diff --git a/-SUNntP3dWo.txt b/-SUNntP3dWo.txt new file mode 100644 index 0000000000000000000000000000000000000000..ab11eb154a06fc7fdad4ac4e003f26c276c75963 --- /dev/null +++ b/-SUNntP3dWo.txt @@ -0,0 +1,307 @@ +align:start position:0% + +okay so the course is at its core very + + align:start position:0% +okay so the course is at its core very + + + align:start position:0% +okay so the course is at its core very +intensive nary so every single text that + + align:start position:0% +intensive nary so every single text that + + + align:start position:0% +intensive nary so every single text that +we read includes at least two + + align:start position:0% +we read includes at least two + + + align:start position:0% +we read includes at least two +disciplines so when we talk about say + + align:start position:0% +disciplines so when we talk about say + + + align:start position:0% +disciplines so when we talk about say +linguistics we look at linguistics from + + align:start position:0% +linguistics we look at linguistics from + + + align:start position:0% +linguistics we look at linguistics from +a very historical perspective but also + + align:start position:0% +a very historical perspective but also + + + align:start position:0% +a very historical perspective but also +from a very social perspective so + + align:start position:0% +from a very social perspective so + + + align:start position:0% +from a very social perspective so +basically we look at language and + + align:start position:0% +basically we look at language and + + + align:start position:0% +basically we look at language and +society you don't just focus on language + + align:start position:0% +society you don't just focus on language + + + align:start position:0% +society you don't just focus on language +per se and we do the same with found + + align:start position:0% +per se and we do the same with found + + + align:start position:0% +per se and we do the same with found +with writing with literature with an + + align:start position:0% +with writing with literature with an + + + align:start position:0% +with writing with literature with an +apology there is always a larger lens + + align:start position:0% +apology there is always a larger lens + + + align:start position:0% +apology there is always a larger lens +that brings in at least two or three + + align:start position:0% +that brings in at least two or three + + + align:start position:0% +that brings in at least two or three +disciplines so and plus we also bring in + + align:start position:0% +disciplines so and plus we also bring in + + + align:start position:0% +disciplines so and plus we also bring in +guest speakers from various disciplines + + align:start position:0% +guest speakers from various disciplines + + + align:start position:0% +guest speakers from various disciplines +having to do with the International + + align:start position:0% +having to do with the International + + + align:start position:0% +having to do with the International +Studies at apology history of course + + align:start position:0% +Studies at apology history of course + + + align:start position:0% +Studies at apology history of course +linguistics my own field but and also to + + align:start position:0% +linguistics my own field but and also to + + + align:start position:0% +linguistics my own field but and also to +submit themselves they they come from + + align:start position:0% +submit themselves they they come from + + + align:start position:0% +submit themselves they they come from +interdisciplinary background so some of + + align:start position:0% +interdisciplinary background so some of + + + align:start position:0% +interdisciplinary background so some of +them are scientists but also others do + + align:start position:0% +them are scientists but also others do + + + align:start position:0% +them are scientists but also others do +women's studies at apology biology so we + + align:start position:0% +women's studies at apology biology so we + + + align:start position:0% +women's studies at apology biology so we +all I think in the course will prime to + + align:start position:0% +all I think in the course will prime to + + + align:start position:0% +all I think in the course will prime to +look at these issues of of blacks in the + + align:start position:0% +look at these issues of of blacks in the + + + align:start position:0% +look at these issues of of blacks in the +u.s. from a very interdisciplinary + + align:start position:0% +u.s. from a very interdisciplinary + + + align:start position:0% +u.s. from a very interdisciplinary +perspective from the student perspective + + align:start position:0% +perspective from the student perspective + + + align:start position:0% +perspective from the student perspective +if we think of this notion of + + align:start position:0% +if we think of this notion of + + + align:start position:0% +if we think of this notion of +interdisciplinary I think many of them + + align:start position:0% +interdisciplinary I think many of them + + + align:start position:0% +interdisciplinary I think many of them +come from from the science for example + + align:start position:0% +come from from the science for example + + + align:start position:0% +come from from the science for example +so they're engineers I think we have + + align:start position:0% +so they're engineers I think we have + + + align:start position:0% +so they're engineers I think we have +mostly engineers in the course and we + + align:start position:0% +mostly engineers in the course and we + + + align:start position:0% +mostly engineers in the course and we +have also some scientists biology been + + align:start position:0% +have also some scientists biology been + + + align:start position:0% +have also some scientists biology been +considered science and in these fields + + align:start position:0% +considered science and in these fields + + + align:start position:0% +considered science and in these fields +often they look at particular problems + + align:start position:0% +often they look at particular problems + + + align:start position:0% +often they look at particular problems +from very rich even narrow perspective + + align:start position:0% +from very rich even narrow perspective + + + align:start position:0% +from very rich even narrow perspective +so I think that for many of them indeed + + align:start position:0% +so I think that for many of them indeed + + + align:start position:0% +so I think that for many of them indeed +it may have been the first course they + + align:start position:0% +it may have been the first course they + + + align:start position:0% +it may have been the first course they +did they took that exposed them to a + + align:start position:0% +did they took that exposed them to a + + + align:start position:0% +did they took that exposed them to a +broad range of fields within one course \ No newline at end of file diff --git a/13UPhn32Mjs.txt b/13UPhn32Mjs.txt new file mode 100644 index 0000000000000000000000000000000000000000..556275a82b362777063f028ce2c4236883e3fbf0 --- /dev/null +++ b/13UPhn32Mjs.txt @@ -0,0 +1,2704 @@ +align:start position:0% + +welcome back to recitation this video + + align:start position:0% +welcome back to recitation this video + + + align:start position:0% +welcome back to recitation this video +we're going to be working on + + align:start position:0% +we're going to be working on + + + align:start position:0% +we're going to be working on +establishing the best technique for + + align:start position:0% +establishing the best technique for + + + align:start position:0% +establishing the best technique for +finding an integral or finding an + + align:start position:0% +finding an integral or finding an + + + align:start position:0% +finding an integral or finding an +anti-derivative we'll be doing this as + + align:start position:0% +anti-derivative we'll be doing this as + + + align:start position:0% +anti-derivative we'll be doing this as +you've seen probably in a lot of these + + align:start position:0% +you've seen probably in a lot of these + + + align:start position:0% +you've seen probably in a lot of these +videos in a row um and so in this one in + + align:start position:0% +videos in a row um and so in this one in + + + align:start position:0% +videos in a row um and so in this one in +particular we're going to work on these + + align:start position:0% +particular we're going to work on these + + + align:start position:0% +particular we're going to work on these +two so what I'd like us to find is for + + align:start position:0% +two so what I'd like us to find is for + + + align:start position:0% +two so what I'd like us to find is for +letter A I'd like us to find an actual + + align:start position:0% +letter A I'd like us to find an actual + + + align:start position:0% +letter A I'd like us to find an actual +value uh if we take the integral from + + align:start position:0% +value uh if we take the integral from + + + align:start position:0% +value uh if we take the integral from +Min -1 to 0 of this fraction 5x^2 - 2x + + + align:start position:0% +Min -1 to 0 of this fraction 5x^2 - 2x + + + + align:start position:0% +Min -1 to 0 of this fraction 5x^2 - 2x + +3 over the quantity x^2 + 1 * x - one + + align:start position:0% +3 over the quantity x^2 + 1 * x - one + + + align:start position:0% +3 over the quantity x^2 + 1 * x - one +and then the second problem we're just + + align:start position:0% +and then the second problem we're just + + + align:start position:0% +and then the second problem we're just +going to be finding an anti-derivative + + align:start position:0% +going to be finding an anti-derivative + + + align:start position:0% +going to be finding an anti-derivative +so it's finding an anti-derivative of + + align:start position:0% +so it's finding an anti-derivative of + + + align:start position:0% +so it's finding an anti-derivative of +the of the function 1/x + 1 * the < TK + + align:start position:0% +the of the function 1/x + 1 * the < TK + + + align:start position:0% +the of the function 1/x + 1 * the < TK +of x^2 - 2x now this does have a domain + + align:start position:0% +of x^2 - 2x now this does have a domain + + + align:start position:0% +of x^2 - 2x now this does have a domain +over which this function is well defined + + align:start position:0% +over which this function is well defined + + + align:start position:0% +over which this function is well defined +um as long as the the as long as what's + + align:start position:0% +um as long as the the as long as what's + + + align:start position:0% +um as long as the the as long as what's +inside the square root is positive and + + align:start position:0% +inside the square root is positive and + + + align:start position:0% +inside the square root is positive and +there are values of X for which that's + + align:start position:0% +there are values of X for which that's + + + align:start position:0% +there are values of X for which that's +positive I just didn't want us to have + + align:start position:0% +positive I just didn't want us to have + + + align:start position:0% +positive I just didn't want us to have +to compute this one exactly so we're + + align:start position:0% +to compute this one exactly so we're + + + align:start position:0% +to compute this one exactly so we're +just looking for an anti-derivative here + + align:start position:0% +just looking for an anti-derivative here + + + align:start position:0% +just looking for an anti-derivative here +so the goal is figure out what strategy + + align:start position:0% +so the goal is figure out what strategy + + + align:start position:0% +so the goal is figure out what strategy +you want to use um work through that + + align:start position:0% +you want to use um work through that + + + align:start position:0% +you want to use um work through that +strategy and then I'll be back and I'll + + align:start position:0% +strategy and then I'll be back and I'll + + + align:start position:0% +strategy and then I'll be back and I'll +show you which strategy I picked and the + + align:start position:0% +show you which strategy I picked and the + + + align:start position:0% +show you which strategy I picked and the +the solution that I + + align:start position:0% + + + + align:start position:0% + +got okay welcome back well hopefully you + + align:start position:0% +got okay welcome back well hopefully you + + + align:start position:0% +got okay welcome back well hopefully you +were able to make some Headway in both + + align:start position:0% +were able to make some Headway in both + + + align:start position:0% +were able to make some Headway in both +of these and so what do right away is + + align:start position:0% +of these and so what do right away is + + + align:start position:0% +of these and so what do right away is +just we'll start with with the first one + + align:start position:0% +just we'll start with with the first one + + + align:start position:0% +just we'll start with with the first one +so in the first one we should be able to + + align:start position:0% +so in the first one we should be able to + + + align:start position:0% +so in the first one we should be able to +get an actual numerical value at the + + align:start position:0% +get an actual numerical value at the + + + align:start position:0% +get an actual numerical value at the +conclusion of the problem and if you + + align:start position:0% +conclusion of the problem and if you + + + align:start position:0% +conclusion of the problem and if you +look at the first one it it's probably + + align:start position:0% +look at the first one it it's probably + + + align:start position:0% +look at the first one it it's probably +pretty obvious you want to use uh + + align:start position:0% +pretty obvious you want to use uh + + + align:start position:0% +pretty obvious you want to use uh +partial fraction decomposition um you + + align:start position:0% +partial fraction decomposition um you + + + align:start position:0% +partial fraction decomposition um you +you already have a denominator that's + + align:start position:0% +you already have a denominator that's + + + align:start position:0% +you already have a denominator that's +factored and so this is going to be + + align:start position:0% +factored and so this is going to be + + + align:start position:0% +factored and so this is going to be +fairly easy to do now what's one thing + + align:start position:0% +fairly easy to do now what's one thing + + + align:start position:0% +fairly easy to do now what's one thing +you want to check with partial fractions + + align:start position:0% +you want to check with partial fractions + + + align:start position:0% +you want to check with partial fractions +is you want to make sure that the degree + + align:start position:0% +is you want to make sure that the degree + + + align:start position:0% +is you want to make sure that the degree +of the numerator is smaller than the + + align:start position:0% +of the numerator is smaller than the + + + align:start position:0% +of the numerator is smaller than the +degree of the denominator notice that + + align:start position:0% +degree of the denominator notice that + + + align:start position:0% +degree of the denominator notice that +the numerator degree is two and the + + align:start position:0% +the numerator degree is two and the + + + align:start position:0% +the numerator degree is two and the +denominator degree is 3 because we have + + align:start position:0% +denominator degree is 3 because we have + + + align:start position:0% +denominator degree is 3 because we have +an x^2 * X so we don't have to do any + + align:start position:0% +an x^2 * X so we don't have to do any + + + align:start position:0% +an x^2 * X so we don't have to do any +long division we can just start the + + align:start position:0% +long division we can just start the + + + align:start position:0% +long division we can just start the +problem so what I'm going to do is I'm + + align:start position:0% +problem so what I'm going to do is I'm + + + align:start position:0% +problem so what I'm going to do is I'm +I'm going to actually decompose it + + align:start position:0% +I'm going to actually decompose it + + + align:start position:0% +I'm going to actually decompose it +without showing you how I did it and um + + align:start position:0% +without showing you how I did it and um + + + align:start position:0% +without showing you how I did it and um +you've you've done that practice enough + + align:start position:0% +you've you've done that practice enough + + + align:start position:0% +you've you've done that practice enough +so I'm just going to show you what I got + + align:start position:0% +so I'm just going to show you what I got + + + align:start position:0% +so I'm just going to show you what I got +with my decomposition and we'll go from + + align:start position:0% +with my decomposition and we'll go from + + + align:start position:0% +with my decomposition and we'll go from +there so when I decompose for letter A I + + align:start position:0% +there so when I decompose for letter A I + + + align:start position:0% +there so when I decompose for letter A I +actually get two integrals and the first + + align:start position:0% +actually get two integrals and the first + + + align:start position:0% +actually get two integrals and the first +one I get is the integral from minus one + + align:start position:0% +one I get is the integral from minus one + + + align:start position:0% +one I get is the integral from minus one +to zero of + + align:start position:0% +to zero of + + + align:start position:0% +to zero of +2x over x^2 + 1 DX and the second one I + + align:start position:0% +2x over x^2 + 1 DX and the second one I + + + align:start position:0% +2x over x^2 + 1 DX and the second one I +get is the integral from minus1 to0 of + + align:start position:0% +get is the integral from minus1 to0 of + + + align:start position:0% +get is the integral from minus1 to0 of +uh 3 overx -1 DX let me just double + + align:start position:0% +uh 3 overx -1 DX let me just double + + + align:start position:0% +uh 3 overx -1 DX let me just double +check and make sure yes that's what I + + align:start position:0% +check and make sure yes that's what I + + + align:start position:0% +check and make sure yes that's what I +got uh when I did this problem earlier + + align:start position:0% +got uh when I did this problem earlier + + + align:start position:0% +got uh when I did this problem earlier +so this is not magic I actually did this + + align:start position:0% +so this is not magic I actually did this + + + align:start position:0% +so this is not magic I actually did this +already that's how I got these and now + + align:start position:0% +already that's how I got these and now + + + align:start position:0% +already that's how I got these and now +from here we just have to have to + + align:start position:0% +from here we just have to have to + + + align:start position:0% +from here we just have to have to +determine we just have to integrate both + + align:start position:0% +determine we just have to integrate both + + + align:start position:0% +determine we just have to integrate both +of these now what would would be the + + align:start position:0% +of these now what would would be the + + + align:start position:0% +of these now what would would be the +strategy at this point well this one um + + align:start position:0% +strategy at this point well this one um + + + align:start position:0% +strategy at this point well this one um +if if this had just been a two and no X + + align:start position:0% +if if this had just been a two and no X + + + align:start position:0% +if if this had just been a two and no X +you'd be dealing with an arctan uh type + + align:start position:0% +you'd be dealing with an arctan uh type + + + align:start position:0% +you'd be dealing with an arctan uh type +of problem because you'd be integrating + + align:start position:0% +of problem because you'd be integrating + + + align:start position:0% +of problem because you'd be integrating +1 over x^2 + 1 but actually because we + + align:start position:0% +1 over x^2 + 1 but actually because we + + + align:start position:0% +1 over x^2 + 1 but actually because we +have this 2x here this is really a a + + align:start position:0% +have this 2x here this is really a a + + + align:start position:0% +have this 2x here this is really a a +substitution problem right the + + align:start position:0% +substitution problem right the + + + align:start position:0% +substitution problem right the +derivative of x^2 + 1 is + + align:start position:0% +derivative of x^2 + 1 is + + + align:start position:0% +derivative of x^2 + 1 is +2x right so so we see that really what + + align:start position:0% +2x right so so we see that really what + + + align:start position:0% +2x right so so we see that really what +we're integrating is something like du + + align:start position:0% +we're integrating is something like du + + + align:start position:0% +we're integrating is something like du +over U and so if you did the + + align:start position:0% +over U and so if you did the + + + align:start position:0% +over U and so if you did the +substitution problem you should get + + align:start position:0% +substitution problem you should get + + + align:start position:0% +substitution problem you should get +something like natural log of x^2 + 1 + + align:start position:0% +something like natural log of x^2 + 1 + + + align:start position:0% +something like natural log of x^2 + 1 +let me just double check and make sure + + align:start position:0% +let me just double check and make sure + + + align:start position:0% +let me just double check and make sure +that gives me the derivative here the + + align:start position:0% +that gives me the derivative here the + + + align:start position:0% +that gives me the derivative here the +derivative of natural log of X2 + 1 is + + align:start position:0% +derivative of natural log of X2 + 1 is + + + align:start position:0% +derivative of natural log of X2 + 1 is +1x^2 + 1 * 2x it gives me exactly what's + + align:start position:0% +1x^2 + 1 * 2x it gives me exactly what's + + + align:start position:0% +1x^2 + 1 * 2x it gives me exactly what's +here I don't need absolute values here + + align:start position:0% +here I don't need absolute values here + + + align:start position:0% +here I don't need absolute values here +because this is always positive and I + + align:start position:0% +because this is always positive and I + + + align:start position:0% +because this is always positive and I +know I need to evaluate it at minus one + + align:start position:0% +know I need to evaluate it at minus one + + + align:start position:0% +know I need to evaluate it at minus one +and zero okay so that takes care of the + + align:start position:0% +and zero okay so that takes care of the + + + align:start position:0% +and zero okay so that takes care of the +left one now the right one is again it's + + align:start position:0% +left one now the right one is again it's + + + align:start position:0% +left one now the right one is again it's +a pretty straightforward one because + + align:start position:0% +a pretty straightforward one because + + + align:start position:0% +a pretty straightforward one because +it's just 3x -1 that's a natural log + + align:start position:0% +it's just 3x -1 that's a natural log + + + align:start position:0% +it's just 3x -1 that's a natural log +again + + align:start position:0% +again + + + align:start position:0% +again +so this natural log is even simpler it's + + align:start position:0% +so this natural log is even simpler it's + + + align:start position:0% +so this natural log is even simpler it's +going to be 3 times the natural log + + align:start position:0% +going to be 3 times the natural log + + + align:start position:0% +going to be 3 times the natural log +absolute x + + align:start position:0% +absolute x + + + align:start position:0% +absolute x +-1 from minus one to zero and so now we + + align:start position:0% +-1 from minus one to zero and so now we + + + align:start position:0% +-1 from minus one to zero and so now we +just have to plug in everything okay so + + align:start position:0% +just have to plug in everything okay so + + + align:start position:0% +just have to plug in everything okay so +let's just do this one step at a time + + align:start position:0% +let's just do this one step at a time + + + align:start position:0% +let's just do this one step at a time +starting over here so the natural log + + align:start position:0% +starting over here so the natural log + + + align:start position:0% +starting over here so the natural log +when I put in zero I get the natural log + + align:start position:0% +when I put in zero I get the natural log + + + align:start position:0% +when I put in zero I get the natural log +of one that's + + align:start position:0% +of one that's + + + align:start position:0% +of one that's +zero and I subtract what I get when I + + align:start position:0% +zero and I subtract what I get when I + + + align:start position:0% +zero and I subtract what I get when I +put in negative 1 for x soga - 1^ squar + + align:start position:0% +put in negative 1 for x soga - 1^ squar + + + align:start position:0% +put in negative 1 for x soga - 1^ squar +gives me 1 so this is minus the natural + + align:start position:0% +gives me 1 so this is minus the natural + + + align:start position:0% +gives me 1 so this is minus the natural +log of + + align:start position:0% +log of + + + align:start position:0% +log of +two and then I have plus three times + + align:start position:0% +two and then I have plus three times + + + align:start position:0% +two and then I have plus three times +whatever is over here so now let's look + + align:start position:0% +whatever is over here so now let's look + + + align:start position:0% +whatever is over here so now let's look +at this when I plug in zero I get + + align:start position:0% +at this when I plug in zero I get + + + align:start position:0% +at this when I plug in zero I get +natural log of 0 minus one absolute + + align:start position:0% +natural log of 0 minus one absolute + + + align:start position:0% +natural log of 0 minus one absolute +value that's natural log one that's zero + + align:start position:0% +value that's natural log one that's zero + + + align:start position:0% +value that's natural log one that's zero +again and then I get a minus and then I + + align:start position:0% +again and then I get a minus and then I + + + align:start position:0% +again and then I get a minus and then I +put in Nega 1 1 - 1 is -2 absolute value + + align:start position:0% +put in Nega 1 1 - 1 is -2 absolute value + + + align:start position:0% +put in Nega 1 1 - 1 is -2 absolute value +so it's natural log of + + align:start position:0% + + + + align:start position:0% + +two and so if I look it all the way + + align:start position:0% +two and so if I look it all the way + + + align:start position:0% +two and so if I look it all the way +across I see I have a negative natural + + align:start position:0% +across I see I have a negative natural + + + align:start position:0% +across I see I have a negative natural +log of two and then I have three + + align:start position:0% +log of two and then I have three + + + align:start position:0% +log of two and then I have three +negative natural logs of two so the the + + align:start position:0% +negative natural logs of two so the the + + + align:start position:0% +negative natural logs of two so the the +final answer is just -4 natural log of + + align:start position:0% +final answer is just -4 natural log of + + + align:start position:0% +final answer is just -4 natural log of +two and that is where we'll stop with + + align:start position:0% +two and that is where we'll stop with + + + align:start position:0% +two and that is where we'll stop with +with a okay so let me just remind you + + align:start position:0% +with a okay so let me just remind you + + + align:start position:0% +with a okay so let me just remind you +actually before we go uh to B what we + + align:start position:0% +actually before we go uh to B what we + + + align:start position:0% +actually before we go uh to B what we +did in a was we did partial fraction + + align:start position:0% +did in a was we did partial fraction + + + align:start position:0% +did in a was we did partial fraction +decomposition and I gave you the the + + align:start position:0% +decomposition and I gave you the the + + + align:start position:0% +decomposition and I gave you the the +numerators and then on the first one we + + align:start position:0% +numerators and then on the first one we + + + align:start position:0% +numerators and then on the first one we +had to use maybe a substitution to + + align:start position:0% +had to use maybe a substitution to + + + align:start position:0% +had to use maybe a substitution to +figure it out I didn't write explicitly + + align:start position:0% +figure it out I didn't write explicitly + + + align:start position:0% +figure it out I didn't write explicitly +the substitution but a substitution + + align:start position:0% +the substitution but a substitution + + + align:start position:0% +the substitution but a substitution +gives us that integral and this one is + + align:start position:0% +gives us that integral and this one is + + + align:start position:0% +gives us that integral and this one is +directly a natural log okay now let's + + align:start position:0% +directly a natural log okay now let's + + + align:start position:0% +directly a natural log okay now let's +look at + + align:start position:0% +look at + + + align:start position:0% +look at +B so + + align:start position:0% +B so + + + align:start position:0% +B so +B let me let me rewrite uh the the + + align:start position:0% +B let me let me rewrite uh the the + + + align:start position:0% +B let me let me rewrite uh the the +problem because it's now a little far + + align:start position:0% +problem because it's now a little far + + + align:start position:0% +problem because it's now a little far +away uh I think it's x + 1 square < TK + + align:start position:0% +away uh I think it's x + 1 square < TK + + + align:start position:0% +away uh I think it's x + 1 square < TK +of x^2 - + + align:start position:0% +of x^2 - + + + align:start position:0% +of x^2 - +2x okay so B the reason I I I wanted to + + align:start position:0% +2x okay so B the reason I I I wanted to + + + align:start position:0% +2x okay so B the reason I I I wanted to +make sure we did a did a trig + + align:start position:0% +make sure we did a did a trig + + + align:start position:0% +make sure we did a did a trig +substitution in a particular way because + + align:start position:0% +substitution in a particular way because + + + align:start position:0% +substitution in a particular way because +I haven't demonstrated those very much + + align:start position:0% +I haven't demonstrated those very much + + + align:start position:0% +I haven't demonstrated those very much +so the denominator wound up looking a + + align:start position:0% +so the denominator wound up looking a + + + align:start position:0% +so the denominator wound up looking a +little awkward to force you to do it in + + align:start position:0% +little awkward to force you to do it in + + + align:start position:0% +little awkward to force you to do it in +that way um but what we want to do is we + + align:start position:0% +that way um but what we want to do is we + + + align:start position:0% +that way um but what we want to do is we +want to actually complete the square on + + align:start position:0% +want to actually complete the square on + + + align:start position:0% +want to actually complete the square on +what's in here and that might make you a + + align:start position:0% +what's in here and that might make you a + + + align:start position:0% +what's in here and that might make you a +little bit nervous but let me just do a + + align:start position:0% +little bit nervous but let me just do a + + + align:start position:0% +little bit nervous but let me just do a +little sidebar work down here and point + + align:start position:0% +little sidebar work down here and point + + + align:start position:0% +little sidebar work down here and point +out what we get if we factor out a + + align:start position:0% +out what we get if we factor out a + + + align:start position:0% +out what we get if we factor out a +negative here we get an X2 + + + align:start position:0% +negative here we get an X2 + + + + align:start position:0% +negative here we get an X2 + +2x okay so we're going to complete the + + align:start position:0% +2x okay so we're going to complete the + + + align:start position:0% +2x okay so we're going to complete the +square on the inside now this might make + + align:start position:0% +square on the inside now this might make + + + align:start position:0% +square on the inside now this might make +some people nervous they might say you + + align:start position:0% +some people nervous they might say you + + + align:start position:0% +some people nervous they might say you +have a negative under the square root + + align:start position:0% +have a negative under the square root + + + align:start position:0% +have a negative under the square root +but I want to point out that I have a + + align:start position:0% +but I want to point out that I have a + + + align:start position:0% +but I want to point out that I have a +negative here but I could always make X2 + + align:start position:0% +negative here but I could always make X2 + + + align:start position:0% +negative here but I could always make X2 ++ 2x a negative number and then I would + + align:start position:0% ++ 2x a negative number and then I would + + + align:start position:0% ++ 2x a negative number and then I would +have that the negative times the + + align:start position:0% +have that the negative times the + + + align:start position:0% +have that the negative times the +negative is a positive for instance I + + align:start position:0% +negative is a positive for instance I + + + align:start position:0% +negative is a positive for instance I +think negative 1 right if I put in + + align:start position:0% +think negative 1 right if I put in + + + align:start position:0% +think negative 1 right if I put in +negative 1 for X I get -2 + 1 is a + + align:start position:0% +negative 1 for X I get -2 + 1 is a + + + align:start position:0% +negative 1 for X I get -2 + 1 is a +negative value so if I put a negative 1 + + align:start position:0% +negative value so if I put a negative 1 + + + align:start position:0% +negative value so if I put a negative 1 +for X I'm taking the square root of a + + align:start position:0% +for X I'm taking the square root of a + + + align:start position:0% +for X I'm taking the square root of a +positive number so there are values of X + + align:start position:0% +positive number so there are values of X + + + align:start position:0% +positive number so there are values of X +that make this this Den this uh under + + align:start position:0% +that make this this Den this uh under + + + align:start position:0% +that make this this Den this uh under +the square root positive okay so you + + align:start position:0% +the square root positive okay so you + + + align:start position:0% +the square root positive okay so you +don't have to worry about that now if I + + align:start position:0% +don't have to worry about that now if I + + + align:start position:0% +don't have to worry about that now if I +want to complete the square on what's in + + align:start position:0% +want to complete the square on what's in + + + align:start position:0% +want to complete the square on what's in +here what do I do I have x^2 + 2x I + + align:start position:0% +here what do I do I have x^2 + 2x I + + + align:start position:0% +here what do I do I have x^2 + 2x I +obviously need to add a one to complete + + align:start position:0% +obviously need to add a one to complete + + + align:start position:0% +obviously need to add a one to complete +the square why is that because you take + + align:start position:0% +the square why is that because you take + + + align:start position:0% +the square why is that because you take +what's here you divide it by two when + + align:start position:0% +what's here you divide it by two when + + + align:start position:0% +what's here you divide it by two when +you square it and so this actually + + align:start position:0% +you square it and so this actually + + + align:start position:0% +you square it and so this actually +equals Square < TK + + align:start position:0% +equals Square < TK + + + align:start position:0% +equals Square < TK +of x^2 + 2x + 1 and I want to subtract + + align:start position:0% +of x^2 + 2x + 1 and I want to subtract + + + align:start position:0% +of x^2 + 2x + 1 and I want to subtract +one so that I haven't changed anything + + align:start position:0% +one so that I haven't changed anything + + + align:start position:0% +one so that I haven't changed anything +but when I pull it out from the negative + + align:start position:0% +but when I pull it out from the negative + + + align:start position:0% +but when I pull it out from the negative +it's another plus one okay let's make + + align:start position:0% +it's another plus one okay let's make + + + align:start position:0% +it's another plus one okay let's make +sure we buy that I've added one inside + + align:start position:0% +sure we buy that I've added one inside + + + align:start position:0% +sure we buy that I've added one inside +here so if I add one on the outside this + + align:start position:0% +here so if I add one on the outside this + + + align:start position:0% +here so if I add one on the outside this +is this is actually a minus one and so + + align:start position:0% +is this is actually a minus one and so + + + align:start position:0% +is this is actually a minus one and so +this is a plus one so together they add + + align:start position:0% +this is a plus one so together they add + + + align:start position:0% +this is a plus one so together they add +up to zero so I haven't changed what's + + align:start position:0% +up to zero so I haven't changed what's + + + align:start position:0% +up to zero so I haven't changed what's +in the square root so if I come back and + + align:start position:0% +in the square root so if I come back and + + + align:start position:0% +in the square root so if I come back and +put that in right here what do I get I + + align:start position:0% +put that in right here what do I get I + + + align:start position:0% +put that in right here what do I get I +get the integral DX over x + + + align:start position:0% +get the integral DX over x + + + + align:start position:0% +get the integral DX over x + +1 square root let me move this over I'm + + align:start position:0% +1 square root let me move this over I'm + + + align:start position:0% +1 square root let me move this over I'm +going to bring this to the front one + + align:start position:0% +going to bring this to the front one + + + align:start position:0% +going to bring this to the front one +minus x + 1^ + + align:start position:0% +minus x + 1^ + + + align:start position:0% +minus x + 1^ +sared all right so from here we have to + + align:start position:0% +sared all right so from here we have to + + + align:start position:0% +sared all right so from here we have to +do a trig substitution now what trig + + align:start position:0% +do a trig substitution now what trig + + + align:start position:0% +do a trig substitution now what trig +substitution we want to do we could do s + + align:start position:0% +substitution we want to do we could do s + + + align:start position:0% +substitution we want to do we could do s +or cosine but I'm going to do cosine + + align:start position:0% +or cosine but I'm going to do cosine + + + align:start position:0% +or cosine but I'm going to do cosine +because I like secants better than + + align:start position:0% +because I like secants better than + + + align:start position:0% +because I like secants better than +cosecants because I have those memorized + + align:start position:0% +cosecants because I have those memorized + + + align:start position:0% +cosecants because I have those memorized +better so that's why I'm choosing cosine + + align:start position:0% +better so that's why I'm choosing cosine + + + align:start position:0% +better so that's why I'm choosing cosine +you'll see uh wh why I chose that way in + + align:start position:0% +you'll see uh wh why I chose that way in + + + align:start position:0% +you'll see uh wh why I chose that way in +a little bit but it would be you will + + align:start position:0% +a little bit but it would be you will + + + align:start position:0% +a little bit but it would be you will +get the same answer if you do if you do + + align:start position:0% +get the same answer if you do if you do + + + align:start position:0% +get the same answer if you do if you do +sign Okay so I'm going to come to the + + align:start position:0% +sign Okay so I'm going to come to the + + + align:start position:0% +sign Okay so I'm going to come to the +other side um let's see so I'm choosing + + align:start position:0% +other side um let's see so I'm choosing + + + align:start position:0% +other side um let's see so I'm choosing +cine Theta = x + 1 that's the + + align:start position:0% +cine Theta = x + 1 that's the + + + align:start position:0% +cine Theta = x + 1 that's the +substitution I'm making and why am I + + align:start position:0% +substitution I'm making and why am I + + + align:start position:0% +substitution I'm making and why am I +making that substitution I'm making that + + align:start position:0% +making that substitution I'm making that + + + align:start position:0% +making that substitution I'm making that +substitution because when I do one minus + + align:start position:0% +substitution because when I do one minus + + + align:start position:0% +substitution because when I do one minus +x + 1^ SAR that's actually 1 minus + + align:start position:0% +x + 1^ SAR that's actually 1 minus + + + align:start position:0% +x + 1^ SAR that's actually 1 minus +cosine 2 + + align:start position:0% +cosine 2 + + + align:start position:0% +cosine 2 +Theta so that's this in here is sin squ + + align:start position:0% +Theta so that's this in here is sin squ + + + align:start position:0% +Theta so that's this in here is sin squ +Theta and when I take the square root I + + align:start position:0% +Theta and when I take the square root I + + + align:start position:0% +Theta and when I take the square root I +just get a s Theta so that should be + + align:start position:0% +just get a s Theta so that should be + + + align:start position:0% +just get a s Theta so that should be +pretty familiar to you by now this + + align:start position:0% +pretty familiar to you by now this + + + align:start position:0% +pretty familiar to you by now this +strategy y but the point I'm making is + + align:start position:0% +strategy y but the point I'm making is + + + align:start position:0% +strategy y but the point I'm making is +the X+ 1 will be a cosine Theta and this + + align:start position:0% +the X+ 1 will be a cosine Theta and this + + + align:start position:0% +the X+ 1 will be a cosine Theta and this +whole square root is what becomes a sin + + align:start position:0% +whole square root is what becomes a sin + + + align:start position:0% +whole square root is what becomes a sin +Theta so you've seen that a fair amount + + align:start position:0% +Theta so you've seen that a fair amount + + + align:start position:0% +Theta so you've seen that a fair amount +but just to remind you that and then the + + align:start position:0% +but just to remind you that and then the + + + align:start position:0% +but just to remind you that and then the +other thing we need is to replace the DX + + align:start position:0% +other thing we need is to replace the DX + + + align:start position:0% +other thing we need is to replace the DX +so the DX is going to be derivative of + + align:start position:0% +so the DX is going to be derivative of + + + align:start position:0% +so the DX is going to be derivative of +cosine is negative s so you're going to + + align:start position:0% +cosine is negative s so you're going to + + + align:start position:0% +cosine is negative s so you're going to +get Negative sin Theta D + + align:start position:0% +get Negative sin Theta D + + + align:start position:0% +get Negative sin Theta D +Theta so now we know all the pieces we + + align:start position:0% +Theta so now we know all the pieces we + + + align:start position:0% +Theta so now we know all the pieces we +said this was cosine we said the square + + align:start position:0% +said this was cosine we said the square + + + align:start position:0% +said this was cosine we said the square +root is s and the DX is negative sin D + + align:start position:0% +root is s and the DX is negative sin D + + + align:start position:0% +root is s and the DX is negative sin D +Theta so let's rewrite that over + + align:start position:0% + + + + align:start position:0% + +here so we have I'm going to put the + + align:start position:0% +here so we have I'm going to put the + + + align:start position:0% +here so we have I'm going to put the +negative in front so I don't have to + + align:start position:0% +negative in front so I don't have to + + + align:start position:0% +negative in front so I don't have to +deal with it anymore negative sin + + align:start position:0% +deal with it anymore negative sin + + + align:start position:0% +deal with it anymore negative sin +Theta over cosine Theta sin Theta D + + align:start position:0% +Theta over cosine Theta sin Theta D + + + align:start position:0% +Theta over cosine Theta sin Theta D +Theta these divide out and I get 1 over + + align:start position:0% +Theta these divide out and I get 1 over + + + align:start position:0% +Theta these divide out and I get 1 over +cosine Theta which is just equal to + + align:start position:0% +cosine Theta which is just equal to + + + align:start position:0% +cosine Theta which is just equal to +negative secant + + align:start position:0% +negative secant + + + align:start position:0% +negative secant +Theta okay so I have negative secant + + align:start position:0% +Theta okay so I have negative secant + + + align:start position:0% +Theta okay so I have negative secant +Theta let me actually write that here + + align:start position:0% +Theta let me actually write that here + + + align:start position:0% +Theta let me actually write that here +negative integral of secant Theta D + + align:start position:0% +negative integral of secant Theta D + + + align:start position:0% +negative integral of secant Theta D +Theta and now what is that well we know + + align:start position:0% +Theta and now what is that well we know + + + align:start position:0% +Theta and now what is that well we know +uh we know how to integrate secant so + + align:start position:0% +uh we know how to integrate secant so + + + align:start position:0% +uh we know how to integrate secant so +let me write that in terms of + + align:start position:0% +let me write that in terms of + + + align:start position:0% +let me write that in terms of +theta it's going to be negative natural + + align:start position:0% +theta it's going to be negative natural + + + align:start position:0% +theta it's going to be negative natural +log absolute value secant theta plus + + align:start position:0% +log absolute value secant theta plus + + + align:start position:0% +log absolute value secant theta plus +tangent Theta and then we have the plus + + align:start position:0% +tangent Theta and then we have the plus + + + align:start position:0% +tangent Theta and then we have the plus +C out here what's the point of this + + align:start position:0% +C out here what's the point of this + + + align:start position:0% +C out here what's the point of this +let's well we should maybe have this + + align:start position:0% +let's well we should maybe have this + + + align:start position:0% +let's well we should maybe have this +memorized if you have to look it up you + + align:start position:0% +memorized if you have to look it up you + + + align:start position:0% +memorized if you have to look it up you +have to look it up but you saw this one + + align:start position:0% +have to look it up but you saw this one + + + align:start position:0% +have to look it up but you saw this one +in class and the negative is just + + align:start position:0% +in class and the negative is just + + + align:start position:0% +in class and the negative is just +dropping down here so don't think I + + align:start position:0% +dropping down here so don't think I + + + align:start position:0% +dropping down here so don't think I +added that negative in when I was taking + + align:start position:0% +added that negative in when I was taking + + + align:start position:0% +added that negative in when I was taking +anti-derivative it was already there all + + align:start position:0% +anti-derivative it was already there all + + + align:start position:0% +anti-derivative it was already there all +right so we're done oh but we're not + + align:start position:0% +right so we're done oh but we're not + + + align:start position:0% +right so we're done oh but we're not +done why are we not done we're not done + + align:start position:0% +done why are we not done we're not done + + + align:start position:0% +done why are we not done we're not done +because we started off with something in + + align:start position:0% +because we started off with something in + + + align:start position:0% +because we started off with something in +terms of X and now we have something in + + align:start position:0% +terms of X and now we have something in + + + align:start position:0% +terms of X and now we have something in +terms of theta so we have to finish up + + align:start position:0% +terms of theta so we have to finish up + + + align:start position:0% +terms of theta so we have to finish up +and how we do that is we go back we look + + align:start position:0% +and how we do that is we go back we look + + + align:start position:0% +and how we do that is we go back we look +at the substitution we made we make a + + align:start position:0% +at the substitution we made we make a + + + align:start position:0% +at the substitution we made we make a +triangle based on that substitution we + + align:start position:0% +triangle based on that substitution we + + + align:start position:0% +triangle based on that substitution we +figure out the values of secant Theta + + align:start position:0% +figure out the values of secant Theta + + + align:start position:0% +figure out the values of secant Theta +and tangent Theta and then we can plug + + align:start position:0% +and tangent Theta and then we can plug + + + align:start position:0% +and tangent Theta and then we can plug +those in in terms of X so let's remind + + align:start position:0% +those in in terms of X so let's remind + + + align:start position:0% +those in in terms of X so let's remind +ourselves I'm going to draw the triangle + + align:start position:0% +ourselves I'm going to draw the triangle + + + align:start position:0% +ourselves I'm going to draw the triangle +in the middle here let's remind + + align:start position:0% +in the middle here let's remind + + + align:start position:0% +in the middle here let's remind +ourselves of the relationship we had + + align:start position:0% +ourselves of the relationship we had + + + align:start position:0% +ourselves of the relationship we had +between Theta and + + align:start position:0% +between Theta and + + + align:start position:0% +between Theta and +X if this is Theta we said cosine Theta + + align:start position:0% +X if this is Theta we said cosine Theta + + + align:start position:0% +X if this is Theta we said cosine Theta +right here cosine Theta was equal to x + + + align:start position:0% +right here cosine Theta was equal to x + + + + align:start position:0% +right here cosine Theta was equal to x + +1 cosine Theta is adjacent over + + align:start position:0% +1 cosine Theta is adjacent over + + + align:start position:0% +1 cosine Theta is adjacent over +hypotenuse so we want to say this is X+ + + align:start position:0% +hypotenuse so we want to say this is X+ + + + align:start position:0% +hypotenuse so we want to say this is X+ +one and this is one and that implies by + + align:start position:0% +one and this is one and that implies by + + + align:start position:0% +one and this is one and that implies by +the Pythagorean theorem that this is of + + align:start position:0% +the Pythagorean theorem that this is of + + + align:start position:0% +the Pythagorean theorem that this is of + + align:start position:0% + + + align:start position:0% +minus x + 1^ + + align:start position:0% +minus x + 1^ + + + align:start position:0% +minus x + 1^ +2 let me move that over notice then this + + align:start position:0% +2 let me move that over notice then this + + + align:start position:0% +2 let me move that over notice then this +also makes sense why sin Theta is what + + align:start position:0% +also makes sense why sin Theta is what + + + align:start position:0% +also makes sense why sin Theta is what +it is sin Theta is this value divided + + align:start position:0% +it is sin Theta is this value divided + + + align:start position:0% +it is sin Theta is this value divided +one so that also helps you understand + + align:start position:0% +one so that also helps you understand + + + align:start position:0% +one so that also helps you understand +that all right so now what do we need to + + align:start position:0% +that all right so now what do we need to + + + align:start position:0% +that all right so now what do we need to +read off we need to read off secant and + + align:start position:0% +read off we need to read off secant and + + + align:start position:0% +read off we need to read off secant and +we need to read off tangent so secant is + + align:start position:0% +we need to read off tangent so secant is + + + align:start position:0% +we need to read off tangent so secant is +one over cosine so actually we could + + align:start position:0% +one over cosine so actually we could + + + align:start position:0% +one over cosine so actually we could +have gotten that one for free from the + + align:start position:0% +have gotten that one for free from the + + + align:start position:0% +have gotten that one for free from the +cosine so this one over cosine is 1 + + align:start position:0% +cosine so this one over cosine is 1 + + + align:start position:0% +cosine so this one over cosine is 1 +overx + one so this thing is equal to + + align:start position:0% +overx + one so this thing is equal to + + + align:start position:0% +overx + one so this thing is equal to +negative natural log absolute value 1 /x + + align:start position:0% +negative natural log absolute value 1 /x + + + align:start position:0% +negative natural log absolute value 1 /x ++ 1 + + align:start position:0% ++ 1 + + + align:start position:0% ++ 1 +plus now what's tangent if I come back + + align:start position:0% +plus now what's tangent if I come back + + + align:start position:0% +plus now what's tangent if I come back +and look at the triangle tangent Theta + + align:start position:0% +and look at the triangle tangent Theta + + + align:start position:0% +and look at the triangle tangent Theta +is opposite over adjacent right so I can + + align:start position:0% +is opposite over adjacent right so I can + + + align:start position:0% +is opposite over adjacent right so I can +actually just put it all over X plus one + + align:start position:0% +actually just put it all over X plus one + + + align:start position:0% +actually just put it all over X plus one +if I wanted but I already started + + align:start position:0% +if I wanted but I already started + + + align:start position:0% +if I wanted but I already started +writing it separately so I'll leave it + + align:start position:0% +writing it separately so I'll leave it + + + align:start position:0% +writing it separately so I'll leave it +like this sare < TK of 1us x + 1 + + align:start position:0% +like this sare < TK of 1us x + 1 + + + align:start position:0% +like this sare < TK of 1us x + 1 +quantity squared and then close that and + + align:start position:0% +quantity squared and then close that and + + + align:start position:0% +quantity squared and then close that and +then my plus C so now I'm actually + + align:start position:0% +then my plus C so now I'm actually + + + align:start position:0% +then my plus C so now I'm actually +finished with the problem because now I + + align:start position:0% +finished with the problem because now I + + + align:start position:0% +finished with the problem because now I +have an anti- derivative in terms of X + + align:start position:0% +have an anti- derivative in terms of X + + + align:start position:0% +have an anti- derivative in terms of X +so let me just remind you where this + + align:start position:0% +so let me just remind you where this + + + align:start position:0% +so let me just remind you where this +problem where we started the problem + + align:start position:0% +problem where we started the problem + + + align:start position:0% +problem where we started the problem +kind of take us through quickly and then + + align:start position:0% +kind of take us through quickly and then + + + align:start position:0% +kind of take us through quickly and then +we'll be done so back to the beginning + + align:start position:0% +we'll be done so back to the beginning + + + align:start position:0% +we'll be done so back to the beginning +what we had was we had an integral uh + + align:start position:0% +what we had was we had an integral uh + + + align:start position:0% +what we had was we had an integral uh +that was a a fractional problem but we + + align:start position:0% +that was a a fractional problem but we + + + align:start position:0% +that was a a fractional problem but we +had an X plus one here and then we had + + align:start position:0% +had an X plus one here and then we had + + + align:start position:0% +had an X plus one here and then we had +this really messy looking quadratic in + + align:start position:0% +this really messy looking quadratic in + + + align:start position:0% +this really messy looking quadratic in +here to make it easy to deal with I + + align:start position:0% +here to make it easy to deal with I + + + align:start position:0% +here to make it easy to deal with I +factored out a negative sign and then I + + align:start position:0% +factored out a negative sign and then I + + + align:start position:0% +factored out a negative sign and then I +saw I could complete the square once you + + align:start position:0% +saw I could complete the square once you + + + align:start position:0% +saw I could complete the square once you +complete the square you actually get + + align:start position:0% +complete the square you actually get + + + align:start position:0% +complete the square you actually get +another X+ one in there which helps us + + align:start position:0% +another X+ one in there which helps us + + + align:start position:0% +another X+ one in there which helps us +to see immediately it should be a trig + + align:start position:0% +to see immediately it should be a trig + + + align:start position:0% +to see immediately it should be a trig +substitution so the substitution that's + + align:start position:0% +substitution so the substitution that's + + + align:start position:0% +substitution so the substitution that's +natural to make because you have a one + + align:start position:0% +natural to make because you have a one + + + align:start position:0% +natural to make because you have a one +minus something involving an X is going + + align:start position:0% +minus something involving an X is going + + + align:start position:0% +minus something involving an X is going +to be either cosine or S I chose cosine + + align:start position:0% +to be either cosine or S I chose cosine + + + align:start position:0% +to be either cosine or S I chose cosine +if you'd chosen s you probably would + + align:start position:0% +if you'd chosen s you probably would + + + align:start position:0% +if you'd chosen s you probably would +have gotten a cosecant up there instead + + align:start position:0% +have gotten a cosecant up there instead + + + align:start position:0% +have gotten a cosecant up there instead +of a uh secant when you were taking an + + align:start position:0% +of a uh secant when you were taking an + + + align:start position:0% +of a uh secant when you were taking an +anti-derivative at the very end so you + + align:start position:0% +anti-derivative at the very end so you + + + align:start position:0% +anti-derivative at the very end so you +you would have gotten the same answer + + align:start position:0% +you would have gotten the same answer + + + align:start position:0% +you would have gotten the same answer +because of the substitutions in the end + + align:start position:0% +because of the substitutions in the end + + + align:start position:0% +because of the substitutions in the end +um but so I chose cosine Theta is equal + + align:start position:0% +um but so I chose cosine Theta is equal + + + align:start position:0% +um but so I chose cosine Theta is equal +X+ 1 you do that you can replace this + + align:start position:0% +X+ 1 you do that you can replace this + + + align:start position:0% +X+ 1 you do that you can replace this +with cosine this with a sign this + + align:start position:0% +with cosine this with a sign this + + + align:start position:0% +with cosine this with a sign this +becomes a negative sign and then you + + align:start position:0% +becomes a negative sign and then you + + + align:start position:0% +becomes a negative sign and then you +start simplifying so once we came over + + align:start position:0% +start simplifying so once we came over + + + align:start position:0% +start simplifying so once we came over +here and simplified we got it into + + align:start position:0% +here and simplified we got it into + + + align:start position:0% +here and simplified we got it into +something we recognized we got it into + + align:start position:0% +something we recognized we got it into + + + align:start position:0% +something we recognized we got it into +secant we know an we know the + + align:start position:0% +secant we know an we know the + + + align:start position:0% +secant we know an we know the +anti-derivative for secant in terms of + + align:start position:0% +anti-derivative for secant in terms of + + + align:start position:0% +anti-derivative for secant in terms of +secant and tangent we know it's exactly + + align:start position:0% +secant and tangent we know it's exactly + + + align:start position:0% +secant and tangent we know it's exactly +this and then we went back to the + + align:start position:0% +this and then we went back to the + + + align:start position:0% +this and then we went back to the +relationship we had we made ourselves a + + align:start position:0% +relationship we had we made ourselves a + + + align:start position:0% +relationship we had we made ourselves a +triangle in terms of the Theta and the X + + align:start position:0% +triangle in terms of the Theta and the X + + + align:start position:0% +triangle in terms of the Theta and the X +values and then we were able to + + align:start position:0% +values and then we were able to + + + align:start position:0% +values and then we were able to +substitute in for secant and tangent + + align:start position:0% +substitute in for secant and tangent + + + align:start position:0% +substitute in for secant and tangent +all right so hopefully that was + + align:start position:0% +all right so hopefully that was + + + align:start position:0% +all right so hopefully that was +successful for you and uh that's where + + align:start position:0% +successful for you and uh that's where + + + align:start position:0% +successful for you and uh that's where +I'll stop \ No newline at end of file diff --git a/14UeTjQOx50.txt b/14UeTjQOx50.txt new file mode 100644 index 0000000000000000000000000000000000000000..e94bdf504ec96cb95feb878b9a3c7f6ab05c343a --- /dev/null +++ b/14UeTjQOx50.txt @@ -0,0 +1,13352 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following content is provided by MIT +open courseware under a Creative Commons + + align:start position:0% +open courseware under a Creative Commons + + + align:start position:0% +open courseware under a Creative Commons +license additional information about our + + align:start position:0% +license additional information about our + + + align:start position:0% +license additional information about our +license and MIT open courseware in + + align:start position:0% +license and MIT open courseware in + + + align:start position:0% +license and MIT open courseware in +general is available at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay we could + + align:start position:0% +ocw.mit.edu okay we could + + + align:start position:0% +ocw.mit.edu okay we could +continue last time I was talking about + + align:start position:0% +continue last time I was talking about + + + align:start position:0% +continue last time I was talking about +cognition and and and uh framing the the + + align:start position:0% +cognition and and and uh framing the the + + + align:start position:0% +cognition and and and uh framing the the +argument in part in saying that we're + + align:start position:0% +argument in part in saying that we're + + + align:start position:0% +argument in part in saying that we're +not like computers even though computers + + align:start position:0% +not like computers even though computers + + + align:start position:0% +not like computers even though computers +are nice metaphors for various + + align:start position:0% +are nice metaphors for various + + + align:start position:0% +are nice metaphors for various +aspects of of of cognitive function we + + align:start position:0% +aspects of of of cognitive function we + + + align:start position:0% +aspects of of of cognitive function we +could continue that today when you get + + align:start position:0% +could continue that today when you get + + + align:start position:0% +could continue that today when you get +an off-the-shelf computer you expect + + align:start position:0% +an off-the-shelf computer you expect + + + align:start position:0% +an off-the-shelf computer you expect +that um its basic uh way of thinking is + + align:start position:0% +that um its basic uh way of thinking is + + + align:start position:0% +that um its basic uh way of thinking is +going to be you know it's there you + + align:start position:0% +going to be you know it's there you + + + align:start position:0% +going to be you know it's there you +might have to put some you uh uh + + align:start position:0% +might have to put some you uh uh + + + align:start position:0% +might have to put some you uh uh +programs on it to teach it to do + + align:start position:0% +programs on it to teach it to do + + + align:start position:0% +programs on it to teach it to do +specific things but you you you don't + + align:start position:0% +specific things but you you you don't + + + align:start position:0% +specific things but you you you don't +have to educate its motherboard or + + align:start position:0% +have to educate its motherboard or + + + align:start position:0% +have to educate its motherboard or +something of that sort um with kids it's + + align:start position:0% +something of that sort um with kids it's + + + align:start position:0% +something of that sort um with kids it's +not clear that that's the case that if + + align:start position:0% +not clear that that's the case that if + + + align:start position:0% +not clear that that's the case that if +you take an off-the-shelf baby it's not + + align:start position:0% +you take an off-the-shelf baby it's not + + + align:start position:0% +you take an off-the-shelf baby it's not +clear that that baby is thinking the way + + align:start position:0% +clear that that baby is thinking the way + + + align:start position:0% +clear that that baby is thinking the way +that an adult is thinking and that's + + align:start position:0% +that an adult is thinking and that's + + + align:start position:0% +that an adult is thinking and that's +really what I want to uh want to talk + + align:start position:0% +really what I want to uh want to talk + + + align:start position:0% +really what I want to uh want to talk +about today + + align:start position:0% +about today + + + align:start position:0% +about today +um let me put up a picture that I can + + align:start position:0% +um let me put up a picture that I can + + + align:start position:0% +um let me put up a picture that I can +then return + + align:start position:0% +then return + + + align:start position:0% +then return +to multiple times if this + + align:start position:0% +to multiple times if this + + + align:start position:0% +to multiple times if this +is age and we're interested in + + align:start position:0% +is age and we're interested in + + + align:start position:0% +is age and we're interested in +development um what we were talking + + align:start position:0% +development um what we were talking + + + align:start position:0% +development um what we were talking +about last time is the adult state + + align:start position:0% +about last time is the adult state + + + align:start position:0% +about last time is the adult state +something about the adult State what we + + align:start position:0% +something about the adult State what we + + + align:start position:0% +something about the adult State what we +want to + + align:start position:0% +want to + + + align:start position:0% +want to +know in studying cognitive development + + align:start position:0% +know in studying cognitive development + + + align:start position:0% +know in studying cognitive development +or any sort of development is what's the + + align:start position:0% +or any sort of development is what's the + + + align:start position:0% +or any sort of development is what's the +starting + + align:start position:0% +starting + + + align:start position:0% +starting +point if you have a newborn baby is that + + align:start position:0% +point if you have a newborn baby is that + + + align:start position:0% +point if you have a newborn baby is that +baby starting at zero or does that baby + + align:start position:0% +baby starting at zero or does that baby + + + align:start position:0% +baby starting at zero or does that baby +come with some sort of an innate + + align:start position:0% +come with some sort of an innate + + + align:start position:0% +come with some sort of an innate +endowment that allows them uh that that + + align:start position:0% +endowment that allows them uh that that + + + align:start position:0% +endowment that allows them uh that that +that that that that gets them on the way + + align:start position:0% +that that that that gets them on the way + + + align:start position:0% +that that that that gets them on the way +towards the adult State and then what + + align:start position:0% +towards the adult State and then what + + + align:start position:0% +towards the adult State and then what +does the uh what does the um + + align:start position:0% +does the uh what does the um + + + align:start position:0% +does the uh what does the um +uh the transition from the kid state to + + align:start position:0% +uh the transition from the kid state to + + + align:start position:0% +uh the transition from the kid state to +the adult State look like does it look + + align:start position:0% +the adult State look like does it look + + + align:start position:0% +the adult State look like does it look +like some sort of gradual Improvement + + align:start position:0% +like some sort of gradual Improvement + + + align:start position:0% +like some sort of gradual Improvement +does it look like some sort of Step + + align:start position:0% +does it look like some sort of Step + + + align:start position:0% +does it look like some sort of Step +function it might be useful to uh to + + align:start position:0% +function it might be useful to uh to + + + align:start position:0% +function it might be useful to uh to +describe um from the realm of vision um + + align:start position:0% +describe um from the realm of vision um + + + align:start position:0% +describe um from the realm of vision um +a couple of examples just to show you + + align:start position:0% +a couple of examples just to show you + + + align:start position:0% +a couple of examples just to show you +what what this means um if you want to + + align:start position:0% +what what this means um if you want to + + + align:start position:0% +what what this means um if you want to +know what a baby sees if you go and + + align:start position:0% +know what a baby sees if you go and + + + align:start position:0% +know what a baby sees if you go and +we'll go over here if you you know you + + align:start position:0% +we'll go over here if you you know you + + + align:start position:0% +we'll go over here if you you know you +give yourself get get yourself a newborn + + align:start position:0% +give yourself get get yourself a newborn + + + align:start position:0% +give yourself get get yourself a newborn +off-the-shelf baby and give them um well + + align:start position:0% +off-the-shelf baby and give them um well + + + align:start position:0% +off-the-shelf baby and give them um well +you can't give them an ey chart to read + + align:start position:0% +you can't give them an ey chart to read + + + align:start position:0% +you can't give them an ey chart to read +because they can't read so you know you + + align:start position:0% +because they can't read so you know you + + + align:start position:0% +because they can't read so you know you +give them the illiterate e chart as it's + + align:start position:0% +give them the illiterate e chart as it's + + + align:start position:0% +give them the illiterate e chart as it's +called in the trade and whoops + + align:start position:0% + + + + align:start position:0% + +well you know and so on and you ask them + + align:start position:0% +well you know and so on and you ask them + + + align:start position:0% +well you know and so on and you ask them +which way did the the letters point the + + align:start position:0% +which way did the the letters point the + + + align:start position:0% +which way did the the letters point the +kid doesn't tell you anything useful + + align:start position:0% +kid doesn't tell you anything useful + + + align:start position:0% +kid doesn't tell you anything useful +right cuz the kid can't answer that + + align:start position:0% +right cuz the kid can't answer that + + + align:start position:0% +right cuz the kid can't answer that +question however convenience ly + + align:start position:0% +question however convenience ly + + + align:start position:0% +question however convenience ly +enough um if you take even a newborn + + align:start position:0% +enough um if you take even a newborn + + + align:start position:0% +enough um if you take even a newborn +baby as young as you can test them and + + align:start position:0% +baby as young as you can test them and + + + align:start position:0% +baby as young as you can test them and +put them in front of a couple of + + align:start position:0% +put them in front of a couple of + + + align:start position:0% +put them in front of a couple of +screens little peephole here you guys + + align:start position:0% +screens little peephole here you guys + + + align:start position:0% +screens little peephole here you guys +can all be + + align:start position:0% +can all be + + + align:start position:0% +can all be +babies and I the experimentor be looking + + align:start position:0% +babies and I the experimentor be looking + + + align:start position:0% +babies and I the experimentor be looking +out at at you through this peephole if + + align:start position:0% +out at at you through this peephole if + + + align:start position:0% +out at at you through this peephole if +you put black and white bars on one + + align:start position:0% +you put black and white bars on one + + + align:start position:0% +you put black and white bars on one +screen and you put on the other screen a + + align:start position:0% +screen and you put on the other screen a + + + align:start position:0% +screen and you put on the other screen a +gray the same average luminance so if + + align:start position:0% +gray the same average luminance so if + + + align:start position:0% +gray the same average luminance so if +this is you know zero and that's 100 + + align:start position:0% +this is you know zero and that's 100 + + + align:start position:0% +this is you know zero and that's 100 +this is 50 all over the place if the + + align:start position:0% +this is 50 all over the place if the + + + align:start position:0% +this is 50 all over the place if the +baby can see the bars conveniently + + align:start position:0% +baby can see the bars conveniently + + + align:start position:0% +baby can see the bars conveniently +enough that baby will look at the + + align:start position:0% +enough that baby will look at the + + + align:start position:0% +enough that baby will look at the +bars um and uh if you are looking at the + + align:start position:0% +bars um and uh if you are looking at the + + + align:start position:0% +bars um and uh if you are looking at the +baby you can figure out you move the + + align:start position:0% +baby you can figure out you move the + + + align:start position:0% +baby you can figure out you move the +bars from side to side from trial to + + align:start position:0% +bars from side to side from trial to + + + align:start position:0% +bars from side to side from trial to +trial you can figure out where that baby + + align:start position:0% +trial you can figure out where that baby + + + align:start position:0% +trial you can figure out where that baby +is looking and you can figure out where + + align:start position:0% +is looking and you can figure out where + + + align:start position:0% +is looking and you can figure out where +the bars are based on what what the B + + align:start position:0% +the bars are based on what what the B + + + align:start position:0% +the bars are based on what what the B +where the baby is looking that's known + + align:start position:0% +where the baby is looking that's known + + + align:start position:0% +where the baby is looking that's known +as pref a preferential looking method me + + align:start position:0% +as pref a preferential looking method me + + + align:start position:0% +as pref a preferential looking method me +very useful in in + + align:start position:0% +very useful in in + + + align:start position:0% +very useful in in +infant research um and what you discover + + align:start position:0% +infant research um and what you discover + + + align:start position:0% +infant research um and what you discover +if you do experiments like this studying + + align:start position:0% +if you do experiments like this studying + + + align:start position:0% +if you do experiments like this studying +infant visual Acuity is that babies + + align:start position:0% +infant visual Acuity is that babies + + + align:start position:0% +infant visual Acuity is that babies +don't start at zero babies don't start + + align:start position:0% +don't start at zero babies don't start + + + align:start position:0% +don't start at zero babies don't start +you know newborn baby isn't + + align:start position:0% +you know newborn baby isn't + + + align:start position:0% +you know newborn baby isn't +blind newborn baby can see something if + + align:start position:0% +blind newborn baby can see something if + + + align:start position:0% +blind newborn baby can see something if +normal adult vision is around + + align:start position:0% +normal adult vision is around + + + align:start position:0% +normal adult vision is around +2020 um newborn baby vision is around + + align:start position:0% +2020 um newborn baby vision is around + + + align:start position:0% +2020 um newborn baby vision is around +2400 it's the Big E at the top of the + + align:start position:0% +2400 it's the Big E at the top of the + + + align:start position:0% +2400 it's the Big E at the top of the +eye chart roughly + + align:start position:0% +eye chart roughly + + + align:start position:0% +eye chart roughly +um and um the progression from the + + align:start position:0% +um and um the progression from the + + + align:start position:0% +um and um the progression from the +infant state to the adult state is a + + align:start position:0% +infant state to the adult state is a + + + align:start position:0% +infant state to the adult state is a +gradual relatively steady increase over + + align:start position:0% +gradual relatively steady increase over + + + align:start position:0% +gradual relatively steady increase over +um about the first couple of years of + + align:start position:0% +um about the first couple of years of + + + align:start position:0% +um about the first couple of years of +life every month you get roughly the + + align:start position:0% +life every month you get roughly the + + + align:start position:0% +life every month you get roughly the +same kind of uh Improvement until you + + align:start position:0% +same kind of uh Improvement until you + + + align:start position:0% +same kind of uh Improvement until you +hit the uh adult level so not a zero + + align:start position:0% +hit the uh adult level so not a zero + + + align:start position:0% +hit the uh adult level so not a zero +starting + + align:start position:0% +starting + + + align:start position:0% +starting +point um and a gradual Improvement to + + align:start position:0% +point um and a gradual Improvement to + + + align:start position:0% +point um and a gradual Improvement to +adult levels now let's take a different + + align:start position:0% +adult levels now let's take a different + + + align:start position:0% +adult levels now let's take a different +example from the same realm um remember + + align:start position:0% +example from the same realm um remember + + + align:start position:0% +example from the same realm um remember +you've got two eyes the differences in + + align:start position:0% +you've got two eyes the differences in + + + align:start position:0% +you've got two eyes the differences in +those two eyes are are a depth Q um + + align:start position:0% +those two eyes are are a depth Q um + + + align:start position:0% +those two eyes are are a depth Q um +known as binocular stereopsis well the Q + + align:start position:0% +known as binocular stereopsis well the Q + + + align:start position:0% +known as binocular stereopsis well the Q +is binocular disparity the ability is + + align:start position:0% +is binocular disparity the ability is + + + align:start position:0% +is binocular disparity the ability is +stereoscopic depth perception um if you + + align:start position:0% +stereoscopic depth perception um if you + + + align:start position:0% +stereoscopic depth perception um if you +test a baby so babies it turns out also + + align:start position:0% +test a baby so babies it turns out also + + + align:start position:0% +test a baby so babies it turns out also +like things that stand out in depth + + align:start position:0% +like things that stand out in depth + + + align:start position:0% +like things that stand out in depth +better than they like flat stuff so if + + align:start position:0% +better than they like flat stuff so if + + + align:start position:0% +better than they like flat stuff so if +you show a baby bar is standing out in + + align:start position:0% +you show a baby bar is standing out in + + + align:start position:0% +you show a baby bar is standing out in +depth a newborn + + align:start position:0% +depth a newborn + + + align:start position:0% +depth a newborn +baby gives you + + align:start position:0% +baby gives you + + + align:start position:0% +baby gives you +squat to all appearances there is no + + align:start position:0% +squat to all appearances there is no + + + align:start position:0% +squat to all appearances there is no +binocular stereo Vision in in a uh in a + + align:start position:0% +binocular stereo Vision in in a uh in a + + + align:start position:0% +binocular stereo Vision in in a uh in a +newborn baby um and for about the first + + align:start position:0% +newborn baby um and for about the first + + + align:start position:0% +newborn baby um and for about the first +3 to five months nothing happens and + + align:start position:0% +3 to five months nothing happens and + + + align:start position:0% +3 to five months nothing happens and +then over a very short period of time I + + align:start position:0% +then over a very short period of time I + + + align:start position:0% +then over a very short period of time I +should get rid of this other step + + align:start position:0% +should get rid of this other step + + + align:start position:0% +should get rid of this other step +function just + + align:start position:0% +function just + + + align:start position:0% +function just +to not confuse matters over a very short + + align:start position:0% +to not confuse matters over a very short + + + align:start position:0% +to not confuse matters over a very short +period of time performance Rises to + + align:start position:0% +period of time performance Rises to + + + align:start position:0% +period of time performance Rises to +essentially the adult level as if this + + align:start position:0% +essentially the adult level as if this + + + align:start position:0% +essentially the adult level as if this +was waiting for something to get wired + + align:start position:0% +was waiting for something to get wired + + + align:start position:0% +was waiting for something to get wired +up in the brain when it got wired up in + + align:start position:0% +up in the brain when it got wired up in + + + align:start position:0% +up in the brain when it got wired up in +the brain Bingo the uh the kid is fine + + align:start position:0% +the brain Bingo the uh the kid is fine + + + align:start position:0% +the brain Bingo the uh the kid is fine +oh by the way if you are a woman person + + align:start position:0% +oh by the way if you are a woman person + + + align:start position:0% +oh by the way if you are a woman person +you got there first it turns out to be a + + align:start position:0% +you got there first it turns out to be a + + + align:start position:0% +you got there first it turns out to be a +reliable sex difference that uh females + + align:start position:0% +reliable sex difference that uh females + + + align:start position:0% +reliable sex difference that uh females +get uh binocular stereo Vision a month + + align:start position:0% +get uh binocular stereo Vision a month + + + align:start position:0% +get uh binocular stereo Vision a month +or so before males um does this make any + + align:start position:0% +or so before males um does this make any + + + align:start position:0% +or so before males um does this make any +difference to anything no but we found + + align:start position:0% +difference to anything no but we found + + + align:start position:0% +difference to anything no but we found +it years and years ago when I was a grad + + align:start position:0% +it years and years ago when I was a grad + + + align:start position:0% +it years and years ago when I was a grad +student so I still remember it um so + + align:start position:0% +student so I still remember it um so + + + align:start position:0% +student so I still remember it um so +these are are two of the various + + align:start position:0% +these are are two of the various + + + align:start position:0% +these are are two of the various +possibilities for a function like this + + align:start position:0% +possibilities for a function like this + + + align:start position:0% +possibilities for a function like this +uh for for a a developmental course and + + align:start position:0% +uh for for a a developmental course and + + + align:start position:0% +uh for for a a developmental course and +and we're going to look at um we're + + align:start position:0% +and we're going to look at um we're + + + align:start position:0% +and we're going to look at um we're +going to talk about three um specific + + align:start position:0% +going to talk about three um specific + + + align:start position:0% +going to talk about three um specific +Realms of cognitive + + align:start position:0% +Realms of cognitive + + + align:start position:0% +Realms of cognitive +development um in which there are + + align:start position:0% +development um in which there are + + + align:start position:0% +development um in which there are +classic + + align:start position:0% +classic + + + align:start position:0% +classic +demonstrations of children doing things + + align:start position:0% +demonstrations of children doing things + + + align:start position:0% +demonstrations of children doing things +different differently than adults do + + align:start position:0% +different differently than adults do + + + align:start position:0% +different differently than adults do +them and I will try to take each of + + align:start position:0% +them and I will try to take each of + + + align:start position:0% +them and I will try to take each of +those apart and to give you some idea of + + align:start position:0% +those apart and to give you some idea of + + + align:start position:0% +those apart and to give you some idea of +what's the starting point what's the + + align:start position:0% +what's the starting point what's the + + + align:start position:0% +what's the starting point what's the +ending point and how do we get between + + align:start position:0% +ending point and how do we get between + + + align:start position:0% +ending point and how do we get between +those the three which are uh outlined on + + align:start position:0% +those the three which are uh outlined on + + + align:start position:0% +those the three which are uh outlined on +the uh handout are um have to do with uh + + align:start position:0% +the uh handout are um have to do with uh + + + align:start position:0% +the uh handout are um have to do with uh +uh number CH so-called childhood animism + + align:start position:0% +uh number CH so-called childhood animism + + + align:start position:0% +uh number CH so-called childhood animism +and egocentric Behavior let me describe + + align:start position:0% +and egocentric Behavior let me describe + + + align:start position:0% +and egocentric Behavior let me describe +each of these problems to you in turn + + align:start position:0% +each of these problems to you in turn + + + align:start position:0% +each of these problems to you in turn +and uh and then we'll take each of them + + align:start position:0% +and uh and then we'll take each of them + + + align:start position:0% +and uh and then we'll take each of them +um apart the classic the these are all + + align:start position:0% +um apart the classic the these are all + + + align:start position:0% +um apart the classic the these are all +demonstrations that + + align:start position:0% +demonstrations that + + + align:start position:0% +demonstrations that +um originally come from the work of Jean + + align:start position:0% +um originally come from the work of Jean + + + align:start position:0% +um originally come from the work of Jean +P the + + align:start position:0% +P the + + + align:start position:0% +P the +um uh the great early mid 20th century + + align:start position:0% +um uh the great early mid 20th century + + + align:start position:0% +um uh the great early mid 20th century +uh developmental psychologist who among + + align:start position:0% +uh developmental psychologist who among + + + align:start position:0% +uh developmental psychologist who among +other things bequeathed to us a great + + align:start position:0% +other things bequeathed to us a great + + + align:start position:0% +other things bequeathed to us a great +collection of phenomena um that show + + align:start position:0% +collection of phenomena um that show + + + align:start position:0% +collection of phenomena um that show +striking differences between the way + + align:start position:0% +striking differences between the way + + + align:start position:0% +striking differences between the way +kids behave and the way adults behave + + align:start position:0% +kids behave and the way adults behave + + + align:start position:0% +kids behave and the way adults behave +and that that cry out for explanation so + + align:start position:0% +and that that cry out for explanation so + + + align:start position:0% +and that that cry out for explanation so +here would be one of them these are + + align:start position:0% +here would be one of them these are + + + align:start position:0% +here would be one of them these are +M&M's let us + + align:start position:0% + + + + align:start position:0% + +say that'll + + align:start position:0% + + + + align:start position:0% + +do uhoh I'm running out of space here + + align:start position:0% +do uhoh I'm running out of space here + + + align:start position:0% +do uhoh I'm running out of space here +for MY + + align:start position:0% +for MY + + + align:start position:0% +for MY +M&M's well people over there can't see + + align:start position:0% +M&M's well people over there can't see + + + align:start position:0% +M&M's well people over there can't see +them can you can you can you see that + + align:start position:0% +them can you can you can you see that + + + align:start position:0% +them can you can you can you see that +Eminem uh wait a second I'll put them + + align:start position:0% +Eminem uh wait a second I'll put them + + + align:start position:0% +Eminem uh wait a second I'll put them +down + + align:start position:0% +down + + + align:start position:0% +down +here that'll + + align:start position:0% + + + + align:start position:0% + +work there we go don't worry about these + + align:start position:0% +work there we go don't worry about these + + + align:start position:0% +work there we go don't worry about these +M&M's okay + + align:start position:0% +M&M's okay + + + align:start position:0% +M&M's okay +um this is another one of those Force + + align:start position:0% +um this is another one of those Force + + + align:start position:0% +um this is another one of those Force +Choice kind of things so think hard + + align:start position:0% +Choice kind of things so think hard + + + align:start position:0% +Choice kind of things so think hard +about this are there more M&M's here or + + align:start position:0% +about this are there more M&M's here or + + + align:start position:0% +about this are there more M&M's here or +here how many vote + + align:start position:0% +here how many vote + + + align:start position:0% +here how many vote +up that's + + align:start position:0% +up that's + + + align:start position:0% +up that's +good however if you were three four five + + align:start position:0% +good however if you were three four five + + + align:start position:0% +good however if you were three four five +maybe even six um you'd say here you you + + align:start position:0% +maybe even six um you'd say here you you + + + align:start position:0% +maybe even six um you'd say here you you +you would you would be perfectly happy + + align:start position:0% +you would you would be perfectly happy + + + align:start position:0% +you would you would be perfectly happy +yeah you think it's that's good that's + + align:start position:0% +yeah you think it's that's good that's + + + align:start position:0% +yeah you think it's that's good that's +that's that's nice it makes math a + + align:start position:0% +that's that's nice it makes math a + + + align:start position:0% +that's that's nice it makes math a +little more difficult here at MIT but + + align:start position:0% +little more difficult here at MIT but + + + align:start position:0% +little more difficult here at MIT but +but you should that we shouldn't stifle + + align:start position:0% +but you should that we shouldn't stifle + + + align:start position:0% +but you should that we shouldn't stifle +your creativity that's that's that's + + align:start position:0% +your creativity that's that's that's + + + align:start position:0% +your creativity that's that's that's +good um and so the first obvious thought + + align:start position:0% +good um and so the first obvious thought + + + align:start position:0% +good um and so the first obvious thought +is but the kids just not quite + + align:start position:0% +is but the kids just not quite + + + align:start position:0% +is but the kids just not quite +understanding the the question uh it's a + + align:start position:0% + + + + align:start position:0% + +languageyoutube and they're saying which + + align:start position:0% +languageyoutube and they're saying which + + + align:start position:0% +languageyoutube and they're saying which +is longer so that's why it's important + + align:start position:0% +is longer so that's why it's important + + + align:start position:0% +is longer so that's why it's important +that you use M&M's you say okay kid + + align:start position:0% +that you use M&M's you say okay kid + + + align:start position:0% +that you use M&M's you say okay kid +which pile would you + + align:start position:0% +which pile would you + + + align:start position:0% +which pile would you +like kid says I want this pile H why do + + align:start position:0% +like kid says I want this pile H why do + + + align:start position:0% +like kid says I want this pile H why do +you want this pile well there's more + + align:start position:0% +you want this pile well there's more + + + align:start position:0% +you want this pile well there's more +there the um so and in fact this is why + + align:start position:0% +there the um so and in fact this is why + + + align:start position:0% +there the um so and in fact this is why +you shouldn't be born to a psychologist + + align:start position:0% +you shouldn't be born to a psychologist + + + align:start position:0% +you shouldn't be born to a psychologist +because your psychologist dad is always + + align:start position:0% +because your psychologist dad is always + + + align:start position:0% +because your psychologist dad is always +tricking you out of the Candy by playing + + align:start position:0% +tricking you out of the Candy by playing + + + align:start position:0% +tricking you out of the Candy by playing +this game on you it it works it's it's + + align:start position:0% +this game on you it it works it's it's + + + align:start position:0% +this game on you it it works it's it's +good it's you know you teach this stuff + + align:start position:0% +good it's you know you teach this stuff + + + align:start position:0% +good it's you know you teach this stuff +long enough you think is this really + + align:start position:0% +long enough you think is this really + + + align:start position:0% +long enough you think is this really +true and then you've got yourself like a + + align:start position:0% +true and then you've got yourself like a + + + align:start position:0% +true and then you've got yourself like a +a three-year-old kid and you mess with + + align:start position:0% +a three-year-old kid and you mess with + + + align:start position:0% +a three-year-old kid and you mess with +his brain and yeah it's true this + + align:start position:0% +his brain and yeah it's true this + + + align:start position:0% +his brain and yeah it's true this +this this is good stuff + + align:start position:0% +this this is good stuff + + + align:start position:0% +this this is good stuff +um but so so you want to know what's the + + align:start position:0% +um but so so you want to know what's the + + + align:start position:0% +um but so so you want to know what's the +the question here of course is then + + align:start position:0% +the question here of course is then + + + align:start position:0% +the question here of course is then +what's what's going on um it this is + + align:start position:0% +what's what's going on um it this is + + + align:start position:0% +what's what's going on um it this is +part of a general problem um if you take + + align:start position:0% +part of a general problem um if you take + + + align:start position:0% +part of a general problem um if you take +so let's take a a a fat Beaker here's a + + align:start position:0% +so let's take a a a fat Beaker here's a + + + align:start position:0% +so let's take a a a fat Beaker here's a +big fat Beaker with this much fluid in + + align:start position:0% +big fat Beaker with this much fluid in + + + align:start position:0% +big fat Beaker with this much fluid in +it now I pour that into a narrow speaker + + align:start position:0% +it now I pour that into a narrow speaker + + + align:start position:0% +it now I pour that into a narrow speaker +the water uh the the fluid level + + align:start position:0% +the water uh the the fluid level + + + align:start position:0% +the water uh the the fluid level +is higher is there more fluid now than + + align:start position:0% +is higher is there more fluid now than + + + align:start position:0% +is higher is there more fluid now than +there was when it was here + + align:start position:0% +there was when it was here + + + align:start position:0% +there was when it was here +no um does a a little kid think there is + + align:start position:0% +no um does a a little kid think there is + + + align:start position:0% +no um does a a little kid think there is +yes if you let the little kid pour it + + align:start position:0% +yes if you let the little kid pour it + + + align:start position:0% +yes if you let the little kid pour it +back into the big bowl now he thinks + + align:start position:0% +back into the big bowl now he thinks + + + align:start position:0% +back into the big bowl now he thinks +there's less now take a ball of clay + + align:start position:0% +there's less now take a ball of clay + + + align:start position:0% +there's less now take a ball of clay +roll it out into a snake there's more + + align:start position:0% +roll it out into a snake there's more + + + align:start position:0% +roll it out into a snake there's more +clay says the little kid squish it back + + align:start position:0% +clay says the little kid squish it back + + + align:start position:0% +clay says the little kid squish it back +together now there's less um these These + + align:start position:0% +together now there's less um these These + + + align:start position:0% +together now there's less um these These +are so-called conservation problems + + align:start position:0% +are so-called conservation problems + + + align:start position:0% +are so-called conservation problems +we're particularly interested in the + + align:start position:0% +we're particularly interested in the + + + align:start position:0% +we're particularly interested in the +version that has to do with number how + + align:start position:0% +version that has to do with number how + + + align:start position:0% +version that has to do with number how +come they think in this case that five + + align:start position:0% +come they think in this case that five + + + align:start position:0% +come they think in this case that five +is bigger than six um second problem is + + align:start position:0% +is bigger than six um second problem is + + + align:start position:0% +is bigger than six um second problem is +uh uh what's called childhood animism + + align:start position:0% +uh uh what's called childhood animism + + + align:start position:0% +uh uh what's called childhood animism +the uh the classic + + align:start position:0% +the uh the classic + + + align:start position:0% +the uh the classic +petan version would involve something + + align:start position:0% +petan version would involve something + + + align:start position:0% +petan version would involve something +like well something exactly like a his + + align:start position:0% +like well something exactly like a his + + + align:start position:0% +like well something exactly like a his +so-called three + + align:start position:0% +so-called three + + + align:start position:0% +so-called three +Mountain apparatus where he had a sort + + align:start position:0% +Mountain apparatus where he had a sort + + + align:start position:0% +Mountain apparatus where he had a sort +of a + + align:start position:0% +of a + + + align:start position:0% +of a +tabletop he's from Switzerland so he's + + align:start position:0% +tabletop he's from Switzerland so he's + + + align:start position:0% +tabletop he's from Switzerland so he's +into the Alps right see it's a tabletop + + align:start position:0% +into the Alps right see it's a tabletop + + + align:start position:0% +into the Alps right see it's a tabletop +version of the Alps and on the Alps are + + align:start position:0% +version of the Alps and on the Alps are + + + align:start position:0% +version of the Alps and on the Alps are +things like a that's a + + align:start position:0% +things like a that's a + + + align:start position:0% +things like a that's a +river and that's that's a Hut + + align:start position:0% +river and that's that's a Hut + + + align:start position:0% +river and that's that's a Hut +um it's a it's yeah it's it's it's where + + align:start position:0% +um it's a it's yeah it's it's it's where + + + align:start position:0% +um it's a it's yeah it's it's it's where +the pie maker lives right you know the + + align:start position:0% +the pie maker lives right you know the + + + align:start position:0% +the pie maker lives right you know the +um so anyway that the point is that + + align:start position:0% +um so anyway that the point is that + + + align:start position:0% +um so anyway that the point is that +you're sitting here looking at this + + align:start position:0% +you're sitting here looking at this + + + align:start position:0% +you're sitting here looking at this +thing you're you're you're you're like a + + align:start position:0% +thing you're you're you're you're like a + + + align:start position:0% +thing you're you're you're you're like a +three-year-old or something looking at + + align:start position:0% +three-year-old or something looking at + + + align:start position:0% +three-year-old or something looking at +this and and mom's over there on the + + align:start position:0% +this and and mom's over there on the + + + align:start position:0% +this and and mom's over there on the +other side you can see mom um and and + + align:start position:0% +other side you can see mom um and and + + + align:start position:0% +other side you can see mom um and and +the question that that that you're asked + + align:start position:0% +the question that that that you're asked + + + align:start position:0% +the question that that that you're asked +is can your mother see the river and you + + align:start position:0% +is can your mother see the river and you + + + align:start position:0% +is can your mother see the river and you +say yeah sure as if the fact that you + + align:start position:0% +say yeah sure as if the fact that you + + + align:start position:0% +say yeah sure as if the fact that you +could see the river makes it uh uh makes + + align:start position:0% +could see the river makes it uh uh makes + + + align:start position:0% +could see the river makes it uh uh makes +you think that she can see the river as + + align:start position:0% +you think that she can see the river as + + + align:start position:0% +you think that she can see the river as +if you couldn't take her point of view + + align:start position:0% +if you couldn't take her point of view + + + align:start position:0% +if you couldn't take her point of view +at least P thought that the problem here + + align:start position:0% +at least P thought that the problem here + + + align:start position:0% +at least P thought that the problem here +is that you can't quite take somebody + + align:start position:0% +is that you can't quite take somebody + + + align:start position:0% +is that you can't quite take somebody +else's point of view my favorite my + + align:start position:0% +else's point of view my favorite my + + + align:start position:0% +else's point of view my favorite my +favorite anecdotal version of this this + + align:start position:0% +favorite anecdotal version of this this + + + align:start position:0% +favorite anecdotal version of this this +is a story of a little kid um out to uh + + align:start position:0% +is a story of a little kid um out to uh + + + align:start position:0% +is a story of a little kid um out to uh +um eat with his brother at some burger + + align:start position:0% +um eat with his brother at some burger + + + align:start position:0% +um eat with his brother at some burger +place little kid wants more french fries + + align:start position:0% +place little kid wants more french fries + + + align:start position:0% +place little kid wants more french fries +and so he does + + align:start position:0% +and so he does + + + align:start position:0% +and so he does +this on the theory presumably if I can't + + align:start position:0% +this on the theory presumably if I can't + + + align:start position:0% +this on the theory presumably if I can't +see what I'm doing you can't see what + + align:start position:0% +see what I'm doing you can't see what + + + align:start position:0% +see what I'm doing you can't see what +I'm doing um so they mo most most people + + align:start position:0% +I'm doing um so they mo most most people + + + align:start position:0% +I'm doing um so they mo most most people +don't do that by the time they reach + + align:start position:0% +don't do that by the time they reach + + + align:start position:0% +don't do that by the time they reach +adulthood right that that's so there's + + align:start position:0% +adulthood right that that's so there's + + + align:start position:0% +adulthood right that that's so there's +there's something to explain there + + align:start position:0% +there's something to explain there + + + align:start position:0% +there's something to explain there +that's childhood um um that's not + + align:start position:0% +that's childhood um um that's not + + + align:start position:0% +that's childhood um um that's not +childhood animism at + + align:start position:0% +childhood animism at + + + align:start position:0% +childhood animism at +all EXA actually that's e that's + + align:start position:0% +all EXA actually that's e that's + + + align:start position:0% +all EXA actually that's e that's +egocentric Behavior sorry I I I I + + align:start position:0% +egocentric Behavior sorry I I I I + + + align:start position:0% +egocentric Behavior sorry I I I I +misspoke that's the third example that + + align:start position:0% +misspoke that's the third example that + + + align:start position:0% +misspoke that's the third example that +we'll get to so ocent makes more sense + + align:start position:0% +we'll get to so ocent makes more sense + + + align:start position:0% +we'll get to so ocent makes more sense +egocentric is the inability to see + + align:start position:0% +egocentric is the inability to see + + + align:start position:0% +egocentric is the inability to see +things from somebody else's vantage + + align:start position:0% +things from somebody else's vantage + + + align:start position:0% +things from somebody else's vantage +point so I've just described to you the + + align:start position:0% +point so I've just described to you the + + + align:start position:0% +point so I've just described to you the +problem of of childhood egocentrism + + align:start position:0% +problem of of childhood egocentrism + + + align:start position:0% +problem of of childhood egocentrism +childhood animism um is uh a a tendency + + align:start position:0% +childhood animism um is uh a a tendency + + + align:start position:0% +childhood animism um is uh a a tendency +to declare things to be alive that you + + align:start position:0% +to declare things to be alive that you + + + align:start position:0% +to declare things to be alive that you +would not declare to be alive um is the + + align:start position:0% +would not declare to be alive um is the + + + align:start position:0% +would not declare to be alive um is the +cat alive yeah fine is the sun alive yes + + align:start position:0% +cat alive yeah fine is the sun alive yes + + + align:start position:0% +cat alive yeah fine is the sun alive yes +is the CL are the clouds alive yes + + align:start position:0% +is the CL are the clouds alive yes + + + align:start position:0% +is the CL are the clouds alive yes +little kids will will assert that and + + align:start position:0% +little kids will will assert that and + + + align:start position:0% +little kids will will assert that and +you typically will not um that's uh + + align:start position:0% +you typically will not um that's uh + + + align:start position:0% +you typically will not um that's uh +that's animism uh P understood that as a + + align:start position:0% +that's animism uh P understood that as a + + + align:start position:0% +that's animism uh P understood that as a +problem with mapping um Concepts onto a + + align:start position:0% +problem with mapping um Concepts onto a + + + align:start position:0% +problem with mapping um Concepts onto a +a discrete set of entities out in the + + align:start position:0% +a discrete set of entities out in the + + + align:start position:0% +a discrete set of entities out in the +world and so we'll take a look at uh at + + align:start position:0% +world and so we'll take a look at uh at + + + align:start position:0% +world and so we'll take a look at uh at +that too so number animism egocentric + + align:start position:0% +that too so number animism egocentric + + + align:start position:0% +that too so number animism egocentric +Behavior those are the things that I + + align:start position:0% +Behavior those are the things that I + + + align:start position:0% +Behavior those are the things that I +want to talk about today let's start + + align:start position:0% +want to talk about today let's start + + + align:start position:0% +want to talk about today let's start +with um with numer with with number and + + align:start position:0% +with um with numer with with number and + + + align:start position:0% +with um with numer with with number and +let's start by um taking apart the idea + + align:start position:0% +let's start by um taking apart the idea + + + align:start position:0% +let's start by um taking apart the idea +of number a bit because you and I tend + + align:start position:0% +of number a bit because you and I tend + + + align:start position:0% +of number a bit because you and I tend +to think of number as + + align:start position:0% +to think of number as + + + align:start position:0% +to think of number as +um uh you know there's five of those + + align:start position:0% +um uh you know there's five of those + + + align:start position:0% +um uh you know there's five of those +things and six of those things number + + align:start position:0% +things and six of those things number + + + align:start position:0% +things and six of those things number +the the concept of Number the idea of + + align:start position:0% +the the concept of Number the idea of + + + align:start position:0% +the the concept of Number the idea of +number can be broken down into uh three + + align:start position:0% +number can be broken down into uh three + + + align:start position:0% +number can be broken down into uh three +different bits at least and let's see if + + align:start position:0% +different bits at least and let's see if + + + align:start position:0% +different bits at least and let's see if +I can do this right + + align:start position:0% +I can do this right + + + align:start position:0% +I can do this right +who oh well they went by how many + + align:start position:0% +who oh well they went by how many + + + align:start position:0% +who oh well they went by how many +warthogs were + + align:start position:0% +warthogs were + + + align:start position:0% +warthogs were +there six who know some now wait a + + align:start position:0% +there six who know some now wait a + + + align:start position:0% +there six who know some now wait a +second let's try this + + align:start position:0% + + + + align:start position:0% + +again 9 + + align:start position:0% +again 9 + + + align:start position:0% +again 9 +8 seven some number like that it wasn't + + align:start position:0% +8 seven some number like that it wasn't + + + align:start position:0% +8 seven some number like that it wasn't +150 but how about this two yeah okay + + align:start position:0% +150 but how about this two yeah okay + + + align:start position:0% +150 but how about this two yeah okay +that's good whoops how about this three + + align:start position:0% +that's good whoops how about this three + + + align:start position:0% +that's good whoops how about this three +whoops how about that that was + + align:start position:0% +whoops how about that that was + + + align:start position:0% +whoops how about that that was +a how about this this is data + + align:start position:0% +a how about this this is data + + + align:start position:0% +a how about this this is data +um if you do this + + align:start position:0% +um if you do this + + + align:start position:0% +um if you do this +task um what what you find is that + + align:start position:0% +task um what what you find is that + + + align:start position:0% +task um what what you find is that +people are essentially perfect for one + + align:start position:0% +people are essentially perfect for one + + + align:start position:0% +people are essentially perfect for one +two and three maybe four and then it + + align:start position:0% +two and three maybe four and then it + + + align:start position:0% +two and three maybe four and then it +falls off they start I I think the + + align:start position:0% +falls off they start I I think the + + + align:start position:0% +falls off they start I I think the +answer was eight before but you you know + + align:start position:0% +answer was eight before but you you know + + + align:start position:0% +answer was eight before but you you know +sometimes you say seven sometimes you + + align:start position:0% +sometimes you say seven sometimes you + + + align:start position:0% +sometimes you say seven sometimes you +say nine and so your percent correct + + align:start position:0% +say nine and so your percent correct + + + align:start position:0% +say nine and so your percent correct +being absolutely correct will will will + + align:start position:0% +being absolutely correct will will will + + + align:start position:0% +being absolutely correct will will will +will systematically fall off and if I + + align:start position:0% +will systematically fall off and if I + + + align:start position:0% +will systematically fall off and if I +put 1,500 warthogs up there you'll just + + align:start position:0% +put 1,500 warthogs up there you'll just + + + align:start position:0% +put 1,500 warthogs up there you'll just +not get it right at all um similarly if + + align:start position:0% +not get it right at all um similarly if + + + align:start position:0% +not get it right at all um similarly if +I was to measure not percent correct but + + align:start position:0% +I was to measure not percent correct but + + + align:start position:0% +I was to measure not percent correct but +reaction time the reaction time for 1 2 + + align:start position:0% +reaction time the reaction time for 1 2 + + + align:start position:0% +reaction time the reaction time for 1 2 +3 4 would be essentially + + align:start position:0% +3 4 would be essentially + + + align:start position:0% +3 4 would be essentially +flat and then start to roughly linearly + + align:start position:0% +flat and then start to roughly linearly + + + align:start position:0% +flat and then start to roughly linearly +increase that linear increase could be + + align:start position:0% +increase that linear increase could be + + + align:start position:0% +increase that linear increase could be +uh for a number like eight could either + + align:start position:0% +uh for a number like eight could either + + + align:start position:0% +uh for a number like eight could either +be due to some sort of counting + + align:start position:0% +be due to some sort of counting + + + align:start position:0% +be due to some sort of counting +operation or how many people + + align:start position:0% +operation or how many people + + + align:start position:0% +operation or how many people +um somebody tell somebody who thinks + + align:start position:0% +um somebody tell somebody who thinks + + + align:start position:0% +um somebody tell somebody who thinks +they saw eight of them tell me how they + + align:start position:0% +they saw eight of them tell me how they + + + align:start position:0% +they saw eight of them tell me how they +figured that out yeah you saw five and + + align:start position:0% +figured that out yeah you saw five and + + + align:start position:0% +figured that out yeah you saw five and +two and one a line of five and two and + + align:start position:0% +two and one a line of five and two and + + + align:start position:0% +two and one a line of five and two and +one okay well that that that's that's + + align:start position:0% +one okay well that that that's that's + + + align:start position:0% +one okay well that that that's that's +yeah yeah I kind of went away you oh + + align:start position:0% +yeah yeah I kind of went away you oh + + + align:start position:0% +yeah yeah I kind of went away you oh +okay yes if if I was doing this as a + + align:start position:0% +okay yes if if I was doing this as a + + + align:start position:0% +okay yes if if I was doing this as a +proper experiment I would have masked it + + align:start position:0% +proper experiment I would have masked it + + + align:start position:0% +proper experiment I would have masked it +so you couldn't count like the after + + align:start position:0% +so you couldn't count like the after + + + align:start position:0% +so you couldn't count like the after +image or the iconic memory so there yep + + align:start position:0% +image or the iconic memory so there yep + + + align:start position:0% +image or the iconic memory so there yep +just recall the + + align:start position:0% +just recall the + + + align:start position:0% +just recall the +picture okay so you were on o dumping it + + align:start position:0% +picture okay so you were on o dumping it + + + align:start position:0% +picture okay so you were on o dumping it +out of iconic memory in some fashion the + + align:start position:0% +out of iconic memory in some fashion the + + + align:start position:0% +out of iconic memory in some fashion the +the the answer I was fishing for is + + align:start position:0% +the the answer I was fishing for is + + + align:start position:0% +the the answer I was fishing for is +something like the 52 in one thing that + + align:start position:0% +something like the 52 in one thing that + + + align:start position:0% +something like the 52 in one thing that +you can count those displays and in fact + + align:start position:0% +you can count those displays and in fact + + + align:start position:0% +you can count those displays and in fact +the people who got them back later might + + align:start position:0% +the people who got them back later might + + + align:start position:0% +the people who got them back later might +have done this too by uh more typically + + align:start position:0% +have done this too by uh more typically + + + align:start position:0% +have done this too by uh more typically +saying oh there's one group of four + + align:start position:0% +saying oh there's one group of four + + + align:start position:0% +saying oh there's one group of four +there's another group of four this + + align:start position:0% +there's another group of four this + + + align:start position:0% +there's another group of four this +ability to handle small numbers is + + align:start position:0% +ability to handle small numbers is + + + align:start position:0% +ability to handle small numbers is +called + + align:start position:0% +called + + + align:start position:0% +called +subitizing and it works for small + + align:start position:0% +subitizing and it works for small + + + align:start position:0% +subitizing and it works for small +numbers like 1 2 34 you have some + + align:start position:0% +numbers like 1 2 34 you have some + + + align:start position:0% +numbers like 1 2 34 you have some +immediate appreciation of that number of + + align:start position:0% +immediate appreciation of that number of + + + align:start position:0% +immediate appreciation of that number of +of those small numbers um that's + + align:start position:0% +of those small numbers um that's + + + align:start position:0% +of those small numbers um that's +different than your appreciation of + + align:start position:0% +different than your appreciation of + + + align:start position:0% +different than your appreciation of +eight or 17 or + + align:start position:0% +eight or 17 or + + + align:start position:0% +eight or 17 or +150 um okay that's uh um that's one + + align:start position:0% +150 um okay that's uh um that's one + + + align:start position:0% +150 um okay that's uh um that's one +warthog demonstration um how + + align:start position:0% +warthog demonstration um how + + + align:start position:0% +warthog demonstration um how +about which one has more + + align:start position:0% + + + + align:start position:0% + +warthogs how many vote that there were + + align:start position:0% +warthogs how many vote that there were + + + align:start position:0% +warthogs how many vote that there were +more here how many vote that there were + + align:start position:0% +more here how many vote that there were + + + align:start position:0% +more here how many vote that there were +more here yeah okay you got that right + + align:start position:0% +more here yeah okay you got that right + + + align:start position:0% +more here yeah okay you got that right +you you you you knew how many War Hogs + + align:start position:0% +you you you you knew how many War Hogs + + + align:start position:0% +you you you you knew how many War Hogs +were there + + align:start position:0% +were there + + + align:start position:0% +were there +here3 a lot a lot yeah uh and how many + + align:start position:0% +here3 a lot a lot yeah uh and how many + + + align:start position:0% +here3 a lot a lot yeah uh and how many +War Hogs were here L uh a lot but not as + + align:start position:0% +War Hogs were here L uh a lot but not as + + + align:start position:0% +War Hogs were here L uh a lot but not as +many well you can go back there we go um + + align:start position:0% +many well you can go back there we go um + + + align:start position:0% +many well you can go back there we go um +You can count these obviously but you + + align:start position:0% +You can count these obviously but you + + + align:start position:0% +You can count these obviously but you +didn't count them and you didn't + + align:start position:0% +didn't count them and you didn't + + + align:start position:0% +didn't count them and you didn't +subitize them what you did was you got + + align:start position:0% +subitize them what you did was you got + + + align:start position:0% +subitize them what you did was you got +some sort of general impression of their + + align:start position:0% +some sort of general impression of their + + + align:start position:0% +some sort of general impression of their +numerosity because + + align:start position:0% +numerosity because + + + align:start position:0% +numerosity because +um uh well this is this is if you go + + align:start position:0% +um uh well this is this is if you go + + + align:start position:0% +um uh well this is this is if you go +back to the perception chapter this is + + align:start position:0% +back to the perception chapter this is + + + align:start position:0% +back to the perception chapter this is +another Vapor's law kind of thing or the + + align:start position:0% +another Vapor's law kind of thing or the + + + align:start position:0% +another Vapor's law kind of thing or the +money example from last time you can + + align:start position:0% +money example from last time you can + + + align:start position:0% +money example from last time you can +also decide something about how many + + align:start position:0% +also decide something about how many + + + align:start position:0% +also decide something about how many +things there are there by a sort of a + + align:start position:0% +things there are there by a sort of a + + + align:start position:0% +things there are there by a sort of a +ratio um comparison there's more here + + align:start position:0% +ratio um comparison there's more here + + + align:start position:0% +ratio um comparison there's more here +than here if uh if there were 750 here + + align:start position:0% +than here if uh if there were 750 here + + + align:start position:0% +than here if uh if there were 750 here +and 745 here you wouldn't know that + + align:start position:0% +and 745 here you wouldn't know that + + + align:start position:0% +and 745 here you wouldn't know that +there has to be a critical um + + align:start position:0% +there has to be a critical um + + + align:start position:0% +there has to be a critical um +proportional difference between the two + + align:start position:0% +proportional difference between the two + + + align:start position:0% +proportional difference between the two +but given a proportional difference that + + align:start position:0% +but given a proportional difference that + + + align:start position:0% +but given a proportional difference that +this is something like 2: one like that + + align:start position:0% +this is something like 2: one like that + + + align:start position:0% +this is something like 2: one like that +it doesn't matter how many things there + + align:start position:0% +it doesn't matter how many things there + + + align:start position:0% +it doesn't matter how many things there +are simply know that there's more here + + align:start position:0% +are simply know that there's more here + + + align:start position:0% +are simply know that there's more here +and less here that's a sort of a crude + + align:start position:0% +and less here that's a sort of a crude + + + align:start position:0% +and less here that's a sort of a crude +sense of + + align:start position:0% +sense of + + + align:start position:0% +sense of +numerosity the um the variety of what + + align:start position:0% +numerosity the um the variety of what + + + align:start position:0% +numerosity the um the variety of what +what we typically think of when we think + + align:start position:0% +what we typically think of when we think + + + align:start position:0% +what we typically think of when we think +about numbers is counting things and + + align:start position:0% +about numbers is counting things and + + + align:start position:0% +about numbers is counting things and +that's the third propert so so here you + + align:start position:0% +that's the third propert so so here you + + + align:start position:0% +that's the third propert so so here you +can count them somebody can go and + + align:start position:0% +can count them somebody can go and + + + align:start position:0% +can count them somebody can go and +figure out exactly how many warthogs + + align:start position:0% +figure out exactly how many warthogs + + + align:start position:0% +figure out exactly how many warthogs +there are there you just have to go + + align:start position:0% +there are there you just have to go + + + align:start position:0% +there are there you just have to go +through and use your uh um your your + + align:start position:0% +through and use your uh um your your + + + align:start position:0% +through and use your uh um your your +counting ability to uh to to figure that + + align:start position:0% +counting ability to uh to to figure that + + + align:start position:0% +counting ability to uh to to figure that +out um you have that ability it seems to + + align:start position:0% +out um you have that ability it seems to + + + align:start position:0% +out um you have that ability it seems to +be critically piggybacked on your + + align:start position:0% +be critically piggybacked on your + + + align:start position:0% +be critically piggybacked on your +ability uh on on linguistic ability um + + align:start position:0% +ability uh on on linguistic ability um + + + align:start position:0% +ability uh on on linguistic ability um +recent interesting evidence for that + + align:start position:0% +recent interesting evidence for that + + + align:start position:0% +recent interesting evidence for that +comes from I don't know how to pronounce + + align:start position:0% +comes from I don't know how to pronounce + + + align:start position:0% +comes from I don't know how to pronounce +it properly but something like the + + align:start position:0% +it properly but something like the + + + align:start position:0% +it properly but something like the +paraha tribe in the Amazon their number + + align:start position:0% +paraha tribe in the Amazon their number + + + align:start position:0% +paraha tribe in the Amazon their number +terms consist of um one two and more + + align:start position:0% +terms consist of um one two and more + + + align:start position:0% +terms consist of um one two and more +than that and um and the result is that + + align:start position:0% +than that and um and the result is that + + + align:start position:0% +than that and um and the result is that +they bomb + + align:start position:0% +they bomb + + + align:start position:0% +they bomb +tasks um that require counting they can + + align:start position:0% +tasks um that require counting they can + + + align:start position:0% +tasks um that require counting they can +do subitizing tasks they can do + + align:start position:0% +do subitizing tasks they can do + + + align:start position:0% +do subitizing tasks they can do +numerosity tasks but they don't do + + align:start position:0% +numerosity tasks but they don't do + + + align:start position:0% +numerosity tasks but they don't do +counting tasks um and they will fail you + + align:start position:0% +counting tasks um and they will fail you + + + align:start position:0% +counting tasks um and they will fail you +know they they fail versions of the &m + + align:start position:0% +know they they fail versions of the &m + + + align:start position:0% +know they they fail versions of the &m +task in effect you know you say which of + + align:start position:0% +task in effect you know you say which of + + + align:start position:0% +task in effect you know you say which of +these boxes um has do you want you know + + align:start position:0% +these boxes um has do you want you know + + + align:start position:0% +these boxes um has do you want you know +they got fish in them or something like + + align:start position:0% +they got fish in them or something like + + + align:start position:0% +they got fish in them or something like +that and one has a little label with I + + align:start position:0% +that and one has a little label with I + + + align:start position:0% +that and one has a little label with I +think four fish on the top and another + + align:start position:0% +think four fish on the top and another + + + align:start position:0% +think four fish on the top and another +has five fish on the top and as far as + + align:start position:0% +has five fish on the top and as far as + + + align:start position:0% +has five fish on the top and as far as +the these guys are concerned it's all + + align:start position:0% +the these guys are concerned it's all + + + align:start position:0% +the these guys are concerned it's all +just got lots of fish + + align:start position:0% +just got lots of fish + + + align:start position:0% +just got lots of fish +um what you see here is a task where + + align:start position:0% +um what you see here is a task where + + + align:start position:0% +um what you see here is a task where +they were uh this was the experimentor + + align:start position:0% +they were uh this was the experimentor + + + align:start position:0% +they were uh this was the experimentor +marks and the uh the uh paraha person + + align:start position:0% +marks and the uh the uh paraha person + + + align:start position:0% +marks and the uh the uh paraha person +was asked to just copy it so you know + + align:start position:0% +was asked to just copy it so you know + + + align:start position:0% +was asked to just copy it so you know +one I make one Mark too I can make you + + align:start position:0% +one I make one Mark too I can make you + + + align:start position:0% +one I make one Mark too I can make you +know that two marks three three all + + align:start position:0% +know that two marks three three all + + + align:start position:0% +know that two marks three three all +that's just a bunch I'll make a bunch of + + align:start position:0% +that's just a bunch I'll make a bunch of + + + align:start position:0% +that's just a bunch I'll make a bunch of +marks once you got out of the subitizing + + align:start position:0% +marks once you got out of the subitizing + + + align:start position:0% +marks once you got out of the subitizing +range they simply didn't do the um they + + align:start position:0% +range they simply didn't do the um they + + + align:start position:0% +range they simply didn't do the um they +simply didn't do the task I think I put + + align:start position:0% +simply didn't do the task I think I put + + + align:start position:0% +simply didn't do the task I think I put +these guys on the uh + + align:start position:0% +these guys on the uh + + + align:start position:0% +these guys on the uh +uh the this article from which I stole + + align:start position:0% +uh the this article from which I stole + + + align:start position:0% +uh the this article from which I stole +this picture may live on the website um + + align:start position:0% +this picture may live on the website um + + + align:start position:0% +this picture may live on the website um +I seem to remember that that was one of + + align:start position:0% +I seem to remember that that was one of + + + align:start position:0% +I seem to remember that that was one of +the things that I I posted there so what + + align:start position:0% +the things that I I posted there so what + + + align:start position:0% +the things that I I posted there so what +do kids have and how does that tie into + + align:start position:0% +do kids have and how does that tie into + + + align:start position:0% +do kids have and how does that tie into +the uh to the &m problem well um turns + + align:start position:0% +the uh to the &m problem well um turns + + + align:start position:0% +the uh to the &m problem well um turns +out that little kids have um babies uh + + align:start position:0% +out that little kids have um babies uh + + + align:start position:0% +out that little kids have um babies uh +have this + + align:start position:0% +have this + + + align:start position:0% +have this +numerosity uh vaper's law comparison + + align:start position:0% +numerosity uh vaper's law comparison + + + align:start position:0% +numerosity uh vaper's law comparison +kind of numerosity ability + + align:start position:0% +kind of numerosity ability + + + align:start position:0% +kind of numerosity ability +and uh here's an experiment done by Shu + + align:start position:0% +and uh here's an experiment done by Shu + + + align:start position:0% +and uh here's an experiment done by Shu +and Liz spelly up at Harvard um that + + align:start position:0% +and Liz spelly up at Harvard um that + + + align:start position:0% +and Liz spelly up at Harvard um that +illustrates that um you're a baby you're + + align:start position:0% +illustrates that um you're a baby you're + + + align:start position:0% +illustrates that um you're a baby you're +looking at this okay and every now and + + align:start position:0% +looking at this okay and every now and + + + align:start position:0% +looking at this okay and every now and +then the display changes boink yeah okay + + align:start position:0% +then the display changes boink yeah okay + + + align:start position:0% +then the display changes boink yeah okay +there's another bunch of + + align:start position:0% +there's another bunch of + + + align:start position:0% +there's another bunch of +dots and another bunch of dots and what + + align:start position:0% +dots and another bunch of dots and what + + + align:start position:0% +dots and another bunch of dots and what +I'm doing is I the experiment I'm + + align:start position:0% +I'm doing is I the experiment I'm + + + align:start position:0% +I'm doing is I the experiment I'm +measuring how long you look at this um + + align:start position:0% +measuring how long you look at this um + + + align:start position:0% +measuring how long you look at this um +and I'm changing the shape and the + + align:start position:0% +and I'm changing the shape and the + + + align:start position:0% +and I'm changing the shape and the +distribution of these guys but I'm not + + align:start position:0% +distribution of these guys but I'm not + + + align:start position:0% +distribution of these guys but I'm not +changing the + + align:start position:0% +changing the + + + align:start position:0% +changing the +number and you are slowly getting + + align:start position:0% +number and you are slowly getting + + + align:start position:0% +number and you are slowly getting +bored um or to be more technical about + + align:start position:0% +bored um or to be more technical about + + + align:start position:0% +bored um or to be more technical about +it you're + + align:start position:0% +it you're + + + align:start position:0% +it you're +habituating you may recall that from uh + + align:start position:0% +habituating you may recall that from uh + + + align:start position:0% +habituating you may recall that from uh +from the learning chapter I don't think + + align:start position:0% +from the learning chapter I don't think + + + align:start position:0% +from the learning chapter I don't think +we talked about it in in the chapter + + align:start position:0% +we talked about it in in the chapter + + + align:start position:0% +we talked about it in in the chapter +well we can talk about it right + + align:start position:0% +well we can talk about it right + + + align:start position:0% +well we can talk about it right +now oh bunch of people oriented to + + align:start position:0% + + + + align:start position:0% + +that and now those people are having a + + align:start position:0% +that and now those people are having a + + + align:start position:0% +that and now those people are having a +no problem at all Zing back out again + + align:start position:0% +no problem at all Zing back out again + + + align:start position:0% +no problem at all Zing back out again +again right that's habituation you do it + + align:start position:0% +again right that's habituation you do it + + + align:start position:0% +again right that's habituation you do it +babies do it slugs do it everybody does + + align:start position:0% +babies do it slugs do it everybody does + + + align:start position:0% +babies do it slugs do it everybody does +it it's great um useful technique + + align:start position:0% +it it's great um useful technique + + + align:start position:0% +it it's great um useful technique +because the baby sitting here saying + + align:start position:0% +because the baby sitting here saying + + + align:start position:0% +because the baby sitting here saying +this is all kind of more or less the + + align:start position:0% +this is all kind of more or less the + + + align:start position:0% +this is all kind of more or less the +same and it's just not that + + align:start position:0% +same and it's just not that + + + align:start position:0% +same and it's just not that +interesting whoa wait a second that's + + align:start position:0% +interesting whoa wait a second that's + + + align:start position:0% +interesting whoa wait a second that's +interesting says the baby and the baby + + align:start position:0% +interesting says the baby and the baby + + + align:start position:0% +interesting says the baby and the baby +says it by looking more what happens + + align:start position:0% +says it by looking more what happens + + + align:start position:0% +says it by looking more what happens +here is that you know looking time goes + + align:start position:0% +here is that you know looking time goes + + + align:start position:0% +here is that you know looking time goes +down down down down is the number on + + align:start position:0% +down down down down is the number on + + + align:start position:0% +down down down down is the number on +each trial stays the same then when you + + align:start position:0% +each trial stays the same then when you + + + align:start position:0% +each trial stays the same then when you +jump from 8 to 16 the baby says hey + + align:start position:0% +jump from 8 to 16 the baby says hey + + + align:start position:0% +jump from 8 to 16 the baby says hey +something's happened I got to take a + + align:start position:0% +something's happened I got to take a + + + align:start position:0% +something's happened I got to take a +look at this do 16 for a + + align:start position:0% +look at this do 16 for a + + + align:start position:0% +look at this do 16 for a +while and um what this tells you is that + + align:start position:0% +while and um what this tells you is that + + + align:start position:0% +while and um what this tells you is that +the baby could tell the difference + + align:start position:0% +the baby could tell the difference + + + align:start position:0% +the baby could tell the difference +between 8 and + + align:start position:0% +between 8 and + + + align:start position:0% +between 8 and +16 the reason for changing the shape and + + align:start position:0% +16 the reason for changing the shape and + + + align:start position:0% +16 the reason for changing the shape and +the distribution and the density and + + align:start position:0% +the distribution and the density and + + + align:start position:0% +the distribution and the density and +stuff like that is to make sure that + + align:start position:0% +stuff like that is to make sure that + + + align:start position:0% +stuff like that is to make sure that +that's not what you're picking up on and + + align:start position:0% +that's not what you're picking up on and + + + align:start position:0% +that's not what you're picking up on and +Shu and spelly were careful about that + + align:start position:0% +Shu and spelly were careful about that + + + align:start position:0% +Shu and spelly were careful about that +so what you're picking up on here is um + + align:start position:0% +so what you're picking up on here is um + + + align:start position:0% +so what you're picking up on here is um +is numerosity babies can do that um but + + align:start position:0% +is numerosity babies can do that um but + + + align:start position:0% +is numerosity babies can do that um but +it it's you know if you go from 8 to n + + align:start position:0% +it it's you know if you go from 8 to n + + + align:start position:0% +it it's you know if you go from 8 to n +nothing happens here in fact if you go + + align:start position:0% +nothing happens here in fact if you go + + + align:start position:0% +nothing happens here in fact if you go +from 8 to 12 a 50% increase in dots + + align:start position:0% +from 8 to 12 a 50% increase in dots + + + align:start position:0% +from 8 to 12 a 50% increase in dots +nothing happens here with how old are + + align:start position:0% +nothing happens here with how old are + + + align:start position:0% +nothing happens here with how old are +these babies 6month old babies not so 8 + + align:start position:0% +these babies 6month old babies not so 8 + + + align:start position:0% +these babies 6month old babies not so 8 +to 16 a 2 to1 change that baby's pick up + + align:start position:0% +to 16 a 2 to1 change that baby's pick up + + + align:start position:0% +to 16 a 2 to1 change that baby's pick up +on so one thing we know uh let me get + + align:start position:0% +on so one thing we know uh let me get + + + align:start position:0% +on so one thing we know uh let me get +my graph back here oops graph come back + + align:start position:0% +my graph back here oops graph come back + + + align:start position:0% +my graph back here oops graph come back +graph get my graph back down here um so + + align:start position:0% +graph get my graph back down here um so + + + align:start position:0% +graph get my graph back down here um so +we know that if we're talking about + + align:start position:0% +we know that if we're talking about + + + align:start position:0% +we know that if we're talking about +number the starting spot isn't zero for + + align:start position:0% +number the starting spot isn't zero for + + + align:start position:0% +number the starting spot isn't zero for +um for number sense in uh in infants um + + align:start position:0% +um for number sense in uh in infants um + + + align:start position:0% +um for number sense in uh in infants um +the numerosity piece some chunk of the + + align:start position:0% +the numerosity piece some chunk of the + + + align:start position:0% +the numerosity piece some chunk of the +numerosity piece is there for starters + + align:start position:0% +numerosity piece is there for starters + + + align:start position:0% +numerosity piece is there for starters +perhaps more dramatically + + align:start position:0% +perhaps more dramatically + + + align:start position:0% +perhaps more dramatically +um the subitizing piece is there and the + + align:start position:0% +um the subitizing piece is there and the + + + align:start position:0% +um the subitizing piece is there and the +subitizing piece is there along with um + + align:start position:0% +subitizing piece is there along with um + + + align:start position:0% +subitizing piece is there along with um +a uh what seems to be an innate + + align:start position:0% +a uh what seems to be an innate + + + align:start position:0% +a uh what seems to be an innate +mathematical ability little kids can add + + align:start position:0% +mathematical ability little kids can add + + + align:start position:0% +mathematical ability little kids can add +and subtract babies can add and subtract + + align:start position:0% +and subtract babies can add and subtract + + + align:start position:0% +and subtract babies can add and subtract +um this this this is this was a surprise + + align:start position:0% +um this this this is this was a surprise + + + align:start position:0% +um this this this is this was a surprise +um and I can I I this is work done by + + align:start position:0% +um and I can I I this is work done by + + + align:start position:0% +um and I can I I this is work done by +Karen win and it is worth making the + + align:start position:0% +Karen win and it is worth making the + + + align:start position:0% +Karen win and it is worth making the +historical note that uh um she was a TA + + align:start position:0% +historical note that uh um she was a TA + + + align:start position:0% +historical note that uh um she was a TA +for this course Once Upon a Time um now + + align:start position:0% +for this course Once Upon a Time um now + + + align:start position:0% +for this course Once Upon a Time um now +a professor at Yale but in any case she + + align:start position:0% +a professor at Yale but in any case she + + + align:start position:0% +a professor at Yale but in any case she +figured out that that that babies can + + align:start position:0% +figured out that that that babies can + + + align:start position:0% +figured out that that that babies can +add and subtract look if you ask a baby + + align:start position:0% +add and subtract look if you ask a baby + + + align:start position:0% +add and subtract look if you ask a baby +what's 1+ one you get much the same + + align:start position:0% +what's 1+ one you get much the same + + + align:start position:0% +what's 1+ one you get much the same +answer as if you ask the baby which ways + + align:start position:0% +answer as if you ask the baby which ways + + + align:start position:0% +answer as if you ask the baby which ways +the E pointing you got to get clever + + align:start position:0% +the E pointing you got to get clever + + + align:start position:0% +the E pointing you got to get clever +about this sort of thing and um here's + + align:start position:0% +about this sort of thing and um here's + + + align:start position:0% +about this sort of thing and um here's +how Karen got clever about it so you're + + align:start position:0% +how Karen got clever about it so you're + + + align:start position:0% +how Karen got clever about it so you're +looking at a screen you're you're a + + align:start position:0% +looking at a screen you're you're a + + + align:start position:0% +looking at a screen you're you're a +you're a little baby looking at a screen + + align:start position:0% +you're a little baby looking at a screen + + + align:start position:0% +you're a little baby looking at a screen +like this + + align:start position:0% +like this + + + align:start position:0% +like this +and you see a hand come in with an + + align:start position:0% +and you see a hand come in with an + + + align:start position:0% +and you see a hand come in with an +object sticking uh it probably wasn't a + + align:start position:0% +object sticking uh it probably wasn't a + + + align:start position:0% +object sticking uh it probably wasn't a +warthog um but I had this warthog lying + + align:start position:0% +warthog um but I had this warthog lying + + + align:start position:0% +warthog um but I had this warthog lying +around as a as a image on my computer + + align:start position:0% +around as a as a image on my computer + + + align:start position:0% +around as a as a image on my computer +for some reason okay so and you see a + + align:start position:0% +for some reason okay so and you see a + + + align:start position:0% +for some reason okay so and you see a +hand come in with another one okay you + + align:start position:0% +hand come in with another one okay you + + + align:start position:0% +hand come in with another one okay you +got a pretty good idea what's going on + + align:start position:0% +got a pretty good idea what's going on + + + align:start position:0% +got a pretty good idea what's going on +here right so if I lift the + + align:start position:0% +here right so if I lift the + + + align:start position:0% +here right so if I lift the +screen what do you expect to + + align:start position:0% + + + + align:start position:0% + +see + + align:start position:0% +see + + + align:start position:0% +see +all right now let's do we can do this + + align:start position:0% +all right now let's do we can do this + + + align:start position:0% +all right now let's do we can do this +again okay the speed would be the same + + align:start position:0% +again okay the speed would be the same + + + align:start position:0% +again okay the speed would be the same +of course I just didn't want to keep + + align:start position:0% +of course I just didn't want to keep + + + align:start position:0% +of course I just didn't want to keep +sliding them in + + align:start position:0% +sliding them in + + + align:start position:0% +sliding them in +slowly we move the screen + + align:start position:0% +slowly we move the screen + + + align:start position:0% +slowly we move the screen +again they + + align:start position:0% +again they + + + align:start position:0% +again they +uh um and the baby will respond to this + + align:start position:0% +uh um and the baby will respond to this + + + align:start position:0% +uh um and the baby will respond to this +by looking + + align:start position:0% +by looking + + + align:start position:0% +by looking +longer the baby will say are baby will + + align:start position:0% +longer the baby will say are baby will + + + align:start position:0% +longer the baby will say are baby will +say who knows what the baby will say but + + align:start position:0% +say who knows what the baby will say but + + + align:start position:0% +say who knows what the baby will say but +the baby is apparently in effect saying + + align:start position:0% +the baby is apparently in effect saying + + + align:start position:0% +the baby is apparently in effect saying +all I put one thing in there two things + + align:start position:0% +all I put one thing in there two things + + + align:start position:0% +all I put one thing in there two things +in there I guess two that must be two + + align:start position:0% +in there I guess two that must be two + + + align:start position:0% +in there I guess two that must be two +stuffs there's two warthogs back there + + align:start position:0% +stuffs there's two warthogs back there + + + align:start position:0% +stuffs there's two warthogs back there +lifted up and now there's only one + + align:start position:0% +lifted up and now there's only one + + + align:start position:0% +lifted up and now there's only one +warthog and this violates the rules of + + align:start position:0% +warthog and this violates the rules of + + + align:start position:0% +warthog and this violates the rules of +the universe and I better look at this + + align:start position:0% +the universe and I better look at this + + + align:start position:0% +the universe and I better look at this +for a while to figure out what's going + + align:start position:0% +for a while to figure out what's going + + + align:start position:0% +for a while to figure out what's going +on um and you can use this + + align:start position:0% +on um and you can use this + + + align:start position:0% +on um and you can use this +technique to um to show you to to show + + align:start position:0% +technique to um to show you to to show + + + align:start position:0% +technique to um to show you to to show +that babies can do um do I have a + + align:start position:0% +that babies can do um do I have a + + + align:start position:0% +that babies can do um do I have a +subtraction one here I forget no that's + + align:start position:0% +subtraction one here I forget no that's + + + align:start position:0% +subtraction one here I forget no that's +going to I did that + + align:start position:0% +going to I did that + + + align:start position:0% +going to I did that +already yeah yeah yeah na did habituate + + align:start position:0% +already yeah yeah yeah na did habituate + + + align:start position:0% +already yeah yeah yeah na did habituate +uh oh no it works for monkeys too we'll + + align:start position:0% +uh oh no it works for monkeys too we'll + + + align:start position:0% +uh oh no it works for monkeys too we'll +talk about that in a minute um but you + + align:start position:0% +talk about that in a minute um but you + + + align:start position:0% +talk about that in a minute um but you +can do this you can do addition you can + + align:start position:0% +can do this you can do addition you can + + + align:start position:0% +can do this you can do addition you can +do subtraction so subtraction you put + + align:start position:0% +do subtraction so subtraction you put + + + align:start position:0% +do subtraction so subtraction you put +you have two the two things here you put + + align:start position:0% +you have two the two things here you put + + + align:start position:0% +you have two the two things here you put +down the screen the hand comes in and + + align:start position:0% +down the screen the hand comes in and + + + align:start position:0% +down the screen the hand comes in and +pulls one out when the screen comes up + + align:start position:0% +pulls one out when the screen comes up + + + align:start position:0% +pulls one out when the screen comes up +the baby expects to see one if the baby + + align:start position:0% +the baby expects to see one if the baby + + + align:start position:0% +the baby expects to see one if the baby +sees zero or the baby sees two the baby + + align:start position:0% +sees zero or the baby sees two the baby + + + align:start position:0% +sees zero or the baby sees two the baby +says you know something weirds going on + + align:start position:0% +says you know something weirds going on + + + align:start position:0% +says you know something weirds going on +here I need to uh I need to think about + + align:start position:0% +here I need to uh I need to think about + + + align:start position:0% +here I need to uh I need to think about +this for uh for a while now if you do + + align:start position:0% +this for uh for a while now if you do + + + align:start position:0% +this for uh for a while now if you do +this with big numbers outside of the + + align:start position:0% +this with big numbers outside of the + + + align:start position:0% +this with big numbers outside of the +subitizing range you don't get the + + align:start position:0% +subitizing range you don't get the + + + align:start position:0% +subitizing range you don't get the +result so you know you stick 15 warthogs + + align:start position:0% +result so you know you stick 15 warthogs + + + align:start position:0% +result so you know you stick 15 warthogs +back there and you lift up the screen + + align:start position:0% +back there and you lift up the screen + + + align:start position:0% +back there and you lift up the screen +and there's 13 warthogs and the kid says + + align:start position:0% +and there's 13 warthogs and the kid says + + + align:start position:0% +and there's 13 warthogs and the kid says +I don't care um once you get above about + + align:start position:0% +I don't care um once you get above about + + + align:start position:0% +I don't care um once you get above about +three with babies um uh it doesn't work + + align:start position:0% +three with babies um uh it doesn't work + + + align:start position:0% +three with babies um uh it doesn't work +anymore so what you get is evidence for + + align:start position:0% + + + + align:start position:0% + +subitizing being + + align:start position:0% +subitizing being + + + align:start position:0% +subitizing being +present um and uh and and and some sort + + align:start position:0% +present um and uh and and and some sort + + + align:start position:0% +present um and uh and and and some sort +of addition and subtraction kind of + + align:start position:0% +of addition and subtraction kind of + + + align:start position:0% +of addition and subtraction kind of +operation um for essentially as early as + + align:start position:0% +operation um for essentially as early as + + + align:start position:0% +operation um for essentially as early as +you want to test it you can also get + + align:start position:0% +you want to test it you can also get + + + align:start position:0% +you want to test it you can also get +these abilities in animals that's what + + align:start position:0% +these abilities in animals that's what + + + align:start position:0% +these abilities in animals that's what +this this uh slide is intended to remind + + align:start position:0% +this this uh slide is intended to remind + + + align:start position:0% +this this uh slide is intended to remind +me to tell you um animals certainly uh + + align:start position:0% +me to tell you um animals certainly uh + + + align:start position:0% +me to tell you um animals certainly uh +Mako monkeys will show numerosity + + align:start position:0% +Mako monkeys will show numerosity + + + align:start position:0% +Mako monkeys will show numerosity +effects and they they can also do do + + align:start position:0% +effects and they they can also do do + + + align:start position:0% +effects and they they can also do do +this sort of Karen win style math they + + align:start position:0% +this sort of Karen win style math they + + + align:start position:0% +this sort of Karen win style math they +prefer eggplants um at least Mark + + align:start position:0% +prefer eggplants um at least Mark + + + align:start position:0% +prefer eggplants um at least Mark +Howser's uh monkeys like eggplants so + + align:start position:0% +Howser's uh monkeys like eggplants so + + + align:start position:0% +Howser's uh monkeys like eggplants so +that's why they are eggplants here um + + align:start position:0% +that's why they are eggplants here um + + + align:start position:0% +that's why they are eggplants here um +and you worry about doing this at the in + + align:start position:0% +and you worry about doing this at the in + + + align:start position:0% +and you worry about doing this at the in +the lab because maybe your lab monkeys + + align:start position:0% +the lab because maybe your lab monkeys + + + align:start position:0% +the lab because maybe your lab monkeys +have you know LED this elaborately uh + + align:start position:0% +have you know LED this elaborately uh + + + align:start position:0% +have you know LED this elaborately uh +studied life and are kind of smart so um + + align:start position:0% +studied life and are kind of smart so um + + + align:start position:0% +studied life and are kind of smart so um +Hower went down to this island in the + + align:start position:0% +Hower went down to this island in the + + + align:start position:0% +Hower went down to this island in the +Caribbean where he's got a free ranging + + align:start position:0% +Caribbean where he's got a free ranging + + + align:start position:0% +Caribbean where he's got a free ranging +troop of monkeys and then you kind of + + align:start position:0% +troop of monkeys and then you kind of + + + align:start position:0% +troop of monkeys and then you kind of +have to coax them into playing your game + + align:start position:0% +have to coax them into playing your game + + + align:start position:0% +have to coax them into playing your game +so you're hanging there this great video + + align:start position:0% +so you're hanging there this great video + + + align:start position:0% +so you're hanging there this great video +that Mark has of of of monkeys he's + + align:start position:0% +that Mark has of of of monkeys he's + + + align:start position:0% +that Mark has of of of monkeys he's +hanging out with his + + align:start position:0% +hanging out with his + + + align:start position:0% +hanging out with his +eggplants then he's starting to do this + + align:start position:0% +eggplants then he's starting to do this + + + align:start position:0% +eggplants then he's starting to do this +eggplant puppet show with with the makco + + align:start position:0% +eggplant puppet show with with the makco + + + align:start position:0% +eggplant puppet show with with the makco +is looking longer at the weird ones + + align:start position:0% +is looking longer at the weird ones + + + align:start position:0% +is looking longer at the weird ones +right I put twoo two eggplants there and + + align:start position:0% +right I put twoo two eggplants there and + + + align:start position:0% +right I put twoo two eggplants there and +there's only one there now man hope he's + + align:start position:0% +there's only one there now man hope he's + + + align:start position:0% +there's only one there now man hope he's +going to feed me some of these eggplants + + align:start position:0% +going to feed me some of these eggplants + + + align:start position:0% +going to feed me some of these eggplants +eventually but in any case monkeys can + + align:start position:0% +eventually but in any case monkeys can + + + align:start position:0% +eventually but in any case monkeys can +do the task monkeys will look longer at + + align:start position:0% +do the task monkeys will look longer at + + + align:start position:0% +do the task monkeys will look longer at +things that that uh violate their + + align:start position:0% +things that that uh violate their + + + align:start position:0% +things that that uh violate their +expectations + + align:start position:0% +expectations + + + align:start position:0% +expectations +however monkeys don't count at least + + align:start position:0% +however monkeys don't count at least + + + align:start position:0% +however monkeys don't count at least +they don't count the way that you and I + + align:start position:0% +they don't count the way that you and I + + + align:start position:0% +they don't count the way that you and I +count um and this goes for great apes + + align:start position:0% +count um and this goes for great apes + + + align:start position:0% +count um and this goes for great apes +you know you know fine let's let's go + + align:start position:0% +you know you know fine let's let's go + + + align:start position:0% +you know you know fine let's let's go +find the brightest uh uh Beast other + + align:start position:0% +find the brightest uh uh Beast other + + + align:start position:0% +find the brightest uh uh Beast other +than humans that we can um there's uh at + + align:start position:0% +than humans that we can um there's uh at + + + align:start position:0% +than humans that we can um there's uh at +least one chimp who's been trained for + + align:start position:0% +least one chimp who's been trained for + + + align:start position:0% +least one chimp who's been trained for + + align:start position:0% + + + align:start position:0% +years um oh I misspoke when I talked + + align:start position:0% +years um oh I misspoke when I talked + + + align:start position:0% +years um oh I misspoke when I talked +about this in Concourse I said he' been + + align:start position:0% +about this in Concourse I said he' been + + + align:start position:0% +about this in Concourse I said he' been +trained for nine years and never gotten + + align:start position:0% +trained for nine years and never gotten + + + align:start position:0% +trained for nine years and never gotten +past 20 it's worse than that he's been + + align:start position:0% +past 20 it's worse than that he's been + + + align:start position:0% +past 20 it's worse than that he's been +trained for 20 years and he's never + + align:start position:0% +trained for 20 years and he's never + + + align:start position:0% +trained for 20 years and he's never +gotten past nine counting he can count + + align:start position:0% +gotten past nine counting he can count + + + align:start position:0% +gotten past nine counting he can count +to nine and do do do pretty good stuff + + align:start position:0% +to nine and do do do pretty good stuff + + + align:start position:0% +to nine and do do do pretty good stuff +up to nine but he's doing this by um + + align:start position:0% +up to nine but he's doing this by um + + + align:start position:0% +up to nine but he's doing this by um +basically Association learning up you go + + align:start position:0% +basically Association learning up you go + + + align:start position:0% +basically Association learning up you go +and let's turn that on and let it come + + align:start position:0% +and let's turn that on and let it come + + + align:start position:0% +and let's turn that on and let it come +back up um you know you you you can + + align:start position:0% +back up um you know you you you can + + + align:start position:0% +back up um you know you you you can +train the monkey to realize that this + + align:start position:0% +train the monkey to realize that this + + + align:start position:0% +train the monkey to realize that this +sign or this IM this this uh graphic or + + align:start position:0% +sign or this IM this this uh graphic or + + + align:start position:0% +sign or this IM this this uh graphic or +something means nine things but but this + + align:start position:0% +something means nine things but but this + + + align:start position:0% +something means nine things but but this +is very different from what you and I + + align:start position:0% +is very different from what you and I + + + align:start position:0% +is very different from what you and I +can do it didn't take you 20 years and + + align:start position:0% +can do it didn't take you 20 years and + + + align:start position:0% +can do it didn't take you 20 years and +you got well beyond um + + align:start position:0% +you got well beyond um + + + align:start position:0% +you got well beyond um +nine counting seems to be heavily + + align:start position:0% +nine counting seems to be heavily + + + align:start position:0% +nine counting seems to be heavily +dependent on um two things one is + + align:start position:0% +dependent on um two things one is + + + align:start position:0% +dependent on um two things one is +language and the other is an act of of + + align:start position:0% +language and the other is an act of of + + + align:start position:0% +language and the other is an act of of +inductive reasoning and you can sort of + + align:start position:0% +inductive reasoning and you can sort of + + + align:start position:0% +inductive reasoning and you can sort of +see counting happening the development + + align:start position:0% +see counting happening the development + + + align:start position:0% +see counting happening the development +of counting in a in a uh in a series of + + align:start position:0% +of counting in a in a uh in a series of + + + align:start position:0% +of counting in a in a uh in a series of +of of steps um kids as they are learning + + align:start position:0% +of of steps um kids as they are learning + + + align:start position:0% +of of steps um kids as they are learning +language learn that + + align:start position:0% +language learn that + + + align:start position:0% +language learn that +um uh that that there that there's this + + align:start position:0% +um uh that that there that there's this + + + align:start position:0% +um uh that that there that there's this +uh kind of game about saying 1 two 3 4 + + align:start position:0% +uh kind of game about saying 1 two 3 4 + + + align:start position:0% +uh kind of game about saying 1 two 3 4 +um and so on that uh that that parents + + align:start position:0% +um and so on that uh that that parents + + + align:start position:0% +um and so on that uh that that parents +really like to play if you if you start + + align:start position:0% +really like to play if you if you start + + + align:start position:0% +really like to play if you if you start +counting they'll give you the cookies + + align:start position:0% +counting they'll give you the cookies + + + align:start position:0% +counting they'll give you the cookies +and stuff you know good good good things + + align:start position:0% +and stuff you know good good good things + + + align:start position:0% +and stuff you know good good good things +happen um they don't have any particular + + align:start position:0% +happen um they don't have any particular + + + align:start position:0% +happen um they don't have any particular +clue that this initially that this maps + + align:start position:0% +clue that this initially that this maps + + + align:start position:0% +clue that this initially that this maps +on to anything um in um in particular um + + align:start position:0% +on to anything um in um in particular um + + + align:start position:0% +on to anything um in um in particular um +and um so so what you get with like two + + align:start position:0% +and um so so what you get with like two + + + align:start position:0% +and um so so what you get with like two +and a halfy old kids is a two two and a + + align:start position:0% +and a halfy old kids is a two two and a + + + align:start position:0% +and a halfy old kids is a two two and a +halfy old + + align:start position:0% +halfy old + + + align:start position:0% +halfy old +kid if you ask for one cookie we'll give + + align:start position:0% +kid if you ask for one cookie we'll give + + + align:start position:0% +kid if you ask for one cookie we'll give +you one cookie but if you ask for + + align:start position:0% +you one cookie but if you ask for + + + align:start position:0% +you one cookie but if you ask for +anything else give me two cookies give + + align:start position:0% +anything else give me two cookies give + + + align:start position:0% +anything else give me two cookies give +me four cookies give me whatever they'll + + align:start position:0% +me four cookies give me whatever they'll + + + align:start position:0% +me four cookies give me whatever they'll +give you some random BN you know have + + align:start position:0% +give you some random BN you know have + + + align:start position:0% +give you some random BN you know have +some cookies it's one and other stuff + + align:start position:0% +some cookies it's one and other stuff + + + align:start position:0% +some cookies it's one and other stuff +stuff um eventually they learn um to map + + align:start position:0% +stuff um eventually they learn um to map + + + align:start position:0% +stuff um eventually they learn um to map +the counting onto uh the subitizing + + align:start position:0% +the counting onto uh the subitizing + + + align:start position:0% +the counting onto uh the subitizing +range and then start blowing it later so + + align:start position:0% +range and then start blowing it later so + + + align:start position:0% +range and then start blowing it later so +I if you have little sibs or uh cousins + + align:start position:0% +I if you have little sibs or uh cousins + + + align:start position:0% +I if you have little sibs or uh cousins +or stuff that you've hung around with + + align:start position:0% +or stuff that you've hung around with + + + align:start position:0% +or stuff that you've hung around with +you may have seen them counting things + + align:start position:0% +you may have seen them counting things + + + align:start position:0% +you may have seen them counting things +one two 3 4 5 7 12 you they got this + + align:start position:0% +one two 3 4 5 7 12 you they got this + + + align:start position:0% +one two 3 4 5 7 12 you they got this +notion that the numbers keep going in + + align:start position:0% +notion that the numbers keep going in + + + align:start position:0% +notion that the numbers keep going in +some fashion but but but once you get + + align:start position:0% +some fashion but but but once you get + + + align:start position:0% +some fashion but but but once you get +out of the small numbers it's it's not + + align:start position:0% +out of the small numbers it's it's not + + + align:start position:0% +out of the small numbers it's it's not +terribly clear what's going on there but + + align:start position:0% +terribly clear what's going on there but + + + align:start position:0% +terribly clear what's going on there but +even in this stage you can start to see + + align:start position:0% +even in this stage you can start to see + + + align:start position:0% +even in this stage you can start to see +the development of something more + + align:start position:0% +the development of something more + + + align:start position:0% +the development of something more +sophisticated um six they may not know + + align:start position:0% +sophisticated um six they may not know + + + align:start position:0% +sophisticated um six they may not know +how many sixes they know six is a lot of + + align:start position:0% +how many sixes they know six is a lot of + + + align:start position:0% +how many sixes they know six is a lot of +stuff if you ask for six cookies you'll + + align:start position:0% +stuff if you ask for six cookies you'll + + + align:start position:0% +stuff if you ask for six cookies you'll +get some you know arbitrary number of of + + align:start position:0% +get some you know arbitrary number of of + + + align:start position:0% +get some you know arbitrary number of of +of cookies um but if you ask a little + + align:start position:0% +of cookies um but if you ask a little + + + align:start position:0% +of cookies um but if you ask a little +kid + + align:start position:0% +kid + + + align:start position:0% +kid +um you know if I take a lot of + + align:start position:0% +um you know if I take a lot of + + + align:start position:0% +um you know if I take a lot of +cookies and I add a few do I still have + + align:start position:0% +cookies and I add a few do I still have + + + align:start position:0% +cookies and I add a few do I still have +a lot of + + align:start position:0% +a lot of + + + align:start position:0% +a lot of +cookies kid says yeah yeah that works + + align:start position:0% +cookies kid says yeah yeah that works + + + align:start position:0% +cookies kid says yeah yeah that works +kid said and so all right so we know + + align:start position:0% +kid said and so all right so we know + + + align:start position:0% +kid said and so all right so we know +that okay now if I have six cookies can + + align:start position:0% +that okay now if I have six cookies can + + + align:start position:0% +that okay now if I have six cookies can +you give me six + + align:start position:0% +you give me six + + + align:start position:0% +you give me six +cookies some random number of cookies + + align:start position:0% +cookies some random number of cookies + + + align:start position:0% +cookies some random number of cookies +okay if I have six cookies and I give + + align:start position:0% +okay if I have six cookies and I give + + + align:start position:0% +okay if I have six cookies and I give +and I add some more cookies do I still + + align:start position:0% +and I add some more cookies do I still + + + align:start position:0% +and I add some more cookies do I still +have six cookies + + align:start position:0% +have six cookies + + + align:start position:0% +have six cookies +no you got a lot of cookies but it's not + + align:start position:0% +no you got a lot of cookies but it's not + + + align:start position:0% +no you got a lot of cookies but it's not +the same a lot of right so even when + + align:start position:0% +the same a lot of right so even when + + + align:start position:0% +the same a lot of right so even when +they don't really know how many cookies + + align:start position:0% +they don't really know how many cookies + + + align:start position:0% +they don't really know how many cookies +you've got um they they have the notion + + align:start position:0% +you've got um they they have the notion + + + align:start position:0% +you've got um they they have the notion +that the the the the number names are + + align:start position:0% +that the the the the number names are + + + align:start position:0% +that the the the the number names are +naming something specific they don't + + align:start position:0% +naming something specific they don't + + + align:start position:0% +naming something specific they don't +quite get what it is but it's something + + align:start position:0% +quite get what it is but it's something + + + align:start position:0% +quite get what it is but it's something +specific in a way that a term like a lot + + align:start position:0% +specific in a way that a term like a lot + + + align:start position:0% +specific in a way that a term like a lot +is not um + + align:start position:0% +is not um + + + align:start position:0% +is not um +eventually you you make the break + + align:start position:0% +eventually you you make the break + + + align:start position:0% +eventually you you make the break +through um that you can count basically + + align:start position:0% +through um that you can count basically + + + align:start position:0% +through um that you can count basically +and that you can keep and if you add one + + align:start position:0% +and that you can keep and if you add one + + + align:start position:0% +and that you can keep and if you add one +to each of them you can just keep doing + + align:start position:0% +to each of them you can just keep doing + + + align:start position:0% +to each of them you can just keep doing +this forever this is I I again I don't + + align:start position:0% +this forever this is I I again I don't + + + align:start position:0% +this forever this is I I again I don't +know how much you hang around with + + align:start position:0% +know how much you hang around with + + + align:start position:0% +know how much you hang around with +little kids or or remember your own + + align:start position:0% +little kids or or remember your own + + + align:start position:0% +little kids or or remember your own +experience because this this is getting + + align:start position:0% +experience because this this is getting + + + align:start position:0% +experience because this this is getting +old enough that you might actually + + align:start position:0% +old enough that you might actually + + + align:start position:0% +old enough that you might actually +remember this state yourself of um uh + + align:start position:0% +remember this state yourself of um uh + + + align:start position:0% +remember this state yourself of um uh +asking what the biggest number in the + + align:start position:0% +asking what the biggest number in the + + + align:start position:0% +asking what the biggest number in the +world is anybody remember asking what + + align:start position:0% +world is anybody remember asking what + + + align:start position:0% +world is anybody remember asking what +the biggest number in the world is yeah + + align:start position:0% +the biggest number in the world is yeah + + + align:start position:0% +the biggest number in the world is yeah +all right most of you got that's the + + align:start position:0% +all right most of you got that's the + + + align:start position:0% +all right most of you got that's the +problem with MIT students right they + + align:start position:0% +problem with MIT students right they + + + align:start position:0% +problem with MIT students right they +figured all this stuff out when they + + align:start position:0% +figured all this stuff out when they + + + align:start position:0% +figured all this stuff out when they +were like two instead of so anyway yeah + + align:start position:0% +were like two instead of so anyway yeah + + + align:start position:0% +were like two instead of so anyway yeah +little kids want to know what the + + align:start position:0% +little kids want to know what the + + + align:start position:0% +little kids want to know what the +biggest number in the world is and so + + align:start position:0% +biggest number in the world is and so + + + align:start position:0% +biggest number in the world is and so +you say to the little kid well what do + + align:start position:0% +you say to the little kid well what do + + + align:start position:0% +you say to the little kid well what do +you think the biggest number in the + + align:start position:0% +you think the biggest number in the + + + align:start position:0% +you think the biggest number in the +world is well uh it's it's a million + + align:start position:0% +world is well uh it's it's a million + + + align:start position:0% +world is well uh it's it's a million +okay what happens if we had a a million + + align:start position:0% +okay what happens if we had a a million + + + align:start position:0% +okay what happens if we had a a million +plus one is there a number for + + align:start position:0% +plus one is there a number for + + + align:start position:0% +plus one is there a number for +that oh yeah it's a million in one I + + align:start position:0% +that oh yeah it's a million in one I + + + align:start position:0% +that oh yeah it's a million in one I +guess well I guess a million and one is + + align:start position:0% +guess well I guess a million and one is + + + align:start position:0% +guess well I guess a million and one is +the biggest number in the world you know + + align:start position:0% +the biggest number in the world you know + + + align:start position:0% +the biggest number in the world you know +or for adward you know million and two + + align:start position:0% +or for adward you know million and two + + + align:start position:0% +or for adward you know million and two +you can keep doing this for a while + + align:start position:0% +you can keep doing this for a while + + + align:start position:0% +you can keep doing this for a while +eventually around that around the time + + align:start position:0% +eventually around that around the time + + + align:start position:0% +eventually around that around the time +when you get in this conversation the + + align:start position:0% +when you get in this conversation the + + + align:start position:0% +when you get in this conversation the +kid catches on to the notion um that you + + align:start position:0% +kid catches on to the notion um that you + + + align:start position:0% +kid catches on to the notion um that you +can always get a bigger one and this is + + align:start position:0% +can always get a bigger one and this is + + + align:start position:0% +can always get a bigger one and this is +really this is leads to very boring car + + align:start position:0% +really this is leads to very boring car + + + align:start position:0% +really this is leads to very boring car +rides sometimes right do you want to see + + align:start position:0% +rides sometimes right do you want to see + + + align:start position:0% +rides sometimes right do you want to see +how high I can count that's a kind of + + align:start position:0% +how high I can count that's a kind of + + + align:start position:0% +how high I can count that's a kind of +cute game with a three-year-old oh look + + align:start position:0% +cute game with a three-year-old oh look + + + align:start position:0% +cute game with a three-year-old oh look +he can get all the way to 20 you know by + + align:start position:0% +he can get all the way to 20 you know by + + + align:start position:0% +he can get all the way to 20 you know by +the time you get four or fiveyear old + + align:start position:0% +the time you get four or fiveyear old + + + align:start position:0% +the time you get four or fiveyear old +million and one million and two million + + align:start position:0% +million and one million and two million + + + align:start position:0% +million and one million and two million +and three okay we've made it to + + align:start position:0% +and three okay we've made it to + + + align:start position:0% +and three okay we've made it to +California Kid shut up the so what you + + align:start position:0% +California Kid shut up the so what you + + + align:start position:0% +California Kid shut up the so what you +get is um you've got this Bas uh you've + + align:start position:0% +get is um you've got this Bas uh you've + + + align:start position:0% +get is um you've got this Bas uh you've +got this basic numeric competence or + + align:start position:0% +got this basic numeric competence or + + + align:start position:0% +got this basic numeric competence or +core knowledge as Liz spelly would call + + align:start position:0% +core knowledge as Liz spelly would call + + + align:start position:0% +core knowledge as Liz spelly would call +it um and + + align:start position:0% +it um and + + + align:start position:0% +it um and +then um you're waiting for the + + align:start position:0% +then um you're waiting for the + + + align:start position:0% +then um you're waiting for the +development of language when you get + + align:start position:0% +development of language when you get + + + align:start position:0% +development of language when you get +language you can then get this counting + + align:start position:0% +language you can then get this counting + + + align:start position:0% +language you can then get this counting +piece to work when you got the counting + + align:start position:0% +piece to work when you got the counting + + + align:start position:0% +piece to work when you got the counting +piece to work you can combine it with + + align:start position:0% +piece to work you can combine it with + + + align:start position:0% +piece to work you can combine it with +your ability to make the inductive leap + + align:start position:0% +your ability to make the inductive leap + + + align:start position:0% +your ability to make the inductive leap +that numbers go on forever and then + + align:start position:0% +that numbers go on forever and then + + + align:start position:0% +that numbers go on forever and then +you're in a position to go off to school + + align:start position:0% +you're in a position to go off to school + + + align:start position:0% +you're in a position to go off to school +and learn some math um so the ability I + + align:start position:0% +and learn some math um so the ability I + + + align:start position:0% +and learn some math um so the ability I +mean there's in a sense not an adult + + align:start position:0% +mean there's in a sense not an adult + + + align:start position:0% +mean there's in a sense not an adult +level of numerical competence you guys + + align:start position:0% +level of numerical competence you guys + + + align:start position:0% +level of numerical competence you guys +know more about numbers than I know um I + + align:start position:0% +know more about numbers than I know um I + + + align:start position:0% +know more about numbers than I know um I +would imagine um but the the ability to + + align:start position:0% +would imagine um but the the ability to + + + align:start position:0% +would imagine um but the the ability to +go off and learn that kind of math is + + align:start position:0% +go off and learn that kind of math is + + + align:start position:0% +go off and learn that kind of math is +way is based on this core knowledge than + + align:start position:0% +way is based on this core knowledge than + + + align:start position:0% +way is based on this core knowledge than +waiting on language um before you can + + align:start position:0% +waiting on language um before you can + + + align:start position:0% +waiting on language um before you can +make the leap to and ability to use um + + align:start position:0% +make the leap to and ability to use um + + + align:start position:0% +make the leap to and ability to use um +uh to do you know 18 or whatever um so + + align:start position:0% +uh to do you know 18 or whatever um so + + + align:start position:0% +uh to do you know 18 or whatever um so +it's a an example if you like of the + + align:start position:0% +it's a an example if you like of the + + + align:start position:0% +it's a an example if you like of the +synergistic combination of information + + align:start position:0% +synergistic combination of information + + + align:start position:0% +synergistic combination of information +from from a couple of different Realms + + align:start position:0% +from from a couple of different Realms + + + align:start position:0% +from from a couple of different Realms +let's switch to the problem of childhood + + align:start position:0% +let's switch to the problem of childhood + + + align:start position:0% +let's switch to the problem of childhood +animism that in if you're not completely + + align:start position:0% +animism that in if you're not completely + + + align:start position:0% +animism that in if you're not completely +confused from my earlier misspeaking + + align:start position:0% +confused from my earlier misspeaking + + + align:start position:0% +confused from my earlier misspeaking +animism is the tendency to say you know + + align:start position:0% +animism is the tendency to say you know + + + align:start position:0% +animism is the tendency to say you know +is the son of alive yes are clouds alive + + align:start position:0% +is the son of alive yes are clouds alive + + + align:start position:0% +is the son of alive yes are clouds alive +yes that seems quite different from what + + align:start position:0% +yes that seems quite different from what + + + align:start position:0% +yes that seems quite different from what +you and I + + align:start position:0% +you and I + + + align:start position:0% +you and I +do um one might wonder exactly how + + align:start position:0% +do um one might wonder exactly how + + + align:start position:0% +do um one might wonder exactly how +different it really is does it really + + align:start position:0% +different it really is does it really + + + align:start position:0% +different it really is does it really +reflect a fundamental problem with the + + align:start position:0% +reflect a fundamental problem with the + + + align:start position:0% +reflect a fundamental problem with the +concept um alive um it's not that + + align:start position:0% +concept um alive um it's not that + + + align:start position:0% +concept um alive um it's not that +obvious how you map these a concept like + + align:start position:0% +obvious how you map these a concept like + + + align:start position:0% +obvious how you map these a concept like +that um even even as an adult it perhaps + + align:start position:0% +that um even even as an adult it perhaps + + + align:start position:0% +that um even even as an adult it perhaps +um + + align:start position:0% +um + + + align:start position:0% +um +straight easier to to think about in + + align:start position:0% +straight easier to to think about in + + + align:start position:0% +straight easier to to think about in +connection with with uh dead um mapping + + align:start position:0% +connection with with uh dead um mapping + + + align:start position:0% +connection with with uh dead um mapping +dead onto a discret set of things is not + + align:start position:0% +dead onto a discret set of things is not + + + align:start position:0% +dead onto a discret set of things is not +that trivial is a rock dead H probably + + align:start position:0% +that trivial is a rock dead H probably + + + align:start position:0% +that trivial is a rock dead H probably +not because it was never alive right um + + align:start position:0% +not because it was never alive right um + + + align:start position:0% +not because it was never alive right um +is George Washington dead that seems + + align:start position:0% +is George Washington dead that seems + + + align:start position:0% +is George Washington dead that seems +about right is he dead in the same way + + align:start position:0% +about right is he dead in the same way + + + align:start position:0% +about right is he dead in the same way +that something that you can that like a + + align:start position:0% +that something that you can that like a + + + align:start position:0% +that something that you can that like a +cat that just recently died you know + + align:start position:0% +cat that just recently died you know + + + align:start position:0% +cat that just recently died you know +that's here dead now is that the same is + + align:start position:0% +that's here dead now is that the same is + + + align:start position:0% +that's here dead now is that the same is +that the same how about a + + align:start position:0% +that the same how about a + + + align:start position:0% +that the same how about a +dinosaur or the dinosaurs are the + + align:start position:0% +dinosaur or the dinosaurs are the + + + align:start position:0% +dinosaur or the dinosaurs are the +dinosaurs dead well yes they're dead but + + align:start position:0% +dinosaurs dead well yes they're dead but + + + align:start position:0% +dinosaurs dead well yes they're dead but +they're also extinct which is somehow + + align:start position:0% +they're also extinct which is somehow + + + align:start position:0% +they're also extinct which is somehow +kind of um different it's or or to use + + align:start position:0% +kind of um different it's or or to use + + + align:start position:0% +kind of um different it's or or to use +an example from driving around now that + + align:start position:0% +an example from driving around now that + + + align:start position:0% +an example from driving around now that +my kids have gotten out of the counting + + align:start position:0% +my kids have gotten out of the counting + + + align:start position:0% +my kids have gotten out of the counting +to a million + + align:start position:0% +to a million + + + align:start position:0% +to a million +stage um I don't know how we got on the + + align:start position:0% +stage um I don't know how we got on the + + + align:start position:0% +stage um I don't know how we got on the +subject of of uh of what is alive maybe + + align:start position:0% +subject of of uh of what is alive maybe + + + align:start position:0% +subject of of uh of what is alive maybe +because I was thinking about this + + align:start position:0% +because I was thinking about this + + + align:start position:0% +because I was thinking about this +lecture but anyway my 10th grader asked + + align:start position:0% +lecture but anyway my 10th grader asked + + + align:start position:0% +lecture but anyway my 10th grader asked +my third grader is fire + + align:start position:0% +my third grader is fire + + + align:start position:0% +my third grader is fire +alive uh well I don't know about the + + align:start position:0% +alive uh well I don't know about the + + + align:start position:0% +alive uh well I don't know about the +third grader but it took Dad in the + + align:start position:0% +third grader but it took Dad in the + + + align:start position:0% +third grader but it took Dad in the +front seat a surprisingly long time to + + align:start position:0% +front seat a surprisingly long time to + + + align:start position:0% +front seat a surprisingly long time to +to figure well dad knew that the answer + + align:start position:0% +to figure well dad knew that the answer + + + align:start position:0% +to figure well dad knew that the answer +is no but the principled reason why it's + + align:start position:0% +is no but the principled reason why it's + + + align:start position:0% +is no but the principled reason why it's +no takes to took took me a couple of + + align:start position:0% +no takes to took took me a couple of + + + align:start position:0% +no takes to took took me a couple of +Beats to get to because well you know + + align:start position:0% +Beats to get to because well you know + + + align:start position:0% +Beats to get to because well you know +fire breathes right it grows it + + align:start position:0% +fire breathes right it grows it + + + align:start position:0% +fire breathes right it grows it +reproduces it can die it can do all + + align:start position:0% +reproduces it can die it can do all + + + align:start position:0% +reproduces it can die it can do all +those good things turns out in 10th + + align:start position:0% +those good things turns out in 10th + + + align:start position:0% +those good things turns out in 10th +grade biology they teach you that if + + align:start position:0% +grade biology they teach you that if + + + align:start position:0% +grade biology they teach you that if +you're going to be alive you've got to + + align:start position:0% +you're going to be alive you've got to + + + align:start position:0% +you're going to be alive you've got to +be made you got to be made of cells and + + align:start position:0% +be made you got to be made of cells and + + + align:start position:0% +be made you got to be made of cells and +fires not made of of of cells except + + align:start position:0% +fires not made of of of cells except + + + align:start position:0% +fires not made of of of cells except +that you know then you get into 11th + + align:start position:0% +that you know then you get into 11th + + + align:start position:0% +that you know then you get into 11th +grade English and you read some sci-fi + + align:start position:0% +grade English and you read some sci-fi + + + align:start position:0% +grade English and you read some sci-fi +novel where this thing is alive but it's + + align:start position:0% +novel where this thing is alive but it's + + + align:start position:0% +novel where this thing is alive but it's +just a force field in deep space or + + align:start position:0% +just a force field in deep space or + + + align:start position:0% +just a force field in deep space or +something like that I don't know what to + + align:start position:0% +something like that I don't know what to + + + align:start position:0% +something like that I don't know what to +do about that but + + align:start position:0% +do about that but + + + align:start position:0% +do about that but +um Concepts like alive are are are are + + align:start position:0% +um Concepts like alive are are are are + + + align:start position:0% +um Concepts like alive are are are are +pretty complex stuff and the fact that a + + align:start position:0% +pretty complex stuff and the fact that a + + + align:start position:0% +pretty complex stuff and the fact that a +kid doesn't map it exactly the same way + + align:start position:0% +kid doesn't map it exactly the same way + + + align:start position:0% +kid doesn't map it exactly the same way +you map it may not be that definitive um + + align:start position:0% +you map it may not be that definitive um + + + align:start position:0% +you map it may not be that definitive um +does the kid have a concept at all that + + align:start position:0% +does the kid have a concept at all that + + + align:start position:0% +does the kid have a concept at all that +they can use that's what we really want + + align:start position:0% +they can use that's what we really want + + + align:start position:0% +they can use that's what we really want +to know what's really going on there um + + align:start position:0% +to know what's really going on there um + + + align:start position:0% +to know what's really going on there um +so maybe we ought to ask the question a + + align:start position:0% +so maybe we ought to ask the question a + + + align:start position:0% +so maybe we ought to ask the question a +little bit differently kid has some + + align:start position:0% +little bit differently kid has some + + + align:start position:0% +little bit differently kid has some +notion of what alive things do so + + align:start position:0% +notion of what alive things do so + + + align:start position:0% +notion of what alive things do so +suppose we ask a kid um uh does a cat + + align:start position:0% +suppose we ask a kid um uh does a cat + + + align:start position:0% +suppose we ask a kid um uh does a cat +breathe yeah cat breathes how about a + + align:start position:0% +breathe yeah cat breathes how about a + + + align:start position:0% +breathe yeah cat breathes how about a +how about a a cow yeah cow breeds um how + + align:start position:0% +how about a a cow yeah cow breeds um how + + + align:start position:0% +how about a a cow yeah cow breeds um how +about the sun no I don't think so the + + align:start position:0% +about the sun no I don't think so the + + + align:start position:0% +about the sun no I don't think so the +moon no the clouds No so that and you + + align:start position:0% +moon no the clouds No so that and you + + + align:start position:0% +moon no the clouds No so that and you +can do the same thing with + + align:start position:0% +can do the same thing with + + + align:start position:0% +can do the same thing with +babies not not not asking the babies but + + align:start position:0% +babies not not not asking the babies but + + + align:start position:0% +babies not not not asking the babies but +talking about you know does a cat can a + + align:start position:0% +talking about you know does a cat can a + + + align:start position:0% +talking about you know does a cat can a +cat have + + align:start position:0% +cat have + + + align:start position:0% +cat have +babies yeah sure can the Sun have + + align:start position:0% +babies yeah sure can the Sun have + + + align:start position:0% +babies yeah sure can the Sun have +babies + + align:start position:0% +babies + + + align:start position:0% +babies +no and you get the feeling that there's + + align:start position:0% +no and you get the feeling that there's + + + align:start position:0% +no and you get the feeling that there's +a concept there that they're just not + + align:start position:0% +a concept there that they're just not + + + align:start position:0% +a concept there that they're just not +using the word alive the way that uh + + align:start position:0% +using the word alive the way that uh + + + align:start position:0% +using the word alive the way that uh +that you and I are using it well maybe + + align:start position:0% +that you and I are using it well maybe + + + align:start position:0% +that you and I are using it well maybe +all you're looking at here is the fact + + align:start position:0% +all you're looking at here is the fact + + + align:start position:0% +all you're looking at here is the fact +that that they don't actually have a + + align:start position:0% +that that they don't actually have a + + + align:start position:0% +that that they don't actually have a +concept what they have is a long list of + + align:start position:0% +concept what they have is a long list of + + + align:start position:0% +concept what they have is a long list of +learned instances they all hang out at + + align:start position:0% +learned instances they all hang out at + + + align:start position:0% +learned instances they all hang out at +these fancy you know upper middle class + + align:start position:0% +these fancy you know upper middle class + + + align:start position:0% +these fancy you know upper middle class +preschools where they get taught Kitty + + align:start position:0% +preschools where they get taught Kitty + + + align:start position:0% +preschools where they get taught Kitty +has babies cow has babies and they never + + align:start position:0% +has babies cow has babies and they never + + + align:start position:0% +has babies cow has babies and they never +get taught sun has babies because the + + align:start position:0% +get taught sun has babies because the + + + align:start position:0% +get taught sun has babies because the +sun doesn't have babies and so they + + align:start position:0% +sun doesn't have babies and so they + + + align:start position:0% +sun doesn't have babies and so they +learn all this stuff maybe it's not a + + align:start position:0% +learn all this stuff maybe it's not a + + + align:start position:0% +learn all this stuff maybe it's not a +concept maybe it's just a list of + + align:start position:0% +concept maybe it's just a list of + + + align:start position:0% +concept maybe it's just a list of +instances how can we figure this out + + align:start position:0% +instances how can we figure this out + + + align:start position:0% +instances how can we figure this out +well um Sue carry did an experiment + + align:start position:0% +well um Sue carry did an experiment + + + align:start position:0% +well um Sue carry did an experiment +where what she did was she taught kids + + align:start position:0% +where what she did was she taught kids + + + align:start position:0% +where what she did was she taught kids +something new she + + align:start position:0% +something new she + + + align:start position:0% +something new she +said see this cat this cat has an + + align:start position:0% +said see this cat this cat has an + + + align:start position:0% +said see this cat this cat has an +momentum and you have an momentum and + + align:start position:0% +momentum and you have an momentum and + + + align:start position:0% +momentum and you have an momentum and +the cow has an + + align:start position:0% +the cow has an + + + align:start position:0% +the cow has an +momentum now how about the Sheep think + + align:start position:0% +momentum now how about the Sheep think + + + align:start position:0% +momentum now how about the Sheep think +it's got no + + align:start position:0% +it's got no + + + align:start position:0% +it's got no +mum probably got no mum how and and and + + align:start position:0% +mum probably got no mum how and and and + + + align:start position:0% +mum probably got no mum how and and and +and the dog yeah the dog's probably got + + align:start position:0% +and the dog yeah the dog's probably got + + + align:start position:0% +and the dog yeah the dog's probably got +one how about a + + align:start position:0% +one how about a + + + align:start position:0% +one how about a +fish yeah probably probably could be + + align:start position:0% +fish yeah probably probably could be + + + align:start position:0% +fish yeah probably probably could be +worm I don't know Poss Rock nah Rock + + align:start position:0% +worm I don't know Poss Rock nah Rock + + + align:start position:0% +worm I don't know Poss Rock nah Rock +doesn't have momentum and about son nah + + align:start position:0% +doesn't have momentum and about son nah + + + align:start position:0% +doesn't have momentum and about son nah +son doesn't have an momentum you don't + + align:start position:0% +son doesn't have an momentum you don't + + + align:start position:0% +son doesn't have an momentum you don't +have one either it turns out uh she she + + align:start position:0% +have one either it turns out uh she she + + + align:start position:0% +have one either it turns out uh she she +wanted a real biological term but she + + align:start position:0% +wanted a real biological term but she + + + align:start position:0% +wanted a real biological term but she +took I I think it's some weird membrane + + align:start position:0% +took I I think it's some weird membrane + + + align:start position:0% +took I I think it's some weird membrane +that an insect has or something like + + align:start position:0% +that an insect has or something like + + + align:start position:0% +that an insect has or something like +that but the point was that it wasn't + + align:start position:0% +that but the point was that it wasn't + + + align:start position:0% +that but the point was that it wasn't +something that you would have ever + + align:start position:0% +something that you would have ever + + + align:start position:0% +something that you would have ever +learned it's a new piece of knowledge + + align:start position:0% +learned it's a new piece of knowledge + + + align:start position:0% +learned it's a new piece of knowledge +and if you say that things in this + + align:start position:0% +and if you say that things in this + + + align:start position:0% +and if you say that things in this +category things in the category that is + + align:start position:0% +category things in the category that is + + + align:start position:0% +category things in the category that is +are encompassed by cats cows and you all + + align:start position:0% +are encompassed by cats cows and you all + + + align:start position:0% +are encompassed by cats cows and you all +have this who else has it and little + + align:start position:0% +have this who else has it and little + + + align:start position:0% +have this who else has it and little +kids three four-year-old kids map this + + align:start position:0% +kids three four-year-old kids map this + + + align:start position:0% +kids three four-year-old kids map this +in a plausible kind of a way so it might + + align:start position:0% +in a plausible kind of a way so it might + + + align:start position:0% +in a plausible kind of a way so it might +map something like mammal it might map + + align:start position:0% +map something like mammal it might map + + + align:start position:0% +map something like mammal it might map +something like animal um I don't + + align:start position:0% +something like animal um I don't + + + align:start position:0% +something like animal um I don't +remember if any of her kids mapped + + align:start position:0% +remember if any of her kids mapped + + + align:start position:0% +remember if any of her kids mapped +something like alive in which case they + + align:start position:0% +something like alive in which case they + + + align:start position:0% +something like alive in which case they +would assert that a tree had it too or + + align:start position:0% +would assert that a tree had it too or + + + align:start position:0% +would assert that a tree had it too or +something but it Maps a uh a a concept + + align:start position:0% +something but it Maps a uh a a concept + + + align:start position:0% +something but it Maps a uh a a concept +that has a + + align:start position:0% +that has a + + + align:start position:0% +that has a +biological um ring to it what's the + + align:start position:0% +biological um ring to it what's the + + + align:start position:0% +biological um ring to it what's the +difference between the childhood use of + + align:start position:0% +difference between the childhood use of + + + align:start position:0% +difference between the childhood use of +these Concepts and the adult use of + + align:start position:0% +these Concepts and the adult use of + + + align:start position:0% +these Concepts and the adult use of +these Concepts it seems to be in this + + align:start position:0% +these Concepts it seems to be in this + + + align:start position:0% +these Concepts it seems to be in this +case um e education you go to school to + + align:start position:0% +case um e education you go to school to + + + align:start position:0% +case um e education you go to school to +learn the right Concepts in this sense + + align:start position:0% +learn the right Concepts in this sense + + + align:start position:0% +learn the right Concepts in this sense +there is no firm adult uh State I mean + + align:start position:0% +there is no firm adult uh State I mean + + + align:start position:0% +there is no firm adult uh State I mean +my job here is to teach you um a + + align:start position:0% +my job here is to teach you um a + + + align:start position:0% +my job here is to teach you um a +collection of facts and the right + + align:start position:0% +collection of facts and the right + + + align:start position:0% +collection of facts and the right +Concepts in Psychology but um but I can + + align:start position:0% +Concepts in Psychology but um but I can + + + align:start position:0% +Concepts in Psychology but um but I can +teach you some of them and I keep + + align:start position:0% +teach you some of them and I keep + + + align:start position:0% +teach you some of them and I keep +learning new ones and the you know the + + align:start position:0% +learning new ones and the you know the + + + align:start position:0% +learning new ones and the you know the +adult bar keeps sort of um drifting + + align:start position:0% +adult bar keeps sort of um drifting + + + align:start position:0% +adult bar keeps sort of um drifting +there you sort of go off to learn these + + align:start position:0% +there you sort of go off to learn these + + + align:start position:0% +there you sort of go off to learn these +sort of Concepts but you don't learn to + + align:start position:0% +sort of Concepts but you don't learn to + + + align:start position:0% +sort of Concepts but you don't learn to +have a uh a a concept per se what the + + align:start position:0% +have a uh a a concept per se what the + + + align:start position:0% +have a uh a a concept per se what the +kid is doing well actually it's rather + + align:start position:0% +kid is doing well actually it's rather + + + align:start position:0% +kid is doing well actually it's rather +similar to what we're doing here the kid + + align:start position:0% +similar to what we're doing here the kid + + + align:start position:0% +similar to what we're doing here the kid +is + + align:start position:0% +is + + + align:start position:0% +is +mustering the + + align:start position:0% +mustering the + + + align:start position:0% +mustering the +data uh that that is available to + + align:start position:0% +data uh that that is available to + + + align:start position:0% +data uh that that is available to +him and uh and and working with the + + align:start position:0% +him and uh and and working with the + + + align:start position:0% +him and uh and and working with the +concept as long so what what do you + + align:start position:0% +concept as long so what what do you + + + align:start position:0% +concept as long so what what do you +figure what do you think the concept of + + align:start position:0% +figure what do you think the concept of + + + align:start position:0% +figure what do you think the concept of +a lot is for a little kid what do you + + align:start position:0% +a lot is for a little kid what do you + + + align:start position:0% +a lot is for a little kid what do you +think goes into it that that that causes + + align:start position:0% +think goes into it that that that causes + + + align:start position:0% +think goes into it that that that causes +little kids to give the wrong answer + + align:start position:0% +little kids to give the wrong answer + + + align:start position:0% +little kids to give the wrong answer +when asked by P what's alive and what's + + align:start position:0% +when asked by P what's alive and what's + + + align:start position:0% +when asked by P what's alive and what's +not what what what's the critical + + align:start position:0% +not what what what's the critical + + + align:start position:0% +not what what what's the critical +difference between your notion of alive + + align:start position:0% +difference between your notion of alive + + + align:start position:0% +difference between your notion of alive +that you picked up in in 10th grade + + align:start position:0% +that you picked up in in 10th grade + + + align:start position:0% +that you picked up in in 10th grade +biology um and and and a four-year-old's + + align:start position:0% +biology um and and and a four-year-old's + + + align:start position:0% +biology um and and and a four-year-old's +notion of + + align:start position:0% +notion of + + + align:start position:0% +notion of +alive anybody yeah something alive is + + align:start position:0% +alive anybody yeah something alive is + + + align:start position:0% +alive anybody yeah something alive is +something that moves and you didn't see + + align:start position:0% +something that moves and you didn't see + + + align:start position:0% +something that moves and you didn't see +how why it mov yeah so so moving on it + + align:start position:0% +how why it mov yeah so so moving on it + + + align:start position:0% +how why it mov yeah so so moving on it +own seems to be an important so cars + + align:start position:0% +own seems to be an important so cars + + + align:start position:0% +own seems to be an important so cars +aren't alive because you've got to make + + align:start position:0% +aren't alive because you've got to make + + + align:start position:0% +aren't alive because you've got to make +them move in some fashion but but but uh + + align:start position:0% +them move in some fashion but but but uh + + + align:start position:0% +them move in some fashion but but but uh +um but self-produced motion seems to be + + align:start position:0% +um but self-produced motion seems to be + + + align:start position:0% +um but self-produced motion seems to be +an important part of the definition and + + align:start position:0% +an important part of the definition and + + + align:start position:0% +an important part of the definition and +the Sun and the clouds and and and and + + align:start position:0% +the Sun and the clouds and and and and + + + align:start position:0% +the Sun and the clouds and and and and +the moon seem to scooch around in the + + align:start position:0% +the moon seem to scooch around in the + + + align:start position:0% +the moon seem to scooch around in the +sky particularly if you're driving in + + align:start position:0% +sky particularly if you're driving in + + + align:start position:0% +sky particularly if you're driving in +that car um in ways that suggest that it + + align:start position:0% +that car um in ways that suggest that it + + + align:start position:0% +that car um in ways that suggest that it +might be alive it it gets a little more + + align:start position:0% +might be alive it it gets a little more + + + align:start position:0% +might be alive it it gets a little more +complicated because kids have also + + align:start position:0% +complicated because kids have also + + + align:start position:0% +complicated because kids have also +learned that uh that trees are alive and + + align:start position:0% +learned that uh that trees are alive and + + + align:start position:0% +learned that uh that trees are alive and +and outside of Lord of the Rings trees + + align:start position:0% +and outside of Lord of the Rings trees + + + align:start position:0% +and outside of Lord of the Rings trees +don't do much in the way of wandering + + align:start position:0% +don't do much in the way of wandering + + + align:start position:0% +don't do much in the way of wandering +around um but growing on your own is + + align:start position:0% +around um but growing on your own is + + + align:start position:0% +around um but growing on your own is +good too um and and and that's that that + + align:start position:0% +good too um and and and that's that that + + + align:start position:0% +good too um and and and that's that that +would be part of the biological + + align:start position:0% +would be part of the biological + + + align:start position:0% +would be part of the biological +definition but it's it's the + + align:start position:0% +definition but it's it's the + + + align:start position:0% +definition but it's it's the +self-produced motion thing that kids + + align:start position:0% +self-produced motion thing that kids + + + align:start position:0% +self-produced motion thing that kids +regard that o that kids overuse in in + + align:start position:0% +regard that o that kids overuse in in + + + align:start position:0% +regard that o that kids overuse in in +their definition seemingly that uh that + + align:start position:0% +their definition seemingly that uh that + + + align:start position:0% +their definition seemingly that uh that +you don't use you can see if you get uh + + align:start position:0% +you don't use you can see if you get uh + + + align:start position:0% +you don't use you can see if you get uh +transcripts of little kids using + + align:start position:0% +transcripts of little kids using + + + align:start position:0% +transcripts of little kids using +language you can see you can get a + + align:start position:0% +language you can see you can get a + + + align:start position:0% +language you can see you can get a +feeling for this little scientist aspect + + align:start position:0% +feeling for this little scientist aspect + + + align:start position:0% +feeling for this little scientist aspect +of childhood concept well you know of + + align:start position:0% +of childhood concept well you know of + + + align:start position:0% +of childhood concept well you know of +concept formation concept verification + + align:start position:0% +concept formation concept verification + + + align:start position:0% +concept formation concept verification +um so here from the um what is alive uh + + align:start position:0% +um so here from the um what is alive uh + + + align:start position:0% +um so here from the um what is alive uh +literature um is a is a kid + + align:start position:0% +literature um is a is a kid + + + align:start position:0% +literature um is a is a kid +who um is asked are rocks alive and the + + align:start position:0% +who um is asked are rocks alive and the + + + align:start position:0% +who um is asked are rocks alive and the +answer is yes rocks um are are alive um + + align:start position:0% +answer is yes rocks um are are alive um + + + align:start position:0% +answer is yes rocks um are are alive um +but they're only alive until you step on + + align:start position:0% +but they're only alive until you step on + + + align:start position:0% +but they're only alive until you step on +them and then they die um which is kind + + align:start position:0% +them and then they die um which is kind + + + align:start position:0% +them and then they die um which is kind +of reasonable right the kids got + + align:start position:0% +of reasonable right the kids got + + + align:start position:0% +of reasonable right the kids got +presumably some experience with other + + align:start position:0% +presumably some experience with other + + + align:start position:0% +presumably some experience with other +things like that this ant the ant's + + align:start position:0% +things like that this ant the ant's + + + align:start position:0% +things like that this ant the ant's +alive I step on is not alive anymore um + + align:start position:0% +alive I step on is not alive anymore um + + + align:start position:0% +alive I step on is not alive anymore um +and he can actually and this kid + + align:start position:0% +and he can actually and this kid + + + align:start position:0% +and he can actually and this kid +produces some evidence in favor of this + + align:start position:0% +produces some evidence in favor of this + + + align:start position:0% +produces some evidence in favor of this +Theory um which is if you look on a + + align:start position:0% +Theory um which is if you look on a + + + align:start position:0% +Theory um which is if you look on a +path how big are the rocks on + + align:start position:0% +path how big are the rocks on + + + align:start position:0% +path how big are the rocks on +average you know could take a walk in + + align:start position:0% +average you know could take a walk in + + + align:start position:0% +average you know could take a walk in +the woods down a rocky kind of path + + align:start position:0% +the woods down a rocky kind of path + + + align:start position:0% +the woods down a rocky kind of path +there are rocks on there they're kind of + + align:start position:0% +there are rocks on there they're kind of + + + align:start position:0% +there are rocks on there they're kind of +small rocks you look off across you know + + align:start position:0% +small rocks you look off across you know + + + align:start position:0% +small rocks you look off across you know +at the at the mountains how big are the + + align:start position:0% +at the at the mountains how big are the + + + align:start position:0% +at the at the mountains how big are the +Rocks well they're huge what's going on + + align:start position:0% +Rocks well they're huge what's going on + + + align:start position:0% +Rocks well they're huge what's going on +here well on a path people are walking + + align:start position:0% +here well on a path people are walking + + + align:start position:0% +here well on a path people are walking +all the time so the Rocks die real young + + align:start position:0% +all the time so the Rocks die real young + + + align:start position:0% +all the time so the Rocks die real young +they never get to grow big um whereas + + align:start position:0% +they never get to grow big um whereas + + + align:start position:0% +they never get to grow big um whereas +the Rocks off the path out in the + + align:start position:0% +the Rocks off the path out in the + + + align:start position:0% +the Rocks off the path out in the +mountains they got to grow to be really + + align:start position:0% +mountains they got to grow to be really + + + align:start position:0% +mountains they got to grow to be really +big rocks it's not a correct Theory but + + align:start position:0% +big rocks it's not a correct Theory but + + + align:start position:0% +big rocks it's not a correct Theory but +you can see the kid using the data he's + + align:start position:0% +you can see the kid using the data he's + + + align:start position:0% +you can see the kid using the data he's +got right certain amount of data there + + align:start position:0% +got right certain amount of data there + + + align:start position:0% +got right certain amount of data there +if I step on it it + + align:start position:0% +if I step on it it + + + align:start position:0% +if I step on it it +dies maybe that's what happens to rocks + + align:start position:0% +dies maybe that's what happens to rocks + + + align:start position:0% +dies maybe that's what happens to rocks +and the people step more here than they + + align:start position:0% +and the people step more here than they + + + align:start position:0% +and the people step more here than they +step there so big rocks little rocks it + + align:start position:0% +step there so big rocks little rocks it + + + align:start position:0% +step there so big rocks little rocks it +all hangs together I got a great Theory + + align:start position:0% +all hangs together I got a great Theory + + + align:start position:0% +all hangs together I got a great Theory +here or um the another one are rocks + + align:start position:0% +here or um the another one are rocks + + + align:start position:0% +here or um the another one are rocks +alive yes can they have babies yes are + + align:start position:0% +alive yes can they have babies yes are + + + align:start position:0% +alive yes can they have babies yes are +all rocks alive no some rocks are dead + + align:start position:0% +all rocks alive no some rocks are dead + + + align:start position:0% +all rocks alive no some rocks are dead +how can you tell the how can you tell if + + align:start position:0% +how can you tell the how can you tell if + + + align:start position:0% +how can you tell the how can you tell if +a rock is dead well the dead ones just + + align:start position:0% +a rock is dead well the dead ones just + + + align:start position:0% +a rock is dead well the dead ones just +lie + + align:start position:0% +lie + + + align:start position:0% +lie +there this is this is capturing the + + align:start position:0% +there this is this is capturing the + + + align:start position:0% +there this is this is capturing the +notion of that that motion is important + + align:start position:0% +notion of that that motion is important + + + align:start position:0% +notion of that that motion is important +in in in little kids definitions of the + + align:start position:0% +in in in little kids definitions of the + + + align:start position:0% +in in in little kids definitions of the +of of the notion of + + align:start position:0% +of of the notion of + + + align:start position:0% +of of the notion of +aliveness um and then uh um well I don't + + align:start position:0% +aliveness um and then uh um well I don't + + + align:start position:0% +aliveness um and then uh um well I don't +know how many rocks you saw moving under + + align:start position:0% +know how many rocks you saw moving under + + + align:start position:0% +know how many rocks you saw moving under +their own their own power but in any + + align:start position:0% +their own their own power but in any + + + align:start position:0% +their own their own power but in any +case you can see the little uh the + + align:start position:0% +case you can see the little uh the + + + align:start position:0% +case you can see the little uh the +little scientist aspect of this okay so + + align:start position:0% +little scientist aspect of this okay so + + + align:start position:0% +little scientist aspect of this okay so +what's the starting point here + + align:start position:0% +what's the starting point here + + + align:start position:0% +what's the starting point here +um the concepts that you're + + align:start position:0% +um the concepts that you're + + + align:start position:0% +um the concepts that you're +building + + align:start position:0% +building + + + align:start position:0% +building +um see seem to have some foundations + + align:start position:0% +um see seem to have some foundations + + + align:start position:0% +um see seem to have some foundations +that can be picked up very early and are + + align:start position:0% +that can be picked up very early and are + + + align:start position:0% +that can be picked up very early and are +probably innate I'll just talk about two + + align:start position:0% +probably innate I'll just talk about two + + + align:start position:0% +probably innate I'll just talk about two +of them uh here so Concepts like about + + align:start position:0% +of them uh here so Concepts like about + + + align:start position:0% +of them uh here so Concepts like about +things like aliveness um if you're going + + align:start position:0% +things like aliveness um if you're going + + + align:start position:0% +things like aliveness um if you're going +to decide that a thing is alive you need + + align:start position:0% +to decide that a thing is alive you need + + + align:start position:0% +to decide that a thing is alive you need +for starters to know that it is a thing + + align:start position:0% +for starters to know that it is a thing + + + align:start position:0% +for starters to know that it is a thing +so you need to have some notion of an + + align:start position:0% +so you need to have some notion of an + + + align:start position:0% +so you need to have some notion of an +object + + align:start position:0% +object + + + align:start position:0% +object +um and uh the other thing you need is + + align:start position:0% +um and uh the other thing you need is + + + align:start position:0% +um and uh the other thing you need is +some Notions that objects classes of + + align:start position:0% +some Notions that objects classes of + + + align:start position:0% +some Notions that objects classes of +objects have Essences this is I think + + align:start position:0% +objects have Essences this is I think + + + align:start position:0% +objects have Essences this is I think +it's on the handout somewhere as did I + + align:start position:0% +it's on the handout somewhere as did I + + + align:start position:0% +it's on the handout somewhere as did I +write yes I uh oh yes towards the bottom + + align:start position:0% +write yes I uh oh yes towards the bottom + + + align:start position:0% +write yes I uh oh yes towards the bottom +of page to says Essence and there's a + + align:start position:0% +of page to says Essence and there's a + + + align:start position:0% +of page to says Essence and there's a +reference to Susan gelman's work on + + align:start position:0% +reference to Susan gelman's work on + + + align:start position:0% +reference to Susan gelman's work on +psychological essentialism the notion of + + align:start position:0% +psychological essentialism the notion of + + + align:start position:0% +psychological essentialism the notion of +an Essence is a property that's um + + align:start position:0% +an Essence is a property that's um + + + align:start position:0% +an Essence is a property that's um +that's not visible or at least not + + align:start position:0% +that's not visible or at least not + + + align:start position:0% +that's not visible or at least not +currently visible it's got to be in in + + align:start position:0% +currently visible it's got to be in in + + + align:start position:0% +currently visible it's got to be in in +order to have these sort of category + + align:start position:0% +order to have these sort of category + + + align:start position:0% +order to have these sort of category +things you've got to have the notion + + align:start position:0% +things you've got to have the notion + + + align:start position:0% +things you've got to have the notion +that you that there are that that + + align:start position:0% +that you that there are that that + + + align:start position:0% +that you that there are that that +objects continue to have properties even + + align:start position:0% +objects continue to have properties even + + + align:start position:0% +objects continue to have properties even +if you can't see that so for example um + + align:start position:0% +if you can't see that so for example um + + + align:start position:0% +if you can't see that so for example um +well I won't embarrass anybody but um + + align:start position:0% +well I won't embarrass anybody but um + + + align:start position:0% +well I won't embarrass anybody but um +there are people here presently who are + + align:start position:0% +there are people here presently who are + + + align:start position:0% +there are people here presently who are +not moving who are not to all + + align:start position:0% +not moving who are not to all + + + align:start position:0% +not moving who are not to all +appearances growing I can't tell from + + align:start position:0% +appearances growing I can't tell from + + + align:start position:0% +appearances growing I can't tell from +this distance whether they're made of + + align:start position:0% +this distance whether they're made of + + + align:start position:0% +this distance whether they're made of +cells and they don't appear to be having + + align:start position:0% +cells and they don't appear to be having + + + align:start position:0% +cells and they don't appear to be having +babies or anything like that + + align:start position:0% +babies or anything like that + + + align:start position:0% +babies or anything like that +nevertheless I can I assume that they + + align:start position:0% +nevertheless I can I assume that they + + + align:start position:0% +nevertheless I can I assume that they +are + + align:start position:0% +are + + + align:start position:0% +are +alive that that that's part of their + + align:start position:0% +alive that that that's part of their + + + align:start position:0% +alive that that that's part of their +Essence um that this aliveness is + + align:start position:0% +Essence um that this aliveness is + + + align:start position:0% +Essence um that this aliveness is +something that uh that I attribute to + + align:start position:0% +something that uh that I attribute to + + + align:start position:0% +something that uh that I attribute to +that object without without being able + + align:start position:0% +that object without without being able + + + align:start position:0% +that object without without being able +to see it now what's the evidence that + + align:start position:0% +to see it now what's the evidence that + + + align:start position:0% +to see it now what's the evidence that +little kids um have that well I'll tell + + align:start position:0% +little kids um have that well I'll tell + + + align:start position:0% +little kids um have that well I'll tell +you that and then before and then we'll + + align:start position:0% +you that and then before and then we'll + + + align:start position:0% +you that and then before and then we'll +go on have a break and then we'll go on + + align:start position:0% +go on have a break and then we'll go on + + + align:start position:0% +go on have a break and then we'll go on +to the uh to the problem of egocentric + + align:start position:0% +to the uh to the problem of egocentric + + + align:start position:0% +to the uh to the problem of egocentric +Behavior so um uh uh I need a + + align:start position:0% +Behavior so um uh uh I need a + + + align:start position:0% +Behavior so um uh uh I need a +tube this is um let's start with + + align:start position:0% +tube this is um let's start with + + + align:start position:0% +tube this is um let's start with +evidence that children know babies know + + align:start position:0% +evidence that children know babies know + + + align:start position:0% +evidence that children know babies know +something about objects + + align:start position:0% +something about objects + + + align:start position:0% +something about objects +so here's a tube if I was doing this + + align:start position:0% +so here's a tube if I was doing this + + + align:start position:0% +so here's a tube if I was doing this +right I'd show you that there's nothing + + align:start position:0% +right I'd show you that there's nothing + + + align:start position:0% +right I'd show you that there's nothing +in the + + align:start position:0% +in the + + + align:start position:0% +in the +tube and uh it's it's and and then I + + align:start position:0% +tube and uh it's it's and and then I + + + align:start position:0% +tube and uh it's it's and and then I +would take a stuffed + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +animal he's a duck oh okay so we take + + align:start position:0% +animal he's a duck oh okay so we take + + + align:start position:0% +animal he's a duck oh okay so we take +the duck and and and he's he's he's a + + align:start position:0% +the duck and and and he's he's he's a + + + align:start position:0% +the duck and and and he's he's he's a +you know a squishy duck so I can I'm + + align:start position:0% +you know a squishy duck so I can I'm + + + align:start position:0% +you know a squishy duck so I can I'm +going to stuff him in the tube okay and + + align:start position:0% +going to stuff him in the tube okay and + + + align:start position:0% +going to stuff him in the tube okay and +then so the baby's watching all this + + align:start position:0% +then so the baby's watching all this + + + align:start position:0% +then so the baby's watching all this +cool stuff happening here this is a + + align:start position:0% +cool stuff happening here this is a + + + align:start position:0% +cool stuff happening here this is a +little little little baby's watching + + align:start position:0% +little little little baby's watching + + + align:start position:0% +little little little baby's watching +this stuff and then I I take uh you know + + align:start position:0% +this stuff and then I I take uh you know + + + align:start position:0% +this stuff and then I I take uh you know +Nemo or + + align:start position:0% +Nemo or + + + align:start position:0% +Nemo or +whatever my little plush Nemo um and i + + align:start position:0% +whatever my little plush Nemo um and i + + + align:start position:0% +whatever my little plush Nemo um and i +stuff him in the + + align:start position:0% +stuff him in the + + + align:start position:0% +stuff him in the +tube okay you're with me so far baby + + align:start position:0% +tube okay you're with me so far baby + + + align:start position:0% +tube okay you're with me so far baby +IES now I reach into the tube and I pull + + align:start position:0% + + + + align:start position:0% + +out I pull out the + + align:start position:0% +out I pull out the + + + align:start position:0% +out I pull out the +fish and you being good babies stare at + + align:start position:0% +fish and you being good babies stare at + + + align:start position:0% +fish and you being good babies stare at +this you say this is weird stuff because + + align:start position:0% +this you say this is weird stuff because + + + align:start position:0% +this you say this is weird stuff because +I saw the duck go in first and this is + + align:start position:0% +I saw the duck go in first and this is + + + align:start position:0% +I saw the duck go in first and this is +not quite Liz spy's experiment I I'm I'm + + align:start position:0% +not quite Liz spy's experiment I I'm I'm + + + align:start position:0% +not quite Liz spy's experiment I I'm I'm +I realize I'm getting the methods a + + align:start position:0% +I realize I'm getting the methods a + + + align:start position:0% +I realize I'm getting the methods a +little screwed up but the principle is + + align:start position:0% +little screwed up but the principle is + + + align:start position:0% +little screwed up but the principle is +right um I saw the duck go in then the + + align:start position:0% +right um I saw the duck go in then the + + + align:start position:0% +right um I saw the duck go in then the +fish went in and I know about objects + + align:start position:0% +fish went in and I know about objects + + + align:start position:0% +fish went in and I know about objects +objects do not + + align:start position:0% +objects do not + + + align:start position:0% +objects do not +interpenetrate right objects are solid + + align:start position:0% +interpenetrate right objects are solid + + + align:start position:0% +interpenetrate right objects are solid +things and if the if if the fish is out + + align:start position:0% +things and if the if if the fish is out + + + align:start position:0% +things and if the if if the fish is out +here where'd the duck go and Spell's + + align:start position:0% +here where'd the duck go and Spell's + + + align:start position:0% +here where'd the duck go and Spell's +done a series of experiments like this + + align:start position:0% +done a series of experiments like this + + + align:start position:0% +done a series of experiments like this +that suggest that kids know about object + + align:start position:0% +that suggest that kids know about object + + + align:start position:0% +that suggest that kids know about object +babies young babies as early as you can + + align:start position:0% +babies young babies as early as you can + + + align:start position:0% +babies young babies as early as you can +successfully test them so getting very + + align:start position:0% +successfully test them so getting very + + + align:start position:0% +successfully test them so getting very +close to being at the starting point + + align:start position:0% +close to being at the starting point + + + align:start position:0% +close to being at the starting point +know about objects um and and know a few + + align:start position:0% +know about objects um and and know a few + + + align:start position:0% +know about objects um and and know a few +things about those objects not notably + + align:start position:0% +things about those objects not notably + + + align:start position:0% +things about those objects not notably +things like uh that that objects don't + + align:start position:0% +things like uh that that objects don't + + + align:start position:0% +things like uh that that objects don't +interpenetrate um they don't know + + align:start position:0% +interpenetrate um they don't know + + + align:start position:0% +interpenetrate um they don't know +everything about objects so they don't + + align:start position:0% +everything about objects so they don't + + + align:start position:0% +everything about objects so they don't +for instance if if you show if you set + + align:start position:0% +for instance if if you show if you set + + + align:start position:0% +for instance if if you show if you set +up some you know fish and ducky kind of + + align:start position:0% +up some you know fish and ducky kind of + + + align:start position:0% +up some you know fish and ducky kind of +thing that violates the law of gravity + + align:start position:0% +thing that violates the law of gravity + + + align:start position:0% +thing that violates the law of gravity +kid doesn't care they don't seem to be + + align:start position:0% +kid doesn't care they don't seem to be + + + align:start position:0% +kid doesn't care they don't seem to be +particularly sensitive to uh to Gra gra + + align:start position:0% +particularly sensitive to uh to Gra gra + + + align:start position:0% +particularly sensitive to uh to Gra gra +it yet a 2-year-old or so in his high + + align:start position:0% +it yet a 2-year-old or so in his high + + + align:start position:0% +it yet a 2-year-old or so in his high +chair 2-year-old in the high chair + + align:start position:0% +chair 2-year-old in the high chair + + + align:start position:0% +chair 2-year-old in the high chair +thinks gravity is great right you know + + align:start position:0% +thinks gravity is great right you know + + + align:start position:0% +thinks gravity is great right you know +here's here's the hot + + align:start position:0% +here's here's the hot + + + align:start position:0% +here's here's the hot +dog oh yeah okay so dad picks up the hot + + align:start position:0% +dog oh yeah okay so dad picks up the hot + + + align:start position:0% +dog oh yeah okay so dad picks up the hot +dog and puts it back on the plate and + + align:start position:0% +dog and puts it back on the plate and + + + align:start position:0% +dog and puts it back on the plate and +the kid drops it again cuz he's got a + + align:start position:0% +the kid drops it again cuz he's got a + + + align:start position:0% +the kid drops it again cuz he's got a +check little scientist right you got to + + align:start position:0% +check little scientist right you got to + + + align:start position:0% +check little scientist right you got to +check that that gravity is is still + + align:start position:0% +check that that gravity is is still + + + align:start position:0% +check that that gravity is is still +you'll get there the uh um no not Mara + + align:start position:0% +you'll get there the uh um no not Mara + + + align:start position:0% +you'll get there the uh um no not Mara +knows about gravity but but her her like + + align:start position:0% +knows about gravity but but her her like + + + align:start position:0% +knows about gravity but but her her like +baby doesn't know about it yet her baby + + align:start position:0% +baby doesn't know about it yet her baby + + + align:start position:0% +baby doesn't know about it yet her baby +looks at gravity demonstrations and says + + align:start position:0% +looks at gravity demonstrations and says + + + align:start position:0% +looks at gravity demonstrations and says +this is is really boring but her baby + + align:start position:0% +this is is really boring but her baby + + + align:start position:0% +this is is really boring but her baby +knows that that the duck cannot that the + + align:start position:0% +knows that that the duck cannot that the + + + align:start position:0% +knows that that the duck cannot that the +fish cannot go through the duck it just + + align:start position:0% +fish cannot go through the duck it just + + + align:start position:0% +fish cannot go through the duck it just +would be bad news for the uh for the + + align:start position:0% +would be bad news for the uh for the + + + align:start position:0% +would be bad news for the uh for the +duct babies don't care about inertia + + align:start position:0% +duct babies don't care about inertia + + + align:start position:0% +duct babies don't care about inertia +either you know things like objects in + + align:start position:0% +either you know things like objects in + + + align:start position:0% +either you know things like objects in +motion continue in motion unless acted + + align:start position:0% +motion continue in motion unless acted + + + align:start position:0% +motion continue in motion unless acted +on by you tell that to a baby baby says + + align:start position:0% +on by you tell that to a baby baby says + + + align:start position:0% +on by you tell that to a baby baby says +yeah right don't care about that but I + + align:start position:0% +yeah right don't care about that but I + + + align:start position:0% +yeah right don't care about that but I +know that the fish does not go through + + align:start position:0% +know that the fish does not go through + + + align:start position:0% +know that the fish does not go through +the duck um that so that that's this + + align:start position:0% +the duck um that so that that's this + + + align:start position:0% +the duck um that so that that's this +this notion of objects what about + + align:start position:0% +this notion of objects what about + + + align:start position:0% +this notion of objects what about +essence Essence is harder to get to um + + align:start position:0% +essence Essence is harder to get to um + + + align:start position:0% +essence Essence is harder to get to um +in um in early uh childhood it's harder + + align:start position:0% +in um in early uh childhood it's harder + + + align:start position:0% +in um in early uh childhood it's harder +to ask the question but by the time you + + align:start position:0% +to ask the question but by the time you + + + align:start position:0% +to ask the question but by the time you +get + + align:start position:0% + + + + align:start position:0% + +to how old are we in this + + align:start position:0% +to how old are we in this + + + align:start position:0% +to how old are we in this +experiment you're like 2 or three years + + align:start position:0% +experiment you're like 2 or three years + + + align:start position:0% +experiment you're like 2 or three years +old but you're doing something like this + + align:start position:0% +old but you're doing something like this + + + align:start position:0% +old but you're doing something like this +you take the + + align:start position:0% +you take the + + + align:start position:0% +you take the +duck and you say see see this + + align:start position:0% +duck and you say see see this + + + align:start position:0% +duck and you say see see this +duck what we're going to do is we're + + align:start position:0% +duck what we're going to do is we're + + + align:start position:0% +duck what we're going to do is we're +going to do an operation on the duck I + + align:start position:0% +going to do an operation on the duck I + + + align:start position:0% +going to do an operation on the duck I +promise it's not going to hurt the duck + + align:start position:0% +promise it's not going to hurt the duck + + + align:start position:0% +promise it's not going to hurt the duck +but we're going to take off his skin and + + align:start position:0% +but we're going to take off his skin and + + + align:start position:0% +but we're going to take off his skin and +we're going to put raccoon skin on him + + align:start position:0% +we're going to put raccoon skin on him + + + align:start position:0% +we're going to put raccoon skin on him +he's going to look just like a + + align:start position:0% +he's going to look just like a + + + align:start position:0% +he's going to look just like a +raccoon right now is that + + align:start position:0% +raccoon right now is that + + + align:start position:0% +raccoon right now is that +okay okay is this a duck or a + + align:start position:0% +okay okay is this a duck or a + + + align:start position:0% +okay okay is this a duck or a +raccoon and as soon as the kid can + + align:start position:0% +raccoon and as soon as the kid can + + + align:start position:0% +raccoon and as soon as the kid can +meaningfully answer the question for you + + align:start position:0% +meaningfully answer the question for you + + + align:start position:0% +meaningfully answer the question for you +the kid will say Ah that's a duck I mean + + align:start position:0% +the kid will say Ah that's a duck I mean + + + align:start position:0% +the kid will say Ah that's a duck I mean +you dressed him up like a raccoon but + + align:start position:0% +you dressed him up like a raccoon but + + + align:start position:0% +you dressed him up like a raccoon but +he's a duck inside he's got duck Essence + + align:start position:0% +he's a duck inside he's got duck Essence + + + align:start position:0% +he's a duck inside he's got duck Essence +Hees doesn't say anything about duck + + align:start position:0% +Hees doesn't say anything about duck + + + align:start position:0% +Hees doesn't say anything about duck +Essence but he knows that there's a core + + align:start position:0% +Essence but he knows that there's a core + + + align:start position:0% +Essence but he knows that there's a core +of duck that is not dependent on looking + + align:start position:0% +of duck that is not dependent on looking + + + align:start position:0% +of duck that is not dependent on looking +exactly like a + + align:start position:0% +exactly like a + + + align:start position:0% +exactly like a +duck + + align:start position:0% +duck + + + align:start position:0% +duck +moreover um oh it say so this by the way + + align:start position:0% +moreover um oh it say so this by the way + + + align:start position:0% +moreover um oh it say so this by the way +is H how many of the uh of you are + + align:start position:0% +is H how many of the uh of you are + + + align:start position:0% +is H how many of the uh of you are +familiar with the classic Pepe Lew + + align:start position:0% +familiar with the classic Pepe Lew + + + align:start position:0% +familiar with the classic Pepe Lew +cartoons yeah it's Cartoon Network stuff + + align:start position:0% +cartoons yeah it's Cartoon Network stuff + + + align:start position:0% +cartoons yeah it's Cartoon Network stuff +so the basic plot there's a whole bunch + + align:start position:0% +so the basic plot there's a whole bunch + + + align:start position:0% +so the basic plot there's a whole bunch +of these but the basic plot is always + + align:start position:0% +of these but the basic plot is always + + + align:start position:0% +of these but the basic plot is always +the same pepy law is a French + + align:start position:0% +the same pepy law is a French + + + align:start position:0% +the same pepy law is a French +skunk very you know a French lover skunk + + align:start position:0% +skunk very you know a French lover skunk + + + align:start position:0% +skunk very you know a French lover skunk +um and and this cat female cat gets a + + align:start position:0% +um and and this cat female cat gets a + + + align:start position:0% +um and and this cat female cat gets a +white stripe down her back by some paint + + align:start position:0% +white stripe down her back by some paint + + + align:start position:0% +white stripe down her back by some paint +or something like that and and and Peppe + + align:start position:0% +or something like that and and and Peppe + + + align:start position:0% +or something like that and and and Peppe +spends the next five minutes of the + + align:start position:0% +spends the next five minutes of the + + + align:start position:0% +spends the next five minutes of the +cartoon chasing her around trying to get + + align:start position:0% +cartoon chasing her around trying to get + + + align:start position:0% +cartoon chasing her around trying to get +her to fall in love and she doesn't want + + align:start position:0% +her to fall in love and she doesn't want + + + align:start position:0% +her to fall in love and she doesn't want +to fall in love because she knows he's a + + align:start position:0% +to fall in love because she knows he's a + + + align:start position:0% +to fall in love because she knows he's a +skunk and she knows that she's not a + + align:start position:0% +skunk and she knows that she's not a + + + align:start position:0% +skunk and she knows that she's not a +skunk what's funny about this the reason + + align:start position:0% +skunk what's funny about this the reason + + + align:start position:0% +skunk what's funny about this the reason +this is funny for little kids is that + + align:start position:0% +this is funny for little kids is that + + + align:start position:0% +this is funny for little kids is that +little kids know that the fact that + + align:start position:0% +little kids know that the fact that + + + align:start position:0% +little kids know that the fact that +she's got a white stripe down her + + align:start position:0% +she's got a white stripe down her + + + align:start position:0% +she's got a white stripe down her +doesn't make her into a a skunk she's + + align:start position:0% +doesn't make her into a a skunk she's + + + align:start position:0% +doesn't make her into a a skunk she's +still a cat who happens to look like a + + align:start position:0% +still a cat who happens to look like a + + + align:start position:0% +still a cat who happens to look like a +skunk and isn't that funny cuz the skunk + + align:start position:0% +skunk and isn't that funny cuz the skunk + + + align:start position:0% +skunk and isn't that funny cuz the skunk +is chasing around after her and getting + + align:start position:0% +is chasing around after her and getting + + + align:start position:0% +is chasing around after her and getting +hit in the head with bats and stuff like + + align:start position:0% +hit in the head with bats and stuff like + + + align:start position:0% +hit in the head with bats and stuff like +that all you know it's good things that + + align:start position:0% +that all you know it's good things that + + + align:start position:0% +that all you know it's good things that +happen in cartoons um so not only do + + align:start position:0% +happen in cartoons um so not only do + + + align:start position:0% +happen in cartoons um so not only do +kids know that things have an Essence + + align:start position:0% +kids know that things have an Essence + + + align:start position:0% +kids know that things have an Essence +like that they are also well to be a + + align:start position:0% +like that they are also well to be a + + + align:start position:0% +like that they are also well to be a +little recursive here they're innate + + align:start position:0% +little recursive here they're innate + + + align:start position:0% +little recursive here they're innate +nativists it appears they believe that + + align:start position:0% +nativists it appears they believe that + + + align:start position:0% +nativists it appears they believe that +these properties came with the system + + align:start position:0% +these properties came with the system + + + align:start position:0% +these properties came with the system +and were not learned so Susan Gelman did + + align:start position:0% +and were not learned so Susan Gelman did + + + align:start position:0% +and were not learned so Susan Gelman did +a clever experiment where what she did + + align:start position:0% +a clever experiment where what she did + + + align:start position:0% +a clever experiment where what she did +was she said see see this kangaroo this + + align:start position:0% +was she said see see this kangaroo this + + + align:start position:0% +was she said see see this kangaroo this +can be a kangaroo as well as a duck I'm + + align:start position:0% +can be a kangaroo as well as a duck I'm + + + align:start position:0% +can be a kangaroo as well as a duck I'm +sure anyway take this + + align:start position:0% +sure anyway take this + + + align:start position:0% +sure anyway take this +kangaroo this is a baby kangaroo it's a + + align:start position:0% +kangaroo this is a baby kangaroo it's a + + + align:start position:0% +kangaroo this is a baby kangaroo it's a +newborn kangaroo and you and and you + + align:start position:0% +newborn kangaroo and you and and you + + + align:start position:0% +newborn kangaroo and you and and you +know what we're going to do we're going + + align:start position:0% +know what we're going to do we're going + + + align:start position:0% +know what we're going to do we're going +to take her and we're going to uh give + + align:start position:0% +to take her and we're going to uh give + + + align:start position:0% +to take her and we're going to uh give +her to the goats and she's going to get + + align:start position:0% +her to the goats and she's going to get + + + align:start position:0% +her to the goats and she's going to get +raised by the goats okay and now she's + + align:start position:0% +raised by the goats okay and now she's + + + align:start position:0% +raised by the goats okay and now she's +all grown up let me ask you a few + + align:start position:0% +all grown up let me ask you a few + + + align:start position:0% +all grown up let me ask you a few +questions about her does she have a + + align:start position:0% +questions about her does she have a + + + align:start position:0% +questions about her does she have a +pouch well yeah sure that that that's + + align:start position:0% +pouch well yeah sure that that that's + + + align:start position:0% +pouch well yeah sure that that that's +that's pretty straightforward that's not + + align:start position:0% +that's pretty straightforward that's not + + + align:start position:0% +that's pretty straightforward that's not +the interesting question the interesting + + align:start position:0% +the interesting question the interesting + + + align:start position:0% +the interesting question the interesting +question is is she going to be a hopper + + align:start position:0% +question is is she going to be a hopper + + + align:start position:0% +question is is she going to be a hopper +or a + + align:start position:0% +or a + + + align:start position:0% +or a +climber and little kids two three + + align:start position:0% +climber and little kids two three + + + align:start position:0% +climber and little kids two three +three-year-old kids will say this going + + align:start position:0% +three-year-old kids will say this going + + + align:start position:0% +three-year-old kids will say this going +to be a climber + + align:start position:0% +to be a climber + + + align:start position:0% +to be a climber +it's going to be a hopper so I got to + + align:start position:0% +it's going to be a hopper so I got to + + + align:start position:0% +it's going to be a hopper so I got to +get it right here otherwise you get be + + align:start position:0% +get it right here otherwise you get be + + + align:start position:0% +get it right here otherwise you get be +helplessly it's going to be a hopper it + + align:start position:0% +helplessly it's going to be a hopper it + + + align:start position:0% +helplessly it's going to be a hopper it +was a kangaroo at Birth kangaroos hop + + align:start position:0% +was a kangaroo at Birth kangaroos hop + + + align:start position:0% +was a kangaroo at Birth kangaroos hop +it's part of their Essence the fact that + + align:start position:0% +it's part of their Essence the fact that + + + align:start position:0% +it's part of their Essence the fact that +she lived with the um uh the goats isn't + + align:start position:0% +she lived with the um uh the goats isn't + + + align:start position:0% +she lived with the um uh the goats isn't +going to change that this is this is + + align:start position:0% +going to change that this is this is + + + align:start position:0% +going to change that this is this is +this is the amusement value of of the + + align:start position:0% +this is the amusement value of of the + + + align:start position:0% +this is the amusement value of of the +the the um Disney Tarzan uh Cartoon + + align:start position:0% +the the um Disney Tarzan uh Cartoon + + + align:start position:0% +the the um Disney Tarzan uh Cartoon +right Tarzan gets raised by a gorilla by + + align:start position:0% +right Tarzan gets raised by a gorilla by + + + align:start position:0% +right Tarzan gets raised by a gorilla by +the gorillas he think how many you seen + + align:start position:0% +the gorillas he think how many you seen + + + align:start position:0% +the gorillas he think how many you seen +that oh man when did that come out it + + align:start position:0% +that oh man when did that come out it + + + align:start position:0% +that oh man when did that come out it +must have + + align:start position:0% +must have + + + align:start position:0% +must have +come I guess said all right I got to I + + align:start position:0% +come I guess said all right I got to I + + + align:start position:0% +come I guess said all right I got to I +got to calibrate my Disney here what + + align:start position:0% +got to calibrate my Disney here what + + + align:start position:0% +got to calibrate my Disney here what +which Disney movies came out when you + + align:start position:0% +which Disney movies came out when you + + + align:start position:0% +which Disney movies came out when you +were of an age to watch + + align:start position:0% +were of an age to watch + + + align:start position:0% +were of an age to watch +them Aladdin oh you were too old when + + align:start position:0% +them Aladdin oh you were too old when + + + align:start position:0% +them Aladdin oh you were too old when +when when Tarzan came + + align:start position:0% +when when Tarzan came + + + align:start position:0% +when when Tarzan came +out oh say you're you're you're the + + align:start position:0% +out oh say you're you're you're the + + + align:start position:0% +out oh say you're you're you're the +you're you're the Aladdin + + align:start position:0% +you're you're the Aladdin + + + align:start position:0% +you're you're the Aladdin +cohort Jungle Book jungle jungle book + + align:start position:0% +cohort Jungle Book jungle jungle book + + + align:start position:0% +cohort Jungle Book jungle jungle book +came out when I was kid not well no not + + align:start position:0% +came out when I was kid not well no not + + + align:start position:0% +came out when I was kid not well no not +twice actually Jungle Book is a the the + + align:start position:0% +twice actually Jungle Book is a the the + + + align:start position:0% +twice actually Jungle Book is a the the +the the one the one that it was the ones + + align:start position:0% +the the one the one that it was the ones + + + align:start position:0% +the the one the one that it was the ones +that came out when I was a kid with + + align:start position:0% +that came out when I was a kid with + + + align:start position:0% +that came out when I was a kid with +things like Sword and the stone I + + align:start position:0% +things like Sword and the stone I + + + align:start position:0% +things like Sword and the stone I +thought that was great that was that was + + align:start position:0% +thought that was great that was that was + + + align:start position:0% +thought that was great that was that was +good stuff and don't claim that I was a + + align:start position:0% +good stuff and don't claim that I was a + + + align:start position:0% +good stuff and don't claim that I was a +kid when Snow White came out that was my + + align:start position:0% +kid when Snow White came out that was my + + + align:start position:0% +kid when Snow White came out that was my +father um but anyway um so in in Jungle + + align:start position:0% +father um but anyway um so in in Jungle + + + align:start position:0% +father um but anyway um so in in Jungle +Book The Jungle Book in in well Jungle + + align:start position:0% +Book The Jungle Book in in well Jungle + + + align:start position:0% +Book The Jungle Book in in well Jungle +Book works right J Jung Jungle Book + + align:start position:0% +Book works right J Jung Jungle Book + + + align:start position:0% +Book works right J Jung Jungle Book +works but Tarzan works get raised by the + + align:start position:0% +works but Tarzan works get raised by the + + + align:start position:0% +works but Tarzan works get raised by the +wild animals but you're essentially a + + align:start position:0% +wild animals but you're essentially a + + + align:start position:0% +wild animals but you're essentially a +human and that eventually um eventually + + align:start position:0% +human and that eventually um eventually + + + align:start position:0% +human and that eventually um eventually +catches um up with you actually kids are + + align:start position:0% +catches um up with you actually kids are + + + align:start position:0% +catches um up with you actually kids are +more are incorrect + + align:start position:0% +more are incorrect + + + align:start position:0% +more are incorrect +nativists um because they believe things + + align:start position:0% +nativists um because they believe things + + + align:start position:0% +nativists um because they believe things +that turn out it's true that the + + align:start position:0% +that turn out it's true that the + + + align:start position:0% +that turn out it's true that the +kangaroo will probably hop even if it + + align:start position:0% +kangaroo will probably hop even if it + + + align:start position:0% +kangaroo will probably hop even if it +gets uh uh raised by a uh a goat um but + + align:start position:0% +gets uh uh raised by a uh a goat um but + + + align:start position:0% +gets uh uh raised by a uh a goat um but +suppose you are suppose we have here a a + + align:start position:0% +suppose you are suppose we have here a a + + + align:start position:0% +suppose you are suppose we have here a a +Chinese baby and we take this Chinese + + align:start position:0% +Chinese baby and we take this Chinese + + + align:start position:0% +Chinese baby and we take this Chinese +baby and we bring it uh to the United + + align:start position:0% +baby and we bring it uh to the United + + + align:start position:0% +baby and we bring it uh to the United +States and it's raised um in in + + align:start position:0% +States and it's raised um in in + + + align:start position:0% +States and it's raised um in in +California will that uh when that kid + + align:start position:0% +California will that uh when that kid + + + align:start position:0% +California will that uh when that kid +grows up will she be able to speak + + align:start position:0% +grows up will she be able to speak + + + align:start position:0% +grows up will she be able to speak +Chinese depends depends on the what is + + align:start position:0% +Chinese depends depends on the what is + + + align:start position:0% +Chinese depends depends on the what is +it's in California in California yes it + + align:start position:0% +it's in California in California yes it + + + align:start position:0% +it's in California in California yes it +depends on the neighborhood um + + align:start position:0% +depends on the neighborhood um + + + align:start position:0% +depends on the neighborhood um +but I I kids aren't kids aren't quite + + align:start position:0% +but I I kids aren't kids aren't quite + + + align:start position:0% +but I I kids aren't kids aren't quite +clear on these demographic issues to the + + align:start position:0% +clear on these demographic issues to the + + + align:start position:0% +clear on these demographic issues to the +same way but a little kid will figure um + + align:start position:0% +same way but a little kid will figure um + + + align:start position:0% +same way but a little kid will figure um +incorrectly that that language is one of + + align:start position:0% +incorrectly that that language is one of + + + align:start position:0% +incorrectly that that language is one of +these essential properties that if + + align:start position:0% +these essential properties that if + + + align:start position:0% +these essential properties that if +you're Chinese that means you can speak + + align:start position:0% +you're Chinese that means you can speak + + + align:start position:0% +you're Chinese that means you can speak +CH you might be able to speak English + + align:start position:0% +CH you might be able to speak English + + + align:start position:0% +CH you might be able to speak English +too you could learn that they can figure + + align:start position:0% +too you could learn that they can figure + + + align:start position:0% +too you could learn that they can figure +that out but that you'd be you you You' + + align:start position:0% +that out but that you'd be you you You' + + + align:start position:0% +that out but that you'd be you you You' +you'd have a a privileged ability to + + align:start position:0% +you'd have a a privileged ability to + + + align:start position:0% +you'd have a a privileged ability to +speak Chinese because after all you were + + align:start position:0% +speak Chinese because after all you were + + + align:start position:0% +speak Chinese because after all you were +a Chinese kid um and and and that that + + align:start position:0% +a Chinese kid um and and and that that + + + align:start position:0% +a Chinese kid um and and and that that +ought to work um if you're a Chinese kid + + align:start position:0% +ought to work um if you're a Chinese kid + + + align:start position:0% +ought to work um if you're a Chinese kid +who grew up in an Anglo uh linguistic + + align:start position:0% +who grew up in an Anglo uh linguistic + + + align:start position:0% +who grew up in an Anglo uh linguistic +environment you may have discovered that + + align:start position:0% +environment you may have discovered that + + + align:start position:0% +environment you may have discovered that +there were plenty of your relatives who + + align:start position:0% +there were plenty of your relatives who + + + align:start position:0% +there were plenty of your relatives who +also thought you should be able to speak + + align:start position:0% +also thought you should be able to speak + + + align:start position:0% +also thought you should be able to speak +Chinese um but that's a different issue + + align:start position:0% +Chinese um but that's a different issue + + + align:start position:0% +Chinese um but that's a different issue +um in any case little kids + + align:start position:0% +um in any case little kids + + + align:start position:0% +um in any case little kids +start certainly with a notion of + + align:start position:0% +start certainly with a notion of + + + align:start position:0% +start certainly with a notion of +objectness and um and probably quite + + align:start position:0% +objectness and um and probably quite + + + align:start position:0% +objectness and um and probably quite +early with a notion that objects have + + align:start position:0% +early with a notion that objects have + + + align:start position:0% +early with a notion that objects have +Essences and then they build on that in + + align:start position:0% +Essences and then they build on that in + + + align:start position:0% +Essences and then they build on that in +this little scientist kind of a way um + + align:start position:0% +this little scientist kind of a way um + + + align:start position:0% +this little scientist kind of a way um +to uh to get closer and closer to what + + align:start position:0% +to uh to get closer and closer to what + + + align:start position:0% +to uh to get closer and closer to what +we consider to be the adult concept of + + align:start position:0% +we consider to be the adult concept of + + + align:start position:0% +we consider to be the adult concept of +whatever alive or um kangaroo or any of + + align:start position:0% +whatever alive or um kangaroo or any of + + + align:start position:0% +whatever alive or um kangaroo or any of +those um any of those sorts of things um + + align:start position:0% +those um any of those sorts of things um + + + align:start position:0% +those um any of those sorts of things um +that here's a case where the adult state + + align:start position:0% +that here's a case where the adult state + + + align:start position:0% +that here's a case where the adult state +is not not particularly fixed um but + + align:start position:0% +is not not particularly fixed um but + + + align:start position:0% +is not not particularly fixed um but +where nevertheless uh what what you're + + align:start position:0% +where nevertheless uh what what you're + + + align:start position:0% +where nevertheless uh what what you're +doing is you're elaborating on juvenile + + align:start position:0% +doing is you're elaborating on juvenile + + + align:start position:0% +doing is you're elaborating on juvenile +Concepts not suddenly discovering the + + align:start position:0% +Concepts not suddenly discovering the + + + align:start position:0% +Concepts not suddenly discovering the +notion that there is such a thing as as + + align:start position:0% +notion that there is such a thing as as + + + align:start position:0% +notion that there is such a thing as as +a concept okay I I want to do + + align:start position:0% +a concept okay I I want to do + + + align:start position:0% +a concept okay I I want to do +egocentrism still but uh I will start + + align:start position:0% +egocentrism still but uh I will start + + + align:start position:0% +egocentrism still but uh I will start +doing that when that thing says + + align:start position:0% +doing that when that thing says + + + align:start position:0% +doing that when that thing says +310 If You Can + + align:start position:0% + + + + align:start position:0% + +Count what happens if you ask a kid he's + + align:start position:0% +Count what happens if you ask a kid he's + + + align:start position:0% +Count what happens if you ask a kid he's +alive oh yeah it'll say it's alive what + + align:start position:0% +alive oh yeah it'll say it's alive what + + + align:start position:0% +alive oh yeah it'll say it's alive what +F here you + + align:start position:0% + + + + align:start position:0% + +go he can breathe he can you know he can + + align:start position:0% +go he can breathe he can you know he can + + + align:start position:0% +go he can breathe he can you know he can +do he can do the things that he thinks + + align:start position:0% +do he can do the things that he thinks + + + align:start position:0% +do he can do the things that he thinks +alive might mean oh I got to draw + + align:start position:0% +alive might mean oh I got to draw + + + align:start position:0% +alive might mean oh I got to draw +another picture + + align:start position:0% +another picture + + + align:start position:0% +another picture +[Applause] + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah the um a little experiment was a + + align:start position:0% +yeah the um a little experiment was a + + + align:start position:0% +yeah the um a little experiment was a +wind the car a winded or whatever with + + align:start position:0% +wind the car a winded or whatever with + + + align:start position:0% +wind the car a winded or whatever with +the the Box + + align:start position:0% +the the Box + + + align:start position:0% +the the Box +the a question now could you are kids + + align:start position:0% +the a question now could you are kids + + + align:start position:0% +the a question now could you are kids +also capable of multiplication seems + + align:start position:0% +also capable of multiplication seems + + + align:start position:0% +also capable of multiplication seems +like you can use probably the same + + align:start position:0% +like you can use probably the same + + + align:start position:0% +like you can use probably the same +experiment and change it by a little bit + + align:start position:0% +experiment and change it by a little bit + + + align:start position:0% +experiment and change it by a little bit +for instance the Box could change color + + align:start position:0% +for instance the Box could change color + + + align:start position:0% +for instance the Box could change color +and you could have like more objects + + align:start position:0% +and you could have like more objects + + + align:start position:0% +and you could have like more objects +or exponents I guess yeah that that that + + align:start position:0% +or exponents I guess yeah that that that + + + align:start position:0% +or exponents I guess yeah that that that +sounds more symbolic than kids the color + + align:start position:0% +sounds more symbolic than kids the color + + + align:start position:0% +sounds more symbolic than kids the color +change to indicate that this is what's + + align:start position:0% +change to indicate that this is what's + + + align:start position:0% +change to indicate that this is what's +happening it sounds too symbolic um I + + align:start position:0% +happening it sounds too symbolic um I + + + align:start position:0% +happening it sounds too symbolic um I +don't know if any anybody's tried to + + align:start position:0% +don't know if any anybody's tried to + + + align:start position:0% +don't know if any anybody's tried to +find uh multiplication evidence in + + align:start position:0% +find uh multiplication evidence in + + + align:start position:0% +find uh multiplication evidence in +kids oh maybe what you could do wait + + align:start position:0% +kids oh maybe what you could do wait + + + align:start position:0% +kids oh maybe what you could do wait +wait wait the Box tumble the Box no no + + align:start position:0% +wait wait the Box tumble the Box no no + + + align:start position:0% +wait wait the Box tumble the Box no no +no no I I think somebody has done + + align:start position:0% +no no I I think somebody has done + + + align:start position:0% +no no I I think somebody has done +something like you've got a box you put + + align:start position:0% +something like you've got a box you put + + + align:start position:0% +something like you've got a box you put +two thingies in it now you move in an + + align:start position:0% +two thingies in it now you move in an + + + align:start position:0% +two thingies in it now you move in an +identical box next to it what would you + + align:start position:0% +identical box next to it what would you + + + align:start position:0% +identical box next to it what would you +expect to see you know presumably 2 * 2 + + align:start position:0% +expect to see you know presumably 2 * 2 + + + align:start position:0% +expect to see you know presumably 2 * 2 +is 4 or 2 plus 2 is anyway I think + + align:start position:0% +is 4 or 2 plus 2 is anyway I think + + + align:start position:0% +is 4 or 2 plus 2 is anyway I think +somebody's tried that I don't remember + + align:start position:0% +somebody's tried that I don't remember + + + align:start position:0% +somebody's tried that I don't remember +if it works but what about like it seems + + align:start position:0% +if it works but what about like it seems + + + align:start position:0% +if it works but what about like it seems +like with the with the first experiment + + align:start position:0% +like with the with the first experiment + + + align:start position:0% +like with the with the first experiment +did the kids actually take a little bit + + align:start position:0% +did the kids actually take a little bit + + + align:start position:0% +did the kids actually take a little bit +to learn that what was going on in the + + align:start position:0% +to learn that what was going on in the + + + align:start position:0% +to learn that what was going on in the +Box didn't affect the number of um + + align:start position:0% +Box didn't affect the number of um + + + align:start position:0% +Box didn't affect the number of um +things inside or what or like if you did + + align:start position:0% +things inside or what or like if you did + + + align:start position:0% +things inside or what or like if you did +the suppose you put the box down and + + align:start position:0% +the suppose you put the box down and + + + align:start position:0% +the suppose you put the box down and +took it away and there was only one + + align:start position:0% +took it away and there was only one + + + align:start position:0% +took it away and there was only one +thing there at the for the first trial + + align:start position:0% +thing there at the for the first trial + + + align:start position:0% +thing there at the for the first trial +would the kid be surprised even at the + + align:start position:0% +would the kid be surprised even at the + + + align:start position:0% +would the kid be surprised even at the +very first trial I think the answer is + + align:start position:0% +very first trial I think the answer is + + + align:start position:0% +very first trial I think the answer is +yes but I'm not quite sure of that I + + align:start position:0% +yes but I'm not quite sure of that I + + + align:start position:0% +yes but I'm not quite sure of that I +would if if it wasn't then I'm just + + align:start position:0% +would if if it wasn't then I'm just + + + align:start position:0% +would if if it wasn't then I'm just +thinking that it implies to kid add to + + align:start position:0% +thinking that it implies to kid add to + + + align:start position:0% +thinking that it implies to kid add to +Lear a little bit no I I think I think I + + align:start position:0% +Lear a little bit no I I think I think I + + + align:start position:0% +Lear a little bit no I I think I think I +think the evidence I think the evidence + + align:start position:0% +think the evidence I think the evidence + + + align:start position:0% +think the evidence I think the evidence +is that it's there to start okay but I'd + + align:start position:0% +is that it's there to start okay but I'd + + + align:start position:0% +is that it's there to start okay but I'd +have to I'd actually have to look that + + align:start position:0% +have to I'd actually have to look that + + + align:start position:0% +have to I'd actually have to look that +up okay whoops I'm a minute later than I + + align:start position:0% +up okay whoops I'm a minute later than I + + + align:start position:0% +up okay whoops I'm a minute later than I +claimed I would be oh well um let us + + align:start position:0% +claimed I would be oh well um let us + + + align:start position:0% +claimed I would be oh well um let us +talk about egocentrism so you will + + align:start position:0% +talk about egocentrism so you will + + + align:start position:0% +talk about egocentrism so you will +recall that the basic problem here um + + align:start position:0% +recall that the basic problem here um + + + align:start position:0% +recall that the basic problem here um +was that the kid seemed unable to take + + align:start position:0% +was that the kid seemed unable to take + + + align:start position:0% +was that the kid seemed unable to take +the point of view of another in this + + align:start position:0% +the point of view of another in this + + + align:start position:0% +the point of view of another in this +case the mother on the other side of + + align:start position:0% +case the mother on the other side of + + + align:start position:0% +case the mother on the other side of +this table you know the kid a asked + + align:start position:0% +this table you know the kid a asked + + + align:start position:0% +this table you know the kid a asked +about things like the river and and and + + align:start position:0% +about things like the river and and and + + + align:start position:0% +about things like the river and and and +and the Hut um claimed that the mom + + align:start position:0% +and the Hut um claimed that the mom + + + align:start position:0% +and the Hut um claimed that the mom +could see them even though mom couldn't + + align:start position:0% +could see them even though mom couldn't + + + align:start position:0% +could see them even though mom couldn't +see them only the kid could see them + + align:start position:0% +see them only the kid could see them + + + align:start position:0% +see them only the kid could see them +um you can get kids to perform quite + + align:start position:0% +um you can get kids to perform quite + + + align:start position:0% +um you can get kids to perform quite +well on this task if you come from like + + align:start position:0% +well on this task if you come from like + + + align:start position:0% +well on this task if you come from like +Nebraska instead of coming from the Alp + + align:start position:0% +Nebraska instead of coming from the Alp + + + align:start position:0% +Nebraska instead of coming from the Alp +so in one version of this + + align:start position:0% +so in one version of this + + + align:start position:0% +so in one version of this +experiment um so for your how how does + + align:start position:0% +experiment um so for your how how does + + + align:start position:0% +experiment um so for your how how does +this so I think the answer is that + + align:start position:0% +this so I think the answer is that + + + align:start position:0% +this so I think the answer is that +four-year-olds fail this you can get + + align:start position:0% +four-year-olds fail this you can get + + + align:start position:0% +four-year-olds fail this you can get +three-year-olds to be successful in a in + + align:start position:0% +three-year-olds to be successful in a in + + + align:start position:0% +three-year-olds to be successful in a in +an equivalent task if what you do is um + + align:start position:0% +an equivalent task if what you do is um + + + align:start position:0% +an equivalent task if what you do is um +just simplify the situation so there's a + + align:start position:0% +just simplify the situation so there's a + + + align:start position:0% +just simplify the situation so there's a +version of this that may have a picture + + align:start position:0% +version of this that may have a picture + + + align:start position:0% +version of this that may have a picture +in the book still I don't remember of of + + align:start position:0% +in the book still I don't remember of of + + + align:start position:0% +in the book still I don't remember of of +a sort of a city block with a car in it + + align:start position:0% +a sort of a city block with a car in it + + + align:start position:0% +a sort of a city block with a car in it +um and a Sesame Street character and you + + align:start position:0% +um and a Sesame Street character and you + + + align:start position:0% +um and a Sesame Street character and you +drive like Drive Grover around the block + + align:start position:0% +drive like Drive Grover around the block + + + align:start position:0% +drive like Drive Grover around the block +or something and ask questions about + + align:start position:0% +or something and ask questions about + + + align:start position:0% +or something and ask questions about +that much simpler situation and then the + + align:start position:0% +that much simpler situation and then the + + + align:start position:0% +that much simpler situation and then the +kid can um successfully answer questions + + align:start position:0% +kid can um successfully answer questions + + + align:start position:0% +kid can um successfully answer questions +from the vantage point of of the mother + + align:start position:0% +from the vantage point of of the mother + + + align:start position:0% +from the vantage point of of the mother +as if part of the issue here was that + + align:start position:0% +as if part of the issue here was that + + + align:start position:0% +as if part of the issue here was that +the task was just too uh too complicated + + align:start position:0% +the task was just too uh too complicated + + + align:start position:0% +the task was just too uh too complicated +oh I never mentioned the M&Ms are under + + align:start position:0% +oh I never mentioned the M&Ms are under + + + align:start position:0% +oh I never mentioned the M&Ms are under +there somewhere I never mentioned well + + align:start position:0% +there somewhere I never mentioned well + + + align:start position:0% +there somewhere I never mentioned well +why is it that the kids bomb the &m task + + align:start position:0% +why is it that the kids bomb the &m task + + + align:start position:0% +why is it that the kids bomb the &m task +that seems to be the case + + align:start position:0% +that seems to be the case + + + align:start position:0% +that seems to be the case +an an issue where um you're asking kids + + align:start position:0% +an an issue where um you're asking kids + + + align:start position:0% +an an issue where um you're asking kids +who haven't gotten to the counting + + align:start position:0% +who haven't gotten to the counting + + + align:start position:0% +who haven't gotten to the counting +successful counting stage to do this and + + align:start position:0% +successful counting stage to do this and + + + align:start position:0% +successful counting stage to do this and +they can't do it either with the + + align:start position:0% +they can't do it either with the + + + align:start position:0% +they can't do it either with the +numerosity or the subitizing piece so + + align:start position:0% +numerosity or the subitizing piece so + + + align:start position:0% +numerosity or the subitizing piece so +they fail the task if you make the + + align:start position:0% +they fail the task if you make the + + + align:start position:0% +they fail the task if you make the +Eminem task um if you put that into + + align:start position:0% +Eminem task um if you put that into + + + align:start position:0% +Eminem task um if you put that into +either the numerosity range or the + + align:start position:0% +either the numerosity range or the + + + align:start position:0% +either the numerosity range or the +subitizing range little kids will + + align:start position:0% +subitizing range little kids will + + + align:start position:0% +subitizing range little kids will +succeed in doing the task so if you say + + align:start position:0% +succeed in doing the task so if you say + + + align:start position:0% +succeed in doing the task so if you say +would you rather have this pile with two + + align:start position:0% +would you rather have this pile with two + + + align:start position:0% +would you rather have this pile with two +M&M's or three M&M's you little kids + + align:start position:0% +M&M's or three M&M's you little kids + + + align:start position:0% +M&M's or three M&M's you little kids +don't bomb that they bom you know 5 + + align:start position:0% +don't bomb that they bom you know 5 + + + align:start position:0% +don't bomb that they bom you know 5 +versus 6 or 6 versus 8 things like that + + align:start position:0% +versus 6 or 6 versus 8 things like that + + + align:start position:0% +versus 6 or 6 versus 8 things like that +um and a similar sort of thing seems to + + align:start position:0% +um and a similar sort of thing seems to + + + align:start position:0% +um and a similar sort of thing seems to +be going on here that the task um is in + + align:start position:0% +be going on here that the task um is in + + + align:start position:0% +be going on here that the task um is in +some fashion uh a little too complicated + + align:start position:0% +some fashion uh a little too complicated + + + align:start position:0% +some fashion uh a little too complicated +for them how far can we push this back + + align:start position:0% +for them how far can we push this back + + + align:start position:0% +for them how far can we push this back +well if you take + + align:start position:0% +well if you take + + + align:start position:0% +well if you take +two-year-olds suppose you take twoyear + + align:start position:0% +two-year-olds suppose you take twoyear + + + align:start position:0% +two-year-olds suppose you take twoyear +olds and you give them a pair of + + align:start position:0% +olds and you give them a pair of + + + align:start position:0% +olds and you give them a pair of +sunglasses put the sunglasses on the kid + + align:start position:0% +sunglasses put the sunglasses on the kid + + + align:start position:0% +sunglasses put the sunglasses on the kid +kid looks around for a while now we take + + align:start position:0% +kid looks around for a while now we take + + + align:start position:0% +kid looks around for a while now we take +the sunglasses they may have been + + align:start position:0% +the sunglasses they may have been + + + align:start position:0% +the sunglasses they may have been +mirrored Shades even and anyway put the + + align:start position:0% +mirrored Shades even and anyway put the + + + align:start position:0% +mirrored Shades even and anyway put the +glasses on Mommy and you ask can Mommy + + align:start position:0% +glasses on Mommy and you ask can Mommy + + + align:start position:0% +glasses on Mommy and you ask can Mommy +see you well you can't see mommy's eyes + + align:start position:0% +see you well you can't see mommy's eyes + + + align:start position:0% +see you well you can't see mommy's eyes +anymore because of the glasses but the + + align:start position:0% +anymore because of the glasses but the + + + align:start position:0% +anymore because of the glasses but the +kid even a 2-year-old will be able to + + align:start position:0% +kid even a 2-year-old will be able to + + + align:start position:0% +kid even a 2-year-old will be able to +say yes indeed Mommy can see me even + + align:start position:0% +say yes indeed Mommy can see me even + + + align:start position:0% +say yes indeed Mommy can see me even +though I cannot see mommy's eyes + + align:start position:0% +though I cannot see mommy's eyes + + + align:start position:0% +though I cannot see mommy's eyes +normally if mommy is doing this it's a + + align:start position:0% +normally if mommy is doing this it's a + + + align:start position:0% +normally if mommy is doing this it's a +pretty good bet that um Mommy can't see + + align:start position:0% +pretty good bet that um Mommy can't see + + + align:start position:0% +pretty good bet that um Mommy can't see +you and that's the root of a lot of you + + align:start position:0% +you and that's the root of a lot of you + + + align:start position:0% +you and that's the root of a lot of you +know entertaining games um + + align:start position:0% +know entertaining games um + + + align:start position:0% +know entertaining games um +but they can manage to solve the problem + + align:start position:0% +but they can manage to solve the problem + + + align:start position:0% +but they can manage to solve the problem +at the uh uh at the if it's you know if + + align:start position:0% +at the uh uh at the if it's you know if + + + align:start position:0% +at the uh uh at the if it's you know if +it's simplified to the point of + + align:start position:0% +it's simplified to the point of + + + align:start position:0% +it's simplified to the point of +sunglasses on + + align:start position:0% +sunglasses on + + + align:start position:0% +sunglasses on +or uh or off and and you know this if I + + align:start position:0% +or uh or off and and you know this if I + + + align:start position:0% +or uh or off and and you know this if I +can see you can you see me thing um you + + align:start position:0% +can see you can you see me thing um you + + + align:start position:0% +can see you can you see me thing um you +can see as you get more and more + + align:start position:0% +can see as you get more and more + + + align:start position:0% +can see as you get more and more +complicated that uh that that it takes + + align:start position:0% +complicated that uh that that it takes + + + align:start position:0% +complicated that uh that that it takes +you longer and longer to solve the more + + align:start position:0% +you longer and longer to solve the more + + + align:start position:0% +you longer and longer to solve the more +and more complicated versions of it you + + align:start position:0% +and more complicated versions of it you + + + align:start position:0% +and more complicated versions of it you +may you don't remember what it was like + + align:start position:0% +may you don't remember what it was like + + + align:start position:0% +may you don't remember what it was like +to be thinking when you were a + + align:start position:0% +to be thinking when you were a + + + align:start position:0% +to be thinking when you were a +2-year-old but you may remember a stage + + align:start position:0% +2-year-old but you may remember a stage + + + align:start position:0% +2-year-old but you may remember a stage +later in your life when it was not clear + + align:start position:0% +later in your life when it was not clear + + + align:start position:0% +later in your life when it was not clear +to you um how mirrors worked that that + + align:start position:0% +to you um how mirrors worked that that + + + align:start position:0% +to you um how mirrors worked that that +that Mir that you know if a can see b b + + align:start position:0% +that Mir that you know if a can see b b + + + align:start position:0% +that Mir that you know if a can see b b +can see a in a mirror this is the sort + + align:start position:0% +can see a in a mirror this is the sort + + + align:start position:0% +can see a in a mirror this is the sort +of thing that that amuses sort of early + + align:start position:0% +of thing that that amuses sort of early + + + align:start position:0% +of thing that that amuses sort of early +school age kids often you can see around + + align:start position:0% +school age kids often you can see around + + + align:start position:0% +school age kids often you can see around +the corner I can see Dad around the + + align:start position:0% +the corner I can see Dad around the + + + align:start position:0% +the corner I can see Dad around the +corner there I bet he can't see me and + + align:start position:0% +corner there I bet he can't see me and + + + align:start position:0% +corner there I bet he can't see me and +it comes as a shock that Dad can see you + + align:start position:0% +it comes as a shock that Dad can see you + + + align:start position:0% +it comes as a shock that Dad can see you +cuz the mirror kind of works both ways + + align:start position:0% +cuz the mirror kind of works both ways + + + align:start position:0% +cuz the mirror kind of works both ways +and then there are more complicated + + align:start position:0% +and then there are more complicated + + + align:start position:0% +and then there are more complicated +arrangements with you know key holes and + + align:start position:0% +arrangements with you know key holes and + + + align:start position:0% +arrangements with you know key holes and +stuff like that where um it takes even + + align:start position:0% +stuff like that where um it takes even + + + align:start position:0% +stuff like that where um it takes even +longer to be able to take the point of + + align:start position:0% +longer to be able to take the point of + + + align:start position:0% +longer to be able to take the point of +view of the person on the other side so + + align:start position:0% +view of the person on the other side so + + + align:start position:0% +view of the person on the other side so +some examp some aspect of this is simply + + align:start position:0% +some examp some aspect of this is simply + + + align:start position:0% +some examp some aspect of this is simply +a matter of of um complexity in fact um + + align:start position:0% +a matter of of um complexity in fact um + + + align:start position:0% +a matter of of um complexity in fact um +Paul Bloom and his student actually I + + align:start position:0% +Paul Bloom and his student actually I + + + align:start position:0% +Paul Bloom and his student actually I +should mention Paul Bloom is married to + + align:start position:0% +should mention Paul Bloom is married to + + + align:start position:0% +should mention Paul Bloom is married to +Karen win they were both students both + + align:start position:0% +Karen win they were both students both + + + align:start position:0% +Karen win they were both students both +both paas for this course and are now + + align:start position:0% +both paas for this course and are now + + + align:start position:0% +both paas for this course and are now +both professors at Yale anyway Paul + + align:start position:0% +both professors at Yale anyway Paul + + + align:start position:0% +both professors at Yale anyway Paul +works on similar sorts of problems and + + align:start position:0% +works on similar sorts of problems and + + + align:start position:0% +works on similar sorts of problems and +talks about the curse of + + align:start position:0% +talks about the curse of + + + align:start position:0% +talks about the curse of +knowledge um that shows up in adult + + align:start position:0% +knowledge um that shows up in adult + + + align:start position:0% +knowledge um that shows up in adult +Behavior too that is very difficult it's + + align:start position:0% +Behavior too that is very difficult it's + + + align:start position:0% +Behavior too that is very difficult it's +often very difficult to remember that + + align:start position:0% +often very difficult to remember that + + + align:start position:0% +often very difficult to remember that +somebody else doesn't know what you know + + align:start position:0% +somebody else doesn't know what you know + + + align:start position:0% +somebody else doesn't know what you know +and so um it's a problem for uh for me + + align:start position:0% +and so um it's a problem for uh for me + + + align:start position:0% +and so um it's a problem for uh for me +teaching it's the the things that are + + align:start position:0% +teaching it's the the things that are + + + align:start position:0% +teaching it's the the things that are +hardest to teach are the things that I + + align:start position:0% +hardest to teach are the things that I + + + align:start position:0% +hardest to teach are the things that I +don't know anything about that's not + + align:start position:0% +don't know anything about that's not + + + align:start position:0% +don't know anything about that's not +surprising the second hardest category + + align:start position:0% +surprising the second hardest category + + + align:start position:0% +surprising the second hardest category +are things that I know too much about + + align:start position:0% +are things that I know too much about + + + align:start position:0% +are things that I know too much about +because it's hard to + + align:start position:0% +because it's hard to + + + align:start position:0% +because it's hard to +remember um how little you know about + + align:start position:0% +remember um how little you know about + + + align:start position:0% +remember um how little you know about +Vision how can it be that you haven't + + align:start position:0% +Vision how can it be that you haven't + + + align:start position:0% +Vision how can it be that you haven't +actually spent the last 18 years of your + + align:start position:0% +actually spent the last 18 years of your + + + align:start position:0% +actually spent the last 18 years of your +life bathed in visual phenomenology I + + align:start position:0% +life bathed in visual phenomenology I + + + align:start position:0% +life bathed in visual phenomenology I +forget that from time you can try using + + align:start position:0% +forget that from time you can try using + + + align:start position:0% +forget that from time you can try using +that as an excuse on the exam but forget + + align:start position:0% +that as an excuse on the exam but forget + + + align:start position:0% +that as an excuse on the exam but forget +it we'll still take the points off so + + align:start position:0% +it we'll still take the points off so + + + align:start position:0% +it we'll still take the points off so +that that that turns out to be um an + + align:start position:0% +that that that turns out to be um an + + + align:start position:0% +that that that turns out to be um an +example of the curse of knowledge or + + align:start position:0% +example of the curse of knowledge or + + + align:start position:0% +example of the curse of knowledge or +another example um would be uh if if + + align:start position:0% +another example um would be uh if if + + + align:start position:0% +another example um would be uh if if +you've ever been giving somebody + + align:start position:0% +you've ever been giving somebody + + + align:start position:0% +you've ever been giving somebody +directions while you're sitting next to + + align:start position:0% +directions while you're sitting next to + + + align:start position:0% +directions while you're sitting next to +them in the car you might discover that + + align:start position:0% +them in the car you might discover that + + + align:start position:0% +them in the car you might discover that +you go past the street where they were + + align:start position:0% +you go past the street where they were + + + align:start position:0% +you go past the street where they were +supposed to turn because you knew you + + align:start position:0% +supposed to turn because you knew you + + + align:start position:0% +supposed to turn because you knew you +were supposed to turn there um and you + + align:start position:0% +were supposed to turn there um and you + + + align:start position:0% +were supposed to turn there um and you +just kind of forgot that they wouldn't + + align:start position:0% +just kind of forgot that they wouldn't + + + align:start position:0% +just kind of forgot that they wouldn't +know that and that's why you were + + align:start position:0% +know that and that's why you were + + + align:start position:0% +know that and that's why you were +sitting there supposedly giving them uh + + align:start position:0% +sitting there supposedly giving them uh + + + align:start position:0% +sitting there supposedly giving them uh +directions it's + + align:start position:0% +directions it's + + + align:start position:0% +directions it's +hard even for adults necessarily it's + + align:start position:0% +hard even for adults necessarily it's + + + align:start position:0% +hard even for adults necessarily it's +hard for adults sometimes to take the + + align:start position:0% +hard for adults sometimes to take the + + + align:start position:0% +hard for adults sometimes to take the +Vantage Point um of of another person um + + align:start position:0% +Vantage Point um of of another person um + + + align:start position:0% +Vantage Point um of of another person um +now one of the great examples of this + + align:start position:0% +now one of the great examples of this + + + align:start position:0% +now one of the great examples of this +um in in in kid Behavior a paradigm + + align:start position:0% +um in in in kid Behavior a paradigm + + + align:start position:0% +um in in in kid Behavior a paradigm +that's yielded an awful lot of of of + + align:start position:0% +that's yielded an awful lot of of of + + + align:start position:0% +that's yielded an awful lot of of of +research which gives you some insight + + align:start position:0% +research which gives you some insight + + + align:start position:0% +research which gives you some insight +into this um if you like this curse of + + align:start position:0% +into this um if you like this curse of + + + align:start position:0% +into this um if you like this curse of +knowledge problem is what's known as the + + align:start position:0% +knowledge problem is what's known as the + + + align:start position:0% +knowledge problem is what's known as the +false belief task um uh and well the + + align:start position:0% +false belief task um uh and well the + + + align:start position:0% +false belief task um uh and well the +first false belief you need is that this + + align:start position:0% +first false belief you need is that this + + + align:start position:0% +first false belief you need is that this +is Big Bird from Sesame Street um all + + align:start position:0% +is Big Bird from Sesame Street um all + + + align:start position:0% +is Big Bird from Sesame Street um all +right so here's here's how a typical + + align:start position:0% +right so here's here's how a typical + + + align:start position:0% +right so here's here's how a typical +here here's how a typical iCal uh false + + align:start position:0% +here here's how a typical iCal uh false + + + align:start position:0% +here here's how a typical iCal uh false +belief task experiment white might work + + align:start position:0% +belief task experiment white might work + + + align:start position:0% +belief task experiment white might work +Big Bird comes you're you're watching + + align:start position:0% +Big Bird comes you're you're watching + + + align:start position:0% +Big Bird comes you're you're watching +this big bird comes in to the scene and + + align:start position:0% +this big bird comes in to the scene and + + + align:start position:0% +this big bird comes in to the scene and +he has candy and he puts the candy in + + align:start position:0% +he has candy and he puts the candy in + + + align:start position:0% +he has candy and he puts the candy in +what is this I don't it's this the + + align:start position:0% +what is this I don't it's this the + + + align:start position:0% +what is this I don't it's this the +refrigerator he puts the candy in the + + align:start position:0% +refrigerator he puts the candy in the + + + align:start position:0% +refrigerator he puts the candy in the +refrigerator and he goes + + align:start position:0% +refrigerator and he goes + + + align:start position:0% +refrigerator and he goes +out okay um now I didn't + + align:start position:0% +out okay um now I didn't + + + align:start position:0% +out okay um now I didn't +draw uh I I didn't draw Grover or + + align:start position:0% +draw uh I I didn't draw Grover or + + + align:start position:0% +draw uh I I didn't draw Grover or +whatever but Grover + + align:start position:0% +whatever but Grover + + + align:start position:0% +whatever but Grover +comes + + align:start position:0% +comes + + + align:start position:0% +comes +in takes the candy out of the + + align:start position:0% +in takes the candy out of the + + + align:start position:0% +in takes the candy out of the +refrigerator and puts it in the + + align:start position:0% +refrigerator and puts it in the + + + align:start position:0% +refrigerator and puts it in the +drawer okay + + align:start position:0% +drawer okay + + + align:start position:0% +drawer okay +now Big Bird comes back in he didn't see + + align:start position:0% +now Big Bird comes back in he didn't see + + + align:start position:0% +now Big Bird comes back in he didn't see +this but you saw this big bird comes + + align:start position:0% +this but you saw this big bird comes + + + align:start position:0% +this but you saw this big bird comes +back in and uh you are asked where will + + align:start position:0% +back in and uh you are asked where will + + + align:start position:0% +back in and uh you are asked where will +Big Bird look for the + + align:start position:0% +Big Bird look for the + + + align:start position:0% +Big Bird look for the +candy and your answer if you're like a + + align:start position:0% +candy and your answer if you're like a + + + align:start position:0% +candy and your answer if you're like a +four-year-old is that big bird will look + + align:start position:0% +four-year-old is that big bird will look + + + align:start position:0% +four-year-old is that big bird will look +in the + + align:start position:0% +in the + + + align:start position:0% +in the +drawer you cannot somehow access the + + align:start position:0% +drawer you cannot somehow access the + + + align:start position:0% +drawer you cannot somehow access the +fact that big bird thinks you know in in + + align:start position:0% +fact that big bird thinks you know in in + + + align:start position:0% +fact that big bird thinks you know in in +in + + align:start position:0% +in + + + align:start position:0% +in +his + + align:start position:0% +his + + + align:start position:0% +his +brain that the + + align:start position:0% +brain that the + + + align:start position:0% +brain that the +um uh that the cand is in the fridge + + align:start position:0% +um uh that the cand is in the fridge + + + align:start position:0% +um uh that the cand is in the fridge +when you updated your knowledge about + + align:start position:0% +when you updated your knowledge about + + + align:start position:0% +when you updated your knowledge about +the + + align:start position:0% +the + + + align:start position:0% +the +candy you updated his knowledge um about + + align:start position:0% +candy you updated his knowledge um about + + + align:start position:0% +candy you updated his knowledge um about +the candy too in some fashion + + align:start position:0% +the candy too in some fashion + + + align:start position:0% +the candy too in some fashion +um now there are endless versions of of + + align:start position:0% +um now there are endless versions of of + + + align:start position:0% +um now there are endless versions of of +of this experience this this is a task + + align:start position:0% +of this experience this this is a task + + + align:start position:0% +of this experience this this is a task +that four year-olds will fail uh or and + + align:start position:0% +that four year-olds will fail uh or and + + + align:start position:0% +that four year-olds will fail uh or and +well younger than four will fail older + + align:start position:0% +well younger than four will fail older + + + align:start position:0% +well younger than four will fail older +than four roughly will will tend to uh + + align:start position:0% +than four roughly will will tend to uh + + + align:start position:0% +than four roughly will will tend to uh +to get um there are endless tasks that + + align:start position:0% +to get um there are endless tasks that + + + align:start position:0% +to get um there are endless tasks that +look at this and try to break it apart + + align:start position:0% +look at this and try to break it apart + + + align:start position:0% +look at this and try to break it apart +see what's going on here um in + + align:start position:0% +see what's going on here um in + + + align:start position:0% +see what's going on here um in +developing this ability to take into + + align:start position:0% +developing this ability to take into + + + align:start position:0% +developing this ability to take into +account what is in the mind of another + + align:start position:0% +account what is in the mind of another + + + align:start position:0% +account what is in the mind of another +uh person or bird as the case may be + + align:start position:0% +uh person or bird as the case may be + + + align:start position:0% +uh person or bird as the case may be +um this is sometimes talked about as + + align:start position:0% +um this is sometimes talked about as + + + align:start position:0% +um this is sometimes talked about as +mind reading and is sometimes described + + align:start position:0% +mind reading and is sometimes described + + + align:start position:0% +mind reading and is sometimes described +as the major problem or the major social + + align:start position:0% +as the major problem or the major social + + + align:start position:0% +as the major problem or the major social +problem in in autism that may be one of + + align:start position:0% +problem in in autism that may be one of + + + align:start position:0% +problem in in autism that may be one of +the reasons that autistic uh um adults + + align:start position:0% +the reasons that autistic uh um adults + + + align:start position:0% +the reasons that autistic uh um adults +kids and adults have a real problem + + align:start position:0% +kids and adults have a real problem + + + align:start position:0% +kids and adults have a real problem +relating to other people is an inability + + align:start position:0% +relating to other people is an inability + + + align:start position:0% +relating to other people is an inability +to uh understand that other people have + + align:start position:0% +to uh understand that other people have + + + align:start position:0% +to uh understand that other people have +mental States um which you you have that + + align:start position:0% +mental States um which you you have that + + + align:start position:0% +mental States um which you you have that +ability but + + align:start position:0% +ability but + + + align:start position:0% +ability but +you know here you failed the uh you as a + + align:start position:0% +you know here you failed the uh you as a + + + align:start position:0% +you know here you failed the uh you as a +four-year-old have failed to manage to + + align:start position:0% +four-year-old have failed to manage to + + + align:start position:0% +four-year-old have failed to manage to +keep track of Big Bird's mental state + + align:start position:0% +keep track of Big Bird's mental state + + + align:start position:0% +keep track of Big Bird's mental state +okay well let's do a variation on this + + align:start position:0% +okay well let's do a variation on this + + + align:start position:0% +okay well let's do a variation on this +so here's a variation where you don't + + align:start position:0% +so here's a variation where you don't + + + align:start position:0% +so here's a variation where you don't +see that initial + + align:start position:0% +see that initial + + + align:start position:0% +see that initial +scene okay and um now uh you are asked + + align:start position:0% +scene okay and um now uh you are asked + + + align:start position:0% +scene okay and um now uh you are asked +to uh to guess you know the candy is + + align:start position:0% +to uh to guess you know the candy is + + + align:start position:0% +to uh to guess you know the candy is +either here or + + align:start position:0% +either here or + + + align:start position:0% +either here or +here where do you think that the + + align:start position:0% +here where do you think that the + + + align:start position:0% +here where do you think that the +candy might + + align:start position:0% +candy might + + + align:start position:0% +candy might +be well you say you know 50/50 right oh + + align:start position:0% +be well you say you know 50/50 right oh + + + align:start position:0% +be well you say you know 50/50 right oh +I think the cand is in the + + align:start position:0% +I think the cand is in the + + + align:start position:0% +I think the cand is in the +drawer okay now Big Bird comes in and + + align:start position:0% +drawer okay now Big Bird comes in and + + + align:start position:0% +drawer okay now Big Bird comes in and +you're told well you know big bird + + align:start position:0% +you're told well you know big bird + + + align:start position:0% +you're told well you know big bird +thinks it's in the + + align:start position:0% +thinks it's in the + + + align:start position:0% +thinks it's in the +fridge okay where's Big Bird going to + + align:start position:0% +fridge okay where's Big Bird going to + + + align:start position:0% +fridge okay where's Big Bird going to +look and the answer now is even if + + align:start position:0% +look and the answer now is even if + + + align:start position:0% +look and the answer now is even if +you're as young as three that you say + + align:start position:0% +you're as young as three that you say + + + align:start position:0% +you're as young as three that you say +Big Bird's going to look in the + + align:start position:0% +Big Bird's going to look in the + + + align:start position:0% +Big Bird's going to look in the +fridge your guess isn't strong enough to + + align:start position:0% +fridge your guess isn't strong enough to + + + align:start position:0% +fridge your guess isn't strong enough to +overwrite your understanding of what's + + align:start position:0% +overwrite your understanding of what's + + + align:start position:0% +overwrite your understanding of what's +going on in Big Bird's head this tells + + align:start position:0% +going on in Big Bird's head this tells + + + align:start position:0% +going on in Big Bird's head this tells +you something important this tells you + + align:start position:0% +you something important this tells you + + + align:start position:0% +you something important this tells you +immediately that you can you you know + + align:start position:0% +immediately that you can you you know + + + align:start position:0% +immediately that you can you you know +something about the contents uh that + + align:start position:0% +something about the contents uh that + + + align:start position:0% +something about the contents uh that +you're capable of of of understanding + + align:start position:0% +you're capable of of of understanding + + + align:start position:0% +you're capable of of of understanding +something about the contents of Big + + align:start position:0% +something about the contents of Big + + + align:start position:0% +something about the contents of Big +Bird's um head it's it's not a complete + + align:start position:0% +Bird's um head it's it's not a complete + + + align:start position:0% +Bird's um head it's it's not a complete +blank to you um even younger than that + + align:start position:0% +blank to you um even younger than that + + + align:start position:0% +blank to you um even younger than that +little kids can see uh somebody playing + + align:start position:0% +little kids can see uh somebody playing + + + align:start position:0% +little kids can see uh somebody playing +with a banana pretending it's a phone + + align:start position:0% +with a banana pretending it's a phone + + + align:start position:0% +with a banana pretending it's a phone +right and you ask does he know that it's + + align:start position:0% +right and you ask does he know that it's + + + align:start position:0% +right and you ask does he know that it's +a uh that it's not a phone and yeah yeah + + align:start position:0% +a uh that it's not a phone and yeah yeah + + + align:start position:0% +a uh that it's not a phone and yeah yeah +yeah that 2-year-old will tell you yeah + + align:start position:0% +yeah that 2-year-old will tell you yeah + + + align:start position:0% +yeah that 2-year-old will tell you yeah +he he's just pretending and you can have + + align:start position:0% +he he's just pretending and you can have + + + align:start position:0% +he he's just pretending and you can have +the notion that that that somebody else + + align:start position:0% +the notion that that that somebody else + + + align:start position:0% +the notion that that that somebody else +could pretend um to uh pretend something + + align:start position:0% +could pretend um to uh pretend something + + + align:start position:0% +could pretend um to uh pretend something +so again you can push this notion of + + align:start position:0% +so again you can push this notion of + + + align:start position:0% +so again you can push this notion of +some being able to read minds back + + align:start position:0% +some being able to read minds back + + + align:start position:0% +some being able to read minds back +earlier if it gets uh gets simpler um + + align:start position:0% +earlier if it gets uh gets simpler um + + + align:start position:0% +earlier if it gets uh gets simpler um +and maybe maybe this isn't really about + + align:start position:0% +and maybe maybe this isn't really about + + + align:start position:0% +and maybe maybe this isn't really about +the contents of of Big Bird's mind at + + align:start position:0% +the contents of of Big Bird's mind at + + + align:start position:0% +the contents of of Big Bird's mind at +all here's a cute version of the + + align:start position:0% +all here's a cute version of the + + + align:start position:0% +all here's a cute version of the +experiment done by Debbie zek Once Upon + + align:start position:0% +experiment done by Debbie zek Once Upon + + + align:start position:0% +experiment done by Debbie zek Once Upon +a Time Big Bird comes in it's the + + align:start position:0% +a Time Big Bird comes in it's the + + + align:start position:0% +a Time Big Bird comes in it's the +original false memory game a false uh uh + + align:start position:0% +original false memory game a false uh uh + + + align:start position:0% +original false memory game a false uh uh +false belief game Big Bird comes in puts + + align:start position:0% +false belief game Big Bird comes in puts + + + align:start position:0% +false belief game Big Bird comes in puts +the the candy in the fridge but this + + align:start position:0% +the the candy in the fridge but this + + + align:start position:0% +the the candy in the fridge but this +time big bird takes out his camera and + + align:start position:0% +time big bird takes out his camera and + + + align:start position:0% +time big bird takes out his camera and +he photographs it so he's got a picture + + align:start position:0% +he photographs it so he's got a picture + + + align:start position:0% +he photographs it so he's got a picture +of + + align:start position:0% + + + + align:start position:0% + +it there's the candy in the fridge okay + + align:start position:0% +it there's the candy in the fridge okay + + + align:start position:0% +it there's the candy in the fridge okay +now Big Bird goes out + + align:start position:0% +now Big Bird goes out + + + align:start position:0% +now Big Bird goes out +um and uh Grover comes in moves the + + align:start position:0% +um and uh Grover comes in moves the + + + align:start position:0% +um and uh Grover comes in moves the +candy to the to the drawer you now know + + align:start position:0% +candy to the to the drawer you now know + + + align:start position:0% +candy to the to the drawer you now know +that the candy is in the drawer Big Bird + + align:start position:0% +that the candy is in the drawer Big Bird + + + align:start position:0% +that the candy is in the drawer Big Bird +comes in you are asked where's Big Bird + + align:start position:0% +comes in you are asked where's Big Bird + + + align:start position:0% +comes in you are asked where's Big Bird +going to look for the candy even though + + align:start position:0% +going to look for the candy even though + + + align:start position:0% +going to look for the candy even though +big bird has taken a picture of it even + + align:start position:0% +big bird has taken a picture of it even + + + align:start position:0% +big bird has taken a picture of it even +though there's now a physical + + align:start position:0% +though there's now a physical + + + align:start position:0% +though there's now a physical +instantiation of uh the contents of Big + + align:start position:0% +instantiation of uh the contents of Big + + + align:start position:0% +instantiation of uh the contents of Big +Bird's mind you still say it's in the + + align:start position:0% +Bird's mind you still say it's in the + + + align:start position:0% +Bird's mind you still say it's in the +drawer you as a four-year-old are still + + align:start position:0% +drawer you as a four-year-old are still + + + align:start position:0% +drawer you as a four-year-old are still +unable to keep track of this this + + align:start position:0% +unable to keep track of this this + + + align:start position:0% +unable to keep track of this this +suggests that maybe the problem is a + + align:start position:0% +suggests that maybe the problem is a + + + align:start position:0% +suggests that maybe the problem is a +less with your ability to see into + + align:start position:0% +less with your ability to see into + + + align:start position:0% +less with your ability to see into +somebody else's mind and more um with + + align:start position:0% +somebody else's mind and more um with + + + align:start position:0% +somebody else's mind and more um with +something like the capacity of your + + align:start position:0% +something like the capacity of your + + + align:start position:0% +something like the capacity of your +working memory so if you think about it + + align:start position:0% +working memory so if you think about it + + + align:start position:0% +working memory so if you think about it +this is very parallel to a less + + align:start position:0% +this is very parallel to a less + + + align:start position:0% +this is very parallel to a less +experiment I talked about he did last + + align:start position:0% +experiment I talked about he did last + + + align:start position:0% +experiment I talked about he did last +time or the time before you see somebody + + align:start position:0% +time or the time before you see somebody + + + align:start position:0% +time or the time before you see somebody +go through a yield sign you later hear + + align:start position:0% +go through a yield sign you later hear + + + align:start position:0% +go through a yield sign you later hear +that it was a stop sign and you believe + + align:start position:0% +that it was a stop sign and you believe + + + align:start position:0% +that it was a stop sign and you believe +you come to have a false memory or a + + align:start position:0% +you come to have a false memory or a + + + align:start position:0% +you come to have a false memory or a +false belief if you like that it really + + align:start position:0% +false belief if you like that it really + + + align:start position:0% +false belief if you like that it really +was a stop sign because we've managed to + + align:start position:0% +was a stop sign because we've managed to + + + align:start position:0% +was a stop sign because we've managed to +somehow overwrite your your memory here + + align:start position:0% +somehow overwrite your your memory here + + + align:start position:0% +somehow overwrite your your memory here +maybe in this case what you're dealing + + align:start position:0% +maybe in this case what you're dealing + + + align:start position:0% +maybe in this case what you're dealing +with is not the development uh a a a + + align:start position:0% +with is not the development uh a a a + + + align:start position:0% +with is not the development uh a a a +qualitative change where you're seeing a + + align:start position:0% +qualitative change where you're seeing a + + + align:start position:0% +qualitative change where you're seeing a +change in the ability to see into + + align:start position:0% +change in the ability to see into + + + align:start position:0% +change in the ability to see into +somebody else's mind but a big enough + + align:start position:0% +somebody else's mind but a big enough + + + align:start position:0% +somebody else's mind but a big enough +working memory that you can keep track + + align:start position:0% +working memory that you can keep track + + + align:start position:0% +working memory that you can keep track +of the task so another case where the uh + + align:start position:0% +of the task so another case where the uh + + + align:start position:0% +of the task so another case where the uh +the development here Waits on the uh the + + align:start position:0% +the development here Waits on the uh the + + + align:start position:0% +the development here Waits on the uh the +development of another ability a + + align:start position:0% +development of another ability a + + + align:start position:0% +development of another ability a +separate ability in this case working + + align:start position:0% +separate ability in this case working + + + align:start position:0% +separate ability in this case working +memory um okay that's as good a place to + + align:start position:0% +memory um okay that's as good a place to + + + align:start position:0% +memory um okay that's as good a place to +stop as any so I'll stop \ No newline at end of file diff --git a/2PP1QHvBECo.txt b/2PP1QHvBECo.txt new file mode 100644 index 0000000000000000000000000000000000000000..16565d20674fd6a2ff0d9d3626c26a1725d05df5 --- /dev/null +++ b/2PP1QHvBECo.txt @@ -0,0 +1,13035 @@ +align:start position:0% + +the following content is provided by mit + + align:start position:0% +the following content is provided by mit + + + align:start position:0% +the following content is provided by mit +opencourseware under a creative commons + + align:start position:0% +opencourseware under a creative commons + + + align:start position:0% +opencourseware under a creative commons +license + + align:start position:0% +license + + + align:start position:0% +license +additional information about our license + + align:start position:0% +additional information about our license + + + align:start position:0% +additional information about our license +and mit opencourseware in general is + + align:start position:0% +and mit opencourseware in general is + + + align:start position:0% +and mit opencourseware in general is +available at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +yeah the internet i had + + align:start position:0% +yeah the internet i had + + + align:start position:0% +yeah the internet i had +i was really trying to uh + + align:start position:0% +i was really trying to uh + + + align:start position:0% +i was really trying to uh +well push is not the word but something + + align:start position:0% +well push is not the word but something + + + align:start position:0% +well push is not the word but something +close to + + align:start position:0% +close to + + + align:start position:0% +close to +dr ing to do something + + align:start position:0% +dr ing to do something + + + align:start position:0% +dr ing to do something +on that + + align:start position:0% + + + + align:start position:0% + +see one of the things about the internet + + align:start position:0% +see one of the things about the internet + + + align:start position:0% +see one of the things about the internet +is + + align:start position:0% + + + + align:start position:0% + +that um + + align:start position:0% + + + + align:start position:0% + +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +produced a generation + + align:start position:0% + + + + align:start position:0% + +and the we is the world + + align:start position:0% + + + + align:start position:0% + +let me tell you what i mean by that one + + align:start position:0% +let me tell you what i mean by that one + + + align:start position:0% +let me tell you what i mean by that one +now that i don't know if i ever told you + + align:start position:0% +now that i don't know if i ever told you + + + align:start position:0% +now that i don't know if i ever told you +this i was in + + align:start position:0% +this i was in + + + align:start position:0% +this i was in +south africa + + align:start position:0% +south africa + + + align:start position:0% +south africa +and i was up in the sutu + + align:start position:0% +and i was up in the sutu + + + align:start position:0% +and i was up in the sutu +and + + align:start position:0% +and + + + align:start position:0% +and +i'm riding down this road + + align:start position:0% +i'm riding down this road + + + align:start position:0% +i'm riding down this road +and it's total desolation + + align:start position:0% + + + + align:start position:0% + +totally up in the mountains total + + align:start position:0% +totally up in the mountains total + + + align:start position:0% +totally up in the mountains total +desolation + + align:start position:0% +desolation + + + align:start position:0% +desolation +and all of a sudden there's this guy + + align:start position:0% +and all of a sudden there's this guy + + + align:start position:0% +and all of a sudden there's this guy +walking alongside the road herself + + align:start position:0% + + + + align:start position:0% + +and i asked my my driver said who was he + + align:start position:0% +and i asked my my driver said who was he + + + align:start position:0% +and i asked my my driver said who was he +talking to somebody back in his village + + align:start position:0% +talking to somebody back in his village + + + align:start position:0% +talking to somebody back in his village +he said no he's probably talking to a + + align:start position:0% +he said no he's probably talking to a + + + align:start position:0% +he said no he's probably talking to a +relative + + align:start position:0% +relative + + + align:start position:0% +relative +in france you know + + align:start position:0% +in france you know + + + align:start position:0% +in france you know +i mean + + align:start position:0% +i mean + + + align:start position:0% +i mean +so when i say we + + align:start position:0% +so when i say we + + + align:start position:0% +so when i say we +and i mean the world i really mean + + align:start position:0% +and i mean the world i really mean + + + align:start position:0% +and i mean the world i really mean +we have produced a + + align:start position:0% +we have produced a + + + align:start position:0% +we have produced a +generation that + + align:start position:0% + + + + align:start position:0% + +that is probably in some ways wired into + + align:start position:0% +that is probably in some ways wired into + + + align:start position:0% +that is probably in some ways wired into +the internet and other things + + align:start position:0% +the internet and other things + + + align:start position:0% +the internet and other things +that i am not wired into and that you + + align:start position:0% +that i am not wired into and that you + + + align:start position:0% +that i am not wired into and that you +all are probably just + + align:start position:0% +all are probably just + + + align:start position:0% +all are probably just +i don't even know if i count you all in + + align:start position:0% +i don't even know if i count you all in + + + align:start position:0% +i don't even know if i count you all in +it's + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +and what i what i what i've gotten from + + align:start position:0% +and what i what i what i've gotten from + + + align:start position:0% +and what i what i what i've gotten from +students is um + + align:start position:0% +students is um + + + align:start position:0% +students is um +a basic uh + + align:start position:0% +a basic uh + + + align:start position:0% +a basic uh +moral sensibility about the internet + + align:start position:0% +moral sensibility about the internet + + + align:start position:0% +moral sensibility about the internet +that i don't have + + align:start position:0% +that i don't have + + + align:start position:0% +that i don't have +and that i can argue against + + align:start position:0% +and that i can argue against + + + align:start position:0% +and that i can argue against +but they have a basic sentimental + + align:start position:0% +but they have a basic sentimental + + + align:start position:0% +but they have a basic sentimental +sentimentality about it which i think + + align:start position:0% +sentimentality about it which i think + + + align:start position:0% +sentimentality about it which i think +gives rise to all ethics you have to + + align:start position:0% +gives rise to all ethics you have to + + + align:start position:0% +gives rise to all ethics you have to +have a sentiment + + align:start position:0% +have a sentiment + + + align:start position:0% +have a sentiment +you have to have a passion about + + align:start position:0% +you have to have a passion about + + + align:start position:0% +you have to have a passion about +something you have to feel something + + align:start position:0% +something you have to feel something + + + align:start position:0% +something you have to feel something +and one of them is um + + align:start position:0% +and one of them is um + + + align:start position:0% +and one of them is um +that no matter what the law says + + align:start position:0% +that no matter what the law says + + + align:start position:0% +that no matter what the law says +whatever you can get from the net + + align:start position:0% +whatever you can get from the net + + + align:start position:0% +whatever you can get from the net +belongs to you it's like free water you + + align:start position:0% +belongs to you it's like free water you + + + align:start position:0% +belongs to you it's like free water you +know uh pierre passed out past the + + align:start position:0% +know uh pierre passed out past the + + + align:start position:0% +know uh pierre passed out past the +12-mile limit there's a + + align:start position:0% +12-mile limit there's a + + + align:start position:0% +12-mile limit there's a +sensibility they have that no matter + + align:start position:0% +sensibility they have that no matter + + + align:start position:0% +sensibility they have that no matter +what you put up there once it gets up + + align:start position:0% +what you put up there once it gets up + + + align:start position:0% +what you put up there once it gets up +there + + align:start position:0% +there + + + align:start position:0% +there +it's in + + align:start position:0% +it's in + + + align:start position:0% +it's in +public domain and i say no you know what + + align:start position:0% +public domain and i say no you know what + + + align:start position:0% +public domain and i say no you know what +i mean i'm able to argue all of that + + align:start position:0% +i mean i'm able to argue all of that + + + align:start position:0% +i mean i'm able to argue all of that +stuff and they okay they believe + + align:start position:0% +stuff and they okay they believe + + + align:start position:0% +stuff and they okay they believe +whatever but i look at them in their + + align:start position:0% +whatever but i look at them in their + + + align:start position:0% +whatever but i look at them in their +faces after i've argued they're not + + align:start position:0% +faces after i've argued they're not + + + align:start position:0% +faces after i've argued they're not +buying it + + align:start position:0% + + + + align:start position:0% + +and the only argument that i can give to + + align:start position:0% +and the only argument that i can give to + + + align:start position:0% +and the only argument that i can give to +them that confuses them + + align:start position:0% +them that confuses them + + + align:start position:0% +them that confuses them +is the one where + + align:start position:0% +is the one where + + + align:start position:0% +is the one where +i say that + + align:start position:0% +i say that + + + align:start position:0% +i say that +i ran into this + + align:start position:0% +i ran into this + + + align:start position:0% +i ran into this +undergraduate student one day at howard + + align:start position:0% +undergraduate student one day at howard + + + align:start position:0% +undergraduate student one day at howard +he was a chemical engineering major i + + align:start position:0% +he was a chemical engineering major i + + + align:start position:0% +he was a chemical engineering major i +hadn't had him in the class but i knew + + align:start position:0% +hadn't had him in the class but i knew + + + align:start position:0% +hadn't had him in the class but i knew +him + + align:start position:0% +him + + + align:start position:0% +him +he's walking down the hall with a guitar + + align:start position:0% +he's walking down the hall with a guitar + + + align:start position:0% +he's walking down the hall with a guitar +i said i know you played a guitar he + + align:start position:0% +i said i know you played a guitar he + + + align:start position:0% +i said i know you played a guitar he +said well i play at the guitar i'm not + + align:start position:0% +said well i play at the guitar i'm not + + + align:start position:0% +said well i play at the guitar i'm not +really good at it but i write songs i + + align:start position:0% +really good at it but i write songs i + + + align:start position:0% +really good at it but i write songs i +say oh really + + align:start position:0% +say oh really + + + align:start position:0% +say oh really +so he opens up his guitar and pulls out + + align:start position:0% +so he opens up his guitar and pulls out + + + align:start position:0% +so he opens up his guitar and pulls out +shows me this little sheet of paper + + align:start position:0% +shows me this little sheet of paper + + + align:start position:0% +shows me this little sheet of paper +about that much of it + + align:start position:0% +about that much of it + + + align:start position:0% +about that much of it +as a song + + align:start position:0% +as a song + + + align:start position:0% +as a song +i said oh how nice + + align:start position:0% +i said oh how nice + + + align:start position:0% +i said oh how nice +he sold it to prince + + align:start position:0% +he sold it to prince + + + align:start position:0% +he sold it to prince +so i said how much did you make for that + + align:start position:0% +so i said how much did you make for that + + + align:start position:0% +so i said how much did you make for that +and it was about twice the salary i'm + + align:start position:0% +and it was about twice the salary i'm + + + align:start position:0% +and it was about twice the salary i'm +making a year + + align:start position:0% + + + + align:start position:0% + +what do you got from that royalties and + + align:start position:0% +what do you got from that royalties and + + + align:start position:0% +what do you got from that royalties and +all + + align:start position:0% +all + + + align:start position:0% +all +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so i say now if if you wrote a song + + align:start position:0% +so i say now if if you wrote a song + + + align:start position:0% +so i say now if if you wrote a song +and it's yours i don't care if you spent + + align:start position:0% +and it's yours i don't care if you spent + + + align:start position:0% +and it's yours i don't care if you spent +12 years on it or 12 minutes on it + + align:start position:0% +12 years on it or 12 minutes on it + + + align:start position:0% +12 years on it or 12 minutes on it +you know don't do you want everybody + + align:start position:0% +you know don't do you want everybody + + + align:start position:0% +you know don't do you want everybody +downloading your + + align:start position:0% +downloading your + + + align:start position:0% +downloading your +song + + align:start position:0% +song + + + align:start position:0% +song +and + + align:start position:0% +and + + + align:start position:0% +and +they will sit and think and they they + + align:start position:0% +they will sit and think and they they + + + align:start position:0% +they will sit and think and they they +they got problems with that + + align:start position:0% +they got problems with that + + + align:start position:0% +they got problems with that +okay but i still think that there's a + + align:start position:0% +okay but i still think that there's a + + + align:start position:0% +okay but i still think that there's a +possibility we have to contend with + + align:start position:0% +possibility we have to contend with + + + align:start position:0% +possibility we have to contend with +uh a sensibility about the net + + align:start position:0% +uh a sensibility about the net + + + align:start position:0% +uh a sensibility about the net +that uh my generation was developing + + align:start position:0% +that uh my generation was developing + + + align:start position:0% +that uh my generation was developing +about robots + + align:start position:0% +about robots + + + align:start position:0% +about robots +so my generation was about willing to + + align:start position:0% +so my generation was about willing to + + + align:start position:0% +so my generation was about willing to +say that a robot + + align:start position:0% +say that a robot + + + align:start position:0% +say that a robot +was sentient not really + + align:start position:0% +was sentient not really + + + align:start position:0% +was sentient not really +that the robot was central ascension but + + align:start position:0% +that the robot was central ascension but + + + align:start position:0% +that the robot was central ascension but +that we could have feelings + + align:start position:0% +that we could have feelings + + + align:start position:0% +that we could have feelings +for a machine + + align:start position:0% + + + + align:start position:0% + +and i don't think we ever got quite got + + align:start position:0% +and i don't think we ever got quite got + + + align:start position:0% +and i don't think we ever got quite got +there mainly because we're dying off + + align:start position:0% +there mainly because we're dying off + + + align:start position:0% +there mainly because we're dying off +first + + align:start position:0% +first + + + align:start position:0% +first +uh but + + align:start position:0% + + + + align:start position:0% + +i don't know + + align:start position:0% +i don't know + + + align:start position:0% +i don't know +if you ever meet somebody my age or + + align:start position:0% +if you ever meet somebody my age or + + + align:start position:0% +if you ever meet somebody my age or +older + + align:start position:0% +older + + + align:start position:0% +older +ask what they feel about their car + + align:start position:0% + + + + align:start position:0% + +might feel that + + align:start position:0% + + + + align:start position:0% + +well i mean some people feel about a + + align:start position:0% +well i mean some people feel about a + + + align:start position:0% +well i mean some people feel about a +copy they get out and kiss the engine if + + align:start position:0% +copy they get out and kiss the engine if + + + align:start position:0% +copy they get out and kiss the engine if +you let them it wasn't hot i mean they + + align:start position:0% +you let them it wasn't hot i mean they + + + align:start position:0% +you let them it wasn't hot i mean they +feel + + align:start position:0% +feel + + + align:start position:0% +feel +uh sentimentality about it + + align:start position:0% +uh sentimentality about it + + + align:start position:0% +uh sentimentality about it +so i don't know it's an interesting + + align:start position:0% +so i don't know it's an interesting + + + align:start position:0% +so i don't know it's an interesting +thing to speculate about the important + + align:start position:0% +thing to speculate about the important + + + align:start position:0% +thing to speculate about the important +thing for this class is + + align:start position:0% +thing for this class is + + + align:start position:0% +thing for this class is +to + + align:start position:0% +to + + + align:start position:0% +to +to speculate about keep it in mind watch + + align:start position:0% +to speculate about keep it in mind watch + + + align:start position:0% +to speculate about keep it in mind watch +people ask them questions because your + + align:start position:0% +people ask them questions because your + + + align:start position:0% +people ask them questions because your +arguments may not sync in with them past + + align:start position:0% +arguments may not sync in with them past + + + align:start position:0% +arguments may not sync in with them past +the rational level + + align:start position:0% + + + + align:start position:0% + +okay what i want to do today is go into + + align:start position:0% +okay what i want to do today is go into + + + align:start position:0% +okay what i want to do today is go into +some depth on these codes of ethics but + + align:start position:0% +some depth on these codes of ethics but + + + align:start position:0% +some depth on these codes of ethics but +i want to entertain q a first + + align:start position:0% + + + + align:start position:0% + +any burning issues outstanding stuff + + align:start position:0% + + + + align:start position:0% + +related to anything + + align:start position:0% +related to anything + + + align:start position:0% +related to anything +so that i can start + + align:start position:0% +so that i can start + + + align:start position:0% +so that i can start +into the code of ethics with a clear + + align:start position:0% +into the code of ethics with a clear + + + align:start position:0% +into the code of ethics with a clear +conscience + + align:start position:0% + + + + align:start position:0% + +ethics as i believe most engineers + + align:start position:0% +ethics as i believe most engineers + + + align:start position:0% +ethics as i believe most engineers +understand and practice it + + align:start position:0% +understand and practice it + + + align:start position:0% +understand and practice it +hot dog involves the carefully + + align:start position:0% +hot dog involves the carefully + + + align:start position:0% +hot dog involves the carefully +calculated + + align:start position:0% +calculated + + + align:start position:0% +calculated +responsible application + + align:start position:0% +responsible application + + + align:start position:0% +responsible application +of well-understood principles + + align:start position:0% +of well-understood principles + + + align:start position:0% +of well-understood principles +in accordance with established public + + align:start position:0% +in accordance with established public + + + align:start position:0% +in accordance with established public +and professional standards to produce + + align:start position:0% +and professional standards to produce + + + align:start position:0% +and professional standards to produce +results + + align:start position:0% +results + + + align:start position:0% +results +that are both safe and beneficial to + + align:start position:0% +that are both safe and beneficial to + + + align:start position:0% +that are both safe and beneficial to +society's argument you cannot call + + align:start position:0% +society's argument you cannot call + + + align:start position:0% +society's argument you cannot call +genetic what's done with genes genetic + + align:start position:0% +genetic what's done with genes genetic + + + align:start position:0% +genetic what's done with genes genetic +engineering these people who manipulate + + align:start position:0% +engineering these people who manipulate + + + align:start position:0% +engineering these people who manipulate +the genetics you know + + align:start position:0% +the genetics you know + + + align:start position:0% +the genetics you know +organisms they can't assume that they + + align:start position:0% +organisms they can't assume that they + + + align:start position:0% +organisms they can't assume that they +can't say + + align:start position:0% +can't say + + + align:start position:0% +can't say +it's in a safe way and no one really + + align:start position:0% +it's in a safe way and no one really + + + align:start position:0% +it's in a safe way and no one really +there's so much uncertainty you really + + align:start position:0% +there's so much uncertainty you really + + + align:start position:0% +there's so much uncertainty you really +can't call it engineering + + align:start position:0% + + + + align:start position:0% + +yeah that's that's a that's an argument + + align:start position:0% +yeah that's that's a that's an argument + + + align:start position:0% +yeah that's that's a that's an argument +if you'll recall you have no reason to + + align:start position:0% +if you'll recall you have no reason to + + + align:start position:0% +if you'll recall you have no reason to +recall this because it was at the very + + align:start position:0% +recall this because it was at the very + + + align:start position:0% +recall this because it was at the very +very very the last thing i said + + align:start position:0% +very very the last thing i said + + + align:start position:0% +very very the last thing i said +but when we + + align:start position:0% +but when we + + + align:start position:0% +but when we +uh + + align:start position:0% +uh + + + align:start position:0% +uh +went to the um + + align:start position:0% +went to the um + + + align:start position:0% +went to the um +you know the norwegian + + align:start position:0% +you know the norwegian + + + align:start position:0% +you know the norwegian +uh + + align:start position:0% +uh + + + align:start position:0% +uh +lecture my very last recommendation + + align:start position:0% +lecture my very last recommendation + + + align:start position:0% +lecture my very last recommendation +was that we think about + + align:start position:0% +was that we think about + + + align:start position:0% +was that we think about +competency + + align:start position:0% +competency + + + align:start position:0% +competency +we define competency in terms of + + align:start position:0% +we define competency in terms of + + + align:start position:0% +we define competency in terms of +the good + + align:start position:0% +the good + + + align:start position:0% +the good +not competent and then ask whether it's + + align:start position:0% +not competent and then ask whether it's + + + align:start position:0% +not competent and then ask whether it's +good + + align:start position:0% +good + + + align:start position:0% +good +but it is not competent + + align:start position:0% +but it is not competent + + + align:start position:0% +but it is not competent +unless it is also good + + align:start position:0% +unless it is also good + + + align:start position:0% +unless it is also good +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +the group didn't seem uh to want to + + align:start position:0% +the group didn't seem uh to want to + + + align:start position:0% +the group didn't seem uh to want to +spend much time on that part they wanted + + align:start position:0% +spend much time on that part they wanted + + + align:start position:0% +spend much time on that part they wanted +to spend time on the + + align:start position:0% +to spend time on the + + + align:start position:0% +to spend time on the +character development part + + align:start position:0% +character development part + + + align:start position:0% +character development part +but that part + + align:start position:0% +but that part + + + align:start position:0% +but that part +was + + align:start position:0% + + + + align:start position:0% + +was significant + + align:start position:0% +was significant + + + align:start position:0% +was significant +because + + align:start position:0% +because + + + align:start position:0% +because +well for two reasons + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +well let me just say for one reason if + + align:start position:0% +well let me just say for one reason if + + + align:start position:0% +well let me just say for one reason if +if i want to put the element in that way + + align:start position:0% +if i want to put the element in that way + + + align:start position:0% +if i want to put the element in that way +and that is + + align:start position:0% + + + + align:start position:0% + +that if you take the ethics out of the + + align:start position:0% +that if you take the ethics out of the + + + align:start position:0% +that if you take the ethics out of the +definition of competency what you have + + align:start position:0% +definition of competency what you have + + + align:start position:0% +definition of competency what you have +is + + align:start position:0% +is + + + align:start position:0% +is +a lower order + + align:start position:0% +a lower order + + + align:start position:0% +a lower order +standard for confidence you don't have + + align:start position:0% +standard for confidence you don't have + + + align:start position:0% +standard for confidence you don't have +to be really good at what you do + + align:start position:0% +to be really good at what you do + + + align:start position:0% +to be really good at what you do +because let's say for example + + align:start position:0% +because let's say for example + + + align:start position:0% +because let's say for example +okay uh three children come in here and + + align:start position:0% +okay uh three children come in here and + + + align:start position:0% +okay uh three children come in here and +one of them's got a disease that we'll + + align:start position:0% +one of them's got a disease that we'll + + + align:start position:0% +one of them's got a disease that we'll +all catch in this in 10 minutes + + align:start position:0% +all catch in this in 10 minutes + + + align:start position:0% +all catch in this in 10 minutes +well one way to solve the problem kill + + align:start position:0% +well one way to solve the problem kill + + + align:start position:0% +well one way to solve the problem kill +all the children + + align:start position:0% +all the children + + + align:start position:0% +all the children +i wouldn't call that competent + + align:start position:0% +i wouldn't call that competent + + + align:start position:0% +i wouldn't call that competent +all right but that's + + align:start position:0% +all right but that's + + + align:start position:0% +all right but that's +that's a okay so i want to say that + + align:start position:0% +that's a okay so i want to say that + + + align:start position:0% +that's a okay so i want to say that +that competency really includes ethics + + align:start position:0% +that competency really includes ethics + + + align:start position:0% +that competency really includes ethics +as + + align:start position:0% +as + + + align:start position:0% +as +a condition + + align:start position:0% +a condition + + + align:start position:0% +a condition +because it not only means that + + align:start position:0% +because it not only means that + + + align:start position:0% +because it not only means that +you have to be + + align:start position:0% +you have to be + + + align:start position:0% +you have to be +really highly confident + + align:start position:0% +really highly confident + + + align:start position:0% +really highly confident +but you build incompetence into the + + align:start position:0% +but you build incompetence into the + + + align:start position:0% +but you build incompetence into the +culture + + align:start position:0% +culture + + + align:start position:0% +culture +that people do not look for + + align:start position:0% +that people do not look for + + + align:start position:0% +that people do not look for +the uh one that's not ethical and i + + align:start position:0% +the uh one that's not ethical and i + + + align:start position:0% +the uh one that's not ethical and i +guess i'll put the other one in there + + align:start position:0% +guess i'll put the other one in there + + + align:start position:0% +guess i'll put the other one in there +because + + align:start position:0% +because + + + align:start position:0% +because +it actually means the same thing it goes + + align:start position:0% +it actually means the same thing it goes + + + align:start position:0% +it actually means the same thing it goes +back to my lecture again about faust + + align:start position:0% +back to my lecture again about faust + + + align:start position:0% +back to my lecture again about faust +that if you leave out the ethics part + + align:start position:0% +that if you leave out the ethics part + + + align:start position:0% +that if you leave out the ethics part +you're going to get what you call a + + align:start position:0% +you're going to get what you call a + + + align:start position:0% +you're going to get what you call a +competent dissolution but it'd be + + align:start position:0% +competent dissolution but it'd be + + + align:start position:0% +competent dissolution but it'd be +something you don't want + + align:start position:0% +something you don't want + + + align:start position:0% +something you don't want +all right the monkey's paw again all + + align:start position:0% +all right the monkey's paw again all + + + align:start position:0% +all right the monkey's paw again all +right + + align:start position:0% +right + + + align:start position:0% +right +so i think the monkey's par really + + align:start position:0% +so i think the monkey's par really + + + align:start position:0% +so i think the monkey's par really +defines + + align:start position:0% +defines + + + align:start position:0% +defines +competency without ethics + + align:start position:0% +competency without ethics + + + align:start position:0% +competency without ethics +and that's something that + + align:start position:0% +and that's something that + + + align:start position:0% +and that's something that +nobody wants + + align:start position:0% +nobody wants + + + align:start position:0% +nobody wants +even though you have agreed + + align:start position:0% +even though you have agreed + + + align:start position:0% +even though you have agreed +our priority + + align:start position:0% +our priority + + + align:start position:0% +our priority +that + + align:start position:0% +that + + + align:start position:0% +that +on the terms of the contract + + align:start position:0% +on the terms of the contract + + + align:start position:0% +on the terms of the contract +okay so um + + align:start position:0% +okay so um + + + align:start position:0% +okay so um +so those are my arguments about that so + + align:start position:0% +so those are my arguments about that so + + + align:start position:0% +so those are my arguments about that so +yeah i'd like to see that paper um + + align:start position:0% +yeah i'd like to see that paper um + + + align:start position:0% +yeah i'd like to see that paper um +and i'd like to actually i'm trying to + + align:start position:0% +and i'd like to actually i'm trying to + + + align:start position:0% +and i'd like to actually i'm trying to +get stephanie byrd in here um + + align:start position:0% +get stephanie byrd in here um + + + align:start position:0% +get stephanie byrd in here um +to talk she she does us + + align:start position:0% +to talk she she does us + + + align:start position:0% +to talk she she does us +ethics in science + + align:start position:0% +ethics in science + + + align:start position:0% +ethics in science +so she wants to talk about those kinds + + align:start position:0% +so she wants to talk about those kinds + + + align:start position:0% +so she wants to talk about those kinds +of issues too and i want to bring her in + + align:start position:0% +of issues too and i want to bring her in + + + align:start position:0% +of issues too and i want to bring her in +here to talk about these issues because + + align:start position:0% +here to talk about these issues because + + + align:start position:0% +here to talk about these issues because +i think when you say what something is + + align:start position:0% +i think when you say what something is + + + align:start position:0% +i think when you say what something is +you clarify by saying what did what it + + align:start position:0% +you clarify by saying what did what it + + + align:start position:0% +you clarify by saying what did what it +is not + + align:start position:0% +is not + + + align:start position:0% +is not +so we're not talking about ethics and + + align:start position:0% +so we're not talking about ethics and + + + align:start position:0% +so we're not talking about ethics and +science but how do we know well let's + + align:start position:0% +science but how do we know well let's + + + align:start position:0% +science but how do we know well let's +have a course lecture in ethics and + + align:start position:0% +have a course lecture in ethics and + + + align:start position:0% +have a course lecture in ethics and +science + + align:start position:0% +science + + + align:start position:0% +science +uh so what you'll find in ethics and + + align:start position:0% +uh so what you'll find in ethics and + + + align:start position:0% +uh so what you'll find in ethics and +science + + align:start position:0% +science + + + align:start position:0% +science +uh + + align:start position:0% +uh + + + align:start position:0% +uh +is uh + + align:start position:0% +is uh + + + align:start position:0% +is uh +two kinds of uh + + align:start position:0% +two kinds of uh + + + align:start position:0% +two kinds of uh +two categories of issues basically one + + align:start position:0% +two categories of issues basically one + + + align:start position:0% +two categories of issues basically one +is + + align:start position:0% +is + + + align:start position:0% +is +ethics and research + + align:start position:0% +ethics and research + + + align:start position:0% +ethics and research +research ethics which is what i talked + + align:start position:0% +research ethics which is what i talked + + + align:start position:0% +research ethics which is what i talked +about is today almost always considered + + align:start position:0% +about is today almost always considered + + + align:start position:0% +about is today almost always considered +science research ethics and sciences + + align:start position:0% +science research ethics and sciences + + + align:start position:0% +science research ethics and sciences +even though it can include anything else + + align:start position:0% +even though it can include anything else + + + align:start position:0% +even though it can include anything else +but all of the issues have come up + + align:start position:0% +but all of the issues have come up + + + align:start position:0% +but all of the issues have come up +with big scientists + + align:start position:0% +with big scientists + + + align:start position:0% +with big scientists +doing making gross + + align:start position:0% +doing making gross + + + align:start position:0% +doing making gross +violations of + + align:start position:0% +violations of + + + align:start position:0% +violations of +your basic sensitivity + + align:start position:0% +your basic sensitivity + + + align:start position:0% +your basic sensitivity +the other uh category has to do with + + align:start position:0% +the other uh category has to do with + + + align:start position:0% +the other uh category has to do with +what i would call um + + align:start position:0% +what i would call um + + + align:start position:0% +what i would call um +uh political issues abortion + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +stem cells + + align:start position:0% +stem cells + + + align:start position:0% +stem cells +that's right + + align:start position:0% +that's right + + + align:start position:0% +that's right +should we be doing it at all + + align:start position:0% +should we be doing it at all + + + align:start position:0% +should we be doing it at all +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and some people will tell you if you get + + align:start position:0% +and some people will tell you if you get + + + align:start position:0% +and some people will tell you if you get +uh four philosophers in this room one of + + align:start position:0% +uh four philosophers in this room one of + + + align:start position:0% +uh four philosophers in this room one of +them will say + + align:start position:0% +them will say + + + align:start position:0% +them will say +that + + align:start position:0% +that + + + align:start position:0% +that +those issues really aren't ethical + + align:start position:0% +those issues really aren't ethical + + + align:start position:0% +those issues really aren't ethical +issues + + align:start position:0% + + + + align:start position:0% + +they are scientific issues + + align:start position:0% +they are scientific issues + + + align:start position:0% +they are scientific issues +because we want + + align:start position:0% +because we want + + + align:start position:0% +because we want +a scientific definition of a human being + + align:start position:0% +a scientific definition of a human being + + + align:start position:0% +a scientific definition of a human being +we all agree that we shouldn't be doing + + align:start position:0% +we all agree that we shouldn't be doing + + + align:start position:0% +we all agree that we shouldn't be doing +these things to human beings + + align:start position:0% +these things to human beings + + + align:start position:0% +these things to human beings +but is that a human being + + align:start position:0% + + + + align:start position:0% + +that feed us or whatever okay + + align:start position:0% +that feed us or whatever okay + + + align:start position:0% +that feed us or whatever okay +and so that person will say + + align:start position:0% +and so that person will say + + + align:start position:0% +and so that person will say +i'm done walk out of the room not that + + align:start position:0% +i'm done walk out of the room not that + + + align:start position:0% +i'm done walk out of the room not that +he doesn't want to talk about it but + + align:start position:0% +he doesn't want to talk about it but + + + align:start position:0% +he doesn't want to talk about it but +it's not ethics for him or her + + align:start position:0% + + + + align:start position:0% + +is a matter of + + align:start position:0% +is a matter of + + + align:start position:0% +is a matter of +definition it's + + align:start position:0% +definition it's + + + align:start position:0% +definition it's +not just science + + align:start position:0% +not just science + + + align:start position:0% +not just science +that's sort of the other side + + align:start position:0% +that's sort of the other side + + + align:start position:0% +that's sort of the other side +of the other side + + align:start position:0% + + + + align:start position:0% + +scientists + + align:start position:0% + + + + align:start position:0% + +about + + align:start position:0% +about + + + align:start position:0% +about +what + + align:start position:0% + + + + align:start position:0% + +well that + + align:start position:0% +well that + + + align:start position:0% +well that +that takes time right + + align:start position:0% +that takes time right + + + align:start position:0% +that takes time right +you have to sit out you have to think + + align:start position:0% +you have to sit out you have to think + + + align:start position:0% +you have to sit out you have to think +about that one um + + align:start position:0% +about that one um + + + align:start position:0% +about that one um +actually what i say + + align:start position:0% +actually what i say + + + align:start position:0% +actually what i say +excuse me + + align:start position:0% +excuse me + + + align:start position:0% +excuse me +what i say is first of all it is a + + align:start position:0% +what i say is first of all it is a + + + align:start position:0% +what i say is first of all it is a +philosophical argument because it + + align:start position:0% +philosophical argument because it + + + align:start position:0% +philosophical argument because it +belongs to the category of metaphysics + + align:start position:0% +belongs to the category of metaphysics + + + align:start position:0% +belongs to the category of metaphysics +you're talking about + + align:start position:0% +you're talking about + + + align:start position:0% +you're talking about +how you're going to divide the world up + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +scientific definition can only + + align:start position:0% +scientific definition can only + + + align:start position:0% +scientific definition can only +contribute uh one part of that + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +the other thing is about it is that uh + + align:start position:0% +the other thing is about it is that uh + + + align:start position:0% +the other thing is about it is that uh +the affected parties are not only the + + align:start position:0% +the affected parties are not only the + + + align:start position:0% +the affected parties are not only the +fetus + + align:start position:0% +fetus + + + align:start position:0% +fetus +you got the mother got the father you + + align:start position:0% +you got the mother got the father you + + + align:start position:0% +you got the mother got the father you +got a whole bunch of other people who + + align:start position:0% +got a whole bunch of other people who + + + align:start position:0% +got a whole bunch of other people who +are concerned about all that + + align:start position:0% +are concerned about all that + + + align:start position:0% +are concerned about all that +then + + align:start position:0% +then + + + align:start position:0% +then +it when what the more you step into the + + align:start position:0% +it when what the more you step into the + + + align:start position:0% +it when what the more you step into the +political domain on this issue the more + + align:start position:0% +political domain on this issue the more + + + align:start position:0% +political domain on this issue the more +you get into the religious domain + + align:start position:0% +you get into the religious domain + + + align:start position:0% +you get into the religious domain +so you got to start dividing the house + + align:start position:0% +so you got to start dividing the house + + + align:start position:0% +so you got to start dividing the house +there what are we going to talk about + + align:start position:0% +there what are we going to talk about + + + align:start position:0% +there what are we going to talk about +here we're gonna use faith as a uh + + align:start position:0% +here we're gonna use faith as a uh + + + align:start position:0% +here we're gonna use faith as a uh +uh as a as an appeal a legitimate source + + align:start position:0% +uh as a as an appeal a legitimate source + + + align:start position:0% +uh as a as an appeal a legitimate source +of appeal or we're gonna stay with uh + + align:start position:0% +of appeal or we're gonna stay with uh + + + align:start position:0% +of appeal or we're gonna stay with uh +reason + + align:start position:0% +reason + + + align:start position:0% +reason +okay so you've got to continue to divide + + align:start position:0% +okay so you've got to continue to divide + + + align:start position:0% +okay so you've got to continue to divide +the house and once you do that + + align:start position:0% +the house and once you do that + + + align:start position:0% +the house and once you do that +still solve the problem but uh + + align:start position:0% + + + + align:start position:0% + +okay so um so i think that uh having her + + align:start position:0% +okay so um so i think that uh having her + + + align:start position:0% +okay so um so i think that uh having her +in here i i need i order a paper by the + + align:start position:0% +in here i i need i order a paper by the + + + align:start position:0% +in here i i need i order a paper by the +way + + align:start position:0% +way + + + align:start position:0% +way +one that i'm reading for not one that + + align:start position:0% +one that i'm reading for not one that + + + align:start position:0% +one that i'm reading for not one that +i've written + + align:start position:0% +i've written + + + align:start position:0% +i've written +uh so that would be helpful and i hope + + align:start position:0% +uh so that would be helpful and i hope + + + align:start position:0% +uh so that would be helpful and i hope +you all have the stomach for one lecture + + align:start position:0% +you all have the stomach for one lecture + + + align:start position:0% +you all have the stomach for one lecture +on this + + align:start position:0% +on this + + + align:start position:0% +on this +you might + + align:start position:0% +you might + + + align:start position:0% +you might +yeah so um + + align:start position:0% +yeah so um + + + align:start position:0% +yeah so um +and then we'll talk about whether or not + + align:start position:0% +and then we'll talk about whether or not + + + align:start position:0% +and then we'll talk about whether or not +any of this genetic engineering or + + align:start position:0% +any of this genetic engineering or + + + align:start position:0% +any of this genetic engineering or +whether it's really bio engineering + + align:start position:0% + + + + align:start position:0% + +because you are + + align:start position:0% +because you are + + + align:start position:0% +because you are +making something + + align:start position:0% +making something + + + align:start position:0% +making something +like you take clay and make bricks + + align:start position:0% +like you take clay and make bricks + + + align:start position:0% +like you take clay and make bricks +or + + align:start position:0% +or + + + align:start position:0% +or +like take iron and make steel + + align:start position:0% +like take iron and make steel + + + align:start position:0% +like take iron and make steel +you're making something + + align:start position:0% +you're making something + + + align:start position:0% +you're making something +there's a design process involved + + align:start position:0% + + + + align:start position:0% + +there's lots of engineering + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% + + + + align:start position:0% + +i'm giving consideration to all of this + + align:start position:0% +i'm giving consideration to all of this + + + align:start position:0% +i'm giving consideration to all of this +and in my research work and + + align:start position:0% +and in my research work and + + + align:start position:0% +and in my research work and +i haven't finished i haven't finished it + + align:start position:0% +i haven't finished i haven't finished it + + + align:start position:0% +i haven't finished i haven't finished it +but where i am now + + align:start position:0% +but where i am now + + + align:start position:0% +but where i am now +is that um + + align:start position:0% +is that um + + + align:start position:0% +is that um +it goes back to the manhattan project + + align:start position:0% +it goes back to the manhattan project + + + align:start position:0% +it goes back to the manhattan project +actually it goes back before the + + align:start position:0% +actually it goes back before the + + + align:start position:0% +actually it goes back before the +manhattan project it goes back really to + + align:start position:0% +manhattan project it goes back really to + + + align:start position:0% +manhattan project it goes back really to +uh + + align:start position:0% +uh + + + align:start position:0% +uh +radar + + align:start position:0% +radar + + + align:start position:0% +radar +and that's when scientists were doing + + align:start position:0% +and that's when scientists were doing + + + align:start position:0% +and that's when scientists were doing +engineering + + align:start position:0% +engineering + + + align:start position:0% +engineering +so if you get a scientist who is doing + + align:start position:0% +so if you get a scientist who is doing + + + align:start position:0% +so if you get a scientist who is doing +engineering + + align:start position:0% +engineering + + + align:start position:0% +engineering +basically + + align:start position:0% +basically + + + align:start position:0% +basically +they might not do it right so + + align:start position:0% +they might not do it right so + + + align:start position:0% +they might not do it right so +you can call it engineering i think but + + align:start position:0% +you can call it engineering i think but + + + align:start position:0% +you can call it engineering i think but +it's not + + align:start position:0% +it's not + + + align:start position:0% +it's not +what i would call sophisticated + + align:start position:0% +what i would call sophisticated + + + align:start position:0% +what i would call sophisticated +engineering because they are it's like + + align:start position:0% +engineering because they are it's like + + + align:start position:0% +engineering because they are it's like +when engineers sometimes do science i + + align:start position:0% +when engineers sometimes do science i + + + align:start position:0% +when engineers sometimes do science i +think a good example of that + + align:start position:0% +think a good example of that + + + align:start position:0% +think a good example of that +is + + align:start position:0% +is + + + align:start position:0% +is +the invention of thermodynamics + + align:start position:0% +the invention of thermodynamics + + + align:start position:0% +the invention of thermodynamics +if you look into the history of + + align:start position:0% +if you look into the history of + + + align:start position:0% +if you look into the history of +thermodynamics + + align:start position:0% +thermodynamics + + + align:start position:0% +thermodynamics +engineers boilers + + align:start position:0% +engineers boilers + + + align:start position:0% +engineers boilers +and boilers for trains + + align:start position:0% +and boilers for trains + + + align:start position:0% +and boilers for trains +uh + + align:start position:0% +uh + + + align:start position:0% +uh +approached developed a science + + align:start position:0% +approached developed a science + + + align:start position:0% +approached developed a science +using what scientists would call + + align:start position:0% +using what scientists would call + + + align:start position:0% +using what scientists would call +herky-jerky methods + + align:start position:0% +herky-jerky methods + + + align:start position:0% +herky-jerky methods +okay + + align:start position:0% + + + + align:start position:0% + +and so that's what i'm trying trying to + + align:start position:0% +and so that's what i'm trying trying to + + + align:start position:0% +and so that's what i'm trying trying to +reconcile now + + align:start position:0% +reconcile now + + + align:start position:0% +reconcile now +i think i'll have to reconcile before + + align:start position:0% +i think i'll have to reconcile before + + + align:start position:0% +i think i'll have to reconcile before +the month is out + + align:start position:0% +the month is out + + + align:start position:0% +the month is out +but what happens to a thing + + align:start position:0% +but what happens to a thing + + + align:start position:0% +but what happens to a thing +when it is practiced by + + align:start position:0% +when it is practiced by + + + align:start position:0% +when it is practiced by +a non-practitioner uh uh here's a good + + align:start position:0% +a non-practitioner uh uh here's a good + + + align:start position:0% +a non-practitioner uh uh here's a good +example here's a good example i'll tell + + align:start position:0% +example here's a good example i'll tell + + + align:start position:0% +example here's a good example i'll tell +you a good example i was uh + + align:start position:0% +you a good example i was uh + + + align:start position:0% +you a good example i was uh +getting on the elevator with this + + align:start position:0% +getting on the elevator with this + + + align:start position:0% +getting on the elevator with this +researcher here at mit + + align:start position:0% + + + + align:start position:0% + +uh who is doing research on systems + + align:start position:0% +uh who is doing research on systems + + + align:start position:0% +uh who is doing research on systems +actually i was getting on the elevator + + align:start position:0% +actually i was getting on the elevator + + + align:start position:0% +actually i was getting on the elevator +with him at the airport we ran into each + + align:start position:0% +with him at the airport we ran into each + + + align:start position:0% +with him at the airport we ran into each +other at the airport + + align:start position:0% +other at the airport + + + align:start position:0% +other at the airport +and he's going to this conference + + align:start position:0% +and he's going to this conference + + + align:start position:0% +and he's going to this conference +on systems there's another person here + + align:start position:0% +on systems there's another person here + + + align:start position:0% +on systems there's another person here +at mit who's the president of the + + align:start position:0% +at mit who's the president of the + + + align:start position:0% +at mit who's the president of the +organization + + align:start position:0% +organization + + + align:start position:0% +organization +named pat hale h-a-l-e i don't know if + + align:start position:0% +named pat hale h-a-l-e i don't know if + + + align:start position:0% +named pat hale h-a-l-e i don't know if +you've been + + align:start position:0% +you've been + + + align:start position:0% +you've been +and we were discussing that and he had + + align:start position:0% +and we were discussing that and he had + + + align:start position:0% +and we were discussing that and he had +organized a + + align:start position:0% +organized a + + + align:start position:0% +organized a +session + + align:start position:0% +session + + + align:start position:0% +session +and so i said well you know uh what did + + align:start position:0% +and so i said well you know uh what did + + + align:start position:0% +and so i said well you know uh what did +you organize your session on + + align:start position:0% +you organize your session on + + + align:start position:0% +you organize your session on +and really what he said what he said was + + align:start position:0% + + + + align:start position:0% + +that he belongs to the first generation + + align:start position:0% +that he belongs to the first generation + + + align:start position:0% +that he belongs to the first generation +of systems engineers does it hold up + + align:start position:0% +of systems engineers does it hold up + + + align:start position:0% +of systems engineers does it hold up +what are you talking about systems + + align:start position:0% +what are you talking about systems + + + align:start position:0% +what are you talking about systems +engineers been around before you were + + align:start position:0% +engineers been around before you were + + + align:start position:0% +engineers been around before you were +around he says no they were all + + align:start position:0% +around he says no they were all + + + align:start position:0% +around he says no they were all +this engineer or that + + align:start position:0% +this engineer or that + + + align:start position:0% +this engineer or that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +business person or the other doing + + align:start position:0% +business person or the other doing + + + align:start position:0% +business person or the other doing +systems but we're the first ones who are + + align:start position:0% +systems but we're the first ones who are + + + align:start position:0% +systems but we're the first ones who are +really systems engineer everybody who + + align:start position:0% +really systems engineer everybody who + + + align:start position:0% +really systems engineer everybody who +was my teacher my faculty advisor all of + + align:start position:0% +was my teacher my faculty advisor all of + + + align:start position:0% +was my teacher my faculty advisor all of +these people + + align:start position:0% +these people + + + align:start position:0% +these people +were people who were doing engineering + + align:start position:0% +were people who were doing engineering + + + align:start position:0% +were people who were doing engineering +but they mainly had it from this + + align:start position:0% +but they mainly had it from this + + + align:start position:0% +but they mainly had it from this +perspective of another district + + align:start position:0% +perspective of another district + + + align:start position:0% +perspective of another district +and so we want to organize the young + + align:start position:0% +and so we want to organize the young + + + align:start position:0% +and so we want to organize the young +people to start developing you know + + align:start position:0% +people to start developing you know + + + align:start position:0% +people to start developing you know +a purely systems idea + + align:start position:0% +a purely systems idea + + + align:start position:0% +a purely systems idea +and so + + align:start position:0% +and so + + + align:start position:0% +and so +i think that tells a story about a lot + + align:start position:0% +i think that tells a story about a lot + + + align:start position:0% +i think that tells a story about a lot +of things it tells it about engineering + + align:start position:0% +of things it tells it about engineering + + + align:start position:0% +of things it tells it about engineering +ethics because + + align:start position:0% +ethics because + + + align:start position:0% +ethics because +the the + + align:start position:0% +the the + + + align:start position:0% +the the +people involved were basically mostly + + align:start position:0% +people involved were basically mostly + + + align:start position:0% +people involved were basically mostly +philosophers + + align:start position:0% +philosophers + + + align:start position:0% +philosophers +and they got some engineers and half of + + align:start position:0% +and they got some engineers and half of + + + align:start position:0% +and they got some engineers and half of +the engineers were practicing engineers + + align:start position:0% +the engineers were practicing engineers + + + align:start position:0% +the engineers were practicing engineers +many of them have been whistleblowers + + align:start position:0% +many of them have been whistleblowers + + + align:start position:0% +many of them have been whistleblowers +half of them were academic engineers + + align:start position:0% +half of them were academic engineers + + + align:start position:0% +half of them were academic engineers +so who becomes the first engineering + + align:start position:0% +so who becomes the first engineering + + + align:start position:0% +so who becomes the first engineering +ethicist + + align:start position:0% +ethicist + + + align:start position:0% +ethicist +okay + + align:start position:0% +okay + + + align:start position:0% +okay +well i felt that way when i came out i + + align:start position:0% +well i felt that way when i came out i + + + align:start position:0% +well i felt that way when i came out i +felt that i was in a generation that was + + align:start position:0% +felt that i was in a generation that was + + + align:start position:0% +felt that i was in a generation that was +the first + + align:start position:0% +the first + + + align:start position:0% +the first +engine person who not the first person + + align:start position:0% +engine person who not the first person + + + align:start position:0% +engine person who not the first person +but in the first generation at least not + + align:start position:0% +but in the first generation at least not + + + align:start position:0% +but in the first generation at least not +the first age generation + + align:start position:0% +the first age generation + + + align:start position:0% +the first age generation +but in the first + + align:start position:0% +but in the first + + + align:start position:0% +but in the first +academic generation + + align:start position:0% +academic generation + + + align:start position:0% +academic generation +uh who was doing was doing engineering + + align:start position:0% +uh who was doing was doing engineering + + + align:start position:0% +uh who was doing was doing engineering +ethics with a combined + + align:start position:0% +ethics with a combined + + + align:start position:0% +ethics with a combined +uh approach + + align:start position:0% +uh approach + + + align:start position:0% +uh approach +that some + + align:start position:0% +that some + + + align:start position:0% +that some +that that on occasion developed + + align:start position:0% +that that on occasion developed + + + align:start position:0% +that that on occasion developed +something that was different from the + + align:start position:0% +something that was different from the + + + align:start position:0% +something that was different from the +two things that made it + + align:start position:0% +two things that made it + + + align:start position:0% +two things that made it +and you can do that by + + align:start position:0% +and you can do that by + + + align:start position:0% +and you can do that by +adding to or violating one of the + + align:start position:0% +adding to or violating one of the + + + align:start position:0% +adding to or violating one of the +principles of one of the + + align:start position:0% +principles of one of the + + + align:start position:0% +principles of one of the +one of the participating disciplines + + align:start position:0% +one of the participating disciplines + + + align:start position:0% +one of the participating disciplines +okay and an example of that is the one + + align:start position:0% +okay and an example of that is the one + + + align:start position:0% +okay and an example of that is the one +that where i talk about uh + + align:start position:0% +that where i talk about uh + + + align:start position:0% +that where i talk about uh +the virtue ethics from the standpoint of + + align:start position:0% +the virtue ethics from the standpoint of + + + align:start position:0% +the virtue ethics from the standpoint of +what i had first called african ethics + + align:start position:0% +what i had first called african ethics + + + align:start position:0% +what i had first called african ethics +but now i haven't + + align:start position:0% +but now i haven't + + + align:start position:0% +but now i haven't +i realized that there's all around the + + align:start position:0% +i realized that there's all around the + + + align:start position:0% +i realized that there's all around the +world that there's this whole other + + align:start position:0% +world that there's this whole other + + + align:start position:0% +world that there's this whole other +point of view that's non-western + + align:start position:0% +point of view that's non-western + + + align:start position:0% +point of view that's non-western +and so the question is and + + align:start position:0% +and so the question is and + + + align:start position:0% +and so the question is and +my colleagues at howard are debating me + + align:start position:0% +my colleagues at howard are debating me + + + align:start position:0% +my colleagues at howard are debating me +uh is this an extension of + + align:start position:0% +uh is this an extension of + + + align:start position:0% +uh is this an extension of +greek ethics + + align:start position:0% +greek ethics + + + align:start position:0% +greek ethics +western ethics + + align:start position:0% +western ethics + + + align:start position:0% +western ethics +or is this something different + + align:start position:0% + + + + align:start position:0% + +all right so um + + align:start position:0% + + + + align:start position:0% + +yeah i think that uh + + align:start position:0% + + + + align:start position:0% + +one makes a big mistake when one defines + + align:start position:0% +one makes a big mistake when one defines + + + align:start position:0% +one makes a big mistake when one defines +competency that in in + + align:start position:0% +competency that in in + + + align:start position:0% +competency that in in +in a manner that does not have a moral + + align:start position:0% +in a manner that does not have a moral + + + align:start position:0% +in a manner that does not have a moral +dimension + + align:start position:0% +dimension + + + align:start position:0% +dimension +now and scientists argue now this one + + align:start position:0% +now and scientists argue now this one + + + align:start position:0% +now and scientists argue now this one +used to be a big issue then i'll get on + + align:start position:0% +used to be a big issue then i'll get on + + + align:start position:0% +used to be a big issue then i'll get on +to the point of the + + align:start position:0% + + + + align:start position:0% + +of the um + + align:start position:0% +of the um + + + align:start position:0% +of the um +codes of ethics + + align:start position:0% + + + + align:start position:0% + +there was there were big debates in the + + align:start position:0% +there was there were big debates in the + + + align:start position:0% +there was there were big debates in the +in the 70s and 80s + + align:start position:0% +in the 70s and 80s + + + align:start position:0% +in the 70s and 80s +over the question is + + align:start position:0% +over the question is + + + align:start position:0% +over the question is +science value-free + + align:start position:0% +science value-free + + + align:start position:0% +science value-free +then it got narrowed down to truth + + align:start position:0% +then it got narrowed down to truth + + + align:start position:0% +then it got narrowed down to truth +okay + + align:start position:0% +okay + + + align:start position:0% +okay +squirrel got enough + + align:start position:0% +squirrel got enough + + + align:start position:0% +squirrel got enough +what's the value in that + + align:start position:0% + + + + align:start position:0% + +somebody would argue okay + + align:start position:0% +somebody would argue okay + + + align:start position:0% +somebody would argue okay +so truth + + align:start position:0% +so truth + + + align:start position:0% +so truth +can be separate from values + + align:start position:0% +can be separate from values + + + align:start position:0% +can be separate from values +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you have to ask yourself + + align:start position:0% +you have to ask yourself + + + align:start position:0% +you have to ask yourself +if truth + + align:start position:0% +if truth + + + align:start position:0% +if truth +was not separate from values why would + + align:start position:0% +was not separate from values why would + + + align:start position:0% +was not separate from values why would +we need two different words + + align:start position:0% + + + + align:start position:0% + +truth and values + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +my take on it has come out since you all + + align:start position:0% +my take on it has come out since you all + + + align:start position:0% +my take on it has come out since you all +got me on this road + + align:start position:0% +got me on this road + + + align:start position:0% +got me on this road +i didn't ask i didn't ask for this + + align:start position:0% +i didn't ask i didn't ask for this + + + align:start position:0% +i didn't ask i didn't ask for this +um my take on it + + align:start position:0% + + + + align:start position:0% + +is uh + + align:start position:0% + + + + align:start position:0% + +that truth is value free you can think + + align:start position:0% +that truth is value free you can think + + + align:start position:0% +that truth is value free you can think +about + + align:start position:0% +about + + + align:start position:0% +about +a truthful a truthful statement + + align:start position:0% + + + + align:start position:0% + +and then make a valid judgment about it + + align:start position:0% +and then make a valid judgment about it + + + align:start position:0% +and then make a valid judgment about it +separately + + align:start position:0% +separately + + + align:start position:0% +separately +okay but then i come back and say what + + align:start position:0% +okay but then i come back and say what + + + align:start position:0% +okay but then i come back and say what +is scientific truth + + align:start position:0% + + + + align:start position:0% + +what is scientific truth + + align:start position:0% + + + + align:start position:0% + +and then there's a book if i have two + + align:start position:0% +and then there's a book if i have two + + + align:start position:0% +and then there's a book if i have two +books and + + align:start position:0% +books and + + + align:start position:0% +books and +three books + + align:start position:0% + + + + align:start position:0% + +well let's say two + + align:start position:0% +well let's say two + + + align:start position:0% +well let's say two +um + + align:start position:0% +um + + + align:start position:0% +um +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +i hadn't intended the lecture about but + + align:start position:0% +i hadn't intended the lecture about but + + + align:start position:0% +i hadn't intended the lecture about but +why not + + align:start position:0% +why not + + + align:start position:0% +why not +um we'll just + + align:start position:0% + + + + align:start position:0% + +uh one is called + + align:start position:0% + + + + align:start position:0% + +one is called patterns of discovery + + align:start position:0% + + + + align:start position:0% + +by hanson + + align:start position:0% + + + + align:start position:0% + +and the other is called + + align:start position:0% +and the other is called + + + align:start position:0% +and the other is called +um + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +okay let me start talking dinner to come + + align:start position:0% +okay let me start talking dinner to come + + + align:start position:0% +okay let me start talking dinner to come +to my mind + + align:start position:0% +to my mind + + + align:start position:0% +to my mind +i hadn't prepared for this + + align:start position:0% +i hadn't prepared for this + + + align:start position:0% +i hadn't prepared for this +um + + align:start position:0% + + + + align:start position:0% + +thomas the nature of scientific + + align:start position:0% +thomas the nature of scientific + + + align:start position:0% +thomas the nature of scientific +revolutions + + align:start position:0% + + + + align:start position:0% + +i think it might even be the structure + + align:start position:0% +i think it might even be the structure + + + align:start position:0% +i think it might even be the structure +structure of scientific revolutions + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +both of them talk about something called + + align:start position:0% +both of them talk about something called + + + align:start position:0% +both of them talk about something called +world view + + align:start position:0% +world view + + + align:start position:0% +world view +both of them talk about something called + + align:start position:0% +both of them talk about something called + + + align:start position:0% +both of them talk about something called +gestalt + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so + + align:start position:0% + + + + align:start position:0% + +both of them will talk about this figure + + align:start position:0% +both of them will talk about this figure + + + align:start position:0% +both of them will talk about this figure +and + + align:start position:0% +and + + + align:start position:0% +and +you would not + + align:start position:0% + + + + align:start position:0% + +believe that this figure has a name + + align:start position:0% +believe that this figure has a name + + + align:start position:0% +believe that this figure has a name +called the necker cube + + align:start position:0% + + + + align:start position:0% + +because the swedish psychology + + align:start position:0% +because the swedish psychology + + + align:start position:0% +because the swedish psychology +psychologist studied it + + align:start position:0% +psychologist studied it + + + align:start position:0% +psychologist studied it +i mean we do it in engineering from day + + align:start position:0% +i mean we do it in engineering from day + + + align:start position:0% +i mean we do it in engineering from day +one right + + align:start position:0% +one right + + + align:start position:0% +one right +this thing here if for no other reason + + align:start position:0% +this thing here if for no other reason + + + align:start position:0% +this thing here if for no other reason +then you'll extend this out call that x + + align:start position:0% +then you'll extend this out call that x + + + align:start position:0% +then you'll extend this out call that x +then this up call that y and then this + + align:start position:0% +then this up call that y and then this + + + align:start position:0% +then this up call that y and then this +i'll call that z + + align:start position:0% + + + + align:start position:0% + +for no other reason + + align:start position:0% + + + + align:start position:0% + +now what they'll do is they'll ask if a + + align:start position:0% +now what they'll do is they'll ask if a + + + align:start position:0% +now what they'll do is they'll ask if a +is in front of b + + align:start position:0% +is in front of b + + + align:start position:0% +is in front of b +or is b in front of a + + align:start position:0% + + + + align:start position:0% + +your mind can switch + + align:start position:0% + + + + align:start position:0% + +you can get both takes a minute + + align:start position:0% + + + + align:start position:0% + +is this thing coming out of the board + + align:start position:0% +is this thing coming out of the board + + + align:start position:0% +is this thing coming out of the board +and down to the right + + align:start position:0% +and down to the right + + + align:start position:0% +and down to the right +or is it coming out of the board and up + + align:start position:0% +or is it coming out of the board and up + + + align:start position:0% +or is it coming out of the board and up +to the left + + align:start position:0% + + + + align:start position:0% + +well the point is + + align:start position:0% +well the point is + + + align:start position:0% +well the point is +that we're dealing with gestalt here + + align:start position:0% +that we're dealing with gestalt here + + + align:start position:0% +that we're dealing with gestalt here +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +the whole range + + align:start position:0% +the whole range + + + align:start position:0% +the whole range +of a choice of gestalts + + align:start position:0% +of a choice of gestalts + + + align:start position:0% +of a choice of gestalts +it's called world view + + align:start position:0% +it's called world view + + + align:start position:0% +it's called world view +so if you choose to see that a is in + + align:start position:0% +so if you choose to see that a is in + + + align:start position:0% +so if you choose to see that a is in +front of b and then you see a lot of + + align:start position:0% +front of b and then you see a lot of + + + align:start position:0% +front of b and then you see a lot of +different things with the same kind of + + align:start position:0% +different things with the same kind of + + + align:start position:0% +different things with the same kind of +choice that whole thing + + align:start position:0% +choice that whole thing + + + align:start position:0% +choice that whole thing +forms your world view and somebody + + align:start position:0% +forms your world view and somebody + + + align:start position:0% +forms your world view and somebody +coming in + + align:start position:0% +coming in + + + align:start position:0% +coming in +the door may have a different or + + align:start position:0% +the door may have a different or + + + align:start position:0% +the door may have a different or +overlapping worldview + + align:start position:0% +overlapping worldview + + + align:start position:0% +overlapping worldview +now what they say is that every learned + + align:start position:0% +now what they say is that every learned + + + align:start position:0% +now what they say is that every learned +discipline has + + align:start position:0% +discipline has + + + align:start position:0% +discipline has +it's world view + + align:start position:0% + + + + align:start position:0% + +and that you can walk into a class + + align:start position:0% +and that you can walk into a class + + + align:start position:0% +and that you can walk into a class +and get lost + + align:start position:0% +and get lost + + + align:start position:0% +and get lost +when you are right + + align:start position:0% +when you are right + + + align:start position:0% +when you are right +but you're just looking at it from a + + align:start position:0% +but you're just looking at it from a + + + align:start position:0% +but you're just looking at it from a +different point you're looking at b is + + align:start position:0% +different point you're looking at b is + + + align:start position:0% +different point you're looking at b is +being behind that + + align:start position:0% +being behind that + + + align:start position:0% +being behind that +everybody else is looking at a in front + + align:start position:0% +everybody else is looking at a in front + + + align:start position:0% +everybody else is looking at a in front +of b + + align:start position:0% +of b + + + align:start position:0% +of b +okay because that's the world view + + align:start position:0% +okay because that's the world view + + + align:start position:0% +okay because that's the world view +associated with this learning discipline + + align:start position:0% +associated with this learning discipline + + + align:start position:0% +associated with this learning discipline +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right + + align:start position:0% + + + + align:start position:0% + +so what they say then is + + align:start position:0% +so what they say then is + + + align:start position:0% +so what they say then is +that + + align:start position:0% +that + + + align:start position:0% +that +when you talk about the truth + + align:start position:0% + + + + align:start position:0% + +that's one thing but when you talk about + + align:start position:0% +that's one thing but when you talk about + + + align:start position:0% +that's one thing but when you talk about +scientific truth in the context of a + + align:start position:0% +scientific truth in the context of a + + + align:start position:0% +scientific truth in the context of a +scientific world view + + align:start position:0% + + + + align:start position:0% + +you're talking about looking at it + + align:start position:0% +you're talking about looking at it + + + align:start position:0% +you're talking about looking at it +this way as opposed to another way + + align:start position:0% +this way as opposed to another way + + + align:start position:0% +this way as opposed to another way +you're not talking about always looking + + align:start position:0% +you're not talking about always looking + + + align:start position:0% +you're not talking about always looking +at the truth + + align:start position:0% +at the truth + + + align:start position:0% +at the truth +and so therefore you have put a value of + + align:start position:0% +and so therefore you have put a value of + + + align:start position:0% +and so therefore you have put a value of +judgment on why you want to look at it + + align:start position:0% +judgment on why you want to look at it + + + align:start position:0% +judgment on why you want to look at it +that way + + align:start position:0% +that way + + + align:start position:0% +that way +as opposed to the other and that value + + align:start position:0% +as opposed to the other and that value + + + align:start position:0% +as opposed to the other and that value +judgment has moral implications + + align:start position:0% + + + + align:start position:0% + +so i go before these people and say yeah + + align:start position:0% +so i go before these people and say yeah + + + align:start position:0% +so i go before these people and say yeah +truth is value free but scientific truth + + align:start position:0% +truth is value free but scientific truth + + + align:start position:0% +truth is value free but scientific truth +isn't + + align:start position:0% +isn't + + + align:start position:0% +isn't +because you have chosen + + align:start position:0% +because you have chosen + + + align:start position:0% +because you have chosen +then + + align:start position:0% +then + + + align:start position:0% +then +to look at it a certain way when you + + align:start position:0% +to look at it a certain way when you + + + align:start position:0% +to look at it a certain way when you +could have + + align:start position:0% +could have + + + align:start position:0% +could have +looked at it another way + + align:start position:0% + + + + align:start position:0% + +and then what kuhn comes along and says + + align:start position:0% +and then what kuhn comes along and says + + + align:start position:0% +and then what kuhn comes along and says +is that's how we get paradigm shifts + + align:start position:0% +is that's how we get paradigm shifts + + + align:start position:0% +is that's how we get paradigm shifts +in the disciplines somebody says we all + + align:start position:0% +in the disciplines somebody says we all + + + align:start position:0% +in the disciplines somebody says we all +better look at it the other way + + align:start position:0% + + + + align:start position:0% + +and when everybody starts changing their + + align:start position:0% +and when everybody starts changing their + + + align:start position:0% +and when everybody starts changing their +world view when they actually + + align:start position:0% +world view when they actually + + + align:start position:0% +world view when they actually +when they look at the same thing and + + align:start position:0% +when they look at the same thing and + + + align:start position:0% +when they look at the same thing and +actually see something different + + align:start position:0% + + + + align:start position:0% + +then you've got + + align:start position:0% +then you've got + + + align:start position:0% +then you've got +a paradigm shift + + align:start position:0% +a paradigm shift + + + align:start position:0% +a paradigm shift +and now you talk about why people get no + + align:start position:0% +and now you talk about why people get no + + + align:start position:0% +and now you talk about why people get no +girlfriends + + align:start position:0% + + + + align:start position:0% + +why people write dissertation + + align:start position:0% +why people write dissertation + + + align:start position:0% +why people write dissertation +master species + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +uh thomas cool was actually here + + align:start position:0% + + + + align:start position:0% + +he was a historian he was a historian + + align:start position:0% + + + + align:start position:0% + +so i and and he uses that thesis + + align:start position:0% +so i and and he uses that thesis + + + align:start position:0% +so i and and he uses that thesis +to do history of science + + align:start position:0% +to do history of science + + + align:start position:0% +to do history of science +and + + align:start position:0% +and + + + align:start position:0% +and +that thesis then tells him how to break + + align:start position:0% +that thesis then tells him how to break + + + align:start position:0% +that thesis then tells him how to break +up the errors + + align:start position:0% +up the errors + + + align:start position:0% +up the errors +and that between this era and that there + + align:start position:0% +and that between this era and that there + + + align:start position:0% +and that between this era and that there +was a paradigm shift and the paradigm + + align:start position:0% +was a paradigm shift and the paradigm + + + align:start position:0% +was a paradigm shift and the paradigm +shift was like that + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and this stuff is very interesting um + + align:start position:0% +and this stuff is very interesting um + + + align:start position:0% +and this stuff is very interesting um +we look at it and everybody agrees that + + align:start position:0% +we look at it and everybody agrees that + + + align:start position:0% +we look at it and everybody agrees that +this in fact is a cube i don't care how + + align:start position:0% +this in fact is a cube i don't care how + + + align:start position:0% +this in fact is a cube i don't care how +many people you get i mean you ask them + + align:start position:0% +many people you get i mean you ask them + + + align:start position:0% +many people you get i mean you ask them +what do they see and everybody will + + align:start position:0% +what do they see and everybody will + + + align:start position:0% +what do they see and everybody will +agree that it's a cute + + align:start position:0% +agree that it's a cute + + + align:start position:0% +agree that it's a cute +let's just think about it + + align:start position:0% +let's just think about it + + + align:start position:0% +let's just think about it +and this is what hanson does i mean what + + align:start position:0% +and this is what hanson does i mean what + + + align:start position:0% +and this is what hanson does i mean what +uh hanson does + + align:start position:0% +uh hanson does + + + align:start position:0% +uh hanson does +he says just think about it i asked you + + align:start position:0% +he says just think about it i asked you + + + align:start position:0% +he says just think about it i asked you +what do you did you see i didn't ask you + + align:start position:0% +what do you did you see i didn't ask you + + + align:start position:0% +what do you did you see i didn't ask you +what this represents + + align:start position:0% +what this represents + + + align:start position:0% +what this represents +i ask you what do you actually see + + align:start position:0% +i ask you what do you actually see + + + align:start position:0% +i ask you what do you actually see +everybody says acute + + align:start position:0% +everybody says acute + + + align:start position:0% +everybody says acute +it's not a cue it's a flat + + align:start position:0% +it's not a cue it's a flat + + + align:start position:0% +it's not a cue it's a flat +it's 12 lines on a flat surface + + align:start position:0% +it's 12 lines on a flat surface + + + align:start position:0% +it's 12 lines on a flat surface +actually what your brain sees is not + + align:start position:0% +actually what your brain sees is not + + + align:start position:0% +actually what your brain sees is not +even a line it's it's a bitmap + + align:start position:0% +even a line it's it's a bitmap + + + align:start position:0% +even a line it's it's a bitmap +you got white dots and black dots in + + align:start position:0% +you got white dots and black dots in + + + align:start position:0% +you got white dots and black dots in +here + + align:start position:0% +here + + + align:start position:0% +here +so your brain is doing all of this work + + align:start position:0% +so your brain is doing all of this work + + + align:start position:0% +so your brain is doing all of this work +to organize what your experience so that + + align:start position:0% +to organize what your experience so that + + + align:start position:0% +to organize what your experience so that +you can understand it so you can get + + align:start position:0% +you can understand it so you can get + + + align:start position:0% +you can understand it so you can get +meaning out of it + + align:start position:0% +meaning out of it + + + align:start position:0% +meaning out of it +but basically this is not even a cube + + align:start position:0% + + + + align:start position:0% + +now there's a artist + + align:start position:0% +now there's a artist + + + align:start position:0% +now there's a artist +that deals with this issue + + align:start position:0% + + + + align:start position:0% + +now i'm going to right tell you who this + + align:start position:0% +now i'm going to right tell you who this + + + align:start position:0% +now i'm going to right tell you who this +artist is + + align:start position:0% +artist is + + + align:start position:0% +artist is +and i'm going to tell you that + + align:start position:0% + + + + align:start position:0% + +only one or two pieces of his work + + align:start position:0% +only one or two pieces of his work + + + align:start position:0% +only one or two pieces of his work +come through to me but maybe you see + + align:start position:0% +come through to me but maybe you see + + + align:start position:0% +come through to me but maybe you see +mondrian + + align:start position:0% + + + + align:start position:0% + +because mondrian knows how to draw and + + align:start position:0% +because mondrian knows how to draw and + + + align:start position:0% +because mondrian knows how to draw and +color a neck of cube so it looks flat + + align:start position:0% + + + + align:start position:0% + +whereas picasso + + align:start position:0% +whereas picasso + + + align:start position:0% +whereas picasso +can use + + align:start position:0% +can use + + + align:start position:0% +can use +six to ten of them + + align:start position:0% +six to ten of them + + + align:start position:0% +six to ten of them +to draw your face + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +well that's the kind of thing we need to + + align:start position:0% +well that's the kind of thing we need to + + + align:start position:0% +well that's the kind of thing we need to +do in this class i mean not we haven't + + align:start position:0% +do in this class i mean not we haven't + + + align:start position:0% +do in this class i mean not we haven't +been doing but + + align:start position:0% +been doing but + + + align:start position:0% +been doing but +yeah what what does it what is + + align:start position:0% + + + + align:start position:0% + +what is truth + + align:start position:0% +what is truth + + + align:start position:0% +what is truth +well let's let's play with that what do + + align:start position:0% +well let's let's play with that what do + + + align:start position:0% +well let's let's play with that what do +you mean absolutely + + align:start position:0% + + + + align:start position:0% + +what does the word truth mean + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +okay + + align:start position:0% +okay + + + align:start position:0% +okay +well um + + align:start position:0% +well um + + + align:start position:0% +well um +aristotle played around with that + + align:start position:0% +aristotle played around with that + + + align:start position:0% +aristotle played around with that +question + + align:start position:0% +question + + + align:start position:0% +question +plato did too and uh they they they went + + align:start position:0% +plato did too and uh they they they went + + + align:start position:0% +plato did too and uh they they they went +very far they went at least 50 percent + + align:start position:0% +very far they went at least 50 percent + + + align:start position:0% +very far they went at least 50 percent +accomplished + + align:start position:0% +accomplished + + + align:start position:0% +accomplished +50 of the question + + align:start position:0% +50 of the question + + + align:start position:0% +50 of the question +and the rest of us have accomplished + + align:start position:0% +and the rest of us have accomplished + + + align:start position:0% +and the rest of us have accomplished +added to that maybe we're at 90 + + align:start position:0% + + + + align:start position:0% + +let's speculate on that + + align:start position:0% + + + + align:start position:0% + +what did we mean by well plato + + align:start position:0% +what did we mean by well plato + + + align:start position:0% +what did we mean by well plato +said + + align:start position:0% +said + + + align:start position:0% +said +you want to think about it + + align:start position:0% +you want to think about it + + + align:start position:0% +you want to think about it +you want me to talk + + align:start position:0% + + + + align:start position:0% + +okay hi tony plato said we're talking + + align:start position:0% +okay hi tony plato said we're talking + + + align:start position:0% +okay hi tony plato said we're talking +about + + align:start position:0% +about + + + align:start position:0% +about +what is truth + + align:start position:0% +what is truth + + + align:start position:0% +what is truth +and i don't consider that a diversion i + + align:start position:0% +and i don't consider that a diversion i + + + align:start position:0% +and i don't consider that a diversion i +wanted to talk about codes of ethics + + align:start position:0% +wanted to talk about codes of ethics + + + align:start position:0% +wanted to talk about codes of ethics +today + + align:start position:0% +today + + + align:start position:0% +today +frankly the question of what is truth is + + align:start position:0% +frankly the question of what is truth is + + + align:start position:0% +frankly the question of what is truth is +more interesting than codes + + align:start position:0% + + + + align:start position:0% + +but i'm looking at the clock we got time + + align:start position:0% +but i'm looking at the clock we got time + + + align:start position:0% +but i'm looking at the clock we got time +we got time we got time we've got time + + align:start position:0% +we got time we got time we've got time + + + align:start position:0% +we got time we got time we've got time +this is what an uh philosophy class is + + align:start position:0% +this is what an uh philosophy class is + + + align:start position:0% +this is what an uh philosophy class is +supposed to be like + + align:start position:0% +supposed to be like + + + align:start position:0% +supposed to be like +uh supposed to be 75 ad hoc + + align:start position:0% + + + + align:start position:0% + +i wouldn't say that that about a math + + align:start position:0% +i wouldn't say that that about a math + + + align:start position:0% +i wouldn't say that that about a math +class + + align:start position:0% +class + + + align:start position:0% +class +but + + align:start position:0% +but + + + align:start position:0% +but +okay let me start talking but i want + + align:start position:0% +okay let me start talking but i want + + + align:start position:0% +okay let me start talking but i want +you all to uh take over the conversation + + align:start position:0% +you all to uh take over the conversation + + + align:start position:0% +you all to uh take over the conversation +if you can get to + + align:start position:0% +if you can get to + + + align:start position:0% +if you can get to +get to it all right + + align:start position:0% +get to it all right + + + align:start position:0% +get to it all right +let me start with plato plato said well + + align:start position:0% + + + + align:start position:0% + +let's not talk about truth first let's + + align:start position:0% +let's not talk about truth first let's + + + align:start position:0% +let's not talk about truth first let's +talk about something else first + + align:start position:0% +talk about something else first + + + align:start position:0% +talk about something else first +let's talk about knowledge what is + + align:start position:0% +let's talk about knowledge what is + + + align:start position:0% +let's talk about knowledge what is +knowledge + + align:start position:0% + + + + align:start position:0% + +and plato said well + + align:start position:0% +and plato said well + + + align:start position:0% +and plato said well +a knowledge + + align:start position:0% +a knowledge + + + align:start position:0% +a knowledge +knowledge is a statement that is a + + align:start position:0% +knowledge is a statement that is a + + + align:start position:0% +knowledge is a statement that is a +sentence that's either true or false + + align:start position:0% + + + + align:start position:0% + +and that there are two kinds of + + align:start position:0% +and that there are two kinds of + + + align:start position:0% +and that there are two kinds of +knowledge + + align:start position:0% +knowledge + + + align:start position:0% +knowledge +statement + + align:start position:0% +statement + + + align:start position:0% +statement +one is a statement + + align:start position:0% +one is a statement + + + align:start position:0% +one is a statement +that agrees + + align:start position:0% + + + + align:start position:0% + +with + + align:start position:0% +with + + + align:start position:0% +with +other + + align:start position:0% +other + + + align:start position:0% +other +knowledge statements by + + align:start position:0% +knowledge statements by + + + align:start position:0% +knowledge statements by +according to the rules of logic and + + align:start position:0% +according to the rules of logic and + + + align:start position:0% +according to the rules of logic and +reason + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% +so um + + + align:start position:0% +so um +and that's called rational + + align:start position:0% +and that's called rational + + + align:start position:0% +and that's called rational +knowledge + + align:start position:0% + + + + align:start position:0% + +the other one + + align:start position:0% +the other one + + + align:start position:0% +the other one +is a statement that agrees + + align:start position:0% +is a statement that agrees + + + align:start position:0% +is a statement that agrees +with observation or experience i'll put + + align:start position:0% +with observation or experience i'll put + + + align:start position:0% +with observation or experience i'll put +observation but i don't mean just the + + align:start position:0% +observation but i don't mean just the + + + align:start position:0% +observation but i don't mean just the +eye i mean all five senses + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +there's a cup of coffee on the table + + align:start position:0% +there's a cup of coffee on the table + + + align:start position:0% +there's a cup of coffee on the table +that's a statement of knowledge + + align:start position:0% + + + + align:start position:0% + +no it's the same thing it's an + + align:start position:0% +no it's the same thing it's an + + + align:start position:0% +no it's the same thing it's an +observation of a fact + + align:start position:0% +observation of a fact + + + align:start position:0% +observation of a fact +it's a statement that describes an + + align:start position:0% +it's a statement that describes an + + + align:start position:0% +it's a statement that describes an +observation of effect + + align:start position:0% +observation of effect + + + align:start position:0% +observation of effect +or it is a fact because + + align:start position:0% +or it is a fact because + + + align:start position:0% +or it is a fact because +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it is information that is coming to my + + align:start position:0% +it is information that is coming to my + + + align:start position:0% +it is information that is coming to my +brain + + align:start position:0% +brain + + + align:start position:0% +brain +from of the type that i call sensory + + align:start position:0% +from of the type that i call sensory + + + align:start position:0% +from of the type that i call sensory +information + + align:start position:0% + + + + align:start position:0% + +and then what i would speculate on is + + align:start position:0% +and then what i would speculate on is + + + align:start position:0% +and then what i would speculate on is +that that sensory information comes from + + align:start position:0% +that that sensory information comes from + + + align:start position:0% +that that sensory information comes from +some place outside of the mind + + align:start position:0% + + + + align:start position:0% + +call it real world + + align:start position:0% + + + + align:start position:0% + +okay so a knowledge statement + + align:start position:0% +okay so a knowledge statement + + + align:start position:0% +okay so a knowledge statement +well + + align:start position:0% +well + + + align:start position:0% +well +you might come along and say i said this + + align:start position:0% +you might come along and say i said this + + + align:start position:0% +you might come along and say i said this +was a cup of coffee + + align:start position:0% +was a cup of coffee + + + align:start position:0% +was a cup of coffee +i analyzed there's some coffee in it but + + align:start position:0% +i analyzed there's some coffee in it but + + + align:start position:0% +i analyzed there's some coffee in it but +there's really strychnine in there + + align:start position:0% +there's really strychnine in there + + + align:start position:0% +there's really strychnine in there +okay pretty soon no more dr drew right + + align:start position:0% +okay pretty soon no more dr drew right + + + align:start position:0% +okay pretty soon no more dr drew right +right so plato had doesn't have any + + align:start position:0% +right so plato had doesn't have any + + + align:start position:0% +right so plato had doesn't have any +problems with that + + align:start position:0% +problems with that + + + align:start position:0% +problems with that +plato says + + align:start position:0% +plato says + + + align:start position:0% +plato says +that you can improve upon your knowledge + + align:start position:0% +that you can improve upon your knowledge + + + align:start position:0% +that you can improve upon your knowledge +statements and in the limit + + align:start position:0% + + + + align:start position:0% + +you get the truth + + align:start position:0% +you get the truth + + + align:start position:0% +you get the truth +that's why plato is very happy to say we + + align:start position:0% +that's why plato is very happy to say we + + + align:start position:0% +that's why plato is very happy to say we +pursue the truth + + align:start position:0% + + + + align:start position:0% + +uh but we make knowledge claims + + align:start position:0% + + + + align:start position:0% + +you do the same thing when it comes to + + align:start position:0% +you do the same thing when it comes to + + + align:start position:0% +you do the same thing when it comes to +um + + align:start position:0% +um + + + align:start position:0% +um +to value judgments + + align:start position:0% +to value judgments + + + align:start position:0% +to value judgments +you make a value judgment and in the + + align:start position:0% +you make a value judgment and in the + + + align:start position:0% +you make a value judgment and in the +limit you get the good + + align:start position:0% + + + + align:start position:0% + +okay so now this is called rational + + align:start position:0% +okay so now this is called rational + + + align:start position:0% +okay so now this is called rational +knowledge + + align:start position:0% + + + + align:start position:0% + +and this is called empirical + + align:start position:0% + + + + align:start position:0% + +knowledge + + align:start position:0% + + + + align:start position:0% + +you can also say values + + align:start position:0% +you can also say values + + + align:start position:0% +you can also say values +value judgments and get the good + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then one then he says plato says + + align:start position:0% + + + + align:start position:0% + +that if you put these two together and + + align:start position:0% +that if you put these two together and + + + align:start position:0% +that if you put these two together and +say that imagine that there is + + align:start position:0% +say that imagine that there is + + + align:start position:0% +say that imagine that there is +that this limit does + + align:start position:0% +that this limit does + + + align:start position:0% +that this limit does +okay + + align:start position:0% +okay + + + align:start position:0% +okay +what do you think plato or what do you + + align:start position:0% +what do you think plato or what do you + + + align:start position:0% +what do you think plato or what do you +think pretty much + + align:start position:0% +think pretty much + + + align:start position:0% +think pretty much +90 of any of the philosophers that are + + align:start position:0% +90 of any of the philosophers that are + + + align:start position:0% +90 of any of the philosophers that are +out here what do you think they would + + align:start position:0% +out here what do you think they would + + + align:start position:0% +out here what do you think they would +call + + align:start position:0% +call + + + align:start position:0% +call +the truth and the good + + align:start position:0% + + + + align:start position:0% + +if there's something out there + + align:start position:0% +if there's something out there + + + align:start position:0% +if there's something out there +that is perfect + + align:start position:0% +that is perfect + + + align:start position:0% +that is perfect +yes + + align:start position:0% +yes + + + align:start position:0% +yes +that's plato's theology he calls this + + align:start position:0% +that's plato's theology he calls this + + + align:start position:0% +that's plato's theology he calls this +god + + align:start position:0% + + + + align:start position:0% + +values that's uh + + align:start position:0% +values that's uh + + + align:start position:0% +values that's uh +an aesthetic value + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +well it's hard to put in words + + align:start position:0% +well it's hard to put in words + + + align:start position:0% +well it's hard to put in words +all right let me let me let me give you + + align:start position:0% +all right let me let me let me give you + + + align:start position:0% +all right let me let me let me give you +a a a starting point mathematics is + + align:start position:0% +a a a starting point mathematics is + + + align:start position:0% +a a a starting point mathematics is +rational novel + + align:start position:0% +rational novel + + + align:start position:0% +rational novel +it makes no + + align:start position:0% +it makes no + + + align:start position:0% +it makes no +reference to experience + + align:start position:0% +reference to experience + + + align:start position:0% +reference to experience +or to objects + + align:start position:0% + + + + align:start position:0% + +all right you ready for this + + align:start position:0% + + + + align:start position:0% + +can you see this + + align:start position:0% +can you see this + + + align:start position:0% +can you see this +uh up at the top + + align:start position:0% +uh up at the top + + + align:start position:0% +uh up at the top +i'll tell you well + + align:start position:0% + + + + align:start position:0% + +so like math + + align:start position:0% +so like math + + + align:start position:0% +so like math +saying that the derivative + + align:start position:0% + + + + align:start position:0% + +of the natural log + + align:start position:0% + + + + align:start position:0% + +is is + + align:start position:0% +is is + + + align:start position:0% +is is +knowledge but it makes no sense unless + + align:start position:0% +knowledge but it makes no sense unless + + + align:start position:0% +knowledge but it makes no sense unless +you know what the others what derivative + + align:start position:0% +you know what the others what derivative + + + align:start position:0% +you know what the others what derivative +means + + align:start position:0% +means + + + align:start position:0% +means +you got definitions + + align:start position:0% +you got definitions + + + align:start position:0% +you got definitions +start with definitions + + align:start position:0% +start with definitions + + + align:start position:0% +start with definitions +you got symbols + + align:start position:0% +you got symbols + + + align:start position:0% +you got symbols +and you got rules for putting them + + align:start position:0% +and you got rules for putting them + + + align:start position:0% +and you got rules for putting them +together you call that syntax + + align:start position:0% +together you call that syntax + + + align:start position:0% +together you call that syntax +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then you have rules for deducing + + align:start position:0% +and then you have rules for deducing + + + align:start position:0% +and then you have rules for deducing +other + + align:start position:0% +other + + + align:start position:0% +other +uh symbols you call that semantics so + + align:start position:0% +uh symbols you call that semantics so + + + align:start position:0% +uh symbols you call that semantics so +now we're talking about deducing + + align:start position:0% +now we're talking about deducing + + + align:start position:0% +now we're talking about deducing +a theorem + + align:start position:0% +a theorem + + + align:start position:0% +a theorem +from an accident + + align:start position:0% +from an accident + + + align:start position:0% +from an accident +uh + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +or i'm gonna be a little bit more + + align:start position:0% +or i'm gonna be a little bit more + + + align:start position:0% +or i'm gonna be a little bit more +it is not empirical + + align:start position:0% + + + + align:start position:0% + +i don't want to say that it can opposite + + align:start position:0% +i don't want to say that it can opposite + + + align:start position:0% +i don't want to say that it can opposite +we throw that all out it's all + + align:start position:0% +we throw that all out it's all + + + align:start position:0% +we throw that all out it's all +mental and it's all reasonable + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +right i can put a rock here and then a + + align:start position:0% +right i can put a rock here and then a + + + align:start position:0% +right i can put a rock here and then a +smaller rock and a smaller one and a + + align:start position:0% +smaller rock and a smaller one and a + + + align:start position:0% +smaller rock and a smaller one and a +smaller one + + align:start position:0% +smaller one + + + align:start position:0% +smaller one +we can even go down to + + align:start position:0% +we can even go down to + + + align:start position:0% +we can even go down to +an atomic particle + + align:start position:0% +an atomic particle + + + align:start position:0% +an atomic particle +and keep going we still haven't got a + + align:start position:0% +and keep going we still haven't got a + + + align:start position:0% +and keep going we still haven't got a +point + + align:start position:0% +point + + + align:start position:0% +point +but we can still talk about a point + + align:start position:0% + + + + align:start position:0% + +and all kinds of stuff + + align:start position:0% + + + + align:start position:0% + +that's right + + align:start position:0% + + + + align:start position:0% + +so what kant wanted to do is take that + + align:start position:0% +so what kant wanted to do is take that + + + align:start position:0% +so what kant wanted to do is take that +kind of thinking out of the + + align:start position:0% +kind of thinking out of the + + + align:start position:0% +kind of thinking out of the +scientific realm + + align:start position:0% +scientific realm + + + align:start position:0% +scientific realm +and say i want + + align:start position:0% +and say i want + + + align:start position:0% +and say i want +to base a value judgment + + align:start position:0% + + + + align:start position:0% + +strictly off of the rational process + + align:start position:0% +strictly off of the rational process + + + align:start position:0% +strictly off of the rational process +quickly + + align:start position:0% +quickly + + + align:start position:0% +quickly +and bill said i want to make a rational + + align:start position:0% +and bill said i want to make a rational + + + align:start position:0% +and bill said i want to make a rational +judgment + + align:start position:0% +judgment + + + align:start position:0% +judgment +strictly out of the empirical + + align:start position:0% +strictly out of the empirical + + + align:start position:0% +strictly out of the empirical +uh thinking knowledge statements + + align:start position:0% +uh thinking knowledge statements + + + align:start position:0% +uh thinking knowledge statements +so they took all of this stuff and put + + align:start position:0% +so they took all of this stuff and put + + + align:start position:0% +so they took all of this stuff and put +it into the value domain + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now let's let's talk some more + + align:start position:0% +now let's let's talk some more + + + align:start position:0% +now let's let's talk some more +about empirical knowledge + + align:start position:0% +about empirical knowledge + + + align:start position:0% +about empirical knowledge +all right + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +let's talk some more + + align:start position:0% +let's talk some more + + + align:start position:0% +let's talk some more +there is um + + align:start position:0% + + + + align:start position:0% + +a genre of story + + align:start position:0% + + + + align:start position:0% + +that all start the same way they end + + align:start position:0% +that all start the same way they end + + + align:start position:0% +that all start the same way they end +slightly differently but they all start + + align:start position:0% +slightly differently but they all start + + + align:start position:0% +slightly differently but they all start +the same way + + align:start position:0% + + + + align:start position:0% + +and we get a lot out of this + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you're driving along someplace + + align:start position:0% + + + + align:start position:0% + +you look down something looks funny + + align:start position:0% +you look down something looks funny + + + align:start position:0% +you look down something looks funny +about your car + + align:start position:0% +about your car + + + align:start position:0% +about your car +okay + + align:start position:0% +okay + + + align:start position:0% +okay +or for whatever reason you get off 95 + + align:start position:0% +or for whatever reason you get off 95 + + + align:start position:0% +or for whatever reason you get off 95 +that the main highway get on some little + + align:start position:0% +that the main highway get on some little + + + align:start position:0% +that the main highway get on some little +road + + align:start position:0% +road + + + align:start position:0% +road +going down this little road and then + + align:start position:0% +going down this little road and then + + + align:start position:0% +going down this little road and then +no houses no gas stations + + align:start position:0% +no houses no gas stations + + + align:start position:0% +no houses no gas stations +just driving down this little road it's + + align:start position:0% +just driving down this little road it's + + + align:start position:0% +just driving down this little road it's +getting dark + + align:start position:0% +getting dark + + + align:start position:0% +getting dark +and your car stops and the road comes to + + align:start position:0% +and your car stops and the road comes to + + + align:start position:0% +and your car stops and the road comes to +an end and you're nothing but there with + + align:start position:0% +an end and you're nothing but there with + + + align:start position:0% +an end and you're nothing but there with +the woods + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +for some reason you decide to get out of + + align:start position:0% +for some reason you decide to get out of + + + align:start position:0% +for some reason you decide to get out of +your car and walk through the woods you + + align:start position:0% +your car and walk through the woods you + + + align:start position:0% +your car and walk through the woods you +gotta run into something shopping center + + align:start position:0% + + + + align:start position:0% + +you run into a monastery + + align:start position:0% + + + + align:start position:0% + +and you knock on the door + + align:start position:0% +and you knock on the door + + + align:start position:0% +and you knock on the door +and hear a voice on the other side + + align:start position:0% +and hear a voice on the other side + + + align:start position:0% +and hear a voice on the other side +talking to you there's a little window + + align:start position:0% +talking to you there's a little window + + + align:start position:0% +talking to you there's a little window +in the door a little window with + + align:start position:0% +in the door a little window with + + + align:start position:0% +in the door a little window with +these can pass + + align:start position:0% +these can pass + + + align:start position:0% +these can pass +and + + align:start position:0% +and + + + align:start position:0% +and +everybody has + + align:start position:0% +everybody has + + + align:start position:0% +everybody has +can speak the same like english + + align:start position:0% +can speak the same like english + + + align:start position:0% +can speak the same like english +all right + + align:start position:0% +all right + + + align:start position:0% +all right +now all of the stories thought the same + + align:start position:0% +now all of the stories thought the same + + + align:start position:0% +now all of the stories thought the same +way i'm gonna + + align:start position:0% +way i'm gonna + + + align:start position:0% +way i'm gonna +tell two of them + + align:start position:0% + + + + align:start position:0% + +now uh one of them is that + + align:start position:0% + + + + align:start position:0% + +they tell you to go away at first you + + align:start position:0% +they tell you to go away at first you + + + align:start position:0% +they tell you to go away at first you +say you're hungry you need a place to + + align:start position:0% +say you're hungry you need a place to + + + align:start position:0% +say you're hungry you need a place to +sleep and tell you to go away you keep + + align:start position:0% +sleep and tell you to go away you keep + + + align:start position:0% +sleep and tell you to go away you keep +knocking on the banging on the door + + align:start position:0% +knocking on the banging on the door + + + align:start position:0% +knocking on the banging on the door +and + + align:start position:0% + + + + align:start position:0% + +all of a sudden + + align:start position:0% +all of a sudden + + + align:start position:0% +all of a sudden +that little window falls open by itself + + align:start position:0% +that little window falls open by itself + + + align:start position:0% +that little window falls open by itself +nobody opened it it just falls open and + + align:start position:0% +nobody opened it it just falls open and + + + align:start position:0% +nobody opened it it just falls open and +you get a peek inside + + align:start position:0% + + + + align:start position:0% + +and you look in there + + align:start position:0% +and you look in there + + + align:start position:0% +and you look in there +and + + align:start position:0% +and + + + align:start position:0% +and +everything + + align:start position:0% +everything + + + align:start position:0% +everything +is yellow + + align:start position:0% + + + + align:start position:0% + +floor + + align:start position:0% + + + + align:start position:0% + +walls chairs the desk their food + + align:start position:0% + + + + align:start position:0% + +their skin + + align:start position:0% +their skin + + + align:start position:0% +their skin +their eyes their hair + + align:start position:0% +their eyes their hair + + + align:start position:0% +their eyes their hair +everything is yellow + + align:start position:0% + + + + align:start position:0% + +everything is yellow + + align:start position:0% + + + + align:start position:0% + +then you say why is everything yellow + + align:start position:0% +then you say why is everything yellow + + + align:start position:0% +then you say why is everything yellow +they don't have the word yellow + + align:start position:0% +they don't have the word yellow + + + align:start position:0% +they don't have the word yellow +in their vocabulary + + align:start position:0% + + + + align:start position:0% + +then you reach in your hand and for some + + align:start position:0% +then you reach in your hand and for some + + + align:start position:0% +then you reach in your hand and for some +let's say you had a pen that had red ink + + align:start position:0% +let's say you had a pen that had red ink + + + align:start position:0% +let's say you had a pen that had red ink +in it so you squirt some red ink in + + align:start position:0% +in it so you squirt some red ink in + + + align:start position:0% +in it so you squirt some red ink in +there + + align:start position:0% +there + + + align:start position:0% +there +all of a sudden two words comes into the + + align:start position:0% +all of a sudden two words comes into the + + + align:start position:0% +all of a sudden two words comes into the +vocabulary at the same time red and + + align:start position:0% +vocabulary at the same time red and + + + align:start position:0% +vocabulary at the same time red and +yellow + + align:start position:0% + + + + align:start position:0% + +then they get to talk and then they + + align:start position:0% +then they get to talk and then they + + + align:start position:0% +then they get to talk and then they +might then they find the word color to + + align:start position:0% +might then they find the word color to + + + align:start position:0% +might then they find the word color to +account for both of them and distinguish + + align:start position:0% +account for both of them and distinguish + + + align:start position:0% +account for both of them and distinguish +color from other things but they were + + align:start position:0% +color from other things but they were + + + align:start position:0% +color from other things but they were +they had yellow in front of them all + + align:start position:0% +they had yellow in front of them all + + + align:start position:0% +they had yellow in front of them all +along but they couldn't see + + align:start position:0% +along but they couldn't see + + + align:start position:0% +along but they couldn't see +or they could see it + + align:start position:0% +or they could see it + + + align:start position:0% +or they could see it +couldn't distinguish it + + align:start position:0% +couldn't distinguish it + + + align:start position:0% +couldn't distinguish it +only when they got that other color in + + align:start position:0% +only when they got that other color in + + + align:start position:0% +only when they got that other color in +there could they distinguish it but then + + align:start position:0% +there could they distinguish it but then + + + align:start position:0% +there could they distinguish it but then +red and yellow come in + + align:start position:0% +red and yellow come in + + + align:start position:0% +red and yellow come in +their + + align:start position:0% +their + + + align:start position:0% +their +language at the same time + + align:start position:0% +language at the same time + + + align:start position:0% +language at the same time +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so now that's what kuhn is talking about + + align:start position:0% +so now that's what kuhn is talking about + + + align:start position:0% +so now that's what kuhn is talking about +when he says + + align:start position:0% +when he says + + + align:start position:0% +when he says +apparent a new paradigm + + align:start position:0% +apparent a new paradigm + + + align:start position:0% +apparent a new paradigm +he's not saying that somebody's going to + + align:start position:0% +he's not saying that somebody's going to + + + align:start position:0% +he's not saying that somebody's going to +show you something that you've never + + align:start position:0% +show you something that you've never + + + align:start position:0% +show you something that you've never +seen before + + align:start position:0% +seen before + + + align:start position:0% +seen before +what he's going to say is you're going + + align:start position:0% +what he's going to say is you're going + + + align:start position:0% +what he's going to say is you're going +to say + + align:start position:0% +to say + + + align:start position:0% +to say +i don't know what word to use + + align:start position:0% +i don't know what word to use + + + align:start position:0% +i don't know what word to use +about my experience with this thing it + + align:start position:0% +about my experience with this thing it + + + align:start position:0% +about my experience with this thing it +was here all along + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +did i see it + + align:start position:0% +did i see it + + + align:start position:0% +did i see it +no then you have to find a lot of + + align:start position:0% +no then you have to find a lot of + + + align:start position:0% +no then you have to find a lot of +different words to describe what you did + + align:start position:0% +different words to describe what you did + + + align:start position:0% +different words to describe what you did +see + + align:start position:0% +see + + + align:start position:0% +see +and you still won't be and you'll wind + + align:start position:0% +and you still won't be and you'll wind + + + align:start position:0% +and you still won't be and you'll wind +up speaking what people call tongues + + align:start position:0% +up speaking what people call tongues + + + align:start position:0% +up speaking what people call tongues +it's very abstract + + align:start position:0% +it's very abstract + + + align:start position:0% +it's very abstract +it's only when the other one came in + + align:start position:0% +it's only when the other one came in + + + align:start position:0% +it's only when the other one came in +there that you can see both of them + + align:start position:0% +there that you can see both of them + + + align:start position:0% +there that you can see both of them +all right + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now let's get to einstein + + align:start position:0% +now let's get to einstein + + + align:start position:0% +now let's get to einstein +same same genre story walk go to you're + + align:start position:0% +same same genre story walk go to you're + + + align:start position:0% +same same genre story walk go to you're +at the uh monastery + + align:start position:0% +at the uh monastery + + + align:start position:0% +at the uh monastery +the monks won't let you in + + align:start position:0% +the monks won't let you in + + + align:start position:0% +the monks won't let you in +okay the door opens up + + align:start position:0% +okay the door opens up + + + align:start position:0% +okay the door opens up +this time + + align:start position:0% +this time + + + align:start position:0% +this time +you look in there + + align:start position:0% +you look in there + + + align:start position:0% +you look in there +and all of the monks are blind + + align:start position:0% + + + + align:start position:0% + +you don't answer the question about + + align:start position:0% +you don't answer the question about + + + align:start position:0% +you don't answer the question about +generations + + align:start position:0% +generations + + + align:start position:0% +generations +that's not + + align:start position:0% +that's not + + + align:start position:0% +that's not +they've always been black everybody's + + align:start position:0% +they've always been black everybody's + + + align:start position:0% +they've always been black everybody's +been blind + + align:start position:0% + + + + align:start position:0% + +so what you do is + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you finally talk them into letting you + + align:start position:0% +you finally talk them into letting you + + + align:start position:0% +you finally talk them into letting you +in + + align:start position:0% +in + + + align:start position:0% +in +and when you get in there + + align:start position:0% + + + + align:start position:0% + +you find that there's a rack in a closet + + align:start position:0% +you find that there's a rack in a closet + + + align:start position:0% +you find that there's a rack in a closet +a rack of t-shirts + + align:start position:0% + + + + align:start position:0% + +now all of the t-shirts are the same + + align:start position:0% +now all of the t-shirts are the same + + + align:start position:0% +now all of the t-shirts are the same +size + + align:start position:0% +size + + + align:start position:0% +size +smell the same way made out of some + + align:start position:0% +smell the same way made out of some + + + align:start position:0% +smell the same way made out of some +material + + align:start position:0% +material + + + align:start position:0% +material +they are all the same except that they + + align:start position:0% +they are all the same except that they + + + align:start position:0% +they are all the same except that they +have different colors but the blind men + + align:start position:0% +have different colors but the blind men + + + align:start position:0% +have different colors but the blind men +can't see it + + align:start position:0% + + + + align:start position:0% + +the blind man cannot distinguish one + + align:start position:0% +the blind man cannot distinguish one + + + align:start position:0% +the blind man cannot distinguish one +from the other + + align:start position:0% +from the other + + + align:start position:0% +from the other +he's sitting there he knows he pulls out + + align:start position:0% +he's sitting there he knows he pulls out + + + align:start position:0% +he's sitting there he knows he pulls out +one and they're all the same + + align:start position:0% + + + + align:start position:0% + +you can tell + + align:start position:0% +you can tell + + + align:start position:0% +you can tell +that + + align:start position:0% +that + + + align:start position:0% +that +half of them are dark red + + align:start position:0% +half of them are dark red + + + align:start position:0% +half of them are dark red +and the other half are white + + align:start position:0% + + + + align:start position:0% + +they can't see it + + align:start position:0% +they can't see it + + + align:start position:0% +they can't see it +but there's one thing the blind men know + + align:start position:0% +but there's one thing the blind men know + + + align:start position:0% +but there's one thing the blind men know +and that is + + align:start position:0% +and that is + + + align:start position:0% +and that is +that if + + align:start position:0% +that if + + + align:start position:0% +that if +when they put on some t-shirts + + align:start position:0% +when they put on some t-shirts + + + align:start position:0% +when they put on some t-shirts +and sit out in the sun they get warm and + + align:start position:0% +and sit out in the sun they get warm and + + + align:start position:0% +and sit out in the sun they get warm and +when they put on other t-shirts + + align:start position:0% +when they put on other t-shirts + + + align:start position:0% +when they put on other t-shirts +they sit down to the sun and they don't + + align:start position:0% +they sit down to the sun and they don't + + + align:start position:0% +they sit down to the sun and they don't +get one they stay a little bit cool + + align:start position:0% +get one they stay a little bit cool + + + align:start position:0% +get one they stay a little bit cool +you can you go in there and say well + + align:start position:0% +you can you go in there and say well + + + align:start position:0% +you can you go in there and say well +where are the red ones when you want to + + align:start position:0% +where are the red ones when you want to + + + align:start position:0% +where are the red ones when you want to +get warm and wear the white ones when + + align:start position:0% +get warm and wear the white ones when + + + align:start position:0% +get warm and wear the white ones when +you want to get cool they don't know + + align:start position:0% +you want to get cool they don't know + + + align:start position:0% +you want to get cool they don't know +what you're talking about + + align:start position:0% +what you're talking about + + + align:start position:0% +what you're talking about +okay einstein says that cause that + + align:start position:0% +okay einstein says that cause that + + + align:start position:0% +okay einstein says that cause that +hyperspace + + align:start position:0% +hyperspace + + + align:start position:0% +hyperspace +says that we have five + + align:start position:0% +says that we have five + + + align:start position:0% +says that we have five +uh senses + + align:start position:0% +uh senses + + + align:start position:0% +uh senses +if we had a sixth one + + align:start position:0% +if we had a sixth one + + + align:start position:0% +if we had a sixth one +we could perceive other things + + align:start position:0% +we could perceive other things + + + align:start position:0% +we could perceive other things +with our five senses we can still + + align:start position:0% +with our five senses we can still + + + align:start position:0% +with our five senses we can still +perceive + + align:start position:0% +perceive + + + align:start position:0% +perceive +some of those things but their behaviors + + align:start position:0% +some of those things but their behaviors + + + align:start position:0% +some of those things but their behaviors +don't fit into patterns + + align:start position:0% +don't fit into patterns + + + align:start position:0% +don't fit into patterns +you know + + align:start position:0% +you know + + + align:start position:0% +you know +like these traces of particles they see + + align:start position:0% +like these traces of particles they see + + + align:start position:0% +like these traces of particles they see +these + + align:start position:0% +these + + + align:start position:0% +these +particle physicists see even to this day + + align:start position:0% +particle physicists see even to this day + + + align:start position:0% +particle physicists see even to this day +they know that they're there but they + + align:start position:0% +they know that they're there but they + + + align:start position:0% +they know that they're there but they +don't behave they don't + + align:start position:0% +don't behave they don't + + + align:start position:0% +don't behave they don't +they don't + + align:start position:0% +they don't + + + align:start position:0% +they don't +according to newton's laws + + align:start position:0% +according to newton's laws + + + align:start position:0% +according to newton's laws +the einstein's special theory + + align:start position:0% +the einstein's special theory + + + align:start position:0% +the einstein's special theory +as a matter of fact there's no pattern + + align:start position:0% +as a matter of fact there's no pattern + + + align:start position:0% +as a matter of fact there's no pattern +that you can see they don't behave and + + align:start position:0% +that you can see they don't behave and + + + align:start position:0% +that you can see they don't behave and +so what they say is that a pattern would + + align:start position:0% +so what they say is that a pattern would + + + align:start position:0% +so what they say is that a pattern would +exist if some alien came down here with + + align:start position:0% +exist if some alien came down here with + + + align:start position:0% +exist if some alien came down here with +a sixth sense + + align:start position:0% + + + + align:start position:0% + +who could perceive something like that + + align:start position:0% +who could perceive something like that + + + align:start position:0% +who could perceive something like that +we don't have the sixth sense we know + + align:start position:0% +we don't have the sixth sense we know + + + align:start position:0% +we don't have the sixth sense we know +that this thing is behaving like this + + align:start position:0% +that this thing is behaving like this + + + align:start position:0% +that this thing is behaving like this +so here's what einstein and these + + align:start position:0% +so here's what einstein and these + + + align:start position:0% +so here's what einstein and these +physicists try to do + + align:start position:0% +physicists try to do + + + align:start position:0% +physicists try to do +what they try to do is write a position + + align:start position:0% +what they try to do is write a position + + + align:start position:0% +what they try to do is write a position +vector + + align:start position:0% + + + + align:start position:0% + +not just in x y z and say + + align:start position:0% +not just in x y z and say + + + align:start position:0% +not just in x y z and say +that these are dependent variables and + + align:start position:0% +that these are dependent variables and + + + align:start position:0% +that these are dependent variables and +they're all dependent on time + + align:start position:0% +they're all dependent on time + + + align:start position:0% +they're all dependent on time +einstein comes back and says + + align:start position:0% +einstein comes back and says + + + align:start position:0% +einstein comes back and says +let's put in alpha + + align:start position:0% +let's put in alpha + + + align:start position:0% +let's put in alpha +call it the fourth dimension + + align:start position:0% +call it the fourth dimension + + + align:start position:0% +call it the fourth dimension +do our arithmetic and we will be able to + + align:start position:0% +do our arithmetic and we will be able to + + + align:start position:0% +do our arithmetic and we will be able to +account + + align:start position:0% +account + + + align:start position:0% +account +for that behavior even though we don't + + align:start position:0% +for that behavior even though we don't + + + align:start position:0% +for that behavior even though we don't +belong or can't sense this hyper the + + align:start position:0% +belong or can't sense this hyper the + + + align:start position:0% +belong or can't sense this hyper the +rest of this hyperspace just like the + + align:start position:0% +rest of this hyperspace just like the + + + align:start position:0% +rest of this hyperspace just like the +blind men + + align:start position:0% +blind men + + + align:start position:0% +blind men +can account + + align:start position:0% +can account + + + align:start position:0% +can account +for the difference in t-shirts by going + + align:start position:0% +for the difference in t-shirts by going + + + align:start position:0% +for the difference in t-shirts by going +out in the sun + + align:start position:0% + + + + align:start position:0% + +but can't see the difference or + + align:start position:0% +but can't see the difference or + + + align:start position:0% +but can't see the difference or +otherwise perceive it + + align:start position:0% +otherwise perceive it + + + align:start position:0% +otherwise perceive it +so that's what hyperspace is + + align:start position:0% +so that's what hyperspace is + + + align:start position:0% +so that's what hyperspace is +all right it's an attempt to account for + + align:start position:0% +all right it's an attempt to account for + + + align:start position:0% +all right it's an attempt to account for +something you can't + + align:start position:0% +something you can't + + + align:start position:0% +something you can't +perceive fully perceive but you can you + + align:start position:0% +perceive fully perceive but you can you + + + align:start position:0% +perceive fully perceive but you can you +can't perceive but you can perceive the + + align:start position:0% +can't perceive but you can perceive the + + + align:start position:0% +can't perceive but you can perceive the +effects + + align:start position:0% +effects + + + align:start position:0% +effects +so what you say is that in order to + + align:start position:0% +so what you say is that in order to + + + align:start position:0% +so what you say is that in order to +understand this position vector + + align:start position:0% +understand this position vector + + + align:start position:0% +understand this position vector +you have to speculate another dimension + + align:start position:0% +you have to speculate another dimension + + + align:start position:0% +you have to speculate another dimension +and if you do your math right you'll get + + align:start position:0% +and if you do your math right you'll get + + + align:start position:0% +and if you do your math right you'll get +right answers + + align:start position:0% +right answers + + + align:start position:0% +right answers +you will find better stated you will + + align:start position:0% +you will find better stated you will + + + align:start position:0% +you will find better stated you will +find a pattern + + align:start position:0% + + + + align:start position:0% + +and then you use this alpha to make the + + align:start position:0% +and then you use this alpha to make the + + + align:start position:0% +and then you use this alpha to make the +fit in so that you fit to the pattern + + align:start position:0% +fit in so that you fit to the pattern + + + align:start position:0% +fit in so that you fit to the pattern +and if that has a predictive quality + + align:start position:0% +and if that has a predictive quality + + + align:start position:0% +and if that has a predictive quality +then you've got + + align:start position:0% +then you've got + + + align:start position:0% +then you've got +a law + + align:start position:0% + + + + align:start position:0% + +you just have to live with it + + align:start position:0% +you just have to live with it + + + align:start position:0% +you just have to live with it +like the black men just have to live + + align:start position:0% +like the black men just have to live + + + align:start position:0% +like the black men just have to live +with the fact + + align:start position:0% + + + + align:start position:0% + +and they're not even sure before they go + + align:start position:0% +and they're not even sure before they go + + + align:start position:0% +and they're not even sure before they go +out which ones are + + align:start position:0% +out which ones are + + + align:start position:0% +out which ones are +so you take two or three of them you go + + align:start position:0% +so you take two or three of them you go + + + align:start position:0% +so you take two or three of them you go +out you put them on take a chance that + + align:start position:0% +out you put them on take a chance that + + + align:start position:0% +out you put them on take a chance that +one of them will + + align:start position:0% +one of them will + + + align:start position:0% +one of them will +but you've tied down things a bit you've + + align:start position:0% +but you've tied down things a bit you've + + + align:start position:0% +but you've tied down things a bit you've +got a science they've got a science in + + align:start position:0% +got a science they've got a science in + + + align:start position:0% +got a science they've got a science in +there + + align:start position:0% +there + + + align:start position:0% +there +in that monastery + + align:start position:0% + + + + align:start position:0% + +okay so that's where you get a lot of + + align:start position:0% +okay so that's where you get a lot of + + + align:start position:0% +okay so that's where you get a lot of +this abstract thinking coming along + + align:start position:0% +this abstract thinking coming along + + + align:start position:0% +this abstract thinking coming along +later + + align:start position:0% +later + + + align:start position:0% +later +uh + + align:start position:0% +uh + + + align:start position:0% +uh +with people like kierkegaard and sock + + align:start position:0% +with people like kierkegaard and sock + + + align:start position:0% +with people like kierkegaard and sock +let me see if i can get my + + align:start position:0% +let me see if i can get my + + + align:start position:0% +let me see if i can get my +get my french right i qualified in + + align:start position:0% +get my french right i qualified in + + + align:start position:0% +get my french right i qualified in +french but i don't count myself as a + + align:start position:0% +french but i don't count myself as a + + + align:start position:0% +french but i don't count myself as a +person who knows reference but it's fart + + align:start position:0% +person who knows reference but it's fart + + + align:start position:0% +person who knows reference but it's fart +s-a-r-t-r-e i feel more comfortable in + + align:start position:0% +s-a-r-t-r-e i feel more comfortable in + + + align:start position:0% +s-a-r-t-r-e i feel more comfortable in +saying sartre + + align:start position:0% +saying sartre + + + align:start position:0% +saying sartre +okay um you know sartre + + align:start position:0% +okay um you know sartre + + + align:start position:0% +okay um you know sartre +won + + align:start position:0% +won + + + align:start position:0% +won +the nobel prize twice + + align:start position:0% +the nobel prize twice + + + align:start position:0% +the nobel prize twice +he turned i think he wanted three times + + align:start position:0% +he turned i think he wanted three times + + + align:start position:0% +he turned i think he wanted three times +but he turned it down + + align:start position:0% +but he turned it down + + + align:start position:0% +but he turned it down +one time + + align:start position:0% +one time + + + align:start position:0% +one time +um + + align:start position:0% +um + + + align:start position:0% +um +these are + + align:start position:0% + + + + align:start position:0% + +people who talk about existentialism + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +if you + + align:start position:0% +if you + + + align:start position:0% +if you +go talk to a zen buddhist + + align:start position:0% +go talk to a zen buddhist + + + align:start position:0% +go talk to a zen buddhist +uh + + align:start position:0% +uh + + + align:start position:0% +uh +he or she will talk about + + align:start position:0% +he or she will talk about + + + align:start position:0% +he or she will talk about +nirvana + + align:start position:0% + + + + align:start position:0% + +and if you talk to einstein + + align:start position:0% +and if you talk to einstein + + + align:start position:0% +and if you talk to einstein +or any of his uh intellectual + + align:start position:0% +or any of his uh intellectual + + + align:start position:0% +or any of his uh intellectual +descendants descendants + + align:start position:0% +descendants descendants + + + align:start position:0% +descendants descendants +he will talk about hyperspace + + align:start position:0% + + + + align:start position:0% + +there's a lot of similarity in those + + align:start position:0% +there's a lot of similarity in those + + + align:start position:0% +there's a lot of similarity in those +concepts + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +a lot of similarity in those concepts + + align:start position:0% +a lot of similarity in those concepts + + + align:start position:0% +a lot of similarity in those concepts +and + + align:start position:0% +and + + + align:start position:0% +and +uh there is um + + align:start position:0% +uh there is um + + + align:start position:0% +uh there is um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +kierkegaard will talk about + + align:start position:0% +kierkegaard will talk about + + + align:start position:0% +kierkegaard will talk about +existentialism and then he'll talk he + + align:start position:0% +existentialism and then he'll talk he + + + align:start position:0% +existentialism and then he'll talk he +does the same thing + + align:start position:0% +does the same thing + + + align:start position:0% +does the same thing +that these two two guys did when they + + align:start position:0% +that these two two guys did when they + + + align:start position:0% +that these two two guys did when they +looked at knowledge and truth values and + + align:start position:0% +looked at knowledge and truth values and + + + align:start position:0% +looked at knowledge and truth values and +the good + + align:start position:0% +the good + + + align:start position:0% +the good +then they and you look at knowledge in + + align:start position:0% +then they and you look at knowledge in + + + align:start position:0% +then they and you look at knowledge in +terms of empirical knowledge and + + align:start position:0% +terms of empirical knowledge and + + + align:start position:0% +terms of empirical knowledge and +rational analysis these people talk + + align:start position:0% +rational analysis these people talk + + + align:start position:0% +rational analysis these people talk +about + + align:start position:0% +about + + + align:start position:0% +about +actually empirical + + align:start position:0% +actually empirical + + + align:start position:0% +actually empirical +uh values and irrational things + + align:start position:0% +uh values and irrational things + + + align:start position:0% +uh values and irrational things +okay so kierkegaard comes along and says + + align:start position:0% +okay so kierkegaard comes along and says + + + align:start position:0% +okay so kierkegaard comes along and says +let's stretch out + + align:start position:0% +let's stretch out + + + align:start position:0% +let's stretch out +hyperspace can we talk about good and + + align:start position:0% +hyperspace can we talk about good and + + + align:start position:0% +hyperspace can we talk about good and +bad in high respect + + align:start position:0% +bad in high respect + + + align:start position:0% +bad in high respect +in other words not just the real world + + align:start position:0% +in other words not just the real world + + + align:start position:0% +in other words not just the real world +but things that you cannot totally + + align:start position:0% +but things that you cannot totally + + + align:start position:0% +but things that you cannot totally +observe but they're there anyway + + align:start position:0% +observe but they're there anyway + + + align:start position:0% +observe but they're there anyway +all right + + align:start position:0% +all right + + + align:start position:0% +all right +and you get a lot of sympathy from that + + align:start position:0% +and you get a lot of sympathy from that + + + align:start position:0% +and you get a lot of sympathy from that +if you go over to the art department + + align:start position:0% + + + + align:start position:0% + +you don't have to go to the school of + + align:start position:0% +you don't have to go to the school of + + + align:start position:0% +you don't have to go to the school of +religion you go to the art department + + align:start position:0% +religion you go to the art department + + + align:start position:0% +religion you go to the art department +uh ballet + + align:start position:0% +uh ballet + + + align:start position:0% +uh ballet +they'll tell you there's a hyper space + + align:start position:0% +they'll tell you there's a hyper space + + + align:start position:0% +they'll tell you there's a hyper space +out there + + align:start position:0% +out there + + + align:start position:0% +out there +there's a hyper real world out there + + align:start position:0% +there's a hyper real world out there + + + align:start position:0% +there's a hyper real world out there +and some people are in touch with it and + + align:start position:0% +and some people are in touch with it and + + + align:start position:0% +and some people are in touch with it and +some people most of the rest of us + + align:start position:0% +some people most of the rest of us + + + align:start position:0% +some people most of the rest of us +aren't + + align:start position:0% + + + + align:start position:0% + +and they don't know what it is out there + + align:start position:0% +and they don't know what it is out there + + + align:start position:0% +and they don't know what it is out there +but they know when you got it + + align:start position:0% +but they know when you got it + + + align:start position:0% +but they know when you got it +like the + + align:start position:0% +like the + + + align:start position:0% +like the +monks did they knew when you had the red + + align:start position:0% +monks did they knew when you had the red + + + align:start position:0% +monks did they knew when you had the red +shirt + + align:start position:0% +shirt + + + align:start position:0% +shirt +they didn't know about red and white + + align:start position:0% +they didn't know about red and white + + + align:start position:0% +they didn't know about red and white +shirts + + align:start position:0% +shirts + + + align:start position:0% +shirts +but they know when you've got it and + + align:start position:0% +but they know when you've got it and + + + align:start position:0% +but they know when you've got it and +those are the ones you call the geniuses + + align:start position:0% +those are the ones you call the geniuses + + + align:start position:0% +those are the ones you call the geniuses +not genius in terms of intellect but + + align:start position:0% +not genius in terms of intellect but + + + align:start position:0% +not genius in terms of intellect but +just people who can just who's it who + + align:start position:0% +just people who can just who's it who + + + align:start position:0% +just people who can just who's it who +just got it + + align:start position:0% +just got it + + + align:start position:0% +just got it +some people just got it + + align:start position:0% +some people just got it + + + align:start position:0% +some people just got it +and they can touch that other world + + align:start position:0% +and they can touch that other world + + + align:start position:0% +and they can touch that other world +um + + align:start position:0% +um + + + align:start position:0% +um +ancient people knew about this stuff + + align:start position:0% + + + + align:start position:0% + +i'll tell you how they knew about it + + align:start position:0% + + + + align:start position:0% + +they knew it in a very common way in a + + align:start position:0% +they knew it in a very common way in a + + + align:start position:0% +they knew it in a very common way in a +way that we call very concrete + + align:start position:0% +way that we call very concrete + + + align:start position:0% +way that we call very concrete +they knew about it in terms of + + align:start position:0% +they knew about it in terms of + + + align:start position:0% +they knew about it in terms of +consciousness and unconsciousness + + align:start position:0% + + + + align:start position:0% + +uh they knew about the dream state + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the um + + align:start position:0% +the um + + + align:start position:0% +the um +when i say ancient i want to go i'm + + align:start position:0% +when i say ancient i want to go i'm + + + align:start position:0% +when i say ancient i want to go i'm +talking about beyond + + align:start position:0% +talking about beyond + + + align:start position:0% +talking about beyond +way back i'm talking about + + align:start position:0% +way back i'm talking about + + + align:start position:0% +way back i'm talking about +uh + + align:start position:0% + + + + align:start position:0% + +ten thousand years ago + + align:start position:0% +ten thousand years ago + + + align:start position:0% +ten thousand years ago +i'm talking about even probably before + + align:start position:0% +i'm talking about even probably before + + + align:start position:0% +i'm talking about even probably before +that but when human beings + + align:start position:0% +that but when human beings + + + align:start position:0% +that but when human beings +began to have dreams + + align:start position:0% +began to have dreams + + + align:start position:0% +began to have dreams +they say + + align:start position:0% +they say + + + align:start position:0% +they say +some animals have dreams dogs + + align:start position:0% + + + + align:start position:0% + +they know when dreams became + + align:start position:0% +they know when dreams became + + + align:start position:0% +they know when dreams became +uh + + align:start position:0% +uh + + + align:start position:0% +uh +a factor in your daily life + + align:start position:0% + + + + align:start position:0% + +they know that because they were able to + + align:start position:0% +they know that because they were able to + + + align:start position:0% +they know that because they were able to +see what we call religious artifacts + + align:start position:0% +see what we call religious artifacts + + + align:start position:0% +see what we call religious artifacts +and burial i think burial was what the + + align:start position:0% +and burial i think burial was what the + + + align:start position:0% +and burial i think burial was what the +archaeologists cultural archaeologists + + align:start position:0% +archaeologists cultural archaeologists + + + align:start position:0% +archaeologists cultural archaeologists +say is + + align:start position:0% +say is + + + align:start position:0% +say is +the first + + align:start position:0% +the first + + + align:start position:0% +the first +uh then came drawings on walls art + + align:start position:0% +uh then came drawings on walls art + + + align:start position:0% +uh then came drawings on walls art +but burial the notion that somebody + + align:start position:0% +but burial the notion that somebody + + + align:start position:0% +but burial the notion that somebody +deserves some kind of ceremony + + align:start position:0% +deserves some kind of ceremony + + + align:start position:0% +deserves some kind of ceremony +uh after they after they die and have to + + align:start position:0% +uh after they after they die and have to + + + align:start position:0% +uh after they after they die and have to +be buried and something goes into the + + align:start position:0% +be buried and something goes into the + + + align:start position:0% +be buried and something goes into the +grave with them to notice the notion + + align:start position:0% +grave with them to notice the notion + + + align:start position:0% +grave with them to notice the notion +that there is another world and the + + align:start position:0% +that there is another world and the + + + align:start position:0% +that there is another world and the +other world that they thought was that + + align:start position:0% +other world that they thought was that + + + align:start position:0% +other world that they thought was that +you're just going to the + + align:start position:0% +you're just going to the + + + align:start position:0% +you're just going to the +dream state and you'll never get out of + + align:start position:0% +dream state and you'll never get out of + + + align:start position:0% +dream state and you'll never get out of +it now + + align:start position:0% + + + + align:start position:0% + +and that the dream state was just as + + align:start position:0% +and that the dream state was just as + + + align:start position:0% +and that the dream state was just as +valid + + align:start position:0% +valid + + + align:start position:0% +valid +as the conscious state + + align:start position:0% +as the conscious state + + + align:start position:0% +as the conscious state +the price we pay + + align:start position:0% +the price we pay + + + align:start position:0% +the price we pay +for saying that the dream stay + + align:start position:0% +for saying that the dream stay + + + align:start position:0% +for saying that the dream stay +it doesn't it's not worth anything + + align:start position:0% +it doesn't it's not worth anything + + + align:start position:0% +it doesn't it's not worth anything +unless you're unless you've got a real + + align:start position:0% +unless you're unless you've got a real + + + align:start position:0% +unless you're unless you've got a real +disease mental problem + + align:start position:0% +disease mental problem + + + align:start position:0% +disease mental problem +the price we pay for that is that we + + align:start position:0% +the price we pay for that is that we + + + align:start position:0% +the price we pay for that is that we +forget the obvious and that is that + + align:start position:0% +forget the obvious and that is that + + + align:start position:0% +forget the obvious and that is that +there + + align:start position:0% +there + + + align:start position:0% +there +that our conscious mind minds can't be + + align:start position:0% +that our conscious mind minds can't be + + + align:start position:0% +that our conscious mind minds can't be +entirely trusted because there are a lot + + align:start position:0% +entirely trusted because there are a lot + + + align:start position:0% +entirely trusted because there are a lot +of truths that are in our mind that our + + align:start position:0% +of truths that are in our mind that our + + + align:start position:0% +of truths that are in our mind that our +conscious minds do not want to face and + + align:start position:0% +conscious minds do not want to face and + + + align:start position:0% +conscious minds do not want to face and +we put them in our unconscious and they + + align:start position:0% +we put them in our unconscious and they + + + align:start position:0% +we put them in our unconscious and they +come out in dreams in the forms of + + align:start position:0% +come out in dreams in the forms of + + + align:start position:0% +come out in dreams in the forms of +dragons and + + align:start position:0% +dragons and + + + align:start position:0% +dragons and +trolls and all that + + align:start position:0% +trolls and all that + + + align:start position:0% +trolls and all that +so there is truth down there and that's + + align:start position:0% +so there is truth down there and that's + + + align:start position:0% +so there is truth down there and that's +what the + + align:start position:0% +what the + + + align:start position:0% +what the +that's what the mythic hero has got to + + align:start position:0% +that's what the mythic hero has got to + + + align:start position:0% +that's what the mythic hero has got to +do is got to kill that dragon + + align:start position:0% +do is got to kill that dragon + + + align:start position:0% +do is got to kill that dragon +that's the symbol that is the metaphor + + align:start position:0% +that's the symbol that is the metaphor + + + align:start position:0% +that's the symbol that is the metaphor +for solving your biggest problems in + + align:start position:0% +for solving your biggest problems in + + + align:start position:0% +for solving your biggest problems in +life you have to say that you've got all + + align:start position:0% +life you have to say that you've got all + + + align:start position:0% +life you have to say that you've got all +of the truth necessary to solve this + + align:start position:0% +of the truth necessary to solve this + + + align:start position:0% +of the truth necessary to solve this +problem but some of it you have hidden + + align:start position:0% +problem but some of it you have hidden + + + align:start position:0% +problem but some of it you have hidden +so you have to go down in the + + align:start position:0% +so you have to go down in the + + + align:start position:0% +so you have to go down in the +unconscious get it + + align:start position:0% +unconscious get it + + + align:start position:0% +unconscious get it +bring it up the consciousness and make + + align:start position:0% +bring it up the consciousness and make + + + align:start position:0% +bring it up the consciousness and make +it fit + + align:start position:0% +it fit + + + align:start position:0% +it fit +mostly morally + + align:start position:0% +mostly morally + + + align:start position:0% +mostly morally +because a lot of the things you have + + align:start position:0% +because a lot of the things you have + + + align:start position:0% +because a lot of the things you have +hidden down there don't fit because you + + align:start position:0% +hidden down there don't fit because you + + + align:start position:0% +hidden down there don't fit because you +don't want to accept the moral truth of + + align:start position:0% +don't want to accept the moral truth of + + + align:start position:0% +don't want to accept the moral truth of +it + + align:start position:0% +it + + + align:start position:0% +it +notice i said moral truth + + align:start position:0% +notice i said moral truth + + + align:start position:0% +notice i said moral truth +okay so there are truths down there so + + align:start position:0% +okay so there are truths down there so + + + align:start position:0% +okay so there are truths down there so +what the + + align:start position:0% +what the + + + align:start position:0% +what the +the the + + align:start position:0% +the the + + + align:start position:0% +the the +primitive that's the word i'm looking + + align:start position:0% +primitive that's the word i'm looking + + + align:start position:0% +primitive that's the word i'm looking +for beyond behind + + align:start position:0% +for beyond behind + + + align:start position:0% +for beyond behind +ancient primitive uh human beings + + align:start position:0% +ancient primitive uh human beings + + + align:start position:0% +ancient primitive uh human beings +uh understood the two different worlds + + align:start position:0% + + + + align:start position:0% + +and they believed that both were valid + + align:start position:0% +and they believed that both were valid + + + align:start position:0% +and they believed that both were valid +and that whatever was down in one + + align:start position:0% +and that whatever was down in one + + + align:start position:0% +and that whatever was down in one +uh + + align:start position:0% +uh + + + align:start position:0% +uh +some of them had mirror images of what + + align:start position:0% +some of them had mirror images of what + + + align:start position:0% +some of them had mirror images of what +was up in the other + + align:start position:0% +was up in the other + + + align:start position:0% +was up in the other +uh but there were other things and you + + align:start position:0% +uh but there were other things and you + + + align:start position:0% +uh but there were other things and you +had to deal learn how to live in both + + align:start position:0% +had to deal learn how to live in both + + + align:start position:0% +had to deal learn how to live in both +and there was always one individual + + align:start position:0% +and there was always one individual + + + align:start position:0% +and there was always one individual +that could that that understood both of + + align:start position:0% +that could that that understood both of + + + align:start position:0% +that could that that understood both of +them + + align:start position:0% +them + + + align:start position:0% +them +you know what they call them + + align:start position:0% +you know what they call them + + + align:start position:0% +you know what they call them +go ahead and say it + + align:start position:0% +go ahead and say it + + + align:start position:0% +go ahead and say it +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +the shame + + align:start position:0% + + + + align:start position:0% + +shaman understands + + align:start position:0% +shaman understands + + + align:start position:0% +shaman understands +those those two different worlds + + align:start position:0% +those those two different worlds + + + align:start position:0% +those those two different worlds +and uh connecticut + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +um yeah so uh so hyperspace + + align:start position:0% + + + + align:start position:0% + +all right let's let's take this thing + + align:start position:0% +all right let's let's take this thing + + + align:start position:0% +all right let's let's take this thing +one more time and then we'll try one or + + align:start position:0% +one more time and then we'll try one or + + + align:start position:0% +one more time and then we'll try one or +two of these codes before we get out of + + align:start position:0% +two of these codes before we get out of + + + align:start position:0% +two of these codes before we get out of +here + + align:start position:0% +here + + + align:start position:0% +here +uh + + align:start position:0% +uh + + + align:start position:0% +uh +hyperspace + + align:start position:0% +hyperspace + + + align:start position:0% +hyperspace +let's go back to knowledge in the first + + align:start position:0% +let's go back to knowledge in the first + + + align:start position:0% +let's go back to knowledge in the first +place go back to knowledge + + align:start position:0% + + + + align:start position:0% + +we're talking now about there's a + + align:start position:0% +we're talking now about there's a + + + align:start position:0% +we're talking now about there's a +there's a term of art + + align:start position:0% + + + + align:start position:0% + +uh in philosophy and it's called + + align:start position:0% +uh in philosophy and it's called + + + align:start position:0% +uh in philosophy and it's called +i'm put it in quotes because i want you + + align:start position:0% +i'm put it in quotes because i want you + + + align:start position:0% +i'm put it in quotes because i want you +to memorize this it's called the mind + + align:start position:0% + + + + align:start position:0% + +body + + align:start position:0% + + + + align:start position:0% + +problem + + align:start position:0% + + + + align:start position:0% + +now the mind body problem is this + + align:start position:0% +now the mind body problem is this + + + align:start position:0% +now the mind body problem is this +we know that there's there exists a mind + + align:start position:0% +we know that there's there exists a mind + + + align:start position:0% +we know that there's there exists a mind +does there exist the body + + align:start position:0% + + + + align:start position:0% + +or you just get or is the mind just + + align:start position:0% +or you just get or is the mind just + + + align:start position:0% +or you just get or is the mind just +telling you + + align:start position:0% +telling you + + + align:start position:0% +telling you +that things are going on + + align:start position:0% +that things are going on + + + align:start position:0% +that things are going on +and somehow another you believe that + + align:start position:0% +and somehow another you believe that + + + align:start position:0% +and somehow another you believe that +there's a physical world out here that + + align:start position:0% +there's a physical world out here that + + + align:start position:0% +there's a physical world out here that +that will be there even if you're dead + + align:start position:0% + + + + align:start position:0% + +believe it or not there's a lot of + + align:start position:0% +believe it or not there's a lot of + + + align:start position:0% +believe it or not there's a lot of +serious debate about all that right now + + align:start position:0% +serious debate about all that right now + + + align:start position:0% +serious debate about all that right now +whether or not + + align:start position:0% +whether or not + + + align:start position:0% +whether or not +you know there's only + + align:start position:0% +you know there's only + + + align:start position:0% +you know there's only +the mind + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the thing you've got to take seriously + + align:start position:0% +the thing you've got to take seriously + + + align:start position:0% +the thing you've got to take seriously +about it is some of the best thinkers + + align:start position:0% +about it is some of the best thinkers + + + align:start position:0% +about it is some of the best thinkers +at least that the western world has ever + + align:start position:0% +at least that the western world has ever + + + align:start position:0% +at least that the western world has ever +had + + align:start position:0% +had + + + align:start position:0% +had +uh has put their have tried to tackle + + align:start position:0% +uh has put their have tried to tackle + + + align:start position:0% +uh has put their have tried to tackle +this thing + + align:start position:0% +this thing + + + align:start position:0% +this thing +the car tried to tackle + + align:start position:0% +the car tried to tackle + + + align:start position:0% +the car tried to tackle +he got a big chunk of it you remember + + align:start position:0% +he got a big chunk of it you remember + + + align:start position:0% +he got a big chunk of it you remember +what it was + + align:start position:0% + + + + align:start position:0% + +there it is + + align:start position:0% +there it is + + + align:start position:0% +there it is +right he said there is one world for + + align:start position:0% +right he said there is one world for + + + align:start position:0% +right he said there is one world for +sure and that you do exist because it's + + align:start position:0% +sure and that you do exist because it's + + + align:start position:0% +sure and that you do exist because it's +in your mind your mind exists now that + + align:start position:0% +in your mind your mind exists now that + + + align:start position:0% +in your mind your mind exists now that +why because you think + + align:start position:0% +why because you think + + + align:start position:0% +why because you think +do you think everybody said yeah i think + + align:start position:0% +do you think everybody said yeah i think + + + align:start position:0% +do you think everybody said yeah i think +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right uh then um + + align:start position:0% +all right uh then um + + + align:start position:0% +all right uh then um +they they start playing games with you + + align:start position:0% +they they start playing games with you + + + align:start position:0% +they they start playing games with you +well what about this desk how do you + + align:start position:0% +well what about this desk how do you + + + align:start position:0% +well what about this desk how do you +know that you're not just dreaming + + align:start position:0% +know that you're not just dreaming + + + align:start position:0% +know that you're not just dreaming +how do you know that this isn't in fact + + align:start position:0% +how do you know that this isn't in fact + + + align:start position:0% +how do you know that this isn't in fact +a desk because i can play a game with + + align:start position:0% +a desk because i can play a game with + + + align:start position:0% +a desk because i can play a game with +you + + align:start position:0% +you + + + align:start position:0% +you +and i can make this thing out of water + + align:start position:0% +and i can make this thing out of water + + + align:start position:0% +and i can make this thing out of water +and you just won't know there + + align:start position:0% +and you just won't know there + + + align:start position:0% +and you just won't know there +until you touch it + + align:start position:0% + + + + align:start position:0% + +so uh i can manipulate your world + + align:start position:0% +so uh i can manipulate your world + + + align:start position:0% +so uh i can manipulate your world +what do you know is there is this valid + + align:start position:0% +what do you know is there is this valid + + + align:start position:0% +what do you know is there is this valid +this business of observation + + align:start position:0% + + + + align:start position:0% + +uh or is it just you and your mind + + align:start position:0% + + + + align:start position:0% + +there's some other thinking + + align:start position:0% +there's some other thinking + + + align:start position:0% +there's some other thinking +that + + align:start position:0% +that + + + align:start position:0% +that +the only valid statement you can make + + align:start position:0% +the only valid statement you can make + + + align:start position:0% +the only valid statement you can make +about knowledge is your mind but is the + + align:start position:0% +about knowledge is your mind but is the + + + align:start position:0% +about knowledge is your mind but is the +mind + + align:start position:0% +mind + + + align:start position:0% +mind +but not your mind because what you say + + align:start position:0% +but not your mind because what you say + + + align:start position:0% +but not your mind because what you say +is yours is only part of a whole + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +all of this has to do with um + + align:start position:0% + + + + align:start position:0% + +just finds its way into ethical thought + + align:start position:0% +just finds its way into ethical thought + + + align:start position:0% +just finds its way into ethical thought +one way or another + + align:start position:0% + + + + align:start position:0% + +and like i said if you read kierkegaard + + align:start position:0% + + + + align:start position:0% + +a-a-r-d + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +some of these other people are + + align:start position:0% + + + + align:start position:0% + +dealing with that hyperspace + + align:start position:0% + + + + align:start position:0% + +you know any artists that deal with + + align:start position:0% +you know any artists that deal with + + + align:start position:0% +you know any artists that deal with +hyperspaces and all of this stuff + + align:start position:0% + + + + align:start position:0% + +can you imagine a fourth + + align:start position:0% + + + + align:start position:0% + +dimension i thought i couldn't imagine + + align:start position:0% +dimension i thought i couldn't imagine + + + align:start position:0% +dimension i thought i couldn't imagine +one until i met till + + align:start position:0% +one until i met till + + + align:start position:0% +one until i met till +i had this discussion with a cousin of + + align:start position:0% +i had this discussion with a cousin of + + + align:start position:0% +i had this discussion with a cousin of +mine + + align:start position:0% +mine + + + align:start position:0% +mine +well my cousin this cousin of mine has + + align:start position:0% +well my cousin this cousin of mine has + + + align:start position:0% +well my cousin this cousin of mine has +the same mentality as a shaman + + align:start position:0% +the same mentality as a shaman + + + align:start position:0% +the same mentality as a shaman +uh he was diagnosed as schizophrenic + + align:start position:0% + + + + align:start position:0% + +long time + + align:start position:0% +long time + + + align:start position:0% +long time +20 30 years + + align:start position:0% +20 30 years + + + align:start position:0% +20 30 years +40 years ago + + align:start position:0% + + + + align:start position:0% + +he had uh + + align:start position:0% +he had uh + + + align:start position:0% +he had uh +some um + + align:start position:0% +some um + + + align:start position:0% +some um +he had all of the he had all the makings + + align:start position:0% +he had all of the he had all the makings + + + align:start position:0% +he had all of the he had all the makings +of machinery he had a + + align:start position:0% +of machinery he had a + + + align:start position:0% +of machinery he had a +terrible experience as a child + + align:start position:0% +terrible experience as a child + + + align:start position:0% +terrible experience as a child +and + + align:start position:0% +and + + + align:start position:0% +and +he never had a job + + align:start position:0% +he never had a job + + + align:start position:0% +he never had a job +he's at home with his mother + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +i was sitting there + + align:start position:0% +i was sitting there + + + align:start position:0% +i was sitting there +his mother asked me to go talk to him + + align:start position:0% +his mother asked me to go talk to him + + + align:start position:0% +his mother asked me to go talk to him +one day + + align:start position:0% +one day + + + align:start position:0% +one day +i went and sat down and talked to him i + + align:start position:0% +i went and sat down and talked to him i + + + align:start position:0% +i went and sat down and talked to him i +said we don't have to talk about talking + + align:start position:0% +said we don't have to talk about talking + + + align:start position:0% +said we don't have to talk about talking +if you don't want to + + align:start position:0% +if you don't want to + + + align:start position:0% +if you don't want to +i said i want you i said well you know + + align:start position:0% + + + + align:start position:0% + +everybody says you got a problem what's + + align:start position:0% +everybody says you got a problem what's + + + align:start position:0% +everybody says you got a problem what's +your problem + + align:start position:0% +your problem + + + align:start position:0% +your problem +he said + + align:start position:0% + + + + align:start position:0% + +sometimes he goes to sleep + + align:start position:0% + + + + align:start position:0% + +and he doesn't wake up for a month + + align:start position:0% + + + + align:start position:0% + +and he's not laying in the bed for a + + align:start position:0% +and he's not laying in the bed for a + + + align:start position:0% +and he's not laying in the bed for a +month he's walking around talking but he + + align:start position:0% +month he's walking around talking but he + + + align:start position:0% +month he's walking around talking but he +said he's in the dream state + + align:start position:0% + + + + align:start position:0% + +and then he comes out of it he only + + align:start position:0% +and then he comes out of it he only + + + align:start position:0% +and then he comes out of it he only +knows that he was in the dream state + + align:start position:0% +knows that he was in the dream state + + + align:start position:0% +knows that he was in the dream state +when he comes out of it + + align:start position:0% +when he comes out of it + + + align:start position:0% +when he comes out of it +it's like the yellow + + align:start position:0% +it's like the yellow + + + align:start position:0% +it's like the yellow +he only knows there's this + + align:start position:0% +he only knows there's this + + + align:start position:0% +he only knows there's this +red + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +people tell him + + align:start position:0% +people tell him + + + align:start position:0% +people tell him +he has a distorted concept of time + + align:start position:0% + + + + align:start position:0% + +but there's a there's a there's there's + + align:start position:0% +but there's a there's a there's there's + + + align:start position:0% +but there's a there's a there's there's +some there are some talents that he has + + align:start position:0% +some there are some talents that he has + + + align:start position:0% +some there are some talents that he has +and one of those talents is the talent + + align:start position:0% +and one of those talents is the talent + + + align:start position:0% +and one of those talents is the talent +that um + + align:start position:0% + + + + align:start position:0% + +that uh + + align:start position:0% + + + + align:start position:0% + +i got you i got the what's the oh what's + + align:start position:0% +i got you i got the what's the oh what's + + + align:start position:0% +i got you i got the what's the oh what's +his name problem again + + align:start position:0% +his name problem again + + + align:start position:0% +his name problem again +is that um + + align:start position:0% +is that um + + + align:start position:0% +is that um +the the the book + + align:start position:0% +the the the book + + + align:start position:0% +the the the book +in the movie is called uh + + align:start position:0% + + + + align:start position:0% + +it's called the picture of dorian gray + + align:start position:0% + + + + align:start position:0% + +what's the author's name + + align:start position:0% +what's the author's name + + + align:start position:0% +what's the author's name +keep who + + align:start position:0% +keep who + + + align:start position:0% +keep who +oscar wilde yes + + align:start position:0% +oscar wilde yes + + + align:start position:0% +oscar wilde yes +yeah oscar + + align:start position:0% +yeah oscar + + + align:start position:0% +yeah oscar +wilde uh + + align:start position:0% + + + + align:start position:0% + +there's a movie that i've gotten also + + align:start position:0% +there's a movie that i've gotten also + + + align:start position:0% +there's a movie that i've gotten also +it's written in french + + align:start position:0% +it's written in french + + + align:start position:0% +it's written in french +i haven't looked at it + + align:start position:0% +i haven't looked at it + + + align:start position:0% +i haven't looked at it +i looked at it once on television i went + + align:start position:0% +i looked at it once on television i went + + + align:start position:0% +i looked at it once on television i went +and ordered the movie he's got subtitles + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +there's this young artist + + align:start position:0% +there's this young artist + + + align:start position:0% +there's this young artist +who falls in love with this young girl + + align:start position:0% + + + + align:start position:0% + +and he tries to paint her + + align:start position:0% +and he tries to paint her + + + align:start position:0% +and he tries to paint her +and he can't get it right + + align:start position:0% +and he can't get it right + + + align:start position:0% +and he can't get it right +says he just can't bring out the + + align:start position:0% +says he just can't bring out the + + + align:start position:0% +says he just can't bring out the +in her inner beauty every time he paints + + align:start position:0% +in her inner beauty every time he paints + + + align:start position:0% +in her inner beauty every time he paints +her she looks like + + align:start position:0% +her she looks like + + + align:start position:0% +her she looks like +some uh like picture door great looks + + align:start position:0% +some uh like picture door great looks + + + align:start position:0% +some uh like picture door great looks +like something else + + align:start position:0% +like something else + + + align:start position:0% +like something else +so he says he knows of this + + align:start position:0% +so he says he knows of this + + + align:start position:0% +so he says he knows of this +old man + + align:start position:0% + + + + align:start position:0% + +and lives up in the hills + + align:start position:0% +and lives up in the hills + + + align:start position:0% +and lives up in the hills +who's a famous artist + + align:start position:0% +who's a famous artist + + + align:start position:0% +who's a famous artist +and he's an artist who's just got it + + align:start position:0% +and he's an artist who's just got it + + + align:start position:0% +and he's an artist who's just got it +everybody says the artist and then some + + align:start position:0% +everybody says the artist and then some + + + align:start position:0% +everybody says the artist and then some +people just got it so he says + + align:start position:0% +people just got it so he says + + + align:start position:0% +people just got it so he says +he's a friend of mine i'm gonna take you + + align:start position:0% +he's a friend of mine i'm gonna take you + + + align:start position:0% +he's a friend of mine i'm gonna take you +up to his house + + align:start position:0% +up to his house + + + align:start position:0% +up to his house +and i'm gonna ask him to paint you + + align:start position:0% + + + + align:start position:0% + +so he goes up to this man's house + + align:start position:0% +so he goes up to this man's house + + + align:start position:0% +so he goes up to this man's house +small villa + + align:start position:0% +small villa + + + align:start position:0% +small villa +man's there with his wife + + align:start position:0% +man's there with his wife + + + align:start position:0% +man's there with his wife +and the old man is very reluctant to + + align:start position:0% +and the old man is very reluctant to + + + align:start position:0% +and the old man is very reluctant to +take on this job of painting this girl + + align:start position:0% +take on this job of painting this girl + + + align:start position:0% +take on this job of painting this girl +and there's a real nice line in there + + align:start position:0% +and there's a real nice line in there + + + align:start position:0% +and there's a real nice line in there +where the old man says well + + align:start position:0% +where the old man says well + + + align:start position:0% +where the old man says well +if when i start painting her + + align:start position:0% +if when i start painting her + + + align:start position:0% +if when i start painting her +i don't know + + align:start position:0% +i don't know + + + align:start position:0% +i don't know +what the ink or i mean what the paint on + + align:start position:0% +what the ink or i mean what the paint on + + + align:start position:0% +what the ink or i mean what the paint on +my brush is going to do when it hits the + + align:start position:0% +my brush is going to do when it hits the + + + align:start position:0% +my brush is going to do when it hits the +canvas + + align:start position:0% +canvas + + + align:start position:0% +canvas +you may not like what you see + + align:start position:0% + + + + align:start position:0% + +and it goes on and at the end the last + + align:start position:0% +and it goes on and at the end the last + + + align:start position:0% +and it goes on and at the end the last +scene he's completed the painting + + align:start position:0% +scene he's completed the painting + + + align:start position:0% +scene he's completed the painting +he puts the cover over the painting + + align:start position:0% +he puts the cover over the painting + + + align:start position:0% +he puts the cover over the painting +he takes a + + align:start position:0% +he takes a + + + align:start position:0% +he takes a +sledgehammer and he breaks a hole in the + + align:start position:0% +sledgehammer and he breaks a hole in the + + + align:start position:0% +sledgehammer and he breaks a hole in the +brick wall + + align:start position:0% +brick wall + + + align:start position:0% +brick wall +he takes the painting we never see the + + align:start position:0% +he takes the painting we never see the + + + align:start position:0% +he takes the painting we never see the +painting he puts it in the hole and he + + align:start position:0% +painting he puts it in the hole and he + + + align:start position:0% +painting he puts it in the hole and he +got some water he covered the hole back + + align:start position:0% +got some water he covered the hole back + + + align:start position:0% +got some water he covered the hole back +up in other words + + align:start position:0% +up in other words + + + align:start position:0% +up in other words +he was able to capture her quote unquote + + align:start position:0% +he was able to capture her quote unquote + + + align:start position:0% +he was able to capture her quote unquote +true self + + align:start position:0% +true self + + + align:start position:0% +true self +and she looked like a beast + + align:start position:0% +and she looked like a beast + + + align:start position:0% +and she looked like a beast +and he just could not give that picture + + align:start position:0% +and he just could not give that picture + + + align:start position:0% +and he just could not give that picture +to that young boy because + + align:start position:0% +to that young boy because + + + align:start position:0% +to that young boy because +it would tear us harder that's the whole + + align:start position:0% +it would tear us harder that's the whole + + + align:start position:0% +it would tear us harder that's the whole +point of the thing the whole point of + + align:start position:0% +point of the thing the whole point of + + + align:start position:0% +point of the thing the whole point of +the thing is that some people like my + + align:start position:0% +the thing is that some people like my + + + align:start position:0% +the thing is that some people like my +cousin + + align:start position:0% +cousin + + + align:start position:0% +cousin +can see that into you + + align:start position:0% +can see that into you + + + align:start position:0% +can see that into you +and i don't like the because i don't + + align:start position:0% +and i don't like the because i don't + + + align:start position:0% +and i don't like the because i don't +want him to see this + + align:start position:0% + + + + align:start position:0% + +but i mean we got along so i guess it's + + align:start position:0% +but i mean we got along so i guess it's + + + align:start position:0% +but i mean we got along so i guess it's +not so bad but he + + align:start position:0% +not so bad but he + + + align:start position:0% +not so bad but he +he's got that he doesn't have the skill + + align:start position:0% +he's got that he doesn't have the skill + + + align:start position:0% +he's got that he doesn't have the skill +to put + + align:start position:0% +to put + + + align:start position:0% +to put +brush to paint and paint the canvas + + align:start position:0% +brush to paint and paint the canvas + + + align:start position:0% +brush to paint and paint the canvas +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and i always try to tell him you know he + + align:start position:0% +and i always try to tell him you know he + + + align:start position:0% +and i always try to tell him you know he +developed poetic skills and all poetic + + align:start position:0% +developed poetic skills and all poetic + + + align:start position:0% +developed poetic skills and all poetic +skills + + align:start position:0% +skills + + + align:start position:0% +skills +don't uh you don't have to rhyme you + + align:start position:0% +don't uh you don't have to rhyme you + + + align:start position:0% +don't uh you don't have to rhyme you +know + + align:start position:0% +know + + + align:start position:0% +know +but if he can see those things in people + + align:start position:0% +but if he can see those things in people + + + align:start position:0% +but if he can see those things in people +then he is a special he's got a special + + align:start position:0% +then he is a special he's got a special + + + align:start position:0% +then he is a special he's got a special +talent + + align:start position:0% +talent + + + align:start position:0% +talent +um + + align:start position:0% +um + + + align:start position:0% +um +and uh a lot of artists like that + + align:start position:0% +and uh a lot of artists like that + + + align:start position:0% +and uh a lot of artists like that +he really it's like jackson pollock + + align:start position:0% + + + + align:start position:0% + +i would not go to an ice cream polisher + + align:start position:0% +i would not go to an ice cream polisher + + + align:start position:0% +i would not go to an ice cream polisher +jacket jackson pollock + + align:start position:0% + + + + align:start position:0% + +but they in other words what they what + + align:start position:0% +but they in other words what they what + + + align:start position:0% +but they in other words what they what +what uh + + align:start position:0% +what uh + + + align:start position:0% +what uh +i think + + align:start position:0% +i think + + + align:start position:0% +i think +is healthy for us to say + + align:start position:0% +is healthy for us to say + + + align:start position:0% +is healthy for us to say +is that so far as our senses are + + align:start position:0% +is that so far as our senses are + + + align:start position:0% +is that so far as our senses are +concerned some of these people are in + + align:start position:0% +concerned some of these people are in + + + align:start position:0% +concerned some of these people are in +high perspective + + align:start position:0% +high perspective + + + align:start position:0% +high perspective +they're perceiving things that we could + + align:start position:0% +they're perceiving things that we could + + + align:start position:0% +they're perceiving things that we could +perceive if we could purge our our + + align:start position:0% +perceive if we could purge our our + + + align:start position:0% +perceive if we could purge our our +unconsciousnesses + + align:start position:0% +unconsciousnesses + + + align:start position:0% +unconsciousnesses +of their demons + + align:start position:0% +of their demons + + + align:start position:0% +of their demons +and reconcile all that's down there with + + align:start position:0% +and reconcile all that's down there with + + + align:start position:0% +and reconcile all that's down there with +our conscience and our reason and our + + align:start position:0% +our conscience and our reason and our + + + align:start position:0% +our conscience and our reason and our +morals + + align:start position:0% +morals + + + align:start position:0% +morals +and that's what's supposed to happen + + align:start position:0% +and that's what's supposed to happen + + + align:start position:0% +and that's what's supposed to happen +when you become wise + + align:start position:0% +when you become wise + + + align:start position:0% +when you become wise +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +you're supposed to be able to purge your + + align:start position:0% +you're supposed to be able to purge your + + + align:start position:0% +you're supposed to be able to purge your +unconscious of all of his demons + + align:start position:0% +unconscious of all of his demons + + + align:start position:0% +unconscious of all of his demons +carl jung said that + + align:start position:0% +carl jung said that + + + align:start position:0% +carl jung said that +and that he said it happens only in the + + align:start position:0% +and that he said it happens only in the + + + align:start position:0% +and that he said it happens only in the +old because + + align:start position:0% +old because + + + align:start position:0% +old because +in order for the rest of us the + + align:start position:0% +in order for the rest of us the + + + align:start position:0% +in order for the rest of us the +non-shaming for the rest of us to do it + + align:start position:0% +non-shaming for the rest of us to do it + + + align:start position:0% +non-shaming for the rest of us to do it +and remain healthy + + align:start position:0% +and remain healthy + + + align:start position:0% +and remain healthy +uh we have to see death + + align:start position:0% +uh we have to see death + + + align:start position:0% +uh we have to see death +and when we see the grim reaper not far + + align:start position:0% +and when we see the grim reaper not far + + + align:start position:0% +and when we see the grim reaper not far +away and these demons just don't mean + + align:start position:0% +away and these demons just don't mean + + + align:start position:0% +away and these demons just don't mean +that much + + align:start position:0% +that much + + + align:start position:0% +that much +and + + align:start position:0% +and + + + align:start position:0% +and +and if we can find a moral way to accept + + align:start position:0% +and if we can find a moral way to accept + + + align:start position:0% +and if we can find a moral way to accept +uh y'all know what i mean by moral way + + align:start position:0% +uh y'all know what i mean by moral way + + + align:start position:0% +uh y'all know what i mean by moral way +to accept the stuff that's down there + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +well one that's unforgettable is freud + + align:start position:0% +well one that's unforgettable is freud + + + align:start position:0% +well one that's unforgettable is freud +when he talked about + + align:start position:0% +when he talked about + + + align:start position:0% +when he talked about +how a boy can have a sexual attraction + + align:start position:0% +how a boy can have a sexual attraction + + + align:start position:0% +how a boy can have a sexual attraction +to his mother + + align:start position:0% +to his mother + + + align:start position:0% +to his mother +okay + + align:start position:0% +okay + + + align:start position:0% +okay +well that's kept down in the unconscious + + align:start position:0% +well that's kept down in the unconscious + + + align:start position:0% +well that's kept down in the unconscious +because that's morally unacceptable + + align:start position:0% + + + + align:start position:0% + +so there's a demon that + + align:start position:0% +so there's a demon that + + + align:start position:0% +so there's a demon that +but if you're getting old and you and + + align:start position:0% +but if you're getting old and you and + + + align:start position:0% +but if you're getting old and you and +the grim reaper is right over there you + + align:start position:0% +the grim reaper is right over there you + + + align:start position:0% +the grim reaper is right over there you +don't know when you're going that + + align:start position:0% +don't know when you're going that + + + align:start position:0% +don't know when you're going that +becomes no longer significant + + align:start position:0% +becomes no longer significant + + + align:start position:0% +becomes no longer significant +okay you can bring that to consciousness + + align:start position:0% +okay you can bring that to consciousness + + + align:start position:0% +okay you can bring that to consciousness +and deal with it so a wise person is + + align:start position:0% +and deal with it so a wise person is + + + align:start position:0% +and deal with it so a wise person is +purged + + align:start position:0% +purged + + + align:start position:0% +purged +is unconscious of all these demons and + + align:start position:0% +is unconscious of all these demons and + + + align:start position:0% +is unconscious of all these demons and +takes on some of these skills of the + + align:start position:0% +takes on some of these skills of the + + + align:start position:0% +takes on some of these skills of the +shame + + align:start position:0% +shame + + + align:start position:0% +shame +and can see + + align:start position:0% +and can see + + + align:start position:0% +and can see +into + + align:start position:0% +into + + + align:start position:0% +into +certain kinds of hype space + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +in this class i wouldn't say this in in + + align:start position:0% +in this class i wouldn't say this in in + + + align:start position:0% +in this class i wouldn't say this in in +an engineering class but in this class + + align:start position:0% +an engineering class but in this class + + + align:start position:0% +an engineering class but in this class +i'm no longer in the mood to talk about + + align:start position:0% +i'm no longer in the mood to talk about + + + align:start position:0% +i'm no longer in the mood to talk about +code + + align:start position:0% + + + + align:start position:0% + +so i'm gonna make that an assignment + + align:start position:0% +so i'm gonna make that an assignment + + + align:start position:0% +so i'm gonna make that an assignment +uh we have a surprise did you read your + + align:start position:0% +uh we have a surprise did you read your + + + align:start position:0% +uh we have a surprise did you read your +email + + align:start position:0% +email + + + align:start position:0% +email +we have a visitor coming on tuesday + + align:start position:0% + + + + align:start position:0% + +uh it's not + + align:start position:0% +uh it's not + + + align:start position:0% +uh it's not +it what's what's what is definite is + + align:start position:0% +it what's what's what is definite is + + + align:start position:0% +it what's what's what is definite is +that apparently he had asked about this + + align:start position:0% +that apparently he had asked about this + + + align:start position:0% +that apparently he had asked about this +about a class like this this is a + + align:start position:0% +about a class like this this is a + + + align:start position:0% +about a class like this this is a +visitor from + + align:start position:0% +visitor from + + + align:start position:0% +visitor from +the netherlands + + align:start position:0% +the netherlands + + + align:start position:0% +the netherlands +uh chairman of the department of an + + align:start position:0% +uh chairman of the department of an + + + align:start position:0% +uh chairman of the department of an +engineering department + + align:start position:0% +engineering department + + + align:start position:0% +engineering department +uh + + align:start position:0% +uh + + + align:start position:0% +uh +apparently part of this whole + + align:start position:0% +apparently part of this whole + + + align:start position:0% +apparently part of this whole +um + + align:start position:0% +um + + + align:start position:0% +um +reconstruction of education in europe + + align:start position:0% +reconstruction of education in europe + + + align:start position:0% +reconstruction of education in europe +and um + + align:start position:0% +and um + + + align:start position:0% +and um +engineering ethics is + + align:start position:0% +engineering ethics is + + + align:start position:0% +engineering ethics is +getting on everybody's agenda over there \ No newline at end of file diff --git a/2UpHyGPVdgg.txt b/2UpHyGPVdgg.txt new file mode 100644 index 0000000000000000000000000000000000000000..40ae95bb8ef30a34c3ba7b2d6f6dc95a6c63ef40 --- /dev/null +++ b/2UpHyGPVdgg.txt @@ -0,0 +1,10848 @@ +align:start position:0% + +so we're going to make a good part of + + align:start position:0% +so we're going to make a good part of + + + align:start position:0% +so we're going to make a good part of +today about talking about some of the + + align:start position:0% +today about talking about some of the + + + align:start position:0% +today about talking about some of the +other people who have thought about + + align:start position:0% +other people who have thought about + + + align:start position:0% +other people who have thought about +music representation or or talking about + + align:start position:0% +music representation or or talking about + + + align:start position:0% +music representation or or talking about +other people's thoughts and whether we + + align:start position:0% +other people's thoughts and whether we + + + align:start position:0% +other people's thoughts and whether we +agree with them or not specifically to + + align:start position:0% +agree with them or not specifically to + + + align:start position:0% +agree with them or not specifically to +Giants of the field uh elanar suffrage + + align:start position:0% +Giants of the field uh elanar suffrage + + + align:start position:0% +Giants of the field uh elanar suffrage +field um her article on um music + + align:start position:0% +field um her article on um music + + + align:start position:0% +field um her article on um music +representation and uh Nicholas cook on + + align:start position:0% +representation and uh Nicholas cook on + + + align:start position:0% +representation and uh Nicholas cook on +what's comparative musicology and what's + + align:start position:0% +what's comparative musicology and what's + + + align:start position:0% +what's comparative musicology and what's +computational musicology and what they + + align:start position:0% +computational musicology and what they + + + align:start position:0% +computational musicology and what they +might have to do with each other if + + align:start position:0% +might have to do with each other if + + + align:start position:0% +might have to do with each other if +anything so let's um let's start by by + + align:start position:0% +anything so let's um let's start by by + + + align:start position:0% +anything so let's um let's start by by +talking uh a little bit about the Elanor + + align:start position:0% +talking uh a little bit about the Elanor + + + align:start position:0% +talking uh a little bit about the Elanor +self field article um she's a before + + align:start position:0% +self field article um she's a before + + + align:start position:0% +self field article um she's a before +getting into computers and continuing + + align:start position:0% +getting into computers and continuing + + + align:start position:0% +getting into computers and continuing +afterwards she's a specialist in broke + + align:start position:0% +afterwards she's a specialist in broke + + + align:start position:0% +afterwards she's a specialist in broke +music which is sort of uh Western + + align:start position:0% +music which is sort of uh Western + + + align:start position:0% +music which is sort of uh Western +European musical era from a lot of + + align:start position:0% +European musical era from a lot of + + + align:start position:0% +European musical era from a lot of +people say 1600 to 17750 roughly 1580 to + + align:start position:0% +people say 1600 to 17750 roughly 1580 to + + + align:start position:0% +people say 1600 to 17750 roughly 1580 to +1770 but with the previous areas + + align:start position:0% +1770 but with the previous areas + + + align:start position:0% +1770 but with the previous areas +overlapping and previous and next ones + + align:start position:0% +overlapping and previous and next ones + + + align:start position:0% +overlapping and previous and next ones +for a bit + + align:start position:0% +for a bit + + + align:start position:0% +for a bit +um and so she talks about uh about some + + align:start position:0% +um and so she talks about uh about some + + + align:start position:0% +um and so she talks about uh about some +some things in her article um anyone + + align:start position:0% +some things in her article um anyone + + + align:start position:0% +some things in her article um anyone +remember anything about um the article + + align:start position:0% +remember anything about um the article + + + align:start position:0% +remember anything about um the article +that has this diagram what's what's she + + align:start position:0% +that has this diagram what's what's she + + + align:start position:0% +that has this diagram what's what's she +kind of showing + + align:start position:0% +kind of showing + + + align:start position:0% +kind of showing +here we + + align:start position:0% + + + + align:start position:0% + +call I know you do you're just + + align:start position:0% + + + + align:start position:0% + +shy a note has a lot of parameters note + + align:start position:0% +shy a note has a lot of parameters note + + + align:start position:0% +shy a note has a lot of parameters note +has a lot of parameters yes no has a lot + + align:start position:0% +has a lot of parameters yes no has a lot + + + align:start position:0% +has a lot of parameters yes no has a lot +of parameters what kind of relationship + + align:start position:0% +of parameters what kind of relationship + + + align:start position:0% +of parameters what kind of relationship +are we talking about has a + + align:start position:0% +are we talking about has a + + + align:start position:0% +are we talking about has a +means what word pops into your head when + + align:start position:0% +means what word pops into your head when + + + align:start position:0% +means what word pops into your head when +you think of Haas + + align:start position:0% + + + + align:start position:0% + +so into your ontologies that forgotten + + align:start position:0% +so into your ontologies that forgotten + + + align:start position:0% +so into your ontologies that forgotten +what are the two + + align:start position:0% +what are the two + + + align:start position:0% +what are the two +choices yeah go ahead morom tonomy and + + align:start position:0% +choices yeah go ahead morom tonomy and + + + align:start position:0% +choices yeah go ahead morom tonomy and +morony Hann did you have your hand for + + align:start position:0% +morony Hann did you have your hand for + + + align:start position:0% +morony Hann did you have your hand for +which one of those two that would be is + + align:start position:0% +which one of those two that would be is + + + align:start position:0% +which one of those two that would be is +it morom moromi yes yes yes because the + + align:start position:0% +it morom moromi yes yes yes because the + + + align:start position:0% +it morom moromi yes yes yes because the +taxonomy is the one that we use for uh + + align:start position:0% +taxonomy is the one that we use for uh + + + align:start position:0% +taxonomy is the one that we use for uh +Kingdom film you know what what kind of + + align:start position:0% +Kingdom film you know what what kind of + + + align:start position:0% +Kingdom film you know what what kind of +thing is something yeah so note has a + + align:start position:0% +thing is something yeah so note has a + + + align:start position:0% +thing is something yeah so note has a +lot of um different + + align:start position:0% +lot of um different + + + align:start position:0% +lot of um different +different parameters and it's made up of + + align:start position:0% +different parameters and it's made up of + + + align:start position:0% +different parameters and it's made up of +a lot of different parameters I think + + align:start position:0% +a lot of different parameters I think + + + align:start position:0% +a lot of different parameters I think +it's it's something that maybe just + + align:start position:0% +it's it's something that maybe just + + + align:start position:0% +it's it's something that maybe just +sounds so obvious but but this was you + + align:start position:0% +sounds so obvious but but this was you + + + align:start position:0% +sounds so obvious but but this was you +know a really revolutionary way of + + align:start position:0% +know a really revolutionary way of + + + align:start position:0% +know a really revolutionary way of +thinking about some of these things and + + align:start position:0% +thinking about some of these things and + + + align:start position:0% +thinking about some of these things and +this diagram has become sort of the one + + align:start position:0% +this diagram has become sort of the one + + + align:start position:0% +this diagram has become sort of the one +of the legendary diagrams in the field + + align:start position:0% +of the legendary diagrams in the field + + + align:start position:0% +of the legendary diagrams in the field +every field has these legendary diagrams + + align:start position:0% +every field has these legendary diagrams + + + align:start position:0% +every field has these legendary diagrams +and I know um that Dr suff field would + + align:start position:0% +and I know um that Dr suff field would + + + align:start position:0% +and I know um that Dr suff field would +have drawn that flat a little bit better + + align:start position:0% +have drawn that flat a little bit better + + + align:start position:0% +have drawn that flat a little bit better +uh if she had known that this was going + + align:start position:0% +uh if she had known that this was going + + + align:start position:0% +uh if she had known that this was going +to become so famous but yeah this is + + align:start position:0% +to become so famous but yeah this is + + + align:start position:0% +to become so famous but yeah this is +this is the one that we oh yeah we're + + align:start position:0% +this is the one that we oh yeah we're + + + align:start position:0% +this is the one that we oh yeah we're +talking about components of a note and + + align:start position:0% +talking about components of a note and + + + align:start position:0% +talking about components of a note and +we're going to argue about certain + + align:start position:0% +we're going to argue about certain + + + align:start position:0% +we're going to argue about certain +things um and we can see that some of + + align:start position:0% +things um and we can see that some of + + + align:start position:0% +things um and we can see that some of +these things are + + align:start position:0% +these things are + + + align:start position:0% +these things are +um what kind of a thing is duration she + + align:start position:0% +um what kind of a thing is duration she + + + align:start position:0% +um what kind of a thing is duration she +talks about is it a graphical thing can + + align:start position:0% +talks about is it a graphical thing can + + + align:start position:0% +talks about is it a graphical thing can +you see + + align:start position:0% + + + + align:start position:0% + +duration it's interesting that's that's + + align:start position:0% +duration it's interesting that's that's + + + align:start position:0% +duration it's interesting that's that's +good that's good that you're you're + + align:start position:0% +good that's good that you're you're + + + align:start position:0% +good that's good that you're you're +puzzling over it + + align:start position:0% +puzzling over it + + + align:start position:0% +puzzling over it +there's well let's um let's try to + + align:start position:0% +there's well let's um let's try to + + + align:start position:0% +there's well let's um let's try to +figure out the context that I'm talking + + align:start position:0% +figure out the context that I'm talking + + + align:start position:0% +figure out the context that I'm talking +about when we talk about duration she + + align:start position:0% +about when we talk about duration she + + + align:start position:0% +about when we talk about duration she +talks about three contexts that musical + + align:start position:0% +talks about three contexts that musical + + + align:start position:0% +talks about three contexts that musical +representation happens in if you + + align:start position:0% +representation happens in if you + + + align:start position:0% +representation happens in if you +remember them three + + align:start position:0% +remember them three + + + align:start position:0% +remember them three +contexts it's a big part + + align:start position:0% +contexts it's a big part + + + align:start position:0% +contexts it's a big part +of one of the early parts of our + + align:start position:0% +of one of the early parts of our + + + align:start position:0% +of one of the early parts of our +article give the first letter + + align:start position:0% +article give the first letter + + + align:start position:0% +article give the first letter +of each of + + align:start position:0% + + + + align:start position:0% + +them that trigger anything what what is + + align:start position:0% +them that trigger anything what what is + + + align:start position:0% +them that trigger anything what what is +some ways music's represented + + align:start position:0% +some ways music's represented + + + align:start position:0% +some ways music's represented +yeah the graphical yep the graphical how + + align:start position:0% +yeah the graphical yep the graphical how + + + align:start position:0% +yeah the graphical yep the graphical how +it looks + + align:start position:0% + + + + align:start position:0% + +right great let's let's fill out the + + align:start position:0% +right great let's let's fill out the + + + align:start position:0% +right great let's let's fill out the +other two before getting back to the + + align:start position:0% +other two before getting back to the + + + align:start position:0% +other two before getting back to the +question I was talking about yeah go + + align:start position:0% +question I was talking about yeah go + + + align:start position:0% +question I was talking about yeah go +ahead what's that the sound + + align:start position:0% +ahead what's that the sound + + + align:start position:0% +ahead what's that the sound +sound good and then the other one she + + align:start position:0% +sound good and then the other one she + + + align:start position:0% +sound good and then the other one she +uses kind of um + + align:start position:0% +uses kind of um + + + align:start position:0% +uses kind of um +two words at different + + align:start position:0% +two words at different + + + align:start position:0% +two words at different +points or the graph the sound + + align:start position:0% +points or the graph the sound + + + align:start position:0% +points or the graph the sound +graphical uh is that semantical semantic + + align:start position:0% +graphical uh is that semantical semantic + + + align:start position:0% +graphical uh is that semantical semantic +yep and semantic or semantical I like + + align:start position:0% +yep and semantic or semantical I like + + + align:start position:0% +yep and semantic or semantical I like +semantical um and um what would the L be + + align:start position:0% +semantical um and um what would the L be + + + align:start position:0% +semantical um and um what would the L be +it's a in this case for her logical + + align:start position:0% +it's a in this case for her logical + + + align:start position:0% +it's a in this case for her logical +logical yeah so the semantic yeah you're + + align:start position:0% +logical yeah so the semantic yeah you're + + + align:start position:0% +logical yeah so the semantic yeah you're +right it should be sort of alls + + align:start position:0% +right it should be sort of alls + + + align:start position:0% +right it should be sort of alls +logical great so what's duration in this + + align:start position:0% +logical great so what's duration in this + + + align:start position:0% +logical great so what's duration in this +which context are we talking about + + align:start position:0% +which context are we talking about + + + align:start position:0% +which context are we talking about +we in this + + align:start position:0% + + + + align:start position:0% + +diagram what's that I just can't hear + + align:start position:0% +diagram what's that I just can't hear + + + align:start position:0% +diagram what's that I just can't hear +Graal graphic and or logical graphical + + align:start position:0% +Graal graphic and or logical graphical + + + align:start position:0% +Graal graphic and or logical graphical +or logical great so definitely not sound + + align:start position:0% +or logical great so definitely not sound + + + align:start position:0% +or logical great so definitely not sound +right are we all in agreement with Jake + + align:start position:0% +right are we all in agreement with Jake + + + align:start position:0% +right are we all in agreement with Jake +that uh that that that this doesn't + + align:start position:0% +that uh that that that this doesn't + + + align:start position:0% +that uh that that that this doesn't +sound very good unless you have a good + + align:start position:0% +sound very good unless you have a good + + + align:start position:0% +sound very good unless you have a good +internal imagination right this is we're + + align:start position:0% +internal imagination right this is we're + + + align:start position:0% +internal imagination right this is we're +not hearing anything good + + align:start position:0% +not hearing anything good + + + align:start position:0% +not hearing anything good +so what's and who you got to take a + + align:start position:0% +so what's and who you got to take a + + + align:start position:0% +so what's and who you got to take a +stand on this if even if you're wrong + + align:start position:0% +stand on this if even if you're wrong + + + align:start position:0% +stand on this if even if you're wrong +who who wants to say that that this + + align:start position:0% +who who wants to say that that this + + + align:start position:0% +who who wants to say that that this +duration here is more in the graphical + + align:start position:0% +duration here is more in the graphical + + + align:start position:0% +duration here is more in the graphical +domain I mean we're seeing a picture + + align:start position:0% +domain I mean we're seeing a picture + + + align:start position:0% +domain I mean we're seeing a picture +here good and who thinks is more in The + + align:start position:0% +here good and who thinks is more in The + + + align:start position:0% +here good and who thinks is more in The +Logical domain great great super so we + + align:start position:0% +Logical domain great great super so we + + + align:start position:0% +Logical domain great great super so we +have have a little bit of disagreement + + align:start position:0% +have have a little bit of disagreement + + + align:start position:0% +have have a little bit of disagreement +more people on the graphical side what + + align:start position:0% +more people on the graphical side what + + + align:start position:0% +more people on the graphical side what +what would be the argument that um that + + align:start position:0% +what would be the argument that um that + + + align:start position:0% +what would be the argument that um that +it's a graphical duration somebody who + + align:start position:0% +it's a graphical duration somebody who + + + align:start position:0% +it's a graphical duration somebody who +who went for the graphical yeah Vanessa + + align:start position:0% +who went for the graphical yeah Vanessa + + + align:start position:0% +who went for the graphical yeah Vanessa +it's a visual representation there are a + + align:start position:0% +it's a visual representation there are a + + + align:start position:0% +it's a visual representation there are a +bunch of different visual + + align:start position:0% +bunch of different visual + + + align:start position:0% +bunch of different visual +representations that represent how long + + align:start position:0% +representations that represent how long + + + align:start position:0% +representations that represent how long +a note is supposed to be so you can like + + align:start position:0% +a note is supposed to be so you can like + + + align:start position:0% +a note is supposed to be so you can like +look at it and'll make sense what it's + + align:start position:0% +look at it and'll make sense what it's + + + align:start position:0% +look at it and'll make sense what it's +supposed to be great super so we can + + align:start position:0% +supposed to be great super so we can + + + align:start position:0% +supposed to be great super so we can +look at it and we can see what's going + + align:start position:0% +look at it and we can see what's going + + + align:start position:0% +look at it and we can see what's going +to be we a graphic and we see the + + align:start position:0% +to be we a graphic and we see the + + + align:start position:0% +to be we a graphic and we see the +graphic and go there who wants to make + + align:start position:0% +graphic and go there who wants to make + + + align:start position:0% +graphic and go there who wants to make +an argument for The Logical on + + align:start position:0% + + + + align:start position:0% + +this three people yeah um I guess like + + align:start position:0% +this three people yeah um I guess like + + + align:start position:0% +this three people yeah um I guess like +even just seeing this it's all relative + + align:start position:0% +even just seeing this it's all relative + + + align:start position:0% +even just seeing this it's all relative +to other parts of the like you need the + + align:start position:0% +to other parts of the like you need the + + + align:start position:0% +to other parts of the like you need the +conly the sycal context of like beats + + align:start position:0% +conly the sycal context of like beats + + + align:start position:0% +conly the sycal context of like beats +per minute or like yeah um and the times + + align:start position:0% +per minute or like yeah um and the times + + + align:start position:0% +per minute or like yeah um and the times +are sharing right so so we're we're + + align:start position:0% +are sharing right so so we're we're + + + align:start position:0% +are sharing right so so we're we're +going quite a bit further and saying + + align:start position:0% +going quite a bit further and saying + + + align:start position:0% +going quite a bit further and saying +yeah the duration only makes sense in a + + align:start position:0% +yeah the duration only makes sense in a + + + align:start position:0% +yeah the duration only makes sense in a +larger context of things super um let me + + align:start position:0% +larger context of things super um let me + + + align:start position:0% +larger context of things super um let me +come up with two ways that you might uh + + align:start position:0% +come up with two ways that you might uh + + + align:start position:0% +come up with two ways that you might uh +describe something we'll stop + + align:start position:0% + + + + align:start position:0% + +there describe what I did what I have on + + align:start position:0% +there describe what I did what I have on + + + align:start position:0% +there describe what I did what I have on +the board in the most purely graphical + + align:start position:0% +the board in the most purely graphical + + + align:start position:0% +the board in the most purely graphical +description possible + + align:start position:0% + + + + align:start position:0% + +take yeah + + align:start position:0% +take yeah + + + align:start position:0% +take yeah +John three notes ofal with have three + + align:start position:0% +John three notes ofal with have three + + + align:start position:0% +John three notes ofal with have three +notes of equal duration + + align:start position:0% + + + + align:start position:0% + +great dur um dur yeah not + + align:start position:0% +great dur um dur yeah not + + + align:start position:0% +great dur um dur yeah not +dur anyone want to see if we can go even + + align:start position:0% +dur anyone want to see if we can go even + + + align:start position:0% +dur anyone want to see if we can go even +more graphically yes go ahead Jason uh + + align:start position:0% +more graphically yes go ahead Jason uh + + + align:start position:0% +more graphically yes go ahead Jason uh +two vertical lines with three three + + align:start position:0% +two vertical lines with three three + + + align:start position:0% +two vertical lines with three three +filled in circles with sticks attached + + align:start position:0% +filled in circles with sticks attached + + + align:start position:0% +filled in circles with sticks attached +two vertical lines with three filled in + + align:start position:0% +two vertical lines with three filled in + + + align:start position:0% +two vertical lines with three filled in +circles with sticks attached I like + + align:start position:0% +circles with sticks attached I like + + + align:start position:0% +circles with sticks attached I like +everything about that except the word + + align:start position:0% +everything about that except the word + + + align:start position:0% +everything about that except the word +that came before attached why don't I + + align:start position:0% +that came before attached why don't I + + + align:start position:0% +that came before attached why don't I +like + + align:start position:0% + + + + align:start position:0% + +sticks I like stems even + + align:start position:0% +sticks I like stems even + + + align:start position:0% +sticks I like stems even +less lines yeah what what don't I like + + align:start position:0% +less lines yeah what what don't I like + + + align:start position:0% +less lines yeah what what don't I like +about stems if we're going for + + align:start position:0% +about stems if we're going for + + + align:start position:0% +about stems if we're going for +sticks yeah Adam they already give a + + align:start position:0% +sticks yeah Adam they already give a + + + align:start position:0% +sticks yeah Adam they already give a +contextualization for an abstract symbol + + align:start position:0% +contextualization for an abstract symbol + + + align:start position:0% +contextualization for an abstract symbol +yes we're already abstracting something + + align:start position:0% +yes we're already abstracting something + + + align:start position:0% +yes we're already abstracting something +Jason that was + + align:start position:0% +Jason that was + + + align:start position:0% +Jason that was +fantastic and and and Adam great to the + + align:start position:0% +fantastic and and and Adam great to the + + + align:start position:0% +fantastic and and and Adam great to the +yeah so so we can go we're already + + align:start position:0% +yeah so so we can go we're already + + + align:start position:0% +yeah so so we can go we're already +making assumptions that well you know a + + align:start position:0% +making assumptions that well you know a + + + align:start position:0% +making assumptions that well you know a +line could represent a stick so um it + + align:start position:0% +line could represent a stick so um it + + + align:start position:0% +line could represent a stick so um it +was uh John's thing that two notes of + + align:start position:0% +was uh John's thing that two notes of + + + align:start position:0% +was uh John's thing that two notes of +equal durations is a great description + + align:start position:0% +equal durations is a great description + + + align:start position:0% +equal durations is a great description +but which one um but three filled in + + align:start position:0% +but which one um but three filled in + + + align:start position:0% +but which one um but three filled in +circles and by the way we're already um + + align:start position:0% +circles and by the way we're already um + + + align:start position:0% +circles and by the way we're already um +we're already doing some sort of uh + + align:start position:0% +we're already doing some sort of uh + + + align:start position:0% +we're already doing some sort of uh +we're already interpreting a little bit + + align:start position:0% +we're already interpreting a little bit + + + align:start position:0% +we're already interpreting a little bit +that u a bunch of continuous lines that + + align:start position:0% +that u a bunch of continuous lines that + + + align:start position:0% +that u a bunch of continuous lines that +um are kind of oline and stick out we + + align:start position:0% +um are kind of oline and stick out we + + + align:start position:0% +um are kind of oline and stick out we +think oh that kind of represents a + + align:start position:0% +think oh that kind of represents a + + + align:start position:0% +think oh that kind of represents a +circle but yeah but we'll go with that + + align:start position:0% +circle but yeah but we'll go with that + + + align:start position:0% +circle but yeah but we'll go with that +three build in circles + + align:start position:0% + + + + align:start position:0% + +between two + + align:start position:0% +between two + + + align:start position:0% +between two +lines with more lines okay something + + align:start position:0% +lines with more lines okay something + + + align:start position:0% +lines with more lines okay something +like like that + + align:start position:0% +like like that + + + align:start position:0% +like like that +which one of these does suffrage field + + align:start position:0% +which one of these does suffrage field + + + align:start position:0% +which one of these does suffrage field +consider to be on the graphical domain + + align:start position:0% +consider to be on the graphical domain + + + align:start position:0% +consider to be on the graphical domain +and which one to be on The + + align:start position:0% + + + + align:start position:0% + +Logical too + + align:start position:0% +Logical too + + + align:start position:0% +Logical too +obvious shout it out which graphical or + + align:start position:0% +obvious shout it out which graphical or + + + align:start position:0% +obvious shout it out which graphical or +logical + + align:start position:0% + + + + align:start position:0% + +logical Des describe the thing that it's + + align:start position:0% +logical Des describe the thing that it's + + + align:start position:0% +logical Des describe the thing that it's +pointing to you in the most graphical + + align:start position:0% +pointing to you in the most graphical + + + align:start position:0% +pointing to you in the most graphical +form you + + align:start position:0% + + + + align:start position:0% + +can so you want to take a shot at this + + align:start position:0% +can so you want to take a shot at this + + + align:start position:0% +can so you want to take a shot at this +Matthew do you want to take a shot what + + align:start position:0% +Matthew do you want to take a shot what + + + align:start position:0% +Matthew do you want to take a shot what +it's pointing to in the most + + align:start position:0% +it's pointing to in the most + + + align:start position:0% +it's pointing to in the most +graphical it's a flag hanging off the + + align:start position:0% +graphical it's a flag hanging off the + + + align:start position:0% +graphical it's a flag hanging off the +end of the stem it's a flag hanging off + + align:start position:0% +end of the stem it's a flag hanging off + + + align:start position:0% +end of the stem it's a flag hanging off +the end of the stem who who wants to uh + + align:start position:0% +the end of the stem who who wants to uh + + + align:start position:0% +the end of the stem who who wants to uh +go even even further back this corner + + align:start position:0% +go even even further back this corner + + + align:start position:0% +go even even further back this corner +take a shot + + align:start position:0% + + + + align:start position:0% + +I mean a strip that like decreases in + + align:start position:0% +I mean a strip that like decreases in + + + align:start position:0% +I mean a strip that like decreases in +width in a curled a strip that decreases + + align:start position:0% +width in a curled a strip that decreases + + + align:start position:0% +width in a curled a strip that decreases +in width in a curled uh manner yeah so I + + align:start position:0% +in width in a curled uh manner yeah so I + + + align:start position:0% +in width in a curled uh manner yeah so I +think we can go further even than a flag + + align:start position:0% +think we can go further even than a flag + + + align:start position:0% +think we can go further even than a flag +but we can but we sort of have curled + + align:start position:0% +but we can but we sort of have curled + + + align:start position:0% +but we can but we sort of have curled +strip thing your interpretation says oh + + align:start position:0% +strip thing your interpretation says oh + + + align:start position:0% +strip thing your interpretation says oh +that's a flag and then there sort of a + + align:start position:0% +that's a flag and then there sort of a + + + align:start position:0% +that's a flag and then there sort of a +Next Level Up says Flags represent + + align:start position:0% +Next Level Up says Flags represent + + + align:start position:0% +Next Level Up says Flags represent +duration so we can go in all these world + + align:start position:0% +duration so we can go in all these world + + + align:start position:0% +duration so we can go in all these world +and what um why I love this article even + + align:start position:0% +and what um why I love this article even + + + align:start position:0% +and what um why I love this article even +though it's you know now over 20 years + + align:start position:0% +though it's you know now over 20 years + + + align:start position:0% +though it's you know now over 20 years +old is that nobody puts out so clearly + + align:start position:0% +old is that nobody puts out so clearly + + + align:start position:0% +old is that nobody puts out so clearly +to me to um to think about what all + + align:start position:0% +to me to um to think about what all + + + align:start position:0% +to me to um to think about what all +these things actually mean so we have + + align:start position:0% +these things actually mean so we have + + + align:start position:0% +these things actually mean so we have +three domains that she's talking about + + align:start position:0% +three domains that she's talking about + + + align:start position:0% +three domains that she's talking about +the sound a context she says ter she + + align:start position:0% +the sound a context she says ter she + + + align:start position:0% +the sound a context she says ter she +uses uh I call them domains in my head + + align:start position:0% +uses uh I call them domains in my head + + + align:start position:0% +uses uh I call them domains in my head +we'll use her term uh context sound + + align:start position:0% +we'll use her term uh context sound + + + align:start position:0% +we'll use her term uh context sound +graphical or she most uses the word + + align:start position:0% +graphical or she most uses the word + + + align:start position:0% +graphical or she most uses the word +logical um but um + + align:start position:0% +logical um but um + + + align:start position:0% +logical um but um +semantic or semantical could also be uh + + align:start position:0% +semantic or semantical could also be uh + + + align:start position:0% +semantic or semantical could also be uh +is also a you term that's use and that + + align:start position:0% +is also a you term that's use and that + + + align:start position:0% +is also a you term that's use and that +one is coming up a lot + + align:start position:0% +one is coming up a lot + + + align:start position:0% +one is coming up a lot +more together these last two parts and + + align:start position:0% +more together these last two parts and + + + align:start position:0% +more together these last two parts and +and we're pretty good at distinguishing + + align:start position:0% +and we're pretty good at distinguishing + + + align:start position:0% +and we're pretty good at distinguishing +between sound and either of these other + + align:start position:0% +between sound and either of these other + + + align:start position:0% +between sound and either of these other +ones right yeah + + align:start position:0% +ones right yeah + + + align:start position:0% +ones right yeah +um together these last two will + + align:start position:0% +um together these last two will + + + align:start position:0% +um together these last two will +sometimes put them together as + + align:start position:0% + + + + align:start position:0% + +symbolic that these are things that deal + + align:start position:0% +symbolic that these are things that deal + + + align:start position:0% +symbolic that these are things that deal +with symbols on a page or conceptually + + align:start position:0% +with symbols on a page or conceptually + + + align:start position:0% +with symbols on a page or conceptually +on a page or conceptually written + + align:start position:0% +on a page or conceptually written + + + align:start position:0% +on a page or conceptually written +written or conceptually written um great + + align:start position:0% +written or conceptually written um great + + + align:start position:0% +written or conceptually written um great +now uh she says in her article which one + + align:start position:0% +now uh she says in her article which one + + + align:start position:0% +now uh she says in her article which one +of these holds the most + + align:start position:0% + + + + align:start position:0% + +interest BL + + align:start position:0% + + + + align:start position:0% + +remember this it's okay it's a longish + + align:start position:0% +remember this it's okay it's a longish + + + align:start position:0% +remember this it's okay it's a longish +article but yeah it's a graphical + + align:start position:0% +article but yeah it's a graphical + + + align:start position:0% +article but yeah it's a graphical +graphical unfortunately not but thanks + + align:start position:0% +graphical unfortunately not but thanks + + + align:start position:0% +graphical unfortunately not but thanks +thanks for taking a bold stand stuff's + + align:start position:0% +thanks for taking a bold stand stuff's + + + align:start position:0% +thanks for taking a bold stand stuff's +good we've eliminated graphical which + + align:start position:0% +good we've eliminated graphical which + + + align:start position:0% +good we've eliminated graphical which +one want I take a + + align:start position:0% + + + + align:start position:0% + +guess um I'm I'm gonna say sound you + + align:start position:0% +guess um I'm I'm gonna say sound you + + + align:start position:0% +guess um I'm I'm gonna say sound you +would say sound and you would + + align:start position:0% +would say sound and you would + + + align:start position:0% +would say sound and you would +be with most human beings because most + + align:start position:0% +be with most human beings because most + + + align:start position:0% +be with most human beings because most +people buy uh many more CDs than they + + align:start position:0% +people buy uh many more CDs than they + + + align:start position:0% +people buy uh many more CDs than they +buy abstract musical scores encoded in + + align:start position:0% +buy abstract musical scores encoded in + + + align:start position:0% +buy abstract musical scores encoded in +computers but she's really on The + + align:start position:0% +computers but she's really on The + + + align:start position:0% +computers but she's really on The +Logical so it's good um so sound yeah + + align:start position:0% +Logical so it's good um so sound yeah + + + align:start position:0% +Logical so it's good um so sound yeah +sound is is what most of us work with + + align:start position:0% +sound is is what most of us work with + + + align:start position:0% +sound is is what most of us work with +the music but for for her purposes for + + align:start position:0% +the music but for for her purposes for + + + align:start position:0% +the music but for for her purposes for +the purposes of representation she + + align:start position:0% +the purposes of representation she + + + align:start position:0% +the purposes of representation she +especially she was really interested in + + align:start position:0% +especially she was really interested in + + + align:start position:0% +especially she was really interested in +logical things thanks uh right everybody + + align:start position:0% +logical things thanks uh right everybody + + + align:start position:0% +logical things thanks uh right everybody +who didn't speak was thinking of logical + + align:start position:0% +who didn't speak was thinking of logical + + + align:start position:0% +who didn't speak was thinking of logical +and and think no thank you um bold + + align:start position:0% +and and think no thank you um bold + + + align:start position:0% +and and think no thank you um bold +people for for taking a stab at this + + align:start position:0% +people for for taking a stab at this + + + align:start position:0% +people for for taking a stab at this +um great + + align:start position:0% +um great + + + align:start position:0% +um great +so one of the things that she talks + + align:start position:0% +so one of the things that she talks + + + align:start position:0% +so one of the things that she talks +about um later on do you remember that + + align:start position:0% +about um later on do you remember that + + + align:start position:0% +about um later on do you remember that +she talks about musical scores and + + align:start position:0% +she talks about musical scores and + + + align:start position:0% +she talks about musical scores and +anyone remember any sorts of musical + + align:start position:0% +anyone remember any sorts of musical + + + align:start position:0% +anyone remember any sorts of musical +scores she brings + + align:start position:0% +scores she brings + + + align:start position:0% +scores she brings +in some funny ones and some pretty + + align:start position:0% +in some funny ones and some pretty + + + align:start position:0% +in some funny ones and some pretty +normal + + align:start position:0% + + + + align:start position:0% + +ones we had a lot more fun on our on our + + align:start position:0% +ones we had a lot more fun on our on our + + + align:start position:0% +ones we had a lot more fun on our on our +problem set this weekend than read time + + align:start position:0% +problem set this weekend than read time + + + align:start position:0% +problem set this weekend than read time +I can tell went in but not in the depth + + align:start position:0% + + + + align:start position:0% + +that second Trio from the Mozart Claret + + align:start position:0% +that second Trio from the Mozart Claret + + + align:start position:0% +that second Trio from the Mozart Claret +quintet was the first one she also thank + + align:start position:0% +quintet was the first one she also thank + + + align:start position:0% +quintet was the first one she also thank +you thank you Jake I was uh you know + + align:start position:0% +you thank you Jake I was uh you know + + + align:start position:0% +you thank you Jake I was uh you know +you're allowed to have computers open so + + align:start position:0% +you're allowed to have computers open so + + + align:start position:0% +you're allowed to have computers open so +you can also uh look at these if you + + align:start position:0% +you can also uh look at these if you + + + align:start position:0% +you can also uh look at these if you +want yeah uh she also talks oops sorry + + align:start position:0% +want yeah uh she also talks oops sorry + + + align:start position:0% +want yeah uh she also talks oops sorry +thank you somebody I'm going to going to + + align:start position:0% +thank you somebody I'm going to going to + + + align:start position:0% +thank you somebody I'm going to going to +assign tasks for each person to fix VAR + + align:start position:0% +assign tasks for each person to fix VAR + + + align:start position:0% +assign tasks for each person to fix VAR +stupid CU prisms so I'm going to want + + align:start position:0% +stupid CU prisms so I'm going to want + + + align:start position:0% +stupid CU prisms so I'm going to want +one person to be the um we can't see + + align:start position:0% +one person to be the um we can't see + + + align:start position:0% +one person to be the um we can't see +anything task and one person for the um + + align:start position:0% +anything task and one person for the um + + + align:start position:0% +anything task and one person for the um +the the thing is rolled up okay yeah so + + align:start position:0% +the the thing is rolled up okay yeah so + + + align:start position:0% +the the thing is rolled up okay yeah so +this particular one she also does some + + align:start position:0% +this particular one she also does some + + + align:start position:0% +this particular one she also does some +other things including Gregorian chant + + align:start position:0% +other things including Gregorian chant + + + align:start position:0% +other things including Gregorian chant +um a lot of things representing sort of + + align:start position:0% +um a lot of things representing sort of + + + align:start position:0% +um a lot of things representing sort of +a music historical perspective um and + + align:start position:0% +a music historical perspective um and + + + align:start position:0% +a music historical perspective um and +each one chosen uh many of the later + + align:start position:0% +each one chosen uh many of the later + + + align:start position:0% +each one chosen uh many of the later +ones chosen because they have a + + align:start position:0% +ones chosen because they have a + + + align:start position:0% +ones chosen because they have a +particular interest and difficulty in + + align:start position:0% +particular interest and difficulty in + + + align:start position:0% +particular interest and difficulty in +representing part of your problem set + + align:start position:0% +representing part of your problem set + + + align:start position:0% +representing part of your problem set +too is to make a contribution to that + + align:start position:0% +too is to make a contribution to that + + + align:start position:0% +too is to make a contribution to that +set of + + align:start position:0% +set of + + + align:start position:0% +set of +Repertory that um when you say and you + + align:start position:0% +Repertory that um when you say and you + + + align:start position:0% +Repertory that um when you say and you +will hear software people and coming up + + align:start position:0% +will hear software people and coming up + + + align:start position:0% +will hear software people and coming up +with things who haven't been taking you + + align:start position:0% +with things who haven't been taking you + + + align:start position:0% +with things who haven't been taking you +the full liberal arts education and + + align:start position:0% +the full liberal arts education and + + + align:start position:0% +the full liberal arts education and +music you know oh I have a system that + + align:start position:0% +music you know oh I have a system that + + + align:start position:0% +music you know oh I have a system that +can represent all music I want to be + + align:start position:0% +can represent all music I want to be + + + align:start position:0% +can represent all music I want to be +like great here's DDR show me how your + + align:start position:0% +like great here's DDR show me how your + + + align:start position:0% +like great here's DDR show me how your +system represents here's here's um South + + align:start position:0% +system represents here's here's um South + + + align:start position:0% +system represents here's here's um South +Indian music how does it so these are + + align:start position:0% +Indian music how does it so these are + + + align:start position:0% +Indian music how does it so these are +are all challenges and there'll never be + + align:start position:0% +are all challenges and there'll never be + + + align:start position:0% +are all challenges and there'll never be +a system that can represent all of them + + align:start position:0% +a system that can represent all of them + + + align:start position:0% +a system that can represent all of them +but + + align:start position:0% +but + + + align:start position:0% +but +um hence why most of us will avoid the + + align:start position:0% +um hence why most of us will avoid the + + + align:start position:0% +um hence why most of us will avoid the +all music + + align:start position:0% +all music + + + align:start position:0% +all music +things this particular score has had a + + align:start position:0% +things this particular score has had a + + + align:start position:0% +things this particular score has had a +um about as much impact from the article + + align:start position:0% +um about as much impact from the article + + + align:start position:0% +um about as much impact from the article +as this diagram had um it's sort of + + align:start position:0% +as this diagram had um it's sort of + + + align:start position:0% +as this diagram had um it's sort of +become the Hol world a little bit more + + align:start position:0% +become the Hol world a little bit more + + + align:start position:0% +become the Hol world a little bit more +complex than Holo world of Music in + + align:start position:0% +complex than Holo world of Music in + + + align:start position:0% +complex than Holo world of Music in +representation encoding I want know + + align:start position:0% +representation encoding I want know + + + align:start position:0% +representation encoding I want know +computers explain what a h world + + align:start position:0% +computers explain what a h world + + + align:start position:0% +computers explain what a h world +is yeah the basic file that everyone + + align:start position:0% +is yeah the basic file that everyone + + + align:start position:0% +is yeah the basic file that everyone +writes at the beginning as a sample yep + + align:start position:0% +writes at the beginning as a sample yep + + + align:start position:0% +writes at the beginning as a sample yep +and what do you do with hello world you + + align:start position:0% +and what do you do with hello world you + + + align:start position:0% +and what do you do with hello world you +you print it out print it out somewhere + + align:start position:0% +you print it out print it out somewhere + + + align:start position:0% +you print it out print it out somewhere +great and um some languages you put that + + align:start position:0% +great and um some languages you put that + + + align:start position:0% +great and um some languages you put that +back slash n otherwise nothing prints + + align:start position:0% +back slash n otherwise nothing prints + + + align:start position:0% +back slash n otherwise nothing prints +yep great so it's how do you get how do + + align:start position:0% +yep great so it's how do you get how do + + + align:start position:0% +yep great so it's how do you get how do +you do something very simple in a + + align:start position:0% +you do something very simple in a + + + align:start position:0% +you do something very simple in a +programming language this piece piece or + + align:start position:0% +programming language this piece piece or + + + align:start position:0% +programming language this piece piece or +at least the clarinet part the top part + + align:start position:0% +at least the clarinet part the top part + + + align:start position:0% +at least the clarinet part the top part +of the five has become that um that + + align:start position:0% +of the five has become that um that + + + align:start position:0% +of the five has become that um that +piece so um at least one of it so I + + align:start position:0% +piece so um at least one of it so I + + + align:start position:0% +piece so um at least one of it so I +think we should at least hear it once so + + align:start position:0% +think we should at least hear it once so + + + align:start position:0% +think we should at least hear it once so +we can get it in our head oh and uh just + + align:start position:0% +we can get it in our head oh and uh just + + + align:start position:0% +we can get it in our head oh and uh just +just so you just so I can kind of hear + + align:start position:0% +just so you just so I can kind of hear + + + align:start position:0% +just so you just so I can kind of hear +kind of go when um you might do it + + align:start position:0% +kind of go when um you might do it + + + align:start position:0% +kind of go when um you might do it +involuntarily when something happens + + align:start position:0% +involuntarily when something happens + + + align:start position:0% +involuntarily when something happens +that's not in the score from this + + align:start position:0% +that's not in the score from this + + + align:start position:0% +that's not in the score from this +recording + + align:start position:0% +recording + + + align:start position:0% +recording +[Music] + + align:start position:0% + + + + align:start position:0% + +I didn't + + align:start position:0% +I didn't + + + align:start position:0% +I didn't +hear + + align:start position:0% + + + + align:start position:0% + +repeat now Adam on it anybody + + align:start position:0% +repeat now Adam on it anybody + + + align:start position:0% +repeat now Adam on it anybody +else yeah what + + align:start position:0% +else yeah what + + + align:start position:0% +else yeah what +was uh they kind of glazed over the + + align:start position:0% +was uh they kind of glazed over the + + + align:start position:0% +was uh they kind of glazed over the +triplet at glazed over the triplet yeah + + align:start position:0% +triplet at glazed over the triplet yeah + + + align:start position:0% +triplet at glazed over the triplet yeah +great which is uh which is kind of a + + align:start position:0% +great which is uh which is kind of a + + + align:start position:0% +great which is uh which is kind of a +problematic per uh performance for this + + align:start position:0% +problematic per uh performance for this + + + align:start position:0% +problematic per uh performance for this +particular one because one of the + + align:start position:0% +particular one because one of the + + + align:start position:0% +particular one because one of the +reasons why this is almost certainly + + align:start position:0% +reasons why this is almost certainly + + + align:start position:0% +reasons why this is almost certainly +chosen was can your system represent + + align:start position:0% +chosen was can your system represent + + + align:start position:0% +chosen was can your system represent +triplets um the performers playing on a + + align:start position:0% +triplets um the performers playing on a + + + align:start position:0% +triplets um the performers playing on a +clarinet that uh we hypothesized mozar + + align:start position:0% +clarinet that uh we hypothesized mozar + + + align:start position:0% +clarinet that uh we hypothesized mozar +originally wrote this for that could go + + align:start position:0% +originally wrote this for that could go + + + align:start position:0% +originally wrote this for that could go +two notes lower than this and so played + + align:start position:0% +two notes lower than this and so played + + + align:start position:0% +two notes lower than this and so played +those low notes instead of um instead of + + align:start position:0% +those low notes instead of um instead of + + + align:start position:0% +those low notes instead of um instead of +starting high and going down good so + + align:start position:0% +starting high and going down good so + + + align:start position:0% +starting high and going down good so +this is um the hello world piece that + + align:start position:0% +this is um the hello world piece that + + + align:start position:0% +this is um the hello world piece that +you'll be getting uh any other thoughts + + align:start position:0% +you'll be getting uh any other thoughts + + + align:start position:0% +you'll be getting uh any other thoughts +about uh Elena suffrage Fields work will + + align:start position:0% +about uh Elena suffrage Fields work will + + + align:start position:0% +about uh Elena suffrage Fields work will +come back to her more as the semester + + align:start position:0% +come back to her more as the semester + + + align:start position:0% +come back to her more as the semester +comes + + align:start position:0% + + + + align:start position:0% + +on well um just a just a reminder uh + + align:start position:0% +on well um just a just a reminder uh + + + align:start position:0% +on well um just a just a reminder uh +there's one um exam in this class and + + align:start position:0% +there's one um exam in this class and + + + align:start position:0% +there's one um exam in this class and +it's um sort of the midterm but it's + + align:start position:0% +it's um sort of the midterm but it's + + + align:start position:0% +it's um sort of the midterm but it's +about two-thirds of the way through the + + align:start position:0% +about two-thirds of the way through the + + + align:start position:0% +about two-thirds of the way through the +semester and it's the one uh the only + + align:start position:0% +semester and it's the one uh the only + + + align:start position:0% +semester and it's the one uh the only +one that's not based at all on + + align:start position:0% +one that's not based at all on + + + align:start position:0% +one that's not based at all on +programming but based on readings and um + + align:start position:0% +programming but based on readings and um + + + align:start position:0% +programming but based on readings and um +and the big thoughts I put it that way + + align:start position:0% +and the big thoughts I put it that way + + + align:start position:0% +and the big thoughts I put it that way +so that you have these readings and big + + align:start position:0% +so that you have these readings and big + + + align:start position:0% +so that you have these readings and big +thoughts going through your head as you + + align:start position:0% +thoughts going through your head as you + + + align:start position:0% +thoughts going through your head as you +start working on your final projects um + + align:start position:0% +start working on your final projects um + + + align:start position:0% +start working on your final projects um +I think this is I think you can pretty + + align:start position:0% +I think this is I think you can pretty + + + align:start position:0% +I think this is I think you can pretty +much count um that some thoughts this + + align:start position:0% +much count um that some thoughts this + + + align:start position:0% +much count um that some thoughts this +and some of these questions might be on + + align:start position:0% +and some of these questions might be on + + + align:start position:0% +and some of these questions might be on +there so give it another read when you + + align:start position:0% +there so give it another read when you + + + align:start position:0% +there so give it another read when you +get a chance and let's move on to + + align:start position:0% +get a chance and let's move on to + + + align:start position:0% +get a chance and let's move on to +um Nicholas Cook's uh comparative versus + + align:start position:0% +um Nicholas Cook's uh comparative versus + + + align:start position:0% +um Nicholas Cook's uh comparative versus +computational musicology article and + + align:start position:0% +computational musicology article and + + + align:start position:0% +computational musicology article and +here I've given you the questions I'm + + align:start position:0% +here I've given you the questions I'm + + + align:start position:0% +here I've given you the questions I'm +going to be asking uh written down on + + align:start position:0% +going to be asking uh written down on + + + align:start position:0% +going to be asking uh written down on +the outline today um and I and so take a + + align:start position:0% +the outline today um and I and so take a + + + align:start position:0% +the outline today um and I and so take a +second to um you jot down some some of + + align:start position:0% +second to um you jot down some some of + + + align:start position:0% +second to um you jot down some some of +the notes so you probably already have + + align:start position:0% +the notes so you probably already have + + + align:start position:0% +the notes so you probably already have +them because I gave you these also on + + align:start position:0% +them because I gave you these also on + + + align:start position:0% +them because I gave you these also on +the um on the canvas s right + + align:start position:0% +the um on the canvas s right + + + align:start position:0% +the um on the canvas s right +thinking about um take a second while I + + align:start position:0% +thinking about um take a second while I + + + align:start position:0% +thinking about um take a second while I +play uh a little example from the first + + align:start position:0% +play uh a little example from the first + + + align:start position:0% +play uh a little example from the first +piece that + + align:start position:0% + + + + align:start position:0% + +um that he discusses + + align:start position:0% +um that he discusses + + + align:start position:0% +um that he discusses +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +would know 2001 Space Odyssey this one + + align:start position:0% +would know 2001 Space Odyssey this one + + + align:start position:0% +would know 2001 Space Odyssey this one +of the + + align:start position:0% + + + + align:start position:0% + +pieces okay so + + align:start position:0% +pieces okay so + + + align:start position:0% +pieces okay so +um we'll get back to this and you what + + align:start position:0% +um we'll get back to this and you what + + + align:start position:0% +um we'll get back to this and you what +he uses this piece for in a little bit + + align:start position:0% +he uses this piece for in a little bit + + + align:start position:0% +he uses this piece for in a little bit +but first thing is kind of the + + align:start position:0% +but first thing is kind of the + + + align:start position:0% +but first thing is kind of the +fundamental question one of the a couple + + align:start position:0% +fundamental question one of the a couple + + + align:start position:0% +fundamental question one of the a couple +of the fundamental questions about CL + + align:start position:0% +of the fundamental questions about CL + + + align:start position:0% +of the fundamental questions about CL +what um what does he mean there's no + + align:start position:0% +what um what does he mean there's no + + + align:start position:0% +what um what does he mean there's no +such thing as a good or bad + + align:start position:0% +such thing as a good or bad + + + align:start position:0% +such thing as a good or bad +representation of Music per se yeah + + align:start position:0% +representation of Music per se yeah + + + align:start position:0% +representation of Music per se yeah +Vanessa like just of the point is that + + align:start position:0% +Vanessa like just of the point is that + + + align:start position:0% +Vanessa like just of the point is that +like it's all that's particularly good + + align:start position:0% +like it's all that's particularly good + + + align:start position:0% +like it's all that's particularly good +or bad about it it's like depending on + + align:start position:0% +or bad about it it's like depending on + + + align:start position:0% +or bad about it it's like depending on +what you're attempting to use it for + + align:start position:0% +what you're attempting to use it for + + + align:start position:0% +what you're attempting to use it for +there are different situations where + + align:start position:0% +there are different situations where + + + align:start position:0% +there are different situations where +like certain characteristics might be + + align:start position:0% +like certain characteristics might be + + + align:start position:0% +like certain characteristics might be +more beneficial than others and in that + + align:start position:0% +more beneficial than others and in that + + + align:start position:0% +more beneficial than others and in that +scenario you can make a good or a bad + + align:start position:0% +scenario you can make a good or a bad + + + align:start position:0% +scenario you can make a good or a bad +choice but it doesn't mean it's all + + align:start position:0% +choice but it doesn't mean it's all + + + align:start position:0% +choice but it doesn't mean it's all +around great so so fantastic I think + + align:start position:0% +around great so so fantastic I think + + + align:start position:0% +around great so so fantastic I think +that really captures a lot of what cook + + align:start position:0% +that really captures a lot of what cook + + + align:start position:0% +that really captures a lot of what cook +saying it all depends on what you're + + align:start position:0% +saying it all depends on what you're + + + align:start position:0% +saying it all depends on what you're +trying to get out of it what are you + + align:start position:0% +trying to get out of it what are you + + + align:start position:0% +trying to get out of it what are you +trying to do so U some of your own + + align:start position:0% +trying to do so U some of your own + + + align:start position:0% +trying to do so U some of your own +representations um are going to be + + align:start position:0% +representations um are going to be + + + align:start position:0% +representations um are going to be +really bad representations even if you + + align:start position:0% +really bad representations even if you + + + align:start position:0% +really bad representations even if you +get an A+ for certain things + + align:start position:0% +get an A+ for certain things + + + align:start position:0% +get an A+ for certain things +but um o did I like have the whole + + align:start position:0% +but um o did I like have the whole + + + align:start position:0% +but um o did I like have the whole +recording going um but they could be + + align:start position:0% +recording going um but they could be + + + align:start position:0% +recording going um but they could be +great representations for some other + + align:start position:0% +great representations for some other + + + align:start position:0% +great representations for some other +things um somebody want to give an + + align:start position:0% +things um somebody want to give an + + + align:start position:0% +things um somebody want to give an +example either from the reading or um or + + align:start position:0% +example either from the reading or um or + + + align:start position:0% +example either from the reading or um or +from your own thoughts but maybe + + align:start position:0% +from your own thoughts but maybe + + + align:start position:0% +from your own thoughts but maybe +preferably from the reading if you have + + align:start position:0% +preferably from the reading if you have + + + align:start position:0% +preferably from the reading if you have +it of of what one representation that + + align:start position:0% +it of of what one representation that + + + align:start position:0% +it of of what one representation that +would be uh bad in a specific case and a + + align:start position:0% +would be uh bad in a specific case and a + + + align:start position:0% +would be uh bad in a specific case and a +rep and the same representation how it + + align:start position:0% +rep and the same representation how it + + + align:start position:0% +rep and the same representation how it +could be really good for something + + align:start position:0% +could be really good for something + + + align:start position:0% +could be really good for something +else yeah go ahead + + align:start position:0% +else yeah go ahead + + + align:start position:0% +else yeah go ahead +um I guess the is more detailed but like + + align:start position:0% +um I guess the is more detailed but like + + + align:start position:0% +um I guess the is more detailed but like +at the beginning they had a lot of um + + align:start position:0% +at the beginning they had a lot of um + + + align:start position:0% +at the beginning they had a lot of um +charts that represented pieces and they + + align:start position:0% +charts that represented pieces and they + + + align:start position:0% +charts that represented pieces and they +mentioned that this would be really good + + align:start position:0% +mentioned that this would be really good + + + align:start position:0% +mentioned that this would be really good +for like comparing the formats of + + align:start position:0% +for like comparing the formats of + + + align:start position:0% +for like comparing the formats of +different pieces to each other or like + + align:start position:0% +different pieces to each other or like + + + align:start position:0% +different pieces to each other or like +finding similarities between repertoire + + align:start position:0% +finding similarities between repertoire + + + align:start position:0% +finding similarities between repertoire +but for example like a performer + + align:start position:0% +but for example like a performer + + + align:start position:0% +but for example like a performer +wouldn't be able to use this + + align:start position:0% +wouldn't be able to use this + + + align:start position:0% +wouldn't be able to use this +representation fantastic so cook begins + + align:start position:0% +representation fantastic so cook begins + + + align:start position:0% +representation fantastic so cook begins +uh his article by showing certain charts + + align:start position:0% +uh his article by showing certain charts + + + align:start position:0% +uh his article by showing certain charts +that might uh help compare similarities + + align:start position:0% +that might uh help compare similarities + + + align:start position:0% +that might uh help compare similarities +across pieces but not not be very good + + align:start position:0% +across pieces but not not be very good + + + align:start position:0% +across pieces but not not be very good +for a performer so this is + + align:start position:0% +for a performer so this is + + + align:start position:0% +for a performer so this is +um from the same piece from Luke's + + align:start position:0% +um from the same piece from Luke's + + + align:start position:0% +um from the same piece from Luke's +etterna one of the parts showing at any + + align:start position:0% +etterna one of the parts showing at any + + + align:start position:0% +etterna one of the parts showing at any +given moment what the full range of the + + align:start position:0% +given moment what the full range of the + + + align:start position:0% +given moment what the full range of the +piece is um what's the um what can you + + align:start position:0% +piece is um what's the um what can you + + + align:start position:0% +piece is um what's the um what can you +say about what happens to the range of + + align:start position:0% +say about what happens to the range of + + + align:start position:0% +say about what happens to the range of +the piece around measure 60 + + align:start position:0% + + + + align:start position:0% + +65 I want to take it + + align:start position:0% +65 I want to take it + + + align:start position:0% +65 I want to take it +yeah go + + align:start position:0% +yeah go + + + align:start position:0% +yeah go +ahead like the average pitch just + + align:start position:0% +ahead like the average pitch just + + + align:start position:0% +ahead like the average pitch just +increases overall the average pitch what + + align:start position:0% +increases overall the average pitch what + + + align:start position:0% +increases overall the average pitch what +frequency frequency the average + + align:start position:0% +frequency frequency the average + + + align:start position:0% +frequency frequency the average +frequency increases quite a bit there + + align:start position:0% +frequency increases quite a bit there + + + align:start position:0% +frequency increases quite a bit there +right anything else you could say about + + align:start position:0% +right anything else you could say about + + + align:start position:0% +right anything else you could say about +it it's going more specific even that + + align:start position:0% +it it's going more specific even that + + + align:start position:0% +it it's going more specific even that +that the average pitch because that + + align:start position:0% +that the average pitch because that + + + align:start position:0% +that the average pitch because that +that's also a very good representation + + align:start position:0% +that's also a very good representation + + + align:start position:0% +that's also a very good representation +average pitch yeah Adam there's a + + align:start position:0% +average pitch yeah Adam there's a + + + align:start position:0% +average pitch yeah Adam there's a +descending sequence that goes throughout + + align:start position:0% +descending sequence that goes throughout + + + align:start position:0% +descending sequence that goes throughout +the can there's there's a yeah there's a + + align:start position:0% +the can there's there's a yeah there's a + + + align:start position:0% +the can there's there's a yeah there's a +descending uh line sequence something + + align:start position:0% +descending uh line sequence something + + + align:start position:0% +descending uh line sequence something +like that that's continuing on and then + + align:start position:0% +like that that's continuing on and then + + + align:start position:0% +like that that's continuing on and then +it continues but what else + + align:start position:0% + + + + align:start position:0% + +happens yeah Jason a bunch of voices + + align:start position:0% +happens yeah Jason a bunch of voices + + + align:start position:0% +happens yeah Jason a bunch of voices +appear in the top great yeah a bunch of + + align:start position:0% +appear in the top great yeah a bunch of + + + align:start position:0% +appear in the top great yeah a bunch of +voices comeing in the + + align:start position:0% +voices comeing in the + + + align:start position:0% +voices comeing in the +top and the top most ones maybe also + + align:start position:0% +top and the top most ones maybe also + + + align:start position:0% +top and the top most ones maybe also +have a descending sequence that's it's + + align:start position:0% +have a descending sequence that's it's + + + align:start position:0% +have a descending sequence that's it's +great now I mean you can get all of this + + align:start position:0% +great now I mean you can get all of this + + + align:start position:0% +great now I mean you can get all of this +from a musical score but we'll go back + + align:start position:0% +from a musical score but we'll go back + + + align:start position:0% +from a musical score but we'll go back +here where's the first um first point + + align:start position:0% +here where's the first um first point + + + align:start position:0% +here where's the first um first point +that there's two different + + align:start position:0% +that there's two different + + + align:start position:0% +that there's two different +notes this measure here + + align:start position:0% + + + + align:start position:0% + +here you could do it you can do it but + + align:start position:0% +here you could do it you can do it but + + + align:start position:0% +here you could do it you can do it but +that is what this is not a very good + + align:start position:0% +that is what this is not a very good + + + align:start position:0% +that is what this is not a very good +representation of on the other hand it's + + align:start position:0% +representation of on the other hand it's + + + align:start position:0% +representation of on the other hand it's +a very good representation for seeing Oh + + align:start position:0% +a very good representation for seeing Oh + + + align:start position:0% +a very good representation for seeing Oh +my gosh I'm going to have to count + + align:start position:0% +my gosh I'm going to have to count + + + align:start position:0% +my gosh I'm going to have to count +really hard if I want to get in exactly + + align:start position:0% +really hard if I want to get in exactly + + + align:start position:0% +really hard if I want to get in exactly +at that right moment right but um second + + align:start position:0% +at that right moment right but um second + + + align:start position:0% +at that right moment right but um second +representation showing the number of + + align:start position:0% +representation showing the number of + + + align:start position:0% +representation showing the number of +different notes pitch count graph how + + align:start position:0% +different notes pitch count graph how + + + align:start position:0% +different notes pitch count graph how +many different notes are being sung is a + + align:start position:0% +many different notes are being sung is a + + + align:start position:0% +many different notes are being sung is a +very good representation if you just + + align:start position:0% +very good representation if you just + + + align:start position:0% +very good representation if you just +wanted to um now now you're doing your + + align:start position:0% +wanted to um now now you're doing your + + + align:start position:0% +wanted to um now now you're doing your +uh next horror film or something and + + align:start position:0% +uh next horror film or something and + + + align:start position:0% +uh next horror film or something and +you're a big Stanley Kubrick fan so + + align:start position:0% +you're a big Stanley Kubrick fan so + + + align:start position:0% +you're a big Stanley Kubrick fan so +you're going to rip off uh what he did + + align:start position:0% +you're going to rip off uh what he did + + + align:start position:0% +you're going to rip off uh what he did +in 2001 uh but you just need a 5-second + + align:start position:0% +in 2001 uh but you just need a 5-second + + + align:start position:0% +in 2001 uh but you just need a 5-second +clip for your scariest part where are + + align:start position:0% +clip for your scariest part where are + + + align:start position:0% +clip for your scariest part where are +you going to choose give me a measure + + align:start position:0% + + + + align:start position:0% + +number that give me a shot 52 53 52 53 + + align:start position:0% +number that give me a shot 52 53 52 53 + + + align:start position:0% +number that give me a shot 52 53 52 53 +yeah right we have a whole bunch of + + align:start position:0% +yeah right we have a whole bunch of + + + align:start position:0% +yeah right we have a whole bunch of +different pitches all sounding at the + + align:start position:0% +different pitches all sounding at the + + + align:start position:0% +different pitches all sounding at the +same time that could be really tense I + + align:start position:0% +same time that could be really tense I + + + align:start position:0% +same time that could be really tense I +think this is talking about um pitches + + align:start position:0% +think this is talking about um pitches + + + align:start position:0% +think this is talking about um pitches +without octave pitch classes you all + + align:start position:0% +without octave pitch classes you all + + + align:start position:0% +without octave pitch classes you all +know that term now um so yeah a lot of + + align:start position:0% +know that term now um so yeah a lot of + + + align:start position:0% +know that term now um so yeah a lot of +things happening very easy to do in this + + align:start position:0% +things happening very easy to do in this + + + align:start position:0% +things happening very easy to do in this +graph but very hard to do in + + align:start position:0% +graph but very hard to do in + + + align:start position:0% +graph but very hard to do in +others so + + align:start position:0% +others so + + + align:start position:0% +others so +um goes through some of the different + + align:start position:0% +um goes through some of the different + + + align:start position:0% +um goes through some of the different +things now + + align:start position:0% +things now + + + align:start position:0% +things now +oh this gra sorry I just forgot on this + + align:start position:0% +oh this gra sorry I just forgot on this + + + align:start position:0% +oh this gra sorry I just forgot on this +this one per can you perform from this + + align:start position:0% +this one per can you perform from this + + + align:start position:0% +this one per can you perform from this +one from this + + align:start position:0% +one from this + + + align:start position:0% +one from this +graph see a lot of I see some up I I see + + align:start position:0% +graph see a lot of I see some up I I see + + + align:start position:0% +graph see a lot of I see some up I I see +I see some yeah it's not the + + align:start position:0% +I see some yeah it's not the + + + align:start position:0% +I see some yeah it's not the +best thing for being able to perform + + align:start position:0% +best thing for being able to perform + + + align:start position:0% +best thing for being able to perform +that piece probably not the best thing + + align:start position:0% +that piece probably not the best thing + + + align:start position:0% +that piece probably not the best thing +but you can almost perform from it from + + align:start position:0% +but you can almost perform from it from + + + align:start position:0% +but you can almost perform from it from +the range graph thing so there's some + + align:start position:0% +the range graph thing so there's some + + + align:start position:0% +the range graph thing so there's some +things that are in between um better the + + align:start position:0% +things that are in between um better the + + + align:start position:0% +things that are in between um better the +pitch count graph can you perform from + + align:start position:0% +pitch count graph can you perform from + + + align:start position:0% +pitch count graph can you perform from +this no though you could I mean thinking + + align:start position:0% +this no though you could I mean thinking + + + align:start position:0% +this no though you could I mean thinking +about in the future you could take a + + align:start position:0% +about in the future you could take a + + + align:start position:0% +about in the future you could take a +piece's pitch count graph and uh use a + + align:start position:0% +piece's pitch count graph and uh use a + + + align:start position:0% +piece's pitch count graph and uh use a +computer to write a different piece that + + align:start position:0% +computer to write a different piece that + + + align:start position:0% +computer to write a different piece that +had the same pitch count profile um and + + align:start position:0% +had the same pitch count profile um and + + + align:start position:0% +had the same pitch count profile um and +it might be an interesting type of thing + + align:start position:0% +it might be an interesting type of thing + + + align:start position:0% +it might be an interesting type of thing +um but yeah you couldn't perform this + + align:start position:0% +um but yeah you couldn't perform this + + + align:start position:0% +um but yeah you couldn't perform this +the same piece for some ontological + + align:start position:0% +the same piece for some ontological + + + align:start position:0% +the same piece for some ontological +definition of the same piece right good + + align:start position:0% +definition of the same piece right good + + + align:start position:0% +definition of the same piece right good +we can skip the entrance graph uh second + + align:start position:0% +we can skip the entrance graph uh second + + + align:start position:0% +we can skip the entrance graph uh second +piece talks about um oh this is the B + + align:start position:0% +piece talks about um oh this is the B + + + align:start position:0% +piece talks about um oh this is the B +talk string quartet number four oops + + align:start position:0% +talk string quartet number four oops + + + align:start position:0% +talk string quartet number four oops +we'll get a tiny if it's working a few + + align:start position:0% +we'll get a tiny if it's working a few + + + align:start position:0% +we'll get a tiny if it's working a few +seconds that if it doesn't give me a + + align:start position:0% +seconds that if it doesn't give me a + + + align:start position:0% +seconds that if it doesn't give me a +YouTube + + align:start position:0% +YouTube + + + align:start position:0% +YouTube +ad no okay + + align:start position:0% +ad no okay + + + align:start position:0% +ad no okay +um B talk similar uh similar era a + + align:start position:0% +um B talk similar uh similar era a + + + align:start position:0% +um B talk similar uh similar era a +little bit earlier uh composer also + + align:start position:0% +little bit earlier uh composer also + + + align:start position:0% +little bit earlier uh composer also +Hungarian um so this is + + align:start position:0% +Hungarian um so this is + + + align:start position:0% +Hungarian um so this is +showing what is this showing I remember + + align:start position:0% +showing what is this showing I remember + + + align:start position:0% +showing what is this showing I remember +somebody who I haven't heard from + + align:start position:0% +somebody who I haven't heard from + + + align:start position:0% +somebody who I haven't heard from +yet Jonathan do you remember + + align:start position:0% + + + + align:start position:0% + +this soundes sound waves what particular + + align:start position:0% +this soundes sound waves what particular + + + align:start position:0% +this soundes sound waves what particular +parts of it + + align:start position:0% +parts of it + + + align:start position:0% +parts of it +anybody + + align:start position:0% +anybody + + + align:start position:0% +anybody +that not sure you're not sure okay good + + align:start position:0% +that not sure you're not sure okay good + + + align:start position:0% +that not sure you're not sure okay good +good not not sure saves the whole class + + align:start position:0% +good not not sure saves the whole class + + + align:start position:0% +good not not sure saves the whole class +great super harmonics harmonics no not + + align:start position:0% +great super harmonics harmonics no not + + + align:start position:0% +great super harmonics harmonics no not +exactly this yeah def amplitude how loud + + align:start position:0% +exactly this yeah def amplitude how loud + + + align:start position:0% +exactly this yeah def amplitude how loud +each part is what does it mean when the + + align:start position:0% +each part is what does it mean when the + + + align:start position:0% +each part is what does it mean when the +V is really really really really + + align:start position:0% +V is really really really really + + + align:start position:0% +V is really really really really +quiet it's not playing yep so you can + + align:start position:0% +quiet it's not playing yep so you can + + + align:start position:0% +quiet it's not playing yep so you can +quickly see which parts are playing + + align:start position:0% +quickly see which parts are playing + + + align:start position:0% +quickly see which parts are playing +where and then somehow make a composite + + align:start position:0% +where and then somehow make a composite + + + align:start position:0% +where and then somehow make a composite +that is more like the um the uh what do + + align:start position:0% +that is more like the um the uh what do + + + align:start position:0% +that is more like the um the uh what do +you call it the amplitude wave type the + + align:start position:0% +you call it the amplitude wave type the + + + align:start position:0% +you call it the amplitude wave type the +um the sound wave um of of the piece as + + align:start position:0% +um the sound wave um of of the piece as + + + align:start position:0% +um the sound wave um of of the piece as +a whole so yeah um I don't this is this + + align:start position:0% +a whole so yeah um I don't this is this + + + align:start position:0% +a whole so yeah um I don't this is this +is one of the ones in that article that + + align:start position:0% +is one of the ones in that article that + + + align:start position:0% +is one of the ones in that article that +one of the most so I'm always like eh + + align:start position:0% +one of the most so I'm always like eh + + + align:start position:0% +one of the most so I'm always like eh +doesn't get so much out of it but um but + + align:start position:0% +doesn't get so much out of it but um but + + + align:start position:0% +doesn't get so much out of it but um but +because this is the type of thing + + align:start position:0% +because this is the type of thing + + + align:start position:0% +because this is the type of thing +computational people do wrote my own + + align:start position:0% +computational people do wrote my own + + + align:start position:0% +computational people do wrote my own +program to generate the same thing um + + align:start position:0% +program to generate the same thing um + + + align:start position:0% +program to generate the same thing um +this is a piece by hien's uh uh by uh + + align:start position:0% +this is a piece by hien's uh uh by uh + + + align:start position:0% +this is a piece by hien's uh uh by uh +yoseph Heiden uh around I guess 1790 uh + + align:start position:0% +yoseph Heiden uh around I guess 1790 uh + + + align:start position:0% +yoseph Heiden uh around I guess 1790 uh +called the surprise symy uh anyone know + + align:start position:0% +called the surprise symy uh anyone know + + + align:start position:0% +called the surprise symy uh anyone know +where the surprise happens from looking + + align:start position:0% +where the surprise happens from looking + + + align:start position:0% +where the surprise happens from looking +at this yeah so sometimes these things + + align:start position:0% +at this yeah so sometimes these things + + + align:start position:0% +at this yeah so sometimes these things +can be uh very great I didn't even + + align:start position:0% +can be uh very great I didn't even + + + align:start position:0% +can be uh very great I didn't even +realize though that the Dynamics were + + align:start position:0% +realize though that the Dynamics were + + + align:start position:0% +realize though that the Dynamics were +kind of thinning out leading up to it I + + align:start position:0% +kind of thinning out leading up to it I + + + align:start position:0% +kind of thinning out leading up to it I +always knew that there was one gigantic + + align:start position:0% +always knew that there was one gigantic + + + align:start position:0% +always knew that there was one gigantic +cord right about here um go on and you + + align:start position:0% +cord right about here um go on and you + + + align:start position:0% +cord right about here um go on and you +can see the various other places that + + align:start position:0% +can see the various other places that + + + align:start position:0% +can see the various other places that +these things happen so so these can be + + align:start position:0% +these things happen so so these can be + + + align:start position:0% +these things happen so so these can be +good representations for some + + align:start position:0% +good representations for some + + + align:start position:0% +good representations for some +things so what's this hum drum that he's + + align:start position:0% +things so what's this hum drum that he's + + + align:start position:0% +things so what's this hum drum that he's +talking about anybody + + align:start position:0% +talking about anybody + + + align:start position:0% +talking about anybody +remember this part yeah + + align:start position:0% + + + + align:start position:0% + +a to manipulate + + align:start position:0% +a to manipulate + + + align:start position:0% +a to manipulate +dat great so it's a I think I heard it's + + align:start position:0% +dat great so it's a I think I heard it's + + + align:start position:0% +dat great so it's a I think I heard it's +a framework that's used to manipulate + + align:start position:0% +a framework that's used to manipulate + + + align:start position:0% +a framework that's used to manipulate +musical data uh in the Unix uh terminal + + align:start position:0% +musical data uh in the Unix uh terminal + + + align:start position:0% +musical data uh in the Unix uh terminal +great um it's written by um it was + + align:start position:0% +great um it's written by um it was + + + align:start position:0% +great um it's written by um it was +originally uh written by um music cogn + + align:start position:0% +originally uh written by um music cogn + + + align:start position:0% +originally uh written by um music cogn +cognition perception and Theory + + align:start position:0% +cognition perception and Theory + + + align:start position:0% +cognition perception and Theory +specialist uh David hiron and um who + + align:start position:0% +specialist uh David hiron and um who + + + align:start position:0% +specialist uh David hiron and um who +we're going to read a lot about what he + + align:start position:0% +we're going to read a lot about what he + + + align:start position:0% +we're going to read a lot about what he +used hum drum to kind of demonstrate new + + align:start position:0% +used hum drum to kind of demonstrate new + + + align:start position:0% +used hum drum to kind of demonstrate new +about music but right now we're mostly + + align:start position:0% +about music but right now we're mostly + + + align:start position:0% +about music but right now we're mostly +you know we're looking at oh what he did + + align:start position:0% +you know we're looking at oh what he did + + + align:start position:0% +you know we're looking at oh what he did +um humdrum is uh in many ways the pred + + align:start position:0% +um humdrum is uh in many ways the pred + + + align:start position:0% +um humdrum is uh in many ways the pred +the predecessor to music 21 and a + + align:start position:0% +the predecessor to music 21 and a + + + align:start position:0% +the predecessor to music 21 and a +lecture that David hon the inventor gave + + align:start position:0% +lecture that David hon the inventor gave + + + align:start position:0% +lecture that David hon the inventor gave +when I was uh I think I was a first year + + align:start position:0% +when I was uh I think I was a first year + + + align:start position:0% +when I was uh I think I was a first year +grad student to like change my life I'm + + align:start position:0% +grad student to like change my life I'm + + + align:start position:0% +grad student to like change my life I'm +like oh my gosh I want to do this but uh + + align:start position:0% +like oh my gosh I want to do this but uh + + + align:start position:0% +like oh my gosh I want to do this but uh +your system the system was already 10 15 + + align:start position:0% +your system the system was already 10 15 + + + align:start position:0% +your system the system was already 10 15 +years old by then 20 years old maybe and + + align:start position:0% +years old by then 20 years old maybe and + + + align:start position:0% +years old by then 20 years old maybe and +um like we have these things called + + align:start position:0% +um like we have these things called + + + align:start position:0% +um like we have these things called +objects now so but um so it's a non-ob + + align:start position:0% +objects now so but um so it's a non-ob + + + align:start position:0% +objects now so but um so it's a non-ob +oriented it's shell shell scripting + + align:start position:0% +oriented it's shell shell scripting + + + align:start position:0% +oriented it's shell shell scripting +things which is pretty cool if anybody + + align:start position:0% +things which is pretty cool if anybody + + + align:start position:0% +things which is pretty cool if anybody +anyone ever pipe a script from one thing + + align:start position:0% +anyone ever pipe a script from one thing + + + align:start position:0% +anyone ever pipe a script from one thing +to the next you yeah youve input send it + + align:start position:0% +to the next you yeah youve input send it + + + align:start position:0% +to the next you yeah youve input send it +to a program uh input text usually or or + + align:start position:0% +to a program uh input text usually or or + + + align:start position:0% +to a program uh input text usually or or +bytes and then it sends something out + + align:start position:0% +bytes and then it sends something out + + + align:start position:0% +bytes and then it sends something out +and you can send it to the next program + + align:start position:0% +and you can send it to the next program + + + align:start position:0% +and you can send it to the next program +so you could have one program that just + + align:start position:0% +so you could have one program that just + + + align:start position:0% +so you could have one program that just +goes through and strips all the ties + + align:start position:0% +goes through and strips all the ties + + + align:start position:0% +goes through and strips all the ties +from notes and then you have another + + align:start position:0% +from notes and then you have another + + + align:start position:0% +from notes and then you have another +program that you know labels the pitch + + align:start position:0% +program that you know labels the pitch + + + align:start position:0% +program that you know labels the pitch +classes of everything um very very cool + + align:start position:0% +classes of everything um very very cool + + + align:start position:0% +classes of everything um very very cool +very um new things and so hum drum had + + align:start position:0% +very um new things and so hum drum had + + + align:start position:0% +very um new things and so hum drum had +its own format which was called um + + align:start position:0% +its own format which was called um + + + align:start position:0% +its own format which was called um +actually I'm going to jump through some + + align:start position:0% +actually I'm going to jump through some + + + align:start position:0% +actually I'm going to jump through some +some of these questions don't don't seem + + align:start position:0% +some of these questions don't don't seem + + + align:start position:0% +some of these questions don't don't seem +as relevant for class discussion called + + align:start position:0% +as relevant for class discussion called + + + align:start position:0% +as relevant for class discussion called +Kern which was basically a musical score + + align:start position:0% +Kern which was basically a musical score + + + align:start position:0% +Kern which was basically a musical score +turned sideways so first part going + + align:start position:0% +turned sideways so first part going + + + align:start position:0% +turned sideways so first part going +vertically here second part vertically + + align:start position:0% +vertically here second part vertically + + + align:start position:0% +vertically here second part vertically +here third part and so on + + align:start position:0% +here third part and so on + + + align:start position:0% +here third part and so on +um and um and so this was a way that + + align:start position:0% +um and um and so this was a way that + + + align:start position:0% +um and um and so this was a way that +meant that looking horizontally you + + align:start position:0% +meant that looking horizontally you + + + align:start position:0% +meant that looking horizontally you +could see anything that was happening at + + align:start position:0% +could see anything that was happening at + + + align:start position:0% +could see anything that was happening at +the same time and very useful back + + align:start position:0% +the same time and very useful back + + + align:start position:0% +the same time and very useful back +before graphical editors where you can + + align:start position:0% +before graphical editors where you can + + + align:start position:0% +before graphical editors where you can +uh tab among + + align:start position:0% +uh tab among + + + align:start position:0% +uh tab among +them oops contrasting um uh in the + + align:start position:0% +them oops contrasting um uh in the + + + align:start position:0% +them oops contrasting um uh in the +article was this particular um + + align:start position:0% +article was this particular um + + + align:start position:0% +article was this particular um +format ESS code and this is um one of + + align:start position:0% +format ESS code and this is um one of + + + align:start position:0% +format ESS code and this is um one of +ones how do we read + + align:start position:0% +ones how do we read + + + align:start position:0% +ones how do we read +this some people Adam great but I want + + align:start position:0% +this some people Adam great but I want + + + align:start position:0% +this some people Adam great but I want +to want to get some more reluctant + + align:start position:0% +to want to get some more reluctant + + + align:start position:0% +to want to get some more reluctant +participants and we'll come + + align:start position:0% +participants and we'll come + + + align:start position:0% +participants and we'll come +back anyone want to take a guess what + + align:start position:0% +back anyone want to take a guess what + + + align:start position:0% +back anyone want to take a guess what +anything means um yeah John like some + + align:start position:0% +anything means um yeah John like some + + + align:start position:0% +anything means um yeah John like some +sort of figured base some sort of + + align:start position:0% +sort of figured base some sort of + + + align:start position:0% +sort of figured base some sort of +figured base yeah does totally look like + + align:start position:0% +figured base yeah does totally look like + + + align:start position:0% +figured base yeah does totally look like +that not exactly what what it actually + + align:start position:0% +that not exactly what what it actually + + + align:start position:0% +that not exactly what what it actually +is but great great first first guess + + align:start position:0% +is but great great first first guess + + + align:start position:0% +is but great great first first guess +what what numbers do you see that um + + align:start position:0% +what what numbers do you see that um + + + align:start position:0% +what what numbers do you see that um +that that make you think it's like + + align:start position:0% +that that make you think it's like + + + align:start position:0% +that that make you think it's like +figured base so scale degrees scale + + align:start position:0% +figured base so scale degrees scale + + + align:start position:0% +figured base so scale degrees scale +degrees Yeah so something maybe to do + + align:start position:0% +degrees Yeah so something maybe to do + + + align:start position:0% +degrees Yeah so something maybe to do +with scale degrees do we see eights and + + align:start position:0% +with scale degrees do we see eights and + + + align:start position:0% +with scale degrees do we see eights and +nines are zeros no no so so that can be + + align:start position:0% +nines are zeros no no so so that can be + + + align:start position:0% +nines are zeros no no so so that can be +a good good thing what so great great + + align:start position:0% +a good good thing what so great great + + + align:start position:0% +a good good thing what so great great +guess that moved us into toward the + + align:start position:0% +guess that moved us into toward the + + + align:start position:0% +guess that moved us into toward the +right direction um these are scale + + align:start position:0% +right direction um these are scale + + + align:start position:0% +right direction um these are scale +degrees what's all this other stuff + + align:start position:0% +degrees what's all this other stuff + + + align:start position:0% +degrees what's all this other stuff +might + + align:start position:0% +might + + + align:start position:0% +might +be yeah Hannah is like the sharps and + + align:start position:0% +be yeah Hannah is like the sharps and + + + align:start position:0% +be yeah Hannah is like the sharps and +the dashes represent like The Accidental + + align:start position:0% +the dashes represent like The Accidental + + + align:start position:0% +the dashes represent like The Accidental +so Sharps probably a good one do um with + + align:start position:0% +so Sharps probably a good one do um with + + + align:start position:0% +so Sharps probably a good one do um with +this part so this piece would have a lot + + align:start position:0% +this part so this piece would have a lot + + + align:start position:0% +this part so this piece would have a lot +of accidentals if the underscore did and + + align:start position:0% +of accidentals if the underscore did and + + + align:start position:0% +of accidentals if the underscore did and +might like the shorter Dash oh the + + align:start position:0% +might like the shorter Dash oh the + + + align:start position:0% +might like the shorter Dash oh the +shorter Dash can you tell me where one + + align:start position:0% +shorter Dash can you tell me where one + + + align:start position:0% +shorter Dash can you tell me where one +is uh I guess like in the first line the + + align:start position:0% +is uh I guess like in the first line the + + + align:start position:0% +is uh I guess like in the first line the +one before the seven yeah I should be + + align:start position:0% +one before the seven yeah I should be + + + align:start position:0% +one before the seven yeah I should be +like can somebody point out one that I + + align:start position:0% +like can somebody point out one that I + + + align:start position:0% +like can somebody point out one that I +can reach yeah this one or this one good + + align:start position:0% +can reach yeah this one or this one good + + + align:start position:0% +can reach yeah this one or this one good +good yeah so um minus signs you've I + + align:start position:0% +good yeah so um minus signs you've I + + + align:start position:0% +good yeah so um minus signs you've I +think we've already seen that as a way + + align:start position:0% +think we've already seen that as a way + + + align:start position:0% +think we've already seen that as a way +of representing um maybe Flats flats and + + align:start position:0% +of representing um maybe Flats flats and + + + align:start position:0% +of representing um maybe Flats flats and +Shar shs I mean when we say there is no + + align:start position:0% +Shar shs I mean when we say there is no + + + align:start position:0% +Shar shs I mean when we say there is no +such thing as a good representation or + + align:start position:0% +such thing as a good representation or + + + align:start position:0% +such thing as a good representation or +bad representation per se I will say it + + align:start position:0% +bad representation per se I will say it + + + align:start position:0% +bad representation per se I will say it +is a bad representation If this means + + align:start position:0% +is a bad representation If this means + + + align:start position:0% +is a bad representation If this means +flat and that means sharp but if we + + align:start position:0% +flat and that means sharp but if we + + + align:start position:0% +flat and that means sharp but if we +reverse them so I'll assume that good uh + + align:start position:0% +reverse them so I'll assume that good uh + + + align:start position:0% +reverse them so I'll assume that good uh +What are some of the other symbols we + + align:start position:0% +What are some of the other symbols we + + + align:start position:0% +What are some of the other symbols we +see yeah Adam then symbols in the melody + + align:start position:0% +see yeah Adam then symbols in the melody + + + align:start position:0% +see yeah Adam then symbols in the melody +or any what's some other things you see + + align:start position:0% +or any what's some other things you see + + + align:start position:0% +or any what's some other things you see +up here top is the composer top is the + + align:start position:0% +up here top is the composer top is the + + + align:start position:0% +up here top is the composer top is the +composer maybe + + align:start position:0% +composer maybe + + + align:start position:0% +composer maybe +boam it's not actually but but good + + align:start position:0% +boam it's not actually but but good + + + align:start position:0% +boam it's not actually but but good +guess good guess that's great + + align:start position:0% +guess good guess that's great + + + align:start position:0% +guess good guess that's great +um yeah Vincent sorry sorry V and then I + + align:start position:0% +um yeah Vincent sorry sorry V and then I + + + align:start position:0% +um yeah Vincent sorry sorry V and then I +I don't think he's going to fire + + align:start position:0% +I don't think he's going to fire + + + align:start position:0% +I don't think he's going to fire +everything yep the underscores represent + + align:start position:0% +everything yep the underscores represent + + + align:start position:0% +everything yep the underscores represent +duration and then like the 16y + + align:start position:0% +duration and then like the 16y + + + align:start position:0% +duration and then like the 16y +represents like the lowest okay okay + + align:start position:0% +represents like the lowest okay okay + + + align:start position:0% +represents like the lowest okay okay +good good good so we'll start we'll + + align:start position:0% +good good good so we'll start we'll + + + align:start position:0% +good good good so we'll start we'll +start with one thing the underscores + + align:start position:0% +start with one thing the underscores + + + align:start position:0% +start with one thing the underscores +might represent duration so what does + + align:start position:0% +might represent duration so what does + + + align:start position:0% +might represent duration so what does +that what's that mean think think about + + align:start position:0% +that what's that mean think think about + + + align:start position:0% +that what's that mean think think about +that for a second we'll come back that's + + align:start position:0% +that for a second we'll come back that's + + + align:start position:0% +that for a second we'll come back that's +totally what I say okay well then fill + + align:start position:0% +totally what I say okay well then fill + + + align:start position:0% +totally what I say okay well then fill +it out a little bit um well I was going + + align:start position:0% +it out a little bit um well I was going + + + align:start position:0% +it out a little bit um well I was going +to guess that like one underscore would + + align:start position:0% +to guess that like one underscore would + + + align:start position:0% +to guess that like one underscore would +be some standard like maybe a coordinate + + align:start position:0% +be some standard like maybe a coordinate + + + align:start position:0% +be some standard like maybe a coordinate +or something like that and then two is + + align:start position:0% +or something like that and then two is + + + align:start position:0% +or something like that and then two is +more yep and then two is more how it's + + align:start position:0% +more yep and then two is more how it's + + + align:start position:0% +more yep and then two is more how it's +it's a fixed width font but it's + + align:start position:0% +it's a fixed width font but it's + + + align:start position:0% +it's a fixed width font but it's +stilling hard to see do we what are the + + align:start position:0% +stilling hard to see do we what are the + + + align:start position:0% +stilling hard to see do we what are the +lengths that we see the + + align:start position:0% +lengths that we see the + + + align:start position:0% +lengths that we see the +most + + align:start position:0% +most + + + align:start position:0% +most +one two do we see three a + + align:start position:0% +one two do we see three a + + + align:start position:0% +one two do we see three a +lot not too many no end of the line end + + align:start position:0% +lot not too many no end of the line end + + + align:start position:0% +lot not too many no end of the line end +of the line line yeah so there's some + + align:start position:0% +of the line line yeah so there's some + + + align:start position:0% +of the line line yeah so there's some +places where you see through good good + + align:start position:0% +places where you see through good good + + + align:start position:0% +places where you see through good good +so that might have something to do with + + align:start position:0% +so that might have something to do with + + + align:start position:0% +so that might have something to do with +things + + align:start position:0% +things + + + align:start position:0% +things +um any places where there's two that are + + align:start position:0% +um any places where there's two that are + + + align:start position:0% +um any places where there's two that are +uh numbers that + + align:start position:0% +uh numbers that + + + align:start position:0% +uh numbers that +are without uh separating + + align:start position:0% + + + + align:start position:0% + +underscore John where do you see one + + align:start position:0% +underscore John where do you see one + + + align:start position:0% +underscore John where do you see one +bottom left bottom left good thanks for + + align:start position:0% +bottom left bottom left good thanks for + + + align:start position:0% +bottom left bottom left good thanks for +finding one I can point to you yep so + + align:start position:0% +finding one I can point to you yep so + + + align:start position:0% +finding one I can point to you yep so +and what's right proceeding it + + align:start position:0% +and what's right proceeding it + + + align:start position:0% +and what's right proceeding it +period period what period might + + align:start position:0% +period period what period might + + + align:start position:0% +period period what period might +represent rest might represent a rest + + align:start position:0% +represent rest might represent a rest + + + align:start position:0% +represent rest might represent a rest +what else might it represent + + align:start position:0% +what else might it represent + + + align:start position:0% +what else might it represent +yeah good a DOT a DOT so it could be one + + align:start position:0% +yeah good a DOT a DOT so it could be one + + + align:start position:0% +yeah good a DOT a DOT so it could be one +of those + + align:start position:0% +of those + + + align:start position:0% +of those +things quite often after let's see so + + align:start position:0% +things quite often after let's see so + + + align:start position:0% +things quite often after let's see so +one of the ways we can figure out is if + + align:start position:0% +one of the ways we can figure out is if + + + align:start position:0% +one of the ways we can figure out is if +we get a particular length and then does + + align:start position:0% +we get a particular length and then does + + + align:start position:0% +we get a particular length and then does +everything else work what do you think + + align:start position:0% +everything else work what do you think + + + align:start position:0% +everything else work what do you think +the space + + align:start position:0% + + + + align:start position:0% + +means measure separation measure + + align:start position:0% +means measure separation measure + + + align:start position:0% +means measure separation measure +separation some measures seem to be a + + align:start position:0% +separation some measures seem to be a + + + align:start position:0% +separation some measures seem to be a +lot shorter than others but yeah it + + align:start position:0% +lot shorter than others but yeah it + + + align:start position:0% +lot shorter than others but yeah it +could be a measure separation could also + + align:start position:0% +could be a measure separation could also + + + align:start position:0% +could be a measure separation could also +be as a lot of these formats are just to + + align:start position:0% +be as a lot of these formats are just to + + + align:start position:0% +be as a lot of these formats are just to +make it easier for us to read that + + align:start position:0% +make it easier for us to read that + + + align:start position:0% +make it easier for us to read that +there's a certain readability that's + + align:start position:0% +there's a certain readability that's + + + align:start position:0% +there's a certain readability that's +built into some good good um and uh + + align:start position:0% +built into some good good um and uh + + + align:start position:0% +built into some good good um and uh +Vincent you were starting to say + + align:start position:0% +Vincent you were starting to say + + + align:start position:0% +Vincent you were starting to say +something about the 16 up there having + + align:start position:0% +something about the 16 up there having + + + align:start position:0% +something about the 16 up there having +something to do with the uh so like how + + align:start position:0% +something to do with the uh so like how + + + align:start position:0% +something to do with the uh so like how +the UND duration how some have like one + + align:start position:0% +the UND duration how some have like one + + + align:start position:0% +the UND duration how some have like one +or two um but those would all be + + align:start position:0% +or two um but those would all be + + + align:start position:0% +or two um but those would all be +multiples of like whatever is best right + + align:start position:0% +multiples of like whatever is best right + + + align:start position:0% +multiples of like whatever is best right +there would be the 16 so like the first + + align:start position:0% +there would be the 16 so like the first + + + align:start position:0% +there would be the 16 so like the first +one would be like two 16 notes or an E + + align:start position:0% +one would be like two 16 notes or an E + + + align:start position:0% +one would be like two 16 notes or an E +note so this would be two 16th notes or + + align:start position:0% +note so this would be two 16th notes or + + + align:start position:0% +note so this would be two 16th notes or +uhuh oh so like got that five where + + align:start position:0% +uhuh oh so like got that five where + + + align:start position:0% +uhuh oh so like got that five where +there's one one be one 16th note and + + align:start position:0% +there's one one be one 16th note and + + + align:start position:0% +there's one one be one 16th note and +then the six great so let's see what do + + align:start position:0% +then the six great so let's see what do + + + align:start position:0% +then the six great so let's see what do +you think 44 means everybody 44 right + + align:start position:0% +you think 44 means everybody 44 right + + + align:start position:0% +you think 44 means everybody 44 right +good M do you want to say something on + + align:start position:0% +good M do you want to say something on + + + align:start position:0% +good M do you want to say something on +that um yeah yeah um basically along + + align:start position:0% +that um yeah yeah um basically along + + + align:start position:0% +that um yeah yeah um basically along +these lines and yeah I think the thing + + align:start position:0% +these lines and yeah I think the thing + + + align:start position:0% +these lines and yeah I think the thing +that we're probably trying to get to now + + align:start position:0% +that we're probably trying to get to now + + + align:start position:0% +that we're probably trying to get to now +is that like it doesn't quite seem to + + align:start position:0% +is that like it doesn't quite seem to + + + align:start position:0% +is that like it doesn't quite seem to +add up if it's 44 on each one with one + + align:start position:0% +add up if it's 44 on each one with one + + + align:start position:0% +add up if it's 44 on each one with one +um is uh 16th so like there are a lot of + + align:start position:0% +um is uh 16th so like there are a lot of + + + align:start position:0% +um is uh 16th so like there are a lot of +measures with three and I believe it's + + align:start position:0% +measures with three and I believe it's + + + align:start position:0% +measures with three and I believe it's +two underscores like the the the I'm + + align:start position:0% +two underscores like the the the I'm + + + align:start position:0% +two underscores like the the the I'm +sorry to make you point super high maybe + + align:start position:0% +sorry to make you point super high maybe + + + align:start position:0% +sorry to make you point super high maybe +there's an example lower but the the Top + + align:start position:0% +there's an example lower but the the Top + + + align:start position:0% +there's an example lower but the the Top +Line the the first one it seems like the + + align:start position:0% +Line the the first one it seems like the + + + align:start position:0% +Line the the first one it seems like the +full um measure yeah yep so it's two + + align:start position:0% +full um measure yeah yep so it's two + + + align:start position:0% +full um measure yeah yep so it's two +underscores yeah two two which would + + align:start position:0% +underscores yeah two two which would + + + align:start position:0% +underscores yeah two two which would +imply that they're all quarter nodes if + + align:start position:0% +imply that they're all quarter nodes if + + + align:start position:0% +imply that they're all quarter nodes if +it's in four4 which means that like and + + align:start position:0% +it's in four4 which means that like and + + + align:start position:0% +it's in four4 which means that like and +then the one right below it has the + + align:start position:0% +then the one right below it has the + + + align:start position:0% +then the one right below it has the +exact same but like in the last + + align:start position:0% +exact same but like in the last + + + align:start position:0% +exact same but like in the last +um with the duration of the coord note + + align:start position:0% +um with the duration of the coord note + + + align:start position:0% +um with the duration of the coord note +splits it up so those seem like eth + + align:start position:0% +splits it up so those seem like eth + + + align:start position:0% +splits it up so those seem like eth +notes rather than 16th notes great super + + align:start position:0% +notes rather than 16th notes great super + + + align:start position:0% +notes rather than 16th notes great super +awesome great let's let's do a tiny bit + + align:start position:0% +awesome great let's let's do a tiny bit + + + align:start position:0% +awesome great let's let's do a tiny bit +of the metadata um you can take a guess + + align:start position:0% +of the metadata um you can take a guess + + + align:start position:0% +of the metadata um you can take a guess +what language is the + + align:start position:0% + + + + align:start position:0% + +metadata anybody + + align:start position:0% +metadata anybody + + + align:start position:0% +metadata anybody +know see just yeah Jason I this is the + + align:start position:0% +know see just yeah Jason I this is the + + + align:start position:0% +know see just yeah Jason I this is the +code from the reading Yep this isak code + + align:start position:0% +code from the reading Yep this isak code + + + align:start position:0% +code from the reading Yep this isak code +and what what's the uh isach or Essen is + + align:start position:0% +and what what's the uh isach or Essen is + + + align:start position:0% +and what what's the uh isach or Essen is +the the two ways of putting it yep and + + align:start position:0% +the the two ways of putting it yep and + + + align:start position:0% +the the two ways of putting it yep and +um anyone know where Essen is yeah + + align:start position:0% +um anyone know where Essen is yeah + + + align:start position:0% +um anyone know where Essen is yeah +Germany Germany do we see some German + + align:start position:0% +Germany Germany do we see some German + + + align:start position:0% +Germany Germany do we see some German +things good so this is a a very famous + + align:start position:0% +things good so this is a a very famous + + + align:start position:0% +things good so this is a a very famous +piece and I want to say um as you're + + align:start position:0% +piece and I want to say um as you're + + + align:start position:0% +piece and I want to say um as you're +choosing things to represent and + + align:start position:0% +choosing things to represent and + + + align:start position:0% +choosing things to represent and +choosing things in it um and Nicholas + + align:start position:0% +choosing things in it um and Nicholas + + + align:start position:0% +choosing things in it um and Nicholas +cook is amazing I think Nicholas CH + + align:start position:0% +cook is amazing I think Nicholas CH + + + align:start position:0% +cook is amazing I think Nicholas CH +chose the absolute worst piece he + + align:start position:0% +chose the absolute worst piece he + + + align:start position:0% +chose the absolute worst piece he +possibly could have chosen to be the + + align:start position:0% +possibly could have chosen to be the + + + align:start position:0% +possibly could have chosen to be the +demonstration this and I've thought of + + align:start position:0% +demonstration this and I've thought of + + + align:start position:0% +demonstration this and I've thought of +switching out + + align:start position:0% +switching out + + + align:start position:0% +switching out +um cut might be it's not sent for cuer + + align:start position:0% +um cut might be it's not sent for cuer + + + align:start position:0% +um cut might be it's not sent for cuer +it's the something about the title + + align:start position:0% +it's the something about the title + + + align:start position:0% +it's the something about the title +Germany Germany anyone El + + align:start position:0% +Germany Germany anyone El + + + align:start position:0% +Germany Germany anyone El +overall it's the Nazi national + + align:start position:0% +overall it's the Nazi national + + + align:start position:0% +overall it's the Nazi national +anthem so I I wish that he had chosen + + align:start position:0% +anthem so I I wish that he had chosen + + + align:start position:0% +anthem so I I wish that he had chosen +better but fortunately if we crop off + + align:start position:0% +better but fortunately if we crop off + + + align:start position:0% +better but fortunately if we crop off +the top um it is also the pre-nazi + + align:start position:0% +the top um it is also the pre-nazi + + + align:start position:0% +the top um it is also the pre-nazi +National Anthem with different words and + + align:start position:0% +National Anthem with different words and + + + align:start position:0% +National Anthem with different words and +the current national anthem and a piece + + align:start position:0% +the current national anthem and a piece + + + align:start position:0% +the current national anthem and a piece +composed by yoseph Heiden so the + + align:start position:0% +composed by yoseph Heiden so the + + + align:start position:0% +composed by yoseph Heiden so the +Surprise Symphony composer and I wanted + + align:start position:0% +Surprise Symphony composer and I wanted + + + align:start position:0% +Surprise Symphony composer and I wanted +to um put it up it's rather small might + + align:start position:0% +to um put it up it's rather small might + + + align:start position:0% +to um put it up it's rather small might +need to zoom in or or get up but see or + + align:start position:0% +need to zoom in or or get up but see or + + + align:start position:0% +need to zoom in or or get up but see or +you can look at the article see if you + + align:start position:0% +you can look at the article see if you + + + align:start position:0% +you can look at the article see if you +can re Now read the notation from + + align:start position:0% +can re Now read the notation from + + + align:start position:0% +can re Now read the notation from +hearing this assuming YouTube's going to + + align:start position:0% +hearing this assuming YouTube's going to + + + align:start position:0% +hearing this assuming YouTube's going to +work this time and this is the modern + + align:start position:0% +work this time and this is the modern + + + align:start position:0% +work this time and this is the modern +word + + align:start position:0% + + + + align:start position:0% + +word second + + align:start position:0% +word second + + + align:start position:0% +word second +line 31 1 + + align:start position:0% +line 31 1 + + + align:start position:0% +line 31 1 +5 1 2 3 2 4 3 + + align:start position:0% + + + + align:start position:0% + +2 oh was that a + + align:start position:0% +2 oh was that a + + + align:start position:0% +2 oh was that a +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +flat might be an otive + + align:start position:0% +flat might be an otive + + + align:start position:0% +flat might be an otive +[Music] + + align:start position:0% + + + + align:start position:0% + +sign you can hear the sharps are + + align:start position:0% +sign you can hear the sharps are + + + align:start position:0% +sign you can hear the sharps are +definitely Sharps those who can hear + + align:start position:0% +definitely Sharps those who can hear + + + align:start position:0% +definitely Sharps those who can hear +secondary + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +dominance anyhow we don't have to hear + + align:start position:0% +dominance anyhow we don't have to hear + + + align:start position:0% +dominance anyhow we don't have to hear +the + + align:start position:0% +the + + + align:start position:0% +the +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +rest yeah yeah yeah you win the World + + align:start position:0% +rest yeah yeah yeah you win the World + + + align:start position:0% +rest yeah yeah yeah you win the World +Cup more than us we know + + align:start position:0% +Cup more than us we know + + + align:start position:0% +Cup more than us we know +um okay um + + align:start position:0% +um okay um + + + align:start position:0% +um okay um +so two more two more questions one I + + align:start position:0% +so two more two more questions one I + + + align:start position:0% +so two more two more questions one I +didn't put on here before we move on to + + align:start position:0% +didn't put on here before we move on to + + + align:start position:0% +didn't put on here before we move on to +another topic + + align:start position:0% +another topic + + + align:start position:0% +another topic +um what does comparative + + align:start position:0% +um what does comparative + + + align:start position:0% +um what does comparative +musicology mean and how's it have + + align:start position:0% +musicology mean and how's it have + + + align:start position:0% +musicology mean and how's it have +anything to do with computational + + align:start position:0% +anything to do with computational + + + align:start position:0% +anything to do with computational +musicology and that's the main title of + + align:start position:0% +musicology and that's the main title of + + + align:start position:0% +musicology and that's the main title of +the piece the + + align:start position:0% +the piece the + + + align:start position:0% +the piece the +article anyone let's take stand take the + + align:start position:0% +article anyone let's take stand take the + + + align:start position:0% +article anyone let's take stand take the +first one what is + + align:start position:0% +first one what is + + + align:start position:0% +first one what is +comparative + + align:start position:0% + + + + align:start position:0% + +musicology we can probably figure it out + + align:start position:0% +musicology we can probably figure it out + + + align:start position:0% +musicology we can probably figure it out +from the words so yep I believe it was + + align:start position:0% +from the words so yep I believe it was + + + align:start position:0% +from the words so yep I believe it was +like just that concept of comparing + + align:start position:0% +like just that concept of comparing + + + align:start position:0% +like just that concept of comparing +music to each other regardless of where + + align:start position:0% +music to each other regardless of where + + + align:start position:0% +music to each other regardless of where +necessarily far yeah uh so it's it's + + align:start position:0% +necessarily far yeah uh so it's it's + + + align:start position:0% +necessarily far yeah uh so it's it's +comparing pieces of music to each other + + align:start position:0% +comparing pieces of music to each other + + + align:start position:0% +comparing pieces of music to each other +but not necessarily you know close + + align:start position:0% +but not necessarily you know close + + + align:start position:0% +but not necessarily you know close +things not oh let's look at the first + + align:start position:0% +things not oh let's look at the first + + + align:start position:0% +things not oh let's look at the first +movement and compare it to the second + + align:start position:0% +movement and compare it to the second + + + align:start position:0% +movement and compare it to the second +movement but let's look at oh um let's + + align:start position:0% +movement but let's look at oh um let's + + + align:start position:0% +movement but let's look at oh um let's +look at a nationalist song from Germany + + align:start position:0% +look at a nationalist song from Germany + + + align:start position:0% +look at a nationalist song from Germany +and let's look at a nationalist song + + align:start position:0% +and let's look at a nationalist song + + + align:start position:0% +and let's look at a nationalist song +from Kenya and see if they have any + + align:start position:0% +from Kenya and see if they have any + + + align:start position:0% +from Kenya and see if they have any +connection let's look at um oh shoot I + + align:start position:0% +connection let's look at um oh shoot I + + + align:start position:0% +connection let's look at um oh shoot I +forgot to put it into into the slides um + + align:start position:0% +forgot to put it into into the slides um + + + align:start position:0% +forgot to put it into into the slides um +the person uh I BL on her name not + + align:start position:0% +the person uh I BL on her name not + + + align:start position:0% +the person uh I BL on her name not +checking my email I I have the picture + + align:start position:0% +checking my email I I have the picture + + + align:start position:0% +checking my email I I have the picture +to put into the slide and I didn't get + + align:start position:0% +to put into the slide and I didn't get + + + align:start position:0% +to put into the slide and I didn't get +uh her name is uh trout uh sorry uh yeah + + align:start position:0% +uh her name is uh trout uh sorry uh yeah + + + align:start position:0% +uh her name is uh trout uh sorry uh yeah +trob um big New York Times obituary and + + align:start position:0% +trob um big New York Times obituary and + + + align:start position:0% +trob um big New York Times obituary and +I have a notification that won't Sandra + + align:start position:0% +I have a notification that won't Sandra + + + align:start position:0% +I have a notification that won't Sandra +CH the Pioneer one of the Pioneers in + + align:start position:0% +CH the Pioneer one of the Pioneers in + + + align:start position:0% +CH the Pioneer one of the Pioneers in +the psychology of comp comparative music + + align:start position:0% +the psychology of comp comparative music + + + align:start position:0% +the psychology of comp comparative music +uh mus musicology died very recently and + + align:start position:0% +uh mus musicology died very recently and + + + align:start position:0% +uh mus musicology died very recently and +she was the one who famously did + + align:start position:0% +she was the one who famously did + + + align:start position:0% +she was the one who famously did +experiments to show that people could + + align:start position:0% +experiments to show that people could + + + align:start position:0% +experiments to show that people could +identify here or two songs from the same + + align:start position:0% +identify here or two songs from the same + + + align:start position:0% +identify here or two songs from the same +culture which one's the lullabi and + + align:start position:0% +culture which one's the lullabi and + + + align:start position:0% +culture which one's the lullabi and +which one is not all throughout the + + align:start position:0% +which one is not all throughout the + + + align:start position:0% +which one is not all throughout the +world and this experiment's been um + + align:start position:0% +world and this experiment's been um + + + align:start position:0% +world and this experiment's been um +replicated with other uh musics uh quite + + align:start position:0% +replicated with other uh musics uh quite + + + align:start position:0% +replicated with other uh musics uh quite +a lot uh recently um over in the lab at + + align:start position:0% +a lot uh recently um over in the lab at + + + align:start position:0% +a lot uh recently um over in the lab at +at Harvard but she was a big one so this + + align:start position:0% +at Harvard but she was a big one so this + + + align:start position:0% +at Harvard but she was a big one so this +notion of looking across + + align:start position:0% +notion of looking across + + + align:start position:0% +notion of looking across +cultures uh anybody take um in class I + + align:start position:0% +cultures uh anybody take um in class I + + + align:start position:0% +cultures uh anybody take um in class I +think a couple people have uh intro to + + align:start position:0% +think a couple people have uh intro to + + + align:start position:0% +think a couple people have uh intro to +um to Global Music or World music yeah + + align:start position:0% +um to Global Music or World music yeah + + + align:start position:0% +um to Global Music or World music yeah +so great so um did did the word + + align:start position:0% +so great so um did did the word + + + align:start position:0% +so great so um did did the word +comparative musicology come up much in + + align:start position:0% +comparative musicology come up much in + + + align:start position:0% +comparative musicology come up much in +your class not really not really good + + align:start position:0% +your class not really not really good + + + align:start position:0% +your class not really not really good +the paper it says that that was what + + align:start position:0% +the paper it says that that was what + + + align:start position:0% +the paper it says that that was what +used to be that's what used to be + + align:start position:0% +used to be that's what used to be + + + align:start position:0% +used to be that's what used to be +ethnomusicology the study of music and + + align:start position:0% +ethnomusicology the study of music and + + + align:start position:0% +ethnomusicology the study of music and +cultures and it yeah did you you also + + align:start position:0% +cultures and it yeah did you you also + + + align:start position:0% +cultures and it yeah did you you also +didn't see in your classes yeah so + + align:start position:0% +didn't see in your classes yeah so + + + align:start position:0% +didn't see in your classes yeah so +comparativist approaches is of looking + + align:start position:0% +comparativist approaches is of looking + + + align:start position:0% +comparativist approaches is of looking +at things um from here and you know + + align:start position:0% +at things um from here and you know + + + align:start position:0% +at things um from here and you know +there and saying what's similar to them + + align:start position:0% +there and saying what's similar to them + + + align:start position:0% +there and saying what's similar to them +got a um so gave way to Modern + + align:start position:0% +got a um so gave way to Modern + + + align:start position:0% +got a um so gave way to Modern +ethnomusicology which is the study of + + align:start position:0% +ethnomusicology which is the study of + + + align:start position:0% +ethnomusicology which is the study of +Music in its culture and so the notion + + align:start position:0% +Music in its culture and so the notion + + + align:start position:0% +Music in its culture and so the notion +that um that you go to a culture you get + + align:start position:0% +that um that you go to a culture you get + + + align:start position:0% +that um that you go to a culture you get +to know the culture very well um and + + align:start position:0% +to know the culture very well um and + + + align:start position:0% +to know the culture very well um and +then learn from how the culture itself + + align:start position:0% +then learn from how the culture itself + + + align:start position:0% +then learn from how the culture itself +is describing its music in order to um + + align:start position:0% +is describing its music in order to um + + + align:start position:0% +is describing its music in order to um +say something uh valuable and and that + + align:start position:0% +say something uh valuable and and that + + + align:start position:0% +say something uh valuable and and that +the more you get to know one culture and + + align:start position:0% +the more you get to know one culture and + + + align:start position:0% +the more you get to know one culture and +the less you spend time comparing you + + align:start position:0% +the less you spend time comparing you + + + align:start position:0% +the less you spend time comparing you +know this culture in Paraguay to that + + align:start position:0% +know this culture in Paraguay to that + + + align:start position:0% +know this culture in Paraguay to that +culture in lap land uh the the more that + + align:start position:0% +culture in lap land uh the the more that + + + align:start position:0% +culture in lap land uh the the more that +you just F focus on one place the more + + align:start position:0% +you just F focus on one place the more + + + align:start position:0% +you just F focus on one place the more +depth of knowledge you'll get and in + + align:start position:0% +depth of knowledge you'll get and in + + + align:start position:0% +depth of knowledge you'll get and in +part because uh the early negative + + align:start position:0% +part because uh the early negative + + + align:start position:0% +part because uh the early negative +history of comparative um musicology uh + + align:start position:0% +history of comparative um musicology uh + + + align:start position:0% +history of comparative um musicology uh +deserves its very bad rap and we have to + + align:start position:0% +deserves its very bad rap and we have to + + + align:start position:0% +deserves its very bad rap and we have to +still be really careful for it because + + align:start position:0% +still be really careful for it because + + + align:start position:0% +still be really careful for it because +we're always going to be comparing you + + align:start position:0% +we're always going to be comparing you + + + align:start position:0% +we're always going to be comparing you +know what what are the countries I keep + + align:start position:0% +know what what are the countries I keep + + + align:start position:0% +know what what are the countries I keep +you know Paraguay and Lapland and uh and + + align:start position:0% +you know Paraguay and Lapland and uh and + + + align:start position:0% +you know Paraguay and Lapland and uh and +you know Kenya and uh okanawa and Japan + + align:start position:0% +you know Kenya and uh okanawa and Japan + + + align:start position:0% +you know Kenya and uh okanawa and Japan +and all these things together and then + + align:start position:0% +and all these things together and then + + + align:start position:0% +and all these things together and then +we're also going to compare with bein's + + align:start position:0% +we're also going to compare with bein's + + + align:start position:0% +we're also going to compare with bein's +Ninth Symphony in order to demonstrate + + align:start position:0% +Ninth Symphony in order to demonstrate + + + align:start position:0% +Ninth Symphony in order to demonstrate +uh what if you're a German around 1914 + + align:start position:0% +uh what if you're a German around 1914 + + + align:start position:0% +uh what if you're a German around 1914 +or a German around 1933 what is the + + align:start position:0% +or a German around 1933 what is the + + + align:start position:0% +or a German around 1933 what is the +conclusion you will always come after + + align:start position:0% +conclusion you will always come after + + + align:start position:0% +conclusion you will always come after +comparing all these + + align:start position:0% + + + + align:start position:0% + +things someone take a guess give a + + align:start position:0% +things someone take a guess give a + + + align:start position:0% +things someone take a guess give a +hypothal mind what's that is the best + + align:start position:0% +hypothal mind what's that is the best + + + align:start position:0% +hypothal mind what's that is the best +the who's is the best your whoever like + + align:start position:0% +the who's is the best your whoever like + + + align:start position:0% +the who's is the best your whoever like +you identify with yeah and the people + + align:start position:0% +you identify with yeah and the people + + + align:start position:0% +you identify with yeah and the people +doing this were mostly white + + align:start position:0% +doing this were mostly white + + + align:start position:0% +doing this were mostly white +Europeans so uh the comparativist + + align:start position:0% +Europeans so uh the comparativist + + + align:start position:0% +Europeans so uh the comparativist +project while it gathered a lot of data + + align:start position:0% +project while it gathered a lot of data + + + align:start position:0% +project while it gathered a lot of data +um we would now say it was embodied in + + align:start position:0% +um we would now say it was embodied in + + + align:start position:0% +um we would now say it was embodied in +the uh Narrative of of white supremacy + + align:start position:0% +the uh Narrative of of white supremacy + + + align:start position:0% +the uh Narrative of of white supremacy +oh now this class can't be shown in in + + align:start position:0% +oh now this class can't be shown in in + + + align:start position:0% +oh now this class can't be shown in in +Florida um uh but uh you know it and and + + align:start position:0% +Florida um uh but uh you know it and and + + + align:start position:0% +Florida um uh but uh you know it and and +that really really happened and the + + align:start position:0% +that really really happened and the + + + align:start position:0% +that really really happened and the +issue is um and so ethnomusicology this + + align:start position:0% +issue is um and so ethnomusicology this + + + align:start position:0% +issue is um and so ethnomusicology this +Focus tried to to say let's stop making + + align:start position:0% +Focus tried to to say let's stop making + + + align:start position:0% +Focus tried to to say let's stop making +this comparative um type of project so + + align:start position:0% +this comparative um type of project so + + + align:start position:0% +this comparative um type of project so +that um so that we can actually + + align:start position:0% +that um so that we can actually + + + align:start position:0% +that um so that we can actually +understand + + align:start position:0% +understand + + + align:start position:0% +understand +why individual pieces of music are great + + align:start position:0% +why individual pieces of music are great + + + align:start position:0% +why individual pieces of music are great +and interesting and valuable and + + align:start position:0% +and interesting and valuable and + + + align:start position:0% +and interesting and valuable and +meaningful and touching to people all + + align:start position:0% +meaningful and touching to people all + + + align:start position:0% +meaningful and touching to people all +over the world and a lot of people even + + align:start position:0% +over the world and a lot of people even + + + align:start position:0% +over the world and a lot of people even +in Germany don't like Bean's Ninth + + align:start position:0% +in Germany don't like Bean's Ninth + + + align:start position:0% +in Germany don't like Bean's Ninth +Symphony um so working as particular + + align:start position:0% +Symphony um so working as particular + + + align:start position:0% +Symphony um so working as particular +things and then the irony that comes out + + align:start position:0% +things and then the irony that comes out + + + align:start position:0% +things and then the irony that comes out +is that the comparativists were still + + align:start position:0% +is that the comparativists were still + + + align:start position:0% +is that the comparativists were still +you know looking at a small number of + + align:start position:0% +you know looking at a small number of + + + align:start position:0% +you know looking at a small number of +pieces to compare I mean quite often + + align:start position:0% +pieces to compare I mean quite often + + + align:start position:0% +pieces to compare I mean quite often +look at comparative uh musicology uh + + align:start position:0% +look at comparative uh musicology uh + + + align:start position:0% +look at comparative uh musicology uh +also called systematic at that time um + + align:start position:0% +also called systematic at that time um + + + align:start position:0% +also called systematic at that time um +systematic musicological Works we're + + align:start position:0% +systematic musicological Works we're + + + align:start position:0% +systematic musicological Works we're +talking about one piece from here one + + align:start position:0% +talking about one piece from here one + + + align:start position:0% +talking about one piece from here one +piece from here because that's all that + + align:start position:0% +piece from here because that's all that + + + align:start position:0% +piece from here because that's all that +people had um and so this go out a style + + align:start position:0% +people had um and so this go out a style + + + align:start position:0% +people had um and so this go out a style +right + + align:start position:0% +right + + + align:start position:0% +right +when this thing comes + + align:start position:0% +when this thing comes + + + align:start position:0% +when this thing comes +along and suddenly I mean not not this + + align:start position:0% +along and suddenly I mean not not this + + + align:start position:0% +along and suddenly I mean not not this +particular uh lightweight thing but the + + align:start position:0% +particular uh lightweight thing but the + + + align:start position:0% +particular uh lightweight thing but the +gigantic you know hunking ones that you + + align:start position:0% +gigantic you know hunking ones that you + + + align:start position:0% +gigantic you know hunking ones that you +can still see in the computer museums + + align:start position:0% +can still see in the computer museums + + + align:start position:0% +can still see in the computer museums +and stuff uh that were able to compare + + align:start position:0% +and stuff uh that were able to compare + + + align:start position:0% +and stuff uh that were able to compare +large numbers of information and at + + align:start position:0% +large numbers of information and at + + + align:start position:0% +large numbers of information and at +least encode their + + align:start position:0% +least encode their + + + align:start position:0% +least encode their +biases if not you know at least you + + align:start position:0% +biases if not you know at least you + + + align:start position:0% +biases if not you know at least you +could see what had been encoded into it + + align:start position:0% +could see what had been encoded into it + + + align:start position:0% +could see what had been encoded into it +so this is where the comparativist + + align:start position:0% +so this is where the comparativist + + + align:start position:0% +so this is where the comparativist +project comes together with the uh + + align:start position:0% +project comes together with the uh + + + align:start position:0% +project comes together with the uh +computational + + align:start position:0% +computational + + + align:start position:0% +computational +project but as you can see I mean the + + align:start position:0% +project but as you can see I mean the + + + align:start position:0% +project but as you can see I mean the +danger is that by using a computer we + + align:start position:0% +danger is that by using a computer we + + + align:start position:0% +danger is that by using a computer we +can still be replicating the kinds of + + align:start position:0% +can still be replicating the kinds of + + + align:start position:0% +can still be replicating the kinds of +mistakes that were made quite a bit + + align:start position:0% + + + + align:start position:0% + +ago so we're going to have to be hyper + + align:start position:0% +ago so we're going to have to be hyper + + + align:start position:0% +ago so we're going to have to be hyper +Vigilant the more + + align:start position:0% +Vigilant the more + + + align:start position:0% +Vigilant the more +more hyper Vigilant against + + align:start position:0% + + + + align:start position:0% + +that we're going to be hypervigilant and + + align:start position:0% +that we're going to be hypervigilant and + + + align:start position:0% +that we're going to be hypervigilant and +it probably means that some sometimes uh + + align:start position:0% +it probably means that some sometimes uh + + + align:start position:0% +it probably means that some sometimes uh +if for that we shouldn't be focusing on + + align:start position:0% +if for that we shouldn't be focusing on + + + align:start position:0% +if for that we shouldn't be focusing on +um on musical um things for our major + + align:start position:0% +um on musical um things for our major + + + align:start position:0% +um on musical um things for our major +projects that we don't know anything + + align:start position:0% +projects that we don't know anything + + + align:start position:0% +projects that we don't know anything +about so I'm very glad um that the + + align:start position:0% +about so I'm very glad um that the + + + align:start position:0% +about so I'm very glad um that the +encoding of of South Indian music that + + align:start position:0% +encoding of of South Indian music that + + + align:start position:0% +encoding of of South Indian music that +we have somebody in the group who is a + + align:start position:0% +we have somebody in the group who is a + + + align:start position:0% +we have somebody in the group who is a +of expert can can I call you an expert + + align:start position:0% +of expert can can I call you an expert + + + align:start position:0% +of expert can can I call you an expert +on on a a very very strong um + + align:start position:0% +on on a a very very strong um + + + align:start position:0% +on on a a very very strong um +understanding this and that we want to + + align:start position:0% +understanding this and that we want to + + + align:start position:0% +understanding this and that we want to +get to know our repertories before we + + align:start position:0% +get to know our repertories before we + + + align:start position:0% +get to know our repertories before we +work too much on them and I think it + + align:start position:0% +work too much on them and I think it + + + align:start position:0% +work too much on them and I think it +kind of comes back to um to this anyhow + + align:start position:0% +kind of comes back to um to this anyhow + + + align:start position:0% +kind of comes back to um to this anyhow +even for repertories that um might be + + align:start position:0% +even for repertories that um might be + + + align:start position:0% +even for repertories that um might be +more conventionally studied so we're + + align:start position:0% +more conventionally studied so we're + + + align:start position:0% +more conventionally studied so we're +going to look at some pieces in a bit um + + align:start position:0% +going to look at some pieces in a bit um + + + align:start position:0% +going to look at some pieces in a bit um +and uh we're going to start by jumping + + align:start position:0% +and uh we're going to start by jumping + + + align:start position:0% +and uh we're going to start by jumping +into a particular Buck Coral um and I + + align:start position:0% +into a particular Buck Coral um and I + + + align:start position:0% +into a particular Buck Coral um and I +want everybody to at some point to do + + align:start position:0% +want everybody to at some point to do + + + align:start position:0% +want everybody to at some point to do +all the things of trying to get into the + + align:start position:0% +all the things of trying to get into the + + + align:start position:0% +all the things of trying to get into the +style of that piece by hand because we + + align:start position:0% +style of that piece by hand because we + + + align:start position:0% +style of that piece by hand because we +don't want we want to be able to at + + align:start position:0% +don't want we want to be able to at + + + align:start position:0% +don't want we want to be able to at +least be a little expert ourselves on a + + align:start position:0% +least be a little expert ourselves on a + + + align:start position:0% +least be a little expert ourselves on a +particular Repertory before we turn it + + align:start position:0% +particular Repertory before we turn it + + + align:start position:0% +particular Repertory before we turn it +over to the computer helps to avoid the + + align:start position:0% +over to the computer helps to avoid the + + + align:start position:0% +over to the computer helps to avoid the +gigo or goo problem anyone know what + + align:start position:0% +gigo or goo problem anyone know what + + + align:start position:0% +gigo or goo problem anyone know what +that is + + align:start position:0% +that is + + + align:start position:0% +that is +Gio know Garing garbage out garbage in + + align:start position:0% +Gio know Garing garbage out garbage in + + + align:start position:0% +Gio know Garing garbage out garbage in +equals garbage out so we want to make + + align:start position:0% +equals garbage out so we want to make + + + align:start position:0% +equals garbage out so we want to make +sure that we're not um putting garbage + + align:start position:0% +sure that we're not um putting garbage + + + align:start position:0% +sure that we're not um putting garbage +in + + align:start position:0% +in + + + align:start position:0% +in +great I think I'm going to skip number + + align:start position:0% +great I think I'm going to skip number + + + align:start position:0% +great I think I'm going to skip number +three for now we'll do it um the sign + + align:start position:0% +three for now we'll do it um the sign + + + align:start position:0% +three for now we'll do it um the sign +score to sound because that one's a + + align:start position:0% +score to sound because that one's a + + + align:start position:0% +score to sound because that one's a +little bit me talking more and let's + + align:start position:0% +little bit me talking more and let's + + + align:start position:0% +little bit me talking more and let's +jump to a little bit of programming + + align:start position:0% +jump to a little bit of programming + + + align:start position:0% +jump to a little bit of programming +because we haven't done that in class um + + align:start position:0% +because we haven't done that in class um + + + align:start position:0% +because we haven't done that in class um +in a while so go ahead and take take a + + align:start position:0% +in a while so go ahead and take take a + + + align:start position:0% +in a while so go ahead and take take a +second or two and um grab a Jupiter + + align:start position:0% +second or two and um grab a Jupiter + + + align:start position:0% +second or two and um grab a Jupiter +notebook while I try to get my screen + + align:start position:0% +notebook while I try to get my screen + + + align:start position:0% +notebook while I try to get my screen +set up to have two things at once how + + align:start position:0% +set up to have two things at once how + + + align:start position:0% +set up to have two things at once how +about that um great you've already we're + + align:start position:0% +about that um great you've already we're + + + align:start position:0% +about that um great you've already we're +going to do some unlocking as know that + + align:start position:0% +going to do some unlocking as know that + + + align:start position:0% +going to do some unlocking as know that +this means that um from here on out + + align:start position:0% +this means that um from here on out + + + align:start position:0% +this means that um from here on out +unless you're told otherwise you may use + + align:start position:0% +unless you're told otherwise you may use + + + align:start position:0% +unless you're told otherwise you may use +um these materials in any problem Set uh + + align:start position:0% +um these materials in any problem Set uh + + + align:start position:0% +um these materials in any problem Set uh +going forward so you've already unlocked + + align:start position:0% +going forward so you've already unlocked + + + align:start position:0% +going forward so you've already unlocked +the pitch module lowercase p meaning + + align:start position:0% +the pitch module lowercase p meaning + + + align:start position:0% +the pitch module lowercase p meaning +it's a module and we'll also unlock the + + align:start position:0% +it's a module and we'll also unlock the + + + align:start position:0% +it's a module and we'll also unlock the +Note and the duration modules right + + align:start position:0% + + + + align:start position:0% + +now and we don't even we're not even + + align:start position:0% +now and we don't even we're not even + + + align:start position:0% +now and we don't even we're not even +really going to need the pitch or the + + align:start position:0% +really going to need the pitch or the + + + align:start position:0% +really going to need the pitch or the +duration module so let's start with + + align:start position:0% +duration module so let's start with + + + align:start position:0% +duration module so let's start with +everything on the Note let's um okay I'm + + align:start position:0% +everything on the Note let's um okay I'm + + + align:start position:0% +everything on the Note let's um okay I'm +going to need to get this later + + align:start position:0% +going to need to get this later + + + align:start position:0% +going to need to get this later +um + + align:start position:0% +um + + + align:start position:0% +um +let's start with one of my favorite + + align:start position:0% +let's start with one of my favorite + + + align:start position:0% +let's start with one of my favorite +notes I don't know why C five became one + + align:start position:0% +notes I don't know why C five became one + + + align:start position:0% +notes I don't know why C five became one +of my favorite notes I think it just + + align:start position:0% +of my favorite notes I think it just + + + align:start position:0% +of my favorite notes I think it just +demonstrates something and it's right in + + align:start position:0% +demonstrates something and it's right in + + + align:start position:0% +demonstrates something and it's right in +the middle screen good and + + align:start position:0% + + + + align:start position:0% + +um always remember that you can get a + + align:start position:0% +um always remember that you can get a + + + align:start position:0% +um always remember that you can get a +list of um of what any object can do and + + align:start position:0% +list of um of what any object can do and + + + align:start position:0% +list of um of what any object can do and +by the way you all got its upper and um + + align:start position:0% +by the way you all got its upper and um + + + align:start position:0% +by the way you all got its upper and um +the class rule is I go too fast you say + + align:start position:0% +the class rule is I go too fast you say + + + align:start position:0% +the class rule is I go too fast you say +slow down okay everybody practice that + + align:start position:0% +slow down okay everybody practice that + + + align:start position:0% +slow down okay everybody practice that +say It Out Slow Down slow down good you + + align:start position:0% +say It Out Slow Down slow down good you + + + align:start position:0% +say It Out Slow Down slow down good you +don't want me to slow down right now but + + align:start position:0% +don't want me to slow down right now but + + + align:start position:0% +don't want me to slow down right now but +at some point you will and just shout it + + align:start position:0% +at some point you will and just shout it + + + align:start position:0% +at some point you will and just shout it +out great so you can always get this uh + + align:start position:0% +out great so you can always get this uh + + + align:start position:0% +out great so you can always get this uh +python unhelpfully uh gives it an + + align:start position:0% +python unhelpfully uh gives it an + + + align:start position:0% +python unhelpfully uh gives it an +alphabetical order which means the + + align:start position:0% +alphabetical order which means the + + + align:start position:0% +alphabetical order which means the +things you don't want to know about the + + align:start position:0% +things you don't want to know about the + + + align:start position:0% +things you don't want to know about the +private things come first but um you can + + align:start position:0% +private things come first but um you can + + + align:start position:0% +private things come first but um you can +see some of the things are happening + + align:start position:0% +see some of the things are happening + + + align:start position:0% +see some of the things are happening +here and very nicely uh you'll see that + + align:start position:0% +here and very nicely uh you'll see that + + + align:start position:0% +here and very nicely uh you'll see that +duration is one of the attributes or + + align:start position:0% +duration is one of the attributes or + + + align:start position:0% +duration is one of the attributes or +Properties or something of of a note + + align:start position:0% +Properties or something of of a note + + + align:start position:0% +Properties or something of of a note +and Pitch is also a property of a note + + align:start position:0% +and Pitch is also a property of a note + + + align:start position:0% +and Pitch is also a property of a note +so that's pretty good + + align:start position:0% +so that's pretty good + + + align:start position:0% +so that's pretty good +yep so we can get that pitch from the + + align:start position:0% +yep so we can get that pitch from the + + + align:start position:0% +yep so we can get that pitch from the +note object and it's + + align:start position:0% +note object and it's + + + align:start position:0% +note object and it's +looks pretty similar to um the other + + align:start position:0% +looks pretty similar to um the other + + + align:start position:0% +looks pretty similar to um the other +note + + align:start position:0% + + + + align:start position:0% + +things so can we get the Octave of a + + align:start position:0% +things so can we get the Octave of a + + + align:start position:0% +things so can we get the Octave of a +note yes we can can we get the name of + + align:start position:0% +note yes we can can we get the name of + + + align:start position:0% +note yes we can can we get the name of +the note yes we can what are some other + + align:start position:0% +the note yes we can what are some other + + + align:start position:0% +the note yes we can what are some other +things we did with pitch can we get the + + align:start position:0% +things we did with pitch can we get the + + + align:start position:0% +things we did with pitch can we get the +accidental from a pitch yep can we get + + align:start position:0% +accidental from a pitch yep can we get + + + align:start position:0% +accidental from a pitch yep can we get +the + + align:start position:0% +the + + + align:start position:0% +the +accidental of note no we cannot so one + + align:start position:0% +accidental of note no we cannot so one + + + align:start position:0% +accidental of note no we cannot so one +of the things you'll find in the music + + align:start position:0% +of the things you'll find in the music + + + align:start position:0% +of the things you'll find in the music +21 and again music 21 is just one + + align:start position:0% +21 and again music 21 is just one + + + align:start position:0% +21 and again music 21 is just one +framework you can use hum drum you can + + align:start position:0% +framework you can use hum drum you can + + + align:start position:0% +framework you can use hum drum you can +use build your own um but one of the + + align:start position:0% +use build your own um but one of the + + + align:start position:0% +use build your own um but one of the +things is it started with uh this that + + align:start position:0% +things is it started with uh this that + + + align:start position:0% +things is it started with uh this that +there's some things about a pitch that + + align:start position:0% +there's some things about a pitch that + + + align:start position:0% +there's some things about a pitch that +seemed like you're going to use so often + + align:start position:0% +seemed like you're going to use so often + + + align:start position:0% +seemed like you're going to use so often +that we might as well put it on the Note + + align:start position:0% +that we might as well put it on the Note + + + align:start position:0% +that we might as well put it on the Note +make it a um a shortcut and then a lot + + align:start position:0% +make it a um a shortcut and then a lot + + + align:start position:0% +make it a um a shortcut and then a lot +of things just too complicated so you'll + + align:start position:0% +of things just too complicated so you'll + + + align:start position:0% +of things just too complicated so you'll +if you want something deeper go grab it + + align:start position:0% +if you want something deeper go grab it + + + align:start position:0% +if you want something deeper go grab it +from The + + align:start position:0% +from The + + + align:start position:0% +from The +Accidental or to grab it from the pitch + + align:start position:0% +Accidental or to grab it from the pitch + + + align:start position:0% +Accidental or to grab it from the pitch +object + + align:start position:0% +object + + + align:start position:0% +object +um notes also have a + + align:start position:0% +um notes also have a + + + align:start position:0% +um notes also have a +duration note. pitch and pitches do not + + align:start position:0% +duration note. pitch and pitches do not + + + align:start position:0% +duration note. pitch and pitches do not +have a duration so this is sort of going + + align:start position:0% +have a duration so this is sort of going + + + align:start position:0% +have a duration so this is sort of going +into the logical representation mode um + + align:start position:0% +into the logical representation mode um + + + align:start position:0% +into the logical representation mode um +that some things have durations and some + + align:start position:0% +that some things have durations and some + + + align:start position:0% +that some things have durations and some +things + + align:start position:0% +things + + + align:start position:0% +things +don't let's see what we can um do with + + align:start position:0% +don't let's see what we can um do with + + + align:start position:0% +don't let's see what we can um do with +this let's let's look at the duration + + align:start position:0% +this let's let's look at the duration + + + align:start position:0% +this let's let's look at the duration +since we haven't looked at the duration + + align:start position:0% +since we haven't looked at the duration + + + align:start position:0% +since we haven't looked at the duration +module + + align:start position:0% +module + + + align:start position:0% +module +yet or the duration + + align:start position:0% +yet or the duration + + + align:start position:0% +yet or the duration +class okay so we have a duration and we + + align:start position:0% +class okay so we have a duration and we + + + align:start position:0% +class okay so we have a duration and we +can see some of the things um duration. + + align:start position:0% +can see some of the things um duration. + + + align:start position:0% +can see some of the things um duration. +almond unfortunately I did not go with + + align:start position:0% +almond unfortunately I did not go with + + + align:start position:0% +almond unfortunately I did not go with +that great idea uh what anyone remember + + align:start position:0% +that great idea uh what anyone remember + + + align:start position:0% +that great idea uh what anyone remember +what I said I went with boring term + + align:start position:0% +what I said I went with boring term + + + align:start position:0% +what I said I went with boring term +type so everything starts off as a + + align:start position:0% +type so everything starts off as a + + + align:start position:0% +type so everything starts off as a +quarter note but we can make it + + align:start position:0% + + + + align:start position:0% + +half + + align:start position:0% +half + + + align:start position:0% +half +and remember early on in the semester we + + align:start position:0% +and remember early on in the semester we + + + align:start position:0% +and remember early on in the semester we +talked about representations a duration + + align:start position:0% +talked about representations a duration + + + align:start position:0% +talked about representations a duration +uh before it was a duration of one now + + align:start position:0% +uh before it was a duration of one now + + + align:start position:0% +uh before it was a duration of one now +it's some sort of a duration of two two + + align:start position:0% +it's some sort of a duration of two two + + + align:start position:0% +it's some sort of a duration of two two +whats could be a lot of things could be + + align:start position:0% +whats could be a lot of things could be + + + align:start position:0% +whats could be a lot of things could be +2 seconds with a tempo of 60 could be + + align:start position:0% +2 seconds with a tempo of 60 could be + + + align:start position:0% +2 seconds with a tempo of 60 could be +two beats two ticks + + align:start position:0% +two beats two ticks + + + align:start position:0% +two beats two ticks +um music 21 has chosen to represent + + align:start position:0% +um music 21 has chosen to represent + + + align:start position:0% +um music 21 has chosen to represent +everything in numbers of quarter + + align:start position:0% +everything in numbers of quarter + + + align:start position:0% +everything in numbers of quarter +notes so duration is one um duration of + + align:start position:0% +notes so duration is one um duration of + + + align:start position:0% +notes so duration is one um duration of +two is a half + + align:start position:0% +two is a half + + + align:start position:0% +two is a half +note + + align:start position:0% +note + + + align:start position:0% +note +let's have dots zero so let's add some + + align:start position:0% + + + + align:start position:0% + +dots and now we added six dots to the + + align:start position:0% +dots and now we added six dots to the + + + align:start position:0% +dots and now we added six dots to the +notes um and we get something + + align:start position:0% +notes um and we get something + + + align:start position:0% +notes um and we get something +like like this um my favorite random MIT + + align:start position:0% +like like this um my favorite random MIT + + + align:start position:0% +like like this um my favorite random MIT +thing that you all can figure out based + + align:start position:0% +thing that you all can figure out based + + + align:start position:0% +thing that you all can figure out based +on that uh thing + + align:start position:0% +on that uh thing + + + align:start position:0% +on that uh thing +what what is the limit of half note as + + align:start position:0% +what what is the limit of half note as + + + align:start position:0% +what what is the limit of half note as +the dots approaches Infinity + + align:start position:0% + + + + align:start position:0% + +sorry whole note good good yall can play + + align:start position:0% +sorry whole note good good yall can play + + + align:start position:0% +sorry whole note good good yall can play +with the Easter egg and set the um dots + + align:start position:0% +with the Easter egg and set the um dots + + + align:start position:0% +with the Easter egg and set the um dots +to Infinity later and see what happens + + align:start position:0% +to Infinity later and see what happens + + + align:start position:0% +to Infinity later and see what happens +um okay + + align:start position:0% +um okay + + + align:start position:0% +um okay +so we have some of these things let's + + align:start position:0% +so we have some of these things let's + + + align:start position:0% +so we have some of these things let's +put the dots back down to I don't know + + align:start position:0% +put the dots back down to I don't know + + + align:start position:0% +put the dots back down to I don't know +something + + align:start position:0% +something + + + align:start position:0% +something +manageable and quarter + + align:start position:0% +manageable and quarter + + + align:start position:0% +manageable and quarter +length each of these things affects each + + align:start position:0% +length each of these things affects each + + + align:start position:0% +length each of these things affects each +other and they're almost all setable so + + align:start position:0% +other and they're almost all setable so + + + align:start position:0% +other and they're almost all setable so +that can be helpful in your programming + + align:start position:0% +that can be helpful in your programming + + + align:start position:0% +that can be helpful in your programming +like + + align:start position:0% +like + + + align:start position:0% +like +3.5 and now we get that it's a double + + align:start position:0% + + + + align:start position:0% + +dotted and um probably a mistake on my + + align:start position:0% +dotted and um probably a mistake on my + + + align:start position:0% +dotted and um probably a mistake on my +original part but everything U most of + + align:start position:0% +original part but everything U most of + + + align:start position:0% +original part but everything U most of +these objects are are mutable so if we + + align:start position:0% +these objects are are mutable so if we + + + align:start position:0% +these objects are are mutable so if we +go back to the original and duration + + align:start position:0% +go back to the original and duration + + + align:start position:0% +go back to the original and duration +it's still now has the quarter length so + + align:start position:0% +it's still now has the quarter length so + + + align:start position:0% +it's still now has the quarter length so +you can change the duration on the side + + align:start position:0% +you can change the duration on the side + + + align:start position:0% +you can change the duration on the side +similarly with pitch do + + align:start position:0% +similarly with pitch do + + + align:start position:0% +similarly with pitch do +um pitch. + + align:start position:0% +um pitch. + + + align:start position:0% +um pitch. +Step it's already C we'll make it a + + align:start position:0% +Step it's already C we'll make it a + + + align:start position:0% +Step it's already C we'll make it a +d and now we've changed the step of the + + align:start position:0% +d and now we've changed the step of the + + + align:start position:0% +d and now we've changed the step of the +pitch to D but not change it's + + align:start position:0% +pitch to D but not change it's + + + align:start position:0% +pitch to D but not change it's +accidental and now this is still on here + + align:start position:0% +accidental and now this is still on here + + + align:start position:0% +accidental and now this is still on here +give everyone a second or two to catch + + align:start position:0% +give everyone a second or two to catch + + + align:start position:0% +give everyone a second or two to catch +up I'll make it a little small smaller + + align:start position:0% +up I'll make it a little small smaller + + + align:start position:0% +up I'll make it a little small smaller +so that any parts that people have + + align:start position:0% +so that any parts that people have + + + align:start position:0% +so that any parts that people have +missed you don't have to you don't have + + align:start position:0% +missed you don't have to you don't have + + + align:start position:0% +missed you don't have to you don't have +to write down everything that I write + + align:start position:0% +to write down everything that I write + + + align:start position:0% +to write down everything that I write +down uh only write things down as + + align:start position:0% +down uh only write things down as + + + align:start position:0% +down uh only write things down as +they're helpful for you to finger memory + + align:start position:0% +they're helpful for you to finger memory + + + align:start position:0% +they're helpful for you to finger memory +remember + + align:start position:0% +remember + + + align:start position:0% +remember +it okay um that's all I'm going to talk + + align:start position:0% +it okay um that's all I'm going to talk + + + align:start position:0% +it okay um that's all I'm going to talk +about with unlocking notes and durations + + align:start position:0% +about with unlocking notes and durations + + + align:start position:0% +about with unlocking notes and durations +at this point um I'll don't think I've + + align:start position:0% +at this point um I'll don't think I've + + + align:start position:0% +at this point um I'll don't think I've +put a per a prominent enough link but + + align:start position:0% +put a per a prominent enough link but + + + align:start position:0% +put a per a prominent enough link but +you can Google it music 21 has a users + + align:start position:0% +you can Google it music 21 has a users + + + align:start position:0% +you can Google it music 21 has a users +guide and so you've kind of gone through + + align:start position:0% +guide and so you've kind of gone through + + + align:start position:0% +guide and so you've kind of gone through +chapters one through two um in this + + align:start position:0% +chapters one through two um in this + + + align:start position:0% +chapters one through two um in this +class so far but let's let's unlock some + + align:start position:0% +class so far but let's let's unlock some + + + align:start position:0% +class so far but let's let's unlock some +other + + align:start position:0% +other + + + align:start position:0% +other +things uh + + align:start position:0% +things uh + + + align:start position:0% +things uh +unlocking + + align:start position:0% +unlocking + + + align:start position:0% +unlocking +scores so we're going to give you your + + align:start position:0% +scores so we're going to give you your + + + align:start position:0% +scores so we're going to give you your +first larger representation things and + + align:start position:0% +first larger representation things and + + + align:start position:0% +first larger representation things and +to do this we're going to um from music + + align:start position:0% +to do this we're going to um from music + + + align:start position:0% +to do this we're going to um from music + + align:start position:0% + + + align:start position:0% +import something called stream and + + align:start position:0% +import something called stream and + + + align:start position:0% +import something called stream and +something called + + align:start position:0% +something called + + + align:start position:0% +something called +Corpus oops no + + align:start position:0% +Corpus oops no + + + align:start position:0% +Corpus oops no +trailing um I was putting that there + + align:start position:0% +trailing um I was putting that there + + + align:start position:0% +trailing um I was putting that there +because you can also invert import sign + + align:start position:0% +because you can also invert import sign + + + align:start position:0% +because you can also invert import sign +called converter I'm not going to talk + + align:start position:0% +called converter I'm not going to talk + + + align:start position:0% +called converter I'm not going to talk +about it um but converter is a way of + + align:start position:0% +about it um but converter is a way of + + + align:start position:0% +about it um but converter is a way of +loading things from your hard drive + + align:start position:0% +loading things from your hard drive + + + align:start position:0% +loading things from your hard drive +Corpus uses um a batteries included set + + align:start position:0% +Corpus uses um a batteries included set + + + align:start position:0% +Corpus uses um a batteries included set +of about 8,000 pieces that comes that + + align:start position:0% +of about 8,000 pieces that comes that + + + align:start position:0% +of about 8,000 pieces that comes that +come with music 21 so there's about + + align:start position:0% +come with music 21 so there's about + + + align:start position:0% +come with music 21 so there's about +8,000 pieces in there and and we'll grab + + align:start position:0% +8,000 pieces in there and and we'll grab + + + align:start position:0% +8,000 pieces in there and and we'll grab +one of them and when I'm not um thinking + + align:start position:0% +one of them and when I'm not um thinking + + + align:start position:0% +one of them and when I'm not um thinking +very much I apologize I go to this Bo so + + align:start position:0% +very much I apologize I go to this Bo so + + + align:start position:0% +very much I apologize I go to this Bo so +we'll load from the Corpus we're going + + align:start position:0% +we'll load from the Corpus we're going + + + align:start position:0% +we'll load from the Corpus we're going +to parse meaning make sense of the of + + align:start position:0% +to parse meaning make sense of the of + + + align:start position:0% +to parse meaning make sense of the of +the um representation Bach bwv + + align:start position:0% +the um representation Bach bwv + + + align:start position:0% +the um representation Bach bwv +66.6 bwv means the + + align:start position:0% +66.6 bwv means the + + + align:start position:0% +66.6 bwv means the +Bess the box work um uh index and by Bo + + align:start position:0% +Bess the box work um uh index and by Bo + + + align:start position:0% +Bess the box work um uh index and by Bo +in this case um I mean Johan Sebastian + + align:start position:0% +in this case um I mean Johan Sebastian + + + align:start position:0% +in this case um I mean Johan Sebastian +Bach daddy Bach there's some other boxs + + align:start position:0% +Bach daddy Bach there's some other boxs + + + align:start position:0% +Bach daddy Bach there's some other boxs +in there and this is um the work number + + align:start position:0% +in there and this is um the work number + + + align:start position:0% +in there and this is um the work number +66 6 movement um it's the one that we're + + align:start position:0% +66 6 movement um it's the one that we're + + + align:start position:0% +66 6 movement um it's the one that we're +going to use quite a bit because it's + + align:start position:0% +going to use quite a bit because it's + + + align:start position:0% +going to use quite a bit because it's +the smallest uh shortest Corral he + + align:start position:0% +the smallest uh shortest Corral he + + + align:start position:0% +the smallest uh shortest Corral he +wrote and um what I'm going to ask you + + align:start position:0% +wrote and um what I'm going to ask you + + + align:start position:0% +wrote and um what I'm going to ask you +to + + align:start position:0% +to + + + align:start position:0% +to +do over the next couple classes as part + + align:start position:0% +do over the next couple classes as part + + + align:start position:0% +do over the next couple classes as part +of the avoiding garbage in garbage out + + align:start position:0% +of the avoiding garbage in garbage out + + + align:start position:0% +of the avoiding garbage in garbage out +want you to learn to sing Your Part from + + align:start position:0% +want you to learn to sing Your Part from + + + align:start position:0% +want you to learn to sing Your Part from +this + + align:start position:0% + + + + align:start position:0% + +Coral can you can you do that can you go + + align:start position:0% +Coral can you can you do that can you go + + + align:start position:0% +Coral can you can you do that can you go +to the piano and match pitch on one of + + align:start position:0% +to the piano and match pitch on one of + + + align:start position:0% +to the piano and match pitch on one of +the parts if you're really not um you + + align:start position:0% +the parts if you're really not um you + + + align:start position:0% +the parts if you're really not um you +feeling very confident you're singing + + align:start position:0% +feeling very confident you're singing + + + align:start position:0% +feeling very confident you're singing +you can do the soprano part at whatever + + align:start position:0% +you can do the soprano part at whatever + + + align:start position:0% +you can do the soprano part at whatever +um octave is most comfortable but it + + align:start position:0% +um octave is most comfortable but it + + + align:start position:0% +um octave is most comfortable but it +would be nice to be able to sing this as + + align:start position:0% +would be nice to be able to sing this as + + + align:start position:0% +would be nice to be able to sing this as +a group and we'll come back to this one + + align:start position:0% +a group and we'll come back to this one + + + align:start position:0% +a group and we'll come back to this one +um next class so you now have sorry + + align:start position:0% +um next class so you now have sorry + + + align:start position:0% +um next class so you now have sorry +should have slowed down I was like + + align:start position:0% +should have slowed down I was like + + + align:start position:0% +should have slowed down I was like +talking about something else B we're + + align:start position:0% +talking about something else B we're + + + align:start position:0% +talking about something else B we're +going to store this piece as a variable + + align:start position:0% +going to store this piece as a variable + + + align:start position:0% +going to store this piece as a variable +and one of the things you're going to + + align:start position:0% +and one of the things you're going to + + + align:start position:0% +and one of the things you're going to +find very helpful is do show um can you + + align:start position:0% +find very helpful is do show um can you + + + align:start position:0% +find very helpful is do show um can you +raise your hand if you have gotten + + align:start position:0% +raise your hand if you have gotten + + + align:start position:0% +raise your hand if you have gotten +everything installed so that you can see + + align:start position:0% +everything installed so that you can see + + + align:start position:0% +everything installed so that you can see +uh scores when you call show on things + + align:start position:0% +uh scores when you call show on things + + + align:start position:0% +uh scores when you call show on things +anybody anybody still having some + + align:start position:0% +anybody anybody still having some + + + align:start position:0% +anybody anybody still having some +difficulty that on okay great super + + align:start position:0% +difficulty that on okay great super + + + align:start position:0% +difficulty that on okay great super +we'll make sure that we can uh get that + + align:start position:0% +we'll make sure that we can uh get that + + + align:start position:0% +we'll make sure that we can uh get that +up and um and and see if we can uh get + + align:start position:0% +up and um and and see if we can uh get + + + align:start position:0% +up and um and and see if we can uh get +that straightened out there were some + + align:start position:0% +that straightened out there were some + + + align:start position:0% +that straightened out there were some +some helpful hints put onto one of the + + align:start position:0% +some helpful hints put onto one of the + + + align:start position:0% +some helpful hints put onto one of the +discussion points about um dealing with + + align:start position:0% +discussion points about um dealing with + + + align:start position:0% +discussion points about um dealing with +M score 4 but want to get that yeah when + + align:start position:0% +M score 4 but want to get that yeah when + + + align:start position:0% +M score 4 but want to get that yeah when +we get this um this a notebook chance + + align:start position:0% +we get this um this a notebook chance + + + align:start position:0% +we get this um this a notebook chance +yeah I can make sure to do that just if + + align:start position:0% +yeah I can make sure to do that just if + + + align:start position:0% +yeah I can make sure to do that just if +there's something that I create in the + + align:start position:0% +there's something that I create in the + + + align:start position:0% +there's something that I create in the +middle of class and it's not a one + + align:start position:0% +middle of class and it's not a one + + + align:start position:0% +middle of class and it's not a one +button thing and you don't see it by uh + + align:start position:0% +button thing and you don't see it by uh + + + align:start position:0% +button thing and you don't see it by uh +9:00 a.m. the next day just drop me a + + align:start position:0% +9:00 a.m. the next day just drop me a + + + align:start position:0% +9:00 a.m. the next day just drop me a +line but I'll try to do that and + + align:start position:0% +line but I'll try to do that and + + + align:start position:0% +line but I'll try to do that and +sometimes I'll give you the cleaned up + + align:start position:0% +sometimes I'll give you the cleaned up + + + align:start position:0% +sometimes I'll give you the cleaned up +one I should have a script on my other + + align:start position:0% +one I should have a script on my other + + + align:start position:0% +one I should have a script on my other +monitor but I'm not uh getting it now + + align:start position:0% +monitor but I'm not uh getting it now + + + align:start position:0% +monitor but I'm not uh getting it now +great so let's look at that boach thing + + align:start position:0% +great so let's look at that boach thing + + + align:start position:0% +great so let's look at that boach thing +it is + + align:start position:0% +it is + + + align:start position:0% +it is +something in the project is music 21 + + align:start position:0% +something in the project is music 21 + + + align:start position:0% +something in the project is music 21 +stream is a what is it Shout It + + align:start position:0% +stream is a what is it Shout It + + + align:start position:0% +stream is a what is it Shout It +Out module and score is a class class + + align:start position:0% +Out module and score is a class class + + + align:start position:0% +Out module and score is a class class +class good so this is an object of class + + align:start position:0% +class good so this is an object of class + + + align:start position:0% +class good so this is an object of class +score in the Stream module in the music + + align:start position:0% +score in the Stream module in the music + + + align:start position:0% +score in the Stream module in the music +21 package project whatever you call it + + align:start position:0% +21 package project whatever you call it + + + align:start position:0% +21 package project whatever you call it +and this is the particular memory + + align:start position:0% +and this is the particular memory + + + align:start position:0% +and this is the particular memory +location that you can hack on my + + align:start position:0% +location that you can hack on my + + + align:start position:0% +location that you can hack on my +computer to uh to deal with the stream + + align:start position:0% +computer to uh to deal with the stream + + + align:start position:0% +computer to uh to deal with the stream +we can change we'll just make this + + align:start position:0% +we can change we'll just make this + + + align:start position:0% +we can change we'll just make this +change its ID to BU short something like + + align:start position:0% +change its ID to BU short something like + + + align:start position:0% +change its ID to BU short something like +that and then we'll see something nicer + + align:start position:0% +that and then we'll see something nicer + + + align:start position:0% +that and then we'll see something nicer +than just a memory location that's + + align:start position:0% +than just a memory location that's + + + align:start position:0% +than just a memory location that's +sometimes helpful okay + + align:start position:0% +sometimes helpful okay + + + align:start position:0% +sometimes helpful okay +so this we call at the beginning of the + + align:start position:0% +so this we call at the beginning of the + + + align:start position:0% +so this we call at the beginning of the +uh semester we have how many things are + + align:start position:0% +uh semester we have how many things are + + + align:start position:0% +uh semester we have how many things are +in bck this was a trick question on the + + align:start position:0% +in bck this was a trick question on the + + + align:start position:0% +in bck this was a trick question on the +first day you all stuck around well a + + align:start position:0% +first day you all stuck around well a + + + align:start position:0% +first day you all stuck around well a +lot of trick questions and + + align:start position:0% +lot of trick questions and + + + align:start position:0% +lot of trick questions and +um there are six things in the bo what + + align:start position:0% +um there are six things in the bo what + + + align:start position:0% +um there are six things in the bo what +what's what are two basic answers that + + align:start position:0% +what's what are two basic answers that + + + align:start position:0% +what's what are two basic answers that +you thought might be the um a good + + align:start position:0% +you thought might be the um a good + + + align:start position:0% +you thought might be the um a good +answer to how many things there are in + + align:start position:0% +answer to how many things there are in + + + align:start position:0% +answer to how many things there are in +the Box ballpark + + align:start position:0% + + + + align:start position:0% + +figures 100 100 yep why maybe about 100 + + align:start position:0% +figures 100 100 yep why maybe about 100 + + + align:start position:0% +figures 100 100 yep why maybe about 100 +what's notes notes good what's another + + align:start position:0% +what's notes notes good what's another + + + align:start position:0% +what's notes notes good what's another +number that you might have thought could + + align:start position:0% +number that you might have thought could + + + align:start position:0% +number that you might have thought could +be there four four why number of parts + + align:start position:0% +be there four four why number of parts + + + align:start position:0% +be there four four why number of parts +of parts good so let's see what those + + align:start position:0% +of parts good so let's see what those + + + align:start position:0% +of parts good so let's see what those +things are um well one of the things + + align:start position:0% +things are um well one of the things + + + align:start position:0% +things are um well one of the things +streams um scores are a type of stream + + align:start position:0% +streams um scores are a type of stream + + + align:start position:0% +streams um scores are a type of stream +everything in there's a type of stream + + align:start position:0% +everything in there's a type of stream + + + align:start position:0% +everything in there's a type of stream +can be treated like um like lists so you + + align:start position:0% +can be treated like um like lists so you + + + align:start position:0% +can be treated like um like lists so you +can index them get what zeroth object is + + align:start position:0% +can index them get what zeroth object is + + + align:start position:0% +can index them get what zeroth object is +get the first + + align:start position:0% +get the first + + + align:start position:0% +get the first +object ah there's our part second + + align:start position:0% +object ah there's our part second + + + align:start position:0% +object ah there's our part second +and so + + align:start position:0% +and so + + + align:start position:0% +and so +on so what's that last object everyone + + align:start position:0% +on so what's that last object everyone + + + align:start position:0% +on so what's that last object everyone +remember python give negative one + + align:start position:0% +remember python give negative one + + + align:start position:0% +remember python give negative one +indexing uh we have something that says + + align:start position:0% +indexing uh we have something that says + + + align:start position:0% +indexing uh we have something that says +all of these soprano Alto tenor base are + + align:start position:0% +all of these soprano Alto tenor base are + + + align:start position:0% +all of these soprano Alto tenor base are +all have these what do you call it this + + align:start position:0% +all have these what do you call it this + + + align:start position:0% +all have these what do you call it this +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +little thing around them so that's how + + align:start position:0% +little thing around them so that's how + + + align:start position:0% +little thing around them so that's how +we get six things we have metadata which + + align:start position:0% +we get six things we have metadata which + + + align:start position:0% +we get six things we have metadata which +is data about data that is usually + + align:start position:0% +is data about data that is usually + + + align:start position:0% +is data about data that is usually +having the title of it so and things + + align:start position:0% +having the title of it so and things + + + align:start position:0% +having the title of it so and things +like that we'll get to met dat later but + + align:start position:0% +like that we'll get to met dat later but + + + align:start position:0% +like that we'll get to met dat later but +I know you want to get so let's see + + align:start position:0% +I know you want to get so let's see + + + align:start position:0% +I know you want to get so let's see +what's what's an index I can use to get + + align:start position:0% +what's what's an index I can use to get + + + align:start position:0% +what's what's an index I can use to get +something that might have notes in it + + align:start position:0% +something that might have notes in it + + + align:start position:0% +something that might have notes in it +zero probably not negative one which one + + align:start position:0% +zero probably not negative one which one + + + align:start position:0% +zero probably not negative one which one +do we want to look + + align:start position:0% + + + + align:start position:0% + +at give me a number to put in here two + + align:start position:0% +at give me a number to put in here two + + + align:start position:0% +at give me a number to put in here two +two okay so two is in this case the Alto + + align:start position:0% +two okay so two is in this case the Alto + + + align:start position:0% +two okay so two is in this case the Alto +part and you would think if you don't + + align:start position:0% +part and you would think if you don't + + + align:start position:0% +part and you would think if you don't +get that metadata as zero that this + + align:start position:0% +get that metadata as zero that this + + + align:start position:0% +get that metadata as zero that this +would be um this might be uh you know + + align:start position:0% +would be um this might be uh you know + + + align:start position:0% +would be um this might be uh you know +that one indexed or something right one + + align:start position:0% +that one indexed or something right one + + + align:start position:0% +that one indexed or something right one +is soprano 2 but no it's zero index but + + align:start position:0% +is soprano 2 but no it's zero index but + + + align:start position:0% +is soprano 2 but no it's zero index but +the zero is metadata um there might be + + align:start position:0% +the zero is metadata um there might be + + + align:start position:0% +the zero is metadata um there might be +multiple things at the beginning not + + align:start position:0% +multiple things at the beginning not + + + align:start position:0% +multiple things at the beginning not +just one metadata there could be more + + align:start position:0% +just one metadata there could be more + + + align:start position:0% +just one metadata there could be more +could be metadata lists so it's you + + align:start position:0% +could be metadata lists so it's you + + + align:start position:0% +could be metadata lists so it's you +might not always get this so you could + + align:start position:0% +might not always get this so you could + + + align:start position:0% +might not always get this so you could +do something like like this for B for + + align:start position:0% +do something like like this for B for + + + align:start position:0% +do something like like this for B for +thing I always use thing in b um because + + align:start position:0% +thing I always use thing in b um because + + + align:start position:0% +thing I always use thing in b um because +I don't know what it is if is instance + + align:start position:0% +I don't know what it is if is instance + + + align:start position:0% +I don't know what it is if is instance +thing music21 Dost + + align:start position:0% +thing music21 Dost + + + align:start position:0% +thing music21 Dost +stream. + + align:start position:0% +stream. + + + align:start position:0% +stream. +part print + + align:start position:0% +part print + + + align:start position:0% +part print +thing oops what did I do um I + + align:start position:0% +thing oops what did I do um I + + + align:start position:0% +thing oops what did I do um I +didn't sorry streamed up part because I + + align:start position:0% +didn't sorry streamed up part because I + + + align:start position:0% +didn't sorry streamed up part because I +imported that um I imported stream into + + align:start position:0% +imported that um I imported stream into + + + align:start position:0% +imported that um I imported stream into +it so that can be one way to get this + + align:start position:0% +it so that can be one way to get this + + + align:start position:0% +it so that can be one way to get this +I'm going to tell you all of the most + + align:start position:0% +I'm going to tell you all of the most + + + align:start position:0% +I'm going to tell you all of the most +General ways of doing things now so that + + align:start position:0% +General ways of doing things now so that + + + align:start position:0% +General ways of doing things now so that +it sort of forms a mental habit but um + + align:start position:0% +it sort of forms a mental habit but um + + + align:start position:0% +it sort of forms a mental habit but um +but we want to um but just just to know + + align:start position:0% +but we want to um but just just to know + + + align:start position:0% +but we want to um but just just to know +you will learn some shortcuts so you + + align:start position:0% +you will learn some shortcuts so you + + + align:start position:0% +you will learn some shortcuts so you +won't need to have to code all this uh + + align:start position:0% +won't need to have to code all this uh + + + align:start position:0% +won't need to have to code all this uh +later great so now we have all the parts + + align:start position:0% +later great so now we have all the parts + + + align:start position:0% +later great so now we have all the parts +what do you um let's do this we we got + + align:start position:0% +what do you um let's do this we we got + + + align:start position:0% +what do you um let's do this we we got +the bach two let's see four thing in + + align:start position:0% +the bach two let's see four thing in + + + align:start position:0% +the bach two let's see four thing in +Bach two that's let just call that Alto + + align:start position:0% +Bach two that's let just call that Alto + + + align:start position:0% +Bach two that's let just call that Alto +let's call that Alto right Alto equals + + align:start position:0% +let's call that Alto right Alto equals + + + align:start position:0% +let's call that Alto right Alto equals +Bach two for thing in Alto I always like + + align:start position:0% +Bach two for thing in Alto I always like + + + align:start position:0% +Bach two for thing in Alto I always like +good naming see I'm calling it thing + + align:start position:0% +good naming see I'm calling it thing + + + align:start position:0% +good naming see I'm calling it thing +thing's the best naming when you don't + + align:start position:0% +thing's the best naming when you don't + + + align:start position:0% +thing's the best naming when you don't +know what something is yet suppose you + + align:start position:0% +know what something is yet suppose you + + + align:start position:0% +know what something is yet suppose you +could call it L for element or something + + align:start position:0% +could call it L for element or something + + + align:start position:0% +could call it L for element or something +print thing and what and when we call + + align:start position:0% +print thing and what and when we call + + + align:start position:0% +print thing and what and when we call +from the very fast thing for stay what + + align:start position:0% +from the very fast thing for stay what + + + align:start position:0% +from the very fast thing for stay what +it's going to + + align:start position:0% +it's going to + + + align:start position:0% +it's going to +be so it's a bunch of measures but also + + align:start position:0% +be so it's a bunch of measures but also + + + align:start position:0% +be so it's a bunch of measures but also +an + + align:start position:0% +an + + + align:start position:0% +an +instrument I think that that's been + + align:start position:0% +instrument I think that that's been + + + align:start position:0% +instrument I think that that's been +fixed in the latest version and it looks + + align:start position:0% +fixed in the latest version and it looks + + + align:start position:0% +fixed in the latest version and it looks +like everything else but yeah so we have + + align:start position:0% +like everything else but yeah so we have + + + align:start position:0% +like everything else but yeah so we have +an instrument there so we can do this + + align:start position:0% +an instrument there so we can do this + + + align:start position:0% +an instrument there so we can do this +again I'm going to copy I just copied + + align:start position:0% +again I'm going to copy I just copied + + + align:start position:0% +again I'm going to copy I just copied +here I'm going to go here and paste um + + align:start position:0% +here I'm going to go here and paste um + + + align:start position:0% +here I'm going to go here and paste um +and we'll again do that is instance + + align:start position:0% +and we'll again do that is instance + + + align:start position:0% +and we'll again do that is instance +checking if is instance that means is a + + align:start position:0% +checking if is instance that means is a + + + align:start position:0% +checking if is instance that means is a +member of this class thing um stream. + + align:start position:0% +member of this class thing um stream. + + + align:start position:0% +member of this class thing um stream. +measure + + align:start position:0% +measure + + + align:start position:0% +measure +print thing okay now we've gotten just + + align:start position:0% +print thing okay now we've gotten just + + + align:start position:0% +print thing okay now we've gotten just +the measures and + + align:start position:0% +the measures and + + + align:start position:0% +the measures and +and we can get um oh I don't know + + align:start position:0% +and we can get um oh I don't know + + + align:start position:0% +and we can get um oh I don't know +measure 2 equals Alto three I think we + + align:start position:0% +measure 2 equals Alto three I think we + + + align:start position:0% +measure 2 equals Alto three I think we +got that is that I guess right okay and + + align:start position:0% +got that is that I guess right okay and + + + align:start position:0% +got that is that I guess right okay and +we can keep writing the same type of + + align:start position:0% +we can keep writing the same type of + + + align:start position:0% +we can keep writing the same type of +thing for thing + + align:start position:0% +thing for thing + + + align:start position:0% +thing for thing +in in + + align:start position:0% + + + + align:start position:0% + +M2 we don't need that because we're + + align:start position:0% +M2 we don't need that because we're + + + align:start position:0% +M2 we don't need that because we're +already in a measure and finally we get + + align:start position:0% +already in a measure and finally we get + + + align:start position:0% +already in a measure and finally we get +to + + align:start position:0% +to + + + align:start position:0% +to +notes finally we get to notes + + align:start position:0% + + + + align:start position:0% + +so that's where I'm going to end um this + + align:start position:0% +so that's where I'm going to end um this + + + align:start position:0% +so that's where I'm going to end um this +part now um that I've given you a very + + align:start position:0% +part now um that I've given you a very + + + align:start position:0% +part now um that I've given you a very +tedious way to get two notes from a + + align:start position:0% +tedious way to get two notes from a + + + align:start position:0% +tedious way to get two notes from a +score that you go through all the + + align:start position:0% +score that you go through all the + + + align:start position:0% +score that you go through all the +parts um you go through everything + + align:start position:0% +parts um you go through everything + + + align:start position:0% +parts um you go through everything +that's in the score find the things that + + align:start position:0% +that's in the score find the things that + + + align:start position:0% +that's in the score find the things that +are parts and then you could do a next + + align:start position:0% +are parts and then you could do a next + + + align:start position:0% +are parts and then you could do a next +iteration on here another uh for Loop + + align:start position:0% +iteration on here another uh for Loop + + + align:start position:0% +iteration on here another uh for Loop +another if go through each of the parts + + align:start position:0% +another if go through each of the parts + + + align:start position:0% +another if go through each of the parts +and figure out everything that's a + + align:start position:0% +and figure out everything that's a + + + align:start position:0% +and figure out everything that's a +measure and what oh sorry everything + + align:start position:0% +measure and what oh sorry everything + + + align:start position:0% +measure and what oh sorry everything +that's a measure and go through each of + + align:start position:0% +that's a measure and go through each of + + + align:start position:0% +that's a measure and go through each of +the measures and do this a for Loop + + align:start position:0% +the measures and do this a for Loop + + + align:start position:0% +the measures and do this a for Loop +within a for Loop within a for Loop um + + align:start position:0% +within a for Loop within a for Loop um + + + align:start position:0% +within a for Loop within a for Loop um +but we're going to learn some better + + align:start position:0% +but we're going to learn some better + + + align:start position:0% +but we're going to learn some better +ways to do this later but I want to + + align:start position:0% +ways to do this later but I want to + + + align:start position:0% +ways to do this later but I want to +leave you at least two days with trying + + align:start position:0% +leave you at least two days with trying + + + align:start position:0% +leave you at least two days with trying +to do everything the hard way before we + + align:start position:0% +to do everything the hard way before we + + + align:start position:0% +to do everything the hard way before we +start to get to the easier ways um so + + align:start position:0% +start to get to the easier ways um so + + + align:start position:0% +start to get to the easier ways um so +you can do this so that's that your only + + align:start position:0% +you can do this so that's that your only + + + align:start position:0% +you can do this so that's that your only +assign assignments continue working with + + align:start position:0% +assign assignments continue working with + + + align:start position:0% +assign assignments continue working with +um your um on your problem sets and to + + align:start position:0% +um your um on your problem sets and to + + + align:start position:0% +um your um on your problem sets and to +learn to sing your little part of bwv + + align:start position:0% +learn to sing your little part of bwv + + + align:start position:0% +learn to sing your little part of bwv +66.6 \ No newline at end of file diff --git a/4A9bGL-_ilA.txt b/4A9bGL-_ilA.txt new file mode 100644 index 0000000000000000000000000000000000000000..14a971d16d2c801362fbfb12fef4838cc22651bb --- /dev/null +++ b/4A9bGL-_ilA.txt @@ -0,0 +1,13603 @@ +align:start position:0% + +okay let's go ahead and get started so + + align:start position:0% +okay let's go ahead and get started so + + + align:start position:0% +okay let's go ahead and get started so +uh last time uh we ended well we were + + align:start position:0% +uh last time uh we ended well we were + + + align:start position:0% +uh last time uh we ended well we were +talking about functions of random + + align:start position:0% +talking about functions of random + + + align:start position:0% +talking about functions of random +variables of + + align:start position:0% +variables of + + + align:start position:0% +variables of +course and there um we talked in + + align:start position:0% +course and there um we talked in + + + align:start position:0% +course and there um we talked in +particular one of the uh sort of + + align:start position:0% +particular one of the uh sort of + + + align:start position:0% +particular one of the uh sort of +standard examples that I did was uh the + + align:start position:0% +standard examples that I did was uh the + + + align:start position:0% +standard examples that I did was uh the +probability integral transformation and + + align:start position:0% +probability integral transformation and + + + align:start position:0% +probability integral transformation and +I talked about how this could be useful + + align:start position:0% +I talked about how this could be useful + + + align:start position:0% +I talked about how this could be useful +for generating random draws like if for + + align:start position:0% +for generating random draws like if for + + + align:start position:0% +for generating random draws like if for +instance if you were interested in + + align:start position:0% +instance if you were interested in + + + align:start position:0% +instance if you were interested in +writing a program where um you wanted to + + align:start position:0% +writing a program where um you wanted to + + + align:start position:0% +writing a program where um you wanted to +simulate random draws from some + + align:start position:0% +simulate random draws from some + + + align:start position:0% +simulate random draws from some +distribution that sort of using kind of + + align:start position:0% +distribution that sort of using kind of + + + align:start position:0% +distribution that sort of using kind of +the reverse of the probability integral + + align:start position:0% +the reverse of the probability integral + + + align:start position:0% +the reverse of the probability integral +transformation could be uh useful and + + align:start position:0% +transformation could be uh useful and + + + align:start position:0% +transformation could be uh useful and +there seem to be some demand for an + + align:start position:0% +there seem to be some demand for an + + + align:start position:0% +there seem to be some demand for an +example so what I'm going to do I'm not + + align:start position:0% +example so what I'm going to do I'm not + + + align:start position:0% +example so what I'm going to do I'm not +going to do exactly that but I'm going + + align:start position:0% +going to do exactly that but I'm going + + + align:start position:0% +going to do exactly that but I'm going +to do an example that uh is quite + + align:start position:0% +to do an example that uh is quite + + + align:start position:0% +to do an example that uh is quite +related and then we'll sort of talk + + align:start position:0% +related and then we'll sort of talk + + + align:start position:0% +related and then we'll sort of talk +about the relation in a second okay oh + + align:start position:0% +about the relation in a second okay oh + + + align:start position:0% +about the relation in a second okay oh +let's start with housekeeping notes I + + align:start position:0% +let's start with housekeeping notes I + + + align:start position:0% +let's start with housekeeping notes I +don't think there's anything uh sort of + + align:start position:0% +don't think there's anything uh sort of + + + align:start position:0% +don't think there's anything uh sort of +controversial here uh problems that + + align:start position:0% +controversial here uh problems that + + + align:start position:0% +controversial here uh problems that +three is do on Wednesday keep an eye out + + align:start position:0% +three is do on Wednesday keep an eye out + + + align:start position:0% +three is do on Wednesday keep an eye out +for problem set four um today more on + + align:start position:0% +for problem set four um today more on + + + align:start position:0% +for problem set four um today more on +functions of random variables uh we will + + align:start position:0% +functions of random variables uh we will + + + align:start position:0% +functions of random variables uh we will +start talking about moments of + + align:start position:0% +start talking about moments of + + + align:start position:0% +start talking about moments of +distributions today and I'm going to + + align:start position:0% +distributions today and I'm going to + + + align:start position:0% +distributions today and I'm going to +finish off the lecture today with kind + + align:start position:0% +finish off the lecture today with kind + + + align:start position:0% +finish off the lecture today with kind +of an extended example uh of um auction + + align:start position:0% +of an extended example uh of um auction + + + align:start position:0% +of an extended example uh of um auction +auction Theory basically um and then uh + + align:start position:0% +auction Theory basically um and then uh + + + align:start position:0% +auction Theory basically um and then uh +Wednesday we're going to talk about + + align:start position:0% +Wednesday we're going to talk about + + + align:start position:0% +Wednesday we're going to talk about +properties of moments conditional + + align:start position:0% +properties of moments conditional + + + align:start position:0% +properties of moments conditional +moments and so forth + + align:start position:0% +moments and so forth + + + align:start position:0% +moments and so forth +okay okay so here is the example and um + + align:start position:0% +okay okay so here is the example and um + + + align:start position:0% +okay okay so here is the example and um +just uh sit tight there will be a + + align:start position:0% +just uh sit tight there will be a + + + align:start position:0% +just uh sit tight there will be a +connection to the probability integral + + align:start position:0% +connection to the probability integral + + + align:start position:0% +connection to the probability integral +transformation example uh here okay so + + align:start position:0% +transformation example uh here okay so + + + align:start position:0% +transformation example uh here okay so +suppose we start with a random variable + + align:start position:0% +suppose we start with a random variable + + + align:start position:0% +suppose we start with a random variable +X that has a uniform Distribution on the + + align:start position:0% +X that has a uniform Distribution on the + + + align:start position:0% +X that has a uniform Distribution on the +unit interval and we have some function + + align:start position:0% +unit interval and we have some function + + + align:start position:0% +unit interval and we have some function +we just were given this function or came + + align:start position:0% +we just were given this function or came + + + align:start position:0% +we just were given this function or came +up with this function that we want to + + align:start position:0% +up with this function that we want to + + + align:start position:0% +up with this function that we want to +use to transform uh X okay so what is uh + + align:start position:0% +use to transform uh X okay so what is uh + + + align:start position:0% +use to transform uh X okay so what is uh +the uh distribution of this transformed + + align:start position:0% +the uh distribution of this transformed + + + align:start position:0% +the uh distribution of this transformed +random variable well we know how to do + + align:start position:0% +random variable well we know how to do + + + align:start position:0% +random variable well we know how to do +this remember we can figure out first + + align:start position:0% +this remember we can figure out first + + + align:start position:0% +this remember we can figure out first +what the CDF of Y is and we do that in + + align:start position:0% +what the CDF of Y is and we do that in + + + align:start position:0% +what the CDF of Y is and we do that in +steps we sort of argue what it is in + + align:start position:0% +steps we sort of argue what it is in + + + align:start position:0% +steps we sort of argue what it is in +steps and then once we have the CDF then + + align:start position:0% +steps and then once we have the CDF then + + + align:start position:0% +steps and then once we have the CDF then +we take the derivative and we get the + + align:start position:0% +we take the derivative and we get the + + + align:start position:0% +we take the derivative and we get the +PDF right so let's do that oh but first + + align:start position:0% +PDF right so let's do that oh but first + + + align:start position:0% +PDF right so let's do that oh but first +note that the induced support of Y is uh + + align:start position:0% +note that the induced support of Y is uh + + + align:start position:0% +note that the induced support of Y is uh +just the um sort of non- negative uh + + align:start position:0% +just the um sort of non- negative uh + + + align:start position:0% +just the um sort of non- negative uh +real values yep do zero is undefined + + align:start position:0% +real values yep do zero is undefined + + + align:start position:0% +real values yep do zero is undefined +right pardon me zero yeah so it it + + align:start position:0% +right pardon me zero yeah so it it + + + align:start position:0% +right pardon me zero yeah so it it +doesn't it doesn't actually matter too + + align:start position:0% +doesn't it doesn't actually matter too + + + align:start position:0% +doesn't it doesn't actually matter too +much because the probability at any + + align:start position:0% +much because the probability at any + + + align:start position:0% +much because the probability at any +particular point is equal to zero so we + + align:start position:0% +particular point is equal to zero so we + + + align:start position:0% +particular point is equal to zero so we +don't have to worry too much about what + + align:start position:0% +don't have to worry too much about what + + + align:start position:0% +don't have to worry too much about what +happens at any particular point but + + align:start position:0% +happens at any particular point but + + + align:start position:0% +happens at any particular point but +yeah okay so the in the induced support + + align:start position:0% +yeah okay so the in the induced support + + + align:start position:0% +yeah okay so the in the induced support +is uh is is the following okay and we'll + + align:start position:0% +is uh is is the following okay and we'll + + + align:start position:0% +is uh is is the following okay and we'll +use that in a + + align:start position:0% +use that in a + + + align:start position:0% +use that in a +second okay so now let's go through step + + align:start position:0% +second okay so now let's go through step + + + align:start position:0% +second okay so now let's go through step +by step figure out what the CDF of Y is + + align:start position:0% +by step figure out what the CDF of Y is + + + align:start position:0% +by step figure out what the CDF of Y is +so remember we'll start with uh the + + align:start position:0% +so remember we'll start with uh the + + + align:start position:0% +so remember we'll start with uh the +definition of the + + align:start position:0% +definition of the + + + align:start position:0% +definition of the +CDF and then we plug in this function + + align:start position:0% +CDF and then we plug in this function + + + align:start position:0% +CDF and then we plug in this function +that we have so we plug in negative log + + align:start position:0% +that we have so we plug in negative log + + + align:start position:0% +that we have so we plug in negative log +of x over + + align:start position:0% +of x over + + + align:start position:0% +of x over +Lambda and into the probability + + align:start position:0% +Lambda and into the probability + + + align:start position:0% +Lambda and into the probability +statement we solve for x okay standard + + align:start position:0% +statement we solve for x okay standard + + + align:start position:0% +statement we solve for x okay standard +stuff and then um we don't actually have + + align:start position:0% +stuff and then um we don't actually have + + + align:start position:0% +stuff and then um we don't actually have +to do the integral so most of the time + + align:start position:0% +to do the integral so most of the time + + + align:start position:0% +to do the integral so most of the time +at this point what we do is we we write + + align:start position:0% +at this point what we do is we we write + + + align:start position:0% +at this point what we do is we we write +down the PDF of X and then we integrate + + align:start position:0% +down the PDF of X and then we integrate + + + align:start position:0% +down the PDF of X and then we integrate +over the relevant area defined by this + + align:start position:0% +over the relevant area defined by this + + + align:start position:0% +over the relevant area defined by this +probability statement but we're going to + + align:start position:0% +probability statement but we're going to + + + align:start position:0% +probability statement but we're going to +take a shortcut today and that's because + + align:start position:0% +take a shortcut today and that's because + + + align:start position:0% +take a shortcut today and that's because +X has a uniform distribution and so the + + align:start position:0% +X has a uniform distribution and so the + + + align:start position:0% +X has a uniform distribution and so the +probability that + + align:start position:0% + + + + align:start position:0% + +X so X is uniform 01 the probability + + align:start position:0% +X so X is uniform 01 the probability + + + align:start position:0% +X so X is uniform 01 the probability +that X is greater than any number is + + align:start position:0% +that X is greater than any number is + + + align:start position:0% +that X is greater than any number is +just one minus that number okay that's + + align:start position:0% +just one minus that number okay that's + + + align:start position:0% +just one minus that number okay that's +that's only because uh X has a uniform + + align:start position:0% +that's only because uh X has a uniform + + + align:start position:0% +that's only because uh X has a uniform +01 distribution okay so um when we're + + align:start position:0% +01 distribution okay so um when we're + + + align:start position:0% +01 distribution okay so um when we're +dealing with uniform random variables we + + align:start position:0% +dealing with uniform random variables we + + + align:start position:0% +dealing with uniform random variables we +can often skip the step where we have to + + align:start position:0% +can often skip the step where we have to + + + align:start position:0% +can often skip the step where we have to +do the integral + + align:start position:0% +do the integral + + + align:start position:0% +do the integral +okay okay so here's what we have that's + + align:start position:0% +okay okay so here's what we have that's + + + align:start position:0% +okay okay so here's what we have that's +the induced support that's the CDF of + + align:start position:0% +the induced support that's the CDF of + + + align:start position:0% +the induced support that's the CDF of +the new random variable + + align:start position:0% +the new random variable + + + align:start position:0% +the new random variable +okay and so we just take the derivative + + align:start position:0% +okay and so we just take the derivative + + + align:start position:0% +okay and so we just take the derivative +to get the PDF and here's what we get + + align:start position:0% +to get the PDF and here's what we get + + + align:start position:0% +to get the PDF and here's what we get +okay fine everything's standard does + + align:start position:0% +okay fine everything's standard does + + + align:start position:0% +okay fine everything's standard does +this distribution look familiar so we've + + align:start position:0% +this distribution look familiar so we've + + + align:start position:0% +this distribution look familiar so we've +seen this least a couple times this + + align:start position:0% +seen this least a couple times this + + + align:start position:0% +seen this least a couple times this +semester I think it might be familiar + + align:start position:0% +semester I think it might be familiar + + + align:start position:0% +semester I think it might be familiar +from other + + align:start position:0% +from other + + + align:start position:0% +from other +contexts exponential + + align:start position:0% + + + + align:start position:0% + +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +okay so now recall that I said that if + + align:start position:0% +okay so now recall that I said that if + + + align:start position:0% +okay so now recall that I said that if +you have a distribution and you + + align:start position:0% +you have a distribution and you + + + align:start position:0% +you have a distribution and you +want say you you want um the function + + align:start position:0% +want say you you want um the function + + + align:start position:0% +want say you you want um the function +that transforms a a a uniform 01 to that + + align:start position:0% +that transforms a a a uniform 01 to that + + + align:start position:0% +that transforms a a a uniform 01 to that +distribution what you do is you just + + align:start position:0% +distribution what you do is you just + + + align:start position:0% +distribution what you do is you just +take the inverse of the CDF and you use + + align:start position:0% +take the inverse of the CDF and you use + + + align:start position:0% +take the inverse of the CDF and you use +that uh function to transform the random + + align:start position:0% +that uh function to transform the random + + + align:start position:0% +that uh function to transform the random +variable okay so now let's just go back + + align:start position:0% +variable okay so now let's just go back + + + align:start position:0% +variable okay so now let's just go back +take a step back uh take the inverse of + + align:start position:0% +take a step back uh take the inverse of + + + align:start position:0% +take a step back uh take the inverse of +the CDF uh that we found above and let's + + align:start position:0% +the CDF uh that we found above and let's + + + align:start position:0% +the CDF uh that we found above and let's +see if it's the same function that we + + align:start position:0% +see if it's the same function that we + + + align:start position:0% +see if it's the same function that we +used to transform the random variable or + + align:start position:0% + + + + align:start position:0% + +originally okay so here's our + + align:start position:0% +originally okay so here's our + + + align:start position:0% +originally okay so here's our +CDF + + align:start position:0% +CDF + + + align:start position:0% +CDF +and let's just find the inverse function + + align:start position:0% +and let's just find the inverse function + + + align:start position:0% +and let's just find the inverse function +okay so we're just writing x = 1 - uh e + + align:start position:0% +okay so we're just writing x = 1 - uh e + + + align:start position:0% +okay so we're just writing x = 1 - uh e +to the Lambda Y and solving uh for y + + align:start position:0% +to the Lambda Y and solving uh for y + + + align:start position:0% +to the Lambda Y and solving uh for y +okay we do that in a couple steps and + + align:start position:0% +okay we do that in a couple steps and + + + align:start position:0% +okay we do that in a couple steps and +then we plug in the capital X and Y + + align:start position:0% +then we plug in the capital X and Y + + + align:start position:0% +then we plug in the capital X and Y +because this is now the function we're + + align:start position:0% +because this is now the function we're + + + align:start position:0% +because this is now the function we're +going to use to transform the random + + align:start position:0% +going to use to transform the random + + + align:start position:0% +going to use to transform the random +variable X + + align:start position:0% + + + + align:start position:0% + +right but that's not the same function + + align:start position:0% +right but that's not the same function + + + align:start position:0% +right but that's not the same function +that we used in the + + align:start position:0% +that we used in the + + + align:start position:0% +that we used in the +example what's going on + + align:start position:0% + + + + align:start position:0% + +any thoughts about what's going on + + align:start position:0% +any thoughts about what's going on + + + align:start position:0% +any thoughts about what's going on +here x sorry x and one- x is the same + + align:start position:0% +here x sorry x and one- x is the same + + + align:start position:0% +here x sorry x and one- x is the same +distribution same distribution exactly + + align:start position:0% +distribution same distribution exactly + + + align:start position:0% +distribution same distribution exactly +okay so when I said that you can take + + align:start position:0% +okay so when I said that you can take + + + align:start position:0% +okay so when I said that you can take +the inverse of the CDF and use that to + + align:start position:0% +the inverse of the CDF and use that to + + + align:start position:0% +the inverse of the CDF and use that to +transform a uniform 01 random variable + + align:start position:0% +transform a uniform 01 random variable + + + align:start position:0% +transform a uniform 01 random variable +to get the distribution of of or to get + + align:start position:0% +to get the distribution of of or to get + + + align:start position:0% +to get the distribution of of or to get +you know sort of the the PDF of the the + + align:start position:0% +you know sort of the the PDF of the the + + + align:start position:0% +you know sort of the the PDF of the the +random variable that had this that your + + align:start position:0% +random variable that had this that your + + + align:start position:0% +random variable that had this that your +whose CDF you're using okay when I said + + align:start position:0% +whose CDF you're using okay when I said + + + align:start position:0% +whose CDF you're using okay when I said +that I didn't say that was unique okay + + align:start position:0% +that I didn't say that was unique okay + + + align:start position:0% +that I didn't say that was unique okay +so in particular there might be lots of + + align:start position:0% +so in particular there might be lots of + + + align:start position:0% +so in particular there might be lots of +different functions that are going to + + align:start position:0% +different functions that are going to + + + align:start position:0% +different functions that are going to +transform a uniform 01 random variable + + align:start position:0% +transform a uniform 01 random variable + + + align:start position:0% +transform a uniform 01 random variable +into an exponential random variable and + + align:start position:0% +into an exponential random variable and + + + align:start position:0% +into an exponential random variable and +these happen to be two of the + + align:start position:0% +these happen to be two of the + + + align:start position:0% +these happen to be two of the +functions and in fact if you uh you know + + align:start position:0% +functions and in fact if you uh you know + + + align:start position:0% +functions and in fact if you uh you know +if you sort of look at the functions you + + align:start position:0% +if you sort of look at the functions you + + + align:start position:0% +if you sort of look at the functions you +might be able to convince yourself that + + align:start position:0% +might be able to convince yourself that + + + align:start position:0% +might be able to convince yourself that +these are going to um give you the same + + align:start position:0% +these are going to um give you the same + + + align:start position:0% +these are going to um give you the same +distribution if you use the these two + + align:start position:0% +distribution if you use the these two + + + align:start position:0% +distribution if you use the these two +different functions to transform a + + align:start position:0% +different functions to transform a + + + align:start position:0% +different functions to transform a +uniform Z1 random variable why because 1 + + align:start position:0% +uniform Z1 random variable why because 1 + + + align:start position:0% +uniform Z1 random variable why because 1 +- x this random variable is also going + + align:start position:0% +- x this random variable is also going + + + align:start position:0% +- x this random variable is also going +to have a uniform 01 distribution okay I + + align:start position:0% +to have a uniform 01 distribution okay I + + + align:start position:0% +to have a uniform 01 distribution okay I +didn't prove it but it's probably not + + align:start position:0% +didn't prove it but it's probably not + + + align:start position:0% +didn't prove it but it's probably not +very hard to believe that that's true + + align:start position:0% +very hard to believe that that's true + + + align:start position:0% +very hard to believe that that's true +okay and you can prove it if you want + + align:start position:0% +okay and you can prove it if you want + + + align:start position:0% +okay and you can prove it if you want +okay okay so what's going on both of + + align:start position:0% +okay okay so what's going on both of + + + align:start position:0% +okay okay so what's going on both of +these functions work and and um the in + + align:start position:0% +these functions work and and um the in + + + align:start position:0% +these functions work and and um the in +particular the reason why both of them + + align:start position:0% +particular the reason why both of them + + + align:start position:0% +particular the reason why both of them +work is that um as I said if x is + + align:start position:0% +work is that um as I said if x is + + + align:start position:0% +work is that um as I said if x is +uniform 01 one - x is as well okay so + + align:start position:0% +uniform 01 one - x is as well okay so + + + align:start position:0% +uniform 01 one - x is as well okay so +there is a lot of information in a PDF a + + align:start position:0% +there is a lot of information in a PDF a + + + align:start position:0% +there is a lot of information in a PDF a +PDF contains just you know it's it's + + align:start position:0% +PDF contains just you know it's it's + + + align:start position:0% +PDF contains just you know it's it's +it's a it's a whole function it sort of + + align:start position:0% +it's a it's a whole function it sort of + + + align:start position:0% +it's a it's a whole function it sort of +tells you all kinds of things and + + align:start position:0% +tells you all kinds of things and + + + align:start position:0% +tells you all kinds of things and +sometimes it tells you a lot uh of + + align:start position:0% +sometimes it tells you a lot uh of + + + align:start position:0% +sometimes it tells you a lot uh of +things that we don't actually care about + + align:start position:0% +things that we don't actually care about + + + align:start position:0% +things that we don't actually care about +okay perhaps we don't care you know + + align:start position:0% +okay perhaps we don't care you know + + + align:start position:0% +okay perhaps we don't care you know +precisely what the shape of the + + align:start position:0% +precisely what the shape of the + + + align:start position:0% +precisely what the shape of the +distribution of our random variable is + + align:start position:0% +distribution of our random variable is + + + align:start position:0% +distribution of our random variable is +in every region of the the reals or + + align:start position:0% +in every region of the the reals or + + + align:start position:0% +in every region of the the reals or +something like that U maybe what we + + align:start position:0% +something like that U maybe what we + + + align:start position:0% +something like that U maybe what we +really want is we want some way to + + align:start position:0% +really want is we want some way to + + + align:start position:0% +really want is we want some way to +summarize uh and and I should say + + align:start position:0% +summarize uh and and I should say + + + align:start position:0% +summarize uh and and I should say +sometimes we do care about that and + + align:start position:0% +sometimes we do care about that and + + + align:start position:0% +sometimes we do care about that and +sometimes we don't okay but in the times + + align:start position:0% +sometimes we don't okay but in the times + + + align:start position:0% +sometimes we don't okay but in the times +that we don't uh maybe what we want to + + align:start position:0% +that we don't uh maybe what we want to + + + align:start position:0% +that we don't uh maybe what we want to +do is just just summarize some of the + + align:start position:0% +do is just just summarize some of the + + + align:start position:0% +do is just just summarize some of the +most Salient features of a distribution + + align:start position:0% +most Salient features of a distribution + + + align:start position:0% +most Salient features of a distribution +okay where it is centered uh where it + + align:start position:0% +okay where it is centered uh where it + + + align:start position:0% +okay where it is centered uh where it +reaches it Peak how spread out it is uh + + align:start position:0% +reaches it Peak how spread out it is uh + + + align:start position:0% +reaches it Peak how spread out it is uh +whether it's symmetric how thick its + + align:start position:0% +whether it's symmetric how thick its + + + align:start position:0% +whether it's symmetric how thick its +tails are Etc okay and so what we do is + + align:start position:0% +tails are Etc okay and so what we do is + + + align:start position:0% +tails are Etc okay and so what we do is +we Define something called a moment or a + + align:start position:0% +we Define something called a moment or a + + + align:start position:0% +we Define something called a moment or a +series of moments of a distribution to + + align:start position:0% +series of moments of a distribution to + + + align:start position:0% +series of moments of a distribution to +help us summarize some of these most + + align:start position:0% +help us summarize some of these most + + + align:start position:0% +help us summarize some of these most +Salient features and that's what we're + + align:start position:0% +Salient features and that's what we're + + + align:start position:0% +Salient features and that's what we're +going to talk about + + align:start position:0% +going to talk about + + + align:start position:0% +going to talk about +next okay so here's some distributions I + + align:start position:0% +next okay so here's some distributions I + + + align:start position:0% +next okay so here's some distributions I +just drew them I don't know what they + + align:start position:0% +just drew them I don't know what they + + + align:start position:0% +just drew them I don't know what they +are um and the one moment or I guess + + align:start position:0% +are um and the one moment or I guess + + + align:start position:0% +are um and the one moment or I guess +three different of moments that are + + align:start position:0% +three different of moments that are + + + align:start position:0% +three different of moments that are +somewhat related uh that you've probably + + align:start position:0% +somewhat related uh that you've probably + + + align:start position:0% +somewhat related uh that you've probably +all run across in one context or another + + align:start position:0% +all run across in one context or another + + + align:start position:0% +all run across in one context or another +um are mean median and mode and they all + + align:start position:0% +um are mean median and mode and they all + + + align:start position:0% +um are mean median and mode and they all +describe in different ways where the + + align:start position:0% +describe in different ways where the + + + align:start position:0% +describe in different ways where the +distribution is located or centered okay + + align:start position:0% +distribution is located or centered okay + + + align:start position:0% +distribution is located or centered okay +so all of these uh all of these moments + + align:start position:0% +so all of these uh all of these moments + + + align:start position:0% +so all of these uh all of these moments +are going to be um sort of useful in in + + align:start position:0% +are going to be um sort of useful in in + + + align:start position:0% +are going to be um sort of useful in in +various ways okay so the mode is the + + align:start position:0% +various ways okay so the mode is the + + + align:start position:0% +various ways okay so the mode is the +point where the PDF reaches its highest + + align:start position:0% +point where the PDF reaches its highest + + + align:start position:0% +point where the PDF reaches its highest +value indicated it on these three + + align:start position:0% +value indicated it on these three + + + align:start position:0% +value indicated it on these three +distributions the median is the point + + align:start position:0% +distributions the median is the point + + + align:start position:0% +distributions the median is the point +above and below which the integral of + + align:start position:0% +above and below which the integral of + + + align:start position:0% +above and below which the integral of +the PDF is equal to 1/2 okay so uh + + align:start position:0% +the PDF is equal to 1/2 okay so uh + + + align:start position:0% +the PDF is equal to 1/2 okay so uh +whatever uh whatever point is the point + + align:start position:0% +whatever uh whatever point is the point + + + align:start position:0% +whatever uh whatever point is the point +at which the integral below is equal to + + align:start position:0% +at which the integral below is equal to + + + align:start position:0% +at which the integral below is equal to +1/2 and above is equal to 1/2 is the + + align:start position:0% +1/2 and above is equal to 1/2 is the + + + align:start position:0% +1/2 and above is equal to 1/2 is the +median of the + + align:start position:0% +median of the + + + align:start position:0% +median of the +distribution and then the mean also + + align:start position:0% +distribution and then the mean also + + + align:start position:0% +distribution and then the mean also +known as the expectation or expected + + align:start position:0% +known as the expectation or expected + + + align:start position:0% +known as the expectation or expected +value the distribution is defined in + + align:start position:0% +value the distribution is defined in + + + align:start position:0% +value the distribution is defined in +this way I'll give you a sort of a + + align:start position:0% +this way I'll give you a sort of a + + + align:start position:0% +this way I'll give you a sort of a +geometric interpretation of it in just a + + align:start position:0% +geometric interpretation of it in just a + + + align:start position:0% +geometric interpretation of it in just a +second but um basically the way we + + align:start position:0% +second but um basically the way we + + + align:start position:0% +second but um basically the way we +Define the mean of the distribution or + + align:start position:0% +Define the mean of the distribution or + + + align:start position:0% +Define the mean of the distribution or +the expectation is just the integral + + align:start position:0% +the expectation is just the integral + + + align:start position:0% +the expectation is just the integral +over the support of the distribution of + + align:start position:0% +over the support of the distribution of + + + align:start position:0% +over the support of the distribution of +uh x times the PDF of X + + align:start position:0% +uh x times the PDF of X + + + align:start position:0% +uh x times the PDF of X +okay okay so if we need to find the + + align:start position:0% +okay okay so if we need to find the + + + align:start position:0% +okay okay so if we need to find the +expectation of a continuous random + + align:start position:0% +expectation of a continuous random + + + align:start position:0% +expectation of a continuous random +variable we just integrate the PDF times + + align:start position:0% +variable we just integrate the PDF times + + + align:start position:0% +variable we just integrate the PDF times +the value over the support that's just + + align:start position:0% +the value over the support that's just + + + align:start position:0% +the value over the support that's just +what I had on the previous + + align:start position:0% +what I had on the previous + + + align:start position:0% +what I had on the previous +slide and I should also point out uh + + align:start position:0% +slide and I should also point out uh + + + align:start position:0% +slide and I should also point out uh +because this comes in handy quite a bit + + align:start position:0% +because this comes in handy quite a bit + + + align:start position:0% +because this comes in handy quite a bit +uh the discret analog is just what you + + align:start position:0% +uh the discret analog is just what you + + + align:start position:0% +uh the discret analog is just what you +would expect it to be instead of uh + + align:start position:0% +would expect it to be instead of uh + + + align:start position:0% +would expect it to be instead of uh +integrating we sum but we sum up all + + align:start position:0% +integrating we sum but we sum up all + + + align:start position:0% +integrating we sum but we sum up all +over all of the possible values of X + + align:start position:0% +over all of the possible values of X + + + align:start position:0% +over all of the possible values of X +okay so it's just summing up uh x times + + align:start position:0% +okay so it's just summing up uh x times + + + align:start position:0% +okay so it's just summing up uh x times +the the probability that X you know + + align:start position:0% +the the probability that X you know + + + align:start position:0% +the the probability that X you know +probability of X at that point okay + + align:start position:0% +probability of X at that point okay + + + align:start position:0% +probability of X at that point okay +couple comments about uh you know sort + + align:start position:0% +couple comments about uh you know sort + + + align:start position:0% +couple comments about uh you know sort +of notation and + + align:start position:0% +of notation and + + + align:start position:0% +of notation and +terminology um I will often use capital + + align:start position:0% +terminology um I will often use capital + + + align:start position:0% +terminology um I will often use capital +E of x to denote the the mean of a + + align:start position:0% +E of x to denote the the mean of a + + + align:start position:0% +E of x to denote the the mean of a +distribution the expectation of a + + align:start position:0% +distribution the expectation of a + + + align:start position:0% +distribution the expectation of a +distribution um but we I'll often also + + align:start position:0% +distribution um but we I'll often also + + + align:start position:0% +distribution um but we I'll often also +use the uh Greek letter mu and so those + + align:start position:0% +use the uh Greek letter mu and so those + + + align:start position:0% +use the uh Greek letter mu and so those +uh are sometimes used + + align:start position:0% +uh are sometimes used + + + align:start position:0% +uh are sometimes used +interchangeably and this is the sort of + + align:start position:0% +interchangeably and this is the sort of + + + align:start position:0% +interchangeably and this is the sort of +geometric uh distribution I prom or + + align:start position:0% +geometric uh distribution I prom or + + + align:start position:0% +geometric uh distribution I prom or +geometric interpretation I promised you + + align:start position:0% +geometric interpretation I promised you + + + align:start position:0% +geometric interpretation I promised you +so if we think of the PDF literally + + align:start position:0% +so if we think of the PDF literally + + + align:start position:0% +so if we think of the PDF literally +as a density the expectation is the + + align:start position:0% +as a density the expectation is the + + + align:start position:0% +as a density the expectation is the +balancing point of that density okay so + + align:start position:0% +balancing point of that density okay so + + + align:start position:0% +balancing point of that density okay so +this is different from the median of a + + align:start position:0% +this is different from the median of a + + + align:start position:0% +this is different from the median of a +distribution because uh if you think + + align:start position:0% +distribution because uh if you think + + + align:start position:0% +distribution because uh if you think +about um how I describe the median it's + + align:start position:0% +about um how I describe the median it's + + + align:start position:0% +about um how I describe the median it's +the point at which the integral uh both + + align:start position:0% +the point at which the integral uh both + + + align:start position:0% +the point at which the integral uh both +above and below is equal to one half if + + align:start position:0% +above and below is equal to one half if + + + align:start position:0% +above and below is equal to one half if +you set you know if you have a median of + + align:start position:0% +you set you know if you have a median of + + + align:start position:0% +you set you know if you have a median of +a distribution and you shift probability + + align:start position:0% +a distribution and you shift probability + + + align:start position:0% +a distribution and you shift probability +on one side of it the median doesn't + + align:start position:0% +on one side of it the median doesn't + + + align:start position:0% +on one side of it the median doesn't +change okay because the the um the the + + align:start position:0% +change okay because the the um the the + + + align:start position:0% +change okay because the the um the the +uh integral on that side is still equal + + align:start position:0% +uh integral on that side is still equal + + + align:start position:0% +uh integral on that side is still equal +to 1/2 but uh the expectation might + + align:start position:0% +to 1/2 but uh the expectation might + + + align:start position:0% +to 1/2 but uh the expectation might +change okay you take a chunk of + + align:start position:0% +change okay you take a chunk of + + + align:start position:0% +change okay you take a chunk of +probability and you shift it out uh then + + align:start position:0% +probability and you shift it out uh then + + + align:start position:0% +probability and you shift it out uh then +the sort of um the expectation of the + + align:start position:0% +the sort of um the expectation of the + + + align:start position:0% +the sort of um the expectation of the +distribution shifts out as well okay and + + align:start position:0% +distribution shifts out as well okay and + + + align:start position:0% +distribution shifts out as well okay and +the the terminology does get a little + + align:start position:0% +the the terminology does get a little + + + align:start position:0% +the the terminology does get a little +more complicated complicating or + + align:start position:0% +more complicated complicating or + + + align:start position:0% +more complicated complicating or +complicated when we start talking about + + align:start position:0% +complicated when we start talking about + + + align:start position:0% +complicated when we start talking about +estimation because we're going to talk + + align:start position:0% +estimation because we're going to talk + + + align:start position:0% +estimation because we're going to talk +about something called a sample mean + + align:start position:0% +about something called a sample mean + + + align:start position:0% +about something called a sample mean +which is quite definitely different from + + align:start position:0% +which is quite definitely different from + + + align:start position:0% +which is quite definitely different from +this it's related but it's different uh + + align:start position:0% +this it's related but it's different uh + + + align:start position:0% +this it's related but it's different uh +and so then we've got to keep mean and + + align:start position:0% +and so then we've got to keep mean and + + + align:start position:0% +and so then we've got to keep mean and +Sample Bean kind of straight in our + + align:start position:0% +Sample Bean kind of straight in our + + + align:start position:0% +Sample Bean kind of straight in our +heads but I we'll be able to do + + align:start position:0% +heads but I we'll be able to do + + + align:start position:0% +heads but I we'll be able to do +it okay oh + + align:start position:0% +it okay oh + + + align:start position:0% +it okay oh +here okay so uh here's just a quick + + align:start position:0% +here okay so uh here's just a quick + + + align:start position:0% +here okay so uh here's just a quick +example of uh calculating the + + align:start position:0% +example of uh calculating the + + + align:start position:0% +example of uh calculating the +expectation of a distribution okay so + + align:start position:0% +expectation of a distribution okay so + + + align:start position:0% +expectation of a distribution okay so +let's suppose we have an exponential PDF + + align:start position:0% +let's suppose we have an exponential PDF + + + align:start position:0% +let's suppose we have an exponential PDF +and how do we calculate uh its + + align:start position:0% +and how do we calculate uh its + + + align:start position:0% +and how do we calculate uh its +expectation well if it's just plugging + + align:start position:0% +expectation well if it's just plugging + + + align:start position:0% +expectation well if it's just plugging +into the formula it's just going to be + + align:start position:0% +into the formula it's just going to be + + + align:start position:0% +into the formula it's just going to be +the integral over the support of the + + align:start position:0% +the integral over the support of the + + + align:start position:0% +the integral over the support of the +exponential which is 0 to uh infinity of + + align:start position:0% +exponential which is 0 to uh infinity of + + + align:start position:0% +exponential which is 0 to uh infinity of +x times the PDF of X okay if we didn't + + align:start position:0% +x times the PDF of X okay if we didn't + + + align:start position:0% +x times the PDF of X okay if we didn't +put X in here of course we know that + + align:start position:0% +put X in here of course we know that + + + align:start position:0% +put X in here of course we know that +integral is just equal to one right but + + align:start position:0% +integral is just equal to one right but + + + align:start position:0% +integral is just equal to one right but +then we put we uh uh put the X in the + + align:start position:0% +then we put we uh uh put the X in the + + + align:start position:0% +then we put we uh uh put the X in the +formula and that's the formula for + + align:start position:0% +formula and that's the formula for + + + align:start position:0% +formula and that's the formula for +calculating the + + align:start position:0% + + + + align:start position:0% + +expectation okay so specifically in the + + align:start position:0% +expectation okay so specifically in the + + + align:start position:0% +expectation okay so specifically in the +case of the exponential that's what it + + align:start position:0% +case of the exponential that's what it + + + align:start position:0% +case of the exponential that's what it +looks + + align:start position:0% +looks + + + align:start position:0% +looks +like + + align:start position:0% +like + + + align:start position:0% +like +um I'm skipping the uh calculus and just + + align:start position:0% +um I'm skipping the uh calculus and just + + + align:start position:0% +um I'm skipping the uh calculus and just +giving you the answer and it turns out + + align:start position:0% +giving you the answer and it turns out + + + align:start position:0% +giving you the answer and it turns out +there's a good reason for me to skip + + align:start position:0% +there's a good reason for me to skip + + + align:start position:0% +there's a good reason for me to skip +skip the calculus this time I didn't + + align:start position:0% +skip the calculus this time I didn't + + + align:start position:0% +skip the calculus this time I didn't +realize when I picked this example uh + + align:start position:0% +realize when I picked this example uh + + + align:start position:0% +realize when I picked this example uh +you have to um do integration by parts + + align:start position:0% +you have to um do integration by parts + + + align:start position:0% +you have to um do integration by parts +to get it so if you want a little + + align:start position:0% +to get it so if you want a little + + + align:start position:0% +to get it so if you want a little +practice on your Calculus skills go + + align:start position:0% +practice on your Calculus skills go + + + align:start position:0% +practice on your Calculus skills go +ahead and do it if you don't you can + + align:start position:0% +ahead and do it if you don't you can + + + align:start position:0% +ahead and do it if you don't you can +just take my word for it this is the + + align:start position:0% +just take my word for it this is the + + + align:start position:0% +just take my word for it this is the +expectation of an + + align:start position:0% +expectation of an + + + align:start position:0% +expectation of an +exponential uh distribution + + align:start position:0% + + + + align:start position:0% + +okay so now um sort of having having a + + align:start position:0% +okay so now um sort of having having a + + + align:start position:0% +okay so now um sort of having having a +few of these things under our belt we're + + align:start position:0% +few of these things under our belt we're + + + align:start position:0% +few of these things under our belt we're +going to uh take a little side trip into + + align:start position:0% +going to uh take a little side trip into + + + align:start position:0% +going to uh take a little side trip into +auction Theory okay so why what do + + align:start position:0% +auction Theory okay so why what do + + + align:start position:0% +auction Theory okay so why what do +auctions have to do with probabilities + + align:start position:0% +auctions have to do with probabilities + + + align:start position:0% +auctions have to do with probabilities +well there's there's sort of a number of + + align:start position:0% +well there's there's sort of a number of + + + align:start position:0% +well there's there's sort of a number of +reasons that uh I want to take this + + align:start position:0% +reasons that uh I want to take this + + + align:start position:0% +reasons that uh I want to take this +little side trip um one reason is that + + align:start position:0% +little side trip um one reason is that + + + align:start position:0% +little side trip um one reason is that +uh we have um last lecture we talked + + align:start position:0% +uh we have um last lecture we talked + + + align:start position:0% +uh we have um last lecture we talked +about um order statistics and it turns + + align:start position:0% +about um order statistics and it turns + + + align:start position:0% +about um order statistics and it turns +out that order statistics are a very + + align:start position:0% +out that order statistics are a very + + + align:start position:0% +out that order statistics are a very +useful mathematical tool to analyze um + + align:start position:0% +useful mathematical tool to analyze um + + + align:start position:0% +useful mathematical tool to analyze um +auctions why is that um an an obvious + + align:start position:0% +auctions why is that um an an obvious + + + align:start position:0% +auctions why is that um an an obvious +thing to do when you're talking about + + align:start position:0% +thing to do when you're talking about + + + align:start position:0% +thing to do when you're talking about +auctions is to model bids in an auction + + align:start position:0% +auctions is to model bids in an auction + + + align:start position:0% +auctions is to model bids in an auction +as an IID random sample and the winning + + align:start position:0% +as an IID random sample and the winning + + + align:start position:0% +as an IID random sample and the winning +bid which is typically the highest bid + + align:start position:0% +bid which is typically the highest bid + + + align:start position:0% +bid which is typically the highest bid +as the nth order statistic from that + + align:start position:0% +as the nth order statistic from that + + + align:start position:0% +as the nth order statistic from that +random sample okay so we will do + + align:start position:0% +random sample okay so we will do + + + align:start position:0% +random sample okay so we will do +that um another reason that I like uh + + align:start position:0% +that um another reason that I like uh + + + align:start position:0% +that um another reason that I like uh +you know I want to take this little side + + align:start position:0% +you know I want to take this little side + + + align:start position:0% +you know I want to take this little side +trip into auction theory is that you + + align:start position:0% +trip into auction theory is that you + + + align:start position:0% +trip into auction theory is that you +know most of this class we're going to + + align:start position:0% +know most of this class we're going to + + + align:start position:0% +know most of this class we're going to +be sort of giving you tools that help + + align:start position:0% +be sort of giving you tools that help + + + align:start position:0% +be sort of giving you tools that help +you uh sort of empirically analyze uh + + align:start position:0% +you uh sort of empirically analyze uh + + + align:start position:0% +you uh sort of empirically analyze uh +questions in social science and here is + + align:start position:0% +questions in social science and here is + + + align:start position:0% +questions in social science and here is +an example of probability tools that + + align:start position:0% +an example of probability tools that + + + align:start position:0% +an example of probability tools that +help you theoretically analyze uh some + + align:start position:0% +help you theoretically analyze uh some + + + align:start position:0% +help you theoretically analyze uh some +questions in social science so it's not + + align:start position:0% +questions in social science so it's not + + + align:start position:0% +questions in social science so it's not +really the main focus of of the class I + + align:start position:0% +really the main focus of of the class I + + + align:start position:0% +really the main focus of of the class I +mean the main focus of the class is sort + + align:start position:0% +mean the main focus of the class is sort + + + align:start position:0% +mean the main focus of the class is sort +of data analysis and and empirically + + align:start position:0% +of data analysis and and empirically + + + align:start position:0% +of data analysis and and empirically +analyzing questions and social science + + align:start position:0% +analyzing questions and social science + + + align:start position:0% +analyzing questions and social science +but I did want to show you one example + + align:start position:0% +but I did want to show you one example + + + align:start position:0% +but I did want to show you one example +where you could take tools from + + align:start position:0% +where you could take tools from + + + align:start position:0% +where you could take tools from +probability and help you uh sort of help + + align:start position:0% +probability and help you uh sort of help + + + align:start position:0% +probability and help you uh sort of help +you do some theoretical uh analysis of + + align:start position:0% +you do some theoretical uh analysis of + + + align:start position:0% +you do some theoretical uh analysis of +questions in social science okay and + + align:start position:0% +questions in social science okay and + + + align:start position:0% +questions in social science okay and +furthermore uh we also will uh compute + + align:start position:0% +furthermore uh we also will uh compute + + + align:start position:0% +furthermore uh we also will uh compute +some expectations along the way so we'll + + align:start position:0% +some expectations along the way so we'll + + + align:start position:0% +some expectations along the way so we'll +get a little practice with that + + align:start position:0% + + + + align:start position:0% + +okay so here are some things that are + + align:start position:0% +okay so here are some things that are + + + align:start position:0% +okay so here are some things that are +sold at + + align:start position:0% +sold at + + + align:start position:0% +sold at +auction okay uh there's over here + + align:start position:0% +auction okay uh there's over here + + + align:start position:0% +auction okay uh there's over here +there's a + + align:start position:0% +there's a + + + align:start position:0% +there's a +Picasso so if you have a Picasso sitting + + align:start position:0% +Picasso so if you have a Picasso sitting + + + align:start position:0% +Picasso so if you have a Picasso sitting +around and you'd like to liquidate that + + align:start position:0% +around and you'd like to liquidate that + + + align:start position:0% +around and you'd like to liquidate that +and maybe you know use it to pay for + + align:start position:0% +and maybe you know use it to pay for + + + align:start position:0% +and maybe you know use it to pay for +your MIT tuition or something um what + + align:start position:0% +your MIT tuition or something um what + + + align:start position:0% +your MIT tuition or something um what +would you do you probably wouldn't just + + align:start position:0% +would you do you probably wouldn't just + + + align:start position:0% +would you do you probably wouldn't just +put it up on Craigs List at a posted + + align:start position:0% +put it up on Craigs List at a posted + + + align:start position:0% +put it up on Craigs List at a posted +price uh you probably go to Chris or sou + + align:start position:0% +price uh you probably go to Chris or sou + + + align:start position:0% +price uh you probably go to Chris or sou +bees and auction it off okay we'll talk + + align:start position:0% +bees and auction it off okay we'll talk + + + align:start position:0% +bees and auction it off okay we'll talk +about we can talk about the the the + + align:start position:0% +about we can talk about the the the + + + align:start position:0% +about we can talk about the the the +decision between posted price and + + align:start position:0% +decision between posted price and + + + align:start position:0% +decision between posted price and +auction in in a second but start + + align:start position:0% +auction in in a second but start + + + align:start position:0% +auction in in a second but start +thinking about that question why would + + align:start position:0% +thinking about that question why would + + + align:start position:0% +thinking about that question why would +you decide to sell that at auction as + + align:start position:0% +you decide to sell that at auction as + + + align:start position:0% +you decide to sell that at auction as +opposed to a posted price uh down here's + + align:start position:0% +opposed to a posted price uh down here's + + + align:start position:0% +opposed to a posted price uh down here's +some livestock uh Livestock in in the US + + align:start position:0% +some livestock uh Livestock in in the US + + + align:start position:0% +some livestock uh Livestock in in the US +is typically sold at auction uh before + + align:start position:0% +is typically sold at auction uh before + + + align:start position:0% +is typically sold at auction uh before +um going to The Butcher Shop uh this is + + align:start position:0% +um going to The Butcher Shop uh this is + + + align:start position:0% +um going to The Butcher Shop uh this is +a picture of radio spectrum okay so it + + align:start position:0% +a picture of radio spectrum okay so it + + + align:start position:0% +a picture of radio spectrum okay so it +used to be in in the United States and + + align:start position:0% +used to be in in the United States and + + + align:start position:0% +used to be in in the United States and +pretty much all countries radio spectrum + + align:start position:0% +pretty much all countries radio spectrum + + + align:start position:0% +pretty much all countries radio spectrum +uh was sort of controlled by the + + align:start position:0% +uh was sort of controlled by the + + + align:start position:0% +uh was sort of controlled by the +government and given away for free uh to + + align:start position:0% +government and given away for free uh to + + + align:start position:0% +government and given away for free uh to +radio stations and uh television + + align:start position:0% +radio stations and uh television + + + align:start position:0% +radio stations and uh television +stations and things like that um and it + + align:start position:0% +stations and things like that um and it + + + align:start position:0% +stations and things like that um and it +was given away typically with uh + + align:start position:0% +was given away typically with uh + + + align:start position:0% +was given away typically with uh +conditions like you have to put on + + align:start position:0% +conditions like you have to put on + + + align:start position:0% +conditions like you have to put on +programming that's you know uh uh useful + + align:start position:0% +programming that's you know uh uh useful + + + align:start position:0% +programming that's you know uh uh useful +for the public good or something like + + align:start position:0% +for the public good or something like + + + align:start position:0% +for the public good or something like +that but you know was just given away + + align:start position:0% +that but you know was just given away + + + align:start position:0% +that but you know was just given away +and then at some point I think it was in + + align:start position:0% +and then at some point I think it was in + + + align:start position:0% +and then at some point I think it was in +the 80s or '90s maybe I'm not sure uh + + align:start position:0% +the 80s or '90s maybe I'm not sure uh + + + align:start position:0% +the 80s or '90s maybe I'm not sure uh +the US government decided we're sitting + + align:start position:0% +the US government decided we're sitting + + + align:start position:0% +the US government decided we're sitting +on a gold mine we have hugely valuable + + align:start position:0% +on a gold mine we have hugely valuable + + + align:start position:0% +on a gold mine we have hugely valuable +asset here and furthermore we don't + + align:start position:0% +asset here and furthermore we don't + + + align:start position:0% +asset here and furthermore we don't +actually know we know it's hugely + + align:start position:0% +actually know we know it's hugely + + + align:start position:0% +actually know we know it's hugely +valuable we don't know exactly how + + align:start position:0% +valuable we don't know exactly how + + + align:start position:0% +valuable we don't know exactly how +valuable it is why don't we start + + align:start position:0% +valuable it is why don't we start + + + align:start position:0% +valuable it is why don't we start +auctioning it off and so the United + + align:start position:0% +auctioning it off and so the United + + + align:start position:0% +auctioning it off and so the United +States uh started uh running uh Spectrum + + align:start position:0% +States uh started uh running uh Spectrum + + + align:start position:0% +States uh started uh running uh Spectrum +auctions they still do for various parts + + align:start position:0% +auctions they still do for various parts + + + align:start position:0% +auctions they still do for various parts +of the spectrum uh and now this is sort + + align:start position:0% +of the spectrum uh and now this is sort + + + align:start position:0% +of the spectrum uh and now this is sort +of common practice among lots of + + align:start position:0% +of common practice among lots of + + + align:start position:0% +of common practice among lots of +countries + + align:start position:0% +countries + + + align:start position:0% +countries +okay uh down here is a picture of an + + align:start position:0% +okay uh down here is a picture of an + + + align:start position:0% +okay uh down here is a picture of an +F-16 so um lock who who produces these + + align:start position:0% +F-16 so um lock who who produces these + + + align:start position:0% +F-16 so um lock who who produces these +locky Martin I'm not sure okay so locky + + align:start position:0% +locky Martin I'm not sure okay so locky + + + align:start position:0% +locky Martin I'm not sure okay so locky +Martin does not sell f-16s at auction + + align:start position:0% +Martin does not sell f-16s at auction + + + align:start position:0% +Martin does not sell f-16s at auction +obviously but in fact they are acquired + + align:start position:0% +obviously but in fact they are acquired + + + align:start position:0% +obviously but in fact they are acquired +through an auction mechanism kind of a + + align:start position:0% +through an auction mechanism kind of a + + + align:start position:0% +through an auction mechanism kind of a +reverse auction so when the US + + align:start position:0% +reverse auction so when the US + + + align:start position:0% +reverse auction so when the US +government wants + + align:start position:0% +government wants + + + align:start position:0% +government wants +uh to buy the sixth generation fighter + + align:start position:0% +uh to buy the sixth generation fighter + + + align:start position:0% +uh to buy the sixth generation fighter +jets what did they do they sort of write + + align:start position:0% +jets what did they do they sort of write + + + align:start position:0% +jets what did they do they sort of write +down the specifications that they want + + align:start position:0% +down the specifications that they want + + + align:start position:0% +down the specifications that they want +in the sixth generation fighter jets and + + align:start position:0% +in the sixth generation fighter jets and + + + align:start position:0% +in the sixth generation fighter jets and +then they let all of the people who + + align:start position:0% +then they let all of the people who + + + align:start position:0% +then they let all of the people who +would all of the firms who would like to + + align:start position:0% +would all of the firms who would like to + + + align:start position:0% +would all of the firms who would like to +produce those fighter jets bid so they + + align:start position:0% +produce those fighter jets bid so they + + + align:start position:0% +produce those fighter jets bid so they +you know the bids can be very + + align:start position:0% +you know the bids can be very + + + align:start position:0% +you know the bids can be very +complicated but they boil down to here's + + align:start position:0% +complicated but they boil down to here's + + + align:start position:0% +complicated but they boil down to here's +how we can fulfill your specifications + + align:start position:0% +how we can fulfill your specifications + + + align:start position:0% +how we can fulfill your specifications +and here's what we'll charge and then + + align:start position:0% +and here's what we'll charge and then + + + align:start position:0% +and here's what we'll charge and then +the US government uh buys the fighter + + align:start position:0% +the US government uh buys the fighter + + + align:start position:0% +the US government uh buys the fighter +jets from the lowest bidder so that's + + align:start position:0% +jets from the lowest bidder so that's + + + align:start position:0% +jets from the lowest bidder so that's +called a procurement auction and it's + + align:start position:0% +called a procurement auction and it's + + + align:start position:0% +called a procurement auction and it's +kind of a reverse auction okay so + + align:start position:0% +kind of a reverse auction okay so + + + align:start position:0% +kind of a reverse auction okay so +instead of the highest bidder winning um + + align:start position:0% +instead of the highest bidder winning um + + + align:start position:0% +instead of the highest bidder winning um +and purchasing the lowest bidder wins + + align:start position:0% +and purchasing the lowest bidder wins + + + align:start position:0% +and purchasing the lowest bidder wins +and sells sells the product okay um I + + align:start position:0% +and sells sells the product okay um I + + + align:start position:0% +and sells sells the product okay um I +went on eBay uh a couple days ago and I + + align:start position:0% +went on eBay uh a couple days ago and I + + + align:start position:0% +went on eBay uh a couple days ago and I +was making up this slide and I found + + align:start position:0% +was making up this slide and I found + + + align:start position:0% +was making up this slide and I found +some uh + + align:start position:0% +some uh + + + align:start position:0% +some uh +collectible uh beer trade tin signs I + + align:start position:0% +collectible uh beer trade tin signs I + + + align:start position:0% +collectible uh beer trade tin signs I +guess they're just beer trays I don't + + align:start position:0% +guess they're just beer trays I don't + + + align:start position:0% +guess they're just beer trays I don't +know did anyone has anyone heard of tech + + align:start position:0% +know did anyone has anyone heard of tech + + + align:start position:0% +know did anyone has anyone heard of tech +beer did you know Tech beer existed no + + align:start position:0% +beer did you know Tech beer existed no + + + align:start position:0% +beer did you know Tech beer existed no +I've never heard of tech beer I don't I + + align:start position:0% +I've never heard of tech beer I don't I + + + align:start position:0% +I've never heard of tech beer I don't I +I didn't know if it was like maybe the + + align:start position:0% +I didn't know if it was like maybe the + + + align:start position:0% +I didn't know if it was like maybe the +official MIT beer or something like that + + align:start position:0% +official MIT beer or something like that + + + align:start position:0% +official MIT beer or something like that +but but if you're inclined you can buy + + align:start position:0% +but but if you're inclined you can buy + + + align:start position:0% +but but if you're inclined you can buy +memorabilia like Tech beer trays on eBay + + align:start position:0% +memorabilia like Tech beer trays on eBay + + + align:start position:0% +memorabilia like Tech beer trays on eBay +and I think the starting bid was only + + align:start position:0% +and I think the starting bid was only + + + align:start position:0% +and I think the starting bid was only +eight bucks there so you can get them + + align:start position:0% +eight bucks there so you can get them + + + align:start position:0% +eight bucks there so you can get them +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +cheaply um up on the very top where it + + align:start position:0% +cheaply um up on the very top where it + + + align:start position:0% +cheaply um up on the very top where it +says + + align:start position:0% +says + + + align:start position:0% +says +amama uh do you know what that is you've + + align:start position:0% +amama uh do you know what that is you've + + + align:start position:0% +amama uh do you know what that is you've +seen a zillion of them so you should + + align:start position:0% +seen a zillion of them so you should + + + align:start position:0% +seen a zillion of them so you should +they should should look familiar it's an + + align:start position:0% +they should should look familiar it's an + + + align:start position:0% +they should should look familiar it's an +ad on you don't necessarily know but + + align:start position:0% +ad on you don't necessarily know but + + + align:start position:0% +ad on you don't necessarily know but +Google yeah turns out it's an ad on + + align:start position:0% +Google yeah turns out it's an ad on + + + align:start position:0% +Google yeah turns out it's an ad on +Google so one thing which you may or may + + align:start position:0% +Google so one thing which you may or may + + + align:start position:0% +Google so one thing which you may or may +not know is every time you type in a + + align:start position:0% +not know is every time you type in a + + + align:start position:0% +not know is every time you type in a +search term on Google an auction is run + + align:start position:0% +search term on Google an auction is run + + + align:start position:0% +search term on Google an auction is run +every time anyone anywhere in the world + + align:start position:0% +every time anyone anywhere in the world + + + align:start position:0% +every time anyone anywhere in the world +types in a search term on Google an + + align:start position:0% +types in a search term on Google an + + + align:start position:0% +types in a search term on Google an +auction is run R and that auction + + align:start position:0% +auction is run R and that auction + + + align:start position:0% +auction is run R and that auction +determines which ads you are served so I + + align:start position:0% +determines which ads you are served so I + + + align:start position:0% +determines which ads you are served so I +went on Google and I typed auto + + align:start position:0% +went on Google and I typed auto + + + align:start position:0% +went on Google and I typed auto +insurance and that was one of the ads I + + align:start position:0% +insurance and that was one of the ads I + + + align:start position:0% +insurance and that was one of the ads I +was served okay someone paid Google for + + align:start position:0% +was served okay someone paid Google for + + + align:start position:0% +was served okay someone paid Google for +the um for the you know ability to serve + + align:start position:0% +the um for the you know ability to serve + + + align:start position:0% +the um for the you know ability to serve +me an ad when I typed in auto + + align:start position:0% +me an ad when I typed in auto + + + align:start position:0% +me an ad when I typed in auto +insurance okay does anyone know what + + align:start position:0% +insurance okay does anyone know what + + + align:start position:0% +insurance okay does anyone know what +this is in the upper right + + align:start position:0% +this is in the upper right + + + align:start position:0% +this is in the upper right +corner tulip bolts right + + align:start position:0% +corner tulip bolts right + + + align:start position:0% +corner tulip bolts right +so + + align:start position:0% + + + + align:start position:0% + +um so I I'll I'll talk I have one slide + + align:start position:0% +um so I I'll I'll talk I have one slide + + + align:start position:0% +um so I I'll I'll talk I have one slide +just for fun on uh the tulip bulbs in + + align:start position:0% +just for fun on uh the tulip bulbs in + + + align:start position:0% +just for fun on uh the tulip bulbs in +just a second so we'll get to those but + + align:start position:0% +just a second so we'll get to those but + + + align:start position:0% +just a second so we'll get to those but +basically in um well tulip bulbs uh not + + align:start position:0% +basically in um well tulip bulbs uh not + + + align:start position:0% +basically in um well tulip bulbs uh not +only were auctioned off in the 1600s in + + align:start position:0% +only were auctioned off in the 1600s in + + + align:start position:0% +only were auctioned off in the 1600s in +Amsterdam but uh you know sort of a new + + align:start position:0% +Amsterdam but uh you know sort of a new + + + align:start position:0% +Amsterdam but uh you know sort of a new +auction mechanism was devised to handle + + align:start position:0% +auction mechanism was devised to handle + + + align:start position:0% +auction mechanism was devised to handle +um you know sort of the the auctioning + + align:start position:0% +um you know sort of the the auctioning + + + align:start position:0% +um you know sort of the the auctioning +off of of tulip bulbs and I I'll mention + + align:start position:0% +off of of tulip bulbs and I I'll mention + + + align:start position:0% +off of of tulip bulbs and I I'll mention +more about this in a second uh does + + align:start position:0% +more about this in a second uh does + + + align:start position:0% +more about this in a second uh does +anyone know what this + + align:start position:0% + + + + align:start position:0% + +is old map but actually it's it's it's + + align:start position:0% +is old map but actually it's it's it's + + + align:start position:0% +is old map but actually it's it's it's +what's on the map I'm trying to + + align:start position:0% +what's on the map I'm trying to + + + align:start position:0% +what's on the map I'm trying to +represent not the map + + align:start position:0% +represent not the map + + + align:start position:0% +represent not the map +itself Roman Empire the Roman Empire + + align:start position:0% +itself Roman Empire the Roman Empire + + + align:start position:0% +itself Roman Empire the Roman Empire +exactly so the Roman Empire was actually + + align:start position:0% +exactly so the Roman Empire was actually + + + align:start position:0% +exactly so the Roman Empire was actually +auctioned off believe it or not okay so + + align:start position:0% +auctioned off believe it or not okay so + + + align:start position:0% +auctioned off believe it or not okay so +let me go to the next slide and I'll + + align:start position:0% +let me go to the next slide and I'll + + + align:start position:0% +let me go to the next slide and I'll +give you a couple details so this is + + align:start position:0% +give you a couple details so this is + + + align:start position:0% +give you a couple details so this is +again these next two slides are just for + + align:start position:0% +again these next two slides are just for + + + align:start position:0% +again these next two slides are just for +fun but so the petorian guard which was + + align:start position:0% +fun but so the petorian guard which was + + + align:start position:0% +fun but so the petorian guard which was +sort of the the elite uh Military + + align:start position:0% +sort of the the elite uh Military + + + align:start position:0% +sort of the the elite uh Military +Officers the in the um Roman Empire um + + align:start position:0% +Officers the in the um Roman Empire um + + + align:start position:0% +Officers the in the um Roman Empire um +found themselves without an emperor and + + align:start position:0% +found themselves without an emperor and + + + align:start position:0% +found themselves without an emperor and +they decided to auction off the Roman + + align:start position:0% +they decided to auction off the Roman + + + align:start position:0% +they decided to auction off the Roman +Empire to the highest bidder this is in + + align:start position:0% +Empire to the highest bidder this is in + + + align:start position:0% +Empire to the highest bidder this is in +193 CE okay so Marcus didus seus + + align:start position:0% +193 CE okay so Marcus didus seus + + + align:start position:0% +193 CE okay so Marcus didus seus +julianus uh was the highest bidder and + + align:start position:0% +julianus uh was the highest bidder and + + + align:start position:0% +julianus uh was the highest bidder and +he ended up paying 25,000 cies per + + align:start position:0% +he ended up paying 25,000 cies per + + + align:start position:0% +he ended up paying 25,000 cies per +Soldier uh for the Roman + + align:start position:0% +Soldier uh for the Roman + + + align:start position:0% +Soldier uh for the Roman +Empire so he served as Empire for + + align:start position:0% +Empire so he served as Empire for + + + align:start position:0% +Empire so he served as Empire for +Emperor for 66 days before being + + align:start position:0% +Emperor for 66 days before being + + + align:start position:0% +Emperor for 66 days before being +executed um I don't know precisely what + + align:start position:0% +executed um I don't know precisely what + + + align:start position:0% +executed um I don't know precisely what +happened whether there was a followon + + align:start position:0% +happened whether there was a followon + + + align:start position:0% +happened whether there was a followon +auction after he was executed if there + + align:start position:0% +auction after he was executed if there + + + align:start position:0% +auction after he was executed if there +was I can bet that the bids were lower + + align:start position:0% +was I can bet that the bids were lower + + + align:start position:0% +was I can bet that the bids were lower +that's my guess but did they like not + + align:start position:0% +that's my guess but did they like not + + + align:start position:0% +that's my guess but did they like not +have democracy + + align:start position:0% +have democracy + + + align:start position:0% +have democracy +yet vote for well I don't know I'm sort + + align:start position:0% +yet vote for well I don't know I'm sort + + + align:start position:0% +yet vote for well I don't know I'm sort +of not an expert on um on this on this + + align:start position:0% +of not an expert on um on this on this + + + align:start position:0% +of not an expert on um on this on this +uh time in in history in the Roman + + align:start position:0% +uh time in in history in the Roman + + + align:start position:0% +uh time in in history in the Roman +Empire um I just that was a time when + + align:start position:0% +Empire um I just that was a time when + + + align:start position:0% +Empire um I just that was a time when +the petorian guard had a lot of power so + + align:start position:0% +the petorian guard had a lot of power so + + + align:start position:0% +the petorian guard had a lot of power so +they just decided to exploit that power + + align:start position:0% +they just decided to exploit that power + + + align:start position:0% +they just decided to exploit that power +and auction off the end so + + align:start position:0% +and auction off the end so + + + align:start position:0% +and auction off the end so +yes they already had democracy and then + + align:start position:0% +yes they already had democracy and then + + + align:start position:0% +yes they already had democracy and then +they got overthrown by some by Cesar + + align:start position:0% +they got overthrown by some by Cesar + + + align:start position:0% +they got overthrown by some by Cesar +with the Army but apparently this + + align:start position:0% +with the Army but apparently this + + + align:start position:0% +with the Army but apparently this +sparked the Civil War oh this the the + + align:start position:0% +sparked the Civil War oh this the the + + + align:start position:0% +sparked the Civil War oh this the the +the execution sparked a civil war okay + + align:start position:0% +the execution sparked a civil war okay + + + align:start position:0% +the execution sparked a civil war okay +oh interesting okay + + align:start position:0% +oh interesting okay + + + align:start position:0% +oh interesting okay +good so um so the word auction actually + + align:start position:0% +good so um so the word auction actually + + + align:start position:0% +good so um so the word auction actually +comes from the Latin ooco meaning + + align:start position:0% +comes from the Latin ooco meaning + + + align:start position:0% +comes from the Latin ooco meaning +increase and that is a description or a + + align:start position:0% +increase and that is a description or a + + + align:start position:0% +increase and that is a description or a +partial description of one of the very + + align:start position:0% +partial description of one of the very + + + align:start position:0% +partial description of one of the very +common auction mechanisms where the + + align:start position:0% +common auction mechanisms where the + + + align:start position:0% +common auction mechanisms where the +price increases until all but one bidder + + align:start position:0% +price increases until all but one bidder + + + align:start position:0% +price increases until all but one bidder +um drops + + align:start position:0% +um drops + + + align:start position:0% +um drops +out and uh the highest bidder um is uh + + align:start position:0% +out and uh the highest bidder um is uh + + + align:start position:0% +out and uh the highest bidder um is uh +in in an auction in ancient Rome was + + align:start position:0% +in in an auction in ancient Rome was + + + align:start position:0% +in in an auction in ancient Rome was +called the empor that's the the Latin + + align:start position:0% +called the empor that's the the Latin + + + align:start position:0% +called the empor that's the the Latin +term for it okay and obviously we we + + align:start position:0% +term for it okay and obviously we we + + + align:start position:0% +term for it okay and obviously we we +sort of use you know we are familiar + + align:start position:0% +sort of use you know we are familiar + + + align:start position:0% +sort of use you know we are familiar +with that term from um you know the the + + align:start position:0% +with that term from um you know the the + + + align:start position:0% +with that term from um you know the the +uh uh phrase buyer beware a caveat empor + + align:start position:0% +uh uh phrase buyer beware a caveat empor + + + align:start position:0% +uh uh phrase buyer beware a caveat empor +okay um auctions were used very + + align:start position:0% +okay um auctions were used very + + + align:start position:0% +okay um auctions were used very +extensively in ancient Rome they were + + align:start position:0% +extensively in ancient Rome they were + + + align:start position:0% +extensively in ancient Rome they were +used to sell plunder household effects + + align:start position:0% +used to sell plunder household effects + + + align:start position:0% +used to sell plunder household effects +slaves wives Commodities + + align:start position:0% +slaves wives Commodities + + + align:start position:0% +slaves wives Commodities +Etc + + align:start position:0% +Etc + + + align:start position:0% +Etc +okay um okay and now uh the to the tulip + + align:start position:0% +okay um okay and now uh the to the tulip + + + align:start position:0% +okay um okay and now uh the to the tulip +bulbs so as I said in 1600s Traders from + + align:start position:0% +bulbs so as I said in 1600s Traders from + + + align:start position:0% +bulbs so as I said in 1600s Traders from +the Ottoman Empire U brought tulip bulbs + + align:start position:0% +the Ottoman Empire U brought tulip bulbs + + + align:start position:0% +the Ottoman Empire U brought tulip bulbs +back to Holland they were unknown in + + align:start position:0% +back to Holland they were unknown in + + + align:start position:0% +back to Holland they were unknown in +Holland so um so no one knew exactly + + align:start position:0% +Holland so um so no one knew exactly + + + align:start position:0% +Holland so um so no one knew exactly +what the demand was going to be and + + align:start position:0% +what the demand was going to be and + + + align:start position:0% +what the demand was going to be and +furthermore Supply was fixed in the + + align:start position:0% +furthermore Supply was fixed in the + + + align:start position:0% +furthermore Supply was fixed in the +short run there was no way that they + + align:start position:0% +short run there was no way that they + + + align:start position:0% +short run there was no way that they +could sort of generate more tulip bulbs + + align:start position:0% +could sort of generate more tulip bulbs + + + align:start position:0% +could sort of generate more tulip bulbs +in the short run because it takes 7 to + + align:start position:0% +in the short run because it takes 7 to + + + align:start position:0% +in the short run because it takes 7 to +12 years to go from a tulip seed I you + + align:start position:0% +12 years to go from a tulip seed I you + + + align:start position:0% +12 years to go from a tulip seed I you +know what existed anyhow a tulip SE to a + + align:start position:0% +know what existed anyhow a tulip SE to a + + + align:start position:0% +know what existed anyhow a tulip SE to a +tradable bulb so the the whatever the + + align:start position:0% +tradable bulb so the the whatever the + + + align:start position:0% +tradable bulb so the the whatever the +the Traders brought back from the + + align:start position:0% +the Traders brought back from the + + + align:start position:0% +the Traders brought back from the +Ottoman Empire that was sort of what + + align:start position:0% +Ottoman Empire that was sort of what + + + align:start position:0% +Ottoman Empire that was sort of what +they had so it turns out demand was + + align:start position:0% +they had so it turns out demand was + + + align:start position:0% +they had so it turns out demand was +really high and what the Traders did is + + align:start position:0% +really high and what the Traders did is + + + align:start position:0% +really high and what the Traders did is +they invented uh basically an auction + + align:start position:0% +they invented uh basically an auction + + + align:start position:0% +they invented uh basically an auction +mechanism called The Dutch auction uh + + align:start position:0% +mechanism called The Dutch auction uh + + + align:start position:0% +mechanism called The Dutch auction uh +where you start at a high price and you + + align:start position:0% +where you start at a high price and you + + + align:start position:0% +where you start at a high price and you +decrease the price until someone uh buys + + align:start position:0% +decrease the price until someone uh buys + + + align:start position:0% +decrease the price until someone uh buys +the tulip bulb and I don't remember off + + align:start position:0% +the tulip bulb and I don't remember off + + + align:start position:0% +the tulip bulb and I don't remember off +the top of my head what tulip bulbs + + align:start position:0% +the top of my head what tulip bulbs + + + align:start position:0% +the top of my head what tulip bulbs +ended up selling for but it was you know + + align:start position:0% +ended up selling for but it was you know + + + align:start position:0% +ended up selling for but it was you know +sort of thousands of dollars in you know + + align:start position:0% +sort of thousands of dollars in you know + + + align:start position:0% +sort of thousands of dollars in you know +sort of uh current dollars or something + + align:start position:0% +sort of uh current dollars or something + + + align:start position:0% +sort of uh current dollars or something +I mean huge amounts of money you have a + + align:start position:0% +I mean huge amounts of money you have a + + + align:start position:0% +I mean huge amounts of money you have a +question um so what if multiple people + + align:start position:0% +question um so what if multiple people + + + align:start position:0% +question um so what if multiple people +pick a bit do they start going up + + align:start position:0% +pick a bit do they start going up + + + align:start position:0% +pick a bit do they start going up +again oh so how you're asking how are + + align:start position:0% +again oh so how you're asking how are + + + align:start position:0% +again oh so how you're asking how are +ties resolved I don't know maybe they + + align:start position:0% +ties resolved I don't know maybe they + + + align:start position:0% +ties resolved I don't know maybe they +have some you know maybe if two people + + align:start position:0% +have some you know maybe if two people + + + align:start position:0% +have some you know maybe if two people +put up their hand at exactly the same + + align:start position:0% +put up their hand at exactly the same + + + align:start position:0% +put up their hand at exactly the same +time then the auctioneer picks one of + + align:start position:0% +time then the auctioneer picks one of + + + align:start position:0% +time then the auctioneer picks one of +them at random but yeah so there's this + + align:start position:0% +them at random but yeah so there's this + + + align:start position:0% +them at random but yeah so there's this +I actually have a board game called + + align:start position:0% +I actually have a board game called + + + align:start position:0% +I actually have a board game called +merchants of amster Dam has anyone ever + + align:start position:0% +merchants of amster Dam has anyone ever + + + align:start position:0% +merchants of amster Dam has anyone ever +played this no okay so it has this + + align:start position:0% +played this no okay so it has this + + + align:start position:0% +played this no okay so it has this +little thing where you you like you um a + + align:start position:0% +little thing where you you like you um a + + + align:start position:0% +little thing where you you like you um a +timer kind of thing it's like a it's a + + align:start position:0% +timer kind of thing it's like a it's a + + + align:start position:0% +timer kind of thing it's like a it's a +it's it's to to uh do this the Dutch + + align:start position:0% +it's it's to to uh do this the Dutch + + + align:start position:0% +it's it's to to uh do this the Dutch +mechanism or Dutch auction mechanism so + + align:start position:0% +mechanism or Dutch auction mechanism so + + + align:start position:0% +mechanism or Dutch auction mechanism so +you turn the timer and then basically + + align:start position:0% +you turn the timer and then basically + + + align:start position:0% +you turn the timer and then basically +everyone's watching the price of the + + align:start position:0% +everyone's watching the price of the + + + align:start position:0% +everyone's watching the price of the +commodity tick down and then you you're + + align:start position:0% +commodity tick down and then you you're + + + align:start position:0% +commodity tick down and then you you're +all sort of like sitting around the + + align:start position:0% +all sort of like sitting around the + + + align:start position:0% +all sort of like sitting around the +timer and whoever presses the timer + + align:start position:0% +timer and whoever presses the timer + + + align:start position:0% +timer and whoever presses the timer +first wins the auction and so you know + + align:start position:0% +first wins the auction and so you know + + + align:start position:0% +first wins the auction and so you know +that's I mean at least in that case + + align:start position:0% +that's I mean at least in that case + + + align:start position:0% +that's I mean at least in that case +someone is actually pressing it and + + align:start position:0% +someone is actually pressing it and + + + align:start position:0% +someone is actually pressing it and +that's how the ties get resolved but + + align:start position:0% +that's how the ties get resolved but + + + align:start position:0% +that's how the ties get resolved but +okay and for people who are interested + + align:start position:0% +okay and for people who are interested + + + align:start position:0% +okay and for people who are interested +in uh Financial Innovation the Tulip + + align:start position:0% +in uh Financial Innovation the Tulip + + + align:start position:0% +in uh Financial Innovation the Tulip +Panic the Dutch tulip Panic so I should + + align:start position:0% +Panic the Dutch tulip Panic so I should + + + align:start position:0% +Panic the Dutch tulip Panic so I should +say prices went went up very high but + + align:start position:0% +say prices went went up very high but + + + align:start position:0% +say prices went went up very high but +then they also there were ALS there was + + align:start position:0% +then they also there were ALS there was + + + align:start position:0% +then they also there were ALS there was +also sort of a spectacular crash um and + + align:start position:0% +also sort of a spectacular crash um and + + + align:start position:0% +also sort of a spectacular crash um and +that was why it was called the Tulip + + align:start position:0% +that was why it was called the Tulip + + + align:start position:0% +that was why it was called the Tulip +Panic um and but for people interested + + align:start position:0% +Panic um and but for people interested + + + align:start position:0% +Panic um and but for people interested +in financial aid + + align:start position:0% +in financial aid + + + align:start position:0% +in financial aid +options and future contracts were also + + align:start position:0% +options and future contracts were also + + + align:start position:0% +options and future contracts were also +pioneered during this period uh to sort + + align:start position:0% +pioneered during this period uh to sort + + + align:start position:0% +pioneered during this period uh to sort +of help deal with the sort of uh + + align:start position:0% +of help deal with the sort of uh + + + align:start position:0% +of help deal with the sort of uh +interesting uh Financial setting uh that + + align:start position:0% +interesting uh Financial setting uh that + + + align:start position:0% +interesting uh Financial setting uh that +was caused by these uh tulip bulbs okay + + align:start position:0% +was caused by these uh tulip bulbs okay + + + align:start position:0% +was caused by these uh tulip bulbs okay +yes that I don't know does anyone know + + align:start position:0% +yes that I don't know does anyone know + + + align:start position:0% +yes that I don't know does anyone know +how long did the Dutch tulip bulb bubble + + align:start position:0% +how long did the Dutch tulip bulb bubble + + + align:start position:0% +how long did the Dutch tulip bulb bubble +last it last like a year year and two + + align:start position:0% +last it last like a year year and two + + + align:start position:0% +last it last like a year year and two +year and a half year and a half okay + + align:start position:0% +year and a half year and a half okay + + + align:start position:0% +year and a half year and a half okay +cool okay so those those uh those couple + + align:start position:0% +cool okay so those those uh those couple + + + align:start position:0% +cool okay so those those uh those couple +slides were mostly for fun but um let's + + align:start position:0% +slides were mostly for fun but um let's + + + align:start position:0% +slides were mostly for fun but um let's +go back to the question of uh you know + + align:start position:0% +go back to the question of uh you know + + + align:start position:0% +go back to the question of uh you know +sort of selling a product at posted + + align:start position:0% +sort of selling a product at posted + + + align:start position:0% +sort of selling a product at posted +price uh versus auctioning okay so here + + align:start position:0% +price uh versus auctioning okay so here + + + align:start position:0% +price uh versus auctioning okay so here +now is a slide of things that are sold + + align:start position:0% +now is a slide of things that are sold + + + align:start position:0% +now is a slide of things that are sold +at Post-it price you buy fruit at posted + + align:start position:0% +at Post-it price you buy fruit at posted + + + align:start position:0% +at Post-it price you buy fruit at posted +prices you would never go into the Stop + + align:start position:0% +prices you would never go into the Stop + + + align:start position:0% +prices you would never go into the Stop +and Shop and you know sort of like + + align:start position:0% +and Shop and you know sort of like + + + align:start position:0% +and Shop and you know sort of like +engage in some kind of an auction in the + + align:start position:0% +engage in some kind of an auction in the + + + align:start position:0% +engage in some kind of an auction in the +produce aisle or something like that you + + align:start position:0% +produce aisle or something like that you + + + align:start position:0% +produce aisle or something like that you +just pay whatever price is posted um + + align:start position:0% +just pay whatever price is posted um + + + align:start position:0% +just pay whatever price is posted um +when I bought my iPhone I just bought it + + align:start position:0% +when I bought my iPhone I just bought it + + + align:start position:0% +when I bought my iPhone I just bought it +at a posted price uh when I buy IC tea + + align:start position:0% +at a posted price uh when I buy IC tea + + + align:start position:0% +at a posted price uh when I buy IC tea +every day um I just go in you know I buy + + align:start position:0% +every day um I just go in you know I buy + + + align:start position:0% +every day um I just go in you know I buy +whatever the price is posted clothing is + + align:start position:0% +whatever the price is posted clothing is + + + align:start position:0% +whatever the price is posted clothing is +the same uh the new mammore and Ryan + + align:start position:0% +the same uh the new mammore and Ryan + + + align:start position:0% +the same uh the new mammore and Ryan +Lewis uh CD uh you will just if you buy + + align:start position:0% +Lewis uh CD uh you will just if you buy + + + align:start position:0% +Lewis uh CD uh you will just if you buy +that you will just buy it at a posted + + align:start position:0% +that you will just buy it at a posted + + + align:start position:0% +that you will just buy it at a posted +price I heard it wasn't very good that's + + align:start position:0% +price I heard it wasn't very good that's + + + align:start position:0% +price I heard it wasn't very good that's +what the reviews say but I I I'm not an + + align:start position:0% +what the reviews say but I I I'm not an + + + align:start position:0% +what the reviews say but I I I'm not an +expert yeah but this is in the US right + + align:start position:0% +expert yeah but this is in the US right + + + align:start position:0% +expert yeah but this is in the US right +in the in other culture so so that's + + align:start position:0% +in the in other culture so so that's + + + align:start position:0% +in the in other culture so so that's +right there are cultural differences + + align:start position:0% +right there are cultural differences + + + align:start position:0% +right there are cultural differences +between what is what is sold at posted + + align:start position:0% +between what is what is sold at posted + + + align:start position:0% +between what is what is sold at posted +prices and what is auctioned that's + + align:start position:0% +prices and what is auctioned that's + + + align:start position:0% +prices and what is auctioned that's +absolutely right yeah post price not + + align:start position:0% +absolutely right yeah post price not + + + align:start position:0% +absolutely right yeah post price not +sometimes really and sometimes you can + + align:start position:0% +sometimes really and sometimes you can + + + align:start position:0% +sometimes really and sometimes you can +negotiate a poster price which is a + + align:start position:0% +negotiate a poster price which is a + + + align:start position:0% +negotiate a poster price which is a +negotiation is a little bit different + + align:start position:0% +negotiation is a little bit different + + + align:start position:0% +negotiation is a little bit different +than than you know selling something at + + align:start position:0% +than than you know selling something at + + + align:start position:0% +than than you know selling something at +auction but uh but it has some of the + + align:start position:0% +auction but uh but it has some of the + + + align:start position:0% +auction but uh but it has some of the +elements of of an auction for + + align:start position:0% +elements of of an auction for + + + align:start position:0% +elements of of an auction for +sure I it was + + align:start position:0% +sure I it was + + + align:start position:0% +sure I it was +inter buying vegetables from vegetable + + align:start position:0% +inter buying vegetables from vegetable + + + align:start position:0% +inter buying vegetables from vegetable +seller in India is a reverse auction you + + align:start position:0% +seller in India is a reverse auction you + + + align:start position:0% +seller in India is a reverse auction you +keep reducing the price until he refuses + + align:start position:0% +keep reducing the price until he refuses + + + align:start position:0% +keep reducing the price until he refuses +to sell at a lower price and then you + + align:start position:0% +to sell at a lower price and then you + + + align:start position:0% +to sell at a lower price and then you +bu so so he has a posted + + align:start position:0% +bu so so he has a posted + + + align:start position:0% +bu so so he has a posted +price right is that what you're saying + + align:start position:0% +price right is that what you're saying + + + align:start position:0% +price right is that what you're saying +and then you say no I'll give you a half + + align:start position:0% +and then you say no I'll give you a half + + + align:start position:0% +and then you say no I'll give you a half +of that yeah and and then he says okay + + align:start position:0% +of that yeah and and then he says okay + + + align:start position:0% +of that yeah and and then he says okay +and then you say no I'll give you a + + align:start position:0% +and then you say no I'll give you a + + + align:start position:0% +and then you say no I'll give you a +quarter of that well no well you start + + align:start position:0% +quarter of that well no well you start + + + align:start position:0% +quarter of that well no well you start +with the lowest oh okay fine yeah yeah + + align:start position:0% +with the lowest oh okay fine yeah yeah + + + align:start position:0% +with the lowest oh okay fine yeah yeah +yeah so it's a standard bargaining yeah + + align:start position:0% +yeah so it's a standard bargaining yeah + + + align:start position:0% +yeah so it's a standard bargaining yeah +exactly yeah yeah that's right so so so + + align:start position:0% +exactly yeah yeah that's right so so so + + + align:start position:0% +exactly yeah yeah that's right so so so +definitely so that's that's a a very + + align:start position:0% +definitely so that's that's a a very + + + align:start position:0% +definitely so that's that's a a very +important point that there are cultural + + align:start position:0% +important point that there are cultural + + + align:start position:0% +important point that there are cultural +differences we'll get to that in a + + align:start position:0% +differences we'll get to that in a + + + align:start position:0% +differences we'll get to that in a +second uh you know sort of across across + + align:start position:0% +second uh you know sort of across across + + + align:start position:0% +second uh you know sort of across across +cultures about what's uh auctioned Andor + + align:start position:0% +cultures about what's uh auctioned Andor + + + align:start position:0% +cultures about what's uh auctioned Andor +you know sort of haggled over and what's + + align:start position:0% +you know sort of haggled over and what's + + + align:start position:0% +you know sort of haggled over and what's +sold at a posted price um and then yeah + + align:start position:0% +sold at a posted price um and then yeah + + + align:start position:0% +sold at a posted price um and then yeah +the the I guess the other point is that + + align:start position:0% +the the I guess the other point is that + + + align:start position:0% +the the I guess the other point is that +uh haggling isn't quite the same as an + + align:start position:0% +uh haggling isn't quite the same as an + + + align:start position:0% +uh haggling isn't quite the same as an +auction but it has has some many of the + + align:start position:0% +auction but it has has some many of the + + + align:start position:0% +auction but it has has some many of the +same characteristics um so in the US uh + + align:start position:0% +same characteristics um so in the US uh + + + align:start position:0% +same characteristics um so in the US uh +houses are also sold at posted prices + + align:start position:0% +houses are also sold at posted prices + + + align:start position:0% +houses are also sold at posted prices +which has always been a little puzzling + + align:start position:0% +which has always been a little puzzling + + + align:start position:0% +which has always been a little puzzling +uh for me and it doesn't a house doesn't + + align:start position:0% +uh for me and it doesn't a house doesn't + + + align:start position:0% +uh for me and it doesn't a house doesn't +quite fit in to the you know in terms of + + align:start position:0% +quite fit in to the you know in terms of + + + align:start position:0% +quite fit in to the you know in terms of +the its characteristics it doesn't quite + + align:start position:0% +the its characteristics it doesn't quite + + + align:start position:0% +the its characteristics it doesn't quite +fit into to what uh other things are + + align:start position:0% +fit into to what uh other things are + + + align:start position:0% +fit into to what uh other things are +sold at posted prices in the US now of + + align:start position:0% +sold at posted prices in the US now of + + + align:start position:0% +sold at posted prices in the US now of +course there often is is a a bargaining + + align:start position:0% +course there often is is a a bargaining + + + align:start position:0% +course there often is is a a bargaining +that goes on after U you know sort of in + + align:start position:0% +that goes on after U you know sort of in + + + align:start position:0% +that goes on after U you know sort of in +in the process of buying a house heavy B + + align:start position:0% +in the process of buying a house heavy B + + + align:start position:0% +in the process of buying a house heavy B +Wars as well if you have a + + align:start position:0% +Wars as well if you have a + + + align:start position:0% +Wars as well if you have a +certain that's right that's right I + + align:start position:0% +certain that's right that's right I + + + align:start position:0% +certain that's right that's right I +tried to talk my parents into auctioning + + align:start position:0% +tried to talk my parents into auctioning + + + align:start position:0% +tried to talk my parents into auctioning +their house off and it didn't they they + + align:start position:0% +their house off and it didn't they they + + + align:start position:0% +their house off and it didn't they they +they said you know you and all your + + align:start position:0% +they said you know you and all your + + + align:start position:0% +they said you know you and all your +crazy economics ideas no way um yeah + + align:start position:0% +crazy economics ideas no way um yeah + + + align:start position:0% +crazy economics ideas no way um yeah +okay and and actually um I don't know if + + align:start position:0% +okay and and actually um I don't know if + + + align:start position:0% +okay and and actually um I don't know if +you guys have been on eBay uh recently + + align:start position:0% +you guys have been on eBay uh recently + + + align:start position:0% +you guys have been on eBay uh recently +if you buy things on eBay uh it's it's + + align:start position:0% +if you buy things on eBay uh it's it's + + + align:start position:0% +if you buy things on eBay uh it's it's +true that most things on eBay today are + + align:start position:0% +true that most things on eBay today are + + + align:start position:0% +true that most things on eBay today are +sold at posted prices not uh through an + + align:start position:0% +sold at posted prices not uh through an + + + align:start position:0% +sold at posted prices not uh through an +auction mechanism okay and that's a big + + align:start position:0% +auction mechanism okay and that's a big + + + align:start position:0% +auction mechanism okay and that's a big +change we'll we'll talk about that as + + align:start position:0% +change we'll we'll talk about that as + + + align:start position:0% +change we'll we'll talk about that as +well okay so what determines whether a + + align:start position:0% +well okay so what determines whether a + + + align:start position:0% +well okay so what determines whether a +seller will decide to sell an item at a + + align:start position:0% +seller will decide to sell an item at a + + + align:start position:0% +seller will decide to sell an item at a +posted price or auction it off so based + + align:start position:0% +posted price or auction it off so based + + + align:start position:0% +posted price or auction it off so based +on your own experience based on the + + align:start position:0% +on your own experience based on the + + + align:start position:0% +on your own experience based on the +products that we saw here what would you + + align:start position:0% +products that we saw here what would you + + + align:start position:0% +products that we saw here what would you +say are some of the factors that a + + align:start position:0% +say are some of the factors that a + + + align:start position:0% +say are some of the factors that a +seller might consider yes Supply pardon + + align:start position:0% +seller might consider yes Supply pardon + + + align:start position:0% +seller might consider yes Supply pardon +me Supply Supply meaning can you + + align:start position:0% +me Supply Supply meaning can you + + + align:start position:0% +me Supply Supply meaning can you +elaborate a little bit like if the thing + + align:start position:0% +elaborate a little bit like if the thing + + + align:start position:0% +elaborate a little bit like if the thing +is common then it doesn't make sense to + + align:start position:0% +is common then it doesn't make sense to + + + align:start position:0% +is common then it doesn't make sense to +auction it because right like you can + + align:start position:0% +auction it because right like you can + + + align:start position:0% +auction it because right like you can +spite anywhere but if the thing is + + align:start position:0% +spite anywhere but if the thing is + + + align:start position:0% +spite anywhere but if the thing is +really unique and you want to auction it + + align:start position:0% +really unique and you want to auction it + + + align:start position:0% +really unique and you want to auction it +because you and if it's hard to + + align:start position:0% +because you and if it's hard to + + + align:start position:0% +because you and if it's hard to +determine the value of your good then + + align:start position:0% +determine the value of your good then + + + align:start position:0% +determine the value of your good then +you use the option yeah absolutely right + + align:start position:0% +you use the option yeah absolutely right + + + align:start position:0% +you use the option yeah absolutely right +so if you have a product that's unique + + align:start position:0% +so if you have a product that's unique + + + align:start position:0% +so if you have a product that's unique +and or hard to determine its value then + + align:start position:0% +and or hard to determine its value then + + + align:start position:0% +and or hard to determine its value then +you're more likely to auction it off + + align:start position:0% +you're more likely to auction it off + + + align:start position:0% +you're more likely to auction it off +than sell it at a posted price okay um + + align:start position:0% +than sell it at a posted price okay um + + + align:start position:0% +than sell it at a posted price okay um +and I guess you know maybe this is sort + + align:start position:0% +and I guess you know maybe this is sort + + + align:start position:0% +and I guess you know maybe this is sort +of an obvious point but the the reason + + align:start position:0% +of an obvious point but the the reason + + + align:start position:0% +of an obvious point but the the reason +that that's the case is because the when + + align:start position:0% +that that's the case is because the when + + + align:start position:0% +that that's the case is because the when +you auction off a product then you're + + align:start position:0% +you auction off a product then you're + + + align:start position:0% +you auction off a product then you're +getting a lot of price information um + + align:start position:0% +getting a lot of price information um + + + align:start position:0% +getting a lot of price information um +for free or a lot sorry a lot of value a + + align:start position:0% +for free or a lot sorry a lot of value a + + + align:start position:0% +for free or a lot sorry a lot of value a +lot of information the valuation of that + + align:start position:0% +lot of information the valuation of that + + + align:start position:0% +lot of information the valuation of that +product for free okay so um you know you + + align:start position:0% +product for free okay so um you know you + + + align:start position:0% +product for free okay so um you know you +you're getting not only I mean depending + + align:start position:0% +you're getting not only I mean depending + + + align:start position:0% +you're getting not only I mean depending +on the mechanism you get not only the + + align:start position:0% +on the mechanism you get not only the + + + align:start position:0% +on the mechanism you get not only the +winning bid but you may get sort of lots + + align:start position:0% +winning bid but you may get sort of lots + + + align:start position:0% +winning bid but you may get sort of lots +of information on the entire + + align:start position:0% +of information on the entire + + + align:start position:0% +of information on the entire +distribution of valuations for this + + align:start position:0% +distribution of valuations for this + + + align:start position:0% +distribution of valuations for this +product okay um you also hinted at + + align:start position:0% +product okay um you also hinted at + + + align:start position:0% +product okay um you also hinted at +another thing which was that there could + + align:start position:0% +another thing which was that there could + + + align:start position:0% +another thing which was that there could +be um relatedly there could be an + + align:start position:0% +be um relatedly there could be an + + + align:start position:0% +be um relatedly there could be an +asymmetry of information between the + + align:start position:0% +asymmetry of information between the + + + align:start position:0% +asymmetry of information between the +buyer and the seller there could be situ + + align:start position:0% +buyer and the seller there could be situ + + + align:start position:0% +buyer and the seller there could be situ +situations where um there is a lot of + + align:start position:0% +situations where um there is a lot of + + + align:start position:0% +situations where um there is a lot of +information about the value of a product + + align:start position:0% +information about the value of a product + + + align:start position:0% +information about the value of a product +out there but the seller doesn't have + + align:start position:0% +out there but the seller doesn't have + + + align:start position:0% +out there but the seller doesn't have +that information so go back to the um to + + align:start position:0% +that information so go back to the um to + + + align:start position:0% +that information so go back to the um to +the case of the spectrum auction when + + align:start position:0% +the case of the spectrum auction when + + + align:start position:0% +the case of the spectrum auction when +the US government is auctioning off a + + align:start position:0% +the US government is auctioning off a + + + align:start position:0% +the US government is auctioning off a +slice of the radio spectrum um they know + + align:start position:0% +slice of the radio spectrum um they know + + + align:start position:0% +slice of the radio spectrum um they know +that the people bidding on that slice of + + align:start position:0% +that the people bidding on that slice of + + + align:start position:0% +that the people bidding on that slice of +the spectrum have done huge amounts of + + align:start position:0% +the spectrum have done huge amounts of + + + align:start position:0% +the spectrum have done huge amounts of +research and they they they sell + + align:start position:0% +research and they they they sell + + + align:start position:0% +research and they they they sell +products that are going to be using the + + align:start position:0% +products that are going to be using the + + + align:start position:0% +products that are going to be using the +spectrum they have lots of Engineers and + + align:start position:0% +spectrum they have lots of Engineers and + + + align:start position:0% +spectrum they have lots of Engineers and +experts uh you know sort of predicting + + align:start position:0% +experts uh you know sort of predicting + + + align:start position:0% +experts uh you know sort of predicting +what uh they'll be able to sell their + + align:start position:0% +what uh they'll be able to sell their + + + align:start position:0% +what uh they'll be able to sell their +product for and what products they'll be + + align:start position:0% +product for and what products they'll be + + + align:start position:0% +product for and what products they'll be +able to to uh invent that take advantage + + align:start position:0% +able to to uh invent that take advantage + + + align:start position:0% +able to to uh invent that take advantage +of that spectrum and so forth and the + + align:start position:0% +of that spectrum and so forth and the + + + align:start position:0% +of that spectrum and so forth and the +the US government doesn't have isn't + + align:start position:0% +the US government doesn't have isn't + + + align:start position:0% +the US government doesn't have isn't +privy to any of that research okay so + + align:start position:0% +privy to any of that research okay so + + + align:start position:0% +privy to any of that research okay so +there's really sort of a big + + align:start position:0% +there's really sort of a big + + + align:start position:0% +there's really sort of a big +informational asymmetry there between + + align:start position:0% +informational asymmetry there between + + + align:start position:0% +informational asymmetry there between +the seller and the buyer okay um other + + align:start position:0% +the seller and the buyer okay um other + + + align:start position:0% +the seller and the buyer okay um other +let me see what I have + + align:start position:0% +let me see what I have + + + align:start position:0% +let me see what I have +here well actually that's okay so we've + + align:start position:0% +here well actually that's okay so we've + + + align:start position:0% +here well actually that's okay so we've +been talking mostly about this sort of + + align:start position:0% +been talking mostly about this sort of + + + align:start position:0% +been talking mostly about this sort of +second Point information uh the seller + + align:start position:0% +second Point information uh the seller + + + align:start position:0% +second Point information uh the seller +receives free information on the value + + align:start position:0% +receives free information on the value + + + align:start position:0% +receives free information on the value +of the good and in fact possibly + + align:start position:0% +of the good and in fact possibly + + + align:start position:0% +of the good and in fact possibly +information on the whole + + align:start position:0% +information on the whole + + + align:start position:0% +information on the whole +distribution um but how about + + align:start position:0% +distribution um but how about + + + align:start position:0% +distribution um but how about +transactions + + align:start position:0% +transactions + + + align:start position:0% +transactions +costs so it's re it's sort of a little + + align:start position:0% +costs so it's re it's sort of a little + + + align:start position:0% +costs so it's re it's sort of a little +ridiculous to think about me going into + + align:start position:0% +ridiculous to think about me going into + + + align:start position:0% +ridiculous to think about me going into +the Stop and Shop and you know + + align:start position:0% +the Stop and Shop and you know + + + align:start position:0% +the Stop and Shop and you know +bargaining over um you know sort of + + align:start position:0% +bargaining over um you know sort of + + + align:start position:0% +bargaining over um you know sort of +every single thing that I buy in the + + align:start position:0% +every single thing that I buy in the + + + align:start position:0% +every single thing that I buy in the +Stop and Shop or you know having to + + align:start position:0% +Stop and Shop or you know having to + + + align:start position:0% +Stop and Shop or you know having to +engage in some kind of an auction uh on + + align:start position:0% +engage in some kind of an auction uh on + + + align:start position:0% +engage in some kind of an auction uh on +every single thing that I'm buying in in + + align:start position:0% +every single thing that I'm buying in in + + + align:start position:0% +every single thing that I'm buying in in +my trip to the Stop and Shop right and + + align:start position:0% +my trip to the Stop and Shop right and + + + align:start position:0% +my trip to the Stop and Shop right and +again you know so there there are + + align:start position:0% +again you know so there there are + + + align:start position:0% +again you know so there there are +cultural differences there are places + + align:start position:0% +cultural differences there are places + + + align:start position:0% +cultural differences there are places +where if I go to the market I might in + + align:start position:0% +where if I go to the market I might in + + + align:start position:0% +where if I go to the market I might in +fact haggle over everything but there's + + align:start position:0% +fact haggle over everything but there's + + + align:start position:0% +fact haggle over everything but there's +big transactions costs associated with + + align:start position:0% +big transactions costs associated with + + + align:start position:0% +big transactions costs associated with +that right and so you would think that + + align:start position:0% +that right and so you would think that + + + align:start position:0% +that right and so you would think that +maybe small ticket items um the seller + + align:start position:0% +maybe small ticket items um the seller + + + align:start position:0% +maybe small ticket items um the seller +is not likely to lose that much I'm not + + align:start position:0% +is not likely to lose that much I'm not + + + align:start position:0% +is not likely to lose that much I'm not +likely to lose that much if I you know + + align:start position:0% +likely to lose that much if I you know + + + align:start position:0% +likely to lose that much if I you know +uh if I pay too you know if I pay + + align:start position:0% +uh if I pay too you know if I pay + + + align:start position:0% +uh if I pay too you know if I pay +slightly higher price it might not be + + align:start position:0% +slightly higher price it might not be + + + align:start position:0% +slightly higher price it might not be +worth it to either of us to engage in an + + align:start position:0% +worth it to either of us to engage in an + + + align:start position:0% +worth it to either of us to engage in an +auction it might just be a you know we + + align:start position:0% +auction it might just be a you know we + + + align:start position:0% +auction it might just be a you know we +might be able to minimize our + + align:start position:0% +might be able to minimize our + + + align:start position:0% +might be able to minimize our +transactions cost by just doing the + + align:start position:0% +transactions cost by just doing the + + + align:start position:0% +transactions cost by just doing the +transaction at a posted price + + align:start position:0% +transaction at a posted price + + + align:start position:0% +transaction at a posted price +okay I don't know if um this information + + align:start position:0% +okay I don't know if um this information + + + align:start position:0% +okay I don't know if um this information +is current is like available but + + align:start position:0% +is current is like available but + + + align:start position:0% +is current is like available but +historically was were posted prices like + + align:start position:0% +historically was were posted prices like + + + align:start position:0% +historically was were posted prices like +coming quite much later than say like an + + align:start position:0% +coming quite much later than say like an + + + align:start position:0% +coming quite much later than say like an +auction type + + align:start position:0% +auction type + + + align:start position:0% +auction type +mechanism the barter system I'm + + align:start position:0% +mechanism the barter system I'm + + + align:start position:0% +mechanism the barter system I'm +sure yeah so you you bring up a very + + align:start position:0% +sure yeah so you you bring up a very + + + align:start position:0% +sure yeah so you you bring up a very +interesting point so the question was in + + align:start position:0% +interesting point so the question was in + + + align:start position:0% +interesting point so the question was in +various markets do auctions kind of uh + + align:start position:0% +various markets do auctions kind of uh + + + align:start position:0% +various markets do auctions kind of uh +preedee posted prices and um I you know + + align:start position:0% +preedee posted prices and um I you know + + + align:start position:0% +preedee posted prices and um I you know +I think that's that's an interesting + + align:start position:0% +I think that's that's an interesting + + + align:start position:0% +I think that's that's an interesting +question I can't say with great + + align:start position:0% +question I can't say with great + + + align:start position:0% +question I can't say with great +certainty um that you know I'm sort of + + align:start position:0% +certainty um that you know I'm sort of + + + align:start position:0% +certainty um that you know I'm sort of +not a historian of so I can't say with + + align:start position:0% +not a historian of so I can't say with + + + align:start position:0% +not a historian of so I can't say with +great certainty if that's true but there + + align:start position:0% +great certainty if that's true but there + + + align:start position:0% +great certainty if that's true but there +are reasons to believe why it that it + + align:start position:0% +are reasons to believe why it that it + + + align:start position:0% +are reasons to believe why it that it +could and um this sort of second bullet + + align:start position:0% +could and um this sort of second bullet + + + align:start position:0% +could and um this sort of second bullet +point + + align:start position:0% +point + + + align:start position:0% +point +suggests um one reason which is that + + align:start position:0% +suggests um one reason which is that + + + align:start position:0% +suggests um one reason which is that +when a market is new um there's a lot of + + align:start position:0% +when a market is new um there's a lot of + + + align:start position:0% +when a market is new um there's a lot of +uh there there's a lot of sort of um + + align:start position:0% +uh there there's a lot of sort of um + + + align:start position:0% +uh there there's a lot of sort of um +information asymmetry and then once a + + align:start position:0% +information asymmetry and then once a + + + align:start position:0% +information asymmetry and then once a +market becomes more mature the sellers + + align:start position:0% +market becomes more mature the sellers + + + align:start position:0% +market becomes more mature the sellers +know what they're going to be able to + + align:start position:0% +know what they're going to be able to + + + align:start position:0% +know what they're going to be able to +sell this product for and um so yeah + + align:start position:0% +sell this product for and um so yeah + + + align:start position:0% +sell this product for and um so yeah +there are definitely reasons to believe + + align:start position:0% +there are definitely reasons to believe + + + align:start position:0% +there are definitely reasons to believe +that that kind of evolution can happen + + align:start position:0% +that that kind of evolution can happen + + + align:start position:0% +that that kind of evolution can happen +and actually that could be a a part of + + align:start position:0% +and actually that could be a a part of + + + align:start position:0% +and actually that could be a a part of +what's uh going on in eBay which we'll + + align:start position:0% +what's uh going on in eBay which we'll + + + align:start position:0% +what's uh going on in eBay which we'll +talk about in a few + + align:start position:0% +talk about in a few + + + align:start position:0% +talk about in a few +minutes + + align:start position:0% +minutes + + + align:start position:0% +minutes +okay so uh what did these two you know + + align:start position:0% +okay so uh what did these two you know + + + align:start position:0% +okay so uh what did these two you know +sort of keeping in mind this sort of + + align:start position:0% +sort of keeping in mind this sort of + + + align:start position:0% +sort of keeping in mind this sort of +information story and the transactions + + align:start position:0% +information story and the transactions + + + align:start position:0% +information story and the transactions +cost story what are the goods that are + + align:start position:0% +cost story what are the goods that are + + + align:start position:0% +cost story what are the goods that are +likely to be auctioned instead of sold + + align:start position:0% +likely to be auctioned instead of sold + + + align:start position:0% +likely to be auctioned instead of sold +at posted prices unique goods are likely + + align:start position:0% +at posted prices unique goods are likely + + + align:start position:0% +at posted prices unique goods are likely +to be auctioned because people don't + + align:start position:0% +to be auctioned because people don't + + + align:start position:0% +to be auctioned because people don't +know you know the sellers don't know + + align:start position:0% +know you know the sellers don't know + + + align:start position:0% +know you know the sellers don't know +what they're worth expensive Goods might + + align:start position:0% +what they're worth expensive Goods might + + + align:start position:0% +what they're worth expensive Goods might +be more likely to be sold at auction + + align:start position:0% +be more likely to be sold at auction + + + align:start position:0% +be more likely to be sold at auction +than cheaper Goods just because the + + align:start position:0% +than cheaper Goods just because the + + + align:start position:0% +than cheaper Goods just because the +transactions costs might be a fixed cost + + align:start position:0% +transactions costs might be a fixed cost + + + align:start position:0% +transactions costs might be a fixed cost +that doesn't scale with the size of the + + align:start position:0% +that doesn't scale with the size of the + + + align:start position:0% +that doesn't scale with the size of the +transaction um but any loss uh or + + align:start position:0% +transaction um but any loss uh or + + + align:start position:0% +transaction um but any loss uh or +foregone Surplus from uncertainty might + + align:start position:0% +foregone Surplus from uncertainty might + + + align:start position:0% +foregone Surplus from uncertainty might +scale with the the size of the + + align:start position:0% +scale with the the size of the + + + align:start position:0% +scale with the the size of the +transaction uh Goods where + + align:start position:0% +transaction uh Goods where + + + align:start position:0% +transaction uh Goods where +characteristics are costly to assess uh + + align:start position:0% +characteristics are costly to assess uh + + + align:start position:0% +characteristics are costly to assess uh +Goods where buyers know more than the + + align:start position:0% +Goods where buyers know more than the + + + align:start position:0% +Goods where buyers know more than the +sellers Goods with heterogene + + align:start position:0% +sellers Goods with heterogene + + + align:start position:0% +sellers Goods with heterogene +heterogeneity and buyer valuation okay + + align:start position:0% +heterogeneity and buyer valuation okay + + + align:start position:0% +heterogeneity and buyer valuation okay +so these are the kinds of things that we + + align:start position:0% +so these are the kinds of things that we + + + align:start position:0% +so these are the kinds of things that we +would expect to be auctioned instead of + + align:start position:0% +would expect to be auctioned instead of + + + align:start position:0% +would expect to be auctioned instead of +uh sold at posted + + align:start position:0% +uh sold at posted + + + align:start position:0% +uh sold at posted +prices okay so now let's consider a + + align:start position:0% +prices okay so now let's consider a + + + align:start position:0% +prices okay so now let's consider a +simple model to illustrate this point + + align:start position:0% +simple model to illustrate this point + + + align:start position:0% +simple model to illustrate this point +about information in particular okay so + + align:start position:0% +about information in particular okay so + + + align:start position:0% +about information in particular okay so +we're going to start with n potential + + align:start position:0% +we're going to start with n potential + + + align:start position:0% +we're going to start with n potential +buyers of some good and let's suppose + + align:start position:0% +buyers of some good and let's suppose + + + align:start position:0% +buyers of some good and let's suppose +that their valuations are independent so + + align:start position:0% +that their valuations are independent so + + + align:start position:0% +that their valuations are independent so +I'm I'm auctioning off some good and all + + align:start position:0% +I'm I'm auctioning off some good and all + + + align:start position:0% +I'm I'm auctioning off some good and all +all of the potential buyers have a + + align:start position:0% +all of the potential buyers have a + + + align:start position:0% +all of the potential buyers have a +valuation all the valuations are + + align:start position:0% +valuation all the valuations are + + + align:start position:0% +valuation all the valuations are +independent and they're distributed + + align:start position:0% +independent and they're distributed + + + align:start position:0% +independent and they're distributed +uniformly on the unit interval okay they + + align:start position:0% +uniformly on the unit interval okay they + + + align:start position:0% +uniformly on the unit interval okay they +have a a uniform 01 distribution of + + align:start position:0% +have a a uniform 01 distribution of + + + align:start position:0% +have a a uniform 01 distribution of +valuations now the seller has a choice + + align:start position:0% +valuations now the seller has a choice + + + align:start position:0% +valuations now the seller has a choice +seller can offer the good at no cost at + + align:start position:0% +seller can offer the good at no cost at + + + align:start position:0% +seller can offer the good at no cost at +a posted price or the seller can auction + + align:start position:0% +a posted price or the seller can auction + + + align:start position:0% +a posted price or the seller can auction +it + + align:start position:0% +it + + + align:start position:0% +it +off the seller knows the distribution of + + align:start position:0% +off the seller knows the distribution of + + + align:start position:0% +off the seller knows the distribution of +the valuations so knows this uniform 01 + + align:start position:0% +the valuations so knows this uniform 01 + + + align:start position:0% +the valuations so knows this uniform 01 +piece but doesn't know what the + + align:start position:0% +piece but doesn't know what the + + + align:start position:0% +piece but doesn't know what the +individual potential buyers what their + + align:start position:0% +individual potential buyers what their + + + align:start position:0% +individual potential buyers what their +valuations + + align:start position:0% +valuations + + + align:start position:0% +valuations +are so let's consider the posted price + + align:start position:0% +are so let's consider the posted price + + + align:start position:0% +are so let's consider the posted price +first so the seller is going to PO is + + align:start position:0% +first so the seller is going to PO is + + + align:start position:0% +first so the seller is going to PO is +going to set a price p and sell the good + + align:start position:0% +going to set a price p and sell the good + + + align:start position:0% +going to set a price p and sell the good +if there's any potential buyer who has + + align:start position:0% +if there's any potential buyer who has + + + align:start position:0% +if there's any potential buyer who has +valuation greater than or equal to P + + align:start position:0% +valuation greater than or equal to P + + + align:start position:0% +valuation greater than or equal to P +right is that agreed make sense okay so + + align:start position:0% +right is that agreed make sense okay so + + + align:start position:0% +right is that agreed make sense okay so +we can write down a a um an expression + + align:start position:0% +we can write down a a um an expression + + + align:start position:0% +we can write down a a um an expression +for the expected profit in this case and + + align:start position:0% +for the expected profit in this case and + + + align:start position:0% +for the expected profit in this case and +that's just going to be equal to the + + align:start position:0% +that's just going to be equal to the + + + align:start position:0% +that's just going to be equal to the +price times the probability that uh + + align:start position:0% +price times the probability that uh + + + align:start position:0% +price times the probability that uh +there is at least one person with a + + align:start position:0% +there is at least one person with a + + + align:start position:0% +there is at least one person with a +valuation above P okay where did I get + + align:start position:0% +valuation above P okay where did I get + + + align:start position:0% +valuation above P okay where did I get +this expected profit well let + + align:start position:0% +this expected profit well let + + + align:start position:0% +this expected profit well let +me okay so let me just first emphasize + + align:start position:0% +me okay so let me just first emphasize + + + align:start position:0% +me okay so let me just first emphasize +uh what these what the notation means + + align:start position:0% +uh what these what the notation means + + + align:start position:0% +uh what these what the notation means +here so this is what I get if I sell the + + align:start position:0% +here so this is what I get if I sell the + + + align:start position:0% +here so this is what I get if I sell the +product and this is + + align:start position:0% +product and this is + + + align:start position:0% +product and this is +one + + align:start position:0% +one + + + align:start position:0% +one +oh yes the the second term there is one + + align:start position:0% +oh yes the the second term there is one + + + align:start position:0% +oh yes the the second term there is one +minus the CDF of the nth order statistic + + align:start position:0% +minus the CDF of the nth order statistic + + + align:start position:0% +minus the CDF of the nth order statistic +from a uniform uh 01 evaluated at + + align:start position:0% + + + + align:start position:0% + +P does everyone understand where this + + align:start position:0% +P does everyone understand where this + + + align:start position:0% +P does everyone understand where this +came + + align:start position:0% +came + + + align:start position:0% +came +from nope okay so remember the + + align:start position:0% +from nope okay so remember the + + + align:start position:0% +from nope okay so remember the +definition of the anthor statistic so + + align:start position:0% +definition of the anthor statistic so + + + align:start position:0% +definition of the anthor statistic so +enor statistic from a uniform 01 + + align:start position:0% +enor statistic from a uniform 01 + + + align:start position:0% +enor statistic from a uniform 01 +distribution is just the um is just the + + align:start position:0% +distribution is just the um is just the + + + align:start position:0% +distribution is just the um is just the +highest value highest realization okay + + align:start position:0% +highest value highest realization okay + + + align:start position:0% +highest value highest realization okay +from a from a IID random sample from + + align:start position:0% +from a from a IID random sample from + + + align:start position:0% +from a from a IID random sample from +this uh uniform 01 and so basically in + + align:start position:0% +this uh uniform 01 and so basically in + + + align:start position:0% +this uh uniform 01 and so basically in +order to sell this good I need to have + + align:start position:0% +order to sell this good I need to have + + + align:start position:0% +order to sell this good I need to have +the nth order statistic there there can + + align:start position:0% +the nth order statistic there there can + + + align:start position:0% +the nth order statistic there there can +be other order statistics that are + + align:start position:0% +be other order statistics that are + + + align:start position:0% +be other order statistics that are +greater than greater than p as well but + + align:start position:0% +greater than greater than p as well but + + + align:start position:0% +greater than greater than p as well but +I need to have at least one in other + + align:start position:0% +I need to have at least one in other + + + align:start position:0% +I need to have at least one in other +words the nth order statistic greater + + align:start position:0% +words the nth order statistic greater + + + align:start position:0% +words the nth order statistic greater +than + + align:start position:0% +than + + + align:start position:0% +than +P okay and so this this is in + + align:start position:0% +P okay and so this this is in + + + align:start position:0% +P okay and so this this is in +fact this is this is uh the probability + + align:start position:0% +fact this is this is uh the probability + + + align:start position:0% +fact this is this is uh the probability +that I sell the good and this is how I + + align:start position:0% +that I sell the good and this is how I + + + align:start position:0% +that I sell the good and this is how I +how I calculate that + + align:start position:0% +how I calculate that + + + align:start position:0% +how I calculate that +probability yes this probability is + + align:start position:0% +probability yes this probability is + + + align:start position:0% +probability yes this probability is +basically just the number of people who + + align:start position:0% +basically just the number of people who + + + align:start position:0% +basically just the number of people who +are ready to purchase it for a price + + align:start position:0% +are ready to purchase it for a price + + + align:start position:0% +are ready to purchase it for a price +field the number of people who are + + align:start position:0% +field the number of people who are + + + align:start position:0% +field the number of people who are +willing to purchase it no it's just it's + + align:start position:0% +willing to purchase it no it's just it's + + + align:start position:0% +willing to purchase it no it's just it's +just the uh probability so I'm going to + + align:start position:0% +just the uh probability so I'm going to + + + align:start position:0% +just the uh probability so I'm going to +you know I can sort of uh get the + + align:start position:0% +you know I can sort of uh get the + + + align:start position:0% +you know I can sort of uh get the +distribution of the nth order statistic + + align:start position:0% +distribution of the nth order statistic + + + align:start position:0% +distribution of the nth order statistic +from this uniform 01 distribution and + + align:start position:0% +from this uniform 01 distribution and + + + align:start position:0% +from this uniform 01 distribution and +I'm just saying what's the probability + + align:start position:0% +I'm just saying what's the probability + + + align:start position:0% +I'm just saying what's the probability +that the inth order statistic is greater + + align:start position:0% +that the inth order statistic is greater + + + align:start position:0% +that the inth order statistic is greater +than or equal to some value if you think + + align:start position:0% +than or equal to some value if you think + + + align:start position:0% +than or equal to some value if you think +of it this way that uh that P number of + + align:start position:0% +of it this way that uh that P number of + + + align:start position:0% +of it this way that uh that P number of +people sorry number of people who are + + align:start position:0% +people sorry number of people who are + + + align:start position:0% +people sorry number of people who are +ready to buy it at a price of P or more + + align:start position:0% +ready to buy it at a price of P or more + + + align:start position:0% +ready to buy it at a price of P or more +the probability of that so out of us n + + align:start position:0% +the probability of that so out of us n + + + align:start position:0% +the probability of that so out of us n +people over here if suppose 10 of us are + + align:start position:0% +people over here if suppose 10 of us are + + + align:start position:0% +people over here if suppose 10 of us are +ready to purchase it at P or more so + + align:start position:0% +ready to purchase it at P or more so + + + align:start position:0% +ready to purchase it at P or more so +then that probity times the price is the + + align:start position:0% +then that probity times the price is the + + + align:start position:0% +then that probity times the price is the +expected I don't think that's quite the + + align:start position:0% +expected I don't think that's quite the + + + align:start position:0% +expected I don't think that's quite the +right intuition um so all I care about + + align:start position:0% +right intuition um so all I care about + + + align:start position:0% +right intuition um so all I care about +is the the probability that that one + + align:start position:0% +is the the probability that that one + + + align:start position:0% +is the the probability that that one +person is is going to buy it if I post + + align:start position:0% +person is is going to buy it if I post + + + align:start position:0% +person is is going to buy it if I post +the price at P that's all I care about I + + align:start position:0% +the price at P that's all I care about I + + + align:start position:0% +the price at P that's all I care about I +don't care about how many other people + + align:start position:0% +don't care about how many other people + + + align:start position:0% +don't care about how many other people +and furthermore we know how to find the + + align:start position:0% +and furthermore we know how to find the + + + align:start position:0% +and furthermore we know how to find the +distribution of that highest price + + align:start position:0% +distribution of that highest price + + + align:start position:0% +distribution of that highest price +because it's just the inth order + + align:start position:0% +because it's just the inth order + + + align:start position:0% +because it's just the inth order +statistic so I it it's I I think that + + align:start position:0% +statistic so I it it's I I think that + + + align:start position:0% +statistic so I it it's I I think that +the + + align:start position:0% +the + + + align:start position:0% +the +intuition uh that you're coming up with + + align:start position:0% +intuition uh that you're coming up with + + + align:start position:0% +intuition uh that you're coming up with +is kind of heading in the right + + align:start position:0% +is kind of heading in the right + + + align:start position:0% +is kind of heading in the right +direction but I don't think it's + + align:start position:0% +direction but I don't think it's + + + align:start position:0% +direction but I don't think it's +precisely correct and so I yeah I think + + align:start position:0% +precisely correct and so I yeah I think + + + align:start position:0% +precisely correct and so I yeah I think +it's it's more useful to just think of + + align:start position:0% +it's it's more useful to just think of + + + align:start position:0% +it's it's more useful to just think of +you need at least one person who has + + align:start position:0% +you need at least one person who has + + + align:start position:0% +you need at least one person who has +valuation above the price you post and + + align:start position:0% +valuation above the price you post and + + + align:start position:0% +valuation above the price you post and +what's the distribution of the the the + + align:start position:0% +what's the distribution of the the the + + + align:start position:0% +what's the distribution of the the the +highest value well it's just the the nth + + align:start position:0% +highest value well it's just the the nth + + + align:start position:0% +highest value well it's just the the nth +order + + align:start position:0% +order + + + align:start position:0% +order +statistic + + align:start position:0% + + + + align:start position:0% + +okay okay and I I should step back uh + + align:start position:0% +okay okay and I I should step back uh + + + align:start position:0% +okay okay and I I should step back uh +just uh for a moment and + + align:start position:0% +just uh for a moment and + + + align:start position:0% +just uh for a moment and +um mention how does this formula for + + align:start position:0% +um mention how does this formula for + + + align:start position:0% +um mention how does this formula for +expectation here square with the for + + align:start position:0% +expectation here square with the for + + + align:start position:0% +expectation here square with the for +formula we saw for expectation so + + align:start position:0% +formula we saw for expectation so + + + align:start position:0% +formula we saw for expectation so +obviously the the formula that you that + + align:start position:0% +obviously the the formula that you that + + + align:start position:0% +obviously the the formula that you that +you saw most often for expectation the + + align:start position:0% +you saw most often for expectation the + + + align:start position:0% +you saw most often for expectation the +beginning of the lecture was this sort + + align:start position:0% +beginning of the lecture was this sort + + + align:start position:0% +beginning of the lecture was this sort +of integral it was a expectation of a + + align:start position:0% +of integral it was a expectation of a + + + align:start position:0% +of integral it was a expectation of a +continuous random variable this is a + + align:start position:0% +continuous random variable this is a + + + align:start position:0% +continuous random variable this is a +discrete random variable here so we have + + align:start position:0% +discrete random variable here so we have + + + align:start position:0% +discrete random variable here so we have +to go back to to um when I flashed up + + align:start position:0% +to go back to to um when I flashed up + + + align:start position:0% +to go back to to um when I flashed up +the the um uh the equation for computing + + align:start position:0% +the the um uh the equation for computing + + + align:start position:0% +the the um uh the equation for computing +the expectation from a discret random + + align:start position:0% +the expectation from a discret random + + + align:start position:0% +the expectation from a discret random +variable okay so think about that it's + + align:start position:0% + + + + align:start position:0% + +um okay so we're just summing up uh the + + align:start position:0% +um okay so we're just summing up uh the + + + align:start position:0% +um okay so we're just summing up uh the +um you know sort of uh probability + + align:start position:0% +um you know sort of uh probability + + + align:start position:0% +um you know sort of uh probability +function for each value of x times x + + align:start position:0% +function for each value of x times x + + + align:start position:0% +function for each value of x times x +okay to get the expectation and here the + + align:start position:0% +okay to get the expectation and here the + + + align:start position:0% +okay to get the expectation and here the +um this is this distribution has only + + align:start position:0% +um this is this distribution has only + + + align:start position:0% +um this is this distribution has only +two points it's a discrete distribution + + align:start position:0% +two points it's a discrete distribution + + + align:start position:0% +two points it's a discrete distribution +that has only two points um one is um + + align:start position:0% +that has only two points um one is um + + + align:start position:0% +that has only two points um one is um +the probability that we get zero from + + align:start position:0% +the probability that we get zero from + + + align:start position:0% +the probability that we get zero from +this transaction and that's the + + align:start position:0% +this transaction and that's the + + + align:start position:0% +this transaction and that's the +probability that's basically uh the CDF + + align:start position:0% +probability that's basically uh the CDF + + + align:start position:0% +probability that's basically uh the CDF +of the nth order statistic evaluated at + + align:start position:0% +of the nth order statistic evaluated at + + + align:start position:0% +of the nth order statistic evaluated at +P so it's a probability it's one minus + + align:start position:0% +P so it's a probability it's one minus + + + align:start position:0% +P so it's a probability it's one minus +uh that probability okay but then that + + align:start position:0% +uh that probability okay but then that + + + align:start position:0% +uh that probability okay but then that +gets multiplied by P or sorry gets + + align:start position:0% +gets multiplied by P or sorry gets + + + align:start position:0% +gets multiplied by P or sorry gets +multiplied by zero and so that term goes + + align:start position:0% +multiplied by zero and so that term goes + + + align:start position:0% +multiplied by zero and so that term goes +away and so basically we have two terms + + align:start position:0% +away and so basically we have two terms + + + align:start position:0% +away and so basically we have two terms +in the expectation + + align:start position:0% +in the expectation + + + align:start position:0% +in the expectation +one term is the probability that you + + align:start position:0% +one term is the probability that you + + + align:start position:0% +one term is the probability that you +don't sell it times zero which is what + + align:start position:0% +don't sell it times zero which is what + + + align:start position:0% +don't sell it times zero which is what +you get if you don't sell it so that + + align:start position:0% +you get if you don't sell it so that + + + align:start position:0% +you get if you don't sell it so that +term goes away plus the probability that + + align:start position:0% +term goes away plus the probability that + + + align:start position:0% +term goes away plus the probability that +you sell it times what you get if you do + + align:start position:0% +you sell it times what you get if you do + + + align:start position:0% +you sell it times what you get if you do +sell it and + + align:start position:0% +sell it and + + + align:start position:0% +sell it and +that's uh this equation + + align:start position:0% + + + + align:start position:0% + +okay okay + + align:start position:0% +okay okay + + + align:start position:0% +okay okay +so and now um oh I said just apply the + + align:start position:0% +so and now um oh I said just apply the + + + align:start position:0% +so and now um oh I said just apply the +discrete formula note that the first + + align:start position:0% +discrete formula note that the first + + + align:start position:0% +discrete formula note that the first +term is zero + + align:start position:0% +term is zero + + + align:start position:0% +term is zero +Okay so we've got an expression for the + + align:start position:0% +Okay so we've got an expression for the + + + align:start position:0% +Okay so we've got an expression for the +expected profit and um if I go back to + + align:start position:0% +expected profit and um if I go back to + + + align:start position:0% +expected profit and um if I go back to +my notes on um order + + align:start position:0% +my notes on um order + + + align:start position:0% +my notes on um order +statistics I can uh remind myself what + + align:start position:0% +statistics I can uh remind myself what + + + align:start position:0% +statistics I can uh remind myself what +the CDF for the nth order statistic from + + align:start position:0% +the CDF for the nth order statistic from + + + align:start position:0% +the CDF for the nth order statistic from +a uniform uh 01 distribution is and so I + + align:start position:0% +a uniform uh 01 distribution is and so I + + + align:start position:0% +a uniform uh 01 distribution is and so I +can plug that in and I get this + + align:start position:0% +can plug that in and I get this + + + align:start position:0% +can plug that in and I get this +expression for expected + + align:start position:0% +expression for expected + + + align:start position:0% +expression for expected +profits okay + + align:start position:0% + + + + align:start position:0% + +okay so now for a little economics if + + align:start position:0% +okay so now for a little economics if + + + align:start position:0% +okay so now for a little economics if +this if this didn't confuse you enough + + align:start position:0% +this if this didn't confuse you enough + + + align:start position:0% +this if this didn't confuse you enough +already yep explain the P to the power n + + align:start position:0% +already yep explain the P to the power n + + + align:start position:0% +already yep explain the P to the power n +this is just the if you go back and you + + align:start position:0% +this is just the if you go back and you + + + align:start position:0% +this is just the if you go back and you +look uh on your notes about where we + + align:start position:0% +look uh on your notes about where we + + + align:start position:0% +look uh on your notes about where we +talked about um uh in sort of order + + align:start position:0% +talked about um uh in sort of order + + + align:start position:0% +talked about um uh in sort of order +statistics and we talked about the CDF + + align:start position:0% +statistics and we talked about the CDF + + + align:start position:0% +statistics and we talked about the CDF +of order statistics basically what I'm + + align:start position:0% +of order statistics basically what I'm + + + align:start position:0% +of order statistics basically what I'm +doing is I'm just getting the formula + + align:start position:0% +doing is I'm just getting the formula + + + align:start position:0% +doing is I'm just getting the formula +for the CDF of the uh anthor statistic + + align:start position:0% +for the CDF of the uh anthor statistic + + + align:start position:0% +for the CDF of the uh anthor statistic +and pluging get in + + align:start position:0% +and pluging get in + + + align:start position:0% +and pluging get in +okay okay so now for a little bit of + + align:start position:0% +okay okay so now for a little bit of + + + align:start position:0% +okay okay so now for a little bit of +Economics so we've got U an expression + + align:start position:0% +Economics so we've got U an expression + + + align:start position:0% +Economics so we've got U an expression +for expected profit but um as we often + + align:start position:0% +for expected profit but um as we often + + + align:start position:0% +for expected profit but um as we often +do as economists often do we assume that + + align:start position:0% +do as economists often do we assume that + + + align:start position:0% +do as economists often do we assume that +the seller is going to do what's in his + + align:start position:0% +the seller is going to do what's in his + + + align:start position:0% +the seller is going to do what's in his +best interest okay even though we + + align:start position:0% +best interest okay even though we + + + align:start position:0% +best interest okay even though we +realize that doesn't always happen uh in + + align:start position:0% +realize that doesn't always happen uh in + + + align:start position:0% +realize that doesn't always happen uh in +order to sort of solve our models this + + align:start position:0% +order to sort of solve our models this + + + align:start position:0% +order to sort of solve our models this +is typically the Assumption we make we + + align:start position:0% +is typically the Assumption we make we + + + align:start position:0% +is typically the Assumption we make we +figure that the seller is going to do do + + align:start position:0% +figure that the seller is going to do do + + + align:start position:0% +figure that the seller is going to do do +what's in its best interest in other + + align:start position:0% +what's in its best interest in other + + + align:start position:0% +what's in its best interest in other +words set P to maximize his profits okay + + align:start position:0% +words set P to maximize his profits okay + + + align:start position:0% +words set P to maximize his profits okay +given that he knows what distribution + + align:start position:0% +given that he knows what distribution + + + align:start position:0% +given that he knows what distribution +the valuations are coming from okay so + + align:start position:0% +the valuations are coming from okay so + + + align:start position:0% +the valuations are coming from okay so +how do we find what that optimal p is + + align:start position:0% +how do we find what that optimal p is + + + align:start position:0% +how do we find what that optimal p is +well it's just a little calculous okay + + align:start position:0% +well it's just a little calculous okay + + + align:start position:0% +well it's just a little calculous okay +so we take the derivative of the + + align:start position:0% +so we take the derivative of the + + + align:start position:0% +so we take the derivative of the +expected profit function with respect to + + align:start position:0% +expected profit function with respect to + + + align:start position:0% +expected profit function with respect to +price we set that equal to zero and then + + align:start position:0% +price we set that equal to zero and then + + + align:start position:0% +price we set that equal to zero and then +we solve for Price + + align:start position:0% +we solve for Price + + + align:start position:0% +we solve for Price +okay so by the way this isn't + + align:start position:0% +okay so by the way this isn't + + + align:start position:0% +okay so by the way this isn't +I we know this isn't an economics class + + align:start position:0% +I we know this isn't an economics class + + + align:start position:0% +I we know this isn't an economics class +and we don't have an economics + + align:start position:0% +and we don't have an economics + + + align:start position:0% +and we don't have an economics +prerequisite we're not going to hold you + + align:start position:0% +prerequisite we're not going to hold you + + + align:start position:0% +prerequisite we're not going to hold you +guys responsible for profit maximizing + + align:start position:0% +guys responsible for profit maximizing + + + align:start position:0% +guys responsible for profit maximizing +behavior of of uh of um you know sellers + + align:start position:0% +behavior of of uh of um you know sellers + + + align:start position:0% +behavior of of uh of um you know sellers +but I think it's good to be exposed to + + align:start position:0% +but I think it's good to be exposed to + + + align:start position:0% +but I think it's good to be exposed to +this kind of thinking regardless + + align:start position:0% +this kind of thinking regardless + + + align:start position:0% +this kind of thinking regardless +it's it's very um sort of powerful way + + align:start position:0% +it's it's very um sort of powerful way + + + align:start position:0% +it's it's very um sort of powerful way +of uh of thinking and and solving + + align:start position:0% +of uh of thinking and and solving + + + align:start position:0% +of uh of thinking and and solving +problems okay so what we do is we just + + align:start position:0% +problems okay so what we do is we just + + + align:start position:0% +problems okay so what we do is we just +take the derivative we set it equal to + + align:start position:0% +take the derivative we set it equal to + + + align:start position:0% +take the derivative we set it equal to +zero and we solve for the optimal price + + align:start position:0% +zero and we solve for the optimal price + + + align:start position:0% +zero and we solve for the optimal price +and that's what it is okay so we get + + align:start position:0% +and that's what it is okay so we get + + + align:start position:0% +and that's what it is okay so we get +that it's the nth root of 1 over n + one + + align:start position:0% +that it's the nth root of 1 over n + one + + + align:start position:0% +that it's the nth root of 1 over n + one +remember n is the number of + + align:start position:0% +remember n is the number of + + + align:start position:0% +remember n is the number of +biders or sorry the number of potential + + align:start position:0% +biders or sorry the number of potential + + + align:start position:0% +biders or sorry the number of potential +buyers not biders in this case Okay + + align:start position:0% +buyers not biders in this case Okay + + + align:start position:0% +buyers not biders in this case Okay +potential what number of potential + + align:start position:0% +potential what number of potential + + + align:start position:0% +potential what number of potential +buyers okay so and then we can also take + + align:start position:0% +buyers okay so and then we can also take + + + align:start position:0% +buyers okay so and then we can also take +this optimal price plug it back into the + + align:start position:0% +this optimal price plug it back into the + + + align:start position:0% +this optimal price plug it back into the +expected profit profit formula and we + + align:start position:0% +expected profit profit formula and we + + + align:start position:0% +expected profit profit formula and we +get the expected profit under that + + align:start position:0% +get the expected profit under that + + + align:start position:0% +get the expected profit under that +optimal price is uh this value here + + align:start position:0% +optimal price is uh this value here + + + align:start position:0% +optimal price is uh this value here +okay okay so now we can just plug in + + align:start position:0% +okay okay so now we can just plug in + + + align:start position:0% +okay okay so now we can just plug in +different ends and we can see what price + + align:start position:0% +different ends and we can see what price + + + align:start position:0% +different ends and we can see what price +this seller's going to set for different + + align:start position:0% +this seller's going to set for different + + + align:start position:0% +this seller's going to set for different +ends and we can see what profit he makes + + align:start position:0% +ends and we can see what profit he makes + + + align:start position:0% +ends and we can see what profit he makes +the different + + align:start position:0% +the different + + + align:start position:0% +the different +ends okay so here's a little table uh n + + align:start position:0% +ends okay so here's a little table uh n + + + align:start position:0% +ends okay so here's a little table uh n +goes from one to nine so if you only + + align:start position:0% +goes from one to nine so if you only + + + align:start position:0% +goes from one to nine so if you only +have one potential buyer and you know + + align:start position:0% +have one potential buyer and you know + + + align:start position:0% +have one potential buyer and you know +that his valuation is drawn from uniform + + align:start position:0% +that his valuation is drawn from uniform + + + align:start position:0% +that his valuation is drawn from uniform +01 distribution the optimal price that + + align:start position:0% +01 distribution the optimal price that + + + align:start position:0% +01 distribution the optimal price that +you're going to set is one half you're + + align:start position:0% +you're going to set is one half you're + + + align:start position:0% +you're going to set is one half you're +going to sell the product half of the + + align:start position:0% +going to sell the product half of the + + + align:start position:0% +going to sell the product half of the +time that makes sense right you you're + + align:start position:0% +time that makes sense right you you're + + + align:start position:0% +time that makes sense right you you're +going to be out of luck half the time uh + + align:start position:0% +going to be out of luck half the time uh + + + align:start position:0% +going to be out of luck half the time uh +but then uh that because you sell it + + align:start position:0% +but then uh that because you sell it + + + align:start position:0% +but then uh that because you sell it +half the time and you get profit uh one + + align:start position:0% +half the time and you get profit uh one + + + align:start position:0% +half the time and you get profit uh one +half when you do sell it your expected + + align:start position:0% +half when you do sell it your expected + + + align:start position:0% +half when you do sell it your expected +profit is one quarter okay and then you + + align:start position:0% +profit is one quarter okay and then you + + + align:start position:0% +profit is one quarter okay and then you +know the the the you know sort of + + align:start position:0% +know the the the you know sort of + + + align:start position:0% +know the the the you know sort of +reasoning applies as you go down the + + align:start position:0% +reasoning applies as you go down the + + + align:start position:0% +reasoning applies as you go down the +table to get this table of course I'm + + align:start position:0% +table to get this table of course I'm + + + align:start position:0% +table to get this table of course I'm +just plugging into the uh the formulas + + align:start position:0% +just plugging into the uh the formulas + + + align:start position:0% +just plugging into the uh the formulas +for optimal pricing that that we DED + + align:start position:0% +for optimal pricing that that we DED + + + align:start position:0% +for optimal pricing that that we DED +before + + align:start position:0% +before + + + align:start position:0% +before +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yes but why is + + align:start position:0% +yes but why is + + + align:start position:0% +yes but why is +there sorry that's that's the um + + align:start position:0% +there sorry that's that's the um + + + align:start position:0% +there sorry that's that's the um +notation we use for + + align:start position:0% + + + + align:start position:0% + +profit + + align:start position:0% +profit + + + align:start position:0% +profit +so in a probability class it's not + + align:start position:0% +so in a probability class it's not + + + align:start position:0% +so in a probability class it's not +always Pi is not always going to stand + + align:start position:0% +always Pi is not always going to stand + + + align:start position:0% +always Pi is not always going to stand +for profit but uh yeah in in this + + align:start position:0% +for profit but uh yeah in in this + + + align:start position:0% +for profit but uh yeah in in this +particular example uh Pi just means + + align:start position:0% +particular example uh Pi just means + + + align:start position:0% +particular example uh Pi just means +profit yeah so that's that's an + + align:start position:0% +profit yeah so that's that's an + + + align:start position:0% +profit yeah so that's that's an +economics + + align:start position:0% + + + + align:start position:0% + +thing okay so the posted price is rising + + align:start position:0% +thing okay so the posted price is rising + + + align:start position:0% +thing okay so the posted price is rising +as the number of potential buyers goes + + align:start position:0% +as the number of potential buyers goes + + + align:start position:0% +as the number of potential buyers goes +up does this make sense sort of + + align:start position:0% +up does this make sense sort of + + + align:start position:0% +up does this make sense sort of +intuitively you have like a 100 buyers + + align:start position:0% +intuitively you have like a 100 buyers + + + align:start position:0% +intuitively you have like a 100 buyers +you know we know something about the + + align:start position:0% +you know we know something about the + + + align:start position:0% +you know we know something about the +inth order statistic when you have a 100 + + align:start position:0% +inth order statistic when you have a 100 + + + align:start position:0% +inth order statistic when you have a 100 +buyers right it's going to be really + + align:start position:0% +buyers right it's going to be really + + + align:start position:0% +buyers right it's going to be really +close to one it's going to have high + + align:start position:0% +close to one it's going to have high + + + align:start position:0% +close to one it's going to have high +probability it's close to one so you're + + align:start position:0% +probability it's close to one so you're + + + align:start position:0% +probability it's close to one so you're +going to set a higher price so that + + align:start position:0% +going to set a higher price so that + + + align:start position:0% +going to set a higher price so that +makes sense and expected profits also go + + align:start position:0% +makes sense and expected profits also go + + + align:start position:0% +makes sense and expected profits also go +up okay as in goes + + align:start position:0% +up okay as in goes + + + align:start position:0% +up okay as in goes +up okay oh so I said this this is a + + align:start position:0% +up okay oh so I said this this is a + + + align:start position:0% +up okay oh so I said this this is a +consequence of the distribution of the + + align:start position:0% +consequence of the distribution of the + + + align:start position:0% +consequence of the distribution of the +nth order statistic and how it changes + + align:start position:0% +nth order statistic and how it changes + + + align:start position:0% +nth order statistic and how it changes +as in and increases + + align:start position:0% + + + + align:start position:0% + +okay so now we know what profit the + + align:start position:0% +okay so now we know what profit the + + + align:start position:0% +okay so now we know what profit the +seller is going to make uh for uh posted + + align:start position:0% +seller is going to make uh for uh posted + + + align:start position:0% +seller is going to make uh for uh posted +price as a function of the number of + + align:start position:0% +price as a function of the number of + + + align:start position:0% +price as a function of the number of +potential buyers so let's see how he's + + align:start position:0% +potential buyers so let's see how he's + + + align:start position:0% +potential buyers so let's see how he's +going to do in the auction okay so we're + + align:start position:0% +going to do in the auction okay so we're + + + align:start position:0% +going to do in the auction okay so we're +going to assume uh what's called an + + align:start position:0% +going to assume uh what's called an + + + align:start position:0% +going to assume uh what's called an +English auction where the price of the + + align:start position:0% +English auction where the price of the + + + align:start position:0% +English auction where the price of the +good is going to gradually increase and + + align:start position:0% +good is going to gradually increase and + + + align:start position:0% +good is going to gradually increase and +potential buyers ERS you can think about + + align:start position:0% +potential buyers ERS you can think about + + + align:start position:0% +potential buyers ERS you can think about +everyone starting with their hand up who + + align:start position:0% +everyone starting with their hand up who + + + align:start position:0% +everyone starting with their hand up who +wants this Picasso for a dollar everyone + + align:start position:0% +wants this Picasso for a dollar everyone + + + align:start position:0% +wants this Picasso for a dollar everyone +has their hand up who wants it for $2 + + align:start position:0% +has their hand up who wants it for $2 + + + align:start position:0% +has their hand up who wants it for $2 +everyone has their hands up who wants it + + align:start position:0% +everyone has their hands up who wants it + + + align:start position:0% +everyone has their hands up who wants it +for 40 million the hands start going + + align:start position:0% +for 40 million the hands start going + + + align:start position:0% +for 40 million the hands start going +down okay so um until there's only one + + align:start position:0% +down okay so um until there's only one + + + align:start position:0% +down okay so um until there's only one +person left okay and that buyer's + + align:start position:0% +person left okay and that buyer's + + + align:start position:0% +person left okay and that buyer's +valuation sorry uh there's sorry there's + + align:start position:0% +valuation sorry uh there's sorry there's + + + align:start position:0% +valuation sorry uh there's sorry there's +only one person left okay we're using + + align:start position:0% +only one person left okay we're using + + + align:start position:0% +only one person left okay we're using +Visa buy to stand for buyer eyes + + align:start position:0% +Visa buy to stand for buyer eyes + + + align:start position:0% +Visa buy to stand for buyer eyes +valuation for the product then when only + + align:start position:0% +valuation for the product then when only + + + align:start position:0% +valuation for the product then when only +one buyer is left he gets the good at V + + align:start position:0% +one buyer is left he gets the good at V + + + align:start position:0% +one buyer is left he gets the good at V +sub n minus + + align:start position:0% +sub n minus + + + align:start position:0% +sub n minus +one the second highest valuation why is + + align:start position:0% +one the second highest valuation why is + + + align:start position:0% +one the second highest valuation why is +that why does he get it at the second + + align:start position:0% +that why does he get it at the second + + + align:start position:0% +that why does he get it at the second +highest valuation yep until the last + + align:start position:0% +highest valuation yep until the last + + + align:start position:0% +highest valuation yep until the last +person falls away he might have a higher + + align:start position:0% +person falls away he might have a higher + + + align:start position:0% +person falls away he might have a higher +price than he would that's right he the + + align:start position:0% +price than he would that's right he the + + + align:start position:0% +price than he would that's right he the +the auction's done when the second to + + align:start position:0% +the auction's done when the second to + + + align:start position:0% +the auction's done when the second to +last person uh takes his hand down okay + + align:start position:0% +last person uh takes his hand down okay + + + align:start position:0% +last person uh takes his hand down okay +so we have no idea what the value + + align:start position:0% +so we have no idea what the value + + + align:start position:0% +so we have no idea what the value +valuation of the winner is it's we just + + align:start position:0% +valuation of the winner is it's we just + + + align:start position:0% +valuation of the winner is it's we just +know it's it's above the second highest + + align:start position:0% +know it's it's above the second highest + + + align:start position:0% +know it's it's above the second highest +valuation but he gets it at the second + + align:start position:0% +valuation but he gets it at the second + + + align:start position:0% +valuation but he gets it at the second +highest valuation okay so this + + align:start position:0% +highest valuation okay so this + + + align:start position:0% +highest valuation okay so this +is um the classic open out cry auction + + align:start position:0% +is um the classic open out cry auction + + + align:start position:0% +is um the classic open out cry auction +that you see you know on TV shows and + + align:start position:0% +that you see you know on TV shows and + + + align:start position:0% +that you see you know on TV shows and +things like that + + align:start position:0% +things like that + + + align:start position:0% +things like that +okay okay so here to compute the + + align:start position:0% +okay okay so here to compute the + + + align:start position:0% +okay okay so here to compute the +expected profits we're going to need the + + align:start position:0% +expected profits we're going to need the + + + align:start position:0% +expected profits we're going to need the +distribution of the N minus first order + + align:start position:0% +distribution of the N minus first order + + + align:start position:0% +distribution of the N minus first order +statistic uh from the the uniform 01 so + + align:start position:0% +statistic uh from the the uniform 01 so + + + align:start position:0% +statistic uh from the the uniform 01 so +why the N minus first order statistic + + align:start position:0% +why the N minus first order statistic + + + align:start position:0% +why the N minus first order statistic +because that's the the price at which + + align:start position:0% +because that's the the price at which + + + align:start position:0% +because that's the the price at which +this thing gets auctioned off + + align:start position:0% +this thing gets auctioned off + + + align:start position:0% +this thing gets auctioned off +okay okay so if I look up if I go back + + align:start position:0% +okay okay so if I look up if I go back + + + align:start position:0% +okay okay so if I look up if I go back +to my notes actually I don't think this + + align:start position:0% +to my notes actually I don't think this + + + align:start position:0% +to my notes actually I don't think this +is in your notes I'd have to figure it + + align:start position:0% +is in your notes I'd have to figure it + + + align:start position:0% +is in your notes I'd have to figure it +out or or look it up in some other you + + align:start position:0% +out or or look it up in some other you + + + align:start position:0% +out or or look it up in some other you +know textbook or something uh I can + + align:start position:0% +know textbook or something uh I can + + + align:start position:0% +know textbook or something uh I can +figure out what the PDF of the N minus + + align:start position:0% +figure out what the PDF of the N minus + + + align:start position:0% +figure out what the PDF of the N minus +first order statistic from the unifor + + align:start position:0% +first order statistic from the unifor + + + align:start position:0% +first order statistic from the unifor +form 01 distribution is and this is what + + align:start position:0% +form 01 distribution is and this is what + + + align:start position:0% +form 01 distribution is and this is what +it + + align:start position:0% +it + + + align:start position:0% +it +is + + align:start position:0% +is + + + align:start position:0% +is +okay and so we'll just to to uh + + align:start position:0% +okay and so we'll just to to uh + + + align:start position:0% +okay and so we'll just to to uh +compute oh yeah and again we're assuming + + align:start position:0% +compute oh yeah and again we're assuming + + + align:start position:0% +compute oh yeah and again we're assuming +this is the distribution of the + + align:start position:0% + + + + align:start position:0% + +valuations okay so then to compute the + + align:start position:0% +valuations okay so then to compute the + + + align:start position:0% +valuations okay so then to compute the +expected profit in the auction all we do + + align:start position:0% +expected profit in the auction all we do + + + align:start position:0% +expected profit in the auction all we do +is we integrate over the support of the + + align:start position:0% +is we integrate over the support of the + + + align:start position:0% +is we integrate over the support of the +distribution the + + align:start position:0% +distribution the + + + align:start position:0% +distribution the +Pro the the PDF of the N minus first + + align:start position:0% +Pro the the PDF of the N minus first + + + align:start position:0% +Pro the the PDF of the N minus first +order statistic that's what the seller + + align:start position:0% +order statistic that's what the seller + + + align:start position:0% +order statistic that's what the seller +is going to get at auction for this + + align:start position:0% +is going to get at auction for this + + + align:start position:0% +is going to get at auction for this +product times x I put the X at the end + + align:start position:0% +product times x I put the X at the end + + + align:start position:0% +product times x I put the X at the end +so it's right before the the little + + align:start position:0% +so it's right before the the little + + + align:start position:0% +so it's right before the the little +DX okay and this is just the formula for + + align:start position:0% +DX okay and this is just the formula for + + + align:start position:0% +DX okay and this is just the formula for +uh calculating expectation from a um + + align:start position:0% +uh calculating expectation from a um + + + align:start position:0% +uh calculating expectation from a um +from a continuous random + + align:start position:0% +from a continuous random + + + align:start position:0% +from a continuous random +variable okay so everyone on board with + + align:start position:0% +variable okay so everyone on board with + + + align:start position:0% +variable okay so everyone on board with +this so then + + align:start position:0% +this so then + + + align:start position:0% +this so then +we just uh you know sort of perform the + + align:start position:0% +we just uh you know sort of perform the + + + align:start position:0% +we just uh you know sort of perform the +integral and we end up getting n minus + + align:start position:0% +integral and we end up getting n minus + + + align:start position:0% +integral and we end up getting n minus +one over n + + + align:start position:0% +one over n + + + + align:start position:0% +one over n + +one + + align:start position:0% +one + + + align:start position:0% +one +okay that's the that's the + + align:start position:0% + + + + align:start position:0% + +formula and so we can make a similar + + align:start position:0% +formula and so we can make a similar + + + align:start position:0% +formula and so we can make a similar +table to the one we saw before where we + + align:start position:0% +table to the one we saw before where we + + + align:start position:0% +table to the one we saw before where we +have n here I'm I'm not going to put p + + align:start position:0% +have n here I'm I'm not going to put p + + + align:start position:0% +have n here I'm I'm not going to put p +on the table here because in an auction + + align:start position:0% +on the table here because in an auction + + + align:start position:0% +on the table here because in an auction +you're not setting a price okay it's + + align:start position:0% +you're not setting a price okay it's + + + align:start position:0% +you're not setting a price okay it's +just uh you know sort of it just gets + + align:start position:0% +just uh you know sort of it just gets + + + align:start position:0% +just uh you know sort of it just gets +sold at uh the the N minus first uh + + align:start position:0% +sold at uh the the N minus first uh + + + align:start position:0% +sold at uh the the N minus first uh +order statistic but we can also put the + + align:start position:0% +order statistic but we can also put the + + + align:start position:0% +order statistic but we can also put the +um uh expected profit in the case of the + + align:start position:0% +um uh expected profit in the case of the + + + align:start position:0% +um uh expected profit in the case of the +auction and let me put up the last + + align:start position:0% +auction and let me put up the last + + + align:start position:0% +auction and let me put up the last +column of the previous table to compare + + align:start position:0% +column of the previous table to compare + + + align:start position:0% +column of the previous table to compare +okay so if we only have why do we get no + + align:start position:0% +okay so if we only have why do we get no + + + align:start position:0% +okay so if we only have why do we get no +profit if uh there's only one potential + + align:start position:0% +profit if uh there's only one potential + + + align:start position:0% +profit if uh there's only one potential +buyer or one + + align:start position:0% +buyer or one + + + align:start position:0% +buyer or one +bidder + + align:start position:0% + + + + align:start position:0% + +yeah exactly I mean that you the + + align:start position:0% +yeah exactly I mean that you the + + + align:start position:0% +yeah exactly I mean that you the +auction's over when there's only one guy + + align:start position:0% +auction's over when there's only one guy + + + align:start position:0% +auction's over when there's only one guy +left if you start with one guy he gets + + align:start position:0% +left if you start with one guy he gets + + + align:start position:0% +left if you start with one guy he gets +it for free okay so um so anyhow the the + + align:start position:0% +it for free okay so um so anyhow the the + + + align:start position:0% +it for free okay so um so anyhow the the +for one if there's one potential buyer + + align:start position:0% +for one if there's one potential buyer + + + align:start position:0% +for one if there's one potential buyer +or one bidder um you you do a ve you do + + align:start position:0% +or one bidder um you you do a ve you do + + + align:start position:0% +or one bidder um you you do a ve you do +very poorly if you auction it off okay + + align:start position:0% +very poorly if you auction it off okay + + + align:start position:0% +very poorly if you auction it off okay +and that's uh compared to expected + + align:start position:0% +and that's uh compared to expected + + + align:start position:0% +and that's uh compared to expected +profit from a posted price of a + + align:start position:0% +profit from a posted price of a + + + align:start position:0% +profit from a posted price of a +order if you have two um then you end up + + align:start position:0% +order if you have two um then you end up + + + align:start position:0% +order if you have two um then you end up +doing a little bit better uh with the + + align:start position:0% +doing a little bit better uh with the + + + align:start position:0% +doing a little bit better uh with the +posted price in the auction but uh the + + align:start position:0% +posted price in the auction but uh the + + + align:start position:0% +posted price in the auction but uh the +auction's catching up and then for n + + align:start position:0% +auction's catching up and then for n + + + align:start position:0% +auction's catching up and then for n +equals 3 and above you you do better uh + + align:start position:0% +equals 3 and above you you do better uh + + + align:start position:0% +equals 3 and above you you do better uh +with the auction than the Post-it price + + align:start position:0% +with the auction than the Post-it price + + + align:start position:0% +with the auction than the Post-it price +so I think I have + + align:start position:0% +so I think I have + + + align:start position:0% +so I think I have +yeah and I should say by the way this is + + align:start position:0% +yeah and I should say by the way this is + + + align:start position:0% +yeah and I should say by the way this is +not just um it it's not that uh this is + + align:start position:0% +not just um it it's not that uh this is + + + align:start position:0% +not just um it it's not that uh this is +true for Nal ALS 2 through 9 and then + + align:start position:0% +true for Nal ALS 2 through 9 and then + + + align:start position:0% +true for Nal ALS 2 through 9 and then +something crazy happens below this is + + align:start position:0% +something crazy happens below this is + + + align:start position:0% +something crazy happens below this is +General you can show that uh for uh any + + align:start position:0% +General you can show that uh for uh any + + + align:start position:0% +General you can show that uh for uh any +value of n greater than two in this + + align:start position:0% +value of n greater than two in this + + + align:start position:0% +value of n greater than two in this +particular um model uh the auction does + + align:start position:0% +particular um model uh the auction does + + + align:start position:0% +particular um model uh the auction does +do + + align:start position:0% +do + + + align:start position:0% +do +better + + align:start position:0% + + + + align:start position:0% + +okay so what did this model tell us well + + align:start position:0% +okay so what did this model tell us well + + + align:start position:0% +okay so what did this model tell us well +conditional on the assumptions of the + + align:start position:0% +conditional on the assumptions of the + + + align:start position:0% +conditional on the assumptions of the +model of course it told us that uh the + + align:start position:0% +model of course it told us that uh the + + + align:start position:0% +model of course it told us that uh the +seller is going to do better with an + + align:start position:0% +seller is going to do better with an + + + align:start position:0% +seller is going to do better with an +auction when uh the number of biders is + + align:start position:0% +auction when uh the number of biders is + + + align:start position:0% +auction when uh the number of biders is +large okay so that might might be + + align:start position:0% +large okay so that might might be + + + align:start position:0% +large okay so that might might be +consistent with intuition you have or it + + align:start position:0% +consistent with intuition you have or it + + + align:start position:0% +consistent with intuition you have or it +might not be I mean I'm not sure that I + + align:start position:0% +might not be I mean I'm not sure that I + + + align:start position:0% +might not be I mean I'm not sure that I +had a really strong intuition certainly + + align:start position:0% +had a really strong intuition certainly + + + align:start position:0% +had a really strong intuition certainly +in both cases of the posted price and + + align:start position:0% +in both cases of the posted price and + + + align:start position:0% +in both cases of the posted price and +the auction the seller is going to do + + align:start position:0% +the auction the seller is going to do + + + align:start position:0% +the auction the seller is going to do +better if there are more buyers okay + + align:start position:0% +better if there are more buyers okay + + + align:start position:0% +better if there are more buyers okay +that's that seems pretty clear to me um + + align:start position:0% +that's that seems pretty clear to me um + + + align:start position:0% +that's that seems pretty clear to me um +but this model at least this simple + + align:start position:0% +but this model at least this simple + + + align:start position:0% +but this model at least this simple +model shows us that uh the seller does + + align:start position:0% +model shows us that uh the seller does + + + align:start position:0% +model shows us that uh the seller does +better with an auction when n is large + + align:start position:0% +better with an auction when n is large + + + align:start position:0% +better with an auction when n is large +um large enough okay + + align:start position:0% +um large enough okay + + + align:start position:0% +um large enough okay +and but here here was the here was the + + align:start position:0% +and but here here was the here was the + + + align:start position:0% +and but here here was the here was the +sort of um amazing thing that you might + + align:start position:0% +sort of um amazing thing that you might + + + align:start position:0% +sort of um amazing thing that you might +not have realized when we were going + + align:start position:0% +not have realized when we were going + + + align:start position:0% +not have realized when we were going +through the the example or going through + + align:start position:0% +through the the example or going through + + + align:start position:0% +through the the example or going through +this model the seller didn't need to + + align:start position:0% +this model the seller didn't need to + + + align:start position:0% +this model the seller didn't need to +know anything about the distribution of + + align:start position:0% +know anything about the distribution of + + + align:start position:0% +know anything about the distribution of +the valuations in the + + align:start position:0% +the valuations in the + + + align:start position:0% +the valuations in the +auction + + align:start position:0% +auction + + + align:start position:0% +auction +okay so um the this the seller did in + + align:start position:0% +okay so um the this the seller did in + + + align:start position:0% +okay so um the this the seller did in +fact need to know the distribution + + align:start position:0% +fact need to know the distribution + + + align:start position:0% +fact need to know the distribution +for the post to set the optimal posted + + align:start position:0% +for the post to set the optimal posted + + + align:start position:0% +for the post to set the optimal posted +price but in the auction the the + + align:start position:0% +price but in the auction the the + + + align:start position:0% +price but in the auction the the +seller's not setting a posted price or + + align:start position:0% +seller's not setting a posted price or + + + align:start position:0% +seller's not setting a posted price or +not setting a price okay so the seller + + align:start position:0% +not setting a price okay so the seller + + + align:start position:0% +not setting a price okay so the seller +actually didn't need to know um what the + + align:start position:0% +actually didn't need to know um what the + + + align:start position:0% +actually didn't need to know um what the +uh what the the sort of underlying + + align:start position:0% +uh what the the sort of underlying + + + align:start position:0% +uh what the the sort of underlying +distribution of valuations was in the + + align:start position:0% +distribution of valuations was in the + + + align:start position:0% +distribution of valuations was in the +auction model okay and furthermore you + + align:start position:0% +auction model okay and furthermore you + + + align:start position:0% +auction model okay and furthermore you +could work through the same example + + align:start position:0% +could work through the same example + + + align:start position:0% +could work through the same example +using different distri contributions uh + + align:start position:0% +using different distri contributions uh + + + align:start position:0% +using different distri contributions uh +for the fixed price part of it so like + + align:start position:0% +for the fixed price part of it so like + + + align:start position:0% +for the fixed price part of it so like +assume that the seller got you know got + + align:start position:0% +assume that the seller got you know got + + + align:start position:0% +assume that the seller got you know got +the distribution wrong and thought that + + align:start position:0% +the distribution wrong and thought that + + + align:start position:0% +the distribution wrong and thought that +the the valuations were uniform on zero + + align:start position:0% +the the valuations were uniform on zero + + + align:start position:0% +the the valuations were uniform on zero +to 1 half or uniform 0 to2 when in fact + + align:start position:0% +to 1 half or uniform 0 to2 when in fact + + + align:start position:0% +to 1 half or uniform 0 to2 when in fact +they were uniform 0 to one and you'll + + align:start position:0% +they were uniform 0 to one and you'll + + + align:start position:0% +they were uniform 0 to one and you'll +see that the posted price does much + + align:start position:0% +see that the posted price does much + + + align:start position:0% +see that the posted price does much +worse in that case Okay so the the + + align:start position:0% +worse in that case Okay so the the + + + align:start position:0% +worse in that case Okay so the the +important Point here is that there's a + + align:start position:0% +important Point here is that there's a + + + align:start position:0% +important Point here is that there's a +large Reliance when you're setting a + + align:start position:0% +large Reliance when you're setting a + + + align:start position:0% +large Reliance when you're setting a +posted price on knowing the distribution + + align:start position:0% +posted price on knowing the distribution + + + align:start position:0% +posted price on knowing the distribution +of valuations that Reliance isn't there + + align:start position:0% +of valuations that Reliance isn't there + + + align:start position:0% +of valuations that Reliance isn't there +with the + + align:start position:0% +with the + + + align:start position:0% +with the +auction + + align:start position:0% +auction + + + align:start position:0% +auction +okay and then the third thing to point + + align:start position:0% +okay and then the third thing to point + + + align:start position:0% +okay and then the third thing to point +out this model doesn't have any + + align:start position:0% +out this model doesn't have any + + + align:start position:0% +out this model doesn't have any +transactions cost in it so we talked + + align:start position:0% +transactions cost in it so we talked + + + align:start position:0% +transactions cost in it so we talked +about how transactions costs might be + + align:start position:0% +about how transactions costs might be + + + align:start position:0% +about how transactions costs might be +important and you might not want to + + align:start position:0% +important and you might not want to + + + align:start position:0% +important and you might not want to +auction off things that you know are + + align:start position:0% +auction off things that you know are + + + align:start position:0% +auction off things that you know are +kind of low value items uh just because + + align:start position:0% +kind of low value items uh just because + + + align:start position:0% +kind of low value items uh just because +it's a hassle and selling it posted + + align:start position:0% +it's a hassle and selling it posted + + + align:start position:0% +it's a hassle and selling it posted +price is easier this model doesn't have + + align:start position:0% +price is easier this model doesn't have + + + align:start position:0% +price is easier this model doesn't have +have that in it at all and so um you + + align:start position:0% +have that in it at all and so um you + + + align:start position:0% +have that in it at all and so um you +know that you have to sort of keep that + + align:start position:0% +know that you have to sort of keep that + + + align:start position:0% +know that you have to sort of keep that +in mind when you're interpreting the the + + align:start position:0% + + + + align:start position:0% + +results okay + + align:start position:0% +results okay + + + align:start position:0% +results okay +yep um is there like a transaction cost + + align:start position:0% +yep um is there like a transaction cost + + + align:start position:0% +yep um is there like a transaction cost +to gather all the people op yeah + + align:start position:0% +to gather all the people op yeah + + + align:start position:0% +to gather all the people op yeah +absolutely and that's like I said that + + align:start position:0% +absolutely and that's like I said that + + + align:start position:0% +absolutely and that's like I said that +none of those transactions costs are in + + align:start position:0% +none of those transactions costs are in + + + align:start position:0% +none of those transactions costs are in +this model so you could write another + + align:start position:0% +this model so you could write another + + + align:start position:0% +this model so you could write another +model that had transactions costs that + + align:start position:0% +model that had transactions costs that + + + align:start position:0% +model that had transactions costs that +could be a function of the number of or + + align:start position:0% +could be a function of the number of or + + + align:start position:0% +could be a function of the number of or +something like that and the transactions + + align:start position:0% +something like that and the transactions + + + align:start position:0% +something like that and the transactions +cost could you know I mean you know you + + align:start position:0% +cost could you know I mean you know you + + + align:start position:0% +cost could you know I mean you know you +could think of various ways to model it + + align:start position:0% +could think of various ways to model it + + + align:start position:0% +could think of various ways to model it +but if it's like a like I don't know if + + align:start position:0% +but if it's like a like I don't know if + + + align:start position:0% +but if it's like a like I don't know if +it's like wealthy people then you have + + align:start position:0% +it's like wealthy people then you have + + + align:start position:0% +it's like wealthy people then you have +to like give them food it's like a + + align:start position:0% +to like give them food it's like a + + + align:start position:0% +to like give them food it's like a +that's right yeah that's like yeah if + + align:start position:0% +that's right yeah that's like yeah if + + + align:start position:0% +that's right yeah that's like yeah if +you're running an auction at SBE you + + align:start position:0% +you're running an auction at SBE you + + + align:start position:0% +you're running an auction at SBE you +can't like serve chicken fingers or + + align:start position:0% +can't like serve chicken fingers or + + + align:start position:0% +can't like serve chicken fingers or +something yeah that's right you have to + + align:start position:0% +something yeah that's right you have to + + + align:start position:0% +something yeah that's right you have to +have sort of a nice auction house and + + align:start position:0% +have sort of a nice auction house and + + + align:start position:0% +have sort of a nice auction house and +yeah exactly this mod tell you how much + + align:start position:0% +yeah exactly this mod tell you how much + + + align:start position:0% +yeah exactly this mod tell you how much +you able to to spend to make an auction + + align:start position:0% +you able to to spend to make an auction + + + align:start position:0% +you able to to spend to make an auction +happen this is the optimal optimal fix + + align:start position:0% +happen this is the optimal optimal fix + + + align:start position:0% +happen this is the optimal optimal fix +price the Gap is the money you can spend + + align:start position:0% +price the Gap is the money you can spend + + + align:start position:0% +price the Gap is the money you can spend +to for the + + align:start position:0% +to for the + + + align:start position:0% +to for the +option remain that's right you could you + + align:start position:0% +option remain that's right you could you + + + align:start position:0% +option remain that's right you could you +could sort of think of yeah think of + + align:start position:0% +could sort of think of yeah think of + + + align:start position:0% +could sort of think of yeah think of +have that interpretation of the Gap as + + align:start position:0% +have that interpretation of the Gap as + + + align:start position:0% +have that interpretation of the Gap as +well yes um so I don't understand the + + align:start position:0% +well yes um so I don't understand the + + + align:start position:0% +well yes um so I don't understand the +part where we the doing this calculation + + align:start position:0% +part where we the doing this calculation + + + align:start position:0% +part where we the doing this calculation +we don't need to know about an oxgen + + align:start position:0% +we don't need to know about an oxgen + + + align:start position:0% +we don't need to know about an oxgen +distribution because in N minus one + + align:start position:0% +distribution because in N minus one + + + align:start position:0% +distribution because in N minus one +first statistics we are assuming that we + + align:start position:0% +first statistics we are assuming that we + + + align:start position:0% +first statistics we are assuming that we +know the oh we needed to know + + align:start position:0% +know the oh we needed to know + + + align:start position:0% +know the oh we needed to know +but the seller didn't need to know cuz + + align:start position:0% +but the seller didn't need to know cuz + + + align:start position:0% +but the seller didn't need to know cuz +the seller is not setting a price what + + align:start position:0% +the seller is not setting a price what + + + align:start position:0% +the seller is not setting a price what +is the seller + + align:start position:0% +is the seller + + + align:start position:0% +is the seller +doing seller's just auctioning it off + + align:start position:0% +doing seller's just auctioning it off + + + align:start position:0% +doing seller's just auctioning it off +right so we needed to know in order to + + align:start position:0% +right so we needed to know in order to + + + align:start position:0% +right so we needed to know in order to +calculate the expected profit um and but + + align:start position:0% +calculate the expected profit um and but + + + align:start position:0% +calculate the expected profit um and but +yeah but he didn't need to know I + + align:start position:0% +yeah but he didn't need to know I + + + align:start position:0% +yeah but he didn't need to know I +thought the seller is doing disc + + align:start position:0% +thought the seller is doing disc + + + align:start position:0% +thought the seller is doing disc +competitions to see with options that + + align:start position:0% +competitions to see with options that + + + align:start position:0% +competitions to see with options that +are op not if if the seller wants to do + + align:start position:0% +are op not if if the seller wants to do + + + align:start position:0% +are op not if if the seller wants to do +this calculation then the seller would + + align:start position:0% +this calculation then the seller would + + + align:start position:0% +this calculation then the seller would +would have to know in both cases + + align:start position:0% +would have to know in both cases + + + align:start position:0% +would have to know in both cases +absolutely yep yep you're right no I'm + + align:start position:0% +absolutely yep yep you're right no I'm + + + align:start position:0% +absolutely yep yep you're right no I'm +glad for for that clarification yep to + + align:start position:0% +glad for for that clarification yep to + + + align:start position:0% +glad for for that clarification yep to +choose but if he gets it home then + + align:start position:0% +choose but if he gets it home then + + + align:start position:0% +choose but if he gets it home then +just maybe just chosen the WR mechanism + + align:start position:0% +just maybe just chosen the WR mechanism + + + align:start position:0% +just maybe just chosen the WR mechanism +but has chosen the wrong price you just + + align:start position:0% +but has chosen the wrong price you just + + + align:start position:0% +but has chosen the wrong price you just +need to know to choose the scope error + + align:start position:0% +need to know to choose the scope error + + + align:start position:0% +need to know to choose the scope error +less bad you actually you have to know + + align:start position:0% +less bad you actually you have to know + + + align:start position:0% +less bad you actually you have to know +very + + align:start position:0% +very + + + align:start position:0% +very +specifically then you can show that + + align:start position:0% +specifically then you can show that + + + align:start position:0% +specifically then you can show that +the pro for example that the two + + align:start position:0% +the pro for example that the two + + + align:start position:0% +the pro for example that the two +distribution was uniform from 0 to two + + align:start position:0% +distribution was uniform from 0 to two + + + align:start position:0% +distribution was uniform from 0 to two +and you think it's from0 to one you're + + align:start position:0% +and you think it's from0 to one you're + + + align:start position:0% +and you think it's from0 to one you're +going to do your comparison under the + + align:start position:0% +going to do your comparison under the + + + align:start position:0% +going to do your comparison under the +same models you're still probably going + + align:start position:0% +same models you're still probably going + + + align:start position:0% +same models you're still probably going +to still roughly going to tell you when + + align:start position:0% +to still roughly going to tell you when + + + align:start position:0% +to still roughly going to tell you when +you're going + + align:start position:0% +you're going + + + align:start position:0% +you're going +to to shoot go for option versus fixed + + align:start position:0% +to to shoot go for option versus fixed + + + align:start position:0% +to to shoot go for option versus fixed +price the number of the end is going to + + align:start position:0% +price the number of the end is going to + + + align:start position:0% +price the number of the end is going to +change the critical end but that's for + + align:start position:0% +change the critical end but that's for + + + align:start position:0% +change the critical end but that's for +most ends you're still going to get the + + align:start position:0% +most ends you're still going to get the + + + align:start position:0% +most ends you're still going to get the +right choice but then if you go for a + + align:start position:0% +right choice but then if you go for a + + + align:start position:0% +right choice but then if you go for a +fixed price you get the price completely + + align:start position:0% +fixed price you get the price completely + + + align:start position:0% +fixed price you get the price completely +WR as if it turns out to be B option + + align:start position:0% +WR as if it turns out to be B option + + + align:start position:0% +WR as if it turns out to be B option +you you would have an issue because the + + align:start position:0% +you you would have an issue because the + + + align:start position:0% +you you would have an issue because the +5% y + + align:start position:0% +5% y + + + align:start position:0% +5% y +exactly was there another question yeah + + align:start position:0% +exactly was there another question yeah + + + align:start position:0% +exactly was there another question yeah +a quick clarification as well um so the + + align:start position:0% +a quick clarification as well um so the + + + align:start position:0% +a quick clarification as well um so the +the um I can go back if yeah don't mind + + align:start position:0% +the um I can go back if yeah don't mind + + + align:start position:0% +the um I can go back if yeah don't mind +going back to the equation or option is + + align:start position:0% +going back to the equation or option is + + + align:start position:0% +going back to the equation or option is +how Universal is that is that model so + + align:start position:0% +how Universal is that is that model so + + + align:start position:0% +how Universal is that is that model so +it so uh in order to compute the + + align:start position:0% +it so uh in order to compute the + + + align:start position:0% +it so uh in order to compute the +expected profit from the the auction I + + align:start position:0% +expected profit from the the auction I + + + align:start position:0% +expected profit from the the auction I +had to make an assumption about the + + align:start position:0% +had to make an assumption about the + + + align:start position:0% +had to make an assumption about the +distribution of valuations and keep in + + align:start position:0% +distribution of valuations and keep in + + + align:start position:0% +distribution of valuations and keep in +mind I also made an assumption that + + align:start position:0% +mind I also made an assumption that + + + align:start position:0% +mind I also made an assumption that +those valuations were + + align:start position:0% +those valuations were + + + align:start position:0% +those valuations were +independent so there are lots of cases + + align:start position:0% +independent so there are lots of cases + + + align:start position:0% +independent so there are lots of cases +in an auction model where you wouldn't + + align:start position:0% +in an auction model where you wouldn't + + + align:start position:0% +in an auction model where you wouldn't +want to to where you might be hesitant + + align:start position:0% +want to to where you might be hesitant + + + align:start position:0% +want to to where you might be hesitant +or might not be particularly confident + + align:start position:0% +or might not be particularly confident + + + align:start position:0% +or might not be particularly confident +in the distribution of the the uh + + align:start position:0% +in the distribution of the the uh + + + align:start position:0% +in the distribution of the the uh +valuations but in particular you + + align:start position:0% +valuations but in particular you + + + align:start position:0% +valuations but in particular you +wouldn't want to make the assumption + + align:start position:0% +wouldn't want to make the assumption + + + align:start position:0% +wouldn't want to make the assumption +that the valuations were + + align:start position:0% +that the valuations were + + + align:start position:0% +that the valuations were +independent um that's the most common + + align:start position:0% +independent um that's the most common + + + align:start position:0% +independent um that's the most common +and Lees in reality in in some in some + + align:start position:0% +and Lees in reality in in some in some + + + align:start position:0% +and Lees in reality in in some in some +auctions it's that's a reasonable + + align:start position:0% +auctions it's that's a reasonable + + + align:start position:0% +auctions it's that's a reasonable +assumption and in other auctions it's + + align:start position:0% +assumption and in other auctions it's + + + align:start position:0% +assumption and in other auctions it's +just not a reasonable assumption yeah so + + align:start position:0% +just not a reasonable assumption yeah so + + + align:start position:0% +just not a reasonable assumption yeah so +so anyhow it's um I would say it's this + + align:start position:0% +so anyhow it's um I would say it's this + + + align:start position:0% +so anyhow it's um I would say it's this +is a somewhat General model but but not + + align:start position:0% +is a somewhat General model but but not + + + align:start position:0% +is a somewhat General model but but not +completely General it's not going to be + + align:start position:0% +completely General it's not going to be + + + align:start position:0% +completely General it's not going to be +a good and the other thing is that we + + align:start position:0% +a good and the other thing is that we + + + align:start position:0% +a good and the other thing is that we +ruled out things + + align:start position:0% +ruled out things + + + align:start position:0% +ruled out things +like um we ruled out being able to + + align:start position:0% +like um we ruled out being able to + + + align:start position:0% +like um we ruled out being able to +bargain over the posted price + + align:start position:0% +bargain over the posted price + + + align:start position:0% +bargain over the posted price +we ruled that out completely we ruled + + align:start position:0% +we ruled that out completely we ruled + + + align:start position:0% +we ruled that out completely we ruled +out setting um a reserve price in the + + align:start position:0% +out setting um a reserve price in the + + + align:start position:0% +out setting um a reserve price in the +auction and not selling if if you're + + align:start position:0% +auction and not selling if if you're + + + align:start position:0% +auction and not selling if if you're +below that reserve price so you know + + align:start position:0% +below that reserve price so you know + + + align:start position:0% +below that reserve price so you know +there were certain things we ruled out + + align:start position:0% +there were certain things we ruled out + + + align:start position:0% +there were certain things we ruled out +just to simplify the model Yep this is + + align:start position:0% +just to simplify the model Yep this is + + + align:start position:0% +just to simplify the model Yep this is +this English auction D Auction so + + align:start position:0% +this English auction D Auction so + + + align:start position:0% +this English auction D Auction so +there's actually sort of a very famous + + align:start position:0% +there's actually sort of a very famous + + + align:start position:0% +there's actually sort of a very famous +theorem in auction theory that says that + + align:start position:0% +theorem in auction theory that says that + + + align:start position:0% +theorem in auction theory that says that +um in some kind of limited sense + + align:start position:0% +um in some kind of limited sense + + + align:start position:0% +um in some kind of limited sense +all standard auction mechanisms are + + align:start position:0% +all standard auction mechanisms are + + + align:start position:0% +all standard auction mechanisms are +equivalent okay and so that doesn't that + + align:start position:0% +equivalent okay and so that doesn't that + + + align:start position:0% +equivalent okay and so that doesn't that +doesn't mean they're equivalent in all + + align:start position:0% +doesn't mean they're equivalent in all + + + align:start position:0% +doesn't mean they're equivalent in all +ways but it means like the expected + + align:start position:0% +ways but it means like the expected + + + align:start position:0% +ways but it means like the expected +Revenue that the seller gets from a a + + align:start position:0% +Revenue that the seller gets from a a + + + align:start position:0% +Revenue that the seller gets from a a +whole big set of standard auctions + + align:start position:0% +whole big set of standard auctions + + + align:start position:0% +whole big set of standard auctions +regardless of what mechanism and the + + align:start position:0% +regardless of what mechanism and the + + + align:start position:0% +regardless of what mechanism and the +English and the Dutch auction are in + + align:start position:0% +English and the Dutch auction are in + + + align:start position:0% +English and the Dutch auction are in +that Set uh the their the expected + + align:start position:0% +that Set uh the their the expected + + + align:start position:0% +that Set uh the their the expected +revenue is going to be the same so yeah + + align:start position:0% +revenue is going to be the same so yeah + + + align:start position:0% +revenue is going to be the same so yeah +the that's it's called not surprisingly + + align:start position:0% +the that's it's called not surprisingly + + + align:start position:0% +the that's it's called not surprisingly +the revenue equivalence theorem so + + align:start position:0% +the revenue equivalence theorem so + + + align:start position:0% +the revenue equivalence theorem so +yes I'm just wondering under what + + align:start position:0% +yes I'm just wondering under what + + + align:start position:0% +yes I'm just wondering under what +conditions can we assume Independence + + align:start position:0% +conditions can we assume Independence + + + align:start position:0% +conditions can we assume Independence +because it seems to me that the prices + + align:start position:0% +because it seems to me that the prices + + + align:start position:0% +because it seems to me that the prices +that one person might offer will be + + align:start position:0% +that one person might offer will be + + + align:start position:0% +that one person might offer will be +conditional unlik the other people are + + align:start position:0% +conditional unlik the other people are + + + align:start position:0% +conditional unlik the other people are +yeah no it's a good question so the the + + align:start position:0% +yeah no it's a good question so the the + + + align:start position:0% +yeah no it's a good question so the the +question is under what circumstances + + align:start position:0% +question is under what circumstances + + + align:start position:0% +question is under what circumstances +does Independence make sense so let's + + align:start position:0% +does Independence make sense so let's + + + align:start position:0% +does Independence make sense so let's +suppose I'm auctioning off a bottle of + + align:start position:0% +suppose I'm auctioning off a bottle of + + + align:start position:0% +suppose I'm auctioning off a bottle of +wine and it's a bottle of wine that the + + align:start position:0% +wine and it's a bottle of wine that the + + + align:start position:0% +wine and it's a bottle of wine that the +person who buys it is going to drink + + align:start position:0% +person who buys it is going to drink + + + align:start position:0% +person who buys it is going to drink +okay so not likely to resell it not + + align:start position:0% +okay so not likely to resell it not + + + align:start position:0% +okay so not likely to resell it not +likely to you know sort of do anything + + align:start position:0% +likely to you know sort of do anything + + + align:start position:0% +likely to you know sort of do anything +else with uh do anything else with it + + align:start position:0% +else with uh do anything else with it + + + align:start position:0% +else with uh do anything else with it +but just drink it well then we can think + + align:start position:0% +but just drink it well then we can think + + + align:start position:0% +but just drink it well then we can think +the valuation that those buyers are are + + align:start position:0% +the valuation that those buyers are are + + + align:start position:0% +the valuation that those buyers are are +going to get from that bottle of wine + + align:start position:0% +going to get from that bottle of wine + + + align:start position:0% +going to get from that bottle of wine +can can reasonably be assumed to be + + align:start position:0% +can can reasonably be assumed to be + + + align:start position:0% +can can reasonably be assumed to be +independent Okay C + + align:start position:0% +independent Okay C + + + align:start position:0% +independent Okay C +ass that's right and you know sort of + + align:start position:0% +ass that's right and you know sort of + + + align:start position:0% +ass that's right and you know sort of +the the the enjoyment you get from + + align:start position:0% +the the the enjoyment you get from + + + align:start position:0% +the the the enjoyment you get from +drinking that bottle of wine does + + align:start position:0% +drinking that bottle of wine does + + + align:start position:0% +drinking that bottle of wine does +doesn't really uh have anything to do + + align:start position:0% +doesn't really uh have anything to do + + + align:start position:0% +doesn't really uh have anything to do +with the enjoyment I would get from + + align:start position:0% +with the enjoyment I would get from + + + align:start position:0% +with the enjoyment I would get from +drinking that bottle of wine so if you + + align:start position:0% +drinking that bottle of wine so if you + + + align:start position:0% +drinking that bottle of wine so if you +had envelopes for example for the price + + align:start position:0% +had envelopes for example for the price + + + align:start position:0% +had envelopes for example for the price +then they're independent I don't know + + align:start position:0% +then they're independent I don't know + + + align:start position:0% +then they're independent I don't know +what other people are writing and I just + + align:start position:0% +what other people are writing and I just + + + align:start position:0% +what other people are writing and I just +well no no no so that that's so the + + align:start position:0% +well no no no so that that's so the + + + align:start position:0% +well no no no so that that's so the +you're talking about the dependence in + + align:start position:0% +you're talking about the dependence in + + + align:start position:0% +you're talking about the dependence in +bidding as opposed to valuations and I + + align:start position:0% +bidding as opposed to valuations and I + + + align:start position:0% +bidding as opposed to valuations and I +kind of glossed over the distinction + + align:start position:0% +kind of glossed over the distinction + + + align:start position:0% +kind of glossed over the distinction +between a bid and a valuation here + + align:start position:0% +between a bid and a valuation here + + + align:start position:0% +between a bid and a valuation here +that's one reason why I use the English + + align:start position:0% +that's one reason why I use the English + + + align:start position:0% +that's one reason why I use the English +auction mechanism uh because in fact the + + align:start position:0% +auction mechanism uh because in fact the + + + align:start position:0% +auction mechanism uh because in fact the +optimal thing for bid we didn't talk + + align:start position:0% +optimal thing for bid we didn't talk + + + align:start position:0% +optimal thing for bid we didn't talk +about uh what the optimal thing for + + align:start position:0% +about uh what the optimal thing for + + + align:start position:0% +about uh what the optimal thing for +biders to do but in the English auction + + align:start position:0% +biders to do but in the English auction + + + align:start position:0% +biders to do but in the English auction +the optimal thing for them to do is to + + align:start position:0% +the optimal thing for them to do is to + + + align:start position:0% +the optimal thing for them to do is to +bid their valuations in some auctions + + align:start position:0% +bid their valuations in some auctions + + + align:start position:0% +bid their valuations in some auctions +the optimal thing to do is not to bid + + align:start position:0% +the optimal thing to do is not to bid + + + align:start position:0% +the optimal thing to do is not to bid +your valuation so there is a distinction + + align:start position:0% +your valuation so there is a distinction + + + align:start position:0% +your valuation so there is a distinction +between a bid and a valuation here we + + align:start position:0% +between a bid and a valuation here we + + + align:start position:0% +between a bid and a valuation here we +didn't have to worry about it because of + + align:start position:0% +didn't have to worry about it because of + + + align:start position:0% +didn't have to worry about it because of +the mechanism I + + align:start position:0% +the mechanism I + + + align:start position:0% +the mechanism I +chose did you have a question no I just + + align:start position:0% +chose did you have a question no I just + + + align:start position:0% +chose did you have a question no I just +think if you have enough large enough + + align:start position:0% +think if you have enough large enough + + + align:start position:0% +think if you have enough large enough +end sort of dependence in most cases you + + align:start position:0% +end sort of dependence in most cases you + + + align:start position:0% +end sort of dependence in most cases you +have like three people and there from + + align:start position:0% +have like three people and there from + + + align:start position:0% +have like three people and there from +the same well no not necessar no not + + align:start position:0% +the same well no not necessar no not + + + align:start position:0% +the same well no not necessar no not +necessarily I mean I if if for instance + + align:start position:0% +necessarily I mean I if if for instance + + + align:start position:0% +necessarily I mean I if if for instance +um so let's think of a case where the + + align:start position:0% +um so let's think of a case where the + + + align:start position:0% +um so let's think of a case where the +government is auctioning off the rights + + align:start position:0% +government is auctioning off the rights + + + align:start position:0% +government is auctioning off the rights +to cut + + align:start position:0% +to cut + + + align:start position:0% +to cut +down timber in a tract of land so they + + align:start position:0% +down timber in a tract of land so they + + + align:start position:0% +down timber in a tract of land so they +have public lands and they're auctioning + + align:start position:0% +have public lands and they're auctioning + + + align:start position:0% +have public lands and they're auctioning +and there's sort of a bunch of firms who + + align:start position:0% +and there's sort of a bunch of firms who + + + align:start position:0% +and there's sort of a bunch of firms who +are going to go and sort of cut down + + align:start position:0% +are going to go and sort of cut down + + + align:start position:0% +are going to go and sort of cut down +Timber and and Mill it and sell it um so + + align:start position:0% +Timber and and Mill it and sell it um so + + + align:start position:0% +Timber and and Mill it and sell it um so +for instance my + + align:start position:0% +for instance my + + + align:start position:0% +for instance my +valuation I mean this is kind of a more + + align:start position:0% +valuation I mean this is kind of a more + + + align:start position:0% +valuation I mean this is kind of a more +complicated model but in in my valuation + + align:start position:0% +complicated model but in in my valuation + + + align:start position:0% +complicated model but in in my valuation +should depend on everyone else's + + align:start position:0% +should depend on everyone else's + + + align:start position:0% +should depend on everyone else's +valuations if I'm you know one of the + + align:start position:0% +valuations if I'm you know one of the + + + align:start position:0% +valuations if I'm you know one of the +potential biders there because there's + + align:start position:0% +potential biders there because there's + + + align:start position:0% +potential biders there because there's +information in all of their valuations + + align:start position:0% +information in all of their valuations + + + align:start position:0% +information in all of their valuations +about how much Timber is actually you + + align:start position:0% +about how much Timber is actually you + + + align:start position:0% +about how much Timber is actually you +know can be cut down and mil and and + + align:start position:0% +know can be cut down and mil and and + + + align:start position:0% +know can be cut down and mil and and +what its market value is this is like + + align:start position:0% +what its market value is this is like + + + align:start position:0% +what its market value is this is like +sort of a complicated um there's a + + align:start position:0% +sort of a complicated um there's a + + + align:start position:0% +sort of a complicated um there's a +complicated question of you know how to + + align:start position:0% +complicated question of you know how to + + + align:start position:0% +complicated question of you know how to +estimate the valuation and so uh your + + align:start position:0% +estimate the valuation and so uh your + + + align:start position:0% +estimate the valuation and so uh your +valuation is going to be um relevant + + align:start position:0% +valuation is going to be um relevant + + + align:start position:0% +valuation is going to be um relevant +information for me as + + align:start position:0% +information for me as + + + align:start position:0% +information for me as +well in a case like + + align:start position:0% +well in a case like + + + align:start position:0% +well in a case like +that okay so this just gives you a a a + + align:start position:0% +that okay so this just gives you a a a + + + align:start position:0% +that okay so this just gives you a a a +little taste of auction Theory I I + + align:start position:0% +little taste of auction Theory I I + + + align:start position:0% +little taste of auction Theory I I +happen to like auctions and I hope you + + align:start position:0% +happen to like auctions and I hope you + + + align:start position:0% +happen to like auctions and I hope you +thought it was uh interesting uh but + + align:start position:0% +thought it was uh interesting uh but + + + align:start position:0% +thought it was uh interesting uh but +there's sort of uh lots of other um + + align:start position:0% +there's sort of uh lots of other um + + + align:start position:0% +there's sort of uh lots of other um +interesting and and sometimes + + align:start position:0% +interesting and and sometimes + + + align:start position:0% +interesting and and sometimes +complicated economic issues having to do + + align:start position:0% +complicated economic issues having to do + + + align:start position:0% +complicated economic issues having to do +with uh auctions and auction Theory and + + align:start position:0% +with uh auctions and auction Theory and + + + align:start position:0% +with uh auctions and auction Theory and +uh um you know but it's also a nice + + align:start position:0% +uh um you know but it's also a nice + + + align:start position:0% +uh um you know but it's also a nice +illustration to show you that um order + + align:start position:0% +illustration to show you that um order + + + align:start position:0% +illustration to show you that um order +statistics you know are important in the + + align:start position:0% +statistics you know are important in the + + + align:start position:0% +statistics you know are important in the +real world too so okay so let's see I + + align:start position:0% +real world too so okay so let's see I + + + align:start position:0% +real world too so okay so let's see I +still have a couple other things to say + + align:start position:0% +still have a couple other things to say + + + align:start position:0% +still have a couple other things to say +about auctions that will take us to the + + align:start position:0% +about auctions that will take us to the + + + align:start position:0% +about auctions that will take us to the +end of the lecture so as I mentioned + + align:start position:0% +end of the lecture so as I mentioned + + + align:start position:0% +end of the lecture so as I mentioned +earlier eBay which was founded in 1995 + + align:start position:0% +earlier eBay which was founded in 1995 + + + align:start position:0% +earlier eBay which was founded in 1995 +as an online auction site + + align:start position:0% +as an online auction site + + + align:start position:0% +as an online auction site +exclusively uh now only has about 15% of + + align:start position:0% +exclusively uh now only has about 15% of + + + align:start position:0% +exclusively uh now only has about 15% of +its listings in + + align:start position:0% +its listings in + + + align:start position:0% +its listings in +auctions okay so the vast majority of + + align:start position:0% +auctions okay so the vast majority of + + + align:start position:0% +auctions okay so the vast majority of +its listings are Buy It Now listings + + align:start position:0% +its listings are Buy It Now listings + + + align:start position:0% +its listings are Buy It Now listings +there's also some um kind of best offer + + align:start position:0% +there's also some um kind of best offer + + + align:start position:0% +there's also some um kind of best offer +listings which are kind of a hybrid but + + align:start position:0% +listings which are kind of a hybrid but + + + align:start position:0% +listings which are kind of a hybrid but +the the um the number of pure the + + align:start position:0% +the the um the number of pure the + + + align:start position:0% +the the um the number of pure the +percentage of pure auction listings is + + align:start position:0% +percentage of pure auction listings is + + + align:start position:0% +percentage of pure auction listings is +down to about 15% maybe lower by now 15% + + align:start position:0% +down to about 15% maybe lower by now 15% + + + align:start position:0% +down to about 15% maybe lower by now 15% +by sort of the the last time I saw the + + align:start position:0% +by sort of the the last time I saw the + + + align:start position:0% +by sort of the the last time I saw the +data okay so here's a graph illustrating + + align:start position:0% +data okay so here's a graph illustrating + + + align:start position:0% +data okay so here's a graph illustrating +that point so this is taken from an NBR + + align:start position:0% +that point so this is taken from an NBR + + + align:start position:0% +that point so this is taken from an NBR +working paper um sort of mentioned up + + align:start position:0% +working paper um sort of mentioned up + + + align:start position:0% +working paper um sort of mentioned up +above and what they did is looked at so + + align:start position:0% +above and what they did is looked at so + + + align:start position:0% +above and what they did is looked at so +the darker line is the share of active + + align:start position:0% +the darker line is the share of active + + + align:start position:0% +the darker line is the share of active +listings on eBay uh as that are uh + + align:start position:0% +listings on eBay uh as that are uh + + + align:start position:0% +listings on eBay uh as that are uh +listed in auction format and you can see + + align:start position:0% +listed in auction format and you can see + + + align:start position:0% +listed in auction format and you can see +as recently as January of + + align:start position:0% +as recently as January of + + + align:start position:0% +as recently as January of +2003 uh that was almost 100% of active + + align:start position:0% +2003 uh that was almost 100% of active + + + align:start position:0% +2003 uh that was almost 100% of active +listings on eBay were auctions + + align:start position:0% +listings on eBay were auctions + + + align:start position:0% +listings on eBay were auctions +and there have been some sort of changes + + align:start position:0% +and there have been some sort of changes + + + align:start position:0% +and there have been some sort of changes +in the rules the listing rules in eBay + + align:start position:0% +in the rules the listing rules in eBay + + + align:start position:0% +in the rules the listing rules in eBay +over the years but there has also been + + align:start position:0% +over the years but there has also been + + + align:start position:0% +over the years but there has also been +this sort of gradual decline over this + + align:start position:0% +this sort of gradual decline over this + + + align:start position:0% +this sort of gradual decline over this +period of um of auction listings so now + + align:start position:0% +period of um of auction listings so now + + + align:start position:0% +period of um of auction listings so now +we're down to like I said about 15% and + + align:start position:0% +we're down to like I said about 15% and + + + align:start position:0% +we're down to like I said about 15% and +maybe even lower of active listings or + + align:start position:0% +maybe even lower of active listings or + + + align:start position:0% +maybe even lower of active listings or +auction + + align:start position:0% +auction + + + align:start position:0% +auction +listings was uh January of 09 where they + + align:start position:0% +listings was uh January of 09 where they + + + align:start position:0% +listings was uh January of 09 where they +kind of reevaluated their structure so I + + align:start position:0% +kind of reevaluated their structure so I + + + align:start position:0% +kind of reevaluated their structure so I +should I should have I should have + + align:start position:0% +should I should have I should have + + + align:start position:0% +should I should have I should have +looked that up to double check before I + + align:start position:0% +looked that up to double check before I + + + align:start position:0% +looked that up to double check before I +came in today um there was some kind of + + align:start position:0% +came in today um there was some kind of + + + align:start position:0% +came in today um there was some kind of +a yeah there was some kind of a rule + + align:start position:0% +a yeah there was some kind of a rule + + + align:start position:0% +a yeah there was some kind of a rule +change that occurred there maybe it was + + align:start position:0% +change that occurred there maybe it was + + + align:start position:0% +change that occurred there maybe it was +sort of a um a difference in the the uh + + align:start position:0% +sort of a um a difference in the the uh + + + align:start position:0% +sort of a um a difference in the the uh +fees that they charge for different + + align:start position:0% +fees that they charge for different + + + align:start position:0% +fees that they charge for different +types of listings and I knew that at one + + align:start position:0% +types of listings and I knew that at one + + + align:start position:0% +types of listings and I knew that at one +point and I forgot to look it up but + + align:start position:0% +point and I forgot to look it up but + + + align:start position:0% +point and I forgot to look it up but +yeah final crisis pardon me it h yeah + + align:start position:0% +yeah final crisis pardon me it h yeah + + + align:start position:0% +yeah final crisis pardon me it h yeah +although I mean this is keep in mind + + align:start position:0% +although I mean this is keep in mind + + + align:start position:0% +although I mean this is keep in mind +this is kind of this is probably a + + align:start position:0% +this is kind of this is probably a + + + align:start position:0% +this is kind of this is probably a +decision that that the + + align:start position:0% +decision that that the + + + align:start position:0% +decision that that the +macroeconomic uh variables are not going + + align:start position:0% +macroeconomic uh variables are not going + + + align:start position:0% +macroeconomic uh variables are not going +to have a huge effect on you're just a + + align:start position:0% +to have a huge effect on you're just a + + + align:start position:0% +to have a huge effect on you're just a +seller and you're like auction or posted + + align:start position:0% +seller and you're like auction or posted + + + align:start position:0% +seller and you're like auction or posted +price so this isn't not this is just the + + align:start position:0% +price so this isn't not this is just the + + + align:start position:0% +price so this isn't not this is just the +fraction of the listings that are + + align:start position:0% +fraction of the listings that are + + + align:start position:0% +fraction of the listings that are +auction versus posted + + align:start position:0% +auction versus posted + + + align:start position:0% +auction versus posted +price okay so it's not it's not like the + + align:start position:0% +price okay so it's not it's not like the + + + align:start position:0% +price okay so it's not it's not like the +number of listings plummeted it's the + + align:start position:0% +number of listings plummeted it's the + + + align:start position:0% +number of listings plummeted it's the +the fraction that was uh auctions versus + + align:start position:0% +the fraction that was uh auctions versus + + + align:start position:0% +the fraction that was uh auctions versus +posted price plummeted + + align:start position:0% +posted price plummeted + + + align:start position:0% +posted price plummeted +okay um so I said that says + + align:start position:0% +okay um so I said that says + + + align:start position:0% +okay um so I said that says +itop in 2008 coincides with the decision + + align:start position:0% +itop in 2008 coincides with the decision + + + align:start position:0% +itop in 2008 coincides with the decision +september8 to allow good till cancel oh + + align:start position:0% +september8 to allow good till cancel oh + + + align:start position:0% +september8 to allow good till cancel oh +great thank you + + align:start position:0% +great thank you + + + align:start position:0% +great thank you +okay okay and here's another graph that + + align:start position:0% +okay okay and here's another graph that + + + align:start position:0% +okay okay and here's another graph that +illustrates kind of a similar phenomenon + + align:start position:0% +illustrates kind of a similar phenomenon + + + align:start position:0% +illustrates kind of a similar phenomenon +uh using different data so this from the + + align:start position:0% +uh using different data so this from the + + + align:start position:0% +uh using different data so this from the +same + + align:start position:0% +same + + + align:start position:0% +same +paper and what they did is they used + + align:start position:0% +paper and what they did is they used + + + align:start position:0% +paper and what they did is they used +Google Trends data has anyone used + + align:start position:0% +Google Trends data has anyone used + + + align:start position:0% +Google Trends data has anyone used +Google Trends data what did you use + + align:start position:0% +Google Trends data what did you use + + + align:start position:0% +Google Trends data what did you use +Google Trends data for just look up + + align:start position:0% +Google Trends data for just look up + + + align:start position:0% +Google Trends data for just look up +different companies see how they change + + align:start position:0% +different companies see how they change + + + align:start position:0% +different companies see how they change +Rel term popular okay so um so for those + + align:start position:0% +Rel term popular okay so um so for those + + + align:start position:0% +Rel term popular okay so um so for those +of you who are not familiar with Google + + align:start position:0% +of you who are not familiar with Google + + + align:start position:0% +of you who are not familiar with Google +Trends Google Trends is a sort of a free + + align:start position:0% +Trends Google Trends is a sort of a free + + + align:start position:0% +Trends Google Trends is a sort of a free +facility that Google makes available to + + align:start position:0% +facility that Google makes available to + + + align:start position:0% +facility that Google makes available to +anyone who wants to use it and you can + + align:start position:0% +anyone who wants to use it and you can + + + align:start position:0% +anyone who wants to use it and you can +go on uh to Google Trends and download + + align:start position:0% +go on uh to Google Trends and download + + + align:start position:0% +go on uh to Google Trends and download +data on the number of searches that have + + align:start position:0% +data on the number of searches that have + + + align:start position:0% +data on the number of searches that have +been done on particular Search terms and + + align:start position:0% +been done on particular Search terms and + + + align:start position:0% +been done on particular Search terms and +you can download the data over time + + align:start position:0% +you can download the data over time + + + align:start position:0% +you can download the data over time +which is what they did here so they were + + align:start position:0% +which is what they did here so they were + + + align:start position:0% +which is what they did here so they were +looking at the search term online + + align:start position:0% +looking at the search term online + + + align:start position:0% +looking at the search term online +auction versus the search term online + + align:start position:0% +auction versus the search term online + + + align:start position:0% +auction versus the search term online +prices and they saw these sort of Trends + + align:start position:0% +prices and they saw these sort of Trends + + + align:start position:0% +prices and they saw these sort of Trends +uh you know over time changing uh you + + align:start position:0% +uh you know over time changing uh you + + + align:start position:0% +uh you know over time changing uh you +can also use Google Trends to look at + + align:start position:0% +can also use Google Trends to look at + + + align:start position:0% +can also use Google Trends to look at +Google searches uh geographically so + + align:start position:0% +Google searches uh geographically so + + + align:start position:0% +Google searches uh geographically so +they they can give you you can sort of + + align:start position:0% +they they can give you you can sort of + + + align:start position:0% +they they can give you you can sort of +ask them to give you data on Google + + align:start position:0% +ask them to give you data on Google + + + align:start position:0% +ask them to give you data on Google +searches um you know sort of by region + + align:start position:0% +searches um you know sort of by region + + + align:start position:0% +searches um you know sort of by region +or by state or by City And so this this + + align:start position:0% +or by state or by City And so this this + + + align:start position:0% +or by state or by City And so this this +is actually sort of an aside but Google + + align:start position:0% +is actually sort of an aside but Google + + + align:start position:0% +is actually sort of an aside but Google +Trends can be a very useful tool uh for + + align:start position:0% +Trends can be a very useful tool uh for + + + align:start position:0% +Trends can be a very useful tool uh for +you know sort of gathering uh data for + + align:start position:0% +you know sort of gathering uh data for + + + align:start position:0% +you know sort of gathering uh data for +various purposes so it basically just + + align:start position:0% +various purposes so it basically just + + + align:start position:0% +various purposes so it basically just +tells you how popular Search terms on + + align:start position:0% +tells you how popular Search terms on + + + align:start position:0% +tells you how popular Search terms on +Google are okay so what they did is they + + align:start position:0% +Google are okay so what they did is they + + + align:start position:0% +Google are okay so what they did is they +downloaded Google Trends data on it and + + align:start position:0% +downloaded Google Trends data on it and + + + align:start position:0% +downloaded Google Trends data on it and +I should say also so that Google Trends + + align:start position:0% +I should say also so that Google Trends + + + align:start position:0% +I should say also so that Google Trends +doesn't give you the raw number of + + align:start position:0% +doesn't give you the raw number of + + + align:start position:0% +doesn't give you the raw number of +searches what they do is they give you + + align:start position:0% +searches what they do is they give you + + + align:start position:0% +searches what they do is they give you +some kind of a um I don't know a + + align:start position:0% +some kind of a um I don't know a + + + align:start position:0% +some kind of a um I don't know a +normalized or uh you know a search + + align:start position:0% +normalized or uh you know a search + + + align:start position:0% +normalized or uh you know a search +volume index I guess they call it + + align:start position:0% +volume index I guess they call it + + + align:start position:0% +volume index I guess they call it +okay um so what they did here is they + + align:start position:0% +okay um so what they did here is they + + + align:start position:0% +okay um so what they did here is they +got Google Trends data on two Search + + align:start position:0% +got Google Trends data on two Search + + + align:start position:0% +got Google Trends data on two Search +terms Online Auctions and online + + align:start position:0% +terms Online Auctions and online + + + align:start position:0% +terms Online Auctions and online +prices and um you can see that there has + + align:start position:0% +prices and um you can see that there has + + + align:start position:0% +prices and um you can see that there has +been this sort of decrease from uh the + + align:start position:0% +been this sort of decrease from uh the + + + align:start position:0% +been this sort of decrease from uh the +index high of around 90 to now uh down + + align:start position:0% +index high of around 90 to now uh down + + + align:start position:0% +index high of around 90 to now uh down +to around 20 for the um for the search + + align:start position:0% +to around 20 for the um for the search + + + align:start position:0% +to around 20 for the um for the search +term uh Online Auctions the search term + + align:start position:0% +term uh Online Auctions the search term + + + align:start position:0% +term uh Online Auctions the search term +uh online prices has you know has you + + align:start position:0% +uh online prices has you know has you + + + align:start position:0% +uh online prices has you know has you +know bounced around quite a bit but has + + align:start position:0% +know bounced around quite a bit but has + + + align:start position:0% +know bounced around quite a bit but has +maintained uh something like the same + + align:start position:0% +maintained uh something like the same + + + align:start position:0% +maintained uh something like the same +Google search volume okay so this is an + + align:start position:0% +Google search volume okay so this is an + + + align:start position:0% +Google search volume okay so this is an +indication that people are just they're + + align:start position:0% +indication that people are just they're + + + align:start position:0% +indication that people are just they're +as interested in online prices as they + + align:start position:0% +as interested in online prices as they + + + align:start position:0% +as interested in online prices as they +have been for a long time they're + + align:start position:0% +have been for a long time they're + + + align:start position:0% +have been for a long time they're +getting less interested in online + + align:start position:0% +getting less interested in online + + + align:start position:0% +getting less interested in online +auctions + + align:start position:0% +auctions + + + align:start position:0% +auctions +okay I would just be interested to see + + align:start position:0% +okay I would just be interested to see + + + align:start position:0% +okay I would just be interested to see +if we just aggregated the data by the + + align:start position:0% +if we just aggregated the data by the + + + align:start position:0% +if we just aggregated the data by the +type of goods how that would as well + + align:start position:0% +type of goods how that would as well + + + align:start position:0% +type of goods how that would as well +well strange strange that you mention + + align:start position:0% +well strange strange that you mention + + + align:start position:0% +well strange strange that you mention +that so um so what's going on okay um so + + align:start position:0% +that so um so what's going on okay um so + + + align:start position:0% +that so um so what's going on okay um so +we s we have a theory that we developed + + align:start position:0% +we s we have a theory that we developed + + + align:start position:0% +we s we have a theory that we developed +just a few minutes ago suggesting when a + + align:start position:0% +just a few minutes ago suggesting when a + + + align:start position:0% +just a few minutes ago suggesting when a +seller might prefer to sell an item with + + align:start position:0% +seller might prefer to sell an item with + + + align:start position:0% +seller might prefer to sell an item with +a posted price versus versus an auction + + align:start position:0% +a posted price versus versus an auction + + + align:start position:0% +a posted price versus versus an auction +and that theory is useful for thinking + + align:start position:0% +and that theory is useful for thinking + + + align:start position:0% +and that theory is useful for thinking +about you know information a symmetries + + align:start position:0% +about you know information a symmetries + + + align:start position:0% +about you know information a symmetries +but it was an incomplete theory in the + + align:start position:0% +but it was an incomplete theory in the + + + align:start position:0% +but it was an incomplete theory in the +sense that the model didn't include + + align:start position:0% +sense that the model didn't include + + + align:start position:0% +sense that the model didn't include +anything about transactions costs okay + + align:start position:0% +anything about transactions costs okay + + + align:start position:0% +anything about transactions costs okay +um and furthermore these eBay graphs + + align:start position:0% +um and furthermore these eBay graphs + + + align:start position:0% +um and furthermore these eBay graphs +suggest that something has been changing + + align:start position:0% +suggest that something has been changing + + + align:start position:0% +suggest that something has been changing +over time but that could be you know our + + align:start position:0% +over time but that could be you know our + + + align:start position:0% +over time but that could be you know our +Theory could sort of suggest what has + + align:start position:0% +Theory could sort of suggest what has + + + align:start position:0% +Theory could sort of suggest what has +been changing over time that that's + + align:start position:0% +been changing over time that that's + + + align:start position:0% +been changing over time that that's +driving these uh Trends + + align:start position:0% +driving these uh Trends + + + align:start position:0% +driving these uh Trends +okay so uh three broad hypotheses and I + + align:start position:0% +okay so uh three broad hypotheses and I + + + align:start position:0% +okay so uh three broad hypotheses and I +should say these um these these are sort + + align:start position:0% +should say these um these these are sort + + + align:start position:0% +should say these um these these are sort +of more or less discussed in the in the + + align:start position:0% +of more or less discussed in the in the + + + align:start position:0% +of more or less discussed in the in the +NBR um working paper that I mentioned um + + align:start position:0% +NBR um working paper that I mentioned um + + + align:start position:0% +NBR um working paper that I mentioned um +although actually they don't dis discuss + + align:start position:0% +although actually they don't dis discuss + + + align:start position:0% +although actually they don't dis discuss +three very much which I think is kind of + + align:start position:0% +three very much which I think is kind of + + + align:start position:0% +three very much which I think is kind of +an important hypothesis so um one + + align:start position:0% +an important hypothesis so um one + + + align:start position:0% +an important hypothesis so um one +hypothesis is that there has been a + + align:start position:0% +hypothesis is that there has been a + + + align:start position:0% +hypothesis is that there has been a +compositional shift of Sellers and types + + align:start position:0% +compositional shift of Sellers and types + + + align:start position:0% +compositional shift of Sellers and types +of products on eBay okay so it used to + + align:start position:0% +of products on eBay okay so it used to + + + align:start position:0% +of products on eBay okay so it used to +be that eBay was mostly used for + + align:start position:0% +be that eBay was mostly used for + + + align:start position:0% +be that eBay was mostly used for +memorabilia Collectibles antiques you + + align:start position:0% +memorabilia Collectibles antiques you + + + align:start position:0% +memorabilia Collectibles antiques you +know uh + + align:start position:0% +know uh + + + align:start position:0% +know uh +Estate Jewelry things like that and now + + align:start position:0% +Estate Jewelry things like that and now + + + align:start position:0% +Estate Jewelry things like that and now +it's being used mostly for iPhones or + + align:start position:0% +it's being used mostly for iPhones or + + + align:start position:0% +it's being used mostly for iPhones or +Xboxes or whatever okay and those + + align:start position:0% +Xboxes or whatever okay and those + + + align:start position:0% +Xboxes or whatever okay and those +products the sort of new mix of products + + align:start position:0% +products the sort of new mix of products + + + align:start position:0% +products the sort of new mix of products +is not a a bunch of products that where + + align:start position:0% +is not a a bunch of products that where + + + align:start position:0% +is not a a bunch of products that where +auction the auction mechanism makes + + align:start position:0% +auction the auction mechanism makes + + + align:start position:0% +auction the auction mechanism makes +sense basically could be that consumer + + align:start position:0% +sense basically could be that consumer + + + align:start position:0% +sense basically could be that consumer +tastes have changed Online Auctions are + + align:start position:0% +tastes have changed Online Auctions are + + + align:start position:0% +tastes have changed Online Auctions are +just not as fun as they used to be so + + align:start position:0% +just not as fun as they used to be so + + + align:start position:0% +just not as fun as they used to be so +like in the late 1990s everyone was just + + align:start position:0% +like in the late 1990s everyone was just + + + align:start position:0% +like in the late 1990s everyone was just +like hey I'm going to go on eBay and I'm + + align:start position:0% +like hey I'm going to go on eBay and I'm + + + align:start position:0% +like hey I'm going to go on eBay and I'm +going to buy something on auction and + + align:start position:0% +going to buy something on auction and + + + align:start position:0% +going to buy something on auction and +then you know the sort of novelty wears + + align:start position:0% +then you know the sort of novelty wears + + + align:start position:0% +then you know the sort of novelty wears +off and then you're like the + + align:start position:0% +off and then you're like the + + + align:start position:0% +off and then you're like the +transactions costs are killing me I'm + + align:start position:0% +transactions costs are killing me I'm + + + align:start position:0% +transactions costs are killing me I'm +sick of this so that's certainly my I + + align:start position:0% +sick of this so that's certainly my I + + + align:start position:0% +sick of this so that's certainly my I +can tell you from my uh you know + + align:start position:0% +can tell you from my uh you know + + + align:start position:0% +can tell you from my uh you know +experience that's that's what happened + + align:start position:0% +experience that's that's what happened + + + align:start position:0% +experience that's that's what happened +um and then also as was pointed out + + align:start position:0% +um and then also as was pointed out + + + align:start position:0% +um and then also as was pointed out +earlier the price Discovery benefits of + + align:start position:0% +earlier the price Discovery benefits of + + + align:start position:0% +earlier the price Discovery benefits of +auctions have declined over time okay so + + align:start position:0% +auctions have declined over time okay so + + + align:start position:0% +auctions have declined over time okay so +online search has made it easier to find + + align:start position:0% +online search has made it easier to find + + + align:start position:0% +online search has made it easier to find +prices for comp a items but eBay + + align:start position:0% +prices for comp a items but eBay + + + align:start position:0% +prices for comp a items but eBay +itself might have killed the market for + + align:start position:0% +itself might have killed the market for + + + align:start position:0% +itself might have killed the market for +online auctions because eBay has created + + align:start position:0% +online auctions because eBay has created + + + align:start position:0% +online auctions because eBay has created +thick National markets for lots of + + align:start position:0% +thick National markets for lots of + + + align:start position:0% +thick National markets for lots of +things that didn't exist before those + + align:start position:0% +things that didn't exist before those + + + align:start position:0% +things that didn't exist before those +thick National markets provide + + align:start position:0% +thick National markets provide + + + align:start position:0% +thick National markets provide +information on uh price and so now maybe + + align:start position:0% +information on uh price and so now maybe + + + align:start position:0% +information on uh price and so now maybe +you just you just go on eBay and you see + + align:start position:0% +you just you just go on eBay and you see + + + align:start position:0% +you just you just go on eBay and you see +oh what did this um this uh uh Liberty + + align:start position:0% +oh what did this um this uh uh Liberty + + + align:start position:0% +oh what did this um this uh uh Liberty +Head silver or um Liberty Head gold + + align:start position:0% +Head silver or um Liberty Head gold + + + align:start position:0% +Head silver or um Liberty Head gold +dollar from 1863 sell for on eBay okay + + align:start position:0% +dollar from 1863 sell for on eBay okay + + + align:start position:0% +dollar from 1863 sell for on eBay okay +well I got it you know I have like 20 + + align:start position:0% +well I got it you know I have like 20 + + + align:start position:0% +well I got it you know I have like 20 +auctions date on 20 auctions so now I + + align:start position:0% +auctions date on 20 auctions so now I + + + align:start position:0% +auctions date on 20 auctions so now I +know how to set my price okay so eBay + + align:start position:0% +know how to set my price okay so eBay + + + align:start position:0% +know how to set my price okay so eBay +may have may have sort of been + + align:start position:0% +may have may have sort of been + + + align:start position:0% +may have may have sort of been +victimized by its own success in some in + + align:start position:0% +victimized by its own success in some in + + + align:start position:0% +victimized by its own success in some in +some + + align:start position:0% +some + + + align:start position:0% +some +sense okay so um the the the paper does + + align:start position:0% +sense okay so um the the the paper does + + + align:start position:0% +sense okay so um the the the paper does +a little bit of this and let me just + + align:start position:0% +a little bit of this and let me just + + + align:start position:0% +a little bit of this and let me just +mention briefly um I won't go into any + + align:start position:0% +mention briefly um I won't go into any + + + align:start position:0% +mention briefly um I won't go into any +detail but what they can do what they've + + align:start position:0% +detail but what they can do what they've + + + align:start position:0% +detail but what they can do what they've +done the paper as they can decompose the + + align:start position:0% +done the paper as they can decompose the + + + align:start position:0% +done the paper as they can decompose the +shift over time from auction to posted + + align:start position:0% +shift over time from auction to posted + + + align:start position:0% +shift over time from auction to posted +Price look exactly as you were + + align:start position:0% +Price look exactly as you were + + + align:start position:0% +Price look exactly as you were +suggesting look at the different product + + align:start position:0% +suggesting look at the different product + + + align:start position:0% +suggesting look at the different product +categories um and look also at the + + align:start position:0% +categories um and look also at the + + + align:start position:0% +categories um and look also at the +experience of the typical seller because + + align:start position:0% +experience of the typical seller because + + + align:start position:0% +experience of the typical seller because +that lets you get it sort some of these + + align:start position:0% +that lets you get it sort some of these + + + align:start position:0% +that lets you get it sort some of these +informational questions like if the + + align:start position:0% +informational questions like if the + + + align:start position:0% +informational questions like if the +sellers that are selling on eBay are + + align:start position:0% +sellers that are selling on eBay are + + + align:start position:0% +sellers that are selling on eBay are +just much more experienced than the + + align:start position:0% +just much more experienced than the + + + align:start position:0% +just much more experienced than the +sellers that were on eBay 15 years ago + + align:start position:0% +sellers that were on eBay 15 years ago + + + align:start position:0% +sellers that were on eBay 15 years ago +uh then maybe they don't need the the + + align:start position:0% +uh then maybe they don't need the the + + + align:start position:0% +uh then maybe they don't need the the +sort of auction mechanism to tell them + + align:start position:0% +sort of auction mechanism to tell them + + + align:start position:0% +sort of auction mechanism to tell them +about the price distribution and what + + align:start position:0% +about the price distribution and what + + + align:start position:0% +about the price distribution and what +they found actually was that uh these + + align:start position:0% +they found actually was that uh these + + + align:start position:0% +they found actually was that uh these +explanations only account for a fairly + + align:start position:0% +explanations only account for a fairly + + + align:start position:0% +explanations only account for a fairly +small fraction of the shift and instead + + align:start position:0% +small fraction of the shift and instead + + + align:start position:0% +small fraction of the shift and instead +the returns to sellers uh using auctions + + align:start position:0% +the returns to sellers uh using auctions + + + align:start position:0% +the returns to sellers uh using auctions +have diminished okay and uh if you're uh + + align:start position:0% +have diminished okay and uh if you're uh + + + align:start position:0% +have diminished okay and uh if you're uh +interested um you can check it check + + align:start position:0% +interested um you can check it check + + + align:start position:0% +interested um you can check it check +that paper but um it's it's sort of a + + align:start position:0% +that paper but um it's it's sort of a + + + align:start position:0% +that paper but um it's it's sort of a +it's not a hard paper to read and it's + + align:start position:0% +it's not a hard paper to read and it's + + + align:start position:0% +it's not a hard paper to read and it's +sort of a nice illustration of how you + + align:start position:0% +sort of a nice illustration of how you + + + align:start position:0% +sort of a nice illustration of how you +can uh you know sort of take a data set + + align:start position:0% +can uh you know sort of take a data set + + + align:start position:0% +can uh you know sort of take a data set +and sort of decompose it to to answer + + align:start position:0% +and sort of decompose it to to answer + + + align:start position:0% +and sort of decompose it to to answer +different economic + + align:start position:0% +different economic + + + align:start position:0% +different economic +questions okay so okay we'll call it a + + align:start position:0% + + + + align:start position:0% + +day \ No newline at end of file diff --git a/4ql4kfIBMX8.txt b/4ql4kfIBMX8.txt new file mode 100644 index 0000000000000000000000000000000000000000..bbc9f545514cda2775810c39afaeec0d0a4dc7fb --- /dev/null +++ b/4ql4kfIBMX8.txt @@ -0,0 +1,4587 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu Okay so we've talked we've + + align:start position:0% +ocw.mit.edu Okay so we've talked we've + + + align:start position:0% +ocw.mit.edu Okay so we've talked we've +talked about value stream and we've + + align:start position:0% +talked about value stream and we've + + + align:start position:0% +talked about value stream and we've +talked about process maps in this module + + align:start position:0% +talked about process maps in this module + + + align:start position:0% +talked about process maps in this module +we're really doing just one thing which + + align:start position:0% +we're really doing just one thing which + + + align:start position:0% +we're really doing just one thing which +is to link those two together in what we + + align:start position:0% +is to link those two together in what we + + + align:start position:0% +is to link those two together in what we +call Value stream + + align:start position:0% +call Value stream + + + align:start position:0% +call Value stream +mapping + + align:start position:0% +mapping + + + align:start position:0% +mapping +okay and we're going + + align:start position:0% +okay and we're going + + + align:start position:0% +okay and we're going +to actually create a value stream map + + align:start position:0% +to actually create a value stream map + + + align:start position:0% +to actually create a value stream map +and look at some of we're going to + + align:start position:0% +and look at some of we're going to + + + align:start position:0% +and look at some of we're going to +demonstrate what some of these + + align:start position:0% +demonstrate what some of these + + + align:start position:0% +demonstrate what some of these +principles of analysis of the value + + align:start position:0% +principles of analysis of the value + + + align:start position:0% +principles of analysis of the value +stream map are and recognize some + + align:start position:0% +stream map are and recognize some + + + align:start position:0% +stream map are and recognize some +process Improvement using value stream + + align:start position:0% +process Improvement using value stream + + + align:start position:0% +process Improvement using value stream +mapping okay so this was this is the + + align:start position:0% +mapping okay so this was this is the + + + align:start position:0% +mapping okay so this was this is the +chart that's in the middle of your table + + align:start position:0% +chart that's in the middle of your table + + + align:start position:0% +chart that's in the middle of your table +so let's go with this as the Baseline + + align:start position:0% +so let's go with this as the Baseline + + + align:start position:0% +so let's go with this as the Baseline +chart and now the question is how can + + align:start position:0% +chart and now the question is how can + + + align:start position:0% +chart and now the question is how can +given that Sasha and Andy have a process + + align:start position:0% +given that Sasha and Andy have a process + + + align:start position:0% +given that Sasha and Andy have a process +map and they have the data how can we + + align:start position:0% +map and they have the data how can we + + + align:start position:0% +map and they have the data how can we +combine the data and the process map to + + align:start position:0% +combine the data and the process map to + + + align:start position:0% +combine the data and the process map to +figure out quantitatively where we need + + align:start position:0% +figure out quantitatively where we need + + + align:start position:0% +figure out quantitatively where we need +to focus for process Improvement so + + align:start position:0% +to focus for process Improvement so + + + align:start position:0% +to focus for process Improvement so +value stream mapping is a very + + align:start position:0% +value stream mapping is a very + + + align:start position:0% +value stream mapping is a very +quantitative activity it's going out and + + align:start position:0% +quantitative activity it's going out and + + + align:start position:0% +quantitative activity it's going out and +getting act we heard claudo say go see + + align:start position:0% +getting act we heard claudo say go see + + + align:start position:0% +getting act we heard claudo say go see +for yourself it's going out in whatever + + align:start position:0% +for yourself it's going out in whatever + + + align:start position:0% +for yourself it's going out in whatever +the the uh production process is or + + align:start position:0% +the the uh production process is or + + + align:start position:0% +the the uh production process is or +activity is and actually getting data + + align:start position:0% +activity is and actually getting data + + + align:start position:0% +activity is and actually getting data +that can populate this process map and + + align:start position:0% +that can populate this process map and + + + align:start position:0% +that can populate this process map and +and once people have data then they can + + align:start position:0% +and once people have data then they can + + + align:start position:0% +and once people have data then they can +make uh informed + + align:start position:0% +make uh informed + + + align:start position:0% +make uh informed +decisions okay so we're on this second + + align:start position:0% +decisions okay so we're on this second + + + align:start position:0% +decisions okay so we're on this second +stage of the five stages of lean + + align:start position:0% +stage of the five stages of lean + + + align:start position:0% +stage of the five stages of lean +thinking the value stream stage okay so + + align:start position:0% +thinking the value stream stage okay so + + + align:start position:0% +thinking the value stream stage okay so +a value stream appap is a + + align:start position:0% +a value stream appap is a + + + align:start position:0% +a value stream appap is a +tool it's a tool to use to identify and + + align:start position:0% +tool it's a tool to use to identify and + + + align:start position:0% +tool it's a tool to use to identify and +eliminate waste and I've mentioned this + + align:start position:0% +eliminate waste and I've mentioned this + + + align:start position:0% +eliminate waste and I've mentioned this +it's a map with process data added and + + align:start position:0% +it's a map with process data added and + + + align:start position:0% +it's a map with process data added and +what kind of data do you add you add the + + align:start position:0% +what kind of data do you add you add the + + + align:start position:0% +what kind of data do you add you add the +kind of data you need to improve proove + + align:start position:0% +kind of data you need to improve proove + + + align:start position:0% +kind of data you need to improve proove +that process and here are some typical + + align:start position:0% +that process and here are some typical + + + align:start position:0% +that process and here are some typical +ones but you don't have to feel you have + + align:start position:0% +ones but you don't have to feel you have + + + align:start position:0% +ones but you don't have to feel you have +to add use all these data use what's + + align:start position:0% +to add use all these data use what's + + + align:start position:0% +to add use all these data use what's +what's necessary so usually Times show + + align:start position:0% +what's necessary so usually Times show + + + align:start position:0% +what's necessary so usually Times show +up in there certainly if you have + + align:start position:0% +up in there certainly if you have + + + align:start position:0% +up in there certainly if you have +quality issues you want to capture those + + align:start position:0% +quality issues you want to capture those + + + align:start position:0% +quality issues you want to capture those +if you're um find you may want to find + + align:start position:0% +if you're um find you may want to find + + + align:start position:0% +if you're um find you may want to find +out how much is in inventory you might + + align:start position:0% +out how much is in inventory you might + + + align:start position:0% +out how much is in inventory you might +need to say how many people or space is + + align:start position:0% +need to say how many people or space is + + + align:start position:0% +need to say how many people or space is +being used another one that's often used + + align:start position:0% +being used another one that's often used + + + align:start position:0% +being used another one that's often used +is how far you've traveling okay + + align:start position:0% +is how far you've traveling okay + + + align:start position:0% +is how far you've traveling okay +whatever is useful you want to capture + + align:start position:0% +whatever is useful you want to capture + + + align:start position:0% +whatever is useful you want to capture +for your value stream + + align:start position:0% +for your value stream + + + align:start position:0% +for your value stream +map and then here are the steps for + + align:start position:0% +map and then here are the steps for + + + align:start position:0% +map and then here are the steps for +doing value stream mapping and again + + align:start position:0% +doing value stream mapping and again + + + align:start position:0% +doing value stream mapping and again +you've already heard these and this just + + align:start position:0% +you've already heard these and this just + + + align:start position:0% +you've already heard these and this just +writes them down what you've heard you + + align:start position:0% +writes them down what you've heard you + + + align:start position:0% +writes them down what you've heard you +wanted to find what is what is value for + + align:start position:0% +wanted to find what is what is value for + + + align:start position:0% +wanted to find what is what is value for +your value stream then you create a + + align:start position:0% +your value stream then you create a + + + align:start position:0% +your value stream then you create a +current state map an Asis map so that's + + align:start position:0% +current state map an Asis map so that's + + + align:start position:0% +current state map an Asis map so that's +what we're going to do for Sasha and + + align:start position:0% +what we're going to do for Sasha and + + + align:start position:0% +what we're going to do for Sasha and +Andy we're going to say what is our + + align:start position:0% +Andy we're going to say what is our + + + align:start position:0% +Andy we're going to say what is our +current + + align:start position:0% +current + + + align:start position:0% +current +state and and they've collected the data + + align:start position:0% +state and and they've collected the data + + + align:start position:0% +state and and they've collected the data +for us then you want to analyze that map + + align:start position:0% +for us then you want to analyze that map + + + align:start position:0% +for us then you want to analyze that map +and see where's the value added in waste + + align:start position:0% +and see where's the value added in waste + + + align:start position:0% +and see where's the value added in waste +activities and then brainstorm and how + + align:start position:0% +activities and then brainstorm and how + + + align:start position:0% +activities and then brainstorm and how +to eliminate the waste and add more + + align:start position:0% +to eliminate the waste and add more + + + align:start position:0% +to eliminate the waste and add more +value and then once you have that you + + align:start position:0% +value and then once you have that you + + + align:start position:0% +value and then once you have that you +create a future state map you remap your + + align:start position:0% +create a future state map you remap your + + + align:start position:0% +create a future state map you remap your +process + + align:start position:0% +process + + + align:start position:0% +process +now where you think you can get to and + + align:start position:0% +now where you think you can get to and + + + align:start position:0% +now where you think you can get to and +um sometimes you might create What's + + align:start position:0% +um sometimes you might create What's + + + align:start position:0% +um sometimes you might create What's +called the ideal State the best you can + + align:start position:0% +called the ideal State the best you can + + + align:start position:0% +called the ideal State the best you can +possibly think of but that may be too + + align:start position:0% +possibly think of but that may be too + + + align:start position:0% +possibly think of but that may be too +big a step to take it once and so you + + align:start position:0% +big a step to take it once and so you + + + align:start position:0% +big a step to take it once and so you +you create the future state may be a + + align:start position:0% +you create the future state may be a + + + align:start position:0% +you create the future state may be a +step towards that ideal state but you + + align:start position:0% +step towards that ideal state but you + + + align:start position:0% +step towards that ideal state but you +want to get a future state map and then + + align:start position:0% +want to get a future state map and then + + + align:start position:0% +want to get a future state map and then +you have to have a plan for how you're + + align:start position:0% +you have to have a plan for how you're + + + align:start position:0% +you have to have a plan for how you're +going to implement that future State how + + align:start position:0% +going to implement that future State how + + + align:start position:0% +going to implement that future State how +you actually going to change the process + + align:start position:0% +you actually going to change the process + + + align:start position:0% +you actually going to change the process +and you know we heard a lot about that + + align:start position:0% +and you know we heard a lot about that + + + align:start position:0% +and you know we heard a lot about that +at New Balance uh how they actually move + + align:start position:0% +at New Balance uh how they actually move + + + align:start position:0% +at New Balance uh how they actually move +things around they reordered things they + + align:start position:0% +things around they reordered things they + + + align:start position:0% +things around they reordered things they +trained people uh they on our tour Walda + + align:start position:0% +trained people uh they on our tour Walda + + + align:start position:0% +trained people uh they on our tour Walda +said you know we did a little step first + + align:start position:0% +said you know we did a little step first + + + align:start position:0% +said you know we did a little step first +we didn't you know we changed a little + + align:start position:0% +we didn't you know we changed a little + + + align:start position:0% +we didn't you know we changed a little +bit we got started and then we did a + + align:start position:0% +bit we got started and then we did a + + + align:start position:0% +bit we got started and then we did a +little bit more so you don't want to + + align:start position:0% +little bit more so you don't want to + + + align:start position:0% +little bit more so you don't want to +break the system usually you're in the + + align:start position:0% +break the system usually you're in the + + + align:start position:0% +break the system usually you're in the +middle of a production while this is + + align:start position:0% +middle of a production while this is + + + align:start position:0% +middle of a production while this is +going on so you you have to keep + + align:start position:0% +going on so you you have to keep + + + align:start position:0% +going on so you you have to keep +producing your + + align:start position:0% +producing your + + + align:start position:0% +producing your +units Okay so so here's our value our + + align:start position:0% +units Okay so so here's our value our + + + align:start position:0% +units Okay so so here's our value our +customer + + align:start position:0% +customer + + + align:start position:0% +customer +value is they want good food but they + + align:start position:0% +value is they want good food but they + + + align:start position:0% +value is they want good food but they +want faster service so they're happy + + align:start position:0% +want faster service so they're happy + + + align:start position:0% +want faster service so they're happy +with the quality but they want to get + + align:start position:0% +with the quality but they want to get + + + align:start position:0% +with the quality but they want to get +faster service and here's our current + + align:start position:0% +faster service and here's our current + + + align:start position:0% +faster service and here's our current +demand 50 customers and 100 hot + + align:start position:0% +demand 50 customers and 100 hot + + + align:start position:0% +demand 50 customers and 100 hot +dogs now + + align:start position:0% +dogs now + + + align:start position:0% +dogs now +um I've taken the the + + align:start position:0% +um I've taken the the + + + align:start position:0% +um I've taken the the +data that's on here the cycle time data + + align:start position:0% +data that's on here the cycle time data + + + align:start position:0% +data that's on here the cycle time data +and just put it next to each of the + + align:start position:0% +and just put it next to each of the + + + align:start position:0% +and just put it next to each of the +boxes on the process proc map and then + + align:start position:0% +boxes on the process proc map and then + + + align:start position:0% +boxes on the process proc map and then +the quality we've also captured quality + + align:start position:0% +the quality we've also captured quality + + + align:start position:0% +the quality we've also captured quality +data and so we have here we have 10% + + align:start position:0% +data and so we have here we have 10% + + + align:start position:0% +data and so we have here we have 10% +rejects on this but otherwise we're + + align:start position:0% +rejects on this but otherwise we're + + + align:start position:0% +rejects on this but otherwise we're +okay okay so that's the kind of data you + + align:start position:0% +okay okay so that's the kind of data you + + + align:start position:0% +okay okay so that's the kind of data you +might show see showing up on a a value + + align:start position:0% +might show see showing up on a a value + + + align:start position:0% +might show see showing up on a a value +stream + + align:start position:0% +stream + + + align:start position:0% +stream +map and now what we're going to do is T + + align:start position:0% +map and now what we're going to do is T + + + align:start position:0% +map and now what we're going to do is T +take uh about 10 + + align:start position:0% +take uh about 10 + + + align:start position:0% +take uh about 10 +minutes and the first thing we want you + + align:start position:0% +minutes and the first thing we want you + + + align:start position:0% +minutes and the first thing we want you +to do is to take some colored + + align:start position:0% +to do is to take some colored + + + align:start position:0% +to do is to take some colored +dots and on this map just as a group try + + align:start position:0% +dots and on this map just as a group try + + + align:start position:0% +dots and on this map just as a group try +to identify what these states are are + + align:start position:0% +to identify what these states are are + + + align:start position:0% +to identify what these states are are +red that is pure waste there's no value + + align:start position:0% +red that is pure waste there's no value + + + align:start position:0% +red that is pure waste there's no value +being added at all what steps are + + align:start position:0% +being added at all what steps are + + + align:start position:0% +being added at all what steps are +yellow that is that they're they're not + + align:start position:0% +yellow that is that they're they're not + + + align:start position:0% +yellow that is that they're they're not +adding value in the eyes of the customer + + align:start position:0% +adding value in the eyes of the customer + + + align:start position:0% +adding value in the eyes of the customer +but they're needed given the current + + align:start position:0% +but they're needed given the current + + + align:start position:0% +but they're needed given the current +process okay and then what steps are + + align:start position:0% +process okay and then what steps are + + + align:start position:0% +process okay and then what steps are +green what steps really contribute to + + align:start position:0% +green what steps really contribute to + + + align:start position:0% +green what steps really contribute to +the customer so take about three or four + + align:start position:0% +the customer so take about three or four + + + align:start position:0% +the customer so take about three or four +minutes to do that and you'll find out + + align:start position:0% +minutes to do that and you'll find out + + + align:start position:0% +minutes to do that and you'll find out +there may + + align:start position:0% +there may + + + align:start position:0% +there may +be there's going to be some ambiguity + + align:start position:0% +be there's going to be some ambiguity + + + align:start position:0% +be there's going to be some ambiguity +okay there's going to be some ambiguity + + align:start position:0% +okay there's going to be some ambiguity + + + align:start position:0% +okay there's going to be some ambiguity +waste necessary waste and absolute waste + + align:start position:0% +waste necessary waste and absolute waste + + + align:start position:0% +waste necessary waste and absolute waste +just do the best you can okay it's don't + + align:start position:0% +just do the best you can okay it's don't + + + align:start position:0% +just do the best you can okay it's don't +spend all the rest of the afternoon + + align:start position:0% +spend all the rest of the afternoon + + + align:start position:0% +spend all the rest of the afternoon +arguing about that but then once you + + align:start position:0% +arguing about that but then once you + + + align:start position:0% +arguing about that but then once you +find + + align:start position:0% +find + + + align:start position:0% +find +out + + align:start position:0% +out + + + align:start position:0% +out +uh what's value add nonv value add and + + align:start position:0% +uh what's value add nonv value add and + + + align:start position:0% +uh what's value add nonv value add and +and uh and the red is wait time here + + align:start position:0% +and uh and the red is wait time here + + + align:start position:0% +and uh and the red is wait time here +fill in the blanks for the time and also + + align:start position:0% +fill in the blanks for the time and also + + + align:start position:0% +fill in the blanks for the time and also +fill in uh how much time of this is + + align:start position:0% +fill in uh how much time of this is + + + align:start position:0% +fill in uh how much time of this is +allocated to Sasha how much time is + + align:start position:0% +allocated to Sasha how much time is + + + align:start position:0% +allocated to Sasha how much time is +allocated to Andy and how much time + + align:start position:0% +allocated to Andy and how much time + + + align:start position:0% +allocated to Andy and how much time +neither of them are working because + + align:start position:0% +neither of them are working because + + + align:start position:0% +neither of them are working because +we're going to find out how hard they're + + align:start position:0% +we're going to find out how hard they're + + + align:start position:0% +we're going to find out how hard they're +working how how much of the time they're + + align:start position:0% +working how how much of the time they're + + + align:start position:0% +working how how much of the time they're +actually spending on executing this + + align:start position:0% +actually spending on executing this + + + align:start position:0% +actually spending on executing this +value stream okay so go ahead and go to + + align:start position:0% +value stream okay so go ahead and go to + + + align:start position:0% +value stream okay so go ahead and go to +that and I'll walk around and see if you + + align:start position:0% +that and I'll walk around and see if you + + + align:start position:0% +that and I'll walk around and see if you +need any help on that and we'll then ask + + align:start position:0% +need any help on that and we'll then ask + + + align:start position:0% +need any help on that and we'll then ask +for your answers uh on these these + + align:start position:0% +for your answers uh on these these + + + align:start position:0% +for your answers uh on these these +different uh times + + align:start position:0% +different uh times + + + align:start position:0% +different uh times +here okay let's uh let's see where we're + + align:start position:0% +here okay let's uh let's see where we're + + + align:start position:0% +here okay let's uh let's see where we're +at like the last exercise we got some uh + + align:start position:0% +at like the last exercise we got some uh + + + align:start position:0% +at like the last exercise we got some uh +we got some instructor solutions to hand + + align:start position:0% +we got some instructor solutions to hand + + + align:start position:0% +we got some instructor solutions to hand +out to you so how much time is allocated + + align:start position:0% +out to you so how much time is allocated + + + align:start position:0% +out to you so how much time is allocated +that neither of them are spending time + + align:start position:0% +that neither of them are spending time + + + align:start position:0% +that neither of them are spending time +doing it but it's taking some time + + align:start position:0% +doing it but it's taking some time + + + align:start position:0% +doing it but it's taking some time +sitting and wait or + + align:start position:0% +sitting and wait or + + + align:start position:0% +sitting and wait or +whatever 63 yeah okay that's + + align:start position:0% + + + + align:start position:0% + +good okay was anybody able to calculate + + align:start position:0% +good okay was anybody able to calculate + + + align:start position:0% +good okay was anybody able to calculate +the total value added time in this + + align:start position:0% + + + + align:start position:0% + +process + + align:start position:0% +process + + + align:start position:0% +process +no why don't we go ahead and hand out + + align:start position:0% +no why don't we go ahead and hand out + + + align:start position:0% +no why don't we go ahead and hand out +those + + align:start position:0% +those + + + align:start position:0% +those +sheets let's take a look at it okay so + + align:start position:0% +sheets let's take a look at it okay so + + + align:start position:0% +sheets let's take a look at it okay so +this is this is one way of what we have + + align:start position:0% +this is this is one way of what we have + + + align:start position:0% +this is this is one way of what we have +is two sheets one is is this slide which + + align:start position:0% +is two sheets one is is this slide which + + + align:start position:0% +is two sheets one is is this slide which +is blank in your student notebooks and + + align:start position:0% +is blank in your student notebooks and + + + align:start position:0% +is blank in your student notebooks and +the other is the worksheet you were + + align:start position:0% +the other is the worksheet you were + + + align:start position:0% +the other is the worksheet you were +working on it's the same data just shown + + align:start position:0% +working on it's the same data just shown + + + align:start position:0% +working on it's the same data just shown +two different ways the instructors + + align:start position:0% +two different ways the instructors + + + align:start position:0% +two different ways the instructors +calculated that Andy spending + + align:start position:0% +calculated that Andy spending + + + align:start position:0% +calculated that Andy spending +224 seconds of the total of 446 + + align:start position:0% +224 seconds of the total of 446 + + + align:start position:0% +224 seconds of the total of 446 +seconds and the Sasha is spending 159 + + align:start position:0% +seconds and the Sasha is spending 159 + + + align:start position:0% +seconds and the Sasha is spending 159 +and the 63 seconds the order is just + + align:start position:0% +and the 63 seconds the order is just + + + align:start position:0% +and the 63 seconds the order is just +sitting there in in the uh order in or + + align:start position:0% +sitting there in in the uh order in or + + + align:start position:0% +sitting there in in the uh order in or +the order out box now what's value added + + align:start position:0% +the order out box now what's value added + + + align:start position:0% +the order out box now what's value added +time and non-value add this is a little + + align:start position:0% +time and non-value add this is a little + + + align:start position:0% +time and non-value add this is a little +bit more uh + + align:start position:0% +bit more uh + + + align:start position:0% +bit more uh +subjective + + align:start position:0% +subjective + + + align:start position:0% +subjective +uh the uh instructor solution was that + + align:start position:0% +uh the uh instructor solution was that + + + align:start position:0% +uh the uh instructor solution was that +taking order was value added now you + + align:start position:0% +taking order was value added now you + + + align:start position:0% +taking order was value added now you +could argue does Sasha need to spend 60 + + align:start position:0% +could argue does Sasha need to spend 60 + + + align:start position:0% +could argue does Sasha need to spend 60 +seconds taking the order you know okay + + align:start position:0% +seconds taking the order you know okay + + + align:start position:0% +seconds taking the order you know okay +okay so you know that's questionable but + + align:start position:0% +okay so you know that's questionable but + + + align:start position:0% +okay so you know that's questionable but +we we we we booked at his value ated + + align:start position:0% +we we we we booked at his value ated + + + align:start position:0% +we we we we booked at his value ated +time but certainly that's an opportunity + + align:start position:0% +time but certainly that's an opportunity + + + align:start position:0% +time but certainly that's an opportunity +for improvement you know she is gain the + + align:start position:0% +for improvement you know she is gain the + + + align:start position:0% +for improvement you know she is gain the +customer feedback and seeing if they + + align:start position:0% +customer feedback and seeing if they + + + align:start position:0% +customer feedback and seeing if they +satisfied and all that kind of stuff but + + align:start position:0% +satisfied and all that kind of stuff but + + + align:start position:0% +satisfied and all that kind of stuff but +60 seconds you know is a long time okay + + align:start position:0% +60 seconds you know is a long time okay + + + align:start position:0% +60 seconds you know is a long time okay +we got 30 seconds that's just sitting + + align:start position:0% +we got 30 seconds that's just sitting + + + align:start position:0% +we got 30 seconds that's just sitting +there with nothing being done in the + + align:start position:0% +there with nothing being done in the + + + align:start position:0% +there with nothing being done in the +order in box for for Andy then Andy's + + align:start position:0% +order in box for for Andy then Andy's + + + align:start position:0% +order in box for for Andy then Andy's +takes 100 seconds to cook two hot + + align:start position:0% +takes 100 seconds to cook two hot + + + align:start position:0% +takes 100 seconds to cook two hot +dogs okay so under our current process + + align:start position:0% +dogs okay so under our current process + + + align:start position:0% +dogs okay so under our current process +we'd say that's value added time we're + + align:start position:0% +we'd say that's value added time we're + + + align:start position:0% +we'd say that's value added time we're +delivering that to the customer could he + + align:start position:0% +delivering that to the customer could he + + + align:start position:0% +delivering that to the customer could he +do it faster than 100 seconds maybe but + + align:start position:0% +do it faster than 100 seconds maybe but + + + align:start position:0% +do it faster than 100 seconds maybe but +given the current process but certainly + + align:start position:0% +given the current process but certainly + + + align:start position:0% +given the current process but certainly +the rework is nonv value added + + align:start position:0% +the rework is nonv value added + + + align:start position:0% +the rework is nonv value added +but now the question is is that pure + + align:start position:0% +but now the question is is that pure + + + align:start position:0% +but now the question is is that pure +waste or necessary + + align:start position:0% +waste or necessary + + + align:start position:0% +waste or necessary +waste now we booked it as necessary + + align:start position:0% +waste now we booked it as necessary + + + align:start position:0% +waste now we booked it as necessary +waste because if we didn't check that + + align:start position:0% +waste because if we didn't check that + + + align:start position:0% +waste because if we didn't check that +order and it went to the + + align:start position:0% +order and it went to the + + + align:start position:0% +order and it went to the +customer without being properly filled + + align:start position:0% +customer without being properly filled + + + align:start position:0% +customer without being properly filled +then then it would not satisfy the + + align:start position:0% +then then it would not satisfy the + + + align:start position:0% +then then it would not satisfy the +customers need on the other hand the + + align:start position:0% +customers need on the other hand the + + + align:start position:0% +customers need on the other hand the +customer doesn't really care about the + + align:start position:0% +customer doesn't really care about the + + + align:start position:0% +customer doesn't really care about the +inspection so we added under the current + + align:start position:0% +inspection so we added under the current + + + align:start position:0% +inspection so we added under the current +process it was a non-value added but + + align:start position:0% +process it was a non-value added but + + + align:start position:0% +process it was a non-value added but +necessary waste but one could argue that + + align:start position:0% +necessary waste but one could argue that + + + align:start position:0% +necessary waste but one could argue that +it was pure waste I mean you could argue + + align:start position:0% +it was pure waste I mean you could argue + + + align:start position:0% +it was pure waste I mean you could argue +either way + + align:start position:0% +either way + + + align:start position:0% +either way +probably + + align:start position:0% +probably + + + align:start position:0% +probably +same thing here with Andy's wrapping up + + align:start position:0% +same thing here with Andy's wrapping up + + + align:start position:0% +same thing here with Andy's wrapping up +the + + align:start position:0% +the + + + align:start position:0% +the +bun + + align:start position:0% +bun + + + align:start position:0% +bun +uh this is another thing where Andy's + + align:start position:0% +uh this is another thing where Andy's + + + align:start position:0% +uh this is another thing where Andy's +have having to check does he need to go + + align:start position:0% +have having to check does he need to go + + + align:start position:0% +have having to check does he need to go +cook another hot dog or not well the + + align:start position:0% +cook another hot dog or not well the + + + align:start position:0% +cook another hot dog or not well the +customer really doesn't care about that + + align:start position:0% +customer really doesn't care about that + + + align:start position:0% +customer really doesn't care about that +but but um on the other hand if he + + align:start position:0% +but but um on the other hand if he + + + align:start position:0% +but but um on the other hand if he +doesn't see whether the order is + + align:start position:0% +doesn't see whether the order is + + + align:start position:0% +doesn't see whether the order is +complete the customer is not going to be + + align:start position:0% +complete the customer is not going to be + + + align:start position:0% +complete the customer is not going to be +happy so that's non-value added + + align:start position:0% +happy so that's non-value added + + + align:start position:0% +happy so that's non-value added +necessary waste hereis just sitting + + align:start position:0% +necessary waste hereis just sitting + + + align:start position:0% +necessary waste hereis just sitting +there're waiting with nothing happening + + align:start position:0% +there're waiting with nothing happening + + + align:start position:0% +there're waiting with nothing happening +in the order out so we'll call that pure + + align:start position:0% +in the order out so we'll call that pure + + + align:start position:0% +in the order out so we'll call that pure +waste and then Sasha doesn't another + + align:start position:0% +waste and then Sasha doesn't another + + + align:start position:0% +waste and then Sasha doesn't another +inspection okay that's an inspection + + align:start position:0% +inspection okay that's an inspection + + + align:start position:0% +inspection okay that's an inspection +that's a + + align:start position:0% +that's a + + + align:start position:0% +that's a +NE under our current system that's a + + align:start position:0% +NE under our current system that's a + + + align:start position:0% +NE under our current system that's a +necessary waste because we don't have + + align:start position:0% +necessary waste because we don't have + + + align:start position:0% +necessary waste because we don't have +quality control working yet we add the + + align:start position:0% +quality control working yet we add the + + + align:start position:0% +quality control working yet we add the +beverage we deliver to the customer + + align:start position:0% +beverage we deliver to the customer + + + align:start position:0% +beverage we deliver to the customer +again you could argue she doesn't need + + align:start position:0% +again you could argue she doesn't need + + + align:start position:0% +again you could argue she doesn't need +to take 30 seconds to deliver it to the + + align:start position:0% +to take 30 seconds to deliver it to the + + + align:start position:0% +to take 30 seconds to deliver it to the +customer and then uh we booked this + + align:start position:0% +customer and then uh we booked this + + + align:start position:0% +customer and then uh we booked this +cleanup stuff as sort of customer + + align:start position:0% +cleanup stuff as sort of customer + + + align:start position:0% +cleanup stuff as sort of customer +doesn't really care whether the counter + + align:start position:0% +doesn't really care whether the counter + + + align:start position:0% +doesn't really care whether the counter +is cleaned up or not on your hand you + + align:start position:0% +is cleaned up or not on your hand you + + + align:start position:0% +is cleaned up or not on your hand you +want to somebody's got to do it so it's + + align:start position:0% +want to somebody's got to do it so it's + + + align:start position:0% +want to somebody's got to do it so it's +again nonv value added but necessary + + align:start position:0% +again nonv value added but necessary + + + align:start position:0% +again nonv value added but necessary +waste so that's that's how we booked it + + align:start position:0% +waste so that's that's how we booked it + + + align:start position:0% +waste so that's that's how we booked it +again you could you could come up with + + align:start position:0% +again you could you could come up with + + + align:start position:0% +again you could you could come up with +different bookings and and we'd be happy + + align:start position:0% +different bookings and and we'd be happy + + + align:start position:0% +different bookings and and we'd be happy +to accept those but you have to kind of + + align:start position:0% +to accept those but you have to kind of + + + align:start position:0% +to accept those but you have to kind of +make some decision so of that total of + + align:start position:0% +make some decision so of that total of + + + align:start position:0% +make some decision so of that total of +446 seconds the value added times about + + align:start position:0% +446 seconds the value added times about + + + align:start position:0% +446 seconds the value added times about +50% okay that's not an unusual number + + align:start position:0% +50% okay that's not an unusual number + + + align:start position:0% +50% okay that's not an unusual number +actually that's somewhat high for a + + align:start position:0% +actually that's somewhat high for a + + + align:start position:0% +actually that's somewhat high for a +first time through uh but again we could + + align:start position:0% +first time through uh but again we could + + + align:start position:0% +first time through uh but again we could +argue about whether some of these things + + align:start position:0% +argue about whether some of these things + + + align:start position:0% +argue about whether some of these things +are really true value added about 32% + + align:start position:0% +are really true value added about 32% + + + align:start position:0% +are really true value added about 32% +necessary waste and 14% pure waste + + align:start position:0% +necessary waste and 14% pure waste + + + align:start position:0% +necessary waste and 14% pure waste +okay so value added times only about 50% + + align:start position:0% +okay so value added times only about 50% + + + align:start position:0% +okay so value added times only about 50% +ah opportunity for improvement okay we + + align:start position:0% +ah opportunity for improvement okay we + + + align:start position:0% +ah opportunity for improvement okay we +should be able to do something better + + align:start position:0% +should be able to do something better + + + align:start position:0% +should be able to do something better +than that let's look at the now the + + align:start position:0% +than that let's look at the now the + + + align:start position:0% +than that let's look at the now the +analysis part so this is the value + + align:start position:0% +analysis part so this is the value + + + align:start position:0% +analysis part so this is the value +stream mapping now we're doing the + + align:start position:0% +stream mapping now we're doing the + + + align:start position:0% +stream mapping now we're doing the +analysis we have a total available time + + align:start position:0% +analysis we have a total available time + + + align:start position:0% +analysis we have a total available time +of 240 + + align:start position:0% +of 240 + + + align:start position:0% +of 240 +minutes so + + align:start position:0% +minutes so + + + align:start position:0% +minutes so +sash's working here + + align:start position:0% +sash's working here + + + align:start position:0% +sash's working here +159 uh divided by 60 minutes per hour + + align:start position:0% +159 uh divided by 60 minutes per hour + + + align:start position:0% +159 uh divided by 60 minutes per hour +times she Services that's per order she + + align:start position:0% +times she Services that's per order she + + + align:start position:0% +times she Services that's per order she +Services 50 customers so she's working + + align:start position:0% +Services 50 customers so she's working + + + align:start position:0% +Services 50 customers so she's working +132 1/2 hours a minutes out of 240 + + align:start position:0% +132 1/2 hours a minutes out of 240 + + + align:start position:0% +132 1/2 hours a minutes out of 240 +minutes so she's uh load she's about + + align:start position:0% +minutes so she's uh load she's about + + + align:start position:0% +minutes so she's uh load she's about +55% at capacity she's got almost 50% + + align:start position:0% +55% at capacity she's got almost 50% + + + align:start position:0% +55% at capacity she's got almost 50% +capacity that she's just not doing + + align:start position:0% +capacity that she's just not doing + + + align:start position:0% +capacity that she's just not doing +anything okay Andy is a little bit more + + align:start position:0% +anything okay Andy is a little bit more + + + align:start position:0% +anything okay Andy is a little bit more +overloaded we got the 224 minutes times + + align:start position:0% +overloaded we got the 224 minutes times + + + align:start position:0% +overloaded we got the 224 minutes times +of 50 customers 186 minutes + + align:start position:0% +of 50 customers 186 minutes + + + align:start position:0% +of 50 customers 186 minutes +total uh + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +uh I think I see a bug + + align:start position:0% +uh I think I see a bug + + + align:start position:0% +uh I think I see a bug +here + + align:start position:0% +here + + + align:start position:0% +here +yeah Anisa can you note a correction on + + align:start position:0% +yeah Anisa can you note a correction on + + + align:start position:0% +yeah Anisa can you note a correction on +this + + align:start position:0% +this + + + align:start position:0% +this +chart + + align:start position:0% +chart + + + align:start position:0% +chart +okay anyway + + align:start position:0% +okay anyway + + + align:start position:0% +okay anyway +um it's this should be 186 over 240 + + align:start position:0% +um it's this should be 186 over 240 + + + align:start position:0% +um it's this should be 186 over 240 +which is 78% utilized so Andy's Andy's + + align:start position:0% +which is 78% utilized so Andy's Andy's + + + align:start position:0% +which is 78% utilized so Andy's Andy's +working hard harder than Sasha now what + + align:start position:0% +working hard harder than Sasha now what + + + align:start position:0% +working hard harder than Sasha now what +do we what do we see here then we have + + align:start position:0% +do we what do we see here then we have + + + align:start position:0% +do we what do we see here then we have +an + + align:start position:0% +an + + + align:start position:0% +an +imbalance okay we don't have balanced + + align:start position:0% +imbalance okay we don't have balanced + + + align:start position:0% +imbalance okay we don't have balanced +work we don't have them working at the + + align:start position:0% +work we don't have them working at the + + + align:start position:0% +work we don't have them working at the +same rate remember we talked about + + align:start position:0% +same rate remember we talked about + + + align:start position:0% +same rate remember we talked about +balanced work okay what's the total + + align:start position:0% +balanced work okay what's the total + + + align:start position:0% +balanced work okay what's the total +capacity they have working with this + + align:start position:0% +capacity they have working with this + + + align:start position:0% +capacity they have working with this +current broken process they should be + + align:start position:0% +current broken process they should be + + + align:start position:0% +current broken process they should be +able to service about 65 on average + + align:start position:0% +able to service about 65 on average + + + align:start position:0% +able to service about 65 on average +about 65 customers a day + + align:start position:0% +about 65 customers a day + + + align:start position:0% +about 65 customers a day +okay okay so that's an example of how + + align:start position:0% +okay okay so that's an example of how + + + align:start position:0% +okay okay so that's an example of how +you would do a value stream mapping and + + align:start position:0% +you would do a value stream mapping and + + + align:start position:0% +you would do a value stream mapping and +Analysis + + align:start position:0% +Analysis + + + align:start position:0% +Analysis +okay okay their Tac time + + align:start position:0% +okay okay their Tac time + + + align:start position:0% +okay okay their Tac time +uh we already computed up here was 4.8 + + align:start position:0% +uh we already computed up here was 4.8 + + + align:start position:0% +uh we already computed up here was 4.8 +minutes okay for 50 for 50 customers + + align:start position:0% +minutes okay for 50 for 50 customers + + + align:start position:0% +minutes okay for 50 for 50 customers +they have to work at 4.8 minutes uh + + align:start position:0% +they have to work at 4.8 minutes uh + + + align:start position:0% +they have to work at 4.8 minutes uh +their cycle time is 446 seconds which is + + align:start position:0% +their cycle time is 446 seconds which is + + + align:start position:0% +their cycle time is 446 seconds which is +7.43 minutes but remember that chart + + align:start position:0% +7.43 minutes but remember that chart + + + align:start position:0% +7.43 minutes but remember that chart +that had cycle time and balanced work + + align:start position:0% +that had cycle time and balanced work + + + align:start position:0% +that had cycle time and balanced work +cycle time and Tac time so I got two + + align:start position:0% +cycle time and Tac time so I got two + + + align:start position:0% +cycle time and Tac time so I got two +employees so they they can both work in + + align:start position:0% +employees so they they can both work in + + + align:start position:0% +employees so they they can both work in +parallel so that's why they can deliver + + align:start position:0% +parallel so that's why they can deliver + + + align:start position:0% +parallel so that's why they can deliver +every 4.8 minutes uh hot dog because + + align:start position:0% +every 4.8 minutes uh hot dog because + + + align:start position:0% +every 4.8 minutes uh hot dog because +this is really divided by two if if + + align:start position:0% +this is really divided by two if if + + + align:start position:0% +this is really divided by two if if +because they're both + + align:start position:0% +because they're both + + + align:start position:0% +because they're both +working their Productions is okay + + align:start position:0% +working their Productions is okay + + + align:start position:0% +working their Productions is okay +they're below their absolute capacity + + align:start position:0% +they're below their absolute capacity + + + align:start position:0% +they're below their absolute capacity +but they got a growing + + align:start position:0% +but they got a growing + + + align:start position:0% +but they got a growing +demand both of them are + + align:start position:0% +demand both of them are + + + align:start position:0% +demand both of them are +underutilized but there's utilization + + align:start position:0% +underutilized but there's utilization + + + align:start position:0% +underutilized but there's utilization +not balanced between them and this is a + + align:start position:0% +not balanced between them and this is a + + + align:start position:0% +not balanced between them and this is a +long time for making a customer wait to + + align:start position:0% +long time for making a customer wait to + + + align:start position:0% +long time for making a customer wait to +get a hot dog okay s minutes okay we + + align:start position:0% +get a hot dog okay s minutes okay we + + + align:start position:0% +get a hot dog okay s minutes okay we +should be able to shorten the cycle time + + align:start position:0% +should be able to shorten the cycle time + + + align:start position:0% +should be able to shorten the cycle time +so in order to get through next week + + align:start position:0% +so in order to get through next week + + + align:start position:0% +so in order to get through next week +Sasha and Andy are going to have to to + + align:start position:0% +Sasha and Andy are going to have to to + + + align:start position:0% +Sasha and Andy are going to have to to +improve their process now we're just + + align:start position:0% +improve their process now we're just + + + align:start position:0% +improve their process now we're just +going to do this as a group but um what + + align:start position:0% +going to do this as a group but um what + + + align:start position:0% +going to do this as a group but um what +are some ideas how the utilization can + + align:start position:0% +are some ideas how the utilization can + + + align:start position:0% +are some ideas how the utilization can +be improved between for Sasha and + + align:start position:0% +be improved between for Sasha and + + + align:start position:0% +be improved between for Sasha and +Andy yeah Sasha take the next order + + align:start position:0% +Andy yeah Sasha take the next order + + + align:start position:0% +Andy yeah Sasha take the next order +while Andy's + + align:start position:0% +while Andy's + + + align:start position:0% +while Andy's +preparing okay actually she's doing that + + align:start position:0% +preparing okay actually she's doing that + + + align:start position:0% +preparing okay actually she's doing that +she's taking the next order while Andy's + + align:start position:0% +she's taking the next order while Andy's + + + align:start position:0% +she's taking the next order while Andy's +preparing it already and it's going in + + align:start position:0% +preparing it already and it's going in + + + align:start position:0% +preparing it already and it's going in +the order in boox yeah yeah could pass + + align:start position:0% +the order in boox yeah yeah could pass + + + align:start position:0% +the order in boox yeah yeah could pass +the order directly from Sasha toy yeah + + align:start position:0% +the order directly from Sasha toy yeah + + + align:start position:0% +the order directly from Sasha toy yeah +get rid of the order in right okay + + align:start position:0% +get rid of the order in right okay + + + align:start position:0% +get rid of the order in right okay +that's that's only value yet yeah Sasha + + align:start position:0% +that's that's only value yet yeah Sasha + + + align:start position:0% +that's that's only value yet yeah Sasha +can do the fruit Sasha could do the + + align:start position:0% +can do the fruit Sasha could do the + + + align:start position:0% +can do the fruit Sasha could do the +fruit right that could balance the work + + align:start position:0% +fruit right that could balance the work + + + align:start position:0% +fruit right that could balance the work +between okay yeah other IDE and you + + align:start position:0% +between okay yeah other IDE and you + + + align:start position:0% +between okay yeah other IDE and you +could have more hot dogs on a grill than + + align:start position:0% +could have more hot dogs on a grill than + + + align:start position:0% +could have more hot dogs on a grill than +doing yeah they're doing them in series + + align:start position:0% +doing yeah they're doing them in series + + + align:start position:0% +doing yeah they're doing them in series +and they they could be doing the + + align:start position:0% +and they they could be doing the + + + align:start position:0% +and they they could be doing the +parall I mean you go into Burger King + + align:start position:0% +parall I mean you go into Burger King + + + align:start position:0% +parall I mean you go into Burger King +and you know how many of they're cooking + + align:start position:0% +and you know how many of they're cooking + + + align:start position:0% +and you know how many of they're cooking +at the same time or the next time you + + align:start position:0% +at the same time or the next time you + + + align:start position:0% +at the same time or the next time you +sit at the C and watch somebody make + + align:start position:0% +sit at the C and watch somebody make + + + align:start position:0% +sit at the C and watch somebody make +pizzas they got about four or five piz + + align:start position:0% +pizzas they got about four or five piz + + + align:start position:0% +pizzas they got about four or five piz +right yeah so they have anything like a + + align:start position:0% +right yeah so they have anything like a + + + align:start position:0% +right yeah so they have anything like a +conon system going here you know I mean + + align:start position:0% +conon system going here you know I mean + + + align:start position:0% +conon system going here you know I mean +maybe Andy could be putting up hot dogs + + align:start position:0% +maybe Andy could be putting up hot dogs + + + align:start position:0% +maybe Andy could be putting up hot dogs +and Sasha you know she takes the order + + align:start position:0% +and Sasha you know she takes the order + + + align:start position:0% +and Sasha you know she takes the order +turns around takes a hot dog puts the + + align:start position:0% +turns around takes a hot dog puts the + + + align:start position:0% +turns around takes a hot dog puts the +fruit serves the order and Andy's maybe + + align:start position:0% +fruit serves the order and Andy's maybe + + + align:start position:0% +fruit serves the order and Andy's maybe +trying to keep her you know her box + + align:start position:0% +trying to keep her you know her box + + + align:start position:0% +trying to keep her you know her box +about full not not over full but about + + align:start position:0% +about full not not over full but about + + + align:start position:0% +about full not not over full but about +full so they got this kind of convoluted + + align:start position:0% +full so they got this kind of convoluted + + + align:start position:0% +full so they got this kind of convoluted +process where he's and this is not + + align:start position:0% +process where he's and this is not + + + align:start position:0% +process where he's and this is not +unusual by the way this is the way often + + align:start position:0% +unusual by the way this is the way often + + + align:start position:0% +unusual by the way this is the way often +things they take an order they put put + + align:start position:0% +things they take an order they put put + + + align:start position:0% +things they take an order they put put +it on a board he takes that order he + + align:start position:0% +it on a board he takes that order he + + + align:start position:0% +it on a board he takes that order he +does his thing he puts it out she does + + align:start position:0% +does his thing he puts it out she does + + + align:start position:0% +does his thing he puts it out she does +her thing you know but you could be + + align:start position:0% +her thing you know but you could be + + + align:start position:0% +her thing you know but you could be +thinking more of like a conon approach + + align:start position:0% +thinking more of like a conon approach + + + align:start position:0% +thinking more of like a conon approach +where where Andy is kind of looking out + + align:start position:0% +where where Andy is kind of looking out + + + align:start position:0% +where where Andy is kind of looking out +and saying you know I'll keep I'll try + + align:start position:0% +and saying you know I'll keep I'll try + + + align:start position:0% +and saying you know I'll keep I'll try +to keep two or three hot dogs up there + + align:start position:0% +to keep two or three hot dogs up there + + + align:start position:0% +to keep two or three hot dogs up there +at a time or demands about that level + + align:start position:0% +at a time or demands about that level + + + align:start position:0% +at a time or demands about that level +and uh and he's in the back room cooking + + align:start position:0% +and uh and he's in the back room cooking + + + align:start position:0% +and uh and he's in the back room cooking +hot dogs and she's serving the customers + + align:start position:0% +hot dogs and she's serving the customers + + + align:start position:0% +hot dogs and she's serving the customers +and filling the is there anybody I just + + align:start position:0% +and filling the is there anybody I just + + + align:start position:0% +and filling the is there anybody I just +happened to come back from a schi trip + + align:start position:0% +happened to come back from a schi trip + + + align:start position:0% +happened to come back from a schi trip +this weekend and we on the way up we + + align:start position:0% +this weekend and we on the way up we + + + align:start position:0% +this weekend and we on the way up we +stopped at Burger King on the way back + + align:start position:0% +stopped at Burger King on the way back + + + align:start position:0% +stopped at Burger King on the way back +we stopped at McDonald's and and uh + + align:start position:0% +we stopped at McDonald's and and uh + + + align:start position:0% +we stopped at McDonald's and and uh +there's a real difference in industrial + + align:start position:0% +there's a real difference in industrial + + + align:start position:0% +there's a real difference in industrial +engineering difference between the way + + align:start position:0% +engineering difference between the way + + + align:start position:0% +engineering difference between the way +they do it uh in Burger King you form a + + align:start position:0% +they do it uh in Burger King you form a + + + align:start position:0% +they do it uh in Burger King you form a +a sequential line and you place your + + align:start position:0% +a sequential line and you place your + + + align:start position:0% +a sequential line and you place your +order and you walk over here to try to + + align:start position:0% +order and you walk over here to try to + + + align:start position:0% +order and you walk over here to try to +pick it up in in the McDonald's there's + + align:start position:0% +pick it up in in the McDonald's there's + + + align:start position:0% +pick it up in in the McDonald's there's +like three or four cash registers and + + align:start position:0% +like three or four cash registers and + + + align:start position:0% +like three or four cash registers and +it's like a group grope everybody goes + + align:start position:0% +it's like a group grope everybody goes + + + align:start position:0% +it's like a group grope everybody goes +up to three or four of the cash + + align:start position:0% +up to three or four of the cash + + + align:start position:0% +up to three or four of the cash +registers you know and it's a different + + align:start position:0% +registers you know and it's a different + + + align:start position:0% +registers you know and it's a different +process + + align:start position:0% +process + + + align:start position:0% +process +yeah okay so some things you know let's + + align:start position:0% +yeah okay so some things you know let's + + + align:start position:0% +yeah okay so some things you know let's +eliminate + + align:start position:0% +eliminate + + + align:start position:0% +eliminate +this this uh pure waste of things just + + align:start position:0% +this this uh pure waste of things just + + + align:start position:0% +this this uh pure waste of things just +sitting there waiting for some action + + align:start position:0% +sitting there waiting for some action + + + align:start position:0% +sitting there waiting for some action +you know let's get rid of this inp + + align:start position:0% +you know let's get rid of this inp + + + align:start position:0% +you know let's get rid of this inp +inection you know let's balance the work + + align:start position:0% +inection you know let's balance the work + + + align:start position:0% +inection you know let's balance the work +between them with a little bit of simple + + align:start position:0% +between them with a little bit of simple + + + align:start position:0% +between them with a little bit of simple +process Improvement using actually using + + align:start position:0% +process Improvement using actually using + + + align:start position:0% +process Improvement using actually using +the tools you've heard about today you + + align:start position:0% +the tools you've heard about today you + + + align:start position:0% +the tools you've heard about today you +could go in and probably triple their + + align:start position:0% +could go in and probably triple their + + + align:start position:0% +could go in and probably triple their +capacity and the customers would be + + align:start position:0% +capacity and the customers would be + + + align:start position:0% +capacity and the customers would be +getting hot dogs you know in 10 seconds + + align:start position:0% +getting hot dogs you know in 10 seconds + + + align:start position:0% +getting hot dogs you know in 10 seconds +or 20 30 seconds or less than a minute + + align:start position:0% +or 20 30 seconds or less than a minute + + + align:start position:0% +or 20 30 seconds or less than a minute +yeah how do you account for how much of + + align:start position:0% +yeah how do you account for how much of + + + align:start position:0% +yeah how do you account for how much of +the employees get to paid like is there + + align:start position:0% +the employees get to paid like is there + + + align:start position:0% +the employees get to paid like is there +more value to employee that gets paid + + align:start position:0% +more value to employee that gets paid + + + align:start position:0% +more value to employee that gets paid +less working more because then it's it's + + align:start position:0% +less working more because then it's it's + + + align:start position:0% +less working more because then it's it's +cost it's cost you know I mean we're + + align:start position:0% +cost it's cost you know I mean we're + + + align:start position:0% +cost it's cost you know I mean we're +measuring everything in units of time + + align:start position:0% +measuring everything in units of time + + + align:start position:0% +measuring everything in units of time +but isn't there a dollars and cense + + align:start position:0% +but isn't there a dollars and cense + + + align:start position:0% +but isn't there a dollars and cense +equivalent well there is a dollars and + + align:start position:0% +equivalent well there is a dollars and + + + align:start position:0% +equivalent well there is a dollars and +cense but + + align:start position:0% + + + + align:start position:0% + +uh looking at certainly from a lean + + align:start position:0% +uh looking at certainly from a lean + + + align:start position:0% +uh looking at certainly from a lean +thinking point of view thinking about + + align:start position:0% +thinking point of view thinking about + + + align:start position:0% +thinking point of view thinking about +how I can reduce my labor costs as a + + align:start position:0% +how I can reduce my labor costs as a + + + align:start position:0% +how I can reduce my labor costs as a +starting position is is taking the the + + align:start position:0% +starting position is is taking the the + + + align:start position:0% +starting position is is taking the the +suboptimization what you want to do is + + align:start position:0% +suboptimization what you want to do is + + + align:start position:0% +suboptimization what you want to do is +look at how you can use those those + + align:start position:0% +look at how you can use those those + + + align:start position:0% +look at how you can use those those +employees more effectively and get rid + + align:start position:0% +employees more effectively and get rid + + + align:start position:0% +employees more effectively and get rid +of the + + align:start position:0% +of the + + + align:start position:0% +of the +the other costs you have or the other + + align:start position:0% +the other costs you have or the other + + + align:start position:0% +the other costs you have or the other +Inc capacity problems you have and you + + align:start position:0% +Inc capacity problems you have and you + + + align:start position:0% +Inc capacity problems you have and you +know reward your employees so now in the + + align:start position:0% +know reward your employees so now in the + + + align:start position:0% +know reward your employees so now in the +end you know there is a limit to + + align:start position:0% +end you know there is a limit to + + + align:start position:0% +end you know there is a limit to +everything of course I mean if you got + + align:start position:0% +everything of course I mean if you got + + + align:start position:0% +everything of course I mean if you got +$80,000 hot dog flippers you know you're + + align:start position:0% +$80,000 hot dog flippers you know you're + + + align:start position:0% +$80,000 hot dog flippers you know you're +not going to be competitive but uh I + + align:start position:0% +not going to be competitive but uh I + + + align:start position:0% +not going to be competitive but uh I +mean look what we saw at New Balance you + + align:start position:0% +mean look what we saw at New Balance you + + + align:start position:0% +mean look what we saw at New Balance you +know those ladies up there are making + + align:start position:0% +know those ladies up there are making + + + align:start position:0% +know those ladies up there are making +shoes that are competitive in the + + align:start position:0% +shoes that are competitive in the + + + align:start position:0% +shoes that are competitive in the +marketplace and they're not going to + + align:start position:0% +marketplace and they're not going to + + + align:start position:0% +marketplace and they're not going to +China they're probably getting paid + + align:start position:0% +China they're probably getting paid + + + align:start position:0% +China they're probably getting paid +what's the labor rate between US and + + align:start position:0% +what's the labor rate between US and + + + align:start position:0% +what's the labor rate between US and +China 20 20 factor of 20 sure at least + + align:start position:0% +China 20 20 factor of 20 sure at least + + + align:start position:0% +China 20 20 factor of 20 sure at least +you know but new balance is managing + + align:start position:0% +you know but new balance is managing + + + align:start position:0% +you know but new balance is managing +it's a privately held company so they + + align:start position:0% +it's a privately held company so they + + + align:start position:0% +it's a privately held company so they +making money okay and uh so thinking of + + align:start position:0% +making money okay and uh so thinking of + + + align:start position:0% +making money okay and uh so thinking of +just reducing labor costs as the first + + align:start position:0% +just reducing labor costs as the first + + + align:start position:0% +just reducing labor costs as the first +thing is not it's just not a lean + + align:start position:0% +thing is not it's just not a lean + + + align:start position:0% +thing is not it's just not a lean +thinking principle uh another thing that + + align:start position:0% +thinking principle uh another thing that + + + align:start position:0% +thinking principle uh another thing that +Earl seen out there we took uh one of + + align:start position:0% +Earl seen out there we took uh one of + + + align:start position:0% +Earl seen out there we took uh one of +the the Arizona State team through the + + align:start position:0% +the the Arizona State team through the + + + align:start position:0% +the the Arizona State team through the +Apache production line and we actually + + align:start position:0% +Apache production line and we actually + + + align:start position:0% +Apache production line and we actually +incentivize the employees to beat they + + align:start position:0% +incentivize the employees to beat they + + + align:start position:0% +incentivize the employees to beat they +they they help schedule but that we + + align:start position:0% +they they help schedule but that we + + + align:start position:0% +they they help schedule but that we +there's a schedule goal a cost goal and + + align:start position:0% +there's a schedule goal a cost goal and + + + align:start position:0% +there's a schedule goal a cost goal and +a quality goal if they they beat that + + align:start position:0% +a quality goal if they they beat that + + + align:start position:0% +a quality goal if they they beat that +goal and actually reduce the learning + + align:start position:0% +goal and actually reduce the learning + + + align:start position:0% +goal and actually reduce the learning +curve better than what we in fact put in + + align:start position:0% +curve better than what we in fact put in + + + align:start position:0% +curve better than what we in fact put in +the business plan we share that underrun + + align:start position:0% +the business plan we share that underrun + + + align:start position:0% +the business plan we share that underrun +with the employees so they're motivated + + align:start position:0% +with the employees so they're motivated + + + align:start position:0% +with the employees so they're motivated +to beat all three goals and it's not + + align:start position:0% +to beat all three goals and it's not + + + align:start position:0% +to beat all three goals and it's not +just pushing out the door it's got to be + + align:start position:0% +just pushing out the door it's got to be + + + align:start position:0% +just pushing out the door it's got to be +high quality the Army w't accept it so + + align:start position:0% +high quality the Army w't accept it so + + + align:start position:0% +high quality the Army w't accept it so +they have to beat all three goals but + + align:start position:0% +they have to beat all three goals but + + + align:start position:0% +they have to beat all three goals but +those are those teams are self-managed + + align:start position:0% +those are those teams are self-managed + + + align:start position:0% +those are those teams are self-managed +and they they work so you can you have + + align:start position:0% +and they they work so you can you have + + + align:start position:0% +and they they work so you can you have +you have to put the dollar incentives on + + align:start position:0% +you have to put the dollar incentives on + + + align:start position:0% +you have to put the dollar incentives on +the right things and that's delivering + + align:start position:0% +the right things and that's delivering + + + align:start position:0% +the right things and that's delivering +value to the customer scheduled cost and + + align:start position:0% +value to the customer scheduled cost and + + + align:start position:0% +value to the customer scheduled cost and +quality uh but you can in fact share + + align:start position:0% +quality uh but you can in fact share + + + align:start position:0% +quality uh but you can in fact share +that with the employees and they're very + + align:start position:0% +that with the employees and they're very + + + align:start position:0% +that with the employees and they're very +motivated so a a mass production + + align:start position:0% +motivated so a a mass production + + + align:start position:0% +motivated so a a mass production +thinking is that the workers are + + align:start position:0% +thinking is that the workers are + + + align:start position:0% +thinking is that the workers are +interchangeable cogs and you know if we + + align:start position:0% +interchangeable cogs and you know if we + + + align:start position:0% +interchangeable cogs and you know if we +don't need them now we'll get rid of + + align:start position:0% +don't need them now we'll get rid of + + + align:start position:0% +don't need them now we'll get rid of +them and we'll go down to the job Hall + + align:start position:0% +them and we'll go down to the job Hall + + + align:start position:0% +them and we'll go down to the job Hall +and hire more when we need them and that + + align:start position:0% +and hire more when we need them and that + + + align:start position:0% +and hire more when we need them and that +they're just and the lean the lean + + align:start position:0% +they're just and the lean the lean + + + align:start position:0% +they're just and the lean the lean +approach is the workers are your most + + align:start position:0% +approach is the workers are your most + + + align:start position:0% +approach is the workers are your most +valuable resource and and let them help + + align:start position:0% +valuable resource and and let them help + + + align:start position:0% +valuable resource and and let them help +you make the system better and compens + + align:start position:0% +you make the system better and compens + + + align:start position:0% +you make the system better and compens +them + + align:start position:0% +them + + + align:start position:0% +them +okay okay we're about ready to wrap up + + align:start position:0% +okay okay we're about ready to wrap up + + + align:start position:0% +okay okay we're about ready to wrap up +this module okay so we we kind of you + + align:start position:0% +this module okay so we we kind of you + + + align:start position:0% +this module okay so we we kind of you +know quickly gone through the first + + align:start position:0% +know quickly gone through the first + + + align:start position:0% +know quickly gone through the first +three steps of value stream mapping + + align:start position:0% +three steps of value stream mapping + + + align:start position:0% +three steps of value stream mapping +obviously you know we we've kind of + + align:start position:0% +obviously you know we we've kind of + + + align:start position:0% +obviously you know we we've kind of +rushed it but you've been through a + + align:start position:0% +rushed it but you've been through a + + + align:start position:0% +rushed it but you've been through a +cycle now tomorrow you're going to go + + align:start position:0% +cycle now tomorrow you're going to go + + + align:start position:0% +cycle now tomorrow you're going to go +through this again in a in a Lego + + align:start position:0% +through this again in a in a Lego + + + align:start position:0% +through this again in a in a Lego +simulation okay so what would you know + + align:start position:0% +simulation okay so what would you know + + + align:start position:0% +simulation okay so what would you know +do now where we're at well you would say + + align:start position:0% +do now where we're at well you would say + + + align:start position:0% +do now where we're at well you would say +Sasha and Andy would sit down and say + + align:start position:0% +Sasha and Andy would sit down and say + + + align:start position:0% +Sasha and Andy would sit down and say +let's let's now we have this data and + + align:start position:0% +let's let's now we have this data and + + + align:start position:0% +let's let's now we have this data and +see how bad our process really is let's + + align:start position:0% +see how bad our process really is let's + + + align:start position:0% +see how bad our process really is let's +Envision a much better process and you + + align:start position:0% +Envision a much better process and you + + + align:start position:0% +Envision a much better process and you +would map that out + + align:start position:0% +would map that out + + + align:start position:0% +would map that out +and then you'd go implement it for them + + align:start position:0% +and then you'd go implement it for them + + + align:start position:0% +and then you'd go implement it for them +that would be pretty simple and you + + align:start position:0% +that would be pretty simple and you + + + align:start position:0% +that would be pretty simple and you +would do it again kind of you know + + align:start position:0% +would do it again kind of you know + + + align:start position:0% +would do it again kind of you know +taking the the the lowrisk steps first + + align:start position:0% +taking the the the lowrisk steps first + + + align:start position:0% +taking the the the lowrisk steps first +you don't want to break the + + align:start position:0% +you don't want to break the + + + align:start position:0% +you don't want to break the +system okay so why is value stream + + align:start position:0% +system okay so why is value stream + + + align:start position:0% +system okay so why is value stream +mapping so useful boy we heard about and + + align:start position:0% +mapping so useful boy we heard about and + + + align:start position:0% +mapping so useful boy we heard about and +we heard about it today okay first of + + align:start position:0% +we heard about it today okay first of + + + align:start position:0% +we heard about it today okay first of +all multiple people can visualize the + + align:start position:0% +all multiple people can visualize the + + + align:start position:0% +all multiple people can visualize the +whole process and see what the whole + + align:start position:0% +whole process and see what the whole + + + align:start position:0% +whole process and see what the whole +process is opposed to just their little + + align:start position:0% +process is opposed to just their little + + + align:start position:0% +process is opposed to just their little +piece and it's really very hard to do + + align:start position:0% +piece and it's really very hard to do + + + align:start position:0% +piece and it's really very hard to do +without some visual tool it's hard to + + align:start position:0% +without some visual tool it's hard to + + + align:start position:0% +without some visual tool it's hard to +describe you know it's hard if you and I + + align:start position:0% +describe you know it's hard if you and I + + + align:start position:0% +describe you know it's hard if you and I +sit down and say what do you do and what + + align:start position:0% +sit down and say what do you do and what + + + align:start position:0% +sit down and say what do you do and what +do I do it's not the same as us + + align:start position:0% +do I do it's not the same as us + + + align:start position:0% +do I do it's not the same as us +collectively sitting down and building a + + align:start position:0% +collectively sitting down and building a + + + align:start position:0% +collectively sitting down and building a +value stream map then we really + + align:start position:0% +value stream map then we really + + + align:start position:0% +value stream map then we really +understand it it's it's like Active + + align:start position:0% +understand it it's it's like Active + + + align:start position:0% +understand it it's it's like Active +Learning it's internalizing it okay you + + align:start position:0% +Learning it's internalizing it okay you + + + align:start position:0% +Learning it's internalizing it okay you +can see what the linkages are in the in + + align:start position:0% +can see what the linkages are in the in + + + align:start position:0% +can see what the linkages are in the in +the + + align:start position:0% +the + + + align:start position:0% +the +process uh it by working together you + + align:start position:0% +process uh it by working together you + + + align:start position:0% +process uh it by working together you +develop a Common Language so you can + + align:start position:0% +develop a Common Language so you can + + + align:start position:0% +develop a Common Language so you can +communicate with your workers and and we + + align:start position:0% +communicate with your workers and and we + + + align:start position:0% +communicate with your workers and and we +saw up at New Balance how they uh at + + align:start position:0% +saw up at New Balance how they uh at + + + align:start position:0% +saw up at New Balance how they uh at +least on our tour that Walda took us on + + align:start position:0% +least on our tour that Walda took us on + + + align:start position:0% +least on our tour that Walda took us on +she said you know someone uh is missing + + align:start position:0% +she said you know someone uh is missing + + + align:start position:0% +she said you know someone uh is missing +for a day here or something this person + + align:start position:0% +for a day here or something this person + + + align:start position:0% +for a day here or something this person +can step in and do their job because + + align:start position:0% +can step in and do their job because + + + align:start position:0% +can step in and do their job because +they understand what that job is and how + + align:start position:0% +they understand what that job is and how + + + align:start position:0% +they understand what that job is and how +that job fits in the overall flow okay + + align:start position:0% +that job fits in the overall flow okay + + + align:start position:0% +that job fits in the overall flow okay +and then you can find out where the + + align:start position:0% +and then you can find out where the + + + align:start position:0% +and then you can find out where the +constraints are in the system so it's a + + align:start position:0% +constraints are in the system so it's a + + + align:start position:0% +constraints are in the system so it's a +again a system level thing find out + + align:start position:0% +again a system level thing find out + + + align:start position:0% +again a system level thing find out +where the constraints are uh and how + + align:start position:0% +where the constraints are uh and how + + + align:start position:0% +where the constraints are uh and how +that matches up against capacity and the + + align:start position:0% +that matches up against capacity and the + + + align:start position:0% +that matches up against capacity and the +Wast and their sources so it's it's a + + align:start position:0% +Wast and their sources so it's it's a + + + align:start position:0% +Wast and their sources so it's it's a +very powerful tool so finally where are + + align:start position:0% +very powerful tool so finally where are + + + align:start position:0% +very powerful tool so finally where are +some tips involve every everybody don't + + align:start position:0% +some tips involve every everybody don't + + + align:start position:0% +some tips involve every everybody don't +this isn't something where you hire + + align:start position:0% +this isn't something where you hire + + + align:start position:0% +this isn't something where you hire +McKenzie to come in and do a value + + align:start position:0% +McKenzie to come in and do a value + + + align:start position:0% +McKenzie to come in and do a value +stream map and then give it to everybody + + align:start position:0% +stream map and then give it to everybody + + + align:start position:0% +stream map and then give it to everybody +because they won't understand it okay + + align:start position:0% +because they won't understand it okay + + + align:start position:0% +because they won't understand it okay +they have to do it themselves okay and + + align:start position:0% +they have to do it themselves okay and + + + align:start position:0% +they have to do it themselves okay and +it takes a little bit of time mark it + + align:start position:0% +it takes a little bit of time mark it + + + align:start position:0% +it takes a little bit of time mark it +takes time takes them away from their + + align:start position:0% +takes time takes them away from their + + + align:start position:0% +takes time takes them away from their +job but the payoffs usually much greater + + align:start position:0% +job but the payoffs usually much greater + + + align:start position:0% +job but the payoffs usually much greater +you actually strap yourself to the + + align:start position:0% +you actually strap yourself to the + + + align:start position:0% +you actually strap yourself to the +process you walk through it um from + + align:start position:0% +process you walk through it um from + + + align:start position:0% +process you walk through it um from +beginning to end you know do it in some + + align:start position:0% +beginning to end you know do it in some + + + align:start position:0% +beginning to end you know do it in some +environment like this where you can move + + align:start position:0% +environment like this where you can move + + + align:start position:0% +environment like this where you can move +the poits around uh you can collectively + + align:start position:0% +the poits around uh you can collectively + + + align:start position:0% +the poits around uh you can collectively +gather around as a group and you know + + align:start position:0% +gather around as a group and you know + + + align:start position:0% +gather around as a group and you know +look at this chart you know you can put + + align:start position:0% +look at this chart you know you can put + + + align:start position:0% +look at this chart you know you can put +your Post-its here and you can all + + align:start position:0% +your Post-its here and you can all + + + align:start position:0% +your Post-its here and you can all +participate it's a very flexible + + align:start position:0% +participate it's a very flexible + + + align:start position:0% +participate it's a very flexible +environment uh at this level a software + + align:start position:0% +environment uh at this level a software + + + align:start position:0% +environment uh at this level a software +tool is not nearly as effective as just + + align:start position:0% +tool is not nearly as effective as just + + + align:start position:0% +tool is not nearly as effective as just +butcher paper and Post-its uh now if + + align:start position:0% +butcher paper and Post-its uh now if + + + align:start position:0% +butcher paper and Post-its uh now if +you're if you're mapping the whole value + + align:start position:0% +you're if you're mapping the whole value + + + align:start position:0% +you're if you're mapping the whole value +stream of the + + align:start position:0% +stream of the + + + align:start position:0% +stream of the +787 you know you're eventually probably + + align:start position:0% +787 you know you're eventually probably + + + align:start position:0% +787 you know you're eventually probably +going to have to get into some form that + + align:start position:0% +going to have to get into some form that + + + align:start position:0% +going to have to get into some form that +you can distribute but at a starting + + align:start position:0% +you can distribute but at a starting + + + align:start position:0% +you can distribute but at a starting +point you want to use something that's + + align:start position:0% +point you want to use something that's + + + align:start position:0% +point you want to use something that's +very simple use meaningful icons agree + + align:start position:0% +very simple use meaningful icons agree + + + align:start position:0% +very simple use meaningful icons agree +on what they are that so that you're + + align:start position:0% +on what they are that so that you're + + + align:start position:0% +on what they are that so that you're +communicating with each other and that + + align:start position:0% +communicating with each other and that + + + align:start position:0% +communicating with each other and that +those are the basic + + align:start position:0% +those are the basic + + + align:start position:0% +those are the basic +steps okay if you want to get more + + align:start position:0% +steps okay if you want to get more + + + align:start position:0% +steps okay if you want to get more +information on this there's a book + + align:start position:0% +information on this there's a book + + + align:start position:0% +information on this there's a book +called learning to see that really uh + + align:start position:0% +called learning to see that really uh + + + align:start position:0% +called learning to see that really uh +lays this whole thing out uh this is + + align:start position:0% +lays this whole thing out uh this is + + + align:start position:0% +lays this whole thing out uh this is +really for factory type operations like + + align:start position:0% +really for factory type operations like + + + align:start position:0% +really for factory type operations like +we saw at New Balance humic Manis has + + align:start position:0% +we saw at New Balance humic Manis has + + + align:start position:0% +we saw at New Balance humic Manis has +created a version of that for + + align:start position:0% +created a version of that for + + + align:start position:0% +created a version of that for +engineering for what we call product + + align:start position:0% +engineering for what we call product + + + align:start position:0% +engineering for what we call product +development okay so that's the value + + align:start position:0% +development okay so that's the value + + + align:start position:0% +development okay so that's the value +stream mapping + + align:start position:0% +stream mapping + + + align:start position:0% +stream mapping +module \ No newline at end of file diff --git a/5auv_xrvoJk.txt b/5auv_xrvoJk.txt new file mode 100644 index 0000000000000000000000000000000000000000..d19f79b993992d60ab83be71728f87053d986d55 --- /dev/null +++ b/5auv_xrvoJk.txt @@ -0,0 +1,11867 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so today what we're going to be doing is + + align:start position:0% +so today what we're going to be doing is + + + align:start position:0% +so today what we're going to be doing is +last week you gave us some feedback what + + align:start position:0% +last week you gave us some feedback what + + + align:start position:0% +last week you gave us some feedback what +you want it to do in the class we're + + align:start position:0% +you want it to do in the class we're + + + align:start position:0% +you want it to do in the class we're +gonna go through that and talk about the + + align:start position:0% +gonna go through that and talk about the + + + align:start position:0% +gonna go through that and talk about the +readings I'm going to do a little + + align:start position:0% +readings I'm going to do a little + + + align:start position:0% +readings I'm going to do a little +calling on you and helping you take the + + align:start position:0% +calling on you and helping you take the + + + align:start position:0% +calling on you and helping you take the +class through the readings and then the + + align:start position:0% +class through the readings and then the + + + align:start position:0% +class through the readings and then the +six or seven things I'm going to do + + align:start position:0% +six or seven things I'm going to do + + + align:start position:0% +six or seven things I'm going to do +history of money ledgers fiat currency + + align:start position:0% +history of money ledgers fiat currency + + + align:start position:0% +history of money ledgers fiat currency +central banks and credit cards the role + + align:start position:0% +central banks and credit cards the role + + + align:start position:0% +central banks and credit cards the role +of money some early digital money you + + align:start position:0% +of money some early digital money you + + + align:start position:0% +of money some early digital money you +had the clerk reading as to a bunch of + + align:start position:0% +had the clerk reading as to a bunch of + + + align:start position:0% +had the clerk reading as to a bunch of +failed attempts just all the way through + + align:start position:0% +failed attempts just all the way through + + + align:start position:0% +failed attempts just all the way through +a little bit of mobile money all the way + + align:start position:0% +a little bit of mobile money all the way + + + align:start position:0% +a little bit of mobile money all the way +up to Starbucks and and Allie pay and + + align:start position:0% +up to Starbucks and and Allie pay and + + + align:start position:0% +up to Starbucks and and Allie pay and +yet the riddle remains we're gonna get + + align:start position:0% +yet the riddle remains we're gonna get + + + align:start position:0% +yet the riddle remains we're gonna get +really deep into Bitcoin then the next + + align:start position:0% +really deep into Bitcoin then the next + + + align:start position:0% +really deep into Bitcoin then the next +three classes but this is to give some + + align:start position:0% +three classes but this is to give some + + + align:start position:0% +three classes but this is to give some +foundational bits of money and Ledger's + + align:start position:0% +foundational bits of money and Ledger's + + + align:start position:0% +foundational bits of money and Ledger's +and central banking and Technology and + + align:start position:0% +and central banking and Technology and + + + align:start position:0% +and central banking and Technology and +then of course I always like to finish + + align:start position:0% +then of course I always like to finish + + + align:start position:0% +then of course I always like to finish +the class talking a little bit about why + + align:start position:0% +the class talking a little bit about why + + + align:start position:0% +the class talking a little bit about why +we're doing what we're doing between now + + align:start position:0% +we're doing what we're doing between now + + + align:start position:0% +we're doing what we're doing between now +and then even though the readings are + + align:start position:0% +and then even though the readings are + + + align:start position:0% +and then even though the readings are +required I know you're all busy I know + + align:start position:0% +required I know you're all busy I know + + + align:start position:0% +required I know you're all busy I know +that you've all got a bunch of classes + + align:start position:0% +that you've all got a bunch of classes + + + align:start position:0% +that you've all got a bunch of classes +and like good business students and + + align:start position:0% +and like good business students and + + + align:start position:0% +and like good business students and +business people you optimized so I'm + + align:start position:0% +business people you optimized so I'm + + + align:start position:0% +business people you optimized so I'm +trying to give you a sense of why you + + align:start position:0% +trying to give you a sense of why you + + + align:start position:0% +trying to give you a sense of why you +might read it rather than it's required + + align:start position:0% +might read it rather than it's required + + + align:start position:0% +might read it rather than it's required +at the end of each class and how it fits + + align:start position:0% +at the end of each class and how it fits + + + align:start position:0% +at the end of each class and how it fits +into the the course narrative and then + + align:start position:0% +into the the course narrative and then + + + align:start position:0% +into the the course narrative and then +we'll do a little bit of conclusions so + + align:start position:0% +we'll do a little bit of conclusions so + + + align:start position:0% +we'll do a little bit of conclusions so +the survey results what did you want to + + align:start position:0% +the survey results what did you want to + + + align:start position:0% +the survey results what did you want to +learn this is really your class and I'm + + align:start position:0% +learn this is really your class and I'm + + + align:start position:0% +learn this is really your class and I'm +gonna learn as much from you but + + align:start position:0% +gonna learn as much from you but + + + align:start position:0% +gonna learn as much from you but +hopefully we're gonna cover what you + + align:start position:0% +hopefully we're gonna cover what you + + + align:start position:0% +hopefully we're gonna cover what you +want so here's a list of those things + + align:start position:0% +want so here's a list of those things + + + align:start position:0% +want so here's a list of those things +that were at least written by two of you + + align:start position:0% +that were at least written by two of you + + + align:start position:0% +that were at least written by two of you +first was technical things eighteen of + + align:start position:0% +first was technical things eighteen of + + + align:start position:0% +first was technical things eighteen of +you said understanding blockchain + + align:start position:0% +you said understanding blockchain + + + align:start position:0% +you said understanding blockchain +technology hopefully we get to that but + + align:start position:0% +technology hopefully we get to that but + + + align:start position:0% +technology hopefully we get to that but +you might find that you'll want to do + + align:start position:0% +you might find that you'll want to do + + + align:start position:0% +you might find that you'll want to do +more after this class the ecosystem and + + align:start position:0% +more after this class the ecosystem and + + + align:start position:0% +more after this class the ecosystem and +being able to have an educated + + align:start position:0% +being able to have an educated + + + align:start position:0% +being able to have an educated +discussion sort of the dinner party + + align:start position:0% +discussion sort of the dinner party + + + align:start position:0% +discussion sort of the dinner party +conversation around blockchain I I think + + align:start position:0% +conversation around blockchain I I think + + + align:start position:0% +conversation around blockchain I I think +will be successful but at the end of the + + align:start position:0% +will be successful but at the end of the + + + align:start position:0% +will be successful but at the end of the +semester we're gonna pull these slides + + align:start position:0% +semester we're gonna pull these slides + + + align:start position:0% +semester we're gonna pull these slides +up again and we'll see how we did as a + + align:start position:0% +up again and we'll see how we did as a + + + align:start position:0% +up again and we'll see how we did as a +group you all talked a lot about + + align:start position:0% +group you all talked a lot about + + + align:start position:0% +group you all talked a lot about +applications how can you actually apply + + align:start position:0% +applications how can you actually apply + + + align:start position:0% +applications how can you actually apply +it learning it in the venture space and + + align:start position:0% +it learning it in the venture space and + + + align:start position:0% +it learning it in the venture space and +about where it really works in the world + + align:start position:0% +about where it really works in the world + + + align:start position:0% +about where it really works in the world +and I think we're gonna spend a lot of + + align:start position:0% +and I think we're gonna spend a lot of + + + align:start position:0% +and I think we're gonna spend a lot of +time on that in the second half but all + + align:start position:0% +time on that in the second half but all + + + align:start position:0% +time on that in the second half but all +throughout we're gonna be talking about + + align:start position:0% +throughout we're gonna be talking about + + + align:start position:0% +throughout we're gonna be talking about +the economics and what's the reality + + align:start position:0% +the economics and what's the reality + + + align:start position:0% +the economics and what's the reality +versus the hype you also wanted to + + align:start position:0% +versus the hype you also wanted to + + + align:start position:0% +versus the hype you also wanted to +understand its impact on people's lives + + align:start position:0% +understand its impact on people's lives + + + align:start position:0% +understand its impact on people's lives +the regulation about six of you said + + align:start position:0% +the regulation about six of you said + + + align:start position:0% +the regulation about six of you said +something about regulation I'm glad + + align:start position:0% +something about regulation I'm glad + + + align:start position:0% +something about regulation I'm glad +because we're only doing one lecture on + + align:start position:0% +because we're only doing one lecture on + + + align:start position:0% +because we're only doing one lecture on +that but we're gonna spread it out + + align:start position:0% +that but we're gonna spread it out + + + align:start position:0% +that but we're gonna spread it out +because as we talked about in our first + + align:start position:0% +because as we talked about in our first + + + align:start position:0% +because as we talked about in our first +class and I'm honored Larry's here again + + align:start position:0% +class and I'm honored Larry's here again + + + align:start position:0% +class and I'm honored Larry's here again +but you know we're gonna always be + + align:start position:0% +but you know we're gonna always be + + + align:start position:0% +but you know we're gonna always be +thinking about Larry's four ways and I + + align:start position:0% +thinking about Larry's four ways and I + + + align:start position:0% +thinking about Larry's four ways and I +see is it he where Larry Lessig's you + + align:start position:0% +see is it he where Larry Lessig's you + + + align:start position:0% +see is it he where Larry Lessig's you +shook your head yes does anybody want to + + align:start position:0% +shook your head yes does anybody want to + + + align:start position:0% +shook your head yes does anybody want to +say how that relates to blockchain why + + align:start position:0% +say how that relates to blockchain why + + + align:start position:0% +say how that relates to blockchain why +we're chatting about that oh my god I'm + + align:start position:0% +we're chatting about that oh my god I'm + + + align:start position:0% +we're chatting about that oh my god I'm +gonna have to cold call fast right oh + + align:start position:0% +gonna have to cold call fast right oh + + + align:start position:0% +gonna have to cold call fast right oh +you're from r3 maybe not + + align:start position:0% +you're from r3 maybe not + + + align:start position:0% +you're from r3 maybe not +Ilan help your your table made out this + + align:start position:0% +Ilan help your your table made out this + + + align:start position:0% +Ilan help your your table made out this +isn't it I'm having fun you know this is + + align:start position:0% +isn't it I'm having fun you know this is + + + align:start position:0% +isn't it I'm having fun you know this is +what I'm gonna do I'm just gonna have + + align:start position:0% +what I'm gonna do I'm just gonna have + + + align:start position:0% +what I'm gonna do I'm just gonna have +fun twere e about it all so why to + + align:start position:0% +fun twere e about it all so why to + + + align:start position:0% +fun twere e about it all so why to +markets code law did I hear did I can't + + align:start position:0% +markets code law did I hear did I can't + + + align:start position:0% +markets code law did I hear did I can't +see your name but it's it the doric yeah + + align:start position:0% +see your name but it's it the doric yeah + + + align:start position:0% +see your name but it's it the doric yeah +why why is that relate to all this + + align:start position:0% + + + + align:start position:0% + +jihee you're gonna repeat the question + + align:start position:0% +jihee you're gonna repeat the question + + + align:start position:0% +jihee you're gonna repeat the question +because you you went through it wery + + align:start position:0% +because you you went through it wery + + + align:start position:0% +because you you went through it wery +larry's for horses relate to our + + align:start position:0% +larry's for horses relate to our + + + align:start position:0% +larry's for horses relate to our +commerce our topic of watch for horses + + align:start position:0% +commerce our topic of watch for horses + + + align:start position:0% +commerce our topic of watch for horses +again our markets so business law code + + align:start position:0% +again our markets so business law code + + + align:start position:0% +again our markets so business law code +or architecture call it technology and + + align:start position:0% +or architecture call it technology and + + + align:start position:0% +or architecture call it technology and +social norms so what I got from the real + + align:start position:0% +social norms so what I got from the real + + + align:start position:0% +social norms so what I got from the real +you today these Ledger's for me already + + align:start position:0% +you today these Ledger's for me already + + + align:start position:0% +you today these Ledger's for me already +existed but giving that now we have + + align:start position:0% +existed but giving that now we have + + + align:start position:0% +existed but giving that now we have +makes you think for example and more + + align:start position:0% +makes you think for example and more + + + align:start position:0% +makes you think for example and more +things going on help society good way to + + align:start position:0% +things going on help society good way to + + + align:start position:0% +things going on help society good way to +say look it's unfair of me it wasn't one + + align:start position:0% +say look it's unfair of me it wasn't one + + + align:start position:0% +say look it's unfair of me it wasn't one +of the readings I'm just saying in + + align:start position:0% +of the readings I'm just saying in + + + align:start position:0% +of the readings I'm just saying in +everything in life I find these things + + align:start position:0% +everything in life I find these things + + + align:start position:0% +everything in life I find these things +grind up against each other I spent a + + align:start position:0% +grind up against each other I spent a + + + align:start position:0% +grind up against each other I spent a +lot of time in Washington in politics + + align:start position:0% +lot of time in Washington in politics + + + align:start position:0% +lot of time in Washington in politics +but the markets and how the commercial + + align:start position:0% +but the markets and how the commercial + + + align:start position:0% +but the markets and how the commercial +enterprise and the economy grinds up + + align:start position:0% +enterprise and the economy grinds up + + + align:start position:0% +enterprise and the economy grinds up +against technology and sort of grinds up + + align:start position:0% +against technology and sort of grinds up + + + align:start position:0% +against technology and sort of grinds up +against the law and then of course to + + align:start position:0% +against the law and then of course to + + + align:start position:0% +against the law and then of course to +social normative behavior these four + + align:start position:0% +social normative behavior these four + + + align:start position:0% +social normative behavior these four +forces and almost everything one does in + + align:start position:0% +forces and almost everything one does in + + + align:start position:0% +forces and almost everything one does in +life you will find and so I I just ask + + align:start position:0% +life you will find and so I I just ask + + + align:start position:0% +life you will find and so I I just ask +you to always whether it's one reading + + align:start position:0% +you to always whether it's one reading + + + align:start position:0% +you to always whether it's one reading +or another reading bring that to your + + align:start position:0% +or another reading bring that to your + + + align:start position:0% +or another reading bring that to your +thought process of this class I'm not + + align:start position:0% +thought process of this class I'm not + + + align:start position:0% +thought process of this class I'm not +gonna sign Larry's assignment I didn't + + align:start position:0% +gonna sign Larry's assignment I didn't + + + align:start position:0% +gonna sign Larry's assignment I didn't +know he was even gonna be here but I've + + align:start position:0% +know he was even gonna be here but I've + + + align:start position:0% +know he was even gonna be here but I've +always thought these is it's a good + + align:start position:0% +always thought these is it's a good + + + align:start position:0% +always thought these is it's a good +discipline to think okay what are the + + align:start position:0% +discipline to think okay what are the + + + align:start position:0% +discipline to think okay what are the +commercial realities the markets what's + + align:start position:0% +commercial realities the markets what's + + + align:start position:0% +commercial realities the markets what's +the technology even if it's in an + + align:start position:0% +the technology even if it's in an + + + align:start position:0% +the technology even if it's in an +earlier day and it's a technology of the + + align:start position:0% +earlier day and it's a technology of the + + + align:start position:0% +earlier day and it's a technology of the +car replacing the horse and carriage had + + align:start position:0% +car replacing the horse and carriage had + + + align:start position:0% +car replacing the horse and carriage had +it had US government or the official + + align:start position:0% +it had US government or the official + + + align:start position:0% +it had US government or the official +sector put it into a set of standards + + align:start position:0% +sector put it into a set of standards + + + align:start position:0% +sector put it into a set of standards +that are required and then how do we a + + align:start position:0% +that are required and then how do we a + + + align:start position:0% +that are required and then how do we a +society even if it's not required just + + align:start position:0% +society even if it's not required just + + + align:start position:0% +society even if it's not required just +have our behaviors those are the four + + align:start position:0% +have our behaviors those are the four + + + align:start position:0% +have our behaviors those are the four +forces so that's why and I probably just + + align:start position:0% +forces so that's why and I probably just + + + align:start position:0% +forces so that's why and I probably just +failed Larry's class but + + align:start position:0% +failed Larry's class but + + + align:start position:0% +failed Larry's class but +so I've thought of it I did probably + + align:start position:0% +so I've thought of it I did probably + + + align:start position:0% +so I've thought of it I did probably +right you know he's he's shaking his + + align:start position:0% +right you know he's he's shaking his + + + align:start position:0% +right you know he's he's shaking his +head but regulation is just one of those + + align:start position:0% +head but regulation is just one of those + + + align:start position:0% +head but regulation is just one of those +four forces and that's why I pause there + + align:start position:0% +four forces and that's why I pause there + + + align:start position:0% +four forces and that's why I pause there +and so we'll have it in every class but + + align:start position:0% +and so we'll have it in every class but + + + align:start position:0% +and so we'll have it in every class but +only one lecture money and markets + + align:start position:0% +only one lecture money and markets + + + align:start position:0% +only one lecture money and markets +that's a one of the other forces five of + + align:start position:0% +that's a one of the other forces five of + + + align:start position:0% +that's a one of the other forces five of +you said you want to make money and I + + align:start position:0% +you said you want to make money and I + + + align:start position:0% +you said you want to make money and I +applaud those who said that because own + + align:start position:0% +applaud those who said that because own + + + align:start position:0% +applaud those who said that because own +it you're in a business school why not + + align:start position:0% +it you're in a business school why not + + + align:start position:0% +it you're in a business school why not +but investing in trance now there was a + + align:start position:0% +but investing in trance now there was a + + + align:start position:0% +but investing in trance now there was a +bunch of other miscellaneous topics I'm + + align:start position:0% +bunch of other miscellaneous topics I'm + + + align:start position:0% +bunch of other miscellaneous topics I'm +not going to go through them I kind of + + align:start position:0% +not going to go through them I kind of + + + align:start position:0% +not going to go through them I kind of +thought the last two were interesting + + align:start position:0% +thought the last two were interesting + + + align:start position:0% +thought the last two were interesting +anecdotes from my past I'm not sure who + + align:start position:0% +anecdotes from my past I'm not sure who + + + align:start position:0% +anecdotes from my past I'm not sure who +said that not sure what you want to know + + align:start position:0% +said that not sure what you want to know + + + align:start position:0% +said that not sure what you want to know +about my three daughter is my running or + + align:start position:0% +about my three daughter is my running or + + + align:start position:0% +about my three daughter is my running or +this you know Wall Street stuff in + + align:start position:0% +this you know Wall Street stuff in + + + align:start position:0% +this you know Wall Street stuff in +finance and I'd like to understand hyper + + align:start position:0% +finance and I'd like to understand hyper + + + align:start position:0% +finance and I'd like to understand hyper +bitcoin ization as well but I don't know + + align:start position:0% +bitcoin ization as well but I don't know + + + align:start position:0% +bitcoin ization as well but I don't know +who asked that question I don't know + + align:start position:0% +who asked that question I don't know + + + align:start position:0% +who asked that question I don't know +what it is so I'll try to figure out + + align:start position:0% +what it is so I'll try to figure out + + + align:start position:0% +what it is so I'll try to figure out +what hyper does anyone want to own up to + + align:start position:0% +what hyper does anyone want to own up to + + + align:start position:0% +what hyper does anyone want to own up to +that question + + align:start position:0% +that question + + + align:start position:0% +that question +they were anonymous alright alright so + + align:start position:0% +they were anonymous alright alright so + + + align:start position:0% +they were anonymous alright alright so +today's study questions what's the role + + align:start position:0% +today's study questions what's the role + + + align:start position:0% +today's study questions what's the role +of money historically and in today's + + align:start position:0% +of money historically and in today's + + + align:start position:0% +of money historically and in today's +digital economy and this is what I'm + + align:start position:0% +digital economy and this is what I'm + + + align:start position:0% +digital economy and this is what I'm +gonna look for discussions so as anybody + + align:start position:0% +gonna look for discussions so as anybody + + + align:start position:0% +gonna look for discussions so as anybody +want to tell me what the role of money + + align:start position:0% +want to tell me what the role of money + + + align:start position:0% +want to tell me what the role of money +what would be your answer to this three + + align:start position:0% +what would be your answer to this three + + + align:start position:0% +what would be your answer to this three +three classic roles of money that people + + align:start position:0% +three classic roles of money that people + + + align:start position:0% +three classic roles of money that people +talk about Kelly you want to repeat what + + align:start position:0% +talk about Kelly you want to repeat what + + + align:start position:0% +talk about Kelly you want to repeat what +he just said you know in conquering + + align:start position:0% +he just said you know in conquering + + + align:start position:0% +he just said you know in conquering +various lands awards and also funding + + align:start position:0% + + + + align:start position:0% + +and what we'll discuss today and what it + + align:start position:0% +and what we'll discuss today and what it + + + align:start position:0% +and what we'll discuss today and what it +is is that money is a social construct + + align:start position:0% +is is that money is a social construct + + + align:start position:0% +is is that money is a social construct +it's something that societies came + + align:start position:0% +it's something that societies came + + + align:start position:0% +it's something that societies came +together whether it's hard to tell + + align:start position:0% +together whether it's hard to tell + + + align:start position:0% +together whether it's hard to tell +whether it was five thousand years ago + + align:start position:0% +whether it was five thousand years ago + + + align:start position:0% +whether it was five thousand years ago +or eight or ten thousand years ago that + + align:start position:0% +or eight or ten thousand years ago that + + + align:start position:0% +or eight or ten thousand years ago that +it's really it's a social consensus + + align:start position:0% +it's really it's a social consensus + + + align:start position:0% +it's really it's a social consensus +mechanism but we're gonna chat about the + + align:start position:0% +mechanism but we're gonna chat about the + + + align:start position:0% +mechanism but we're gonna chat about the +readings in a minute and come back to + + align:start position:0% +readings in a minute and come back to + + + align:start position:0% +readings in a minute and come back to +that question what is fiat currency is + + align:start position:0% +that question what is fiat currency is + + + align:start position:0% +that question what is fiat currency is +anybody want to Tom you want to tell us + + align:start position:0% +anybody want to Tom you want to tell us + + + align:start position:0% +anybody want to Tom you want to tell us +what fiat currency is right so you said + + align:start position:0% +what fiat currency is right so you said + + + align:start position:0% +what fiat currency is right so you said +it's a central currency and it's by + + align:start position:0% +it's a central currency and it's by + + + align:start position:0% +it's a central currency and it's by +government anybody else want to add some + + align:start position:0% +government anybody else want to add some + + + align:start position:0% +government anybody else want to add some +things as a Kyle not backed by any + + align:start position:0% +things as a Kyle not backed by any + + + align:start position:0% +things as a Kyle not backed by any +physical commodity do you want to add + + align:start position:0% +physical commodity do you want to add + + + align:start position:0% +physical commodity do you want to add +anything was it always that way the + + align:start position:0% +anything was it always that way the + + + align:start position:0% +anything was it always that way the +currency might be backed by something + + align:start position:0% +currency might be backed by something + + + align:start position:0% +currency might be backed by something +physical was there other remind me your + + align:start position:0% +physical was there other remind me your + + + align:start position:0% +physical was there other remind me your +name I'm sorry for taxes and remind me + + align:start position:0% +name I'm sorry for taxes and remind me + + + align:start position:0% +name I'm sorry for taxes and remind me +your name cuz I can't see a card so + + align:start position:0% +your name cuz I can't see a card so + + + align:start position:0% +your name cuz I can't see a card so +here's a question for the class is there + + align:start position:0% +here's a question for the class is there + + + align:start position:0% +here's a question for the class is there +inherent value to non fiat currencies + + align:start position:0% +inherent value to non fiat currencies + + + align:start position:0% +inherent value to non fiat currencies +because Shawn sang there may be a + + align:start position:0% +because Shawn sang there may be a + + + align:start position:0% +because Shawn sang there may be a +distinguishing characteristic of fiat is + + align:start position:0% +distinguishing characteristic of fiat is + + + align:start position:0% +distinguishing characteristic of fiat is +it has no inherent value + + align:start position:0% +it has no inherent value + + + align:start position:0% +it has no inherent value +well actually the same applies to any + + align:start position:0% +well actually the same applies to any + + + align:start position:0% +well actually the same applies to any +commodity that's used as purity you know + + align:start position:0% +commodity that's used as purity you know + + + align:start position:0% +commodity that's used as purity you know +because it's just this car to be of some + + align:start position:0% +because it's just this car to be of some + + + align:start position:0% +because it's just this car to be of some +specific resource and social common + + align:start position:0% +specific resource and social common + + + align:start position:0% +specific resource and social common +agreement that that's going to be the + + align:start position:0% + + + + align:start position:0% + +how many people are more in line with + + align:start position:0% +how many people are more in line with + + + align:start position:0% +how many people are more in line with +Eric or there's not one right answer to + + align:start position:0% +Eric or there's not one right answer to + + + align:start position:0% +Eric or there's not one right answer to +this this is this is a question that's + + align:start position:0% +this this is this is a question that's + + + align:start position:0% +this this is this is a question that's +been debated for decades or centuries + + align:start position:0% +been debated for decades or centuries + + + align:start position:0% +been debated for decades or centuries +but how many are more in Shawn's camp + + align:start position:0% +but how many are more in Shawn's camp + + + align:start position:0% +but how many are more in Shawn's camp +today for example gold is definitely + + align:start position:0% +today for example gold is definitely + + + align:start position:0% +today for example gold is definitely +like a social concept we decide that as + + align:start position:0% +like a social concept we decide that as + + + align:start position:0% +like a social concept we decide that as +a human society that gold is going to be + + align:start position:0% +a human society that gold is going to be + + + align:start position:0% +a human society that gold is going to be +something valuable but like if it's like + + align:start position:0% +something valuable but like if it's like + + + align:start position:0% +something valuable but like if it's like +you know grain that humans can't it it + + align:start position:0% +you know grain that humans can't it it + + + align:start position:0% +you know grain that humans can't it it +and you know that I've been quietly here + + align:start position:0% +and you know that I've been quietly here + + + align:start position:0% +and you know that I've been quietly here +in college so I think there are non camp + + align:start position:0% +in college so I think there are non camp + + + align:start position:0% +in college so I think there are non camp +currencies dad go ahead inherent values + + align:start position:0% +currencies dad go ahead inherent values + + + align:start position:0% +currencies dad go ahead inherent values +and does not have it embodies all right + + align:start position:0% +and does not have it embodies all right + + + align:start position:0% +and does not have it embodies all right +anybody which are cheeky yeah Tom Thomas + + align:start position:0% + + + + align:start position:0% + +it is a legal thing how does foster + + align:start position:0% +it is a legal thing how does foster + + + align:start position:0% +it is a legal thing how does foster +society to use the food which makes more + + align:start position:0% +society to use the food which makes more + + + align:start position:0% +society to use the food which makes more +people to use it is saying that fiat + + align:start position:0% +people to use it is saying that fiat + + + align:start position:0% +people to use it is saying that fiat +currency is legal tender so first we + + align:start position:0% +currency is legal tender so first we + + + align:start position:0% +currency is legal tender so first we +have to discuss what is legal tenders + + align:start position:0% +have to discuss what is legal tenders + + + align:start position:0% +have to discuss what is legal tenders +anybody want to knock that one out of + + align:start position:0% +anybody want to knock that one out of + + + align:start position:0% +anybody want to knock that one out of +the ballpark + + align:start position:0% +the ballpark + + + align:start position:0% +the ballpark +who hasn't raised their hand yet so you + + align:start position:0% +who hasn't raised their hand yet so you + + + align:start position:0% +who hasn't raised their hand yet so you +can use the money it can be a store + + align:start position:0% +can use the money it can be a store + + + align:start position:0% +can use the money it can be a store +value it can be a means + + align:start position:0% +value it can be a means + + + align:start position:0% +value it can be a means +you can't pay your taxes right is that + + align:start position:0% +you can't pay your taxes right is that + + + align:start position:0% +you can't pay your taxes right is that +correct + + align:start position:0% +correct + + + align:start position:0% +correct +so 19th century could you pay your taxes + + align:start position:0% +so 19th century could you pay your taxes + + + align:start position:0% +so 19th century could you pay your taxes +in gold in the US and in Britain in + + align:start position:0% +in gold in the US and in Britain in + + + align:start position:0% +in gold in the US and in Britain in +other countries that had gold currency + + align:start position:0% +other countries that had gold currency + + + align:start position:0% +other countries that had gold currency +is it just a yes or no but James + + align:start position:0% +is it just a yes or no but James + + + align:start position:0% +is it just a yes or no but James +yes but seventies that don't be the + + align:start position:0% +yes but seventies that don't be the + + + align:start position:0% +yes but seventies that don't be the +currency of paper currencies attach the + + align:start position:0% +currency of paper currencies attach the + + + align:start position:0% +currency of paper currencies attach the +gold standard so inherently there is in + + align:start position:0% +gold standard so inherently there is in + + + align:start position:0% +gold standard so inherently there is in +the exchange of value that is pegged by + + align:start position:0% +the exchange of value that is pegged by + + + align:start position:0% +the exchange of value that is pegged by +the government or bank or the central + + align:start position:0% +the government or bank or the central + + + align:start position:0% +the government or bank or the central +bank so it's almost one of the same + + align:start position:0% +bank so it's almost one of the same + + + align:start position:0% +bank so it's almost one of the same +thing at that time until more recent + + align:start position:0% +thing at that time until more recent + + + align:start position:0% +thing at that time until more recent +years James is saying you could use gold + + align:start position:0% +years James is saying you could use gold + + + align:start position:0% +years James is saying you could use gold +as legal tender legal tender again is + + align:start position:0% +as legal tender legal tender again is + + + align:start position:0% +as legal tender legal tender again is +something that a society comes together + + align:start position:0% +something that a society comes together + + + align:start position:0% +something that a society comes together +and creates a law you know back to the + + align:start position:0% +and creates a law you know back to the + + + align:start position:0% +and creates a law you know back to the +lesyk for that's a you know society + + align:start position:0% +lesyk for that's a you know society + + + align:start position:0% +lesyk for that's a you know society +together it says it's not just a social + + align:start position:0% +together it says it's not just a social + + + align:start position:0% +together it says it's not just a social +normative behavior it's it's a law one + + align:start position:0% +normative behavior it's it's a law one + + + align:start position:0% +normative behavior it's it's a law one +must accept this in the US and the UK in + + align:start position:0% +must accept this in the US and the UK in + + + align:start position:0% +must accept this in the US and the UK in +many countries it says for for all debts + + align:start position:0% +many countries it says for for all debts + + + align:start position:0% +many countries it says for for all debts +public and private so a debt to the + + align:start position:0% +public and private so a debt to the + + + align:start position:0% +public and private so a debt to the +government or a debt in a store we're + + align:start position:0% +government or a debt in a store we're + + + align:start position:0% +government or a debt in a store we're +going to get to later as to when is it + + align:start position:0% +going to get to later as to when is it + + + align:start position:0% +going to get to later as to when is it +true that somebody has to take your cash + + align:start position:0% +true that somebody has to take your cash + + + align:start position:0% +true that somebody has to take your cash +but I'm gonna hold off on that in a + + align:start position:0% +but I'm gonna hold off on that in a + + + align:start position:0% +but I'm gonna hold off on that in a +minute and and talk about it but I think + + align:start position:0% +minute and and talk about it but I think + + + align:start position:0% +minute and and talk about it but I think +also gee he said it was somewhere + + align:start position:0% +also gee he said it was somewhere + + + align:start position:0% +also gee he said it was somewhere +between Sean and Eric both physically in + + align:start position:0% +between Sean and Eric both physically in + + + align:start position:0% +between Sean and Eric both physically in +the class and in terms of her + + align:start position:0% +the class and in terms of her + + + align:start position:0% +the class and in terms of her +articulation that fiat currency might + + align:start position:0% +articulation that fiat currency might + + + align:start position:0% +articulation that fiat currency might +not have anything inherently behind it + + align:start position:0% +not have anything inherently behind it + + + align:start position:0% +not have anything inherently behind it +and but gold mostly doesn't have + + align:start position:0% +and but gold mostly doesn't have + + + align:start position:0% +and but gold mostly doesn't have +anything inherently behind it and then + + align:start position:0% +anything inherently behind it and then + + + align:start position:0% +anything inherently behind it and then +some forms of currency like grain had + + align:start position:0% +some forms of currency like grain had + + + align:start position:0% +some forms of currency like grain had +more so it may be it's a it's a + + align:start position:0% +more so it may be it's a it's a + + + align:start position:0% +more so it may be it's a it's a +continuum maybe it's not you know black + + align:start position:0% +continuum maybe it's not you know black + + + align:start position:0% +continuum maybe it's not you know black +and white a hundred percent or zero + + align:start position:0% +and white a hundred percent or zero + + + align:start position:0% +and white a hundred percent or zero +percent and then we're gonna talk a + + align:start position:0% +percent and then we're gonna talk a + + + align:start position:0% +percent and then we're gonna talk a +little bit about how Bitcoin fits into + + align:start position:0% +little bit about how Bitcoin fits into + + + align:start position:0% +little bit about how Bitcoin fits into +it and and our next three classes are + + align:start position:0% +it and and our next three classes are + + + align:start position:0% +it and and our next three classes are +gonna be really into the technology of + + align:start position:0% +gonna be really into the technology of + + + align:start position:0% +gonna be really into the technology of +Bitcoin but just just a little bit of + + align:start position:0% +Bitcoin but just just a little bit of + + + align:start position:0% +Bitcoin but just just a little bit of +teasing out before I go through some + + align:start position:0% +teasing out before I go through some + + + align:start position:0% +teasing out before I go through some +lecture slides who wants to talk about + + align:start position:0% +lecture slides who wants to talk about + + + align:start position:0% +lecture slides who wants to talk about +how Bitcoin might fit into this history + + align:start position:0% +how Bitcoin might fit into this history + + + align:start position:0% +how Bitcoin might fit into this history +of money and then I'm gonna return to + + align:start position:0% +of money and then I'm gonna return to + + + align:start position:0% +of money and then I'm gonna return to +that question + + align:start position:0% +that question + + + align:start position:0% +that question +in in about 45 minutes and ask you again + + align:start position:0% +in in about 45 minutes and ask you again + + + align:start position:0% +in in about 45 minutes and ask you again +but does anybody want to say from the + + align:start position:0% +but does anybody want to say from the + + + align:start position:0% +but does anybody want to say from the +readings and you remind me your name is + + align:start position:0% +readings and you remind me your name is + + + align:start position:0% +readings and you remind me your name is +about twins have the same where the + + align:start position:0% +about twins have the same where the + + + align:start position:0% +about twins have the same where the +value is given by society except with + + align:start position:0% +value is given by society except with + + + align:start position:0% +value is given by society except with +Bitcoin it's not that I think a central + + align:start position:0% +Bitcoin it's not that I think a central + + + align:start position:0% +Bitcoin it's not that I think a central +bank so people don't think that there is + + align:start position:0% +bank so people don't think that there is + + + align:start position:0% +bank so people don't think that there is +an inherent value but it like that the + + align:start position:0% +an inherent value but it like that the + + + align:start position:0% +an inherent value but it like that the +readings pointed out that there's sort + + align:start position:0% +readings pointed out that there's sort + + + align:start position:0% +readings pointed out that there's sort +of that same history Isabel was saying + + align:start position:0% +of that same history Isabel was saying + + + align:start position:0% +of that same history Isabel was saying +that Bitcoin fits into the history of + + align:start position:0% +that Bitcoin fits into the history of + + + align:start position:0% +that Bitcoin fits into the history of +money because like fiat currencies and + + align:start position:0% +money because like fiat currencies and + + + align:start position:0% +money because like fiat currencies and +like G he said about gold it doesn't + + align:start position:0% +like G he said about gold it doesn't + + + align:start position:0% +like G he said about gold it doesn't +necessarily have any inherent money + + align:start position:0% +necessarily have any inherent money + + + align:start position:0% +necessarily have any inherent money +monetary value but it's a societal set + + align:start position:0% +monetary value but it's a societal set + + + align:start position:0% +monetary value but it's a societal set +of norms the people are accepting it as + + align:start position:0% +of norms the people are accepting it as + + + align:start position:0% +of norms the people are accepting it as +having value but the key distinction + + align:start position:0% +having value but the key distinction + + + align:start position:0% +having value but the key distinction +that Isabel said was that it's no + + align:start position:0% +that Isabel said was that it's no + + + align:start position:0% +that Isabel said was that it's no +central it's not backed by central bank + + align:start position:0% +central it's not backed by central bank + + + align:start position:0% +central it's not backed by central bank +or a central authority + + align:start position:0% +or a central authority + + + align:start position:0% +or a central authority +so my pin is unique because I think the + + align:start position:0% +so my pin is unique because I think the + + + align:start position:0% +so my pin is unique because I think the +value of Bitcoin changes over time not + + align:start position:0% +value of Bitcoin changes over time not + + + align:start position:0% +value of Bitcoin changes over time not +the fluctuation that we see like 6,000 + + align:start position:0% +the fluctuation that we see like 6,000 + + + align:start position:0% +the fluctuation that we see like 6,000 +or $90,000 but in terms of the power + + align:start position:0% +or $90,000 but in terms of the power + + + align:start position:0% +or $90,000 but in terms of the power +utility off the point itself and so + + align:start position:0% +utility off the point itself and so + + + align:start position:0% +utility off the point itself and so +today for example we might be able to + + align:start position:0% +today for example we might be able to + + + align:start position:0% +today for example we might be able to +buy pizza or popular whatever would be + + align:start position:0% +buy pizza or popular whatever would be + + + align:start position:0% +buy pizza or popular whatever would be +point so there is an ignorant value in + + align:start position:0% +point so there is an ignorant value in + + + align:start position:0% +point so there is an ignorant value in +terms of many loops of exchange and it + + align:start position:0% +terms of many loops of exchange and it + + + align:start position:0% +terms of many loops of exchange and it +will change society adopts it more and + + align:start position:0% +will change society adopts it more and + + + align:start position:0% +will change society adopts it more and +more so I think it's hard to define if + + align:start position:0% +more so I think it's hard to define if + + + align:start position:0% +more so I think it's hard to define if +there is raising that Bitcoin if I can + + align:start position:0% +there is raising that Bitcoin if I can + + + align:start position:0% +there is raising that Bitcoin if I can +put some words in your mouth and tell me + + align:start position:0% +put some words in your mouth and tell me + + + align:start position:0% +put some words in your mouth and tell me +if I'm correct that Bitcoin might have + + align:start position:0% +if I'm correct that Bitcoin might have + + + align:start position:0% +if I'm correct that Bitcoin might have +some distinguishing features from even + + align:start position:0% +some distinguishing features from even + + + align:start position:0% +some distinguishing features from even +fiat currency that its value is shifting + + align:start position:0% +fiat currency that its value is shifting + + + align:start position:0% +fiat currency that its value is shifting +over time with adoption is that I mean + + align:start position:0% +over time with adoption is that I mean + + + align:start position:0% +over time with adoption is that I mean +you didn't use that word please let me + + align:start position:0% +you didn't use that word please let me + + + align:start position:0% +you didn't use that word please let me +know your name Ian right like British + + align:start position:0% +know your name Ian right like British + + + align:start position:0% +know your name Ian right like British +but with an O you told me earlier + + align:start position:0% +but with an O you told me earlier + + + align:start position:0% +but with an O you told me earlier +British + + align:start position:0% + + + + align:start position:0% + +the evolution of the lady technologic + + align:start position:0% +the evolution of the lady technologic + + + align:start position:0% +the evolution of the lady technologic +like accounting and and evolution of + + align:start position:0% +like accounting and and evolution of + + + align:start position:0% +like accounting and and evolution of +money along with how we happened in the + + align:start position:0% +money along with how we happened in the + + + align:start position:0% +money along with how we happened in the +great for agent and the advent of the + + align:start position:0% +great for agent and the advent of the + + + align:start position:0% +great for agent and the advent of the +tea ladies and then distributed layer + + align:start position:0% +tea ladies and then distributed layer + + + align:start position:0% +tea ladies and then distributed layer +which is kind of the fundamental what + + align:start position:0% +which is kind of the fundamental what + + + align:start position:0% +which is kind of the fundamental what +are the fundamental blocks of another + + align:start position:0% +are the fundamental blocks of another + + + align:start position:0% +are the fundamental blocks of another +kind of natural progression of how money + + align:start position:0% +kind of natural progression of how money + + + align:start position:0% +kind of natural progression of how money +so purchase yeah so what bro Tisch is + + align:start position:0% +so purchase yeah so what bro Tisch is + + + align:start position:0% +so purchase yeah so what bro Tisch is +raised is also Bitcoin fits into the + + align:start position:0% +raised is also Bitcoin fits into the + + + align:start position:0% +raised is also Bitcoin fits into the +history of Ledger's whether it's double + + align:start position:0% +history of Ledger's whether it's double + + + align:start position:0% +history of Ledger's whether it's double +entry Ledger's is recognized through T + + align:start position:0% +entry Ledger's is recognized through T + + + align:start position:0% +entry Ledger's is recognized through T +accounts or other forms of Ledger's that + + align:start position:0% +accounts or other forms of Ledger's that + + + align:start position:0% +accounts or other forms of Ledger's that +it adds to this whole long history of + + align:start position:0% +it adds to this whole long history of + + + align:start position:0% +it adds to this whole long history of +Ledger's I agree with that and it's a + + align:start position:0% +Ledger's I agree with that and it's a + + + align:start position:0% +Ledger's I agree with that and it's a +new form of keeping Ledger's Elaine it + + align:start position:0% +new form of keeping Ledger's Elaine it + + + align:start position:0% +new form of keeping Ledger's Elaine it +seems like scarcity and Ledger's are + + align:start position:0% +seems like scarcity and Ledger's are + + + align:start position:0% +seems like scarcity and Ledger's are +important components of Viva in terms of + + align:start position:0% +important components of Viva in terms of + + + align:start position:0% +important components of Viva in terms of +scarcity but the more we adopted the + + align:start position:0% +scarcity but the more we adopted the + + + align:start position:0% +scarcity but the more we adopted the +more it becomes divisible in terms of + + align:start position:0% +more it becomes divisible in terms of + + + align:start position:0% +more it becomes divisible in terms of +units and so we can increase its use + + align:start position:0% +units and so we can increase its use + + + align:start position:0% +units and so we can increase its use +because this ability is another + + align:start position:0% +because this ability is another + + + align:start position:0% +because this ability is another +characteristic of money scarcity + + align:start position:0% +characteristic of money scarcity + + + align:start position:0% +characteristic of money scarcity +adoption is Ilan said Ledger's sorry + + align:start position:0% +adoption is Ilan said Ledger's sorry + + + align:start position:0% +adoption is Ilan said Ledger's sorry +tomas the bitcoin that makes people to + + align:start position:0% +tomas the bitcoin that makes people to + + + align:start position:0% +tomas the bitcoin that makes people to +implement discussed in the decentralized + + align:start position:0% +implement discussed in the decentralized + + + align:start position:0% +implement discussed in the decentralized +environment so without any i will take + + align:start position:0% +environment so without any i will take + + + align:start position:0% +environment so without any i will take +one more and then I'll start to toy with + + align:start position:0% +one more and then I'll start to toy with + + + align:start position:0% +one more and then I'll start to toy with +history why don't we go here + + align:start position:0% +history why don't we go here + + + align:start position:0% +history why don't we go here +revive username like money in like other + + align:start position:0% +revive username like money in like other + + + align:start position:0% +revive username like money in like other +forms of currency even if it's not + + align:start position:0% +forms of currency even if it's not + + + align:start position:0% +forms of currency even if it's not +controlled by like there's a hooker in + + align:start position:0% +controlled by like there's a hooker in + + + align:start position:0% +controlled by like there's a hooker in +mint or something like there's no fixed + + align:start position:0% +mint or something like there's no fixed + + + align:start position:0% +mint or something like there's no fixed +exchange rate which way to extremely + + align:start position:0% +exchange rate which way to extremely + + + align:start position:0% +exchange rate which way to extremely +quickly currency so I mean it's still + + align:start position:0% +quickly currency so I mean it's still + + + align:start position:0% +quickly currency so I mean it's still +very different Alexis if I understand + + align:start position:0% +very different Alexis if I understand + + + align:start position:0% +very different Alexis if I understand +alexis is point is that there's no fixed + + align:start position:0% +alexis is point is that there's no fixed + + + align:start position:0% +alexis is point is that there's no fixed +exchange rate about Bitcoin we're + + align:start position:0% +exchange rate about Bitcoin we're + + + align:start position:0% +exchange rate about Bitcoin we're +talking about but couldn't we really + + align:start position:0% +talking about but couldn't we really + + + align:start position:0% +talking about but couldn't we really +broaden that to all forms of currency I + + align:start position:0% +broaden that to all forms of currency I + + + align:start position:0% +broaden that to all forms of currency I +mean what what really is the exchange + + align:start position:0% +mean what what really is the exchange + + + align:start position:0% +mean what what really is the exchange +rate between an ounce of gold and a + + align:start position:0% +rate between an ounce of gold and a + + + align:start position:0% +rate between an ounce of gold and a +bushel of corn yes and no because some + + align:start position:0% +bushel of corn yes and no because some + + + align:start position:0% +bushel of corn yes and no because some +governments try to fix now back to + + align:start position:0% +governments try to fix now back to + + + align:start position:0% +governments try to fix now back to +markets how well is that worked when + + align:start position:0% +markets how well is that worked when + + + align:start position:0% +markets how well is that worked when +governments try to fix an exchange rate + + align:start position:0% +governments try to fix an exchange rate + + + align:start position:0% +governments try to fix an exchange rate +I mean just a sense of the class does + + align:start position:0% +I mean just a sense of the class does + + + align:start position:0% +I mean just a sense of the class does +that work well so it sort of might work + + align:start position:0% +that work well so it sort of might work + + + align:start position:0% +that work well so it sort of might work +well in temporal short periods works + + align:start position:0% +well in temporal short periods works + + + align:start position:0% +well in temporal short periods works +less well for you know decades on end + + align:start position:0% +less well for you know decades on end + + + align:start position:0% +less well for you know decades on end +I'll take one more and then I'm just I + + align:start position:0% +I'll take one more and then I'm just I + + + align:start position:0% +I'll take one more and then I'm just I +want to go through a couple what is a + + align:start position:0% +want to go through a couple what is a + + + align:start position:0% +want to go through a couple what is a +ledger very good question I'm gonna be + + align:start position:0% +ledger very good question I'm gonna be + + + align:start position:0% +ledger very good question I'm gonna be +chatting about that in a minute but does + + align:start position:0% +chatting about that in a minute but does + + + align:start position:0% +chatting about that in a minute but does +anybody want to hit that I'm sorry no we + + align:start position:0% +anybody want to hit that I'm sorry no we + + + align:start position:0% +anybody want to hit that I'm sorry no we +over here because the American record of + + align:start position:0% +over here because the American record of + + + align:start position:0% +over here because the American record of +anything recorded in a fashion a + + align:start position:0% +anything recorded in a fashion a + + + align:start position:0% +anything recorded in a fashion a +numerical record I think that's a good + + align:start position:0% +numerical record I think that's a good + + + align:start position:0% +numerical record I think that's a good +thing a ledger is basically a way to + + align:start position:0% +thing a ledger is basically a way to + + + align:start position:0% +thing a ledger is basically a way to +record economic activity or social + + align:start position:0% +record economic activity or social + + + align:start position:0% +record economic activity or social +relationships or financial relationships + + align:start position:0% +relationships or financial relationships + + + align:start position:0% +relationships or financial relationships +I would say it's both a way to record + + align:start position:0% +I would say it's both a way to record + + + align:start position:0% +I would say it's both a way to record +economic activity and it's a system of + + align:start position:0% +economic activity and it's a system of + + + align:start position:0% +economic activity and it's a system of +recording + + align:start position:0% +recording + + + align:start position:0% +recording +financial relationships and while I + + align:start position:0% +financial relationships and while I + + + align:start position:0% +financial relationships and while I +didn't assign these readings some some + + align:start position:0% +didn't assign these readings some some + + + align:start position:0% +didn't assign these readings some some +very good academic research suggests + + align:start position:0% +very good academic research suggests + + + align:start position:0% +very good academic research suggests +that the first methods of writing and + + align:start position:0% +that the first methods of writing and + + + align:start position:0% +that the first methods of writing and +symbols of writing had to do with + + align:start position:0% +symbols of writing had to do with + + + align:start position:0% +symbols of writing had to do with +numbers and had to do with Ledger's + + align:start position:0% +numbers and had to do with Ledger's + + + align:start position:0% +numbers and had to do with Ledger's +rather than words and communication + + align:start position:0% +rather than words and communication + + + align:start position:0% +rather than words and communication +because it's so fundamental to society + + align:start position:0% +because it's so fundamental to society + + + align:start position:0% +because it's so fundamental to society +to record various economic transactions + + align:start position:0% +to record various economic transactions + + + align:start position:0% +to record various economic transactions +or to record the financial relationships + + align:start position:0% +or to record the financial relationships + + + align:start position:0% +or to record the financial relationships +amongst them between members of a + + align:start position:0% +amongst them between members of a + + + align:start position:0% +amongst them between members of a +community whether it was a small village + + align:start position:0% +community whether it was a small village + + + align:start position:0% +community whether it was a small village +or when when society bursts out of + + align:start position:0% +or when when society bursts out of + + + align:start position:0% +or when when society bursts out of +villages thousands of years ago so help + + align:start position:0% +villages thousands of years ago so help + + + align:start position:0% +villages thousands of years ago so help +will be back to it and better that you + + align:start position:0% +will be back to it and better that you + + + align:start position:0% +will be back to it and better that you +ask that here than in your accounting + + align:start position:0% +ask that here than in your accounting + + + align:start position:0% +ask that here than in your accounting +fundamentals class so the readings we've + + align:start position:0% +fundamentals class so the readings we've + + + align:start position:0% +fundamentals class so the readings we've +we've sort of talked about the readings + + align:start position:0% +we've sort of talked about the readings + + + align:start position:0% +we've sort of talked about the readings +how many of you actually watch the + + align:start position:0% +how many of you actually watch the + + + align:start position:0% +how many of you actually watch the +little three minute video did you what + + align:start position:0% +little three minute video did you what + + + align:start position:0% +little three minute video did you what +do you think just I mean just as a I'm + + align:start position:0% +do you think just I mean just as a I'm + + + align:start position:0% +do you think just I mean just as a I'm +sorry here we have in chat it was just + + align:start position:0% +sorry here we have in chat it was just + + + align:start position:0% +sorry here we have in chat it was just +it was a nice little did Ian Hawaii + + align:start position:0% +it was a nice little did Ian Hawaii + + + align:start position:0% +it was a nice little did Ian Hawaii +Matthew I'm sorry you would have given + + align:start position:0% +Matthew I'm sorry you would have given + + + align:start position:0% +Matthew I'm sorry you would have given +him a dollar + + align:start position:0% +him a dollar + + + align:start position:0% +him a dollar +great would anybody else have given him + + align:start position:0% +great would anybody else have given him + + + align:start position:0% +great would anybody else have given him +a dollar for it no maybe you would have + + align:start position:0% + + + + align:start position:0% + +we refer back to each of these readings + + align:start position:0% +we refer back to each of these readings + + + align:start position:0% +we refer back to each of these readings +as we go through the next 45 minutes but + + align:start position:0% +as we go through the next 45 minutes but + + + align:start position:0% +as we go through the next 45 minutes but +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +he was actually breaking the law by + + align:start position:0% +he was actually breaking the law by + + + align:start position:0% +he was actually breaking the law by +launching his own collar that + + align:start position:0% +launching his own collar that + + + align:start position:0% +launching his own collar that +illegitimate you know obviously didn't + + align:start position:0% +illegitimate you know obviously didn't + + + align:start position:0% +illegitimate you know obviously didn't +compete with the US dollar + + align:start position:0% +compete with the US dollar + + + align:start position:0% +compete with the US dollar +very cool question I'm not aware of any + + align:start position:0% +very cool question I'm not aware of any + + + align:start position:0% +very cool question I'm not aware of any +statute federal or state that says + + align:start position:0% +statute federal or state that says + + + align:start position:0% +statute federal or state that says +there's an absolute monopoly or in forms + + align:start position:0% +there's an absolute monopoly or in forms + + + align:start position:0% +there's an absolute monopoly or in forms +of currency as there is and other things + + align:start position:0% +of currency as there is and other things + + + align:start position:0% +of currency as there is and other things +like you know that that that that's slot + + align:start position:0% +like you know that that that that's slot + + + align:start position:0% +like you know that that that that's slot +in the door that's called the the where + + align:start position:0% +in the door that's called the the where + + + align:start position:0% +in the door that's called the the where +you can put a letter through the door or + + align:start position:0% +you can put a letter through the door or + + + align:start position:0% +you can put a letter through the door or +a mailbox there's actually a law that + + align:start position:0% +a mailbox there's actually a law that + + + align:start position:0% +a mailbox there's actually a law that +says that the US Postal Service has a + + align:start position:0% +says that the US Postal Service has a + + + align:start position:0% +says that the US Postal Service has a +monopoly and that's why UPS is not + + align:start position:0% +monopoly and that's why UPS is not + + + align:start position:0% +monopoly and that's why UPS is not +allowed to put their boxes or anything + + align:start position:0% +allowed to put their boxes or anything + + + align:start position:0% +allowed to put their boxes or anything +in there there is a government Fiat + + align:start position:0% +in there there is a government Fiat + + + align:start position:0% +in there there is a government Fiat +monopoly but you raise a very good + + align:start position:0% +monopoly but you raise a very good + + + align:start position:0% +monopoly but you raise a very good +question what we've found in the last 10 + + align:start position:0% +question what we've found in the last 10 + + + align:start position:0% +question what we've found in the last 10 +years with Bitcoin without with really + + align:start position:0% +years with Bitcoin without with really + + + align:start position:0% +years with Bitcoin without with really +oversimplifying is that it is legal to + + align:start position:0% +oversimplifying is that it is legal to + + + align:start position:0% +oversimplifying is that it is legal to +create your own form of money as as + + align:start position:0% +create your own form of money as as + + + align:start position:0% +create your own form of money as as +Bitcoin is possibly this money but you + + align:start position:0% +Bitcoin is possibly this money but you + + + align:start position:0% +Bitcoin is possibly this money but you +have to comply with all the other laws + + align:start position:0% +have to comply with all the other laws + + + align:start position:0% +have to comply with all the other laws +and all those other laws that we'll talk + + align:start position:0% +and all those other laws that we'll talk + + + align:start position:0% +and all those other laws that we'll talk +about in other lectures in essence fall + + align:start position:0% +about in other lectures in essence fall + + + align:start position:0% +about in other lectures in essence fall +into buckets of guarding against illicit + + align:start position:0% +into buckets of guarding against illicit + + + align:start position:0% +into buckets of guarding against illicit +activity so the Bank Secrecy Act and all + + align:start position:0% +activity so the Bank Secrecy Act and all + + + align:start position:0% +activity so the Bank Secrecy Act and all +the laws related to any money laundering + + align:start position:0% +the laws related to any money laundering + + + align:start position:0% +the laws related to any money laundering +and terrorism finance and so forth that + + align:start position:0% +and terrorism finance and so forth that + + + align:start position:0% +and terrorism finance and so forth that +one still has to pay your taxes if + + align:start position:0% +one still has to pay your taxes if + + + align:start position:0% +one still has to pay your taxes if +you're gaining or losing on this + + align:start position:0% +you're gaining or losing on this + + + align:start position:0% +you're gaining or losing on this +investment that the Federal Reserve and + + align:start position:0% +investment that the Federal Reserve and + + + align:start position:0% +investment that the Federal Reserve and +other authorities around the globe still + + align:start position:0% +other authorities around the globe still + + + align:start position:0% +other authorities around the globe still +want to insure for financial stability + + align:start position:0% +want to insure for financial stability + + + align:start position:0% +want to insure for financial stability +the fellow on the streets of I don't + + align:start position:0% +the fellow on the streets of I don't + + + align:start position:0% +the fellow on the streets of I don't +remember what city New York selling his + + align:start position:0% +remember what city New York selling his + + + align:start position:0% +remember what city New York selling his +dollars when Mathew bought it for a + + align:start position:0% +dollars when Mathew bought it for a + + + align:start position:0% +dollars when Mathew bought it for a +dollar and I think over here + + align:start position:0% +dollar and I think over here + + + align:start position:0% +dollar and I think over here +Briona what's that yes + + align:start position:0% +Briona what's that yes + + + align:start position:0% +Briona what's that yes +Brigade bought it that's probably we're + + align:start position:0% +Brigade bought it that's probably we're + + + align:start position:0% +Brigade bought it that's probably we're +gonna have the society is still gonna be + + align:start position:0% +gonna have the society is still gonna be + + + align:start position:0% +gonna have the society is still gonna be +stable it's gonna be alright + + align:start position:0% +stable it's gonna be alright + + + align:start position:0% +stable it's gonna be alright +but if millions of people were buying it + + align:start position:0% +but if millions of people were buying it + + + align:start position:0% +but if millions of people were buying it +then then people might worry and then + + align:start position:0% +then then people might worry and then + + + align:start position:0% +then then people might worry and then +there's the third big bucket that we + + align:start position:0% +there's the third big bucket that we + + + align:start position:0% +there's the third big bucket that we +look at is investor and consumer + + align:start position:0% +look at is investor and consumer + + + align:start position:0% +look at is investor and consumer +protection but I think it's allowed so + + align:start position:0% +protection but I think it's allowed so + + + align:start position:0% +protection but I think it's allowed so +we'll refer to these and Joe Quinn and + + align:start position:0% +we'll refer to these and Joe Quinn and + + + align:start position:0% +we'll refer to these and Joe Quinn and +then + + align:start position:0% +then + + + align:start position:0% +then +you gotta pay for example salaries you'd + + align:start position:0% +you gotta pay for example salaries you'd + + + align:start position:0% +you gotta pay for example salaries you'd +be in the US yes and why is it that you + + align:start position:0% +be in the US yes and why is it that you + + + align:start position:0% +be in the US yes and why is it that you +can legally pay for four wages in + + align:start position:0% +can legally pay for four wages in + + + align:start position:0% +can legally pay for four wages in +Bitcoin in the US so anybody I know it's + + align:start position:0% +Bitcoin in the US so anybody I know it's + + + align:start position:0% +Bitcoin in the US so anybody I know it's +outside of the readings but why do you + + align:start position:0% +outside of the readings but why do you + + + align:start position:0% +outside of the readings but why do you +think it is allowed in this society is + + align:start position:0% +think it is allowed in this society is + + + align:start position:0% +think it is allowed in this society is +it Kyle most things you could pay + + align:start position:0% +it Kyle most things you could pay + + + align:start position:0% +it Kyle most things you could pay +somebody in these placards I doubt + + align:start position:0% +somebody in these placards I doubt + + + align:start position:0% +somebody in these placards I doubt +really that you're gonna value that much + + align:start position:0% +really that you're gonna value that much + + + align:start position:0% +really that you're gonna value that much +but you could pay somebody in this you + + align:start position:0% +but you could pay somebody in this you + + + align:start position:0% +but you could pay somebody in this you +could pay somebody in gold euros Bitcoin + + align:start position:0% +could pay somebody in gold euros Bitcoin + + + align:start position:0% +could pay somebody in gold euros Bitcoin +and there are firms that are paying + + align:start position:0% +and there are firms that are paying + + + align:start position:0% +and there are firms that are paying +usually they are developing blockchain + + align:start position:0% +usually they are developing blockchain + + + align:start position:0% +usually they are developing blockchain +applications and interestingly they have + + align:start position:0% +applications and interestingly they have + + + align:start position:0% +applications and interestingly they have +to compute the value of the wages to do + + align:start position:0% +to compute the value of the wages to do + + + align:start position:0% +to compute the value of the wages to do +withholding taxes because the US + + align:start position:0% +withholding taxes because the US + + + align:start position:0% +withholding taxes because the US +government will not accept taxes in + + align:start position:0% +government will not accept taxes in + + + align:start position:0% +government will not accept taxes in +Bitcoin so they they figure out the fair + + align:start position:0% +Bitcoin so they they figure out the fair + + + align:start position:0% +Bitcoin so they they figure out the fair +market value and there are companies in + + align:start position:0% +market value and there are companies in + + + align:start position:0% +market value and there are companies in +the US that pay people in Bitcoin who + + align:start position:0% +the US that pay people in Bitcoin who + + + align:start position:0% +the US that pay people in Bitcoin who +are doing development work around + + align:start position:0% +are doing development work around + + + align:start position:0% +are doing development work around +blockchain applications but the taxes + + align:start position:0% +blockchain applications but the taxes + + + align:start position:0% +blockchain applications but the taxes +need to be computed and and analyzed and + + align:start position:0% +need to be computed and and analyzed and + + + align:start position:0% +need to be computed and and analyzed and +then paid in US dollars because and + + align:start position:0% +then paid in US dollars because and + + + align:start position:0% +then paid in US dollars because and +there was a legislative initiative in + + align:start position:0% +there was a legislative initiative in + + + align:start position:0% +there was a legislative initiative in +Arizona earlier this year where a state + + align:start position:0% +Arizona earlier this year where a state + + + align:start position:0% +Arizona earlier this year where a state +legislature wanted to have Arizona be + + align:start position:0% +legislature wanted to have Arizona be + + + align:start position:0% +legislature wanted to have Arizona be +the first state in the land to accept + + align:start position:0% +the first state in the land to accept + + + align:start position:0% +the first state in the land to accept +Bitcoin for taxes but it failed in + + align:start position:0% +Bitcoin for taxes but it failed in + + + align:start position:0% +Bitcoin for taxes but it failed in +committee it didn't even get a full vote + + align:start position:0% +committee it didn't even get a full vote + + + align:start position:0% +committee it didn't even get a full vote +of I can't remember it was the Arizona + + align:start position:0% +of I can't remember it was the Arizona + + + align:start position:0% +of I can't remember it was the Arizona +Senate or the Arizona House of Delegates + + align:start position:0% +Senate or the Arizona House of Delegates + + + align:start position:0% +Senate or the Arizona House of Delegates +but so just a little walk through the + + align:start position:0% +but so just a little walk through the + + + align:start position:0% +but so just a little walk through the +history I was going to do a little + + align:start position:0% +history I was going to do a little + + + align:start position:0% +history I was going to do a little +history of money and have some fun + + align:start position:0% +history of money and have some fun + + + align:start position:0% +history of money and have some fun +so in Ethiopia people put together sawed + + align:start position:0% +so in Ethiopia people put together sawed + + + align:start position:0% +so in Ethiopia people put together sawed +bores these this is not that long ago + + align:start position:0% +bores these this is not that long ago + + + align:start position:0% +bores these this is not that long ago +saw it as gee he would have said earlier + + align:start position:0% +saw it as gee he would have said earlier + + + align:start position:0% +saw it as gee he would have said earlier +is really valuable in society and they + + align:start position:0% +is really valuable in society and they + + + align:start position:0% +is really valuable in society and they +standardized the shape and size and said + + align:start position:0% +standardized the shape and size and said + + + align:start position:0% +standardized the shape and size and said +here's sawed boars + + align:start position:0% +here's sawed boars + + + align:start position:0% +here's sawed boars +we're gonna get to a little bit later + + align:start position:0% +we're gonna get to a little bit later + + + align:start position:0% +we're gonna get to a little bit later +all the characteristics of money but + + align:start position:0% +all the characteristics of money but + + + align:start position:0% +all the characteristics of money but +what else do you think a sawed bar in + + align:start position:0% +what else do you think a sawed bar in + + + align:start position:0% +what else do you think a sawed bar in +Ethiopia + + align:start position:0% +Ethiopia + + + align:start position:0% +Ethiopia +as opposed to maybe some other country + + align:start position:0% +as opposed to maybe some other country + + + align:start position:0% +as opposed to maybe some other country +what what what did it have as well as to + + align:start position:0% +what what what did it have as well as to + + + align:start position:0% +what what what did it have as well as to +why people might use that crude oil + + align:start position:0% +why people might use that crude oil + + + align:start position:0% +why people might use that crude oil +alright I hadn't thought of that I'm + + align:start position:0% +alright I hadn't thought of that I'm + + + align:start position:0% +alright I hadn't thought of that I'm +gonna I'm gonna keep thinking about that + + align:start position:0% +gonna I'm gonna keep thinking about that + + + align:start position:0% +gonna I'm gonna keep thinking about that +it's not a it's not a common + + align:start position:0% +it's not a it's not a common + + + align:start position:0% +it's not a it's not a common +characteristic of money but why + + align:start position:0% +characteristic of money but why + + + align:start position:0% +characteristic of money but why +sophomores what else might it have in in + + align:start position:0% +sophomores what else might it have in in + + + align:start position:0% +sophomores what else might it have in in +Ethiopia we preserve food but because it + + align:start position:0% +Ethiopia we preserve food but because it + + + align:start position:0% +Ethiopia we preserve food but because it +was mined there was some scarcity as + + align:start position:0% +was mined there was some scarcity as + + + align:start position:0% +was mined there was some scarcity as +well and a lot of currencies a lot of + + align:start position:0% +well and a lot of currencies a lot of + + + align:start position:0% +well and a lot of currencies a lot of +monies over time to have that + + align:start position:0% +monies over time to have that + + + align:start position:0% +monies over time to have that +fundamental issue Cowie shells from West + + align:start position:0% +fundamental issue Cowie shells from West + + + align:start position:0% +fundamental issue Cowie shells from West +Africa does anyone know the history of + + align:start position:0% +Africa does anyone know the history of + + + align:start position:0% +Africa does anyone know the history of +when Cowie shells got really debased and + + align:start position:0% +when Cowie shells got really debased and + + + align:start position:0% +when Cowie shells got really debased and +and stopped being used from the readings + + align:start position:0% +and stopped being used from the readings + + + align:start position:0% +and stopped being used from the readings +I can't remember if that was in in the + + align:start position:0% +I can't remember if that was in in the + + + align:start position:0% +I can't remember if that was in in the +readings or not they got to baste when + + align:start position:0% +readings or not they got to baste when + + + align:start position:0% +readings or not they got to baste when +Europeans started to realize that they + + align:start position:0% +Europeans started to realize that they + + + align:start position:0% +Europeans started to realize that they +were accepted as a value and as a very + + align:start position:0% +were accepted as a value and as a very + + + align:start position:0% +were accepted as a value and as a very +sad and terrible history - because it's + + align:start position:0% +sad and terrible history - because it's + + + align:start position:0% +sad and terrible history - because it's +related to the whole slave trade but + + align:start position:0% +related to the whole slave trade but + + + align:start position:0% +related to the whole slave trade but +that that the Europeans could figure out + + align:start position:0% +that that the Europeans could figure out + + + align:start position:0% +that that the Europeans could figure out +that that societies accepted this as + + align:start position:0% +that that societies accepted this as + + + align:start position:0% +that that societies accepted this as +something of value but they also debase + + align:start position:0% +something of value but they also debase + + + align:start position:0% +something of value but they also debase +that currency and they debase the land + + align:start position:0% +that currency and they debase the land + + + align:start position:0% +that currency and they debase the land +and capture people as slaves I mean was + + align:start position:0% +and capture people as slaves I mean was + + + align:start position:0% +and capture people as slaves I mean was +a quite a collection of not particularly + + align:start position:0% +a quite a collection of not particularly + + + align:start position:0% +a quite a collection of not particularly +good things going on tally sticks in + + align:start position:0% +good things going on tally sticks in + + + align:start position:0% +good things going on tally sticks in +England so anybody from the readings + + align:start position:0% +England so anybody from the readings + + + align:start position:0% +England so anybody from the readings +because there was a little bit of the + + align:start position:0% +because there was a little bit of the + + + align:start position:0% +because there was a little bit of the +debate in the first reading about the + + align:start position:0% +debate in the first reading about the + + + align:start position:0% +debate in the first reading about the +history of money want a chat and I'll + + align:start position:0% +history of money want a chat and I'll + + + align:start position:0% +history of money want a chat and I'll +pull up the rice tones from yeah how + + align:start position:0% +pull up the rice tones from yeah how + + + align:start position:0% +pull up the rice tones from yeah how +this fits into that first reading in the + + align:start position:0% +this fits into that first reading in the + + + align:start position:0% +this fits into that first reading in the +debate between has the money come from a + + align:start position:0% +debate between has the money come from a + + + align:start position:0% +debate between has the money come from a +history of border or did money come from + + align:start position:0% +history of border or did money come from + + + align:start position:0% +history of border or did money come from +a history of Ledger's and credit which + + align:start position:0% +a history of Ledger's and credit which + + + align:start position:0% +a history of Ledger's and credit which +is kind of a set up of that first I + + align:start position:0% +is kind of a set up of that first I + + + align:start position:0% +is kind of a set up of that first I +think the first reading any thoughts + + align:start position:0% + + + + align:start position:0% + +which ones that is these four bits of + + align:start position:0% +which ones that is these four bits of + + + align:start position:0% +which ones that is these four bits of +money early money or more about maybe + + align:start position:0% +money early money or more about maybe + + + align:start position:0% +money early money or more about maybe +border so cool theory right dead which + + align:start position:0% +border so cool theory right dead which + + + align:start position:0% +border so cool theory right dead which +corresponds to these one way to metric + + align:start position:0% +corresponds to these one way to metric + + + align:start position:0% +corresponds to these one way to metric +that with which one bit sticks six the + + align:start position:0% +that with which one bit sticks six the + + + align:start position:0% +that with which one bit sticks six the +tally says yes correct which is the + + align:start position:0% +tally says yes correct which is the + + + align:start position:0% +tally says yes correct which is the +second one on here that has to do with + + align:start position:0% +second one on here that has to do with + + + align:start position:0% +second one on here that has to do with +debts actually and credits rise dots so + + align:start position:0% +debts actually and credits rise dots so + + + align:start position:0% +debts actually and credits rise dots so +it's remarkable the right stones were so + + align:start position:0% +it's remarkable the right stones were so + + + align:start position:0% +it's remarkable the right stones were so +heavy that on this island of Yap they + + align:start position:0% +heavy that on this island of Yap they + + + align:start position:0% +heavy that on this island of Yap they +couldn't possibly lug it around and use + + align:start position:0% +couldn't possibly lug it around and use + + + align:start position:0% +couldn't possibly lug it around and use +it you know in traditional medium of + + align:start position:0% +it you know in traditional medium of + + + align:start position:0% +it you know in traditional medium of +exchange but it was viewed as well I + + align:start position:0% +exchange but it was viewed as well I + + + align:start position:0% +exchange but it was viewed as well I +have one sixth of this rise stone you + + align:start position:0% +have one sixth of this rise stone you + + + align:start position:0% +have one sixth of this rise stone you +have one sixteenth and then if I make an + + align:start position:0% +have one sixteenth and then if I make an + + + align:start position:0% +have one sixteenth and then if I make an +exchange we'd remember and a society was + + align:start position:0% +exchange we'd remember and a society was + + + align:start position:0% +exchange we'd remember and a society was +small enough to keep a form of Ledger's + + align:start position:0% +small enough to keep a form of Ledger's + + + align:start position:0% +small enough to keep a form of Ledger's +even to the extent that when a rise + + align:start position:0% +even to the extent that when a rise + + + align:start position:0% +even to the extent that when a rise +stone was lost in a river they said you + + align:start position:0% +stone was lost in a river they said you + + + align:start position:0% +stone was lost in a river they said you +know the river of rice stone + + align:start position:0% +know the river of rice stone + + + align:start position:0% +know the river of rice stone +we each have this piece so in the island + + align:start position:0% +we each have this piece so in the island + + + align:start position:0% +we each have this piece so in the island +of Yap okay I can assure you these + + align:start position:0% +of Yap okay I can assure you these + + + align:start position:0% +of Yap okay I can assure you these +stones could not be used for anything + + align:start position:0% +stones could not be used for anything + + + align:start position:0% +stones could not be used for anything +else does anyone know because it was + + align:start position:0% +else does anyone know because it was + + + align:start position:0% +else does anyone know because it was +outside the readings what made these + + align:start position:0% +outside the readings what made these + + + align:start position:0% +outside the readings what made these +stones so scarce so rye stones were + + align:start position:0% +stones so scarce so rye stones were + + + align:start position:0% +stones so scarce so rye stones were +quarried on an island about two hundred + + align:start position:0% +quarried on an island about two hundred + + + align:start position:0% +quarried on an island about two hundred +kilometers away from Yap so we're the + + align:start position:0% +kilometers away from Yap so we're the + + + align:start position:0% +kilometers away from Yap so we're the +exceedingly hard to get like gold like + + align:start position:0% +exceedingly hard to get like gold like + + + align:start position:0% +exceedingly hard to get like gold like +mining of gold what else has mined these + + align:start position:0% +mining of gold what else has mined these + + + align:start position:0% +mining of gold what else has mined these +days that might be a money what's that + + align:start position:0% +days that might be a money what's that + + + align:start position:0% +days that might be a money what's that +can I hear everybody what's that is + + align:start position:0% +can I hear everybody what's that is + + + align:start position:0% +can I hear everybody what's that is +gonna be very difficult in the future + + align:start position:0% +gonna be very difficult in the future + + + align:start position:0% +gonna be very difficult in the future +for electric battery tomorrow what's + + align:start position:0% +for electric battery tomorrow what's + + + align:start position:0% +for electric battery tomorrow what's +mine + + align:start position:0% +mine + + + align:start position:0% +mine +right now that's at the center of this + + align:start position:0% +right now that's at the center of this + + + align:start position:0% +right now that's at the center of this +class Bitcoin right the Yap stone was in + + align:start position:0% +class Bitcoin right the Yap stone was in + + + align:start position:0% +class Bitcoin right the Yap stone was in +essence quarried a couple hundred + + align:start position:0% +essence quarried a couple hundred + + + align:start position:0% +essence quarried a couple hundred +kilometers away and what debase to that + + align:start position:0% +kilometers away and what debase to that + + + align:start position:0% +kilometers away and what debase to that +currency was when sailors from England + + align:start position:0% +currency was when sailors from England + + + align:start position:0% +currency was when sailors from England +came there's a specific sailor I think + + align:start position:0% +came there's a specific sailor I think + + + align:start position:0% +came there's a specific sailor I think +his name was O'Keefe in the late 19th + + align:start position:0% +his name was O'Keefe in the late 19th + + + align:start position:0% +his name was O'Keefe in the late 19th +century and he realized that these + + align:start position:0% +century and he realized that these + + + align:start position:0% +century and he realized that these +stones were valuable and he went to the + + align:start position:0% +stones were valuable and he went to the + + + align:start position:0% +stones were valuable and he went to the +other Island and he started querying and + + align:start position:0% +other Island and he started querying and + + + align:start position:0% +other Island and he started querying and +came back + + align:start position:0% +came back + + + align:start position:0% +came back +forth and within a few years the whole + + align:start position:0% +forth and within a few years the whole + + + align:start position:0% +forth and within a few years the whole +economic system collapsed we moved to + + align:start position:0% +economic system collapsed we moved to + + + align:start position:0% +economic system collapsed we moved to +metal money at first it wasn't really + + align:start position:0% +metal money at first it wasn't really + + + align:start position:0% +metal money at first it wasn't really +stamped it was just heavy it was hard to + + align:start position:0% +stamped it was just heavy it was hard to + + + align:start position:0% +stamped it was just heavy it was hard to +quarry bronze in Rome there's some + + align:start position:0% +quarry bronze in Rome there's some + + + align:start position:0% +quarry bronze in Rome there's some +chiness in Sweden + + align:start position:0% +chiness in Sweden + + + align:start position:0% +chiness in Sweden +these were starting to be stamped by the + + align:start position:0% +these were starting to be stamped by the + + + align:start position:0% +these were starting to be stamped by the +official sector and then we had minted + + align:start position:0% +official sector and then we had minted + + + align:start position:0% +official sector and then we had minted +money starting somewhere around 2,500 + + align:start position:0% +money starting somewhere around 2,500 + + + align:start position:0% +money starting somewhere around 2,500 +years ago and there's debates as to + + align:start position:0% +years ago and there's debates as to + + + align:start position:0% +years ago and there's debates as to +whether it started in Greece or in China + + align:start position:0% +whether it started in Greece or in China + + + align:start position:0% +whether it started in Greece or in China +and but but we're an official emblem was + + align:start position:0% +and but but we're an official emblem was + + + align:start position:0% +and but but we're an official emblem was +placed upon a scarce resource that was + + align:start position:0% +placed upon a scarce resource that was + + + align:start position:0% +placed upon a scarce resource that was +used paper money came along in a sense + + align:start position:0% +used paper money came along in a sense + + + align:start position:0% +used paper money came along in a sense +for what reason why why did why did + + align:start position:0% +for what reason why why did why did + + + align:start position:0% +for what reason why why did why did +society first tip into paper money gold + + align:start position:0% + + + + align:start position:0% + +it's kind of heavy especially if there + + align:start position:0% +it's kind of heavy especially if there + + + align:start position:0% +it's kind of heavy especially if there +wasn't gold and if it was copper bronze + + align:start position:0% +wasn't gold and if it was copper bronze + + + align:start position:0% +wasn't gold and if it was copper bronze +it was just heavy or if it was wheat you + + align:start position:0% +it was just heavy or if it was wheat you + + + align:start position:0% +it was just heavy or if it was wheat you +have to put it in a storage unit + + align:start position:0% +have to put it in a storage unit + + + align:start position:0% +have to put it in a storage unit +so the first paper money's from China + + align:start position:0% +so the first paper money's from China + + + align:start position:0% +so the first paper money's from China +were basically warehouse receipts and I + + align:start position:0% +were basically warehouse receipts and I + + + align:start position:0% +were basically warehouse receipts and I +spent five years running something + + align:start position:0% +spent five years running something + + + align:start position:0% +spent five years running something +called Commodity Futures Trading + + align:start position:0% +called Commodity Futures Trading + + + align:start position:0% +called Commodity Futures Trading +Commission and so I guess I learned a + + align:start position:0% +Commission and so I guess I learned a + + + align:start position:0% +Commission and so I guess I learned a +lot about warehouse receipts commodity + + align:start position:0% +lot about warehouse receipts commodity + + + align:start position:0% +lot about warehouse receipts commodity +receipts where you put a commodity in a + + align:start position:0% +receipts where you put a commodity in a + + + align:start position:0% +receipts where you put a commodity in a +warehouse and then you got a piece of + + align:start position:0% +warehouse and then you got a piece of + + + align:start position:0% +warehouse and then you got a piece of +paper that said yes you have that + + align:start position:0% +paper that said yes you have that + + + align:start position:0% +paper that said yes you have that +commodity the air so the first paper + + align:start position:0% +commodity the air so the first paper + + + align:start position:0% +commodity the air so the first paper +monies were basically warehouse receipts + + align:start position:0% +monies were basically warehouse receipts + + + align:start position:0% +monies were basically warehouse receipts +in China because whatever it was grain + + align:start position:0% +in China because whatever it was grain + + + align:start position:0% +in China because whatever it was grain +or gold and then you had a piece of + + align:start position:0% +or gold and then you had a piece of + + + align:start position:0% +or gold and then you had a piece of +paper backing it + + align:start position:0% +paper backing it + + + align:start position:0% +paper backing it +these are five-pound notes from England + + align:start position:0% +these are five-pound notes from England + + + align:start position:0% +these are five-pound notes from England +and the Continental notes in the US but + + align:start position:0% +and the Continental notes in the US but + + + align:start position:0% +and the Continental notes in the US but +between so that that note in China is + + align:start position:0% +between so that that note in China is + + + align:start position:0% +between so that that note in China is +about 700 years old but before between + + align:start position:0% +about 700 years old but before between + + + align:start position:0% +about 700 years old but before between +that first paper money and the 18th + + align:start position:0% +that first paper money and the 18th + + + align:start position:0% +that first paper money and the 18th +century who do you think we're kind of + + align:start position:0% +century who do you think we're kind of + + + align:start position:0% +century who do you think we're kind of +the first bankers in the seven late 17th + + align:start position:0% +the first bankers in the seven late 17th + + + align:start position:0% +the first bankers in the seven late 17th +century early 18th century who were what + + align:start position:0% +century early 18th century who were what + + + align:start position:0% +century early 18th century who were what +what Kraft had they been + + align:start position:0% +what Kraft had they been + + + align:start position:0% +what Kraft had they been +before they were in banking + + align:start position:0% + + + + align:start position:0% + +international trade they actually did + + align:start position:0% +international trade they actually did + + + align:start position:0% +international trade they actually did +something more local like the ones that + + align:start position:0% +something more local like the ones that + + + align:start position:0% +something more local like the ones that +have maids and all the lanes land land + + align:start position:0% +have maids and all the lanes land land + + + align:start position:0% +have maids and all the lanes land land +no they had something else that they + + align:start position:0% +no they had something else that they + + + align:start position:0% +no they had something else that they +were doing Tom Chris I like that we're + + align:start position:0% +were doing Tom Chris I like that we're + + + align:start position:0% +were doing Tom Chris I like that we're +not there yet insurance a little bit + + align:start position:0% +not there yet insurance a little bit + + + align:start position:0% +not there yet insurance a little bit +later outside of the reading there + + align:start position:0% +later outside of the reading there + + + align:start position:0% +later outside of the reading there +Goldsmith's + + align:start position:0% + + + + align:start position:0% + +the sum of the first dominant bankers in + + align:start position:0% +the sum of the first dominant bankers in + + + align:start position:0% +the sum of the first dominant bankers in +London there they were small Goldsmith's + + align:start position:0% +London there they were small Goldsmith's + + + align:start position:0% +London there they were small Goldsmith's +and they took the gold they gave you a + + align:start position:0% +and they took the gold they gave you a + + + align:start position:0% +and they took the gold they gave you a +piece of paper and then they went from + + align:start position:0% +piece of paper and then they went from + + + align:start position:0% +piece of paper and then they went from +there and then all of a sudden they + + align:start position:0% +there and then all of a sudden they + + + align:start position:0% +there and then all of a sudden they +figured out how to do credit later in + + align:start position:0% +figured out how to do credit later in + + + align:start position:0% +figured out how to do credit later in +the semester we're gonna talk about + + align:start position:0% +the semester we're gonna talk about + + + align:start position:0% +the semester we're gonna talk about +Bitcoin credit it's not there yet by the + + align:start position:0% +Bitcoin credit it's not there yet by the + + + align:start position:0% +Bitcoin credit it's not there yet by the +way I think in the next 18 to 36 months + + align:start position:0% +way I think in the next 18 to 36 months + + + align:start position:0% +way I think in the next 18 to 36 months +we're gonna start seeing crypto lending + + align:start position:0% +we're gonna start seeing crypto lending + + + align:start position:0% +we're gonna start seeing crypto lending +and and and crypto finance in the form + + align:start position:0% +and and and crypto finance in the form + + + align:start position:0% +and and and crypto finance in the form +similar to what the Goldsmith's were + + align:start position:0% +similar to what the Goldsmith's were + + + align:start position:0% +similar to what the Goldsmith's were +doing in the early 1700 sin England a + + align:start position:0% + + + + align:start position:0% + +very good question is it scalable to + + align:start position:0% +very good question is it scalable to + + + align:start position:0% +very good question is it scalable to +lend against a finite currency I I think + + align:start position:0% +lend against a finite currency I I think + + + align:start position:0% +lend against a finite currency I I think +so but it's not it's not done yet + + align:start position:0% +so but it's not it's not done yet + + + align:start position:0% +so but it's not it's not done yet +right this is exactly the central of + + align:start position:0% +right this is exactly the central of + + + align:start position:0% +right this is exactly the central of +commercial banking today it's called + + align:start position:0% +commercial banking today it's called + + + align:start position:0% +commercial banking today it's called +fractional banking we'll be talking + + align:start position:0% +fractional banking we'll be talking + + + align:start position:0% +fractional banking we'll be talking +about that in a bit but as to yes you + + align:start position:0% +about that in a bit but as to yes you + + + align:start position:0% +about that in a bit but as to yes you +could you could you could lend and then + + align:start position:0% +could you could you could lend and then + + + align:start position:0% +could you could you could lend and then +have a multiplier effect + + align:start position:0% +have a multiplier effect + + + align:start position:0% +have a multiplier effect +you also had then banks come up and + + align:start position:0% +you also had then banks come up and + + + align:start position:0% +you also had then banks come up and +started to issue private banknotes + + align:start position:0% +started to issue private banknotes + + + align:start position:0% +started to issue private banknotes +private banknotes effectively a + + align:start position:0% +private banknotes effectively a + + + align:start position:0% +private banknotes effectively a +liability of that back and saying it + + align:start position:0% +liability of that back and saying it + + + align:start position:0% +liability of that back and saying it +would trade and the history of private + + align:start position:0% +would trade and the history of private + + + align:start position:0% +would trade and the history of private +banknotes is usually what you know good + + align:start position:0% +banknotes is usually what you know good + + + align:start position:0% +banknotes is usually what you know good +until it's really bad + + align:start position:0% +until it's really bad + + + align:start position:0% +until it's really bad +and the history of money a lot of + + align:start position:0% +and the history of money a lot of + + + align:start position:0% +and the history of money a lot of +private banks went bust in this country + + align:start position:0% +private banks went bust in this country + + + align:start position:0% +private banks went bust in this country +around the Revolutionary period again + + align:start position:0% +around the Revolutionary period again + + + align:start position:0% +around the Revolutionary period again +around the Civil War and in essence + + align:start position:0% +around the Civil War and in essence + + + align:start position:0% +around the Civil War and in essence +that's what we have now with sixteen + + align:start position:0% +that's what we have now with sixteen + + + align:start position:0% +that's what we have now with sixteen +hundred different crypto currencies we + + align:start position:0% +hundred different crypto currencies we + + + align:start position:0% +hundred different crypto currencies we +have a sort of a new period of a little + + align:start position:0% +have a sort of a new period of a little + + + align:start position:0% +have a sort of a new period of a little +bit of private currencies and I only ask + + align:start position:0% +bit of private currencies and I only ask + + + align:start position:0% +bit of private currencies and I only ask +you to remember that as we start to look + + align:start position:0% +you to remember that as we start to look + + + align:start position:0% +you to remember that as we start to look +at icos initial coin offerings and so + + align:start position:0% +at icos initial coin offerings and so + + + align:start position:0% +at icos initial coin offerings and so +forth so Ledger's the earlier question + + align:start position:0% +forth so Ledger's the earlier question + + + align:start position:0% +forth so Ledger's the earlier question +is what was a ledger + + align:start position:0% + + + + align:start position:0% + +you you asked it can you remember what's + + align:start position:0% +you you asked it can you remember what's + + + align:start position:0% +you you asked it can you remember what's +a ledger principal recordings of + + align:start position:0% +a ledger principal recordings of + + + align:start position:0% +a ledger principal recordings of +accounts and five thousand years ago + + align:start position:0% +accounts and five thousand years ago + + + align:start position:0% +accounts and five thousand years ago +you've had a little reading on this just + + align:start position:0% +you've had a little reading on this just + + + align:start position:0% +you've had a little reading on this just +a medium post it wasn't meant to be a + + align:start position:0% +a medium post it wasn't meant to be a + + + align:start position:0% +a medium post it wasn't meant to be a +deep act economic academic paper but it + + align:start position:0% +deep act economic academic paper but it + + + align:start position:0% +deep act economic academic paper but it +was to try to get get the class thinking + + align:start position:0% +was to try to get get the class thinking + + + align:start position:0% +was to try to get get the class thinking +about Ledger's this is the personal + + align:start position:0% +about Ledger's this is the personal + + + align:start position:0% +about Ledger's this is the personal +ledger of George Washington our first + + align:start position:0% +ledger of George Washington our first + + + align:start position:0% +ledger of George Washington our first +president he was 15 years old when he + + align:start position:0% +president he was 15 years old when he + + + align:start position:0% +president he was 15 years old when he +kept this ledger and he apparently kept + + align:start position:0% +kept this ledger and he apparently kept + + + align:start position:0% +kept this ledger and he apparently kept +Ledger's until his his death and let's + + align:start position:0% +Ledger's until his his death and let's + + + align:start position:0% +Ledger's until his his death and let's +see 52 years later but so Ledger's can + + align:start position:0% +see 52 years later but so Ledger's can + + + align:start position:0% +see 52 years later but so Ledger's can +be kept Justin record the transactions + + align:start position:0% +be kept Justin record the transactions + + + align:start position:0% +be kept Justin record the transactions +of the day he's got one up there mayor + + align:start position:0% +of the day he's got one up there mayor + + + align:start position:0% +of the day he's got one up there mayor +Washington it must have been a cousin or + + align:start position:0% +Washington it must have been a cousin or + + + align:start position:0% +Washington it must have been a cousin or +I can't remember if it was his mother so + + align:start position:0% +I can't remember if it was his mother so + + + align:start position:0% +I can't remember if it was his mother so +if they're the principal recordings of + + align:start position:0% +if they're the principal recordings of + + + align:start position:0% +if they're the principal recordings of +accounts and I've already sort of said + + align:start position:0% +accounts and I've already sort of said + + + align:start position:0% +accounts and I've already sort of said +this they record economic activity and + + align:start position:0% +this they record economic activity and + + + align:start position:0% +this they record economic activity and +financial relationships economic + + align:start position:0% +financial relationships economic + + + align:start position:0% +financial relationships economic +activity and in a sense of transactions + + align:start position:0% +activity and in a sense of transactions + + + align:start position:0% +activity and in a sense of transactions +financial relationships + + align:start position:0% +financial relationships + + + align:start position:0% +financial relationships +what's a the key financial relationship + + align:start position:0% +what's a the key financial relationship + + + align:start position:0% +what's a the key financial relationship +a ledger might record I'm sorry Kelly + + align:start position:0% +a ledger might record I'm sorry Kelly + + + align:start position:0% +a ledger might record I'm sorry Kelly +said it debt and it goes back to the + + align:start position:0% +said it debt and it goes back to the + + + align:start position:0% +said it debt and it goes back to the +debate you had in the reading is money + + align:start position:0% +debate you had in the reading is money + + + align:start position:0% +debate you had in the reading is money +history of border did it come out of + + align:start position:0% +history of border did it come out of + + + align:start position:0% +history of border did it come out of +border did it come out of a sense of + + align:start position:0% +border did it come out of a sense of + + + align:start position:0% +border did it come out of a sense of +debts and credit and store value for + + align:start position:0% +debts and credit and store value for + + + align:start position:0% +debts and credit and store value for +this purpose today it doesn't really + + align:start position:0% +this purpose today it doesn't really + + + align:start position:0% +this purpose today it doesn't really +matter it may have come from both but + + align:start position:0% +matter it may have come from both but + + + align:start position:0% +matter it may have come from both but +know that it has both sides and Ledger's + + align:start position:0% +know that it has both sides and Ledger's + + + align:start position:0% +know that it has both sides and Ledger's +have both sides too and when we're + + align:start position:0% +have both sides too and when we're + + + align:start position:0% +have both sides too and when we're +talking about Bitcoin Bitcoin you will + + align:start position:0% +talking about Bitcoin Bitcoin you will + + + align:start position:0% +talking about Bitcoin Bitcoin you will +see is a is a mechanism to store + + align:start position:0% +see is a is a mechanism to store + + + align:start position:0% +see is a is a mechanism to store +transactions some other block chains + + align:start position:0% +transactions some other block chains + + + align:start position:0% +transactions some other block chains +like etherium stores balances so even in + + align:start position:0% +like etherium stores balances so even in + + + align:start position:0% +like etherium stores balances so even in +the blockchain world you will see some + + align:start position:0% +the blockchain world you will see some + + + align:start position:0% +the blockchain world you will see some +that are balance Ledger's and some which + + align:start position:0% +that are balance Ledger's and some which + + + align:start position:0% +that are balance Ledger's and some which +are transaction Ledger's not to lose you + + align:start position:0% +are transaction Ledger's not to lose you + + + align:start position:0% +are transaction Ledger's not to lose you +and confuse you it's an important part + + align:start position:0% +and confuse you it's an important part + + + align:start position:0% +and confuse you it's an important part +of what is blockchain some types of + + align:start position:0% +of what is blockchain some types of + + + align:start position:0% +of what is blockchain some types of +Ledger's I just mentioned one + + align:start position:0% +Ledger's I just mentioned one + + + align:start position:0% +Ledger's I just mentioned one +transactions versus balance George + + align:start position:0% +transactions versus balance George + + + align:start position:0% +transactions versus balance George +Washington's ledger by the way I think + + align:start position:0% +Washington's ledger by the way I think + + + align:start position:0% +Washington's ledger by the way I think +was a transaction ledger he was just + + align:start position:0% +was a transaction ledger he was just + + + align:start position:0% +was a transaction ledger he was just +keeping you know a list of sales and + + align:start position:0% +keeping you know a list of sales and + + + align:start position:0% +keeping you know a list of sales and +movements but I haven't studied + + align:start position:0% +movements but I haven't studied + + + align:start position:0% +movements but I haven't studied +President George Washington's ledger + + align:start position:0% +President George Washington's ledger + + + align:start position:0% +President George Washington's ledger +close enough so anybody know enough + + align:start position:0% +close enough so anybody know enough + + + align:start position:0% +close enough so anybody know enough +accounting to tell me the difference + + align:start position:0% +accounting to tell me the difference + + + align:start position:0% +accounting to tell me the difference +between a general ledger and a sub + + align:start position:0% +between a general ledger and a sub + + + align:start position:0% +between a general ledger and a sub +ledger or a general ledger and a + + align:start position:0% +ledger or a general ledger and a + + + align:start position:0% +ledger or a general ledger and a +supporting ledger I mean I don't want to + + align:start position:0% +supporting ledger I mean I don't want to + + + align:start position:0% +supporting ledger I mean I don't want to +do the whole lecture myself how many of + + align:start position:0% +do the whole lecture myself how many of + + + align:start position:0% +do the whole lecture myself how many of +you have taken accounting I taught + + align:start position:0% +you have taken accounting I taught + + + align:start position:0% +you have taken accounting I taught +undergraduate accounting once sorry so + + align:start position:0% +undergraduate accounting once sorry so + + + align:start position:0% +undergraduate accounting once sorry so +those of you who just put up your hand + + align:start position:0% +those of you who just put up your hand + + + align:start position:0% +those of you who just put up your hand +who took accounting did I see in the + + align:start position:0% +who took accounting did I see in the + + + align:start position:0% +who took accounting did I see in the +back of the room did you take the + + align:start position:0% +back of the room did you take the + + + align:start position:0% +back of the room did you take the +accounting and that's Aviva + + align:start position:0% + + + + align:start position:0% + +alright alright did you pass the CPA oh + + align:start position:0% +alright alright did you pass the CPA oh + + + align:start position:0% +alright alright did you pass the CPA oh +we have a certified public accountant is + + align:start position:0% +we have a certified public accountant is + + + align:start position:0% +we have a certified public accountant is +gonna tell us the difference between a + + align:start position:0% +gonna tell us the difference between a + + + align:start position:0% +gonna tell us the difference between a +general ledger you can call them as like + + align:start position:0% +general ledger you can call them as like + + + align:start position:0% +general ledger you can call them as like +a specialization so let's say if there's + + align:start position:0% +a specialization so let's say if there's + + + align:start position:0% +a specialization so let's say if there's +a salary or to be paid your salary sub + + align:start position:0% +a salary or to be paid your salary sub + + + align:start position:0% +a salary or to be paid your salary sub +ledger but it'll also go in the general + + align:start position:0% +ledger but it'll also go in the general + + + align:start position:0% +ledger but it'll also go in the general +ledger and the other part of the + + align:start position:0% +ledger and the other part of the + + + align:start position:0% +ledger and the other part of the +transaction some new stuff that you buy + + align:start position:0% +transaction some new stuff that you buy + + + align:start position:0% +transaction some new stuff that you buy +so all of that goes specifically in the + + align:start position:0% +so all of that goes specifically in the + + + align:start position:0% +so all of that goes specifically in the +general agent each of them have their + + align:start position:0% +general agent each of them have their + + + align:start position:0% +general agent each of them have their +own specific lectures if you want to say + + align:start position:0% +own specific lectures if you want to say + + + align:start position:0% +own specific lectures if you want to say +how much you spend on salaries for the + + align:start position:0% +how much you spend on salaries for the + + + align:start position:0% +how much you spend on salaries for the +month then you go to your salary agency + + align:start position:0% +month then you go to your salary agency + + + align:start position:0% +month then you go to your salary agency +but if you want to see overall how much + + align:start position:0% +but if you want to see overall how much + + + align:start position:0% +but if you want to see overall how much +money you spend and how much is moved + + align:start position:0% +money you spend and how much is moved + + + align:start position:0% +money you spend and how much is moved +around then you look at your general + + align:start position:0% +around then you look at your general + + + align:start position:0% +around then you look at your general +ledger + + align:start position:0% +ledger + + + align:start position:0% +ledger +Aviva clearly said it better than I + + align:start position:0% +Aviva clearly said it better than I + + + align:start position:0% +Aviva clearly said it better than I +could have thank you now we know we have + + align:start position:0% +could have thank you now we know we have + + + align:start position:0% +could have thank you now we know we have +one CPA in the class but the importance + + align:start position:0% +one CPA in the class but the importance + + + align:start position:0% +one CPA in the class but the importance +it's not just a passing note the + + align:start position:0% +it's not just a passing note the + + + align:start position:0% +it's not just a passing note the +importance of a general ledger and sub + + align:start position:0% +importance of a general ledger and sub + + + align:start position:0% +importance of a general ledger and sub +Ledger's is there's a hierarchy as well + + align:start position:0% +Ledger's is there's a hierarchy as well + + + align:start position:0% +Ledger's is there's a hierarchy as well +sub Ledger's have more detail and maybe + + align:start position:0% +sub Ledger's have more detail and maybe + + + align:start position:0% +sub Ledger's have more detail and maybe +the net number is kept on the general + + align:start position:0% +the net number is kept on the general + + + align:start position:0% +the net number is kept on the general +ledger that is at the heart of our + + align:start position:0% +ledger that is at the heart of our + + + align:start position:0% +ledger that is at the heart of our +system of banking and is at the heart of + + align:start position:0% +system of banking and is at the heart of + + + align:start position:0% +system of banking and is at the heart of +our system of financial markets where + + align:start position:0% +our system of financial markets where + + + align:start position:0% +our system of financial markets where +the central bank is like a general + + align:start position:0% +the central bank is like a general + + + align:start position:0% +the central bank is like a general +ledger for money in every commercial + + align:start position:0% +ledger for money in every commercial + + + align:start position:0% +ledger for money in every commercial +bank on 9,000 of them or so in the u.s. + + align:start position:0% +bank on 9,000 of them or so in the u.s. + + + align:start position:0% +bank on 9,000 of them or so in the u.s. +in essence keep a sub ledger for money + + align:start position:0% +in essence keep a sub ledger for money + + + align:start position:0% +in essence keep a sub ledger for money +but they do not have control of what I + + align:start position:0% +but they do not have control of what I + + + align:start position:0% +but they do not have control of what I +will call the master ledger or general + + align:start position:0% +will call the master ledger or general + + + align:start position:0% +will call the master ledger or general +ledger at the Federal Reserve + + align:start position:0% + + + + align:start position:0% + +then a third distinction about ledger is + + align:start position:0% +then a third distinction about ledger is + + + align:start position:0% +then a third distinction about ledger is +a single entry a little young 15 year + + align:start position:0% +a single entry a little young 15 year + + + align:start position:0% +a single entry a little young 15 year +old George Washington was keeping a + + align:start position:0% +old George Washington was keeping a + + + align:start position:0% +old George Washington was keeping a +single-entry ledger just a list of + + align:start position:0% +single-entry ledger just a list of + + + align:start position:0% +single-entry ledger just a list of +things that was going on and I didn't + + align:start position:0% +things that was going on and I didn't + + + align:start position:0% +things that was going on and I didn't +think I was gonna bore the class with + + align:start position:0% +think I was gonna bore the class with + + + align:start position:0% +think I was gonna bore the class with +readings about double-entry bookkeeping + + align:start position:0% +readings about double-entry bookkeeping + + + align:start position:0% +readings about double-entry bookkeeping +because you've taken accounting but does + + align:start position:0% +because you've taken accounting but does + + + align:start position:0% +because you've taken accounting but does +anybody want to tell me other than Aviva + + align:start position:0% +anybody want to tell me other than Aviva + + + align:start position:0% +anybody want to tell me other than Aviva +what double-entry bookkeeping and she'll + + align:start position:0% +what double-entry bookkeeping and she'll + + + align:start position:0% +what double-entry bookkeeping and she'll +bail you out + + align:start position:0% +bail you out + + + align:start position:0% +bail you out +yeah double-entry bookkeeping basically + + align:start position:0% +yeah double-entry bookkeeping basically + + + align:start position:0% +yeah double-entry bookkeeping basically +means that any transaction has two + + align:start position:0% +means that any transaction has two + + + align:start position:0% +means that any transaction has two +places in the ledger one on the credit + + align:start position:0% +places in the ledger one on the credit + + + align:start position:0% +places in the ledger one on the credit +side and one on the debit side every + + align:start position:0% +side and one on the debit side every + + + align:start position:0% +side and one on the debit side every +transaction was 1% 90 - hundred percent + + align:start position:0% +transaction was 1% 90 - hundred percent + + + align:start position:0% +transaction was 1% 90 - hundred percent +this is getting it works for me + + align:start position:0% +this is getting it works for me + + + align:start position:0% +this is getting it works for me +anybody else want a different view + + align:start position:0% + + + + align:start position:0% + +there's a balancing between assets and + + align:start position:0% +there's a balancing between assets and + + + align:start position:0% +there's a balancing between assets and +liabilities and then the resulting bit + + align:start position:0% +liabilities and then the resulting bit + + + align:start position:0% +liabilities and then the resulting bit +of capitalism in it is if assets or more + + align:start position:0% +of capitalism in it is if assets or more + + + align:start position:0% +of capitalism in it is if assets or more +than liabilities the rest is capital so + + align:start position:0% +than liabilities the rest is capital so + + + align:start position:0% +than liabilities the rest is capital so +at the heart of capitalism in a sense is + + align:start position:0% +at the heart of capitalism in a sense is + + + align:start position:0% +at the heart of capitalism in a sense is +double entry bookkeeping and in fact + + align:start position:0% +double entry bookkeeping and in fact + + + align:start position:0% +double entry bookkeeping and in fact +while it probably goes back a little + + align:start position:0% +while it probably goes back a little + + + align:start position:0% +while it probably goes back a little +over a thousand years when it was truly + + align:start position:0% +over a thousand years when it was truly + + + align:start position:0% +over a thousand years when it was truly +written up by the Italians in the 1300s + + align:start position:0% +written up by the Italians in the 1300s + + + align:start position:0% +written up by the Italians in the 1300s +it starts started to help you or come + + align:start position:0% +it starts started to help you or come + + + align:start position:0% +it starts started to help you or come +out of the Dark Ages I mean the + + align:start position:0% +out of the Dark Ages I mean the + + + align:start position:0% +out of the Dark Ages I mean the +commercial Renaissance of the Middle + + align:start position:0% +commercial Renaissance of the Middle + + + align:start position:0% +commercial Renaissance of the Middle +Ages some would say was in part not + + align:start position:0% +Ages some would say was in part not + + + align:start position:0% +Ages some would say was in part not +entirely but in part bet on the backs of + + align:start position:0% +entirely but in part bet on the backs of + + + align:start position:0% +entirely but in part bet on the backs of +double entry bookkeeping so Ledger's + + align:start position:0% +double entry bookkeeping so Ledger's + + + align:start position:0% +double entry bookkeeping so Ledger's +matter is my point they're not going to + + align:start position:0% +matter is my point they're not going to + + + align:start position:0% +matter is my point they're not going to +be the heart and soul of this class but + + align:start position:0% +be the heart and soul of this class but + + + align:start position:0% +be the heart and soul of this class but +Bitcoin which is a transaction ledger + + align:start position:0% +Bitcoin which is a transaction ledger + + + align:start position:0% +Bitcoin which is a transaction ledger +aetherium which is a balance ledger our + + align:start position:0% +aetherium which is a balance ledger our + + + align:start position:0% +aetherium which is a balance ledger our +financial system which is all set up on + + align:start position:0% +financial system which is all set up on + + + align:start position:0% +financial system which is all set up on +Ledger's is a relevant sort of subtext + + align:start position:0% +Ledger's is a relevant sort of subtext + + + align:start position:0% +Ledger's is a relevant sort of subtext +you don't have to be afraid of it just + + align:start position:0% +you don't have to be afraid of it just + + + align:start position:0% +you don't have to be afraid of it just +as you don't have to be afraid of + + align:start position:0% +as you don't have to be afraid of + + + align:start position:0% +as you don't have to be afraid of +hashing power that we'll be talking + + align:start position:0% +hashing power that we'll be talking + + + align:start position:0% +hashing power that we'll be talking +about on Thursday in cryptography but + + align:start position:0% +about on Thursday in cryptography but + + + align:start position:0% +about on Thursday in cryptography but +you'd have to have some you know sort of + + align:start position:0% +you'd have to have some you know sort of + + + align:start position:0% +you'd have to have some you know sort of +basic sense of where's where's Bitcoin + + align:start position:0% +basic sense of where's where's Bitcoin + + + align:start position:0% +basic sense of where's where's Bitcoin +fit in terms of Ledger's does anybody I + + align:start position:0% +fit in terms of Ledger's does anybody I + + + align:start position:0% +fit in terms of Ledger's does anybody I +I didn't fill this slide in you'll find + + align:start position:0% +I didn't fill this slide in you'll find + + + align:start position:0% +I didn't fill this slide in you'll find +out it's blank does anybody want to tell + + align:start position:0% +out it's blank does anybody want to tell + + + align:start position:0% +out it's blank does anybody want to tell +me what some characteristics of a good + + align:start position:0% +me what some characteristics of a good + + + align:start position:0% +me what some characteristics of a good +ledger because again as you start to + + align:start position:0% +ledger because again as you start to + + + align:start position:0% +ledger because again as you start to +think about your blockchain projects + + align:start position:0% +think about your blockchain projects + + + align:start position:0% +think about your blockchain projects +later in the semester it's like what + + align:start position:0% +later in the semester it's like what + + + align:start position:0% +later in the semester it's like what +makes a good ledger I don't have any + + align:start position:0% +makes a good ledger I don't have any + + + align:start position:0% +makes a good ledger I don't have any +answers here the world immutable want to + + align:start position:0% +answers here the world immutable want to + + + align:start position:0% +answers here the world immutable want to +be immutable maybe talita can you do me + + align:start position:0% +be immutable maybe talita can you do me + + + align:start position:0% +be immutable maybe talita can you do me +a favor and keep these we'll put them on + + align:start position:0% +a favor and keep these we'll put them on + + + align:start position:0% +a favor and keep these we'll put them on +the slides when we put will keep the + + align:start position:0% +the slides when we put will keep the + + + align:start position:0% +the slides when we put will keep the +classes list and we'll put them in the + + align:start position:0% +classes list and we'll put them in the + + + align:start position:0% +classes list and we'll put them in the +slides immutable I like + + align:start position:0% +slides immutable I like + + + align:start position:0% +slides immutable I like +that anybody else want to grab something + + align:start position:0% +that anybody else want to grab something + + + align:start position:0% +that anybody else want to grab something +which is a good ledger time stand all + + align:start position:0% +which is a good ledger time stand all + + + align:start position:0% +which is a good ledger time stand all +right so that you know when you made + + align:start position:0% +right so that you know when you made + + + align:start position:0% +right so that you know when you made +your entry Kelly so there's a + + align:start position:0% +your entry Kelly so there's a + + + align:start position:0% +your entry Kelly so there's a +transaction the two counterparties to + + align:start position:0% +transaction the two counterparties to + + + align:start position:0% +transaction the two counterparties to +the transaction right and if it's a + + align:start position:0% +the transaction right and if it's a + + + align:start position:0% +the transaction right and if it's a +balance then who owns the balance I was + + align:start position:0% +balance then who owns the balance I was + + + align:start position:0% +balance then who owns the balance I was +just adding a little bit to let's see if + + align:start position:0% +just adding a little bit to let's see if + + + align:start position:0% +just adding a little bit to let's see if +we have a new name or face back here on + + align:start position:0% +we have a new name or face back here on + + + align:start position:0% +we have a new name or face back here on +the back table I haven't chatted with + + align:start position:0% +the back table I haven't chatted with + + + align:start position:0% +the back table I haven't chatted with +you yet what is it + + align:start position:0% +you yet what is it + + + align:start position:0% +you yet what is it +Ross thank you Ross good to meet you + + align:start position:0% + + + + align:start position:0% + +Ross says accuracy and can we take one + + align:start position:0% +Ross says accuracy and can we take one + + + align:start position:0% +Ross says accuracy and can we take one +or two more just a description of the + + align:start position:0% +or two more just a description of the + + + align:start position:0% +or two more just a description of the +transaction and last so all good + + align:start position:0% +transaction and last so all good + + + align:start position:0% +transaction and last so all good +attributes of characteristics somebody's + + align:start position:0% +attributes of characteristics somebody's + + + align:start position:0% +attributes of characteristics somebody's +burning desire that we missed one or two + + align:start position:0% +burning desire that we missed one or two + + + align:start position:0% +burning desire that we missed one or two +GE all right well I think that's inside + + align:start position:0% +GE all right well I think that's inside + + + align:start position:0% +GE all right well I think that's inside +of immutability that in essence that + + align:start position:0% +of immutability that in essence that + + + align:start position:0% +of immutability that in essence that +it's valid that you can't you can't + + align:start position:0% +it's valid that you can't you can't + + + align:start position:0% +it's valid that you can't you can't +change it + + align:start position:0% +change it + + + align:start position:0% +change it +you can't counterfeit it and alike and + + align:start position:0% +you can't counterfeit it and alike and + + + align:start position:0% +you can't counterfeit it and alike and +what you'll find is it's the + + align:start position:0% +what you'll find is it's the + + + align:start position:0% +what you'll find is it's the +characteristics of a good ledger is also + + align:start position:0% +characteristics of a good ledger is also + + + align:start position:0% +characteristics of a good ledger is also +in some part similar to the + + align:start position:0% +in some part similar to the + + + align:start position:0% +in some part similar to the +characteristics of good money they're + + align:start position:0% +characteristics of good money they're + + + align:start position:0% +characteristics of good money they're +not identical but they overlap a lot + + align:start position:0% +not identical but they overlap a lot + + + align:start position:0% +not identical but they overlap a lot +payment systems I'm just going to say + + align:start position:0% +payment systems I'm just going to say + + + align:start position:0% +payment systems I'm just going to say +one line about it it's a method + + align:start position:0% +one line about it it's a method + + + align:start position:0% +one line about it it's a method +basically to amend and record changes in + + align:start position:0% +basically to amend and record changes in + + + align:start position:0% +basically to amend and record changes in +a ledger for money I know it's not what + + align:start position:0% +a ledger for money I know it's not what + + + align:start position:0% +a ledger for money I know it's not what +you usually think about a payment system + + align:start position:0% +you usually think about a payment system + + + align:start position:0% +you usually think about a payment system +but if you go into Starbucks and buy a + + align:start position:0% +but if you go into Starbucks and buy a + + + align:start position:0% +but if you go into Starbucks and buy a +cup of coffee and use your cell phone + + align:start position:0% +cup of coffee and use your cell phone + + + align:start position:0% +cup of coffee and use your cell phone +what you're really just amending a set + + align:start position:0% +what you're really just amending a set + + + align:start position:0% +what you're really just amending a set +of Ledger's Starbucks's ledger goes up + + align:start position:0% +of Ledger's Starbucks's ledger goes up + + + align:start position:0% +of Ledger's Starbucks's ledger goes up +and yep your ledger goes down well your + + align:start position:0% +and yep your ledger goes down well your + + + align:start position:0% +and yep your ledger goes down well your +monetary ledger goes up your utility + + align:start position:0% +monetary ledger goes up your utility + + + align:start position:0% +monetary ledger goes up your utility +your + + align:start position:0% +your + + + align:start position:0% +your +fulfillment from that lot I might go up + + align:start position:0% +fulfillment from that lot I might go up + + + align:start position:0% +fulfillment from that lot I might go up +I'm talking about the financial ledger + + align:start position:0% +I'm talking about the financial ledger + + + align:start position:0% +I'm talking about the financial ledger +so I just wanted to ground when we talk + + align:start position:0% +so I just wanted to ground when we talk + + + align:start position:0% +so I just wanted to ground when we talk +about payment systems to think about + + align:start position:0% +about payment systems to think about + + + align:start position:0% +about payment systems to think about +it's really just a way to amend + + align:start position:0% +it's really just a way to amend + + + align:start position:0% +it's really just a way to amend +usually two parties Ledger's one going + + align:start position:0% +usually two parties Ledger's one going + + + align:start position:0% +usually two parties Ledger's one going +up one going down now in an earlier time + + align:start position:0% +up one going down now in an earlier time + + + align:start position:0% +up one going down now in an earlier time +it was handing somebody a bit of gold + + align:start position:0% +it was handing somebody a bit of gold + + + align:start position:0% +it was handing somebody a bit of gold +there's a bit of silver and it was not + + align:start position:0% +there's a bit of silver and it was not + + + align:start position:0% +there's a bit of silver and it was not +recorded on central Ledger's but we + + align:start position:0% +recorded on central Ledger's but we + + + align:start position:0% +recorded on central Ledger's but we +already live in a age of electronics so + + align:start position:0% +already live in a age of electronics so + + + align:start position:0% +already live in a age of electronics so +this is really what a payment system + + align:start position:0% +this is really what a payment system + + + align:start position:0% +this is really what a payment system +largely is it's not entirely there's + + align:start position:0% +largely is it's not entirely there's + + + align:start position:0% +largely is it's not entirely there's +still some other ways to do for the + + align:start position:0% +still some other ways to do for the + + + align:start position:0% +still some other ways to do for the +Nance so what were some early forms of + + align:start position:0% +Nance so what were some early forms of + + + align:start position:0% +Nance so what were some early forms of +payment systems that did just that that + + align:start position:0% +payment systems that did just that that + + + align:start position:0% +payment systems that did just that that +moved and changed Ledger's they're + + align:start position:0% +moved and changed Ledger's they're + + + align:start position:0% +moved and changed Ledger's they're +called negotiable orders I would dare + + align:start position:0% +called negotiable orders I would dare + + + align:start position:0% +called negotiable orders I would dare +say that most of you probably have not + + align:start position:0% +say that most of you probably have not + + + align:start position:0% +say that most of you probably have not +used negotiable orders of withdrawal + + align:start position:0% +used negotiable orders of withdrawal + + + align:start position:0% +used negotiable orders of withdrawal +that much in the last week or the last + + align:start position:0% +that much in the last week or the last + + + align:start position:0% +that much in the last week or the last +month + + align:start position:0% +month + + + align:start position:0% +month +does anybody here written a personal + + align:start position:0% +does anybody here written a personal + + + align:start position:0% +does anybody here written a personal +cheque in the last week right but in an + + align:start position:0% +cheque in the last week right but in an + + + align:start position:0% +cheque in the last week right but in an +earlier era it would have been the whole + + align:start position:0% +earlier era it would have been the whole + + + align:start position:0% +earlier era it would have been the whole +class anybody in the class not even have + + align:start position:0% +class anybody in the class not even have + + + align:start position:0% +class anybody in the class not even have +a checkbook three-quarters of the class + + align:start position:0% +a checkbook three-quarters of the class + + + align:start position:0% +a checkbook three-quarters of the class +Larry how's that make you feel but a + + align:start position:0% +Larry how's that make you feel but a + + + align:start position:0% +Larry how's that make you feel but a +checkbook is in essence a with a what do + + align:start position:0% +checkbook is in essence a with a what do + + + align:start position:0% +checkbook is in essence a with a what do +you put on a cheque what's it where + + align:start position:0% +you put on a cheque what's it where + + + align:start position:0% +you put on a cheque what's it where +these are this is all about Bitcoin now + + align:start position:0% +these are this is all about Bitcoin now + + + align:start position:0% +these are this is all about Bitcoin now +I'm not doing this just as a walk down + + align:start position:0% +I'm not doing this just as a walk down + + + align:start position:0% +I'm not doing this just as a walk down +memory lane for Larry and myself what + + align:start position:0% +memory lane for Larry and myself what + + + align:start position:0% +memory lane for Larry and myself what +what's that what are the important + + align:start position:0% +what's that what are the important + + + align:start position:0% +what's that what are the important +pieces of a negotiable order withdraw or + + align:start position:0% +pieces of a negotiable order withdraw or + + + align:start position:0% +pieces of a negotiable order withdraw or +check so there's a signature what else + + align:start position:0% +check so there's a signature what else + + + align:start position:0% +check so there's a signature what else +is there I want to just people I haven't + + align:start position:0% +is there I want to just people I haven't + + + align:start position:0% +is there I want to just people I haven't +talked to in the back that I can't + + align:start position:0% +talked to in the back that I can't + + + align:start position:0% +talked to in the back that I can't +remember your name yeah all right so + + align:start position:0% +remember your name yeah all right so + + + align:start position:0% +remember your name yeah all right so +there's a bunch so a signature a payee + + align:start position:0% +there's a bunch so a signature a payee + + + align:start position:0% +there's a bunch so a signature a payee +how much and what it was for what else + + align:start position:0% +how much and what it was for what else + + + align:start position:0% +how much and what it was for what else +number and rally account numbers and + + align:start position:0% +number and rally account numbers and + + + align:start position:0% +number and rally account numbers and +routing numbers + + align:start position:0% +routing numbers + + + align:start position:0% +routing numbers +so think about count numbers and routing + + align:start position:0% +so think about count numbers and routing + + + align:start position:0% +so think about count numbers and routing +numbers is to say in essence what ledger + + align:start position:0% +numbers is to say in essence what ledger + + + align:start position:0% +numbers is to say in essence what ledger +is this coming from + + align:start position:0% +is this coming from + + + align:start position:0% +is this coming from +and the payee is the ledger it's to whom + + align:start position:0% +and the payee is the ledger it's to whom + + + align:start position:0% +and the payee is the ledger it's to whom +it's going and I'm sorry Dan so there's + + align:start position:0% +it's going and I'm sorry Dan so there's + + + align:start position:0% +it's going and I'm sorry Dan so there's +a time stamp a signature a payee the + + align:start position:0% +a time stamp a signature a payee the + + + align:start position:0% +a time stamp a signature a payee the +payor in the form of the account number + + align:start position:0% +payor in the form of the account number + + + align:start position:0% +payor in the form of the account number +and an amount those five are really + + align:start position:0% +and an amount those five are really + + + align:start position:0% +and an amount those five are really +critical and you'll find them all gonna + + align:start position:0% +critical and you'll find them all gonna + + + align:start position:0% +critical and you'll find them all gonna +be right in the middle of all this + + align:start position:0% +be right in the middle of all this + + + align:start position:0% +be right in the middle of all this +Bitcoin and then the reason why you're + + align:start position:0% +Bitcoin and then the reason why you're + + + align:start position:0% +Bitcoin and then the reason why you're +you know some other information I'm + + align:start position:0% +you know some other information I'm + + + align:start position:0% +you know some other information I'm +sorry was there something else they may + + align:start position:0% +sorry was there something else they may + + + align:start position:0% +sorry was there something else they may +be they may be new forms there's + + align:start position:0% +be they may be new forms there's + + + align:start position:0% +be they may be new forms there's +certainly parts of the payment system + + align:start position:0% +certainly parts of the payment system + + + align:start position:0% +certainly parts of the payment system +why they might not be negotiable orders + + align:start position:0% +why they might not be negotiable orders + + + align:start position:0% +why they might not be negotiable orders +withdraw they might not be a direct + + align:start position:0% +withdraw they might not be a direct + + + align:start position:0% +withdraw they might not be a direct +authorization for a bank with one ledger + + align:start position:0% +authorization for a bank with one ledger + + + align:start position:0% +authorization for a bank with one ledger +to move money to another ledger they + + align:start position:0% +to move money to another ledger they + + + align:start position:0% +to move money to another ledger they +might be moving in on their own ledger + + align:start position:0% +might be moving in on their own ledger + + + align:start position:0% +might be moving in on their own ledger +that's it's but you're you're asking the + + align:start position:0% +that's it's but you're you're asking the + + + align:start position:0% +that's it's but you're you're asking the +right question so some early money that + + align:start position:0% +right question so some early money that + + + align:start position:0% +right question so some early money that +we already talked about that was ledger + + align:start position:0% +we already talked about that was ledger + + + align:start position:0% +we already talked about that was ledger +where the tally sticks in England and + + align:start position:0% +where the tally sticks in England and + + + align:start position:0% +where the tally sticks in England and +the Yap stone these were ledger types + + align:start position:0% +the Yap stone these were ledger types + + + align:start position:0% +the Yap stone these were ledger types +and forms of money and it was kind of + + align:start position:0% +and forms of money and it was kind of + + + align:start position:0% +and forms of money and it was kind of +interesting so Ledger's didn't just come + + align:start position:0% +interesting so Ledger's didn't just come + + + align:start position:0% +interesting so Ledger's didn't just come +with electricity and computers so now + + align:start position:0% +with electricity and computers so now + + + align:start position:0% +with electricity and computers so now +let's get back to fiat currency the + + align:start position:0% +let's get back to fiat currency the + + + align:start position:0% +let's get back to fiat currency the +heart of the earlier question and and we + + align:start position:0% +heart of the earlier question and and we + + + align:start position:0% +heart of the earlier question and and we +already talked about it so let's see how + + align:start position:0% +already talked about it so let's see how + + + align:start position:0% +already talked about it so let's see how +the professor did cuz you already said + + align:start position:0% +the professor did cuz you already said + + + align:start position:0% +the professor did cuz you already said +some of the things that you said were + + align:start position:0% +some of the things that you said were + + + align:start position:0% +some of the things that you said were +fiat currency one social and economic + + align:start position:0% +fiat currency one social and economic + + + align:start position:0% +fiat currency one social and economic +consensus I don't I'm in this school + + align:start position:0% +consensus I don't I'm in this school + + + align:start position:0% +consensus I don't I'm in this school +that it's just part of the history it's + + align:start position:0% +that it's just part of the history it's + + + align:start position:0% +that it's just part of the history it's +not that different than everything + + align:start position:0% +not that different than everything + + + align:start position:0% +not that different than everything +became even though it built on that + + align:start position:0% +became even though it built on that + + + align:start position:0% +became even though it built on that +promissory note from China 700 years ago + + align:start position:0% +promissory note from China 700 years ago + + + align:start position:0% +promissory note from China 700 years ago +and the private banknotes it got in the + + align:start position:0% +and the private banknotes it got in the + + + align:start position:0% +and the private banknotes it got in the +Goldsmith's in the 1700s but ultimately + + align:start position:0% +Goldsmith's in the 1700s but ultimately + + + align:start position:0% +Goldsmith's in the 1700s but ultimately +governments took control it represents + + align:start position:0% +governments took control it represents + + + align:start position:0% +governments took control it represents +central bank liabilities and that's + + align:start position:0% +central bank liabilities and that's + + + align:start position:0% +central bank liabilities and that's +important it's a liability of a central + + align:start position:0% +important it's a liability of a central + + + align:start position:0% +important it's a liability of a central +bank it's not an asset it's their + + align:start position:0% +bank it's not an asset it's their + + + align:start position:0% +bank it's not an asset it's their +liability side but it's also guess what + + align:start position:0% +liability side but it's also guess what + + + align:start position:0% +liability side but it's also guess what +there's a second form of money and + + align:start position:0% +there's a second form of money and + + + align:start position:0% +there's a second form of money and +that's when you make a you have a + + align:start position:0% +that's when you make a you have a + + + align:start position:0% +that's when you make a you have a +deposit in a bank that's a liability of + + align:start position:0% +deposit in a bank that's a liability of + + + align:start position:0% +deposit in a bank that's a liability of +a commercial bank central bank is the + + align:start position:0% +a commercial bank central bank is the + + + align:start position:0% +a commercial bank central bank is the +top gold standard a sense using the word + + align:start position:0% +top gold standard a sense using the word + + + align:start position:0% +top gold standard a sense using the word +gold but it's the top ledger commercial + + align:start position:0% +gold but it's the top ledger commercial + + + align:start position:0% +gold but it's the top ledger commercial +banks are like sub ledgers in a sense + + align:start position:0% +banks are like sub ledgers in a sense + + + align:start position:0% +banks are like sub ledgers in a sense +please so before I answer does anybody + + align:start position:0% +please so before I answer does anybody + + + align:start position:0% +please so before I answer does anybody +want to try to answer what it is is a + + align:start position:0% + + + + align:start position:0% + +because it's a social consensus it's + + align:start position:0% +because it's a social consensus it's + + + align:start position:0% +because it's a social consensus it's +it's a it's a very good question that + + align:start position:0% +it's a it's a very good question that + + + align:start position:0% +it's a it's a very good question that +only nask is what does it mean to be a + + align:start position:0% +only nask is what does it mean to be a + + + align:start position:0% +only nask is what does it mean to be a +liability of a central bank when it's + + align:start position:0% +liability of a central bank when it's + + + align:start position:0% +liability of a central bank when it's +just the currency in our pocket right + + align:start position:0% +just the currency in our pocket right + + + align:start position:0% +just the currency in our pocket right +this Federal Reserve Note this says + + align:start position:0% +this Federal Reserve Note this says + + + align:start position:0% +this Federal Reserve Note this says +Federal Reserve Note on it and right we + + align:start position:0% +Federal Reserve Note on it and right we + + + align:start position:0% +Federal Reserve Note on it and right we +can passed around them I'm not afraid + + align:start position:0% +can passed around them I'm not afraid + + + align:start position:0% +can passed around them I'm not afraid +it's only a dollar but you know right + + align:start position:0% +it's only a dollar but you know right + + + align:start position:0% +it's only a dollar but you know right +join me pass around twenties and then I + + align:start position:0% +join me pass around twenties and then I + + + align:start position:0% +join me pass around twenties and then I +went them back you know but it's just + + align:start position:0% +went them back you know but it's just + + + align:start position:0% +went them back you know but it's just +better Reserve Note right so it's a + + align:start position:0% +better Reserve Note right so it's a + + + align:start position:0% +better Reserve Note right so it's a +liability of the commercial bank in a + + align:start position:0% +liability of the commercial bank in a + + + align:start position:0% +liability of the commercial bank in a +earlier day it was said you could + + align:start position:0% +earlier day it was said you could + + + align:start position:0% +earlier day it was said you could +exchange it for gold or silver by the + + align:start position:0% +exchange it for gold or silver by the + + + align:start position:0% +exchange it for gold or silver by the +1930s for retail deposits in the middle + + align:start position:0% +1930s for retail deposits in the middle + + + align:start position:0% +1930s for retail deposits in the middle +of the Depression President Roosevelt + + align:start position:0% +of the Depression President Roosevelt + + + align:start position:0% +of the Depression President Roosevelt +said no more you cannot you could not + + align:start position:0% +said no more you cannot you could not + + + align:start position:0% +said no more you cannot you could not +redeem gold and silver and then + + align:start position:0% +redeem gold and silver and then + + + align:start position:0% +redeem gold and silver and then +President Nixon in the 1970s said in the + + align:start position:0% +President Nixon in the 1970s said in the + + + align:start position:0% +President Nixon in the 1970s said in the +official sector that he was going off of + + align:start position:0% +official sector that he was going off of + + + align:start position:0% +official sector that he was going off of +the until that point in time other + + align:start position:0% +the until that point in time other + + + align:start position:0% +the until that point in time other +governments could redeem in gold but + + align:start position:0% +governments could redeem in gold but + + + align:start position:0% +governments could redeem in gold but +when paper money started it was not + + align:start position:0% +when paper money started it was not + + + align:start position:0% +when paper money started it was not +backed by coal + + align:start position:0% +backed by coal + + + align:start position:0% +backed by coal +we had a period of the gold-standard we + + align:start position:0% +we had a period of the gold-standard we + + + align:start position:0% +we had a period of the gold-standard we +were on and off of it we fell off of it + + align:start position:0% +were on and off of it we fell off of it + + + align:start position:0% +were on and off of it we fell off of it +after world war in World War one we went + + align:start position:0% +after world war in World War one we went + + + align:start position:0% +after world war in World War one we went +back on it it's it would be a false + + align:start position:0% +back on it it's it would be a false + + + align:start position:0% +back on it it's it would be a false +narrative to say that we were on the + + align:start position:0% +narrative to say that we were on the + + + align:start position:0% +narrative to say that we were on the +gold standard for our first hundred and + + align:start position:0% +gold standard for our first hundred and + + + align:start position:0% +gold standard for our first hundred and +forty years I just wanted to clear that + + align:start position:0% +forty years I just wanted to clear that + + + align:start position:0% +forty years I just wanted to clear that +up I mean we sort of went on the gold + + align:start position:0% +up I mean we sort of went on the gold + + + align:start position:0% +up I mean we sort of went on the gold +standard we went off we went back one + + align:start position:0% +standard we went off we went back one + + + align:start position:0% +standard we went off we went back one +and so forth but it is a liability on + + align:start position:0% +and so forth but it is a liability on + + + align:start position:0% +and so forth but it is a liability on +the books and records so as a matter of + + align:start position:0% +the books and records so as a matter of + + + align:start position:0% +the books and records so as a matter of +accounting and double-entry bookkeeping + + align:start position:0% +accounting and double-entry bookkeeping + + + align:start position:0% +accounting and double-entry bookkeeping +I will show you in a minute the balance + + align:start position:0% +I will show you in a minute the balance + + + align:start position:0% +I will show you in a minute the balance +sheet of the Federal Reserve and I'll + + align:start position:0% +sheet of the Federal Reserve and I'll + + + align:start position:0% +sheet of the Federal Reserve and I'll +come back to this question is that all + + align:start position:0% +come back to this question is that all + + + align:start position:0% +come back to this question is that all +right it is in essence a social it's the + + align:start position:0% +right it is in essence a social it's the + + + align:start position:0% +right it is in essence a social it's the +first point they I'm a separate the + + align:start position:0% +first point they I'm a separate the + + + align:start position:0% +first point they I'm a separate the +central bank is liable that they will + + align:start position:0% +central bank is liable that they will + + + align:start position:0% +central bank is liable that they will +move one it's Ledger's if you want to + + align:start position:0% +move one it's Ledger's if you want to + + + align:start position:0% +move one it's Ledger's if you want to +move that to somewhere else so you could + + align:start position:0% +move that to somewhere else so you could + + + align:start position:0% +move that to somewhere else so you could +take that physical $1.00 in and say I + + align:start position:0% +take that physical $1.00 in and say I + + + align:start position:0% +take that physical $1.00 in and say I +want to deposit this in a bank and they + + align:start position:0% +want to deposit this in a bank and they + + + align:start position:0% +want to deposit this in a bank and they +have to record it on the ledger of that + + align:start position:0% +have to record it on the ledger of that + + + align:start position:0% +have to record it on the ledger of that +back that is what they're that that is + + align:start position:0% +back that is what they're that that is + + + align:start position:0% +back that is what they're that that is +and the US government which is + + align:start position:0% +and the US government which is + + + align:start position:0% +and the US government which is +technically separate from the central + + align:start position:0% +technically separate from the central + + + align:start position:0% +technically separate from the central +bank or the or the UK government or the + + align:start position:0% +bank or the or the UK government or the + + + align:start position:0% +bank or the or the UK government or the +Chinese government they're all + + align:start position:0% +Chinese government they're all + + + align:start position:0% +Chinese government they're all +technically separate from their banks + + align:start position:0% +technically separate from their banks + + + align:start position:0% +technically separate from their banks +People's Bank of China or the Bank of + + align:start position:0% +People's Bank of China or the Bank of + + + align:start position:0% +People's Bank of China or the Bank of +England their governments are saying + + align:start position:0% +England their governments are saying + + + align:start position:0% +England their governments are saying +they will accept it for payments against + + align:start position:0% +they will accept it for payments against + + + align:start position:0% +they will accept it for payments against +taxes so there's a set of social + + align:start position:0% +taxes so there's a set of social + + + align:start position:0% +taxes so there's a set of social +constructs it relies on us I'm gonna + + align:start position:0% +constructs it relies on us I'm gonna + + + align:start position:0% +constructs it relies on us I'm gonna +just go through this to answer your + + align:start position:0% +just go through this to answer your + + + align:start position:0% +just go through this to answer your +question it relies on a system of + + align:start position:0% +question it relies on a system of + + + align:start position:0% +question it relies on a system of +Ledger's and it's an integration of + + align:start position:0% +Ledger's and it's an integration of + + + align:start position:0% +Ledger's and it's an integration of +those Ledger's between the banking + + align:start position:0% +those Ledger's between the banking + + + align:start position:0% +those Ledger's between the banking +system and the commercial banks in the + + align:start position:0% +system and the commercial banks in the + + + align:start position:0% +system and the commercial banks in the +u.s. we have about nine thousand + + align:start position:0% +u.s. we have about nine thousand + + + align:start position:0% +u.s. we have about nine thousand +commercial banks and what the Federal + + align:start position:0% +commercial banks and what the Federal + + + align:start position:0% +commercial banks and what the Federal +Reserve is saying but it's true about + + align:start position:0% +Reserve is saying but it's true about + + + align:start position:0% +Reserve is saying but it's true about +the People's Bank of China it's true + + align:start position:0% +the People's Bank of China it's true + + + align:start position:0% +the People's Bank of China it's true +about the European Central Bank each of + + align:start position:0% +about the European Central Bank each of + + + align:start position:0% +about the European Central Bank each of +these central banks are basically saying + + align:start position:0% +these central banks are basically saying + + + align:start position:0% +these central banks are basically saying +if you bring your paper money in will + + align:start position:0% +if you bring your paper money in will + + + align:start position:0% +if you bring your paper money in will +record it on the ledger of a commercial + + align:start position:0% +record it on the ledger of a commercial + + + align:start position:0% +record it on the ledger of a commercial +bank and you can pay your taxes to our + + align:start position:0% +bank and you can pay your taxes to our + + + align:start position:0% +bank and you can pay your taxes to our +sis + + align:start position:0% +sis + + + align:start position:0% +sis +sir over here called the government + + align:start position:0% +sir over here called the government + + + align:start position:0% +sir over here called the government +that's I'm sorry to let you down it's + + align:start position:0% +that's I'm sorry to let you down it's + + + align:start position:0% +that's I'm sorry to let you down it's +it's not more than that sorry alone I + + align:start position:0% +it's not more than that sorry alone I + + + align:start position:0% +it's not more than that sorry alone I +think it's a legal and sustainable way + + align:start position:0% +think it's a legal and sustainable way + + + align:start position:0% +think it's a legal and sustainable way +to conduct to conduct a pondus even with + + align:start position:0% +to conduct to conduct a pondus even with + + + align:start position:0% +to conduct to conduct a pondus even with +a proper policy where where the value + + align:start position:0% +a proper policy where where the value + + + align:start position:0% +a proper policy where where the value +will increase by 1 to 3 percent if you + + align:start position:0% +will increase by 1 to 3 percent if you + + + align:start position:0% +will increase by 1 to 3 percent if you +get to central bank reaches the goal of + + align:start position:0% +get to central bank reaches the goal of + + + align:start position:0% +get to central bank reaches the goal of +inflation + + align:start position:0% +inflation + + + align:start position:0% +inflation +all right any other points of view and + + align:start position:0% +all right any other points of view and + + + align:start position:0% +all right any other points of view and +that I saw I saw I'm not sure your name + + align:start position:0% +that I saw I saw I'm not sure your name + + + align:start position:0% +that I saw I saw I'm not sure your name +oh no you don't you don't want to say + + align:start position:0% +oh no you don't you don't want to say + + + align:start position:0% +oh no you don't you don't want to say +anything + + align:start position:0% +anything + + + align:start position:0% +anything +no all right it's a construct that + + align:start position:0% +no all right it's a construct that + + + align:start position:0% +no all right it's a construct that +someone would give you something so your + + align:start position:0% +someone would give you something so your + + + align:start position:0% +someone would give you something so your +dollar the central bank central bank + + align:start position:0% +dollar the central bank central bank + + + align:start position:0% +dollar the central bank central bank +owes you that dollars worth of whatever + + align:start position:0% +owes you that dollars worth of whatever + + + align:start position:0% +owes you that dollars worth of whatever +you desire and some were happy to take + + align:start position:0% +you desire and some were happy to take + + + align:start position:0% +you desire and some were happy to take +that Donna from the central bank and + + align:start position:0% +that Donna from the central bank and + + + align:start position:0% +that Donna from the central bank and +give you the good say you want so it's + + align:start position:0% +give you the good say you want so it's + + + align:start position:0% +give you the good say you want so it's +it's a roundabout way of it's a way of + + align:start position:0% +it's a roundabout way of it's a way of + + + align:start position:0% +it's a roundabout way of it's a way of +transacting something knows it's so + + align:start position:0% +transacting something knows it's so + + + align:start position:0% +transacting something knows it's so +that's what's a liability because you + + align:start position:0% +that's what's a liability because you + + + align:start position:0% +that's what's a liability because you +can only issue notes against a certain + + align:start position:0% +can only issue notes against a certain + + + align:start position:0% +can only issue notes against a certain +amount of reserves at you so that's why + + align:start position:0% +amount of reserves at you so that's why + + + align:start position:0% +amount of reserves at you so that's why +that's why you refer to it as a + + align:start position:0% +that's why you refer to it as a + + + align:start position:0% +that's why you refer to it as a +liability because you can't just issue + + align:start position:0% +liability because you can't just issue + + + align:start position:0% +liability because you can't just issue +new notes whenever you need them you can + + align:start position:0% +new notes whenever you need them you can + + + align:start position:0% +new notes whenever you need them you can +just make new money out of thin air I'm + + align:start position:0% +just make new money out of thin air I'm + + + align:start position:0% +just make new money out of thin air I'm +gonna take one more comment on this and + + align:start position:0% +gonna take one more comment on this and + + + align:start position:0% +gonna take one more comment on this and +then give a couple more things there I + + align:start position:0% +then give a couple more things there I + + + align:start position:0% +then give a couple more things there I +think maybe the bank reserves I'm very + + align:start position:0% +think maybe the bank reserves I'm very + + + align:start position:0% +think maybe the bank reserves I'm very +pleased with this discussion even even + + align:start position:0% +pleased with this discussion even even + + + align:start position:0% +pleased with this discussion even even +Alliance contribution had the scheme's + + align:start position:0% +Alliance contribution had the scheme's + + + align:start position:0% +Alliance contribution had the scheme's +this is the this is the debate if j-pal + + align:start position:0% +this is the this is the debate if j-pal + + + align:start position:0% +this is the this is the debate if j-pal +were here how many of you know who J Pao + + align:start position:0% +were here how many of you know who J Pao + + + align:start position:0% +were here how many of you know who J Pao +is who's J pal + + align:start position:0% + + + + align:start position:0% + +a lot J how you know who's j-pal head of + + align:start position:0% +a lot J how you know who's j-pal head of + + + align:start position:0% +a lot J how you know who's j-pal head of +the Federal Reserve thank you sorry but + + align:start position:0% +the Federal Reserve thank you sorry but + + + align:start position:0% +the Federal Reserve thank you sorry but +if J Pat were here he'd have a laugh + + align:start position:0% +if J Pat were here he'd have a laugh + + + align:start position:0% +if J Pat were here he'd have a laugh +along with what Alon just said but he + + align:start position:0% +along with what Alon just said but he + + + align:start position:0% +along with what Alon just said but he +would say also the liability is a social + + align:start position:0% +would say also the liability is a social + + + align:start position:0% +would say also the liability is a social +liability as well that a central banker + + align:start position:0% +liability as well that a central banker + + + align:start position:0% +liability as well that a central banker +to their core believes that what they + + align:start position:0% +to their core believes that what they + + + align:start position:0% +to their core believes that what they +are trying to do is ensure for the + + align:start position:0% +are trying to do is ensure for the + + + align:start position:0% +are trying to do is ensure for the +stability of this social thing we call + + align:start position:0% +stability of this social thing we call + + + align:start position:0% +stability of this social thing we call +money and to make sure that it doesn't + + align:start position:0% +money and to make sure that it doesn't + + + align:start position:0% +money and to make sure that it doesn't +get to based and it has some value and + + align:start position:0% +get to based and it has some value and + + + align:start position:0% +get to based and it has some value and +so it's accepted for taxes we talked + + align:start position:0% +so it's accepted for taxes we talked + + + align:start position:0% +so it's accepted for taxes we talked +about notes and coins or legal tender + + align:start position:0% +about notes and coins or legal tender + + + align:start position:0% +about notes and coins or legal tender +for all debts public and private I walk + + align:start position:0% +for all debts public and private I walk + + + align:start position:0% +for all debts public and private I walk +into a Starbucks and I say I'd like a + + align:start position:0% +into a Starbucks and I say I'd like a + + + align:start position:0% +into a Starbucks and I say I'd like a +cup of coffee here's my five dollars or + + align:start position:0% +cup of coffee here's my five dollars or + + + align:start position:0% +cup of coffee here's my five dollars or +whatever it costs these days does the + + align:start position:0% +whatever it costs these days does the + + + align:start position:0% +whatever it costs these days does the +person behind the counter have to brew + + align:start position:0% +person behind the counter have to brew + + + align:start position:0% +person behind the counter have to brew +the coffee he says just a yes or no can + + align:start position:0% +the coffee he says just a yes or no can + + + align:start position:0% +the coffee he says just a yes or no can +I say who wants to go for it there's a + + align:start position:0% +I say who wants to go for it there's a + + + align:start position:0% +I say who wants to go for it there's a +now from Christopher what Chris all + + align:start position:0% +now from Christopher what Chris all + + + align:start position:0% +now from Christopher what Chris all +right there's an O from Chris who agrees + + align:start position:0% +right there's an O from Chris who agrees + + + align:start position:0% +right there's an O from Chris who agrees +with Chris okay they brew the cup of + + align:start position:0% +with Chris okay they brew the cup of + + + align:start position:0% +with Chris okay they brew the cup of +coffee I go to the other side of the + + align:start position:0% +coffee I go to the other side of the + + + align:start position:0% +coffee I go to the other side of the +counter the coffee sitting there now do + + align:start position:0% +counter the coffee sitting there now do + + + align:start position:0% +counter the coffee sitting there now do +they have to accept my five dollars at + + align:start position:0% +they have to accept my five dollars at + + + align:start position:0% +they have to accept my five dollars at +that point yes before they brew the + + align:start position:0% +that point yes before they brew the + + + align:start position:0% +that point yes before they brew the +coffee nobody has to take dollars but + + align:start position:0% +coffee nobody has to take dollars but + + + align:start position:0% +coffee nobody has to take dollars but +once a debt is established they've + + align:start position:0% +once a debt is established they've + + + align:start position:0% +once a debt is established they've +produced the good they provided the + + align:start position:0% +produced the good they provided the + + + align:start position:0% +produced the good they provided the +service they have to take it just a + + align:start position:0% +service they have to take it just a + + + align:start position:0% +service they have to take it just a +small little thing that's what legal + + align:start position:0% +small little thing that's what legal + + + align:start position:0% +small little thing that's what legal +tender is and so there's many + + align:start position:0% +tender is and so there's many + + + align:start position:0% +tender is and so there's many +establishments around the globe that are + + align:start position:0% +establishments around the globe that are + + + align:start position:0% +establishments around the globe that are +basically now putting little signs out + + align:start position:0% +basically now putting little signs out + + + align:start position:0% +basically now putting little signs out +we don't take Swedish Krona we don't + + align:start position:0% +we don't take Swedish Krona we don't + + + align:start position:0% +we don't take Swedish Krona we don't +take this we don't take that in paper + + align:start position:0% +take this we don't take that in paper + + + align:start position:0% +take this we don't take that in paper +form they'll still take it + + align:start position:0% +form they'll still take it + + + align:start position:0% +form they'll still take it +electronically and there's sort of + + align:start position:0% +electronically and there's sort of + + + align:start position:0% +electronically and there's sort of +there's a new a little bit of + + align:start position:0% +there's a new a little bit of + + + align:start position:0% +there's a new a little bit of +definitional thing going on about legal + + align:start position:0% +definitional thing going on about legal + + + align:start position:0% +definitional thing going on about legal +tender there's also some unique tax + + align:start position:0% +tender there's also some unique tax + + + align:start position:0% +tender there's also some unique tax +treatments but I'm not going to go + + align:start position:0% +treatments but I'm not going to go + + + align:start position:0% +treatments but I'm not going to go +through the currency + + align:start position:0% +through the currency + + + align:start position:0% +through the currency +central banking and money we talked + + align:start position:0% +central banking and money we talked + + + align:start position:0% +central banking and money we talked +about a little bit this is a kind of + + align:start position:0% +about a little bit this is a kind of + + + align:start position:0% +about a little bit this is a kind of +short that I borrowed from from somebody + + align:start position:0% +short that I borrowed from from somebody + + + align:start position:0% +short that I borrowed from from somebody +else's paper but the central banks at + + align:start position:0% +else's paper but the central banks at + + + align:start position:0% +else's paper but the central banks at +the top is at the center and if Alice + + align:start position:0% +the top is at the center and if Alice + + + align:start position:0% +the top is at the center and if Alice +and Bob and we'll be talking about Alice + + align:start position:0% +and Bob and we'll be talking about Alice + + + align:start position:0% +and Bob and we'll be talking about Alice +and Bob and Bitcoin time so you can pull + + align:start position:0% +and Bob and Bitcoin time so you can pull + + + align:start position:0% +and Bob and Bitcoin time so you can pull +this chart down later want to transact + + align:start position:0% +this chart down later want to transact + + + align:start position:0% +this chart down later want to transact +and they're at the same commercial bank + + align:start position:0% +and they're at the same commercial bank + + + align:start position:0% +and they're at the same commercial bank +bank number one then commercial bank + + align:start position:0% +bank number one then commercial bank + + + align:start position:0% +bank number one then commercial bank +number one has to change their Ledger's + + align:start position:0% +number one has to change their Ledger's + + + align:start position:0% +number one has to change their Ledger's +moving money from Alice to Bob in + + align:start position:0% +moving money from Alice to Bob in + + + align:start position:0% +moving money from Alice to Bob in +essence if you're both two people at + + align:start position:0% +essence if you're both two people at + + + align:start position:0% +essence if you're both two people at +Bank of America you can move the your + + align:start position:0% +Bank of America you can move the your + + + align:start position:0% +Bank of America you can move the your +balance at Bank of America but if you're + + align:start position:0% +balance at Bank of America but if you're + + + align:start position:0% +balance at Bank of America but if you're +a Bank of America going over to Citicorp + + align:start position:0% +a Bank of America going over to Citicorp + + + align:start position:0% +a Bank of America going over to Citicorp +then something has to go between two + + align:start position:0% +then something has to go between two + + + align:start position:0% +then something has to go between two +Ledger's Bank of America's ledger and + + align:start position:0% +Ledger's Bank of America's ledger and + + + align:start position:0% +Ledger's Bank of America's ledger and +City corpse ledger and the only way to + + align:start position:0% +City corpse ledger and the only way to + + + align:start position:0% +City corpse ledger and the only way to +transact between two banks Ledger's is + + align:start position:0% +transact between two banks Ledger's is + + + align:start position:0% +transact between two banks Ledger's is +some balancing act has to happen at the + + align:start position:0% +some balancing act has to happen at the + + + align:start position:0% +some balancing act has to happen at the +top ledger called the central bank and + + align:start position:0% +top ledger called the central bank and + + + align:start position:0% +top ledger called the central bank and +later when we talk about payment systems + + align:start position:0% +later when we talk about payment systems + + + align:start position:0% +later when we talk about payment systems +and running I'm gonna use this slide + + align:start position:0% +and running I'm gonna use this slide + + + align:start position:0% +and running I'm gonna use this slide +again later in the semester that's why + + align:start position:0% +again later in the semester that's why + + + align:start position:0% +again later in the semester that's why +I'm not going to spend as much time now + + align:start position:0% +I'm not going to spend as much time now + + + align:start position:0% +I'm not going to spend as much time now +on it we're gonna talk about Ledger's + + align:start position:0% +on it we're gonna talk about Ledger's + + + align:start position:0% +on it we're gonna talk about Ledger's +and when you move money between two + + align:start position:0% +and when you move money between two + + + align:start position:0% +and when you move money between two +banks it's all within one closed system + + align:start position:0% +banks it's all within one closed system + + + align:start position:0% +banks it's all within one closed system +that countries are that societies + + align:start position:0% +that countries are that societies + + + align:start position:0% +that countries are that societies +central banking system but then it gets + + align:start position:0% +central banking system but then it gets + + + align:start position:0% +central banking system but then it gets +really a little bit more iffy and wooly + + align:start position:0% +really a little bit more iffy and wooly + + + align:start position:0% +really a little bit more iffy and wooly +when you're moving from one currency to + + align:start position:0% +when you're moving from one currency to + + + align:start position:0% +when you're moving from one currency to +another currency because how do you make + + align:start position:0% +another currency because how do you make + + + align:start position:0% +another currency because how do you make +two closed ledger systems operable not + + align:start position:0% +two closed ledger systems operable not + + + align:start position:0% +two closed ledger systems operable not +for today but we'll go through that + + align:start position:0% +for today but we'll go through that + + + align:start position:0% +for today but we'll go through that +later when we do payment systems and + + align:start position:0% +later when we do payment systems and + + + align:start position:0% +later when we do payment systems and +they'll and the like the Central Bank + + align:start position:0% +they'll and the like the Central Bank + + + align:start position:0% +they'll and the like the Central Bank +the US central bank this was the only + + align:start position:0% +the US central bank this was the only + + + align:start position:0% +the US central bank this was the only +good slide I could find which was about + + align:start position:0% +good slide I could find which was about + + + align:start position:0% +good slide I could find which was about +a year old its liabilities and assets + + align:start position:0% +a year old its liabilities and assets + + + align:start position:0% +a year old its liabilities and assets +are about four and a quarter trillion + + align:start position:0% +are about four and a quarter trillion + + + align:start position:0% +are about four and a quarter trillion +dollars four point three trillion one + + align:start position:0% +dollars four point three trillion one + + + align:start position:0% +dollars four point three trillion one +point seven trillion of that is in + + align:start position:0% +point seven trillion of that is in + + + align:start position:0% +point seven trillion of that is in +currency do I get my $1 back by the way + + align:start position:0% +currency do I get my $1 back by the way + + + align:start position:0% +currency do I get my $1 back by the way +I mean my life L is a yeah yeah so one + + align:start position:0% +I mean my life L is a yeah yeah so one + + + align:start position:0% +I mean my life L is a yeah yeah so one +point seven trillion dollars of those + + align:start position:0% +point seven trillion dollars of those + + + align:start position:0% +point seven trillion dollars of those +greenbacks are in circulation + + align:start position:0% +greenbacks are in circulation + + + align:start position:0% +greenbacks are in circulation +and remarkably even though half of you + + align:start position:0% +and remarkably even though half of you + + + align:start position:0% +and remarkably even though half of you +probably don't use cash that much you + + align:start position:0% +probably don't use cash that much you + + + align:start position:0% +probably don't use cash that much you +don't even have checking accounts the + + align:start position:0% +don't even have checking accounts the + + + align:start position:0% +don't even have checking accounts the +amount of cash and circulation is + + align:start position:0% +amount of cash and circulation is + + + align:start position:0% +amount of cash and circulation is +growing faster than the economy and most + + align:start position:0% +growing faster than the economy and most + + + align:start position:0% +growing faster than the economy and most +developed nations why do you think that + + align:start position:0% +developed nations why do you think that + + + align:start position:0% +developed nations why do you think that +is what one probably one word that's + + align:start position:0% +is what one probably one word that's + + + align:start position:0% +is what one probably one word that's +more than one word drugs Oh trust I + + align:start position:0% +more than one word drugs Oh trust I + + + align:start position:0% +more than one word drugs Oh trust I +thought you said drugs trust well it + + align:start position:0% +thought you said drugs trust well it + + + align:start position:0% +thought you said drugs trust well it +does have to do with trust but it also + + align:start position:0% +does have to do with trust but it also + + + align:start position:0% +does have to do with trust but it also +has to do with drugs paper currency is a + + align:start position:0% +has to do with drugs paper currency is a + + + align:start position:0% +has to do with drugs paper currency is a +wonderful method of money-laundering + + align:start position:0% +wonderful method of money-laundering + + + align:start position:0% +wonderful method of money-laundering +drug-running and a store of value so + + align:start position:0% +drug-running and a store of value so + + + align:start position:0% +drug-running and a store of value so +there's certain segments of our economy + + align:start position:0% +there's certain segments of our economy + + + align:start position:0% +there's certain segments of our economy +and segments of the worldwide economy + + align:start position:0% +and segments of the worldwide economy + + + align:start position:0% +and segments of the worldwide economy +that does not want to be in the + + align:start position:0% +that does not want to be in the + + + align:start position:0% +that does not want to be in the +electronic banking system I'm gonna slip + + align:start position:0% +electronic banking system I'm gonna slip + + + align:start position:0% +electronic banking system I'm gonna slip +through these quickly but there's + + align:start position:0% +through these quickly but there's + + + align:start position:0% +through these quickly but there's +another piece that we need for this + + align:start position:0% +another piece that we need for this + + + align:start position:0% +another piece that we need for this +whole class and for the semester is + + align:start position:0% +whole class and for the semester is + + + align:start position:0% +whole class and for the semester is +credit and credit intermediating but + + align:start position:0% +credit and credit intermediating but + + + align:start position:0% +credit and credit intermediating but +just a little thing + + align:start position:0% +just a little thing + + + align:start position:0% +just a little thing +credit cards started only 60 or 70 years + + align:start position:0% +credit cards started only 60 or 70 years + + + align:start position:0% +credit cards started only 60 or 70 years +ago but they go back to a book a little + + align:start position:0% +ago but they go back to a book a little + + + align:start position:0% +ago but they go back to a book a little +over a hundred years ago the word credit + + align:start position:0% +over a hundred years ago the word credit + + + align:start position:0% +over a hundred years ago the word credit +cards used eighteen times in this book + + align:start position:0% +cards used eighteen times in this book + + + align:start position:0% +cards used eighteen times in this book +where a science fiction writer in 1887 + + align:start position:0% +where a science fiction writer in 1887 + + + align:start position:0% +where a science fiction writer in 1887 +said what would the world be like in the + + align:start position:0% +said what would the world be like in the + + + align:start position:0% +said what would the world be like in the +year 2000 and it was the first we used + + align:start position:0% +year 2000 and it was the first we used + + + align:start position:0% +year 2000 and it was the first we used +the word credit card and he said they + + align:start position:0% +the word credit card and he said they + + + align:start position:0% +the word credit card and he said they +would society would have a form of money + + align:start position:0% +would society would have a form of money + + + align:start position:0% +would society would have a form of money +and you would have credit against it and + + align:start position:0% +and you would have credit against it and + + + align:start position:0% +and you would have credit against it and +it's a fascinating thing that somebody + + align:start position:0% +it's a fascinating thing that somebody + + + align:start position:0% +it's a fascinating thing that somebody +could be that visionary but there were + + align:start position:0% +could be that visionary but there were + + + align:start position:0% +could be that visionary but there were +merchants cards starting so maybe he + + align:start position:0% +merchants cards starting so maybe he + + + align:start position:0% +merchants cards starting so maybe he +wasn't so visionary oil companies in the + + align:start position:0% +wasn't so visionary oil companies in the + + + align:start position:0% +wasn't so visionary oil companies in the +1920s Georg cords were starting but they + + align:start position:0% +1920s Georg cords were starting but they + + + align:start position:0% +1920s Georg cords were starting but they +were single merchant cords you could + + align:start position:0% +were single merchant cords you could + + + align:start position:0% +were single merchant cords you could +have credit from that merchants in 1946 + + align:start position:0% +have credit from that merchants in 1946 + + + align:start position:0% +have credit from that merchants in 1946 +in a bank in Brooklyn a guy named big + + align:start position:0% +in a bank in Brooklyn a guy named big + + + align:start position:0% +in a bank in Brooklyn a guy named big +uns started with that that was the first + + align:start position:0% +uns started with that that was the first + + + align:start position:0% +uns started with that that was the first +real charge it you could charge things + + align:start position:0% +real charge it you could charge things + + + align:start position:0% +real charge it you could charge things +in a few dozen places in Brooklyn + + align:start position:0% +in a few dozen places in Brooklyn + + + align:start position:0% +in a few dozen places in Brooklyn +literally and then all of a sudden it + + align:start position:0% +literally and then all of a sudden it + + + align:start position:0% +literally and then all of a sudden it +took + + align:start position:0% +took + + + align:start position:0% +took +diners club started in the early 1950s + + align:start position:0% +diners club started in the early 1950s + + + align:start position:0% +diners club started in the early 1950s +they found that they could get a bunch + + align:start position:0% +they found that they could get a bunch + + + align:start position:0% +they found that they could get a bunch +of restaurants to say wouldn't you want + + align:start position:0% +of restaurants to say wouldn't you want + + + align:start position:0% +of restaurants to say wouldn't you want +to extend credit and we'll back it + + align:start position:0% +to extend credit and we'll back it + + + align:start position:0% +to extend credit and we'll back it +American Express in the mid 1950s and + + align:start position:0% +American Express in the mid 1950s and + + + align:start position:0% +American Express in the mid 1950s and +then finally in the mid 1960s Bank + + align:start position:0% +then finally in the mid 1960s Bank + + + align:start position:0% +then finally in the mid 1960s Bank +America which is that time was a + + align:start position:0% +America which is that time was a + + + align:start position:0% +America which is that time was a +California bank figured out they would + + align:start position:0% +California bank figured out they would + + + align:start position:0% +California bank figured out they would +create a cooperative with a bunch of + + align:start position:0% +create a cooperative with a bunch of + + + align:start position:0% +create a cooperative with a bunch of +other US banks to extend credit and and + + align:start position:0% +other US banks to extend credit and and + + + align:start position:0% +other US banks to extend credit and and +and the credit boom took off and what + + align:start position:0% +and the credit boom took off and what + + + align:start position:0% +and the credit boom took off and what +was interesting the laws to regulate all + + align:start position:0% +was interesting the laws to regulate all + + + align:start position:0% +was interesting the laws to regulate all +this didn't come until the 1970s at + + align:start position:0% +this didn't come until the 1970s at + + + align:start position:0% +this didn't come until the 1970s at +least in the u.s. the Fair Credit + + align:start position:0% +least in the u.s. the Fair Credit + + + align:start position:0% +least in the u.s. the Fair Credit +Reporting Act in all all the other laws + + align:start position:0% +Reporting Act in all all the other laws + + + align:start position:0% +Reporting Act in all all the other laws +there's three big ones in the 1970s so + + align:start position:0% +there's three big ones in the 1970s so + + + align:start position:0% +there's three big ones in the 1970s so +those who I go to conferences sometime + + align:start position:0% +those who I go to conferences sometime + + + align:start position:0% +those who I go to conferences sometime +to talk about Bitcoin regulation and + + align:start position:0% +to talk about Bitcoin regulation and + + + align:start position:0% +to talk about Bitcoin regulation and +they say well why can't the government + + align:start position:0% +they say well why can't the government + + + align:start position:0% +they say well why can't the government +solve this now I sort of remind them + + align:start position:0% +solve this now I sort of remind them + + + align:start position:0% +solve this now I sort of remind them +that it took fifteen to twenty years + + align:start position:0% +that it took fifteen to twenty years + + + align:start position:0% +that it took fifteen to twenty years +from the introduction of credit cards + + align:start position:0% +from the introduction of credit cards + + + align:start position:0% +from the introduction of credit cards +kind of in the early to mid 1950s and + + align:start position:0% +kind of in the early to mid 1950s and + + + align:start position:0% +kind of in the early to mid 1950s and +the real take off in the 1960s it was + + align:start position:0% +the real take off in the 1960s it was + + + align:start position:0% +the real take off in the 1960s it was +1974 1977 t7 the three big credit laws + + align:start position:0% +1974 1977 t7 the three big credit laws + + + align:start position:0% +1974 1977 t7 the three big credit laws +so if you're going to be an entrepreneur + + align:start position:0% +so if you're going to be an entrepreneur + + + align:start position:0% +so if you're going to be an entrepreneur +in Bitcoin know that it could be 15 + + align:start position:0% +in Bitcoin know that it could be 15 + + + align:start position:0% +in Bitcoin know that it could be 15 +years until there's some crypto laws in + + align:start position:0% +years until there's some crypto laws in + + + align:start position:0% +years until there's some crypto laws in +the future + + align:start position:0% +the future + + + align:start position:0% +the future +that was the processing machine from the + + align:start position:0% +that was the processing machine from the + + + align:start position:0% +that was the processing machine from the +1950s I know I made it too small sorry + + align:start position:0% +1950s I know I made it too small sorry + + + align:start position:0% +1950s I know I made it too small sorry +visa made it better and then of course + + align:start position:0% +visa made it better and then of course + + + align:start position:0% +visa made it better and then of course +that's what we all see today how your + + align:start position:0% +that's what we all see today how your + + + align:start position:0% +that's what we all see today how your +cords get processed so the role of money + + align:start position:0% +cords get processed so the role of money + + + align:start position:0% +cords get processed so the role of money +we've talked about so I'm gonna skip + + align:start position:0% +we've talked about so I'm gonna skip + + + align:start position:0% +we've talked about so I'm gonna skip +over that but now the characteristics of + + align:start position:0% +over that but now the characteristics of + + + align:start position:0% +over that but now the characteristics of +money what makes a good money we talked + + align:start position:0% +money what makes a good money we talked + + + align:start position:0% +money what makes a good money we talked +about some of this earlier it's durable + + align:start position:0% +about some of this earlier it's durable + + + align:start position:0% +about some of this earlier it's durable +meaning that you that that saut cube + + align:start position:0% +meaning that you that that saut cube + + + align:start position:0% +meaning that you that that saut cube +wasn't the greatest because of a lot of + + align:start position:0% +wasn't the greatest because of a lot of + + + align:start position:0% +wasn't the greatest because of a lot of +rain came that would kind of wash away + + align:start position:0% +rain came that would kind of wash away + + + align:start position:0% +rain came that would kind of wash away +gold and silver metals are durable + + align:start position:0% +gold and silver metals are durable + + + align:start position:0% +gold and silver metals are durable +they're portable the heavier it is the + + align:start position:0% +they're portable the heavier it is the + + + align:start position:0% +they're portable the heavier it is the +less portable it is and that's why gold + + align:start position:0% +less portable it is and that's why gold + + + align:start position:0% +less portable it is and that's why gold +was a better money than silver you could + + align:start position:0% +was a better money than silver you could + + + align:start position:0% +was a better money than silver you could +move it or and better than copper or + + align:start position:0% +move it or and better than copper or + + + align:start position:0% +move it or and better than copper or +bronze it was divisible easily you could + + align:start position:0% +bronze it was divisible easily you could + + + align:start position:0% +bronze it was divisible easily you could +slice things up uniform and fungible and + + align:start position:0% +slice things up uniform and fungible and + + + align:start position:0% +slice things up uniform and fungible and +anyone who's down the rabbit hole on + + align:start position:0% +anyone who's down the rabbit hole on + + + align:start position:0% +anyone who's down the rabbit hole on +this stuff + + align:start position:0% +this stuff + + + align:start position:0% +this stuff +if you really want to learn about money + + align:start position:0% +if you really want to learn about money + + + align:start position:0% +if you really want to learn about money +read about Crawford versus royal back in + + align:start position:0% +read about Crawford versus royal back in + + + align:start position:0% +read about Crawford versus royal back in +1749 there was a gentleman at the early + + align:start position:0% +1749 there was a gentleman at the early + + + align:start position:0% +1749 there was a gentleman at the early +part of paper money that mailed 220 + + align:start position:0% +part of paper money that mailed 220 + + + align:start position:0% +part of paper money that mailed 220 +pound notes and he wrote his name on + + align:start position:0% +pound notes and he wrote his name on + + + align:start position:0% +pound notes and he wrote his name on +them they got lost in the mail and he + + align:start position:0% +them they got lost in the mail and he + + + align:start position:0% +them they got lost in the mail and he +took the banks to court to say those + + align:start position:0% +took the banks to court to say those + + + align:start position:0% +took the banks to court to say those +were mine when they were found and there + + align:start position:0% +were mine when they were found and there + + + align:start position:0% +were mine when they were found and there +was no law in Scotland or in England at + + align:start position:0% +was no law in Scotland or in England at + + + align:start position:0% +was no law in Scotland or in England at +the time as to what to do about it but + + align:start position:0% +the time as to what to do about it but + + + align:start position:0% +the time as to what to do about it but +if you lose or somebody stole a piece of + + align:start position:0% +if you lose or somebody stole a piece of + + + align:start position:0% +if you lose or somebody stole a piece of +art you get it back and the law was + + align:start position:0% +art you get it back and the law was + + + align:start position:0% +art you get it back and the law was +settled in 1749 that you actually don't + + align:start position:0% +settled in 1749 that you actually don't + + + align:start position:0% +settled in 1749 that you actually don't +get your money back does anybody want to + + align:start position:0% +get your money back does anybody want to + + + align:start position:0% +get your money back does anybody want to +guess as to why the courts it was a + + align:start position:0% +guess as to why the courts it was a + + + align:start position:0% +guess as to why the courts it was a +matter of first interpretation the court + + align:start position:0% +matter of first interpretation the court + + + align:start position:0% +matter of first interpretation the court +said no look they had no jurisprudence + + align:start position:0% +said no look they had no jurisprudence + + + align:start position:0% +said no look they had no jurisprudence +on this before 1749 why did the courts + + align:start position:0% +on this before 1749 why did the courts + + + align:start position:0% +on this before 1749 why did the courts +decide that a piece of art was different + + align:start position:0% +decide that a piece of art was different + + + align:start position:0% +decide that a piece of art was different +than currency and it goes to the + + align:start position:0% +than currency and it goes to the + + + align:start position:0% +than currency and it goes to the +fundamental of what money is fiat money + + align:start position:0% +fundamental of what money is fiat money + + + align:start position:0% +fundamental of what money is fiat money +yes anybody want to take a guess as to + + align:start position:0% +yes anybody want to take a guess as to + + + align:start position:0% +yes anybody want to take a guess as to +why the courts they could have gone the + + align:start position:0% +why the courts they could have gone the + + + align:start position:0% +why the courts they could have gone the +other way it was it was actually the + + align:start position:0% +other way it was it was actually the + + + align:start position:0% +other way it was it was actually the +facts were clear it was the currency he + + align:start position:0% +facts were clear it was the currency he + + + align:start position:0% +facts were clear it was the currency he +signed I'm just helping ya out so that + + align:start position:0% +signed I'm just helping ya out so that + + + align:start position:0% +signed I'm just helping ya out so that +that's a good point but he signed it if + + align:start position:0% +that's a good point but he signed it if + + + align:start position:0% +that's a good point but he signed it if +I'm you know the medium of this game + + align:start position:0% + + + + align:start position:0% + +since if you would go back and read + + align:start position:0% +since if you would go back and read + + + align:start position:0% +since if you would go back and read +there's some history on this and read + + align:start position:0% +there's some history on this and read + + + align:start position:0% +there's some history on this and read +the court cases this was the point the + + align:start position:0% +the court cases this was the point the + + + align:start position:0% +the court cases this was the point the +court basically said we have to make + + align:start position:0% +court basically said we have to make + + + align:start position:0% +court basically said we have to make +this a medium of exchange this is the + + align:start position:0% +this a medium of exchange this is the + + + align:start position:0% +this a medium of exchange this is the +greater social good it has to be + + align:start position:0% +greater social good it has to be + + + align:start position:0% +greater social good it has to be +fungible and the Royal Bank of Scotland + + align:start position:0% +fungible and the Royal Bank of Scotland + + + align:start position:0% +fungible and the Royal Bank of Scotland +was of course kind of you know closer to + + align:start position:0% +was of course kind of you know closer to + + + align:start position:0% +was of course kind of you know closer to +the courts than this gentleman Crawford + + align:start position:0% +the courts than this gentleman Crawford + + + align:start position:0% +the courts than this gentleman Crawford +but the banks were also saying that we + + align:start position:0% +but the banks were also saying that we + + + align:start position:0% +but the banks were also saying that we +can't keep track of this so it was a + + align:start position:0% +can't keep track of this so it was a + + + align:start position:0% +can't keep track of this so it was a +mixture of the two but it made it + + align:start position:0% +mixture of the two but it made it + + + align:start position:0% +mixture of the two but it made it +fungible err + + align:start position:0% + + + + align:start position:0% + +yeah and in 1749 they all had serial + + align:start position:0% +yeah and in 1749 they all had serial + + + align:start position:0% +yeah and in 1749 they all had serial +numbers and they were signed in a way + + align:start position:0% +numbers and they were signed in a way + + + align:start position:0% +numbers and they were signed in a way +that not today of course they're + + align:start position:0% +that not today of course they're + + + align:start position:0% +that not today of course they're +acceptable and they're stable and we're + + align:start position:0% +acceptable and they're stable and we're + + + align:start position:0% +acceptable and they're stable and we're +going to talk a lot about the last point + + align:start position:0% +going to talk a lot about the last point + + + align:start position:0% +going to talk a lot about the last point +they're stable because they're hard to + + align:start position:0% +they're stable because they're hard to + + + align:start position:0% +they're stable because they're hard to +mine and Bitcoin has that embedded in it + + align:start position:0% +mine and Bitcoin has that embedded in it + + + align:start position:0% +mine and Bitcoin has that embedded in it +as well the design of money is really + + align:start position:0% +as well the design of money is really + + + align:start position:0% +as well the design of money is really +important as well you can make it a + + align:start position:0% +important as well you can make it a + + + align:start position:0% +important as well you can make it a +token a token is like something physical + + align:start position:0% +token a token is like something physical + + + align:start position:0% +token a token is like something physical +or a count based where of course now + + align:start position:0% +or a count based where of course now + + + align:start position:0% +or a count based where of course now +live in a world of account based money + + align:start position:0% +live in a world of account based money + + + align:start position:0% +live in a world of account based money +and it's digital not physical it can be + + align:start position:0% +and it's digital not physical it can be + + + align:start position:0% +and it's digital not physical it can be +issued by the private sector just like + + align:start position:0% +issued by the private sector just like + + + align:start position:0% +issued by the private sector just like +banknotes in the 18th century or a + + align:start position:0% +banknotes in the 18th century or a + + + align:start position:0% +banknotes in the 18th century or a +private sector like Bitcoin or it can be + + align:start position:0% +private sector like Bitcoin or it can be + + + align:start position:0% +private sector like Bitcoin or it can be +central it can be widely acceptable or + + align:start position:0% +central it can be widely acceptable or + + + align:start position:0% +central it can be widely acceptable or +just ho sale there are forms of + + align:start position:0% +just ho sale there are forms of + + + align:start position:0% +just ho sale there are forms of +wholesale money one of the biggest forms + + align:start position:0% +wholesale money one of the biggest forms + + + align:start position:0% +wholesale money one of the biggest forms +that Oso money is the central bank's + + align:start position:0% +that Oso money is the central bank's + + + align:start position:0% +that Oso money is the central bank's +reserves are only available to the + + align:start position:0% +reserves are only available to the + + + align:start position:0% +reserves are only available to the +commercial banking system we're gonna + + align:start position:0% +commercial banking system we're gonna + + + align:start position:0% +commercial banking system we're gonna +study this money flower later but I put + + align:start position:0% +study this money flower later but I put + + + align:start position:0% +study this money flower later but I put +it in the slides because this I didn't + + align:start position:0% +it in the slides because this I didn't + + + align:start position:0% +it in the slides because this I didn't +create this flower you have a reading + + align:start position:0% +create this flower you have a reading + + + align:start position:0% +create this flower you have a reading +later in the semester from the Bank of + + align:start position:0% +later in the semester from the Bank of + + + align:start position:0% +later in the semester from the Bank of +International Settlement it has this + + align:start position:0% +International Settlement it has this + + + align:start position:0% +International Settlement it has this +money flower in it but it's basically + + align:start position:0% +money flower in it but it's basically + + + align:start position:0% +money flower in it but it's basically +across these four things as a token or + + align:start position:0% +across these four things as a token or + + + align:start position:0% +across these four things as a token or +account based physical and digital + + align:start position:0% +account based physical and digital + + + align:start position:0% +account based physical and digital +private or central or widely accessible + + align:start position:0% +private or central or widely accessible + + + align:start position:0% +private or central or widely accessible +and then all monies fall into one piece + + align:start position:0% +and then all monies fall into one piece + + + align:start position:0% +and then all monies fall into one piece +of this money flower + + align:start position:0% +of this money flower + + + align:start position:0% +of this money flower +there's a professor garret that came up + + align:start position:0% +there's a professor garret that came up + + + align:start position:0% +there's a professor garret that came up +with this flower and and there's an + + align:start position:0% +with this flower and and there's an + + + align:start position:0% +with this flower and and there's an +optional reading later in the semester + + align:start position:0% +optional reading later in the semester + + + align:start position:0% +optional reading later in the semester +from him you had a reading from Clark + + align:start position:0% +from him you had a reading from Clark + + + align:start position:0% +from him you had a reading from Clark +there's not enough time but all this + + align:start position:0% +there's not enough time but all this + + + align:start position:0% +there's not enough time but all this +stuff failed does anybody want to give + + align:start position:0% +stuff failed does anybody want to give + + + align:start position:0% +stuff failed does anybody want to give +me a flavor for one or two reasons why a + + align:start position:0% +me a flavor for one or two reasons why a + + + align:start position:0% +me a flavor for one or two reasons why a +bunch of digital cache failed did + + align:start position:0% +bunch of digital cache failed did + + + align:start position:0% +bunch of digital cache failed did +anybody read the Clark reading the + + align:start position:0% +anybody read the Clark reading the + + + align:start position:0% +anybody read the Clark reading the +history of some digit cache no alignment + + align:start position:0% +history of some digit cache no alignment + + + align:start position:0% +history of some digit cache no alignment +anybody else read it over here I can't + + align:start position:0% +anybody else read it over here I can't + + + align:start position:0% +anybody else read it over here I can't +Don so what did you do what Zhan Zhan + + align:start position:0% +Don so what did you do what Zhan Zhan + + + align:start position:0% +Don so what did you do what Zhan Zhan +what did you take from the reading why + + align:start position:0% +what did you take from the reading why + + + align:start position:0% +what did you take from the reading why +did these all fail what's like the one + + align:start position:0% +did these all fail what's like the one + + + align:start position:0% +did these all fail what's like the one +or two biggest reasons they failed + + align:start position:0% +or two biggest reasons they failed + + + align:start position:0% +or two biggest reasons they failed +most of them still relied on kind of + + align:start position:0% +most of them still relied on kind of + + + align:start position:0% +most of them still relied on kind of +some form of a central authority any + + align:start position:0% +some form of a central authority any + + + align:start position:0% +some form of a central authority any +other big reason the lien did you have + + align:start position:0% + + + + align:start position:0% + +not adoption by merchants very good + + align:start position:0% +not adoption by merchants very good + + + align:start position:0% +not adoption by merchants very good +third reason why they failed one that's + + align:start position:0% +third reason why they failed one that's + + + align:start position:0% +third reason why they failed one that's +at the core of what Bitcoin solved + + align:start position:0% + + + + align:start position:0% + +couldn't spend a double spent problem + + align:start position:0% +couldn't spend a double spent problem + + + align:start position:0% +couldn't spend a double spent problem +could a currency be spent not just once + + align:start position:0% +could a currency be spent not just once + + + align:start position:0% +could a currency be spent not just once +but twice so there's four things that + + align:start position:0% +but twice so there's four things that + + + align:start position:0% +but twice so there's four things that +were raised four things there's about + + align:start position:0% +were raised four things there's about + + + align:start position:0% +were raised four things there's about +centralization the double spend they + + align:start position:0% +centralization the double spend they + + + align:start position:0% +centralization the double spend they +couldn't get merchants to adopt it and + + align:start position:0% +couldn't get merchants to adopt it and + + + align:start position:0% +couldn't get merchants to adopt it and +there was couldn't some form of + + align:start position:0% +there was couldn't some form of + + + align:start position:0% +there was couldn't some form of +consensus as to what the ledger was I'm + + align:start position:0% +consensus as to what the ledger was I'm + + + align:start position:0% +consensus as to what the ledger was I'm +gonna flip through these quickly but + + align:start position:0% +gonna flip through these quickly but + + + align:start position:0% +gonna flip through these quickly but +digital and mobile money did happen we + + align:start position:0% +digital and mobile money did happen we + + + align:start position:0% +digital and mobile money did happen we +were asked about PayPal earlier it was + + align:start position:0% +were asked about PayPal earlier it was + + + align:start position:0% +were asked about PayPal earlier it was +1998 in in Norway Eriksson and Telenor + + align:start position:0% +1998 in in Norway Eriksson and Telenor + + + align:start position:0% +1998 in in Norway Eriksson and Telenor +had the first mobile app and it was to + + align:start position:0% +had the first mobile app and it was to + + + align:start position:0% +had the first mobile app and it was to +get movies on your mobile phone $19.99 a + + align:start position:0% +get movies on your mobile phone $19.99 a + + + align:start position:0% +get movies on your mobile phone $19.99 a +leap a comes along that we'll talk a lot + + align:start position:0% +leap a comes along that we'll talk a lot + + + align:start position:0% +leap a comes along that we'll talk a lot +about when we do payments later + + align:start position:0% +about when we do payments later + + + align:start position:0% +about when we do payments later +and of course em pay so that we talked + + align:start position:0% +and of course em pay so that we talked + + + align:start position:0% +and of course em pay so that we talked +about a little last week in Kenya where + + align:start position:0% +about a little last week in Kenya where + + + align:start position:0% +about a little last week in Kenya where +it was Safaricom notice that a bunch of + + align:start position:0% +it was Safaricom notice that a bunch of + + + align:start position:0% +it was Safaricom notice that a bunch of +money near money it was mobile minutes + + align:start position:0% +money near money it was mobile minutes + + + align:start position:0% +money near money it was mobile minutes +that was being used as money in Kenya + + align:start position:0% +that was being used as money in Kenya + + + align:start position:0% +that was being used as money in Kenya +and now there's 20 million users of that + + align:start position:0% +and now there's 20 million users of that + + + align:start position:0% +and now there's 20 million users of that +and of course there's a bunch of + + align:start position:0% +and of course there's a bunch of + + + align:start position:0% +and of course there's a bunch of +regulations now and so forth + + align:start position:0% +regulations now and so forth + + + align:start position:0% +regulations now and so forth +Starbucks started in 2011 and then of + + align:start position:0% +Starbucks started in 2011 and then of + + + align:start position:0% +Starbucks started in 2011 and then of +course it's now off to the races in + + align:start position:0% +course it's now off to the races in + + + align:start position:0% +course it's now off to the races in +mobile money one of the key things about + + align:start position:0% +mobile money one of the key things about + + + align:start position:0% +mobile money one of the key things about +mobile money we will discuss and learn + + align:start position:0% +mobile money we will discuss and learn + + + align:start position:0% +mobile money we will discuss and learn +together is the question each one of + + align:start position:0% +together is the question each one of + + + align:start position:0% +together is the question each one of +these is where is the stored value and I + + align:start position:0% +these is where is the stored value and I + + + align:start position:0% +these is where is the stored value and I +have to tell you sometimes I get quite + + align:start position:0% +have to tell you sometimes I get quite + + + align:start position:0% +have to tell you sometimes I get quite +confused when I research a new app are + + align:start position:0% +confused when I research a new app are + + + align:start position:0% +confused when I research a new app are +they storing the value or are they just + + align:start position:0% +they storing the value or are they just + + + align:start position:0% +they storing the value or are they just +a processing provider to move as we said + + align:start position:0% +a processing provider to move as we said + + + align:start position:0% +a processing provider to move as we said +earlier payment systems move and change + + align:start position:0% +earlier payment systems move and change + + + align:start position:0% +earlier payment systems move and change +and amend other Ledger's + + align:start position:0% +and amend other Ledger's + + + align:start position:0% +and amend other Ledger's +in a number of these like m-pesa + + align:start position:0% +in a number of these like m-pesa + + + align:start position:0% +in a number of these like m-pesa +initially they were storing the value + + align:start position:0% +initially they were storing the value + + + align:start position:0% +initially they were storing the value +and mobile app store blocks stores the + + align:start position:0% +and mobile app store blocks stores the + + + align:start position:0% +and mobile app store blocks stores the +value but many of them are just + + align:start position:0% +value but many of them are just + + + align:start position:0% +value but many of them are just +applications computer code to move the + + align:start position:0% +applications computer code to move the + + + align:start position:0% +applications computer code to move the +ledger somewhere else but the riddle + + align:start position:0% +ledger somewhere else but the riddle + + + align:start position:0% +ledger somewhere else but the riddle +remained you remember that riddle how to + + align:start position:0% +remained you remember that riddle how to + + + align:start position:0% +remained you remember that riddle how to +move money peer-to-peer with that + + align:start position:0% +move money peer-to-peer with that + + + align:start position:0% +move money peer-to-peer with that +essential Authority and that's what I'm + + align:start position:0% +essential Authority and that's what I'm + + + align:start position:0% +essential Authority and that's what I'm +asking for next class Thursday to + + align:start position:0% +asking for next class Thursday to + + + align:start position:0% +asking for next class Thursday to +actually read I wouldn't wing it and I + + align:start position:0% +actually read I wouldn't wing it and I + + + align:start position:0% +actually read I wouldn't wing it and I +wouldn't be afraid of it Satoshi + + align:start position:0% +wouldn't be afraid of it Satoshi + + + align:start position:0% +wouldn't be afraid of it Satoshi +Nakamoto wrote a paper that everybody in + + align:start position:0% +Nakamoto wrote a paper that everybody in + + + align:start position:0% +Nakamoto wrote a paper that everybody in +this class if you're at MIT and a few of + + align:start position:0% +this class if you're at MIT and a few of + + + align:start position:0% +this class if you're at MIT and a few of +you are at Harvard I'm telling you you + + align:start position:0% +you are at Harvard I'm telling you you + + + align:start position:0% +you are at Harvard I'm telling you you +can read it you'll understand maybe 1/2 + + align:start position:0% +can read it you'll understand maybe 1/2 + + + align:start position:0% +can read it you'll understand maybe 1/2 +to 2/3 of it it's not deeply technical + + align:start position:0% +to 2/3 of it it's not deeply technical + + + align:start position:0% +to 2/3 of it it's not deeply technical +it's it's it's it's and it's only 8 or 9 + + align:start position:0% +it's it's it's it's and it's only 8 or 9 + + + align:start position:0% +it's it's it's it's and it's only 8 or 9 +pages I've also assigned National + + align:start position:0% +pages I've also assigned National + + + align:start position:0% +pages I've also assigned National +Institute of Science Technology about 20 + + align:start position:0% +Institute of Science Technology about 20 + + + align:start position:0% +Institute of Science Technology about 20 +pages of reading from NIST the question + + align:start position:0% +pages of reading from NIST the question + + + align:start position:0% +pages of reading from NIST the question +is whether that's Bitcoin I'm gonna skip + + align:start position:0% +is whether that's Bitcoin I'm gonna skip + + + align:start position:0% +is whether that's Bitcoin I'm gonna skip +through the study questions but the + + align:start position:0% +through the study questions but the + + + align:start position:0% +through the study questions but the +study questions are really about + + align:start position:0% +study questions are really about + + + align:start position:0% +study questions are really about +cryptography and hal append-only + + align:start position:0% +cryptography and hal append-only + + + align:start position:0% +cryptography and hal append-only +timestamping we are gonna get into the + + align:start position:0% +timestamping we are gonna get into the + + + align:start position:0% +timestamping we are gonna get into the +nitty-gritty over three lectures I + + align:start position:0% +nitty-gritty over three lectures I + + + align:start position:0% +nitty-gritty over three lectures I +couldn't commit the whole clip the + + align:start position:0% +couldn't commit the whole clip the + + + align:start position:0% +couldn't commit the whole clip the +course the whole semester but I think + + align:start position:0% +course the whole semester but I think + + + align:start position:0% +course the whole semester but I think +three lectures Thursday and the two next + + align:start position:0% +three lectures Thursday and the two next + + + align:start position:0% +three lectures Thursday and the two next +week any time you want to come to see me + + align:start position:0% +week any time you want to come to see me + + + align:start position:0% +week any time you want to come to see me +Sabrina somewhere here or who's one of + + align:start position:0% +Sabrina somewhere here or who's one of + + + align:start position:0% +Sabrina somewhere here or who's one of +our TAS is a computer science master + + align:start position:0% +our TAS is a computer science master + + + align:start position:0% +our TAS is a computer science master +student and knows more about all of this + + align:start position:0% +student and knows more about all of this + + + align:start position:0% +student and knows more about all of this +medoras who was here last week I don't + + align:start position:0% +medoras who was here last week I don't + + + align:start position:0% +medoras who was here last week I don't +know if medoras is here he was part of + + align:start position:0% +know if medoras is here he was part of + + + align:start position:0% +know if medoras is here he was part of +the digital currency initiative over + + align:start position:0% +the digital currency initiative over + + + align:start position:0% +the digital currency initiative over +three lectures we're gonna try to work + + align:start position:0% +three lectures we're gonna try to work + + + align:start position:0% +three lectures we're gonna try to work +through what's the cryptography and why + + align:start position:0% +through what's the cryptography and why + + + align:start position:0% +through what's the cryptography and why +is that matter how does the + + align:start position:0% +is that matter how does the + + + align:start position:0% +is that matter how does the +time-stamping happen how's this look + + align:start position:0% +time-stamping happen how's this look + + + align:start position:0% +time-stamping happen how's this look +like money and how do the transactions + + align:start position:0% +like money and how do the transactions + + + align:start position:0% +like money and how do the transactions +kept yes you get to close it out almost + + align:start position:0% +kept yes you get to close it out almost + + + align:start position:0% +kept yes you get to close it out almost +I can answer that but the assignment was + + align:start position:0% +I can answer that but the assignment was + + + align:start position:0% +I can answer that but the assignment was +to answer it by Thursday right + + align:start position:0% +to answer it by Thursday right + + + align:start position:0% +to answer it by Thursday right +so by Thursday what's your first name + + align:start position:0% +so by Thursday what's your first name + + + align:start position:0% +so by Thursday what's your first name +Caroline did I say we I was going to + + align:start position:0% +Caroline did I say we I was going to + + + align:start position:0% +Caroline did I say we I was going to +answer it today oh did I say today no is + + align:start position:0% +answer it today oh did I say today no is + + + align:start position:0% +answer it today oh did I say today no is +there a mutable record of what I said + + align:start position:0% +there a mutable record of what I said + + + align:start position:0% +there a mutable record of what I said +I'll answer it now if you want but does + + align:start position:0% +I'll answer it now if you want but does + + + align:start position:0% +I'll answer it now if you want but does +anyone have the answer in the whole + + align:start position:0% +anyone have the answer in the whole + + + align:start position:0% +anyone have the answer in the whole +class + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +it's good to raise the question I + + align:start position:0% +it's good to raise the question I + + + align:start position:0% +it's good to raise the question I +thought it was for Thursday but thank + + align:start position:0% +thought it was for Thursday but thank + + + align:start position:0% +thought it was for Thursday but thank +you + + align:start position:0% +you + + + align:start position:0% +you +Stuart Haber a cryptographer and a + + align:start position:0% +Stuart Haber a cryptographer and a + + + align:start position:0% +Stuart Haber a cryptographer and a +colleague at Bell Labs in the early 90s + + align:start position:0% +colleague at Bell Labs in the early 90s + + + align:start position:0% +colleague at Bell Labs in the early 90s +said how do we notarize information + + align:start position:0% +said how do we notarize information + + + align:start position:0% +said how do we notarize information +digitally notarized and we're gonna be + + align:start position:0% +digitally notarized and we're gonna be + + + align:start position:0% +digitally notarized and we're gonna be +talking about this Thursday a lot + + align:start position:0% +talking about this Thursday a lot + + + align:start position:0% +talking about this Thursday a lot +they used a cryptographic method called + + align:start position:0% +they used a cryptographic method called + + + align:start position:0% +they used a cryptographic method called +hash functions and they were just trying + + align:start position:0% +hash functions and they were just trying + + + align:start position:0% +hash functions and they were just trying +to notarize information and by 1995 they + + align:start position:0% +to notarize information and by 1995 they + + + align:start position:0% +to notarize information and by 1995 they +took the they were entrepreneurs they + + align:start position:0% +took the they were entrepreneurs they + + + align:start position:0% +took the they were entrepreneurs they +created a company called surety and once + + align:start position:0% +created a company called surety and once + + + align:start position:0% +created a company called surety and once +a week they published in the New York + + align:start position:0% +a week they published in the New York + + + align:start position:0% +a week they published in the New York +Times and they still do it you can get + + align:start position:0% +Times and they still do it you can get + + + align:start position:0% +Times and they still do it you can get +in New York Times I believe it's on + + align:start position:0% +in New York Times I believe it's on + + + align:start position:0% +in New York Times I believe it's on +Saturday or Sunday and they take it's in + + align:start position:0% +Saturday or Sunday and they take it's in + + + align:start position:0% +Saturday or Sunday and they take it's in +the classified section and they have the + + align:start position:0% +the classified section and they have the + + + align:start position:0% +the classified section and they have the +hash function which you'll read about + + align:start position:0% +hash function which you'll read about + + + align:start position:0% +hash function which you'll read about +between now and Thursday they have the + + align:start position:0% +between now and Thursday they have the + + + align:start position:0% +between now and Thursday they have the +hash of all the pre-existing information + + align:start position:0% +hash of all the pre-existing information + + + align:start position:0% +hash of all the pre-existing information +and so they timestamp it by using the + + align:start position:0% +and so they timestamp it by using the + + + align:start position:0% +and so they timestamp it by using the +New York Times and they use cryptography + + align:start position:0% +New York Times and they use cryptography + + + align:start position:0% +New York Times and they use cryptography +and it's currently 23 years in running + + align:start position:0% + + + + align:start position:0% + +correct because block bitcoin is about + + align:start position:0% +correct because block bitcoin is about + + + align:start position:0% +correct because block bitcoin is about +550,000 blocks and this would be + + align:start position:0% +550,000 blocks and this would be + + + align:start position:0% +550,000 blocks and this would be +whatever 23 years times 52 is longest in + + align:start position:0% +whatever 23 years times 52 is longest in + + + align:start position:0% +whatever 23 years times 52 is longest in +time thank you I look forward to seeing + + align:start position:0% +time thank you I look forward to seeing + + + align:start position:0% +time thank you I look forward to seeing +you + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/6B8FySbsUsM.txt b/6B8FySbsUsM.txt new file mode 100644 index 0000000000000000000000000000000000000000..af7f08e21dedc6b006637032f443c1d4e873e30c --- /dev/null +++ b/6B8FySbsUsM.txt @@ -0,0 +1,11315 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu Cora's rashan uh is a + + align:start position:0% +ocw.mit.edu Cora's rashan uh is a + + + align:start position:0% +ocw.mit.edu Cora's rashan uh is a +particularly dramatic example of a film + + align:start position:0% +particularly dramatic example of a film + + + align:start position:0% +particularly dramatic example of a film +that understands itself to have the kind + + align:start position:0% +that understands itself to have the kind + + + align:start position:0% +that understands itself to have the kind +of claim on its audience that the + + align:start position:0% +of claim on its audience that the + + + align:start position:0% +of claim on its audience that the +greatest art has always imagined itself + + align:start position:0% +greatest art has always imagined itself + + + align:start position:0% +greatest art has always imagined itself +to have on its + + align:start position:0% +to have on its + + + align:start position:0% +to have on its +audience so I want to begin by talking + + align:start position:0% +audience so I want to begin by talking + + + align:start position:0% +audience so I want to begin by talking +very briefly about what I call the + + align:start position:0% +very briefly about what I call the + + + align:start position:0% +very briefly about what I call the +moment of rashan there's a bit of + + align:start position:0% +moment of rashan there's a bit of + + + align:start position:0% +moment of rashan there's a bit of +confusion or at least + + align:start position:0% +confusion or at least + + + align:start position:0% +confusion or at least +historical chronological confusion or + + align:start position:0% +historical chronological confusion or + + + align:start position:0% +historical chronological confusion or +inconsistency in the notion that in the + + align:start position:0% +inconsistency in the notion that in the + + + align:start position:0% +inconsistency in the notion that in the +in the principle that we end the course + + align:start position:0% +in the principle that we end the course + + + align:start position:0% +in the principle that we end the course +with a film that was made uh and and + + align:start position:0% +with a film that was made uh and and + + + align:start position:0% +with a film that was made uh and and +shown internationally before the some + + align:start position:0% +shown internationally before the some + + + align:start position:0% +shown internationally before the some +the the the last two films that we've + + align:start position:0% +the the the last two films that we've + + + align:start position:0% +the the the last two films that we've +seen in our course my reasons for that + + align:start position:0% +seen in our course my reasons for that + + + align:start position:0% +seen in our course my reasons for that +as I partly explained in an earlier + + align:start position:0% +as I partly explained in an earlier + + + align:start position:0% +as I partly explained in an earlier +lecture had to do with the fact with + + align:start position:0% +lecture had to do with the fact with + + + align:start position:0% +lecture had to do with the fact with +with my desire to show a certain + + align:start position:0% +with my desire to show a certain + + + align:start position:0% +with my desire to show a certain +continuity uh amongst forms of European + + align:start position:0% +continuity uh amongst forms of European + + + align:start position:0% +continuity uh amongst forms of European +Cinema and the link between uh Jean + + align:start position:0% +Cinema and the link between uh Jean + + + align:start position:0% +Cinema and the link between uh Jean +Renoir and the Italian neorealists and + + align:start position:0% +Renoir and the Italian neorealists and + + + align:start position:0% +Renoir and the Italian neorealists and +the French Nel vag is so intimate that + + align:start position:0% +the French Nel vag is so intimate that + + + align:start position:0% +the French Nel vag is so intimate that +it seemed to me important to show you + + align:start position:0% +it seemed to me important to show you + + + align:start position:0% +it seemed to me important to show you +that progression in in in sequence but + + align:start position:0% +that progression in in in sequence but + + + align:start position:0% +that progression in in in sequence but +if had been going by strict + + align:start position:0% +if had been going by strict + + + align:start position:0% +if had been going by strict +chronological order we would have + + align:start position:0% +chronological order we would have + + + align:start position:0% +chronological order we would have +introduced this kurasawa film a bit + + align:start position:0% +introduced this kurasawa film a bit + + + align:start position:0% +introduced this kurasawa film a bit +earlier because it was made in 1950 and + + align:start position:0% +earlier because it was made in 1950 and + + + align:start position:0% +earlier because it was made in 1950 and +uh and in 1951 it won an important + + align:start position:0% +uh and in 1951 it won an important + + + align:start position:0% +uh and in 1951 it won an important +International prize the Golden Lion the + + align:start position:0% +International prize the Golden Lion the + + + align:start position:0% +International prize the Golden Lion the +highest prize available at the Venice + + align:start position:0% +highest prize available at the Venice + + + align:start position:0% +highest prize available at the Venice +film festival in 1951 and this had a a + + align:start position:0% +film festival in 1951 and this had a a + + + align:start position:0% +film festival in 1951 and this had a a +seismic effect on internet on on movies + + align:start position:0% +seismic effect on internet on on movies + + + align:start position:0% +seismic effect on internet on on movies +around the world uh the dramatic and + + align:start position:0% +around the world uh the dramatic and + + + align:start position:0% +around the world uh the dramatic and +Powerful subject matter of kurosawa's + + align:start position:0% +Powerful subject matter of kurosawa's + + + align:start position:0% +Powerful subject matter of kurosawa's +film of course riveted attention but + + align:start position:0% +film of course riveted attention but + + + align:start position:0% +film of course riveted attention but +even more than that uh the the the + + align:start position:0% +even more than that uh the the the + + + align:start position:0% +even more than that uh the the the +freedom and imaginative energy of his + + align:start position:0% +freedom and imaginative energy of his + + + align:start position:0% +freedom and imaginative energy of his +stylistic Innovations in the film had a + + align:start position:0% +stylistic Innovations in the film had a + + + align:start position:0% +stylistic Innovations in the film had a +profound impact on on filmmakers around + + align:start position:0% +profound impact on on filmmakers around + + + align:start position:0% +profound impact on on filmmakers around +the world and the the uh when the film + + align:start position:0% +the world and the the uh when the film + + + align:start position:0% +the world and the the uh when the film +was shown in at at Venice in + + align:start position:0% +was shown in at at Venice in + + + align:start position:0% +was shown in at at Venice in +1951 um uh another effect it had when it + + align:start position:0% +1951 um uh another effect it had when it + + + align:start position:0% +1951 um uh another effect it had when it +when when it won the prize was to + + align:start position:0% +when when it won the prize was to + + + align:start position:0% +when when it won the prize was to +introduce Japanese Cinema to to a wider + + align:start position:0% +introduce Japanese Cinema to to a wider + + + align:start position:0% +introduce Japanese Cinema to to a wider +world it was the first significant + + align:start position:0% +world it was the first significant + + + align:start position:0% +world it was the first significant +Japanese film kurasawa the first + + align:start position:0% +Japanese film kurasawa the first + + + align:start position:0% +Japanese film kurasawa the first +important Japanese director to gain + + align:start position:0% +important Japanese director to gain + + + align:start position:0% +important Japanese director to gain +reput a reputation outside of Japan + + align:start position:0% +reput a reputation outside of Japan + + + align:start position:0% +reput a reputation outside of Japan +itself in fact there are many film Buffs + + align:start position:0% +itself in fact there are many film Buffs + + + align:start position:0% +itself in fact there are many film Buffs +and especially specialists in Japanese + + align:start position:0% +and especially specialists in Japanese + + + align:start position:0% +and especially specialists in Japanese +film uh uh who are somewhat resentful of + + align:start position:0% +film uh uh who are somewhat resentful of + + + align:start position:0% +film uh uh who are somewhat resentful of +kurosawa's eminence even though no one + + align:start position:0% +kurosawa's eminence even though no one + + + align:start position:0% +kurosawa's eminence even though no one +denies that he is an eminent director + + align:start position:0% +denies that he is an eminent director + + + align:start position:0% +denies that he is an eminent director +because there are other directors the + + align:start position:0% +because there are other directors the + + + align:start position:0% +because there are other directors the +two I've listed under item two in our in + + align:start position:0% +two I've listed under item two in our in + + + align:start position:0% +two I've listed under item two in our in +our outline are the most most dramatic + + align:start position:0% +our outline are the most most dramatic + + + align:start position:0% +our outline are the most most dramatic +examples uh mizuguchi and U who are + + align:start position:0% +examples uh mizuguchi and U who are + + + align:start position:0% +examples uh mizuguchi and U who are +often thought to be his Superior even + + align:start position:0% +often thought to be his Superior even + + + align:start position:0% +often thought to be his Superior even +greater directors than kurasa this is a + + align:start position:0% +greater directors than kurasa this is a + + + align:start position:0% +greater directors than kurasa this is a +debate for this is a debate of nuances + + align:start position:0% +debate for this is a debate of nuances + + + align:start position:0% +debate for this is a debate of nuances +all three of these directors are major + + align:start position:0% +all three of these directors are major + + + align:start position:0% +all three of these directors are major +artists uh but but it is true I think + + align:start position:0% +artists uh but but it is true I think + + + align:start position:0% +artists uh but but it is true I think +and it is widely recognized that + + align:start position:0% +and it is widely recognized that + + + align:start position:0% +and it is widely recognized that +kurasawa was the director who who uh + + align:start position:0% +kurasawa was the director who who uh + + + align:start position:0% +kurasawa was the director who who uh +crossed that barrier more more + + align:start position:0% +crossed that barrier more more + + + align:start position:0% +crossed that barrier more more +immediately more dramatically than any + + align:start position:0% +immediately more dramatically than any + + + align:start position:0% +immediately more dramatically than any +other and opened the world not just to + + align:start position:0% +other and opened the world not just to + + + align:start position:0% +other and opened the world not just to +Japanese cinem in some degree but open + + align:start position:0% +Japanese cinem in some degree but open + + + align:start position:0% +Japanese cinem in some degree but open +the world in some longer sense to Asian + + align:start position:0% +the world in some longer sense to Asian + + + align:start position:0% +the world in some longer sense to Asian +Cinema more generally that that that the + + align:start position:0% +Cinema more generally that that that the + + + align:start position:0% +Cinema more generally that that that the +the so-called Western World the the the + + align:start position:0% +the so-called Western World the the the + + + align:start position:0% +the so-called Western World the the the +the European and and American Cinema + + align:start position:0% +the European and and American Cinema + + + align:start position:0% +the European and and American Cinema +universes uh had been fairly oblivious + + align:start position:0% +universes uh had been fairly oblivious + + + align:start position:0% +universes uh had been fairly oblivious +to Asian Cinema and certainly to + + align:start position:0% +to Asian Cinema and certainly to + + + align:start position:0% +to Asian Cinema and certainly to +Japanese Cinema uh uh prior to this and + + align:start position:0% +Japanese Cinema uh uh prior to this and + + + align:start position:0% +Japanese Cinema uh uh prior to this and +and the appearance of rashan uh its + + align:start position:0% +and the appearance of rashan uh its + + + align:start position:0% +and the appearance of rashan uh its +enormous uh uh impact in 1951 began to + + align:start position:0% +enormous uh uh impact in 1951 began to + + + align:start position:0% +enormous uh uh impact in 1951 began to +change that um so that what was + + align:start position:0% +change that um so that what was + + + align:start position:0% +change that um so that what was +demonstrated in part in that moment in + + align:start position:0% +demonstrated in part in that moment in + + + align:start position:0% +demonstrated in part in that moment in +when when rashan won this award won the + + align:start position:0% +when when rashan won this award won the + + + align:start position:0% +when when rashan won this award won the +Golden Lion at at at the Venice Film + + align:start position:0% +Golden Lion at at at the Venice Film + + + align:start position:0% +Golden Lion at at at the Venice Film +Festival was a reinforcement of a + + align:start position:0% +Festival was a reinforcement of a + + + align:start position:0% +Festival was a reinforcement of a +principle I've been discussing + + align:start position:0% +principle I've been discussing + + + align:start position:0% +principle I've been discussing +throughout the semester the notion of + + align:start position:0% +throughout the semester the notion of + + + align:start position:0% +throughout the semester the notion of +film as an international medium uh the + + align:start position:0% +film as an international medium uh the + + + align:start position:0% +film as an international medium uh the +idea that the the notion that that uh + + align:start position:0% +idea that the the notion that that uh + + + align:start position:0% +idea that the the notion that that uh +directors from different National + + align:start position:0% +directors from different National + + + align:start position:0% +directors from different National +Cinemas were now being deeply influenced + + align:start position:0% +Cinemas were now being deeply influenced + + + align:start position:0% +Cinemas were now being deeply influenced +by directors from from other nations uh + + align:start position:0% +by directors from from other nations uh + + + align:start position:0% +by directors from from other nations uh +and that and that film itself was in + + align:start position:0% +and that and that film itself was in + + + align:start position:0% +and that and that film itself was in +some deep way a global phenomenon this + + align:start position:0% +some deep way a global phenomenon this + + + align:start position:0% +some deep way a global phenomenon this +uh even even an international form uh + + align:start position:0% +uh even even an international form uh + + + align:start position:0% +uh even even an international form uh +and and uh this I I think it was in the + + align:start position:0% +and and uh this I I think it was in the + + + align:start position:0% +and and uh this I I think it was in the +50s and early 60s that this idea began + + align:start position:0% +50s and early 60s that this idea began + + + align:start position:0% +50s and early 60s that this idea began +to become more and more widely embraced + + align:start position:0% +to become more and more widely embraced + + + align:start position:0% +to become more and more widely embraced +by filmgoers in the United States and in + + align:start position:0% +by filmgoers in the United States and in + + + align:start position:0% +by filmgoers in the United States and in +Europe but perhaps especially in the + + align:start position:0% +Europe but perhaps especially in the + + + align:start position:0% +Europe but perhaps especially in the +United States and uh one mark of this of + + align:start position:0% +United States and uh one mark of this of + + + align:start position:0% +United States and uh one mark of this of +this of this the emergence of Cinema as + + align:start position:0% +this of this the emergence of Cinema as + + + align:start position:0% +this of this the emergence of Cinema as +a as a fully recognized independent art + + align:start position:0% +a as a fully recognized independent art + + + align:start position:0% +a as a fully recognized independent art +form obviously people had thought this + + align:start position:0% +form obviously people had thought this + + + align:start position:0% +form obviously people had thought this +and many directors had achieved artistic + + align:start position:0% +and many directors had achieved artistic + + + align:start position:0% +and many directors had achieved artistic +distinction before this but I'm talking + + align:start position:0% +distinction before this but I'm talking + + + align:start position:0% +distinction before this but I'm talking +about sort of the public understanding + + align:start position:0% +about sort of the public understanding + + + align:start position:0% +about sort of the public understanding +of movies the way people in different + + align:start position:0% +of movies the way people in different + + + align:start position:0% +of movies the way people in different +cultures actually recognized and thought + + align:start position:0% +cultures actually recognized and thought + + + align:start position:0% +cultures actually recognized and thought +about thought about movies it was as if + + align:start position:0% +about thought about movies it was as if + + + align:start position:0% +about thought about movies it was as if +this is the moment in which movies uh + + align:start position:0% +this is the moment in which movies uh + + + align:start position:0% +this is the moment in which movies uh +were understood to enter the museum in a + + align:start position:0% +were understood to enter the museum in a + + + align:start position:0% +were understood to enter the museum in a +certain way to earn uh in in public in a + + align:start position:0% +certain way to earn uh in in public in a + + + align:start position:0% +certain way to earn uh in in public in a +public sense uh the status that that + + align:start position:0% +public sense uh the status that that + + + align:start position:0% +public sense uh the status that that +more traditional art forms had had and + + align:start position:0% +more traditional art forms had had and + + + align:start position:0% +more traditional art forms had had and +one of the explanations for why this + + align:start position:0% +one of the explanations for why this + + + align:start position:0% +one of the explanations for why this +would have been so uh uh why it would + + align:start position:0% +would have been so uh uh why it would + + + align:start position:0% +would have been so uh uh why it would +have had such a powerful impact now I + + align:start position:0% +have had such a powerful impact now I + + + align:start position:0% +have had such a powerful impact now I +think I mentioned last time that this + + align:start position:0% +think I mentioned last time that this + + + align:start position:0% +think I mentioned last time that this +sight was partial in the United States + + align:start position:0% +sight was partial in the United States + + + align:start position:0% +sight was partial in the United States +especially that is to say in the 50s and + + align:start position:0% +especially that is to say in the 50s and + + + align:start position:0% +especially that is to say in the 50s and +early 60s it began to Dawn on movie + + align:start position:0% +early 60s it began to Dawn on movie + + + align:start position:0% +early 60s it began to Dawn on movie +critics and and and Scholars and of whom + + align:start position:0% +critics and and and Scholars and of whom + + + align:start position:0% +critics and and and Scholars and of whom +there were only a few at that time and + + align:start position:0% +there were only a few at that time and + + + align:start position:0% +there were only a few at that time and +and then movie audiences that European + + align:start position:0% +and then movie audiences that European + + + align:start position:0% +and then movie audiences that European +films and Asian films especially + + align:start position:0% +films and Asian films especially + + + align:start position:0% +films and Asian films especially +Japanese films might have great artistic + + align:start position:0% +Japanese films might have great artistic + + + align:start position:0% +Japanese films might have great artistic +value but it was it was a longer time + + align:start position:0% +value but it was it was a longer time + + + align:start position:0% +value but it was it was a longer time +before Americans began to realize that + + align:start position:0% +before Americans began to realize that + + + align:start position:0% +before Americans began to realize that +their own native uh forms of films uh + + align:start position:0% +their own native uh forms of films uh + + + align:start position:0% +their own native uh forms of films uh +had had a similar kind of authority and + + align:start position:0% +had had a similar kind of authority and + + + align:start position:0% +had had a similar kind of authority and +so this moment uh uh in the in the early + + align:start position:0% +so this moment uh uh in the in the early + + + align:start position:0% +so this moment uh uh in the in the early +1950s was a deeply significant one let's + + align:start position:0% +1950s was a deeply significant one let's + + + align:start position:0% +1950s was a deeply significant one let's +remember uh historically what it + + align:start position:0% +remember uh historically what it + + + align:start position:0% +remember uh historically what it +represented in in in Europe and in the + + align:start position:0% +represented in in in Europe and in the + + + align:start position:0% +represented in in in Europe and in the +United States it's the moment of the + + align:start position:0% +United States it's the moment of the + + + align:start position:0% +United States it's the moment of the +emergence of Italian neorealism which + + align:start position:0% +emergence of Italian neorealism which + + + align:start position:0% +emergence of Italian neorealism which +itself begins to establish a kind of + + align:start position:0% +itself begins to establish a kind of + + + align:start position:0% +itself begins to establish a kind of +very powerful claim on people's on + + align:start position:0% +very powerful claim on people's on + + + align:start position:0% +very powerful claim on people's on +people's attention one irony of rashim + + align:start position:0% +people's attention one irony of rashim + + + align:start position:0% +people's attention one irony of rashim +Mon's success was that it was not very + + align:start position:0% +Mon's success was that it was not very + + + align:start position:0% +Mon's success was that it was not very +successful in Japan when it was released + + align:start position:0% +successful in Japan when it was released + + + align:start position:0% +successful in Japan when it was released +in 1950 and the producer the production + + align:start position:0% +in 1950 and the producer the production + + + align:start position:0% +in 1950 and the producer the production +company responsible for the film was + + align:start position:0% +company responsible for the film was + + + align:start position:0% +company responsible for the film was +very dubious about entering it in the + + align:start position:0% +very dubious about entering it in the + + + align:start position:0% +very dubious about entering it in the +competition uh didn't think it was a a + + align:start position:0% +competition uh didn't think it was a a + + + align:start position:0% +competition uh didn't think it was a a +significant film uh even though it + + align:start position:0% +significant film uh even though it + + + align:start position:0% +significant film uh even though it +transformed korus sawa's career because + + align:start position:0% +transformed korus sawa's career because + + + align:start position:0% +transformed korus sawa's career because +of the immense recognition it finally + + align:start position:0% +of the immense recognition it finally + + + align:start position:0% +of the immense recognition it finally +got and kusawa himself recognized he'd + + align:start position:0% +got and kusawa himself recognized he'd + + + align:start position:0% +got and kusawa himself recognized he'd +been making films for almost a decade + + align:start position:0% +been making films for almost a decade + + + align:start position:0% +been making films for almost a decade +before that but rashan was his most + + align:start position:0% +before that but rashan was his most + + + align:start position:0% +before that but rashan was his most +ambitious uh film to that point and it + + align:start position:0% +ambitious uh film to that point and it + + + align:start position:0% +ambitious uh film to that point and it +also Incorporated more Innovative + + align:start position:0% +also Incorporated more Innovative + + + align:start position:0% +also Incorporated more Innovative +strategy visual strategies than any he + + align:start position:0% +strategy visual strategies than any he + + + align:start position:0% +strategy visual strategies than any he +had tried before um established him as + + align:start position:0% +had tried before um established him as + + + align:start position:0% +had tried before um established him as +an international director and I + + align:start position:0% +an international director and I + + + align:start position:0% +an international director and I +mentioned the names of two other + + align:start position:0% +mentioned the names of two other + + + align:start position:0% +mentioned the names of two other +directors uh uh just as a from different + + align:start position:0% +directors uh uh just as a from different + + + align:start position:0% +directors uh uh just as a from different +uh Traditions as a way of reminding you + + align:start position:0% +uh Traditions as a way of reminding you + + + align:start position:0% +uh Traditions as a way of reminding you +of of of another feature of this + + align:start position:0% +of of of another feature of this + + + align:start position:0% +of of of another feature of this +phenomenon another reason uh as I began + + align:start position:0% +phenomenon another reason uh as I began + + + align:start position:0% +phenomenon another reason uh as I began +to say earlier for why this moment was + + align:start position:0% +to say earlier for why this moment was + + + align:start position:0% +to say earlier for why this moment was +such a significant one and the term I + + align:start position:0% +such a significant one and the term I + + + align:start position:0% +such a significant one and the term I +use here is modernism modernist Cinema + + align:start position:0% +use here is modernism modernist Cinema + + + align:start position:0% +use here is modernism modernist Cinema +remember one of the ways to understand + + align:start position:0% +remember one of the ways to understand + + + align:start position:0% +remember one of the ways to understand +this idea is to recognize that a great + + align:start position:0% +this idea is to recognize that a great + + + align:start position:0% +this idea is to recognize that a great +revolution in the Arts had occurred at + + align:start position:0% +revolution in the Arts had occurred at + + + align:start position:0% +revolution in the Arts had occurred at +the turn of the 20th century the end of + + align:start position:0% +the turn of the 20th century the end of + + + align:start position:0% +the turn of the 20th century the end of +the 19th and at the turn of the 20 + + align:start position:0% +the 19th and at the turn of the 20 + + + align:start position:0% +the 19th and at the turn of the 20 +Century we've talked about this earlier + + align:start position:0% +Century we've talked about this earlier + + + align:start position:0% +Century we've talked about this earlier +it's the movement we call modernism + + align:start position:0% +it's the movement we call modernism + + + align:start position:0% +it's the movement we call modernism +right it's the moment of Picasso it's + + align:start position:0% +right it's the moment of Picasso it's + + + align:start position:0% +right it's the moment of Picasso it's +the moment of James Joyce uh and uh uh + + align:start position:0% +the moment of James Joyce uh and uh uh + + + align:start position:0% +the moment of James Joyce uh and uh uh +it was a kind of revolution in both art + + align:start position:0% +it was a kind of revolution in both art + + + align:start position:0% +it was a kind of revolution in both art +uh uh visual art literature music uh + + align:start position:0% +uh uh visual art literature music uh + + + align:start position:0% +uh uh visual art literature music uh +took place in this period and and uh uh + + align:start position:0% +took place in this period and and uh uh + + + align:start position:0% +took place in this period and and uh uh +what what was characteristic of among + + align:start position:0% +what what was characteristic of among + + + align:start position:0% +what what was characteristic of among +the characteristics of this modernist + + align:start position:0% +the characteristics of this modernist + + + align:start position:0% +the characteristics of this modernist +movement was a was a was a a a newly + + align:start position:0% +movement was a was a was a a a newly + + + align:start position:0% +movement was a was a was a a a newly +complicated and self-conscious attitude + + align:start position:0% +complicated and self-conscious attitude + + + align:start position:0% +complicated and self-conscious attitude +toward narrative itself toward + + align:start position:0% +toward narrative itself toward + + + align:start position:0% +toward narrative itself toward +storytelling uh so it was a modernism in + + align:start position:0% +storytelling uh so it was a modernism in + + + align:start position:0% +storytelling uh so it was a modernism in +literature and in art uh involved among + + align:start position:0% +literature and in art uh involved among + + + align:start position:0% +literature and in art uh involved among +other things a kind of a kind if not a + + align:start position:0% +other things a kind of a kind if not a + + + align:start position:0% +other things a kind of a kind if not a +hostility at least a kind of a kind of + + align:start position:0% +hostility at least a kind of a kind of + + + align:start position:0% +hostility at least a kind of a kind of +or antagonism at least a kind of + + align:start position:0% +or antagonism at least a kind of + + + align:start position:0% +or antagonism at least a kind of +skepticism about inherited traditional + + align:start position:0% +skepticism about inherited traditional + + + align:start position:0% +skepticism about inherited traditional +categories and ways of doing things one + + align:start position:0% +categories and ways of doing things one + + + align:start position:0% +categories and ways of doing things one +form this took in narrative was to dis + + align:start position:0% +form this took in narrative was to dis + + + align:start position:0% +form this took in narrative was to dis +to dislocate or disorient the narrative + + align:start position:0% +to dislocate or disorient the narrative + + + align:start position:0% +to dislocate or disorient the narrative +line instead of telling a story in a + + align:start position:0% +line instead of telling a story in a + + + align:start position:0% +line instead of telling a story in a +Chron chronological sequence a lot of + + align:start position:0% +Chron chronological sequence a lot of + + + align:start position:0% +Chron chronological sequence a lot of +the great works of fiction of of the + + align:start position:0% +the great works of fiction of of the + + + align:start position:0% +the great works of fiction of of the +modern of the modernist era uh books + + align:start position:0% +modern of the modernist era uh books + + + align:start position:0% +modern of the modernist era uh books +books by writers like Joseph Conrad or + + align:start position:0% +books by writers like Joseph Conrad or + + + align:start position:0% +books by writers like Joseph Conrad or +or PR uh the great French novelist who + + align:start position:0% +or PR uh the great French novelist who + + + align:start position:0% +or PR uh the great French novelist who +was so preoccupied by memory and human + + align:start position:0% +was so preoccupied by memory and human + + + align:start position:0% +was so preoccupied by memory and human +subjectivity or uh the great uh German + + align:start position:0% +subjectivity or uh the great uh German + + + align:start position:0% +subjectivity or uh the great uh German +novelist uh Tomas man number of other uh + + align:start position:0% +novelist uh Tomas man number of other uh + + + align:start position:0% +novelist uh Tomas man number of other uh +great figures that we could mention + + align:start position:0% +great figures that we could mention + + + align:start position:0% +great figures that we could mention +began to construct stories in which the + + align:start position:0% +began to construct stories in which the + + + align:start position:0% +began to construct stories in which the +uh in which chronological order was + + align:start position:0% +uh in which chronological order was + + + align:start position:0% +uh in which chronological order was +profoundly disrupted and they also began + + align:start position:0% +profoundly disrupted and they also began + + + align:start position:0% +profoundly disrupted and they also began +to connect create stories in which there + + align:start position:0% +to connect create stories in which there + + + align:start position:0% +to connect create stories in which there +were multiple narrators in which and the + + align:start position:0% +were multiple narrators in which and the + + + align:start position:0% +were multiple narrators in which and the +effect of multiple narrators begins in a + + align:start position:0% +effect of multiple narrators begins in a + + + align:start position:0% +effect of multiple narrators begins in a +even in it even if you do nothing more + + align:start position:0% +even in it even if you do nothing more + + + align:start position:0% +even in it even if you do nothing more +than have multiple narrators you begin + + align:start position:0% +than have multiple narrators you begin + + + align:start position:0% +than have multiple narrators you begin +to raise questions about the about the + + align:start position:0% +to raise questions about the about the + + + align:start position:0% +to raise questions about the about the +veracity the truthfulness of the of any + + align:start position:0% +veracity the truthfulness of the of any + + + align:start position:0% +veracity the truthfulness of the of any +single perspective uh and you will + + align:start position:0% +single perspective uh and you will + + + align:start position:0% +single perspective uh and you will +understand when you look at rasham on + + align:start position:0% +understand when you look at rasham on + + + align:start position:0% +understand when you look at rasham on +why this movie embodies the many of + + align:start position:0% +why this movie embodies the many of + + + align:start position:0% +why this movie embodies the many of +these same modernist principles but the + + align:start position:0% +these same modernist principles but the + + + align:start position:0% +these same modernist principles but the +point is that Cinema as a as a as as a + + align:start position:0% +point is that Cinema as a as a as as a + + + align:start position:0% +point is that Cinema as a as a as as a +narrative form uh lagged Behind These + + align:start position:0% +narrative form uh lagged Behind These + + + align:start position:0% +narrative form uh lagged Behind These +more traditional arts and it really + + align:start position:0% +more traditional arts and it really + + + align:start position:0% +more traditional arts and it really +wasn't until the 1950s uh and partly + + align:start position:0% +wasn't until the 1950s uh and partly + + + align:start position:0% +wasn't until the 1950s uh and partly +because of films like Rashon that it + + align:start position:0% +because of films like Rashon that it + + + align:start position:0% +because of films like Rashon that it +began to be recognized that the movies + + align:start position:0% +began to be recognized that the movies + + + align:start position:0% +began to be recognized that the movies +too could Embrace and embody the + + align:start position:0% +too could Embrace and embody the + + + align:start position:0% +too could Embrace and embody the +principles of modernism so one way to + + align:start position:0% +principles of modernism so one way to + + + align:start position:0% +principles of modernism so one way to +understand what happened in the 1950s + + align:start position:0% +understand what happened in the 1950s + + + align:start position:0% +understand what happened in the 1950s +was uh was to uh is to is to recognize + + align:start position:0% +was uh was to uh is to is to recognize + + + align:start position:0% +was uh was to uh is to is to recognize +that directors like kurasawa and ingar + + align:start position:0% +that directors like kurasawa and ingar + + + align:start position:0% +that directors like kurasawa and ingar +Bergman the great Swedish director and + + align:start position:0% +Bergman the great Swedish director and + + + align:start position:0% +Bergman the great Swedish director and +felini the great Italian director and + + align:start position:0% +felini the great Italian director and + + + align:start position:0% +felini the great Italian director and +the inheritor and expander of the + + align:start position:0% +the inheritor and expander of the + + + align:start position:0% +the inheritor and expander of the +neorealist tradition going far beyond a + + align:start position:0% +neorealist tradition going far beyond a + + + align:start position:0% +neorealist tradition going far beyond a +narrow realism uh that directors like + + align:start position:0% +narrow realism uh that directors like + + + align:start position:0% +narrow realism uh that directors like +that uh began to create films that in a + + align:start position:0% +that uh began to create films that in a + + + align:start position:0% +that uh began to create films that in a +in a in a in a formal sense in a + + align:start position:0% +in a in a in a formal sense in a + + + align:start position:0% +in a in a in a formal sense in a +structural sense in and also in terms of + + align:start position:0% +structural sense in and also in terms of + + + align:start position:0% +structural sense in and also in terms of +their content had the kind of complexity + + align:start position:0% +their content had the kind of complexity + + + align:start position:0% +their content had the kind of complexity +nuance and skepticism that uh and even + + align:start position:0% +nuance and skepticism that uh and even + + + align:start position:0% +nuance and skepticism that uh and even +the philosophic U uh self-awareness that + + align:start position:0% +the philosophic U uh self-awareness that + + + align:start position:0% +the philosophic U uh self-awareness that +that was characteristic of high + + align:start position:0% +that was characteristic of high + + + align:start position:0% +that was characteristic of high +modernism at the turn of the 20th + + align:start position:0% +modernism at the turn of the 20th + + + align:start position:0% +modernism at the turn of the 20th +century so it's as if what was going on + + align:start position:0% +century so it's as if what was going on + + + align:start position:0% +century so it's as if what was going on +was the movies themselves were now + + align:start position:0% +was the movies themselves were now + + + align:start position:0% +was the movies themselves were now +asserting themselves as a modernist art + + align:start position:0% +asserting themselves as a modernist art + + + align:start position:0% +asserting themselves as a modernist art +right uh I don't mean as a contemporary + + align:start position:0% +right uh I don't mean as a contemporary + + + align:start position:0% +right uh I don't mean as a contemporary +art right I'm I'm referring specifically + + align:start position:0% +art right I'm I'm referring specifically + + + align:start position:0% +art right I'm I'm referring specifically +to the modernist movement and to the and + + align:start position:0% +to the modernist movement and to the and + + + align:start position:0% +to the modernist movement and to the and +to the and to the + + align:start position:0% +to the and to the + + + align:start position:0% +to the and to the +dislocated uh and and and and uh uh much + + align:start position:0% +dislocated uh and and and and uh uh much + + + align:start position:0% +dislocated uh and and and and uh uh much +more demanding kinds of narrative + + align:start position:0% +more demanding kinds of narrative + + + align:start position:0% +more demanding kinds of narrative +strategies that are characteristic of + + align:start position:0% +strategies that are characteristic of + + + align:start position:0% +strategies that are characteristic of +the modernist movement so so rasham man + + align:start position:0% +the modernist movement so so rasham man + + + align:start position:0% +the modernist movement so so rasham man +played a fundamental role in this sort + + align:start position:0% +played a fundamental role in this sort + + + align:start position:0% +played a fundamental role in this sort +of transformation of what we might call + + align:start position:0% +of transformation of what we might call + + + align:start position:0% +of transformation of what we might call +the cultural understanding of movies + + align:start position:0% +the cultural understanding of movies + + + align:start position:0% +the cultural understanding of movies +among ordinary people as well as among + + align:start position:0% +among ordinary people as well as among + + + align:start position:0% +among ordinary people as well as among +Scholars critics and other filmmakers I + + align:start position:0% +Scholars critics and other filmmakers I + + + align:start position:0% +Scholars critics and other filmmakers I +want to mention one other point give you + + align:start position:0% +want to mention one other point give you + + + align:start position:0% +want to mention one other point give you +a kind of note to + + align:start position:0% +a kind of note to + + + align:start position:0% +a kind of note to +clarify um uh some of what I've been + + align:start position:0% +clarify um uh some of what I've been + + + align:start position:0% +clarify um uh some of what I've been +implying uh when I some of what I + + align:start position:0% +implying uh when I some of what I + + + align:start position:0% +implying uh when I some of what I +implied when I talked about mizuchi and + + align:start position:0% +implied when I talked about mizuchi and + + + align:start position:0% +implied when I talked about mizuchi and +mizuchi and U as directors who are often + + align:start position:0% +mizuchi and U as directors who are often + + + align:start position:0% +mizuchi and U as directors who are often +even more highly regarded than Kurosawa + + align:start position:0% +even more highly regarded than Kurosawa + + + align:start position:0% +even more highly regarded than Kurosawa +I'll leave that to uh uh each individual + + align:start position:0% +I'll leave that to uh uh each individual + + + align:start position:0% +I'll leave that to uh uh each individual +filmgoer all three directors are + + align:start position:0% +filmgoer all three directors are + + + align:start position:0% +filmgoer all three directors are +astonishing and REM remarkable but it + + align:start position:0% +astonishing and REM remarkable but it + + + align:start position:0% +astonishing and REM remarkable but it +wouldn't be appropriate to talk uh even + + align:start position:0% +wouldn't be appropriate to talk uh even + + + align:start position:0% +wouldn't be appropriate to talk uh even +about this single film rashan without + + align:start position:0% +about this single film rashan without + + + align:start position:0% +about this single film rashan without +paying uh respects to those two great + + align:start position:0% +paying uh respects to those two great + + + align:start position:0% +paying uh respects to those two great +directors whose dates I've put on your + + align:start position:0% +directors whose dates I've put on your + + + align:start position:0% +directors whose dates I've put on your +on your uh uh uh uh outline U I won't + + align:start position:0% +on your uh uh uh uh outline U I won't + + + align:start position:0% +on your uh uh uh uh outline U I won't +talk about individual films by these + + align:start position:0% +talk about individual films by these + + + align:start position:0% +talk about individual films by these +directors but I urge you all to look + + align:start position:0% +directors but I urge you all to look + + + align:start position:0% +directors but I urge you all to look +them up in in in read about them in + + align:start position:0% +them up in in in read about them in + + + align:start position:0% +them up in in in read about them in +David Cook's history of narrative film + + align:start position:0% +David Cook's history of narrative film + + + align:start position:0% +David Cook's history of narrative film +and think about experimenting by + + align:start position:0% +and think about experimenting by + + + align:start position:0% +and think about experimenting by +extending your knowledge of Japanese + + align:start position:0% +extending your knowledge of Japanese + + + align:start position:0% +extending your knowledge of Japanese +cinema by trying films by these two + + align:start position:0% +cinema by trying films by these two + + + align:start position:0% +cinema by trying films by these two +remark aable + + align:start position:0% +remark aable + + + align:start position:0% +remark aable +directors one of the things that's + + align:start position:0% +directors one of the things that's + + + align:start position:0% +directors one of the things that's +characteristic of all three of these + + align:start position:0% +characteristic of all three of these + + + align:start position:0% +characteristic of all three of these +directors of kurasawa even more fully of + + align:start position:0% +directors of kurasawa even more fully of + + + align:start position:0% +directors of kurasawa even more fully of +mizuchi and oou U most fundamentally of + + align:start position:0% +mizuchi and oou U most fundamentally of + + + align:start position:0% +mizuchi and oou U most fundamentally of +all is that their films are marked by a + + align:start position:0% +all is that their films are marked by a + + + align:start position:0% +all is that their films are marked by a +kind of impulse toward stylization + + align:start position:0% +kind of impulse toward stylization + + + align:start position:0% +kind of impulse toward stylization +toward fabular fabl likee Creations uh + + align:start position:0% +toward fabular fabl likee Creations uh + + + align:start position:0% +toward fabular fabl likee Creations uh +that distinguish them in some ways from + + align:start position:0% +that distinguish them in some ways from + + + align:start position:0% +that distinguish them in some ways from +Western from European and American films + + align:start position:0% +Western from European and American films + + + align:start position:0% +Western from European and American films +and I think that one reason one + + align:start position:0% +and I think that one reason one + + + align:start position:0% +and I think that one reason one +explanation for this has to do with the + + align:start position:0% +explanation for this has to do with the + + + align:start position:0% +explanation for this has to do with the +long longer uh artistic traditions of + + align:start position:0% +long longer uh artistic traditions of + + + align:start position:0% +long longer uh artistic traditions of +Japanese Society Japanese film grows out + + align:start position:0% +Japanese Society Japanese film grows out + + + align:start position:0% +Japanese Society Japanese film grows out +of theatrical Traditions like Kabuki + + align:start position:0% +of theatrical Traditions like Kabuki + + + align:start position:0% +of theatrical Traditions like Kabuki +theater or no drama no drama both of + + align:start position:0% +theater or no drama no drama both of + + + align:start position:0% +theater or no drama no drama both of +which have profoundly stylized and Fable + + align:start position:0% +which have profoundly stylized and Fable + + + align:start position:0% +which have profoundly stylized and Fable +likee qualities they're anti-narrative + + align:start position:0% +likee qualities they're anti-narrative + + + align:start position:0% +likee qualities they're anti-narrative +in some sense and any of you who have + + align:start position:0% +in some sense and any of you who have + + + align:start position:0% +in some sense and any of you who have +ever had even a minimal experience with + + align:start position:0% +ever had even a minimal experience with + + + align:start position:0% +ever had even a minimal experience with +either of these two tra uh theatrical + + align:start position:0% +either of these two tra uh theatrical + + + align:start position:0% +either of these two tra uh theatrical +Traditions will understand what I'm what + + align:start position:0% +Traditions will understand what I'm what + + + align:start position:0% +Traditions will understand what I'm what +I'm discussing it was these are theater + + align:start position:0% +I'm discussing it was these are theater + + + align:start position:0% +I'm discussing it was these are theater +of gesture and of and of and of a very + + align:start position:0% +of gesture and of and of and of a very + + + align:start position:0% +of gesture and of and of and of a very +uh uh decisive sort of symbolic + + align:start position:0% +uh uh decisive sort of symbolic + + + align:start position:0% +uh uh decisive sort of symbolic +representation uh uh they are uh they + + align:start position:0% +representation uh uh they are uh they + + + align:start position:0% +representation uh uh they are uh they +what what we would think of as sort of + + align:start position:0% +what what we would think of as sort of + + + align:start position:0% +what what we would think of as sort of +realistic characters or realistic + + align:start position:0% +realistic characters or realistic + + + align:start position:0% +realistic characters or realistic +stories are are not a part of these very + + align:start position:0% +stories are are not a part of these very + + + align:start position:0% +stories are are not a part of these very +ancient Traditions these theatrical + + align:start position:0% +ancient Traditions these theatrical + + + align:start position:0% +ancient Traditions these theatrical +Traditions go back hundreds even + + align:start position:0% +Traditions go back hundreds even + + + align:start position:0% +Traditions go back hundreds even +thousands of years so there's a there's + + align:start position:0% +thousands of years so there's a there's + + + align:start position:0% +thousands of years so there's a there's +a tradition in Japan of a kind of + + align:start position:0% +a tradition in Japan of a kind of + + + align:start position:0% +a tradition in Japan of a kind of +stylized of symbolic representation uh + + align:start position:0% +stylized of symbolic representation uh + + + align:start position:0% +stylized of symbolic representation uh +um and and you'll you'll see I think how + + align:start position:0% +um and and you'll you'll see I think how + + + align:start position:0% +um and and you'll you'll see I think how +how in rashim how powerful this + + align:start position:0% +how in rashim how powerful this + + + align:start position:0% +how in rashim how powerful this +principal operate how powerfully this + + align:start position:0% +principal operate how powerfully this + + + align:start position:0% +principal operate how powerfully this +principle operates in rashan uh even + + align:start position:0% +principle operates in rashan uh even + + + align:start position:0% +principle operates in rashan uh even +when the film even when film itself + + align:start position:0% +when the film even when film itself + + + align:start position:0% +when the film even when film itself +emerged in Japan in the silent era it + + align:start position:0% +emerged in Japan in the silent era it + + + align:start position:0% +emerged in Japan in the silent era it +emerged in a slightly different way and + + align:start position:0% +emerged in a slightly different way and + + + align:start position:0% +emerged in a slightly different way and +one of the most interesting features of + + align:start position:0% +one of the most interesting features of + + + align:start position:0% +one of the most interesting features of +the uh silent film tradition in in U of + + align:start position:0% +the uh silent film tradition in in U of + + + align:start position:0% +the uh silent film tradition in in U of +Japan was the appearance of a character + + align:start position:0% +Japan was the appearance of a character + + + align:start position:0% +Japan was the appearance of a character +who has no counterpart in Western Cinema + + align:start position:0% +who has no counterpart in Western Cinema + + + align:start position:0% +who has no counterpart in Western Cinema +a character called called a Beni b n Shi + + align:start position:0% +a character called called a Beni b n Shi + + + align:start position:0% +a character called called a Beni b n Shi +any of you heard of it none uh what he + + align:start position:0% +any of you heard of it none uh what he + + + align:start position:0% +any of you heard of it none uh what he +was essentially was a narrator and + + align:start position:0% +was essentially was a narrator and + + + align:start position:0% +was essentially was a narrator and +explainer and he stood next to the + + align:start position:0% +explainer and he stood next to the + + + align:start position:0% +explainer and he stood next to the +movies in a way and gave explanations + + align:start position:0% +movies in a way and gave explanations + + + align:start position:0% +movies in a way and gave explanations +right he said now we will introduce the + + align:start position:0% +right he said now we will introduce the + + + align:start position:0% +right he said now we will introduce the +villain now we will introduce the you + + align:start position:0% +villain now we will introduce the you + + + align:start position:0% +villain now we will introduce the you +know he was like a kind of intermediary + + align:start position:0% +know he was like a kind of intermediary + + + align:start position:0% +know he was like a kind of intermediary +a narrator uh or a or a concierge who + + align:start position:0% +a narrator uh or a or a concierge who + + + align:start position:0% +a narrator uh or a or a concierge who +who who mediated between the audience + + align:start position:0% +who who mediated between the audience + + + align:start position:0% +who who mediated between the audience +and the text who gave the audience + + align:start position:0% +and the text who gave the audience + + + align:start position:0% +and the text who gave the audience +information again it's a deep in one + + align:start position:0% +information again it's a deep in one + + + align:start position:0% +information again it's a deep in one +sense we might think of it as as a as a + + align:start position:0% +sense we might think of it as as a as a + + + align:start position:0% +sense we might think of it as as a as a +as an anti-narrative tradition as a + + align:start position:0% +as an anti-narrative tradition as a + + + align:start position:0% +as an anti-narrative tradition as a +tradition in which things are are are + + align:start position:0% +tradition in which things are are are + + + align:start position:0% +tradition in which things are are are +presented or spoken rather than + + align:start position:0% +presented or spoken rather than + + + align:start position:0% +presented or spoken rather than +literally acted out or and certainly one + + align:start position:0% +literally acted out or and certainly one + + + align:start position:0% +literally acted out or and certainly one +in which in which in which the details + + align:start position:0% +in which in which in which the details + + + align:start position:0% +in which in which in which the details +of a story are less important than it's + + align:start position:0% +of a story are less important than it's + + + align:start position:0% +of a story are less important than it's +than its General than its General + + align:start position:0% +than its General than its General + + + align:start position:0% +than its General than its General +outline so when we talk about + + align:start position:0% +outline so when we talk about + + + align:start position:0% +outline so when we talk about +stylization one of the things we're + + align:start position:0% +stylization one of the things we're + + + align:start position:0% +stylization one of the things we're +talking about is an Impulse toward what + + align:start position:0% +talking about is an Impulse toward what + + + align:start position:0% +talking about is an Impulse toward what +we might think of as generalized uh + + align:start position:0% +we might think of as generalized uh + + + align:start position:0% +we might think of as generalized uh +argument instead of specific argument uh + + align:start position:0% +argument instead of specific argument uh + + + align:start position:0% +argument instead of specific argument uh +an an Impulse to have uh one moment + + align:start position:0% +an an Impulse to have uh one moment + + + align:start position:0% +an an Impulse to have uh one moment +stand symbolically for many other + + align:start position:0% +stand symbolically for many other + + + align:start position:0% +stand symbolically for many other +moments and what we might think of as a + + align:start position:0% +moments and what we might think of as a + + + align:start position:0% +moments and what we might think of as a +simplification or a or a distillation of + + align:start position:0% +simplification or a or a distillation of + + + align:start position:0% +simplification or a or a distillation of +reality uh into certain symbolic moments + + align:start position:0% +reality uh into certain symbolic moments + + + align:start position:0% +reality uh into certain symbolic moments +that are that are uh thought to be + + align:start position:0% +that are that are uh thought to be + + + align:start position:0% +that are that are uh thought to be +emblematic in certain ways but don't + + align:start position:0% +emblematic in certain ways but don't + + + align:start position:0% +emblematic in certain ways but don't +necessarily have a realistic feel and + + align:start position:0% +necessarily have a realistic feel and + + + align:start position:0% +necessarily have a realistic feel and +you'll see almost instantly when this + + align:start position:0% +you'll see almost instantly when this + + + align:start position:0% +you'll see almost instantly when this +film begins I mean there's a there's a + + align:start position:0% +film begins I mean there's a there's a + + + align:start position:0% +film begins I mean there's a there's a +kind of prologue uh uh uh and then when + + align:start position:0% +kind of prologue uh uh uh and then when + + + align:start position:0% +kind of prologue uh uh uh and then when +the film makes a transition into the + + align:start position:0% +the film makes a transition into the + + + align:start position:0% +the film makes a transition into the +first sequence that takes place in the + + align:start position:0% +first sequence that takes place in the + + + align:start position:0% +first sequence that takes place in the +forest you'll begin to see uh what I + + align:start position:0% +forest you'll begin to see uh what I + + + align:start position:0% +forest you'll begin to see uh what I +mean when I say that the seems to enter + + align:start position:0% +mean when I say that the seems to enter + + + align:start position:0% +mean when I say that the seems to enter +into a kind of symbolic realm uh in + + align:start position:0% +into a kind of symbolic realm uh in + + + align:start position:0% +into a kind of symbolic realm uh in +which your in which your uh uh sense of + + align:start position:0% +which your in which your uh uh sense of + + + align:start position:0% +which your in which your uh uh sense of +reality is in some sense of of U + + align:start position:0% +reality is in some sense of of U + + + align:start position:0% +reality is in some sense of of U +undermined uh as if you're entering into + + align:start position:0% +undermined uh as if you're entering into + + + align:start position:0% +undermined uh as if you're entering into +a dream or a symbolic space kurasawa + + align:start position:0% +a dream or a symbolic space kurasawa + + + align:start position:0% +a dream or a symbolic space kurasawa +talking about that um uh astonishing + + align:start position:0% +talking about that um uh astonishing + + + align:start position:0% +talking about that um uh astonishing +sequence at the beginning of rashan said + + align:start position:0% +sequence at the beginning of rashan said + + + align:start position:0% +sequence at the beginning of rashan said +that the C the camera's complex + + align:start position:0% +that the C the camera's complex + + + align:start position:0% +that the C the camera's complex +movements and the uh uh uh movements of + + align:start position:0% +movements and the uh uh uh movements of + + + align:start position:0% +movements and the uh uh uh movements of +the of the uh character himself + + align:start position:0% +the of the uh character himself + + + align:start position:0% +the of the uh character himself +everything is in Motion in that + + align:start position:0% +everything is in Motion in that + + + align:start position:0% +everything is in Motion in that +remarkable o opening sequence uh some + + align:start position:0% +remarkable o opening sequence uh some + + + align:start position:0% +remarkable o opening sequence uh some +people have called it the most visually + + align:start position:0% +people have called it the most visually + + + align:start position:0% +people have called it the most visually +poetic sequence in the history of movies + + align:start position:0% +poetic sequence in the history of movies + + + align:start position:0% +poetic sequence in the history of movies +uh what you kusawa called This Moment a + + align:start position:0% +uh what you kusawa called This Moment a + + + align:start position:0% +uh what you kusawa called This Moment a +moment in which uh the camera was shown + + align:start position:0% +moment in which uh the camera was shown + + + align:start position:0% +moment in which uh the camera was shown +to be penetrating where the into a space + + align:start position:0% +to be penetrating where the into a space + + + align:start position:0% +to be penetrating where the into a space +where the heart loses its way as if + + align:start position:0% +where the heart loses its way as if + + + align:start position:0% +where the heart loses its way as if +you're penetrating into a into an + + align:start position:0% +you're penetrating into a into an + + + align:start position:0% +you're penetrating into a into an +ancestral space into a into a a a space + + align:start position:0% +ancestral space into a into a a a space + + + align:start position:0% +ancestral space into a into a a a space +of a space that's dreamlike uh uh in + + align:start position:0% +of a space that's dreamlike uh uh in + + + align:start position:0% +of a space that's dreamlike uh uh in +fundamental ways so that very opening of + + align:start position:0% +fundamental ways so that very opening of + + + align:start position:0% +fundamental ways so that very opening of +the film EST or almost the very opening + + align:start position:0% +the film EST or almost the very opening + + + align:start position:0% +the film EST or almost the very opening +of the film establishes this kind of uh + + align:start position:0% +of the film establishes this kind of uh + + + align:start position:0% +of the film establishes this kind of uh +complexity this kind I I don't want + + align:start position:0% +complexity this kind I I don't want + + + align:start position:0% +complexity this kind I I don't want +exactly call it an ambiguity but this + + align:start position:0% +exactly call it an ambiguity but this + + + align:start position:0% +exactly call it an ambiguity but this +this this complexity uh about the about + + align:start position:0% +this this complexity uh about the about + + + align:start position:0% +this this complexity uh about the about +the nature of the reality that you're + + align:start position:0% +the nature of the reality that you're + + + align:start position:0% +the nature of the reality that you're +watching and this is even before the + + align:start position:0% +watching and this is even before the + + + align:start position:0% +watching and this is even before the +film proceeds to to present essentially + + align:start position:0% +film proceeds to to present essentially + + + align:start position:0% +film proceeds to to present essentially +four different accounts of the same + + align:start position:0% +four different accounts of the same + + + align:start position:0% +four different accounts of the same +event these four different accounts + + align:start position:0% +event these four different accounts + + + align:start position:0% +event these four different accounts +conflicting with each other in a variety + + align:start position:0% +conflicting with each other in a variety + + + align:start position:0% +conflicting with each other in a variety +of ways U so these these abstracting or + + align:start position:0% +of ways U so these these abstracting or + + + align:start position:0% +of ways U so these these abstracting or +symbol izing uh or stylizing narrative + + align:start position:0% +symbol izing uh or stylizing narrative + + + align:start position:0% +symbol izing uh or stylizing narrative +and dramatic Traditions lie behind and + + align:start position:0% +and dramatic Traditions lie behind and + + + align:start position:0% +and dramatic Traditions lie behind and +shape the movies in Japan even movies + + align:start position:0% +shape the movies in Japan even movies + + + align:start position:0% +shape the movies in Japan even movies +like kosa which Embrace uh uh the + + align:start position:0% +like kosa which Embrace uh uh the + + + align:start position:0% +like kosa which Embrace uh uh the +camera's freedom in a way that's much + + align:start position:0% +camera's freedom in a way that's much + + + align:start position:0% +camera's freedom in a way that's much +more uh uh characteristic of Western of + + align:start position:0% +more uh uh characteristic of Western of + + + align:start position:0% +more uh uh characteristic of Western of +uh directors than of than of Eastern + + align:start position:0% +uh directors than of than of Eastern + + + align:start position:0% +uh directors than of than of Eastern +ones oo the the the the the um uh second + + align:start position:0% +ones oo the the the the the um uh second + + + align:start position:0% +ones oo the the the the the um uh second +of the two directors I've listed on your + + align:start position:0% +of the two directors I've listed on your + + + align:start position:0% +of the two directors I've listed on your +on your outline is especially famous for + + align:start position:0% +on your outline is especially famous for + + + align:start position:0% +on your outline is especially famous for +holding his camera almost stationary for + + align:start position:0% +holding his camera almost stationary for + + + align:start position:0% +holding his camera almost stationary for +tremendously long time for a uh and in + + align:start position:0% +tremendously long time for a uh and in + + + align:start position:0% +tremendously long time for a uh and in +fact he sometimes it's sometimes called + + align:start position:0% +fact he sometimes it's sometimes called + + + align:start position:0% +fact he sometimes it's sometimes called +he sometimes called uh a director who + + align:start position:0% +he sometimes called uh a director who + + + align:start position:0% +he sometimes called uh a director who +tries to create a a Zen aesthetic uh + + align:start position:0% +tries to create a a Zen aesthetic uh + + + align:start position:0% +tries to create a a Zen aesthetic uh +because the camera is so quiet and so + + align:start position:0% +because the camera is so quiet and so + + + align:start position:0% +because the camera is so quiet and so +stationary and so uh uh in relatively + + align:start position:0% +stationary and so uh uh in relatively + + + align:start position:0% +stationary and so uh uh in relatively +inactive it's a it's a style that lays + + align:start position:0% +inactive it's a it's a style that lays + + + align:start position:0% +inactive it's a it's a style that lays +tremendous emphasis on the nuances of + + align:start position:0% +tremendous emphasis on the nuances of + + + align:start position:0% +tremendous emphasis on the nuances of +facial expression and and vocal uh tone + + align:start position:0% +facial expression and and vocal uh tone + + + align:start position:0% +facial expression and and vocal uh tone +uh uh so that and both mizuguchi and u + + align:start position:0% +uh uh so that and both mizuguchi and u + + + align:start position:0% +uh uh so that and both mizuguchi and u +do in some sense have an even greater + + align:start position:0% +do in some sense have an even greater + + + align:start position:0% +do in some sense have an even greater +sense of stylization in many of their + + align:start position:0% +sense of stylization in many of their + + + align:start position:0% +sense of stylization in many of their +films than than uh kurasawa does but I + + align:start position:0% +films than than uh kurasawa does but I + + + align:start position:0% +films than than uh kurasawa does but I +don't want to oversimplify because they + + align:start position:0% +don't want to oversimplify because they + + + align:start position:0% +don't want to oversimplify because they +are also capable of very great realistic + + align:start position:0% +are also capable of very great realistic + + + align:start position:0% +are also capable of very great realistic +moments and and uh uh they have a moral + + align:start position:0% +moments and and uh uh they have a moral + + + align:start position:0% +moments and and uh uh they have a moral +realism that's at least as powerful in + + align:start position:0% +realism that's at least as powerful in + + + align:start position:0% +realism that's at least as powerful in +their films as Kurosawa himself + + align:start position:0% +their films as Kurosawa himself + + + align:start position:0% +their films as Kurosawa himself +kurosawa's career is a very remarkable + + align:start position:0% +kurosawa's career is a very remarkable + + + align:start position:0% +kurosawa's career is a very remarkable +one uh and and I wish I had time to talk + + align:start position:0% +one uh and and I wish I had time to talk + + + align:start position:0% +one uh and and I wish I had time to talk +about it in detail organizational + + align:start position:0% +about it in detail organizational + + + align:start position:0% +about it in detail organizational +structure of Japanese Cinema was not + + align:start position:0% +structure of Japanese Cinema was not + + + align:start position:0% +structure of Japanese Cinema was not +unlike the uh structures that developed + + align:start position:0% +unlike the uh structures that developed + + + align:start position:0% +unlike the uh structures that developed +in in Western Societies in the United + + align:start position:0% +in in Western Societies in the United + + + align:start position:0% +in in Western Societies in the United +States or in France uh there + + align:start position:0% +States or in France uh there + + + align:start position:0% +States or in France uh there +were essentially monopolies of uh not + + align:start position:0% +were essentially monopolies of uh not + + + align:start position:0% +were essentially monopolies of uh not +not a small number but a relatively + + align:start position:0% +not a small number but a relatively + + + align:start position:0% +not a small number but a relatively +larger number of of uh of film + + align:start position:0% +larger number of of uh of film + + + align:start position:0% +larger number of of uh of film +production companies operating at at + + align:start position:0% +production companies operating at at + + + align:start position:0% +production companies operating at at +different levels of significance so + + align:start position:0% +different levels of significance so + + + align:start position:0% +different levels of significance so +there were second rate and there were + + align:start position:0% +there were second rate and there were + + + align:start position:0% +there were second rate and there were +second level and third level production + + align:start position:0% +second level and third level production + + + align:start position:0% +second level and third level production +companies as well but all of them + + align:start position:0% +companies as well but all of them + + + align:start position:0% +companies as well but all of them +operated in a similar way there was a + + align:start position:0% +operated in a similar way there was a + + + align:start position:0% +operated in a similar way there was a +the director was a was a more dominant + + align:start position:0% +the director was a was a more dominant + + + align:start position:0% +the director was a was a more dominant +and major figure in this system and they + + align:start position:0% +and major figure in this system and they + + + align:start position:0% +and major figure in this system and they +surround surrounding each director were + + align:start position:0% +surround surrounding each director were + + + align:start position:0% +surround surrounding each director were +were a group of workers and a group of + + align:start position:0% +were a group of workers and a group of + + + align:start position:0% +were a group of workers and a group of +uh uh creative people including usually + + align:start position:0% +uh uh creative people including usually + + + align:start position:0% +uh uh creative people including usually +performers who went with the director + + align:start position:0% +performers who went with the director + + + align:start position:0% +performers who went with the director +from space to Spa from film to film as + + align:start position:0% +from space to Spa from film to film as + + + align:start position:0% +from space to Spa from film to film as +well as his technical people he would + + align:start position:0% +well as his technical people he would + + + align:start position:0% +well as his technical people he would +often use they would often use the same + + align:start position:0% +often use they would often use the same + + + align:start position:0% +often use they would often use the same +people to write the music and the same + + align:start position:0% +people to write the music and the same + + + align:start position:0% +people to write the music and the same +crew to work on the film the same if + + align:start position:0% +crew to work on the film the same if + + + align:start position:0% +crew to work on the film the same if +they could succeed get the same + + align:start position:0% +they could succeed get the same + + + align:start position:0% +they could succeed get the same +cinematographer and the kurasa was so it + + align:start position:0% +cinematographer and the kurasa was so it + + + align:start position:0% +cinematographer and the kurasa was so it +was called kurosawa's group was called + + align:start position:0% +was called kurosawa's group was called + + + align:start position:0% +was called kurosawa's group was called +the kurasawa Gumi gu Mii it means the + + align:start position:0% +the kurasawa Gumi gu Mii it means the + + + align:start position:0% +the kurasawa Gumi gu Mii it means the +group or or cadra the kusawa group + + align:start position:0% +group or or cadra the kusawa group + + + align:start position:0% +group or or cadra the kusawa group +worked with on a on a series of fil I + + align:start position:0% +worked with on a on a series of fil I + + + align:start position:0% +worked with on a on a series of fil I +don't mean it was always identical there + + align:start position:0% +don't mean it was always identical there + + + align:start position:0% +don't mean it was always identical there +were changes but it was a stable group + + align:start position:0% +were changes but it was a stable group + + + align:start position:0% +were changes but it was a stable group +unified especially by kurosawa's vision + + align:start position:0% +unified especially by kurosawa's vision + + + align:start position:0% +unified especially by kurosawa's vision +and and supervision uh and I've listed + + align:start position:0% +and and supervision uh and I've listed + + + align:start position:0% +and and supervision uh and I've listed +uh here a few of his most famous and + + align:start position:0% +uh here a few of his most famous and + + + align:start position:0% +uh here a few of his most famous and +fundamental films besides rashan uh + + align:start position:0% +fundamental films besides rashan uh + + + align:start position:0% +fundamental films besides rashan uh +akiru maybe his greatest film a + + align:start position:0% +akiru maybe his greatest film a + + + align:start position:0% +akiru maybe his greatest film a +realistic film set in the modern world + + align:start position:0% +realistic film set in the modern world + + + align:start position:0% +realistic film set in the modern world +the title means to live uh and it's + + align:start position:0% +the title means to live uh and it's + + + align:start position:0% +the title means to live uh and it's +about a man who discovers that he has + + align:start position:0% +about a man who discovers that he has + + + align:start position:0% +about a man who discovers that he has +only a few months to live and it stars + + align:start position:0% +only a few months to live and it stars + + + align:start position:0% +only a few months to live and it stars +uh uh the the actor uh uh takishi + + align:start position:0% +uh uh the the actor uh uh takishi + + + align:start position:0% +uh uh the the actor uh uh takishi +shimura who plays the wood cutter in + + align:start position:0% +shimura who plays the wood cutter in + + + align:start position:0% +shimura who plays the wood cutter in +rashan uh the actor the other actor that + + align:start position:0% +rashan uh the actor the other actor that + + + align:start position:0% +rashan uh the actor the other actor that +you'll see in in uh rashan that I that + + align:start position:0% +you'll see in in uh rashan that I that + + + align:start position:0% +you'll see in in uh rashan that I that +that uh is one of kurosawa's favorites + + align:start position:0% +that uh is one of kurosawa's favorites + + + align:start position:0% +that uh is one of kurosawa's favorites +and appears again and again in + + align:start position:0% +and appears again and again in + + + align:start position:0% +and appears again and again in +kurosawa's films uh is the toshiro mauni + + align:start position:0% +kurosawa's films uh is the toshiro mauni + + + align:start position:0% +kurosawa's films uh is the toshiro mauni +in rashan he plays the Bandon you'll see + + align:start position:0% +in rashan he plays the Bandon you'll see + + + align:start position:0% +in rashan he plays the Bandon you'll see +what a remarkable figure he is so so + + align:start position:0% +what a remarkable figure he is so so + + + align:start position:0% +what a remarkable figure he is so so +I've only listed a few of his films here + + align:start position:0% +I've only listed a few of his films here + + + align:start position:0% +I've only listed a few of his films here +but among his most important rashan + + align:start position:0% +but among his most important rashan + + + align:start position:0% +but among his most important rashan +akiru Seven Samurai many people would + + align:start position:0% +akiru Seven Samurai many people would + + + align:start position:0% +akiru Seven Samurai many people would +say the greatest of all Samurai movies + + align:start position:0% +say the greatest of all Samurai movies + + + align:start position:0% +say the greatest of all Samurai movies +and probably the greatest of all Western + + align:start position:0% +and probably the greatest of all Western + + + align:start position:0% +and probably the greatest of all Western +movies because it puts most westerns + + align:start position:0% +movies because it puts most westerns + + + align:start position:0% +movies because it puts most westerns +American westerns to shame it's + + align:start position:0% +American westerns to shame it's + + + align:start position:0% +American westerns to shame it's +influenced by American westerns as as + + align:start position:0% +influenced by American westerns as as + + + align:start position:0% +influenced by American westerns as as +kurasawa himself acknowledged and it was + + align:start position:0% +kurasawa himself acknowledged and it was + + + align:start position:0% +kurasawa himself acknowledged and it was +itself that film made in 1954 remade uh + + align:start position:0% +itself that film made in 1954 remade uh + + + align:start position:0% +itself that film made in 1954 remade uh +as an as an American Film some years + + align:start position:0% +as an as an American Film some years + + + align:start position:0% +as an as an American Film some years +later under the title The Magnificent + + align:start position:0% +later under the title The Magnificent + + + align:start position:0% +later under the title The Magnificent +Seven and it was so successful that it + + align:start position:0% +Seven and it was so successful that it + + + align:start position:0% +Seven and it was so successful that it +was then a sequel was made Something + + align:start position:0% +was then a sequel was made Something + + + align:start position:0% +was then a sequel was made Something +Like This Magnificent Seven return uh + + align:start position:0% +Like This Magnificent Seven return uh + + + align:start position:0% +Like This Magnificent Seven return uh +and in fact one of the deep features of + + align:start position:0% +and in fact one of the deep features of + + + align:start position:0% +and in fact one of the deep features of +kurosawa's work is that many of his + + align:start position:0% +kurosawa's work is that many of his + + + align:start position:0% +kurosawa's work is that many of his +films have been remade by other + + align:start position:0% +films have been remade by other + + + align:start position:0% +films have been remade by other +directors both American and European + + align:start position:0% +directors both American and European + + + align:start position:0% +directors both American and European +directors russan was made 14 years later + + align:start position:0% +directors russan was made 14 years later + + + align:start position:0% +directors russan was made 14 years later +or remade 14 years later with kurasawa + + align:start position:0% +or remade 14 years later with kurasawa + + + align:start position:0% +or remade 14 years later with kurasawa +given script scen playay uh credit um in + + align:start position:0% +given script scen playay uh credit um in + + + align:start position:0% +given script scen playay uh credit um in +a film uh uh directed by Martin rit in + + align:start position:0% +a film uh uh directed by Martin rit in + + + align:start position:0% +a film uh uh directed by Martin rit in +the United States called the outrage and + + align:start position:0% +the United States called the outrage and + + + align:start position:0% +the United States called the outrage and +it retells the story that's at the heart + + align:start position:0% +it retells the story that's at the heart + + + align:start position:0% +it retells the story that's at the heart +of of kurosawa's film it starred Paul + + align:start position:0% +of of kurosawa's film it starred Paul + + + align:start position:0% +of of kurosawa's film it starred Paul +Newman among others and Edward J + + align:start position:0% +Newman among others and Edward J + + + align:start position:0% +Newman among others and Edward J +Robinson among other significant + + align:start position:0% +Robinson among other significant + + + align:start position:0% +Robinson among other significant +American actors uh Throne of blood I + + align:start position:0% +American actors uh Throne of blood I + + + align:start position:0% +American actors uh Throne of blood I +mentioned because many people see it as + + align:start position:0% +mentioned because many people see it as + + + align:start position:0% +mentioned because many people see it as +the most successful of all adaptations + + align:start position:0% +the most successful of all adaptations + + + align:start position:0% +the most successful of all adaptations +of Shakespeare it's a Japanese uh + + align:start position:0% + + + + align:start position:0% + +and many people at starring toiro mauni + + align:start position:0% +and many people at starring toiro mauni + + + align:start position:0% +and many people at starring toiro mauni +and many people think of it as the + + align:start position:0% +and many people think of it as the + + + align:start position:0% +and many people think of it as the +greatest of all Shakespearean + + align:start position:0% +greatest of all Shakespearean + + + align:start position:0% +greatest of all Shakespearean +adaptations Yojimbo uh is a samurai film + + align:start position:0% +adaptations Yojimbo uh is a samurai film + + + align:start position:0% +adaptations Yojimbo uh is a samurai film +a much more straightforward Samurai film + + align:start position:0% +a much more straightforward Samurai film + + + align:start position:0% +a much more straightforward Samurai film +in many ways than Seven Samurai also + + align:start position:0% +in many ways than Seven Samurai also + + + align:start position:0% +in many ways than Seven Samurai also +Stars Muni and it has brilliant + + align:start position:0% +Stars Muni and it has brilliant + + + align:start position:0% +Stars Muni and it has brilliant +brilliant swordfight sequences in it + + align:start position:0% +brilliant swordfight sequences in it + + + align:start position:0% +brilliant swordfight sequences in it +that anticipate uh the kind of thing + + align:start position:0% +that anticipate uh the kind of thing + + + align:start position:0% +that anticipate uh the kind of thing +that is now common uh in in in Asian + + align:start position:0% +that is now common uh in in in Asian + + + align:start position:0% +that is now common uh in in in Asian +Cinema but much less trivially done in + + align:start position:0% +Cinema but much less trivially done in + + + align:start position:0% +Cinema but much less trivially done in +kurasawa than in many of these uh later + + align:start position:0% +kurasawa than in many of these uh later + + + align:start position:0% +kurasawa than in many of these uh later +films that merely seem to want to + + align:start position:0% +films that merely seem to want to + + + align:start position:0% +films that merely seem to want to +entertain us by their Sword Play and and + + align:start position:0% +entertain us by their Sword Play and and + + + align:start position:0% +entertain us by their Sword Play and and +the physical Grace of their of their + + align:start position:0% +the physical Grace of their of their + + + align:start position:0% +the physical Grace of their of their +actors but don't connect nearly so + + align:start position:0% +actors but don't connect nearly so + + + align:start position:0% +actors but don't connect nearly so +powerfully as kusawa films do to a + + align:start position:0% +powerfully as kusawa films do to a + + + align:start position:0% +powerfully as kusawa films do to a +profound and serious historical setting + + align:start position:0% +profound and serious historical setting + + + align:start position:0% +profound and serious historical setting +and story um yo Jimbo was also made into + + align:start position:0% +and story um yo Jimbo was also made into + + + align:start position:0% +and story um yo Jimbo was also made into +an American movie called Last Man + + align:start position:0% +an American movie called Last Man + + + align:start position:0% +an American movie called Last Man +Standing in + + align:start position:0% +Standing in + + + align:start position:0% +Standing in +1966 I mentioned kagam Musha only + + align:start position:0% +1966 I mentioned kagam Musha only + + + align:start position:0% +1966 I mentioned kagam Musha only +because it's a later film and it's so + + align:start position:0% +because it's a later film and it's so + + + align:start position:0% +because it's a later film and it's so +many people many people uh uh admire it + + align:start position:0% +many people many people uh uh admire it + + + align:start position:0% +many people many people uh uh admire it +uh because it shows that kurasawa was + + align:start position:0% +uh because it shows that kurasawa was + + + align:start position:0% +uh because it shows that kurasawa was +working effectively even in old age uh + + align:start position:0% +working effectively even in old age uh + + + align:start position:0% +working effectively even in old age uh +he made another film in 1985 one of his + + align:start position:0% +he made another film in 1985 one of his + + + align:start position:0% +he made another film in 1985 one of his +final films called Ron RN which is a + + align:start position:0% +final films called Ron RN which is a + + + align:start position:0% +final films called Ron RN which is a +remake of King Lear and these two older + + align:start position:0% +remake of King Lear and these two older + + + align:start position:0% +remake of King Lear and these two older +films later films kagam Musha and Ron uh + + align:start position:0% +films later films kagam Musha and Ron uh + + + align:start position:0% +films later films kagam Musha and Ron uh +uh show his V show kurosawa's visual + + align:start position:0% +uh show his V show kurosawa's visual + + + align:start position:0% +uh show his V show kurosawa's visual +sense uh visual imagination to great + + align:start position:0% +sense uh visual imagination to great + + + align:start position:0% +sense uh visual imagination to great +effect but they feel stylized in a way + + align:start position:0% +effect but they feel stylized in a way + + + align:start position:0% +effect but they feel stylized in a way +that or stylized may not be the right + + align:start position:0% +that or stylized may not be the right + + + align:start position:0% +that or stylized may not be the right +word they feel + + align:start position:0% +word they feel + + + align:start position:0% +word they feel +abstract in a way that earlier uh + + align:start position:0% +abstract in a way that earlier uh + + + align:start position:0% +abstract in a way that earlier uh +kurasawa films do not they are + + align:start position:0% +kurasawa films do not they are + + + align:start position:0% +kurasawa films do not they are +extraordinary spectacles but they don't + + align:start position:0% +extraordinary spectacles but they don't + + + align:start position:0% +extraordinary spectacles but they don't +have the same interest in character uh + + align:start position:0% +have the same interest in character uh + + + align:start position:0% +have the same interest in character uh +the same focus on character that his + + align:start position:0% +the same focus on character that his + + + align:start position:0% +the same focus on character that his +earlier films despite their stylization + + align:start position:0% +earlier films despite their stylization + + + align:start position:0% +earlier films despite their stylization +seemed to do I've saved my uh most of my + + align:start position:0% +seemed to do I've saved my uh most of my + + + align:start position:0% +seemed to do I've saved my uh most of my +time today to talk about Rashon itself + + align:start position:0% +time today to talk about Rashon itself + + + align:start position:0% +time today to talk about Rashon itself +because it's such a central and + + align:start position:0% +because it's such a central and + + + align:start position:0% +because it's such a central and +significant film and I hope when you + + align:start position:0% +significant film and I hope when you + + + align:start position:0% +significant film and I hope when you +when you uh watch it you'll uh uh + + align:start position:0% +when you uh watch it you'll uh uh + + + align:start position:0% +when you uh watch it you'll uh uh +um not being impatient and you and and + + align:start position:0% +um not being impatient and you and and + + + align:start position:0% +um not being impatient and you and and +especially that you'll watch for the + + align:start position:0% +especially that you'll watch for the + + + align:start position:0% +especially that you'll watch for the +ways in which from sequence to sequence + + align:start position:0% +ways in which from sequence to sequence + + + align:start position:0% +ways in which from sequence to sequence +the visual style Alters it's a very it's + + align:start position:0% +the visual style Alters it's a very it's + + + align:start position:0% +the visual style Alters it's a very it's +a very demanding film in that sense um + + align:start position:0% +a very demanding film in that sense um + + + align:start position:0% +a very demanding film in that sense um +let let's begin by talking a little bit + + align:start position:0% +let let's begin by talking a little bit + + + align:start position:0% +let let's begin by talking a little bit +about the problem of rape in cultural + + align:start position:0% +about the problem of rape in cultural + + + align:start position:0% +about the problem of rape in cultural +stories because uh I think that one of + + align:start position:0% +stories because uh I think that one of + + + align:start position:0% +stories because uh I think that one of +the problems with uh responding fully to + + align:start position:0% +the problems with uh responding fully to + + + align:start position:0% +the problems with uh responding fully to +Rashon is is that we especially in in um + + align:start position:0% +Rashon is is that we especially in in um + + + align:start position:0% +Rashon is is that we especially in in um +uh in the in in the Western world uh are + + align:start position:0% +uh in the in in the Western world uh are + + + align:start position:0% +uh in the in in the Western world uh are +are are newly struggling with Notions of + + align:start position:0% +are are newly struggling with Notions of + + + align:start position:0% +are are newly struggling with Notions of +of of of of gender identity and and and + + align:start position:0% +of of of of gender identity and and and + + + align:start position:0% +of of of of gender identity and and and +and of the legacy of patriarchy uh that + + align:start position:0% +and of the legacy of patriarchy uh that + + + align:start position:0% +and of the legacy of patriarchy uh that +give us a particularly uh uh fraught and + + align:start position:0% +give us a particularly uh uh fraught and + + + align:start position:0% +give us a particularly uh uh fraught and +complex uh put us in a fraud and complex + + align:start position:0% +complex uh put us in a fraud and complex + + + align:start position:0% +complex uh put us in a fraud and complex +position in relation to stories like + + align:start position:0% +position in relation to stories like + + + align:start position:0% +position in relation to stories like +that of this film and I want to be I + + align:start position:0% +that of this film and I want to be I + + + align:start position:0% +that of this film and I want to be I +want to confront it right right in the + + align:start position:0% +want to confront it right right in the + + + align:start position:0% +want to confront it right right in the +beginning as some of you may know uh the + + align:start position:0% +beginning as some of you may know uh the + + + align:start position:0% +beginning as some of you may know uh the +story of rashan is the story of a rape + + align:start position:0% +story of rashan is the story of a rape + + + align:start position:0% +story of rashan is the story of a rape +uh there are four different a rape + + align:start position:0% +uh there are four different a rape + + + align:start position:0% +uh there are four different a rape +occurs at the center of the film and the + + align:start position:0% +occurs at the center of the film and the + + + align:start position:0% +occurs at the center of the film and the +and there are four different accounts of + + align:start position:0% +and there are four different accounts of + + + align:start position:0% +and there are four different accounts of +what happened of how the rape occurred + + align:start position:0% +what happened of how the rape occurred + + + align:start position:0% +what happened of how the rape occurred +and the film is partly a meditation on + + align:start position:0% +and the film is partly a meditation on + + + align:start position:0% +and the film is partly a meditation on +why would what what motives do do the + + align:start position:0% +why would what what motives do do the + + + align:start position:0% +why would what what motives do do the +different tellers have for for putting + + align:start position:0% +different tellers have for for putting + + + align:start position:0% +different tellers have for for putting +this particular spin on the story how uh + + align:start position:0% +this particular spin on the story how uh + + + align:start position:0% +this particular spin on the story how uh +and and uh part of what's subtle and + + align:start position:0% +and and uh part of what's subtle and + + + align:start position:0% +and and uh part of what's subtle and +disturbing about the movie is that when + + align:start position:0% +disturbing about the movie is that when + + + align:start position:0% +disturbing about the movie is that when +when the first testimony is given it's + + align:start position:0% +when the first testimony is given it's + + + align:start position:0% +when the first testimony is given it's +not fully clear yet to us that we should + + align:start position:0% +not fully clear yet to us that we should + + + align:start position:0% +not fully clear yet to us that we should +be skeptical of the testimony and and I + + align:start position:0% +be skeptical of the testimony and and I + + + align:start position:0% +be skeptical of the testimony and and I +think the first time uh I think the + + align:start position:0% +think the first time uh I think the + + + align:start position:0% +think the first time uh I think the +first the one of the test one of the + + align:start position:0% +first the one of the test one of the + + + align:start position:0% +first the one of the test one of the +people whose testimony we heard is the + + align:start position:0% +people whose testimony we heard is the + + + align:start position:0% +people whose testimony we heard is the +murderer himself or the or is the rapist + + align:start position:0% +murderer himself or the or is the rapist + + + align:start position:0% +murderer himself or the or is the rapist +himself uh the Mafi character he's the + + align:start position:0% +himself uh the Mafi character he's the + + + align:start position:0% +himself uh the Mafi character he's the +first one to testify and it's as he's + + align:start position:0% +first one to testify and it's as he's + + + align:start position:0% +first one to testify and it's as he's +testifying it begins to Dawn on an + + align:start position:0% +testifying it begins to Dawn on an + + + align:start position:0% +testifying it begins to Dawn on an +attentive viewer that maybe his + + align:start position:0% +attentive viewer that maybe his + + + align:start position:0% +attentive viewer that maybe his +testimony is self- serving in certain + + align:start position:0% +testimony is self- serving in certain + + + align:start position:0% +testimony is self- serving in certain +ways that there's certain way things + + align:start position:0% +ways that there's certain way things + + + align:start position:0% +ways that there's certain way things +he's saying that maybe we shouldn't + + align:start position:0% +he's saying that maybe we shouldn't + + + align:start position:0% +he's saying that maybe we shouldn't +fully accept uh and and then when the + + align:start position:0% +fully accept uh and and then when the + + + align:start position:0% +fully accept uh and and then when the +next uh account comes our sense of + + align:start position:0% +next uh account comes our sense of + + + align:start position:0% +next uh account comes our sense of +skepticism is reinfored forced uh uh and + + align:start position:0% +skepticism is reinfored forced uh uh and + + + align:start position:0% +skepticism is reinfored forced uh uh and +and fortified we begin to worry about + + align:start position:0% +and fortified we begin to worry about + + + align:start position:0% +and fortified we begin to worry about +what what and and the and then the film + + align:start position:0% +what what and and the and then the film + + + align:start position:0% +what what and and the and then the film +itself reminds us of the fact that these + + align:start position:0% +itself reminds us of the fact that these + + + align:start position:0% +itself reminds us of the fact that these +Tales are problematic because the film + + align:start position:0% +Tales are problematic because the film + + + align:start position:0% +Tales are problematic because the film +structure is so uh interesting uh + + align:start position:0% +structure is so uh interesting uh + + + align:start position:0% +structure is so uh interesting uh +roughly every 10 minutes or so I've + + align:start position:0% +roughly every 10 minutes or so I've + + + align:start position:0% +roughly every 10 minutes or so I've +timed most of them uh you you or a + + align:start position:0% +timed most of them uh you you or a + + + align:start position:0% +timed most of them uh you you or a +little less than 10 minutes in some + + align:start position:0% +little less than 10 minutes in some + + + align:start position:0% +little less than 10 minutes in some +cases a little longer than some some uh + + align:start position:0% +cases a little longer than some some uh + + + align:start position:0% +cases a little longer than some some uh +you you you'll have a an extended + + align:start position:0% +you you you'll have a an extended + + + align:start position:0% +you you you'll have a an extended +narrative sequence of which will last + + align:start position:0% +narrative sequence of which will last + + + align:start position:0% +narrative sequence of which will last +about 10 minutes usually it's the + + align:start position:0% +about 10 minutes usually it's the + + + align:start position:0% +about 10 minutes usually it's the +testimony of one of the of one of the um + + align:start position:0% +testimony of one of the of one of the um + + + align:start position:0% +testimony of one of the of one of the um +um uh people appearing before the before + + align:start position:0% +um uh people appearing before the before + + + align:start position:0% +um uh people appearing before the before +the court and then when that after that + + align:start position:0% +the court and then when that after that + + + align:start position:0% +the court and then when that after that +happens uh the the film the film sort of + + align:start position:0% +happens uh the the film the film sort of + + + align:start position:0% +happens uh the the film the film sort of +shifts into a shifts into another mode + + align:start position:0% +shifts into a shifts into another mode + + + align:start position:0% +shifts into a shifts into another mode +and the way you can tell is that it + + align:start position:0% +and the way you can tell is that it + + + align:start position:0% +and the way you can tell is that it +shifts back to the scene with which the + + align:start position:0% +shifts back to the scene with which the + + + align:start position:0% +shifts back to the scene with which the +film opens and words all the way through + + align:start position:0% +film opens and words all the way through + + + align:start position:0% +film opens and words all the way through +the scene it's marked by this but the + + align:start position:0% +the scene it's marked by this but the + + + align:start position:0% +the scene it's marked by this but the +structure of the film is marked by this + + align:start position:0% +structure of the film is marked by this + + + align:start position:0% +structure of the film is marked by this +return to a scene at at rashan gate + + align:start position:0% +return to a scene at at rashan gate + + + align:start position:0% +return to a scene at at rashan gate +which I'll explain in a moment so so uh + + align:start position:0% +which I'll explain in a moment so so uh + + + align:start position:0% +which I'll explain in a moment so so uh +the PO the point of one point that I'm + + align:start position:0% +the PO the point of one point that I'm + + + align:start position:0% +the PO the point of one point that I'm +that I'm trying to get to here is the + + align:start position:0% +that I'm trying to get to here is the + + + align:start position:0% +that I'm trying to get to here is the +idea that uh um as we watch the film uh + + align:start position:0% +idea that uh um as we watch the film uh + + + align:start position:0% +idea that uh um as we watch the film uh +and we begin to sort of weigh the + + align:start position:0% +and we begin to sort of weigh the + + + align:start position:0% +and we begin to sort of weigh the +accounts that different people give of + + align:start position:0% +accounts that different people give of + + + align:start position:0% +accounts that different people give of +this of of this rape uh uh many of us + + align:start position:0% +this of of this rape uh uh many of us + + + align:start position:0% +this of of this rape uh uh many of us +are likely to feel uneasy and diff and + + align:start position:0% +are likely to feel uneasy and diff and + + + align:start position:0% +are likely to feel uneasy and diff and +disturbed because one of the things that + + align:start position:0% +disturbed because one of the things that + + + align:start position:0% +disturbed because one of the things that +disturbs me in the film is the woman's + + align:start position:0% +disturbs me in the film is the woman's + + + align:start position:0% +disturbs me in the film is the woman's +reaction to her rape she feels terrible + + align:start position:0% +reaction to her rape she feels terrible + + + align:start position:0% +reaction to her rape she feels terrible +shame it's as if she have felt and and + + align:start position:0% +shame it's as if she have felt and and + + + align:start position:0% +shame it's as if she have felt and and +there's an Impulse there seems to be + + align:start position:0% +there's an Impulse there seems to be + + + align:start position:0% +there's an Impulse there seems to be +impulse in the film that certainly some + + align:start position:0% +impulse in the film that certainly some + + + align:start position:0% +impulse in the film that certainly some +people have certainly gotten there they + + align:start position:0% +people have certainly gotten there they + + + align:start position:0% +people have certainly gotten there they +at least they perceive an Impulse in the + + align:start position:0% +at least they perceive an Impulse in the + + + align:start position:0% +at least they perceive an Impulse in the +film in or an Impulse in the narrative + + align:start position:0% +film in or an Impulse in the narrative + + + align:start position:0% +film in or an Impulse in the narrative +to blame the victim right but we have to + + align:start position:0% +to blame the victim right but we have to + + + align:start position:0% +to blame the victim right but we have to +get in some sense what I'm suggesting is + + align:start position:0% +get in some sense what I'm suggesting is + + + align:start position:0% +get in some sense what I'm suggesting is +that uh uh not that that response is + + align:start position:0% +that uh uh not that that response is + + + align:start position:0% +that uh uh not that that response is +inappropriate but that that that it's a + + align:start position:0% +inappropriate but that that that it's a + + + align:start position:0% +inappropriate but that that that it's a +little bit off key off off center + + align:start position:0% +little bit off key off off center + + + align:start position:0% +little bit off key off off center +because if you recall the idea that the + + align:start position:0% +because if you recall the idea that the + + + align:start position:0% +because if you recall the idea that the +film is deeply stylized that it's said + + align:start position:0% +film is deeply stylized that it's said + + + align:start position:0% +film is deeply stylized that it's said +in an in an ancestral past in a in in in + + align:start position:0% +in an in an ancestral past in a in in in + + + align:start position:0% +in an in an ancestral past in a in in in +in a in a in a in a in the m in in a in + + align:start position:0% +in a in a in a in a in the m in in a in + + + align:start position:0% +in a in a in a in a in the m in in a in +a medieval Japan in a moment of terrible + + align:start position:0% +a medieval Japan in a moment of terrible + + + align:start position:0% +a medieval Japan in a moment of terrible +social breakdown uh um uh in which + + align:start position:0% +social breakdown uh um uh in which + + + align:start position:0% +social breakdown uh um uh in which +vestigal or ancestral attitudes towards + + align:start position:0% +vestigal or ancestral attitudes towards + + + align:start position:0% +vestigal or ancestral attitudes towards +sexuality and gender are being are being + + align:start position:0% +sexuality and gender are being are being + + + align:start position:0% +sexuality and gender are being are being +uh mobilized or awakened right and if we + + align:start position:0% +uh mobilized or awakened right and if we + + + align:start position:0% +uh mobilized or awakened right and if we +understand it in that way uh we can + + align:start position:0% +understand it in that way uh we can + + + align:start position:0% +understand it in that way uh we can +begin to recognize that our own + + align:start position:0% +begin to recognize that our own + + + align:start position:0% +begin to recognize that our own +discomfort with the subject matter is a + + align:start position:0% +discomfort with the subject matter is a + + + align:start position:0% +discomfort with the subject matter is a +discomfort uh that the film itself may + + align:start position:0% +discomfort uh that the film itself may + + + align:start position:0% +discomfort uh that the film itself may +even be aware of and may even be + + align:start position:0% +even be aware of and may even be + + + align:start position:0% +even be aware of and may even be +encouraging and I as you're watching the + + align:start position:0% +encouraging and I as you're watching the + + + align:start position:0% +encouraging and I as you're watching the +film watch how in some sense it uh uh uh + + align:start position:0% +film watch how in some sense it uh uh uh + + + align:start position:0% +film watch how in some sense it uh uh uh +especially in in one moment where the + + align:start position:0% +especially in in one moment where the + + + align:start position:0% +especially in in one moment where the +where the uh victim of rape makes an + + align:start position:0% +where the uh victim of rape makes an + + + align:start position:0% +where the uh victim of rape makes an +appeal to her husband right after + + align:start position:0% +appeal to her husband right after + + + align:start position:0% +appeal to her husband right after +there's a sequence where where we see + + align:start position:0% +there's a sequence where where we see + + + align:start position:0% +there's a sequence where where we see +her embracing her husband and looking + + align:start position:0% +her embracing her husband and looking + + + align:start position:0% +her embracing her husband and looking +into his face now the problem is she's + + align:start position:0% +into his face now the problem is she's + + + align:start position:0% +into his face now the problem is she's +giving this testimony and there's some + + align:start position:0% +giving this testimony and there's some + + + align:start position:0% +giving this testimony and there's some +reason to it's after the fact and + + align:start position:0% +reason to it's after the fact and + + + align:start position:0% +reason to it's after the fact and +there's some reason to doubt what she's + + align:start position:0% +there's some reason to doubt what she's + + + align:start position:0% +there's some reason to doubt what she's +saying uh especially as the film goes on + + align:start position:0% +saying uh especially as the film goes on + + + align:start position:0% +saying uh especially as the film goes on +nonetheless it's a it's a moment of uh + + align:start position:0% +nonetheless it's a it's a moment of uh + + + align:start position:0% +nonetheless it's a it's a moment of uh +of great power and what and and that + + align:start position:0% +of great power and what and and that + + + align:start position:0% +of great power and what and and that +moment at least mobilizes a a sympathy + + align:start position:0% +moment at least mobilizes a a sympathy + + + align:start position:0% +moment at least mobilizes a a sympathy +for + + align:start position:0% +for + + + align:start position:0% +for +the victim of rape that is uh uh very + + align:start position:0% +the victim of rape that is uh uh very + + + align:start position:0% +the victim of rape that is uh uh very +significant because you hear so little + + align:start position:0% +significant because you hear so little + + + align:start position:0% +significant because you hear so little +of it elsewhere uh elsewhere in the film + + align:start position:0% +of it elsewhere uh elsewhere in the film + + + align:start position:0% +of it elsewhere uh elsewhere in the film +not that the woman is is is treated + + align:start position:0% +not that the woman is is is treated + + + align:start position:0% +not that the woman is is is treated +badly but but she's subjected to the + + align:start position:0% +badly but but she's subjected to the + + + align:start position:0% +badly but but she's subjected to the +same suspicions as the other as the + + align:start position:0% +same suspicions as the other as the + + + align:start position:0% +same suspicions as the other as the +other Central characters but there's a + + align:start position:0% +other Central characters but there's a + + + align:start position:0% +other Central characters but there's a +larger thing to think about a larger a + + align:start position:0% +larger thing to think about a larger a + + + align:start position:0% +larger thing to think about a larger a +larger way a larger way in which we can + + align:start position:0% +larger way a larger way in which we can + + + align:start position:0% +larger way a larger way in which we can +accommodate ourselves to the slight + + align:start position:0% +accommodate ourselves to the slight + + + align:start position:0% +accommodate ourselves to the slight +discomfort we might feel at turning a + + align:start position:0% +discomfort we might feel at turning a + + + align:start position:0% +discomfort we might feel at turning a +story of rape into a philosophic + + align:start position:0% +story of rape into a philosophic + + + align:start position:0% +story of rape into a philosophic +discourse as this film does and that's + + align:start position:0% +discourse as this film does and that's + + + align:start position:0% +discourse as this film does and that's +simply here's how we might do that let + + align:start position:0% +simply here's how we might do that let + + + align:start position:0% +simply here's how we might do that let +me just remind you that stories about + + align:start position:0% +me just remind you that stories about + + + align:start position:0% +me just remind you that stories about +rape are at the heart of many cultures + + align:start position:0% +rape are at the heart of many cultures + + + align:start position:0% +rape are at the heart of many cultures +how how many of you have heard of the + + align:start position:0% +how how many of you have heard of the + + + align:start position:0% +how how many of you have heard of the +story of the rape of Europa it's a Greek + + align:start position:0% +story of the rape of Europa it's a Greek + + + align:start position:0% +story of the rape of Europa it's a Greek +myth none of you in many ways it's the + + align:start position:0% +myth none of you in many ways it's the + + + align:start position:0% +myth none of you in many ways it's the +story of the foundation of Europe Zeus + + align:start position:0% +story of the foundation of Europe Zeus + + + align:start position:0% +story of the foundation of Europe Zeus +disguised as a white bull is the great + + align:start position:0% +disguised as a white bull is the great + + + align:start position:0% +disguised as a white bull is the great +Greek god right the God of all gods one + + align:start position:0% +Greek god right the God of all gods one + + + align:start position:0% +Greek god right the God of all gods one +of one of Zeus's best habits or most + + align:start position:0% +of one of Zeus's best habits or most + + + align:start position:0% +of one of Zeus's best habits or most +most remarkable habits in the in the in + + align:start position:0% +most remarkable habits in the in the in + + + align:start position:0% +most remarkable habits in the in the in +in this in the in these mythological + + align:start position:0% +in this in the in these mythological + + + align:start position:0% +in this in the in these mythological +stories is that when he gets a Yen for a + + align:start position:0% +stories is that when he gets a Yen for a + + + align:start position:0% +stories is that when he gets a Yen for a +human female he will disguise himself as + + align:start position:0% +human female he will disguise himself as + + + align:start position:0% +human female he will disguise himself as +a as a creature of the earth and rape + + align:start position:0% +a as a creature of the earth and rape + + + align:start position:0% +a as a creature of the earth and rape +her go down and Raper right and he does + + align:start position:0% +her go down and Raper right and he does + + + align:start position:0% +her go down and Raper right and he does +this with Europa the story the rape of + + align:start position:0% +this with Europa the story the rape of + + + align:start position:0% +this with Europa the story the rape of +Europa is a kind of symbolic story which + + align:start position:0% +Europa is a kind of symbolic story which + + + align:start position:0% +Europa is a kind of symbolic story which +is which which later uh uh uh Europeans + + align:start position:0% +is which which later uh uh uh Europeans + + + align:start position:0% +is which which later uh uh uh Europeans +actually took as a kind of one of the + + align:start position:0% +actually took as a kind of one of the + + + align:start position:0% +actually took as a kind of one of the +founding Tales of how Europe itself was + + align:start position:0% +founding Tales of how Europe itself was + + + align:start position:0% +founding Tales of how Europe itself was +found + + align:start position:0% +found + + + align:start position:0% +found +can you think of another story in which + + align:start position:0% +can you think of another story in which + + + align:start position:0% +can you think of another story in which +Zeus is a rapist how about L how many of + + align:start position:0% +Zeus is a rapist how about L how many of + + + align:start position:0% +Zeus is a rapist how about L how many of +you know the story of Lita and the swan + + align:start position:0% +you know the story of Lita and the swan + + + align:start position:0% +you know the story of Lita and the swan +about about which Yates wrote so so such + + align:start position:0% +about about which Yates wrote so so such + + + align:start position:0% +about about which Yates wrote so so such +beautiful poems again Zeus the god of + + align:start position:0% +beautiful poems again Zeus the god of + + + align:start position:0% +beautiful poems again Zeus the god of +gods disguises himself as a great Swan + + align:start position:0% +gods disguises himself as a great Swan + + + align:start position:0% +gods disguises himself as a great Swan +and swoops down on Lita this beautiful + + align:start position:0% +and swoops down on Lita this beautiful + + + align:start position:0% +and swoops down on Lita this beautiful +woman uh and rapes her as in the in in + + align:start position:0% +woman uh and rapes her as in the in in + + + align:start position:0% +woman uh and rapes her as in the in in +the guise of the Swan and there's a + + align:start position:0% +the guise of the Swan and there's a + + + align:start position:0% +the guise of the Swan and there's a +brilliant almost pornographically + + align:start position:0% +brilliant almost pornographically + + + align:start position:0% +brilliant almost pornographically +powerful poem by WB Yates in which he + + align:start position:0% +powerful poem by WB Yates in which he + + + align:start position:0% +powerful poem by WB Yates in which he +describes this terrible moment of rape + + align:start position:0% +describes this terrible moment of rape + + + align:start position:0% +describes this terrible moment of rape +it's one of the it's one of the great + + align:start position:0% +it's one of the it's one of the great + + + align:start position:0% +it's one of the it's one of the great +poems of the western world and it it's + + align:start position:0% +poems of the western world and it it's + + + align:start position:0% +poems of the western world and it it's +about this rape it so so that what I'm + + align:start position:0% +about this rape it so so that what I'm + + + align:start position:0% +about this rape it so so that what I'm +what I'm reminding you of is that the + + align:start position:0% +what I'm reminding you of is that the + + + align:start position:0% +what I'm reminding you of is that the +misogyny that you may sense there is a + + align:start position:0% +misogyny that you may sense there is a + + + align:start position:0% +misogyny that you may sense there is a +misogyny that's embedded in culture it's + + align:start position:0% +misogyny that's embedded in culture it's + + + align:start position:0% +misogyny that's embedded in culture it's +a misogyny that's embedded it's a + + align:start position:0% +a misogyny that's embedded it's a + + + align:start position:0% +a misogyny that's embedded it's a +misogyny that's embedded in in all the + + align:start position:0% +misogyny that's embedded in in all the + + + align:start position:0% +misogyny that's embedded in in all the +stories that human beings tell in many + + align:start position:0% +stories that human beings tell in many + + + align:start position:0% +stories that human beings tell in many +of the stories that human beings tell + + align:start position:0% +of the stories that human beings tell + + + align:start position:0% +of the stories that human beings tell +themselves about about the world about + + align:start position:0% +themselves about about the world about + + + align:start position:0% +themselves about about the world about +the relations of men and women and often + + align:start position:0% +the relations of men and women and often + + + align:start position:0% +the relations of men and women and often +especially about the foundations of + + align:start position:0% +especially about the foundations of + + + align:start position:0% +especially about the foundations of +society so so that so that this so that + + align:start position:0% +society so so that so that this so that + + + align:start position:0% +society so so that so that this so that +this meditation uh on on uh uh + + align:start position:0% +this meditation uh on on uh uh + + + align:start position:0% +this meditation uh on on uh uh +uh human Frailty and human uh deceit uh + + align:start position:0% +uh human Frailty and human uh deceit uh + + + align:start position:0% +uh human Frailty and human uh deceit uh +uh focused on a rape uh is from that + + align:start position:0% +uh focused on a rape uh is from that + + + align:start position:0% +uh focused on a rape uh is from that +perspective is one of many such stories + + align:start position:0% +perspective is one of many such stories + + + align:start position:0% +perspective is one of many such stories +not a unique object at all and uh it + + align:start position:0% +not a unique object at all and uh it + + + align:start position:0% +not a unique object at all and uh it +seems to me that's that that the that + + align:start position:0% +seems to me that's that that the that + + + align:start position:0% +seems to me that's that that the that +that that's one of the ways in which we + + align:start position:0% +that that's one of the ways in which we + + + align:start position:0% +that that's one of the ways in which we +can recognize that what kurasawa is + + align:start position:0% +can recognize that what kurasawa is + + + align:start position:0% +can recognize that what kurasawa is +doing is part of a long and complex and + + align:start position:0% +doing is part of a long and complex and + + + align:start position:0% +doing is part of a long and complex and +and and in many ways very disturbing uh + + align:start position:0% +and and in many ways very disturbing uh + + + align:start position:0% +and and in many ways very disturbing uh +uh uh + + align:start position:0% +uh uh + + + align:start position:0% +uh uh +uh Habit of mind uh that many many + + align:start position:0% +uh Habit of mind uh that many many + + + align:start position:0% +uh Habit of mind uh that many many +cultures + + align:start position:0% +cultures + + + align:start position:0% +cultures +share the title rashan Western People + + align:start position:0% +share the title rashan Western People + + + align:start position:0% +share the title rashan Western People +students are often puzzled by it it's a + + align:start position:0% +students are often puzzled by it it's a + + + align:start position:0% +students are often puzzled by it it's a +reference to the name of the gate but + + align:start position:0% +reference to the name of the gate but + + + align:start position:0% +reference to the name of the gate but +the word gate is complicated too because + + align:start position:0% +the word gate is complicated too because + + + align:start position:0% +the word gate is complicated too because +it's not an American gate that just + + align:start position:0% +it's not an American gate that just + + + align:start position:0% +it's not an American gate that just +opens and closes it's a great great + + align:start position:0% +opens and closes it's a great great + + + align:start position:0% +opens and closes it's a great great +massive entrance to the city of Kyoto in + + align:start position:0% +massive entrance to the city of Kyoto in + + + align:start position:0% +massive entrance to the city of Kyoto in +the southern part of Japan in the late + + align:start position:0% +the southern part of Japan in the late + + + align:start position:0% +the southern part of Japan in the late +11th or early 12th century it's a period + + align:start position:0% +11th or early 12th century it's a period + + + align:start position:0% +11th or early 12th century it's a period +of complete disillusion uh uh and and + + align:start position:0% +of complete disillusion uh uh and and + + + align:start position:0% +of complete disillusion uh uh and and +and and and and destructive poverty in + + align:start position:0% +and and and and destructive poverty in + + + align:start position:0% +and and and and destructive poverty in +uh political chaos and the broken down + + align:start position:0% +uh political chaos and the broken down + + + align:start position:0% +uh political chaos and the broken down +condition of the gate which you get long + + align:start position:0% +condition of the gate which you get long + + + align:start position:0% +condition of the gate which you get long +shots of you know you see this massive + + align:start position:0% +shots of you know you see this massive + + + align:start position:0% +shots of you know you see this massive +structure in under which it's a terrible + + align:start position:0% +structure in under which it's a terrible + + + align:start position:0% +structure in under which it's a terrible +rainstorm going on under which certain + + align:start position:0% +rainstorm going on under which certain + + + align:start position:0% +rainstorm going on under which certain +people come to get Shelter From the rain + + align:start position:0% +people come to get Shelter From the rain + + + align:start position:0% +people come to get Shelter From the rain +and that is rashan gate right uh and and + + align:start position:0% +and that is rashan gate right uh and and + + + align:start position:0% +and that is rashan gate right uh and and +it's broken down condition simp + + align:start position:0% +it's broken down condition simp + + + align:start position:0% +it's broken down condition simp +symbolizes the broken down condition + + align:start position:0% +symbolizes the broken down condition + + + align:start position:0% +symbolizes the broken down condition +politically and socially of the society + + align:start position:0% +politically and socially of the society + + + align:start position:0% +politically and socially of the society +repres that that that that is + + align:start position:0% +repres that that that that is + + + align:start position:0% +repres that that that that is +represented there and again and again + + align:start position:0% +represented there and again and again + + + align:start position:0% +represented there and again and again +the characters gathered beneath the gate + + align:start position:0% +the characters gathered beneath the gate + + + align:start position:0% +the characters gathered beneath the gate +to protect themselves from the weather + + align:start position:0% +to protect themselves from the weather + + + align:start position:0% +to protect themselves from the weather +engage in conversation about the about + + align:start position:0% +engage in conversation about the about + + + align:start position:0% +engage in conversation about the about +the nature of about human nature are + + align:start position:0% +the nature of about human nature are + + + align:start position:0% +the nature of about human nature are +human beings innately evil do they + + align:start position:0% +human beings innately evil do they + + + align:start position:0% +human beings innately evil do they +always lie can we never trust them and + + align:start position:0% +always lie can we never trust them and + + + align:start position:0% +always lie can we never trust them and +one of the characters uh who carries on + + align:start position:0% +one of the characters uh who carries on + + + align:start position:0% +one of the characters uh who carries on +this discourse is a is a priest uh who + + align:start position:0% +this discourse is a is a priest uh who + + + align:start position:0% +this discourse is a is a priest uh who +has a kind who has an idealizing + + align:start position:0% +has a kind who has an idealizing + + + align:start position:0% +has a kind who has an idealizing +tendency which another of the characters + + align:start position:0% +tendency which another of the characters + + + align:start position:0% +tendency which another of the characters +a commoner he's called the commoner he's + + align:start position:0% +a commoner he's called the commoner he's + + + align:start position:0% +a commoner he's called the commoner he's +an ordinary man is constantly mocking + + align:start position:0% +an ordinary man is constantly mocking + + + align:start position:0% +an ordinary man is constantly mocking +and arguing against it's almost a kind + + align:start position:0% +and arguing against it's almost a kind + + + align:start position:0% +and arguing against it's almost a kind +of argument that reminds me in some ways + + align:start position:0% +of argument that reminds me in some ways + + + align:start position:0% +of argument that reminds me in some ways +of the argument between spirit and flesh + + align:start position:0% +of the argument between spirit and flesh + + + align:start position:0% +of the argument between spirit and flesh +in in in cervant Don kote in which in + + align:start position:0% +in in in cervant Don kote in which in + + + align:start position:0% +in in in cervant Don kote in which in +which Sancho Pon is constantly reminding + + align:start position:0% +which Sancho Pon is constantly reminding + + + align:start position:0% +which Sancho Pon is constantly reminding +the idealizing kote of the miserable + + align:start position:0% +the idealizing kote of the miserable + + + align:start position:0% +the idealizing kote of the miserable +actuality of the world look when you get + + align:start position:0% +actuality of the world look when you get + + + align:start position:0% +actuality of the world look when you get +stabbed you bleed when you're when you + + align:start position:0% +stabbed you bleed when you're when you + + + align:start position:0% +stabbed you bleed when you're when you +haven't eaten you're hungry hungry right + + align:start position:0% +haven't eaten you're hungry hungry right + + + align:start position:0% +haven't eaten you're hungry hungry right +the world is real in a way that uh uh uh + + align:start position:0% +the world is real in a way that uh uh uh + + + align:start position:0% +the world is real in a way that uh uh uh +that that ideal that IDE and miserable + + align:start position:0% +that that ideal that IDE and miserable + + + align:start position:0% +that that ideal that IDE and miserable +in some respects in a way that idealists + + align:start position:0% +in some respects in a way that idealists + + + align:start position:0% +in some respects in a way that idealists +don't like and so that's a kind of + + align:start position:0% +don't like and so that's a kind of + + + align:start position:0% +don't like and so that's a kind of +argument that runs through these + + align:start position:0% +argument that runs through these + + + align:start position:0% +argument that runs through these +interludes as the as the film goes on so + + align:start position:0% +interludes as the as the film goes on so + + + align:start position:0% +interludes as the as the film goes on so +so the title refers to the rasham manate + + align:start position:0% +so the title refers to the rasham manate + + + align:start position:0% +so the title refers to the rasham manate +and rashim manate is itself a massive + + align:start position:0% +and rashim manate is itself a massive + + + align:start position:0% +and rashim manate is itself a massive +symbol for the breakdown of order for + + align:start position:0% +symbol for the breakdown of order for + + + align:start position:0% +symbol for the breakdown of order for +the misery of indiv for the miserable + + align:start position:0% +the misery of indiv for the miserable + + + align:start position:0% +the misery of indiv for the miserable +circumstances that individuals find + + align:start position:0% +circumstances that individuals find + + + align:start position:0% +circumstances that individuals find +themselves in and what you one of the + + align:start position:0% +themselves in and what you one of the + + + align:start position:0% +themselves in and what you one of the +things you'll see is that it's chilly + + align:start position:0% +things you'll see is that it's chilly + + + align:start position:0% +things you'll see is that it's chilly +it's cold it's raining like mad a + + align:start position:0% +it's cold it's raining like mad a + + + align:start position:0% +it's cold it's raining like mad a +tremendous torrent a downpour + + align:start position:0% +tremendous torrent a downpour + + + align:start position:0% +tremendous torrent a downpour +incidentally created partly by fire + + align:start position:0% +incidentally created partly by fire + + + align:start position:0% +incidentally created partly by fire +trucks in his autobiography kusawa talks + + align:start position:0% +trucks in his autobiography kusawa talks + + + align:start position:0% +trucks in his autobiography kusawa talks +about uh how difficult it was to create + + align:start position:0% +about uh how difficult it was to create + + + align:start position:0% +about uh how difficult it was to create +this sense of an immense ongoing almost + + align:start position:0% +this sense of an immense ongoing almost + + + align:start position:0% +this sense of an immense ongoing almost +a tsunami of rain uh and he talked about + + align:start position:0% +a tsunami of rain uh and he talked about + + + align:start position:0% +a tsunami of rain uh and he talked about +the technical difficulties of of of of + + align:start position:0% +the technical difficulties of of of of + + + align:start position:0% +the technical difficulties of of of of +doing so uh very impressive very + + align:start position:0% +doing so uh very impressive very + + + align:start position:0% +doing so uh very impressive very +impressive rain the most impressive + + align:start position:0% +impressive rain the most impressive + + + align:start position:0% +impressive rain the most impressive +rainstorm in the history of movies I + + align:start position:0% +rainstorm in the history of movies I + + + align:start position:0% +rainstorm in the history of movies I +think uh and uh so so these these these + + align:start position:0% +think uh and uh so so these these these + + + align:start position:0% +think uh and uh so so these these these +uh people are gathered beneath the gate + + align:start position:0% +uh people are gathered beneath the gate + + + align:start position:0% +uh people are gathered beneath the gate +in order to in order to protect + + align:start position:0% +in order to in order to protect + + + align:start position:0% +in order to in order to protect +themselves and the gate symbolic + + align:start position:0% +themselves and the gate symbolic + + + align:start position:0% +themselves and the gate symbolic +significance is is is is important uh + + align:start position:0% +significance is is is is important uh + + + align:start position:0% +significance is is is is important uh +you will notice that one of the things + + align:start position:0% +you will notice that one of the things + + + align:start position:0% +you will notice that one of the things +they do when they get cold is they go + + align:start position:0% +they do when they get cold is they go + + + align:start position:0% +they do when they get cold is they go +over to certain parts of the of the + + align:start position:0% +over to certain parts of the of the + + + align:start position:0% +over to certain parts of the of the +building it's wooden structure already + + align:start position:0% +building it's wooden structure already + + + align:start position:0% +building it's wooden structure already +half broken down and and and in Decay + + align:start position:0% +half broken down and and and in Decay + + + align:start position:0% +half broken down and and and in Decay +and they'll break off banisters or other + + align:start position:0% +and they'll break off banisters or other + + + align:start position:0% +and they'll break off banisters or other +pieces of wood and break them up and + + align:start position:0% +pieces of wood and break them up and + + + align:start position:0% +pieces of wood and break them up and +turn and and and and burn them up and + + align:start position:0% +turn and and and and burn them up and + + + align:start position:0% +turn and and and and burn them up and +the implication is if things go on like + + align:start position:0% +the implication is if things go on like + + + align:start position:0% +the implication is if things go on like +this pretty soon the whole gate will + + align:start position:0% +this pretty soon the whole gate will + + + align:start position:0% +this pretty soon the whole gate will +have will have been consumed by people + + align:start position:0% +have will have been consumed by people + + + align:start position:0% +have will have been consumed by people +who have tried to take shelter under it + + align:start position:0% +who have tried to take shelter under it + + + align:start position:0% +who have tried to take shelter under it +so it's a so it's a symbol of the + + align:start position:0% +so it's a so it's a symbol of the + + + align:start position:0% +so it's a so it's a symbol of the +breakdown of social order and of and of + + align:start position:0% +breakdown of social order and of and of + + + align:start position:0% +breakdown of social order and of and of +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh and and of the society uh I've + + align:start position:0% +uh and and of the society uh I've + + + align:start position:0% +uh and and of the society uh I've +already mentioned the medium the name + + align:start position:0% +already mentioned the medium the name + + + align:start position:0% +already mentioned the medium the name +the Japanese word is moo and I just + + align:start position:0% +the Japanese word is moo and I just + + + align:start position:0% +the Japanese word is moo and I just +mention it here just because I wanted to + + align:start position:0% +mention it here just because I wanted to + + + align:start position:0% +mention it here just because I wanted to +uh uh clarify I wanted to be sure all of + + align:start position:0% +uh uh clarify I wanted to be sure all of + + + align:start position:0% +uh uh clarify I wanted to be sure all of +you understood what was going on there + + align:start position:0% +you understood what was going on there + + + align:start position:0% +you understood what was going on there +the husband is dead when the testimony + + align:start position:0% +the husband is dead when the testimony + + + align:start position:0% +the husband is dead when the testimony +uh begins he's a samurai soul + + align:start position:0% +uh begins he's a samurai soul + + + align:start position:0% +uh begins he's a samurai soul +husband of a samurai who was the husband + + align:start position:0% +husband of a samurai who was the husband + + + align:start position:0% +husband of a samurai who was the husband +of the of the rape victim uh and as the + + align:start position:0% +of the of the rape victim uh and as the + + + align:start position:0% +of the of the rape victim uh and as the +story unfolds you'll see what what + + align:start position:0% +story unfolds you'll see what what + + + align:start position:0% +story unfolds you'll see what what +you'll get the basic facts but you'll + + align:start position:0% +you'll get the basic facts but you'll + + + align:start position:0% +you'll get the basic facts but you'll +also by the even when the film is over + + align:start position:0% +also by the even when the film is over + + + align:start position:0% +also by the even when the film is over +there are many fundamental things you + + align:start position:0% +there are many fundamental things you + + + align:start position:0% +there are many fundamental things you +won't be able to uh have decided and I + + align:start position:0% +won't be able to uh have decided and I + + + align:start position:0% +won't be able to uh have decided and I +think that's part of certainly part of + + align:start position:0% +think that's part of certainly part of + + + align:start position:0% +think that's part of certainly part of +kurosawa's point so the medium is just + + align:start position:0% +kurosawa's point so the medium is just + + + align:start position:0% +kurosawa's point so the medium is just +this this U uh uh Clairvoyant type of + + align:start position:0% +this this U uh uh Clairvoyant type of + + + align:start position:0% +this this U uh uh Clairvoyant type of +apparently uh characters real characters + + align:start position:0% +apparently uh characters real characters + + + align:start position:0% +apparently uh characters real characters +believed in and and uh uh so socially + + align:start position:0% +believed in and and uh uh so socially + + + align:start position:0% +believed in and and uh uh so socially +recognizable in late middle uh in late + + align:start position:0% +recognizable in late middle uh in late + + + align:start position:0% +recognizable in late middle uh in late +medieval Japan a character who claims to + + align:start position:0% +medieval Japan a character who claims to + + + align:start position:0% +medieval Japan a character who claims to +have access to the words and beliefs of + + align:start position:0% +have access to the words and beliefs of + + + align:start position:0% +have access to the words and beliefs of +dead people so the dead man testifies in + + align:start position:0% +dead people so the dead man testifies in + + + align:start position:0% +dead people so the dead man testifies in +the and another way of reminding you + + align:start position:0% +the and another way of reminding you + + + align:start position:0% +the and another way of reminding you +that we're looking at a very stylized a + + align:start position:0% +that we're looking at a very stylized a + + + align:start position:0% +that we're looking at a very stylized a +dream a story that isn't in a narrow + + align:start position:0% +dream a story that isn't in a narrow + + + align:start position:0% +dream a story that isn't in a narrow +sense realistic at + + align:start position:0% +sense realistic at + + + align:start position:0% +sense realistic at +all the visual style of the film is + + align:start position:0% +all the visual style of the film is + + + align:start position:0% +all the visual style of the film is +especially remarkable and and astounding + + align:start position:0% +especially remarkable and and astounding + + + align:start position:0% +especially remarkable and and astounding +uh in some ways it's almost as if each + + align:start position:0% +uh in some ways it's almost as if each + + + align:start position:0% +uh in some ways it's almost as if each +of the test each form of testimony has + + align:start position:0% +of the test each form of testimony has + + + align:start position:0% +of the test each form of testimony has +its own style uh and you might want to + + align:start position:0% +its own style uh and you might want to + + + align:start position:0% +its own style uh and you might want to +watch uh the the way in which kusawa + + align:start position:0% +watch uh the the way in which kusawa + + + align:start position:0% +watch uh the the way in which kusawa +sort of builds uh uh his eclectic and + + align:start position:0% +sort of builds uh uh his eclectic and + + + align:start position:0% +sort of builds uh uh his eclectic and +dynamic sense of of of of The Eclectic + + align:start position:0% +dynamic sense of of of of The Eclectic + + + align:start position:0% +dynamic sense of of of of The Eclectic +and dynamic way in which in which + + align:start position:0% +and dynamic way in which in which + + + align:start position:0% +and dynamic way in which in which +kurosawa's editing camera work use of + + align:start position:0% +kurosawa's editing camera work use of + + + align:start position:0% +kurosawa's editing camera work use of +Music uh combin to create a kind of + + align:start position:0% +Music uh combin to create a kind of + + + align:start position:0% +Music uh combin to create a kind of +almost constant visual excitement one of + + align:start position:0% +almost constant visual excitement one of + + + align:start position:0% +almost constant visual excitement one of +the most remarkable things about the + + align:start position:0% +the most remarkable things about the + + + align:start position:0% +the most remarkable things about the +film is how many sequences in it are + + align:start position:0% +film is how many sequences in it are + + + align:start position:0% +film is how many sequences in it are +without + + align:start position:0% +without + + + align:start position:0% +without +dialogue EX Ed wordless sequences truly + + align:start position:0% +dialogue EX Ed wordless sequences truly + + + align:start position:0% +dialogue EX Ed wordless sequences truly +entirely cinematic uh the opening + + align:start position:0% +entirely cinematic uh the opening + + + align:start position:0% +entirely cinematic uh the opening +sequence I almost the opening sequence + + align:start position:0% +sequence I almost the opening sequence + + + align:start position:0% +sequence I almost the opening sequence +the first extended sequence in a forest + + align:start position:0% +the first extended sequence in a forest + + + align:start position:0% +the first extended sequence in a forest +uh which comes after the sort of + + align:start position:0% +uh which comes after the sort of + + + align:start position:0% +uh which comes after the sort of +introduction um which I've described + + align:start position:0% +introduction um which I've described + + + align:start position:0% +introduction um which I've described +earlier is a magnificently uh clear + + align:start position:0% +earlier is a magnificently uh clear + + + align:start position:0% +earlier is a magnificently uh clear +example of that process and in that one + + align:start position:0% +example of that process and in that one + + + align:start position:0% +example of that process and in that one +of the things that you you may notice uh + + align:start position:0% +of the things that you you may notice uh + + + align:start position:0% +of the things that you you may notice uh +in that sequence especially uh is the + + align:start position:0% +in that sequence especially uh is the + + + align:start position:0% +in that sequence especially uh is the +way in which you become increasingly + + align:start position:0% +way in which you become increasingly + + + align:start position:0% +way in which you become increasingly +disoriented about the dire direction in + + align:start position:0% +disoriented about the dire direction in + + + align:start position:0% +disoriented about the dire direction in +which the wood cutter is going he's + + align:start position:0% +which the wood cutter is going he's + + + align:start position:0% +which the wood cutter is going he's +apparently narrating the story and his + + align:start position:0% +apparently narrating the story and his + + + align:start position:0% +apparently narrating the story and his +narration sort of Segways into a visual + + align:start position:0% +narration sort of Segways into a visual + + + align:start position:0% +narration sort of Segways into a visual +experience as happens again and again in + + align:start position:0% +experience as happens again and again in + + + align:start position:0% +experience as happens again and again in +the film and the visual experience we + + align:start position:0% +the film and the visual experience we + + + align:start position:0% +the film and the visual experience we +have shows him going into the woods + + align:start position:0% +have shows him going into the woods + + + align:start position:0% +have shows him going into the woods +walking and then discovering first the + + align:start position:0% +walking and then discovering first the + + + align:start position:0% +walking and then discovering first the +woman's hat and then discovering a other + + align:start position:0% +woman's hat and then discovering a other + + + align:start position:0% +woman's hat and then discovering a other +things and discovering a body and then + + align:start position:0% +things and discovering a body and then + + + align:start position:0% +things and discovering a body and then +running away in fear uh and and uh as he + + align:start position:0% +running away in fear uh and and uh as he + + + align:start position:0% +running away in fear uh and and uh as he +penetrates into the woods one of the + + align:start position:0% +penetrates into the woods one of the + + + align:start position:0% +penetrates into the woods one of the +things that happens is the camera is + + align:start position:0% +things that happens is the camera is + + + align:start position:0% +things that happens is the camera is +always moving and and and the camera + + align:start position:0% +always moving and and and the camera + + + align:start position:0% +always moving and and and the camera +becomes as interested in the in the + + align:start position:0% +becomes as interested in the in the + + + align:start position:0% +becomes as interested in the in the +forest itself in this densely wooded + + align:start position:0% +forest itself in this densely wooded + + + align:start position:0% +forest itself in this densely wooded +forest and in the play of light and dark + + align:start position:0% +forest and in the play of light and dark + + + align:start position:0% +forest and in the play of light and dark +uh because the sunlight comes through + + align:start position:0% +uh because the sunlight comes through + + + align:start position:0% +uh because the sunlight comes through +the wooded canopy uh in in odd and + + align:start position:0% +the wooded canopy uh in in odd and + + + align:start position:0% +the wooded canopy uh in in odd and +profoundly uh visually powerful ways um + + align:start position:0% +profoundly uh visually powerful ways um + + + align:start position:0% +profoundly uh visually powerful ways um +uh it's it's as if the you begin to have + + align:start position:0% +uh it's it's as if the you begin to have + + + align:start position:0% +uh it's it's as if the you begin to have +a sense that that that the camera is at + + align:start position:0% +a sense that that that the camera is at + + + align:start position:0% +a sense that that that the camera is at +least as interested in the woods and in + + align:start position:0% +least as interested in the woods and in + + + align:start position:0% +least as interested in the woods and in +the play of sunlight as it is in the + + align:start position:0% +the play of sunlight as it is in the + + + align:start position:0% +the play of sunlight as it is in the +Motions of the of the wood cutter and + + align:start position:0% +Motions of the of the wood cutter and + + + align:start position:0% +Motions of the of the wood cutter and +the the whole sequence has a kind of + + align:start position:0% +the the whole sequence has a kind of + + + align:start position:0% +the the whole sequence has a kind of +profoundly uh lyrical but also in some + + align:start position:0% +profoundly uh lyrical but also in some + + + align:start position:0% +profoundly uh lyrical but also in some +degree disoriented ing sense that as + + align:start position:0% +degree disoriented ing sense that as + + + align:start position:0% +degree disoriented ing sense that as +kusawa said you're entering a space in + + align:start position:0% +kusawa said you're entering a space in + + + align:start position:0% +kusawa said you're entering a space in +which in you're you're you're entering a + + align:start position:0% +which in you're you're you're entering a + + + align:start position:0% +which in you're you're you're entering a +space that's dreamlike that's dangerous + + align:start position:0% +space that's dreamlike that's dangerous + + + align:start position:0% +space that's dreamlike that's dangerous +a a place where the heart will lose its + + align:start position:0% +a a place where the heart will lose its + + + align:start position:0% +a a place where the heart will lose its +way right as if you're as if you're + + align:start position:0% +way right as if you're as if you're + + + align:start position:0% +way right as if you're as if you're +entering a symbolic space not a + + align:start position:0% +entering a symbolic space not a + + + align:start position:0% +entering a symbolic space not a +realistic space right a stylized space + + align:start position:0% +realistic space right a stylized space + + + align:start position:0% +realistic space right a stylized space +in in some in some in some deep way um + + align:start position:0% +in in some in some in some deep way um + + + align:start position:0% +in in some in some in some deep way um +um and there are there are a couple of + + align:start position:0% +um and there are there are a couple of + + + align:start position:0% +um and there are there are a couple of +specific strategies that kurasawa uses + + align:start position:0% +specific strategies that kurasawa uses + + + align:start position:0% +specific strategies that kurasawa uses +in in the in the film to uh uh reinforce + + align:start position:0% +in in the in the film to uh uh reinforce + + + align:start position:0% +in in the in the film to uh uh reinforce +I think our sense that he is Eng that + + align:start position:0% +I think our sense that he is Eng that + + + align:start position:0% +I think our sense that he is Eng that +he's engaging every element of the of of + + align:start position:0% +he's engaging every element of the of of + + + align:start position:0% +he's engaging every element of the of of +his of his cinematic pallet uh in order + + align:start position:0% +his of his cinematic pallet uh in order + + + align:start position:0% +his of his cinematic pallet uh in order +to create his effects one thing he does + + align:start position:0% +to create his effects one thing he does + + + align:start position:0% +to create his effects one thing he does +uh he violates certain rules that at + + align:start position:0% +uh he violates certain rules that at + + + align:start position:0% +uh he violates certain rules that at +especially at the time where would have + + align:start position:0% +especially at the time where would have + + + align:start position:0% +especially at the time where would have +been tremendously shocking to + + align:start position:0% +been tremendously shocking to + + + align:start position:0% +been tremendously shocking to +professional directors one thing he does + + align:start position:0% +professional directors one thing he does + + + align:start position:0% +professional directors one thing he does +in the film was he points the camera at + + align:start position:0% +in the film was he points the camera at + + + align:start position:0% +in the film was he points the camera at +the Sun and he creates Sun effects right + + align:start position:0% +the Sun and he creates Sun effects right + + + align:start position:0% +the Sun and he creates Sun effects right +that was a no no it was a sort of rule + + align:start position:0% +that was a no no it was a sort of rule + + + align:start position:0% +that was a no no it was a sort of rule +that directors should never do that + + align:start position:0% +that directors should never do that + + + align:start position:0% +that directors should never do that +kusawa doesn't it does and you watch how + + align:start position:0% +kusawa doesn't it does and you watch how + + + align:start position:0% +kusawa doesn't it does and you watch how +he does it it's very it's it's very + + align:start position:0% +he does it it's very it's it's very + + + align:start position:0% +he does it it's very it's it's very +powerful it has it also has a + + align:start position:0% +powerful it has it also has a + + + align:start position:0% +powerful it has it also has a +disorienting effect of the effect of + + align:start position:0% +disorienting effect of the effect of + + + align:start position:0% +disorienting effect of the effect of +making us understand more deeply what + + align:start position:0% +making us understand more deeply what + + + align:start position:0% +making us understand more deeply what +it's like to work to work our way + + align:start position:0% +it's like to work to work our way + + + align:start position:0% +it's like to work to work our way +through this the incredible dense forest + + align:start position:0% +through this the incredible dense forest + + + align:start position:0% +through this the incredible dense forest +in which the event occur in in which the + + align:start position:0% +in which the event occur in in which the + + + align:start position:0% +in which the event occur in in which the +um uh crime occurs as if the forest + + align:start position:0% +um uh crime occurs as if the forest + + + align:start position:0% +um uh crime occurs as if the forest +itself is a space so complex and so + + align:start position:0% +itself is a space so complex and so + + + align:start position:0% +itself is a space so complex and so +private uh so cut off from from uh uh + + align:start position:0% +private uh so cut off from from uh uh + + + align:start position:0% +private uh so cut off from from uh uh +the outer world that almost anything + + align:start position:0% +the outer world that almost anything + + + align:start position:0% +the outer world that almost anything +could could happen there a space of + + align:start position:0% +could could happen there a space of + + + align:start position:0% +could could happen there a space of +dream a space of Terror a space of + + align:start position:0% +dream a space of Terror a space of + + + align:start position:0% +dream a space of Terror a space of +symbolic Fable um and and uh uh there's + + align:start position:0% +symbolic Fable um and and uh uh there's + + + align:start position:0% +symbolic Fable um and and uh uh there's +there there are a couple of other things + + align:start position:0% +there there are a couple of other things + + + align:start position:0% +there there are a couple of other things +I wanted to mention about the way his + + align:start position:0% +I wanted to mention about the way his + + + align:start position:0% +I wanted to mention about the way his +camera behaves one is that he kusawa + + align:start position:0% +camera behaves one is that he kusawa + + + align:start position:0% +camera behaves one is that he kusawa +uses here a device at certain points in + + align:start position:0% +uses here a device at certain points in + + + align:start position:0% +uses here a device at certain points in +the film that a very interesting device + + align:start position:0% +the film that a very interesting device + + + align:start position:0% +the film that a very interesting device +it's the official name for it the the + + align:start position:0% +it's the official name for it the the + + + align:start position:0% +it's the official name for it the the +the fancy name for it the technical name + + align:start position:0% +the fancy name for it the technical name + + + align:start position:0% +the fancy name for it the technical name +for it is he makes what is called an + + align:start position:0% +for it is he makes what is called an + + + align:start position:0% +for it is he makes what is called an +axial cut axi L it's really a form of a + + align:start position:0% +axial cut axi L it's really a form of a + + + align:start position:0% +axial cut axi L it's really a form of a +jump cut uh that is to say you know an + + align:start position:0% +jump cut uh that is to say you know an + + + align:start position:0% +jump cut uh that is to say you know an +Abrupt edit which which are not fully + + align:start position:0% +Abrupt edit which which are not fully + + + align:start position:0% +Abrupt edit which which are not fully +prepared for which breaks in it it a + + align:start position:0% +prepared for which breaks in it it a + + + align:start position:0% +prepared for which breaks in it it a +jump cut as you know breaks uh the the + + align:start position:0% +jump cut as you know breaks uh the the + + + align:start position:0% +jump cut as you know breaks uh the the +action in in mid stride or in mid-action + + align:start position:0% +action in in mid stride or in mid-action + + + align:start position:0% +action in in mid stride or in mid-action +and then jumps to something else in a + + align:start position:0% +and then jumps to something else in a + + + align:start position:0% +and then jumps to something else in a +kind of in a way that's slightly + + align:start position:0% +kind of in a way that's slightly + + + align:start position:0% +kind of in a way that's slightly +disorienting that eliminates right it's + + align:start position:0% +disorienting that eliminates right it's + + + align:start position:0% +disorienting that eliminates right it's +elliptical it eliminates it eliminates + + align:start position:0% +elliptical it eliminates it eliminates + + + align:start position:0% +elliptical it eliminates it eliminates +connection or transitions right and you + + align:start position:0% +connection or transitions right and you + + + align:start position:0% +connection or transitions right and you +but but the axial cut does this in a + + align:start position:0% +but but the axial cut does this in a + + + align:start position:0% +but but the axial cut does this in a +very dramatic way that also calls + + align:start position:0% +very dramatic way that also calls + + + align:start position:0% +very dramatic way that also calls +attention to the apparatus of the movies + + align:start position:0% +attention to the apparatus of the movies + + + align:start position:0% +attention to the apparatus of the movies +uh the most dramatic places in which + + align:start position:0% +uh the most dramatic places in which + + + align:start position:0% +uh the most dramatic places in which +this occurs in the film are certain + + align:start position:0% +this occurs in the film are certain + + + align:start position:0% +this occurs in the film are certain +scenes in which you see the samurai + + align:start position:0% +scenes in which you see the samurai + + + align:start position:0% +scenes in which you see the samurai +husband tied up sitting on the ground + + align:start position:0% +husband tied up sitting on the ground + + + align:start position:0% +husband tied up sitting on the ground +tied up like this kneeling on the ground + + align:start position:0% +tied up like this kneeling on the ground + + + align:start position:0% +tied up like this kneeling on the ground +and the camera's at some distance from + + align:start position:0% +and the camera's at some distance from + + + align:start position:0% +and the camera's at some distance from +him and moves toward him but it doesn't + + align:start position:0% +him and moves toward him but it doesn't + + + align:start position:0% +him and moves toward him but it doesn't +move toward him in a smooth uh uh + + align:start position:0% +move toward him in a smooth uh uh + + + align:start position:0% +move toward him in a smooth uh uh +tracking motion that is characteristic + + align:start position:0% +tracking motion that is characteristic + + + align:start position:0% +tracking motion that is characteristic +or Trucking motion characteristic of + + align:start position:0% +or Trucking motion characteristic of + + + align:start position:0% +or Trucking motion characteristic of +most films what it does is it moves + + align:start position:0% +most films what it does is it moves + + + align:start position:0% +most films what it does is it moves +forward and it stops and then it jumps + + align:start position:0% +forward and it stops and then it jumps + + + align:start position:0% +forward and it stops and then it jumps +it moves forward and then it and what + + align:start position:0% +it moves forward and then it and what + + + align:start position:0% +it moves forward and then it and what +you feel is it it leaps forward I and + + align:start position:0% +you feel is it it leaps forward I and + + + align:start position:0% +you feel is it it leaps forward I and +what what's happening of course is that + + align:start position:0% +what what's happening of course is that + + + align:start position:0% +what what's happening of course is that +he stops the camera's forward movement + + align:start position:0% +he stops the camera's forward movement + + + align:start position:0% +he stops the camera's forward movement +moves it further makes a cut so that + + align:start position:0% +moves it further makes a cut so that + + + align:start position:0% +moves it further makes a cut so that +what you so the effect is the camera + + align:start position:0% +what you so the effect is the camera + + + align:start position:0% +what you so the effect is the camera +moves like not that the camera is jerky + + align:start position:0% +moves like not that the camera is jerky + + + align:start position:0% +moves like not that the camera is jerky +but but it's it's it's as if it's it's + + align:start position:0% +but but it's it's it's as if it's it's + + + align:start position:0% +but but it's it's it's as if it's it's +as if it's speed it up in some sense uh + + align:start position:0% +as if it's speed it up in some sense uh + + + align:start position:0% +as if it's speed it up in some sense uh +we can feel that the camera is becoming + + align:start position:0% +we can feel that the camera is becoming + + + align:start position:0% +we can feel that the camera is becoming +elliptical so say this fellow in the + + align:start position:0% +elliptical so say this fellow in the + + + align:start position:0% +elliptical so say this fellow in the +front is the person I'm focusing on I'll + + align:start position:0% +front is the person I'm focusing on I'll + + + align:start position:0% +front is the person I'm focusing on I'll +be here that you'll see this shot then + + align:start position:0% +be here that you'll see this shot then + + + align:start position:0% +be here that you'll see this shot then +you'll make two minut then you'll see + + align:start position:0% +you'll make two minut then you'll see + + + align:start position:0% +you'll make two minut then you'll see +this shot and you'll and the effect is + + align:start position:0% +this shot and you'll and the effect is + + + align:start position:0% +this shot and you'll and the effect is +very abrupt and you watch how it happens + + align:start position:0% +very abrupt and you watch how it happens + + + align:start position:0% +very abrupt and you watch how it happens +so one Effect one one consequence of + + align:start position:0% +so one Effect one one consequence of + + + align:start position:0% +so one Effect one one consequence of +this kind of a shot uh is that you + + align:start position:0% +this kind of a shot uh is that you + + + align:start position:0% +this kind of a shot uh is that you +watching it you can feel how mechanical + + align:start position:0% +watching it you can feel how mechanical + + + align:start position:0% +watching it you can feel how mechanical +it is you you begin to think to yourself + + align:start position:0% +it is you you begin to think to yourself + + + align:start position:0% +it is you you begin to think to yourself +well how could that have been created + + align:start position:0% +well how could that have been created + + + align:start position:0% +well how could that have been created +you're aware of its mechanical qualities + + align:start position:0% +you're aware of its mechanical qualities + + + align:start position:0% +you're aware of its mechanical qualities +that is to say you become partly aware + + align:start position:0% +that is to say you become partly aware + + + align:start position:0% +that is to say you become partly aware +of the apparatus behind the making of + + align:start position:0% +of the apparatus behind the making of + + + align:start position:0% +of the apparatus behind the making of +the movie it's a moment of + + align:start position:0% +the movie it's a moment of + + + align:start position:0% +the movie it's a moment of +self-consciousness that other elements + + align:start position:0% +self-consciousness that other elements + + + align:start position:0% +self-consciousness that other elements +on the film also + + align:start position:0% +on the film also + + + align:start position:0% +on the film also +reinforce um um so the visual style is + + align:start position:0% +reinforce um um so the visual style is + + + align:start position:0% +reinforce um um so the visual style is +profoundly eclectic and dynamic uh um + + align:start position:0% +profoundly eclectic and dynamic uh um + + + align:start position:0% +profoundly eclectic and dynamic uh um +I've mentioned the axial cut in pointing + + align:start position:0% +I've mentioned the axial cut in pointing + + + align:start position:0% +I've mentioned the axial cut in pointing +the camera at the sun maybe I'll mention + + align:start position:0% +the camera at the sun maybe I'll mention + + + align:start position:0% +the camera at the sun maybe I'll mention +one other device that he one of other uh + + align:start position:0% +one other device that he one of other uh + + + align:start position:0% +one other device that he one of other uh +uh technically intricate and and at the + + align:start position:0% +uh technically intricate and and at the + + + align:start position:0% +uh technically intricate and and at the +time revolutionary thing that kurasawa + + align:start position:0% +time revolutionary thing that kurasawa + + + align:start position:0% +time revolutionary thing that kurasawa +did was he violates What's called the + + align:start position:0% +did was he violates What's called the + + + align:start position:0% +did was he violates What's called the +180 degree Rule and the 180 degree rule + + align:start position:0% +180 degree Rule and the 180 degree rule + + + align:start position:0% +180 degree Rule and the 180 degree rule +essentially has to do with the your + + align:start position:0% +essentially has to do with the your + + + align:start position:0% +essentially has to do with the your +sense of spatial orientation in a within + + align:start position:0% +sense of spatial orientation in a within + + + align:start position:0% +sense of spatial orientation in a within +the frame right essentially the 180 + + align:start position:0% +the frame right essentially the 180 + + + align:start position:0% +the frame right essentially the 180 +degree rule holds that if you're showing + + align:start position:0% +degree rule holds that if you're showing + + + align:start position:0% +degree rule holds that if you're showing +characters moving in this direction + + align:start position:0% +characters moving in this direction + + + align:start position:0% +characters moving in this direction +right uh uh you're showing a character + + align:start position:0% +right uh uh you're showing a character + + + align:start position:0% +right uh uh you're showing a character +moving this way you won't suddenly if + + align:start position:0% +moving this way you won't suddenly if + + + align:start position:0% +moving this way you won't suddenly if +he's still going in the same direction + + align:start position:0% +he's still going in the same direction + + + align:start position:0% +he's still going in the same direction +show them walking this way because it + + align:start position:0% +show them walking this way because it + + + align:start position:0% +show them walking this way because it +disorients the viewer right so that if + + align:start position:0% +disorients the viewer right so that if + + + align:start position:0% +disorients the viewer right so that if +but + + align:start position:0% +but + + + align:start position:0% +but +what in in in our film in in in rashan + + align:start position:0% +what in in in our film in in in rashan + + + align:start position:0% +what in in in our film in in in rashan +there are certain moments there are + + align:start position:0% +there are certain moments there are + + + align:start position:0% +there are certain moments there are +hints of it in that opening sequence + + align:start position:0% +hints of it in that opening sequence + + + align:start position:0% +hints of it in that opening sequence +that lyrical first sequence in the + + align:start position:0% +that lyrical first sequence in the + + + align:start position:0% +that lyrical first sequence in the +forest that I've mentioned in which you + + align:start position:0% +forest that I've mentioned in which you + + + align:start position:0% +forest that I've mentioned in which you +in which you can see that the camera's + + align:start position:0% +in which you can see that the camera's + + + align:start position:0% +in which you can see that the camera's +own movements uh uh complicate and in + + align:start position:0% +own movements uh uh complicate and in + + + align:start position:0% +own movements uh uh complicate and in +some sense confuse our sense of where + + align:start position:0% +some sense confuse our sense of where + + + align:start position:0% +some sense confuse our sense of where +the wood cutter is going and and and uh + + align:start position:0% +the wood cutter is going and and and uh + + + align:start position:0% +the wood cutter is going and and and uh +it's in that sequence and some other + + align:start position:0% +it's in that sequence and some other + + + align:start position:0% +it's in that sequence and some other +places in the film as well where the 100 + + align:start position:0% +places in the film as well where the 100 + + + align:start position:0% +places in the film as well where the 100 +degree rule is violated and the effect + + align:start position:0% +degree rule is violated and the effect + + + align:start position:0% +degree rule is violated and the effect +again is to disorient us is to feel gee + + align:start position:0% +again is to disorient us is to feel gee + + + align:start position:0% +again is to disorient us is to feel gee +uh I don't know whether I'm coming or + + align:start position:0% +uh I don't know whether I'm coming or + + + align:start position:0% +uh I don't know whether I'm coming or +going this guy doesn't know whether he's + + align:start position:0% +going this guy doesn't know whether he's + + + align:start position:0% +going this guy doesn't know whether he's +coming or going what kind of a space is + + align:start position:0% +coming or going what kind of a space is + + + align:start position:0% +coming or going what kind of a space is +he in again violating certain + + align:start position:0% +he in again violating certain + + + align:start position:0% +he in again violating certain +conventions of traditional film making + + align:start position:0% +conventions of traditional film making + + + align:start position:0% +conventions of traditional film making +in order to create new effects so it's a + + align:start position:0% +in order to create new effects so it's a + + + align:start position:0% +in order to create new effects so it's a +and the the the uh consequence of these + + align:start position:0% +and the the the uh consequence of these + + + align:start position:0% +and the the the uh consequence of these +choices of the impact of these choices + + align:start position:0% +choices of the impact of these choices + + + align:start position:0% +choices of the impact of these choices +in 1951 when the film won its prize was + + align:start position:0% +in 1951 when the film won its prize was + + + align:start position:0% +in 1951 when the film won its prize was +profound + + align:start position:0% +profound + + + align:start position:0% +profound +um I want to say one other thing about + + align:start position:0% +um I want to say one other thing about + + + align:start position:0% +um I want to say one other thing about +uh uh another aspect of the film's + + align:start position:0% +uh uh another aspect of the film's + + + align:start position:0% +uh uh another aspect of the film's +structure which I've described + + align:start position:0% +structure which I've described + + + align:start position:0% +structure which I've described +imperfectly and I apologize for being so + + align:start position:0% +imperfectly and I apologize for being so + + + align:start position:0% +imperfectly and I apologize for being so +Tongue Tied about it but as I tried to + + align:start position:0% +Tongue Tied about it but as I tried to + + + align:start position:0% +Tongue Tied about it but as I tried to +describe earlier the basic structure of + + align:start position:0% +describe earlier the basic structure of + + + align:start position:0% +describe earlier the basic structure of +the film becomes fairly clear what + + align:start position:0% +the film becomes fairly clear what + + + align:start position:0% +the film becomes fairly clear what +happens is you get testimony then there + + align:start position:0% +happens is you get testimony then there + + + align:start position:0% +happens is you get testimony then there +are interruptions in which you + + align:start position:0% +are interruptions in which you + + + align:start position:0% +are interruptions in which you +essentially all four of the primary + + align:start position:0% +essentially all four of the primary + + + align:start position:0% +essentially all four of the primary +pieces of testimony take place in the + + align:start position:0% +pieces of testimony take place in the + + + align:start position:0% +pieces of testimony take place in the +past right uh so they're so what we have + + align:start position:0% +past right uh so they're so what we have + + + align:start position:0% +past right uh so they're so what we have +are flashbacks but competing flashbacks + + align:start position:0% +are flashbacks but competing flashbacks + + + align:start position:0% +are flashbacks but competing flashbacks +and at various points the film returns + + align:start position:0% +and at various points the film returns + + + align:start position:0% +and at various points the film returns +to our scene of rain at rasham man gate + + align:start position:0% +to our scene of rain at rasham man gate + + + align:start position:0% +to our scene of rain at rasham man gate +in which the people under the gate the + + align:start position:0% +in which the people under the gate the + + + align:start position:0% +in which the people under the gate the +three people under the gate two of them + + align:start position:0% +three people under the gate two of them + + + align:start position:0% +three people under the gate two of them +are actually partial participants uh the + + align:start position:0% +are actually partial participants uh the + + + align:start position:0% +are actually partial participants uh the +third the commoner is just a kind of + + align:start position:0% +third the commoner is just a kind of + + + align:start position:0% +third the commoner is just a kind of +listener to the story although a + + align:start position:0% +listener to the story although a + + + align:start position:0% +listener to the story although a +profound commentator on it right the + + align:start position:0% +profound commentator on it right the + + + align:start position:0% +profound commentator on it right the +Sano pona type who's who says look the + + align:start position:0% +Sano pona type who's who says look the + + + align:start position:0% +Sano pona type who's who says look the +world is miserable why should you why + + align:start position:0% +world is miserable why should you why + + + align:start position:0% +world is miserable why should you why +should you believe anyone and the priest + + align:start position:0% +should you believe anyone and the priest + + + align:start position:0% +should you believe anyone and the priest +is constantly resisting him well when we + + align:start position:0% +is constantly resisting him well when we + + + align:start position:0% +is constantly resisting him well when we +return to these moments so so we return + + align:start position:0% +return to these moments so so we return + + + align:start position:0% +return to these moments so so we return +to rashan gate several times many times + + align:start position:0% +to rashan gate several times many times + + + align:start position:0% +to rashan gate several times many times +in the film and every time we return to + + align:start position:0% +in the film and every time we return to + + + align:start position:0% +in the film and every time we return to +that spot where are we we're in the + + align:start position:0% +that spot where are we we're in the + + + align:start position:0% +that spot where are we we're in the +present time of the film so one of the + + align:start position:0% +present time of the film so one of the + + + align:start position:0% +present time of the film so one of the +things the film does it creates what I + + align:start position:0% +things the film does it creates what I + + + align:start position:0% +things the film does it creates what I +call a drama of the telling of the story + + align:start position:0% +call a drama of the telling of the story + + + align:start position:0% +call a drama of the telling of the story +in which the conversation that's going + + align:start position:0% +in which the conversation that's going + + + align:start position:0% +in which the conversation that's going +on in underneath rashan gate is a kind + + align:start position:0% +on in underneath rashan gate is a kind + + + align:start position:0% +on in underneath rashan gate is a kind +of meta commentary on the story that + + align:start position:0% +of meta commentary on the story that + + + align:start position:0% +of meta commentary on the story that +we're we're watching right the + + align:start position:0% +we're we're watching right the + + + align:start position:0% +we're we're watching right the +characters inside the film comment on + + align:start position:0% +characters inside the film comment on + + + align:start position:0% +characters inside the film comment on +well can we believe her is this credible + + align:start position:0% +well can we believe her is this credible + + + align:start position:0% +well can we believe her is this credible +why did she say this right and the + + align:start position:0% +why did she say this right and the + + + align:start position:0% +why did she say this right and the +effect of this meta commentary is to + + align:start position:0% +effect of this meta commentary is to + + + align:start position:0% +effect of this meta commentary is to +create essentially a separate story + + align:start position:0% +create essentially a separate story + + + align:start position:0% +create essentially a separate story +what's the separate story it's a + + align:start position:0% +what's the separate story it's a + + + align:start position:0% +what's the separate story it's a +philosophic topic the topic is the + + align:start position:0% +philosophic topic the topic is the + + + align:start position:0% +philosophic topic the topic is the +telling of stories in other words this + + align:start position:0% +telling of stories in other words this + + + align:start position:0% +telling of stories in other words this +Interruption creates a new kind of moral + + align:start position:0% +Interruption creates a new kind of moral + + + align:start position:0% +Interruption creates a new kind of moral +and thematic complexity in the film + + align:start position:0% +and thematic complexity in the film + + + align:start position:0% +and thematic complexity in the film +something that's characteristic of the + + align:start position:0% +something that's characteristic of the + + + align:start position:0% +something that's characteristic of the +great novels and fiction works I + + align:start position:0% +great novels and fiction works I + + + align:start position:0% +great novels and fiction works I +mentioned earlier in our in the lecture + + align:start position:0% +mentioned earlier in our in the lecture + + + align:start position:0% +mentioned earlier in our in the lecture +that appeared at the turn of the 20th + + align:start position:0% +that appeared at the turn of the 20th + + + align:start position:0% +that appeared at the turn of the 20th +century what we have not only are the is + + align:start position:0% +century what we have not only are the is + + + align:start position:0% +century what we have not only are the is +the principle of unreliable narration + + align:start position:0% +the principle of unreliable narration + + + align:start position:0% +the principle of unreliable narration +being introduced and the principle of of + + align:start position:0% +being introduced and the principle of of + + + align:start position:0% +being introduced and the principle of of +competing flashbacks being introduced + + align:start position:0% +competing flashbacks being introduced + + + align:start position:0% +competing flashbacks being introduced +and the principle of dislocated + + align:start position:0% +and the principle of dislocated + + + align:start position:0% +and the principle of dislocated +chronology being introduced all of those + + align:start position:0% +chronology being introduced all of those + + + align:start position:0% +chronology being introduced all of those +things are operating but what is even + + align:start position:0% +things are operating but what is even + + + align:start position:0% +things are operating but what is even +more important about it is that this Mo + + align:start position:0% +more important about it is that this Mo + + + align:start position:0% +more important about it is that this Mo +these moments of conversation amongst + + align:start position:0% +these moments of conversation amongst + + + align:start position:0% +these moments of conversation amongst +this those three characters at rashim + + align:start position:0% +this those three characters at rashim + + + align:start position:0% +this those three characters at rashim +mon gate also constitute a kind of + + align:start position:0% +mon gate also constitute a kind of + + + align:start position:0% +mon gate also constitute a kind of +philosophic meditation on the nature of + + align:start position:0% +philosophic meditation on the nature of + + + align:start position:0% +philosophic meditation on the nature of +Storytelling and on the nature of truth + + align:start position:0% +Storytelling and on the nature of truth + + + align:start position:0% +Storytelling and on the nature of truth +right and they actually say oh how can + + align:start position:0% +right and they actually say oh how can + + + align:start position:0% +right and they actually say oh how can +you believe a person or what is truth + + align:start position:0% +you believe a person or what is truth + + + align:start position:0% +you believe a person or what is truth +how can we believe what anybody says so + + align:start position:0% +how can we believe what anybody says so + + + align:start position:0% +how can we believe what anybody says so +the the so the film calls attention not + + align:start position:0% +the the so the film calls attention not + + + align:start position:0% +the the so the film calls attention not +only to the profound subjectivity of + + align:start position:0% +only to the profound subjectivity of + + + align:start position:0% +only to the profound subjectivity of +human responses and the profoundly + + align:start position:0% +human responses and the profoundly + + + align:start position:0% +human responses and the profoundly +unreliable nature of memory right uh but + + align:start position:0% +unreliable nature of memory right uh but + + + align:start position:0% +unreliable nature of memory right uh but +also the extent to which individuals + + align:start position:0% +also the extent to which individuals + + + align:start position:0% +also the extent to which individuals +themselves have reasons developing from + + align:start position:0% +themselves have reasons developing from + + + align:start position:0% +themselves have reasons developing from +their egos right to to distort and tell + + align:start position:0% +their egos right to to distort and tell + + + align:start position:0% +their egos right to to distort and tell +stories that are more flattering to + + align:start position:0% +stories that are more flattering to + + + align:start position:0% +stories that are more flattering to +themselves right and so that by the time + + align:start position:0% +themselves right and so that by the time + + + align:start position:0% +themselves right and so that by the time +we come to the end of the film it isn't + + align:start position:0% +we come to the end of the film it isn't + + + align:start position:0% +we come to the end of the film it isn't +clear at all when the film is over + + align:start position:0% +clear at all when the film is over + + + align:start position:0% +clear at all when the film is over +whether there is a truth that whether + + align:start position:0% +whether there is a truth that whether + + + align:start position:0% +whether there is a truth that whether +there is any final truth that we can + + align:start position:0% +there is any final truth that we can + + + align:start position:0% +there is any final truth that we can +Embrace uh the the issues are not + + align:start position:0% +Embrace uh the the issues are not + + + align:start position:0% +Embrace uh the the issues are not +finally resolved but what is resolved + + align:start position:0% +finally resolved but what is resolved + + + align:start position:0% +finally resolved but what is resolved +for us is the idea that human reality is + + align:start position:0% +for us is the idea that human reality is + + + align:start position:0% +for us is the idea that human reality is +immensely complex that that human beings + + align:start position:0% +immensely complex that that human beings + + + align:start position:0% +immensely complex that that human beings +are endlessly + + align:start position:0% +are endlessly + + + align:start position:0% +are endlessly +deceitful that that the stories they + + align:start position:0% +deceitful that that the stories they + + + align:start position:0% +deceitful that that the stories they +tell about themselves and others may not + + align:start position:0% +tell about themselves and others may not + + + align:start position:0% +tell about themselves and others may not +be trustworthy so that in other words + + align:start position:0% +be trustworthy so that in other words + + + align:start position:0% +be trustworthy so that in other words +the the the film opens out into a kind + + align:start position:0% +the the the film opens out into a kind + + + align:start position:0% +the the the film opens out into a kind +of philosophic profundity that's partly + + align:start position:0% +of philosophic profundity that's partly + + + align:start position:0% +of philosophic profundity that's partly +a function of its structure so it's + + align:start position:0% +a function of its structure so it's + + + align:start position:0% +a function of its structure so it's +another example one of the most + + align:start position:0% +another example one of the most + + + align:start position:0% +another example one of the most +remarkable examples that we've seen in + + align:start position:0% +remarkable examples that we've seen in + + + align:start position:0% +remarkable examples that we've seen in +our course of what I call organic form + + align:start position:0% +our course of what I call organic form + + + align:start position:0% +our course of what I call organic form +of a of a film who of a of a of a text + + align:start position:0% +of a of a film who of a of a of a text + + + align:start position:0% +of a of a film who of a of a of a text +whose whose structure helps us + + align:start position:0% +whose whose structure helps us + + + align:start position:0% +whose whose structure helps us +understand what it's about and whose + + align:start position:0% +understand what it's about and whose + + + align:start position:0% +understand what it's about and whose +structure is part of what it means whose + + align:start position:0% +structure is part of what it means whose + + + align:start position:0% +structure is part of what it means whose +structure is essential to its meaning we + + align:start position:0% +structure is essential to its meaning we + + + align:start position:0% +structure is essential to its meaning we +couldn't imagine this film as a + + align:start position:0% +couldn't imagine this film as a + + + align:start position:0% +couldn't imagine this film as a +straightforward chronological sequence + + align:start position:0% +straightforward chronological sequence + + + align:start position:0% +straightforward chronological sequence +it wouldn't be it wouldn't be able to do + + align:start position:0% +it wouldn't be it wouldn't be able to do + + + align:start position:0% +it wouldn't be it wouldn't be able to do +what it does so this so what I what I + + align:start position:0% +what it does so this so what I what I + + + align:start position:0% +what it does so this so what I what I +mean by the drama of the telling of the + + align:start position:0% +mean by the drama of the telling of the + + + align:start position:0% +mean by the drama of the telling of the +story is literally that that to say + + align:start position:0% +story is literally that that to say + + + align:start position:0% +story is literally that that to say +there's a second story that a second + + align:start position:0% +there's a second story that a second + + + align:start position:0% +there's a second story that a second +subject matter in these interlude let's + + align:start position:0% +subject matter in these interlude let's + + + align:start position:0% +subject matter in these interlude let's +call them interludes in these + + align:start position:0% +call them interludes in these + + + align:start position:0% +call them interludes in these +interruptions in which we return to the + + align:start position:0% +interruptions in which we return to the + + + align:start position:0% +interruptions in which we return to the +present time get out of the past and + + align:start position:0% +present time get out of the past and + + + align:start position:0% +present time get out of the past and +those those interludes are a an extended + + align:start position:0% +those those interludes are a an extended + + + align:start position:0% +those those interludes are a an extended +philosophic and moral conversation about + + align:start position:0% +philosophic and moral conversation about + + + align:start position:0% +philosophic and moral conversation about +human nature about the nature of the + + align:start position:0% +human nature about the nature of the + + + align:start position:0% +human nature about the nature of the +human of of our human capacity to + + align:start position:0% +human of of our human capacity to + + + align:start position:0% +human of of our human capacity to +understand the + + align:start position:0% +understand the + + + align:start position:0% +understand the +world and and and our capacity to talk + + align:start position:0% +world and and and our capacity to talk + + + align:start position:0% +world and and and our capacity to talk +about it to narrate it accurately L and + + align:start position:0% +about it to narrate it accurately L and + + + align:start position:0% +about it to narrate it accurately L and +fully so this drama of the telling of + + align:start position:0% +fully so this drama of the telling of + + + align:start position:0% +fully so this drama of the telling of +the story this drama of the screening + + align:start position:0% +the story this drama of the screening + + + align:start position:0% +the story this drama of the screening +this drama of the making of the story is + + align:start position:0% +this drama of the making of the story is + + + align:start position:0% +this drama of the making of the story is +as important a dimension of the film as + + align:start position:0% +as important a dimension of the film as + + + align:start position:0% +as important a dimension of the film as +its actual story uh as the actual uh + + align:start position:0% +its actual story uh as the actual uh + + + align:start position:0% +its actual story uh as the actual uh +story that it wants to + + align:start position:0% + + + + align:start position:0% + +tell I have two other points to make + + align:start position:0% +tell I have two other points to make + + + align:start position:0% +tell I have two other points to make +about this remarkable film and I'll be + + align:start position:0% +about this remarkable film and I'll be + + + align:start position:0% +about this remarkable film and I'll be +done the first is that one of the things + + align:start position:0% +done the first is that one of the things + + + align:start position:0% +done the first is that one of the things +I think you'll notice uh as The Story + + align:start position:0% +I think you'll notice uh as The Story + + + align:start position:0% +I think you'll notice uh as The Story +Goes On And as different different + + align:start position:0% +Goes On And as different different + + + align:start position:0% +Goes On And as different different +people give different accounts of what + + align:start position:0% +people give different accounts of what + + + align:start position:0% +people give different accounts of what +happened + + align:start position:0% +happened + + + align:start position:0% +happened +is that the actual + + align:start position:0% +is that the actual + + + align:start position:0% +is that the actual +physical conflict between the two male + + align:start position:0% +physical conflict between the two male + + + align:start position:0% +physical conflict between the two male +characters uh uh which one would expect + + align:start position:0% +characters uh uh which one would expect + + + align:start position:0% +characters uh uh which one would expect +to be grand and heroic is almost always + + align:start position:0% +to be grand and heroic is almost always + + + align:start position:0% +to be grand and heroic is almost always +clownish and + + align:start position:0% +clownish and + + + align:start position:0% +clownish and +unheroic we expect this great he's a + + align:start position:0% +unheroic we expect this great he's a + + + align:start position:0% +unheroic we expect this great he's a +samurai warrior after all and the man + + align:start position:0% +samurai warrior after all and the man + + + align:start position:0% +samurai warrior after all and the man +he's doing battle with is a very famous + + align:start position:0% +he's doing battle with is a very famous + + + align:start position:0% +he's doing battle with is a very famous +uh or inFAMOUS uh Bandit criminal uh so + + align:start position:0% +uh or inFAMOUS uh Bandit criminal uh so + + + align:start position:0% +uh or inFAMOUS uh Bandit criminal uh so +gifted a criminal that he that he's + + align:start position:0% +gifted a criminal that he that he's + + + align:start position:0% +gifted a criminal that he that he's +famous right uh uh and yet in their and + + align:start position:0% +famous right uh uh and yet in their and + + + align:start position:0% +famous right uh uh and yet in their and +and both uh one one one realizes in + + align:start position:0% +and both uh one one one realizes in + + + align:start position:0% +and both uh one one one realizes in +retrospect that when the criminal the T + + align:start position:0% +retrospect that when the criminal the T + + + align:start position:0% +retrospect that when the criminal the T +toshiro maoni character gives his gives + + align:start position:0% +toshiro maoni character gives his gives + + + align:start position:0% +toshiro maoni character gives his gives +his testimony in the beginning of the uh + + align:start position:0% +his testimony in the beginning of the uh + + + align:start position:0% +his testimony in the beginning of the uh +in the early part of the film uh he's + + align:start position:0% +in the early part of the film uh he's + + + align:start position:0% +in the early part of the film uh he's +exaggerating his own his own Marshal + + align:start position:0% +exaggerating his own his own Marshal + + + align:start position:0% +exaggerating his own his own Marshal +genius although we don't fully realize + + align:start position:0% +genius although we don't fully realize + + + align:start position:0% +genius although we don't fully realize +that at first but it becomes clearer and + + align:start position:0% +that at first but it becomes clearer and + + + align:start position:0% +that at first but it becomes clearer and +clearer to us as the film goes on that + + align:start position:0% +clearer to us as the film goes on that + + + align:start position:0% +clearer to us as the film goes on that +he has a motive to sort of exaggerate + + align:start position:0% +he has a motive to sort of exaggerate + + + align:start position:0% +he has a motive to sort of exaggerate +his heroic stature and his strength and + + align:start position:0% +his heroic stature and his strength and + + + align:start position:0% +his heroic stature and his strength and +so forth not to mention a motive to ex + + align:start position:0% +so forth not to mention a motive to ex + + + align:start position:0% +so forth not to mention a motive to ex +exaggerate and maybe to lie about the + + align:start position:0% +exaggerate and maybe to lie about the + + + align:start position:0% +exaggerate and maybe to lie about the +woman's reaction to his to his forced + + align:start position:0% +woman's reaction to his to his forced + + + align:start position:0% +woman's reaction to his to his forced +attentions um um so + + align:start position:0% +attentions um um so + + + align:start position:0% +attentions um um so +so so all of that is uh is is is is is + + align:start position:0% +so so all of that is uh is is is is is + + + align:start position:0% +so so all of that is uh is is is is is +is is a a central part of of our of our + + align:start position:0% +is is a a central part of of our of our + + + align:start position:0% +is is a a central part of of our of our +of our understanding of what of what is + + align:start position:0% +of our understanding of what of what is + + + align:start position:0% +of our understanding of what of what is +at this U uh of what is at stake I guess + + align:start position:0% +at this U uh of what is at stake I guess + + + align:start position:0% +at this U uh of what is at stake I guess +uh when when we think about the the + + align:start position:0% +uh when when we think about the the + + + align:start position:0% +uh when when we think about the the +subject that rasham the various subjects + + align:start position:0% +subject that rasham the various subjects + + + align:start position:0% +subject that rasham the various subjects +that rashan gestures toward uh + + align:start position:0% +that rashan gestures toward uh + + + align:start position:0% +that rashan gestures toward uh +so if the clownish unheroic behavior of + + align:start position:0% +so if the clownish unheroic behavior of + + + align:start position:0% +so if the clownish unheroic behavior of +these Fighters is something to note + + align:start position:0% +these Fighters is something to note + + + align:start position:0% +these Fighters is something to note +because there's a deep skepticism in the + + align:start position:0% +because there's a deep skepticism in the + + + align:start position:0% +because there's a deep skepticism in the +film itself about uh uh about all forms + + align:start position:0% +film itself about uh uh about all forms + + + align:start position:0% +film itself about uh uh about all forms +of a grand of human aggrandisement + + align:start position:0% +of a grand of human aggrandisement + + + align:start position:0% +of a grand of human aggrandisement +there's a there's a skepticism that the + + align:start position:0% +there's a there's a skepticism that the + + + align:start position:0% +there's a there's a skepticism that the +film shares with the commoner who said + + align:start position:0% +film shares with the commoner who said + + + align:start position:0% +film shares with the commoner who said +who who maybe is too negative about + + align:start position:0% +who who maybe is too negative about + + + align:start position:0% +who who maybe is too negative about +human nature who thinks human human + + align:start position:0% +human nature who thinks human human + + + align:start position:0% +human nature who thinks human human +beings are completely AB object and that + + align:start position:0% +beings are completely AB object and that + + + align:start position:0% +beings are completely AB object and that +uh this is a justification for the most + + align:start position:0% +uh this is a justification for the most + + + align:start position:0% +uh this is a justification for the most +selfish kind of behavior because no one + + align:start position:0% +selfish kind of behavior because no one + + + align:start position:0% +selfish kind of behavior because no one +can behave well all right uh I I I I + + align:start position:0% +can behave well all right uh I I I I + + + align:start position:0% +can behave well all right uh I I I I +have hardly exhausted the film but I + + align:start position:0% +have hardly exhausted the film but I + + + align:start position:0% +have hardly exhausted the film but I +hope I've said some things that will be + + align:start position:0% +hope I've said some things that will be + + + align:start position:0% +hope I've said some things that will be +valuable and useful to you on your first + + align:start position:0% +valuable and useful to you on your first + + + align:start position:0% +valuable and useful to you on your first +viewing but let me end by talking about + + align:start position:0% +viewing but let me end by talking about + + + align:start position:0% +viewing but let me end by talking about +the ending because the ending of rashan + + align:start position:0% +the ending because the ending of rashan + + + align:start position:0% +the ending because the ending of rashan +presents us with a problem similar to + + align:start position:0% +presents us with a problem similar to + + + align:start position:0% +presents us with a problem similar to +the problem that we confronted in a film + + align:start position:0% +the problem that we confronted in a film + + + align:start position:0% +the problem that we confronted in a film +like uh uh the last laugh dman in which + + align:start position:0% +like uh uh the last laugh dman in which + + + align:start position:0% +like uh uh the last laugh dman in which +there seems to be a kind of optimis IC + + align:start position:0% +there seems to be a kind of optimis IC + + + align:start position:0% +there seems to be a kind of optimis IC +or or reassuring ending uh to the to to + + align:start position:0% +or or reassuring ending uh to the to to + + + align:start position:0% +or or reassuring ending uh to the to to +this film the film has been very dark + + align:start position:0% +this film the film has been very dark + + + align:start position:0% +this film the film has been very dark +and rainy and in fact one of the ways + + align:start position:0% +and rainy and in fact one of the ways + + + align:start position:0% +and rainy and in fact one of the ways +you can tell that the film has changed + + align:start position:0% +you can tell that the film has changed + + + align:start position:0% +you can tell that the film has changed +registers is that the rain finally + + align:start position:0% +registers is that the rain finally + + + align:start position:0% +registers is that the rain finally +disappears uh well as you're watching + + align:start position:0% +disappears uh well as you're watching + + + align:start position:0% +disappears uh well as you're watching +the ending uh which which is quite + + align:start position:0% +the ending uh which which is quite + + + align:start position:0% +the ending uh which which is quite +explicit even heavy-handed about its + + align:start position:0% +explicit even heavy-handed about its + + + align:start position:0% +explicit even heavy-handed about its +attempt to return us to a sort of more + + align:start position:0% +attempt to return us to a sort of more + + + align:start position:0% +attempt to return us to a sort of more +hopeful view of mankind uh you should + + align:start position:0% +hopeful view of mankind uh you should + + + align:start position:0% +hopeful view of mankind uh you should +ask yourself does it deserve to be + + align:start position:0% +ask yourself does it deserve to be + + + align:start position:0% +ask yourself does it deserve to be +deleted uh all through the 40s when + + align:start position:0% +deleted uh all through the 40s when + + + align:start position:0% +deleted uh all through the 40s when +kurasa was first learning his trade he + + align:start position:0% +kurasa was first learning his trade he + + + align:start position:0% +kurasa was first learning his trade he +began to direct early in the' 40s and he + + align:start position:0% +began to direct early in the' 40s and he + + + align:start position:0% +began to direct early in the' 40s and he +directed this film in 1950 is his is his + + align:start position:0% +directed this film in 1950 is his is his + + + align:start position:0% +directed this film in 1950 is his is his +first real Masterwork uh he'd become + + align:start position:0% +first real Masterwork uh he'd become + + + align:start position:0% +first real Masterwork uh he'd become +more and more confident and ambitious as + + align:start position:0% +more and more confident and ambitious as + + + align:start position:0% +more and more confident and ambitious as +a director during this period uh uh but + + align:start position:0% +a director during this period uh uh but + + + align:start position:0% +a director during this period uh uh but +he hadn't sort of displayed his full + + align:start position:0% +he hadn't sort of displayed his full + + + align:start position:0% +he hadn't sort of displayed his full +capacities as a director until this + + align:start position:0% +capacities as a director until this + + + align:start position:0% +capacities as a director until this +point most accounts of his career + + align:start position:0% +point most accounts of his career + + + align:start position:0% +point most accounts of his career +suggest uh but during this period in in + + align:start position:0% +suggest uh but during this period in in + + + align:start position:0% +suggest uh but during this period in in +the in the uh 1940s kurasawa took up on + + align:start position:0% +the in the uh 1940s kurasawa took up on + + + align:start position:0% +the in the uh 1940s kurasawa took up on +himself what he regarded as a social + + align:start position:0% +himself what he regarded as a social + + + align:start position:0% +himself what he regarded as a social +project which was to try to help + + align:start position:0% +project which was to try to help + + + align:start position:0% +project which was to try to help +renovate Japan after the devastations of + + align:start position:0% +renovate Japan after the devastations of + + + align:start position:0% +renovate Japan after the devastations of +the war and his films of the 40s almost + + align:start position:0% +the war and his films of the 40s almost + + + align:start position:0% +the war and his films of the 40s almost +always tried to suggest various forms of + + align:start position:0% +always tried to suggest various forms of + + + align:start position:0% +always tried to suggest various forms of +uh various ways in which people could + + align:start position:0% +uh various ways in which people could + + + align:start position:0% +uh various ways in which people could +behave decently and heroically uh not + + align:start position:0% +behave decently and heroically uh not + + + align:start position:0% +behave decently and heroically uh not +decent not heroically at least decent + + align:start position:0% +decent not heroically at least decent + + + align:start position:0% +decent not heroically at least decent +decently in an effort to sort of + + align:start position:0% +decently in an effort to sort of + + + align:start position:0% +decently in an effort to sort of +renovate and re reconstitute a damaged + + align:start position:0% +renovate and re reconstitute a damaged + + + align:start position:0% +renovate and re reconstitute a damaged +Society a broken Society one of the + + align:start position:0% +Society a broken Society one of the + + + align:start position:0% +Society a broken Society one of the +reasons that the that the breakdown of + + align:start position:0% +reasons that the that the breakdown of + + + align:start position:0% +reasons that the that the breakdown of +ancient Japan uh is so powerful in + + align:start position:0% +ancient Japan uh is so powerful in + + + align:start position:0% +ancient Japan uh is so powerful in +rashan is that no question that uh is + + align:start position:0% +rashan is that no question that uh is + + + align:start position:0% +rashan is that no question that uh is +that kurasawa and his and his cast + + align:start position:0% +that kurasawa and his and his cast + + + align:start position:0% +that kurasawa and his and his cast +believed that in some sense there was a + + align:start position:0% +believed that in some sense there was a + + + align:start position:0% +believed that in some sense there was a +symbolic analogy to be made between + + align:start position:0% +symbolic analogy to be made between + + + align:start position:0% +symbolic analogy to be made between +conditions in Japan in actual Japan in + + align:start position:0% +conditions in Japan in actual Japan in + + + align:start position:0% +conditions in Japan in actual Japan in +19 in the 1940s and early 50s and the + + align:start position:0% +19 in the 1940s and early 50s and the + + + align:start position:0% +19 in the 1940s and early 50s and the +broken terrifying conditions of society + + align:start position:0% +broken terrifying conditions of society + + + align:start position:0% +broken terrifying conditions of society +in the in the 11th and 12th + + align:start position:0% +in the in the 11th and 12th + + + align:start position:0% +in the in the 11th and 12th +centuries uh in the past par Parable + + align:start position:0% +centuries uh in the past par Parable + + + align:start position:0% +centuries uh in the past par Parable +that the narrative is telling us and so + + align:start position:0% +that the narrative is telling us and so + + + align:start position:0% +that the narrative is telling us and so +and this film continues that tradition + + align:start position:0% +and this film continues that tradition + + + align:start position:0% +and this film continues that tradition +uh um but but I think I think many many + + align:start position:0% +uh um but but I think I think many many + + + align:start position:0% +uh um but but I think I think many many +viewers I among them have the feeling + + align:start position:0% +viewers I among them have the feeling + + + align:start position:0% +viewers I among them have the feeling +that that this is more wish fulfillment + + align:start position:0% +that that this is more wish fulfillment + + + align:start position:0% +that that this is more wish fulfillment +on kurosawa's part than reality and one + + align:start position:0% +on kurosawa's part than reality and one + + + align:start position:0% +on kurosawa's part than reality and one +could say from an artistic standpoint + + align:start position:0% +could say from an artistic standpoint + + + align:start position:0% +could say from an artistic standpoint +then one might conclude that it's a + + align:start position:0% +then one might conclude that it's a + + + align:start position:0% +then one might conclude that it's a +weakness in the film I think I might say + + align:start position:0% +weakness in the film I think I might say + + + align:start position:0% +weakness in the film I think I might say +that uh that the film might be more + + align:start position:0% +that uh that the film might be more + + + align:start position:0% +that uh that the film might be more +powerful more truthful to itself that it + + align:start position:0% +powerful more truthful to itself that it + + + align:start position:0% +powerful more truthful to itself that it +may that that that the ending that that + + align:start position:0% +may that that that the ending that that + + + align:start position:0% +may that that that the ending that that +the ending that's tacked on May + + align:start position:0% +the ending that's tacked on May + + + align:start position:0% +the ending that's tacked on May +undermine its uh deepest energies uh in + + align:start position:0% +undermine its uh deepest energies uh in + + + align:start position:0% +undermine its uh deepest energies uh in +in in disturbing ways so it's another + + align:start position:0% +in in disturbing ways so it's another + + + align:start position:0% +in in disturbing ways so it's another +example of a of of a uh in + + align:start position:0% +example of a of of a uh in + + + align:start position:0% +example of a of of a uh in +which commercial and social imperatives + + align:start position:0% +which commercial and social imperatives + + + align:start position:0% +which commercial and social imperatives +may be may be interfering with uh the + + align:start position:0% +may be may be interfering with uh the + + + align:start position:0% +may be may be interfering with uh the +Artistic integrity of the text uh but + + align:start position:0% +Artistic integrity of the text uh but + + + align:start position:0% +Artistic integrity of the text uh but +it's significant uh important to + + align:start position:0% +it's significant uh important to + + + align:start position:0% +it's significant uh important to +understand that this was a tendency that + + align:start position:0% +understand that this was a tendency that + + + align:start position:0% +understand that this was a tendency that +was present in Cora's work all the way + + align:start position:0% +was present in Cora's work all the way + + + align:start position:0% +was present in Cora's work all the way +through the 40s uh and that therefore + + align:start position:0% +through the 40s uh and that therefore + + + align:start position:0% +through the 40s uh and that therefore +it's a kind of expression of of a of a + + align:start position:0% +it's a kind of expression of of a of a + + + align:start position:0% +it's a kind of expression of of a of a +of a + + align:start position:0% +of a + + + align:start position:0% +of a +a of a moral sense that the director had + + align:start position:0% +a of a moral sense that the director had + + + align:start position:0% +a of a moral sense that the director had +that be that that that that begins to + + align:start position:0% +that be that that that that begins to + + + align:start position:0% +that be that that that that begins to +become less powerful after rashan and uh + + align:start position:0% +become less powerful after rashan and uh + + + align:start position:0% +become less powerful after rashan and uh +uh although although he remains a deeply + + align:start position:0% +uh although although he remains a deeply + + + align:start position:0% +uh although although he remains a deeply +moral director so the ending is a + + align:start position:0% +moral director so the ending is a + + + align:start position:0% +moral director so the ending is a +question and and you might want to ask + + align:start position:0% +question and and you might want to ask + + + align:start position:0% +question and and you might want to ask +yourself what uh how how how you would + + align:start position:0% +yourself what uh how how how you would + + + align:start position:0% +yourself what uh how how how you would +react how how you would respond to the + + align:start position:0% +react how how you would respond to the + + + align:start position:0% +react how how you would respond to the +question of the relevance of the of the + + align:start position:0% +question of the relevance of the of the + + + align:start position:0% +question of the relevance of the of the +uh ending to the rest to the rest of the + + align:start position:0% +uh ending to the rest to the rest of the + + + align:start position:0% +uh ending to the rest to the rest of the +film + + align:start position:0% +film + + + align:start position:0% +film +let me end with a a reminder about maybe + + align:start position:0% +let me end with a a reminder about maybe + + + align:start position:0% +let me end with a a reminder about maybe +what is in some ways the most uh + + align:start position:0% +what is in some ways the most uh + + + align:start position:0% +what is in some ways the most uh +powerful aspect of what happens when + + align:start position:0% +powerful aspect of what happens when + + + align:start position:0% +powerful aspect of what happens when +you're watching rashan I've said that + + align:start position:0% +you're watching rashan I've said that + + + align:start position:0% +you're watching rashan I've said that +you feel that you've entered into a kind + + align:start position:0% +you feel that you've entered into a kind + + + align:start position:0% +you feel that you've entered into a kind +of if not a dream into a kind of + + align:start position:0% +of if not a dream into a kind of + + + align:start position:0% +of if not a dream into a kind of +uniquely stylized space in which what + + align:start position:0% +uniquely stylized space in which what + + + align:start position:0% +uniquely stylized space in which what +happens resembles what happens in real + + align:start position:0% +happens resembles what happens in real + + + align:start position:0% +happens resembles what happens in real +life but is but but + + align:start position:0% +life but is but but + + + align:start position:0% +life but is but but +also distills what happens in real life + + align:start position:0% +also distills what happens in real life + + + align:start position:0% +also distills what happens in real life +highlights it in a way that isn't true + + align:start position:0% +highlights it in a way that isn't true + + + align:start position:0% +highlights it in a way that isn't true +of actual uality right and I think you + + align:start position:0% +of actual uality right and I think you + + + align:start position:0% +of actual uality right and I think you +feel this I think you feel this U um + + align:start position:0% +feel this I think you feel this U um + + + align:start position:0% +feel this I think you feel this U um +this Mythic tendency all the way all the + + align:start position:0% +this Mythic tendency all the way all the + + + align:start position:0% +this Mythic tendency all the way all the +way through the film + + align:start position:0% +way through the film + + + align:start position:0% +way through the film +uh it's what I'm in in a in a certain in + + align:start position:0% +uh it's what I'm in in a in a certain in + + + align:start position:0% +uh it's what I'm in in a in a certain in +a certain sense um uh uh it's a way one + + align:start position:0% +a certain sense um uh uh it's a way one + + + align:start position:0% +a certain sense um uh uh it's a way one +way one way of capturing what I'm saying + + align:start position:0% +way one way of capturing what I'm saying + + + align:start position:0% +way one way of capturing what I'm saying +is to say that there is a tension in the + + align:start position:0% +is to say that there is a tension in the + + + align:start position:0% +is to say that there is a tension in the +film between this impulse to be Mythic + + align:start position:0% +film between this impulse to be Mythic + + + align:start position:0% +film between this impulse to be Mythic +to tell a story that it understands to + + align:start position:0% +to tell a story that it understands to + + + align:start position:0% +to tell a story that it understands to +have a fable likee significance and its + + align:start position:0% +have a fable likee significance and its + + + align:start position:0% +have a fable likee significance and its +sense of the complex + + align:start position:0% +sense of the complex + + + align:start position:0% +sense of the complex +and and concreteness of actuality one + + align:start position:0% +and and concreteness of actuality one + + + align:start position:0% +and and concreteness of actuality one +that is to say so there's this wonderful + + align:start position:0% +that is to say so there's this wonderful + + + align:start position:0% +that is to say so there's this wonderful +constant tension in the film between the + + align:start position:0% +constant tension in the film between the + + + align:start position:0% +constant tension in the film between the +enormous persuasiveness of the + + align:start position:0% +enormous persuasiveness of the + + + align:start position:0% +enormous persuasiveness of the +individual images that you see but your + + align:start position:0% +individual images that you see but your + + + align:start position:0% +individual images that you see but your +sense also that you're in a world that's + + align:start position:0% +sense also that you're in a world that's + + + align:start position:0% +sense also that you're in a world that's +not totally real so this this the + + align:start position:0% +not totally real so this this the + + + align:start position:0% +not totally real so this this the +tension I'm trying to get you to feel + + align:start position:0% +tension I'm trying to get you to feel + + + align:start position:0% +tension I'm trying to get you to feel +you can feel it in the dialogue you can + + align:start position:0% +you can feel it in the dialogue you can + + + align:start position:0% +you can feel it in the dialogue you can +feel it but especially you can feel it + + align:start position:0% +feel it but especially you can feel it + + + align:start position:0% +feel it but especially you can feel it +in the visual images uh in the in the + + align:start position:0% +in the visual images uh in the in the + + + align:start position:0% +in the visual images uh in the in the +visual texture of the film you can feel + + align:start position:0% +visual texture of the film you can feel + + + align:start position:0% +visual texture of the film you can feel +a kind of tension between an Impulse to + + align:start position:0% +a kind of tension between an Impulse to + + + align:start position:0% +a kind of tension between an Impulse to +mythologize and to faize and an Impulse + + align:start position:0% +mythologize and to faize and an Impulse + + + align:start position:0% +mythologize and to faize and an Impulse +to show the world in its in its in its + + align:start position:0% +to show the world in its in its in its + + + align:start position:0% +to show the world in its in its in its +deepest and most concrete elements in + + align:start position:0% +deepest and most concrete elements in + + + align:start position:0% +deepest and most concrete elements in +its most in its most authentic actuality + + align:start position:0% +its most in its most authentic actuality + + + align:start position:0% +its most in its most authentic actuality +and the tension between the two gee this + + align:start position:0% +and the tension between the two gee this + + + align:start position:0% +and the tension between the two gee this +is so real gee this is so unreal this is + + align:start position:0% +is so real gee this is so unreal this is + + + align:start position:0% +is so real gee this is so unreal this is +so Fable likee uh is part of the secret + + align:start position:0% +so Fable likee uh is part of the secret + + + align:start position:0% +so Fable likee uh is part of the secret +of the movie and one way you can feel it + + align:start position:0% +of the movie and one way you can feel it + + + align:start position:0% +of the movie and one way you can feel it +with immensely intense power is + + align:start position:0% +with immensely intense power is + + + align:start position:0% +with immensely intense power is +sometimes when you see the way the film + + align:start position:0% +sometimes when you see the way the film + + + align:start position:0% +sometimes when you see the way the film +deals with human flesh there are certain + + align:start position:0% +deals with human flesh there are certain + + + align:start position:0% +deals with human flesh there are certain +scenes for example where a woman's hand + + align:start position:0% +scenes for example where a woman's hand + + + align:start position:0% +scenes for example where a woman's hand +will be on on a man's body right talk + + align:start position:0% +will be on on a man's body right talk + + + align:start position:0% +will be on on a man's body right talk +about what you how you can be erotic + + align:start position:0% +about what you how you can be erotic + + + align:start position:0% +about what you how you can be erotic +without without offending anyone there's + + align:start position:0% +without without offending anyone there's + + + align:start position:0% +without without offending anyone there's +a moment where you can see the woman's + + align:start position:0% +a moment where you can see the woman's + + + align:start position:0% +a moment where you can see the woman's +fingers pressing into the man's flesh + + align:start position:0% +fingers pressing into the man's flesh + + + align:start position:0% +fingers pressing into the man's flesh +right it's an immensely erotic and + + align:start position:0% +right it's an immensely erotic and + + + align:start position:0% +right it's an immensely erotic and +powerfully concretizing moment it + + align:start position:0% +powerfully concretizing moment it + + + align:start position:0% +powerfully concretizing moment it +reminds you of Flesh it reminds you of + + align:start position:0% +reminds you of Flesh it reminds you of + + + align:start position:0% +reminds you of Flesh it reminds you of +the act of of film's power to capture + + align:start position:0% +the act of of film's power to capture + + + align:start position:0% +the act of of film's power to capture +actuality with a vividness that goes far + + align:start position:0% +actuality with a vividness that goes far + + + align:start position:0% +actuality with a vividness that goes far +beyond what words could ever do right + + align:start position:0% +beyond what words could ever do right + + + align:start position:0% +beyond what words could ever do right +the visual power of moving and that's + + align:start position:0% +the visual power of moving and that's + + + align:start position:0% +the visual power of moving and that's +what I mean when I say that there's this + + align:start position:0% +what I mean when I say that there's this + + + align:start position:0% +what I mean when I say that there's this +constant tension in the F in the film + + align:start position:0% +constant tension in the F in the film + + + align:start position:0% +constant tension in the F in the film +between the mythologizing Tendencies of + + align:start position:0% +between the mythologizing Tendencies of + + + align:start position:0% +between the mythologizing Tendencies of +the story and of Cora's imagination and + + align:start position:0% +the story and of Cora's imagination and + + + align:start position:0% +the story and of Cora's imagination and +what we might call the breaking tendency + + align:start position:0% +what we might call the breaking tendency + + + align:start position:0% +what we might call the breaking tendency +the the the concretizing tendency uh of + + align:start position:0% +the the the concretizing tendency uh of + + + align:start position:0% +the the the concretizing tendency uh of +the of the of the film medium which + + align:start position:0% +the of the of the film medium which + + + align:start position:0% +the of the of the film medium which +which has this grow this capacity to + + align:start position:0% +which has this grow this capacity to + + + align:start position:0% +which has this grow this capacity to +register the gross concrete reality of + + align:start position:0% +register the gross concrete reality of + + + align:start position:0% +register the gross concrete reality of +our experiences with a detail and a + + align:start position:0% +our experiences with a detail and a + + + align:start position:0% +our experiences with a detail and a +power that no other medium can well this + + align:start position:0% +power that no other medium can well this + + + align:start position:0% +power that no other medium can well this +sense of tension between a story that + + align:start position:0% +sense of tension between a story that + + + align:start position:0% +sense of tension between a story that +wants to be a f and a story that wants + + align:start position:0% +wants to be a f and a story that wants + + + align:start position:0% +wants to be a f and a story that wants +to persuade you of its of its concrete + + align:start position:0% +to persuade you of its of its concrete + + + align:start position:0% +to persuade you of its of its concrete +reality is part of what makes the film + + align:start position:0% +reality is part of what makes the film + + + align:start position:0% +reality is part of what makes the film +so memorable and so and so + + align:start position:0% + + + + align:start position:0% + +significant \ No newline at end of file diff --git a/6Rq2VFCGQfE.txt b/6Rq2VFCGQfE.txt new file mode 100644 index 0000000000000000000000000000000000000000..d7e4a2cdd3d978a0b108948eb4f97e4d5bae3009 --- /dev/null +++ b/6Rq2VFCGQfE.txt @@ -0,0 +1,11891 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +talk a bit about the politics of + + align:start position:0% +talk a bit about the politics of + + + align:start position:0% +talk a bit about the politics of +regulation and a bit more about EPA and + + align:start position:0% +regulation and a bit more about EPA and + + + align:start position:0% +regulation and a bit more about EPA and +how it works and how it has worked just + + align:start position:0% +how it works and how it has worked just + + + align:start position:0% +how it works and how it has worked just +by way of why are we doing this in a + + align:start position:0% +by way of why are we doing this in a + + + align:start position:0% +by way of why are we doing this in a +course on energy policy an awful lot of + + align:start position:0% +course on energy policy an awful lot of + + + align:start position:0% +course on energy policy an awful lot of +energy policy is set by environmental + + align:start position:0% +energy policy is set by environmental + + + align:start position:0% +energy policy is set by environmental +regulation all the much of the + + align:start position:0% +regulation all the much of the + + + align:start position:0% +regulation all the much of the +discussion of doing co2 controls for + + align:start position:0% +discussion of doing co2 controls for + + + align:start position:0% +discussion of doing co2 controls for +climate change comes down to shaping + + align:start position:0% +climate change comes down to shaping + + + align:start position:0% +climate change comes down to shaping +energy policy so you really do need to + + align:start position:0% +energy policy so you really do need to + + + align:start position:0% +energy policy so you really do need to +think about the environmental regulation + + align:start position:0% +think about the environmental regulation + + + align:start position:0% +think about the environmental regulation +when thinking about where energy is + + align:start position:0% +when thinking about where energy is + + + align:start position:0% +when thinking about where energy is +going and where energy policy is going + + align:start position:0% +going and where energy policy is going + + + align:start position:0% +going and where energy policy is going +and we'll talk about a trading regime we + + align:start position:0% +and we'll talk about a trading regime we + + + align:start position:0% +and we'll talk about a trading regime we +talked about cap-and-trade earlier + + align:start position:0% +talked about cap-and-trade earlier + + + align:start position:0% +talked about cap-and-trade earlier +briefly when we talked about climate + + align:start position:0% +briefly when we talked about climate + + + align:start position:0% +briefly when we talked about climate +change we'll talk about it in the + + align:start position:0% +change we'll talk about it in the + + + align:start position:0% +change we'll talk about it in the +context of so2 in the case you've all + + align:start position:0% +context of so2 in the case you've all + + + align:start position:0% +context of so2 in the case you've all +read and subsequent developments and + + align:start position:0% +read and subsequent developments and + + + align:start position:0% +read and subsequent developments and +then say a little bit about generally + + align:start position:0% +then say a little bit about generally + + + align:start position:0% +then say a little bit about generally +what the how the regime looks it's worth + + align:start position:0% +what the how the regime looks it's worth + + + align:start position:0% +what the how the regime looks it's worth +stepping back a minute just to relate to + + align:start position:0% +stepping back a minute just to relate to + + + align:start position:0% +stepping back a minute just to relate to +some of the earlier discussions we had + + align:start position:0% +some of the earlier discussions we had + + + align:start position:0% +some of the earlier discussions we had +about politics and interest groups + + align:start position:0% +about politics and interest groups + + + align:start position:0% +about politics and interest groups +I like the Wilson piece because it it + + align:start position:0% +I like the Wilson piece because it it + + + align:start position:0% +I like the Wilson piece because it it +splits politics into recognizable + + align:start position:0% +splits politics into recognizable + + + align:start position:0% +splits politics into recognizable +categories I had a little trouble I + + align:start position:0% +categories I had a little trouble I + + + align:start position:0% +categories I had a little trouble I +confess as a non political science a + + align:start position:0% +confess as a non political science a + + + align:start position:0% +confess as a non political science a +scientist getting my head around lowey's + + align:start position:0% +scientist getting my head around lowey's + + + align:start position:0% +scientist getting my head around lowey's +four categories Wilson's are easy who + + align:start position:0% +four categories Wilson's are easy who + + + align:start position:0% +four categories Wilson's are easy who +bears the costs are they concentrated + + align:start position:0% +bears the costs are they concentrated + + + align:start position:0% +bears the costs are they concentrated +who bears the benefits are they + + align:start position:0% +who bears the benefits are they + + + align:start position:0% +who bears the benefits are they +concentrated in the case of where the + + align:start position:0% +concentrated in the case of where the + + + align:start position:0% +concentrated in the case of where the +cost of regulation are concentrated and + + align:start position:0% +cost of regulation are concentrated and + + + align:start position:0% +cost of regulation are concentrated and +the benefits of regulation are + + align:start position:0% +the benefits of regulation are + + + align:start position:0% +the benefits of regulation are +concentrated you get interest classic + + align:start position:0% +concentrated you get interest classic + + + align:start position:0% +concentrated you get interest classic +interest group competition cargoes + + align:start position:0% +interest group competition cargoes + + + align:start position:0% +interest group competition cargoes +between US ports have to be carried in + + align:start position:0% +between US ports have to be carried in + + + align:start position:0% +between US ports have to be carried in +US ships by very long-standing law + + align:start position:0% +US ships by very long-standing law + + + align:start position:0% +US ships by very long-standing law +those rates are regulated by the those + + align:start position:0% +those rates are regulated by the those + + + align:start position:0% +those rates are regulated by the those +US flag ships wouldn't exist but for + + align:start position:0% +US flag ships wouldn't exist but for + + + align:start position:0% +US flag ships wouldn't exist but for +that law this really affects people who + + align:start position:0% +that law this really affects people who + + + align:start position:0% +that law this really affects people who +live in Hawaii and who get cargoes from + + align:start position:0% +live in Hawaii and who get cargoes from + + + align:start position:0% +live in Hawaii and who get cargoes from +the mainland there a small number of + + align:start position:0% +the mainland there a small number of + + + align:start position:0% +the mainland there a small number of +shippers there a small number of + + align:start position:0% +shippers there a small number of + + + align:start position:0% +shippers there a small number of +customers there regulated by the Federal + + align:start position:0% +customers there regulated by the Federal + + + align:start position:0% +customers there regulated by the Federal +Maritime Commission that you've never + + align:start position:0% +Maritime Commission that you've never + + + align:start position:0% +Maritime Commission that you've never +heard of and they care a lot and that is + + align:start position:0% +heard of and they care a lot and that is + + + align:start position:0% +heard of and they care a lot and that is +the ultimate inside baseball + + align:start position:0% +the ultimate inside baseball + + + align:start position:0% +the ultimate inside baseball +so that's maritime regulation client + + align:start position:0% +so that's maritime regulation client + + + align:start position:0% +so that's maritime regulation client +politics is where the benefits are + + align:start position:0% +politics is where the benefits are + + + align:start position:0% +politics is where the benefits are +concentrated and the costs are dispersed + + align:start position:0% +concentrated and the costs are dispersed + + + align:start position:0% +concentrated and the costs are dispersed +and there's a lot of that we talked + + align:start position:0% +and there's a lot of that we talked + + + align:start position:0% +and there's a lot of that we talked +about concentrated versus dispersed + + align:start position:0% +about concentrated versus dispersed + + + align:start position:0% +about concentrated versus dispersed +interests milk price supports a small + + align:start position:0% +interests milk price supports a small + + + align:start position:0% +interests milk price supports a small +number of milk producers benefit the + + align:start position:0% +number of milk producers benefit the + + + align:start position:0% +number of milk producers benefit the +costs are dispersed among consumers in + + align:start position:0% +costs are dispersed among consumers in + + + align:start position:0% +costs are dispersed among consumers in +the old days of airline regulation it + + align:start position:0% +the old days of airline regulation it + + + align:start position:0% +the old days of airline regulation it +sort of looked like that the reverse + + align:start position:0% +sort of looked like that the reverse + + + align:start position:0% +sort of looked like that the reverse +then he talks about majoritarian we're + + align:start position:0% +then he talks about majoritarian we're + + + align:start position:0% +then he talks about majoritarian we're +like antitrust where you really can't + + align:start position:0% +like antitrust where you really can't + + + align:start position:0% +like antitrust where you really can't +identify the benefits and the costs + + align:start position:0% +identify the benefits and the costs + + + align:start position:0% +identify the benefits and the costs +they're both quite dispersed the + + align:start position:0% +they're both quite dispersed the + + + align:start position:0% +they're both quite dispersed the +interesting case in the case we have + + align:start position:0% +interesting case in the case we have + + + align:start position:0% +interesting case in the case we have +today is where the costs are + + align:start position:0% +today is where the costs are + + + align:start position:0% +today is where the costs are +concentrated and the benefits are + + align:start position:0% +concentrated and the benefits are + + + align:start position:0% +concentrated and the benefits are +dispersed and by our earlier discussions + + align:start position:0% +dispersed and by our earlier discussions + + + align:start position:0% +dispersed and by our earlier discussions +of what shapes interest group influence + + align:start position:0% +of what shapes interest group influence + + + align:start position:0% +of what shapes interest group influence +that shouldn't happen and the examples + + align:start position:0% +that shouldn't happen and the examples + + + align:start position:0% +that shouldn't happen and the examples +of that are cases where there was a + + align:start position:0% +of that are cases where there was a + + + align:start position:0% +of that are cases where there was a +social movement EPA the Food and Drug + + align:start position:0% +social movement EPA the Food and Drug + + + align:start position:0% +social movement EPA the Food and Drug +Administration came out of scandals in + + align:start position:0% +Administration came out of scandals in + + + align:start position:0% +Administration came out of scandals in +the early part of the last century and + + align:start position:0% +the early part of the last century and + + + align:start position:0% +the early part of the last century and +you could talk about a lot of a lot of + + align:start position:0% +you could talk about a lot of a lot of + + + align:start position:0% +you could talk about a lot of a lot of +regulation that has that character but + + align:start position:0% +regulation that has that character but + + + align:start position:0% +regulation that has that character but +that comes from a social movement + + align:start position:0% +that comes from a social movement + + + align:start position:0% +that comes from a social movement +he calls it entrepreneurial and that's + + align:start position:0% +he calls it entrepreneurial and that's + + + align:start position:0% +he calls it entrepreneurial and that's +because usually an entrepreneur drove + + align:start position:0% +because usually an entrepreneur drove + + + align:start position:0% +because usually an entrepreneur drove +the movement so it is it's useful to + + align:start position:0% +the movement so it is it's useful to + + + align:start position:0% +the movement so it is it's useful to +think about sort of where the regulation + + align:start position:0% +think about sort of where the regulation + + + align:start position:0% +think about sort of where the regulation +came from it's also useful to think + + align:start position:0% +came from it's also useful to think + + + align:start position:0% +came from it's also useful to think +about who does it does anybody recall + + align:start position:0% +about who does it does anybody recall + + + align:start position:0% +about who does it does anybody recall +the the types that Wilson has of people + + align:start position:0% +the the types that Wilson has of people + + + align:start position:0% +the the types that Wilson has of people +who work in regulatory agencies why + + align:start position:0% +who work in regulatory agencies why + + + align:start position:0% +who work in regulatory agencies why +would you work in a regulatory agency + + align:start position:0% + + + + align:start position:0% + +yeah it's + + align:start position:0% +yeah it's + + + align:start position:0% +yeah it's +a equal person like it's it's very it + + align:start position:0% +a equal person like it's it's very it + + + align:start position:0% +a equal person like it's it's very it +doesn't oscillate as much in the market + + align:start position:0% +doesn't oscillate as much in the market + + + align:start position:0% +doesn't oscillate as much in the market +so you might make a career out of it you + + align:start position:0% +so you might make a career out of it you + + + align:start position:0% +so you might make a career out of it you +might say I want to work in the Food and + + align:start position:0% +might say I want to work in the Food and + + + align:start position:0% +might say I want to work in the Food and +Drug Administration as opposed to a drug + + align:start position:0% +Drug Administration as opposed to a drug + + + align:start position:0% +Drug Administration as opposed to a drug +company because it's really safe and its + + align:start position:0% +company because it's really safe and its + + + align:start position:0% +company because it's really safe and its +steady okay so that's the usual civil + + align:start position:0% +steady okay so that's the usual civil + + + align:start position:0% +steady okay so that's the usual civil +service argument any other reason you + + align:start position:0% +service argument any other reason you + + + align:start position:0% +service argument any other reason you +might care a lot about what you're doing + + align:start position:0% +might care a lot about what you're doing + + + align:start position:0% +might care a lot about what you're doing +you might care a lot about what you're + + align:start position:0% +you might care a lot about what you're + + + align:start position:0% +you might care a lot about what you're +doing so you might you might be a I + + align:start position:0% +doing so you might you might be a I + + + align:start position:0% +doing so you might you might be a I +guess an advocate which isn't quite what + + align:start position:0% +guess an advocate which isn't quite what + + + align:start position:0% +guess an advocate which isn't quite what +quite one of his one of his categories + + align:start position:0% +quite one of his one of his categories + + + align:start position:0% +quite one of his one of his categories +anything else you might any other reason + + align:start position:0% +anything else you might any other reason + + + align:start position:0% +anything else you might any other reason +you might write work with political + + align:start position:0% +you might write work with political + + + align:start position:0% +you might write work with political +leaders you might have political + + align:start position:0% +leaders you might have political + + + align:start position:0% +leaders you might have political +ambitions it doesn't arise so much at + + align:start position:0% +ambitions it doesn't arise so much at + + + align:start position:0% +ambitions it doesn't arise so much at +the EPA but it can arise in other + + align:start position:0% +the EPA but it can arise in other + + + align:start position:0% +the EPA but it can arise in other +settings you might also it's this is + + align:start position:0% +settings you might also it's this is + + + align:start position:0% +settings you might also it's this is +kind of obscure but you might why would + + align:start position:0% +kind of obscure but you might why would + + + align:start position:0% +kind of obscure but you might why would +an economist go to work for the + + align:start position:0% +an economist go to work for the + + + align:start position:0% +an economist go to work for the +Antitrust Division in the Department of + + align:start position:0% +Antitrust Division in the Department of + + + align:start position:0% +Antitrust Division in the Department of +Justice - or a lawyer for that matter to + + align:start position:0% +Justice - or a lawyer for that matter to + + + align:start position:0% +Justice - or a lawyer for that matter to +build a professional reputation and then + + align:start position:0% +build a professional reputation and then + + + align:start position:0% +build a professional reputation and then +move out so Wilson talks about + + align:start position:0% +move out so Wilson talks about + + + align:start position:0% +move out so Wilson talks about +careerists politicians and professionals + + align:start position:0% +careerists politicians and professionals + + + align:start position:0% +careerists politicians and professionals +careerists are those who really believe + + align:start position:0% +careerists are those who really believe + + + align:start position:0% +careerists are those who really believe +within the agency and they're David's + + align:start position:0% +within the agency and they're David's + + + align:start position:0% +within the agency and they're David's +people who if you work for the EPA + + align:start position:0% +people who if you work for the EPA + + + align:start position:0% +people who if 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align:start position:0% +lawyer you work for a Washington agency +and you get known who worked in the EPA + + align:start position:0% +and you get known who worked in the EPA + + + align:start position:0% +and you get known who worked in the EPA +early on who would you guess David who + + align:start position:0% +early on who would you guess David who + + + align:start position:0% +early on who would you guess David who +would work for the EPA when it starts + + align:start position:0% +would work for the EPA when it starts + + + align:start position:0% +would work for the EPA when it starts +people who care a lot about the + + align:start position:0% +people who care a lot about the + + + align:start position:0% +people who care a lot about the +environment that means and it's still + + align:start position:0% +environment that means and it's still + + + align:start position:0% +environment that means and it's still +true that you know how the EPA thinks as + + align:start position:0% 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like reliable abundant + + align:start position:0% +well you'd like reliable abundant + + + align:start position:0% +well you'd like reliable abundant +supplies of energy you care about that + + align:start position:0% +supplies of energy you care about that + + + align:start position:0% +supplies of energy you care about that +maybe you want to move into the + + align:start position:0% +maybe you want to move into the + + + align:start position:0% +maybe you want to move into the +energy industry EPA you may want to move + + align:start position:0% +energy industry EPA you may want to move + + + align:start position:0% +energy industry EPA you may want to move +into one of the environmental groups the + + align:start position:0% +into one of the environmental groups the + + + align:start position:0% +into one of the environmental groups the +Department of Energy you know how they + + align:start position:0% +Department of Energy you know how they + + + align:start position:0% +Department of Energy you know how they +think going into the room if you have a + + align:start position:0% +think going into the room if you have a + + + align:start position:0% +think going into the room if you have a +meeting with EPA and energy as I had + + align:start position:0% +meeting with EPA and energy as I had + + + align:start position:0% +meeting with EPA and energy as I had +many of you know you don't have to know + + align:start position:0% +many of you know you don't have to know + + + align:start position:0% +many of you know you don't have to know +who they are you know where they come + + align:start position:0% +who they are you know where they come + + + align:start position:0% +who they are you know where they come +from you know how they think because you + + align:start position:0% +from you know how they think because you + + + align:start position:0% +from you know how they think because you +know why they got there one needs to + + align:start position:0% +know why they got there one needs to + + + align:start position:0% +know why they got there one needs to +think about this recall when we talked + + align:start position:0% +think about this recall when we talked + + + align:start position:0% +think about this recall when we talked +about biodiesel at MIT we talked about + + align:start position:0% +about biodiesel at MIT we talked about + + + align:start position:0% +about biodiesel at MIT we talked about +what do those people do what is their + + align:start position:0% +what do those people do what is their + + + align:start position:0% +what do those people do what is their +job what is their responsibility you + + align:start position:0% +job what is their responsibility you + + + align:start position:0% +job what is their responsibility you +didn't have to know them to know how + + align:start position:0% +didn't have to know them to know how + + + align:start position:0% +didn't have to know them to know how +they'd act in a meeting you had to know + + align:start position:0% +they'd act in a meeting you had to know + + + align:start position:0% +they'd act in a meeting you had to know +where they sat where they said where you + + align:start position:0% +where they sat where they said where you + + + align:start position:0% +where they sat where they said where you +stand depends on where you sit okay just + + align:start position:0% +stand depends on where you sit okay just + + + align:start position:0% +stand depends on where you sit okay just +talking now about EPA they do water air + + align:start position:0% +talking now about EPA they do water air + + + align:start position:0% +talking now about EPA they do water air +toxics of Arius kinds regulation mostly + + align:start position:0% +toxics of Arius kinds regulation mostly + + + align:start position:0% +toxics of Arius kinds regulation mostly +what we care about here is air they set + + align:start position:0% +what we care about here is air they set + + + align:start position:0% +what we care about here is air they set +national air quality ambient air quality + + align:start position:0% +national air quality ambient air quality + + + align:start position:0% +national air quality ambient air quality +standards for six pollutants Arizona + + align:start position:0% +standards for six pollutants Arizona + + + align:start position:0% +standards for six pollutants Arizona +ozone particulate Scarpa monoxide oxides + + align:start position:0% +ozone particulate Scarpa monoxide oxides + + + align:start position:0% +ozone particulate Scarpa monoxide oxides +of nitrogen Sox and lead all of them + + align:start position:0% +of nitrogen Sox and lead all of them + + + align:start position:0% +of nitrogen Sox and lead all of them +because the lead came from leaded + + align:start position:0% +because the lead came from leaded + + + align:start position:0% +because the lead came from leaded +gasoline primarily are driven by energy + + align:start position:0% +gasoline primarily are driven by energy + + + align:start position:0% +gasoline primarily are driven by energy +use so those standards and other + + align:start position:0% +use so those standards and other + + + align:start position:0% +use so those standards and other +regulations that energy policy in effect + + align:start position:0% + + + + align:start position:0% + +the law requires them to set standards + + align:start position:0% +the law requires them to set standards + + + align:start position:0% +the law requires them to set standards +to protect human health with an adequate + + align:start position:0% +to protect human health with an adequate + + + align:start position:0% +to protect human health with an adequate +margin of safety which presumes a + + align:start position:0% +margin of safety which presumes a + + + align:start position:0% +margin of safety which presumes a +threshold people have said for thirty + + align:start position:0% +threshold people have said for thirty + + + align:start position:0% +threshold people have said for thirty +years and more there aren't any + + align:start position:0% +years and more there aren't any + + + align:start position:0% +years and more there aren't any +thresholds the law presumes thresholds + + align:start position:0% +thresholds the law presumes thresholds + + + align:start position:0% +thresholds the law presumes thresholds +as we discussed last time they control + + align:start position:0% +as we discussed last time they control + + + align:start position:0% +as we discussed last time they control +they review States state implementation + + align:start position:0% +they review States state implementation + + + align:start position:0% +they review States state implementation +plans the reference to MIT parking is to + + align:start position:0% +plans the reference to MIT parking is to + + + align:start position:0% +plans the reference to MIT parking is to +remind me to tell you that the + + align:start position:0% +remind me to tell you that the + + + align:start position:0% +remind me to tell you that the +Massachusetts state implementation plan + + align:start position:0% +Massachusetts state implementation plan + + + align:start position:0% +Massachusetts state implementation plan +limits the number of parking spots MIT + + align:start position:0% +limits the number of parking spots MIT + + + align:start position:0% +limits the number of parking spots MIT +can have and one of the reasons there's + + align:start position:0% +can have and one of the reasons there's + + + align:start position:0% +can have and one of the reasons there's +a large garage under this building is + + align:start position:0% +a large garage under this building is + + + align:start position:0% +a large garage under this building is +that MIT wasn't using its limit and was + + align:start position:0% +that MIT wasn't using its limit and was + + + align:start position:0% +that MIT wasn't using its limit and was +a phrase the limit would be lowered so + + align:start position:0% +a phrase the limit would be lowered so + + + align:start position:0% +a phrase the limit would be lowered so +state implementation plans can go into + + align:start position:0% +state implementation plans can go into + + + align:start position:0% +state implementation plans can go into +great detail and are reviewed by the EPA + + align:start position:0% + + + + align:start position:0% + +they we talked about taxes to limit + + align:start position:0% +they we talked about taxes to limit + + + align:start position:0% +they we talked about taxes to limit +pollution EPA has never done that they + + align:start position:0% +pollution EPA has never done that they + + + align:start position:0% +pollution EPA has never done that they +do early on they did very little trading + + align:start position:0% +do early on they did very little trading + + + align:start position:0% +do early on they did very little trading +we talked about offsets and so forth + + align:start position:0% +we talked about offsets and so forth + + + align:start position:0% +we talked about offsets and so forth +I'll come back to that in a second + + align:start position:0% +I'll come back to that in a second + + + align:start position:0% +I'll come back to that in a second +mostly they set standards most + + align:start position:0% +mostly they set standards most + + + align:start position:0% +mostly they set standards most +regulation is so many grams of this per + + align:start position:0% +regulation is so many grams of this per + + + align:start position:0% +regulation is so many grams of this per +unit of that or use this technology The + + align:start position:0% +unit of that or use this technology The + + + align:start position:0% +unit of that or use this technology The +Economist alternative is put a price on + + align:start position:0% +Economist alternative is put a price on + + + align:start position:0% +Economist alternative is put a price on +it or limit its amount and let people + + align:start position:0% +it or limit its amount and let people + + + align:start position:0% +it or limit its amount and let people +trade the right to emit when might a + + align:start position:0% +trade the right to emit when might a + + + align:start position:0% +trade the right to emit when might a +standard be better why might a standard + + align:start position:0% +standard be better why might a standard + + + align:start position:0% +standard be better why might a standard +be better in some cases not to be too + + align:start position:0% +be better in some cases not to be too + + + align:start position:0% +be better in some cases not to be too +dogmatic yep just setting how well that + + align:start position:0% +dogmatic yep just setting how well that + + + align:start position:0% +dogmatic yep just setting how well that +stands a standard versus the technology + + align:start position:0% +stands a standard versus the technology + + + align:start position:0% +stands a standard versus the technology +how about a standard versus a tax or + + align:start position:0% +how about a standard versus a tax or + + + align:start position:0% +how about a standard versus a tax or +trade because the standard standard + + align:start position:0% +trade because the standard standard + + + align:start position:0% +trade because the standard standard +tells you what you must achieve doesn't + + align:start position:0% +tells you what you must achieve doesn't + + + align:start position:0% +tells you what you must achieve doesn't +necessarily tell you how now that's an + + align:start position:0% +necessarily tell you how now that's an + + + align:start position:0% +necessarily tell you how now that's an +interesting distinction tell me about + + align:start position:0% +interesting distinction tell me about + + + align:start position:0% +interesting distinction tell me about +why you if for whatever reason specific + + align:start position:0% +why you if for whatever reason specific + + + align:start position:0% +why you if for whatever reason specific +credit begins so so let me let me just + + align:start position:0% +credit begins so so let me let me just + + + align:start position:0% +credit begins so so let me let me just +let me just cut you there what you're + + align:start position:0% +let me just cut you there what you're + + + align:start position:0% +let me just cut you there what you're +saying is it doesn't necessarily it you + + align:start position:0% +saying is it doesn't necessarily it you + + + align:start position:0% +saying is it doesn't necessarily it you +could have intense pollution in some + + align:start position:0% +could have intense pollution in some + + + align:start position:0% +could have intense pollution in some +areas now for carbon dioxide that isn't + + align:start position:0% +areas now for carbon dioxide that isn't + + + align:start position:0% +areas now for carbon dioxide that isn't +going to matter is it because it mixes + + align:start position:0% +going to matter is it because it mixes + + + align:start position:0% +going to matter is it because it mixes +but it might matter if it doesn't mix so + + align:start position:0% +but it might matter if it doesn't mix so + + + align:start position:0% +but it might matter if it doesn't mix so +suppose you have a pollutant that + + align:start position:0% +suppose you have a pollutant that + + + align:start position:0% +suppose you have a pollutant that +basically travels 50 feet from the plant + + align:start position:0% +basically travels 50 feet from the plant + + + align:start position:0% +basically travels 50 feet from the plant +then you wouldn't want to use trading + + align:start position:0% +then you wouldn't want to use trading + + + align:start position:0% +then you wouldn't want to use trading +from plants in widely separated areas + + align:start position:0% +from plants in widely separated areas + + + align:start position:0% +from plants in widely separated areas +because you'd have a hot spot + + align:start position:0% +because you'd have a hot spot + + + align:start position:0% +because you'd have a hot spot +okay so standards can deal with hot + + align:start position:0% +okay so standards can deal with hot + + + align:start position:0% +okay so standards can deal with hot +spots and that's called the hot spot + + align:start position:0% +spots and that's called the hot spot + + + align:start position:0% +spots and that's called the hot spot +you had a comment rekelen well that's + + align:start position:0% +you had a comment rekelen well that's + + + align:start position:0% +you had a comment rekelen well that's +the same issue hazardous substances you + + align:start position:0% +the same issue hazardous substances you + + + align:start position:0% +the same issue hazardous substances you +might be they're really hazardous you + + align:start position:0% +might be they're really hazardous you + + + align:start position:0% +might be they're really hazardous you +might want to ban them and if they don't + + align:start position:0% +might want to ban them and if they don't + + + align:start position:0% +might want to ban them and if they don't +travel all that stuff's hazardous to + + align:start position:0% +travel all that stuff's hazardous to + + + align:start position:0% +travel all that stuff's hazardous to +some extent if they don't travel and + + align:start position:0% +some extent if they don't travel and + + + align:start position:0% +some extent if they don't travel and +they don't mix then you don't want to + + align:start position:0% +they don't mix then you don't want to + + + align:start position:0% +they don't mix then you don't want to +say an emission here is equivalent to an + + align:start position:0% +say an emission here is equivalent to an + + + align:start position:0% +say an emission here is equivalent to an +emission there you know lots of + + align:start position:0% +emission there you know lots of + + + align:start position:0% +emission there you know lots of +emissions here and none there is the + + align:start position:0% +emissions here and none there is the + + + align:start position:0% +emissions here and none there is the +same thing as none there and lots there + + align:start position:0% +same thing as none there and lots there + + + align:start position:0% +same thing as none there and lots there +it may not be true people may live over + + align:start position:0% +it may not be true people may live over + + + align:start position:0% +it may not be true people may live over +here and not over there so that's the + + align:start position:0% +here and not over there so that's the + + + align:start position:0% +here and not over there so that's the +hotspot problem where things don't mix + + align:start position:0% +hotspot problem where things don't mix + + + align:start position:0% +hotspot problem where things don't mix +any other reason why you might want to + + align:start position:0% +any other reason why you might want to + + + align:start position:0% +any other reason why you might want to +suppose you couldn't measure emissions + + align:start position:0% +suppose you couldn't measure emissions + + + align:start position:0% +suppose you couldn't measure emissions +very well like automobiles we don't do + + align:start position:0% +very well like automobiles we don't do + + + align:start position:0% +very well like automobiles we don't do +cap-and-trade for automobiles can we + + align:start position:0% +cap-and-trade for automobiles can we + + + align:start position:0% +cap-and-trade for automobiles can we +measure what comes out of the tailpipe + + align:start position:0% +measure what comes out of the tailpipe + + + align:start position:0% +measure what comes out of the tailpipe +of your car not real easily we can + + align:start position:0% +of your car not real easily we can + + + align:start position:0% +of your car not real easily we can +measure per mile when you go to get it + + align:start position:0% +measure per mile when you go to get it + + + align:start position:0% +measure per mile when you go to get it +inspected but it's you know aside from + + align:start position:0% +inspected but it's you know aside from + + + align:start position:0% +inspected but it's you know aside from +monitoring your driving putting a meter + + align:start position:0% +monitoring your driving putting a meter + + + align:start position:0% +monitoring your driving putting a meter +on your tailpipe we can't we couldn't do + + align:start position:0% +on your tailpipe we can't we couldn't do + + + align:start position:0% +on your tailpipe we can't we couldn't do +cap and trade we can't measure it so + + align:start position:0% +cap and trade we can't measure it so + + + align:start position:0% +cap and trade we can't measure it so +their enforcement issues right if I say + + align:start position:0% +their enforcement issues right if I say + + + align:start position:0% +their enforcement issues right if I say +to the power plant you have to put this + + align:start position:0% +to the power plant you have to put this + + + align:start position:0% +to the power plant you have to put this +device on your smokestack and it has to + + align:start position:0% +device on your smokestack and it has to + + + align:start position:0% +device on your smokestack and it has to +be working when our inspectors come + + align:start position:0% +be working when our inspectors come + + + align:start position:0% +be working when our inspectors come +that's easy I can go check that that's + + align:start position:0% +that's easy I can go check that that's + + + align:start position:0% +that's easy I can go check that that's +why UPA one reason UPA love standards + + align:start position:0% +why UPA one reason UPA love standards + + + align:start position:0% +why UPA one reason UPA love standards +and particularly technology standards do + + align:start position:0% +and particularly technology standards do + + + align:start position:0% +and particularly technology standards do +you have the Box is it working easy not + + align:start position:0% +you have the Box is it working easy not + + + align:start position:0% +you have the Box is it working easy not +how many how many tons did you produce + + align:start position:0% +how many how many tons did you produce + + + align:start position:0% +how many how many tons did you produce +did you run at the day time or night so + + align:start position:0% +did you run at the day time or night so + + + align:start position:0% +did you run at the day time or night so +there are there enforcement issues and + + align:start position:0% +there are there enforcement issues and + + + align:start position:0% +there are there enforcement issues and +there hotspot issues the let me see is + + align:start position:0% +there hotspot issues the let me see is + + + align:start position:0% +there hotspot issues the let me see is +there is there anything else you can + + align:start position:0% +there is there anything else you can + + + align:start position:0% +there is there anything else you can +think of anybody look at the Sandell + + align:start position:0% +think of anybody look at the Sandell + + + align:start position:0% +think of anybody look at the Sandell +piece that's all that's on it and + + align:start position:0% +piece that's all that's on it and + + + align:start position:0% +piece that's all that's on it and +recommended probably not it's late in + + align:start position:0% +recommended probably not it's late in + + + align:start position:0% +recommended probably not it's late in +the semester Sandell argues that none of + + align:start position:0% +the semester Sandell argues that none of + + + align:start position:0% +the semester Sandell argues that none of +us would agree that you ought to be able + + align:start position:0% +us would agree that you ought to be able + + + align:start position:0% +us would agree that you ought to be able +to buy a license to dump garbage in the + + align:start position:0% +to buy a license to dump garbage in the + + + align:start position:0% +to buy a license to dump garbage in the +street so he would even if you know we + + align:start position:0% +street so he would even if you know we + + + align:start position:0% +street so he would even if you know we +could we could we could do that we could + + align:start position:0% +could we could we could do that we could + + + align:start position:0% +could we could we could do that we could +have licences to just dump + + align:start position:0% +have licences to just dump + + + align:start position:0% +have licences to just dump +garbage in the street but we'd all sort + + align:start position:0% +garbage in the street but we'd all sort + + + align:start position:0% +garbage in the street but we'd all sort +of think that's wrong if you could buy + + align:start position:0% +of think that's wrong if you could buy + + + align:start position:0% +of think that's wrong if you could buy +the right to dump garbage in the street + + align:start position:0% +the right to dump garbage in the street + + + align:start position:0% +the right to dump garbage in the street +you'd eliminate the stigma and if you + + align:start position:0% +you'd eliminate the stigma and if you + + + align:start position:0% +you'd eliminate the stigma and if you +eliminate the stigma you eliminate a + + align:start position:0% +eliminate the stigma you eliminate a + + + align:start position:0% +eliminate the stigma you eliminate a +force for cleaning up so Sandell would + + align:start position:0% +force for cleaning up so Sandell would + + + align:start position:0% +force for cleaning up so Sandell would +say it's wrong to do trading because it + + align:start position:0% +say it's wrong to do trading because it + + + align:start position:0% +say it's wrong to do trading because it +sort of eliminates the stigma now carbon + + align:start position:0% +sort of eliminates the stigma now carbon + + + align:start position:0% +sort of eliminates the stigma now carbon +dioxide versus hazardous chemicals you + + align:start position:0% +dioxide versus hazardous chemicals you + + + align:start position:0% +dioxide versus hazardous chemicals you +may want to argue whether a stigma is + + align:start position:0% +may want to argue whether a stigma is + + + align:start position:0% +may want to argue whether a stigma is +appropriate right as we breathe out co2 + + align:start position:0% +appropriate right as we breathe out co2 + + + align:start position:0% +appropriate right as we breathe out co2 +maybe that's not such a terrible thing + + align:start position:0% +maybe that's not such a terrible thing + + + align:start position:0% +maybe that's not such a terrible thing +to be doing but the other issue you + + align:start position:0% +to be doing but the other issue you + + + align:start position:0% +to be doing but the other issue you +might think about if I can put if I can + + align:start position:0% +might think about if I can put if I can + + + align:start position:0% +might think about if I can put if I can +put a device on the smokestack and I'm + + align:start position:0% +put a device on the smokestack and I'm + + + align:start position:0% +put a device on the smokestack and I'm +done I get no credit for doing better so + + align:start position:0% +done I get no credit for doing better so + + + align:start position:0% +done I get no credit for doing better so +I get no credit for beating a standard + + align:start position:0% +I get no credit for beating a standard + + + align:start position:0% +I get no credit for beating a standard +if a standard is set so there's no + + align:start position:0% +if a standard is set so there's no + + + align:start position:0% +if a standard is set so there's no +reason to innovate if you've told me + + align:start position:0% +reason to innovate if you've told me + + + align:start position:0% +reason to innovate if you've told me +that what all I have to do to comply + + align:start position:0% +that what all I have to do to comply + + + align:start position:0% +that what all I have to do to comply +with the law is X then I'm done if you + + align:start position:0% +with the law is X then I'm done if you + + + align:start position:0% +with the law is X then I'm done if you +tell tell me it costs five dollars a + + align:start position:0% +tell tell me it costs five dollars a + + + align:start position:0% +tell tell me it costs five dollars a +tonne every time I admit I owe I have a + + align:start position:0% +tonne every time I admit I owe I have a + + + align:start position:0% +tonne every time I admit I owe I have a +constant incentive to figure out ways to + + align:start position:0% +constant incentive to figure out ways to + + + align:start position:0% +constant incentive to figure out ways to +avoid it so standards ease enforcement + + align:start position:0% +avoid it so standards ease enforcement + + + align:start position:0% +avoid it so standards ease enforcement +they avoid the hotspot problem + + align:start position:0% +they avoid the hotspot problem + + + align:start position:0% +they avoid the hotspot problem +environmentalists don't like markets + + align:start position:0% +environmentalists don't like markets + + + align:start position:0% +environmentalists don't like markets +traditionally because they like the + + align:start position:0% +traditionally because they like the + + + align:start position:0% +traditionally because they like the +stigma which I guess would apply I think + + align:start position:0% +stigma which I guess would apply I think + + + align:start position:0% +stigma which I guess would apply I think +makes more sense in the case of toxics + + align:start position:0% +makes more sense in the case of toxics + + + align:start position:0% +makes more sense in the case of toxics +than in the case of co2 + + align:start position:0% +than in the case of co2 + + + align:start position:0% +than in the case of co2 +I love plenty of people would like to + + align:start position:0% +I love plenty of people would like to + + + align:start position:0% +I love plenty of people would like to +stigmatize SUVs + + align:start position:0% +stigmatize SUVs + + + align:start position:0% +stigmatize SUVs +it's raises costs may raise costs which + + align:start position:0% +it's raises costs may raise costs which + + + align:start position:0% +it's raises costs may raise costs which +we talked about we'll come back to and + + align:start position:0% +we talked about we'll come back to and + + + align:start position:0% +we talked about we'll come back to and +there's no reward for innovation there's + + align:start position:0% +there's no reward for innovation there's + + + align:start position:0% +there's no reward for innovation there's +no reward for beating the standard ok a + + align:start position:0% +no reward for beating the standard ok a + + + align:start position:0% +no reward for beating the standard ok a +little bit about early trading which is + + align:start position:0% +little bit about early trading which is + + + align:start position:0% +little bit about early trading which is +in the the text assignment let me just + + align:start position:0% +in the the text assignment let me just + + + align:start position:0% +in the the text assignment let me just +mention this this is + + align:start position:0% +mention this this is + + + align:start position:0% +mention this this is +for 1990 did did we have any trading + + align:start position:0% +for 1990 did did we have any trading + + + align:start position:0% +for 1990 did did we have any trading +allowed in the US apart from the lead + + align:start position:0% +allowed in the US apart from the lead + + + align:start position:0% +allowed in the US apart from the lead +lead phase-out well there were a few + + align:start position:0% +lead phase-out well there were a few + + + align:start position:0% +lead phase-out well there were a few +netting says you can go to you you can + + align:start position:0% +netting says you can go to you you can + + + align:start position:0% +netting says you can go to you you can +go to your regulator you have an oil + + align:start position:0% +go to your regulator you have an oil + + + align:start position:0% +go to your regulator you have an oil +refinery the emissions here are + + align:start position:0% +refinery the emissions here are + + + align:start position:0% +refinery the emissions here are +regulated and emissions there are + + align:start position:0% +regulated and emissions there are + + + align:start position:0% +regulated and emissions there are +regulated different parts of the same + + align:start position:0% +regulated different parts of the same + + + align:start position:0% +regulated different parts of the same +factory and you say to the regulator + + align:start position:0% +factory and you say to the regulator + + + align:start position:0% +factory and you say to the regulator +look I'd really like to admit a little + + align:start position:0% +look I'd really like to admit a little + + + align:start position:0% +look I'd really like to admit a little +more here in exchange for a lot less + + align:start position:0% +more here in exchange for a lot less + + + align:start position:0% +more here in exchange for a lot less +there or maybe it's it's even that's + + align:start position:0% +there or maybe it's it's even that's + + + align:start position:0% +there or maybe it's it's even that's +called netting it's in the same internal + + align:start position:0% +called netting it's in the same internal + + + align:start position:0% +called netting it's in the same internal +transactions or within an entity within + + align:start position:0% +transactions or within an entity within + + + align:start position:0% +transactions or within an entity within +a plant external transactions are + + align:start position:0% +a plant external transactions are + + + align:start position:0% +a plant external transactions are +outside these are inside they happened + + align:start position:0% + + + + align:start position:0% + +thousands of them offsets I think we + + align:start position:0% +thousands of them offsets I think we + + + align:start position:0% +thousands of them offsets I think we +talked about offsets are I'm gonna I'm + + align:start position:0% +talked about offsets are I'm gonna I'm + + + align:start position:0% +talked about offsets are I'm gonna I'm +gonna do more than is required in my + + align:start position:0% +gonna do more than is required in my + + + align:start position:0% +gonna do more than is required in my +factory or less than is required in my + + align:start position:0% +factory or less than is required in my + + + align:start position:0% +factory or less than is required in my +factory in exchange for which he'll do a + + align:start position:0% +factory in exchange for which he'll do a + + + align:start position:0% +factory in exchange for which he'll do a +lot more than is required in his factory + + align:start position:0% +lot more than is required in his factory + + + align:start position:0% +lot more than is required in his factory +he'll do more than he would have done + + align:start position:0% +he'll do more than he would have done + + + align:start position:0% +he'll do more than he would have done +and those are very complicated + + align:start position:0% +and those are very complicated + + + align:start position:0% +and those are very complicated +negotiations that happen in Los Angeles + + align:start position:0% +negotiations that happen in Los Angeles + + + align:start position:0% +negotiations that happen in Los Angeles +heavily because you couldn't build in + + align:start position:0% +heavily because you couldn't build in + + + align:start position:0% +heavily because you couldn't build in +Los Angeles you couldn't add anything + + align:start position:0% +Los Angeles you couldn't add anything + + + align:start position:0% +Los Angeles you couldn't add anything +new in Los Angeles unless you shut + + align:start position:0% +new in Los Angeles unless you shut + + + align:start position:0% +new in Los Angeles unless you shut +something down so if you happened not to + + align:start position:0% +something down so if you happened not to + + + align:start position:0% +something down so if you happened not to +have anything to shut down you did a + + align:start position:0% +have anything to shut down you did a + + + align:start position:0% +have anything to shut down you did a +deal and the local regulators would + + align:start position:0% +deal and the local regulators would + + + align:start position:0% +deal and the local regulators would +either approve it on the grounds that + + align:start position:0% +either approve it on the grounds that + + + align:start position:0% +either approve it on the grounds that +you were actually reducing emissions + + align:start position:0% +you were actually reducing emissions + + + align:start position:0% +you were actually reducing emissions +over there more than would have happened + + align:start position:0% +over there more than would have happened + + + align:start position:0% +over there more than would have happened +or they'll disapprove it because what + + align:start position:0% +or they'll disapprove it because what + + + align:start position:0% +or they'll disapprove it because what +what the typical thing is you take an + + align:start position:0% +what the typical thing is you take an + + + align:start position:0% +what the typical thing is you take an +old factory and you pay them to shut + + align:start position:0% +old factory and you pay them to shut + + + align:start position:0% +old factory and you pay them to shut +down and the regulator would say but + + align:start position:0% +down and the regulator would say but + + + align:start position:0% +down and the regulator would say but +that's an old factory it would have shut + + align:start position:0% +that's an old factory it would have shut + + + align:start position:0% +that's an old factory it would have shut +down anyway so prove to me it wouldn't + + align:start position:0% +down anyway so prove to me it wouldn't + + + align:start position:0% +down anyway so prove to me it wouldn't +have shut down if you hadn't paid it + + align:start position:0% +have shut down if you hadn't paid it + + + align:start position:0% +have shut down if you hadn't paid it +well that's either impossible if the + + align:start position:0% +well that's either impossible if the + + + align:start position:0% +well that's either impossible if the +burden of proof is is set high or easy + + align:start position:0% +burden of proof is is set high or easy + + + align:start position:0% +burden of proof is is set high or easy +if it's set low bubbles are where you + + align:start position:0% +if it's set low bubbles are where you + + + align:start position:0% +if it's set low bubbles are where you +take an area and you worry about + + align:start position:0% +take an area and you worry about + + + align:start position:0% +take an area and you worry about +emissions within the area you put a + + align:start position:0% +emissions within the area you put a + + + align:start position:0% +emissions within the area you put a +bubble over it some experiments were + + align:start position:0% +bubble over it some experiments were + + + align:start position:0% +bubble over it some experiments were +done banking is where I'll do more than + + align:start position:0% +done banking is where I'll do more than + + + align:start position:0% +done banking is where I'll do more than +I have to today in exchange for less + + align:start position:0% +I have to today in exchange for less + + + align:start position:0% +I have to today in exchange for less +I have to tomorrow very little of that + + align:start position:0% +I have to tomorrow very little of that + + + align:start position:0% +I have to tomorrow very little of that +was done so these are kinds of trading + + align:start position:0% +was done so these are kinds of trading + + + align:start position:0% +was done so these are kinds of trading +that the regulator's fiddled with early + + align:start position:0% +that the regulator's fiddled with early + + + align:start position:0% +that the regulator's fiddled with early +on but not in high volume except for + + align:start position:0% +on but not in high volume except for + + + align:start position:0% +on but not in high volume except for +netting and and not much not much impact + + align:start position:0% +netting and and not much not much impact + + + align:start position:0% +netting and and not much not much impact +so let us go to a one last thing before + + align:start position:0% +so let us go to a one last thing before + + + align:start position:0% +so let us go to a one last thing before +I go to the I go to the case I want to + + align:start position:0% +I go to the I go to the case I want to + + + align:start position:0% +I go to the I go to the case I want to +say a little bit about cost-benefit + + align:start position:0% +say a little bit about cost-benefit + + + align:start position:0% +say a little bit about cost-benefit +analysis just a very little bit we + + align:start position:0% +analysis just a very little bit we + + + align:start position:0% +analysis just a very little bit we +talked about it early on but it comes up + + align:start position:0% +talked about it early on but it comes up + + + align:start position:0% +talked about it early on but it comes up +sort of in the case sort of EPA has to + + align:start position:0% +sort of in the case sort of EPA has to + + + align:start position:0% +sort of in the case sort of EPA has to +produce a cost-benefit analysis of + + align:start position:0% +produce a cost-benefit analysis of + + + align:start position:0% +produce a cost-benefit analysis of +defending any regulation at issues + + align:start position:0% +defending any regulation at issues + + + align:start position:0% +defending any regulation at issues +that's been a requirement really the + + align:start position:0% +that's been a requirement really the + + + align:start position:0% +that's been a requirement really the +case talks about the first sort of + + align:start position:0% +case talks about the first sort of + + + align:start position:0% +case talks about the first sort of +instances of it under Carter it's been + + align:start position:0% +instances of it under Carter it's been + + + align:start position:0% +instances of it under Carter it's been +every president has revised this rule + + align:start position:0% +every president has revised this rule + + + align:start position:0% +every president has revised this rule +for executive branch agencies usually + + align:start position:0% +for executive branch agencies usually + + + align:start position:0% +for executive branch agencies usually +however the agencies make a decision and + + align:start position:0% +however the agencies make a decision and + + + align:start position:0% +however the agencies make a decision and +then do cost-benefit to prove it was a + + align:start position:0% +then do cost-benefit to prove it was a + + + align:start position:0% +then do cost-benefit to prove it was a +good idea which drives other people + + align:start position:0% +good idea which drives other people + + + align:start position:0% +good idea which drives other people +crazy it's supposed to be used to make a + + align:start position:0% +crazy it's supposed to be used to make a + + + align:start position:0% +crazy it's supposed to be used to make a +decision they it's generally used to + + align:start position:0% +decision they it's generally used to + + + align:start position:0% +decision they it's generally used to +defend a decision you never ever have BP + + align:start position:0% +defend a decision you never ever have BP + + + align:start position:0% +defend a decision you never ever have BP +a producer rule and say well we have to + + align:start position:0% +a producer rule and say well we have to + + + align:start position:0% +a producer rule and say well we have to +produce this rule but in fact it has no + + align:start position:0% +produce this rule but in fact it has no + + + align:start position:0% +produce this rule but in fact it has no +benefits there's always a benefit some + + align:start position:0% +benefits there's always a benefit some + + + align:start position:0% +benefits there's always a benefit some +controversies some of which are + + align:start position:0% +controversies some of which are + + + align:start position:0% +controversies some of which are +mentioned in the text EPA having found + + align:start position:0% +mentioned in the text EPA having found + + + align:start position:0% +mentioned in the text EPA having found +carbon dioxide emissions to be dangerous + + align:start position:0% +carbon dioxide emissions to be dangerous + + + align:start position:0% +carbon dioxide emissions to be dangerous +is legally obliged to regulate it + + align:start position:0% +is legally obliged to regulate it + + + align:start position:0% +is legally obliged to regulate it +EPA has issued draft regulations for new + + align:start position:0% +EPA has issued draft regulations for new + + + align:start position:0% +EPA has issued draft regulations for new +power plants those regulations are being + + align:start position:0% +power plants those regulations are being + + + align:start position:0% +power plants those regulations are being +challenged in court for among other + + align:start position:0% +challenged in court for among other + + + align:start position:0% +challenged in court for among other +reasons being arbitrary and capricious + + align:start position:0% +reasons being arbitrary and capricious + + + align:start position:0% +reasons being arbitrary and capricious +because they will have no benefits + + align:start position:0% +because they will have no benefits + + + align:start position:0% +because they will have no benefits +regulation of carbon dioxide from us + + align:start position:0% +regulation of carbon dioxide from us + + + align:start position:0% +regulation of carbon dioxide from us +from new US power plants in a slow + + align:start position:0% +from new US power plants in a slow + + + align:start position:0% +from new US power plants in a slow +growth period when we're a small part of + + align:start position:0% +growth period when we're a small part of + + + align:start position:0% +growth period when we're a small part of +the world will have no detectable + + align:start position:0% +the world will have no detectable + + + align:start position:0% +the world will have no detectable +benefits true fact + + align:start position:0% +benefits true fact + + + align:start position:0% +benefits true fact +EPA is legally obliged to issue a + + align:start position:0% +EPA is legally obliged to issue a + + + align:start position:0% +EPA is legally obliged to issue a +regulation however it will be very + + align:start position:0% +regulation however it will be very + + + align:start position:0% +regulation however it will be very +interesting to see how the court rules + + align:start position:0% +interesting to see how the court rules + + + align:start position:0% +interesting to see how the court rules +on this one which is now before the DS + + align:start position:0% +on this one which is now before the DS + + + align:start position:0% +on this one which is now before the DS +circuit there a set of controversies + + align:start position:0% +circuit there a set of controversies + + + align:start position:0% +circuit there a set of controversies +about well when you do cost-benefit + + align:start position:0% +about well when you do cost-benefit + + + align:start position:0% +about well when you do cost-benefit +analysis what discount rate do you use + + align:start position:0% +analysis what discount rate do you use + + + align:start position:0% +analysis what discount rate do you use +what do you do you value carbon dioxide + + align:start position:0% +what do you do you value carbon dioxide + + + align:start position:0% +what do you do you value carbon dioxide +emissions as a cost and how do you value + + align:start position:0% +emissions as a cost and how do you value + + + align:start position:0% +emissions as a cost and how do you value +a life saved there our White House + + align:start position:0% +a life saved there our White House + + + align:start position:0% +a life saved there our White House +Office of Management and Budget + + align:start position:0% +Office of Management and Budget + + + align:start position:0% +Office of Management and Budget +directives on all of those the tell + + align:start position:0% +directives on all of those the tell + + + align:start position:0% +directives on all of those the tell +agencies how to proceed you can imagine + + align:start position:0% +agencies how to proceed you can imagine + + + align:start position:0% +agencies how to proceed you can imagine +those are the outcomes of significant + + align:start position:0% +those are the outcomes of significant + + + align:start position:0% +those are the outcomes of significant +fights within within each administration + + align:start position:0% +fights within within each administration + + + align:start position:0% +fights within within each administration +another significant fight is the senior + + align:start position:0% +another significant fight is the senior + + + align:start position:0% +another significant fight is the senior +discount which the text talks about and + + align:start position:0% +discount which the text talks about and + + + align:start position:0% +discount which the text talks about and +the way to think about this one is do + + align:start position:0% +the way to think about this one is do + + + align:start position:0% +the way to think about this one is do +you count small particles that are small + + align:start position:0% +you count small particles that are small + + + align:start position:0% +you count small particles that are small +particulates that result from sulfate + + align:start position:0% +particulates that result from sulfate + + + align:start position:0% +particulates that result from sulfate +emissions cause acute respiratory + + align:start position:0% +emissions cause acute respiratory + + + align:start position:0% +emissions cause acute respiratory +episodes under certain conditions those + + align:start position:0% +episodes under certain conditions those + + + align:start position:0% +episodes under certain conditions those +tend to kill elderly people so if you + + align:start position:0% +tend to kill elderly people so if you + + + align:start position:0% +tend to kill elderly people so if you +value the average life saved it's a six + + align:start position:0% +value the average life saved it's a six + + + align:start position:0% +value the average life saved it's a six +million dollars how do you value the + + align:start position:0% +million dollars how do you value the + + + align:start position:0% +million dollars how do you value the +life of an 85 year old some people say + + align:start position:0% +life of an 85 year old some people say + + + align:start position:0% +life of an 85 year old some people say +well you shouldn't do lives you should + + align:start position:0% +well you shouldn't do lives you should + + + align:start position:0% +well you shouldn't do lives you should +do life years that 85 year old is only + + align:start position:0% +do life years that 85 year old is only + + + align:start position:0% +do life years that 85 year old is only +expected to live a few years if in fact + + align:start position:0% +expected to live a few years if in fact + + + align:start position:0% +expected to live a few years if in fact +you killed a teenager you're costing a + + align:start position:0% +you killed a teenager you're costing a + + + align:start position:0% +you killed a teenager you're costing a +lot more life years the EPA discussed + + align:start position:0% +lot more life years the EPA discussed + + + align:start position:0% +lot more life years the EPA discussed +this at one point and proposed to do it + + align:start position:0% +this at one point and proposed to do it + + + align:start position:0% +this at one point and proposed to do it +that was the senior discount who votes + + align:start position:0% +that was the senior discount who votes + + + align:start position:0% +that was the senior discount who votes +that proposal died I think most + + align:start position:0% +that proposal died I think most + + + align:start position:0% +that proposal died I think most +economists think although we're a little + + align:start position:0% +economists think although we're a little + + + align:start position:0% +economists think although we're a little +uneasy about this that it sort of makes + + align:start position:0% +uneasy about this that it sort of makes + + + align:start position:0% +uneasy about this that it sort of makes +sense to ask are you killing somebody + + align:start position:0% +sense to ask are you killing somebody + + + align:start position:0% +sense to ask are you killing somebody +two weeks early or 50 years early how + + align:start position:0% +two weeks early or 50 years early how + + + align:start position:0% +two weeks early or 50 years early how +you want to deal with that difference + + align:start position:0% +you want to deal with that difference + + + align:start position:0% +you want to deal with that difference +you can argue about for days but it sort + + align:start position:0% +you can argue about for days but it sort + + + align:start position:0% +you can argue about for days but it sort +of seems to matter but the the 80 year + + align:start position:0% +of seems to matter but the the 80 year + + + align:start position:0% +of seems to matter but the the 80 year +old votes so the senior discount seems + + align:start position:0% +old votes so the senior discount seems + + + align:start position:0% +old votes so the senior discount seems +to have vanished from from government + + align:start position:0% +to have vanished from from government + + + align:start position:0% +to have vanished from from government +government decision-making it appears + + align:start position:0% +government decision-making it appears + + + align:start position:0% +government decision-making it appears +all the time + + align:start position:0% +all the time + + + align:start position:0% +all the time +in academic analysis contingent + + align:start position:0% +in academic analysis contingent + + + align:start position:0% +in academic analysis contingent +valuation just one last topic it's not + + align:start position:0% +valuation just one last topic it's not + + + align:start position:0% +valuation just one last topic it's not +quite as hot a topic as it used to used + + align:start position:0% +quite as hot a topic as it used to used + + + align:start position:0% +quite as hot a topic as it used to used +to be when we had the big Exxon Valdez + + align:start position:0% +to be when we had the big Exxon Valdez + + + align:start position:0% +to be when we had the big Exxon Valdez +oil spill in Alaska that was notorious + + align:start position:0% +oil spill in Alaska that was notorious + + + align:start position:0% +oil spill in Alaska that was notorious +the question was what are the damages + + align:start position:0% +the question was what are the damages + + + align:start position:0% +the question was what are the damages +the damages were mostly to wildlife in + + align:start position:0% +the damages were mostly to wildlife in + + + align:start position:0% +the damages were mostly to wildlife in +the natural environment and nobody lived + + align:start position:0% +the natural environment and nobody lived + + + align:start position:0% +the natural environment and nobody lived +there to a first approximation so be + + align:start position:0% +there to a first approximation so be + + + align:start position:0% +there to a first approximation so be +hard to say that a lot of people were + + align:start position:0% +hard to say that a lot of people were + + + align:start position:0% +hard to say that a lot of people were +directly damaged so if you asked you + + align:start position:0% +directly damaged so if you asked you + + + align:start position:0% +directly damaged so if you asked you +know loss of fishing revenue six bucks + + align:start position:0% +know loss of fishing revenue six bucks + + + align:start position:0% +know loss of fishing revenue six bucks +loss of campsites $12 so the following + + align:start position:0% +loss of campsites $12 so the following + + + align:start position:0% +loss of campsites $12 so the following +technique was adopted they sent out a + + align:start position:0% +technique was adopted they sent out a + + + align:start position:0% +technique was adopted they sent out a +survey to people in the lower 48 states + + align:start position:0% +survey to people in the lower 48 states + + + align:start position:0% +survey to people in the lower 48 states +how much would you be willing to pay to + + align:start position:0% +how much would you be willing to pay to + + + align:start position:0% +how much would you be willing to pay to +undo the damages caused by the Exxon + + align:start position:0% +undo the damages caused by the Exxon + + + align:start position:0% +undo the damages caused by the Exxon +Valdez and then they would list a bunch + + align:start position:0% +Valdez and then they would list a bunch + + + align:start position:0% +Valdez and then they would list a bunch +of things and you get a really big + + align:start position:0% +of things and you get a really big + + + align:start position:0% +of things and you get a really big +number when you ask that question and + + align:start position:0% +number when you ask that question and + + + align:start position:0% +number when you ask that question and +add it up because most people a lot of + + align:start position:0% +add it up because most people a lot of + + + align:start position:0% +add it up because most people a lot of +people will pay zero that's the most + + align:start position:0% +people will pay zero that's the most + + + align:start position:0% +people will pay zero that's the most +common answer but among those people who + + align:start position:0% +common answer but among those people who + + + align:start position:0% +common answer but among those people who +would pay something standard answers $20 + + align:start position:0% +would pay something standard answers $20 + + + align:start position:0% +would pay something standard answers $20 +so since it's not real money you + + align:start position:0% +so since it's not real money you + + + align:start position:0% +so since it's not real money you +multiply that across 60 70 million + + align:start position:0% +multiply that across 60 70 million + + + align:start position:0% +multiply that across 60 70 million +people you get a and a few people will + + align:start position:0% +people you get a and a few people will + + + align:start position:0% +people you get a and a few people will +put out you know a thousand two thousand + + align:start position:0% +put out you know a thousand two thousand + + + align:start position:0% +put out you know a thousand two thousand +five thousand you'll get hundreds of + + align:start position:0% +five thousand you'll get hundreds of + + + align:start position:0% +five thousand you'll get hundreds of +millions of dollars easily with a + + align:start position:0% +millions of dollars easily with a + + + align:start position:0% +millions of dollars easily with a +question like that does that mean + + align:start position:0% +question like that does that mean + + + align:start position:0% +question like that does that mean +anything this one was also in court in a + + align:start position:0% +anything this one was also in court in a + + + align:start position:0% +anything this one was also in court in a +number of cases does that mean anything + + align:start position:0% +number of cases does that mean anything + + + align:start position:0% +number of cases does that mean anything +one response to it was to do surveys + + align:start position:0% +one response to it was to do surveys + + + align:start position:0% +one response to it was to do surveys +where they took they asked other people + + align:start position:0% +where they took they asked other people + + + align:start position:0% +where they took they asked other people +the same kind of question but they + + align:start position:0% +the same kind of question but they + + + align:start position:0% +the same kind of question but they +doubled the number of birds killed and + + align:start position:0% +doubled the number of birds killed and + + + align:start position:0% +doubled the number of birds killed and +then they asked other people the same + + align:start position:0% +then they asked other people the same + + + align:start position:0% +then they asked other people the same +kind of question they cut the number of + + align:start position:0% +kind of question they cut the number of + + + align:start position:0% +kind of question they cut the number of +birds killed in half that didn't affect + + align:start position:0% +birds killed in half that didn't affect + + + align:start position:0% +birds killed in half that didn't affect +the answers they say oh maybe what I'm + + align:start position:0% +the answers they say oh maybe what I'm + + + align:start position:0% +the answers they say oh maybe what I'm +getting is general environment sentiment + + align:start position:0% +getting is general environment sentiment + + + align:start position:0% +getting is general environment sentiment +that has nothing to do with this + + align:start position:0% +that has nothing to do with this + + + align:start position:0% +that has nothing to do with this +accident but then how do I value the + + align:start position:0% +accident but then how do I value the + + + align:start position:0% +accident but then how do I value the +fact that there was enormous damage to + + align:start position:0% +fact that there was enormous damage to + + + align:start position:0% +fact that there was enormous damage to +natural systems and wildlife if I can't + + align:start position:0% +natural systems and wildlife if I can't + + + align:start position:0% +natural systems and wildlife if I can't +relate it to people in + + align:start position:0% +relate it to people in + + + align:start position:0% +relate it to people in +birds don't vote I'd say that remains an + + align:start position:0% +birds don't vote I'd say that remains an + + + align:start position:0% +birds don't vote I'd say that remains an +unanswered question this notion of + + align:start position:0% +unanswered question this notion of + + + align:start position:0% +unanswered question this notion of +asking people how much would you pay to + + align:start position:0% +asking people how much would you pay to + + + align:start position:0% +asking people how much would you pay to +save a million Birds gives answers that + + align:start position:0% +save a million Birds gives answers that + + + align:start position:0% +save a million Birds gives answers that +seem quite unreliable because you get + + align:start position:0% +seem quite unreliable because you get + + + align:start position:0% +seem quite unreliable because you get +the same answer for a thousand and you + + align:start position:0% +the same answer for a thousand and you + + + align:start position:0% +the same answer for a thousand and you +get the same answer for ten million so + + align:start position:0% +get the same answer for ten million so + + + align:start position:0% +get the same answer for ten million so +you say I don't know what that means but + + align:start position:0% +you say I don't know what that means but + + + align:start position:0% +you say I don't know what that means but +I don't think it's a real it's a real + + align:start position:0% +I don't think it's a real it's a real + + + align:start position:0% +I don't think it's a real it's a real +answer but then how do you value the + + align:start position:0% +answer but then how do you value the + + + align:start position:0% +answer but then how do you value the +birds so number of questions lots of fun + + align:start position:0% +birds so number of questions lots of fun + + + align:start position:0% +birds so number of questions lots of fun +let's go to the case we passed the 1970 + + align:start position:0% +let's go to the case we passed the 1970 + + + align:start position:0% +let's go to the case we passed the 1970 +Clean Air Act Amendments and instructed + + align:start position:0% +Clean Air Act Amendments and instructed + + + align:start position:0% +Clean Air Act Amendments and instructed +EPA to do a lot of things including the + + align:start position:0% +EPA to do a lot of things including the + + + align:start position:0% +EPA to do a lot of things including the +1971 new source performance standard for + + align:start position:0% +1971 new source performance standard for + + + align:start position:0% +1971 new source performance standard for +coal-fired generators we talked last + + align:start position:0% +coal-fired generators we talked last + + + align:start position:0% +coal-fired generators we talked last +time about who were the interest groups + + align:start position:0% +time about who were the interest groups + + + align:start position:0% +time about who were the interest groups +reviewed the bidding who was involved in + + align:start position:0% +reviewed the bidding who was involved in + + + align:start position:0% +reviewed the bidding who was involved in +in setting the 71 standard who were the + + align:start position:0% +in setting the 71 standard who were the + + + align:start position:0% +in setting the 71 standard who were the +interest groups we did this last time + + align:start position:0% +interest groups we did this last time + + + align:start position:0% +interest groups we did this last time +consult your memory what well tree + + align:start position:0% +consult your memory what well tree + + + align:start position:0% +consult your memory what well tree +huggers were very heavily involved + + align:start position:0% +huggers were very heavily involved + + + align:start position:0% +huggers were very heavily involved +getting the Act passed but you don't + + align:start position:0% +getting the Act passed but you don't + + + align:start position:0% +getting the Act passed but you don't +hear the much mention in connection with + + align:start position:0% +hear the much mention in connection with + + + align:start position:0% +hear the much mention in connection with +making this administrative decision this + + align:start position:0% +making this administrative decision this + + + align:start position:0% +making this administrative decision this +was lobbying who are the lobbyists EPA + + align:start position:0% +was lobbying who are the lobbyists EPA + + + align:start position:0% +was lobbying who are the lobbyists EPA +made the decision Casey + + align:start position:0% + + + + align:start position:0% + +we're all the coal producers in + + align:start position:0% +we're all the coal producers in + + + align:start position:0% +we're all the coal producers in +agreement so yeah Eastern coal and + + align:start position:0% +agreement so yeah Eastern coal and + + + align:start position:0% +agreement so yeah Eastern coal and +Western coal and I'm about to lead you + + align:start position:0% +Western coal and I'm about to lead you + + + align:start position:0% +Western coal and I'm about to lead you +to the next question which is why did + + align:start position:0% +to the next question which is why did + + + align:start position:0% +to the next question which is why did +that make it hard we're afraid that an + + align:start position:0% +that make it hard we're afraid that an + + + align:start position:0% +that make it hard we're afraid that an +EPA required heavy emission cuts without + + align:start position:0% +EPA required heavy emission cuts without + + + align:start position:0% +EPA required heavy emission cuts without +specific technology in place to achieve + + align:start position:0% +specific technology in place to achieve + + + align:start position:0% +specific technology in place to achieve +those cuts and people would just switch + + align:start position:0% +those cuts and people would just switch + + + align:start position:0% +those cuts and people would just switch +to using West + + align:start position:0% +to using West + + + align:start position:0% +to using West +that's the problem coal in the u.s. + + align:start position:0% +that's the problem coal in the u.s. + + + align:start position:0% +that's the problem coal in the u.s. +differs dramatically in sulfur content + + align:start position:0% +differs dramatically in sulfur content + + + align:start position:0% +differs dramatically in sulfur content +there's a range particularly in the east + + align:start position:0% +there's a range particularly in the east + + + align:start position:0% +there's a range particularly in the east +it's tends to be low in the West so if + + align:start position:0% +it's tends to be low in the West so if + + + align:start position:0% +it's tends to be low in the West so if +you say you have to have low emissions + + align:start position:0% +you say you have to have low emissions + + + align:start position:0% +you say you have to have low emissions +per kilowatt per megawatt hour kilowatt + + align:start position:0% +per kilowatt per megawatt hour kilowatt + + + align:start position:0% +per kilowatt per megawatt hour kilowatt +hour whichever then for a lot of people + + align:start position:0% +hour whichever then for a lot of people + + + align:start position:0% +hour whichever then for a lot of people +it'll be cheaper to switch to Western + + align:start position:0% +it'll be cheaper to switch to Western + + + align:start position:0% +it'll be cheaper to switch to Western +coal if you say what you have to do is + + align:start position:0% +coal if you say what you have to do is + + + align:start position:0% +coal if you say what you have to do is +scrub that is to say remove sulfur from + + align:start position:0% +scrub that is to say remove sulfur from + + + align:start position:0% +scrub that is to say remove sulfur from +the exhaust then particular if you say + + align:start position:0% +the exhaust then particular if you say + + + align:start position:0% +the exhaust then particular if you say +the percentage you have to remove it may + + align:start position:0% +the percentage you have to remove it may + + + align:start position:0% +the percentage you have to remove it may +be cheaper to use Eastern coal and the + + align:start position:0% +be cheaper to use Eastern coal and the + + + align:start position:0% +be cheaper to use Eastern coal and the +people in the West will go nuts right if + + align:start position:0% +people in the West will go nuts right if + + + align:start position:0% +people in the West will go nuts right if +they're burning really clean coal and + + align:start position:0% +they're burning really clean coal and + + + align:start position:0% +they're burning really clean coal and +they have to also clean the stack they + + align:start position:0% +they have to also clean the stack they + + + align:start position:0% +they have to also clean the stack they +get angry so you have these two very + + align:start position:0% +get angry so you have these two very + + + align:start position:0% +get angry so you have these two very +clearly opposed interests the ones in + + align:start position:0% +clearly opposed interests the ones in + + + align:start position:0% +clearly opposed interests the ones in +the East favored a scrubbing standard + + align:start position:0% +the East favored a scrubbing standard + + + align:start position:0% +the East favored a scrubbing standard +the ones in the West favored an emission + + align:start position:0% +the ones in the West favored an emission + + + align:start position:0% +the ones in the West favored an emission +standard the seventy one performance + + align:start position:0% +standard the seventy one performance + + + align:start position:0% +standard the seventy one performance +standard was a an emission standard 1.2 + + align:start position:0% +standard was a an emission standard 1.2 + + + align:start position:0% +standard was a an emission standard 1.2 +pounds of sulfur dioxide per million Btu + + align:start position:0% +pounds of sulfur dioxide per million Btu + + + align:start position:0% +pounds of sulfur dioxide per million Btu +burned of coal burned + + align:start position:0% +burned of coal burned + + + align:start position:0% +burned of coal burned +what was the cost-benefit analysis + + align:start position:0% +what was the cost-benefit analysis + + + align:start position:0% +what was the cost-benefit analysis +behind that standard yeah + + align:start position:0% + + + + align:start position:0% + +you're giving me a political answer + + align:start position:0% +you're giving me a political answer + + + align:start position:0% +you're giving me a political answer +you're not giving me the cost/benefit + + align:start position:0% +you're not giving me the cost/benefit + + + align:start position:0% +you're not giving me the cost/benefit +did they do any cost-benefit does the + + align:start position:0% +did they do any cost-benefit does the + + + align:start position:0% +did they do any cost-benefit does the +case mention any analysis of costs or + + align:start position:0% +case mention any analysis of costs or + + + align:start position:0% +case mention any analysis of costs or +benefit no no they didn't they just kind + + align:start position:0% +benefit no no they didn't they just kind + + + align:start position:0% +benefit no no they didn't they just kind +of casually you're getting the answer + + align:start position:0% +of casually you're getting the answer + + + align:start position:0% +of casually you're getting the answer +they gave was you can burn most east you + + align:start position:0% +they gave was you can burn most east you + + + align:start position:0% +they gave was you can burn most east you +can scrub most Eastern coal and meet + + align:start position:0% +can scrub most Eastern coal and meet + + + align:start position:0% +can scrub most Eastern coal and meet +that standard that was that was the + + align:start position:0% +that standard that was that was the + + + align:start position:0% +that standard that was that was the +thinking which was very very casual very + + align:start position:0% +thinking which was very very casual very + + + align:start position:0% +thinking which was very very casual very +casual this was challenged + + align:start position:0% +casual this was challenged + + + align:start position:0% +casual this was challenged +does anybody recall what had what the + + align:start position:0% +does anybody recall what had what the + + + align:start position:0% +does anybody recall what had what the +court challenge was all about + + align:start position:0% +court challenge was all about + + + align:start position:0% +court challenge was all about +why was challenge that EPA didn't + + align:start position:0% +why was challenge that EPA didn't + + + align:start position:0% +why was challenge that EPA didn't +adequately consider sludge that would + + align:start position:0% +adequately consider sludge that would + + + align:start position:0% +adequately consider sludge that would +result when you when you when you take + + align:start position:0% +result when you when you when you take + + + align:start position:0% +result when you when you when you take +the when you take the junk out of the + + align:start position:0% +the when you take the junk out of the + + + align:start position:0% +the when you take the junk out of the +emissions you get sludge and you got to + + align:start position:0% +emissions you get sludge and you got to + + + align:start position:0% +emissions you get sludge and you got to +you got to treat that or worry about it + + align:start position:0% +you got to treat that or worry about it + + + align:start position:0% +you got to treat that or worry about it +and it went back you they didn't + + align:start position:0% +and it went back you they didn't + + + align:start position:0% +and it went back you they didn't +adequately consider it and it was sent + + align:start position:0% +adequately consider it and it was sent + + + align:start position:0% +adequately consider it and it was sent +back to consider it and they considered + + align:start position:0% +back to consider it and they considered + + + align:start position:0% +back to consider it and they considered +it and didn't change the rule right the + + align:start position:0% +it and didn't change the rule right the + + + align:start position:0% +it and didn't change the rule right the +requirement isn't about outcome the + + align:start position:0% +requirement isn't about outcome the + + + align:start position:0% +requirement isn't about outcome the +requirements about process did you + + align:start position:0% +requirements about process did you + + + align:start position:0% +requirements about process did you +adequately consider that requires + + align:start position:0% +adequately consider that requires + + + align:start position:0% +adequately consider that requires +somebody to write something that says + + align:start position:0% +somebody to write something that says + + + align:start position:0% +somebody to write something that says +here's what they said here's what we + + align:start position:0% +here's what they said here's what we + + + align:start position:0% +here's what they said here's what we +think about it here's why it doesn't + + align:start position:0% +think about it here's why it doesn't + + + align:start position:0% +think about it here's why it doesn't +change our conclusion you delegate that + + align:start position:0% +change our conclusion you delegate that + + + align:start position:0% +change our conclusion you delegate that +somewhere down in the organization deal + + align:start position:0% +somewhere down in the organization deal + + + align:start position:0% +somewhere down in the organization deal +with this write me up write me five + + align:start position:0% +with this write me up write me five + + + align:start position:0% +with this write me up write me five +pages okay would you have done anything + + align:start position:0% +pages okay would you have done anything + + + align:start position:0% +pages okay would you have done anything +else the case makes the interesting + + align:start position:0% +else the case makes the interesting + + + align:start position:0% +else the case makes the interesting +point that EPA was doing a lot of stuff + + align:start position:0% +point that EPA was doing a lot of stuff + + + align:start position:0% +point that EPA was doing a lot of stuff +Congress does this all the time you set + + align:start position:0% +Congress does this all the time you set + + + align:start position:0% +Congress does this all the time you set +up a new agency or you pass a + + align:start position:0% +up a new agency or you pass a + + + align:start position:0% +up a new agency or you pass a +comprehensive law like dodd-frank and + + align:start position:0% +comprehensive law like dodd-frank and + + + align:start position:0% +comprehensive law like dodd-frank and +you say to the agencies we need the + + align:start position:0% +you say to the agencies we need the + + + align:start position:0% +you say to the agencies we need the +following five thousand rules issued + + align:start position:0% +following five thousand rules issued + + + align:start position:0% +following five thousand rules issued +within 18 months and the agency says + + align:start position:0% +within 18 months and the agency says + + + align:start position:0% +within 18 months and the agency says +I've got six people and you do what you + + align:start position:0% +I've got six people and you do what you + + + align:start position:0% +I've got six people and you do what you +can but you don't spend your lifetime on + + align:start position:0% +can but you don't spend your lifetime on + + + align:start position:0% +can but you don't spend your lifetime on +this one because this is new coal-fired + + align:start position:0% +this one because this is new coal-fired + + + align:start position:0% +this one because this is new coal-fired +power plants we've got this whole + + align:start position:0% +power plants we've got this whole + + + align:start position:0% +power plants we've got this whole +problem with dealing with existing + + align:start position:0% +problem with dealing with existing + + + align:start position:0% +problem with dealing with existing +sources with sip plans what's a sip look + + align:start position:0% +sources with sip plans what's a sip look + + + align:start position:0% +sources with sip plans what's a sip look +like what are sip + + align:start position:0% +like what are sip + + + align:start position:0% +like what are sip +review state implementation plans what's + + align:start position:0% +review state implementation plans what's + + + align:start position:0% +review state implementation plans what's +all that about what are our air quality + + align:start position:0% +all that about what are our air quality + + + align:start position:0% +all that about what are our air quality +standards and oh by the way we've got to + + align:start position:0% +standards and oh by the way we've got to + + + align:start position:0% +standards and oh by the way we've got to +do this thing so they did it pretty + + align:start position:0% +do this thing so they did it pretty + + + align:start position:0% +do this thing so they did it pretty +casually would you is it obvious that + + align:start position:0% +casually would you is it obvious that + + + align:start position:0% +casually would you is it obvious that +there was a better approach would you + + align:start position:0% +there was a better approach would you + + + align:start position:0% +there was a better approach would you +have done a scrubbing standard KC I mean + + align:start position:0% +have done a scrubbing standard KC I mean + + + align:start position:0% +have done a scrubbing standard KC I mean +you were you probably would have done + + align:start position:0% +you were you probably would have done + + + align:start position:0% +you were you probably would have done +what they did + + align:start position:0% + + + + align:start position:0% + +we'll keep the can we'll kick the can + + align:start position:0% +we'll keep the can we'll kick the can + + + align:start position:0% +we'll keep the can we'll kick the can +down the road okay so this cruises this + + align:start position:0% +down the road okay so this cruises this + + + align:start position:0% +down the road okay so this cruises this +cruise is along now Wyatt what puts + + align:start position:0% +cruise is along now Wyatt what puts + + + align:start position:0% +cruise is along now Wyatt what puts +scrubbing on the table would reduce + + align:start position:0% +scrubbing on the table would reduce + + + align:start position:0% +scrubbing on the table would reduce +pollution in their area they were + + align:start position:0% +pollution in their area they were + + + align:start position:0% +pollution in their area they were +particularly worried maybe came a little + + align:start position:0% +particularly worried maybe came a little + + + align:start position:0% +particularly worried maybe came a little +later but they were particularly worried + + align:start position:0% +later but they were particularly worried + + + align:start position:0% +later but they were particularly worried +at this point about haze and you still + + align:start position:0% +at this point about haze and you still + + + align:start position:0% +at this point about haze and you still +see it in the West that you get what you + + align:start position:0% +see it in the West that you get what you + + + align:start position:0% +see it in the West that you get what you +get a lot more haze than you used to + + align:start position:0% +get a lot more haze than you used to + + + align:start position:0% +get a lot more haze than you used to +have and it's not hazardous to human + + align:start position:0% +have and it's not hazardous to human + + + align:start position:0% +have and it's not hazardous to human +health but it's obnoxious haze in the + + align:start position:0% +health but it's obnoxious haze in the + + + align:start position:0% +health but it's obnoxious haze in the +Grand Canyon means you just don't have + + align:start position:0% +Grand Canyon means you just don't have + + + align:start position:0% +Grand Canyon means you just don't have +those wonderful views so the navajo sued + + align:start position:0% +those wonderful views so the navajo sued + + + align:start position:0% +those wonderful views so the navajo sued +they lost the environmentalists the + + align:start position:0% +they lost the environmentalists the + + + align:start position:0% +they lost the environmentalists the +other issue was the court some states in + + align:start position:0% +other issue was the court some states in + + + align:start position:0% +other issue was the court some states in +the West that were in full compliance + + align:start position:0% +the West that were in full compliance + + + align:start position:0% +the West that were in full compliance +submitted state implementation plans + + align:start position:0% +submitted state implementation plans + + + align:start position:0% +submitted state implementation plans +that let them get dirtier but still be + + align:start position:0% +that let them get dirtier but still be + + + align:start position:0% +that let them get dirtier but still be +in compliance with the law and the + + align:start position:0% +in compliance with the law and the + + + align:start position:0% +in compliance with the law and the +courts rejected those so what do you do + + align:start position:0% +courts rejected those so what do you do + + + align:start position:0% +courts rejected those so what do you do +about that because you'd like to develop + + align:start position:0% +about that because you'd like to develop + + + align:start position:0% +about that because you'd like to develop +in the West you'd like to grow you'd + + align:start position:0% +in the West you'd like to grow you'd + + + align:start position:0% +in the West you'd like to grow you'd +like to build stuff the court says if + + align:start position:0% +like to build stuff the court says if + + + align:start position:0% +like to build stuff the court says if +even if you're clean you can't get + + align:start position:0% +even if you're clean you can't get + + + align:start position:0% +even if you're clean you can't get +dirtier and people were installing the + + align:start position:0% +dirtier and people were installing the + + + align:start position:0% +dirtier and people were installing the +the air quality standards were nearby + + align:start position:0% +the air quality standards were nearby + + + align:start position:0% +the air quality standards were nearby +right so one of the ways people were + + align:start position:0% +right so one of the ways people were + + + align:start position:0% +right so one of the ways people were +dealing with sulfur dioxide was to build + + align:start position:0% +dealing with sulfur dioxide was to build + + + align:start position:0% +dealing with sulfur dioxide was to build +these monstrously high stacks which + + align:start position:0% +these monstrously high stacks which + + + align:start position:0% +these monstrously high stacks which +would just let the stuff diffuse over a + + align:start position:0% +would just let the stuff diffuse over a + + + align:start position:0% +would just let the stuff diffuse over a +wide area + + align:start position:0% +wide area + + + align:start position:0% +wide area +so the standard which is about + + align:start position:0% +so the standard which is about + + + align:start position:0% +so the standard which is about +concentration wasn't violated + + align:start position:0% +concentration wasn't violated + + + align:start position:0% +concentration wasn't violated +the environmentalists were not happy to + + align:start position:0% +the environmentalists were not happy to + + + align:start position:0% +the environmentalists were not happy to +say the least that just didn't seem like + + align:start position:0% +say the least that just didn't seem like + + + align:start position:0% +say the least that just didn't seem like +the right approach to the problem that's + + align:start position:0% +the right approach to the problem that's + + + align:start position:0% +the right approach to the problem that's +take the dirt spread the dirt it's not + + align:start position:0% +take the dirt spread the dirt it's not + + + align:start position:0% +take the dirt spread the dirt it's not +too dirty anyplace see same dirt spread + + align:start position:0% +too dirty anyplace see same dirt spread + + + align:start position:0% +too dirty anyplace see same dirt spread +so everybody the Navajos wanted stuff + + align:start position:0% +so everybody the Navajos wanted stuff + + + align:start position:0% +so everybody the Navajos wanted stuff +scrubbed the scrubbers were potential + + align:start position:0% +scrubbed the scrubbers were potential + + + align:start position:0% +scrubbed the scrubbers were potential +way of dealing with this western states + + align:start position:0% +way of dealing with this western states + + + align:start position:0% +way of dealing with this western states +problem there may be other ways but in + + align:start position:0% +problem there may be other ways but in + + + align:start position:0% +problem there may be other ways but in +any case you had to go you had to reopen + + align:start position:0% +any case you had to go you had to reopen + + + align:start position:0% +any case you had to go you had to reopen +the law to deal with western states to + + align:start position:0% +the law to deal with western states to + + + align:start position:0% +the law to deal with western states to +deal with that court decision that + + align:start position:0% +deal with that court decision that + + + align:start position:0% +deal with that court decision that +basically didn't let him build anything + + align:start position:0% +basically didn't let him build anything + + + align:start position:0% +basically didn't let him build anything +okay + + align:start position:0% +okay + + + align:start position:0% +okay +who are the who are the interest groups + + align:start position:0% +who are the who are the interest groups + + + align:start position:0% +who are the who are the interest groups +here we're in we're now in the process + + align:start position:0% +here we're in we're now in the process + + + align:start position:0% +here we're in we're now in the process +of writing it shouldn't say NSPS it + + align:start position:0% +of writing it shouldn't say NSPS it + + + align:start position:0% +of writing it shouldn't say NSPS it +should say Clean Air Act legislation so + + align:start position:0% +should say Clean Air Act legislation so + + + align:start position:0% +should say Clean Air Act legislation so +we go through 76 77 amending process of + + align:start position:0% +we go through 76 77 amending process of + + + align:start position:0% +we go through 76 77 amending process of +amending the bill and I left all that + + align:start position:0% +amending the bill and I left all that + + + align:start position:0% +amending the bill and I left all that +stuff in the case because it's + + align:start position:0% +stuff in the case because it's + + + align:start position:0% +stuff in the case because it's +interesting I think to see it once to + + align:start position:0% +interesting I think to see it once to + + + align:start position:0% +interesting I think to see it once to +see the process of trying to write + + align:start position:0% +see the process of trying to write + + + align:start position:0% +see the process of trying to write +something it gets passed here it gets + + align:start position:0% +something it gets passed here it gets + + + align:start position:0% +something it gets passed here it gets +rejected there the session ends you + + align:start position:0% +rejected there the session ends you + + + align:start position:0% +rejected there the session ends you +start over again you try issues get + + align:start position:0% +start over again you try issues get + + + align:start position:0% +start over again you try issues get +debated multiple times often before + + align:start position:0% +debated multiple times often before + + + align:start position:0% +debated multiple times often before +things are finally passed into law and + + align:start position:0% +things are finally passed into law and + + + align:start position:0% +things are finally passed into law and +this is an example there was the 76 + + align:start position:0% +this is an example there was the 76 + + + align:start position:0% +this is an example there was the 76 +process then there was a 77 process who + + align:start position:0% +process then there was a 77 process who + + + align:start position:0% +process then there was a 77 process who +are the players Sierra Club were the + + align:start position:0% +are the players Sierra Club were the + + + align:start position:0% +are the players Sierra Club were the +environmental groups generally notice + + align:start position:0% +environmental groups generally notice + + + align:start position:0% +environmental groups generally notice +they're not marching in the streets + + align:start position:0% +they're not marching in the streets + + + align:start position:0% +they're not marching in the streets +they're lobbying so we've sort of seen + + align:start position:0% +they're lobbying so we've sort of seen + + + align:start position:0% +they're lobbying so we've sort of seen +the environmental movement transformed + + align:start position:0% +the environmental movement transformed + + + align:start position:0% +the environmental movement transformed +in part into something that looks more + + align:start position:0% +in part into something that looks more + + + align:start position:0% +in part into something that looks more +like a conventional interest group they + + align:start position:0% +like a conventional interest group they + + + align:start position:0% +like a conventional interest group they +have lawyers the lawyers are in the + + align:start position:0% +have lawyers the lawyers are in the + + + align:start position:0% +have lawyers the lawyers are in the +details the lawyers are in the lobby + + align:start position:0% +details the lawyers are in the lobby + + + align:start position:0% +details the lawyers are in the lobby +talking to people they threaten you know + + align:start position:0% +talking to people they threaten you know + + + align:start position:0% +talking to people they threaten you know +we can have 9 million people write their + + align:start position:0% +we can have 9 million people write their + + + align:start position:0% +we can have 9 million people write their +congressmen about this because we're a + + align:start position:0% +congressmen about this because we're a + + + align:start position:0% +congressmen about this because we're a +grassroots organization so they're a + + align:start position:0% +grassroots organization so they're a + + + align:start position:0% +grassroots organization so they're a +little bit of a social movement still + + align:start position:0% +little bit of a social movement still + + + align:start position:0% +little bit of a social movement still +but they're lobbying who else anybody + + align:start position:0% +but they're lobbying who else anybody + + + align:start position:0% +but they're lobbying who else anybody +else the environmentalists wrote that + + align:start position:0% +else the environmentalists wrote that + + + align:start position:0% +else the environmentalists wrote that +law + + align:start position:0% + + + + align:start position:0% + +coal producers fell asleep both both + + align:start position:0% +coal producers fell asleep both both + + + align:start position:0% +coal producers fell asleep both both +sets east and west I mean is this a + + align:start position:0% +sets east and west I mean is this a + + + align:start position:0% +sets east and west I mean is this a +we're now back in play we're now back in + + align:start position:0% +we're now back in play we're now back in + + + align:start position:0% +we're now back in play we're now back in +play worrying about scrubbing worrying + + align:start position:0% +play worrying about scrubbing worrying + + + align:start position:0% +play worrying about scrubbing worrying +about high sulfur coal low sulfur coal + + align:start position:0% +about high sulfur coal low sulfur coal + + + align:start position:0% +about high sulfur coal low sulfur coal +and of course the people well in the + + align:start position:0% +and of course the people well in the + + + align:start position:0% +and of course the people well in the +western states also the utilities I'm + + align:start position:0% +western states also the utilities I'm + + + align:start position:0% +western states also the utilities I'm +not quite sure why I put the utilities + + align:start position:0% +not quite sure why I put the utilities + + + align:start position:0% +not quite sure why I put the utilities +there it didn't have the utilities there + + align:start position:0% +there it didn't have the utilities there + + + align:start position:0% +there it didn't have the utilities there +but the utilities are also involved + + align:start position:0% +but the utilities are also involved + + + align:start position:0% +but the utilities are also involved +because they're gonna bear the cost of + + align:start position:0% +because they're gonna bear the cost of + + + align:start position:0% +because they're gonna bear the cost of +all this scrubbing is not cheap so the + + align:start position:0% +all this scrubbing is not cheap so the + + + align:start position:0% +all this scrubbing is not cheap so the +question of do you scrub don't you scrub + + align:start position:0% +question of do you scrub don't you scrub + + + align:start position:0% +question of do you scrub don't you scrub +can you develop in the West ok where was + + align:start position:0% +can you develop in the West ok where was + + + align:start position:0% +can you develop in the West ok where was +the Carter Administration you recall so + + align:start position:0% +the Carter Administration you recall so + + + align:start position:0% +the Carter Administration you recall so +they were willing to scrub so they + + align:start position:0% +they were willing to scrub so they + + + align:start position:0% +they were willing to scrub so they +wanted us to scrub to sell the + + align:start position:0% +wanted us to scrub to sell the + + + align:start position:0% +wanted us to scrub to sell the +environmental movement on the use of + + align:start position:0% +environmental movement on the use of + + + align:start position:0% +environmental movement on the use of +coal for energy security if you made + + align:start position:0% +coal for energy security if you made + + + align:start position:0% +coal for energy security if you made +coal too expensive people were still + + align:start position:0% +coal too expensive people were still + + + align:start position:0% +coal too expensive people were still +generating a lot of power from oil and + + align:start position:0% +generating a lot of power from oil and + + + align:start position:0% +generating a lot of power from oil and +they really wanted to move away from oil + + align:start position:0% +they really wanted to move away from oil + + + align:start position:0% +they really wanted to move away from oil +for security reasons so hay scrubbing + + align:start position:0% +for security reasons so hay scrubbing + + + align:start position:0% +for security reasons so hay scrubbing +costs money but it's a security issue ok + + align:start position:0% +costs money but it's a security issue ok + + + align:start position:0% +costs money but it's a security issue ok +so you have the Carter Administration + + align:start position:0% +so you have the Carter Administration + + + align:start position:0% +so you have the Carter Administration +kind of positioned in favor of scrubbing + + align:start position:0% +kind of positioned in favor of scrubbing + + + align:start position:0% +kind of positioned in favor of scrubbing +at least at the White House you got + + align:start position:0% +at least at the White House you got + + + align:start position:0% +at least at the White House you got +Eastern coal that loves scrubbing + + align:start position:0% +Eastern coal that loves scrubbing + + + align:start position:0% +Eastern coal that loves scrubbing +Western coal that hates scrubbing + + align:start position:0% +Western coal that hates scrubbing + + + align:start position:0% +Western coal that hates scrubbing +environmentalists have come to love it + + align:start position:0% +environmentalists have come to love it + + + align:start position:0% +environmentalists have come to love it +right because it's now a technology + + align:start position:0% +right because it's now a technology + + + align:start position:0% +right because it's now a technology +solution it's a standard it's the kind + + align:start position:0% +solution it's a standard it's the kind + + + align:start position:0% +solution it's a standard it's the kind +of thing they tend to like put the thing + + align:start position:0% +of thing they tend to like put the thing + + + align:start position:0% +of thing they tend to like put the thing +on the smokestack make sure it's running + + align:start position:0% +on the smokestack make sure it's running + + + align:start position:0% +on the smokestack make sure it's running +that's swell + + align:start position:0% +that's swell + + + align:start position:0% +that's swell +don't give me any nonsense the western + + align:start position:0% +don't give me any nonsense the western + + + align:start position:0% +don't give me any nonsense the western +states say well whatever you do we have + + align:start position:0% +states say well whatever you do we have + + + align:start position:0% +states say well whatever you do we have +to be able to grow we have to be able to + + align:start position:0% +to be able to grow we have to be able to + + + align:start position:0% +to be able to grow we have to be able to +build things in pristine areas at least + + align:start position:0% +build things in pristine areas at least + + + align:start position:0% +build things in pristine areas at least +some of them so what's the final outcome + + align:start position:0% +some of them so what's the final outcome + + + align:start position:0% +some of them so what's the final outcome +and well we talk about the outcome but + + align:start position:0% +and well we talk about the outcome but + + + align:start position:0% +and well we talk about the outcome but +who favored it what did we get we got + + align:start position:0% +who favored it what did we get we got + + + align:start position:0% +who favored it what did we get we got +confused + + align:start position:0% +confused + + + align:start position:0% +confused +language right we got confused languages + + align:start position:0% +language right we got confused languages + + + align:start position:0% +language right we got confused languages +the final outcome and the confused + + align:start position:0% +the final outcome and the confused + + + align:start position:0% +the final outcome and the confused +language if you read that and I actually + + align:start position:0% +language if you read that and I actually + + + align:start position:0% +language if you read that and I actually +I did this case out of a larger piece + + align:start position:0% +I did this case out of a larger piece + + + align:start position:0% +I did this case out of a larger piece +I'd left out a lot of detail because + + align:start position:0% +I'd left out a lot of detail because + + + align:start position:0% +I'd left out a lot of detail because +there this also happens legislation goes + + align:start position:0% +there this also happens legislation goes + + + align:start position:0% +there this also happens legislation goes +to staff and you do not see senators at + + align:start position:0% +to staff and you do not see senators at + + + align:start position:0% +to staff and you do not see senators at +3:00 in the morning rewriting details of + + align:start position:0% +3:00 in the morning rewriting details of + + + align:start position:0% +3:00 in the morning rewriting details of +thousand-page bills + + align:start position:0% +thousand-page bills + + + align:start position:0% +thousand-page bills +you see senators giving instruction to + + align:start position:0% +you see senators giving instruction to + + + align:start position:0% +you see senators giving instruction to +people saying look the bill ayat the + + align:start position:0% +people saying look the bill ayat the + + + align:start position:0% +people saying look the bill ayat the +bill has to get this done + + align:start position:0% +bill has to get this done + + + align:start position:0% +bill has to get this done +and so at 3:00 in the morning over pizza + + align:start position:0% +and so at 3:00 in the morning over pizza + + + align:start position:0% +and so at 3:00 in the morning over pizza +people are saying well let me just add + + align:start position:0% +people are saying well let me just add + + + align:start position:0% +people are saying well let me just add +this and then it goes from the Senate to + + align:start position:0% +this and then it goes from the Senate to + + + align:start position:0% +this and then it goes from the Senate to +the house and somebody in the house says + + align:start position:0% +the house and somebody in the house says + + + align:start position:0% +the house and somebody in the house says +now we can't have that let you take that + + align:start position:0% +now we can't have that let you take that + + + align:start position:0% +now we can't have that let you take that +out I'll put this in and then the bill + + align:start position:0% +out I'll put this in and then the bill + + + align:start position:0% +out I'll put this in and then the bill +gets passed and then somebody says well + + align:start position:0% +gets passed and then somebody says well + + + align:start position:0% +gets passed and then somebody says well +but that doesn't read right so let me + + align:start position:0% +but that doesn't read right so let me + + + align:start position:0% +but that doesn't read right so let me +make sure the report on the bill says + + align:start position:0% +make sure the report on the bill says + + + align:start position:0% +make sure the report on the bill says +what we really mean and then somebody + + align:start position:0% +what we really mean and then somebody + + + align:start position:0% +what we really mean and then somebody +else is no no so what you got in this + + align:start position:0% +else is no no so what you got in this + + + align:start position:0% +else is no no so what you got in this +case was confused language that sort of + + align:start position:0% +case was confused language that sort of + + + align:start position:0% +case was confused language that sort of +seemed to favor scrubbing but was + + align:start position:0% +seemed to favor scrubbing but was + + + align:start position:0% +seemed to favor scrubbing but was +sufficiently ambiguous to give some + + align:start position:0% +sufficiently ambiguous to give some + + + align:start position:0% +sufficiently ambiguous to give some +leeway who liked that who was in favor + + align:start position:0% +leeway who liked that who was in favor + + + align:start position:0% +leeway who liked that who was in favor +of that who pushed was happy at the end + + align:start position:0% +of that who pushed was happy at the end + + + align:start position:0% +of that who pushed was happy at the end +of the day who felt they'd won + + align:start position:0% + + + + align:start position:0% + +Western Western call you're saying yeah + + align:start position:0% +Western Western call you're saying yeah + + + align:start position:0% +Western Western call you're saying yeah +it kind of favored scrubbing all the + + align:start position:0% +it kind of favored scrubbing all the + + + align:start position:0% +it kind of favored scrubbing all the +ambiguity yeah yeah yeah but they would + + align:start position:0% +ambiguity yeah yeah yeah but they would + + + align:start position:0% +ambiguity yeah yeah yeah but they would +rather have had oh nothing that that + + align:start position:0% +rather have had oh nothing that that + + + align:start position:0% +rather have had oh nothing that that +it's the administrators job to set a + + align:start position:0% +it's the administrators job to set a + + + align:start position:0% +it's the administrators job to set a +standard and the administrator had done + + align:start position:0% +standard and the administrator had done + + + align:start position:0% +standard and the administrator had done +it once and that was a performance + + align:start position:0% +it once and that was a performance + + + align:start position:0% +it once and that was a performance +standard this now said the administrator + + align:start position:0% +standard this now said the administrator + + + align:start position:0% +standard this now said the administrator +also has to cassette a percentage + + align:start position:0% +also has to cassette a percentage + + + align:start position:0% +also has to cassette a percentage +removal doesn't say it has to be + + align:start position:0% +removal doesn't say it has to be + + + align:start position:0% +removal doesn't say it has to be +positive but has to set a percentage + + align:start position:0% +positive but has to set a percentage + + + align:start position:0% +positive but has to set a percentage +remove has to consider costs has to set + + align:start position:0% +remove has to consider costs has to set + + + align:start position:0% +remove has to consider costs has to set +a percentage removal has to at least + + align:start position:0% +a percentage removal has to at least + + + align:start position:0% +a percentage removal has to at least +look at scrubbing the earlier law didn't + + align:start position:0% +look at scrubbing the earlier law didn't + + + align:start position:0% +look at scrubbing the earlier law didn't +say had to look at scrubbing who would + + align:start position:0% +say had to look at scrubbing who would + + + align:start position:0% +say had to look at scrubbing who would +like that yeah + + align:start position:0% +like that yeah + + + align:start position:0% +like that yeah +utilities sort of liked it Eastern coal + + align:start position:0% +utilities sort of liked it Eastern coal + + + align:start position:0% +utilities sort of liked it Eastern coal +sort of liked it because Eastern coal + + align:start position:0% +sort of liked it because Eastern coal + + + align:start position:0% +sort of liked it because Eastern coal +liked anything that moved towards + + align:start position:0% +liked anything that moved towards + + + align:start position:0% +liked anything that moved towards +scrubbing and environmentalists liked it + + align:start position:0% +scrubbing and environmentalists liked it + + + align:start position:0% +scrubbing and environmentalists liked it +because it favored scrubbing so that's + + align:start position:0% +because it favored scrubbing so that's + + + align:start position:0% +because it favored scrubbing so that's +that's the interesting the interesting + + align:start position:0% +that's the interesting the interesting + + + align:start position:0% +that's the interesting the interesting +little little irony right I mean you had + + align:start position:0% +little little irony right I mean you had + + + align:start position:0% +little little irony right I mean you had +environmentalists and Eastern coal + + align:start position:0% +environmentalists and Eastern coal + + + align:start position:0% +environmentalists and Eastern coal +favoring the use of a dirty fuel that's + + align:start position:0% +favoring the use of a dirty fuel that's + + + align:start position:0% +favoring the use of a dirty fuel that's +an alliance and the great quote in the + + align:start position:0% +an alliance and the great quote in the + + + align:start position:0% +an alliance and the great quote in the +case you almost never hear anything like + + align:start position:0% +case you almost never hear anything like + + + align:start position:0% +case you almost never hear anything like +this it's just amazing it says it made + + align:start position:0% +this it's just amazing it says it made + + + align:start position:0% +this it's just amazing it says it made +sense for the dirty coal producers to + + align:start position:0% +sense for the dirty coal producers to + + + align:start position:0% +sense for the dirty coal producers to +abandon their campaign to weaken + + align:start position:0% +abandon their campaign to weaken + + + align:start position:0% +abandon their campaign to weaken +standards and support the most expensive + + align:start position:0% +standards and support the most expensive + + + align:start position:0% +standards and support the most expensive +possible clean air solution Universal + + align:start position:0% +possible clean air solution Universal + + + align:start position:0% +possible clean air solution Universal +scrubbing which is what they thought + + align:start position:0% +scrubbing which is what they thought + + + align:start position:0% +scrubbing which is what they thought +they got from Congress they thought they + + align:start position:0% +they got from Congress they thought they + + + align:start position:0% +they got from Congress they thought they +got Universal scrubbing you could read + + align:start position:0% +got Universal scrubbing you could read + + + align:start position:0% +got Universal scrubbing you could read +the law that way and this is a Sierra + + align:start position:0% +the law that way and this is a Sierra + + + align:start position:0% +the law that way and this is a Sierra +Club a lawyer on behalf of the Sierra + + align:start position:0% +Club a lawyer on behalf of the Sierra + + + align:start position:0% +Club a lawyer on behalf of the Sierra +Club he condemned that 1.2 pound + + align:start position:0% +Club he condemned that 1.2 pound + + + align:start position:0% +Club he condemned that 1.2 pound +standard because quote Eastern high + + align:start position:0% +standard because quote Eastern high + + + align:start position:0% +standard because quote Eastern high +sulfur coal which is now available is + + align:start position:0% +sulfur coal which is now available is + + + align:start position:0% +sulfur coal which is now available is +having a hard time getting a market + + align:start position:0% +having a hard time getting a market + + + align:start position:0% +having a hard time getting a market +because of the comparative cheapness of + + align:start position:0% +because of the comparative cheapness of + + + align:start position:0% +because of the comparative cheapness of +bringing in Western low sulfur coal + + align:start position:0% +bringing in Western low sulfur coal + + + align:start position:0% +bringing in Western low sulfur coal +eastern dirty coal isn't selling well + + align:start position:0% +eastern dirty coal isn't selling well + + + align:start position:0% +eastern dirty coal isn't selling well +because Western clean coal is cheaper + + align:start position:0% +because Western clean coal is cheaper + + + align:start position:0% +because Western clean coal is cheaper +says the Sierra Club + + align:start position:0% +says the Sierra Club + + + align:start position:0% +says the Sierra Club +okay this is a picture of politics + + align:start position:0% +okay this is a picture of politics + + + align:start position:0% +okay this is a picture of politics +people are getting what they can get + + align:start position:0% +people are getting what they can get + + + align:start position:0% +people are getting what they can get +building coalitions this is not the + + align:start position:0% +building coalitions this is not the + + + align:start position:0% +building coalitions this is not the +Sierra Club trashing the environment + + align:start position:0% +Sierra Club trashing the environment + + + align:start position:0% +Sierra Club trashing the environment +this is the Sierra Club pushing + + align:start position:0% +this is the Sierra Club pushing + + + align:start position:0% +this is the Sierra Club pushing +scrubbing the Sierra Club wants + + align:start position:0% +scrubbing the Sierra Club wants + + + align:start position:0% +scrubbing the Sierra Club wants +scrubbing and to get scrubbing they are + + align:start position:0% +scrubbing and to get scrubbing they are + + + align:start position:0% +scrubbing and to get scrubbing they are +they have an alliance with Eastern coal + + align:start position:0% +they have an alliance with Eastern coal + + + align:start position:0% +they have an alliance with Eastern coal +producers who also want scrubbing you + + align:start position:0% +producers who also want scrubbing you + + + align:start position:0% +producers who also want scrubbing you +might say gee wouldn't the Sierra Club + + align:start position:0% +might say gee wouldn't the Sierra Club + + + align:start position:0% +might say gee wouldn't the Sierra Club +serve the environment better if the + + align:start position:0% +serve the environment better if the + + + align:start position:0% +serve the environment better if the +Sierra Club said just tighten the + + align:start position:0% +Sierra Club said just tighten the + + + align:start position:0% +Sierra Club said just tighten the +standard well they weren't going to get + + align:start position:0% +standard well they weren't going to get + + + align:start position:0% +standard well they weren't going to get +it because Eastern coal producers were + + align:start position:0% +it because Eastern coal producers were + + + align:start position:0% +it because Eastern coal producers were +too strong so what they thought they + + align:start position:0% +too strong so what they thought they + + + align:start position:0% +too strong so what they thought they +could get was scrub the dirty coal may + + align:start position:0% +could get was scrub the dirty coal may + + + align:start position:0% +could get was scrub the dirty coal may +be cynical + + align:start position:0% +be cynical + + + align:start position:0% +be cynical +maybe not cynical was it irrational well + + align:start position:0% +maybe not cynical was it irrational well + + + align:start position:0% +maybe not cynical was it irrational well +that's you know people jumped up and + + align:start position:0% +that's you know people jumped up and + + + align:start position:0% +that's you know people jumped up and +down about this what does what a bizarre + + align:start position:0% +down about this what does what a bizarre + + + align:start position:0% +down about this what does what a bizarre +alliance the environmental interest + + align:start position:0% +alliance the environmental interest + + + align:start position:0% +alliance the environmental interest +groups arm-in-arm with the dirty coal + + align:start position:0% +groups arm-in-arm with the dirty coal + + + align:start position:0% +groups arm-in-arm with the dirty coal +producers well they both got what they + + align:start position:0% +producers well they both got what they + + + align:start position:0% +producers well they both got what they +wanted scrubbing or they thought they + + align:start position:0% +wanted scrubbing or they thought they + + + align:start position:0% +wanted scrubbing or they thought they +got scrubbing okay I'll walk a little + + align:start position:0% +got scrubbing okay I'll walk a little + + + align:start position:0% +got scrubbing okay I'll walk a little +bit just in the interest of time through + + align:start position:0% +bit just in the interest of time through + + + align:start position:0% +bit just in the interest of time through +through how we got to the new source + + align:start position:0% +through how we got to the new source + + + align:start position:0% +through how we got to the new source +performance standard because I want to + + align:start position:0% +performance standard because I want to + + + align:start position:0% +performance standard because I want to +spend more time on 1980 so what you had + + align:start position:0% +spend more time on 1980 so what you had + + + align:start position:0% +spend more time on 1980 so what you had +in the administration was a split right + + align:start position:0% +in the administration was a split right + + + align:start position:0% +in the administration was a split right +the EIR office says these guys won in + + align:start position:0% +the EIR office says these guys won in + + + align:start position:0% +the EIR office says these guys won in +Congress they went in trying to get + + align:start position:0% +Congress they went in trying to get + + + align:start position:0% +Congress they went in trying to get +scrubbing they got scrubbing let's give + + align:start position:0% +scrubbing they got scrubbing let's give + + + align:start position:0% +scrubbing they got scrubbing let's give +them scrubbing we'll set the new + + align:start position:0% +them scrubbing we'll set the new + + + align:start position:0% +them scrubbing we'll set the new +performance standard is requiring 90 + + align:start position:0% +performance standard is requiring 90 + + + align:start position:0% +performance standard is requiring 90 +percent scrubbing The Economist's always + + align:start position:0% +percent scrubbing The Economist's always + + + align:start position:0% +percent scrubbing The Economist's always +the heroes of my story the Department of + + align:start position:0% +the heroes of my story the Department of + + + align:start position:0% +the heroes of my story the Department of +Energy the planning office in EPA said + + align:start position:0% +Energy the planning office in EPA said + + + align:start position:0% +Energy the planning office in EPA said +why don't we just tighten the standard + + align:start position:0% +why don't we just tighten the standard + + + align:start position:0% +why don't we just tighten the standard +the law says we have to consider a + + align:start position:0% +the law says we have to consider a + + + align:start position:0% +the law says we have to consider a +percentage removal we'll make it zero + + align:start position:0% +percentage removal we'll make it zero + + + align:start position:0% +percentage removal we'll make it zero +tighten the standard from one point two + + align:start position:0% +tighten the standard from one point two + + + align:start position:0% +tighten the standard from one point two +pounds per million Btu to 0.55 pounds + + align:start position:0% +pounds per million Btu to 0.55 pounds + + + align:start position:0% +pounds per million Btu to 0.55 pounds +per million Btu you do it in the West + + align:start position:0% +per million Btu you do it in the West + + + align:start position:0% +per million Btu you do it in the West +with low sulfur coal you do it in these + + align:start position:0% +with low sulfur coal you do it in these + + + align:start position:0% +with low sulfur coal you do it in these +a little tough to do it in the East but + + align:start position:0% +a little tough to do it in the East but + + + align:start position:0% +a little tough to do it in the East but +we're gonna tighten the standard that's + + align:start position:0% +we're gonna tighten the standard that's + + + align:start position:0% +we're gonna tighten the standard that's +displayed within the administration + + align:start position:0% +displayed within the administration + + + align:start position:0% +displayed within the administration +right EPA's rules are reviewed by the + + align:start position:0% +right EPA's rules are reviewed by the + + + align:start position:0% +right EPA's rules are reviewed by the +White House the Department of Energy + + align:start position:0% +White House the Department of Energy + + + align:start position:0% +White House the Department of Energy +gets to sit at the table everybody has + + align:start position:0% +gets to sit at the table everybody has + + + align:start position:0% +gets to sit at the table everybody has +fun would require scrubbing gas but not + + align:start position:0% +fun would require scrubbing gas but not + + + align:start position:0% +fun would require scrubbing gas but not +with Western Colvard not much scrubbing + + align:start position:0% +with Western Colvard not much scrubbing + + + align:start position:0% +with Western Colvard not much scrubbing +with Western coal you could some Western + + align:start position:0% +with Western coal you could some Western + + + align:start position:0% +with Western coal you could some Western +coal you could meet that straight most + + align:start position:0% +coal you could meet that straight most + + + align:start position:0% +coal you could meet that straight most +of it you'd have to scrub but you + + align:start position:0% +of it you'd have to scrub but you + + + align:start position:0% +of it you'd have to scrub but you +wouldn't have to remove 90 percent of + + align:start position:0% +wouldn't have to remove 90 percent of + + + align:start position:0% +wouldn't have to remove 90 percent of +the sulfur to get it how had they + + align:start position:0% +the sulfur to get it how had they + + + align:start position:0% +the sulfur to get it how had they +shifted well this gets interesting + + align:start position:0% +shifted well this gets interesting + + + align:start position:0% +shifted well this gets interesting +the environmentalist could count the + + align:start position:0% +the environmentalist could count the + + + align:start position:0% +the environmentalist could count the +0.55 standard as a win so they now + + align:start position:0% +0.55 standard as a win so they now + + + align:start position:0% +0.55 standard as a win so they now +didn't much care about scrubbing what + + align:start position:0% +didn't much care about scrubbing what + + + align:start position:0% +didn't much care about scrubbing what +was on the table now both of those were + + align:start position:0% +was on the table now both of those were + + + align:start position:0% +was on the table now both of those were +wins the 0.55 would probably be cleaner + + align:start position:0% +wins the 0.55 would probably be cleaner + + + align:start position:0% +wins the 0.55 would probably be cleaner +would be cleaner than one-point-two so + + align:start position:0% +would be cleaner than one-point-two so + + + align:start position:0% +would be cleaner than one-point-two so +the environmental movement switched + + align:start position:0% +the environmental movement switched + + + align:start position:0% +the environmental movement switched +Eastern coal wanted scrubbing the + + align:start position:0% +Eastern coal wanted scrubbing the + + + align:start position:0% +Eastern coal wanted scrubbing the +utilities for some reason that I don't + + align:start position:0% +utilities for some reason that I don't + + + align:start position:0% +utilities for some reason that I don't +quite understand because I didn't think + + align:start position:0% +quite understand because I didn't think + + + align:start position:0% +quite understand because I didn't think +it was the cheapest alternative the + + align:start position:0% +it was the cheapest alternative the + + + align:start position:0% +it was the cheapest alternative the +utilities sided with Eastern coal so you + + align:start position:0% +utilities sided with Eastern coal so you + + + align:start position:0% +utilities sided with Eastern coal so you +have a switch when it went from passing + + align:start position:0% +have a switch when it went from passing + + + align:start position:0% +have a switch when it went from passing +the law to making the rule the + + align:start position:0% +the law to making the rule the + + + align:start position:0% +the law to making the rule the +environmentalists switch sides + + align:start position:0% +environmentalists switch sides + + + align:start position:0% +environmentalists switch sides +they were allied with the Eastern coal + + align:start position:0% +they were allied with the Eastern coal + + + align:start position:0% +they were allied with the Eastern coal +interests in the legislative process + + align:start position:0% +interests in the legislative process + + + align:start position:0% +interests in the legislative process +they switched in the administrative + + align:start position:0% +they switched in the administrative + + + align:start position:0% +they switched in the administrative +process as the agenda changed again this + + align:start position:0% +process as the agenda changed again this + + + align:start position:0% +process as the agenda changed again this +is not a picture this is a kind of a + + align:start position:0% +is not a picture this is a kind of a + + + align:start position:0% +is not a picture this is a kind of a +particularly striking case which is why + + align:start position:0% +particularly striking case which is why + + + align:start position:0% +particularly striking case which is why +it's here and it matters for energy + + align:start position:0% +it's here and it matters for energy + + + align:start position:0% +it's here and it matters for energy +which is why it's here but it's not that + + align:start position:0% +which is why it's here but it's not that + + + align:start position:0% +which is why it's here but it's not that +unusual that interest groups switch + + align:start position:0% +unusual that interest groups switch + + + align:start position:0% +unusual that interest groups switch +sides for tactical reasons this is + + align:start position:0% +sides for tactical reasons this is + + + align:start position:0% +sides for tactical reasons this is +there's no religious issue here this is + + align:start position:0% +there's no religious issue here this is + + + align:start position:0% +there's no religious issue here this is +this is a pro or anti this is how do you + + align:start position:0% +this is a pro or anti this is how do you + + + align:start position:0% +this is a pro or anti this is how do you +how do you get forward they want a + + align:start position:0% +how do you get forward they want a + + + align:start position:0% +how do you get forward they want a +cleaner air and they want it scrubbing + + align:start position:0% +cleaner air and they want it scrubbing + + + align:start position:0% +cleaner air and they want it scrubbing +okay once you get really clean air will + + align:start position:0% +okay once you get really clean air will + + + align:start position:0% +okay once you get really clean air will +give up on scrubbing let the eastern + + align:start position:0% +give up on scrubbing let the eastern + + + align:start position:0% +give up on scrubbing let the eastern +coal guys go the utilities now have a + + align:start position:0% +coal guys go the utilities now have a + + + align:start position:0% +coal guys go the utilities now have a +now have a distinct point of view yep + + align:start position:0% +now have a distinct point of view yep + + + align:start position:0% +now have a distinct point of view yep +the new NSPS just to go to it quickly + + align:start position:0% +the new NSPS just to go to it quickly + + + align:start position:0% +the new NSPS just to go to it quickly +we had a two-tier solution you could + + align:start position:0% +we had a two-tier solution you could + + + align:start position:0% +we had a two-tier solution you could +either + + align:start position:0% +either + + + align:start position:0% +either +scrubbed 90% and emit 1.2 pounds or you + + align:start position:0% +scrubbed 90% and emit 1.2 pounds or you + + + align:start position:0% +scrubbed 90% and emit 1.2 pounds or you +could scrub 70% and emit 0.6 pounds it's + + align:start position:0% +could scrub 70% and emit 0.6 pounds it's + + + align:start position:0% +could scrub 70% and emit 0.6 pounds it's +a little weird if you look at it why not + + align:start position:0% +a little weird if you look at it why not + + + align:start position:0% +a little weird if you look at it why not +just require these plants to be clean + + align:start position:0% +just require these plants to be clean + + + align:start position:0% +just require these plants to be clean +it's a political solution + + align:start position:0% +it's a political solution + + + align:start position:0% +it's a political solution +it made Eastern coal economical in the + + align:start position:0% +it made Eastern coal economical in the + + + align:start position:0% +it made Eastern coal economical in the +east and Western coal economical in the + + align:start position:0% +east and Western coal economical in the + + + align:start position:0% +east and Western coal economical in the +West + + align:start position:0% +West + + + align:start position:0% +West +nobody's thrilled not clear that those + + align:start position:0% +nobody's thrilled not clear that those + + + align:start position:0% +nobody's thrilled not clear that those +70 percent scrubbers actually work + + align:start position:0% +70 percent scrubbers actually work + + + align:start position:0% +70 percent scrubbers actually work +people have a tendency to do this in + + align:start position:0% +people have a tendency to do this in + + + align:start position:0% +people have a tendency to do this in +Washington they've heard about a + + align:start position:0% +Washington they've heard about a + + + align:start position:0% +Washington they've heard about a +technology they'll require it even if + + align:start position:0% +technology they'll require it even if + + + align:start position:0% +technology they'll require it even if +it's not necessarily proven that's a + + align:start position:0% +it's not necessarily proven that's a + + + align:start position:0% +it's not necessarily proven that's a +political that I won't I won't press you + + align:start position:0% +political that I won't I won't press you + + + align:start position:0% +political that I won't I won't press you +on that one what would you have done + + align:start position:0% +on that one what would you have done + + + align:start position:0% +on that one what would you have done +instead who knows it's a political + + align:start position:0% +instead who knows it's a political + + + align:start position:0% +instead who knows it's a political +answer it's a political answer ok let me + + align:start position:0% +answer it's a political answer ok let me + + + align:start position:0% +answer it's a political answer ok let me +go after that let me pass out the the B + + align:start position:0% +go after that let me pass out the the B + + + align:start position:0% +go after that let me pass out the the B +case new sources under this we talked + + align:start position:0% +case new sources under this we talked + + + align:start position:0% +case new sources under this we talked +about this under the 70 act in today + + align:start position:0% +about this under the 70 act in today + + + align:start position:0% +about this under the 70 act in today +have to meet stricter standards and old + + align:start position:0% +have to meet stricter standards and old + + + align:start position:0% +have to meet stricter standards and old +sources old sources have to be approved + + align:start position:0% +sources old sources have to be approved + + + align:start position:0% +sources old sources have to be approved +by the state there are plenty of really + + align:start position:0% +by the state there are plenty of really + + + align:start position:0% +by the state there are plenty of really +dirty power plants still running so by + + align:start position:0% +dirty power plants still running so by + + + align:start position:0% +dirty power plants still running so by +the mid 80s this is called new source + + align:start position:0% +the mid 80s this is called new source + + + align:start position:0% +the mid 80s this is called new source +bias and leads to this wonderful + + align:start position:0% +bias and leads to this wonderful + + + align:start position:0% +bias and leads to this wonderful +question on which I spent some time in + + align:start position:0% +question on which I spent some time in + + + align:start position:0% +question on which I spent some time in +Washington the outcome of which I cannot + + align:start position:0% +Washington the outcome of which I cannot + + + align:start position:0% +Washington the outcome of which I cannot +remember because it was so stupid what + + align:start position:0% +remember because it was so stupid what + + + align:start position:0% +remember because it was so stupid what +changes can you make to an old plant + + align:start position:0% +changes can you make to an old plant + + + align:start position:0% +changes can you make to an old plant +before it becomes a new plant the + + align:start position:0% +before it becomes a new plant the + + + align:start position:0% +before it becomes a new plant the +Environmental Protection Agency's + + align:start position:0% +Environmental Protection Agency's + + + align:start position:0% +Environmental Protection Agency's +position was if you replace a piece of + + align:start position:0% +position was if you replace a piece of + + + align:start position:0% +position was if you replace a piece of +capital equipment like oh say a faucet + + align:start position:0% +capital equipment like oh say a faucet + + + align:start position:0% +capital equipment like oh say a faucet +it's a new plant it's not the same as it + + align:start position:0% +it's a new plant it's not the same as it + + + align:start position:0% +it's a new plant it's not the same as it +was it's a new plant it has to meet new + + align:start position:0% +was it's a new plant it has to meet new + + + align:start position:0% +was it's a new plant it has to meet new +source standards the Department of + + align:start position:0% +source standards the Department of + + + align:start position:0% +source standards the Department of +Energy's position was well if there's + + align:start position:0% +Energy's position was well if there's + + + align:start position:0% +Energy's position was well if there's +still a brick from the old plant it's an + + align:start position:0% +still a brick from the old plant it's an + + + align:start position:0% +still a brick from the old plant it's an +old plant you know as long as there's + + align:start position:0% +old plant you know as long as there's + + + align:start position:0% +old plant you know as long as there's +something left we reached a compromise + + align:start position:0% +something left we reached a compromise + + + align:start position:0% +something left we reached a compromise +that was challenged in court by both + + align:start position:0% +that was challenged in court by both + + + align:start position:0% +that was challenged in court by both +sides and upheld and I cannot tell you + + align:start position:0% +sides and upheld and I cannot tell you + + + align:start position:0% +sides and upheld and I cannot tell you +what it was because that's a question + + align:start position:0% +what it was because that's a question + + + align:start position:0% +what it was because that's a question +that has no answer what can you do well + + align:start position:0% +that has no answer what can you do well + + + align:start position:0% +that has no answer what can you do well +that's that there's no principled answer + + align:start position:0% +that's that there's no principled answer + + + align:start position:0% +that's that there's no principled answer +to that question it's a compromise + + align:start position:0% +to that question it's a compromise + + + align:start position:0% +to that question it's a compromise +answer an enormous waste of time but in + + align:start position:0% +answer an enormous waste of time but in + + + align:start position:0% +answer an enormous waste of time but in +any case so by the mid-nineteen + + align:start position:0% +any case so by the mid-nineteen + + + align:start position:0% +any case so by the mid-nineteen +ATS we had more than 80% of the so2 + + align:start position:0% +ATS we had more than 80% of the so2 + + + align:start position:0% +ATS we had more than 80% of the so2 +emitted was emitted by power plants that + + align:start position:0% +emitted was emitted by power plants that + + + align:start position:0% +emitted was emitted by power plants that +failed the 71 standard right because + + align:start position:0% +failed the 71 standard right because + + + align:start position:0% +failed the 71 standard right because +people and this is the this is you know + + align:start position:0% +people and this is the this is you know + + + align:start position:0% +people and this is the this is you know +Ages of power plants we saw that at the + + align:start position:0% +Ages of power plants we saw that at the + + + align:start position:0% +Ages of power plants we saw that at the +start of the semester there's an awful + + align:start position:0% +start of the semester there's an awful + + + align:start position:0% +start of the semester there's an awful +lot of coal-fired it's black for + + align:start position:0% +lot of coal-fired it's black for + + + align:start position:0% +lot of coal-fired it's black for +symbolic reasons all a whole lot of old + + align:start position:0% +symbolic reasons all a whole lot of old + + + align:start position:0% +symbolic reasons all a whole lot of old +coal fired power plants put in place + + align:start position:0% +coal fired power plants put in place + + + align:start position:0% +coal fired power plants put in place +before 1970 still there were a lot more + + align:start position:0% +before 1970 still there were a lot more + + + align:start position:0% +before 1970 still there were a lot more +in 1985 so all this hullabaloo about the + + align:start position:0% +in 1985 so all this hullabaloo about the + + + align:start position:0% +in 1985 so all this hullabaloo about the +new source performance standard isn't + + align:start position:0% +new source performance standard isn't + + + align:start position:0% +new source performance standard isn't +actually going to do much you know + + align:start position:0% +actually going to do much you know + + + align:start position:0% +actually going to do much you know +you're not not huge growth in capacity + + align:start position:0% +you're not not huge growth in capacity + + + align:start position:0% +you're not not huge growth in capacity +here in the 80s it's growing but not + + align:start position:0% +here in the 80s it's growing but not + + + align:start position:0% +here in the 80s it's growing but not +rapidly so nobody people want to extend + + align:start position:0% +rapidly so nobody people want to extend + + + align:start position:0% +rapidly so nobody people want to extend +the lives of old plants the old plants + + align:start position:0% +the lives of old plants the old plants + + + align:start position:0% +the lives of old plants the old plants +are dirty people aren't building new + + align:start position:0% +are dirty people aren't building new + + + align:start position:0% +are dirty people aren't building new +plants and acid rain gets to be an issue + + align:start position:0% +plants and acid rain gets to be an issue + + + align:start position:0% +plants and acid rain gets to be an issue +so acid rain says particularly with high + + align:start position:0% +so acid rain says particularly with high + + + align:start position:0% +so acid rain says particularly with high +smokestacks the stuff blows hundreds of + + align:start position:0% +smokestacks the stuff blows hundreds of + + + align:start position:0% +smokestacks the stuff blows hundreds of +miles was the argument and damages lakes + + align:start position:0% +miles was the argument and damages lakes + + + align:start position:0% +miles was the argument and damages lakes +in the Northeast + + align:start position:0% +in the Northeast + + + align:start position:0% +in the Northeast +so what do you do well in the 80s what + + align:start position:0% +so what do you do well in the 80s what + + + align:start position:0% +so what do you do well in the 80s what +you did was debate legislation that + + align:start position:0% +you did was debate legislation that + + + align:start position:0% +you did was debate legislation that +required every old plants to scrub and + + align:start position:0% +required every old plants to scrub and + + + align:start position:0% +required every old plants to scrub and +those laws didn't get anywhere in part + + align:start position:0% +those laws didn't get anywhere in part + + + align:start position:0% +those laws didn't get anywhere in part +because the costs varied so enormous Lee + + align:start position:0% +because the costs varied so enormous Lee + + + align:start position:0% +because the costs varied so enormous Lee +you have to have land to put a scrubber + + align:start position:0% +you have to have land to put a scrubber + + + align:start position:0% +you have to have land to put a scrubber +in some plants didn't have any land they + + align:start position:0% +in some plants didn't have any land they + + + align:start position:0% +in some plants didn't have any land they +just have to shut down does that make + + align:start position:0% +just have to shut down does that make + + + align:start position:0% +just have to shut down does that make +any sense and then the question is how + + align:start position:0% +any sense and then the question is how + + + align:start position:0% +any sense and then the question is how +you gonna pay for this monstrous thing + + align:start position:0% +you gonna pay for this monstrous thing + + + align:start position:0% +you gonna pay for this monstrous thing +how about we put on a national + + align:start position:0% +how about we put on a national + + + align:start position:0% +how about we put on a national +electricity tax we didn't burn much coal + + align:start position:0% +electricity tax we didn't burn much coal + + + align:start position:0% +electricity tax we didn't burn much coal +in New England you could imagine the New + + align:start position:0% +in New England you could imagine the New + + + align:start position:0% +in New England you could imagine the New +England response to that let's see + + align:start position:0% +England response to that let's see + + + align:start position:0% +England response to that let's see +you're gonna tax us so Ohio can clean up + + align:start position:0% +you're gonna tax us so Ohio can clean up + + + align:start position:0% +you're gonna tax us so Ohio can clean up +good idea No + + align:start position:0% +good idea No + + + align:start position:0% +good idea No +so the politics were bad and of course + + align:start position:0% +so the politics were bad and of course + + + align:start position:0% +so the politics were bad and of course +the Senate Majority Leader was from a + + align:start position:0% +the Senate Majority Leader was from a + + + align:start position:0% +the Senate Majority Leader was from a +Eastern coal producing state and the + + align:start position:0% +Eastern coal producing state and the + + + align:start position:0% +Eastern coal producing state and the +president was Ronald Reagan so nothing + + align:start position:0% +president was Ronald Reagan so nothing + + + align:start position:0% +president was Ronald Reagan so nothing +was going to pass and nothing was going + + align:start position:0% +was going to pass and nothing was going + + + align:start position:0% +was going to pass and nothing was going +to be signed but + + align:start position:0% + + + + align:start position:0% + +it was a question to do what do you do + + align:start position:0% +it was a question to do what do you do + + + align:start position:0% +it was a question to do what do you do +so that case the B case which you have + + align:start position:0% +so that case the B case which you have + + + align:start position:0% +so that case the B case which you have +described sort of the process that got + + align:start position:0% +described sort of the process that got + + + align:start position:0% +described sort of the process that got +us to the trading position of the + + align:start position:0% +us to the trading position of the + + + align:start position:0% +us to the trading position of the +trading provision title 4 in the 1990 + + align:start position:0% +trading provision title 4 in the 1990 + + + align:start position:0% +trading provision title 4 in the 1990 +Clean Air Act one environmental group + + align:start position:0% +Clean Air Act one environmental group + + + align:start position:0% +Clean Air Act one environmental group +the Environmental Defense Fund decided + + align:start position:0% +the Environmental Defense Fund decided + + + align:start position:0% +the Environmental Defense Fund decided +the only way we could deal with this + + align:start position:0% +the only way we could deal with this + + + align:start position:0% +the only way we could deal with this +problem was to put in place trading + + align:start position:0% +problem was to put in place trading + + + align:start position:0% +problem was to put in place trading +which the environmental movement had + + align:start position:0% +which the environmental movement had + + + align:start position:0% +which the environmental movement had +traditionally hated because it removed + + align:start position:0% +traditionally hated because it removed + + + align:start position:0% +traditionally hated because it removed +stigma licensed to pollute trading in + + align:start position:0% +stigma licensed to pollute trading in + + + align:start position:0% +stigma licensed to pollute trading in +filth etc smark it's in garbage all + + align:start position:0% +filth etc smark it's in garbage all + + + align:start position:0% +filth etc smark it's in garbage all +kinds of great slogans but once they saw + + align:start position:0% +kinds of great slogans but once they saw + + + align:start position:0% +kinds of great slogans but once they saw +there was no other way to do it and we + + align:start position:0% +there was no other way to do it and we + + + align:start position:0% +there was no other way to do it and we +suddenly had a senate majority leader + + align:start position:0% +suddenly had a senate majority leader + + + align:start position:0% +suddenly had a senate majority leader +from maine who cared about acid rain and + + align:start position:0% +from maine who cared about acid rain and + + + align:start position:0% +from maine who cared about acid rain and +a president who had a summer home in + + align:start position:0% +a president who had a summer home in + + + align:start position:0% +a president who had a summer home in +maine who cared about acid rain we were + + align:start position:0% +maine who cared about acid rain we were + + + align:start position:0% +maine who cared about acid rain we were +going to get a bill so this was this was + + align:start position:0% +going to get a bill so this was this was + + + align:start position:0% +going to get a bill so this was this was +the way forward + + align:start position:0% +the way forward + + + align:start position:0% +the way forward +it was a wild scramble for the tradable + + align:start position:0% +it was a wild scramble for the tradable + + + align:start position:0% +it was a wild scramble for the tradable +things I was involved in this it was + + align:start position:0% +things I was involved in this it was + + + align:start position:0% +things I was involved in this it was +horse trading at its worst but didn't + + align:start position:0% +horse trading at its worst but didn't + + + align:start position:0% +horse trading at its worst but didn't +affect equal marginal costs we talked + + align:start position:0% +affect equal marginal costs we talked + + + align:start position:0% +affect equal marginal costs we talked +about national trading for some + + align:start position:0% +about national trading for some + + + align:start position:0% +about national trading for some +pollutants it doesn't make sense for all + + align:start position:0% +pollutants it doesn't make sense for all + + + align:start position:0% +pollutants it doesn't make sense for all +pollutants because of the hotspot + + align:start position:0% +pollutants because of the hotspot + + + align:start position:0% +pollutants because of the hotspot +problem but in any case this law which + + align:start position:0% +problem but in any case this law which + + + align:start position:0% +problem but in any case this law which +was a national cap and trade for sulfur + + align:start position:0% +was a national cap and trade for sulfur + + + align:start position:0% +was a national cap and trade for sulfur +dioxide which by the way doesn't mix + + align:start position:0% +dioxide which by the way doesn't mix + + + align:start position:0% +dioxide which by the way doesn't mix +like carbon dioxide it doesn't mix + + align:start position:0% +like carbon dioxide it doesn't mix + + + align:start position:0% +like carbon dioxide it doesn't mix +around the globe it travels travels + + align:start position:0% +around the globe it travels travels + + + align:start position:0% +around the globe it travels travels +maybe a few hundred miles sulphur + + align:start position:0% +maybe a few hundred miles sulphur + + + align:start position:0% +maybe a few hundred miles sulphur +dioxide emitted in Miami does not affect + + align:start position:0% +dioxide emitted in Miami does not affect + + + align:start position:0% +dioxide emitted in Miami does not affect +the forests in Maine at all affects the + + align:start position:0% +the forests in Maine at all affects the + + + align:start position:0% +the forests in Maine at all affects the +oceans but doesn't affect the forests in + + align:start position:0% +oceans but doesn't affect the forests in + + + align:start position:0% +oceans but doesn't affect the forests in +Maine directly and sulphur dioxide + + align:start position:0% +Maine directly and sulphur dioxide + + + align:start position:0% +Maine directly and sulphur dioxide +emitted in Arizona boy there may be a + + align:start position:0% +emitted in Arizona boy there may be a + + + align:start position:0% +emitted in Arizona boy there may be a +few molecules who get east but not that + + align:start position:0% +few molecules who get east but not that + + + align:start position:0% +few molecules who get east but not that +that get east not that many so it took + + align:start position:0% +that get east not that many so it took + + + align:start position:0% +that get east not that many so it took +effect in 1995 so we're now after that + + align:start position:0% +effect in 1995 so we're now after that + + + align:start position:0% +effect in 1995 so we're now after that +be case if you have any questions about + + align:start position:0% +be case if you have any questions about + + + align:start position:0% +be case if you have any questions about +it about the case let me know I've got a + + align:start position:0% +it about the case let me know I've got a + + + align:start position:0% +it about the case let me know I've got a +bit to cover I want to make sure I get + + align:start position:0% +bit to cover I want to make sure I get + + + align:start position:0% +bit to cover I want to make sure I get +it done + + align:start position:0% +it done + + + align:start position:0% +it done +so here's what happened one thing that + + align:start position:0% +so here's what happened one thing that + + + align:start position:0% +so here's what happened one thing that +happened the law created an asset this + + align:start position:0% +happened the law created an asset this + + + align:start position:0% +happened the law created an asset this +tradable allowance and it gave it away + + align:start position:0% +tradable allowance and it gave it away + + + align:start position:0% +tradable allowance and it gave it away +now that's interesting right that's + + align:start position:0% +now that's interesting right that's + + + align:start position:0% +now that's interesting right that's +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +it gave away the rights to emit sulfur + + align:start position:0% +it gave away the rights to emit sulfur + + + align:start position:0% +it gave away the rights to emit sulfur +dioxide now if it were a competitive + + align:start position:0% +dioxide now if it were a competitive + + + align:start position:0% +dioxide now if it were a competitive +market right let's suppose it it took + + align:start position:0% +market right let's suppose it it took + + + align:start position:0% +market right let's suppose it it took +one of those things to them to generate + + align:start position:0% +one of those things to them to generate + + + align:start position:0% +one of those things to them to generate +a megawatt of electricity then you'd + + align:start position:0% +a megawatt of electricity then you'd + + + align:start position:0% +a megawatt of electricity then you'd +expect the price of electricity to rise + + align:start position:0% +expect the price of electricity to rise + + + align:start position:0% +expect the price of electricity to rise +by the cost of an allowance on + + align:start position:0% +by the cost of an allowance on + + + align:start position:0% +by the cost of an allowance on +opportunity cost on an opportunity cost + + align:start position:0% +opportunity cost on an opportunity cost + + + align:start position:0% +opportunity cost on an opportunity cost +basis right if you give it to me for + + align:start position:0% +basis right if you give it to me for + + + align:start position:0% +basis right if you give it to me for +free but if I don't use it myself I can + + align:start position:0% +free but if I don't use it myself I can + + + align:start position:0% +free but if I don't use it myself I can +sell it so the cost of using it is the + + align:start position:0% +sell it so the cost of using it is the + + + align:start position:0% +sell it so the cost of using it is the +price on the market even though I got it + + align:start position:0% +price on the market even though I got it + + + align:start position:0% +price on the market even though I got it +for free so what you would expect is in + + align:start position:0% +for free so what you would expect is in + + + align:start position:0% +for free so what you would expect is in +a competitive market it's a gift in a in + + align:start position:0% +a competitive market it's a gift in a in + + + align:start position:0% +a competitive market it's a gift in a in +a regulated market it's not so clear and + + align:start position:0% +a regulated market it's not so clear and + + + align:start position:0% +a regulated market it's not so clear and +states had different ways of dealing + + align:start position:0% +states had different ways of dealing + + + align:start position:0% +states had different ways of dealing +with this this picture illustrates sort + + align:start position:0% +with this this picture illustrates sort + + + align:start position:0% +with this this picture illustrates sort +of the distinction between the value of + + align:start position:0% +of the distinction between the value of + + + align:start position:0% +of the distinction between the value of +the allowances and the cost of cleanup + + align:start position:0% +the allowances and the cost of cleanup + + + align:start position:0% +the allowances and the cost of cleanup +which is often a confusion right so we + + align:start position:0% +which is often a confusion right so we + + + align:start position:0% +which is often a confusion right so we +have allowances to emit sulfur dioxide + + align:start position:0% +have allowances to emit sulfur dioxide + + + align:start position:0% +have allowances to emit sulfur dioxide +each one gives you the right to emit a + + align:start position:0% +each one gives you the right to emit a + + + align:start position:0% +each one gives you the right to emit a +ton there's a demand for those what's + + align:start position:0% +ton there's a demand for those what's + + + align:start position:0% +ton there's a demand for those what's +the demand determined by well is + + align:start position:0% +the demand determined by well is + + + align:start position:0% +the demand determined by well is +determined by the marginal cost of + + align:start position:0% +determined by the marginal cost of + + + align:start position:0% +determined by the marginal cost of +cleaning up if this is what I would emit + + align:start position:0% +cleaning up if this is what I would emit + + + align:start position:0% +cleaning up if this is what I would emit +this is what the industry would emit if + + align:start position:0% +this is what the industry would emit if + + + align:start position:0% +this is what the industry would emit if +there were no price on allowances and + + align:start position:0% +there were no price on allowances and + + + align:start position:0% +there were no price on allowances and +this is what they emit when the price is + + align:start position:0% +this is what they emit when the price is + + + align:start position:0% +this is what they emit when the price is +higher this curve must reflect the + + align:start position:0% +higher this curve must reflect the + + + align:start position:0% +higher this curve must reflect the +marginal cost of cleanup all right + + align:start position:0% +marginal cost of cleanup all right + + + align:start position:0% +marginal cost of cleanup all right +because you you you you will emit until + + align:start position:0% +because you you you you will emit until + + + align:start position:0% +because you you you you will emit until +the cost of cleanup exceeds the cost or + + align:start position:0% +the cost of cleanup exceeds the cost or + + + align:start position:0% +the cost of cleanup exceeds the cost or +that you'll clean up until the cost of + + align:start position:0% +that you'll clean up until the cost of + + + align:start position:0% +that you'll clean up until the cost of +cleanup exceeds the value of an + + align:start position:0% +cleanup exceeds the value of an + + + align:start position:0% +cleanup exceeds the value of an +allowance because I have a choice I can + + align:start position:0% +allowance because I have a choice I can + + + align:start position:0% +allowance because I have a choice I can +reduce emissions or buy an allowance so + + align:start position:0% +reduce emissions or buy an allowance so + + + align:start position:0% +reduce emissions or buy an allowance so +the area if this is the cap the area + + align:start position:0% +the area if this is the cap the area + + + align:start position:0% +the area if this is the cap the area +under the curve to here and that this is + + align:start position:0% +under the curve to here and that this is + + + align:start position:0% +under the curve to here and that this is +the price this area must be the cost of + + align:start position:0% +the price this area must be the cost of + + + align:start position:0% +the price this area must be the cost of +clean up you know just just like the + + align:start position:0% +clean up you know just just like the + + + align:start position:0% +clean up you know just just like the +demand for a good is the marginal value + + align:start position:0% +demand for a good is the marginal value + + + align:start position:0% +demand for a good is the marginal value +consumers place on it here the marginal + + align:start position:0% +consumers place on it here the marginal + + + align:start position:0% +consumers place on it here the marginal +value is the cost of cleanup so the cost + + align:start position:0% +value is the cost of cleanup so the cost + + + align:start position:0% +value is the cost of cleanup so the cost +the area under this curve from here to + + align:start position:0% +the area under this curve from here to + + + align:start position:0% +the area under this curve from here to +here is the cost this rant is the value + + align:start position:0% +here is the cost this rant is the value + + + align:start position:0% +here is the cost this rant is the value +of the allow of the allowances that were + + align:start position:0% +of the allow of the allowances that were + + + align:start position:0% +of the allow of the allowances that were +given out now if this were a competitive + + align:start position:0% +given out now if this were a competitive + + + align:start position:0% +given out now if this were a competitive +unregulated market and that picture were + + align:start position:0% +unregulated market and that picture were + + + align:start position:0% +unregulated market and that picture were +right + + align:start position:0% +right + + + align:start position:0% +right +well I don't have that I don't have the + + align:start position:0% +well I don't have that I don't have the + + + align:start position:0% +well I don't have that I don't have the +rest of the story so I can't say that + + align:start position:0% +rest of the story so I can't say that + + + align:start position:0% +rest of the story so I can't say that +normally however it's a it's a gift you + + align:start position:0% +normally however it's a it's a gift you + + + align:start position:0% +normally however it's a it's a gift you +probably haven't followed this but + + align:start position:0% +probably haven't followed this but + + + align:start position:0% +probably haven't followed this but +there's a controversy about the European + + align:start position:0% +there's a controversy about the European + + + align:start position:0% +there's a controversy about the European +carbon trading system is now being + + align:start position:0% +carbon trading system is now being + + + align:start position:0% +carbon trading system is now being +expanded to include Airlines which + + align:start position:0% +expanded to include Airlines which + + + align:start position:0% +expanded to include Airlines which +requires airlines flying into Europe to + + align:start position:0% +requires airlines flying into Europe to + + + align:start position:0% +requires airlines flying into Europe to +buy allowances to cover the carbon they + + align:start position:0% +buy allowances to cover the carbon they + + + align:start position:0% +buy allowances to cover the carbon they +admit flying in Airlines including US + + align:start position:0% +admit flying in Airlines including US + + + align:start position:0% +admit flying in Airlines including US +airlines are being given allowances not + + align:start position:0% +airlines are being given allowances not + + + align:start position:0% +airlines are being given allowances not +enough but they're being given + + align:start position:0% +enough but they're being given + + + align:start position:0% +enough but they're being given +allowances to cover most of their + + align:start position:0% +allowances to cover most of their + + + align:start position:0% +allowances to cover most of their +emissions US airlines are berserk about + + align:start position:0% +emissions US airlines are berserk about + + + align:start position:0% +emissions US airlines are berserk about +this the administration is berserk about + + align:start position:0% +this the administration is berserk about + + + align:start position:0% +this the administration is berserk about +this you're taxing our people the + + align:start position:0% +this you're taxing our people the + + + align:start position:0% +this you're taxing our people the +analysis done over in building e 19 + + align:start position:0% +analysis done over in building e 19 + + + align:start position:0% +analysis done over in building e 19 +concludes very persuasively that the US + + align:start position:0% +concludes very persuasively that the US + + + align:start position:0% +concludes very persuasively that the US +airlines will in fact make money because + + align:start position:0% +airlines will in fact make money because + + + align:start position:0% +airlines will in fact make money because +they've been given almost enough + + align:start position:0% +they've been given almost enough + + + align:start position:0% +they've been given almost enough +allowances and the price of airline + + align:start position:0% +allowances and the price of airline + + + align:start position:0% +allowances and the price of airline +fares is going to go up to cover the + + align:start position:0% +fares is going to go up to cover the + + + align:start position:0% +fares is going to go up to cover the +opportunity cost not the out-of-pocket + + align:start position:0% +opportunity cost not the out-of-pocket + + + align:start position:0% +opportunity cost not the out-of-pocket +cost the opportunity cost right even if + + align:start position:0% +cost the opportunity cost right even if + + + align:start position:0% +cost the opportunity cost right even if +I've been given it the cost of using it + + align:start position:0% +I've been given it the cost of using it + + + align:start position:0% +I've been given it the cost of using it +to me is the market price the price I + + align:start position:0% +to me is the market price the price I + + + align:start position:0% +to me is the market price the price I +charge will have to cover that my + + align:start position:0% +charge will have to cover that my + + + align:start position:0% +charge will have to cover that my +profits will go up US airlines hate this + + align:start position:0% +profits will go up US airlines hate this + + + align:start position:0% +profits will go up US airlines hate this +analysis they paid for it + + align:start position:0% +analysis they paid for it + + + align:start position:0% +analysis they paid for it +they now reject that is fatally flawed + + align:start position:0% +they now reject that is fatally flawed + + + align:start position:0% +they now reject that is fatally flawed +it is if you think about it for a little + + align:start position:0% +it is if you think about it for a little + + + align:start position:0% +it is if you think about it for a little +while + + align:start position:0% +while + + + align:start position:0% +while +pretty simple economics a little more + + align:start position:0% +pretty simple economics a little more + + + align:start position:0% +pretty simple economics a little more +complicated under regulation so what + + align:start position:0% +complicated under regulation so what + + + align:start position:0% +complicated under regulation so what +else happened question on this okay what + + align:start position:0% +else happened question on this okay what + + + align:start position:0% +else happened question on this okay what +else happened + + align:start position:0% +else happened + + + align:start position:0% +else happened +this is the pretty picture these were + + align:start position:0% +this is the pretty picture these were + + + align:start position:0% +this is the pretty picture these were +this was actual emissions u.s. emissions + + align:start position:0% +this was actual emissions u.s. emissions + + + align:start position:0% +this was actual emissions u.s. emissions +and millions of tons these were you + + align:start position:0% +and millions of tons these were you + + + align:start position:0% +and millions of tons these were you +could you can you can estimate that + + align:start position:0% +could you can you can estimate that + + + align:start position:0% +could you can you can estimate that +pretty well by the fuel they burned + + align:start position:0% +pretty well by the fuel they burned + + + align:start position:0% +pretty well by the fuel they burned +after 1995 they had monitors on the + + align:start position:0% +after 1995 they had monitors on the + + + align:start position:0% +after 1995 they had monitors on the +stack so we know it for sure here's the + + align:start position:0% +stack so we know it for sure here's the + + + align:start position:0% +stack so we know it for sure here's the +cap this this line here it went down + + align:start position:0% +cap this this line here it went down + + + align:start position:0% +cap this this line here it went down +over time it's a little complicated + + align:start position:0% +over time it's a little complicated + + + align:start position:0% +over time it's a little complicated +because more units were covered which is + + align:start position:0% +because more units were covered which is + + + align:start position:0% +because more units were covered which is +one reason that one a lot of things + + align:start position:0% +one reason that one a lot of things + + + align:start position:0% +one reason that one a lot of things +happen but but this is the aggregate cap + + align:start position:0% +happen but but this is the aggregate cap + + + align:start position:0% +happen but but this is the aggregate cap +pretty clearly these are some estimates + + align:start position:0% +pretty clearly these are some estimates + + + align:start position:0% +pretty clearly these are some estimates +of what might have happened absent the + + align:start position:0% +of what might have happened absent the + + + align:start position:0% +of what might have happened absent the +law the law the law was passed in 1990 + + align:start position:0% +law the law the law was passed in 1990 + + + align:start position:0% +law the law the law was passed in 1990 +but there was some anticipation of it + + align:start position:0% +but there was some anticipation of it + + + align:start position:0% +but there was some anticipation of it +and some investments made but the key + + align:start position:0% +and some investments made but the key + + + align:start position:0% +and some investments made but the key +the key thing is in the oval look at + + align:start position:0% +the key thing is in the oval look at + + + align:start position:0% +the key thing is in the oval look at +what happened to emissions environmental + + align:start position:0% +what happened to emissions environmental + + + align:start position:0% +what happened to emissions environmental +programs don't do that people litigate + + align:start position:0% +programs don't do that people litigate + + + align:start position:0% +programs don't do that people litigate +they resist the devices don't work look + + align:start position:0% +they resist the devices don't work look + + + align:start position:0% +they resist the devices don't work look +at that drop it dropped below the cap + + align:start position:0% +at that drop it dropped below the cap + + + align:start position:0% +at that drop it dropped below the cap +way below the cap why did that happen do + + align:start position:0% +way below the cap why did that happen do + + + align:start position:0% +way below the cap why did that happen do +you think well give you this yeah go + + align:start position:0% +you think well give you this yeah go + + + align:start position:0% +you think well give you this yeah go +ahead Jacqueline was begging exactly + + align:start position:0% +ahead Jacqueline was begging exactly + + + align:start position:0% +ahead Jacqueline was begging exactly +there was banking the cap gets pretty + + align:start position:0% +there was banking the cap gets pretty + + + align:start position:0% +there was banking the cap gets pretty +low out here around 2000 a lot of people + + align:start position:0% +low out here around 2000 a lot of people + + + align:start position:0% +low out here around 2000 a lot of people +said all right I'm gonna look to mm I'm + + align:start position:0% +said all right I'm gonna look to mm I'm + + + align:start position:0% +said all right I'm gonna look to mm I'm +gonna over control I'm going to do more + + align:start position:0% +gonna over control I'm going to do more + + + align:start position:0% +gonna over control I'm going to do more +than I need to do now so that when I + + align:start position:0% +than I need to do now so that when I + + + align:start position:0% +than I need to do now so that when I +come here I can notice emissions are + + align:start position:0% +come here I can notice emissions are + + + align:start position:0% +come here I can notice emissions are +above the cap here I can draw down the + + align:start position:0% +above the cap here I can draw down the + + + align:start position:0% +above the cap here I can draw down the +bank that can draw down that makes sense + + align:start position:0% +bank that can draw down that makes sense + + + align:start position:0% +bank that can draw down that makes sense +yeah it probably made sense because + + align:start position:0% +yeah it probably made sense because + + + align:start position:0% +yeah it probably made sense because +you've got early emissions reductions + + align:start position:0% +you've got early emissions reductions + + + align:start position:0% +you've got early emissions reductions +you got early control cumulative + + align:start position:0% +you got early control cumulative + + + align:start position:0% +you got early control cumulative +emissions were the same eventually the + + align:start position:0% +emissions were the same eventually the + + + align:start position:0% +emissions were the same eventually the +banks is exhausted the other thing you + + align:start position:0% +banks is exhausted the other thing you + + + align:start position:0% +banks is exhausted the other thing you +saw this business about always having an + + align:start position:0% +saw this business about always having an + + + align:start position:0% +saw this business about always having an +incentive to cut the incentive to cut + + align:start position:0% +incentive to cut the incentive to cut + + + align:start position:0% +incentive to cut the incentive to cut +here was the value of the banked + + align:start position:0% +here was the value of the banked + + + align:start position:0% +here was the value of the banked +allowance later on the other thing that + + align:start position:0% +allowance later on the other thing that + + + align:start position:0% +allowance later on the other thing that +happened is you wouldn't have had it + + align:start position:0% +happened is you wouldn't have had it + + + align:start position:0% +happened is you wouldn't have had it +happen in standards as people innovated + + align:start position:0% +happen in standards as people innovated + + + align:start position:0% +happen in standards as people innovated +well you know how I'm talking about + + align:start position:0% +well you know how I'm talking about + + + align:start position:0% +well you know how I'm talking about +burning high sulfur coal and burning low + + align:start position:0% +burning high sulfur coal and burning low + + + align:start position:0% +burning high sulfur coal and burning low +sulfur coal people said wait a minute + + align:start position:0% +sulfur coal people said wait a minute + + + align:start position:0% +sulfur coal people said wait a minute +high sulfur coal is now really cheap + + align:start position:0% +high sulfur coal is now really cheap + + + align:start position:0% +high sulfur coal is now really cheap +because it's really dirty + + align:start position:0% +because it's really dirty + + + align:start position:0% +because it's really dirty +but I can mix it it's not a trivial + + align:start position:0% +but I can mix it it's not a trivial + + + align:start position:0% +but I can mix it it's not a trivial +thing to do but it's not that hard + + align:start position:0% +thing to do but it's not that hard + + + align:start position:0% +thing to do but it's not that hard +people figured out how to blend it in + + align:start position:0% +people figured out how to blend it in + + + align:start position:0% +people figured out how to blend it in +which lowered their costs while still + + align:start position:0% +which lowered their costs while still + + + align:start position:0% +which lowered their costs while still +keeping under under allowances people + + align:start position:0% +keeping under under allowances people + + + align:start position:0% +keeping under under allowances people +invented new ways to scrub didn't remove + + align:start position:0% +invented new ways to scrub didn't remove + + + align:start position:0% +invented new ways to scrub didn't remove +90% but were lots cheaper people did a + + align:start position:0% +90% but were lots cheaper people did a + + + align:start position:0% +90% but were lots cheaper people did a +variety of things + + align:start position:0% +variety of things + + + align:start position:0% +variety of things +railroad deregulation brought Western + + align:start position:0% +railroad deregulation brought Western + + + align:start position:0% +railroad deregulation brought Western +coal East so we had this huge reduction + + align:start position:0% +coal East so we had this huge reduction + + + align:start position:0% +coal East so we had this huge reduction +in emissions and you saw it on the + + align:start position:0% +in emissions and you saw it on the + + + align:start position:0% +in emissions and you saw it on the +ground now it turns out acid rain wasn't + + align:start position:0% +ground now it turns out acid rain wasn't + + + align:start position:0% +ground now it turns out acid rain wasn't +as damaging as people thought there was + + align:start position:0% +as damaging as people thought there was + + + align:start position:0% +as damaging as people thought there was +a large study funded on impact of acid + + align:start position:0% +a large study funded on impact of acid + + + align:start position:0% +a large study funded on impact of acid +rain it wasn't finished before the bill + + align:start position:0% +rain it wasn't finished before the bill + + + align:start position:0% +rain it wasn't finished before the bill +was passed + + align:start position:0% +was passed + + + align:start position:0% +was passed +hey but in terms of of deposition you + + align:start position:0% +hey but in terms of of deposition you + + + align:start position:0% +hey but in terms of of deposition you +saw a great reduction in the Northeast + + align:start position:0% +saw a great reduction in the Northeast + + + align:start position:0% +saw a great reduction in the Northeast +still some hot spots but nothing like + + align:start position:0% +still some hot spots but nothing like + + + align:start position:0% +still some hot spots but nothing like +what they were before this was why the + + align:start position:0% +what they were before this was why the + + + align:start position:0% +what they were before this was why the +fiction worked it was going to be + + align:start position:0% +fiction worked it was going to be + + + align:start position:0% +fiction worked it was going to be +cheapest to control in here and + + align:start position:0% +cheapest to control in here and + + + align:start position:0% +cheapest to control in here and +everybody knew it so if you had even if + + align:start position:0% +everybody knew it so if you had even if + + + align:start position:0% +everybody knew it so if you had even if +you had a national regime and yes you + + align:start position:0% +you had a national regime and yes you + + + align:start position:0% +you had a national regime and yes you +could control down here you can control + + align:start position:0% +could control down here you can control + + + align:start position:0% +could control down here you can control +over there you can control up here it + + align:start position:0% +over there you can control up here it + + + align:start position:0% +over there you can control up here it +was going to be cheapest to make + + align:start position:0% +was going to be cheapest to make + + + align:start position:0% +was going to be cheapest to make +reductions here and so that's where they + + align:start position:0% +reductions here and so that's where they + + + align:start position:0% +reductions here and so that's where they +were gonna get made all all the models + + align:start position:0% +were gonna get made all all the models + + + align:start position:0% +were gonna get made all all the models +said that everybody was very quiet about + + align:start position:0% +said that everybody was very quiet about + + + align:start position:0% +said that everybody was very quiet about +the fact that this stuff doesn't mix + + align:start position:0% +the fact that this stuff doesn't mix + + + align:start position:0% +the fact that this stuff doesn't mix +because the models were pretty clear + + align:start position:0% +because the models were pretty clear + + + align:start position:0% +because the models were pretty clear +that we're going to get what we want + + align:start position:0% +that we're going to get what we want + + + align:start position:0% +that we're going to get what we want +because here's where it's cheap and + + align:start position:0% +because here's where it's cheap and + + + align:start position:0% +because here's where it's cheap and +here's where we want the cuts made but + + align:start position:0% +here's where we want the cuts made but + + + align:start position:0% +here's where we want the cuts made but +the different but the the point to keep + + align:start position:0% +the different but the the point to keep + + + align:start position:0% +the different but the the point to keep +in mind is even in these regions the + + align:start position:0% +in mind is even in these regions the + + + align:start position:0% +in mind is even in these regions the +costs of control differed enormous ly + + align:start position:0% +costs of control differed enormous ly + + + align:start position:0% +costs of control differed enormous ly +among plants so yeah regionally its + + align:start position:0% +among plants so yeah regionally its + + + align:start position:0% +among plants so yeah regionally its +cheapest in there but not plant by plant + + align:start position:0% +cheapest in there but not plant by plant + + + align:start position:0% +cheapest in there but not plant by plant +so trading worked it got it where it was + + align:start position:0% +so trading worked it got it where it was + + + align:start position:0% +so trading worked it got it where it was +cheapest and where it was cheapest was + + align:start position:0% +cheapest and where it was cheapest was + + + align:start position:0% +cheapest and where it was cheapest was +where we wanted it this is the price + + align:start position:0% +where we wanted it this is the price + + + align:start position:0% +where we wanted it this is the price +these are the price of these rights to + + align:start position:0% +these are the price of these rights to + + + align:start position:0% +these are the price of these rights to +emit a ton running through the end of + + align:start position:0% +emit a ton running through the end of + + + align:start position:0% +emit a ton running through the end of +2003 the initial estimates were higher + + align:start position:0% +2003 the initial estimates were higher + + + align:start position:0% +2003 the initial estimates were higher +the initial estimates were about three + + align:start position:0% +the initial estimates were about three + + + align:start position:0% +the initial estimates were about three +hundred dollars a ton so we got some + + align:start position:0% +hundred dollars a ton so we got some + + + align:start position:0% +hundred dollars a ton so we got some +mixture of innovation and cheap Western + + align:start position:0% +mixture of innovation and cheap Western + + + align:start position:0% +mixture of innovation and cheap Western +coal held the price down but you will + + align:start position:0% +coal held the price down but you will + + + align:start position:0% +coal held the price down but you will +notice the price bounces around people + + align:start position:0% +notice the price bounces around people + + + align:start position:0% +notice the price bounces around people +were making a living trading these + + align:start position:0% +were making a living trading these + + + align:start position:0% +were making a living trading these +things how could you make a living well + + align:start position:0% +things how could you make a living well + + + align:start position:0% +things how could you make a living well +why did they bounce well if you think + + align:start position:0% +why did they bounce well if you think + + + align:start position:0% +why did they bounce well if you think +about it for just a minute it's like + + align:start position:0% +about it for just a minute it's like + + + align:start position:0% +about it for just a minute it's like +sort of like we talked about oil there's + + align:start position:0% +sort of like we talked about oil there's + + + align:start position:0% +sort of like we talked about oil there's +a demand for emissions it depends on the + + align:start position:0% +a demand for emissions it depends on the + + + align:start position:0% +a demand for emissions it depends on the +economy it depends on coal prices it + + align:start position:0% +economy it depends on coal prices it + + + align:start position:0% +economy it depends on coal prices it +depends on a lot of things but in the + + align:start position:0% +depends on a lot of things but in the + + + align:start position:0% +depends on a lot of things but in the +short run it's pretty inelastic + + align:start position:0% +short run it's pretty inelastic + + + align:start position:0% +short run it's pretty inelastic +short-run a few months you don't change + + align:start position:0% +short-run a few months you don't change + + + align:start position:0% +short-run a few months you don't change +a coal plant in a few months the supply + + align:start position:0% +a coal plant in a few months the supply + + + align:start position:0% +a coal plant in a few months the supply +curve is that vertical line it's a cap + + align:start position:0% +curve is that vertical line it's a cap + + + align:start position:0% +curve is that vertical line it's a cap +so the supply is really an elastic the + + align:start position:0% +so the supply is really an elastic the + + + align:start position:0% +so the supply is really an elastic the +demand is pretty inelastic and the price + + align:start position:0% +demand is pretty inelastic and the price + + + align:start position:0% +demand is pretty inelastic and the price +bounces so if you look at it you say + + align:start position:0% +bounces so if you look at it you say + + + align:start position:0% +bounces so if you look at it you say +well alright the price moved from say + + align:start position:0% +well alright the price moved from say + + + align:start position:0% +well alright the price moved from say +$75 to $200 over a period of a few years + + align:start position:0% +$75 to $200 over a period of a few years + + + align:start position:0% +$75 to $200 over a period of a few years +terrible horrible oh by the way there + + align:start position:0% +terrible horrible oh by the way there + + + align:start position:0% +terrible horrible oh by the way there +were speculators of course there were + + align:start position:0% +were speculators of course there were + + + align:start position:0% +were speculators of course there were +speculators how could there not be + + align:start position:0% +speculators how could there not be + + + align:start position:0% +speculators how could there not be +speculators did the speculators do this + + align:start position:0% +speculators did the speculators do this + + + align:start position:0% +speculators did the speculators do this +not really they may have amplified but + + align:start position:0% +not really they may have amplified but + + + align:start position:0% +not really they may have amplified but +but the main story was inelastic demand + + align:start position:0% +but the main story was inelastic demand + + + align:start position:0% +but the main story was inelastic demand +and inelastic supply industry hated this + + align:start position:0% +and inelastic supply industry hated this + + + align:start position:0% +and inelastic supply industry hated this +as you could imagine not such a big deal + + align:start position:0% +as you could imagine not such a big deal + + + align:start position:0% +as you could imagine not such a big deal +for sulphur because it's a small cost + + align:start position:0% +for sulphur because it's a small cost + + + align:start position:0% +for sulphur because it's a small cost +but makes it hard to plan when you don't + + align:start position:0% +but makes it hard to plan when you don't + + + align:start position:0% +but makes it hard to plan when you don't +know within a factor of three what that + + align:start position:0% +know within a factor of three what that + + + align:start position:0% +know within a factor of three what that +cost is going to be the alternative and + + align:start position:0% +cost is going to be the alternative and + + + align:start position:0% +cost is going to be the alternative and +I will say we were asked a lot those of + + align:start position:0% +I will say we were asked a lot those of + + + align:start position:0% +I will say we were asked a lot those of +us who were involved in in doing this + + align:start position:0% +us who were involved in in doing this + + + align:start position:0% +us who were involved in in doing this +thing why didn't you do a tax tax would + + align:start position:0% +thing why didn't you do a tax tax would + + + align:start position:0% +thing why didn't you do a tax tax would +avoid that kind of uncertainty you know + + align:start position:0% +avoid that kind of uncertainty you know + + + align:start position:0% +avoid that kind of uncertainty you know +you buy the government would buy is or + + align:start position:0% +you buy the government would buy is or + + + align:start position:0% +you buy the government would buy is or +sell you just put it in effect you just + + align:start position:0% +sell you just put it in effect you just + + + align:start position:0% +sell you just put it in effect you just +put a tax on so2 emissions wouldn't that + + align:start position:0% +put a tax on so2 emissions wouldn't that + + + align:start position:0% +put a tax on so2 emissions wouldn't that +be better yes and no it would mean there + + align:start position:0% +be better yes and no it would mean there + + + align:start position:0% +be better yes and no it would mean there +was a risk the risk would transfer as + + align:start position:0% +was a risk the risk would transfer as + + + align:start position:0% +was a risk the risk would transfer as +you can see to quantity the + + align:start position:0% +you can see to quantity the + + + align:start position:0% +you can see to quantity the +environmentalists hey + + align:start position:0% +environmentalists hey + + + align:start position:0% +environmentalists hey +that you don't know how much is gonna be + + align:start position:0% +that you don't know how much is gonna be + + + align:start position:0% +that you don't know how much is gonna be +omitted rather not know the price and + + align:start position:0% +omitted rather not know the price and + + + align:start position:0% +omitted rather not know the price and +the utilities really hated it because + + align:start position:0% +the utilities really hated it because + + + align:start position:0% +the utilities really hated it because +instead of being given these rights + + align:start position:0% +instead of being given these rights + + + align:start position:0% +instead of being given these rights +you'd actually have to pay out-of-pocket + + align:start position:0% +you'd actually have to pay out-of-pocket + + + align:start position:0% +you'd actually have to pay out-of-pocket +no no no no no so that was a non-starter + + align:start position:0% +no no no no no so that was a non-starter + + + align:start position:0% +no no no no no so that was a non-starter +that was a non-starter okay let us now + + align:start position:0% +that was a non-starter okay let us now + + + align:start position:0% +that was a non-starter okay let us now +go I think this is where we go to the C + + align:start position:0% +go I think this is where we go to the C + + + align:start position:0% +go I think this is where we go to the C +case so what the C case tells us is the + + align:start position:0% +case so what the C case tells us is the + + + align:start position:0% +case so what the C case tells us is the +game shifted in the early 90s people + + align:start position:0% +game shifted in the early 90s people + + + align:start position:0% +game shifted in the early 90s people +worry less about acid rain and they + + align:start position:0% +worry less about acid rain and they + + + align:start position:0% +worry less about acid rain and they +worried a lot more about small fine + + align:start position:0% +worried a lot more about small fine + + + align:start position:0% +worried a lot more about small fine +particulates began to get + + align:start position:0% +particulates began to get + + + align:start position:0% +particulates began to get +epidemiological studies that said that + + align:start position:0% +epidemiological studies that said that + + + align:start position:0% +epidemiological studies that said that +fine particulate skilled people most did + + align:start position:0% +fine particulate skilled people most did + + + align:start position:0% +fine particulate skilled people most did +they kill old people but old people vote + + align:start position:0% +they kill old people but old people vote + + + align:start position:0% +they kill old people but old people vote +so EPA had to EPA issued a standard for + + align:start position:0% +so EPA had to EPA issued a standard for + + + align:start position:0% +so EPA had to EPA issued a standard for +fine particulates in 1997 and it had to + + align:start position:0% +fine particulates in 1997 and it had to + + + align:start position:0% +fine particulates in 1997 and it had to +figure out how to meet that standard the + + align:start position:0% +figure out how to meet that standard the + + + align:start position:0% +figure out how to meet that standard the +problem being this the acid rain problem + + align:start position:0% +problem being this the acid rain problem + + + align:start position:0% +problem being this the acid rain problem +in different clothing small particulates + + align:start position:0% +in different clothing small particulates + + + align:start position:0% +in different clothing small particulates +are caused by so2 among other things and + + align:start position:0% +are caused by so2 among other things and + + + align:start position:0% +are caused by so2 among other things and +thus they travel in effect they travel + + align:start position:0% +thus they travel in effect they travel + + + align:start position:0% +thus they travel in effect they travel +so EPA which has interstate Authority + + align:start position:0% +so EPA which has interstate Authority + + + align:start position:0% +so EPA which has interstate Authority +had to do something about fine + + align:start position:0% +had to do something about fine + + + align:start position:0% +had to do something about fine +particulates so what he tried to do was + + align:start position:0% +particulates so what he tried to do was + + + align:start position:0% +particulates so what he tried to do was +brilliant in a way it said we'll tighten + + align:start position:0% +brilliant in a way it said we'll tighten + + + align:start position:0% +brilliant in a way it said we'll tighten +the acid rain program how do we tighten + + align:start position:0% +the acid rain program how do we tighten + + + align:start position:0% +the acid rain program how do we tighten +the acid rain program we require I think + + align:start position:0% +the acid rain program we require I think + + + align:start position:0% +the acid rain program we require I think +it was to two allowances to be omitted + + align:start position:0% +it was to two allowances to be omitted + + + align:start position:0% +it was to two allowances to be omitted +now for every ton instead of one + + align:start position:0% +now for every ton instead of one + + + align:start position:0% +now for every ton instead of one +allowance how perfect is that + + align:start position:0% +allowance how perfect is that + + + align:start position:0% +allowance how perfect is that +we just cut the ceiling cut the cap in + + align:start position:0% +we just cut the ceiling cut the cap in + + + align:start position:0% +we just cut the ceiling cut the cap in +half surely that's going to reduce + + align:start position:0% +half surely that's going to reduce + + + align:start position:0% +half surely that's going to reduce +emissions enough to cut these + + align:start position:0% +emissions enough to cut these + + + align:start position:0% +emissions enough to cut these +particulate swayback well here's what + + align:start position:0% +particulate swayback well here's what + + + align:start position:0% +particulate swayback well here's what +happened to price + + align:start position:0% +happened to price + + + align:start position:0% +happened to price +yeah well what I showed you early on ran + + align:start position:0% +yeah well what I showed you early on ran + + + align:start position:0% +yeah well what I showed you early on ran +up to about there this drastic + + align:start position:0% +up to about there this drastic + + + align:start position:0% +up to about there this drastic +tightening was being debated uh and that + + align:start position:0% +tightening was being debated uh and that + + + align:start position:0% +tightening was being debated uh and that +must be somebody cornering the market + + align:start position:0% +must be somebody cornering the market + + + align:start position:0% +must be somebody cornering the market +but but the run up are trying to but the + + align:start position:0% +but but the run up are trying to but the + + + align:start position:0% +but but the run up are trying to but the +run up to the shoulders the run up the + + align:start position:0% +run up to the shoulders the run up the + + + align:start position:0% +run up to the shoulders the run up the +shoulders was fear of this regulation so + + align:start position:0% +shoulders was fear of this regulation so + + + align:start position:0% +shoulders was fear of this regulation so +again if you read the C case this was a + + align:start position:0% +again if you read the C case this was a + + + align:start position:0% +again if you read the C case this was a +brilliant idea to keep the trading + + align:start position:0% +brilliant idea to keep the trading + + + align:start position:0% +brilliant idea to keep the trading +system intact to make it deal with the + + align:start position:0% +system intact to make it deal with the + + + align:start position:0% +system intact to make it deal with the +new the new problem by tightening it if + + align:start position:0% +new the new problem by tightening it if + + + align:start position:0% +new the new problem by tightening it if +you if you want to read oh I didn't put + + align:start position:0% +you if you want to read oh I didn't put + + + align:start position:0% +you if you want to read oh I didn't put +the citation in if you want to read + + align:start position:0% +the citation in if you want to read + + + align:start position:0% +the citation in if you want to read +something really depressing read the + + align:start position:0% +something really depressing read the + + + align:start position:0% +something really depressing read the +Circuit Court opinion the dealt with the + + align:start position:0% +Circuit Court opinion the dealt with the + + + align:start position:0% +Circuit Court opinion the dealt with the +maybe forty people who challenged this + + align:start position:0% +maybe forty people who challenged this + + + align:start position:0% +maybe forty people who challenged this +rule hundreds of reasons why you + + align:start position:0% +rule hundreds of reasons why you + + + align:start position:0% +rule hundreds of reasons why you +couldn't do this why it was arbitrary + + align:start position:0% +couldn't do this why it was arbitrary + + + align:start position:0% +couldn't do this why it was arbitrary +capricious and a an abuse of discretion + + align:start position:0% +capricious and a an abuse of discretion + + + align:start position:0% +capricious and a an abuse of discretion +and what the Court did was throw it out + + align:start position:0% +and what the Court did was throw it out + + + align:start position:0% +and what the Court did was throw it out +and by throwing it out threw out the + + align:start position:0% +and by throwing it out threw out the + + + align:start position:0% +and by throwing it out threw out the +acid rain program you see that the + + align:start position:0% +acid rain program you see that the + + + align:start position:0% +acid rain program you see that the +little quotation there it said sources + + align:start position:0% +little quotation there it said sources + + + align:start position:0% +little quotation there it said sources +in Alabama which contribute to + + align:start position:0% +in Alabama which contribute to + + + align:start position:0% +in Alabama which contribute to +non-attainment of the fine particulate + + align:start position:0% +non-attainment of the fine particulate + + + align:start position:0% +non-attainment of the fine particulate +standard in Davidson County North + + align:start position:0% +standard in Davidson County North + + + align:start position:0% +standard in Davidson County North +Carolina would not need to reduce their + + align:start position:0% +Carolina would not need to reduce their + + + align:start position:0% +Carolina would not need to reduce their +emissions at all they could just buy the + + align:start position:0% +emissions at all they could just buy the + + + align:start position:0% +emissions at all they could just buy the +right to emit therefore they could keep + + align:start position:0% +right to emit therefore they could keep + + + align:start position:0% +right to emit therefore they could keep +contributing to non-attainment in North + + align:start position:0% +contributing to non-attainment in North + + + align:start position:0% +contributing to non-attainment in North +Carolina therefore a rule that allows + + align:start position:0% +Carolina therefore a rule that allows + + + align:start position:0% +Carolina therefore a rule that allows +that is invalid it doesn't solve the + + align:start position:0% +that is invalid it doesn't solve the + + + align:start position:0% +that is invalid it doesn't solve the +North Carolina problem you've got to + + align:start position:0% +North Carolina problem you've got to + + + align:start position:0% +North Carolina problem you've got to +come up with something that does and + + align:start position:0% +come up with something that does and + + + align:start position:0% +come up with something that does and +what EPA has come up with and what's in + + align:start position:0% +what EPA has come up with and what's in + + + align:start position:0% +what EPA has come up with and what's in +process is something that basically + + align:start position:0% +process is something that basically + + + align:start position:0% +process is something that basically +eliminates interstate trading so this is + + align:start position:0% +eliminates interstate trading so this is + + + align:start position:0% +eliminates interstate trading so this is +the short happy life of interstate + + align:start position:0% +the short happy life of interstate + + + align:start position:0% +the short happy life of interstate +trading of sulfur dioxide allowances it + + align:start position:0% +trading of sulfur dioxide allowances it + + + align:start position:0% +trading of sulfur dioxide allowances it +worked it didn't in the lives of the + + align:start position:0% +worked it didn't in the lives of the + + + align:start position:0% +worked it didn't in the lives of the +court solve the next problem that came + + align:start position:0% +court solve the next problem that came + + + align:start position:0% +court solve the next problem that came +along but it worked so let me say a + + align:start position:0% +along but it worked so let me say a + + + align:start position:0% +along but it worked so let me say a +little bit generally about the the Clean + + align:start position:0% +little bit generally about the the Clean + + + align:start position:0% +little bit generally about the the Clean +Air Act + + align:start position:0% +Air Act + + + align:start position:0% +Air Act +from some EPA propaganda stepping back + + align:start position:0% +from some EPA propaganda stepping back + + + align:start position:0% +from some EPA propaganda stepping back +from this program and I'll let you + + align:start position:0% +from this program and I'll let you + + + align:start position:0% +from this program and I'll let you +digest this stuff and we'll have a few + + align:start position:0% +digest this stuff and we'll have a few + + + align:start position:0% +digest this stuff and we'll have a few +minutes for questions if you look over + + align:start position:0% +minutes for questions if you look over + + + align:start position:0% +minutes for questions if you look over +the long term from 1970 to 2005 real GDP + + align:start position:0% +the long term from 1970 to 2005 real GDP + + + align:start position:0% +the long term from 1970 to 2005 real GDP +almost doubled vehicle miles traveled + + align:start position:0% +almost doubled vehicle miles traveled + + + align:start position:0% +almost doubled vehicle miles traveled +almost doubled let emissions went almost + + align:start position:0% +almost doubled let emissions went almost + + + align:start position:0% +almost doubled let emissions went almost +to zero well I was easy we phased let + + align:start position:0% +to zero well I was easy we phased let + + + align:start position:0% +to zero well I was easy we phased let +out of gasoline that was that was a good + + align:start position:0% +out of gasoline that was that was a good + + + align:start position:0% +out of gasoline that was that was a good +trick + + align:start position:0% +trick + + + align:start position:0% +trick +but large particulates went down by 83% + + align:start position:0% +but large particulates went down by 83% + + + align:start position:0% +but large particulates went down by 83% +but the small particulates not so much + + align:start position:0% +but the small particulates not so much + + + align:start position:0% +but the small particulates not so much +so this problem is still with us + + align:start position:0% +so this problem is still with us + + + align:start position:0% +so this problem is still with us +smoke the small particulate stir not the + + align:start position:0% +smoke the small particulate stir not the + + + align:start position:0% +smoke the small particulate stir not the +big ones you see the small ones kill you + + align:start position:0% +big ones you see the small ones kill you + + + align:start position:0% +big ones you see the small ones kill you +too it is a short hand carbon monoxide + + align:start position:0% +too it is a short hand carbon monoxide + + + align:start position:0% +too it is a short hand carbon monoxide +is down better than more than half + + align:start position:0% +is down better than more than half + + + align:start position:0% +is down better than more than half +sulfur dioxide is down half oxides if + + align:start position:0% +sulfur dioxide is down half oxides if + + + align:start position:0% +sulfur dioxide is down half oxides if +these are national emissions not + + align:start position:0% +these are national emissions not + + + align:start position:0% +these are national emissions not +concentrations oxides of nitrogen 30% + + align:start position:0% +concentrations oxides of nitrogen 30% + + + align:start position:0% +concentrations oxides of nitrogen 30% +that's stubborn because because you get + + align:start position:0% +that's stubborn because because you get + + + align:start position:0% +that's stubborn because because you get +it from automobiles and you got that + + align:start position:0% +it from automobiles and you got that + + + align:start position:0% +it from automobiles and you got that +doubling of vehicle miles traveled but + + align:start position:0% +doubling of vehicle miles traveled but + + + align:start position:0% +doubling of vehicle miles traveled but +still down down a third volatile + + align:start position:0% +still down down a third volatile + + + align:start position:0% +still down down a third volatile +organics down 52 percent and that's + + align:start position:0% +organics down 52 percent and that's + + + align:start position:0% +organics down 52 percent and that's +catalytic converters so if you look at + + align:start position:0% +catalytic converters so if you look at + + + align:start position:0% +catalytic converters so if you look at +that again if you look at that relative + + align:start position:0% +that again if you look at that relative + + + align:start position:0% +that again if you look at that relative +to that paper that was so pessimistic + + align:start position:0% +to that paper that was so pessimistic + + + align:start position:0% +to that paper that was so pessimistic +about the environmental progress that's + + align:start position:0% +about the environmental progress that's + + + align:start position:0% +about the environmental progress that's +not bad if you hadn't had a PA it would + + align:start position:0% +not bad if you hadn't had a PA it would + + + align:start position:0% +not bad if you hadn't had a PA it would +have been worse most of this stuff would + + align:start position:0% +have been worse most of this stuff would + + + align:start position:0% +have been worse most of this stuff would +have gone up with GDP or vehicle miles + + align:start position:0% +have gone up with GDP or vehicle miles + + + align:start position:0% +have gone up with GDP or vehicle miles +traveled not great not great you still + + align:start position:0% +traveled not great not great you still + + + align:start position:0% +traveled not great not great you still +have a zone to devolve small + + align:start position:0% +have a zone to devolve small + + + align:start position:0% +have a zone to devolve small +particulates stubborn stubborn the + + align:start position:0% +particulates stubborn stubborn the + + + align:start position:0% +particulates stubborn stubborn the +eastern eastern seaboard and of course + + align:start position:0% +eastern eastern seaboard and of course + + + align:start position:0% +eastern eastern seaboard and of course +southern california but but you'll + + align:start position:0% +southern california but but you'll + + + align:start position:0% +southern california but but you'll +notice Cape Cod is in non-attainment for + + align:start position:0% +notice Cape Cod is in non-attainment for + + + align:start position:0% +notice Cape Cod is in non-attainment for +ozone not because of the terrible things + + align:start position:0% +ozone not because of the terrible things + + + align:start position:0% +ozone not because of the terrible things +they do there because it moves yeah the + + align:start position:0% +they do there because it moves yeah the + + + align:start position:0% +they do there because it moves yeah the +random wood + + align:start position:0% + + + + align:start position:0% + +in Colorado that's that's good that I + + align:start position:0% +in Colorado that's that's good that I + + + align:start position:0% +in Colorado that's that's good that I +believe is is carbon monoxide and it has + + align:start position:0% +believe is is carbon monoxide and it has + + + align:start position:0% +believe is is carbon monoxide and it has +to do with automobiles I think I don't + + align:start position:0% +to do with automobiles I think I don't + + + align:start position:0% +to do with automobiles I think I don't +think it's ozone no no no no no this is + + align:start position:0% +think it's ozone no no no no no this is + + + align:start position:0% +think it's ozone no no no no no this is +this is Denver this is Denver ha do you + + align:start position:0% +this is Denver this is Denver ha do you + + + align:start position:0% +this is Denver this is Denver ha do you +have a clue what that is I know there + + align:start position:0% +have a clue what that is I know there + + + align:start position:0% +have a clue what that is I know there +was there was some issues with fuel + + align:start position:0% +was there was some issues with fuel + + + align:start position:0% +was there was some issues with fuel +formulation there in particular so I + + align:start position:0% +formulation there in particular so I + + + align:start position:0% +formulation there in particular so I +think it's a it is a I think it's an + + align:start position:0% +think it's a it is a I think it's an + + + align:start position:0% +think it's a it is a I think it's an +ozone or a carbon monoxide problem I + + align:start position:0% + + + + align:start position:0% + +could be wrong but there are people + + align:start position:0% +could be wrong but there are people + + + align:start position:0% +could be wrong but there are people +there there are people there it's not + + align:start position:0% +there there are people there it's not + + + align:start position:0% +there there are people there it's not +just skiing that skiing's for the west + + align:start position:0% +just skiing that skiing's for the west + + + align:start position:0% +just skiing that skiing's for the west +so you know there are parts of the + + align:start position:0% +so you know there are parts of the + + + align:start position:0% +so you know there are parts of the +country that where the air still counts + + align:start position:0% +country that where the air still counts + + + align:start position:0% +country that where the air still counts +is dirty and that's ozone and other + + align:start position:0% +is dirty and that's ozone and other + + + align:start position:0% +is dirty and that's ozone and other +criteria pollutants are you know again + + align:start position:0% +criteria pollutants are you know again + + + align:start position:0% +criteria pollutants are you know again +in some places you've got the well some + + align:start position:0% +in some places you've got the well some + + + align:start position:0% +in some places you've got the well some +of these are some of these are quite + + align:start position:0% +of these are some of these are quite + + + align:start position:0% +of these are some of these are quite +quite unpleasant Southern Cal not + + align:start position:0% +quite unpleasant Southern Cal not + + + align:start position:0% +quite unpleasant Southern Cal not +unpleasant but Southern California for + + align:start position:0% +unpleasant but Southern California for + + + align:start position:0% +unpleasant but Southern California for +instance persists as for that matter + + align:start position:0% +instance persists as for that matter + + + align:start position:0% +instance persists as for that matter +does the Pittsburgh area as in + + align:start position:0% +does the Pittsburgh area as in + + + align:start position:0% +does the Pittsburgh area as in +non-attainment for a number of a number + + align:start position:0% +non-attainment for a number of a number + + + align:start position:0% +non-attainment for a number of a number +of pollutants so let me pause there + + align:start position:0% +of pollutants so let me pause there + + + align:start position:0% +of pollutants so let me pause there +that's that's a lot of ground to cover + + align:start position:0% +that's that's a lot of ground to cover + + + align:start position:0% +that's that's a lot of ground to cover +and I rush through it so let me see if + + align:start position:0% +and I rush through it so let me see if + + + align:start position:0% +and I rush through it so let me see if +you have questions on any of it oh yes + + align:start position:0% +you have questions on any of it oh yes + + + align:start position:0% +you have questions on any of it oh yes +absolutely that's easy + + align:start position:0% +absolutely that's easy + + + align:start position:0% +absolutely that's easy +so in California like waters border of + + align:start position:0% +so in California like waters border of + + + align:start position:0% +so in California like waters border of +California Nevada yep looks like pretty + + align:start position:0% +California Nevada yep looks like pretty + + + align:start position:0% +California Nevada yep looks like pretty +much all of that border in California I + + align:start position:0% + + + + align:start position:0% + +think what you have here is is this is + + align:start position:0% +think what you have here is is this is + + + align:start position:0% +think what you have here is is this is +this may be Imperial County which is + + align:start position:0% +this may be Imperial County which is + + + align:start position:0% +this may be Imperial County which is +gigantic so it may be that the problem + + align:start position:0% +gigantic so it may be that the problem + + + align:start position:0% +gigantic so it may be that the problem +is is over here so it's being done by + + align:start position:0% +is is over here so it's being done by + + + align:start position:0% +is is over here so it's being done by +County it's being done there certain + + align:start position:0% +County it's being done there certain + + + align:start position:0% +County it's being done there certain +monitoring stations in each County and + + align:start position:0% +monitoring stations in each County and + + + align:start position:0% +monitoring stations in each County and +my guess is you know Death Valley's + + align:start position:0% +my guess is you know Death Valley's + + + align:start position:0% +my guess is you know Death Valley's +probably not a non-attainment area for + + align:start position:0% +probably not a non-attainment area for + + + align:start position:0% +probably not a non-attainment area for +much but over here near la I'm guessing + + align:start position:0% +much but over here near la I'm guessing + + + align:start position:0% +much but over here near la I'm guessing +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah it's a certain number of monitoring + + align:start position:0% +yeah it's a certain number of monitoring + + + align:start position:0% +yeah it's a certain number of monitoring +stations sort of thing yeah + + align:start position:0% + + + + align:start position:0% + +sure sure you could even do you could + + align:start position:0% +sure sure you could even do you could + + + align:start position:0% +sure sure you could even do you could +even do better than that let me get + + align:start position:0% +even do better than that let me get + + + align:start position:0% +even do better than that let me get +there yeah here over here but rather + + align:start position:0% +there yeah here over here but rather + + + align:start position:0% +there yeah here over here but rather +here what people did talk about in the + + align:start position:0% +here what people did talk about in the + + + align:start position:0% +here what people did talk about in the +context of co2 right so we talked about + + align:start position:0% +context of co2 right so we talked about + + + align:start position:0% +context of co2 right so we talked about +the kit there was a cap-and-trade bill + + align:start position:0% +the kit there was a cap-and-trade bill + + + align:start position:0% +the kit there was a cap-and-trade bill +and environmentalists said well you know + + align:start position:0% +and environmentalists said well you know + + + align:start position:0% +and environmentalists said well you know +the price could get so low there + + align:start position:0% +the price could get so low there + + + align:start position:0% +the price could get so low there +wouldn't be any incentives and industry + + align:start position:0% +wouldn't be any incentives and industry + + + align:start position:0% +wouldn't be any incentives and industry +said the price could be so high it had + + align:start position:0% +said the price could be so high it had + + + align:start position:0% +said the price could be so high it had +kill us if we had sudden economic growth + + align:start position:0% +kill us if we had sudden economic growth + + + align:start position:0% +kill us if we had sudden economic growth +we could get really high prices that + + align:start position:0% +we could get really high prices that + + + align:start position:0% +we could get really high prices that +would choke off growth or if the growth + + align:start position:0% +would choke off growth or if the growth + + + align:start position:0% +would choke off growth or if the growth +was slow you could have what you have in + + align:start position:0% +was slow you could have what you have in + + + align:start position:0% +was slow you could have what you have in +Europe which is really slow prices + + align:start position:0% +Europe which is really slow prices + + + align:start position:0% +Europe which is really slow prices +really low prices so people proposed how + + align:start position:0% +really low prices so people proposed how + + + align:start position:0% +really low prices so people proposed how +about we have a floor and a ceiling the + + align:start position:0% +about we have a floor and a ceiling the + + + align:start position:0% +about we have a floor and a ceiling the +floor would be if the price drops below + + align:start position:0% +floor would be if the price drops below + + + align:start position:0% +floor would be if the price drops below +this floor some agency starts buying + + align:start position:0% +this floor some agency starts buying + + + align:start position:0% +this floor some agency starts buying +these things on the market if the price + + align:start position:0% +these things on the market if the price + + + align:start position:0% +these things on the market if the price +gets above this ceiling we start selling + + align:start position:0% +gets above this ceiling we start selling + + + align:start position:0% +gets above this ceiling we start selling +them at the ceiling price so you stand + + align:start position:0% +them at the ceiling price so you stand + + + align:start position:0% +them at the ceiling price so you stand +ready to buy it the floor price and sell + + align:start position:0% +ready to buy it the floor price and sell + + + align:start position:0% +ready to buy it the floor price and sell +it the ceiling price to limit the + + align:start position:0% +it the ceiling price to limit the + + + align:start position:0% +it the ceiling price to limit the +fluctuations and if the floor and + + align:start position:0% +fluctuations and if the floor and + + + align:start position:0% +fluctuations and if the floor and +ceiling are close enough together it + + align:start position:0% +ceiling are close enough together it + + + align:start position:0% +ceiling are close enough together it +looks like a tax right so that that was + + align:start position:0% +looks like a tax right so that that was + + + align:start position:0% +looks like a tax right so that that was +a serious a serious set of proposals in + + align:start position:0% +a serious a serious set of proposals in + + + align:start position:0% +a serious a serious set of proposals in +the climate context for exactly the + + align:start position:0% +the climate context for exactly the + + + align:start position:0% +the climate context for exactly the +reasons I think you're thinking of too + + align:start position:0% +reasons I think you're thinking of too + + + align:start position:0% +reasons I think you're thinking of too +low removes incentives too high is very + + align:start position:0% +low removes incentives too high is very + + + align:start position:0% +low removes incentives too high is very +expensive you you give up quantity + + align:start position:0% +expensive you you give up quantity + + + align:start position:0% +expensive you you give up quantity +control but you give up quantity control + + align:start position:0% +control but you give up quantity control + + + align:start position:0% +control but you give up quantity control +sort of at the edges you know if growth + + align:start position:0% +sort of at the edges you know if growth + + + align:start position:0% +sort of at the edges you know if growth +is really slow then emissions are going + + align:start position:0% +is really slow then emissions are going + + + align:start position:0% +is really slow then emissions are going +to be low the problem is up here if + + align:start position:0% +to be low the problem is up here if + + + align:start position:0% +to be low the problem is up here if +growth is really fast you're going to + + align:start position:0% +growth is really fast you're going to + + + align:start position:0% +growth is really fast you're going to +let emissions grow some so maybe you + + align:start position:0% +let emissions grow some so maybe you + + + align:start position:0% +let emissions grow some so maybe you +want this curve to be steep up here a + + align:start position:0% +want this curve to be steep up here a + + + align:start position:0% +want this curve to be steep up here a +supply curve but you could they're + + align:start position:0% +supply curve but you could they're + + + align:start position:0% +supply curve but you could they're +they're very there ways to combine these + + align:start position:0% +they're very there ways to combine these + + + align:start position:0% +they're very there ways to combine these +two and variations on a theme yeah + + align:start position:0% +two and variations on a theme yeah + + + align:start position:0% +two and variations on a theme yeah +anything else okay \ No newline at end of file diff --git a/7KOwsepQcXI.txt b/7KOwsepQcXI.txt new file mode 100644 index 0000000000000000000000000000000000000000..4145f76cc7e12bf0d42f2765b1ee08686ed17a9e --- /dev/null +++ b/7KOwsepQcXI.txt @@ -0,0 +1,11427 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu uh we revised 1805 at an MIT + + align:start position:0% +ocw.mit.edu uh we revised 1805 at an MIT + + + align:start position:0% +ocw.mit.edu uh we revised 1805 at an MIT +1805 is the introductory probability and + + align:start position:0% +1805 is the introductory probability and + + + align:start position:0% +1805 is the introductory probability and +statistics class for mostly non maath + + align:start position:0% +statistics class for mostly non maath + + + align:start position:0% +statistics class for mostly non maath +Majors it for most of them it's the only + + align:start position:0% +Majors it for most of them it's the only + + + align:start position:0% +Majors it for most of them it's the only +probability and statistics class they'll + + align:start position:0% +probability and statistics class they'll + + + align:start position:0% +probability and statistics class they'll +take a lot of them will go on to be + + align:start position:0% +take a lot of them will go on to be + + + align:start position:0% +take a lot of them will go on to be +doctors and so our goal is to have at + + align:start position:0% +doctors and so our goal is to have at + + + align:start position:0% +doctors and so our goal is to have at +least statistically literate + + align:start position:0% +least statistically literate + + + align:start position:0% +least statistically literate +doctors uh out there that that that's + + align:start position:0% +doctors uh out there that that that's + + + align:start position:0% +doctors uh out there that that that's +important the uh no let's keep back + + align:start position:0% + + + + align:start position:0% + +there we've been supported for two years + + align:start position:0% +there we've been supported for two years + + + align:start position:0% +there we've been supported for two years +by a Davis Foundation Grant the pi on + + align:start position:0% +by a Davis Foundation Grant the pi on + + + align:start position:0% +by a Davis Foundation Grant the pi on +the grant is Haynes Miller and and I + + align:start position:0% +the grant is Haynes Miller and and I + + + align:start position:0% +the grant is Haynes Miller and and I +classify him as our PI and Visionary + + align:start position:0% +classify him as our PI and Visionary + + + align:start position:0% +classify him as our PI and Visionary +because the vision of bringing Active + + align:start position:0% +because the vision of bringing Active + + + align:start position:0% +because the vision of bringing Active +Learning into the math department was + + align:start position:0% +Learning into the math department was + + + align:start position:0% +Learning into the math department was +his and it it takes some effort + + align:start position:0% +his and it it takes some effort + + + align:start position:0% +his and it it takes some effort +so thank you thank you for that and it's + + align:start position:0% +so thank you thank you for that and it's + + + align:start position:0% +so thank you thank you for that and it's +uh it's working in some way you'll see + + align:start position:0% +uh it's working in some way you'll see + + + align:start position:0% +uh it's working in some way you'll see +here's the outline of the talk we'll + + align:start position:0% +here's the outline of the talk we'll + + + align:start position:0% +here's the outline of the talk we'll +talk about what we inherited what we + + align:start position:0% +talk about what we inherited what we + + + align:start position:0% +talk about what we inherited what we +came into with 1805 what we've done and + + align:start position:0% +came into with 1805 what we've done and + + + align:start position:0% +came into with 1805 what we've done and +what we've learned and along the way + + align:start position:0% +what we've learned and along the way + + + align:start position:0% +what we've learned and along the way +we'll do a little + + align:start position:0% +we'll do a little + + + align:start position:0% +we'll do a little +demonstration so what we found when we + + align:start position:0% +demonstration so what we found when we + + + align:start position:0% +demonstration so what we found when we +or what what the state of 1805 3 years + + align:start position:0% +or what what the state of 1805 3 years + + + align:start position:0% +or what what the state of 1805 3 years +ago was it was a traditional lecture + + align:start position:0% +ago was it was a traditional lecture + + + align:start position:0% +ago was it was a traditional lecture +class taught at MIT as a lecture with a + + align:start position:0% +class taught at MIT as a lecture with a + + + align:start position:0% +class taught at MIT as a lecture with a +recitation + + align:start position:0% +recitation + + + align:start position:0% +recitation +component and the enrollment was was + + align:start position:0% +component and the enrollment was was + + + align:start position:0% +component and the enrollment was was +dwindling students were not taking it + + align:start position:0% +dwindling students were not taking it + + + align:start position:0% +dwindling students were not taking it +they' migrated to another class part of + + align:start position:0% +they' migrated to another class part of + + + align:start position:0% +they' migrated to another class part of +it was that the faculty who were + + align:start position:0% +it was that the faculty who were + + + align:start position:0% +it was that the faculty who were +teaching it were not uh how do I say + + align:start position:0% +teaching it were not uh how do I say + + + align:start position:0% +teaching it were not uh how do I say +it gently we're not so interested in + + align:start position:0% +it gently we're not so interested in + + + align:start position:0% +it gently we're not so interested in +this section of undergraduate education + + align:start position:0% +this section of undergraduate education + + + align:start position:0% +this section of undergraduate education +and in fact uh the year we took it over + + align:start position:0% +and in fact uh the year we took it over + + + align:start position:0% +and in fact uh the year we took it over +I think we were faced haes can correct + + align:start position:0% +I think we were faced haes can correct + + + align:start position:0% +I think we were faced haes can correct +me if I'm wrong with the choice of + + align:start position:0% +me if I'm wrong with the choice of + + + align:start position:0% +me if I'm wrong with the choice of +either us taking it over or not teaching + + align:start position:0% +either us taking it over or not teaching + + + align:start position:0% +either us taking it over or not teaching +the + + align:start position:0% +the + + + align:start position:0% +the +class so the first year we did teach it + + align:start position:0% +class so the first year we did teach it + + + align:start position:0% +class so the first year we did teach it +as a lecture class John was a recitation + + align:start position:0% +as a lecture class John was a recitation + + + align:start position:0% +as a lecture class John was a recitation +instructor I was a lecturer and then in + + align:start position:0% +instructor I was a lecturer and then in + + + align:start position:0% +instructor I was a lecturer and then in +the next two years we converted to + + align:start position:0% +the next two years we converted to + + + align:start position:0% +the next two years we converted to +a uh fully flipped classroom Active + + align:start position:0% +a uh fully flipped classroom Active + + + align:start position:0% +a uh fully flipped classroom Active +Learning and we co- te it + + align:start position:0% +Learning and we co- te it + + + align:start position:0% +Learning and we co- te it +now so what we found is just that Haynes + + align:start position:0% +now so what we found is just that Haynes + + + align:start position:0% +now so what we found is just that Haynes +had a big interest in active learning + + align:start position:0% +had a big interest in active learning + + + align:start position:0% +had a big interest in active learning +he's been pushing them in recitations + + align:start position:0% +he's been pushing them in recitations + + + align:start position:0% +he's been pushing them in recitations +for years uh with some success I would + + align:start position:0% +for years uh with some success I would + + + align:start position:0% +for years uh with some success I would +say now it's built up + + align:start position:0% +say now it's built up + + + align:start position:0% +say now it's built up +and Davis and everyone is interested in + + align:start position:0% +and Davis and everyone is interested in + + + align:start position:0% +and Davis and everyone is interested in +the world of online learning and what + + align:start position:0% +the world of online learning and what + + + align:start position:0% +the world of online learning and what +can happen there so we have a component + + align:start position:0% +can happen there so we have a component + + + align:start position:0% +can happen there so we have a component +of the class online the class itself + + align:start position:0% +of the class online the class itself + + + align:start position:0% +of the class online the class itself +will be put on open courseware uh + + align:start position:0% +will be put on open courseware uh + + + align:start position:0% +will be put on open courseware uh +educator at the end of this + + align:start position:0% +educator at the end of this + + + align:start position:0% +educator at the end of this +year + + align:start position:0% +year + + + align:start position:0% +year +so what did we do we changed everything + + align:start position:0% +so what did we do we changed everything + + + align:start position:0% +so what did we do we changed everything +at once in retrospect I would say I + + align:start position:0% +at once in retrospect I would say I + + + align:start position:0% +at once in retrospect I would say I +don't recommend it but having gotten + + align:start position:0% +don't recommend it but having gotten + + + align:start position:0% +don't recommend it but having gotten +through it you're always glad that you + + align:start position:0% +through it you're always glad that you + + + align:start position:0% +through it you're always glad that you +did it all at once because now we don't + + align:start position:0% +did it all at once because now we don't + + + align:start position:0% +did it all at once because now we don't +have to do any of these pieces we can + + align:start position:0% +have to do any of these pieces we can + + + align:start position:0% +have to do any of these pieces we can +just keep refining them it's a lot to + + align:start position:0% +just keep refining them it's a lot to + + + align:start position:0% +just keep refining them it's a lot to +talk about so we're not going to focus + + align:start position:0% +talk about so we're not going to focus + + + align:start position:0% +talk about so we're not going to focus +much on the new curriculum I'll just say + + align:start position:0% +much on the new curriculum I'll just say + + + align:start position:0% +much on the new curriculum I'll just say +a few words that we're really proud of + + align:start position:0% +a few words that we're really proud of + + + align:start position:0% +a few words that we're really proud of +the curriculum we have we've introduced + + align:start position:0% +the curriculum we have we've introduced + + + align:start position:0% +the curriculum we have we've introduced +a unit on Basi and inference sanj mahen + + align:start position:0% +a unit on Basi and inference sanj mahen + + + align:start position:0% +a unit on Basi and inference sanj mahen +who's here here is our uh + + align:start position:0% +who's here here is our uh + + + align:start position:0% +who's here here is our uh +basian uh can I say + + align:start position:0% +basian uh can I say + + + align:start position:0% +basian uh can I say +Zealot does it say that's your religion + + align:start position:0% +Zealot does it say that's your religion + + + align:start position:0% +Zealot does it say that's your religion +on your Facebook site no that's me + + align:start position:0% +on your Facebook site no that's me + + + align:start position:0% +on your Facebook site no that's me +that's oh that's + + align:start position:0% +that's oh that's + + + align:start position:0% +that's oh that's +John okay that's all it's on John's site + + align:start position:0% +John okay that's all it's on John's site + + + align:start position:0% +John okay that's all it's on John's site +John is a convert + + align:start position:0% +John is a convert + + + align:start position:0% +John is a convert +um a basing unit what that has done for + + align:start position:0% +um a basing unit what that has done for + + + align:start position:0% +um a basing unit what that has done for +us it allows us to bridge the gap + + align:start position:0% +us it allows us to bridge the gap + + + align:start position:0% +us it allows us to bridge the gap +between the probability and statistics + + align:start position:0% +between the probability and statistics + + + align:start position:0% +between the probability and statistics +part which is always a hard Gap + + align:start position:0% +part which is always a hard Gap + + + align:start position:0% +part which is always a hard Gap +probability I'll say is a mathematical + + align:start position:0% +probability I'll say is a mathematical + + + align:start position:0% +probability I'll say is a mathematical +science statistic is a statistic ICS are + + align:start position:0% +science statistic is a statistic ICS are + + + align:start position:0% +science statistic is a statistic ICS are +at least as much art as science and so + + align:start position:0% +at least as much art as science and so + + + align:start position:0% +at least as much art as science and so +it allows us to bridge that basian + + align:start position:0% +it allows us to bridge that basian + + + align:start position:0% +it allows us to bridge that basian +inference and basian learning are + + align:start position:0% +inference and basian learning are + + + align:start position:0% +inference and basian learning are +becoming more and more important uh + + align:start position:0% +becoming more and more important uh + + + align:start position:0% +becoming more and more important uh +today so it's good that they see it and + + align:start position:0% +today so it's good that they see it and + + + align:start position:0% +today so it's good that they see it and +finally even if they're just doctors who + + align:start position:0% +finally even if they're just doctors who + + + align:start position:0% +finally even if they're just doctors who +need to know what a P value is we feel + + align:start position:0% +need to know what a P value is we feel + + + align:start position:0% +need to know what a P value is we feel +we can explain a P value better by + + align:start position:0% +we can explain a P value better by + + + align:start position:0% +we can explain a P value better by +having introduced this unit so we + + align:start position:0% +having introduced this unit so we + + + align:start position:0% +having introduced this unit so we +actually added three weeks worth of + + align:start position:0% +actually added three weeks worth of + + + align:start position:0% +actually added three weeks worth of +material to the class and we'll talk a + + align:start position:0% +material to the class and we'll talk a + + + align:start position:0% +material to the class and we'll talk a +little bit about that later then we'll + + align:start position:0% +little bit about that later then we'll + + + align:start position:0% +little bit about that later then we'll +speak more about the pedagogy the + + align:start position:0% +speak more about the pedagogy the + + + align:start position:0% +speak more about the pedagogy the +importance of the classroom and what + + align:start position:0% +importance of the classroom and what + + + align:start position:0% +importance of the classroom and what +technology we have in the class we have + + align:start position:0% +technology we have in the class we have + + + align:start position:0% +technology we have in the class we have +a video oh and now we actually we're + + align:start position:0% +a video oh and now we actually we're + + + align:start position:0% +a video oh and now we actually we're +going to show you this is a video a + + align:start position:0% +going to show you this is a video a + + + align:start position:0% +going to show you this is a video a +little bit what you should pay attention + + align:start position:0% +little bit what you should pay attention + + + align:start position:0% +little bit what you should pay attention +while you're watching the video is the + + align:start position:0% +while you're watching the video is the + + + align:start position:0% +while you're watching the video is the +energy in the classroom and particularly + + align:start position:0% +energy in the classroom and particularly + + + align:start position:0% +energy in the classroom and particularly +the comments and the oo and a that come + + align:start position:0% +the comments and the oo and a that come + + + align:start position:0% +the comments and the oo and a that come +at the end when you'll see John talking + + align:start position:0% +at the end when you'll see John talking + + + align:start position:0% +at the end when you'll see John talking +to some students on the today we're + + align:start position:0% +to some students on the today we're + + + align:start position:0% +to some students on the today we're +going to do basian updating which is to + + align:start position:0% +going to do basian updating which is to + + + align:start position:0% +going to do basian updating which is to +say we're going to be using base theorem + + align:start position:0% +say we're going to be using base theorem + + + align:start position:0% +say we're going to be using base theorem +to learn from data which treatment would + + align:start position:0% +to learn from data which treatment would + + + align:start position:0% +to learn from data which treatment would +you choose if you needed a treatment + + align:start position:0% +you choose if you needed a treatment + + + align:start position:0% +you choose if you needed a treatment +treatment one cured 100% of the patients + + align:start position:0% +treatment one cured 100% of the patients + + + align:start position:0% +treatment one cured 100% of the patients +treatment two cured + + align:start position:0% +treatment two cured + + + align:start position:0% +treatment two cured +95% in a trial and treatment three cured + + align:start position:0% +95% in a trial and treatment three cured + + + align:start position:0% +95% in a trial and treatment three cured +90% all right there there's some + + align:start position:0% +90% all right there there's some + + + align:start position:0% +90% all right there there's some +holdouts for the 95% cure I'm not sure + + align:start position:0% +holdouts for the 95% cure I'm not sure + + + align:start position:0% +holdouts for the 95% cure I'm not sure +why what if I gave you this + + align:start position:0% +why what if I gave you this + + + align:start position:0% +why what if I gave you this +information treatment one cured three + + align:start position:0% +information treatment one cured three + + + align:start position:0% +information treatment one cured three +out of three patients that's 100% + + align:start position:0% +out of three patients that's 100% + + + align:start position:0% +out of three patients that's 100% +treatment two cured 19 out of 20 + + align:start position:0% +treatment two cured 19 out of 20 + + + align:start position:0% +treatment two cured 19 out of 20 +patients that's + + align:start position:0% +patients that's + + + align:start position:0% +patients that's +95% or you have a standard treatment + + align:start position:0% +95% or you have a standard treatment + + + align:start position:0% +95% or you have a standard treatment +which has cured 990,000 out of 100,000 + + align:start position:0% +which has cured 990,000 out of 100,000 + + + align:start position:0% +which has cured 990,000 out of 100,000 +patients 90% so suppose in this MIT + + align:start position:0% +patients 90% so suppose in this MIT + + + align:start position:0% +patients 90% so suppose in this MIT +mug I have dice of two types foursided + + align:start position:0% +mug I have dice of two types foursided + + + align:start position:0% +mug I have dice of two types foursided +and 20-sided I'm going to randomly pull + + align:start position:0% +and 20-sided I'm going to randomly pull + + + align:start position:0% +and 20-sided I'm going to randomly pull +out a die roll + + align:start position:0% +out a die roll + + + align:start position:0% +out a die roll +it all right I got a + + align:start position:0% +it all right I got a + + + align:start position:0% +it all right I got a +one which type of D do you think I + + align:start position:0% +one which type of D do you think I + + + align:start position:0% +one which type of D do you think I +randomly + + align:start position:0% +randomly + + + align:start position:0% +randomly +chose okay that was actually what I had + + align:start position:0% +chose okay that was actually what I had + + + align:start position:0% +chose okay that was actually what I had +in this cup does this change at all your + + align:start position:0% +in this cup does this change at all your + + + align:start position:0% +in this cup does this change at all your +analysis of which die you think I rolled + + align:start position:0% +analysis of which die you think I rolled + + + align:start position:0% +analysis of which die you think I rolled +and got a one with so this is the first + + align:start position:0% +and got a one with so this is the first + + + align:start position:0% +and got a one with so this is the first +board question all right I want you to + + align:start position:0% +board question all right I want you to + + + align:start position:0% +board question all right I want you to +practice making the table Jerry showed + + align:start position:0% +practice making the table Jerry showed + + + align:start position:0% +practice making the table Jerry showed +you make one for if it were 13 make one + + align:start position:0% +you make one for if it were 13 make one + + + align:start position:0% +you make one for if it were 13 make one +if it were if I had rolled a five + + align:start position:0% +if it were if I had rolled a five + + + align:start position:0% +if it were if I had rolled a five +instead or do the same question if I had + + align:start position:0% +instead or do the same question if I had + + + align:start position:0% +instead or do the same question if I had +rolled a + + align:start position:0% + + + + align:start position:0% + +nine you knew it was a 20 set of Die + + align:start position:0% +nine you knew it was a 20 set of Die + + + align:start position:0% +nine you knew it was a 20 set of Die +yeah all right your beliefs have changed + + align:start position:0% +yeah all right your beliefs have changed + + + align:start position:0% +yeah all right your beliefs have changed +based on that about the probability that + + align:start position:0% +based on that about the probability that + + + align:start position:0% +based on that about the probability that +you have each of the five dice so if you + + align:start position:0% +you have each of the five dice so if you + + + align:start position:0% +you have each of the five dice so if you +take that and you use that as your prior + + align:start position:0% +take that and you use that as your prior + + + align:start position:0% +take that and you use that as your prior +here + + align:start position:0% +here + + + align:start position:0% +here +then the likelihood multiply and Su + + align:start position:0% +then the likelihood multiply and Su + + + align:start position:0% +then the likelihood multiply and Su +there we go that should give + + align:start position:0% +there we go that should give + + + align:start position:0% +there we go that should give +you I like + + align:start position:0% +you I like + + + align:start position:0% +you I like +that right so I I I've lectured for + + align:start position:0% +that right so I I I've lectured for + + + align:start position:0% +that right so I I I've lectured for +years I don't know that I've ever heard + + align:start position:0% +years I don't know that I've ever heard + + + align:start position:0% +years I don't know that I've ever heard +of that many oenas or a statement I like + + align:start position:0% +of that many oenas or a statement I like + + + align:start position:0% +of that many oenas or a statement I like +that at the end sometimes there's a + + align:start position:0% +that at the end sometimes there's a + + + align:start position:0% +that at the end sometimes there's a +student who nods very + + align:start position:0% +student who nods very + + + align:start position:0% +student who nods very +enthusiastically + + align:start position:0% +enthusiastically + + + align:start position:0% +enthusiastically +um okay so what I'm going to go through + + align:start position:0% +um okay so what I'm going to go through + + + align:start position:0% +um okay so what I'm going to go through +here is just what we do I'm going to + + align:start position:0% +here is just what we do I'm going to + + + align:start position:0% +here is just what we do I'm going to +resist the urge to talk a lot about why + + align:start position:0% +resist the urge to talk a lot about why + + + align:start position:0% +resist the urge to talk a lot about why +we like doing it because that'll come + + align:start position:0% +we like doing it because that'll come + + + align:start position:0% +we like doing it because that'll come +later and John will talk about that the + + align:start position:0% +later and John will talk about that the + + + align:start position:0% +later and John will talk about that the +the structure is we meet three times 80 + + align:start position:0% +the structure is we meet three times 80 + + + align:start position:0% +the structure is we meet three times 80 +minutes so that's 240 minutes which + + align:start position:0% +minutes so that's 240 minutes which + + + align:start position:0% +minutes so that's 240 minutes which +matches the 5times 50 minutes that a + + align:start position:0% +matches the 5times 50 minutes that a + + + align:start position:0% +matches the 5times 50 minutes that a +traditional class meets three lecture + + align:start position:0% +traditional class meets three lecture + + + align:start position:0% +traditional class meets three lecture +hours to recitation so it's not more + + align:start position:0% +hours to recitation so it's not more + + + align:start position:0% +hours to recitation so it's not more +time but at all times we have uh two + + align:start position:0% +time but at all times we have uh two + + + align:start position:0% +time but at all times we have uh two +teachers this year and three assistant + + align:start position:0% +teachers this year and three assistant + + + align:start position:0% +teachers this year and three assistant +teachers in the room so there's five + + align:start position:0% +teachers in the room so there's five + + + align:start position:0% +teachers in the room so there's five +instructors in the room at all times + + align:start position:0% + + + + align:start position:0% + +what we have them do before class they + + align:start position:0% +what we have them do before class they + + + align:start position:0% +what we have them do before class they +do some reading to get them to do the + + align:start position:0% +do some reading to get them to do the + + + align:start position:0% +do some reading to get them to do the +reading there's reading questions which + + align:start position:0% +reading there's reading questions which + + + align:start position:0% +reading there's reading questions which +they get credit for these are all online + + align:start position:0% +they get credit for these are all online + + + align:start position:0% +they get credit for these are all online +it's hosted on mitx and they get + + align:start position:0% +it's hosted on mitx and they get + + + align:start position:0% +it's hosted on mitx and they get +immediate feedback they know whether + + align:start position:0% +immediate feedback they know whether + + + align:start position:0% +immediate feedback they know whether +they got the question right or wrong + + align:start position:0% +they got the question right or wrong + + + align:start position:0% +they got the question right or wrong +it's possible to ask lots and lots of + + align:start position:0% +it's possible to ask lots and lots of + + + align:start position:0% +it's possible to ask lots and lots of +different types of questions although we + + align:start position:0% +different types of questions although we + + + align:start position:0% +different types of questions although we +restrict ourselves mostly to multiple + + align:start position:0% +restrict ourselves mostly to multiple + + + align:start position:0% +restrict ourselves mostly to multiple +choice and fill in a number type of + + align:start position:0% +choice and fill in a number type of + + + align:start position:0% +choice and fill in a number type of +questions um Jenny French who's here has + + align:start position:0% +questions um Jenny French who's here has + + + align:start position:0% +questions um Jenny French who's here has +done the same thing for 1803 and she's + + align:start position:0% +done the same thing for 1803 and she's + + + align:start position:0% +done the same thing for 1803 and she's +been more ambitious with the types of + + align:start position:0% +been more ambitious with the types of + + + align:start position:0% +been more ambitious with the types of +questions they come to class and we do a + + align:start position:0% +questions they come to class and we do a + + + align:start position:0% +questions they come to class and we do a +minimal amount of lecturing what gets + + align:start position:0% +minimal amount of lecturing what gets + + + align:start position:0% +minimal amount of lecturing what gets +left out of a math class of our class as + + align:start position:0% +left out of a math class of our class as + + + align:start position:0% +left out of a math class of our class as +opposed to a traditional class lecture + + align:start position:0% +opposed to a traditional class lecture + + + align:start position:0% +opposed to a traditional class lecture +class is we don't do examples we're + + align:start position:0% +class is we don't do examples we're + + + align:start position:0% +class is we don't do examples we're +going to have the students work examples + + align:start position:0% +going to have the students work examples + + + align:start position:0% +going to have the students work examples +and it's much more better much more + + align:start position:0% +and it's much more better much more + + + align:start position:0% +and it's much more better much more +better much better for students to work + + align:start position:0% +better much better for students to work + + + align:start position:0% +better much better for students to work +one example than for the teacher to work + + align:start position:0% +one example than for the teacher to work + + + align:start position:0% +one example than for the teacher to work +two we feel this + + align:start position:0% +two we feel this + + + align:start position:0% +two we feel this +strongly you saw that you saw a little + + align:start position:0% +strongly you saw that you saw a little + + + align:start position:0% +strongly you saw that you saw a little +bit of lecturing it was cut I maybe + + align:start position:0% +bit of lecturing it was cut I maybe + + + align:start position:0% +bit of lecturing it was cut I maybe +lectured a little more in the video than + + align:start position:0% +lectured a little more in the video than + + + align:start position:0% +lectured a little more in the video than +you saw but very quickly we have them up + + align:start position:0% +you saw but very quickly we have them up + + + align:start position:0% +you saw but very quickly we have them up +at the boards doing group problems as + + align:start position:0% +at the boards doing group problems as + + + align:start position:0% +at the boards doing group problems as +you saw in the video while the teachers + + align:start position:0% +you saw in the video while the teachers + + + align:start position:0% +you saw in the video while the teachers +and the assistants are circulating and + + align:start position:0% +and the assistants are circulating and + + + align:start position:0% +and the assistants are circulating and +talking to people and helping them get + + align:start position:0% +talking to people and helping them get + + + align:start position:0% +talking to people and helping them get +past stumbling part points and assessing + + align:start position:0% +past stumbling part points and assessing + + + align:start position:0% +past stumbling part points and assessing +what they're understanding and + + align:start position:0% +what they're understanding and + + + align:start position:0% +what they're understanding and +correcting + + align:start position:0% + + + + align:start position:0% + +misconceptions other components of the + + align:start position:0% +misconceptions other components of the + + + align:start position:0% +misconceptions other components of the +class which you didn't see as much we + + align:start position:0% +class which you didn't see as much we + + + align:start position:0% +class which you didn't see as much we +have whole class discussions we'll have + + align:start position:0% +have whole class discussions we'll have + + + align:start position:0% +have whole class discussions we'll have +them discuss things at their tables in + + align:start position:0% +them discuss things at their tables in + + + align:start position:0% +them discuss things at their tables in +groups we can operate on many levels of + + align:start position:0% +groups we can operate on many levels of + + + align:start position:0% +groups we can operate on many levels of +interaction between students and + + align:start position:0% +interaction between students and + + + align:start position:0% +interaction between students and +students and students and teachers we + + align:start position:0% +students and students and teachers we + + + align:start position:0% +students and students and teachers we +also use a little bit of Technology + + align:start position:0% +also use a little bit of Technology + + + align:start position:0% +also use a little bit of Technology +clicker questions where we'll ask a + + align:start position:0% +clicker questions where we'll ask a + + + align:start position:0% +clicker questions where we'll ask a +multiple choice usually a kind of + + align:start position:0% +multiple choice usually a kind of + + + align:start position:0% +multiple choice usually a kind of +concept question to see if they've + + align:start position:0% +concept question to see if they've + + + align:start position:0% +concept question to see if they've +understood + + align:start position:0% +understood + + + align:start position:0% +understood +one idea and it also allows us to take + + align:start position:0% +one idea and it also allows us to take + + + align:start position:0% +one idea and it also allows us to take +attendance and the students see it that + + align:start position:0% +attendance and the students see it that + + + align:start position:0% +attendance and the students see it that +way once a week on Fridays we actually + + align:start position:0% +way once a week on Fridays we actually + + + align:start position:0% +way once a week on Fridays we actually +do comp a computer-based studio where + + align:start position:0% +do comp a computer-based studio where + + + align:start position:0% +do comp a computer-based studio where +they have their computers it's the one + + align:start position:0% +they have their computers it's the one + + + align:start position:0% +they have their computers it's the one +time we let them take their computers + + align:start position:0% +time we let them take their computers + + + align:start position:0% +time we let them take their computers +out and we do it in + + align:start position:0% +out and we do it in + + + align:start position:0% +out and we do it in +our typically we're not introducing new + + align:start position:0% +our typically we're not introducing new + + + align:start position:0% +our typically we're not introducing new +material we're doing more advanced work + + align:start position:0% +material we're doing more advanced work + + + align:start position:0% +material we're doing more advanced work +or simulations that you can do on the + + align:start position:0% +or simulations that you can do on the + + + align:start position:0% +or simulations that you can do on the +computer and finally uh we do have + + align:start position:0% +computer and finally uh we do have + + + align:start position:0% +computer and finally uh we do have +traditional problem sets they have to + + align:start position:0% +traditional problem sets they have to + + + align:start position:0% +traditional problem sets they have to +turn in the problem set on paper once a + + align:start position:0% +turn in the problem set on paper once a + + + align:start position:0% +turn in the problem set on paper once a +week and it's graded in the usual way uh + + align:start position:0% +week and it's graded in the usual way uh + + + align:start position:0% +week and it's graded in the usual way uh +the pet Checker is not traditional this + + align:start position:0% +the pet Checker is not traditional this + + + align:start position:0% +the pet Checker is not traditional this +is something we borrowed from the + + align:start position:0% +is something we borrowed from the + + + align:start position:0% +is something we borrowed from the +physics people safe is here I think and + + align:start position:0% +physics people safe is here I think and + + + align:start position:0% +physics people safe is here I think and +I think you guys pioneered this it + + align:start position:0% +I think you guys pioneered this it + + + align:start position:0% +I think you guys pioneered this it +allows the students to check their + + align:start position:0% +allows the students to check their + + + align:start position:0% +allows the students to check their +answers to their + + align:start position:0% +answers to their + + + align:start position:0% +answers to their +homework ahead of time which allows us + + align:start position:0% +homework ahead of time which allows us + + + align:start position:0% +homework ahead of time which allows us +to tell them we care about how you + + align:start position:0% +to tell them we care about how you + + + align:start position:0% +to tell them we care about how you +present it that your logic and your + + align:start position:0% +present it that your logic and your + + + align:start position:0% +present it that your logic and your +thinking is correct it allows the + + align:start position:0% +thinking is correct it allows the + + + align:start position:0% +thinking is correct it allows the +students I can't resist saying this one + + align:start position:0% +students I can't resist saying this one + + + align:start position:0% +students I can't resist saying this one +thing on I'm sorry it allows the + + align:start position:0% +thing on I'm sorry it allows the + + + align:start position:0% +thing on I'm sorry it allows the +students to reflect on the pets as + + align:start position:0% +students to reflect on the pets as + + + align:start position:0% +students to reflect on the pets as +they're doing it one of the things we + + align:start position:0% +they're doing it one of the things we + + + align:start position:0% +they're doing it one of the things we +know is when we turn back a he said A + + align:start position:0% +know is when we turn back a he said A + + + align:start position:0% +know is when we turn back a he said A +week later it's gone cold they barely + + align:start position:0% +week later it's gone cold they barely + + + align:start position:0% +week later it's gone cold they barely +look at it to see what they've done + + align:start position:0% +look at it to see what they've done + + + align:start position:0% +look at it to see what they've done +wrong here they see immediately it's + + align:start position:0% +wrong here they see immediately it's + + + align:start position:0% +wrong here they see immediately it's +wrong and they can + + align:start position:0% +wrong and they can + + + align:start position:0% +wrong and they can +reflect okay I think now we + + align:start position:0% +reflect okay I think now we + + + align:start position:0% +reflect okay I think now we +have yeah an active part of this John is + + align:start position:0% +have yeah an active part of this John is + + + align:start position:0% +have yeah an active part of this John is +going to uh we believe strongly in + + align:start position:0% +going to uh we believe strongly in + + + align:start position:0% +going to uh we believe strongly in +active learning so we got to do some + + align:start position:0% +active learning so we got to do some + + + align:start position:0% +active learning so we got to do some +Active Learning uh but really what I + + align:start position:0% +Active Learning uh but really what I + + + align:start position:0% +Active Learning uh but really what I +want to take you through is how we might + + align:start position:0% +want to take you through is how we might + + + align:start position:0% +want to take you through is how we might +Envision a particular New Concept being + + align:start position:0% +Envision a particular New Concept being + + + align:start position:0% +Envision a particular New Concept being +introduced to the students what are the + + align:start position:0% +introduced to the students what are the + + + align:start position:0% +introduced to the students what are the +very components and how do they fit + + align:start position:0% +very components and how do they fit + + + align:start position:0% +very components and how do they fit +together so Jer mentioned that we have + + align:start position:0% +together so Jer mentioned that we have + + + align:start position:0% +together so Jer mentioned that we have +this unit the middle unit of our course + + align:start position:0% +this unit the middle unit of our course + + + align:start position:0% +this unit the middle unit of our course +on basian inference and the first day we + + align:start position:0% +on basian inference and the first day we + + + align:start position:0% +on basian inference and the first day we +do a number of problems that involve + + align:start position:0% +do a number of problems that involve + + + align:start position:0% +do a number of problems that involve +dice in particular at the beginning of + + align:start position:0% +dice in particular at the beginning of + + + align:start position:0% +dice in particular at the beginning of +the term we actually give students dice + + align:start position:0% +the term we actually give students dice + + + align:start position:0% +the term we actually give students dice +that we expect them to keep with them + + align:start position:0% +that we expect them to keep with them + + + align:start position:0% +that we expect them to keep with them +throughout the term and we use them to + + align:start position:0% +throughout the term and we use them to + + + align:start position:0% +throughout the term and we use them to +generate data and to do probability + + align:start position:0% +generate data and to do probability + + + align:start position:0% +generate data and to do probability +experiments but also just to make + + align:start position:0% +experiments but also just to make + + + align:start position:0% +experiments but also just to make +something tangible and so in particular + + align:start position:0% +something tangible and so in particular + + + align:start position:0% +something tangible and so in particular +on this first day the students will have + + align:start position:0% +on this first day the students will have + + + align:start position:0% +on this first day the students will have +come in having done reading maybe we had + + align:start position:0% +come in having done reading maybe we had + + + align:start position:0% +come in having done reading maybe we had +about 10 pages they read they they + + align:start position:0% +about 10 pages they read they they + + + align:start position:0% +about 10 pages they read they they +answer some reading questions and this + + align:start position:0% +answer some reading questions and this + + + align:start position:0% +answer some reading questions and this +introduces them to some new Concepts but + + align:start position:0% +introduces them to some new Concepts but + + + align:start position:0% +introduces them to some new Concepts but +doesn't expect them to have mastered it + + align:start position:0% +doesn't expect them to have mastered it + + + align:start position:0% +doesn't expect them to have mastered it +and then in the beginning of that class + + align:start position:0% +and then in the beginning of that class + + + align:start position:0% +and then in the beginning of that class +that you saw filmed uh we had some + + align:start position:0% +that you saw filmed uh we had some + + + align:start position:0% +that you saw filmed uh we had some +discussions surrounding these dice so + + align:start position:0% +discussions surrounding these dice so + + + align:start position:0% +discussions surrounding these dice so +what you see here is I have five dice uh + + align:start position:0% +what you see here is I have five dice uh + + + align:start position:0% +what you see here is I have five dice uh +this four-sided uh this is a six-sided + + align:start position:0% +this four-sided uh this is a six-sided + + + align:start position:0% +this four-sided uh this is a six-sided +regular old die 8 12 and 20 so these are + + align:start position:0% +regular old die 8 12 and 20 so these are + + + align:start position:0% +regular old die 8 12 and 20 so these are +platonic Dice and the question I have + + align:start position:0% +platonic Dice and the question I have + + + align:start position:0% +platonic Dice and the question I have +for you is is as follows so I actually + + align:start position:0% +for you is is as follows so I actually + + + align:start position:0% +for you is is as follows so I actually +have smaller versions I'm going to take + + align:start position:0% +have smaller versions I'm going to take + + + align:start position:0% +have smaller versions I'm going to take +them and put them in this + + align:start position:0% +them and put them in this + + + align:start position:0% +them and put them in this +cup all right I'll shake it around + + align:start position:0% +cup all right I'll shake it around + + + align:start position:0% +cup all right I'll shake it around +all right Alison reach in and grab one + + align:start position:0% +all right Alison reach in and grab one + + + align:start position:0% +all right Alison reach in and grab one +at random don't + + align:start position:0% + + + + align:start position:0% + +look all right hand it to me thank you + + align:start position:0% +look all right hand it to me thank you + + + align:start position:0% +look all right hand it to me thank you +and then lus can you come up and be our + + align:start position:0% +and then lus can you come up and be our + + + align:start position:0% +and then lus can you come up and be our +verifier + + align:start position:0% +verifier + + + align:start position:0% +verifier +here all right so four dice are still in + + align:start position:0% +here all right so four dice are still in + + + align:start position:0% +here all right so four dice are still in +this cup and lus is going to + + align:start position:0% +this cup and lus is going to + + + align:start position:0% +this cup and lus is going to +tell no I'll do I can I'll do it in the + + align:start position:0% +tell no I'll do I can I'll do it in the + + + align:start position:0% +tell no I'll do I can I'll do it in the +cup so you're G to say what I roll okay + + align:start position:0% +cup so you're G to say what I roll okay + + + align:start position:0% +cup so you're G to say what I roll okay +I'm GNA drop it in shake it around all + + align:start position:0% +I'm GNA drop it in shake it around all + + + align:start position:0% +I'm GNA drop it in shake it around all +right just say the number do not say + + align:start position:0% +right just say the number do not say + + + align:start position:0% +right just say the number do not say +which die okay what number do you see + + align:start position:0% +which die okay what number do you see + + + align:start position:0% +which die okay what number do you see +four a four great so which die do you + + align:start position:0% +four a four great so which die do you + + + align:start position:0% +four a four great so which die do you +think I + + align:start position:0% +think I + + + align:start position:0% +think I +chose raise your hand if you think it's + + align:start position:0% +chose raise your hand if you think it's + + + align:start position:0% +chose raise your hand if you think it's +the four-sided die let's say which is + + align:start position:0% +the four-sided die let's say which is + + + align:start position:0% +the four-sided die let's say which is +the most likely raise your hand if you + + align:start position:0% +the most likely raise your hand if you + + + align:start position:0% +the most likely raise your hand if you +think it's the six-sided + + align:start position:0% +think it's the six-sided + + + align:start position:0% +think it's the six-sided +okay eight 12 20 raise your hand if you + + align:start position:0% +okay eight 12 20 raise your hand if you + + + align:start position:0% +okay eight 12 20 raise your hand if you +think actually they're all equally + + align:start position:0% +think actually they're all equally + + + align:start position:0% +think actually they're all equally +likely at this + + align:start position:0% +likely at this + + + align:start position:0% +likely at this +point great so this is an example of an + + align:start position:0% +point great so this is an example of an + + + align:start position:0% +point great so this is an example of an +excellent opportunity to have a whole + + align:start position:0% +excellent opportunity to have a whole + + + align:start position:0% +excellent opportunity to have a whole +class discussion because clearly you + + align:start position:0% +class discussion because clearly you + + + align:start position:0% +class discussion because clearly you +don't all agree so in our class since + + align:start position:0% +don't all agree so in our class since + + + align:start position:0% +don't all agree so in our class since +they sit around these tables of nine + + align:start position:0% +they sit around these tables of nine + + + align:start position:0% +they sit around these tables of nine +people we might have them say okay well + + align:start position:0% +people we might have them say okay well + + + align:start position:0% +people we might have them say okay well +discuss at the level of your table you + + align:start position:0% +discuss at the level of your table you + + + align:start position:0% +discuss at the level of your table you +know you're all facing each other and + + align:start position:0% +know you're all facing each other and + + + align:start position:0% +know you're all facing each other and +see if you can come to some consensus + + align:start position:0% +see if you can come to some consensus + + + align:start position:0% +see if you can come to some consensus +they'll try to convince each other all + + align:start position:0% +they'll try to convince each other all + + + align:start position:0% +they'll try to convince each other all +right well I'm not going to tell you the + + align:start position:0% +right well I'm not going to tell you the + + + align:start position:0% +right well I'm not going to tell you the +answer just yet uh let's let's do + + align:start position:0% +answer just yet uh let's let's do + + + align:start position:0% +answer just yet uh let's let's do +another roll maybe that'll help it's the + + align:start position:0% +another roll maybe that'll help it's the + + + align:start position:0% +another roll maybe that'll help it's the +same die I didn't you you saw it's not + + align:start position:0% +same die I didn't you you saw it's not + + + align:start position:0% +same die I didn't you you saw it's not +magic all right what did I just roll + + align:start position:0% +magic all right what did I just roll + + + align:start position:0% +magic all right what did I just roll +five a five oo okay so now raise your + + align:start position:0% +five a five oo okay so now raise your + + + align:start position:0% +five a five oo okay so now raise your +hand is it the four-sided + + align:start position:0% +hand is it the four-sided + + + align:start position:0% +hand is it the four-sided +die + + align:start position:0% +die + + + align:start position:0% +die +very good six-sided + + align:start position:0% +very good six-sided + + + align:start position:0% +very good six-sided +die okay + + align:start position:0% +die okay + + + align:start position:0% +die okay +eight 12 20 are they all equally likely + + align:start position:0% +eight 12 20 are they all equally likely + + + align:start position:0% +eight 12 20 are they all equally likely +raise your hand if you still think + + align:start position:0% +raise your hand if you still think + + + align:start position:0% +raise your hand if you still think +they're all equally likely that's + + align:start position:0% +they're all equally likely that's + + + align:start position:0% +they're all equally likely that's +interesting right so there's been some + + align:start position:0% +interesting right so there's been some + + + align:start position:0% +interesting right so there's been some +progress here maybe discuss with your + + align:start position:0% +progress here maybe discuss with your + + + align:start position:0% +progress here maybe discuss with your +neighbors now I'll give you 10 seconds + + align:start position:0% +neighbors now I'll give you 10 seconds + + + align:start position:0% +neighbors now I'll give you 10 seconds +all right th this is great usually it + + align:start position:0% +all right th this is great usually it + + + align:start position:0% +all right th this is great usually it +takes us about a week and a half before + + align:start position:0% +takes us about a week and a half before + + + align:start position:0% +takes us about a week and a half before +we get people to discuss this animatedly + + align:start position:0% +we get people to discuss this animatedly + + + align:start position:0% +we get people to discuss this animatedly +when we do things they have to learn to + + align:start position:0% +when we do things they have to learn to + + + align:start position:0% +when we do things they have to learn to +trust us all right so you've had some + + align:start position:0% +trust us all right so you've had some + + + align:start position:0% +trust us all right so you've had some +discussions I might call on people to + + align:start position:0% +discussions I might call on people to + + + align:start position:0% +discussions I might call on people to +give explanations but in the interest of + + align:start position:0% +give explanations but in the interest of + + + align:start position:0% +give explanations but in the interest of +time let me just flip it a few more + + align:start position:0% +time let me just flip it a few more + + + align:start position:0% +time let me just flip it a few more +times now I got a six now I got a three + + align:start position:0% +times now I got a six now I got a three + + + align:start position:0% +times now I got a six now I got a three +now I got a two now I got a one now I + + align:start position:0% +now I got a two now I got a one now I + + + align:start position:0% +now I got a two now I got a one now I +got a six okay raise your hand if you + + align:start position:0% +got a six okay raise your hand if you + + + align:start position:0% +got a six okay raise your hand if you +think it's a six-sided + + align:start position:0% +think it's a six-sided + + + align:start position:0% +think it's a six-sided +die wonderful all right + + align:start position:0% +die wonderful all right + + + align:start position:0% +die wonderful all right +so it is you never know in science you + + align:start position:0% +so it is you never know in science you + + + align:start position:0% +so it is you never know in science you +never know this is statistics I'm not + + align:start position:0% +never know this is statistics I'm not + + + align:start position:0% +never know this is statistics I'm not +going to tell you + + align:start position:0% + + + + align:start position:0% + +sorry all + + align:start position:0% +sorry all + + + align:start position:0% +sorry all +right no that's the difference between + + align:start position:0% +right no that's the difference between + + + align:start position:0% +right no that's the difference between +probability and statistics you never + + align:start position:0% +probability and statistics you never + + + align:start position:0% +probability and statistics you never +know right so + + align:start position:0% +know right so + + + align:start position:0% +know right so +so great we've gotten the students to + + align:start position:0% +so great we've gotten the students to + + + align:start position:0% +so great we've gotten the students to +appreciate there's some some some + + align:start position:0% +appreciate there's some some some + + + align:start position:0% +appreciate there's some some some +interesting question here maybe some + + align:start position:0% +interesting question here maybe some + + + align:start position:0% +interesting question here maybe some +intuition they've discussed it next what + + align:start position:0% +intuition they've discussed it next what + + + align:start position:0% +intuition they've discussed it next what +you saw in the video was the students at + + align:start position:0% +you saw in the video was the students at + + + align:start position:0% +you saw in the video was the students at +the boards working on problems so + + align:start position:0% +the boards working on problems so + + + align:start position:0% +the boards working on problems so +they're actually doing computations + + align:start position:0% +they're actually doing computations + + + align:start position:0% +they're actually doing computations +meant to you know take them to the next + + align:start position:0% +meant to you know take them to the next + + + align:start position:0% +meant to you know take them to the next +level where they're not just beginning + + align:start position:0% +level where they're not just beginning + + + align:start position:0% +level where they're not just beginning +to appreciate that something's going on + + align:start position:0% +to appreciate that something's going on + + + align:start position:0% +to appreciate that something's going on +but to actually rigorously + + align:start position:0% +but to actually rigorously + + + align:start position:0% +but to actually rigorously +mathematically uh do some computations + + align:start position:0% +mathematically uh do some computations + + + align:start position:0% +mathematically uh do some computations +and they've seen examples of this + + align:start position:0% +and they've seen examples of this + + + align:start position:0% +and they've seen examples of this +computation in their reading and we're + + align:start position:0% +computation in their reading and we're + + + align:start position:0% +computation in their reading and we're +all going around the room and we're + + align:start position:0% +all going around the room and we're + + + align:start position:0% +all going around the room and we're +helping interacting with the groups and + + align:start position:0% +helping interacting with the groups and + + + align:start position:0% +helping interacting with the groups and +uh after they do this they come back + + align:start position:0% +uh after they do this they come back + + + align:start position:0% +uh after they do this they come back +together we might discuss the solution + + align:start position:0% +together we might discuss the solution + + + align:start position:0% +together we might discuss the solution +maybe there'll be some clicker questions + + align:start position:0% +maybe there'll be some clicker questions + + + align:start position:0% +maybe there'll be some clicker questions +involved and they'll still have on + + align:start position:0% +involved and they'll still have on + + + align:start position:0% +involved and they'll still have on +Friday the studio in the studio they + + align:start position:0% +Friday the studio in the studio they + + + align:start position:0% +Friday the studio in the studio they +might use R perhaps we've written a + + align:start position:0% +might use R perhaps we've written a + + + align:start position:0% +might use R perhaps we've written a +script that simulates this rolling of + + align:start position:0% +script that simulates this rolling of + + + align:start position:0% +script that simulates this rolling of +the die and updates the prior to the + + align:start position:0% +the die and updates the prior to the + + + align:start position:0% +the die and updates the prior to the +posterior about which die it is and then + + align:start position:0% +posterior about which die it is and then + + + align:start position:0% +posterior about which die it is and then +they'll experiment with different + + align:start position:0% +they'll experiment with different + + + align:start position:0% +they'll experiment with different +situations with the simulation or + + align:start position:0% +situations with the simulation or + + + align:start position:0% +situations with the simulation or +changing some component of it we don't + + align:start position:0% +changing some component of it we don't + + + align:start position:0% +changing some component of it we don't +expect them to be experts in R but we + + align:start position:0% +expect them to be experts in R but we + + + align:start position:0% +expect them to be experts in R but we +expect them to be able to understand + + align:start position:0% +expect them to be able to understand + + + align:start position:0% +expect them to be able to understand +code we've written and modified in some + + align:start position:0% +code we've written and modified in some + + + align:start position:0% +code we've written and modified in some +way to build their concept understanding + + align:start position:0% +way to build their concept understanding + + + align:start position:0% +way to build their concept understanding +and then they'll have a problem set the + + align:start position:0% +and then they'll have a problem set the + + + align:start position:0% +and then they'll have a problem set the +problem set will ask them some questions + + align:start position:0% +problem set will ask them some questions + + + align:start position:0% +problem set will ask them some questions +that build further and they'll be exams + + align:start position:0% +that build further and they'll be exams + + + align:start position:0% +that build further and they'll be exams +and so on so that's that's the the sort + + align:start position:0% +and so on so that's that's the the sort + + + align:start position:0% +and so on so that's that's the the sort +of trajectory of seeing a topic sort of + + align:start position:0% +of trajectory of seeing a topic sort of + + + align:start position:0% +of trajectory of seeing a topic sort of +building up your your level of + + align:start position:0% +building up your your level of + + + align:start position:0% +building up your your level of +understanding so + + align:start position:0% +understanding so + + + align:start position:0% +understanding so +now uh I'm going to say a little bit now + + align:start position:0% +now uh I'm going to say a little bit now + + + align:start position:0% +now uh I'm going to say a little bit now +about the why so Jerry told you the what + + align:start position:0% +about the why so Jerry told you the what + + + align:start position:0% +about the why so Jerry told you the what +of what we do here's a little bit about + + align:start position:0% +of what we do here's a little bit about + + + align:start position:0% +of what we do here's a little bit about +why we do it or what we've learned from + + align:start position:0% +why we do it or what we've learned from + + + align:start position:0% +why we do it or what we've learned from +the experience of doing it and what we + + align:start position:0% +the experience of doing it and what we + + + align:start position:0% +the experience of doing it and what we +like so in terms of active learning + + align:start position:0% +like so in terms of active learning + + + align:start position:0% +like so in terms of active learning +versus traditional lecture + + align:start position:0% +versus traditional lecture + + + align:start position:0% +versus traditional lecture +the first thing to note is that just the + + align:start position:0% +the first thing to note is that just the + + + align:start position:0% +the first thing to note is that just the +physical act of standing up serves many + + align:start position:0% +physical act of standing up serves many + + + align:start position:0% +physical act of standing up serves many +very useful purposes the first is that + + align:start position:0% +very useful purposes the first is that + + + align:start position:0% +very useful purposes the first is that +in a given 80-minute session the + + align:start position:0% +in a given 80-minute session the + + + align:start position:0% +in a given 80-minute session the +students might be out out of their feet + + align:start position:0% +students might be out out of their feet + + + align:start position:0% +students might be out out of their feet +on their feet two or three times for 10 + + align:start position:0% +on their feet two or three times for 10 + + + align:start position:0% +on their feet two or three times for 10 +to 15 minutes and when they're up + + align:start position:0% +to 15 minutes and when they're up + + + align:start position:0% +to 15 minutes and when they're up +they're not on their phone they're not + + align:start position:0% +they're not on their phone they're not + + + align:start position:0% +they're not on their phone they're not +on their computer and they're not asleep + + align:start position:0% +on their computer and they're not asleep + + + align:start position:0% +on their computer and they're not asleep +so those are all good things but but + + align:start position:0% +so those are all good things but but + + + align:start position:0% +so those are all good things but but +even more just the act of standing it + + align:start position:0% +even more just the act of standing it + + + align:start position:0% +even more just the act of standing it +sort of in some ways activates your + + align:start position:0% +sort of in some ways activates your + + + align:start position:0% +sort of in some ways activates your +focus you're at the board there aren't + + align:start position:0% +focus you're at the board there aren't + + + align:start position:0% +focus you're at the board there aren't +distractions you're with your group + + align:start position:0% +distractions you're with your group + + + align:start position:0% +distractions you're with your group +members and you have a task at hand + + align:start position:0% +members and you have a task at hand + + + align:start position:0% +members and you have a task at hand +and so that just the physical act of + + align:start position:0% +and so that just the physical act of + + + align:start position:0% +and so that just the physical act of +standing we find is a way to raise the + + align:start position:0% +standing we find is a way to raise the + + + align:start position:0% +standing we find is a way to raise the +energy in the room now I'm not make you + + align:start position:0% +energy in the room now I'm not make you + + + align:start position:0% +energy in the room now I'm not make you +all you stand while we talk about this + + align:start position:0% +all you stand while we talk about this + + + align:start position:0% +all you stand while we talk about this +but I think you you would agree that + + align:start position:0% +but I think you you would agree that + + + align:start position:0% +but I think you you would agree that +standing wakes you up the physical space + + align:start position:0% +standing wakes you up the physical space + + + align:start position:0% +standing wakes you up the physical space +this is teal room is kind of amazing but + + align:start position:0% +this is teal room is kind of amazing but + + + align:start position:0% +this is teal room is kind of amazing but +what's most amazing about it is not that + + align:start position:0% +what's most amazing about it is not that + + + align:start position:0% +what's most amazing about it is not that +it has all these computers at the tables + + align:start position:0% +it has all these computers at the tables + + + align:start position:0% +it has all these computers at the tables +which at this stage Isn't So useful + + align:start position:0% +which at this stage Isn't So useful + + + align:start position:0% +which at this stage Isn't So useful +because everyone has laptops uh it's not + + align:start position:0% +because everyone has laptops uh it's not + + + align:start position:0% +because everyone has laptops uh it's not +even really the video cameras and the + + align:start position:0% +even really the video cameras and the + + + align:start position:0% +even really the video cameras and the +projectors it's just the physical space + + align:start position:0% +projectors it's just the physical space + + + align:start position:0% +projectors it's just the physical space +is such that students can rapid get out + + align:start position:0% +is such that students can rapid get out + + + align:start position:0% +is such that students can rapid get out +of their seats find room on the board + + align:start position:0% +of their seats find room on the board + + + align:start position:0% +of their seats find room on the board +work on a problem comfortably come back + + align:start position:0% +work on a problem comfortably come back + + + align:start position:0% +work on a problem comfortably come back +sit at these tables their cheers swivel + + align:start position:0% +sit at these tables their cheers swivel + + + align:start position:0% +sit at these tables their cheers swivel +without them getting up because they + + align:start position:0% +without them getting up because they + + + align:start position:0% +without them getting up because they +have little rollers it's carpeted so + + align:start position:0% +have little rollers it's carpeted so + + + align:start position:0% +have little rollers it's carpeted so +it's not too noisy there's just lots of + + align:start position:0% +it's not too noisy there's just lots of + + + align:start position:0% +it's not too noisy there's just lots of +things about the physical space that are + + align:start position:0% +things about the physical space that are + + + align:start position:0% +things about the physical space that are +really nice and make the class possible + + align:start position:0% +really nice and make the class possible + + + align:start position:0% +really nice and make the class possible +so if we had a choice between technology + + align:start position:0% +so if we had a choice between technology + + + align:start position:0% +so if we had a choice between technology +versus just physical space we would + + align:start position:0% +versus just physical space we would + + + align:start position:0% +versus just physical space we would +choose the ladder in a heartbeat and + + align:start position:0% +choose the ladder in a heartbeat and + + + align:start position:0% +choose the ladder in a heartbeat and +that means that in classrooms where you + + align:start position:0% +that means that in classrooms where you + + + align:start position:0% +that means that in classrooms where you +might not have whiteboards everywhere + + align:start position:0% +might not have whiteboards everywhere + + + align:start position:0% +might not have whiteboards everywhere +you might want to think about putting + + align:start position:0% +you might want to think about putting + + + align:start position:0% +you might want to think about putting +some up in Haiti we actually put up we + + align:start position:0% +some up in Haiti we actually put up we + + + align:start position:0% +some up in Haiti we actually put up we +put up paper on the wall in order to do + + align:start position:0% +put up paper on the wall in order to do + + + align:start position:0% +put up paper on the wall in order to do +simulations with professors there to get + + align:start position:0% +simulations with professors there to get + + + align:start position:0% +simulations with professors there to get +them to feel what Active Learning was + + align:start position:0% +them to feel what Active Learning was + + + align:start position:0% +them to feel what Active Learning was +like at least the way we were trying it + + align:start position:0% +like at least the way we were trying it + + + align:start position:0% +like at least the way we were trying it +peer and teacher instruction so here + + align:start position:0% +peer and teacher instruction so here + + + align:start position:0% +peer and teacher instruction so here +there's a lot of talk about peer + + align:start position:0% +there's a lot of talk about peer + + + align:start position:0% +there's a lot of talk about peer +instruction about how students can help + + align:start position:0% +instruction about how students can help + + + align:start position:0% +instruction about how students can help +teach one another and that's really + + align:start position:0% +teach one another and that's really + + + align:start position:0% +teach one another and that's really +important and there's also teacher + + align:start position:0% +important and there's also teacher + + + align:start position:0% +important and there's also teacher +instruction where the teacher is + + align:start position:0% +instruction where the teacher is + + + align:start position:0% +instruction where the teacher is +interacting with the student uh and + + align:start position:0% +interacting with the student uh and + + + align:start position:0% +interacting with the student uh and +helping them move along in their + + align:start position:0% +helping them move along in their + + + align:start position:0% +helping them move along in their +understanding and what we find in the + + align:start position:0% +understanding and what we find in the + + + align:start position:0% +understanding and what we find in the +classroom is really happening is a lot + + align:start position:0% +classroom is really happening is a lot + + + align:start position:0% +classroom is really happening is a lot +of both they're both important so the + + align:start position:0% +of both they're both important so the + + + align:start position:0% +of both they're both important so the +peer instruction happens because they + + align:start position:0% +peer instruction happens because they + + + align:start position:0% +peer instruction happens because they +have these discussions at the table or + + align:start position:0% +have these discussions at the table or + + + align:start position:0% +have these discussions at the table or +because they're working together at go + + align:start position:0% +because they're working together at go + + + align:start position:0% +because they're working together at go +groups in the board in particular at the + + align:start position:0% +groups in the board in particular at the + + + align:start position:0% +groups in the board in particular at the +board you know you might have one + + align:start position:0% +board you know you might have one + + + align:start position:0% +board you know you might have one +student who's very strong a couple + + align:start position:0% +student who's very strong a couple + + + align:start position:0% +student who's very strong a couple +others who aren't as strong on a + + align:start position:0% +others who aren't as strong on a + + + align:start position:0% +others who aren't as strong on a +particular problem and us going around + + align:start position:0% +particular problem and us going around + + + align:start position:0% +particular problem and us going around +can very much encourage the student who + + align:start position:0% +can very much encourage the student who + + + align:start position:0% +can very much encourage the student who +seems to be taking the lead to make sure + + align:start position:0% +seems to be taking the lead to make sure + + + align:start position:0% +seems to be taking the lead to make sure +the other group members understand or to + + align:start position:0% +the other group members understand or to + + + align:start position:0% +the other group members understand or to +try to vary who's who's taking that lead + + align:start position:0% +try to vary who's who's taking that lead + + + align:start position:0% +try to vary who's who's taking that lead +but you see a lot of students explaining + + align:start position:0% +but you see a lot of students explaining + + + align:start position:0% +but you see a lot of students explaining +to each other students being able to + + align:start position:0% +to each other students being able to + + + align:start position:0% +to each other students being able to +look over at the next group if they're + + align:start position:0% +look over at the next group if they're + + + align:start position:0% +look over at the next group if they're +stuck uh all of this is a kind of peer + + align:start position:0% +stuck uh all of this is a kind of peer + + + align:start position:0% +stuck uh all of this is a kind of peer +instruction then there's also the + + align:start position:0% +instruction then there's also the + + + align:start position:0% +instruction then there's also the +teacher instruction which is the fact + + align:start position:0% +teacher instruction which is the fact + + + align:start position:0% +teacher instruction which is the fact +that Jerry and I and then um several a + + align:start position:0% +that Jerry and I and then um several a + + + align:start position:0% +that Jerry and I and then um several a +graduate student and two undergrads are + + align:start position:0% +graduate student and two undergrads are + + + align:start position:0% +graduate student and two undergrads are +in the room able to basically distribute + + align:start position:0% +in the room able to basically distribute + + + align:start position:0% +in the room able to basically distribute +ourselves like zone defense and monitor + + align:start position:0% +ourselves like zone defense and monitor + + + align:start position:0% +ourselves like zone defense and monitor +a certain number of groups and really + + align:start position:0% +a certain number of groups and really + + + align:start position:0% +a certain number of groups and really +keep tabs on the progress they're making + + align:start position:0% +keep tabs on the progress they're making + + + align:start position:0% +keep tabs on the progress they're making +because you're going to have groups that + + align:start position:0% +because you're going to have groups that + + + align:start position:0% +because you're going to have groups that +are faster and slower and you want to + + align:start position:0% +are faster and slower and you want to + + + align:start position:0% +are faster and slower and you want to +kind of bring them to about the same + + align:start position:0% +kind of bring them to about the same + + + align:start position:0% +kind of bring them to about the same +point at the same time so they can get + + align:start position:0% +point at the same time so they can get + + + align:start position:0% +point at the same time so they can get +the most out of the time when you come + + align:start position:0% +the most out of the time when you come + + + align:start position:0% +the most out of the time when you come +back to the explanation so that's that + + align:start position:0% +back to the explanation so that's that + + + align:start position:0% +back to the explanation so that's that +sort of interaction between the teachers + + align:start position:0% +sort of interaction between the teachers + + + align:start position:0% +sort of interaction between the teachers +and the students is also really huge + + align:start position:0% +and the students is also really huge + + + align:start position:0% +and the students is also really huge +because the students actually feel like + + align:start position:0% +because the students actually feel like + + + align:start position:0% +because the students actually feel like +they get to know us and we get get to + + align:start position:0% +they get to know us and we get get to + + + align:start position:0% +they get to know us and we get get to +feel like we know them the student self + + align:start position:0% +feel like we know them the student self + + + align:start position:0% +feel like we know them the student self +assessment that's referring to the idea + + align:start position:0% +assessment that's referring to the idea + + + align:start position:0% +assessment that's referring to the idea +that you know there's a really rich + + align:start position:0% +that you know there's a really rich + + + align:start position:0% +that you know there's a really rich +Forma of assessment happening in the + + align:start position:0% +Forma of assessment happening in the + + + align:start position:0% +Forma of assessment happening in the +classroom when the students are asked + + align:start position:0% +classroom when the students are asked + + + align:start position:0% +classroom when the students are asked +especially to get up and solve problems + + align:start position:0% +especially to get up and solve problems + + + align:start position:0% +especially to get up and solve problems +at the board when you listen to a + + align:start position:0% +at the board when you listen to a + + + align:start position:0% +at the board when you listen to a +teacher lecture at + + align:start position:0% +teacher lecture at + + + align:start position:0% +teacher lecture at +you doing an example you may nod your + + align:start position:0% +you doing an example you may nod your + + + align:start position:0% +you doing an example you may nod your +head and think you understand it but + + align:start position:0% +head and think you understand it but + + + align:start position:0% +head and think you understand it but +when you're at a board or when you're + + align:start position:0% +when you're at a board or when you're + + + align:start position:0% +when you're at a board or when you're +using a clicker you actually have to do + + align:start position:0% +using a clicker you actually have to do + + + align:start position:0% +using a clicker you actually have to do +the problem you figure out really + + align:start position:0% +the problem you figure out really + + + align:start position:0% +the problem you figure out really +quickly if you understand it because if + + align:start position:0% +quickly if you understand it because if + + + align:start position:0% +quickly if you understand it because if +you're standing there and you have no + + align:start position:0% +you're standing there and you have no + + + align:start position:0% +you're standing there and you have no +idea where to get started + + align:start position:0% +idea where to get started + + + align:start position:0% +idea where to get started +you don't understand it and you know but + + align:start position:0% +you don't understand it and you know but + + + align:start position:0% +you don't understand it and you know but +you want to create an environment where + + align:start position:0% +you want to create an environment where + + + align:start position:0% +you want to create an environment where +that's okay because maybe your + + align:start position:0% +that's okay because maybe your + + + align:start position:0% +that's okay because maybe your +groupmates know or maybe we know and + + align:start position:0% +groupmates know or maybe we know and + + + align:start position:0% +groupmates know or maybe we know and +they're comfortable saying hey John + + align:start position:0% +they're comfortable saying hey John + + + align:start position:0% +they're comfortable saying hey John +Jerry you know can you help us get + + align:start position:0% +Jerry you know can you help us get + + + align:start position:0% +Jerry you know can you help us get +started or even better we're on top of + + align:start position:0% +started or even better we're on top of + + + align:start position:0% +started or even better we're on top of +them even before they get to that point + + align:start position:0% +them even before they get to that point + + + align:start position:0% +them even before they get to that point +because we have a sense at this point + + align:start position:0% +because we have a sense at this point + + + align:start position:0% +because we have a sense at this point +which groups are going to have the most + + align:start position:0% +which groups are going to have the most + + + align:start position:0% +which groups are going to have the most +trouble getting started and there are + + align:start position:0% +trouble getting started and there are + + + align:start position:0% +trouble getting started and there are +some groups where once you get them + + align:start position:0% +some groups where once you get them + + + align:start position:0% +some groups where once you get them +started they fly and it's just a matter + + align:start position:0% +started they fly and it's just a matter + + + align:start position:0% +started they fly and it's just a matter +of being there at the beginning there + + align:start position:0% +of being there at the beginning there + + + align:start position:0% +of being there at the beginning there +are other groups which are the reverse + + align:start position:0% +are other groups which are the reverse + + + align:start position:0% +are other groups which are the reverse +so you get to learn that through this + + align:start position:0% +so you get to learn that through this + + + align:start position:0% +so you get to learn that through this +Rich interaction and that self + + align:start position:0% +Rich interaction and that self + + + align:start position:0% +Rich interaction and that self +assessment students say really helps + + align:start position:0% +assessment students say really helps + + + align:start position:0% +assessment students say really helps +them know if they know right teacher + + align:start position:0% +them know if they know right teacher + + + align:start position:0% +them know if they know right teacher +formative assessment I guess I just + + align:start position:0% +formative assessment I guess I just + + + align:start position:0% +formative assessment I guess I just +mentioned that that's us being able to + + align:start position:0% +mentioned that that's us being able to + + + align:start position:0% +mentioned that that's us being able to +see where these groups are at so the + + align:start position:0% +see where these groups are at so the + + + align:start position:0% +see where these groups are at so the +advantage of them standing up at the + + align:start position:0% +advantage of them standing up at the + + + align:start position:0% +advantage of them standing up at the +boards is that from a distance you can + + align:start position:0% +boards is that from a distance you can + + + align:start position:0% +boards is that from a distance you can +scan the room and see very quickly how + + align:start position:0% +scan the room and see very quickly how + + + align:start position:0% +scan the room and see very quickly how +far each student or group has gotten on + + align:start position:0% +far each student or group has gotten on + + + align:start position:0% +far each student or group has gotten on +these problems which students is holding + + align:start position:0% +these problems which students is holding + + + align:start position:0% +these problems which students is holding +the pen or explaining uh you by the time + + align:start position:0% +the pen or explaining uh you by the time + + + align:start position:0% +the pen or explaining uh you by the time +this period has ended where they've been + + align:start position:0% +this period has ended where they've been + + + align:start position:0% +this period has ended where they've been +working on these problems you've helped + + align:start position:0% +working on these problems you've helped + + + align:start position:0% +working on these problems you've helped +several groups get past several + + align:start position:0% +several groups get past several + + + align:start position:0% +several groups get past several +stumbling points so now it comes time to + + align:start position:0% +stumbling points so now it comes time to + + + align:start position:0% +stumbling points so now it comes time to +bring the class back together and go + + align:start position:0% +bring the class back together and go + + + align:start position:0% +bring the class back together and go +through an explanation of those parts + + align:start position:0% +through an explanation of those parts + + + align:start position:0% +through an explanation of those parts +which are most helpful and you know + + align:start position:0% +which are most helpful and you know + + + align:start position:0% +which are most helpful and you know +because you actually already help them + + align:start position:0% +because you actually already help them + + + align:start position:0% +because you actually already help them +it's like you had an office hour where + + align:start position:0% +it's like you had an office hour where + + + align:start position:0% +it's like you had an office hour where +everyone attended and now you get to + + align:start position:0% +everyone attended and now you get to + + + align:start position:0% +everyone attended and now you get to +explain the answer right and so that's + + align:start position:0% +explain the answer right and so that's + + + align:start position:0% +explain the answer right and so that's +that's been really exciting uh for us so + + align:start position:0% +that's been really exciting uh for us so + + + align:start position:0% +that's been really exciting uh for us so +those are some of the active learning + + align:start position:0% +those are some of the active learning + + + align:start position:0% +those are some of the active learning +benefits we found and then in terms of + + align:start position:0% +benefits we found and then in terms of + + + align:start position:0% +benefits we found and then in terms of +Technology there are I guess three ways + + align:start position:0% +Technology there are I guess three ways + + + align:start position:0% +Technology there are I guess three ways +we're using technology to enhance the + + align:start position:0% +we're using technology to enhance the + + + align:start position:0% +we're using technology to enhance the +class the reading questions as Jerry + + align:start position:0% +class the reading questions as Jerry + + + align:start position:0% +class the reading questions as Jerry +said these are by and large a way to get + + align:start position:0% +said these are by and large a way to get + + + align:start position:0% +said these are by and large a way to get +students to at least open the PDF that + + align:start position:0% +students to at least open the PDF that + + + align:start position:0% +students to at least open the PDF that +has the reading students at MIT are + + align:start position:0% +has the reading students at MIT are + + + align:start position:0% +has the reading students at MIT are +going to play some Game Theory and + + align:start position:0% +going to play some Game Theory and + + + align:start position:0% +going to play some Game Theory and +manage their time to balance a lot of + + align:start position:0% +manage their time to balance a lot of + + + align:start position:0% +manage their time to balance a lot of +obligations and it's very hard to you + + align:start position:0% +obligations and it's very hard to you + + + align:start position:0% +obligations and it's very hard to you +know you can't expect them to say your + + align:start position:0% +know you can't expect them to say your + + + align:start position:0% +know you can't expect them to say your +course is the most important course and + + align:start position:0% +course is the most important course and + + + align:start position:0% +course is the most important course and +of course I'm going to do this before I + + align:start position:0% +of course I'm going to do this before I + + + align:start position:0% +of course I'm going to do this before I +do anything else but at least if they + + align:start position:0% +do anything else but at least if they + + + align:start position:0% +do anything else but at least if they +get to the stage where they open the + + align:start position:0% +get to the stage where they open the + + + align:start position:0% +get to the stage where they open the +document because they know they're going + + align:start position:0% +document because they know they're going + + + align:start position:0% +document because they know they're going +to get graded 5% of their grade on + + align:start position:0% +to get graded 5% of their grade on + + + align:start position:0% +to get graded 5% of their grade on +answering these reading questions you + + align:start position:0% +answering these reading questions you + + + align:start position:0% +answering these reading questions you +have a good chance that they're going to + + align:start position:0% +have a good chance that they're going to + + + align:start position:0% +have a good chance that they're going to +have some first exposure and if you + + align:start position:0% +have some first exposure and if you + + + align:start position:0% +have some first exposure and if you +create an expectation at the beginning + + align:start position:0% +create an expectation at the beginning + + + align:start position:0% +create an expectation at the beginning +of the term that we're going to assume + + align:start position:0% +of the term that we're going to assume + + + align:start position:0% +of the term that we're going to assume +that they've done the reading and not go + + align:start position:0% +that they've done the reading and not go + + + align:start position:0% +that they've done the reading and not go +over it as if they didn't then that also + + align:start position:0% +over it as if they didn't then that also + + + align:start position:0% +over it as if they didn't then that also +helps to inforce and get students to + + align:start position:0% +helps to inforce and get students to + + + align:start position:0% +helps to inforce and get students to +actually do it so they are actually + + align:start position:0% +actually do it so they are actually + + + align:start position:0% +actually do it so they are actually +graded on these questions in terms of + + align:start position:0% +graded on these questions in terms of + + + align:start position:0% +graded on these questions in terms of +whether they're right or wrong uh and + + align:start position:0% +whether they're right or wrong uh and + + + align:start position:0% +whether they're right or wrong uh and +they're not meant to be particularly + + align:start position:0% +they're not meant to be particularly + + + align:start position:0% +they're not meant to be particularly +hard questions they're more like + + align:start position:0% +hard questions they're more like + + + align:start position:0% +hard questions they're more like +questions that are exactly parallel to + + align:start position:0% +questions that are exactly parallel to + + + align:start position:0% +questions that are exactly parallel to +an example so at least they have to look + + align:start position:0% +an example so at least they have to look + + + align:start position:0% +an example so at least they have to look +through the example change the numbers + + align:start position:0% +through the example change the numbers + + + align:start position:0% +through the example change the numbers +you know plug in an answer clickers and + + align:start position:0% +you know plug in an answer clickers and + + + align:start position:0% +you know plug in an answer clickers and +attendance when you do an active + + align:start position:0% +attendance when you do an active + + + align:start position:0% +attendance when you do an active +learning course it's even more important + + align:start position:0% +learning course it's even more important + + + align:start position:0% +learning course it's even more important +that students come to class you can't + + align:start position:0% +that students come to class you can't + + + align:start position:0% +that students come to class you can't +watch an active learning course on video + + align:start position:0% +watch an active learning course on video + + + align:start position:0% +watch an active learning course on video +like you can watch a lecture and so in + + align:start position:0% +like you can watch a lecture and so in + + + align:start position:0% +like you can watch a lecture and so in +some sense it's a way to bring value + + align:start position:0% +some sense it's a way to bring value + + + align:start position:0% +some sense it's a way to bring value +back to you know campus in the face of + + align:start position:0% +back to you know campus in the face of + + + align:start position:0% +back to you know campus in the face of +mukes and + + align:start position:0% +mukes and + + + align:start position:0% +mukes and +so well one way to force attendance is + + align:start position:0% +so well one way to force attendance is + + + align:start position:0% +so well one way to force attendance is +to actually take attendance but we can + + align:start position:0% +to actually take attendance but we can + + + align:start position:0% +to actually take attendance but we can +do that implicitly with the clickers so + + align:start position:0% +do that implicitly with the clickers so + + + align:start position:0% +do that implicitly with the clickers so +students know that if they don't show up + + align:start position:0% +students know that if they don't show up + + + align:start position:0% +students know that if they don't show up +they're not clicking in to certain + + align:start position:0% +they're not clicking in to certain + + + align:start position:0% +they're not clicking in to certain +questions they don't get any points for + + align:start position:0% +questions they don't get any points for + + + align:start position:0% +questions they don't get any points for +that that's 5% of their grade now we + + align:start position:0% +that that's 5% of their grade now we + + + align:start position:0% +that that's 5% of their grade now we +definitely have a few students who are + + align:start position:0% +definitely have a few students who are + + + align:start position:0% +definitely have a few students who are +not still not going to show up at all + + align:start position:0% +not still not going to show up at all + + + align:start position:0% +not still not going to show up at all +because they Ace every exam they learn + + align:start position:0% +because they Ace every exam they learn + + + align:start position:0% +because they Ace every exam they learn +it on their own great they'll get 95% + + align:start position:0% +it on their own great they'll get 95% + + + align:start position:0% +it on their own great they'll get 95% +they'll get an A in the course right but + + align:start position:0% +they'll get an A in the course right but + + + align:start position:0% +they'll get an A in the course right but +and that's okay it's not necessarily + + align:start position:0% +and that's okay it's not necessarily + + + align:start position:0% +and that's okay it's not necessarily +everyone has to learn the same way but + + align:start position:0% +everyone has to learn the same way but + + + align:start position:0% +everyone has to learn the same way but +it's really important for those students + + align:start position:0% +it's really important for those students + + + align:start position:0% +it's really important for those students +who aren't able to do everything on + + align:start position:0% +who aren't able to do everything on + + + align:start position:0% +who aren't able to do everything on +their own that they come to class and we + + align:start position:0% +their own that they come to class and we + + + align:start position:0% +their own that they come to class and we +get a pretty good attendance rate uh and + + align:start position:0% +get a pretty good attendance rate uh and + + + align:start position:0% +get a pretty good attendance rate uh and +we think the clickers help incentivize + + align:start position:0% +we think the clickers help incentivize + + + align:start position:0% +we think the clickers help incentivize +that the pet Checker Jerry mentioned is + + align:start position:0% +that the pet Checker Jerry mentioned is + + + align:start position:0% +that the pet Checker Jerry mentioned is +a tool to get students to know ahead of + + align:start position:0% +a tool to get students to know ahead of + + + align:start position:0% +a tool to get students to know ahead of +time whether or not they got their + + align:start position:0% +time whether or not they got their + + + align:start position:0% +time whether or not they got their +answer correct so that they still have + + align:start position:0% +answer correct so that they still have + + + align:start position:0% +answer correct so that they still have +time to reflect and ask a friend or + + align:start position:0% +time to reflect and ask a friend or + + + align:start position:0% +time to reflect and ask a friend or +think about it some more while they they + + align:start position:0% +think about it some more while they they + + + align:start position:0% +think about it some more while they they +might still get some credit so they're + + align:start position:0% +might still get some credit so they're + + + align:start position:0% +might still get some credit so they're +still incentive as opposed to a couple + + align:start position:0% +still incentive as opposed to a couple + + + align:start position:0% +still incentive as opposed to a couple +weeks later when the problem set comes + + align:start position:0% +weeks later when the problem set comes + + + align:start position:0% +weeks later when the problem set comes +back they have three other problem sets + + align:start position:0% +back they have three other problem sets + + + align:start position:0% +back they have three other problem sets +they have an exam it's not in + + align:start position:0% +they have an exam it's not in + + + align:start position:0% +they have an exam it's not in +Ram might as well not give it back to + + align:start position:0% +Ram might as well not give it back to + + + align:start position:0% +Ram might as well not give it back to +them at all I can't tell you how big the + + align:start position:0% +them at all I can't tell you how big the + + + align:start position:0% +them at all I can't tell you how big the +stack of problem sets I have that + + align:start position:0% +stack of problem sets I have that + + + align:start position:0% +stack of problem sets I have that +students I mean every day every week I + + align:start position:0% +students I mean every day every week I + + + align:start position:0% +students I mean every day every week I +bring them the class I'm like please + + align:start position:0% +bring them the class I'm like please + + + align:start position:0% +bring them the class I'm like please +unburden me take back these problem sets + + align:start position:0% +unburden me take back these problem sets + + + align:start position:0% +unburden me take back these problem sets +most students don't even want them back + + align:start position:0% +most students don't even want them back + + + align:start position:0% +most students don't even want them back +it just tells you how little their + + align:start position:0% +it just tells you how little their + + + align:start position:0% +it just tells you how little their +benefiting from the grading of the + + align:start position:0% +benefiting from the grading of the + + + align:start position:0% +benefiting from the grading of the +problem sets and I think this tool in + + align:start position:0% +problem sets and I think this tool in + + + align:start position:0% +problem sets and I think this tool in +particular transfers very broadly very + + align:start position:0% +particular transfers very broadly very + + + align:start position:0% +particular transfers very broadly very +easily it doesn't have to be a math + + align:start position:0% +easily it doesn't have to be a math + + + align:start position:0% +easily it doesn't have to be a math +class or a Physics course it just has to + + align:start position:0% +class or a Physics course it just has to + + + align:start position:0% +class or a Physics course it just has to +be a course where there's some way to do + + align:start position:0% +be a course where there's some way to do + + + align:start position:0% +be a course where there's some way to do +some assessment of or some some way to + + align:start position:0% +some assessment of or some some way to + + + align:start position:0% +some assessment of or some some way to +evaluate if a student has made progress + + align:start position:0% +evaluate if a student has made progress + + + align:start position:0% +evaluate if a student has made progress +uh it might be there's a formula and you + + align:start position:0% +uh it might be there's a formula and you + + + align:start position:0% +uh it might be there's a formula and you +just plug in some number and that's how + + align:start position:0% +just plug in some number and that's how + + + align:start position:0% +just plug in some number and that's how +you know granted they don't learn what + + align:start position:0% +you know granted they don't learn what + + + align:start position:0% +you know granted they don't learn what +the answer is they just get told that + + align:start position:0% +the answer is they just get told that + + + align:start position:0% +the answer is they just get told that +3.58 is not the right answer it's not + + align:start position:0% +3.58 is not the right answer it's not + + + align:start position:0% +3.58 is not the right answer it's not +very efficient for them to then try 3.59 + + align:start position:0% +very efficient for them to then try 3.59 + + + align:start position:0% +very efficient for them to then try 3.59 +3.57 you know it won't help them so they + + align:start position:0% +3.57 you know it won't help them so they + + + align:start position:0% +3.57 you know it won't help them so they +use it in a way that's very satisfying + + align:start position:0% +use it in a way that's very satisfying + + + align:start position:0% +use it in a way that's very satisfying +if you've ever taken a Muk which is you + + align:start position:0% +if you've ever taken a Muk which is you + + + align:start position:0% +if you've ever taken a Muk which is you +get those green checks when your + + align:start position:0% +get those green checks when your + + + align:start position:0% +get those green checks when your +answerers correct it feels great and so + + align:start position:0% +answerers correct it feels great and so + + + align:start position:0% +answerers correct it feels great and so +they know great I figured these out I + + align:start position:0% +they know great I figured these out I + + + align:start position:0% +they know great I figured these out I +got green checks I'm turning this in + + align:start position:0% +got green checks I'm turning this in + + + align:start position:0% +got green checks I'm turning this in +it's going to be correct but they still + + align:start position:0% +it's going to be correct but they still + + + align:start position:0% +it's going to be correct but they still +get graded on their logic and on on + + align:start position:0% +get graded on their logic and on on + + + align:start position:0% +get graded on their logic and on on +their their writing that's the only part + + align:start position:0% +their their writing that's the only part + + + align:start position:0% +their their writing that's the only part +of the problem set that actually counts + + align:start position:0% +of the problem set that actually counts + + + align:start position:0% +of the problem set that actually counts +uh toward the + + align:start position:0% +uh toward the + + + align:start position:0% +uh toward the +grade so I think those are those points + + align:start position:0% +grade so I think those are those points + + + align:start position:0% +grade so I think those are those points +right we I can add that since it's on + + align:start position:0% +right we I can add that since it's on + + + align:start position:0% +right we I can add that since it's on +mitx we have analytics they use the pet + + align:start position:0% +mitx we have analytics they use the pet + + + align:start position:0% +mitx we have analytics they use the pet +Checker a + + align:start position:0% +Checker a + + + align:start position:0% +Checker a +lot most students are using it um I'd + + align:start position:0% +lot most students are using it um I'd + + + align:start position:0% +lot most students are using it um I'd +say well over 2third and they go through + + align:start position:0% +say well over 2third and they go through + + + align:start position:0% +say well over 2third and they go through +you can see how many attempts they're + + align:start position:0% +you can see how many attempts they're + + + align:start position:0% +you can see how many attempts they're +making for the various + + align:start position:0% +making for the various + + + align:start position:0% +making for the various +questions next + + align:start position:0% + + + + align:start position:0% + +slide I think it's both of us oh yeah so + + align:start position:0% +slide I think it's both of us oh yeah so + + + align:start position:0% +slide I think it's both of us oh yeah so +uh we'll give our own takes on this + + align:start position:0% +uh we'll give our own takes on this + + + align:start position:0% +uh we'll give our own takes on this +so when you talk about Active Learning + + align:start position:0% +so when you talk about Active Learning + + + align:start position:0% +so when you talk about Active Learning +there's some common questions so how + + align:start position:0% +there's some common questions so how + + + align:start position:0% +there's some common questions so how +much work was all this uh the answer was + + align:start position:0% +much work was all this uh the answer was + + + align:start position:0% +much work was all this uh the answer was +an unbelievably large amount of work for + + align:start position:0% +an unbelievably large amount of work for + + + align:start position:0% +an unbelievably large amount of work for +us but part of that was we changed + + align:start position:0% +us but part of that was we changed + + + align:start position:0% +us but part of that was we changed +everything so it's hard to say what it + + align:start position:0% +everything so it's hard to say what it + + + align:start position:0% +everything so it's hard to say what it +would be had we taught this as a lecture + + align:start position:0% +would be had we taught this as a lecture + + + align:start position:0% +would be had we taught this as a lecture +course for three or four years had we + + align:start position:0% +course for three or four years had we + + + align:start position:0% +course for three or four years had we +changed our curriculum and added the + + align:start position:0% +changed our curriculum and added the + + + align:start position:0% +changed our curriculum and added the +basian unit + + align:start position:0% +basian unit + + + align:start position:0% +basian unit +before converting into an active + + align:start position:0% +before converting into an active + + + align:start position:0% +before converting into an active +learning class had we not been so + + align:start position:0% +learning class had we not been so + + + align:start position:0% +learning class had we not been so +ambitious in using the mitx platform it + + align:start position:0% +ambitious in using the mitx platform it + + + align:start position:0% +ambitious in using the mitx platform it +would have all of those things would + + align:start position:0% +would have all of those things would + + + align:start position:0% +would have all of those things would +have lessened the work but I think you + + align:start position:0% +have lessened the work but I think you + + + align:start position:0% +have lessened the work but I think you +can say it's still a lot of work to + + align:start position:0% +can say it's still a lot of work to + + + align:start position:0% +can say it's still a lot of work to +convert from a lecture to + + align:start position:0% +convert from a lecture to + + + align:start position:0% +convert from a lecture to +a Active Learning format for one + + align:start position:0% +a Active Learning format for one + + + align:start position:0% +a Active Learning format for one +thing there's no faking what you're + + align:start position:0% +thing there's no faking what you're + + + align:start position:0% +thing there's no faking what you're +going to do in an active learning format + + align:start position:0% +going to do in an active learning format + + + align:start position:0% +going to do in an active learning format +we have slides we have to have questions + + align:start position:0% +we have slides we have to have questions + + + align:start position:0% +we have slides we have to have questions +wellth thought out questions ahead of + + align:start position:0% +wellth thought out questions ahead of + + + align:start position:0% +wellth thought out questions ahead of +time you can't pull examples kind of out + + align:start position:0% +time you can't pull examples kind of out + + + align:start position:0% +time you can't pull examples kind of out +of your hat uh the way I would never do + + align:start position:0% +of your hat uh the way I would never do + + + align:start position:0% +of your hat uh the way I would never do +but I've heard that some people do when + + align:start position:0% +but I've heard that some people do when + + + align:start position:0% +but I've heard that some people do when +they + + align:start position:0% +they + + + align:start position:0% +they +lecture uh how much are you able to + + align:start position:0% +lecture uh how much are you able to + + + align:start position:0% +lecture uh how much are you able to +cover this is also a typical question + + align:start position:0% +cover this is also a typical question + + + align:start position:0% +cover this is also a typical question +how can you cover as much the answer is + + align:start position:0% +how can you cover as much the answer is + + + align:start position:0% +how can you cover as much the answer is +we find we can cover at least as much + + align:start position:0% +we find we can cover at least as much + + + align:start position:0% +we find we can cover at least as much +I'll I'll say a little more about + + align:start position:0% +I'll I'll say a little more about + + + align:start position:0% +I'll I'll say a little more about +that you're cutting out examples you + + align:start position:0% +that you're cutting out examples you + + + align:start position:0% +that you're cutting out examples you +spend a lot of time in a math class + + align:start position:0% +spend a lot of time in a math class + + + align:start position:0% +spend a lot of time in a math class +working through examples the students + + align:start position:0% +working through examples the students + + + align:start position:0% +working through examples the students +are doing the examples so they're + + align:start position:0% +are doing the examples so they're + + + align:start position:0% +are doing the examples so they're +learning the material better than your + + align:start position:0% +learning the material better than your + + + align:start position:0% +learning the material better than your +than you're doing the examples and that + + align:start position:0% +than you're doing the examples and that + + + align:start position:0% +than you're doing the examples and that +time is from you're doing the examples + + align:start position:0% +time is from you're doing the examples + + + align:start position:0% +time is from you're doing the examples +is safe for them to work in terms of + + align:start position:0% +is safe for them to work in terms of + + + align:start position:0% +is safe for them to work in terms of +1805 it's a little hard to measure we + + align:start position:0% +1805 it's a little hard to measure we + + + align:start position:0% +1805 it's a little hard to measure we +know we've added three weeks worth of + + align:start position:0% +know we've added three weeks worth of + + + align:start position:0% +know we've added three weeks worth of +material to the class we inherited it's + + align:start position:0% +material to the class we inherited it's + + + align:start position:0% +material to the class we inherited it's +possible that the class we inherited was + + align:start position:0% +possible that the class we inherited was + + + align:start position:0% +possible that the class we inherited was +under ambitious and we could have added + + align:start position:0% +under ambitious and we could have added + + + align:start position:0% +under ambitious and we could have added +that in a lecture class we know we cover + + align:start position:0% +that in a lecture class we know we cover + + + align:start position:0% +that in a lecture class we know we cover +the first unit the probability unit in I + + align:start position:0% +the first unit the probability unit in I + + + align:start position:0% +the first unit the probability unit in I +think five weeks instead of seven five + + align:start position:0% +think five weeks instead of seven five + + + align:start position:0% +think five weeks instead of seven five +weeks instead of seven and they do just + + align:start position:0% +weeks instead of seven and they do just + + + align:start position:0% +weeks instead of seven and they do just +as well on comparable exams so I I think + + align:start position:0% +as well on comparable exams so I I think + + + align:start position:0% +as well on comparable exams so I I think +I feel safe and saying that we can cover + + align:start position:0% +I feel safe and saying that we can cover + + + align:start position:0% +I feel safe and saying that we can cover +at least as much + + align:start position:0% +at least as much + + + align:start position:0% +at least as much +material we are more of us in in the + + align:start position:0% +material we are more of us in in the + + + align:start position:0% +material we are more of us in in the +there's you spend more time in the + + align:start position:0% +there's you spend more time in the + + + align:start position:0% +there's you spend more time in the +classroom because the as a teachers + + align:start position:0% +classroom because the as a teachers + + + align:start position:0% +classroom because the as a teachers +we're in there for all 240 minutes none + + align:start position:0% +we're in there for all 240 minutes none + + + align:start position:0% +we're in there for all 240 minutes none +of it is upon off on recitation leaders + + align:start position:0% +of it is upon off on recitation leaders + + + align:start position:0% +of it is upon off on recitation leaders +it might be interesting to know whether + + align:start position:0% +it might be interesting to know whether + + + align:start position:0% +it might be interesting to know whether +that's really necessary for one all the + + align:start position:0% +that's really necessary for one all the + + + align:start position:0% +that's really necessary for one all the +teachers to be there all the time do you + + align:start position:0% +teachers to be there all the time do you + + + align:start position:0% +teachers to be there all the time do you +have anything to add to that John well I + + align:start position:0% +have anything to add to that John well I + + + align:start position:0% +have anything to add to that John well I +think for us one thing that added a lot + + align:start position:0% +think for us one thing that added a lot + + + align:start position:0% +think for us one thing that added a lot +of work was that when we decided to + + align:start position:0% +of work was that when we decided to + + + align:start position:0% +of work was that when we decided to +change the curriculum we realized there + + align:start position:0% +change the curriculum we realized there + + + align:start position:0% +change the curriculum we realized there +was no textbook that taught what we + + align:start position:0% +was no textbook that taught what we + + + align:start position:0% +was no textbook that taught what we +wanted to teach so we had wrote The + + align:start position:0% +wanted to teach so we had wrote The + + + align:start position:0% +wanted to teach so we had wrote The +Textbook and that takes a lot of time + + align:start position:0% +Textbook and that takes a lot of time + + + align:start position:0% +Textbook and that takes a lot of time +yeah that that was in November for a + + align:start position:0% +yeah that that was in November for a + + + align:start position:0% +yeah that that was in November for a +class that was starting in January that + + align:start position:0% +class that was starting in January that + + + align:start position:0% +class that was starting in January that +we finally decided we had to throw away + + align:start position:0% +we finally decided we had to throw away + + + align:start position:0% +we finally decided we had to throw away +the textbook right so so in the end you + + align:start position:0% +the textbook right so so in the end you + + + align:start position:0% +the textbook right so so in the end you +know we wrote These materials but I can + + align:start position:0% +know we wrote These materials but I can + + + align:start position:0% +know we wrote These materials but I can +say that the the students really + + align:start position:0% +say that the the students really + + + align:start position:0% +say that the the students really +appreciated that the reading they were + + align:start position:0% +appreciated that the reading they were + + + align:start position:0% +appreciated that the reading they were +doing was very targeted it told them the + + align:start position:0% +doing was very targeted it told them the + + + align:start position:0% +doing was very targeted it told them the +objectives exactly what we expected of + + align:start position:0% +objectives exactly what we expected of + + + align:start position:0% +objectives exactly what we expected of +them what kinds of problems at what + + align:start position:0% +them what kinds of problems at what + + + align:start position:0% +them what kinds of problems at what +level um and and so it turned out to + + align:start position:0% +level um and and so it turned out to + + + align:start position:0% +level um and and so it turned out to +have other benefits we didn't foresee uh + + align:start position:0% +have other benefits we didn't foresee uh + + + align:start position:0% +have other benefits we didn't foresee uh +going in and then in terms of how much + + align:start position:0% +going in and then in terms of how much + + + align:start position:0% +going in and then in terms of how much +you're able to cover like Jerry said we + + align:start position:0% +you're able to cover like Jerry said we + + + align:start position:0% +you're able to cover like Jerry said we +gave basically the same First Mid + + align:start position:0% +gave basically the same First Mid + + + align:start position:0% +gave basically the same First Mid +actually we gave exactly the same first + + align:start position:0% +actually we gave exactly the same first + + + align:start position:0% +actually we gave exactly the same first +midterm three years in a row we're not + + align:start position:0% +midterm three years in a row we're not + + + align:start position:0% +midterm three years in a row we're not +going to give it a fourth year in a row + + align:start position:0% +going to give it a fourth year in a row + + + align:start position:0% +going to give it a fourth year in a row +no no we added one question plus one + + align:start position:0% +no no we added one question plus one + + + align:start position:0% +no no we added one question plus one +question so we took because we gave the + + align:start position:0% +question so we took because we gave the + + + align:start position:0% +question so we took because we gave the +exam at seven + + align:start position:0% +exam at seven + + + align:start position:0% +exam at seven +weeks the first time we taught it that + + align:start position:0% +weeks the first time we taught it that + + + align:start position:0% +weeks the first time we taught it that +was just the probability unit the second + + align:start position:0% +was just the probability unit the second + + + align:start position:0% +was just the probability unit the second +and third time we taught it so third + + align:start position:0% +and third time we taught it so third + + + align:start position:0% +and third time we taught it so third +time is right now that was the + + align:start position:0% +time is right now that was the + + + align:start position:0% +time is right now that was the +probability unit plus like a week or two + + align:start position:0% +probability unit plus like a week or two + + + align:start position:0% +probability unit plus like a week or two +of more stuff right so it had one more + + align:start position:0% +of more stuff right so it had one more + + + align:start position:0% +of more stuff right so it had one more +question like six instead of five + + align:start position:0% +question like six instead of five + + + align:start position:0% +question like six instead of five +questions and if you remove the one more + + align:start position:0% +questions and if you remove the one more + + + align:start position:0% +questions and if you remove the one more +question they actually did as well or + + align:start position:0% +question they actually did as well or + + + align:start position:0% +question they actually did as well or +slightly better on compared to the first + + align:start position:0% +slightly better on compared to the first + + + align:start position:0% +slightly better on compared to the first +year and if you include it they did + + align:start position:0% +year and if you include it they did + + + align:start position:0% +year and if you include it they did +pretty much the same but you have the + + align:start position:0% +pretty much the same but you have the + + + align:start position:0% +pretty much the same but you have the +same amount of time to take the exam so + + align:start position:0% +same amount of time to take the exam so + + + align:start position:0% +same amount of time to take the exam so +it's a it's a pretty concrete measure + + align:start position:0% +it's a it's a pretty concrete measure + + + align:start position:0% +it's a it's a pretty concrete measure +that that they did better now we don't + + align:start position:0% +that that they did better now we don't + + + align:start position:0% +that that they did better now we don't +know that that's because in part we + + align:start position:0% +know that that's because in part we + + + align:start position:0% +know that that's because in part we +actually understood a little more + + align:start position:0% +actually understood a little more + + + align:start position:0% +actually understood a little more +statistics and could explain it better + + align:start position:0% +statistics and could explain it better + + + align:start position:0% +statistics and could explain it better +the second time around this was just + + align:start position:0% +the second time around this was just + + + align:start position:0% +the second time around this was just +probability we understand we did + + align:start position:0% +probability we understand we did + + + align:start position:0% +probability we understand we did +understand probability yeah okay that + + align:start position:0% +understand probability yeah okay that + + + align:start position:0% +understand probability yeah okay that +was good so yeah yeah yeah we should say + + align:start position:0% +was good so yeah yeah yeah we should say + + + align:start position:0% +was good so yeah yeah yeah we should say +so neither of us are statisticians going + + align:start position:0% +so neither of us are statisticians going + + + align:start position:0% +so neither of us are statisticians going +in we've learned a lot of statistics and + + align:start position:0% +in we've learned a lot of statistics and + + + align:start position:0% +in we've learned a lot of statistics and +particularly how to teach it I don't + + align:start position:0% +particularly how to teach it I don't + + + align:start position:0% +particularly how to teach it I don't +think at a mathematical level the + + align:start position:0% +think at a mathematical level the + + + align:start position:0% +think at a mathematical level the +statistics we're doing + + align:start position:0% +statistics we're doing + + + align:start position:0% +statistics we're doing +is terribly hard but we all believe I + + align:start position:0% +is terribly hard but we all believe I + + + align:start position:0% +is terribly hard but we all believe I +think as teachers that the more + + align:start position:0% +think as teachers that the more + + + align:start position:0% +think as teachers that the more +expertise you have so Sanji who I + + align:start position:0% +expertise you have so Sanji who I + + + align:start position:0% +expertise you have so Sanji who I +mentioned earlier does know a lot of + + align:start position:0% +mentioned earlier does know a lot of + + + align:start position:0% +mentioned earlier does know a lot of +statistics and has been Consulting with + + align:start position:0% +statistics and has been Consulting with + + + align:start position:0% +statistics and has been Consulting with +us and been a tremendous asset in + + align:start position:0% +us and been a tremendous asset in + + + align:start position:0% +us and been a tremendous asset in +getting us up to speed on this question + + align:start position:0% +getting us up to speed on this question + + + align:start position:0% +getting us up to speed on this question +M how did you know that the students + + align:start position:0% +M how did you know that the students + + + align:start position:0% +M how did you know that the students +didn't cheat for example and have access + + align:start position:0% +didn't cheat for example and have access + + + align:start position:0% +didn't cheat for example and have access +to the previous year's exams you ask a + + align:start position:0% +to the previous year's exams you ask a + + + align:start position:0% +to the previous year's exams you ask a +really good question but I think you can + + align:start position:0% +really good question but I think you can + + + align:start position:0% +really good question but I think you can +infer that from Reading their papers + + align:start position:0% +infer that from Reading their papers + + + align:start position:0% +infer that from Reading their papers +they're not they're if you read the + + align:start position:0% +they're not they're if you read the + + + align:start position:0% +they're not they're if you read the +papers students are not getting + + align:start position:0% +papers students are not getting + + + align:start position:0% +papers students are not getting +everything + + align:start position:0% +everything + + + align:start position:0% +everything +right and we did by the way we did + + align:start position:0% +right and we did by the way we did + + + align:start position:0% +right and we did by the way we did +change the the wording the topic and the + + align:start position:0% +change the the wording the topic and the + + + align:start position:0% +change the the wording the topic and the +numbers I mean we didn't leave it so you + + align:start position:0% +numbers I mean we didn't leave it so you + + + align:start position:0% +numbers I mean we didn't leave it so you +could just put the same answer certainly + + align:start position:0% +could just put the same answer certainly + + + align:start position:0% +could just put the same answer certainly +um and and doing it a third year was + + align:start position:0% +um and and doing it a third year was + + + align:start position:0% +um and and doing it a third year was +kind of stretching the limits of what + + align:start position:0% +kind of stretching the limits of what + + + align:start position:0% +kind of stretching the limits of what +you're exactly asking we don't we don't + + align:start position:0% +you're exactly asking we don't we don't + + + align:start position:0% +you're exactly asking we don't we don't +want to we won't we won't do it again I + + align:start position:0% +want to we won't we won't do it again I + + + align:start position:0% +want to we won't we won't do it again I +will say this and I often get into a + + align:start position:0% +will say this and I often get into a + + + align:start position:0% +will say this and I often get into a +discussion about cheating which is I + + align:start position:0% +discussion about cheating which is I + + + align:start position:0% +discussion about cheating which is I +could give I know from lecture classes + + align:start position:0% +could give I know from lecture classes + + + align:start position:0% +could give I know from lecture classes +and maybe Arthur will verify this who's + + align:start position:0% +and maybe Arthur will verify this who's + + + align:start position:0% +and maybe Arthur will verify this who's +sitting there there uh Arthur Matic + + align:start position:0% +sitting there there uh Arthur Matic + + + align:start position:0% +sitting there there uh Arthur Matic +who's done a lot of lecturing I've seen + + align:start position:0% +who's done a lot of lecturing I've seen + + + align:start position:0% +who's done a lot of lecturing I've seen +when I've teach recitation that I can + + align:start position:0% +when I've teach recitation that I can + + + align:start position:0% +when I've teach recitation that I can +tell my students the teacher has given + + align:start position:0% +tell my students the teacher has given + + + align:start position:0% +tell my students the teacher has given +you practice questions three of them + + align:start position:0% +you practice questions three of them + + + align:start position:0% +you practice questions three of them +will be on the exam two of the questions + + align:start position:0% +will be on the exam two of the questions + + + align:start position:0% +will be on the exam two of the questions +on the exam will be just small changes + + align:start position:0% +on the exam will be just small changes + + + align:start position:0% +on the exam will be just small changes +of this and I still know that many + + align:start position:0% +of this and I still know that many + + + align:start position:0% +of this and I still know that many +students won't find time to do the + + align:start position:0% +students won't find time to do the + + + align:start position:0% +students won't find time to do the +practice + + align:start position:0% +practice + + + align:start position:0% +practice +exam I I think it's it's kind of a myth + + align:start position:0% +exam I I think it's it's kind of a myth + + + align:start position:0% +exam I I think it's it's kind of a myth +if they found my my exam in The copier + + align:start position:0% +if they found my my exam in The copier + + + align:start position:0% +if they found my my exam in The copier +well actually most of them would return + + align:start position:0% +well actually most of them would return + + + align:start position:0% +well actually most of them would return +it to me but so might cheat but they + + align:start position:0% +it to me but so might cheat but they + + + align:start position:0% +it to me but so might cheat but they +it the effort of going to try to do + + align:start position:0% +it the effort of going to try to do + + + align:start position:0% +it the effort of going to try to do +something like this without being + + align:start position:0% +something like this without being + + + align:start position:0% +something like this without being +certain that you're going to be getting + + align:start position:0% +certain that you're going to be getting + + + align:start position:0% +certain that you're going to be getting +something that's going to be on the exam + + align:start position:0% +something that's going to be on the exam + + + align:start position:0% +something that's going to be on the exam +it just doesn't happen that often so I + + align:start position:0% +it just doesn't happen that often so I + + + align:start position:0% +it just doesn't happen that often so I +think now if if it comes out that we'd + + align:start position:0% +think now if if it comes out that we'd + + + align:start position:0% +think now if if it comes out that we'd +give the same exam year in and year out + + align:start position:0% +give the same exam year in and year out + + + align:start position:0% +give the same exam year in and year out +people will look at it but so we won't + + align:start position:0% +people will look at it but so we won't + + + align:start position:0% +people will look at it but so we won't +do that again what is that oh other + + align:start position:0% +do that again what is that oh other + + + align:start position:0% +do that again what is that oh other +observations + + align:start position:0% +observations + + + align:start position:0% +observations +uh this this is kind of the + + align:start position:0% +uh this this is kind of the + + + align:start position:0% +uh this this is kind of the +psychological observations Active + + align:start position:0% +psychological observations Active + + + align:start position:0% +psychological observations Active +Learning is a lot more fun for the + + align:start position:0% +Learning is a lot more fun for the + + + align:start position:0% +Learning is a lot more fun for the +students you could see even in that + + align:start position:0% +students you could see even in that + + + align:start position:0% +students you could see even in that +video when they stand up there's a lot + + align:start position:0% +video when they stand up there's a lot + + + align:start position:0% +video when they stand up there's a lot +of energy in the classroom you could + + align:start position:0% +of energy in the classroom you could + + + align:start position:0% +of energy in the classroom you could +hear the buzz people are not sleeping + + align:start position:0% +hear the buzz people are not sleeping + + + align:start position:0% +hear the buzz people are not sleeping +co- teing if you can do it is tremendous + + align:start position:0% +co- teing if you can do it is tremendous + + + align:start position:0% +co- teing if you can do it is tremendous +fun I can't get away with anything with + + align:start position:0% +fun I can't get away with anything with + + + align:start position:0% +fun I can't get away with anything with +John standing there uh I'm a little more + + align:start position:0% +John standing there uh I'm a little more + + + align:start position:0% +John standing there uh I'm a little more +generous to him I let him make mistakes + + align:start position:0% +generous to him I let him make mistakes + + + align:start position:0% +generous to him I let him make mistakes +um students like getting to know their + + align:start position:0% +um students like getting to know their + + + align:start position:0% +um students like getting to know their +teachers this is a really important + + align:start position:0% +teachers this is a really important + + + align:start position:0% +teachers this is a really important +value at MIT a number of students + + align:start position:0% +value at MIT a number of students + + + align:start position:0% +value at MIT a number of students +graduate from MIT without having knowing + + align:start position:0% +graduate from MIT without having knowing + + + align:start position:0% +graduate from MIT without having knowing +enough teachers well enough to get three + + align:start position:0% +enough teachers well enough to get three + + + align:start position:0% +enough teachers well enough to get three +letters of + + align:start position:0% +letters of + + + align:start position:0% +letters of +recommendation here we're walking around + + align:start position:0% +recommendation here we're walking around + + + align:start position:0% +recommendation here we're walking around +we're meeting them both of us like + + align:start position:0% +we're meeting them both of us like + + + align:start position:0% +we're meeting them both of us like +students and like talking to students + + align:start position:0% +students and like talking to students + + + align:start position:0% +students and like talking to students +and they appreciate it they do get to + + align:start position:0% +and they appreciate it they do get to + + + align:start position:0% +and they appreciate it they do get to +know us we have to write a lot more + + align:start position:0% +know us we have to write a lot more + + + align:start position:0% +know us we have to write a lot more +letters of + + align:start position:0% +letters of + + + align:start position:0% +letters of +recommendation than we ever did before + + align:start position:0% +recommendation than we ever did before + + + align:start position:0% +recommendation than we ever did before +uh there's a downside to + + align:start position:0% +uh there's a downside to + + + align:start position:0% +uh there's a downside to +everything uh the students like The + + align:start position:0% +everything uh the students like The + + + align:start position:0% +everything uh the students like The +targeted reading in fact Glenda who is + + align:start position:0% +targeted reading in fact Glenda who is + + + align:start position:0% +targeted reading in fact Glenda who is +with the teaching and learning + + align:start position:0% +with the teaching and learning + + + align:start position:0% +with the teaching and learning +laboratory here and has done uh surveys + + align:start position:0% +laboratory here and has done uh surveys + + + align:start position:0% +laboratory here and has done uh surveys +of our students and interviews with our + + align:start position:0% +of our students and interviews with our + + + align:start position:0% +of our students and interviews with our +students the report and this was + + align:start position:0% +students the report and this was + + + align:start position:0% +students the report and this was +interesting to us they like the reading + + align:start position:0% +interesting to us they like the reading + + + align:start position:0% +interesting to us they like the reading +more than they like watching videos + + align:start position:0% +more than they like watching videos + + + align:start position:0% +more than they like watching videos +videos take longer the targeted reading + + align:start position:0% +videos take longer the targeted reading + + + align:start position:0% +videos take longer the targeted reading +is just what they need to know we're + + align:start position:0% +is just what they need to know we're + + + align:start position:0% +is just what they need to know we're +telling them this is what we expect you + + align:start position:0% +telling them this is what we expect you + + + align:start position:0% +telling them this is what we expect you +uh to learn and it doesn't take as much + + align:start position:0% +uh to learn and it doesn't take as much + + + align:start position:0% +uh to learn and it doesn't take as much +time as a + + align:start position:0% +time as a + + + align:start position:0% +time as a +video and finally students really love + + align:start position:0% +video and finally students really love + + + align:start position:0% +video and finally students really love +the pet Checker it gives them a very + + align:start position:0% +the pet Checker it gives them a very + + + align:start position:0% +the pet Checker it gives them a very +comfortable + + align:start position:0% + + + + align:start position:0% + +feeling so finally looking forward + + align:start position:0% +feeling so finally looking forward + + + align:start position:0% +feeling so finally looking forward +Glenda is continuing to study what we're + + align:start position:0% +Glenda is continuing to study what we're + + + align:start position:0% +Glenda is continuing to study what we're +doing at some point there'll be a paper + + align:start position:0% +doing at some point there'll be a paper + + + align:start position:0% +doing at some point there'll be a paper +a report that comes out of this the + + align:start position:0% +a report that comes out of this the + + + align:start position:0% +a report that comes out of this the +course will be on open courseware and + + align:start position:0% +course will be on open courseware and + + + align:start position:0% +course will be on open courseware and +the ocw educator where we'll give it's + + align:start position:0% +the ocw educator where we'll give it's + + + align:start position:0% +the ocw educator where we'll give it's +being videotaped here so this talk might + + align:start position:0% +being videotaped here so this talk might + + + align:start position:0% +being videotaped here so this talk might +show up on open course for educator to + + align:start position:0% +show up on open course for educator to + + + align:start position:0% +show up on open course for educator to +tell other teachers about what we're + + align:start position:0% +tell other teachers about what we're + + + align:start position:0% +tell other teachers about what we're +doing as well as present the course + + align:start position:0% +doing as well as present the course + + + align:start position:0% +doing as well as present the course +materials and finally and this is + + align:start position:0% +materials and finally and this is + + + align:start position:0% +materials and finally and this is +important we've had a we've overstaffed + + align:start position:0% +important we've had a we've overstaffed + + + align:start position:0% +important we've had a we've overstaffed +the class in the sense of what the + + align:start position:0% +the class in the sense of what the + + + align:start position:0% +the class in the sense of what the +budgets will really allow we've had a + + align:start position:0% +budgets will really allow we've had a + + + align:start position:0% +budgets will really allow we've had a +Davis Foundation grant that helps with + + align:start position:0% +Davis Foundation grant that helps with + + + align:start position:0% +Davis Foundation grant that helps with +it the math department has supported it + + align:start position:0% +it the math department has supported it + + + align:start position:0% +it the math department has supported it +we have to move to a more traditional + + align:start position:0% +we have to move to a more traditional + + + align:start position:0% +we have to move to a more traditional +Staffing so actually next year I'll + + align:start position:0% +Staffing so actually next year I'll + + + align:start position:0% +Staffing so actually next year I'll +teach the class by myself without John's + + align:start position:0% +teach the class by myself without John's + + + align:start position:0% +teach the class by myself without John's +help uh we'll see what we do I'll have + + align:start position:0% +help uh we'll see what we do I'll have + + + align:start position:0% +help uh we'll see what we do I'll have +to learn how to do these sort of demos + + align:start position:0% +to learn how to do these sort of demos + + + align:start position:0% +to learn how to do these sort of demos +because we leave that to John + + align:start position:0% +because we leave that to John + + + align:start position:0% +because we leave that to John +um + + align:start position:0% +um + + + align:start position:0% +um +and with just undergraduates and maybe a + + align:start position:0% +and with just undergraduates and maybe a + + + align:start position:0% +and with just undergraduates and maybe a +graduate student in the class this year + + align:start position:0% +graduate student in the class this year + + + align:start position:0% +graduate student in the class this year +John didn't say it but we have actually + + align:start position:0% +John didn't say it but we have actually + + + align:start position:0% +John didn't say it but we have actually +another instructor who's a statistician + + align:start position:0% +another instructor who's a statistician + + + align:start position:0% +another instructor who's a statistician +in the class with us Peter kempthorne at + + align:start position:0% +in the class with us Peter kempthorne at + + + align:start position:0% +in the class with us Peter kempthorne at +all times and then equally important for + + align:start position:0% +all times and then equally important for + + + align:start position:0% +all times and then equally important for +a project like this is making a + + align:start position:0% +a project like this is making a + + + align:start position:0% +a project like this is making a +transition to the next teacher we're + + align:start position:0% +transition to the next teacher we're + + + align:start position:0% +transition to the next teacher we're +going to have to convince someone else + + align:start position:0% +going to have to convince someone else + + + align:start position:0% +going to have to convince someone else +that they want to teach like this and + + align:start position:0% +that they want to teach like this and + + + align:start position:0% +that they want to teach like this and +they want to do it part of our strategy + + align:start position:0% +they want to do it part of our strategy + + + align:start position:0% +they want to do it part of our strategy +will be after three years to have such a + + align:start position:0% +will be after three years to have such a + + + align:start position:0% +will be after three years to have such a +compelling set of materials that is so + + align:start position:0% +compelling set of materials that is so + + + align:start position:0% +compelling set of materials that is so +easy for them to use that it won't feel + + align:start position:0% +easy for them to use that it won't feel + + + align:start position:0% +easy for them to use that it won't feel +like as much work so that that's what + + align:start position:0% +like as much work so that that's what + + + align:start position:0% +like as much work so that that's what +we're looking forward to in the future + + align:start position:0% +we're looking forward to in the future + + + align:start position:0% +we're looking forward to in the future +finally come visit we have had visitors + + align:start position:0% +finally come visit we have had visitors + + + align:start position:0% +finally come visit we have had visitors +we like it when people come to visit if + + align:start position:0% +we like it when people come to visit if + + + align:start position:0% +we like it when people come to visit if +you send us a note we'll tell you what's + + align:start position:0% +you send us a note we'll tell you what's + + + align:start position:0% +you send us a note we'll tell you what's +a good day to visit if not you can take + + align:start position:0% +a good day to visit if not you can take + + + align:start position:0% +a good day to visit if not you can take +your chances and just show up we're in + + align:start position:0% +your chances and just show up we're in + + + align:start position:0% +your chances and just show up we're in +the basement of the status Center in the + + align:start position:0% +the basement of the status Center in the + + + align:start position:0% +the basement of the status Center in the +teal room which we should have mentioned + + align:start position:0% +teal room which we should have mentioned + + + align:start position:0% +teal room which we should have mentioned +this is in part an outgrowth of the + + align:start position:0% +this is in part an outgrowth of the + + + align:start position:0% +this is in part an outgrowth of the +physic + + align:start position:0% +physic + + + align:start position:0% +physic +teal it's a huge room there's plenty of + + align:start position:0% +teal it's a huge room there's plenty of + + + align:start position:0% +teal it's a huge room there's plenty of +space so you don't have to worry it'll + + align:start position:0% +space so you don't have to worry it'll + + + align:start position:0% +space so you don't have to worry it'll +be full yeah but you saw you saw the in + + align:start position:0% +be full yeah but you saw you saw the in + + + align:start position:0% +be full yeah but you saw you saw the in +the video it's it's a a big room sta + + align:start position:0% +the video it's it's a a big room sta + + + align:start position:0% +the video it's it's a a big room sta +Tuesday Thursday and Friday at 1: to + + align:start position:0% +Tuesday Thursday and Friday at 1: to + + + align:start position:0% +Tuesday Thursday and Friday at 1: to +2:30 come for all are part of it and I + + align:start position:0% +2:30 come for all are part of it and I + + + align:start position:0% +2:30 come for all are part of it and I +should say that Tuesday and Thursday are + + align:start position:0% +should say that Tuesday and Thursday are + + + align:start position:0% +should say that Tuesday and Thursday are +really the days are sort of standard + + align:start position:0% +really the days are sort of standard + + + align:start position:0% +really the days are sort of standard +flipped days and then Fridays are when + + align:start position:0% +flipped days and then Fridays are when + + + align:start position:0% +flipped days and then Fridays are when +we do that studio with r and they have + + align:start position:0% +we do that studio with r and they have + + + align:start position:0% +we do that studio with r and they have +their computers so it's a bit different + + align:start position:0% +their computers so it's a bit different + + + align:start position:0% +their computers so it's a bit different +and of course some weeks they have exams + + align:start position:0% +and of course some weeks they have exams + + + align:start position:0% +and of course some weeks they have exams +so you might not want to come on an exam + + align:start position:0% +so you might not want to come on an exam + + + align:start position:0% +so you might not want to come on an exam +day that won't be as interesting so you + + align:start position:0% +day that won't be as interesting so you + + + align:start position:0% +day that won't be as interesting so you +might just let us know when you're going + + align:start position:0% +might just let us know when you're going + + + align:start position:0% +might just let us know when you're going +to show up what's the size of we have + + align:start position:0% +to show up what's the size of we have + + + align:start position:0% +to show up what's the size of we have +about 60 students right now the room + + align:start position:0% +about 60 students right now the room + + + align:start position:0% +about 60 students right now the room +could comfortably hold I think + + align:start position:0% +could comfortably hold I think + + + align:start position:0% +could comfortably hold I think +90 people so the class actually had + + align:start position:0% +90 people so the class actually had + + + align:start position:0% +90 people so the class actually had +about 31 32 students two years ago when + + align:start position:0% +about 31 32 students two years ago when + + + align:start position:0% +about 31 32 students two years ago when +we took it over as a lecture course yeah + + align:start position:0% +we took it over as a lecture course yeah + + + align:start position:0% +we took it over as a lecture course yeah +last year that bumped up to the low 40s + + align:start position:0% +last year that bumped up to the low 40s + + + align:start position:0% +last year that bumped up to the low 40s +um the first time through as a flipped + + align:start position:0% +um the first time through as a flipped + + + align:start position:0% +um the first time through as a flipped +and now we have 60 uh or maybe 58 the + + align:start position:0% +and now we have 60 uh or maybe 58 the + + + align:start position:0% +and now we have 60 uh or maybe 58 the +second time through so we're hoping + + align:start position:0% +second time through so we're hoping + + + align:start position:0% +second time through so we're hoping +that's you know we can keep that that + + align:start position:0% +that's you know we can keep that that + + + align:start position:0% +that's you know we can keep that that +going yeah okay yes + + align:start position:0% +going yeah okay yes + + + align:start position:0% +going yeah okay yes +um do you find that it's more worth to + + align:start position:0% +um do you find that it's more worth to + + + align:start position:0% +um do you find that it's more worth to +teach the class yes no I find it's less + + align:start position:0% +teach the class yes no I find it's less + + + align:start position:0% +teach the class yes no I find it's less +work once you're in the class if you + + align:start position:0% +work once you're in the class if you + + + align:start position:0% +work once you're in the class if you +have the slides prepared + + align:start position:0% +have the slides prepared + + + align:start position:0% +have the slides prepared +and you spend a lot of time walking + + align:start position:0% +and you spend a lot of time walking + + + align:start position:0% +and you spend a lot of time walking +around just smoing with + + align:start position:0% +around just smoing with + + + align:start position:0% +around just smoing with +students and and and working no it's not + + align:start position:0% +students and and and working no it's not + + + align:start position:0% +students and and and working no it's not +it's it's easier it's more energizing + + align:start position:0% +it's it's easier it's more energizing + + + align:start position:0% +it's it's easier it's more energizing +I'm never tired when we're done I never + + align:start position:0% +I'm never tired when we're done I never + + + align:start position:0% +I'm never tired when we're done I never +feel uh that I've just droned on for 40 + + align:start position:0% +feel uh that I've just droned on for 40 + + + align:start position:0% +feel uh that I've just droned on for 40 +minutes and not modulated my voice at + + align:start position:0% +minutes and not modulated my voice at + + + align:start position:0% +minutes and not modulated my voice at +all so it it's not more work to teach + + align:start position:0% +all so it it's not more work to teach + + + align:start position:0% +all so it it's not more work to teach +it's more work to prepare or I should + + align:start position:0% +it's more work to prepare or I should + + + align:start position:0% +it's more work to prepare or I should +say you have to be fully prepared + + align:start position:0% +say you have to be fully prepared + + + align:start position:0% +say you have to be fully prepared +there's no thinking about yeah what is + + align:start position:0% +there's no thinking about yeah what is + + + align:start position:0% +there's no thinking about yeah what is +this topic on the way to the lecture and + + align:start position:0% +this topic on the way to the lecture and + + + align:start position:0% +this topic on the way to the lecture and +and giving the example and being + + align:start position:0% +and giving the example and being + + + align:start position:0% +and giving the example and being +confident you'll be able to work it out + + align:start position:0% +confident you'll be able to work it out + + + align:start position:0% +confident you'll be able to work it out +the next line before you you get + + align:start position:0% + + + + align:start position:0% + +there don't + + align:start position:0% +there don't + + + align:start position:0% +there don't +have how much money you had guess I'm + + align:start position:0% +have how much money you had guess I'm + + + align:start position:0% +have how much money you had guess I'm +wondering how does the scale with enr if + + align:start position:0% +wondering how does the scale with enr if + + + align:start position:0% +wondering how does the scale with enr if +you had students the physics department + + align:start position:0% +you had students the physics department + + + align:start position:0% +you had students the physics department +has been doing this for a lot of years + + align:start position:0% +has been doing this for a lot of years + + + align:start position:0% +has been doing this for a lot of years +they have one instructor in the room and + + align:start position:0% +they have one instructor in the room and + + + align:start position:0% +they have one instructor in the room and +typically a lot of graduate students who + + align:start position:0% +typically a lot of graduate students who + + + align:start position:0% +typically a lot of graduate students who +would be teaching a recitation otherwise + + align:start position:0% +would be teaching a recitation otherwise + + + align:start position:0% +would be teaching a recitation otherwise +so you can staff it in that way with one + + align:start position:0% +so you can staff it in that way with one + + + align:start position:0% +so you can staff it in that way with one +instructor and graduate students + + align:start position:0% +instructor and graduate students + + + align:start position:0% +instructor and graduate students +undergraduates good undergraduates are + + align:start position:0% +undergraduates good undergraduates are + + + align:start position:0% +undergraduates good undergraduates are +also very good it's a little harder to + + align:start position:0% +also very good it's a little harder to + + + align:start position:0% +also very good it's a little harder to +find students who are free Tuesday + + align:start position:0% +find students who are free Tuesday + + + align:start position:0% +find students who are free Tuesday +Thursday and Friday I think maybe next + + align:start position:0% +Thursday and Friday I think maybe next + + + align:start position:0% +Thursday and Friday I think maybe next +year because Friday is just the studio + + align:start position:0% +year because Friday is just the studio + + + align:start position:0% +year because Friday is just the studio +and there's less of a need they do less + + align:start position:0% +and there's less of a need they do less + + + align:start position:0% +and there's less of a need they do less +on Friday if I get students just on + + align:start position:0% +on Friday if I get students just on + + + align:start position:0% +on Friday if I get students just on +Tuesday and Thursday we'll do it but + + align:start position:0% +Tuesday and Thursday we'll do it but + + + align:start position:0% +Tuesday and Thursday we'll do it but +there's a lot of very good + + align:start position:0% +there's a lot of very good + + + align:start position:0% +there's a lot of very good +undergraduates who are are quite helpful + + align:start position:0% +undergraduates who are are quite helpful + + + align:start position:0% +undergraduates who are are quite helpful +I guess a lot of theing is automatic is + + align:start position:0% +I guess a lot of theing is automatic is + + + align:start position:0% +I guess a lot of theing is automatic is +that the only thing no it's not + + align:start position:0% +that the only thing no it's not + + + align:start position:0% +that the only thing no it's not +automatic at all that that's the pets + + align:start position:0% +automatic at all that that's the pets + + + align:start position:0% +automatic at all that that's the pets +are graded by graders on paper + + align:start position:0% +are graded by graders on paper + + + align:start position:0% +are graded by graders on paper +undergraduate graders that's the same as + + align:start position:0% +undergraduate graders that's the same as + + + align:start position:0% +undergraduate graders that's the same as +if we taught it as a lecture you have to + + align:start position:0% +if we taught it as a lecture you have to + + + align:start position:0% +if we taught it as a lecture you have to +hire them it's easier to find graders + + align:start position:0% +hire them it's easier to find graders + + + align:start position:0% +hire them it's easier to find graders +because they don't commit to being in a + + align:start position:0% +because they don't commit to being in a + + + align:start position:0% +because they don't commit to being in a +certain place at a certain + + align:start position:0% + + + + align:start position:0% + +time ask you this lunch um did you get + + align:start position:0% +time ask you this lunch um did you get + + + align:start position:0% +time ask you this lunch um did you get +feedback um from students that um helped + + align:start position:0% +feedback um from students that um helped + + + align:start position:0% +feedback um from students that um helped +you refine it or make you think about + + align:start position:0% +you refine it or make you think about + + + align:start position:0% +you refine it or make you think about +the things that maybe weren't so good or + + align:start position:0% +the things that maybe weren't so good or + + + align:start position:0% +the things that maybe weren't so good or +things that were especially good yes uh + + align:start position:0% +things that were especially good yes uh + + + align:start position:0% +things that were especially good yes uh +so the first year we did the studio in + + align:start position:0% +so the first year we did the studio in + + + align:start position:0% +so the first year we did the studio in +mat lab and it was and it's not mat it's + + align:start position:0% +mat lab and it was and it's not mat it's + + + align:start position:0% +mat lab and it was and it's not mat it's +not mat lab's fault it was our our fault + + align:start position:0% +not mat lab's fault it was our our fault + + + align:start position:0% +not mat lab's fault it was our our fault +it was really tedious we did a lot of + + align:start position:0% +it was really tedious we did a lot of + + + align:start position:0% +it was really tedious we did a lot of +tutorials on using the software and so + + align:start position:0% +tutorials on using the software and so + + + align:start position:0% +tutorials on using the software and so +it was click here click there you have + + align:start position:0% +it was click here click there you have + + + align:start position:0% +it was click here click there you have +students at very different levels mat + + align:start position:0% +students at very different levels mat + + + align:start position:0% +students at very different levels mat +students are very good if you show them + + align:start position:0% +students are very good if you show them + + + align:start position:0% +students are very good if you show them +a program you know a script we don't + + align:start position:0% +a program you know a script we don't + + + align:start position:0% +a program you know a script we don't +write complicated scripts with a lot of + + align:start position:0% +write complicated scripts with a lot of + + + align:start position:0% +write complicated scripts with a lot of +logic it's typically just a series of + + align:start position:0% +logic it's typically just a series of + + + align:start position:0% +logic it's typically just a series of +commands that you can get out of this + + align:start position:0% +commands that you can get out of this + + + align:start position:0% +commands that you can get out of this +they're able to see what's going on and + + align:start position:0% +they're able to see what's going on and + + + align:start position:0% +they're able to see what's going on and +use it so it's based on feedback from + + align:start position:0% +use it so it's based on feedback from + + + align:start position:0% +use it so it's based on feedback from +them part of it is just being in the + + align:start position:0% +them part of it is just being in the + + + align:start position:0% +them part of it is just being in the +room and realizing how d it was but also + + align:start position:0% +room and realizing how d it was but also + + + align:start position:0% +room and realizing how d it was but also +from talking to + + align:start position:0% +from talking to + + + align:start position:0% +from talking to +students uh we changed + + align:start position:0% +students uh we changed + + + align:start position:0% +students uh we changed +that uh what else we did get feedback on + + align:start position:0% +that uh what else we did get feedback on + + + align:start position:0% +that uh what else we did get feedback on +others but I'm forgetting we got + + align:start position:0% +others but I'm forgetting we got + + + align:start position:0% +others but I'm forgetting we got +feedback that it's good to have the full + + align:start position:0% +feedback that it's good to have the full + + + align:start position:0% +feedback that it's good to have the full +week's materials posted before the week + + align:start position:0% +week's materials posted before the week + + + align:start position:0% +week's materials posted before the week +starts which was very challenging the + + align:start position:0% +starts which was very challenging the + + + align:start position:0% +starts which was very challenging the +first year because we were often writing + + align:start position:0% +first year because we were often writing + + + align:start position:0% +first year because we were often writing +it like at that exact moment um this + + align:start position:0% +it like at that exact moment um this + + + align:start position:0% +it like at that exact moment um this +year we've corrected that yeah uh the as + + align:start position:0% +year we've corrected that yeah uh the as + + + align:start position:0% +year we've corrected that yeah uh the as +far as the using the software I think + + align:start position:0% +far as the using the software I think + + + align:start position:0% +far as the using the software I think +exactly what Jerry said plus I'll add + + align:start position:0% +exactly what Jerry said plus I'll add + + + align:start position:0% +exactly what Jerry said plus I'll add +that you know we we had to think we we + + align:start position:0% +that you know we we had to think we we + + + align:start position:0% +that you know we we had to think we we +we thought more what our goals were with + + align:start position:0% +we thought more what our goals were with + + + align:start position:0% +we thought more what our goals were with +them interacting with this software and + + align:start position:0% +them interacting with this software and + + + align:start position:0% +them interacting with this software and +really it was less about making them + + align:start position:0% +really it was less about making them + + + align:start position:0% +really it was less about making them +experts in using mat lab R and more + + align:start position:0% +experts in using mat lab R and more + + + align:start position:0% +experts in using mat lab R and more +about leveraging the software as a way + + align:start position:0% +about leveraging the software as a way + + + align:start position:0% +about leveraging the software as a way +to increase their understanding of the + + align:start position:0% +to increase their understanding of the + + + align:start position:0% +to increase their understanding of the +material and from that point of view + + align:start position:0% +material and from that point of view + + + align:start position:0% +material and from that point of view +it's not quite as necessary to have them + + align:start position:0% +it's not quite as necessary to have them + + + align:start position:0% +it's not quite as necessary to have them +build up complicated things from scratch + + align:start position:0% +build up complicated things from scratch + + + align:start position:0% +build up complicated things from scratch +but rather to be able to understand + + align:start position:0% +but rather to be able to understand + + + align:start position:0% +but rather to be able to understand +something we've written and well enough + + align:start position:0% +something we've written and well enough + + + align:start position:0% +something we've written and well enough +that they can change components play + + align:start position:0% +that they can change components play + + + align:start position:0% +that they can change components play +with it visualize things and so we've + + align:start position:0% +with it visualize things and so we've + + + align:start position:0% +with it visualize things and so we've +really moved in that direction and also + + align:start position:0% +really moved in that direction and also + + + align:start position:0% +really moved in that direction and also +another piece of feedback we got was + + align:start position:0% +another piece of feedback we got was + + + align:start position:0% +another piece of feedback we got was +that students really appreciate real + + align:start position:0% +that students really appreciate real + + + align:start position:0% +that students really appreciate real +world applications especially a lot of + + align:start position:0% +world applications especially a lot of + + + align:start position:0% +world applications especially a lot of +them are Premed they want to see medical + + align:start position:0% +them are Premed they want to see medical + + + align:start position:0% +them are Premed they want to see medical +research papers they want to see they + + align:start position:0% +research papers they want to see they + + + align:start position:0% +research papers they want to see they +want to see data that that that speaks + + align:start position:0% +want to see data that that that speaks + + + align:start position:0% +want to see data that that that speaks +to them and so uh Peter kempthorne for + + align:start position:0% +to them and so uh Peter kempthorne for + + + align:start position:0% +to them and so uh Peter kempthorne for +example has a background in in the + + align:start position:0% +example has a background in in the + + + align:start position:0% +example has a background in in the +financial world so he's helped us create + + align:start position:0% +financial world so he's helped us create + + + align:start position:0% +financial world so he's helped us create +some studios centered around stock + + align:start position:0% +some studios centered around stock + + + align:start position:0% +some studios centered around stock +moving you know stock prices moving + + align:start position:0% +moving you know stock prices moving + + + align:start position:0% +moving you know stock prices moving +around uh we the one we created last + + align:start position:0% +around uh we the one we created last + + + align:start position:0% +around uh we the one we created last +week was a studio where basically they + + align:start position:0% +week was a studio where basically they + + + align:start position:0% +week was a studio where basically they +used a two-dimensional basing updating + + align:start position:0% +used a two-dimensional basing updating + + + align:start position:0% +used a two-dimensional basing updating +to simulate looking for Malaysia Flight + + align:start position:0% +to simulate looking for Malaysia Flight + + + align:start position:0% +to simulate looking for Malaysia Flight +370 under the India ocean by putting a + + align:start position:0% +370 under the India ocean by putting a + + + align:start position:0% +370 under the India ocean by putting a +sensor grid and it was found the next + + align:start position:0% +sensor grid and it was found the next + + + align:start position:0% +sensor grid and it was found the next +day or they got that ping that's right + + align:start position:0% +day or they got that ping that's right + + + align:start position:0% +day or they got that ping that's right +right so so so there they have this you + + align:start position:0% +right so so so there they have this you + + + align:start position:0% +right so so so there they have this you +know they're not going to know how to + + align:start position:0% +know they're not going to know how to + + + align:start position:0% +know they're not going to know how to +make this like sort of heat map + + align:start position:0% +make this like sort of heat map + + + align:start position:0% +make this like sort of heat map +representation or a contour plot + + align:start position:0% +representation or a contour plot + + + align:start position:0% +representation or a contour plot +representation of you know the posterior + + align:start position:0% +representation of you know the posterior + + + align:start position:0% +representation of you know the posterior +of updating based on what sensors + + align:start position:0% +of updating based on what sensors + + + align:start position:0% +of updating based on what sensors +detected and so on but that's okay we + + align:start position:0% +detected and so on but that's okay we + + + align:start position:0% +detected and so on but that's okay we +can then we can instead give them the + + align:start position:0% +can then we can instead give them the + + + align:start position:0% +can then we can instead give them the +framework they can play with it we can + + align:start position:0% +framework they can play with it we can + + + align:start position:0% +framework they can play with it we can +say well what happens if instead of the + + align:start position:0% +say well what happens if instead of the + + + align:start position:0% +say well what happens if instead of the +Black Box being right in the middle of + + align:start position:0% +Black Box being right in the middle of + + + align:start position:0% +Black Box being right in the middle of +this grid of sensors it's up here and + + align:start position:0% +this grid of sensors it's up here and + + + align:start position:0% +this grid of sensors it's up here and +then they realize after playing with it + + align:start position:0% +then they realize after playing with it + + + align:start position:0% +then they realize after playing with it +oh actually it takes long to converge + + align:start position:0% +oh actually it takes long to converge + + + align:start position:0% +oh actually it takes long to converge +and at first the probability sort of + + align:start position:0% +and at first the probability sort of + + + align:start position:0% +and at first the probability sort of +spread out this way and why is that oh + + align:start position:0% +spread out this way and why is that oh + + + align:start position:0% +spread out this way and why is that oh +because it's about the same distance + + align:start position:0% +because it's about the same distance + + + align:start position:0% +because it's about the same distance +left to right those things were coming + + align:start position:0% +left to right those things were coming + + + align:start position:0% +left to right those things were coming +you know naturally to them it didn't + + align:start position:0% +you know naturally to them it didn't + + + align:start position:0% +you know naturally to them it didn't +mean they had to understand how to do + + align:start position:0% +mean they had to understand how to do + + + align:start position:0% +mean they had to understand how to do +this complicated syntax but it was a + + align:start position:0% +this complicated syntax but it was a + + + align:start position:0% +this complicated syntax but it was a +benefit of getting these visuals right + + align:start position:0% +benefit of getting these visuals right + + + align:start position:0% +benefit of getting these visuals right +away being able to play + + align:start position:0% + + + + align:start position:0% + +around well in this case it was relevant + + align:start position:0% +around well in this case it was relevant + + + align:start position:0% +around well in this case it was relevant +to the New York Times report the night + + align:start position:0% +to the New York Times report the night + + + align:start position:0% +to the New York Times report the night +before which said that they were + + align:start position:0% +before which said that they were + + + align:start position:0% +before which said that they were +deploying sensors behind ship so we + + align:start position:0% +deploying sensors behind ship so we + + + align:start position:0% +deploying sensors behind ship so we +talked about how would you modify this + + align:start position:0% +talked about how would you modify this + + + align:start position:0% +talked about how would you modify this +to make it more realistic based on what + + align:start position:0% +to make it more realistic based on what + + + align:start position:0% +to make it more realistic based on what +they're actually doing which isn't so + + align:start position:0% +they're actually doing which isn't so + + + align:start position:0% +they're actually doing which isn't so +hard and they got the idea hopefully + + align:start position:0% +hard and they got the idea hopefully + + + align:start position:0% +hard and they got the idea hopefully +that this stuff is useful so these are + + align:start position:0% +that this stuff is useful so these are + + + align:start position:0% +that this stuff is useful so these are +details I think part of the point is + + align:start position:0% +details I think part of the point is + + + align:start position:0% +details I think part of the point is +we're always getting feedback them from + + align:start position:0% +we're always getting feedback them from + + + align:start position:0% +we're always getting feedback them from +the students because that's part of what + + align:start position:0% +the students because that's part of what + + + align:start position:0% +the students because that's part of what +happens in a classroom the kind of + + align:start position:0% +happens in a classroom the kind of + + + align:start position:0% +happens in a classroom the kind of +formative assessment John mentioned one + + align:start position:0% +formative assessment John mentioned one + + + align:start position:0% +formative assessment John mentioned one +of the things we've done and it differs + + align:start position:0% +of the things we've done and it differs + + + align:start position:0% +of the things we've done and it differs +from what teal does is a question is how + + align:start position:0% +from what teal does is a question is how + + + align:start position:0% +from what teal does is a question is how +long do you let them work on a + + align:start position:0% +long do you let them work on a + + + align:start position:0% +long do you let them work on a +problem and through their feedback + + align:start position:0% +problem and through their feedback + + + align:start position:0% +problem and through their feedback +through talking to them and through + + align:start position:0% +through talking to them and through + + + align:start position:0% +through talking to them and through +observation we've kind of converged on + + align:start position:0% +observation we've kind of converged on + + + align:start position:0% +observation we've kind of converged on +how long you go with a problem and I + + align:start position:0% +how long you go with a problem and I + + + align:start position:0% +how long you go with a problem and I +think one of the differences with teal + + align:start position:0% +think one of the differences with teal + + + align:start position:0% +think one of the differences with teal +is we give them a longer time to solve + + align:start position:0% +is we give them a longer time to solve + + + align:start position:0% +is we give them a longer time to solve +problems than they do in teal and they + + align:start position:0% +problems than they do in teal and they + + + align:start position:0% +problems than they do in teal and they +do Express an appreciation for + + align:start position:0% +do Express an appreciation for + + + align:start position:0% +do Express an appreciation for +that how did you learn to work + + align:start position:0% +that how did you learn to work + + + align:start position:0% +that how did you learn to work +effectively in the teal classroom Did + + align:start position:0% +effectively in the teal classroom Did + + + align:start position:0% +effectively in the teal classroom Did +You observe others have special no we + + align:start position:0% +You observe others have special no we + + + align:start position:0% +You observe others have special no we +went we we went to Peter dermaskin class + + align:start position:0% +went we we went to Peter dermaskin class + + + align:start position:0% +went we we went to Peter dermaskin class +we talked with Peter we the night before + + align:start position:0% +we talked with Peter we the night before + + + align:start position:0% +we talked with Peter we the night before +our first or the day before our first + + align:start position:0% +our first or the day before our first + + + align:start position:0% +our first or the day before our first +class we went into the room and we + + align:start position:0% +class we went into the room and we + + + align:start position:0% +class we went into the room and we +rehearsed it down to the minute um and + + align:start position:0% +rehearsed it down to the minute um and + + + align:start position:0% +rehearsed it down to the minute um and +then we just sort of tried it over and + + align:start position:0% +then we just sort of tried it over and + + + align:start position:0% +then we just sort of tried it over and +over again we were lucky the first day + + align:start position:0% +over again we were lucky the first day + + + align:start position:0% +over again we were lucky the first day +partly I think because of the rehearsal + + align:start position:0% +partly I think because of the rehearsal + + + align:start position:0% +partly I think because of the rehearsal +was so successful Haynes you probably + + align:start position:0% +was so successful Haynes you probably + + + align:start position:0% +was so successful Haynes you probably +remember how high we were flying after + + align:start position:0% +remember how high we were flying after + + + align:start position:0% +remember how high we were flying after +that day uh and + + align:start position:0% +that day uh and + + + align:start position:0% +that day uh and +so the level of preparation quickly you + + align:start position:0% +so the level of preparation quickly you + + + align:start position:0% +so the level of preparation quickly you +know deteriorated no no no no we don't + + align:start position:0% +know deteriorated no no no no we don't + + + align:start position:0% +know deteriorated no no no no we don't +do it down to the minute we're more + + align:start position:0% +do it down to the minute we're more + + + align:start position:0% +do it down to the minute we're more +confident in you know 10minute intervals + + align:start position:0% +confident in you know 10minute intervals + + + align:start position:0% +confident in you know 10minute intervals +but we're we're well prepared the room + + align:start position:0% +but we're we're well prepared the room + + + align:start position:0% +but we're we're well prepared the room +itself is I mean there's a little + + align:start position:0% +itself is I mean there's a little + + + align:start position:0% +itself is I mean there's a little +control panel you just need to learn how + + align:start position:0% +control panel you just need to learn how + + + align:start position:0% +control panel you just need to learn how +to make the screens go up and down or + + align:start position:0% +to make the screens go up and down or + + + align:start position:0% +to make the screens go up and down or +make a video camera go on or off make + + align:start position:0% +make a video camera go on or off make + + + align:start position:0% +make a video camera go on or off make +the lights go up or down it's not it's + + align:start position:0% +the lights go up or down it's not it's + + + align:start position:0% +the lights go up or down it's not it's +not that that's that's challenging but + + align:start position:0% +not that that's that's challenging but + + + align:start position:0% +not that that's that's challenging but +it definitely took a lot of trial and + + align:start position:0% +it definitely took a lot of trial and + + + align:start position:0% +it definitely took a lot of trial and +error to optimize what's the best way to + + align:start position:0% +error to optimize what's the best way to + + + align:start position:0% +error to optimize what's the best way to +use those Technologies and that was + + align:start position:0% +use those Technologies and that was + + + align:start position:0% +use those Technologies and that was +experimentation that kind of we got + + align:start position:0% +experimentation that kind of we got + + + align:start position:0% +experimentation that kind of we got +better as we win yeah I don't think the + + align:start position:0% +better as we win yeah I don't think the + + + align:start position:0% +better as we win yeah I don't think the +technology was as much but things like + + align:start position:0% +technology was as much but things like + + + align:start position:0% +technology was as much but things like +how long do you do a problem in the + + align:start position:0% +how long do you do a problem in the + + + align:start position:0% +how long do you do a problem in the +first year you know I'd be off in the + + align:start position:0% +first year you know I'd be off in the + + + align:start position:0% +first year you know I'd be off in the +corner talking with students and John + + align:start position:0% +corner talking with students and John + + + align:start position:0% +corner talking with students and John +would come and say you know it's been a + + align:start position:0% +would come and say you know it's been a + + + align:start position:0% +would come and say you know it's been a +long time it's time to stop uh and and I + + align:start position:0% +long time it's time to stop uh and and I + + + align:start position:0% +long time it's time to stop uh and and I +think maybe it happened in reverse on + + align:start position:0% +think maybe it happened in reverse on + + + align:start position:0% +think maybe it happened in reverse on +occasion yeah and it's it's a really + + align:start position:0% +occasion yeah and it's it's a really + + + align:start position:0% +occasion yeah and it's it's a really +common problem with with active learning + + align:start position:0% +common problem with with active learning + + + align:start position:0% +common problem with with active learning +is that you do have groups with that + + align:start position:0% +is that you do have groups with that + + + align:start position:0% +is that you do have groups with that +will go at different speeds one + + align:start position:0% +will go at different speeds one + + + align:start position:0% +will go at different speeds one +advantage with having enough Staffing is + + align:start position:0% +advantage with having enough Staffing is + + + align:start position:0% +advantage with having enough Staffing is +that you can try to Target those groups + + align:start position:0% +that you can try to Target those groups + + + align:start position:0% +that you can try to Target those groups +get people to about the same point + + align:start position:0% +get people to about the same point + + + align:start position:0% +get people to about the same point +you're never going to you know there are + + align:start position:0% +you're never going to you know there are + + + align:start position:0% +you're never going to you know there are +always going to be winners and losers in + + align:start position:0% +always going to be winners and losers in + + + align:start position:0% +always going to be winners and losers in +any approach you take to teaching a + + align:start position:0% +any approach you take to teaching a + + + align:start position:0% +any approach you take to teaching a +class we're not claiming that what we're + + align:start position:0% +class we're not claiming that what we're + + + align:start position:0% +class we're not claiming that what we're +doing is better for + + align:start position:0% +doing is better for + + + align:start position:0% +doing is better for +everyone uh but you + + align:start position:0% + + + + align:start position:0% + +know this just this this feedback you + + align:start position:0% +know this just this this feedback you + + + align:start position:0% +know this just this this feedback you +get as you're doing it dynamically in + + align:start position:0% +get as you're doing it dynamically in + + + align:start position:0% +get as you're doing it dynamically in +the hour it really helps it really helps + + align:start position:0% +the hour it really helps it really helps + + + align:start position:0% +the hour it really helps it really helps +you know how to reach them did you have + + align:start position:0% +you know how to reach them did you have + + + align:start position:0% +you know how to reach them did you have +a schedule that we're going to do this + + align:start position:0% +a schedule that we're going to do this + + + align:start position:0% +a schedule that we're going to do this +for 10 minutes we're going to do this + + align:start position:0% +for 10 minutes we're going to do this + + + align:start position:0% +for 10 minutes we're going to do this +for 15 did you have it we have it broken + + align:start position:0% +for 15 did you have it we have it broken + + + align:start position:0% +for 15 did you have it we have it broken +down by slides and so the + + align:start position:0% +down by slides and so the + + + align:start position:0% +down by slides and so the +slides do we have a slide presentation + + align:start position:0% +slides do we have a slide presentation + + + align:start position:0% +slides do we have a slide presentation +that that is prepared ahead so that does + + align:start position:0% +that that is prepared ahead so that does + + + align:start position:0% +that that is prepared ahead so that does +give you an order yeah and at this point + + align:start position:0% +give you an order yeah and at this point + + + align:start position:0% +give you an order yeah and at this point +you know you learn when you prepare + + align:start position:0% +you know you learn when you prepare + + + align:start position:0% +you know you learn when you prepare +lectures at this point we know that 16 + + align:start position:0% +lectures at this point we know that 16 + + + align:start position:0% +lectures at this point we know that 16 +slides we can get through 20 slides + + align:start position:0% +slides we can get through 20 slides + + + align:start position:0% +slides we can get through 20 slides +we're not going to get through we should + + align:start position:0% +we're not going to get through we should + + + align:start position:0% +we're not going to get through we should +also say we fall still into the mistake + + align:start position:0% +also say we fall still into the mistake + + + align:start position:0% +also say we fall still into the mistake +of thinking oh we could do it we could + + align:start position:0% +of thinking oh we could do it we could + + + align:start position:0% +of thinking oh we could do it we could +do it but you never do one thing we also + + align:start position:0% +do it but you never do one thing we also + + + align:start position:0% +do it but you never do one thing we also +do that students I think appreciate is + + align:start position:0% +do that students I think appreciate is + + + align:start position:0% +do that students I think appreciate is +that you know you're still not going to + + align:start position:0% +that you know you're still not going to + + + align:start position:0% +that you know you're still not going to +get every student to understand the + + align:start position:0% +get every student to understand the + + + align:start position:0% +get every student to understand the +problem they just did necessarily in the + + align:start position:0% +problem they just did necessarily in the + + + align:start position:0% +problem they just did necessarily in the +confines of the class time and there + + align:start position:0% +confines of the class time and there + + + align:start position:0% +confines of the class time and there +might be times where it doesn't make + + align:start position:0% +might be times where it doesn't make + + + align:start position:0% +might be times where it doesn't make +sense to go through every detail of a + + align:start position:0% +sense to go through every detail of a + + + align:start position:0% +sense to go through every detail of a +problem because it wouldn't be that + + align:start position:0% +problem because it wouldn't be that + + + align:start position:0% +problem because it wouldn't be that +efficient because most students + + align:start position:0% +efficient because most students + + + align:start position:0% +efficient because most students +basically got it and so the version of + + align:start position:0% +basically got it and so the version of + + + align:start position:0% +basically got it and so the version of +the slides that we post right before and + + align:start position:0% +the slides that we post right before and + + + align:start position:0% +the slides that we post right before and +we use in the class is different from + + align:start position:0% +we use in the class is different from + + + align:start position:0% +we use in the class is different from +the updated version We post after class + + align:start position:0% +the updated version We post after class + + + align:start position:0% +the updated version We post after class +which includes complete careful + + align:start position:0% +which includes complete careful + + + align:start position:0% +which includes complete careful +solutions to every problem that we did + + align:start position:0% +solutions to every problem that we did + + + align:start position:0% +solutions to every problem that we did +in class so students know that that's + + align:start position:0% +in class so students know that that's + + + align:start position:0% +in class so students know that that's +there for them because they still want I + + align:start position:0% +there for them because they still want I + + + align:start position:0% +there for them because they still want I +mean they might feel like they're + + align:start position:0% +mean they might feel like they're + + + align:start position:0% +mean they might feel like they're +missing out they want to see you know an + + align:start position:0% +missing out they want to see you know an + + + align:start position:0% +missing out they want to see you know an +expert solve the problem the right way + + align:start position:0% +expert solve the problem the right way + + + align:start position:0% +expert solve the problem the right way +why should they have to come up with + + align:start position:0% +why should they have to come up with + + + align:start position:0% +why should they have to come up with +that way completely themselves and so we + + align:start position:0% +that way completely themselves and so we + + + align:start position:0% +that way completely themselves and so we +try to recapture some of that by putting + + align:start position:0% +try to recapture some of that by putting + + + align:start position:0% +try to recapture some of that by putting +that in there but you you should say we + + align:start position:0% +that in there but you you should say we + + + align:start position:0% +that in there but you you should say we +usually do solve it for them afterwards + + align:start position:0% +usually do solve it for them afterwards + + + align:start position:0% +usually do solve it for them afterwards +most problems we give them the expert + + align:start position:0% +most problems we give them the expert + + + align:start position:0% +most problems we give them the expert +nice succinct View and I think that's an + + align:start position:0% +nice succinct View and I think that's an + + + align:start position:0% +nice succinct View and I think that's an +important part of the students want to + + align:start position:0% +important part of the students want to + + + align:start position:0% +important part of the students want to +feel that they're getting some of your + + align:start position:0% +feel that they're getting some of your + + + align:start position:0% +feel that they're getting some of your +expertise you mentioned students prefer + + align:start position:0% +expertise you mentioned students prefer + + + align:start position:0% +expertise you mentioned students prefer +the targeted questions reading to U + + align:start position:0% +the targeted questions reading to U + + + align:start position:0% +the targeted questions reading to U +online lectures I wondering what + + align:start position:0% +online lectures I wondering what + + + align:start position:0% +online lectures I wondering what +students felt was so good about the + + align:start position:0% +students felt was so good about the + + + align:start position:0% +students felt was so good about the +targeted reading or what it was that was + + align:start position:0% +targeted reading or what it was that was + + + align:start position:0% +targeted reading or what it was that was +so bad about the online lectures I don't + + align:start position:0% +so bad about the online lectures I don't + + + align:start position:0% +so bad about the online lectures I don't +think they'd say online lectures were + + align:start position:0% +think they'd say online lectures were + + + align:start position:0% +think they'd say online lectures were +bad online lectures take longer to watch + + align:start position:0% +bad online lectures take longer to watch + + + align:start position:0% +bad online lectures take longer to watch +if you tried a Muk and how many people + + align:start position:0% +if you tried a Muk and how many people + + + align:start position:0% +if you tried a Muk and how many people +in this room have tried that the videos + + align:start position:0% +in this room have tried that the videos + + + align:start position:0% +in this room have tried that the videos +are long I mean you always are looking + + align:start position:0% +are long I mean you always are looking + + + align:start position:0% +are long I mean you always are looking +to try to speed it up find the two time + + align:start position:0% +to try to speed it up find the two time + + + align:start position:0% +to try to speed it up find the two time +speed up Etc they can take a long time + + align:start position:0% +speed up Etc they can take a long time + + + align:start position:0% +speed up Etc they can take a long time +the target the fact that the reading is + + align:start position:0% +the target the fact that the reading is + + + align:start position:0% +the target the fact that the reading is +Target fact that we wrote it and it + + align:start position:0% +Target fact that we wrote it and it + + + align:start position:0% +Target fact that we wrote it and it +covers what we expect them to + + align:start position:0% +covers what we expect them to + + + align:start position:0% +covers what we expect them to +learn is I think the main thing they + + align:start position:0% +learn is I think the main thing they + + + align:start position:0% +learn is I think the main thing they +like there's clear signals in there we + + align:start position:0% +like there's clear signals in there we + + + align:start position:0% +like there's clear signals in there we +think this is important not we said read + + align:start position:0% +think this is important not we said read + + + align:start position:0% +think this is important not we said read +chapter five and you have to figure out + + align:start position:0% +chapter five and you have to figure out + + + align:start position:0% +chapter five and you have to figure out +by listening to us which parts of + + align:start position:0% +by listening to us which parts of + + + align:start position:0% +by listening to us which parts of +chapter 5 are important and I mean those + + align:start position:0% +chapter 5 are important and I mean those + + + align:start position:0% +chapter 5 are important and I mean those +are skills that as you go higher up in + + align:start position:0% +are skills that as you go higher up in + + + align:start position:0% +are skills that as you go higher up in +your education in MIT you might be able + + align:start position:0% +your education in MIT you might be able + + + align:start position:0% +your education in MIT you might be able +to do more for yourself and you should + + align:start position:0% +to do more for yourself and you should + + + align:start position:0% +to do more for yourself and you should +learn those skills but but I think the + + align:start position:0% +learn those skills but but I think the + + + align:start position:0% +learn those skills but but I think the +level of this course I mean many of + + align:start position:0% +level of this course I mean many of + + + align:start position:0% +level of this course I mean many of +these students they're strong + + align:start position:0% +these students they're strong + + + align:start position:0% +these students they're strong +mathematically by national standards of + + align:start position:0% +mathematically by national standards of + + + align:start position:0% +mathematically by national standards of +course but maybe within MIT if they're + + align:start position:0% +course but maybe within MIT if they're + + + align:start position:0% +course but maybe within MIT if they're +life science Majors they're not as + + align:start position:0% +life science Majors they're not as + + + align:start position:0% +life science Majors they're not as +confident as some of the math majors and + + align:start position:0% +confident as some of the math majors and + + + align:start position:0% +confident as some of the math majors and +physics Majors it it helps them to have + + align:start position:0% +physics Majors it it helps them to have + + + align:start position:0% +physics Majors it it helps them to have +a little more guidance in what the + + align:start position:0% +a little more guidance in what the + + + align:start position:0% +a little more guidance in what the +expectations + + align:start position:0% +expectations + + + align:start position:0% +expectations +are what do you do for small groups + + align:start position:0% +are what do you do for small groups + + + align:start position:0% +are what do you do for small groups +where there's some there's a group + + align:start position:0% +where there's some there's a group + + + align:start position:0% +where there's some there's a group +that's ahead gotten done and everyone + + align:start position:0% +that's ahead gotten done and everyone + + + align:start position:0% +that's ahead gotten done and everyone +else is still working do you have extra + + align:start position:0% +else is still working do you have extra + + + align:start position:0% +else is still working do you have extra +stuff for them or enrichment or you can + + align:start position:0% +stuff for them or enrichment or you can + + + align:start position:0% +stuff for them or enrichment or you can +walk around and try to challenge them + + align:start position:0% +walk around and try to challenge them + + + align:start position:0% +walk around and try to challenge them +most groups it's rare that there's + + align:start position:0% +most groups it's rare that there's + + + align:start position:0% +most groups it's rare that there's +people who have understood particularly + + align:start position:0% +people who have understood particularly + + + align:start position:0% +people who have understood particularly +say the first time we work through an + + align:start position:0% +say the first time we work through an + + + align:start position:0% +say the first time we work through an +idea have understood it completely so + + align:start position:0% +idea have understood it completely so + + + align:start position:0% +idea have understood it completely so +there's always questions you could say + + align:start position:0% +there's always questions you could say + + + align:start position:0% +there's always questions you could say +have you thought about this or what if + + align:start position:0% +have you thought about this or what if + + + align:start position:0% +have you thought about this or what if +you did + + align:start position:0% +you did + + + align:start position:0% +you did +that how do you form the groups and do + + align:start position:0% +that how do you form the groups and do + + + align:start position:0% +that how do you form the groups and do +you change them during the course of the + + align:start position:0% +you change them during the course of the + + + align:start position:0% +you change them during the course of the +semester no we we let them form + + align:start position:0% +semester no we we let them form + + + align:start position:0% +semester no we we let them form +themselves I think there's a debate in + + align:start position:0% +themselves I think there's a debate in + + + align:start position:0% +themselves I think there's a debate in +the education Community maybe Jenny can + + align:start position:0% +the education Community maybe Jenny can + + + align:start position:0% +the education Community maybe Jenny can +speak to this about whether it's better + + align:start position:0% +speak to this about whether it's better + + + align:start position:0% +speak to this about whether it's better +to form the groups you for you to form + + align:start position:0% +to form the groups you for you to form + + + align:start position:0% +to form the groups you for you to form +them by you know some sort of + + align:start position:0% +them by you know some sort of + + + align:start position:0% +them by you know some sort of +heterogeneous ability or to to let them + + align:start position:0% +heterogeneous ability or to to let them + + + align:start position:0% +heterogeneous ability or to to let them +form we feel that first of all we don't + + align:start position:0% +form we feel that first of all we don't + + + align:start position:0% +form we feel that first of all we don't +know their ability coming in second + + align:start position:0% +know their ability coming in second + + + align:start position:0% +know their ability coming in second +people like autonomy and so allowing + + align:start position:0% +people like autonomy and so allowing + + + align:start position:0% +people like autonomy and so allowing +them to form groups makes them + + align:start position:0% +them to form groups makes them + + + align:start position:0% +them to form groups makes them +comfortable there's students who are + + align:start position:0% +comfortable there's students who are + + + align:start position:0% +comfortable there's students who are +resistant to this idea of active + + align:start position:0% +resistant to this idea of active + + + align:start position:0% +resistant to this idea of active +learning coming in we win them over + + align:start position:0% +learning coming in we win them over + + + align:start position:0% +learning coming in we win them over +quickly and part of it is that we're + + align:start position:0% +quickly and part of it is that we're + + + align:start position:0% +quickly and part of it is that we're +generous say in that sense what do you + + align:start position:0% +generous say in that sense what do you + + + align:start position:0% +generous say in that sense what do you +do you see in one group is a dominant + + align:start position:0% +do you see in one group is a dominant + + + align:start position:0% +do you see in one group is a dominant +member + + align:start position:0% +member + + + align:start position:0% +member +or you know it doesn't happen that much + + align:start position:0% +or you know it doesn't happen that much + + + align:start position:0% +or you know it doesn't happen that much +groups of three they tend to work + + align:start position:0% +groups of three they tend to work + + + align:start position:0% +groups of three they tend to work +together these are largely Juniors and + + align:start position:0% +together these are largely Juniors and + + + align:start position:0% +together these are largely Juniors and +seniors at MIT a few sophomores they + + align:start position:0% +seniors at MIT a few sophomores they + + + align:start position:0% +seniors at MIT a few sophomores they +have + + align:start position:0% +have + + + align:start position:0% +have +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +become uh better at being students and + + align:start position:0% +become uh better at being students and + + + align:start position:0% +become uh better at being students and +making sure they're getting what they + + align:start position:0% +making sure they're getting what they + + + align:start position:0% +making sure they're getting what they +want there are some groups where you + + align:start position:0% +want there are some groups where you + + + align:start position:0% +want there are some groups where you +come and you try to draw people in it + + align:start position:0% +come and you try to draw people in it + + + align:start position:0% +come and you try to draw people in it +tends to be the groups that are overall + + align:start position:0% +tends to be the groups that are overall + + + align:start position:0% +tends to be the groups that are overall +weaker where you see people hanging back + + align:start position:0% +weaker where you see people hanging back + + + align:start position:0% +weaker where you see people hanging back +but those are exactly the groups where + + align:start position:0% +but those are exactly the groups where + + + align:start position:0% +but those are exactly the groups where +you go to first and you spend more time + + align:start position:0% +you go to first and you spend more time + + + align:start position:0% +you go to first and you spend more time +with + + align:start position:0% +with + + + align:start position:0% +with +them you mentioned uh the FP component + + align:start position:0% +them you mentioned uh the FP component + + + align:start position:0% +them you mentioned uh the FP component +of the so can you give a little bit more + + align:start position:0% +of the so can you give a little bit more + + + align:start position:0% +of the so can you give a little bit more +idea about your expectations time wise + + align:start position:0% +idea about your expectations time wise + + + align:start position:0% +idea about your expectations time wise +and material wise and how you coordinate + + align:start position:0% +and material wise and how you coordinate + + + align:start position:0% +and material wise and how you coordinate +it like you said they have these + + align:start position:0% +it like you said they have these + + + align:start position:0% +it like you said they have these +readings maybe 10 pages for every class + + align:start position:0% +readings maybe 10 pages for every class + + + align:start position:0% +readings maybe 10 pages for every class +per week two twice a two twice twice a + + align:start position:0% +per week two twice a two twice twice a + + + align:start position:0% +per week two twice a two twice twice a +week Tuesday and Thursday so prior to + + align:start position:0% +week Tuesday and Thursday so prior to + + + align:start position:0% +week Tuesday and Thursday so prior to +Tuesday and Thursday they need to do + + align:start position:0% +Tuesday and Thursday they need to do + + + align:start position:0% +Tuesday and Thursday they need to do +reading it's about 10 pages it's a very + + align:start position:0% +reading it's about 10 pages it's a very + + + align:start position:0% +reading it's about 10 pages it's a very +fast 10 pages we use a lot of white + + align:start position:0% +fast 10 pages we use a lot of white + + + align:start position:0% +fast 10 pages we use a lot of white +space problem there one problem set per + + align:start position:0% +space problem there one problem set per + + + align:start position:0% +space problem there one problem set per +week and also one more follow question + + align:start position:0% +week and also one more follow question + + + align:start position:0% +week and also one more follow question +on that what's the turn + + align:start position:0% +on that what's the turn + + + align:start position:0% +on that what's the turn +assment feed + + align:start position:0% +assment feed + + + align:start position:0% +assment feed +fors that they could hopefully learn the + + align:start position:0% +fors that they could hopefully learn the + + + align:start position:0% +fors that they could hopefully learn the +next uh they have one pet per week + + align:start position:0% +next uh they have one pet per week + + + align:start position:0% +next uh they have one pet per week +except in weeks where we have an exam uh + + align:start position:0% +except in weeks where we have an exam uh + + + align:start position:0% +except in weeks where we have an exam uh +and Vacations so usually let's say one + + align:start position:0% +and Vacations so usually let's say one + + + align:start position:0% +and Vacations so usually let's say one +per week with some variation we try to + + align:start position:0% +per week with some variation we try to + + + align:start position:0% +per week with some variation we try to +get so the p sets the way we structure + + align:start position:0% +get so the p sets the way we structure + + + align:start position:0% +get so the p sets the way we structure +it right they're they're learning say + + align:start position:0% +it right they're they're learning say + + + align:start position:0% +it right they're they're learning say +some new material Tuesday Thursday + + align:start position:0% +some new material Tuesday Thursday + + + align:start position:0% +some new material Tuesday Thursday +Studio on Friday and then the P set we + + align:start position:0% +Studio on Friday and then the P set we + + + align:start position:0% +Studio on Friday and then the P set we +have due Monday and the idea is that + + align:start position:0% +have due Monday and the idea is that + + + align:start position:0% +have due Monday and the idea is that +they by turning it on Monday they still + + align:start position:0% +they by turning it on Monday they still + + + align:start position:0% +they by turning it on Monday they still +then + + align:start position:0% +then + + + align:start position:0% +then +Monday night can prepare for Tuesday's + + align:start position:0% +Monday night can prepare for Tuesday's + + + align:start position:0% +Monday night can prepare for Tuesday's +class uh we try to get the greaters to + + align:start position:0% +class uh we try to get the greaters to + + + align:start position:0% +class uh we try to get the greaters to +turn back to P set by the end of the + + align:start position:0% +turn back to P set by the end of the + + + align:start position:0% +turn back to P set by the end of the +week by Friday um I'm not convinced that + + align:start position:0% +week by Friday um I'm not convinced that + + + align:start position:0% +week by Friday um I'm not convinced that +getting that problem set back is + + align:start position:0% +getting that problem set back is + + + align:start position:0% +getting that problem set back is +actually helping that many students in + + align:start position:0% +actually helping that many students in + + + align:start position:0% +actually helping that many students in +the end like I said most half the + + align:start position:0% +the end like I said most half the + + + align:start position:0% +the end like I said most half the +students don't even pick them up right + + align:start position:0% +students don't even pick them up right + + + align:start position:0% +students don't even pick them up right +but it is nice for the students that + + align:start position:0% +but it is nice for the students that + + + align:start position:0% +but it is nice for the students that +that want it so we we it's been good + + align:start position:0% +that want it so we we it's been good + + + align:start position:0% +that want it so we we it's been good +they get it the graders get it back by + + align:start position:0% +they get it the graders get it back by + + + align:start position:0% +they get it the graders get it back by +Frid oh yeah the graders abely like how + + align:start position:0% +Frid oh yeah the graders abely like how + + + align:start position:0% +Frid oh yeah the graders abely like how +many uh questions do you expect them to + + align:start position:0% +many uh questions do you expect them to + + + align:start position:0% +many uh questions do you expect them to +work through through that okay so the + + align:start position:0% +work through through that okay so the + + + align:start position:0% +work through through that okay so the +pet is just the challenging part of a + + align:start position:0% +pet is just the challenging part of a + + + align:start position:0% +pet is just the challenging part of a +problem set we would ask in a regular + + align:start position:0% +problem set we would ask in a regular + + + align:start position:0% +problem set we would ask in a regular +lecture class they've done more of the + + align:start position:0% +lecture class they've done more of the + + + align:start position:0% +lecture class they've done more of the +drill problems in class and somewhat on + + align:start position:0% +drill problems in class and somewhat on + + + align:start position:0% +drill problems in class and somewhat on +the reading questions so five or six + + align:start position:0% +the reading questions so five or six + + + align:start position:0% +the reading questions so five or six +questions which is about what we would + + align:start position:0% +questions which is about what we would + + + align:start position:0% +questions which is about what we would +have on what we call the part two part + + align:start position:0% +have on what we call the part two part + + + align:start position:0% +have on what we call the part two part +of a + + align:start position:0% +of a + + + align:start position:0% +of a +regular lecture class what they would + + align:start position:0% +regular lecture class what they would + + + align:start position:0% +regular lecture class what they would +see in uh 1801 or 1802 or + + align:start position:0% +see in uh 1801 or 1802 or + + + align:start position:0% +see in uh 1801 or 1802 or +1803 sounds right about the grading of + + align:start position:0% +1803 sounds right about the grading of + + + align:start position:0% +1803 sounds right about the grading of +the problem set I mean one thing that a + + align:start position:0% +the problem set I mean one thing that a + + + align:start position:0% +the problem set I mean one thing that a +lot of Education research shows is that + + align:start position:0% +lot of Education research shows is that + + + align:start position:0% +lot of Education research shows is that +if there's a delay between the act of + + align:start position:0% +if there's a delay between the act of + + + align:start position:0% +if there's a delay between the act of +doing a problem feedback they don't pay + + align:start position:0% +doing a problem feedback they don't pay + + + align:start position:0% +doing a problem feedback they don't pay +any attention which is what you're + + align:start position:0% +any attention which is what you're + + + align:start position:0% +any attention which is what you're +saying right what if you force them to + + align:start position:0% +saying right what if you force them to + + + align:start position:0% +saying right what if you force them to +actually think about it again by grading + + align:start position:0% +actually think about it again by grading + + + align:start position:0% +actually think about it again by grading +the problem that himself so you could + + align:start position:0% +the problem that himself so you could + + + align:start position:0% +the problem that himself so you could +say everyone upload their problem set + + align:start position:0% +say everyone upload their problem set + + + align:start position:0% +say everyone upload their problem set +and then you get somebody else's problem + + align:start position:0% +and then you get somebody else's problem + + + align:start position:0% +and then you get somebody else's problem +set and you have to been gred with your + + align:start position:0% +set and you have to been gred with your + + + align:start position:0% +set and you have to been gred with your +solution I think it's a a great idea but + + align:start position:0% +solution I think it's a a great idea but + + + align:start position:0% +solution I think it's a a great idea but +my questions about it would be twofold + + align:start position:0% +my questions about it would be twofold + + + align:start position:0% +my questions about it would be twofold +students are not going to like it + + align:start position:0% +students are not going to like it + + + align:start position:0% +students are not going to like it +especially when you start them doing it + + align:start position:0% +especially when you start them doing it + + + align:start position:0% +especially when you start them doing it +and is it the best use of their + + align:start position:0% +and is it the best use of their + + + align:start position:0% +and is it the best use of their +time I don't know what the research + + align:start position:0% +time I don't know what the research + + + align:start position:0% +time I don't know what the research +shows on that the solution said it's + + align:start position:0% +shows on that the solution said it's + + + align:start position:0% +shows on that the solution said it's +probably wor their their time reading it + + align:start position:0% +probably wor their their time reading it + + + align:start position:0% +probably wor their their time reading it +oh I see if they have to grade they have + + align:start position:0% +oh I see if they have to grade they have + + + align:start position:0% +oh I see if they have to grade they have +to read our + + align:start position:0% +to read our + + + align:start position:0% +to read our +Solutions and really understand them and + + align:start position:0% +Solutions and really understand them and + + + align:start position:0% +Solutions and really understand them and +also learn what counts as a good + + align:start position:0% +also learn what counts as a good + + + align:start position:0% +also learn what counts as a good +argument and what doesn't yeah just + + align:start position:0% +argument and what doesn't yeah just + + + align:start position:0% +argument and what doesn't yeah just +hopefully transfers I can tell you this + + align:start position:0% +hopefully transfers I can tell you this + + + align:start position:0% +hopefully transfers I can tell you this +analia brones who I teach with in in the + + align:start position:0% +analia brones who I teach with in in the + + + align:start position:0% +analia brones who I teach with in in the +experimental study group who teaches + + align:start position:0% +experimental study group who teaches + + + align:start position:0% +experimental study group who teaches +physics there she did try to do this at + + align:start position:0% +physics there she did try to do this at + + + align:start position:0% +physics there she did try to do this at +some point and she did learn that + + align:start position:0% +some point and she did learn that + + + align:start position:0% +some point and she did learn that +students become good at grading it you + + align:start position:0% +students become good at grading it you + + + align:start position:0% +students become good at grading it you +don't have to worry about that over time + + align:start position:0% +don't have to worry about that over time + + + align:start position:0% +don't have to worry about that over time +with your feedback they learn to grade + + align:start position:0% +with your feedback they learn to grade + + + align:start position:0% +with your feedback they learn to grade +pretty close to what you would grade the + + align:start position:0% +pretty close to what you would grade the + + + align:start position:0% +pretty close to what you would grade the +questions she would give them a rubric + + align:start position:0% +questions she would give them a rubric + + + align:start position:0% +questions she would give them a rubric +but she no longer does it there was a + + align:start position:0% +but she no longer does it there was a + + + align:start position:0% +but she no longer does it there was a +lot of resistance to + + align:start position:0% +lot of resistance to + + + align:start position:0% +lot of resistance to +it by the students by the students you + + align:start position:0% +it by the students by the students you + + + align:start position:0% +it by the students by the students you +would hope that a little bit of that + + align:start position:0% +would hope that a little bit of that + + + align:start position:0% +would hope that a little bit of that +occurs before exams but I'm not sure + + align:start position:0% +occurs before exams but I'm not sure + + + align:start position:0% +occurs before exams but I'm not sure +yeah excuse me are you collecting data + + align:start position:0% +yeah excuse me are you collecting data + + + align:start position:0% +yeah excuse me are you collecting data +more than you would in a regular class + + align:start position:0% +more than you would in a regular class + + + align:start position:0% +more than you would in a regular class +just so you mean like the the sort of + + align:start position:0% +just so you mean like the the sort of + + + align:start position:0% +just so you mean like the the sort of +data coming in from the + + align:start position:0% +data coming in from the + + + align:start position:0% +data coming in from the +students here's the data that we have we + + align:start position:0% +students here's the data that we have we + + + align:start position:0% +students here's the data that we have we +there's something called the statistics + + align:start position:0% +there's something called the statistics + + + align:start position:0% +there's something called the statistics +concept inventory and we had them last + + align:start position:0% +concept inventory and we had them last + + + align:start position:0% +concept inventory and we had them last +year do a pre-test and we had them do a + + align:start position:0% +year do a pre-test and we had them do a + + + align:start position:0% +year do a pre-test and we had them do a +post test but we got to it too late so + + align:start position:0% +post test but we got to it too late so + + + align:start position:0% +post test but we got to it too late so +we couldn't assign it to them it was in + + align:start position:0% +we couldn't assign it to them it was in + + + align:start position:0% +we couldn't assign it to them it was in +the last week of class where you can't + + align:start position:0% +the last week of class where you can't + + + align:start position:0% +the last week of class where you can't +assign things at MIT so we didn't get a + + align:start position:0% +assign things at MIT so we didn't get a + + + align:start position:0% +assign things at MIT so we didn't get a +lot of compliance there this year they + + align:start position:0% +lot of compliance there this year they + + + align:start position:0% +lot of compliance there this year they +did the preest and the post test will be + + align:start position:0% +did the preest and the post test will be + + + align:start position:0% +did the preest and the post test will be +an assigned + + align:start position:0% +an assigned + + + align:start position:0% +an assigned +for them to do so we'll be able to + + align:start position:0% +for them to do so we'll be able to + + + align:start position:0% +for them to do so we'll be able to +measure how well they improve on the + + align:start position:0% +measure how well they improve on the + + + align:start position:0% +measure how well they improve on the +concept inventory it's not a perfect + + align:start position:0% +concept inventory it's not a perfect + + + align:start position:0% +concept inventory it's not a perfect +match for what we do it has no basian + + align:start position:0% +match for what we do it has no basian + + + align:start position:0% +match for what we do it has no basian +component to it but we'll get a measure + + align:start position:0% +component to it but we'll get a measure + + + align:start position:0% +component to it but we'll get a measure +there uh the other is what Glenda has + + align:start position:0% +there uh the other is what Glenda has + + + align:start position:0% +there uh the other is what Glenda has +done with surveys and interviews and + + align:start position:0% +done with surveys and interviews and + + + align:start position:0% +done with surveys and interviews and +finally there are analytics on mitx so + + align:start position:0% +finally there are analytics on mitx so + + + align:start position:0% +finally there are analytics on mitx so +we can see how long they've spent at + + align:start position:0% +we can see how long they've spent at + + + align:start position:0% +we can see how long they've spent at +least with the PDFs open how of how many + + align:start position:0% +least with the PDFs open how of how many + + + align:start position:0% +least with the PDFs open how of how many +tries they took at various questions we + + align:start position:0% +tries they took at various questions we + + + align:start position:0% +tries they took at various questions we +haven't tried to analyze that data yet + + align:start position:0% +haven't tried to analyze that data yet + + + align:start position:0% +haven't tried to analyze that data yet +but we + + align:start position:0% +but we + + + align:start position:0% +but we +could okay I think so we won't have + + align:start position:0% +could okay I think so we won't have + + + align:start position:0% +could okay I think so we won't have +people starting to get up and leave um + + align:start position:0% +people starting to get up and leave um + + + align:start position:0% +people starting to get up and leave um +thank you guys I think strikes me as one + + align:start position:0% +thank you guys I think strikes me as one + + + align:start position:0% +thank you guys I think strikes me as one +of those real in the trenches talks + + align:start position:0% +of those real in the trenches talks + + + align:start position:0% +of those real in the trenches talks +you're actually doing it and you can + + align:start position:0% +you're actually doing it and you can + + + align:start position:0% +you're actually doing it and you can +hear the with from the questions this + + align:start position:0% +hear the with from the questions this + + + align:start position:0% +hear the with from the questions this +time we sort of mve from a sort of + + align:start position:0% +time we sort of mve from a sort of + + + align:start position:0% +time we sort of mve from a sort of +theoretical construct of you could do it + + align:start position:0% +theoretical construct of you could do it + + + align:start position:0% +theoretical construct of you could do it +this way it's actually happening around + + align:start position:0% +this way it's actually happening around + + + align:start position:0% +this way it's actually happening around +a lot of people are thinking about it + + align:start position:0% +a lot of people are thinking about it + + + align:start position:0% +a lot of people are thinking about it +and just thank you so much for coming + + align:start position:0% +and just thank you so much for coming + + + align:start position:0% +and just thank you so much for coming +really + + align:start position:0% +really + + + align:start position:0% +really +all \ No newline at end of file diff --git a/7TljYDljC5w.txt b/7TljYDljC5w.txt new file mode 100644 index 0000000000000000000000000000000000000000..2974766b287dc4d386ce1e7ff6e4cc7fabafd833 --- /dev/null +++ b/7TljYDljC5w.txt @@ -0,0 +1,403 @@ +align:start position:0% + +so we've now drawn pictures of the + + align:start position:0% +so we've now drawn pictures of the + + + align:start position:0% +so we've now drawn pictures of the +interaction of a person jumping off a + + align:start position:0% +interaction of a person jumping off a + + + align:start position:0% +interaction of a person jumping off a +cart in both the ground frame and a + + align:start position:0% +cart in both the ground frame and a + + + align:start position:0% +cart in both the ground frame and a +reference frame moving with velocity VC + + align:start position:0% +reference frame moving with velocity VC + + + align:start position:0% +reference frame moving with velocity VC +which is the final speed of the cart + + align:start position:0% +which is the final speed of the cart + + + align:start position:0% +which is the final speed of the cart +these were pictures in the reference + + align:start position:0% +these were pictures in the reference + + + align:start position:0% +these were pictures in the reference +frame moving with VC and these are the + + align:start position:0% +frame moving with VC and these are the + + + align:start position:0% +frame moving with VC and these are the +pictures momentum diagrams of the person + + align:start position:0% +pictures momentum diagrams of the person + + + align:start position:0% +pictures momentum diagrams of the person +in the cart in the ground frame now we + + align:start position:0% +in the cart in the ground frame now we + + + align:start position:0% +in the cart in the ground frame now we +would like to apply the momentum + + align:start position:0% +would like to apply the momentum + + + align:start position:0% +would like to apply the momentum +principle to solve for VP and VC we are + + align:start position:0% +principle to solve for VP and VC we are + + + align:start position:0% +principle to solve for VP and VC we are +given that the relative velocity of the + + align:start position:0% +given that the relative velocity of the + + + align:start position:0% +given that the relative velocity of the +person in the moving frame you will + + align:start position:0% +person in the moving frame you will + + + align:start position:0% +person in the moving frame you will +treat this as a given quantity and will + + align:start position:0% +treat this as a given quantity and will + + + align:start position:0% +treat this as a given quantity and will +express the velocity VC and so we want + + align:start position:0% +express the velocity VC and so we want + + + align:start position:0% +express the velocity VC and so we want +to find BC and VP in terms of U MP and + + align:start position:0% +to find BC and VP in terms of U MP and + + + align:start position:0% +to find BC and VP in terms of U MP and +MC now we'll use the ground frame first + + align:start position:0% +MC now we'll use the ground frame first + + + align:start position:0% +MC now we'll use the ground frame first +and our assumption here is that the + + align:start position:0% +and our assumption here is that the + + + align:start position:0% +and our assumption here is that the +person jumped horizontally and that + + align:start position:0% +person jumped horizontally and that + + + align:start position:0% +person jumped horizontally and that +there are no external forces in the + + align:start position:0% +there are no external forces in the + + + align:start position:0% +there are no external forces in the +horizontal direction so all of the + + align:start position:0% +horizontal direction so all of the + + + align:start position:0% +horizontal direction so all of the +vectors we've drawn are horizontal and + + align:start position:0% +vectors we've drawn are horizontal and + + + align:start position:0% +vectors we've drawn are horizontal and +there's no external forces in the + + align:start position:0% +there's no external forces in the + + + align:start position:0% +there's no external forces in the +horizontal direction then we know that + + align:start position:0% +horizontal direction then we know that + + + align:start position:0% +horizontal direction then we know that +the initial momentum of the system is + + align:start position:0% +the initial momentum of the system is + + + align:start position:0% +the initial momentum of the system is +equal to the final momentum of the + + align:start position:0% +equal to the final momentum of the + + + align:start position:0% +equal to the final momentum of the +system in our initial picture nothing is + + align:start position:0% +system in our initial picture nothing is + + + align:start position:0% +system in our initial picture nothing is +moving and in our final picture we have + + align:start position:0% +moving and in our final picture we have + + + align:start position:0% +moving and in our final picture we have +M cart D cart plus M person B person is + + align:start position:0% +M cart D cart plus M person B person is + + + align:start position:0% +M cart D cart plus M person B person is +0 now recall that we also showed that + + align:start position:0% +0 now recall that we also showed that + + + align:start position:0% +0 now recall that we also showed that +the velocity of the person in the ground + + align:start position:0% +the velocity of the person in the ground + + + align:start position:0% +the velocity of the person in the ground +frame is related to the velocity of the + + align:start position:0% +frame is related to the velocity of the + + + align:start position:0% +frame is related to the velocity of the +person in the moving frame by adding the + + align:start position:0% +person in the moving frame by adding the + + + align:start position:0% +person in the moving frame by adding the +relative velocity of the two frames the + + align:start position:0% +relative velocity of the two frames the + + + align:start position:0% +relative velocity of the two frames the +relative velocity of the two frames is + + align:start position:0% +relative velocity of the two frames is + + + align:start position:0% +relative velocity of the two frames is +the velocity of the car BC so what we + + align:start position:0% +the velocity of the car BC so what we + + + align:start position:0% +the velocity of the car BC so what we +have is VC plus u so this is how VP is + + align:start position:0% +have is VC plus u so this is how VP is + + + align:start position:0% +have is VC plus u so this is how VP is +related to you and now I can use this + + align:start position:0% +related to you and now I can use this + + + align:start position:0% +related to you and now I can use this +start equation to write it as zero + + align:start position:0% +start equation to write it as zero + + + align:start position:0% +start equation to write it as zero +equals MC VC plus MP x vc plus u and by + + align:start position:0% +equals MC VC plus MP x vc plus u and by + + + align:start position:0% +equals MC VC plus MP x vc plus u and by +adding terms + + align:start position:0% +adding terms + + + align:start position:0% +adding terms +I get that MC plus MP v C equals minus + + align:start position:0% +I get that MC plus MP v C equals minus + + + align:start position:0% +I get that MC plus MP v C equals minus +MP u or the velocity of the cart is + + align:start position:0% +MP u or the velocity of the cart is + + + align:start position:0% +MP u or the velocity of the cart is +equal to minus MP u divided by MC plus + + align:start position:0% +equal to minus MP u divided by MC plus + + + align:start position:0% +equal to minus MP u divided by MC plus +MP now that I have the velocity of the + + align:start position:0% +MP now that I have the velocity of the + + + align:start position:0% +MP now that I have the velocity of the +cart I can just substitute that in here + + align:start position:0% +cart I can just substitute that in here + + + align:start position:0% +cart I can just substitute that in here +to find the velocity the person which + + align:start position:0% +to find the velocity the person which + + + align:start position:0% +to find the velocity the person which +remember was the velocity of the cart + + align:start position:0% +remember was the velocity of the cart + + + align:start position:0% +remember was the velocity of the cart +Plus u so now I've solved this problem + + align:start position:0% +Plus u so now I've solved this problem + + + align:start position:0% +Plus u so now I've solved this problem +in the ground frame next I'll do the + + align:start position:0% +in the ground frame next I'll do the + + + align:start position:0% +in the ground frame next I'll do the +same analysis in the moving frame \ No newline at end of file diff --git a/83NmtaE7fEk.txt b/83NmtaE7fEk.txt new file mode 100644 index 0000000000000000000000000000000000000000..e4de02493fb42a06898bf6898cde2ea7a8424f2b --- /dev/null +++ b/83NmtaE7fEk.txt @@ -0,0 +1,923 @@ +align:start position:0% + +one of the most common motions we see in + + align:start position:0% +one of the most common motions we see in + + + align:start position:0% +one of the most common motions we see in +our everyday lives is the path of an + + align:start position:0% +our everyday lives is the path of an + + + align:start position:0% +our everyday lives is the path of an +object moving thrown and moving through + + align:start position:0% +object moving thrown and moving through + + + align:start position:0% +object moving thrown and moving through +space now this type of motion has a very + + align:start position:0% +space now this type of motion has a very + + + align:start position:0% +space now this type of motion has a very +famous name called projectile motion and + + align:start position:0% +famous name called projectile motion and + + + align:start position:0% +famous name called projectile motion and +when we look at it let's introduce a + + align:start position:0% +when we look at it let's introduce a + + + align:start position:0% +when we look at it let's introduce a +coordinate system I hat and J hat here's + + align:start position:0% +coordinate system I hat and J hat here's + + + align:start position:0% +coordinate system I hat and J hat here's +our y plus y axis and our plus X axis + + align:start position:0% +our y plus y axis and our plus X axis + + + align:start position:0% +our y plus y axis and our plus X axis +then in order to understand the + + align:start position:0% +then in order to understand the + + + align:start position:0% +then in order to understand the +kinematics of this motion we would like + + align:start position:0% +kinematics of this motion we would like + + + align:start position:0% +kinematics of this motion we would like +to apply Newton's second law + + align:start position:0% +to apply Newton's second law + + + align:start position:0% +to apply Newton's second law +so separately we'll draw our object it + + align:start position:0% +so separately we'll draw our object it + + + align:start position:0% +so separately we'll draw our object it +has gravitational force acting downward + + align:start position:0% +has gravitational force acting downward + + + align:start position:0% +has gravitational force acting downward +remember our unit vectors in the J hat + + align:start position:0% +remember our unit vectors in the J hat + + + align:start position:0% +remember our unit vectors in the J hat +direction and so when we write our + + align:start position:0% +direction and so when we write our + + + align:start position:0% +direction and so when we write our +equations of motion F equals MA we have + + align:start position:0% +equations of motion F equals MA we have + + + align:start position:0% +equations of motion F equals MA we have +two different directions in the J hat + + align:start position:0% +two different directions in the J hat + + + align:start position:0% +two different directions in the J hat +direction we have the gravitational + + align:start position:0% +direction we have the gravitational + + + align:start position:0% +direction we have the gravitational +force downward minus mg and remember + + align:start position:0% +force downward minus mg and remember + + + align:start position:0% +force downward minus mg and remember +here that G is our positive quantity 9.8 + + align:start position:0% +here that G is our positive quantity 9.8 + + + align:start position:0% +here that G is our positive quantity 9.8 +meters per second and we have ma Y + + align:start position:0% +meters per second and we have ma Y + + + align:start position:0% +meters per second and we have ma Y +Newton's second law equates these two + + align:start position:0% +Newton's second law equates these two + + + align:start position:0% +Newton's second law equates these two +different things and that's we'll write + + align:start position:0% +different things and that's we'll write + + + align:start position:0% +different things and that's we'll write +it like that so those two quantities are + + align:start position:0% +it like that so those two quantities are + + + align:start position:0% +it like that so those two quantities are +equal and so our conclusion is that the + + align:start position:0% +equal and so our conclusion is that the + + + align:start position:0% +equal and so our conclusion is that the +acceleration is equal to minus G in the + + align:start position:0% +acceleration is equal to minus G in the + + + align:start position:0% +acceleration is equal to minus G in the +Y direction now likewise keep in mind + + align:start position:0% +Y direction now likewise keep in mind + + + align:start position:0% +Y direction now likewise keep in mind +that we have our horizontal direction as + + align:start position:0% +that we have our horizontal direction as + + + align:start position:0% +that we have our horizontal direction as +well and notice there we're now assuming + + align:start position:0% +well and notice there we're now assuming + + + align:start position:0% +well and notice there we're now assuming +that there's no horizontal forces in the + + align:start position:0% +that there's no horizontal forces in the + + + align:start position:0% +that there's no horizontal forces in the +real world there can be all types of air + + align:start position:0% +real world there can be all types of air + + + align:start position:0% +real world there can be all types of air +resistances but here for the simplicity + + align:start position:0% +resistances but here for the simplicity + + + align:start position:0% +resistances but here for the simplicity +of this model we have no horizontal + + align:start position:0% +of this model we have no horizontal + + + align:start position:0% +of this model we have no horizontal +forces so we have zero equals ma X and + + align:start position:0% +forces so we have zero equals ma X and + + + align:start position:0% +forces so we have zero equals ma X and +so we have our separate equation ax + + align:start position:0% +so we have our separate equation ax + + + align:start position:0% +so we have our separate equation ax +equals zero now both of these equations + + align:start position:0% +equals zero now both of these equations + + + align:start position:0% +equals zero now both of these equations +are equations that we've already been + + align:start position:0% +are equations that we've already been + + + align:start position:0% +are equations that we've already been +working with in kinematics here we have + + align:start position:0% +working with in kinematics here we have + + + align:start position:0% +working with in kinematics here we have +a constant acceleration and here we have + + align:start position:0% +a constant acceleration and here we have + + + align:start position:0% +a constant acceleration and here we have +zero acceleration so using the results + + align:start position:0% +zero acceleration so using the results + + + align:start position:0% +zero acceleration so using the results +that we had earlier from integration we + + align:start position:0% +that we had earlier from integration we + + + align:start position:0% +that we had earlier from integration we +can write down the equations of motion + + align:start position:0% +can write down the equations of motion + + + align:start position:0% +can write down the equations of motion +in the Y and the X directions first + + align:start position:0% +in the Y and the X directions first + + + align:start position:0% +in the Y and the X directions first +we'll write the velocity V Y as a + + align:start position:0% +we'll write the velocity V Y as a + + + align:start position:0% +we'll write the velocity V Y as a +function of time is equal to some in + + align:start position:0% +function of time is equal to some in + + + align:start position:0% +function of time is equal to some in +value and because the acceleration is + + align:start position:0% +value and because the acceleration is + + + align:start position:0% +value and because the acceleration is +negative minus GT you can test your + + align:start position:0% +negative minus GT you can test your + + + align:start position:0% +negative minus GT you can test your +integration technique to see that and + + align:start position:0% +integration technique to see that and + + + align:start position:0% +integration technique to see that and +the position as a function of time + + align:start position:0% +the position as a function of time + + + align:start position:0% +the position as a function of time +remember is just some constant value + + align:start position:0% +remember is just some constant value + + + align:start position:0% +remember is just some constant value +this is our constant Y naught and we + + align:start position:0% +this is our constant Y naught and we + + + align:start position:0% +this is our constant Y naught and we +have plus V y naught t minus one-half GT + + align:start position:0% +have plus V y naught t minus one-half GT + + + align:start position:0% +have plus V y naught t minus one-half GT +squared again doing integration now the + + align:start position:0% +squared again doing integration now the + + + align:start position:0% +squared again doing integration now the +horizontal equation of motion the X of T + + align:start position:0% +horizontal equation of motion the X of T + + + align:start position:0% +horizontal equation of motion the X of T +because there's no acceleration in the + + align:start position:0% +because there's no acceleration in the + + + align:start position:0% +because there's no acceleration in the +horizontal direction this is a constant + + align:start position:0% +horizontal direction this is a constant + + + align:start position:0% +horizontal direction this is a constant +value given by the initial value of the + + align:start position:0% +value given by the initial value of the + + + align:start position:0% +value given by the initial value of the +component of the velocity in the X + + align:start position:0% +component of the velocity in the X + + + align:start position:0% +component of the velocity in the X +direction and the position X of T is + + align:start position:0% +direction and the position X of T is + + + align:start position:0% +direction and the position X of T is +then equal to some initial position plus + + align:start position:0% +then equal to some initial position plus + + + align:start position:0% +then equal to some initial position plus +VX not T and so those are our functions + + align:start position:0% +VX not T and so those are our functions + + + align:start position:0% +VX not T and so those are our functions +of time for little components of the + + align:start position:0% +of time for little components of the + + + align:start position:0% +of time for little components of the +velocity and the components of position + + align:start position:0% +velocity and the components of position + + + align:start position:0% +velocity and the components of position +now for our particular example it's much + + align:start position:0% +now for our particular example it's much + + + align:start position:0% +now for our particular example it's much +easier here we have X not equal to zero + + align:start position:0% +easier here we have X not equal to zero + + + align:start position:0% +easier here we have X not equal to zero +notice that our object is starting at + + align:start position:0% +notice that our object is starting at + + + align:start position:0% +notice that our object is starting at +the origin and so that tells us that X + + align:start position:0% +the origin and so that tells us that X + + + align:start position:0% +the origin and so that tells us that X +as a function of time is just V X naught + + align:start position:0% +as a function of time is just V X naught + + + align:start position:0% +as a function of time is just V X naught +T I'm dropping the parentheses T + + align:start position:0% +T I'm dropping the parentheses T + + + align:start position:0% +T I'm dropping the parentheses T +remember that's not a product it's just + + align:start position:0% +remember that's not a product it's just + + + align:start position:0% +remember that's not a product it's just +a function of time and given this fact + + align:start position:0% +a function of time and given this fact + + + align:start position:0% +a function of time and given this fact +that tells us that T is X divided by B X + + align:start position:0% +that tells us that T is X divided by B X + + + align:start position:0% +that tells us that T is X divided by B X +naught and now I can take this value of + + align:start position:0% +naught and now I can take this value of + + + align:start position:0% +naught and now I can take this value of +T and put it into our vertical equation + + align:start position:0% +T and put it into our vertical equation + + + align:start position:0% +T and put it into our vertical equation +and I get V Y is some initial value plus + + align:start position:0% +and I get V Y is some initial value plus + + + align:start position:0% +and I get V Y is some initial value plus +V y naught X over V X naught + + align:start position:0% +V y naught X over V X naught + + + align:start position:0% +V y naught X over V X naught +substituting for t minus one-half g x + + align:start position:0% +substituting for t minus one-half g x + + + align:start position:0% +substituting for t minus one-half g x +squared over V X naught squared when we + + align:start position:0% +squared over V X naught squared when we + + + align:start position:0% +squared over V X naught squared when we +describe projectile motion we had a + + align:start position:0% +describe projectile motion we had a + + + align:start position:0% +describe projectile motion we had a +equation describing Y as a function of T + + align:start position:0% +equation describing Y as a function of T + + + align:start position:0% +equation describing Y as a function of T +an equation describing X as a function + + align:start position:0% +an equation describing X as a function + + + align:start position:0% +an equation describing X as a function +of T the horizontal motion the vertical + + align:start position:0% +of T the horizontal motion the vertical + + + align:start position:0% +of T the horizontal motion the vertical +motion and here we have a separate + + align:start position:0% +motion and here we have a separate + + + align:start position:0% +motion and here we have a separate +equation which is describing the Y as + + align:start position:0% +equation which is describing the Y as + + + align:start position:0% +equation which is describing the Y as +function of X notice there is no time + + align:start position:0% +function of X notice there is no time + + + align:start position:0% +function of X notice there is no time +involved in this equation now let's try + + align:start position:0% +involved in this equation now let's try + + + align:start position:0% +involved in this equation now let's try +to look at graphically what we're seeing + + align:start position:0% +to look at graphically what we're seeing + + + align:start position:0% +to look at graphically what we're seeing +here so for instance when we look at a + + align:start position:0% +here so for instance when we look at a + + + align:start position:0% +here so for instance when we look at a +plot of the motion of y versus of X we + + align:start position:0% +plot of the motion of y versus of X we + + + align:start position:0% +plot of the motion of y versus of X we +can see the vertical component going up + + align:start position:0% +can see the vertical component going up + + + align:start position:0% +can see the vertical component going up +and down and we can see the horizontal + + align:start position:0% +and down and we can see the horizontal + + + align:start position:0% +and down and we can see the horizontal +component moving to the right while the + + align:start position:0% +component moving to the right while the + + + align:start position:0% +component moving to the right while the +object is following this trajectory and + + align:start position:0% +object is following this trajectory and + + + align:start position:0% +object is following this trajectory and +this is a parabolic trajectory of Y as a + + align:start position:0% +this is a parabolic trajectory of Y as a + + + align:start position:0% +this is a parabolic trajectory of Y as a +function of X now if we wanted to + + align:start position:0% +function of X now if we wanted to + + + align:start position:0% +function of X now if we wanted to +actually plot out Y as a function of T + + align:start position:0% +actually plot out Y as a function of T + + + align:start position:0% +actually plot out Y as a function of T +then here we can look at the simulation + + align:start position:0% +then here we can look at the simulation + + + align:start position:0% +then here we can look at the simulation +where we're just looking at the Y + + align:start position:0% +where we're just looking at the Y + + + align:start position:0% +where we're just looking at the Y +component and you can see that that + + align:start position:0% +component and you can see that that + + + align:start position:0% +component and you can see that that +motion too is a parabola however what's + + align:start position:0% +motion too is a parabola however what's + + + align:start position:0% +motion too is a parabola however what's +crucial to look at is that it's Y as a + + align:start position:0% +crucial to look at is that it's Y as a + + + align:start position:0% +crucial to look at is that it's Y as a +function of T and not Y as a function of + + align:start position:0% +function of T and not Y as a function of + + + align:start position:0% +function of T and not Y as a function of +X finally we can look at the horizontal + + align:start position:0% +X finally we can look at the horizontal + + + align:start position:0% +X finally we can look at the horizontal +motion and again recall that when we + + align:start position:0% +motion and again recall that when we + + + align:start position:0% +motion and again recall that when we +looked at the trajectory as Y is a + + align:start position:0% +looked at the trajectory as Y is a + + + align:start position:0% +looked at the trajectory as Y is a +function of X you can see the horizontal + + align:start position:0% +function of X you can see the horizontal + + + align:start position:0% +function of X you can see the horizontal +motion component let's plot that + + align:start position:0% +motion component let's plot that + + + align:start position:0% +motion component let's plot that +separately X as a function of T and when + + align:start position:0% +separately X as a function of T and when + + + align:start position:0% +separately X as a function of T and when +we make that plot you can see that this + + align:start position:0% +we make that plot you can see that this + + + align:start position:0% +we make that plot you can see that this +is just a linear equation in time where + + align:start position:0% +is just a linear equation in time where + + + align:start position:0% +is just a linear equation in time where +there's some initial condition X naught + + align:start position:0% +there's some initial condition X naught + + + align:start position:0% +there's some initial condition X naught +and so that's the plot of X as a + + align:start position:0% +and so that's the plot of X as a + + + align:start position:0% +and so that's the plot of X as a +function of T and so we see three + + align:start position:0% +function of T and so we see three + + + align:start position:0% +function of T and so we see three +separate representations of this motion + + align:start position:0% +separate representations of this motion + + + align:start position:0% +separate representations of this motion +Y as a function of X Y as a function of + + align:start position:0% +Y as a function of X Y as a function of + + + align:start position:0% +Y as a function of X Y as a function of +T and X as a function of T \ No newline at end of file diff --git a/9aKidJvppF0.txt b/9aKidJvppF0.txt new file mode 100644 index 0000000000000000000000000000000000000000..326271e80855f09d2450e5cfecae057d13599ef1 --- /dev/null +++ b/9aKidJvppF0.txt @@ -0,0 +1,912 @@ +align:start position:0% + +in this lecture we'll see how + + align:start position:0% +in this lecture we'll see how + + + align:start position:0% +in this lecture we'll see how +optimization can be used to construct + + align:start position:0% +optimization can be used to construct + + + align:start position:0% +optimization can be used to construct +sport schedules + + align:start position:0% +sport schedules + + + align:start position:0% +sport schedules +specifically we'll introduce the method + + align:start position:0% +specifically we'll introduce the method + + + align:start position:0% +specifically we'll introduce the method +of integer optimization sports is a + + align:start position:0% +of integer optimization sports is a + + + align:start position:0% +of integer optimization sports is a +three-hundred billion dollar industry + + align:start position:0% +three-hundred billion dollar industry + + + align:start position:0% +three-hundred billion dollar industry +this is twice as big as the automobile + + align:start position:0% +this is twice as big as the automobile + + + align:start position:0% +this is twice as big as the automobile +industry and seven times as big as the + + align:start position:0% +industry and seven times as big as the + + + align:start position:0% +industry and seven times as big as the +movie industry this includes tickets for + + align:start position:0% +movie industry this includes tickets for + + + align:start position:0% +movie industry this includes tickets for +games team merchandise salaries for + + align:start position:0% +games team merchandise salaries for + + + align:start position:0% +games team merchandise salaries for +players etc almost every single country + + align:start position:0% +players etc almost every single country + + + align:start position:0% +players etc almost every single country +participates in the sports industry for + + align:start position:0% +participates in the sports industry for + + + align:start position:0% +participates in the sports industry for +this industry to remain so large sports + + align:start position:0% +this industry to remain so large sports + + + align:start position:0% +this industry to remain so large sports +teams are very important the key revenue + + align:start position:0% +teams are very important the key revenue + + + align:start position:0% +teams are very important the key revenue +for sports teams comes from TV networks + + align:start position:0% +for sports teams comes from TV networks + + + align:start position:0% +for sports teams comes from TV networks +TV networks paid five hundred and + + align:start position:0% +TV networks paid five hundred and + + + align:start position:0% +TV networks paid five hundred and +thirteen million dollars per year for + + align:start position:0% +thirteen million dollars per year for + + + align:start position:0% +thirteen million dollars per year for +English Premier League Soccer seven + + align:start position:0% +English Premier League Soccer seven + + + align:start position:0% +English Premier League Soccer seven +hundred and sixty-six million dollars + + align:start position:0% +hundred and sixty-six million dollars + + + align:start position:0% +hundred and sixty-six million dollars +per year for the National Basketball + + align:start position:0% +per year for the National Basketball + + + align:start position:0% +per year for the National Basketball +Association or NBA and three billion + + align:start position:0% +Association or NBA and three billion + + + align:start position:0% +Association or NBA and three billion +dollars per year for the National + + align:start position:0% +dollars per year for the National + + + align:start position:0% +dollars per year for the National +Football League or NFL these TV networks + + align:start position:0% +Football League or NFL these TV networks + + + align:start position:0% +Football League or NFL these TV networks +are paying such large amounts to ensure + + align:start position:0% +are paying such large amounts to ensure + + + align:start position:0% +are paying such large amounts to ensure +that they will have a good schedule of + + align:start position:0% +that they will have a good schedule of + + + align:start position:0% +that they will have a good schedule of +sports games to convince fans to tune in + + align:start position:0% +sports games to convince fans to tune in + + + align:start position:0% +sports games to convince fans to tune in +and watch the games on their network in + + align:start position:0% +and watch the games on their network in + + + align:start position:0% +and watch the games on their network in +addition to the TV networks good sports + + align:start position:0% +addition to the TV networks good sports + + + align:start position:0% +addition to the TV networks good sports +schedules are important for other + + align:start position:0% +schedules are important for other + + + align:start position:0% +schedules are important for other +reasons too one is that extensive + + align:start position:0% +reasons too one is that extensive + + + align:start position:0% +reasons too one is that extensive +traveling caused by a poor schedule can + + align:start position:0% +traveling caused by a poor schedule can + + + align:start position:0% +traveling caused by a poor schedule can +cause player fatigue which can reflect + + align:start position:0% +cause player fatigue which can reflect + + + align:start position:0% +cause player fatigue which can reflect +badly on the team also ticket sales tend + + align:start position:0% +badly on the team also ticket sales tend + + + align:start position:0% +badly on the team also ticket sales tend +to be better on the weekends so teams + + align:start position:0% +to be better on the weekends so teams + + + align:start position:0% +to be better on the weekends so teams +like to have games scheduled for + + align:start position:0% +like to have games scheduled for + + + align:start position:0% +like to have games scheduled for +weekends to increase revenue + + align:start position:0% +weekends to increase revenue + + + align:start position:0% +weekends to increase revenue +additionally it's better to play + + align:start position:0% +additionally it's better to play + + + align:start position:0% +additionally it's better to play +division teams or direct competitors for + + align:start position:0% +division teams or direct competitors for + + + align:start position:0% +division teams or direct competitors for +playoff spots near the end of the season + + align:start position:0% +playoff spots near the end of the season + + + align:start position:0% +playoff spots near the end of the season +since teams have more information for + + align:start position:0% +since teams have more information for + + + align:start position:0% +since teams have more information for +these reasons and many more everyone in + + align:start position:0% +these reasons and many more everyone in + + + align:start position:0% +these reasons and many more everyone in +the sports industry is incentivized to + + align:start position:0% +the sports industry is incentivized to + + + align:start position:0% +the sports industry is incentivized to +have a good schedule of games all + + align:start position:0% +have a good schedule of games all + + + align:start position:0% +have a good schedule of games all +competitive sports require schedules + + align:start position:0% +competitive sports require schedules + + + align:start position:0% +competitive sports require schedules +defining which pairs of teams play each + + align:start position:0% +defining which pairs of teams play each + + + align:start position:0% +defining which pairs of teams play each +other and win until recently sports + + align:start position:0% +other and win until recently sports + + + align:start position:0% +other and win until recently sports +schedules were mostly constructed by + + align:start position:0% +schedules were mostly constructed by + + + align:start position:0% +schedules were mostly constructed by +hand + + align:start position:0% +hand + + + align:start position:0% +hand +this is incredibly time-consuming with + + align:start position:0% +this is incredibly time-consuming with + + + align:start position:0% +this is incredibly time-consuming with +just 10 teams there are over 1 trillion + + align:start position:0% +just 10 teams there are over 1 trillion + + + align:start position:0% +just 10 teams there are over 1 trillion +possible schedules where every team + + align:start position:0% +possible schedules where every team + + + align:start position:0% +possible schedules where every team +plays every other team there are many + + align:start position:0% +plays every other team there are many + + + align:start position:0% +plays every other team there are many +constraints defined by the TV networks + + align:start position:0% +constraints defined by the TV networks + + + align:start position:0% +constraints defined by the TV networks +teams cities and others TV networks want + + align:start position:0% +teams cities and others TV networks want + + + align:start position:0% +teams cities and others TV networks want +games to occur at prime times like in + + align:start position:0% +games to occur at prime times like in + + + align:start position:0% +games to occur at prime times like in +the evening teams went games on the + + align:start position:0% +the evening teams went games on the + + + align:start position:0% +the evening teams went games on the +weekends cities went games that don't + + align:start position:0% +weekends cities went games that don't + + + align:start position:0% +weekends cities went games that don't +conflict with other major events etc + + align:start position:0% +conflict with other major events etc + + + align:start position:0% +conflict with other major events etc +this requires looking through all + + align:start position:0% +this requires looking through all + + + align:start position:0% +this requires looking through all +trillion possible schedules to find one + + align:start position:0% +trillion possible schedules to find one + + + align:start position:0% +trillion possible schedules to find one +that satisfies all of the constraints + + align:start position:0% +that satisfies all of the constraints + + + align:start position:0% +that satisfies all of the constraints +for Major League Baseball a husband and + + align:start position:0% +for Major League Baseball a husband and + + + align:start position:0% +for Major League Baseball a husband and +wife team constructed the schedules for + + align:start position:0% +wife team constructed the schedules for + + + align:start position:0% +wife team constructed the schedules for +24 years + + align:start position:0% +24 years + + + align:start position:0% +24 years +they mostly built the schedule by hand + + align:start position:0% +they mostly built the schedule by hand + + + align:start position:0% +they mostly built the schedule by hand +and used a giant wall of magnets to + + align:start position:0% +and used a giant wall of magnets to + + + align:start position:0% +and used a giant wall of magnets to +schedule 2430 games each year not only + + align:start position:0% +schedule 2430 games each year not only + + + align:start position:0% +schedule 2430 games each year not only +is this approach time-consuming but it's + + align:start position:0% +is this approach time-consuming but it's + + + align:start position:0% +is this approach time-consuming but it's +very difficult to add new constraints if + + align:start position:0% +very difficult to add new constraints if + + + align:start position:0% +very difficult to add new constraints if +one new constraint is added that might + + align:start position:0% +one new constraint is added that might + + + align:start position:0% +one new constraint is added that might +make this schedule infeasible and the + + align:start position:0% +make this schedule infeasible and the + + + align:start position:0% +make this schedule infeasible and the +process would have to start all over + + align:start position:0% +process would have to start all over + + + align:start position:0% +process would have to start all over +again there have been many interesting + + align:start position:0% +again there have been many interesting + + + align:start position:0% +again there have been many interesting +constraints that have been added by + + align:start position:0% +constraints that have been added by + + + align:start position:0% +constraints that have been added by +interesting people in 2008 the owners + + align:start position:0% +interesting people in 2008 the owners + + + align:start position:0% +interesting people in 2008 the owners +and TV networks were not the only ones + + align:start position:0% +and TV networks were not the only ones + + + align:start position:0% +and TV networks were not the only ones +who cared about the schedule President + + align:start position:0% +who cared about the schedule President + + + align:start position:0% +who cared about the schedule President +Barack Obama and Senator John McCain + + align:start position:0% +Barack Obama and Senator John McCain + + + align:start position:0% +Barack Obama and Senator John McCain +complained about the schedule 2008 was + + align:start position:0% +complained about the schedule 2008 was + + + align:start position:0% +complained about the schedule 2008 was +an election year and President Obama and + + align:start position:0% +an election year and President Obama and + + + align:start position:0% +an election year and President Obama and +Senator McCain were the leading + + align:start position:0% +Senator McCain were the leading + + + align:start position:0% +Senator McCain were the leading +presidential nominees the Democratic and + + align:start position:0% +presidential nominees the Democratic and + + + align:start position:0% +presidential nominees the Democratic and +Republican national conventions + + align:start position:0% +Republican national conventions + + + align:start position:0% +Republican national conventions +conflicted with the game scheduling so + + align:start position:0% +conflicted with the game scheduling so + + + align:start position:0% +conflicted with the game scheduling so +the schedule had to be adjusted after + + align:start position:0% +the schedule had to be adjusted after + + + align:start position:0% +the schedule had to be adjusted after +that was settled the Pope complained + + align:start position:0% +that was settled the Pope complained + + + align:start position:0% +that was settled the Pope complained +about the schedule the Pope visited New + + align:start position:0% +about the schedule the Pope visited New + + + align:start position:0% +about the schedule the Pope visited New +York on April 20th 2008 he traditionally + + align:start position:0% +York on April 20th 2008 he traditionally + + + align:start position:0% +York on April 20th 2008 he traditionally +always holds mass in Yankee Stadium but + + align:start position:0% +always holds mass in Yankee Stadium but + + + align:start position:0% +always holds mass in Yankee Stadium but +a game was scheduled that same day the + + align:start position:0% +a game was scheduled that same day the + + + align:start position:0% +a game was scheduled that same day the +schedule had to be readjusted to move + + align:start position:0% +schedule had to be readjusted to move + + + align:start position:0% +schedule had to be readjusted to move +the Yankee game these are just a couple + + align:start position:0% +the Yankee game these are just a couple + + + align:start position:0% +the Yankee game these are just a couple +examples of the wide variety of + + align:start position:0% +examples of the wide variety of + + + align:start position:0% +examples of the wide variety of +constraints that have to be accounted + + align:start position:0% +constraints that have to be accounted + + + align:start position:0% +constraints that have to be accounted +for when building a sport schedule + + align:start position:0% + + + + align:start position:0% + +recognizing how difficult it was to + + align:start position:0% +recognizing how difficult it was to + + + align:start position:0% +recognizing how difficult it was to +construct sports schedules by hand in + + align:start position:0% +construct sports schedules by hand in + + + align:start position:0% +construct sports schedules by hand in + + align:start position:0% + + + align:start position:0% +six a company called the sports + + align:start position:0% +six a company called the sports + + + align:start position:0% +six a company called the sports +scheduling group was started the + + align:start position:0% +scheduling group was started the + + + align:start position:0% +scheduling group was started the +founders were Doug bjurman a former + + align:start position:0% +founders were Doug bjurman a former + + + align:start position:0% +founders were Doug bjurman a former +baseball vice-president and three + + align:start position:0% +baseball vice-president and three + + + align:start position:0% +baseball vice-president and three +academics george nemhauser michael trick + + align:start position:0% +academics george nemhauser michael trick + + + align:start position:0% +academics george nemhauser michael trick +and Kelly Easton instead of generated + + align:start position:0% +and Kelly Easton instead of generated + + + align:start position:0% +and Kelly Easton instead of generated +sport schedules by hand they use a + + align:start position:0% +sport schedules by hand they use a + + + align:start position:0% +sport schedules by hand they use a +computer + + align:start position:0% +computer + + + align:start position:0% +computer +they've been scheduling college sports + + align:start position:0% +they've been scheduling college sports + + + align:start position:0% +they've been scheduling college sports +since 1999 and Major League Baseball + + align:start position:0% +since 1999 and Major League Baseball + + + align:start position:0% +since 1999 and Major League Baseball +since 2005 they rely on optimization to + + align:start position:0% +since 2005 they rely on optimization to + + + align:start position:0% +since 2005 they rely on optimization to +build the schedules which can easily + + align:start position:0% +build the schedules which can easily + + + align:start position:0% +build the schedules which can easily +adapt when new constraints are added in + + align:start position:0% +adapt when new constraints are added in + + + align:start position:0% +adapt when new constraints are added in +this lecture we'll introduce one of the + + align:start position:0% +this lecture we'll introduce one of the + + + align:start position:0% +this lecture we'll introduce one of the +techniques they use called integer + + align:start position:0% +techniques they use called integer + + + align:start position:0% +techniques they use called integer +optimization to construct a sport + + align:start position:0% +optimization to construct a sport + + + align:start position:0% +optimization to construct a sport +schedule \ No newline at end of file diff --git a/9tIifUIgcXU.txt b/9tIifUIgcXU.txt new file mode 100644 index 0000000000000000000000000000000000000000..b75314258bc27ee4a7e0495c6035a6cc61d26059 --- /dev/null +++ b/9tIifUIgcXU.txt @@ -0,0 +1,723 @@ +align:start position:0% + +hello Within the Music 21 Corpus there's + + align:start position:0% +hello Within the Music 21 Corpus there's + + + align:start position:0% +hello Within the Music 21 Corpus there's +another subcorpus which is a pretty + + align:start position:0% +another subcorpus which is a pretty + + + align:start position:0% +another subcorpus which is a pretty +useful one and that is the Corpus of the + + align:start position:0% +useful one and that is the Corpus of the + + + align:start position:0% +useful one and that is the Corpus of the +complete corals of jsbach I'm really + + align:start position:0% +complete corals of jsbach I'm really + + + align:start position:0% +complete corals of jsbach I'm really +thankful to Margaret Green Tree who + + align:start position:0% +thankful to Margaret Green Tree who + + + align:start position:0% +thankful to Margaret Green Tree who +contributed all of these before her + + align:start position:0% +contributed all of these before her + + + align:start position:0% +contributed all of these before her +untimely passing so within music 21 + + align:start position:0% +untimely passing so within music 21 + + + align:start position:0% +untimely passing so within music 21 +let's go ahead and import Corpus because + + align:start position:0% +let's go ahead and import Corpus because + + + align:start position:0% +let's go ahead and import Corpus because +that's going to be pretty useful + + align:start position:0% +that's going to be pretty useful + + + align:start position:0% +that's going to be pretty useful +and we + + align:start position:0% +and we + + + align:start position:0% +and we +can have within the Corpus a sign called + + align:start position:0% +can have within the Corpus a sign called + + + align:start position:0% +can have within the Corpus a sign called +Corpus doc + + align:start position:0% +Corpus doc + + + align:start position:0% +Corpus doc +corals and see that there and there's a + + align:start position:0% +corals and see that there and there's a + + + align:start position:0% +corals and see that there and there's a +sign called the Corpus Coral's iterator + + align:start position:0% +sign called the Corpus Coral's iterator + + + align:start position:0% +sign called the Corpus Coral's iterator +which will go through this and so we can + + align:start position:0% +which will go through this and so we can + + + align:start position:0% +which will go through this and so we can +say for Coral in the Corpus Coral + + align:start position:0% +say for Coral in the Corpus Coral + + + align:start position:0% +say for Coral in the Corpus Coral +iterator print Coral do metadata that's + + align:start position:0% +iterator print Coral do metadata that's + + + align:start position:0% +iterator print Coral do metadata that's +the data about the data the data about + + align:start position:0% +the data about the data the data about + + + align:start position:0% +the data about the data the data about +the piece and we can print its title and + + align:start position:0% +the piece and we can print its title and + + + align:start position:0% +the piece and we can print its title and +it's going through and it's a little bit + + align:start position:0% +it's going through and it's a little bit + + + align:start position:0% +it's going through and it's a little bit +slow because it's actually parsing them + + align:start position:0% +slow because it's actually parsing them + + + align:start position:0% +slow because it's actually parsing them +and along the way as it's going that'll + + align:start position:0% +and along the way as it's going that'll + + + align:start position:0% +and along the way as it's going that'll +take some time so you can go ahead and + + align:start position:0% +take some time so you can go ahead and + + + align:start position:0% +take some time so you can go ahead and +interrupt that uh while it's going so + + align:start position:0% +interrupt that uh while it's going so + + + align:start position:0% +interrupt that uh while it's going so +not every Corral has four parts so + + align:start position:0% +not every Corral has four parts so + + + align:start position:0% +not every Corral has four parts so +sometimes as we want to do um if + + align:start position:0% +sometimes as we want to do um if + + + align:start position:0% +sometimes as we want to do um if +Coral L + + align:start position:0% +Coral L + + + align:start position:0% +Coral L +Coral or spell + + align:start position:0% +Coral or spell + + + align:start position:0% +Coral or spell +Parts not equals 4 will + + align:start position:0% +Parts not equals 4 will + + + align:start position:0% +Parts not equals 4 will +continue then let's do this let's print + + align:start position:0% +continue then let's do this let's print + + + align:start position:0% +continue then let's do this let's print +Coral + + align:start position:0% +Coral + + + align:start position:0% +Coral +metadata title and we'll + + align:start position:0% +metadata title and we'll + + + align:start position:0% +metadata title and we'll +say that we just put a call in at the + + align:start position:0% +say that we just put a call in at the + + + align:start position:0% +say that we just put a call in at the +end and then for I in range 4 012 3 + + align:start position:0% +end and then for I in range 4 012 3 + + + align:start position:0% +end and then for I in range 4 012 3 +right P equals coral. Parts + + align:start position:0% +right P equals coral. Parts + + + align:start position:0% +right P equals coral. Parts +I print + + align:start position:0% + + + + align:start position:0% + +I and then the the length of P do flat. + + align:start position:0% +I and then the the length of P do flat. + + + align:start position:0% +I and then the the length of P do flat. +notes we curse will be a little faster + + align:start position:0% +notes we curse will be a little faster + + + align:start position:0% +notes we curse will be a little faster +but we'll have to do that and we'll + + align:start position:0% +but we'll have to do that and we'll + + + align:start position:0% +but we'll have to do that and we'll +say the end of that + + align:start position:0% +say the end of that + + + align:start position:0% +say the end of that +is let's I'll put comma space something + + align:start position:0% +is let's I'll put comma space something + + + align:start position:0% +is let's I'll put comma space something +like that and now we can go through oops + + align:start position:0% +like that and now we can go through oops + + + align:start position:0% +like that and now we can go through oops +or interrupt + + align:start position:0% +or interrupt + + + align:start position:0% +or interrupt +that I think it's probably useful to + + align:start position:0% +that I think it's probably useful to + + + align:start position:0% +that I think it's probably useful to +print a new line afterwards and we can + + align:start position:0% +print a new line afterwards and we can + + + align:start position:0% +print a new line afterwards and we can +kind of see how the various parts are + + align:start position:0% +kind of see how the various parts are + + + align:start position:0% +kind of see how the various parts are +and you can imagine that you can go + + align:start position:0% +and you can imagine that you can go + + + align:start position:0% +and you can imagine that you can go +through this and play with it and have + + align:start position:0% +through this and play with it and have + + + align:start position:0% +through this and play with it and have +um so interesting things on which parts + + align:start position:0% +um so interesting things on which parts + + + align:start position:0% +um so interesting things on which parts +have more notes and which parts have + + align:start position:0% +have more notes and which parts have + + + align:start position:0% +have more notes and which parts have +fewer notes and so + + align:start position:0% +fewer notes and so + + + align:start position:0% +fewer notes and so +on some of the things that we could do + + align:start position:0% +on some of the things that we could do + + + align:start position:0% +on some of the things that we could do +with a complete Corpus of crows are look + + align:start position:0% +with a complete Corpus of crows are look + + + align:start position:0% +with a complete Corpus of crows are look +at the types of motion where do climaxes + + align:start position:0% +at the types of motion where do climaxes + + + align:start position:0% +at the types of motion where do climaxes +appear here where can uh + + align:start position:0% +appear here where can uh + + + align:start position:0% +appear here where can uh +we find uh repeats uh what are the kinds + + align:start position:0% +we find uh repeats uh what are the kinds + + + align:start position:0% +we find uh repeats uh what are the kinds +of time signatures that appear in Cals + + align:start position:0% +of time signatures that appear in Cals + + + align:start position:0% +of time signatures that appear in Cals +basically all the things that you guys + + align:start position:0% +basically all the things that you guys + + + align:start position:0% +basically all the things that you guys +did uh in problem set three which is + + align:start position:0% +did uh in problem set three which is + + + align:start position:0% +did uh in problem set three which is +just wonderful um or probably yeah to + + align:start position:0% +just wonderful um or probably yeah to + + + align:start position:0% +just wonderful um or probably yeah to +talk about what you can do with the + + align:start position:0% +talk about what you can do with the + + + align:start position:0% +talk about what you can do with the +Corpus corals so this is the coral + + align:start position:0% +Corpus corals so this is the coral + + + align:start position:0% +Corpus corals so this is the coral +Corpus if you want to quickly go through + + align:start position:0% +Corpus if you want to quickly go through + + + align:start position:0% +Corpus if you want to quickly go through +and just find particular ones you can + + align:start position:0% +and just find particular ones you can + + + align:start position:0% +and just find particular ones you can +say that the + + align:start position:0% + + + + align:start position:0% + +return type is something else uh file + + align:start position:0% + + + + align:start position:0% + +name and this will allow you to pass + + align:start position:0% +name and this will allow you to pass + + + align:start position:0% +name and this will allow you to pass +them into the converter + + align:start position:0% +them into the converter + + + align:start position:0% +them into the converter +if1 + + align:start position:0% +if1 + + + align:start position:0% +if1 +one in + + align:start position:0% +one in + + + align:start position:0% +one in +Coral real + + align:start position:0% +Coral real + + + align:start position:0% +Coral real +Coral equals Corpus + + align:start position:0% +Coral equals Corpus + + + align:start position:0% +Coral equals Corpus +parse + + align:start position:0% + + + + align:start position:0% + +C and there are all the CRS with 11 in + + align:start position:0% +C and there are all the CRS with 11 in + + + align:start position:0% +C and there are all the CRS with 11 in +the name so these are just some things + + align:start position:0% +the name so these are just some things + + + align:start position:0% +the name so these are just some things +that you could um be working with and + + align:start position:0% +that you could um be working with and + + + align:start position:0% +that you could um be working with and +you can even this is a small enough + + align:start position:0% +you can even this is a small enough + + + align:start position:0% +you can even this is a small enough +number we can show each of + + align:start position:0% +number we can show each of + + + align:start position:0% +number we can show each of +them and I'll take a little bit of time + + align:start position:0% +them and I'll take a little bit of time + + + align:start position:0% +them and I'll take a little bit of time +but we'll start getting to see all all + + align:start position:0% +but we'll start getting to see all all + + + align:start position:0% +but we'll start getting to see all all +the crows in a + + align:start position:0% +the crows in a + + + align:start position:0% +the crows in a +piece our friends at Intel bum bum bum + + align:start position:0% +piece our friends at Intel bum bum bum + + + align:start position:0% +piece our friends at Intel bum bum bum +bum have created a tutorial on how you + + align:start position:0% +bum have created a tutorial on how you + + + align:start position:0% +bum have created a tutorial on how you +can use B Cals and work through the + + align:start position:0% +can use B Cals and work through the + + + align:start position:0% +can use B Cals and work through the +iterators and explore the data and begin + + align:start position:0% +iterators and explore the data and begin + + + align:start position:0% +iterators and explore the data and begin +looking on emotion recognition and so on + + align:start position:0% +looking on emotion recognition and so on + + + align:start position:0% +looking on emotion recognition and so on +from the bach corals and even do + + align:start position:0% +from the bach corals and even do + + + align:start position:0% +from the bach corals and even do +artificial intelligence and plot various + + align:start position:0% +artificial intelligence and plot various + + + align:start position:0% +artificial intelligence and plot various +things we'll show you this in a second + + align:start position:0% +things we'll show you this in a second + + + align:start position:0% +things we'll show you this in a second +and Pitch throughout tie very short + + align:start position:0% +and Pitch throughout tie very short + + + align:start position:0% +and Pitch throughout tie very short +video thanks for watching \ No newline at end of file diff --git a/BCQ9h1PxW08.txt b/BCQ9h1PxW08.txt new file mode 100644 index 0000000000000000000000000000000000000000..91576a521f2028b10cc16781df49cb0859006eb0 --- /dev/null +++ b/BCQ9h1PxW08.txt @@ -0,0 +1,1971 @@ +align:start position:0% + +welcome back to 8701 + + align:start position:0% +welcome back to 8701 + + + align:start position:0% +welcome back to 8701 +in this video we talk about nuclear + + align:start position:0% +in this video we talk about nuclear + + + align:start position:0% +in this video we talk about nuclear +binding energies + + align:start position:0% +binding energies + + + align:start position:0% +binding energies +but before we get started on this topic + + align:start position:0% +but before we get started on this topic + + + align:start position:0% +but before we get started on this topic +i would like you + + align:start position:0% +i would like you + + + align:start position:0% +i would like you +to have a look at this table or this + + align:start position:0% +to have a look at this table or this + + + align:start position:0% +to have a look at this table or this +diagram which shows nuclear abundances + + align:start position:0% +diagram which shows nuclear abundances + + + align:start position:0% +diagram which shows nuclear abundances +in our + + align:start position:0% +in our + + + align:start position:0% +in our +solar system so how many atoms of the + + align:start position:0% +solar system so how many atoms of the + + + align:start position:0% +solar system so how many atoms of the +various types are + + align:start position:0% +various types are + + + align:start position:0% +various types are +present in our solar system and you see + + align:start position:0% +present in our solar system and you see + + + align:start position:0% +present in our solar system and you see +this super interesting + + align:start position:0% +this super interesting + + + align:start position:0% +this super interesting +structure most of it is is hydrogen here + + align:start position:0% +structure most of it is is hydrogen here + + + align:start position:0% +structure most of it is is hydrogen here +but and then there seems to be some sort + + align:start position:0% +but and then there seems to be some sort + + + align:start position:0% +but and then there seems to be some sort +of an excess of iron + + align:start position:0% +of an excess of iron + + + align:start position:0% +of an excess of iron +um and you know the stable goes all the + + align:start position:0% +um and you know the stable goes all the + + + align:start position:0% +um and you know the stable goes all the +way to let + + align:start position:0% +way to let + + + align:start position:0% +way to let +and beyond there's a little bit of a gap + + align:start position:0% +and beyond there's a little bit of a gap + + + align:start position:0% +and beyond there's a little bit of a gap +here + + align:start position:0% +here + + + align:start position:0% +here +so how is this possible how did this + + align:start position:0% +so how is this possible how did this + + + align:start position:0% +so how is this possible how did this +particle get there in the first place + + align:start position:0% +particle get there in the first place + + + align:start position:0% +particle get there in the first place +uh why is there some which are more + + align:start position:0% +uh why is there some which are more + + + align:start position:0% +uh why is there some which are more +frequent than others + + align:start position:0% +frequent than others + + + align:start position:0% +frequent than others +you know a very interesting question + + align:start position:0% +you know a very interesting question + + + align:start position:0% +you know a very interesting question +which we will be able to answer at the + + align:start position:0% +which we will be able to answer at the + + + align:start position:0% +which we will be able to answer at the +end of the discussion of nuclear physics + + align:start position:0% +end of the discussion of nuclear physics + + + align:start position:0% +end of the discussion of nuclear physics +and the first starting point is to + + align:start position:0% +and the first starting point is to + + + align:start position:0% +and the first starting point is to +understand why + + align:start position:0% +understand why + + + align:start position:0% +understand why +nuclei are stable in the first place + + align:start position:0% +nuclei are stable in the first place + + + align:start position:0% +nuclei are stable in the first place +what holds them together + + align:start position:0% +what holds them together + + + align:start position:0% +what holds them together +and that's the discussion of binding + + align:start position:0% +and that's the discussion of binding + + + align:start position:0% +and that's the discussion of binding +energies + + align:start position:0% +energies + + + align:start position:0% +energies +so we can just very simply write the + + align:start position:0% +so we can just very simply write the + + + align:start position:0% +so we can just very simply write the +binding energy + + align:start position:0% +binding energy + + + align:start position:0% +binding energy +down we just you know sum up all the + + align:start position:0% +down we just you know sum up all the + + + align:start position:0% +down we just you know sum up all the +ingredients + + align:start position:0% +ingredients + + + align:start position:0% +ingredients +the number of protons and electrons + + align:start position:0% +the number of protons and electrons + + + align:start position:0% +the number of protons and electrons +times z the number of + + align:start position:0% +times z the number of + + + align:start position:0% +times z the number of +neutrons aim the mass number minus z + + align:start position:0% +neutrons aim the mass number minus z + + + align:start position:0% +neutrons aim the mass number minus z +and then we subtract from this the mass + + align:start position:0% +and then we subtract from this the mass + + + align:start position:0% +and then we subtract from this the mass +of the nuclei itself + + align:start position:0% +of the nuclei itself + + + align:start position:0% +of the nuclei itself +what remains is the binding energy + + align:start position:0% +what remains is the binding energy + + + align:start position:0% +what remains is the binding energy +just for record the mass of the proton + + align:start position:0% +just for record the mass of the proton + + + align:start position:0% +just for record the mass of the proton +the mass of the proton the mass of the + + align:start position:0% +the mass of the proton the mass of the + + + align:start position:0% +the mass of the proton the mass of the +neutron you see that the neutron + + align:start position:0% +neutron you see that the neutron + + + align:start position:0% +neutron you see that the neutron +is slightly heavier than the proton and + + align:start position:0% +is slightly heavier than the proton and + + + align:start position:0% +is slightly heavier than the proton and +the neutron itself + + align:start position:0% +the neutron itself + + + align:start position:0% +the neutron itself +decays into the proton a free proton + + align:start position:0% +decays into the proton a free proton + + + align:start position:0% +decays into the proton a free proton +does not decay + + align:start position:0% +does not decay + + + align:start position:0% +does not decay +however inside the nucleus the proton + + align:start position:0% +however inside the nucleus the proton + + + align:start position:0% +however inside the nucleus the proton +can also decay + + align:start position:0% +can also decay + + + align:start position:0% +can also decay +and then we have the mass of the + + align:start position:0% +and then we have the mass of the + + + align:start position:0% +and then we have the mass of the +electron you see there's a factor of + + align:start position:0% +electron you see there's a factor of + + + align:start position:0% +electron you see there's a factor of +almost 2000 between the mass scales of + + align:start position:0% +almost 2000 between the mass scales of + + + align:start position:0% +almost 2000 between the mass scales of +an electron and the mass of the neutron + + align:start position:0% +an electron and the mass of the neutron + + + align:start position:0% +an electron and the mass of the neutron +so for all practical purposes we can + + align:start position:0% +so for all practical purposes we can + + + align:start position:0% +so for all practical purposes we can +ignore this but if it comes to precision + + align:start position:0% +ignore this but if it comes to precision + + + align:start position:0% +ignore this but if it comes to precision +measurements + + align:start position:0% +measurements + + + align:start position:0% +measurements +then the mass of the neutron which is + + align:start position:0% +then the mass of the neutron which is + + + align:start position:0% +then the mass of the neutron which is +half in mav + + align:start position:0% +half in mav + + + align:start position:0% +half in mav +becomes a of an electron which is half + + align:start position:0% +becomes a of an electron which is half + + + align:start position:0% +becomes a of an electron which is half +an mav becomes relevant + + align:start position:0% +an mav becomes relevant + + + align:start position:0% +an mav becomes relevant +this plot here shows the average binding + + align:start position:0% +this plot here shows the average binding + + + align:start position:0% +this plot here shows the average binding +energy per nuclei + + align:start position:0% +energy per nuclei + + + align:start position:0% +energy per nuclei +as a function of the mass number and you + + align:start position:0% +as a function of the mass number and you + + + align:start position:0% +as a function of the mass number and you +see that with the exception of those + + align:start position:0% +see that with the exception of those + + + align:start position:0% +see that with the exception of those +light elements you see that this is + + align:start position:0% +light elements you see that this is + + + align:start position:0% +light elements you see that this is +fairly stable + + align:start position:0% +fairly stable + + + align:start position:0% +fairly stable +and in the range of 7.5 to 9 mev + + align:start position:0% +and in the range of 7.5 to 9 mev + + + align:start position:0% +and in the range of 7.5 to 9 mev +you also see that there seem to be a + + align:start position:0% +you also see that there seem to be a + + + align:start position:0% +you also see that there seem to be a +maximum around iron + + align:start position:0% +maximum around iron + + + align:start position:0% +maximum around iron +um which then leads to you know an + + align:start position:0% +um which then leads to you know an + + + align:start position:0% +um which then leads to you know an +advantage + + align:start position:0% +advantage + + + align:start position:0% +advantage +in gaining energy when you or + + align:start position:0% +in gaining energy when you or + + + align:start position:0% +in gaining energy when you or +gaining energy going to lower energy + + align:start position:0% +gaining energy going to lower energy + + + align:start position:0% +gaining energy going to lower energy +state when you go in this direction and + + align:start position:0% +state when you go in this direction and + + + align:start position:0% +state when you go in this direction and +in this direction + + align:start position:0% +in this direction + + + align:start position:0% +in this direction +this part is called this part is called + + align:start position:0% +this part is called this part is called + + + align:start position:0% +this part is called this part is called +fission this part is called fusion both + + align:start position:0% +fission this part is called fusion both + + + align:start position:0% +fission this part is called fusion both +processes because we go to a + + align:start position:0% +processes because we go to a + + + align:start position:0% +processes because we go to a +more energy preferred state are possible + + align:start position:0% +more energy preferred state are possible + + + align:start position:0% +more energy preferred state are possible +and they're you know + + align:start position:0% + + + + align:start position:0% + +they they can be used in order to attain + + align:start position:0% +they they can be used in order to attain + + + align:start position:0% +they they can be used in order to attain +energy from nuclear processes + + align:start position:0% + + + + align:start position:0% + +this diagram here can be parameterized + + align:start position:0% +this diagram here can be parameterized + + + align:start position:0% +this diagram here can be parameterized +um and the rest of this video will talk + + align:start position:0% +um and the rest of this video will talk + + + align:start position:0% +um and the rest of this video will talk +about + + align:start position:0% +about + + + align:start position:0% +about +a very you know popular parametrization + + align:start position:0% +a very you know popular parametrization + + + align:start position:0% +a very you know popular parametrization +of the binding energy + + align:start position:0% +of the binding energy + + + align:start position:0% +of the binding energy +so this is semi-empirical um it's + + align:start position:0% +so this is semi-empirical um it's + + + align:start position:0% +so this is semi-empirical um it's +called the white sector formula because + + align:start position:0% +called the white sector formula because + + + align:start position:0% +called the white sector formula because +it was proposed by a german called + + align:start position:0% +it was proposed by a german called + + + align:start position:0% +it was proposed by a german called +whiteseeker + + align:start position:0% +whiteseeker + + + align:start position:0% +whiteseeker +sometimes it's called the semi empirical + + align:start position:0% +sometimes it's called the semi empirical + + + align:start position:0% +sometimes it's called the semi empirical +mass formula + + align:start position:0% +mass formula + + + align:start position:0% +mass formula +and sometimes the discussion is + + align:start position:0% +and sometimes the discussion is + + + align:start position:0% +and sometimes the discussion is +summarized as a little liquid + + align:start position:0% +summarized as a little liquid + + + align:start position:0% +summarized as a little liquid +drop model and you'll see why in a + + align:start position:0% +drop model and you'll see why in a + + + align:start position:0% +drop model and you'll see why in a +second + + align:start position:0% +second + + + align:start position:0% +second +what we see here is very similar to what + + align:start position:0% +what we see here is very similar to what + + + align:start position:0% +what we see here is very similar to what +before we can calculate the mass + + align:start position:0% +before we can calculate the mass + + + align:start position:0% +before we can calculate the mass +and from that the binding energy + + align:start position:0% +and from that the binding energy + + + align:start position:0% +and from that the binding energy +by having those first elements here and + + align:start position:0% +by having those first elements here and + + + align:start position:0% +by having those first elements here and +this part then here + + align:start position:0% +this part then here + + + align:start position:0% +this part then here +is our binding energies and there's one + + align:start position:0% +is our binding energies and there's one + + + align:start position:0% +is our binding energies and there's one +two three four + + align:start position:0% +two three four + + + align:start position:0% +two three four +five terms which we're discussing now on + + align:start position:0% +five terms which we're discussing now on + + + align:start position:0% +five terms which we're discussing now on +the next slide + + align:start position:0% +the next slide + + + align:start position:0% +the next slide +which gives what this is shown here is a + + align:start position:0% +which gives what this is shown here is a + + + align:start position:0% +which gives what this is shown here is a +parameterization + + align:start position:0% +parameterization + + + align:start position:0% +parameterization +um so you can fix the data and get a + + align:start position:0% +um so you can fix the data and get a + + + align:start position:0% +um so you can fix the data and get a +best estimate + + align:start position:0% +best estimate + + + align:start position:0% +best estimate +um for the individual parameters in this + + align:start position:0% +um for the individual parameters in this + + + align:start position:0% +um for the individual parameters in this +equation + + align:start position:0% +equation + + + align:start position:0% +equation +all right so as the name said liquid + + align:start position:0% +all right so as the name said liquid + + + align:start position:0% +all right so as the name said liquid +drop model + + align:start position:0% +drop model + + + align:start position:0% +drop model +we can think about in some essence about + + align:start position:0% +we can think about in some essence about + + + align:start position:0% +we can think about in some essence about +a nuclei nucle nucleolite + + align:start position:0% +a nuclei nucle nucleolite + + + align:start position:0% +a nuclei nucle nucleolite +an atom as being built out of a + + align:start position:0% +an atom as being built out of a + + + align:start position:0% +an atom as being built out of a +soup a liquid of protons and neutrons + + align:start position:0% +soup a liquid of protons and neutrons + + + align:start position:0% +soup a liquid of protons and neutrons +which are bound together + + align:start position:0% +which are bound together + + + align:start position:0% +which are bound together +so the first term which contributes to + + align:start position:0% +so the first term which contributes to + + + align:start position:0% +so the first term which contributes to +the binding energy is the so-called + + align:start position:0% +the binding energy is the so-called + + + align:start position:0% +the binding energy is the so-called +volume term + + align:start position:0% +volume term + + + align:start position:0% +volume term +this dominates the binding energy and is + + align:start position:0% +this dominates the binding energy and is + + + align:start position:0% +this dominates the binding energy and is +proportional to the number + + align:start position:0% +proportional to the number + + + align:start position:0% +proportional to the number +the mass number remember the mass number + + align:start position:0% +the mass number remember the mass number + + + align:start position:0% +the mass number remember the mass number +is proportional to the + + align:start position:0% +is proportional to the + + + align:start position:0% +is proportional to the +third power of the radius hence + + align:start position:0% +third power of the radius hence + + + align:start position:0% +third power of the radius hence +proportional to the volume + + align:start position:0% +proportional to the volume + + + align:start position:0% +proportional to the volume +of the of the nuclei + + align:start position:0% +of the of the nuclei + + + align:start position:0% +of the of the nuclei +and you know this contributes with about + + align:start position:0% +and you know this contributes with about + + + align:start position:0% +and you know this contributes with about +16 mev per nucleon for proton and + + align:start position:0% +16 mev per nucleon for proton and + + + align:start position:0% +16 mev per nucleon for proton and +neutron um from this we can conclude + + align:start position:0% +neutron um from this we can conclude + + + align:start position:0% +neutron um from this we can conclude +that the nuclear force must be very + + align:start position:0% +that the nuclear force must be very + + + align:start position:0% +that the nuclear force must be very +short range why is that + + align:start position:0% +short range why is that + + + align:start position:0% +short range why is that +because in order for the binding energy + + align:start position:0% +because in order for the binding energy + + + align:start position:0% +because in order for the binding energy +to depend dominantly on the volume + + align:start position:0% +to depend dominantly on the volume + + + align:start position:0% +to depend dominantly on the volume +the individual nucleis can only see its + + align:start position:0% +the individual nucleis can only see its + + + align:start position:0% +the individual nucleis can only see its +nearest neighbor + + align:start position:0% +nearest neighbor + + + align:start position:0% +nearest neighbor +so this corresponds to a short-range + + align:start position:0% +so this corresponds to a short-range + + + align:start position:0% +so this corresponds to a short-range +force + + align:start position:0% +force + + + align:start position:0% +force +which is roughly of the distance of two + + align:start position:0% +which is roughly of the distance of two + + + align:start position:0% +which is roughly of the distance of two +nuclei + + align:start position:0% +nuclei + + + align:start position:0% +nuclei +if any given nuclei would be able to see + + align:start position:0% +if any given nuclei would be able to see + + + align:start position:0% +if any given nuclei would be able to see +everybody else you would see a a term + + align:start position:0% +everybody else you would see a a term + + + align:start position:0% +everybody else you would see a a term +quadratic in the in + + align:start position:0% +quadratic in the in + + + align:start position:0% +quadratic in the in +in the in the number of nuclei and + + align:start position:0% +in the in the number of nuclei and + + + align:start position:0% +in the in the number of nuclei and +available um as a result of this you can + + align:start position:0% +available um as a result of this you can + + + align:start position:0% +available um as a result of this you can +calculate a central density + + align:start position:0% +calculate a central density + + + align:start position:0% +calculate a central density +which is about 0.17 nucleons + + align:start position:0% +which is about 0.17 nucleons + + + align:start position:0% +which is about 0.17 nucleons +per cubic fermi meters + + align:start position:0% +per cubic fermi meters + + + align:start position:0% +per cubic fermi meters +or an average distance between protons + + align:start position:0% +or an average distance between protons + + + align:start position:0% +or an average distance between protons +and neutrons + + align:start position:0% +and neutrons + + + align:start position:0% +and neutrons +of 1.8 empty meters + + align:start position:0% +of 1.8 empty meters + + + align:start position:0% +of 1.8 empty meters +okay so they're really tightly packed + + align:start position:0% +okay so they're really tightly packed + + + align:start position:0% +okay so they're really tightly packed +the size of a proton is about + + align:start position:0% +the size of a proton is about + + + align:start position:0% +the size of a proton is about +a femtometer + + align:start position:0% + + + + align:start position:0% + +all right however + + align:start position:0% +all right however + + + align:start position:0% +all right however +the proton the neutrons which are on the + + align:start position:0% +the proton the neutrons which are on the + + + align:start position:0% +the proton the neutrons which are on the +surface of this + + align:start position:0% +surface of this + + + align:start position:0% +surface of this +uh construct they see less + + align:start position:0% +uh construct they see less + + + align:start position:0% +uh construct they see less +nuclear they see um less nuclear + + align:start position:0% +nuclear they see um less nuclear + + + align:start position:0% +nuclear they see um less nuclear +nucleons around them + + align:start position:0% +nucleons around them + + + align:start position:0% +nucleons around them +so if therefore the binding energy needs + + align:start position:0% +so if therefore the binding energy needs + + + align:start position:0% +so if therefore the binding energy needs +to be reduced + + align:start position:0% +to be reduced + + + align:start position:0% +to be reduced +and it needs to be reduced with the area + + align:start position:0% +and it needs to be reduced with the area + + + align:start position:0% +and it needs to be reduced with the area +the area of of the surface of the of the + + align:start position:0% +the area of of the surface of the of the + + + align:start position:0% +the area of of the surface of the of the +nucleus so it needs to be proportional + + align:start position:0% +nucleus so it needs to be proportional + + + align:start position:0% +nucleus so it needs to be proportional +to r square + + align:start position:0% +to r square + + + align:start position:0% +to r square +and therefore proportional to a the mass + + align:start position:0% +and therefore proportional to a the mass + + + align:start position:0% +and therefore proportional to a the mass +number + + align:start position:0% +number + + + align:start position:0% +number +to the two thirds okay + + align:start position:0% +to the two thirds okay + + + align:start position:0% +to the two thirds okay +then the protons in the nucleus + + align:start position:0% +then the protons in the nucleus + + + align:start position:0% +then the protons in the nucleus +they are electrically charged so they + + align:start position:0% +they are electrically charged so they + + + align:start position:0% +they are electrically charged so they +want to get it apart + + align:start position:0% +want to get it apart + + + align:start position:0% +want to get it apart +and that itself also reduces the binding + + align:start position:0% +and that itself also reduces the binding + + + align:start position:0% +and that itself also reduces the binding +energy so this is proportional to the + + align:start position:0% +energy so this is proportional to the + + + align:start position:0% +energy so this is proportional to the +number of charges squared + + align:start position:0% +number of charges squared + + + align:start position:0% +number of charges squared +and then you normalize this by the + + align:start position:0% +and then you normalize this by the + + + align:start position:0% +and then you normalize this by the +radius so charged square over + + align:start position:0% +radius so charged square over + + + align:start position:0% +radius so charged square over +no normal charge square over r + + align:start position:0% +no normal charge square over r + + + align:start position:0% +no normal charge square over r +so this is q square over r + + align:start position:0% + + + + align:start position:0% + +all right there's two more terms which + + align:start position:0% +all right there's two more terms which + + + align:start position:0% +all right there's two more terms which +are + + align:start position:0% +are + + + align:start position:0% +are +quite interesting the first one is + + align:start position:0% +quite interesting the first one is + + + align:start position:0% +quite interesting the first one is +sensitive to the asymmetry + + align:start position:0% +sensitive to the asymmetry + + + align:start position:0% +sensitive to the asymmetry +between the number of neutrons and the + + align:start position:0% +between the number of neutrons and the + + + align:start position:0% +between the number of neutrons and the +number of protons + + align:start position:0% +number of protons + + + align:start position:0% +number of protons +and it can be explained by the pauli + + align:start position:0% +and it can be explained by the pauli + + + align:start position:0% +and it can be explained by the pauli +exclusion principle + + align:start position:0% +exclusion principle + + + align:start position:0% +exclusion principle +which allows only two identical fermions + + align:start position:0% +which allows only two identical fermions + + + align:start position:0% +which allows only two identical fermions +neutrons or two protons to occupy the + + align:start position:0% +neutrons or two protons to occupy the + + + align:start position:0% +neutrons or two protons to occupy the +same energy state so you basically fill + + align:start position:0% +same energy state so you basically fill + + + align:start position:0% +same energy state so you basically fill +up the energy states + + align:start position:0% +up the energy states + + + align:start position:0% +up the energy states +now as is shown in this picture here you + + align:start position:0% +now as is shown in this picture here you + + + align:start position:0% +now as is shown in this picture here you +reach + + align:start position:0% +reach + + + align:start position:0% +reach +a the lowest energy state if the number + + align:start position:0% +a the lowest energy state if the number + + + align:start position:0% +a the lowest energy state if the number +of neutrons + + align:start position:0% +of neutrons + + + align:start position:0% +of neutrons +and the number of protons is actually + + align:start position:0% +and the number of protons is actually + + + align:start position:0% +and the number of protons is actually +the same you have higher energies if + + align:start position:0% +the same you have higher energies if + + + align:start position:0% +the same you have higher energies if +there is + + align:start position:0% +there is + + + align:start position:0% +there is +enough symmetry between those two + + align:start position:0% +enough symmetry between those two + + + align:start position:0% +enough symmetry between those two +numbers so we have yet another term + + align:start position:0% +numbers so we have yet another term + + + align:start position:0% +numbers so we have yet another term +which is sensitive to the asymmetry + + align:start position:0% +which is sensitive to the asymmetry + + + align:start position:0% +which is sensitive to the asymmetry +between the number of neutrons and + + align:start position:0% +between the number of neutrons and + + + align:start position:0% +between the number of neutrons and +protons + + align:start position:0% +protons + + + align:start position:0% +protons +which reduces the binding energy + + align:start position:0% +which reduces the binding energy + + + align:start position:0% +which reduces the binding energy +and last but not least the pairing term + + align:start position:0% +and last but not least the pairing term + + + align:start position:0% +and last but not least the pairing term +which has + + align:start position:0% +which has + + + align:start position:0% +which has +a very similar origin so what we're + + align:start position:0% +a very similar origin so what we're + + + align:start position:0% +a very similar origin so what we're +looking at here is + + align:start position:0% +looking at here is + + + align:start position:0% +looking at here is +you know the energy is lower if you have + + align:start position:0% +you know the energy is lower if you have + + + align:start position:0% +you know the energy is lower if you have +an even number of neutrons + + align:start position:0% +an even number of neutrons + + + align:start position:0% +an even number of neutrons +or protons it's higher and we have an + + align:start position:0% +or protons it's higher and we have an + + + align:start position:0% +or protons it's higher and we have an +odd number so you can have an odd number + + align:start position:0% +odd number so you can have an odd number + + + align:start position:0% +odd number so you can have an odd number +for the protons + + align:start position:0% +for the protons + + + align:start position:0% +for the protons +or the neutrons in which case a is odd + + align:start position:0% +or the neutrons in which case a is odd + + + align:start position:0% +or the neutrons in which case a is odd +and + + align:start position:0% +and + + + align:start position:0% +and +the worst case or the the worst energy + + align:start position:0% +the worst case or the the worst energy + + + align:start position:0% +the worst case or the the worst energy +state is achieved + + align:start position:0% +state is achieved + + + align:start position:0% +state is achieved +having both the protons and the neutrons + + align:start position:0% +having both the protons and the neutrons + + + align:start position:0% +having both the protons and the neutrons +um + + align:start position:0% +um + + + align:start position:0% +um +hot so that's why this is a little bit + + align:start position:0% +hot so that's why this is a little bit + + + align:start position:0% +hot so that's why this is a little bit +more complicated way to write this + + align:start position:0% +more complicated way to write this + + + align:start position:0% +more complicated way to write this +you have the three different cases uh + + align:start position:0% +you have the three different cases uh + + + align:start position:0% +you have the three different cases uh +number of protons number of neutrons + + align:start position:0% +number of protons number of neutrons + + + align:start position:0% +number of protons number of neutrons +even + + align:start position:0% +even + + + align:start position:0% +even +um a odd or both z and n + + align:start position:0% +um a odd or both z and n + + + align:start position:0% +um a odd or both z and n +odd in which case a is even + + align:start position:0% +odd in which case a is even + + + align:start position:0% +odd in which case a is even +just to add to the confusion a little + + align:start position:0% +just to add to the confusion a little + + + align:start position:0% +just to add to the confusion a little +bit all right then you can make a + + align:start position:0% +bit all right then you can make a + + + align:start position:0% +bit all right then you can make a +drawing + + align:start position:0% +drawing + + + align:start position:0% +drawing +of the binding energy as a function of + + align:start position:0% +of the binding energy as a function of + + + align:start position:0% +of the binding energy as a function of +the mass + + align:start position:0% +the mass + + + align:start position:0% +the mass +and you see again those individual terms + + align:start position:0% +and you see again those individual terms + + + align:start position:0% +and you see again those individual terms +the volume energy energy + + align:start position:0% +the volume energy energy + + + align:start position:0% +the volume energy energy +the volume term your constant the volume + + align:start position:0% +the volume term your constant the volume + + + align:start position:0% +the volume term your constant the volume +plus surface reduced + + align:start position:0% +plus surface reduced + + + align:start position:0% +plus surface reduced +the volume plus surface column further + + align:start position:0% +the volume plus surface column further + + + align:start position:0% +the volume plus surface column further +reduced and then all terms + + align:start position:0% +reduced and then all terms + + + align:start position:0% +reduced and then all terms +put together here and you see again this + + align:start position:0% +put together here and you see again this + + + align:start position:0% +put together here and you see again this +binding energy + + align:start position:0% +binding energy + + + align:start position:0% +binding energy +parameterization which we just discussed + + align:start position:0% +parameterization which we just discussed + + + align:start position:0% +parameterization which we just discussed +we saw the actual values + + align:start position:0% +we saw the actual values + + + align:start position:0% +we saw the actual values +with the maximum maximum around here + + align:start position:0% +with the maximum maximum around here + + + align:start position:0% +with the maximum maximum around here +for for iron \ No newline at end of file diff --git a/CUygqWS7occ.txt b/CUygqWS7occ.txt new file mode 100644 index 0000000000000000000000000000000000000000..bf7cea47acd255a1ba0c88b4d5ed8e1d5c97bc75 --- /dev/null +++ b/CUygqWS7occ.txt @@ -0,0 +1,11198 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu So today we're going to talk + + align:start position:0% +ocw.mit.edu So today we're going to talk + + + align:start position:0% +ocw.mit.edu So today we're going to talk +about the + + align:start position:0% +about the + + + align:start position:0% +about the +uh dynamics of running and ask questions + + align:start position:0% +uh dynamics of running and ask questions + + + align:start position:0% +uh dynamics of running and ask questions +as freely as possible and also if my + + align:start position:0% +as freely as possible and also if my + + + align:start position:0% +as freely as possible and also if my +handwriting is bad let me know um it + + align:start position:0% +handwriting is bad let me know um it + + + align:start position:0% +handwriting is bad let me know um it +generally is + + align:start position:0% + + + + align:start position:0% + +so so this is actually a really fun + + align:start position:0% +so so this is actually a really fun + + + align:start position:0% +so so this is actually a really fun +lecture um we have a lot of cool videos + + align:start position:0% +lecture um we have a lot of cool videos + + + align:start position:0% +lecture um we have a lot of cool videos +I don't know if you seen rer Hoppers and + + align:start position:0% +I don't know if you seen rer Hoppers and + + + align:start position:0% +I don't know if you seen rer Hoppers and +stuff before but we have some cool + + align:start position:0% +stuff before but we have some cool + + + align:start position:0% +stuff before but we have some cool +models and some cool analysis too so + + align:start position:0% +models and some cool analysis too so + + + align:start position:0% +models and some cool analysis too so +hopefully uh you'll be as excited as I + + align:start position:0% +hopefully uh you'll be as excited as I + + + align:start position:0% +hopefully uh you'll be as excited as I +am to uh participate in this learning + + align:start position:0% +am to uh participate in this learning + + + align:start position:0% +am to uh participate in this learning +experience so here we + + align:start position:0% +experience so here we + + + align:start position:0% +experience so here we +go so the uh the basic model we look at + + align:start position:0% +go so the uh the basic model we look at + + + align:start position:0% +go so the uh the basic model we look at +today in several different sort of + + align:start position:0% +today in several different sort of + + + align:start position:0% +today in several different sort of +versions of this is the slip + + align:start position:0% +versions of this is the slip + + + align:start position:0% +versions of this is the slip +model this is the springloaded inverted + + align:start position:0% + + + + align:start position:0% + +pendulum + + align:start position:0% +pendulum + + + align:start position:0% +pendulum +right + + align:start position:0% +right + + + align:start position:0% +right +um it's sort of like the uh running + + align:start position:0% +um it's sort of like the uh running + + + align:start position:0% +um it's sort of like the uh running +version of the rimless wheel or compus + + align:start position:0% +version of the rimless wheel or compus + + + align:start position:0% +version of the rimless wheel or compus +gate um it's pretty simple you just have + + align:start position:0% +gate um it's pretty simple you just have + + + align:start position:0% +gate um it's pretty simple you just have +a mass at the end of a pendulum you have + + align:start position:0% +a mass at the end of a pendulum you have + + + align:start position:0% +a mass at the end of a pendulum you have +a spring here spring constant k + + align:start position:0% +a spring here spring constant k + + + align:start position:0% +a spring here spring constant k +um the spring is a rest + + align:start position:0% + + + + align:start position:0% + +length R not and a uh said spring + + align:start position:0% +length R not and a uh said spring + + + align:start position:0% +length R not and a uh said spring +constant and so then this the + + align:start position:0% +constant and so then this the + + + align:start position:0% +constant and so then this the +coordinates then are this length + + align:start position:0% +coordinates then are this length + + + align:start position:0% +coordinates then are this length +R + + align:start position:0% +R + + + align:start position:0% +R +and the angle Theta from the upright + + align:start position:0% +and the angle Theta from the upright + + + align:start position:0% +and the angle Theta from the upright +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the uh what we're going to want to + + align:start position:0% +so the uh what we're going to want to + + + align:start position:0% +so the uh what we're going to want to +look at here is not just this model but + + align:start position:0% +look at here is not just this model but + + + align:start position:0% +look at here is not just this model but +also in the same way we had for the uh + + align:start position:0% +also in the same way we had for the uh + + + align:start position:0% +also in the same way we had for the uh +rless wheel as you remember is a + + align:start position:0% +rless wheel as you remember is a + + + align:start position:0% +rless wheel as you remember is a +1D iterated + + align:start position:0% +1D iterated + + + align:start position:0% +1D iterated +map so you probably remember that for + + align:start position:0% +map so you probably remember that for + + + align:start position:0% +map so you probably remember that for +the uh compis gate that lets you look at + + align:start position:0% +the uh compis gate that lets you look at + + + align:start position:0% +the uh compis gate that lets you look at +the stability of it and there's all + + align:start position:0% +the stability of it and there's all + + + align:start position:0% +the stability of it and there's all +these interesting dynamics that are + + align:start position:0% +these interesting dynamics that are + + + align:start position:0% +these interesting dynamics that are +captured by that simple + + align:start position:0% +captured by that simple + + + align:start position:0% +captured by that simple +system um so we're going to look at the + + align:start position:0% +system um so we're going to look at the + + + align:start position:0% +system um so we're going to look at the +one iterated map and the other thing I'm + + align:start position:0% +one iterated map and the other thing I'm + + + align:start position:0% +one iterated map and the other thing I'm +going to try to convince you is that + + align:start position:0% +going to try to convince you is that + + + align:start position:0% +going to try to convince you is that +this is + + align:start position:0% +this is + + + align:start position:0% +this is +a biologically plausible + + align:start position:0% +a biologically plausible + + + align:start position:0% +a biologically plausible +system + + align:start position:0% + + + + align:start position:0% + +so if you look at the rimless wheel it + + align:start position:0% +so if you look at the rimless wheel it + + + align:start position:0% +so if you look at the rimless wheel it +sort of feels like something that's + + align:start position:0% +sort of feels like something that's + + + align:start position:0% +sort of feels like something that's +walking um confiscate even more so and + + align:start position:0% +walking um confiscate even more so and + + + align:start position:0% +walking um confiscate even more so and +your knees these things all sort of just + + align:start position:0% +your knees these things all sort of just + + + align:start position:0% +your knees these things all sort of just +intuitively you can believe that they're + + align:start position:0% +intuitively you can believe that they're + + + align:start position:0% +intuitively you can believe that they're +sorry a uh well that's probably going to + + align:start position:0% +sorry a uh well that's probably going to + + + align:start position:0% +sorry a uh well that's probably going to +be bad that you could believe that + + align:start position:0% +be bad that you could believe that + + + align:start position:0% +be bad that you could believe that +they're uh that they're walking systems + + align:start position:0% +they're uh that they're walking systems + + + align:start position:0% +they're uh that they're walking systems +but this one maybe doesn't seem to you + + align:start position:0% +but this one maybe doesn't seem to you + + + align:start position:0% +but this one maybe doesn't seem to you +immediately like a a running system + + align:start position:0% +immediately like a a running system + + + align:start position:0% +immediately like a a running system +maybe it seems like a jumping system or + + align:start position:0% +maybe it seems like a jumping system or + + + align:start position:0% +maybe it seems like a jumping system or +bouncing system or something but + + align:start position:0% +bouncing system or something but + + + align:start position:0% +bouncing system or something but +actually it actually is a pretty good + + align:start position:0% +actually it actually is a pretty good + + + align:start position:0% +actually it actually is a pretty good +model for uh running systems so the two + + align:start position:0% +model for uh running systems so the two + + + align:start position:0% +model for uh running systems so the two +things that we're going to have to go + + align:start position:0% +things that we're going to have to go + + + align:start position:0% +things that we're going to have to go +through how do you get a 1D iterated map + + align:start position:0% +through how do you get a 1D iterated map + + + align:start position:0% +through how do you get a 1D iterated map +now that maybe is a bit surprising for + + align:start position:0% +now that maybe is a bit surprising for + + + align:start position:0% +now that maybe is a bit surprising for +you because if you look at this uh the + + align:start position:0% +you because if you look at this uh the + + + align:start position:0% +you because if you look at this uh the +full State Bas of this inverted pendulum + + align:start position:0% +full State Bas of this inverted pendulum + + + align:start position:0% +full State Bas of this inverted pendulum +right now um it has states of R + + align:start position:0% +right now um it has states of R + + + align:start position:0% +right now um it has states of R +sorry R Theta r dot Theta dot now that's + + align:start position:0% +sorry R Theta r dot Theta dot now that's + + + align:start position:0% +sorry R Theta r dot Theta dot now that's +four parameters so when you you remember + + align:start position:0% +four parameters so when you you remember + + + align:start position:0% +four parameters so when you you remember +when you slice through and you pick a a + + align:start position:0% +when you slice through and you pick a a + + + align:start position:0% +when you slice through and you pick a a +surface of section you can cut it down + + align:start position:0% +surface of section you can cut it down + + + align:start position:0% +surface of section you can cut it down +by one so for the this wheel you know + + align:start position:0% +by one so for the this wheel you know + + + align:start position:0% +by one so for the this wheel you know +maybe you have Theta Theta dot you cut + + align:start position:0% +maybe you have Theta Theta dot you cut + + + align:start position:0% +maybe you have Theta Theta dot you cut +out Theta Dot and you're in pretty good + + align:start position:0% +out Theta Dot and you're in pretty good + + + align:start position:0% +out Theta Dot and you're in pretty good +shape here we have four but we're + + align:start position:0% +shape here we have four but we're + + + align:start position:0% +shape here we have four but we're +actually going to show that we can + + align:start position:0% +actually going to show that we can + + + align:start position:0% +actually going to show that we can +actually get this down to a 1D system + + align:start position:0% +actually get this down to a 1D system + + + align:start position:0% +actually get this down to a 1D system +and actually look at the iterated map + + align:start position:0% +and actually look at the iterated map + + + align:start position:0% +and actually look at the iterated map +for this so that's kind of cool um and + + align:start position:0% +for this so that's kind of cool um and + + + align:start position:0% +for this so that's kind of cool um and +the other thing is that also this system + + align:start position:0% +the other thing is that also this system + + + align:start position:0% +the other thing is that also this system +bounces and takes off so actually we + + align:start position:0% +bounces and takes off so actually we + + + align:start position:0% +bounces and takes off so actually we +need two coordinate systems one is this + + align:start position:0% +need two coordinate systems one is this + + + align:start position:0% +need two coordinate systems one is this +R Theta R do theta Dot and other one + + align:start position:0% +R Theta R do theta Dot and other one + + + align:start position:0% +R Theta R do theta Dot and other one +when it's in Flight we're going to have + + align:start position:0% +when it's in Flight we're going to have + + + align:start position:0% +when it's in Flight we're going to have +x y x dot y dot all right and both of + + align:start position:0% +x y x dot y dot all right and both of + + + align:start position:0% +x y x dot y dot all right and both of +these are 4D so you have to deal with + + align:start position:0% +these are 4D so you have to deal with + + + align:start position:0% +these are 4D so you have to deal with +that either way um but first the uh + + align:start position:0% +that either way um but first the uh + + + align:start position:0% +that either way um but first the uh +convincing part + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so the justification here comes from a + + align:start position:0% +so the justification here comes from a + + + align:start position:0% +so the justification here comes from a +field called comparative + + align:start position:0% + + + + align:start position:0% + +biomechanics now this is + + align:start position:0% +biomechanics now this is + + + align:start position:0% +biomechanics now this is +a pretty cool field + + align:start position:0% + + + + align:start position:0% + +um they uh they look at all sorts of + + align:start position:0% +um they uh they look at all sorts of + + + align:start position:0% +um they uh they look at all sorts of +different systems and try to sort of + + align:start position:0% +different systems and try to sort of + + + align:start position:0% +different systems and try to sort of +figure out these commonalities in the + + align:start position:0% +figure out these commonalities in the + + + align:start position:0% +figure out these commonalities in the +kinematics the Dynamics or certain + + align:start position:0% +kinematics the Dynamics or certain + + + align:start position:0% +kinematics the Dynamics or certain +properties and figure out sort of what + + align:start position:0% +properties and figure out sort of what + + + align:start position:0% +properties and figure out sort of what +are the fundamental you know common + + align:start position:0% +are the fundamental you know common + + + align:start position:0% +are the fundamental you know common +features of these these uh of these + + align:start position:0% +features of these these uh of these + + + align:start position:0% +features of these these uh of these +different biological systems so this + + align:start position:0% +different biological systems so this + + + align:start position:0% +different biological systems so this +running model um actually you can look + + align:start position:0% +running model um actually you can look + + + align:start position:0% +running model um actually you can look +at it in the context of things + + align:start position:0% + + + + align:start position:0% + +from cockroaches which are on the order + + align:start position:0% +from cockroaches which are on the order + + + align:start position:0% +from cockroaches which are on the order +of + + align:start position:0% +of + + + align:start position:0% +of +uh a gram in Mass + + align:start position:0% + + + + align:start position:0% + +horses which are on the order of well + + align:start position:0% +horses which are on the order of well + + + align:start position:0% +horses which are on the order of well +some of them at least are 135 kg it's + + align:start position:0% +some of them at least are 135 kg it's + + + align:start position:0% +some of them at least are 135 kg it's +not that heavy really you imagine maybe + + align:start position:0% +not that heavy really you imagine maybe + + + align:start position:0% +not that heavy really you imagine maybe +heavier horses um crabs now you can + + align:start position:0% +heavier horses um crabs now you can + + + align:start position:0% +heavier horses um crabs now you can +think about the kinematics of these + + align:start position:0% +think about the kinematics of these + + + align:start position:0% +think about the kinematics of these +systems and just how wildly different + + align:start position:0% +systems and just how wildly different + + + align:start position:0% +systems and just how wildly different +they are cockroach is six leg bouncing + + align:start position:0% +they are cockroach is six leg bouncing + + + align:start position:0% +they are cockroach is six leg bouncing +all around follows a tripod gate horses + + align:start position:0% +all around follows a tripod gate horses + + + align:start position:0% +all around follows a tripod gate horses +quadrupeds um crabs actually they run + + align:start position:0% +quadrupeds um crabs actually they run + + + align:start position:0% +quadrupeds um crabs actually they run +sideways um with eight legs well this is + + align:start position:0% +sideways um with eight legs well this is + + + align:start position:0% +sideways um with eight legs well this is +different information so I want put + + align:start position:0% +different information so I want put + + + align:start position:0% +different information so I want put +there but crabs actually will run + + align:start position:0% +there but crabs actually will run + + + align:start position:0% +there but crabs actually will run +sideways using their eight legs it's + + align:start position:0% +sideways using their eight legs it's + + + align:start position:0% +sideways using their eight legs it's +actually pretty cool I don't know if + + align:start position:0% +actually pretty cool I don't know if + + + align:start position:0% +actually pretty cool I don't know if +you've seen it but um and then humans + + align:start position:0% +you've seen it but um and then humans + + + align:start position:0% +you've seen it but um and then humans +which maybe is the one that we most well + + align:start position:0% +which maybe is the one that we most well + + + align:start position:0% +which maybe is the one that we most well +that's probably unfairly biocentric so + + align:start position:0% +that's probably unfairly biocentric so + + + align:start position:0% +that's probably unfairly biocentric so +there + + align:start position:0% +there + + + align:start position:0% +there +humans um and all of these despite the + + align:start position:0% +humans um and all of these despite the + + + align:start position:0% +humans um and all of these despite the +very different kinematics despite what + + align:start position:0% +very different kinematics despite what + + + align:start position:0% +very different kinematics despite what +this five orders of magnitude in Mass um + + align:start position:0% +this five orders of magnitude in Mass um + + + align:start position:0% +this five orders of magnitude in Mass um +they all have incredible Dynamic + + align:start position:0% + + + + align:start position:0% + +similarity let's hope I'm not getting + + align:start position:0% +similarity let's hope I'm not getting + + + align:start position:0% +similarity let's hope I'm not getting +graded on spelling cuz I'm pretty sure + + align:start position:0% +graded on spelling cuz I'm pretty sure + + + align:start position:0% +graded on spelling cuz I'm pretty sure +that's way + + align:start position:0% + + + + align:start position:0% + +off um and so if you look at them in the + + align:start position:0% +off um and so if you look at them in the + + + align:start position:0% +off um and so if you look at them in the +right way you can actually see that all + + align:start position:0% +right way you can actually see that all + + + align:start position:0% +right way you can actually see that all +of these systems cockroaches horses + + align:start position:0% +of these systems cockroaches horses + + + align:start position:0% +of these systems cockroaches horses +crabs camels cats bunny rabbits all + + align:start position:0% +crabs camels cats bunny rabbits all + + + align:start position:0% +crabs camels cats bunny rabbits all +these things actually look very similar + + align:start position:0% +these things actually look very similar + + + align:start position:0% +these things actually look very similar +um + + align:start position:0% + + + + align:start position:0% + +and so Bob full um some of you may know + + align:start position:0% +and so Bob full um some of you may know + + + align:start position:0% +and so Bob full um some of you may know +Bob full I think Berkeley um he looks at + + align:start position:0% +Bob full I think Berkeley um he looks at + + + align:start position:0% +Bob full I think Berkeley um he looks at +a lot of these things especially the + + align:start position:0% +a lot of these things especially the + + + align:start position:0% +a lot of these things especially the +cockroach he has a lot of cool work on + + align:start position:0% +cockroach he has a lot of cool work on + + + align:start position:0% +cockroach he has a lot of cool work on +cockroaches + + align:start position:0% +cockroaches + + + align:start position:0% +cockroaches +um and he also has this paper + + align:start position:0% +um and he also has this paper + + + align:start position:0% +um and he also has this paper +which see if I + + align:start position:0% +which see if I + + + align:start position:0% +which see if I +can what page is this + + align:start position:0% +can what page is this + + + align:start position:0% +can what page is this +on sorry here uh there we + + align:start position:0% +on sorry here uh there we + + + align:start position:0% +on sorry here uh there we +go is that clear up + + align:start position:0% +go is that clear up + + + align:start position:0% +go is that clear up +there oh + + align:start position:0% +there oh + + + align:start position:0% +there oh +sorry so here you can look at the uh let + + align:start position:0% +sorry so here you can look at the uh let + + + align:start position:0% +sorry so here you can look at the uh let +me dim the lights a bit um if you look + + align:start position:0% +me dim the lights a bit um if you look + + + align:start position:0% +me dim the lights a bit um if you look +at + + align:start position:0% +at + + + align:start position:0% +at +the uh plot on the left this is speed + + align:start position:0% +the uh plot on the left this is speed + + + align:start position:0% +the uh plot on the left this is speed +and the stride length so if you plot + + align:start position:0% +and the stride length so if you plot + + + align:start position:0% +and the stride length so if you plot +speed and stride lengths here they've + + align:start position:0% +speed and stride lengths here they've + + + align:start position:0% +speed and stride lengths here they've +got Geral dogs and camels but you can do + + align:start position:0% +got Geral dogs and camels but you can do + + + align:start position:0% +got Geral dogs and camels but you can do +this for a very wide variety of systems + + align:start position:0% +this for a very wide variety of systems + + + align:start position:0% +this for a very wide variety of systems +um you can see that they're sort of all + + align:start position:0% +um you can see that they're sort of all + + + align:start position:0% +um you can see that they're sort of all +bounced over the place um you don't have + + align:start position:0% +bounced over the place um you don't have + + + align:start position:0% +bounced over the place um you don't have +I mean they're all behaving very + + align:start position:0% +I mean they're all behaving very + + + align:start position:0% +I mean they're all behaving very +differently that's so that's not + + align:start position:0% +differently that's so that's not + + + align:start position:0% +differently that's so that's not +necessar the right way to look at them + + align:start position:0% +necessar the right way to look at them + + + align:start position:0% +necessar the right way to look at them +if you want to sort of see what is what + + align:start position:0% +if you want to sort of see what is what + + + align:start position:0% +if you want to sort of see what is what +is fundamentally similar between them if + + align:start position:0% +is fundamentally similar between them if + + + align:start position:0% +is fundamentally similar between them if +you look at the right this is the froud + + align:start position:0% +you look at the right this is the froud + + + align:start position:0% +you look at the right this is the froud +number um in this case you can see it's + + align:start position:0% +number um in this case you can see it's + + + align:start position:0% +number um in this case you can see it's +just the ratio well it's two times the + + align:start position:0% +just the ratio well it's two times the + + + align:start position:0% +just the ratio well it's two times the +ratio of uh kinetic energy to uh + + align:start position:0% +ratio of uh kinetic energy to uh + + + align:start position:0% +ratio of uh kinetic energy to uh +potential energy so it's just this + + align:start position:0% +potential energy so it's just this + + + align:start position:0% +potential energy so it's just this +non-dimensional quantity if you plot + + align:start position:0% +non-dimensional quantity if you plot + + + align:start position:0% +non-dimensional quantity if you plot +this and you look at the relative stride + + align:start position:0% +this and you look at the relative stride + + + align:start position:0% +this and you look at the relative stride +length which + + align:start position:0% +length which + + + align:start position:0% +length which +is you can see they all sort of collapse + + align:start position:0% +is you can see they all sort of collapse + + + align:start position:0% +is you can see they all sort of collapse +very tightly on this line and so that's + + align:start position:0% +very tightly on this line and so that's + + + align:start position:0% +very tightly on this line and so that's +actually sort of like that's impressive + + align:start position:0% +actually sort of like that's impressive + + + align:start position:0% +actually sort of like that's impressive +agreement you see that these are you + + align:start position:0% +agreement you see that these are you + + + align:start position:0% +agreement you see that these are you +know camels dogs and geros are all sort + + align:start position:0% +know camels dogs and geros are all sort + + + align:start position:0% +know camels dogs and geros are all sort +of look very similar when you look at + + align:start position:0% +of look very similar when you look at + + + align:start position:0% +of look very similar when you look at +them in this sort of non-dimensional way + + align:start position:0% +them in this sort of non-dimensional way + + + align:start position:0% +them in this sort of non-dimensional way +so all these uh these systems orders of + + align:start position:0% +so all these uh these systems orders of + + + align:start position:0% +so all these uh these systems orders of +magnitude again of uh difference in + + align:start position:0% +magnitude again of uh difference in + + + align:start position:0% +magnitude again of uh difference in +masses um St links too probably uh all + + align:start position:0% +masses um St links too probably uh all + + + align:start position:0% +masses um St links too probably uh all +look very similar when you compare them + + align:start position:0% +look very similar when you compare them + + + align:start position:0% +look very similar when you compare them +in the right in the right framework and + + align:start position:0% +in the right in the right framework and + + + align:start position:0% +in the right in the right framework and +that's sort of what comparative + + align:start position:0% +that's sort of what comparative + + + align:start position:0% +that's sort of what comparative +biomechanics tries to do um in addition + + align:start position:0% +biomechanics tries to do um in addition + + + align:start position:0% +biomechanics tries to do um in addition +to other things obviously but so here's + + align:start position:0% +to other things obviously but so here's + + + align:start position:0% +to other things obviously but so here's +something that's really cool and that + + align:start position:0% +something that's really cool and that + + + align:start position:0% +something that's really cool and that +connects us back to our slip model if we + + align:start position:0% +connects us back to our slip model if we + + + align:start position:0% +connects us back to our slip model if we +look at the next + + align:start position:0% +look at the next + + + align:start position:0% +look at the next +page let's see + + align:start position:0% +page let's see + + + align:start position:0% +page let's see +right + + align:start position:0% +right + + + align:start position:0% +right +here here in this is the relative spring + + align:start position:0% +here here in this is the relative spring + + + align:start position:0% +here here in this is the relative spring +constant for individual leg for all + + align:start position:0% +constant for individual leg for all + + + align:start position:0% +constant for individual leg for all +surfing systems cockroach to Kangaroo um + + align:start position:0% +surfing systems cockroach to Kangaroo um + + + align:start position:0% +surfing systems cockroach to Kangaroo um +Five O of magnitude you can see that + + align:start position:0% +Five O of magnitude you can see that + + + align:start position:0% +Five O of magnitude you can see that +they're all pretty similar right this is + + align:start position:0% +they're all pretty similar right this is + + + align:start position:0% +they're all pretty similar right this is +huge spectrum of masses and yet in the + + align:start position:0% +huge spectrum of masses and yet in the + + + align:start position:0% +huge spectrum of masses and yet in the +framework of the slip models you know + + align:start position:0% +framework of the slip models you know + + + align:start position:0% +framework of the slip models you know +spring constant they all behave pretty + + align:start position:0% +spring constant they all behave pretty + + + align:start position:0% +spring constant they all behave pretty +similarly you know humans all these + + align:start position:0% +similarly you know humans all these + + + align:start position:0% +similarly you know humans all these +things and so if you look at these uh + + align:start position:0% +things and so if you look at these uh + + + align:start position:0% +things and so if you look at these uh +systems through this simple model they + + align:start position:0% +systems through this simple model they + + + align:start position:0% +systems through this simple model they +all not only look like similar to one + + align:start position:0% +all not only look like similar to one + + + align:start position:0% +all not only look like similar to one +another but their Dynamics and their + + align:start position:0% +another but their Dynamics and their + + + align:start position:0% +another but their Dynamics and their +Center M everything like that are pretty + + align:start position:0% +Center M everything like that are pretty + + + align:start position:0% +Center M everything like that are pretty +well described by this kind of behavior + + align:start position:0% +well described by this kind of behavior + + + align:start position:0% +well described by this kind of behavior +Sorry by that kind of + + align:start position:0% + + + + align:start position:0% + +behavior so + + align:start position:0% +behavior so + + + align:start position:0% +behavior so +uh so hopefully that'll + + align:start position:0% +uh so hopefully that'll + + + align:start position:0% +uh so hopefully that'll +be you know somewhat compelling argument + + align:start position:0% +be you know somewhat compelling argument + + + align:start position:0% +be you know somewhat compelling argument +that you know this model is + + align:start position:0% +that you know this model is + + + align:start position:0% +that you know this model is +representative of actual running + + align:start position:0% +representative of actual running + + + align:start position:0% +representative of actual running +Behavior not just you know something + + align:start position:0% +Behavior not just you know something + + + align:start position:0% +Behavior not just you know something +that comes out of nowhere um and a lot + + align:start position:0% +that comes out of nowhere um and a lot + + + align:start position:0% +that comes out of nowhere um and a lot +of work was done on this in the ' 80s + + align:start position:0% +of work was done on this in the ' 80s + + + align:start position:0% +of work was done on this in the ' 80s +and 90s um on trying to sort of study + + align:start position:0% +and 90s um on trying to sort of study + + + align:start position:0% +and 90s um on trying to sort of study +this model and connect it to animals and + + align:start position:0% +this model and connect it to animals and + + + align:start position:0% +this model and connect it to animals and +that sort of stuff and I don't know if + + align:start position:0% +that sort of stuff and I don't know if + + + align:start position:0% +that sort of stuff and I don't know if +you've seen Raber's uh Raber's work um + + align:start position:0% +you've seen Raber's uh Raber's work um + + + align:start position:0% +you've seen Raber's uh Raber's work um +but he has robots that are very similar + + align:start position:0% +but he has robots that are very similar + + + align:start position:0% +but he has robots that are very similar +so they sort of slit model that run and + + align:start position:0% +so they sort of slit model that run and + + + align:start position:0% +so they sort of slit model that run and +jump and actually from the the AG and + + align:start position:0% +jump and actually from the the AG and + + + align:start position:0% +jump and actually from the the AG and +such like that actually some of the + + align:start position:0% +such like that actually some of the + + + align:start position:0% +such like that actually some of the +really cool robots and I'll show you um + + align:start position:0% +really cool robots and I'll show you um + + + align:start position:0% +really cool robots and I'll show you um +some of those + + align:start position:0% +some of those + + + align:start position:0% +some of those +so he actually didn't even call them + + align:start position:0% +so he actually didn't even call them + + + align:start position:0% +so he actually didn't even call them +slip he actually made them before slip + + align:start position:0% +slip he actually made them before slip + + + align:start position:0% +slip he actually made them before slip +and that motivated some of the work on + + align:start position:0% +and that motivated some of the work on + + + align:start position:0% +and that motivated some of the work on +slip models um I can show you I'll show + + align:start position:0% +slip models um I can show you I'll show + + + align:start position:0% +slip models um I can show you I'll show +you a picture of a robot so you can see + + align:start position:0% +you a picture of a robot so you can see + + + align:start position:0% +you a picture of a robot so you can see +the kind of cool + + align:start position:0% +the kind of cool + + + align:start position:0% +the kind of cool +stuff that we're getting to um + + align:start position:0% +stuff that we're getting to um + + + align:start position:0% +stuff that we're getting to um +um I don't know are many of you familiar + + align:start position:0% +um I don't know are many of you familiar + + + align:start position:0% +um I don't know are many of you familiar +with the leg lab used to be around yeah + + align:start position:0% +with the leg lab used to be around yeah + + + align:start position:0% +with the leg lab used to be around yeah +they had a lot of cool robots um and + + align:start position:0% +they had a lot of cool robots um and + + + align:start position:0% +they had a lot of cool robots um and +here see if I can give you just + + align:start position:0% +here see if I can give you just + + + align:start position:0% +here see if I can give you just +a little picture + + align:start position:0% +a little picture + + + align:start position:0% +a little picture +this hope a so that's the biped R this + + align:start position:0% +this hope a so that's the biped R this + + + align:start position:0% +this hope a so that's the biped R this +thing's bouncing but that's not really + + align:start position:0% +thing's bouncing but that's not really + + + align:start position:0% +thing's bouncing but that's not really +the picture I wanted to show you + + align:start position:0% + + + + align:start position:0% + +um ah here we go yeah + + align:start position:0% +um ah here we go yeah + + + align:start position:0% +um ah here we go yeah +so this little + + align:start position:0% +so this little + + + align:start position:0% +so this little +robot you can + + align:start position:0% +robot you can + + + align:start position:0% +robot you can +see um that's the sort of tracing its + + align:start position:0% +see um that's the sort of tracing its + + + align:start position:0% +see um that's the sort of tracing its +foot this up here is tracing its Center + + align:start position:0% +foot this up here is tracing its Center + + + align:start position:0% +foot this up here is tracing its Center +Mass and you see how it Center Mass + + align:start position:0% +Mass and you see how it Center Mass + + + align:start position:0% +Mass and you see how it Center Mass +actually compresses right above the foot + + align:start position:0% +actually compresses right above the foot + + + align:start position:0% +actually compresses right above the foot +and that's sort of what you expect here + + align:start position:0% +and that's sort of what you expect here + + + align:start position:0% +and that's sort of what you expect here +it lands and squishes down and so + + align:start position:0% +it lands and squishes down and so + + + align:start position:0% +it lands and squishes down and so +instead of when you're walking and you + + align:start position:0% +instead of when you're walking and you + + + align:start position:0% +instead of when you're walking and you +sort of Vault over this leg like you + + align:start position:0% +sort of Vault over this leg like you + + + align:start position:0% +sort of Vault over this leg like you +think about that rimless wheel Cent our + + align:start position:0% +think about that rimless wheel Cent our + + + align:start position:0% +think about that rimless wheel Cent our +Mass rolls up over its foot this one um + + align:start position:0% +Mass rolls up over its foot this one um + + + align:start position:0% +Mass rolls up over its foot this one um +both intuitively in the model and you + + align:start position:0% +both intuitively in the model and you + + + align:start position:0% +both intuitively in the model and you +can see right here this robot which is + + align:start position:0% +can see right here this robot which is + + + align:start position:0% +can see right here this robot which is +similar to the model in many ways is + + align:start position:0% +similar to the model in many ways is + + + align:start position:0% +similar to the model in many ways is +squishing down into its foot all right + + align:start position:0% +squishing down into its foot all right + + + align:start position:0% +squishing down into its foot all right +and that actually is one of the ways of + + align:start position:0% +and that actually is one of the ways of + + + align:start position:0% +and that actually is one of the ways of +looking at the difference between uh + + align:start position:0% +looking at the difference between uh + + + align:start position:0% +looking at the difference between uh +what is running what is walking so uh + + align:start position:0% +what is running what is walking so uh + + + align:start position:0% +what is running what is walking so uh +one of the definitions for running is + + align:start position:0% +one of the definitions for running is + + + align:start position:0% +one of the definitions for running is +that you're supposed to have an aerial + + align:start position:0% +that you're supposed to have an aerial + + + align:start position:0% +that you're supposed to have an aerial +phase um but not every running animal + + align:start position:0% +phase um but not every running animal + + + align:start position:0% +phase um but not every running animal +has an aerial phase so this is actually + + align:start position:0% +has an aerial phase so this is actually + + + align:start position:0% +has an aerial phase so this is actually +I think comparative biome mechanicians + + align:start position:0% +I think comparative biome mechanicians + + + align:start position:0% +I think comparative biome mechanicians +look at this sort of Center Mass to + + align:start position:0% +look at this sort of Center Mass to + + + align:start position:0% +look at this sort of Center Mass to +Center pressure kind of trajectory + + align:start position:0% +Center pressure kind of trajectory + + + align:start position:0% +Center pressure kind of trajectory +because I don't know if you know Groucho + + align:start position:0% +because I don't know if you know Groucho + + + align:start position:0% +because I don't know if you know Groucho +marks Groucho marks at this funny run + + align:start position:0% +marks Groucho marks at this funny run + + + align:start position:0% +marks Groucho marks at this funny run +maybe maybe I'll do it so different + + align:start position:0% +maybe maybe I'll do it so different + + + align:start position:0% +maybe maybe I'll do it so different +posterity but sort of like this you know + + align:start position:0% +posterity but sort of like this you know + + + align:start position:0% +posterity but sort of like this you know +that kind of goofy thing where your feet + + align:start position:0% +that kind of goofy thing where your feet + + + align:start position:0% +that kind of goofy thing where your feet +aren't coming up the ground that doesn't + + align:start position:0% +aren't coming up the ground that doesn't + + + align:start position:0% +aren't coming up the ground that doesn't +seem natural but actually some animals + + align:start position:0% +seem natural but actually some animals + + + align:start position:0% +seem natural but actually some animals +do that there's actually elephants that + + align:start position:0% +do that there's actually elephants that + + + align:start position:0% +do that there's actually elephants that +sort of do that Groucho run um so maybe + + align:start position:0% +sort of do that Groucho run um so maybe + + + align:start position:0% +sort of do that Groucho run um so maybe +if you're big enough it makes sense uh + + align:start position:0% +if you're big enough it makes sense uh + + + align:start position:0% +if you're big enough it makes sense uh +but yeah so you see this is very + + align:start position:0% +but yeah so you see this is very + + + align:start position:0% +but yeah so you see this is very +different from walking um and it's + + align:start position:0% +different from walking um and it's + + + align:start position:0% +different from walking um and it's +actually quite similar to to running and + + align:start position:0% +actually quite similar to to running and + + + align:start position:0% +actually quite similar to to running and +actually if you look at these animals um + + align:start position:0% +actually if you look at these animals um + + + align:start position:0% +actually if you look at these animals um +it captures a lot of + + align:start position:0% +it captures a lot of + + + align:start position:0% +it captures a lot of +Dynamics so um yeah and another + + align:start position:0% +Dynamics so um yeah and another + + + align:start position:0% +Dynamics so um yeah and another +important thing is that these kind of + + align:start position:0% +important thing is that these kind of + + + align:start position:0% +important thing is that these kind of +robots which came around the 80s um + + align:start position:0% +robots which came around the 80s um + + + align:start position:0% +robots which came around the 80s um +where sort of a similar kind of work in + + align:start position:0% +where sort of a similar kind of work in + + + align:start position:0% +where sort of a similar kind of work in +robotics because again again at the same + + align:start position:0% +robotics because again again at the same + + + align:start position:0% +robotics because again again at the same +time when they have these sort of slow + + align:start position:0% +time when they have these sort of slow + + + align:start position:0% +time when they have these sort of slow +careful kind of walking robots again + + align:start position:0% +careful kind of walking robots again + + + align:start position:0% +careful kind of walking robots again +here these robots that are flying + + align:start position:0% +here these robots that are flying + + + align:start position:0% +here these robots that are flying +through the air um I'll show you some in + + align:start position:0% +through the air um I'll show you some in + + + align:start position:0% +through the air um I'll show you some in +the videos later but they did flips and + + align:start position:0% +the videos later but they did flips and + + + align:start position:0% +the videos later but they did flips and +all kinds of crazy stuff I mean they + + align:start position:0% +all kinds of crazy stuff I mean they + + + align:start position:0% +all kinds of crazy stuff I mean they +were throwing themselves around wildly + + align:start position:0% +were throwing themselves around wildly + + + align:start position:0% +were throwing themselves around wildly +which is not what people sort of thought + + align:start position:0% +which is not what people sort of thought + + + align:start position:0% +which is not what people sort of thought +of when they thought of these sort of + + align:start position:0% +of when they thought of these sort of + + + align:start position:0% +of when they thought of these sort of +you know legged robots + + align:start position:0% +you know legged robots + + + align:start position:0% +you know legged robots +um so oh and the other thing this is + + align:start position:0% +um so oh and the other thing this is + + + align:start position:0% +um so oh and the other thing this is +cool too um if you look at animals like + + align:start position:0% +cool too um if you look at animals like + + + align:start position:0% +cool too um if you look at animals like +we're talking about this Springs and + + align:start position:0% +we're talking about this Springs and + + + align:start position:0% +we're talking about this Springs and +stuff like that that's not just sort of + + align:start position:0% +stuff like that that's not just sort of + + + align:start position:0% +stuff like that that's not just sort of +some sort of obtuse model that comes out + + align:start position:0% +some sort of obtuse model that comes out + + + align:start position:0% +some sort of obtuse model that comes out +of nowhere if you look at uh horse and + + align:start position:0% +of nowhere if you look at uh horse and + + + align:start position:0% +of nowhere if you look at uh horse and +stuff well animals actually are full of + + align:start position:0% +stuff well animals actually are full of + + + align:start position:0% +stuff well animals actually are full of +Springs like their tendons can store up + + align:start position:0% +Springs like their tendons can store up + + + align:start position:0% +Springs like their tendons can store up +energy and stuff and actually horses + + align:start position:0% +energy and stuff and actually horses + + + align:start position:0% +energy and stuff and actually horses +have a big tendon that runs um through + + align:start position:0% +have a big tendon that runs um through + + + align:start position:0% +have a big tendon that runs um through +their leg all the way up I think behind + + align:start position:0% +their leg all the way up I think behind + + + align:start position:0% +their leg all the way up I think behind +their hip and apparently one of the + + align:start position:0% +their hip and apparently one of the + + + align:start position:0% +their hip and apparently one of the +limiting factors in trying to run fast + + align:start position:0% +limiting factors in trying to run fast + + + align:start position:0% +limiting factors in trying to run fast +is that you can't pull your leg forward + + align:start position:0% +is that you can't pull your leg forward + + + align:start position:0% +is that you can't pull your leg forward +fast enough to get to the next stride + + align:start position:0% +fast enough to get to the next stride + + + align:start position:0% +fast enough to get to the next stride +and so what they actually can do is they + + align:start position:0% +and so what they actually can do is they + + + align:start position:0% +and so what they actually can do is they +can they can preload when they're + + align:start position:0% +can they can preload when they're + + + align:start position:0% +can they can preload when they're +pushing and then that tendon actually + + align:start position:0% +pushing and then that tendon actually + + + align:start position:0% +pushing and then that tendon actually +acts like a spring actually stores + + align:start position:0% +acts like a spring actually stores + + + align:start position:0% +acts like a spring actually stores +energy and lets them swing for forward + + align:start position:0% +energy and lets them swing for forward + + + align:start position:0% +energy and lets them swing for forward +faster than they would be able to if + + align:start position:0% +faster than they would be able to if + + + align:start position:0% +faster than they would be able to if +they just use the motor and if you look + + align:start position:0% +they just use the motor and if you look + + + align:start position:0% +they just use the motor and if you look +at the oxygen intake of these animals + + align:start position:0% +at the oxygen intake of these animals + + + align:start position:0% +at the oxygen intake of these animals +you can see that they're behaving much + + align:start position:0% +you can see that they're behaving much + + + align:start position:0% +you can see that they're behaving much +more efficiently than you could hope to + + align:start position:0% +more efficiently than you could hope to + + + align:start position:0% +more efficiently than you could hope to +accomplish if you just had uh if you + + align:start position:0% +accomplish if you just had uh if you + + + align:start position:0% +accomplish if you just had uh if you +were simulating a spring with you know a + + align:start position:0% +were simulating a spring with you know a + + + align:start position:0% +were simulating a spring with you know a +bunch of motor with it with like your + + align:start position:0% +bunch of motor with it with like your + + + align:start position:0% +bunch of motor with it with like your +muscles acting like a spring right so + + align:start position:0% +muscles acting like a spring right so + + + align:start position:0% +muscles acting like a spring right so +it's actually their physical Springs + + align:start position:0% +it's actually their physical Springs + + + align:start position:0% +it's actually their physical Springs +like actually the this tendon in there + + align:start position:0% +like actually the this tendon in there + + + align:start position:0% +like actually the this tendon in there +actually have this actual Behavior so + + align:start position:0% +actually have this actual Behavior so + + + align:start position:0% +actually have this actual Behavior so +hopefully maybe + + align:start position:0% +hopefully maybe + + + align:start position:0% +hopefully maybe +I'm dwelling on that point too much but + + align:start position:0% +I'm dwelling on that point too much but + + + align:start position:0% +I'm dwelling on that point too much but +I think that's really cool that these + + align:start position:0% +I think that's really cool that these + + + align:start position:0% +I think that's really cool that these +animals actually have this kind of + + align:start position:0% +animals actually have this kind of + + + align:start position:0% +animals actually have this kind of +spring Behavior you can see it in their + + align:start position:0% +spring Behavior you can see it in their + + + align:start position:0% +spring Behavior you can see it in their +uh in their Dynamics and actually this + + align:start position:0% +uh in their Dynamics and actually this + + + align:start position:0% +uh in their Dynamics and actually this +model of captures that all that + + align:start position:0% +model of captures that all that + + + align:start position:0% +model of captures that all that +um oh oh and here's one other thing that + + align:start position:0% +um oh oh and here's one other thing that + + + align:start position:0% +um oh oh and here's one other thing that +Russ likes I'll bring you up and it's + + align:start position:0% +Russ likes I'll bring you up and it's + + + align:start position:0% +Russ likes I'll bring you up and it's +pretty cool too if you think about uh + + align:start position:0% +pretty cool too if you think about uh + + + align:start position:0% +pretty cool too if you think about uh +this is sort of a tangent but you think + + align:start position:0% +this is sort of a tangent but you think + + + align:start position:0% +this is sort of a tangent but you think +about how birds like sit on perches + + align:start position:0% +about how birds like sit on perches + + + align:start position:0% +about how birds like sit on perches +forever right I mean it seems like that' + + align:start position:0% +forever right I mean it seems like that' + + + align:start position:0% +forever right I mean it seems like that' +be tiring to go like hang there forever + + align:start position:0% +be tiring to go like hang there forever + + + align:start position:0% +be tiring to go like hang there forever +just squeezing right but they actually + + align:start position:0% +just squeezing right but they actually + + + align:start position:0% +just squeezing right but they actually +have tendons too um such that when they + + align:start position:0% +have tendons too um such that when they + + + align:start position:0% +have tendons too um such that when they +sit on the perch and their weight sort + + align:start position:0% +sit on the perch and their weight sort + + + align:start position:0% +sit on the perch and their weight sort +of squishes their legs down it actually + + align:start position:0% +of squishes their legs down it actually + + + align:start position:0% +of squishes their legs down it actually +will + + align:start position:0% +will + + + align:start position:0% +will +clamp their uh their talons and let them + + align:start position:0% +clamp their uh their talons and let them + + + align:start position:0% +clamp their uh their talons and let them +hold on so that's that's sort of cool + + align:start position:0% +hold on so that's that's sort of cool + + + align:start position:0% +hold on so that's that's sort of cool +too that these animals have all these + + align:start position:0% +too that these animals have all these + + + align:start position:0% +too that these animals have all these +sort of interesting sort of like passive + + align:start position:0% +sort of interesting sort of like passive + + + align:start position:0% +sort of interesting sort of like passive +structures and you know spr and stuff + + align:start position:0% +structures and you know spr and stuff + + + align:start position:0% +structures and you know spr and stuff +like that that help them do all these + + align:start position:0% +like that that help them do all these + + + align:start position:0% +like that that help them do all these +kind of things and so it's not just like + + align:start position:0% +kind of things and so it's not just like + + + align:start position:0% +kind of things and so it's not just like +you know it's not like the uh you know + + align:start position:0% +you know it's not like the uh you know + + + align:start position:0% +you know it's not like the uh you know +just use your muscles and just dominate + + align:start position:0% +just use your muscles and just dominate + + + align:start position:0% +just use your muscles and just dominate +all these kind of things it's there's a + + align:start position:0% +all these kind of things it's there's a + + + align:start position:0% +all these kind of things it's there's a +lot of sort of passive structures that + + align:start position:0% +lot of sort of passive structures that + + + align:start position:0% +lot of sort of passive structures that +capture like do a lot of this sort of + + align:start position:0% +capture like do a lot of this sort of + + + align:start position:0% +capture like do a lot of this sort of +for free um well so hopefully you all + + align:start position:0% +for free um well so hopefully you all + + + align:start position:0% +for free um well so hopefully you all +think that's + + align:start position:0% +think that's + + + align:start position:0% +think that's +awesome all right um all right so + + align:start position:0% +awesome all right um all right so + + + align:start position:0% +awesome all right um all right so +getting back to the + + align:start position:0% +getting back to the + + + align:start position:0% +getting back to the +system um looking at this uh sorry at + + align:start position:0% +system um looking at this uh sorry at + + + align:start position:0% +system um looking at this uh sorry at +this model again uh + + align:start position:0% +this model again uh + + + align:start position:0% +this model again uh +see where I put my + + align:start position:0% + + + + align:start position:0% + +chalk all right so going back to the + + align:start position:0% +chalk all right so going back to the + + + align:start position:0% +chalk all right so going back to the +slip system + + align:start position:0% +slip system + + + align:start position:0% +slip system +um see all right again the state space + + align:start position:0% +um see all right again the state space + + + align:start position:0% +um see all right again the state space +here is it is it is that still dark in + + align:start position:0% +here is it is it is that still dark in + + + align:start position:0% +here is it is it is that still dark in +here all + + align:start position:0% + + + + align:start position:0% + +right all + + align:start position:0% +right all + + + align:start position:0% +right all +right so + + align:start position:0% + + + + align:start position:0% + +all + + align:start position:0% +all + + + align:start position:0% +all +right so going back to the system again + + align:start position:0% +right so going back to the system again + + + align:start position:0% +right so going back to the system again +we have R Theta r dot Theta Dot and in + + align:start position:0% +we have R Theta r dot Theta Dot and in + + + align:start position:0% +we have R Theta r dot Theta Dot and in +the aerial phase XY x dot y + + align:start position:0% +the aerial phase XY x dot y + + + align:start position:0% +the aerial phase XY x dot y +dot all right I'll bring this one back + + align:start position:0% + + + + align:start position:0% + +down + + align:start position:0% +down + + + align:start position:0% +down +and let me put in the + + align:start position:0% +and let me put in the + + + align:start position:0% +and let me put in the +uh the assumptions really clearly of + + align:start position:0% +uh the assumptions really clearly of + + + align:start position:0% +uh the assumptions really clearly of +what this model um is going to have so + + align:start position:0% +what this model um is going to have so + + + align:start position:0% +what this model um is going to have so +the assumptions for the slip + + align:start position:0% + + + + align:start position:0% + +model so one is that you have a + + align:start position:0% +model so one is that you have a + + + align:start position:0% +model so one is that you have a +massless well that's terrible + + align:start position:0% +massless well that's terrible + + + align:start position:0% +massless well that's terrible +massless leg and toe all right so all + + align:start position:0% +massless leg and toe all right so all + + + align:start position:0% +massless leg and toe all right so all +your mass is concentrated in that uh + + align:start position:0% +your mass is concentrated in that uh + + + align:start position:0% +your mass is concentrated in that uh +Point messenger at the body all right + + align:start position:0% +Point messenger at the body all right + + + align:start position:0% +Point messenger at the body all right +um you have an + + align:start position:0% +um you have an + + + align:start position:0% +um you have an +ideal uh lossless + + align:start position:0% + + + + align:start position:0% + +spring in your + + align:start position:0% +spring in your + + + align:start position:0% +spring in your +leg um and that means that effectively + + align:start position:0% +leg um and that means that effectively + + + align:start position:0% +leg um and that means that effectively +your collisions with the ground unlike + + align:start position:0% +your collisions with the ground unlike + + + align:start position:0% +your collisions with the ground unlike +all the walking models are perfectly + + align:start position:0% +all the walking models are perfectly + + + align:start position:0% +all the walking models are perfectly +elastic + + align:start position:0% + + + + align:start position:0% + +all right now you can see that that's + + align:start position:0% +all right now you can see that that's + + + align:start position:0% +all right now you can see that that's +not like an extra assumption that that + + align:start position:0% +not like an extra assumption that that + + + align:start position:0% +not like an extra assumption that that +is dered from these when it hits even + + align:start position:0% +is dered from these when it hits even + + + align:start position:0% +is dered from these when it hits even +though like this toe you know CL like + + align:start position:0% +though like this toe you know CL like + + + align:start position:0% +though like this toe you know CL like +sticks in right away and you know kind + + align:start position:0% +sticks in right away and you know kind + + + align:start position:0% +sticks in right away and you know kind +an Ines C with that toe because there's + + align:start position:0% +an Ines C with that toe because there's + + + align:start position:0% +an Ines C with that toe because there's +no Mass there there's no energy there's + + align:start position:0% +no Mass there there's no energy there's + + + align:start position:0% +no Mass there there's no energy there's +no momentum in it sorry this is um you + + align:start position:0% +no momentum in it sorry this is um you + + + align:start position:0% +no momentum in it sorry this is um you +don't lose any energy and so it's + + align:start position:0% +don't lose any energy and so it's + + + align:start position:0% +don't lose any energy and so it's +actually conservative as it runs through + + align:start position:0% +actually conservative as it runs through + + + align:start position:0% +actually conservative as it runs through +and then if you you know flying through + + align:start position:0% +and then if you you know flying through + + + align:start position:0% +and then if you you know flying through +the air there's no drag or anything it's + + align:start position:0% +the air there's no drag or anything it's + + + align:start position:0% +the air there's no drag or anything it's +conservative when it flies through the + + align:start position:0% +conservative when it flies through the + + + align:start position:0% +conservative when it flies through the +air as well and so this system actually + + align:start position:0% +air as well and so this system actually + + + align:start position:0% +air as well and so this system actually +um is completely conservative in its + + align:start position:0% +um is completely conservative in its + + + align:start position:0% +um is completely conservative in its +full + + align:start position:0% +full + + + align:start position:0% +full +operation um so yeah so it's very + + align:start position:0% +operation um so yeah so it's very + + + align:start position:0% +operation um so yeah so it's very +different than rimless wheel um and also + + align:start position:0% +different than rimless wheel um and also + + + align:start position:0% +different than rimless wheel um and also +then the other assumption we have to + + align:start position:0% +then the other assumption we have to + + + align:start position:0% +then the other assumption we have to +make is that the leg + + align:start position:0% + + + + align:start position:0% + +instantly + + align:start position:0% +instantly + + + align:start position:0% +instantly +goes to like the + + align:start position:0% + + + + align:start position:0% + +desired Theta and rest length so again + + align:start position:0% +desired Theta and rest length so again + + + align:start position:0% +desired Theta and rest length so again +when it's Mass l the rest length it'll + + align:start position:0% +when it's Mass l the rest length it'll + + + align:start position:0% +when it's Mass l the rest length it'll +do that automatically but you have to + + align:start position:0% +do that automatically but you have to + + + align:start position:0% +do that automatically but you have to +assume that you can sort of teleport it + + align:start position:0% +assume that you can sort of teleport it + + + align:start position:0% +assume that you can sort of teleport it +to that Theta so you don't worry about + + align:start position:0% +to that Theta so you don't worry about + + + align:start position:0% +to that Theta so you don't worry about +collisions with the ground or everything + + align:start position:0% +collisions with the ground or everything + + + align:start position:0% +collisions with the ground or everything +like that your leg just goes to the + + align:start position:0% +like that your leg just goes to the + + + align:start position:0% +like that your leg just goes to the +Theta of touchdown so the moment you + + align:start position:0% +Theta of touchdown so the moment you + + + align:start position:0% +Theta of touchdown so the moment you +take off it's in this new + + align:start position:0% +take off it's in this new + + + align:start position:0% +take off it's in this new +configuration all + + align:start position:0% + + + + align:start position:0% + +right so now what we have to do is now + + align:start position:0% +right so now what we have to do is now + + + align:start position:0% +right so now what we have to do is now +that we have the system in the model we + + align:start position:0% +that we have the system in the model we + + + align:start position:0% +that we have the system in the model we +want to pick our surface of section + + align:start position:0% +want to pick our surface of section + + + align:start position:0% +want to pick our surface of section +because our goal here sort of is to turn + + align:start position:0% +because our goal here sort of is to turn + + + align:start position:0% +because our goal here sort of is to turn +this into a 1D iterated map right so + + align:start position:0% +this into a 1D iterated map right so + + + align:start position:0% +this into a 1D iterated map right so +that's sort of what this is all about + + align:start position:0% +that's sort of what this is all about + + + align:start position:0% +that's sort of what this is all about +we're going to try to figure out how do + + align:start position:0% +we're going to try to figure out how do + + + align:start position:0% +we're going to try to figure out how do +we pick a spot we can just look at one + + align:start position:0% +we pick a spot we can just look at one + + + align:start position:0% +we pick a spot we can just look at one +section and describe all the Dynamics + + align:start position:0% +section and describe all the Dynamics + + + align:start position:0% +section and describe all the Dynamics +just being like okay we're here simulate + + align:start position:0% +just being like okay we're here simulate + + + align:start position:0% +just being like okay we're here simulate +no to the next one and then we can just + + align:start position:0% +no to the next one and then we can just + + + align:start position:0% +no to the next one and then we can just +sort of iterate this map and figure out + + align:start position:0% +sort of iterate this map and figure out + + + align:start position:0% +sort of iterate this map and figure out +the fixed points figure out a lot of + + align:start position:0% +the fixed points figure out a lot of + + + align:start position:0% +the fixed points figure out a lot of +things as we did with the rimless wheel + + align:start position:0% +things as we did with the rimless wheel + + + align:start position:0% +things as we did with the rimless wheel +so does anyone have an idea of what a + + align:start position:0% +so does anyone have an idea of what a + + + align:start position:0% +so does anyone have an idea of what a +good surface of section would + + align:start position:0% + + + + align:start position:0% + +be no what sort of like special + + align:start position:0% +be no what sort of like special + + + align:start position:0% +be no what sort of like special +configurations are there that we could + + align:start position:0% +configurations are there that we could + + + align:start position:0% +configurations are there that we could +look + + align:start position:0% +look + + + align:start position:0% +look +at take off take off what else that's + + align:start position:0% +at take off take off what else that's + + + align:start position:0% +at take off take off what else that's +one + + align:start position:0% + + + + align:start position:0% + +full compression full + + align:start position:0% +full compression full + + + align:start position:0% +full compression full +rest at at the rest length that's true + + align:start position:0% +rest at at the rest length that's true + + + align:start position:0% +rest at at the rest length that's true +full compression you could do but that + + align:start position:0% +full compression you could do but that + + + align:start position:0% +full compression you could do but that +would be like there be a zero r dot or + + align:start position:0% +would be like there be a zero r dot or + + + align:start position:0% +would be like there be a zero r dot or +something like that but yeah no I mean + + align:start position:0% +something like that but yeah no I mean + + + align:start position:0% +something like that but yeah no I mean +you could there's a lot of these sort of + + align:start position:0% +you could there's a lot of these sort of + + + align:start position:0% +you could there's a lot of these sort of +special configurations but the one that + + align:start position:0% +special configurations but the one that + + + align:start position:0% +special configurations but the one that +you really want to look at the one that + + align:start position:0% +you really want to look at the one that + + + align:start position:0% +you really want to look at the one that +sort of comp collaps things down the + + align:start position:0% +sort of comp collaps things down the + + + align:start position:0% +sort of comp collaps things down the +most is if you look at the Apex so you + + align:start position:0% +most is if you look at the Apex so you + + + align:start position:0% +most is if you look at the Apex so you +look at sort of the maximum height of + + align:start position:0% +look at sort of the maximum height of + + + align:start position:0% +look at sort of the maximum height of +this flight right so then we can just + + align:start position:0% +this flight right so then we can just + + + align:start position:0% +this flight right so then we can just +look at that Y and the reason we can do + + align:start position:0% +look at that Y and the reason we can do + + + align:start position:0% +look at that Y and the reason we can do +this I'm going describe right here so we + + align:start position:0% +this I'm going describe right here so we + + + align:start position:0% +this I'm going describe right here so we +look in the flight phase + + align:start position:0% + + + + align:start position:0% + +now first of all X we don't really care + + align:start position:0% +now first of all X we don't really care + + + align:start position:0% +now first of all X we don't really care +about what x is for the stability right + + align:start position:0% +about what x is for the stability right + + + align:start position:0% +about what x is for the stability right +doesn't matter where it is along that + + align:start position:0% +doesn't matter where it is along that + + + align:start position:0% +doesn't matter where it is along that +position that doesn't affect the + + align:start position:0% +position that doesn't affect the + + + align:start position:0% +position that doesn't affect the +Dynamics directly so we sort of don't + + align:start position:0% +Dynamics directly so we sort of don't + + + align:start position:0% +Dynamics directly so we sort of don't +care about + + align:start position:0% + + + + align:start position:0% + +X so y we definitely do care about this + + align:start position:0% + + + + align:start position:0% + +matters x dot well x dot because we know + + align:start position:0% +matters x dot well x dot because we know + + + align:start position:0% +matters x dot well x dot because we know +it's conservative and we know that since + + align:start position:0% +it's conservative and we know that since + + + align:start position:0% +it's conservative and we know that since +the Apex y dot equal + + align:start position:0% +the Apex y dot equal + + + align:start position:0% +the Apex y dot equal +0 then x dot is purely a function of Y + + align:start position:0% +0 then x dot is purely a function of Y + + + align:start position:0% +0 then x dot is purely a function of Y +right we can look at the total energy of + + align:start position:0% +right we can look at the total energy of + + + align:start position:0% +right we can look at the total energy of +the + + align:start position:0% +the + + + align:start position:0% +the +system which is 12 m v ^ + + align:start position:0% +system which is 12 m v ^ + + + align:start position:0% +system which is 12 m v ^ +2+ mg y right we know y zero so that + + align:start position:0% +2+ mg y right we know y zero so that + + + align:start position:0% +2+ mg y right we know y zero so that +means that V is just x dot and so you + + align:start position:0% +means that V is just x dot and so you + + + align:start position:0% +means that V is just x dot and so you +can write x dot is a function of Y + + align:start position:0% +can write x dot is a function of Y + + + align:start position:0% +can write x dot is a function of Y +all right and so here we know this is + + align:start position:0% +all right and so here we know this is + + + align:start position:0% +all right and so here we know this is +zero we don't care about this this one + + align:start position:0% +zero we don't care about this this one + + + align:start position:0% +zero we don't care about this this one +we can find directly from Y and so + + align:start position:0% +we can find directly from Y and so + + + align:start position:0% +we can find directly from Y and so +everything that happens between one Apex + + align:start position:0% +everything that happens between one Apex + + + align:start position:0% +everything that happens between one Apex +another Apex we know if we just know why + + align:start position:0% +another Apex we know if we just know why + + + align:start position:0% +another Apex we know if we just know why +you see that yes we're always adjusting + + align:start position:0% +you see that yes we're always adjusting + + + align:start position:0% +you see that yes we're always adjusting +the angle the spring Landing so that it + + align:start position:0% +the angle the spring Landing so that it + + + align:start position:0% +the angle the spring Landing so that it +is vertical it's it's set at whatever + + align:start position:0% +is vertical it's it's set at whatever + + + align:start position:0% +is vertical it's it's set at whatever +desired angle we're at so there's some + + align:start position:0% +desired angle we're at so there's some + + + align:start position:0% +desired angle we're at so there's some +nominal angle we want on this touchdown + + align:start position:0% +nominal angle we want on this touchdown + + + align:start position:0% +nominal angle we want on this touchdown +so let's say it's you know 30° or + + align:start position:0% +so let's say it's you know 30° or + + + align:start position:0% +so let's say it's you know 30° or +whatever and so that means that you take + + align:start position:0% +whatever and so that means that you take + + + align:start position:0% +whatever and so that means that you take +off your angle your leg goes to 30° and + + align:start position:0% +off your angle your leg goes to 30° and + + + align:start position:0% +off your angle your leg goes to 30° and +then you hit there and so the touchdown + + align:start position:0% +then you hit there and so the touchdown + + + align:start position:0% +then you hit there and so the touchdown +angle is always the same right and so + + align:start position:0% +angle is always the same right and so + + + align:start position:0% +angle is always the same right and so +there's there's no control in this at + + align:start position:0% +there's there's no control in this at + + + align:start position:0% +there's there's no control in this at +the moment right it's just the the + + align:start position:0% +the moment right it's just the the + + + align:start position:0% +the moment right it's just the the +passive stability of this bouncing + + align:start position:0% +passive stability of this bouncing + + + align:start position:0% +passive stability of this bouncing +system does that make sense everyone how + + align:start position:0% +system does that make sense everyone how + + + align:start position:0% +system does that make sense everyone how +we can collapse all these + + align:start position:0% + + + + align:start position:0% + +things all right + + align:start position:0% +things all right + + + align:start position:0% +things all right +um why don't you about X again cuz that + + align:start position:0% +um why don't you about X again cuz that + + + align:start position:0% +um why don't you about X again cuz that +doesn't affect the stability of the + + align:start position:0% +doesn't affect the stability of the + + + align:start position:0% +doesn't affect the stability of the +system right so like if we're trying to + + align:start position:0% +system right so like if we're trying to + + + align:start position:0% +system right so like if we're trying to +get somewhere hit a Target yeah then we + + align:start position:0% +get somewhere hit a Target yeah then we + + + align:start position:0% +get somewhere hit a Target yeah then we +have to look at X in controller but + + align:start position:0% +have to look at X in controller but + + + align:start position:0% +have to look at X in controller but +because the X doesn't figure in the + + align:start position:0% +because the X doesn't figure in the + + + align:start position:0% +because the X doesn't figure in the +Dynamics anywhere right doesn't matter + + align:start position:0% +Dynamics anywhere right doesn't matter + + + align:start position:0% +Dynamics anywhere right doesn't matter +because again this sorry this is + + align:start position:0% +because again this sorry this is + + + align:start position:0% +because again this sorry this is +something I probably should mention in + + align:start position:0% +something I probably should mention in + + + align:start position:0% +something I probably should mention in +the beginning um it's not going downhill + + align:start position:0% +the beginning um it's not going downhill + + + align:start position:0% +the beginning um it's not going downhill +or anything like that right so how far + + align:start position:0% +or anything like that right so how far + + + align:start position:0% +or anything like that right so how far +it goes an X doesn't matter the Dynamics + + align:start position:0% +it goes an X doesn't matter the Dynamics + + + align:start position:0% +it goes an X doesn't matter the Dynamics +are going to be the same sort of + + align:start position:0% +are going to be the same sort of + + + align:start position:0% +are going to be the same sort of +invariant to that that makes sense and + + align:start position:0% +invariant to that that makes sense and + + + align:start position:0% +invariant to that that makes sense and +so because of that I mean X will be + + align:start position:0% +so because of that I mean X will be + + + align:start position:0% +so because of that I mean X will be +changing but it won't affect sort of the + + align:start position:0% +changing but it won't affect sort of the + + + align:start position:0% +changing but it won't affect sort of the +next Apex height because doesn't figur + + align:start position:0% +next Apex height because doesn't figur + + + align:start position:0% +next Apex height because doesn't figur +into the Dynamics like that does that + + align:start position:0% +into the Dynamics like that does that + + + align:start position:0% +into the Dynamics like that does that +make + + align:start position:0% + + + + align:start position:0% + +sense all right + + align:start position:0% +sense all right + + + align:start position:0% +sense all right +so we can represent the whole thing just + + align:start position:0% +so we can represent the whole thing just + + + align:start position:0% +so we can represent the whole thing just +using Y I guess that's the important + + align:start position:0% +using Y I guess that's the important + + + align:start position:0% +using Y I guess that's the important +thing to realize so what do I want to + + align:start position:0% +thing to realize so what do I want to + + + align:start position:0% +thing to realize so what do I want to +erase I'll erase this + + align:start position:0% + + + + align:start position:0% + +stuff throw this back + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +up this isn't deal + + align:start position:0% + + + + align:start position:0% + +I guess it's not going to get better + + align:start position:0% +I guess it's not going to get better + + + align:start position:0% +I guess it's not going to get better +than that all right so we go through + + align:start position:0% +than that all right so we go through + + + align:start position:0% +than that all right so we go through +this transition we go from Apex to Apex + + align:start position:0% +this transition we go from Apex to Apex + + + align:start position:0% +this transition we go from Apex to Apex +we can look at is we have y + + align:start position:0% +we can look at is we have y + + + align:start position:0% +we can look at is we have y +Apex at n now we need to figure out how + + align:start position:0% +Apex at n now we need to figure out how + + + align:start position:0% +Apex at n now we need to figure out how +that translates into the + + align:start position:0% +that translates into the + + + align:start position:0% +that translates into the +Y uh X do and Y dot at that + + align:start position:0% +Y uh X do and Y dot at that + + + align:start position:0% +Y uh X do and Y dot at that +Apex right so we need to sort of map + + align:start position:0% +Apex right so we need to sort of map + + + align:start position:0% +Apex right so we need to sort of map +this one piece of information into all + + align:start position:0% +this one piece of information into all + + + align:start position:0% +this one piece of information into all +of + + align:start position:0% +of + + + align:start position:0% +of +these then we can map that + + align:start position:0% +these then we can map that + + + align:start position:0% +these then we can map that +into uh the y x dot y + + align:start position:0% +into uh the y x dot y + + + align:start position:0% +into uh the y x dot y +do at the touchdown so when it comes in + + align:start position:0% +do at the touchdown so when it comes in + + + align:start position:0% +do at the touchdown so when it comes in +and hits now we have to change our + + align:start position:0% +and hits now we have to change our + + + align:start position:0% +and hits now we have to change our +coordinate system to R Theta R do theta + + align:start position:0% +coordinate system to R Theta R do theta + + + align:start position:0% +coordinate system to R Theta R do theta +dot this is still a + + align:start position:0% +dot this is still a + + + align:start position:0% +dot this is still a +touchdown and we swing that through in + + align:start position:0% +touchdown and we swing that through in + + + align:start position:0% +touchdown and we swing that through in +the stance phase and we get that to our + + align:start position:0% +the stance phase and we get that to our + + + align:start position:0% +the stance phase and we get that to our +R Theta r dot Theta dot at take off so + + align:start position:0% +R Theta r dot Theta dot at take off so + + + align:start position:0% +R Theta r dot Theta dot at take off so +my D and my o are as different as I can + + align:start position:0% +my D and my o are as different as I can + + + align:start position:0% +my D and my o are as different as I can +make them + + align:start position:0% +make them + + + align:start position:0% +make them +look + + align:start position:0% +look + + + align:start position:0% +look +um then at takeoff again we switch to + + align:start position:0% +um then at takeoff again we switch to + + + align:start position:0% +um then at takeoff again we switch to +our aerial phase we go back to + + align:start position:0% +our aerial phase we go back to + + + align:start position:0% +our aerial phase we go back to +y x dot y dot at + + align:start position:0% + + + + align:start position:0% + +takeoff + + align:start position:0% +takeoff + + + align:start position:0% +takeoff +and that brings us then to a y x do y + + align:start position:0% +and that brings us then to a y x do y + + + align:start position:0% +and that brings us then to a y x do y +dot + + align:start position:0% +dot + + + align:start position:0% +dot +Apex and then here of course we grab y n + + align:start position:0% +Apex and then here of course we grab y n + + + align:start position:0% +Apex and then here of course we grab y n ++ 1 + + align:start position:0% + + + + align:start position:0% + +Apex so these transitions I'll I'll + + align:start position:0% +Apex so these transitions I'll I'll + + + align:start position:0% +Apex so these transitions I'll I'll +number them make this a little bit clear + + align:start position:0% +number them make this a little bit clear + + + align:start position:0% +number them make this a little bit clear +it's one 2 + + align:start position:0% +it's one 2 + + + align:start position:0% +it's one 2 + + align:start position:0% + + + align:start position:0% + + align:start position:0% + + + + align:start position:0% + +sorry so all + + align:start position:0% +sorry so all + + + align:start position:0% +sorry so all +right and the key now is to uh is sort + + align:start position:0% +right and the key now is to uh is sort + + + align:start position:0% +right and the key now is to uh is sort +of figure out how to push our system + + align:start position:0% +of figure out how to push our system + + + align:start position:0% +of figure out how to push our system +through all these all these transitions + + align:start position:0% +through all these all these transitions + + + align:start position:0% +through all these all these transitions +so you can figure out what this mapping + + align:start position:0% +so you can figure out what this mapping + + + align:start position:0% +so you can figure out what this mapping +is going to be + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so some of these are pretty easy to do + + align:start position:0% +so some of these are pretty easy to do + + + align:start position:0% +so some of these are pretty easy to do +and some of them can be quite tricky to + + align:start position:0% +and some of them can be quite tricky to + + + align:start position:0% +and some of them can be quite tricky to +do um but all of them are quite + + align:start position:0% +do um but all of them are quite + + + align:start position:0% +do um but all of them are quite +manageable so + + align:start position:0% + + + + align:start position:0% + +we look at first is the + + align:start position:0% +we look at first is the + + + align:start position:0% +we look at first is the +energy which is our ktic kinetic plus + + align:start position:0% +energy which is our ktic kinetic plus + + + align:start position:0% +energy which is our ktic kinetic plus +potential again is 12 m v ^2 + mg + + align:start position:0% +potential again is 12 m v ^2 + mg + + + align:start position:0% +potential again is 12 m v ^2 + mg +y right so at the first step you want to + + align:start position:0% +y right so at the first step you want to + + + align:start position:0% +y right so at the first step you want to +convert if we want to take y Apex and + + align:start position:0% +convert if we want to take y Apex and + + + align:start position:0% +convert if we want to take y Apex and +turn into these guys right again we can + + align:start position:0% +turn into these guys right again we can + + + align:start position:0% +turn into these guys right again we can +have the energy of the Apex + + align:start position:0% +have the energy of the Apex + + + align:start position:0% +have the energy of the Apex +we know is 12 MX dot again because we + + align:start position:0% +we know is 12 MX dot again because we + + + align:start position:0% +we know is 12 MX dot again because we +know y + + align:start position:0% +know y + + + align:start position:0% +know y +do0 plus + + align:start position:0% +do0 plus + + + align:start position:0% +do0 plus +mgy and is equal to a + + align:start position:0% +mgy and is equal to a + + + align:start position:0% +mgy and is equal to a +constant and so then this means that we + + align:start position:0% +constant and so then this means that we + + + align:start position:0% +constant and so then this means that we +can say all right x dot + + align:start position:0% +can say all right x dot + + + align:start position:0% +can say all right x dot +equals this function of + + align:start position:0% + + + + align:start position:0% + +Y so we can figure out what x dot is for + + align:start position:0% +Y so we can figure out what x dot is for + + + align:start position:0% +Y so we can figure out what x dot is for +why it is and then we know also sorry we + + align:start position:0% +why it is and then we know also sorry we + + + align:start position:0% +why it is and then we know also sorry we +know y do equals z and so here then that + + align:start position:0% +know y do equals z and so here then that + + + align:start position:0% +know y do equals z and so here then that +gets our Sur first + + align:start position:0% +gets our Sur first + + + align:start position:0% +gets our Sur first +transition two + + align:start position:0% + + + + align:start position:0% + +then you want we know that x dot at + + align:start position:0% +then you want we know that x dot at + + + align:start position:0% +then you want we know that x dot at +touchdown so this is the sort of + + align:start position:0% +touchdown so this is the sort of + + + align:start position:0% +touchdown so this is the sort of +ballistic phase coming down from Apex is + + align:start position:0% +ballistic phase coming down from Apex is + + + align:start position:0% +ballistic phase coming down from Apex is +equal to X do Apex because there's no + + align:start position:0% +equal to X do Apex because there's no + + + align:start position:0% +equal to X do Apex because there's no +forces on it so it's just going to keep + + align:start position:0% +forces on it so it's just going to keep + + + align:start position:0% +forces on it so it's just going to keep +carrying forward in X then we know y + + align:start position:0% +carrying forward in X then we know y + + + align:start position:0% +carrying forward in X then we know y +touchdown + + align:start position:0% +touchdown + + + align:start position:0% +touchdown +is going to be R KN cine Theta KN so + + align:start position:0% +is going to be R KN cine Theta KN so + + + align:start position:0% +is going to be R KN cine Theta KN so +this is what I was talking about with + + align:start position:0% +this is what I was talking about with + + + align:start position:0% +this is what I was talking about with +there's the desired Theta right so + + align:start position:0% +there's the desired Theta right so + + + align:start position:0% +there's the desired Theta right so +you're touchdown you know you're going + + align:start position:0% +you're touchdown you know you're going + + + align:start position:0% +you're touchdown you know you're going +to touch down at this desired Theta + + align:start position:0% +to touch down at this desired Theta + + + align:start position:0% +to touch down at this desired Theta +right and this then again since we know + + align:start position:0% +right and this then again since we know + + + align:start position:0% +right and this then again since we know +our energy we can get y. touchdown all + + align:start position:0% +our energy we can get y. touchdown all + + + align:start position:0% +our energy we can get y. touchdown all +right + + align:start position:0% +right + + + align:start position:0% +right +so here that gets our transition from + + align:start position:0% +so here that gets our transition from + + + align:start position:0% +so here that gets our transition from +Apex to touchdown now this is just a + + align:start position:0% +Apex to touchdown now this is just a + + + align:start position:0% +Apex to touchdown now this is just a +coordinate transformation um it's pretty + + align:start position:0% +coordinate transformation um it's pretty + + + align:start position:0% +coordinate transformation um it's pretty +easy to do too just make sure you get + + align:start position:0% +easy to do too just make sure you get + + + align:start position:0% +easy to do too just make sure you get +your velocities right you have to be POS + + align:start position:0% +your velocities right you have to be POS + + + align:start position:0% +your velocities right you have to be POS +them properly but you just transform + + align:start position:0% +them properly but you just transform + + + align:start position:0% +them properly but you just transform +those coordinates and you get that + + align:start position:0% +those coordinates and you get that + + + align:start position:0% +those coordinates and you get that +without too much difficulty but then you + + align:start position:0% +without too much difficulty but then you + + + align:start position:0% +without too much difficulty but then you +get to the tricky one um and the tricky + + align:start position:0% +get to the tricky one um and the tricky + + + align:start position:0% +get to the tricky one um and the tricky +one great the tricky one is The Stance + + align:start position:0% +one great the tricky one is The Stance + + + align:start position:0% +one great the tricky one is The Stance +phase + + align:start position:0% +phase + + + align:start position:0% +phase +so how do you push yourself from + + align:start position:0% +so how do you push yourself from + + + align:start position:0% +so how do you push yourself from +uh sort of from when you come in and hit + + align:start position:0% +uh sort of from when you come in and hit + + + align:start position:0% +uh sort of from when you come in and hit +to squishing down and launching back out + + align:start position:0% +to squishing down and launching back out + + + align:start position:0% +to squishing down and launching back out +so that's that's the that's the of the + + align:start position:0% +so that's that's the that's the of the + + + align:start position:0% +so that's that's the that's the of the +involved part of this + + align:start position:0% +involved part of this + + + align:start position:0% +involved part of this +so or + + align:start position:0% +so or + + + align:start position:0% +so or +is + + align:start position:0% +is + + + align:start position:0% +is +stance + + align:start position:0% + + + + align:start position:0% + +Dynamics + + align:start position:0% + + + + align:start position:0% + +pardon oh yeah this is touched down um + + align:start position:0% +pardon oh yeah this is touched down um + + + align:start position:0% +pardon oh yeah this is touched down um +sorry so to get to two to get this + + align:start position:0% +sorry so to get to two to get this + + + align:start position:0% +sorry so to get to two to get this +falling phase you know X doesn't change + + align:start position:0% +falling phase you know X doesn't change + + + align:start position:0% +falling phase you know X doesn't change +there's no forces in the X Direction y + + align:start position:0% +there's no forces in the X Direction y + + + align:start position:0% +there's no forces in the X Direction y +touchdown you fix this angle that's + + align:start position:0% +touchdown you fix this angle that's + + + align:start position:0% +touchdown you fix this angle that's +instantaneous sort of like warp of the + + align:start position:0% +instantaneous sort of like warp of the + + + align:start position:0% +instantaneous sort of like warp of the +leg so you know when it touches down + + align:start position:0% +leg so you know when it touches down + + + align:start position:0% +leg so you know when it touches down +it's going to be this High because + + align:start position:0% +it's going to be this High because + + + align:start position:0% +it's going to be this High because +that's sort of when touchdown is defined + + align:start position:0% +that's sort of when touchdown is defined + + + align:start position:0% +that's sort of when touchdown is defined +is when the toe hits the ground and then + + align:start position:0% +is when the toe hits the ground and then + + + align:start position:0% +is when the toe hits the ground and then +here you know your height you know this + + align:start position:0% +here you know your height you know this + + + align:start position:0% +here you know your height you know this +and again conservation of energy will + + align:start position:0% +and again conservation of energy will + + + align:start position:0% +and again conservation of energy will +give you this at the Y dot touchdown + + align:start position:0% +give you this at the Y dot touchdown + + + align:start position:0% +give you this at the Y dot touchdown +right and so that's just allows you to + + align:start position:0% +right and so that's just allows you to + + + align:start position:0% +right and so that's just allows you to +figure out your state when you come + + align:start position:0% +figure out your state when you come + + + align:start position:0% +figure out your state when you come +in all + + align:start position:0% +in all + + + align:start position:0% +in all +right so stance Dynamics so here + + align:start position:0% +right so stance Dynamics so here + + + align:start position:0% +right so stance Dynamics so here +um you sort of get a idea of what you + + align:start position:0% +um you sort of get a idea of what you + + + align:start position:0% +um you sort of get a idea of what you +expect the system to do you have a + + align:start position:0% +expect the system to do you have a + + + align:start position:0% +expect the system to do you have a +Sprint + + align:start position:0% +Sprint + + + align:start position:0% +Sprint +and I if you're running in steady state + + align:start position:0% +and I if you're running in steady state + + + align:start position:0% +and I if you're running in steady state +um I believe you take off the same angle + + align:start position:0% +um I believe you take off the same angle + + + align:start position:0% +um I believe you take off the same angle +you come in but so you can imagine + + align:start position:0% +you come in but so you can imagine + + + align:start position:0% +you come in but so you can imagine +happens is this thing sort of swings + + align:start position:0% +happens is this thing sort of swings + + + align:start position:0% +happens is this thing sort of swings +around like this but the center of mass + + align:start position:0% +around like this but the center of mass + + + align:start position:0% +around like this but the center of mass +you know goes + + align:start position:0% +you know goes + + + align:start position:0% +you know goes +in and comes back out so again do that + + align:start position:0% +in and comes back out so again do that + + + align:start position:0% +in and comes back out so again do that +compression and then launching itself + + align:start position:0% +compression and then launching itself + + + align:start position:0% +compression and then launching itself +right so I think it's a assumption + + align:start position:0% +right so I think it's a assumption + + + align:start position:0% +right so I think it's a assumption +rabert did so stady State operation it + + align:start position:0% +rabert did so stady State operation it + + + align:start position:0% +rabert did so stady State operation it +comes in out the same angle and as + + align:start position:0% +comes in out the same angle and as + + + align:start position:0% +comes in out the same angle and as +compression in the middle and so again + + align:start position:0% +compression in the middle and so again + + + align:start position:0% +compression in the middle and so again +this is this kind of behavior is again + + align:start position:0% +this is this kind of behavior is again + + + align:start position:0% +this is this kind of behavior is again +one of those ways of defining running + + align:start position:0% +one of those ways of defining running + + + align:start position:0% +one of those ways of defining running +like for the grouo kind of running is + + align:start position:0% +like for the grouo kind of running is + + + align:start position:0% +like for the grouo kind of running is +that you see the center Mass come in to + + align:start position:0% +that you see the center Mass come in to + + + align:start position:0% +that you see the center Mass come in to +the center of pressure as opposed to + + align:start position:0% +the center of pressure as opposed to + + + align:start position:0% +the center of pressure as opposed to +vaulting over it right if this was a + + align:start position:0% +vaulting over it right if this was a + + + align:start position:0% +vaulting over it right if this was a +stiff leg it would go like this right so + + align:start position:0% +stiff leg it would go like this right so + + + align:start position:0% +stiff leg it would go like this right so +that distinction is is one way of + + align:start position:0% +that distinction is is one way of + + + align:start position:0% +that distinction is is one way of +defining + + align:start position:0% +defining + + + align:start position:0% +defining +running + + align:start position:0% + + + + align:start position:0% + +um all right yeah so we can Define + + align:start position:0% +um all right yeah so we can Define + + + align:start position:0% +um all right yeah so we can Define +takeoff so we know sort of our final + + align:start position:0% +takeoff so we know sort of our final + + + align:start position:0% +takeoff so we know sort of our final +condition + + align:start position:0% + + + + align:start position:0% + +um so takeoff happens when r t equals + + align:start position:0% +um so takeoff happens when r t equals + + + align:start position:0% +um so takeoff happens when r t equals +are not so when you get back to your + + align:start position:0% +are not so when you get back to your + + + align:start position:0% +are not so when you get back to your +rest length you assume that your your + + align:start position:0% +rest length you assume that your your + + + align:start position:0% +rest length you assume that your your +body then it goes back to the ballistic + + align:start position:0% +body then it goes back to the ballistic + + + align:start position:0% +body then it goes back to the ballistic +phase then we can write down + + align:start position:0% +phase then we can write down + + + align:start position:0% +phase then we can write down +our energies here now again we're in the + + align:start position:0% +our energies here now again we're in the + + + align:start position:0% +our energies here now again we're in the +uh we're in the polar coordinates now so + + align:start position:0% +uh we're in the polar coordinates now so + + + align:start position:0% +uh we're in the polar coordinates now so +our energies look a little bit different + + align:start position:0% +our energies look a little bit different + + + align:start position:0% +our energies look a little bit different +um our kinetic + + align:start position:0% + + + + align:start position:0% + +energy looks like that and our potential + + align:start position:0% +energy looks like that and our potential + + + align:start position:0% +energy looks like that and our potential +energy um + + align:start position:0% +energy um + + + align:start position:0% +energy um +is this term and what else do we + + align:start position:0% +is this term and what else do we + + + align:start position:0% +is this term and what else do we +need + + align:start position:0% +need + + + align:start position:0% +need +else spring poti spring yeah how much + + align:start position:0% +else spring poti spring yeah how much + + + align:start position:0% +else spring poti spring yeah how much +it's K over + + align:start position:0% +it's K over + + + align:start position:0% +it's K over +two + + align:start position:0% +two + + + align:start position:0% +two +um X + + align:start position:0% +um X + + + align:start position:0% +um X +sorry R minus r + + align:start position:0% +sorry R minus r + + + align:start position:0% +sorry R minus r +squared and so using + + align:start position:0% +squared and so using + + + align:start position:0% +squared and so using +that you probably remember lrange it's + + align:start position:0% +that you probably remember lrange it's + + + align:start position:0% +that you probably remember lrange it's +not that bad the system + + align:start position:0% +not that bad the system + + + align:start position:0% +not that bad the system +um you can get the equations of + + align:start position:0% +um you can get the equations of + + + align:start position:0% +um you can get the equations of +motion equation motion + + align:start position:0% + + + + align:start position:0% + +here you + + align:start position:0% + + + + align:start position:0% + +get oh sorry + + align:start position:0% + + + + align:start position:0% + +and so you have all your expected terms + + align:start position:0% +and so you have all your expected terms + + + align:start position:0% +and so you have all your expected terms +centrifugal terms coris terms all that + + align:start position:0% +centrifugal terms coris terms all that + + + align:start position:0% +centrifugal terms coris terms all that +if you TR to make sense of what this is + + align:start position:0% +if you TR to make sense of what this is + + + align:start position:0% +if you TR to make sense of what this is +um + + align:start position:0% +um + + + align:start position:0% +um +and so if you want to get from touchdown + + align:start position:0% +and so if you want to get from touchdown + + + align:start position:0% +and so if you want to get from touchdown +to + + align:start position:0% +to + + + align:start position:0% +to +takeoff you can't get a close form + + align:start position:0% +takeoff you can't get a close form + + + align:start position:0% +takeoff you can't get a close form +solution from this you can simulate + + align:start position:0% +solution from this you can simulate + + + align:start position:0% +solution from this you can simulate +pretty easily obviously but you don't + + align:start position:0% +pretty easily obviously but you don't + + + align:start position:0% +pretty easily obviously but you don't +get the close forms you can't get sort + + align:start position:0% +get the close forms you can't get sort + + + align:start position:0% +get the close forms you can't get sort +of this analytical kind of mapping but + + align:start position:0% +of this analytical kind of mapping but + + + align:start position:0% +of this analytical kind of mapping but +if you use a small angle and small + + align:start position:0% +if you use a small angle and small + + + align:start position:0% +if you use a small angle and small +displacement approximation you can + + align:start position:0% +displacement approximation you can + + + align:start position:0% +displacement approximation you can +linearize the system and you can get the + + align:start position:0% +linearize the system and you can get the + + + align:start position:0% +linearize the system and you can get the +uh a close form solution for this + + align:start position:0% +uh a close form solution for this + + + align:start position:0% +uh a close form solution for this +touchdown to take off phase all right + + align:start position:0% +touchdown to take off phase all right + + + align:start position:0% +touchdown to take off phase all right +and so that's sort of is the assumption + + align:start position:0% +and so that's sort of is the assumption + + + align:start position:0% +and so that's sort of is the assumption +that Theta is much much less than one + + align:start position:0% +that Theta is much much less than one + + + align:start position:0% +that Theta is much much less than one +your Delta r r + + align:start position:0% +your Delta r r + + + align:start position:0% +your Delta r r +one all right and so then you can get to + + align:start position:0% +one all right and so then you can get to + + + align:start position:0% +one all right and so then you can get to +a close from solution it's it's kind of + + align:start position:0% +a close from solution it's it's kind of + + + align:start position:0% +a close from solution it's it's kind of +ugly it's not really ugly I mean it's + + align:start position:0% +ugly it's not really ugly I mean it's + + + align:start position:0% +ugly it's not really ugly I mean it's +not so ugly as to be prohibitive but I'm + + align:start position:0% +not so ugly as to be prohibitive but I'm + + + align:start position:0% +not so ugly as to be prohibitive but I'm +not going to write it down + + align:start position:0% +not going to write it down + + + align:start position:0% +not going to write it down +um but that lets you actually get a + + align:start position:0% +um but that lets you actually get a + + + align:start position:0% +um but that lets you actually get a +close form return map all right and + + align:start position:0% +close form return map all right and + + + align:start position:0% +close form return map all right and +something cool about that is that you + + align:start position:0% +something cool about that is that you + + + align:start position:0% +something cool about that is that you +get + + align:start position:0% +get + + + align:start position:0% +get +these two fixed points you get one + + align:start position:0% +these two fixed points you get one + + + align:start position:0% +these two fixed points you get one +stable fix point and one unstable fix + + align:start position:0% +stable fix point and one unstable fix + + + align:start position:0% +stable fix point and one unstable fix +point and + + align:start position:0% + + + + align:start position:0% + +H and actually a number of people + + align:start position:0% +H and actually a number of people + + + align:start position:0% +H and actually a number of people +thought that a system like this this + + align:start position:0% +thought that a system like this this + + + align:start position:0% +thought that a system like this this +conservative system shouldn't be able to + + align:start position:0% +conservative system shouldn't be able to + + + align:start position:0% +conservative system shouldn't be able to +get that sort of stability um CU if you + + align:start position:0% +get that sort of stability um CU if you + + + align:start position:0% +get that sort of stability um CU if you +remember in the uh in the rimless wheel + + align:start position:0% +remember in the uh in the rimless wheel + + + align:start position:0% +remember in the uh in the rimless wheel +the sort of energy loss was critical + + align:start position:0% +the sort of energy loss was critical + + + align:start position:0% +the sort of energy loss was critical +towards achieving the stability is that + + align:start position:0% +towards achieving the stability is that + + + align:start position:0% +towards achieving the stability is that +when you went faster you hit harder you + + align:start position:0% +when you went faster you hit harder you + + + align:start position:0% +when you went faster you hit harder you +lost more energy um and when you went + + align:start position:0% +lost more energy um and when you went + + + align:start position:0% +lost more energy um and when you went +slower you uh you know you you didn't + + align:start position:0% +slower you uh you know you you didn't + + + align:start position:0% +slower you uh you know you you didn't +lose as much energy so you're able to + + align:start position:0% +lose as much energy so you're able to + + + align:start position:0% +lose as much energy so you're able to +speed up as you went down this + + align:start position:0% +speed up as you went down this + + + align:start position:0% +speed up as you went down this +ramp so the fact that you can achieve + + align:start position:0% +ramp so the fact that you can achieve + + + align:start position:0% +ramp so the fact that you can achieve +stability in the system is kind of cool + + align:start position:0% +stability in the system is kind of cool + + + align:start position:0% +stability in the system is kind of cool +too because it's completely conservative + + align:start position:0% +too because it's completely conservative + + + align:start position:0% +too because it's completely conservative +yet somehow able to actually sort of + + align:start position:0% +yet somehow able to actually sort of + + + align:start position:0% +yet somehow able to actually sort of +push it towards a repeatable state so + + align:start position:0% +push it towards a repeatable state so + + + align:start position:0% +push it towards a repeatable state so +again then looking at uh we want to see + + align:start position:0% +again then looking at uh we want to see + + + align:start position:0% +again then looking at uh we want to see +this return map um this is + + align:start position:0% +this return map um this is + + + align:start position:0% +this return map um this is +from H uh gu's thesis work I believe + + align:start position:0% +from H uh gu's thesis work I believe + + + align:start position:0% +from H uh gu's thesis work I believe +um + + align:start position:0% + + + + align:start position:0% + +and it's pretty cool if I can get to for + + align:start position:0% +and it's pretty cool if I can get to for + + + align:start position:0% +and it's pretty cool if I can get to for +you all + + align:start position:0% + + + + align:start position:0% + +right there we + + align:start position:0% + + + + align:start position:0% + +go there we + + align:start position:0% +go there we + + + align:start position:0% +go there we +go all right so this is actually um the + + align:start position:0% +go all right so this is actually um the + + + align:start position:0% +go all right so this is actually um the +return map for this sort of small angle + + align:start position:0% +return map for this sort of small angle + + + align:start position:0% +return map for this sort of small angle +approximation you can get analytically + + align:start position:0% +approximation you can get analytically + + + align:start position:0% +approximation you can get analytically +and you see there's this unstable fix + + align:start position:0% +and you see there's this unstable fix + + + align:start position:0% +and you see there's this unstable fix +point and then down there there's that + + align:start position:0% +point and then down there there's that + + + align:start position:0% +point and then down there there's that +stable fix point so you zoom in and you + + align:start position:0% +stable fix point so you zoom in and you + + + align:start position:0% +stable fix point so you zoom in and you +can + + align:start position:0% +can + + + align:start position:0% +can +see um s the stability region that that + + align:start position:0% +see um s the stability region that that + + + align:start position:0% +see um s the stability region that that +unstable one is s of defining the + + align:start position:0% +unstable one is s of defining the + + + align:start position:0% +unstable one is s of defining the +boundary and the stability for that um + + align:start position:0% +boundary and the stability for that um + + + align:start position:0% +boundary and the stability for that um +the Apex height um you know the why does + + align:start position:0% +the Apex height um you know the why does + + + align:start position:0% +the Apex height um you know the why does +it get to that minimum there why does it + + align:start position:0% +it get to that minimum there why does it + + + align:start position:0% +it get to that minimum there why does it +go below that + + align:start position:0% +go below that + + + align:start position:0% +go below that + + align:start position:0% + + + + align:start position:0% + +no why don't we look at it below that + + align:start position:0% +no why don't we look at it below that + + + align:start position:0% +no why don't we look at it below that +that's the maximum L of yeah that's your + + align:start position:0% +that's the maximum L of yeah that's your + + + align:start position:0% +that's the maximum L of yeah that's your +sort of height at the cosine Theta + + align:start position:0% +sort of height at the cosine Theta + + + align:start position:0% +sort of height at the cosine Theta +length of the leg and so you can't get + + align:start position:0% +length of the leg and so you can't get + + + align:start position:0% +length of the leg and so you can't get +below that and then the weird thing is + + align:start position:0% +below that and then the weird thing is + + + align:start position:0% +below that and then the weird thing is +and this is something I was talking + + align:start position:0% +and this is something I was talking + + + align:start position:0% +and this is something I was talking +about with Russ just before he went home + + align:start position:0% +about with Russ just before he went home + + + align:start position:0% +about with Russ just before he went home +um was why does it keep climbing like + + align:start position:0% + + + + align:start position:0% + +that does it keep cling well cuz right + + align:start position:0% +that does it keep cling well cuz right + + + align:start position:0% +that does it keep cling well cuz right +this this is conservative right so how + + align:start position:0% +this this is conservative right so how + + + align:start position:0% +this this is conservative right so how +does how can you have an instability + + align:start position:0% +does how can you have an instability + + + align:start position:0% +does how can you have an instability +that pushes you up to larger and larger + + align:start position:0% +that pushes you up to larger and larger + + + align:start position:0% +that pushes you up to larger and larger +Apex + + align:start position:0% +Apex + + + align:start position:0% +Apex +Heights more vertical at some point + + align:start position:0% +Heights more vertical at some point + + + align:start position:0% +Heights more vertical at some point +though it should cap right there should + + align:start position:0% +though it should cap right there should + + + align:start position:0% +though it should cap right there should +be another stable fix Point bouncing + + align:start position:0% +be another stable fix Point bouncing + + + align:start position:0% +be another stable fix Point bouncing +straight up + + align:start position:0% +straight up + + + align:start position:0% +straight up +right there isn't the thing is that what + + align:start position:0% +right there isn't the thing is that what + + + align:start position:0% +right there isn't the thing is that what +we think is that that unstable one right + + align:start position:0% +we think is that that unstable one right + + + align:start position:0% +we think is that that unstable one right +there is your vertical bouncing and + + align:start position:0% +there is your vertical bouncing and + + + align:start position:0% +there is your vertical bouncing and +thing is that actually if you when you + + align:start position:0% +thing is that actually if you when you + + + align:start position:0% +thing is that actually if you when you +linearize these they don't quite + + align:start position:0% +linearize these they don't quite + + + align:start position:0% +linearize these they don't quite +conserve energy anymore there actually + + align:start position:0% +conserve energy anymore there actually + + + align:start position:0% +conserve energy anymore there actually +can be a non-conservative term so I + + align:start position:0% +can be a non-conservative term so I + + + align:start position:0% +can be a non-conservative term so I +think that's what this is from so it + + align:start position:0% +think that's what this is from so it + + + align:start position:0% +think that's what this is from so it +really shouldn't be climbing up like + + align:start position:0% +really shouldn't be climbing up like + + + align:start position:0% +really shouldn't be climbing up like +that cuz when you simulate these things + + align:start position:0% +that cuz when you simulate these things + + + align:start position:0% +that cuz when you simulate these things +um you don't get above that sort of + + align:start position:0% +um you don't get above that sort of + + + align:start position:0% +um you don't get above that sort of +second fix point it sort of rolls up to + + align:start position:0% +second fix point it sort of rolls up to + + + align:start position:0% +second fix point it sort of rolls up to +that and you have this unstable one and + + align:start position:0% +that and you have this unstable one and + + + align:start position:0% +that and you have this unstable one and +so then but then looking at this again + + align:start position:0% +so then but then looking at this again + + + align:start position:0% +so then but then looking at this again +now here's another strange thing it + + align:start position:0% +now here's another strange thing it + + + align:start position:0% +now here's another strange thing it +looks like it should be globally stable + + align:start position:0% +looks like it should be globally stable + + + align:start position:0% +looks like it should be globally stable +then right because if in practice we + + align:start position:0% +then right because if in practice we + + + align:start position:0% +then right because if in practice we +can't get above that unstable fix point + + align:start position:0% +can't get above that unstable fix point + + + align:start position:0% +can't get above that unstable fix point +and if you look at this uh this Apex + + align:start position:0% +and if you look at this uh this Apex + + + align:start position:0% +and if you look at this uh this Apex +axis right the higher it is the slower + + align:start position:0% +axis right the higher it is the slower + + + align:start position:0% +axis right the higher it is the slower +it moves so at your minimum sort of Apex + + align:start position:0% +it moves so at your minimum sort of Apex + + + align:start position:0% +it moves so at your minimum sort of Apex +height right that's when you're moving + + align:start position:0% +height right that's when you're moving + + + align:start position:0% +height right that's when you're moving +fastest it looks like it's stable + + align:start position:0% +fastest it looks like it's stable + + + align:start position:0% +fastest it looks like it's stable +throughout the entire sort of operating + + align:start position:0% +throughout the entire sort of operating + + + align:start position:0% +throughout the entire sort of operating +regime right the fastest it can move is + + align:start position:0% +regime right the fastest it can move is + + + align:start position:0% +regime right the fastest it can move is +that little guy on the far left where + + align:start position:0% +that little guy on the far left where + + + align:start position:0% +that little guy on the far left where +it's apparently stable and the slowest + + align:start position:0% +it's apparently stable and the slowest + + + align:start position:0% +it's apparently stable and the slowest +can moves is vertical bouncing is that + + align:start position:0% +can moves is vertical bouncing is that + + + align:start position:0% +can moves is vertical bouncing is that +then a fix point so how do you explain + + align:start position:0% + + + + align:start position:0% + +that soon as you always you always the + + align:start position:0% +that soon as you always you always the + + + align:start position:0% +that soon as you always you always the +same angle that's the thing is that it + + align:start position:0% +same angle that's the thing is that it + + + align:start position:0% +same angle that's the thing is that it +that's that's pretty much exactly the + + align:start position:0% +that's that's pretty much exactly the + + + align:start position:0% +that's that's pretty much exactly the +issue is that your your failure mode can + + align:start position:0% +issue is that your your failure mode can + + + align:start position:0% +issue is that your your failure mode can +come from like coming in squishing + + align:start position:0% +come from like coming in squishing + + + align:start position:0% +come from like coming in squishing +really low I'm going to fall on my face + + align:start position:0% +really low I'm going to fall on my face + + + align:start position:0% +really low I'm going to fall on my face +here so I should let everyone see it um + + align:start position:0% +here so I should let everyone see it um + + + align:start position:0% +here so I should let everyone see it um +you compress and get really low and then + + align:start position:0% +you compress and get really low and then + + + align:start position:0% +you compress and get really low and then +you bounce forward and if you bounce + + align:start position:0% +you bounce forward and if you bounce + + + align:start position:0% +you bounce forward and if you bounce +forward it's such a trajectory that you + + align:start position:0% +forward it's such a trajectory that you + + + align:start position:0% +forward it's such a trajectory that you +never get high enough for your leg to be + + align:start position:0% +never get high enough for your leg to be + + + align:start position:0% +never get high enough for your leg to be +out touch it down then you're just going + + align:start position:0% +out touch it down then you're just going + + + align:start position:0% +out touch it down then you're just going +to bounce forward sort of land in your + + align:start position:0% +to bounce forward sort of land in your + + + align:start position:0% +to bounce forward sort of land in your +face you can't actually warp your leg + + align:start position:0% +face you can't actually warp your leg + + + align:start position:0% +face you can't actually warp your leg +right does that make sense so that can + + align:start position:0% +right does that make sense so that can + + + align:start position:0% +right does that make sense so that can +be your feeling you bounce in you shoot + + align:start position:0% +be your feeling you bounce in you shoot + + + align:start position:0% +be your feeling you bounce in you shoot +across and then if you're never if you + + align:start position:0% +across and then if you're never if you + + + align:start position:0% +across and then if you're never if you +never have an apex high enough you'll + + align:start position:0% +never have an apex high enough you'll + + + align:start position:0% +never have an apex high enough you'll +never get your leg ahead of you so + + align:start position:0% +never get your leg ahead of you so + + + align:start position:0% +never get your leg ahead of you so +that's the failure modes that's actually + + align:start position:0% +that's the failure modes that's actually + + + align:start position:0% +that's the failure modes that's actually +thing what we see when we simulate it um + + align:start position:0% +thing what we see when we simulate it um + + + align:start position:0% +thing what we see when we simulate it um +and the simulation actually looks a + + align:start position:0% +and the simulation actually looks a + + + align:start position:0% +and the simulation actually looks a +little bit different there's actually um + + align:start position:0% +little bit different there's actually um + + + align:start position:0% +little bit different there's actually um +this guy looks pretty good but if you if + + align:start position:0% +this guy looks pretty good but if you if + + + align:start position:0% +this guy looks pretty good but if you if +you simulate it um you have SL different + + align:start position:0% +you simulate it um you have SL different + + + align:start position:0% +you simulate it um you have SL different +parameters that um that curve there + + align:start position:0% +parameters that um that curve there + + + align:start position:0% +parameters that um that curve there +comes down a little bit lower and so + + align:start position:0% +comes down a little bit lower and so + + + align:start position:0% +comes down a little bit lower and so +you're actually able to sort of be the + + align:start position:0% +you're actually able to sort of be the + + + align:start position:0% +you're actually able to sort of be the +top and bounce in and overshoot and go + + align:start position:0% +top and bounce in and overshoot and go + + + align:start position:0% +top and bounce in and overshoot and go +unstable so it's not like you're + + align:start position:0% +unstable so it's not like you're + + + align:start position:0% +unstable so it's not like you're +guaranteed stability by starting to + + align:start position:0% +guaranteed stability by starting to + + + align:start position:0% +guaranteed stability by starting to +bounce vertically either so this is this + + align:start position:0% +bounce vertically either so this is this + + + align:start position:0% +bounce vertically either so this is this +will change with different energies + + align:start position:0% +will change with different energies + + + align:start position:0% +will change with different energies +different parameter settings and + + align:start position:0% +different parameter settings and + + + align:start position:0% +different parameter settings and +everything like that but the the take + + align:start position:0% +everything like that but the the take + + + align:start position:0% +everything like that but the the take +home thing I think what cool is that + + align:start position:0% +home thing I think what cool is that + + + align:start position:0% +home thing I think what cool is that +even this like sort of simplified + + align:start position:0% +even this like sort of simplified + + + align:start position:0% +even this like sort of simplified +perspective of it um you get the + + align:start position:0% +perspective of it um you get the + + + align:start position:0% +perspective of it um you get the +stability in this conservative system + + align:start position:0% +stability in this conservative system + + + align:start position:0% +stability in this conservative system +you get the stability that you can see + + align:start position:0% +you get the stability that you can see + + + align:start position:0% +you get the stability that you can see +in the simulation and that even though + + align:start position:0% +in the simulation and that even though + + + align:start position:0% +in the simulation and that even though +it's not damping on any energy or + + align:start position:0% +it's not damping on any energy or + + + align:start position:0% +it's not damping on any energy or +anything like that is able to uh to + + align:start position:0% +anything like that is able to uh to + + + align:start position:0% +anything like that is able to uh to +bounce along and right itself and + + align:start position:0% +bounce along and right itself and + + + align:start position:0% +bounce along and right itself and +apparently what that's related to + + align:start position:0% +apparently what that's related to + + + align:start position:0% +apparently what that's related to +apparently people didn't used to think + + align:start position:0% +apparently people didn't used to think + + + align:start position:0% +apparently people didn't used to think +that was possible um but the coordinate + + align:start position:0% +that was possible um but the coordinate + + + align:start position:0% +that was possible um but the coordinate +transform is actually enough to get that + + align:start position:0% +transform is actually enough to get that + + + align:start position:0% +transform is actually enough to get that +kind of stability is that it's called + + align:start position:0% +kind of stability is that it's called + + + align:start position:0% +kind of stability is that it's called +peie wise homic um and by switching sort + + align:start position:0% +peie wise homic um and by switching sort + + + align:start position:0% +peie wise homic um and by switching sort +of these coordinates you're actually + + align:start position:0% +of these coordinates you're actually + + + align:start position:0% +of these coordinates you're actually +able to get the sort of that allows the + + align:start position:0% +able to get the sort of that allows the + + + align:start position:0% +able to get the sort of that allows the +Dynamics to to stabilize themselves + + align:start position:0% +Dynamics to to stabilize themselves + + + align:start position:0% +Dynamics to to stabilize themselves +apparently as opposed to a normal homic + + align:start position:0% +apparently as opposed to a normal homic + + + align:start position:0% +apparently as opposed to a normal homic +system apparently couldn't actually you + + align:start position:0% +system apparently couldn't actually you + + + align:start position:0% +system apparently couldn't actually you +know converge in back towards this uh + + align:start position:0% +know converge in back towards this uh + + + align:start position:0% +know converge in back towards this uh +fixed point if you think about like the + + align:start position:0% +fixed point if you think about like the + + + align:start position:0% +fixed point if you think about like the +pendulum on damp something like that + + align:start position:0% +pendulum on damp something like that + + + align:start position:0% +pendulum on damp something like that +that's not going to converge in right it + + align:start position:0% +that's not going to converge in right it + + + align:start position:0% +that's not going to converge in right it +has to conserve the energy but + + align:start position:0% +has to conserve the energy but + + + align:start position:0% +has to conserve the energy but +apparently with peic systems it's + + align:start position:0% +apparently with peic systems it's + + + align:start position:0% +apparently with peic systems it's +available um but you can read some + + align:start position:0% +available um but you can read some + + + align:start position:0% +available um but you can read some +papers and get into that but + + align:start position:0% +papers and get into that but + + + align:start position:0% +papers and get into that but +I I don't know uh I don't know much more + + align:start position:0% +I I don't know uh I don't know much more + + + align:start position:0% +I I don't know uh I don't know much more +than I just told you + + align:start position:0% +than I just told you + + + align:start position:0% +than I just told you +so + + align:start position:0% +so + + + align:start position:0% +so +um all right so here's another thing um + + align:start position:0% +um all right so here's another thing um + + + align:start position:0% +um all right so here's another thing um +that's interesting is that if you look + + align:start position:0% +that's interesting is that if you look + + + align:start position:0% +that's interesting is that if you look +at if you want to model those uh those + + align:start position:0% +at if you want to model those uh those + + + align:start position:0% +at if you want to model those uh those +rir Hoppers right they obviously aren't + + align:start position:0% +rir Hoppers right they obviously aren't + + + align:start position:0% +rir Hoppers right they obviously aren't +completely conservative right they do + + align:start position:0% +completely conservative right they do + + + align:start position:0% +completely conservative right they do +have some mass of the toe and in the leg + + align:start position:0% +have some mass of the toe and in the leg + + + align:start position:0% +have some mass of the toe and in the leg +um and so when they hit they do lose + + align:start position:0% +um and so when they hit they do lose + + + align:start position:0% +um and so when they hit they do lose +some energy cuz when that toe hits and + + align:start position:0% +some energy cuz when that toe hits and + + + align:start position:0% +some energy cuz when that toe hits and +sticks to the ground it's going to be a + + align:start position:0% +sticks to the ground it's going to be a + + + align:start position:0% +sticks to the ground it's going to be a +dissipative reaction + + align:start position:0% +dissipative reaction + + + align:start position:0% +dissipative reaction +so you can look at this model by I think + + align:start position:0% +so you can look at this model by I think + + + align:start position:0% +so you can look at this model by I think +kod and ber um in + + align:start position:0% +kod and ber um in + + + align:start position:0% +kod and ber um in +91 let me use my big chalk again and + + align:start position:0% +91 let me use my big chalk again and + + + align:start position:0% +91 let me use my big chalk again and +here's my old big + + align:start position:0% +here's my old big + + + align:start position:0% +here's my old big +chalk + + align:start position:0% +chalk + + + align:start position:0% +chalk +so looking at + + align:start position:0% +so looking at + + + align:start position:0% +so looking at +this + + align:start position:0% + + + + align:start position:0% + +right so here we have a toe Mass so we + + align:start position:0% +right so here we have a toe Mass so we + + + align:start position:0% +right so here we have a toe Mass so we +have the mass of the body and mass of + + align:start position:0% +have the mass of the body and mass of + + + align:start position:0% +have the mass of the body and mass of +the toe all right and this spring can + + align:start position:0% +the toe all right and this spring can + + + align:start position:0% +the toe all right and this spring can +possibly be + + align:start position:0% +possibly be + + + align:start position:0% +possibly be +nonlinear if you + + align:start position:0% +nonlinear if you + + + align:start position:0% +nonlinear if you +want um and this was largely they did + + align:start position:0% +want um and this was largely they did + + + align:start position:0% +want um and this was largely they did +some analytics but a lot of it was + + align:start position:0% +some analytics but a lot of it was + + + align:start position:0% +some analytics but a lot of it was +computationally driven the analysis they + + align:start position:0% +computationally driven the analysis they + + + align:start position:0% +computationally driven the analysis they +did this system and so thing is because + + align:start position:0% +did this system and so thing is because + + + align:start position:0% +did this system and so thing is because +of this uh this hit here you have a + + align:start position:0% + + + + align:start position:0% + +loss due to the toe + + align:start position:0% + + + + align:start position:0% + +Mass so must + + align:start position:0% +Mass so must + + + align:start position:0% +Mass so must +add + + align:start position:0% + + + + align:start position:0% + +energy and I do this with a sort of + + align:start position:0% +energy and I do this with a sort of + + + align:start position:0% +energy and I do this with a sort of +control on the uh on the spring if you + + align:start position:0% +control on the uh on the spring if you + + + align:start position:0% +control on the uh on the spring if you +can vary your spring con something like + + align:start position:0% +can vary your spring con something like + + + align:start position:0% +can vary your spring con something like +that you can add you can add energy to + + align:start position:0% +that you can add you can add energy to + + + align:start position:0% +that you can add you can add energy to +the + + align:start position:0% +the + + + align:start position:0% +the +system um and so the control on the + + align:start position:0% +system um and so the control on the + + + align:start position:0% +system um and so the control on the +spring is sort of their only control + + align:start position:0% +spring is sort of their only control + + + align:start position:0% +spring is sort of their only control +then um and you actually can get similar + + align:start position:0% +then um and you actually can get similar + + + align:start position:0% +then um and you actually can get similar +stability properties to the slip model + + align:start position:0% +stability properties to the slip model + + + align:start position:0% +stability properties to the slip model +you can get these when you simulate it + + align:start position:0% +you can get these when you simulate it + + + align:start position:0% +you can get these when you simulate it +you can find the same sort of uh stable + + align:start position:0% +you can find the same sort of uh stable + + + align:start position:0% +you can find the same sort of uh stable +fix Point unstable fix Point um kind of + + align:start position:0% +fix Point unstable fix Point um kind of + + + align:start position:0% +fix Point unstable fix Point um kind of +behavior and so this is all what we've + + align:start position:0% +behavior and so this is all what we've + + + align:start position:0% +behavior and so this is all what we've +been talking about sort of the image we + + align:start position:0% +been talking about sort of the image we + + + align:start position:0% +been talking about sort of the image we +have is this sort of sagittal plane + + align:start position:0% +have is this sort of sagittal plane + + + align:start position:0% +have is this sort of sagittal plane +Dynamics right the sagittal plane is + + align:start position:0% +Dynamics right the sagittal plane is + + + align:start position:0% +Dynamics right the sagittal plane is +this plane and sort of the sort of idea + + align:start position:0% +this plane and sort of the sort of idea + + + align:start position:0% +this plane and sort of the sort of idea +of running through like that right + + align:start position:0% +of running through like that right + + + align:start position:0% +of running through like that right +getting a little bit aerial face so it + + align:start position:0% +getting a little bit aerial face so it + + + align:start position:0% +getting a little bit aerial face so it +look less + + align:start position:0% +look less + + + align:start position:0% +look less +ridiculous and so the other thing though + + align:start position:0% +ridiculous and so the other thing though + + + align:start position:0% +ridiculous and so the other thing though +is that it's good for the lateral plane + + align:start position:0% +is that it's good for the lateral plane + + + align:start position:0% +is that it's good for the lateral plane +if you look at the sort of lateral plane + + align:start position:0% +if you look at the sort of lateral plane + + + align:start position:0% +if you look at the sort of lateral plane +Dynamics certain animals um the same + + align:start position:0% +Dynamics certain animals um the same + + + align:start position:0% +Dynamics certain animals um the same +kind of slit model and that kind of + + align:start position:0% +kind of slit model and that kind of + + + align:start position:0% +kind of slit model and that kind of +behavior can actually be witnessed so + + align:start position:0% +behavior can actually be witnessed so + + + align:start position:0% +behavior can actually be witnessed so +this is uh again something Bob F spent a + + align:start position:0% +this is uh again something Bob F spent a + + + align:start position:0% +this is uh again something Bob F spent a +lot of time on um if you look at a + + align:start position:0% +lot of time on um if you look at a + + + align:start position:0% +lot of time on um if you look at a +cockroach which has a tripod + + align:start position:0% +cockroach which has a tripod + + + align:start position:0% +cockroach which has a tripod +gate um here's a cockroach I wish they + + align:start position:0% +gate um here's a cockroach I wish they + + + align:start position:0% +gate um here's a cockroach I wish they +actually looked like that probably + + align:start position:0% +actually looked like that probably + + + align:start position:0% +actually looked like that probably +wouldn't be as + + align:start position:0% + + + + align:start position:0% + +disturbing + + align:start position:0% +disturbing + + + align:start position:0% +disturbing +there and so what you have is they sort + + align:start position:0% +there and so what you have is they sort + + + align:start position:0% +there and so what you have is they sort +of use three legs at a time and they're + + align:start position:0% +of use three legs at a time and they're + + + align:start position:0% +of use three legs at a time and they're +springy + + align:start position:0% + + + + align:start position:0% + +legs as it runs if you look at the + + align:start position:0% +legs as it runs if you look at the + + + align:start position:0% +legs as it runs if you look at the +Dynamics you actually can see the uh + + align:start position:0% +Dynamics you actually can see the uh + + + align:start position:0% +Dynamics you actually can see the uh +actually you'd see that these legs are + + align:start position:0% +actually you'd see that these legs are + + + align:start position:0% +actually you'd see that these legs are +acting sort of like Springs and actually + + align:start position:0% +acting sort of like Springs and actually + + + align:start position:0% +acting sort of like Springs and actually +the same kind of slip Behavior you'd + + align:start position:0% +the same kind of slip Behavior you'd + + + align:start position:0% +the same kind of slip Behavior you'd +expect you witness in + + align:start position:0% +expect you witness in + + + align:start position:0% +expect you witness in +uh you witness in the + + align:start position:0% +uh you witness in the + + + align:start position:0% +uh you witness in the +Cockroaches um and so there's some cool + + align:start position:0% +Cockroaches um and so there's some cool + + + align:start position:0% +Cockroaches um and so there's some cool +things here um let me show you some of + + align:start position:0% +things here um let me show you some of + + + align:start position:0% +things here um let me show you some of +these have any of you heard of + + align:start position:0% +these have any of you heard of + + + align:start position:0% +these have any of you heard of +preflex as opposed to reflex it's sort + + align:start position:0% +preflex as opposed to reflex it's sort + + + align:start position:0% +preflex as opposed to reflex it's sort +of like piy kind of name I guess um so + + align:start position:0% +of like piy kind of name I guess um so + + + align:start position:0% +of like piy kind of name I guess um so +the uh preflex is where actually you can + + align:start position:0% +the uh preflex is where actually you can + + + align:start position:0% +the uh preflex is where actually you can +actually look at the top time constant + + align:start position:0% +actually look at the top time constant + + + align:start position:0% +actually look at the top time constant +required for + + align:start position:0% +required for + + + align:start position:0% +required for +uh um for the monoptic reflex which is s + + align:start position:0% +uh um for the monoptic reflex which is s + + + align:start position:0% +uh um for the monoptic reflex which is s +the electrical signal to go through and + + align:start position:0% +the electrical signal to go through and + + + align:start position:0% +the electrical signal to go through and +actually to the spinal cord and back so + + align:start position:0% +actually to the spinal cord and back so + + + align:start position:0% +actually to the spinal cord and back so +not to the brain to like the full path + + align:start position:0% +not to the brain to like the full path + + + align:start position:0% +not to the brain to like the full path +but just like the sort of quick reflex + + align:start position:0% +but just like the sort of quick reflex + + + align:start position:0% +but just like the sort of quick reflex +kind of response and actually some of + + align:start position:0% +kind of response and actually some of + + + align:start position:0% +kind of response and actually some of +these um creatures actually respond + + align:start position:0% +these um creatures actually respond + + + align:start position:0% +these um creatures actually respond +faster than that so the theory is is + + align:start position:0% +faster than that so the theory is is + + + align:start position:0% +faster than that so the theory is is +that it's actually a muscular skeletal + + align:start position:0% +that it's actually a muscular skeletal + + + align:start position:0% +that it's actually a muscular skeletal +response right so it's not even it's not + + align:start position:0% +response right so it's not even it's not + + + align:start position:0% +response right so it's not even it's not +control at all it's not going to muscles + + align:start position:0% +control at all it's not going to muscles + + + align:start position:0% +control at all it's not going to muscles +or anything like that it's tendons it's + + align:start position:0% +or anything like that it's tendons it's + + + align:start position:0% +or anything like that it's tendons it's +the sort of springness in the leg and + + align:start position:0% +the sort of springness in the leg and + + + align:start position:0% +the sort of springness in the leg and +that is actually what's providing some + + align:start position:0% +that is actually what's providing some + + + align:start position:0% +that is actually what's providing some +of the control here and some of the + + align:start position:0% +of the control here and some of the + + + align:start position:0% +of the control here and some of the +stability and so there's a really + + align:start position:0% +stability and so there's a really + + + align:start position:0% +stability and so there's a really +incredibly awesome video + + align:start position:0% +incredibly awesome video + + + align:start position:0% +incredibly awesome video +that + + align:start position:0% +that + + + align:start position:0% +that +I I'm definitely going to show you + + align:start position:0% +I I'm definitely going to show you + + + align:start position:0% +I I'm definitely going to show you +regardless of how inconvenient this + + align:start position:0% +regardless of how inconvenient this + + + align:start position:0% +regardless of how inconvenient this +thing comes up + + align:start position:0% +thing comes up + + + align:start position:0% +thing comes up +um it's not an anticipatory neural it's + + align:start position:0% +um it's not an anticipatory neural it's + + + align:start position:0% +um it's not an anticipatory neural it's +not and and that's because you can + + align:start position:0% +not and and that's because you can + + + align:start position:0% +not and and that's because you can +actually you can perturb them um sort of + + align:start position:0% +actually you can perturb them um sort of + + + align:start position:0% +actually you can perturb them um sort of +almost instantaneous right like sort of + + align:start position:0% +almost instantaneous right like sort of + + + align:start position:0% +almost instantaneous right like sort of +Slam with a perturbation and so they + + align:start position:0% +Slam with a perturbation and so they + + + align:start position:0% +Slam with a perturbation and so they +can't anticipate this right and actually + + align:start position:0% +can't anticipate this right and actually + + + align:start position:0% +can't anticipate this right and actually +you can see like within one footstep + + align:start position:0% +you can see like within one footstep + + + align:start position:0% +you can see like within one footstep +within one step a cockroach step they'll + + align:start position:0% +within one step a cockroach step they'll + + + align:start position:0% +within one step a cockroach step they'll +spring back in their Center Mass + + align:start position:0% +spring back in their Center Mass + + + align:start position:0% +spring back in their Center Mass +trajectory will get back on track and so + + align:start position:0% +trajectory will get back on track and so + + + align:start position:0% +trajectory will get back on track and so +it's not it's not like they see + + align:start position:0% +it's not it's not like they see + + + align:start position:0% +it's not it's not like they see +something coming or there's like you + + align:start position:0% +something coming or there's like you + + + align:start position:0% +something coming or there's like you +know they're going to step something + + align:start position:0% +know they're going to step something + + + align:start position:0% +know they're going to step something +it's going to hit them it's that there's + + align:start position:0% +it's going to hit them it's that there's + + + align:start position:0% +it's going to hit them it's that there's +just they're running along a + + align:start position:0% +just they're running along a + + + align:start position:0% +just they're running along a +perturbation and then they start + + align:start position:0% +perturbation and then they start + + + align:start position:0% +perturbation and then they start +balancing right + + align:start position:0% +balancing right + + + align:start position:0% +balancing right +away um I'm sorry about this I don't + + align:start position:0% +away um I'm sorry about this I don't + + + align:start position:0% +away um I'm sorry about this I don't +know + + align:start position:0% + + + + align:start position:0% + +what what's happening here um + + align:start position:0% + + + + align:start position:0% + +yeah now I have + + align:start position:0% +yeah now I have + + + align:start position:0% +yeah now I have +to in that model is it now the spring is + + align:start position:0% +to in that model is it now the spring is + + + align:start position:0% +to in that model is it now the spring is +actually in three + + align:start position:0% +actually in three + + + align:start position:0% +actually in three +dimensions you have XY z um and it's at + + align:start position:0% +dimensions you have XY z um and it's at + + + align:start position:0% +dimensions you have XY z um and it's at +an + + align:start position:0% +an + + + align:start position:0% +an +angle yeah I mean you is that how you + + align:start position:0% +angle yeah I mean you is that how you + + + align:start position:0% +angle yeah I mean you is that how you +that there's if you're doing the lateral + + align:start position:0% +that there's if you're doing the lateral + + + align:start position:0% +that there's if you're doing the lateral +plane you have to have some sort of + + align:start position:0% +plane you have to have some sort of + + + align:start position:0% +plane you have to have some sort of +bring this like that that can push you + + align:start position:0% +bring this like that that can push you + + + align:start position:0% +bring this like that that can push you +through through but you can actually + + align:start position:0% +through through but you can actually + + + align:start position:0% +through through but you can actually +look at the Cockroach um running in + + align:start position:0% +look at the Cockroach um running in + + + align:start position:0% +look at the Cockroach um running in +along the sadal plane and you don't need + + align:start position:0% +along the sadal plane and you don't need + + + align:start position:0% +along the sadal plane and you don't need +that you mention you + + align:start position:0% +that you mention you + + + align:start position:0% +that you mention you +can yeah you you can you can treat + + align:start position:0% +can yeah you you can you can treat + + + align:start position:0% +can yeah you you can you can treat +several legs if they're just sort of + + align:start position:0% +several legs if they're just sort of + + + align:start position:0% +several legs if they're just sort of +like one spring in the Tripod um if + + align:start position:0% +like one spring in the Tripod um if + + + align:start position:0% +like one spring in the Tripod um if +there's something called I don't know if + + align:start position:0% +there's something called I don't know if + + + align:start position:0% +there's something called I don't know if +you've seen you know Bob FS work at all + + align:start position:0% +you've seen you know Bob FS work at all + + + align:start position:0% +you've seen you know Bob FS work at all +on sort of these uh templates and + + align:start position:0% +on sort of these uh templates and + + + align:start position:0% +on sort of these uh templates and +anchors where there's anchors are the + + align:start position:0% +anchors where there's anchors are the + + + align:start position:0% +anchors where there's anchors are the +more complicated systems and the + + align:start position:0% +more complicated systems and the + + + align:start position:0% +more complicated systems and the +templates are these really simplified + + align:start position:0% +templates are these really simplified + + + align:start position:0% +templates are these really simplified +systems so your slip little thing here + + align:start position:0% +systems so your slip little thing here + + + align:start position:0% +systems so your slip little thing here +can be like a template which is a really + + align:start position:0% +can be like a template which is a really + + + align:start position:0% +can be like a template which is a really +sort of minimalist model but captures + + align:start position:0% +sort of minimalist model but captures + + + align:start position:0% +sort of minimalist model but captures +some of the essential Dynamics and does + + align:start position:0% +some of the essential Dynamics and does + + + align:start position:0% +some of the essential Dynamics and does +so in a sort of concise way um and you + + align:start position:0% +so in a sort of concise way um and you + + + align:start position:0% +so in a sort of concise way um and you +can look at just a which is + + align:start position:0% +can look at just a which is + + + align:start position:0% +can look at just a which is +following this kind of running I mean + + align:start position:0% +following this kind of running I mean + + + align:start position:0% +following this kind of running I mean +and it actually captures a lot of it I + + align:start position:0% +and it actually captures a lot of it I + + + align:start position:0% +and it actually captures a lot of it I +mean there's more complicated ones if + + align:start position:0% +mean there's more complicated ones if + + + align:start position:0% +mean there's more complicated ones if +you want look at the lateral playe + + align:start position:0% +you want look at the lateral playe + + + align:start position:0% +you want look at the lateral playe +Dynamics I you probably need a more + + align:start position:0% +Dynamics I you probably need a more + + + align:start position:0% +Dynamics I you probably need a more +complicated model um but + + align:start position:0% + + + + align:start position:0% + +so see what did you say this model was + + align:start position:0% +so see what did you say this model was + + + align:start position:0% +so see what did you say this model was +called again um this is slip oh but Cod + + align:start position:0% +called again um this is slip oh but Cod + + + align:start position:0% +called again um this is slip oh but Cod +and beer came with this so this is sort + + align:start position:0% +and beer came with this so this is sort + + + align:start position:0% +and beer came with this so this is sort +of yeah it has a mass of the toe I don't + + align:start position:0% +of yeah it has a mass of the toe I don't + + + align:start position:0% +of yeah it has a mass of the toe I don't +know if it has a different I don't think + + align:start position:0% +know if it has a different I don't think + + + align:start position:0% +know if it has a different I don't think +it has a different name um yeah so let + + align:start position:0% +it has a different name um yeah so let + + + align:start position:0% +it has a different name um yeah so let +me get to this + + align:start position:0% + + + + align:start position:0% + +there you go all right so first the less + + align:start position:0% +there you go all right so first the less + + + align:start position:0% +there you go all right so first the less +exciting thing I think right here but + + align:start position:0% +exciting thing I think right here but + + + align:start position:0% +exciting thing I think right here but +still pretty cool + + align:start position:0% +still pretty cool + + + align:start position:0% +still pretty cool +um so measuring the force on these + + align:start position:0% +um so measuring the force on these + + + align:start position:0% +um so measuring the force on these +cockroaches steps you could imagine + + align:start position:0% +cockroaches steps you could imagine + + + align:start position:0% +cockroaches steps you could imagine +difficult something they did actually to + + align:start position:0% +difficult something they did actually to + + + align:start position:0% +difficult something they did actually to +sort of facilitate these experiments is + + align:start position:0% +sort of facilitate these experiments is + + + align:start position:0% +sort of facilitate these experiments is +they actually have these guys running on + + align:start position:0% +they actually have these guys running on + + + align:start position:0% +they actually have these guys running on +Jello and you can set up defraction + + align:start position:0% +Jello and you can set up defraction + + + align:start position:0% +Jello and you can set up defraction +gretings on this Jell-O and so you see + + align:start position:0% +gretings on this Jell-O and so you see + + + align:start position:0% +gretings on this Jell-O and so you see +that how it changes color when they're + + align:start position:0% +that how it changes color when they're + + + align:start position:0% +that how it changes color when they're +pushing they're actually able to figure + + align:start position:0% +pushing they're actually able to figure + + + align:start position:0% +pushing they're actually able to figure +out the magnitude and direction of the + + align:start position:0% +out the magnitude and direction of the + + + align:start position:0% +out the magnitude and direction of the +force you know to some level of accuracy + + align:start position:0% +force you know to some level of accuracy + + + align:start position:0% +force you know to some level of accuracy +by looking at that apparently orange + + align:start position:0% +by looking at that apparently orange + + + align:start position:0% +by looking at that apparently orange +jell works really well I don't know what + + align:start position:0% +jell works really well I don't know what + + + align:start position:0% +jell works really well I don't know what +is about orange Jello but if you ever + + align:start position:0% +is about orange Jello but if you ever + + + align:start position:0% +is about orange Jello but if you ever +want to analyze the forces on a + + align:start position:0% +want to analyze the forces on a + + + align:start position:0% +want to analyze the forces on a +cockroach's legs start with orange + + align:start position:0% +cockroach's legs start with orange + + + align:start position:0% +cockroach's legs start with orange +Jell-O + + align:start position:0% +Jell-O + + + align:start position:0% +Jell-O +that's if that's the only thing you get + + align:start position:0% +that's if that's the only thing you get + + + align:start position:0% +that's if that's the only thing you get +out of this + + align:start position:0% +out of this + + + align:start position:0% +out of this +lecture um yeah so that's pretty cool + + align:start position:0% +lecture um yeah so that's pretty cool + + + align:start position:0% +lecture um yeah so that's pretty cool +but that's just sort of analyzing when + + align:start position:0% +but that's just sort of analyzing when + + + align:start position:0% +but that's just sort of analyzing when +it's turning they can sort of figure out + + align:start position:0% +it's turning they can sort of figure out + + + align:start position:0% +it's turning they can sort of figure out +that's to look at sort of some of the + + align:start position:0% +that's to look at sort of some of the + + + align:start position:0% +that's to look at sort of some of the +springiness and the uh how the force + + align:start position:0% +springiness and the uh how the force + + + align:start position:0% +springiness and the uh how the force +response and the center Mass response + + align:start position:0% +response and the center Mass response + + + align:start position:0% +response and the center Mass response +connect but here this is one of the + + align:start position:0% +connect but here this is one of the + + + align:start position:0% +connect but here this is one of the +greatest experiments of all time all + + align:start position:0% +greatest experiments of all time all + + + align:start position:0% +greatest experiments of all time all +right so this is looking at the + + align:start position:0% +right so this is looking at the + + + align:start position:0% +right so this is looking at the +perturbation experienced by these + + align:start position:0% +perturbation experienced by these + + + align:start position:0% +perturbation experienced by these +cockroaches so what they did they bolt a + + align:start position:0% +cockroaches so what they did they bolt a + + + align:start position:0% +cockroaches so what they did they bolt a +cannon to the back because pulling + + align:start position:0% +cannon to the back because pulling + + + align:start position:0% +cannon to the back because pulling +strings and stuff like that it's not + + align:start position:0% +strings and stuff like that it's not + + + align:start position:0% +strings and stuff like that it's not +fast enough it's nowhere near fast + + align:start position:0% +fast enough it's nowhere near fast + + + align:start position:0% +fast enough it's nowhere near fast +enough this cockro is running a come + + align:start position:0% +enough this cockro is running a come + + + align:start position:0% +enough this cockro is running a come +on what's going on + + align:start position:0% +on what's going on + + + align:start position:0% +on what's going on +here all + + align:start position:0% + + + + align:start position:0% + +right really sorry + + align:start position:0% + + + + align:start position:0% + +it's running + + align:start position:0% +it's running + + + align:start position:0% +it's running +bam perturbation the little canon ball + + align:start position:0% +bam perturbation the little canon ball + + + align:start position:0% +bam perturbation the little canon ball +actually hits it on the way back you see + + align:start position:0% +actually hits it on the way back you see + + + align:start position:0% +actually hits it on the way back you see +that's not really fair that's a double + + align:start position:0% +that's not really fair that's a double + + + align:start position:0% +that's not really fair that's a double +perturbation but they track the center + + align:start position:0% +perturbation but they track the center + + + align:start position:0% +perturbation but they track the center +mass of this guy and actually you could + + align:start position:0% +mass of this guy and actually you could + + + align:start position:0% +mass of this guy and actually you could +see it gets back on in like less than a + + align:start position:0% +see it gets back on in like less than a + + + align:start position:0% +see it gets back on in like less than a +step and if you look at the time scale + + align:start position:0% +step and if you look at the time scale + + + align:start position:0% +step and if you look at the time scale +of this and the time scale of their uh + + align:start position:0% +of this and the time scale of their uh + + + align:start position:0% +of this and the time scale of their uh +of their monosynaptic + + align:start position:0% + + + + align:start position:0% + +reflex this is uh it happens too quickly + + align:start position:0% +reflex this is uh it happens too quickly + + + align:start position:0% +reflex this is uh it happens too quickly +and so they think it's actually + + align:start position:0% +and so they think it's actually + + + align:start position:0% +and so they think it's actually +compliance in the legs and everything + + align:start position:0% +compliance in the legs and everything + + + align:start position:0% +compliance in the legs and everything +like that that sort of just passively + + align:start position:0% +like that that sort of just passively + + + align:start position:0% +like that that sort of just passively +tuned such that gets banged to the side + + align:start position:0% +tuned such that gets banged to the side + + + align:start position:0% +tuned such that gets banged to the side +and writes itself you put this on the + + align:start position:0% +and writes itself you put this on the + + + align:start position:0% +and writes itself you put this on the +first I I think I mean it's Bob F's + + align:start position:0% +first I I think I mean it's Bob F's + + + align:start position:0% +first I I think I mean it's Bob F's +video but he may have it available but a + + align:start position:0% +video but he may have it available but a + + + align:start position:0% +video but he may have it available but a +great thing is that the guy who did this + + align:start position:0% +great thing is that the guy who did this + + + align:start position:0% +great thing is that the guy who did this +I think Devin did it um and he uh he + + align:start position:0% +I think Devin did it um and he uh he + + + align:start position:0% +I think Devin did it um and he uh he +said and this is like all he said um so + + align:start position:0% +said and this is like all he said um so + + + align:start position:0% +said and this is like all he said um so +he didn't like go through the full thing + + align:start position:0% +he didn't like go through the full thing + + + align:start position:0% +he didn't like go through the full thing +but he's like you'd be surprised by how + + align:start position:0% +but he's like you'd be surprised by how + + + align:start position:0% +but he's like you'd be surprised by how +little gunpowder is necessary to perturb + + align:start position:0% +little gunpowder is necessary to perturb + + + align:start position:0% +little gunpowder is necessary to perturb +a cockroach that's you can only imagine + + align:start position:0% +a cockroach that's you can only imagine + + + align:start position:0% +a cockroach that's you can only imagine +the first cockroach they got out there + + align:start position:0% +the first cockroach they got out there + + + align:start position:0% +the first cockroach they got out there +they're like ah this is about the right + + align:start position:0% +they're like ah this is about the right + + + align:start position:0% +they're like ah this is about the right +amount and + + align:start position:0% +amount and + + + align:start position:0% +amount and +just blows the Cockroach up or launches + + align:start position:0% +just blows the Cockroach up or launches + + + align:start position:0% +just blows the Cockroach up or launches +across the room or so that would have + + align:start position:0% +across the room or so that would have + + + align:start position:0% +across the room or so that would have +been a fun trial and experiment to to + + align:start position:0% +been a fun trial and experiment to to + + + align:start position:0% +been a fun trial and experiment to to +watch from a different room I think all + + align:start position:0% +watch from a different room I think all + + + align:start position:0% +watch from a different room I think all +right yeah we'll watch this one more + + align:start position:0% +right yeah we'll watch this one more + + + align:start position:0% +right yeah we'll watch this one more +time I don't know but you see I mean + + align:start position:0% +time I don't know but you see I mean + + + align:start position:0% +time I don't know but you see I mean +that's just that's just a fantastic + + align:start position:0% +that's just that's just a fantastic + + + align:start position:0% +that's just that's just a fantastic +little experiment and the perturbation + + align:start position:0% +little experiment and the perturbation + + + align:start position:0% +little experiment and the perturbation +as you see I mean like it doesn't know + + align:start position:0% +as you see I mean like it doesn't know + + + align:start position:0% +as you see I mean like it doesn't know +that's coming that hits it like that it + + align:start position:0% +that's coming that hits it like that it + + + align:start position:0% +that's coming that hits it like that it +just responds almost instantaneously so + + align:start position:0% +just responds almost instantaneously so + + + align:start position:0% +just responds almost instantaneously so +I think that's + + align:start position:0% +I think that's + + + align:start position:0% +I think that's +uh that's really cool and that sort of + + align:start position:0% +uh that's really cool and that sort of + + + align:start position:0% +uh that's really cool and that sort of +shows this uh I mean that's that slip in + + align:start position:0% +shows this uh I mean that's that slip in + + + align:start position:0% +shows this uh I mean that's that slip in +the lateral plane and it sort of shows + + align:start position:0% +the lateral plane and it sort of shows + + + align:start position:0% +the lateral plane and it sort of shows +that these Springs and this compliance + + align:start position:0% +that these Springs and this compliance + + + align:start position:0% +that these Springs and this compliance +in the actual you know in the animal can + + align:start position:0% +in the actual you know in the animal can + + + align:start position:0% +in the actual you know in the animal can +actually do things that just control + + align:start position:0% +actually do things that just control + + + align:start position:0% +actually do things that just control +couldn't do that the time scale of the + + align:start position:0% +couldn't do that the time scale of the + + + align:start position:0% +couldn't do that the time scale of the +response can be faster than control + + align:start position:0% +response can be faster than control + + + align:start position:0% +response can be faster than control +could achieve um I don't know if I + + align:start position:0% +could achieve um I don't know if I + + + align:start position:0% +could achieve um I don't know if I +have yeah I don't think I have any + + align:start position:0% +have yeah I don't think I have any + + + align:start position:0% +have yeah I don't think I have any +so do anyone have a + + align:start position:0% +so do anyone have a + + + align:start position:0% +so do anyone have a +question um + + align:start position:0% + + + + align:start position:0% + +yeah okay so that's nature sort of + + align:start position:0% +yeah okay so that's nature sort of + + + align:start position:0% +yeah okay so that's nature sort of +having this kind of spring bouncy + + align:start position:0% +having this kind of spring bouncy + + + align:start position:0% +having this kind of spring bouncy +compliance um but you can see rabert + + align:start position:0% +compliance um but you can see rabert + + + align:start position:0% +compliance um but you can see rabert +Hoppers back in this the 80s and 90s did + + align:start position:0% +Hoppers back in this the 80s and 90s did + + + align:start position:0% +Hoppers back in this the 80s and 90s did +amazing things too um if you look at see + + align:start position:0% +amazing things too um if you look at see + + + align:start position:0% +amazing things too um if you look at see +where's this 1D moned there some of + + align:start position:0% +where's this 1D moned there some of + + + align:start position:0% +where's this 1D moned there some of +these videos are pretty crappy but there + + align:start position:0% +these videos are pretty crappy but there + + + align:start position:0% +these videos are pretty crappy but there +so that's just a little uh like a little + + align:start position:0% +so that's just a little uh like a little + + + align:start position:0% +so that's just a little uh like a little +monopad running around you see and it's + + align:start position:0% +monopad running around you see and it's + + + align:start position:0% +monopad running around you see and it's +I mean it's constraint to me the plane + + align:start position:0% +I mean it's constraint to me the plane + + + align:start position:0% +I mean it's constraint to me the plane +it's on a boom but it could fall down + + align:start position:0% +it's on a boom but it could fall down + + + align:start position:0% +it's on a boom but it could fall down +forward and everything like that it's + + align:start position:0% +forward and everything like that it's + + + align:start position:0% +forward and everything like that it's +not like it's you know for you to roll + + align:start position:0% +not like it's you know for you to roll + + + align:start position:0% +not like it's you know for you to roll +so it's achieved the sort of stability + + align:start position:0% +so it's achieved the sort of stability + + + align:start position:0% +so it's achieved the sort of stability +bouncing around that Circle um but + + align:start position:0% +bouncing around that Circle um but + + + align:start position:0% +bouncing around that Circle um but +thought they could do more than that if + + align:start position:0% +thought they could do more than that if + + + align:start position:0% +thought they could do more than that if +you look at uh they built + + align:start position:0% +you look at uh they built + + + align:start position:0% +you look at uh they built +bipeds um this is I think yeah rust + + align:start position:0% +bipeds um this is I think yeah rust + + + align:start position:0% +bipeds um this is I think yeah rust +grabbed these from uh VHS tape so this + + align:start position:0% +grabbed these from uh VHS tape so this + + + align:start position:0% +grabbed these from uh VHS tape so this +is actually what's funny is that I think + + align:start position:0% +is actually what's funny is that I think + + + align:start position:0% +is actually what's funny is that I think +this is the fastest biped around but it + + align:start position:0% +this is the fastest biped around but it + + + align:start position:0% +this is the fastest biped around but it +wasn't quite that fast oh that's + + align:start position:0% +wasn't quite that fast oh that's + + + align:start position:0% +wasn't quite that fast oh that's +skipping frames but I think it's still + + align:start position:0% +skipping frames but I think it's still + + + align:start position:0% +skipping frames but I think it's still +um unless something has changed in the + + align:start position:0% +um unless something has changed in the + + + align:start position:0% +um unless something has changed in the +last year it runs like 2.2 m a second I + + align:start position:0% +last year it runs like 2.2 m a second I + + + align:start position:0% +last year it runs like 2.2 m a second I +think it's actually still the fastest + + align:start position:0% +think it's actually still the fastest + + + align:start position:0% +think it's actually still the fastest +bipad uh but I Russ would know if + + align:start position:0% +bipad uh but I Russ would know if + + + align:start position:0% +bipad uh but I Russ would know if +anything has changed um is it spinning + + align:start position:0% +anything has changed um is it spinning + + + align:start position:0% +anything has changed um is it spinning +around + + align:start position:0% +around + + + align:start position:0% +around +Fon sorry it looks like it's kind of + + align:start position:0% +Fon sorry it looks like it's kind of + + + align:start position:0% +Fon sorry it looks like it's kind of +spinning around but it's not yeah oh but + + align:start position:0% +spinning around but it's not yeah oh but + + + align:start position:0% +spinning around but it's not yeah oh but +check out + + align:start position:0% +check out + + + align:start position:0% +check out +that so + + align:start position:0% +that so + + + align:start position:0% +that so +here oh come on there so they figured + + align:start position:0% +here oh come on there so they figured + + + align:start position:0% +here oh come on there so they figured +they could do more here's a biped so + + align:start position:0% +they could do more here's a biped so + + + align:start position:0% +they could do more here's a biped so +this one isn't on a + + align:start position:0% +this one isn't on a + + + align:start position:0% +this one isn't on a +boom bam check that out that's one more + + align:start position:0% +boom bam check that out that's one more + + + align:start position:0% +boom bam check that out that's one more +time running there + + align:start position:0% +time running there + + + align:start position:0% +time running there +speed like gymnastics that's like a + + align:start position:0% +speed like gymnastics that's like a + + + align:start position:0% +speed like gymnastics that's like a +robot doing a front flip and here this + + align:start position:0% +robot doing a front flip and here this + + + align:start position:0% +robot doing a front flip and here this +is pretty impressive + + align:start position:0% + + + + align:start position:0% + +too + + align:start position:0% +too + + + align:start position:0% +too +yeah right over those stairs like + + align:start position:0% +yeah right over those stairs like + + + align:start position:0% +yeah right over those stairs like +nobody's business right + + align:start position:0% +nobody's business right + + + align:start position:0% +nobody's business right +if they were out of + + align:start position:0% + + + + align:start position:0% + +phase if what were out of phase if the + + align:start position:0% +phase if what were out of phase if the + + + align:start position:0% +phase if what were out of phase if the +the stairs were out of phase um I don't + + align:start position:0% +the stairs were out of phase um I don't + + + align:start position:0% +the stairs were out of phase um I don't +know I mean you could probably imagine + + align:start position:0% +know I mean you could probably imagine + + + align:start position:0% +know I mean you could probably imagine +sitting upstairs that would make it + + align:start position:0% +sitting upstairs that would make it + + + align:start position:0% +sitting upstairs that would make it +easier and stairs would make it harder + + align:start position:0% +easier and stairs would make it harder + + + align:start position:0% +easier and stairs would make it harder +so yeah you probably could come up with + + align:start position:0% +so yeah you probably could come up with + + + align:start position:0% +so yeah you probably could come up with +something that would be problematic if + + align:start position:0% +something that would be problematic if + + + align:start position:0% +something that would be problematic if +it had to like hop well maybe it could + + align:start position:0% +it had to like hop well maybe it could + + + align:start position:0% +it had to like hop well maybe it could +hop on one foot for a while I don't know + + align:start position:0% +hop on one foot for a while I don't know + + + align:start position:0% +hop on one foot for a while I don't know +it's on a boom but yeah so I mean these + + align:start position:0% +it's on a boom but yeah so I mean these + + + align:start position:0% +it's on a boom but yeah so I mean these +are I mean even now you can look at + + align:start position:0% +are I mean even now you can look at + + + align:start position:0% +are I mean even now you can look at +these things and I mean there they would + + align:start position:0% +these things and I mean there they would + + + align:start position:0% +these things and I mean there they would +be amazing if someone just achieved this + + align:start position:0% +be amazing if someone just achieved this + + + align:start position:0% +be amazing if someone just achieved this +but these were back in the ' 80s and + + align:start position:0% +but these were back in the ' 80s and + + + align:start position:0% +but these were back in the ' 80s and +'90s that people did this + + align:start position:0% +'90s that people did this + + + align:start position:0% +'90s that people did this +and so uh I mean you've probably seen + + align:start position:0% +and so uh I mean you've probably seen + + + align:start position:0% +and so uh I mean you've probably seen +big dog um R worked on big dog too and + + align:start position:0% +big dog um R worked on big dog too and + + + align:start position:0% +big dog um R worked on big dog too and +that's like 20 years later and this + + align:start position:0% +that's like 20 years later and this + + + align:start position:0% +that's like 20 years later and this +stuff and it's still sort of like + + align:start position:0% +stuff and it's still sort of like + + + align:start position:0% +stuff and it's still sort of like +state-ofthe-art that kind of control + + align:start position:0% +state-ofthe-art that kind of control + + + align:start position:0% +state-ofthe-art that kind of control +similar control in a lot of ways um do + + align:start position:0% +similar control in a lot of ways um do + + + align:start position:0% +similar control in a lot of ways um do +some more the oh there's one that's + + align:start position:0% +some more the oh there's one that's + + + align:start position:0% +some more the oh there's one that's +let's see + + align:start position:0% +let's see + + + align:start position:0% +let's see +that's and the thing is that not only do + + align:start position:0% +that's and the thing is that not only do + + + align:start position:0% +that's and the thing is that not only do +these guys do these crazy + + align:start position:0% +these guys do these crazy + + + align:start position:0% +these guys do these crazy +things but their + + align:start position:0% +things but their + + + align:start position:0% +things but their +robustness is really pretty incredible + + align:start position:0% +robustness is really pretty incredible + + + align:start position:0% +robustness is really pretty incredible +able um I mean a lot of these like the + + align:start position:0% +able um I mean a lot of these like the + + + align:start position:0% +able um I mean a lot of these like the +Honda robots you know walk on you know + + align:start position:0% +Honda robots you know walk on you know + + + align:start position:0% +Honda robots you know walk on you know +carefully show the ground everything + + align:start position:0% +carefully show the ground everything + + + align:start position:0% +carefully show the ground everything +like that here I + + align:start position:0% +like that here I + + + align:start position:0% +like that here I +mean Towing them along it's probably not + + align:start position:0% +mean Towing them along it's probably not + + + align:start position:0% +mean Towing them along it's probably not +the most comfortable it looks like it's + + align:start position:0% +the most comfortable it looks like it's + + + align:start position:0% +the most comfortable it looks like it's +a little bit less smooth + + align:start position:0% +a little bit less smooth + + + align:start position:0% +a little bit less smooth +but I mean it's it's running along + + align:start position:0% +but I mean it's it's running along + + + align:start position:0% +but I mean it's it's running along +sidewalks outside of + + align:start position:0% +sidewalks outside of + + + align:start position:0% +sidewalks outside of +MIT + + align:start position:0% +MIT + + + align:start position:0% +MIT +um they have uh there's other ones of + + align:start position:0% +um they have uh there's other ones of + + + align:start position:0% +um they have uh there's other ones of +just running by itself on grass and + + align:start position:0% +just running by itself on grass and + + + align:start position:0% +just running by itself on grass and +everything too um + + align:start position:0% +everything too um + + + align:start position:0% +everything too um +oh quadri Peds are pretty cool + + align:start position:0% +oh quadri Peds are pretty cool + + + align:start position:0% +oh quadri Peds are pretty cool +too that's a quadraped running down the + + align:start position:0% +too that's a quadraped running down the + + + align:start position:0% +too that's a quadraped running down the +hallway see and they actually did a cool + + align:start position:0% +hallway see and they actually did a cool + + + align:start position:0% +hallway see and they actually did a cool +paper called uh four legs running as one + + align:start position:0% +paper called uh four legs running as one + + + align:start position:0% +paper called uh four legs running as one +four legs that run as one running with + + align:start position:0% +four legs that run as one running with + + + align:start position:0% +four legs that run as one running with +four legs as if it were one there you go + + align:start position:0% +four legs as if it were one there you go + + + align:start position:0% +four legs as if it were one there you go +um that sort of use the same kind of + + align:start position:0% +um that sort of use the same kind of + + + align:start position:0% +um that sort of use the same kind of +control ideas but actually can get these + + align:start position:0% +control ideas but actually can get these + + + align:start position:0% +control ideas but actually can get these +quadrip heads and actually run sort of + + align:start position:0% +quadrip heads and actually run sort of + + + align:start position:0% +quadrip heads and actually run sort of +based on the same ideas and you see that + + align:start position:0% +based on the same ideas and you see that + + + align:start position:0% +based on the same ideas and you see that +thing moving prettyy fast and pretty + + align:start position:0% +thing moving prettyy fast and pretty + + + align:start position:0% +thing moving prettyy fast and pretty +robustly right down all we like that so + + align:start position:0% +robustly right down all we like that so + + + align:start position:0% +robustly right down all we like that so +it's really pretty uh pretty amazing + + align:start position:0% +it's really pretty uh pretty amazing + + + align:start position:0% +it's really pretty uh pretty amazing +capabilities um even + + align:start position:0% + + + + align:start position:0% + +today I really there's one I really wish + + align:start position:0% +today I really there's one I really wish + + + align:start position:0% +today I really there's one I really wish +I could find for + + align:start position:0% +I could find for + + + align:start position:0% +I could find for +you yeah and so interesting thing that + + align:start position:0% +you yeah and so interesting thing that + + + align:start position:0% +you yeah and so interesting thing that +some more recent work they've + + align:start position:0% +some more recent work they've + + + align:start position:0% +some more recent work they've +uh let's let's look at + + align:start position:0% + + + + align:start position:0% + +aerial + + align:start position:0% +aerial + + + align:start position:0% +aerial +yeah check that out + + align:start position:0% + + + + align:start position:0% + +isn't that kind of just amazing right um + + align:start position:0% +isn't that kind of just amazing right um + + + align:start position:0% +isn't that kind of just amazing right um +and the actuators that these guys use is + + align:start position:0% +and the actuators that these guys use is + + + align:start position:0% +and the actuators that these guys use is +uh Hydraulics at the hips and then + + align:start position:0% +uh Hydraulics at the hips and then + + + align:start position:0% +uh Hydraulics at the hips and then +pneumatics along the leg so with a + + align:start position:0% +pneumatics along the leg so with a + + + align:start position:0% +pneumatics along the leg so with a +Pneumatic need that so you can rocket + + align:start position:0% +Pneumatic need that so you can rocket + + + align:start position:0% +Pneumatic need that so you can rocket +yourself that far + + align:start position:0% +yourself that far + + + align:start position:0% +yourself that far +but just + + align:start position:0% +but just + + + align:start position:0% +but just +incredible um yeah so something that + + align:start position:0% +incredible um yeah so something that + + + align:start position:0% +incredible um yeah so something that +people are are working on more + + align:start position:0% +people are are working on more + + + align:start position:0% +people are are working on more +recently is uh something called slip + + align:start position:0% +recently is uh something called slip + + + align:start position:0% +recently is uh something called slip +Walkers so + + align:start position:0% +Walkers so + + + align:start position:0% +Walkers so +you can imagine if you have like a + + align:start position:0% +you can imagine if you have like a + + + align:start position:0% +you can imagine if you have like a +compass gate with springy legs right as + + align:start position:0% +compass gate with springy legs right as + + + align:start position:0% +compass gate with springy legs right as +it spring constant gets very high it + + align:start position:0% +it spring constant gets very high it + + + align:start position:0% +it spring constant gets very high it +starts behaving just like a compass gate + + align:start position:0% +starts behaving just like a compass gate + + + align:start position:0% +starts behaving just like a compass gate +right I mean if spring H goes to + + align:start position:0% +right I mean if spring H goes to + + + align:start position:0% +right I mean if spring H goes to +Infinity it's rigid it's going to be + + align:start position:0% +Infinity it's rigid it's going to be + + + align:start position:0% +Infinity it's rigid it's going to be +just like a compass gate right if you + + align:start position:0% +just like a compass gate right if you + + + align:start position:0% +just like a compass gate right if you +let those Springs get looser and looser + + align:start position:0% +let those Springs get looser and looser + + + align:start position:0% +let those Springs get looser and looser +it's going to start being more like one + + align:start position:0% +it's going to start being more like one + + + align:start position:0% +it's going to start being more like one +of these sort of bouncy bipeds right + + align:start position:0% +of these sort of bouncy bipeds right + + + align:start position:0% +of these sort of bouncy bipeds right +sort of more like this kind of slip + + align:start position:0% +sort of more like this kind of slip + + + align:start position:0% +sort of more like this kind of slip +behavior and so actually you can get + + align:start position:0% +behavior and so actually you can get + + + align:start position:0% +behavior and so actually you can get +stability properties I mean you can be + + align:start position:0% +stability properties I mean you can be + + + align:start position:0% +stability properties I mean you can be +stable through a relatively uh broad + + align:start position:0% +stable through a relatively uh broad + + + align:start position:0% +stable through a relatively uh broad +range of sort of bounciness so that sort + + align:start position:0% +range of sort of bounciness so that sort + + + align:start position:0% +range of sort of bounciness so that sort +of the same robot can sort of you know + + align:start position:0% +of the same robot can sort of you know + + + align:start position:0% +of the same robot can sort of you know +Vault over its legs and walking and then + + align:start position:0% +Vault over its legs and walking and then + + + align:start position:0% +Vault over its legs and walking and then +start bouncing and start of running that + + align:start position:0% +start bouncing and start of running that + + + align:start position:0% +start bouncing and start of running that +actually do that transition and that's a + + align:start position:0% +actually do that transition and that's a + + + align:start position:0% +actually do that transition and that's a +cool thing also that you see I should + + align:start position:0% +cool thing also that you see I should + + + align:start position:0% +cool thing also that you see I should +have brought this up at the beginning we + + align:start position:0% +have brought this up at the beginning we + + + align:start position:0% +have brought this up at the beginning we +were talking about biology but um those + + align:start position:0% +were talking about biology but um those + + + align:start position:0% +were talking about biology but um those +transitions are interesting because if + + align:start position:0% +transitions are interesting because if + + + align:start position:0% +transitions are interesting because if +you look at the efficiency of human + + align:start position:0% +you look at the efficiency of human + + + align:start position:0% +you look at the efficiency of human +Locomotion so you can measure O2 + + align:start position:0% +Locomotion so you can measure O2 + + + align:start position:0% +Locomotion so you can measure O2 +consumption and you can see sort of how + + align:start position:0% +consumption and you can see sort of how + + + align:start position:0% +consumption and you can see sort of how +efficient it is to walk at different + + align:start position:0% +efficient it is to walk at different + + + align:start position:0% +efficient it is to walk at different +speeds um and to run at different speeds + + align:start position:0% +speeds um and to run at different speeds + + + align:start position:0% +speeds um and to run at different speeds +you can look at the efficiency curve for + + align:start position:0% +you can look at the efficiency curve for + + + align:start position:0% +you can look at the efficiency curve for +believe this is like + + align:start position:0% +believe this is like + + + align:start position:0% +believe this is like +speed and this is let's say efficiency + + align:start position:0% +speed and this is let's say efficiency + + + align:start position:0% +speed and this is let's say efficiency +see all right and so you have something + + align:start position:0% +see all right and so you have something + + + align:start position:0% +see all right and so you have something +with walking you have some + + align:start position:0% +with walking you have some + + + align:start position:0% +with walking you have some +curve like + + align:start position:0% + + + + align:start position:0% + +this and then + + align:start position:0% +this and then + + + align:start position:0% +this and then +running you have some curve like + + align:start position:0% +running you have some curve like + + + align:start position:0% +running you have some curve like +this I mean quantitatively these could + + align:start position:0% +this I mean quantitatively these could + + + align:start position:0% +this I mean quantitatively these could +be wrong but this is a qualitative + + align:start position:0% +be wrong but this is a qualitative + + + align:start position:0% +be wrong but this is a qualitative +feature so if you look at the efficiency + + align:start position:0% +feature so if you look at the efficiency + + + align:start position:0% +feature so if you look at the efficiency +of a person walking and you just like + + align:start position:0% +of a person walking and you just like + + + align:start position:0% +of a person walking and you just like +put them on a treadmill and just tell + + align:start position:0% +put them on a treadmill and just tell + + + align:start position:0% +put them on a treadmill and just tell +them you know like start walking speed + + align:start position:0% +them you know like start walking speed + + + align:start position:0% +them you know like start walking speed +it up speed it up and tell them just to + + align:start position:0% +it up speed it up and tell them just to + + + align:start position:0% +it up speed it up and tell them just to +transition to running whatever they want + + align:start position:0% +transition to running whatever they want + + + align:start position:0% +transition to running whatever they want +they they'll transition right here that + + align:start position:0% +they they'll transition right here that + + + align:start position:0% +they they'll transition right here that +switches and so sort of like you know + + align:start position:0% +switches and so sort of like you know + + + align:start position:0% +switches and so sort of like you know +the feeling I'm sure where you're like + + align:start position:0% +the feeling I'm sure where you're like + + + align:start position:0% +the feeling I'm sure where you're like +walking fast and Fast and suddenly it + + align:start position:0% +walking fast and Fast and suddenly it + + + align:start position:0% +walking fast and Fast and suddenly it +just feels more comfortable to just + + align:start position:0% +just feels more comfortable to just + + + align:start position:0% +just feels more comfortable to just +start jogging apparently that happens + + align:start position:0% +start jogging apparently that happens + + + align:start position:0% +start jogging apparently that happens +when the efficiency of that motion + + align:start position:0% +when the efficiency of that motion + + + align:start position:0% +when the efficiency of that motion +outweighs that of walking because + + align:start position:0% +outweighs that of walking because + + + align:start position:0% +outweighs that of walking because +obviously you can walk where it's + + align:start position:0% +obviously you can walk where it's + + + align:start position:0% +obviously you can walk where it's +uncomfortable to walk and run where it's + + align:start position:0% +uncomfortable to walk and run where it's + + + align:start position:0% +uncomfortable to walk and run where it's +uncomfortable to run but the natural + + align:start position:0% +uncomfortable to run but the natural + + + align:start position:0% +uncomfortable to run but the natural +transition happens at that sort of + + align:start position:0% +transition happens at that sort of + + + align:start position:0% +transition happens at that sort of +efficiency pardon yeah that should be + + align:start position:0% +efficiency pardon yeah that should be + + + align:start position:0% +efficiency pardon yeah that should be +cost + + align:start position:0% +cost + + + align:start position:0% +cost +here + + align:start position:0% + + + + align:start position:0% + +right now it's even more skewed + + align:start position:0% +right now it's even more skewed + + + align:start position:0% +right now it's even more skewed +[Music] + + align:start position:0% + + + + align:start position:0% + +so there we + + align:start position:0% +so there we + + + align:start position:0% +so there we +go thank you um yeah so these new sort + + align:start position:0% +go thank you um yeah so these new sort + + + align:start position:0% +go thank you um yeah so these new sort +of slip Walkers I think hope you can get + + align:start position:0% +of slip Walkers I think hope you can get + + + align:start position:0% +of slip Walkers I think hope you can get +some of this transition but I'm not not + + align:start position:0% +some of this transition but I'm not not + + + align:start position:0% +some of this transition but I'm not not +sure exactly where they right now I + + align:start position:0% +sure exactly where they right now I + + + align:start position:0% +sure exactly where they right now I +don't know if they have any videos of + + align:start position:0% +don't know if they have any videos of + + + align:start position:0% +don't know if they have any videos of +those there's some papers about them um + + align:start position:0% +those there's some papers about them um + + + align:start position:0% +those there's some papers about them um +and I think + + align:start position:0% + + + + align:start position:0% + +I think that's all the stuff that Russ + + align:start position:0% +I think that's all the stuff that Russ + + + align:start position:0% +I think that's all the stuff that Russ +wanted me to convey + + align:start position:0% + + + + align:start position:0% + +um so we just have some idea of the sort + + align:start position:0% +um so we just have some idea of the sort + + + align:start position:0% +um so we just have some idea of the sort +of culture of these cool running models + + align:start position:0% +of culture of these cool running models + + + align:start position:0% +of culture of these cool running models +and these springy things and these pre + + align:start position:0% +and these springy things and these pre + + + align:start position:0% +and these springy things and these pre +flexes and stuff and in nature the fact + + align:start position:0% +flexes and stuff and in nature the fact + + + align:start position:0% +flexes and stuff and in nature the fact +that Springs are critical to sort of you + + align:start position:0% +that Springs are critical to sort of you + + + align:start position:0% +that Springs are critical to sort of you +know Locomotion of horses and the + + align:start position:0% +know Locomotion of horses and the + + + align:start position:0% +know Locomotion of horses and the +stability of this cockroach running and + + align:start position:0% +stability of this cockroach running and + + + align:start position:0% +stability of this cockroach running and +everything like that so anyone has any + + align:start position:0% +everything like that so anyone has any + + + align:start position:0% +everything like that so anyone has any +questions I'd love to answer them about + + align:start position:0% +questions I'd love to answer them about + + + align:start position:0% +questions I'd love to answer them about +anything but yeah and when you were + + align:start position:0% +anything but yeah and when you were + + + align:start position:0% +anything but yeah and when you were +saying how they were the transitioning + + align:start position:0% +saying how they were the transitioning + + + align:start position:0% +saying how they were the transitioning +using the string model between walking + + align:start position:0% +using the string model between walking + + + align:start position:0% +using the string model between walking +to like running oh the slip Walkers yeah + + align:start position:0% +to like running oh the slip Walkers yeah + + + align:start position:0% +to like running oh the slip Walkers yeah +the slip Walkers the slip Walkers uh do + + align:start position:0% +the slip Walkers the slip Walkers uh do + + + align:start position:0% +the slip Walkers the slip Walkers uh do +they is it still the completely ltic + + align:start position:0% +they is it still the completely ltic + + + align:start position:0% +they is it still the completely ltic +Collis or do they need the I + + align:start position:0% +Collis or do they need the I + + + align:start position:0% +Collis or do they need the I +mean I mean I I think in practice I + + align:start position:0% +mean I mean I I think in practice I + + + align:start position:0% +mean I mean I I think in practice I +think they have idealized + + align:start position:0% +think they have idealized + + + align:start position:0% +think they have idealized +legs + + align:start position:0% +legs + + + align:start position:0% +legs +um I think they've done simulations with + + align:start position:0% +um I think they've done simulations with + + + align:start position:0% +um I think they've done simulations with +idealized legs too but you can do either + + align:start position:0% +idealized legs too but you can do either + + + align:start position:0% +idealized legs too but you can do either +way I'm pretty sure I haven't I haven't + + align:start position:0% +way I'm pretty sure I haven't I haven't + + + align:start position:0% +way I'm pretty sure I haven't I haven't +looked at that work as closely as I + + align:start position:0% +looked at that work as closely as I + + + align:start position:0% +looked at that work as closely as I +probably should have but yeah I mean for + + align:start position:0% +probably should have but yeah I mean for + + + align:start position:0% +probably should have but yeah I mean for +the The Walking kind of vaulting + + align:start position:0% +the The Walking kind of vaulting + + + align:start position:0% +the The Walking kind of vaulting +Behavior you need either a toe thing + + align:start position:0% +Behavior you need either a toe thing + + + align:start position:0% +Behavior you need either a toe thing +that's going to or or you can let your + + align:start position:0% +that's going to or or you can let your + + + align:start position:0% +that's going to or or you can let your +spring constant go to Infinity right and + + align:start position:0% +spring constant go to Infinity right and + + + align:start position:0% +spring constant go to Infinity right and +then you'll then you'll have a rigid + + align:start position:0% +then you'll then you'll have a rigid + + + align:start position:0% +then you'll then you'll have a rigid +impact right so with uh with you can + + align:start position:0% +impact right so with uh with you can + + + align:start position:0% +impact right so with uh with you can +treat it that way too but then yeah if + + align:start position:0% +treat it that way too but then yeah if + + + align:start position:0% +treat it that way too but then yeah if +you loosen it up then you're not going + + align:start position:0% +you loosen it up then you're not going + + + align:start position:0% +you loosen it up then you're not going +to have the sort of intermediate still + + align:start position:0% +to have the sort of intermediate still + + + align:start position:0% +to have the sort of intermediate still +lossy Behavior but I think they have + + align:start position:0% +lossy Behavior but I think they have + + + align:start position:0% +lossy Behavior but I think they have +done stuff with idealized legs and + + align:start position:0% +done stuff with idealized legs and + + + align:start position:0% +done stuff with idealized legs and +probably non idealis ones too + + align:start position:0% +probably non idealis ones too + + + align:start position:0% +probably non idealis ones too +so anything else + + align:start position:0% +so anything else + + + align:start position:0% +so anything else +if you um if you get it just right can + + align:start position:0% +if you um if you get it just right can + + + align:start position:0% +if you um if you get it just right can +you adjust the spring constants so that + + align:start position:0% +you adjust the spring constants so that + + + align:start position:0% +you adjust the spring constants so that +you'll get the kind of push off right + + align:start position:0% +you'll get the kind of push off right + + + align:start position:0% +you'll get the kind of push off right +before + + align:start position:0% +before + + + align:start position:0% +before +landing Oh you mean like toe off kind of + + align:start position:0% +landing Oh you mean like toe off kind of + + + align:start position:0% +landing Oh you mean like toe off kind of +or the kind of like toe off thing that + + align:start position:0% +or the kind of like toe off thing that + + + align:start position:0% +or the kind of like toe off thing that +pushes you forward that gra you some + + align:start position:0% +pushes you forward that gra you some + + + align:start position:0% +pushes you forward that gra you some +efficiency um I think you should I mean + + align:start position:0% +efficiency um I think you should I mean + + + align:start position:0% +efficiency um I think you should I mean +I'm not sure about how the tuning would + + align:start position:0% +I'm not sure about how the tuning would + + + align:start position:0% +I'm not sure about how the tuning would +relate to the walking things but when + + align:start position:0% +relate to the walking things but when + + + align:start position:0% +relate to the walking things but when +you have these idealized legs with the + + align:start position:0% +you have these idealized legs with the + + + align:start position:0% +you have these idealized legs with the +spring I mean you can be more efficient + + align:start position:0% +spring I mean you can be more efficient + + + align:start position:0% +spring I mean you can be more efficient +than if you're vaulting over them so I + + align:start position:0% +than if you're vaulting over them so I + + + align:start position:0% +than if you're vaulting over them so I +don't know if it connects to the I mean + + align:start position:0% +don't know if it connects to the I mean + + + align:start position:0% +don't know if it connects to the I mean +seems like it could connect to that toe + + align:start position:0% +seems like it could connect to that toe + + + align:start position:0% +seems like it could connect to that toe +off kind of launch but I'm not sure if + + align:start position:0% +off kind of launch but I'm not sure if + + + align:start position:0% +off kind of launch but I'm not sure if +they like if that is explicit you know + + align:start position:0% +they like if that is explicit you know + + + align:start position:0% +they like if that is explicit you know +just by having like your leg not you + + align:start position:0% +just by having like your leg not you + + + align:start position:0% +just by having like your leg not you +know be a strike with the dissipative + + align:start position:0% +know be a strike with the dissipative + + + align:start position:0% +know be a strike with the dissipative +kind of you know uh an elastic Collision + + align:start position:0% +kind of you know uh an elastic Collision + + + align:start position:0% +kind of you know uh an elastic Collision +is going to help you but I don't know if + + align:start position:0% +is going to help you but I don't know if + + + align:start position:0% +is going to help you but I don't know if +you get the same kind of yeah it seems + + align:start position:0% +you get the same kind of yeah it seems + + + align:start position:0% +you get the same kind of yeah it seems +like you should but I I don't know if if + + align:start position:0% +like you should but I I don't know if if + + + align:start position:0% +like you should but I I don't know if if +that exact point I haven't seen that + + align:start position:0% +that exact point I haven't seen that + + + align:start position:0% +that exact point I haven't seen that +exact point but it could easily be + + align:start position:0% +exact point but it could easily be + + + align:start position:0% +exact point but it could easily be +addressed in one of their papers I + + align:start position:0% +addressed in one of their papers I + + + align:start position:0% +addressed in one of their papers I +should uh I don't know if I have the + + align:start position:0% +should uh I don't know if I have the + + + align:start position:0% +should uh I don't know if I have the +references right now but I can make sure + + align:start position:0% +references right now but I can make sure + + + align:start position:0% +references right now but I can make sure +that Russ gives those to you or give + + align:start position:0% +that Russ gives those to you or give + + + align:start position:0% +that Russ gives those to you or give +those to you my myself next lecture if + + align:start position:0% +those to you my myself next lecture if + + + align:start position:0% +those to you my myself next lecture if +you want to look up some of the slip + + align:start position:0% +you want to look up some of the slip + + + align:start position:0% +you want to look up some of the slip +Walkers that's pretty new stuff I think \ No newline at end of file diff --git a/CsHQ35j_1kY.txt b/CsHQ35j_1kY.txt new file mode 100644 index 0000000000000000000000000000000000000000..62becca68dde6682c1a187f3a3f925df647e1b3f --- /dev/null +++ b/CsHQ35j_1kY.txt @@ -0,0 +1,747 @@ +align:start position:0% + +we've so far described abstractly what + + align:start position:0% +we've so far described abstractly what + + + align:start position:0% +we've so far described abstractly what +we mean by a dot product by a definition + + align:start position:0% +we mean by a dot product by a definition + + + align:start position:0% +we mean by a dot product by a definition +of a B equals the magnitude of a times + + align:start position:0% +of a B equals the magnitude of a times + + + align:start position:0% +of a B equals the magnitude of a times +cosine theta times the magnitude of B + + align:start position:0% +cosine theta times the magnitude of B + + + align:start position:0% +cosine theta times the magnitude of B +but many times in physics problems we + + align:start position:0% +but many times in physics problems we + + + align:start position:0% +but many times in physics problems we +actually have vectors in space and we + + align:start position:0% +actually have vectors in space and we + + + align:start position:0% +actually have vectors in space and we +want to see how to do this in terms of a + + align:start position:0% +want to see how to do this in terms of a + + + align:start position:0% +want to see how to do this in terms of a +Cartesian or any coordinate system in + + align:start position:0% +Cartesian or any coordinate system in + + + align:start position:0% +Cartesian or any coordinate system in +particular so let's set up a coordinate + + align:start position:0% +particular so let's set up a coordinate + + + align:start position:0% +particular so let's set up a coordinate +system we will call it Cartesian a and J + + align:start position:0% +system we will call it Cartesian a and J + + + align:start position:0% +system we will call it Cartesian a and J +and now this is very important let's + + align:start position:0% +and now this is very important let's + + + align:start position:0% +and now this is very important let's +define a vector a here and let's have + + align:start position:0% +define a vector a here and let's have + + + align:start position:0% +define a vector a here and let's have +another vector in a completely different + + align:start position:0% +another vector in a completely different + + + align:start position:0% +another vector in a completely different +point B we're still can take the dot + + align:start position:0% +point B we're still can take the dot + + + align:start position:0% +point B we're still can take the dot +product of these two vectors but in + + align:start position:0% +product of these two vectors but in + + + align:start position:0% +product of these two vectors but in +order this is our plus X plus y and I'm + + align:start position:0% +order this is our plus X plus y and I'm + + + align:start position:0% +order this is our plus X plus y and I'm +only doing things in two dimensions so + + align:start position:0% +only doing things in two dimensions so + + + align:start position:0% +only doing things in two dimensions so +how do we calculate the dot product well + + align:start position:0% +how do we calculate the dot product well + + + align:start position:0% +how do we calculate the dot product well +the first thing that we want to look at + + align:start position:0% +the first thing that we want to look at + + + align:start position:0% +the first thing that we want to look at +is our unit vectors what are the dot + + align:start position:0% +is our unit vectors what are the dot + + + align:start position:0% +is our unit vectors what are the dot +products of unit vectors well if we take + + align:start position:0% +products of unit vectors well if we take + + + align:start position:0% +products of unit vectors well if we take +I hat dot I hat that's the magnitude of + + align:start position:0% +I hat dot I hat that's the magnitude of + + + align:start position:0% +I hat dot I hat that's the magnitude of +I hat times cosine of the angle 0 times + + align:start position:0% +I hat times cosine of the angle 0 times + + + align:start position:0% +I hat times cosine of the angle 0 times +the magnitude of I hat and cosine of 0 + + align:start position:0% +the magnitude of I hat and cosine of 0 + + + align:start position:0% +the magnitude of I hat and cosine of 0 +is 1 and the magnitude of unit vectors + + align:start position:0% +is 1 and the magnitude of unit vectors + + + align:start position:0% +is 1 and the magnitude of unit vectors +are 1 so when you dot product the unit + + align:start position:0% +are 1 so when you dot product the unit + + + align:start position:0% +are 1 so when you dot product the unit +vector with itself you get 1 and + + align:start position:0% +vector with itself you get 1 and + + + align:start position:0% +vector with itself you get 1 and +therefore it's also true for the J hat J + + align:start position:0% +therefore it's also true for the J hat J + + + align:start position:0% +therefore it's also true for the J hat J +hat J hat is 1 what happens when you dot + + align:start position:0% +hat J hat is 1 what happens when you dot + + + align:start position:0% +hat J hat is 1 what happens when you dot +product two vectors that are + + align:start position:0% +product two vectors that are + + + align:start position:0% +product two vectors that are +perpendicular well in this case this is + + align:start position:0% +perpendicular well in this case this is + + + align:start position:0% +perpendicular well in this case this is +0 because the angle theta is 90 degrees + + align:start position:0% +0 because the angle theta is 90 degrees + + + align:start position:0% +0 because the angle theta is 90 degrees +and remember that cosine of 90 degrees + + align:start position:0% +and remember that cosine of 90 degrees + + + align:start position:0% +and remember that cosine of 90 degrees +is 0 and anyway + + align:start position:0% +is 0 and anyway + + + align:start position:0% +is 0 and anyway +when two vectors are perpendicular + + align:start position:0% +when two vectors are perpendicular + + + align:start position:0% +when two vectors are perpendicular +there's no component of one vector + + align:start position:0% +there's no component of one vector + + + align:start position:0% +there's no component of one vector +that's parallel to the other so these + + align:start position:0% +that's parallel to the other so these + + + align:start position:0% +that's parallel to the other so these +are the essential facts that we're going + + align:start position:0% +are the essential facts that we're going + + + align:start position:0% +are the essential facts that we're going +to need to calculate the dot product of + + align:start position:0% +to need to calculate the dot product of + + + align:start position:0% +to need to calculate the dot product of +two vectors that are separated in space + + align:start position:0% +two vectors that are separated in space + + + align:start position:0% +two vectors that are separated in space +so the way we do that is we'll begin by + + align:start position:0% +so the way we do that is we'll begin by + + + align:start position:0% +so the way we do that is we'll begin by +drawing writing down the vectors in + + align:start position:0% +drawing writing down the vectors in + + + align:start position:0% +drawing writing down the vectors in +Cartesian coordinates where ax is a + + align:start position:0% +Cartesian coordinates where ax is a + + + align:start position:0% +Cartesian coordinates where ax is a +scalar and the vector part is in the + + align:start position:0% +scalar and the vector part is in the + + + align:start position:0% +scalar and the vector part is in the +unit vector and we have a Y J hat and + + align:start position:0% +unit vector and we have a Y J hat and + + + align:start position:0% +unit vector and we have a Y J hat and +likewise we can write B as B X I hat + + align:start position:0% +likewise we can write B as B X I hat + + + align:start position:0% +likewise we can write B as B X I hat +plus B Y J hat and now when we take the + + align:start position:0% +plus B Y J hat and now when we take the + + + align:start position:0% +plus B Y J hat and now when we take the +dot product + + align:start position:0% +dot product + + + align:start position:0% +dot product +of these two vectors that's we're gonna + + align:start position:0% +of these two vectors that's we're gonna + + + align:start position:0% +of these two vectors that's we're gonna +write out all the terms here so that you + + align:start position:0% +write out all the terms here so that you + + + align:start position:0% +write out all the terms here so that you +see them so here is our scalar or dot + + align:start position:0% +see them so here is our scalar or dot + + + align:start position:0% +see them so here is our scalar or dot +product we use those words + + align:start position:0% +product we use those words + + + align:start position:0% +product we use those words +interchangeably now notice that we've + + align:start position:0% +interchangeably now notice that we've + + + align:start position:0% +interchangeably now notice that we've +already shown that the dot product + + align:start position:0% +already shown that the dot product + + + align:start position:0% +already shown that the dot product +distributes over vector addition and + + align:start position:0% +distributes over vector addition and + + + align:start position:0% +distributes over vector addition and +also if you multiply a scalar by a + + align:start position:0% +also if you multiply a scalar by a + + + align:start position:0% +also if you multiply a scalar by a +vector you can pull the scalar out so + + align:start position:0% +vector you can pull the scalar out so + + + align:start position:0% +vector you can pull the scalar out so +there's four terms here ax I hat dot BX + + align:start position:0% +there's four terms here ax I hat dot BX + + + align:start position:0% +there's four terms here ax I hat dot BX +I huh plus ax I huh + + align:start position:0% +I huh plus ax I huh + + + align:start position:0% +I huh plus ax I huh +dot B Y jaehun plus ay Y J hat dot BX I + + align:start position:0% +dot B Y jaehun plus ay Y J hat dot BX I + + + align:start position:0% +dot B Y jaehun plus ay Y J hat dot BX I +had this is a little tedious to write + + align:start position:0% +had this is a little tedious to write + + + align:start position:0% +had this is a little tedious to write +out B Y J huh and now because these are + + align:start position:0% +out B Y J huh and now because these are + + + align:start position:0% +out B Y J huh and now because these are +scalars we can pull them out and the + + align:start position:0% +scalars we can pull them out and the + + + align:start position:0% +scalars we can pull them out and the +only part of a dot product that matters + + align:start position:0% +only part of a dot product that matters + + + align:start position:0% +only part of a dot product that matters +is how the unit vectors dot and that's + + align:start position:0% +is how the unit vectors dot and that's + + + align:start position:0% +is how the unit vectors dot and that's +why we have these two results I had that + + align:start position:0% +why we have these two results I had that + + + align:start position:0% +why we have these two results I had that +I had as one J Hutta + + align:start position:0% +I had as one J Hutta + + + align:start position:0% +I had as one J Hutta +J hat is one and I hat J hat is zero so + + align:start position:0% +J hat is one and I hat J hat is zero so + + + align:start position:0% +J hat is one and I hat J hat is zero so +the first term is ax BX I hat J hat is + + align:start position:0% +the first term is ax BX I hat J hat is + + + align:start position:0% +the first term is ax BX I hat J hat is +zero so we don't need that J huh dot I + + align:start position:0% +zero so we don't need that J huh dot I + + + align:start position:0% +zero so we don't need that J huh dot I +hat is zero and finally J hat J hat is + + align:start position:0% +hat is zero and finally J hat J hat is + + + align:start position:0% +hat is zero and finally J hat J hat is +one and so we get plus ay Y B Y and + + align:start position:0% +one and so we get plus ay Y B Y and + + + align:start position:0% +one and so we get plus ay Y B Y and +that's how we define the dot product in + + align:start position:0% +that's how we define the dot product in + + + align:start position:0% +that's how we define the dot product in +Cartesian coordinates of two vectors now + + align:start position:0% +Cartesian coordinates of two vectors now + + + align:start position:0% +Cartesian coordinates of two vectors now +notice that if we dotted a vector a dot + + align:start position:0% +notice that if we dotted a vector a dot + + + align:start position:0% +notice that if we dotted a vector a dot +with itself that would just be ax ax + + align:start position:0% +with itself that would just be ax ax + + + align:start position:0% +with itself that would just be ax ax +plus ay Y a Y which is the components + + align:start position:0% +plus ay Y a Y which is the components + + + align:start position:0% +plus ay Y a Y which is the components +squared and that's equal to the + + align:start position:0% +squared and that's equal to the + + + align:start position:0% +squared and that's equal to the +magnitude of the vector squared and so + + align:start position:0% +magnitude of the vector squared and so + + + align:start position:0% +magnitude of the vector squared and so +we can say that the magnitude of the + + align:start position:0% +we can say that the magnitude of the + + + align:start position:0% +we can say that the magnitude of the +vector of any vector is you take its dot + + align:start position:0% +vector of any vector is you take its dot + + + align:start position:0% +vector of any vector is you take its dot +product with itself you take the square + + align:start position:0% +product with itself you take the square + + + align:start position:0% +product with itself you take the square +root but remember we always take the + + align:start position:0% +root but remember we always take the + + + align:start position:0% +root but remember we always take the +positive square root because magnitudes + + align:start position:0% +positive square root because magnitudes + + + align:start position:0% +positive square root because magnitudes +are positive and that's how we calculate + + align:start position:0% +are positive and that's how we calculate + + + align:start position:0% +are positive and that's how we calculate +the scalar product for vectors + + align:start position:0% +the scalar product for vectors + + + align:start position:0% +the scalar product for vectors +many times in the application of physics + + align:start position:0% +many times in the application of physics + + + align:start position:0% +many times in the application of physics +when we have physical quantities that + + align:start position:0% +when we have physical quantities that + + + align:start position:0% +when we have physical quantities that +are vectors in different places we use + + align:start position:0% +are vectors in different places we use + + + align:start position:0% +are vectors in different places we use +vector decomposition and we use this + + align:start position:0% +vector decomposition and we use this + + + align:start position:0% +vector decomposition and we use this +procedure we'll learn how to do this in + + align:start position:0% +procedure we'll learn how to do this in + + + align:start position:0% +procedure we'll learn how to do this in +cup this is the Cartesian picture we'll + + align:start position:0% +cup this is the Cartesian picture we'll + + + align:start position:0% +cup this is the Cartesian picture we'll +learn how to do that in polar + + align:start position:0% +learn how to do that in polar + + + align:start position:0% +learn how to do that in polar +coordinates when we need it later on \ No newline at end of file diff --git a/Du0HgYO3E6U.txt b/Du0HgYO3E6U.txt new file mode 100644 index 0000000000000000000000000000000000000000..e5fa696e14e48ce54a2d35ec7eba07354dffa7df --- /dev/null +++ b/Du0HgYO3E6U.txt @@ -0,0 +1,1203 @@ +align:start position:0% + +in our our console let's start by + + align:start position:0% +in our our console let's start by + + + align:start position:0% +in our our console let's start by +loading our dataset don't forget to make + + align:start position:0% +loading our dataset don't forget to make + + + align:start position:0% +loading our dataset don't forget to make +sure you're in the directory containing + + align:start position:0% +sure you're in the directory containing + + + align:start position:0% +sure you're in the directory containing +the file wine dot CSV first we'll call + + align:start position:0% +the file wine dot CSV first we'll call + + + align:start position:0% +the file wine dot CSV first we'll call +our data frame wine and we'll use the + + align:start position:0% +our data frame wine and we'll use the + + + align:start position:0% +our data frame wine and we'll use the +read dot CSV function to read in the + + align:start position:0% +read dot CSV function to read in the + + + align:start position:0% +read dot CSV function to read in the +data file wine dot CSV we can look at + + align:start position:0% +data file wine dot CSV we can look at + + + align:start position:0% +data file wine dot CSV we can look at +the structure of our data by using the + + align:start position:0% +the structure of our data by using the + + + align:start position:0% +the structure of our data by using the +STR function we can see that we have a + + align:start position:0% +STR function we can see that we have a + + + align:start position:0% +STR function we can see that we have a +data frame with 25 observations of seven + + align:start position:0% +data frame with 25 observations of seven + + + align:start position:0% +data frame with 25 observations of seven +different variables year gives the year + + align:start position:0% +different variables year gives the year + + + align:start position:0% +different variables year gives the year +the wine was produced and it's just a + + align:start position:0% +the wine was produced and it's just a + + + align:start position:0% +the wine was produced and it's just a +unique identifier for each observation + + align:start position:0% +unique identifier for each observation + + + align:start position:0% +unique identifier for each observation +price is the dependent variable we're + + align:start position:0% +price is the dependent variable we're + + + align:start position:0% +price is the dependent variable we're +trying to predict and winter rain' + + align:start position:0% +trying to predict and winter rain' + + + align:start position:0% +trying to predict and winter rain' +average growing season temperature + + align:start position:0% +average growing season temperature + + + align:start position:0% +average growing season temperature +harvest rain age and France population + + align:start position:0% +harvest rain age and France population + + + align:start position:0% +harvest rain age and France population +are the independent variables we'll use + + align:start position:0% +are the independent variables we'll use + + + align:start position:0% +are the independent variables we'll use +to predict price we can also look at the + + align:start position:0% +to predict price we can also look at the + + + align:start position:0% +to predict price we can also look at the +statistical summary of our data using + + align:start position:0% +statistical summary of our data using + + + align:start position:0% +statistical summary of our data using +the summary function this gives us + + align:start position:0% +the summary function this gives us + + + align:start position:0% +the summary function this gives us +information about the range of values + + align:start position:0% +information about the range of values + + + align:start position:0% +information about the range of values +for each variable in our data set let's + + align:start position:0% +for each variable in our data set let's + + + align:start position:0% +for each variable in our data set let's +now create a one variable linear + + align:start position:0% +now create a one variable linear + + + align:start position:0% +now create a one variable linear +regression equation using average + + align:start position:0% +regression equation using average + + + align:start position:0% +regression equation using average +growing season temperature to predict + + align:start position:0% +growing season temperature to predict + + + align:start position:0% +growing season temperature to predict +price we'll call our regression model + + align:start position:0% +price we'll call our regression model + + + align:start position:0% +price we'll call our regression model +model one and we'll use the LM function + + align:start position:0% +model one and we'll use the LM function + + + align:start position:0% +model one and we'll use the LM function +which stands for linear model this is + + align:start position:0% +which stands for linear model this is + + + align:start position:0% +which stands for linear model this is +the function we'll use whenever we want + + align:start position:0% +the function we'll use whenever we want + + + align:start position:0% +the function we'll use whenever we want +to build a linear regression model then + + align:start position:0% +to build a linear regression model then + + + align:start position:0% +to build a linear regression model then +inside parentheses type price our + + align:start position:0% +inside parentheses type price our + + + align:start position:0% +inside parentheses type price our +dependent variable and then a tilde + + align:start position:0% +dependent variable and then a tilde + + + align:start position:0% +dependent variable and then a tilde +symbol and then average growing season + + align:start position:0% +symbol and then average growing season + + + align:start position:0% +symbol and then average growing season +temperature the independent variable + + align:start position:0% +temperature the independent variable + + + align:start position:0% +temperature the independent variable +we'll use in this model then after a + + align:start position:0% +we'll use in this model then after a + + + align:start position:0% +we'll use in this model then after a +comma we need to add data equals wine to + + align:start position:0% +comma we need to add data equals wine to + + + align:start position:0% +comma we need to add data equals wine to +tell the LM function what data set to + + align:start position:0% +tell the LM function what data set to + + + align:start position:0% +tell the LM function what data set to +use to build the model we're saving the + + align:start position:0% +use to build the model we're saving the + + + align:start position:0% +use to build the model we're saving the +output of the LM function to the + + align:start position:0% +output of the LM function to the + + + align:start position:0% +output of the LM function to the +variable named model 1 so when + + align:start position:0% +variable named model 1 so when + + + align:start position:0% +variable named model 1 so when +hit enter we didn't see any output + + align:start position:0% +hit enter we didn't see any output + + + align:start position:0% +hit enter we didn't see any output +because it's been saved to the variable + + align:start position:0% +because it's been saved to the variable + + + align:start position:0% +because it's been saved to the variable +model 1 let's take a look at the summary + + align:start position:0% +model 1 let's take a look at the summary + + + align:start position:0% +model 1 let's take a look at the summary +of model 1 the first thing we see is a + + align:start position:0% +of model 1 the first thing we see is a + + + align:start position:0% +of model 1 the first thing we see is a +description of the function we use to + + align:start position:0% +description of the function we use to + + + align:start position:0% +description of the function we use to +build the model then we see a summary of + + align:start position:0% +build the model then we see a summary of + + + align:start position:0% +build the model then we see a summary of +the residuals or errors following that + + align:start position:0% +the residuals or errors following that + + + align:start position:0% +the residuals or errors following that +is a description of the coefficients of + + align:start position:0% +is a description of the coefficients of + + + align:start position:0% +is a description of the coefficients of +our model the first row corresponds to + + align:start position:0% +our model the first row corresponds to + + + align:start position:0% +our model the first row corresponds to +the intersect term and the second row + + align:start position:0% +the intersect term and the second row + + + align:start position:0% +the intersect term and the second row +corresponds to our independent variable + + align:start position:0% +corresponds to our independent variable + + + align:start position:0% +corresponds to our independent variable +average growing season temperature the + + align:start position:0% +average growing season temperature the + + + align:start position:0% +average growing season temperature the +estimate column gives estimates of the + + align:start position:0% +estimate column gives estimates of the + + + align:start position:0% +estimate column gives estimates of the +beta values for our model so here beta 0 + + align:start position:0% +beta values for our model so here beta 0 + + + align:start position:0% +beta values for our model so here beta 0 +or the coefficient for the intercept + + align:start position:0% +or the coefficient for the intercept + + + align:start position:0% +or the coefficient for the intercept +term is estimated to be negative 3.4 and + + align:start position:0% +term is estimated to be negative 3.4 and + + + align:start position:0% +term is estimated to be negative 3.4 and +beta 1 or the coefficient for our + + align:start position:0% +beta 1 or the coefficient for our + + + align:start position:0% +beta 1 or the coefficient for our +independent variable is estimated to be + + align:start position:0% +independent variable is estimated to be + + + align:start position:0% +independent variable is estimated to be +0.6 35 there's additional information in + + align:start position:0% +0.6 35 there's additional information in + + + align:start position:0% +0.6 35 there's additional information in +this table that we'll discuss in the + + align:start position:0% +this table that we'll discuss in the + + + align:start position:0% +this table that we'll discuss in the +next video towards a bottom of the + + align:start position:0% +next video towards a bottom of the + + + align:start position:0% +next video towards a bottom of the +output you can see multiple r-squared + + align:start position:0% +output you can see multiple r-squared + + + align:start position:0% +output you can see multiple r-squared +0.43 5 which is the r-squared value that + + align:start position:0% +0.43 5 which is the r-squared value that + + + align:start position:0% +0.43 5 which is the r-squared value that +we discussed in the previous video + + align:start position:0% +we discussed in the previous video + + + align:start position:0% +we discussed in the previous video +beside it is a number labeled adjusted + + align:start position:0% +beside it is a number labeled adjusted + + + align:start position:0% +beside it is a number labeled adjusted +r-squared in this case it's point 4 1 + + align:start position:0% +r-squared in this case it's point 4 1 + + + align:start position:0% +r-squared in this case it's point 4 1 +this number adjusts the r-squared value + + align:start position:0% +this number adjusts the r-squared value + + + align:start position:0% +this number adjusts the r-squared value +to account for the number of independent + + align:start position:0% +to account for the number of independent + + + align:start position:0% +to account for the number of independent +variables used relative to the number of + + align:start position:0% +variables used relative to the number of + + + align:start position:0% +variables used relative to the number of +data points multiple r-squared will + + align:start position:0% +data points multiple r-squared will + + + align:start position:0% +data points multiple r-squared will +always increase if you add more + + align:start position:0% +always increase if you add more + + + align:start position:0% +always increase if you add more +independent variables but adjusted + + align:start position:0% +independent variables but adjusted + + + align:start position:0% +independent variables but adjusted +r-squared will decrease if you add an + + align:start position:0% +r-squared will decrease if you add an + + + align:start position:0% +r-squared will decrease if you add an +independent variable that doesn't help + + align:start position:0% +independent variable that doesn't help + + + align:start position:0% +independent variable that doesn't help +the model this is a good way to + + align:start position:0% +the model this is a good way to + + + align:start position:0% +the model this is a good way to +determine if an additional variable + + align:start position:0% +determine if an additional variable + + + align:start position:0% +determine if an additional variable +should even be included in the model + + align:start position:0% +should even be included in the model + + + align:start position:0% +should even be included in the model +we'll also discuss other ways to select + + align:start position:0% +we'll also discuss other ways to select + + + align:start position:0% +we'll also discuss other ways to select +important independent variables in the + + align:start position:0% +important independent variables in the + + + align:start position:0% +important independent variables in the +next video let's also compute the sum of + + align:start position:0% +next video let's also compute the sum of + + + align:start position:0% +next video let's also compute the sum of +squared errors or SSE for our model our + + align:start position:0% +squared errors or SSE for our model our + + + align:start position:0% +squared errors or SSE for our model our +residuals or air terms are stored in the + + align:start position:0% +residuals or air terms are stored in the + + + align:start position:0% +residuals or air terms are stored in the +vector model 1 dollar signs + + align:start position:0% +vector model 1 dollar signs + + + align:start position:0% +vector model 1 dollar signs +residuals + + align:start position:0% +residuals + + + align:start position:0% +residuals +by hitting enter we can see the values + + align:start position:0% +by hitting enter we can see the values + + + align:start position:0% +by hitting enter we can see the values +of all of our residuals we can compute + + align:start position:0% +of all of our residuals we can compute + + + align:start position:0% +of all of our residuals we can compute +the sum of squared errors or SSE by + + align:start position:0% +the sum of squared errors or SSE by + + + align:start position:0% +the sum of squared errors or SSE by +taking the sum of model one residuals + + align:start position:0% +taking the sum of model one residuals + + + align:start position:0% +taking the sum of model one residuals +squared if we type SSE and hit enter we + + align:start position:0% +squared if we type SSE and hit enter we + + + align:start position:0% +squared if we type SSE and hit enter we +can see that our sum of squared errors + + align:start position:0% +can see that our sum of squared errors + + + align:start position:0% +can see that our sum of squared errors +is five point seven three now let's add + + align:start position:0% +is five point seven three now let's add + + + align:start position:0% +is five point seven three now let's add +another variable to our regression model + + align:start position:0% +another variable to our regression model + + + align:start position:0% +another variable to our regression model +harvest rain we'll call our new model + + align:start position:0% +harvest rain we'll call our new model + + + align:start position:0% +harvest rain we'll call our new model +model two and again we'll use the LM + + align:start position:0% +model two and again we'll use the LM + + + align:start position:0% +model two and again we'll use the LM +function to predict price but this time + + align:start position:0% +function to predict price but this time + + + align:start position:0% +function to predict price but this time +using average growing season temperature + + align:start position:0% +using average growing season temperature + + + align:start position:0% +using average growing season temperature +and harvest rain when you want to use + + align:start position:0% +and harvest rain when you want to use + + + align:start position:0% +and harvest rain when you want to use +more than one independent variable you + + align:start position:0% +more than one independent variable you + + + align:start position:0% +more than one independent variable you +can just separate them with a plus sign + + align:start position:0% +can just separate them with a plus sign + + + align:start position:0% +can just separate them with a plus sign +like we did here then we again need to + + align:start position:0% +like we did here then we again need to + + + align:start position:0% +like we did here then we again need to +indicate that the data that should be + + align:start position:0% +indicate that the data that should be + + + align:start position:0% +indicate that the data that should be +used is wine let's take a look at the + + align:start position:0% +used is wine let's take a look at the + + + align:start position:0% +used is wine let's take a look at the +summary of our new model using the + + align:start position:0% +summary of our new model using the + + + align:start position:0% +summary of our new model using the +summary function we have a third row in + + align:start position:0% +summary function we have a third row in + + + align:start position:0% +summary function we have a third row in +our coefficients table now corresponding + + align:start position:0% +our coefficients table now corresponding + + + align:start position:0% +our coefficients table now corresponding +to harvest rain the coefficient estimate + + align:start position:0% +to harvest rain the coefficient estimate + + + align:start position:0% +to harvest rain the coefficient estimate +for this new independent variable is + + align:start position:0% +for this new independent variable is + + + align:start position:0% +for this new independent variable is +negative point zero zero four five seven + + align:start position:0% +negative point zero zero four five seven + + + align:start position:0% +negative point zero zero four five seven +and if you look at the r-squared near + + align:start position:0% +and if you look at the r-squared near + + + align:start position:0% +and if you look at the r-squared near +the bottom of the output you can see + + align:start position:0% +the bottom of the output you can see + + + align:start position:0% +the bottom of the output you can see +that this variable really helped our + + align:start position:0% +that this variable really helped our + + + align:start position:0% +that this variable really helped our +model our multiple r-squared and + + align:start position:0% +model our multiple r-squared and + + + align:start position:0% +model our multiple r-squared and +adjusted r-squared both increase + + align:start position:0% +adjusted r-squared both increase + + + align:start position:0% +adjusted r-squared both increase +significantly compared to the previous + + align:start position:0% +significantly compared to the previous + + + align:start position:0% +significantly compared to the previous +model this indicates that this new model + + align:start position:0% +model this indicates that this new model + + + align:start position:0% +model this indicates that this new model +is probably better than the previous + + align:start position:0% +is probably better than the previous + + + align:start position:0% +is probably better than the previous +model + + align:start position:0% +model + + + align:start position:0% +model +let's now also compute the sum of + + align:start position:0% +let's now also compute the sum of + + + align:start position:0% +let's now also compute the sum of +squared errors for this new model so SSE + + align:start position:0% +squared errors for this new model so SSE + + + align:start position:0% +squared errors for this new model so SSE +equals and then sum of model two + + align:start position:0% +equals and then sum of model two + + + align:start position:0% +equals and then sum of model two +residuals squared if we type SSE we can + + align:start position:0% +residuals squared if we type SSE we can + + + align:start position:0% +residuals squared if we type SSE we can +see that the sum of squared errors for + + align:start position:0% +see that the sum of squared errors for + + + align:start position:0% +see that the sum of squared errors for +model two is two point nine seven which + + align:start position:0% +model two is two point nine seven which + + + align:start position:0% +model two is two point nine seven which +is much better than the sum of squared + + align:start position:0% +is much better than the sum of squared + + + align:start position:0% +is much better than the sum of squared +errors for model one + + align:start position:0% +errors for model one + + + align:start position:0% +errors for model one +now let's build a third model this time + + align:start position:0% +now let's build a third model this time + + + align:start position:0% +now let's build a third model this time +with all of our independent variables + + align:start position:0% +with all of our independent variables + + + align:start position:0% +with all of our independent variables +we'll call this one model three and + + align:start position:0% +we'll call this one model three and + + + align:start position:0% +we'll call this one model three and +again use the LM function to predict + + align:start position:0% +again use the LM function to predict + + + align:start position:0% +again use the LM function to predict +price using average growing season + + align:start position:0% +price using average growing season + + + align:start position:0% +price using average growing season +temperature and harvest rain and winter + + align:start position:0% +temperature and harvest rain and winter + + + align:start position:0% +temperature and harvest rain and winter +rain and age and France population again + + align:start position:0% +rain and age and France population again + + + align:start position:0% +rain and age and France population again +we need to tell the LM function to use + + align:start position:0% +we need to tell the LM function to use + + + align:start position:0% +we need to tell the LM function to use +the data set wine let's take a look at + + align:start position:0% +the data set wine let's take a look at + + + align:start position:0% +the data set wine let's take a look at +the summary of model three now the + + align:start position:0% +the summary of model three now the + + + align:start position:0% +the summary of model three now the +coefficients table has six rows one for + + align:start position:0% +coefficients table has six rows one for + + + align:start position:0% +coefficients table has six rows one for +the intercept and one for each of the + + align:start position:0% +the intercept and one for each of the + + + align:start position:0% +the intercept and one for each of the +five independent variables if we look at + + align:start position:0% +five independent variables if we look at + + + align:start position:0% +five independent variables if we look at +the bottom of the output we can again + + align:start position:0% +the bottom of the output we can again + + + align:start position:0% +the bottom of the output we can again +see that the multiple r-squared and + + align:start position:0% +see that the multiple r-squared and + + + align:start position:0% +see that the multiple r-squared and +adjusted r-squared have both increased + + align:start position:0% +adjusted r-squared have both increased + + + align:start position:0% +adjusted r-squared have both increased +let's now compute the sum of squared + + align:start position:0% +let's now compute the sum of squared + + + align:start position:0% +let's now compute the sum of squared +errors for this new model SSE equals the + + align:start position:0% +errors for this new model SSE equals the + + + align:start position:0% +errors for this new model SSE equals the +sum of model three residuals squared if + + align:start position:0% +sum of model three residuals squared if + + + align:start position:0% +sum of model three residuals squared if +we type sfe we can see that the sum of + + align:start position:0% +we type sfe we can see that the sum of + + + align:start position:0% +we type sfe we can see that the sum of +squared errors for model three is one + + align:start position:0% +squared errors for model three is one + + + align:start position:0% +squared errors for model three is one +point seven even better than before in + + align:start position:0% +point seven even better than before in + + + align:start position:0% +point seven even better than before in +the next video we'll determine if we + + align:start position:0% +the next video we'll determine if we + + + align:start position:0% +the next video we'll determine if we +should keep all of these variables in + + align:start position:0% +should keep all of these variables in + + + align:start position:0% +should keep all of these variables in +our final model \ No newline at end of file diff --git a/E-AQf4uR_Bw.txt b/E-AQf4uR_Bw.txt new file mode 100644 index 0000000000000000000000000000000000000000..3b51a79cb90eb392ae560d0c81f83ab643bb8959 --- /dev/null +++ b/E-AQf4uR_Bw.txt @@ -0,0 +1,451 @@ +align:start position:0% + +the field and inductance of a spherical + + align:start position:0% +the field and inductance of a spherical + + + align:start position:0% +the field and inductance of a spherical +coil illustrate the model of a + + align:start position:0% +coil illustrate the model of a + + + align:start position:0% +coil illustrate the model of a +distributed surface current density and + + align:start position:0% +distributed surface current density and + + + align:start position:0% +distributed surface current density and +the associated laplacian fields this is + + align:start position:0% +the associated laplacian fields this is + + + align:start position:0% +the associated laplacian fields this is +a coil wound on the surface of a sphere + + align:start position:0% +a coil wound on the surface of a sphere + + + align:start position:0% +a coil wound on the surface of a sphere +here are the terminals a current through + + align:start position:0% +here are the terminals a current through + + + align:start position:0% +here are the terminals a current through +the wire results in a magnetic field + + align:start position:0% +the wire results in a magnetic field + + + align:start position:0% +the wire results in a magnetic field +inside the sphere that is uniform + + align:start position:0% +inside the sphere that is uniform + + + align:start position:0% +inside the sphere that is uniform +outside the field is that of a dipole + + align:start position:0% +outside the field is that of a dipole + + + align:start position:0% +outside the field is that of a dipole +because these fields are so simple this + + align:start position:0% +because these fields are so simple this + + + align:start position:0% +because these fields are so simple this +flux ball example is a valuable resource + + align:start position:0% +flux ball example is a valuable resource + + + align:start position:0% +flux ball example is a valuable resource +for dealing with other situations and + + align:start position:0% +for dealing with other situations and + + + align:start position:0% +for dealing with other situations and +forgetting basic notions straight such + + align:start position:0% +forgetting basic notions straight such + + + align:start position:0% +forgetting basic notions straight such +as how to compute the inductance of a + + align:start position:0% +as how to compute the inductance of a + + + align:start position:0% +as how to compute the inductance of a +coil every turn of which links a + + align:start position:0% +coil every turn of which links a + + + align:start position:0% +coil every turn of which links a +different amount of magnetic flux a Hall + + align:start position:0% +different amount of magnetic flux a Hall + + + align:start position:0% +different amount of magnetic flux a Hall +magnetometer with the transverse probe + + align:start position:0% +magnetometer with the transverse probe + + + align:start position:0% +magnetometer with the transverse probe +make it possible to probe the field we + + align:start position:0% +make it possible to probe the field we + + + align:start position:0% +make it possible to probe the field we +use the oscilloscope to show the output + + align:start position:0% +use the oscilloscope to show the output + + + align:start position:0% +use the oscilloscope to show the output +of the hall probe the upper trace is the + + align:start position:0% +of the hall probe the upper trace is the + + + align:start position:0% +of the hall probe the upper trace is the +coil current the lower is from the probe + + align:start position:0% + + + + align:start position:0% + +here at the North Pole the magnetic flux + + align:start position:0% +here at the North Pole the magnetic flux + + + align:start position:0% +here at the North Pole the magnetic flux +density should be perpendicular to the + + align:start position:0% +density should be perpendicular to the + + + align:start position:0% +density should be perpendicular to the +sphere surface the probe detects the + + align:start position:0% +sphere surface the probe detects the + + + align:start position:0% +sphere surface the probe detects the +field perpendicular to its flat face so + + align:start position:0% +field perpendicular to its flat face so + + + align:start position:0% +field perpendicular to its flat face so +we can see that the field is + + align:start position:0% +we can see that the field is + + + align:start position:0% +we can see that the field is +perpendicular to the surface of the + + align:start position:0% +perpendicular to the surface of the + + + align:start position:0% +perpendicular to the surface of the +North Pole at the equator the field is + + align:start position:0% +North Pole at the equator the field is + + + align:start position:0% +North Pole at the equator the field is +tangential and in the opposite direction + + align:start position:0% + + + + align:start position:0% + +by latching the phase of the lower trace + + align:start position:0% +by latching the phase of the lower trace + + + align:start position:0% +by latching the phase of the lower trace +we can see that the field at the South + + align:start position:0% +we can see that the field at the South + + + align:start position:0% +we can see that the field at the South +Pole is in the same direction as at the + + align:start position:0% +Pole is in the same direction as at the + + + align:start position:0% +Pole is in the same direction as at the +North Pole the phase is the same at the + + align:start position:0% +North Pole the phase is the same at the + + + align:start position:0% +North Pole the phase is the same at the +two poles so the field is upward at both + + align:start position:0% +two poles so the field is upward at both + + + align:start position:0% +two poles so the field is upward at both +poles + + align:start position:0% + + + + align:start position:0% + +watch the vertical component of the + + align:start position:0% +watch the vertical component of the + + + align:start position:0% +watch the vertical component of the +field as we go from the north to the + + align:start position:0% +field as we go from the north to the + + + align:start position:0% +field as we go from the north to the +south + + align:start position:0% + + + + align:start position:0% + +we have a whole from the south to the + + align:start position:0% +we have a whole from the south to the + + + align:start position:0% +we have a whole from the south to the +North Pole + + align:start position:0% + + + + align:start position:0% + +we can insert another probe by contrast + + align:start position:0% +we can insert another probe by contrast + + + align:start position:0% +we can insert another probe by contrast +with our transfers probe this axial + + align:start position:0% +with our transfers probe this axial + + + align:start position:0% +with our transfers probe this axial +probe measures the magnetic field along + + align:start position:0% +probe measures the magnetic field along + + + align:start position:0% +probe measures the magnetic field along +its axis + + align:start position:0% + + + + align:start position:0% + +the magnetic flux density inside the + + align:start position:0% +the magnetic flux density inside the + + + align:start position:0% +the magnetic flux density inside the +sphere is essentially uniform + + align:start position:0% + + + + align:start position:0% + +outside it has the decay of a dipole + + align:start position:0% + + + + align:start position:0% + +inside we measure 5.4 Gauss RMS + + align:start position:0% + + + + align:start position:0% + +the flex ball is a classic example where + + align:start position:0% +the flex ball is a classic example where + + + align:start position:0% +the flex ball is a classic example where +the fields are simple to represent a + + align:start position:0% +the fields are simple to represent a + + + align:start position:0% +the fields are simple to represent a +uniform field inside and a dipole field + + align:start position:0% +uniform field inside and a dipole field + + + align:start position:0% +uniform field inside and a dipole field +outside and yet interesting enough to + + align:start position:0% +outside and yet interesting enough to + + + align:start position:0% +outside and yet interesting enough to +give insight into more complex + + align:start position:0% +give insight into more complex + + + align:start position:0% +give insight into more complex +situations for example the vertical + + align:start position:0% +situations for example the vertical + + + align:start position:0% +situations for example the vertical +field at the North Pole should be twice + + align:start position:0% +field at the North Pole should be twice + + + align:start position:0% +field at the North Pole should be twice +what it is at the equator + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/EBVNbRN805o.txt b/EBVNbRN805o.txt new file mode 100644 index 0000000000000000000000000000000000000000..3e8f4732fe26a6cd3db8ac5c7783e76ee3e4c309 --- /dev/null +++ b/EBVNbRN805o.txt @@ -0,0 +1,1171 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu in this demo we're going to + + align:start position:0% +ocw.mit.edu in this demo we're going to + + + align:start position:0% +ocw.mit.edu in this demo we're going to +illustrate the basic use of a quarter + + align:start position:0% +illustrate the basic use of a quarter + + + align:start position:0% +illustrate the basic use of a quarter +wave play + + align:start position:0% +wave play + + + align:start position:0% +wave play +and as we know a quarter wave plate is + + align:start position:0% +and as we know a quarter wave plate is + + + align:start position:0% +and as we know a quarter wave plate is +used to change the state of polarization + + align:start position:0% +used to change the state of polarization + + + align:start position:0% +used to change the state of polarization +of light from plain polarized for + + align:start position:0% +of light from plain polarized for + + + align:start position:0% +of light from plain polarized for +example to elliptical and under certain + + align:start position:0% +example to elliptical and under certain + + + align:start position:0% +example to elliptical and under certain +conditions to Circular polarized light + + align:start position:0% +conditions to Circular polarized light + + + align:start position:0% +conditions to Circular polarized light +so we'd like to do that using using this + + align:start position:0% +so we'd like to do that using using this + + + align:start position:0% +so we'd like to do that using using this +setup we have a a laser a helium neon + + align:start position:0% +setup we have a a laser a helium neon + + + align:start position:0% +setup we have a a laser a helium neon +laser and here's the beam from the laser + + align:start position:0% +laser and here's the beam from the laser + + + align:start position:0% +laser and here's the beam from the laser +we're going to reflect it through this + + align:start position:0% +we're going to reflect it through this + + + align:start position:0% +we're going to reflect it through this +mirror and then reflect it again through + + align:start position:0% +mirror and then reflect it again through + + + align:start position:0% +mirror and then reflect it again through +a second mirror then we pass it through + + align:start position:0% +a second mirror then we pass it through + + + align:start position:0% +a second mirror then we pass it through +this uh + + align:start position:0% +this uh + + + align:start position:0% +this uh +polarizer and the the beam coming out of + + align:start position:0% +polarizer and the the beam coming out of + + + align:start position:0% +polarizer and the the beam coming out of +the through the polarizer then hits the + + align:start position:0% +the through the polarizer then hits the + + + align:start position:0% +the through the polarizer then hits the +hits the + + align:start position:0% +hits the + + + align:start position:0% +hits the +screen this polarizer the transmission + + align:start position:0% +screen this polarizer the transmission + + + align:start position:0% +screen this polarizer the transmission +axis of which is shown by the white + + align:start position:0% +axis of which is shown by the white + + + align:start position:0% +axis of which is shown by the white +Arrow sets the state of polarization of + + align:start position:0% +Arrow sets the state of polarization of + + + align:start position:0% +Arrow sets the state of polarization of +the light here in this region no matter + + align:start position:0% +the light here in this region no matter + + + align:start position:0% +the light here in this region no matter +what the state of polarization is before + + align:start position:0% +what the state of polarization is before + + + align:start position:0% +what the state of polarization is before +the Light reaches the polarizer the + + align:start position:0% +the Light reaches the polarizer the + + + align:start position:0% +the Light reaches the polarizer the +polarizer then will clean it up and set + + align:start position:0% +polarizer then will clean it up and set + + + align:start position:0% +polarizer then will clean it up and set +it uh according to the transmission axis + + align:start position:0% +it uh according to the transmission axis + + + align:start position:0% +it uh according to the transmission axis +and right now the transmission axis is + + align:start position:0% +and right now the transmission axis is + + + align:start position:0% +and right now the transmission axis is +along the uh vertical as shown by the + + align:start position:0% +along the uh vertical as shown by the + + + align:start position:0% +along the uh vertical as shown by the +white Arrow but just to check this we + + align:start position:0% +white Arrow but just to check this we + + + align:start position:0% +white Arrow but just to check this we +will use the analyzer which is another + + align:start position:0% +will use the analyzer which is another + + + align:start position:0% +will use the analyzer which is another +polarizer and we place it over + + align:start position:0% + + + + align:start position:0% + +here the white + + align:start position:0% +here the white + + + align:start position:0% +here the white +arrow is along the vertical Direction + + align:start position:0% +arrow is along the vertical Direction + + + align:start position:0% +arrow is along the vertical Direction +and labels the transmission axis of this + + align:start position:0% +and labels the transmission axis of this + + + align:start position:0% +and labels the transmission axis of this +polarizer so let's see indeed whether + + align:start position:0% +polarizer so let's see indeed whether + + + align:start position:0% +polarizer so let's see indeed whether +the light here is plain + + align:start position:0% +the light here is plain + + + align:start position:0% +the light here is plain +polarized so I'm going to rotate the + + align:start position:0% +polarized so I'm going to rotate the + + + align:start position:0% +polarized so I'm going to rotate the +analyzer and see if I can extinguish the + + align:start position:0% +analyzer and see if I can extinguish the + + + align:start position:0% +analyzer and see if I can extinguish the +light + + align:start position:0% +light + + + align:start position:0% +light +now what I would like to do is is uh + + align:start position:0% +now what I would like to do is is uh + + + align:start position:0% +now what I would like to do is is uh +look at this uh extinguishing of the + + align:start position:0% +look at this uh extinguishing of the + + + align:start position:0% +look at this uh extinguishing of the +light more closely in a uh in the in the + + align:start position:0% +light more closely in a uh in the in the + + + align:start position:0% +light more closely in a uh in the in the +bottom left hand Corner which is a + + align:start position:0% +bottom left hand Corner which is a + + + align:start position:0% +bottom left hand Corner which is a +closeup of of what you see on the screen + + align:start position:0% +closeup of of what you see on the screen + + + align:start position:0% +closeup of of what you see on the screen +and here you can see that that the + + align:start position:0% +and here you can see that that the + + + align:start position:0% +and here you can see that that the +extinguishing is pretty complete which + + align:start position:0% +extinguishing is pretty complete which + + + align:start position:0% +extinguishing is pretty complete which +shows that indeed the light in this + + align:start position:0% +shows that indeed the light in this + + + align:start position:0% +shows that indeed the light in this +region is uh is plain polarized so let + + align:start position:0% +region is uh is plain polarized so let + + + align:start position:0% +region is uh is plain polarized so let +me set the analyzer back so that we're + + align:start position:0% +me set the analyzer back so that we're + + + align:start position:0% +me set the analyzer back so that we're +transmitting uh the maximum intensity + + align:start position:0% +transmitting uh the maximum intensity + + + align:start position:0% +transmitting uh the maximum intensity +which means the transmission axis is + + align:start position:0% +which means the transmission axis is + + + align:start position:0% +which means the transmission axis is +lined up with the transmission axis of + + align:start position:0% +lined up with the transmission axis of + + + align:start position:0% +lined up with the transmission axis of +this polarizer now we're ready to bring + + align:start position:0% +this polarizer now we're ready to bring + + + align:start position:0% +this polarizer now we're ready to bring +in the quarter wave plate plate here's + + align:start position:0% +in the quarter wave plate plate here's + + + align:start position:0% +in the quarter wave plate plate here's +the quarter wave plate I'm going to + + align:start position:0% +the quarter wave plate I'm going to + + + align:start position:0% +the quarter wave plate I'm going to +place it in this + + align:start position:0% +place it in this + + + align:start position:0% +place it in this +position secure + + align:start position:0% +position secure + + + align:start position:0% +position secure +it now this quarter W plate has as we + + align:start position:0% +it now this quarter W plate has as we + + + align:start position:0% +it now this quarter W plate has as we +know has two principal axes one of them + + align:start position:0% +know has two principal axes one of them + + + align:start position:0% +know has two principal axes one of them +is labeled by the white Arrow here and + + align:start position:0% +is labeled by the white Arrow here and + + + align:start position:0% +is labeled by the white Arrow here and +uh and again we know that when light + + align:start position:0% +uh and again we know that when light + + + align:start position:0% +uh and again we know that when light +when this light is propagated along the + + align:start position:0% +when this light is propagated along the + + + align:start position:0% +when this light is propagated along the +principal axis of the Quad wave plate + + align:start position:0% +principal axis of the Quad wave plate + + + align:start position:0% +principal axis of the Quad wave plate +there is no change in the polarization + + align:start position:0% +there is no change in the polarization + + + align:start position:0% +there is no change in the polarization +just like a piece of glass let's check + + align:start position:0% +just like a piece of glass let's check + + + align:start position:0% +just like a piece of glass let's check +that so we take the analyzer again and + + align:start position:0% +that so we take the analyzer again and + + + align:start position:0% +that so we take the analyzer again and +we rotate the analyzer to see indeed + + align:start position:0% +we rotate the analyzer to see indeed + + + align:start position:0% +we rotate the analyzer to see indeed +whether the light is PL + + align:start position:0% +whether the light is PL + + + align:start position:0% +whether the light is PL +polarized and as you can see maybe I + + align:start position:0% +polarized and as you can see maybe I + + + align:start position:0% +polarized and as you can see maybe I +didn't get the labeling here but as you + + align:start position:0% +didn't get the labeling here but as you + + + align:start position:0% +didn't get the labeling here but as you +can see the light + + align:start position:0% +can see the light + + + align:start position:0% +can see the light +[Music] + + align:start position:0% + + + + align:start position:0% + +is is pretty close + + align:start position:0% +is is pretty close + + + align:start position:0% +is is pretty close +to Flame + + align:start position:0% +to Flame + + + align:start position:0% +to Flame +polarized now we know that there are two + + align:start position:0% +polarized now we know that there are two + + + align:start position:0% +polarized now we know that there are two +principal axes so let's turn the arrow + + align:start position:0% +principal axes so let's turn the arrow + + + align:start position:0% +principal axes so let's turn the arrow +to + + align:start position:0% + + + + align:start position:0% + +90° and show + + align:start position:0% +90° and show + + + align:start position:0% +90° and show +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the fact that when light propagates + + align:start position:0% +the fact that when light propagates + + + align:start position:0% +the fact that when light propagates +along the other principal axis the the + + align:start position:0% +along the other principal axis the the + + + align:start position:0% +along the other principal axis the the +light here is again PL polarized which + + align:start position:0% +light here is again PL polarized which + + + align:start position:0% +light here is again PL polarized which +means it cannot get get past this + + align:start position:0% +means it cannot get get past this + + + align:start position:0% +means it cannot get get past this +polarizer when the transmission axis is + + align:start position:0% +polarizer when the transmission axis is + + + align:start position:0% +polarizer when the transmission axis is +orthogonal to the initial polarization + + align:start position:0% +orthogonal to the initial polarization + + + align:start position:0% +orthogonal to the initial polarization +set by this polarizer so now we've + + align:start position:0% +set by this polarizer so now we've + + + align:start position:0% +set by this polarizer so now we've +established that indeed when we + + align:start position:0% +established that indeed when we + + + align:start position:0% +established that indeed when we +propagate along principal axis of the qu + + align:start position:0% +propagate along principal axis of the qu + + + align:start position:0% +propagate along principal axis of the qu +plate nothing happens to the light it + + align:start position:0% +plate nothing happens to the light it + + + align:start position:0% +plate nothing happens to the light it +just stays plain + + align:start position:0% +just stays plain + + + align:start position:0% +just stays plain +polarized now we're going to demonstrate + + align:start position:0% +polarized now we're going to demonstrate + + + align:start position:0% +polarized now we're going to demonstrate +the actual use of a quarterway plate + + align:start position:0% +the actual use of a quarterway plate + + + align:start position:0% +the actual use of a quarterway plate +which would changes for example in this + + align:start position:0% +which would changes for example in this + + + align:start position:0% +which would changes for example in this +case from plain changes the state of + + align:start position:0% +case from plain changes the state of + + + align:start position:0% +case from plain changes the state of +polarization from plain polarized light + + align:start position:0% +polarization from plain polarized light + + + align:start position:0% +polarization from plain polarized light +to Elliptical depending on the the + + align:start position:0% +to Elliptical depending on the the + + + align:start position:0% +to Elliptical depending on the the +angular position that we that we set the + + align:start position:0% +angular position that we that we set the + + + align:start position:0% +angular position that we that we set the +quarter wave plate + + align:start position:0% +quarter wave plate + + + align:start position:0% +quarter wave plate +at okay so let's start with a very small + + align:start position:0% +at okay so let's start with a very small + + + align:start position:0% +at okay so let's start with a very small +angle away from uh from the principal + + align:start position:0% +angle away from uh from the principal + + + align:start position:0% +angle away from uh from the principal +axis and and now we want to look at the + + align:start position:0% +axis and and now we want to look at the + + + align:start position:0% +axis and and now we want to look at the +intensity on the screen and also in the + + align:start position:0% +intensity on the screen and also in the + + + align:start position:0% +intensity on the screen and also in the +insert uh to see whether the + + align:start position:0% +insert uh to see whether the + + + align:start position:0% +insert uh to see whether the +light first of all whether the light + + align:start position:0% +light first of all whether the light + + + align:start position:0% +light first of all whether the light +gets + + align:start position:0% +gets + + + align:start position:0% +gets +extinguished and + + align:start position:0% +extinguished and + + + align:start position:0% +extinguished and +also watch the intensity as I as I + + align:start position:0% +also watch the intensity as I as I + + + align:start position:0% +also watch the intensity as I as I +rotate my analyzer now you can see the + + align:start position:0% +rotate my analyzer now you can see the + + + align:start position:0% +rotate my analyzer now you can see the +minimum is around + + align:start position:0% +minimum is around + + + align:start position:0% +minimum is around +here it's not zero and the maximum is + + align:start position:0% +here it's not zero and the maximum is + + + align:start position:0% +here it's not zero and the maximum is +around here which shows that the light + + align:start position:0% +around here which shows that the light + + + align:start position:0% +around here which shows that the light +is tically polarized certainly not plain + + align:start position:0% +is tically polarized certainly not plain + + + align:start position:0% +is tically polarized certainly not plain +polarized as it was + + align:start position:0% +polarized as it was + + + align:start position:0% +polarized as it was +before now if you want circular + + align:start position:0% +before now if you want circular + + + align:start position:0% +before now if you want circular +polarization we have to rotate the + + align:start position:0% +polarization we have to rotate the + + + align:start position:0% +polarization we have to rotate the +quarter wave plate to about 45° from one + + align:start position:0% +quarter wave plate to about 45° from one + + + align:start position:0% +quarter wave plate to about 45° from one +of the principal axes and if the light + + align:start position:0% +of the principal axes and if the light + + + align:start position:0% +of the principal axes and if the light +is indeed circularly polarized then we + + align:start position:0% +is indeed circularly polarized then we + + + align:start position:0% +is indeed circularly polarized then we +would we wouldn't see any change in + + align:start position:0% +would we wouldn't see any change in + + + align:start position:0% +would we wouldn't see any change in +intensity as we rotate the transmission + + align:start position:0% +intensity as we rotate the transmission + + + align:start position:0% +intensity as we rotate the transmission +axis of the analyze and let's see if if + + align:start position:0% +axis of the analyze and let's see if if + + + align:start position:0% +axis of the analyze and let's see if if +we got this close now you can see is I'm + + align:start position:0% +we got this close now you can see is I'm + + + align:start position:0% +we got this close now you can see is I'm +rotating the uh the analyzer you can see + + align:start position:0% +rotating the uh the analyzer you can see + + + align:start position:0% +rotating the uh the analyzer you can see +that the + + align:start position:0% +that the + + + align:start position:0% +that the +intensity on the screen doesn't change + + align:start position:0% +intensity on the screen doesn't change + + + align:start position:0% +intensity on the screen doesn't change +all that much which shows that the light + + align:start position:0% +all that much which shows that the light + + + align:start position:0% +all that much which shows that the light +is circularly + + align:start position:0% +is circularly + + + align:start position:0% +is circularly +polarized in summary we've shown that a + + align:start position:0% +polarized in summary we've shown that a + + + align:start position:0% +polarized in summary we've shown that a +quarterway plate can change the state of + + align:start position:0% +quarterway plate can change the state of + + + align:start position:0% +quarterway plate can change the state of +polarization of light in particular + + align:start position:0% +polarization of light in particular + + + align:start position:0% +polarization of light in particular +we've demonstrated that if plain + + align:start position:0% +we've demonstrated that if plain + + + align:start position:0% +we've demonstrated that if plain +polarized light is incident on the + + align:start position:0% +polarized light is incident on the + + + align:start position:0% +polarized light is incident on the +quarter wave plate and the quarterwave + + align:start position:0% +quarter wave plate and the quarterwave + + + align:start position:0% +quarter wave plate and the quarterwave +plate is oriented appropriately we can + + align:start position:0% +plate is oriented appropriately we can + + + align:start position:0% +plate is oriented appropriately we can +get elliptically polarized light if the + + align:start position:0% +get elliptically polarized light if the + + + align:start position:0% +get elliptically polarized light if the +quarterwave plate is oriented at 45° + + align:start position:0% +quarterwave plate is oriented at 45° + + + align:start position:0% +quarterwave plate is oriented at 45° +with respect to the state of + + align:start position:0% +with respect to the state of + + + align:start position:0% +with respect to the state of +polarization of the light then we can + + align:start position:0% +polarization of the light then we can + + + align:start position:0% +polarization of the light then we can +get circularly polarized light \ No newline at end of file diff --git a/FRoD9TOJxso.txt b/FRoD9TOJxso.txt new file mode 100644 index 0000000000000000000000000000000000000000..f76bb018c08834b1eb16c9ad1326c9e174a32316 --- /dev/null +++ b/FRoD9TOJxso.txt @@ -0,0 +1,6235 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license + + align:start position:0% +a Creative Commons license + + + align:start position:0% +a Creative Commons license +your support will help MIT + + align:start position:0% +your support will help MIT + + + align:start position:0% +your support will help MIT +OpenCourseWare continue to offer high + + align:start position:0% +OpenCourseWare continue to offer high + + + align:start position:0% +OpenCourseWare continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +great pleasure to be in Woods Hole my + + align:start position:0% +great pleasure to be in Woods Hole my + + + align:start position:0% +great pleasure to be in Woods Hole my +first visit here had a wonderful swim in + + align:start position:0% +first visit here had a wonderful swim in + + + align:start position:0% +first visit here had a wonderful swim in +the sea yesterday Southfield robotics is + + align:start position:0% +the sea yesterday Southfield robotics is + + + align:start position:0% +the sea yesterday Southfield robotics is +across both universities in Sheffield + + align:start position:0% +across both universities in Sheffield + + + align:start position:0% +across both universities in Sheffield +and it's been founded since 2011 but + + align:start position:0% +and it's been founded since 2011 but + + + align:start position:0% +and it's been founded since 2011 but +we've really been doing robotics since + + align:start position:0% +we've really been doing robotics since + + + align:start position:0% +we've really been doing robotics since +the 1980s and I joined them in 1989 and + + align:start position:0% +the 1980s and I joined them in 1989 and + + + align:start position:0% +the 1980s and I joined them in 1989 and +we do pretty much every different kind + + align:start position:0% +we do pretty much every different kind + + + align:start position:0% +we do pretty much every different kind +of robotics but I talk about biomimetics + + align:start position:0% +of robotics but I talk about biomimetics + + + align:start position:0% +of robotics but I talk about biomimetics +I also do or what you might call + + align:start position:0% +I also do or what you might call + + + align:start position:0% +I also do or what you might call +cognitive robotics and I collaborate + + align:start position:0% +cognitive robotics and I collaborate + + + align:start position:0% +cognitive robotics and I collaborate +with Georgia matter on that but since + + align:start position:0% +with Georgia matter on that but since + + + align:start position:0% +with Georgia matter on that but since +he's speaking to I'm going to focus on + + align:start position:0% +he's speaking to I'm going to focus on + + + align:start position:0% +he's speaking to I'm going to focus on +the more animal-like robots that we've + + align:start position:0% +the more animal-like robots that we've + + + align:start position:0% +the more animal-like robots that we've +been developing so this is one of our + + align:start position:0% +been developing so this is one of our + + + align:start position:0% +been developing so this is one of our +latest projects this is a small + + align:start position:0% +latest projects this is a small + + + align:start position:0% +latest projects this is a small +autonomous mobile robot which is a + + align:start position:0% +autonomous mobile robot which is a + + + align:start position:0% +autonomous mobile robot which is a +commercial platform which will be + + align:start position:0% +commercial platform which will be + + + align:start position:0% +commercial platform which will be +available in the UK I think next January + + align:start position:0% +available in the UK I think next January + + + align:start position:0% +available in the UK I think next January +and there will hopefully be a Developer + + align:start position:0% +and there will hopefully be a Developer + + + align:start position:0% +and there will hopefully be a Developer +Program for people that are interested + + align:start position:0% +Program for people that are interested + + + align:start position:0% +Program for people that are interested +in helping to develop the intelligence + + align:start position:0% +in helping to develop the intelligence + + + align:start position:0% +in helping to develop the intelligence +for this robot so this is at a + + align:start position:0% +for this robot so this is at a + + + align:start position:0% +for this robot so this is at a +conference we had in Barcelona last + + align:start position:0% +conference we had in Barcelona last + + + align:start position:0% +conference we had in Barcelona last +month and you can see that it's a robot + + align:start position:0% +month and you can see that it's a robot + + + align:start position:0% +month and you can see that it's a robot +pet and we've been focusing on giving it + + align:start position:0% +pet and we've been focusing on giving it + + + align:start position:0% +pet and we've been focusing on giving it +some effective communication abilities + + align:start position:0% +some effective communication abilities + + + align:start position:0% +some effective communication abilities +responding particularly to touch you can + + align:start position:0% +responding particularly to touch you can + + + align:start position:0% +responding particularly to touch you can +see that it's orienting to similarly it + + align:start position:0% +see that it's orienting to similarly it + + + align:start position:0% +see that it's orienting to similarly it +has stereo vision it has stereo sound + + align:start position:0% +has stereo vision it has stereo sound + + + align:start position:0% +has stereo vision it has stereo sound +and it can orient to visual stimuli and + + align:start position:0% +and it can orient to visual stimuli and + + + align:start position:0% +and it can orient to visual stimuli and +also to auditory stimuli here we're + + align:start position:0% +also to auditory stimuli here we're + + + align:start position:0% +also to auditory stimuli here we're +showing it a picture of itself on this + + align:start position:0% +showing it a picture of itself on this + + + align:start position:0% +showing it a picture of itself on this +magazine cover and the goal is to + + align:start position:0% +magazine cover and the goal is to + + + align:start position:0% +magazine cover and the goal is to +demonstrate that we can in a commercial + + align:start position:0% +demonstrate that we can in a commercial + + + align:start position:0% +demonstrate that we can in a commercial +robot that will cost less than a + + align:start position:0% +robot that will cost less than a + + + align:start position:0% +robot that will cost less than a +thousand dollars considerably less some + + align:start position:0% +thousand dollars considerably less some + + + align:start position:0% +thousand dollars considerably less some +of the principles of how the brain + + align:start position:0% +of the principles of how the brain + + + align:start position:0% +of the principles of how the brain +generates behavior so this robot that's + + align:start position:0% +generates behavior so this robot that's + + + align:start position:0% +generates behavior so this robot that's +called Miro is + + align:start position:0% +called Miro is + + + align:start position:0% +called Miro is +based on some high-level principles + + align:start position:0% +based on some high-level principles + + + align:start position:0% +based on some high-level principles +abstracted from what we know about how + + align:start position:0% +abstracted from what we know about how + + + align:start position:0% +abstracted from what we know about how +Amalia means controlled behavior so it's + + align:start position:0% +Amalia means controlled behavior so it's + + + align:start position:0% +Amalia means controlled behavior so it's +a relatively complex robot 13 degrees of + + align:start position:0% +a relatively complex robot 13 degrees of + + + align:start position:0% +a relatively complex robot 13 degrees of +freedom 3 ARM processors corresponding + + align:start position:0% +freedom 3 ARM processors corresponding + + + align:start position:0% +freedom 3 ARM processors corresponding +to different levels if you like of the + + align:start position:0% +to different levels if you like of the + + + align:start position:0% +to different levels if you like of the +neuraxis the central nervous system so + + align:start position:0% +neuraxis the central nervous system so + + + align:start position:0% +neuraxis the central nervous system so +once you sort of start out with some + + align:start position:0% +once you sort of start out with some + + + align:start position:0% +once you sort of start out with some +general ideas and questions and issues + + align:start position:0% +general ideas and questions and issues + + + align:start position:0% +general ideas and questions and issues +about how we might learn from the + + align:start position:0% +about how we might learn from the + + + align:start position:0% +about how we might learn from the +biology in the brain how to develop + + align:start position:0% +biology in the brain how to develop + + + align:start position:0% +biology in the brain how to develop +robots and how we might use robots to + + align:start position:0% +robots and how we might use robots to + + + align:start position:0% +robots and how we might use robots to +help us understand the brain and a + + align:start position:0% +help us understand the brain and a + + + align:start position:0% +help us understand the brain and a +central question I think that robotics + + align:start position:0% +central question I think that robotics + + + align:start position:0% +central question I think that robotics +can help us answer and I think that's a + + align:start position:0% +can help us answer and I think that's a + + + align:start position:0% +can help us answer and I think that's a +core question in neuroscience is what + + align:start position:0% +core question in neuroscience is what + + + align:start position:0% +core question in neuroscience is what +you might call the problem of behavioral + + align:start position:0% +you might call the problem of behavioral + + + align:start position:0% +you might call the problem of behavioral +integration and the neuroscientist + + align:start position:0% +integration and the neuroscientist + + + align:start position:0% +integration and the neuroscientist +Ernest barrington summarized this quite + + align:start position:0% +Ernest barrington summarized this quite + + + align:start position:0% +Ernest barrington summarized this quite +nicely + + align:start position:0% +nicely + + + align:start position:0% +nicely +he said the phenomenon so characteristic + + align:start position:0% +he said the phenomenon so characteristic + + + align:start position:0% +he said the phenomenon so characteristic +of living organisms so very difficult to + + align:start position:0% +of living organisms so very difficult to + + + align:start position:0% +of living organisms so very difficult to +analyze the fact that they behave as + + align:start position:0% +analyze the fact that they behave as + + + align:start position:0% +analyze the fact that they behave as +holes rather than as the sum of their + + align:start position:0% +holes rather than as the sum of their + + + align:start position:0% +holes rather than as the sum of their +constituent parts their behavior shows + + align:start position:0% +constituent parts their behavior shows + + + align:start position:0% +constituent parts their behavior shows +integration a process unifying the + + align:start position:0% +integration a process unifying the + + + align:start position:0% +integration a process unifying the +actions of an organism into patterns + + align:start position:0% +actions of an organism into patterns + + + align:start position:0% +actions of an organism into patterns +that involve the whole individual and + + align:start position:0% +that involve the whole individual and + + + align:start position:0% +that involve the whole individual and +this picture of a squirrel over here I + + align:start position:0% +this picture of a squirrel over here I + + + align:start position:0% +this picture of a squirrel over here I +think nicely demonstrates this so of + + align:start position:0% +think nicely demonstrates this so of + + + align:start position:0% +think nicely demonstrates this so of +course this the squirrel is leaping from + + align:start position:0% +course this the squirrel is leaping from + + + align:start position:0% +course this the squirrel is leaping from +one batch to the next and you can see + + align:start position:0% +one batch to the next and you can see + + + align:start position:0% +one batch to the next and you can see +that every part of his body is + + align:start position:0% +that every part of his body is + + + align:start position:0% +that every part of his body is +coordinated and organized for this + + align:start position:0% +coordinated and organized for this + + + align:start position:0% +coordinated and organized for this +action so you can see that his eyes + + align:start position:0% +action so you can see that his eyes + + + align:start position:0% +action so you can see that his eyes +looking straight ahead is his whiskers + + align:start position:0% +looking straight ahead is his whiskers + + + align:start position:0% +looking straight ahead is his whiskers +and I'll talk a lot more about whiskers + + align:start position:0% +and I'll talk a lot more about whiskers + + + align:start position:0% +and I'll talk a lot more about whiskers +are pointing forward his his arms and + + align:start position:0% +are pointing forward his his arms and + + + align:start position:0% +are pointing forward his his arms and +his feet are already and that they're + + align:start position:0% +his feet are already and that they're + + + align:start position:0% +his feet are already and that they're +ready to catch his fall even his tail is + + align:start position:0% +ready to catch his fall even his tail is + + + align:start position:0% +ready to catch his fall even his tail is +is angled and positioned to help him fly + + align:start position:0% +is angled and positioned to help him fly + + + align:start position:0% +is angled and positioned to help him fly +through the air so it's the coordination + + align:start position:0% +through the air so it's the coordination + + + align:start position:0% +through the air so it's the coordination +of the different parts of the body in + + align:start position:0% +of the different parts of the body in + + + align:start position:0% +of the different parts of the body in +the multiple degrees of freedom of the + + align:start position:0% +the multiple degrees of freedom of the + + + align:start position:0% +the multiple degrees of freedom of the +body and the sensory systems in space + + align:start position:0% +body and the sensory systems in space + + + align:start position:0% +body and the sensory systems in space +and in time which i think is a critical + + align:start position:0% +and in time which i think is a critical + + + align:start position:0% +and in time which i think is a critical +problem for biological control and also + + align:start position:0% +problem for biological control and also + + + align:start position:0% +problem for biological control and also +a problem for robots which were still + + align:start position:0% +a problem for robots which were still + + + align:start position:0% +a problem for robots which were still +struggling to address with our robots + + align:start position:0% +struggling to address with our robots + + + align:start position:0% +struggling to address with our robots +and I want to give you two very general + + align:start position:0% +and I want to give you two very general + + + align:start position:0% +and I want to give you two very general +principles for thinking about how brains + + align:start position:0% +principles for thinking about how brains + + + align:start position:0% +principles for thinking about how brains +solve this problem so many of you will + + align:start position:0% +solve this problem so many of you will + + + align:start position:0% +solve this problem so many of you will +have come across Rodney Brooks + + align:start position:0% +have come across Rodney Brooks + + + align:start position:0% +have come across Rodney Brooks +yes from MIT and he's famous for in + + align:start position:0% +yes from MIT and he's famous for in + + + align:start position:0% +yes from MIT and he's famous for in +robotics a notion of LED control which + + align:start position:0% +robotics a notion of LED control which + + + align:start position:0% +robotics a notion of LED control which +he called subsumption and I think the + + align:start position:0% +he called subsumption and I think the + + + align:start position:0% +he called subsumption and I think the +ideas that he brought into robotics + + align:start position:0% +ideas that he brought into robotics + + + align:start position:0% +ideas that he brought into robotics +really changed how people thought about + + align:start position:0% +really changed how people thought about + + + align:start position:0% +really changed how people thought about +robots in the 1980s but if we go back to + + align:start position:0% +robots in the 1980s but if we go back to + + + align:start position:0% +robots in the 1980s but if we go back to +the 1880s John Herlings Jackson who was + + align:start position:0% +the 1880s John Herlings Jackson who was + + + align:start position:0% +the 1880s John Herlings Jackson who was +British neurologist proposed a similar + + align:start position:0% +British neurologist proposed a similar + + + align:start position:0% +British neurologist proposed a similar +idea but with respect to the nervous + + align:start position:0% +idea but with respect to the nervous + + + align:start position:0% +idea but with respect to the nervous +system so in the 1880s people thought + + align:start position:0% +system so in the 1880s people thought + + + align:start position:0% +system so in the 1880s people thought +about the higher areas of the brain + + align:start position:0% +about the higher areas of the brain + + + align:start position:0% +about the higher areas of the brain +particularly the the cortex as being + + align:start position:0% +particularly the the cortex as being + + + align:start position:0% +particularly the the cortex as being +about higher thought and reasoning and + + align:start position:0% +about higher thought and reasoning and + + + align:start position:0% +about higher thought and reasoning and +language and not so much about + + align:start position:0% +language and not so much about + + + align:start position:0% +language and not so much about +perception and action and healings + + align:start position:0% +perception and action and healings + + + align:start position:0% +perception and action and healings +Jackson I think was revolutionary in his + + align:start position:0% +Jackson I think was revolutionary in his + + + align:start position:0% +Jackson I think was revolutionary in his +day in saying that the highest motor + + align:start position:0% +day in saying that the highest motor + + + align:start position:0% +day in saying that the highest motor +senses represent over again in more + + align:start position:0% +senses represent over again in more + + + align:start position:0% +senses represent over again in more +complex combinations what the middle + + align:start position:0% +complex combinations what the middle + + + align:start position:0% +complex combinations what the middle +motor centers represent in other words + + align:start position:0% +motor centers represent in other words + + + align:start position:0% +motor centers represent in other words +he was saying that the whole of the + + align:start position:0% +he was saying that the whole of the + + + align:start position:0% +he was saying that the whole of the +brain all the way up is about + + align:start position:0% +brain all the way up is about + + + align:start position:0% +brain all the way up is about +coordinating perception with action and + + align:start position:0% +coordinating perception with action and + + + align:start position:0% +coordinating perception with action and +he described it in many senses as a + + align:start position:0% +he described it in many senses as a + + + align:start position:0% +he described it in many senses as a +layered system he talked about how you + + align:start position:0% +layered system he talked about how you + + + align:start position:0% +layered system he talked about how you +could take off the top layers of the + + align:start position:0% +could take off the top layers of the + + + align:start position:0% +could take off the top layers of the +system and the competences of the lower + + align:start position:0% +system and the competences of the lower + + + align:start position:0% +system and the competences of the lower +layers remained intact which of course + + align:start position:0% +layers remained intact which of course + + + align:start position:0% +layers remained intact which of course +is very much the idea of rodney brooks + + align:start position:0% +is very much the idea of rodney brooks + + + align:start position:0% +is very much the idea of rodney brooks +subsumption architecture and some old + + align:start position:0% +subsumption architecture and some old + + + align:start position:0% +subsumption architecture and some old +studies the transaction in animals like + + align:start position:0% +studies the transaction in animals like + + + align:start position:0% +studies the transaction in animals like +cats and rats demonstrate this nicely so + + align:start position:0% +cats and rats demonstrate this nicely so + + + align:start position:0% +cats and rats demonstrate this nicely so +if you take a cat or a rat particularly + + align:start position:0% +if you take a cat or a rat particularly + + + align:start position:0% +if you take a cat or a rat particularly +a rat and you remove in fact all of the + + align:start position:0% +a rat and you remove in fact all of the + + + align:start position:0% +a rat and you remove in fact all of the +cerebral cortex so if you make a slice + + align:start position:0% +cerebral cortex so if you make a slice + + + align:start position:0% +cerebral cortex so if you make a slice +here that takes away cortex you get an + + align:start position:0% +here that takes away cortex you get an + + + align:start position:0% +here that takes away cortex you get an +animal that actually to all appearances + + align:start position:0% +animal that actually to all appearances + + + align:start position:0% +animal that actually to all appearances +looks fairly normal it does motivated + + align:start position:0% +looks fairly normal it does motivated + + + align:start position:0% +looks fairly normal it does motivated +behavioral sequences so it will get + + align:start position:0% +behavioral sequences so it will get + + + align:start position:0% +behavioral sequences so it will get +hungry and it will look for food and it + + align:start position:0% +hungry and it will look for food and it + + + align:start position:0% +hungry and it will look for food and it +will eat if there's an appropriate mate + + align:start position:0% +will eat if there's an appropriate mate + + + align:start position:0% +will eat if there's an appropriate mate +nearby it will look to have a sexual + + align:start position:0% +nearby it will look to have a sexual + + + align:start position:0% +nearby it will look to have a sexual +relationship and it it will fail in some + + align:start position:0% +relationship and it it will fail in some + + + align:start position:0% +relationship and it it will fail in some +challenges such as learning and perhaps + + align:start position:0% +challenges such as learning and perhaps + + + align:start position:0% +challenges such as learning and perhaps +also in dexterous construct control but + + align:start position:0% +also in dexterous construct control but + + + align:start position:0% +also in dexterous construct control but +in many ways that will look normal if + + align:start position:0% +in many ways that will look normal if + + + align:start position:0% +in many ways that will look normal if +you slice below the other part of the + + align:start position:0% +you slice below the other part of the + + + align:start position:0% +you slice below the other part of the +forebrain that the the pharmacist and + + align:start position:0% +forebrain that the the pharmacist and + + + align:start position:0% +forebrain that the the pharmacist and +the hypothalamus you remove these areas + + align:start position:0% +the hypothalamus you remove these areas + + + align:start position:0% +the hypothalamus you remove these areas +then you remove this capacity for + + align:start position:0% +then you remove this capacity for + + + align:start position:0% +then you remove this capacity for +motivated behavior but you leave intact + + align:start position:0% +motivated behavior but you leave intact + + + align:start position:0% +motivated behavior but you leave intact +midbrain systems + + align:start position:0% +midbrain systems + + + align:start position:0% +midbrain systems +that can still generate individual + + align:start position:0% +that can still generate individual + + + align:start position:0% +that can still generate individual +actions and if you remove parts of the + + align:start position:0% +actions and if you remove parts of the + + + align:start position:0% +actions and if you remove parts of the +midbrain you leave intact still + + align:start position:0% +midbrain you leave intact still + + + align:start position:0% +midbrain you leave intact still +component movements so for example + + align:start position:0% +component movements so for example + + + align:start position:0% +component movements so for example +animals that can run on a treadmill so + + align:start position:0% +animals that can run on a treadmill so + + + align:start position:0% +animals that can run on a treadmill so +we are with our mirror robot loosely + + align:start position:0% +we are with our mirror robot loosely + + + align:start position:0% +we are with our mirror robot loosely +recapitulating this architecture so we + + align:start position:0% +recapitulating this architecture so we + + + align:start position:0% +recapitulating this architecture so we +have three processes and the idea with + + align:start position:0% +have three processes and the idea with + + + align:start position:0% +have three processes and the idea with +this robots actually a part work so you + + align:start position:0% +this robots actually a part work so you + + + align:start position:0% +this robots actually a part work so you +build it up you get a magazine every + + align:start position:0% +build it up you get a magazine every + + + align:start position:0% +build it up you get a magazine every +week with a new part for the robot and + + align:start position:0% +week with a new part for the robot and + + + align:start position:0% +week with a new part for the robot and +you build essentially a spinal robot + + align:start position:0% +you build essentially a spinal robot + + + align:start position:0% +you build essentially a spinal robot +first and then you add a midbrain + + align:start position:0% +first and then you add a midbrain + + + align:start position:0% +first and then you add a midbrain +processor eventually you add a cortical + + align:start position:0% +processor eventually you add a cortical + + + align:start position:0% +processor eventually you add a cortical +processor which gives with it some + + align:start position:0% +processor which gives with it some + + + align:start position:0% +processor which gives with it some +learning capacities some pattern + + align:start position:0% +learning capacities some pattern + + + align:start position:0% +learning capacities some pattern +recognition some navigation so that's + + align:start position:0% +recognition some navigation so that's + + + align:start position:0% +recognition some navigation so that's +one principle layered architecture which + + align:start position:0% +one principle layered architecture which + + + align:start position:0% +one principle layered architecture which +seems to work both for biology and + + align:start position:0% +seems to work both for biology and + + + align:start position:0% +seems to work both for biology and +perhaps in robotics so second principle + + align:start position:0% +perhaps in robotics so second principle + + + align:start position:0% +perhaps in robotics so second principle +and this goes back to another famous + + align:start position:0% +and this goes back to another famous + + + align:start position:0% +and this goes back to another famous +neuroscientist this time will depend + + align:start position:0% +neuroscientist this time will depend + + + align:start position:0% +neuroscientist this time will depend +field who has known too many people for + + align:start position:0% +field who has known too many people for + + + align:start position:0% +field who has known too many people for +his discovery of somatic topic maps in + + align:start position:0% +his discovery of somatic topic maps in + + + align:start position:0% +his discovery of somatic topic maps in +the brain that if you stimulate in the + + align:start position:0% +the brain that if you stimulate in the + + + align:start position:0% +the brain that if you stimulate in the +brain in the area the sensory area then + + align:start position:0% +brain in the area the sensory area then + + + align:start position:0% +brain in the area the sensory area then +you find that people have experience of + + align:start position:0% +you find that people have experience of + + + align:start position:0% +you find that people have experience of +tickling on parts of the body and + + align:start position:0% +tickling on parts of the body and + + + align:start position:0% +tickling on parts of the body and +adjacent parts of cortex correspond to + + align:start position:0% +adjacent parts of cortex correspond to + + + align:start position:0% +adjacent parts of cortex correspond to +adjacent parts of the body and he found + + align:start position:0% +adjacent parts of the body and he found + + + align:start position:0% +adjacent parts of the body and he found +a similar homunculus in the motor area + + align:start position:0% +a similar homunculus in the motor area + + + align:start position:0% +a similar homunculus in the motor area +that you stimulate and you get movement + + align:start position:0% +that you stimulate and you get movement + + + align:start position:0% +that you stimulate and you get movement +in adjacent parts of the body and he + + align:start position:0% +in adjacent parts of the body and he + + + align:start position:0% +in adjacent parts of the body and he +also proposed another idea and that was + + align:start position:0% +also proposed another idea and that was + + + align:start position:0% +also proposed another idea and that was +a sort of a central transcendence + + align:start position:0% +a sort of a central transcendence + + + align:start position:0% +a sort of a central transcendence +cephalic dimension to know a system + + align:start position:0% +cephalic dimension to know a system + + + align:start position:0% +cephalic dimension to know a system +organization and last to say that down + + align:start position:0% +organization and last to say that down + + + align:start position:0% +organization and last to say that down +the midline of the central nervous + + align:start position:0% +the midline of the central nervous + + + align:start position:0% +the midline of the central nervous +system there are a group of structures + + align:start position:0% +system there are a group of structures + + + align:start position:0% +system there are a group of structures +that don't seem to be specifically + + align:start position:0% +that don't seem to be specifically + + + align:start position:0% +that don't seem to be specifically +involved in specific aspects of + + align:start position:0% +involved in specific aspects of + + + align:start position:0% +involved in specific aspects of +perception and action but seem to be + + align:start position:0% +perception and action but seem to be + + + align:start position:0% +perception and action but seem to be +about integration and amongst them + + align:start position:0% +about integration and amongst them + + + align:start position:0% +about integration and amongst them +particularly the basal ganglia he noted + + align:start position:0% +particularly the basal ganglia he noted + + + align:start position:0% +particularly the basal ganglia he noted +as being important and parts of the + + align:start position:0% +as being important and parts of the + + + align:start position:0% +as being important and parts of the +reticular formation + + align:start position:0% +reticular formation + + + align:start position:0% +reticular formation +so Michael Frank was here talking to you + + align:start position:0% +so Michael Frank was here talking to you + + + align:start position:0% +so Michael Frank was here talking to you +about basal ganglia so I'm not going to + + align:start position:0% +about basal ganglia so I'm not going to + + + align:start position:0% +about basal ganglia so I'm not going to +say much more about this but this is + + align:start position:0% +say much more about this but this is + + + align:start position:0% +say much more about this but this is +just to point out in in a slice in the + + align:start position:0% +just to point out in in a slice in the + + + align:start position:0% +just to point out in in a slice in the +rat brain these are the elements of the + + align:start position:0% +rat brain these are the elements of the + + + align:start position:0% +rat brain these are the elements of the +basal ganglia particularly the striatum + + align:start position:0% +basal ganglia particularly the striatum + + + align:start position:0% +basal ganglia particularly the striatum +is the input system in the rat + + align:start position:0% +is the input system in the rat + + + align:start position:0% +is the input system in the rat +substantial Niagra and part of the + + align:start position:0% +substantial Niagra and part of the + + + align:start position:0% +substantial Niagra and part of the +globus pallidus at the output systems + + align:start position:0% +globus pallidus at the output systems + + + align:start position:0% +globus pallidus at the output systems +and then you have in the rat brain and + + align:start position:0% +and then you have in the rat brain and + + + align:start position:0% +and then you have in the rat brain and +also in in our brains you have massive + + align:start position:0% +also in in our brains you have massive + + + align:start position:0% +also in in our brains you have massive +convergence onto the input area the + + align:start position:0% +convergence onto the input area the + + + align:start position:0% +convergence onto the input area the +codec but a minute is also called from + + align:start position:0% +codec but a minute is also called from + + + align:start position:0% +codec but a minute is also called from +the cortex and from the brainstem so you + + align:start position:0% +the cortex and from the brainstem so you + + + align:start position:0% +the cortex and from the brainstem so you +have signals coming in from all over the + + align:start position:0% +have signals coming in from all over the + + + align:start position:0% +have signals coming in from all over the +brain to the striatum which could be + + align:start position:0% +brain to the striatum which could be + + + align:start position:0% +brain to the striatum which could be +interpreted as a request for action and + + align:start position:0% +interpreted as a request for action and + + + align:start position:0% +interpreted as a request for action and +then you have inhibition coming out from + + align:start position:0% +then you have inhibition coming out from + + + align:start position:0% +then you have inhibition coming out from +the output structures of the basal + + align:start position:0% +the output structures of the basal + + + align:start position:0% +the output structures of the basal +ganglia here I'm showing it for the + + align:start position:0% +ganglia here I'm showing it for the + + + align:start position:0% +ganglia here I'm showing it for the +substantia going back to all of + + align:start position:0% +substantia going back to all of + + + align:start position:0% +substantia going back to all of +those areas of the brain and this + + align:start position:0% +those areas of the brain and this + + + align:start position:0% +those areas of the brain and this +inhibition is tonic and in order to have + + align:start position:0% +inhibition is tonic and in order to have + + + align:start position:0% +inhibition is tonic and in order to have +voluntary action you have to remove the + + align:start position:0% +voluntary action you have to remove the + + + align:start position:0% +voluntary action you have to remove the +inhibition so this is a system that can + + align:start position:0% +inhibition so this is a system that can + + + align:start position:0% +inhibition so this is a system that can +give you some of that behavior + + align:start position:0% +give you some of that behavior + + + align:start position:0% +give you some of that behavior +integration that you need the ability to + + align:start position:0% +integration that you need the ability to + + + align:start position:0% +integration that you need the ability to +ensure that you do one thing at a time + + align:start position:0% +ensure that you do one thing at a time + + + align:start position:0% +ensure that you do one thing at a time +you do that quickly you do that + + align:start position:0% +you do that quickly you do that + + + align:start position:0% +you do that quickly you do that +consistently you dedicate all of your + + align:start position:0% +consistently you dedicate all of your + + + align:start position:0% +consistently you dedicate all of your +resources to the action that you want to + + align:start position:0% +resources to the action that you want to + + + align:start position:0% +resources to the action that you want to +do here's a little video of a rat and + + align:start position:0% +do here's a little video of a rat and + + + align:start position:0% +do here's a little video of a rat and +I'm showing you some integrated behavior + + align:start position:0% +I'm showing you some integrated behavior + + + align:start position:0% +I'm showing you some integrated behavior +over time in an intact rat so this is a + + align:start position:0% +over time in an intact rat so this is a + + + align:start position:0% +over time in an intact rat so this is a +rat exploring in a large container and + + align:start position:0% +rat exploring in a large container and + + + align:start position:0% +rat exploring in a large container and +rats generally don't like open spaces so + + align:start position:0% +rats generally don't like open spaces so + + + align:start position:0% +rats generally don't like open spaces so +when you first put the animal into this + + align:start position:0% +when you first put the animal into this + + + align:start position:0% +when you first put the animal into this +space it will trend to stay near the + + align:start position:0% +space it will trend to stay near the + + + align:start position:0% +space it will trend to stay near the +walls and it prefers this corner which + + align:start position:0% +walls and it prefers this corner which + + + align:start position:0% +walls and it prefers this corner which +is dark and of course it's hungry too so + + align:start position:0% +is dark and of course it's hungry too so + + + align:start position:0% +is dark and of course it's hungry too so +there's a dish of food here and + + align:start position:0% +there's a dish of food here and + + + align:start position:0% +there's a dish of food here and +eventually it gets up the courage to go + + align:start position:0% +eventually it gets up the courage to go + + + align:start position:0% +eventually it gets up the courage to go +out collect a piece of food and it will + + align:start position:0% +out collect a piece of food and it will + + + align:start position:0% +out collect a piece of food and it will +take it back into this dark corner to + + align:start position:0% +take it back into this dark corner to + + + align:start position:0% +take it back into this dark corner to +consume it and one of the first models + + align:start position:0% +consume it and one of the first models + + + align:start position:0% +consume it and one of the first models +that we built was a model of basal + + align:start position:0% +that we built was a model of basal + + + align:start position:0% +that we built was a model of basal +ganglia operating is this kind of action + + align:start position:0% +ganglia operating is this kind of action + + + align:start position:0% +ganglia operating is this kind of action +selection device and with a simple cap + + align:start position:0% +selection device and with a simple cap + + + align:start position:0% +selection device and with a simple cap +or a robot this is a robot that just + + align:start position:0% +or a robot this is a robot that just + + + align:start position:0% +or a robot this is a robot that just +really uses infrared sensors and a + + align:start position:0% +really uses infrared sensors and a + + + align:start position:0% +really uses infrared sensors and a +gripper arm and we are using a model of + + align:start position:0% +gripper arm and we are using a model of + + + align:start position:0% +gripper arm and we are using a model of +the basal ganglia to control + + align:start position:0% +the basal ganglia to control + + + align:start position:0% +the basal ganglia to control +decision-making about which actions to + + align:start position:0% +decision-making about which actions to + + + align:start position:0% +decision-making about which actions to +do at which time and to generate + + align:start position:0% +do at which time and to generate + + + align:start position:0% +do at which time and to generate +sequences sequencing of those actions so + + align:start position:0% +sequences sequencing of those actions so + + + align:start position:0% +sequences sequencing of those actions so +as then the needs dear stay close to + + align:start position:0% +as then the needs dear stay close to + + + align:start position:0% +as then the needs dear stay close to +walls diminishes the robot like the rat + + align:start position:0% +walls diminishes the robot like the rat + + + align:start position:0% +walls diminishes the robot like the rat +goes and collects these cylinders and it + + align:start position:0% +goes and collects these cylinders and it + + + align:start position:0% +goes and collects these cylinders and it +carries them back into the corners and + + align:start position:0% +carries them back into the corners and + + + align:start position:0% +carries them back into the corners and +deposits them so a model of these + + align:start position:0% +deposits them so a model of these + + + align:start position:0% +deposits them so a model of these +central brain structures and + + align:start position:0% +central brain structures and + + + align:start position:0% +central brain structures and +I'm happy to discuss in more detail + + align:start position:0% +I'm happy to discuss in more detail + + + align:start position:0% +I'm happy to discuss in more detail +about how that model operates it has + + align:start position:0% +about how that model operates it has + + + align:start position:0% +about how that model operates it has +similarities to the model that Michael + + align:start position:0% +similarities to the model that Michael + + + align:start position:0% +similarities to the model that Michael +will describe to you but that's + + align:start position:0% +will describe to you but that's + + + align:start position:0% +will describe to you but that's +controlling the behavior switching if + + align:start position:0% +controlling the behavior switching if + + + align:start position:0% +controlling the behavior switching if +you like in this robot so I spent some + + align:start position:0% +you like in this robot so I spent some + + + align:start position:0% +you like in this robot so I spent some +time working on this this question of + + align:start position:0% +time working on this this question of + + + align:start position:0% +time working on this this question of +how central systems in the brain + + align:start position:0% +how central systems in the brain + + + align:start position:0% +how central systems in the brain +particularly the basal ganglia are + + align:start position:0% +particularly the basal ganglia are + + + align:start position:0% +particularly the basal ganglia are +involved in the integration of behavior + + align:start position:0% +involved in the integration of behavior + + + align:start position:0% +involved in the integration of behavior +but I became frustrated with not + + align:start position:0% +but I became frustrated with not + + + align:start position:0% +but I became frustrated with not +understanding what were the signals + + align:start position:0% +understanding what were the signals + + + align:start position:0% +understanding what were the signals +coming in to the central brain + + align:start position:0% +coming in to the central brain + + + align:start position:0% +coming in to the central brain +structures and not understanding what + + align:start position:0% +structures and not understanding what + + + align:start position:0% +structures and not understanding what +effects those brain structures were + + align:start position:0% +effects those brain structures were + + + align:start position:0% +effects those brain structures were +having on the the motor system of the + + align:start position:0% +having on the the motor system of the + + + align:start position:0% +having on the the motor system of the +animal so I thought that what we needed + + align:start position:0% +animal so I thought that what we needed + + + align:start position:0% +animal so I thought that what we needed +to do was look at complete sensory motor + + align:start position:0% +to do was look at complete sensory motor + + + align:start position:0% +to do was look at complete sensory motor +loops who look needed to look at sensing + + align:start position:0% +loops who look needed to look at sensing + + + align:start position:0% +loops who look needed to look at sensing +in action and how those interact and in + + align:start position:0% +in action and how those interact and in + + + align:start position:0% +in action and how those interact and in +our at psychology department we have a + + align:start position:0% +our at psychology department we have a + + + align:start position:0% +our at psychology department we have a +neuroscience group that works mainly + + align:start position:0% +neuroscience group that works mainly + + + align:start position:0% +neuroscience group that works mainly +with rats so it was natural for us to + + align:start position:0% +with rats so it was natural for us to + + + align:start position:0% +with rats so it was natural for us to +look at the rat and in the rat we know + + align:start position:0% +look at the rat and in the rat we know + + + align:start position:0% +look at the rat and in the rat we know +that one of the key perception systems + + align:start position:0% +that one of the key perception systems + + + align:start position:0% +that one of the key perception systems +is the verb bristle system so here you + + align:start position:0% +is the verb bristle system so here you + + + align:start position:0% +is the verb bristle system so here you +see this is actually a pet rat wandering + + align:start position:0% +see this is actually a pet rat wandering + + + align:start position:0% +see this is actually a pet rat wandering +around on my windowsill in my house in + + align:start position:0% +around on my windowsill in my house in + + + align:start position:0% +around on my windowsill in my house in +Sheffield and the thing to notice is the + + align:start position:0% +Sheffield and the thing to notice is the + + + align:start position:0% +Sheffield and the thing to notice is the +whiskers here and the whiskers are + + align:start position:0% +whiskers here and the whiskers are + + + align:start position:0% +whiskers here and the whiskers are +moving back and forth pretty much all + + align:start position:0% +moving back and forth pretty much all + + + align:start position:0% +moving back and forth pretty much all +the time that the rat is exploring and + + align:start position:0% + + + + align:start position:0% + +we understand from nearly a hundred + + align:start position:0% +we understand from nearly a hundred + + + align:start position:0% +we understand from nearly a hundred +years now of research that this system + + align:start position:0% +years now of research that this system + + + align:start position:0% +years now of research that this system +is very important for the rat to + + align:start position:0% +is very important for the rat to + + + align:start position:0% +is very important for the rat to +understand the environment in fact if + + align:start position:0% +understand the environment in fact if + + + align:start position:0% +understand the environment in fact if +it's completely dark the rat would move + + align:start position:0% +it's completely dark the rat would move + + + align:start position:0% +it's completely dark the rat would move +around in much the same way and it would + + align:start position:0% +around in much the same way and it would + + + align:start position:0% +around in much the same way and it would +be able to understand the world through + + align:start position:0% +be able to understand the world through + + + align:start position:0% +be able to understand the world through +touch pretty pretty well even in the + + align:start position:0% +touch pretty pretty well even in the + + + align:start position:0% +touch pretty pretty well even in the +absence of vision so this is the same + + align:start position:0% +absence of vision so this is the same + + + align:start position:0% +absence of vision so this is the same +video but now slowed down ten times and + + align:start position:0% +video but now slowed down ten times and + + + align:start position:0% +video but now slowed down ten times and +just to show you these movements of the + + align:start position:0% +just to show you these movements of the + + + align:start position:0% +just to show you these movements of the +whiskers and how quite precise they are + + align:start position:0% +whiskers and how quite precise they are + + + align:start position:0% +whiskers and how quite precise they are +because the rat isn't just in a + + align:start position:0% +because the rat isn't just in a + + + align:start position:0% +because the rat isn't just in a +stereotypical way banging its whiskers + + align:start position:0% +stereotypical way banging its whiskers + + + align:start position:0% +stereotypical way banging its whiskers +against the floor it is lightly touching + + align:start position:0% +against the floor it is lightly touching + + + align:start position:0% +against the floor it is lightly touching +the whiskers and places that will get + + align:start position:0% +the whiskers and places that will get + + + align:start position:0% +the whiskers and places that will get +useful information and you can see when + + align:start position:0% +useful information and you can see when + + + align:start position:0% +useful information and you can see when +he puts his own head over the windowsill + + align:start position:0% +he puts his own head over the windowsill + + + align:start position:0% +he puts his own head over the windowsill +here the whiskers push forward as if he + + align:start position:0% +here the whiskers push forward as if he + + + align:start position:0% +here the whiskers push forward as if he +knows that he's going to have to reach + + align:start position:0% +knows that he's going to have to reach + + + align:start position:0% +knows that he's going to have to reach +further forward if he's going to find + + align:start position:0% +further forward if he's going to find + + + align:start position:0% +further forward if he's going to find +anything here you see I'm exploring this + + align:start position:0% +anything here you see I'm exploring this + + + align:start position:0% +anything here you see I'm exploring this +wooden cup and you can see light touches + + align:start position:0% +wooden cup and you can see light touches + + + align:start position:0% +wooden cup and you can see light touches +by the whiskers + + align:start position:0% +by the whiskers + + + align:start position:0% +by the whiskers +and you can also see that the movement + + align:start position:0% +and you can also see that the movement + + + align:start position:0% +and you can also see that the movement +of the whiskers is being modulated by + + align:start position:0% +of the whiskers is being modulated by + + + align:start position:0% +of the whiskers is being modulated by +the shape of the surface that he's + + align:start position:0% +the shape of the surface that he's + + + align:start position:0% +the shape of the surface that he's +investigating so there's some fairly + + align:start position:0% +investigating so there's some fairly + + + align:start position:0% +investigating so there's some fairly +subtle control happening here and I + + align:start position:0% +subtle control happening here and I + + + align:start position:0% +subtle control happening here and I +think it's not too much to say that the + + align:start position:0% +think it's not too much to say that the + + + align:start position:0% +think it's not too much to say that the +way in which the rat controls its + + align:start position:0% +way in which the rat controls its + + + align:start position:0% +way in which the rat controls its +whiskers has almost the same richness as + + align:start position:0% +whiskers has almost the same richness as + + + align:start position:0% +whiskers has almost the same richness as +the way that we control our fingertips + + align:start position:0% +the way that we control our fingertips + + + align:start position:0% +the way that we control our fingertips +so I'm interested in how this plays out + + align:start position:0% +so I'm interested in how this plays out + + + align:start position:0% +so I'm interested in how this plays out +in terms of a layered architecture story + + align:start position:0% +in terms of a layered architecture story + + + align:start position:0% +in terms of a layered architecture story +and of course many people study this + + align:start position:0% +and of course many people study this + + + align:start position:0% +and of course many people study this +system the beauty of it is if you're a + + align:start position:0% +system the beauty of it is if you're a + + + align:start position:0% +system the beauty of it is if you're a +neuroscientist that you can look in the + + align:start position:0% +neuroscientist that you can look in the + + + align:start position:0% +neuroscientist that you can look in the +cortex this is this is rat cortex here + + align:start position:0% +cortex this is this is rat cortex here + + + align:start position:0% +cortex this is this is rat cortex here +and a huge area of rat cortex is + + align:start position:0% +and a huge area of rat cortex is + + + align:start position:0% +and a huge area of rat cortex is +dedicated to so at a sensation to touch + + align:start position:0% +dedicated to so at a sensation to touch + + + align:start position:0% +dedicated to so at a sensation to touch +of which a large area is dedicated to + + align:start position:0% +of which a large area is dedicated to + + + align:start position:0% +of which a large area is dedicated to +whiskers in fact you zoom in you can + + align:start position:0% +whiskers in fact you zoom in you can + + + align:start position:0% +whiskers in fact you zoom in you can +find this area called barrel cortex and + + align:start position:0% +find this area called barrel cortex and + + + align:start position:0% +find this area called barrel cortex and +with the right kind of staining you can + + align:start position:0% +with the right kind of staining you can + + + align:start position:0% +with the right kind of staining you can +find groups of cells which + + align:start position:0% +find groups of cells which + + + align:start position:0% +find groups of cells which +preferentially receive signals from + + align:start position:0% +preferentially receive signals from + + + align:start position:0% +preferentially receive signals from +individual whiskers so for example you + + align:start position:0% +individual whiskers so for example you + + + align:start position:0% +individual whiskers so for example you +can move one whisker here and you can + + align:start position:0% +can move one whisker here and you can + + + align:start position:0% +can move one whisker here and you can +know exactly where to record in the + + align:start position:0% +know exactly where to record in the + + + align:start position:0% +know exactly where to record in the +barrel cortex to get a very strong + + align:start position:0% +barrel cortex to get a very strong + + + align:start position:0% +barrel cortex to get a very strong +response from that whisker and this + + align:start position:0% +response from that whisker and this + + + align:start position:0% +response from that whisker and this +means that barrel cortex and the whisker + + align:start position:0% +means that barrel cortex and the whisker + + + align:start position:0% +means that barrel cortex and the whisker +system has become one of the prepared + + align:start position:0% +system has become one of the prepared + + + align:start position:0% +system has become one of the prepared +preferred preparations in which to study + + align:start position:0% +preferred preparations in which to study + + + align:start position:0% +preferred preparations in which to study +in a cortical microcircuitry altogether + + align:start position:0% +in a cortical microcircuitry altogether + + + align:start position:0% +in a cortical microcircuitry altogether +so people study this system to really + + align:start position:0% +so people study this system to really + + + align:start position:0% +so people study this system to really +understand how cortex operates now if we + + align:start position:0% +understand how cortex operates now if we + + + align:start position:0% +understand how cortex operates now if we +think about this system as a pathway + + align:start position:0% +think about this system as a pathway + + + align:start position:0% +think about this system as a pathway +from the whiskers up to Val cortex we're + + align:start position:0% +from the whiskers up to Val cortex we're + + + align:start position:0% +from the whiskers up to Val cortex we're +really only capturing one element of + + align:start position:0% +really only capturing one element of + + + align:start position:0% +really only capturing one element of +what's going on in the four bristle + + align:start position:0% +what's going on in the four bristle + + + align:start position:0% +what's going on in the four bristle +system and that's this pathway here from + + align:start position:0% +system and that's this pathway here from + + + align:start position:0% +system and that's this pathway here from +the verb reside via the trigeminal + + align:start position:0% +the verb reside via the trigeminal + + + align:start position:0% +the verb reside via the trigeminal +complex goes by the farmers up to + + align:start position:0% +complex goes by the farmers up to + + + align:start position:0% +complex goes by the farmers up to +sensory cortex and this is probably + + align:start position:0% +sensory cortex and this is probably + + + align:start position:0% +sensory cortex and this is probably +where 9 out of 10 papers on this system + + align:start position:0% +where 9 out of 10 papers on this system + + + align:start position:0% +where 9 out of 10 papers on this system +are published but actually this system + + align:start position:0% +are published but actually this system + + + align:start position:0% +are published but actually this system +is only part of a looped architecture or + + align:start position:0% +is only part of a looped architecture or + + + align:start position:0% +is only part of a looped architecture or +we might say a layered architecture and + + align:start position:0% +we might say a layered architecture and + + + align:start position:0% +we might say a layered architecture and +at each level of this layered + + align:start position:0% +at each level of this layered + + + align:start position:0% +at each level of this layered +architecture there's a completed loop so + + align:start position:0% +architecture there's a completed loop so + + + align:start position:0% +architecture there's a completed loop so +that sensing can affect action so + + align:start position:0% +that sensing can affect action so + + + align:start position:0% +that sensing can affect action so +sensing on the verb ris i can affect the + + align:start position:0% +sensing on the verb ris i can affect the + + + align:start position:0% +sensing on the verb ris i can affect the +movement and control of the verb ris i + + align:start position:0% +movement and control of the verb ris i + + + align:start position:0% +movement and control of the verb ris i +so there's a loop via the brainstem here + + align:start position:0% +so there's a loop via the brainstem here + + + align:start position:0% +so there's a loop via the brainstem here +so that directly from the tremolo + + align:start position:0% +so that directly from the tremolo + + + align:start position:0% +so that directly from the tremolo +complex signals come back to the + + align:start position:0% +complex signals come back to the + + + align:start position:0% +complex signals come back to the +a nucleus which is where the motor + + align:start position:0% +a nucleus which is where the motor + + + align:start position:0% +a nucleus which is where the motor +neurons are that move the whiskers + + align:start position:0% +neurons are that move the whiskers + + + align:start position:0% +neurons are that move the whiskers +there's a loop via the midbrain here so + + align:start position:0% +there's a loop via the midbrain here so + + + align:start position:0% +there's a loop via the midbrain here so +that sensory signals are sent very + + align:start position:0% +that sensory signals are sent very + + + align:start position:0% +that sensory signals are sent very +quickly to the midbrain superior + + align:start position:0% +quickly to the midbrain superior + + + align:start position:0% +quickly to the midbrain superior +colliculus and they come back to affect + + align:start position:0% +colliculus and they come back to affect + + + align:start position:0% +colliculus and they come back to affect +how the whiskers move and then of course + + align:start position:0% +how the whiskers move and then of course + + + align:start position:0% +how the whiskers move and then of course +there's the loop via the cortex too so + + align:start position:0% +there's the loop via the cortex too so + + + align:start position:0% +there's the loop via the cortex too so +there's essentially those three loops at + + align:start position:0% +there's essentially those three loops at + + + align:start position:0% +there's essentially those three loops at +least that we need to think about so + + align:start position:0% +least that we need to think about so + + + align:start position:0% +least that we need to think about so +since 2003 we've been building different + + align:start position:0% +since 2003 we've been building different + + + align:start position:0% +since 2003 we've been building different +whisker robots the aim being to + + align:start position:0% +whisker robots the aim being to + + + align:start position:0% +whisker robots the aim being to +instantiate our theories about how + + align:start position:0% +instantiate our theories about how + + + align:start position:0% +instantiate our theories about how +whiskered control works in this laird + + align:start position:0% +whiskered control works in this laird + + + align:start position:0% +whiskered control works in this laird +architecture and demonstrate it in a + + align:start position:0% +architecture and demonstrate it in a + + + align:start position:0% +architecture and demonstrate it in a +robot platform and often actually + + align:start position:0% +robot platform and often actually + + + align:start position:0% +robot platform and often actually +building a robot platform it causes us + + align:start position:0% +building a robot platform it causes us + + + align:start position:0% +building a robot platform it causes us +to ask new questions that might not be + + align:start position:0% +to ask new questions that might not be + + + align:start position:0% +to ask new questions that might not be +obvious to you just by doing biological + + align:start position:0% +obvious to you just by doing biological + + + align:start position:0% +obvious to you just by doing biological +experiments or even by doing simulation + + align:start position:0% +experiments or even by doing simulation + + + align:start position:0% +experiments or even by doing simulation +before I show you some robots just + + align:start position:0% +before I show you some robots just + + + align:start position:0% +before I show you some robots just +quickly show you a little bit more about + + align:start position:0% +quickly show you a little bit more about + + + align:start position:0% +quickly show you a little bit more about +the rat and its whiskers + + align:start position:0% +the rat and its whiskers + + + align:start position:0% +the rat and its whiskers +so we began thinking we could just build + + align:start position:0% +so we began thinking we could just build + + + align:start position:0% +so we began thinking we could just build +robots but we quickly realized that we + + align:start position:0% +robots but we quickly realized that we + + + align:start position:0% +robots but we quickly realized that we +didn't know enough about how rats used + + align:start position:0% +didn't know enough about how rats used + + + align:start position:0% +didn't know enough about how rats used +their whiskers to do that and that's + + align:start position:0% +their whiskers to do that and that's + + + align:start position:0% +their whiskers to do that and that's +partly because the experiments that had + + align:start position:0% +partly because the experiments that had + + + align:start position:0% +partly because the experiments that had +been done hadn't been done with the + + align:start position:0% +been done hadn't been done with the + + + align:start position:0% +been done hadn't been done with the +purpose of building a whiskered robot so + + align:start position:0% +purpose of building a whiskered robot so + + + align:start position:0% +purpose of building a whiskered robot so +when you try and build a whisker robot + + align:start position:0% +when you try and build a whisker robot + + + align:start position:0% +when you try and build a whisker robot +you have to ask questions like how do + + align:start position:0% +you have to ask questions like how do + + + align:start position:0% +you have to ask questions like how do +the whiskers move and when you look at a + + align:start position:0% +the whiskers move and when you look at a + + + align:start position:0% +the whiskers move and when you look at a +video like this film from above this is + + align:start position:0% +video like this film from above this is + + + align:start position:0% +video like this film from above this is +with a high-speed camera you think well + + align:start position:0% +with a high-speed camera you think well + + + align:start position:0% +with a high-speed camera you think well +the whiskers are sweeping + + align:start position:0% +the whiskers are sweeping + + + align:start position:0% +the whiskers are sweeping +backward and forward like this but in + + align:start position:0% +backward and forward like this but in + + + align:start position:0% +backward and forward like this but in +fact if you put a mirror just tilt it + + align:start position:0% +fact if you put a mirror just tilt it + + + align:start position:0% +fact if you put a mirror just tilt it +down here and you see what happens and + + align:start position:0% +down here and you see what happens and + + + align:start position:0% +down here and you see what happens and +it turns out to be a little bit + + align:start position:0% +it turns out to be a little bit + + + align:start position:0% +it turns out to be a little bit +different so you see that the whiskers + + align:start position:0% +different so you see that the whiskers + + + align:start position:0% +different so you see that the whiskers +are going up and down as much as they're + + align:start position:0% +are going up and down as much as they're + + + align:start position:0% +are going up and down as much as they're +going backwards and forwards so the + + align:start position:0% +going backwards and forwards so the + + + align:start position:0% +going backwards and forwards so the +whiskers are actually sweeping like this + + align:start position:0% +whiskers are actually sweeping like this + + + align:start position:0% +whiskers are actually sweeping like this +and they're making a series of touches + + align:start position:0% +and they're making a series of touches + + + align:start position:0% +and they're making a series of touches +on the surface and if you watch you can + + align:start position:0% +on the surface and if you watch you can + + + align:start position:0% +on the surface and if you watch you can +see that the whiskers are sort of + + align:start position:0% +see that the whiskers are sort of + + + align:start position:0% +see that the whiskers are sort of +playing down on the surface sort of in a + + align:start position:0% +playing down on the surface sort of in a + + + align:start position:0% +playing down on the surface sort of in a +sequence quite quickly so that + + align:start position:0% +sequence quite quickly so that + + + align:start position:0% +sequence quite quickly so that +information but it might be giving you + + align:start position:0% +information but it might be giving you + + + align:start position:0% +information but it might be giving you +details about the shape of the surfaces + + align:start position:0% +details about the shape of the surfaces + + + align:start position:0% +details about the shape of the surfaces +in your world + + align:start position:0% +in your world + + + align:start position:0% +in your world +so we mainly look at the long whiskers + + align:start position:0% +so we mainly look at the long whiskers + + + align:start position:0% +so we mainly look at the long whiskers +this is a rat that's running up an alley + + align:start position:0% +this is a rat that's running up an alley + + + align:start position:0% +this is a rat that's running up an alley +and we put an unexpected object in the + + align:start position:0% +and we put an unexpected object in the + + + align:start position:0% +and we put an unexpected object in the +alley which could be this aluminium + + align:start position:0% +alley which could be this aluminium + + + align:start position:0% +alley which could be this aluminium +rectangle or it could be this plastic + + align:start position:0% +rectangle or it could be this plastic + + + align:start position:0% +rectangle or it could be this plastic +step and what you see is if the + + align:start position:0% +step and what you see is if the + + + align:start position:0% +step and what you see is if the +encounters something unexpected with his + + align:start position:0% +encounters something unexpected with his + + + align:start position:0% +encounters something unexpected with his +long whiskers then it turns very quickly + + align:start position:0% +long whiskers then it turns very quickly + + + align:start position:0% +long whiskers then it turns very quickly +and investigates it so the long whiskers + + align:start position:0% +and investigates it so the long whiskers + + + align:start position:0% +and investigates it so the long whiskers +are like the periphery of a sensory + + align:start position:0% +are like the periphery of a sensory + + + align:start position:0% +are like the periphery of a sensory +system that has a phobia and the phobia + + align:start position:0% +system that has a phobia and the phobia + + + align:start position:0% +system that has a phobia and the phobia +at the center of that system is a set of + + align:start position:0% +at the center of that system is a set of + + + align:start position:0% +at the center of that system is a set of +short whiskers around the mouth also the + + align:start position:0% +short whiskers around the mouth also the + + + align:start position:0% +short whiskers around the mouth also the +lips and the nose so that you can sniff + + align:start position:0% +lips and the nose so that you can sniff + + + align:start position:0% +lips and the nose so that you can sniff +and smell the surface that you're + + align:start position:0% +and smell the surface that you're + + + align:start position:0% +and smell the surface that you're +investigating so we can zoom in and see + + align:start position:0% +investigating so we can zoom in and see + + + align:start position:0% +investigating so we can zoom in and see +that sensory fovea here you see these + + align:start position:0% +that sensory fovea here you see these + + + align:start position:0% +that sensory fovea here you see these +short whiskers that are being used to + + align:start position:0% +short whiskers that are being used to + + + align:start position:0% +short whiskers that are being used to +investigate this plastic pup puck and + + align:start position:0% +investigate this plastic pup puck and + + + align:start position:0% +investigate this plastic pup puck and +the longer whiskers investigating around + + align:start position:0% +the longer whiskers investigating around + + + align:start position:0% +the longer whiskers investigating around +the outside so we have recap + + align:start position:0% +the outside so we have recap + + + align:start position:0% +the outside so we have recap +recapitulated elements of this layered + + align:start position:0% +recapitulated elements of this layered + + + align:start position:0% +recapitulated elements of this layered +architecture in our robot and this is + + align:start position:0% +architecture in our robot and this is + + + align:start position:0% +architecture in our robot and this is +the these are the loops and this was + + align:start position:0% +the these are the loops and this was + + + align:start position:0% +the these are the loops and this was +about five years ago we'd built a system + + align:start position:0% +about five years ago we'd built a system + + + align:start position:0% +about five years ago we'd built a system +with a brainstem loop and really a + + align:start position:0% +with a brainstem loop and really a + + + align:start position:0% +with a brainstem loop and really a +midbrain loop and this is our a robot + + align:start position:0% +midbrain loop and this is our a robot + + + align:start position:0% +midbrain loop and this is our a robot +scratch bot which is the first of the + + align:start position:0% +scratch bot which is the first of the + + + align:start position:0% +scratch bot which is the first of the +whiskered robots that we felt really was + + align:start position:0% +whiskered robots that we felt really was + + + align:start position:0% +whiskered robots that we felt really was +capturing whisking and the way that the + + align:start position:0% +capturing whisking and the way that the + + + align:start position:0% +capturing whisking and the way that the +wrap does it it's running at about four + + align:start position:0% +wrap does it it's running at about four + + + align:start position:0% +wrap does it it's running at about four +Hertz whereas the real rat is whisking + + align:start position:0% +Hertz whereas the real rat is whisking + + + align:start position:0% +Hertz whereas the real rat is whisking +from eight to 12 Hertz but you know it's + + align:start position:0% +from eight to 12 Hertz but you know it's + + + align:start position:0% +from eight to 12 Hertz but you know it's +scaled up to be about four times rat + + align:start position:0% +scaled up to be about four times rat + + + align:start position:0% +scaled up to be about four times rat +size and what it's doing here is it's + + align:start position:0% +size and what it's doing here is it's + + + align:start position:0% +size and what it's doing here is it's +using the whiskers to orient to stimuli + + align:start position:0% +using the whiskers to orient to stimuli + + + align:start position:0% +using the whiskers to orient to stimuli +so this is Martin Pearson from Bristol + + align:start position:0% +so this is Martin Pearson from Bristol + + + align:start position:0% +so this is Martin Pearson from Bristol +robotics lab he's putting an object in + + align:start position:0% +robotics lab he's putting an object in + + + align:start position:0% +robotics lab he's putting an object in +the whisker field and the robot is + + align:start position:0% +the whisker field and the robot is + + + align:start position:0% +the whisker field and the robot is +turning and orienting to the touch with + + align:start position:0% +turning and orienting to the touch with + + + align:start position:0% +turning and orienting to the touch with +the object it's putting it short + + align:start position:0% +the object it's putting it short + + + align:start position:0% +the object it's putting it short +microbrew sight in fact against the + + align:start position:0% +microbrew sight in fact against the + + + align:start position:0% +microbrew sight in fact against the +object and exploring it now - to do that + + align:start position:0% +object and exploring it now - to do that + + + align:start position:0% +object and exploring it now - to do that +to detect a stimulus on the whiskers and + + align:start position:0% +to detect a stimulus on the whiskers and + + + align:start position:0% +to detect a stimulus on the whiskers and +then turn it's not a fantastically hard + + align:start position:0% +then turn it's not a fantastically hard + + + align:start position:0% +then turn it's not a fantastically hard +task the main challenge is to work out + + align:start position:0% +task the main challenge is to work out + + + align:start position:0% +task the main challenge is to work out +where the whisker was in its sweep when + + align:start position:0% +where the whisker was in its sweep when + + + align:start position:0% +where the whisker was in its sweep when +you make contact with an object because + + align:start position:0% +you make contact with an object because + + + align:start position:0% +you make contact with an object because +the whiskers sweeping back and forth so + + align:start position:0% +the whiskers sweeping back and forth so + + + align:start position:0% +the whiskers sweeping back and forth so +if you want to know the location of the + + align:start position:0% +if you want to know the location of the + + + align:start position:0% +if you want to know the location of the +point of contact you need to integrate + + align:start position:0% +point of contact you need to integrate + + + align:start position:0% +point of contact you need to integrate +the position of the whisker in his sleep + + align:start position:0% +the position of the whisker in his sleep + + + align:start position:0% +the position of the whisker in his sleep +in its sweep what you might call a theta + + align:start position:0% +in its sweep what you might call a theta + + + align:start position:0% +in its sweep what you might call a theta +signal and the presence of a contact on + + align:start position:0% +signal and the presence of a contact on + + + align:start position:0% +signal and the presence of a contact on +the whiskers and the quittance + + align:start position:0% +the whiskers and the quittance + + + align:start position:0% +the whiskers and the quittance +coincidence of those two is detected in + + align:start position:0% +coincidence of those two is detected in + + + align:start position:0% +coincidence of those two is detected in +the brain and we know that there are + + align:start position:0% +the brain and we know that there are + + + align:start position:0% +the brain and we know that there are +cells in the bowel cortex that respond + + align:start position:0% +cells in the bowel cortex that respond + + + align:start position:0% +cells in the bowel cortex that respond +to that coincidence + + align:start position:0% +to that coincidence + + + align:start position:0% +to that coincidence +so we have in our robot a model of + + align:start position:0% +so we have in our robot a model of + + + align:start position:0% +so we have in our robot a model of +superior colliculus which is the + + align:start position:0% +superior colliculus which is the + + + align:start position:0% +superior colliculus which is the +location in the brain which we think + + align:start position:0% +location in the brain which we think + + + align:start position:0% +location in the brain which we think +is involved in orienting and in our + + align:start position:0% +is involved in orienting and in our + + + align:start position:0% +is involved in orienting and in our +model of the colliculus we have a head + + align:start position:0% +model of the colliculus we have a head + + + align:start position:0% +model of the colliculus we have a head +centered map which looks for this + + align:start position:0% +centered map which looks for this + + + align:start position:0% +centered map which looks for this +coincidence between a cell encoding the + + align:start position:0% +coincidence between a cell encoding the + + + align:start position:0% +coincidence between a cell encoding the +position of the whisker in its sweep and + + align:start position:0% +position of the whisker in its sweep and + + + align:start position:0% +position of the whisker in its sweep and +a cell encoding at contact and makes a + + align:start position:0% +a cell encoding at contact and makes a + + + align:start position:0% +a cell encoding at contact and makes a +turn to orient and explore that position + + align:start position:0% +turn to orient and explore that position + + + align:start position:0% +turn to orient and explore that position +and then if we want to actually create + + align:start position:0% +and then if we want to actually create + + + align:start position:0% +and then if we want to actually create +behavior which is integrated over time + + align:start position:0% +behavior which is integrated over time + + + align:start position:0% +behavior which is integrated over time +so if the robot was just to orient every + + align:start position:0% +so if the robot was just to orient every + + + align:start position:0% +so if the robot was just to orient every +time it cuts something that wouldn't be + + align:start position:0% +time it cuts something that wouldn't be + + + align:start position:0% +time it cuts something that wouldn't be +very animal-like particularly you don't + + align:start position:0% +very animal-like particularly you don't + + + align:start position:0% +very animal-like particularly you don't +want to orient and every time you touch + + align:start position:0% +want to orient and every time you touch + + + align:start position:0% +want to orient and every time you touch +the ground so you just want to orient + + align:start position:0% +the ground so you just want to orient + + + align:start position:0% +the ground so you just want to orient +when you touch important stimuli so we + + align:start position:0% +when you touch important stimuli so we + + + align:start position:0% +when you touch important stimuli so we +we put into our model the basal ganglia + + align:start position:0% +we put into our model the basal ganglia + + + align:start position:0% +we put into our model the basal ganglia +so that we can decide whether the + + align:start position:0% +so that we can decide whether the + + + align:start position:0% +so that we can decide whether the +contact we've just made is something we + + align:start position:0% +contact we've just made is something we + + + align:start position:0% +contact we've just made is something we +want to investigate or something that + + align:start position:0% +want to investigate or something that + + + align:start position:0% +want to investigate or something that +doesn't interest us so much so we have a + + align:start position:0% +doesn't interest us so much so we have a + + + align:start position:0% +doesn't interest us so much so we have a +system now with a midbrain that does + + align:start position:0% +system now with a midbrain that does + + + align:start position:0% +system now with a midbrain that does +orienting a basal ganglia that makes + + align:start position:0% +orienting a basal ganglia that makes + + + align:start position:0% +orienting a basal ganglia that makes +decisions about sequencing and those two + + align:start position:0% +decisions about sequencing and those two + + + align:start position:0% +decisions about sequencing and those two +things together give way give us + + align:start position:0% +things together give way give us + + + align:start position:0% +things together give way give us +reasonably lifelike behavior in a + + align:start position:0% +reasonably lifelike behavior in a + + + align:start position:0% +reasonably lifelike behavior in a +robot's ratch bot and that's quite a lot + + align:start position:0% +robot's ratch bot and that's quite a lot + + + align:start position:0% +robot's ratch bot and that's quite a lot +of what we have running now on the new + + align:start position:0% +of what we have running now on the new + + + align:start position:0% +of what we have running now on the new +robot Miro is this system it's for + + align:start position:0% +robot Miro is this system it's for + + + align:start position:0% +robot Miro is this system it's for +orienting and exploring and we can use + + align:start position:0% +orienting and exploring and we can use + + + align:start position:0% +orienting and exploring and we can use +it we use it here for tactile orienting + + align:start position:0% +it we use it here for tactile orienting + + + align:start position:0% +it we use it here for tactile orienting +but of course the same system can + + align:start position:0% +but of course the same system can + + + align:start position:0% +but of course the same system can +underlie orienting to sounds if you can + + align:start position:0% +underlie orienting to sounds if you can + + + align:start position:0% +underlie orienting to sounds if you can +localize those in space and orienting to + + align:start position:0% +localize those in space and orienting to + + + align:start position:0% +localize those in space and orienting to +visual stimuli too so it turns out that + + align:start position:0% +visual stimuli too so it turns out that + + + align:start position:0% +visual stimuli too so it turns out that +this isn't a complete solution to the + + align:start position:0% +this isn't a complete solution to the + + + align:start position:0% +this isn't a complete solution to the +problem of orienting for our whiskered + + align:start position:0% +problem of orienting for our whiskered + + + align:start position:0% +problem of orienting for our whiskered +robot and that's because sometimes our + + align:start position:0% +robot and that's because sometimes our + + + align:start position:0% +robot and that's because sometimes our +robot would stop as it was moving around + + align:start position:0% +robot would stop as it was moving around + + + align:start position:0% +robot would stop as it was moving around +and just move and investigate a point in + + align:start position:0% +and just move and investigate a point in + + + align:start position:0% +and just move and investigate a point in +space where nothing was happening we + + align:start position:0% +space where nothing was happening we + + + align:start position:0% +space where nothing was happening we +called that a ghost orient and the + + align:start position:0% +called that a ghost orient and the + + + align:start position:0% +called that a ghost orient and the +problem is that the whiskers because + + align:start position:0% +problem is that the whiskers because + + + align:start position:0% +problem is that the whiskers because +they're moving back and forth + + align:start position:0% +they're moving back and forth + + + align:start position:0% +they're moving back and forth +they sometimes generate signals in the + + align:start position:0% +they sometimes generate signals in the + + + align:start position:0% +they sometimes generate signals in the +strain gauges that are detecting bending + + align:start position:0% +strain gauges that are detecting bending + + + align:start position:0% +strain gauges that are detecting bending +of the whisker and sometimes those + + align:start position:0% +of the whisker and sometimes those + + + align:start position:0% +of the whisker and sometimes those +signals just as a consequence of the + + align:start position:0% +signals just as a consequence of the + + + align:start position:0% +signals just as a consequence of the +movement and the mass of the whisker are + + align:start position:0% +movement and the mass of the whisker are + + + align:start position:0% +movement and the mass of the whisker are +strong enough to be above threshold to + + align:start position:0% +strong enough to be above threshold to + + + align:start position:0% +strong enough to be above threshold to +generate an Orient so you get if you + + align:start position:0% +generate an Orient so you get if you + + + align:start position:0% +generate an Orient so you get if you +like these ghosts orienting movements + + align:start position:0% +like these ghosts orienting movements + + + align:start position:0% +like these ghosts orienting movements +towards stimuli that don't exist and we + + align:start position:0% +towards stimuli that don't exist and we + + + align:start position:0% +towards stimuli that don't exist and we +know that rats don't make these kind of + + align:start position:0% +know that rats don't make these kind of + + + align:start position:0% +know that rats don't make these kind of +ghosts Orient's so something else must + + align:start position:0% +ghosts Orient's so something else must + + + align:start position:0% +ghosts Orient's so something else must +be going on in the brain + + align:start position:0% +be going on in the brain + + + align:start position:0% +be going on in the brain +and one part of the brain that might be + + align:start position:0% +and one part of the brain that might be + + + align:start position:0% +and one part of the brain that might be +helping here is a region called the + + align:start position:0% +helping here is a region called the + + + align:start position:0% +helping here is a region called the +cerebellum which I'm not sure if you've + + align:start position:0% +cerebellum which I'm not sure if you've + + + align:start position:0% +cerebellum which I'm not sure if you've +covered that in the summer school but + + align:start position:0% +covered that in the summer school but + + + align:start position:0% +covered that in the summer school but +the cerebellum this large structure at + + align:start position:0% +the cerebellum this large structure at + + + align:start position:0% +the cerebellum this large structure at +the back of the rat brain one of its key + + align:start position:0% +the back of the rat brain one of its key + + + align:start position:0% +the back of the rat brain one of its key +functions seems to be to make + + align:start position:0% +functions seems to be to make + + + align:start position:0% +functions seems to be to make +predictions about sensory signals and + + align:start position:0% +predictions about sensory signals and + + + align:start position:0% +predictions about sensory signals and +particularly to be able to predict + + align:start position:0% +particularly to be able to predict + + + align:start position:0% +particularly to be able to predict +sensory signals that have been caused by + + align:start position:0% +sensory signals that have been caused by + + + align:start position:0% +sensory signals that have been caused by +your own movement + + align:start position:0% +your own movement + + + align:start position:0% +your own movement +there's a lovely experiment that's been + + align:start position:0% +there's a lovely experiment that's been + + + align:start position:0% +there's a lovely experiment that's been +done by Blackmore et al where they put + + align:start position:0% +done by Blackmore et al where they put + + + align:start position:0% +done by Blackmore et al where they put +people into a scanner and they + + align:start position:0% +people into a scanner and they + + + align:start position:0% +people into a scanner and they +investigated how they responded to + + align:start position:0% +investigated how they responded to + + + align:start position:0% +investigated how they responded to +tickling stimuli so of course if + + align:start position:0% +tickling stimuli so of course if + + + align:start position:0% +tickling stimuli so of course if +somebody tickles you that can be quite + + align:start position:0% +somebody tickles you that can be quite + + + align:start position:0% +somebody tickles you that can be quite +amusing but unfortunately if you try to + + align:start position:0% +amusing but unfortunately if you try to + + + align:start position:0% +amusing but unfortunately if you try to +tickle yourself it's really + + align:start position:0% +tickle yourself it's really + + + align:start position:0% +tickle yourself it's really +uninteresting it doesn't work as a + + align:start position:0% +uninteresting it doesn't work as a + + + align:start position:0% +uninteresting it doesn't work as a +stimulus and it's it's it's worth + + align:start position:0% +stimulus and it's it's it's worth + + + align:start position:0% +stimulus and it's it's it's worth +thinking about why it is that self + + align:start position:0% +thinking about why it is that self + + + align:start position:0% +thinking about why it is that self +tickling is so unrewarding and one of + + align:start position:0% +tickling is so unrewarding and one of + + + align:start position:0% +tickling is so unrewarding and one of +the reasons is that it's just not + + align:start position:0% +the reasons is that it's just not + + + align:start position:0% +the reasons is that it's just not +surprising you know what's what's going + + align:start position:0% +surprising you know what's what's going + + + align:start position:0% +surprising you know what's what's going +to happen when you tickle yourself + + align:start position:0% +to happen when you tickle yourself + + + align:start position:0% +to happen when you tickle yourself +whereas if somebody else is doing it + + align:start position:0% +whereas if somebody else is doing it + + + align:start position:0% +whereas if somebody else is doing it +it's unexpected and surprising so why is + + align:start position:0% +it's unexpected and surprising so why is + + + align:start position:0% +it's unexpected and surprising so why is +self tickling unexpected why is it not + + align:start position:0% +self tickling unexpected why is it not + + + align:start position:0% +self tickling unexpected why is it not +surprising it must be because the brain + + align:start position:0% +surprising it must be because the brain + + + align:start position:0% +surprising it must be because the brain +expects and anticipates the signal + + align:start position:0% +expects and anticipates the signal + + + align:start position:0% +expects and anticipates the signal +that's going to get and what Blakemore + + align:start position:0% +that's going to get and what Blakemore + + + align:start position:0% +that's going to get and what Blakemore +ital did was to show that the cerebellum + + align:start position:0% +ital did was to show that the cerebellum + + + align:start position:0% +ital did was to show that the cerebellum +really lights up when you try to tickle + + align:start position:0% +really lights up when you try to tickle + + + align:start position:0% +really lights up when you try to tickle +yourself because it's estimating + + align:start position:0% +yourself because it's estimating + + + align:start position:0% +yourself because it's estimating +predicting the sensory signal and using + + align:start position:0% +predicting the sensory signal and using + + + align:start position:0% +predicting the sensory signal and using +that to cancel out if you like + + align:start position:0% +that to cancel out if you like + + + align:start position:0% +that to cancel out if you like +the signaling that the signal is coming + + align:start position:0% +the signaling that the signal is coming + + + align:start position:0% +the signaling that the signal is coming +from your skin the same thing is + + align:start position:0% +from your skin the same thing is + + + align:start position:0% +from your skin the same thing is +happening in electric fish which which + + align:start position:0% +happening in electric fish which which + + + align:start position:0% +happening in electric fish which which +generate this broad electric field which + + align:start position:0% +generate this broad electric field which + + + align:start position:0% +generate this broad electric field which +they use for catching prey and they need + + align:start position:0% +they use for catching prey and they need + + + align:start position:0% +they use for catching prey and they need +to be able to tell the difference + + align:start position:0% +to be able to tell the difference + + + align:start position:0% +to be able to tell the difference +between a distortion to the electric + + align:start position:0% +between a distortion to the electric + + + align:start position:0% +between a distortion to the electric +field caused by a prey animal and a + + align:start position:0% +field caused by a prey animal and a + + + align:start position:0% +field caused by a prey animal and a +distortion caused by their own movement + + align:start position:0% +distortion caused by their own movement + + + align:start position:0% +distortion caused by their own movement +by swimming and they do that by having a + + align:start position:0% +by swimming and they do that by having a + + + align:start position:0% +by swimming and they do that by having a +very large cerebellum so we put a model + + align:start position:0% +very large cerebellum so we put a model + + + align:start position:0% +very large cerebellum so we put a model +of cerebellum in our whiskered robot and + + align:start position:0% +of cerebellum in our whiskered robot and + + + align:start position:0% +of cerebellum in our whiskered robot and +the cerebellum predicts the noise that + + align:start position:0% +the cerebellum predicts the noise that + + + align:start position:0% +the cerebellum predicts the noise that +you might get due to the movement of the + + align:start position:0% +you might get due to the movement of the + + + align:start position:0% +you might get due to the movement of the +whiskers and it learns online to + + align:start position:0% +whiskers and it learns online to + + + align:start position:0% +whiskers and it learns online to +accurately predict what noise signals + + align:start position:0% +accurately predict what noise signals + + + align:start position:0% +accurately predict what noise signals +you might get and to cancel them out so + + align:start position:0% +you might get and to cancel them out so + + + align:start position:0% +you might get and to cancel them out so +you get a much better signal-to-noise + + align:start position:0% +you get a much better signal-to-noise + + + align:start position:0% +you get a much better signal-to-noise +ratio in the robot + + align:start position:0% +ratio in the robot + + + align:start position:0% +ratio in the robot +so we've dealt with whisking and we've + + align:start position:0% +so we've dealt with whisking and we've + + + align:start position:0% +so we've dealt with whisking and we've +dealt with orienting but as you saw with + + align:start position:0% +dealt with orienting but as you saw with + + + align:start position:0% +dealt with orienting but as you saw with +that rat on the windowsill the whisker + + align:start position:0% +that rat on the windowsill the whisker + + + align:start position:0% +that rat on the windowsill the whisker +movements are really precise and they're + + align:start position:0% +movements are really precise and they're + + + align:start position:0% +movements are really precise and they're +really controlled and the rat seems to + + align:start position:0% +really controlled and the rat seems to + + + align:start position:0% +really controlled and the rat seems to +really care about how it's moving its + + align:start position:0% +really care about how it's moving its + + + align:start position:0% +really care about how it's moving its +whiskers and how it's touching we call + + align:start position:0% +whiskers and how it's touching we call + + + align:start position:0% +whiskers and how it's touching we call +this active sensing and if you look at + + align:start position:0% +this active sensing and if you look at + + + align:start position:0% +this active sensing and if you look at +these high-speed videos you can see for + + align:start position:0% +these high-speed videos you can see for + + + align:start position:0% +these high-speed videos you can see for +instance this rat when it's exploring + + align:start position:0% +instance this rat when it's exploring + + + align:start position:0% +instance this rat when it's exploring +this perspex block the whiskers aren't + + align:start position:0% +this perspex block the whiskers aren't + + + align:start position:0% +this perspex block the whiskers aren't +moving in a stereotyped symmetric way + + align:start position:0% +moving in a stereotyped symmetric way + + + align:start position:0% +moving in a stereotyped symmetric way +you can see that here the whiskers on + + align:start position:0% +you can see that here the whiskers on + + + align:start position:0% +you can see that here the whiskers on +the right hand side are really reaching + + align:start position:0% +the right hand side are really reaching + + + align:start position:0% +the right hand side are really reaching +round to try and reach the other side of + + align:start position:0% +round to try and reach the other side of + + + align:start position:0% +round to try and reach the other side of +the block if you watch this rat here you + + align:start position:0% +the block if you watch this rat here you + + + align:start position:0% +the block if you watch this rat here you +see that - you got a symmetry and you'll + + align:start position:0% +see that - you got a symmetry and you'll + + + align:start position:0% +see that - you got a symmetry and you'll +see that even as the the rat comes up to + + align:start position:0% +see that even as the the rat comes up to + + + align:start position:0% +see that even as the the rat comes up to +the cylinder here the whiskers at the + + align:start position:0% +the cylinder here the whiskers at the + + + align:start position:0% +the cylinder here the whiskers at the +front are pushing forward while the ones + + align:start position:0% +front are pushing forward while the ones + + + align:start position:0% +front are pushing forward while the ones +at the back are hardly moving at all so + + align:start position:0% +at the back are hardly moving at all so + + + align:start position:0% +at the back are hardly moving at all so +there's some ability to control even the + + align:start position:0% +there's some ability to control even the + + + align:start position:0% +there's some ability to control even the +whiskers on one side of the head and + + align:start position:0% +whiskers on one side of the head and + + + align:start position:0% +whiskers on one side of the head and +when you move your fingers of course + + align:start position:0% +when you move your fingers of course + + + align:start position:0% +when you move your fingers of course +there's some coupling between your + + align:start position:0% +there's some coupling between your + + + align:start position:0% +there's some coupling between your +finger movements you can't move them + + align:start position:0% +finger movements you can't move them + + + align:start position:0% +finger movements you can't move them +entirely independently and each of these + + align:start position:0% +entirely independently and each of these + + + align:start position:0% +entirely independently and each of these +whiskers has its own muscle so there's + + align:start position:0% +whiskers has its own muscle so there's + + + align:start position:0% +whiskers has its own muscle so there's +there's a degree of independence and how + + align:start position:0% +there's a degree of independence and how + + + align:start position:0% +there's a degree of independence and how +the whiskers can move and we find that + + align:start position:0% +the whiskers can move and we find that + + + align:start position:0% +the whiskers can move and we find that +when we record over long intervals so + + align:start position:0% +when we record over long intervals so + + + align:start position:0% +when we record over long intervals so +this was in which we recorded the + + align:start position:0% +this was in which we recorded the + + + align:start position:0% +this was in which we recorded the +whisking muscles using EMG that's the + + align:start position:0% +whisking muscles using EMG that's the + + + align:start position:0% +whisking muscles using EMG that's the +sound that you can hear as a rat + + align:start position:0% +sound that you can hear as a rat + + + align:start position:0% +sound that you can hear as a rat +explored and we tracked the rat as he + + align:start position:0% +explored and we tracked the rat as he + + + align:start position:0% +explored and we tracked the rat as he +was moving around and we showed that + + align:start position:0% +was moving around and we showed that + + + align:start position:0% +was moving around and we showed that +whenever he came close to the edge of + + align:start position:0% +whenever he came close to the edge of + + + align:start position:0% +whenever he came close to the edge of +the box here the whiskers would become + + align:start position:0% +the box here the whiskers would become + + + align:start position:0% +the box here the whiskers would become +asymmetric and the whiskers that were + + align:start position:0% +asymmetric and the whiskers that were + + + align:start position:0% +asymmetric and the whiskers that were +furthest away from the wall would push + + align:start position:0% +furthest away from the wall would push + + + align:start position:0% +furthest away from the wall would push +round to try and touch the sides of the + + align:start position:0% +round to try and touch the sides of the + + + align:start position:0% +round to try and touch the sides of the +box the whiskers that were close to the + + align:start position:0% +box the whiskers that were close to the + + + align:start position:0% +box the whiskers that were close to the +wall would barely move at all so we want + + align:start position:0% +wall would barely move at all so we want + + + align:start position:0% +wall would barely move at all so we want +to put that kind of control into our + + align:start position:0% +to put that kind of control into our + + + align:start position:0% +to put that kind of control into our +robot so I briefly want to come back to + + align:start position:0% +robot so I briefly want to come back to + + + align:start position:0% +robot so I briefly want to come back to +this question of how we decomposed + + align:start position:0% +this question of how we decomposed + + + align:start position:0% +this question of how we decomposed +control so in our original robot that + + align:start position:0% +control so in our original robot that + + + align:start position:0% +control so in our original robot that +was controlled by the basal ganglion + + align:start position:0% +was controlled by the basal ganglion + + + align:start position:0% +was controlled by the basal ganglion +it's collecting cans weeded decomposed + + align:start position:0% +it's collecting cans weeded decomposed + + + align:start position:0% +it's collecting cans weeded decomposed +behaviors into the different elements of + + align:start position:0% +behaviors into the different elements of + + + align:start position:0% +behaviors into the different elements of +behavior looking for a kin picking it up + + align:start position:0% +behavior looking for a kin picking it up + + + align:start position:0% +behavior looking for a kin picking it up +carrying it to the wall these sorts of + + align:start position:0% +carrying it to the wall these sorts of + + + align:start position:0% +carrying it to the wall these sorts of +things and if we look in the ethology + + align:start position:0% +things and if we look in the ethology + + + align:start position:0% +things and if we look in the ethology +literature we find that people have + + align:start position:0% +literature we find that people have + + + align:start position:0% +literature we find that people have +talked about these kinds of + + align:start position:0% +talked about these kinds of + + + align:start position:0% +talked about these kinds of +decompositions there's a very famous + + align:start position:0% +decompositions there's a very famous + + + align:start position:0% +decompositions there's a very famous +paper by Barron's about the herring gull + + align:start position:0% +paper by Barron's about the herring gull + + + align:start position:0% +paper by Barron's about the herring gull +and with the herring goal is there's + + align:start position:0% +and with the herring goal is there's + + + align:start position:0% +and with the herring goal is there's +this famous experiment where the the egg + + align:start position:0% +this famous experiment where the the egg + + + align:start position:0% +this famous experiment where the the egg +rolls out the nest and the bird will + + align:start position:0% +rolls out the nest and the bird will + + + align:start position:0% +rolls out the nest and the bird will +retrieve the egg with its bill and push + + align:start position:0% +retrieve the egg with its bill and push + + + align:start position:0% +retrieve the egg with its bill and push +it back into the nest and it will do + + align:start position:0% +it back into the nest and it will do + + + align:start position:0% +it back into the nest and it will do +this same action really reliably and + + align:start position:0% +this same action really reliably and + + + align:start position:0% +this same action really reliably and +repeatedly + + align:start position:0% +repeatedly + + + align:start position:0% +repeatedly +and it can do it with eggs of various + + align:start position:0% +and it can do it with eggs of various + + + align:start position:0% +and it can do it with eggs of various +size it might even do it for a coke can + + align:start position:0% +size it might even do it for a coke can + + + align:start position:0% +size it might even do it for a coke can +and if you take the egg away during the + + align:start position:0% +and if you take the egg away during the + + + align:start position:0% +and if you take the egg away during the +movement it will still complete the + + align:start position:0% +movement it will still complete the + + + align:start position:0% +movement it will still complete the +movement and it's all adjusts of call + + align:start position:0% +movement and it's all adjusts of call + + + align:start position:0% +movement and it's all adjusts of call +this a fixed action pattern so it may be + + align:start position:0% +this a fixed action pattern so it may be + + + align:start position:0% +this a fixed action pattern so it may be +that behavior is decomposed into action + + align:start position:0% +that behavior is decomposed into action + + + align:start position:0% +that behavior is decomposed into action +patterns and that's one of the ways for + + align:start position:0% +patterns and that's one of the ways for + + + align:start position:0% +patterns and that's one of the ways for +instance in which Rodney Brooks wantedly + + align:start position:0% +instance in which Rodney Brooks wantedly + + + align:start position:0% +instance in which Rodney Brooks wantedly +decomposed robot behavior we decompose + + align:start position:0% +decomposed robot behavior we decompose + + + align:start position:0% +decomposed robot behavior we decompose +it into different things you might want + + align:start position:0% +it into different things you might want + + + align:start position:0% +it into different things you might want +the robot to do and we can do that with + + align:start position:0% +the robot to do and we can do that with + + + align:start position:0% +the robot to do and we can do that with +ours good robots here's another one + + align:start position:0% +ours good robots here's another one + + + align:start position:0% +ours good robots here's another one +whether it's behavior decomposed into + + align:start position:0% +whether it's behavior decomposed into + + + align:start position:0% +whether it's behavior decomposed into +different kinds of if you like orienting + + align:start position:0% +different kinds of if you like orienting + + + align:start position:0% +different kinds of if you like orienting +behaviors and fixed action patterns + + align:start position:0% +behaviors and fixed action patterns + + + align:start position:0% +behaviors and fixed action patterns +another way to decompose behavior is to + + align:start position:0% +another way to decompose behavior is to + + + align:start position:0% +another way to decompose behavior is to +think about where your attention is so + + align:start position:0% +think about where your attention is so + + + align:start position:0% +think about where your attention is so +where you put your attention might + + align:start position:0% +where you put your attention might + + + align:start position:0% +where you put your attention might +decide what you're going to do next and + + align:start position:0% +decide what you're going to do next and + + + align:start position:0% +decide what you're going to do next and +for an animal that doesn't have arms and + + align:start position:0% +for an animal that doesn't have arms and + + + align:start position:0% +for an animal that doesn't have arms and +of course most animals except humans and + + align:start position:0% +of course most animals except humans and + + + align:start position:0% +of course most animals except humans and +some primates don't usually use their + + align:start position:0% +some primates don't usually use their + + + align:start position:0% +some primates don't usually use their +fore limbs for much much else other than + + align:start position:0% +fore limbs for much much else other than + + + align:start position:0% +fore limbs for much much else other than +locomotion and they primarily are + + align:start position:0% +locomotion and they primarily are + + + align:start position:0% +locomotion and they primarily are +positioning their head in their face and + + align:start position:0% +positioning their head in their face and + + + align:start position:0% +positioning their head in their face and +their main effective then is their + + align:start position:0% +their main effective then is their + + + align:start position:0% +their main effective then is their +mouths so where you position your + + align:start position:0% +mouths so where you position your + + + align:start position:0% +mouths so where you position your +attention could determine what you're + + align:start position:0% +attention could determine what you're + + + align:start position:0% +attention could determine what you're +going to do next so another way of + + align:start position:0% +going to do next so another way of + + + align:start position:0% +going to do next so another way of +decomposing control is to solve the + + align:start position:0% +decomposing control is to solve the + + + align:start position:0% +decomposing control is to solve the +attention problem first and then once + + align:start position:0% +attention problem first and then once + + + align:start position:0% +attention problem first and then once +you've solved that the problem of what + + align:start position:0% +you've solved that the problem of what + + + align:start position:0% +you've solved that the problem of what +you're going to do is simplified so in + + align:start position:0% +you're going to do is simplified so in + + + align:start position:0% +you're going to do is simplified so in +this robot we're controlling it by + + align:start position:0% +this robot we're controlling it by + + + align:start position:0% +this robot we're controlling it by +deciding where its attention should go + + align:start position:0% +deciding where its attention should go + + + align:start position:0% +deciding where its attention should go +and then the rest of the body kind of + + align:start position:0% +and then the rest of the body kind of + + + align:start position:0% +and then the rest of the body kind of +follows when humans have spatial + + align:start position:0% +follows when humans have spatial + + + align:start position:0% +follows when humans have spatial +attention of course we we explore that + + align:start position:0% +attention of course we we explore that + + + align:start position:0% +attention of course we we explore that +in the visual modality and we look at + + align:start position:0% +in the visual modality and we look at + + + align:start position:0% +in the visual modality and we look at +the saccadic eye movements that people + + align:start position:0% +the saccadic eye movements that people + + + align:start position:0% +the saccadic eye movements that people +make so in a famous experiment + + align:start position:0% +make so in a famous experiment + + + align:start position:0% +make so in a famous experiment +Albert yabas had people looking at this + + align:start position:0% +Albert yabas had people looking at this + + + align:start position:0% +Albert yabas had people looking at this +picture and tracking where their eyes + + align:start position:0% +picture and tracking where their eyes + + + align:start position:0% +picture and tracking where their eyes +would look and of course we look at the + + align:start position:0% +would look and of course we look at the + + + align:start position:0% +would look and of course we look at the +socially significant elements of the + + align:start position:0% +socially significant elements of the + + + align:start position:0% +socially significant elements of the +picture people's faces and so on not + + align:start position:0% +picture people's faces and so on not + + + align:start position:0% +picture people's faces and so on not +just + + align:start position:0% +just + + + align:start position:0% +just +arbitrary points of light or corners and + + align:start position:0% +arbitrary points of light or corners and + + + align:start position:0% +arbitrary points of light or corners and +so on and we can actually calculate a + + align:start position:0% +so on and we can actually calculate a + + + align:start position:0% +so on and we can actually calculate a +sailin see map for space and say what + + align:start position:0% +sailin see map for space and say what + + + align:start position:0% +sailin see map for space and say what +are the important parts of space for + + align:start position:0% +are the important parts of space for + + + align:start position:0% +are the important parts of space for +exploring and attending to and we've + + align:start position:0% +exploring and attending to and we've + + + align:start position:0% +exploring and attending to and we've +taken that idea and transferred it into + + align:start position:0% +taken that idea and transferred it into + + + align:start position:0% +taken that idea and transferred it into +our model for understanding the rat and + + align:start position:0% +our model for understanding the rat and + + + align:start position:0% +our model for understanding the rat and +we've thought about tactile salience e + + align:start position:0% +we've thought about tactile salience e + + + align:start position:0% +we've thought about tactile salience e +maps so can we with a sense of touch + + align:start position:0% +maps so can we with a sense of touch + + + align:start position:0% +maps so can we with a sense of touch +think about days of the world which are + + align:start position:0% +think about days of the world which are + + + align:start position:0% +think about days of the world which are +important to explore and understand + + align:start position:0% +important to explore and understand + + + align:start position:0% +important to explore and understand +through touch and can we use that to + + align:start position:0% +through touch and can we use that to + + + align:start position:0% +through touch and can we use that to +control the movement of our robot or in + + align:start position:0% +control the movement of our robot or in + + + align:start position:0% +control the movement of our robot or in +this case our simulation so here we have + + align:start position:0% +this case our simulation so here we have + + + align:start position:0% +this case our simulation so here we have +a form of emergent wall following which + + align:start position:0% +a form of emergent wall following which + + + align:start position:0% +a form of emergent wall following which +is a consequence of the rats spatial + + align:start position:0% +is a consequence of the rats spatial + + + align:start position:0% +is a consequence of the rats spatial +attention being driven by contact with + + align:start position:0% +attention being driven by contact with + + + align:start position:0% +attention being driven by contact with +vertical objects which we we program it + + align:start position:0% +vertical objects which we we program it + + + align:start position:0% +vertical objects which we we program it +so that that vertical surfaces are + + align:start position:0% +so that that vertical surfaces are + + + align:start position:0% +so that that vertical surfaces are +salient and interesting and it has this + + align:start position:0% +salient and interesting and it has this + + + align:start position:0% +salient and interesting and it has this +salient zone and it tries to put its + + align:start position:0% +salient zone and it tries to put its + + + align:start position:0% +salient zone and it tries to put its +whiskers into the salient zone and then + + align:start position:0% +whiskers into the salient zone and then + + + align:start position:0% +whiskers into the salient zone and then +here is his a robot instantiating this + + align:start position:0% +here is his a robot instantiating this + + + align:start position:0% +here is his a robot instantiating this +this is Ben Mitch Anson whose program + + align:start position:0% +this is Ben Mitch Anson whose program + + + align:start position:0% +this is Ben Mitch Anson whose program +many of these robots and so what we're + + align:start position:0% +many of these robots and so what we're + + + align:start position:0% +many of these robots and so what we're +doing now is following this biologically + + align:start position:0% +doing now is following this biologically + + + align:start position:0% +doing now is following this biologically +inspired orienting system to explore + + align:start position:0% +inspired orienting system to explore + + + align:start position:0% +inspired orienting system to explore +shapes and in this case he he put his + + align:start position:0% +shapes and in this case he he put his + + + align:start position:0% +shapes and in this case he he put his +own face in front of the robot and you + + align:start position:0% +own face in front of the robot and you + + + align:start position:0% +own face in front of the robot and you +can see the robot making light touches + + align:start position:0% +can see the robot making light touches + + + align:start position:0% +can see the robot making light touches +against his face and investigating it + + align:start position:0% +against his face and investigating it + + + align:start position:0% +against his face and investigating it +looking making a series of people like + + align:start position:0% +looking making a series of people like + + + align:start position:0% +looking making a series of people like +exploratory touches somewhat like + + align:start position:0% +exploratory touches somewhat like + + + align:start position:0% +exploratory touches somewhat like +saccades somewhat what you might like + + align:start position:0% +saccades somewhat what you might like + + + align:start position:0% +saccades somewhat what you might like +what you might imagine a blind person + + align:start position:0% +what you might imagine a blind person + + + align:start position:0% +what you might imagine a blind person +would do if they were investigating your + + align:start position:0% +would do if they were investigating your + + + align:start position:0% +would do if they were investigating your +face to try and recognize you and Mitra + + align:start position:0% +face to try and recognize you and Mitra + + + align:start position:0% +face to try and recognize you and Mitra +hartwin from Northwestern has shown that + + align:start position:0% +hartwin from Northwestern has shown that + + + align:start position:0% +hartwin from Northwestern has shown that +you can take signals off these kinds of + + align:start position:0% +you can take signals off these kinds of + + + align:start position:0% +you can take signals off these kinds of +whiskers and and reconstruct a face so + + align:start position:0% +whiskers and and reconstruct a face so + + + align:start position:0% +whiskers and and reconstruct a face so +it should be possible from this to to + + align:start position:0% +it should be possible from this to to + + + align:start position:0% +it should be possible from this to to +build up from the touch as the sequence + + align:start position:0% +build up from the touch as the sequence + + + align:start position:0% +build up from the touch as the sequence +of touches a lot of rich information + + align:start position:0% +of touches a lot of rich information + + + align:start position:0% +of touches a lot of rich information +about the object that's being + + align:start position:0% +about the object that's being + + + align:start position:0% +about the object that's being +investigated how much time I need to + + align:start position:0% +investigated how much time I need to + + + align:start position:0% +investigated how much time I need to +finish ok let me just skip through so + + align:start position:0% +finish ok let me just skip through so + + + align:start position:0% +finish ok let me just skip through so +we've been doing working on there on the + + align:start position:0% +we've been doing working on there on the + + + align:start position:0% +we've been doing working on there on the +cortex we have number of models of that + + align:start position:0% +cortex we have number of models of that + + + align:start position:0% +cortex we have number of models of that +which I'd like to show you but I wanted + + align:start position:0% +which I'd like to show you but I wanted + + + align:start position:0% +which I'd like to show you but I wanted +to just finish just to make contact with + + align:start position:0% +to just finish just to make contact with + + + align:start position:0% +to just finish just to make contact with +John's talk is that we've been doing in + + align:start position:0% +John's talk is that we've been doing in + + + align:start position:0% +John's talk is that we've been doing in +our robots tactile simultaneous + + align:start position:0% +our robots tactile simultaneous + + + align:start position:0% +our robots tactile simultaneous +localization and mapping so this is our + + align:start position:0% +localization and mapping so this is our + + + align:start position:0% +localization and mapping so this is our +our whiskered robot + + align:start position:0% +our whiskered robot + + + align:start position:0% +our whiskered robot +and we have various models for this some + + align:start position:0% +and we have various models for this some + + + align:start position:0% +and we have various models for this some +of which are more hippocampal like this + + align:start position:0% +of which are more hippocampal like this + + + align:start position:0% +of which are more hippocampal like this +one I think was more of an engineered + + align:start position:0% +one I think was more of an engineered + + + align:start position:0% +one I think was more of an engineered +model but you can see the robot just + + align:start position:0% +model but you can see the robot just + + + align:start position:0% +model but you can see the robot just +using touch on these artificial whiskers + + align:start position:0% +using touch on these artificial whiskers + + + align:start position:0% +using touch on these artificial whiskers +building up a map of its environment + + align:start position:0% +building up a map of its environment + + + align:start position:0% +building up a map of its environment +these two lines show it's dead reckoning + + align:start position:0% +these two lines show it's dead reckoning + + + align:start position:0% +these two lines show it's dead reckoning +position and it's calculated position + + align:start position:0% +position and it's calculated position + + + align:start position:0% +position and it's calculated position +and just using touch we can build up a + + align:start position:0% +and just using touch we can build up a + + + align:start position:0% +and just using touch we can build up a +reasonably accurate map of the world + + align:start position:0% +reasonably accurate map of the world + + + align:start position:0% +reasonably accurate map of the world +that we're exploring so a giorgo will + + align:start position:0% +that we're exploring so a giorgo will + + + align:start position:0% +that we're exploring so a giorgo will +we'll talk about the iCub and I just + + align:start position:0% +we'll talk about the iCub and I just + + + align:start position:0% +we'll talk about the iCub and I just +wanted to mention that in the work we're + + align:start position:0% +wanted to mention that in the work we're + + + align:start position:0% +wanted to mention that in the work we're +doing with Giorgio we are very much + + align:start position:0% +doing with Giorgio we are very much + + + align:start position:0% +doing with Giorgio we are very much +trying to understand human cognition I + + align:start position:0% +trying to understand human cognition I + + + align:start position:0% +trying to understand human cognition I +wrote a short article for new scientists + + align:start position:0% +wrote a short article for new scientists + + + align:start position:0% +wrote a short article for new scientists +on the possibility that robots might one + + align:start position:0% +on the possibility that robots might one + + + align:start position:0% +on the possibility that robots might one +day have selves + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/FqVRwxc8hqQ.txt b/FqVRwxc8hqQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..3f1e8f9918fcc67f74cc7423f6aab64805e1176a --- /dev/null +++ b/FqVRwxc8hqQ.txt @@ -0,0 +1,8608 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT opencourseware continue to + + align:start position:0% +will help MIT opencourseware continue to + + + align:start position:0% +will help MIT opencourseware continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay instead of a quiz I'm + + align:start position:0% +okay instead of a quiz I'm + + + align:start position:0% +okay instead of a quiz I'm +trying to write some homework and some + + align:start position:0% +trying to write some homework and some + + + align:start position:0% +trying to write some homework and some +of them will be extra credit + + align:start position:0% +of them will be extra credit + + + align:start position:0% +of them will be extra credit +some of them will be + + align:start position:0% +some of them will be + + + align:start position:0% +some of them will be +part of the required homework + + align:start position:0% + + + + align:start position:0% + +now today + + align:start position:0% +now today + + + align:start position:0% +now today +we still have a lot to do + + align:start position:0% +we still have a lot to do + + + align:start position:0% +we still have a lot to do +chapter 26 for the + + align:start position:0% + + + + align:start position:0% + +concerning core Pathways of the limbic + + align:start position:0% +concerning core Pathways of the limbic + + + align:start position:0% +concerning core Pathways of the limbic +system and + + align:start position:0% +system and + + + align:start position:0% +system and +we had + + align:start position:0% +we had + + + align:start position:0% +we had +this is where we finished last time + + align:start position:0% +this is where we finished last time + + + align:start position:0% +this is where we finished last time +we won't we may not even get to the part + + align:start position:0% +we won't we may not even get to the part + + + align:start position:0% +we won't we may not even get to the part +on hormones and brain development and + + align:start position:0% +on hormones and brain development and + + + align:start position:0% +on hormones and brain development and +effects on the brain but + + align:start position:0% +effects on the brain but + + + align:start position:0% +effects on the brain but +we may just do most of that with the + + align:start position:0% +we may just do most of that with the + + + align:start position:0% +we may just do most of that with the +reading because I really need the time + + align:start position:0% +reading because I really need the time + + + align:start position:0% +reading because I really need the time +to + + align:start position:0% +to + + + align:start position:0% +to +talk to you about the + + align:start position:0% +talk to you about the + + + align:start position:0% +talk to you about the +recent changes in understanding of the + + align:start position:0% +recent changes in understanding of the + + + align:start position:0% +recent changes in understanding of the +hippocampus and the pathways related to + + align:start position:0% +hippocampus and the pathways related to + + + align:start position:0% +hippocampus and the pathways related to +it + + align:start position:0% + + + + align:start position:0% + +okay we + + align:start position:0% + + + + align:start position:0% + +we answered this question + + align:start position:0% + + + + align:start position:0% + +the information about the internal + + align:start position:0% +the information about the internal + + + align:start position:0% +the information about the internal +environment of the body reaches the + + align:start position:0% +environment of the body reaches the + + + align:start position:0% +environment of the body reaches the +hypothalamus by both the bloodstream and + + align:start position:0% +hypothalamus by both the bloodstream and + + + align:start position:0% +hypothalamus by both the bloodstream and +sensory pathways + + align:start position:0% +sensory pathways + + + align:start position:0% +sensory pathways +and then I asked this about well how do + + align:start position:0% +and then I asked this about well how do + + + align:start position:0% +and then I asked this about well how do +these molecules even get in the brain we + + align:start position:0% +these molecules even get in the brain we + + + align:start position:0% +these molecules even get in the brain we +know that there's a blood brain barrier + + align:start position:0% + + + + align:start position:0% + +small molecules can get in but not the + + align:start position:0% +small molecules can get in but not the + + + align:start position:0% +small molecules can get in but not the +larger organic molecules so and yet + + align:start position:0% +larger organic molecules so and yet + + + align:start position:0% +larger organic molecules so and yet +things like Angiotensin II + + align:start position:0% +things like Angiotensin II + + + align:start position:0% +things like Angiotensin II +do get in but they get in only at + + align:start position:0% +do get in but they get in only at + + + align:start position:0% +do get in but they get in only at +certain places places where the + + align:start position:0% +certain places places where the + + + align:start position:0% +certain places places where the +blood-brain barrier is weak + + align:start position:0% +blood-brain barrier is weak + + + align:start position:0% +blood-brain barrier is weak +I think the figure in the book is a + + align:start position:0% +I think the figure in the book is a + + + align:start position:0% +I think the figure in the book is a +little better than this one but this is + + align:start position:0% +little better than this one but this is + + + align:start position:0% +little better than this one but this is +a similar one it just shows the + + align:start position:0% +a similar one it just shows the + + + align:start position:0% +a similar one it just shows the +sites in the walls of the third and + + align:start position:0% +sites in the walls of the third and + + + align:start position:0% +sites in the walls of the third and +fourth ventricles where the blood-brain + + align:start position:0% +fourth ventricles where the blood-brain + + + align:start position:0% +fourth ventricles where the blood-brain +barriers lacking once you hear about + + align:start position:0% +barriers lacking once you hear about + + + align:start position:0% +barriers lacking once you hear about +here mainly we talked very early about + + align:start position:0% +here mainly we talked very early about + + + align:start position:0% +here mainly we talked very early about +the area of postrema where toxins in the + + align:start position:0% +the area of postrema where toxins in the + + + align:start position:0% +the area of postrema where toxins in the +blood can get in and elicit vomiting + + align:start position:0% +blood can get in and elicit vomiting + + + align:start position:0% +blood can get in and elicit vomiting +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the subpornical organ + + align:start position:0% +the subpornical organ + + + align:start position:0% +the subpornical organ +has a weak blood brain barrier and + + align:start position:0% +has a weak blood brain barrier and + + + align:start position:0% +has a weak blood brain barrier and +the + + align:start position:0% +the + + + align:start position:0% +the +the median Eminence of a hypothalamus + + align:start position:0% +the median Eminence of a hypothalamus + + + align:start position:0% +the median Eminence of a hypothalamus +and that's where I want to look now just + + align:start position:0% +and that's where I want to look now just + + + align:start position:0% +and that's where I want to look now just +to show you an experiment + + align:start position:0% +to show you an experiment + + + align:start position:0% +to show you an experiment +on the blood-brain barrier this is where + + align:start position:0% +on the blood-brain barrier this is where + + + align:start position:0% +on the blood-brain barrier this is where +with injection of horseradish peroxidase + + align:start position:0% +with injection of horseradish peroxidase + + + align:start position:0% +with injection of horseradish peroxidase +which is a tracer because it's + + align:start position:0% +which is a tracer because it's + + + align:start position:0% +which is a tracer because it's +transported + + align:start position:0% +transported + + + align:start position:0% +transported +though they enter greatly and retrograde + + align:start position:0% +though they enter greatly and retrograde + + + align:start position:0% +though they enter greatly and retrograde +the in axons but if you just put it in + + align:start position:0% +the in axons but if you just put it in + + + align:start position:0% +the in axons but if you just put it in +the bloodstream not in the brain + + align:start position:0% + + + + align:start position:0% + +it doesn't get in the brain everywhere + + align:start position:0% +it doesn't get in the brain everywhere + + + align:start position:0% +it doesn't get in the brain everywhere +just where the blood-brain barrier is + + align:start position:0% +just where the blood-brain barrier is + + + align:start position:0% +just where the blood-brain barrier is +weak + + align:start position:0% +weak + + + align:start position:0% +weak +and so here we are at the base of the + + align:start position:0% +and so here we are at the base of the + + + align:start position:0% +and so here we are at the base of the +third ventricle + + align:start position:0% +third ventricle + + + align:start position:0% +third ventricle +so we're in the hypothalamic region this + + align:start position:0% +so we're in the hypothalamic region this + + + align:start position:0% +so we're in the hypothalamic region this +region is called the median eminence uh + + align:start position:0% +region is called the median eminence uh + + + align:start position:0% +region is called the median eminence uh +it's near the stock of the pituitary + + align:start position:0% +it's near the stock of the pituitary + + + align:start position:0% +it's near the stock of the pituitary +and and most of the hyper problems here + + align:start position:0% +and and most of the hyper problems here + + + align:start position:0% +and and most of the hyper problems here +and of course Thalamus and other areas + + align:start position:0% +and of course Thalamus and other areas + + + align:start position:0% +and of course Thalamus and other areas +that you can't see here you see the hrp + + align:start position:0% +that you can't see here you see the hrp + + + align:start position:0% +that you can't see here you see the hrp +in the blood so it's in the + + align:start position:0% +in the blood so it's in the + + + align:start position:0% +in the blood so it's in the +crappelleries these are all little + + align:start position:0% +crappelleries these are all little + + + align:start position:0% +crappelleries these are all little +capillaries and some larger vessels + + align:start position:0% +capillaries and some larger vessels + + + align:start position:0% +capillaries and some larger vessels +it's always + + align:start position:0% +it's always + + + align:start position:0% +it's always +with this particular method it's uh + + align:start position:0% +with this particular method it's uh + + + align:start position:0% +with this particular method it's uh +showing as bright white + + align:start position:0% +showing as bright white + + + align:start position:0% +showing as bright white +but look at the median eminence + + align:start position:0% +but look at the median eminence + + + align:start position:0% +but look at the median eminence +the hrp is + + align:start position:0% +the hrp is + + + align:start position:0% +the hrp is +pervades the tissue and the median + + align:start position:0% +pervades the tissue and the median + + + align:start position:0% +pervades the tissue and the median +eminence + + align:start position:0% +eminence + + + align:start position:0% +eminence +and that's the kind of experiments that + + align:start position:0% +and that's the kind of experiments that + + + align:start position:0% +and that's the kind of experiments that +have been done now in a number of + + align:start position:0% +have been done now in a number of + + + align:start position:0% +have been done now in a number of +different animals to show + + align:start position:0% +different animals to show + + + align:start position:0% +different animals to show +you know these areas + + align:start position:0% +you know these areas + + + align:start position:0% +you know these areas +and in those areas there's always + + align:start position:0% +and in those areas there's always + + + align:start position:0% +and in those areas there's always +receptors + + align:start position:0% + + + + align:start position:0% + +in neurons generally that respond to + + align:start position:0% +in neurons generally that respond to + + + align:start position:0% +in neurons generally that respond to +specific things + + align:start position:0% +specific things + + + align:start position:0% +specific things +like Angiotensin for example + + align:start position:0% +like Angiotensin for example + + + align:start position:0% +like Angiotensin for example +and other things that + + align:start position:0% +and other things that + + + align:start position:0% +and other things that +here in the median Eminence you would + + align:start position:0% +here in the median Eminence you would + + + align:start position:0% +here in the median Eminence you would +have sexual hormones for example + + align:start position:0% +have sexual hormones for example + + + align:start position:0% +have sexual hormones for example +secreted by the gonads that can affect + + align:start position:0% +secreted by the gonads that can affect + + + align:start position:0% +secreted by the gonads that can affect +the brain by + + align:start position:0% +the brain by + + + align:start position:0% +the brain by +getting in in this in this route + + align:start position:0% +getting in in this in this route + + + align:start position:0% +getting in in this in this route +now what about sensory inputs + + align:start position:0% +now what about sensory inputs + + + align:start position:0% +now what about sensory inputs +well we know the vagus nerve carries + + align:start position:0% +well we know the vagus nerve carries + + + align:start position:0% +well we know the vagus nerve carries +inputs about pain temperature stomach + + align:start position:0% +inputs about pain temperature stomach + + + align:start position:0% +inputs about pain temperature stomach +distension + + align:start position:0% +distension + + + align:start position:0% +distension +other visceral inputs uh and and there's + + align:start position:0% +other visceral inputs uh and and there's + + + align:start position:0% +other visceral inputs uh and and there's +also inputs coming from the sacral + + align:start position:0% +also inputs coming from the sacral + + + align:start position:0% +also inputs coming from the sacral +region + + align:start position:0% +region + + + align:start position:0% +region +[Music] + + align:start position:0% + + + + align:start position:0% + +including inputs from the genital region + + align:start position:0% +including inputs from the genital region + + + align:start position:0% +including inputs from the genital region +and basically the lower of Israel and uh + + align:start position:0% + + + + align:start position:0% + +just come in through the dorsal Roots + + align:start position:0% +just come in through the dorsal Roots + + + align:start position:0% +just come in through the dorsal Roots +Pathways carrying pain information for + + align:start position:0% +Pathways carrying pain information for + + + align:start position:0% +Pathways carrying pain information for +example and there this is an interesting + + align:start position:0% +example and there this is an interesting + + + align:start position:0% +example and there this is an interesting +one because pain information can reach + + align:start position:0% +one because pain information can reach + + + align:start position:0% +one because pain information can reach +the hypothalamus directly + + align:start position:0% +the hypothalamus directly + + + align:start position:0% +the hypothalamus directly +from secondary Sensory neurons and + + align:start position:0% +from secondary Sensory neurons and + + + align:start position:0% +from secondary Sensory neurons and +tertiary Sensory neurons in the spinal + + align:start position:0% +tertiary Sensory neurons in the spinal + + + align:start position:0% +tertiary Sensory neurons in the spinal +cord so it comes directly from the + + align:start position:0% +cord so it comes directly from the + + + align:start position:0% +cord so it comes directly from the +dorsal horn + + align:start position:0% +dorsal horn + + + align:start position:0% +dorsal horn +there are long Pathways that do reach + + align:start position:0% +there are long Pathways that do reach + + + align:start position:0% +there are long Pathways that do reach +the hypothalamus + + align:start position:0% + + + + align:start position:0% + +it's a mystical pathway that I don't + + align:start position:0% +it's a mystical pathway that I don't + + + align:start position:0% +it's a mystical pathway that I don't +think I mentioned it's not a real large + + align:start position:0% +think I mentioned it's not a real large + + + align:start position:0% +think I mentioned it's not a real large +one but it does exist and could be very + + align:start position:0% +one but it does exist and could be very + + + align:start position:0% +one but it does exist and could be very +important + + align:start position:0% +important + + + align:start position:0% +important +responses to pain + + align:start position:0% +responses to pain + + + align:start position:0% +responses to pain +we know it that pain elicits + + align:start position:0% +we know it that pain elicits + + + align:start position:0% +we know it that pain elicits +activation of + + align:start position:0% +activation of + + + align:start position:0% +activation of +the sympathetic nervous system and + + align:start position:0% +the sympathetic nervous system and + + + align:start position:0% +the sympathetic nervous system and +results in + + align:start position:0% +results in + + + align:start position:0% +results in +inhibition of most parasympathetic + + align:start position:0% +inhibition of most parasympathetic + + + align:start position:0% +inhibition of most parasympathetic +functions + + align:start position:0% +functions + + + align:start position:0% +functions +and it does so very quickly through this + + align:start position:0% +and it does so very quickly through this + + + align:start position:0% +and it does so very quickly through this +pathway + + align:start position:0% + + + + align:start position:0% + +okay then there's inputs + + align:start position:0% + + + + align:start position:0% + +from neurons in the hypothalamus that + + align:start position:0% +from neurons in the hypothalamus that + + + align:start position:0% +from neurons in the hypothalamus that +respond to temperature + + align:start position:0% +respond to temperature + + + align:start position:0% +respond to temperature +or to the osmolarity of the blood + + align:start position:0% + + + + align:start position:0% + +if you required from those neurons for + + align:start position:0% +if you required from those neurons for + + + align:start position:0% +if you required from those neurons for +example I may have mentioned this we've + + align:start position:0% +example I may have mentioned this we've + + + align:start position:0% +example I may have mentioned this we've +talked about + + align:start position:0% +talked about + + + align:start position:0% +talked about +hypothalamic about regulation of the + + align:start position:0% +hypothalamic about regulation of the + + + align:start position:0% +hypothalamic about regulation of the +internal environment before but these + + align:start position:0% +internal environment before but these + + + align:start position:0% +internal environment before but these +these neurons + + align:start position:0% +these neurons + + + align:start position:0% +these neurons +change their firing in very precise ways + + align:start position:0% +change their firing in very precise ways + + + align:start position:0% +change their firing in very precise ways +with the temperature + + align:start position:0% + + + + align:start position:0% + +obviously pretty important for the brain + + align:start position:0% +obviously pretty important for the brain + + + align:start position:0% +obviously pretty important for the brain +to get that information it's going to + + align:start position:0% +to get that information it's going to + + + align:start position:0% +to get that information it's going to +control temperature regulating + + align:start position:0% +control temperature regulating + + + align:start position:0% +control temperature regulating +mechanisms + + align:start position:0% + + + + align:start position:0% + +they're in the anterior hypothalamic + + align:start position:0% +they're in the anterior hypothalamic + + + align:start position:0% +they're in the anterior hypothalamic +region and then we know there's some + + align:start position:0% +region and then we know there's some + + + align:start position:0% +region and then we know there's some +olfactory inputs that reach pretty + + align:start position:0% +olfactory inputs that reach pretty + + + align:start position:0% +olfactory inputs that reach pretty +directly impact many + + align:start position:0% +directly impact many + + + align:start position:0% +directly impact many +many lore animals the old factory bulbs + + align:start position:0% +many lore animals the old factory bulbs + + + align:start position:0% +many lore animals the old factory bulbs +project directly into the hypothalamus + + align:start position:0% + + + + align:start position:0% + +but they project indirectly therein + + align:start position:0% +but they project indirectly therein + + + align:start position:0% +but they project indirectly therein +in + + align:start position:0% +in + + + align:start position:0% +in +all the vertebrates + + align:start position:0% +all the vertebrates + + + align:start position:0% +all the vertebrates +and we know the retina projects directly + + align:start position:0% +and we know the retina projects directly + + + align:start position:0% +and we know the retina projects directly +to the hypothalamus + + align:start position:0% +to the hypothalamus + + + align:start position:0% +to the hypothalamus +mainly to the superchiasmatic nucleus + + align:start position:0% +mainly to the superchiasmatic nucleus + + + align:start position:0% +mainly to the superchiasmatic nucleus +where you have the biological clock + + align:start position:0% +where you have the biological clock + + + align:start position:0% +where you have the biological clock +mechanism but we there's other regions + + align:start position:0% +mechanism but we there's other regions + + + align:start position:0% +mechanism but we there's other regions +too that get sparser inputs from the + + align:start position:0% +too that get sparser inputs from the + + + align:start position:0% +too that get sparser inputs from the +retina we talked about that + + align:start position:0% +retina we talked about that + + + align:start position:0% +retina we talked about that +in uh chapter 20. + + align:start position:0% + + + + align:start position:0% + +okay now I want to start talking about + + align:start position:0% +okay now I want to start talking about + + + align:start position:0% +okay now I want to start talking about +some of the circuitry that links + + align:start position:0% +some of the circuitry that links + + + align:start position:0% +some of the circuitry that links +hypothalamus + + align:start position:0% +hypothalamus + + + align:start position:0% +hypothalamus +to + + align:start position:0% +to + + + align:start position:0% +to +end brain structures + + align:start position:0% +end brain structures + + + align:start position:0% +end brain structures +the limbic in brain structures + + align:start position:0% +the limbic in brain structures + + + align:start position:0% +the limbic in brain structures +and + + align:start position:0% +and + + + align:start position:0% +and +these studies were given a lot of + + align:start position:0% +these studies were given a lot of + + + align:start position:0% +these studies were given a lot of +impetus by James papes a neuronatomist + + align:start position:0% +impetus by James papes a neuronatomist + + + align:start position:0% +impetus by James papes a neuronatomist +working at Cornell in the 1930s + + align:start position:0% +working at Cornell in the 1930s + + + align:start position:0% +working at Cornell in the 1930s +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and there's been a big Revival of + + align:start position:0% +and there's been a big Revival of + + + align:start position:0% +and there's been a big Revival of +interest in that circuit I mean there + + align:start position:0% +interest in that circuit I mean there + + + align:start position:0% +interest in that circuit I mean there +are a few neuroanatomy texts for medical + + align:start position:0% +are a few neuroanatomy texts for medical + + + align:start position:0% +are a few neuroanatomy texts for medical +schools that don't even mention James + + align:start position:0% +schools that don't even mention James + + + align:start position:0% +schools that don't even mention James +peeps anymore + + align:start position:0% +peeps anymore + + + align:start position:0% +peeps anymore +but that's because they're not keeping + + align:start position:0% +but that's because they're not keeping + + + align:start position:0% +but that's because they're not keeping +up with all the recent uh + + align:start position:0% +up with all the recent uh + + + align:start position:0% +up with all the recent uh +interest in + + align:start position:0% +interest in + + + align:start position:0% +interest in +in research labs in some of these + + align:start position:0% +in research labs in some of these + + + align:start position:0% +in research labs in some of these +Pathways so I want to go through + + align:start position:0% +Pathways so I want to go through + + + align:start position:0% +Pathways so I want to go through +so we talk about Peach circuit which is + + align:start position:0% +so we talk about Peach circuit which is + + + align:start position:0% +so we talk about Peach circuit which is +interesting because it it's a complete + + align:start position:0% +interesting because it it's a complete + + + align:start position:0% +interesting because it it's a complete +circuit + + align:start position:0% +circuit + + + align:start position:0% +circuit +uh + + align:start position:0% +uh + + + align:start position:0% +uh +if you start you can start any point in + + align:start position:0% +if you start you can start any point in + + + align:start position:0% +if you start you can start any point in +but if you go to the singular cortex we + + align:start position:0% +but if you go to the singular cortex we + + + align:start position:0% +but if you go to the singular cortex we +know that cingulate is one of the + + align:start position:0% +know that cingulate is one of the + + + align:start position:0% +know that cingulate is one of the +paralympic areas that + + align:start position:0% +paralympic areas that + + + align:start position:0% +paralympic areas that +sends projections to hippocampal para + + align:start position:0% +sends projections to hippocampal para + + + align:start position:0% +sends projections to hippocampal para +hippocampal regions which then project + + align:start position:0% +hippocampal regions which then project + + + align:start position:0% +hippocampal regions which then project +directly into the hippocampus + + align:start position:0% +directly into the hippocampus + + + align:start position:0% +directly into the hippocampus +and the hippocampus then projects + + align:start position:0% + + + + align:start position:0% + +to subclitical Regions through the + + align:start position:0% +to subclitical Regions through the + + + align:start position:0% +to subclitical Regions through the +fornix major a major output not the only + + align:start position:0% +fornix major a major output not the only + + + align:start position:0% +fornix major a major output not the only +output but a major it's the major output + + align:start position:0% +output but a major it's the major output + + + align:start position:0% +output but a major it's the major output +going subcortically + + align:start position:0% +going subcortically + + + align:start position:0% +going subcortically +it goes to the subtle area but it + + align:start position:0% +it goes to the subtle area but it + + + align:start position:0% +it goes to the subtle area but it +continues long actions continue right + + align:start position:0% +continues long actions continue right + + + align:start position:0% +continues long actions continue right +to the height of powerless + + align:start position:0% +to the height of powerless + + + align:start position:0% +to the height of powerless +most of them terminate in the mammary + + align:start position:0% +most of them terminate in the mammary + + + align:start position:0% +most of them terminate in the mammary +bodies at the very caudal into the + + align:start position:0% +bodies at the very caudal into the + + + align:start position:0% +bodies at the very caudal into the +hypothalamus + + align:start position:0% + + + + align:start position:0% + +and that those structures + + align:start position:0% +and that those structures + + + align:start position:0% +and that those structures +project to the thalamus the anterior + + align:start position:0% +project to the thalamus the anterior + + + align:start position:0% +project to the thalamus the anterior +nuclei which connects to singular cortex + + align:start position:0% +nuclei which connects to singular cortex + + + align:start position:0% +nuclei which connects to singular cortex +so it forms then a complete Loop + + align:start position:0% + + + + align:start position:0% + +so papes published this paper in 1937 it + + align:start position:0% +so papes published this paper in 1937 it + + + align:start position:0% +so papes published this paper in 1937 it +was called a proposed mechanism of + + align:start position:0% +was called a proposed mechanism of + + + align:start position:0% +was called a proposed mechanism of +emotion + + align:start position:0% +emotion + + + align:start position:0% +emotion +and basically he argued that people had + + align:start position:0% +and basically he argued that people had + + + align:start position:0% +and basically he argued that people had +Associated a group of structures + + align:start position:0% +Associated a group of structures + + + align:start position:0% +Associated a group of structures +in the + + align:start position:0% +in the + + + align:start position:0% +in the +forebrain especially the end brain with + + align:start position:0% +forebrain especially the end brain with + + + align:start position:0% +forebrain especially the end brain with +olfaction + + align:start position:0% +olfaction + + + align:start position:0% +olfaction +and he said they weren't really + + align:start position:0% +and he said they weren't really + + + align:start position:0% +and he said they weren't really +olfactory in humans + + align:start position:0% +olfactory in humans + + + align:start position:0% +olfactory in humans +because the clinical information and he + + align:start position:0% +because the clinical information and he + + + align:start position:0% +because the clinical information and he +reviewed it a lot of it + + align:start position:0% +reviewed it a lot of it + + + align:start position:0% +reviewed it a lot of it +indicates if it really involved in + + align:start position:0% +indicates if it really involved in + + + align:start position:0% +indicates if it really involved in +Emotion emotional expression uh + + align:start position:0% +Emotion emotional expression uh + + + align:start position:0% +Emotion emotional expression uh +emotional disturbances + + align:start position:0% +emotional disturbances + + + align:start position:0% +emotional disturbances +and + + align:start position:0% + + + + align:start position:0% + +the feelings accompanying emotions + + align:start position:0% +the feelings accompanying emotions + + + align:start position:0% +the feelings accompanying emotions +and they + + align:start position:0% +and they + + + align:start position:0% +and they +he also noted one other thing that + + align:start position:0% +he also noted one other thing that + + + align:start position:0% +he also noted one other thing that +people often forget about they have a + + align:start position:0% +people often forget about they have a + + + align:start position:0% +people often forget about they have a +low threshold procedure so seizures that + + align:start position:0% +low threshold procedure so seizures that + + + align:start position:0% +low threshold procedure so seizures that +tend to start in one of these structures + + align:start position:0% +tend to start in one of these structures + + + align:start position:0% +tend to start in one of these structures +will spread through all of them because + + align:start position:0% +will spread through all of them because + + + align:start position:0% +will spread through all of them because +they're closely interconnected which was + + align:start position:0% +they're closely interconnected which was + + + align:start position:0% +they're closely interconnected which was +one of his arguments remember he didn't + + align:start position:0% +one of his arguments remember he didn't + + + align:start position:0% +one of his arguments remember he didn't +have the + + align:start position:0% +have the + + + align:start position:0% +have the +the precise neuranatomical methods that + + align:start position:0% +the precise neuranatomical methods that + + + align:start position:0% +the precise neuranatomical methods that +we have now + + align:start position:0% +we have now + + + align:start position:0% +we have now +and believe me diffusion tester Imaging + + align:start position:0% +and believe me diffusion tester Imaging + + + align:start position:0% +and believe me diffusion tester Imaging +is not going to give you these + + align:start position:0% +is not going to give you these + + + align:start position:0% +is not going to give you these +connections adequately + + align:start position:0% +connections adequately + + + align:start position:0% +connections adequately +you know to tell you the main tracks + + align:start position:0% +you know to tell you the main tracks + + + align:start position:0% +you know to tell you the main tracks +it's not useful for this you need good + + align:start position:0% +it's not useful for this you need good + + + align:start position:0% +it's not useful for this you need good +anatomical techniques + + align:start position:0% +anatomical techniques + + + align:start position:0% +anatomical techniques +where you can use animals to do + + align:start position:0% +where you can use animals to do + + + align:start position:0% +where you can use animals to do +experiments and Trace connections to + + align:start position:0% +experiments and Trace connections to + + + align:start position:0% +experiments and Trace connections to +synaptic endings + + align:start position:0% +synaptic endings + + + align:start position:0% +synaptic endings +but papes was remarkably accurate in his + + align:start position:0% +but papes was remarkably accurate in his + + + align:start position:0% +but papes was remarkably accurate in his +basic description of the circuit + + align:start position:0% +basic description of the circuit + + + align:start position:0% +basic description of the circuit +based on clinical work + + align:start position:0% + + + + align:start position:0% + +but now we can take that original + + align:start position:0% +but now we can take that original + + + align:start position:0% +but now we can take that original +Circuit of his and show + + align:start position:0% +Circuit of his and show + + + align:start position:0% +Circuit of his and show +expanded a little bit from + + align:start position:0% +expanded a little bit from + + + align:start position:0% +expanded a little bit from +more recent studies using experimental + + align:start position:0% +more recent studies using experimental + + + align:start position:0% +more recent studies using experimental +or anatomical techniques of the Nara + + align:start position:0% +or anatomical techniques of the Nara + + + align:start position:0% +or anatomical techniques of the Nara +type okay and many people that have + + align:start position:0% +type okay and many people that have + + + align:start position:0% +type okay and many people that have +followed maora with various kinds of + + align:start position:0% +followed maora with various kinds of + + + align:start position:0% +followed maora with various kinds of +track tracing techniques + + align:start position:0% + + + + align:start position:0% + +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +I should also point out here that it was + + align:start position:0% +I should also point out here that it was + + + align:start position:0% +I should also point out here that it was +during this time after papes that the + + align:start position:0% +during this time after papes that the + + + align:start position:0% +during this time after papes that the +term limbic system was coined based on + + align:start position:0% +term limbic system was coined based on + + + align:start position:0% +term limbic system was coined based on +Broca's term the great limbic lobe + + align:start position:0% +Broca's term the great limbic lobe + + + align:start position:0% +Broca's term the great limbic lobe +uh but + + align:start position:0% +uh but + + + align:start position:0% +uh but +in modern times it was Paul McClain at + + align:start position:0% +in modern times it was Paul McClain at + + + align:start position:0% +in modern times it was Paul McClain at +the National Institute Health colleague + + align:start position:0% +the National Institute Health colleague + + + align:start position:0% +the National Institute Health colleague +of notice + + align:start position:0% +of notice + + + align:start position:0% +of notice +uh + + align:start position:0% +uh + + + align:start position:0% +uh +that actually coined that term + + align:start position:0% +that actually coined that term + + + align:start position:0% +that actually coined that term +the limbic system + + align:start position:0% +the limbic system + + + align:start position:0% +the limbic system +and now to then extended it into their + + align:start position:0% +and now to then extended it into their + + + align:start position:0% +and now to then extended it into their +midbrain + + align:start position:0% +midbrain + + + align:start position:0% +midbrain +and did a number of studies of + + align:start position:0% +and did a number of studies of + + + align:start position:0% +and did a number of studies of +connections of that system in in the end + + align:start position:0% +connections of that system in in the end + + + align:start position:0% +connections of that system in in the end +brain + + align:start position:0% + + + + align:start position:0% + +but I'll focus on the way our + + align:start position:0% +but I'll focus on the way our + + + align:start position:0% +but I'll focus on the way our +understanding of the system has changed + + align:start position:0% +understanding of the system has changed + + + align:start position:0% +understanding of the system has changed +that won't sound like we're discussing + + align:start position:0% +that won't sound like we're discussing + + + align:start position:0% +that won't sound like we're discussing +mechanisms of emotion for the most part + + align:start position:0% +mechanisms of emotion for the most part + + + align:start position:0% +mechanisms of emotion for the most part +but we will we will get to that also + + align:start position:0% +but we will we will get to that also + + + align:start position:0% +but we will we will get to that also +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the the reason there's such a Revival of + + align:start position:0% +the the reason there's such a Revival of + + + align:start position:0% +the the reason there's such a Revival of +interest of course is because of the + + align:start position:0% +interest of course is because of the + + + align:start position:0% +interest of course is because of the +involvement of the hippocampus in + + align:start position:0% +involvement of the hippocampus in + + + align:start position:0% +involvement of the hippocampus in +in memory for long-term memory formation + + align:start position:0% +in memory for long-term memory formation + + + align:start position:0% +in memory for long-term memory formation +and what we call it exotic memory not + + align:start position:0% +and what we call it exotic memory not + + + align:start position:0% +and what we call it exotic memory not +habit formation not striatal memory + + align:start position:0% +habit formation not striatal memory + + + align:start position:0% +habit formation not striatal memory +which we've mentioned a number of times + + align:start position:0% + + + + align:start position:0% + +but the kind of memory that we usually + + align:start position:0% +but the kind of memory that we usually + + + align:start position:0% +but the kind of memory that we usually +mean when we say I remember something + + align:start position:0% +mean when we say I remember something + + + align:start position:0% +mean when we say I remember something +yes I remember something and something + + align:start position:0% +yes I remember something and something + + + align:start position:0% +yes I remember something and something +happened I remember something that + + align:start position:0% +happened I remember something that + + + align:start position:0% +happened I remember something that +happened over there + + align:start position:0% +happened over there + + + align:start position:0% +happened over there +that's what we're talking about here and + + align:start position:0% +that's what we're talking about here and + + + align:start position:0% +that's what we're talking about here and +that certainly adds to the importance of + + align:start position:0% +that certainly adds to the importance of + + + align:start position:0% +that certainly adds to the importance of +understanding these circuits and how + + align:start position:0% +understanding these circuits and how + + + align:start position:0% +understanding these circuits and how +they work now if you look at a medical + + align:start position:0% +they work now if you look at a medical + + + align:start position:0% +they work now if you look at a medical +school text you're likely to see + + align:start position:0% +school text you're likely to see + + + align:start position:0% +school text you're likely to see +something like this + + align:start position:0% +something like this + + + align:start position:0% +something like this +just to + + align:start position:0% +just to + + + align:start position:0% +just to +show you it can be really difficult + + align:start position:0% +show you it can be really difficult + + + align:start position:0% +show you it can be really difficult +because they only give you human brain + + align:start position:0% +because they only give you human brain + + + align:start position:0% +because they only give you human brain +so I'm not going to do that I want to + + align:start position:0% +so I'm not going to do that I want to + + + align:start position:0% +so I'm not going to do that I want to +expect you to you will understand it + + align:start position:0% +expect you to you will understand it + + + align:start position:0% +expect you to you will understand it +once you begin to understand the + + align:start position:0% +once you begin to understand the + + + align:start position:0% +once you begin to understand the +circuitry + + align:start position:0% +circuitry + + + align:start position:0% +circuitry +so we're going to take our diagrams here + + align:start position:0% +so we're going to take our diagrams here + + + align:start position:0% +so we're going to take our diagrams here +of the mammalian brain let's take this + + align:start position:0% +of the mammalian brain let's take this + + + align:start position:0% +of the mammalian brain let's take this +one and turn it around like this + + align:start position:0% +one and turn it around like this + + + align:start position:0% +one and turn it around like this +and now let's just slice off the + + align:start position:0% +and now let's just slice off the + + + align:start position:0% +and now let's just slice off the +hemispheres like this + + align:start position:0% +hemispheres like this + + + align:start position:0% +hemispheres like this +okay we'll throw this one away + + align:start position:0% + + + + align:start position:0% + +and turn this on its side so we get this + + align:start position:0% +and turn this on its side so we get this + + + align:start position:0% +and turn this on its side so we get this +here's the hemisphere up here and here's + + align:start position:0% +here's the hemisphere up here and here's + + + align:start position:0% +here's the hemisphere up here and here's +the brain stem down here + + align:start position:0% + + + + align:start position:0% + +we're looking at it from the side + + align:start position:0% +we're looking at it from the side + + + align:start position:0% +we're looking at it from the side +showing where some of the a few of the + + align:start position:0% +showing where some of the a few of the + + + align:start position:0% +showing where some of the a few of the +pathways are + + align:start position:0% +pathways are + + + align:start position:0% +pathways are +so we made the brain transparent + + align:start position:0% +so we made the brain transparent + + + align:start position:0% +so we made the brain transparent +and the same here in the hemisphere + + align:start position:0% +and the same here in the hemisphere + + + align:start position:0% +and the same here in the hemisphere +where I've shown the campus there + + align:start position:0% +where I've shown the campus there + + + align:start position:0% +where I've shown the campus there +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and now + + align:start position:0% +and now + + + align:start position:0% +and now +I want to know how this was the original + + align:start position:0% +I want to know how this was the original + + + align:start position:0% +I want to know how this was the original +figure here I want to show you where you + + align:start position:0% +figure here I want to show you where you + + + align:start position:0% +figure here I want to show you where you +get tight circuit in that very straight + + align:start position:0% +get tight circuit in that very straight + + + align:start position:0% +get tight circuit in that very straight +quote + + align:start position:0% +quote + + + align:start position:0% +quote +okay so let's start this time with the + + align:start position:0% +okay so let's start this time with the + + + align:start position:0% +okay so let's start this time with the +mammary bodies here we are at the caudal + + align:start position:0% +mammary bodies here we are at the caudal + + + align:start position:0% +mammary bodies here we are at the caudal +in the hypothalance + + align:start position:0% +in the hypothalance + + + align:start position:0% +in the hypothalance +the mammillary bodies project by a very + + align:start position:0% +the mammillary bodies project by a very + + + align:start position:0% +the mammillary bodies project by a very +direct route you always see this in + + align:start position:0% +direct route you always see this in + + + align:start position:0% +direct route you always see this in +Cross sections you know here in the in + + align:start position:0% +Cross sections you know here in the in + + + align:start position:0% +Cross sections you know here in the in +the diencephalon + + align:start position:0% +the diencephalon + + + align:start position:0% +the diencephalon +trace the mammalo thalamic track to the + + align:start position:0% +trace the mammalo thalamic track to the + + + align:start position:0% +trace the mammalo thalamic track to the +anterior nuclei + + align:start position:0% +anterior nuclei + + + align:start position:0% +anterior nuclei +there's three main nuclei the project + + align:start position:0% +there's three main nuclei the project + + + align:start position:0% +there's three main nuclei the project +various parts + + align:start position:0% + + + + align:start position:0% + +they follow + + align:start position:0% +they follow + + + align:start position:0% +they follow +a route to the cortex through what we + + align:start position:0% +a route to the cortex through what we + + + align:start position:0% +a route to the cortex through what we +call the anterior thalanic radiation so + + align:start position:0% +call the anterior thalanic radiation so + + + align:start position:0% +call the anterior thalanic radiation so +they don't go out the side like say the + + align:start position:0% +they don't go out the side like say the + + + align:start position:0% +they don't go out the side like say the +genicular bodies do they go forward + + align:start position:0% +genicular bodies do they go forward + + + align:start position:0% +genicular bodies do they go forward +and then + + align:start position:0% + + + + align:start position:0% + +of course just above the corpus callosum + + align:start position:0% +of course just above the corpus callosum + + + align:start position:0% +of course just above the corpus callosum +throughout the entire length of the + + align:start position:0% +throughout the entire length of the + + + align:start position:0% +throughout the entire length of the +corpus callosum terminating + + align:start position:0% +corpus callosum terminating + + + align:start position:0% +corpus callosum terminating +in the singular cortex at all these + + align:start position:0% +in the singular cortex at all these + + + align:start position:0% +in the singular cortex at all these +different levels and terminating also in + + align:start position:0% +different levels and terminating also in + + + align:start position:0% +different levels and terminating also in +the area just behind us + + align:start position:0% +the area just behind us + + + align:start position:0% +the area just behind us +the close and an area we call the + + align:start position:0% +the close and an area we call the + + + align:start position:0% +the close and an area we call the +retrosplenial area meaning behind the + + align:start position:0% +retrosplenial area meaning behind the + + + align:start position:0% +retrosplenial area meaning behind the +splenium + + align:start position:0% +splenium + + + align:start position:0% +splenium +of the corpus callosum that's the caudal + + align:start position:0% +of the corpus callosum that's the caudal + + + align:start position:0% +of the corpus callosum that's the caudal +end of the Corpus clause + + align:start position:0% +end of the Corpus clause + + + align:start position:0% +end of the Corpus clause +the anterior and just the genuine + + align:start position:0% +the anterior and just the genuine + + + align:start position:0% +the anterior and just the genuine +or caudulent is explaining + + align:start position:0% +or caudulent is explaining + + + align:start position:0% +or caudulent is explaining +because of its shape in humans + + align:start position:0% +because of its shape in humans + + + align:start position:0% +because of its shape in humans +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +cingulate and these other para + + align:start position:0% +cingulate and these other para + + + align:start position:0% +cingulate and these other para +hippocampal areas including the + + align:start position:0% +hippocampal areas including the + + + align:start position:0% +hippocampal areas including the +anterional cortex which gets heavy input + + align:start position:0% +anterional cortex which gets heavy input + + + align:start position:0% +anterional cortex which gets heavy input +from the singular just polenial areas + + align:start position:0% +from the singular just polenial areas + + + align:start position:0% +from the singular just polenial areas +they project directly into the + + align:start position:0% +they project directly into the + + + align:start position:0% +they project directly into the +hippocampal formation + + align:start position:0% + + + + align:start position:0% + +and then here's the output of the + + align:start position:0% +and then here's the output of the + + + align:start position:0% +and then here's the output of the +hippocampus through these this thick + + align:start position:0% +hippocampus through these this thick + + + align:start position:0% +hippocampus through these this thick +column of fibers of course is just in + + align:start position:0% +column of fibers of course is just in + + + align:start position:0% +column of fibers of course is just in +through the call end of the septum in + + align:start position:0% +through the call end of the septum in + + + align:start position:0% +through the call end of the septum in +front of the thalamus + + align:start position:0% +front of the thalamus + + + align:start position:0% +front of the thalamus +and then because I've separated it here + + align:start position:0% +and then because I've separated it here + + + align:start position:0% +and then because I've separated it here +I pick it up again right here + + align:start position:0% +I pick it up again right here + + + align:start position:0% +I pick it up again right here +and there's the fornix columns coming + + align:start position:0% +and there's the fornix columns coming + + + align:start position:0% +and there's the fornix columns coming +through the hypothalms + + align:start position:0% +through the hypothalms + + + align:start position:0% +through the hypothalms +there are some axons that terminate on + + align:start position:0% +there are some axons that terminate on + + + align:start position:0% +there are some axons that terminate on +the weight but most of them are ending + + align:start position:0% +the weight but most of them are ending + + + align:start position:0% +the weight but most of them are ending +there on the mammary bodies okay + + align:start position:0% +there on the mammary bodies okay + + + align:start position:0% +there on the mammary bodies okay +so now let's take that circuit + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and see how + + align:start position:0% +and see how + + + align:start position:0% +and see how +I mean just a circuit what good is that + + align:start position:0% +I mean just a circuit what good is that + + + align:start position:0% +I mean just a circuit what good is that +you've got to know what's coming into it + + align:start position:0% +you've got to know what's coming into it + + + align:start position:0% +you've got to know what's coming into it +what's coming out of it you know what is + + align:start position:0% +what's coming out of it you know what is + + + align:start position:0% +what's coming out of it you know what is +it and what purpose what kind of + + align:start position:0% +it and what purpose what kind of + + + align:start position:0% +it and what purpose what kind of +information is it here + + align:start position:0% +information is it here + + + align:start position:0% +information is it here +and there we were initially the anatomy + + align:start position:0% +and there we were initially the anatomy + + + align:start position:0% +and there we were initially the anatomy +was way ahead of the physiology + + align:start position:0% +was way ahead of the physiology + + + align:start position:0% +was way ahead of the physiology +but then the anatomy was done well + + align:start position:0% +but then the anatomy was done well + + + align:start position:0% +but then the anatomy was done well +enough that the physiologists had better + + align:start position:0% +enough that the physiologists had better + + + align:start position:0% +enough that the physiologists had better +guides and they started doing + + align:start position:0% +guides and they started doing + + + align:start position:0% +guides and they started doing +different kinds of study so I'm going to + + align:start position:0% +different kinds of study so I'm going to + + + align:start position:0% +different kinds of study so I'm going to +talk about some physiology here + + align:start position:0% +talk about some physiology here + + + align:start position:0% +talk about some physiology here +okay so here's the diagram + + align:start position:0% +okay so here's the diagram + + + align:start position:0% +okay so here's the diagram +up to a more up-to-date version of paid + + align:start position:0% +up to a more up-to-date version of paid + + + align:start position:0% +up to a more up-to-date version of paid +circuit and I've shown in red the + + align:start position:0% +circuit and I've shown in red the + + + align:start position:0% +circuit and I've shown in red the +structures the tapes named + + align:start position:0% +structures the tapes named + + + align:start position:0% +structures the tapes named +for human + + align:start position:0% +for human + + + align:start position:0% +for human +analy bodies anterior nuclei + + align:start position:0% +analy bodies anterior nuclei + + + align:start position:0% +analy bodies anterior nuclei +singular cortex + + align:start position:0% +singular cortex + + + align:start position:0% +singular cortex +the hippocampal formation which includes + + align:start position:0% +the hippocampal formation which includes + + + align:start position:0% +the hippocampal formation which includes +these are the major + + align:start position:0% +these are the major + + + align:start position:0% +these are the major +components + + align:start position:0% +components + + + align:start position:0% +components +seviculum and hippocampus are one line + + align:start position:0% +seviculum and hippocampus are one line + + + align:start position:0% +seviculum and hippocampus are one line +of cells and then the dentate gyrus went + + align:start position:0% +of cells and then the dentate gyrus went + + + align:start position:0% +of cells and then the dentate gyrus went +in and we're going to be looking at that + + align:start position:0% +in and we're going to be looking at that + + + align:start position:0% +in and we're going to be looking at that +very soon in a little more detail + + align:start position:0% +very soon in a little more detail + + + align:start position:0% +very soon in a little more detail +and then there's that output the fornix + + align:start position:0% +and then there's that output the fornix + + + align:start position:0% +and then there's that output the fornix +and notice that there's a less direct + + align:start position:0% +and notice that there's a less direct + + + align:start position:0% +and notice that there's a less direct +route + + align:start position:0% +route + + + align:start position:0% +route +that goes through the subtle area + + align:start position:0% +that goes through the subtle area + + + align:start position:0% +that goes through the subtle area +to the hypothalamus as well + + align:start position:0% +to the hypothalamus as well + + + align:start position:0% +to the hypothalamus as well +so I've included all that here and I've + + align:start position:0% +so I've included all that here and I've + + + align:start position:0% +so I've included all that here and I've +included some accents that go in the + + align:start position:0% +included some accents that go in the + + + align:start position:0% +included some accents that go in the +reverse Direction and I've shown that + + align:start position:0% +reverse Direction and I've shown that + + + align:start position:0% +reverse Direction and I've shown that +many of these in fact are two-way + + align:start position:0% +many of these in fact are two-way + + + align:start position:0% +many of these in fact are two-way +connections like between singular cortex + + align:start position:0% +connections like between singular cortex + + + align:start position:0% +connections like between singular cortex +as like most cortex it gets input from + + align:start position:0% +as like most cortex it gets input from + + + align:start position:0% +as like most cortex it gets input from +the balance those coricularies project + + align:start position:0% +the balance those coricularies project + + + align:start position:0% +the balance those coricularies project +back to the thalamus too okay + + align:start position:0% + + + + align:start position:0% + +okay well + + align:start position:0% + + + + align:start position:0% + +and I'm I asked here in this question + + align:start position:0% +and I'm I asked here in this question + + + align:start position:0% +and I'm I asked here in this question +how is it connected to neocortical areas + + align:start position:0% +how is it connected to neocortical areas + + + align:start position:0% +how is it connected to neocortical areas +well let's look right here see this + + align:start position:0% +well let's look right here see this + + + align:start position:0% +well let's look right here see this +wasn't discussed so much by papes but we + + align:start position:0% +wasn't discussed so much by papes but we + + + align:start position:0% +wasn't discussed so much by papes but we +know that + + align:start position:0% +know that + + + align:start position:0% +know that +these singular areas + + align:start position:0% +these singular areas + + + align:start position:0% +these singular areas +and other paralympic areas like the + + align:start position:0% +and other paralympic areas like the + + + align:start position:0% +and other paralympic areas like the +internal area are closely connected to + + align:start position:0% +internal area are closely connected to + + + align:start position:0% +internal area are closely connected to +neocortex they get major inputs from + + align:start position:0% +neocortex they get major inputs from + + + align:start position:0% +neocortex they get major inputs from +association areas not from primary + + align:start position:0% +association areas not from primary + + + align:start position:0% +association areas not from primary +sensory areas they're not getting it + + align:start position:0% +sensory areas they're not getting it + + + align:start position:0% +sensory areas they're not getting it +from visual error visual cortex or + + align:start position:0% +from visual error visual cortex or + + + align:start position:0% +from visual error visual cortex or +auditory cortex medicines or cortex so + + align:start position:0% +auditory cortex medicines or cortex so + + + align:start position:0% +auditory cortex medicines or cortex so +getting it from association areas + + align:start position:0% +getting it from association areas + + + align:start position:0% +getting it from association areas +particularly from the multimodal + + align:start position:0% +particularly from the multimodal + + + align:start position:0% +particularly from the multimodal +association areas okay + + align:start position:0% +association areas okay + + + align:start position:0% +association areas okay +it's an interesting thing those + + align:start position:0% +it's an interesting thing those + + + align:start position:0% +it's an interesting thing those +multimodal association areas are like + + align:start position:0% +multimodal association areas are like + + + align:start position:0% +multimodal association areas are like +the most primitive cortex but they're + + align:start position:0% +the most primitive cortex but they're + + + align:start position:0% +the most primitive cortex but they're +the areas that have expanded the most in + + align:start position:0% +the areas that have expanded the most in + + + align:start position:0% +the areas that have expanded the most in +recent evolution + + align:start position:0% +recent evolution + + + align:start position:0% +recent evolution +and they're getting major inputs from + + align:start position:0% +and they're getting major inputs from + + + align:start position:0% +and they're getting major inputs from +the unimodal + + align:start position:0% +the unimodal + + + align:start position:0% +the unimodal +sensory areas + + align:start position:0% + + + + align:start position:0% + +get their input from primary sensor + + align:start position:0% +get their input from primary sensor + + + align:start position:0% +get their input from primary sensor +sensors okay so the association areas + + align:start position:0% +sensors okay so the association areas + + + align:start position:0% +sensors okay so the association areas +then connect in the Pape circuit + + align:start position:0% +then connect in the Pape circuit + + + align:start position:0% +then connect in the Pape circuit +through these roots I'm showing through + + align:start position:0% +through these roots I'm showing through + + + align:start position:0% +through these roots I'm showing through +singulate + + align:start position:0% +singulate + + + align:start position:0% +singulate +uh + + align:start position:0% +uh + + + align:start position:0% +uh +retroflenial and into Rhino areas + + align:start position:0% +retroflenial and into Rhino areas + + + align:start position:0% +retroflenial and into Rhino areas +which then project directly into the + + align:start position:0% +which then project directly into the + + + align:start position:0% +which then project directly into the +cortex there are there's more than one + + align:start position:0% +cortex there are there's more than one + + + align:start position:0% +cortex there are there's more than one +group + + align:start position:0% +group + + + align:start position:0% +group +there + + align:start position:0% +there + + + align:start position:0% +there +I just indicate a couple of them + + align:start position:0% +I just indicate a couple of them + + + align:start position:0% +I just indicate a couple of them +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +what kind of signals are + + align:start position:0% +what kind of signals are + + + align:start position:0% +what kind of signals are +what is going on this route here + + align:start position:0% +what is going on this route here + + + align:start position:0% +what is going on this route here +what is the mammalary body telling the + + align:start position:0% +what is the mammalary body telling the + + + align:start position:0% +what is the mammalary body telling the +cellulocortex + + align:start position:0% +cellulocortex + + + align:start position:0% +cellulocortex +hippocampus + + align:start position:0% + + + + align:start position:0% + +concerns our sense of direction + + align:start position:0% + + + + align:start position:0% + +pain is a big surprise to many people + + align:start position:0% +pain is a big surprise to many people + + + align:start position:0% +pain is a big surprise to many people +because we were thinking all the time in + + align:start position:0% +because we were thinking all the time in + + + align:start position:0% +because we were thinking all the time in +terms of papes and emotion and all this + + align:start position:0% +terms of papes and emotion and all this + + + align:start position:0% +terms of papes and emotion and all this +but you'll see how in fact that wasn't + + align:start position:0% +but you'll see how in fact that wasn't + + + align:start position:0% +but you'll see how in fact that wasn't +wrong + + align:start position:0% + + + + align:start position:0% + +what is our sense of direction in the + + align:start position:0% +what is our sense of direction in the + + + align:start position:0% +what is our sense of direction in the +world come from + + align:start position:0% + + + + align:start position:0% + +how do you know where you are + + align:start position:0% +how do you know where you are + + + align:start position:0% +how do you know where you are +say you're taking a walk + + align:start position:0% + + + + align:start position:0% + +it's it's a little harder to think of + + align:start position:0% +it's it's a little harder to think of + + + align:start position:0% +it's it's a little harder to think of +when you're inside a building but really + + align:start position:0% +when you're inside a building but really + + + align:start position:0% +when you're inside a building but really +not that much + + align:start position:0% +not that much + + + align:start position:0% +not that much +but think of an animal walking he always + + align:start position:0% +but think of an animal walking he always + + + align:start position:0% +but think of an animal walking he always +has a sense of direction when he doesn't + + align:start position:0% +has a sense of direction when he doesn't + + + align:start position:0% +has a sense of direction when he doesn't +we say he's disoriented and we feel very + + align:start position:0% +we say he's disoriented and we feel very + + + align:start position:0% +we say he's disoriented and we feel very +disoriented well what happens + + align:start position:0% +disoriented well what happens + + + align:start position:0% +disoriented well what happens +when we lose the landmarks we were + + align:start position:0% +when we lose the landmarks we were + + + align:start position:0% +when we lose the landmarks we were +depending on and for primates and many + + align:start position:0% +depending on and for primates and many + + + align:start position:0% +depending on and for primates and many +other animals it's primarily visual even + + align:start position:0% +other animals it's primarily visual even + + + align:start position:0% +other animals it's primarily visual even +a rat not such a visual animal but yet + + align:start position:0% +a rat not such a visual animal but yet + + + align:start position:0% +a rat not such a visual animal but yet +his major landmarks are still visual + + align:start position:0% +his major landmarks are still visual + + + align:start position:0% +his major landmarks are still visual +it's how he knows where he is + + align:start position:0% +it's how he knows where he is + + + align:start position:0% +it's how he knows where he is +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and they're + + align:start position:0% +and they're + + + align:start position:0% +and they're +and that's usually detected by + + align:start position:0% +and that's usually detected by + + + align:start position:0% +and that's usually detected by +cortex + + align:start position:0% +cortex + + + align:start position:0% +cortex +neocortex + + align:start position:0% +neocortex + + + align:start position:0% +neocortex +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we know what direction we're going + + align:start position:0% +so we know what direction we're going + + + align:start position:0% +so we know what direction we're going +with respect to landmarks even when + + align:start position:0% +with respect to landmarks even when + + + align:start position:0% +with respect to landmarks even when +we're not really aware of which + + align:start position:0% +we're not really aware of which + + + align:start position:0% +we're not really aware of which +landmarks we're using + + align:start position:0% +landmarks we're using + + + align:start position:0% +landmarks we're using +okay + + align:start position:0% + + + + align:start position:0% + +that head Direction + + align:start position:0% +that head Direction + + + align:start position:0% +that head Direction +with respect to landmarks is you can + + align:start position:0% +with respect to landmarks is you can + + + align:start position:0% +with respect to landmarks is you can +call it allocentric head Direction when + + align:start position:0% +call it allocentric head Direction when + + + align:start position:0% +call it allocentric head Direction when +we talk about where if I want to know + + align:start position:0% +we talk about where if I want to know + + + align:start position:0% +we talk about where if I want to know +where that object is with respect to my + + align:start position:0% +where that object is with respect to my + + + align:start position:0% +where that object is with respect to my +head that's not what I'm talking about + + align:start position:0% +head that's not what I'm talking about + + + align:start position:0% +head that's not what I'm talking about +here that's egocentric that has to do + + align:start position:0% +here that's egocentric that has to do + + + align:start position:0% +here that's egocentric that has to do +with where it is with respect to my head + + align:start position:0% +with where it is with respect to my head + + + align:start position:0% +with where it is with respect to my head +you're nice + + align:start position:0% +you're nice + + + align:start position:0% +you're nice +here now I'm talking about where we are + + align:start position:0% +here now I'm talking about where we are + + + align:start position:0% +here now I'm talking about where we are +with respect + + align:start position:0% +with respect + + + align:start position:0% +with respect +to some landmark + + align:start position:0% +to some landmark + + + align:start position:0% +to some landmark +I know where I am here with respect to + + align:start position:0% +I know where I am here with respect to + + + align:start position:0% +I know where I am here with respect to +the doors with respect to the status + + align:start position:0% +the doors with respect to the status + + + align:start position:0% +the doors with respect to the status +Center things like that + + align:start position:0% + + + + align:start position:0% + +that's allocentric Hendrix + + align:start position:0% +that's allocentric Hendrix + + + align:start position:0% +that's allocentric Hendrix +well but that's changing all the time + + align:start position:0% +well but that's changing all the time + + + align:start position:0% +well but that's changing all the time +I'm I'm moving my head around + + align:start position:0% +I'm I'm moving my head around + + + align:start position:0% +I'm I'm moving my head around +an animal is moving Etc + + align:start position:0% +an animal is moving Etc + + + align:start position:0% +an animal is moving Etc +okay he's taught in a wonderful system + + align:start position:0% +okay he's taught in a wonderful system + + + align:start position:0% +okay he's taught in a wonderful system +for taking those changes in head + + align:start position:0% +for taking those changes in head + + + align:start position:0% +for taking those changes in head +Direction + + align:start position:0% +Direction + + + align:start position:0% +Direction +and affecting the activity + + align:start position:0% +and affecting the activity + + + align:start position:0% +and affecting the activity +detect that's being sent by hippocampus + + align:start position:0% +detect that's being sent by hippocampus + + + align:start position:0% +detect that's being sent by hippocampus +down to the mammary bodies and + + align:start position:0% +down to the mammary bodies and + + + align:start position:0% +down to the mammary bodies and +correcting it firm changes in head + + align:start position:0% +correcting it firm changes in head + + + align:start position:0% +correcting it firm changes in head +Direction + + align:start position:0% +Direction + + + align:start position:0% +Direction +that's what's happening there in the + + align:start position:0% +that's what's happening there in the + + + align:start position:0% +that's what's happening there in the +mail everybody + + align:start position:0% + + + + align:start position:0% + +so from moment to moment the signal + + align:start position:0% +so from moment to moment the signal + + + align:start position:0% +so from moment to moment the signal +going from ammonary bodies + + align:start position:0% +going from ammonary bodies + + + align:start position:0% +going from ammonary bodies +back to the + + align:start position:0% +back to the + + + align:start position:0% +back to the +cingulate and hippocampus + + align:start position:0% +cingulate and hippocampus + + + align:start position:0% +cingulate and hippocampus +is always corrected for the + + align:start position:0% +is always corrected for the + + + align:start position:0% +is always corrected for the +momentary head Direction + + align:start position:0% +momentary head Direction + + + align:start position:0% +momentary head Direction +so it's constantly changing that's why + + align:start position:0% +so it's constantly changing that's why + + + align:start position:0% +so it's constantly changing that's why +it's so important + + align:start position:0% +it's so important + + + align:start position:0% +it's so important +why is that so important + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% + + + + align:start position:0% + +the way my head is pointed is + + align:start position:0% +the way my head is pointed is + + + align:start position:0% +the way my head is pointed is +potentially where I can go + + align:start position:0% +potentially where I can go + + + align:start position:0% +potentially where I can go +think of an animal I'll foraging + + align:start position:0% +think of an animal I'll foraging + + + align:start position:0% +think of an animal I'll foraging +he can turn this way and then + + align:start position:0% + + + + align:start position:0% + +what is important for him to know what's + + align:start position:0% +what is important for him to know what's + + + align:start position:0% +what is important for him to know what's +important for him to know is what's in + + align:start position:0% +important for him to know is what's in + + + align:start position:0% +important for him to know is what's in +front of it + + align:start position:0% +front of it + + + align:start position:0% +front of it +and + + align:start position:0% +and + + + align:start position:0% +and +he remembers things that are in front of + + align:start position:0% +he remembers things that are in front of + + + align:start position:0% +he remembers things that are in front of +him he has a map of the environment that + + align:start position:0% +him he has a map of the environment that + + + align:start position:0% +him he has a map of the environment that +he's learned + + align:start position:0% +he's learned + + + align:start position:0% +he's learned +so all the time he's + + align:start position:0% + + + + align:start position:0% + +at the hippocampus + + align:start position:0% +at the hippocampus + + + align:start position:0% +at the hippocampus +is connected through the cortex and is + + align:start position:0% +is connected through the cortex and is + + + align:start position:0% +is connected through the cortex and is +activating these memories things that + + align:start position:0% +activating these memories things that + + + align:start position:0% +activating these memories things that +happen in those areas so he knows am I + + align:start position:0% +happen in those areas so he knows am I + + + align:start position:0% +happen in those areas so he knows am I +going towards a good area or a bad area + + align:start position:0% +going towards a good area or a bad area + + + align:start position:0% +going towards a good area or a bad area +we know are we going towards food or not + + align:start position:0% +we know are we going towards food or not + + + align:start position:0% +we know are we going towards food or not +food are we going towards our friends or + + align:start position:0% +food are we going towards our friends or + + + align:start position:0% +food are we going towards our friends or +not towards our friends are we going to + + align:start position:0% +not towards our friends are we going to + + + align:start position:0% +not towards our friends are we going to +our classroom or not + + align:start position:0% + + + + align:start position:0% + +so you begin to see the connection of + + align:start position:0% +so you begin to see the connection of + + + align:start position:0% +so you begin to see the connection of +the circuit with memory now + + align:start position:0% +the circuit with memory now + + + align:start position:0% +the circuit with memory now +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yeah + + align:start position:0% + + + + align:start position:0% + +so how does that change in head + + align:start position:0% +so how does that change in head + + + align:start position:0% +so how does that change in head +Direction work let's go back to the tape + + align:start position:0% +Direction work let's go back to the tape + + + align:start position:0% +Direction work let's go back to the tape +circuit here well here's the mammary + + align:start position:0% +circuit here well here's the mammary + + + align:start position:0% +circuit here well here's the mammary +bodies and they're getting input from + + align:start position:0% +bodies and they're getting input from + + + align:start position:0% +bodies and they're getting input from +these structures the caudal into the + + align:start position:0% +these structures the caudal into the + + + align:start position:0% +these structures the caudal into the +midbrain some books say they're + + align:start position:0% +midbrain some books say they're + + + align:start position:0% +midbrain some books say they're +Australian but they're they're right at + + align:start position:0% +Australian but they're they're right at + + + align:start position:0% +Australian but they're they're right at +the caudal in the midbrain in most folks + + align:start position:0% +the caudal in the midbrain in most folks + + + align:start position:0% +the caudal in the midbrain in most folks +okay they're the technical nuclei of + + align:start position:0% +okay they're the technical nuclei of + + + align:start position:0% +okay they're the technical nuclei of +goodies okay and they they carry + + align:start position:0% +goodies okay and they they carry + + + align:start position:0% +goodies okay and they they carry +information derived mainly from the + + align:start position:0% +information derived mainly from the + + + align:start position:0% +information derived mainly from the +vestibular sense probably from + + align:start position:0% +vestibular sense probably from + + + align:start position:0% +vestibular sense probably from +proprioception as well + + align:start position:0% +proprioception as well + + + align:start position:0% +proprioception as well +about any change + + align:start position:0% +about any change + + + align:start position:0% +about any change +in the direction of the head + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +and you find these you can record head + + align:start position:0% +and you find these you can record head + + + align:start position:0% +and you find these you can record head +directions and you find them all along + + align:start position:0% +directions and you find them all along + + + align:start position:0% +directions and you find them all along +that circuit + + align:start position:0% +that circuit + + + align:start position:0% +that circuit +so the information they're carrying is + + align:start position:0% +so the information they're carrying is + + + align:start position:0% +so the information they're carrying is +always correct being is corrected is + + align:start position:0% +always correct being is corrected is + + + align:start position:0% +always correct being is corrected is +changing every time the animal moves his + + align:start position:0% +changing every time the animal moves his + + + align:start position:0% +changing every time the animal moves his +head + + align:start position:0% + + + + align:start position:0% + +well there's other ways we know we've + + align:start position:0% +well there's other ways we know we've + + + align:start position:0% +well there's other ways we know we've +moved our head not just from distributor + + align:start position:0% +moved our head not just from distributor + + + align:start position:0% +moved our head not just from distributor +sense we also know it from vision + + align:start position:0% +sense we also know it from vision + + + align:start position:0% +sense we also know it from vision +as I put in here + + align:start position:0% + + + + align:start position:0% + +lateral shifts and head directions do + + align:start position:0% +lateral shifts and head directions do + + + align:start position:0% +lateral shifts and head directions do +excite cells in the pre-technical area + + align:start position:0% +excite cells in the pre-technical area + + + align:start position:0% +excite cells in the pre-technical area +okay and there's a pathway from the + + align:start position:0% +okay and there's a pathway from the + + + align:start position:0% +okay and there's a pathway from the +pretential area that goes to this + + align:start position:0% +pretential area that goes to this + + + align:start position:0% +pretential area that goes to this +nucleus the lateral dorsal nucleus which + + align:start position:0% +nucleus the lateral dorsal nucleus which + + + align:start position:0% +nucleus the lateral dorsal nucleus which +sits right next to the anterior nuclea + + align:start position:0% +sits right next to the anterior nuclea + + + align:start position:0% +sits right next to the anterior nuclea +so I put that in here because they're + + align:start position:0% +so I put that in here because they're + + + align:start position:0% +so I put that in here because they're +tearing head direction information to + + align:start position:0% +tearing head direction information to + + + align:start position:0% +tearing head direction information to +the lateral dorsal nucleus + + align:start position:0% +the lateral dorsal nucleus + + + align:start position:0% +the lateral dorsal nucleus +and it's a system + + align:start position:0% +and it's a system + + + align:start position:0% +and it's a system +completely parallel to the mammalary + + align:start position:0% +completely parallel to the mammalary + + + align:start position:0% +completely parallel to the mammalary +body + + align:start position:0% +body + + + align:start position:0% +body +to anterior nucleus pathway + + align:start position:0% +to anterior nucleus pathway + + + align:start position:0% +to anterior nucleus pathway +so you're getting changes in head + + align:start position:0% +so you're getting changes in head + + + align:start position:0% +so you're getting changes in head +Direction coming into the lateral dorsal + + align:start position:0% +Direction coming into the lateral dorsal + + + align:start position:0% +Direction coming into the lateral dorsal +nucleus + + align:start position:0% +nucleus + + + align:start position:0% +nucleus +which also gets connect projections from + + align:start position:0% +which also gets connect projections from + + + align:start position:0% +which also gets connect projections from +hippocampal flamation + + align:start position:0% +hippocampal flamation + + + align:start position:0% +hippocampal flamation +so in both places you're constantly + + align:start position:0% +so in both places you're constantly + + + align:start position:0% +so in both places you're constantly +correcting + + align:start position:0% +correcting + + + align:start position:0% +correcting +that information about where we are with + + align:start position:0% +that information about where we are with + + + align:start position:0% +that information about where we are with +respect to landmarks correcting it for + + align:start position:0% +respect to landmarks correcting it for + + + align:start position:0% +respect to landmarks correcting it for +changes in head Direction + + align:start position:0% +changes in head Direction + + + align:start position:0% +changes in head Direction +I know this makes it seem a little more + + align:start position:0% +I know this makes it seem a little more + + + align:start position:0% +I know this makes it seem a little more +complicated + + align:start position:0% +complicated + + + align:start position:0% +complicated +this is the simpler diagram here + + align:start position:0% +this is the simpler diagram here + + + align:start position:0% +this is the simpler diagram here +you can just remember there's a parallel + + align:start position:0% +you can just remember there's a parallel + + + align:start position:0% +you can just remember there's a parallel +pathway there for visual information + + align:start position:0% + + + + align:start position:0% + +I want to point out that the axons in + + align:start position:0% +I want to point out that the axons in + + + align:start position:0% +I want to point out that the axons in +the paper circuit + + align:start position:0% +the paper circuit + + + align:start position:0% +the paper circuit +are more than one type and the one + + align:start position:0% +are more than one type and the one + + + align:start position:0% +are more than one type and the one +signaling head direction of the one + + align:start position:0% +signaling head direction of the one + + + align:start position:0% +signaling head direction of the one +physiologists have characterize the best + + align:start position:0% +physiologists have characterize the best + + + align:start position:0% +physiologists have characterize the best +we often don't know what the others do + + align:start position:0% +we often don't know what the others do + + + align:start position:0% +we often don't know what the others do +but it's a large number okay a lot of + + align:start position:0% +but it's a large number okay a lot of + + + align:start position:0% +but it's a large number okay a lot of +the axons the mammal Islamic track are + + align:start position:0% +the axons the mammal Islamic track are + + + align:start position:0% +the axons the mammal Islamic track are +involved in this + + align:start position:0% +involved in this + + + align:start position:0% +involved in this +I don't want to give you the sense that + + align:start position:0% +I don't want to give you the sense that + + + align:start position:0% +I don't want to give you the sense that +we know everything about it but we do + + align:start position:0% +we know everything about it but we do + + + align:start position:0% +we know everything about it but we do +know about this + + align:start position:0% +know about this + + + align:start position:0% +know about this +a major component + + align:start position:0% +a major component + + + align:start position:0% +a major component +we also know the hippocampus through the + + align:start position:0% +we also know the hippocampus through the + + + align:start position:0% +we also know the hippocampus through the +fornix is sending information to other + + align:start position:0% +fornix is sending information to other + + + align:start position:0% +fornix is sending information to other +areas than just the mammalary bodies + + align:start position:0% + + + + align:start position:0% + +it may be altering motivations + + align:start position:0% +it may be altering motivations + + + align:start position:0% +it may be altering motivations +motivational level according to you know + + align:start position:0% +motivational level according to you know + + + align:start position:0% +motivational level according to you know +what you're facing + + align:start position:0% +what you're facing + + + align:start position:0% +what you're facing +uh but that in fact hasn't been + + align:start position:0% +uh but that in fact hasn't been + + + align:start position:0% +uh but that in fact hasn't been +specifically + + align:start position:0% +specifically + + + align:start position:0% +specifically +we know it more from what it might be + + align:start position:0% +we know it more from what it might be + + + align:start position:0% +we know it more from what it might be +doing from behavioral work than we do + + align:start position:0% +doing from behavioral work than we do + + + align:start position:0% +doing from behavioral work than we do +from anatomical and physiological work + + align:start position:0% +from anatomical and physiological work + + + align:start position:0% +from anatomical and physiological work +okay + + align:start position:0% +okay + + + align:start position:0% +okay +a few other terms here you should know + + align:start position:0% +a few other terms here you should know + + + align:start position:0% +a few other terms here you should know +what the basal poor brain is + + align:start position:0% +what the basal poor brain is + + + align:start position:0% +what the basal poor brain is +if I go back to this picture + + align:start position:0% +if I go back to this picture + + + align:start position:0% +if I go back to this picture +when you talk about basal foreign + + align:start position:0% +when you talk about basal foreign + + + align:start position:0% +when you talk about basal foreign +if you look at the bottom one here + + align:start position:0% +if you look at the bottom one here + + + align:start position:0% +if you look at the bottom one here +here's hypothalamus it's a little bit + + align:start position:0% +here's hypothalamus it's a little bit + + + align:start position:0% +here's hypothalamus it's a little bit +arbitrary where hypothalamus ends here + + align:start position:0% +arbitrary where hypothalamus ends here + + + align:start position:0% +arbitrary where hypothalamus ends here +we know we say it ends about at the + + align:start position:0% +we know we say it ends about at the + + + align:start position:0% +we know we say it ends about at the +level of the out if this is the optic + + align:start position:0% +level of the out if this is the optic + + + align:start position:0% +level of the out if this is the optic +chiasm the optic tract is Crossing + + align:start position:0% +chiasm the optic tract is Crossing + + + align:start position:0% +chiasm the optic tract is Crossing +the areas in Chrono the opticism are + + align:start position:0% +the areas in Chrono the opticism are + + + align:start position:0% +the areas in Chrono the opticism are +basal forebrain + + align:start position:0% + + + + align:start position:0% + +if you look at sections let's look at + + align:start position:0% +if you look at sections let's look at + + + align:start position:0% +if you look at sections let's look at +these sections for a minute + + align:start position:0% +these sections for a minute + + + align:start position:0% +these sections for a minute +and start back here with things we we've + + align:start position:0% +and start back here with things we we've + + + align:start position:0% +and start back here with things we we've +studied before here's the midbrain + + align:start position:0% +studied before here's the midbrain + + + align:start position:0% +studied before here's the midbrain +section there's the central gray and the + + align:start position:0% +section there's the central gray and the + + + align:start position:0% +section there's the central gray and the +ventral pigmental area so this is the + + align:start position:0% +ventral pigmental area so this is the + + + align:start position:0% +ventral pigmental area so this is the +limbic midbrain areas + + align:start position:0% +limbic midbrain areas + + + align:start position:0% +limbic midbrain areas +and you follow these forward both + + align:start position:0% +and you follow these forward both + + + align:start position:0% +and you follow these forward both +Central gray and ventraltigmental area + + align:start position:0% +Central gray and ventraltigmental area + + + align:start position:0% +Central gray and ventraltigmental area +are continuous with hypothalamus + + align:start position:0% +are continuous with hypothalamus + + + align:start position:0% +are continuous with hypothalamus +you father follow eel of them forward + + align:start position:0% +you father follow eel of them forward + + + align:start position:0% +you father follow eel of them forward +and come right into hypothalamus + + align:start position:0% +and come right into hypothalamus + + + align:start position:0% +and come right into hypothalamus +posterior I put down so here we are in + + align:start position:0% +posterior I put down so here we are in + + + align:start position:0% +posterior I put down so here we are in +the middle by bones + + align:start position:0% +the middle by bones + + + align:start position:0% +the middle by bones +forming the ventral part of the twin + + align:start position:0% +forming the ventral part of the twin + + + align:start position:0% +forming the ventral part of the twin +brain + + align:start position:0% +brain + + + align:start position:0% +brain +here we are a little further forward you + + align:start position:0% +here we are a little further forward you + + + align:start position:0% +here we are a little further forward you +see the optic track now just behind the + + align:start position:0% +see the optic track now just behind the + + + align:start position:0% +see the optic track now just behind the +chiasm + + align:start position:0% +chiasm + + + align:start position:0% +chiasm +they're the Forex fibers are a bundled + + align:start position:0% +they're the Forex fibers are a bundled + + + align:start position:0% +they're the Forex fibers are a bundled +at the medial edge of the medial + + align:start position:0% +at the medial edge of the medial + + + align:start position:0% +at the medial edge of the medial +forebrain bundle there which basically + + align:start position:0% +forebrain bundle there which basically + + + align:start position:0% +forebrain bundle there which basically +courses through the whole lateral + + align:start position:0% +courses through the whole lateral + + + align:start position:0% +courses through the whole lateral +hypothalamus + + align:start position:0% +hypothalamus + + + align:start position:0% +hypothalamus +okay but then you go forward + + align:start position:0% +okay but then you go forward + + + align:start position:0% +okay but then you go forward +okay and when the thalamus stops + + align:start position:0% +okay and when the thalamus stops + + + align:start position:0% +okay and when the thalamus stops +okay the ball in the stops in here + + align:start position:0% +okay the ball in the stops in here + + + align:start position:0% +okay the ball in the stops in here +now there's the hemispheres with the + + align:start position:0% +now there's the hemispheres with the + + + align:start position:0% +now there's the hemispheres with the +septum in between the septillary which + + align:start position:0% +septum in between the septillary which + + + align:start position:0% +septum in between the septillary which +is lumens is very thin but in rats + + align:start position:0% +is lumens is very thin but in rats + + + align:start position:0% +is lumens is very thin but in rats +and other rodents it's very thick + + align:start position:0% +and other rodents it's very thick + + + align:start position:0% +and other rodents it's very thick +this is basil for brain at the bottom + + align:start position:0% +this is basil for brain at the bottom + + + align:start position:0% +this is basil for brain at the bottom +the old factory tumors that's the + + align:start position:0% +the old factory tumors that's the + + + align:start position:0% +the old factory tumors that's the +ventral most part of the striata + + align:start position:0% +ventral most part of the striata + + + align:start position:0% +ventral most part of the striata +the part that's been there since the + + align:start position:0% +the part that's been there since the + + + align:start position:0% +the part that's been there since the +most ancient chordates + + align:start position:0% +most ancient chordates + + + align:start position:0% +most ancient chordates +getting the olfactory input + + align:start position:0% + + + + align:start position:0% + +and that's how impaction + + align:start position:0% +and that's how impaction + + + align:start position:0% +and that's how impaction +still influences + + align:start position:0% + + + + align:start position:0% + +into this region + + align:start position:0% +into this region + + + align:start position:0% +into this region +okay but notice other things in that + + align:start position:0% +okay but notice other things in that + + + align:start position:0% +okay but notice other things in that +region + + align:start position:0% + + + + align:start position:0% + +if you go back a little bit you're in + + align:start position:0% +if you go back a little bit you're in + + + align:start position:0% +if you go back a little bit you're in +amygdala + + align:start position:0% + + + + align:start position:0% + +and this note here that + + align:start position:0% +and this note here that + + + align:start position:0% +and this note here that +the whole ventral medial striatum + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +I've got it colored here the same way as + + align:start position:0% +I've got it colored here the same way as + + + align:start position:0% +I've got it colored here the same way as +the basal forebrain because in fact + + align:start position:0% +the basal forebrain because in fact + + + align:start position:0% +the basal forebrain because in fact +they're all part of the ventral striatum + + align:start position:0% +they're all part of the ventral striatum + + + align:start position:0% +they're all part of the ventral striatum +okay + + align:start position:0% +okay + + + align:start position:0% +okay +we usually we don't say the septums part + + align:start position:0% +we usually we don't say the septums part + + + align:start position:0% +we usually we don't say the septums part +of this three atom + + align:start position:0% + + + + align:start position:0% + +okay because it was embryonic Origins + + align:start position:0% +okay because it was embryonic Origins + + + align:start position:0% +okay because it was embryonic Origins +but the rest of these structures are all + + align:start position:0% +but the rest of these structures are all + + + align:start position:0% +but the rest of these structures are all +part of infrastructure and if we go + + align:start position:0% +part of infrastructure and if we go + + + align:start position:0% +part of infrastructure and if we go +forward we're now + + align:start position:0% +forward we're now + + + align:start position:0% +forward we're now +divides into the hemispheres + + align:start position:0% +divides into the hemispheres + + + align:start position:0% +divides into the hemispheres +you can see that you can follow it this + + align:start position:0% +you can see that you can follow it this + + + align:start position:0% +you can see that you can follow it this +is still all basal floor brain probably + + align:start position:0% +is still all basal floor brain probably + + + align:start position:0% +is still all basal floor brain probably +the septum + + align:start position:0% +the septum + + + align:start position:0% +the septum +and it includes the most medial part + + align:start position:0% +and it includes the most medial part + + + align:start position:0% +and it includes the most medial part +ventral medial part of it + + align:start position:0% +ventral medial part of it + + + align:start position:0% +ventral medial part of it +the + + align:start position:0% + + + + align:start position:0% + +Street atom here so + + align:start position:0% +Street atom here so + + + align:start position:0% +Street atom here so +most of this we call the interest-free + + align:start position:0% +most of this we call the interest-free + + + align:start position:0% +most of this we call the interest-free +atom + + align:start position:0% +atom + + + align:start position:0% +atom +and it has specific structures in it + + align:start position:0% +and it has specific structures in it + + + align:start position:0% +and it has specific structures in it +like nucleus accumbens + + align:start position:0% + + + + align:start position:0% + +bad nucleus history of terminology + + align:start position:0% +bad nucleus history of terminology + + + align:start position:0% +bad nucleus history of terminology +the basal nucleus is mine art and so + + align:start position:0% +the basal nucleus is mine art and so + + + align:start position:0% +the basal nucleus is mine art and so +forth all right + + align:start position:0% +forth all right + + + align:start position:0% +forth all right +it's nice to review these a little bit + + align:start position:0% +it's nice to review these a little bit + + + align:start position:0% +it's nice to review these a little bit +I've not named everything + + align:start position:0% + + + + align:start position:0% + +let's talk about a couple of other + + align:start position:0% +let's talk about a couple of other + + + align:start position:0% +let's talk about a couple of other +things here quickly + + align:start position:0% +things here quickly + + + align:start position:0% +things here quickly +that + + align:start position:0% +that + + + align:start position:0% +that +you should understand a little bit I'm + + align:start position:0% +you should understand a little bit I'm + + + align:start position:0% +you should understand a little bit I'm +interested in ways the hypothalamus can + + align:start position:0% +interested in ways the hypothalamus can + + + align:start position:0% +interested in ways the hypothalamus can +influence the neocortex + + align:start position:0% +influence the neocortex + + + align:start position:0% +influence the neocortex +and I want you to remember the major + + align:start position:0% +and I want you to remember the major + + + align:start position:0% +and I want you to remember the major +reward pathway in mammalian CNS can + + align:start position:0% +reward pathway in mammalian CNS can + + + align:start position:0% +reward pathway in mammalian CNS can +someone answer that what's the major + + align:start position:0% +someone answer that what's the major + + + align:start position:0% +someone answer that what's the major +reward pathway if you hear that phrase + + align:start position:0% +reward pathway if you hear that phrase + + + align:start position:0% +reward pathway if you hear that phrase +we've known about it for many years + + align:start position:0% + + + + align:start position:0% + +these are the accents that use dopamine + + align:start position:0% +these are the accents that use dopamine + + + align:start position:0% +these are the accents that use dopamine +as a transmitter where are they coming + + align:start position:0% +as a transmitter where are they coming + + + align:start position:0% +as a transmitter where are they coming +from + + align:start position:0% + + + + align:start position:0% + +usually we're talking about the ones + + align:start position:0% +usually we're talking about the ones + + + align:start position:0% +usually we're talking about the ones +coming from the ventral pigment already + + align:start position:0% +coming from the ventral pigment already + + + align:start position:0% +coming from the ventral pigment already +here okay + + align:start position:0% +here okay + + + align:start position:0% +here okay +but in fact the function of the ones + + align:start position:0% +but in fact the function of the ones + + + align:start position:0% +but in fact the function of the ones +that come from the here which are + + align:start position:0% +that come from the here which are + + + align:start position:0% +that come from the here which are +the medial part of the here + + align:start position:0% +the medial part of the here + + + align:start position:0% +the medial part of the here +perhaps should be + + align:start position:0% +perhaps should be + + + align:start position:0% +perhaps should be +shaded pink here too because it's really + + align:start position:0% +shaded pink here too because it's really + + + align:start position:0% +shaded pink here too because it's really +part of the limbic system as well + + align:start position:0% +part of the limbic system as well + + + align:start position:0% +part of the limbic system as well +they're really also a reward pathway but + + align:start position:0% +they're really also a reward pathway but + + + align:start position:0% +they're really also a reward pathway but +a different nature usually we're talking + + align:start position:0% +a different nature usually we're talking + + + align:start position:0% +a different nature usually we're talking +about + + align:start position:0% +about + + + align:start position:0% +about +the dopamine axons that go through the + + align:start position:0% +the dopamine axons that go through the + + + align:start position:0% +the dopamine axons that go through the +medial forebrain Rumble + + align:start position:0% +medial forebrain Rumble + + + align:start position:0% +medial forebrain Rumble +and the lateral hypothalamus here and + + align:start position:0% +and the lateral hypothalamus here and + + + align:start position:0% +and the lateral hypothalamus here and +project into the basal forward + + align:start position:0% + + + + align:start position:0% + +so what about this first one describe + + align:start position:0% +so what about this first one describe + + + align:start position:0% +so what about this first one describe +two ways the hypothalamus can influence + + align:start position:0% +two ways the hypothalamus can influence + + + align:start position:0% +two ways the hypothalamus can influence +the neocortex well actually there's a + + align:start position:0% +the neocortex well actually there's a + + + align:start position:0% +the neocortex well actually there's a +lot of ways + + align:start position:0% +lot of ways + + + align:start position:0% +lot of ways +you could say welders + + align:start position:0% +you could say welders + + + align:start position:0% +you could say welders +the hypothalamus is connected to in a + + align:start position:0% +the hypothalamus is connected to in a + + + align:start position:0% +the hypothalamus is connected to in a +two-directional way with limbic + + align:start position:0% +two-directional way with limbic + + + align:start position:0% +two-directional way with limbic +structures + + align:start position:0% +structures + + + align:start position:0% +structures +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +subcortical limbic structures and those + + align:start position:0% +subcortical limbic structures and those + + + align:start position:0% +subcortical limbic structures and those +are connected with the + + align:start position:0% +are connected with the + + + align:start position:0% +are connected with the +more you could say corticoid limbic + + align:start position:0% +more you could say corticoid limbic + + + align:start position:0% +more you could say corticoid limbic +structures including hippocampus + + align:start position:0% +structures including hippocampus + + + align:start position:0% +structures including hippocampus +which are connected to the paralympic + + align:start position:0% +which are connected to the paralympic + + + align:start position:0% +which are connected to the paralympic +areas which are connected to the + + align:start position:0% +areas which are connected to the + + + align:start position:0% +areas which are connected to the +cortical areas this is Muslims diagram + + align:start position:0% +cortical areas this is Muslims diagram + + + align:start position:0% +cortical areas this is Muslims diagram +shows just major roots from + + align:start position:0% +shows just major roots from + + + align:start position:0% +shows just major roots from +sensory areas this is primary sensory + + align:start position:0% +sensory areas this is primary sensory + + + align:start position:0% +sensory areas this is primary sensory +areas here the height valves down here + + align:start position:0% +areas here the height valves down here + + + align:start position:0% +areas here the height valves down here +but + + align:start position:0% + + + + align:start position:0% + +first of all + + align:start position:0% +first of all + + + align:start position:0% +first of all +would you expect the hypothalamus to + + align:start position:0% +would you expect the hypothalamus to + + + align:start position:0% +would you expect the hypothalamus to +influence the neocortical area and what + + align:start position:0% +influence the neocortical area and what + + + align:start position:0% +influence the neocortical area and what +kind of influence have we talked under + + align:start position:0% + + + + align:start position:0% + +well you know what functions the + + align:start position:0% +well you know what functions the + + + align:start position:0% +well you know what functions the +hypothalamus is involved in + + align:start position:0% +hypothalamus is involved in + + + align:start position:0% +hypothalamus is involved in +so we're talking about influences of the + + align:start position:0% +so we're talking about influences of the + + + align:start position:0% +so we're talking about influences of the +moods motivational States + + align:start position:0% +moods motivational States + + + align:start position:0% +moods motivational States +on you know cortical processes + + align:start position:0% +on you know cortical processes + + + align:start position:0% +on you know cortical processes +we know that moods and especially the + + align:start position:0% +we know that moods and especially the + + + align:start position:0% +we know that moods and especially the +motivational States influence the way + + align:start position:0% +motivational States influence the way + + + align:start position:0% +motivational States influence the way +decisions are being made in by + + align:start position:0% +decisions are being made in by + + + align:start position:0% +decisions are being made in by +neocortical + + align:start position:0% +neocortical + + + align:start position:0% +neocortical +existence + + align:start position:0% + + + + align:start position:0% + +no matter how cognitive we we may be + + align:start position:0% +no matter how cognitive we we may be + + + align:start position:0% +no matter how cognitive we we may be +talking about cognitive functions but + + align:start position:0% +talking about cognitive functions but + + + align:start position:0% +talking about cognitive functions but +you don't get away from motivation + + align:start position:0% +you don't get away from motivation + + + align:start position:0% +you don't get away from motivation +you don't behave without motivation + + align:start position:0% +you don't behave without motivation + + + align:start position:0% +you don't behave without motivation +and motivation often involves + + align:start position:0% + + + + align:start position:0% + +changes in motivation of all changes in + + align:start position:0% +changes in motivation of all changes in + + + align:start position:0% +changes in motivation of all changes in +emotional states as well + + align:start position:0% +emotional states as well + + + align:start position:0% +emotional states as well +all right so here I've outlined many + + align:start position:0% +all right so here I've outlined many + + + align:start position:0% +all right so here I've outlined many +different ways the hyperbalances in your + + align:start position:0% +different ways the hyperbalances in your + + + align:start position:0% +different ways the hyperbalances in your +cartridge + + align:start position:0% + + + + align:start position:0% + +we just talked about tape circuit the + + align:start position:0% +we just talked about tape circuit the + + + align:start position:0% +we just talked about tape circuit the +more direct and more indirect way + + align:start position:0% +more direct and more indirect way + + + align:start position:0% +more direct and more indirect way +through Page circuit to get from + + align:start position:0% +through Page circuit to get from + + + align:start position:0% +through Page circuit to get from +hypothalamus to Cortex and your cortex + + align:start position:0% +hypothalamus to Cortex and your cortex + + + align:start position:0% +hypothalamus to Cortex and your cortex +earlier we talked about the gating of + + align:start position:0% +earlier we talked about the gating of + + + align:start position:0% +earlier we talked about the gating of +information by hypothalamus the gating + + align:start position:0% +information by hypothalamus the gating + + + align:start position:0% +information by hypothalamus the gating +of information going through the films + + align:start position:0% +of information going through the films + + + align:start position:0% +of information going through the films +these are the chapters where I mentioned + + align:start position:0% +these are the chapters where I mentioned + + + align:start position:0% +these are the chapters where I mentioned +that that's certainly a way the + + align:start position:0% +that that's certainly a way the + + + align:start position:0% +that that's certainly a way the +hypothalamus is influencing inner cortex + + align:start position:0% +hypothalamus is influencing inner cortex + + + align:start position:0% +hypothalamus is influencing inner cortex +we talked in chapter 17 about the + + align:start position:0% +we talked in chapter 17 about the + + + align:start position:0% +we talked in chapter 17 about the +widespread act Center systems + + align:start position:0% +widespread act Center systems + + + align:start position:0% +widespread act Center systems +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +I mentioned a few of them here again + + align:start position:0% +I mentioned a few of them here again + + + align:start position:0% +I mentioned a few of them here again +that's certainly an influence of + + align:start position:0% +that's certainly an influence of + + + align:start position:0% +that's certainly an influence of +hypothalamus on your cortex + + align:start position:0% + + + + align:start position:0% + +but then there's a very direct way + + align:start position:0% +but then there's a very direct way + + + align:start position:0% +but then there's a very direct way +by way of the media dorsal nucleus and I + + align:start position:0% +by way of the media dorsal nucleus and I + + + align:start position:0% +by way of the media dorsal nucleus and I +show it here + + align:start position:0% +show it here + + + align:start position:0% +show it here +'s your hypothalamus down here here's + + align:start position:0% +'s your hypothalamus down here here's + + + align:start position:0% +'s your hypothalamus down here here's +the thalamus and I'm showing here the + + align:start position:0% +the thalamus and I'm showing here the + + + align:start position:0% +the thalamus and I'm showing here the +media dorsal nucleus which projects + + align:start position:0% +media dorsal nucleus which projects + + + align:start position:0% +media dorsal nucleus which projects +prefrontal areas of Cortex and the + + align:start position:0% +prefrontal areas of Cortex and the + + + align:start position:0% +prefrontal areas of Cortex and the +medial part which contains the larger + + align:start position:0% +medial part which contains the larger + + + align:start position:0% +medial part which contains the larger +cells + + align:start position:0% +cells + + + align:start position:0% +cells +receives axons I've just shown them here + + align:start position:0% +receives axons I've just shown them here + + + align:start position:0% +receives axons I've just shown them here +on the left with an arrow a red arrow + + align:start position:0% +on the left with an arrow a red arrow + + + align:start position:0% +on the left with an arrow a red arrow +the hypothalamus projects as does + + align:start position:0% +the hypothalamus projects as does + + + align:start position:0% +the hypothalamus projects as does +olfactory system + + align:start position:0% +olfactory system + + + align:start position:0% +olfactory system +to that part of the meteor synthesis + + align:start position:0% +to that part of the meteor synthesis + + + align:start position:0% +to that part of the meteor synthesis +and + + align:start position:0% +and + + + align:start position:0% +and +so a fairly this is probably the most + + align:start position:0% +so a fairly this is probably the most + + + align:start position:0% +so a fairly this is probably the most +directly hypothalamus can enter + + align:start position:0% +directly hypothalamus can enter + + + align:start position:0% +directly hypothalamus can enter +cortex + + align:start position:0% +cortex + + + align:start position:0% +cortex +but all as in Less Direct ways are very + + align:start position:0% +but all as in Less Direct ways are very + + + align:start position:0% +but all as in Less Direct ways are very +important as well + + align:start position:0% +important as well + + + align:start position:0% +important as well +the influences + + align:start position:0% +the influences + + + align:start position:0% +the influences +very widespread + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so I point out here that a person's + + align:start position:0% +so I point out here that a person's + + + align:start position:0% +so I point out here that a person's +mental state can influence the endocrine + + align:start position:0% +mental state can influence the endocrine + + + align:start position:0% +mental state can influence the endocrine +endocrine organs I wear the hypothalamus + + align:start position:0% + + + + align:start position:0% + +and of course you've got to consider + + align:start position:0% +and of course you've got to consider + + + align:start position:0% +and of course you've got to consider +what we mean by mental state + + align:start position:0% + + + + align:start position:0% + +let's talk about how the hypothalamus + + align:start position:0% +let's talk about how the hypothalamus + + + align:start position:0% +let's talk about how the hypothalamus +can influence that mental state + + align:start position:0% + + + + align:start position:0% + +the influences go in both directions + + align:start position:0% + + + + align:start position:0% + +so let's one way to get experimental + + align:start position:0% +so let's one way to get experimental + + + align:start position:0% +so let's one way to get experimental +data on it is to look at disturbances of + + align:start position:0% +data on it is to look at disturbances of + + + align:start position:0% +data on it is to look at disturbances of +the hypothalamus during their surgical + + align:start position:0% +the hypothalamus during their surgical + + + align:start position:0% +the hypothalamus during their surgical +procedures because this often during + + align:start position:0% +procedures because this often during + + + align:start position:0% +procedures because this often during +those surgical procedures the patient is + + align:start position:0% +those surgical procedures the patient is + + + align:start position:0% +those surgical procedures the patient is +conscious + + align:start position:0% +conscious + + + align:start position:0% +conscious +okay the brain doesn't contain pain + + align:start position:0% +okay the brain doesn't contain pain + + + align:start position:0% +okay the brain doesn't contain pain +receptors so pain pain path was + + align:start position:0% +receptors so pain pain path was + + + align:start position:0% +receptors so pain pain path was +originate in the brain itself so you can + + align:start position:0% +originate in the brain itself so you can + + + align:start position:0% +originate in the brain itself so you can +operate on the brain as long as you + + align:start position:0% +operate on the brain as long as you + + + align:start position:0% +operate on the brain as long as you +anesthetized + + align:start position:0% +anesthetized + + + align:start position:0% +anesthetized +structures that you have to open up to + + align:start position:0% +structures that you have to open up to + + + align:start position:0% +structures that you have to open up to +get in + + align:start position:0% +get in + + + align:start position:0% +get in +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +you can get + + align:start position:0% +you can get + + + align:start position:0% +you can get +pretty drastic changes in autonomic + + align:start position:0% +pretty drastic changes in autonomic + + + align:start position:0% +pretty drastic changes in autonomic +activity you can get changes in mood + + align:start position:0% +activity you can get changes in mood + + + align:start position:0% +activity you can get changes in mood +changes in emotional expression changes + + align:start position:0% +changes in emotional expression changes + + + align:start position:0% +changes in emotional expression changes +and feelings being reported + + align:start position:0% + + + + align:start position:0% + +the founder of our departments Weber + + align:start position:0% +the founder of our departments Weber + + + align:start position:0% +the founder of our departments Weber +always in his introductory lectures in + + align:start position:0% +always in his introductory lectures in + + + align:start position:0% +always in his introductory lectures in + + align:start position:0% + + + align:start position:0% +you know would talk about + + align:start position:0% +you know would talk about + + + align:start position:0% +you know would talk about +a soldier + + align:start position:0% +a soldier + + + align:start position:0% +a soldier +during World War II who + + align:start position:0% + + + + align:start position:0% + +ended up with a piece of shrapnel in his + + align:start position:0% +ended up with a piece of shrapnel in his + + + align:start position:0% +ended up with a piece of shrapnel in his +third ventricle + + align:start position:0% +third ventricle + + + align:start position:0% +third ventricle +that they + + align:start position:0% + + + + align:start position:0% + +very difficult at that time anyway to + + align:start position:0% +very difficult at that time anyway to + + + align:start position:0% +very difficult at that time anyway to +get it out + + align:start position:0% +get it out + + + align:start position:0% +get it out +so they left it there and + + align:start position:0% +so they left it there and + + + align:start position:0% +so they left it there and +every time he moved his head a lot + + align:start position:0% +every time he moved his head a lot + + + align:start position:0% +every time he moved his head a lot +that piece of shrapnel would + + align:start position:0% +that piece of shrapnel would + + + align:start position:0% +that piece of shrapnel would +rattle around inside his third ventricle + + align:start position:0% +rattle around inside his third ventricle + + + align:start position:0% +rattle around inside his third ventricle +and stimulate structures mechanically + + align:start position:0% +and stimulate structures mechanically + + + align:start position:0% +and stimulate structures mechanically +near the walls of The ventricle + + align:start position:0% +near the walls of The ventricle + + + align:start position:0% +near the walls of The ventricle +he was start crying uncontrollably + + align:start position:0% +he was start crying uncontrollably + + + align:start position:0% +he was start crying uncontrollably +it was only when he sat still well that + + align:start position:0% +it was only when he sat still well that + + + align:start position:0% +it was only when he sat still well that +that stimulation stopped + + align:start position:0% + + + + align:start position:0% + +what interested me the most is that + + align:start position:0% +what interested me the most is that + + + align:start position:0% +what interested me the most is that +when you asked him why he was crying he + + align:start position:0% +when you asked him why he was crying he + + + align:start position:0% +when you asked him why he was crying he +would say things like well it cries in + + align:start position:0% +would say things like well it cries in + + + align:start position:0% +would say things like well it cries in +me in other words that's not me crying + + align:start position:0% +me in other words that's not me crying + + + align:start position:0% +me in other words that's not me crying +it's just something happening to me + + align:start position:0% +it's just something happening to me + + + align:start position:0% +it's just something happening to me +but later + + align:start position:0% +but later + + + align:start position:0% +but later +as time went on he began identifying + + align:start position:0% +as time went on he began identifying + + + align:start position:0% +as time went on he began identifying +with his States and he would say + + align:start position:0% +with his States and he would say + + + align:start position:0% +with his States and he would say +I feel really sad and unhappy and that's + + align:start position:0% +I feel really sad and unhappy and that's + + + align:start position:0% +I feel really sad and unhappy and that's +why I'm crying + + align:start position:0% +why I'm crying + + + align:start position:0% +why I'm crying +and I think that's a real lesson + + align:start position:0% +and I think that's a real lesson + + + align:start position:0% +and I think that's a real lesson +when things happen to us + + align:start position:0% +when things happen to us + + + align:start position:0% +when things happen to us +you don't really have to identify with + + align:start position:0% +you don't really have to identify with + + + align:start position:0% +you don't really have to identify with +the States you can separate yourself + + align:start position:0% +the States you can separate yourself + + + align:start position:0% +the States you can separate yourself +from them and that is the way you have + + align:start position:0% +from them and that is the way you have + + + align:start position:0% +from them and that is the way you have +more self-control + + align:start position:0% +more self-control + + + align:start position:0% +more self-control +all right uh + + align:start position:0% + + + + align:start position:0% + +Marta goes on and talks about the + + align:start position:0% +Marta goes on and talks about the + + + align:start position:0% +Marta goes on and talks about the +concepts of autonomic and voluntary + + align:start position:0% +concepts of autonomic and voluntary + + + align:start position:0% +concepts of autonomic and voluntary +we talk about voluntary nervous system + + align:start position:0% +we talk about voluntary nervous system + + + align:start position:0% +we talk about voluntary nervous system +for the pyramidal tract for example it's + + align:start position:0% +for the pyramidal tract for example it's + + + align:start position:0% +for the pyramidal tract for example it's +part of the voluntary nervous system + + align:start position:0% + + + + align:start position:0% + +we talk about the + + align:start position:0% + + + + align:start position:0% + +involuntary nervous system the autonomic + + align:start position:0% +involuntary nervous system the autonomic + + + align:start position:0% +involuntary nervous system the autonomic +nervous system + + align:start position:0% +nervous system + + + align:start position:0% +nervous system +and other subcortical and + + align:start position:0% +and other subcortical and + + + align:start position:0% +and other subcortical and +non-extra pyramidal motor system like + + align:start position:0% +non-extra pyramidal motor system like + + + align:start position:0% +non-extra pyramidal motor system like +involving cerebellum and striatum + + align:start position:0% +involving cerebellum and striatum + + + align:start position:0% +involving cerebellum and striatum +okay and various structures of the brain + + align:start position:0% +okay and various structures of the brain + + + align:start position:0% +okay and various structures of the brain +stem + + align:start position:0% + + + + align:start position:0% + +and now they're pointed out that that's + + align:start position:0% +and now they're pointed out that that's + + + align:start position:0% +and now they're pointed out that that's +a little bit misleading because in fact + + align:start position:0% + + + + align:start position:0% + +first of all the so-called voluntary + + align:start position:0% +first of all the so-called voluntary + + + align:start position:0% +first of all the so-called voluntary +nervous system corticospinal projections + + align:start position:0% +nervous system corticospinal projections + + + align:start position:0% +nervous system corticospinal projections +and so forth + + align:start position:0% +and so forth + + + align:start position:0% +and so forth +are engaged in unconscious habits + + align:start position:0% +are engaged in unconscious habits + + + align:start position:0% +are engaged in unconscious habits +performance of habits + + align:start position:0% +performance of habits + + + align:start position:0% +performance of habits +that you can do with very little + + align:start position:0% +that you can do with very little + + + align:start position:0% +that you can do with very little +awareness + + align:start position:0% + + + + align:start position:0% + +it's not just voluntary movements + + align:start position:0% +it's not just voluntary movements + + + align:start position:0% +it's not just voluntary movements +and just pointing out that we don't + + align:start position:0% +and just pointing out that we don't + + + align:start position:0% +and just pointing out that we don't +fully understand what we mean we talk + + align:start position:0% +fully understand what we mean we talk + + + align:start position:0% +fully understand what we mean we talk +about volunteering voluntary in terms of + + align:start position:0% +about volunteering voluntary in terms of + + + align:start position:0% +about volunteering voluntary in terms of +brain structures + + align:start position:0% +brain structures + + + align:start position:0% +brain structures +similarly autonomic is usually + + align:start position:0% + + + + align:start position:0% + +things happening automatically but in + + align:start position:0% +things happening automatically but in + + + align:start position:0% +things happening automatically but in +fact people some people get quite a bit + + align:start position:0% +fact people some people get quite a bit + + + align:start position:0% +fact people some people get quite a bit +of control out of the raw Dynamic + + align:start position:0% +of control out of the raw Dynamic + + + align:start position:0% +of control out of the raw Dynamic +nervous system + + align:start position:0% +nervous system + + + align:start position:0% +nervous system +the best known is reported + + align:start position:0% +the best known is reported + + + align:start position:0% +the best known is reported +yogic exercises where people learn to + + align:start position:0% +yogic exercises where people learn to + + + align:start position:0% +yogic exercises where people learn to +control their heart rate they can even + + align:start position:0% +control their heart rate they can even + + + align:start position:0% +control their heart rate they can even +change the body temperature because even + + align:start position:0% +change the body temperature because even + + + align:start position:0% +change the body temperature because even +some yogis that are able to make the one + + align:start position:0% +some yogis that are able to make the one + + + align:start position:0% +some yogis that are able to make the one +hand warmer than the other and things + + align:start position:0% +hand warmer than the other and things + + + align:start position:0% +hand warmer than the other and things +like that + + align:start position:0% +like that + + + align:start position:0% +like that +but I point out here that it's very + + align:start position:0% +but I point out here that it's very + + + align:start position:0% +but I point out here that it's very +limited because most people + + align:start position:0% +limited because most people + + + align:start position:0% +limited because most people +can't do those things at all + + align:start position:0% + + + + align:start position:0% + +at least not directly + + align:start position:0% +at least not directly + + + align:start position:0% +at least not directly +not also points out + + align:start position:0% +not also points out + + + align:start position:0% +not also points out +high performance has very few long + + align:start position:0% +high performance has very few long + + + align:start position:0% +high performance has very few long +Pathways either leading out of it or + + align:start position:0% +Pathways either leading out of it or + + + align:start position:0% +Pathways either leading out of it or +coming into it I mentioned the long + + align:start position:0% +coming into it I mentioned the long + + + align:start position:0% +coming into it I mentioned the long +pathway carrying pain information + + align:start position:0% +pathway carrying pain information + + + align:start position:0% +pathway carrying pain information +but that's very unusual most of them are + + align:start position:0% +but that's very unusual most of them are + + + align:start position:0% +but that's very unusual most of them are +polysynaptic unlike pyramidal tract + + align:start position:0% +polysynaptic unlike pyramidal tract + + + align:start position:0% +polysynaptic unlike pyramidal tract +unlike + + align:start position:0% +unlike + + + align:start position:0% +unlike +the dorsal columnistic system which are + + align:start position:0% +the dorsal columnistic system which are + + + align:start position:0% +the dorsal columnistic system which are +long accidents + + align:start position:0% +long accidents + + + align:start position:0% +long accidents +characteristic of hypothalamic + + align:start position:0% +characteristic of hypothalamic + + + align:start position:0% +characteristic of hypothalamic +connections are the shorter pathways + + align:start position:0% + + + + align:start position:0% + +one more topic here + + align:start position:0% +one more topic here + + + align:start position:0% +one more topic here +should know about we talked about + + align:start position:0% +should know about we talked about + + + align:start position:0% +should know about we talked about +disconnecting hypothalamus from other + + align:start position:0% +disconnecting hypothalamus from other + + + align:start position:0% +disconnecting hypothalamus from other +structures it's a very interesting + + align:start position:0% +structures it's a very interesting + + + align:start position:0% +structures it's a very interesting +experiment I did not talk about and we + + align:start position:0% +experiment I did not talk about and we + + + align:start position:0% +experiment I did not talk about and we +talked about those earlier experiments + + align:start position:0% +talked about those earlier experiments + + + align:start position:0% +talked about those earlier experiments +it's particularly interesting to me + + align:start position:0% +it's particularly interesting to me + + + align:start position:0% +it's particularly interesting to me +because I'm interested in mechanisms for + + align:start position:0% +because I'm interested in mechanisms for + + + align:start position:0% +because I'm interested in mechanisms for +recovery and I talked about diastesis + + align:start position:0% +recovery and I talked about diastesis + + + align:start position:0% +recovery and I talked about diastesis +effects well this involves that if you + + align:start position:0% +effects well this involves that if you + + + align:start position:0% +effects well this involves that if you +take rabbit okay + + align:start position:0% +take rabbit okay + + + align:start position:0% +take rabbit okay +and you you can Loop a wire + + align:start position:0% +and you you can Loop a wire + + + align:start position:0% +and you you can Loop a wire +it's a difficult surgical procedure but + + align:start position:0% +it's a difficult surgical procedure but + + + align:start position:0% +it's a difficult surgical procedure but +you can get a wire in there that Loops + + align:start position:0% +you can get a wire in there that Loops + + + align:start position:0% +you can get a wire in there that Loops +below + + align:start position:0% + + + + align:start position:0% + +coddle into the hypothalamus so if the + + align:start position:0% +coddle into the hypothalamus so if the + + + align:start position:0% +coddle into the hypothalamus so if the +wire is pulled so now the animal's + + align:start position:0% +wire is pulled so now the animal's + + + align:start position:0% +wire is pulled so now the animal's +conscious but he's got that wire + + align:start position:0% +conscious but he's got that wire + + + align:start position:0% +conscious but he's got that wire +and you put it so you can pull the wire + + align:start position:0% +and you put it so you can pull the wire + + + align:start position:0% +and you put it so you can pull the wire +and you're not causing any pain but you + + align:start position:0% +and you're not causing any pain but you + + + align:start position:0% +and you're not causing any pain but you +are basically slicing the pathways + + align:start position:0% +are basically slicing the pathways + + + align:start position:0% +are basically slicing the pathways +between + + align:start position:0% +between + + + align:start position:0% +between +hypothalamus and midbrain + + align:start position:0% +hypothalamus and midbrain + + + align:start position:0% +hypothalamus and midbrain +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and if you pull it up high enough you'll + + align:start position:0% +and if you pull it up high enough you'll + + + align:start position:0% +and if you pull it up high enough you'll +completely disconnect the hypothalamus + + align:start position:0% +completely disconnect the hypothalamus + + + align:start position:0% +completely disconnect the hypothalamus +from the midbrain okay if you do that in + + align:start position:0% +from the midbrain okay if you do that in + + + align:start position:0% +from the midbrain okay if you do that in +one quick step + + align:start position:0% +one quick step + + + align:start position:0% +one quick step +you will have a lot of trouble keeping + + align:start position:0% +you will have a lot of trouble keeping + + + align:start position:0% +you will have a lot of trouble keeping +that animal alive because he can't + + align:start position:0% +that animal alive because he can't + + + align:start position:0% +that animal alive because he can't +direct he can't directly controls + + align:start position:0% +direct he can't directly controls + + + align:start position:0% +direct he can't directly controls +feedings temperature and various things + + align:start position:0% +feedings temperature and various things + + + align:start position:0% +feedings temperature and various things +like that but Thalamus is so important + + align:start position:0% +like that but Thalamus is so important + + + align:start position:0% +like that but Thalamus is so important +but if you do it in small steps + + align:start position:0% + + + + align:start position:0% + +and wait every time you do a little more + + align:start position:0% +and wait every time you do a little more + + + align:start position:0% +and wait every time you do a little more +damage you wait he will recover + + align:start position:0% + + + + align:start position:0% + +and if you keep doing it you'll + + align:start position:0% +and if you keep doing it you'll + + + align:start position:0% +and if you keep doing it you'll +eventually completely separate the + + align:start position:0% +eventually completely separate the + + + align:start position:0% +eventually completely separate the +hypothalamus + + align:start position:0% +hypothalamus + + + align:start position:0% +hypothalamus +from the midbrain + + align:start position:0% +from the midbrain + + + align:start position:0% +from the midbrain +and he still recovers + + align:start position:0% +and he still recovers + + + align:start position:0% +and he still recovers +that's called a multi-stage lesion what + + align:start position:0% +that's called a multi-stage lesion what + + + align:start position:0% +that's called a multi-stage lesion what +kind of damage to the brain can you + + align:start position:0% +kind of damage to the brain can you + + + align:start position:0% +kind of damage to the brain can you +think of this like that + + align:start position:0% +think of this like that + + + align:start position:0% +think of this like that +in patience + + align:start position:0% +in patience + + + align:start position:0% +in patience +think of a tumor that's slow growing + + align:start position:0% +think of a tumor that's slow growing + + + align:start position:0% +think of a tumor that's slow growing +one reason they're so difficult to + + align:start position:0% +one reason they're so difficult to + + + align:start position:0% +one reason they're so difficult to +detect and one reason a person will come + + align:start position:0% +detect and one reason a person will come + + + align:start position:0% +detect and one reason a person will come +to see the doctor only when it's huge is + + align:start position:0% +to see the doctor only when it's huge is + + + align:start position:0% +to see the doctor only when it's huge is +because it's like that wire being pulled + + align:start position:0% +because it's like that wire being pulled + + + align:start position:0% +because it's like that wire being pulled +really slowly + + align:start position:0% +really slowly + + + align:start position:0% +really slowly +keep his recovering all the time from + + align:start position:0% +keep his recovering all the time from + + + align:start position:0% +keep his recovering all the time from +the damage being done yes + + align:start position:0% + + + + align:start position:0% + +that's one reason why people with + + align:start position:0% +that's one reason why people with + + + align:start position:0% +that's one reason why people with +Alzheimer's or people with Parkinson's + + align:start position:0% +Alzheimer's or people with Parkinson's + + + align:start position:0% +Alzheimer's or people with Parkinson's +say you don't notice the symptoms until + + align:start position:0% +say you don't notice the symptoms until + + + align:start position:0% +say you don't notice the symptoms until +the damage is very far along because + + align:start position:0% +the damage is very far along because + + + align:start position:0% +the damage is very far along because +it's happening gradually + + align:start position:0% +it's happening gradually + + + align:start position:0% +it's happening gradually +it's a good parallel + + align:start position:0% +it's a good parallel + + + align:start position:0% +it's a good parallel +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so that's Rudolph Powell was the one who + + align:start position:0% +so that's Rudolph Powell was the one who + + + align:start position:0% +so that's Rudolph Powell was the one who +did that + + align:start position:0% +did that + + + align:start position:0% +did that +with with rabbits that experiment I was + + align:start position:0% +with with rabbits that experiment I was + + + align:start position:0% +with with rabbits that experiment I was +just describing + + align:start position:0% +just describing + + + align:start position:0% +just describing +okay and then I just discuss I just + + align:start position:0% +okay and then I just discuss I just + + + align:start position:0% +okay and then I just discuss I just +point out some of the things you should + + align:start position:0% +point out some of the things you should + + + align:start position:0% +point out some of the things you should +review and I also showed the figure from + + align:start position:0% +review and I also showed the figure from + + + align:start position:0% +review and I also showed the figure from +a paper + + align:start position:0% +a paper + + + align:start position:0% +a paper +that studied how the central gray area + + align:start position:0% +that studied how the central gray area + + + align:start position:0% +that studied how the central gray area +of the midbrain + + align:start position:0% +of the midbrain + + + align:start position:0% +of the midbrain +uh + + align:start position:0% +uh + + + align:start position:0% +uh +especially in an animal that's got this + + align:start position:0% +especially in an animal that's got this + + + align:start position:0% +especially in an animal that's got this +kind of disconnection + + align:start position:0% +kind of disconnection + + + align:start position:0% +kind of disconnection +actually has different areas that serve + + align:start position:0% +actually has different areas that serve + + + align:start position:0% +actually has different areas that serve +say fight and fight sexual behaviors + + align:start position:0% +say fight and fight sexual behaviors + + + align:start position:0% +say fight and fight sexual behaviors +defense Behavior + + align:start position:0% +defense Behavior + + + align:start position:0% +defense Behavior +uh and even feeding okay + + align:start position:0% +uh and even feeding okay + + + align:start position:0% +uh and even feeding okay +and uh so it is possible for animals to + + align:start position:0% +and uh so it is possible for animals to + + + align:start position:0% +and uh so it is possible for animals to +recover a lot + + align:start position:0% +recover a lot + + + align:start position:0% +recover a lot +the problem is if the midbrain + + align:start position:0% +the problem is if the midbrain + + + align:start position:0% +the problem is if the midbrain +they don't have much control of the end + + align:start position:0% +they don't have much control of the end + + + align:start position:0% +they don't have much control of the end +brain at all so they're completely + + align:start position:0% +brain at all so they're completely + + + align:start position:0% +brain at all so they're completely +abnormal and they will not initiate very + + align:start position:0% +abnormal and they will not initiate very + + + align:start position:0% +abnormal and they will not initiate very +much Behavior as we said before + + align:start position:0% + + + + align:start position:0% + +that's one of my favorite quotes from + + align:start position:0% +that's one of my favorite quotes from + + + align:start position:0% +that's one of my favorite quotes from +Rumi + + align:start position:0% +Rumi + + + align:start position:0% +Rumi +when we're studying hypothalamus this is + + align:start position:0% +when we're studying hypothalamus this is + + + align:start position:0% +when we're studying hypothalamus this is +the way I feel + + align:start position:0% +the way I feel + + + align:start position:0% +the way I feel +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +I will post the slides here from + + align:start position:0% +I will post the slides here from + + + align:start position:0% +I will post the slides here from +the discussed hormone and other + + align:start position:0% +the discussed hormone and other + + + align:start position:0% +the discussed hormone and other +influences will spend just a little time + + align:start position:0% +influences will spend just a little time + + + align:start position:0% +influences will spend just a little time +at the beginning of the next class + + align:start position:0% +at the beginning of the next class + + + align:start position:0% +at the beginning of the next class +going over just a few things here + + align:start position:0% +going over just a few things here + + + align:start position:0% +going over just a few things here +I think it's it's a very interesting + + align:start position:0% +I think it's it's a very interesting + + + align:start position:0% +I think it's it's a very interesting +topic and I know a lot of you are + + align:start position:0% +topic and I know a lot of you are + + + align:start position:0% +topic and I know a lot of you are +interested in it + + align:start position:0% +interested in it + + + align:start position:0% +interested in it +but read + + align:start position:0% +but read + + + align:start position:0% +but read +chapter 27 + + align:start position:0% +chapter 27 + + + align:start position:0% +chapter 27 +and then we'll go to chapter 28 because + + align:start position:0% +and then we'll go to chapter 28 because + + + align:start position:0% +and then we'll go to chapter 28 because +I need more than one I I need at least a + + align:start position:0% +I need more than one I I need at least a + + + align:start position:0% +I need more than one I I need at least a +full class to talk about hippocampus so + + align:start position:0% +full class to talk about hippocampus so + + + align:start position:0% +full class to talk about hippocampus so +we'll do that + + align:start position:0% +we'll do that + + + align:start position:0% +we'll do that +second part of the next class and then + + align:start position:0% +second part of the next class and then + + + align:start position:0% +second part of the next class and then +that's Friday and then on Monday we'll + + align:start position:0% +that's Friday and then on Monday we'll + + + align:start position:0% +that's Friday and then on Monday we'll +we'll finish talking about hippocampus + + align:start position:0% +we'll finish talking about hippocampus + + + align:start position:0% +we'll finish talking about hippocampus +so we can talk about the amygdala and + + align:start position:0% +so we can talk about the amygdala and + + + align:start position:0% +so we can talk about the amygdala and +the basal forebrain + + align:start position:0% +the basal forebrain + + + align:start position:0% +the basal forebrain +okay \ No newline at end of file diff --git a/GAF78dg8-nE.txt b/GAF78dg8-nE.txt new file mode 100644 index 0000000000000000000000000000000000000000..2bdae81cbcde0655d82c7c3acadaaa0a3340eab6 --- /dev/null +++ b/GAF78dg8-nE.txt @@ -0,0 +1,11107 @@ +align:start position:0% + +next thing I want to do now that we have + + align:start position:0% +next thing I want to do now that we have + + + align:start position:0% +next thing I want to do now that we have +fear CH so now what do we know we have + + align:start position:0% +fear CH so now what do we know we have + + + align:start position:0% +fear CH so now what do we know we have +this protocol again I'm always think of + + align:start position:0% +this protocol again I'm always think of + + + align:start position:0% +this protocol again I'm always think of +this protocol as parall repetition + + align:start position:0% +this protocol as parall repetition + + + align:start position:0% +this protocol as parall repetition +parallel repeated and we know the sound + + align:start position:0% +parallel repeated and we know the sound + + + align:start position:0% +parallel repeated and we know the sound +on it now what's really nice about it + + align:start position:0% +on it now what's really nice about it + + + align:start position:0% +on it now what's really nice about it +that this gives us so now I wanted to + + align:start position:0% +that this gives us so now I wanted to + + + align:start position:0% +that this gives us so now I wanted to +say two things in the hour or so + + align:start position:0% +say two things in the hour or so + + + align:start position:0% +say two things in the hour or so +remaining one thing I want to say is + + align:start position:0% +remaining one thing I want to say is + + + align:start position:0% +remaining one thing I want to say is +that it gives us an isic okay + + align:start position:0% +that it gives us an isic okay + + + align:start position:0% +that it gives us an isic okay +non-interactive a zero knowledge uh + + align:start position:0% +non-interactive a zero knowledge uh + + + align:start position:0% +non-interactive a zero knowledge uh +proof and the second and so I want to + + align:start position:0% +proof and the second and so I want to + + + align:start position:0% +proof and the second and so I want to +explain what that is and the second + + align:start position:0% +explain what that is and the second + + + align:start position:0% +explain what that is and the second +thing I want to say is uh to mention a + + align:start position:0% +thing I want to say is uh to mention a + + + align:start position:0% +thing I want to say is uh to mention a +little bit what was me the question uh + + align:start position:0% +little bit what was me the question uh + + + align:start position:0% +little bit what was me the question uh +here in the beginning which was wait + + align:start position:0% +here in the beginning which was wait + + + align:start position:0% +here in the beginning which was wait +this contradicts all this idea with + + align:start position:0% +this contradicts all this idea with + + + align:start position:0% +this contradicts all this idea with +something weird is going on so I want to + + align:start position:0% +something weird is going on so I want to + + + align:start position:0% +something weird is going on so I want to +talk about that and I want to end with + + align:start position:0% +talk about that and I want to end with + + + align:start position:0% +talk about that and I want to end with +explaining why this technique is more + + align:start position:0% +explaining why this technique is more + + + align:start position:0% +explaining why this technique is more +General okay + + align:start position:0% +General okay + + + align:start position:0% +General okay +H okay so let's first see why + + align:start position:0% +H okay so let's first see why + + + align:start position:0% +H okay so let's first see why +why why we get an isic okay + + align:start position:0% + + + + align:start position:0% + +so okay so now what did we get Once once + + align:start position:0% +so okay so now what did we get Once once + + + align:start position:0% +so okay so now what did we get Once once +we apply the fum we have an + + align:start position:0% +we apply the fum we have an + + + align:start position:0% +we apply the fum we have an +uninteractive protocol so let's look at + + align:start position:0% +uninteractive protocol so let's look at + + + align:start position:0% +uninteractive protocol so let's look at +this protocol and + + align:start position:0% +this protocol and + + + align:start position:0% +this protocol and +see what this protocol becomes when we + + align:start position:0% +see what this protocol becomes when we + + + align:start position:0% +see what this protocol becomes when we +apply the F Paradigm to it + + align:start position:0% + + + + align:start position:0% + +so let me just write it down Actually I + + align:start position:0% +so let me just write it down Actually I + + + align:start position:0% +so let me just write it down Actually I +don't even want to write the + + align:start position:0% +don't even want to write the + + + align:start position:0% +don't even want to write the +explicit + + align:start position:0% +explicit + + + align:start position:0% +explicit +uh constru like everything explicitly + + align:start position:0% +uh constru like everything explicitly + + + align:start position:0% +uh constru like everything explicitly +let me just say this protocol had like a + + align:start position:0% +let me just say this protocol had like a + + + align:start position:0% +let me just say this protocol had like a +public key associated with + + align:start position:0% +public key associated with + + + align:start position:0% +public key associated with +it now it also has a a hash function + + align:start position:0% +it now it also has a a hash function + + + align:start position:0% +it now it also has a a hash function +associated with hash key which we use + + align:start position:0% +associated with hash key which we use + + + align:start position:0% +associated with hash key which we use +for the fure hash function and now + + align:start position:0% +for the fure hash function and now + + + align:start position:0% +for the fure hash function and now +essentially the + + align:start position:0% +essentially the + + + align:start position:0% +essentially the +verifier he sends Alpha which is the + + align:start position:0% +verifier he sends Alpha which is the + + + align:start position:0% +verifier he sends Alpha which is the +other commitments FAL repetition like + + align:start position:0% +other commitments FAL repetition like + + + align:start position:0% +other commitments FAL repetition like +the first message and then he tells you + + align:start position:0% +the first message and then he tells you + + + align:start position:0% +the first message and then he tells you +beta he doesn't need to send it + + align:start position:0% +beta he doesn't need to send it + + + align:start position:0% +beta he doesn't need to send it +everybody comput it but that's kind of + + align:start position:0% +everybody comput it but that's kind of + + + align:start position:0% +everybody comput it but that's kind of +evaluating with a hash key Alpha by the + + align:start position:0% +evaluating with a hash key Alpha by the + + + align:start position:0% +evaluating with a hash key Alpha by the +way I abuse notation a little bit and + + align:start position:0% +way I abuse notation a little bit and + + + align:start position:0% +way I abuse notation a little bit and +actually every time you don't you + + align:start position:0% +actually every time you don't you + + + align:start position:0% +actually every time you don't you +you uh let's see there's also a g here + + align:start position:0% +you uh let's see there's also a g here + + + align:start position:0% +you uh let's see there's also a g here +like the instance the + + align:start position:0% +like the instance the + + + align:start position:0% +like the instance the +graph really what you where you hash is + + align:start position:0% +graph really what you where you hash is + + + align:start position:0% +graph really what you where you hash is +the graph in Alpha I kind of omitted the + + align:start position:0% +the graph in Alpha I kind of omitted the + + + align:start position:0% +the graph in Alpha I kind of omitted the +graph from the notation because it's + + align:start position:0% +graph from the notation because it's + + + align:start position:0% +graph from the notation because it's +kind of cumbersome and it's kind of + + align:start position:0% +kind of cumbersome and it's kind of + + + align:start position:0% +kind of cumbersome and it's kind of +fixed in advance the alpha is the one + + align:start position:0% +fixed in advance the alpha is the one + + + align:start position:0% +fixed in advance the alpha is the one +that's not fixed so I the G but the G is + + align:start position:0% +that's not fixed so I the G but the G is + + + align:start position:0% +that's not fixed so I the G but the G is +always there when you apply F you apply + + align:start position:0% +always there when you apply F you apply + + + align:start position:0% +always there when you apply F you apply +it to the first message and the + + align:start position:0% +it to the first message and the + + + align:start position:0% +it to the first message and the +instance okay so that's the beta and + + align:start position:0% +instance okay so that's the beta and + + + align:start position:0% +instance okay so that's the beta and +gamma this is the pro that's the it's + + align:start position:0% +gamma this is the pro that's the it's + + + align:start position:0% +gamma this is the pro that's the it's +one message right because we applied F + + align:start position:0% +one message right because we applied F + + + align:start position:0% +one message right because we applied F +okay so this protocol which consists of + + align:start position:0% +okay so this protocol which consists of + + + align:start position:0% +okay so this protocol which consists of +three messages Alpha Beta gamma now once + + align:start position:0% +three messages Alpha Beta gamma now once + + + align:start position:0% +three messages Alpha Beta gamma now once +we applied F we have not only the public + + align:start position:0% +we applied F we have not only the public + + + align:start position:0% +we applied F we have not only the public +key in the CRS we also have the hash key + + align:start position:0% +key in the CRS we also have the hash key + + + align:start position:0% +key in the CRS we also have the hash key +corresponding to the fiir + + align:start position:0% +corresponding to the fiir + + + align:start position:0% +corresponding to the fiir +and now this Alpha Beta gamma are sent + + align:start position:0% +and now this Alpha Beta gamma are sent + + + align:start position:0% +and now this Alpha Beta gamma are sent +all at once there's no interaction + + align:start position:0% +all at once there's no interaction + + + align:start position:0% +all at once there's no interaction +that's what F + + align:start position:0% +that's what F + + + align:start position:0% +that's what F +does but beta the PR's hands are tied + + align:start position:0% +does but beta the PR's hands are tied + + + align:start position:0% +does but beta the PR's hands are tied +and they it should be the evaluation of + + align:start position:0% +and they it should be the evaluation of + + + align:start position:0% +and they it should be the evaluation of +G and Alpha the hash function evaluated + + align:start position:0% +G and Alpha the hash function evaluated + + + align:start position:0% +G and Alpha the hash function evaluated +on G and Alpha so this is completely + + align:start position:0% +on G and Alpha so this is completely + + + align:start position:0% +on G and Alpha so this is completely +noninteractive and it's sound because we + + align:start position:0% +noninteractive and it's sound because we + + + align:start position:0% +noninteractive and it's sound because we +just worked hard to prove that it's + + align:start position:0% +just worked hard to prove that it's + + + align:start position:0% +just worked hard to prove that it's +sound if we use this hash + + align:start position:0% +sound if we use this hash + + + align:start position:0% +sound if we use this hash +function under Circle Circ yeah is + + align:start position:0% +function under Circle Circ yeah is + + + align:start position:0% +function under Circle Circ yeah is +this a isic argument now then because we + + align:start position:0% +this a isic argument now then because we + + + align:start position:0% +this a isic argument now then because we +used like f SEC good a we'll see there's + + align:start position:0% +used like f SEC good a we'll see there's + + + align:start position:0% +used like f SEC good a we'll see there's +you can make it and is a proof or + + align:start position:0% +you can make it and is a proof or + + + align:start position:0% +you can make it and is a proof or +argument so we'll talk about that in a + + align:start position:0% +argument so we'll talk about that in a + + + align:start position:0% +argument so we'll talk about that in a +second but uh so this is a one message + + align:start position:0% +second but uh so this is a one message + + + align:start position:0% +second but uh so this is a one message +it's sound and it's complete now what + + align:start position:0% +it's sound and it's complete now what + + + align:start position:0% +it's sound and it's complete now what +happened to the zero knowledge let's see + + align:start position:0% +happened to the zero knowledge let's see + + + align:start position:0% +happened to the zero knowledge let's see +what happened here we said we had zero + + align:start position:0% +what happened here we said we had zero + + + align:start position:0% +what happened here we said we had zero +knowledge we could simulate + + align:start position:0% +knowledge we could simulate + + + align:start position:0% +knowledge we could simulate +it what happens + + align:start position:0% +it what happens + + + align:start position:0% +it what happens +here and what I want to argue is that + + align:start position:0% +here and what I want to argue is that + + + align:start position:0% +here and what I want to argue is that +it's still you have zero knowledge even + + align:start position:0% +it's still you have zero knowledge even + + + align:start position:0% +it's still you have zero knowledge even +though before we said f actually Ru zero + + align:start position:0% +though before we said f actually Ru zero + + + align:start position:0% +though before we said f actually Ru zero +knowledge supp it's not zero + + align:start position:0% +knowledge supp it's not zero + + + align:start position:0% +knowledge supp it's not zero +knowledge this non intractive version + + align:start position:0% +knowledge this non intractive version + + + align:start position:0% +knowledge this non intractive version +you can can prove that it's zero + + align:start position:0% +you can can prove that it's zero + + + align:start position:0% +you can can prove that it's zero +knowledge however the definition of zero + + align:start position:0% +knowledge however the definition of zero + + + align:start position:0% +knowledge however the definition of zero +knowledge here is a different bit + + align:start position:0% +knowledge here is a different bit + + + align:start position:0% +knowledge here is a different bit +different because we have a common + + align:start position:0% +different because we have a common + + + align:start position:0% +different because we have a common +random string so now this common random + + align:start position:0% +random string so now this common random + + + align:start position:0% +random string so now this common random +or common reference string denoted by + + align:start position:0% +or common reference string denoted by + + + align:start position:0% +or common reference string denoted by +CRS it consists of the public + + align:start position:0% +CRS it consists of the public + + + align:start position:0% +CRS it consists of the public +key used for the commitment for the + + align:start position:0% +key used for the commitment for the + + + align:start position:0% +key used for the commitment for the +message Alpha + + align:start position:0% +message Alpha + + + align:start position:0% +message Alpha +and the hash use for the + + align:start position:0% +and the hash use for the + + + align:start position:0% +and the hash use for the +CRS now let me I want to argue that this + + align:start position:0% +CRS now let me I want to argue that this + + + align:start position:0% +CRS now let me I want to argue that this +protocol is a non-interactive zero + + align:start position:0% +protocol is a non-interactive zero + + + align:start position:0% +protocol is a non-interactive zero +knowledge or is an isic non-interactive + + align:start position:0% +knowledge or is an isic non-interactive + + + align:start position:0% +knowledge or is an isic non-interactive +zero + + align:start position:0% +zero + + + align:start position:0% +zero +knowledge but to prove that let me + + align:start position:0% +knowledge but to prove that let me + + + align:start position:0% +knowledge but to prove that let me +Define first what noninteractive zero + + align:start position:0% +Define first what noninteractive zero + + + align:start position:0% +Define first what noninteractive zero +knowledge is okay because it's the + + align:start position:0% +knowledge is okay because it's the + + + align:start position:0% +knowledge is okay because it's the +definition is similar to the interactive + + align:start position:0% +definition is similar to the interactive + + + align:start position:0% +definition is similar to the interactive +setting but slightly different so the + + align:start position:0% +setting but slightly different so the + + + align:start position:0% +setting but slightly different so the +definition is the following anic for a + + align:start position:0% +definition is the following anic for a + + + align:start position:0% +definition is the following anic for a +language out + + align:start position:0% +language out + + + align:start position:0% +language out +is the following it says that for any PP + + align:start position:0% +is the following it says that for any PP + + + align:start position:0% +is the following it says that for any PP +VAR or poly size it can be non it can be + + align:start position:0% +VAR or poly size it can be non it can be + + + align:start position:0% +VAR or poly size it can be non it can be +poly but okay me for any PPT V + + align:start position:0% +poly but okay me for any PPT V + + + align:start position:0% +poly but okay me for any PPT V +Star there exists a simulator a PPT + + align:start position:0% +Star there exists a simulator a PPT + + + align:start position:0% +Star there exists a simulator a PPT +simulator po time + + align:start position:0% +simulator po time + + + align:start position:0% +simulator po time +simulator such that the simulator can + + align:start position:0% +simulator such that the simulator can + + + align:start position:0% +simulator such that the simulator can +simulate everything that the verifier + + align:start position:0% +simulate everything that the verifier + + + align:start position:0% +simulate everything that the verifier +learns in the real world so what does + + align:start position:0% +learns in the real world so what does + + + align:start position:0% +learns in the real world so what does +the What is the view of the verifier in + + align:start position:0% +the What is the view of the verifier in + + + align:start position:0% +the What is the view of the verifier in +the real world such that the view of the + + align:start position:0% +the real world such that the view of the + + + align:start position:0% +the real world such that the view of the +verifier in the real world which is what + + align:start position:0% +verifier in the real world which is what + + + align:start position:0% +verifier in the real world which is what +it's the + + align:start position:0% +it's the + + + align:start position:0% +it's the +CRS so every niic is a it's not + + align:start position:0% +CRS so every niic is a it's not + + + align:start position:0% +CRS so every niic is a it's not +interactive and there's a CRS so the + + align:start position:0% +interactive and there's a CRS so the + + + align:start position:0% +interactive and there's a CRS so the +verifier learns the CRS and he learns + + align:start position:0% +verifier learns the CRS and he learns + + + align:start position:0% +verifier learns the CRS and he learns +what he got he learns uh H such that + + align:start position:0% +what he got he learns uh H such that + + + align:start position:0% +what he got he learns uh H such that +sorry for every X and L I forgot to say + + align:start position:0% +sorry for every X and L I forgot to say + + + align:start position:0% +sorry for every X and L I forgot to say +for every X in the language he learns + + align:start position:0% +for every X in the language he learns + + + align:start position:0% +for every X in the language he learns +this and he learns the proof of the + + align:start position:0% +this and he learns the proof of the + + + align:start position:0% +this and he learns the proof of the +actual prover so I guess what the actual + + align:start position:0% +actual prover so I guess what the actual + + + align:start position:0% +actual prover so I guess what the actual +prover gives is when he gets + + align:start position:0% +prover gives is when he gets + + + align:start position:0% +prover gives is when he gets +CRS X and + + align:start position:0% +CRS X and + + + align:start position:0% +CRS X and +witness this is what the verifier learns + + align:start position:0% +witness this is what the verifier learns + + + align:start position:0% +witness this is what the verifier learns +in the real world he sees the CRS and he + + align:start position:0% +in the real world he sees the CRS and he + + + align:start position:0% +in the real world he sees the CRS and he +sees the actual proof produced by the + + align:start position:0% +sees the actual proof produced by the + + + align:start position:0% +sees the actual proof produced by the +prover and the prover is given CRS X and + + align:start position:0% +prover and the prover is given CRS X and + + + align:start position:0% +prover and the prover is given CRS X and +A Witness instance and + + align:start position:0% +A Witness instance and + + + align:start position:0% +A Witness instance and +witness and zero knowledge says that the + + align:start position:0% +witness and zero knowledge says that the + + + align:start position:0% +witness and zero knowledge says that the +simulator can simulate this so I forgot + + align:start position:0% +simulator can simulate this so I forgot + + + align:start position:0% +simulator can simulate this so I forgot +to say security parameter there's also + + align:start position:0% +to say security parameter there's also + + + align:start position:0% +to say security parameter there's also +security param oh actually you know what + + align:start position:0% +security param oh actually you know what + + + align:start position:0% +security param oh actually you know what +you don't need security parameter + + align:start position:0% +you don't need security parameter + + + align:start position:0% +you don't need security parameter +because the CRS you can think of + + align:start position:0% +because the CRS you can think of + + + align:start position:0% +because the CRS you can think of +including in this + + align:start position:0% +including in this + + + align:start position:0% +including in this +includes also security parameter you can + + align:start position:0% +includes also security parameter you can + + + align:start position:0% +includes also security parameter you can +always assume the CRS includes a + + align:start position:0% +always assume the CRS includes a + + + align:start position:0% +always assume the CRS includes a +security parameter so here what the + + align:start position:0% +security parameter so here what the + + + align:start position:0% +security parameter so here what the +verifier learns in the real world he + + align:start position:0% +verifier learns in the real world he + + + align:start position:0% +verifier learns in the real world he +sees the CRS which includes a security + + align:start position:0% +sees the CRS which includes a security + + + align:start position:0% +sees the CRS which includes a security +parameter and he sees the proof that the + + align:start position:0% +parameter and he sees the proof that the + + + align:start position:0% +parameter and he sees the proof that the +verifier gave and now I want to argue + + align:start position:0% +verifier gave and now I want to argue + + + align:start position:0% +verifier gave and now I want to argue +that the simulator can simulate this + + align:start position:0% +that the simulator can simulate this + + + align:start position:0% +that the simulator can simulate this +entire thing + + align:start position:0% +entire thing + + + align:start position:0% +entire thing +okay typically we also allow auxiliary + + align:start position:0% +okay typically we also allow auxiliary + + + align:start position:0% +okay typically we also allow auxiliary +information so for any ax and for every + + align:start position:0% +information so for any ax and for every + + + align:start position:0% +information so for any ax and for every +auxiliary information + + align:start position:0% +auxiliary information + + + align:start position:0% +auxiliary information +augs + + align:start position:0% +augs + + + align:start position:0% +augs +a the Dy also see sees augs and still he + + align:start position:0% +a the Dy also see sees augs and still he + + + align:start position:0% +a the Dy also see sees augs and still he +cannot tell the + + align:start position:0% + + + + align:start position:0% + +difference so when we talk about Zer + + align:start position:0% +difference so when we talk about Zer + + + align:start position:0% +difference so when we talk about Zer +there's just Zer and then there's + + align:start position:0% +there's just Zer and then there's + + + align:start position:0% +there's just Zer and then there's +auxiliary input Zer knowledge this is + + align:start position:0% +auxiliary input Zer knowledge this is + + + align:start position:0% +auxiliary input Zer knowledge this is +stronger we usually want this so I'm + + align:start position:0% +stronger we usually want this so I'm + + + align:start position:0% +stronger we usually want this so I'm +just writing it but uh there's also the + + align:start position:0% +just writing it but uh there's also the + + + align:start position:0% +just writing it but uh there's also the +without auxilary information uh + + align:start position:0% +without auxilary information uh + + + align:start position:0% +without auxilary information uh +definition but again what is zero uh NK + + align:start position:0% +definition but again what is zero uh NK + + + align:start position:0% +definition but again what is zero uh NK +non interactive zero knowledge it says + + align:start position:0% +non interactive zero knowledge it says + + + align:start position:0% +non interactive zero knowledge it says +that for any efficient + + align:start position:0% +that for any efficient + + + align:start position:0% +that for any efficient +varar there exists an efficient + + align:start position:0% +varar there exists an efficient + + + align:start position:0% +varar there exists an efficient +simulator said that for every X in the + + align:start position:0% +simulator said that for every X in the + + + align:start position:0% +simulator said that for every X in the +language that had a witness and for any + + align:start position:0% +language that had a witness and for any + + + align:start position:0% +language that had a witness and for any +auxiliary information that the you know + + align:start position:0% +auxiliary information that the you know + + + align:start position:0% +auxiliary information that the you know +the simulator may have or the verifier + + align:start position:0% +the simulator may have or the verifier + + + align:start position:0% +the simulator may have or the verifier +may + + align:start position:0% +may + + + align:start position:0% +may +have what the verifier learns in the + + align:start position:0% +have what the verifier learns in the + + + align:start position:0% +have what the verifier learns in the +real world can be simulated by the + + align:start position:0% +real world can be simulated by the + + + align:start position:0% +real world can be simulated by the +simulator + + align:start position:0% +simulator + + + align:start position:0% +simulator +yeah here we don't even need + + align:start position:0% +yeah here we don't even need + + + align:start position:0% +yeah here we don't even need +right yeah sorry there's no + + align:start position:0% +right yeah sorry there's no + + + align:start position:0% +right yeah sorry there's no +v ah yeah there's no V whatever you can + + align:start position:0% +v ah yeah there's no V whatever you can + + + align:start position:0% +v ah yeah there's no V whatever you can +learn you're right thank you for every L + + align:start position:0% +learn you're right thank you for every L + + + align:start position:0% +learn you're right thank you for every L +there exist a simulator for every X for + + align:start position:0% +there exist a simulator for every X for + + + align:start position:0% +there exist a simulator for every X for +any auxilary that's it that's the + + align:start position:0% +any auxilary that's it that's the + + + align:start position:0% +any auxilary that's it that's the +definition okay cuz V doesn't send + + align:start position:0% +definition okay cuz V doesn't send + + + align:start position:0% +definition okay cuz V doesn't send +anything okay now here's note what what + + align:start position:0% +anything okay now here's note what what + + + align:start position:0% +anything okay now here's note what what +the reason this is still zero knowledge + + align:start position:0% +the reason this is still zero knowledge + + + align:start position:0% +the reason this is still zero knowledge +is + + align:start position:0% +is + + + align:start position:0% +is +that now the simulator he gets to choose + + align:start position:0% +that now the simulator he gets to choose + + + align:start position:0% +that now the simulator he gets to choose +the + + align:start position:0% +the + + + align:start position:0% +the +CRS the simulator he outputs this + + align:start position:0% +CRS the simulator he outputs this + + + align:start position:0% +CRS the simulator he outputs this +simulator outputs a CRS and some fake + + align:start position:0% +simulator outputs a CRS and some fake + + + align:start position:0% +simulator outputs a CRS and some fake +proof P that should be + + align:start position:0% +proof P that should be + + + align:start position:0% +proof P that should be +indistinguishable even given + + align:start position:0% + + + + align:start position:0% + +augs so really it's + + align:start position:0% +augs so really it's + + + align:start position:0% +augs so really it's +um a and the point is the simulator he + + align:start position:0% +um a and the point is the simulator he + + + align:start position:0% +um a and the point is the simulator he +can he can he has the power to choose + + align:start position:0% +can he can he has the power to choose + + + align:start position:0% +can he can he has the power to choose +the CRS this is a power that the + + align:start position:0% +the CRS this is a power that the + + + align:start position:0% +the CRS this is a power that the +cheating prover does not + + align:start position:0% +cheating prover does not + + + align:start position:0% +cheating prover does not +have and that's + + align:start position:0% +have and that's + + + align:start position:0% +have and that's +why if you could prove that Fe the the + + align:start position:0% +why if you could prove that Fe the the + + + align:start position:0% +why if you could prove that Fe the the +fact that F works for the fact that you + + align:start position:0% +fact that F works for the fact that you + + + align:start position:0% +fact that F works for the fact that you +have a it's it doesn't there's no + + align:start position:0% +have a it's it doesn't there's no + + + align:start position:0% +have a it's it doesn't there's no +contradiction with the fact that it's + + align:start position:0% +contradiction with the fact that it's + + + align:start position:0% +contradiction with the fact that it's +zero knowledge and F chir sound because + + align:start position:0% +zero knowledge and F chir sound because + + + align:start position:0% +zero knowledge and F chir sound because +the fact that it's zero knowled the fact + + align:start position:0% +the fact that it's zero knowled the fact + + + align:start position:0% +the fact that it's zero knowled the fact +that it's F chir sound + + align:start position:0% +that it's F chir sound + + + align:start position:0% +that it's F chir sound +or in other words the fact that it's + + align:start position:0% +or in other words the fact that it's + + + align:start position:0% +or in other words the fact that it's +zero + + align:start position:0% +zero + + + align:start position:0% +zero +knowledge does not mean that you can use + + align:start position:0% +knowledge does not mean that you can use + + + align:start position:0% +knowledge does not mean that you can use +the simulator as a cheating prover the + + align:start position:0% +the simulator as a cheating prover the + + + align:start position:0% +the simulator as a cheating prover the +simulator succeeds in simulating because + + align:start position:0% +simulator succeeds in simulating because + + + align:start position:0% +simulator succeeds in simulating because +he has the power to fake the CRS the + + align:start position:0% +he has the power to fake the CRS the + + + align:start position:0% +he has the power to fake the CRS the +cheating Pro does not have that + + align:start position:0% +cheating Pro does not have that + + + align:start position:0% +cheating Pro does not have that +power okay again remember before we said + + align:start position:0% +power okay again remember before we said + + + align:start position:0% +power okay again remember before we said +oh if you have fear then the simulator + + align:start position:0% +oh if you have fear then the simulator + + + align:start position:0% +oh if you have fear then the simulator +because he can + + align:start position:0% +because he can + + + align:start position:0% +because he can +simulate uh the view he can he can also + + align:start position:0% +simulate uh the view he can he can also + + + align:start position:0% +simulate uh the view he can he can also +simulate a view in the case of cheating + + align:start position:0% +simulate a view in the case of cheating + + + align:start position:0% +simulate a view in the case of cheating +so he can actually break Fe here he + + align:start position:0% +so he can actually break Fe here he + + + align:start position:0% +so he can actually break Fe here he +can't break F because I mean the prover + + align:start position:0% +can't break F because I mean the prover + + + align:start position:0% +can't break F because I mean the prover +can't the simulator can because he has + + align:start position:0% +can't the simulator can because he has + + + align:start position:0% +can't the simulator can because he has +an additional power that a cheating + + align:start position:0% +an additional power that a cheating + + + align:start position:0% +an additional power that a cheating +prover does not have he can fake the + + align:start position:0% +prover does not have he can fake the + + + align:start position:0% +prover does not have he can fake the +he's the one who gets to choose the CRS + + align:start position:0% +he's the one who gets to choose the CRS + + + align:start position:0% +he's the one who gets to choose the CRS +and that's the only reason why we can + + align:start position:0% +and that's the only reason why we can + + + align:start position:0% +and that's the only reason why we can +actually get ank here because he's we're + + align:start position:0% +actually get ank here because he's we're + + + align:start position:0% +actually get ank here because he's we're +gonna he's going to choose the CRS to + + align:start position:0% +gonna he's going to choose the CRS to + + + align:start position:0% +gonna he's going to choose the CRS to +his liking in an indistinguishable way + + align:start position:0% +his liking in an indistinguishable way + + + align:start position:0% +his liking in an indistinguishable way +of + + align:start position:0% +of + + + align:start position:0% +of +course but I mean this CRS and This Ss + + align:start position:0% +course but I mean this CRS and This Ss + + + align:start position:0% +course but I mean this CRS and This Ss +are + + align:start position:0% +are + + + align:start position:0% +are +indistinguishable but he can kind of + + align:start position:0% +indistinguishable but he can kind of + + + align:start position:0% +indistinguishable but he can kind of +program it that's that's the idea + + align:start position:0% +program it that's that's the idea + + + align:start position:0% +program it that's that's the idea +so let me just tell you why it's zero + + align:start position:0% +so let me just tell you why it's zero + + + align:start position:0% +so let me just tell you why it's zero +knowledge and then you'll see because + + align:start position:0% +knowledge and then you'll see because + + + align:start position:0% +knowledge and then you'll see because +you know why it's F secure I'll tell you + + align:start position:0% +you know why it's F secure I'll tell you + + + align:start position:0% +you know why it's F secure I'll tell you +why it's Z knowledge and then you'll see + + align:start position:0% +why it's Z knowledge and then you'll see + + + align:start position:0% +why it's Z knowledge and then you'll see +how I'm where how I'm abusing the power + + align:start position:0% +how I'm where how I'm abusing the power + + + align:start position:0% +how I'm where how I'm abusing the power +of the + + align:start position:0% +of the + + + align:start position:0% +of the +simulator + + align:start position:0% +simulator + + + align:start position:0% +simulator +okay so the way the reason why it's uh + + align:start position:0% +okay so the way the reason why it's uh + + + align:start position:0% +okay so the way the reason why it's uh +Zer it's NK it's nonactive zeron so I + + align:start position:0% +Zer it's NK it's nonactive zeron so I + + + align:start position:0% +Zer it's NK it's nonactive zeron so I +need to come up with a simulator I need + + align:start position:0% +need to come up with a simulator I need + + + align:start position:0% +need to come up with a simulator I need +to simulate the F + + align:start position:0% +to simulate the F + + + align:start position:0% +to simulate the F +protocol and actually if you think about + + align:start position:0% +protocol and actually if you think about + + + align:start position:0% +protocol and actually if you think about +it how can I simulate it I need to come + + align:start position:0% +it how can I simulate it I need to come + + + align:start position:0% +it how can I simulate it I need to come +up with an think what I need to do I'm + + align:start position:0% +up with an think what I need to do I'm + + + align:start position:0% +up with an think what I need to do I'm +the simulator it seems like a hard task + + align:start position:0% +the simulator it seems like a hard task + + + align:start position:0% +the simulator it seems like a hard task +for me what do I need to do as a + + align:start position:0% +for me what do I need to do as a + + + align:start position:0% +for me what do I need to do as a +simulator so what does the Sim do Sim + + align:start position:0% +simulator so what does the Sim do Sim + + + align:start position:0% +simulator so what does the Sim do Sim +needs to he he needs to generate CRS + + align:start position:0% +needs to he he needs to generate CRS + + + align:start position:0% +needs to he he needs to generate CRS +somehow I don't know okay I can just + + align:start position:0% +somehow I don't know okay I can just + + + align:start position:0% +somehow I don't know okay I can just +generate publicly and hash key but + + align:start position:0% +generate publicly and hash key but + + + align:start position:0% +generate publicly and hash key but +then I need to find like Alpha Beta + + align:start position:0% +then I need to find like Alpha Beta + + + align:start position:0% +then I need to find like Alpha Beta +gamma accepting so I guess first note + + align:start position:0% +gamma accepting so I guess first note + + + align:start position:0% +gamma accepting so I guess first note +look the simulator is given oh wait he's + + align:start position:0% +look the simulator is given oh wait he's + + + align:start position:0% +look the simulator is given oh wait he's +given also X forgot to write X he's + + align:start position:0% +given also X forgot to write X he's + + + align:start position:0% +given also X forgot to write X he's +given the instance X and + + align:start position:0% +given the instance X and + + + align:start position:0% +given the instance X and +augs now note I'm the Simulator X can be + + align:start position:0% +augs now note I'm the Simulator X can be + + + align:start position:0% +augs now note I'm the Simulator X can be +in the language X cannot be in the + + align:start position:0% +in the language X cannot be in the + + + align:start position:0% +in the language X cannot be in the +language I have no idea what x + + align:start position:0% +language I have no idea what x + + + align:start position:0% +language I have no idea what x +is okay so in if I if I succeed I should + + align:start position:0% +is okay so in if I if I succeed I should + + + align:start position:0% +is okay so in if I if I succeed I should +also succeed for some for some x's not + + align:start position:0% +also succeed for some for some x's not + + + align:start position:0% +also succeed for some for some x's not +in the language because I I can't break + + align:start position:0% +in the language because I I can't break + + + align:start position:0% +in the language because I I can't break +the language now if to succeed for X9 in + + align:start position:0% +the language now if to succeed for X9 in + + + align:start position:0% +the language now if to succeed for X9 in +the language I need to generate beta + + align:start position:0% +the language I need to generate beta + + + align:start position:0% +the language I need to generate beta +that's bad otherwise I can't + + align:start position:0% +that's bad otherwise I can't + + + align:start position:0% +that's bad otherwise I can't +succeed but how can I generate B bet + + align:start position:0% +succeed but how can I generate B bet + + + align:start position:0% +succeed but how can I generate B bet +that's bad I remember the encryption H + + align:start position:0% +that's bad I remember the encryption H + + + align:start position:0% +that's bad I remember the encryption H +it's a problem the reason it's not a + + align:start position:0% +it's a problem the reason it's not a + + + align:start position:0% +it's a problem the reason it's not a +problem because I'm going to break the + + align:start position:0% +problem because I'm going to break the + + + align:start position:0% +problem because I'm going to break the +encryption I get to choose it I choose + + align:start position:0% +encryption I get to choose it I choose + + + align:start position:0% +encryption I get to choose it I choose +the encryption I chose it with a secret + + align:start position:0% +the encryption I chose it with a secret + + + align:start position:0% +the encryption I chose it with a secret +key and actually actually let me be a + + align:start position:0% +key and actually actually let me be a + + + align:start position:0% +key and actually actually let me be a +um actually for this specific hash + + align:start position:0% +um actually for this specific hash + + + align:start position:0% +um actually for this specific hash +function I actually don't know how to + + align:start position:0% +function I actually don't know how to + + + align:start position:0% +function I actually don't know how to +prove that it's an isic it may be I + + align:start position:0% +prove that it's an isic it may be I + + + align:start position:0% +prove that it's an isic it may be I +don't know but I don't know how to prove + + align:start position:0% +don't know but I don't know how to prove + + + align:start position:0% +don't know but I don't know how to prove +it but if you slightly change that hash + + align:start position:0% +it but if you slightly change that hash + + + align:start position:0% +it but if you slightly change that hash +function in a way that doesn't affect + + align:start position:0% +function in a way that doesn't affect + + + align:start position:0% +function in a way that doesn't affect +soundness at all then I can prove that + + align:start position:0% +soundness at all then I can prove that + + + align:start position:0% +soundness at all then I can prove that +it's AIC so I'm going to slightly change + + align:start position:0% +it's AIC so I'm going to slightly change + + + align:start position:0% +it's AIC so I'm going to slightly change +the hash function the F hash function + + align:start position:0% +the hash function the F hash function + + + align:start position:0% +the hash function the F hash function +okay I'm going to slightly change it + + align:start position:0% +okay I'm going to slightly change it + + + align:start position:0% +okay I'm going to slightly change it +just add a constant to + + align:start position:0% +just add a constant to + + + align:start position:0% +just add a constant to +it I'm going to argue that it doesn't + + align:start position:0% +it I'm going to argue that it doesn't + + + align:start position:0% +it I'm going to argue that it doesn't +change the uh soundness and uh but now I + + align:start position:0% +change the uh soundness and uh but now I + + + align:start position:0% +change the uh soundness and uh but now I +can use it for niic so let me show you + + align:start position:0% +can use it for niic so let me show you + + + align:start position:0% +can use it for niic so let me show you +how this is + + align:start position:0% +how this is + + + align:start position:0% +how this is +done so how do I generate this Alpha + + align:start position:0% +done so how do I generate this Alpha + + + align:start position:0% +done so how do I generate this Alpha +Beta gamma so the first thing I'm going + + align:start position:0% +Beta gamma so the first thing I'm going + + + align:start position:0% +Beta gamma so the first thing I'm going +to do I'm going to you know what I'm + + align:start position:0% +to do I'm going to you know what I'm + + + align:start position:0% +to do I'm going to you know what I'm +going to just generate beta completely + + align:start position:0% +going to just generate beta completely + + + align:start position:0% +going to just generate beta completely +random okay so I'm going to actually use + + align:start position:0% +random okay so I'm going to actually use + + + align:start position:0% +random okay so I'm going to actually use +kind of a the way remember last time we + + align:start position:0% +kind of a the way remember last time we + + + align:start position:0% +kind of a the way remember last time we +showed why the + + align:start position:0% +showed why the + + + align:start position:0% +showed why the +single um uh the the one bit protocol is + + align:start position:0% +single um uh the the one bit protocol is + + + align:start position:0% +single um uh the the one bit protocol is +zero knowledge I'm going to use that + + align:start position:0% +zero knowledge I'm going to use that + + + align:start position:0% +zero knowledge I'm going to use that +that idea or in other words I'm going to + + align:start position:0% +that idea or in other words I'm going to + + + align:start position:0% +that idea or in other words I'm going to +first use a simulator first I'm going to + + align:start position:0% +first use a simulator first I'm going to + + + align:start position:0% +first use a simulator first I'm going to +use a honest verifier ZK simulator this + + align:start position:0% +use a honest verifier ZK simulator this + + + align:start position:0% +use a honest verifier ZK simulator this +is just short for honest verifier + + align:start position:0% + + + + align:start position:0% + +so I'm going to use a simul I want to + + align:start position:0% +so I'm going to use a simul I want to + + + align:start position:0% +so I'm going to use a simul I want to +First argue this protocol alpab beta + + align:start position:0% +First argue this protocol alpab beta + + + align:start position:0% +First argue this protocol alpab beta +gamma even repeat it in parallel repeat + + align:start position:0% +gamma even repeat it in parallel repeat + + + align:start position:0% +gamma even repeat it in parallel repeat +it in parallel right so it's honest + + align:start position:0% +it in parallel right so it's honest + + + align:start position:0% +it in parallel right so it's honest +verifi your knowledge what does it mean + + align:start position:0% +verifi your knowledge what does it mean + + + align:start position:0% +verifi your knowledge what does it mean +honest verifier the verifier just sends + + align:start position:0% +honest verifier the verifier just sends + + + align:start position:0% +honest verifier the verifier just sends +beta completely and random so B1 B2 up + + align:start position:0% +beta completely and random so B1 B2 up + + + align:start position:0% +beta completely and random so B1 B2 up +to B Lambda completely + + align:start position:0% +to B Lambda completely + + + align:start position:0% +to B Lambda completely +randomly then it's zero + + align:start position:0% +randomly then it's zero + + + align:start position:0% +randomly then it's zero +knowledge okay so that we kind of saw + + align:start position:0% +knowledge okay so that we kind of saw + + + align:start position:0% +knowledge okay so that we kind of saw +last time so first of all I want to + + align:start position:0% +last time so first of all I want to + + + align:start position:0% +last time so first of all I want to +argue that we have honest verifier of + + align:start position:0% +argue that we have honest verifier of + + + align:start position:0% +argue that we have honest verifier of +zero knowledge that's the first thing H + + align:start position:0% +zero knowledge that's the first thing H + + + align:start position:0% +zero knowledge that's the first thing H +the interactive protocol the interactive + + align:start position:0% +the interactive protocol the interactive + + + align:start position:0% +the interactive protocol the interactive +but parel repeated okay the interactive + + align:start position:0% +but parel repeated okay the interactive + + + align:start position:0% +but parel repeated okay the interactive +par repeated protocol is onest verifier + + align:start position:0% +par repeated protocol is onest verifier + + + align:start position:0% +par repeated protocol is onest verifier +zero + + align:start position:0% +zero + + + align:start position:0% +zero +knowledge + + align:start position:0% +knowledge + + + align:start position:0% +knowledge +why well it's very easy what I'm going + + align:start position:0% +why well it's very easy what I'm going + + + align:start position:0% +why well it's very easy what I'm going +to do I'm the simulator what I'm going + + align:start position:0% +to do I'm the simulator what I'm going + + + align:start position:0% +to do I'm the simulator what I'm going +to do I'm going to first I need to + + align:start position:0% +to do I'm going to first I need to + + + align:start position:0% +to do I'm going to first I need to +generate a transcript what I'm going to + + align:start position:0% +generate a transcript what I'm going to + + + align:start position:0% +generate a transcript what I'm going to +do I'm going to first generate it + + align:start position:0% +do I'm going to first generate it + + + align:start position:0% +do I'm going to first generate it +generate the B's B1 B2 up to B Lambda at + + align:start position:0% +generate the B's B1 B2 up to B Lambda at + + + align:start position:0% +generate the B's B1 B2 up to B Lambda at +random now I know what I'm now I know + + align:start position:0% +random now I know what I'm now I know + + + align:start position:0% +random now I know what I'm now I know +okay if B equals zero I'm going to just + + align:start position:0% +okay if B equals zero I'm going to just + + + align:start position:0% +okay if B equals zero I'm going to just +commit to uh I'm going to commit here + + align:start position:0% +commit to uh I'm going to commit here + + + align:start position:0% +commit to uh I'm going to commit here +just a completely random hamiltonian + + align:start position:0% +just a completely random hamiltonian + + + align:start position:0% +just a completely random hamiltonian +cycle have nothing to do with the graph + + align:start position:0% +cycle have nothing to do with the graph + + + align:start position:0% +cycle have nothing to do with the graph +if I need to open if B was one I'm going + + align:start position:0% +if I need to open if B was one I'm going + + + align:start position:0% +if I need to open if B was one I'm going +to just really commit to Pi of G won't + + align:start position:0% +to just really commit to Pi of G won't + + + align:start position:0% +to just really commit to Pi of G won't +have any antonian cycle in it but I'm + + align:start position:0% +have any antonian cycle in it but I'm + + + align:start position:0% +have any antonian cycle in it but I'm +going to commit the pi + + align:start position:0% +going to commit the pi + + + align:start position:0% +going to commit the pi +ofg so that's going to be my simulation + + align:start position:0% +ofg so that's going to be my simulation + + + align:start position:0% +ofg so that's going to be my simulation +okay we it's kind of a little bit of + + align:start position:0% +okay we it's kind of a little bit of + + + align:start position:0% +okay we it's kind of a little bit of +what we did it's similar to what we did + + align:start position:0% +what we did it's similar to what we did + + + align:start position:0% +what we did it's similar to what we did +last time but it's even easier because + + align:start position:0% +last time but it's even easier because + + + align:start position:0% +last time but it's even easier because +the verifire is completely honest + + align:start position:0% +the verifire is completely honest + + + align:start position:0% +the verifire is completely honest +okay and let me repeat it how do I + + align:start position:0% +okay and let me repeat it how do I + + + align:start position:0% +okay and let me repeat it how do I +generate this transcript repeated Lambda + + align:start position:0% +generate this transcript repeated Lambda + + + align:start position:0% +generate this transcript repeated Lambda +times in parallel I need to generate + + align:start position:0% +times in parallel I need to generate + + + align:start position:0% +times in parallel I need to generate +Alpha Beta gamma that looks like real + + align:start position:0% +Alpha Beta gamma that looks like real + + + align:start position:0% +Alpha Beta gamma that looks like real +I'm going to first generate the beta so + + align:start position:0% +I'm going to first generate the beta so + + + align:start position:0% +I'm going to first generate the beta so +B one of to B Lambda that's the first + + align:start position:0% +B one of to B Lambda that's the first + + + align:start position:0% +B one of to B Lambda that's the first +thing then I'm going to generate Alpha + + align:start position:0% +thing then I'm going to generate Alpha + + + align:start position:0% +thing then I'm going to generate Alpha +I'm gonna take it out of order how do I + + align:start position:0% +I'm gonna take it out of order how do I + + + align:start position:0% +I'm gonna take it out of order how do I +generate Alpha well if the B + + align:start position:0% +generate Alpha well if the B + + + align:start position:0% +generate Alpha well if the B +corresponding to the let's say how the + + align:start position:0% +corresponding to the let's say how the + + + align:start position:0% +corresponding to the let's say how the +first Alpha if the B was Zero I know I + + align:start position:0% +first Alpha if the B was Zero I know I + + + align:start position:0% +first Alpha if the B was Zero I know I +need to open to the hamiltonian cycle + + align:start position:0% +need to open to the hamiltonian cycle + + + align:start position:0% +need to open to the hamiltonian cycle +I'll I'll I'll commit down random aonian + + align:start position:0% +I'll I'll I'll commit down random aonian + + + align:start position:0% +I'll I'll I'll commit down random aonian +cycle if the bit B was one I know that I + + align:start position:0% +cycle if the bit B was one I know that I + + + align:start position:0% +cycle if the bit B was one I know that I +will need to open the pi and the + + align:start position:0% +will need to open the pi and the + + + align:start position:0% +will need to open the pi and the +non-edges then I'll just commit to Pi G + + align:start position:0% +non-edges then I'll just commit to Pi G + + + align:start position:0% +non-edges then I'll just commit to Pi G +honestly there's not going to be a homon + + align:start position:0% +honestly there's not going to be a homon + + + align:start position:0% +honestly there's not going to be a homon +cycle in there but I know I'm not going + + align:start position:0% +cycle in there but I know I'm not going + + + align:start position:0% +cycle in there but I know I'm not going +to be asked to open it and that's what I + + align:start position:0% +to be asked to open it and that's what I + + + align:start position:0% +to be asked to open it and that's what I +do bit by + + align:start position:0% +do bit by + + + align:start position:0% +do bit by +bit so because I know beta I choose + + align:start position:0% +bit so because I know beta I choose + + + align:start position:0% +bit so because I know beta I choose +Alpha to be kind of I exactly choose + + align:start position:0% +Alpha to be kind of I exactly choose + + + align:start position:0% +Alpha to be kind of I exactly choose +Alpha to hit the bad on + + align:start position:0% +Alpha to hit the bad on + + + align:start position:0% +Alpha to hit the bad on +purpose okay so that's I I so I I can + + align:start position:0% +purpose okay so that's I I so I I can + + + align:start position:0% +purpose okay so that's I I so I I can +choose Alpha so I can choose Alpha Beta + + align:start position:0% +choose Alpha so I can choose Alpha Beta + + + align:start position:0% +choose Alpha so I can choose Alpha Beta +G + + align:start position:0% +G + + + align:start position:0% +G +to hit the bad but now what do I do with + + align:start position:0% +to hit the bad but now what do I do with + + + align:start position:0% +to hit the bad but now what do I do with +the hash function how do I I didn't + + align:start position:0% +the hash function how do I I didn't + + + align:start position:0% +the hash function how do I I didn't +choose the hash function yet remember + + align:start position:0% +choose the hash function yet remember + + + align:start position:0% +choose the hash function yet remember +now I'm going to choose the hash + + align:start position:0% +now I'm going to choose the hash + + + align:start position:0% +now I'm going to choose the hash +function so now I want to be able now I + + align:start position:0% +function so now I want to be able now I + + + align:start position:0% +function so now I want to be able now I +want to + + align:start position:0% + + + + align:start position:0% + +choose hash key such that you know eval + + align:start position:0% +choose hash key such that you know eval + + + align:start position:0% +choose hash key such that you know eval +the hash key and Alpha actually an G of + + align:start position:0% +the hash key and Alpha actually an G of + + + align:start position:0% +the hash key and Alpha actually an G of +alpha but I'm going to Adit G for + + align:start position:0% +alpha but I'm going to Adit G for + + + align:start position:0% +alpha but I'm going to Adit G for +Simplicity is equal to that beta which + + align:start position:0% +Simplicity is equal to that beta which + + + align:start position:0% +Simplicity is equal to that beta which +is the bad beta + + align:start position:0% + + + + align:start position:0% + +how can I do this is it so can I choose + + align:start position:0% +how can I do this is it so can I choose + + + align:start position:0% +how can I do this is it so can I choose +hash key subject to + + align:start position:0% + + + + align:start position:0% + +this I I can choose the public key the + + align:start position:0% +this I I can choose the public key the + + + align:start position:0% +this I I can choose the public key the +secret key everything you know I can + + align:start position:0% +secret key everything you know I can + + + align:start position:0% +secret key everything you know I can +break the encryption but can I choose it + + align:start position:0% +break the encryption but can I choose it + + + align:start position:0% +break the encryption but can I choose it +subject to so actually to tell you the + + align:start position:0% +subject to so actually to tell you the + + + align:start position:0% +subject to so actually to tell you the +truth I don't really know if you can do + + align:start position:0% +truth I don't really know if you can do + + + align:start position:0% +truth I don't really know if you can do +it but let me change slightly the hash + + align:start position:0% +it but let me change slightly the hash + + + align:start position:0% +it but let me change slightly the hash +function and now I'll be able to do that + + align:start position:0% +function and now I'll be able to do that + + + align:start position:0% +function and now I'll be able to do that +how do I change the hash + + align:start position:0% +how do I change the hash + + + align:start position:0% +how do I change the hash +function my hash function + + align:start position:0% +function my hash function + + + align:start position:0% +function my hash function +it's going to be the original hash + + align:start position:0% +it's going to be the original hash + + + align:start position:0% +it's going to be the original hash +function plus some fixed kind of Lambda + + align:start position:0% +function plus some fixed kind of Lambda + + + align:start position:0% +function plus some fixed kind of Lambda +so the hash function outputs some string + + align:start position:0% +so the hash function outputs some string + + + align:start position:0% +so the hash function outputs some string +0 one to the Lambda small Lambda I'm + + align:start position:0% +0 one to the Lambda small Lambda I'm + + + align:start position:0% +0 one to the Lambda small Lambda I'm +going to just add a random completely + + align:start position:0% +going to just add a random completely + + + align:start position:0% +going to just add a random completely +random Lambda bit string to it ah now I + + align:start position:0% +random Lambda bit string to it ah now I + + + align:start position:0% +random Lambda bit string to it ah now I +don't like this letter because it + + align:start position:0% +don't like this letter because it + + + align:start position:0% +don't like this letter because it +sound I'm going to add Z in 0 one to the + + align:start position:0% +sound I'm going to add Z in 0 one to the + + + align:start position:0% +sound I'm going to add Z in 0 one to the +Lambda a random Lambda bit string + + align:start position:0% +Lambda a random Lambda bit string + + + align:start position:0% +Lambda a random Lambda bit string +now now I'm in business that's easy now + + align:start position:0% +now now I'm in business that's easy now + + + align:start position:0% +now now I'm in business that's easy now +because now I want to make sure that + + align:start position:0% +because now I want to make sure that + + + align:start position:0% +because now I want to make sure that +okay so now I need this to be equal to + + align:start position:0% +okay so now I need this to be equal to + + + align:start position:0% +okay so now I need this to be equal to +Beta no problem I'll choose hash key + + align:start position:0% +Beta no problem I'll choose hash key + + + align:start position:0% +Beta no problem I'll choose hash key +honestly I'll compute this and I'll just + + align:start position:0% +honestly I'll compute this and I'll just + + + align:start position:0% +honestly I'll compute this and I'll just +in in the CRS so I told you how I + + align:start position:0% +in in the CRS so I told you how I + + + align:start position:0% +in in the CRS so I told you how I +simulate Alpha Beta gamma now I need to + + align:start position:0% +simulate Alpha Beta gamma now I need to + + + align:start position:0% +simulate Alpha Beta gamma now I need to +simulate the CRS what does the CRS + + align:start position:0% +simulate the CRS what does the CRS + + + align:start position:0% +simulate the CRS what does the CRS +consists of it consists of the public + + align:start position:0% +consists of it consists of the public + + + align:start position:0% +consists of it consists of the public +key and the hash key I'll choose the + + align:start position:0% +key and the hash key I'll choose the + + + align:start position:0% +key and the hash key I'll choose the +public key randomly now the hash key + + align:start position:0% +public key randomly now the hash key + + + align:start position:0% +public key randomly now the hash key +consists of of this part and this part + + align:start position:0% +consists of of this part and this part + + + align:start position:0% +consists of of this part and this part +it's like now two hash keys because it's + + align:start position:0% +it's like now two hash keys because it's + + + align:start position:0% +it's like now two hash keys because it's +the original hash keys but I also add a + + align:start position:0% +the original hash keys but I also add a + + + align:start position:0% +the original hash keys but I also add a +fixed Z to it that's my new hash key + + align:start position:0% +fixed Z to it that's my new hash key + + + align:start position:0% +fixed Z to it that's my new hash key +okay my new hash + + align:start position:0% +okay my new hash + + + align:start position:0% +okay my new hash +function does the previous hash function + + align:start position:0% +function does the previous hash function + + + align:start position:0% +function does the previous hash function +and adds z z is fixed it's part of the + + align:start position:0% +and adds z z is fixed it's part of the + + + align:start position:0% +and adds z z is fixed it's part of the +description of the hash + + align:start position:0% +description of the hash + + + align:start position:0% +description of the hash +function so now how do I generate the + + align:start position:0% +function so now how do I generate the + + + align:start position:0% +function so now how do I generate the +CRS so for CRS so to generate a CRS I'm + + align:start position:0% +CRS so for CRS so to generate a CRS I'm + + + align:start position:0% +CRS so for CRS so to generate a CRS I'm +going to choose a random public key a + + align:start position:0% +going to choose a random public key a + + + align:start position:0% +going to choose a random public key a +random hash key + + align:start position:0% +random hash key + + + align:start position:0% +random hash key +and Z such that this equation is + + align:start position:0% +and Z such that this equation is + + + align:start position:0% +and Z such that this equation is +satisfied I'm going to choose Z which is + + align:start position:0% +satisfied I'm going to choose Z which is + + + align:start position:0% +satisfied I'm going to choose Z which is +equal to I chose Alpha Beta gamma I + + align:start position:0% +equal to I chose Alpha Beta gamma I + + + align:start position:0% +equal to I chose Alpha Beta gamma I +chose the I chose already Hashi so this + + align:start position:0% +chose the I chose already Hashi so this + + + align:start position:0% +chose the I chose already Hashi so this +defines this the the eval so Z is just + + align:start position:0% +defines this the the eval so Z is just + + + align:start position:0% +defines this the the eval so Z is just +going to be beta minus or xor I'm in I'm + + align:start position:0% +going to be beta minus or xor I'm in I'm + + + align:start position:0% +going to be beta minus or xor I'm in I'm +over strings so xor this + + align:start position:0% + + + + align:start position:0% + +Evan and this is a good simulation + + align:start position:0% + + + + align:start position:0% + +so now let me go back to your question + + align:start position:0% +so now let me go back to your question + + + align:start position:0% +so now let me go back to your question +which + + align:start position:0% +which + + + align:start position:0% +which +was so okay so the question was so this + + align:start position:0% +was so okay so the question was so this + + + align:start position:0% +was so okay so the question was so this +is going to be it's zero knowledge it's + + align:start position:0% +is going to be it's zero knowledge it's + + + align:start position:0% +is going to be it's zero knowledge it's +computational zero knowledge it's not + + align:start position:0% +computational zero knowledge it's not + + + align:start position:0% +computational zero knowledge it's not +statistical zero knowledge because the + + align:start position:0% +statistical zero knowledge because the + + + align:start position:0% +statistical zero knowledge because the +alpha contains actually the when I + + align:start position:0% +alpha contains actually the when I + + + align:start position:0% +alpha contains actually the when I +simulate it I don't simulate it with a + + align:start position:0% +simulate it I don't simulate it with a + + + align:start position:0% +simulate it I don't simulate it with a +real Pi of c i simulate it with junk so + + align:start position:0% +real Pi of c i simulate it with junk so + + + align:start position:0% +real Pi of c i simulate it with junk so +it's only computational zero knowledge + + align:start position:0% +it's only computational zero knowledge + + + align:start position:0% +it's only computational zero knowledge +but it's statistical um and it's not + + align:start position:0% +but it's statistical um and it's not + + + align:start position:0% +but it's statistical um and it's not +even statistical soundness because I'm + + align:start position:0% +even statistical soundness because I'm + + + align:start position:0% +even statistical soundness because I'm +using FH so I don't I I don't get + + align:start position:0% +using FH so I don't I I don't get + + + align:start position:0% +using FH so I don't I I don't get +anything computation is zero knowledge + + align:start position:0% +anything computation is zero knowledge + + + align:start position:0% +anything computation is zero knowledge +and computational + + align:start position:0% + + + + align:start position:0% + +soundness there is a way to get + + align:start position:0% +soundness there is a way to get + + + align:start position:0% +soundness there is a way to get +statistical if you play with it but this + + align:start position:0% +statistical if you play with it but this + + + align:start position:0% +statistical if you play with it but this +the way I I explained it it's everything + + align:start position:0% +the way I I explained it it's everything + + + align:start position:0% +the way I I explained it it's everything +is + + align:start position:0% + + + + align:start position:0% + +computational + + align:start position:0% + + + + align:start position:0% + +yeah the final + + align:start position:0% +yeah the final + + + align:start position:0% +yeah the final +key is the and then you have that random + + align:start position:0% +key is the and then you have that random + + + align:start position:0% +key is the and then you have that random +but in real case it will be just good + + align:start position:0% +but in real case it will be just good + + + align:start position:0% +but in real case it will be just good +good good great great great question so + + align:start position:0% +good good great great great question so + + + align:start position:0% +good good great great great question so +you're saying you're saying wait so I + + align:start position:0% +you're saying you're saying wait so I + + + align:start position:0% +you're saying you're saying wait so I +changed the I changed the hash key on + + align:start position:0% +changed the I changed the hash key on + + + align:start position:0% +changed the I changed the hash key on +you so before + + align:start position:0% +you so before + + + align:start position:0% +you so before +a let me erase + + align:start position:0% +a let me erase + + + align:start position:0% +a let me erase +this before the hash key was exactly + + align:start position:0% +this before the hash key was exactly + + + align:start position:0% +this before the hash key was exactly +what we wrote there that was the hash + + align:start position:0% +what we wrote there that was the hash + + + align:start position:0% +what we wrote there that was the hash +key now I changed the hash key now the + + align:start position:0% +key now I changed the hash key now the + + + align:start position:0% +key now I changed the hash key now the +hash key is + + align:start position:0% + + + + align:start position:0% + +what tell me first now the hatch key is + + align:start position:0% +what tell me first now the hatch key is + + + align:start position:0% +what tell me first now the hatch key is +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +this and + + align:start position:0% + + + + align:start position:0% + +z h a random Z so the has key consists + + align:start position:0% +z h a random Z so the has key consists + + + align:start position:0% +z h a random Z so the has key consists +of the + + align:start position:0% +of the + + + align:start position:0% +of the +a public encrypt FH public key publicy + + align:start position:0% +a public encrypt FH public key publicy + + + align:start position:0% +a public encrypt FH public key publicy +for fully homic encryption an encryption + + align:start position:0% +for fully homic encryption an encryption + + + align:start position:0% +for fully homic encryption an encryption +of a g that's in the analysis going to + + align:start position:0% +of a g that's in the analysis going to + + + align:start position:0% +of a g that's in the analysis going to +be okay in the analysis we're going to + + align:start position:0% +be okay in the analysis we're going to + + + align:start position:0% +be okay in the analysis we're going to +see what it's now changing a little + + align:start position:0% +see what it's now changing a little + + + align:start position:0% +see what it's now changing a little +because it's the Z but some G of fixed + + align:start position:0% +because it's the Z but some G of fixed + + + align:start position:0% +because it's the Z but some G of fixed +size like uh 0 to the T okay and a + + align:start position:0% +size like uh 0 to the T okay and a + + + align:start position:0% +size like uh 0 to the T okay and a +random Z and 01 to the Lambda that's it + + align:start position:0% +random Z and 01 to the Lambda that's it + + + align:start position:0% +random Z and 01 to the Lambda that's it +now I still want to argue I still want + + align:start position:0% +now I still want to argue I still want + + + align:start position:0% +now I still want to argue I still want +to argue that that um a that this G is + + align:start position:0% +to argue that that um a that this G is + + + align:start position:0% +to argue that that um a that this G is +not bad right I want to argue that I + + align:start position:0% +not bad right I want to argue that I + + + align:start position:0% +not bad right I want to argue that I +want to say that uh when I en when I do + + align:start position:0% +want to say that uh when I en when I do + + + align:start position:0% +want to say that uh when I en when I do +the for every Alpha when I do this fom + + align:start position:0% +the for every Alpha when I do this fom + + + align:start position:0% +the for every Alpha when I do this fom +morphic encryption it's it's not bad so + + align:start position:0% +morphic encryption it's it's not bad so + + + align:start position:0% +morphic encryption it's it's not bad so +for which G for which G Star when I do + + align:start position:0% +for which G for which G Star when I do + + + align:start position:0% +for which G for which G Star when I do +this so now okay now what I want to + + align:start position:0% +this so now okay now what I want to + + + align:start position:0% +this so now okay now what I want to +argue let me change this a little bit I + + align:start position:0% +argue let me change this a little bit I + + + align:start position:0% +argue let me change this a little bit I +guess now I want to argue that when I do + + align:start position:0% +guess now I want to argue that when I do + + + align:start position:0% +guess now I want to argue that when I do +this and I add Z it's not bad because I + + align:start position:0% +this and I add Z it's not bad because I + + + align:start position:0% +this and I add Z it's not bad because I +add Z so I want to argue that this is + + align:start position:0% +add Z so I want to argue that this is + + + align:start position:0% +add Z so I want to argue that this is +not equal to this minus Z or I guess xor + + align:start position:0% +not equal to this minus Z or I guess xor + + + align:start position:0% +not equal to this minus Z or I guess xor +we're doing everything xor so minus plus + + align:start position:0% +we're doing everything xor so minus plus + + + align:start position:0% +we're doing everything xor so minus plus +it's uh don't worry about it we'll we'll + + align:start position:0% +it's uh don't worry about it we'll we'll + + + align:start position:0% +it's uh don't worry about it we'll we'll +get it later um so I want to AR arue + + align:start position:0% +get it later um so I want to AR arue + + + align:start position:0% +get it later um so I want to AR arue +that this does not equal beta X or Z + + align:start position:0% +that this does not equal beta X or Z + + + align:start position:0% +that this does not equal beta X or Z +because my hash is not just this it's + + align:start position:0% +because my hash is not just this it's + + + align:start position:0% +because my hash is not just this it's +this X or Z that's my hash so I want to + + align:start position:0% +this X or Z that's my hash so I want to + + + align:start position:0% +this X or Z that's my hash so I want to +arue that this X or Z is not beta which + + align:start position:0% +arue that this X or Z is not beta which + + + align:start position:0% +arue that this X or Z is not beta which +is the same as saying that this is + + align:start position:0% +is the same as saying that this is + + + align:start position:0% +is the same as saying that this is +different than beta X or + + align:start position:0% +different than beta X or + + + align:start position:0% +different than beta X or +Z so now what I'm going to do I'm just + + align:start position:0% +Z so now what I'm going to do I'm just + + + align:start position:0% +Z so now what I'm going to do I'm just +going + + align:start position:0% +going + + + align:start position:0% +going +to here I'm going to exore in the + + align:start position:0% +to here I'm going to exore in the + + + align:start position:0% +to here I'm going to exore in the +analysis I'm going to say sure let me + + align:start position:0% +analysis I'm going to say sure let me + + + align:start position:0% +analysis I'm going to say sure let me +tell you if you change the G + + align:start position:0% +tell you if you change the G + + + align:start position:0% +tell you if you change the G +Star if you take G Star to be the + + align:start position:0% +Star if you take G Star to be the + + + align:start position:0% +Star if you take G Star to be the +decryption of bad X or Z and then change + + align:start position:0% +decryption of bad X or Z and then change + + + align:start position:0% +decryption of bad X or Z and then change +it a little bit xort was just one like 0 + + align:start position:0% +it a little bit xort was just one like 0 + + + align:start position:0% +it a little bit xort was just one like 0 +z0 one or then I can argue that you get + + align:start position:0% +z0 one or then I can argue that you get + + + align:start position:0% +z0 one or then I can argue that you get +statistical soundness so in the analysis + + align:start position:0% +statistical soundness so in the analysis + + + align:start position:0% +statistical soundness so in the analysis +I'm going to say okay you started with + + align:start position:0% +I'm going to say okay you started with + + + align:start position:0% +I'm going to say okay you started with +this g whatever it was suppose it was + + align:start position:0% +this g whatever it was suppose it was + + + align:start position:0% +this g whatever it was suppose it was +just this G and then I can argue that + + align:start position:0% +just this G and then I can argue that + + + align:start position:0% +just this G and then I can argue that +for this G it's never equal to this + + align:start position:0% +for this G it's never equal to this + + + align:start position:0% +for this G it's never equal to this +because exactly as before well if for + + align:start position:0% +because exactly as before well if for + + + align:start position:0% +because exactly as before well if for +this G star it will it was it was equal + + align:start position:0% +this G star it will it was it was equal + + + align:start position:0% +this G star it will it was it was equal +to a so now I guess a if it was equal to + + align:start position:0% +to a so now I guess a if it was equal to + + + align:start position:0% +to a so now I guess a if it was equal to +you + + align:start position:0% +you + + + align:start position:0% +you +know beta X or Z then if then the + + align:start position:0% +know beta X or Z then if then the + + + align:start position:0% +know beta X or Z then if then the +decryption would be equal and we got a + + align:start position:0% +decryption would be equal and we got a + + + align:start position:0% +decryption would be equal and we got a +contradiction so it's exactly the fact + + align:start position:0% +contradiction so it's exactly the fact + + + align:start position:0% +contradiction so it's exactly the fact +that I did I added Z has no significance + + align:start position:0% +that I did I added Z has no significance + + + align:start position:0% +that I did I added Z has no significance +on the proof it's exactly the same + + align:start position:0% + + + + align:start position:0% + +proof okay + + align:start position:0% +proof okay + + + align:start position:0% +proof okay +so uh so and that's how I I simulate and + + align:start position:0% +so uh so and that's how I I simulate and + + + align:start position:0% +so uh so and that's how I I simulate and +now I have a simulator so essentially + + align:start position:0% +now I have a simulator so essentially + + + align:start position:0% +now I have a simulator so essentially +the way I proved that it's zero + + align:start position:0% +the way I proved that it's zero + + + align:start position:0% +the way I proved that it's zero +knowledge is by doing just the honest + + align:start position:0% +knowledge is by doing just the honest + + + align:start position:0% +knowledge is by doing just the honest +verifier zero + + align:start position:0% +verifier zero + + + align:start position:0% +verifier zero +knowledge and then what I did in the + + align:start position:0% +knowledge and then what I did in the + + + align:start position:0% +knowledge and then what I did in the +with the CRS I chose the Z I chose I + + align:start position:0% +with the CRS I chose the Z I chose I + + + align:start position:0% +with the CRS I chose the Z I chose I +programmed part of the hash key if the + + align:start position:0% +programmed part of the hash key if the + + + align:start position:0% +programmed part of the hash key if the +hash key was programmed by someone else + + align:start position:0% +hash key was programmed by someone else + + + align:start position:0% +hash key was programmed by someone else +ahead of time and I couldn't touch it I + + align:start position:0% +ahead of time and I couldn't touch it I + + + align:start position:0% +ahead of time and I couldn't touch it I +don't know how to prove a soundness + + align:start position:0% +don't know how to prove a soundness + + + align:start position:0% +don't know how to prove a soundness +okay but I I don't know how to + + align:start position:0% +okay but I I don't know how to + + + align:start position:0% +okay but I I don't know how to +simulate but because I could I could uh + + align:start position:0% +simulate but because I could I could uh + + + align:start position:0% +simulate but because I could I could uh +do it I could simulate so the fact that + + align:start position:0% +do it I could simulate so the fact that + + + align:start position:0% +do it I could simulate so the fact that +I could I I had the freedom to program + + align:start position:0% +I could I I had the freedom to program + + + align:start position:0% +I could I I had the freedom to program +the hash key that's what allowed me to + + align:start position:0% +the hash key that's what allowed me to + + + align:start position:0% +the hash key that's what allowed me to +simulate and that's + + align:start position:0% +simulate and that's + + + align:start position:0% +simulate and that's +why there's no that's what broke the + + align:start position:0% +why there's no that's what broke the + + + align:start position:0% +why there's no that's what broke the +tension between and zero knowledge + + align:start position:0% +tension between and zero knowledge + + + align:start position:0% +tension between and zero knowledge +because in the interactive setting when + + align:start position:0% +because in the interactive setting when + + + align:start position:0% +because in the interactive setting when +there's no + + align:start position:0% +there's no + + + align:start position:0% +there's no +CRS then a simulator really has the same + + align:start position:0% +CRS then a simulator really has the same + + + align:start position:0% +CRS then a simulator really has the same +power as a cheating prover and now say + + align:start position:0% +power as a cheating prover and now say + + + align:start position:0% +power as a cheating prover and now say +if there's a simulator there's a + + align:start position:0% +if there's a simulator there's a + + + align:start position:0% +if there's a simulator there's a +cheating prover and when you think about + + align:start position:0% +cheating prover and when you think about + + + align:start position:0% +cheating prover and when you think about +the simulator thing about like a + + align:start position:0% +the simulator thing about like a + + + align:start position:0% +the simulator thing about like a +verifier who's like a f verifier like + + align:start position:0% +verifier who's like a f verifier like + + + align:start position:0% +verifier who's like a f verifier like +verifier that behaves like a f hash + + align:start position:0% +verifier that behaves like a f hash + + + align:start position:0% +verifier that behaves like a f hash +function then the simulator is exactly + + align:start position:0% +function then the simulator is exactly + + + align:start position:0% +function then the simulator is exactly +like a cheating Pro and then you say + + align:start position:0% +like a cheating Pro and then you say + + + align:start position:0% +like a cheating Pro and then you say +well there's no cheating Pro they can't + + align:start position:0% +well there's no cheating Pro they can't + + + align:start position:0% +well there's no cheating Pro they can't +exist a simulator but in the niic the + + align:start position:0% +exist a simulator but in the niic the + + + align:start position:0% +exist a simulator but in the niic the +simulator has much more power than this + + align:start position:0% +simulator has much more power than this + + + align:start position:0% +simulator has much more power than this +cheating prover he can choose the CRS he + + align:start position:0% +cheating prover he can choose the CRS he + + + align:start position:0% +cheating prover he can choose the CRS he +can program the CRS to his desire and + + align:start position:0% +can program the CRS to his desire and + + + align:start position:0% +can program the CRS to his desire and +that's what breaks that's kind of what + + align:start position:0% +that's what breaks that's kind of what + + + align:start position:0% +that's what breaks that's kind of what +allows us to get like both F and + + align:start position:0% +allows us to get like both F and + + + align:start position:0% +allows us to get like both F and +noninteractive z and the non like both + + align:start position:0% +noninteractive z and the non like both + + + align:start position:0% +noninteractive z and the non like both +sist and noninteractive zero + + align:start position:0% + + + + align:start position:0% + +knowledge any questions yeah does the r + + align:start position:0% +knowledge any questions yeah does the r + + + align:start position:0% +knowledge any questions yeah does the r +help is + + align:start position:0% +help is + + + align:start position:0% +help is +not ah okay okay good good good so now + + align:start position:0% +not ah okay okay good good good so now + + + align:start position:0% +not ah okay okay good good good so now +the qu okay so now the question is what + + align:start position:0% +the qu okay so now the question is what + + + align:start position:0% +the qu okay so now the question is what +if beta bad was not unique okay so let + + align:start position:0% +if beta bad was not unique okay so let + + + align:start position:0% +if beta bad was not unique okay so let +me I'll answer that because I have a + + align:start position:0% +me I'll answer that because I have a + + + align:start position:0% +me I'll answer that because I have a +longer question a longer answer to that + + align:start position:0% +longer question a longer answer to that + + + align:start position:0% +longer question a longer answer to that +but are there any other questions about + + align:start position:0% +but are there any other questions about + + + align:start position:0% +but are there any other questions about +this before I I answer that + + align:start position:0% +this before I I answer that + + + align:start position:0% +this before I I answer that +question okay + + align:start position:0% +question okay + + + align:start position:0% +question okay +so let's step back and see where where + + align:start position:0% +so let's step back and see where where + + + align:start position:0% +so let's step back and see where where +we are I I'm I'm on my way to your to + + align:start position:0% +we are I I'm I'm on my way to your to + + + align:start position:0% +we are I I'm I'm on my way to your to +answer your question because it's about + + align:start position:0% +answer your question because it's about + + + align:start position:0% +answer your question because it's about +how General this technique is so I want + + align:start position:0% +how General this technique is so I want + + + align:start position:0% +how General this technique is so I want +I'll get there uh but before I go to J + + align:start position:0% +I'll get there uh but before I go to J + + + align:start position:0% +I'll get there uh but before I go to J +technique let's see what we did today so + + align:start position:0% +technique let's see what we did today so + + + align:start position:0% +technique let's see what we did today so +far so we uh started + + align:start position:0% +far so we uh started + + + align:start position:0% +far so we uh started +by a we looked at this protocol the + + align:start position:0% +by a we looked at this protocol the + + + align:start position:0% +by a we looked at this protocol the +parallel repeated version and we said + + align:start position:0% +parallel repeated version and we said + + + align:start position:0% +parallel repeated version and we said +okay this protocol guess what it's F we + + align:start position:0% +okay this protocol guess what it's F we + + + align:start position:0% +okay this protocol guess what it's F we +actually constructed a certain hash + + align:start position:0% +actually constructed a certain hash + + + align:start position:0% +actually constructed a certain hash +function very specific hash function + + align:start position:0% +function very specific hash function + + + align:start position:0% +function very specific hash function +said that with respect to this hash + + align:start position:0% +said that with respect to this hash + + + align:start position:0% +said that with respect to this hash +function we proved + + align:start position:0% +function we proved + + + align:start position:0% +function we proved +sness and then we proved not only is it + + align:start position:0% +sness and then we proved not only is it + + + align:start position:0% +sness and then we proved not only is it +sound respect to now that it's not + + align:start position:0% +sound respect to now that it's not + + + align:start position:0% +sound respect to now that it's not +interactive we can also prove that it's + + align:start position:0% +interactive we can also prove that it's + + + align:start position:0% +interactive we can also prove that it's +zero knowledge like zero knowledge still + + align:start position:0% +zero knowledge like zero knowledge still + + + align:start position:0% +zero knowledge like zero knowledge still +maintains by playing with a + + align:start position:0% +maintains by playing with a + + + align:start position:0% +maintains by playing with a +CRS okay so uh so even before talking + + align:start position:0% +CRS okay so uh so even before talking + + + align:start position:0% +CRS okay so uh so even before talking +about generalization I just want to + + align:start position:0% +about generalization I just want to + + + align:start position:0% +about generalization I just want to +point this this was a huge open problem + + align:start position:0% +point this this was a huge open problem + + + align:start position:0% +point this this was a huge open problem +for a very long time to get niic under + + align:start position:0% +for a very long time to get niic under + + + align:start position:0% +for a very long time to get niic under +lwe uh even though what you saw it's + + align:start position:0% +lwe uh even though what you saw it's + + + align:start position:0% +lwe uh even though what you saw it's +only circular secure LW or under if you + + align:start position:0% +only circular secure LW or under if you + + + align:start position:0% +only circular secure LW or under if you +think under fhe you just saw the + + align:start position:0% +think under fhe you just saw the + + + align:start position:0% +think under fhe you just saw the +circular secure version but even with a + + align:start position:0% +circular secure version but even with a + + + align:start position:0% +circular secure version but even with a +circle secure + + align:start position:0% +circle secure + + + align:start position:0% +circle secure +version It's I still find it remarkable + + align:start position:0% +version It's I still find it remarkable + + + align:start position:0% +version It's I still find it remarkable +that I'm able to teach it like from + + align:start position:0% +that I'm able to teach it like from + + + align:start position:0% +that I'm able to teach it like from +beginning to end uh in one class uh I + + align:start position:0% +beginning to end uh in one class uh I + + + align:start position:0% +beginning to end uh in one class uh I +hope you understood but it seems like + + align:start position:0% +hope you understood but it seems like + + + align:start position:0% +hope you understood but it seems like +from your question you were pretty good + + align:start position:0% +from your question you were pretty good + + + align:start position:0% +from your question you were pretty good +A so um I don't know I wish I I could + + align:start position:0% +A so um I don't know I wish I I could + + + align:start position:0% +A so um I don't know I wish I I could +torture you with previous attempts that + + align:start position:0% +torture you with previous attempts that + + + align:start position:0% +torture you with previous attempts that +were much worse and much more + + align:start position:0% +were much worse and much more + + + align:start position:0% +were much worse and much more +complicated so you will really kind of + + align:start position:0% +complicated so you will really kind of + + + align:start position:0% +complicated so you will really kind of +appreciate this one uh but uh for me who + + align:start position:0% +appreciate this one uh but uh for me who + + + align:start position:0% +appreciate this one uh but uh for me who +you know uh shed a lot of tears and + + align:start position:0% +you know uh shed a lot of tears and + + + align:start position:0% +you know uh shed a lot of tears and +sweat with these previous approaches I + + align:start position:0% +sweat with these previous approaches I + + + align:start position:0% +sweat with these previous approaches I +totally appreciate the beauty of of this + + align:start position:0% +totally appreciate the beauty of of this + + + align:start position:0% +totally appreciate the beauty of of this +one uh + + align:start position:0% +one uh + + + align:start position:0% +one uh +okay but now so so far it was kind of + + align:start position:0% +okay but now so so far it was kind of + + + align:start position:0% +okay but now so so far it was kind of +the focus was on this protocol you know + + align:start position:0% +the focus was on this protocol you know + + + align:start position:0% +the focus was on this protocol you know +had this protocol we now we have under + + align:start position:0% +had this protocol we now we have under + + + align:start position:0% +had this protocol we now we have under +lwe great but how General is this + + align:start position:0% +lwe great but how General is this + + + align:start position:0% +lwe great but how General is this +technique and that's what I want to talk + + align:start position:0% +technique and that's what I want to talk + + + align:start position:0% +technique and that's what I want to talk +about next okay how General is it and I + + align:start position:0% +about next okay how General is it and I + + + align:start position:0% +about next okay how General is it and I +want to point out actually we said we + + align:start position:0% +want to point out actually we said we + + + align:start position:0% +want to point out actually we said we +used this specific structure very little + + align:start position:0% +used this specific structure very little + + + align:start position:0% +used this specific structure very little +what did we use a so let me actually a a + + align:start position:0% +what did we use a so let me actually a a + + + align:start position:0% +what did we use a so let me actually a a +let's see what I should + + align:start position:0% + + + + align:start position:0% + +erase let me start here + + align:start position:0% + + + + align:start position:0% + +so we use the fact what did we use here + + align:start position:0% +so we use the fact what did we use here + + + align:start position:0% +so we use the fact what did we use here +we used the fact that the beta was + + align:start position:0% +we used the fact that the beta was + + + align:start position:0% +we used the fact that the beta was +unique that's one thing we used can we + + align:start position:0% +unique that's one thing we used can we + + + align:start position:0% +unique that's one thing we used can we +do non-unique betas we can do non-unique + + align:start position:0% +do non-unique betas we can do non-unique + + + align:start position:0% +do non-unique betas we can do non-unique +betas but we pay so the number of bad + + align:start position:0% +betas but we pay so the number of bad + + + align:start position:0% +betas but we pay so the number of bad +betas can be let me we call it uh D but + + align:start position:0% +betas can be let me we call it uh D but + + + align:start position:0% +betas can be let me we call it uh D but +our assumption degrades with one over D + + align:start position:0% +our assumption degrades with one over D + + + align:start position:0% +our assumption degrades with one over D +because the way we deal with if there's + + align:start position:0% +because the way we deal with if there's + + + align:start position:0% +because the way we deal with if there's +many bads then essentially what I do is + + align:start position:0% +many bads then essentially what I do is + + + align:start position:0% +many bads then essentially what I do is +I'm going to guess which bad the the + + align:start position:0% +I'm going to guess which bad the the + + + align:start position:0% +I'm going to guess which bad the the +approver is going to cheat with and if + + align:start position:0% +approver is going to cheat with and if + + + align:start position:0% +approver is going to cheat with and if +I'm going to choose a b a a random beta + + align:start position:0% +I'm going to choose a b a a random beta + + + align:start position:0% +I'm going to choose a b a a random beta +out of this you know dbad betas with + + align:start position:0% +out of this you know dbad betas with + + + align:start position:0% +out of this you know dbad betas with +probably one over D I got I got the I + + align:start position:0% +probably one over D I got I got the I + + + align:start position:0% +probably one over D I got I got the I +guess his beta correctly and then + + align:start position:0% +guess his beta correctly and then + + + align:start position:0% +guess his beta correctly and then +everything else goes kind of continues + + align:start position:0% +everything else goes kind of continues + + + align:start position:0% +everything else goes kind of continues +as if it was unique so we canal with + + align:start position:0% +as if it was unique so we canal with + + + align:start position:0% +as if it was unique so we canal with +more betas but we pay with the number of + + align:start position:0% +more betas but we pay with the number of + + + align:start position:0% +more betas but we pay with the number of +betas of number of bad betas so if it's + + align:start position:0% +betas of number of bad betas so if it's + + + align:start position:0% +betas of number of bad betas so if it's +really really huge then it's a problem + + align:start position:0% +really really huge then it's a problem + + + align:start position:0% +really really huge then it's a problem +okay so we use the fact that it's Unique + + align:start position:0% +okay so we use the fact that it's Unique + + + align:start position:0% +okay so we use the fact that it's Unique +beta but we also used one more thing + + align:start position:0% +beta but we also used one more thing + + + align:start position:0% +beta but we also used one more thing +which is that we can efficiently compute + + align:start position:0% +which is that we can efficiently compute + + + align:start position:0% +which is that we can efficiently compute +the bad + + align:start position:0% +the bad + + + align:start position:0% +the bad +beta okay and that the the number + + align:start position:0% +beta okay and that the the number + + + align:start position:0% +beta okay and that the the number +actually I feel like the unique beta as + + align:start position:0% +actually I feel like the unique beta as + + + align:start position:0% +actually I feel like the unique beta as +I think your intuition was well you can + + align:start position:0% +I think your intuition was well you can + + + align:start position:0% +I think your intuition was well you can +get around it a little bit like is it + + align:start position:0% +get around it a little bit like is it + + + align:start position:0% +get around it a little bit like is it +unique well you know we can more as long + + align:start position:0% +unique well you know we can more as long + + + align:start position:0% +unique well you know we can more as long +as I'll guess it and as long as you know + + align:start position:0% +as I'll guess it and as long as you know + + + align:start position:0% +as I'll guess it and as long as you know +there is some degradation but the + + align:start position:0% +there is some degradation but the + + + align:start position:0% +there is some degradation but the +efficiency of the beta we really used it + + align:start position:0% +efficiency of the beta we really used it + + + align:start position:0% +efficiency of the beta we really used it +uh you know and the the C the hash + + align:start position:0% +uh you know and the the C the hash + + + align:start position:0% +uh you know and the the C the hash +function computes the bad data so I + + align:start position:0% +function computes the bad data so I + + + align:start position:0% +function computes the bad data so I +don't know at all how to deal with + + align:start position:0% +don't know at all how to deal with + + + align:start position:0% +don't know at all how to deal with +inefficient a bad betas but let me just + + align:start position:0% +inefficient a bad betas but let me just + + + align:start position:0% +inefficient a bad betas but let me just +um mention that still this result is + + align:start position:0% +um mention that still this result is + + + align:start position:0% +um mention that still this result is +very uh + + align:start position:0% +very uh + + + align:start position:0% +very uh +General and actually you can frame this + + align:start position:0% +General and actually you can frame this + + + align:start position:0% +General and actually you can frame this +result in a much more General framework + + align:start position:0% +result in a much more General framework + + + align:start position:0% +result in a much more General framework +uh which is than than kind of for this + + align:start position:0% +uh which is than than kind of for this + + + align:start position:0% +uh which is than than kind of for this +specific protocol and the general + + align:start position:0% +specific protocol and the general + + + align:start position:0% +specific protocol and the general +framework is the framework that's called + + align:start position:0% +framework is the framework that's called + + + align:start position:0% +framework is the framework that's called +correlation intractable so let me tell + + align:start position:0% +correlation intractable so let me tell + + + align:start position:0% +correlation intractable so let me tell +give you like let me just start with the + + align:start position:0% +give you like let me just start with the + + + align:start position:0% +give you like let me just start with the +definition what is a correlation and + + align:start position:0% +definition what is a correlation and + + + align:start position:0% +definition what is a correlation and +tractable hash function so correlation + + align:start position:0% +tractable hash function so correlation + + + align:start position:0% +tractable hash function so correlation +tractable hash function was you was + + align:start position:0% +tractable hash function was you was + + + align:start position:0% +tractable hash function was you was +defined in order in an attempt to + + align:start position:0% +defined in order in an attempt to + + + align:start position:0% +defined in order in an attempt to +prove and a hash function is correlation + + align:start position:0% +prove and a hash function is correlation + + + align:start position:0% +prove and a hash function is correlation +and tractable essentially if it if works + + align:start position:0% +and tractable essentially if it if works + + + align:start position:0% +and tractable essentially if it if works +with it that's kind of the idea so let + + align:start position:0% +with it that's kind of the idea so let + + + align:start position:0% +with it that's kind of the idea so let +me Define a Spector relation R so here's + + align:start position:0% +me Define a Spector relation R so here's + + + align:start position:0% +me Define a Spector relation R so here's +a + + align:start position:0% +a + + + align:start position:0% +a +definition a + + align:start position:0% +definition a + + + align:start position:0% +definition a +correlation + + align:start position:0% + + + + align:start position:0% + +intractable hash function Hash Hash + + align:start position:0% + + + + align:start position:0% + +family with respect to a relation R so + + align:start position:0% +family with respect to a relation R so + + + align:start position:0% +family with respect to a relation R so +we have some + + align:start position:0% +we have some + + + align:start position:0% +we have some +relation + + align:start position:0% +relation + + + align:start position:0% +relation +r r is a relation it's like a subset of + + align:start position:0% +r r is a relation it's like a subset of + + + align:start position:0% +r r is a relation it's like a subset of +X comma + + align:start position:0% +X comma + + + align:start position:0% +X comma +y okay you can think of X as let's say + + align:start position:0% +y okay you can think of X as let's say + + + align:start position:0% +y okay you can think of X as let's say +in 0 1 to the + + align:start position:0% +in 0 1 to the + + + align:start position:0% +in 0 1 to the +n and y I know 0 1 to the + + align:start position:0% +n and y I know 0 1 to the + + + align:start position:0% +n and y I know 0 1 to the +n and you can think of both n and M is + + align:start position:0% +n and you can think of both n and M is + + + align:start position:0% +n and you can think of both n and M is +like functions of security parameter so + + align:start position:0% +like functions of security parameter so + + + align:start position:0% +like functions of security parameter so +n is like n of Lambda so for any + + align:start position:0% +n is like n of Lambda so for any + + + align:start position:0% +n is like n of Lambda so for any +security + + align:start position:0% +security + + + align:start position:0% +security +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +parameter you have like a a uh length n + + align:start position:0% +parameter you have like a a uh length n + + + align:start position:0% +parameter you have like a a uh length n +and M and you have a + + align:start position:0% +and M and you have a + + + align:start position:0% +and M and you have a +relation and the hash family's + + align:start position:0% +relation and the hash family's + + + align:start position:0% +relation and the hash family's +correlation intractable with respect to + + align:start position:0% +correlation intractable with respect to + + + align:start position:0% +correlation intractable with respect to +this relation it essentially means that + + align:start position:0% +this relation it essentially means that + + + align:start position:0% +this relation it essentially means that +for any for every poly signs + + align:start position:0% + + + + align:start position:0% + +adversary the probability that this + + align:start position:0% +adversary the probability that this + + + align:start position:0% +adversary the probability that this +adversary who gets hash key so the + + align:start position:0% +adversary who gets hash key so the + + + align:start position:0% +adversary who gets hash key so the +adversary gets a hash key there's a hash + + align:start position:0% +adversary gets a hash key there's a hash + + + align:start position:0% +adversary gets a hash key there's a hash +family let me call it h + + align:start position:0% + + + + align:start position:0% + +that has gen + + align:start position:0% + + + + align:start position:0% + +andal now the aders he gets hash key + + align:start position:0% +andal now the aders he gets hash key + + + align:start position:0% +andal now the aders he gets hash key +generated according to + + align:start position:0% +generated according to + + + align:start position:0% +generated according to +gen and his goal is to Output + + align:start position:0% +gen and his goal is to Output + + + align:start position:0% +gen and his goal is to Output +X such + + align:start position:0% + + + + align:start position:0% + +that h of + + align:start position:0% +that h of + + + align:start position:0% +that h of +X is or such that X comma h of X is in + + align:start position:0% +X is or such that X comma h of X is in + + + align:start position:0% +X is or such that X comma h of X is in +the relation such that X + + align:start position:0% +the relation such that X + + + align:start position:0% +the relation such that X +comma eval hash key of + + align:start position:0% +comma eval hash key of + + + align:start position:0% +comma eval hash key of +X is in + + align:start position:0% +X is in + + + align:start position:0% +X is in +R okay so + + align:start position:0% +R okay so + + + align:start position:0% +R okay so +again a correlation intractable hash + + align:start position:0% +again a correlation intractable hash + + + align:start position:0% +again a correlation intractable hash +family with suspect to a c relation + + align:start position:0% +family with suspect to a c relation + + + align:start position:0% +family with suspect to a c relation +R satisfies that for any poly siiz + + align:start position:0% +R satisfies that for any poly siiz + + + align:start position:0% +R satisfies that for any poly siiz +adversary he gets a hash in the family + + align:start position:0% +adversary he gets a hash in the family + + + align:start position:0% +adversary he gets a hash in the family +his goal is to find an X that hashes to + + align:start position:0% +his goal is to find an X that hashes to + + + align:start position:0% +his goal is to find an X that hashes to +a y said that X and Y is an r and we say + + align:start position:0% +a y said that X and Y is an r and we say + + + align:start position:0% +a y said that X and Y is an r and we say +that this probability is + + align:start position:0% +that this probability is + + + align:start position:0% +that this probability is +negligible I didn't finish to write + + align:start position:0% +negligible I didn't finish to write + + + align:start position:0% +negligible I didn't finish to write +it okay so for every poly size a there + + align:start position:0% +it okay so for every poly size a there + + + align:start position:0% +it okay so for every poly size a there +exists a + + align:start position:0% +exists a + + + align:start position:0% +exists a +negligible + + align:start position:0% +negligible + + + align:start position:0% +negligible +Lambda such that the probability so any + + align:start position:0% +Lambda such that the probability so any + + + align:start position:0% +Lambda such that the probability so any +poly siiz adversary he gets a random + + align:start position:0% +poly siiz adversary he gets a random + + + align:start position:0% +poly siiz adversary he gets a random +hash key in the family and he's able to + + align:start position:0% +hash key in the family and he's able to + + + align:start position:0% +hash key in the family and he's able to +find X at that h of X so that X comma h + + align:start position:0% +find X at that h of X so that X comma h + + + align:start position:0% +find X at that h of X so that X comma h +of x is in R only with n probability so + + align:start position:0% +of x is in R only with n probability so + + + align:start position:0% +of x is in R only with n probability so +he he always EV kind of uh evades the + + align:start position:0% +he he always EV kind of uh evades the + + + align:start position:0% +he he always EV kind of uh evades the +why in the + + align:start position:0% +why in the + + + align:start position:0% +why in the +relation that's called correlation + + align:start position:0% +relation that's called correlation + + + align:start position:0% +relation that's called correlation +attractable hash + + align:start position:0% +attractable hash + + + align:start position:0% +attractable hash +family for for specific + + align:start position:0% +family for for specific + + + align:start position:0% +family for for specific +R questions about about the + + align:start position:0% + + + + align:start position:0% + +definition so first note this makes + + align:start position:0% +definition so first note this makes + + + align:start position:0% +definition so first note this makes +sense so I want to say do we have a + + align:start position:0% +sense so I want to say do we have a + + + align:start position:0% +sense so I want to say do we have a +correlation tractable hash family and + + align:start position:0% +correlation tractable hash family and + + + align:start position:0% +correlation tractable hash family and +for which relations + + align:start position:0% +for which relations + + + align:start position:0% +for which relations +okay so this is kind of a major open + + align:start position:0% +okay so this is kind of a major open + + + align:start position:0% +okay so this is kind of a major open +question because this is very related to + + align:start position:0% +question because this is very related to + + + align:start position:0% +question because this is very related to +F so F we know take x n in the + + align:start position:0% +F so F we know take x n in the + + + align:start position:0% +F so F we know take x n in the +language we want so think of Alpha Beta + + align:start position:0% +language we want so think of Alpha Beta + + + align:start position:0% +language we want so think of Alpha Beta +gamma just think for three messages + + align:start position:0% +gamma just think for three messages + + + align:start position:0% +gamma just think for three messages +everything I say now extends to more but + + align:start position:0% +everything I say now extends to more but + + + align:start position:0% +everything I say now extends to more but +let's think of of three it extends to + + align:start position:0% +let's think of of three it extends to + + + align:start position:0% +let's think of of three it extends to +constant at least but let's think of + + align:start position:0% +constant at least but let's think of + + + align:start position:0% +constant at least but let's think of +three for + + align:start position:0% +three for + + + align:start position:0% +three for +Simplicity so we want to evade like not + + align:start position:0% +Simplicity so we want to evade like not + + + align:start position:0% +Simplicity so we want to evade like not +to tach to be correlation TR so the + + align:start position:0% +to tach to be correlation TR so the + + + align:start position:0% +to tach to be correlation TR so the +relation in our case in F CH the + + align:start position:0% +relation in our case in F CH the + + + align:start position:0% +relation in our case in F CH the +relation is like Alpha and beta are in + + align:start position:0% +relation is like Alpha and beta are in + + + align:start position:0% +relation is like Alpha and beta are in +the relation if there exists a gamma + + align:start position:0% +the relation if there exists a gamma + + + align:start position:0% +the relation if there exists a gamma +that will make it + + align:start position:0% +that will make it + + + align:start position:0% +that will make it +accept Okay so for the relation contains + + align:start position:0% +accept Okay so for the relation contains + + + align:start position:0% +accept Okay so for the relation contains +Alpha and the bad betas and we want to + + align:start position:0% +Alpha and the bad betas and we want to + + + align:start position:0% +Alpha and the bad betas and we want to +avoid these bad betas so we want to say + + align:start position:0% +avoid these bad betas so we want to say + + + align:start position:0% +avoid these bad betas so we want to say +that any adversary that gets a hash key + + align:start position:0% +that any adversary that gets a hash key + + + align:start position:0% +that any adversary that gets a hash key +managed to hit a bad beta onlyn with + + align:start position:0% + + + + align:start position:0% + +probability so there may there may exist + + align:start position:0% +probability so there may there may exist + + + align:start position:0% +probability so there may there may exist +Alphas but he won't find them it'll be + + align:start position:0% +Alphas but he won't find them it'll be + + + align:start position:0% +Alphas but he won't find them it'll be +hard for him to find kind of a X or an + + align:start position:0% +hard for him to find kind of a X or an + + + align:start position:0% +hard for him to find kind of a X or an +alpha that hashes to Beta that is + + align:start position:0% + + + + align:start position:0% + +bad okay and here I'm the idea is here + + align:start position:0% +bad okay and here I'm the idea is here + + + align:start position:0% +bad okay and here I'm the idea is here +take any inter take any think of any + + align:start position:0% +take any inter take any think of any + + + align:start position:0% +take any inter take any think of any +interactive proof like of the form Alpha + + align:start position:0% +interactive proof like of the form Alpha + + + align:start position:0% +interactive proof like of the form Alpha +Beta + + align:start position:0% +Beta + + + align:start position:0% +Beta +gamma and I want to say think the + + align:start position:0% +gamma and I want to say think the + + + align:start position:0% +gamma and I want to say think the +relation think of the relation being all + + align:start position:0% +relation think of the relation being all + + + align:start position:0% +relation think of the relation being all +the the relations of X take X not in the + + align:start position:0% +the the relations of X take X not in the + + + align:start position:0% +the the relations of X take X not in the +language I guess now this x this x + + align:start position:0% +language I guess now this x this x + + + align:start position:0% +language I guess now this x this x +corresponds to Alpha here but takes any + + align:start position:0% +corresponds to Alpha here but takes any + + + align:start position:0% +corresponds to Alpha here but takes any +X not in the language and the relation + + align:start position:0% +X not in the language and the relation + + + align:start position:0% +X not in the language and the relation +is all the alpha + + align:start position:0% +is all the alpha + + + align:start position:0% +is all the alpha +beta so that exists a gamma + + align:start position:0% +beta so that exists a gamma + + + align:start position:0% +beta so that exists a gamma +accepting so that Alpha Beta gamma is + + align:start position:0% + + + + align:start position:0% + +accepting and I know that for every + + align:start position:0% +accepting and I know that for every + + + align:start position:0% +accepting and I know that for every +Alpha there's very very few betas and I + + align:start position:0% +Alpha there's very very few betas and I + + + align:start position:0% +Alpha there's very very few betas and I +want to say that the adversary output + + align:start position:0% +want to say that the adversary output + + + align:start position:0% +want to say that the adversary output +Alpha Beta and the the relation like + + align:start position:0% +Alpha Beta and the the relation like + + + align:start position:0% +Alpha Beta and the the relation like +alpas that the hash of alpha is in the + + align:start position:0% +alpas that the hash of alpha is in the + + + align:start position:0% +alpas that the hash of alpha is in the +relation only with NE probability then I + + align:start position:0% +relation only with NE probability then I + + + align:start position:0% +relation only with NE probability then I +have soundness of the + + align:start position:0% + + + + align:start position:0% + +Fe was that too fast should I repeat the + + align:start position:0% +Fe was that too fast should I repeat the + + + align:start position:0% +Fe was that too fast should I repeat the +connection to + + align:start position:0% + + + + align:start position:0% + +F let me repeat it once more okay so I + + align:start position:0% +F let me repeat it once more okay so I + + + align:start position:0% +F let me repeat it once more okay so I +want to argue that I have correlation + + align:start position:0% +want to argue that I have correlation + + + align:start position:0% +want to argue that I have correlation +tractable hash family for a lot of + + align:start position:0% +tractable hash family for a lot of + + + align:start position:0% +tractable hash family for a lot of +relations + + align:start position:0% +relations + + + align:start position:0% +relations +actually before I I go note I can't hope + + align:start position:0% +actually before I I go note I can't hope + + + align:start position:0% +actually before I I go note I can't hope +to have it for any relation the relation + + align:start position:0% +to have it for any relation the relation + + + align:start position:0% +to have it for any relation the relation +has to be sparse if the relation is + + align:start position:0% +has to be sparse if the relation is + + + align:start position:0% +has to be sparse if the relation is +everything maybe the everything every X + + align:start position:0% +everything maybe the everything every X + + + align:start position:0% +everything maybe the everything every X +Y is in the relation then of course a + + align:start position:0% +Y is in the relation then of course a + + + align:start position:0% +Y is in the relation then of course a +hash will hit like + + align:start position:0% +hash will hit like + + + align:start position:0% +hash will hit like +trivial so the most I can hope for so + + align:start position:0% +trivial so the most I can hope for so + + + align:start position:0% +trivial so the most I can hope for so +the question I really want to ask or the + + align:start position:0% +the question I really want to ask or the + + + align:start position:0% +the question I really want to ask or the +most like the most general question + + align:start position:0% +most like the most general question + + + align:start position:0% +most like the most general question +is + + align:start position:0% +is + + + align:start position:0% +is +does there + + align:start position:0% + + + + align:start position:0% + +exist uh correlation intractable hash + + align:start position:0% +exist uh correlation intractable hash + + + align:start position:0% +exist uh correlation intractable hash +for every + + align:start position:0% +for every + + + align:start position:0% +for every +evasive or also people sometimes call it + + align:start position:0% +evasive or also people sometimes call it + + + align:start position:0% +evasive or also people sometimes call it +sparse + + align:start position:0% + + + + align:start position:0% + +relation that's the question and by a + + align:start position:0% +relation that's the question and by a + + + align:start position:0% +relation that's the question and by a +vas of over by sparse I just mean that + + align:start position:0% +vas of over by sparse I just mean that + + + align:start position:0% +vas of over by sparse I just mean that +for every X there are very few y's that + + align:start position:0% +for every X there are very few y's that + + + align:start position:0% +for every X there are very few y's that +are in the + + align:start position:0% +are in the + + + align:start position:0% +are in the +relation so sparse means ah forgot me + + align:start position:0% +relation so sparse means ah forgot me + + + align:start position:0% +relation so sparse means ah forgot me +sparse means this + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% +this + + + align:start position:0% +this +means that for every X the probability + + align:start position:0% +means that for every X the probability + + + align:start position:0% +means that for every X the probability +over a random + + align:start position:0% + + + + align:start position:0% + +y that XY is in R is + + align:start position:0% + + + + align:start position:0% + +negligible + + align:start position:0% +negligible + + + align:start position:0% +negligible +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +for yes yes yes yes yes good okay good + + align:start position:0% +for yes yes yes yes yes good okay good + + + align:start position:0% +for yes yes yes yes yes good okay good +so now let's go to yeah so now let's go + + align:start position:0% +so now let's go to yeah so now let's go + + + align:start position:0% +so now let's go to yeah so now let's go +to F good so I want to ask if the exist + + align:start position:0% +to F good so I want to ask if the exist + + + align:start position:0% +to F good so I want to ask if the exist +a correlation trable for every such + + align:start position:0% +a correlation trable for every such + + + align:start position:0% +a correlation trable for every such +evasive or sparse language uh relation + + align:start position:0% +evasive or sparse language uh relation + + + align:start position:0% +evasive or sparse language uh relation +now if there is I'm done why if there if + + align:start position:0% +now if there is I'm done why if there if + + + align:start position:0% +now if there is I'm done why if there if +you can prove that there's correlation + + align:start position:0% +you can prove that there's correlation + + + align:start position:0% +you can prove that there's correlation +tractable hat for every sparse + + align:start position:0% +tractable hat for every sparse + + + align:start position:0% +tractable hat for every sparse +language I here's now I'll tell you now + + align:start position:0% +language I here's now I'll tell you now + + + align:start position:0% +language I here's now I'll tell you now +here's the fature take X not in the + + align:start position:0% + + + + align:start position:0% + +language the uh so take the correlation + + align:start position:0% +language the uh so take the correlation + + + align:start position:0% +language the uh so take the correlation +tractable hash you had said there's a + + align:start position:0% +tractable hash you had said there's a + + + align:start position:0% +tractable hash you had said there's a +correlation tractable hash take that + + align:start position:0% +correlation tractable hash take that + + + align:start position:0% +correlation tractable hash take that +hash function now what I'm going to do + + align:start position:0% +hash function now what I'm going to do + + + align:start position:0% +hash function now what I'm going to do +now I want to now take ex the language I + + align:start position:0% +now I want to now take ex the language I + + + align:start position:0% +now I want to now take ex the language I +my the evasive relation that I look at + + align:start position:0% +my the evasive relation that I look at + + + align:start position:0% +my the evasive relation that I look at +is this relation Alpha Beta is in the + + align:start position:0% +is this relation Alpha Beta is in the + + + align:start position:0% +is this relation Alpha Beta is in the +relation if there exists gamma of course + + align:start position:0% +relation if there exists gamma of course + + + align:start position:0% +relation if there exists gamma of course +it's evasive because it's a proof mean + + align:start position:0% +it's evasive because it's a proof mean + + + align:start position:0% +it's evasive because it's a proof mean +there there's only negligible amount of + + align:start position:0% +there there's only negligible amount of + + + align:start position:0% +there there's only negligible amount of +betas I can answer so it's evasive and + + align:start position:0% +betas I can answer so it's evasive and + + + align:start position:0% +betas I can answer so it's evasive and +therefore the probability that you hit a + + align:start position:0% +therefore the probability that you hit a + + + align:start position:0% +therefore the probability that you hit a +bad beta is negligible I'm done + + align:start position:0% +bad beta is negligible I'm done + + + align:start position:0% +bad beta is negligible I'm done +proof so if I have a collision hash that + + align:start position:0% +proof so if I have a collision hash that + + + align:start position:0% +proof so if I have a collision hash that +works for any Bas so for any Bas of + + align:start position:0% +works for any Bas so for any Bas of + + + align:start position:0% +works for any Bas so for any Bas of +relation this holds for any R then I'm + + align:start position:0% +relation this holds for any R then I'm + + + align:start position:0% +relation this holds for any R then I'm +good okay so if that for any R yes that + + align:start position:0% +good okay so if that for any R yes that + + + align:start position:0% +good okay so if that for any R yes that +for any + + align:start position:0% +for any + + + align:start position:0% +for any +R you don't hit it then I'm done + + align:start position:0% +R you don't hit it then I'm done + + + align:start position:0% +R you don't hit it then I'm done +sound okay so then this was actually um + + align:start position:0% +sound okay so then this was actually um + + + align:start position:0% +sound okay so then this was actually um +defined in an earlier work like 2004 + + align:start position:0% +defined in an earlier work like 2004 + + + align:start position:0% +defined in an earlier work like 2004 +maybe I don't really remember but a + + align:start position:0% +maybe I don't really remember but a + + + align:start position:0% +maybe I don't really remember but a +while a while + + align:start position:0% +while a while + + + align:start position:0% +while a while +back and then people ask okay so we need + + align:start position:0% +back and then people ask okay so we need + + + align:start position:0% +back and then people ask okay so we need +to construct this evasive + + align:start position:0% +to construct this evasive + + + align:start position:0% +to construct this evasive +functions so they proed that the random + + align:start position:0% +functions so they proed that the random + + + align:start position:0% +functions so they proed that the random +Oracle model is the random Oracle is an + + align:start position:0% +Oracle model is the random Oracle is an + + + align:start position:0% +Oracle model is the random Oracle is an +evasive function but beyond that they + + align:start position:0% +evasive function but beyond that they + + + align:start position:0% +evasive function but beyond that they +were + + align:start position:0% + + + + align:start position:0% + +stuck and what this result that the + + align:start position:0% +stuck and what this result that the + + + align:start position:0% +stuck and what this result that the +ketti Lombardi weeks result show so let + + align:start position:0% +ketti Lombardi weeks result show so let + + + align:start position:0% +ketti Lombardi weeks result show so let +me now uh def uh State the result in in + + align:start position:0% +me now uh def uh State the result in in + + + align:start position:0% +me now uh def uh State the result in in +more general terms what it shows that + + align:start position:0% +more general terms what it shows that + + + align:start position:0% +more general terms what it shows that +there exists a correlation intractable + + align:start position:0% +there exists a correlation intractable + + + align:start position:0% +there exists a correlation intractable +hash for every + + align:start position:0% +hash for every + + + align:start position:0% +hash for every +relation that is + + align:start position:0% +relation that is + + + align:start position:0% +relation that is +a here okay for any relation that is + + align:start position:0% +a here okay for any relation that is + + + align:start position:0% +a here okay for any relation that is +they call it + + align:start position:0% +they call it + + + align:start position:0% +they call it +searchable I'll + + align:start position:0% + + + + align:start position:0% + +explain in + + align:start position:0% +explain in + + + align:start position:0% +explain in +time + + align:start position:0% +time + + + align:start position:0% +time +T So search on time T just means that + + align:start position:0% +T So search on time T just means that + + + align:start position:0% +T So search on time T just means that +searchable means that for every Alpha + + align:start position:0% +searchable means that for every Alpha + + + align:start position:0% +searchable means that for every Alpha +there's a unique beta it's a search + + align:start position:0% +there's a unique beta it's a search + + + align:start position:0% +there's a unique beta it's a search +problem it's like for every Alpha + + align:start position:0% +problem it's like for every Alpha + + + align:start position:0% +problem it's like for every Alpha +there's a unique beta beta and this beta + + align:start position:0% +there's a unique beta beta and this beta + + + align:start position:0% +there's a unique beta beta and this beta +can be computed in time + + align:start position:0% +can be computed in time + + + align:start position:0% +can be computed in time +T so what they show is there exists a + + align:start position:0% +T so what they show is there exists a + + + align:start position:0% +T so what they show is there exists a +coration in hash correlation intractable + + align:start position:0% +coration in hash correlation intractable + + + align:start position:0% +coration in hash correlation intractable +hash for every that that is correlation + + align:start position:0% +hash for every that that is correlation + + + align:start position:0% +hash for every that that is correlation +intractable for every relation + + align:start position:0% +intractable for every relation + + + align:start position:0% +intractable for every relation +searchable in time T and this hash the + + align:start position:0% +searchable in time T and this hash the + + + align:start position:0% +searchable in time T and this hash the +time to compute the hash grows with + + align:start position:0% + + + + align:start position:0% + +T so essentially what they say is for + + align:start position:0% +T so essentially what they say is for + + + align:start position:0% +T so essentially what they say is for +every polinomial t because the hatch + + align:start position:0% +every polinomial t because the hatch + + + align:start position:0% +every polinomial t because the hatch +grows with T so for every polinomial + + align:start position:0% + + + + align:start position:0% + +T there exists a Corr a a hash function + + align:start position:0% +T there exists a Corr a a hash function + + + align:start position:0% +T there exists a Corr a a hash function +that grow depends on T and it's + + align:start position:0% +that grow depends on T and it's + + + align:start position:0% +that grow depends on T and it's +correlation intractable with respect to + + align:start position:0% +correlation intractable with respect to + + + align:start position:0% +correlation intractable with respect to +all relations that are searchable in + + align:start position:0% +all relations that are searchable in + + + align:start position:0% +all relations that are searchable in +time T and again relation searchable in + + align:start position:0% +time T and again relation searchable in + + + align:start position:0% +time T and again relation searchable in +time t + + align:start position:0% +time t + + + align:start position:0% +time t +means that for every uh Alpha let me + + align:start position:0% +means that for every uh Alpha let me + + + align:start position:0% +means that for every uh Alpha let me +don't note the relation in by this and + + align:start position:0% +don't note the relation in by this and + + + align:start position:0% +don't note the relation in by this and +not X because + + align:start position:0% +not X because + + + align:start position:0% +not X because +X often + + align:start position:0% +X often + + + align:start position:0% +X often +denotes uh input and I want to think of + + align:start position:0% +denotes uh input and I want to think of + + + align:start position:0% +denotes uh input and I want to think of +the relation as Alpha Beta instead of X + + align:start position:0% +the relation as Alpha Beta instead of X + + + align:start position:0% +the relation as Alpha Beta instead of X +Y because then there's a confusion + + align:start position:0% +Y because then there's a confusion + + + align:start position:0% +Y because then there's a confusion +between the X here and the X instance so + + align:start position:0% +between the X here and the X instance so + + + align:start position:0% +between the X here and the X instance so +it just means that for that the relation + + align:start position:0% +it just means that for that the relation + + + align:start position:0% +it just means that for that the relation +is a set of alpha + + align:start position:0% +is a set of alpha + + + align:start position:0% +is a set of alpha +betas such that for every Alpha there + + align:start position:0% +betas such that for every Alpha there + + + align:start position:0% +betas such that for every Alpha there +exists a + + align:start position:0% +exists a + + + align:start position:0% +exists a +unique at most a unique maybe less but + + align:start position:0% +unique at most a unique maybe less but + + + align:start position:0% +unique at most a unique maybe less but +at most uh so + + align:start position:0% +at most uh so + + + align:start position:0% +at most uh so +at + + align:start position:0% +at + + + align:start position:0% +at +most + + align:start position:0% +most + + + align:start position:0% +most +unique + + align:start position:0% +unique + + + align:start position:0% +unique +beta such that Alpha Beta is in R + + align:start position:0% +beta such that Alpha Beta is in R + + + align:start position:0% +beta such that Alpha Beta is in R +and to go from alpha to Beta or B if + + align:start position:0% +and to go from alpha to Beta or B if + + + align:start position:0% +and to go from alpha to Beta or B if +there's no beta is + + align:start position:0% +there's no beta is + + + align:start position:0% +there's no beta is +computable in time + + align:start position:0% + + + + align:start position:0% + +t Okay so a searchable relation means + + align:start position:0% +t Okay so a searchable relation means + + + align:start position:0% +t Okay so a searchable relation means +for every Alpha there's a unique beta at + + align:start position:0% +for every Alpha there's a unique beta at + + + align:start position:0% +for every Alpha there's a unique beta at +most unique maybe there's no beta but if + + align:start position:0% +most unique maybe there's no beta but if + + + align:start position:0% +most unique maybe there's no beta but if +there is a beta it's Unique and from + + align:start position:0% +there is a beta it's Unique and from + + + align:start position:0% +there is a beta it's Unique and from +alpha to compute the beta corresponding + + align:start position:0% +alpha to compute the beta corresponding + + + align:start position:0% +alpha to compute the beta corresponding +to it in the relation can be done in + + align:start position:0% +to it in the relation can be done in + + + align:start position:0% +to it in the relation can be done in +time + + align:start position:0% +time + + + align:start position:0% +time +T and what they showed is that there + + align:start position:0% +T and what they showed is that there + + + align:start position:0% +T and what they showed is that there +exists a single hash family so first + + align:start position:0% +exists a single hash family so first + + + align:start position:0% +exists a single hash family so first +note of course of course if you fix a + + align:start position:0% +note of course of course if you fix a + + + align:start position:0% +note of course of course if you fix a +relation that's searchable in time T of + + align:start position:0% +relation that's searchable in time T of + + + align:start position:0% +relation that's searchable in time T of +course there's a hash that's correlation + + align:start position:0% +course there's a hash that's correlation + + + align:start position:0% +course there's a hash that's correlation +tractable with respect to it just take + + align:start position:0% +tractable with respect to it just take + + + align:start position:0% +tractable with respect to it just take +compute the beta and add + + align:start position:0% +compute the beta and add + + + align:start position:0% +compute the beta and add +one okay again let me + + align:start position:0% +one okay again let me + + + align:start position:0% +one okay again let me +uh let me move there so we'll have + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +this so we want to show a correlation + + align:start position:0% +this so we want to show a correlation + + + align:start position:0% +this so we want to show a correlation +intractable hash with respect + + align:start position:0% +intractable hash with respect + + + align:start position:0% +intractable hash with respect +to any relation that's searchable in + + align:start position:0% +to any relation that's searchable in + + + align:start position:0% +to any relation that's searchable in +time te + + align:start position:0% +time te + + + align:start position:0% +time te +and first I want to note I want one hash + + align:start position:0% +and first I want to note I want one hash + + + align:start position:0% +and first I want to note I want one hash +that's correlation attractable for all + + align:start position:0% +that's correlation attractable for all + + + align:start position:0% +that's correlation attractable for all +relations of course if you first choose + + align:start position:0% +relations of course if you first choose + + + align:start position:0% +relations of course if you first choose +a relation if you first Cho of course + + align:start position:0% +a relation if you first Cho of course + + + align:start position:0% +a relation if you first Cho of course +this what I'm saying now is a trivial + + align:start position:0% +this what I'm saying now is a trivial + + + align:start position:0% +this what I'm saying now is a trivial +for any T + + align:start position:0% +for any T + + + align:start position:0% +for any T +time + + align:start position:0% + + + + align:start position:0% + +searchable relation there exists a + + align:start position:0% +searchable relation there exists a + + + align:start position:0% +searchable relation there exists a +correlation intractable hash running in + + align:start position:0% +correlation intractable hash running in + + + align:start position:0% +correlation intractable hash running in +time t + + align:start position:0% + + + + align:start position:0% + +or close to + + align:start position:0% +or close to + + + align:start position:0% +or close to +T that's easy what is the hash the hash + + align:start position:0% +T that's easy what is the hash the hash + + + align:start position:0% +T that's easy what is the hash the hash +of + + align:start position:0% +of + + + align:start position:0% +of +alpha will just be the beta that you're + + align:start position:0% +alpha will just be the beta that you're + + + align:start position:0% +alpha will just be the beta that you're +searching for in the relation plus + + align:start position:0% +searching for in the relation plus + + + align:start position:0% +searching for in the relation plus +one just avoid it somehow plus I + + align:start position:0% +one just avoid it somehow plus I + + + align:start position:0% +one just avoid it somehow plus I +whatever one like just move move out of + + align:start position:0% +whatever one like just move move out of + + + align:start position:0% +whatever one like just move move out of +the beta that's it that's + + align:start position:0% +the beta that's it that's + + + align:start position:0% +the beta that's it that's +easy but what they show is something + + align:start position:0% +easy but what they show is something + + + align:start position:0% +easy but what they show is something +much stronger they show the oppos they + + align:start position:0% +much stronger they show the oppos they + + + align:start position:0% +much stronger they show the oppos they +show the the reverse order of + + align:start position:0% +show the the reverse order of + + + align:start position:0% +show the the reverse order of +quantifiers they show that there exist + + align:start position:0% +quantifiers they show that there exist + + + align:start position:0% +quantifiers they show that there exist +one hash + + align:start position:0% + + + + align:start position:0% + +family and this has family is + + align:start position:0% +family and this has family is + + + align:start position:0% +family and this has family is +correlation intractable for all T time + + align:start position:0% + + + + align:start position:0% + +searchable + + align:start position:0% +searchable + + + align:start position:0% +searchable +relations that's the difference + + align:start position:0% + + + + align:start position:0% + +okay so let's so that's kind of what I + + align:start position:0% +okay so let's so that's kind of what I + + + align:start position:0% +okay so let's so that's kind of what I +want to end end with I'm I want to prove + + align:start position:0% +want to end end with I'm I want to prove + + + align:start position:0% +want to end end with I'm I want to prove +it to you because we we saw this proof + + align:start position:0% +it to you because we we saw this proof + + + align:start position:0% +it to you because we we saw this proof +it's exactly the same thing but let's + + align:start position:0% +it's exactly the same thing but let's + + + align:start position:0% +it's exactly the same thing but let's +just see it in this language but before + + align:start position:0% +just see it in this language but before + + + align:start position:0% +just see it in this language but before +we go over the proof again or or just + + align:start position:0% +we go over the proof again or or just + + + align:start position:0% +we go over the proof again or or just +remind the proof it's a so this is a + + align:start position:0% +remind the proof it's a so this is a + + + align:start position:0% +remind the proof it's a so this is a +much stronger a this is a pretty general + + align:start position:0% + + + + align:start position:0% + +statement and this thing + + align:start position:0% +statement and this thing + + + align:start position:0% +statement and this thing +ment uh is used in many follow-up works + + align:start position:0% +ment uh is used in many follow-up works + + + align:start position:0% +ment uh is used in many follow-up works +for + + align:start position:0% +for + + + align:start position:0% +for +example this can be used uh almost to + + align:start position:0% +example this can be used uh almost to + + + align:start position:0% +example this can be used uh almost to +prove the soundness of gkr for example + + align:start position:0% +prove the soundness of gkr for example + + + align:start position:0% +prove the soundness of gkr for example +so or or some check let's do some check + + align:start position:0% +so or or some check let's do some check + + + align:start position:0% +so or or some check let's do some check +for Simplicity because that's all the + + align:start position:0% +for Simplicity because that's all the + + + align:start position:0% +for Simplicity because that's all the +ideas are there how can you do how can + + align:start position:0% +ideas are there how can you do how can + + + align:start position:0% +ideas are there how can you do how can +you prove F sound for some check let's + + align:start position:0% +you prove F sound for some check let's + + + align:start position:0% +you prove F sound for some check let's +just recall just for a + + align:start position:0% +just recall just for a + + + align:start position:0% +just recall just for a +minute what the sum check is just so you + + align:start position:0% +minute what the sum check is just so you + + + align:start position:0% +minute what the sum check is just so you +see how it it's not immediate by the way + + align:start position:0% +see how it it's not immediate by the way + + + align:start position:0% +see how it it's not immediate by the way +it requires more crypto but I want to + + align:start position:0% +it requires more crypto but I want to + + + align:start position:0% +it requires more crypto but I want to +give you a sense a little bit of the why + + align:start position:0% +give you a sense a little bit of the why + + + align:start position:0% +give you a sense a little bit of the why +this is very useful so it's not + + align:start position:0% +this is very useful so it's not + + + align:start position:0% +this is very useful so it's not +immediate but it definitely uses this + + align:start position:0% + + + + align:start position:0% + +fact okay so let's see why let's as an + + align:start position:0% +fact okay so let's see why let's as an + + + align:start position:0% +fact okay so let's see why let's as an +example let's look at the sum check so + + align:start position:0% +example let's look at the sum check so + + + align:start position:0% +example let's look at the sum check so +suppose I have I want to prove that sum + + align:start position:0% +suppose I have I want to prove that sum + + + align:start position:0% +suppose I have I want to prove that sum +of G B1 up to BM is equal to some value + + align:start position:0% +of G B1 up to BM is equal to some value + + + align:start position:0% +of G B1 up to BM is equal to some value +V and I wanted do it in the in in the + + align:start position:0% +V and I wanted do it in the in in the + + + align:start position:0% +V and I wanted do it in the in in the +F so what is the relation let's see it's + + align:start position:0% +F so what is the relation let's see it's + + + align:start position:0% +F so what is the relation let's see it's +many rounds so it's harder but let's + + align:start position:0% +many rounds so it's harder but let's + + + align:start position:0% +many rounds so it's harder but let's +just look at the first round for a + + align:start position:0% +just look at the first round for a + + + align:start position:0% +just look at the first round for a +second so or the first three rounds so + + align:start position:0% +second so or the first three rounds so + + + align:start position:0% +second so or the first three rounds so +we have a prover and a verifier suppose + + align:start position:0% +we have a prover and a verifier suppose + + + align:start position:0% +we have a prover and a verifier suppose +this is false right so it's this is + + align:start position:0% +this is false right so it's this is + + + align:start position:0% +this is false right so it's this is +actually it's actually + + align:start position:0% +actually it's actually + + + align:start position:0% +actually it's actually +false but the Prov is trying to cheat me + + align:start position:0% +false but the Prov is trying to cheat me + + + align:start position:0% +false but the Prov is trying to cheat me +so now the first thing the prover does + + align:start position:0% +so now the first thing the prover does + + + align:start position:0% +so now the first thing the prover does +if you remember he gives a univariant + + align:start position:0% +if you remember he gives a univariant + + + align:start position:0% +if you remember he gives a univariant +polinomial + + align:start position:0% + + + + align:start position:0% + +now this uni mod is wrong I I'll put + + align:start position:0% +now this uni mod is wrong I I'll put + + + align:start position:0% +now this uni mod is wrong I I'll put +star because it's wrong why because I + + align:start position:0% +star because it's wrong why because I + + + align:start position:0% +star because it's wrong why because I +know the value here is actually not v + + align:start position:0% +know the value here is actually not v + + + align:start position:0% +know the value here is actually not v +he's proving that it's V he should be + + align:start position:0% +he's proving that it's V he should be + + + align:start position:0% +he's proving that it's V he should be +giving the value that he should be + + align:start position:0% +giving the value that he should be + + + align:start position:0% +giving the value that he should be +giving is + + align:start position:0% + + + + align:start position:0% + +G1 which is sum of G of + + align:start position:0% +G1 which is sum of G of + + + align:start position:0% +G1 which is sum of G of +G on B2 up to BM + + align:start position:0% + + + + align:start position:0% + +that's what he should be + + align:start position:0% +that's what he should be + + + align:start position:0% +that's what he should be +giving and I would check that when you + + align:start position:0% +giving and I would check that when you + + + align:start position:0% +giving and I would check that when you +take this and sum it only over B1 you + + align:start position:0% +take this and sum it only over B1 you + + + align:start position:0% +take this and sum it only over B1 you +get V but of course he's not going to + + align:start position:0% +get V but of course he's not going to + + + align:start position:0% +get V but of course he's not going to +give me this because when you sum this + + align:start position:0% +give me this because when you sum this + + + align:start position:0% +give me this because when you sum this +over B1 it's not V because the real + + align:start position:0% +over B1 it's not V because the real + + + align:start position:0% +over B1 it's not V because the real +answer this is not V so he will give me + + align:start position:0% +answer this is not V so he will give me + + + align:start position:0% +answer this is not V so he will give me +another one + + align:start position:0% +another one + + + align:start position:0% +another one +star what are the bad betas the bad + + align:start position:0% +star what are the bad betas the bad + + + align:start position:0% +star what are the bad betas the bad +betas so now beta bad + + align:start position:0% + + + + align:start position:0% + +are all the elements T in the + + align:start position:0% +are all the elements T in the + + + align:start position:0% +are all the elements T in the +field such that G1 + + align:start position:0% +field such that G1 + + + align:start position:0% +field such that G1 +star is equal now with this now he can + + align:start position:0% +star is equal now with this now he can + + + align:start position:0% +star is equal now with this now he can +cheat if he managed to give me G star + + align:start position:0% +cheat if he managed to give me G star + + + align:start position:0% +cheat if he managed to give me G star +that's equal to GT now he kind of + + align:start position:0% +that's equal to GT now he kind of + + + align:start position:0% +that's equal to GT now he kind of +continues like with a good now he has a + + align:start position:0% +continues like with a good now he has a + + + align:start position:0% +continues like with a good now he has a +true statement lucky him so these are + + align:start position:0% +true statement lucky him so these are + + + align:start position:0% +true statement lucky him so these are +going to be really bad for me but there + + align:start position:0% +going to be really bad for me but there + + + align:start position:0% +going to be really bad for me but there +are very few of them like the degree the + + align:start position:0% +are very few of them like the degree the + + + align:start position:0% +are very few of them like the degree the +univ degree of this G so as long as I + + align:start position:0% +univ degree of this G so as long as I + + + align:start position:0% +univ degree of this G so as long as I +don't hit the degrees d as long as I + + align:start position:0% +don't hit the degrees d as long as I + + + align:start position:0% +don't hit the degrees d as long as I +don't hit this D bad I'm + + align:start position:0% +don't hit this D bad I'm + + + align:start position:0% +don't hit this D bad I'm +good and it's pretty easy to compute + + align:start position:0% +good and it's pretty easy to compute + + + align:start position:0% +good and it's pretty easy to compute +this thing because I'm gonna hard like I + + align:start position:0% +this thing because I'm gonna hard like I + + + align:start position:0% +this thing because I'm gonna hard like I +I'm gonna so Computing G1 may be hard + + align:start position:0% +I'm gonna so Computing G1 may be hard + + + align:start position:0% +I'm gonna so Computing G1 may be hard +but I can hardwire it it's like a trapo + + align:start position:0% +but I can hardwire it it's like a trapo + + + align:start position:0% +but I can hardwire it it's like a trapo +I have this I have this statement I can + + align:start position:0% +I have this I have this statement I can + + + align:start position:0% +I have this I have this statement I can +use G1 as a + + align:start position:0% +use G1 as a + + + align:start position:0% +use G1 as a +trapo and now compute once I have G1 as + + align:start position:0% +trapo and now compute once I have G1 as + + + align:start position:0% +trapo and now compute once I have G1 as +a trapo given G1 star Computing all the + + align:start position:0% +a trapo given G1 star Computing all the + + + align:start position:0% +a trapo given G1 star Computing all the +inputs that collide with my G1 there + + align:start position:0% +inputs that collide with my G1 there + + + align:start position:0% +inputs that collide with my G1 there +algorithms there's efficient algorithms + + align:start position:0% +algorithms there's efficient algorithms + + + align:start position:0% +algorithms there's efficient algorithms +for this so now it's efficient so all I + + align:start position:0% +for this so now it's efficient so all I + + + align:start position:0% +for this so now it's efficient so all I +I need to avoid so it's not searchable + + align:start position:0% +I need to avoid so it's not searchable + + + align:start position:0% +I need to avoid so it's not searchable +it's not one beta like we have here it's + + align:start position:0% +it's not one beta like we have here it's + + + align:start position:0% +it's not one beta like we have here it's +D betas but to go from one to d as I + + align:start position:0% +D betas but to go from one to d as I + + + align:start position:0% +D betas but to go from one to d as I +said you just guess you lose a factor of + + align:start position:0% +said you just guess you lose a factor of + + + align:start position:0% +said you just guess you lose a factor of +D it's really extends pretty easily so + + align:start position:0% +D it's really extends pretty easily so + + + align:start position:0% +D it's really extends pretty easily so +you apply + + align:start position:0% +you apply + + + align:start position:0% +you apply +done okay it's not that easy the reason + + align:start position:0% +done okay it's not that easy the reason + + + align:start position:0% +done okay it's not that easy the reason +it's not that easy is because now a t + + align:start position:0% +it's not that easy is because now a t + + + align:start position:0% +it's not that easy is because now a t +comes out from the + + align:start position:0% +comes out from the + + + align:start position:0% +comes out from the +F and the next G depends on this T + + align:start position:0% +F and the next G depends on this T + + + align:start position:0% +F and the next G depends on this T +because the next G is going to be the + + align:start position:0% +because the next G is going to be the + + + align:start position:0% +because the next G is going to be the +next G Star the next real G G2 is going + + align:start position:0% +next G Star the next real G G2 is going + + + align:start position:0% +next G Star the next real G G2 is going +to + + align:start position:0% +to + + + align:start position:0% +to +be some G that the real G here + + align:start position:0% +be some G that the real G here + + + align:start position:0% +be some G that the real G here +T1 and then B3 da d d d d d da so I + + align:start position:0% +T1 and then B3 da d d d d d da so I + + + align:start position:0% +T1 and then B3 da d d d d d da so I +don't I I I can't hardwire G2 ahead of + + align:start position:0% +don't I I I can't hardwire G2 ahead of + + + align:start position:0% +don't I I I can't hardwire G2 ahead of +time I don't know what T1 is things are + + align:start position:0% +time I don't know what T1 is things are + + + align:start position:0% +time I don't know what T1 is things are +not as simple so there's more it's not a + + align:start position:0% +not as simple so there's more it's not a + + + align:start position:0% +not as simple so there's more it's not a +but the first me the first part is + + align:start position:0% +but the first me the first part is + + + align:start position:0% +but the first me the first part is +Trivial and then you need to add add to + + align:start position:0% +Trivial and then you need to add add to + + + align:start position:0% +Trivial and then you need to add add to +throw on it a little more crypto and do + + align:start position:0% +throw on it a little more crypto and do + + + align:start position:0% +throw on it a little more crypto and do +some more work but it's this technique + + align:start position:0% +some more work but it's this technique + + + align:start position:0% +some more work but it's this technique +is used to prove gkr this technique is + + align:start position:0% +is used to prove gkr this technique is + + + align:start position:0% +is used to prove gkr this technique is +also used to prove the result of churi + + align:start position:0% +also used to prove the result of churi + + + align:start position:0% +also used to prove the result of churi +Jin and Jen Jen and Jin where Jen Jong + + align:start position:0% +Jin and Jen Jen and Jin where Jen Jong + + + align:start position:0% +Jin and Jen Jen and Jin where Jen Jong +Jin is gonna uh present next class where + + align:start position:0% +Jin is gonna uh present next class where + + + align:start position:0% +Jin is gonna uh present next class where +they use FIA to prove uh this uh the + + align:start position:0% +they use FIA to prove uh this uh the + + + align:start position:0% +they use FIA to prove uh this uh the +existence of a batch AR batch + + align:start position:0% +existence of a batch AR batch + + + align:start position:0% +existence of a batch AR batch +non-interactive argument so he'll + + align:start position:0% +non-interactive argument so he'll + + + align:start position:0% +non-interactive argument so he'll +explain what that is next time but again + + align:start position:0% +explain what that is next time but again + + + align:start position:0% +explain what that is next time but again +this technique so this technique is + + align:start position:0% +this technique so this technique is + + + align:start position:0% +this technique so this technique is +really is pretty + + align:start position:0% +really is pretty + + + align:start position:0% +really is pretty +General + + align:start position:0% +General + + + align:start position:0% +General +okay question before I just kind of REM + + align:start position:0% +okay question before I just kind of REM + + + align:start position:0% +okay question before I just kind of REM +remind you why why this + + align:start position:0% + + + + align:start position:0% + +holds questions yeah so you + + align:start position:0% +holds questions yeah so you + + + align:start position:0% +holds questions yeah so you +said compute all + + align:start position:0% +said compute all + + + align:start position:0% +said compute all +the keys Pi a random one okay exactly so + + align:start position:0% +the keys Pi a random one okay exactly so + + + align:start position:0% +the keys Pi a random one okay exactly so +in the analysis you can think of it yeah + + align:start position:0% +in the analysis you can think of it yeah + + + align:start position:0% +in the analysis you can think of it yeah +I'm going to so I have a cheating prover + + align:start position:0% +I'm going to so I have a cheating prover + + + align:start position:0% +I'm going to so I have a cheating prover +and ah okay it's a bit complicated but + + align:start position:0% +and ah okay it's a bit complicated but + + + align:start position:0% +and ah okay it's a bit complicated but +yes in in the analysis I'm going to say + + align:start position:0% +yes in in the analysis I'm going to say + + + align:start position:0% +yes in in the analysis I'm going to say +look I have a cheating prover so it + + align:start position:0% +look I have a cheating prover so it + + + align:start position:0% +look I have a cheating prover so it +means he he cheats with respect to one + + align:start position:0% +means he he cheats with respect to one + + + align:start position:0% +means he he cheats with respect to one +random with a random one here with + + align:start position:0% +random with a random one here with + + + align:start position:0% +random with a random one here with +probability one over D and then I'm + + align:start position:0% +probability one over D and then I'm + + + align:start position:0% +probability one over D and then I'm +going to get a contradict contradiction + + align:start position:0% +going to get a contradict contradiction + + + align:start position:0% +going to get a contradict contradiction +because it's going to cheat with anyone + + align:start position:0% +because it's going to cheat with anyone + + + align:start position:0% +because it's going to cheat with anyone +with netive probability for each one fix + + align:start position:0% +with netive probability for each one fix + + + align:start position:0% +with netive probability for each one fix +it with that he's going to CH with that + + align:start position:0% +it with that he's going to CH with that + + + align:start position:0% +it with that he's going to CH with that +with negtive probability so then you + + align:start position:0% +with negtive probability so then you + + + align:start position:0% +with negtive probability so then you +Union bound kind of and say okay so for + + align:start position:0% +Union bound kind of and say okay so for + + + align:start position:0% +Union bound kind of and say okay so for +he cheat the probability that he cheats + + align:start position:0% +he cheat the probability that he cheats + + + align:start position:0% +he cheat the probability that he cheats +with any of these is D times negligible + + align:start position:0% +with any of these is D times negligible + + + align:start position:0% +with any of these is D times negligible +so as long as D is polinomial you're + + align:start position:0% +so as long as D is polinomial you're + + + align:start position:0% +so as long as D is polinomial you're +good what will our function look like + + align:start position:0% +good what will our function look like + + + align:start position:0% +good what will our function look like +it's the exact same so okay so actually + + align:start position:0% +it's the exact same so okay so actually + + + align:start position:0% +it's the exact same so okay so actually +let me what so the question what was our + + align:start position:0% +let me what so the question what was our + + + align:start position:0% +let me what so the question what was our +hash function look like I'll I'll tell + + align:start position:0% +hash function look like I'll I'll tell + + + align:start position:0% +hash function look like I'll I'll tell +you exactly what it is when I prove this + + align:start position:0% +you exactly what it is when I prove this + + + align:start position:0% +you exactly what it is when I prove this +and you'll see it's the exact same hash + + align:start position:0% +and you'll see it's the exact same hash + + + align:start position:0% +and you'll see it's the exact same hash +function so I say here and that's the + + align:start position:0% +function so I say here and that's the + + + align:start position:0% +function so I say here and that's the +hash function that I'll use up there I + + align:start position:0% +hash function that I'll use up there I + + + align:start position:0% +hash function that I'll use up there I +say here + + align:start position:0% +say here + + + align:start position:0% +say here +that there exists a hash function that's + + align:start position:0% +that there exists a hash function that's + + + align:start position:0% +that there exists a hash function that's +correlation tractable respect to any T + + align:start position:0% +correlation tractable respect to any T + + + align:start position:0% +correlation tractable respect to any T +time searchable relation what is this + + align:start position:0% +time searchable relation what is this + + + align:start position:0% +time searchable relation what is this +hash function I'll tell you so the hash + + align:start position:0% +hash function I'll tell you so the hash + + + align:start position:0% +hash function I'll tell you so the hash +function so to say hash family I need to + + align:start position:0% +function so to say hash family I need to + + + align:start position:0% +function so to say hash family I need to +say what's + + align:start position:0% +say what's + + + align:start position:0% +say what's +gen and what's + + align:start position:0% +gen and what's + + + align:start position:0% +gen and what's +Ian so here is the + + align:start position:0% + + + + align:start position:0% + +Gen help me out what do the gend do + + align:start position:0% + + + + align:start position:0% + +key exactly he computes a public key for + + align:start position:0% +key exactly he computes a public key for + + + align:start position:0% +key exactly he computes a public key for +the fhe and encrypt something nobody + + align:start position:0% +the fhe and encrypt something nobody + + + align:start position:0% +the fhe and encrypt something nobody +cares we're never going to decrypt it it + + align:start position:0% +cares we're never going to decrypt it it + + + align:start position:0% +cares we're never going to decrypt it it +encrypts with public key just let's say + + align:start position:0% +encrypts with public key just let's say + + + align:start position:0% +encrypts with public key just let's say +the all zero string so it's not exactly + + align:start position:0% +the all zero string so it's not exactly + + + align:start position:0% +the all zero string so it's not exactly +T it's a little more than T we'll it's + + align:start position:0% +T it's a little more than T we'll it's + + + align:start position:0% +T it's a little more than T we'll it's +the T we'll see what encrypts T Prime + + align:start position:0% +the T we'll see what encrypts T Prime + + + align:start position:0% +the T we'll see what encrypts T Prime +like 0 t Prime T Prime is going to be + + align:start position:0% +like 0 t Prime T Prime is going to be + + + align:start position:0% +like 0 t Prime T Prime is going to be +very similar to T but tiny bit more t + + align:start position:0% +very similar to T but tiny bit more t + + + align:start position:0% +very similar to T but tiny bit more t +plus the decryption plus one we'll see + + align:start position:0% +plus the decryption plus one we'll see + + + align:start position:0% +plus the decryption plus one we'll see +but that that's the that's gen it + + align:start position:0% +but that that's the that's gen it + + + align:start position:0% +but that that's the that's gen it +outputs a publicy an encryption of a + + align:start position:0% +outputs a publicy an encryption of a + + + align:start position:0% +outputs a publicy an encryption of a +bunch of zeros how many a little more + + align:start position:0% +bunch of zeros how many a little more + + + align:start position:0% +bunch of zeros how many a little more +than T we'll see the exact number that's + + align:start position:0% +than T we'll see the exact number that's + + + align:start position:0% +than T we'll see the exact number that's +what gen does what does eval + + align:start position:0% +what gen does what does eval + + + align:start position:0% +what gen does what does eval +do eval given this this hash key so this + + align:start position:0% +do eval given this this hash key so this + + + align:start position:0% +do eval given this this hash key so this +is a hash key and given + + align:start position:0% +is a hash key and given + + + align:start position:0% +is a hash key and given +alpha or yeah Alpha what it does it + + align:start position:0% +alpha or yeah Alpha what it does it + + + align:start position:0% +alpha or yeah Alpha what it does it +simply + + align:start position:0% +simply + + + align:start position:0% +simply +computes the eval of the FH + + align:start position:0% +computes the eval of the FH + + + align:start position:0% +computes the eval of the FH +so FH can be evaluated a new Alpha and + + align:start position:0% +so FH can be evaluated a new Alpha and + + + align:start position:0% +so FH can be evaluated a new Alpha and +the cipher text and let me call this G + + align:start position:0% +the cipher text and let me call this G + + + align:start position:0% +the cipher text and let me call this G +hat because it's kind of describes a + + align:start position:0% +hat because it's kind of describes a + + + align:start position:0% +hat because it's kind of describes a +circuit and G hat which is what it does + + align:start position:0% +circuit and G hat which is what it does + + + align:start position:0% +circuit and G hat which is what it does +it essentially computes G of alpha + + align:start position:0% +it essentially computes G of alpha + + + align:start position:0% +it essentially computes G of alpha +encryption that's what this eval of f + + align:start position:0% +encryption that's what this eval of f + + + align:start position:0% +encryption that's what this eval of f +does it takes this is a universal + + align:start position:0% +does it takes this is a universal + + + align:start position:0% +does it takes this is a universal +circuit takes this input a circuit g a + + align:start position:0% +circuit takes this input a circuit g a + + + align:start position:0% +circuit takes this input a circuit g a +description of circuit G and outputs G + + align:start position:0% +description of circuit G and outputs G + + + align:start position:0% +description of circuit G and outputs G +of alpha + + align:start position:0% +of alpha + + + align:start position:0% +of alpha +and this event does this under the hood + + align:start position:0% +and this event does this under the hood + + + align:start position:0% +and this event does this under the hood +so he outputs whatever is encrypted here + + align:start position:0% +so he outputs whatever is encrypted here + + + align:start position:0% +so he outputs whatever is encrypted here +the all zero circuit whatever a + + align:start position:0% +the all zero circuit whatever a + + + align:start position:0% +the all zero circuit whatever a +description of this is let's say + + align:start position:0% +description of this is let's say + + + align:start position:0% +description of this is let's say +description of + + align:start position:0% +description of + + + align:start position:0% +description of +circuit so in that case it'll be + + align:start position:0% +circuit so in that case it'll be + + + align:start position:0% +circuit so in that case it'll be +encryption of zero that's what it does + + align:start position:0% +encryption of zero that's what it does + + + align:start position:0% +encryption of zero that's what it does +that's the that's the hash function that + + align:start position:0% +that's the that's the hash function that + + + align:start position:0% +that's the that's the hash function that +I'm going to argue as correlation + + align:start position:0% +I'm going to argue as correlation + + + align:start position:0% +I'm going to argue as correlation +intractable for every relation uh for + + align:start position:0% +intractable for every relation uh for + + + align:start position:0% +intractable for every relation uh for +every T time searchable + + align:start position:0% +every T time searchable + + + align:start position:0% +every T time searchable +relation so now give me your favorite T + + align:start position:0% +relation so now give me your favorite T + + + align:start position:0% +relation so now give me your favorite T +time searchable relation and I'll show + + align:start position:0% +time searchable relation and I'll show + + + align:start position:0% +time searchable relation and I'll show +you why it's a correlation tractable + + align:start position:0% +you why it's a correlation tractable + + + align:start position:0% +you why it's a correlation tractable +with respect to it so okay you give me + + align:start position:0% +with respect to it so okay you give me + + + align:start position:0% +with respect to it so okay you give me +your favorite relation let me say a + + align:start position:0% +your favorite relation let me say a + + + align:start position:0% +your favorite relation let me say a +relation is a bunch of Alpha and F of + + align:start position:0% +relation is a bunch of Alpha and F of + + + align:start position:0% +relation is a bunch of Alpha and F of +alpha it's searchable so there's + + align:start position:0% +alpha it's searchable so there's + + + align:start position:0% +alpha it's searchable so there's +some function that for every Alpha + + align:start position:0% +some function that for every Alpha + + + align:start position:0% +some function that for every Alpha +there's a unique beta find the unique + + align:start position:0% +there's a unique beta find the unique + + + align:start position:0% +there's a unique beta find the unique +beta okay if if in in the more General + + align:start position:0% +beta okay if if in in the more General + + + align:start position:0% +beta okay if if in in the more General +case where there's D think of there's d + + align:start position:0% +case where there's D think of there's d + + + align:start position:0% +case where there's D think of there's d +fs like so there's a few more but for + + align:start position:0% +fs like so there's a few more but for + + + align:start position:0% +fs like so there's a few more but for +one you can think of just one okay so + + align:start position:0% +one you can think of just one okay so + + + align:start position:0% +one you can think of just one okay so +now now I want to argue there's no way + + align:start position:0% +now now I want to argue there's no way + + + align:start position:0% +now now I want to argue there's no way +you can find okay so I'm going to I'm + + align:start position:0% +you can find okay so I'm going to I'm + + + align:start position:0% +you can find okay so I'm going to I'm +going to argue you can't find F1 but if + + align:start position:0% +going to argue you can't find F1 but if + + + align:start position:0% +going to argue you can't find F1 but if +there's more I'll I'll then you also + + align:start position:0% +there's more I'll I'll then you also + + + align:start position:0% +there's more I'll I'll then you also +can't find F2 and F3 but let me focus on + + align:start position:0% +can't find F2 and F3 but let me focus on + + + align:start position:0% +can't find F2 and F3 but let me focus on +the first F let's see if there's only + + align:start position:0% +the first F let's see if there's only + + + align:start position:0% +the first F let's see if there's only +one I'm going to show you on the first F + + align:start position:0% +one I'm going to show you on the first F + + + align:start position:0% +one I'm going to show you on the first F +so you cannot there's no way why + + align:start position:0% +so you cannot there's no way why + + + align:start position:0% +so you cannot there's no way why +because if you could if the adversary + + align:start position:0% +because if you could if the adversary + + + align:start position:0% +because if you could if the adversary +given hash + + align:start position:0% +given hash + + + align:start position:0% +given hash +key could find Alpha so that the hash of + + align:start position:0% +key could find Alpha so that the hash of + + + align:start position:0% +key could find Alpha so that the hash of +alpha is f of alpha then he could also + + align:start position:0% +alpha is f of alpha then he could also + + + align:start position:0% +alpha is f of alpha then he could also +do it in the case where I + + align:start position:0% +do it in the case where I + + + align:start position:0% +do it in the case where I +replace Alpha with where I replace G + + align:start position:0% +replace Alpha with where I replace G + + + align:start position:0% +replace Alpha with where I replace G +with a fake G and my fake G that I'm + + align:start position:0% +with a fake G and my fake G that I'm + + + align:start position:0% +with a fake G and my fake G that I'm +going to replace it + + align:start position:0% +going to replace it + + + align:start position:0% +going to replace it +with + + align:start position:0% +with + + + align:start position:0% +with +so so + + align:start position:0% + + + + align:start position:0% + +Suppose there exists an adversary that + + align:start position:0% +Suppose there exists an adversary that + + + align:start position:0% +Suppose there exists an adversary that +breaks then okay so uh that so there + + align:start position:0% +breaks then okay so uh that so there + + + align:start position:0% +breaks then okay so uh that so there +exists an adversary that such that + + align:start position:0% +exists an adversary that such that + + + align:start position:0% +exists an adversary that such that +the adversary given hash key outputs + + align:start position:0% +the adversary given hash key outputs + + + align:start position:0% +the adversary given hash key outputs +Alpha such + + align:start position:0% +Alpha such + + + align:start position:0% +Alpha such +that eval of H key and + + align:start position:0% +that eval of H key and + + + align:start position:0% +that eval of H key and +Alpha is equal to F of alpha that's what + + align:start position:0% +Alpha is equal to F of alpha that's what + + + align:start position:0% +Alpha is equal to F of alpha that's what +we want to avoid we say no you shouldn't + + align:start position:0% +we want to avoid we say no you shouldn't + + + align:start position:0% +we want to avoid we say no you shouldn't +be able to find something in in the + + align:start position:0% +be able to find something in in the + + + align:start position:0% +be able to find something in in the +relation if you can if you can do that + + align:start position:0% +relation if you can if you can do that + + + align:start position:0% +relation if you can if you can do that +with probability greater than some + + align:start position:0% +with probability greater than some + + + align:start position:0% +with probability greater than some +Epsilon then I claim then + + align:start position:0% +Epsilon then I claim then + + + align:start position:0% +Epsilon then I claim then +a succeeds in the same thing + + align:start position:0% +a succeeds in the same thing + + + align:start position:0% +a succeeds in the same thing +succeeds with probability close like + + align:start position:0% +succeeds with probability close like + + + align:start position:0% +succeeds with probability close like +close to Epsilon + + align:start position:0% +close to Epsilon + + + align:start position:0% +close to Epsilon +also by semantic security also with HK + + align:start position:0% +also by semantic security also with HK + + + align:start position:0% +also by semantic security also with HK +star a different HK and what is HK star + + align:start position:0% +star a different HK and what is HK star + + + align:start position:0% +star a different HK and what is HK star +this it generates the same public key + + align:start position:0% +this it generates the same public key + + + align:start position:0% +this it generates the same public key +but it generates an encryption of G Star + + align:start position:0% +but it generates an encryption of G Star + + + align:start position:0% +but it generates an encryption of G Star +not of G so here I encrypted all zero g + + align:start position:0% +not of G so here I encrypted all zero g + + + align:start position:0% +not of G so here I encrypted all zero g +was all zero I'm encrypting a new g a g + + align:start position:0% +was all zero I'm encrypting a new g a g + + + align:start position:0% +was all zero I'm encrypting a new g a g +star what is + + align:start position:0% + + + + align:start position:0% + +gar g + + align:start position:0% + + + + align:start position:0% + +star uh an + + align:start position:0% + + + + align:start position:0% + +input Alpha outputs the decryption I + + align:start position:0% +input Alpha outputs the decryption I + + + align:start position:0% +input Alpha outputs the decryption I +know weird it has secret key hard wired + + align:start position:0% +know weird it has secret key hard wired + + + align:start position:0% +know weird it has secret key hard wired +in it and it outputs the + + align:start position:0% +in it and it outputs the + + + align:start position:0% +in it and it outputs the +decryption of kind of the bad + + align:start position:0% +decryption of kind of the bad + + + align:start position:0% +decryption of kind of the bad +function an alpha + + align:start position:0% +function an alpha + + + align:start position:0% +function an alpha +XR with + + align:start position:0% + + + + align:start position:0% + +one and we show that actually if this is + + align:start position:0% +one and we show that actually if this is + + + align:start position:0% +one and we show that actually if this is +what you put + + align:start position:0% +what you put + + + align:start position:0% +what you put +there you really that you you never it's + + align:start position:0% +there you really that you you never it's + + + align:start position:0% +there you really that you you never it's +impossible to Output F ofx this is never + + align:start position:0% +impossible to Output F ofx this is never + + + align:start position:0% +impossible to Output F ofx this is never +it's never the case so we want to say + + align:start position:0% +it's never the case so we want to say + + + align:start position:0% +it's never the case so we want to say +that G Star + + align:start position:0% +that G Star + + + align:start position:0% +that G Star +theal G Star + + align:start position:0% +theal G Star + + + align:start position:0% +theal G Star +Alpha is never F of f of alpha it's just + + align:start position:0% +Alpha is never F of f of alpha it's just + + + align:start position:0% +Alpha is never F of f of alpha it's just +never why because if it was then if you + + align:start position:0% +never why because if it was then if you + + + align:start position:0% +never why because if it was then if you +decrypt this and decrypt this you would + + align:start position:0% +decrypt this and decrypt this you would + + + align:start position:0% +decrypt this and decrypt this you would +get the same value but if you decrypt + + align:start position:0% +get the same value but if you decrypt + + + align:start position:0% +get the same value but if you decrypt +this you get G Star Alpha and if you + + align:start position:0% +this you get G Star Alpha and if you + + + align:start position:0% +this you get G Star Alpha and if you +decrypt this you get this and they're + + align:start position:0% +decrypt this you get this and they're + + + align:start position:0% +decrypt this you get this and they're +not the + + align:start position:0% + + + + align:start position:0% + +same + + align:start position:0% +same + + + align:start position:0% +same +yeah what + + align:start position:0% +yeah what + + + align:start position:0% +yeah what +is no F sorry I'm uh let me so we have a + + align:start position:0% +is no F sorry I'm uh let me so we have a + + + align:start position:0% +is no F sorry I'm uh let me so we have a +a t time searchable relation T time + + align:start position:0% +a t time searchable relation T time + + + align:start position:0% +a t time searchable relation T time +searchable relation it means that for + + align:start position:0% +searchable relation it means that for + + + align:start position:0% +searchable relation it means that for +every alha there's a unique beta so I + + align:start position:0% +every alha there's a unique beta so I + + + align:start position:0% +every alha there's a unique beta so I +call this beta sorry sorry so then is + + align:start position:0% +call this beta sorry sorry so then is + + + align:start position:0% +call this beta sorry sorry so then is +this over like all + + align:start position:0% +this over like all + + + align:start position:0% +this over like all +good so exactly so I want to say I say I + + align:start position:0% +good so exactly so I want to say I say I + + + align:start position:0% +good so exactly so I want to say I say I +constructed this hash family that just + + align:start position:0% +constructed this hash family that just + + + align:start position:0% +constructed this hash family that just +has an encryption and he does + + align:start position:0% +has an encryption and he does + + + align:start position:0% +has an encryption and he does +computation under the hood and I'm + + align:start position:0% +computation under the hood and I'm + + + align:start position:0% +computation under the hood and I'm +saying this hash family it's a + + align:start position:0% +saying this hash family it's a + + + align:start position:0% +saying this hash family it's a +correlation and tractable with respect + + align:start position:0% +correlation and tractable with respect + + + align:start position:0% +correlation and tractable with respect +to every T time searchable relation why + + align:start position:0% +to every T time searchable relation why + + + align:start position:0% +to every T time searchable relation why +fix your favorite T time searchable + + align:start position:0% +fix your favorite T time searchable + + + align:start position:0% +fix your favorite T time searchable +relation your favorite one the fact that + + align:start position:0% +relation your favorite one the fact that + + + align:start position:0% +relation your favorite one the fact that +it's searchable means that for every + + align:start position:0% +it's searchable means that for every + + + align:start position:0% +it's searchable means that for every +Alpha there's a unique beta and it's + + align:start position:0% +Alpha there's a unique beta and it's + + + align:start position:0% +Alpha there's a unique beta and it's +computable in time T so I call F the + + align:start position:0% +computable in time T so I call F the + + + align:start position:0% +computable in time T so I call F the +function that computes this beta and now + + align:start position:0% +function that computes this beta and now + + + align:start position:0% +function that computes this beta and now +I say look there's no way an adversary + + align:start position:0% +I say look there's no way an adversary + + + align:start position:0% +I say look there's no way an adversary +can find Alpha for which the hash + + align:start position:0% +can find Alpha for which the hash + + + align:start position:0% +can find Alpha for which the hash +function takes him to to Beta to F of + + align:start position:0% +function takes him to to Beta to F of + + + align:start position:0% +function takes him to to Beta to F of +alpha because if he could he could also + + align:start position:0% +alpha because if he could he could also + + + align:start position:0% +alpha because if he could he could also +do it where I where the hash key which + + align:start position:0% +do it where I where the hash key which + + + align:start position:0% +do it where I where the hash key which +encrypts zero actually + + align:start position:0% +encrypts zero actually + + + align:start position:0% +encrypts zero actually +encrypts this G Star another G what is g + + align:start position:0% +encrypts this G Star another G what is g + + + align:start position:0% +encrypts this G Star another G what is g +g star now G star depends on this F but + + align:start position:0% +g star now G star depends on this F but + + + align:start position:0% +g star now G star depends on this F but +it's under the hood nobody can tell the + + align:start position:0% +it's under the hood nobody can tell the + + + align:start position:0% +it's under the hood nobody can tell the +difference and this G Star it decrypts + + align:start position:0% +difference and this G Star it decrypts + + + align:start position:0% +difference and this G Star it decrypts +this F even though f is not a cipher + + align:start position:0% +this F even though f is not a cipher + + + align:start position:0% +this F even though f is not a cipher +attack so it's a very weird thing to do + + align:start position:0% +attack so it's a very weird thing to do + + + align:start position:0% +attack so it's a very weird thing to do +but it decrypts this F and changes + + align:start position:0% +but it decrypts this F and changes + + + align:start position:0% +but it decrypts this F and changes +something changes a bit and now I want + + align:start position:0% +something changes a bit and now I want + + + align:start position:0% +something changes a bit and now I want +to say the hash gives you encryption of + + align:start position:0% +to say the hash gives you encryption of + + + align:start position:0% +to say the hash gives you encryption of +G Star Alpha an encryption of gar Alpha + + align:start position:0% +G Star Alpha an encryption of gar Alpha + + + align:start position:0% +G Star Alpha an encryption of gar Alpha +cannot be F of alpha there's no way + + align:start position:0% +cannot be F of alpha there's no way + + + align:start position:0% +cannot be F of alpha there's no way +because if it was any encryption + + align:start position:0% +because if it was any encryption + + + align:start position:0% +because if it was any encryption +actually because if it was if you + + align:start position:0% +actually because if it was if you + + + align:start position:0% +actually because if it was if you +decrypted this and decrypted this you + + align:start position:0% +decrypted this and decrypted this you + + + align:start position:0% +decrypted this and decrypted this you +would get the same thing but you decrypt + + align:start position:0% +would get the same thing but you decrypt + + + align:start position:0% +would get the same thing but you decrypt +this you get G Star + + align:start position:0% +this you get G Star + + + align:start position:0% +this you get G Star +Alpha and G starpha is not decryption of + + align:start position:0% +Alpha and G starpha is not decryption of + + + align:start position:0% +Alpha and G starpha is not decryption of +f of alpha by by Design + + align:start position:0% +f of alpha by by Design + + + align:start position:0% +f of alpha by by Design +so once you change the hash key to this + + align:start position:0% +so once you change the hash key to this + + + align:start position:0% +so once you change the hash key to this +you're + + align:start position:0% +you're + + + align:start position:0% +you're +statistically C and and all powerful + + align:start position:0% +statistically C and and all powerful + + + align:start position:0% +statistically C and and all powerful +adversary cannot hit F so there's some + + align:start position:0% +adversary cannot hit F so there's some + + + align:start position:0% +adversary cannot hit F so there's some +kind of we use computational assumption + + align:start position:0% +kind of we use computational assumption + + + align:start position:0% +kind of we use computational assumption +but then once we once we move to Gar we + + align:start position:0% +but then once we once we move to Gar we + + + align:start position:0% +but then once we once we move to Gar we +we can we don't care about the + + align:start position:0% +we can we don't care about the + + + align:start position:0% +we can we don't care about the +Assumption anymore we're in statistical + + align:start position:0% +Assumption anymore we're in statistical + + + align:start position:0% +Assumption anymore we're in statistical +land even in all powerful adversary + + align:start position:0% +land even in all powerful adversary + + + align:start position:0% +land even in all powerful adversary +cannot + + align:start position:0% + + + + align:start position:0% + +cheat sorry I don't to ask no no it's + + align:start position:0% +cheat sorry I don't to ask no no it's + + + align:start position:0% +cheat sorry I don't to ask no no it's +fantastic question this still fine if + + align:start position:0% +fantastic question this still fine if + + + align:start position:0% +fantastic question this still fine if +the adversary picks the relation after + + align:start position:0% +the adversary picks the relation after + + + align:start position:0% +the adversary picks the relation after +it knows the hash key exact H yeah yeah + + align:start position:0% +it knows the hash key exact H yeah yeah + + + align:start position:0% +it knows the hash key exact H yeah yeah +exactly you're right so think about this + + align:start position:0% +exactly you're right so think about this + + + align:start position:0% +exactly you're right so think about this +the adversary get the hash key public + + align:start position:0% +the adversary get the hash key public + + + align:start position:0% +the adversary get the hash key public +key and encryption of something + + align:start position:0% +key and encryption of something + + + align:start position:0% +key and encryption of something +encryption of zero now he gives me f he + + align:start position:0% +encryption of zero now he gives me f he + + + align:start position:0% +encryption of zero now he gives me f he +tells me f with this F I can cheat I can + + align:start position:0% +tells me f with this F I can cheat I can + + + align:start position:0% +tells me f with this F I can cheat I can +find I can I'm get really okay can you + + align:start position:0% +find I can I'm get really okay can you + + + align:start position:0% +find I can I'm get really okay can you +distinguish between encryption of the + + align:start position:0% +distinguish between encryption of the + + + align:start position:0% +distinguish between encryption of the +all zero and encryption assuming + + align:start position:0% +all zero and encryption assuming + + + align:start position:0% +all zero and encryption assuming +circular security yeah cuz this is kind + + align:start position:0% +circular security yeah cuz this is kind + + + align:start position:0% +circular security yeah cuz this is kind +of subse secret key but let's so it's + + align:start position:0% +of subse secret key but let's so it's + + + align:start position:0% +of subse secret key but let's so it's +I'm I'm using semantic this gar depends + + align:start position:0% +I'm I'm using semantic this gar depends + + + align:start position:0% +I'm I'm using semantic this gar depends +on F and then the secret key but + + align:start position:0% +on F and then the secret key but + + + align:start position:0% +on F and then the secret key but +assuming you can't break semantic + + align:start position:0% +assuming you can't break semantic + + + align:start position:0% +assuming you can't break semantic +security circle of + + align:start position:0% +security circle of + + + align:start position:0% +security circle of +security then he even if he chooses F he + + align:start position:0% +security then he even if he chooses F he + + + align:start position:0% +security then he even if he chooses F he +cannot distinguish between encryption of + + align:start position:0% +cannot distinguish between encryption of + + + align:start position:0% +cannot distinguish between encryption of +G star and encryption of zero assuming + + align:start position:0% +G star and encryption of zero assuming + + + align:start position:0% +G star and encryption of zero assuming +circular secure F I guess what prevents + + align:start position:0% +circular secure F I guess what prevents + + + align:start position:0% +circular secure F I guess what prevents +from just piing like f evaluation of + + align:start position:0% +from just piing like f evaluation of + + + align:start position:0% +from just piing like f evaluation of +Alpha and + + align:start position:0% +Alpha and + + + align:start position:0% +Alpha and +why can't F just be like + + align:start position:0% +why can't F just be like + + + align:start position:0% +why can't F just be like +evaluation like why can't he's just said + + align:start position:0% +evaluation like why can't he's just said + + + align:start position:0% +evaluation like why can't he's just said +oh okay good point hold on you're saying + + align:start position:0% +oh okay good point hold on you're saying + + + align:start position:0% +oh okay good point hold on you're saying +why + + align:start position:0% +why + + + align:start position:0% +why +a no okay okay okay sorry + + align:start position:0% +a no okay okay okay sorry + + + align:start position:0% +a no okay okay okay sorry +a no it's kind of weird yeah yeah yeah + + align:start position:0% +a no it's kind of weird yeah yeah yeah + + + align:start position:0% +a no it's kind of weird yeah yeah yeah +yeah yeah no no no you're right okay + + align:start position:0% +yeah yeah no no no you're right okay + + + align:start position:0% +yeah yeah no no no you're right okay +sorry sorry sorry uh he can choose f + + align:start position:0% +sorry sorry sorry uh he can choose f + + + align:start position:0% +sorry sorry sorry uh he can choose f +after he sees the hash family the hash + + align:start position:0% +after he sees the hash family the hash + + + align:start position:0% +after he sees the hash family the hash +family the hash family no once you have + + align:start position:0% +family the hash family no once you have + + + align:start position:0% +family the hash family no once you have +the specific key then you're right + + align:start position:0% +the specific key then you're right + + + align:start position:0% +the specific key then you're right +you'll just be the hash key sorry I I + + align:start position:0% +you'll just be the hash key sorry I I + + + align:start position:0% +you'll just be the hash key sorry I I +miss I yeah there's one hash family + + align:start position:0% +miss I yeah there's one hash family + + + align:start position:0% +miss I yeah there's one hash family +after he sees the hash family he can + + align:start position:0% +after he sees the hash family he can + + + align:start position:0% +after he sees the hash family he can +choose the relation but of course for + + align:start position:0% +choose the relation but of course for + + + align:start position:0% +choose the relation but of course for +the specific hash + + align:start position:0% +the specific hash + + + align:start position:0% +the specific hash +key + + align:start position:0% +key + + + align:start position:0% +key +he'll yeah then yeah and and yeah + + align:start position:0% +he'll yeah then yeah and and yeah + + + align:start position:0% +he'll yeah then yeah and and yeah +exactly and that should just follow like + + align:start position:0% +exactly and that should just follow like + + + align:start position:0% +exactly and that should just follow like +the fact the cyer text is randomized + + align:start position:0% +the fact the cyer text is randomized + + + align:start position:0% +the fact the cyer text is randomized +right like once you have an an + + align:start position:0% +right like once you have an an + + + align:start position:0% +right like once you have an an +encryption of had like predicting the + + align:start position:0% +encryption of had like predicting the + + + align:start position:0% +encryption of had like predicting the +evaluation should be very exactly + + align:start position:0% +evaluation should be very exactly + + + align:start position:0% +evaluation should be very exactly +exactly exactly and just going back this + + align:start position:0% +exactly exactly and just going back this + + + align:start position:0% +exactly exactly and just going back this +T Prime is the time the the size of G + + align:start position:0% +T Prime is the time the the size of G + + + align:start position:0% +T Prime is the time the the size of G +Star so it's a little more than F + + align:start position:0% +Star so it's a little more than F + + + align:start position:0% +Star so it's a little more than F +because you also need to decrypt but + + align:start position:0% +because you also need to decrypt but + + + align:start position:0% +because you also need to decrypt but +it's very very similar to have just + + align:start position:0% +it's very very similar to have just + + + align:start position:0% +it's very very similar to have just +uh + + align:start position:0% +uh + + + align:start position:0% +uh +question this like the same kind of + + align:start position:0% +question this like the same kind of + + + align:start position:0% +question this like the same kind of +issue as to why it mattered that in some + + align:start position:0% +issue as to why it mattered that in some + + + align:start position:0% +issue as to why it mattered that in some +TR like the later bad relations depended + + align:start position:0% +TR like the later bad relations depended + + + align:start position:0% +TR like the later bad relations depended +on the verifier messages it's like if + + align:start position:0% +on the verifier messages it's like if + + + align:start position:0% +on the verifier messages it's like if +that wasn't the case then this exactly + + align:start position:0% +that wasn't the case then this exactly + + + align:start position:0% +that wasn't the case then this exactly +exactly exactly that was the same issue + + align:start position:0% +exactly exactly that was the same issue + + + align:start position:0% +exactly exactly that was the same issue +that came in GK that the things the T + + align:start position:0% +that came in GK that the things the T + + + align:start position:0% +that came in GK that the things the T +dependent yeah yeah that me yeah great + + align:start position:0% +dependent yeah yeah that me yeah great + + + align:start position:0% +dependent yeah yeah that me yeah great +great great question anybody else yeah I + + align:start position:0% +great great question anybody else yeah I + + + align:start position:0% +great great question anybody else yeah I +still don't + + align:start position:0% +still don't + + + align:start position:0% +still don't +see + + align:start position:0% + + + + align:start position:0% + +how if f is if f is what is not unique + + align:start position:0% +how if f is if f is what is not unique + + + align:start position:0% +how if f is if f is what is not unique +okay good so if f is what not unique + + align:start position:0% +okay good so if f is what not unique + + + align:start position:0% +okay good so if f is what not unique +what I'm going to show suppose Alpha has + + align:start position:0% +what I'm going to show suppose Alpha has + + + align:start position:0% +what I'm going to show suppose Alpha has +many FS F1 up to FD associated with them + + align:start position:0% +many FS F1 up to FD associated with them + + + align:start position:0% +many FS F1 up to FD associated with them +then I'm going to say look first let me + + align:start position:0% +then I'm going to say look first let me + + + align:start position:0% +then I'm going to say look first let me +argue that adversary cannot the + + align:start position:0% +argue that adversary cannot the + + + align:start position:0% +argue that adversary cannot the +probability that he outputs F1 is + + align:start position:0% +probability that he outputs F1 is + + + align:start position:0% +probability that he outputs F1 is +negligible so for every the probability + + align:start position:0% +negligible so for every the probability + + + align:start position:0% +negligible so for every the probability +that he outputs Alpha and F1 of alpha is + + align:start position:0% +that he outputs Alpha and F1 of alpha is + + + align:start position:0% +that he outputs Alpha and F1 of alpha is +negligible this I kind of convinced + + align:start position:0% +negligible this I kind of convinced + + + align:start position:0% +negligible this I kind of convinced +you but that's Al also for F2 and for F3 + + align:start position:0% +you but that's Al also for F2 and for F3 + + + align:start position:0% +you but that's Al also for F2 and for F3 +oh so you use many yeah I'm just using + + align:start position:0% +oh so you use many yeah I'm just using + + + align:start position:0% +oh so you use many yeah I'm just using +exactly in the anal exactly so I'm + + align:start position:0% +exactly in the anal exactly so I'm + + + align:start position:0% +exactly in the anal exactly so I'm +saying exactly in the analysis I'm going + + align:start position:0% +saying exactly in the analysis I'm going + + + align:start position:0% +saying exactly in the analysis I'm going +to change my G Star exactly + + align:start position:0% +to change my G Star exactly + + + align:start position:0% +to change my G Star exactly +fantastic yeah so a simar idea how you + + align:start position:0% +fantastic yeah so a simar idea how you + + + align:start position:0% +fantastic yeah so a simar idea how you +define like our Cal or like relations + + align:start position:0% +define like our Cal or like relations + + + align:start position:0% +define like our Cal or like relations +that have like many Bas instead of + + align:start position:0% +that have like many Bas instead of + + + align:start position:0% +that have like many Bas instead of +exactly the the doing the many betas the + + align:start position:0% +exactly the the doing the many betas the + + + align:start position:0% +exactly the the doing the many betas the +only difference is it's exact same proof + + align:start position:0% +only difference is it's exact same proof + + + align:start position:0% +only difference is it's exact same proof +except that I'll I'll need to kind of + + align:start position:0% +except that I'll I'll need to kind of + + + align:start position:0% +except that I'll I'll need to kind of +choose one of them a I I'll degrade with + + align:start position:0% +choose one of them a I I'll degrade with + + + align:start position:0% +choose one of them a I I'll degrade with +d because I'm going to show for each one + + align:start position:0% +d because I'm going to show for each one + + + align:start position:0% +d because I'm going to show for each one +the probability that with that one you + + align:start position:0% +the probability that with that one you + + + align:start position:0% +the probability that with that one you +succeed is negligible and then I'll just + + align:start position:0% +succeed is negligible and then I'll just + + + align:start position:0% +succeed is negligible and then I'll just +do a union bound I guess my question a + + align:start position:0% +do a union bound I guess my question a + + + align:start position:0% +do a union bound I guess my question a +little I guess in + + align:start position:0% +little I guess in + + + align:start position:0% +little I guess in +cist uh CI function for all relations + + align:start position:0% +cist uh CI function for all relations + + + align:start position:0% +cist uh CI function for all relations +that are searchable in time and I was + + align:start position:0% +that are searchable in time and I was + + + align:start position:0% +that are searchable in time and I was +trying to how to extend the r definition + + align:start position:0% +trying to how to extend the r definition + + + align:start position:0% +trying to how to extend the r definition +to handle like cases where beta isn't + + align:start position:0% +to handle like cases where beta isn't + + + align:start position:0% +to handle like cases where beta isn't +easy yeah exactly so yeah essentially + + align:start position:0% +easy yeah exactly so yeah essentially + + + align:start position:0% +easy yeah exactly so yeah essentially +think of r instead of searchable it's + + align:start position:0% +think of r instead of searchable it's + + + align:start position:0% +think of r instead of searchable it's +like it has like F1 so for each Alpha + + align:start position:0% +like it has like F1 so for each Alpha + + + align:start position:0% +like it has like F1 so for each Alpha +there's F1 of alpha up to FD of alpha + + align:start position:0% +there's F1 of alpha up to FD of alpha + + + align:start position:0% +there's F1 of alpha up to FD of alpha +these are the betas corresponding to it + + align:start position:0% +these are the betas corresponding to it + + + align:start position:0% +these are the betas corresponding to it +so now that's your relation that's yeah + + align:start position:0% +so now that's your relation that's yeah + + + align:start position:0% +so now that's your relation that's yeah +okay great okay we're out of time guys + + align:start position:0% +okay great okay we're out of time guys + + + align:start position:0% +okay great okay we're out of time guys +thank you so much have a great peaceful + + align:start position:0% +thank you so much have a great peaceful + + + align:start position:0% +thank you so much have a great peaceful +fun Thanksgiving and I'll see you + + align:start position:0% +fun Thanksgiving and I'll see you + + + align:start position:0% +fun Thanksgiving and I'll see you +uh not the week after but the week after + + align:start position:0% +uh not the week after but the week after + + + align:start position:0% +uh not the week after but the week after +after \ No newline at end of file diff --git a/HWRHTNzwELo.txt b/HWRHTNzwELo.txt new file mode 100644 index 0000000000000000000000000000000000000000..381cf2e796f92bf3f4d37e0491b9c422c72a1fa7 --- /dev/null +++ b/HWRHTNzwELo.txt @@ -0,0 +1,8915 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay let's get + + align:start position:0% +ocw.mit.edu okay let's get + + + align:start position:0% +ocw.mit.edu okay let's get +started settle down couple of + + align:start position:0% +started settle down couple of + + + align:start position:0% +started settle down couple of +announcements to make um it's with great + + align:start position:0% +announcements to make um it's with great + + + align:start position:0% +announcements to make um it's with great +sadness that I announced that there will + + align:start position:0% +sadness that I announced that there will + + + align:start position:0% +sadness that I announced that there will +be no lecture on + + align:start position:0% +be no lecture on + + + align:start position:0% +be no lecture on +Monday yeah I know + + align:start position:0% +Monday yeah I know + + + align:start position:0% +Monday yeah I know +I with all the kleenex consumed Kimberly + + align:start position:0% +I with all the kleenex consumed Kimberly + + + align:start position:0% +I with all the kleenex consumed Kimberly +Clark went up two points on the New York + + align:start position:0% +Clark went up two points on the New York + + + align:start position:0% +Clark went up two points on the New York +Stock Exchange yesterday just incredible + + align:start position:0% +Stock Exchange yesterday just incredible + + + align:start position:0% +Stock Exchange yesterday just incredible +um and in view of the the the timing of + + align:start position:0% +um and in view of the the the timing of + + + align:start position:0% +um and in view of the the the timing of +where we are in the lectures versus the + + align:start position:0% +where we are in the lectures versus the + + + align:start position:0% +where we are in the lectures versus the +um homework and uh no opportunity to + + align:start position:0% +um homework and uh no opportunity to + + + align:start position:0% +um homework and uh no opportunity to +interact with the recitation instructors + + align:start position:0% +interact with the recitation instructors + + + align:start position:0% +interact with the recitation instructors +on Monday what we're doing just uh this + + align:start position:0% +on Monday what we're doing just uh this + + + align:start position:0% +on Monday what we're doing just uh this +one time I'm going to slide the the + + align:start position:0% +one time I'm going to slide the the + + + align:start position:0% +one time I'm going to slide the the +weekly quiz over to Thursday that gives + + align:start position:0% +weekly quiz over to Thursday that gives + + + align:start position:0% +weekly quiz over to Thursday that gives +more time for uh people to contact their + + align:start position:0% +more time for uh people to contact their + + + align:start position:0% +more time for uh people to contact their +recitation + + align:start position:0% +recitation + + + align:start position:0% +recitation +instructors um well let's get on with + + align:start position:0% +instructors um well let's get on with + + + align:start position:0% +instructors um well let's get on with +the lesson uh you know I perhaps some of + + align:start position:0% +the lesson uh you know I perhaps some of + + + align:start position:0% +the lesson uh you know I perhaps some of +you haven't figured out but the lecture + + align:start position:0% +you haven't figured out but the lecture + + + align:start position:0% +you haven't figured out but the lecture +has started and I still hear talking and + + align:start position:0% +has started and I still hear talking and + + + align:start position:0% +has started and I still hear talking and +I will invite people to leave if they + + align:start position:0% +I will invite people to leave if they + + + align:start position:0% +I will invite people to leave if they +insist + + align:start position:0% +insist + + + align:start position:0% +insist +on talking + + align:start position:0% + + + + align:start position:0% + +so last day we talked about secondary + + align:start position:0% +so last day we talked about secondary + + + align:start position:0% +so last day we talked about secondary +bonding and uh we looked at uh various + + align:start position:0% +bonding and uh we looked at uh various + + + align:start position:0% +bonding and uh we looked at uh various +forms of secondary bonding here's the + + align:start position:0% +forms of secondary bonding here's the + + + align:start position:0% +forms of secondary bonding here's the +cartoons dipole dipole interactions + + align:start position:0% +cartoons dipole dipole interactions + + + align:start position:0% +cartoons dipole dipole interactions +dipole induced dipole ins Solutions a + + align:start position:0% +dipole induced dipole ins Solutions a + + + align:start position:0% +dipole induced dipole ins Solutions a +little bit of a diversion induc dipo and + + align:start position:0% +little bit of a diversion induc dipo and + + + align:start position:0% +little bit of a diversion induc dipo and +de dipole which was the London + + align:start position:0% +de dipole which was the London + + + align:start position:0% +de dipole which was the London +dispersion forces uh or vander's bonds + + align:start position:0% +dispersion forces uh or vander's bonds + + + align:start position:0% +dispersion forces uh or vander's bonds +and uh also hydrogen bonding and all of + + align:start position:0% +and uh also hydrogen bonding and all of + + + align:start position:0% +and uh also hydrogen bonding and all of +these helped us answer the question + + align:start position:0% +these helped us answer the question + + + align:start position:0% +these helped us answer the question +what's the state of aggregation the + + align:start position:0% +what's the state of aggregation the + + + align:start position:0% +what's the state of aggregation the +reason we want to know the state of + + align:start position:0% +reason we want to know the state of + + + align:start position:0% +reason we want to know the state of +aggregation is that this is solid state + + align:start position:0% +aggregation is that this is solid state + + + align:start position:0% +aggregation is that this is solid state +chemistry and we want to know when + + align:start position:0% +chemistry and we want to know when + + + align:start position:0% +chemistry and we want to know when +something's a solid so this helps us get + + align:start position:0% +something's a solid so this helps us get + + + align:start position:0% +something's a solid so this helps us get +to that conclusion and then we came to + + align:start position:0% +to that conclusion and then we came to + + + align:start position:0% +to that conclusion and then we came to +the point where we realized that three + + align:start position:0% +the point where we realized that three + + + align:start position:0% +the point where we realized that three +quarters of the periodic table wasn't + + align:start position:0% +quarters of the periodic table wasn't + + + align:start position:0% +quarters of the periodic table wasn't +covered by either ionic bonding coent + + align:start position:0% +covered by either ionic bonding coent + + + align:start position:0% +covered by either ionic bonding coent +bonding + + align:start position:0% +bonding + + + align:start position:0% +bonding +or Vander Fall's bonding as a primary + + align:start position:0% +or Vander Fall's bonding as a primary + + + align:start position:0% +or Vander Fall's bonding as a primary +form of bonding so we had to come up + + align:start position:0% +form of bonding so we had to come up + + + align:start position:0% +form of bonding so we had to come up +with something else and that something + + align:start position:0% +with something else and that something + + + align:start position:0% +with something else and that something +else was metallic bonding we saw uh Paul + + align:start position:0% +else was metallic bonding we saw uh Paul + + + align:start position:0% +else was metallic bonding we saw uh Paul +duda's early attempt in 1900 to model + + align:start position:0% +duda's early attempt in 1900 to model + + + align:start position:0% +duda's early attempt in 1900 to model +Metals at a gas of free electrons moving + + align:start position:0% +Metals at a gas of free electrons moving + + + align:start position:0% +Metals at a gas of free electrons moving +about ion cores where the ion core in + + align:start position:0% +about ion cores where the ion core in + + + align:start position:0% +about ion cores where the ion core in +fact is a mix of the nucleus plus all + + align:start position:0% +fact is a mix of the nucleus plus all + + + align:start position:0% +fact is a mix of the nucleus plus all +the inner shell electrons and uh we + + align:start position:0% +the inner shell electrons and uh we + + + align:start position:0% +the inner shell electrons and uh we +recognized that that didn't take us very + + align:start position:0% +recognized that that didn't take us very + + + align:start position:0% +recognized that that didn't take us very +far so what we want to do is continue + + align:start position:0% +far so what we want to do is continue + + + align:start position:0% +far so what we want to do is continue +the discussion and today we're going to + + align:start position:0% +the discussion and today we're going to + + + align:start position:0% +the discussion and today we're going to +look at um the next installments which + + align:start position:0% +look at um the next installments which + + + align:start position:0% +look at um the next installments which +took place about 30 years later as part + + align:start position:0% +took place about 30 years later as part + + + align:start position:0% +took place about 30 years later as part +of the quantum Revolution and there's + + align:start position:0% +of the quantum Revolution and there's + + + align:start position:0% +of the quantum Revolution and there's +really two benchmarks here the first one + + align:start position:0% +really two benchmarks here the first one + + + align:start position:0% +really two benchmarks here the first one +is by f Felix + + align:start position:0% +is by f Felix + + + align:start position:0% +is by f Felix +block Felix block and this came out in + + align:start position:0% +block Felix block and this came out in + + + align:start position:0% +block Felix block and this came out in +1928 this was his PhD thesis this was + + align:start position:0% +1928 this was his PhD thesis this was + + + align:start position:0% +1928 this was his PhD thesis this was +his PhD thesis what he did for his PhD + + align:start position:0% +his PhD thesis what he did for his PhD + + + align:start position:0% +his PhD thesis what he did for his PhD +thesis which was done under the + + align:start position:0% +thesis which was done under the + + + align:start position:0% +thesis which was done under the +supervision of Heisenberg at + + align:start position:0% +supervision of Heisenberg at + + + align:start position:0% +supervision of Heisenberg at +leipsig took on a interesting problem so + + align:start position:0% +leipsig took on a interesting problem so + + + align:start position:0% +leipsig took on a interesting problem so +far you've seen quantum theory applied + + align:start position:0% +far you've seen quantum theory applied + + + align:start position:0% +far you've seen quantum theory applied +to gases right applied to gases bore + + align:start position:0% +to gases right applied to gases bore + + + align:start position:0% +to gases right applied to gases bore +talk talked about Atomic hydrogen Atomic + + align:start position:0% +talk talked about Atomic hydrogen Atomic + + + align:start position:0% +talk talked about Atomic hydrogen Atomic +hydrogen and you know the complexities + + align:start position:0% +hydrogen and you know the complexities + + + align:start position:0% +hydrogen and you know the complexities +of condensed matter blocks PhD thesis + + align:start position:0% +of condensed matter blocks PhD thesis + + + align:start position:0% +of condensed matter blocks PhD thesis +quantum theory of solids let's take + + align:start position:0% +quantum theory of solids let's take + + + align:start position:0% +quantum theory of solids let's take +quantum theory and apply it to solids + + align:start position:0% +quantum theory and apply it to solids + + + align:start position:0% +quantum theory and apply it to solids +not bad for an opener okay quantum + + align:start position:0% +not bad for an opener okay quantum + + + align:start position:0% +not bad for an opener okay quantum +theory of + + align:start position:0% +theory of + + + align:start position:0% +theory of +solids was his PhD + + align:start position:0% + + + + align:start position:0% + +thesis and here's what he did you can + + align:start position:0% +thesis and here's what he did you can + + + align:start position:0% +thesis and here's what he did you can +follow not going to give you the + + align:start position:0% +follow not going to give you the + + + align:start position:0% +follow not going to give you the +derivations but it's quite simple first + + align:start position:0% +derivations but it's quite simple first + + + align:start position:0% +derivations but it's quite simple first +he recognizes that atoms in a metal are + + align:start position:0% +he recognizes that atoms in a metal are + + + align:start position:0% +he recognizes that atoms in a metal are +arranged in periodic positions there's + + align:start position:0% +arranged in periodic positions there's + + + align:start position:0% +arranged in periodic positions there's +an array it's not just thrown together + + align:start position:0% +an array it's not just thrown together + + + align:start position:0% +an array it's not just thrown together +in some jumble so + + align:start position:0% +in some jumble so + + + align:start position:0% +in some jumble so +atoms atoms in + + align:start position:0% +atoms atoms in + + + align:start position:0% +atoms atoms in +solid uh uh set in + + align:start position:0% +solid uh uh set in + + + align:start position:0% +solid uh uh set in +regular + + align:start position:0% +regular + + + align:start position:0% +regular +patterns we're going to learn these + + align:start position:0% +patterns we're going to learn these + + + align:start position:0% +patterns we're going to learn these +patterns next week arrays and such + + align:start position:0% +patterns next week arrays and such + + + align:start position:0% +patterns next week arrays and such +solids where the atoms are found in + + align:start position:0% +solids where the atoms are found in + + + align:start position:0% +solids where the atoms are found in +regular patterns are called crystals + + align:start position:0% +regular patterns are called crystals + + + align:start position:0% +regular patterns are called crystals +crystals so he took that as one + + align:start position:0% +crystals so he took that as one + + + align:start position:0% +crystals so he took that as one +Benchmark the second thing he says that + + align:start position:0% +Benchmark the second thing he says that + + + align:start position:0% +Benchmark the second thing he says that +remember druda says that the veence + + align:start position:0% +remember druda says that the veence + + + align:start position:0% +remember druda says that the veence +electrons are free to move around he + + align:start position:0% +electrons are free to move around he + + + align:start position:0% +electrons are free to move around he +says well if if these valence electrons + + align:start position:0% +says well if if these valence electrons + + + align:start position:0% +says well if if these valence electrons +are free to move around what would they + + align:start position:0% +are free to move around what would they + + + align:start position:0% +are free to move around what would they +be subjected to they would be subjected + + align:start position:0% +be subjected to they would be subjected + + + align:start position:0% +be subjected to they would be subjected +to a potential this is how we derive the + + align:start position:0% +to a potential this is how we derive the + + + align:start position:0% +to a potential this is how we derive the +energy levels in even a single hydrogen + + align:start position:0% +energy levels in even a single hydrogen + + + align:start position:0% +energy levels in even a single hydrogen +atom we've got the positive charge of + + align:start position:0% +atom we've got the positive charge of + + + align:start position:0% +atom we've got the positive charge of +the core we got the negative charge of + + align:start position:0% +the core we got the negative charge of + + + align:start position:0% +the core we got the negative charge of +the electron so now I've got an electron + + align:start position:0% +the electron so now I've got an electron + + + align:start position:0% +the electron so now I've got an electron +and it sees the net positive charge of + + align:start position:0% +and it sees the net positive charge of + + + align:start position:0% +and it sees the net positive charge of +the atomic core but it sees an array it + + align:start position:0% +the atomic core but it sees an array it + + + align:start position:0% +the atomic core but it sees an array it +sees periodic variation potential so + + align:start position:0% +sees periodic variation potential so + + + align:start position:0% +sees periodic variation potential so +that's the second thing he says so + + align:start position:0% +that's the second thing he says so + + + align:start position:0% +that's the second thing he says so +periodic periodic + + align:start position:0% +periodic periodic + + + align:start position:0% +periodic periodic +potential periodic potential acts on the + + align:start position:0% +potential periodic potential acts on the + + + align:start position:0% +potential periodic potential acts on the +veence + + align:start position:0% + + + + align:start position:0% + +electrons and then he invokes wave + + align:start position:0% + + + + align:start position:0% + +mechanics he invokes wave mechanics + + align:start position:0% +mechanics he invokes wave mechanics + + + align:start position:0% +mechanics he invokes wave mechanics +remember shreder equation was only + + align:start position:0% +remember shreder equation was only + + + align:start position:0% +remember shreder equation was only +enunciated a couple of years earlier + + align:start position:0% +enunciated a couple of years earlier + + + align:start position:0% +enunciated a couple of years earlier +1926 there's a PhD student hears about + + align:start position:0% +1926 there's a PhD student hears about + + + align:start position:0% +1926 there's a PhD student hears about +the sheringer equation as applied to a + + align:start position:0% +the sheringer equation as applied to a + + + align:start position:0% +the sheringer equation as applied to a +gous atom and he's applying it to + + align:start position:0% +gous atom and he's applying it to + + + align:start position:0% +gous atom and he's applying it to +condensed matter and so he solves the + + align:start position:0% +condensed matter and so he solves the + + + align:start position:0% +condensed matter and so he solves the +shredding equation with these + + align:start position:0% + + + + align:start position:0% + +constraints and what does he get he gets + + align:start position:0% +constraints and what does he get he gets + + + align:start position:0% +constraints and what does he get he gets +a set of solutions he gets a family of + + align:start position:0% + + + + align:start position:0% + +solutions a family of solutions and + + align:start position:0% +solutions a family of solutions and + + + align:start position:0% +solutions a family of solutions and +these give rise to a set + + align:start position:0% +these give rise to a set + + + align:start position:0% +these give rise to a set +of wavelengths of the electron that + + align:start position:0% +of wavelengths of the electron that + + + align:start position:0% +of wavelengths of the electron that +could move quickly through the crystal + + align:start position:0% +could move quickly through the crystal + + + align:start position:0% +could move quickly through the crystal +they could propagate in other words by + + align:start position:0% +they could propagate in other words by + + + align:start position:0% +they could propagate in other words by +invoking the wavelike properties of the + + align:start position:0% +invoking the wavelike properties of the + + + align:start position:0% +invoking the wavelike properties of the +electron he can rationalize how these + + align:start position:0% +electron he can rationalize how these + + + align:start position:0% +electron he can rationalize how these +veence electrons can move through + + align:start position:0% +veence electrons can move through + + + align:start position:0% +veence electrons can move through +barriers that classical physics would + + align:start position:0% +barriers that classical physics would + + + align:start position:0% +barriers that classical physics would +impose and so pretty soon outfalls + + align:start position:0% +impose and so pretty soon outfalls + + + align:start position:0% +impose and so pretty soon outfalls +electronic + + align:start position:0% +electronic + + + align:start position:0% +electronic +conductivity electronic + + align:start position:0% +conductivity electronic + + + align:start position:0% +conductivity electronic +conductivity so this is pretty good for + + align:start position:0% +conductivity so this is pretty good for + + + align:start position:0% +conductivity so this is pretty good for +a for an opening uh volley not bad for a + + align:start position:0% +a for an opening uh volley not bad for a + + + align:start position:0% +a for an opening uh volley not bad for a +PhD and he uh eventually U took on some + + align:start position:0% +PhD and he uh eventually U took on some + + + align:start position:0% +PhD and he uh eventually U took on some +faculty positions and then in the 1930s + + align:start position:0% +faculty positions and then in the 1930s + + + align:start position:0% +faculty positions and then in the 1930s +when the Nazis came to power block as + + align:start position:0% +when the Nazis came to power block as + + + align:start position:0% +when the Nazis came to power block as +did many of the scientists from Europe + + align:start position:0% +did many of the scientists from Europe + + + align:start position:0% +did many of the scientists from Europe +left and came to the United States and + + align:start position:0% +left and came to the United States and + + + align:start position:0% +left and came to the United States and +he settled at Stanford and eventually he + + align:start position:0% +he settled at Stanford and eventually he + + + align:start position:0% +he settled at Stanford and eventually he +won a Nobel prize but not for this work + + align:start position:0% +won a Nobel prize but not for this work + + + align:start position:0% +won a Nobel prize but not for this work +this this was okay but he got Nobel + + align:start position:0% +this this was okay but he got Nobel + + + align:start position:0% +this this was okay but he got Nobel +Prize in + + align:start position:0% +Prize in + + + align:start position:0% +Prize in +1952 for work he started in 1945 it had + + align:start position:0% +1952 for work he started in 1945 it had + + + align:start position:0% +1952 for work he started in 1945 it had +to do with uh magnetic moments in the + + align:start position:0% +to do with uh magnetic moments in the + + + align:start position:0% +to do with uh magnetic moments in the +nucleus so he had more than one good + + align:start position:0% +nucleus so he had more than one good + + + align:start position:0% +nucleus so he had more than one good +idea so that's the first thing that we + + align:start position:0% +idea so that's the first thing that we + + + align:start position:0% +idea so that's the first thing that we +need to take into account uh in the Band + + align:start position:0% +need to take into account uh in the Band + + + align:start position:0% +need to take into account uh in the Band +Theory the second was uh a pair of + + align:start position:0% +Theory the second was uh a pair of + + + align:start position:0% +Theory the second was uh a pair of +gentlemen Walter + + align:start position:0% +gentlemen Walter + + + align:start position:0% +gentlemen Walter +heitler Walter heitler and same man as + + align:start position:0% +heitler Walter heitler and same man as + + + align:start position:0% +heitler Walter heitler and same man as +from last lecture Fritz London this was + + align:start position:0% +from last lecture Fritz London this was + + + align:start position:0% +from last lecture Fritz London this was +before he came up with the dispersion + + align:start position:0% +before he came up with the dispersion + + + align:start position:0% +before he came up with the dispersion +idea the dispersion bonding uh was 1930 + + align:start position:0% +idea the dispersion bonding uh was 1930 + + + align:start position:0% +idea the dispersion bonding uh was 1930 +but he and heitler decided to go in + + align:start position:0% +but he and heitler decided to go in + + + align:start position:0% +but he and heitler decided to go in +1927 to Zurich and spend a year + + align:start position:0% +1927 to Zurich and spend a year + + + align:start position:0% +1927 to Zurich and spend a year +postdocking with sheringer little did + + align:start position:0% +postdocking with sheringer little did + + + align:start position:0% +postdocking with sheringer little did +they know that sheringer had negotiated + + align:start position:0% +they know that sheringer had negotiated + + + align:start position:0% +they know that sheringer had negotiated +a position at Berlin and they knew son + + align:start position:0% +a position at Berlin and they knew son + + + align:start position:0% +a position at Berlin and they knew son +they no knew no sooner arrived than + + align:start position:0% +they no knew no sooner arrived than + + + align:start position:0% +they no knew no sooner arrived than +sheringer left but anyways that's what + + align:start position:0% +sheringer left but anyways that's what + + + align:start position:0% +sheringer left but anyways that's what +brought them to Zurich and they decided + + align:start position:0% +brought them to Zurich and they decided + + + align:start position:0% +brought them to Zurich and they decided +let's take this idea of linear + + align:start position:0% +let's take this idea of linear + + + align:start position:0% +let's take this idea of linear +combination of atomic orbitals and + + align:start position:0% +combination of atomic orbitals and + + + align:start position:0% +combination of atomic orbitals and +instead of asking Rinky Dink questions + + align:start position:0% +instead of asking Rinky Dink questions + + + align:start position:0% +instead of asking Rinky Dink questions +like is lithium 2 stable is helium 2 + + align:start position:0% +like is lithium 2 stable is helium 2 + + + align:start position:0% +like is lithium 2 stable is helium 2 +stable and looking at bonding versus + + align:start position:0% +stable and looking at bonding versus + + + align:start position:0% +stable and looking at bonding versus +antibonding said let's ask if we take + + align:start position:0% +antibonding said let's ask if we take + + + align:start position:0% +antibonding said let's ask if we take +avagadro's number of wave functions and + + align:start position:0% +avagadro's number of wave functions and + + + align:start position:0% +avagadro's number of wave functions and +blend them in something like copper can + + align:start position:0% +blend them in something like copper can + + + align:start position:0% +blend them in something like copper can +we make sense of what's going on so this + + align:start position:0% +we make sense of what's going on so this + + + align:start position:0% +we make sense of what's going on so this +is what their contribution was it was + + align:start position:0% +is what their contribution was it was + + + align:start position:0% +is what their contribution was it was +linear combination of atomic orbitals + + align:start position:0% +linear combination of atomic orbitals + + + align:start position:0% +linear combination of atomic orbitals +into molecular orbitals for for + + align:start position:0% +into molecular orbitals for for + + + align:start position:0% +into molecular orbitals for for +large + + align:start position:0% +large + + + align:start position:0% +large +ensembles large + + align:start position:0% +ensembles large + + + align:start position:0% +ensembles large +ensembles and so here's what here's how + + align:start position:0% +ensembles and so here's what here's how + + + align:start position:0% +ensembles and so here's what here's how +that goes let's take a look at the + + align:start position:0% +that goes let's take a look at the + + + align:start position:0% +that goes let's take a look at the +cartoon you recall last day we looked at + + align:start position:0% +cartoon you recall last day we looked at + + + align:start position:0% +cartoon you recall last day we looked at +something like if we wanted to ask + + align:start position:0% +something like if we wanted to ask + + + align:start position:0% +something like if we wanted to ask +whether a blends with another a to make + + align:start position:0% +whether a blends with another a to make + + + align:start position:0% +whether a blends with another a to make +A2 we can start at at some level I'm + + align:start position:0% +A2 we can start at at some level I'm + + + align:start position:0% +A2 we can start at at some level I'm +going to just look at the veilance Shell + + align:start position:0% +going to just look at the veilance Shell + + + align:start position:0% +going to just look at the veilance Shell +okay so I look at the veilance uh + + align:start position:0% +okay so I look at the veilance uh + + + align:start position:0% +okay so I look at the veilance uh +orbitals this is atomic orbitals and + + align:start position:0% +orbitals this is atomic orbitals and + + + align:start position:0% +orbitals this is atomic orbitals and +when these two come close together when + + align:start position:0% +when these two come close together when + + + align:start position:0% +when these two come close together when +these two atoms become close enough that + + align:start position:0% +these two atoms become close enough that + + + align:start position:0% +these two atoms become close enough that +they're operating as one system in order + + align:start position:0% +they're operating as one system in order + + + align:start position:0% +they're operating as one system in order +not to violate the poly Exclusion + + align:start position:0% +not to violate the poly Exclusion + + + align:start position:0% +not to violate the poly Exclusion +Principle these energies have to shift a + + align:start position:0% +Principle these energies have to shift a + + + align:start position:0% +Principle these energies have to shift a +little bit otherwise we run the risk of + + align:start position:0% +little bit otherwise we run the risk of + + + align:start position:0% +little bit otherwise we run the risk of +having more than one electron with the + + align:start position:0% +having more than one electron with the + + + align:start position:0% +having more than one electron with the +same set of quantum numbers so these + + align:start position:0% +same set of quantum numbers so these + + + align:start position:0% +same set of quantum numbers so these +will rearrange themselves into what we + + align:start position:0% +will rearrange themselves into what we + + + align:start position:0% +will rearrange themselves into what we +called anti-bonding and bonding orbitals + + align:start position:0% +called anti-bonding and bonding orbitals + + + align:start position:0% +called anti-bonding and bonding orbitals +where anti-bonding are at slightly + + align:start position:0% +where anti-bonding are at slightly + + + align:start position:0% +where anti-bonding are at slightly +higher energy than the + + align:start position:0% +higher energy than the + + + align:start position:0% +higher energy than the +uh parent atomic orbital and bonding are + + align:start position:0% +uh parent atomic orbital and bonding are + + + align:start position:0% +uh parent atomic orbital and bonding are +at slightly lower energy than the parent + + align:start position:0% +at slightly lower energy than the parent + + + align:start position:0% +at slightly lower energy than the parent +orbital so this is A2 now suppose I do + + align:start position:0% +orbital so this is A2 now suppose I do + + + align:start position:0% +orbital so this is A2 now suppose I do +this one more time suppose I take a plus + + align:start position:0% +this one more time suppose I take a plus + + + align:start position:0% +this one more time suppose I take a plus +A2 and I want to make + + align:start position:0% +A2 and I want to make + + + align:start position:0% +A2 and I want to make +A3 what would happen if I took a plus A2 + + align:start position:0% +A3 what would happen if I took a plus A2 + + + align:start position:0% +A3 what would happen if I took a plus A2 +well again not to violate the poly + + align:start position:0% +well again not to violate the poly + + + align:start position:0% +well again not to violate the poly +Exclusion Principle this initial + + align:start position:0% +Exclusion Principle this initial + + + align:start position:0% +Exclusion Principle this initial +whatever this orbital is let's call it + + align:start position:0% +whatever this orbital is let's call it + + + align:start position:0% +whatever this orbital is let's call it +NS I don't know maybe it's 3s whatever + + align:start position:0% +NS I don't know maybe it's 3s whatever + + + align:start position:0% +NS I don't know maybe it's 3s whatever +it's going to have to + + align:start position:0% +it's going to have to + + + align:start position:0% +it's going to have to +allow for that number of + + align:start position:0% +allow for that number of + + + align:start position:0% +allow for that number of +states and I think you can see by + + align:start position:0% +states and I think you can see by + + + align:start position:0% +states and I think you can see by +analogy this is what heitler and London + + align:start position:0% +analogy this is what heitler and London + + + align:start position:0% +analogy this is what heitler and London +did they kept going until they got a n + + align:start position:0% +did they kept going until they got a n + + + align:start position:0% +did they kept going until they got a n +where n is large how large oh Crystal + + align:start position:0% +where n is large how large oh Crystal + + + align:start position:0% +where n is large how large oh Crystal +about the size of your thumb on the + + align:start position:0% +about the size of your thumb on the + + + align:start position:0% +about the size of your thumb on the +order of a cubic centimeter in other + + align:start position:0% +order of a cubic centimeter in other + + + align:start position:0% +order of a cubic centimeter in other +words a block of metal a block of metal + + align:start position:0% +words a block of metal a block of metal + + + align:start position:0% +words a block of metal a block of metal +so when an is large what's happens this + + align:start position:0% +so when an is large what's happens this + + + align:start position:0% +so when an is large what's happens this +thing keeps going there's a little bit + + align:start position:0% +thing keeps going there's a little bit + + + align:start position:0% +thing keeps going there's a little bit +of a broadening but + + align:start position:0% + + + + align:start position:0% + +this is what happens we have many many + + align:start position:0% +this is what happens we have many many + + + align:start position:0% +this is what happens we have many many +levels here starting at the highest + + align:start position:0% +levels here starting at the highest + + + align:start position:0% +levels here starting at the highest +antibonding down to the lowest bonding + + align:start position:0% +antibonding down to the lowest bonding + + + align:start position:0% +antibonding down to the lowest bonding +but now the space the energy difference + + align:start position:0% +but now the space the energy difference + + + align:start position:0% +but now the space the energy difference +between successive levels is getting + + align:start position:0% +between successive levels is getting + + + align:start position:0% +between successive levels is getting +vanishingly small and in fact you can + + align:start position:0% +vanishingly small and in fact you can + + + align:start position:0% +vanishingly small and in fact you can +think about it what's how many how many + + align:start position:0% +think about it what's how many how many + + + align:start position:0% +think about it what's how many how many +uh how many atoms would there be in a + + align:start position:0% +uh how many atoms would there be in a + + + align:start position:0% +uh how many atoms would there be in a +cubic centimeter of uh copper well let's + + align:start position:0% +cubic centimeter of uh copper well let's + + + align:start position:0% +cubic centimeter of uh copper well let's +think about that if I got a cubic + + align:start position:0% +think about that if I got a cubic + + + align:start position:0% +think about that if I got a cubic +centimeter of copper I can look on a + + align:start position:0% +centimeter of copper I can look on a + + + align:start position:0% +centimeter of copper I can look on a +periodic table if you look on the + + align:start position:0% +periodic table if you look on the + + + align:start position:0% +periodic table if you look on the +periodic table the molar volume they + + align:start position:0% +periodic table the molar volume they + + + align:start position:0% +periodic table the molar volume they +call it Atomic volume but the molar + + align:start position:0% +call it Atomic volume but the molar + + + align:start position:0% +call it Atomic volume but the molar +volume the molar volume of copper is uh + + align:start position:0% +volume the molar volume of copper is uh + + + align:start position:0% +volume the molar volume of copper is uh +7.11 cubic cm so there's avagadro's + + align:start position:0% +7.11 cubic cm so there's avagadro's + + + align:start position:0% +7.11 cubic cm so there's avagadro's +number in there right who's buried in + + align:start position:0% +number in there right who's buried in + + + align:start position:0% +number in there right who's buried in +Grant's Tomb Grant how many atoms in a + + align:start position:0% +Grant's Tomb Grant how many atoms in a + + + align:start position:0% +Grant's Tomb Grant how many atoms in a +molar volume one mole so this contains + + align:start position:0% +molar volume one mole so this contains + + + align:start position:0% +molar volume one mole so this contains +this contains an AAG Ro + + align:start position:0% +this contains an AAG Ro + + + align:start position:0% +this contains an AAG Ro +atoms right so divide in + + align:start position:0% +atoms right so divide in + + + align:start position:0% +atoms right so divide in +so an avagadro atoms you can divide + + align:start position:0% +so an avagadro atoms you can divide + + + align:start position:0% +so an avagadro atoms you can divide +through and pretty soon you figure out + + align:start position:0% +through and pretty soon you figure out + + + align:start position:0% +through and pretty soon you figure out +how many states there are right if I go + + align:start position:0% +how many states there are right if I go + + + align:start position:0% +how many states there are right if I go +one cubic centimeter it's roughly 10 the + + align:start position:0% +one cubic centimeter it's roughly 10 the + + + align:start position:0% +one cubic centimeter it's roughly 10 the +23 atoms per cm + + align:start position:0% +23 atoms per cm + + + align:start position:0% +23 atoms per cm +cubed so that means I'm going to have 10 + + align:start position:0% +cubed so that means I'm going to have 10 + + + align:start position:0% +cubed so that means I'm going to have 10 +to the 23 States here and what's this + + align:start position:0% +to the 23 States here and what's this + + + align:start position:0% +to the 23 States here and what's this +energy difference it's on the order of + + align:start position:0% +energy difference it's on the order of + + + align:start position:0% +energy difference it's on the order of +some tens of electron volts so suppose I + + align:start position:0% +some tens of electron volts so suppose I + + + align:start position:0% +some tens of electron volts so suppose I +put in here I'll even give you a th + + align:start position:0% +put in here I'll even give you a th + + + align:start position:0% +put in here I'll even give you a th +electron volts cuz I got I got a lot of + + align:start position:0% +electron volts cuz I got I got a lot of + + + align:start position:0% +electron volts cuz I got I got a lot of +protons in the nucleus suppose this is + + align:start position:0% +protons in the nucleus suppose this is + + + align:start position:0% +protons in the nucleus suppose this is +on the order of 10 the 3 EV but it's + + align:start position:0% +on the order of 10 the 3 EV but it's + + + align:start position:0% +on the order of 10 the 3 EV but it's +divided by 10 the + + align:start position:0% +divided by 10 the + + + align:start position:0% +divided by 10 the +23rd contributors so what's the delta in + + align:start position:0% +23rd contributors so what's the delta in + + + align:start position:0% +23rd contributors so what's the delta in +here it's about + + align:start position:0% +here it's about + + + align:start position:0% +here it's about +10-20 electron volts which is about 10 + + align:start position:0% +10-20 electron volts which is about 10 + + + align:start position:0% +10-20 electron volts which is about 10 +Theus 40 jewles I mean this is less + + align:start position:0% +Theus 40 jewles I mean this is less + + + align:start position:0% +Theus 40 jewles I mean this is less +energy in uh you know the movement of + + align:start position:0% +energy in uh you know the movement of + + + align:start position:0% +energy in uh you know the movement of +the eyeball of mosquito there's nothing + + align:start position:0% +the eyeball of mosquito there's nothing + + + align:start position:0% +the eyeball of mosquito there's nothing +here there's + + align:start position:0% +here there's + + + align:start position:0% +here there's +nothing so from a distance you know if I + + align:start position:0% +nothing so from a distance you know if I + + + align:start position:0% +nothing so from a distance you know if I +get up really close this is still alph + + align:start position:0% +get up really close this is still alph + + + align:start position:0% +get up really close this is still alph +Bal principle so the electrons come in + + align:start position:0% +Bal principle so the electrons come in + + + align:start position:0% +Bal principle so the electrons come in +two by two just as Noah's Arc from the + + align:start position:0% +two by two just as Noah's Arc from the + + + align:start position:0% +two by two just as Noah's Arc from the +bottom up to the top these are all + + align:start position:0% +bottom up to the top these are all + + + align:start position:0% +bottom up to the top these are all +distinct Quantum States but from a + + align:start position:0% +distinct Quantum States but from a + + + align:start position:0% +distinct Quantum States but from a +distance they're so close together that + + align:start position:0% +distance they're so close together that + + + align:start position:0% +distance they're so close together that +this appears to be a + + align:start position:0% +this appears to be a + + + align:start position:0% +this appears to be a +band almost a Continuum a band + + align:start position:0% + + + + align:start position:0% + +so the band is a set of very closely + + align:start position:0% +so the band is a set of very closely + + + align:start position:0% +so the band is a set of very closely +spaced orbitals and now you see how to + + align:start position:0% +spaced orbitals and now you see how to + + + align:start position:0% +spaced orbitals and now you see how to +populate and for something like copper + + align:start position:0% +populate and for something like copper + + + align:start position:0% +populate and for something like copper +we know Copper's got it's uh Copper's + + align:start position:0% +we know Copper's got it's uh Copper's + + + align:start position:0% +we know Copper's got it's uh Copper's +argon + + align:start position:0% +argon + + + align:start position:0% +argon +3d10 + + align:start position:0% +3d10 + + + align:start position:0% +3d10 +4s1 so Copper's 2 by two coming in and + + align:start position:0% +4s1 so Copper's 2 by two coming in and + + + align:start position:0% +4s1 so Copper's 2 by two coming in and +they'll fill up to the halfway point of + + align:start position:0% +they'll fill up to the halfway point of + + + align:start position:0% +they'll fill up to the halfway point of +the band because I can put two per + + align:start position:0% +the band because I can put two per + + + align:start position:0% +the band because I can put two per +orbital but I only have one per copper + + align:start position:0% +orbital but I only have one per copper + + + align:start position:0% +orbital but I only have one per copper +so if I blow this up what do I have I've + + align:start position:0% +so if I blow this up what do I have I've + + + align:start position:0% +so if I blow this up what do I have I've +got this band that's half + + align:start position:0% +got this band that's half + + + align:start position:0% +got this band that's half +filled this is the S band and it's half + + align:start position:0% +filled this is the S band and it's half + + + align:start position:0% +filled this is the S band and it's half +filled and then the next level is a + + align:start position:0% +filled and then the next level is a + + + align:start position:0% +filled and then the next level is a +vanishingly small energy difference and + + align:start position:0% +vanishingly small energy difference and + + + align:start position:0% +vanishingly small energy difference and +so if then I apply a potential and say I + + align:start position:0% +so if then I apply a potential and say I + + + align:start position:0% +so if then I apply a potential and say I +make this side of the crystal negative + + align:start position:0% +make this side of the crystal negative + + + align:start position:0% +make this side of the crystal negative +and I make this side of the crystal + + align:start position:0% +and I make this side of the crystal + + + align:start position:0% +and I make this side of the crystal +positive it takes a tiny bit of energy + + align:start position:0% +positive it takes a tiny bit of energy + + + align:start position:0% +positive it takes a tiny bit of energy +to pull an electron out of the topmost + + align:start position:0% +to pull an electron out of the topmost + + + align:start position:0% +to pull an electron out of the topmost +orbital put it up here and now it's free + + align:start position:0% +orbital put it up here and now it's free + + + align:start position:0% +orbital put it up here and now it's free +to move about the crystal so this + + align:start position:0% +to move about the crystal so this + + + align:start position:0% +to move about the crystal so this +accounts for the high degree of uh + + align:start position:0% +accounts for the high degree of uh + + + align:start position:0% +accounts for the high degree of uh +metallic uh nature of materials because + + align:start position:0% +metallic uh nature of materials because + + + align:start position:0% +metallic uh nature of materials because +the energy levels are so close together + + align:start position:0% +the energy levels are so close together + + + align:start position:0% +the energy levels are so close together +in the past we saw for uh classical + + align:start position:0% +in the past we saw for uh classical + + + align:start position:0% +in the past we saw for uh classical +gasphase atoms it took a substantial + + align:start position:0% +gasphase atoms it took a substantial + + + align:start position:0% +gasphase atoms it took a substantial +amount of energy to move something out + + align:start position:0% +amount of energy to move something out + + + align:start position:0% +amount of energy to move something out +of its ground state in this case to move + + align:start position:0% +of its ground state in this case to move + + + align:start position:0% +of its ground state in this case to move +out of ground state takes a trivial + + align:start position:0% +out of ground state takes a trivial + + + align:start position:0% +out of ground state takes a trivial +amount of energy and I think I've got + + align:start position:0% +amount of energy and I think I've got + + + align:start position:0% +amount of energy and I think I've got +some cartoons that indicate this this + + align:start position:0% +some cartoons that indicate this this + + + align:start position:0% +some cartoons that indicate this this +goes back to druda with his uh cat on + + align:start position:0% +goes back to druda with his uh cat on + + + align:start position:0% +goes back to druda with his uh cat on +some books will actually call the um + + align:start position:0% +some books will actually call the um + + + align:start position:0% +some books will actually call the um +Atomic cores cats but they're they're + + align:start position:0% +Atomic cores cats but they're they're + + + align:start position:0% +Atomic cores cats but they're they're +being sloppy with the terminology + + align:start position:0% +being sloppy with the terminology + + + align:start position:0% +being sloppy with the terminology +because it's the it's the ionic core + + align:start position:0% +because it's the it's the ionic core + + + align:start position:0% +because it's the it's the ionic core +consisting of the protons of the nucleus + + align:start position:0% +consisting of the protons of the nucleus + + + align:start position:0% +consisting of the protons of the nucleus +plus the inner shell electrons but in + + align:start position:0% +plus the inner shell electrons but in + + + align:start position:0% +plus the inner shell electrons but in +electrical engineering they'll refer to + + align:start position:0% +electrical engineering they'll refer to + + + align:start position:0% +electrical engineering they'll refer to +this as cations I and then the Sea of + + align:start position:0% +this as cations I and then the Sea of + + + align:start position:0% +this as cations I and then the Sea of +veence electrons so here's the cartoon + + align:start position:0% +veence electrons so here's the cartoon + + + align:start position:0% +veence electrons so here's the cartoon +showing what's happening as you + + align:start position:0% +showing what's happening as you + + + align:start position:0% +showing what's happening as you +progressively add larger and larger + + align:start position:0% +progressively add larger and larger + + + align:start position:0% +progressively add larger and larger +numbers and not to violate the poly + + align:start position:0% +numbers and not to violate the poly + + + align:start position:0% +numbers and not to violate the poly +Exclusion Principle you have to keep + + align:start position:0% +Exclusion Principle you have to keep + + + align:start position:0% +Exclusion Principle you have to keep +Shifting the energies and since you only + + align:start position:0% +Shifting the energies and since you only + + + align:start position:0% +Shifting the energies and since you only +have one electron here as you move out + + align:start position:0% +have one electron here as you move out + + + align:start position:0% +have one electron here as you move out +in this case sodium you'll find you're + + align:start position:0% +in this case sodium you'll find you're + + + align:start position:0% +in this case sodium you'll find you're +filling 2 by two and all of the bonding + + align:start position:0% +filling 2 by two and all of the bonding + + + align:start position:0% +filling 2 by two and all of the bonding +orbitals are filled with a tiny energy + + align:start position:0% +orbitals are filled with a tiny energy + + + align:start position:0% +orbitals are filled with a tiny energy +difference and this is out of the + + align:start position:0% +difference and this is out of the + + + align:start position:0% +difference and this is out of the +reading this is a same same idea only + + align:start position:0% +reading this is a same same idea only + + + align:start position:0% +reading this is a same same idea only +it's done in the case of of lithium and + + align:start position:0% +it's done in the case of of lithium and + + + align:start position:0% +it's done in the case of of lithium and +lastly this is the idea I was just + + align:start position:0% +lastly this is the idea I was just + + + align:start position:0% +lastly this is the idea I was just +trying to get across that here's the + + align:start position:0% +trying to get across that here's the + + + align:start position:0% +trying to get across that here's the +metal sitting at rest and now there's a + + align:start position:0% +metal sitting at rest and now there's a + + + align:start position:0% +metal sitting at rest and now there's a +electrical potential put across it which + + align:start position:0% +electrical potential put across it which + + + align:start position:0% +electrical potential put across it which +wants to move electrons and even with a + + align:start position:0% +wants to move electrons and even with a + + + align:start position:0% +wants to move electrons and even with a +modest potential that's enough to + + align:start position:0% +modest potential that's enough to + + + align:start position:0% +modest potential that's enough to +disrupt the bonding here in the + + align:start position:0% +disrupt the bonding here in the + + + align:start position:0% +disrupt the bonding here in the +uppermost levels and cause electrons to + + align:start position:0% +uppermost levels and cause electrons to + + + align:start position:0% +uppermost levels and cause electrons to +rise and then move along the uh + + align:start position:0% +rise and then move along the uh + + + align:start position:0% +rise and then move along the uh +anti-bonding orbitals quite + + align:start position:0% +anti-bonding orbitals quite + + + align:start position:0% +anti-bonding orbitals quite +freely so that gives us a sense of + + align:start position:0% +freely so that gives us a sense of + + + align:start position:0% +freely so that gives us a sense of +what's going on in the conductivity of + + align:start position:0% +what's going on in the conductivity of + + + align:start position:0% +what's going on in the conductivity of +something like copper or sodium but now + + align:start position:0% +something like copper or sodium but now + + + align:start position:0% +something like copper or sodium but now +let's think about something like + + align:start position:0% +let's think about something like + + + align:start position:0% +let's think about something like +magnesium magnesium is a metal but let's + + align:start position:0% +magnesium magnesium is a metal but let's + + + align:start position:0% +magnesium magnesium is a metal but let's +think about what's going on with + + align:start position:0% +think about what's going on with + + + align:start position:0% +think about what's going on with +magnesium magnesium has uh + + align:start position:0% +magnesium magnesium has uh + + + align:start position:0% +magnesium magnesium has uh +3s but it has 3s2 + + align:start position:0% +3s but it has 3s2 + + + align:start position:0% +3s but it has 3s2 +of magnesium magnesium is 3 S2 so if we + + align:start position:0% +of magnesium magnesium is 3 S2 so if we + + + align:start position:0% +of magnesium magnesium is 3 S2 so if we +start filling magnesium s band we're + + align:start position:0% +start filling magnesium s band we're + + + align:start position:0% +start filling magnesium s band we're +going to fill 2 by2 all the way up to + + align:start position:0% +going to fill 2 by2 all the way up to + + + align:start position:0% +going to fill 2 by2 all the way up to +the top all the way up to the Top If + + align:start position:0% +the top all the way up to the Top If + + + align:start position:0% +the top all the way up to the Top If +this is s and the P's are up + + align:start position:0% +this is s and the P's are up + + + align:start position:0% +this is s and the P's are up +here what happens when the P split into + + align:start position:0% +here what happens when the P split into + + + align:start position:0% +here what happens when the P split into +the bands that's the real issue and + + align:start position:0% +the bands that's the real issue and + + + align:start position:0% +the bands that's the real issue and +mercifully what happens in the case of + + align:start position:0% +mercifully what happens in the case of + + + align:start position:0% +mercifully what happens in the case of +magnesium is this is the S + + align:start position:0% +magnesium is this is the S + + + align:start position:0% +magnesium is this is the S +band but for magnesium the p band the + + align:start position:0% +band but for magnesium the p band the + + + align:start position:0% +band but for magnesium the p band the +bottom of the P band + + align:start position:0% +bottom of the P band + + + align:start position:0% +bottom of the P band +lies below the top of the sand so in the + + align:start position:0% +lies below the top of the sand so in the + + + align:start position:0% +lies below the top of the sand so in the +case of + + align:start position:0% +case of + + + align:start position:0% +case of +magnesium this is now the P + + align:start position:0% +magnesium this is now the P + + + align:start position:0% +magnesium this is now the P +band and the P band energy levels are + + align:start position:0% +band and the P band energy levels are + + + align:start position:0% +band and the P band energy levels are +available so that when we fill the top + + align:start position:0% +available so that when we fill the top + + + align:start position:0% +available so that when we fill the top +of the sand we can continue to move into + + align:start position:0% +of the sand we can continue to move into + + + align:start position:0% +of the sand we can continue to move into +a range of energy that allows for motion + + align:start position:0% +a range of energy that allows for motion + + + align:start position:0% +a range of energy that allows for motion +so that we're able to account for both + + align:start position:0% +so that we're able to account for both + + + align:start position:0% +so that we're able to account for both +unpaired electron atoms and paired + + align:start position:0% +unpaired electron atoms and paired + + + align:start position:0% +unpaired electron atoms and paired +electron atoms by this overlap of uh + + align:start position:0% +electron atoms by this overlap of uh + + + align:start position:0% +electron atoms by this overlap of uh +energies and I think there's a cartoon + + align:start position:0% +energies and I think there's a cartoon + + + align:start position:0% +energies and I think there's a cartoon +in your reading that indicates that + + align:start position:0% +in your reading that indicates that + + + align:start position:0% +in your reading that indicates that +uh yeah this shows what happens with the + + align:start position:0% +uh yeah this shows what happens with the + + + align:start position:0% +uh yeah this shows what happens with the +energy levels as a function of distance + + align:start position:0% +energy levels as a function of distance + + + align:start position:0% +energy levels as a function of distance +and you can see that the P band is now + + align:start position:0% +and you can see that the P band is now + + + align:start position:0% +and you can see that the P band is now +dropping below the uh top of the sban + + align:start position:0% +dropping below the uh top of the sban + + + align:start position:0% +dropping below the uh top of the sban +and so it allows for continuous filling + + align:start position:0% +and so it allows for continuous filling + + + align:start position:0% +and so it allows for continuous filling +uh into um more States and so this now + + align:start position:0% +uh into um more States and so this now + + + align:start position:0% +uh into um more States and so this now +accounts not only for such things as + + align:start position:0% +accounts not only for such things as + + + align:start position:0% +accounts not only for such things as +electrical connectivity but reflectivity + + align:start position:0% +electrical connectivity but reflectivity + + + align:start position:0% +electrical connectivity but reflectivity +metals have luster because the photons + + align:start position:0% +metals have luster because the photons + + + align:start position:0% +metals have luster because the photons +of visible light have the capacity to + + align:start position:0% +of visible light have the capacity to + + + align:start position:0% +of visible light have the capacity to +excite electrons which immediately + + align:start position:0% +excite electrons which immediately + + + align:start position:0% +excite electrons which immediately +Cascade down and reflect back so you + + align:start position:0% +Cascade down and reflect back so you + + + align:start position:0% +Cascade down and reflect back so you +know Band Theory became uh widespread in + + align:start position:0% +know Band Theory became uh widespread in + + + align:start position:0% +know Band Theory became uh widespread in +popularity in the 20s it was known only + + align:start position:0% +popularity in the 20s it was known only + + + align:start position:0% +popularity in the 20s it was known only +among a few physicists in the 30s the + + align:start position:0% +among a few physicists in the 30s the + + + align:start position:0% +among a few physicists in the 30s the +scientific Community knew it in the 40s + + align:start position:0% +scientific Community knew it in the 40s + + + align:start position:0% +scientific Community knew it in the 40s +it infected the popular culture if you + + align:start position:0% +it infected the popular culture if you + + + align:start position:0% +it infected the popular culture if you +talk to your grandparents they'll refer + + align:start position:0% +talk to your grandparents they'll refer + + + align:start position:0% +talk to your grandparents they'll refer +to the' 40s as the big band era because + + align:start position:0% +to the' 40s as the big band era because + + + align:start position:0% +to the' 40s as the big band era because +of this thing you know maybe you thought + + align:start position:0% +of this thing you know maybe you thought + + + align:start position:0% +of this thing you know maybe you thought +maybe you thought that the reason the + + align:start position:0% +maybe you thought that the reason the + + + align:start position:0% +maybe you thought that the reason the +big band era was named the big band era + + align:start position:0% +big band era was named the big band era + + + align:start position:0% +big band era was named the big band era +was due to people like uh uh Glenn + + align:start position:0% +was due to people like uh uh Glenn + + + align:start position:0% +was due to people like uh uh Glenn +Miller Benny Goodman Tommy dorsy no it + + align:start position:0% +Miller Benny Goodman Tommy dorsy no it + + + align:start position:0% +Miller Benny Goodman Tommy dorsy no it +was due to Felix block Walter heitler + + align:start position:0% +was due to Felix block Walter heitler + + + align:start position:0% +was due to Felix block Walter heitler +and Fritz London so I don't want you + + align:start position:0% +and Fritz London so I don't want you + + + align:start position:0% +and Fritz London so I don't want you +thinking about those band leaders + + align:start position:0% +thinking about those band leaders + + + align:start position:0% +thinking about those band leaders +anymore this is the band this is the big + + align:start position:0% +anymore this is the band this is the big + + + align:start position:0% +anymore this is the band this is the big +band right here all right + + align:start position:0% +band right here all right + + + align:start position:0% +band right here all right +so now let's go on to something a little + + align:start position:0% +so now let's go on to something a little + + + align:start position:0% +so now let's go on to something a little +bit more interesting one of the other + + align:start position:0% +bit more interesting one of the other + + + align:start position:0% +bit more interesting one of the other +shortcomings that was uh uh not um + + align:start position:0% +shortcomings that was uh uh not um + + + align:start position:0% +shortcomings that was uh uh not um +addressed by druda was the ability to + + align:start position:0% +addressed by druda was the ability to + + + align:start position:0% +addressed by druda was the ability to +distinguish between metals and + + align:start position:0% +distinguish between metals and + + + align:start position:0% +distinguish between metals and +insulators so let's see if this Theory + + align:start position:0% +insulators so let's see if this Theory + + + align:start position:0% +insulators so let's see if this Theory +can do that so let's go to something + + align:start position:0% +can do that so let's go to something + + + align:start position:0% +can do that so let's go to something +like diamond so if we start with diamond + + align:start position:0% +like diamond so if we start with diamond + + + align:start position:0% +like diamond so if we start with diamond +if we start here's carbon as a single + + align:start position:0% +if we start here's carbon as a single + + + align:start position:0% +if we start here's carbon as a single +gas molecule and we start off with + + align:start position:0% +gas molecule and we start off with + + + align:start position:0% +gas molecule and we start off with +2s and 2 + + align:start position:0% +2s and 2 + + + align:start position:0% +2s and 2 +p and we know that this then hybridizes + + align:start position:0% +p and we know that this then hybridizes + + + align:start position:0% +p and we know that this then hybridizes +to maximize bonding capability so this + + align:start position:0% +to maximize bonding capability so this + + + align:start position:0% +to maximize bonding capability so this +is now + + align:start position:0% +is now + + + align:start position:0% +is now +sp3 I'm going to put a two here for + + align:start position:0% +sp3 I'm going to put a two here for + + + align:start position:0% +sp3 I'm going to put a two here for +reasons that'll become apparent in a + + align:start position:0% +reasons that'll become apparent in a + + + align:start position:0% +reasons that'll become apparent in a +minute so this is now carbon in the + + align:start position:0% +minute so this is now carbon in the + + + align:start position:0% +minute so this is now carbon in the +diamond configuration as a single gas + + align:start position:0% +diamond configuration as a single gas + + + align:start position:0% +diamond configuration as a single gas +molecule I know this is sort of the + + align:start position:0% +molecule I know this is sort of the + + + align:start position:0% +molecule I know this is sort of the +sound of one hand clapping but this is + + align:start position:0% +sound of one hand clapping but this is + + + align:start position:0% +sound of one hand clapping but this is +this lone lone carbon that is waiting to + + align:start position:0% +this lone lone carbon that is waiting to + + + align:start position:0% +this lone lone carbon that is waiting to +form diamond and I'm going to skip over + + align:start position:0% +form diamond and I'm going to skip over + + + align:start position:0% +form diamond and I'm going to skip over +the di Diamond and the tri Diamond let's + + align:start position:0% +the di Diamond and the tri Diamond let's + + + align:start position:0% +the di Diamond and the tri Diamond let's +just go to diamond crystal so what will + + align:start position:0% +just go to diamond crystal so what will + + + align:start position:0% +just go to diamond crystal so what will +happen is these levels will divide and + + align:start position:0% +happen is these levels will divide and + + + align:start position:0% +happen is these levels will divide and +in accordance with poly Exclusion + + align:start position:0% +in accordance with poly Exclusion + + + align:start position:0% +in accordance with poly Exclusion +Principle we'll start up here with the + + align:start position:0% +Principle we'll start up here with the + + + align:start position:0% +Principle we'll start up here with the +the antibonding and we'll start down + + align:start position:0% +the antibonding and we'll start down + + + align:start position:0% +the antibonding and we'll start down +here with the bonding and what happens + + align:start position:0% +here with the bonding and what happens + + + align:start position:0% +here with the bonding and what happens +in the case of diamond is that when the + + align:start position:0% +in the case of diamond is that when the + + + align:start position:0% +in the case of diamond is that when the +population + + align:start position:0% +population + + + align:start position:0% +population +of + + align:start position:0% +of + + + align:start position:0% +of +antibonding + + align:start position:0% +antibonding + + + align:start position:0% +antibonding +descends there is an energy gap between + + align:start position:0% +descends there is an energy gap between + + + align:start position:0% +descends there is an energy gap between +the bottom of the anti-bonding orbitals + + align:start position:0% +the bottom of the anti-bonding orbitals + + + align:start position:0% +the bottom of the anti-bonding orbitals +and the top of the bonding orbitals so + + align:start position:0% +and the top of the bonding orbitals so + + + align:start position:0% +and the top of the bonding orbitals so +we have two bands here before we simply + + align:start position:0% +we have two bands here before we simply + + + align:start position:0% +we have two bands here before we simply +had a single band this would have given + + align:start position:0% +had a single band this would have given + + + align:start position:0% +had a single band this would have given +us an S band these these would be this + + align:start position:0% +us an S band these these would be this + + + align:start position:0% +us an S band these these would be this +would all come from s sp3 forming Sigma + + align:start position:0% +would all come from s sp3 forming Sigma + + + align:start position:0% +would all come from s sp3 forming Sigma +bonds but in this case there's a big + + align:start position:0% +bonds but in this case there's a big + + + align:start position:0% +bonds but in this case there's a big +divide here so this is the + + align:start position:0% +divide here so this is the + + + align:start position:0% +divide here so this is the +energy gap or some people call it the + + align:start position:0% +energy gap or some people call it the + + + align:start position:0% +energy gap or some people call it the +band Gap and the energy here is given a + + align:start position:0% +band Gap and the energy here is given a + + + align:start position:0% +band Gap and the energy here is given a +symbol e subg the band Gap energy and in + + align:start position:0% +symbol e subg the band Gap energy and in + + + align:start position:0% +symbol e subg the band Gap energy and in +the case of diamond the band Gap energy + + align:start position:0% +the case of diamond the band Gap energy + + + align:start position:0% +the case of diamond the band Gap energy +is 5.4 electron + + align:start position:0% +is 5.4 electron + + + align:start position:0% +is 5.4 electron +volts in Diamond + + align:start position:0% +volts in Diamond + + + align:start position:0% +volts in Diamond +so what happens now now let's fill this + + align:start position:0% +so what happens now now let's fill this + + + align:start position:0% +so what happens now now let's fill this +one two 3 4 and if we count this + + align:start position:0% +one two 3 4 and if we count this + + + align:start position:0% +one two 3 4 and if we count this +properly see we we've + + align:start position:0% +properly see we we've + + + align:start position:0% +properly see we we've +got single occupancy we fill to the top + + align:start position:0% +got single occupancy we fill to the top + + + align:start position:0% +got single occupancy we fill to the top +of the veence band this is known as + + align:start position:0% +of the veence band this is known as + + + align:start position:0% +of the veence band this is known as +veence band because these were these + + align:start position:0% +veence band because these were these + + + align:start position:0% +veence band because these were these +were bonding orbitals we fill to the top + + align:start position:0% +were bonding orbitals we fill to the top + + + align:start position:0% +were bonding orbitals we fill to the top +of the veilance band and now if we want + + align:start position:0% +of the veilance band and now if we want + + + align:start position:0% +of the veilance band and now if we want +to apply an electrical potential to + + align:start position:0% +to apply an electrical potential to + + + align:start position:0% +to apply an electrical potential to +cause these electrons to come out of the + + align:start position:0% +cause these electrons to come out of the + + + align:start position:0% +cause these electrons to come out of the +bonds and move up and down the crystal + + align:start position:0% +bonds and move up and down the crystal + + + align:start position:0% +bonds and move up and down the crystal +we've got to come up with 5.4 EV which + + align:start position:0% +we've got to come up with 5.4 EV which + + + align:start position:0% +we've got to come up with 5.4 EV which +is a substantial amount of energy and + + align:start position:0% +is a substantial amount of energy and + + + align:start position:0% +is a substantial amount of energy and +doesn't happen so as a result this is an + + align:start position:0% +doesn't happen so as a result this is an + + + align:start position:0% +doesn't happen so as a result this is an +insulator so we now have the capacity to + + align:start position:0% +insulator so we now have the capacity to + + + align:start position:0% +insulator so we now have the capacity to +distinguish between metals and + + align:start position:0% +distinguish between metals and + + + align:start position:0% +distinguish between metals and +insulators + + align:start position:0% +insulators + + + align:start position:0% +insulators +insulators + + align:start position:0% + + + + align:start position:0% + +insulators have high band gaps typically + + align:start position:0% +insulators have high band gaps typically + + + align:start position:0% +insulators have high band gaps typically +on the order of about three electron + + align:start position:0% +on the order of about three electron + + + align:start position:0% +on the order of about three electron +volts + + align:start position:0% +volts + + + align:start position:0% +volts +S + + align:start position:0% +S + + + align:start position:0% +S +Metals metals have no band Gap no band + + align:start position:0% +Metals metals have no band Gap no band + + + align:start position:0% +Metals metals have no band Gap no band +Gap continuous availability of these + + align:start position:0% +Gap continuous availability of these + + + align:start position:0% +Gap continuous availability of these +closely spaced + + align:start position:0% +closely spaced + + + align:start position:0% +closely spaced +orbitals uh and while we're in the + + align:start position:0% +orbitals uh and while we're in the + + + align:start position:0% +orbitals uh and while we're in the +neighborhood this upper this upper band + + align:start position:0% +neighborhood this upper this upper band + + + align:start position:0% +neighborhood this upper this upper band +that consists of of all of the + + align:start position:0% +that consists of of all of the + + + align:start position:0% +that consists of of all of the +anti-bonding orbitals is called the + + align:start position:0% +anti-bonding orbitals is called the + + + align:start position:0% +anti-bonding orbitals is called the +conduction + + align:start position:0% +conduction + + + align:start position:0% +conduction +band conduction band because this + + align:start position:0% +band conduction band because this + + + align:start position:0% +band conduction band because this +doesn't involve bonding so if an + + align:start position:0% +doesn't involve bonding so if an + + + align:start position:0% +doesn't involve bonding so if an +electron is in this upper band it's free + + align:start position:0% +electron is in this upper band it's free + + + align:start position:0% +electron is in this upper band it's free +to move and under the influence of + + align:start position:0% +to move and under the influence of + + + align:start position:0% +to move and under the influence of +electrical potential it will do so so we + + align:start position:0% +electrical potential it will do so so we + + + align:start position:0% +electrical potential it will do so so we +have veence band conduction band band + + align:start position:0% + + + + align:start position:0% + +Gap now let's look at one other one + + align:start position:0% +Gap now let's look at one other one + + + align:start position:0% +Gap now let's look at one other one +let's look at silicon let's look at + + align:start position:0% +let's look at silicon let's look at + + + align:start position:0% +let's look at silicon let's look at +silicon silicon is in the same family + + align:start position:0% +silicon silicon is in the same family + + + align:start position:0% +silicon silicon is in the same family +it's group four sp3 hybridized only in + + align:start position:0% +it's group four sp3 hybridized only in + + + align:start position:0% +it's group four sp3 hybridized only in +the case of silicon we're going to start + + align:start position:0% +the case of silicon we're going to start + + + align:start position:0% +the case of silicon we're going to start +with 3s atomic + + align:start position:0% +with 3s atomic + + + align:start position:0% +with 3s atomic +orbital and the 3 p Atomic orbitals + + align:start position:0% +orbital and the 3 p Atomic orbitals + + + align:start position:0% +orbital and the 3 p Atomic orbitals +which h hybridized to give us sp3 but + + align:start position:0% +which h hybridized to give us sp3 but + + + align:start position:0% +which h hybridized to give us sp3 but +now Nal + + align:start position:0% +now Nal + + + align:start position:0% +now Nal +3 and if we bring a large number of + + align:start position:0% +3 and if we bring a large number of + + + align:start position:0% +3 and if we bring a large number of +silicons together we will + + align:start position:0% +silicons together we will + + + align:start position:0% +silicons together we will +form as in the case of diamond a + + align:start position:0% +form as in the case of diamond a + + + align:start position:0% +form as in the case of diamond a +veilance band and a conduction + + align:start position:0% + + + + align:start position:0% + +band the difference here is that let's + + align:start position:0% +band the difference here is that let's + + + align:start position:0% +band the difference here is that let's +think about the strength of these + + align:start position:0% +think about the strength of these + + + align:start position:0% +think about the strength of these +bonds the bonds are down here in the + + align:start position:0% +bonds the bonds are down here in the + + + align:start position:0% +bonds the bonds are down here in the +veence band electrons in pairs these are + + align:start position:0% +veence band electrons in pairs these are + + + align:start position:0% +veence band electrons in pairs these are +Cove valent bonds all the way up to the + + align:start position:0% +Cove valent bonds all the way up to the + + + align:start position:0% +Cove valent bonds all the way up to the +top of the veence band this is n equals + + align:start position:0% +top of the veence band this is n equals + + + align:start position:0% +top of the veence band this is n equals +3 in contrast to n equals 2 so what do + + align:start position:0% +3 in contrast to n equals 2 so what do + + + align:start position:0% +3 in contrast to n equals 2 so what do +we know about the relative strength of a + + align:start position:0% +we know about the relative strength of a + + + align:start position:0% +we know about the relative strength of a +bond in n equals 3 versus n equals 2 is + + align:start position:0% +bond in n equals 3 versus n equals 2 is + + + align:start position:0% +bond in n equals 3 versus n equals 2 is +it going to be stronger or weaker expect + + align:start position:0% +it going to be stronger or weaker expect + + + align:start position:0% +it going to be stronger or weaker expect +it to be weaker it's farther from the + + align:start position:0% +it to be weaker it's farther from the + + + align:start position:0% +it to be weaker it's farther from the +nucleus and indeed this is Manifest by + + align:start position:0% +nucleus and indeed this is Manifest by + + + align:start position:0% +nucleus and indeed this is Manifest by +the fact that the separation between + + align:start position:0% +the fact that the separation between + + + align:start position:0% +the fact that the separation between +anti-bonding and bonding is not as great + + align:start position:0% +anti-bonding and bonding is not as great + + + align:start position:0% +anti-bonding and bonding is not as great +because we know that when something + + align:start position:0% +because we know that when something + + + align:start position:0% +because we know that when something +moves from atomic orbital to molecular + + align:start position:0% +moves from atomic orbital to molecular + + + align:start position:0% +moves from atomic orbital to molecular +orbital this is the change in energy + + align:start position:0% +orbital this is the change in energy + + + align:start position:0% +orbital this is the change in energy +going from the atomic orbital to the + + align:start position:0% +going from the atomic orbital to the + + + align:start position:0% +going from the atomic orbital to the +molecular orbital so if I have a + + align:start position:0% +molecular orbital so if I have a + + + align:start position:0% +molecular orbital so if I have a +stronger Bond doesn't it stand a reason + + align:start position:0% +stronger Bond doesn't it stand a reason + + + align:start position:0% +stronger Bond doesn't it stand a reason +that the energy difference between an + + align:start position:0% +that the energy difference between an + + + align:start position:0% +that the energy difference between an +atomic orbital and the molecular orbital + + align:start position:0% +atomic orbital and the molecular orbital + + + align:start position:0% +atomic orbital and the molecular orbital +will be greater for for a stronger + + align:start position:0% +will be greater for for a stronger + + + align:start position:0% +will be greater for for a stronger +bond this is weaker so therefore this + + align:start position:0% +bond this is weaker so therefore this + + + align:start position:0% +bond this is weaker so therefore this +separation isn't as great as it is in + + align:start position:0% +separation isn't as great as it is in + + + align:start position:0% +separation isn't as great as it is in +diamond and indeed the band Gap in + + align:start position:0% +diamond and indeed the band Gap in + + + align:start position:0% +diamond and indeed the band Gap in +Silicon is on the order of 1.1 electron + + align:start position:0% +Silicon is on the order of 1.1 electron + + + align:start position:0% +Silicon is on the order of 1.1 electron +volts 1.1 electron volts and 1.1 + + align:start position:0% +volts 1.1 electron volts and 1.1 + + + align:start position:0% +volts 1.1 electron volts and 1.1 +electron volts is a special is on a + + align:start position:0% +electron volts is a special is on a + + + align:start position:0% +electron volts is a special is on a +special range what else do we know + + align:start position:0% +special range what else do we know + + + align:start position:0% +special range what else do we know +that's on the order of several electron + + align:start position:0% +that's on the order of several electron + + + align:start position:0% +that's on the order of several electron +volts that's really critical here + + align:start position:0% +volts that's really critical here + + + align:start position:0% +volts that's really critical here +critical here is visible light + + align:start position:0% + + + + align:start position:0% + +visible light is on the order of 2 to + + align:start position:0% +visible light is on the order of 2 to + + + align:start position:0% +visible light is on the order of 2 to +three electron volts 2 to three electron + + align:start position:0% +three electron volts 2 to three electron + + + align:start position:0% +three electron volts 2 to three electron +volts so what happens in this case with + + align:start position:0% +volts so what happens in this case with + + + align:start position:0% +volts so what happens in this case with +the with respect to visible light if + + align:start position:0% +the with respect to visible light if + + + align:start position:0% +the with respect to visible light if +visible light shines on + + align:start position:0% +visible light shines on + + + align:start position:0% +visible light shines on +diamond it's transparent because the + + align:start position:0% +diamond it's transparent because the + + + align:start position:0% +diamond it's transparent because the +energy gap is 5.4 electron volts if + + align:start position:0% +energy gap is 5.4 electron volts if + + + align:start position:0% +energy gap is 5.4 electron volts if +visible light shines on + + align:start position:0% +visible light shines on + + + align:start position:0% +visible light shines on +Silicon it's absorbed because visible + + align:start position:0% +Silicon it's absorbed because visible + + + align:start position:0% +Silicon it's absorbed because visible +light has greater than + + align:start position:0% +light has greater than + + + align:start position:0% +light has greater than +1.1 EV and here's a this is a uh 800 mm + + align:start position:0% +1.1 EV and here's a this is a uh 800 mm + + + align:start position:0% +1.1 EV and here's a this is a uh 800 mm +silicon crystal this has been cut and + + align:start position:0% +silicon crystal this has been cut and + + + align:start position:0% +silicon crystal this has been cut and +Polished from a uh a giant single + + align:start position:0% +Polished from a uh a giant single + + + align:start position:0% +Polished from a uh a giant single +Crystal salami cut and this is down to + + align:start position:0% +Crystal salami cut and this is down to + + + align:start position:0% +Crystal salami cut and this is down to +one atom + + align:start position:0% +one atom + + + align:start position:0% +one atom +Fidelity but you can see it appears + + align:start position:0% +Fidelity but you can see it appears + + + align:start position:0% +Fidelity but you can see it appears +black because the visible light that + + align:start position:0% +black because the visible light that + + + align:start position:0% +black because the visible light that +reaches it is absorbed you say well + + align:start position:0% +reaches it is absorbed you say well + + + align:start position:0% +reaches it is absorbed you say well +what's the reflectivity from well + + align:start position:0% +what's the reflectivity from well + + + align:start position:0% +what's the reflectivity from well +there's a thin oxide filum and that's a + + align:start position:0% +there's a thin oxide filum and that's a + + + align:start position:0% +there's a thin oxide filum and that's a +topic of another lecture but the + + align:start position:0% +topic of another lecture but the + + + align:start position:0% +topic of another lecture but the +material itself is dark because the + + align:start position:0% +material itself is dark because the + + + align:start position:0% +material itself is dark because the +energy + + align:start position:0% +energy + + + align:start position:0% +energy +level here is less than anything that + + align:start position:0% +level here is less than anything that + + + align:start position:0% +level here is less than anything that +you'll find invisible + + align:start position:0% + + + + align:start position:0% + +light you know that's got me thinking if + + align:start position:0% +light you know that's got me thinking if + + + align:start position:0% +light you know that's got me thinking if +a photon comes in like this Photon of + + align:start position:0% +a photon comes in like this Photon of + + + align:start position:0% +a photon comes in like this Photon of +visible light what will happen Photon of + + align:start position:0% +visible light what will happen Photon of + + + align:start position:0% +visible light what will happen Photon of +visible light will hit an electron + + align:start position:0% +visible light will hit an electron + + + align:start position:0% +visible light will hit an electron +sitting here and excite the electron + + align:start position:0% +sitting here and excite the electron + + + align:start position:0% +sitting here and excite the electron +won't it but that electron is going to + + align:start position:0% +won't it but that electron is going to + + + align:start position:0% +won't it but that electron is going to +be the same thing that happen in Balmer + + align:start position:0% +be the same thing that happen in Balmer + + + align:start position:0% +be the same thing that happen in Balmer +in enstrom's gas tube this is a One-Shot + + align:start position:0% +in enstrom's gas tube this is a One-Shot + + + align:start position:0% +in enstrom's gas tube this is a One-Shot +deal the electron Rises but it's not + + align:start position:0% +deal the electron Rises but it's not + + + align:start position:0% +deal the electron Rises but it's not +sustained so what happens immediately + + align:start position:0% +sustained so what happens immediately + + + align:start position:0% +sustained so what happens immediately +thereafter the electron falls back down + + align:start position:0% +thereafter the electron falls back down + + + align:start position:0% +thereafter the electron falls back down +and + + align:start position:0% +and + + + align:start position:0% +and +re-emits re-emits so this is + + align:start position:0% +re-emits re-emits so this is + + + align:start position:0% +re-emits re-emits so this is +photo photo + + align:start position:0% +photo photo + + + align:start position:0% +photo photo +excitation photo + + align:start position:0% +excitation photo + + + align:start position:0% +excitation photo +excitation and if this energy if this e + + align:start position:0% +excitation and if this energy if this e + + + align:start position:0% +excitation and if this energy if this e +incident if this is greater than 1.1 EV + + align:start position:0% +incident if this is greater than 1.1 EV + + + align:start position:0% +incident if this is greater than 1.1 EV +suppose it's 1.5 EV things get more + + align:start position:0% +suppose it's 1.5 EV things get more + + + align:start position:0% +suppose it's 1.5 EV things get more +complicated and we're not going to go + + align:start position:0% +complicated and we're not going to go + + + align:start position:0% +complicated and we're not going to go +into all the quantum mechanics just + + align:start position:0% +into all the quantum mechanics just + + + align:start position:0% +into all the quantum mechanics just +suffice it to say that excess energy + + align:start position:0% +suffice it to say that excess energy + + + align:start position:0% +suffice it to say that excess energy +will go up into the Crystal and will be + + align:start position:0% +will go up into the Crystal and will be + + + align:start position:0% +will go up into the Crystal and will be +dissipated as heat I and as far as 3091 + + align:start position:0% +dissipated as heat I and as far as 3091 + + + align:start position:0% +dissipated as heat I and as far as 3091 +is concerned if the incident energy is + + align:start position:0% +is concerned if the incident energy is + + + align:start position:0% +is concerned if the incident energy is +greater than the band Gap energy expect + + align:start position:0% +greater than the band Gap energy expect + + + align:start position:0% +greater than the band Gap energy expect +excitation loss of excess energy and + + align:start position:0% +excitation loss of excess energy and + + + align:start position:0% +excitation loss of excess energy and +then this electron will fall back down + + align:start position:0% +then this electron will fall back down + + + align:start position:0% +then this electron will fall back down +and give us a an emitted Photon at + + align:start position:0% +and give us a an emitted Photon at + + + align:start position:0% +and give us a an emitted Photon at +exactly equal the band Gap energy right + + align:start position:0% +exactly equal the band Gap energy right + + + align:start position:0% +exactly equal the band Gap energy right +this would be HC over Lambda directly + + align:start position:0% +this would be HC over Lambda directly + + + align:start position:0% +this would be HC over Lambda directly +band + + align:start position:0% + + + + align:start position:0% + +Gap you + + align:start position:0% +Gap you + + + align:start position:0% +Gap you +know there's something here that's + + align:start position:0% +know there's something here that's + + + align:start position:0% +know there's something here that's +intriguing you got this electron up here + + align:start position:0% +intriguing you got this electron up here + + + align:start position:0% +intriguing you got this electron up here +you know wouldn't it be cool if you + + align:start position:0% +you know wouldn't it be cool if you + + + align:start position:0% +you know wouldn't it be cool if you +could take the backside of the silicon + + align:start position:0% +could take the backside of the silicon + + + align:start position:0% +could take the backside of the silicon +and connect it to an external circuit + + align:start position:0% +and connect it to an external circuit + + + align:start position:0% +and connect it to an external circuit +and shine light on the silicon and then + + align:start position:0% +and shine light on the silicon and then + + + align:start position:0% +and shine light on the silicon and then +cause the photons to excite electrons + + align:start position:0% +cause the photons to excite electrons + + + align:start position:0% +cause the photons to excite electrons +which could then power + + align:start position:0% +which could then power + + + align:start position:0% +which could then power +something that would be photovoltaics + + align:start position:0% +something that would be photovoltaics + + + align:start position:0% +something that would be photovoltaics +wouldn't + + align:start position:0% + + + + align:start position:0% + +it that would be how a solar cell works + + align:start position:0% +it that would be how a solar cell works + + + align:start position:0% +it that would be how a solar cell works +wouldn't + + align:start position:0% +wouldn't + + + align:start position:0% +wouldn't +it if you wanted a sensor that took + + align:start position:0% +it if you wanted a sensor that took + + + align:start position:0% +it if you wanted a sensor that took +visible light that strikes it and then + + align:start position:0% +visible light that strikes it and then + + + align:start position:0% +visible light that strikes it and then +captures that + + align:start position:0% +captures that + + + align:start position:0% +captures that +electron and then sends it to a detector + + align:start position:0% +electron and then sends it to a detector + + + align:start position:0% +electron and then sends it to a detector +and maybe if you made an array of + + align:start position:0% + + + + align:start position:0% + +these and so that light that comes at + + align:start position:0% +these and so that light that comes at + + + align:start position:0% +these and so that light that comes at +different intensities on different + + align:start position:0% +different intensities on different + + + align:start position:0% +different intensities on different +pixels sends currents at different + + align:start position:0% +pixels sends currents at different + + + align:start position:0% +pixels sends currents at different +intensities that would be interesting + + align:start position:0% +intensities that would be interesting + + + align:start position:0% +intensities that would be interesting +too wouldn't it can you see why the band + + align:start position:0% +too wouldn't it can you see why the band + + + align:start position:0% +too wouldn't it can you see why the band +Gap being 1.1 EV versus visible light is + + align:start position:0% +Gap being 1.1 EV versus visible light is + + + align:start position:0% +Gap being 1.1 EV versus visible light is +really + + align:start position:0% +really + + + align:start position:0% +really +important how about this what + + align:start position:0% +important how about this what + + + align:start position:0% +important how about this what +if what if instead of having light + + align:start position:0% +if what if instead of having light + + + align:start position:0% +if what if instead of having light +coming in what if I connected this to a + + align:start position:0% +coming in what if I connected this to a + + + align:start position:0% +coming in what if I connected this to a +power + + align:start position:0% +power + + + align:start position:0% +power +supply and I pump the electrons out of + + align:start position:0% +supply and I pump the electrons out of + + + align:start position:0% +supply and I pump the electrons out of +the veence band into the conduction band + + align:start position:0% +the veence band into the conduction band + + + align:start position:0% +the veence band into the conduction band +from which they would + + align:start position:0% +from which they would + + + align:start position:0% +from which they would +fall and then emit + + align:start position:0% +fall and then emit + + + align:start position:0% +fall and then emit +photons so I could make a light emitting + + align:start position:0% +photons so I could make a light emitting + + + align:start position:0% +photons so I could make a light emitting +device by pumping things up and having + + align:start position:0% +device by pumping things up and having + + + align:start position:0% +device by pumping things up and having +them fall down this is why this class of + + align:start position:0% +them fall down this is why this class of + + + align:start position:0% +them fall down this is why this class of +materials is dominating the modern world + + align:start position:0% +materials is dominating the modern world + + + align:start position:0% +materials is dominating the modern world +materials with a band Gap around the + + align:start position:0% +materials with a band Gap around the + + + align:start position:0% +materials with a band Gap around the +value of the energy in visible light are + + align:start position:0% +value of the energy in visible light are + + + align:start position:0% +value of the energy in visible light are +called + + align:start position:0% +called + + + align:start position:0% +called +semiconductors + + align:start position:0% +semiconductors + + + align:start position:0% +semiconductors +semiconductors for a reason you'll see + + align:start position:0% +semiconductors for a reason you'll see + + + align:start position:0% +semiconductors for a reason you'll see +shortly in terms of their conductivity + + align:start position:0% +shortly in terms of their conductivity + + + align:start position:0% +shortly in terms of their conductivity +their electrical conductivity is the + + align:start position:0% +their electrical conductivity is the + + + align:start position:0% +their electrical conductivity is the +least appealing of their properties it's + + align:start position:0% +least appealing of their properties it's + + + align:start position:0% +least appealing of their properties it's +their ability to interact with radiation + + align:start position:0% +their ability to interact with radiation + + + align:start position:0% +their ability to interact with radiation +that makes them so so + + align:start position:0% +that makes them so so + + + align:start position:0% +that makes them so so +exciting and uh actually you know we + + align:start position:0% +exciting and uh actually you know we + + + align:start position:0% +exciting and uh actually you know we +could actually do a test we could we + + align:start position:0% +could actually do a test we could we + + + align:start position:0% +could actually do a test we could we +actually measure measure what these band + + align:start position:0% +actually measure measure what these band + + + align:start position:0% +actually measure measure what these band +gaps are by tuning the value of the + + align:start position:0% +gaps are by tuning the value of the + + + align:start position:0% +gaps are by tuning the value of the +incident radiation so for example if we + + align:start position:0% +incident radiation so for example if we + + + align:start position:0% +incident radiation so for example if we +did this with longwave + + align:start position:0% +did this with longwave + + + align:start position:0% +did this with longwave +radiation keep moving moving moving + + align:start position:0% +radiation keep moving moving moving + + + align:start position:0% +radiation keep moving moving moving +until we get to a value of photon energy + + align:start position:0% +until we get to a value of photon energy + + + align:start position:0% +until we get to a value of photon energy +that causes excitation we could have a + + align:start position:0% +that causes excitation we could have a + + + align:start position:0% +that causes excitation we could have a +sensor that detects when the incident + + align:start position:0% +sensor that detects when the incident + + + align:start position:0% +sensor that detects when the incident +radiation is being absorbed and we could + + align:start position:0% +radiation is being absorbed and we could + + + align:start position:0% +radiation is being absorbed and we could +plot that energy as follows we could + + align:start position:0% +plot that energy as follows we could + + + align:start position:0% +plot that energy as follows we could +have this is say the Lambda of the + + align:start position:0% +have this is say the Lambda of the + + + align:start position:0% +have this is say the Lambda of the +incident + + align:start position:0% + + + + align:start position:0% + +energy Lambda the incident energy and + + align:start position:0% +energy Lambda the incident energy and + + + align:start position:0% +energy Lambda the incident energy and +this is the percent absorption + + align:start position:0% +this is the percent absorption + + + align:start position:0% +this is the percent absorption +this the percent absorption by the by + + align:start position:0% +this the percent absorption by the by + + + align:start position:0% +this the percent absorption by the by +the Crystal and this would go from zero + + align:start position:0% +the Crystal and this would go from zero + + + align:start position:0% +the Crystal and this would go from zero +to 100 so energy moves + + align:start position:0% +to 100 so energy moves + + + align:start position:0% +to 100 so energy moves +from right to left it goes inversely + + align:start position:0% +from right to left it goes inversely + + + align:start position:0% +from right to left it goes inversely +with Lambda so high wavelength is low + + align:start position:0% +with Lambda so high wavelength is low + + + align:start position:0% +with Lambda so high wavelength is low +energy so at low energy we expect + + align:start position:0% +energy so at low energy we expect + + + align:start position:0% +energy so at low energy we expect +materials to be transparent and at high + + align:start position:0% +materials to be transparent and at high + + + align:start position:0% +materials to be transparent and at high +energy they will absorb and it's some + + align:start position:0% +energy they will absorb and it's some + + + align:start position:0% +energy they will absorb and it's some +critical value of energy + + align:start position:0% +critical value of energy + + + align:start position:0% +critical value of energy +absorption begins and this value here is + + align:start position:0% +absorption begins and this value here is + + + align:start position:0% +absorption begins and this value here is +called the absorption Edge the + + align:start position:0% +called the absorption Edge the + + + align:start position:0% +called the absorption Edge the +absorption Edge so out here at very very + + align:start position:0% +absorption Edge so out here at very very + + + align:start position:0% +absorption Edge so out here at very very +high wavelengths or low energies the + + align:start position:0% +high wavelengths or low energies the + + + align:start position:0% +high wavelengths or low energies the +material appears + + align:start position:0% +material appears + + + align:start position:0% +material appears +transparent transparent because e + + align:start position:0% +transparent transparent because e + + + align:start position:0% +transparent transparent because e +incident is less than e of the band Gap + + align:start position:0% +incident is less than e of the band Gap + + + align:start position:0% +incident is less than e of the band Gap +and at high energies the material + + align:start position:0% +and at high energies the material + + + align:start position:0% +and at high energies the material +appears + + align:start position:0% +appears + + + align:start position:0% +appears +opaque it's absorbing because here e + + align:start position:0% +opaque it's absorbing because here e + + + align:start position:0% +opaque it's absorbing because here e +incident is greater than e of the band + + align:start position:0% +incident is greater than e of the band + + + align:start position:0% +incident is greater than e of the band +Gap and this roundedness here is due to + + align:start position:0% +Gap and this roundedness here is due to + + + align:start position:0% +Gap and this roundedness here is due to +defects it's not it's not a perfectly + + align:start position:0% +defects it's not it's not a perfectly + + + align:start position:0% +defects it's not it's not a perfectly +sharp it's not a perfectly sharp edge + + align:start position:0% +sharp it's not a perfectly sharp edge + + + align:start position:0% +sharp it's not a perfectly sharp edge +and so what I did is I said well okay + + align:start position:0% +and so what I did is I said well okay + + + align:start position:0% +and so what I did is I said well okay +let's do the calculation so I compared + + align:start position:0% +let's do the calculation so I compared + + + align:start position:0% +let's do the calculation so I compared +silicon and Diamond silicon and Diamond + + align:start position:0% +silicon and Diamond silicon and Diamond + + + align:start position:0% +silicon and Diamond silicon and Diamond +so the band gaps the band gaps in + + align:start position:0% +so the band gaps the band gaps in + + + align:start position:0% +so the band gaps the band gaps in +electron volts for silicon is 1.1 for + + align:start position:0% +electron volts for silicon is 1.1 for + + + align:start position:0% +electron volts for silicon is 1.1 for +diamond is 5.4 and then all I did is + + align:start position:0% +diamond is 5.4 and then all I did is + + + align:start position:0% +diamond is 5.4 and then all I did is +just said well band Gap energy is now + + align:start position:0% +just said well band Gap energy is now + + + align:start position:0% +just said well band Gap energy is now +converted to Photon energy so just do HC + + align:start position:0% +converted to Photon energy so just do HC + + + align:start position:0% +converted to Photon energy so just do HC +over Lambda so Lambda of the absorption + + align:start position:0% +over Lambda so Lambda of the absorption + + + align:start position:0% +over Lambda so Lambda of the absorption +Edge Lambda of the absorption Edge this + + align:start position:0% +Edge Lambda of the absorption Edge this + + + align:start position:0% +Edge Lambda of the absorption Edge this +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +uh band Gap is equal to HC over Lambda + + align:start position:0% +uh band Gap is equal to HC over Lambda + + + align:start position:0% +uh band Gap is equal to HC over Lambda +of the absorption Edge for silicon it's + + align:start position:0% +of the absorption Edge for silicon it's + + + align:start position:0% +of the absorption Edge for silicon it's +way out in the infrared it's, + + align:start position:0% +way out in the infrared it's, + + + align:start position:0% +way out in the infrared it's, +25 I'm going to use these ugly units + + align:start position:0% +25 I'm going to use these ugly units + + + align:start position:0% +25 I'm going to use these ugly units +nanometers and diamond is down at 229 + + align:start position:0% +nanometers and diamond is down at 229 + + + align:start position:0% +nanometers and diamond is down at 229 +nanometers and where's visible light + + align:start position:0% +nanometers and where's visible light + + + align:start position:0% +nanometers and where's visible light +visible light is round + + align:start position:0% +visible light is round + + + align:start position:0% +visible light is round +numbers 400 to 700 nanometers so you can + + align:start position:0% +numbers 400 to 700 nanometers so you can + + + align:start position:0% +numbers 400 to 700 nanometers so you can +see that this is out in the IR and this + + align:start position:0% +see that this is out in the IR and this + + + align:start position:0% +see that this is out in the IR and this +is down in the + + align:start position:0% +is down in the + + + align:start position:0% +is down in the +UV so we could make a plot here if this + + align:start position:0% +UV so we could make a plot here if this + + + align:start position:0% +UV so we could make a plot here if this +is 400 NM this is 700 NM so this is + + align:start position:0% +is 400 NM this is 700 NM so this is + + + align:start position:0% +is 400 NM this is 700 NM so this is +visible + + align:start position:0% +visible + + + align:start position:0% +visible +light then this would be silicon out + + align:start position:0% +light then this would be silicon out + + + align:start position:0% +light then this would be silicon out +here at 1125 + + align:start position:0% +here at 1125 + + + align:start position:0% +here at 1125 +nanom and + + align:start position:0% +nanom and + + + align:start position:0% +nanom and +diamond diamond over + + align:start position:0% +diamond diamond over + + + align:start position:0% +diamond diamond over +here at + + align:start position:0% +here at + + + align:start position:0% +here at +229 nanometers and visible light right + + align:start position:0% +229 nanometers and visible light right + + + align:start position:0% +229 nanometers and visible light right +in between and I thought well there's + + align:start position:0% +in between and I thought well there's + + + align:start position:0% +in between and I thought well there's +there's probably another chemistry + + align:start position:0% +there's probably another chemistry + + + align:start position:0% +there's probably another chemistry +lesson in here so first of all just to + + align:start position:0% +lesson in here so first of all just to + + + align:start position:0% +lesson in here so first of all just to +summarize here what we've seen we've + + align:start position:0% +summarize here what we've seen we've + + + align:start position:0% +summarize here what we've seen we've +seen here that the metal has no band Gap + + align:start position:0% +seen here that the metal has no band Gap + + + align:start position:0% +seen here that the metal has no band Gap +Gap so there's there's no gap between + + align:start position:0% +Gap so there's there's no gap between + + + align:start position:0% +Gap so there's there's no gap between +the top of the bonding and the bottom of + + align:start position:0% +the top of the bonding and the bottom of + + + align:start position:0% +the top of the bonding and the bottom of +the anti-bonding orbitals in an + + align:start position:0% +the anti-bonding orbitals in an + + + align:start position:0% +the anti-bonding orbitals in an +insulator there's a huge band Gap and in + + align:start position:0% +insulator there's a huge band Gap and in + + + align:start position:0% +insulator there's a huge band Gap and in +the semiconductor there is a moderate + + align:start position:0% +the semiconductor there is a moderate + + + align:start position:0% +the semiconductor there is a moderate +band Gap where moderate is defined + + align:start position:0% +band Gap where moderate is defined + + + align:start position:0% +band Gap where moderate is defined +literally in reference to visible + + align:start position:0% +literally in reference to visible + + + align:start position:0% +literally in reference to visible +light now this was an interesting thing + + align:start position:0% +light now this was an interesting thing + + + align:start position:0% +light now this was an interesting thing +I here's here's your uh group 14 or + + align:start position:0% +I here's here's your uh group 14 or + + + align:start position:0% +I here's here's your uh group 14 or +group four off the periodic table and + + align:start position:0% +group four off the periodic table and + + + align:start position:0% +group four off the periodic table and +these are the values of band Gap energy + + align:start position:0% +these are the values of band Gap energy + + + align:start position:0% +these are the values of band Gap energy +I've already showed you that uh diamond + + align:start position:0% +I've already showed you that uh diamond + + + align:start position:0% +I've already showed you that uh diamond +is 5.4 and so looking as 1.1 and again + + align:start position:0% +is 5.4 and so looking as 1.1 and again + + + align:start position:0% +is 5.4 and so looking as 1.1 and again +now germanium is going out to Nal 4 so + + align:start position:0% +now germanium is going out to Nal 4 so + + + align:start position:0% +now germanium is going out to Nal 4 so +that it's still sp3 hybridizes you see + + align:start position:0% +that it's still sp3 hybridizes you see + + + align:start position:0% +that it's still sp3 hybridizes you see +this is 4s2 4 P2 forms four sp3 hybrid + + align:start position:0% +this is 4s2 4 P2 forms four sp3 hybrid + + + align:start position:0% +this is 4s2 4 P2 forms four sp3 hybrid +orbitals + + align:start position:0% +orbitals + + + align:start position:0% +orbitals +0.72 tin it may surprise you tin has two + + align:start position:0% +0.72 tin it may surprise you tin has two + + + align:start position:0% +0.72 tin it may surprise you tin has two +different crystallographic forms they're + + align:start position:0% +different crystallographic forms they're + + + align:start position:0% +different crystallographic forms they're +called allotropes one of them is + + align:start position:0% +called allotropes one of them is + + + align:start position:0% +called allotropes one of them is +metallic and the other one is sp3 + + align:start position:0% +metallic and the other one is sp3 + + + align:start position:0% +metallic and the other one is sp3 +hybridized so tin actually has a semic + + align:start position:0% +hybridized so tin actually has a semic + + + align:start position:0% +hybridized so tin actually has a semic +inducting form it's a tiny tiny band Gap + + align:start position:0% +inducting form it's a tiny tiny band Gap + + + align:start position:0% +inducting form it's a tiny tiny band Gap +but it's it's + + align:start position:0% +but it's it's + + + align:start position:0% +but it's it's +nonzero and then lastly lead lead is + + align:start position:0% +nonzero and then lastly lead lead is + + + align:start position:0% +nonzero and then lastly lead lead is +it's got so many electrons the outer of + + align:start position:0% +it's got so many electrons the outer of + + + align:start position:0% +it's got so many electrons the outer of +the veence electrons are so weakly held + + align:start position:0% +the veence electrons are so weakly held + + + align:start position:0% +the veence electrons are so weakly held +that there's no propensity for coeny And + + align:start position:0% +that there's no propensity for coeny And + + + align:start position:0% +that there's no propensity for coeny And +So It exists only in metallic form but + + align:start position:0% +So It exists only in metallic form but + + + align:start position:0% +So It exists only in metallic form but +you can see the trends very nicely + + align:start position:0% +you can see the trends very nicely + + + align:start position:0% +you can see the trends very nicely +scaling with the intensity of the + + align:start position:0% +scaling with the intensity of the + + + align:start position:0% +scaling with the intensity of the +bonding uh as exemplified by the pull on + + align:start position:0% +bonding uh as exemplified by the pull on + + + align:start position:0% +bonding uh as exemplified by the pull on +the nucleus on the outer shell + + align:start position:0% +the nucleus on the outer shell + + + align:start position:0% +the nucleus on the outer shell +electrons okay well I talked about uh + + align:start position:0% +electrons okay well I talked about uh + + + align:start position:0% +electrons okay well I talked about uh +photo excitation there's another way to + + align:start position:0% +photo excitation there's another way to + + + align:start position:0% +photo excitation there's another way to +excite electrons and that's by thermal + + align:start position:0% +excite electrons and that's by thermal + + + align:start position:0% +excite electrons and that's by thermal +excitation just the energy in the + + align:start position:0% +excitation just the energy in the + + + align:start position:0% +excitation just the energy in the +environment could lead to promotion of + + align:start position:0% +environment could lead to promotion of + + + align:start position:0% +environment could lead to promotion of +the electrons from the veence band to + + align:start position:0% +the electrons from the veence band to + + + align:start position:0% +the electrons from the veence band to +the conduction band so I'd like to look + + align:start position:0% +the conduction band so I'd like to look + + + align:start position:0% +the conduction band so I'd like to look +at that process let's look at + + align:start position:0% +at that process let's look at + + + align:start position:0% +at that process let's look at +thermal + + align:start position:0% +thermal + + + align:start position:0% +thermal +excitation thermal excitation + + align:start position:0% +excitation thermal excitation + + + align:start position:0% +excitation thermal excitation +so again here's the I'm going to + + align:start position:0% +so again here's the I'm going to + + + align:start position:0% +so again here's the I'm going to +simplify this the upper anti-bonding + + align:start position:0% +simplify this the upper anti-bonding + + + align:start position:0% +simplify this the upper anti-bonding +orbitals uh represented here as the + + align:start position:0% +orbitals uh represented here as the + + + align:start position:0% +orbitals uh represented here as the +conduction band and the lower filled + + align:start position:0% +conduction band and the lower filled + + + align:start position:0% +conduction band and the lower filled +bonding orbitals are represented as the + + align:start position:0% +bonding orbitals are represented as the + + + align:start position:0% +bonding orbitals are represented as the +veence band and you know there there's + + align:start position:0% +veence band and you know there there's + + + align:start position:0% +veence band and you know there there's +fine structure in here these are + + align:start position:0% +fine structure in here these are + + + align:start position:0% +fine structure in here these are +electrons 2 by two all the way up + + align:start position:0% +electrons 2 by two all the way up + + + align:start position:0% +electrons 2 by two all the way up +through here + + align:start position:0% +through here + + + align:start position:0% +through here +right so let's suppose we have enough + + align:start position:0% +right so let's suppose we have enough + + + align:start position:0% +right so let's suppose we have enough +thermal energy so that e thermal is + + align:start position:0% +thermal energy so that e thermal is + + + align:start position:0% +thermal energy so that e thermal is +greater + + align:start position:0% +greater + + + align:start position:0% +greater +than band Gap energy if the thermal + + align:start position:0% +than band Gap energy if the thermal + + + align:start position:0% +than band Gap energy if the thermal +energy of the system were greater than + + align:start position:0% +energy of the system were greater than + + + align:start position:0% +energy of the system were greater than +the band Gap energy we would have the + + align:start position:0% +the band Gap energy we would have the + + + align:start position:0% +the band Gap energy we would have the +ability to break these bonds and promote + + align:start position:0% +ability to break these bonds and promote + + + align:start position:0% +ability to break these bonds and promote +electrons across the band + + align:start position:0% +electrons across the band + + + align:start position:0% +electrons across the band +Gap so what happens let's look at that + + align:start position:0% +Gap so what happens let's look at that + + + align:start position:0% +Gap so what happens let's look at that +process so I'm going to rip an electron + + align:start position:0% +process so I'm going to rip an electron + + + align:start position:0% +process so I'm going to rip an electron +out of an orbital here rip an electron + + align:start position:0% +out of an orbital here rip an electron + + + align:start position:0% +out of an orbital here rip an electron +out of an orbital and send it up to the + + align:start position:0% +out of an orbital and send it up to the + + + align:start position:0% +out of an orbital and send it up to the +conduction + + align:start position:0% +conduction + + + align:start position:0% +conduction +band so one electron is now moved from + + align:start position:0% +band so one electron is now moved from + + + align:start position:0% +band so one electron is now moved from +the veence band to the conduction band + + align:start position:0% +the veence band to the conduction band + + + align:start position:0% +the veence band to the conduction band +leaving behind a half-filled + + align:start position:0% +leaving behind a half-filled + + + align:start position:0% +leaving behind a half-filled +orbital a half-filled orbital so it's + + align:start position:0% +orbital a half-filled orbital so it's + + + align:start position:0% +orbital a half-filled orbital so it's +pretty clear that we now have a new + + align:start position:0% +pretty clear that we now have a new + + + align:start position:0% +pretty clear that we now have a new +carrier in the conduction band okay so + + align:start position:0% +carrier in the conduction band okay so + + + align:start position:0% +carrier in the conduction band okay so +we have a negative negative + + align:start position:0% +we have a negative negative + + + align:start position:0% +we have a negative negative +carrier in the conduction band but + + align:start position:0% +carrier in the conduction band but + + + align:start position:0% +carrier in the conduction band but +what's interesting is what's happening + + align:start position:0% +what's interesting is what's happening + + + align:start position:0% +what's interesting is what's happening +down here in the valance band this + + align:start position:0% +down here in the valance band this + + + align:start position:0% +down here in the valance band this +broken bond this single electron in a + + align:start position:0% +broken bond this single electron in a + + + align:start position:0% +broken bond this single electron in a +bonding orbital it's like a hot po + + align:start position:0% +bonding orbital it's like a hot po + + + align:start position:0% +bonding orbital it's like a hot po +potato nobody wants this thing it's + + align:start position:0% +potato nobody wants this thing it's + + + align:start position:0% +potato nobody wants this thing it's +highly unstable it's highly unstable and + + align:start position:0% +highly unstable it's highly unstable and + + + align:start position:0% +highly unstable it's highly unstable and +so what will happen is if we put this + + align:start position:0% +so what will happen is if we put this + + + align:start position:0% +so what will happen is if we put this +Crystal between two electrodes and let's + + align:start position:0% +Crystal between two electrodes and let's + + + align:start position:0% +Crystal between two electrodes and let's +say we polarize the right electrode + + align:start position:0% +say we polarize the right electrode + + + align:start position:0% +say we polarize the right electrode +negative and the left electrode positive + + align:start position:0% +negative and the left electrode positive + + + align:start position:0% +negative and the left electrode positive +it doesn't surprise you that the + + align:start position:0% +it doesn't surprise you that the + + + align:start position:0% +it doesn't surprise you that the +electron will be repelled by the + + align:start position:0% +electron will be repelled by the + + + align:start position:0% +electron will be repelled by the +negative electrode and drawn to the + + align:start position:0% +negative electrode and drawn to the + + + align:start position:0% +negative electrode and drawn to the +positive electrode it'll move from right + + align:start position:0% +positive electrode it'll move from right + + + align:start position:0% +positive electrode it'll move from right +to left this broken bond I'm I'm drawing + + align:start position:0% +to left this broken bond I'm I'm drawing + + + align:start position:0% +to left this broken bond I'm I'm drawing +it here as in energy space but you can + + align:start position:0% +it here as in energy space but you can + + + align:start position:0% +it here as in energy space but you can +imagine imagine a lattice full of of + + align:start position:0% +imagine imagine a lattice full of of + + + align:start position:0% +imagine imagine a lattice full of of +silicons this this broken bond will + + align:start position:0% +silicons this this broken bond will + + + align:start position:0% +silicons this this broken bond will +actually propagate and since the broken + + align:start position:0% +actually propagate and since the broken + + + align:start position:0% +actually propagate and since the broken +bond is a zero in a Land of minus one it + + align:start position:0% +bond is a zero in a Land of minus one it + + + align:start position:0% +bond is a zero in a Land of minus one it +has an apparent charge of plus and this + + align:start position:0% +has an apparent charge of plus and this + + + align:start position:0% +has an apparent charge of plus and this +is uh it represents essentially a a + + align:start position:0% +is uh it represents essentially a a + + + align:start position:0% +is uh it represents essentially a a +vacancy in a bonding orbital and is + + align:start position:0% +vacancy in a bonding orbital and is + + + align:start position:0% +vacancy in a bonding orbital and is +termed a hole this is termed a hole it's + + align:start position:0% +termed a hole this is termed a hole it's + + + align:start position:0% +termed a hole this is termed a hole it's +designated lowercase H and it has charge + + align:start position:0% +designated lowercase H and it has charge + + + align:start position:0% +designated lowercase H and it has charge ++ one we've got minus one in the + + align:start position:0% ++ one we've got minus one in the + + + align:start position:0% ++ one we've got minus one in the +conduction band we've got plus one in + + align:start position:0% +conduction band we've got plus one in + + + align:start position:0% +conduction band we've got plus one in +the veilance band and so under this same + + align:start position:0% +the veilance band and so under this same + + + align:start position:0% +the veilance band and so under this same +influence of electric field the hole + + align:start position:0% +influence of electric field the hole + + + align:start position:0% +influence of electric field the hole +will move from left to right so one one + + align:start position:0% +will move from left to right so one one + + + align:start position:0% +will move from left to right so one one +promotion one promotion + + align:start position:0% +promotion one promotion + + + align:start position:0% +promotion one promotion +thermally one promotion thermally + + align:start position:0% +thermally one promotion thermally + + + align:start position:0% +thermally one promotion thermally +generates two + + align:start position:0% +generates two + + + align:start position:0% +generates two +carriers two carriers we get an electron + + align:start position:0% +carriers two carriers we get an electron + + + align:start position:0% +carriers two carriers we get an electron +in the conduction band and a hole in the + + align:start position:0% +in the conduction band and a hole in the + + + align:start position:0% +in the conduction band and a hole in the +veilance + + align:start position:0% +veilance + + + align:start position:0% +veilance +band so now we have some conductivity + + align:start position:0% +band so now we have some conductivity + + + align:start position:0% +band so now we have some conductivity +that is quite different from what we're + + align:start position:0% +that is quite different from what we're + + + align:start position:0% +that is quite different from what we're +used to and in fact the numbers are + + align:start position:0% +used to and in fact the numbers are + + + align:start position:0% +used to and in fact the numbers are +equal right the number of electrons that + + align:start position:0% +equal right the number of electrons that + + + align:start position:0% +equal right the number of electrons that +we generate is equal to the number of + + align:start position:0% +we generate is equal to the number of + + + align:start position:0% +we generate is equal to the number of +holes that we + + align:start position:0% +holes that we + + + align:start position:0% +holes that we +generate but electrical engineers will + + align:start position:0% +generate but electrical engineers will + + + align:start position:0% +generate but electrical engineers will +represent this in a more compact + + align:start position:0% +represent this in a more compact + + + align:start position:0% +represent this in a more compact +notation they don't want to know the + + align:start position:0% +notation they don't want to know the + + + align:start position:0% +notation they don't want to know the +chemistry electrical engineers are + + align:start position:0% +chemistry electrical engineers are + + + align:start position:0% +chemistry electrical engineers are +historically were afraid of chemistry + + align:start position:0% +historically were afraid of chemistry + + + align:start position:0% +historically were afraid of chemistry +they just classify these things on the + + align:start position:0% +they just classify these things on the + + + align:start position:0% +they just classify these things on the +basis of their functionality electrons + + align:start position:0% +basis of their functionality electrons + + + align:start position:0% +basis of their functionality electrons +are negative carriers holes are positive + + align:start position:0% +are negative carriers holes are positive + + + align:start position:0% +are negative carriers holes are positive +carriers so in electrical engineering + + align:start position:0% +carriers so in electrical engineering + + + align:start position:0% +carriers so in electrical engineering +parament you'll see this equation n + + align:start position:0% +parament you'll see this equation n + + + align:start position:0% +parament you'll see this equation n +equals P meaning the number of negative + + align:start position:0% +equals P meaning the number of negative + + + align:start position:0% +equals P meaning the number of negative +carriers is equal to the number of + + align:start position:0% +carriers is equal to the number of + + + align:start position:0% +carriers is equal to the number of +positive carriers so this comes out of + + align:start position:0% +positive carriers so this comes out of + + + align:start position:0% +positive carriers so this comes out of +thermal excitation and so now we can say + + align:start position:0% +thermal excitation and so now we can say + + + align:start position:0% +thermal excitation and so now we can say +something intelligent about about + + align:start position:0% +something intelligent about about + + + align:start position:0% +something intelligent about about +conductivity we can say that electrical + + align:start position:0% +conductivity we can say that electrical + + + align:start position:0% +conductivity we can say that electrical +conductivity must be related to this so + + align:start position:0% +conductivity must be related to this so + + + align:start position:0% +conductivity must be related to this so +I know I was using Sigma over there for + + align:start position:0% +I know I was using Sigma over there for + + + align:start position:0% +I know I was using Sigma over there for +bonds we're running out of characters + + align:start position:0% +bonds we're running out of characters + + + align:start position:0% +bonds we're running out of characters +we've we've burned the Latin alphabet + + align:start position:0% +we've we've burned the Latin alphabet + + + align:start position:0% +we've we've burned the Latin alphabet +we've burned through the Greek alphabet + + align:start position:0% +we've burned through the Greek alphabet + + + align:start position:0% +we've burned through the Greek alphabet +but here we are so Sigma now represents + + align:start position:0% +but here we are so Sigma now represents + + + align:start position:0% +but here we are so Sigma now represents +electrical conductivity of the specimen + + align:start position:0% +electrical conductivity of the specimen + + + align:start position:0% +electrical conductivity of the specimen +and we know the electrical conductivity + + align:start position:0% +and we know the electrical conductivity + + + align:start position:0% +and we know the electrical conductivity +of the specim must be related to the + + align:start position:0% +of the specim must be related to the + + + align:start position:0% +of the specim must be related to the +number of carriers the number of + + align:start position:0% +number of carriers the number of + + + align:start position:0% +number of carriers the number of +carriers + + align:start position:0% +carriers + + + align:start position:0% +carriers +population of + + align:start position:0% + + + + align:start position:0% + +carriers all right + + align:start position:0% +carriers all right + + + align:start position:0% +carriers all right +and it must be related to the charge on + + align:start position:0% +and it must be related to the charge on + + + align:start position:0% +and it must be related to the charge on +the carriers to the charge on the + + align:start position:0% +the carriers to the charge on the + + + align:start position:0% +the carriers to the charge on the +carriers in other words if I had plus + + align:start position:0% +carriers in other words if I had plus + + + align:start position:0% +carriers in other words if I had plus +one all other things being equal plus + + align:start position:0% +one all other things being equal plus + + + align:start position:0% +one all other things being equal plus +two all other things being equal the + + align:start position:0% +two all other things being equal the + + + align:start position:0% +two all other things being equal the +plus twos will give me double the + + align:start position:0% +plus twos will give me double the + + + align:start position:0% +plus twos will give me double the +conductivity of the plus one so + + align:start position:0% +conductivity of the plus one so + + + align:start position:0% +conductivity of the plus one so +charge charge or let's say charge + + align:start position:0% +charge charge or let's say charge + + + align:start position:0% +charge charge or let's say charge +on unit + + align:start position:0% + + + + align:start position:0% + +carrier and then lastly there's a term + + align:start position:0% +carrier and then lastly there's a term + + + align:start position:0% +carrier and then lastly there's a term +called called Mobility mobility of the + + align:start position:0% +called called Mobility mobility of the + + + align:start position:0% +called called Mobility mobility of the +carrier Mobility what's the mobility the + + align:start position:0% +carrier Mobility what's the mobility the + + + align:start position:0% +carrier Mobility what's the mobility the +mobility is the ease with which the + + align:start position:0% +mobility is the ease with which the + + + align:start position:0% +mobility is the ease with which the +carrier can move through the crystal you + + align:start position:0% +carrier can move through the crystal you + + + align:start position:0% +carrier can move through the crystal you +can Define mobility as the + + align:start position:0% +can Define mobility as the + + + align:start position:0% +can Define mobility as the +velocity per unit electric field so if I + + align:start position:0% +velocity per unit electric field so if I + + + align:start position:0% +velocity per unit electric field so if I +have two carriers one is in Copper moves + + align:start position:0% +have two carriers one is in Copper moves + + + align:start position:0% +have two carriers one is in Copper moves +very quickly one is in Silicon moves + + align:start position:0% +very quickly one is in Silicon moves + + + align:start position:0% +very quickly one is in Silicon moves +very slowly I apply the same voltage + + align:start position:0% +very slowly I apply the same voltage + + + align:start position:0% +very slowly I apply the same voltage +across equally sized specimens I find + + align:start position:0% +across equally sized specimens I find + + + align:start position:0% +across equally sized specimens I find +one moves more quickly than the other + + align:start position:0% +one moves more quickly than the other + + + align:start position:0% +one moves more quickly than the other +the the concept that captures that is + + align:start position:0% +the the concept that captures that is + + + align:start position:0% +the the concept that captures that is +called Mobility so if I take the product + + align:start position:0% +called Mobility so if I take the product + + + align:start position:0% +called Mobility so if I take the product +of the population the charge and the + + align:start position:0% +of the population the charge and the + + + align:start position:0% +of the population the charge and the +mobility I end up with something that + + align:start position:0% +mobility I end up with something that + + + align:start position:0% +mobility I end up with something that +gives me conductivity and what I'm going + + align:start position:0% +gives me conductivity and what I'm going + + + align:start position:0% +gives me conductivity and what I'm going +to do is I'm going to sum this over all + + align:start position:0% +to do is I'm going to sum this over all + + + align:start position:0% +to do is I'm going to sum this over all +of my + + align:start position:0% +of my + + + align:start position:0% +of my +carriers because each carrier + + align:start position:0% +carriers because each carrier + + + align:start position:0% +carriers because each carrier +contributes a negative current going + + align:start position:0% +contributes a negative current going + + + align:start position:0% +contributes a negative current going +from right to left will contribute to a + + align:start position:0% +from right to left will contribute to a + + + align:start position:0% +from right to left will contribute to a +positive current going from left to + + align:start position:0% +positive current going from left to + + + align:start position:0% +positive current going from left to +right + + align:start position:0% + + + + align:start position:0% + +okay so we can now write this we can + + align:start position:0% +okay so we can now write this we can + + + align:start position:0% +okay so we can now write this we can +write in in the case of this uh uh + + align:start position:0% +write in in the case of this uh uh + + + align:start position:0% +write in in the case of this uh uh +Crystal here we only have two carriers + + align:start position:0% +Crystal here we only have two carriers + + + align:start position:0% +Crystal here we only have two carriers +we've got electrons and we've got holes + + align:start position:0% +we've got electrons and we've got holes + + + align:start position:0% +we've got electrons and we've got holes +so we can say it's the number of + + align:start position:0% +so we can say it's the number of + + + align:start position:0% +so we can say it's the number of +electrons times the charge on the + + align:start position:0% +electrons times the charge on the + + + align:start position:0% +electrons times the charge on the +electron absolute value is the unit + + align:start position:0% +electron absolute value is the unit + + + align:start position:0% +electron absolute value is the unit +charge times the mobility of the + + align:start position:0% +charge times the mobility of the + + + align:start position:0% +charge times the mobility of the +electron plus the number of + + align:start position:0% +electron plus the number of + + + align:start position:0% +electron plus the number of +holes times the charge on a hole which + + align:start position:0% +holes times the charge on a hole which + + + align:start position:0% +holes times the charge on a hole which +is the unit charge and the mobility of + + align:start position:0% +is the unit charge and the mobility of + + + align:start position:0% +is the unit charge and the mobility of +the hole + + align:start position:0% +the hole + + + align:start position:0% +the hole +so we also know that the number of + + align:start position:0% +so we also know that the number of + + + align:start position:0% +so we also know that the number of +electrons equals the number of holes in + + align:start position:0% +electrons equals the number of holes in + + + align:start position:0% +electrons equals the number of holes in +thermal excitation so then that allows + + align:start position:0% +thermal excitation so then that allows + + + align:start position:0% +thermal excitation so then that allows +us to write this is N Sub e it's the + + align:start position:0% +us to write this is N Sub e it's the + + + align:start position:0% +us to write this is N Sub e it's the +same times the elementary + + align:start position:0% +same times the elementary + + + align:start position:0% +same times the elementary +charge times the sum of the mobilities + + align:start position:0% +charge times the sum of the mobilities + + + align:start position:0% +charge times the sum of the mobilities +and those mobilities in many instances + + align:start position:0% +and those mobilities in many instances + + + align:start position:0% +and those mobilities in many instances +in this Crystal are roughly the same so + + align:start position:0% +in this Crystal are roughly the same so + + + align:start position:0% +in this Crystal are roughly the same so +we can get a measure of what the + + align:start position:0% +we can get a measure of what the + + + align:start position:0% +we can get a measure of what the +conductivity is from this now I'm going + + align:start position:0% +conductivity is from this now I'm going + + + align:start position:0% +conductivity is from this now I'm going +to show you an equation that uh we're + + align:start position:0% +to show you an equation that uh we're + + + align:start position:0% +to show you an equation that uh we're +not going to derive from first + + align:start position:0% +not going to derive from first + + + align:start position:0% +not going to derive from first +principles but from the more elaborate + + align:start position:0% +principles but from the more elaborate + + + align:start position:0% +principles but from the more elaborate +form of quantum mechanics allows us to + + align:start position:0% +form of quantum mechanics allows us to + + + align:start position:0% +form of quantum mechanics allows us to +estimate the number of electrons that + + align:start position:0% +estimate the number of electrons that + + + align:start position:0% +estimate the number of electrons that +have been thermally exited in a + + align:start position:0% +have been thermally exited in a + + + align:start position:0% +have been thermally exited in a +crystal and it looks like this it's got + + align:start position:0% +crystal and it looks like this it's got + + + align:start position:0% +crystal and it looks like this it's got +a a preactor times absolute temperature + + align:start position:0% +a a preactor times absolute temperature + + + align:start position:0% +a a preactor times absolute temperature +to the three + + align:start position:0% +to the three + + + align:start position:0% +to the three +Hales and an equation that has a ratio + + align:start position:0% +Hales and an equation that has a ratio + + + align:start position:0% +Hales and an equation that has a ratio +of The Binding energy and the disruptive + + align:start position:0% +of The Binding energy and the disruptive + + + align:start position:0% +of The Binding energy and the disruptive +energy + + align:start position:0% +energy + + + align:start position:0% +energy +and that's done through an exponential + + align:start position:0% +and that's done through an exponential + + + align:start position:0% +and that's done through an exponential +where we put the band Gap energy in the + + align:start position:0% +where we put the band Gap energy in the + + + align:start position:0% +where we put the band Gap energy in the +numerator and some measure of thermal + + align:start position:0% +numerator and some measure of thermal + + + align:start position:0% +numerator and some measure of thermal +energy in the denominator and the way we + + align:start position:0% +energy in the denominator and the way we + + + align:start position:0% +energy in the denominator and the way we +characterize thermal energy is the + + align:start position:0% +characterize thermal energy is the + + + align:start position:0% +characterize thermal energy is the +product of the boltzman constant and + + align:start position:0% +product of the boltzman constant and + + + align:start position:0% +product of the boltzman constant and +absolute temperature so this is a + + align:start position:0% +absolute temperature so this is a + + + align:start position:0% +absolute temperature so this is a +measure of The Binding + + align:start position:0% +measure of The Binding + + + align:start position:0% +measure of The Binding +energy all right and this is a measure + + align:start position:0% +energy all right and this is a measure + + + align:start position:0% +energy all right and this is a measure +of the disruptive energy we've seen that + + align:start position:0% +of the disruptive energy we've seen that + + + align:start position:0% +of the disruptive energy we've seen that +notion before and we're going to see it + + align:start position:0% +notion before and we're going to see it + + + align:start position:0% +notion before and we're going to see it +again where we make an exponential + + align:start position:0% +again where we make an exponential + + + align:start position:0% +again where we make an exponential +is going to be a minus here and because + + align:start position:0% +is going to be a minus here and because + + + align:start position:0% +is going to be a minus here and because +we get two carriers for excitation + + align:start position:0% +we get two carriers for excitation + + + align:start position:0% +we get two carriers for excitation +there'll be a two + + align:start position:0% +there'll be a two + + + align:start position:0% +there'll be a two +here and now we're ready to elaborate + + align:start position:0% +here and now we're ready to elaborate + + + align:start position:0% +here and now we're ready to elaborate +this KB just to be clear is the boltzman + + align:start position:0% + + + + align:start position:0% + +constant boltzman constant and the + + align:start position:0% +constant boltzman constant and the + + + align:start position:0% +constant boltzman constant and the +boltzman constant is uh + + align:start position:0% +boltzman constant is uh + + + align:start position:0% +boltzman constant is uh +1.38 * 10us 23 jewles per Kelvin it's + + align:start position:0% +1.38 * 10us 23 jewles per Kelvin it's + + + align:start position:0% +1.38 * 10us 23 jewles per Kelvin it's +the amount of energy per per degree rise + + align:start position:0% +the amount of energy per per degree rise + + + align:start position:0% +the amount of energy per per degree rise +times temperature will give us an energy + + align:start position:0% +times temperature will give us an energy + + + align:start position:0% +times temperature will give us an energy +term we know the band Gap energy and so + + align:start position:0% +term we know the band Gap energy and so + + + align:start position:0% +term we know the band Gap energy and so +by evaluating this it turns out for + + align:start position:0% +by evaluating this it turns out for + + + align:start position:0% +by evaluating this it turns out for +silicon for silicon at room temperature + + align:start position:0% +silicon for silicon at room temperature + + + align:start position:0% +silicon for silicon at room temperature +uh the value is NE for silicon at room + + align:start position:0% + + + + align:start position:0% + +temperature is equal to + + align:start position:0% +temperature is equal to + + + align:start position:0% +temperature is equal to +13 * 10 the 10th carriers per cm + + align:start position:0% +13 * 10 the 10th carriers per cm + + + align:start position:0% +13 * 10 the 10th carriers per cm +cubed 1.3 * 10 10th you'll say well gee + + align:start position:0% +cubed 1.3 * 10 10th you'll say well gee + + + align:start position:0% +cubed 1.3 * 10 10th you'll say well gee +that's that's 10 billion that's 10 + + align:start position:0% +that's that's 10 billion that's 10 + + + align:start position:0% +that's that's 10 billion that's 10 +billion well how many carriers are there + + align:start position:0% +billion well how many carriers are there + + + align:start position:0% +billion well how many carriers are there +in copper per cubic centimeter in copper + + align:start position:0% +in copper per cubic centimeter in copper + + + align:start position:0% +in copper per cubic centimeter in copper +per cubic centimeter we did the + + align:start position:0% +per cubic centimeter we did the + + + align:start position:0% +per cubic centimeter we did the +calculation for + + align:start position:0% +calculation for + + + align:start position:0% +calculation for +copper we have one carrier per copper + + align:start position:0% +copper we have one carrier per copper + + + align:start position:0% +copper we have one carrier per copper +atom and we said for copper we've got + + align:start position:0% +atom and we said for copper we've got + + + align:start position:0% +atom and we said for copper we've got +roughly avagadro's number of copper + + align:start position:0% +roughly avagadro's number of copper + + + align:start position:0% +roughly avagadro's number of copper +atoms per cubic centimeter so in Copper + + align:start position:0% +atoms per cubic centimeter so in Copper + + + align:start position:0% +atoms per cubic centimeter so in Copper +that analogous quantity is going to be + + align:start position:0% +that analogous quantity is going to be + + + align:start position:0% +that analogous quantity is going to be +on the order of 10 the + + align:start position:0% +on the order of 10 the + + + align:start position:0% +on the order of 10 the +23r per cm cubed so what's the + + align:start position:0% +23r per cm cubed so what's the + + + align:start position:0% +23r per cm cubed so what's the +difference the difference is that + + align:start position:0% +difference the difference is that + + + align:start position:0% +difference the difference is that +silicon native silicon pure undoped + + align:start position:0% +silicon native silicon pure undoped + + + align:start position:0% +silicon native silicon pure undoped +silicon has a value of a carrier + + align:start position:0% +silicon has a value of a carrier + + + align:start position:0% +silicon has a value of a carrier +concentration NE of copper to NE of + + align:start position:0% +concentration NE of copper to NE of + + + align:start position:0% +concentration NE of copper to NE of +silicon at room temperature is on the + + align:start position:0% +silicon at room temperature is on the + + + align:start position:0% +silicon at room temperature is on the +order of about 10 trillion 10 trillion + + align:start position:0% +order of about 10 trillion 10 trillion + + + align:start position:0% +order of about 10 trillion 10 trillion +and so you can see the power of Band + + align:start position:0% +and so you can see the power of Band + + + align:start position:0% +and so you can see the power of Band +Theory because it's now allowing you to + + align:start position:0% +Theory because it's now allowing you to + + + align:start position:0% +Theory because it's now allowing you to +make sense of the + + align:start position:0% +make sense of the + + + align:start position:0% +make sense of the +various values in conductivity look I + + align:start position:0% +various values in conductivity look I + + + align:start position:0% +various values in conductivity look I +showed you last day copper is up at 5.9 + + align:start position:0% +showed you last day copper is up at 5.9 + + + align:start position:0% +showed you last day copper is up at 5.9 +time 10 the 7th SE per meter so if we + + align:start position:0% +time 10 the 7th SE per meter so if we + + + align:start position:0% +time 10 the 7th SE per meter so if we +take now the conductivity of pure + + align:start position:0% +take now the conductivity of pure + + + align:start position:0% +take now the conductivity of pure +silicon in the same units we're down + + align:start position:0% +silicon in the same units we're down + + + align:start position:0% +silicon in the same units we're down +here at 10 Theus 4 and if you take the + + align:start position:0% +here at 10 Theus 4 and if you take the + + + align:start position:0% +here at 10 Theus 4 and if you take the +ratio of 10 the + 7 over 10 Theus 4 it's + + align:start position:0% +ratio of 10 the + 7 over 10 Theus 4 it's + + + align:start position:0% +ratio of 10 the + 7 over 10 Theus 4 it's +about 10 the 11th + + align:start position:0% +about 10 the 11th + + + align:start position:0% +about 10 the 11th +and this is giving us 10 the 13th and + + align:start position:0% +and this is giving us 10 the 13th and + + + align:start position:0% +and this is giving us 10 the 13th and +all I've done is look at this first term + + align:start position:0% +all I've done is look at this first term + + + align:start position:0% +all I've done is look at this first term +population of carriers we're talking + + align:start position:0% +population of carriers we're talking + + + align:start position:0% +population of carriers we're talking +about the same carrier same charge + + align:start position:0% +about the same carrier same charge + + + align:start position:0% +about the same carrier same charge +clearly there's something here that's in + + align:start position:0% +clearly there's something here that's in + + + align:start position:0% +clearly there's something here that's in +the mobility where do you think you're + + align:start position:0% +the mobility where do you think you're + + + align:start position:0% +the mobility where do you think you're +going to have much higher mobility of + + align:start position:0% +going to have much higher mobility of + + + align:start position:0% +going to have much higher mobility of +electrons in a metallically bonded + + align:start position:0% +electrons in a metallically bonded + + + align:start position:0% +electrons in a metallically bonded +structure or in a Cove valent bonded + + align:start position:0% +structure or in a Cove valent bonded + + + align:start position:0% +structure or in a Cove valent bonded +structure I think you can see that the + + align:start position:0% +structure I think you can see that the + + + align:start position:0% +structure I think you can see that the +mobility of electrons in Silicon is + + align:start position:0% +mobility of electrons in Silicon is + + + align:start position:0% +mobility of electrons in Silicon is +going to be much lower whether it's a + + align:start position:0% +going to be much lower whether it's a + + + align:start position:0% +going to be much lower whether it's a +100 times or not is a is a something to + + align:start position:0% +100 times or not is a is a something to + + + align:start position:0% +100 times or not is a is a something to +be seen but I think you can see that the + + align:start position:0% +be seen but I think you can see that the + + + align:start position:0% +be seen but I think you can see that the +Band Theory is helping us make sense of + + align:start position:0% +Band Theory is helping us make sense of + + + align:start position:0% +Band Theory is helping us make sense of +of what's going on so I think this is + + align:start position:0% +of what's going on so I think this is + + + align:start position:0% +of what's going on so I think this is +probably a good place to uh to stop I + + align:start position:0% +probably a good place to uh to stop I + + + align:start position:0% +probably a good place to uh to stop I +just want to give you one thing to + + align:start position:0% +just want to give you one thing to + + + align:start position:0% +just want to give you one thing to +ponder over over the Columbus Day + + align:start position:0% +ponder over over the Columbus Day + + + align:start position:0% +ponder over over the Columbus Day +weekend um I told you that the + + align:start position:0% +weekend um I told you that the + + + align:start position:0% +weekend um I told you that the +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +uh measure of thermal energy is the + + align:start position:0% +uh measure of thermal energy is the + + + align:start position:0% +uh measure of thermal energy is the +product of the bolman's constant times + + align:start position:0% +product of the bolman's constant times + + + align:start position:0% +product of the bolman's constant times +temperature and if you take room + + align:start position:0% +temperature and if you take room + + + align:start position:0% +temperature and if you take room +temperature and you multiply it times + + align:start position:0% +temperature and you multiply it times + + + align:start position:0% +temperature and you multiply it times +the boltzman constant this value at room + + align:start position:0% +the boltzman constant this value at room + + + align:start position:0% +the boltzman constant this value at room +temperature is about 140 + + align:start position:0% +temperature is about 140 + + + align:start position:0% +temperature is about 140 +of an electron volt yet the band Gap + + align:start position:0% +of an electron volt yet the band Gap + + + align:start position:0% +of an electron volt yet the band Gap +energy is 1.1 which + + align:start position:0% +energy is 1.1 which + + + align:start position:0% +energy is 1.1 which +is much much higher than the thermal + + align:start position:0% +is much much higher than the thermal + + + align:start position:0% +is much much higher than the thermal +energy how is it that we get any thermal + + align:start position:0% +energy how is it that we get any thermal + + + align:start position:0% +energy how is it that we get any thermal +excitation that's what I'm going to + + align:start position:0% +excitation that's what I'm going to + + + align:start position:0% +excitation that's what I'm going to +answer next day but uh before you go I + + align:start position:0% +answer next day but uh before you go I + + + align:start position:0% +answer next day but uh before you go I +wanted to go back to Seaman and show one + + align:start position:0% +wanted to go back to Seaman and show one + + + align:start position:0% +wanted to go back to Seaman and show one +of his many inventions uh I've shown you + + align:start position:0% +of his many inventions uh I've shown you + + + align:start position:0% +of his many inventions uh I've shown you +how I've shown you silicon High Purity + + align:start position:0% +how I've shown you silicon High Purity + + + align:start position:0% +how I've shown you silicon High Purity +silicon where do we get silicon from + + align:start position:0% +silicon where do we get silicon from + + + align:start position:0% +silicon where do we get silicon from +this is the Silicon age we live in the + + align:start position:0% +this is the Silicon age we live in the + + + align:start position:0% +this is the Silicon age we live in the +Silicon age so silicon starts on the + + align:start position:0% +Silicon age so silicon starts on the + + + align:start position:0% +Silicon age so silicon starts on the +beach you start with sand Quartzsite + + align:start position:0% +beach you start with sand Quartzsite + + + align:start position:0% +beach you start with sand Quartzsite +okay and we take silica and we feed it + + align:start position:0% +okay and we take silica and we feed it + + + align:start position:0% +okay and we take silica and we feed it +into this furnace which was invented by + + align:start position:0% +into this furnace which was invented by + + + align:start position:0% +into this furnace which was invented by +seens it's an electric Arc furnace it + + align:start position:0% +seens it's an electric Arc furnace it + + + align:start position:0% +seens it's an electric Arc furnace it +has three carbon electrodes and these + + align:start position:0% +has three carbon electrodes and these + + + align:start position:0% +has three carbon electrodes and these +are fed by AC power and we don't we we + + align:start position:0% +are fed by AC power and we don't we we + + + align:start position:0% +are fed by AC power and we don't we we +put the sand in here with a few other + + align:start position:0% +put the sand in here with a few other + + + align:start position:0% +put the sand in here with a few other +ingredients and the action of electric + + align:start position:0% +ingredients and the action of electric + + + align:start position:0% +ingredients and the action of electric +current passing between the electrodes + + align:start position:0% +current passing between the electrodes + + + align:start position:0% +current passing between the electrodes +actually melts the charge so you have + + align:start position:0% +actually melts the charge so you have + + + align:start position:0% +actually melts the charge so you have +this liquid honey like goo of silica and + + align:start position:0% +this liquid honey like goo of silica and + + + align:start position:0% +this liquid honey like goo of silica and +some other ingredients and then the + + align:start position:0% +some other ingredients and then the + + + align:start position:0% +some other ingredients and then the +reaction proceeds the carbon reduces the + + align:start position:0% +reaction proceeds the carbon reduces the + + + align:start position:0% +reaction proceeds the carbon reduces the +silica to Elemental silicon and + + align:start position:0% +silica to Elemental silicon and + + + align:start position:0% +silica to Elemental silicon and +generates carbon monoxide and the carbon + + align:start position:0% +generates carbon monoxide and the carbon + + + align:start position:0% +generates carbon monoxide and the carbon +comes from the electrodes themselves so + + align:start position:0% +comes from the electrodes themselves so + + + align:start position:0% +comes from the electrodes themselves so +you consume the electrodes so the + + align:start position:0% +you consume the electrodes so the + + + align:start position:0% +you consume the electrodes so the +electrodes are constantly being fed like + + align:start position:0% +electrodes are constantly being fed like + + + align:start position:0% +electrodes are constantly being fed like +giant drafting pencils into the into the + + align:start position:0% +giant drafting pencils into the into the + + + align:start position:0% +giant drafting pencils into the into the +charge while they're passing current and + + align:start position:0% +charge while they're passing current and + + + align:start position:0% +charge while they're passing current and +now we make silicon this silicon is full + + align:start position:0% +now we make silicon this silicon is full + + + align:start position:0% +now we make silicon this silicon is full +of impu ities because Sand's got iron in + + align:start position:0% +of impu ities because Sand's got iron in + + + align:start position:0% +of impu ities because Sand's got iron in +it it's got aluminum in it it's got Lord + + align:start position:0% +it it's got aluminum in it it's got Lord + + + align:start position:0% +it it's got aluminum in it it's got Lord +knows what else in it and that's not + + align:start position:0% +knows what else in it and that's not + + + align:start position:0% +knows what else in it and that's not +going to make high Purity silicon for + + align:start position:0% +going to make high Purity silicon for + + + align:start position:0% +going to make high Purity silicon for +microelectronic devices so you might say + + align:start position:0% +microelectronic devices so you might say + + + align:start position:0% +microelectronic devices so you might say +how are we going to make high Purity + + align:start position:0% +how are we going to make high Purity + + + align:start position:0% +how are we going to make high Purity +silicon we're talking about + + align:start position:0% +silicon we're talking about + + + align:start position:0% +silicon we're talking about +99.999999 times people talk about 69 79 + + align:start position:0% +99.999999 times people talk about 69 79 + + + align:start position:0% +99.999999 times people talk about 69 79 +Purity one part per million one part per + + align:start position:0% +Purity one part per million one part per + + + align:start position:0% +Purity one part per million one part per +billion how are you going to get from + + align:start position:0% +billion how are you going to get from + + + align:start position:0% +billion how are you going to get from +this glp here that's full of iron + + align:start position:0% +this glp here that's full of iron + + + align:start position:0% +this glp here that's full of iron +aluminum and also saturated with carbon + + align:start position:0% +aluminum and also saturated with carbon + + + align:start position:0% +aluminum and also saturated with carbon +what are you going to do somebody might + + align:start position:0% +what are you going to do somebody might + + + align:start position:0% +what are you going to do somebody might +say why don't we distill the Silicon + + align:start position:0% +say why don't we distill the Silicon + + + align:start position:0% +say why don't we distill the Silicon +well silicon melts at, 1418 de + + align:start position:0% +well silicon melts at, 1418 de + + + align:start position:0% +well silicon melts at, 1418 de +Centigrade it boils at temperature above + + align:start position:0% +Centigrade it boils at temperature above + + + align:start position:0% +Centigrade it boils at temperature above +2,000 Centigrade at atmospheric pressure + + align:start position:0% +2,000 Centigrade at atmospheric pressure + + + align:start position:0% +2,000 Centigrade at atmospheric pressure +what are you going to contain this stuff + + align:start position:0% +what are you going to contain this stuff + + + align:start position:0% +what are you going to contain this stuff +in how are you going to ensure Purity + + align:start position:0% +in how are you going to ensure Purity + + + align:start position:0% +in how are you going to ensure Purity +and how much energy you're going to + + align:start position:0% +and how much energy you're going to + + + align:start position:0% +and how much energy you're going to +consume that won't work so what happens + + align:start position:0% +consume that won't work so what happens + + + align:start position:0% +consume that won't work so what happens +instead is people get smart and use some + + align:start position:0% +instead is people get smart and use some + + + align:start position:0% +instead is people get smart and use some +chemistry so they take this impure + + align:start position:0% +chemistry so they take this impure + + + align:start position:0% +chemistry so they take this impure +silicon and chlorinate it with HCL see + + align:start position:0% +silicon and chlorinate it with HCL see + + + align:start position:0% +silicon and chlorinate it with HCL see +we've met silicon it's sp3 hybridized + + align:start position:0% +we've met silicon it's sp3 hybridized + + + align:start position:0% +we've met silicon it's sp3 hybridized +we've met HCL it's polar and it forms + + align:start position:0% +we've met HCL it's polar and it forms + + + align:start position:0% +we've met HCL it's polar and it forms +this molecule + + align:start position:0% +this molecule + + + align:start position:0% +this molecule +torosyan and guess what the interatomic + + align:start position:0% +torosyan and guess what the interatomic + + + align:start position:0% +torosyan and guess what the interatomic +right secondary bonding is weak in this + + align:start position:0% +right secondary bonding is weak in this + + + align:start position:0% +right secondary bonding is weak in this +material and it boils at 33 degre C + + align:start position:0% +material and it boils at 33 degre C + + + align:start position:0% +material and it boils at 33 degre C +that's below body temperature you hold + + align:start position:0% +that's below body temperature you hold + + + align:start position:0% +that's below body temperature you hold +this in your hand and the stuff will + + align:start position:0% +this in your hand and the stuff will + + + align:start position:0% +this in your hand and the stuff will +start boiling okay so what can you do + + align:start position:0% +start boiling okay so what can you do + + + align:start position:0% +start boiling okay so what can you do +well what happens to the iron what + + align:start position:0% +well what happens to the iron what + + + align:start position:0% +well what happens to the iron what +happens to the aluminum what happens to + + align:start position:0% +happens to the aluminum what happens to + + + align:start position:0% +happens to the aluminum what happens to +all the other crud it doesn't form this + + align:start position:0% +all the other crud it doesn't form this + + + align:start position:0% +all the other crud it doesn't form this +so now you can + + align:start position:0% +so now you can + + + align:start position:0% +so now you can +selectively transfer with minimal energy + + align:start position:0% +selectively transfer with minimal energy + + + align:start position:0% +selectively transfer with minimal energy +the tri chloros cylene fractionally + + align:start position:0% +the tri chloros cylene fractionally + + + align:start position:0% +the tri chloros cylene fractionally +distill it to get very very high Purity + + align:start position:0% +distill it to get very very high Purity + + + align:start position:0% +distill it to get very very high Purity +TR chloros cylene then you go back and + + align:start position:0% +TR chloros cylene then you go back and + + + align:start position:0% +TR chloros cylene then you go back and +you convert to silicon and how do you do + + align:start position:0% +you convert to silicon and how do you do + + + align:start position:0% +you convert to silicon and how do you do +that you pass it over a hot wire at high + + align:start position:0% +that you pass it over a hot wire at high + + + align:start position:0% +that you pass it over a hot wire at high +temperature this is unstable so see + + align:start position:0% +temperature this is unstable so see + + + align:start position:0% +temperature this is unstable so see +we're playing with chemistry we're + + align:start position:0% +we're playing with chemistry we're + + + align:start position:0% +we're playing with chemistry we're +playing with temperature this is the + + align:start position:0% +playing with temperature this is the + + + align:start position:0% +playing with temperature this is the +these are the tricks this is the + + align:start position:0% +these are the tricks this is the + + + align:start position:0% +these are the tricks this is the +Playbook so now we got high temperature + + align:start position:0% +Playbook so now we got high temperature + + + align:start position:0% +Playbook so now we got high temperature +got a hot wire how do we make a wire hot + + align:start position:0% +got a hot wire how do we make a wire hot + + + align:start position:0% +got a hot wire how do we make a wire hot +with a flame no we pass electri current + + align:start position:0% +with a flame no we pass electri current + + + align:start position:0% +with a flame no we pass electri current +through it and the molecules of Tri TR + + align:start position:0% +through it and the molecules of Tri TR + + + align:start position:0% +through it and the molecules of Tri TR +chloros cylene hit the hot wire in the + + align:start position:0% +chloros cylene hit the hot wire in the + + + align:start position:0% +chloros cylene hit the hot wire in the +presence of hydrogen back react to form + + align:start position:0% +presence of hydrogen back react to form + + + align:start position:0% +presence of hydrogen back react to form +HCL silicon thetr chloride and silicon + + align:start position:0% +HCL silicon thetr chloride and silicon + + + align:start position:0% +HCL silicon thetr chloride and silicon +and it's this silicon that comes out of + + align:start position:0% +and it's this silicon that comes out of + + + align:start position:0% +and it's this silicon that comes out of +that first operation that then goes for + + align:start position:0% +that first operation that then goes for + + + align:start position:0% +that first operation that then goes for +subsequent Zone melting to make the + + align:start position:0% +subsequent Zone melting to make the + + + align:start position:0% +subsequent Zone melting to make the +giant single Crystal from which we cut + + align:start position:0% +giant single Crystal from which we cut + + + align:start position:0% +giant single Crystal from which we cut +this piece right here and all of this + + align:start position:0% +this piece right here and all of this + + + align:start position:0% +this piece right here and all of this +goes back to the + + align:start position:0% +goes back to the + + + align:start position:0% +goes back to the +1800s by about 1870s Seamans was running + + align:start position:0% +1800s by about 1870s Seamans was running + + + align:start position:0% +1800s by about 1870s Seamans was running +furnaces like this there's one other + + align:start position:0% +furnaces like this there's one other + + + align:start position:0% +furnaces like this there's one other +important application for this furnace + + align:start position:0% +important application for this furnace + + + align:start position:0% +important application for this furnace +that's used to this day it's recycling + + align:start position:0% +that's used to this day it's recycling + + + align:start position:0% +that's used to this day it's recycling +steel steel is the number one recycled + + align:start position:0% +steel steel is the number one recycled + + + align:start position:0% +steel steel is the number one recycled +metal by far not the aluminum beverage + + align:start position:0% +metal by far not the aluminum beverage + + + align:start position:0% +metal by far not the aluminum beverage +can Steel in this country there's about + + align:start position:0% +can Steel in this country there's about + + + align:start position:0% +can Steel in this country there's about +12 million tons of steel consumed uh for + + align:start position:0% +12 million tons of steel consumed uh for + + + align:start position:0% +12 million tons of steel consumed uh for +automobile uh industry and about 12 + + align:start position:0% +automobile uh industry and about 12 + + + align:start position:0% +automobile uh industry and about 12 +million tons of steel go back into + + align:start position:0% +million tons of steel go back into + + + align:start position:0% +million tons of steel go back into +recirculation and this is the furnace + + align:start position:0% +recirculation and this is the furnace + + + align:start position:0% +recirculation and this is the furnace +you take scrap metal electric Arc + + align:start position:0% +you take scrap metal electric Arc + + + align:start position:0% +you take scrap metal electric Arc +furnace slag on top remelt purify then + + align:start position:0% +furnace slag on top remelt purify then + + + align:start position:0% +furnace slag on top remelt purify then +it goes back into the + + align:start position:0% +it goes back into the + + + align:start position:0% +it goes back into the +marketplace okay have a nice weekend \ No newline at end of file diff --git a/Hjvy1w4ocQU.txt b/Hjvy1w4ocQU.txt new file mode 100644 index 0000000000000000000000000000000000000000..d4b03b6fce7d1608aef709251a8fec2cac067f4c --- /dev/null +++ b/Hjvy1w4ocQU.txt @@ -0,0 +1,10022 @@ +align:start position:0% + +hello can people hear me are we good in + + align:start position:0% +hello can people hear me are we good in + + + align:start position:0% +hello can people hear me are we good in +the + + align:start position:0% +the + + + align:start position:0% +the +back are we good can can people hear me + + align:start position:0% +back are we good can can people hear me + + + align:start position:0% +back are we good can can people hear me +good good good okay so today we are + + align:start position:0% +good good good okay so today we are + + + align:start position:0% +good good good okay so today we are +going to uh move on from counting and + + align:start position:0% +going to uh move on from counting and + + + align:start position:0% +going to uh move on from counting and +start the last unit on + + align:start position:0% +start the last unit on + + + align:start position:0% +start the last unit on +probability uh probability is uh you + + align:start position:0% +probability uh probability is uh you + + + align:start position:0% +probability uh probability is uh you +know very important it's one of the most + + align:start position:0% +know very important it's one of the most + + + align:start position:0% +know very important it's one of the most +important disciplines you know not just + + align:start position:0% +important disciplines you know not just + + + align:start position:0% +important disciplines you know not just +in computer science but like in in all + + align:start position:0% +in computer science but like in in all + + + align:start position:0% +in computer science but like in in all +of the Sciences uh please don't tell + + align:start position:0% +of the Sciences uh please don't tell + + + align:start position:0% +of the Sciences uh please don't tell +your other you know science instructors + + align:start position:0% +your other you know science instructors + + + align:start position:0% +your other you know science instructors +that I said this um you know you use it + + align:start position:0% +that I said this um you know you use it + + + align:start position:0% +that I said this um you know you use it +in like we've already seen it uh in this + + align:start position:0% +in like we've already seen it uh in this + + + align:start position:0% +in like we've already seen it uh in this +class uh with the Miller Ren algorithm + + align:start position:0% +class uh with the Miller Ren algorithm + + + align:start position:0% +class uh with the Miller Ren algorithm +uh you also see it in like you know + + align:start position:0% +uh you also see it in like you know + + + align:start position:0% +uh you also see it in like you know +other randomized algorithms that you'll + + align:start position:0% +other randomized algorithms that you'll + + + align:start position:0% +other randomized algorithms that you'll +see later in 61210 1220 5220 if you take + + align:start position:0% +see later in 61210 1220 5220 if you take + + + align:start position:0% +see later in 61210 1220 5220 if you take +that uh we see it in Game Theory + + align:start position:0% +that uh we see it in Game Theory + + + align:start position:0% +that uh we see it in Game Theory +information Theory signal processing + + align:start position:0% +information Theory signal processing + + + align:start position:0% +information Theory signal processing +cryptography uh machine learning + + align:start position:0% +cryptography uh machine learning + + + align:start position:0% +cryptography uh machine learning +medicine Stu + + align:start position:0% +medicine Stu + + + align:start position:0% +medicine Stu +forensics uh you know the list goes on + + align:start position:0% +forensics uh you know the list goes on + + + align:start position:0% +forensics uh you know the list goes on +and on uh but unfortunately it's also + + align:start position:0% +and on uh but unfortunately it's also + + + align:start position:0% +and on uh but unfortunately it's also +one of the least understood + + align:start position:0% +one of the least understood + + + align:start position:0% +one of the least understood +disciplines uh so there's a a pretty + + align:start position:0% +disciplines uh so there's a a pretty + + + align:start position:0% +disciplines uh so there's a a pretty +famous quote attributed to uh Mark Twain + + align:start position:0% +famous quote attributed to uh Mark Twain + + + align:start position:0% +famous quote attributed to uh Mark Twain +Benjamin Dy you know several other + + align:start position:0% +Benjamin Dy you know several other + + + align:start position:0% +Benjamin Dy you know several other +people uh there are three kinds of lies + + align:start position:0% +people uh there are three kinds of lies + + + align:start position:0% +people uh there are three kinds of lies +right there are lies there are damned + + align:start position:0% +right there are lies there are damned + + + align:start position:0% +right there are lies there are damned +lies and + + align:start position:0% +lies and + + + align:start position:0% +lies and +statistics uh so like you know you can + + align:start position:0% +statistics uh so like you know you can + + + align:start position:0% +statistics uh so like you know you can +kind of lie with probability and + + align:start position:0% +kind of lie with probability and + + + align:start position:0% +kind of lie with probability and +statistics by you know saying things + + align:start position:0% +statistics by you know saying things + + + align:start position:0% +statistics by you know saying things +that are true that are you know also + + align:start position:0% +that are true that are you know also + + + align:start position:0% +that are true that are you know also +very + + align:start position:0% +very + + + align:start position:0% +very +misleading uh common sense is often very + + align:start position:0% +misleading uh common sense is often very + + + align:start position:0% +misleading uh common sense is often very +demonstrably you know completely + + align:start position:0% +demonstrably you know completely + + + align:start position:0% +demonstrably you know completely +unreliable uh which you know we'll see + + align:start position:0% +unreliable uh which you know we'll see + + + align:start position:0% +unreliable uh which you know we'll see +in a in a moment uh there are many + + align:start position:0% +in a in a moment uh there are many + + + align:start position:0% +in a in a moment uh there are many +graduate students like even in our + + align:start position:0% +graduate students like even in our + + + align:start position:0% +graduate students like even in our +department uh again don't tell people + + align:start position:0% +department uh again don't tell people + + + align:start position:0% +department uh again don't tell people +they said this uh you know that they can + + align:start position:0% +they said this uh you know that they can + + + align:start position:0% +they said this uh you know that they can +they can do all sorts of exciting maths + + align:start position:0% +they can do all sorts of exciting maths + + + align:start position:0% +they can do all sorts of exciting maths +but you know you give them a basic + + align:start position:0% +but you know you give them a basic + + + align:start position:0% +but you know you give them a basic +probability question and you know they + + align:start position:0% +probability question and you know they + + + align:start position:0% +probability question and you know they +don't know where to + + align:start position:0% +don't know where to + + + align:start position:0% +don't know where to +start uh there are many garbage papers + + align:start position:0% +start uh there are many garbage papers + + + align:start position:0% +start uh there are many garbage papers +that are you know based on faulty + + align:start position:0% +that are you know based on faulty + + + align:start position:0% +that are you know based on faulty +understanding of probability uh even + + align:start position:0% +understanding of probability uh even + + + align:start position:0% +understanding of probability uh even +some of our colleagues um have some uh + + align:start position:0% +some of our colleagues um have some uh + + + align:start position:0% +some of our colleagues um have some uh +let's say issues + + align:start position:0% +let's say issues + + + align:start position:0% +let's say issues +um today we are going to look at uh an + + align:start position:0% +um today we are going to look at uh an + + + align:start position:0% +um today we are going to look at uh an +example um who who is sort of the Monty + + align:start position:0% +example um who who is sort of the Monty + + + align:start position:0% +example um who who is sort of the Monty +Hall + + align:start position:0% +Hall + + + align:start position:0% +Hall +problem oh nice decent number of people + + align:start position:0% +problem oh nice decent number of people + + + align:start position:0% +problem oh nice decent number of people +okay um so yeah well we'll basically try + + align:start position:0% +okay um so yeah well we'll basically try + + + align:start position:0% +okay um so yeah well we'll basically try +and use the Monty Hall problem to + + align:start position:0% +and use the Monty Hall problem to + + + align:start position:0% +and use the Monty Hall problem to +illustrate that you know it's it's + + align:start position:0% +illustrate that you know it's it's + + + align:start position:0% +illustrate that you know it's it's +really best to just kind of throw away + + align:start position:0% +really best to just kind of throw away + + + align:start position:0% +really best to just kind of throw away +your intuition and just fall back on + + align:start position:0% +your intuition and just fall back on + + + align:start position:0% +your intuition and just fall back on +rigorous step-by-step analyses okay + + align:start position:0% +rigorous step-by-step analyses okay + + + align:start position:0% +rigorous step-by-step analyses okay +so uh the the Monty Hall problem uh it + + align:start position:0% +so uh the the Monty Hall problem uh it + + + align:start position:0% +so uh the the Monty Hall problem uh it +kind of became famous in 1990 when uh + + align:start position:0% +kind of became famous in 1990 when uh + + + align:start position:0% +kind of became famous in 1990 when uh +this this magazine columnist named uh + + align:start position:0% +this this magazine columnist named uh + + + align:start position:0% +this this magazine columnist named uh +Marilyn vos Sant uh received a letter + + align:start position:0% +Marilyn vos Sant uh received a letter + + + align:start position:0% +Marilyn vos Sant uh received a letter +from a Craig + + align:start position:0% +from a Craig + + + align:start position:0% +from a Craig +Whitaker uh which read as follows + + align:start position:0% +Whitaker uh which read as follows + + + align:start position:0% +Whitaker uh which read as follows +suppose you're on a game show and you're + + align:start position:0% +suppose you're on a game show and you're + + + align:start position:0% +suppose you're on a game show and you're +given the choice of three doors behind + + align:start position:0% +given the choice of three doors behind + + + align:start position:0% +given the choice of three doors behind +one door is a car and behind the others + + align:start position:0% +one door is a car and behind the others + + + align:start position:0% +one door is a car and behind the others +goats you pick a door say number one and + + align:start position:0% +goats you pick a door say number one and + + + align:start position:0% +goats you pick a door say number one and +the host who knows what's behind the + + align:start position:0% +the host who knows what's behind the + + + align:start position:0% +the host who knows what's behind the +doors opens a different door say number + + align:start position:0% +doors opens a different door say number + + + align:start position:0% +doors opens a different door say number +three which has a goat he says to do you + + align:start position:0% +three which has a goat he says to do you + + + align:start position:0% +three which has a goat he says to do you +want to pick door number two now the + + align:start position:0% +want to pick door number two now the + + + align:start position:0% +want to pick door number two now the +question is is it to your advantage to + + align:start position:0% +question is is it to your advantage to + + + align:start position:0% +question is is it to your advantage to +switch okay and uh who thinks who thinks + + align:start position:0% +switch okay and uh who thinks who thinks + + + align:start position:0% +switch okay and uh who thinks who thinks +yes it is advantageous to + + align:start position:0% +yes it is advantageous to + + + align:start position:0% +yes it is advantageous to +switch who thinks no who thinks you're + + align:start position:0% +switch who thinks no who thinks you're + + + align:start position:0% +switch who thinks no who thinks you're +better off sticking with your original + + align:start position:0% +better off sticking with your original + + + align:start position:0% +better off sticking with your original +choice who thinks it doesn't + + align:start position:0% +choice who thinks it doesn't + + + align:start position:0% +choice who thinks it doesn't +matter okay so it looks like most people + + align:start position:0% +matter okay so it looks like most people + + + align:start position:0% +matter okay so it looks like most people +think that it's advantageous to switch + + align:start position:0% +think that it's advantageous to switch + + + align:start position:0% +think that it's advantageous to switch +uh we've had a few extensions uh I'm + + align:start position:0% +uh we've had a few extensions uh I'm + + + align:start position:0% +uh we've had a few extensions uh I'm +going to I'm going to count those as it + + align:start position:0% +going to I'm going to count those as it + + + align:start position:0% +going to I'm going to count those as it +doesn't + + align:start position:0% +doesn't + + + align:start position:0% +doesn't +matter uh so Marilyn replied that it's + + align:start position:0% +matter uh so Marilyn replied that it's + + + align:start position:0% +matter uh so Marilyn replied that it's +indeed advantageous to switch uh if the + + align:start position:0% +indeed advantageous to switch uh if the + + + align:start position:0% +indeed advantageous to switch uh if the +car is behind the originally picked door + + align:start position:0% +car is behind the originally picked door + + + align:start position:0% +car is behind the originally picked door +then you lose by switching but if it's + + align:start position:0% +then you lose by switching but if it's + + + align:start position:0% +then you lose by switching but if it's +not which is twice as likely then you + + align:start position:0% +not which is twice as likely then you + + + align:start position:0% +not which is twice as likely then you +win by + + align:start position:0% +win by + + + align:start position:0% +win by +switching uh and you know of course she + + align:start position:0% +switching uh and you know of course she + + + align:start position:0% +switching uh and you know of course she +soon received a torrent of hate mail uh + + align:start position:0% +soon received a torrent of hate mail uh + + + align:start position:0% +soon received a torrent of hate mail uh +including from professional + + align:start position:0% +including from professional + + + align:start position:0% +including from professional +mathematicians + + align:start position:0% +mathematicians + + + align:start position:0% +mathematicians +adamantly asserting that she was wrong + + align:start position:0% +adamantly asserting that she was wrong + + + align:start position:0% +adamantly asserting that she was wrong +okay uh so the the hypo that was + + align:start position:0% +okay uh so the the hypo that was + + + align:start position:0% +okay uh so the the hypo that was +described in this letter became known as + + align:start position:0% +described in this letter became known as + + + align:start position:0% +described in this letter became known as +the Monty Hall problem uh you know after + + align:start position:0% +the Monty Hall problem uh you know after + + + align:start position:0% +the Monty Hall problem uh you know after +the the host Monty Hall of the game show + + align:start position:0% +the the host Monty Hall of the game show + + + align:start position:0% +the the host Monty Hall of the game show +which you know had games like + + align:start position:0% +which you know had games like + + + align:start position:0% +which you know had games like +this uh where where you know contestants + + align:start position:0% +this uh where where you know contestants + + + align:start position:0% +this uh where where you know contestants +faced very similar + + align:start position:0% +faced very similar + + + align:start position:0% +faced very similar +situations uh so today we're going to + + align:start position:0% +situations uh so today we're going to + + + align:start position:0% +situations uh so today we're going to +analyze it but first can I get uh a + + align:start position:0% +analyze it but first can I get uh a + + + align:start position:0% +analyze it but first can I get uh a +handful of volunteers to come play Let's + + align:start position:0% +handful of volunteers to come play Let's + + + align:start position:0% +handful of volunteers to come play Let's +Make a + + align:start position:0% +Make a + + + align:start position:0% +Make a +Deal okay so empirically at least it + + align:start position:0% +Deal okay so empirically at least it + + + align:start position:0% +Deal okay so empirically at least it +looks like it's better to switch right + + align:start position:0% +looks like it's better to switch right + + + align:start position:0% +looks like it's better to switch right +like you know most people uh switched + + align:start position:0% +like you know most people uh switched + + + align:start position:0% +like you know most people uh switched +and you know most people won the prize + + align:start position:0% +and you know most people won the prize + + + align:start position:0% +and you know most people won the prize +when they did that uh so you know even + + align:start position:0% +when they did that uh so you know even + + + align:start position:0% +when they did that uh so you know even +though there's only one door with the + + align:start position:0% +though there's only one door with the + + + align:start position:0% +though there's only one door with the +prize it it seems to be pretty promising + + align:start position:0% +prize it it seems to be pretty promising + + + align:start position:0% +prize it it seems to be pretty promising +right so let's see if we can analyze + + align:start position:0% +right so let's see if we can analyze + + + align:start position:0% +right so let's see if we can analyze +this mathematically okay so we're going + + align:start position:0% +this mathematically okay so we're going + + + align:start position:0% +this mathematically okay so we're going +to solve the Monty Hall problem using + + align:start position:0% +to solve the Monty Hall problem using + + + align:start position:0% +to solve the Monty Hall problem using +what we call it the the tree method + + align:start position:0% +what we call it the the tree method + + + align:start position:0% +what we call it the the tree method +which is a very simple and Elementary uh + + align:start position:0% +which is a very simple and Elementary uh + + + align:start position:0% +which is a very simple and Elementary uh +approach uh that doesn't rely on + + align:start position:0% +approach uh that doesn't rely on + + + align:start position:0% +approach uh that doesn't rely on +intuition it's just going to rely on + + align:start position:0% +intuition it's just going to rely on + + + align:start position:0% +intuition it's just going to rely on +mathematical break + + align:start position:0% + + + + align:start position:0% + +okay so the tree method uses 4ish steps + + align:start position:0% +okay so the tree method uses 4ish steps + + + align:start position:0% +okay so the tree method uses 4ish steps +uh we used to call it the four step + + align:start position:0% +uh we used to call it the four step + + + align:start position:0% +uh we used to call it the four step +method but like I couldn't for the life + + align:start position:0% +method but like I couldn't for the life + + + align:start position:0% +method but like I couldn't for the life +of me tell you what the four steps are + + align:start position:0% +of me tell you what the four steps are + + + align:start position:0% +of me tell you what the four steps are +if if uh you know they weren't written + + align:start position:0% +if if uh you know they weren't written + + + align:start position:0% +if if uh you know they weren't written +in front of me uh so you know I prefer + + align:start position:0% +in front of me uh so you know I prefer + + + align:start position:0% +in front of me uh so you know I prefer +to call it the tree method uh oh I can't + + align:start position:0% +to call it the tree method uh oh I can't + + + align:start position:0% +to call it the tree method uh oh I can't +even count it kind of has five steps + + align:start position:0% +even count it kind of has five steps + + + align:start position:0% +even count it kind of has five steps +we've got like a Step + + align:start position:0% + + + + align:start position:0% + +Zero before you even start right you + + align:start position:0% +Zero before you even start right you + + + align:start position:0% +Zero before you even start right you +really want to make sure that you are + + align:start position:0% +really want to make sure that you are + + + align:start position:0% +really want to make sure that you are +like you know what question you're + + align:start position:0% +like you know what question you're + + + align:start position:0% +like you know what question you're +trying to answer + + align:start position:0% + + + + align:start position:0% + +okay so before we can even think about + + align:start position:0% +okay so before we can even think about + + + align:start position:0% +okay so before we can even think about +uh solving a mathematical problem we we + + align:start position:0% +uh solving a mathematical problem we we + + + align:start position:0% +uh solving a mathematical problem we we +need to know what the problem is okay uh + + align:start position:0% +need to know what the problem is okay uh + + + align:start position:0% +need to know what the problem is okay uh +we we we need to to understand the setup + + align:start position:0% +we we we need to to understand the setup + + + align:start position:0% +we we we need to to understand the setup +make sure we know what we're trying to + + align:start position:0% +make sure we know what we're trying to + + + align:start position:0% +make sure we know what we're trying to +ask uh you know before we can start + + align:start position:0% +ask uh you know before we can start + + + align:start position:0% +ask uh you know before we can start +analyzing it so the the letter from from + + align:start position:0% +analyzing it so the the letter from from + + + align:start position:0% +analyzing it so the the letter from from +this uh Mr Whitaker was not entirely + + align:start position:0% +this uh Mr Whitaker was not entirely + + + align:start position:0% +this uh Mr Whitaker was not entirely +precise Okay so we've got to kind of + + align:start position:0% +precise Okay so we've got to kind of + + + align:start position:0% +precise Okay so we've got to kind of +figure out what axium we're working with + + align:start position:0% +figure out what axium we're working with + + + align:start position:0% +figure out what axium we're working with +okay so we're going to assume the + + align:start position:0% + + + + align:start position:0% + +following + + align:start position:0% +following + + + align:start position:0% +following +uh prize is equally + + align:start position:0% + + + + align:start position:0% + +likely to + + align:start position:0% +likely to + + + align:start position:0% +likely to +be in any + + align:start position:0% + + + + align:start position:0% + +box + + align:start position:0% +box + + + align:start position:0% +box +okay so you know in principle it's + + align:start position:0% +okay so you know in principle it's + + + align:start position:0% +okay so you know in principle it's +possible that uh you know Monty Hall + + align:start position:0% +possible that uh you know Monty Hall + + + align:start position:0% +possible that uh you know Monty Hall +tries to be tricky and you know tries to + + align:start position:0% +tries to be tricky and you know tries to + + + align:start position:0% +tries to be tricky and you know tries to +you know get into the contestants Minds + + align:start position:0% +you know get into the contestants Minds + + + align:start position:0% +you know get into the contestants Minds +figure out what box they're going to + + align:start position:0% +figure out what box they're going to + + + align:start position:0% +figure out what box they're going to +pick and like put the price somewhere + + align:start position:0% +pick and like put the price somewhere + + + align:start position:0% +pick and like put the price somewhere +else or you know alternatively put the + + align:start position:0% +else or you know alternatively put the + + + align:start position:0% +else or you know alternatively put the +pricee somewhere where they will pick it + + align:start position:0% +pricee somewhere where they will pick it + + + align:start position:0% +pricee somewhere where they will pick it +because it's an exciting game show um + + align:start position:0% +because it's an exciting game show um + + + align:start position:0% +because it's an exciting game show um +but you know we're going to assume that + + align:start position:0% +but you know we're going to assume that + + + align:start position:0% +but you know we're going to assume that +you know Monty is just you know picking + + align:start position:0% +you know Monty is just you know picking + + + align:start position:0% +you know Monty is just you know picking +the boxes randomly okay so the the prize + + align:start position:0% +the boxes randomly okay so the the prize + + + align:start position:0% +the boxes randomly okay so the the prize +is going to go into into a randomly + + align:start position:0% +is going to go into into a randomly + + + align:start position:0% +is going to go into into a randomly +selected box like completely uniform and + + align:start position:0% +selected box like completely uniform and + + + align:start position:0% +selected box like completely uniform and +then the other two will have the goats + + align:start position:0% +then the other two will have the goats + + + align:start position:0% +then the other two will have the goats +okay we're also going to assume that + + align:start position:0% +okay we're also going to assume that + + + align:start position:0% +okay we're also going to assume that +Marilyn + + align:start position:0% +Marilyn + + + align:start position:0% +Marilyn +or you know your colleagues whoever is + + align:start position:0% +or you know your colleagues whoever is + + + align:start position:0% +or you know your colleagues whoever is +is doing the picking is equally + + align:start position:0% + + + + align:start position:0% + +likely to + + align:start position:0% +likely to + + + align:start position:0% +likely to +pick any + + align:start position:0% +pick any + + + align:start position:0% +pick any +ebx okay so for the for the first pick + + align:start position:0% +ebx okay so for the for the first pick + + + align:start position:0% +ebx okay so for the for the first pick +okay uh she doesn't know anything about + + align:start position:0% +okay uh she doesn't know anything about + + + align:start position:0% +okay uh she doesn't know anything about +what Monty is doing she's just going to + + align:start position:0% +what Monty is doing she's just going to + + + align:start position:0% +what Monty is doing she's just going to +you know toss some random coins in her + + align:start position:0% +you know toss some random coins in her + + + align:start position:0% +you know toss some random coins in her +head and you know uniformly at random + + align:start position:0% +head and you know uniformly at random + + + align:start position:0% +head and you know uniformly at random +she'll just pick one of the boxes it + + align:start position:0% +she'll just pick one of the boxes it + + + align:start position:0% +she'll just pick one of the boxes it +doesn't really matter where the where + + align:start position:0% +doesn't really matter where the where + + + align:start position:0% +doesn't really matter where the where +the price is + + align:start position:0% +the price is + + + align:start position:0% +the price is +okay now after Marilyn picks her her box + + align:start position:0% +okay now after Marilyn picks her her box + + + align:start position:0% +okay now after Marilyn picks her her box +right + + align:start position:0% + + + + align:start position:0% + +Monty + + align:start position:0% +Monty + + + align:start position:0% +Monty +must + + align:start position:0% +must + + + align:start position:0% +must +reveal a non + + align:start position:0% + + + + align:start position:0% + +prise okay and moreover it cannot be in + + align:start position:0% +prise okay and moreover it cannot be in + + + align:start position:0% +prise okay and moreover it cannot be in +Maryland's box + + align:start position:0% + + + + align:start position:0% + +okay so you know all that all that Mr + + align:start position:0% +okay so you know all that all that Mr + + + align:start position:0% +okay so you know all that all that Mr +Whitaker said was right Monty did reveal + + align:start position:0% +Whitaker said was right Monty did reveal + + + align:start position:0% +Whitaker said was right Monty did reveal +a non prize that wasn't uh you know + + align:start position:0% +a non prize that wasn't uh you know + + + align:start position:0% +a non prize that wasn't uh you know +behind the chosen door uh it's not + + align:start position:0% +behind the chosen door uh it's not + + + align:start position:0% +behind the chosen door uh it's not +entirely clear that this must happen and + + align:start position:0% +entirely clear that this must happen and + + + align:start position:0% +entirely clear that this must happen and +in fact I believe on the game show there + + align:start position:0% +in fact I believe on the game show there + + + align:start position:0% +in fact I believe on the game show there +were instances where you know he didn't + + align:start position:0% +were instances where you know he didn't + + + align:start position:0% +were instances where you know he didn't +right um so we're just going to assume + + align:start position:0% +right um so we're just going to assume + + + align:start position:0% +right um so we're just going to assume +that you know Monty is going to reveal a + + align:start position:0% +that you know Monty is going to reveal a + + + align:start position:0% +that you know Monty is going to reveal a +prize you know regardless of whether + + align:start position:0% +prize you know regardless of whether + + + align:start position:0% +prize you know regardless of whether +picked the correct uh correct box to + + align:start position:0% +picked the correct uh correct box to + + + align:start position:0% +picked the correct uh correct box to +begin with + + align:start position:0% + + + + align:start position:0% + +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +lastly if Monty has a + + align:start position:0% + + + + align:start position:0% + +choice he picks + + align:start position:0% + + + + align:start position:0% + +randomly okay so if Marilyn has you know + + align:start position:0% +randomly okay so if Marilyn has you know + + + align:start position:0% +randomly okay so if Marilyn has you know +picked a non-price to begin with right + + align:start position:0% +picked a non-price to begin with right + + + align:start position:0% +picked a non-price to begin with right +there's only one other non priz so so + + align:start position:0% +there's only one other non priz so so + + + align:start position:0% +there's only one other non priz so so +Monty has to reveal that one but if + + align:start position:0% +Monty has to reveal that one but if + + + align:start position:0% +Monty has to reveal that one but if +Marilyn has picked the the prize box to + + align:start position:0% +Marilyn has picked the the prize box to + + + align:start position:0% +Marilyn has picked the the prize box to +begin with then Monty could in principle + + align:start position:0% +begin with then Monty could in principle + + + align:start position:0% +begin with then Monty could in principle +open either of the other two boxes that + + align:start position:0% +open either of the other two boxes that + + + align:start position:0% +open either of the other two boxes that +would still follow this role okay so + + align:start position:0% +would still follow this role okay so + + + align:start position:0% +would still follow this role okay so +when Monty has a choice like this we're + + align:start position:0% +when Monty has a choice like this we're + + + align:start position:0% +when Monty has a choice like this we're +going to say that you know he tosses a + + align:start position:0% +going to say that you know he tosses a + + + align:start position:0% +going to say that you know he tosses a +coin and he's going to you know open one + + align:start position:0% +coin and he's going to you know open one + + + align:start position:0% +coin and he's going to you know open one +of them at random + + align:start position:0% + + + + align:start position:0% + +okay so note that these are all axioms + + align:start position:0% +okay so note that these are all axioms + + + align:start position:0% +okay so note that these are all axioms +okay we are just you know taking them on + + align:start position:0% +okay we are just you know taking them on + + + align:start position:0% +okay we are just you know taking them on +faith they may or may not have Merit but + + align:start position:0% +faith they may or may not have Merit but + + + align:start position:0% +faith they may or may not have Merit but +if you accept them then you also have to + + align:start position:0% +if you accept them then you also have to + + + align:start position:0% +if you accept them then you also have to +accept whatever conclusions we draw uh + + align:start position:0% +accept whatever conclusions we draw uh + + + align:start position:0% +accept whatever conclusions we draw uh +from them okay uh but you know I should + + align:start position:0% +from them okay uh but you know I should + + + align:start position:0% +from them okay uh but you know I should +point out that there are other perfectly + + align:start position:0% +point out that there are other perfectly + + + align:start position:0% +point out that there are other perfectly +reasonable sets of + + align:start position:0% +reasonable sets of + + + align:start position:0% +reasonable sets of +axioms uh that would lead us to + + align:start position:0% +axioms uh that would lead us to + + + align:start position:0% +axioms uh that would lead us to +different conclusions right like maybe + + align:start position:0% +different conclusions right like maybe + + + align:start position:0% +different conclusions right like maybe +Monty is you know very rude and if + + align:start position:0% +Monty is you know very rude and if + + + align:start position:0% +Monty is you know very rude and if +Marilyn has you know uh has picked the + + align:start position:0% +Marilyn has you know uh has picked the + + + align:start position:0% +Marilyn has you know uh has picked the +prize then he offers her the option to + + align:start position:0% +prize then he offers her the option to + + + align:start position:0% +prize then he offers her the option to +switch + + align:start position:0% +switch + + + align:start position:0% +switch +and if Marilyn has not picked the prize + + align:start position:0% +and if Marilyn has not picked the prize + + + align:start position:0% +and if Marilyn has not picked the prize +then he forces her to go with whatever + + align:start position:0% +then he forces her to go with whatever + + + align:start position:0% +then he forces her to go with whatever +she picked okay you know like this this + + align:start position:0% +she picked okay you know like this this + + + align:start position:0% +she picked okay you know like this this +is you know a totally reasonable uh + + align:start position:0% +is you know a totally reasonable uh + + + align:start position:0% +is you know a totally reasonable uh +interpretation uh and that would lead us + + align:start position:0% +interpretation uh and that would lead us + + + align:start position:0% +interpretation uh and that would lead us +to to a different conclusion okay or you + + align:start position:0% +to to a different conclusion okay or you + + + align:start position:0% +to to a different conclusion okay or you +know conversely maybe as benevolent + + align:start position:0% +know conversely maybe as benevolent + + + align:start position:0% +know conversely maybe as benevolent +maybe if Marilyn uh maybe if Marilyn + + align:start position:0% +maybe if Marilyn uh maybe if Marilyn + + + align:start position:0% +maybe if Marilyn uh maybe if Marilyn +didn't pick the prize initially he'll + + align:start position:0% +didn't pick the prize initially he'll + + + align:start position:0% +didn't pick the prize initially he'll +always you know try and encourage her to + + align:start position:0% +always you know try and encourage her to + + + align:start position:0% +always you know try and encourage her to +switch uh but if she picked the prize + + align:start position:0% +switch uh but if she picked the prize + + + align:start position:0% +switch uh but if she picked the prize +he'll just be like nope you got to stick + + align:start position:0% +he'll just be like nope you got to stick + + + align:start position:0% +he'll just be like nope you got to stick +with that okay + + align:start position:0% + + + + align:start position:0% + +so now that we've got these + + align:start position:0% +so now that we've got these + + + align:start position:0% +so now that we've got these +axioms we can now pose the mathematical + + align:start position:0% +axioms we can now pose the mathematical + + + align:start position:0% +axioms we can now pose the mathematical +question uh what is the + + align:start position:0% + + + + align:start position:0% + +probability that + + align:start position:0% +probability that + + + align:start position:0% +probability that +Marilyn wins by switching + + align:start position:0% + + + + align:start position:0% + +so uh yes um this is why I I singled you + + align:start position:0% +so uh yes um this is why I I singled you + + + align:start position:0% +so uh yes um this is why I I singled you +out I I don't know where where you've + + align:start position:0% +out I I don't know where where you've + + + align:start position:0% +out I I don't know where where you've +gone um you your colleague who who did + + align:start position:0% +gone um you your colleague who who did + + + align:start position:0% +gone um you your colleague who who did +not switch uh you know we're trying to + + align:start position:0% +not switch uh you know we're trying to + + + align:start position:0% +not switch uh you know we're trying to +analyze this probability which is which + + align:start position:0% +analyze this probability which is which + + + align:start position:0% +analyze this probability which is which +is why single you want so I apologize + + align:start position:0% +is why single you want so I apologize + + + align:start position:0% +is why single you want so I apologize +for that but you know it's for the + + align:start position:0% +for that but you know it's for the + + + align:start position:0% +for that but you know it's for the +mouths don't take it + + align:start position:0% +mouths don't take it + + + align:start position:0% +mouths don't take it +personally uh + + align:start position:0% +personally uh + + + align:start position:0% +personally uh +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now we have you know a well- defined + + align:start position:0% +so now we have you know a well- defined + + + align:start position:0% +so now we have you know a well- defined +question right so now we can analyze it + + align:start position:0% +question right so now we can analyze it + + + align:start position:0% +question right so now we can analyze it +using the four step + + align:start position:0% + + + + align:start position:0% + +method the first of our four steps well + + align:start position:0% +method the first of our four steps well + + + align:start position:0% +method the first of our four steps well +the tree method which has four + + align:start position:0% +the tree method which has four + + + align:start position:0% +the tree method which has four +steps uh we need to figure out what we + + align:start position:0% +steps uh we need to figure out what we + + + align:start position:0% +steps uh we need to figure out what we +call the sample + + align:start position:0% + + + + align:start position:0% + +space + + align:start position:0% +space + + + align:start position:0% +space +okay uh so whenever we're thinking about + + align:start position:0% +okay uh so whenever we're thinking about + + + align:start position:0% +okay uh so whenever we're thinking about +a probability problem uh underlying it + + align:start position:0% +a probability problem uh underlying it + + + align:start position:0% +a probability problem uh underlying it +is always what we call a probability + + align:start position:0% +is always what we call a probability + + + align:start position:0% +is always what we call a probability +space okay and a probability space + + align:start position:0% +space okay and a probability space + + + align:start position:0% +space okay and a probability space +consists of two + + align:start position:0% + + + + align:start position:0% + +things uh these two elements are a set + + align:start position:0% +things uh these two elements are a set + + + align:start position:0% +things uh these two elements are a set +right which we call the sample + + align:start position:0% + + + + align:start position:0% + +space okay and you know for the purposes + + align:start position:0% +space okay and you know for the purposes + + + align:start position:0% +space okay and you know for the purposes +of this class we're we're only going to + + align:start position:0% +of this class we're we're only going to + + + align:start position:0% +of this class we're we're only going to +be looking at discrete probability + + align:start position:0% +be looking at discrete probability + + + align:start position:0% +be looking at discrete probability +spaces so uh s is going to be a + + align:start position:0% +spaces so uh s is going to be a + + + align:start position:0% +spaces so uh s is going to be a +non-empty and countable or finite uh set + + align:start position:0% +non-empty and countable or finite uh set + + + align:start position:0% +non-empty and countable or finite uh set +we're not going to look at sets like r + + align:start position:0% +we're not going to look at sets like r + + + align:start position:0% +we're not going to look at sets like r +or something like that okay so you know + + align:start position:0% +or something like that okay so you know + + + align:start position:0% +or something like that okay so you know +this could be uh you know a set of three + + align:start position:0% +this could be uh you know a set of three + + + align:start position:0% +this could be uh you know a set of three +boxes or it could be you know the + + align:start position:0% +boxes or it could be you know the + + + align:start position:0% +boxes or it could be you know the +natural numbers something like that + + align:start position:0% +natural numbers something like that + + + align:start position:0% +natural numbers something like that +something that's you know discret and + + align:start position:0% +something that's you know discret and + + + align:start position:0% +something that's you know discret and +countable uh and then we also have a + + align:start position:0% +countable uh and then we also have a + + + align:start position:0% +countable uh and then we also have a +function which we're going to denote by + + align:start position:0% +function which we're going to denote by + + + align:start position:0% +function which we're going to denote by +the letters PR + + align:start position:0% +the letters PR + + + align:start position:0% +the letters PR +R which Maps + + align:start position:0% +R which Maps + + + align:start position:0% +R which Maps +s into the unit interval 0 to + + align:start position:0% +s into the unit interval 0 to + + + align:start position:0% +s into the unit interval 0 to +one + + align:start position:0% +one + + + align:start position:0% +one +okay so this this is going to be a total + + align:start position:0% + + + + align:start position:0% + +function + + align:start position:0% + + + + align:start position:0% + +with uh probably shouldn't use S here + + align:start position:0% +with uh probably shouldn't use S here + + + align:start position:0% +with uh probably shouldn't use S here +let's call it + + align:start position:0% + + + + align:start position:0% + +X + + align:start position:0% +X + + + align:start position:0% +X +okay uh and you know slightly oddly when + + align:start position:0% +okay uh and you know slightly oddly when + + + align:start position:0% +okay uh and you know slightly oddly when +we're talking about probabilities we use + + align:start position:0% +we're talking about probabilities we use + + + align:start position:0% +we're talking about probabilities we use +square brackets instead of uh + + align:start position:0% +square brackets instead of uh + + + align:start position:0% +square brackets instead of uh +parenthesis uh to enclose the argument + + align:start position:0% +parenthesis uh to enclose the argument + + + align:start position:0% +parenthesis uh to enclose the argument +um but uh you know this is just a + + align:start position:0% +um but uh you know this is just a + + + align:start position:0% +um but uh you know this is just a +function you can think of it as like + + align:start position:0% +function you can think of it as like + + + align:start position:0% +function you can think of it as like +PR of X + + align:start position:0% +PR of X + + + align:start position:0% +PR of X +okay uh so we're going to have the + + align:start position:0% +okay uh so we're going to have the + + + align:start position:0% +okay uh so we're going to have the +requirement that if you sum up PR of X + + align:start position:0% +requirement that if you sum up PR of X + + + align:start position:0% +requirement that if you sum up PR of X +over all of the X in your sample space + + align:start position:0% +over all of the X in your sample space + + + align:start position:0% +over all of the X in your sample space +you should get one okay that's what it + + align:start position:0% +you should get one okay that's what it + + + align:start position:0% +you should get one okay that's what it +means for this to be a probability + + align:start position:0% + + + + align:start position:0% + +function okay + + align:start position:0% + + + + align:start position:0% + +oh actually why don't we leave both of + + align:start position:0% +oh actually why don't we leave both of + + + align:start position:0% +oh actually why don't we leave both of +these + + align:start position:0% +these + + + align:start position:0% +these +up and move on to this + + align:start position:0% + + + + align:start position:0% + +board + + align:start position:0% +board + + + align:start position:0% +board +okay so this is called our probability + + align:start position:0% + + + + align:start position:0% + +function and uh elements of s are what + + align:start position:0% +function and uh elements of s are what + + + align:start position:0% +function and uh elements of s are what +uh we're going to call those outcomes + + align:start position:0% + + + + align:start position:0% + +Okay + + align:start position:0% +Okay + + + align:start position:0% +Okay +Okay so we've got a sample space s which + + align:start position:0% +Okay so we've got a sample space s which + + + align:start position:0% +Okay so we've got a sample space s which +is a set of outcomes and we've got a + + align:start position:0% +is a set of outcomes and we've got a + + + align:start position:0% +is a set of outcomes and we've got a +probability function which Maps each + + align:start position:0% +probability function which Maps each + + + align:start position:0% +probability function which Maps each +outcome to a number between Z and one + + align:start position:0% +outcome to a number between Z and one + + + align:start position:0% +outcome to a number between Z and one +okay and it should be the case that all + + align:start position:0% +okay and it should be the case that all + + + align:start position:0% +okay and it should be the case that all +of those probabilities should sum to + + align:start position:0% +of those probabilities should sum to + + + align:start position:0% +of those probabilities should sum to +one does that make sense to everybody + + align:start position:0% +one does that make sense to everybody + + + align:start position:0% +one does that make sense to everybody +people people reasonably happy with this + + align:start position:0% +people people reasonably happy with this + + + align:start position:0% +people people reasonably happy with this +questions comments + + align:start position:0% + + + + align:start position:0% + +concerns + + align:start position:0% + + + + align:start position:0% + +okay so our first objective is going to + + align:start position:0% +okay so our first objective is going to + + + align:start position:0% +okay so our first objective is going to +be to figure out what our sample space + + align:start position:0% +be to figure out what our sample space + + + align:start position:0% +be to figure out what our sample space +should be + + align:start position:0% +should be + + + align:start position:0% +should be +okay so we're going to do that using + + align:start position:0% +okay so we're going to do that using + + + align:start position:0% +okay so we're going to do that using +what we call a tree diagram + + align:start position:0% + + + + align:start position:0% + +okay so for the moment we're going to + + align:start position:0% +okay so for the moment we're going to + + + align:start position:0% +okay so for the moment we're going to +disregard the probability function and + + align:start position:0% +disregard the probability function and + + + align:start position:0% +disregard the probability function and +just focus on S okay and then once we + + align:start position:0% +just focus on S okay and then once we + + + align:start position:0% +just focus on S okay and then once we +figured out what s is we can figure out + + align:start position:0% +figured out what s is we can figure out + + + align:start position:0% +figured out what s is we can figure out +how to assign probabilities to + + align:start position:0% +how to assign probabilities to + + + align:start position:0% +how to assign probabilities to +everything okay so the tree diagram you + + align:start position:0% +everything okay so the tree diagram you + + + align:start position:0% +everything okay so the tree diagram you +know as you might expect it's going to + + align:start position:0% +know as you might expect it's going to + + + align:start position:0% +know as you might expect it's going to +be a diagram in the shape of a tree + + align:start position:0% +be a diagram in the shape of a tree + + + align:start position:0% +be a diagram in the shape of a tree +where each level of the tree represents + + align:start position:0% +where each level of the tree represents + + + align:start position:0% +where each level of the tree represents +some step in the random process we're + + align:start position:0% +some step in the random process we're + + + align:start position:0% +some step in the random process we're +trying to model + + align:start position:0% +trying to model + + + align:start position:0% +trying to model +okay so in the case of the Monty Hall + + align:start position:0% +okay so in the case of the Monty Hall + + + align:start position:0% +okay so in the case of the Monty Hall +problem what might be the first + + align:start position:0% +problem what might be the first + + + align:start position:0% +problem what might be the first +step like what's what's the first thing + + align:start position:0% +step like what's what's the first thing + + + align:start position:0% +step like what's what's the first thing +that happens in the Monty Hall problem + + align:start position:0% +that happens in the Monty Hall problem + + + align:start position:0% +that happens in the Monty Hall problem +the the first like source of + + align:start position:0% +the the first like source of + + + align:start position:0% +the the first like source of +Randomness + + align:start position:0% + + + + align:start position:0% + +yeah uh okay there's there's something + + align:start position:0% +yeah uh okay there's there's something + + + align:start position:0% +yeah uh okay there's there's something +random that happens even before that the + + align:start position:0% +random that happens even before that the + + + align:start position:0% +random that happens even before that the +answer was you pick a door + + align:start position:0% + + + + align:start position:0% + +yeah yeah so the the first random thing + + align:start position:0% +yeah yeah so the the first random thing + + + align:start position:0% +yeah yeah so the the first random thing +that happens right is I or or Monty + + align:start position:0% +that happens right is I or or Monty + + + align:start position:0% +that happens right is I or or Monty +picks which store the prize uh the priz + + align:start position:0% +picks which store the prize uh the priz + + + align:start position:0% +picks which store the prize uh the priz +is behind Okay so that's going to be the + + align:start position:0% +is behind Okay so that's going to be the + + + align:start position:0% +is behind Okay so that's going to be the +first level of our tree + + align:start position:0% +first level of our tree + + + align:start position:0% +first level of our tree +diagram okay so let's start drawing out + + align:start position:0% +diagram okay so let's start drawing out + + + align:start position:0% +diagram okay so let's start drawing out +our tree diagram we're going to have our + + align:start position:0% +our tree diagram we're going to have our + + + align:start position:0% +our tree diagram we're going to have our +root here and let's label this with you + + align:start position:0% +root here and let's label this with you + + + align:start position:0% +root here and let's label this with you +know Monty hides + + align:start position:0% + + + + align:start position:0% + +price okay + + align:start position:0% + + + + align:start position:0% + +and we're going to have three edges + + align:start position:0% +and we're going to have three edges + + + align:start position:0% +and we're going to have three edges +which go to you know the three + + align:start position:0% +which go to you know the three + + + align:start position:0% +which go to you know the three +possibilities for what happens here okay + + align:start position:0% +possibilities for what happens here okay + + + align:start position:0% +possibilities for what happens here okay +so it could be in door a door B actually + + align:start position:0% +so it could be in door a door B actually + + + align:start position:0% +so it could be in door a door B actually +why don't I call these you know purple + + align:start position:0% +why don't I call these you know purple + + + align:start position:0% +why don't I call these you know purple +gold and silver uh where's the + + align:start position:0% + + + + align:start position:0% + +Eraser here we + + align:start position:0% + + + + align:start position:0% + +go Okay so we've got our purple box our + + align:start position:0% +go Okay so we've got our purple box our + + + align:start position:0% +go Okay so we've got our purple box our +gold box and our Silver Box + + align:start position:0% + + + + align:start position:0% + +okay uh what's the next random thing + + align:start position:0% +okay uh what's the next random thing + + + align:start position:0% +okay uh what's the next random thing +that + + align:start position:0% + + + + align:start position:0% + +happens + + align:start position:0% +happens + + + align:start position:0% +happens +yeah yeah yeah so as as your colleague + + align:start position:0% +yeah yeah yeah so as as your colleague + + + align:start position:0% +yeah yeah yeah so as as your colleague +said last time you know the the next + + align:start position:0% +said last time you know the the next + + + align:start position:0% +said last time you know the the next +random thing that happens is Marilyn or + + align:start position:0% +random thing that happens is Marilyn or + + + align:start position:0% +random thing that happens is Marilyn or +you know the contestant picks a door + + align:start position:0% +you know the contestant picks a door + + + align:start position:0% +you know the contestant picks a door +okay so um oh dear Monty and Marlin both + + align:start position:0% +okay so um oh dear Monty and Marlin both + + + align:start position:0% +okay so um oh dear Monty and Marlin both +begin with the same letter okay let's + + align:start position:0% +begin with the same letter okay let's + + + align:start position:0% +begin with the same letter okay let's +just call this + + align:start position:0% + + + + align:start position:0% + +student okay so now each of + + align:start position:0% +student okay so now each of + + + align:start position:0% +student okay so now each of +these is going to split into you know + + align:start position:0% +these is going to split into you know + + + align:start position:0% +these is going to split into you know +three more possibilities okay so you + + align:start position:0% +three more possibilities okay so you + + + align:start position:0% +three more possibilities okay so you +know our contestant can pick purple gold + + align:start position:0% +know our contestant can pick purple gold + + + align:start position:0% +know our contestant can pick purple gold +or silver okay for each of these these + + align:start position:0% +or silver okay for each of these these + + + align:start position:0% +or silver okay for each of these these +three things right regardless of where + + align:start position:0% +three things right regardless of where + + + align:start position:0% +three things right regardless of where +Monty has hidden the prize the + + align:start position:0% +Monty has hidden the prize the + + + align:start position:0% +Monty has hidden the prize the +contestant can pick you + + align:start position:0% + + + + align:start position:0% + +know any of the uh any of the + + align:start position:0% + + + + align:start position:0% + +doors + + align:start position:0% + + + + align:start position:0% + +okay okay what's the next random thing + + align:start position:0% +okay okay what's the next random thing + + + align:start position:0% +okay okay what's the next random thing +that could + + align:start position:0% +that could + + + align:start position:0% +that could +happen yeah + + align:start position:0% + + + + align:start position:0% + +were you raising your + + align:start position:0% +were you raising your + + + align:start position:0% +were you raising your +hand oh no + + align:start position:0% + + + + align:start position:0% + +no + + align:start position:0% +no + + + align:start position:0% +no +okay yeah so if Monty has a choice of of + + align:start position:0% +okay yeah so if Monty has a choice of of + + + align:start position:0% +okay yeah so if Monty has a choice of of +door to reveal then he picks one of the + + align:start position:0% +door to reveal then he picks one of the + + + align:start position:0% +door to reveal then he picks one of the +one of the two remaining doors randomly + + align:start position:0% +one of the two remaining doors randomly + + + align:start position:0% +one of the two remaining doors randomly +okay so so far we've got three branches + + align:start position:0% +okay so so far we've got three branches + + + align:start position:0% +okay so so far we've got three branches +where that could happen + + align:start position:0% + + + + align:start position:0% + +right we've got uh you know both Monty + + align:start position:0% +right we've got uh you know both Monty + + + align:start position:0% +right we've got uh you know both Monty +and and uh Marilyn picked door P okay so + + align:start position:0% +and and uh Marilyn picked door P okay so + + + align:start position:0% +and and uh Marilyn picked door P okay so +in that case Monty can reveal either G + + align:start position:0% +in that case Monty can reveal either G + + + align:start position:0% +in that case Monty can reveal either G +or S + + align:start position:0% + + + + align:start position:0% + +okay so let's uh you know make uh make a + + align:start position:0% +okay so let's uh you know make uh make a + + + align:start position:0% +okay so let's uh you know make uh make a +branch for that uh similarly if they + + align:start position:0% +branch for that uh similarly if they + + + align:start position:0% +branch for that uh similarly if they +both pick + + align:start position:0% +both pick + + + align:start position:0% +both pick +G we could have either P or S and if + + align:start position:0% +G we could have either P or S and if + + + align:start position:0% +G we could have either P or S and if +they both pick + + align:start position:0% +they both pick + + + align:start position:0% +they both pick +s then here we could have either P or + + align:start position:0% +s then here we could have either P or + + + align:start position:0% +s then here we could have either P or +G + + align:start position:0% +G + + + align:start position:0% +G +okay now for the remaining ones right + + align:start position:0% +okay now for the remaining ones right + + + align:start position:0% +okay now for the remaining ones right +like we we could you know say that uh + + align:start position:0% +like we we could you know say that uh + + + align:start position:0% +like we we could you know say that uh +there's a random process there where + + align:start position:0% +there's a random process there where + + + align:start position:0% +there's a random process there where +Monti is you know randomly picking from + + align:start position:0% +Monti is you know randomly picking from + + + align:start position:0% +Monti is you know randomly picking from +a single element set so you know it's + + align:start position:0% +a single element set so you know it's + + + align:start position:0% +a single element set so you know it's +always going to be the same thing we + + align:start position:0% +always going to be the same thing we + + + align:start position:0% +always going to be the same thing we +could consider it a random outcome + + align:start position:0% +could consider it a random outcome + + + align:start position:0% +could consider it a random outcome +though so we can also draw these arrows + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +okay uh uh kind of running out of space + + align:start position:0% +okay uh uh kind of running out of space + + + align:start position:0% +okay uh uh kind of running out of space +here so let's + + align:start position:0% +here so let's + + + align:start position:0% +here so let's +uh put this up + + align:start position:0% +uh put this up + + + align:start position:0% +uh put this up +here let's label it on this board + + align:start position:0% +here let's label it on this board + + + align:start position:0% +here let's label it on this board +so + + align:start position:0% +so + + + align:start position:0% +so +Monty + + align:start position:0% +Monty + + + align:start position:0% +Monty +reveals a + + align:start position:0% +reveals a + + + align:start position:0% +reveals a +zon so this is the uh technical term for + + align:start position:0% +zon so this is the uh technical term for + + + align:start position:0% +zon so this is the uh technical term for +a non prize I think the uh the non + + align:start position:0% +a non prize I think the uh the non + + + align:start position:0% +a non prize I think the uh the non +prizes on Monty's show were called zonks + + align:start position:0% +prizes on Monty's show were called zonks + + + align:start position:0% +prizes on Monty's show were called zonks +uh that they weren't always goats you + + align:start position:0% +uh that they weren't always goats you + + + align:start position:0% +uh that they weren't always goats you +know some times it was uh you know + + align:start position:0% +know some times it was uh you know + + + align:start position:0% +know some times it was uh you know +something some other sort of ridiculous + + align:start position:0% +something some other sort of ridiculous + + + align:start position:0% +something some other sort of ridiculous +prize like a garbage can or a potato or + + align:start position:0% +prize like a garbage can or a potato or + + + align:start position:0% +prize like a garbage can or a potato or +something um but yeah they were just + + align:start position:0% +something um but yeah they were just + + + align:start position:0% +something um but yeah they were just +called + + align:start position:0% +called + + + align:start position:0% +called +songs uh + + align:start position:0% + + + + align:start position:0% + +okay so now are we done is there any + + align:start position:0% +okay so now are we done is there any + + + align:start position:0% +okay so now are we done is there any +other Randomness that we haven't modeled + + align:start position:0% + + + + align:start position:0% + +yet who thinks yes + + align:start position:0% +yet who thinks yes + + + align:start position:0% +yet who thinks yes +oh okay so what are we missing + + align:start position:0% +oh okay so what are we missing + + + align:start position:0% +oh okay so what are we missing +then everybody seems to think we're + + align:start position:0% +then everybody seems to think we're + + + align:start position:0% +then everybody seems to think we're +missing somebody or are we just asleep + + align:start position:0% +missing somebody or are we just asleep + + + align:start position:0% +missing somebody or are we just asleep +it is very early in the morning I + + align:start position:0% +it is very early in the morning I + + + align:start position:0% +it is very early in the morning I +understand + + align:start position:0% +understand + + + align:start position:0% +understand +uh are we missing + + align:start position:0% +uh are we missing + + + align:start position:0% +uh are we missing +anything who thinks we're not missing + + align:start position:0% +anything who thinks we're not missing + + + align:start position:0% +anything who thinks we're not missing +anything few hands okay uh well yeah + + align:start position:0% +anything few hands okay uh well yeah + + + align:start position:0% +anything few hands okay uh well yeah +turns out that this is all of the all of + + align:start position:0% +turns out that this is all of the all of + + + align:start position:0% +turns out that this is all of the all of +the randomness um you know you could + + align:start position:0% +the randomness um you know you could + + + align:start position:0% +the randomness um you know you could +think about uh a different problem right + + align:start position:0% +think about uh a different problem right + + + align:start position:0% +think about uh a different problem right +where where Marilyn has a random + + align:start position:0% +where where Marilyn has a random + + + align:start position:0% +where where Marilyn has a random +strategy but for now we're just you know + + align:start position:0% +strategy but for now we're just you know + + + align:start position:0% +strategy but for now we're just you know +our question right is you know Marilyn's + + align:start position:0% +our question right is you know Marilyn's + + + align:start position:0% +our question right is you know Marilyn's +always going to switch what's the + + align:start position:0% +always going to switch what's the + + + align:start position:0% +always going to switch what's the +probability that she wins okay so this + + align:start position:0% +probability that she wins okay so this + + + align:start position:0% +probability that she wins okay so this +is all the randomness that we've + + align:start position:0% +is all the randomness that we've + + + align:start position:0% +is all the randomness that we've +got so + + align:start position:0% + + + + align:start position:0% + +now now that we have our tree structure + + align:start position:0% +now now that we have our tree structure + + + align:start position:0% +now now that we have our tree structure +we can label our outcomes okay and + + align:start position:0% +we can label our outcomes okay and + + + align:start position:0% +we can label our outcomes okay and +that'll tell us what the set s + + align:start position:0% +that'll tell us what the set s + + + align:start position:0% +that'll tell us what the set s +is so the set s is just going to be the + + align:start position:0% +is so the set s is just going to be the + + + align:start position:0% +is so the set s is just going to be the +set of leaves of our + + align:start position:0% +set of leaves of our + + + align:start position:0% +set of leaves of our +tree okay + + align:start position:0% +tree okay + + + align:start position:0% +tree okay +each you know path right corresponds to + + align:start position:0% +each you know path right corresponds to + + + align:start position:0% +each you know path right corresponds to +you know some way that the random + + align:start position:0% +you know some way that the random + + + align:start position:0% +you know some way that the random +process could turn out right those are + + align:start position:0% +process could turn out right those are + + + align:start position:0% +process could turn out right those are +going to be our + + align:start position:0% +going to be our + + + align:start position:0% +going to be our +outcomes + + align:start position:0% +outcomes + + + align:start position:0% +outcomes +okay so formally we could label these as + + align:start position:0% +okay so formally we could label these as + + + align:start position:0% +okay so formally we could label these as +tuples so let's say that this one's + + align:start position:0% +tuples so let's say that this one's + + + align:start position:0% +tuples so let's say that this one's +PPG right so that represents you know + + align:start position:0% +PPG right so that represents you know + + + align:start position:0% +PPG right so that represents you know +Monty hides the prize behind door P + + align:start position:0% +Monty hides the prize behind door P + + + align:start position:0% +Monty hides the prize behind door P +Marilyn picks door p and then Monty + + align:start position:0% +Marilyn picks door p and then Monty + + + align:start position:0% +Marilyn picks door p and then Monty +reveals a zon behind uh door G okay this + + align:start position:0% +reveals a zon behind uh door G okay this + + + align:start position:0% +reveals a zon behind uh door G okay this +one's going to be + + align:start position:0% +one's going to be + + + align:start position:0% +one's going to be +PPS this one's going to be + + align:start position:0% +PPS this one's going to be + + + align:start position:0% +PPS this one's going to be +PG and now I haven't actually labeled + + align:start position:0% +PG and now I haven't actually labeled + + + align:start position:0% +PG and now I haven't actually labeled +The Edge uh but you know if Monty hides + + align:start position:0% +The Edge uh but you know if Monty hides + + + align:start position:0% +The Edge uh but you know if Monty hides +the the prize behind door p and then uh + + align:start position:0% +the the prize behind door p and then uh + + + align:start position:0% +the the prize behind door p and then uh +Marilyn picks door + + align:start position:0% +Marilyn picks door + + + align:start position:0% +Marilyn picks door +G where is Monty revealing the + + align:start position:0% + + + + align:start position:0% + +zon s yeah + + align:start position:0% + + + + align:start position:0% + +so let's uh label that okay and you know + + align:start position:0% +so let's uh label that okay and you know + + + align:start position:0% +so let's uh label that okay and you know +we can continue all the way down + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +s oh I've just realized that I've + + align:start position:0% +s oh I've just realized that I've + + + align:start position:0% +s oh I've just realized that I've +overloaded + + align:start position:0% +overloaded + + + align:start position:0% +overloaded +it it's it's a script DES in my notes + + align:start position:0% +it it's it's a script DES in my notes + + + align:start position:0% +it it's it's a script DES in my notes +and so it looks different I'm I'm I'm + + align:start position:0% +and so it looks different I'm I'm I'm + + + align:start position:0% +and so it looks different I'm I'm I'm +sorry uh okay so our squiggly s is going + + align:start position:0% +sorry uh okay so our squiggly s is going + + + align:start position:0% +sorry uh okay so our squiggly s is going +to be the set of all + + align:start position:0% +to be the set of all + + + align:start position:0% +to be the set of all +tuples uh + + align:start position:0% +tuples uh + + + align:start position:0% +tuples uh +so x y + + align:start position:0% +so x y + + + align:start position:0% +so x y +z + + align:start position:0% +z + + + align:start position:0% +z +in uh + + align:start position:0% +in uh + + + align:start position:0% +in uh +PG s uh + + align:start position:0% +PG s uh + + + align:start position:0% +PG s uh +oops cubed right so it's going to be + + align:start position:0% +oops cubed right so it's going to be + + + align:start position:0% +oops cubed right so it's going to be +triples of you know PG and S such + + align:start position:0% +triples of you know PG and S such + + + align:start position:0% +triples of you know PG and S such +that uh Z is not equal to X and Zed is + + align:start position:0% +that uh Z is not equal to X and Zed is + + + align:start position:0% +that uh Z is not equal to X and Zed is +not equal to + + align:start position:0% +not equal to + + + align:start position:0% +not equal to +Y okay + + align:start position:0% + + + + align:start position:0% + +so that's how we're you know + + align:start position:0% +so that's how we're you know + + + align:start position:0% +so that's how we're you know +mathematically going to represent our + + align:start position:0% +mathematically going to represent our + + + align:start position:0% +mathematically going to represent our +sample space okay so X is the door that + + align:start position:0% +sample space okay so X is the door that + + + align:start position:0% +sample space okay so X is the door that +that Monty hides the the prize behind Y + + align:start position:0% +that Monty hides the the prize behind Y + + + align:start position:0% +that Monty hides the the prize behind Y +is the door that Marilyn initially + + align:start position:0% +is the door that Marilyn initially + + + align:start position:0% +is the door that Marilyn initially +chooses and then Z is going to be the + + align:start position:0% +chooses and then Z is going to be the + + + align:start position:0% +chooses and then Z is going to be the +the door that Monty reveals which has a + + align:start position:0% +the door that Monty reveals which has a + + + align:start position:0% +the door that Monty reveals which has a +goat and by our rule that door cannot be + + align:start position:0% +goat and by our rule that door cannot be + + + align:start position:0% +goat and by our rule that door cannot be +either of the first + + align:start position:0% +either of the first + + + align:start position:0% +either of the first +two okay but anything else is a valid + + align:start position:0% +two okay but anything else is a valid + + + align:start position:0% +two okay but anything else is a valid +outcome + + align:start position:0% + + + + align:start position:0% + +okay do we have any questions about the + + align:start position:0% +okay do we have any questions about the + + + align:start position:0% +okay do we have any questions about the +sample space and and how we computed + + align:start position:0% + + + + align:start position:0% + +it okay so our next + + align:start position:0% + + + + align:start position:0% + +step now that we've got our sample space + + align:start position:0% +step now that we've got our sample space + + + align:start position:0% +step now that we've got our sample space +we want to figure out our probability + + align:start position:0% +we want to figure out our probability + + + align:start position:0% +we want to figure out our probability +function + + align:start position:0% + + + + align:start position:0% + +okay so we'd like to figure out what the + + align:start position:0% +okay so we'd like to figure out what the + + + align:start position:0% +okay so we'd like to figure out what the +probability of each of these outcomes + + align:start position:0% +probability of each of these outcomes + + + align:start position:0% +probability of each of these outcomes +is okay so to do this we're going to + + align:start position:0% +is okay so to do this we're going to + + + align:start position:0% +is okay so to do this we're going to +assign a probability to every Edge that + + align:start position:0% +assign a probability to every Edge that + + + align:start position:0% +assign a probability to every Edge that +we've got in our tree + + align:start position:0% +we've got in our tree + + + align:start position:0% +we've got in our tree +diagram okay uh and so that's that's + + align:start position:0% +diagram okay uh and so that's that's + + + align:start position:0% +diagram okay uh and so that's that's +just going to be the probability that + + align:start position:0% +just going to be the probability that + + + align:start position:0% +just going to be the probability that +you know if we get to the source of that + + align:start position:0% +you know if we get to the source of that + + + align:start position:0% +you know if we get to the source of that +edge you know what's the probability + + align:start position:0% +edge you know what's the probability + + + align:start position:0% +edge you know what's the probability +that we uh you know proceed along that + + align:start position:0% +that we uh you know proceed along that + + + align:start position:0% +that we uh you know proceed along that +edge okay so at the very beginning right + + align:start position:0% +edge okay so at the very beginning right + + + align:start position:0% +edge okay so at the very beginning right +if we're at the + + align:start position:0% + + + + align:start position:0% + +root what's the probability that you + + align:start position:0% +root what's the probability that you + + + align:start position:0% +root what's the probability that you +know given that we're at the start Monty + + align:start position:0% +know given that we're at the start Monty + + + align:start position:0% +know given that we're at the start Monty +hides the uh the prize behind door uh + + align:start position:0% + + + + align:start position:0% + +P yeah one3 + + align:start position:0% +P yeah one3 + + + align:start position:0% +P yeah one3 +yeah so we're going to label this with + + align:start position:0% +yeah so we're going to label this with + + + align:start position:0% +yeah so we're going to label this with +one3 + + align:start position:0% +one3 + + + align:start position:0% +one3 +okay what about G what's the probability + + align:start position:0% +okay what about G what's the probability + + + align:start position:0% +okay what about G what's the probability +that Monty hides the uh prize behind + + align:start position:0% +that Monty hides the uh prize behind + + + align:start position:0% +that Monty hides the uh prize behind +door + + align:start position:0% + + + + align:start position:0% + +G + + align:start position:0% + + + + align:start position:0% + +anybody okay I mean yeah arithmetic is + + align:start position:0% +anybody okay I mean yeah arithmetic is + + + align:start position:0% +anybody okay I mean yeah arithmetic is +pretty difficult but uh I I'll just do + + align:start position:0% +pretty difficult but uh I I'll just do + + + align:start position:0% +pretty difficult but uh I I'll just do +it for you it's also 1/3 + + align:start position:0% +it for you it's also 1/3 + + + align:start position:0% +it for you it's also 1/3 +okay and uh the probability that Monty + + align:start position:0% +okay and uh the probability that Monty + + + align:start position:0% +okay and uh the probability that Monty +hide sit behind door s + + align:start position:0% +hide sit behind door s + + + align:start position:0% +hide sit behind door s +also a third okay yeah + + align:start position:0% + + + + align:start position:0% + +question yeah that's a great observation + + align:start position:0% +question yeah that's a great observation + + + align:start position:0% +question yeah that's a great observation +so all of these three + + align:start position:0% +so all of these three + + + align:start position:0% +so all of these three +probabilities should add up to one right + + align:start position:0% +probabilities should add up to one right + + + align:start position:0% +probabilities should add up to one right +because if we're at this this uh vertex + + align:start position:0% +because if we're at this this uh vertex + + + align:start position:0% +because if we're at this this uh vertex +here we should proceed somewhere + + align:start position:0% +here we should proceed somewhere + + + align:start position:0% +here we should proceed somewhere +right uh so like you know it it wouldn't + + align:start position:0% +right uh so like you know it it wouldn't + + + align:start position:0% +right uh so like you know it it wouldn't +make a whole lot of sense to have like + + align:start position:0% +make a whole lot of sense to have like + + + align:start position:0% +make a whole lot of sense to have like +you know probability 1/3 probability 2/3 + + align:start position:0% +you know probability 1/3 probability 2/3 + + + align:start position:0% +you know probability 1/3 probability 2/3 +and probability one right because then + + align:start position:0% +and probability one right because then + + + align:start position:0% +and probability one right because then +you're like like you have to proceed + + align:start position:0% +you're like like you have to proceed + + + align:start position:0% +you're like like you have to proceed +down this path but then you also have to + + align:start position:0% +down this path but then you also have to + + + align:start position:0% +down this path but then you also have to +proceed down one of the others like it's + + align:start position:0% +proceed down one of the others like it's + + + align:start position:0% +proceed down one of the others like it's +it's a bit sticky okay so given that + + align:start position:0% +it's a bit sticky okay so given that + + + align:start position:0% +it's a bit sticky okay so given that +you're at this this vertex you've got to + + align:start position:0% +you're at this this vertex you've got to + + + align:start position:0% +you're at this this vertex you've got to +reach a leaf somehow you you've got to + + align:start position:0% +reach a leaf somehow you you've got to + + + align:start position:0% +reach a leaf somehow you you've got to +get to some outcome so you've got to + + align:start position:0% +get to some outcome so you've got to + + + align:start position:0% +get to some outcome so you've got to +proceed okay so you know all of these + + align:start position:0% +proceed okay so you know all of these + + + align:start position:0% +proceed okay so you know all of these +edges should uh should sum up to + + align:start position:0% +edges should uh should sum up to + + + align:start position:0% +edges should uh should sum up to +one great + + align:start position:0% +one great + + + align:start position:0% +one great +observation uh it's not quite true + + align:start position:0% +observation uh it's not quite true + + + align:start position:0% +observation uh it's not quite true +though that that holds for the entire + + align:start position:0% +though that that holds for the entire + + + align:start position:0% +though that that holds for the entire +column + + align:start position:0% +column + + + align:start position:0% +column +okay so what happens if we look at the + + align:start position:0% +okay so what happens if we look at the + + + align:start position:0% +okay so what happens if we look at the +next + + align:start position:0% +next + + + align:start position:0% +next +column so given that Monty hides the + + align:start position:0% +column so given that Monty hides the + + + align:start position:0% +column so given that Monty hides the +prize behind door P what's the + + align:start position:0% +prize behind door P what's the + + + align:start position:0% +prize behind door P what's the +probability that Marilyn then picks + + align:start position:0% + + + + align:start position:0% + +DP any + + align:start position:0% +DP any + + + align:start position:0% +DP any +ideas yeah one3 + + align:start position:0% +ideas yeah one3 + + + align:start position:0% +ideas yeah one3 +yeah so Marilyn picks this with + + align:start position:0% +yeah so Marilyn picks this with + + + align:start position:0% +yeah so Marilyn picks this with +probability 1/3 right like Marilyn + + align:start position:0% +probability 1/3 right like Marilyn + + + align:start position:0% +probability 1/3 right like Marilyn +doesn't know or care what's going on + + align:start position:0% +doesn't know or care what's going on + + + align:start position:0% +doesn't know or care what's going on +with where the prize actually is + + align:start position:0% +with where the prize actually is + + + align:start position:0% +with where the prize actually is +she's just picking each door with + + align:start position:0% +she's just picking each door with + + + align:start position:0% +she's just picking each door with +probability 1/3 you know regardless Okay + + align:start position:0% +probability 1/3 you know regardless Okay + + + align:start position:0% +probability 1/3 you know regardless Okay +so we've kind of got the same thing + + align:start position:0% +so we've kind of got the same thing + + + align:start position:0% +so we've kind of got the same thing +going on + + align:start position:0% +going on + + + align:start position:0% +going on +here each of these three edges has + + align:start position:0% +here each of these three edges has + + + align:start position:0% +here each of these three edges has +probability + + align:start position:0% +probability + + + align:start position:0% +probability +1/3 but now the same holds true for this + + align:start position:0% +1/3 but now the same holds true for this + + + align:start position:0% +1/3 but now the same holds true for this +Branch right if Monty has hidden the + + align:start position:0% +Branch right if Monty has hidden the + + + align:start position:0% +Branch right if Monty has hidden the +door or hidden the prize behind door G + + align:start position:0% +door or hidden the prize behind door G + + + align:start position:0% +door or hidden the prize behind door G +you know the same logic applies right + + align:start position:0% +you know the same logic applies right + + + align:start position:0% +you know the same logic applies right +Marilyn's still picking each door with + + align:start position:0% +Marilyn's still picking each door with + + + align:start position:0% +Marilyn's still picking each door with +probability + + align:start position:0% +probability + + + align:start position:0% +probability +1/3 Okay so we've also got 1/3 here 1/3 + + align:start position:0% +1/3 Okay so we've also got 1/3 here 1/3 + + + align:start position:0% +1/3 Okay so we've also got 1/3 here 1/3 +here 1/3 here okay so it's not quite + + align:start position:0% +here 1/3 here okay so it's not quite + + + align:start position:0% +here 1/3 here okay so it's not quite +that all of the uh edges in a column add + + align:start position:0% +that all of the uh edges in a column add + + + align:start position:0% +that all of the uh edges in a column add +up to one but all of the edges coming + + align:start position:0% +up to one but all of the edges coming + + + align:start position:0% +up to one but all of the edges coming +out of a single vertex add up to one + + align:start position:0% +out of a single vertex add up to one + + + align:start position:0% +out of a single vertex add up to one +okay and same thing for this bottom + + align:start position:0% + + + + align:start position:0% + +Branch + + align:start position:0% +Branch + + + align:start position:0% +Branch +okay now what about the last + + align:start position:0% + + + + align:start position:0% + +column if Monty has hidden the prize + + align:start position:0% +column if Monty has hidden the prize + + + align:start position:0% +column if Monty has hidden the prize +behind door p and Marilyn has also + + align:start position:0% +behind door p and Marilyn has also + + + align:start position:0% +behind door p and Marilyn has also +picked door p + + align:start position:0% +picked door p + + + align:start position:0% +picked door p +what's the probability that we get to + + align:start position:0% +what's the probability that we get to + + + align:start position:0% +what's the probability that we get to +outcome + + align:start position:0% + + + + align:start position:0% + +PPG + + align:start position:0% +PPG + + + align:start position:0% +PPG +yeah one half that's + + align:start position:0% +yeah one half that's + + + align:start position:0% +yeah one half that's +right + + align:start position:0% +right + + + align:start position:0% +right +okay and it's also half whoops that's + + align:start position:0% +okay and it's also half whoops that's + + + align:start position:0% +okay and it's also half whoops that's +not a two that's a three there we go 1 + + align:start position:0% +not a two that's a three there we go 1 + + + align:start position:0% +not a two that's a three there we go 1 +half okay so probability one half for + + align:start position:0% +half okay so probability one half for + + + align:start position:0% +half okay so probability one half for +each of them okay we've got probability + + align:start position:0% +each of them okay we've got probability + + + align:start position:0% +each of them okay we've got probability +one/ half that uh that the zon behind G + + align:start position:0% +one/ half that uh that the zon behind G + + + align:start position:0% +one/ half that uh that the zon behind G +is revealed probability one half that + + align:start position:0% +is revealed probability one half that + + + align:start position:0% +is revealed probability one half that +the zon behind s is revealed + + align:start position:0% +the zon behind s is revealed + + + align:start position:0% +the zon behind s is revealed +okay and as we were saying before uh if + + align:start position:0% +okay and as we were saying before uh if + + + align:start position:0% +okay and as we were saying before uh if +Monty hides the prize behind p and + + align:start position:0% +Monty hides the prize behind p and + + + align:start position:0% +Monty hides the prize behind p and +Marilyn picks G Monty now has no choice + + align:start position:0% +Marilyn picks G Monty now has no choice + + + align:start position:0% +Marilyn picks G Monty now has no choice +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we're just going to say that this is + + align:start position:0% +so we're just going to say that this is + + + align:start position:0% +so we're just going to say that this is +probability + + align:start position:0% +probability + + + align:start position:0% +probability +one okay and same with this one this one + + align:start position:0% +one okay and same with this one this one + + + align:start position:0% +one okay and same with this one this one +also has one uh + + align:start position:0% +also has one uh + + + align:start position:0% +also has one uh +PSG + + align:start position:0% +PSG + + + align:start position:0% +PSG +okay and similarly for the other three + + align:start position:0% +okay and similarly for the other three + + + align:start position:0% +okay and similarly for the other three +branches so we've got one 1/2 1/2 one + + align:start position:0% +branches so we've got one 1/2 1/2 one + + + align:start position:0% +branches so we've got one 1/2 1/2 one +one one 1/2 + + align:start position:0% + + + + align:start position:0% + +and2 + + align:start position:0% + + + + align:start position:0% + +okay so did these Edge probabilities + + align:start position:0% +okay so did these Edge probabilities + + + align:start position:0% +okay so did these Edge probabilities +make sense to + + align:start position:0% + + + + align:start position:0% + +everybody okay so now remember what the + + align:start position:0% +everybody okay so now remember what the + + + align:start position:0% +everybody okay so now remember what the +probability function was right right uh + + align:start position:0% +probability function was right right uh + + + align:start position:0% +probability function was right right uh +we have to assign a probability to every + + align:start position:0% +we have to assign a probability to every + + + align:start position:0% +we have to assign a probability to every +outcome okay the outcomes right are the + + align:start position:0% +outcome okay the outcomes right are the + + + align:start position:0% +outcome okay the outcomes right are the +leaves of our tree not the + + align:start position:0% +leaves of our tree not the + + + align:start position:0% +leaves of our tree not the +edges okay so what is the + + align:start position:0% +edges okay so what is the + + + align:start position:0% +edges okay so what is the +probability that we end up with outcome + + align:start position:0% +probability that we end up with outcome + + + align:start position:0% +probability that we end up with outcome +PPG for instance + + align:start position:0% + + + + align:start position:0% + +yeah 1 18th and how are you getting + + align:start position:0% + + + + align:start position:0% + +that yeah 1/3 * 1/3 * + + align:start position:0% +that yeah 1/3 * 1/3 * + + + align:start position:0% +that yeah 1/3 * 1/3 * +1/3 okay we're going to multiply + + align:start position:0% +1/3 okay we're going to multiply + + + align:start position:0% +1/3 okay we're going to multiply +together all of the + + align:start position:0% +together all of the + + + align:start position:0% +together all of the +probabilities along the path from the + + align:start position:0% +probabilities along the path from the + + + align:start position:0% +probabilities along the path from the +route to that to that + + align:start position:0% +route to that to that + + + align:start position:0% +route to that to that +leaf okay so Monty hides the prize + + align:start position:0% +leaf okay so Monty hides the prize + + + align:start position:0% +leaf okay so Monty hides the prize +behind door p with probability + + align:start position:0% +behind door p with probability + + + align:start position:0% +behind door p with probability +1/3 and then you know conditioned on + + align:start position:0% +1/3 and then you know conditioned on + + + align:start position:0% +1/3 and then you know conditioned on +that happening + + align:start position:0% +that happening + + + align:start position:0% +that happening +Marilyn then picks door p with + + align:start position:0% +Marilyn then picks door p with + + + align:start position:0% +Marilyn then picks door p with +probability 1/3 so then there's + + align:start position:0% +probability 1/3 so then there's + + + align:start position:0% +probability 1/3 so then there's +probability 1 nth that we make it to + + align:start position:0% +probability 1 nth that we make it to + + + align:start position:0% +probability 1 nth that we make it to +this vertex + + align:start position:0% +this vertex + + + align:start position:0% +this vertex +here and now that one ninth is split + + align:start position:0% +here and now that one ninth is split + + + align:start position:0% +here and now that one ninth is split +again among these two outcomes okay does + + align:start position:0% +again among these two outcomes okay does + + + align:start position:0% +again among these two outcomes okay does +that make sense to + + align:start position:0% +that make sense to + + + align:start position:0% +that make sense to +everybody so if we do that for every + + align:start position:0% +everybody so if we do that for every + + + align:start position:0% +everybody so if we do that for every +outcome we've got uh oops 1/ 18th not + + align:start position:0% +outcome we've got uh oops 1/ 18th not + + + align:start position:0% +outcome we've got uh oops 1/ 18th not +1/8 another 1/ 18th for + + align:start position:0% +1/8 another 1/ 18th for + + + align:start position:0% +1/8 another 1/ 18th for +PPS then what about pgs + + align:start position:0% + + + + align:start position:0% + +yeah yeah it's just one + + align:start position:0% +yeah yeah it's just one + + + align:start position:0% +yeah yeah it's just one +nth + + align:start position:0% +nth + + + align:start position:0% +nth +okay so same deal for the first two + + align:start position:0% +okay so same deal for the first two + + + align:start position:0% +okay so same deal for the first two +layers but then in the last layer we've + + align:start position:0% +layers but then in the last layer we've + + + align:start position:0% +layers but then in the last layer we've +just got a probability of one we don't + + align:start position:0% +just got a probability of one we don't + + + align:start position:0% +just got a probability of one we don't +have to split again so it's it remains + + align:start position:0% +have to split again so it's it remains + + + align:start position:0% +have to split again so it's it remains +at 1 + + align:start position:0% +at 1 + + + align:start position:0% +at 1 +nth + + align:start position:0% +nth + + + align:start position:0% +nth +okay and you know once again we can + + align:start position:0% +okay and you know once again we can + + + align:start position:0% +okay and you know once again we can +continue we've got uh 1 nth here 11 + + align:start position:0% +continue we've got uh 1 nth here 11 + + + align:start position:0% +continue we've got uh 1 nth here 11 +18th 11 18th 1 n + + align:start position:0% + + + + align:start position:0% + +and we can + + align:start position:0% + + + + align:start position:0% + +continue + + align:start position:0% + + + + align:start position:0% + +okay so we're going to justify this more + + align:start position:0% +okay so we're going to justify this more + + + align:start position:0% +okay so we're going to justify this more +formally later but uh you know for now + + align:start position:0% +formally later but uh you know for now + + + align:start position:0% +formally later but uh you know for now +just take it on faith that in order to + + align:start position:0% +just take it on faith that in order to + + + align:start position:0% +just take it on faith that in order to +get the uh probability of an outcome uh + + align:start position:0% +get the uh probability of an outcome uh + + + align:start position:0% +get the uh probability of an outcome uh +you multiply together the probabilities + + align:start position:0% +you multiply together the probabilities + + + align:start position:0% +you multiply together the probabilities +along the path to that outcome okay like + + align:start position:0% +along the path to that outcome okay like + + + align:start position:0% +along the path to that outcome okay like +hopefully it at least makes intuitive + + align:start position:0% +hopefully it at least makes intuitive + + + align:start position:0% +hopefully it at least makes intuitive +sense uh but you know we'll we'll reason + + align:start position:0% +sense uh but you know we'll we'll reason + + + align:start position:0% +sense uh but you know we'll we'll reason +about it more formally later + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% + + + + align:start position:0% + +now we have our sample space we have our + + align:start position:0% +now we have our sample space we have our + + + align:start position:0% +now we have our sample space we have our +probability function so we've got the + + align:start position:0% +probability function so we've got the + + + align:start position:0% +probability function so we've got the +entire probability space that we're that + + align:start position:0% +entire probability space that we're that + + + align:start position:0% +entire probability space that we're that +we're trying to reason about + + align:start position:0% +we're trying to reason about + + + align:start position:0% +we're trying to reason about +okay uh the next thing that we want + + align:start position:0% + + + + align:start position:0% + +we want to figure out what what we call + + align:start position:0% +we want to figure out what what we call + + + align:start position:0% +we want to figure out what what we call +events we care + + align:start position:0% +events we care + + + align:start position:0% +events we care +about + + align:start position:0% + + + + align:start position:0% + +okay so an event is simply a + + align:start position:0% +okay so an event is simply a + + + align:start position:0% +okay so an event is simply a +subset of our sample + + align:start position:0% + + + + align:start position:0% + +space okay + + align:start position:0% +space okay + + + align:start position:0% +space okay +so it's it's a set of + + align:start position:0% + + + + align:start position:0% + +outcomes + + align:start position:0% +outcomes + + + align:start position:0% +outcomes +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so up here right we could think about + + align:start position:0% +so up here right we could think about + + + align:start position:0% +so up here right we could think about +the event that Marilyn + + align:start position:0% +the event that Marilyn + + + align:start position:0% +the event that Marilyn +wins + + align:start position:0% +wins + + + align:start position:0% +wins +okay so what is that formally as a set + + align:start position:0% + + + + align:start position:0% + +yeah yeah exactly so the answer was it's + + align:start position:0% +yeah yeah exactly so the answer was it's + + + align:start position:0% +yeah yeah exactly so the answer was it's +the subset of events where X and Y are + + align:start position:0% + + + + align:start position:0% + +different so the notation that we + + align:start position:0% +different so the notation that we + + + align:start position:0% +different so the notation that we +usually use for events is is the + + align:start position:0% +usually use for events is is the + + + align:start position:0% +usually use for events is is the +following + + align:start position:0% +following + + + align:start position:0% +following +okay we you know put the description of + + align:start position:0% +okay we you know put the description of + + + align:start position:0% +okay we you know put the description of +the event in square + + align:start position:0% + + + + align:start position:0% + +brackets so this is just going to be the + + align:start position:0% +brackets so this is just going to be the + + + align:start position:0% +brackets so this is just going to be the +set right + + align:start position:0% + + + + align:start position:0% + +pgs + + align:start position:0% +pgs + + + align:start position:0% +pgs +PS + + align:start position:0% + + + + align:start position:0% + +g g + + align:start position:0% + + + + align:start position:0% + +PS + + align:start position:0% + + + + align:start position:0% + +GSP uh s + + align:start position:0% + + + + align:start position:0% + +GP s + + align:start position:0% +GP s + + + align:start position:0% +GP s +PG + + align:start position:0% + + + + align:start position:0% + +okay so the six outcomes right where uh + + align:start position:0% +okay so the six outcomes right where uh + + + align:start position:0% +okay so the six outcomes right where uh +Marilyn and Monty originally pick + + align:start position:0% +Marilyn and Monty originally pick + + + align:start position:0% +Marilyn and Monty originally pick +different doors and then Monty is forced + + align:start position:0% +different doors and then Monty is forced + + + align:start position:0% +different doors and then Monty is forced +to reveal the uh the last + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% +one + + + align:start position:0% +one +okay similarly we could also Define you + + align:start position:0% +okay similarly we could also Define you + + + align:start position:0% +okay similarly we could also Define you +know other events like uh you know + + align:start position:0% +know other events like uh you know + + + align:start position:0% +know other events like uh you know +uh Monty + + align:start position:0% + + + + align:start position:0% + +opens uh door + + align:start position:0% +opens uh door + + + align:start position:0% +opens uh door +P + + align:start position:0% +P + + + align:start position:0% +P +okay so this is going to be the + + align:start position:0% +okay so this is going to be the + + + align:start position:0% +okay so this is going to be the +Set uh g g + + align:start position:0% +Set uh g g + + + align:start position:0% +Set uh g g +p uh s s + + align:start position:0% +p uh s s + + + align:start position:0% +p uh s s +p + + align:start position:0% +p + + + align:start position:0% +p +uh + + align:start position:0% +uh + + + align:start position:0% +uh +GSP and + + align:start position:0% + + + + align:start position:0% + +SGP + + align:start position:0% +SGP + + + align:start position:0% +SGP +okay so does this make sense to + + align:start position:0% +okay so does this make sense to + + + align:start position:0% +okay so does this make sense to +everybody like any subset of + + align:start position:0% +everybody like any subset of + + + align:start position:0% +everybody like any subset of +events uh or sorry any subset of + + align:start position:0% +events uh or sorry any subset of + + + align:start position:0% +events uh or sorry any subset of +outcomes is called an + + align:start position:0% +outcomes is called an + + + align:start position:0% +outcomes is called an +event uh we can kind of take our English + + align:start position:0% +event uh we can kind of take our English + + + align:start position:0% +event uh we can kind of take our English +description and then look at which + + align:start position:0% +description and then look at which + + + align:start position:0% +description and then look at which +actual outcomes uh this corresponds + + align:start position:0% +actual outcomes uh this corresponds + + + align:start position:0% +actual outcomes uh this corresponds +to + + align:start position:0% + + + + align:start position:0% + +okay so what we want to do now + + align:start position:0% +okay so what we want to do now + + + align:start position:0% +okay so what we want to do now +is figure out what event we care about + + align:start position:0% +is figure out what event we care about + + + align:start position:0% +is figure out what event we care about +or possibly what events okay so what are + + align:start position:0% +or possibly what events okay so what are + + + align:start position:0% +or possibly what events okay so what are +the events that we care about for this + + align:start position:0% + + + + align:start position:0% + +problem anybody + + align:start position:0% + + + + align:start position:0% + +what was the probability that we're + + align:start position:0% +what was the probability that we're + + + align:start position:0% +what was the probability that we're +trying to compute + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +pardon yeah so that the events Marilyn + + align:start position:0% +pardon yeah so that the events Marilyn + + + align:start position:0% +pardon yeah so that the events Marilyn +wins and Marilyn loses right these are + + align:start position:0% +wins and Marilyn loses right these are + + + align:start position:0% +wins and Marilyn loses right these are +the events we care about okay so uh you + + align:start position:0% +the events we care about okay so uh you + + + align:start position:0% +the events we care about okay so uh you +know we could + + align:start position:0% +know we could + + + align:start position:0% +know we could +say Marilyn + + align:start position:0% + + + + align:start position:0% + +loses is you + + align:start position:0% +loses is you + + + align:start position:0% +loses is you +know the compx + + align:start position:0% +know the compx + + + align:start position:0% +know the compx +of Maryland WIS which we denote with an + + align:start position:0% +of Maryland WIS which we denote with an + + + align:start position:0% +of Maryland WIS which we denote with an +over + + align:start position:0% +over + + + align:start position:0% +over +bar + + align:start position:0% +bar + + + align:start position:0% +bar +okay so these are the two events we care + + align:start position:0% + + + + align:start position:0% + +about + + align:start position:0% + + + + align:start position:0% + +okay so the final step + + align:start position:0% + + + + align:start position:0% + +is to compute the answer okay we've + + align:start position:0% +is to compute the answer okay we've + + + align:start position:0% +is to compute the answer okay we've +identified the event that we care + + align:start position:0% +identified the event that we care + + + align:start position:0% +identified the event that we care +about okay so now we want to figure out + + align:start position:0% +about okay so now we want to figure out + + + align:start position:0% +about okay so now we want to figure out +the probability that that event + + align:start position:0% + + + + align:start position:0% + +occurs okay so we can extend the + + align:start position:0% +occurs okay so we can extend the + + + align:start position:0% +occurs okay so we can extend the +probability function to + + align:start position:0% + + + + align:start position:0% + +events so if e is an event right we can + + align:start position:0% +events so if e is an event right we can + + + align:start position:0% +events so if e is an event right we can +think about the probability of an event + + align:start position:0% +think about the probability of an event + + + align:start position:0% +think about the probability of an event +just as we think about the probability + + align:start position:0% +just as we think about the probability + + + align:start position:0% +just as we think about the probability +of + + align:start position:0% +of + + + align:start position:0% +of +outcomes and we're going to Define this + + align:start position:0% +outcomes and we're going to Define this + + + align:start position:0% +outcomes and we're going to Define this +to + + align:start position:0% +to + + + align:start position:0% +to +be the + + align:start position:0% + + + + align:start position:0% + +sum over all outcomes Omega and + + align:start position:0% +sum over all outcomes Omega and + + + align:start position:0% +sum over all outcomes Omega and +E of the probability of + + align:start position:0% + + + + align:start position:0% + +Omega + + align:start position:0% +Omega + + + align:start position:0% +Omega +okay so you know hopefully intuitively + + align:start position:0% +okay so you know hopefully intuitively + + + align:start position:0% +okay so you know hopefully intuitively +that makes sense right like all of these + + align:start position:0% +that makes sense right like all of these + + + align:start position:0% +that makes sense right like all of these +outcomes uh you know exactly one outcome + + align:start position:0% +outcomes uh you know exactly one outcome + + + align:start position:0% +outcomes uh you know exactly one outcome +is is going to happen so if we're trying + + align:start position:0% +is is going to happen so if we're trying + + + align:start position:0% +is is going to happen so if we're trying +to figure out the probability that you + + align:start position:0% +to figure out the probability that you + + + align:start position:0% +to figure out the probability that you +know one of a set of outcomes happens + + align:start position:0% +know one of a set of outcomes happens + + + align:start position:0% +know one of a set of outcomes happens +it's just going to be you know the the + + align:start position:0% +it's just going to be you know the the + + + align:start position:0% +it's just going to be you know the the +sum of the probabilities that that each + + align:start position:0% +sum of the probabilities that that each + + + align:start position:0% +sum of the probabilities that that each +individual one + + align:start position:0% +individual one + + + align:start position:0% +individual one +occurs okay so we know the probabilities + + align:start position:0% +occurs okay so we know the probabilities + + + align:start position:0% +occurs okay so we know the probabilities +of each of the outcomes right that's + + align:start position:0% +of each of the outcomes right that's + + + align:start position:0% +of each of the outcomes right that's +what we just + + align:start position:0% +what we just + + + align:start position:0% +what we just +computed + + align:start position:0% + + + + align:start position:0% + +here so now we can use that to compute + + align:start position:0% +here so now we can use that to compute + + + align:start position:0% +here so now we can use that to compute +the probability of the events we just + + align:start position:0% +the probability of the events we just + + + align:start position:0% +the probability of the events we just +uh we just talked + + align:start position:0% +uh we just talked + + + align:start position:0% +uh we just talked +about + + align:start position:0% +about + + + align:start position:0% +about +okay so what is the probability that + + align:start position:0% +okay so what is the probability that + + + align:start position:0% +okay so what is the probability that +Marilyn + + align:start position:0% + + + + align:start position:0% + +wins so we have our set of outcomes + + align:start position:0% +wins so we have our set of outcomes + + + align:start position:0% +wins so we have our set of outcomes +here what's the probability of each one + + align:start position:0% + + + + align:start position:0% + +oh what's what's the probability of + + align:start position:0% +oh what's what's the probability of + + + align:start position:0% +oh what's what's the probability of +outcome + + align:start position:0% +outcome + + + align:start position:0% +outcome +pgs yeah one n yeah that one's written + + align:start position:0% +pgs yeah one n yeah that one's written + + + align:start position:0% +pgs yeah one n yeah that one's written +up up there + + align:start position:0% + + + + align:start position:0% + +explicitly uh what about the probability + + align:start position:0% +explicitly uh what about the probability + + + align:start position:0% +explicitly uh what about the probability +of PSV + + align:start position:0% + + + + align:start position:0% + +same 1 + + align:start position:0% + + + + align:start position:0% + +nth okay what about the probability of + + align:start position:0% +nth okay what about the probability of + + + align:start position:0% +nth okay what about the probability of +GPS also a nth right like you know all + + align:start position:0% +GPS also a nth right like you know all + + + align:start position:0% +GPS also a nth right like you know all +of these are + + align:start position:0% +of these are + + + align:start position:0% +of these are +symmetric + + align:start position:0% + + + + align:start position:0% + +okay what's that + + align:start position:0% +okay what's that + + + align:start position:0% +okay what's that +2/3 okay + + align:start position:0% +2/3 okay + + + align:start position:0% +2/3 okay +so we've got six events or six outcomes + + align:start position:0% +so we've got six events or six outcomes + + + align:start position:0% +so we've got six events or six outcomes +Each of which occurs with probability 1 + + align:start position:0% +Each of which occurs with probability 1 + + + align:start position:0% +Each of which occurs with probability 1 +nth so if you add those all together you + + align:start position:0% +nth so if you add those all together you + + + align:start position:0% +nth so if you add those all together you +get + + align:start position:0% +get + + + align:start position:0% +get +2/3 okay so this seems to support you + + align:start position:0% +2/3 okay so this seems to support you + + + align:start position:0% +2/3 okay so this seems to support you +know what we found + + align:start position:0% +know what we found + + + align:start position:0% +know what we found +empirically right Marilyn wins with + + align:start position:0% +empirically right Marilyn wins with + + + align:start position:0% +empirically right Marilyn wins with +better than probability + + align:start position:0% +better than probability + + + align:start position:0% +better than probability +1/2 right the probability that she loses + + align:start position:0% +1/2 right the probability that she loses + + + align:start position:0% +1/2 right the probability that she loses +is going to be the complement of this + + align:start position:0% + + + + align:start position:0% + +okay so it's going to be the uh sum of + + align:start position:0% +okay so it's going to be the uh sum of + + + align:start position:0% +okay so it's going to be the uh sum of +the probabilities of all of the other + + align:start position:0% +the probabilities of all of the other + + + align:start position:0% +the probabilities of all of the other +outcomes right and we said that all + + align:start position:0% +outcomes right and we said that all + + + align:start position:0% +outcomes right and we said that all +probabilities uh should add to one so + + align:start position:0% +probabilities uh should add to one so + + + align:start position:0% +probabilities uh should add to one so +this is going to be you know the + + align:start position:0% +this is going to be you know the + + + align:start position:0% +this is going to be you know the +complement with respect to + + align:start position:0% +complement with respect to + + + align:start position:0% +complement with respect to +one okay so as it turns out Marilyn was + + align:start position:0% +one okay so as it turns out Marilyn was + + + align:start position:0% +one okay so as it turns out Marilyn was +correct okay we didn't have to rely on + + align:start position:0% +correct okay we didn't have to rely on + + + align:start position:0% +correct okay we didn't have to rely on +Intuition or anything like that no + + align:start position:0% +Intuition or anything like that no + + + align:start position:0% +Intuition or anything like that no +ingenious analogies Etc it's just you + + align:start position:0% +ingenious analogies Etc it's just you + + + align:start position:0% +ingenious analogies Etc it's just you +know arithmetic over Q okay and I think + + align:start position:0% +know arithmetic over Q okay and I think + + + align:start position:0% +know arithmetic over Q okay and I think +the the hardest part of this for many + + align:start position:0% +the the hardest part of this for many + + + align:start position:0% +the the hardest part of this for many +people is resisting the temptation to + + align:start position:0% +people is resisting the temptation to + + + align:start position:0% +people is resisting the temptation to +jump jump to some sort of like obvious + + align:start position:0% +jump jump to some sort of like obvious + + + align:start position:0% +jump jump to some sort of like obvious +conclusion right like you know it might + + align:start position:0% +conclusion right like you know it might + + + align:start position:0% +conclusion right like you know it might +be tempting to you know get to the end + + align:start position:0% +be tempting to you know get to the end + + + align:start position:0% +be tempting to you know get to the end +of the tree diagram and be like oh we've + + align:start position:0% +of the tree diagram and be like oh we've + + + align:start position:0% +of the tree diagram and be like oh we've +got six outcomes where Marilyn wins six + + align:start position:0% +got six outcomes where Marilyn wins six + + + align:start position:0% +got six outcomes where Marilyn wins six +where she loses so probably you know 6 + + align:start position:0% +where she loses so probably you know 6 + + + align:start position:0% +where she loses so probably you know 6 +over 12 is2 right so if we actually you + + align:start position:0% +over 12 is2 right so if we actually you + + + align:start position:0% +over 12 is2 right so if we actually you +know set all of that you know intuition + + align:start position:0% +know set all of that you know intuition + + + align:start position:0% +know set all of that you know intuition +aside go through everything formally + + align:start position:0% +aside go through everything formally + + + align:start position:0% +aside go through everything formally +it's all you know quite simple and + + align:start position:0% +it's all you know quite simple and + + + align:start position:0% +it's all you know quite simple and +straightforward + + align:start position:0% +straightforward + + + align:start position:0% +straightforward +okay so that makes sense to + + align:start position:0% + + + + align:start position:0% + +everybody okay so let's move on to a + + align:start position:0% +everybody okay so let's move on to a + + + align:start position:0% +everybody okay so let's move on to a +different + + align:start position:0% +different + + + align:start position:0% +different +example + + align:start position:0% +example + + + align:start position:0% +example +suppose I have three strange dice okay + + align:start position:0% +suppose I have three strange dice okay + + + align:start position:0% +suppose I have three strange dice okay +so excuse my + + align:start position:0% +so excuse my + + + align:start position:0% +so excuse my +drawing whoops nothing + + align:start position:0% +drawing whoops nothing + + + align:start position:0% +drawing whoops nothing +there okay so I've got one die that has + + align:start position:0% +there okay so I've got one die that has + + + align:start position:0% +there okay so I've got one die that has +two written on two of the faces so you + + align:start position:0% +two written on two of the faces so you + + + align:start position:0% +two written on two of the faces so you +know top and bottom uh six written on + + align:start position:0% +know top and bottom uh six written on + + + align:start position:0% +know top and bottom uh six written on +you know these two faces and seven + + align:start position:0% +you know these two faces and seven + + + align:start position:0% +you know these two faces and seven +written on those two faces okay + + align:start position:0% +written on those two faces okay + + + align:start position:0% +written on those two faces okay +hopefully that you know looks vaguely + + align:start position:0% +hopefully that you know looks vaguely + + + align:start position:0% +hopefully that you know looks vaguely +cubical okay I've got a second ey which + + align:start position:0% +cubical okay I've got a second ey which + + + align:start position:0% +cubical okay I've got a second ey which +is + + align:start position:0% + + + + align:start position:0% + +similar uh but instead of 2 six and + + align:start position:0% +similar uh but instead of 2 six and + + + align:start position:0% +similar uh but instead of 2 six and +seven I've got 1 5 and nine then I've + + align:start position:0% +seven I've got 1 5 and nine then I've + + + align:start position:0% +seven I've got 1 5 and nine then I've +got a third one + + align:start position:0% + + + + align:start position:0% + +which has three four and + + align:start position:0% +which has three four and + + + align:start position:0% +which has three four and +eight + + align:start position:0% +eight + + + align:start position:0% +eight +okay so consider the following game + + align:start position:0% +okay so consider the following game + + + align:start position:0% +okay so consider the following game +okay uh I pick a die right now you pick + + align:start position:0% +okay uh I pick a die right now you pick + + + align:start position:0% +okay uh I pick a die right now you pick +one of the uh other + + align:start position:0% +one of the uh other + + + align:start position:0% +one of the uh other +dies after or dice after seeing what I + + align:start position:0% +dies after or dice after seeing what I + + + align:start position:0% +dies after or dice after seeing what I +pick and we each roll our dice okay and + + align:start position:0% +pick and we each roll our dice okay and + + + align:start position:0% +pick and we each roll our dice okay and +whoever gets the higher number + + align:start position:0% +whoever gets the higher number + + + align:start position:0% +whoever gets the higher number +wins okay + + align:start position:0% +wins okay + + + align:start position:0% +wins okay +who should win should I win or should + + align:start position:0% +who should win should I win or should + + + align:start position:0% +who should win should I win or should +you + + align:start position:0% +you + + + align:start position:0% +you +win who thinks I + + align:start position:0% + + + + align:start position:0% + +win okay who thinks you + + align:start position:0% + + + + align:start position:0% + +win who thinks we should just uh you + + align:start position:0% +win who thinks we should just uh you + + + align:start position:0% +win who thinks we should just uh you +know do the tree diagram and figure it + + align:start position:0% +know do the tree diagram and figure it + + + align:start position:0% +know do the tree diagram and figure it +out yeah good call okay so let's let's + + align:start position:0% +out yeah good call okay so let's let's + + + align:start position:0% +out yeah good call okay so let's let's +call these dice like + + align:start position:0% +call these dice like + + + align:start position:0% +call these dice like +r g and B okay + + align:start position:0% +r g and B okay + + + align:start position:0% +r g and B okay +so yeah let's let's draw out our tree + + align:start position:0% +so yeah let's let's draw out our tree + + + align:start position:0% +so yeah let's let's draw out our tree +diagram + + align:start position:0% +diagram + + + align:start position:0% +diagram +okay so what happens if say I pick the + + align:start position:0% +okay so what happens if say I pick the + + + align:start position:0% +okay so what happens if say I pick the +red D and uh you pick the green + + align:start position:0% +red D and uh you pick the green + + + align:start position:0% +red D and uh you pick the green +Dy okay who should win let's let's + + align:start position:0% +Dy okay who should win let's let's + + + align:start position:0% +Dy okay who should win let's let's +see so we've + + align:start position:0% +see so we've + + + align:start position:0% +see so we've +got when I roll my die right there are + + align:start position:0% +got when I roll my die right there are + + + align:start position:0% +got when I roll my die right there are +three possibilities I could either get a + + align:start position:0% +three possibilities I could either get a + + + align:start position:0% +three possibilities I could either get a +two a six or a seven + + align:start position:0% + + + + align:start position:0% + +and now you roll the green D and you + + align:start position:0% +and now you roll the green D and you + + + align:start position:0% +and now you roll the green D and you +could have either a one a five or a + + align:start position:0% +could have either a one a five or a + + + align:start position:0% +could have either a one a five or a +nine not minus 5 five + + align:start position:0% +nine not minus 5 five + + + align:start position:0% +nine not minus 5 five +1 5 9 + + align:start position:0% +1 5 9 + + + align:start position:0% +1 5 9 + + align:start position:0% + + + align:start position:0% +five + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +okay and now what is the probability or + + align:start position:0% +okay and now what is the probability or + + + align:start position:0% +okay and now what is the probability or +sorry what what are the uh what are the + + align:start position:0% +sorry what what are the uh what are the + + + align:start position:0% +sorry what what are the uh what are the +outcomes + + align:start position:0% +outcomes + + + align:start position:0% +outcomes +we have nine leaves so nine + + align:start position:0% +we have nine leaves so nine + + + align:start position:0% +we have nine leaves so nine +outcomes how are we going to represent + + align:start position:0% + + + + align:start position:0% + +them well we can do it basically the + + align:start position:0% +them well we can do it basically the + + + align:start position:0% +them well we can do it basically the +same as how we uh represented them up + + align:start position:0% +same as how we uh represented them up + + + align:start position:0% +same as how we uh represented them up +here right we can uh just look at a + + align:start position:0% +here right we can uh just look at a + + + align:start position:0% +here right we can uh just look at a +tupal of uh Edge labels okay so our some + + align:start position:0% +tupal of uh Edge labels okay so our some + + + align:start position:0% +tupal of uh Edge labels okay so our some +space is going to be the Set uh + + align:start position:0% + + + + align:start position:0% + +267 uh cartisian product with uh + + align:start position:0% +267 uh cartisian product with uh + + + align:start position:0% +267 uh cartisian product with uh +159 okay so this is going to be ordered + + align:start position:0% +159 okay so this is going to be ordered + + + align:start position:0% +159 okay so this is going to be ordered +pairs where the first element is one of + + align:start position:0% +pairs where the first element is one of + + + align:start position:0% +pairs where the first element is one of +these three things and the second is one + + align:start position:0% +these three things and the second is one + + + align:start position:0% +these three things and the second is one +of these three things okay so this one + + align:start position:0% +of these three things okay so this one + + + align:start position:0% +of these three things okay so this one +for instance is 2 comma 1 this one is 2A + + align:start position:0% +for instance is 2 comma 1 this one is 2A + + + align:start position:0% +for instance is 2 comma 1 this one is 2A +5 Etc + + align:start position:0% + + + + align:start position:0% + +okay now what are the probabilities on + + align:start position:0% +okay now what are the probabilities on + + + align:start position:0% +okay now what are the probabilities on +each + + align:start position:0% + + + + align:start position:0% + +Edge yeah 1 + + align:start position:0% +Edge yeah 1 + + + align:start position:0% +Edge yeah 1 +nth uh so those are the uh probabilities + + align:start position:0% +nth uh so those are the uh probabilities + + + align:start position:0% +nth uh so those are the uh probabilities +on the outcomes yeah one3 on each + + align:start position:0% +on the outcomes yeah one3 on each + + + align:start position:0% +on the outcomes yeah one3 on each +Edge + + align:start position:0% + + + + align:start position:0% + +right okay so when I roll my die I've + + align:start position:0% +right okay so when I roll my die I've + + + align:start position:0% +right okay so when I roll my die I've +got a one3 chance each of getting two + + align:start position:0% +got a one3 chance each of getting two + + + align:start position:0% +got a one3 chance each of getting two +six or seven when you roll yours you've + + align:start position:0% +six or seven when you roll yours you've + + + align:start position:0% +six or seven when you roll yours you've +got a 1/3 chance each of getting five or + + align:start position:0% +got a 1/3 chance each of getting five or + + + align:start position:0% +got a 1/3 chance each of getting five or +n + + align:start position:0% +n + + + align:start position:0% +n +okay and you know it's going to be the + + align:start position:0% +okay and you know it's going to be the + + + align:start position:0% +okay and you know it's going to be the +same for the other two + + align:start position:0% +same for the other two + + + align:start position:0% +same for the other two +branches so when we multiply together + + align:start position:0% +branches so when we multiply together + + + align:start position:0% +branches so when we multiply together +the probabilities uh along paths to + + align:start position:0% +the probabilities uh along paths to + + + align:start position:0% +the probabilities uh along paths to +leaves we get 1 nth for every + + align:start position:0% +leaves we get 1 nth for every + + + align:start position:0% +leaves we get 1 nth for every +outcome + + align:start position:0% +outcome + + + align:start position:0% +outcome +okay so when you have a probability + + align:start position:0% +okay so when you have a probability + + + align:start position:0% +okay so when you have a probability +space like this that's particularly nice + + align:start position:0% +space like this that's particularly nice + + + align:start position:0% +space like this that's particularly nice +this is what we call a uniform + + align:start position:0% +this is what we call a uniform + + + align:start position:0% +this is what we call a uniform +probability + + align:start position:0% +probability + + + align:start position:0% +probability +space + + align:start position:0% +space + + + align:start position:0% +space +uh so let's + + align:start position:0% +uh so let's + + + align:start position:0% +uh so let's +say s comma p r so this is our + + align:start position:0% +say s comma p r so this is our + + + align:start position:0% +say s comma p r so this is our +probability space is + + align:start position:0% + + + + align:start position:0% + +uniform if uh PR is + + align:start position:0% + + + + align:start position:0% + +constant okay so in this this case it's + + align:start position:0% +constant okay so in this this case it's + + + align:start position:0% +constant okay so in this this case it's +a constant function that Maps every + + align:start position:0% +a constant function that Maps every + + + align:start position:0% +a constant function that Maps every +outcome to a probability of 1 nth okay + + align:start position:0% +outcome to a probability of 1 nth okay + + + align:start position:0% +outcome to a probability of 1 nth okay +so it's a uniform probability + + align:start position:0% +so it's a uniform probability + + + align:start position:0% +so it's a uniform probability +space okay and uh uniform spaces are + + align:start position:0% +space okay and uh uniform spaces are + + + align:start position:0% +space okay and uh uniform spaces are +particularly nice because you know we + + align:start position:0% +particularly nice because you know we + + + align:start position:0% +particularly nice because you know we +don't even have to worry about the + + align:start position:0% +don't even have to worry about the + + + align:start position:0% +don't even have to worry about the +addition that we were doing before like + + align:start position:0% +addition that we were doing before like + + + align:start position:0% +addition that we were doing before like +in order to figure out probabilities of + + align:start position:0% +in order to figure out probabilities of + + + align:start position:0% +in order to figure out probabilities of +uh of events you just count up how many + + align:start position:0% +uh of events you just count up how many + + + align:start position:0% +uh of events you just count up how many +outcomes are in the event and then + + align:start position:0% +outcomes are in the event and then + + + align:start position:0% +outcomes are in the event and then +divide by the total number of + + align:start position:0% +divide by the total number of + + + align:start position:0% +divide by the total number of +outcomes okay so it just becomes a + + align:start position:0% +outcomes okay so it just becomes a + + + align:start position:0% +outcomes okay so it just becomes a +counting problem + + align:start position:0% + + + + align:start position:0% + +so using that what's the probability + + align:start position:0% +so using that what's the probability + + + align:start position:0% +so using that what's the probability +that red + + align:start position:0% + + + + align:start position:0% + +wins + + align:start position:0% +wins + + + align:start position:0% +wins +yeah 5 9ths + + align:start position:0% + + + + align:start position:0% + +yeah so let's break this down a bit so + + align:start position:0% +yeah so let's break this down a bit so + + + align:start position:0% +yeah so let's break this down a bit so +we're looking at the probability of the + + align:start position:0% +we're looking at the probability of the + + + align:start position:0% +we're looking at the probability of the +set + + align:start position:0% +set + + + align:start position:0% +set +right 2 comma 1 red wins 6165 red wins + + align:start position:0% +right 2 comma 1 red wins 6165 red wins + + + align:start position:0% +right 2 comma 1 red wins 6165 red wins +and 7175 red wins + + align:start position:0% +and 7175 red wins + + + align:start position:0% +and 7175 red wins +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +21 uh + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% + + align:start position:0% + + + align:start position:0% + + align:start position:0% + + + align:start position:0% +75 we have five of + + align:start position:0% +75 we have five of + + + align:start position:0% +75 we have five of +these so + + align:start position:0% +these so + + + align:start position:0% +these so +that's 5 over 9 + + align:start position:0% + + + + align:start position:0% + +okay now what if instead we had red + + align:start position:0% +okay now what if instead we had red + + + align:start position:0% +okay now what if instead we had red +versus blue instead of red versus green + + align:start position:0% + + + + align:start position:0% + +so if instead of red versus green we + + align:start position:0% +so if instead of red versus green we + + + align:start position:0% +so if instead of red versus green we +have red versus blue this column now + + align:start position:0% +have red versus blue this column now + + + align:start position:0% +have red versus blue this column now +gets replaced with 348 instead of + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +okay so our tree diagram is going to + + align:start position:0% +okay so our tree diagram is going to + + + align:start position:0% +okay so our tree diagram is going to +look like the + + align:start position:0% +look like the + + + align:start position:0% +look like the +following so we've still got uh 267 + + align:start position:0% +following so we've still got uh 267 + + + align:start position:0% +following so we've still got uh 267 +here but this time this is going to be 3 + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + +348 3 + + align:start position:0% +348 3 + + + align:start position:0% +348 3 + + align:start position:0% + + + align:start position:0% +okay and I'm going to omit the + + align:start position:0% +okay and I'm going to omit the + + + align:start position:0% +okay and I'm going to omit the +probabilities because we just + + align:start position:0% +probabilities because we just + + + align:start position:0% +probabilities because we just +established it's uniform so it's just a + + align:start position:0% +established it's uniform so it's just a + + + align:start position:0% +established it's uniform so it's just a +counting + + align:start position:0% + + + + align:start position:0% + +problem but let's write down the + + align:start position:0% +problem but let's write down the + + + align:start position:0% +problem but let's write down the +outcomes + + align:start position:0% + + + + align:start position:0% + +okay so in how many of these outcomes + + align:start position:0% +okay so in how many of these outcomes + + + align:start position:0% +okay so in how many of these outcomes +does red + + align:start position:0% + + + + align:start position:0% + +win well not this one right not this one + + align:start position:0% +win well not this one right not this one + + + align:start position:0% +win well not this one right not this one +not this one okay so if red rolls two + + align:start position:0% +not this one okay so if red rolls two + + + align:start position:0% +not this one okay so if red rolls two +right all of Blue's uh all of Blue's uh + + align:start position:0% +right all of Blue's uh all of Blue's uh + + + align:start position:0% +right all of Blue's uh all of Blue's uh +numbers are going to be higher so blue + + align:start position:0% +numbers are going to be higher so blue + + + align:start position:0% +numbers are going to be higher so blue +is always going to win uh if red rolls + + align:start position:0% +is always going to win uh if red rolls + + + align:start position:0% +is always going to win uh if red rolls +six uh red wins if blue Rolls three or + + align:start position:0% +six uh red wins if blue Rolls three or + + + align:start position:0% +six uh red wins if blue Rolls three or +four loses if uh blue Rolls eight and + + align:start position:0% +four loses if uh blue Rolls eight and + + + align:start position:0% +four loses if uh blue Rolls eight and +same for + + align:start position:0% + + + + align:start position:0% + +seven + + align:start position:0% +seven + + + align:start position:0% +seven +okay so we have + + align:start position:0% + + + + align:start position:0% + +uh four outcomes where red wins so red + + align:start position:0% +uh four outcomes where red wins so red + + + align:start position:0% +uh four outcomes where red wins so red +wins with probability four + + align:start position:0% + + + + align:start position:0% + +nths + + align:start position:0% +nths + + + align:start position:0% +nths +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we just saw that uh red beats + + align:start position:0% + + + + align:start position:0% + +Green but loses to + + align:start position:0% +Green but loses to + + + align:start position:0% +Green but loses to +Blue what does that tell us about blue + + align:start position:0% +Blue what does that tell us about blue + + + align:start position:0% +Blue what does that tell us about blue +and + + align:start position:0% + + + + align:start position:0% + +green if I pick blue and you pick Green + + align:start position:0% +green if I pick blue and you pick Green + + + align:start position:0% +green if I pick blue and you pick Green +what + + align:start position:0% + + + + align:start position:0% + +happens who wins + + align:start position:0% + + + + align:start position:0% + +yeah Green + + align:start position:0% + + + + align:start position:0% + +why okay so green Beats red + + align:start position:0% +why okay so green Beats red + + + align:start position:0% +why okay so green Beats red +uh so I think we just established that + + align:start position:0% +uh so I think we just established that + + + align:start position:0% +uh so I think we just established that +red beats screen + + align:start position:0% + + + + align:start position:0% + +right so here we've got you know red + + align:start position:0% +right so here we've got you know red + + + align:start position:0% +right so here we've got you know red +beat screen + + align:start position:0% +beat screen + + + align:start position:0% +beat screen +here we've got red loses to + + align:start position:0% + + + + align:start position:0% + +Blue so if we + + align:start position:0% +Blue so if we + + + align:start position:0% +Blue so if we +have uh green and blue who thinks that + + align:start position:0% +have uh green and blue who thinks that + + + align:start position:0% +have uh green and blue who thinks that +green should + + align:start position:0% +green should + + + align:start position:0% +green should +win who thinks that blue should win who + + align:start position:0% +win who thinks that blue should win who + + + align:start position:0% +win who thinks that blue should win who +has absolutely no idea who wants to do + + align:start position:0% +has absolutely no idea who wants to do + + + align:start position:0% +has absolutely no idea who wants to do +the tree + + align:start position:0% +the tree + + + align:start position:0% +the tree +diagram oh still pretty enthusiastic + + align:start position:0% +diagram oh still pretty enthusiastic + + + align:start position:0% +diagram oh still pretty enthusiastic +about that even though we've got some + + align:start position:0% +about that even though we've got some + + + align:start position:0% +about that even though we've got some +intuition that's + + align:start position:0% +intuition that's + + + align:start position:0% +intuition that's +great intuition is bad dis SC the + + align:start position:0% + + + + align:start position:0% + +intuition okay so if we've got green + + align:start position:0% +intuition okay so if we've got green + + + align:start position:0% +intuition okay so if we've got green +versus + + align:start position:0% +versus + + + align:start position:0% +versus +blue so this can be the uh green roll + + align:start position:0% +blue so this can be the uh green roll + + + align:start position:0% +blue so this can be the uh green roll +here we've got uh + + align:start position:0% +here we've got uh + + + align:start position:0% +here we've got uh +159 blue roll can be uh 3 + + align:start position:0% + + + + align:start position:0% + +48 3 + + align:start position:0% + + + + align:start position:0% + +48 3 + + align:start position:0% +48 3 + + + align:start position:0% +48 3 +48 okay + + align:start position:0% +48 okay + + + align:start position:0% +48 okay +uh so in which of these does green win + + align:start position:0% +uh so in which of these does green win + + + align:start position:0% +uh so in which of these does green win +well if green rolls one then you know + + align:start position:0% +well if green rolls one then you know + + + align:start position:0% +well if green rolls one then you know +Green is screwed so all of these are bad + + align:start position:0% +Green is screwed so all of these are bad + + + align:start position:0% +Green is screwed so all of these are bad +for + + align:start position:0% +for + + + align:start position:0% +for +green uh if green rolls + + align:start position:0% +green uh if green rolls + + + align:start position:0% +green uh if green rolls +five well five will beat three and four + + align:start position:0% +five well five will beat three and four + + + align:start position:0% +five well five will beat three and four +but not eight + + align:start position:0% +but not eight + + + align:start position:0% +but not eight +so green wins these two and if green + + align:start position:0% +so green wins these two and if green + + + align:start position:0% +so green wins these two and if green +rolles nine then green Beats you know + + align:start position:0% +rolles nine then green Beats you know + + + align:start position:0% +rolles nine then green Beats you know +whatever blue rolls + + align:start position:0% + + + + align:start position:0% + +okay okay + + align:start position:0% +okay okay + + + align:start position:0% +okay okay +so it looks like green is winning in + + align:start position:0% +so it looks like green is winning in + + + align:start position:0% +so it looks like green is winning in +five of + + align:start position:0% + + + + align:start position:0% + +these + + align:start position:0% + + + + align:start position:0% + +okay so this should + + align:start position:0% +okay so this should + + + align:start position:0% +okay so this should +be like + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +okay so red beats green green Beats blue + + align:start position:0% +okay so red beats green green Beats blue + + + align:start position:0% +okay so red beats green green Beats blue +and blue Beats + + align:start position:0% +and blue Beats + + + align:start position:0% +and blue Beats +red what's gone + + align:start position:0% + + + + align:start position:0% + +wrong + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +pardon yeah so nothing's gone wrong all + + align:start position:0% +pardon yeah so nothing's gone wrong all + + + align:start position:0% +pardon yeah so nothing's gone wrong all +that's gone wrong is uh you know I I + + align:start position:0% +that's gone wrong is uh you know I I + + + align:start position:0% +that's gone wrong is uh you know I I +kind of expected that there would be a + + align:start position:0% +kind of expected that there would be a + + + align:start position:0% +kind of expected that there would be a +linear order on them right right like uh + + align:start position:0% +linear order on them right right like uh + + + align:start position:0% +linear order on them right right like uh +you know if red beats green and green + + align:start position:0% +you know if red beats green and green + + + align:start position:0% +you know if red beats green and green +Beats blue it kind of intuitively makes + + align:start position:0% +Beats blue it kind of intuitively makes + + + align:start position:0% +Beats blue it kind of intuitively makes +sense that red should beat blue right + + align:start position:0% +sense that red should beat blue right + + + align:start position:0% +sense that red should beat blue right +no no no intuition just do the tree + + align:start position:0% +no no no intuition just do the tree + + + align:start position:0% +no no no intuition just do the tree +diagram uh so yeah this is perfectly + + align:start position:0% +diagram uh so yeah this is perfectly + + + align:start position:0% +diagram uh so yeah this is perfectly +fine right and in fact it gets even + + align:start position:0% +fine right and in fact it gets even + + + align:start position:0% +fine right and in fact it gets even +weirder right + + align:start position:0% +weirder right + + + align:start position:0% +weirder right +uh what do you think happens if uh we + + align:start position:0% +uh what do you think happens if uh we + + + align:start position:0% +uh what do you think happens if uh we +each choose two dice or sorry we each + + align:start position:0% +each choose two dice or sorry we each + + + align:start position:0% +each choose two dice or sorry we each +roll twice + + align:start position:0% + + + + align:start position:0% + +so what if uh you know what if I pick + + align:start position:0% +so what if uh you know what if I pick + + + align:start position:0% +so what if uh you know what if I pick +the red dy I roll it twice you pick the + + align:start position:0% +the red dy I roll it twice you pick the + + + align:start position:0% +the red dy I roll it twice you pick the +green Dy you roll it + + align:start position:0% +green Dy you roll it + + + align:start position:0% +green Dy you roll it +twice right red probably beats Green so + + align:start position:0% +twice right red probably beats Green so + + + align:start position:0% +twice right red probably beats Green so +is it true that two red rolls probably + + align:start position:0% +is it true that two red rolls probably + + + align:start position:0% +is it true that two red rolls probably +beat two green rolls like if we sum them + + align:start position:0% + + + + align:start position:0% + +up who thinks + + align:start position:0% +up who thinks + + + align:start position:0% +up who thinks +yes who thinks + + align:start position:0% +yes who thinks + + + align:start position:0% +yes who thinks +no who wants to draw the tree + + align:start position:0% +no who wants to draw the tree + + + align:start position:0% +no who wants to draw the tree +diagram oh wow so eager I don't + + align:start position:0% + + + + align:start position:0% + +um like uh what is the tree diagram + + align:start position:0% +um like uh what is the tree diagram + + + align:start position:0% +um like uh what is the tree diagram +going to look like if we if we do + + align:start position:0% +going to look like if we if we do + + + align:start position:0% +going to look like if we if we do +that like I'm rolling twice you're + + align:start position:0% +that like I'm rolling twice you're + + + align:start position:0% +that like I'm rolling twice you're +rolling twice each roll can have you + + align:start position:0% +rolling twice each roll can have you + + + align:start position:0% +rolling twice each roll can have you +know three possible uh uh three + + align:start position:0% +know three possible uh uh three + + + align:start position:0% +know three possible uh uh three +possibilities right so we're going to + + align:start position:0% +possibilities right so we're going to + + + align:start position:0% +possibilities right so we're going to +end up with a pretty massive + + align:start position:0% +end up with a pretty massive + + + align:start position:0% +end up with a pretty massive +tree I I don't want to draw that at + + align:start position:0% +tree I I don't want to draw that at + + + align:start position:0% +tree I I don't want to draw that at +least not on the + + align:start position:0% +least not on the + + + align:start position:0% +least not on the +board does somebody else want to come up + + align:start position:0% +board does somebody else want to come up + + + align:start position:0% +board does somebody else want to come up +and do it + + align:start position:0% +and do it + + + align:start position:0% +and do it +please no nobody okay well instead of + + align:start position:0% +please no nobody okay well instead of + + + align:start position:0% +please no nobody okay well instead of +drawing out the entire tree diagram + + align:start position:0% +drawing out the entire tree diagram + + + align:start position:0% +drawing out the entire tree diagram +let's kind of start drawing it and see + + align:start position:0% +let's kind of start drawing it and see + + + align:start position:0% +let's kind of start drawing it and see +if we can find a + + align:start position:0% + + + + align:start position:0% + +pattern okay so this is uh R2 versus + + align:start position:0% +pattern okay so this is uh R2 versus + + + align:start position:0% +pattern okay so this is uh R2 versus +G2 + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so let's start by + + align:start position:0% +so let's start by + + + align:start position:0% +so let's start by +know drawing as we did before okay so my + + align:start position:0% +know drawing as we did before okay so my + + + align:start position:0% +know drawing as we did before okay so my +first roll as was red could be 2 six or + + align:start position:0% +first roll as was red could be 2 six or + + + align:start position:0% +first roll as was red could be 2 six or +7 second rle could also be 2 six or + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +okay now for + + align:start position:0% +okay now for + + + align:start position:0% +okay now for +green right + + align:start position:0% + + + + align:start position:0% + +we're basically just going to be drawing + + align:start position:0% +we're basically just going to be drawing + + + align:start position:0% +we're basically just going to be drawing +the same tree nine times so you know + + align:start position:0% +the same tree nine times so you know + + + align:start position:0% +the same tree nine times so you know +let's + + align:start position:0% +let's + + + align:start position:0% +let's +not so green could roll you know + + align:start position:0% + + + + align:start position:0% + +159 and then can also roll + + align:start position:0% +159 and then can also roll + + + align:start position:0% +159 and then can also roll +159 for the second + + align:start position:0% + + + + align:start position:0% + +roll + + align:start position:0% +roll + + + align:start position:0% +roll +okay and rather than duplicating this + + align:start position:0% +okay and rather than duplicating this + + + align:start position:0% +okay and rather than duplicating this +three nine times I'm just going to leave + + align:start position:0% +three nine times I'm just going to leave + + + align:start position:0% +three nine times I'm just going to leave +this as it is and you know we can see if + + align:start position:0% +this as it is and you know we can see if + + + align:start position:0% +this as it is and you know we can see if +we can find a + + align:start position:0% +we can find a + + + align:start position:0% +we can find a +pattern + + align:start position:0% +pattern + + + align:start position:0% +pattern +okay does that make sense to + + align:start position:0% + + + + align:start position:0% + +everybody so an outcome now is going to + + align:start position:0% +everybody so an outcome now is going to + + + align:start position:0% +everybody so an outcome now is going to +be a four tupal right instead of a + + align:start position:0% +be a four tupal right instead of a + + + align:start position:0% +be a four tupal right instead of a +pair and in some sense we can kind of + + align:start position:0% +pair and in some sense we can kind of + + + align:start position:0% +pair and in some sense we can kind of +think of it as combining a leaf of this + + align:start position:0% +think of it as combining a leaf of this + + + align:start position:0% +think of it as combining a leaf of this +tree with a leaf of this tree okay we're + + align:start position:0% +tree with a leaf of this tree okay we're + + + align:start position:0% +tree with a leaf of this tree okay we're +going to take a red leaf and a green + + align:start position:0% +going to take a red leaf and a green + + + align:start position:0% +going to take a red leaf and a green +leaf a question or + + align:start position:0% +leaf a question or + + + align:start position:0% +leaf a question or +no no + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so we can then abbreviate it even + + align:start position:0% +so we can then abbreviate it even + + + align:start position:0% +so we can then abbreviate it even +further right instead of looking at the + + align:start position:0% +further right instead of looking at the + + + align:start position:0% +further right instead of looking at the +pair of numbers that we've that we've + + align:start position:0% +pair of numbers that we've that we've + + + align:start position:0% +pair of numbers that we've that we've +rolled let's instead look at you know + + align:start position:0% +rolled let's instead look at you know + + + align:start position:0% +rolled let's instead look at you know +just the SU + + align:start position:0% +just the SU + + + align:start position:0% +just the SU +okay so if red rolls two tws we've got + + align:start position:0% +okay so if red rolls two tws we've got + + + align:start position:0% +okay so if red rolls two tws we've got +four here 2 and six is eight 2 and 7 is + + align:start position:0% +four here 2 and six is eight 2 and 7 is + + + align:start position:0% +four here 2 and six is eight 2 and 7 is +N9 uh 6 2 is + + align:start position:0% +N9 uh 6 2 is + + + align:start position:0% +N9 uh 6 2 is +8 uh 66 is not 9 that's 12 ever trust me + + align:start position:0% +8 uh 66 is not 9 that's 12 ever trust me + + + align:start position:0% +8 uh 66 is not 9 that's 12 ever trust me +to do arithmetic uh 67 is 13 72 is 9 76 + + align:start position:0% +to do arithmetic uh 67 is 13 72 is 9 76 + + + align:start position:0% +to do arithmetic uh 67 is 13 72 is 9 76 +is 13 77 is + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +okay and if we do do the same thing for + + align:start position:0% +okay and if we do do the same thing for + + + align:start position:0% +okay and if we do do the same thing for +uh green we have 2 6 10 6 10 + + align:start position:0% +uh green we have 2 6 10 6 10 + + + align:start position:0% +uh green we have 2 6 10 6 10 +14 10 14 + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +okay so now we can start counting + + align:start position:0% +okay so now we can start counting + + + align:start position:0% +okay so now we can start counting +outcomes if we take this Leaf of the red + + align:start position:0% +outcomes if we take this Leaf of the red + + + align:start position:0% +outcomes if we take this Leaf of the red +tree how many outcomes are there where + + align:start position:0% +tree how many outcomes are there where + + + align:start position:0% +tree how many outcomes are there where +red wins + + align:start position:0% +red wins + + + align:start position:0% +red wins +if red rolls four in total the only way + + align:start position:0% +if red rolls four in total the only way + + + align:start position:0% +if red rolls four in total the only way +that red wins is if green gets Snake + + align:start position:0% +that red wins is if green gets Snake + + + align:start position:0% +that red wins is if green gets Snake +Eyes Okay so we've just got + + align:start position:0% + + + + align:start position:0% + +one if red rules eight which could be + + align:start position:0% +one if red rules eight which could be + + + align:start position:0% +one if red rules eight which could be +either of these + + align:start position:0% +either of these + + + align:start position:0% +either of these +two how many outcomes are there where + + align:start position:0% +two how many outcomes are there where + + + align:start position:0% +two how many outcomes are there where +red + + align:start position:0% +red + + + align:start position:0% +red +wins well we've got a two here a six + + align:start position:0% +wins well we've got a two here a six + + + align:start position:0% +wins well we've got a two here a six +here and a six here so we've got three + + align:start position:0% + + + + align:start position:0% + +and we've got uh two red leaves that + + align:start position:0% +and we've got uh two red leaves that + + + align:start position:0% +and we've got uh two red leaves that +have eight uh what about nine it looks + + align:start position:0% +have eight uh what about nine it looks + + + align:start position:0% +have eight uh what about nine it looks +like we've got two more that have + + align:start position:0% +like we've got two more that have + + + align:start position:0% +like we've got two more that have +nine same deal right we don't have any + + align:start position:0% +nine same deal right we don't have any + + + align:start position:0% +nine same deal right we don't have any +eights or nines over on this + + align:start position:0% + + + + align:start position:0% + +side + + align:start position:0% +side + + + align:start position:0% +side +okay uh what else do we have + + align:start position:0% +okay uh what else do we have + + + align:start position:0% +okay uh what else do we have + + align:start position:0% + + + align:start position:0% +okay well if red rolls 12 then red is + + align:start position:0% +okay well if red rolls 12 then red is + + + align:start position:0% +okay well if red rolls 12 then red is +good if blue Rolls 2 6 10 but not 14 or + + align:start position:0% +good if blue Rolls 2 6 10 but not 14 or + + + align:start position:0% +good if blue Rolls 2 6 10 but not 14 or +18 so we've got 1 2 3 4 five six + + align:start position:0% + + + + align:start position:0% + +outcomes and we have one red leaf where + + align:start position:0% +outcomes and we have one red leaf where + + + align:start position:0% +outcomes and we have one red leaf where +red has + + align:start position:0% +red has + + + align:start position:0% +red has +12 okay then same thing for 13 there are + + align:start position:0% +12 okay then same thing for 13 there are + + + align:start position:0% +12 okay then same thing for 13 there are +no 12 or 13s over here and we have two + + align:start position:0% + + + + align:start position:0% + +13s now what about + + align:start position:0% + + + + align:start position:0% + +14 well if red rolls 14 then you know + + align:start position:0% +14 well if red rolls 14 then you know + + + align:start position:0% +14 well if red rolls 14 then you know +same + + align:start position:0% +same + + + align:start position:0% +same +deal but we've got these two ties + + align:start position:0% + + + + align:start position:0% + +here okay so red + + align:start position:0% + + + + align:start position:0% + +winds draw we've just got two and then + + align:start position:0% +winds draw we've just got two and then + + + align:start position:0% +winds draw we've just got two and then +red loses is going to be the complement + + align:start position:0% + + + + align:start position:0% + +okay so has anybody added all of these + + align:start position:0% +okay so has anybody added all of these + + + align:start position:0% +okay so has anybody added all of these +up yet I + + align:start position:0% + + + + align:start position:0% + +haven't 5 + + align:start position:0% +haven't 5 + + + align:start position:0% +haven't 5 +30 42 43 is that + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +so 43 outcomes for red + + align:start position:0% +so 43 outcomes for red + + + align:start position:0% +so 43 outcomes for red +wins + + align:start position:0% + + + + align:start position:0% + +uh had something wrong this doesn't + + align:start position:0% +uh had something wrong this doesn't + + + align:start position:0% +uh had something wrong this doesn't +match my + + align:start position:0% +match my + + + align:start position:0% +match my +notes + + align:start position:0% +notes + + + align:start position:0% +notes +uh let's + + align:start position:0% +uh let's + + + align:start position:0% +uh let's +see so we've got one for this sub tree + + align:start position:0% +see so we've got one for this sub tree + + + align:start position:0% +see so we've got one for this sub tree +for each of these we have three + + align:start position:0% +for each of these we have three + + + align:start position:0% +for each of these we have three +for each of the + + align:start position:0% +for each of the + + + align:start position:0% +for each of the +nines we also have three so that's those + + align:start position:0% +nines we also have three so that's those + + + align:start position:0% +nines we also have three so that's those +12 13 and + + align:start position:0% + + + + align:start position:0% + +13 oh do I just have too many terms I + + align:start position:0% +13 oh do I just have too many terms I + + + align:start position:0% +13 oh do I just have too many terms I +just have too many + + align:start position:0% + + + + align:start position:0% + +terms okay not 43 it should be + + align:start position:0% + + + + align:start position:0% + +37 is that + + align:start position:0% +37 is that + + + align:start position:0% +37 is that +right yeah are 12 13 13 and 14 each have + + align:start position:0% +right yeah are 12 13 13 and 14 each have + + + align:start position:0% +right yeah are 12 13 13 and 14 each have +six + + align:start position:0% + + + + align:start position:0% + +okay okay uh yeah never trust me to do + + align:start position:0% +okay okay uh yeah never trust me to do + + + align:start position:0% +okay okay uh yeah never trust me to do +arithmetic it's always a bad plan uh + + align:start position:0% +arithmetic it's always a bad plan uh + + + align:start position:0% +arithmetic it's always a bad plan uh +okay so red wins in 37 of the outcomes + + align:start position:0% +okay so red wins in 37 of the outcomes + + + align:start position:0% +okay so red wins in 37 of the outcomes +right there's a draw in two of them and + + align:start position:0% +right there's a draw in two of them and + + + align:start position:0% +right there's a draw in two of them and +how many outcomes are there in + + align:start position:0% + + + + align:start position:0% + +total + + align:start position:0% +total + + + align:start position:0% +total +yeah1 yeah 81 so red loses in 81 - 37 - + + align:start position:0% +yeah1 yeah 81 so red loses in 81 - 37 - + + + align:start position:0% +yeah1 yeah 81 so red loses in 81 - 37 - + + align:start position:0% + + + align:start position:0% +which is that 42 I think that's + + align:start position:0% + + + + align:start position:0% + +42 okay + + align:start position:0% +42 okay + + + align:start position:0% +42 okay +so because this is uniform space we have + + align:start position:0% +so because this is uniform space we have + + + align:start position:0% +so because this is uniform space we have +37 over 81 42 over + + align:start position:0% +37 over 81 42 over + + + align:start position:0% +37 over 81 42 over +81 which is going to be well actually + + align:start position:0% +81 which is going to be well actually + + + align:start position:0% +81 which is going to be well actually +let's not reduce it it's easier to see + + align:start position:0% +let's not reduce it it's easier to see + + + align:start position:0% +let's not reduce it it's easier to see +like + + align:start position:0% +like + + + align:start position:0% +like +that and two out of 81 for a + + align:start position:0% +that and two out of 81 for a + + + align:start position:0% +that and two out of 81 for a +draw okay so if we only had one role + + align:start position:0% +draw okay so if we only had one role + + + align:start position:0% +draw okay so if we only had one role +red had the advantage right red wins + + align:start position:0% +red had the advantage right red wins + + + align:start position:0% +red had the advantage right red wins +with probability 5 9ths if we have two + + align:start position:0% +with probability 5 9ths if we have two + + + align:start position:0% +with probability 5 9ths if we have two +roles right the probability that red + + align:start position:0% +roles right the probability that red + + + align:start position:0% +roles right the probability that red +wins is smaller than the probability + + align:start position:0% +wins is smaller than the probability + + + align:start position:0% +wins is smaller than the probability +that red loses so now suddenly green has + + align:start position:0% +that red loses so now suddenly green has + + + align:start position:0% +that red loses so now suddenly green has +the advantage + + align:start position:0% +the advantage + + + align:start position:0% +the advantage +instead + + align:start position:0% +instead + + + align:start position:0% +instead +okay and um as it turns out you know the + + align:start position:0% +okay and um as it turns out you know the + + + align:start position:0% +okay and um as it turns out you know the +same thing happens with all three pairs + + align:start position:0% +same thing happens with all three pairs + + + align:start position:0% +same thing happens with all three pairs +of dice right so uh you know red beats + + align:start position:0% +of dice right so uh you know red beats + + + align:start position:0% +of dice right so uh you know red beats +Green with with one roll green Beats + + align:start position:0% +Green with with one roll green Beats + + + align:start position:0% +Green with with one roll green Beats +blue with one roll but Blue Beats Green + + align:start position:0% +blue with one roll but Blue Beats Green + + + align:start position:0% +blue with one roll but Blue Beats Green +with two + + align:start position:0% +with two + + + align:start position:0% +with two +rolls right and Blue Beats red with with + + align:start position:0% +rolls right and Blue Beats red with with + + + align:start position:0% +rolls right and Blue Beats red with with +one roll but red beats blue with two + + align:start position:0% +one roll but red beats blue with two + + + align:start position:0% +one roll but red beats blue with two +rolls and + + align:start position:0% +rolls and + + + align:start position:0% +rolls and +uh yeah so the the the dice continue to + + align:start position:0% +uh yeah so the the the dice continue to + + + align:start position:0% +uh yeah so the the the dice continue to +you know not have this transitivity + + align:start position:0% +you know not have this transitivity + + + align:start position:0% +you know not have this transitivity +property but like every time it's + + align:start position:0% +property but like every time it's + + + align:start position:0% +property but like every time it's +switched okay and as it turns out uh you + + align:start position:0% +switched okay and as it turns out uh you + + + align:start position:0% +switched okay and as it turns out uh you +know you can even you know extend this + + align:start position:0% +know you can even you know extend this + + + align:start position:0% +know you can even you know extend this +right right like if you have more dice + + align:start position:0% +right right like if you have more dice + + + align:start position:0% +right right like if you have more dice +with different numbers you can get like + + align:start position:0% +with different numbers you can get like + + + align:start position:0% +with different numbers you can get like +all sorts of weird things that are that + + align:start position:0% +all sorts of weird things that are that + + + align:start position:0% +all sorts of weird things that are that +are that that could happen um so there's + + align:start position:0% +are that that could happen um so there's + + + align:start position:0% +are that that could happen um so there's +a a link to a to a a rather interesting + + align:start position:0% +a a link to a to a a rather interesting + + + align:start position:0% +a a link to a to a a rather interesting +paper on archive if you if you want to + + align:start position:0% +paper on archive if you if you want to + + + align:start position:0% +paper on archive if you if you want to +see it uh in the lecture notes um but uh + + align:start position:0% +see it uh in the lecture notes um but uh + + + align:start position:0% +see it uh in the lecture notes um but uh +yeah for now I think that's all we have + + align:start position:0% +yeah for now I think that's all we have + + + align:start position:0% +yeah for now I think that's all we have +time for feel free to uh come up if you + + align:start position:0% +time for feel free to uh come up if you + + + align:start position:0% +time for feel free to uh come up if you +have questions and otherwise we will see + + align:start position:0% +have questions and otherwise we will see + + + align:start position:0% +have questions and otherwise we will see +you on Thursday \ No newline at end of file diff --git a/IZqwi0wJovM.txt b/IZqwi0wJovM.txt new file mode 100644 index 0000000000000000000000000000000000000000..40883f36c69c3c8f150d2623c14f443d1a098b1b --- /dev/null +++ b/IZqwi0wJovM.txt @@ -0,0 +1,7403 @@ +align:start position:0% + +and lift off on differential equations + + align:start position:0% +and lift off on differential equations + + + align:start position:0% +and lift off on differential equations +so this section is about how to solve a + + align:start position:0% +so this section is about how to solve a + + + align:start position:0% +so this section is about how to solve a +system of first order first derivative + + align:start position:0% +system of first order first derivative + + + align:start position:0% +system of first order first derivative +constant coefficient linear + + align:start position:0% +constant coefficient linear + + + align:start position:0% +constant coefficient linear +equation + + align:start position:0% +equation + + + align:start position:0% +equation +and if we do it right it turns directly + + align:start position:0% +and if we do it right it turns directly + + + align:start position:0% +and if we do it right it turns directly +into linear algebra the the key idea is + + align:start position:0% +into linear algebra the the key idea is + + + align:start position:0% +into linear algebra the the key idea is +the solutions to constant coefficient + + align:start position:0% +the solutions to constant coefficient + + + align:start position:0% +the solutions to constant coefficient +linear equations are + + align:start position:0% +linear equations are + + + align:start position:0% +linear equations are +exponentials so if you look for an + + align:start position:0% +exponentials so if you look for an + + + align:start position:0% +exponentials so if you look for an +exponential then all you have to find is + + align:start position:0% +exponential then all you have to find is + + + align:start position:0% +exponential then all you have to find is +what's up there in the exponent and what + + align:start position:0% +what's up there in the exponent and what + + + align:start position:0% +what's up there in the exponent and what +multiplies the exponential and that's + + align:start position:0% +multiplies the exponential and that's + + + align:start position:0% +multiplies the exponential and that's +the linear algebra so and the result one + + align:start position:0% +the linear algebra so and the result one + + + align:start position:0% +the linear algebra so and the result one +thing we will find it's it's completely + + align:start position:0% +thing we will find it's it's completely + + + align:start position:0% +thing we will find it's it's completely +parallel to powers of a matrix so the + + align:start position:0% +parallel to powers of a matrix so the + + + align:start position:0% +parallel to powers of a matrix so the +last lecture was about how would you + + align:start position:0% +last lecture was about how would you + + + align:start position:0% +last lecture was about how would you +compute a to the k or a to the 100 how + + align:start position:0% +compute a to the k or a to the 100 how + + + align:start position:0% +compute a to the k or a to the 100 how +how do you compute High powers of a + + align:start position:0% +how do you compute High powers of a + + + align:start position:0% +how do you compute High powers of a +matrix now uh it's not Powers anymore + + align:start position:0% +matrix now uh it's not Powers anymore + + + align:start position:0% +matrix now uh it's not Powers anymore +but it's + + align:start position:0% +but it's + + + align:start position:0% +but it's +exponentials that's the natural thing + + align:start position:0% +exponentials that's the natural thing + + + align:start position:0% +exponentials that's the natural thing +for differential equation okay but can I + + align:start position:0% +for differential equation okay but can I + + + align:start position:0% +for differential equation okay but can I +begin with an + + align:start position:0% +begin with an + + + align:start position:0% +begin with an +example and I'll just go through the + + align:start position:0% +example and I'll just go through the + + + align:start position:0% +example and I'll just go through the +mechanics how would I solve + + align:start position:0% +mechanics how would I solve + + + align:start position:0% +mechanics how would I solve +the differential equ two differential + + align:start position:0% +the differential equ two differential + + + align:start position:0% +the differential equ two differential +equations so I'm going to make it I'll + + align:start position:0% +equations so I'm going to make it I'll + + + align:start position:0% +equations so I'm going to make it I'll +have a 2X two Matrix and the + + align:start position:0% +have a 2X two Matrix and the + + + align:start position:0% +have a 2X two Matrix and the +coefficients are min-1 2 1 minus 2 and I + + align:start position:0% +coefficients are min-1 2 1 minus 2 and I + + + align:start position:0% +coefficients are min-1 2 1 minus 2 and I +better give you some initial condition + + align:start position:0% +better give you some initial condition + + + align:start position:0% +better give you some initial condition +so suppose it starts U at time zero this + + align:start position:0% +so suppose it starts U at time zero this + + + align:start position:0% +so suppose it starts U at time zero this +is U1 U2 let it let it suppose + + align:start position:0% +is U1 U2 let it let it suppose + + + align:start position:0% +is U1 U2 let it let it suppose +everything is in U1 at time zero so orig + + align:start position:0% +everything is in U1 at time zero so orig + + + align:start position:0% +everything is in U1 at time zero so orig +at at the start it's all in + + align:start position:0% +at at the start it's all in + + + align:start position:0% +at at the start it's all in +1 but what happens as time goes + + align:start position:0% +1 but what happens as time goes + + + align:start position:0% +1 but what happens as time goes +on du2 DT will will be positive because + + align:start position:0% +on du2 DT will will be positive because + + + align:start position:0% +on du2 DT will will be positive because +of that U1 term so flow will move into + + align:start position:0% +of that U1 term so flow will move into + + + align:start position:0% +of that U1 term so flow will move into +the U2 component and it will go out of + + align:start position:0% +the U2 component and it will go out of + + + align:start position:0% +the U2 component and it will go out of +the U1 component so we'll just follow + + align:start position:0% +the U1 component so we'll just follow + + + align:start position:0% +the U1 component so we'll just follow +that movement as time goes forward by + + align:start position:0% +that movement as time goes forward by + + + align:start position:0% +that movement as time goes forward by +looking at the igen values and igen + + align:start position:0% +looking at the igen values and igen + + + align:start position:0% +looking at the igen values and igen +vectors of that Matrix + + align:start position:0% +vectors of that Matrix + + + align:start position:0% +vectors of that Matrix +that's the first job before you do + + align:start position:0% +that's the first job before you do + + + align:start position:0% +that's the first job before you do +anything else find the find the Matrix + + align:start position:0% +anything else find the find the Matrix + + + align:start position:0% +anything else find the find the Matrix +and its igen values and ion vectors so + + align:start position:0% +and its igen values and ion vectors so + + + align:start position:0% +and its igen values and ion vectors so +let me do + + align:start position:0% +let me do + + + align:start position:0% +let me do +that okay so here's our + + align:start position:0% +that okay so here's our + + + align:start position:0% +that okay so here's our +Matrix maybe you can tell me right away + + align:start position:0% +Matrix maybe you can tell me right away + + + align:start position:0% +Matrix maybe you can tell me right away +what what are the igen values and I and + + align:start position:0% +what what are the igen values and I and + + + align:start position:0% +what what are the igen values and I and +I values anyway uh and then we can check + + align:start position:0% +I values anyway uh and then we can check + + + align:start position:0% +I values anyway uh and then we can check +but can you spot any of the igen values + + align:start position:0% +but can you spot any of the igen values + + + align:start position:0% +but can you spot any of the igen values +of that Matrix we're looking for two + + align:start position:0% +of that Matrix we're looking for two + + + align:start position:0% +of that Matrix we're looking for two +igen values + + align:start position:0% +igen values + + + align:start position:0% +igen values +do you see I mean if I just wrote that + + align:start position:0% +do you see I mean if I just wrote that + + + align:start position:0% +do you see I mean if I just wrote that +Matrix down what what do you notice + + align:start position:0% +Matrix down what what do you notice + + + align:start position:0% +Matrix down what what do you notice +about + + align:start position:0% +about + + + align:start position:0% +about +it it's singular right that that's a + + align:start position:0% +it it's singular right that that's a + + + align:start position:0% +it it's singular right that that's a +singular Matrix that tells me right away + + align:start position:0% +singular Matrix that tells me right away + + + align:start position:0% +singular Matrix that tells me right away +that one of the igen values is Lambda + + align:start position:0% +that one of the igen values is Lambda + + + align:start position:0% +that one of the igen values is Lambda +equals zero I can that's a singular + + align:start position:0% +equals zero I can that's a singular + + + align:start position:0% +equals zero I can that's a singular +Matrix the the second column is min-2 + + align:start position:0% +Matrix the the second column is min-2 + + + align:start position:0% +Matrix the the second column is min-2 +times the First Column the determinant + + align:start position:0% +times the First Column the determinant + + + align:start position:0% +times the First Column the determinant +is zero it's it's singular so zero is an + + align:start position:0% +is zero it's it's singular so zero is an + + + align:start position:0% +is zero it's it's singular so zero is an +i value and the other I value will + + align:start position:0% +i value and the other I value will + + + align:start position:0% +i value and the other I value will +be from the + + align:start position:0% +be from the + + + align:start position:0% +be from the +trace I look at the trace the sum down + + align:start position:0% +trace I look at the trace the sum down + + + align:start position:0% +trace I look at the trace the sum down +the diagonal is minus three that has to + + align:start position:0% +the diagonal is minus three that has to + + + align:start position:0% +the diagonal is minus three that has to +agree with the sum of the IG value so + + align:start position:0% +agree with the sum of the IG value so + + + align:start position:0% +agree with the sum of the IG value so +that second value better be minus three + + align:start position:0% +that second value better be minus three + + + align:start position:0% +that second value better be minus three +I could of course I could compute why + + align:start position:0% +I could of course I could compute why + + + align:start position:0% +I could of course I could compute why +don't I over here compute the + + align:start position:0% +don't I over here compute the + + + align:start position:0% +don't I over here compute the +determinant of a minus Lambda I the + + align:start position:0% +determinant of a minus Lambda I the + + + align:start position:0% +determinant of a minus Lambda I the +determinant of this Min -1 - Lambda 2 1 + + align:start position:0% +determinant of this Min -1 - Lambda 2 1 + + + align:start position:0% +determinant of this Min -1 - Lambda 2 1 +- 2 - Lambda Matrix but we know what's + + align:start position:0% +- 2 - Lambda Matrix but we know what's + + + align:start position:0% +- 2 - Lambda Matrix but we know what's +coming when I do that multiplication I + + align:start position:0% +coming when I do that multiplication I + + + align:start position:0% +coming when I do that multiplication I +get a Lambda + + align:start position:0% +get a Lambda + + + align:start position:0% +get a Lambda +squar I get a 2 Lambda and a one Lambda + + align:start position:0% +squar I get a 2 Lambda and a one Lambda + + + align:start position:0% +squar I get a 2 Lambda and a one Lambda +that's a three Lambda and then the now + + align:start position:0% +that's a three Lambda and then the now + + + align:start position:0% +that's a three Lambda and then the now +I'm going to get the determinant which + + align:start position:0% +I'm going to get the determinant which + + + align:start position:0% +I'm going to get the determinant which +is 2 minus 2 which is zero + + align:start position:0% +is 2 minus 2 which is zero + + + align:start position:0% +is 2 minus 2 which is zero +so there's my characteristic polinomial + + align:start position:0% +so there's my characteristic polinomial + + + align:start position:0% +so there's my characteristic polinomial +this + + align:start position:0% +this + + + align:start position:0% +this +determinant and of course I factor that + + align:start position:0% +determinant and of course I factor that + + + align:start position:0% +determinant and of course I factor that +into Lambda * Lambda + + + align:start position:0% +into Lambda * Lambda + + + + align:start position:0% +into Lambda * Lambda + +3 and I get the two igen values that we + + align:start position:0% +3 and I get the two igen values that we + + + align:start position:0% +3 and I get the two igen values that we +saw + + align:start position:0% +saw + + + align:start position:0% +saw +coming what else do I need the IG + + align:start position:0% +coming what else do I need the IG + + + align:start position:0% +coming what else do I need the IG +vectors so before I even think about the + + align:start position:0% +vectors so before I even think about the + + + align:start position:0% +vectors so before I even think about the +differential equation or what how to + + align:start position:0% +differential equation or what how to + + + align:start position:0% +differential equation or what how to +solve it let me find the IG vectors for + + align:start position:0% +solve it let me find the IG vectors for + + + align:start position:0% +solve it let me find the IG vectors for +this Matrix okay so take Lambda equals + + align:start position:0% +this Matrix okay so take Lambda equals + + + align:start position:0% +this Matrix okay so take Lambda equals +z so that that's the first igon value + + align:start position:0% +z so that that's the first igon value + + + align:start position:0% +z so that that's the first igon value +Lambda 1 equals 0 and the second igon + + align:start position:0% +Lambda 1 equals 0 and the second igon + + + align:start position:0% +Lambda 1 equals 0 and the second igon +value will be Lambda 2 = + + align:start position:0% +value will be Lambda 2 = + + + align:start position:0% +value will be Lambda 2 = +-3 by the + + align:start position:0% +-3 by the + + + align:start position:0% +-3 by the +way I I already know something important + + align:start position:0% +way I I already know something important + + + align:start position:0% +way I I already know something important +about this the igen values are telling + + align:start position:0% +about this the igen values are telling + + + align:start position:0% +about this the igen values are telling +me something you'll see how it comes out + + align:start position:0% +me something you'll see how it comes out + + + align:start position:0% +me something you'll see how it comes out +but let me point to these numbers are + + align:start position:0% +but let me point to these numbers are + + + align:start position:0% +but let me point to these numbers are +this igen value a negative igen value is + + align:start position:0% +this igen value a negative igen value is + + + align:start position:0% +this igen value a negative igen value is +going to disappear there's going to be + + align:start position:0% +going to disappear there's going to be + + + align:start position:0% +going to disappear there's going to be +an e to the minus 3T in the + + align:start position:0% +an e to the minus 3T in the + + + align:start position:0% +an e to the minus 3T in the +answer that e to Theus 3T as time goes + + align:start position:0% +answer that e to Theus 3T as time goes + + + align:start position:0% +answer that e to Theus 3T as time goes +on is going to be very very small the + + align:start position:0% +on is going to be very very small the + + + align:start position:0% +on is going to be very very small the +other part of the answer will will will + + align:start position:0% +other part of the answer will will will + + + align:start position:0% +other part of the answer will will will +involve an e to the 0 t but e to the 0 t + + align:start position:0% +involve an e to the 0 t but e to the 0 t + + + align:start position:0% +involve an e to the 0 t but e to the 0 t +is one and that's a constant so I'm + + align:start position:0% +is one and that's a constant so I'm + + + align:start position:0% +is one and that's a constant so I'm +expecting that this solution will have + + align:start position:0% +expecting that this solution will have + + + align:start position:0% +expecting that this solution will have +two parts an e to the 0o T part and an e + + align:start position:0% +two parts an e to the 0o T part and an e + + + align:start position:0% +two parts an e to the 0o T part and an e +to the minus 3 T part and the and as + + align:start position:0% +to the minus 3 T part and the and as + + + align:start position:0% +to the minus 3 T part and the and as +time goes on the second part will + + align:start position:0% +time goes on the second part will + + + align:start position:0% +time goes on the second part will +disappear and the first part will be a + + align:start position:0% +disappear and the first part will be a + + + align:start position:0% +disappear and the first part will be a +steady state it won't move it will be at + + align:start position:0% +steady state it won't move it will be at + + + align:start position:0% +steady state it won't move it will be at +the end of as T approaches Infinity this + + align:start position:0% +the end of as T approaches Infinity this + + + align:start position:0% +the end of as T approaches Infinity this +part disappears and this is the the the + + align:start position:0% +part disappears and this is the the the + + + align:start position:0% +part disappears and this is the the the +e to the zero T part is what I get and + + align:start position:0% +e to the zero T part is what I get and + + + align:start position:0% +e to the zero T part is what I get and +I'm very interested in these steady stat + + align:start position:0% +I'm very interested in these steady stat + + + align:start position:0% +I'm very interested in these steady stat +so that's I I get a steady state when I + + align:start position:0% +so that's I I get a steady state when I + + + align:start position:0% +so that's I I get a steady state when I +have a zero IG value okay what about + + align:start position:0% +have a zero IG value okay what about + + + align:start position:0% +have a zero IG value okay what about +those IG vectors so what's the igon + + align:start position:0% +those IG vectors so what's the igon + + + align:start position:0% +those IG vectors so what's the igon +vector that goes with IG value zero okay + + align:start position:0% +vector that goes with IG value zero okay + + + align:start position:0% +vector that goes with IG value zero okay +the Matrix is singular as it is the + + align:start position:0% +the Matrix is singular as it is the + + + align:start position:0% +the Matrix is singular as it is the +Vector is is the guy in the null space + + align:start position:0% +Vector is is the guy in the null space + + + align:start position:0% +Vector is is the guy in the null space +so what Vector is in the null space of + + align:start position:0% +so what Vector is in the null space of + + + align:start position:0% +so what Vector is in the null space of +that + + align:start position:0% +that + + + align:start position:0% +that +Matrix uh let's see I guess I probably + + align:start position:0% +Matrix uh let's see I guess I probably + + + align:start position:0% +Matrix uh let's see I guess I probably +give the free variable the value one and + + align:start position:0% +give the free variable the value one and + + + align:start position:0% +give the free variable the value one and +I realize that if I want to get zero I + + align:start position:0% +I realize that if I want to get zero I + + + align:start position:0% +I realize that if I want to get zero I +need a two up + + align:start position:0% +need a two up + + + align:start position:0% +need a two up +here okay so ax1 is + + align:start position:0% +here okay so ax1 is + + + align:start position:0% +here okay so ax1 is +0x1 ax1 is 0x1 fine okay what about the + + align:start position:0% +0x1 ax1 is 0x1 fine okay what about the + + + align:start position:0% +0x1 ax1 is 0x1 fine okay what about the +other igen value Lambda 2 is + + align:start position:0% +other igen value Lambda 2 is + + + align:start position:0% +other igen value Lambda 2 is +-3 okay how do I get the other I value + + align:start position:0% +-3 okay how do I get the other I value + + + align:start position:0% +-3 okay how do I get the other I value +then for the moment can I mentally do it + + align:start position:0% +then for the moment can I mentally do it + + + align:start position:0% +then for the moment can I mentally do it +I subtract minus + + align:start position:0% +I subtract minus + + + align:start position:0% +I subtract minus +three along the diagonal which means I + + align:start position:0% +three along the diagonal which means I + + + align:start position:0% +three along the diagonal which means I +add three can I I'll just do it with an + + align:start position:0% +add three can I I'll just do it with an + + + align:start position:0% +add three can I I'll just do it with an +erase erase for the moment so I'm going + + align:start position:0% +erase erase for the moment so I'm going + + + align:start position:0% +erase erase for the moment so I'm going +to add three to the diagonal so this + + align:start position:0% +to add three to the diagonal so this + + + align:start position:0% +to add three to the diagonal so this +minus one will become a + + align:start position:0% +minus one will become a + + + align:start position:0% +minus one will become a +two and I'll make it in big loopy + + align:start position:0% +two and I'll make it in big loopy + + + align:start position:0% +two and I'll make it in big loopy +letters and when I add three to this guy + + align:start position:0% +letters and when I add three to this guy + + + align:start position:0% +letters and when I add three to this guy +the minus two becomes well I can't make + + align:start position:0% +the minus two becomes well I can't make + + + align:start position:0% +the minus two becomes well I can't make +one very loopy but how's that okay uh + + align:start position:0% +one very loopy but how's that okay uh + + + align:start position:0% +one very loopy but how's that okay uh +now that's a minus 3 I A+ 3 I sorry + + align:start position:0% +now that's a minus 3 I A+ 3 I sorry + + + align:start position:0% +now that's a minus 3 I A+ 3 I sorry +that's a + 3 I it's supposed to be + + align:start position:0% +that's a + 3 I it's supposed to be + + + align:start position:0% +that's a + 3 I it's supposed to be +singular right if if if things if I did + + align:start position:0% +singular right if if if things if I did + + + align:start position:0% +singular right if if if things if I did +it right this Matrix should be singular + + align:start position:0% +it right this Matrix should be singular + + + align:start position:0% +it right this Matrix should be singular +and the X2 the I Vector should be in its + + align:start position:0% +and the X2 the I Vector should be in its + + + align:start position:0% +and the X2 the I Vector should be in its +null space okay what do I get for the + + align:start position:0% +null space okay what do I get for the + + + align:start position:0% +null space okay what do I get for the +null space of this maybe minus1 one or 1 + + align:start position:0% +null space of this maybe minus1 one or 1 + + + align:start position:0% +null space of this maybe minus1 one or 1 +minus one doesn't matter those are both + + align:start position:0% +minus one doesn't matter those are both + + + align:start position:0% +minus one doesn't matter those are both +perfectly good right that's in the null + + align:start position:0% +perfectly good right that's in the null + + + align:start position:0% +perfectly good right that's in the null +space of this now + + align:start position:0% +space of this now + + + align:start position:0% +space of this now +I'll because a * that Vector is 3 * that + + align:start position:0% +I'll because a * that Vector is 3 * that + + + align:start position:0% +I'll because a * that Vector is 3 * that +Vector + + align:start position:0% +Vector + + + align:start position:0% +Vector +ax2 is - 3 + + align:start position:0% +ax2 is - 3 + + + align:start position:0% +ax2 is - 3 +X2 + + align:start position:0% +X2 + + + align:start position:0% +X2 +good okay can I get a again so we see + + align:start position:0% +good okay can I get a again so we see + + + align:start position:0% +good okay can I get a again so we see +that correctly that was a minus one and + + align:start position:0% +that correctly that was a minus one and + + + align:start position:0% +that correctly that was a minus one and +that was a minus two + + align:start position:0% +that was a minus two + + + align:start position:0% +that was a minus two +good + + align:start position:0% +good + + + align:start position:0% +good +okay that that's the first job I values + + align:start position:0% +okay that that's the first job I values + + + align:start position:0% +okay that that's the first job I values +and igen vectors and already the igen + + align:start position:0% +and igen vectors and already the igen + + + align:start position:0% +and igen vectors and already the igen +values are telling me the most important + + align:start position:0% +values are telling me the most important + + + align:start position:0% +values are telling me the most important +information about the answer but now + + align:start position:0% +information about the answer but now + + + align:start position:0% +information about the answer but now +what is the answer the answer is the + + align:start position:0% + + + + align:start position:0% + +solution will be U of + + align:start position:0% +solution will be U of + + + align:start position:0% +solution will be U of +T okay now now I use those igen values + + align:start position:0% +T okay now now I use those igen values + + + align:start position:0% +T okay now now I use those igen values +and igen vectors the solution is some + + align:start position:0% +and igen vectors the solution is some + + + align:start position:0% +and igen vectors the solution is some +there are two I values so so there are + + align:start position:0% +there are two I values so so there are + + + align:start position:0% +there are two I values so so there are +going to be two special Solutions here + + align:start position:0% +going to be two special Solutions here + + + align:start position:0% +going to be two special Solutions here +two pure exponential Solutions the first + + align:start position:0% +two pure exponential Solutions the first + + + align:start position:0% +two pure exponential Solutions the first +one is going to be e the Lambda 1T + + align:start position:0% +one is going to be e the Lambda 1T + + + align:start position:0% +one is going to be e the Lambda 1T +X1 and the SEC so that solves the + + align:start position:0% +X1 and the SEC so that solves the + + + align:start position:0% +X1 and the SEC so that solves the +equation and so does this one they both + + align:start position:0% +equation and so does this one they both + + + align:start position:0% +equation and so does this one they both +are solutions to the differential + + align:start position:0% +are solutions to the differential + + + align:start position:0% +are solutions to the differential +equation that's the general solution the + + align:start position:0% +equation that's the general solution the + + + align:start position:0% +equation that's the general solution the +general solution is a combination of + + align:start position:0% +general solution is a combination of + + + align:start position:0% +general solution is a combination of +that pure exponential solution and that + + align:start position:0% +that pure exponential solution and that + + + align:start position:0% +that pure exponential solution and that +pure exponential solution can I just see + + align:start position:0% +pure exponential solution can I just see + + + align:start position:0% +pure exponential solution can I just see +that those guys do solve the equation so + + align:start position:0% +that those guys do solve the equation so + + + align:start position:0% +that those guys do solve the equation so +let me just check check on this one for + + align:start position:0% +let me just check check on this one for + + + align:start position:0% +let me just check check on this one for +example + + align:start position:0% +example + + + align:start position:0% +example +check I want to check that the my + + align:start position:0% +check I want to check that the my + + + align:start position:0% +check I want to check that the my +equation let's remember the equation du + + align:start position:0% +equation let's remember the equation du + + + align:start position:0% +equation let's remember the equation du +DT is au I plug in + + align:start position:0% + + + + align:start position:0% + +e to the Lambda 1 + + align:start position:0% +e to the Lambda 1 + + + align:start position:0% +e to the Lambda 1 +tx1 and let's just see that that the + + align:start position:0% +tx1 and let's just see that that the + + + align:start position:0% +tx1 and let's just see that that the +equation's okay I believe this is a + + align:start position:0% +equation's okay I believe this is a + + + align:start position:0% +equation's okay I believe this is a +solution to that equation so just plug + + align:start position:0% +solution to that equation so just plug + + + align:start position:0% +solution to that equation so just plug +it in on the left hand side I take the + + align:start position:0% +it in on the left hand side I take the + + + align:start position:0% +it in on the left hand side I take the +time derivative so the left hand side + + align:start position:0% +time derivative so the left hand side + + + align:start position:0% +time derivative so the left hand side +will be Lambda 1 e to the Lambda 1 + + align:start position:0% +will be Lambda 1 e to the Lambda 1 + + + align:start position:0% +will be Lambda 1 e to the Lambda 1 +tx1 right the time derivative this is + + align:start position:0% +tx1 right the time derivative this is + + + align:start position:0% +tx1 right the time derivative this is +the term that depends on time it's just + + align:start position:0% +the term that depends on time it's just + + + align:start position:0% +the term that depends on time it's just +just ordinary exponential its derivative + + align:start position:0% +just ordinary exponential its derivative + + + align:start position:0% +just ordinary exponential its derivative +brings down a Lambda 1 on the other side + + align:start position:0% +brings down a Lambda 1 on the other side + + + align:start position:0% +brings down a Lambda 1 on the other side +of the equation it's a * this thing a * + + align:start position:0% +of the equation it's a * this thing a * + + + align:start position:0% +of the equation it's a * this thing a * +e the Lambda 1 + + align:start position:0% +e the Lambda 1 + + + align:start position:0% +e the Lambda 1 +tx1 and does that check out do we have + + align:start position:0% +tx1 and does that check out do we have + + + align:start position:0% +tx1 and does that check out do we have +equality there yes because e to the + + align:start position:0% +equality there yes because e to the + + + align:start position:0% +equality there yes because e to the +Lambda 1 T appears on both + + align:start position:0% +Lambda 1 T appears on both + + + align:start position:0% +Lambda 1 T appears on both +sides and the other one is ax1 equal + + align:start position:0% +sides and the other one is ax1 equal + + + align:start position:0% +sides and the other one is ax1 equal +Lambda 1x1 check do so we've come to the + + align:start position:0% +Lambda 1x1 check do so we've come to the + + + align:start position:0% +Lambda 1x1 check do so we've come to the +first point to + + align:start position:0% +first point to + + + align:start position:0% +first point to +remember these Pure + + align:start position:0% +remember these Pure + + + align:start position:0% +remember these Pure +Solutions those Pure Solutions are the + + align:start position:0% +Solutions those Pure Solutions are the + + + align:start position:0% +Solutions those Pure Solutions are the +those pure exponentials are the + + align:start position:0% +those pure exponentials are the + + + align:start position:0% +those pure exponentials are the +differential equations analog of last + + align:start position:0% +differential equations analog of last + + + align:start position:0% +differential equations analog of last +time we had pure Powers last time so so + + align:start position:0% +time we had pure Powers last time so so + + + align:start position:0% +time we had pure Powers last time so so +last time the the analog was Lambda + + align:start position:0% +last time the the analog was Lambda + + + align:start position:0% +last time the the analog was Lambda +Lambda 1 to the K power X1 some amount + + align:start position:0% +Lambda 1 to the K power X1 some amount + + + align:start position:0% +Lambda 1 to the K power X1 some amount +of that plus some amount of Lambda 2 to + + align:start position:0% +of that plus some amount of Lambda 2 to + + + align:start position:0% +of that plus some amount of Lambda 2 to +the K power X2 that was our formula from + + align:start position:0% +the K power X2 that was our formula from + + + align:start position:0% +the K power X2 that was our formula from +last time I put it up just so you your + + align:start position:0% +last time I put it up just so you your + + + align:start position:0% +last time I put it up just so you your +eye compares those two formulas powers + + align:start position:0% +eye compares those two formulas powers + + + align:start position:0% +eye compares those two formulas powers +of Lambda in the in the difference + + align:start position:0% +of Lambda in the in the difference + + + align:start position:0% +of Lambda in the in the difference +equation that this was in the this was + + align:start position:0% +equation that this was in the this was + + + align:start position:0% +equation that this was in the this was +for the equation u k + 1 = a + + align:start position:0% +for the equation u k + 1 = a + + + align:start position:0% +for the equation u k + 1 = a +UK that was for the finite step stepping + + align:start position:0% +UK that was for the finite step stepping + + + align:start position:0% +UK that was for the finite step stepping +by one + + align:start position:0% +by one + + + align:start position:0% +by one +and we got powers now this is the one + + align:start position:0% +and we got powers now this is the one + + + align:start position:0% +and we got powers now this is the one +we're interested in the exponentials so + + align:start position:0% +we're interested in the exponentials so + + + align:start position:0% +we're interested in the exponentials so +so that's that's the solution what are + + align:start position:0% +so that's that's the solution what are + + + align:start position:0% +so that's that's the solution what are +C1 and C2 then we're through what are C1 + + align:start position:0% +C1 and C2 then we're through what are C1 + + + align:start position:0% +C1 and C2 then we're through what are C1 +and C2 well of course we know these + + align:start position:0% +and C2 well of course we know these + + + align:start position:0% +and C2 well of course we know these +actual things let me just let me come + + align:start position:0% +actual things let me just let me come + + + align:start position:0% +actual things let me just let me come +back to + + align:start position:0% +back to + + + align:start position:0% +back to +this C1 is we haven't figured out yet + + align:start position:0% +this C1 is we haven't figured out yet + + + align:start position:0% +this C1 is we haven't figured out yet +but e to the Lambda 1 T the Lambda 1 is + + align:start position:0% +but e to the Lambda 1 T the Lambda 1 is + + + align:start position:0% +but e to the Lambda 1 T the Lambda 1 is +zero so that's just a one + + align:start position:0% +zero so that's just a one + + + align:start position:0% +zero so that's just a one +* X1 which is 21 so it's C1 time this + + align:start position:0% +* X1 which is 21 so it's C1 time this + + + align:start position:0% +* X1 which is 21 so it's C1 time this +one that's not moving times the vector + + align:start position:0% +one that's not moving times the vector + + + align:start position:0% +one that's not moving times the vector +the I Vector + + align:start position:0% +the I Vector + + + align:start position:0% +the I Vector +21 and + + align:start position:0% +21 and + + + align:start position:0% +21 and +C2 times what's e to the Lambda 2 + + align:start position:0% +C2 times what's e to the Lambda 2 + + + align:start position:0% +C2 times what's e to the Lambda 2 +T Lambda 2 + + align:start position:0% +T Lambda 2 + + + align:start position:0% +T Lambda 2 +is minus 3 so this is the term that has + + align:start position:0% +is minus 3 so this is the term that has + + + align:start position:0% +is minus 3 so this is the term that has +the minus 3T and its I Vector is this 1 + + align:start position:0% +the minus 3T and its I Vector is this 1 + + + align:start position:0% +the minus 3T and its I Vector is this 1 +minus one + + align:start position:0% + + + + align:start position:0% + +so this + + align:start position:0% +so this + + + align:start position:0% +so this +Vector solves the equation and any + + align:start position:0% +Vector solves the equation and any + + + align:start position:0% +Vector solves the equation and any +multiple of it this Vector solves the + + align:start position:0% +multiple of it this Vector solves the + + + align:start position:0% +multiple of it this Vector solves the +equation if it's got that factor e the + + align:start position:0% +equation if it's got that factor e the + + + align:start position:0% +equation if it's got that factor e the +minus + + align:start position:0% +minus + + + align:start position:0% +minus +3T we've got the answer except for C1 + + align:start position:0% +3T we've got the answer except for C1 + + + align:start position:0% +3T we've got the answer except for C1 +and C2 so so everything I've done is + + align:start position:0% +and C2 so so everything I've done is + + + align:start position:0% +and C2 so so everything I've done is +immediate as soon as you know the igen + + align:start position:0% +immediate as soon as you know the igen + + + align:start position:0% +immediate as soon as you know the igen +values and igen vectors so how do we get + + align:start position:0% +values and igen vectors so how do we get + + + align:start position:0% +values and igen vectors so how do we get +C1 and C2 that has to come from the + + align:start position:0% +C1 and C2 that has to come from the + + + align:start position:0% +C1 and C2 that has to come from the +initial condition so now I now I use U + + align:start position:0% +initial condition so now I now I use U + + + align:start position:0% +initial condition so now I now I use U +of0 is given as one + + align:start position:0% + + + + align:start position:0% + +Z so this is the initial condition that + + align:start position:0% +Z so this is the initial condition that + + + align:start position:0% +Z so this is the initial condition that +we'll find C1 and C2 so let me do that + + align:start position:0% +we'll find C1 and C2 so let me do that + + + align:start position:0% +we'll find C1 and C2 so let me do that +on the board + + align:start position:0% + + + + align:start position:0% + +underneath at T equals z + + align:start position:0% + + + + align:start position:0% + +then I get C1 + + align:start position:0% +then I get C1 + + + align:start position:0% +then I get C1 +times this + + align:start position:0% +times this + + + align:start position:0% +times this +guy plus C2 and now I'm at time zero so + + align:start position:0% +guy plus C2 and now I'm at time zero so + + + align:start position:0% +guy plus C2 and now I'm at time zero so +that's a one and this is a one + + align:start position:0% +that's a one and this is a one + + + align:start position:0% +that's a one and this is a one +-1 and that's supposed to agree with U + + align:start position:0% +-1 and that's supposed to agree with U + + + align:start position:0% +-1 and that's supposed to agree with U +of 0 1 + + align:start position:0% + + + + align:start position:0% + +0 okay that should be two equations that + + align:start position:0% +0 okay that should be two equations that + + + align:start position:0% +0 okay that should be two equations that +should give me C1 and C2 and then I'm + + align:start position:0% +should give me C1 and C2 and then I'm + + + align:start position:0% +should give me C1 and C2 and then I'm +through so what are C1 and C2 let's see + + align:start position:0% +through so what are C1 and C2 let's see + + + align:start position:0% +through so what are C1 and C2 let's see +I guess we could actually spot them by I + + align:start position:0% +I guess we could actually spot them by I + + + align:start position:0% +I guess we could actually spot them by I +or we could solve two equations in two + + align:start position:0% +or we could solve two equations in two + + + align:start position:0% +or we could solve two equations in two +unknowns uh let's see if these were both + + align:start position:0% +unknowns uh let's see if these were both + + + align:start position:0% +unknowns uh let's see if these were both +ones so I'm just adding then I would get + + align:start position:0% +ones so I'm just adding then I would get + + + align:start position:0% +ones so I'm just adding then I would get +three zero so what's this what's the + + align:start position:0% +three zero so what's this what's the + + + align:start position:0% +three zero so what's this what's the +solution + + align:start position:0% + + + + align:start position:0% + +then if if if C1 and C2 are both ones I + + align:start position:0% +then if if if C1 and C2 are both ones I + + + align:start position:0% +then if if if C1 and C2 are both ones I +get three Zer so I want like one3 of + + align:start position:0% +get three Zer so I want like one3 of + + + align:start position:0% +get three Zer so I want like one3 of +that because I want to get one zero so I + + align:start position:0% +that because I want to get one zero so I + + + align:start position:0% +that because I want to get one zero so I +think it's C1 = + + align:start position:0% +think it's C1 = + + + align:start position:0% +think it's C1 = +A3 C2 equal + + align:start position:0% + + + + align:start position:0% + +A3 so finally I have the answer let me + + align:start position:0% +A3 so finally I have the answer let me + + + align:start position:0% +A3 so finally I have the answer let me +keep it in the in this board here + + align:start position:0% +keep it in the in this board here + + + align:start position:0% +keep it in the in this board here +finally the answer + + align:start position:0% +finally the answer + + + align:start position:0% +finally the answer +is 1/3 of + + align:start position:0% +is 1/3 of + + + align:start position:0% +is 1/3 of +this + + align:start position:0% +this + + + align:start position:0% +this +plus 1/3 of + + align:start position:0% + + + + align:start position:0% + +this do you see what what's actually + + align:start position:0% +this do you see what what's actually + + + align:start position:0% +this do you see what what's actually +happening with this flow this flow + + align:start position:0% +happening with this flow this flow + + + align:start position:0% +happening with this flow this flow +started out at the solution started out + + align:start position:0% +started out at the solution started out + + + align:start position:0% +started out at the solution started out +at one Z started at one + + align:start position:0% +at one Z started at one + + + align:start position:0% +at one Z started at one +Z then as time went on people moved + + align:start position:0% +Z then as time went on people moved + + + align:start position:0% +Z then as time went on people moved +essentially some fraction of this one + + align:start position:0% +essentially some fraction of this one + + + align:start position:0% +essentially some fraction of this one +moved + + align:start position:0% +moved + + + align:start position:0% +moved +here + + align:start position:0% +here + + + align:start position:0% +here +and and in the limit there's there's the + + align:start position:0% +and and in the limit there's there's the + + + align:start position:0% +and and in the limit there's there's the +limit as right as T goes to Infinity as + + align:start position:0% +limit as right as T goes to Infinity as + + + align:start position:0% +limit as right as T goes to Infinity as +T gets very large this disappears and + + align:start position:0% +T gets very large this disappears and + + + align:start position:0% +T gets very large this disappears and +this is the steady state so the steady + + align:start position:0% +this is the steady state so the steady + + + align:start position:0% +this is the steady state so the steady +state is so the steady + + align:start position:0% + + + + align:start position:0% + +state U we could call it U at Infinity + + align:start position:0% +state U we could call it U at Infinity + + + align:start position:0% +state U we could call it U at Infinity +is 13 of 2 and one it's it's 2/3 + + align:start position:0% + + + + align:start position:0% + +1/3 so that's the we really I mean + + align:start position:0% +1/3 so that's the we really I mean + + + align:start position:0% +1/3 so that's the we really I mean +you're getting like total uh insight + + align:start position:0% +you're getting like total uh insight + + + align:start position:0% +you're getting like total uh insight +into the behavior of this solution what + + align:start position:0% +into the behavior of this solution what + + + align:start position:0% +into the behavior of this solution what +the differential equation does of course + + align:start position:0% +the differential equation does of course + + + align:start position:0% +the differential equation does of course +we don't wouldn't always have a steady + + align:start position:0% +we don't wouldn't always have a steady + + + align:start position:0% +we don't wouldn't always have a steady +state sometimes we would approach + + align:start position:0% +state sometimes we would approach + + + align:start position:0% +state sometimes we would approach +zero sometimes we would blow up can we + + align:start position:0% +zero sometimes we would blow up can we + + + align:start position:0% +zero sometimes we would blow up can we +straighten out those those cases the + + align:start position:0% +straighten out those those cases the + + + align:start position:0% +straighten out those those cases the +igen values should tell us so when do we + + align:start position:0% +igen values should tell us so when do we + + + align:start position:0% +igen values should tell us so when do we +get uh so so let me ask first when do we + + align:start position:0% +get uh so so let me ask first when do we + + + align:start position:0% +get uh so so let me ask first when do we +get + + align:start position:0% + + + + align:start position:0% + +stability that's U of T going to + + align:start position:0% +stability that's U of T going to + + + align:start position:0% +stability that's U of T going to +zero when when would the solution go to + + align:start position:0% +zero when when would the solution go to + + + align:start position:0% +zero when when would the solution go to +zero no matter what the initial + + align:start position:0% +zero no matter what the initial + + + align:start position:0% +zero no matter what the initial +condition + + align:start position:0% +condition + + + align:start position:0% +condition +is negative igen values right negative + + align:start position:0% +is negative igen values right negative + + + align:start position:0% +is negative igen values right negative +igen values but now I have to I have to + + align:start position:0% +igen values but now I have to I have to + + + align:start position:0% +igen values but now I have to I have to +ask you for one more step suppose the + + align:start position:0% +ask you for one more step suppose the + + + align:start position:0% +ask you for one more step suppose the +igen values are complex numbers because + + align:start position:0% +igen values are complex numbers because + + + align:start position:0% +igen values are complex numbers because +we know they could be then we want + + align:start position:0% +we know they could be then we want + + + align:start position:0% +we know they could be then we want +stability this this we we want we need + + align:start position:0% +stability this this we we want we need + + + align:start position:0% +stability this this we we want we need +all these e to the Lambda T is all going + + align:start position:0% +all these e to the Lambda T is all going + + + align:start position:0% +all these e to the Lambda T is all going +to + + align:start position:0% +to + + + align:start position:0% +to +zero and somehow that asks us to have + + align:start position:0% +zero and somehow that asks us to have + + + align:start position:0% +zero and somehow that asks us to have +Lambda negative but suppose Lambda is a + + align:start position:0% +Lambda negative but suppose Lambda is a + + + align:start position:0% +Lambda negative but suppose Lambda is a +complex number then what's the test what + + align:start position:0% +complex number then what's the test what + + + align:start position:0% +complex number then what's the test what +if Lambda is a complex number + + align:start position:0% +if Lambda is a complex number + + + align:start position:0% +if Lambda is a complex number +like uh suppose Lambda is negative plus + + align:start position:0% +like uh suppose Lambda is negative plus + + + align:start position:0% +like uh suppose Lambda is negative plus +an imaginary part say Lambda is -3 + 6 I + + align:start position:0% +an imaginary part say Lambda is -3 + 6 I + + + align:start position:0% +an imaginary part say Lambda is -3 + 6 I +what what happens then can we just like + + align:start position:0% +what what happens then can we just like + + + align:start position:0% +what what happens then can we just like +do a a case here if if this Lambda is -3 + + align:start position:0% +do a a case here if if this Lambda is -3 + + + align:start position:0% +do a a case here if if this Lambda is -3 ++ 6 i + + align:start position:0% ++ 6 i + + + align:start position:0% ++ 6 i +t how big is that + + align:start position:0% +t how big is that + + + align:start position:0% +t how big is that +number does this does this imaginary + + align:start position:0% +number does this does this imaginary + + + align:start position:0% +number does this does this imaginary +part play a play a play a role here or + + align:start position:0% +part play a play a play a role here or + + + align:start position:0% +part play a play a play a role here or +not but how big is what's the absolute + + align:start position:0% +not but how big is what's the absolute + + + align:start position:0% +not but how big is what's the absolute +value of that of that + + align:start position:0% + + + + align:start position:0% + +quantity it's just eus 3 T right because + + align:start position:0% +quantity it's just eus 3 T right because + + + align:start position:0% +quantity it's just eus 3 T right because +this other part this the the the magnit + + align:start position:0% +this other part this the the the magnit + + + align:start position:0% +this other part this the the the magnit +the this e to the 6 i t what that that + + align:start position:0% +the this e to the 6 i t what that that + + + align:start position:0% +the this e to the 6 i t what that that +has absolute value + + align:start position:0% + + + + align:start position:0% + +one right that's just this cine of 6t + + + align:start position:0% +one right that's just this cine of 6t + + + + align:start position:0% +one right that's just this cine of 6t + +I sin of 6t and the absolute value + + align:start position:0% +I sin of 6t and the absolute value + + + align:start position:0% +I sin of 6t and the absolute value +squared will be cos s + sin 2 will be 1 + + align:start position:0% +squared will be cos s + sin 2 will be 1 + + + align:start position:0% +squared will be cos s + sin 2 will be 1 +this is this complex number is running + + align:start position:0% +this is this complex number is running + + + align:start position:0% +this is this complex number is running +around the unit + + align:start position:0% +around the unit + + + align:start position:0% +around the unit +circle this com this the it's the real + + align:start position:0% +circle this com this the it's the real + + + align:start position:0% +circle this com this the it's the real +part that matters this is what I'm + + align:start position:0% +part that matters this is what I'm + + + align:start position:0% +part that matters this is what I'm +trying to do real part of + + align:start position:0% +trying to do real part of + + + align:start position:0% +trying to do real part of +Lambda has to be negative if Lambda is a + + align:start position:0% +Lambda has to be negative if Lambda is a + + + align:start position:0% +Lambda has to be negative if Lambda is a +complex number it's the real part the + + align:start position:0% +complex number it's the real part the + + + align:start position:0% +complex number it's the real part the +minus three that either makes us go to + + align:start position:0% +minus three that either makes us go to + + + align:start position:0% +minus three that either makes us go to +zero or + + align:start position:0% +zero or + + + align:start position:0% +zero or +doesn't uh or let or or blows up the + + align:start position:0% +doesn't uh or let or or blows up the + + + align:start position:0% +doesn't uh or let or or blows up the +imaginary part won't will just like + + align:start position:0% +imaginary part won't will just like + + + align:start position:0% +imaginary part won't will just like +oscillate between the the two + + align:start position:0% +oscillate between the the two + + + align:start position:0% +oscillate between the the two +components okay so that's stability and + + align:start position:0% +components okay so that's stability and + + + align:start position:0% +components okay so that's stability and +what about uh what about a steady + + align:start position:0% + + + + align:start position:0% + +state when would we have uh a steady + + align:start position:0% +state when would we have uh a steady + + + align:start position:0% +state when would we have uh a steady +state always in the same direction so + + align:start position:0% +state always in the same direction so + + + align:start position:0% +state always in the same direction so +let me I'll take this part away when so + + align:start position:0% +let me I'll take this part away when so + + + align:start position:0% +let me I'll take this part away when so +that was like checking that it's that + + align:start position:0% +that was like checking that it's that + + + align:start position:0% +that was like checking that it's that +it's the real part that we care about uh + + align:start position:0% +it's the real part that we care about uh + + + align:start position:0% +it's the real part that we care about uh +now we have a steady state + + align:start position:0% +now we have a steady state + + + align:start position:0% +now we have a steady state +when when Lambda one is zero and the + + align:start position:0% +when when Lambda one is zero and the + + + align:start position:0% +when when Lambda one is zero and the +other I values have + + align:start position:0% +other I values have + + + align:start position:0% +other I values have +what so I'm looking like that example + + align:start position:0% +what so I'm looking like that example + + + align:start position:0% +what so I'm looking like that example +was like + + align:start position:0% +was like + + + align:start position:0% +was like +perfect for a steady state we have a + + align:start position:0% +perfect for a steady state we have a + + + align:start position:0% +perfect for a steady state we have a +zero I value and the other IG values we + + align:start position:0% +zero I value and the other IG values we + + + align:start position:0% +zero I value and the other IG values we +want those to disappear so the other en + + align:start position:0% +want those to disappear so the other en + + + align:start position:0% +want those to disappear so the other en +values have real part + + align:start position:0% + + + + align:start position:0% + +negative and we blow up for + + align:start position:0% +negative and we blow up for + + + align:start position:0% +negative and we blow up for +sure we blow + + align:start position:0% +sure we blow + + + align:start position:0% +sure we blow +up if + + align:start position:0% +up if + + + align:start position:0% +up if +any real part of Lambda is + + align:start position:0% + + + + align:start position:0% + +positive so if I if I reverse the sign + + align:start position:0% +positive so if I if I reverse the sign + + + align:start position:0% +positive so if I if I reverse the sign +of a of the Matrix + + align:start position:0% +of a of the Matrix + + + align:start position:0% +of a of the Matrix +a suppose instead of the Matrix I had + + align:start position:0% +a suppose instead of the Matrix I had + + + align:start position:0% +a suppose instead of the Matrix I had +the a that I had I changed it I changed + + align:start position:0% +the a that I had I changed it I changed + + + align:start position:0% +the a that I had I changed it I changed +all its signs what would that do to the + + align:start position:0% +all its signs what would that do to the + + + align:start position:0% +all its signs what would that do to the +igen values and igen vectors well if I + + align:start position:0% +igen values and igen vectors well if I + + + align:start position:0% +igen values and igen vectors well if I +if if I know the IG values and IG + + align:start position:0% +if if I know the IG values and IG + + + align:start position:0% +if if I know the IG values and IG +vectors of a tell me about minus + + align:start position:0% +vectors of a tell me about minus + + + align:start position:0% +vectors of a tell me about minus +a what happens to the IG + + align:start position:0% +a what happens to the IG + + + align:start position:0% +a what happens to the IG +values for minus a they'll all change + + align:start position:0% +values for minus a they'll all change + + + align:start position:0% +values for minus a they'll all change +sign so I'll have blow up this instead + + align:start position:0% +sign so I'll have blow up this instead + + + align:start position:0% +sign so I'll have blow up this instead +of the e to the minus 3T if I change + + align:start position:0% +of the e to the minus 3T if I change + + + align:start position:0% +of the e to the minus 3T if I change +that to minus if I change the signs in + + align:start position:0% +that to minus if I change the signs in + + + align:start position:0% +that to minus if I change the signs in +that Matrix I would change the trace to + + align:start position:0% +that Matrix I would change the trace to + + + align:start position:0% +that Matrix I would change the trace to +plus three I would have an e to the plus + + align:start position:0% +plus three I would have an e to the plus + + + align:start position:0% +plus three I would have an e to the plus +3 T and I would have blow + + align:start position:0% +3 T and I would have blow + + + align:start position:0% +3 T and I would have blow +up of course the zero I value would stay + + align:start position:0% +up of course the zero I value would stay + + + align:start position:0% +up of course the zero I value would stay +at zero but the other guy is taking off + + align:start position:0% +at zero but the other guy is taking off + + + align:start position:0% +at zero but the other guy is taking off +in if I reversed all the signs okay so + + align:start position:0% +in if I reversed all the signs okay so + + + align:start position:0% +in if I reversed all the signs okay so +this is this is the the stability + + align:start position:0% +this is this is the the stability + + + align:start position:0% +this is this is the the stability +picture and for a 2X two + + align:start position:0% +picture and for a 2X two + + + align:start position:0% +picture and for a 2X two +Matrix uh we can actually pin down even + + align:start position:0% +Matrix uh we can actually pin down even + + + align:start position:0% +Matrix uh we can actually pin down even +more + + align:start position:0% +more + + + align:start position:0% +more +closely what that means can I can I do + + align:start position:0% +closely what that means can I can I do + + + align:start position:0% +closely what that means can I can I do +that let me do that I want to for a 2 by + + align:start position:0% +that let me do that I want to for a 2 by + + + align:start position:0% +that let me do that I want to for a 2 by +two + + align:start position:0% +two + + + align:start position:0% +two +Matrix I can tell whether the real part + + align:start position:0% +Matrix I can tell whether the real part + + + align:start position:0% +Matrix I can tell whether the real part +of the igen values is negative well let + + align:start position:0% +of the igen values is negative well let + + + align:start position:0% +of the igen values is negative well let +me let me tell you what I have in mind + + align:start position:0% +me let me tell you what I have in mind + + + align:start position:0% +me let me tell you what I have in mind +for that so 2x two stability let me this + + align:start position:0% +for that so 2x two stability let me this + + + align:start position:0% +for that so 2x two stability let me this +is just a little + + align:start position:0% +is just a little + + + align:start position:0% +is just a little +comment 2 by two stability + + align:start position:0% + + + + align:start position:0% + +so my Matrix now is just a b c + + align:start position:0% +so my Matrix now is just a b c + + + align:start position:0% +so my Matrix now is just a b c +d and and I'm looking for the real parts + + align:start position:0% +d and and I'm looking for the real parts + + + align:start position:0% +d and and I'm looking for the real parts +of both igen values to be + + align:start position:0% + + + + align:start position:0% + +negative + + align:start position:0% + + + + align:start position:0% + +okay what how can I tell from looking at + + align:start position:0% +okay what how can I tell from looking at + + + align:start position:0% +okay what how can I tell from looking at +the Matrix without Computing its igen + + align:start position:0% +the Matrix without Computing its igen + + + align:start position:0% +the Matrix without Computing its igen +values + + align:start position:0% +values + + + align:start position:0% +values +whether the two L values are negative or + + align:start position:0% +whether the two L values are negative or + + + align:start position:0% +whether the two L values are negative or +at least their real parts are negative + + align:start position:0% +at least their real parts are negative + + + align:start position:0% +at least their real parts are negative +what would that tell me about the trace + + align:start position:0% +what would that tell me about the trace + + + align:start position:0% +what would that tell me about the trace +so so the + + align:start position:0% +so so the + + + align:start position:0% +so so the +trace that's this a plus + + align:start position:0% +trace that's this a plus + + + align:start position:0% +trace that's this a plus +d what Can you tell me about the + + align:start position:0% +d what Can you tell me about the + + + align:start position:0% +d what Can you tell me about the +trace in the case of a 2X two stable + + align:start position:0% +trace in the case of a 2X two stable + + + align:start position:0% +trace in the case of a 2X two stable +Matrix that means the igen values are + + align:start position:0% +Matrix that means the igen values are + + + align:start position:0% +Matrix that means the igen values are +negative or at least the real parts of + + align:start position:0% +negative or at least the real parts of + + + align:start position:0% +negative or at least the real parts of +those igen values are negative + + align:start position:0% +those igen values are negative + + + align:start position:0% +those igen values are negative +then when I take the when I look at the + + align:start position:0% +then when I take the when I look at the + + + align:start position:0% +then when I take the when I look at the +Matrix and and find its Trace what what + + align:start position:0% +Matrix and and find its Trace what what + + + align:start position:0% +Matrix and and find its Trace what what +do I know about that it's negative right + + align:start position:0% +do I know about that it's negative right + + + align:start position:0% +do I know about that it's negative right +this is the sum of the this equals this + + align:start position:0% +this is the sum of the this equals this + + + align:start position:0% +this is the sum of the this equals this +equals Lambda 1 + Lambda 2 so it's + + align:start position:0% +equals Lambda 1 + Lambda 2 so it's + + + align:start position:0% +equals Lambda 1 + Lambda 2 so it's +negative the two I values by the way + + align:start position:0% +negative the two I values by the way + + + align:start position:0% +negative the two I values by the way +will have if they're complex will have + + align:start position:0% +will have if they're complex will have + + + align:start position:0% +will have if they're complex will have +plus 6 I and minus 6 I the complex parts + + align:start position:0% +plus 6 I and minus 6 I the complex parts + + + align:start position:0% +plus 6 I and minus 6 I the complex parts +will will be conjugates of each other + + align:start position:0% +will will be conjugates of each other + + + align:start position:0% +will will be conjugates of each other +and disappear when we add and the trace + + align:start position:0% +and disappear when we add and the trace + + + align:start position:0% +and disappear when we add and the trace +will be negative okay the trace has to + + align:start position:0% +will be negative okay the trace has to + + + align:start position:0% +will be negative okay the trace has to +be negative is that + + align:start position:0% +be negative is that + + + align:start position:0% +be negative is that +enough is a negative Trace enough to + + align:start position:0% +enough is a negative Trace enough to + + + align:start position:0% +enough is a negative Trace enough to +make the Matrix + + align:start position:0% +make the Matrix + + + align:start position:0% +make the Matrix +stable shouldn't be enough right can I + + align:start position:0% +stable shouldn't be enough right can I + + + align:start position:0% +stable shouldn't be enough right can I +can you make what's a matrix that has a + + align:start position:0% +can you make what's a matrix that has a + + + align:start position:0% +can you make what's a matrix that has a +negative Trace but still it's not + + align:start position:0% +negative Trace but still it's not + + + align:start position:0% +negative Trace but still it's not +stable so it it has a blow it still has + + align:start position:0% +stable so it it has a blow it still has + + + align:start position:0% +stable so it it has a blow it still has +a blow up factor and uh and a and a + + align:start position:0% +a blow up factor and uh and a and a + + + align:start position:0% +a blow up factor and uh and a and a +Decay one so what would be so just just + + align:start position:0% +Decay one so what would be so just just + + + align:start position:0% +Decay one so what would be so just just +to see maybe I just put that here uh + + align:start position:0% +to see maybe I just put that here uh + + + align:start position:0% +to see maybe I just put that here uh +this now I'm looking for an example + + align:start position:0% +this now I'm looking for an example + + + align:start position:0% +this now I'm looking for an example +where the trace could be negative but + + align:start position:0% +where the trace could be negative but + + + align:start position:0% +where the trace could be negative but +still blow + + align:start position:0% + + + + align:start position:0% + +up of + + align:start position:0% +up of + + + align:start position:0% +up of +course yeah let's just take + + align:start position:0% +course yeah let's just take + + + align:start position:0% +course yeah let's just take +one oh look let me let me make it -201 + + align:start position:0% + + + + align:start position:0% + +okay there's a case where that Matrix + + align:start position:0% +okay there's a case where that Matrix + + + align:start position:0% +okay there's a case where that Matrix +has negative Trace I know it's values of + + align:start position:0% +has negative Trace I know it's values of + + + align:start position:0% +has negative Trace I know it's values of +course they're minus 2 and one and it + + align:start position:0% +course they're minus 2 and one and it + + + align:start position:0% +course they're minus 2 and one and it +blows up it's got It's got A plus one I + + align:start position:0% +blows up it's got It's got A plus one I + + + align:start position:0% +blows up it's got It's got A plus one I +value here so there'll be an e to the + + align:start position:0% +value here so there'll be an e to the + + + align:start position:0% +value here so there'll be an e to the +plus T in the solution and it'll blow up + + align:start position:0% +plus T in the solution and it'll blow up + + + align:start position:0% +plus T in the solution and it'll blow up +if it has any second component at all I + + align:start position:0% +if it has any second component at all I + + + align:start position:0% +if it has any second component at all I +need another + + align:start position:0% +need another + + + align:start position:0% +need another +condition and it's a condition on the + + align:start position:0% +condition and it's a condition on the + + + align:start position:0% +condition and it's a condition on the +determin and and what's that condition + + align:start position:0% +determin and and what's that condition + + + align:start position:0% +determin and and what's that condition +if I know that the two I values suppose + + align:start position:0% +if I know that the two I values suppose + + + align:start position:0% +if I know that the two I values suppose +I know they're negative both negative + + align:start position:0% +I know they're negative both negative + + + align:start position:0% +I know they're negative both negative +what does that tell me about the + + align:start position:0% +what does that tell me about the + + + align:start position:0% +what does that tell me about the +determinant let me ask again if I know + + align:start position:0% +determinant let me ask again if I know + + + align:start position:0% +determinant let me ask again if I know +both the I values are + + align:start position:0% +both the I values are + + + align:start position:0% +both the I values are +negative then I know the trace is + + align:start position:0% +negative then I know the trace is + + + align:start position:0% +negative then I know the trace is +negative but the determinant is + + align:start position:0% +negative but the determinant is + + + align:start position:0% +negative but the determinant is +positive cuz it's the product of the two + + align:start position:0% +positive cuz it's the product of the two + + + align:start position:0% +positive cuz it's the product of the two +I + + align:start position:0% +I + + + align:start position:0% +I +vales so this determinant is Lambda 1 * + + align:start position:0% +vales so this determinant is Lambda 1 * + + + align:start position:0% +vales so this determinant is Lambda 1 * +Lambda 2 this is this is Lambda 1 * + + align:start position:0% +Lambda 2 this is this is Lambda 1 * + + + align:start position:0% +Lambda 2 this is this is Lambda 1 * +Lambda 2 and if they're both negative + + align:start position:0% +Lambda 2 and if they're both negative + + + align:start position:0% +Lambda 2 and if they're both negative +the product is positive so positive + + align:start position:0% +the product is positive so positive + + + align:start position:0% +the product is positive so positive +determinant negative + + align:start position:0% +determinant negative + + + align:start position:0% +determinant negative +Trace I can easily track down the this + + align:start position:0% +Trace I can easily track down the this + + + align:start position:0% +Trace I can easily track down the this +condition also for the if if there's an + + align:start position:0% +condition also for the if if there's an + + + align:start position:0% +condition also for the if if there's an +imaginary part hanging around okay so + + align:start position:0% +imaginary part hanging around okay so + + + align:start position:0% +imaginary part hanging around okay so +that's a like a small but quite useful + + align:start position:0% +that's a like a small but quite useful + + + align:start position:0% +that's a like a small but quite useful +uh because 2 by two is always important + + align:start position:0% +uh because 2 by two is always important + + + align:start position:0% +uh because 2 by two is always important +uh uh comment on uh stability okay so uh + + align:start position:0% +uh uh comment on uh stability okay so uh + + + align:start position:0% +uh uh comment on uh stability okay so uh +let's just look at the picture + + align:start position:0% +let's just look at the picture + + + align:start position:0% +let's just look at the picture +again okay the main part of my lecture + + align:start position:0% +again okay the main part of my lecture + + + align:start position:0% +again okay the main part of my lecture +the the one thing you want to be able to + + align:start position:0% +the the one thing you want to be able to + + + align:start position:0% +the the one thing you want to be able to +like just do automatically is this step + + align:start position:0% +like just do automatically is this step + + + align:start position:0% +like just do automatically is this step +of solving the + + align:start position:0% +of solving the + + + align:start position:0% +of solving the +system find the igon values find the IG + + align:start position:0% +system find the igon values find the IG + + + align:start position:0% +system find the igon values find the IG +vectors find the coefficients and notice + + align:start position:0% +vectors find the coefficients and notice + + + align:start position:0% +vectors find the coefficients and notice +what what's the Matrix + + align:start position:0% +what what's the Matrix + + + align:start position:0% +what what's the Matrix +in this linear system here I can't help + + align:start position:0% +in this linear system here I can't help + + + align:start position:0% +in this linear system here I can't help +if if I if I have equations like + + align:start position:0% +if if I if I have equations like + + + align:start position:0% +if if I if I have equations like +that that's that's my equation's column + + align:start position:0% +that that's that's my equation's column + + + align:start position:0% +that that's that's my equation's column +at a time what's the Matrix form of that + + align:start position:0% +at a time what's the Matrix form of that + + + align:start position:0% +at a time what's the Matrix form of that +equation so so this this uh system of + + align:start position:0% +equation so so this this uh system of + + + align:start position:0% +equation so so this this uh system of +equations + + align:start position:0% +equations + + + align:start position:0% +equations +is is some + + align:start position:0% +is is some + + + align:start position:0% +is is some +Matrix multiplying C1 C2 to give U of + + align:start position:0% +Matrix multiplying C1 C2 to give U of + + + align:start position:0% +Matrix multiplying C1 C2 to give U of +Zer one Z + + align:start position:0% +Zer one Z + + + align:start position:0% +Zer one Z +what's the Matrix well it's obviously + + align:start position:0% +what's the Matrix well it's obviously + + + align:start position:0% +what's the Matrix well it's obviously +21 1 minus one but we have a name or at + + align:start position:0% +21 1 minus one but we have a name or at + + + align:start position:0% +21 1 minus one but we have a name or at +least a letter actually a name for that + + align:start position:0% +least a letter actually a name for that + + + align:start position:0% +least a letter actually a name for that +Matrix what what Matrix are we are we + + align:start position:0% +Matrix what what Matrix are we are we + + + align:start position:0% +Matrix what what Matrix are we are we +are we dealing with here in this step of + + align:start position:0% +are we dealing with here in this step of + + + align:start position:0% +are we dealing with here in this step of +finding the + + align:start position:0% +finding the + + + align:start position:0% +finding the +C's its letter is s it's the I Vector + + align:start position:0% +C's its letter is s it's the I Vector + + + align:start position:0% +C's its letter is s it's the I Vector +Matrix of course these are the I vectors + + align:start position:0% +Matrix of course these are the I vectors + + + align:start position:0% +Matrix of course these are the I vectors +they're in The Columns of our Matrix so + + align:start position:0% +they're in The Columns of our Matrix so + + + align:start position:0% +they're in The Columns of our Matrix so +this is SC equals U of + + align:start position:0% +this is SC equals U of + + + align:start position:0% +this is SC equals U of +0 is the is the uh that step where you + + align:start position:0% +0 is the is the uh that step where you + + + align:start position:0% +0 is the is the uh that step where you +find the actual uh coefficients you find + + align:start position:0% +find the actual uh coefficients you find + + + align:start position:0% +find the actual uh coefficients you find +out how much of each uh pure exponential + + align:start position:0% +out how much of each uh pure exponential + + + align:start position:0% +out how much of each uh pure exponential +is in the + + align:start position:0% +is in the + + + align:start position:0% +is in the +solution by getting it right at the + + align:start position:0% +solution by getting it right at the + + + align:start position:0% +solution by getting it right at the +start then it stays right + + align:start position:0% +start then it stays right + + + align:start position:0% +start then it stays right +forever you're you're seeing this + + align:start position:0% +forever you're you're seeing this + + + align:start position:0% +forever you're you're seeing this +picture that that each each pure + + align:start position:0% +picture that that each each pure + + + align:start position:0% +picture that that each each pure +exponential goes on its own way when + + align:start position:0% +exponential goes on its own way when + + + align:start position:0% +exponential goes on its own way when +once you start it from U of0 so you + + align:start position:0% +once you start it from U of0 so you + + + align:start position:0% +once you start it from U of0 so you +start it by figuring out how much each + + align:start position:0% +start it by figuring out how much each + + + align:start position:0% +start it by figuring out how much each +one is present in U of0 and then off + + align:start position:0% +one is present in U of0 and then off + + + align:start position:0% +one is present in U of0 and then off +they go okay so um so that's a system of + + align:start position:0% +they go okay so um so that's a system of + + + align:start position:0% +they go okay so um so that's a system of +two equations in two unknowns + + align:start position:0% +two equations in two unknowns + + + align:start position:0% +two equations in two unknowns +coupled + + align:start position:0% +coupled + + + align:start position:0% +coupled +uh the The Matrix sort of couples U1 and + + align:start position:0% +uh the The Matrix sort of couples U1 and + + + align:start position:0% +uh the The Matrix sort of couples U1 and +U2 and the igen values and igen vectors + + align:start position:0% +U2 and the igen values and igen vectors + + + align:start position:0% +U2 and the igen values and igen vectors +uncouple it diagonalize it actually okay + + align:start position:0% +uncouple it diagonalize it actually okay + + + align:start position:0% +uncouple it diagonalize it actually okay +now can I can I think in terms of s and + + align:start position:0% +now can I can I think in terms of s and + + + align:start position:0% +now can I can I think in terms of s and +Lambda so I want to write the solution + + align:start position:0% +Lambda so I want to write the solution + + + align:start position:0% +Lambda so I want to write the solution +down again in terms of s and Lambda okay + + align:start position:0% +down again in terms of s and Lambda okay + + + align:start position:0% +down again in terms of s and Lambda okay +I'll do that on this far + + align:start position:0% +I'll do that on this far + + + align:start position:0% +I'll do that on this far +board okay so I'm coming back + + align:start position:0% + + + + align:start position:0% + +to I'm coming back to our equation + + align:start position:0% +to I'm coming back to our equation + + + align:start position:0% +to I'm coming back to our equation +DT equals AU + + align:start position:0% + + + + align:start position:0% + +now this this Matrix a couples them the + + align:start position:0% +now this this Matrix a couples them the + + + align:start position:0% +now this this Matrix a couples them the +whole point of I vectors is to uncouple + + align:start position:0% +whole point of I vectors is to uncouple + + + align:start position:0% +whole point of I vectors is to uncouple +so one way to see that is introduce + + align:start position:0% +so one way to see that is introduce + + + align:start position:0% +so one way to see that is introduce +set u equal a not a It's s the I Vector + + align:start position:0% +set u equal a not a It's s the I Vector + + + align:start position:0% +set u equal a not a It's s the I Vector +Matrix that + + align:start position:0% + + + + align:start position:0% + +uncouples so I'm I'm taking this + + align:start position:0% +uncouples so I'm I'm taking this + + + align:start position:0% +uncouples so I'm I'm taking this +equation as I'm given coupled with with + + align:start position:0% +equation as I'm given coupled with with + + + align:start position:0% +equation as I'm given coupled with with +a has is probably full of + + align:start position:0% +a has is probably full of + + + align:start position:0% +a has is probably full of +nonzeros but I'm by uncoupling it I mean + + align:start position:0% +nonzeros but I'm by uncoupling it I mean + + + align:start position:0% +nonzeros but I'm by uncoupling it I mean +I'm diagonalizing it if I can get a + + align:start position:0% +I'm diagonalizing it if I can get a + + + align:start position:0% +I'm diagonalizing it if I can get a +diagonal matrix I'm I'm in okay so I + + align:start position:0% +diagonal matrix I'm I'm in okay so I + + + align:start position:0% +diagonal matrix I'm I'm in okay so I +plug that in this is a + + align:start position:0% +plug that in this is a + + + align:start position:0% +plug that in this is a +SV and this is s + + align:start position:0% + + + + align:start position:0% + +dvdt s is a constant it's this is the I + + align:start position:0% +dvdt s is a constant it's this is the I + + + align:start position:0% +dvdt s is a constant it's this is the I +Vector + + align:start position:0% +Vector + + + align:start position:0% +Vector +Matrix this is the IG Vector + + align:start position:0% + + + + align:start position:0% + +Matrix okay now I'm going to bring s + + align:start position:0% +Matrix okay now I'm going to bring s + + + align:start position:0% +Matrix okay now I'm going to bring s +inverse over + + align:start position:0% + + + + align:start position:0% + +here and what have I + + align:start position:0% + + + + align:start position:0% + +got that combination s inverse as s + + align:start position:0% +got that combination s inverse as s + + + align:start position:0% +got that combination s inverse as s +is Lambda the diagonal + + align:start position:0% +is Lambda the diagonal + + + align:start position:0% +is Lambda the diagonal +matrix that's that's the point that that + + align:start position:0% +matrix that's that's the point that that + + + align:start position:0% +matrix that's that's the point that that +in if I'm using the + + align:start position:0% +in if I'm using the + + + align:start position:0% +in if I'm using the +igen vectors as my + + align:start position:0% +igen vectors as my + + + align:start position:0% +igen vectors as my +basis then my system of equations is + + align:start position:0% +basis then my system of equations is + + + align:start position:0% +basis then my system of equations is +just diagonal each there's no coupling + + align:start position:0% +just diagonal each there's no coupling + + + align:start position:0% +just diagonal each there's no coupling +anymore dv1 DT is Lambda 1 V1 so let's + + align:start position:0% +anymore dv1 DT is Lambda 1 V1 so let's + + + align:start position:0% +anymore dv1 DT is Lambda 1 V1 so let's +just write that down dv1 + + align:start position:0% +just write that down dv1 + + + align:start position:0% +just write that down dv1 +DT is Lambda 1 + + align:start position:0% +DT is Lambda 1 + + + align:start position:0% +DT is Lambda 1 +V1 and so on for all n of the equations + + align:start position:0% +V1 and so on for all n of the equations + + + align:start position:0% +V1 and so on for all n of the equations +it's a system of equations but they're + + align:start position:0% +it's a system of equations but they're + + + align:start position:0% +it's a system of equations but they're +not connected so they're easy to solve + + align:start position:0% +not connected so they're easy to solve + + + align:start position:0% +not connected so they're easy to solve +and why don't I just write down the + + align:start position:0% + + + + align:start position:0% + +solution V well V is now some e to the + + align:start position:0% +solution V well V is now some e to the + + + align:start position:0% +solution V well V is now some e to the +Lambda 1 + + align:start position:0% +Lambda 1 + + + align:start position:0% +Lambda 1 +t uh well + + align:start position:0% +t uh well + + + align:start position:0% +t uh well +okay I guess my idea here now is to + + align:start position:0% +okay I guess my idea here now is to + + + align:start position:0% +okay I guess my idea here now is to +use uh the natural notation V of t + + align:start position:0% +use uh the natural notation V of t + + + align:start position:0% +use uh the natural notation V of t +is e to the Lambda t v + + align:start position:0% +is e to the Lambda t v + + + align:start position:0% +is e to the Lambda t v +of0 and U of + + align:start position:0% +of0 and U of + + + align:start position:0% +of0 and U of +T will be + + align:start position:0% +T will be + + + align:start position:0% +T will be +s e to the Lambda t s inverse U of + + align:start position:0% +s e to the Lambda t s inverse U of + + + align:start position:0% +s e to the Lambda t s inverse U of +zero this is the this is the uh formula + + align:start position:0% +zero this is the this is the uh formula + + + align:start position:0% +zero this is the this is the uh formula +I'm headed + + align:start position:0% + + + + align:start position:0% + +for this this Matrix s e to the Lambda t + + align:start position:0% +for this this Matrix s e to the Lambda t + + + align:start position:0% +for this this Matrix s e to the Lambda t +s + + align:start position:0% +s + + + align:start position:0% +s +inverse that's my exponential that's my + + align:start position:0% +inverse that's my exponential that's my + + + align:start position:0% +inverse that's my exponential that's my +e to the a + + align:start position:0% +e to the a + + + align:start position:0% +e to the a +t is this + + align:start position:0% +t is this + + + align:start position:0% +t is this +s e to the Lambda t s + + align:start position:0% + + + + align:start position:0% + +inverse so my my job really now is to + + align:start position:0% +inverse so my my job really now is to + + + align:start position:0% +inverse so my my job really now is to +explain what's going on with this Matrix + + align:start position:0% +explain what's going on with this Matrix + + + align:start position:0% +explain what's going on with this Matrix +up in the exponential what does that + + align:start position:0% +up in the exponential what does that + + + align:start position:0% +up in the exponential what does that +mean what do it mean to say e to a + + align:start position:0% +mean what do it mean to say e to a + + + align:start position:0% +mean what do it mean to say e to a +matrix + + align:start position:0% + + + + align:start position:0% + +this ought to be easier because this is + + align:start position:0% +this ought to be easier because this is + + + align:start position:0% +this ought to be easier because this is +e to a diagonal matrix but still it's a + + align:start position:0% +e to a diagonal matrix but still it's a + + + align:start position:0% +e to a diagonal matrix but still it's a +matrix what what do what do we mean by e + + align:start position:0% +matrix what what do what do we mean by e + + + align:start position:0% +matrix what what do what do we mean by e +to the a t because + + align:start position:0% +to the a t because + + + align:start position:0% +to the a t because +really e to the a t is my answer here my + + align:start position:0% +really e to the a t is my answer here my + + + align:start position:0% +really e to the a t is my answer here my +my answer to this equation + + align:start position:0% + + + + align:start position:0% + +is this U of T this this is my this is + + align:start position:0% +is this U of T this this is my this is + + + align:start position:0% +is this U of T this this is my this is +my e to the A T U of + + align:start position:0% +my e to the A T U of + + + align:start position:0% +my e to the A T U of +zero so it's + + align:start position:0% +zero so it's + + + align:start position:0% +zero so it's +my my job is really now to to say what + + align:start position:0% +my my job is really now to to say what + + + align:start position:0% +my my job is really now to to say what +what does that mean what's the + + align:start position:0% +what does that mean what's the + + + align:start position:0% +what does that mean what's the +exponential of a matrix and why is that + + align:start position:0% +exponential of a matrix and why is that + + + align:start position:0% +exponential of a matrix and why is that +formula + + align:start position:0% +formula + + + align:start position:0% +formula +correct okay so I'll put that on the + + align:start position:0% +correct okay so I'll put that on the + + + align:start position:0% +correct okay so I'll put that on the +board + + align:start position:0% +board + + + align:start position:0% +board +underneath what's the exponential of a + + align:start position:0% +underneath what's the exponential of a + + + align:start position:0% +underneath what's the exponential of a +matrix let me come back here so I'm + + align:start position:0% +matrix let me come back here so I'm + + + align:start position:0% +matrix let me come back here so I'm +talking about Matrix + + align:start position:0% + + + + align:start position:0% + +exponentials e to the a t okay + + align:start position:0% +exponentials e to the a t okay + + + align:start position:0% +exponentials e to the a t okay +how are we going to define the + + align:start position:0% +how are we going to define the + + + align:start position:0% +how are we going to define the +exponential of a of of + + align:start position:0% +exponential of a of of + + + align:start position:0% +exponential of a of of +something the trick the the idea is the + + align:start position:0% +something the trick the the idea is the + + + align:start position:0% +something the trick the the idea is the +the thing to go back to is + + align:start position:0% +the thing to go back to is + + + align:start position:0% +the thing to go back to is +exponential there's a power series for + + align:start position:0% +exponential there's a power series for + + + align:start position:0% +exponential there's a power series for +exponentials that's how you you the good + + align:start position:0% +exponentials that's how you you the good + + + align:start position:0% +exponentials that's how you you the good +way to define e to the x is the power + + align:start position:0% +way to define e to the x is the power + + + align:start position:0% +way to define e to the x is the power +series 1 + x + 12 x^2 6 x cubed and + + align:start position:0% +series 1 + x + 12 x^2 6 x cubed and + + + align:start position:0% +series 1 + x + 12 x^2 6 x cubed and +we'll do do it now when the when we have + + align:start position:0% +we'll do do it now when the when we have + + + align:start position:0% +we'll do do it now when the when we have +a matrix so the one becomes the identity + + align:start position:0% +a matrix so the one becomes the identity + + + align:start position:0% +a matrix so the one becomes the identity +the x is + + align:start position:0% +the x is + + + align:start position:0% +the x is +a the x squ is a t^ 2ar and I divide by + + align:start position:0% +a the x squ is a t^ 2ar and I divide by + + + align:start position:0% +a the x squ is a t^ 2ar and I divide by +two the the cube the X cube is a cubed + + align:start position:0% +two the the cube the X cube is a cubed + + + align:start position:0% +two the the cube the X cube is a cubed +over 6 and what's the general term in + + align:start position:0% +over 6 and what's the general term in + + + align:start position:0% +over 6 and what's the general term in +here a to the N power divided by and it + + align:start position:0% +here a to the N power divided by and it + + + align:start position:0% +here a to the N power divided by and it +goes on but what do I divide + + align:start position:0% +goes on but what do I divide + + + align:start position:0% +goes on but what do I divide +by so you see the pattern here I divided + + align:start position:0% +by so you see the pattern here I divided + + + align:start position:0% +by so you see the pattern here I divided +by one here I divided by one by two by + + align:start position:0% +by one here I divided by one by two by + + + align:start position:0% +by one here I divided by one by two by +six those are the factorials it's n + + align:start position:0% + + + + align:start position:0% + +factorial that was like the the the one + + align:start position:0% +factorial that was like the the the one + + + align:start position:0% +factorial that was like the the the one +beautiful tayor + + align:start position:0% + + + + align:start position:0% + +series the one beautiful tayor series + + align:start position:0% +series the one beautiful tayor series + + + align:start position:0% +series the one beautiful tayor series +well there are two there are two + + align:start position:0% +well there are two there are two + + + align:start position:0% +well there are two there are two +beautiful tayor Series in this world the + + align:start position:0% +beautiful tayor Series in this world the + + + align:start position:0% +beautiful tayor Series in this world the +tayor series for e x is the sum with X + + align:start position:0% +tayor series for e x is the sum with X + + + align:start position:0% +tayor series for e x is the sum with X +to the N Over N + + align:start position:0% +to the N Over N + + + align:start position:0% +to the N Over N +factorial and all I'm doing is doing the + + align:start position:0% +factorial and all I'm doing is doing the + + + align:start position:0% +factorial and all I'm doing is doing the +same thing for matrices the other + + align:start position:0% +same thing for matrices the other + + + align:start position:0% +same thing for matrices the other +beautiful tailor series is just the sum + + align:start position:0% +beautiful tailor series is just the sum + + + align:start position:0% +beautiful tailor series is just the sum +of x to the + + align:start position:0% +of x to the + + + align:start position:0% +of x to the +N not divided by n factorial can you do + + align:start position:0% +N not divided by n factorial can you do + + + align:start position:0% +N not divided by n factorial can you do +you know what function that one is so if + + align:start position:0% +you know what function that one is so if + + + align:start position:0% +you know what function that one is so if +I take this is the series all these sums + + align:start position:0% +I take this is the series all these sums + + + align:start position:0% +I take this is the series all these sums +are going from zero to Infinity + + align:start position:0% +are going from zero to Infinity + + + align:start position:0% +are going from zero to Infinity +what what function have I got this is + + align:start position:0% +what what function have I got this is + + + align:start position:0% +what what function have I got this is +like a side + + align:start position:0% +like a side + + + align:start position:0% +like a side +comment this is 1 + x + x^2 + x Cub + x + + align:start position:0% +comment this is 1 + x + x^2 + x Cub + x + + + align:start position:0% +comment this is 1 + x + x^2 + x Cub + x +4 not divided by anything what what's + + align:start position:0% +4 not divided by anything what what's + + + align:start position:0% +4 not divided by anything what what's +that + + align:start position:0% +that + + + align:start position:0% +that +function 1 + x + x^2 + x Cub + X4 + + align:start position:0% +function 1 + x + x^2 + x Cub + X4 + + + align:start position:0% +function 1 + x + x^2 + x Cub + X4 +forever is 1 over 1 - x it's the + + align:start position:0% +forever is 1 over 1 - x it's the + + + align:start position:0% +forever is 1 over 1 - x it's the +geometric + + align:start position:0% +geometric + + + align:start position:0% +geometric +series the nicest power series of all so + + align:start position:0% +series the nicest power series of all so + + + align:start position:0% +series the nicest power series of all so +actually of course there would be a + + align:start position:0% +actually of course there would be a + + + align:start position:0% +actually of course there would be a +similar thing here + + align:start position:0% +similar thing here + + + align:start position:0% +similar thing here +uh if I if I wanted IUS a t inverse + + align:start position:0% +uh if I if I wanted IUS a t inverse + + + align:start position:0% +uh if I if I wanted IUS a t inverse +would + + align:start position:0% +would + + + align:start position:0% +would +be now I've got + + align:start position:0% +be now I've got + + + align:start position:0% +be now I've got +matrices I've got to have matrices + + align:start position:0% +matrices I've got to have matrices + + + align:start position:0% +matrices I've got to have matrices +everywhere but it's just like that + + align:start position:0% +everywhere but it's just like that + + + align:start position:0% +everywhere but it's just like that +series with and just like this one + + align:start position:0% +series with and just like this one + + + align:start position:0% +series with and just like this one +without the divisions it's I + a t + a + + align:start position:0% +without the divisions it's I + a t + a + + + align:start position:0% +without the divisions it's I + a t + a +t^ + + align:start position:0% +t^ + + + align:start position:0% +t^ +2 plus a + + align:start position:0% +2 plus a + + + align:start position:0% +2 plus a +cubed and forever + + align:start position:0% + + + + align:start position:0% + +so that's actually a a reasonable way to + + align:start position:0% +so that's actually a a reasonable way to + + + align:start position:0% +so that's actually a a reasonable way to +find the inverse of a matrix if I chop + + align:start position:0% +find the inverse of a matrix if I chop + + + align:start position:0% +find the inverse of a matrix if I chop +it + + align:start position:0% +it + + + align:start position:0% +it +off well it's reasonable if T is small + + align:start position:0% +off well it's reasonable if T is small + + + align:start position:0% +off well it's reasonable if T is small +if T is a small number then then t^2 is + + align:start position:0% +if T is a small number then then t^2 is + + + align:start position:0% +if T is a small number then then t^2 is +extremely small T Cub is even smaller so + + align:start position:0% +extremely small T Cub is even smaller so + + + align:start position:0% +extremely small T Cub is even smaller so +approximately that inverse is I + a t i + + align:start position:0% +approximately that inverse is I + a t i + + + align:start position:0% +approximately that inverse is I + a t i +can keep more terms if I like do you see + + align:start position:0% +can keep more terms if I like do you see + + + align:start position:0% +can keep more terms if I like do you see +what I'm doing I'm just saying we can + + align:start position:0% +what I'm doing I'm just saying we can + + + align:start position:0% +what I'm doing I'm just saying we can +can do the same thing for matrices that + + align:start position:0% +can do the same thing for matrices that + + + align:start position:0% +can do the same thing for matrices that +we do for ordinary + + align:start position:0% +we do for ordinary + + + align:start position:0% +we do for ordinary +functions and the good thing about the + + align:start position:0% +functions and the good thing about the + + + align:start position:0% +functions and the good thing about the +exponential Series so in a way this + + align:start position:0% +exponential Series so in a way this + + + align:start position:0% +exponential Series so in a way this +series is better than this + + align:start position:0% +series is better than this + + + align:start position:0% +series is better than this +one why because this one always + + align:start position:0% +one why because this one always + + + align:start position:0% +one why because this one always +converges I'm dividing by these bigger + + align:start position:0% +converges I'm dividing by these bigger + + + align:start position:0% +converges I'm dividing by these bigger +and bigger numbers so whatever Matrix a + + align:start position:0% +and bigger numbers so whatever Matrix a + + + align:start position:0% +and bigger numbers so whatever Matrix a +and however large T is that series these + + align:start position:0% +and however large T is that series these + + + align:start position:0% +and however large T is that series these +terms go to zero the series adds up to a + + align:start position:0% +terms go to zero the series adds up to a + + + align:start position:0% +terms go to zero the series adds up to a +finite sum e to the a is a is is + + align:start position:0% +finite sum e to the a is a is is + + + align:start position:0% +finite sum e to the a is a is is +completely + + align:start position:0% +completely + + + align:start position:0% +completely +defined whereas the second + + align:start position:0% +defined whereas the second + + + align:start position:0% +defined whereas the second +guy could fail right if a t is Big + + align:start position:0% +guy could fail right if a t is Big + + + align:start position:0% +guy could fail right if a t is Big +somehow if a has an igen value larger + + align:start position:0% +somehow if a has an igen value larger + + + align:start position:0% +somehow if a has an igen value larger +than one then when I Square it it'll + + align:start position:0% +than one then when I Square it it'll + + + align:start position:0% +than one then when I Square it it'll +have that IG value squared when I Cube + + align:start position:0% +have that IG value squared when I Cube + + + align:start position:0% +have that IG value squared when I Cube +it the I value will be cubed that series + + align:start position:0% +it the I value will be cubed that series + + + align:start position:0% +it the I value will be cubed that series +will blow + + align:start position:0% +will blow + + + align:start position:0% +will blow +up unless the I values of a are smaller + + align:start position:0% +up unless the I values of a are smaller + + + align:start position:0% +up unless the I values of a are smaller +than one so when the igen values of a + + align:start position:0% +than one so when the igen values of a + + + align:start position:0% +than one so when the igen values of a +are smaller than one so I better put + + align:start position:0% +are smaller than one so I better put + + + align:start position:0% +are smaller than one so I better put +that in the all IG values of at below + + align:start position:0% +that in the all IG values of at below + + + align:start position:0% +that in the all IG values of at below +one then that series converges and gives + + align:start position:0% +one then that series converges and gives + + + align:start position:0% +one then that series converges and gives +me the inverse okay so this is the guy + + align:start position:0% +me the inverse okay so this is the guy + + + align:start position:0% +me the inverse okay so this is the guy +I'm I'm chiefly interested in and I + + align:start position:0% +I'm I'm chiefly interested in and I + + + align:start position:0% +I'm I'm chiefly interested in and I +wanted + + align:start position:0% +wanted + + + align:start position:0% +wanted +to connect it to oh okay what's how do I + + align:start position:0% +to connect it to oh okay what's how do I + + + align:start position:0% +to connect it to oh okay what's how do I +how do I get this is my like main thing + + align:start position:0% +how do I get this is my like main thing + + + align:start position:0% +how do I get this is my like main thing +now to do + + align:start position:0% +now to do + + + align:start position:0% +now to do +how how do I get e to the a t how do I + + align:start position:0% +how how do I get e to the a t how do I + + + align:start position:0% +how how do I get e to the a t how do I +see that e to the a is the same as + + align:start position:0% + + + + align:start position:0% + +this in other words I can find e to the + + align:start position:0% +this in other words I can find e to the + + + align:start position:0% +this in other words I can find e to the +a by finding s and Lambda because now e + + align:start position:0% +a by finding s and Lambda because now e + + + align:start position:0% +a by finding s and Lambda because now e +to the Lambda T is + + align:start position:0% +to the Lambda T is + + + align:start position:0% +to the Lambda T is +easy Lambda is a diagonal matrix and we + + align:start position:0% +easy Lambda is a diagonal matrix and we + + + align:start position:0% +easy Lambda is a diagonal matrix and we +can write down e to the Lambda T and + + align:start position:0% +can write down e to the Lambda T and + + + align:start position:0% +can write down e to the Lambda T and +will right in a minute but how do you + + align:start position:0% +will right in a minute but how do you + + + align:start position:0% +will right in a minute but how do you +see what do you see that we're hoping + + align:start position:0% +see what do you see that we're hoping + + + align:start position:0% +see what do you see that we're hoping +for + + align:start position:0% +for + + + align:start position:0% +for +a we're hoping that we can compute e to + + align:start position:0% +a we're hoping that we can compute e to + + + align:start position:0% +a we're hoping that we can compute e to +the a from s and + + align:start position:0% +the a from s and + + + align:start position:0% +the a from s and +Lambda and I have to look at that + + align:start position:0% +Lambda and I have to look at that + + + align:start position:0% +Lambda and I have to look at that +definition and say okay how how do I get + + align:start position:0% +definition and say okay how how do I get + + + align:start position:0% +definition and say okay how how do I get +an s in a Lambda to come out of that + + align:start position:0% +an s in a Lambda to come out of that + + + align:start position:0% +an s in a Lambda to come out of that +okay can do you see how I I I want to + + align:start position:0% +okay can do you see how I I I want to + + + align:start position:0% +okay can do you see how I I I want to +connect that to that from that + + align:start position:0% +connect that to that from that + + + align:start position:0% +connect that to that from that +definition so let me erase this uh the + + align:start position:0% +definition so let me erase this uh the + + + align:start position:0% +definition so let me erase this uh the +geometric + + align:start position:0% +geometric + + + align:start position:0% +geometric +series which + + align:start position:0% + + + + align:start position:0% + +isn't part of the differential + + align:start position:0% +isn't part of the differential + + + align:start position:0% +isn't part of the differential +equations case + + align:start position:0% +equations case + + + align:start position:0% +equations case +and get the S and the Lambda into this + + align:start position:0% +and get the S and the Lambda into this + + + align:start position:0% +and get the S and the Lambda into this +picture oh okay uh here we go + + align:start position:0% +picture oh okay uh here we go + + + align:start position:0% +picture oh okay uh here we go +um so identity is + + align:start position:0% +um so identity is + + + align:start position:0% +um so identity is +fine + + align:start position:0% +fine + + + align:start position:0% +fine +now all right you you you can see how + + align:start position:0% +now all right you you you can see how + + + align:start position:0% +now all right you you you can see how +how how am I going to get a replaced by + + align:start position:0% +how how am I going to get a replaced by + + + align:start position:0% +how how am I going to get a replaced by +S and S's and lambdas well I use the + + align:start position:0% +S and S's and lambdas well I use the + + + align:start position:0% +S and S's and lambdas well I use the +fundamental formula of this whole + + align:start position:0% +fundamental formula of this whole + + + align:start position:0% +fundamental formula of this whole +chapter a is s Lambda s inverse and then + + align:start position:0% +chapter a is s Lambda s inverse and then + + + align:start position:0% +chapter a is s Lambda s inverse and then +times T that's a + + align:start position:0% +times T that's a + + + align:start position:0% +times T that's a +t okay what's a 2 + + align:start position:0% +t okay what's a 2 + + + align:start position:0% +t okay what's a 2 +T I can I've got to divide by two I've + + align:start position:0% +T I can I've got to divide by two I've + + + align:start position:0% +T I can I've got to divide by two I've +got the + + align:start position:0% +got the + + + align:start position:0% +got the +t^2 and I've got an A + + align:start position:0% +t^2 and I've got an A + + + align:start position:0% +t^2 and I've got an A +Squared all right + + align:start position:0% +Squared all right + + + align:start position:0% +Squared all right +so I've got to there's a there's + + align:start position:0% +so I've got to there's a there's + + + align:start position:0% +so I've got to there's a there's +a now Square it so what happens when I + + align:start position:0% +a now Square it so what happens when I + + + align:start position:0% +a now Square it so what happens when I +Square it we've seen that before when I + + align:start position:0% +Square it we've seen that before when I + + + align:start position:0% +Square it we've seen that before when I +Square it I get S Lambda squared s + + align:start position:0% +Square it I get S Lambda squared s + + + align:start position:0% +Square it I get S Lambda squared s +inverse + + align:start position:0% +inverse + + + align:start position:0% +inverse +right when I square that thing the the + + align:start position:0% +right when I square that thing the the + + + align:start position:0% +right when I square that thing the the +there's an S an S cancels out an S + + align:start position:0% +there's an S an S cancels out an S + + + align:start position:0% +there's an S an S cancels out an S +inverse I'm left with the S on the left + + align:start position:0% +inverse I'm left with the S on the left + + + align:start position:0% +inverse I'm left with the S on the left +the S inverse on the right and Lambda + + align:start position:0% +the S inverse on the right and Lambda + + + align:start position:0% +the S inverse on the right and Lambda +squar in the middle and so + + align:start position:0% +squar in the middle and so + + + align:start position:0% +squar in the middle and so +on the next one will be S Lambda cubed s + + align:start position:0% +on the next one will be S Lambda cubed s + + + align:start position:0% +on the next one will be S Lambda cubed s +inverse * T Cub over 3 factorial and + + align:start position:0% + + + + align:start position:0% + +now what do I do now I want to pull an S + + align:start position:0% +now what do I do now I want to pull an S + + + align:start position:0% +now what do I do now I want to pull an S +out from everything I want an S + + align:start position:0% +out from everything I want an S + + + align:start position:0% +out from everything I want an S +out of the whole thing oh look I better + + align:start position:0% +out of the whole thing oh look I better + + + align:start position:0% +out of the whole thing oh look I better +write the identity how I I want to be + + align:start position:0% +write the identity how I I want to be + + + align:start position:0% +write the identity how I I want to be +able to pull an S out and an S inverse + + align:start position:0% +able to pull an S out and an S inverse + + + align:start position:0% +able to pull an S out and an S inverse +out from the other side so I just write + + align:start position:0% +out from the other side so I just write + + + align:start position:0% +out from the other side so I just write +the identity as s * s inverse so I have + + align:start position:0% +the identity as s * s inverse so I have + + + align:start position:0% +the identity as s * s inverse so I have +an S there and an S inverse from this + + align:start position:0% +an S there and an S inverse from this + + + align:start position:0% +an S there and an S inverse from this +side and what have I got in the + + align:start position:0% + + + + align:start position:0% + +middle if I pull out an S and an S + + align:start position:0% +middle if I pull out an S and an S + + + align:start position:0% +middle if I pull out an S and an S +inverse what have I got in the middle + + align:start position:0% +inverse what have I got in the middle + + + align:start position:0% +inverse what have I got in the middle +I've got the identity a Lambda t a + + align:start position:0% +I've got the identity a Lambda t a + + + align:start position:0% +I've got the identity a Lambda t a +Lambda 2 t^2 over 2 I've got e to the + + align:start position:0% +Lambda 2 t^2 over 2 I've got e to the + + + align:start position:0% +Lambda 2 t^2 over 2 I've got e to the +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +T that's what's in the middle that's my + + align:start position:0% +T that's what's in the middle that's my + + + align:start position:0% +T that's what's in the middle that's my +formula for E to the a + + align:start position:0% +formula for E to the a + + + align:start position:0% +formula for E to the a +t oh now I have to ask you does this + + align:start position:0% +t oh now I have to ask you does this + + + align:start position:0% +t oh now I have to ask you does this +formula always + + align:start position:0% +formula always + + + align:start position:0% +formula always +work this formula always + + align:start position:0% +work this formula always + + + align:start position:0% +work this formula always +works well except it's an infinite + + align:start position:0% +works well except it's an infinite + + + align:start position:0% +works well except it's an infinite +series but what do I mean by always work + + align:start position:0% +series but what do I mean by always work + + + align:start position:0% +series but what do I mean by always work +and this one doesn't always work and I + + align:start position:0% +and this one doesn't always work and I + + + align:start position:0% +and this one doesn't always work and I +just have to remind you of what + + align:start position:0% +just have to remind you of what + + + align:start position:0% +just have to remind you of what +assumption is built into this formula + + align:start position:0% +assumption is built into this formula + + + align:start position:0% +assumption is built into this formula +that's not built into the + + align:start position:0% +that's not built into the + + + align:start position:0% +that's not built into the +original the assumption that a can be + + align:start position:0% +original the assumption that a can be + + + align:start position:0% +original the assumption that a can be +diagonalized you remember that there are + + align:start position:0% +diagonalized you remember that there are + + + align:start position:0% +diagonalized you remember that there are +some + + align:start position:0% +some + + + align:start position:0% +some +small some subset of matrices that don't + + align:start position:0% +small some subset of matrices that don't + + + align:start position:0% +small some subset of matrices that don't +have an independent igon vectors so we + + align:start position:0% +have an independent igon vectors so we + + + align:start position:0% +have an independent igon vectors so we +don't have an S inverse for those + + align:start position:0% +don't have an S inverse for those + + + align:start position:0% +don't have an S inverse for those +matrices and the whole diagonalization + + align:start position:0% +matrices and the whole diagonalization + + + align:start position:0% +matrices and the whole diagonalization +breaks + + align:start position:0% +breaks + + + align:start position:0% +breaks +down we could still make it triangular + + align:start position:0% +down we could still make it triangular + + + align:start position:0% +down we could still make it triangular +I'll tell you you about that but + + align:start position:0% +I'll tell you you about that but + + + align:start position:0% +I'll tell you you about that but +diagonal we can't do for those + + align:start position:0% +diagonal we can't do for those + + + align:start position:0% +diagonal we can't do for those +particular degenerate matrices that + + align:start position:0% +particular degenerate matrices that + + + align:start position:0% +particular degenerate matrices that +don't have enough independent igen + + align:start position:0% +don't have enough independent igen + + + align:start position:0% +don't have enough independent igen +vectors but otherwise this is golden + + align:start position:0% +vectors but otherwise this is golden + + + align:start position:0% +vectors but otherwise this is golden +okay so that's the formula that's the + + align:start position:0% +okay so that's the formula that's the + + + align:start position:0% +okay so that's the formula that's the +Matrix exponential now it just remains + + align:start position:0% +Matrix exponential now it just remains + + + align:start position:0% +Matrix exponential now it just remains +for me to say what is e to the Lambda T + + align:start position:0% +for me to say what is e to the Lambda T + + + align:start position:0% +for me to say what is e to the Lambda T +can I just do that let me just put that + + align:start position:0% +can I just do that let me just put that + + + align:start position:0% +can I just do that let me just put that +in the corner + + align:start position:0% +in the corner + + + align:start position:0% +in the corner +here what is the exponential + + align:start position:0% +here what is the exponential + + + align:start position:0% +here what is the exponential +of a diagonal + + align:start position:0% +of a diagonal + + + align:start position:0% +of a diagonal +matrix remember Lambda + + align:start position:0% +matrix remember Lambda + + + align:start position:0% +matrix remember Lambda +is diagonal Lambda 1 down to Lambda + + align:start position:0% +is diagonal Lambda 1 down to Lambda + + + align:start position:0% +is diagonal Lambda 1 down to Lambda +n what's the exponential of that + + align:start position:0% +n what's the exponential of that + + + align:start position:0% +n what's the exponential of that +diagonal + + align:start position:0% +diagonal + + + align:start position:0% +diagonal +matrix because our whole point + + align:start position:0% +matrix because our whole point + + + align:start position:0% +matrix because our whole point +is that this ought to be simple our our + + align:start position:0% +is that this ought to be simple our our + + + align:start position:0% +is that this ought to be simple our our +whole point is that when to take the + + align:start position:0% +whole point is that when to take the + + + align:start position:0% +whole point is that when to take the +exponential of a diagonal matrix ought + + align:start position:0% +exponential of a diagonal matrix ought + + + align:start position:0% +exponential of a diagonal matrix ought +to be completely decou + + align:start position:0% +to be completely decou + + + align:start position:0% +to be completely decou +it ought to be diagonal in other words + + align:start position:0% +it ought to be diagonal in other words + + + align:start position:0% +it ought to be diagonal in other words +and it is it's just e to the Lambda 1 + + align:start position:0% +and it is it's just e to the Lambda 1 + + + align:start position:0% +and it is it's just e to the Lambda 1 +t e to the Lambda 2T e to the Lambda n t + + align:start position:0% +t e to the Lambda 2T e to the Lambda n t + + + align:start position:0% +t e to the Lambda 2T e to the Lambda n t +all + + align:start position:0% +all + + + align:start position:0% +all +zeros so so if we have a diagonal + + align:start position:0% +zeros so so if we have a diagonal + + + align:start position:0% +zeros so so if we have a diagonal +matrix and I plug it into this + + align:start position:0% +matrix and I plug it into this + + + align:start position:0% +matrix and I plug it into this +exponential + + align:start position:0% +exponential + + + align:start position:0% +exponential +formula everything's diagonal and the + + align:start position:0% +formula everything's diagonal and the + + + align:start position:0% +formula everything's diagonal and the +diagonal terms are just the ordinary + + align:start position:0% +diagonal terms are just the ordinary + + + align:start position:0% +diagonal terms are just the ordinary +scalar exponentials e to the Lambda + + align:start position:0% +scalar exponentials e to the Lambda + + + align:start position:0% +scalar exponentials e to the Lambda +1T okay so that's + + align:start position:0% +1T okay so that's + + + align:start position:0% +1T okay so that's +that's in a sense I'm doing here on this + + align:start position:0% +that's in a sense I'm doing here on this + + + align:start position:0% +that's in a sense I'm doing here on this +board with with like + + align:start position:0% +board with with like + + + align:start position:0% +board with with like +formulas what I did on the in in the + + align:start position:0% +formulas what I did on the in in the + + + align:start position:0% +formulas what I did on the in in the +first half of the lecture with specific + + align:start position:0% +first half of the lecture with specific + + + align:start position:0% +first half of the lecture with specific +Matrix a and specific igen values and + + align:start position:0% +Matrix a and specific igen values and + + + align:start position:0% +Matrix a and specific igen values and +igen vectors the so let me show you the + + align:start position:0% +igen vectors the so let me show you the + + + align:start position:0% +igen vectors the so let me show you the +formulas again but the so you I guess + + align:start position:0% +formulas again but the so you I guess + + + align:start position:0% +formulas again but the so you I guess +what should you know from this M from + + align:start position:0% +what should you know from this M from + + + align:start position:0% +what should you know from this M from +this lecture you should know what this + + align:start position:0% +this lecture you should know what this + + + align:start position:0% +this lecture you should know what this +Matrix exponential + + align:start position:0% +Matrix exponential + + + align:start position:0% +Matrix exponential +is and like when does it go to zero tell + + align:start position:0% +is and like when does it go to zero tell + + + align:start position:0% +is and like when does it go to zero tell +me again now the answer to that when + + align:start position:0% +me again now the answer to that when + + + align:start position:0% +me again now the answer to that when +does e to the a t approach get smaller + + align:start position:0% +does e to the a t approach get smaller + + + align:start position:0% +does e to the a t approach get smaller +and smaller as T + + align:start position:0% +and smaller as T + + + align:start position:0% +and smaller as T +increases well the S and the S inverse + + align:start position:0% +increases well the S and the S inverse + + + align:start position:0% +increases well the S and the S inverse +aren't moving it's this one that has to + + align:start position:0% +aren't moving it's this one that has to + + + align:start position:0% +aren't moving it's this one that has to +get smaller and smaller and that one has + + align:start position:0% +get smaller and smaller and that one has + + + align:start position:0% +get smaller and smaller and that one has +this simple diagonal form and it goes to + + align:start position:0% +this simple diagonal form and it goes to + + + align:start position:0% +this simple diagonal form and it goes to +zero provided every one of these lambdas + + align:start position:0% +zero provided every one of these lambdas + + + align:start position:0% +zero provided every one of these lambdas +I I need to have each one of these guys + + align:start position:0% +I I need to have each one of these guys + + + align:start position:0% +I I need to have each one of these guys +go to zero so I need every real part of + + align:start position:0% +go to zero so I need every real part of + + + align:start position:0% +go to zero so I need every real part of +every I value + + align:start position:0% + + + + align:start position:0% + +negative right if the real part is + + align:start position:0% +negative right if the real part is + + + align:start position:0% +negative right if the real part is +negative that that takes the exponential + + align:start position:0% +negative that that takes the exponential + + + align:start position:0% +negative that that takes the exponential +that Force the exponential goes to zero + + align:start position:0% +that Force the exponential goes to zero + + + align:start position:0% +that Force the exponential goes to zero +okay so that that's really the the + + align:start position:0% +okay so that that's really the the + + + align:start position:0% +okay so that that's really the the +difference if I can just uh + + align:start position:0% +difference if I can just uh + + + align:start position:0% +difference if I can just uh +draw the here here's a + + align:start position:0% +draw the here here's a + + + align:start position:0% +draw the here here's a +picture of the of the this is the + + align:start position:0% +picture of the of the this is the + + + align:start position:0% +picture of the of the this is the +complex + + align:start position:0% +complex + + + align:start position:0% +complex +plane here's the real axis and here's + + align:start position:0% +plane here's the real axis and here's + + + align:start position:0% +plane here's the real axis and here's +the imaginary + + align:start position:0% +the imaginary + + + align:start position:0% +the imaginary +axis and where do the ion values have to + + align:start position:0% +axis and where do the ion values have to + + + align:start position:0% +axis and where do the ion values have to +be for stability in differential + + align:start position:0% +be for stability in differential + + + align:start position:0% +be for stability in differential +equations they have to be over + + align:start position:0% +equations they have to be over + + + align:start position:0% +equations they have to be over +here in the left half plane so the left + + align:start position:0% +here in the left half plane so the left + + + align:start position:0% +here in the left half plane so the left +half plane is this plane real part of + + align:start position:0% +half plane is this plane real part of + + + align:start position:0% +half plane is this plane real part of +Lambda Less Than Zero + + align:start position:0% +Lambda Less Than Zero + + + align:start position:0% +Lambda Less Than Zero +where do the M where do the igen values + + align:start position:0% +where do the M where do the igen values + + + align:start position:0% +where do the M where do the igen values +have to be for powers of the Matrix to + + align:start position:0% +have to be for powers of the Matrix to + + + align:start position:0% +have to be for powers of the Matrix to +go to + + align:start position:0% +go to + + + align:start position:0% +go to +zero powers on The Matrix go to zero if + + align:start position:0% +zero powers on The Matrix go to zero if + + + align:start position:0% +zero powers on The Matrix go to zero if +the igen values are in here so this is + + align:start position:0% +the igen values are in here so this is + + + align:start position:0% +the igen values are in here so this is +the stability region for Powers this is + + align:start position:0% +the stability region for Powers this is + + + align:start position:0% +the stability region for Powers this is +the region absolute value of Lambda less + + align:start position:0% +the region absolute value of Lambda less + + + align:start position:0% +the region absolute value of Lambda less +than + + align:start position:0% +than + + + align:start position:0% +than +one that's the stability for that tells + + align:start position:0% +one that's the stability for that tells + + + align:start position:0% +one that's the stability for that tells +us that the powers of AO to Z this tells + + align:start position:0% +us that the powers of AO to Z this tells + + + align:start position:0% +us that the powers of AO to Z this tells +us that the exponential of a goes to + + align:start position:0% +us that the exponential of a goes to + + + align:start position:0% +us that the exponential of a goes to +zero okay one final example let me just + + align:start position:0% +zero okay one final example let me just + + + align:start position:0% +zero okay one final example let me just +write down how to deal with a with a + + align:start position:0% +write down how to deal with a with a + + + align:start position:0% +write down how to deal with a with a +final + + align:start position:0% +final + + + align:start position:0% +final +example let's + + align:start position:0% + + + + align:start position:0% + +see so my final example will be a single + + align:start position:0% +see so my final example will be a single + + + align:start position:0% +see so my final example will be a single +equation uble prime plus a Buu Prime + + + align:start position:0% +equation uble prime plus a Buu Prime + + + + align:start position:0% +equation uble prime plus a Buu Prime + +kuu equal Z + + align:start position:0% +kuu equal Z + + + align:start position:0% +kuu equal Z +one equation second + + align:start position:0% +one equation second + + + align:start position:0% +one equation second +order how do + + align:start position:0% +order how do + + + align:start position:0% +order how do +I and maybe I should have use I'll use I + + align:start position:0% +I and maybe I should have use I'll use I + + + align:start position:0% +I and maybe I should have use I'll use I +prefer to use y here because that's what + + align:start position:0% +prefer to use y here because that's what + + + align:start position:0% +prefer to use y here because that's what +you see in differential + + align:start position:0% +you see in differential + + + align:start position:0% +you see in differential +equations and I want you to be a vector + + align:start position:0% +equations and I want you to be a vector + + + align:start position:0% +equations and I want you to be a vector +so how do I change one second order + + align:start position:0% + + + + align:start position:0% + +equation into uh 2x two first order + + align:start position:0% +equation into uh 2x two first order + + + align:start position:0% +equation into uh 2x two first order +system + + align:start position:0% +system + + + align:start position:0% +system +just the way I did for Fibonacci I'll + + align:start position:0% +just the way I did for Fibonacci I'll + + + align:start position:0% +just the way I did for Fibonacci I'll +let U + + align:start position:0% +let U + + + align:start position:0% +let U +be y Prime and + + align:start position:0% +be y Prime and + + + align:start position:0% +be y Prime and +Y what I'm going to do is I'm going to + + align:start position:0% +Y what I'm going to do is I'm going to + + + align:start position:0% +Y what I'm going to do is I'm going to +add uh an extra + + align:start position:0% +add uh an extra + + + align:start position:0% +add uh an extra +equation Y Prime equals y + + align:start position:0% +equation Y Prime equals y + + + align:start position:0% +equation Y Prime equals y +Prime so I take this so + + align:start position:0% +Prime so I take this so + + + align:start position:0% +Prime so I take this so +by so using this as the vector unknown + + align:start position:0% +by so using this as the vector unknown + + + align:start position:0% +by so using this as the vector unknown +now my equation is is U Prime my first + + align:start position:0% +now my equation is is U Prime my first + + + align:start position:0% +now my equation is is U Prime my first +order system is U Prime that'll be y + + align:start position:0% +order system is U Prime that'll be y + + + align:start position:0% +order system is U Prime that'll be y +Prime y Prime the derivative of U okay + + align:start position:0% +Prime y Prime the derivative of U okay + + + align:start position:0% +Prime y Prime the derivative of U okay +now the differential equation is telling + + align:start position:0% +now the differential equation is telling + + + align:start position:0% +now the differential equation is telling +me that y Prime is so I'm I'm just + + align:start position:0% +me that y Prime is so I'm I'm just + + + align:start position:0% +me that y Prime is so I'm I'm just +looking for what's this + + align:start position:0% +looking for what's this + + + align:start position:0% +looking for what's this +Matrix y Prime y I'm looking for the + + align:start position:0% +Matrix y Prime y I'm looking for the + + + align:start position:0% +Matrix y Prime y I'm looking for the +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +a what's the + + align:start position:0% +a what's the + + + align:start position:0% +a what's the +Matrix in case I have a single first + + align:start position:0% +Matrix in case I have a single first + + + align:start position:0% +Matrix in case I have a single first +order equation and I want to make it + + align:start position:0% +order equation and I want to make it + + + align:start position:0% +order equation and I want to make it +into a 2X two system okay simple the the + + align:start position:0% +into a 2X two system okay simple the the + + + align:start position:0% +into a 2X two system okay simple the the +first row of the Matrix is given by the + + align:start position:0% +first row of the Matrix is given by the + + + align:start position:0% +first row of the Matrix is given by the +equation so y Prime is - b y Prime - k y + + align:start position:0% +equation so y Prime is - b y Prime - k y + + + align:start position:0% +equation so y Prime is - b y Prime - k y +no problem and what's the second row of + + align:start position:0% +no problem and what's the second row of + + + align:start position:0% +no problem and what's the second row of +the + + align:start position:0% +the + + + align:start position:0% +the +Matrix then we're done the second row of + + align:start position:0% +Matrix then we're done the second row of + + + align:start position:0% +Matrix then we're done the second row of +the Matrix I want just to be the trivial + + align:start position:0% +the Matrix I want just to be the trivial + + + align:start position:0% +the Matrix I want just to be the trivial +equation Y Prime equals y Prime so I + + align:start position:0% +equation Y Prime equals y Prime so I + + + align:start position:0% +equation Y Prime equals y Prime so I +need a one and a zero there + + align:start position:0% + + + + align:start position:0% + +so matrices like + + align:start position:0% +so matrices like + + + align:start position:0% +so matrices like +these the the general case if I had a 5x + + align:start position:0% +these the the general case if I had a 5x + + + align:start position:0% +these the the general case if I had a 5x +five if I had a fifth order equation and + + align:start position:0% +five if I had a fifth order equation and + + + align:start position:0% +five if I had a fifth order equation and +I wanted a 5x5 Matrix I would see the + + align:start position:0% +I wanted a 5x5 Matrix I would see the + + + align:start position:0% +I wanted a 5x5 Matrix I would see the +coefficients of the equation up there + + align:start position:0% +coefficients of the equation up there + + + align:start position:0% +coefficients of the equation up there +and then my four trivial equations would + + align:start position:0% +and then my four trivial equations would + + + align:start position:0% +and then my four trivial equations would +put ones + + align:start position:0% +put ones + + + align:start position:0% +put ones +here this is the the kind of Matrix that + + align:start position:0% +here this is the the kind of Matrix that + + + align:start position:0% +here this is the the kind of Matrix that +goes from a fifth order + + align:start position:0% +goes from a fifth order + + + align:start position:0% +goes from a fifth order +to uh + + align:start position:0% +to uh + + + align:start position:0% +to uh +5x5 first + + align:start position:0% + + + + align:start position:0% + +order so the and the igen values will + + align:start position:0% +order so the and the igen values will + + + align:start position:0% +order so the and the igen values will +come out in a natural way connected to + + align:start position:0% +come out in a natural way connected to + + + align:start position:0% +come out in a natural way connected to +the differential equation okay that's + + align:start position:0% +the differential equation okay that's + + + align:start position:0% +the differential equation okay that's +differential equations uh the a parallel + + align:start position:0% +differential equations uh the a parallel + + + align:start position:0% +differential equations uh the a parallel +lecture compared to powers of a matrix + + align:start position:0% +lecture compared to powers of a matrix + + + align:start position:0% +lecture compared to powers of a matrix +we can now do exponentials thanks \ No newline at end of file diff --git a/IycOPFmEQk8.txt b/IycOPFmEQk8.txt new file mode 100644 index 0000000000000000000000000000000000000000..3e9b330f580472ef59e1424845838450bbed8dea --- /dev/null +++ b/IycOPFmEQk8.txt @@ -0,0 +1,16723 @@ +align:start position:0% + +why don't we get started + + align:start position:0% +why don't we get started + + + align:start position:0% +why don't we get started +so as i like to do let's just + + align:start position:0% +so as i like to do let's just + + + align:start position:0% +so as i like to do let's just +review where we um have been recently um + + align:start position:0% +review where we um have been recently um + + + align:start position:0% +review where we um have been recently um +which is to + + align:start position:0% +which is to + + + align:start position:0% +which is to +um + + align:start position:0% +um + + + align:start position:0% +um +discuss + + align:start position:0% +discuss + + + align:start position:0% +discuss +context-free languages we talked about + + align:start position:0% +context-free languages we talked about + + + align:start position:0% +context-free languages we talked about +the context-free grammars and the + + align:start position:0% +the context-free grammars and the + + + align:start position:0% +the context-free grammars and the +push-down automata + + align:start position:0% +push-down automata + + + align:start position:0% +push-down automata +as a way of describing the context-free + + align:start position:0% +as a way of describing the context-free + + + align:start position:0% +as a way of describing the context-free +languages + + align:start position:0% +languages + + + align:start position:0% +languages +as you remember + + align:start position:0% +as you remember + + + align:start position:0% +as you remember +the context-free languages are a larger + + align:start position:0% +the context-free languages are a larger + + + align:start position:0% +the context-free languages are a larger +class of languages than the regular + + align:start position:0% +class of languages than the regular + + + align:start position:0% +class of languages than the regular +languages which is where we started the + + align:start position:0% +languages which is where we started the + + + align:start position:0% +languages which is where we started the +languages of the finite automata so when + + align:start position:0% +languages of the finite automata so when + + + align:start position:0% +languages of the finite automata so when +you add a stack you get more power you + + align:start position:0% +you add a stack you get more power you + + + align:start position:0% +you add a stack you get more power you +get more languages that you can do + + align:start position:0% + + + + align:start position:0% + +and we're very rapidly going to be + + align:start position:0% +and we're very rapidly going to be + + + align:start position:0% +and we're very rapidly going to be +moving on today to + + align:start position:0% +moving on today to + + + align:start position:0% +moving on today to +our main model for the semester which is + + align:start position:0% +our main model for the semester which is + + + align:start position:0% +our main model for the semester which is +called the turing machine so let's just + + align:start position:0% +called the turing machine so let's just + + + align:start position:0% +called the turing machine so let's just +take a look at what we're + + align:start position:0% + + + + align:start position:0% + +going to be covering today + + align:start position:0% +going to be covering today + + + align:start position:0% +going to be covering today +and that is + + align:start position:0% +and that is + + + align:start position:0% +and that is +first we're going to show that a + + align:start position:0% +first we're going to show that a + + + align:start position:0% +first we're going to show that a +technique analogous to the one we use + + align:start position:0% +technique analogous to the one we use + + + align:start position:0% +technique analogous to the one we use +for um + + align:start position:0% +for um + + + align:start position:0% +for um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +proving that languages are not regular + + align:start position:0% +proving that languages are not regular + + + align:start position:0% +proving that languages are not regular +but this time for proving languages are + + align:start position:0% +but this time for proving languages are + + + align:start position:0% +but this time for proving languages are +not context free + + align:start position:0% +not context free + + + align:start position:0% +not context free +so the + + align:start position:0% +so the + + + align:start position:0% +so the +push down automate and the grammar still + + align:start position:0% +push down automate and the grammar still + + + align:start position:0% +push down automate and the grammar still +have their limitations in terms of what + + align:start position:0% +have their limitations in terms of what + + + align:start position:0% +have their limitations in terms of what +we normally think a computer can do + + align:start position:0% +we normally think a computer can do + + + align:start position:0% +we normally think a computer can do +and with that we're going to use that as + + align:start position:0% +and with that we're going to use that as + + + align:start position:0% +and with that we're going to use that as +a kind of a lead into our + + align:start position:0% +a kind of a lead into our + + + align:start position:0% +a kind of a lead into our +general purpose model which is the + + align:start position:0% +general purpose model which is the + + + align:start position:0% +general purpose model which is the +turing machine + + align:start position:0% +turing machine + + + align:start position:0% +turing machine +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +so we're going to talk about turing + + align:start position:0% +so we're going to talk about turing + + + align:start position:0% +so we're going to talk about turing +machines + + align:start position:0% +machines + + + align:start position:0% +machines +and of and aspects of of that um + + align:start position:0% +and of and aspects of of that um + + + align:start position:0% +and of and aspects of of that um +and i do i would want to make comment uh + + align:start position:0% +and i do i would want to make comment uh + + + align:start position:0% +and i do i would want to make comment uh +so + + align:start position:0% +so + + + align:start position:0% +so +i have posted the solutions for the + + align:start position:0% +i have posted the solutions for the + + + align:start position:0% +i have posted the solutions for the +first problem set i know you're starting + + align:start position:0% +first problem set i know you're starting + + + align:start position:0% +first problem set i know you're starting +to think about the second problem set + + align:start position:0% +to think about the second problem set + + + align:start position:0% +to think about the second problem set +now which i have posted as well + + align:start position:0% +now which i have posted as well + + + align:start position:0% +now which i have posted as well +if you want to get a sense of what i'm + + align:start position:0% +if you want to get a sense of what i'm + + + align:start position:0% +if you want to get a sense of what i'm +looking for in terms of the level of + + align:start position:0% +looking for in terms of the level of + + + align:start position:0% +looking for in terms of the level of +detail + + align:start position:0% +detail + + + align:start position:0% +detail +you can look at the solutions to problem + + align:start position:0% +you can look at the solutions to problem + + + align:start position:0% +you can look at the solutions to problem +set one because i consider those to be + + align:start position:0% +set one because i consider those to be + + + align:start position:0% +set one because i consider those to be +model solutions uh that's part of the + + align:start position:0% +model solutions uh that's part of the + + + align:start position:0% +model solutions uh that's part of the +reason why i post them just to give you + + align:start position:0% +reason why i post them just to give you + + + align:start position:0% +reason why i post them just to give you +a sense of the level of detail that i'm + + align:start position:0% +a sense of the level of detail that i'm + + + align:start position:0% +a sense of the level of detail that i'm +looking for which is not a whole lot but + + align:start position:0% +looking for which is not a whole lot but + + + align:start position:0% +looking for which is not a whole lot but +i do want to make sure you're capturing + + align:start position:0% +i do want to make sure you're capturing + + + align:start position:0% +i do want to make sure you're capturing +the main ideas um + + align:start position:0% +the main ideas um + + + align:start position:0% +the main ideas um +of what + + align:start position:0% +of what + + + align:start position:0% +of what +of what's involved in solving the + + align:start position:0% +of what's involved in solving the + + + align:start position:0% +of what's involved in solving the +problem + + align:start position:0% +problem + + + align:start position:0% +problem +so have a look at those um + + align:start position:0% +so have a look at those um + + + align:start position:0% +so have a look at those um +and + + align:start position:0% +and + + + align:start position:0% +and +for problem set two which i'll talk + + align:start position:0% +for problem set two which i'll talk + + + align:start position:0% +for problem set two which i'll talk +about um in a second so i'll just say a + + align:start position:0% +about um in a second so i'll just say a + + + align:start position:0% +about um in a second so i'll just say a +few words if you want to pull that up um + + align:start position:0% +few words if you want to pull that up um + + + align:start position:0% +few words if you want to pull that up um +you know you can do that but just to get + + align:start position:0% +you know you can do that but just to get + + + align:start position:0% +you know you can do that but just to get +you started on a few of the problems if + + align:start position:0% +you started on a few of the problems if + + + align:start position:0% +you started on a few of the problems if +you're + + align:start position:0% +you're + + + align:start position:0% +you're +uh finding some challenges there i i + + align:start position:0% +uh finding some challenges there i i + + + align:start position:0% +uh finding some challenges there i i +don't want you to get stuck really + + align:start position:0% +don't want you to get stuck really + + + align:start position:0% +don't want you to get stuck really +before you even understand what the + + align:start position:0% +before you even understand what the + + + align:start position:0% +before you even understand what the +problem is saying + + align:start position:0% +problem is saying + + + align:start position:0% +problem is saying +um + + align:start position:0% +um + + + align:start position:0% +um +so for problem number one if you looked + + align:start position:0% +so for problem number one if you looked + + + align:start position:0% +so for problem number one if you looked +at that so that's a problem where you're + + align:start position:0% +at that so that's a problem where you're + + + align:start position:0% +at that so that's a problem where you're +asked to prove um a certain language is + + align:start position:0% +asked to prove um a certain language is + + + align:start position:0% +asked to prove um a certain language is +not context-free so that's + + align:start position:0% +not context-free so that's + + + align:start position:0% +not context-free so that's +um and by the way all of the problems in + + align:start position:0% +um and by the way all of the problems in + + + align:start position:0% +um and by the way all of the problems in +this problem set except uh perhaps for + + align:start position:0% +this problem set except uh perhaps for + + + align:start position:0% +this problem set except uh perhaps for +the last one for number six you'll be + + align:start position:0% +the last one for number six you'll be + + + align:start position:0% +the last one for number six you'll be +able to solve we'll have enough material + + align:start position:0% +able to solve we'll have enough material + + + align:start position:0% +able to solve we'll have enough material +at the end of today's lecture to solve + + align:start position:0% +at the end of today's lecture to solve + + + align:start position:0% +at the end of today's lecture to solve +all of them um + + align:start position:0% +all of them um + + + align:start position:0% +all of them um +i believe that's right uh + + align:start position:0% +i believe that's right uh + + + align:start position:0% +i believe that's right uh +yeah so number six you should have + + align:start position:0% +yeah so number six you should have + + + align:start position:0% +yeah so number six you should have +enough as of thursday's lecture to solve + + align:start position:0% +enough as of thursday's lecture to solve + + + align:start position:0% +enough as of thursday's lecture to solve +that um + + align:start position:0% +that um + + + align:start position:0% +that um +um + + align:start position:0% +um + + + align:start position:0% +um +uh problem number one um + + align:start position:0% +uh problem number one um + + + align:start position:0% +uh problem number one um +uh it's proving a language is not + + align:start position:0% +uh it's proving a language is not + + + align:start position:0% +uh it's proving a language is not +context-free so we're going to introduce + + align:start position:0% +context-free so we're going to introduce + + + align:start position:0% +context-free so we're going to introduce +a method for doing that that method is + + align:start position:0% +a method for doing that that method is + + + align:start position:0% +a method for doing that that method is +going to come in handy + + align:start position:0% +going to come in handy + + + align:start position:0% +going to come in handy +for parts b and c uh if you look at the + + align:start position:0% +for parts b and c uh if you look at the + + + align:start position:0% +for parts b and c uh if you look at the +problem set it has this strange looking + + align:start position:0% +problem set it has this strange looking + + + align:start position:0% +problem set it has this strange looking +thing sigma sigma sigma and parenthesis + + align:start position:0% +thing sigma sigma sigma and parenthesis + + + align:start position:0% +thing sigma sigma sigma and parenthesis +star it's really just a regular + + align:start position:0% +star it's really just a regular + + + align:start position:0% +star it's really just a regular +expression that's very simple + + align:start position:0% +expression that's very simple + + + align:start position:0% +expression that's very simple +um you know + + align:start position:0% +um you know + + + align:start position:0% +um you know +you should just make sure you understand + + align:start position:0% +you should just make sure you understand + + + align:start position:0% +you should just make sure you understand +that that's a way of representing all + + align:start position:0% +that that's a way of representing all + + + align:start position:0% +that that's a way of representing all +strings whose length is a multiple of + + align:start position:0% +strings whose length is a multiple of + + + align:start position:0% +strings whose length is a multiple of +three + + align:start position:0% +three + + + align:start position:0% +three +um + + align:start position:0% +um + + + align:start position:0% +um +and if i stick a sigma in front of that + + align:start position:0% +and if i stick a sigma in front of that + + + align:start position:0% +and if i stick a sigma in front of that +it's all strings whose length + + align:start position:0% +it's all strings whose length + + + align:start position:0% +it's all strings whose length +is one plus a multiple of three + + align:start position:0% +is one plus a multiple of three + + + align:start position:0% +is one plus a multiple of three +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +once you understand that and if you + + align:start position:0% +once you understand that and if you + + + align:start position:0% +once you understand that and if you +think about what kinds of strings are in + + align:start position:0% +think about what kinds of strings are in + + + align:start position:0% +think about what kinds of strings are in +the language c2 it'll help you want to + + align:start position:0% +the language c2 it'll help you want to + + + align:start position:0% +the language c2 it'll help you want to +understand what happens when you take + + align:start position:0% +understand what happens when you take + + + align:start position:0% +understand what happens when you take +those unions um + + align:start position:0% +those unions um + + + align:start position:0% +those unions um +and um + + align:start position:0% +and um + + + align:start position:0% +and um +parts b and c are not intended to be + + align:start position:0% +parts b and c are not intended to be + + + align:start position:0% +parts b and c are not intended to be +very hard but you just have to + + align:start position:0% +very hard but you just have to + + + align:start position:0% +very hard but you just have to +understand what's going on + + align:start position:0% +understand what's going on + + + align:start position:0% +understand what's going on +uh problem number two is about ambiguous + + align:start position:0% +uh problem number two is about ambiguous + + + align:start position:0% +uh problem number two is about ambiguous +grammars i touched on that briefly in + + align:start position:0% +grammars i touched on that briefly in + + + align:start position:0% +grammars i touched on that briefly in +lecture um + + align:start position:0% +lecture um + + + align:start position:0% +lecture um +it's enough to solve the problem um the + + align:start position:0% +it's enough to solve the problem um the + + + align:start position:0% +it's enough to solve the problem um the +book has a little bit more detail about + + align:start position:0% +book has a little bit more detail about + + + align:start position:0% +book has a little bit more detail about +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um + + align:start position:0% +um + + + align:start position:0% +um +ambiguous languages uh ambiguous + + align:start position:0% +ambiguous languages uh ambiguous + + + align:start position:0% +ambiguous languages uh ambiguous +grammars + + align:start position:0% +grammars + + + align:start position:0% +grammars +uh + + align:start position:0% +uh + + + align:start position:0% +uh +ambiguous grammars i should say um + + align:start position:0% +ambiguous grammars i should say um + + + align:start position:0% +ambiguous grammars i should say um +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +so this is a grammar that's supposed to + + align:start position:0% +so this is a grammar that's supposed to + + + align:start position:0% +so this is a grammar that's supposed to +represent a fragment of a programming + + align:start position:0% +represent a fragment of a programming + + + align:start position:0% +represent a fragment of a programming +language um + + align:start position:0% +language um + + + align:start position:0% +language um +you know with uh if thens um and if then + + align:start position:0% +you know with uh if thens um and if then + + + align:start position:0% +you know with uh if thens um and if then +else's uh you know i'm sure you're all + + align:start position:0% +else's uh you know i'm sure you're all + + + align:start position:0% +else's uh you know i'm sure you're all +familiar with uh those kinds of + + align:start position:0% +familiar with uh those kinds of + + + align:start position:0% +familiar with uh those kinds of +constructs in programming languages + + align:start position:0% +constructs in programming languages + + + align:start position:0% +constructs in programming languages +um and there is a natural ambiguity that + + align:start position:0% +um and there is a natural ambiguity that + + + align:start position:0% +um and there is a natural ambiguity that +comes up in a programming language you + + align:start position:0% +comes up in a programming language you + + + align:start position:0% +comes up in a programming language you +know if you have + + align:start position:0% +know if you have + + + align:start position:0% +know if you have +you know if some condition then + + align:start position:0% +you know if some condition then + + + align:start position:0% +you know if some condition then +statement one else statement two i + + align:start position:0% +statement one else statement two i + + + align:start position:0% +statement one else statement two i +presume you understand what the + + align:start position:0% +presume you understand what the + + + align:start position:0% +presume you understand what the +semantics of that is what that means um + + align:start position:0% +semantics of that is what that means um + + + align:start position:0% +semantics of that is what that means um +and the tricky thing is that if you have + + align:start position:0% +and the tricky thing is that if you have + + + align:start position:0% +and the tricky thing is that if you have +a you know those statements can + + align:start position:0% +a you know those statements can + + + align:start position:0% +a you know those statements can +themselves be if statements and so if + + align:start position:0% +themselves be if statements and so if + + + align:start position:0% +themselves be if statements and so if +you have the situation where you have + + align:start position:0% +you have the situation where you have + + + align:start position:0% +you have the situation where you have +if then + + align:start position:0% +if then + + + align:start position:0% +if then +and if then else is the uh what follows + + align:start position:0% +and if then else is the uh what follows + + + align:start position:0% +and if then else is the uh what follows +that the question is where does the else + + align:start position:0% +that the question is where does the else + + + align:start position:0% +that the question is where does the else +attach is it to the second if foot to + + align:start position:0% +attach is it to the second if foot to + + + align:start position:0% +attach is it to the second if foot to +the first if um so that's kind of a big + + align:start position:0% +the first if um so that's kind of a big + + + align:start position:0% +the first if um so that's kind of a big +hint on this problem but that's okay um + + align:start position:0% +hint on this problem but that's okay um + + + align:start position:0% +hint on this problem but that's okay um +i think you uh should uh + + align:start position:0% +i think you uh should uh + + + align:start position:0% +i think you uh should uh +um uh + + align:start position:0% +um uh + + + align:start position:0% +um uh +you know you need to take that and + + align:start position:0% +you know you need to take that and + + + align:start position:0% +you know you need to take that and +figure out how to get a + + align:start position:0% +figure out how to get a + + + align:start position:0% +figure out how to get a +uh an actual member of the language + + align:start position:0% +uh an actual member of the language + + + align:start position:0% +uh an actual member of the language +which is ambiguously generated um and + + align:start position:0% +which is ambiguously generated um and + + + align:start position:0% +which is ambiguously generated um and +then show that it has that show that it + + align:start position:0% +then show that it has that show that it + + + align:start position:0% +then show that it has that show that it +is by showing two parse trees uh + + align:start position:0% +is by showing two parse trees uh + + + align:start position:0% +is by showing two parse trees uh +now or or two + + align:start position:0% +now or or two + + + align:start position:0% +now or or two +left-most derivations if you read the + + align:start position:0% +left-most derivations if you read the + + + align:start position:0% +left-most derivations if you read the +book you'll see that's an alternative + + align:start position:0% +book you'll see that's an alternative + + + align:start position:0% +book you'll see that's an alternative +way of of representing comparison + + align:start position:0% +way of of representing comparison + + + align:start position:0% +way of of representing comparison +so um + + align:start position:0% +so um + + + align:start position:0% +so um +and then what you're supposed to do is + + align:start position:0% +and then what you're supposed to do is + + + align:start position:0% +and then what you're supposed to do is +give a grammar for the same language + + align:start position:0% +give a grammar for the same language + + + align:start position:0% +give a grammar for the same language +which is unambiguous um you don't have + + align:start position:0% +which is unambiguous um you don't have + + + align:start position:0% +which is unambiguous um you don't have +to prove that it's unambiguous because + + align:start position:0% +to prove that it's unambiguous because + + + align:start position:0% +to prove that it's unambiguous because +that's a bit of a chore but as long as + + align:start position:0% +that's a bit of a chore but as long as + + + align:start position:0% +that's a bit of a chore but as long as +you understand what's going on you + + align:start position:0% +you understand what's going on you + + + align:start position:0% +you understand what's going on you +should be should be able to come up with + + align:start position:0% +should be should be able to come up with + + + align:start position:0% +should be should be able to come up with +an unambiguous grammar which resolves + + align:start position:0% +an unambiguous grammar which resolves + + + align:start position:0% +an unambiguous grammar which resolves +that ambiguity + + align:start position:0% +that ambiguity + + + align:start position:0% +that ambiguity +and i don't have in mind changing the + + align:start position:0% +and i don't have in mind changing the + + + align:start position:0% +and i don't have in mind changing the +language by introducing new uh + + align:start position:0% +language by introducing new uh + + + align:start position:0% +language by introducing new uh +programming languages contra constructs + + align:start position:0% +programming languages contra constructs + + + align:start position:0% +programming languages contra constructs +like a begin end uh that's not in the + + align:start position:0% +like a begin end uh that's not in the + + + align:start position:0% +like a begin end uh that's not in the +spirit of this problem because + + align:start position:0% +spirit of this problem because + + + align:start position:0% +spirit of this problem because +that's a different it's grammar for a + + align:start position:0% +that's a different it's grammar for a + + + align:start position:0% +that's a different it's grammar for a +different language so you need to be + + align:start position:0% +different language so you need to be + + + align:start position:0% +different language so you need to be +generating the same language um without + + align:start position:0% +generating the same language um without + + + align:start position:0% +generating the same language um without +any other extraneous things going on + + align:start position:0% +any other extraneous things going on + + + align:start position:0% +any other extraneous things going on +that are going to resolve the ambiguity + + align:start position:0% +that are going to resolve the ambiguity + + + align:start position:0% +that are going to resolve the ambiguity +the ambiguity needs to be resolved + + align:start position:0% +the ambiguity needs to be resolved + + + align:start position:0% +the ambiguity needs to be resolved +within the structure of the grammar + + align:start position:0% +within the structure of the grammar + + + align:start position:0% +within the structure of the grammar +itself + + align:start position:0% +itself + + + align:start position:0% +itself +so keep that in mind + + align:start position:0% +so keep that in mind + + + align:start position:0% +so keep that in mind +uh for problem number three about the + + align:start position:0% +uh for problem number three about the + + + align:start position:0% +uh for problem number three about the +key automata um you know that came up + + align:start position:0% +key automata um you know that came up + + + align:start position:0% +key automata um you know that came up +actually as a suggestion um uh last + + align:start position:0% +actually as a suggestion um uh last + + + align:start position:0% +actually as a suggestion um uh last +lecture i believe or two lectures back + + align:start position:0% +lecture i believe or two lectures back + + + align:start position:0% +lecture i believe or two lectures back +what happens if you take a push down + + align:start position:0% +what happens if you take a push down + + + align:start position:0% +what happens if you take a push down +automaton but instead of a push down uh + + align:start position:0% +automaton but instead of a push down uh + + + align:start position:0% +automaton but instead of a push down uh +as a instead of a stack you add a q + + align:start position:0% +as a instead of a stack you add a q + + + align:start position:0% +as a instead of a stack you add a q +um what happens then well actually it + + align:start position:0% +um what happens then well actually it + + + align:start position:0% +um what happens then well actually it +turns out that the model you get is very + + align:start position:0% +turns out that the model you get is very + + + align:start position:0% +turns out that the model you get is very +powerful and turns out to be equivalent + + align:start position:0% +powerful and turns out to be equivalent + + + align:start position:0% +powerful and turns out to be equivalent +in power to a turing machine so you'll + + align:start position:0% +in power to a turing machine so you'll + + + align:start position:0% +in power to a turing machine so you'll +see arguments of that kind today how you + + align:start position:0% +see arguments of that kind today how you + + + align:start position:0% +see arguments of that kind today how you +show that um + + align:start position:0% +show that um + + + align:start position:0% +show that um +other models are equivalent no not today + + align:start position:0% +other models are equivalent no not today + + + align:start position:0% +other models are equivalent no not today +that's going to be on um + + align:start position:0% +that's going to be on um + + + align:start position:0% +that's going to be on um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +that's going to so i apologize the key + + align:start position:0% +that's going to so i apologize the key + + + align:start position:0% +that's going to so i apologize the key +this is going to be something that + + align:start position:0% +this is going to be something that + + + align:start position:0% +this is going to be something that +you'll also you know i i i i'm confusing + + align:start position:0% +you'll also you know i i i i'm confusing + + + align:start position:0% +you'll also you know i i i i'm confusing +myself here uh for problems number + + align:start position:0% +myself here uh for problems number + + + align:start position:0% +myself here uh for problems number +problem number three you actually need + + align:start position:0% +problem number three you actually need + + + align:start position:0% +problem number three you actually need +thursday thursday's lecture as well uh + + align:start position:0% +thursday thursday's lecture as well uh + + + align:start position:0% +thursday thursday's lecture as well uh +to really + + align:start position:0% +to really + + + align:start position:0% +to really +at least see examples of how you do that + + align:start position:0% +at least see examples of how you do that + + + align:start position:0% +at least see examples of how you do that +kind of thing + + align:start position:0% +kind of thing + + + align:start position:0% +kind of thing +um + + align:start position:0% +um + + + align:start position:0% +um +and so uh so thursday + + align:start position:0% +and so uh so thursday + + + align:start position:0% +and so uh so thursday +uh + + align:start position:0% +uh + + + align:start position:0% +uh +yeah so i i i'll try to send out a note + + align:start position:0% +yeah so i i i'll try to send out a note + + + align:start position:0% +yeah so i i i'll try to send out a note +clarifying this by the end of thursday + + align:start position:0% +clarifying this by the end of thursday + + + align:start position:0% +clarifying this by the end of thursday +you'll be able to do everything except + + align:start position:0% +you'll be able to do everything except + + + align:start position:0% +you'll be able to do everything except +for problem six and for problem six + + align:start position:0% +for problem six and for problem six + + + align:start position:0% +for problem six and for problem six +you'll need tuesday's lecture a week + + align:start position:0% +you'll need tuesday's lecture a week + + + align:start position:0% +you'll need tuesday's lecture a week +from today's lecture to do + + align:start position:0% +from today's lecture to do + + + align:start position:0% +from today's lecture to do +um + + align:start position:0% +um + + + align:start position:0% +um +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +um all right uh so + + align:start position:0% +um all right uh so + + + align:start position:0% +um all right uh so +um + + align:start position:0% +um + + + align:start position:0% +um +problem number four that one you'll be + + align:start position:0% +problem number four that one you'll be + + + align:start position:0% +problem number four that one you'll be +able to do at the end of today we'll + + align:start position:0% +able to do at the end of today we'll + + + align:start position:0% +able to do at the end of today we'll +that's also gonna you know the problem + + align:start position:0% +that's also gonna you know the problem + + + align:start position:0% +that's also gonna you know the problem +is i'm i'm working on preparing + + align:start position:0% +is i'm i'm working on preparing + + + align:start position:0% +is i'm i'm working on preparing +thursday's lecture too so i'm getting a + + align:start position:0% +thursday's lecture too so i'm getting a + + + align:start position:0% +thursday's lecture too so i'm getting a +little i'm confusing myself uh problem + + align:start position:0% +little i'm confusing myself uh problem + + + align:start position:0% +little i'm confusing myself uh problem +number four you'll be able to do after + + align:start position:0% +number four you'll be able to do after + + + align:start position:0% +number four you'll be able to do after +thursday's lecture maybe we should talk + + align:start position:0% +thursday's lecture maybe we should talk + + + align:start position:0% +thursday's lecture maybe we should talk +about that um + + align:start position:0% +about that um + + + align:start position:0% +about that um +next lecture + + align:start position:0% +next lecture + + + align:start position:0% +next lecture +um + + align:start position:0% +um + + + align:start position:0% +um +problem number five um you can do today + + align:start position:0% +problem number five um you can do today + + + align:start position:0% +problem number five um you can do today +um + + align:start position:0% +um + + + align:start position:0% +um +but maybe i'm not gonna say anything + + align:start position:0% +but maybe i'm not gonna say anything + + + align:start position:0% +but maybe i'm not gonna say anything +about that and problem number six i + + align:start position:0% +about that and problem number six i + + + align:start position:0% +about that and problem number six i +won't say anything about either okay so + + align:start position:0% +won't say anything about either okay so + + + align:start position:0% +won't say anything about either okay so +why don't we just jump in then um and uh + + align:start position:0% +why don't we just jump in then um and uh + + + align:start position:0% +why don't we just jump in then um and uh +look at today's material um what about + + align:start position:0% +look at today's material um what about + + + align:start position:0% +look at today's material um what about +seven seven is uh + + align:start position:0% +seven seven is uh + + + align:start position:0% +seven seven is uh +oh seven is an optional problem oh i + + align:start position:0% +oh seven is an optional problem oh i + + + align:start position:0% +oh seven is an optional problem oh i +should have mentioned that whenever + + align:start position:0% +should have mentioned that whenever + + + align:start position:0% +should have mentioned that whenever +there's seven is always going to be an + + align:start position:0% +there's seven is always going to be an + + + align:start position:0% +there's seven is always going to be an +optional i indicate that with a star i + + align:start position:0% +optional i indicate that with a star i + + + align:start position:0% +optional i indicate that with a star i +should have made that clear um on the + + align:start position:0% +should have made that clear um on the + + + align:start position:0% +should have made that clear um on the +actual description here but seven is + + align:start position:0% +actual description here but seven is + + + align:start position:0% +actual description here but seven is +optional uh it's just like we had for + + align:start position:0% +optional uh it's just like we had for + + + align:start position:0% +optional uh it's just like we had for +problem set one + + align:start position:0% +problem set one + + + align:start position:0% +problem set one +okay let's move let's move on then to uh + + align:start position:0% +okay let's move let's move on then to uh + + + align:start position:0% +okay let's move let's move on then to uh +what we're going to talk about today um + + align:start position:0% +what we're going to talk about today um + + + align:start position:0% +what we're going to talk about today um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and just a little bit of review um + + align:start position:0% +and just a little bit of review um + + + align:start position:0% +and just a little bit of review um +so we talked about the equivalence of + + align:start position:0% +so we talked about the equivalence of + + + align:start position:0% +so we talked about the equivalence of +context-free grammars and push down + + align:start position:0% +context-free grammars and push down + + + align:start position:0% +context-free grammars and push down +automata as you remember oops let me get + + align:start position:0% +automata as you remember oops let me get + + + align:start position:0% +automata as you remember oops let me get +myself out of the picture here um + + align:start position:0% +myself out of the picture here um + + + align:start position:0% +myself out of the picture here um +as we mentioned last time we actually + + align:start position:0% +as we mentioned last time we actually + + + align:start position:0% +as we mentioned last time we actually +proved one direction but the other + + align:start position:0% +proved one direction but the other + + + align:start position:0% +proved one direction but the other +direction of that you just have to know + + align:start position:0% +direction of that you just have to know + + + align:start position:0% +direction of that you just have to know +it's true but you don't have to know the + + align:start position:0% +it's true but you don't have to know the + + + align:start position:0% +it's true but you don't have to know the +proof the proof is a little bit lengthy + + align:start position:0% +proof the proof is a little bit lengthy + + + align:start position:0% +proof the proof is a little bit lengthy +i would say it's a nice proof but it's + + align:start position:0% +i would say it's a nice proof but it's + + + align:start position:0% +i would say it's a nice proof but it's +pretty long + + align:start position:0% +pretty long + + + align:start position:0% +pretty long +um + + align:start position:0% +um + + + align:start position:0% +um +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +there are two uh important corollaries + + align:start position:0% +there are two uh important corollaries + + + align:start position:0% +there are two uh important corollaries +to that um if you know what a corollary + + align:start position:0% +to that um if you know what a corollary + + + align:start position:0% +to that um if you know what a corollary +is just a simple consequence which + + align:start position:0% +is just a simple consequence which + + + align:start position:0% +is just a simple consequence which +doesn't need much of a proof uh sort of + + align:start position:0% +doesn't need much of a proof uh sort of + + + align:start position:0% +doesn't need much of a proof uh sort of +a very straightforward consequence first + + align:start position:0% +a very straightforward consequence first + + + align:start position:0% +a very straightforward consequence first +of all uh as i think we pointed out at + + align:start position:0% +of all uh as i think we pointed out at + + + align:start position:0% +of all uh as i think we pointed out at +last time one one conclusion one + + align:start position:0% +last time one one conclusion one + + + align:start position:0% +last time one one conclusion one +corollary you get is that every regular + + align:start position:0% +corollary you get is that every regular + + + align:start position:0% +corollary you get is that every regular +language is a context-free language + + align:start position:0% +language is a context-free language + + + align:start position:0% +language is a context-free language +because um a + + align:start position:0% +because um a + + + align:start position:0% +because um a +finite automaton is a push down + + align:start position:0% +finite automaton is a push down + + + align:start position:0% +finite automaton is a push down +automaton that just happens not to use + + align:start position:0% +automaton that just happens not to use + + + align:start position:0% +automaton that just happens not to use +its stack + + align:start position:0% +its stack + + + align:start position:0% +its stack +so immediately you get that every + + align:start position:0% +so immediately you get that every + + + align:start position:0% +so immediately you get that every +regular language is context-free + + align:start position:0% +regular language is context-free + + + align:start position:0% +regular language is context-free +and second of all um you also + + align:start position:0% +and second of all um you also + + + align:start position:0% +and second of all um you also +immediately get that + + align:start position:0% +immediately get that + + + align:start position:0% +immediately get that +whenever you have a context-free + + align:start position:0% +whenever you have a context-free + + + align:start position:0% +whenever you have a context-free +language and a + + align:start position:0% +language and a + + + align:start position:0% +language and a +and a regular language and you take + + align:start position:0% +and a regular language and you take + + + align:start position:0% +and a regular language and you take +their intersection + + align:start position:0% +their intersection + + + align:start position:0% +their intersection +you get back a context-free language + + align:start position:0% +you get back a context-free language + + + align:start position:0% +you get back a context-free language +so context-free intersect regular is + + align:start position:0% +so context-free intersect regular is + + + align:start position:0% +so context-free intersect regular is +context-free + + align:start position:0% +context-free + + + align:start position:0% +context-free +okay that that's actually mentioned in + + align:start position:0% +okay that that's actually mentioned in + + + align:start position:0% +okay that that's actually mentioned in +your homework as well as one of the + + align:start position:0% +your homework as well as one of the + + + align:start position:0% +your homework as well as one of the +zero-point x problems um which i give to + + align:start position:0% +zero-point x problems um which i give to + + + align:start position:0% +zero-point x problems um which i give to +try to get you um they're not you don't + + align:start position:0% +try to get you um they're not you don't + + + align:start position:0% +try to get you um they're not you don't +have to turn those in but i suggest you + + align:start position:0% +have to turn those in but i suggest you + + + align:start position:0% +have to turn those in but i suggest you +look at them i don't know how many of + + align:start position:0% +look at them i don't know how many of + + + align:start position:0% +look at them i don't know how many of +you are looking at them but uh this is a + + align:start position:0% +you are looking at them but uh this is a + + + align:start position:0% +you are looking at them but uh this is a +useful fact and and some of those other + + align:start position:0% +useful fact and and some of those other + + + align:start position:0% +useful fact and and some of those other +facts and in zero point x problems are + + align:start position:0% +facts and in zero point x problems are + + + align:start position:0% +facts and in zero point x problems are +useful so i encourage you to look at + + align:start position:0% +useful so i encourage you to look at + + + align:start position:0% +useful so i encourage you to look at +them + + align:start position:0% +them + + + align:start position:0% +them +but anyway intersection of context-free + + align:start position:0% +but anyway intersection of context-free + + + align:start position:0% +but anyway intersection of context-free +and regular is context-free you might + + align:start position:0% +and regular is context-free you might + + + align:start position:0% +and regular is context-free you might +ask what about intersection of + + align:start position:0% +ask what about intersection of + + + align:start position:0% +ask what about intersection of +context-free and context-free do we have + + align:start position:0% +context-free and context-free do we have + + + align:start position:0% +context-free and context-free do we have +closure under intersection the answer is + + align:start position:0% +closure under intersection the answer is + + + align:start position:0% +closure under intersection the answer is +no + + align:start position:0% +no + + + align:start position:0% +no +we do not have close closure under + + align:start position:0% +we do not have close closure under + + + align:start position:0% +we do not have close closure under +intersection we'll talk about that + + align:start position:0% +intersection we'll talk about that + + + align:start position:0% +intersection we'll talk about that +shortly uh so here's the proof sketch + + align:start position:0% +shortly uh so here's the proof sketch + + + align:start position:0% +shortly uh so here's the proof sketch +for um + + align:start position:0% +for um + + + align:start position:0% +for um +i should i wanted to say that the + + align:start position:0% +i should i wanted to say that the + + + align:start position:0% +i should i wanted to say that the +intersection of context free and regular + + align:start position:0% +intersection of context free and regular + + + align:start position:0% +intersection of context free and regular +why do we know that's still context-free + + align:start position:0% +why do we know that's still context-free + + + align:start position:0% +why do we know that's still context-free +because the push down automaton for a + + align:start position:0% + + + + align:start position:0% + +can be simulating the finite automaton + + align:start position:0% +can be simulating the finite automaton + + + align:start position:0% +can be simulating the finite automaton +for b + + align:start position:0% +for b + + + align:start position:0% +for b +inside its finite control + + align:start position:0% +inside its finite control + + + align:start position:0% +inside its finite control +inside its finite memory + + align:start position:0% +inside its finite memory + + + align:start position:0% +inside its finite memory +the problem is if you have two + + align:start position:0% +the problem is if you have two + + + align:start position:0% +the problem is if you have two +context-free languages you have two + + align:start position:0% +context-free languages you have two + + + align:start position:0% +context-free languages you have two +push-down automata you can't simulate + + align:start position:0% +push-down automata you can't simulate + + + align:start position:0% +push-down automata you can't simulate +that with one push-down automaton + + align:start position:0% +that with one push-down automaton + + + align:start position:0% +that with one push-down automaton +because it has only a single stack + + align:start position:0% +because it has only a single stack + + + align:start position:0% +because it has only a single stack +so if you're trying to take the + + align:start position:0% +so if you're trying to take the + + + align:start position:0% +so if you're trying to take the +intersection of two context-free + + align:start position:0% +intersection of two context-free + + + align:start position:0% +intersection of two context-free +language languages with only a single + + align:start position:0% +language languages with only a single + + + align:start position:0% +language languages with only a single +stack you're going to be in trouble + + align:start position:0% +stack you're going to be in trouble + + + align:start position:0% +stack you're going to be in trouble +because it's hard to um + + align:start position:0% +because it's hard to um + + + align:start position:0% +because it's hard to um +anyway i mean that's not a proof but at + + align:start position:0% +anyway i mean that's not a proof but at + + + align:start position:0% +anyway i mean that's not a proof but at +least it shows you what goes wrong if + + align:start position:0% +least it shows you what goes wrong if + + + align:start position:0% +least it shows you what goes wrong if +you try to do the obvious thing + + align:start position:0% +you try to do the obvious thing + + + align:start position:0% +you try to do the obvious thing +um + + align:start position:0% +um + + + align:start position:0% +um +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so if + + align:start position:0% +so if + + + align:start position:0% +so if +if then just here's an important point + + align:start position:0% +if then just here's an important point + + + align:start position:0% +if then just here's an important point +that i was trying to make before if a + + align:start position:0% +that i was trying to make before if a + + + align:start position:0% +that i was trying to make before if a +and b are both context-free and you take + + align:start position:0% +and b are both context-free and you take + + + align:start position:0% +and b are both context-free and you take +the intersection + + align:start position:0% +the intersection + + + align:start position:0% +the intersection +uh the result may not necessarily be a + + align:start position:0% +uh the result may not necessarily be a + + + align:start position:0% +uh the result may not necessarily be a +context-free language um so the class of + + align:start position:0% +context-free language um so the class of + + + align:start position:0% +context-free language um so the class of +context-free languages is not closed + + align:start position:0% +context-free languages is not closed + + + align:start position:0% +context-free languages is not closed +under the intersection we'll comment + + align:start position:0% +under the intersection we'll comment + + + align:start position:0% +under the intersection we'll comment +down that uh uh in a bit + + align:start position:0% +down that uh uh in a bit + + + align:start position:0% +down that uh uh in a bit +um + + align:start position:0% + + + + align:start position:0% + +the context-free languages are closed + + align:start position:0% +the context-free languages are closed + + + align:start position:0% +the context-free languages are closed +under the regular operations however + + align:start position:0% +under the regular operations however + + + align:start position:0% +under the regular operations however +union intersection + + align:start position:0% +union intersection + + + align:start position:0% +union intersection +a union concatenation and star so you + + align:start position:0% +a union concatenation and star so you + + + align:start position:0% +a union concatenation and star so you +should um feel comfortable that you know + + align:start position:0% +should um feel comfortable that you know + + + align:start position:0% +should um feel comfortable that you know +how to prove that it's in the again it's + + align:start position:0% +how to prove that it's in the again it's + + + align:start position:0% +how to prove that it's in the again it's +one of the + + align:start position:0% +one of the + + + align:start position:0% +one of the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i think it's problem 0.2 and i think the + + align:start position:0% +i think it's problem 0.2 and i think the + + + align:start position:0% +i think it's problem 0.2 and i think the +solution is even given in the book for + + align:start position:0% +solution is even given in the book for + + + align:start position:0% +solution is even given in the book for +it so you just should know how to prove + + align:start position:0% +it so you just should know how to prove + + + align:start position:0% +it so you just should know how to prove +that um + + align:start position:0% +that um + + + align:start position:0% +that um +uh not very + + align:start position:0% +uh not very + + + align:start position:0% +uh not very +pretty straightforward um okay + + align:start position:0% +pretty straightforward um okay + + + align:start position:0% +pretty straightforward um okay +so let's move on then + + align:start position:0% +so let's move on then + + + align:start position:0% +so let's move on then +um to uh + + align:start position:0% +um to uh + + + align:start position:0% +um to uh +to really basically conclude our um work + + align:start position:0% +to really basically conclude our um work + + + align:start position:0% +to really basically conclude our um work +on context-free languages and to + + align:start position:0% +on context-free languages and to + + + align:start position:0% +on context-free languages and to +understand the limitations of uh content + + align:start position:0% +understand the limitations of uh content + + + align:start position:0% +understand the limitations of uh content +context-free grammars and what kinds of + + align:start position:0% +context-free grammars and what kinds of + + + align:start position:0% +context-free grammars and what kinds of +languages may not be context-free and + + align:start position:0% +languages may not be context-free and + + + align:start position:0% +languages may not be context-free and +how do you prove that so how do you + + align:start position:0% +how do you prove that so how do you + + + align:start position:0% +how do you prove that so how do you +prove that for some language there is no + + align:start position:0% +prove that for some language there is no + + + align:start position:0% +prove that for some language there is no +grammar + + align:start position:0% +grammar + + + align:start position:0% +grammar +um + + align:start position:0% +um + + + align:start position:0% +um +again you know it's not enough just to + + align:start position:0% +again you know it's not enough just to + + + align:start position:0% +again you know it's not enough just to +say + + align:start position:0% +say + + + align:start position:0% +say +you know + + align:start position:0% +you know + + + align:start position:0% +you know +uh given informal + + align:start position:0% +uh given informal + + + align:start position:0% +uh given informal +uh + + align:start position:0% +uh + + + align:start position:0% +uh +comment that you will i i couldn't think + + align:start position:0% +comment that you will i i couldn't think + + + align:start position:0% +comment that you will i i couldn't think +of a grammar that or some things of that + + align:start position:0% +of a grammar that or some things of that + + + align:start position:0% +of a grammar that or some things of that +kind that's not going to be good enough + + align:start position:0% +kind that's not going to be good enough + + + align:start position:0% +kind that's not going to be good enough +we need to have a proof + + align:start position:0% +we need to have a proof + + + align:start position:0% +we need to have a proof +uh so if we take the language here + + align:start position:0% +uh so if we take the language here + + + align:start position:0% +uh so if we take the language here +0 to the k1 to the k2 to the k so those + + align:start position:0% +0 to the k1 to the k2 to the k so those + + + align:start position:0% +0 to the k1 to the k2 to the k so those +are strings which are runs of zeros + + align:start position:0% +are strings which are runs of zeros + + + align:start position:0% +are strings which are runs of zeros +followed by an equal number of ones + + align:start position:0% +followed by an equal number of ones + + + align:start position:0% +followed by an equal number of ones +followed by an equal number of twos so + + align:start position:0% +followed by an equal number of twos so + + + align:start position:0% +followed by an equal number of twos so +just for zeros then ones then twos all + + align:start position:0% +just for zeros then ones then twos all + + + align:start position:0% +just for zeros then ones then twos all +the same length + + align:start position:0% +the same length + + + align:start position:0% +the same length +um + + align:start position:0% +um + + + align:start position:0% +um +uh that's a language which is not going + + align:start position:0% +uh that's a language which is not going + + + align:start position:0% +uh that's a language which is not going +to be a context-free language and we'll + + align:start position:0% +to be a context-free language and we'll + + + align:start position:0% +to be a context-free language and we'll +we'll give a method for proving that + + align:start position:0% +we'll give a method for proving that + + + align:start position:0% +we'll give a method for proving that +you know if you had a stack you can + + align:start position:0% +you know if you had a stack you can + + + align:start position:0% +you know if you had a stack you can +match the ones with the zeros but then + + align:start position:0% +match the ones with the zeros but then + + + align:start position:0% +match the ones with the zeros but then +once you're done with that the stack is + + align:start position:0% +once you're done with that the stack is + + + align:start position:0% +once you're done with that the stack is +empty and how do you now make sure that + + align:start position:0% +empty and how do you now make sure that + + + align:start position:0% +empty and how do you now make sure that +the number of twos corresponds to the + + align:start position:0% +the number of twos corresponds to the + + + align:start position:0% +the number of twos corresponds to the +number of ones that you had so again + + align:start position:0% +number of ones that you had so again + + + align:start position:0% +number of ones that you had so again +that's an informal argument that's not + + align:start position:0% +that's an informal argument that's not + + + align:start position:0% +that's an informal argument that's not +good enough to uh to be a proof but it + + align:start position:0% +good enough to uh to be a proof but it + + + align:start position:0% +good enough to uh to be a proof but it +sort of gives an intuition um so we're + + align:start position:0% +sort of gives an intuition um so we're + + + align:start position:0% +sort of gives an intuition um so we're +going to give a method for proving + + align:start position:0% +going to give a method for proving + + + align:start position:0% +going to give a method for proving +non-context-free + + align:start position:0% +non-context-free + + + align:start position:0% +non-context-free +languages are not context-free using + + align:start position:0% +languages are not context-free using + + + align:start position:0% +languages are not context-free using +again + + align:start position:0% +again + + + align:start position:0% +again +a pumping lemma + + align:start position:0% +a pumping lemma + + + align:start position:0% +a pumping lemma +but this is going to be a pumping lemma + + align:start position:0% +but this is going to be a pumping lemma + + + align:start position:0% +but this is going to be a pumping lemma +that applies to context-free languages + + align:start position:0% +that applies to context-free languages + + + align:start position:0% +that applies to context-free languages +not to regular languages okay it looks + + align:start position:0% +not to regular languages okay it looks + + + align:start position:0% +not to regular languages okay it looks +very similar but it has some extra + + align:start position:0% +very similar but it has some extra + + + align:start position:0% +very similar but it has some extra +wrinkles thrown in + + align:start position:0% +wrinkles thrown in + + + align:start position:0% +wrinkles thrown in +because the other older + + align:start position:0% +because the other older + + + align:start position:0% +because the other older +pumping dilemma was specific to the + + align:start position:0% +pumping dilemma was specific to the + + + align:start position:0% +pumping dilemma was specific to the +regular languages and this is going to + + align:start position:0% +regular languages and this is going to + + + align:start position:0% +regular languages and this is going to +be something that applies to the context + + align:start position:0% +be something that applies to the context + + + align:start position:0% +be something that applies to the context +free languages + + align:start position:0% +free languages + + + align:start position:0% +free languages +okay so now um let's just read it and + + align:start position:0% +okay so now um let's just read it and + + + align:start position:0% +okay so now um let's just read it and +then we'll um + + align:start position:0% +then we'll um + + + align:start position:0% +then we'll um +try to interpret it again it's very + + align:start position:0% +try to interpret it again it's very + + + align:start position:0% +try to interpret it again it's very +similar in spirit basically it says that + + align:start position:0% +similar in spirit basically it says that + + + align:start position:0% +similar in spirit basically it says that +whenever you have a context-free + + align:start position:0% +whenever you have a context-free + + + align:start position:0% +whenever you have a context-free +language all long strings in the + + align:start position:0% +language all long strings in the + + + align:start position:0% +language all long strings in the +language can be pumped + + align:start position:0% +language can be pumped + + + align:start position:0% +language can be pumped +in some kind of way so it's going to be + + align:start position:0% +in some kind of way so it's going to be + + + align:start position:0% +in some kind of way so it's going to be +a little different kind of pumping than + + align:start position:0% +a little different kind of pumping than + + + align:start position:0% +a little different kind of pumping than +we had before + + align:start position:0% +we had before + + + align:start position:0% +we had before +and you stay in the language + + align:start position:0% +and you stay in the language + + + align:start position:0% +and you stay in the language +okay so + + align:start position:0% + + + + align:start position:0% + +before we broke the string into three + + align:start position:0% +before we broke the string into three + + + align:start position:0% +before we broke the string into three +pieces where we could repeat that center + + align:start position:0% +pieces where we could repeat that center + + + align:start position:0% +pieces where we could repeat that center +piece as many times as as you like um + + align:start position:0% +piece as many times as as you like um + + + align:start position:0% +piece as many times as as you like um +and you stay in the language here we're + + align:start position:0% +and you stay in the language here we're + + + align:start position:0% +and you stay in the language here we're +going to end up breaking the um the + + align:start position:0% +going to end up breaking the um the + + + align:start position:0% +going to end up breaking the um the +string into five pieces so s is going to + + align:start position:0% +string into five pieces so s is going to + + + align:start position:0% +string into five pieces so s is going to +be broken up into u v x y z um + + align:start position:0% +be broken up into u v x y z um + + + align:start position:0% +be broken up into u v x y z um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and + + align:start position:0% +and + + + align:start position:0% +and +the + + align:start position:0% +the + + + align:start position:0% +the +and the way it's gonna work here so here + + align:start position:0% +and the way it's gonna work here so here + + + align:start position:0% +and the way it's gonna work here so here +is a picture so all long strings again + + align:start position:0% +is a picture so all long strings again + + + align:start position:0% +is a picture so all long strings again +there's gonna be a threshold um for + + align:start position:0% +there's gonna be a threshold um for + + + align:start position:0% +there's gonna be a threshold um for +whenever you have a language there's + + align:start position:0% +whenever you have a language there's + + + align:start position:0% +whenever you have a language there's +going to be some cutoff length + + align:start position:0% +going to be some cutoff length + + + align:start position:0% +going to be some cutoff length +so that all the longer strings in that + + align:start position:0% +so that all the longer strings in that + + + align:start position:0% +so that all the longer strings in that +language can be pumped and you stay in + + align:start position:0% +language can be pumped and you stay in + + + align:start position:0% +language can be pumped and you stay in +the language but the shorter strings + + align:start position:0% +the language but the shorter strings + + + align:start position:0% +the language but the shorter strings +there's no guarantee + + align:start position:0% +there's no guarantee + + + align:start position:0% +there's no guarantee +um so if you have a long string in the + + align:start position:0% +um so if you have a long string in the + + + align:start position:0% +um so if you have a long string in the +language length at least this pumping + + align:start position:0% +language length at least this pumping + + + align:start position:0% +language length at least this pumping +length p + + align:start position:0% +length p + + + align:start position:0% +length p +then you can break it up into five + + align:start position:0% +then you can break it up into five + + + align:start position:0% +then you can break it up into five +pieces but now it's that + + align:start position:0% +pieces but now it's that + + + align:start position:0% +pieces but now it's that +second and fourth string that are going + + align:start position:0% +second and fourth string that are going + + + align:start position:0% +second and fourth string that are going +to play that special uh pumping roll um + + align:start position:0% +to play that special uh pumping roll um + + + align:start position:0% +to play that special uh pumping roll um +which means that what you can do is you + + align:start position:0% +which means that what you can do is you + + + align:start position:0% +which means that what you can do is you +can repeat those + + align:start position:0% +can repeat those + + + align:start position:0% +can repeat those +um + + align:start position:0% +um + + + align:start position:0% +um +and you stay in the language + + align:start position:0% +and you stay in the language + + + align:start position:0% +and you stay in the language +and it's important that you repeat them + + align:start position:0% +and it's important that you repeat them + + + align:start position:0% +and it's important that you repeat them +both that v and that y the same number + + align:start position:0% +both that v and that y the same number + + + align:start position:0% +both that v and that y the same number +of times so you're gonna have a picture + + align:start position:0% +of times so you're gonna have a picture + + + align:start position:0% +of times so you're gonna have a picture +that looks something like this + + align:start position:0% +that looks something like this + + + align:start position:0% +that looks something like this +um and that is going to + + align:start position:0% +um and that is going to + + + align:start position:0% +um and that is going to +you you repeat + + align:start position:0% +you you repeat + + + align:start position:0% +you you repeat +uh so you can get you if you repeat the + + align:start position:0% +uh so you can get you if you repeat the + + + align:start position:0% +uh so you can get you if you repeat the +v and repeat the y you get u + + align:start position:0% +v and repeat the y you get u + + + align:start position:0% +v and repeat the y you get u +v v x y y z um or if you look at over + + align:start position:0% +v v x y y z um or if you look at over + + + align:start position:0% +v v x y y z um or if you look at over +here it would be u v squared x y squared + + align:start position:0% +here it would be u v squared x y squared + + + align:start position:0% +here it would be u v squared x y squared +is e + + align:start position:0% +is e + + + align:start position:0% +is e +um + + align:start position:0% +um + + + align:start position:0% +um +and that's going to still be in the + + align:start position:0% +and that's going to still be in the + + + align:start position:0% +and that's going to still be in the +language + + align:start position:0% +language + + + align:start position:0% +language +um and then we have so that's one + + align:start position:0% +um and then we have so that's one + + + align:start position:0% +um and then we have so that's one +condition we'll have to look at all of + + align:start position:0% +condition we'll have to look at all of + + + align:start position:0% +condition we'll have to look at all of +these conditions when we do the proof + + align:start position:0% +these conditions when we do the proof + + + align:start position:0% +these conditions when we do the proof +but we just understand what the + + align:start position:0% +but we just understand what the + + + align:start position:0% +but we just understand what the +statement is right now so the second + + align:start position:0% +statement is right now so the second + + + align:start position:0% +statement is right now so the second +condition is that v and y together + + align:start position:0% +condition is that v and y together + + + align:start position:0% +condition is that v and y together +cannot be empty and really that's + + align:start position:0% +cannot be empty and really that's + + + align:start position:0% +cannot be empty and really that's +another way of saying they can't both be + + align:start position:0% +another way of saying they can't both be + + + align:start position:0% +another way of saying they can't both be +the empty string because if they were + + align:start position:0% +the empty string because if they were + + + align:start position:0% +the empty string because if they were +both the empty string then repeating + + align:start position:0% +both the empty string then repeating + + + align:start position:0% +both the empty string then repeating +them wouldn't change + + align:start position:0% +them wouldn't change + + + align:start position:0% +them wouldn't change +um + + align:start position:0% +um + + + align:start position:0% +um +s + + align:start position:0% +s + + + align:start position:0% +s +and then of course it would stay in the + + align:start position:0% +and then of course it would stay in the + + + align:start position:0% +and then of course it would stay in the +language so it would be kind of + + align:start position:0% +language so it would be kind of + + + align:start position:0% +language so it would be kind of +meaningless if they were allowed to be + + align:start position:0% +meaningless if they were allowed to be + + + align:start position:0% +meaningless if they were allowed to be +empty + + align:start position:0% +empty + + + align:start position:0% +empty +and the last thing is again going to be + + align:start position:0% +and the last thing is again going to be + + + align:start position:0% +and the last thing is again going to be +there as a matter of convenience for + + align:start position:0% +there as a matter of convenience for + + + align:start position:0% +there as a matter of convenience for +proving str proving + + align:start position:0% +proving str proving + + + align:start position:0% +proving str proving +uh languages are not context-free + + align:start position:0% +uh languages are not context-free + + + align:start position:0% +uh languages are not context-free +because + + align:start position:0% +because + + + align:start position:0% +because +you have to make sure there's no + + align:start position:0% +you have to make sure there's no + + + align:start position:0% +you have to make sure there's no +possible way of cutting up the string + + align:start position:0% +possible way of cutting up the string + + + align:start position:0% +possible way of cutting up the string +when you're trying to prove a language + + align:start position:0% +when you're trying to prove a language + + + align:start position:0% +when you're trying to prove a language +is not context-free you have to show the + + align:start position:0% +is not context-free you have to show the + + + align:start position:0% +is not context-free you have to show the +pumping fails and then you + + align:start position:0% +pumping fails and then you + + + align:start position:0% +pumping fails and then you +it's it's going to be helpful sometimes + + align:start position:0% +it's it's going to be helpful sometimes + + + align:start position:0% +it's it's going to be helpful sometimes +to limit the ways in which the string + + align:start position:0% +to limit the ways in which the string + + + align:start position:0% +to limit the ways in which the string +can be cut up because then you have it's + + align:start position:0% +can be cut up because then you have it's + + + align:start position:0% +can be cut up because then you have it's +an easier job for you to work with it um + + align:start position:0% +an easier job for you to work with it um + + + align:start position:0% +an easier job for you to work with it um +so here it's a little different than + + align:start position:0% +so here it's a little different than + + + align:start position:0% +so here it's a little different than +before but sort of similar that v x y + + align:start position:0% +before but sort of similar that v x y + + + align:start position:0% +before but sort of similar that v x y +combined um as a substring so i think i + + align:start position:0% +combined um as a substring so i think i + + + align:start position:0% +combined um as a substring so i think i +show that over here + + align:start position:0% +show that over here + + + align:start position:0% +show that over here +v x y together + + align:start position:0% +v x y together + + + align:start position:0% +v x y together +is a um + + align:start position:0% +is a um + + + align:start position:0% +is a um +is not too long so the v vxy maybe is + + align:start position:0% +is not too long so the v vxy maybe is + + + align:start position:0% +is not too long so the v vxy maybe is +better seen up here is going to be is + + align:start position:0% +better seen up here is going to be is + + + align:start position:0% +better seen up here is going to be is +going to be at most p + + align:start position:0% +going to be at most p + + + align:start position:0% +going to be at most p +um we'll we'll do an example in a minute + + align:start position:0% +um we'll we'll do an example in a minute + + + align:start position:0% +um we'll we'll do an example in a minute +of using this okay so + + align:start position:0% +of using this okay so + + + align:start position:0% +of using this okay so +again here's our pumping limit i just + + align:start position:0% +again here's our pumping limit i just + + + align:start position:0% +again here's our pumping limit i just +restated it so um you know we have it in + + align:start position:0% +restated it so um you know we have it in + + + align:start position:0% +restated it so um you know we have it in +front of us + + align:start position:0% +front of us + + + align:start position:0% +front of us +and we're going to do a proof + + align:start position:0% +and we're going to do a proof + + + align:start position:0% +and we're going to do a proof +i'm just going to give you the idea of + + align:start position:0% +i'm just going to give you the idea of + + + align:start position:0% +i'm just going to give you the idea of +the proof first and then we'll go + + align:start position:0% +the proof first and then we'll go + + + align:start position:0% +the proof first and then we'll go +through some of the details the idea is + + align:start position:0% +through some of the details the idea is + + + align:start position:0% +through some of the details the idea is +actually pretty simple + + align:start position:0% +actually pretty simple + + + align:start position:0% +actually pretty simple +okay + + align:start position:0% +okay + + + align:start position:0% +okay +i give it a call proof by picture + + align:start position:0% + + + + align:start position:0% + +again remember what we're trying to do + + align:start position:0% +again remember what we're trying to do + + + align:start position:0% +again remember what we're trying to do +we're trying to show that we have this + + align:start position:0% +we're trying to show that we have this + + + align:start position:0% +we're trying to show that we have this +context-free language a + + align:start position:0% +context-free language a + + + align:start position:0% +context-free language a +and now + + align:start position:0% +and now + + + align:start position:0% +and now +all long strings in a have this pumping + + align:start position:0% +all long strings in a have this pumping + + + align:start position:0% +all long strings in a have this pumping +quality that you can break them up into + + align:start position:0% +quality that you can break them up into + + + align:start position:0% +quality that you can break them up into +five pieces + + align:start position:0% +five pieces + + + align:start position:0% +five pieces +so that the second and the fourth piece + + align:start position:0% +so that the second and the fourth piece + + + align:start position:0% +so that the second and the fourth piece +can be repeated and you stay in the + + align:start position:0% +can be repeated and you stay in the + + + align:start position:0% +can be repeated and you stay in the +language + + align:start position:0% +language + + + align:start position:0% +language +so how do we know that that's going to + + align:start position:0% +so how do we know that that's going to + + + align:start position:0% +so how do we know that that's going to +be true + + align:start position:0% +be true + + + align:start position:0% +be true +let's take a look at the proof here and + + align:start position:0% +let's take a look at the proof here and + + + align:start position:0% +let's take a look at the proof here and +how why is that going to be true + + align:start position:0% +how why is that going to be true + + + align:start position:0% +how why is that going to be true +so first of all + + align:start position:0% +so first of all + + + align:start position:0% +so first of all +i i i'd like to do it qualitatively + + align:start position:0% +i i i'd like to do it qualitatively + + + align:start position:0% +i i i'd like to do it qualitatively +rather than quantitatively so let's just + + align:start position:0% +rather than quantitatively so let's just + + + align:start position:0% +rather than quantitatively so let's just +imagine instead of what thinking we'll + + align:start position:0% +imagine instead of what thinking we'll + + + align:start position:0% +imagine instead of what thinking we'll +calculate what p is later but just + + align:start position:0% +calculate what p is later but just + + + align:start position:0% +calculate what p is later but just +imagine the s is some really really long + + align:start position:0% +imagine the s is some really really long + + + align:start position:0% +imagine the s is some really really long +string + + align:start position:0% +string + + + align:start position:0% +string +that's the way i like to think about it + + align:start position:0% +that's the way i like to think about it + + + align:start position:0% +that's the way i like to think about it +so s is just really long + + align:start position:0% +so s is just really long + + + align:start position:0% +so s is just really long +what is that going to tell us + + align:start position:0% +what is that going to tell us + + + align:start position:0% +what is that going to tell us +it's going to tell us something + + align:start position:0% +it's going to tell us something + + + align:start position:0% +it's going to tell us something +important + + align:start position:0% +important + + + align:start position:0% +important +about + + align:start position:0% + + + + align:start position:0% + +the way the grammar produces s + + align:start position:0% +the way the grammar produces s + + + align:start position:0% +the way the grammar produces s +which is going to be useful in in + + align:start position:0% +which is going to be useful in in + + + align:start position:0% +which is going to be useful in in +getting a way of pumping + + align:start position:0% +getting a way of pumping + + + align:start position:0% +getting a way of pumping +pumping s + + align:start position:0% +pumping s + + + align:start position:0% +pumping s +so if s is really long + + align:start position:0% +so if s is really long + + + align:start position:0% +so if s is really long +um + + align:start position:0% +um + + + align:start position:0% +um +we're going to look at the parse tree + + align:start position:0% +we're going to look at the parse tree + + + align:start position:0% +we're going to look at the parse tree +for s + + align:start position:0% +for s + + + align:start position:0% +for s +and we're going to conclude that the + + align:start position:0% +and we're going to conclude that the + + + align:start position:0% +and we're going to conclude that the +parse tree has to be really tall + + align:start position:0% +parse tree has to be really tall + + + align:start position:0% +parse tree has to be really tall +because it's impossible for a very + + align:start position:0% +because it's impossible for a very + + + align:start position:0% +because it's impossible for a very +shallow + + align:start position:0% +shallow + + + align:start position:0% +shallow +parse tree to generate a very long + + align:start position:0% +parse tree to generate a very long + + + align:start position:0% +parse tree to generate a very long +string + + align:start position:0% +string + + + align:start position:0% +string +and again we'll quantify that in a + + align:start position:0% +and again we'll quantify that in a + + + align:start position:0% +and again we'll quantify that in a +second but intuitively i think that's + + align:start position:0% +second but intuitively i think that's + + + align:start position:0% +second but intuitively i think that's +not too hard to see why that ought to be + + align:start position:0% +not too hard to see why that ought to be + + + align:start position:0% +not too hard to see why that ought to be +true so if you have a long s the pole + + align:start position:0% +true so if you have a long s the pole + + + align:start position:0% +true so if you have a long s the pole +the parse tree has to be really tall + + align:start position:0% +the parse tree has to be really tall + + + align:start position:0% +the parse tree has to be really tall +because the parse tree can't generate + + align:start position:0% +because the parse tree can't generate + + + align:start position:0% +because the parse tree can't generate +very many it can't expand by very much + + align:start position:0% +very many it can't expand by very much + + + align:start position:0% +very many it can't expand by very much +at each level + + align:start position:0% +at each level + + + align:start position:0% +at each level +so we'll look at how much it can expand + + align:start position:0% +so we'll look at how much it can expand + + + align:start position:0% +so we'll look at how much it can expand +but it depends on the grammar + + align:start position:0% +but it depends on the grammar + + + align:start position:0% +but it depends on the grammar +how much expansion can we have at each + + align:start position:0% +how much expansion can we have at each + + + align:start position:0% +how much expansion can we have at each +level and it's going to be you can't + + align:start position:0% +level and it's going to be you can't + + + align:start position:0% +level and it's going to be you can't +have just in three levels + + align:start position:0% +have just in three levels + + + align:start position:0% +have just in three levels +you know some small grammar generating a + + align:start position:0% +you know some small grammar generating a + + + align:start position:0% +you know some small grammar generating a +string of length a million just you know + + align:start position:0% +string of length a million just you know + + + align:start position:0% +string of length a million just you know +you'll see that that's just impossible + + align:start position:0% +you'll see that that's just impossible + + + align:start position:0% +you'll see that that's just impossible +so once you know that the parse tree is + + align:start position:0% +so once you know that the parse tree is + + + align:start position:0% +so once you know that the parse tree is +really tall here + + align:start position:0% +really tall here + + + align:start position:0% +really tall here +um + + align:start position:0% +um + + + align:start position:0% +um +then you're actually almost done + + align:start position:0% +then you're actually almost done + + + align:start position:0% +then you're actually almost done +because what does it mean to be really + + align:start position:0% +because what does it mean to be really + + + align:start position:0% +because what does it mean to be really +tall it means that there's some path + + align:start position:0% +tall it means that there's some path + + + align:start position:0% +tall it means that there's some path +starting at the start variable e i'm + + align:start position:0% +starting at the start variable e i'm + + + align:start position:0% +starting at the start variable e i'm +calling it uh in this parse tree + + align:start position:0% +calling it uh in this parse tree + + + align:start position:0% +calling it uh in this parse tree +which goes down to some + + align:start position:0% +which goes down to some + + + align:start position:0% +which goes down to some +um + + align:start position:0% +um + + + align:start position:0% +um +terminal + + align:start position:0% +terminal + + + align:start position:0% +terminal +symbol + + align:start position:0% +symbol + + + align:start position:0% +symbol +in s + + align:start position:0% +in s + + + align:start position:0% +in s +which goes through many steps that's + + align:start position:0% +which goes through many steps that's + + + align:start position:0% +which goes through many steps that's +what it means for the tree to be very + + align:start position:0% +what it means for the tree to be very + + + align:start position:0% +what it means for the tree to be very +tall + + align:start position:0% +tall + + + align:start position:0% +tall +and each one of those steps is a + + align:start position:0% +and each one of those steps is a + + + align:start position:0% +and each one of those steps is a +variable until you get down to the very + + align:start position:0% +variable until you get down to the very + + + align:start position:0% +variable until you get down to the very +end + + align:start position:0% + + + + align:start position:0% + +okay so that's the way parse trees look + + align:start position:0% +okay so that's the way parse trees look + + + align:start position:0% +okay so that's the way parse trees look +you keep expanding variables until you + + align:start position:0% +you keep expanding variables until you + + + align:start position:0% +you keep expanding variables until you +get to a terminal + + align:start position:0% +get to a terminal + + + align:start position:0% +get to a terminal +so here's that here you get some some + + align:start position:0% +so here's that here you get some some + + + align:start position:0% +so here's that here you get some some +path that's really a long path + + align:start position:0% +path that's really a long path + + + align:start position:0% +path that's really a long path +and once you have a long path that have + + align:start position:0% +and once you have a long path that have + + + align:start position:0% +and once you have a long path that have +many many variables appearing on here + + align:start position:0% +many many variables appearing on here + + + align:start position:0% +many many variables appearing on here +well + + align:start position:0% +well + + + align:start position:0% +well +the grammar itself has only some fixed + + align:start position:0% +the grammar itself has only some fixed + + + align:start position:0% +the grammar itself has only some fixed +number of variables in it so you're + + align:start position:0% +number of variables in it so you're + + + align:start position:0% +number of variables in it so you're +going to have to have a repetition + + align:start position:0% +going to have to have a repetition + + + align:start position:0% +going to have to have a repetition +coming among the variables that occur on + + align:start position:0% +coming among the variables that occur on + + + align:start position:0% +coming among the variables that occur on +that long path + + align:start position:0% + + + + align:start position:0% + +got that + + align:start position:0% +got that + + + align:start position:0% +got that +so a long string forces a tall + + align:start position:0% +so a long string forces a tall + + + align:start position:0% +so a long string forces a tall +parse tree forces a repetition + + align:start position:0% +parse tree forces a repetition + + + align:start position:0% +parse tree forces a repetition +on some path coming out of the start + + align:start position:0% +on some path coming out of the start + + + align:start position:0% +on some path coming out of the start +variable + + align:start position:0% +variable + + + align:start position:0% +variable +uh of some of some other variable that + + align:start position:0% +uh of some of some other variable that + + + align:start position:0% +uh of some of some other variable that +comes out + + align:start position:0% +comes out + + + align:start position:0% +comes out +now that's going to tell us how to cut + + align:start position:0% +now that's going to tell us how to cut + + + align:start position:0% +now that's going to tell us how to cut +up s + + align:start position:0% +up s + + + align:start position:0% +up s +because if you look at the subtrees of s + + align:start position:0% +because if you look at the subtrees of s + + + align:start position:0% +because if you look at the subtrees of s +that those two r variables are + + align:start position:0% +that those two r variables are + + + align:start position:0% +that those two r variables are +generating + + align:start position:0% +generating + + + align:start position:0% +generating +shown like this + + align:start position:0% +shown like this + + + align:start position:0% +shown like this +i'm going to use that + + align:start position:0% +i'm going to use that + + + align:start position:0% +i'm going to use that +so if you have to follow what i'm saying + + align:start position:0% +so if you have to follow what i'm saying + + + align:start position:0% +so if you have to follow what i'm saying +here so you know the r here is + + align:start position:0% +here so you know the r here is + + + align:start position:0% +here so you know the r here is +generating this + + align:start position:0% +generating this + + + align:start position:0% +generating this +portion of s and the lower r is + + align:start position:0% +portion of s and the lower r is + + + align:start position:0% +portion of s and the lower r is +generating a smaller portion of s + + align:start position:0% +generating a smaller portion of s + + + align:start position:0% +generating a smaller portion of s +just + + align:start position:0% +just + + + align:start position:0% +just +looking at the subtree that you get here + + align:start position:0% +looking at the subtree that you get here + + + align:start position:0% +looking at the subtree that you get here +um and that's going to tell us that we + + align:start position:0% +um and that's going to tell us that we + + + align:start position:0% +um and that's going to tell us that we +can cut up s + + align:start position:0% + + + + align:start position:0% + +accordingly + + align:start position:0% +accordingly + + + align:start position:0% +accordingly +so u is that very first part out here + + align:start position:0% +so u is that very first part out here + + + align:start position:0% +so u is that very first part out here +generated by e but not by the first r r + + align:start position:0% +generated by e but not by the first r r + + + align:start position:0% +generated by e but not by the first r r +is generated v is generated by the first + + align:start position:0% +is generated v is generated by the first + + + align:start position:0% +is generated v is generated by the first +r but not by the second r the second r + + align:start position:0% +r but not by the second r the second r + + + align:start position:0% +r but not by the second r the second r +generates exactly x + + align:start position:0% +generates exactly x + + + align:start position:0% +generates exactly x +and then we have y and z similarly + + align:start position:0% + + + + align:start position:0% + +so that all follows from having a lo a + + align:start position:0% +so that all follows from having a lo a + + + align:start position:0% +so that all follows from having a lo a +tall + + align:start position:0% +tall + + + align:start position:0% +tall +parse tree + + align:start position:0% +parse tree + + + align:start position:0% +parse tree +and now we're finished + + align:start position:0% +and now we're finished + + + align:start position:0% +and now we're finished +now we know how to cut up s how do we + + align:start position:0% +now we know how to cut up s how do we + + + align:start position:0% +now we know how to cut up s how do we +know + + align:start position:0% +know + + + align:start position:0% +know +we can repeat + + align:start position:0% +we can repeat + + + align:start position:0% +we can repeat +uh v and y and still be in the language + + align:start position:0% +uh v and y and still be in the language + + + align:start position:0% +uh v and y and still be in the language +well i'll actually show your and show + + align:start position:0% +well i'll actually show your and show + + + align:start position:0% +well i'll actually show your and show +you that you're in the language by + + align:start position:0% +you that you're in the language by + + + align:start position:0% +you that you're in the language by +exhibiting a parse tree for the string u + + align:start position:0% +exhibiting a parse tree for the string u + + + align:start position:0% +exhibiting a parse tree for the string u +v v x y y z here it is + + align:start position:0% + + + + align:start position:0% + +what i'm gonna get that parse tree by + + align:start position:0% +what i'm gonna get that parse tree by + + + align:start position:0% +what i'm gonna get that parse tree by +when i expand this lower r + + align:start position:0% +when i expand this lower r + + + align:start position:0% +when i expand this lower r +instead of expanding it to get x i'm + + align:start position:0% +instead of expanding it to get x i'm + + + align:start position:0% +instead of expanding it to get x i'm +going to follow the same substitutions + + align:start position:0% +going to follow the same substitutions + + + align:start position:0% +going to follow the same substitutions +that i i had when i expanded the upper r + + align:start position:0% +that i i had when i expanded the upper r + + + align:start position:0% +that i i had when i expanded the upper r +so it's as if i took this larger subtree + + align:start position:0% +so it's as if i took this larger subtree + + + align:start position:0% +so it's as if i took this larger subtree +here and i substituted it in for the + + align:start position:0% +here and i substituted it in for the + + + align:start position:0% +here and i substituted it in for the +smaller uh subtree under under the + + align:start position:0% +smaller uh subtree under under the + + + align:start position:0% +smaller uh subtree under under the +second r and so that i get a picture + + align:start position:0% +second r and so that i get a picture + + + align:start position:0% +second r and so that i get a picture +that looks like this + + align:start position:0% + + + + align:start position:0% + +so here i'm substituting under the + + align:start position:0% +so here i'm substituting under the + + + align:start position:0% +so here i'm substituting under the +second r the same subtree that i had + + align:start position:0% +second r the same subtree that i had + + + align:start position:0% +second r the same subtree that i had +originally coming out of the upper r the + + align:start position:0% +originally coming out of the upper r the + + + align:start position:0% +originally coming out of the upper r the +first r + + align:start position:0% +first r + + + align:start position:0% +first r +and so now this parse tree is generating + + align:start position:0% +and so now this parse tree is generating + + + align:start position:0% +and so now this parse tree is generating +the string u v v x y y z + + align:start position:0% +the string u v v x y y z + + + align:start position:0% +the string u v v x y y z +which is what i'm looking for and of + + align:start position:0% +which is what i'm looking for and of + + + align:start position:0% +which is what i'm looking for and of +course you can do that again and again + + align:start position:0% +course you can do that again and again + + + align:start position:0% +course you can do that again and again +and you're going to keep getting higher + + align:start position:0% +and you're going to keep getting higher + + + align:start position:0% +and you're going to keep getting higher +and higher exponents of v and y + + align:start position:0% +and higher exponents of v and y + + + align:start position:0% +and higher exponents of v and y +um + + align:start position:0% +um + + + align:start position:0% +um +and in fact you can even get the zero + + align:start position:0% +and in fact you can even get the zero + + + align:start position:0% +and in fact you can even get the zero +exponent which means that v and y both + + align:start position:0% +exponent which means that v and y both + + + align:start position:0% +exponent which means that v and y both +disappear altogether + + align:start position:0% +disappear altogether + + + align:start position:0% +disappear altogether +and for that you do something slightly + + align:start position:0% +and for that you do something slightly + + + align:start position:0% +and for that you do something slightly +different which is that you replace + + align:start position:0% +different which is that you replace + + + align:start position:0% +different which is that you replace +the larger subtree by the smaller + + align:start position:0% +the larger subtree by the smaller + + + align:start position:0% +the larger subtree by the smaller +subtree + + align:start position:0% + + + + align:start position:0% + +okay so here which was originally that + + align:start position:0% +okay so here which was originally that + + + align:start position:0% +okay so here which was originally that +larger subtree generating v x y i stick + + align:start position:0% +larger subtree generating v x y i stick + + + align:start position:0% +larger subtree generating v x y i stick +instead the smaller subtree i do the + + align:start position:0% +instead the smaller subtree i do the + + + align:start position:0% +instead the smaller subtree i do the +substitutions from the smaller sub tree + + align:start position:0% +substitutions from the smaller sub tree + + + align:start position:0% +substitutions from the smaller sub tree +and i just get x uh there and so now the + + align:start position:0% +and i just get x uh there and so now the + + + align:start position:0% +and i just get x uh there and so now the +string i generated is u xz which is the + + align:start position:0% +string i generated is u xz which is the + + + align:start position:0% +string i generated is u xz which is the +same as u v to the zero x y to the zero + + align:start position:0% +same as u v to the zero x y to the zero + + + align:start position:0% +same as u v to the zero x y to the zero +z + + align:start position:0% +z + + + align:start position:0% +z +okay that's that is the idea of the + + align:start position:0% +okay that's that is the idea of the + + + align:start position:0% +okay that's that is the idea of the +proof + + align:start position:0% +proof + + + align:start position:0% +proof +now i think + + align:start position:0% +now i think + + + align:start position:0% +now i think +uh you could work out um + + align:start position:0% +uh you could work out um + + + align:start position:0% +uh you could work out um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the quantities that you need in order to + + align:start position:0% +the quantities that you need in order to + + + align:start position:0% +the quantities that you need in order to +drive this proof um i'm gonna do that + + align:start position:0% +drive this proof um i'm gonna do that + + + align:start position:0% +drive this proof um i'm gonna do that +for you i actually hate writing down + + align:start position:0% +for you i actually hate writing down + + + align:start position:0% +for you i actually hate writing down +lots of inequalities and um + + align:start position:0% +lots of inequalities and um + + + align:start position:0% +lots of inequalities and um +equations and so on on the board because + + align:start position:0% +equations and so on on the board because + + + align:start position:0% +equations and so on on the board because +i think they're just almost + + align:start position:0% +i think they're just almost + + + align:start position:0% +i think they're just almost +incomprehensible to follow at least they + + align:start position:0% +incomprehensible to follow at least they + + + align:start position:0% +incomprehensible to follow at least they +would be for me but i'm going to put + + align:start position:0% +would be for me but i'm going to put + + + align:start position:0% +would be for me but i'm going to put +them up there just for completeness sake + + align:start position:0% +them up there just for completeness sake + + + align:start position:0% +them up there just for completeness sake +um + + align:start position:0% +um + + + align:start position:0% +um +so here we're going to give the details + + align:start position:0% +so here we're going to give the details + + + align:start position:0% +so here we're going to give the details +of this proof on the next uh the next + + align:start position:0% +of this proof on the next uh the next + + + align:start position:0% +of this proof on the next uh the next +slide here + + align:start position:0% +slide here + + + align:start position:0% +slide here +oh yeah so i just want to give a name to + + align:start position:0% +oh yeah so i just want to give a name to + + + align:start position:0% +oh yeah so i just want to give a name to +this i'm going to call this the cutting + + align:start position:0% +this i'm going to call this the cutting + + + align:start position:0% +this i'm going to call this the cutting +and pasting argument because i'm cutting + + align:start position:0% +and pasting argument because i'm cutting + + + align:start position:0% +and pasting argument because i'm cutting +apart + + align:start position:0% +apart + + + align:start position:0% +apart +pieces of this parse tree and i'm + + align:start position:0% +pieces of this parse tree and i'm + + + align:start position:0% +pieces of this parse tree and i'm +pasting them into other places within + + align:start position:0% +pasting them into other places within + + + align:start position:0% +pasting them into other places within +the parse tree to get new strings being + + align:start position:0% +the parse tree to get new strings being + + + align:start position:0% +the parse tree to get new strings being +generated + + align:start position:0% +generated + + + align:start position:0% +generated +so this is a cutting and pasting + + align:start position:0% +so this is a cutting and pasting + + + align:start position:0% +so this is a cutting and pasting +argument so okay let's let's take a look + + align:start position:0% +argument so okay let's let's take a look + + + align:start position:0% +argument so okay let's let's take a look +at the details here um + + align:start position:0% +at the details here um + + + align:start position:0% +at the details here um +uh just so we have to understand well + + align:start position:0% +uh just so we have to understand well + + + align:start position:0% +uh just so we have to understand well +how big does p actually need to be + + align:start position:0% +how big does p actually need to be + + + align:start position:0% +how big does p actually need to be +in order for this thing to kick in + + align:start position:0% +in order for this thing to kick in + + + align:start position:0% +in order for this thing to kick in +um + + align:start position:0% +um + + + align:start position:0% +um +well first of all we have to understand + + align:start position:0% +well first of all we have to understand + + + align:start position:0% +well first of all we have to understand +how fast that parse tree can be growing + + align:start position:0% +how fast that parse tree can be growing + + + align:start position:0% +how fast that parse tree can be growing +um as we go level to level and that's + + align:start position:0% +um as we go level to level and that's + + + align:start position:0% +um as we go level to level and that's +going to be dependent on how big the + + align:start position:0% +going to be dependent on how big the + + + align:start position:0% +going to be dependent on how big the +right-hand side sides of rules are i + + align:start position:0% +right-hand side sides of rules are i + + + align:start position:0% +right-hand side sides of rules are i +mean that's expand that really tells you + + align:start position:0% +mean that's expand that really tells you + + + align:start position:0% +mean that's expand that really tells you +how many what's the fan out you know of + + align:start position:0% +how many what's the fan out you know of + + + align:start position:0% +how many what's the fan out you know of +each node + + align:start position:0% +each node + + + align:start position:0% +each node +what's the maximum fanout and that's + + align:start position:0% +what's the maximum fanout and that's + + + align:start position:0% +what's the maximum fanout and that's +going to be the maximum uh + + align:start position:0% +going to be the maximum uh + + + align:start position:0% +going to be the maximum uh +length of a right-hand side of any rule + + align:start position:0% +length of a right-hand side of any rule + + + align:start position:0% +length of a right-hand side of any rule +so for example in that other grammar we + + align:start position:0% +so for example in that other grammar we + + + align:start position:0% +so for example in that other grammar we +had seen last time + + align:start position:0% +had seen last time + + + align:start position:0% +had seen last time +for arithmetic expressions we had this e + + align:start position:0% +for arithmetic expressions we had this e + + + align:start position:0% +for arithmetic expressions we had this e +goes to e plus t and + + align:start position:0% +goes to e plus t and + + + align:start position:0% +goes to e plus t and +uh this rule here and in terms of the + + align:start position:0% +uh this rule here and in terms of the + + + align:start position:0% +uh this rule here and in terms of the +parse tree that would look uh like an a + + align:start position:0% +parse tree that would look uh like an a + + + align:start position:0% +parse tree that would look uh like an a +little element like that + + align:start position:0% +little element like that + + + align:start position:0% +little element like that +and that's actually the longest right + + align:start position:0% +and that's actually the longest right + + + align:start position:0% +and that's actually the longest right +hand side that you can get and so the + + align:start position:0% +hand side that you can get and so the + + + align:start position:0% +hand side that you can get and so the +parse tree can be growing by a factor of + + align:start position:0% +parse tree can be growing by a factor of + + + align:start position:0% +parse tree can be growing by a factor of +three each time + + align:start position:0% +three each time + + + align:start position:0% +three each time +now that's going to tell us + + align:start position:0% +now that's going to tell us + + + align:start position:0% +now that's going to tell us +how + + align:start position:0% +how + + + align:start position:0% +how +big the string uh + + align:start position:0% +big the string uh + + + align:start position:0% +big the string uh +needs to be that's being generated what + + align:start position:0% +needs to be that's being generated what + + + align:start position:0% +needs to be that's being generated what +is the value of p in order to get a + + align:start position:0% +is the value of p in order to get a + + + align:start position:0% +is the value of p in order to get a +high enough parse tree so that you're + + align:start position:0% +high enough parse tree so that you're + + + align:start position:0% +high enough parse tree so that you're +going to get a repeated variable + + align:start position:0% +going to get a repeated variable + + + align:start position:0% +going to get a repeated variable +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +let's call the height of the parse tree + + align:start position:0% +let's call the height of the parse tree + + + align:start position:0% +let's call the height of the parse tree +for sh + + align:start position:0% +for sh + + + align:start position:0% +for sh +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now if you this is just repeating + + align:start position:0% +so now if you this is just repeating + + + align:start position:0% +so now if you this is just repeating +what i just said if you have a tree of + + align:start position:0% +what i just said if you have a tree of + + + align:start position:0% +what i just said if you have a tree of +height h and the maximum branching is b + + align:start position:0% +height h and the maximum branching is b + + + align:start position:0% +height h and the maximum branching is b +then you get it most b to the h leaves + + align:start position:0% +then you get it most b to the h leaves + + + align:start position:0% +then you get it most b to the h leaves +because each level you get another + + align:start position:0% +because each level you get another + + + align:start position:0% +because each level you get another +factor of b coming up because that's how + + align:start position:0% +factor of b coming up because that's how + + + align:start position:0% +factor of b coming up because that's how +much branching you have + + align:start position:0% +much branching you have + + + align:start position:0% +much branching you have +so each node at one level can become b + + align:start position:0% +so each node at one level can become b + + + align:start position:0% +so each node at one level can become b +nodes at the next level down so you're + + align:start position:0% +nodes at the next level down so you're + + + align:start position:0% +nodes at the next level down so you're +multiplying by b each time and if you + + align:start position:0% +multiplying by b each time and if you + + + align:start position:0% +multiplying by b each time and if you +have h levels you're going to have b to + + align:start position:0% +have h levels you're going to have b to + + + align:start position:0% +have h levels you're going to have b to +the h leaves + + align:start position:0% + + + + align:start position:0% + +so the length of s which are really the + + align:start position:0% +so the length of s which are really the + + + align:start position:0% +so the length of s which are really the +leaves here that it is at most b to the + + align:start position:0% +leaves here that it is at most b to the + + + align:start position:0% +leaves here that it is at most b to the +a the reason why i said most and not + + align:start position:0% +a the reason why i said most and not + + + align:start position:0% +a the reason why i said most and not +exactly is you might be doing + + align:start position:0% +exactly is you might be doing + + + align:start position:0% +exactly is you might be doing +substitutions which are shorter right + + align:start position:0% +substitutions which are shorter right + + + align:start position:0% +substitutions which are shorter right +hand sides + + align:start position:0% +hand sides + + + align:start position:0% +hand sides +um + + align:start position:0% +um + + + align:start position:0% +um +okay so to try to show this as a picture + + align:start position:0% +okay so to try to show this as a picture + + + align:start position:0% +okay so to try to show this as a picture +here uh + + align:start position:0% +here uh + + + align:start position:0% +here uh +pulling that same picture we had before + + align:start position:0% +pulling that same picture we had before + + + align:start position:0% +pulling that same picture we had before +we want h + + align:start position:0% +we want h + + + align:start position:0% +we want h +the height to be bigger than the number + + align:start position:0% +the height to be bigger than the number + + + align:start position:0% +the height to be bigger than the number +of variables + + align:start position:0% +of variables + + + align:start position:0% +of variables +to force a repetition + + align:start position:0% +to force a repetition + + + align:start position:0% +to force a repetition +so the number of variables is going to + + align:start position:0% +so the number of variables is going to + + + align:start position:0% +so the number of variables is going to +be written this way v is the variables + + align:start position:0% +be written this way v is the variables + + + align:start position:0% +be written this way v is the variables +uh v with bars around it is going to be + + align:start position:0% +uh v with bars around it is going to be + + + align:start position:0% +uh v with bars around it is going to be +the number of variables and we want that + + align:start position:0% +the number of variables and we want that + + + align:start position:0% +the number of variables and we want that +height to be greater than the number of + + align:start position:0% +height to be greater than the number of + + + align:start position:0% +height to be greater than the number of +variables + + align:start position:0% +variables + + + align:start position:0% +variables +so once you know how high you want that + + align:start position:0% +so once you know how high you want that + + + align:start position:0% +so once you know how high you want that +tree to be in order to force the + + align:start position:0% +tree to be in order to force the + + + align:start position:0% +tree to be in order to force the +repetition + + align:start position:0% +repetition + + + align:start position:0% +repetition +then it tells you how big s has to be + + align:start position:0% +then it tells you how big s has to be + + + align:start position:0% +then it tells you how big s has to be +so b has to be bigger + + align:start position:0% +so b has to be bigger + + + align:start position:0% +so b has to be bigger +than b to the v b to the size of v + + align:start position:0% +than b to the v b to the size of v + + + align:start position:0% +than b to the v b to the size of v +um because then + + align:start position:0% +um because then + + + align:start position:0% +um because then +um the the the height that you're going + + align:start position:0% +um the the the height that you're going + + + align:start position:0% +um the the the height that you're going +to get is going to be greater + + align:start position:0% +to get is going to be greater + + + align:start position:0% +to get is going to be greater +than uh + + align:start position:0% +than uh + + + align:start position:0% +than uh +uh the size of v which is uh so that's + + align:start position:0% +uh the size of v which is uh so that's + + + align:start position:0% +uh the size of v which is uh so that's +what you want you want h to be greater + + align:start position:0% +what you want you want h to be greater + + + align:start position:0% +what you want you want h to be greater +than the size of v + + align:start position:0% +than the size of v + + + align:start position:0% +than the size of v +uh so you're gonna set p to be one more + + align:start position:0% +uh so you're gonna set p to be one more + + + align:start position:0% +uh so you're gonna set p to be one more +than b to the v + + align:start position:0% +than b to the v + + + align:start position:0% +than b to the v +and so if s is at least that length + + align:start position:0% +and so if s is at least that length + + + align:start position:0% +and so if s is at least that length +this whole thing is going to kick in and + + align:start position:0% +this whole thing is going to kick in and + + + align:start position:0% +this whole thing is going to kick in and +you're going to get that repeated + + align:start position:0% +you're going to get that repeated + + + align:start position:0% +you're going to get that repeated +variable um + + align:start position:0% +variable um + + + align:start position:0% +variable um +so we let p to be that value where v is + + align:start position:0% +so we let p to be that value where v is + + + align:start position:0% +so we let p to be that value where v is +the number of variables in the grammar + + align:start position:0% +the number of variables in the grammar + + + align:start position:0% +the number of variables in the grammar +and so if + + align:start position:0% +and so if + + + align:start position:0% +and so if +s + + align:start position:0% +s + + + align:start position:0% +s +is at least p + + align:start position:0% +is at least p + + + align:start position:0% +is at least p +which is greater than b to the v + + align:start position:0% +which is greater than b to the v + + + align:start position:0% +which is greater than b to the v +then the length of s is going to be + + align:start position:0% +then the length of s is going to be + + + align:start position:0% +then the length of s is going to be +greater than + + align:start position:0% +greater than + + + align:start position:0% +greater than +um b to the v so h is going to be what + + align:start position:0% +um b to the v so h is going to be what + + + align:start position:0% +um b to the v so h is going to be what +you want to make this thing work + + align:start position:0% +you want to make this thing work + + + align:start position:0% +you want to make this thing work +i + + align:start position:0% +i + + + align:start position:0% +i +you know if you don't follow that those + + align:start position:0% +you know if you don't follow that those + + + align:start position:0% +you know if you don't follow that those +inequalities i sympathize with you i + + align:start position:0% +inequalities i sympathize with you i + + + align:start position:0% +inequalities i sympathize with you i +would never follow that either in a + + align:start position:0% +would never follow that either in a + + + align:start position:0% +would never follow that either in a +lecture so + + align:start position:0% +lecture so + + + align:start position:0% +lecture so +um but i hope you get the idea um but + + align:start position:0% +um but i hope you get the idea um but + + + align:start position:0% +um but i hope you get the idea um but +you know we're not quite finished yet + + align:start position:0% +you know we're not quite finished yet + + + align:start position:0% +you know we're not quite finished yet +because what i want to now circle back + + align:start position:0% +because what i want to now circle back + + + align:start position:0% +because what i want to now circle back +as and look at these three conditions + + align:start position:0% +as and look at these three conditions + + + align:start position:0% +as and look at these three conditions +and make sure + + align:start position:0% +and make sure + + + align:start position:0% +and make sure +that we've captured them all because + + align:start position:0% +that we've captured them all because + + + align:start position:0% +that we've captured them all because +actually it's not totally + + align:start position:0% +actually it's not totally + + + align:start position:0% +actually it's not totally +uh obvious um + + align:start position:0% +uh obvious um + + + align:start position:0% +uh obvious um +in each of those cases that we've got + + align:start position:0% +in each of those cases that we've got + + + align:start position:0% +in each of those cases that we've got +them um so there's a few extra things we + + align:start position:0% +them um so there's a few extra things we + + + align:start position:0% +them um so there's a few extra things we +need to do um um + + align:start position:0% +need to do um um + + + align:start position:0% +need to do um um +okay so this is concluding the argument + + align:start position:0% +okay so this is concluding the argument + + + align:start position:0% +okay so this is concluding the argument +you know there are going to be at least + + align:start position:0% +you know there are going to be at least + + + align:start position:0% +you know there are going to be at least +three plus one variables in the longest + + align:start position:0% +three plus one variables in the longest + + + align:start position:0% +three plus one variables in the longest +path so there's going to be a repetition + + align:start position:0% +path so there's going to be a repetition + + + align:start position:0% +path so there's going to be a repetition +so now let's go back here and see now + + align:start position:0% +so now let's go back here and see now + + + align:start position:0% +so now let's go back here and see now +that we have this picture + + align:start position:0% +that we have this picture + + + align:start position:0% +that we have this picture +with a repeated uh variable + + align:start position:0% +with a repeated uh variable + + + align:start position:0% +with a repeated uh variable +how do we know we can get condition one + + align:start position:0% +how do we know we can get condition one + + + align:start position:0% +how do we know we can get condition one +well that's just the cutting and pacing + + align:start position:0% +well that's just the cutting and pacing + + + align:start position:0% +well that's just the cutting and pacing +argument from the previous slide + + align:start position:0% + + + + align:start position:0% + +how do we know that v and y are not both + + align:start position:0% +how do we know that v and y are not both + + + align:start position:0% +how do we know that v and y are not both +empty + + align:start position:0% +empty + + + align:start position:0% +empty +well actually that's not totally obvious + + align:start position:0% +well actually that's not totally obvious + + + align:start position:0% +well actually that's not totally obvious +because it's possible + + align:start position:0% +because it's possible + + + align:start position:0% +because it's possible +that when you generated v here and you + + align:start position:0% +that when you generated v here and you + + + align:start position:0% +that when you generated v here and you +generated y + + align:start position:0% +generated y + + + align:start position:0% +generated y +um maybe going from this r to that r you + + align:start position:0% +um maybe going from this r to that r you + + + align:start position:0% +um maybe going from this r to that r you +got nothing new + + align:start position:0% +got nothing new + + + align:start position:0% +got nothing new +you know it could have been that r got + + align:start position:0% +you know it could have been that r got + + + align:start position:0% +you know it could have been that r got +replaced by t + + align:start position:0% +replaced by t + + + align:start position:0% +replaced by t +another variable with nothing new coming + + align:start position:0% +another variable with nothing new coming + + + align:start position:0% +another variable with nothing new coming +out and then t got replaced by r so you + + align:start position:0% +out and then t got replaced by r so you + + + align:start position:0% +out and then t got replaced by r so you +substituted uh + + align:start position:0% +substituted uh + + + align:start position:0% +substituted uh +you know t for r and then r for t and + + align:start position:0% +you know t for r and then r for t and + + + align:start position:0% +you know t for r and then r for t and +you've got nothing new coming out and in + + align:start position:0% +you've got nothing new coming out and in + + + align:start position:0% +you've got nothing new coming out and in +that case uh v and y would both be the + + align:start position:0% +that case uh v and y would both be the + + + align:start position:0% +that case uh v and y would both be the +empty string and that would violate what + + align:start position:0% +empty string and that would violate what + + + align:start position:0% +empty string and that would violate what +we want + + align:start position:0% +we want + + + align:start position:0% +we want +um + + align:start position:0% +um + + + align:start position:0% +um +the way you + + align:start position:0% +the way you + + + align:start position:0% +the way you +get around that and these are details + + align:start position:0% +get around that and these are details + + + align:start position:0% +get around that and these are details +here if you're not totally following + + align:start position:0% +here if you're not totally following + + + align:start position:0% +here if you're not totally following +these points don't worry uh but i do + + align:start position:0% +these points don't worry uh but i do + + + align:start position:0% +these points don't worry uh but i do +want to just try to it's easy they're + + align:start position:0% +want to just try to it's easy they're + + + align:start position:0% +want to just try to it's easy they're +easy to describe so i figure let me + + align:start position:0% +easy to describe so i figure let me + + + align:start position:0% +easy to describe so i figure let me +present the whole thing in full detail + + align:start position:0% + + + + align:start position:0% + +so if going from this r to that r + + align:start position:0% +so if going from this r to that r + + + align:start position:0% +so if going from this r to that r +doesn't generate anything new you're + + align:start position:0% +doesn't generate anything new you're + + + align:start position:0% +doesn't generate anything new you're +getting exactly the same things coming + + align:start position:0% +getting exactly the same things coming + + + align:start position:0% +getting exactly the same things coming +out v and y are just + + align:start position:0% +out v and y are just + + + align:start position:0% +out v and y are just +the empty string + + align:start position:0% +the empty string + + + align:start position:0% +the empty string +um how do we avoid that from happening + + align:start position:0% +um how do we avoid that from happening + + + align:start position:0% +um how do we avoid that from happening +well what there's a simple way to + + align:start position:0% +well what there's a simple way to + + + align:start position:0% +well what there's a simple way to +address that which is to say + + align:start position:0% +address that which is to say + + + align:start position:0% +address that which is to say +uh if you have + + align:start position:0% +uh if you have + + + align:start position:0% +uh if you have +this string s + + align:start position:0% +this string s + + + align:start position:0% +this string s +when you take a parse tree make sure you + + align:start position:0% +when you take a parse tree make sure you + + + align:start position:0% +when you take a parse tree make sure you +take a smallest possible parse tree + + align:start position:0% +take a smallest possible parse tree + + + align:start position:0% +take a smallest possible parse tree +you cannot you're not allowed to start + + align:start position:0% +you cannot you're not allowed to start + + + align:start position:0% +you cannot you're not allowed to start +off with an inefficient parse tree that + + align:start position:0% +off with an inefficient parse tree that + + + align:start position:0% +off with an inefficient parse tree that +can be shortened and still generate s i + + align:start position:0% +can be shortened and still generate s i + + + align:start position:0% +can be shortened and still generate s i +want the smallest possible parse tree + + align:start position:0% +want the smallest possible parse tree + + + align:start position:0% +want the smallest possible parse tree +and that smallest possible parser can't + + align:start position:0% +and that smallest possible parser can't + + + align:start position:0% +and that smallest possible parser can't +have an r going to another r which is + + align:start position:0% +have an r going to another r which is + + + align:start position:0% +have an r going to another r which is +generating nothing new because then you + + align:start position:0% +generating nothing new because then you + + + align:start position:0% +generating nothing new because then you +could always have eliminated that step + + align:start position:0% +could always have eliminated that step + + + align:start position:0% +could always have eliminated that step +and you would still have a parse tree + + align:start position:0% +and you would still have a parse tree + + + align:start position:0% +and you would still have a parse tree +for s but it would be a smaller parse + + align:start position:0% +for s but it would be a smaller parse + + + align:start position:0% +for s but it would be a smaller parse +tree so that would be i want you to + + align:start position:0% +tree so that would be i want you to + + + align:start position:0% +tree so that would be i want you to +start off with the smallest possible + + align:start position:0% +start off with the smallest possible + + + align:start position:0% +start off with the smallest possible +parser tree and then you're going to be + + align:start position:0% +parser tree and then you're going to be + + + align:start position:0% +parser tree and then you're going to be +guaranteed that v or y is going to be + + align:start position:0% +guaranteed that v or y is going to be + + + align:start position:0% +guaranteed that v or y is going to be +something uh not empty so that takes + + align:start position:0% +something uh not empty so that takes + + + align:start position:0% +something uh not empty so that takes +care of + + align:start position:0% + + + + align:start position:0% + +uh condition two + + align:start position:0% +uh condition two + + + align:start position:0% +uh condition two +condition three + + align:start position:0% +condition three + + + align:start position:0% +condition three +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know how do we know that v x + + align:start position:0% +you know how do we know that v x + + + align:start position:0% +you know how do we know that v x +y together is not very long + + align:start position:0% +y together is not very long + + + align:start position:0% +y together is not very long +and basically it's the same argument all + + align:start position:0% +and basically it's the same argument all + + + align:start position:0% +and basically it's the same argument all +over again um you just want to make sure + + align:start position:0% +over again um you just want to make sure + + + align:start position:0% +over again um you just want to make sure +that when you're picking the repetition + + align:start position:0% +that when you're picking the repetition + + + align:start position:0% +that when you're picking the repetition +are the two r's here you pick the lowest + + align:start position:0% +are the two r's here you pick the lowest + + + align:start position:0% +are the two r's here you pick the lowest +possible repetitions that occur if you + + align:start position:0% +possible repetitions that occur if you + + + align:start position:0% +possible repetitions that occur if you +have many many choices + + align:start position:0% +have many many choices + + + align:start position:0% +have many many choices +and those lowest two those lowest + + align:start position:0% +and those lowest two those lowest + + + align:start position:0% +and those lowest two those lowest +repetitions there's not going to be any + + align:start position:0% +repetitions there's not going to be any + + + align:start position:0% +repetitions there's not going to be any +lower repetition here and then by the + + align:start position:0% +lower repetition here and then by the + + + align:start position:0% +lower repetition here and then by the +same argument um the the uh + + align:start position:0% +same argument um the the uh + + + align:start position:0% +same argument um the the uh +since once you have that very first r + + align:start position:0% +since once you have that very first r + + + align:start position:0% +since once you have that very first r +there's no more repetitions occurring + + align:start position:0% +there's no more repetitions occurring + + + align:start position:0% +there's no more repetitions occurring +below + + align:start position:0% +below + + + align:start position:0% +below +the v x y can't be very long um because + + align:start position:0% +the v x y can't be very long um because + + + align:start position:0% +the v x y can't be very long um because +that would again force another + + align:start position:0% +that would again force another + + + align:start position:0% +that would again force another +repetition to occur + + align:start position:0% +repetition to occur + + + align:start position:0% +repetition to occur +um so anyway those are the three + + align:start position:0% +um so anyway those are the three + + + align:start position:0% +um so anyway those are the three +conditions and that's the proof of the + + align:start position:0% +conditions and that's the proof of the + + + align:start position:0% +conditions and that's the proof of the +pumping lemma for context-free languages + + align:start position:0% +pumping lemma for context-free languages + + + align:start position:0% +pumping lemma for context-free languages +let's see how we use that + + align:start position:0% +let's see how we use that + + + align:start position:0% +let's see how we use that +um + + align:start position:0% +um + + + align:start position:0% +um +okay so let's do an example of proving a + + align:start position:0% +okay so let's do an example of proving a + + + align:start position:0% +okay so let's do an example of proving a +language not context free using the + + align:start position:0% +language not context free using the + + + align:start position:0% +language not context free using the +pumping line + + align:start position:0% +pumping line + + + align:start position:0% +pumping line +how do you gonna do a go about doing + + align:start position:0% +how do you gonna do a go about doing + + + align:start position:0% +how do you gonna do a go about doing +that because that's the kind of thing + + align:start position:0% +that because that's the kind of thing + + + align:start position:0% +that because that's the kind of thing +you you know + + align:start position:0% +you you know + + + align:start position:0% +you you know +at the very least you need to know how + + align:start position:0% +at the very least you need to know how + + + align:start position:0% +at the very least you need to know how +to do this in order to do the homework + + align:start position:0% +to do this in order to do the homework + + + align:start position:0% +to do this in order to do the homework +um + + align:start position:0% +um + + + align:start position:0% +um +uh i'd like to motivate you that the + + align:start position:0% +uh i'd like to motivate you that the + + + align:start position:0% +uh i'd like to motivate you that the +stuff is so interesting and fun but it + + align:start position:0% +stuff is so interesting and fun but it + + + align:start position:0% +stuff is so interesting and fun but it +doesn't work for everybody so + + align:start position:0% +doesn't work for everybody so + + + align:start position:0% +doesn't work for everybody so +uh for you practical people out there um + + align:start position:0% +uh for you practical people out there um + + + align:start position:0% +uh for you practical people out there um +pay attention so you can do the homework + + align:start position:0% +pay attention so you can do the homework + + + align:start position:0% +pay attention so you can do the homework +okay let's go back to that language we + + align:start position:0% +okay let's go back to that language we + + + align:start position:0% +okay let's go back to that language we +had a couple of slides back zero to the + + align:start position:0% +had a couple of slides back zero to the + + + align:start position:0% +had a couple of slides back zero to the +g one to the k two to the k it's not a + + align:start position:0% +g one to the k two to the k it's not a + + + align:start position:0% +g one to the k two to the k it's not a +contact three language we're gonna show + + align:start position:0% +contact three language we're gonna show + + + align:start position:0% +contact three language we're gonna show +that now using the pumping lemma for + + align:start position:0% +that now using the pumping lemma for + + + align:start position:0% +that now using the pumping lemma for +context-free languages + + align:start position:0% +context-free languages + + + align:start position:0% +context-free languages +um + + align:start position:0% +um + + + align:start position:0% +um +uh so it's gonna do + + align:start position:0% +uh so it's gonna do + + + align:start position:0% +uh so it's gonna do +similar to the proofs using for + + align:start position:0% +similar to the proofs using for + + + align:start position:0% +similar to the proofs using for +non-regular non-regul not non-regular + + align:start position:0% +non-regular non-regul not non-regular + + + align:start position:0% +non-regular non-regul not non-regular +languages um proof by contradiction so + + align:start position:0% +languages um proof by contradiction so + + + align:start position:0% +languages um proof by contradiction so +you first you assume the language is + + align:start position:0% +you first you assume the language is + + + align:start position:0% +you first you assume the language is +context-free and then we're going to + + align:start position:0% +context-free and then we're going to + + + align:start position:0% +context-free and then we're going to +apply the pumping lemma um and then + + align:start position:0% +apply the pumping lemma um and then + + + align:start position:0% +apply the pumping lemma um and then +we're going to get a contradiction uh + + align:start position:0% +we're going to get a contradiction uh + + + align:start position:0% +we're going to get a contradiction uh +so the pumping limit gives that pumping + + align:start position:0% +so the pumping limit gives that pumping + + + align:start position:0% +so the pumping limit gives that pumping +length as we subscribed above and now we + + align:start position:0% +length as we subscribed above and now we + + + align:start position:0% +length as we subscribed above and now we +just want to pick a longer string in the + + align:start position:0% +just want to pick a longer string in the + + + align:start position:0% +just want to pick a longer string in the +language + + align:start position:0% +language + + + align:start position:0% +language +and show that that + + align:start position:0% +and show that that + + + align:start position:0% +and show that that +longer string which is supposed to be + + align:start position:0% +longer string which is supposed to be + + + align:start position:0% +longer string which is supposed to be +pumpable and stay in the language in + + align:start position:0% +pumpable and stay in the language in + + + align:start position:0% +pumpable and stay in the language in +fact is not pumpable + + align:start position:0% +fact is not pumpable + + + align:start position:0% +fact is not pumpable +um + + align:start position:0% +um + + + align:start position:0% +um +so the pumping dilemma says that you can + + align:start position:0% +so the pumping dilemma says that you can + + + align:start position:0% +so the pumping dilemma says that you can +divide it into five pieces satisfying + + align:start position:0% +divide it into five pieces satisfying + + + align:start position:0% +divide it into five pieces satisfying +the three conditions uh condition three + + align:start position:0% +the three conditions uh condition three + + + align:start position:0% +the three conditions uh condition three +implies + + align:start position:0% +implies + + + align:start position:0% +implies +uh that + + align:start position:0% +uh that + + + align:start position:0% +uh that +so now i'm gonna i'm gonna work through + + align:start position:0% +so now i'm gonna i'm gonna work through + + + align:start position:0% +so now i'm gonna i'm gonna work through +the i'm gonna uh show you get a + + align:start position:0% +the i'm gonna uh show you get a + + + align:start position:0% +the i'm gonna uh show you get a +contradiction so condition three + + align:start position:0% +contradiction so condition three + + + align:start position:0% +contradiction so condition three +implies that you cannot contain both + + align:start position:0% +implies that you cannot contain both + + + align:start position:0% +implies that you cannot contain both +zeros and let's pull up a picture here + + align:start position:0% +zeros and let's pull up a picture here + + + align:start position:0% +zeros and let's pull up a picture here +so here's s + + align:start position:0% +so here's s + + + align:start position:0% +so here's s +uh + + align:start position:0% +uh + + + align:start position:0% +uh +zeros ones and then twos all the same + + align:start position:0% +zeros ones and then twos all the same + + + align:start position:0% +zeros ones and then twos all the same +length condition three + + align:start position:0% +length condition three + + + align:start position:0% +length condition three +uh so if you break it up + + align:start position:0% + + + + align:start position:0% + +condition three says v x y together + + align:start position:0% +condition three says v x y together + + + align:start position:0% +condition three says v x y together +cannot be too long well if v x y + + align:start position:0% +cannot be too long well if v x y + + + align:start position:0% +cannot be too long well if v x y +together is not too long + + align:start position:0% +together is not too long + + + align:start position:0% +together is not too long +uh what you know how could it be that + + align:start position:0% +uh what you know how could it be that + + + align:start position:0% +uh what you know how could it be that +when you're repeating v and y you stay + + align:start position:0% +when you're repeating v and y you stay + + + align:start position:0% +when you're repeating v and y you stay +in the language + + align:start position:0% +in the language + + + align:start position:0% +in the language +uh for one thing you can't have + + align:start position:0% +uh for one thing you can't have + + + align:start position:0% +uh for one thing you can't have +zeros ones and twos all occurring within + + align:start position:0% +zeros ones and twos all occurring within + + + align:start position:0% +zeros ones and twos all occurring within +v x and y + + align:start position:0% +v x and y + + + align:start position:0% +v x and y +um + + align:start position:0% +um + + + align:start position:0% +um +some + + align:start position:0% +some + + + align:start position:0% +some +uh some symbol is going to get left out + + align:start position:0% +uh some symbol is going to get left out + + + align:start position:0% +uh some symbol is going to get left out +so then when you pump up you're going to + + align:start position:0% +so then when you pump up you're going to + + + align:start position:0% +so then when you pump up you're going to +have unequal numbers of symbols + + align:start position:0% +have unequal numbers of symbols + + + align:start position:0% +have unequal numbers of symbols +and so you're going to be out of the + + align:start position:0% +and so you're going to be out of the + + + align:start position:0% +and so you're going to be out of the +language + + align:start position:0% +language + + + align:start position:0% +language +um + + align:start position:0% +um + + + align:start position:0% +um +okay so no matter how you try to cut it + + align:start position:0% +okay so no matter how you try to cut it + + + align:start position:0% +okay so no matter how you try to cut it +up uh following condition three which is + + align:start position:0% +up uh following condition three which is + + + align:start position:0% +up uh following condition three which is +one of the things that restricts the + + align:start position:0% +one of the things that restricts the + + + align:start position:0% +one of the things that restricts the +the ways to cut it up you're going to + + align:start position:0% +the ways to cut it up you're going to + + + align:start position:0% +the ways to cut it up you're going to +end up when you pump up + + align:start position:0% +end up when you pump up + + + align:start position:0% +end up when you pump up +uh going out of the language and so + + align:start position:0% +uh going out of the language and so + + + align:start position:0% +uh going out of the language and so +therefore it's not in + + align:start position:0% +therefore it's not in + + + align:start position:0% +therefore it's not in +d + + align:start position:0% +d + + + align:start position:0% +d +d is wrong + + align:start position:0% +d is wrong + + + align:start position:0% +d is wrong +uh + + align:start position:0% +uh + + + align:start position:0% +uh +b shouldn't say b + + align:start position:0% +b shouldn't say b + + + align:start position:0% +b shouldn't say b +can knife can i + + align:start position:0% +can knife can i + + + align:start position:0% +can knife can i +nice + + align:start position:0% + + + + align:start position:0% + +supposed to be able to write on this + + align:start position:0% +supposed to be able to write on this + + + align:start position:0% +supposed to be able to write on this +thing i guess not + + align:start position:0% +thing i guess not + + + align:start position:0% +thing i guess not +i didn't test that + + align:start position:0% +i didn't test that + + + align:start position:0% +i didn't test that +oh well that's supposed to be a b + + align:start position:0% +oh well that's supposed to be a b + + + align:start position:0% +oh well that's supposed to be a b +um + + align:start position:0% + + + + align:start position:0% + +uh so b is a context free language we + + align:start position:0% +uh so b is a context free language we + + + align:start position:0% +uh so b is a context free language we +close + + align:start position:0% +close + + + align:start position:0% +close +so that's the assumption that b is a + + align:start position:0% +so that's the assumption that b is a + + + align:start position:0% +so that's the assumption that b is a +context-free language that's false and + + align:start position:0% +context-free language that's false and + + + align:start position:0% +context-free language that's false and +we conclude that's not a context-free + + align:start position:0% +we conclude that's not a context-free + + + align:start position:0% +we conclude that's not a context-free +language okay + + align:start position:0% +language okay + + + align:start position:0% +language okay +let's do uh + + align:start position:0% +let's do uh + + + align:start position:0% +let's do uh +oh yeah + + align:start position:0% +oh yeah + + + align:start position:0% +oh yeah +i have a check-in here + + align:start position:0% +i have a check-in here + + + align:start position:0% +i have a check-in here +um + + align:start position:0% +um + + + align:start position:0% +um +so let's see um what we're going to + + align:start position:0% +so let's see um what we're going to + + + align:start position:0% +so let's see um what we're going to +we're going to i'm going to ask you to + + align:start position:0% +we're going to i'm going to ask you to + + + align:start position:0% +we're going to i'm going to ask you to +think about + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +my head is blocking part of the text + + align:start position:0% +my head is blocking part of the text + + + align:start position:0% +my head is blocking part of the text +oh that was a while ago um okay uh + + align:start position:0% + + + + align:start position:0% + +yes so with just one question by the way + + align:start position:0% +yes so with just one question by the way + + + align:start position:0% +yes so with just one question by the way +in in terms of applying the um in in the + + align:start position:0% +in in terms of applying the um in in the + + + align:start position:0% +in in terms of applying the um in in the +pumping dilemma either v or y can be uh + + align:start position:0% +pumping dilemma either v or y can be uh + + + align:start position:0% +pumping dilemma either v or y can be uh +empty but not both but anyway let's get + + align:start position:0% +empty but not both but anyway let's get + + + align:start position:0% +empty but not both but anyway let's get +to this check in here + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so let's look at these two languages a1 + + align:start position:0% +so let's look at these two languages a1 + + + align:start position:0% +so let's look at these two languages a1 +and a2 which look very similar to b + + align:start position:0% +and a2 which look very similar to b + + + align:start position:0% +and a2 which look very similar to b +but a little different + + align:start position:0% +but a little different + + + align:start position:0% +but a little different +um so it's a1 is 0 to the k1 to the gate + + align:start position:0% +um so it's a1 is 0 to the k1 to the gate + + + align:start position:0% +um so it's a1 is 0 to the k1 to the gate +2 to the l + + align:start position:0% +2 to the l + + + align:start position:0% +2 to the l +where k and l could be any numbers any + + align:start position:0% +where k and l could be any numbers any + + + align:start position:0% +where k and l could be any numbers any +positive + + align:start position:0% +positive + + + align:start position:0% +positive +you know uh non-negative numbers + + align:start position:0% +you know uh non-negative numbers + + + align:start position:0% +you know uh non-negative numbers +so basically what this says saying is + + align:start position:0% +so basically what this says saying is + + + align:start position:0% +so basically what this says saying is +that the number of zeros and ones are + + align:start position:0% +that the number of zeros and ones are + + + align:start position:0% +that the number of zeros and ones are +going to be equal but the number of twos + + align:start position:0% +going to be equal but the number of twos + + + align:start position:0% +going to be equal but the number of twos +can be anything + + align:start position:0% +can be anything + + + align:start position:0% +can be anything +whereas a2 + + align:start position:0% +whereas a2 + + + align:start position:0% +whereas a2 +similar + + align:start position:0% +similar + + + align:start position:0% +similar +but here we're requiring the number of + + align:start position:0% +but here we're requiring the number of + + + align:start position:0% +but here we're requiring the number of +two ones and twos + + align:start position:0% +two ones and twos + + + align:start position:0% +two ones and twos +to be equal and the number of zeros can + + align:start position:0% +to be equal and the number of zeros can + + + align:start position:0% +to be equal and the number of zeros can +be anything + + align:start position:0% +be anything + + + align:start position:0% +be anything +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now you can easily make i hope + + align:start position:0% +now you can easily make i hope + + + align:start position:0% +now you can easily make i hope +uh you should make sure you you can + + align:start position:0% +uh you should make sure you you can + + + align:start position:0% +uh you should make sure you you can +push down automata that can recognize a1 + + align:start position:0% +push down automata that can recognize a1 + + + align:start position:0% +push down automata that can recognize a1 +and a2 + + align:start position:0% +and a2 + + + align:start position:0% +and a2 +um because let's just take a1 + + align:start position:0% +um because let's just take a1 + + + align:start position:0% +um because let's just take a1 +the push down automaton can push the + + align:start position:0% +the push down automaton can push the + + + align:start position:0% +the push down automaton can push the +zeros + + align:start position:0% +zeros + + + align:start position:0% +zeros +as it's reading them + + align:start position:0% +as it's reading them + + + align:start position:0% +as it's reading them +pop them as it's reading the ones to + + align:start position:0% +pop them as it's reading the ones to + + + align:start position:0% +pop them as it's reading the ones to +match them off and make sure that + + align:start position:0% +match them off and make sure that + + + align:start position:0% +match them off and make sure that +they're the same number of them + + align:start position:0% +they're the same number of them + + + align:start position:0% +they're the same number of them +and then the twos + + align:start position:0% +and then the twos + + + align:start position:0% +and then the twos +it doesn't care how many there are it + + align:start position:0% +it doesn't care how many there are it + + + align:start position:0% +it doesn't care how many there are it +just has to make sure that there are no + + align:start position:0% +just has to make sure that there are no + + + align:start position:0% +just has to make sure that there are no +strings there are no letters coming out + + align:start position:0% +strings there are no letters coming out + + + align:start position:0% +strings there are no letters coming out +of order but any number of twos is fine + + align:start position:0% +of order but any number of twos is fine + + + align:start position:0% +of order but any number of twos is fine +so you can easily make a presentation + + align:start position:0% +so you can easily make a presentation + + + align:start position:0% +so you can easily make a presentation +recognize a1 similarly for a2 + + align:start position:0% +recognize a1 similarly for a2 + + + align:start position:0% +recognize a1 similarly for a2 +um so what can we conclude from that + + align:start position:0% +um so what can we conclude from that + + + align:start position:0% +um so what can we conclude from that +here are the three possibilities let me + + align:start position:0% +here are the three possibilities let me + + + align:start position:0% +here are the three possibilities let me +uh so look at that the class of content + + align:start position:0% +uh so look at that the class of content + + + align:start position:0% +uh so look at that the class of content +language is not closing intersection + + align:start position:0% +language is not closing intersection + + + align:start position:0% +language is not closing intersection +you know you can read it um so i i want + + align:start position:0% +you know you can read it um so i i want + + + align:start position:0% +you know you can read it um so i i want +to pull up the uh + + align:start position:0% +to pull up the uh + + + align:start position:0% +to pull up the uh +poll and launch that + + align:start position:0% + + + + align:start position:0% + +please fill that out + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +10 seconds + + align:start position:0% + + + + align:start position:0% + +again + + align:start position:0% +again + + + align:start position:0% +again +just + + align:start position:0% +just + + + align:start position:0% +just +if you don't know the answer just give + + align:start position:0% +if you don't know the answer just give + + + align:start position:0% +if you don't know the answer just give +any answers so that uh because we're not + + align:start position:0% +any answers so that uh because we're not + + + align:start position:0% +any answers so that uh because we're not +counting correctness + + align:start position:0% +counting correctness + + + align:start position:0% +counting correctness +um + + align:start position:0% +um + + + align:start position:0% +um +still a few dribbling in + + align:start position:0% +still a few dribbling in + + + align:start position:0% +still a few dribbling in +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh + + align:start position:0% +uh + + + align:start position:0% +uh +five seconds + + align:start position:0% +five seconds + + + align:start position:0% +five seconds +okay end polling uh most of you got that + + align:start position:0% +okay end polling uh most of you got that + + + align:start position:0% +okay end polling uh most of you got that +right + + align:start position:0% +right + + + align:start position:0% +right +um + + align:start position:0% + + + + align:start position:0% + +i know is it okay to share these things + + align:start position:0% +i know is it okay to share these things + + + align:start position:0% +i know is it okay to share these things +i don't want to make people who didn't + + align:start position:0% +i don't want to make people who didn't + + + align:start position:0% +i don't want to make people who didn't +get the right feel bad + + align:start position:0% +get the right feel bad + + + align:start position:0% +get the right feel bad +you know but you should understand i + + align:start position:0% +you know but you should understand i + + + align:start position:0% +you know but you should understand i +think you know if you're missing + + align:start position:0% +think you know if you're missing + + + align:start position:0% +think you know if you're missing +something you should understand + + align:start position:0% +something you should understand + + + align:start position:0% +something you should understand +what is what you're missing the pumping + + align:start position:0% +what is what you're missing the pumping + + + align:start position:0% +what is what you're missing the pumping +limit shows that a1 union a2 is not a + + align:start position:0% +limit shows that a1 union a2 is not a + + + align:start position:0% +limit shows that a1 union a2 is not a +context-free language no as i mentioned + + align:start position:0% +context-free language no as i mentioned + + + align:start position:0% +context-free language no as i mentioned +at the beginning the reg the + + align:start position:0% +at the beginning the reg the + + + align:start position:0% +at the beginning the reg the +context-free languages are closed under + + align:start position:0% +context-free languages are closed under + + + align:start position:0% +context-free languages are closed under +union + + align:start position:0% +union + + + align:start position:0% +union +so the pumping alum had better not show + + align:start position:0% +so the pumping alum had better not show + + + align:start position:0% +so the pumping alum had better not show +that these we already know that these + + align:start position:0% +that these we already know that these + + + align:start position:0% +that these we already know that these +two languages are context-free because + + align:start position:0% +two languages are context-free because + + + align:start position:0% +two languages are context-free because +we get them from push down on top + + align:start position:0% +we get them from push down on top + + + align:start position:0% +we get them from push down on top +and we said at the beginning that + + align:start position:0% +and we said at the beginning that + + + align:start position:0% +and we said at the beginning that +contact free language is closed under + + align:start position:0% +contact free language is closed under + + + align:start position:0% +contact free language is closed under +union so we know that these two are + + align:start position:0% +union so we know that these two are + + + align:start position:0% +union so we know that these two are +context-free so the pumping alignment + + align:start position:0% +context-free so the pumping alignment + + + align:start position:0% +context-free so the pumping alignment +better not show it they're not + + align:start position:0% +better not show it they're not + + + align:start position:0% +better not show it they're not +context-free something would be terribly + + align:start position:0% +context-free something would be terribly + + + align:start position:0% +context-free something would be terribly +gone have gone terribly wrong uh + + align:start position:0% +gone have gone terribly wrong uh + + + align:start position:0% +gone have gone terribly wrong uh +if that were true and also + + align:start position:0% +if that were true and also + + + align:start position:0% +if that were true and also +um + + align:start position:0% +um + + + align:start position:0% +um +we know + + align:start position:0% +we know + + + align:start position:0% +we know +also from a little bit of further + + align:start position:0% +also from a little bit of further + + + align:start position:0% +also from a little bit of further +reasoning that the context-free + + align:start position:0% +reasoning that the context-free + + + align:start position:0% +reasoning that the context-free +languages is not closed under complement + + align:start position:0% +languages is not closed under complement + + + align:start position:0% +languages is not closed under complement +by what we've already what we've already + + align:start position:0% +by what we've already what we've already + + + align:start position:0% +by what we've already what we've already +discussed + + align:start position:0% +discussed + + + align:start position:0% +discussed +uh because they are closed under union + + align:start position:0% +uh because they are closed under union + + + align:start position:0% +uh because they are closed under union +as i pointed out they're not closed + + align:start position:0% +as i pointed out they're not closed + + + align:start position:0% +as i pointed out they're not closed +under intersection + + align:start position:0% +under intersection + + + align:start position:0% +under intersection +and so if they were closed under + + align:start position:0% +and so if they were closed under + + + align:start position:0% +and so if they were closed under +complement + + align:start position:0% +complement + + + align:start position:0% +complement +de morgan's laws would say that closure + + align:start position:0% +de morgan's laws would say that closure + + + align:start position:0% +de morgan's laws would say that closure +under union and closure under complement + + align:start position:0% +under union and closure under complement + + + align:start position:0% +under union and closure under complement +would give you closure under + + align:start position:0% +would give you closure under + + + align:start position:0% +would give you closure under +intersection + + align:start position:0% +intersection + + + align:start position:0% +intersection +but we don't have closer intersections + + align:start position:0% +but we don't have closer intersections + + + align:start position:0% +but we don't have closer intersections +so in fact they're not closed under + + align:start position:0% +so in fact they're not closed under + + + align:start position:0% +so in fact they're not closed under +complement + + align:start position:0% + + + + align:start position:0% + +okay uh so in fact this does show us + + align:start position:0% +okay uh so in fact this does show us + + + align:start position:0% +okay uh so in fact this does show us +that the class of context-free language + + align:start position:0% +that the class of context-free language + + + align:start position:0% +that the class of context-free language +is not closed under intersection because + + align:start position:0% +is not closed under intersection because + + + align:start position:0% +is not closed under intersection because +the intersection of a1 and a2 two + + align:start position:0% +the intersection of a1 and a2 two + + + align:start position:0% +the intersection of a1 and a2 two +context three languages is b + + align:start position:0% +context three languages is b + + + align:start position:0% +context three languages is b +and b + + align:start position:0% +and b + + + align:start position:0% +and b +is not context-free so it shows that um + + align:start position:0% +is not context-free so it shows that um + + + align:start position:0% +is not context-free so it shows that um +this is not the the + + align:start position:0% +this is not the the + + + align:start position:0% +this is not the the +um closure under intersection does not + + align:start position:0% +um closure under intersection does not + + + align:start position:0% +um closure under intersection does not +hold + + align:start position:0% +hold + + + align:start position:0% +hold +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so let us continue then + + align:start position:0% +so let us continue then + + + align:start position:0% +so let us continue then +we have one more uh example then we'll + + align:start position:0% +we have one more uh example then we'll + + + align:start position:0% +we have one more uh example then we'll +take a break + + align:start position:0% +take a break + + + align:start position:0% +take a break +uh so the pumping limit for context-free + + align:start position:0% +uh so the pumping limit for context-free + + + align:start position:0% +uh so the pumping limit for context-free +languages again uh here's a second + + align:start position:0% +languages again uh here's a second + + + align:start position:0% +languages again uh here's a second +example + + align:start position:0% +example + + + align:start position:0% +example +uh here's the language f we have + + align:start position:0% +uh here's the language f we have + + + align:start position:0% +uh here's the language f we have +actually seen what's before ww + + align:start position:0% +actually seen what's before ww + + + align:start position:0% +actually seen what's before ww +uh two copies of a string um in in + + align:start position:0% +uh two copies of a string um in in + + + align:start position:0% +uh two copies of a string um in in +um + + align:start position:0% +um + + + align:start position:0% +um +that + + align:start position:0% +that + + + align:start position:0% +that +two copies of any string um i'm gonna + + align:start position:0% +two copies of any string um i'm gonna + + + align:start position:0% +two copies of any string um i'm gonna +show that's not a context free language + + align:start position:0% +show that's not a context free language + + + align:start position:0% +show that's not a context free language +uh + + align:start position:0% + + + + align:start position:0% + +assume that it is context-free the + + align:start position:0% +assume that it is context-free the + + + align:start position:0% +assume that it is context-free the +pumping limit gives pumping length now + + align:start position:0% +pumping limit gives pumping length now + + + align:start position:0% +pumping limit gives pumping length now +here you have to do a little bit more + + align:start position:0% +here you have to do a little bit more + + + align:start position:0% +here you have to do a little bit more +often the challenge + + align:start position:0% +often the challenge + + + align:start position:0% +often the challenge +in applying + + align:start position:0% +in applying + + + align:start position:0% +in applying +the pumping lemma in either case uh that + + align:start position:0% +the pumping lemma in either case uh that + + + align:start position:0% +the pumping lemma in either case uh that +we've seen uh involves with choosing + + align:start position:0% +we've seen uh involves with choosing + + + align:start position:0% +we've seen uh involves with choosing +that string that you need to pump that + + align:start position:0% +that string that you need to pump that + + + align:start position:0% +that string that you need to pump that +you're gonna pump + + align:start position:0% +you're gonna pump + + + align:start position:0% +you're gonna pump +so you have to choose s uh in f which is + + align:start position:0% +so you have to choose s uh in f which is + + + align:start position:0% +so you have to choose s uh in f which is +longer than p which has to go with so + + align:start position:0% +longer than p which has to go with so + + + align:start position:0% +longer than p which has to go with so +you might try this one first glance here + + align:start position:0% +you might try this one first glance here + + + align:start position:0% +you might try this one first glance here +isn't string it's in the language + + align:start position:0% +isn't string it's in the language + + + align:start position:0% +isn't string it's in the language +because it's + + align:start position:0% +because it's + + + align:start position:0% +because it's +two copies of the string zero to the p1 + + align:start position:0% +two copies of the string zero to the p1 + + + align:start position:0% +two copies of the string zero to the p1 +zero to and then zero to the p1 that's + + align:start position:0% +zero to and then zero to the p1 that's + + + align:start position:0% +zero to and then zero to the p1 that's +in the language + + align:start position:0% +in the language + + + align:start position:0% +in the language +but it's a bad choice + + align:start position:0% +but it's a bad choice + + + align:start position:0% +but it's a bad choice +uh let's say let's before i get ahead of + + align:start position:0% +uh let's say let's before i get ahead of + + + align:start position:0% +uh let's say let's before i get ahead of +myself let's let's draw a picture of + + align:start position:0% +myself let's let's draw a picture of + + + align:start position:0% +myself let's let's draw a picture of +this which i think is always helpful to + + align:start position:0% +this which i think is always helpful to + + + align:start position:0% +this which i think is always helpful to +see + + align:start position:0% +see + + + align:start position:0% +see +um so here is runs of zeros and then a + + align:start position:0% +um so here is runs of zeros and then a + + + align:start position:0% +um so here is runs of zeros and then a +one runs of zeros and then a one um why + + align:start position:0% +one runs of zeros and then a one um why + + + align:start position:0% +one runs of zeros and then a one um why +is this a bad choice + + align:start position:0% +is this a bad choice + + + align:start position:0% +is this a bad choice +because you can pump that string and you + + align:start position:0% +because you can pump that string and you + + + align:start position:0% +because you can pump that string and you +remain in the language um there is a way + + align:start position:0% +remain in the language um there is a way + + + align:start position:0% +remain in the language um there is a way +to cut that string up + + align:start position:0% +to cut that string up + + + align:start position:0% +to cut that string up +um and you'll stay in the language and + + align:start position:0% +um and you'll stay in the language and + + + align:start position:0% +um and you'll stay in the language and +the way to cut it up is to let the x be + + align:start position:0% +the way to cut it up is to let the x be + + + align:start position:0% +the way to cut it up is to let the x be +just that substring which is just the + + align:start position:0% +just that substring which is just the + + + align:start position:0% +just that substring which is just the +one + + align:start position:0% +one + + + align:start position:0% +one +and the v and the y can be a couple of + + align:start position:0% +and the v and the y can be a couple of + + + align:start position:0% +and the v and the y can be a couple of +zeros or a single zero on either side of + + align:start position:0% +zeros or a single zero on either side of + + + align:start position:0% +zeros or a single zero on either side of +that one + + align:start position:0% +that one + + + align:start position:0% +that one +and now that's going to be a small + + align:start position:0% +and now that's going to be a small + + + align:start position:0% +and now that's going to be a small +v x y + + align:start position:0% +v x y + + + align:start position:0% +v x y +but + + align:start position:0% +but + + + align:start position:0% +but +if you repeat v and y you're going to um + + align:start position:0% + + + + align:start position:0% + +if you repeat v and y + + align:start position:0% +if you repeat v and y + + + align:start position:0% +if you repeat v and y +you're going to stay in the language + + align:start position:0% +you're going to stay in the language + + + align:start position:0% +you're going to stay in the language +because you'll just be adding zeros here + + align:start position:0% +because you'll just be adding zeros here + + + align:start position:0% +because you'll just be adding zeros here +you'll be adding same number of zeros + + align:start position:0% +you'll be adding same number of zeros + + + align:start position:0% +you'll be adding same number of zeros +there + + align:start position:0% +there + + + align:start position:0% +there +and then you're going to have a string + + align:start position:0% +and then you're going to have a string + + + align:start position:0% +and then you're going to have a string +which still looks like ww and you'll + + align:start position:0% +which still looks like ww and you'll + + + align:start position:0% +which still looks like ww and you'll +still be in the language + + align:start position:0% +still be in the language + + + align:start position:0% +still be in the language +so that + + align:start position:0% +so that + + + align:start position:0% +so that +that means of cutting it up doesn't get + + align:start position:0% +that means of cutting it up doesn't get + + + align:start position:0% +that means of cutting it up doesn't get +you out of the language under pumping + + align:start position:0% +you out of the language under pumping + + + align:start position:0% +you out of the language under pumping +and the fact is that + + align:start position:0% +and the fact is that + + + align:start position:0% +and the fact is that +that's a bad choice for s because there + + align:start position:0% +that's a bad choice for s because there + + + align:start position:0% +that's a bad choice for s because there +is that way of cutting it up so you have + + align:start position:0% +is that way of cutting it up so you have + + + align:start position:0% +is that way of cutting it up so you have +to show there's no way you can't you + + align:start position:0% +to show there's no way you can't you + + + align:start position:0% +to show there's no way you can't you +don't get to pick the way to cut it up + + align:start position:0% +don't get to pick the way to cut it up + + + align:start position:0% +don't get to pick the way to cut it up +um you have to show that there is no way + + align:start position:0% +um you have to show that there is no way + + + align:start position:0% +um you have to show that there is no way +to cut it up um + + align:start position:0% +to cut it up um + + + align:start position:0% +to cut it up um +uh in order to um + + align:start position:0% +uh in order to um + + + align:start position:0% +uh in order to um +to violate the uh + + align:start position:0% +to violate the uh + + + align:start position:0% +to violate the uh +the pumping lever so + + align:start position:0% +the pumping lever so + + + align:start position:0% +the pumping lever so +if instead you use the string 0 to the + + align:start position:0% +if instead you use the string 0 to the + + + align:start position:0% +if instead you use the string 0 to the +p1 to the p0 to the p1 to the p so this + + align:start position:0% +p1 to the p0 to the p1 to the p so this + + + align:start position:0% +p1 to the p0 to the p1 to the p so this +is zeros followed by one followed by + + align:start position:0% +is zeros followed by one followed by + + + align:start position:0% +is zeros followed by one followed by +zeros followed by ones all the same + + align:start position:0% +zeros followed by ones all the same + + + align:start position:0% +zeros followed by ones all the same +number of them + + align:start position:0% +number of them + + + align:start position:0% +number of them +that can't be pumped satisfying to the + + align:start position:0% +that can't be pumped satisfying to the + + + align:start position:0% +that can't be pumped satisfying to the +three conditions um + + align:start position:0% +three conditions um + + + align:start position:0% +three conditions um +and just going through that + + align:start position:0% +and just going through that + + + align:start position:0% +and just going through that +uh + + align:start position:0% + + + + align:start position:0% + +um now if you try to break it up you're + + align:start position:0% +um now if you try to break it up you're + + + align:start position:0% +um now if you try to break it up you're +going to lose + + align:start position:0% +going to lose + + + align:start position:0% +going to lose +or the or the lemon is going to lose + + align:start position:0% +or the or the lemon is going to lose + + + align:start position:0% +or the or the lemon is going to lose +you're going to be happy but the lemon + + align:start position:0% +you're going to be happy but the lemon + + + align:start position:0% +you're going to be happy but the lemon +is not going to be happy because it's + + align:start position:0% +is not going to be happy because it's + + + align:start position:0% +is not going to be happy because it's +not going it's going to violate the + + align:start position:0% +not going it's going to violate the + + + align:start position:0% +not going it's going to violate the +conditions um + + align:start position:0% +conditions um + + + align:start position:0% +conditions um +condition 3 says + + align:start position:0% +condition 3 says + + + align:start position:0% +condition 3 says +vxy is not + + align:start position:0% +vxy is not + + + align:start position:0% +vxy is not +doesn't span too much and in fact can't + + align:start position:0% +doesn't span too much and in fact can't + + + align:start position:0% +doesn't span too much and in fact can't +span + + align:start position:0% +span + + + align:start position:0% +span +uh two runs of zeros or two runs of ones + + align:start position:0% +uh two runs of zeros or two runs of ones + + + align:start position:0% +uh two runs of zeros or two runs of ones +it's just not big enough because they're + + align:start position:0% +it's just not big enough because they're + + + align:start position:0% +it's just not big enough because they're +more than p things they're p things + + align:start position:0% +more than p things they're p things + + + align:start position:0% +more than p things they're p things +apart + + align:start position:0% +apart + + + align:start position:0% +apart +and this one string this string v x y is + + align:start position:0% +and this one string this string v x y is + + + align:start position:0% +and this one string this string v x y is +only p long + + align:start position:0% +only p long + + + align:start position:0% +only p long +and so therefore if you repeat + + align:start position:0% +and so therefore if you repeat + + + align:start position:0% +and so therefore if you repeat +of uh v and y + + align:start position:0% +of uh v and y + + + align:start position:0% +of uh v and y +you're going to have two runs of zeros + + align:start position:0% +you're going to have two runs of zeros + + + align:start position:0% +you're going to have two runs of zeros +or two runs of ones that have unequal + + align:start position:0% +or two runs of ones that have unequal + + + align:start position:0% +or two runs of ones that have unequal +length and now + + align:start position:0% +length and now + + + align:start position:0% +length and now +that's not going to be of the form w and + + align:start position:0% +that's not going to be of the form w and + + + align:start position:0% +that's not going to be of the form w and +you're going to be out of the language + + align:start position:0% +you're going to be out of the language + + + align:start position:0% +you're going to be out of the language +okay uh so i hope + + align:start position:0% +okay uh so i hope + + + align:start position:0% +okay uh so i hope +you know that's uh you've got a little + + align:start position:0% +you know that's uh you've got a little + + + align:start position:0% +you know that's uh you've got a little +practice with that um i think we're at + + align:start position:0% +practice with that um i think we're at + + + align:start position:0% +practice with that um i think we're at +our + + align:start position:0% +our + + + align:start position:0% +our +uh break and i will see you back here in + + align:start position:0% +uh break and i will see you back here in + + + align:start position:0% +uh break and i will see you back here in +uh five uh minutes um + + align:start position:0% +uh five uh minutes um + + + align:start position:0% +uh five uh minutes um +i can get my timer launched here + + align:start position:0% +i can get my timer launched here + + + align:start position:0% +i can get my timer launched here +okay so see you soon + + align:start position:0% + + + + align:start position:0% + +you can this is a good time by the way + + align:start position:0% +you can this is a good time by the way + + + align:start position:0% +you can this is a good time by the way +to to um + + align:start position:0% +to to um + + + align:start position:0% +to to um +uh message me or the tas and i'll i'll + + align:start position:0% +uh message me or the tas and i'll i'll + + + align:start position:0% +uh message me or the tas and i'll i'll +try to be uh + + align:start position:0% +try to be uh + + + align:start position:0% +try to be uh +looking for if you have any questions + + align:start position:0% +looking for if you have any questions + + + align:start position:0% +looking for if you have any questions +in the pumping limit can x + + align:start position:0% +in the pumping limit can x + + + align:start position:0% +in the pumping limit can x +x can be epsilon in the pumping lemma uh + + align:start position:0% +x can be epsilon in the pumping lemma uh + + + align:start position:0% +x can be epsilon in the pumping lemma uh +but it's not possible x can be epsilon y + + align:start position:0% +but it's not possible x can be epsilon y + + + align:start position:0% +but it's not possible x can be epsilon y +can be epsilon but x and y cannot be + + align:start position:0% +can be epsilon but x and y cannot be + + + align:start position:0% +can be epsilon but x and y cannot be +both cannot both be epsilon + + align:start position:0% +both cannot both be epsilon + + + align:start position:0% +both cannot both be epsilon +because then when you pump you will get + + align:start position:0% +because then when you pump you will get + + + align:start position:0% +because then when you pump you will get +nothing new + + align:start position:0% +nothing new + + + align:start position:0% +nothing new +technically v and y can include both + + align:start position:0% +technically v and y can include both + + + align:start position:0% +technically v and y can include both +zeros and ones + + align:start position:0% +zeros and ones + + + align:start position:0% +zeros and ones +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +v and y can conclude both zeros and ones + + align:start position:0% +v and y can conclude both zeros and ones + + + align:start position:0% +v and y can conclude both zeros and ones +um + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +let me uh + + align:start position:0% +let me uh + + + align:start position:0% +let me uh +try to put that back if that's + + align:start position:0% +try to put that back if that's + + + align:start position:0% +try to put that back if that's +will + + align:start position:0% +will + + + align:start position:0% +will +um + + align:start position:0% +um + + + align:start position:0% +um +[Music] + + align:start position:0% + + + + align:start position:0% + +so v and y can have both zeros and ones + + align:start position:0% +so v and y can have both zeros and ones + + + align:start position:0% +so v and y can have both zeros and ones +but they can't have zeros from two + + align:start position:0% +but they can't have zeros from two + + + align:start position:0% +but they can't have zeros from two +different blocks + + align:start position:0% + + + + align:start position:0% + +and you can't have ones from two + + align:start position:0% +and you can't have ones from two + + + align:start position:0% +and you can't have ones from two +different blocks + + align:start position:0% +different blocks + + + align:start position:0% +different blocks +so what's going to happen is either + + align:start position:0% +so what's going to happen is either + + + align:start position:0% +so what's going to happen is either +you're going to get things out of order + + align:start position:0% +you're going to get things out of order + + + align:start position:0% +you're going to get things out of order +when you repeat like a v has both zeros + + align:start position:0% +when you repeat like a v has both zeros + + + align:start position:0% +when you repeat like a v has both zeros +and ones in it when you repeat + + align:start position:0% +and ones in it when you repeat + + + align:start position:0% +and ones in it when you repeat +v you're going to have uh zeros and ones + + align:start position:0% +v you're going to have uh zeros and ones + + + align:start position:0% +v you're going to have uh zeros and ones +and zeros and ones and zeros and ones + + align:start position:0% +and zeros and ones and zeros and ones + + + align:start position:0% +and zeros and ones and zeros and ones +that's clearly out of the language so + + align:start position:0% +that's clearly out of the language so + + + align:start position:0% +that's clearly out of the language so +that's so that's no good + + align:start position:0% +that's so that's no good + + + align:start position:0% +that's so that's no good +your only hope is to have v to be + + align:start position:0% +your only hope is to have v to be + + + align:start position:0% +your only hope is to have v to be +sticking only inside the zeros and y to + + align:start position:0% +sticking only inside the zeros and y to + + + align:start position:0% +sticking only inside the zeros and y to +be sticking only inside zeros are only + + align:start position:0% +be sticking only inside zeros are only + + + align:start position:0% +be sticking only inside zeros are only +inside once + + align:start position:0% +inside once + + + align:start position:0% +inside once +but now if you repeat that if just look + + align:start position:0% +but now if you repeat that if just look + + + align:start position:0% +but now if you repeat that if just look +at what you're going to get + + align:start position:0% +at what you're going to get + + + align:start position:0% +at what you're going to get +you're going to have a string which is + + align:start position:0% +you're going to have a string which is + + + align:start position:0% +you're going to have a string which is +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +if you try to cut that string in half + + align:start position:0% +if you try to cut that string in half + + + align:start position:0% +if you try to cut that string in half +it's not going to be of the right form + + align:start position:0% +it's not going to be of the right form + + + align:start position:0% +it's not going to be of the right form +it's not going to be two copies of the + + align:start position:0% +it's not going to be two copies of the + + + align:start position:0% +it's not going to be two copies of the +same string because you know it's going + + align:start position:0% +same string because you know it's going + + + align:start position:0% +same string because you know it's going +to have a run of zeros + + align:start position:0% +to have a run of zeros + + + align:start position:0% +to have a run of zeros +um followed by + + align:start position:0% +um followed by + + + align:start position:0% +um followed by +a longer or shorter run of zeros or one + + align:start position:0% +a longer or shorter run of zeros or one + + + align:start position:0% +a longer or shorter run of zeros or one +of ones followed by another run of ones + + align:start position:0% +of ones followed by another run of ones + + + align:start position:0% +of ones followed by another run of ones +of unequal length so there's no way this + + align:start position:0% +of unequal length so there's no way this + + + align:start position:0% +of unequal length so there's no way this +can be two strings + + align:start position:0% +can be two strings + + + align:start position:0% +can be two strings +um + + align:start position:0% +um + + + align:start position:0% +um +two copies of the same string + + align:start position:0% +two copies of the same string + + + align:start position:0% +two copies of the same string +because that that's what you're required + + align:start position:0% +because that that's what you're required + + + align:start position:0% +because that that's what you're required +f has to be two copies of the same + + align:start position:0% +f has to be two copies of the same + + + align:start position:0% +f has to be two copies of the same +string to be in the language + + align:start position:0% + + + + align:start position:0% + +okay uh let me just see where we're + + align:start position:0% +okay uh let me just see where we're + + + align:start position:0% +okay uh let me just see where we're +running out of time here let me just put + + align:start position:0% +running out of time here let me just put + + + align:start position:0% +running out of time here let me just put +my uh + + align:start position:0% +my uh + + + align:start position:0% +my uh +my + + align:start position:0% +my + + + align:start position:0% +my +my + + align:start position:0% +my + + + align:start position:0% +my +timer here + + align:start position:0% +timer here + + + align:start position:0% +timer here +we've only got 30 seconds + + align:start position:0% + + + + align:start position:0% + +okay sorry i'm not getting to answer all + + align:start position:0% +okay sorry i'm not getting to answer all + + + align:start position:0% +okay sorry i'm not getting to answer all +the questions here um + + align:start position:0% +the questions here um + + + align:start position:0% +the questions here um +okay we are done um + + align:start position:0% +okay we are done um + + + align:start position:0% +okay we are done um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +with um + + align:start position:0% +with um + + + align:start position:0% +with um +our break + + align:start position:0% +our break + + + align:start position:0% +our break +it's going to come back + + align:start position:0% + + + + align:start position:0% + +um and now we're shifting gears in a + + align:start position:0% +um and now we're shifting gears in a + + + align:start position:0% +um and now we're shifting gears in a +major way + + align:start position:0% +major way + + + align:start position:0% +major way +because in a sense everything we've done + + align:start position:0% +because in a sense everything we've done + + + align:start position:0% +because in a sense everything we've done +so far + + align:start position:0% +so far + + + align:start position:0% +so far +has been kind of a warm up + + align:start position:0% +has been kind of a warm up + + + align:start position:0% +has been kind of a warm up +these limited + + align:start position:0% +these limited + + + align:start position:0% +these limited +computational models + + align:start position:0% +computational models + + + align:start position:0% +computational models +um + + align:start position:0% +um + + + align:start position:0% +um +really are kind of + + align:start position:0% +really are kind of + + + align:start position:0% +really are kind of +get helping us to set our understanding + + align:start position:0% +get helping us to set our understanding + + + align:start position:0% +get helping us to set our understanding +of automata and the definitions and the + + align:start position:0% +of automata and the definitions and the + + + align:start position:0% +of automata and the definitions and the +notation + + align:start position:0% +notation + + + align:start position:0% +notation +and they're also going to be helpful in + + align:start position:0% +and they're also going to be helpful in + + + align:start position:0% +and they're also going to be helpful in +providing examples later on in the term + + align:start position:0% +providing examples later on in the term + + + align:start position:0% +providing examples later on in the term +um but really in terms of a model of + + align:start position:0% +um but really in terms of a model of + + + align:start position:0% +um but really in terms of a model of +computation they don't cut it because + + align:start position:0% +computation they don't cut it because + + + align:start position:0% +computation they don't cut it because +uh they cannot do very simple things + + align:start position:0% +uh they cannot do very simple things + + + align:start position:0% +uh they cannot do very simple things +that we normally think of a computer as + + align:start position:0% +that we normally think of a computer as + + + align:start position:0% +that we normally think of a computer as +being able to do + + align:start position:0% +being able to do + + + align:start position:0% +being able to do +so here we're introducing another model + + align:start position:0% +so here we're introducing another model + + + align:start position:0% +so here we're introducing another model +of computation called the turing machine + + align:start position:0% +of computation called the turing machine + + + align:start position:0% +of computation called the turing machine +and that's really going to be the model + + align:start position:0% +and that's really going to be the model + + + align:start position:0% +and that's really going to be the model +that we're going to stick with for the + + align:start position:0% +that we're going to stick with for the + + + align:start position:0% +that we're going to stick with for the +rest of the semester because that's + + align:start position:0% +rest of the semester because that's + + + align:start position:0% +rest of the semester because that's +going to be our model of a general + + align:start position:0% +going to be our model of a general + + + align:start position:0% +going to be our model of a general +purpose uh + + align:start position:0% +purpose uh + + + align:start position:0% +purpose uh +computer the way you normally think + + align:start position:0% +computer the way you normally think + + + align:start position:0% +computer the way you normally think +about it + + align:start position:0% +about it + + + align:start position:0% +about it +um + + align:start position:0% +um + + + align:start position:0% +um +so let's uh we'll spend a little time + + align:start position:0% +so let's uh we'll spend a little time + + + align:start position:0% +so let's uh we'll spend a little time +introducing it and then we will um + + align:start position:0% +introducing it and then we will um + + + align:start position:0% +introducing it and then we will um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know we'll + + align:start position:0% +you know we'll + + + align:start position:0% +you know we'll +we'll continue that discussion next time + + align:start position:0% +we'll continue that discussion next time + + + align:start position:0% +we'll continue that discussion next time +um + + align:start position:0% +um + + + align:start position:0% +um +so uh in terms of a schematic actually + + align:start position:0% +so uh in terms of a schematic actually + + + align:start position:0% +so uh in terms of a schematic actually +the turing machine model is pretty + + align:start position:0% +the turing machine model is pretty + + + align:start position:0% +the turing machine model is pretty +simple + + align:start position:0% +simple + + + align:start position:0% +simple +um + + align:start position:0% +um + + + align:start position:0% +um +it has a uh + + align:start position:0% + + + + align:start position:0% + +it has um + + align:start position:0% +it has um + + + align:start position:0% +it has um +it's going to have states and all that + + align:start position:0% +it's going to have states and all that + + + align:start position:0% +it's going to have states and all that +stuff but you know though so there's + + align:start position:0% +stuff but you know though so there's + + + align:start position:0% +stuff but you know though so there's +going to be a finite control here which + + align:start position:0% +going to be a finite control here which + + + align:start position:0% +going to be a finite control here which +is going to include the states and + + align:start position:0% +is going to include the states and + + + align:start position:0% +is going to include the states and +transition function as we'll describe in + + align:start position:0% +transition function as we'll describe in + + + align:start position:0% +transition function as we'll describe in +a minute um the point is is that you + + align:start position:0% +a minute um the point is is that you + + + align:start position:0% +a minute um the point is is that you +know it's going to have the input + + align:start position:0% +know it's going to have the input + + + align:start position:0% +know it's going to have the input +appearing on a tape + + align:start position:0% +appearing on a tape + + + align:start position:0% +appearing on a tape +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the key difference now is that the the + + align:start position:0% +the key difference now is that the the + + + align:start position:0% +the key difference now is that the the +machine is going to be able to change + + align:start position:0% +machine is going to be able to change + + + align:start position:0% +machine is going to be able to change +the symbols on the tape um + + align:start position:0% +the symbols on the tape um + + + align:start position:0% +the symbols on the tape um +and so we think of the machine as being + + align:start position:0% +and so we think of the machine as being + + + align:start position:0% +and so we think of the machine as being +able to write as well as read the tape + + align:start position:0% +able to write as well as read the tape + + + align:start position:0% +able to write as well as read the tape +okay so that's really uh the key + + align:start position:0% +okay so that's really uh the key + + + align:start position:0% +okay so that's really uh the key +uh + + align:start position:0% +uh + + + align:start position:0% +uh +feature + + align:start position:0% +feature + + + align:start position:0% +feature +um of a turing machine is the ability to + + align:start position:0% +um of a turing machine is the ability to + + + align:start position:0% +um of a turing machine is the ability to +write on the tape everything else in a + + align:start position:0% +write on the tape everything else in a + + + align:start position:0% +write on the tape everything else in a +sense follows from that + + align:start position:0% +sense follows from that + + + align:start position:0% +sense follows from that +a few other differences + + align:start position:0% +a few other differences + + + align:start position:0% +a few other differences +but so the fact that he he head can read + + align:start position:0% +but so the fact that he he head can read + + + align:start position:0% +but so the fact that he he head can read +and write + + align:start position:0% +and write + + + align:start position:0% +and write +so we can use the tape as + + align:start position:0% +so we can use the tape as + + + align:start position:0% +so we can use the tape as +storage + + align:start position:0% +storage + + + align:start position:0% +storage +much as we used a stack as storage but + + align:start position:0% +much as we used a stack as storage but + + + align:start position:0% +much as we used a stack as storage but +it doesn't it's not limited in the way + + align:start position:0% +it doesn't it's not limited in the way + + + align:start position:0% +it doesn't it's not limited in the way +we can access it the way a stack is so + + align:start position:0% +we can access it the way a stack is so + + + align:start position:0% +we can access it the way a stack is so +that we kind of have very uh + + align:start position:0% +that we kind of have very uh + + + align:start position:0% +that we kind of have very uh +flexible access of the information on + + align:start position:0% +flexible access of the information on + + + align:start position:0% +flexible access of the information on +the tape + + align:start position:0% +the tape + + + align:start position:0% +the tape +now + + align:start position:0% +now + + + align:start position:0% +now +being able to write on the tape doesn't + + align:start position:0% +being able to write on the tape doesn't + + + align:start position:0% +being able to write on the tape doesn't +do any good if you can't go back and + + align:start position:0% +do any good if you can't go back and + + + align:start position:0% +do any good if you can't go back and +read what you've written later on so + + align:start position:0% +read what you've written later on so + + + align:start position:0% +read what you've written later on so +we're going to make the head to be able + + align:start position:0% +we're going to make the head to be able + + + align:start position:0% +we're going to make the head to be able +to be two-way + + align:start position:0% +to be two-way + + + align:start position:0% +to be two-way +so the head can move left to right as + + align:start position:0% +so the head can move left to right as + + + align:start position:0% +so the head can move left to right as +before but it can also move back left + + align:start position:0% +before but it can also move back left + + + align:start position:0% +before but it can also move back left +and that's going to be under control of + + align:start position:0% +and that's going to be under control of + + + align:start position:0% +and that's going to be under control of +the transition function so under under + + align:start position:0% +the transition function so under under + + + align:start position:0% +the transition function so under under +program control essentially + + align:start position:0% +program control essentially + + + align:start position:0% +program control essentially +the tape is going to be + + align:start position:0% +the tape is going to be + + + align:start position:0% +the tape is going to be +oops + + align:start position:0% +oops + + + align:start position:0% +oops +sorry the tape is infinite to the right + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +so we're not going to limit how much + + align:start position:0% +so we're not going to limit how much + + + align:start position:0% +so we're not going to limit how much +storage the machine can have so the tape + + align:start position:0% +storage the machine can have so the tape + + + align:start position:0% +storage the machine can have so the tape +is going to think of as having instead + + align:start position:0% +is going to think of as having instead + + + align:start position:0% +is going to think of as having instead +of just having the input on it it's + + align:start position:0% +of just having the input on it it's + + + align:start position:0% +of just having the input on it it's +going to have the input but then the + + align:start position:0% +going to have the input but then the + + + align:start position:0% +going to have the input but then the +rest is going to have infinitely many + + align:start position:0% +rest is going to have infinitely many + + + align:start position:0% +rest is going to have infinitely many +blanks + + align:start position:0% +blanks + + + align:start position:0% +blanks +blank symbols following the input so the + + align:start position:0% +blank symbols following the input so the + + + align:start position:0% +blank symbols following the input so the +tape is infinite or + + align:start position:0% +tape is infinite or + + + align:start position:0% +tape is infinite or +in the right right hand direction + + align:start position:0% +in the right right hand direction + + + align:start position:0% +in the right right hand direction +um + + align:start position:0% +um + + + align:start position:0% +um +and uh so there's infinitely many blanks + + align:start position:0% +and uh so there's infinitely many blanks + + + align:start position:0% +and uh so there's infinitely many blanks +i'm going to use that symbol for the + + align:start position:0% +i'm going to use that symbol for the + + + align:start position:0% +i'm going to use that symbol for the +blank to follow the input + + align:start position:0% +blank to follow the input + + + align:start position:0% +blank to follow the input +um you can accept or reject oh yeah so + + align:start position:0% +um you can accept or reject oh yeah so + + + align:start position:0% +um you can accept or reject oh yeah so +that's another thing that's important + + align:start position:0% +that's another thing that's important + + + align:start position:0% +that's another thing that's important +normally we think of the machine in the + + align:start position:0% +normally we think of the machine in the + + + align:start position:0% +normally we think of the machine in the +previous machines + + align:start position:0% +previous machines + + + align:start position:0% +previous machines +finding a time when i pushed down + + align:start position:0% +finding a time when i pushed down + + + align:start position:0% +finding a time when i pushed down +automata when you got to the end of the + + align:start position:0% +automata when you got to the end of the + + + align:start position:0% +automata when you got to the end of the +input that's when you the acceptance of + + align:start position:0% +input that's when you the acceptance of + + + align:start position:0% +input that's when you the acceptance of +rejection was decided if you were in + + align:start position:0% +rejection was decided if you were in + + + align:start position:0% +rejection was decided if you were in +except state at the end of the input + + align:start position:0% +except state at the end of the input + + + align:start position:0% +except state at the end of the input +then you accept it but + + align:start position:0% +then you accept it but + + + align:start position:0% +then you accept it but +you have to be in that location um at + + align:start position:0% +you have to be in that location um at + + + align:start position:0% +you have to be in that location um at +the end of the input in order for that + + align:start position:0% +the end of the input in order for that + + + align:start position:0% +the end of the input in order for that +to take effect + + align:start position:0% +to take effect + + + align:start position:0% +to take effect +that doesn't make any sense anymore + + align:start position:0% +that doesn't make any sense anymore + + + align:start position:0% +that doesn't make any sense anymore +because + + align:start position:0% +because + + + align:start position:0% +because +the machine might go off beyond that and + + align:start position:0% +the machine might go off beyond that and + + + align:start position:0% +the machine might go off beyond that and +still be computing and come back and + + align:start position:0% +still be computing and come back and + + + align:start position:0% +still be computing and come back and +read the tape later on so it only really + + align:start position:0% +read the tape later on so it only really + + + align:start position:0% +read the tape later on so it only really +makes sense to let the machine + + align:start position:0% +makes sense to let the machine + + + align:start position:0% +makes sense to let the machine +accept or reject + + align:start position:0% +accept or reject + + + align:start position:0% +accept or reject +upon entering the accept or the reject + + align:start position:0% +upon entering the accept or the reject + + + align:start position:0% +upon entering the accept or the reject +state so we're going to have a special + + align:start position:0% +state so we're going to have a special + + + align:start position:0% +state so we're going to have a special +accept state and a special reject state + + align:start position:0% +accept state and a special reject state + + + align:start position:0% +accept state and a special reject state +which is also a little different than + + align:start position:0% +which is also a little different than + + + align:start position:0% +which is also a little different than +before + + align:start position:0% +before + + + align:start position:0% +before +and when the machine enters those states + + align:start position:0% +and when the machine enters those states + + + align:start position:0% +and when the machine enters those states +then machine then the action takes + + align:start position:0% +then machine then the action takes + + + align:start position:0% +then machine then the action takes +effect the machine those machine holds + + align:start position:0% +effect the machine those machine holds + + + align:start position:0% +effect the machine those machine holds +and then accepts + + align:start position:0% +and then accepts + + + align:start position:0% +and then accepts +or holds and then it rejects so we'll + + align:start position:0% +or holds and then it rejects so we'll + + + align:start position:0% +or holds and then it rejects so we'll +make that absolutely clear in the formal + + align:start position:0% +make that absolutely clear in the formal + + + align:start position:0% +make that absolutely clear in the formal +definition in a second but just to get + + align:start position:0% +definition in a second but just to get + + + align:start position:0% +definition in a second but just to get +the spirit of it + + align:start position:0% +the spirit of it + + + align:start position:0% +the spirit of it +um + + align:start position:0% +um + + + align:start position:0% +um +so i'm going to give you an example of + + align:start position:0% +so i'm going to give you an example of + + + align:start position:0% +so i'm going to give you an example of +the thing running uh sorry you need to + + align:start position:0% +the thing running uh sorry you need to + + + align:start position:0% +the thing running uh sorry you need to +again my + + align:start position:0% +again my + + + align:start position:0% +again my +powerpoint is having issues + + align:start position:0% +powerpoint is having issues + + + align:start position:0% +powerpoint is having issues +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +okay so here is a turing machine + + align:start position:0% +okay so here is a turing machine + + + align:start position:0% +okay so here is a turing machine +recognizing that language b + + align:start position:0% +recognizing that language b + + + align:start position:0% +recognizing that language b +actually i switched gears on you instead + + align:start position:0% +actually i switched gears on you instead + + + align:start position:0% +actually i switched gears on you instead +of zeros ones and twos i made them a's + + align:start position:0% +of zeros ones and twos i made them a's + + + align:start position:0% +of zeros ones and twos i made them a's +b's and c's but same idea + + align:start position:0% +b's and c's but same idea + + + align:start position:0% +b's and c's but same idea +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so i'm going to show you how the turing + + align:start position:0% +so i'm going to show you how the turing + + + align:start position:0% +so i'm going to show you how the turing +machine operates + + align:start position:0% +machine operates + + + align:start position:0% +machine operates +and then we'll give a formal + + align:start position:0% +and then we'll give a formal + + + align:start position:0% +and then we'll give a formal +uh definition i hope that's on here + + align:start position:0% +uh definition i hope that's on here + + + align:start position:0% +uh definition i hope that's on here +i think it is + + align:start position:0% +i think it is + + + align:start position:0% +i think it is +in a second but let's this is an + + align:start position:0% +in a second but let's this is an + + + align:start position:0% +in a second but let's this is an +informal discussion of how the machine + + align:start position:0% +informal discussion of how the machine + + + align:start position:0% +informal discussion of how the machine +is going to operate to do this language + + align:start position:0% +is going to operate to do this language + + + align:start position:0% +is going to operate to do this language +a to the kb to the kc to the k using its + + align:start position:0% +a to the kb to the kc to the k using its + + + align:start position:0% +a to the kb to the kc to the k using its +ability to write on the tape as well as + + align:start position:0% +ability to write on the tape as well as + + + align:start position:0% +ability to write on the tape as well as +read and move its head in both + + align:start position:0% +read and move its head in both + + + align:start position:0% +read and move its head in both +directions + + align:start position:0% +directions + + + align:start position:0% +directions +okay so let me just first describe + + align:start position:0% +okay so let me just first describe + + + align:start position:0% +okay so let me just first describe +um in english + + align:start position:0% +um in english + + + align:start position:0% +um in english +how this um + + align:start position:0% +how this um + + + align:start position:0% +how this um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +machine operates and then we will um + + align:start position:0% +machine operates and then we will um + + + align:start position:0% +machine operates and then we will um +see it in action on this little uh + + align:start position:0% +see it in action on this little uh + + + align:start position:0% +see it in action on this little uh +picture i have over here okay so the way + + align:start position:0% +picture i have over here okay so the way + + + align:start position:0% +picture i have over here okay so the way +the machine is going to operate is the + + align:start position:0% +the machine is going to operate is the + + + align:start position:0% +the machine is going to operate is the +very first thing is the head is going to + + align:start position:0% +very first thing is the head is going to + + + align:start position:0% +very first thing is the head is going to +start here and the head is going to scan + + align:start position:0% +start here and the head is going to scan + + + align:start position:0% +start here and the head is going to scan +off to the right + + align:start position:0% +off to the right + + + align:start position:0% +off to the right +uh making sure that the symbols appear + + align:start position:0% +uh making sure that the symbols appear + + + align:start position:0% +uh making sure that the symbols appear +in the correct order + + align:start position:0% +in the correct order + + + align:start position:0% +in the correct order +so it's seeing that + + align:start position:0% +so it's seeing that + + + align:start position:0% +so it's seeing that +that there are a's and then b's and then + + align:start position:0% +that there are a's and then b's and then + + + align:start position:0% +that there are a's and then b's and then +c's without checking the quantities just + + align:start position:0% +c's without checking the quantities just + + + align:start position:0% +c's without checking the quantities just +that the order is correct for that you + + align:start position:0% +that the order is correct for that you + + + align:start position:0% +that the order is correct for that you +don't need to write a finite automaton + + align:start position:0% +don't need to write a finite automaton + + + align:start position:0% +don't need to write a finite automaton +can check that the input is of the form + + align:start position:0% +can check that the input is of the form + + + align:start position:0% +can check that the input is of the form +a star b star c star + + align:start position:0% +a star b star c star + + + align:start position:0% +a star b star c star +um + + align:start position:0% +um + + + align:start position:0% +um +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +rioting is not necessary + + align:start position:0% +rioting is not necessary + + + align:start position:0% +rioting is not necessary +the machine if it uh detects symbols out + + align:start position:0% +the machine if it uh detects symbols out + + + align:start position:0% +the machine if it uh detects symbols out +of order it immediately rejects by going + + align:start position:0% +of order it immediately rejects by going + + + align:start position:0% +of order it immediately rejects by going +into a special reject state otherwise + + align:start position:0% +into a special reject state otherwise + + + align:start position:0% +into a special reject state otherwise +it's going to return its head back to + + align:start position:0% +it's going to return its head back to + + + align:start position:0% +it's going to return its head back to +the left end + + align:start position:0% +the left end + + + align:start position:0% +the left end +and um + + align:start position:0% +and um + + + align:start position:0% +and um +uh let me just show that here so here is + + align:start position:0% +uh let me just show that here so here is + + + align:start position:0% +uh let me just show that here so here is +it + + align:start position:0% +it + + + align:start position:0% +it +oh no + + align:start position:0% +oh no + + + align:start position:0% +oh no +i better + + align:start position:0% +i better + + + align:start position:0% +i better +before i illustrate it over here let's + + align:start position:0% +before i illustrate it over here let's + + + align:start position:0% +before i illustrate it over here let's +go through the whole algorithm uh so the + + align:start position:0% +go through the whole algorithm uh so the + + + align:start position:0% +go through the whole algorithm uh so the +next thing that happens is you're going + + align:start position:0% +next thing that happens is you're going + + + align:start position:0% +next thing that happens is you're going +to scan right and now you want to do the + + align:start position:0% +to scan right and now you want to do the + + + align:start position:0% +to scan right and now you want to do the +counting so you're going to scan right + + align:start position:0% +counting so you're going to scan right + + + align:start position:0% +counting so you're going to scan right +again but this time you're going to make + + align:start position:0% +again but this time you're going to make + + + align:start position:0% +again but this time you're going to make +a bunch of passes over the input bunch + + align:start position:0% +a bunch of passes over the input bunch + + + align:start position:0% +a bunch of passes over the input bunch +of scans + + align:start position:0% +of scans + + + align:start position:0% +of scans +and each time you make a scan you're + + align:start position:0% +and each time you make a scan you're + + + align:start position:0% +and each time you make a scan you're +going to cross + + align:start position:0% +going to cross + + + align:start position:0% +going to cross +off one symbol of each type so you're + + align:start position:0% +off one symbol of each type so you're + + + align:start position:0% +off one symbol of each type so you're +going to cross off an a you'll cross off + + align:start position:0% +going to cross off an a you'll cross off + + + align:start position:0% +going to cross off an a you'll cross off +a b you'll cross off a c on a single + + align:start position:0% +a b you'll cross off a c on a single + + + align:start position:0% +a b you'll cross off a c on a single +scan and then repeat that + + align:start position:0% +scan and then repeat that + + + align:start position:0% +scan and then repeat that +crossing off the next a the next b the + + align:start position:0% +crossing off the next a the next b the + + + align:start position:0% +crossing off the next a the next b the +next c + + align:start position:0% +next c + + + align:start position:0% +next c +and + + align:start position:0% +and + + + align:start position:0% +and +you want to make sure that you've + + align:start position:0% +you want to make sure that you've + + + align:start position:0% +you want to make sure that you've +crossed off all of the symbols on the + + align:start position:0% +crossed off all of the symbols on the + + + align:start position:0% +crossed off all of the symbols on the +same run and not crossing off some + + align:start position:0% +same run and not crossing off some + + + align:start position:0% +same run and not crossing off some +symbols before other symbols uh while + + align:start position:0% +symbols before other symbols uh while + + + align:start position:0% +symbols before other symbols uh while +other symbols will remain because that + + align:start position:0% +other symbols will remain because that + + + align:start position:0% +other symbols will remain because that +would mean that the counts were not + + align:start position:0% +would mean that the counts were not + + + align:start position:0% +would mean that the counts were not +equal if you cross them off and they're + + align:start position:0% +equal if you cross them off and they're + + + align:start position:0% +equal if you cross them off and they're +all + + align:start position:0% +all + + + align:start position:0% +all +you know run out on the same scan + + align:start position:0% +you know run out on the same scan + + + align:start position:0% +you know run out on the same scan +same pass + + align:start position:0% +same pass + + + align:start position:0% +same pass +then we know that the numbers have to be + + align:start position:0% +then we know that the numbers have to be + + + align:start position:0% +then we know that the numbers have to be +start off being equal sort of i mean + + align:start position:0% +start off being equal sort of i mean + + + align:start position:0% +start off being equal sort of i mean +this is sort of baby stuff here i but i + + align:start position:0% +this is sort of baby stuff here i but i + + + align:start position:0% +this is sort of baby stuff here i but i +hope you get the idea and we'll kind of + + align:start position:0% +hope you get the idea and we'll kind of + + + align:start position:0% +hope you get the idea and we'll kind of +illustrate in in a second so if at least + + align:start position:0% +illustrate in in a second so if at least + + + align:start position:0% +illustrate in in a second so if at least +one of the if you have the last one of + + align:start position:0% +one of the if you have the last one of + + + align:start position:0% +one of the if you have the last one of +each symbol so what i mean by that is + + align:start position:0% +each symbol so what i mean by that is + + + align:start position:0% +each symbol so what i mean by that is +you you just crossed off the last a the + + align:start position:0% +you you just crossed off the last a the + + + align:start position:0% +you you just crossed off the last a the +last b and the last c then you know that + + align:start position:0% +last b and the last c then you know that + + + align:start position:0% +last b and the last c then you know that +you were originally had an equal number + + align:start position:0% +you were originally had an equal number + + + align:start position:0% +you were originally had an equal number +and so you accept because you're + + align:start position:0% +and so you accept because you're + + + align:start position:0% +and so you accept because you're +crossing off one of each on each scan so + + align:start position:0% +crossing off one of each on each scan so + + + align:start position:0% +crossing off one of each on each scan so +if you cross the + + align:start position:0% +if you cross the + + + align:start position:0% +if you cross the +on the last scan + + align:start position:0% +on the last scan + + + align:start position:0% +on the last scan +each one of them gets crossed off um + + align:start position:0% +each one of them gets crossed off um + + + align:start position:0% +each one of them gets crossed off um +then you accept + + align:start position:0% +then you accept + + + align:start position:0% +then you accept +but if + + align:start position:0% +but if + + + align:start position:0% +but if +uh it was the last of some symbol but + + align:start position:0% +uh it was the last of some symbol but + + + align:start position:0% +uh it was the last of some symbol but +not of other symbols + + align:start position:0% +not of other symbols + + + align:start position:0% +not of other symbols +so you know you crossed off the last a + + align:start position:0% +so you know you crossed off the last a + + + align:start position:0% +so you know you crossed off the last a +but there um there were several b's + + align:start position:0% +but there um there were several b's + + + align:start position:0% +but there um there were several b's +remaining then you started off with an + + align:start position:0% +remaining then you started off with an + + + align:start position:0% +remaining then you started off with an +unequal number of a's b's and c's + + align:start position:0% +unequal number of a's b's and c's + + + align:start position:0% +unequal number of a's b's and c's +and you can reject or + + align:start position:0% +and you can reject or + + + align:start position:0% +and you can reject or +if all symbols still remain after you've + + align:start position:0% +if all symbols still remain after you've + + + align:start position:0% +if all symbols still remain after you've +crossed them uh one of each off + + align:start position:0% +crossed them uh one of each off + + + align:start position:0% +crossed them uh one of each off +then you haven't + + align:start position:0% +then you haven't + + + align:start position:0% +then you haven't +done enough passes and you're gonna + + align:start position:0% +done enough passes and you're gonna + + + align:start position:0% +done enough passes and you're gonna +repeat + + align:start position:0% +repeat + + + align:start position:0% +repeat +from stage three and do that uh again + + align:start position:0% +from stage three and do that uh again + + + align:start position:0% +from stage three and do that uh again +another scan + + align:start position:0% +another scan + + + align:start position:0% +another scan +okay so here's a little um animation + + align:start position:0% +okay so here's a little um animation + + + align:start position:0% +okay so here's a little um animation +which shows this happening on this + + align:start position:0% +which shows this happening on this + + + align:start position:0% +which shows this happening on this +diagram so here is + + align:start position:0% +diagram so here is + + + align:start position:0% +diagram so here is +the very first stage where you're + + align:start position:0% +the very first stage where you're + + + align:start position:0% +the very first stage where you're +scanning across making sure things are + + align:start position:0% +scanning across making sure things are + + + align:start position:0% +scanning across making sure things are +in the right order + + align:start position:0% +in the right order + + + align:start position:0% +in the right order +um didn't have to write on the tape and + + align:start position:0% +um didn't have to write on the tape and + + + align:start position:0% +um didn't have to write on the tape and +now you're gonna + + align:start position:0% +now you're gonna + + + align:start position:0% +now you're gonna +reset the the head back to the beginning + + align:start position:0% + + + + align:start position:0% + +this is by the way not the most + + align:start position:0% +this is by the way not the most + + + align:start position:0% +this is by the way not the most +efficient procedure for doing this um + + align:start position:0% +efficient procedure for doing this um + + + align:start position:0% +efficient procedure for doing this um +so um + + align:start position:0% + + + + align:start position:0% + +now that now we're going to do a scan + + align:start position:0% +now that now we're going to do a scan + + + align:start position:0% +now that now we're going to do a scan +crossing off a single a a single b and a + + align:start position:0% +crossing off a single a a single b and a + + + align:start position:0% +crossing off a single a a single b and a +single c + + align:start position:0% +single c + + + align:start position:0% +single c +so here i'm going to show that here + + align:start position:0% +so here i'm going to show that here + + + align:start position:0% +so here i'm going to show that here +single a single b single c + + align:start position:0% +single a single b single c + + + align:start position:0% +single a single b single c +and now as soon as you've crossed out + + align:start position:0% +and now as soon as you've crossed out + + + align:start position:0% +and now as soon as you've crossed out +that last c we can return back to the + + align:start position:0% +that last c we can return back to the + + + align:start position:0% +that last c we can return back to the +beginning um + + align:start position:0% +beginning um + + + align:start position:0% +beginning um +so scan right cross + + align:start position:0% + + + + align:start position:0% + +uh so if all symbols remain so there are + + align:start position:0% +uh so if all symbols remain so there are + + + align:start position:0% +uh so if all symbols remain so there are +still symbols remaining of each type + + align:start position:0% +still symbols remaining of each type + + + align:start position:0% +still symbols remaining of each type +we're going to return to the left and + + align:start position:0% +we're going to return to the left and + + + align:start position:0% +we're going to return to the left and +repeat and repeat + + align:start position:0% + + + + align:start position:0% + +now we'll get another pass single a + + align:start position:0% +now we'll get another pass single a + + + align:start position:0% +now we'll get another pass single a +single b single c get crossed off + + align:start position:0% +single b single c get crossed off + + + align:start position:0% +single b single c get crossed off +we haven't crossed them all off yet + + align:start position:0% +we haven't crossed them all off yet + + + align:start position:0% +we haven't crossed them all off yet +no there's + + align:start position:0% +no there's + + + align:start position:0% +no there's +of each type there's still our remaining + + align:start position:0% +of each type there's still our remaining + + + align:start position:0% +of each type there's still our remaining +ones so again we return back to the + + align:start position:0% +ones so again we return back to the + + + align:start position:0% +ones so again we return back to the +beginning now we have a last pass + + align:start position:0% +beginning now we have a last pass + + + align:start position:0% +beginning now we have a last pass +crossover the last a the last be the + + align:start position:0% +crossover the last a the last be the + + + align:start position:0% +crossover the last a the last be the +last c the last one of each type was + + align:start position:0% +last c the last one of each type was + + + align:start position:0% +last c the last one of each type was +crossed off so now we know we can accept + + align:start position:0% +crossed off so now we know we can accept + + + align:start position:0% +crossed off so now we know we can accept +because the original string was in the + + align:start position:0% +because the original string was in the + + + align:start position:0% +because the original string was in the +language + + align:start position:0% +language + + + align:start position:0% +language +okay so that's + + align:start position:0% +okay so that's + + + align:start position:0% +okay so that's +uh to give you at least some idea um + + align:start position:0% +uh to give you at least some idea um + + + align:start position:0% +uh to give you at least some idea um +that how the turing machine can operate + + align:start position:0% +that how the turing machine can operate + + + align:start position:0% +that how the turing machine can operate +you know more like the way you would + + align:start position:0% +you know more like the way you would + + + align:start position:0% +you know more like the way you would +think of a computer operating you know + + align:start position:0% +think of a computer operating you know + + + align:start position:0% +think of a computer operating you know +maybe it's very primitive you know you + + align:start position:0% +maybe it's very primitive you know you + + + align:start position:0% +maybe it's very primitive you know you +you could imagine counting also and the + + align:start position:0% +you could imagine counting also and the + + + align:start position:0% +you could imagine counting also and the +termination can count as well but this + + align:start position:0% +termination can count as well but this + + + align:start position:0% +termination can count as well but this +is the simplest uh descript uh procedure + + align:start position:0% +is the simplest uh descript uh procedure + + + align:start position:0% +is the simplest uh descript uh procedure +that i can just describe on um you know + + align:start position:0% +that i can just describe on um you know + + + align:start position:0% +that i can just describe on um you know +uh + + align:start position:0% + + + + align:start position:0% + +for you without getting making too + + align:start position:0% +for you without getting making too + + + align:start position:0% +for you without getting making too +complicated um + + align:start position:0% +complicated um + + + align:start position:0% +complicated um +okay so let's do a little checking on + + align:start position:0% +okay so let's do a little checking on + + + align:start position:0% +okay so let's do a little checking on +that um + + align:start position:0% +that um + + + align:start position:0% +that um +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +the way i'm describing this + + align:start position:0% +the way i'm describing this + + + align:start position:0% +the way i'm describing this +how do we go how do you think + + align:start position:0% +how do we go how do you think + + + align:start position:0% +how do we go how do you think +and you in a sense you don't quite know + + align:start position:0% +and you in a sense you don't quite know + + + align:start position:0% +and you in a sense you don't quite know +enough yet but um + + align:start position:0% +enough yet but um + + + align:start position:0% +enough yet but um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +uh how do you think we're going to get + + align:start position:0% +uh how do you think we're going to get + + + align:start position:0% +uh how do you think we're going to get +this effect + + align:start position:0% +this effect + + + align:start position:0% +this effect +of crossing off with the turing machine + + align:start position:0% +of crossing off with the turing machine + + + align:start position:0% +of crossing off with the turing machine +um are we going to get that by + + align:start position:0% +um are we going to get that by + + + align:start position:0% +um are we going to get that by +changing the model and adding that + + align:start position:0% +changing the model and adding that + + + align:start position:0% +changing the model and adding that +ability to cross off to the model + + align:start position:0% +ability to cross off to the model + + + align:start position:0% +ability to cross off to the model +um are we going to use a tape alphabet + + align:start position:0% +um are we going to use a tape alphabet + + + align:start position:0% +um are we going to use a tape alphabet +that includes those crossed off symbols + + align:start position:0% +that includes those crossed off symbols + + + align:start position:0% +that includes those crossed off symbols +among them + + align:start position:0% +among them + + + align:start position:0% +among them +or um we'll just assume that all turing + + align:start position:0% +or um we'll just assume that all turing + + + align:start position:0% +or um we'll just assume that all turing +machines come with the eraser and they + + align:start position:0% +machines come with the eraser and they + + + align:start position:0% +machines come with the eraser and they +can always cross our stuff + + align:start position:0% +can always cross our stuff + + + align:start position:0% +can always cross our stuff +um so what do you think is the + + align:start position:0% +um so what do you think is the + + + align:start position:0% +um so what do you think is the +nice way sort of mathematically to + + align:start position:0% +nice way sort of mathematically to + + + align:start position:0% +nice way sort of mathematically to +describe + + align:start position:0% +describe + + + align:start position:0% +describe +this + + align:start position:0% + + + + align:start position:0% + +this ability to cross things off + + align:start position:0% + + + + align:start position:0% + +yeah again again most of your again i + + align:start position:0% +yeah again again most of your again i + + + align:start position:0% +yeah again again most of your again i +think are getting this um + + align:start position:0% +think are getting this um + + + align:start position:0% +think are getting this um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so + + align:start position:0% + + + + align:start position:0% + +like 10 laggards here so + + align:start position:0% +like 10 laggards here so + + + align:start position:0% +like 10 laggards here so +please wrap it up um so we can + + align:start position:0% +please wrap it up um so we can + + + align:start position:0% +please wrap it up um so we can +close the poll + + align:start position:0% +close the poll + + + align:start position:0% +close the poll +uh + + align:start position:0% +uh + + + align:start position:0% +uh +five seconds to go + + align:start position:0% +five seconds to go + + + align:start position:0% +five seconds to go +um + + align:start position:0% +um + + + align:start position:0% +um +okay + + align:start position:0% +okay + + + align:start position:0% +okay +polling ending get your last last call + + align:start position:0% +polling ending get your last last call + + + align:start position:0% +polling ending get your last last call +uh + + align:start position:0% +uh + + + align:start position:0% +uh +all right + + align:start position:0% +all right + + + align:start position:0% +all right +share the results + + align:start position:0% +share the results + + + align:start position:0% +share the results +so most of you + + align:start position:0% +so most of you + + + align:start position:0% +so most of you +uh got that right + + align:start position:0% +uh got that right + + + align:start position:0% +uh got that right +all turn machines come with an eraser i + + align:start position:0% +all turn machines come with an eraser i + + + align:start position:0% +all turn machines come with an eraser i +don't know that was thrown in there as a + + align:start position:0% +don't know that was thrown in there as a + + + align:start position:0% +don't know that was thrown in there as a +joke but it got came in second so i + + align:start position:0% +joke but it got came in second so i + + + align:start position:0% +joke but it got came in second so i +don't feel bad if you got it but that's + + align:start position:0% +don't feel bad if you got it but that's + + + align:start position:0% +don't feel bad if you got it but that's +not what i had in mind + + align:start position:0% +not what i had in mind + + + align:start position:0% +not what i had in mind +um the the way the turing machine is + + align:start position:0% +um the the way the turing machine is + + + align:start position:0% +um the the way the turing machine is +going to be riding on the tape is to + + align:start position:0% +going to be riding on the tape is to + + + align:start position:0% +going to be riding on the tape is to +write a crossed off symbol uh instead of + + align:start position:0% +write a crossed off symbol uh instead of + + + align:start position:0% +write a crossed off symbol uh instead of +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +the symbol that was originally there so + + align:start position:0% +the symbol that was originally there so + + + align:start position:0% +the symbol that was originally there so +we're going to add these new crosstalk + + align:start position:0% +we're going to add these new crosstalk + + + align:start position:0% +we're going to add these new crosstalk +symbols and that's going to be a common + + align:start position:0% +symbols and that's going to be a common + + + align:start position:0% +symbols and that's going to be a common +thing for us to do + + align:start position:0% +thing for us to do + + + align:start position:0% +thing for us to do +in um you know when we design turing + + align:start position:0% +in um you know when we design turing + + + align:start position:0% +in um you know when we design turing +machines we're not going to get down to + + align:start position:0% +machines we're not going to get down to + + + align:start position:0% +machines we're not going to get down to +the implementation level for very long + + align:start position:0% +the implementation level for very long + + + align:start position:0% +the implementation level for very long +we're going to very quickly shift to a + + align:start position:0% +we're going to very quickly shift to a + + + align:start position:0% +we're going to very quickly shift to a +higher level of discussion about the + + align:start position:0% +higher level of discussion about the + + + align:start position:0% +higher level of discussion about the +machines but anyway that's how you would + + align:start position:0% +machines but anyway that's how you would + + + align:start position:0% +machines but anyway that's how you would +do it if you were going to actually + + align:start position:0% +do it if you were going to actually + + + align:start position:0% +do it if you were going to actually +build a machine + + align:start position:0% +build a machine + + + align:start position:0% +build a machine +okay so um + + align:start position:0% +okay so um + + + align:start position:0% +okay so um +let us then look at the formal + + align:start position:0% +let us then look at the formal + + + align:start position:0% +let us then look at the formal +definition of the cursing and maybe i + + align:start position:0% +definition of the cursing and maybe i + + + align:start position:0% +definition of the cursing and maybe i +should have done that checking after the + + align:start position:0% +should have done that checking after the + + + align:start position:0% +should have done that checking after the +formal definition that might have been + + align:start position:0% +formal definition that might have been + + + align:start position:0% +formal definition that might have been +clear but oh well + + align:start position:0% +clear but oh well + + + align:start position:0% +clear but oh well +uh + + align:start position:0% +uh + + + align:start position:0% +uh +okay here's the formal definition this + + align:start position:0% +okay here's the formal definition this + + + align:start position:0% +okay here's the formal definition this +time a turing machine is a seven + + align:start position:0% +time a turing machine is a seven + + + align:start position:0% +time a turing machine is a seven +tuple um + + align:start position:0% +tuple um + + + align:start position:0% +tuple um +and + + align:start position:0% +and + + + align:start position:0% +and +there is a + + align:start position:0% +there is a + + + align:start position:0% +there is a +uh + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +now here + + align:start position:0% +now here + + + align:start position:0% +now here +uh we have sigma which is the input + + align:start position:0% +uh we have sigma which is the input + + + align:start position:0% +uh we have sigma which is the input +alphabet gamma is the tape alphabet so + + align:start position:0% +alphabet gamma is the tape alphabet so + + + align:start position:0% +alphabet gamma is the tape alphabet so +now you're it's sort of a little bit + + align:start position:0% +now you're it's sort of a little bit + + + align:start position:0% +now you're it's sort of a little bit +analogous to the stack from before where + + align:start position:0% +analogous to the stack from before where + + + align:start position:0% +analogous to the stack from before where +gamma was the stack alphabet but these + + align:start position:0% +gamma was the stack alphabet but these + + + align:start position:0% +gamma was the stack alphabet but these +are the symbols that you're allowed to + + align:start position:0% +are the symbols that you're allowed to + + + align:start position:0% +are the symbols that you're allowed to +write on the tape um or that are allowed + + align:start position:0% +write on the tape um or that are allowed + + + align:start position:0% +write on the tape um or that are allowed +to be on the tape um + + align:start position:0% +to be on the tape um + + + align:start position:0% +to be on the tape um +so uh obviously all of the input symbols + + align:start position:0% +so uh obviously all of the input symbols + + + align:start position:0% +so uh obviously all of the input symbols +are among the uh tape uh symbols + + align:start position:0% +are among the uh tape uh symbols + + + align:start position:0% +are among the uh tape uh symbols +because they can appear on the tape so + + align:start position:0% +because they can appear on the tape so + + + align:start position:0% +because they can appear on the tape so +you have sigma + + align:start position:0% +you have sigma + + + align:start position:0% +you have sigma +is a subset of gamma um + + align:start position:0% +is a subset of gamma um + + + align:start position:0% +is a subset of gamma um +one thing i didn't mention here is that + + align:start position:0% +one thing i didn't mention here is that + + + align:start position:0% +one thing i didn't mention here is that +the input alphabet + + align:start position:0% +the input alphabet + + + align:start position:0% +the input alphabet +we don't allow the blank symbol to be uh + + align:start position:0% +we don't allow the blank symbol to be uh + + + align:start position:0% +we don't allow the blank symbol to be uh +in the input alphabet so that + + align:start position:0% +in the input alphabet so that + + + align:start position:0% +in the input alphabet so that +you can actually use the blank symbol as + + align:start position:0% +you can actually use the blank symbol as + + + align:start position:0% +you can actually use the blank symbol as +a delimiter for the end of the input + + align:start position:0% + + + + align:start position:0% + +a marker for the end of the input um so + + align:start position:0% +a marker for the end of the input um so + + + align:start position:0% +a marker for the end of the input um so +uh in fact and blank symbol is always + + align:start position:0% +uh in fact and blank symbol is always + + + align:start position:0% +uh in fact and blank symbol is always +going to be in the tape alphabet uh so + + align:start position:0% +going to be in the tape alphabet uh so + + + align:start position:0% +going to be in the tape alphabet uh so +we have um + + align:start position:0% +we have um + + + align:start position:0% +we have um +you know + + align:start position:0% +you know + + + align:start position:0% +you know +the this is actually always going to be + + align:start position:0% +the this is actually always going to be + + + align:start position:0% +the this is actually always going to be +a proper subset uh because of the blank + + align:start position:0% +a proper subset uh because of the blank + + + align:start position:0% +a proper subset uh because of the blank +symbol um what we're just allowing + + align:start position:0% +symbol um what we're just allowing + + + align:start position:0% +symbol um what we're just allowing +doesn't really matter we're allowing the + + align:start position:0% +doesn't really matter we're allowing the + + + align:start position:0% +doesn't really matter we're allowing the +tape alphabet to have + + align:start position:0% +tape alphabet to have + + + align:start position:0% +tape alphabet to have +other symbols for convenience so for + + align:start position:0% +other symbols for convenience so for + + + align:start position:0% +other symbols for convenience so for +example these crossed off symbols + + align:start position:0% +example these crossed off symbols + + + align:start position:0% +example these crossed off symbols +now let's look at what the transition + + align:start position:0% +now let's look at what the transition + + + align:start position:0% +now let's look at what the transition +function how that operates so the + + align:start position:0% +function how that operates so the + + + align:start position:0% +function how that operates so the +transition function remember tells how + + align:start position:0% +transition function remember tells how + + + align:start position:0% +transition function remember tells how +the machine is actually doing its + + align:start position:0% +the machine is actually doing its + + + align:start position:0% +the machine is actually doing its +computation + + align:start position:0% +computation + + + align:start position:0% +computation +and it says that if you're in a certain + + align:start position:0% +and it says that if you're in a certain + + + align:start position:0% +and it says that if you're in a certain +state and the head is looking at a + + align:start position:0% +state and the head is looking at a + + + align:start position:0% +state and the head is looking at a +certain tape symbol + + align:start position:0% +certain tape symbol + + + align:start position:0% +certain tape symbol +um + + align:start position:0% +um + + + align:start position:0% +um +then you can go to a new state you write + + align:start position:0% +then you can go to a new state you write + + + align:start position:0% +then you can go to a new state you write +a new symbol on the uh + + align:start position:0% +a new symbol on the uh + + + align:start position:0% +a new symbol on the uh +at that location on the tape and you can + + align:start position:0% +at that location on the tape and you can + + + align:start position:0% +at that location on the tape and you can +move the head either left or right + + align:start position:0% +move the head either left or right + + + align:start position:0% +move the head either left or right +so that's how we get the effect of the + + align:start position:0% +so that's how we get the effect of the + + + align:start position:0% +so that's how we get the effect of the +head being able to be bi-directional + + align:start position:0% +head being able to be bi-directional + + + align:start position:0% +head being able to be bi-directional +and here's the writing on the tape + + align:start position:0% +and here's the writing on the tape + + + align:start position:0% +and here's the writing on the tape +comes up right here so + + align:start position:0% +comes up right here so + + + align:start position:0% +comes up right here so +you know just an example here we says if + + align:start position:0% +you know just an example here we says if + + + align:start position:0% +you know just an example here we says if +we're in state q and the head is looking + + align:start position:0% +we're in state q and the head is looking + + + align:start position:0% +we're in state q and the head is looking +at an a currently on the tape then we + + align:start position:0% +at an a currently on the tape then we + + + align:start position:0% +at an a currently on the tape then we +can move to state r we change it a to a + + align:start position:0% +can move to state r we change it a to a + + + align:start position:0% +can move to state r we change it a to a +b and we move the head right once one + + align:start position:0% +b and we move the head right once one + + + align:start position:0% +b and we move the head right once one +square + + align:start position:0% +square + + + align:start position:0% +square +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh now here this is important + + align:start position:0% + + + + align:start position:0% + +to + + align:start position:0% +to + + + align:start position:0% +to +on when you're giving a certain input + + align:start position:0% +on when you're giving a certain input + + + align:start position:0% +on when you're giving a certain input +here to the turing machine it may gr + + align:start position:0% +here to the turing machine it may gr + + + align:start position:0% +here to the turing machine it may gr +compute around for a while moving its + + align:start position:0% +compute around for a while moving its + + + align:start position:0% +compute around for a while moving its +head back and forth as we were showing + + align:start position:0% +head back and forth as we were showing + + + align:start position:0% +head back and forth as we were showing +and it may eventually halt by either + + align:start position:0% +and it may eventually halt by either + + + align:start position:0% +and it may eventually halt by either +entering the q accept state or the q + + align:start position:0% +entering the q accept state or the q + + + align:start position:0% +entering the q accept state or the q +reject state which i didn't + + align:start position:0% +reject state which i didn't + + + align:start position:0% +reject state which i didn't +uh bring out here but that's important + + align:start position:0% +uh bring out here but that's important + + + align:start position:0% +uh bring out here but that's important +these are the accepting rejecting + + align:start position:0% +these are the accepting rejecting + + + align:start position:0% +these are the accepting rejecting +special states of the machine um or the + + align:start position:0% +special states of the machine um or the + + + align:start position:0% +special states of the machine um or the +machine may never enter one of those it + + align:start position:0% +machine may never enter one of those it + + + align:start position:0% +machine may never enter one of those it +may just go on and on and on and never + + align:start position:0% +may just go on and on and on and never + + + align:start position:0% +may just go on and on and on and never +halt + + align:start position:0% +halt + + + align:start position:0% +halt +we call that looping + + align:start position:0% +we call that looping + + + align:start position:0% +we call that looping +a little bit of a misnomer because it's + + align:start position:0% +a little bit of a misnomer because it's + + + align:start position:0% +a little bit of a misnomer because it's +the looping implies some sort of a + + align:start position:0% +the looping implies some sort of a + + + align:start position:0% +the looping implies some sort of a +repetition for us looping just means not + + align:start position:0% +repetition for us looping just means not + + + align:start position:0% +repetition for us looping just means not +holding + + align:start position:0% +holding + + + align:start position:0% +holding +um + + align:start position:0% +um + + + align:start position:0% +um +and um + + align:start position:0% +and um + + + align:start position:0% +and um +so therefore m has three possible + + align:start position:0% +so therefore m has three possible + + + align:start position:0% +so therefore m has three possible +outcomes for each um input + + align:start position:0% +outcomes for each um input + + + align:start position:0% +outcomes for each um input +w it might accept w + + align:start position:0% +w it might accept w + + + align:start position:0% +w it might accept w +by uh entering uh the except state + + align:start position:0% +by uh entering uh the except state + + + align:start position:0% +by uh entering uh the except state +it could reject w by entering the reject + + align:start position:0% +it could reject w by entering the reject + + + align:start position:0% +it could reject w by entering the reject +state which means it's going to reject + + align:start position:0% +state which means it's going to reject + + + align:start position:0% +state which means it's going to reject +it by holding + + align:start position:0% +it by holding + + + align:start position:0% +it by holding +or we also say we can reject by looping + + align:start position:0% +or we also say we can reject by looping + + + align:start position:0% +or we also say we can reject by looping +you can reject the string by running + + align:start position:0% +you can reject the string by running + + + align:start position:0% +you can reject the string by running +forever + + align:start position:0% +forever + + + align:start position:0% +forever +um + + align:start position:0% +um + + + align:start position:0% +um +okay that's just the terminology that's + + align:start position:0% +okay that's just the terminology that's + + + align:start position:0% +okay that's just the terminology that's +common in the subject so you either + + align:start position:0% +common in the subject so you either + + + align:start position:0% +common in the subject so you either +accept it um by halting and accepting or + + align:start position:0% +accept it um by halting and accepting or + + + align:start position:0% +accept it um by halting and accepting or +rejecting it by either holding and + + align:start position:0% +rejecting it by either holding and + + + align:start position:0% +rejecting it by either holding and +rejecting or by just going forever + + align:start position:0% +rejecting or by just going forever + + + align:start position:0% +rejecting or by just going forever +that's also considered to be rejecting + + align:start position:0% +that's also considered to be rejecting + + + align:start position:0% +that's also considered to be rejecting +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +sort of rejecting the instance by + + align:start position:0% +sort of rejecting the instance by + + + align:start position:0% +sort of rejecting the instance by +default if you never actually have + + align:start position:0% +default if you never actually have + + + align:start position:0% +default if you never actually have +accepted it then it's going to be + + align:start position:0% +accepted it then it's going to be + + + align:start position:0% +accepted it then it's going to be +rejected + + align:start position:0% + + + + align:start position:0% + +okay uh + + align:start position:0% +okay uh + + + align:start position:0% +okay uh +checking three here + + align:start position:0% +checking three here + + + align:start position:0% +checking three here +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so now um our last check in for the day + + align:start position:0% +so now um our last check in for the day + + + align:start position:0% +so now um our last check in for the day +we say this turing machine model is + + align:start position:0% +we say this turing machine model is + + + align:start position:0% +we say this turing machine model is +deterministic + + align:start position:0% +deterministic + + + align:start position:0% +deterministic +um + + align:start position:0% +um + + + align:start position:0% +um +i'm just saying that but if you look at + + align:start position:0% +i'm just saying that but if you look at + + + align:start position:0% +i'm just saying that but if you look at +the way we set it up + + align:start position:0% +the way we set it up + + + align:start position:0% +the way we set it up +if you've been following these formal + + align:start position:0% +if you've been following these formal + + + align:start position:0% +if you've been following these formal +definitions so far you would understand + + align:start position:0% +definitions so far you would understand + + + align:start position:0% +definitions so far you would understand +why it's deterministic so let's just as + + align:start position:0% +why it's deterministic so let's just as + + + align:start position:0% +why it's deterministic so let's just as +a way of checking that um how would we + + align:start position:0% +a way of checking that um how would we + + + align:start position:0% +a way of checking that um how would we +change this definition because we will + + align:start position:0% +change this definition because we will + + + align:start position:0% +change this definition because we will +look on at the next lecture at + + align:start position:0% +look on at the next lecture at + + + align:start position:0% +look on at the next lecture at +non-deterministic turing machines so a + + align:start position:0% +non-deterministic turing machines so a + + + align:start position:0% +non-deterministic turing machines so a +little bit of a lead into that how would + + align:start position:0% +little bit of a lead into that how would + + + align:start position:0% +little bit of a lead into that how would +we change + + align:start position:0% +we change + + + align:start position:0% +we change +this uh definition to make it a + + align:start position:0% +this uh definition to make it a + + + align:start position:0% +this uh definition to make it a +non-deterministic turing machine which + + align:start position:0% +non-deterministic turing machine which + + + align:start position:0% +non-deterministic turing machine which +of those three options would we use + + align:start position:0% +of those three options would we use + + + align:start position:0% +of those three options would we use +so here i'll launch that poll + + align:start position:0% +so here i'll launch that poll + + + align:start position:0% +so here i'll launch that poll +uh + + align:start position:0% + + + + align:start position:0% + +got about 10 people left let's give them + + align:start position:0% +got about 10 people left let's give them + + + align:start position:0% +got about 10 people left let's give them +another 10 seconds + + align:start position:0% +another 10 seconds + + + align:start position:0% +another 10 seconds +um + + align:start position:0% + + + + align:start position:0% + +okay i think that's everybody who's + + align:start position:0% +okay i think that's everybody who's + + + align:start position:0% +okay i think that's everybody who's +answered it from before + + align:start position:0% +answered it from before + + + align:start position:0% +answered it from before +um + + align:start position:0% +um + + + align:start position:0% +um +here there is so here + + align:start position:0% +here there is so here + + + align:start position:0% +here there is so here +i think you pretty much + + align:start position:0% +i think you pretty much + + + align:start position:0% +i think you pretty much +almost all of you got the right idea uh + + align:start position:0% +almost all of you got the right idea uh + + + align:start position:0% +almost all of you got the right idea uh +it is b in fact uh because when we have + + align:start position:0% +it is b in fact uh because when we have + + + align:start position:0% +it is b in fact uh because when we have +the power set symbol here that means + + align:start position:0% +the power set symbol here that means + + + align:start position:0% +the power set symbol here that means +there might be several there's a subset + + align:start position:0% +there might be several there's a subset + + + align:start position:0% +there might be several there's a subset +of possibilities so that indicates + + align:start position:0% +of possibilities so that indicates + + + align:start position:0% +of possibilities so that indicates +several different ways to go + + align:start position:0% +several different ways to go + + + align:start position:0% +several different ways to go +um + + align:start position:0% +um + + + align:start position:0% +um +uh and that's what the that's the + + align:start position:0% +uh and that's what the that's the + + + align:start position:0% +uh and that's what the that's the +essence of non-determinism + + align:start position:0% +essence of non-determinism + + + align:start position:0% +essence of non-determinism +okay so uh i think we're + + align:start position:0% +okay so uh i think we're + + + align:start position:0% +okay so uh i think we're +uh + + align:start position:0% +uh + + + align:start position:0% +uh +whoops + + align:start position:0% +whoops + + + align:start position:0% +whoops +um + + align:start position:0% +um + + + align:start position:0% +um +okay + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so look + + align:start position:0% +so look + + + align:start position:0% +so look +this is also kind of setting us up for + + align:start position:0% +this is also kind of setting us up for + + + align:start position:0% +this is also kind of setting us up for +next lecture + + align:start position:0% +next lecture + + + align:start position:0% +next lecture +and where we're going to be going with + + align:start position:0% +and where we're going to be going with + + + align:start position:0% +and where we're going to be going with +this um so these are uh + + align:start position:0% +this um so these are uh + + + align:start position:0% +this um so these are uh +basically two in example two or three + + align:start position:0% +basically two in example two or three + + + align:start position:0% +basically two in example two or three +important definitions here um + + align:start position:0% +important definitions here um + + + align:start position:0% +important definitions here um +one is um + + align:start position:0% +one is um + + + align:start position:0% +one is um +we have we talked about the regular + + align:start position:0% +we have we talked about the regular + + + align:start position:0% +we have we talked about the regular +languages + + align:start position:0% +languages + + + align:start position:0% +languages +from fine automata we talked about the + + align:start position:0% +from fine automata we talked about the + + + align:start position:0% +from fine automata we talked about the +context free languages from the grammars + + align:start position:0% +context free languages from the grammars + + + align:start position:0% +context free languages from the grammars +and the push down automata what are the + + align:start position:0% +and the push down automata what are the + + + align:start position:0% +and the push down automata what are the +languages of that the touring machines + + align:start position:0% +languages of that the touring machines + + + align:start position:0% +languages of that the touring machines +can do + + align:start position:0% +can do + + + align:start position:0% +can do +those are called in this course anyway + + align:start position:0% +those are called in this course anyway + + + align:start position:0% +those are called in this course anyway +turing recognizable languages is very + + align:start position:0% +turing recognizable languages is very + + + align:start position:0% +turing recognizable languages is very +orti recognizable um those are the lang + + align:start position:0% +orti recognizable um those are the lang + + + align:start position:0% +orti recognizable um those are the lang +those are the languages that the turing + + align:start position:0% +those are the languages that the turing + + + align:start position:0% +those are the languages that the turing +machine can recognize + + align:start position:0% +machine can recognize + + + align:start position:0% +machine can recognize +and so what + + align:start position:0% +and so what + + + align:start position:0% +and so what +just to make sure we were on the same + + align:start position:0% +just to make sure we were on the same + + + align:start position:0% +just to make sure we were on the same +page on this + + align:start position:0% +page on this + + + align:start position:0% +page on this +the language of the machine is the + + align:start position:0% +the language of the machine is the + + + align:start position:0% +the language of the machine is the +collection of strings that the machine + + align:start position:0% +collection of strings that the machine + + + align:start position:0% +collection of strings that the machine +accepts + + align:start position:0% +accepts + + + align:start position:0% +accepts +so the things that are not in the + + align:start position:0% +so the things that are not in the + + + align:start position:0% +so the things that are not in the +language are the things that are + + align:start position:0% +language are the things that are + + + align:start position:0% +language are the things that are +rejected either by looping or by halting + + align:start position:0% +rejected either by looping or by halting + + + align:start position:0% +rejected either by looping or by halting +and projecting + + align:start position:0% +and projecting + + + align:start position:0% +and projecting +so all the only the ones that are + + align:start position:0% +so all the only the ones that are + + + align:start position:0% +so all the only the ones that are +accepted are the light is the language + + align:start position:0% +accepted are the light is the language + + + align:start position:0% +accepted are the light is the language +every machine has just a single language + + align:start position:0% +every machine has just a single language + + + align:start position:0% +every machine has just a single language +it's a language of all strings that that + + align:start position:0% +it's a language of all strings that that + + + align:start position:0% +it's a language of all strings that that +machine accepts um + + align:start position:0% +machine accepts um + + + align:start position:0% +machine accepts um +and we'll say that m recognize that + + align:start position:0% +and we'll say that m recognize that + + + align:start position:0% +and we'll say that m recognize that +language if that language is + + align:start position:0% +language if that language is + + + align:start position:0% +language if that language is +a collection of such strings that are + + align:start position:0% +a collection of such strings that are + + + align:start position:0% +a collection of such strings that are +accepted + + align:start position:0% +accepted + + + align:start position:0% +accepted +and uh we will call that language a + + align:start position:0% +and uh we will call that language a + + + align:start position:0% +and uh we will call that language a +touring recognizable language + + align:start position:0% +touring recognizable language + + + align:start position:0% +touring recognizable language +okay if there's some turing machine that + + align:start position:0% +okay if there's some turing machine that + + + align:start position:0% +okay if there's some turing machine that +can recognize it + + align:start position:0% + + + + align:start position:0% + +um now uh + + align:start position:0% + + + + align:start position:0% + +this feature of being able to reject by + + align:start position:0% +this feature of being able to reject by + + + align:start position:0% +this feature of being able to reject by +running forever is a little bit weird + + align:start position:0% +running forever is a little bit weird + + + align:start position:0% +running forever is a little bit weird +perhaps um + + align:start position:0% +perhaps um + + + align:start position:0% +perhaps um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and + + align:start position:0% +and + + + align:start position:0% +and +uh for from the standpoint of + + align:start position:0% +uh for from the standpoint of + + + align:start position:0% +uh for from the standpoint of +practicality + + align:start position:0% +practicality + + + align:start position:0% +practicality +uh it's more convenient if the machine + + align:start position:0% +uh it's more convenient if the machine + + + align:start position:0% +uh it's more convenient if the machine +always makes a decision to accept or + + align:start position:0% +always makes a decision to accept or + + + align:start position:0% +always makes a decision to accept or +reject in a finite time + + align:start position:0% +reject in a finite time + + + align:start position:0% +reject in a finite time +and doesn't just reject by going forever + + align:start position:0% +and doesn't just reject by going forever + + + align:start position:0% +and doesn't just reject by going forever +and so we're going to + + align:start position:0% +and so we're going to + + + align:start position:0% +and so we're going to +bring out a special class of turing + + align:start position:0% +bring out a special class of turing + + + align:start position:0% +bring out a special class of turing +machines that have that feature + + align:start position:0% +machines that have that feature + + + align:start position:0% +machines that have that feature +that they always halt they always go to + + align:start position:0% +that they always halt they always go to + + + align:start position:0% +that they always halt they always go to +the holding states by the way maybe + + align:start position:0% +the holding states by the way maybe + + + align:start position:0% +the holding states by the way maybe +didn't say this explicitly are the q + + align:start position:0% +didn't say this explicitly are the q + + + align:start position:0% +didn't say this explicitly are the q +accept and the q eject states the accept + + align:start position:0% +accept and the q eject states the accept + + + align:start position:0% +accept and the q eject states the accept +and reject states are the holding states + + align:start position:0% +and reject states are the holding states + + + align:start position:0% +and reject states are the holding states +so the machine halts that means it ends + + align:start position:0% +so the machine halts that means it ends + + + align:start position:0% +so the machine halts that means it ends +up in one of those two so it has made a + + align:start position:0% +up in one of those two so it has made a + + + align:start position:0% +up in one of those two so it has made a +decision of accepting or rejecting in in + + align:start position:0% +decision of accepting or rejecting in in + + + align:start position:0% +decision of accepting or rejecting in in +by the at the point in which it has + + align:start position:0% +by the at the point in which it has + + + align:start position:0% +by the at the point in which it has +halted + + align:start position:0% +halted + + + align:start position:0% +halted +um so we'll say a machine is a decider + + align:start position:0% +um so we'll say a machine is a decider + + + align:start position:0% +um so we'll say a machine is a decider +if it always holds on every input + + align:start position:0% +if it always holds on every input + + + align:start position:0% +if it always holds on every input +uh so for every w feed in the machine is + + align:start position:0% +uh so for every w feed in the machine is + + + align:start position:0% +uh so for every w feed in the machine is +eventually going to come to a q accept + + align:start position:0% +eventually going to come to a q accept + + + align:start position:0% +eventually going to come to a q accept +or to reject we call such a machine a + + align:start position:0% +or to reject we call such a machine a + + + align:start position:0% +or to reject we call such a machine a +decider + + align:start position:0% +decider + + + align:start position:0% +decider +and now we're going to say a language + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +is that so it will say that the machine + + align:start position:0% +is that so it will say that the machine + + + align:start position:0% +is that so it will say that the machine +decides a language + + align:start position:0% +decides a language + + + align:start position:0% +decides a language +if + + align:start position:0% +if + + + align:start position:0% +if +if it's the language of the machines of + + align:start position:0% +if it's the language of the machines of + + + align:start position:0% +if it's the language of the machines of +the collection of accepted strings uh + + align:start position:0% +the collection of accepted strings uh + + + align:start position:0% +the collection of accepted strings uh +and the machine is a decider so we'll + + align:start position:0% +and the machine is a decider so we'll + + + align:start position:0% +and the machine is a decider so we'll +say that instead of just recognizing the + + align:start position:0% +say that instead of just recognizing the + + + align:start position:0% +say that instead of just recognizing the +language we'll say that it decides the + + align:start position:0% +language we'll say that it decides the + + + align:start position:0% +language we'll say that it decides the +language + + align:start position:0% +language + + + align:start position:0% +language +um + + align:start position:0% +um + + + align:start position:0% +um +and a turing decidable language is a + + align:start position:0% +and a turing decidable language is a + + + align:start position:0% +and a turing decidable language is a +language um + + align:start position:0% +language um + + + align:start position:0% +language um +that the machine + + align:start position:0% +that the machine + + + align:start position:0% +that the machine +of all strings the machine accepts uh + + align:start position:0% +of all strings the machine accepts uh + + + align:start position:0% +of all strings the machine accepts uh +for some turing machine which is is a + + align:start position:0% +for some turing machine which is is a + + + align:start position:0% +for some turing machine which is is a +decider which is a touring machine that + + align:start position:0% +decider which is a touring machine that + + + align:start position:0% +decider which is a touring machine that +always holds + + align:start position:0% +always holds + + + align:start position:0% +always holds +so if a turing machine may sometimes + + align:start position:0% +so if a turing machine may sometimes + + + align:start position:0% +so if a turing machine may sometimes +reject by looping then it's only + + align:start position:0% +reject by looping then it's only + + + align:start position:0% +reject by looping then it's only +recognizing this language if the turing + + align:start position:0% +recognizing this language if the turing + + + align:start position:0% +recognizing this language if the turing +machine is always holding so it's always + + align:start position:0% +machine is always holding so it's always + + + align:start position:0% +machine is always holding so it's always +rejecting by explicitly coming to a + + align:start position:0% +rejecting by explicitly coming to a + + + align:start position:0% +rejecting by explicitly coming to a +reject state and halting then we'll say + + align:start position:0% +reject state and halting then we'll say + + + align:start position:0% +reject state and halting then we'll say +it's actually deciding the language + + align:start position:0% +it's actually deciding the language + + + align:start position:0% +it's actually deciding the language +so in a sense that's better and we're + + align:start position:0% +so in a sense that's better and we're + + + align:start position:0% +so in a sense that's better and we're +going to distinguish between those two + + align:start position:0% +going to distinguish between those two + + + align:start position:0% +going to distinguish between those two +because + + align:start position:0% +because + + + align:start position:0% +because +um + + align:start position:0% +um + + + align:start position:0% +um +they're not the same + + align:start position:0% +they're not the same + + + align:start position:0% +they're not the same +uh there are some languages which can be + + align:start position:0% +uh there are some languages which can be + + + align:start position:0% +uh there are some languages which can be +recognized but not decided + + align:start position:0% +recognized but not decided + + + align:start position:0% +recognized but not decided +and so in fact we're going to get the + + align:start position:0% +and so in fact we're going to get the + + + align:start position:0% +and so in fact we're going to get the +following picture here + + align:start position:0% +following picture here + + + align:start position:0% +following picture here +the deteuring recognizable languages are + + align:start position:0% +the deteuring recognizable languages are + + + align:start position:0% +the deteuring recognizable languages are +a proper subset they include all this + + align:start position:0% +a proper subset they include all this + + + align:start position:0% +a proper subset they include all this +everything that's decidable certainly is + + align:start position:0% +everything that's decidable certainly is + + + align:start position:0% +everything that's decidable certainly is +going to be recognizable + + align:start position:0% +going to be recognizable + + + align:start position:0% +going to be recognizable +because um + + align:start position:0% +because um + + + align:start position:0% +because um +uh you know this being a decider is an + + align:start position:0% +uh you know this being a decider is an + + + align:start position:0% +uh you know this being a decider is an +additional restriction to impose + + align:start position:0% +additional restriction to impose + + + align:start position:0% +additional restriction to impose +additional requirement + + align:start position:0% +additional requirement + + + align:start position:0% +additional requirement +so everything that's decidable is going + + align:start position:0% +so everything that's decidable is going + + + align:start position:0% +so everything that's decidable is going +to be automatically recognizable but + + align:start position:0% +to be automatically recognizable but + + + align:start position:0% +to be automatically recognizable but +there are things which are recognizable + + align:start position:0% +there are things which are recognizable + + + align:start position:0% +there are things which are recognizable +but you're not decidable as we'll see + + align:start position:0% +but you're not decidable as we'll see + + + align:start position:0% +but you're not decidable as we'll see +um + + align:start position:0% +um + + + align:start position:0% +um +i'll actually give an example of that + + align:start position:0% +i'll actually give an example of that + + + align:start position:0% +i'll actually give an example of that +but not prove it next lecture + + align:start position:0% +but not prove it next lecture + + + align:start position:0% +but not prove it next lecture +and just for just to complete out this + + align:start position:0% +and just for just to complete out this + + + align:start position:0% +and just for just to complete out this +picture um + + align:start position:0% +picture um + + + align:start position:0% +picture um +i'm going to uh + + align:start position:0% +i'm going to uh + + + align:start position:0% +i'm going to uh +also point out we haven't proven this + + align:start position:0% +also point out we haven't proven this + + + align:start position:0% +also point out we haven't proven this +yet but uh we will prove it um that the + + align:start position:0% +yet but uh we will prove it um that the + + + align:start position:0% +yet but uh we will prove it um that the +decidable languages also include + + align:start position:0% +decidable languages also include + + + align:start position:0% +decidable languages also include +all the context-free languages which in + + align:start position:0% +all the context-free languages which in + + + align:start position:0% +all the context-free languages which in +turn include the regular languages as it + + align:start position:0% +turn include the regular languages as it + + + align:start position:0% +turn include the regular languages as it +was already seen so we haven't shown + + align:start position:0% +was already seen so we haven't shown + + + align:start position:0% +was already seen so we haven't shown +this inclusion yet but actually this is + + align:start position:0% +this inclusion yet but actually this is + + + align:start position:0% +this inclusion yet but actually this is +the picture we we get um so there's + + align:start position:0% +the picture we we get um so there's + + + align:start position:0% +the picture we we get um so there's +actually a hierarchy of containments + + align:start position:0% +actually a hierarchy of containments + + + align:start position:0% +actually a hierarchy of containments +here + + align:start position:0% +here + + + align:start position:0% +here +regular languages are + + align:start position:0% +regular languages are + + + align:start position:0% +regular languages are +a subset of the + + align:start position:0% +a subset of the + + + align:start position:0% +a subset of the +context-free languages which are in turn + + align:start position:0% +context-free languages which are in turn + + + align:start position:0% +context-free languages which are in turn +a subset of the decidable languages + + align:start position:0% +a subset of the decidable languages + + + align:start position:0% +a subset of the decidable languages +which are in turn are a subset of the + + align:start position:0% +which are in turn are a subset of the + + + align:start position:0% +which are in turn are a subset of the +recognizer turing recognizable languages + + align:start position:0% +recognizer turing recognizable languages + + + align:start position:0% +recognizer turing recognizable languages +um and so + + align:start position:0% +um and so + + + align:start position:0% +um and so +with that i think we're going to move to + + align:start position:0% +with that i think we're going to move to + + + align:start position:0% +with that i think we're going to move to +our little bit of a review of what we've + + align:start position:0% +our little bit of a review of what we've + + + align:start position:0% +our little bit of a review of what we've +done today + + align:start position:0% +done today + + + align:start position:0% +done today +so we proved that pumping lemma + + align:start position:0% +so we proved that pumping lemma + + + align:start position:0% +so we proved that pumping lemma +as a tool for showing that languages are + + align:start position:0% +as a tool for showing that languages are + + + align:start position:0% +as a tool for showing that languages are +not context-free languages + + align:start position:0% +not context-free languages + + + align:start position:0% +not context-free languages +we define turing machines which is going + + align:start position:0% +we define turing machines which is going + + + align:start position:0% +we define turing machines which is going +to be our model um + + align:start position:0% +to be our model um + + + align:start position:0% +to be our model um +that we're going to be focusing on for + + align:start position:0% +that we're going to be focusing on for + + + align:start position:0% +that we're going to be focusing on for +the rest of the term uh not forgetting + + align:start position:0% +the rest of the term uh not forgetting + + + align:start position:0% +the rest of the term uh not forgetting +the other models because they're going + + align:start position:0% +the other models because they're going + + + align:start position:0% +the other models because they're going +to be useful examples for us + + align:start position:0% +to be useful examples for us + + + align:start position:0% +to be useful examples for us +and we define touring deciders turing + + align:start position:0% +and we define touring deciders turing + + + align:start position:0% +and we define touring deciders turing +machine deciders that halt and all + + align:start position:0% +machine deciders that halt and all + + + align:start position:0% +machine deciders that halt and all +inputs + + align:start position:0% +inputs + + + align:start position:0% +inputs +okay so i think with that um we have + + align:start position:0% +okay so i think with that um we have + + + align:start position:0% +okay so i think with that um we have +come to the end of today's lecture + + align:start position:0% +come to the end of today's lecture + + + align:start position:0% +come to the end of today's lecture +um i will stick around a little bit and + + align:start position:0% +um i will stick around a little bit and + + + align:start position:0% +um i will stick around a little bit and +answer questions in the chat um i will + + align:start position:0% +answer questions in the chat um i will + + + align:start position:0% +answer questions in the chat um i will +try to share them with everybody um as + + align:start position:0% +try to share them with everybody um as + + + align:start position:0% +try to share them with everybody um as +i'm answering them so i'm not just + + align:start position:0% +i'm answering them so i'm not just + + + align:start position:0% +i'm answering them so i'm not just +talking to one person + + align:start position:0% + + + + align:start position:0% + +how was the concept of pride applied in + + align:start position:0% +how was the concept of pride applied in + + + align:start position:0% +how was the concept of pride applied in +so i'm getting one question about + + align:start position:0% +so i'm getting one question about + + + align:start position:0% +so i'm getting one question about +the practicality of all this uh bunches + + align:start position:0% +the practicality of all this uh bunches + + + align:start position:0% +the practicality of all this uh bunches +of questions are coming in + + align:start position:0% +of questions are coming in + + + align:start position:0% +of questions are coming in +um + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so look uh + + align:start position:0% +so look uh + + + align:start position:0% +so look uh +is this is this stuff all practical um + + align:start position:0% +is this is this stuff all practical um + + + align:start position:0% +is this is this stuff all practical um +uh i would say um uh yes and no um + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i i don't know which concept you have in + + align:start position:0% +i i don't know which concept you have in + + + align:start position:0% +i i don't know which concept you have in +mind we're going to introduce lots of + + align:start position:0% +mind we're going to introduce lots of + + + align:start position:0% +mind we're going to introduce lots of +concepts in this course and + + align:start position:0% +concepts in this course and + + + align:start position:0% +concepts in this course and +um uh the you know the concept of + + align:start position:0% +um uh the you know the concept of + + + align:start position:0% +um uh the you know the concept of +um + + align:start position:0% +um + + + align:start position:0% +um +uh of you know the fine art automata and + + align:start position:0% +uh of you know the fine art automata and + + + align:start position:0% +uh of you know the fine art automata and +the push down automata and context-free + + align:start position:0% +the push down automata and context-free + + + align:start position:0% +the push down automata and context-free +languages + + align:start position:0% +languages + + + align:start position:0% +languages +definitely used in other + + align:start position:0% +definitely used in other + + + align:start position:0% +definitely used in other +subjects in other fields in computer + + align:start position:0% +subjects in other fields in computer + + + align:start position:0% +subjects in other fields in computer +science and elsewhere these are very + + align:start position:0% +science and elsewhere these are very + + + align:start position:0% +science and elsewhere these are very +basic and fundamental notions + + align:start position:0% +basic and fundamental notions + + + align:start position:0% +basic and fundamental notions +um and so yes and turing machines well i + + align:start position:0% +um and so yes and turing machines well i + + + align:start position:0% +um and so yes and turing machines well i +mean that's a model of a general + + align:start position:0% +mean that's a model of a general + + + align:start position:0% +mean that's a model of a general +computer if you want to understand + + align:start position:0% +computer if you want to understand + + + align:start position:0% +computer if you want to understand +computation you're going to need to + + align:start position:0% +computation you're going to need to + + + align:start position:0% +computation you're going to need to +understand some model and a turing + + align:start position:0% +understand some model and a turing + + + align:start position:0% +understand some model and a turing +machine is a particularly simple model + + align:start position:0% +machine is a particularly simple model + + + align:start position:0% +machine is a particularly simple model +and that's why we use it as it turns out + + align:start position:0% +and that's why we use it as it turns out + + + align:start position:0% +and that's why we use it as it turns out +it doesn't really matter what model you + + align:start position:0% +it doesn't really matter what model you + + + align:start position:0% +it doesn't really matter what model you +use but we'll talk about that next + + align:start position:0% +use but we'll talk about that next + + + align:start position:0% +use but we'll talk about that next +next time but yeah i would say there's a + + align:start position:0% +next time but yeah i would say there's a + + + align:start position:0% +next time but yeah i would say there's a +lot of applied material in this course + + align:start position:0% +lot of applied material in this course + + + align:start position:0% +lot of applied material in this course +as time has shown + + align:start position:0% +as time has shown + + + align:start position:0% +as time has shown +whether it's + + align:start position:0% +whether it's + + + align:start position:0% +whether it's +led to things like public key + + align:start position:0% +led to things like public key + + + align:start position:0% +led to things like public key +cryptography which is + + align:start position:0% +cryptography which is + + + align:start position:0% +cryptography which is +used on the internet + + align:start position:0% +used on the internet + + + align:start position:0% +used on the internet +or you know understanding various + + align:start position:0% +or you know understanding various + + + align:start position:0% +or you know understanding various +algorithms + + align:start position:0% +algorithms + + + align:start position:0% +algorithms +i mean + + align:start position:0% +i mean + + + align:start position:0% +i mean +that's not the reason i study it i'd + + align:start position:0% +that's not the reason i study it i'd + + + align:start position:0% +that's not the reason i study it i'd +study it because i'm more of them coming + + align:start position:0% +study it because i'm more of them coming + + + align:start position:0% +study it because i'm more of them coming +at it from more of a mathematical + + align:start position:0% +at it from more of a mathematical + + + align:start position:0% +at it from more of a mathematical +perspective i just find the material + + align:start position:0% +perspective i just find the material + + + align:start position:0% +perspective i just find the material +very uh beautiful and interesting and + + align:start position:0% +very uh beautiful and interesting and + + + align:start position:0% +very uh beautiful and interesting and +challenging um but it does have + + align:start position:0% +challenging um but it does have + + + align:start position:0% +challenging um but it does have +applications um + + align:start position:0% +applications um + + + align:start position:0% +applications um +any other questions here i think i'm + + align:start position:0% +any other questions here i think i'm + + + align:start position:0% +any other questions here i think i'm +going to sign off then so get myself set + + align:start position:0% +going to sign off then so get myself set + + + align:start position:0% +going to sign off then so get myself set +up for my office hours which is in a + + align:start position:0% +up for my office hours which is in a + + + align:start position:0% +up for my office hours which is in a +different on a different zoom like + + align:start position:0% +different on a different zoom like + + + align:start position:0% +different on a different zoom like +okay so thank you everybody and see you + + align:start position:0% +okay so thank you everybody and see you + + + align:start position:0% +okay so thank you everybody and see you +uh on thursday bye \ No newline at end of file diff --git a/K-6HqJPLybc.txt b/K-6HqJPLybc.txt new file mode 100644 index 0000000000000000000000000000000000000000..86e92764b37047522ba0fe45c34c178cb33effa4 --- /dev/null +++ b/K-6HqJPLybc.txt @@ -0,0 +1,1347 @@ +align:start position:0% + +Episode + + align:start position:0% + + + + align:start position:0% + +two. All great ideas start out bad. + + align:start position:0% + + + + align:start position:0% + +All great ideas start out bad. Most look + + align:start position:0% +All great ideas start out bad. Most look + + + align:start position:0% +All great ideas start out bad. Most look +horrible at the start. And yet, this + + align:start position:0% +horrible at the start. And yet, this + + + align:start position:0% +horrible at the start. And yet, this +should come as a relief. That idea you + + align:start position:0% +should come as a relief. That idea you + + + align:start position:0% +should come as a relief. That idea you +had or heard this morning that everyone + + align:start position:0% +had or heard this morning that everyone + + + align:start position:0% +had or heard this morning that everyone +laughed at could be the start of + + align:start position:0% +laughed at could be the start of + + + align:start position:0% +laughed at could be the start of +something. That's right. The idea does + + align:start position:0% +something. That's right. The idea does + + + align:start position:0% +something. That's right. The idea does +not need to look disruptive or scalable + + align:start position:0% +not need to look disruptive or scalable + + + align:start position:0% +not need to look disruptive or scalable +or exponential or like a business yet. + + align:start position:0% +or exponential or like a business yet. + + + align:start position:0% +or exponential or like a business yet. +You can start with what you have. + + align:start position:0% +You can start with what you have. + + + align:start position:0% +You can start with what you have. +This is often difficult for people to + + align:start position:0% +This is often difficult for people to + + + align:start position:0% +This is often difficult for people to +accept. Most innovation stories are told + + align:start position:0% +accept. Most innovation stories are told + + + align:start position:0% +accept. Most innovation stories are told +in hindsight, which creates a cognitive + + align:start position:0% +in hindsight, which creates a cognitive + + + align:start position:0% +in hindsight, which creates a cognitive +bias. If you have read a lot of + + align:start position:0% +bias. If you have read a lot of + + + align:start position:0% +bias. If you have read a lot of +innovation stories, it may be hard to + + align:start position:0% +innovation stories, it may be hard to + + + align:start position:0% +innovation stories, it may be hard to +accept that the start of those great + + align:start position:0% +accept that the start of those great + + + align:start position:0% +accept that the start of those great +stories is a poor fit for the + + align:start position:0% +stories is a poor fit for the + + + align:start position:0% +stories is a poor fit for the +innovations they became. But success + + align:start position:0% +innovations they became. But success + + + align:start position:0% +innovations they became. But success +isn't hiding in the idea. It follows + + align:start position:0% +isn't hiding in the idea. It follows + + + align:start position:0% +isn't hiding in the idea. It follows +from what you do next. Here are some + + align:start position:0% +from what you do next. Here are some + + + align:start position:0% +from what you do next. Here are some +examples of bad ideas that graduated + + align:start position:0% +examples of bad ideas that graduated + + + align:start position:0% +examples of bad ideas that graduated +into becoming great innovation stories + + align:start position:0% +into becoming great innovation stories + + + align:start position:0% +into becoming great innovation stories +to tell. In 1878, Sir William Priest, + + align:start position:0% +to tell. In 1878, Sir William Priest, + + + align:start position:0% +to tell. In 1878, Sir William Priest, +who at the time was chief engineer of + + align:start position:0% +who at the time was chief engineer of + + + align:start position:0% +who at the time was chief engineer of +the British post office, mentioned that + + align:start position:0% +the British post office, mentioned that + + + align:start position:0% +the British post office, mentioned that +the lack of voice was causing Americans + + align:start position:0% +the lack of voice was causing Americans + + + align:start position:0% +the lack of voice was causing Americans +to adopt an idea that had no future. He + + align:start position:0% +to adopt an idea that had no future. He + + + align:start position:0% +to adopt an idea that had no future. He +was talking about the telephone. + + align:start position:0% +was talking about the telephone. + + + align:start position:0% +was talking about the telephone. +Around 1914, the Ford Motor Company + + align:start position:0% +Around 1914, the Ford Motor Company + + + align:start position:0% +Around 1914, the Ford Motor Company +increased worker wages manyifold above + + align:start position:0% +increased worker wages manyifold above + + + align:start position:0% +increased worker wages manyifold above +the minimum wage. Critics thought Henry + + align:start position:0% +the minimum wage. Critics thought Henry + + + align:start position:0% +the minimum wage. Critics thought Henry +Ford had gone insane. But the Ford Motor + + align:start position:0% +Ford had gone insane. But the Ford Motor + + + align:start position:0% +Ford had gone insane. But the Ford Motor +Company did not go bankrupt like critics + + align:start position:0% +Company did not go bankrupt like critics + + + align:start position:0% +Company did not go bankrupt like critics +expected. Instead, they initiated a + + align:start position:0% +expected. Instead, they initiated a + + + align:start position:0% +expected. Instead, they initiated a +trend in the auto industry that caused + + align:start position:0% +trend in the auto industry that caused + + + align:start position:0% +trend in the auto industry that caused +cars to become affordable. In the late + + align:start position:0% +cars to become affordable. In the late + + + align:start position:0% +cars to become affordable. In the late +1960s, in an interview to the New York + + align:start position:0% +1960s, in an interview to the New York + + + align:start position:0% +1960s, in an interview to the New York +Times, Dr. May, the inventor of the + + align:start position:0% +Times, Dr. May, the inventor of the + + + align:start position:0% +Times, Dr. May, the inventor of the +laser, spoke of it as a solution still + + align:start position:0% +laser, spoke of it as a solution still + + + align:start position:0% +laser, spoke of it as a solution still +seeking for a problem. Today, lasers are + + align:start position:0% +seeking for a problem. Today, lasers are + + + align:start position:0% +seeking for a problem. Today, lasers are +everywhere. + + align:start position:0% +everywhere. + + + align:start position:0% +everywhere. +At the turn of the 21st century, one of + + align:start position:0% +At the turn of the 21st century, one of + + + align:start position:0% +At the turn of the 21st century, one of +the companies from famed investor Vinad + + align:start position:0% +the companies from famed investor Vinad + + + align:start position:0% +the companies from famed investor Vinad +Kosla had a chance to acquire Google for + + align:start position:0% +Kosla had a chance to acquire Google for + + + align:start position:0% +Kosla had a chance to acquire Google for +about $750,000. + + align:start position:0% +about $750,000. + + + align:start position:0% +about $750,000. +They passed. They felt it was too + + align:start position:0% +They passed. They felt it was too + + + align:start position:0% +They passed. They felt it was too +expensive. After exiting PayPal, a young + + align:start position:0% +expensive. After exiting PayPal, a young + + + align:start position:0% +expensive. After exiting PayPal, a young +Elan Musk founded an out for profit + + align:start position:0% +Elan Musk founded an out for profit + + + align:start position:0% +Elan Musk founded an out for profit +called Mars Oasis to take a small + + align:start position:0% +called Mars Oasis to take a small + + + align:start position:0% +called Mars Oasis to take a small +greenhouse to Mars. He and his team + + align:start position:0% +greenhouse to Mars. He and his team + + + align:start position:0% +greenhouse to Mars. He and his team +tried to buy rockets from a group of + + align:start position:0% +tried to buy rockets from a group of + + + align:start position:0% +tried to buy rockets from a group of +Russians, but the Russians laughed at + + align:start position:0% +Russians, but the Russians laughed at + + + align:start position:0% +Russians, but the Russians laughed at +them. So instead, they set out to build + + align:start position:0% +them. So instead, they set out to build + + + align:start position:0% +them. So instead, they set out to build +rockets themselves and ended up founding + + align:start position:0% +rockets themselves and ended up founding + + + align:start position:0% +rockets themselves and ended up founding +SpaceX. + + align:start position:0% +SpaceX. + + + align:start position:0% +SpaceX. +In 2021, a new company called Colossal + + align:start position:0% +In 2021, a new company called Colossal + + + align:start position:0% +In 2021, a new company called Colossal +announced plans to bring back the woolly + + align:start position:0% +announced plans to bring back the woolly + + + align:start position:0% +announced plans to bring back the woolly +mammoth in an attempt to stop climate + + align:start position:0% +mammoth in an attempt to stop climate + + + align:start position:0% +mammoth in an attempt to stop climate +change. You can read about it in the New + + align:start position:0% +change. You can read about it in the New + + + align:start position:0% +change. You can read about it in the New +York Times. These examples cover about + + align:start position:0% +York Times. These examples cover about + + + align:start position:0% +York Times. These examples cover about +150 years worth of unlikely innovation + + align:start position:0% +150 years worth of unlikely innovation + + + align:start position:0% +150 years worth of unlikely innovation +stories across many domains. investment, + + align:start position:0% +stories across many domains. investment, + + + align:start position:0% +stories across many domains. investment, +industrial factories, new technologies, + + align:start position:0% +industrial factories, new technologies, + + + align:start position:0% +industrial factories, new technologies, +entrepreneurship, not for profits. Even + + align:start position:0% +entrepreneurship, not for profits. Even + + + align:start position:0% +entrepreneurship, not for profits. Even +in every case, an idea that seemed + + align:start position:0% +in every case, an idea that seemed + + + align:start position:0% +in every case, an idea that seemed +preposterous at the time it got started + + align:start position:0% +preposterous at the time it got started + + + align:start position:0% +preposterous at the time it got started +has ended up leading to something we now + + align:start position:0% +has ended up leading to something we now + + + align:start position:0% +has ended up leading to something we now +think of as an obvious innovation. Well, + + align:start position:0% +think of as an obvious innovation. Well, + + + align:start position:0% +think of as an obvious innovation. Well, +to be fair, as of the recording of this + + align:start position:0% +to be fair, as of the recording of this + + + align:start position:0% +to be fair, as of the recording of this +video, the jury was still out on whether + + align:start position:0% +video, the jury was still out on whether + + + align:start position:0% +video, the jury was still out on whether +the idea to bring back the woolly + + align:start position:0% +the idea to bring back the woolly + + + align:start position:0% +the idea to bring back the woolly +mammoth will end someplace worth + + align:start position:0% +mammoth will end someplace worth + + + align:start position:0% +mammoth will end someplace worth +inclusion in the list. But that only + + align:start position:0% +inclusion in the list. But that only + + + align:start position:0% +inclusion in the list. But that only +strengthens the point I have been making + + align:start position:0% +strengthens the point I have been making + + + align:start position:0% +strengthens the point I have been making +all along. At the start, preposterous + + align:start position:0% +all along. At the start, preposterous + + + align:start position:0% +all along. At the start, preposterous +ideas and good ideas look the exact + + align:start position:0% +ideas and good ideas look the exact + + + align:start position:0% +ideas and good ideas look the exact +same. After hearing all these, many + + align:start position:0% +same. After hearing all these, many + + + align:start position:0% +same. After hearing all these, many +people still find this notion really + + align:start position:0% +people still find this notion really + + + align:start position:0% +people still find this notion really +difficult to accept. You see, most + + align:start position:0% +difficult to accept. You see, most + + + align:start position:0% +difficult to accept. You see, most +entrepreneurship and innovation + + align:start position:0% +entrepreneurship and innovation + + + align:start position:0% +entrepreneurship and innovation +frameworks create the illusion that you + + align:start position:0% +frameworks create the illusion that you + + + align:start position:0% +frameworks create the illusion that you +just have to find the idea that will + + align:start position:0% +just have to find the idea that will + + + align:start position:0% +just have to find the idea that will +work and then execute. It's as if the + + align:start position:0% +work and then execute. It's as if the + + + align:start position:0% +work and then execute. It's as if the +idea had to have it all before you even + + align:start position:0% +idea had to have it all before you even + + + align:start position:0% +idea had to have it all before you even +start. And so the list of requirements + + align:start position:0% +start. And so the list of requirements + + + align:start position:0% +start. And so the list of requirements +for the idea grows. It has to be + + align:start position:0% +for the idea grows. It has to be + + + align:start position:0% +for the idea grows. It has to be +scalable, disruptive, singular, + + align:start position:0% +scalable, disruptive, singular, + + + align:start position:0% +scalable, disruptive, singular, +exponential. It is easy to see why + + align:start position:0% +exponential. It is easy to see why + + + align:start position:0% +exponential. It is easy to see why +people have a hard time letting go of + + align:start position:0% +people have a hard time letting go of + + + align:start position:0% +people have a hard time letting go of +that illusion. If ideas came pre-labeled + + align:start position:0% +that illusion. If ideas came pre-labeled + + + align:start position:0% +that illusion. If ideas came pre-labeled +as good, bad, slam dunk, etc., then all + + align:start position:0% +as good, bad, slam dunk, etc., then all + + + align:start position:0% +as good, bad, slam dunk, etc., then all +you'd have to do is talk to a few people + + align:start position:0% +you'd have to do is talk to a few people + + + align:start position:0% +you'd have to do is talk to a few people +or users, do a minimum prototype, and + + align:start position:0% +or users, do a minimum prototype, and + + + align:start position:0% +or users, do a minimum prototype, and +pitch it, and you'd be mostly done. In + + align:start position:0% +pitch it, and you'd be mostly done. In + + + align:start position:0% +pitch it, and you'd be mostly done. In +our experience, reality works another + + align:start position:0% +our experience, reality works another + + + align:start position:0% +our experience, reality works another +way. To be clear, there is no guarantee + + align:start position:0% +way. To be clear, there is no guarantee + + + align:start position:0% +way. To be clear, there is no guarantee +that your idea will ever graduate from + + align:start position:0% +that your idea will ever graduate from + + + align:start position:0% +that your idea will ever graduate from +being bad. + + align:start position:0% +being bad. + + + align:start position:0% +being bad. +But all that matters is whether the idea + + align:start position:0% +But all that matters is whether the idea + + + align:start position:0% +But all that matters is whether the idea +can supply you with the spunk you need + + align:start position:0% +can supply you with the spunk you need + + + align:start position:0% +can supply you with the spunk you need +to get you started on the real job. + + align:start position:0% +to get you started on the real job. + + + align:start position:0% +to get you started on the real job. +And the job is to fix the idea. And it + + align:start position:0% +And the job is to fix the idea. And it + + + align:start position:0% +And the job is to fix the idea. And it +amounts to being wrong a lot and + + align:start position:0% +amounts to being wrong a lot and + + + align:start position:0% +amounts to being wrong a lot and +surviving it all. That is what I call + + align:start position:0% +surviving it all. That is what I call + + + align:start position:0% +surviving it all. That is what I call +being productively wrong. When I say + + align:start position:0% +being productively wrong. When I say + + + align:start position:0% +being productively wrong. When I say +this, people often ask, "Oh, you mean + + align:start position:0% +this, people often ask, "Oh, you mean + + + align:start position:0% +this, people often ask, "Oh, you mean +like fail fast?" No, fail fast and being + + align:start position:0% +like fail fast?" No, fail fast and being + + + align:start position:0% +like fail fast?" No, fail fast and being +productively wrong are not the same. + + align:start position:0% +productively wrong are not the same. + + + align:start position:0% +productively wrong are not the same. +This is a key distinction of this new + + align:start position:0% +This is a key distinction of this new + + + align:start position:0% +This is a key distinction of this new +mindset. + + align:start position:0% +mindset. + + + align:start position:0% +mindset. +The fail fast phrase has been used so + + align:start position:0% +The fail fast phrase has been used so + + + align:start position:0% +The fail fast phrase has been used so +much that it now looks like failing is a + + align:start position:0% +much that it now looks like failing is a + + + align:start position:0% +much that it now looks like failing is a +cause for celebration. + + align:start position:0% +cause for celebration. + + + align:start position:0% +cause for celebration. +All you have to do to join the cool kids + + align:start position:0% +All you have to do to join the cool kids + + + align:start position:0% +All you have to do to join the cool kids +club and claim yourself an innovator is + + align:start position:0% +club and claim yourself an innovator is + + + align:start position:0% +club and claim yourself an innovator is +to fail. It isn't. It is still better + + align:start position:0% +to fail. It isn't. It is still better + + + align:start position:0% +to fail. It isn't. It is still better +when things work. I cannot fathom Steve + + align:start position:0% +when things work. I cannot fathom Steve + + + align:start position:0% +when things work. I cannot fathom Steve +Jobs celebrating failure that way. And + + align:start position:0% +Jobs celebrating failure that way. And + + + align:start position:0% +Jobs celebrating failure that way. And +yet a lot of famous people speak often + + align:start position:0% +yet a lot of famous people speak often + + + align:start position:0% +yet a lot of famous people speak often +of failing. Failing fast and failing + + align:start position:0% +of failing. Failing fast and failing + + + align:start position:0% +of failing. Failing fast and failing +often, but we really listen to them + + align:start position:0% +often, but we really listen to them + + + align:start position:0% +often, but we really listen to them +because of their success. So it is hard + + align:start position:0% +because of their success. So it is hard + + + align:start position:0% +because of their success. So it is hard +to know what they mean by failing and + + align:start position:0% +to know what they mean by failing and + + + align:start position:0% +to know what they mean by failing and +what you should get from it. This can + + align:start position:0% +what you should get from it. This can + + + align:start position:0% +what you should get from it. This can +help. Ditch the fail fast mantra. What + + align:start position:0% +help. Ditch the fail fast mantra. What + + + align:start position:0% +help. Ditch the fail fast mantra. What +matters is to realize that the idea you + + align:start position:0% +matters is to realize that the idea you + + + align:start position:0% +matters is to realize that the idea you +start with is a poor fit for what you + + align:start position:0% +start with is a poor fit for what you + + + align:start position:0% +start with is a poor fit for what you +think you want to accomplish. And the + + align:start position:0% +think you want to accomplish. And the + + + align:start position:0% +think you want to accomplish. And the +only way you can discover that is by + + align:start position:0% +only way you can discover that is by + + + align:start position:0% +only way you can discover that is by +making your ideas real and tangible. You + + align:start position:0% +making your ideas real and tangible. You + + + align:start position:0% +making your ideas real and tangible. You +may wonder what I mean by making an idea + + align:start position:0% +may wonder what I mean by making an idea + + + align:start position:0% +may wonder what I mean by making an idea +tangible. Nowadays, very often we talk + + align:start position:0% +tangible. Nowadays, very often we talk + + + align:start position:0% +tangible. Nowadays, very often we talk +about ideas, we create powerpoints, we + + align:start position:0% +about ideas, we create powerpoints, we + + + align:start position:0% +about ideas, we create powerpoints, we +describe them to others, we fall + + align:start position:0% +describe them to others, we fall + + + align:start position:0% +describe them to others, we fall +increasingly in love with the idea we + + align:start position:0% +increasingly in love with the idea we + + + align:start position:0% +increasingly in love with the idea we +had. But that idea only lives on paper. + + align:start position:0% +had. But that idea only lives on paper. + + + align:start position:0% +had. But that idea only lives on paper. +By making it tangible, what I'm asking + + align:start position:0% +By making it tangible, what I'm asking + + + align:start position:0% +By making it tangible, what I'm asking +you to do is find a way to make a + + align:start position:0% +you to do is find a way to make a + + + align:start position:0% +you to do is find a way to make a +physical something that you could point + + align:start position:0% +physical something that you could point + + + align:start position:0% +physical something that you could point +to so that other people can actually see + + align:start position:0% +to so that other people can actually see + + + align:start position:0% +to so that other people can actually see +your idea somehow in action. Making your + + align:start position:0% +your idea somehow in action. Making your + + + align:start position:0% +your idea somehow in action. Making your +idea tangible is how you realize you had + + align:start position:0% +idea tangible is how you realize you had + + + align:start position:0% +idea tangible is how you realize you had +not thought it all through and you start + + align:start position:0% +not thought it all through and you start + + + align:start position:0% +not thought it all through and you start +to learn how you were wrong. + + align:start position:0% +to learn how you were wrong. + + + align:start position:0% +to learn how you were wrong. +I will tell you more about this in + + align:start position:0% +I will tell you more about this in + + + align:start position:0% +I will tell you more about this in +another video. Finding something wrong + + align:start position:0% +another video. Finding something wrong + + + align:start position:0% +another video. Finding something wrong +about your idea isn't failing. Only + + align:start position:0% +about your idea isn't failing. Only + + + align:start position:0% +about your idea isn't failing. Only +people afraid to be wrong confuse that + + align:start position:0% +people afraid to be wrong confuse that + + + align:start position:0% +people afraid to be wrong confuse that +for failing. Finding something wrong + + align:start position:0% +for failing. Finding something wrong + + + align:start position:0% +for failing. Finding something wrong +about your idea is how you start fixing + + align:start position:0% +about your idea is how you start fixing + + + align:start position:0% +about your idea is how you start fixing +it. You can take forever to do this or + + align:start position:0% +it. You can take forever to do this or + + + align:start position:0% +it. You can take forever to do this or +you can find ways to find out how your + + align:start position:0% +you can find ways to find out how your + + + align:start position:0% +you can find ways to find out how your +idea was wrong sooner. But it isn't + + align:start position:0% +idea was wrong sooner. But it isn't + + + align:start position:0% +idea was wrong sooner. But it isn't +failing. It is the precise opposite. It + + align:start position:0% +failing. It is the precise opposite. It + + + align:start position:0% +failing. It is the precise opposite. It +is a pursuit of excellence. + + align:start position:0% +is a pursuit of excellence. + + + align:start position:0% +is a pursuit of excellence. +Innovation rarely emerges from planned + + align:start position:0% +Innovation rarely emerges from planned + + + align:start position:0% +Innovation rarely emerges from planned +sloppiness. You have to care about + + align:start position:0% +sloppiness. You have to care about + + + align:start position:0% +sloppiness. You have to care about +excellence. You need to hate failing, + + align:start position:0% +excellence. You need to hate failing, + + + align:start position:0% +excellence. You need to hate failing, +but you cannot be stigmatized by it. + + align:start position:0% +but you cannot be stigmatized by it. + + + align:start position:0% +but you cannot be stigmatized by it. +There is no merit in failing. There is + + align:start position:0% +There is no merit in failing. There is + + + align:start position:0% +There is no merit in failing. There is +no stigma either. But you're in this to + + align:start position:0% +no stigma either. But you're in this to + + + align:start position:0% +no stigma either. But you're in this to +succeed. So fail only in ways you could + + align:start position:0% +succeed. So fail only in ways you could + + + align:start position:0% +succeed. So fail only in ways you could +not have predicted. As you will see in a + + align:start position:0% +not have predicted. As you will see in a + + + align:start position:0% +not have predicted. As you will see in a +few videos, this mindset, the pursuit of + + align:start position:0% +few videos, this mindset, the pursuit of + + + align:start position:0% +few videos, this mindset, the pursuit of +excellence, and the absolute + + align:start position:0% +excellence, and the absolute + + + align:start position:0% +excellence, and the absolute +determination to not fail is how + + align:start position:0% +determination to not fail is how + + + align:start position:0% +determination to not fail is how +astronauts go to space and back. + + align:start position:0% +astronauts go to space and back. + + + align:start position:0% +astronauts go to space and back. +[Music] \ No newline at end of file diff --git a/K2SC-WPdT6k.txt b/K2SC-WPdT6k.txt new file mode 100644 index 0000000000000000000000000000000000000000..13d3e41f2e6e52a4a59163565f3fe7c6dd127dac --- /dev/null +++ b/K2SC-WPdT6k.txt @@ -0,0 +1,7971 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer high quality educational + + align:start position:0% +to offer high quality educational + + + align:start position:0% +to offer high quality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu hello + + align:start position:0% +ocw.mit.edu hello + + + align:start position:0% +ocw.mit.edu hello +everybody um some + + align:start position:0% +everybody um some + + + align:start position:0% +everybody um some +announcements uh the last reading + + align:start position:0% +announcements uh the last reading + + + align:start position:0% +announcements uh the last reading +assignment of the semester at least from + + align:start position:0% +assignment of the semester at least from + + + align:start position:0% +assignment of the semester at least from +us uh course evaluations are still + + align:start position:0% +us uh course evaluations are still + + + align:start position:0% +us uh course evaluations are still +available um through this this Friday + + align:start position:0% +available um through this this Friday + + + align:start position:0% +available um through this this Friday +but only till noon again I I urge you + + align:start position:0% +but only till noon again I I urge you + + + align:start position:0% +but only till noon again I I urge you +all to do it and then + + align:start position:0% +all to do it and then + + + align:start position:0% +all to do it and then +finally uh for the final exam we're + + align:start position:0% +finally uh for the final exam we're + + + align:start position:0% +finally uh for the final exam we're +going to be giving you some code to + + align:start position:0% +going to be giving you some code to + + + align:start position:0% +going to be giving you some code to +study in advance of the exam and then we + + align:start position:0% +study in advance of the exam and then we + + + align:start position:0% +study in advance of the exam and then we +will ask questions about that code on + + align:start position:0% +will ask questions about that code on + + + align:start position:0% +will ask questions about that code on +the exam + + align:start position:0% +the exam + + + align:start position:0% +the exam +itself uh this was described in the + + align:start position:0% +itself uh this was described in the + + + align:start position:0% +itself uh this was described in the +announcement for the exam and we will be + + align:start position:0% +announcement for the exam and we will be + + + align:start position:0% +announcement for the exam and we will be +making this code available later + + align:start position:0% +making this code available later + + + align:start position:0% +making this code available later +today uh I would suggest that you try + + align:start position:0% +today uh I would suggest that you try + + + align:start position:0% +today uh I would suggest that you try +and get your heads around it if you're + + align:start position:0% +and get your heads around it if you're + + + align:start position:0% +and get your heads around it if you're +confused that's a good thing to talk + + align:start position:0% +confused that's a good thing to talk + + + align:start position:0% +confused that's a good thing to talk +about in office hours to to get some + + align:start position:0% +about in office hours to to get some + + + align:start position:0% +about in office hours to to get some +help with it as opposed to waiting till + + align:start position:0% +help with it as opposed to waiting till + + + align:start position:0% +help with it as opposed to waiting till +20 minutes before the exam and realizing + + align:start position:0% +20 minutes before the exam and realizing + + + align:start position:0% +20 minutes before the exam and realizing +you're confused + + align:start position:0% +you're confused + + + align:start position:0% +you're confused +all right I want to pick up where we + + align:start position:0% +all right I want to pick up where we + + + align:start position:0% +all right I want to pick up where we +left off on + + align:start position:0% +left off on + + + align:start position:0% +left off on +Monday so you may recall that we were + + align:start position:0% +Monday so you may recall that we were + + + align:start position:0% +Monday so you may recall that we were +comparing + + align:start position:0% +comparing + + + align:start position:0% +comparing +results of KNN and logistic regression + + align:start position:0% +results of KNN and logistic regression + + + align:start position:0% +results of KNN and logistic regression +on our Titanic + + align:start position:0% +on our Titanic + + + align:start position:0% +on our Titanic +data and we had this + + align:start position:0% +data and we had this + + + align:start position:0% +data and we had this +up uh using 10 80 20 splits for KN andn + + align:start position:0% +up uh using 10 80 20 splits for KN andn + + + align:start position:0% +up uh using 10 80 20 splits for KN andn +equal 3 and logistic regression with P + + align:start position:0% +equal 3 and logistic regression with P + + + align:start position:0% +equal 3 and logistic regression with P +equal .5 + + align:start position:0% +equal .5 + + + align:start position:0% +equal .5 +and what I observed is that logistic + + align:start position:0% +and what I observed is that logistic + + + align:start position:0% +and what I observed is that logistic +regression happen to perform slightly + + align:start position:0% +regression happen to perform slightly + + + align:start position:0% +regression happen to perform slightly +better but certainly nothing that uh you + + align:start position:0% +better but certainly nothing that uh you + + + align:start position:0% +better but certainly nothing that uh you +would choose to write home about right + + align:start position:0% +would choose to write home about right + + + align:start position:0% +would choose to write home about right +it's it's a little bit better and isn't + + align:start position:0% +it's it's a little bit better and isn't + + + align:start position:0% +it's it's a little bit better and isn't +to say we always be better happens to be + + align:start position:0% +to say we always be better happens to be + + + align:start position:0% +to say we always be better happens to be +here but the point I closed with is one + + align:start position:0% +here but the point I closed with is one + + + align:start position:0% +here but the point I closed with is one +of the things we care about when we use + + align:start position:0% +of the things we care about when we use + + + align:start position:0% +of the things we care about when we use +machine learning is not only our ability + + align:start position:0% +machine learning is not only our ability + + + align:start position:0% +machine learning is not only our ability +to make predictions + + align:start position:0% +to make predictions + + + align:start position:0% +to make predictions +with the model but what can we learn by + + align:start position:0% +with the model but what can we learn by + + + align:start position:0% +with the model but what can we learn by +studying the model + + align:start position:0% +studying the model + + + align:start position:0% +studying the model +itself remember the idea is that the + + align:start position:0% +itself remember the idea is that the + + + align:start position:0% +itself remember the idea is that the +model is somehow + + align:start position:0% +model is somehow + + + align:start position:0% +model is somehow +capturing the system or the process that + + align:start position:0% +capturing the system or the process that + + + align:start position:0% +capturing the system or the process that +generated the data and by studying the + + align:start position:0% +generated the data and by studying the + + + align:start position:0% +generated the data and by studying the +model we can learn something + + align:start position:0% + + + + align:start position:0% + +useful so to do that for logistic + + align:start position:0% +useful so to do that for logistic + + + align:start position:0% +useful so to do that for logistic +regression We Begin by looking at the + + align:start position:0% +regression We Begin by looking at the + + + align:start position:0% +regression We Begin by looking at the +weights of the different variables + + align:start position:0% +weights of the different variables + + + align:start position:0% +weights of the different variables +and we had this up in the last + + align:start position:0% +and we had this up in the last + + + align:start position:0% +and we had this up in the last +slide uh the model classes are died and + + align:start position:0% +slide uh the model classes are died and + + + align:start position:0% +slide uh the model classes are died and +survived for the label + + align:start position:0% +survived for the label + + + align:start position:0% +survived for the label +survived we said that if you were in a + + align:start position:0% +survived we said that if you were in a + + + align:start position:0% +survived we said that if you were in a +first class cabin that had a positive + + align:start position:0% +first class cabin that had a positive + + + align:start position:0% +first class cabin that had a positive +impact on your survival a pretty strong + + align:start position:0% +impact on your survival a pretty strong + + + align:start position:0% +impact on your survival a pretty strong +positive + + align:start position:0% +positive + + + align:start position:0% +positive +impact you can't interpret these weights + + align:start position:0% +impact you can't interpret these weights + + + align:start position:0% +impact you can't interpret these weights +in and of themselves if I said it's 1.6 + + align:start position:0% +in and of themselves if I said it's 1.6 + + + align:start position:0% +in and of themselves if I said it's 1.6 +that really doesn't mean anything so + + align:start position:0% +that really doesn't mean anything so + + + align:start position:0% +that really doesn't mean anything so +what you have to look at is the relative + + align:start position:0% +what you have to look at is the relative + + + align:start position:0% +what you have to look at is the relative +weights not the absolute weights and we + + align:start position:0% +weights not the absolute weights and we + + + align:start position:0% +weights not the absolute weights and we +see that it's a pretty strong relative + + align:start position:0% +see that it's a pretty strong relative + + + align:start position:0% +see that it's a pretty strong relative +weight a second class cabin also has a + + align:start position:0% +weight a second class cabin also has a + + + align:start position:0% +weight a second class cabin also has a +positive weight in this case of 0 + + align:start position:0% +positive weight in this case of 0 + + + align:start position:0% +positive weight in this case of 0 +46 so it was indicating you better + + align:start position:0% +46 so it was indicating you better + + + align:start position:0% +46 so it was indicating you better +better than average chance of + + align:start position:0% +better than average chance of + + + align:start position:0% +better than average chance of +surviving um but much less strong than a + + align:start position:0% +surviving um but much less strong than a + + + align:start position:0% +surviving um but much less strong than a +first class + + align:start position:0% +first class + + + align:start position:0% +first class +and if you were one of those poor people + + align:start position:0% +and if you were one of those poor people + + + align:start position:0% +and if you were one of those poor people +in a third class cabin well that had a + + align:start position:0% +in a third class cabin well that had a + + + align:start position:0% +in a third class cabin well that had a +negative weight on Survival you were + + align:start position:0% +negative weight on Survival you were + + + align:start position:0% +negative weight on Survival you were +less likely to + + align:start position:0% +less likely to + + + align:start position:0% +less likely to +survive uh age had a very small effect + + align:start position:0% +survive uh age had a very small effect + + + align:start position:0% +survive uh age had a very small effect +here uh slightly negative what that + + align:start position:0% +here uh slightly negative what that + + + align:start position:0% +here uh slightly negative what that +meant is the older you were the less + + align:start position:0% +meant is the older you were the less + + + align:start position:0% +meant is the older you were the less +likely you were to have survived but + + align:start position:0% +likely you were to have survived but + + + align:start position:0% +likely you were to have survived but +it's a very small negative + + align:start position:0% +it's a very small negative + + + align:start position:0% +it's a very small negative +value and male gender had a very large L + + align:start position:0% +value and male gender had a very large L + + + align:start position:0% +value and male gender had a very large L +relatively large negative gender + + align:start position:0% +relatively large negative gender + + + align:start position:0% +relatively large negative gender +suggesting that if you were a male you + + align:start position:0% +suggesting that if you were a male you + + + align:start position:0% +suggesting that if you were a male you +were more likely to die than if you were + + align:start position:0% +were more likely to die than if you were + + + align:start position:0% +were more likely to die than if you were +a + + align:start position:0% +a + + + align:start position:0% +a +female um this might be true in the + + align:start position:0% +female um this might be true in the + + + align:start position:0% +female um this might be true in the +general population but it was especially + + align:start position:0% +general population but it was especially + + + align:start position:0% +general population but it was especially +true on the + + align:start position:0% +true on the + + + align:start position:0% +true on the +Titanic finally I warned you that while + + align:start position:0% +Titanic finally I warned you that while + + + align:start position:0% +Titanic finally I warned you that while +what I just went through is something + + align:start position:0% +what I just went through is something + + + align:start position:0% +what I just went through is something +you will read in lots of papers that use + + align:start position:0% +you will read in lots of papers that use + + + align:start position:0% +you will read in lots of papers that use +machine learning you will hear in lots + + align:start position:0% +machine learning you will hear in lots + + + align:start position:0% +machine learning you will hear in lots +of talks about people who used machine + + align:start position:0% +of talks about people who used machine + + + align:start position:0% +of talks about people who used machine +learning but you should be very wary + + align:start position:0% +learning but you should be very wary + + + align:start position:0% +learning but you should be very wary +when people speak that way it's not + + align:start position:0% +when people speak that way it's not + + + align:start position:0% +when people speak that way it's not +nonsense but some cautionary + + align:start position:0% +nonsense but some cautionary + + + align:start position:0% +nonsense but some cautionary +notes in + + align:start position:0% +notes in + + + align:start position:0% +notes in +particular there's a big issue because + + align:start position:0% +particular there's a big issue because + + + align:start position:0% +particular there's a big issue because +the features are often correlated with + + align:start position:0% +the features are often correlated with + + + align:start position:0% +the features are often correlated with +one another and so you can't interpret + + align:start position:0% +one another and so you can't interpret + + + align:start position:0% +one another and so you can't interpret +the weights one feature at a + + align:start position:0% +the weights one feature at a + + + align:start position:0% +the weights one feature at a +time to get a little bit + + align:start position:0% +time to get a little bit + + + align:start position:0% +time to get a little bit +technical there are two + + align:start position:0% +technical there are two + + + align:start position:0% +technical there are two +major ways people use Logistics + + align:start position:0% +major ways people use Logistics + + + align:start position:0% +major ways people use Logistics +regression they're called L1 and + + align:start position:0% +regression they're called L1 and + + + align:start position:0% +regression they're called L1 and +L2 um we used an L2 I'll come back to + + align:start position:0% +L2 um we used an L2 I'll come back to + + + align:start position:0% +L2 um we used an L2 I'll come back to +that in a minute because that's the + + align:start position:0% +that in a minute because that's the + + + align:start position:0% +that in a minute because that's the +default in in in Python s kit uh you can + + align:start position:0% +default in in in Python s kit uh you can + + + align:start position:0% +default in in in Python s kit uh you can +set that parameter to L2 and do that to + + align:start position:0% +set that parameter to L2 and do that to + + + align:start position:0% +set that parameter to L2 and do that to +L1 if you want I experimented with it it + + align:start position:0% +L1 if you want I experimented with it it + + + align:start position:0% +L1 if you want I experimented with it it +didn't change the results that + + align:start position:0% +didn't change the results that + + + align:start position:0% +didn't change the results that +much but what an L1 regression is + + align:start position:0% +much but what an L1 regression is + + + align:start position:0% +much but what an L1 regression is +designed to do is to find some weights + + align:start position:0% +designed to do is to find some weights + + + align:start position:0% +designed to do is to find some weights +and drive them to zero + + align:start position:0% + + + + align:start position:0% + +um this is particularly useful when you + + align:start position:0% +um this is particularly useful when you + + + align:start position:0% +um this is particularly useful when you +have a very high dimensional problem + + align:start position:0% +have a very high dimensional problem + + + align:start position:0% +have a very high dimensional problem +relative to the number of examples and + + align:start position:0% +relative to the number of examples and + + + align:start position:0% +relative to the number of examples and +this gets back to that question we've + + align:start position:0% +this gets back to that question we've + + + align:start position:0% +this gets back to that question we've +talked about many times of + + align:start position:0% +talked about many times of + + + align:start position:0% +talked about many times of +overfitting if you've + + align:start position:0% +overfitting if you've + + + align:start position:0% +overfitting if you've +got a thousand variables and a thousand + + align:start position:0% +got a thousand variables and a thousand + + + align:start position:0% +got a thousand variables and a thousand +examples you're very likely to + + align:start position:0% +examples you're very likely to + + + align:start position:0% +examples you're very likely to +overfit L2 L1 is designed to avoid + + align:start position:0% +overfit L2 L1 is designed to avoid + + + align:start position:0% +overfit L2 L1 is designed to avoid +overfitting + + align:start position:0% +overfitting + + + align:start position:0% +overfitting +by taking many of those thousand + + align:start position:0% +by taking many of those thousand + + + align:start position:0% +by taking many of those thousand +variables and just giving them zero + + align:start position:0% +variables and just giving them zero + + + align:start position:0% +variables and just giving them zero +weight and it does typically generalized + + align:start position:0% +weight and it does typically generalized + + + align:start position:0% +weight and it does typically generalized +better but if you have two variables + + align:start position:0% +better but if you have two variables + + + align:start position:0% +better but if you have two variables +that are + + align:start position:0% +that are + + + align:start position:0% +that are +correlated L1 will drive one to zero and + + align:start position:0% +correlated L1 will drive one to zero and + + + align:start position:0% +correlated L1 will drive one to zero and +it will look like it's + + align:start position:0% +it will look like it's + + + align:start position:0% +it will look like it's +unimportant but in fact it might be + + align:start position:0% +unimportant but in fact it might be + + + align:start position:0% +unimportant but in fact it might be +important it's just correlated with + + align:start position:0% +important it's just correlated with + + + align:start position:0% +important it's just correlated with +another which has gotten all the + + align:start position:0% +another which has gotten all the + + + align:start position:0% +another which has gotten all the +credit L2 which is what we did does the + + align:start position:0% +credit L2 which is what we did does the + + + align:start position:0% +credit L2 which is what we did does the +opposite it spreads the weight across + + align:start position:0% +opposite it spreads the weight across + + + align:start position:0% +opposite it spreads the weight across +the variables so if you have a bunch of + + align:start position:0% +the variables so if you have a bunch of + + + align:start position:0% +the variables so if you have a bunch of +correlated variables it might look like + + align:start position:0% +correlated variables it might look like + + + align:start position:0% +correlated variables it might look like +none of them are very important because + + align:start position:0% +none of them are very important because + + + align:start position:0% +none of them are very important because +each of them gets a small amount of the + + align:start position:0% +each of them gets a small amount of the + + + align:start position:0% +each of them gets a small amount of the +weight again not so important when you + + align:start position:0% +weight again not so important when you + + + align:start position:0% +weight again not so important when you +have four or five variables is what I'm + + align:start position:0% +have four or five variables is what I'm + + + align:start position:0% +have four or five variables is what I'm +showing you but it matters when you have + + align:start position:0% +showing you but it matters when you have + + + align:start position:0% +showing you but it matters when you have +a 100 or a thousand + + align:start position:0% +a 100 or a thousand + + + align:start position:0% +a 100 or a thousand +variables let's look at an + + align:start position:0% +variables let's look at an + + + align:start position:0% +variables let's look at an +example + + align:start position:0% +example + + + align:start position:0% +example +so the cabin + + align:start position:0% +so the cabin + + + align:start position:0% +so the cabin +classes the way we set it up C1 plus C2 + + align:start position:0% +classes the way we set it up C1 plus C2 + + + align:start position:0% +classes the way we set it up C1 plus C2 +plus C3 whoops is not equal to zero what + + align:start position:0% +plus C3 whoops is not equal to zero what + + + align:start position:0% +plus C3 whoops is not equal to zero what +is it equal + + align:start position:0% +is it equal + + + align:start position:0% +is it equal +to I'll fix this right + + align:start position:0% +to I'll fix this right + + + align:start position:0% +to I'll fix this right +now what should that have + + align:start position:0% + + + + align:start position:0% + +said what's the invariant + + align:start position:0% +said what's the invariant + + + align:start position:0% +said what's the invariant +here well a person is in exactly one + + align:start position:0% +here well a person is in exactly one + + + align:start position:0% +here well a person is in exactly one +class right I guess if you're really + + align:start position:0% +class right I guess if you're really + + + align:start position:0% +class right I guess if you're really +rich Maybe you rented two cabins one in + + align:start position:0% +rich Maybe you rented two cabins one in + + + align:start position:0% +rich Maybe you rented two cabins one in +first and one in second but probably not + + align:start position:0% +first and one in second but probably not + + + align:start position:0% +first and one in second but probably not +or if you did you put your servants in + + align:start position:0% +or if you did you put your servants in + + + align:start position:0% +or if you did you put your servants in +second or third but what do this got to + + align:start position:0% +second or third but what do this got to + + + align:start position:0% +second or third but what do this got to +add up to yeah has to add up to one + + align:start position:0% +add up to yeah has to add up to one + + + align:start position:0% +add up to yeah has to add up to one +thank + + align:start position:0% + + + + align:start position:0% + +you so it adds up to + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% +one + + + align:start position:0% +one +oh got his attention at least all right + + align:start position:0% +oh got his attention at least all right + + + align:start position:0% +oh got his attention at least all right +so what this tells us is the values are + + align:start position:0% +so what this tells us is the values are + + + align:start position:0% +so what this tells us is the values are +not + + align:start position:0% +not + + + align:start position:0% +not +independent because if C1 is one then C2 + + align:start position:0% +independent because if C1 is one then C2 + + + align:start position:0% +independent because if C1 is one then C2 +and C3 must be zero + + align:start position:0% +and C3 must be zero + + + align:start position:0% +and C3 must be zero +right and so now we could go back to the + + align:start position:0% +right and so now we could go back to the + + + align:start position:0% +right and so now we could go back to the +previous slide and ask the question well + + align:start position:0% +previous slide and ask the question well + + + align:start position:0% +previous slide and ask the question well +is it that being in first class is + + align:start position:0% +is it that being in first class is + + + align:start position:0% +is it that being in first class is +protective or is it that being in second + + align:start position:0% +protective or is it that being in second + + + align:start position:0% +protective or is it that being in second +or third class is + + align:start position:0% +or third class is + + + align:start position:0% +or third class is +risky and there's no simple answer to + + align:start position:0% +risky and there's no simple answer to + + + align:start position:0% +risky and there's no simple answer to +that + + align:start position:0% +that + + + align:start position:0% +that +so let's do an experiment we have these + + align:start position:0% +so let's do an experiment we have these + + + align:start position:0% +so let's do an experiment we have these +correlated + + align:start position:0% +correlated + + + align:start position:0% +correlated +variables suppose we eliminate C1 all + + align:start position:0% +variables suppose we eliminate C1 all + + + align:start position:0% +variables suppose we eliminate C1 all +together so I did that by changing the + + align:start position:0% +together so I did that by changing the + + + align:start position:0% +together so I did that by changing the +anit method of class + + align:start position:0% +anit method of class + + + align:start position:0% +anit method of class +passenger takes the same + + align:start position:0% +passenger takes the same + + + align:start position:0% +passenger takes the same +arguments + + align:start position:0% +arguments + + + align:start position:0% +arguments +but well we'll look at the + + align:start position:0% +but well we'll look at the + + + align:start position:0% +but well we'll look at the +code because it's a little bit clearer + + align:start position:0% +code because it's a little bit clearer + + + align:start position:0% +code because it's a little bit clearer +there so there was the original + + align:start position:0% +there so there was the original + + + align:start position:0% +there so there was the original +one and I'm going to replace that by + + align:start position:0% + + + + align:start position:0% + +this comment out the original + + align:start position:0% + + + + align:start position:0% + +one so what you see is that instead of + + align:start position:0% +one so what you see is that instead of + + + align:start position:0% +one so what you see is that instead of +having uh five features I now have four + + align:start position:0% +having uh five features I now have four + + + align:start position:0% +having uh five features I now have four +I've eliminated the C1 binary feature + + align:start position:0% +I've eliminated the C1 binary feature + + + align:start position:0% +I've eliminated the C1 binary feature +and then the code is is + + align:start position:0% + + + + align:start position:0% + +straightforward that I've just come + + align:start position:0% +straightforward that I've just come + + + align:start position:0% +straightforward that I've just come +through here and I've just enumerated + + align:start position:0% +through here and I've just enumerated + + + align:start position:0% +through here and I've just enumerated +the + + align:start position:0% +the + + + align:start position:0% +the +possibilities so if you're in first + + align:start position:0% +possibilities so if you're in first + + + align:start position:0% +possibilities so if you're in first +class then second and third are both + + align:start position:0% +class then second and third are both + + + align:start position:0% +class then second and third are both +zero otherwise one of them is a + + align:start position:0% +zero otherwise one of them is a + + + align:start position:0% +zero otherwise one of them is a +one so my invariant is is gone now right + + align:start position:0% +one so my invariant is is gone now right + + + align:start position:0% +one so my invariant is is gone now right +it's not the case that we know that + + align:start position:0% +it's not the case that we know that + + + align:start position:0% +it's not the case that we know that +these two things have to add up to one + + align:start position:0% +these two things have to add up to one + + + align:start position:0% +these two things have to add up to one +because maybe I'm in the third + + align:start position:0% + + + + align:start position:0% + +case okay let's go run that + + align:start position:0% + + + + align:start position:0% + +code and see what happens + + align:start position:0% + + + + align:start position:0% + +well if you remember we see that our + + align:start position:0% +well if you remember we see that our + + + align:start position:0% +well if you remember we see that our +accuracy has not really declined much + + align:start position:0% +accuracy has not really declined much + + + align:start position:0% +accuracy has not really declined much +pretty much the same results we got + + align:start position:0% +pretty much the same results we got + + + align:start position:0% +pretty much the same results we got +before but our weights are really quite + + align:start position:0% +before but our weights are really quite + + + align:start position:0% +before but our weights are really quite +different now suddenly C2 and C3 have + + align:start position:0% +different now suddenly C2 and C3 have + + + align:start position:0% +different now suddenly C2 and C3 have +large negative + + align:start position:0% + + + + align:start position:0% + +weights we can look at them side by side + + align:start position:0% +weights we can look at them side by side + + + align:start position:0% +weights we can look at them side by side +here + + align:start position:0% + + + + align:start position:0% + +so you see not much difference it + + align:start position:0% +so you see not much difference it + + + align:start position:0% +so you see not much difference it +actually performs maybe well really no + + align:start position:0% +actually performs maybe well really no + + + align:start position:0% +actually performs maybe well really no +real difference in performance but + + align:start position:0% +real difference in performance but + + + align:start position:0% +real difference in performance but +you'll notice that the weights are + + align:start position:0% +you'll notice that the weights are + + + align:start position:0% +you'll notice that the weights are +really quite + + align:start position:0% +really quite + + + align:start position:0% +really quite +different that + + align:start position:0% +different that + + + align:start position:0% +different that +now what had been a strong positive + + align:start position:0% +now what had been a strong positive + + + align:start position:0% +now what had been a strong positive +weight and relatively weak negative + + align:start position:0% +weight and relatively weak negative + + + align:start position:0% +weight and relatively weak negative +weights is now replaced by two strong + + align:start position:0% +weights is now replaced by two strong + + + align:start position:0% +weights is now replaced by two strong +negative + + align:start position:0% + + + + align:start position:0% + +weights and age and gender change just a + + align:start position:0% +weights and age and gender change just a + + + align:start position:0% +weights and age and gender change just a +little + + align:start position:0% +little + + + align:start position:0% +little +bit so the whole point here is we have + + align:start position:0% +bit so the whole point here is we have + + + align:start position:0% +bit so the whole point here is we have +to be very careful when you have + + align:start position:0% +to be very careful when you have + + + align:start position:0% +to be very careful when you have +correlated features about over + + align:start position:0% +correlated features about over + + + align:start position:0% +correlated features about over +interpreting the weights it is generally + + align:start position:0% +interpreting the weights it is generally + + + align:start position:0% +interpreting the weights it is generally +pretty safe to rely on the sign whether + + align:start position:0% +pretty safe to rely on the sign whether + + + align:start position:0% +pretty safe to rely on the sign whether +it's negative or + + align:start position:0% +it's negative or + + + align:start position:0% +it's negative or +positive all + + align:start position:0% +positive all + + + align:start position:0% +positive all +right changing the topic but sticking + + align:start position:0% +right changing the topic but sticking + + + align:start position:0% +right changing the topic but sticking +with logistic + + align:start position:0% +with logistic + + + align:start position:0% +with logistic +regression there's this parameter you + + align:start position:0% +regression there's this parameter you + + + align:start position:0% +regression there's this parameter you +may recall P which is the probability + + align:start position:0% +may recall P which is the probability + + + align:start position:0% +may recall P which is the probability +and that was the cut off and we set it + + align:start position:0% +and that was the cut off and we set it + + + align:start position:0% +and that was the cut off and we set it +to0 five saying if it estimates the + + align:start position:0% +to0 five saying if it estimates the + + + align:start position:0% +to0 five saying if it estimates the +probability of survival to be 05 or + + align:start position:0% +probability of survival to be 05 or + + + align:start position:0% +probability of survival to be 05 or +higher then we're going to guess + + align:start position:0% +higher then we're going to guess + + + align:start position:0% +higher then we're going to guess +survived predict survived otherwise + + align:start position:0% +survived predict survived otherwise + + + align:start position:0% +survived predict survived otherwise +deceased you can change + + align:start position:0% +deceased you can change + + + align:start position:0% +deceased you can change +that and so I'm going to try two extreme + + align:start position:0% +that and so I'm going to try two extreme + + + align:start position:0% +that and so I'm going to try two extreme +values setting P to 0.1 and P + + align:start position:0% + + + + align:start position:0% + +.9 now what do we think that's likely to + + align:start position:0% + + + + align:start position:0% + +change remember we looked at a bunch of + + align:start position:0% +change remember we looked at a bunch of + + + align:start position:0% +change remember we looked at a bunch of +different + + align:start position:0% + + + + align:start position:0% + +attributes in particular what attributes + + align:start position:0% +attributes in particular what attributes + + + align:start position:0% +attributes in particular what attributes +we think are most likely to change + + align:start position:0% +we think are most likely to change + + + align:start position:0% +we think are most likely to change +anyone who has not answered a question + + align:start position:0% +anyone who has not answered a question + + + align:start position:0% +anyone who has not answered a question +want to + + align:start position:0% +want to + + + align:start position:0% +want to +volunteer I have nothing against you + + align:start position:0% +volunteer I have nothing against you + + + align:start position:0% +volunteer I have nothing against you +it's just I'm trying to spread the + + align:start position:0% +it's just I'm trying to spread the + + + align:start position:0% +it's just I'm trying to spread the +wealth and I don't want to give you + + align:start position:0% +wealth and I don't want to give you + + + align:start position:0% +wealth and I don't want to give you +diabetes + + align:start position:0% +diabetes + + + align:start position:0% +diabetes +all the candy + + align:start position:0% +all the candy + + + align:start position:0% +all the candy +um all right you get to go + + align:start position:0% +um all right you get to go + + + align:start position:0% +um all right you get to go +again specific pardon sensitivity and + + align:start position:0% +again specific pardon sensitivity and + + + align:start position:0% +again specific pardon sensitivity and +speci sensitivity and specificity + + align:start position:0% +speci sensitivity and specificity + + + align:start position:0% +speci sensitivity and specificity +positive predictive value right because + + align:start position:0% +positive predictive value right because + + + align:start position:0% +positive predictive value right because +we're shifting and we're saying well by + + align:start position:0% +we're shifting and we're saying well by + + + align:start position:0% +we're shifting and we're saying well by +changing the probability we're inclining + + align:start position:0% +changing the probability we're inclining + + + align:start position:0% +changing the probability we're inclining +we're making a decision that it's more + + align:start position:0% +we're making a decision that it's more + + + align:start position:0% +we're making a decision that it's more +important to not miss + + align:start position:0% +important to not miss + + + align:start position:0% +important to not miss +survivors than it is to + + align:start position:0% +survivors than it is to + + + align:start position:0% +survivors than it is to +say ask gets too + + align:start position:0% +say ask gets too + + + align:start position:0% +say ask gets too +high so let's look at what happens when + + align:start position:0% +high so let's look at what happens when + + + align:start position:0% +high so let's look at what happens when +we run + + align:start position:0% + + + + align:start position:0% + +that I won't run it for you but these + + align:start position:0% +that I won't run it for you but these + + + align:start position:0% +that I won't run it for you but these +are the results we + + align:start position:0% +are the results we + + + align:start position:0% +are the results we +got so as it happens 0.9 gave me higher + + align:start position:0% +got so as it happens 0.9 gave me higher + + + align:start position:0% +got so as it happens 0.9 gave me higher +accuracy but the key thing is notice the + + align:start position:0% +accuracy but the key thing is notice the + + + align:start position:0% +accuracy but the key thing is notice the +big difference + + align:start position:0% + + + + align:start position:0% + +here so what is is that telling + + align:start position:0% +here so what is is that telling + + + align:start position:0% +here so what is is that telling +me well it's telling me that if I + + align:start position:0% +me well it's telling me that if I + + + align:start position:0% +me well it's telling me that if I +predict you're going to survive you + + align:start position:0% +predict you're going to survive you + + + align:start position:0% +predict you're going to survive you +probably + + align:start position:0% +probably + + + align:start position:0% +probably +did but look what it did to the + + align:start position:0% + + + + align:start position:0% + +sensitivity right it means that most of + + align:start position:0% +sensitivity right it means that most of + + + align:start position:0% +sensitivity right it means that most of +the survivors I'm predicting they + + align:start position:0% +the survivors I'm predicting they + + + align:start position:0% +the survivors I'm predicting they +died why is the accuracy still + + align:start position:0% +died why is the accuracy still + + + align:start position:0% +died why is the accuracy still +okay well because most people died on + + align:start position:0% +okay well because most people died on + + + align:start position:0% +okay well because most people died on +the boat on the ship right so we would + + align:start position:0% +the boat on the ship right so we would + + + align:start position:0% +the boat on the ship right so we would +have done pretty well you recall if we + + align:start position:0% +have done pretty well you recall if we + + + align:start position:0% +have done pretty well you recall if we +just guess died for + + align:start position:0% + + + + align:start position:0% + +everybody so it's important to + + align:start position:0% +everybody so it's important to + + + align:start position:0% +everybody so it's important to +understand these things um I once did + + align:start position:0% +understand these things um I once did + + + align:start position:0% +understand these things um I once did +some work using machine learning for an + + align:start position:0% +some work using machine learning for an + + + align:start position:0% +some work using machine learning for an +insurance company who's trying to set + + align:start position:0% +insurance company who's trying to set + + + align:start position:0% +insurance company who's trying to set +rates and they I asked them what they + + align:start position:0% +rates and they I asked them what they + + + align:start position:0% +rates and they I asked them what they +wanted to do and they said they wanted + + align:start position:0% +wanted to do and they said they wanted + + + align:start position:0% +wanted to do and they said they wanted +it to uh they didn't want to lose money + + align:start position:0% +it to uh they didn't want to lose money + + + align:start position:0% +it to uh they didn't want to lose money +they didn't want to sure people were + + align:start position:0% +they didn't want to sure people were + + + align:start position:0% +they didn't want to sure people were +going to get in + + align:start position:0% +going to get in + + + align:start position:0% +going to get in +accidents so I was able to change this P + + align:start position:0% +accidents so I was able to change this P + + + align:start position:0% +accidents so I was able to change this P +parameter so that it did a great job the + + align:start position:0% +parameter so that it did a great job the + + + align:start position:0% +parameter so that it did a great job the +problem was they got to write almost no + + align:start position:0% +problem was they got to write almost no + + + align:start position:0% +problem was they got to write almost no +policies because I could pretty much + + align:start position:0% +policies because I could pretty much + + + align:start position:0% +policies because I could pretty much +guarantee the people I said wouldn't get + + align:start position:0% +guarantee the people I said wouldn't get + + + align:start position:0% +guarantee the people I said wouldn't get +in an accident wouldn't but there were a + + align:start position:0% +in an accident wouldn't but there were a + + + align:start position:0% +in an accident wouldn't but there were a +whole bunch of people who didn't who + + align:start position:0% +whole bunch of people who didn't who + + + align:start position:0% +whole bunch of people who didn't who +they wouldn't write policies for so they + + align:start position:0% +they wouldn't write policies for so they + + + align:start position:0% +they wouldn't write policies for so they +ended up not making any money it was a + + align:start position:0% +ended up not making any money it was a + + + align:start position:0% +ended up not making any money it was a +bad + + align:start position:0% + + + + align:start position:0% + +decision all right + + align:start position:0% +decision all right + + + align:start position:0% +decision all right +so we can change the cut + + align:start position:0% +so we can change the cut + + + align:start position:0% +so we can change the cut +off that leads to a really important + + align:start position:0% +off that leads to a really important + + + align:start position:0% +off that leads to a really important +concept of something called the receiver + + align:start position:0% +concept of something called the receiver + + + align:start position:0% +concept of something called the receiver +operating + + align:start position:0% +operating + + + align:start position:0% +operating +characteristic and it's a funny name + + align:start position:0% +characteristic and it's a funny name + + + align:start position:0% +characteristic and it's a funny name +having to do with it originally going + + align:start position:0% +having to do with it originally going + + + align:start position:0% +having to do with it originally going +back to radios radio receivers but we + + align:start position:0% +back to radios radio receivers but we + + + align:start position:0% +back to radios radio receivers but we +can ignore + + align:start position:0% +can ignore + + + align:start position:0% +can ignore +that the goal here is to say suppose I + + align:start position:0% +that the goal here is to say suppose I + + + align:start position:0% +that the goal here is to say suppose I +don't want to to make a decision about + + align:start position:0% +don't want to to make a decision about + + + align:start position:0% +don't want to to make a decision about +where the cut off is but I want to look + + align:start position:0% +where the cut off is but I want to look + + + align:start position:0% +where the cut off is but I want to look +at in some sense all possible cut offs + + align:start position:0% +at in some sense all possible cut offs + + + align:start position:0% +at in some sense all possible cut offs +and sort of look at the shape of + + align:start position:0% +and sort of look at the shape of + + + align:start position:0% +and sort of look at the shape of +it and that's what this code is designed + + align:start position:0% +it and that's what this code is designed + + + align:start position:0% +it and that's what this code is designed +to do so the way it + + align:start position:0% +to do so the way it + + + align:start position:0% +to do so the way it +works is I'll take a training + + align:start position:0% +works is I'll take a training + + + align:start position:0% +works is I'll take a training +set and a test set the usual thing I'll + + align:start position:0% +set and a test set the usual thing I'll + + + align:start position:0% +set and a test set the usual thing I'll +build one model and that's an important + + align:start position:0% +build one model and that's an important + + + align:start position:0% +build one model and that's an important +thing that there's only one model + + align:start position:0% +thing that there's only one model + + + align:start position:0% +thing that there's only one model +getting + + align:start position:0% +getting + + + align:start position:0% +getting +built and then I'm going to vary + + align:start position:0% + + + + align:start position:0% + +p and I'm going to call apply model with + + align:start position:0% +p and I'm going to call apply model with + + + align:start position:0% +p and I'm going to call apply model with +the same model and the same test set but + + align:start position:0% +the same model and the same test set but + + + align:start position:0% +the same model and the same test set but +different + + align:start position:0% +different + + + align:start position:0% +different +P's and keep track of all of those + + align:start position:0% + + + + align:start position:0% + +results I'm then going to + + align:start position:0% +results I'm then going to + + + align:start position:0% +results I'm then going to +plot a two-dimensional plot the Y + + align:start position:0% +plot a two-dimensional plot the Y + + + align:start position:0% +plot a two-dimensional plot the Y +AIS will have + + align:start position:0% + + + + align:start position:0% + +sensitivity and the x axis will have one + + align:start position:0% +sensitivity and the x axis will have one + + + align:start position:0% +sensitivity and the x axis will have one +minus + + align:start position:0% + + + + align:start position:0% + +specificity all right so I am + + align:start position:0% +specificity all right so I am + + + align:start position:0% +specificity all right so I am +accumulating a bunch of results + + align:start position:0% + + + + align:start position:0% + +and then I'm going to produce this curve + + align:start position:0% +and then I'm going to produce this curve + + + align:start position:0% +and then I'm going to produce this curve +calling SK learn. metrics. Au that's not + + align:start position:0% +calling SK learn. metrics. Au that's not + + + align:start position:0% +calling SK learn. metrics. Au that's not +the curve Au stands for + + align:start position:0% + + + + align:start position:0% + +area under the + + align:start position:0% + + + + align:start position:0% + +curve and we'll see why we want to get + + align:start position:0% +curve and we'll see why we want to get + + + align:start position:0% +curve and we'll see why we want to get +that area under the Curve + + align:start position:0% + + + + align:start position:0% + +okay when I run + + align:start position:0% +okay when I run + + + align:start position:0% +okay when I run +that it produces + + align:start position:0% +that it produces + + + align:start position:0% +that it produces +this so here's the curve the blue + + align:start position:0% +this so here's the curve the blue + + + align:start position:0% +this so here's the curve the blue +line there's some things to note about + + align:start position:0% +line there's some things to note about + + + align:start position:0% +line there's some things to note about +it way down at this + + align:start position:0% + + + + align:start position:0% + +end I can + + align:start position:0% +end I can + + + align:start position:0% +end I can +have zero right you know I can set it so + + align:start position:0% +have zero right you know I can set it so + + + align:start position:0% +have zero right you know I can set it so +that I don't make any predictions + + align:start position:0% + + + + align:start position:0% + +so I can be and way and this end is + + align:start position:0% +so I can be and way and this end is + + + align:start position:0% +so I can be and way and this end is +interesting so with this end is saying + + align:start position:0% + + + + align:start position:0% + +what remember that my x axis is not + + align:start position:0% +what remember that my x axis is not + + + align:start position:0% +what remember that my x axis is not +specificity but one minus + + align:start position:0% +specificity but one minus + + + align:start position:0% +specificity but one minus +specificity right so what we see is this + + align:start position:0% +specificity right so what we see is this + + + align:start position:0% +specificity right so what we see is this +corner is highly sensitive and very + + align:start position:0% +corner is highly sensitive and very + + + align:start position:0% +corner is highly sensitive and very +unspecific + + align:start position:0% + + + + align:start position:0% + +so I'll get a lot of false + + align:start position:0% +so I'll get a lot of false + + + align:start position:0% +so I'll get a lot of false +positives this corner is very specific + + align:start position:0% +positives this corner is very specific + + + align:start position:0% +positives this corner is very specific +because one minus specificity is zero + + align:start position:0% +because one minus specificity is zero + + + align:start position:0% +because one minus specificity is zero +and very + + align:start position:0% +and very + + + align:start position:0% +and very +insensitive + + align:start position:0% +insensitive + + + align:start position:0% +insensitive +right so way down at the bottom I'm + + align:start position:0% +right so way down at the bottom I'm + + + align:start position:0% +right so way down at the bottom I'm +declaring nobody to be + + align:start position:0% + + + + align:start position:0% + +positive and way up here everybody + + align:start position:0% +positive and way up here everybody + + + align:start position:0% +positive and way up here everybody +clearly I don't want to be at either of + + align:start position:0% +clearly I don't want to be at either of + + + align:start position:0% +clearly I don't want to be at either of +the places on the curve right and + + align:start position:0% +the places on the curve right and + + + align:start position:0% +the places on the curve right and +typically I want to be somewhere in the + + align:start position:0% +typically I want to be somewhere in the + + + align:start position:0% +typically I want to be somewhere in the +middle and here maybe we can see there's + + align:start position:0% +middle and here maybe we can see there's + + + align:start position:0% +middle and here maybe we can see there's +a nice knee in the curve here we can + + align:start position:0% +a nice knee in the curve here we can + + + align:start position:0% +a nice knee in the curve here we can +choose a + + align:start position:0% +choose a + + + align:start position:0% +choose a +place what does this green line + + align:start position:0% +place what does this green line + + + align:start position:0% +place what does this green line +represent do you + + align:start position:0% + + + + align:start position:0% + +think the green line + + align:start position:0% +think the green line + + + align:start position:0% +think the green line +represents a random class ofier + + align:start position:0% + + + + align:start position:0% + +I flip a coin and I just classify + + align:start position:0% +I flip a coin and I just classify + + + align:start position:0% +I flip a coin and I just classify +something positive or negative depending + + align:start position:0% +something positive or negative depending + + + align:start position:0% +something positive or negative depending +on + + align:start position:0% +on + + + align:start position:0% +on +the heads or tails in this case + + align:start position:0% + + + + align:start position:0% + +right so now we can look at an + + align:start position:0% +right so now we can look at an + + + align:start position:0% +right so now we can look at an +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +region which is this + + align:start position:0% + + + + align:start position:0% + +region the area between the curve and a + + align:start position:0% +region the area between the curve and a + + + align:start position:0% +region the area between the curve and a +random classif fire and that sort of + + align:start position:0% +random classif fire and that sort of + + + align:start position:0% +random classif fire and that sort of +tells me how much better I am than + + align:start position:0% + + + + align:start position:0% + +random I can look at the whole + + align:start position:0% + + + + align:start position:0% + +area the area under the + + align:start position:0% +area the area under the + + + align:start position:0% +area the area under the +curve and + + align:start position:0% +curve and + + + align:start position:0% +curve and +that's this the area under the receiver + + align:start position:0% +that's this the area under the receiver + + + align:start position:0% +that's this the area under the receiver +operating + + align:start position:0% + + + + align:start position:0% + +curve in the best of all + + align:start position:0% +curve in the best of all + + + align:start position:0% +curve in the best of all +Worlds the curve would be shaped like + + align:start position:0% +Worlds the curve would be shaped like + + + align:start position:0% +Worlds the curve would be shaped like +you know it would be one right that + + align:start position:0% +you know it would be one right that + + + align:start position:0% +you know it would be one right that +would be a perfect + + align:start position:0% + + + + align:start position:0% + +classifier and the worst of all worlds + + align:start position:0% +classifier and the worst of all worlds + + + align:start position:0% +classifier and the worst of all worlds +it would be zero but it's never zero + + align:start position:0% +it would be zero but it's never zero + + + align:start position:0% +it would be zero but it's never zero +because we don't do worse than 0. five + + align:start position:0% +because we don't do worse than 0. five + + + align:start position:0% +because we don't do worse than 0. five +right we hope not to do worse than + + align:start position:0% +right we hope not to do worse than + + + align:start position:0% +right we hope not to do worse than +random if so we just reverse our + + align:start position:0% +random if so we just reverse our + + + align:start position:0% +random if so we just reverse our +predictions and then we're better than + + align:start position:0% +predictions and then we're better than + + + align:start position:0% +predictions and then we're better than +random So Random is as bad as you can do + + align:start position:0% +random So Random is as bad as you can do + + + align:start position:0% +random So Random is as bad as you can do +really and so this is a very important + + align:start position:0% +really and so this is a very important + + + align:start position:0% +really and so this is a very important +concept + + align:start position:0% +concept + + + align:start position:0% +concept +and it lets us evaluate how good a + + align:start position:0% +and it lets us evaluate how good a + + + align:start position:0% +and it lets us evaluate how good a +classifier is independently of what we + + align:start position:0% +classifier is independently of what we + + + align:start position:0% +classifier is independently of what we +choose to be the + + align:start position:0% + + + + align:start position:0% + +cutoff so that's when you read the + + align:start position:0% +cutoff so that's when you read the + + + align:start position:0% +cutoff so that's when you read the +literature and people say I have this + + align:start position:0% +literature and people say I have this + + + align:start position:0% +literature and people say I have this +wonderful method of making predictions + + align:start position:0% +wonderful method of making predictions + + + align:start position:0% +wonderful method of making predictions +you'll almost always see them site the + + align:start position:0% + + + + align:start position:0% + +a all + + align:start position:0% +a all + + + align:start position:0% +a all +right any questions about this if so or + + align:start position:0% +right any questions about this if so or + + + align:start position:0% +right any questions about this if so or +about machine learning in general if so + + align:start position:0% +about machine learning in general if so + + + align:start position:0% +about machine learning in general if so +this would be a good time to ask them + + align:start position:0% +this would be a good time to ask them + + + align:start position:0% +this would be a good time to ask them +since I'm about to totally change the + + align:start position:0% + + + + align:start position:0% + +topic + + align:start position:0% + + + + align:start position:0% + +yes right so the question is at what + + align:start position:0% +yes right so the question is at what + + + align:start position:0% +yes right so the question is at what +point does the Aur become statistically + + align:start position:0% +point does the Aur become statistically + + + align:start position:0% +point does the Aur become statistically +significant + + align:start position:0% +significant + + + align:start position:0% +significant +and that is essentially an unanswerable + + align:start position:0% +and that is essentially an unanswerable + + + align:start position:0% +and that is essentially an unanswerable +question + + align:start position:0% + + + + align:start position:0% + +uh oops relay it back um needed to put + + align:start position:0% +uh oops relay it back um needed to put + + + align:start position:0% +uh oops relay it back um needed to put +more air under the + + align:start position:0% +more air under the + + + align:start position:0% +more air under the +throw I look like a quarterback for the + + align:start position:0% +throw I look like a quarterback for the + + + align:start position:0% +throw I look like a quarterback for the +Rams um any rate um if you saw them them + + align:start position:0% +Rams um any rate um if you saw them them + + + align:start position:0% +Rams um any rate um if you saw them them +play + + align:start position:0% +play + + + align:start position:0% +play +lately so if if + + align:start position:0% +lately so if if + + + align:start position:0% +lately so if if +you ask this question about significance + + align:start position:0% +you ask this question about significance + + + align:start position:0% +you ask this question about significance +it will depend upon + + align:start position:0% +it will depend upon + + + align:start position:0% +it will depend upon +a number of things so you're always + + align:start position:0% +a number of things so you're always + + + align:start position:0% +a number of things so you're always +asking is it significantly better than x + + align:start position:0% +asking is it significantly better than x + + + align:start position:0% +asking is it significantly better than x +right and so the question is is + + align:start position:0% +right and so the question is is + + + align:start position:0% +right and so the question is is +significantly better than + + align:start position:0% +significantly better than + + + align:start position:0% +significantly better than +random and you can't just say for + + align:start position:0% +random and you can't just say for + + + align:start position:0% +random and you can't just say for +example that 6 is isn't and 7 is because + + align:start position:0% +example that 6 is isn't and 7 is because + + + align:start position:0% +example that 6 is isn't and 7 is because +it depends how many points you + + align:start position:0% +it depends how many points you + + + align:start position:0% +it depends how many points you +have uh the more points if you have a + + align:start position:0% +have uh the more points if you have a + + + align:start position:0% +have uh the more points if you have a +lot of points it could be only a tiny + + align:start position:0% +lot of points it could be only a tiny + + + align:start position:0% +lot of points it could be only a tiny +bit better than 0.5 and still be + + align:start position:0% +bit better than 0.5 and still be + + + align:start position:0% +bit better than 0.5 and still be +statistically + + align:start position:0% +statistically + + + align:start position:0% +statistically +significant it may be uninterestingly + + align:start position:0% +significant it may be uninterestingly + + + align:start position:0% +significant it may be uninterestingly +better it may not be significant in the + + align:start position:0% +better it may not be significant in the + + + align:start position:0% +better it may not be significant in the +English sense but you still get + + align:start position:0% +English sense but you still get + + + align:start position:0% +English sense but you still get +statistical + + align:start position:0% +statistical + + + align:start position:0% +statistical +significance um so that's a problem when + + align:start position:0% +significance um so that's a problem when + + + align:start position:0% +significance um so that's a problem when +Studies have lots of points in general + + align:start position:0% +Studies have lots of points in general + + + align:start position:0% +Studies have lots of points in general +it depends upon the application for a + + align:start position:0% +it depends upon the application for a + + + align:start position:0% +it depends upon the application for a +lot of applications you'll see things in + + align:start position:0% +lot of applications you'll see things in + + + align:start position:0% +lot of applications you'll see things in +the sevens being considered pretty + + align:start position:0% +the sevens being considered pretty + + + align:start position:0% +the sevens being considered pretty +useful and the real question shouldn't + + align:start position:0% +useful and the real question shouldn't + + + align:start position:0% +useful and the real question shouldn't +be whether it's significant or whether + + align:start position:0% +be whether it's significant or whether + + + align:start position:0% +be whether it's significant or whether +it's useful can you make useful + + align:start position:0% +it's useful can you make useful + + + align:start position:0% +it's useful can you make useful +decisions based upon it + + align:start position:0% +decisions based upon it + + + align:start position:0% +decisions based upon it +and the other thing is typically when + + align:start position:0% +and the other thing is typically when + + + align:start position:0% +and the other thing is typically when +you're talking about that you're + + align:start position:0% +you're talking about that you're + + + align:start position:0% +you're talking about that you're +selecting some + + align:start position:0% +selecting some + + + align:start position:0% +selecting some +point and really talking about a region + + align:start position:0% +point and really talking about a region + + + align:start position:0% +point and really talking about a region +relative to that point you know we + + align:start position:0% +relative to that point you know we + + + align:start position:0% +relative to that point you know we +usually don't really care what it does + + align:start position:0% +usually don't really care what it does + + + align:start position:0% +usually don't really care what it does +out here because we hardly ever operate + + align:start position:0% +out here because we hardly ever operate + + + align:start position:0% +out here because we hardly ever operate +out there anyway right we're usually + + align:start position:0% +out there anyway right we're usually + + + align:start position:0% +out there anyway right we're usually +somewhere in the + + align:start position:0% +somewhere in the + + + align:start position:0% +somewhere in the +middle but good question + + align:start position:0% + + + + align:start position:0% + +yeah why are we doing one minus + + align:start position:0% +yeah why are we doing one minus + + + align:start position:0% +yeah why are we doing one minus +specificity in instead of + + align:start position:0% +specificity in instead of + + + align:start position:0% +specificity in instead of +specificity is is that the question and + + align:start position:0% +specificity is is that the question and + + + align:start position:0% +specificity is is that the question and +the answer is essentially so we can do + + align:start position:0% +the answer is essentially so we can do + + + align:start position:0% +the answer is essentially so we can do +this trick of computing the area it + + align:start position:0% +this trick of computing the area it + + + align:start position:0% +this trick of computing the area it +gives us this nice curve conc this nice + + align:start position:0% +gives us this nice curve conc this nice + + + align:start position:0% +gives us this nice curve conc this nice +if you will concave curve which lets us + + align:start position:0% +if you will concave curve which lets us + + + align:start position:0% +if you will concave curve which lets us +compute this area under here nicely if + + align:start position:0% +compute this area under here nicely if + + + align:start position:0% +compute this area under here nicely if +you were to take specificity and just + + align:start position:0% +you were to take specificity and just + + + align:start position:0% +you were to take specificity and just +draw it it would wouldn't it would look + + align:start position:0% +draw it it would wouldn't it would look + + + align:start position:0% +draw it it would wouldn't it would look +different it just + + align:start position:0% +different it just + + + align:start position:0% +different it just +really obviously mathematically they're + + align:start position:0% +really obviously mathematically they're + + + align:start position:0% +really obviously mathematically they're +in some sense the same right if you have + + align:start position:0% +in some sense the same right if you have + + + align:start position:0% +in some sense the same right if you have +one minus x and x you can get either + + align:start position:0% +one minus x and x you can get either + + + align:start position:0% +one minus x and x you can get either +from the other so it really just has to + + align:start position:0% +from the other so it really just has to + + + align:start position:0% +from the other so it really just has to +do with the way people want to draw this + + align:start position:0% + + + + align:start position:0% + +picture + + align:start position:0% + + + + align:start position:0% + +pardon does it + + align:start position:0% + + + + align:start position:0% + +not well you you you'd have to use a + + align:start position:0% +not well you you you'd have to use a + + + align:start position:0% +not well you you you'd have to use a +different statistic right you couldn't + + align:start position:0% +different statistic right you couldn't + + + align:start position:0% +different statistic right you couldn't +recite the a if you did specificity + + align:start position:0% +recite the a if you did specificity + + + align:start position:0% +recite the a if you did specificity +directly + + align:start position:0% +directly + + + align:start position:0% +directly +right which is why they do one + + align:start position:0% +right which is why they do one + + + align:start position:0% +right which is why they do one +minus right the goal is you want to have + + align:start position:0% +minus right the goal is you want to have + + + align:start position:0% +minus right the goal is you want to have +this point at zero and this point z z + + align:start position:0% +this point at zero and this point z z + + + align:start position:0% +this point at zero and this point z z +and 1 one and playing one minus gives + + align:start position:0% +and 1 one and playing one minus gives + + + align:start position:0% +and 1 one and playing one minus gives +you this trick of anchoring those two + + align:start position:0% +you this trick of anchoring those two + + + align:start position:0% +you this trick of anchoring those two +points and so then you get a curve + + align:start position:0% +points and so then you get a curve + + + align:start position:0% +points and so then you get a curve +connecting them which you can then + + align:start position:0% +connecting them which you can then + + + align:start position:0% +connecting them which you can then +easily compare to the random + + align:start position:0% +easily compare to the random + + + align:start position:0% +easily compare to the random +curve right it's just one of these + + align:start position:0% +curve right it's just one of these + + + align:start position:0% +curve right it's just one of these +little tricks that statisticians like to + + align:start position:0% +little tricks that statisticians like to + + + align:start position:0% +little tricks that statisticians like to +play to make things easy to visualize + + align:start position:0% +play to make things easy to visualize + + + align:start position:0% +play to make things easy to visualize +and easy to + + align:start position:0% +and easy to + + + align:start position:0% +and easy to +compute statistics about it's not a + + align:start position:0% +compute statistics about it's not a + + + align:start position:0% +compute statistics about it's not a +fundamentally important + + align:start position:0% +fundamentally important + + + align:start position:0% +fundamentally important +issue anything + + align:start position:0% + + + + align:start position:0% + +else all right so I told you I was going + + align:start position:0% +else all right so I told you I was going + + + align:start position:0% +else all right so I told you I was going +to change + + align:start position:0% + + + + align:start position:0% + +topics finally got one completed and I + + align:start position:0% +topics finally got one completed and I + + + align:start position:0% +topics finally got one completed and I +am um and this is a topic I approach + + align:start position:0% +am um and this is a topic I approach + + + align:start position:0% +am um and this is a topic I approach +with some + + align:start position:0% +with some + + + align:start position:0% +with some +reluctance so you have probably all + + align:start position:0% +reluctance so you have probably all + + + align:start position:0% +reluctance so you have probably all +heard this expression that there were + + align:start position:0% +heard this expression that there were + + + align:start position:0% +heard this expression that there were +three kinds of + + align:start position:0% +three kinds of + + + align:start position:0% +three kinds of +lies + + align:start position:0% +lies + + + align:start position:0% +lies +lies damned lies and + + align:start position:0% +lies damned lies and + + + align:start position:0% +lies damned lies and +statistics we've been talking a lot + + align:start position:0% +statistics we've been talking a lot + + + align:start position:0% +statistics we've been talking a lot +about statistics and now I want to spend + + align:start position:0% +about statistics and now I want to spend + + + align:start position:0% +about statistics and now I want to spend +the rest of today's lecture and the + + align:start position:0% +the rest of today's lecture and the + + + align:start position:0% +the rest of today's lecture and the +start of next of Wednesday's lecture + + align:start position:0% +start of next of Wednesday's lecture + + + align:start position:0% +start of next of Wednesday's lecture +talking + + align:start position:0% +talking + + + align:start position:0% +talking +about how to lie with + + align:start position:0% +about how to lie with + + + align:start position:0% +about how to lie with +Statistics so at this point I usually + + align:start position:0% +Statistics so at this point I usually + + + align:start position:0% +Statistics so at this point I usually +put on my Numbers Never Lie hat + + align:start position:0% +put on my Numbers Never Lie hat + + + align:start position:0% +put on my Numbers Never Lie hat +but do say that Numbers Never Lie but + + align:start position:0% +but do say that Numbers Never Lie but + + + align:start position:0% +but do say that Numbers Never Lie but +Liars use + + align:start position:0% +Liars use + + + align:start position:0% +Liars use +numbers um and I hope uh none of you + + align:start position:0% +numbers um and I hope uh none of you + + + align:start position:0% +numbers um and I hope uh none of you +will ever go work for a politician and + + align:start position:0% +will ever go work for a politician and + + + align:start position:0% +will ever go work for a politician and +put this knowledge to bad use this quote + + align:start position:0% +put this knowledge to bad use this quote + + + align:start position:0% +put this knowledge to bad use this quote +is well known it's variously attributed + + align:start position:0% +is well known it's variously attributed + + + align:start position:0% +is well known it's variously attributed +often to Mark Twain the fellow in the + + align:start position:0% +often to Mark Twain the fellow in the + + + align:start position:0% +often to Mark Twain the fellow in the +left uh he claimed not to have invented + + align:start position:0% +left uh he claimed not to have invented + + + align:start position:0% +left uh he claimed not to have invented +it but said it was invented by Benjamin + + align:start position:0% +it but said it was invented by Benjamin + + + align:start position:0% +it but said it was invented by Benjamin +Disraeli and I prefer to believe that + + align:start position:0% +Disraeli and I prefer to believe that + + + align:start position:0% +Disraeli and I prefer to believe that +since it does seem like something a + + align:start position:0% +since it does seem like something a + + + align:start position:0% +since it does seem like something a +prime minister would + + align:start position:0% +prime minister would + + + align:start position:0% +prime minister would +invent um so let's think about this the + + align:start position:0% +invent um so let's think about this the + + + align:start position:0% +invent um so let's think about this the +issue here is the way the human mind + + align:start position:0% +issue here is the way the human mind + + + align:start position:0% +issue here is the way the human mind +works and + + align:start position:0% + + + + align:start position:0% + +statistics Daryl Huff a well-known + + align:start position:0% +statistics Daryl Huff a well-known + + + align:start position:0% +statistics Daryl Huff a well-known +statistician who did write a book called + + align:start position:0% +statistician who did write a book called + + + align:start position:0% +statistician who did write a book called +How to lie with Statistics says if you + + align:start position:0% +How to lie with Statistics says if you + + + align:start position:0% +How to lie with Statistics says if you +can't prove what you want to + + align:start position:0% +can't prove what you want to + + + align:start position:0% +can't prove what you want to +prove demonstrate something else and + + align:start position:0% +prove demonstrate something else and + + + align:start position:0% +prove demonstrate something else and +pretend they're the same + + align:start position:0% +pretend they're the same + + + align:start position:0% +pretend they're the same +thing in the days that follow follows + + align:start position:0% +thing in the days that follow follows + + + align:start position:0% +thing in the days that follow follows +the Collision of Statistics with the + + align:start position:0% +the Collision of Statistics with the + + + align:start position:0% +the Collision of Statistics with the +human mind hardly anyone will notice the + + align:start position:0% +human mind hardly anyone will notice the + + + align:start position:0% +human mind hardly anyone will notice the +difference and indeed uh empirically he + + align:start position:0% +difference and indeed uh empirically he + + + align:start position:0% +difference and indeed uh empirically he +seems to be + + align:start position:0% +seems to be + + + align:start position:0% +seems to be +right so let's look at some + + align:start position:0% +right so let's look at some + + + align:start position:0% +right so let's look at some +examples here's one I like this is from + + align:start position:0% +examples here's one I like this is from + + + align:start position:0% +examples here's one I like this is from +another famous statistician called + + align:start position:0% +another famous statistician called + + + align:start position:0% +another famous statistician called +Anum and he invented this thing called + + align:start position:0% +Anum and he invented this thing called + + + align:start position:0% +Anum and he invented this thing called +anam's quartet I take my hat off now + + align:start position:0% +anam's quartet I take my hat off now + + + align:start position:0% +anam's quartet I take my hat off now +it's too hot in here + + align:start position:0% +it's too hot in here + + + align:start position:0% +it's too hot in here +um a bunch of numbers + + align:start position:0% +um a bunch of numbers + + + align:start position:0% +um a bunch of numbers +uh 11 XY + + align:start position:0% + + + + align:start position:0% + +pairs I know you don't want to look at + + align:start position:0% +pairs I know you don't want to look at + + + align:start position:0% +pairs I know you don't want to look at +the numbers so here are some statistics + + align:start position:0% +the numbers so here are some statistics + + + align:start position:0% +the numbers so here are some statistics +about + + align:start position:0% +about + + + align:start position:0% +about +them each of those pairs has the same + + align:start position:0% +them each of those pairs has the same + + + align:start position:0% +them each of those pairs has the same +mean + + align:start position:0% +mean + + + align:start position:0% +mean +value for x the same mean for y the same + + align:start position:0% +value for x the same mean for y the same + + + align:start position:0% +value for x the same mean for y the same +variance for X the same variance for y + + align:start position:0% +variance for X the same variance for y + + + align:start position:0% +variance for X the same variance for y +and then I went I fit a linear + + align:start position:0% +and then I went I fit a linear + + + align:start position:0% +and then I went I fit a linear +regression model to it and lo and behold + + align:start position:0% +regression model to it and lo and behold + + + align:start position:0% +regression model to it and lo and behold +I got the same equation for everyone yal + + align:start position:0% +I got the same equation for everyone yal + + + align:start position:0% +I got the same equation for everyone yal +.5x + + + align:start position:0% +.5x + + + + align:start position:0% +.5x + +3 so that raises the + + align:start position:0% +3 so that raises the + + + align:start position:0% +3 so that raises the +question if we go back is there really + + align:start position:0% +question if we go back is there really + + + align:start position:0% +question if we go back is there really +much difference between these these + + align:start position:0% +much difference between these these + + + align:start position:0% +much difference between these these +pairs of X and + + align:start position:0% + + + + align:start position:0% + +Y are they really similar and the answer + + align:start position:0% +Y are they really similar and the answer + + + align:start position:0% +Y are they really similar and the answer +is that's what they look like if you + + align:start position:0% +is that's what they look like if you + + + align:start position:0% +is that's what they look like if you +plot + + align:start position:0% +plot + + + align:start position:0% +plot +them so even though statistically they + + align:start position:0% +them so even though statistically they + + + align:start position:0% +them so even though statistically they +appear to be kind of the same they could + + align:start position:0% +appear to be kind of the same they could + + + align:start position:0% +appear to be kind of the same they could +hardly be more different right right + + align:start position:0% +hardly be more different right right + + + align:start position:0% +hardly be more different right right +those are not the same + + align:start position:0% +those are not the same + + + align:start position:0% +those are not the same +distributions so there's an important + + align:start position:0% +distributions so there's an important + + + align:start position:0% +distributions so there's an important +moral + + align:start position:0% +moral + + + align:start position:0% +moral +here which is that statistics about data + + align:start position:0% +here which is that statistics about data + + + align:start position:0% +here which is that statistics about data +is not the same thing as the data + + align:start position:0% +is not the same thing as the data + + + align:start position:0% +is not the same thing as the data +itself and this seems obvious but it's + + align:start position:0% +itself and this seems obvious but it's + + + align:start position:0% +itself and this seems obvious but it's +amazing how easy it is to forget it the + + align:start position:0% +amazing how easy it is to forget it the + + + align:start position:0% +amazing how easy it is to forget it the +number of papers I've read where I see a + + align:start position:0% +number of papers I've read where I see a + + + align:start position:0% +number of papers I've read where I see a +bunch of statistics about the data but + + align:start position:0% +bunch of statistics about the data but + + + align:start position:0% +bunch of statistics about the data but +don't see the data is enormous and it's + + align:start position:0% +don't see the data is enormous and it's + + + align:start position:0% +don't see the data is enormous and it's +easy to lose track of the fact that the + + align:start position:0% +easy to lose track of the fact that the + + + align:start position:0% +easy to lose track of the fact that the +statistics don't tell the whole + + align:start position:0% +statistics don't tell the whole + + + align:start position:0% +statistics don't tell the whole +story so the answer is the old Chinese + + align:start position:0% +story so the answer is the old Chinese + + + align:start position:0% +story so the answer is the old Chinese +proverb a picture is worth a thousand + + align:start position:0% +proverb a picture is worth a thousand + + + align:start position:0% +proverb a picture is worth a thousand +words I urge you the first thing you + + align:start position:0% +words I urge you the first thing you + + + align:start position:0% +words I urge you the first thing you +should do when you get a data set is + + align:start position:0% +should do when you get a data set is + + + align:start position:0% +should do when you get a data set is +plot it if it's got too many points to + + align:start position:0% +plot it if it's got too many points to + + + align:start position:0% +plot it if it's got too many points to +plot all the points subsample it and + + align:start position:0% +plot all the points subsample it and + + + align:start position:0% +plot all the points subsample it and +plot a + + align:start position:0% +plot a + + + align:start position:0% +plot a +subsample uh use some visualization tool + + align:start position:0% +subsample uh use some visualization tool + + + align:start position:0% +subsample uh use some visualization tool +to look at the data + + align:start position:0% +to look at the data + + + align:start position:0% +to look at the data +itself now that said + + align:start position:0% +itself now that said + + + align:start position:0% +itself now that said +pictures are + + align:start position:0% +pictures are + + + align:start position:0% +pictures are +wonderful but you can lie with pictures + + align:start position:0% +wonderful but you can lie with pictures + + + align:start position:0% +wonderful but you can lie with pictures +so here's an interesting chart these are + + align:start position:0% +so here's an interesting chart these are + + + align:start position:0% +so here's an interesting chart these are +grades in 601 by + + align:start position:0% +grades in 601 by + + + align:start position:0% +grades in 601 by +gender so the males are blue and the + + align:start position:0% +gender so the males are blue and the + + + align:start position:0% +gender so the males are blue and the +females are pink sorry for being such a + + align:start position:0% +females are pink sorry for being such a + + + align:start position:0% +females are pink sorry for being such a +traditionalist and as you can see the + + align:start position:0% +traditionalist and as you can see the + + + align:start position:0% +traditionalist and as you can see the +women did way better than the + + align:start position:0% +women did way better than the + + + align:start position:0% +women did way better than the +men um now I know for some of you this + + align:start position:0% +men um now I know for some of you this + + + align:start position:0% +men um now I know for some of you this +is confirmation bias you say of course + + align:start position:0% +is confirmation bias you say of course + + + align:start position:0% +is confirmation bias you say of course +others say impossible but in in fact if + + align:start position:0% +others say impossible but in in fact if + + + align:start position:0% +others say impossible but in in fact if +you look carefully you'll see that's not + + align:start position:0% +you look carefully you'll see that's not + + + align:start position:0% +you look carefully you'll see that's not +what this chart says at + + align:start position:0% +what this chart says at + + + align:start position:0% +what this chart says at +all because if you look at the axis + + align:start position:0% +all because if you look at the axis + + + align:start position:0% +all because if you look at the axis +here you'll see that actually there's + + align:start position:0% +here you'll see that actually there's + + + align:start position:0% +here you'll see that actually there's +not much + + align:start position:0% +not much + + + align:start position:0% +not much +difference here's what I get if I plot + + align:start position:0% +difference here's what I get if I plot + + + align:start position:0% +difference here's what I get if I plot +it from zero to + + align:start position:0% +it from zero to + + + align:start position:0% +it from zero to +five yeah the women did a little bit + + align:start position:0% +five yeah the women did a little bit + + + align:start position:0% +five yeah the women did a little bit +better but that's not a statistically + + align:start position:0% +better but that's not a statistically + + + align:start position:0% +better but that's not a statistically +significant + + align:start position:0% +significant + + + align:start position:0% +significant +difference and by the way when I plotted + + align:start position:0% +difference and by the way when I plotted + + + align:start position:0% +difference and by the way when I plotted +it last year for + + align:start position:0% +it last year for + + + align:start position:0% +it last year for +62 I the blue was about that much higher + + align:start position:0% +62 I the blue was about that much higher + + + align:start position:0% +62 I the blue was about that much higher +than the + + align:start position:0% +than the + + + align:start position:0% +than the +pink don't read much into either of them + + align:start position:0% +pink don't read much into either of them + + + align:start position:0% +pink don't read much into either of them +but the trick was here I took the Y AIS + + align:start position:0% +but the trick was here I took the Y AIS + + + align:start position:0% +but the trick was here I took the Y AIS +and ran it from 3.9 to + + align:start position:0% + + + + align:start position:0% + +4.05 I cleverly chose my Baseline in + + align:start position:0% +4.05 I cleverly chose my Baseline in + + + align:start position:0% +4.05 I cleverly chose my Baseline in +such a way to make the difference look + + align:start position:0% +such a way to make the difference look + + + align:start position:0% +such a way to make the difference look +really big much bigger than it + + align:start position:0% + + + + align:start position:0% + +is here I did the honest thing of put + + align:start position:0% +is here I did the honest thing of put + + + align:start position:0% +is here I did the honest thing of put +the Baseline at zero and run it to five + + align:start position:0% +the Baseline at zero and run it to five + + + align:start position:0% +the Baseline at zero and run it to five +because that's the range of grades at + + align:start position:0% +because that's the range of grades at + + + align:start position:0% +because that's the range of grades at +MIT and so when you look at a + + align:start position:0% +MIT and so when you look at a + + + align:start position:0% +MIT and so when you look at a +chart it's important to keep in mind + + align:start position:0% +chart it's important to keep in mind + + + align:start position:0% +chart it's important to keep in mind +that you need to look at the axis + + align:start position:0% +that you need to look at the axis + + + align:start position:0% +that you need to look at the axis +labels and the + + align:start position:0% + + + + align:start position:0% + +scales let's look at another chart just + + align:start position:0% +scales let's look at another chart just + + + align:start position:0% +scales let's look at another chart just +in case you think I'm the only one who + + align:start position:0% +in case you think I'm the only one who + + + align:start position:0% +in case you think I'm the only one who +likes to play with + + align:start position:0% +likes to play with + + + align:start position:0% +likes to play with +Graphics uh this is a chart from Fox + + align:start position:0% +Graphics uh this is a chart from Fox + + + align:start position:0% +Graphics uh this is a chart from Fox +News and uh uh they're arguing here it's + + align:start position:0% +News and uh uh they're arguing here it's + + + align:start position:0% +News and uh uh they're arguing here it's +a shocking statistics that there are 10 + + align:start position:0% +a shocking statistics that there are 10 + + + align:start position:0% +a shocking statistics that there are 10 +18.6 million people on welfare and + + align:start position:0% +18.6 million people on welfare and + + + align:start position:0% +18.6 million people on welfare and +101.7 with a full-time job and you can + + align:start position:0% +101.7 with a full-time job and you can + + + align:start position:0% +101.7 with a full-time job and you can +imagine the rhetoric that accompanies + + align:start position:0% +imagine the rhetoric that accompanies + + + align:start position:0% +imagine the rhetoric that accompanies +this + + align:start position:0% +this + + + align:start position:0% +this +chart + + align:start position:0% +chart + + + align:start position:0% +chart +um this is actually + + align:start position:0% +um this is actually + + + align:start position:0% +um this is actually +correct uh it's from it is true from the + + align:start position:0% +correct uh it's from it is true from the + + + align:start position:0% +correct uh it's from it is true from the +Census Bureau data sort of but notice + + align:start position:0% +Census Bureau data sort of but notice + + + align:start position:0% +Census Bureau data sort of but notice +that + + align:start position:0% +that + + + align:start position:0% +that +I said you should read the labels on the + + align:start position:0% +I said you should read the labels on the + + + align:start position:0% +I said you should read the labels on the +axes There Is No Label + + align:start position:0% +axes There Is No Label + + + align:start position:0% +axes There Is No Label +here + + align:start position:0% +here + + + align:start position:0% +here +so but you can bet that the Y intercept + + align:start position:0% +so but you can bet that the Y intercept + + + align:start position:0% +so but you can bet that the Y intercept +is not + + align:start position:0% +is not + + + align:start position:0% +is not +zero on this right because you can see + + align:start position:0% +zero on this right because you can see + + + align:start position:0% +zero on this right because you can see +how small one 101.7 looks + + align:start position:0% +how small one 101.7 looks + + + align:start position:0% +how small one 101.7 looks +like so it makes the difference look + + align:start position:0% +like so it makes the difference look + + + align:start position:0% +like so it makes the difference look +bigger than it + + align:start position:0% + + + + align:start position:0% + +is now that's not the only funny thing + + align:start position:0% +is now that's not the only funny thing + + + align:start position:0% +is now that's not the only funny thing +about + + align:start position:0% +about + + + align:start position:0% +about +it um I said you should look at the + + align:start position:0% +it um I said you should look at the + + + align:start position:0% +it um I said you should look at the +labels on the x + + align:start position:0% +labels on the x + + + align:start position:0% +labels on the x +axis well they've labeled them but what + + align:start position:0% +axis well they've labeled them but what + + + align:start position:0% +axis well they've labeled them but what +do these things + + align:start position:0% +do these things + + + align:start position:0% +do these things +mean well I looked it up and I'll tell + + align:start position:0% +mean well I looked it up and I'll tell + + + align:start position:0% +mean well I looked it up and I'll tell +you what they actually + + align:start position:0% +you what they actually + + + align:start position:0% +you what they actually +mean people on + + align:start position:0% +mean people on + + + align:start position:0% +mean people on +welfare counts the number of people in a + + align:start position:0% +welfare counts the number of people in a + + + align:start position:0% +welfare counts the number of people in a +household in which at least one person + + align:start position:0% +household in which at least one person + + + align:start position:0% +household in which at least one person +is on + + align:start position:0% +is on + + + align:start position:0% +is on +Welfare so if there is + + align:start position:0% +Welfare so if there is + + + align:start position:0% +Welfare so if there is +say two parents one is working and one + + align:start position:0% +say two parents one is working and one + + + align:start position:0% +say two parents one is working and one +is collecting welfare and there are four + + align:start position:0% +is collecting welfare and there are four + + + align:start position:0% +is collecting welfare and there are four +kids that counts as six people on + + align:start position:0% + + + + align:start position:0% + +welfare people with a full-time job is + + align:start position:0% +welfare people with a full-time job is + + + align:start position:0% +welfare people with a full-time job is +actually does not count + + align:start position:0% +actually does not count + + + align:start position:0% +actually does not count +households so in the same family you + + align:start position:0% +households so in the same family you + + + align:start position:0% +households so in the same family you +would have six on the bar on the left + + align:start position:0% +would have six on the bar on the left + + + align:start position:0% +would have six on the bar on the left +and one on the bar on the + + align:start position:0% +and one on the bar on the + + + align:start position:0% +and one on the bar on the +right clearly giving a very different + + align:start position:0% +right clearly giving a very different + + + align:start position:0% +right clearly giving a very different +impression + + align:start position:0% +impression + + + align:start position:0% +impression +right and so again pictures can be good + + align:start position:0% +right and so again pictures can be good + + + align:start position:0% +right and so again pictures can be good +but if you don't dive deep into them + + align:start position:0% +but if you don't dive deep into them + + + align:start position:0% +but if you don't dive deep into them +they really can fool you now before I + + align:start position:0% +they really can fool you now before I + + + align:start position:0% +they really can fool you now before I +should leave this slide I should say + + align:start position:0% +should leave this slide I should say + + + align:start position:0% +should leave this slide I should say +that it's not the case that you can't + + align:start position:0% +that it's not the case that you can't + + + align:start position:0% +that it's not the case that you can't +believe anything you read on Fox News + + align:start position:0% +believe anything you read on Fox News + + + align:start position:0% +believe anything you read on Fox News +because in fact the Red Sox did beat the + + align:start position:0% +because in fact the Red Sox did beat the + + + align:start position:0% +because in fact the Red Sox did beat the +St Louis Cardinals 4 to two that + + align:start position:0% + + + + align:start position:0% + +day so the moral here is to ask whether + + align:start position:0% +day so the moral here is to ask whether + + + align:start position:0% +day so the moral here is to ask whether +the things being compared are actually + + align:start position:0% +the things being compared are actually + + + align:start position:0% +the things being compared are actually +comparable are you really comparing + + align:start position:0% +comparable are you really comparing + + + align:start position:0% +comparable are you really comparing +apples and oranges as they + + align:start position:0% +apples and oranges as they + + + align:start position:0% +apples and oranges as they +say okay this is probably the most + + align:start position:0% +say okay this is probably the most + + + align:start position:0% +say okay this is probably the most +common statistical sin it's called Geo + + align:start position:0% +common statistical sin it's called Geo + + + align:start position:0% +common statistical sin it's called Geo +and perhaps this picture can tell you + + align:start position:0% +and perhaps this picture can tell you + + + align:start position:0% +and perhaps this picture can tell you +make you guess what the G's stand for + + align:start position:0% +make you guess what the G's stand for + + + align:start position:0% +make you guess what the G's stand for +geo is garbage in garbage out + + align:start position:0% + + + + align:start position:0% + +so here's a great again quote about it + + align:start position:0% +so here's a great again quote about it + + + align:start position:0% +so here's a great again quote about it +so Charles + + align:start position:0% +so Charles + + + align:start position:0% +so Charles +Babbage uh designed the first digital + + align:start position:0% +Babbage uh designed the first digital + + + align:start position:0% +Babbage uh designed the first digital +computer the first actual computation + + align:start position:0% +computer the first actual computation + + + align:start position:0% +computer the first actual computation +engine he was unable to build it but + + align:start position:0% +engine he was unable to build it but + + + align:start position:0% +engine he was unable to build it but +hundreds of years after he died one was + + align:start position:0% +hundreds of years after he died one was + + + align:start position:0% +hundreds of years after he died one was +built according to his design and it + + align:start position:0% +built according to his design and it + + + align:start position:0% +built according to his design and it +actually worked no electronics really so + + align:start position:0% +actually worked no electronics really so + + + align:start position:0% +actually worked no electronics really so +he was a famous person and he was was + + align:start position:0% +he was a famous person and he was was + + + align:start position:0% +he was a famous person and he was was +asked by Parliament about his machine + + align:start position:0% +asked by Parliament about his machine + + + align:start position:0% +asked by Parliament about his machine +which he was asking them to fund well if + + align:start position:0% +which he was asking them to fund well if + + + align:start position:0% +which he was asking them to fund well if +you put wrong numbers into the machine + + align:start position:0% +you put wrong numbers into the machine + + + align:start position:0% +you put wrong numbers into the machine +will the machine have right numbers come + + align:start position:0% +will the machine have right numbers come + + + align:start position:0% +will the machine have right numbers come +out the other + + align:start position:0% +out the other + + + align:start position:0% +out the other +end and of course he was a very smart + + align:start position:0% +end and of course he was a very smart + + + align:start position:0% +end and of course he was a very smart +guy and he was totally baffled this + + align:start position:0% +guy and he was totally baffled this + + + align:start position:0% +guy and he was totally baffled this +question seemed so stupid he couldn't + + align:start position:0% +question seemed so stupid he couldn't + + + align:start position:0% +question seemed so stupid he couldn't +believe it when anyone even ask it that + + align:start position:0% +believe it when anyone even ask it that + + + align:start position:0% +believe it when anyone even ask it that +it was just + + align:start position:0% +it was just + + + align:start position:0% +it was just +computation and the answers you get are + + align:start position:0% +computation and the answers you get are + + + align:start position:0% +computation and the answers you get are +based on the data you put in + + align:start position:0% +based on the data you put in + + + align:start position:0% +based on the data you put in +if you put in garbage you get out + + align:start position:0% +if you put in garbage you get out + + + align:start position:0% +if you put in garbage you get out +garbage so here is an example from the + + align:start position:0% +garbage so here is an example from the + + + align:start position:0% +garbage so here is an example from the +1840s um they did a census in the 1840s + + align:start position:0% +1840s um they did a census in the 1840s + + + align:start position:0% +1840s um they did a census in the 1840s +and for those of you who are not + + align:start position:0% +and for those of you who are not + + + align:start position:0% +and for those of you who are not +familiar with American history it was a + + align:start position:0% +familiar with American history it was a + + + align:start position:0% +familiar with American history it was a +very contentious time in the + + align:start position:0% +very contentious time in the + + + align:start position:0% +very contentious time in the +US uh the country was divided between + + align:start position:0% +US uh the country was divided between + + + align:start position:0% +US uh the country was divided between +states that had slavery and states that + + align:start position:0% +states that had slavery and states that + + + align:start position:0% +states that had slavery and states that +didn't + + align:start position:0% +didn't + + + align:start position:0% +didn't +and that was the dominant political + + align:start position:0% +and that was the dominant political + + + align:start position:0% +and that was the dominant political +issue of the day uh John Calhoun who was + + align:start position:0% +issue of the day uh John Calhoun who was + + + align:start position:0% +issue of the day uh John Calhoun who was +Secretary of State and a leader in the + + align:start position:0% +Secretary of State and a leader in the + + + align:start position:0% +Secretary of State and a leader in the +Senate um was a from South Carolina and + + align:start position:0% +Senate um was a from South Carolina and + + + align:start position:0% +Senate um was a from South Carolina and +a strong probably the strongest + + align:start position:0% +a strong probably the strongest + + + align:start position:0% +a strong probably the strongest +proponent of + + align:start position:0% +proponent of + + + align:start position:0% +proponent of +slavery and he used the sentence the + + align:start position:0% +slavery and he used the sentence the + + + align:start position:0% +slavery and he used the sentence the +sensus data to say that slavery was + + align:start position:0% +sensus data to say that slavery was + + + align:start position:0% +sensus data to say that slavery was +actually good for the + + align:start position:0% +actually good for the + + + align:start position:0% +actually good for the +slaves kind of an amazing thought + + align:start position:0% +slaves kind of an amazing thought + + + align:start position:0% +slaves kind of an amazing thought +basically saying that uh the data + + align:start position:0% +basically saying that uh the data + + + align:start position:0% +basically saying that uh the data +claimed that free + + align:start position:0% +claimed that free + + + align:start position:0% +claimed that free +slaves were more likely to be insane + + align:start position:0% +slaves were more likely to be insane + + + align:start position:0% +slaves were more likely to be insane +than enslaved + + align:start position:0% +than enslaved + + + align:start position:0% +than enslaved +slaves + + align:start position:0% + + + + align:start position:0% + +um he was rebutted in the sentence + + align:start position:0% +um he was rebutted in the sentence + + + align:start position:0% +um he was rebutted in the sentence +senate or in the house by John quinsey + + align:start position:0% +senate or in the house by John quinsey + + + align:start position:0% +senate or in the house by John quinsey +Adams who had formerly been president of + + align:start position:0% +Adams who had formerly been president of + + + align:start position:0% +Adams who had formerly been president of +the United States after he stopped being + + align:start position:0% +the United States after he stopped being + + + align:start position:0% +the United States after he stopped being +president he ran for + + align:start position:0% +president he ran for + + + align:start position:0% +president he ran for +congress uh from brain tree + + align:start position:0% +congress uh from brain tree + + + align:start position:0% +congress uh from brain tree +Massachusetts actually now called + + align:start position:0% +Massachusetts actually now called + + + align:start position:0% +Massachusetts actually now called +quinsey the part he's from after his + + align:start position:0% +quinsey the part he's from after his + + + align:start position:0% +quinsey the part he's from after his +family um and he claimed that atrocious + + align:start position:0% +family um and he claimed that atrocious + + + align:start position:0% +family um and he claimed that atrocious +misrepresentations have been made on a + + align:start position:0% +misrepresentations have been made on a + + + align:start position:0% +misrepresentations have been made on a +subject of deep importance he was an + + align:start position:0% +subject of deep importance he was an + + + align:start position:0% +subject of deep importance he was an +abolitionist so you don't even have to + + align:start position:0% +abolitionist so you don't even have to + + + align:start position:0% +abolitionist so you don't even have to +look at statistics know who to believe + + align:start position:0% +look at statistics know who to believe + + + align:start position:0% +look at statistics know who to believe +just look at these pictures right are + + align:start position:0% +just look at these pictures right are + + + align:start position:0% +just look at these pictures right are +you going to believe this nice gentleman + + align:start position:0% +you going to believe this nice gentleman + + + align:start position:0% +you going to believe this nice gentleman +from Braintree or this scary guy from + + align:start position:0% +from Braintree or this scary guy from + + + align:start position:0% +from Braintree or this scary guy from +South + + align:start position:0% +South + + + align:start position:0% +South +Carolina but setting that looks aside um + + align:start position:0% +Carolina but setting that looks aside um + + + align:start position:0% +Carolina but setting that looks aside um +Calhoun eventually admitted that the the + + align:start position:0% +Calhoun eventually admitted that the the + + + align:start position:0% +Calhoun eventually admitted that the the +census was indeed full of errors + + align:start position:0% +census was indeed full of errors + + + align:start position:0% +census was indeed full of errors +but he said that was fine because there + + align:start position:0% +but he said that was fine because there + + + align:start position:0% +but he said that was fine because there +were so many of them that they would + + align:start position:0% +were so many of them that they would + + + align:start position:0% +were so many of them that they would +balance each other out and lead to the + + align:start position:0% +balance each other out and lead to the + + + align:start position:0% +balance each other out and lead to the +same conclusion as if they were all + + align:start position:0% +same conclusion as if they were all + + + align:start position:0% +same conclusion as if they were all +correct so he didn't believe in garbage + + align:start position:0% +correct so he didn't believe in garbage + + + align:start position:0% +correct so he didn't believe in garbage +in garbage out he said yeah it's re is + + align:start position:0% +in garbage out he said yeah it's re is + + + align:start position:0% +in garbage out he said yeah it's re is +garbage but it'll all come out in in the + + align:start position:0% +garbage but it'll all come out in in the + + + align:start position:0% +garbage but it'll all come out in in the +end + + align:start position:0% +end + + + align:start position:0% +end +okay + + align:start position:0% +okay + + + align:start position:0% +okay +well now we know enough to ask the + + align:start position:0% +well now we know enough to ask the + + + align:start position:0% +well now we know enough to ask the +question this + + align:start position:0% +question this + + + align:start position:0% +question this +isn't totally brain dead and we've + + align:start position:0% +isn't totally brain dead and we've + + + align:start position:0% +isn't totally brain dead and we've +already looked at experiments and said + + align:start position:0% +already looked at experiments and said + + + align:start position:0% +already looked at experiments and said +we get experimental error and under some + + align:start position:0% +we get experimental error and under some + + + align:start position:0% +we get experimental error and under some +circumstances you can manage the + + align:start position:0% +circumstances you can manage the + + + align:start position:0% +circumstances you can manage the +error right the data isn't garbage just + + align:start position:0% +error right the data isn't garbage just + + + align:start position:0% +error right the data isn't garbage just +as errors but it's true if the + + align:start position:0% +as errors but it's true if the + + + align:start position:0% +as errors but it's true if the +measurement errors are + + align:start position:0% +measurement errors are + + + align:start position:0% +measurement errors are +unbiased and independent of each other + + align:start position:0% +unbiased and independent of each other + + + align:start position:0% +unbiased and independent of each other +and almost identically distributed on + + align:start position:0% +and almost identically distributed on + + + align:start position:0% +and almost identically distributed on +either side of the mean right that's why + + align:start position:0% +either side of the mean right that's why + + + align:start position:0% +either side of the mean right that's why +we spend so much time looking at the + + align:start position:0% +we spend so much time looking at the + + + align:start position:0% +we spend so much time looking at the +normal + + align:start position:0% +normal + + + align:start position:0% +normal +distribution and why it's called called + + align:start position:0% +distribution and why it's called called + + + align:start position:0% +distribution and why it's called called +gaussian because gaus said yes I know I + + align:start position:0% +gaussian because gaus said yes I know I + + + align:start position:0% +gaussian because gaus said yes I know I +have errors in my astronomical + + align:start position:0% +have errors in my astronomical + + + align:start position:0% +have errors in my astronomical +measurements but I believe my errors are + + align:start position:0% +measurements but I believe my errors are + + + align:start position:0% +measurements but I believe my errors are +distributed in what we now call a + + align:start position:0% +distributed in what we now call a + + + align:start position:0% +distributed in what we now call a +gaussian curve and therefore I can still + + align:start position:0% +gaussian curve and therefore I can still + + + align:start position:0% +gaussian curve and therefore I can still +work with them and get an accurate + + align:start position:0% +work with them and get an accurate + + + align:start position:0% +work with them and get an accurate +estimate of the + + align:start position:0% + + + + align:start position:0% + +values now of + + align:start position:0% +values now of + + + align:start position:0% +values now of +course that wasn't true here the the + + align:start position:0% +course that wasn't true here the the + + + align:start position:0% +course that wasn't true here the the +errors were not random they were in fact + + align:start position:0% +errors were not random they were in fact + + + align:start position:0% +errors were not random they were in fact +quite systematic designed to produce a + + align:start position:0% +quite systematic designed to produce a + + + align:start position:0% +quite systematic designed to produce a +certain thing + + align:start position:0% +certain thing + + + align:start position:0% +certain thing +and the last word was from another + + align:start position:0% +and the last word was from another + + + align:start position:0% +and the last word was from another +abolitionist who claimed it was the in + + align:start position:0% +abolitionist who claimed it was the in + + + align:start position:0% +abolitionist who claimed it was the in +census that was + + align:start position:0% +census that was + + + align:start position:0% +census that was +insane all right that's garbage in + + align:start position:0% +insane all right that's garbage in + + + align:start position:0% +insane all right that's garbage in +garbage + + align:start position:0% +garbage + + + align:start position:0% +garbage +out the moral here is that analysis of + + align:start position:0% +out the moral here is that analysis of + + + align:start position:0% +out the moral here is that analysis of +bad data is worse than no analysis at + + align:start position:0% +bad data is worse than no analysis at + + + align:start position:0% +bad data is worse than no analysis at +all really right time and again we see + + align:start position:0% +all really right time and again we see + + + align:start position:0% +all really right time and again we see +people doing actually often correct + + align:start position:0% +people doing actually often correct + + + align:start position:0% +people doing actually often correct +statistical analysis of incorrect data + + align:start position:0% +statistical analysis of incorrect data + + + align:start position:0% +statistical analysis of incorrect data +and reaching + + align:start position:0% +and reaching + + + align:start position:0% +and reaching +conclusions right and that's really + + align:start position:0% +conclusions right and that's really + + + align:start position:0% +conclusions right and that's really +risky so before one goes off and starts + + align:start position:0% +risky so before one goes off and starts + + + align:start position:0% +risky so before one goes off and starts +using statistical techniques of the sort + + align:start position:0% +using statistical techniques of the sort + + + align:start position:0% +using statistical techniques of the sort +we've been discussing the first question + + align:start position:0% +we've been discussing the first question + + + align:start position:0% +we've been discussing the first question +you have to ask is is the data itself + + align:start position:0% +you have to ask is is the data itself + + + align:start position:0% +you have to ask is is the data itself +worth + + align:start position:0% +worth + + + align:start position:0% +worth +analyzing and it often + + align:start position:0% +analyzing and it often + + + align:start position:0% +analyzing and it often +isn't now you could argue that this is a + + align:start position:0% +isn't now you could argue that this is a + + + align:start position:0% +isn't now you could argue that this is a +thing of the past and no modern + + align:start position:0% +thing of the past and no modern + + + align:start position:0% +thing of the past and no modern +politician would make these kinds of + + align:start position:0% +politician would make these kinds of + + + align:start position:0% +politician would make these kinds of +mistakes uh I'm not going to insert a + + align:start position:0% +mistakes uh I'm not going to insert a + + + align:start position:0% +mistakes uh I'm not going to insert a +photo here but + + align:start position:0% +photo here but + + + align:start position:0% +photo here but +I leave it to you to think which + + align:start position:0% +I leave it to you to think which + + + align:start position:0% +I leave it to you to think which +politician's photo you might paste in + + align:start position:0% +politician's photo you might paste in + + + align:start position:0% +politician's photo you might paste in +this + + align:start position:0% +this + + + align:start position:0% +this +Frame all right on to another + + align:start position:0% +Frame all right on to another + + + align:start position:0% +Frame all right on to another +statistical sin this is a picture of a + + align:start position:0% +statistical sin this is a picture of a + + + align:start position:0% +statistical sin this is a picture of a +World War II fighter plane I don't know + + align:start position:0% +World War II fighter plane I don't know + + + align:start position:0% +World War II fighter plane I don't know +enough about planes to know what kind of + + align:start position:0% +enough about planes to know what kind of + + + align:start position:0% +enough about planes to know what kind of +plane it is anyone here must be an arrow + + align:start position:0% +plane it is anyone here must be an arrow + + + align:start position:0% +plane it is anyone here must be an arrow +student who will be able to tell me what + + align:start position:0% +student who will be able to tell me what + + + align:start position:0% +student who will be able to tell me what +plane this + + align:start position:0% +plane this + + + align:start position:0% +plane this +is don't they teach you guys anything in + + align:start position:0% +is don't they teach you guys anything in + + + align:start position:0% +is don't they teach you guys anything in +error these + + align:start position:0% +error these + + + align:start position:0% +error these +days shame on them all right anyway it's + + align:start position:0% +days shame on them all right anyway it's + + + align:start position:0% +days shame on them all right anyway it's +a plane that much I know and it has a + + align:start position:0% +a plane that much I know and it has a + + + align:start position:0% +a plane that much I know and it has a +propeller and that's all I can tell you + + align:start position:0% +propeller and that's all I can tell you + + + align:start position:0% +propeller and that's all I can tell you +about the airplane so this was a photo + + align:start position:0% +about the airplane so this was a photo + + + align:start position:0% +about the airplane so this was a photo +taken at a Airfield in + + align:start position:0% +taken at a Airfield in + + + align:start position:0% +taken at a Airfield in +Britain and the Allies would send planes + + align:start position:0% +Britain and the Allies would send planes + + + align:start position:0% +Britain and the Allies would send planes +over Germany for bombing runs and + + align:start position:0% +over Germany for bombing runs and + + + align:start position:0% +over Germany for bombing runs and +fighters to protect the + + align:start position:0% +fighters to protect the + + + align:start position:0% +fighters to protect the +bombers and when they came back the + + align:start position:0% +bombers and when they came back the + + + align:start position:0% +bombers and when they came back the +planes were often damaged and they would + + align:start position:0% +planes were often damaged and they would + + + align:start position:0% +planes were often damaged and they would +inspect the damage and say oh look + + align:start position:0% +inspect the damage and say oh look + + + align:start position:0% +inspect the damage and say oh look +there's a lot of flak there the Germans + + align:start position:0% +there's a lot of flak there the Germans + + + align:start position:0% +there's a lot of flak there the Germans +shot Flack at the planes + + align:start position:0% +shot Flack at the planes + + + align:start position:0% +shot Flack at the planes +and that would be a part of the plane + + align:start position:0% +and that would be a part of the plane + + + align:start position:0% +and that would be a part of the plane +that maybe we should reinforce in the + + align:start position:0% +that maybe we should reinforce in the + + + align:start position:0% +that maybe we should reinforce in the +future so when it gets hit by + + align:start position:0% +future so when it gets hit by + + + align:start position:0% +future so when it gets hit by +flak it survives it does less damage so + + align:start position:0% +flak it survives it does less damage so + + + align:start position:0% +flak it survives it does less damage so +you'd analyze where the Germans were + + align:start position:0% +you'd analyze where the Germans were + + + align:start position:0% +you'd analyze where the Germans were +hitting the planes and you would add a + + align:start position:0% +hitting the planes and you would add a + + + align:start position:0% +hitting the planes and you would add a +little extra armor to that part of the + + align:start position:0% +little extra armor to that part of the + + + align:start position:0% +little extra armor to that part of the +plane what's the flaw in + + align:start position:0% + + + + align:start position:0% + +that yeah + + align:start position:0% + + + + align:start position:0% + +yeah this is what's called in the Jaron + + align:start position:0% +yeah this is what's called in the Jaron + + + align:start position:0% +yeah this is what's called in the Jaron +Survivor + + align:start position:0% + + + + align:start position:0% + +bias s r v i v o + + align:start position:0% + + + + align:start position:0% + +r the planes I really should have been + + align:start position:0% +r the planes I really should have been + + + align:start position:0% +r the planes I really should have been +analyzing were the ones that got shot + + align:start position:0% +analyzing were the ones that got shot + + + align:start position:0% +analyzing were the ones that got shot +down but those were hard to analyze so + + align:start position:0% +down but those were hard to analyze so + + + align:start position:0% +down but those were hard to analyze so +they analyzed the ones they + + align:start position:0% +they analyzed the ones they + + + align:start position:0% +they analyzed the ones they +had and Drew conclusions and perhaps + + align:start position:0% +had and Drew conclusions and perhaps + + + align:start position:0% +had and Drew conclusions and perhaps +totally the wrong conclusion maybe the + + align:start position:0% +totally the wrong conclusion maybe the + + + align:start position:0% +totally the wrong conclusion maybe the +conclusion they should have drawn is + + align:start position:0% +conclusion they should have drawn is + + + align:start position:0% +conclusion they should have drawn is +well it's okay if you get hit here let's + + align:start position:0% +well it's okay if you get hit here let's + + + align:start position:0% +well it's okay if you get hit here let's +reinforce the other places I don't know + + align:start position:0% +reinforce the other places I don't know + + + align:start position:0% +reinforce the other places I don't know +enough to know what the right answer was + + align:start position:0% +enough to know what the right answer was + + + align:start position:0% +enough to know what the right answer was +I do know that this was statistically + + align:start position:0% +I do know that this was statistically + + + align:start position:0% +I do know that this was statistically +the wrong thing to be thinking about + + align:start position:0% +the wrong thing to be thinking about + + + align:start position:0% +the wrong thing to be thinking about +doing and this is an issue we have + + align:start position:0% +doing and this is an issue we have + + + align:start position:0% +doing and this is an issue we have +whenever we do + + align:start position:0% +whenever we do + + + align:start position:0% +whenever we do +sampling all statistical techniques are + + align:start position:0% +sampling all statistical techniques are + + + align:start position:0% +sampling all statistical techniques are +based upon the assumption that by + + align:start position:0% +based upon the assumption that by + + + align:start position:0% +based upon the assumption that by +sampling a subset of the population we + + align:start position:0% +sampling a subset of the population we + + + align:start position:0% +sampling a subset of the population we +can infer things about the population as + + align:start position:0% +can infer things about the population as + + + align:start position:0% +can infer things about the population as +a whole right everything we've done this + + align:start position:0% +a whole right everything we've done this + + + align:start position:0% +a whole right everything we've done this +term has been based on that when we were + + align:start position:0% +term has been based on that when we were + + + align:start position:0% +term has been based on that when we were +fitting curves we were doing that um + + align:start position:0% +fitting curves we were doing that um + + + align:start position:0% +fitting curves we were doing that um +when we were talking about the empirical + + align:start position:0% +when we were talking about the empirical + + + align:start position:0% +when we were talking about the empirical +rule and Monte Carlos simulation we were + + align:start position:0% +rule and Monte Carlos simulation we were + + + align:start position:0% +rule and Monte Carlos simulation we were +doing that we were building models with + + align:start position:0% +doing that we were building models with + + + align:start position:0% +doing that we were building models with +machine learning we were doing + + align:start position:0% + + + + align:start position:0% + +that and if random sampling is used you + + align:start position:0% +that and if random sampling is used you + + + align:start position:0% +that and if random sampling is used you +can make meaningful mathematical + + align:start position:0% +can make meaningful mathematical + + + align:start position:0% +can make meaningful mathematical +statements about the relation of the + + align:start position:0% +statements about the relation of the + + + align:start position:0% +statements about the relation of the +sample to the entire + + align:start position:0% + + + + align:start position:0% + +population and that's why so much of + + align:start position:0% +population and that's why so much of + + + align:start position:0% +population and that's why so much of +what we did works and when we're doing + + align:start position:0% +what we did works and when we're doing + + + align:start position:0% +what we did works and when we're doing +simulations that's really + + align:start position:0% +simulations that's really + + + align:start position:0% +simulations that's really +easy right when we were choosing random + + align:start position:0% +easy right when we were choosing random + + + align:start position:0% +easy right when we were choosing random +values of the U needles for for trying + + align:start position:0% +values of the U needles for for trying + + + align:start position:0% +values of the U needles for for trying +to find pi or random values of the + + align:start position:0% +to find pi or random values of the + + + align:start position:0% +to find pi or random values of the +roulette wheel spins we could be pretty + + align:start position:0% +roulette wheel spins we could be pretty + + + align:start position:0% +roulette wheel spins we could be pretty +sure our samples were indeed random + + align:start position:0% +sure our samples were indeed random + + + align:start position:0% +sure our samples were indeed random +random in the + + align:start position:0% +random in the + + + align:start position:0% +random in the +field it's not so + + align:start position:0% +field it's not so + + + align:start position:0% +field it's not so +easy right because some samples are much + + align:start position:0% +easy right because some samples are much + + + align:start position:0% +easy right because some samples are much +more convenient to acquire than others + + align:start position:0% +more convenient to acquire than others + + + align:start position:0% +more convenient to acquire than others +it's much more it's much easier to + + align:start position:0% +it's much more it's much easier to + + + align:start position:0% +it's much more it's much easier to +acquire a plane on the field in Britain + + align:start position:0% +acquire a plane on the field in Britain + + + align:start position:0% +acquire a plane on the field in Britain +than a plane on the ground in + + align:start position:0% + + + + align:start position:0% + +France convenience sampling as it's + + align:start position:0% +France convenience sampling as it's + + + align:start position:0% +France convenience sampling as it's +often called is not usually + + align:start position:0% +often called is not usually + + + align:start position:0% +often called is not usually +random so you have Survivor bias + + align:start position:0% +random so you have Survivor bias + + + align:start position:0% +random so you have Survivor bias +so I all I I asked you to do course + + align:start position:0% +so I all I I asked you to do course + + + align:start position:0% +so I all I I asked you to do course +evaluations well there's Survivor bias + + align:start position:0% +evaluations well there's Survivor bias + + + align:start position:0% +evaluations well there's Survivor bias +there the people who really hated this + + align:start position:0% +there the people who really hated this + + + align:start position:0% +there the people who really hated this +course have already dropped it and so we + + align:start position:0% +course have already dropped it and so we + + + align:start position:0% +course have already dropped it and so we +won't sample them and that's good for me + + align:start position:0% +won't sample them and that's good for me + + + align:start position:0% +won't sample them and that's good for me +at least um but we see that uh we see + + align:start position:0% +at least um but we see that uh we see + + + align:start position:0% +at least um but we see that uh we see +that with grades the people who are + + align:start position:0% +that with grades the people who are + + + align:start position:0% +that with grades the people who are +really struggling who are most likely to + + align:start position:0% +really struggling who are most likely to + + + align:start position:0% +really struggling who are most likely to +fail have probably dropped the course + + align:start position:0% +fail have probably dropped the course + + + align:start position:0% +fail have probably dropped the course +too that's one of the reasons I don't + + align:start position:0% +too that's one of the reasons I don't + + + align:start position:0% +too that's one of the reasons I don't +think it's fair to say we're going to + + align:start position:0% +think it's fair to say we're going to + + + align:start position:0% +think it's fair to say we're going to +have a curve and we're going to always + + align:start position:0% +have a curve and we're going to always + + + align:start position:0% +have a curve and we're going to always +fail this fraction and give an a to this + + align:start position:0% +fail this fraction and give an a to this + + + align:start position:0% +fail this fraction and give an a to this +fraction Because by the end of the term + + align:start position:0% +fraction Because by the end of the term + + + align:start position:0% +fraction Because by the end of the term +we have a lot of Survivor bias the + + align:start position:0% +we have a lot of Survivor bias the + + + align:start position:0% +we have a lot of Survivor bias the +students who are left are on average + + align:start position:0% +students who are left are on average + + + align:start position:0% +students who are left are on average +better than the students who started the + + align:start position:0% +better than the students who started the + + + align:start position:0% +better than the students who started the +semester so you need to take that into + + align:start position:0% +semester so you need to take that into + + + align:start position:0% +semester so you need to take that into +the + + align:start position:0% +the + + + align:start position:0% +the +count another kind + + align:start position:0% +count another kind + + + align:start position:0% +count another kind +of non-representative sampling or + + align:start position:0% +of non-representative sampling or + + + align:start position:0% +of non-representative sampling or +convenience sampling is opinion + + align:start position:0% +convenience sampling is opinion + + + align:start position:0% +convenience sampling is opinion +polls uh in that you have something + + align:start position:0% +polls uh in that you have something + + + align:start position:0% +polls uh in that you have something +there called nonresponse bias + + align:start position:0% +there called nonresponse bias + + + align:start position:0% +there called nonresponse bias +so I don't know about you but I get + + align:start position:0% +so I don't know about you but I get + + + align:start position:0% +so I don't know about you but I get +phone calls asking my opinion about + + align:start position:0% +phone calls asking my opinion about + + + align:start position:0% +phone calls asking my opinion about +things surveys about products whatever I + + align:start position:0% +things surveys about products whatever I + + + align:start position:0% +things surveys about products whatever I +never answer I just hang up the phone I + + align:start position:0% +never answer I just hang up the phone I + + + align:start position:0% +never answer I just hang up the phone I +get a zillion emails every time I stay + + align:start position:0% +get a zillion emails every time I stay + + + align:start position:0% +get a zillion emails every time I stay +in a hotel I get an email asking me to + + align:start position:0% +in a hotel I get an email asking me to + + + align:start position:0% +in a hotel I get an email asking me to +rate the hotel when I fly I get emails + + align:start position:0% +rate the hotel when I fly I get emails + + + align:start position:0% +rate the hotel when I fly I get emails +from the the airline I don't answer any + + align:start position:0% +from the the airline I don't answer any + + + align:start position:0% +from the the airline I don't answer any +of those + + align:start position:0% +of those + + + align:start position:0% +of those +surveys but some people do or presumably + + align:start position:0% +surveys but some people do or presumably + + + align:start position:0% +surveys but some people do or presumably +or they wouldn't send them out but why + + align:start position:0% +or they wouldn't send them out but why + + + align:start position:0% +or they wouldn't send them out but why +should they think that the people who + + align:start position:0% +should they think that the people who + + + align:start position:0% +should they think that the people who +answer the survey are representative of + + align:start position:0% +answer the survey are representative of + + + align:start position:0% +answer the survey are representative of +all the people who stay in the hotel or + + align:start position:0% +all the people who stay in the hotel or + + + align:start position:0% +all the people who stay in the hotel or +all the people who fly in the plane + + align:start position:0% +all the people who fly in the plane + + + align:start position:0% +all the people who fly in the plane +they're not they're the kind of people + + align:start position:0% +they're not they're the kind of people + + + align:start position:0% +they're not they're the kind of people +who maybe have time to answer + + align:start position:0% +who maybe have time to answer + + + align:start position:0% +who maybe have time to answer +surveys and so you get a nonre + + align:start position:0% +surveys and so you get a nonre + + + align:start position:0% +surveys and so you get a nonre +nonresponse + + align:start position:0% +nonresponse + + + align:start position:0% +nonresponse +bias and that tends to distort your + + align:start position:0% + + + + align:start position:0% + +results when samples are not random and + + align:start position:0% +results when samples are not random and + + + align:start position:0% +results when samples are not random and +independent we can still run statistics + + align:start position:0% +independent we can still run statistics + + + align:start position:0% +independent we can still run statistics +on them we can compute mean and standard + + align:start position:0% +on them we can compute mean and standard + + + align:start position:0% +on them we can compute mean and standard +deviations and that's fine but we can't + + align:start position:0% +deviations and that's fine but we can't + + + align:start position:0% +deviations and that's fine but we can't +draw conclusions using things like the + + align:start position:0% +draw conclusions using things like the + + + align:start position:0% +draw conclusions using things like the +empirical rule or the central limit + + align:start position:0% +empirical rule or the central limit + + + align:start position:0% +empirical rule or the central limit +theorem standard error because the basic + + align:start position:0% +theorem standard error because the basic + + + align:start position:0% +theorem standard error because the basic +assumption underlying all of that is + + align:start position:0% +assumption underlying all of that is + + + align:start position:0% +assumption underlying all of that is +that the samples are random and + + align:start position:0% + + + + align:start position:0% + +independent this is one of the reasons + + align:start position:0% +independent this is one of the reasons + + + align:start position:0% +independent this is one of the reasons +why political polls are so + + align:start position:0% +why political polls are so + + + align:start position:0% +why political polls are so +unreliable they compute statistics using + + align:start position:0% +unreliable they compute statistics using + + + align:start position:0% +unreliable they compute statistics using +standard error assuming that the samples + + align:start position:0% +standard error assuming that the samples + + + align:start position:0% +standard error assuming that the samples +are random and + + align:start position:0% +are random and + + + align:start position:0% +are random and +independent but they for example get + + align:start position:0% +independent but they for example get + + + align:start position:0% +independent but they for example get +them mostly by calling + + align:start position:0% +them mostly by calling + + + align:start position:0% +them mostly by calling +landlines and so they get a bias towards + + align:start position:0% +landlines and so they get a bias towards + + + align:start position:0% +landlines and so they get a bias towards +people who actually answer the phone on + + align:start position:0% +people who actually answer the phone on + + + align:start position:0% +people who actually answer the phone on +a landline as opposed how many of you + + align:start position:0% +a landline as opposed how many of you + + + align:start position:0% +a landline as opposed how many of you +have a landline where you + + align:start position:0% +have a landline where you + + + align:start position:0% +have a landline where you +live not many right mostly you rely on + + align:start position:0% +live not many right mostly you rely on + + + align:start position:0% +live not many right mostly you rely on +your cell phones right and so any survey + + align:start position:0% +your cell phones right and so any survey + + + align:start position:0% +your cell phones right and so any survey +that depends on landlines is going to + + align:start position:0% +that depends on landlines is going to + + + align:start position:0% +that depends on landlines is going to +leave a lot of the population out + + align:start position:0% +leave a lot of the population out + + + align:start position:0% +leave a lot of the population out +they'll get a lot of people of of my + + align:start position:0% +they'll get a lot of people of of my + + + align:start position:0% +they'll get a lot of people of of my +vintage not of your + + align:start position:0% +vintage not of your + + + align:start position:0% +vintage not of your +vintage um and that gets you in + + align:start position:0% +vintage um and that gets you in + + + align:start position:0% +vintage um and that gets you in +trouble so the moral here + + align:start position:0% +trouble so the moral here + + + align:start position:0% +trouble so the moral here +is always understand how the data was + + align:start position:0% +is always understand how the data was + + + align:start position:0% +is always understand how the data was +collected what the assumptions in the + + align:start position:0% +collected what the assumptions in the + + + align:start position:0% +collected what the assumptions in the +analysis + + align:start position:0% +analysis + + + align:start position:0% +analysis +were and whether they're + + align:start position:0% +were and whether they're + + + align:start position:0% +were and whether they're +satisfied if these things are not true + + align:start position:0% +satisfied if these things are not true + + + align:start position:0% +satisfied if these things are not true +you need to be very wary of the + + align:start position:0% +you need to be very wary of the + + + align:start position:0% +you need to be very wary of the +results all right I think I'll stop here + + align:start position:0% +results all right I think I'll stop here + + + align:start position:0% +results all right I think I'll stop here +we'll finish up our panoply of + + align:start position:0% +we'll finish up our panoply of + + + align:start position:0% +we'll finish up our panoply of +statistical sins uh on Wednesday in the + + align:start position:0% +statistical sins uh on Wednesday in the + + + align:start position:0% +statistical sins uh on Wednesday in the +first half then we'll do a course wrap + + align:start position:0% +first half then we'll do a course wrap + + + align:start position:0% +first half then we'll do a course wrap +up then I'll wish you all godp speed in + + align:start position:0% +up then I'll wish you all godp speed in + + + align:start position:0% +up then I'll wish you all godp speed in +a good final see you Wednesday \ No newline at end of file diff --git a/K6jxuRHGVCQ.txt b/K6jxuRHGVCQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..ad2395d3cfd89d204969a5cabc82b2122b4a97f1 --- /dev/null +++ b/K6jxuRHGVCQ.txt @@ -0,0 +1,25939 @@ +align:start position:0% + +a little fuzzy but + + align:start position:0% +a little fuzzy but + + + align:start position:0% +a little fuzzy but +um let me start it please this + + align:start position:0% +um let me start it please this + + + align:start position:0% +um let me start it please this +way um Adriana is going to give a + + align:start position:0% +way um Adriana is going to give a + + + align:start position:0% +way um Adriana is going to give a +presentation + + align:start position:0% +presentation + + + align:start position:0% +presentation +today before that I want to correct my + + align:start position:0% +today before that I want to correct my + + + align:start position:0% +today before that I want to correct my +Mis quotation from the short poem by + + align:start position:0% +Mis quotation from the short poem by + + + align:start position:0% +Mis quotation from the short poem by +darthy Parker that I mentioned last week + + align:start position:0% +darthy Parker that I mentioned last week + + + align:start position:0% +darthy Parker that I mentioned last week +uh you'll remember it when I finished + + align:start position:0% +uh you'll remember it when I finished + + + align:start position:0% +uh you'll remember it when I finished +reading you the authentic + + align:start position:0% +reading you the authentic + + + align:start position:0% +reading you the authentic +version which + + align:start position:0% +version which + + + align:start position:0% +version which +reads oh life is a glorious cycle of + + align:start position:0% +reads oh life is a glorious cycle of + + + align:start position:0% +reads oh life is a glorious cycle of +song A medley of + + align:start position:0% +song A medley of + + + align:start position:0% +song A medley of +extemporanea and love is a thing that + + align:start position:0% +extemporanea and love is a thing that + + + align:start position:0% +extemporanea and love is a thing that +can never go + + align:start position:0% +can never go + + + align:start position:0% +can never go +wrong and I am Maria of + + align:start position:0% +wrong and I am Maria of + + + align:start position:0% +wrong and I am Maria of +Romania that's what I was trying to + + align:start position:0% +Romania that's what I was trying to + + + align:start position:0% +Romania that's what I was trying to +remember um and as I mentioned Maria of + + align:start position:0% +remember um and as I mentioned Maria of + + + align:start position:0% +remember um and as I mentioned Maria of +Romania was the queen of that country at + + align:start position:0% +Romania was the queen of that country at + + + align:start position:0% +Romania was the queen of that country at +that time so you get the idea that the + + align:start position:0% +that time so you get the idea that the + + + align:start position:0% +that time so you get the idea that the +speaker is a little uh confused in her + + align:start position:0% +speaker is a little uh confused in her + + + align:start position:0% +speaker is a little uh confused in her +mind you remember the context When U + + align:start position:0% +mind you remember the context When U + + + align:start position:0% +mind you remember the context When U +Veronica was talking about + + align:start position:0% +Veronica was talking about + + + align:start position:0% +Veronica was talking about +love uh which can have various virtues + + align:start position:0% +love uh which can have various virtues + + + align:start position:0% +love uh which can have various virtues +without at the moment discussing all of + + align:start position:0% +without at the moment discussing all of + + + align:start position:0% +without at the moment discussing all of +the + + align:start position:0% +the + + + align:start position:0% +the +drawbacks all right today Adriana is + + align:start position:0% +drawbacks all right today Adriana is + + + align:start position:0% +drawbacks all right today Adriana is +going to take over so What why don't you + + align:start position:0% +going to take over so What why don't you + + + align:start position:0% +going to take over so What why don't you +start now and do you mind being + + align:start position:0% +start now and do you mind being + + + align:start position:0% +start now and do you mind being +interrupted or not no not at all that + + align:start position:0% +interrupted or not no not at all that + + + align:start position:0% +interrupted or not no not at all that +applies to the rest of you as well as + + align:start position:0% +applies to the rest of you as well as + + + align:start position:0% +applies to the rest of you as well as +me okay so we read two chapters from The + + align:start position:0% +me okay so we read two chapters from The + + + align:start position:0% +me okay so we read two chapters from The +Pursuit Of Love we read the chapter on + + align:start position:0% +Pursuit Of Love we read the chapter on + + + align:start position:0% +Pursuit Of Love we read the chapter on +sexual love and the chapter on love and + + align:start position:0% +sexual love and the chapter on love and + + + align:start position:0% +sexual love and the chapter on love and +Society so first I would like to make + + align:start position:0% +Society so first I would like to make + + + align:start position:0% +Society so first I would like to make +some comments on the chapter of sexual + + align:start position:0% +some comments on the chapter of sexual + + + align:start position:0% +some comments on the chapter of sexual +love um you didn't go very deep into + + align:start position:0% +love um you didn't go very deep into + + + align:start position:0% +love um you didn't go very deep into +the concept of sexual love in the + + align:start position:0% +the concept of sexual love in the + + + align:start position:0% +the concept of sexual love in the +religious aspect so I would like to + + align:start position:0% +religious aspect so I would like to + + + align:start position:0% +religious aspect so I would like to +elaborate a little bit on how this + + align:start position:0% +elaborate a little bit on how this + + + align:start position:0% +elaborate a little bit on how this +evolved entire entirely fitting but for + + align:start position:0% +evolved entire entirely fitting but for + + + align:start position:0% +evolved entire entirely fitting but for +next week you'll be reading a chapter + + align:start position:0% +next week you'll be reading a chapter + + + align:start position:0% +next week you'll be reading a chapter +called religious Love yeah this is just + + align:start position:0% +called religious Love yeah this is just + + + align:start position:0% +called religious Love yeah this is just +but it doesn't matter it doesn't matter + + align:start position:0% +but it doesn't matter it doesn't matter + + + align:start position:0% +but it doesn't matter it doesn't matter +in fact maybe it's better for you to try + + align:start position:0% +in fact maybe it's better for you to try + + + align:start position:0% +in fact maybe it's better for you to try +out your own ideas before you read that + + align:start position:0% +out your own ideas before you read that + + + align:start position:0% +out your own ideas before you read that +chapter um + + align:start position:0% +chapter um + + + align:start position:0% +chapter um +so first of all Aristotle derived the + + align:start position:0% +so first of all Aristotle derived the + + + align:start position:0% +so first of all Aristotle derived the +term filia from Plato's uh + + align:start position:0% +term filia from Plato's uh + + + align:start position:0% +term filia from Plato's uh +arrow and he redefined love as something + + align:start position:0% +arrow and he redefined love as something + + + align:start position:0% +arrow and he redefined love as something +that is more dependent on reason than on + + align:start position:0% +that is more dependent on reason than on + + + align:start position:0% +that is more dependent on reason than on +passion what on than passion uh more + + align:start position:0% +passion what on than passion uh more + + + align:start position:0% +passion what on than passion uh more +dependent on reason than on passion than + + align:start position:0% +dependent on reason than on passion than + + + align:start position:0% +dependent on reason than on passion than +on passion but what does the idea filia + + align:start position:0% +on passion but what does the idea filia + + + align:start position:0% +on passion but what does the idea filia +referred to more like friendship + + align:start position:0% +referred to more like friendship + + + align:start position:0% +referred to more like friendship +friendship that's the big difference it + + align:start position:0% +friendship that's the big difference it + + + align:start position:0% +friendship that's the big difference it +actually means friendship in Greek St + + align:start position:0% +actually means friendship in Greek St + + + align:start position:0% +actually means friendship in Greek St +Roose say it again it actually means + + align:start position:0% +Roose say it again it actually means + + + align:start position:0% +Roose say it again it actually means +friendship exactly yes exactly right as + + align:start position:0% +friendship exactly yes exactly right as + + + align:start position:0% +friendship exactly yes exactly right as +in + + align:start position:0% +in + + + align:start position:0% +in +philanthropic friendly sort of + + align:start position:0% +philanthropic friendly sort of + + + align:start position:0% +philanthropic friendly sort of +relationship not necessarily a + + align:start position:0% +relationship not necessarily a + + + align:start position:0% +relationship not necessarily a +passionate one at all so there are some + + align:start position:0% +passionate one at all so there are some + + + align:start position:0% +passionate one at all so there are some +people who have a passion for philanth + + align:start position:0% +people who have a passion for philanth + + + align:start position:0% +people who have a passion for philanth +philanthropy that's you see a + + align:start position:0% +philanthropy that's you see a + + + align:start position:0% +philanthropy that's you see a +complication but um my point here is + + align:start position:0% +complication but um my point here is + + + align:start position:0% +complication but um my point here is +that then filia gave rise to Agape + + align:start position:0% +that then filia gave rise to Agape + + + align:start position:0% +that then filia gave rise to Agape +Christian + + align:start position:0% +Christian + + + align:start position:0% +Christian +philosophy and in in this concept erotic + + align:start position:0% +philosophy and in in this concept erotic + + + align:start position:0% +philosophy and in in this concept erotic +love is repressed and what is emphasized + + align:start position:0% +love is repressed and what is emphasized + + + align:start position:0% +love is repressed and what is emphasized +is the union of the souls okay I think + + align:start position:0% +is the union of the souls okay I think + + + align:start position:0% +is the union of the souls okay I think +at this point I should interrupt for uh + + align:start position:0% +at this point I should interrupt for uh + + + align:start position:0% +at this point I should interrupt for uh +one of my manyi lectures that I hope + + align:start position:0% +one of my manyi lectures that I hope + + + align:start position:0% +one of my manyi lectures that I hope +you'll help me to keep short in the um + + align:start position:0% +you'll help me to keep short in the um + + + align:start position:0% +you'll help me to keep short in the um +Trilogy the nature of + + align:start position:0% +Trilogy the nature of + + + align:start position:0% +Trilogy the nature of +love talking about Christian love + + align:start position:0% +love talking about Christian love + + + align:start position:0% +love talking about Christian love +they're several hundred pages on + + align:start position:0% +they're several hundred pages on + + + align:start position:0% +they're several hundred pages on +Christian love I distinguish among four + + align:start position:0% +Christian love I distinguish among four + + + align:start position:0% +Christian love I distinguish among four +different concepts that applied all of + + align:start position:0% +different concepts that applied all of + + + align:start position:0% +different concepts that applied all of +the words coming from the Greek not all + + align:start position:0% +the words coming from the Greek not all + + + align:start position:0% +the words coming from the Greek not all +of the ideas did but the words did the + + align:start position:0% +of the ideas did but the words did the + + + align:start position:0% +of the ideas did but the words did the +words are love as eras and I'll explain + + align:start position:0% +words are love as eras and I'll explain + + + align:start position:0% +words are love as eras and I'll explain +that to you love as + + align:start position:0% + + + + align:start position:0% + +filia love as noos + + align:start position:0% + + + + align:start position:0% + +and love as + + align:start position:0% +and love as + + + align:start position:0% +and love as +Agape Agape you've already encountered + + align:start position:0% +Agape Agape you've already encountered + + + align:start position:0% +Agape Agape you've already encountered +in this in this book haven't you yes all + + align:start position:0% +in this in this book haven't you yes all + + + align:start position:0% +in this in this book haven't you yes all +right I say love as but the truth is + + align:start position:0% +right I say love as but the truth is + + + align:start position:0% +right I say love as but the truth is +that the + + align:start position:0% +that the + + + align:start position:0% +that the +medieval system of thought was + + align:start position:0% +medieval system of thought was + + + align:start position:0% +medieval system of thought was +inherently a + + align:start position:0% +inherently a + + + align:start position:0% +inherently a +synthesis and this idea of the synthesis + + align:start position:0% +synthesis and this idea of the synthesis + + + align:start position:0% +synthesis and this idea of the synthesis +of these different properties of Love + + align:start position:0% +of these different properties of Love + + + align:start position:0% +of these different properties of Love +or ingredients in love then became part + + align:start position:0% +or ingredients in love then became part + + + align:start position:0% +or ingredients in love then became part +of the + + align:start position:0% +of the + + + align:start position:0% +of the +controversy + + align:start position:0% +controversy + + + align:start position:0% +controversy +that um erupted in the + + align:start position:0% +that um erupted in the + + + align:start position:0% +that um erupted in the +reformation and the Schism between the + + align:start position:0% +reformation and the Schism between the + + + align:start position:0% +reformation and the Schism between the +Catholics and the + + align:start position:0% +Catholics and the + + + align:start position:0% +Catholics and the +Protestants and that has never been + + align:start position:0% +Protestants and that has never been + + + align:start position:0% +Protestants and that has never been +overcome because they became more and + + align:start position:0% +overcome because they became more and + + + align:start position:0% +overcome because they became more and +more Protestants different sects but uh + + align:start position:0% +more Protestants different sects but uh + + + align:start position:0% +more Protestants different sects but uh +the idea of there being one kind of + + align:start position:0% +the idea of there being one kind of + + + align:start position:0% +the idea of there being one kind of +Christianity um I don't think anyone can + + align:start position:0% +Christianity um I don't think anyone can + + + align:start position:0% +Christianity um I don't think anyone can +affirm anymore there may be ecumenical + + align:start position:0% +affirm anymore there may be ecumenical + + + align:start position:0% +affirm anymore there may be ecumenical +efforts to communicate there may be a + + align:start position:0% +efforts to communicate there may be a + + + align:start position:0% +efforts to communicate there may be a +sense of identity as Christians but + + align:start position:0% +sense of identity as Christians but + + + align:start position:0% +sense of identity as Christians but +still they are different sects and + + align:start position:0% +still they are different sects and + + + align:start position:0% +still they are different sects and +that's related to the question of the + + align:start position:0% +that's related to the question of the + + + align:start position:0% +that's related to the question of the +synthesis among those four ingredients + + align:start position:0% +synthesis among those four ingredients + + + align:start position:0% +synthesis among those four ingredients +of medieval love which is still exists + + align:start position:0% +of medieval love which is still exists + + + align:start position:0% +of medieval love which is still exists +as ingredients in Catholic + + align:start position:0% +as ingredients in Catholic + + + align:start position:0% +as ingredients in Catholic +theology follow me all right the first + + align:start position:0% +theology follow me all right the first + + + align:start position:0% +theology follow me all right the first +one + + align:start position:0% +one + + + align:start position:0% +one +AOS AOS as + + align:start position:0% +AOS AOS as + + + align:start position:0% +AOS AOS as +Adriana just point pointed out is a + + align:start position:0% +Adriana just point pointed out is a + + + align:start position:0% +Adriana just point pointed out is a +platonic + + align:start position:0% +platonic + + + align:start position:0% +platonic +idea and it refers to the way in which + + align:start position:0% +idea and it refers to the way in which + + + align:start position:0% +idea and it refers to the way in which +the human soul is always striving to + + align:start position:0% +the human soul is always striving to + + + align:start position:0% +the human soul is always striving to +improve itself to make itself better why + + align:start position:0% +improve itself to make itself better why + + + align:start position:0% +improve itself to make itself better why +because Plato thought that that's in the + + align:start position:0% +because Plato thought that that's in the + + + align:start position:0% +because Plato thought that that's in the +nature of the universe everything wants + + align:start position:0% +nature of the universe everything wants + + + align:start position:0% +nature of the universe everything wants +to be better um nobody wants something + + align:start position:0% +to be better um nobody wants something + + + align:start position:0% +to be better um nobody wants something +that is + + align:start position:0% +that is + + + align:start position:0% +that is +inferior uh given a choice between um + + align:start position:0% +inferior uh given a choice between um + + + align:start position:0% +inferior uh given a choice between um +something that's good and something + + align:start position:0% +something that's good and something + + + align:start position:0% +something that's good and something +that's best everybody wants what's + + align:start position:0% +that's best everybody wants what's + + + align:start position:0% +that's best everybody wants what's +best at that applies not only uh in + + align:start position:0% +best at that applies not only uh in + + + align:start position:0% +best at that applies not only uh in +advertisements for automobiles and and + + align:start position:0% +advertisements for automobiles and and + + + align:start position:0% +advertisements for automobiles and and +uh food at home but also in terms of the + + align:start position:0% +uh food at home but also in terms of the + + + align:start position:0% +uh food at home but also in terms of the +nature of the self the soul the soul + + align:start position:0% +nature of the self the soul the soul + + + align:start position:0% +nature of the self the soul the soul +always wants to improve itself to make + + align:start position:0% +always wants to improve itself to make + + + align:start position:0% +always wants to improve itself to make +itself better and better better it's + + align:start position:0% +itself better and better better it's + + + align:start position:0% +itself better and better better it's +striving for Perfection and that's built + + align:start position:0% +striving for Perfection and that's built + + + align:start position:0% +striving for Perfection and that's built +into everything in the universe + + align:start position:0% +into everything in the universe + + + align:start position:0% +into everything in the universe +according to Plato uh and most evident + + align:start position:0% +according to Plato uh and most evident + + + align:start position:0% +according to Plato uh and most evident +and most interesting in human + + align:start position:0% +and most interesting in human + + + align:start position:0% +and most interesting in human +beings why because human beings are + + align:start position:0% +beings why because human beings are + + + align:start position:0% +beings why because human beings are +created in the image of God and God is + + align:start position:0% +created in the image of God and God is + + + align:start position:0% +created in the image of God and God is +perfect God not only is perfect but it's + + align:start position:0% +perfect God not only is perfect but it's + + + align:start position:0% +perfect God not only is perfect but it's +part of the uh tradition the Christian + + align:start position:0% +part of the uh tradition the Christian + + + align:start position:0% +part of the uh tradition the Christian +tradition that uh God is + + align:start position:0% +tradition that uh God is + + + align:start position:0% +tradition that uh God is +perfection and also that God since he is + + align:start position:0% +perfection and also that God since he is + + + align:start position:0% +perfection and also that God since he is +perfect loves + + align:start position:0% +perfect loves + + + align:start position:0% +perfect loves +himself now that sounds as if uh there's + + align:start position:0% +himself now that sounds as if uh there's + + + align:start position:0% +himself now that sounds as if uh there's +some kind of um copsis or some kind of U + + align:start position:0% +some kind of um copsis or some kind of U + + + align:start position:0% +some kind of um copsis or some kind of U +selfishness being wrapped up in yourself + + align:start position:0% +selfishness being wrapped up in yourself + + + align:start position:0% +selfishness being wrapped up in yourself +or or narcissism I guess like you + + align:start position:0% +or or narcissism I guess like you + + + align:start position:0% +or or narcissism I guess like you +remember the Greek myth of narcissist + + align:start position:0% +remember the Greek myth of narcissist + + + align:start position:0% +remember the Greek myth of narcissist +who fell in love with his own image the + + align:start position:0% +who fell in love with his own image the + + + align:start position:0% +who fell in love with his own image the +idea is that God is + + align:start position:0% +idea is that God is + + + align:start position:0% +idea is that God is +spiritually perfect and consequently + + align:start position:0% +spiritually perfect and consequently + + + align:start position:0% +spiritually perfect and consequently +falling in love with himself or being in + + align:start position:0% +falling in love with himself or being in + + + align:start position:0% +falling in love with himself or being in +love with not falling in love because + + align:start position:0% +love with not falling in love because + + + align:start position:0% +love with not falling in love because +that's separate concept remember in my + + align:start position:0% +that's separate concept remember in my + + + align:start position:0% +that's separate concept remember in my +analysis but uh uh love for + + align:start position:0% +analysis but uh uh love for + + + align:start position:0% +analysis but uh uh love for +Perfection is a manifestation of the P + + align:start position:0% +Perfection is a manifestation of the P + + + align:start position:0% +Perfection is a manifestation of the P +spiritual + + align:start position:0% +spiritual + + + align:start position:0% +spiritual +Purity that is true in God in a way that + + align:start position:0% +Purity that is true in God in a way that + + + align:start position:0% +Purity that is true in God in a way that +it's not true in anybody else and yet + + align:start position:0% +it's not true in anybody else and yet + + + align:start position:0% +it's not true in anybody else and yet +that's what we strive for in loving + + align:start position:0% +that's what we strive for in loving + + + align:start position:0% +that's what we strive for in loving +God uh Demetri you wanted to say + + align:start position:0% +God uh Demetri you wanted to say + + + align:start position:0% +God uh Demetri you wanted to say +something yeah well you said that + + align:start position:0% +something yeah well you said that + + + align:start position:0% +something yeah well you said that +according to Plato love is the pursuit + + align:start position:0% +according to Plato love is the pursuit + + + align:start position:0% +according to Plato love is the pursuit +of perfection + + align:start position:0% +of perfection + + + align:start position:0% +of perfection +How could a perfect being be in pursuit + + align:start position:0% +How could a perfect being be in pursuit + + + align:start position:0% +How could a perfect being be in pursuit +of perfection or love that's a very big + + align:start position:0% +of perfection or love that's a very big + + + align:start position:0% +of perfection or love that's a very big +problem in Plato um on the platonic view + + align:start position:0% +problem in Plato um on the platonic view + + + align:start position:0% +problem in Plato um on the platonic view +which was not uncommon at that time um + + align:start position:0% +which was not uncommon at that time um + + + align:start position:0% +which was not uncommon at that time um +the gods didn't love because they were + + align:start position:0% +the gods didn't love because they were + + + align:start position:0% +the gods didn't love because they were +perfect to love is to seek for + + align:start position:0% +perfect to love is to seek for + + + align:start position:0% +perfect to love is to seek for +something better than yourself + + align:start position:0% +something better than yourself + + + align:start position:0% +something better than yourself +something outside yourself which will + + align:start position:0% +something outside yourself which will + + + align:start position:0% +something outside yourself which will +make you better but if you are already + + align:start position:0% +make you better but if you are already + + + align:start position:0% +make you better but if you are already +perfect you know there is there is no + + align:start position:0% +perfect you know there is there is no + + + align:start position:0% +perfect you know there is there is no +place for there to be loved so the + + align:start position:0% +place for there to be loved so the + + + align:start position:0% +place for there to be loved so the +traditional view was that the gods did + + align:start position:0% +traditional view was that the gods did + + + align:start position:0% +traditional view was that the gods did +not love because they were already + + align:start position:0% +not love because they were already + + + align:start position:0% +not love because they were already +perfect uh the mythological source is in + + align:start position:0% +perfect uh the mythological source is in + + + align:start position:0% +perfect uh the mythological source is in +the sort of mythological character of + + align:start position:0% +the sort of mythological character of + + + align:start position:0% +the sort of mythological character of +the god called AAS who is the god of + + align:start position:0% +the god called AAS who is the god of + + + align:start position:0% +the god called AAS who is the god of +love the son of Aphrodite the uh the + + align:start position:0% +love the son of Aphrodite the uh the + + + align:start position:0% +love the son of Aphrodite the uh the +uh goddess of love um and the point + + align:start position:0% +uh goddess of love um and the point + + + align:start position:0% +uh goddess of love um and the point +about AOS is that he is always Wayward + + align:start position:0% +about AOS is that he is always Wayward + + + align:start position:0% +about AOS is that he is always Wayward +he's very imperfect he is a an + + align:start position:0% +he's very imperfect he is a an + + + align:start position:0% +he's very imperfect he is a an +individual who will shoot his arrows of + + align:start position:0% +individual who will shoot his arrows of + + + align:start position:0% +individual who will shoot his arrows of +Desire wherever he feels like uh he's a + + align:start position:0% +Desire wherever he feels like uh he's a + + + align:start position:0% +Desire wherever he feels like uh he's a +kind of Rogue a kind of um jigo you + + align:start position:0% +kind of Rogue a kind of um jigo you + + + align:start position:0% +kind of Rogue a kind of um jigo you +might even think of him as a kind of Don + + align:start position:0% +might even think of him as a kind of Don + + + align:start position:0% +might even think of him as a kind of Don +Juan who will + + align:start position:0% +Juan who will + + + align:start position:0% +Juan who will +simply uh for reasons of his own cause + + align:start position:0% +simply uh for reasons of his own cause + + + align:start position:0% +simply uh for reasons of his own cause +people to fall in love + + align:start position:0% +people to fall in love + + + align:start position:0% +people to fall in love +not because he is makes them better but + + align:start position:0% +not because he is makes them better but + + + align:start position:0% +not because he is makes them better but +because that is in his + + align:start position:0% +because that is in his + + + align:start position:0% +because that is in his +nature right all right the now Plato + + align:start position:0% +nature right all right the now Plato + + + align:start position:0% +nature right all right the now Plato +picks this up and says that this typ + + align:start position:0% +picks this up and says that this typ + + + align:start position:0% +picks this up and says that this typ +typifies the way in which only an + + align:start position:0% +typifies the way in which only an + + + align:start position:0% +typifies the way in which only an +imperfect person could love and love in + + align:start position:0% +imperfect person could love and love in + + + align:start position:0% +imperfect person could love and love in +the sense of striving to attain + + align:start position:0% +the sense of striving to attain + + + align:start position:0% +the sense of striving to attain +something that is better rather than + + align:start position:0% +something that is better rather than + + + align:start position:0% +something that is better rather than +what one is or worse than what one is + + align:start position:0% +what one is or worse than what one is + + + align:start position:0% +what one is or worse than what one is +the gods being perfect they're different + + align:start position:0% +the gods being perfect they're different + + + align:start position:0% +the gods being perfect they're different +from Aros and uh they don't don't love + + align:start position:0% +from Aros and uh they don't don't love + + + align:start position:0% +from Aros and uh they don't don't love +they are the object of + + align:start position:0% +they are the object of + + + align:start position:0% +they are the object of +Love + + align:start position:0% +Love + + + align:start position:0% +Love +Mortals uh inferior uh imperfect + + align:start position:0% +Mortals uh inferior uh imperfect + + + align:start position:0% +Mortals uh inferior uh imperfect +creatures like us want to emulate the + + align:start position:0% +creatures like us want to emulate the + + + align:start position:0% +creatures like us want to emulate the +gods to be like them right uh 2,000 + + align:start position:0% +gods to be like them right uh 2,000 + + + align:start position:0% +gods to be like them right uh 2,000 +years later um n says in one + + align:start position:0% +years later um n says in one + + + align:start position:0% +years later um n says in one +place um if + + align:start position:0% +place um if + + + align:start position:0% +place um if +um + + align:start position:0% + + + + align:start position:0% + +um the gods are perfect + + align:start position:0% +um the gods are perfect + + + align:start position:0% +um the gods are perfect +how can I not want to be one of them + + align:start position:0% +how can I not want to be one of them + + + align:start position:0% +how can I not want to be one of them +myself I want in other words to be God + + align:start position:0% +myself I want in other words to be God + + + align:start position:0% +myself I want in other words to be God +and then s picks this up and says that + + align:start position:0% +and then s picks this up and says that + + + align:start position:0% +and then s picks this up and says that +the futility of the human race is that + + align:start position:0% +the futility of the human race is that + + + align:start position:0% +the futility of the human race is that +all men and women all people want to be + + align:start position:0% +all men and women all people want to be + + + align:start position:0% +all men and women all people want to be +perfect but there is only one creature + + align:start position:0% +perfect but there is only one creature + + + align:start position:0% +perfect but there is only one creature +who entity who can be perfect and that's + + align:start position:0% +who entity who can be perfect and that's + + + align:start position:0% +who entity who can be perfect and that's +god with the capital G now because it's + + align:start position:0% +god with the capital G now because it's + + + align:start position:0% +god with the capital G now because it's +20th + + align:start position:0% +20th + + + align:start position:0% +20th +century and uh nature concludes but God + + align:start position:0% +century and uh nature concludes but God + + + align:start position:0% +century and uh nature concludes but God +does not exist and therefore the human + + align:start position:0% +does not exist and therefore the human + + + align:start position:0% +does not exist and therefore the human +search to be God + + align:start position:0% +search to be God + + + align:start position:0% +search to be God +which devout religious person would call + + align:start position:0% +which devout religious person would call + + + align:start position:0% +which devout religious person would call +blasphemous that search according to sat + + align:start position:0% +blasphemous that search according to sat + + + align:start position:0% +blasphemous that search according to sat +uh is futile and so humanity is + + align:start position:0% +uh is futile and so humanity is + + + align:start position:0% +uh is futile and so humanity is +futile that's SRA uh going far beyond n + + align:start position:0% +futile that's SRA uh going far beyond n + + + align:start position:0% +futile that's SRA uh going far beyond n +and n playing upon this idea of + + align:start position:0% +and n playing upon this idea of + + + align:start position:0% +and n playing upon this idea of +imperfect creatures searching to be like + + align:start position:0% +imperfect creatures searching to be like + + + align:start position:0% +imperfect creatures searching to be like +the perfect ones but the only perfect + + align:start position:0% +the perfect ones but the only perfect + + + align:start position:0% +the perfect ones but the only perfect +ones be being the gods or + + align:start position:0% + + + + align:start position:0% + +God um Demetri again do you you want to + + align:start position:0% +God um Demetri again do you you want to + + + align:start position:0% +God um Demetri again do you you want to +say something yeah I I can see I can see + + align:start position:0% +say something yeah I I can see I can see + + + align:start position:0% +say something yeah I I can see I can see +this argument but uh certainly it + + align:start position:0% +this argument but uh certainly it + + + align:start position:0% +this argument but uh certainly it +doesn't mean that you can get much + + align:start position:0% +doesn't mean that you can get much + + + align:start position:0% +doesn't mean that you can get much +better than you + + align:start position:0% +better than you + + + align:start position:0% +better than you +are um the real question is whether you + + align:start position:0% +are um the real question is whether you + + + align:start position:0% +are um the real question is whether you +can truly emulate God because God + + align:start position:0% +can truly emulate God because God + + + align:start position:0% +can truly emulate God because God +belongs to a different domain uh he is + + align:start position:0% +belongs to a different domain uh he is + + + align:start position:0% +belongs to a different domain uh he is +inherently perfect and we're inherently + + align:start position:0% +inherently perfect and we're inherently + + + align:start position:0% +inherently perfect and we're inherently +imperfect he is Immortal and we're + + align:start position:0% +imperfect he is Immortal and we're + + + align:start position:0% +imperfect he is Immortal and we're +Immortal um all sorts of ways in which + + align:start position:0% +Immortal um all sorts of ways in which + + + align:start position:0% +Immortal um all sorts of ways in which +God is infinite in his goodness his + + align:start position:0% +God is infinite in his goodness his + + + align:start position:0% +God is infinite in his goodness his +wisdom his power and we are + + align:start position:0% +wisdom his power and we are + + + align:start position:0% +wisdom his power and we are +finite and the um fact that you want to + + align:start position:0% +finite and the um fact that you want to + + + align:start position:0% +finite and the um fact that you want to +be like that doesn't + + align:start position:0% +be like that doesn't + + + align:start position:0% +be like that doesn't +change the state the nature of The Human + + align:start position:0% +change the state the nature of The Human + + + align:start position:0% +change the state the nature of The Human +Condition that's that's the problem we + + align:start position:0% +Condition that's that's the problem we + + + align:start position:0% +Condition that's that's the problem we +don't have to go through this into too + + align:start position:0% +don't have to go through this into too + + + align:start position:0% +don't have to go through this into too +much detail to try to resolve it I + + align:start position:0% +much detail to try to resolve it I + + + align:start position:0% +much detail to try to resolve it I +wanted to make this little + + align:start position:0% +wanted to make this little + + + align:start position:0% +wanted to make this little +bypass to explain the concept in + + align:start position:0% +bypass to explain the concept in + + + align:start position:0% +bypass to explain the concept in +medieval Christianity which is the + + align:start position:0% +medieval Christianity which is the + + + align:start position:0% +medieval Christianity which is the +concept of AOS the great thinker who + + align:start position:0% +concept of AOS the great thinker who + + + align:start position:0% +concept of AOS the great thinker who +interprets the Christian religion in + + align:start position:0% +interprets the Christian religion in + + + align:start position:0% +interprets the Christian religion in +terms of + + align:start position:0% +terms of + + + align:start position:0% +terms of +Aras is St + + align:start position:0% +Aras is St + + + align:start position:0% +Aras is St +Augustine and I have a lot of discussion + + align:start position:0% +Augustine and I have a lot of discussion + + + align:start position:0% +Augustine and I have a lot of discussion +of him in the first volume of the + + align:start position:0% +of him in the first volume of the + + + align:start position:0% +of him in the first volume of the +trilogy uh the whole first volume of the + + align:start position:0% +trilogy uh the whole first volume of the + + + align:start position:0% +trilogy uh the whole first volume of the +trilogy the part that deals with + + align:start position:0% +trilogy the part that deals with + + + align:start position:0% +trilogy the part that deals with +Christianity which is over over 200 + + align:start position:0% +Christianity which is over over 200 + + + align:start position:0% +Christianity which is over over 200 +Pages works at this analysis into the + + align:start position:0% +Pages works at this analysis into the + + + align:start position:0% +Pages works at this analysis into the +four ingredients and the question of + + align:start position:0% +four ingredients and the question of + + + align:start position:0% +four ingredients and the question of +whether they can be synthesized or not + + align:start position:0% +whether they can be synthesized or not + + + align:start position:0% +whether they can be synthesized or not +so if you're really interested for in + + align:start position:0% +so if you're really interested for in + + + align:start position:0% +so if you're really interested for in +detail go back to the first volume of + + align:start position:0% +detail go back to the first volume of + + + align:start position:0% +detail go back to the first volume of +the love Trilogy uh St Augustine's idea + + align:start position:0% +the love Trilogy uh St Augustine's idea + + + align:start position:0% +the love Trilogy uh St Augustine's idea +comes directly out of Plato he was + + align:start position:0% +comes directly out of Plato he was + + + align:start position:0% +comes directly out of Plato he was +originally a pagan uh uh growing up to + + align:start position:0% +originally a pagan uh uh growing up to + + + align:start position:0% +originally a pagan uh uh growing up to +be a + + align:start position:0% +be a + + + align:start position:0% +be a +platonist and then he um saw the word + + align:start position:0% +platonist and then he um saw the word + + + align:start position:0% +platonist and then he um saw the word +heard the word of God had a revelation + + align:start position:0% +heard the word of God had a revelation + + + align:start position:0% +heard the word of God had a revelation +sort of and uh converted to + + align:start position:0% +sort of and uh converted to + + + align:start position:0% +sort of and uh converted to +Christianity his mother was a Christian + + align:start position:0% +Christianity his mother was a Christian + + + align:start position:0% +Christianity his mother was a Christian +his father was a a pagan um and there + + align:start position:0% +his father was a a pagan um and there + + + align:start position:0% +his father was a a pagan um and there +was this conflict with him he finally + + align:start position:0% +was this conflict with him he finally + + + align:start position:0% +was this conflict with him he finally +became a not only a Christian but also a + + align:start position:0% +became a not only a Christian but also a + + + align:start position:0% +became a not only a Christian but also a +very prolific writer uh and + + align:start position:0% +very prolific writer uh and + + + align:start position:0% +very prolific writer uh and +theologian and uh Bishop uh and finally + + align:start position:0% +theologian and uh Bishop uh and finally + + + align:start position:0% +theologian and uh Bishop uh and finally +um he was Sanctified as he was um + + align:start position:0% +um he was Sanctified as he was um + + + align:start position:0% +um he was Sanctified as he was um +canonized as a + + align:start position:0% +canonized as a + + + align:start position:0% +canonized as a +saint and so St Augustine is one of the + + align:start position:0% +saint and so St Augustine is one of the + + + align:start position:0% +saint and so St Augustine is one of the +pillars of the Catholic faith his + + align:start position:0% +pillars of the Catholic faith his + + + align:start position:0% +pillars of the Catholic faith his +dominant idea is that all human beings + + align:start position:0% +dominant idea is that all human beings + + + align:start position:0% +dominant idea is that all human beings +all Christians are defined in terms of + + align:start position:0% +all Christians are defined in terms of + + + align:start position:0% +all Christians are defined in terms of +their erotic love of a spiritual sort + + align:start position:0% +their erotic love of a spiritual sort + + + align:start position:0% +their erotic love of a spiritual sort +the search to approximate the Perfection + + align:start position:0% +the search to approximate the Perfection + + + align:start position:0% +the search to approximate the Perfection +of God that was the big emphasis in him + + align:start position:0% +of God that was the big emphasis in him + + + align:start position:0% +of God that was the big emphasis in him +now and it came out of Plato Aristotle + + align:start position:0% +now and it came out of Plato Aristotle + + + align:start position:0% +now and it came out of Plato Aristotle +deals with a problem that Demitri + + align:start position:0% +deals with a problem that Demitri + + + align:start position:0% +deals with a problem that Demitri +brought up um in a very late + + align:start position:0% +brought up um in a very late + + + align:start position:0% +brought up um in a very late +dialogue um Plato raises the problem but + + align:start position:0% +dialogue um Plato raises the problem but + + + align:start position:0% +dialogue um Plato raises the problem but +he doesn't do anything about it uh the + + align:start position:0% +he doesn't do anything about it uh the + + + align:start position:0% +he doesn't do anything about it uh the +problem is that if + + align:start position:0% +problem is that if + + + align:start position:0% +problem is that if +love um is + + align:start position:0% +love um is + + + align:start position:0% +love um is +um + + align:start position:0% +um + + + align:start position:0% +um +Perfection it's the best condition one + + align:start position:0% +Perfection it's the best condition one + + + align:start position:0% +Perfection it's the best condition one +can + + align:start position:0% +can + + + align:start position:0% +can +imagine meaning by that the love of the + + align:start position:0% +imagine meaning by that the love of the + + + align:start position:0% +imagine meaning by that the love of the +highest forms the good the beautiful + + align:start position:0% +highest forms the good the beautiful + + + align:start position:0% +highest forms the good the beautiful +which Christianity interpreted as God + + align:start position:0% +which Christianity interpreted as God + + + align:start position:0% +which Christianity interpreted as God +Divinity then Plato says + + align:start position:0% +Divinity then Plato says + + + align:start position:0% +Divinity then Plato says +um how is it possible that loving that + + align:start position:0% +um how is it possible that loving that + + + align:start position:0% +um how is it possible that loving that +should not be a perfection in + + align:start position:0% +should not be a perfection in + + + align:start position:0% +should not be a perfection in +itself so the whole question of Love + + align:start position:0% +itself so the whole question of Love + + + align:start position:0% +itself so the whole question of Love +consisting for a search for Perfection + + align:start position:0% +consisting for a search for Perfection + + + align:start position:0% +consisting for a search for Perfection +but love not being perfect is raised in + + align:start position:0% +but love not being perfect is raised in + + + align:start position:0% +but love not being perfect is raised in +that um dialogue of Plato's but he + + align:start position:0% +that um dialogue of Plato's but he + + + align:start position:0% +that um dialogue of Plato's but he +doesn't resolve it Aristotle does + + align:start position:0% +doesn't resolve it Aristotle does + + + align:start position:0% +doesn't resolve it Aristotle does +resolve it Aristotle says um it is + + align:start position:0% +resolve it Aristotle says um it is + + + align:start position:0% +resolve it Aristotle says um it is +because love is a + + align:start position:0% +because love is a + + + align:start position:0% +because love is a +Perfection that anybody um who searches + + align:start position:0% +Perfection that anybody um who searches + + + align:start position:0% +Perfection that anybody um who searches +for the best will also experience and + + align:start position:0% +for the best will also experience and + + + align:start position:0% +for the best will also experience and +embody the nature of love so that all + + align:start position:0% +embody the nature of love so that all + + + align:start position:0% +embody the nature of love so that all +makes a sharp change from Plato uh + + align:start position:0% +makes a sharp change from Plato uh + + + align:start position:0% +makes a sharp change from Plato uh +Aristotle didn't write very much about + + align:start position:0% +Aristotle didn't write very much about + + + align:start position:0% +Aristotle didn't write very much about +the Panorama of loves there's hardly any + + align:start position:0% +the Panorama of loves there's hardly any + + + align:start position:0% +the Panorama of loves there's hardly any +discussion of sexual love or love uh um + + align:start position:0% +discussion of sexual love or love uh um + + + align:start position:0% +discussion of sexual love or love uh um +between um uh friends marching together + + align:start position:0% +between um uh friends marching together + + + align:start position:0% +between um uh friends marching together +as in Plato in their search for the the + + align:start position:0% +as in Plato in their search for the the + + + align:start position:0% +as in Plato in their search for the the +good but he does have a very important + + align:start position:0% +good but he does have a very important + + + align:start position:0% +good but he does have a very important +chapter in his book The Nick and McKean + + align:start position:0% +chapter in his book The Nick and McKean + + + align:start position:0% +chapter in his book The Nick and McKean +ethics on the nature of + + align:start position:0% +ethics on the nature of + + + align:start position:0% +ethics on the nature of +friendship and he defines friendship as + + align:start position:0% +friendship and he defines friendship as + + + align:start position:0% +friendship and he defines friendship as +a kind of love but it's the kind that is + + align:start position:0% +a kind of love but it's the kind that is + + + align:start position:0% +a kind of love but it's the kind that is +at its best when you have two virtuous + + align:start position:0% +at its best when you have two virtuous + + + align:start position:0% +at its best when you have two virtuous +individuals that is two people who are + + align:start position:0% +individuals that is two people who are + + + align:start position:0% +individuals that is two people who are +inherently good morally good and that'll + + align:start position:0% +inherently good morally good and that'll + + + align:start position:0% +inherently good morally good and that'll +be he thinks among those who are fully + + align:start position:0% +be he thinks among those who are fully + + + align:start position:0% +be he thinks among those who are fully +developed in their rationality so that + + align:start position:0% +developed in their rationality so that + + + align:start position:0% +developed in their rationality so that +this gets back to the point Arana was + + align:start position:0% +this gets back to the point Arana was + + + align:start position:0% +this gets back to the point Arana was +making about love for Aristotle being a + + align:start position:0% +making about love for Aristotle being a + + + align:start position:0% +making about love for Aristotle being a +form of + + align:start position:0% +form of + + + align:start position:0% +form of +Reason um to that extent emotions + + align:start position:0% +Reason um to that extent emotions + + + align:start position:0% +Reason um to that extent emotions +passion all of which a throbbing in + + align:start position:0% +passion all of which a throbbing in + + + align:start position:0% +passion all of which a throbbing in +Plato Plato is really a uh almost a + + align:start position:0% +Plato Plato is really a uh almost a + + + align:start position:0% +Plato Plato is really a uh almost a +romantic poet he was a great writer a + + align:start position:0% +romantic poet he was a great writer a + + + align:start position:0% +romantic poet he was a great writer a +literary writer of the search for the + + align:start position:0% +literary writer of the search for the + + + align:start position:0% +literary writer of the search for the +good you know could bring about what he + + align:start position:0% +good you know could bring about what he + + + align:start position:0% +good you know could bring about what he +called the Divine Madness in which you + + align:start position:0% +called the Divine Madness in which you + + + align:start position:0% +called the Divine Madness in which you +Lo lose your reason because you're + + align:start position:0% +Lo lose your reason because you're + + + align:start position:0% +Lo lose your reason because you're +transported into a different realm and + + align:start position:0% +transported into a different realm and + + + align:start position:0% +transported into a different realm and +you can see 19th century + + align:start position:0% +you can see 19th century + + + align:start position:0% +you can see 19th century +Romanticism uh earning learning a great + + align:start position:0% +Romanticism uh earning learning a great + + + align:start position:0% +Romanticism uh earning learning a great +deal from + + align:start position:0% +deal from + + + align:start position:0% +deal from +Plato uh in Aristotle you don't get much + + align:start position:0% +Plato uh in Aristotle you don't get much + + + align:start position:0% +Plato uh in Aristotle you don't get much +of that but you get a really very + + align:start position:0% +of that but you get a really very + + + align:start position:0% +of that but you get a really very +interesting analysis about different + + align:start position:0% +interesting analysis about different + + + align:start position:0% +interesting analysis about different +kinds of friendship I don't want to get + + align:start position:0% +kinds of friendship I don't want to get + + + align:start position:0% +kinds of friendship I don't want to get +into it right now there's a chapter on + + align:start position:0% +into it right now there's a chapter on + + + align:start position:0% +into it right now there's a chapter on +our stotle in the first volume and a + + align:start position:0% +our stotle in the first volume and a + + + align:start position:0% +our stotle in the first volume and a +long chapter on Plato uh uh in the one + + align:start position:0% +long chapter on Plato uh uh in the one + + + align:start position:0% +long chapter on Plato uh uh in the one +kind that I want to emphasize is the + + align:start position:0% +kind that I want to emphasize is the + + + align:start position:0% +kind that I want to emphasize is the +idea of filia being friendship among + + align:start position:0% +idea of filia being friendship among + + + align:start position:0% +idea of filia being friendship among +people who are alike in their virtuous + + align:start position:0% +people who are alike in their virtuous + + + align:start position:0% +people who are alike in their virtuous +search for the good and who live + + align:start position:0% +search for the good and who live + + + align:start position:0% +search for the good and who live +together in a community so Aristotle is + + align:start position:0% +together in a community so Aristotle is + + + align:start position:0% +together in a community so Aristotle is +almost a political theorist when he + + align:start position:0% +almost a political theorist when he + + + align:start position:0% +almost a political theorist when he +talks about love that love is a way + + align:start position:0% +talks about love that love is a way + + + align:start position:0% +talks about love that love is a way +of unifying the city state and being uh + + align:start position:0% +of unifying the city state and being uh + + + align:start position:0% +of unifying the city state and being uh +managed properly by the people who are + + align:start position:0% +managed properly by the people who are + + + align:start position:0% +managed properly by the people who are +capable of being friends and who who + + align:start position:0% +capable of being friends and who who + + + align:start position:0% +capable of being friends and who who +know the difference between right and + + align:start position:0% +know the difference between right and + + + align:start position:0% +know the difference between right and +wrong it's almost a constitutional view + + align:start position:0% +wrong it's almost a constitutional view + + + align:start position:0% +wrong it's almost a constitutional view +about the nature of love and in fact + + align:start position:0% +about the nature of love and in fact + + + align:start position:0% +about the nature of love and in fact +Aristotle did write constitutions for a + + align:start position:0% +Aristotle did write constitutions for a + + + align:start position:0% +Aristotle did write constitutions for a +large number of cities States throughout + + align:start position:0% +large number of cities States throughout + + + align:start position:0% +large number of cities States throughout +the Greek Empire um that's filia Medi + + align:start position:0% +the Greek Empire um that's filia Medi + + + align:start position:0% +the Greek Empire um that's filia Medi +Christianity appropriates that and in + + align:start position:0% +Christianity appropriates that and in + + + align:start position:0% +Christianity appropriates that and in +the first years uh of Christianity first + + align:start position:0% +the first years uh of Christianity first + + + align:start position:0% +the first years uh of Christianity first +century 2 Century ad there were little + + align:start position:0% +century 2 Century ad there were little + + + align:start position:0% +century 2 Century ad there were little +societies who communes as we would call + + align:start position:0% +societies who communes as we would call + + + align:start position:0% +societies who communes as we would call +them since like the communes of + + align:start position:0% +them since like the communes of + + + align:start position:0% +them since like the communes of +1960 in which men and women would live + + align:start position:0% +1960 in which men and women would live + + + align:start position:0% +1960 in which men and women would live +together uh in a loving + + align:start position:0% +together uh in a loving + + + align:start position:0% +together uh in a loving +friendship one problem is + + align:start position:0% +friendship one problem is + + + align:start position:0% +friendship one problem is +what did love + + align:start position:0% +what did love + + + align:start position:0% +what did love +involve do you have to uh subjugate all + + align:start position:0% +involve do you have to uh subjugate all + + + align:start position:0% +involve do you have to uh subjugate all +of your physical desires your sexual + + align:start position:0% +of your physical desires your sexual + + + align:start position:0% +of your physical desires your sexual +desires was this free love uh among + + align:start position:0% +desires was this free love uh among + + + align:start position:0% +desires was this free love uh among +Christians a lot of them uh seem to have + + align:start position:0% +Christians a lot of them uh seem to have + + + align:start position:0% +Christians a lot of them uh seem to have +bordered on that or even turned into + + align:start position:0% +bordered on that or even turned into + + + align:start position:0% +bordered on that or even turned into +that and they were considered heretical + + align:start position:0% +that and they were considered heretical + + + align:start position:0% +that and they were considered heretical +and thousands and thousands of them were + + align:start position:0% +and thousands and thousands of them were + + + align:start position:0% +and thousands and thousands of them were +murdered by uh those who thought that + + align:start position:0% +murdered by uh those who thought that + + + align:start position:0% +murdered by uh those who thought that +that wasn't good Christianity there were + + align:start position:0% +that wasn't good Christianity there were + + + align:start position:0% +that wasn't good Christianity there were +all the Cru States against the alians + + align:start position:0% +all the Cru States against the alians + + + align:start position:0% +all the Cru States against the alians +but against the um cathars and other + + align:start position:0% +but against the um cathars and other + + + align:start position:0% +but against the um cathars and other +people uh on the grounds that they + + align:start position:0% +people uh on the grounds that they + + + align:start position:0% +people uh on the grounds that they +desecrated the Christian religion they + + align:start position:0% +desecrated the Christian religion they + + + align:start position:0% +desecrated the Christian religion they +were sort of too friendly to each other + + align:start position:0% +were sort of too friendly to each other + + + align:start position:0% +were sort of too friendly to each other +uh but then there were others who like + + align:start position:0% +uh but then there were others who like + + + align:start position:0% +uh but then there were others who like +in a NY or Monastery or a Christian + + align:start position:0% +in a NY or Monastery or a Christian + + + align:start position:0% +in a NY or Monastery or a Christian +commune um subjugated uh conquered their + + align:start position:0% +commune um subjugated uh conquered their + + + align:start position:0% +commune um subjugated uh conquered their +sexual desires and liveed together as + + align:start position:0% +sexual desires and liveed together as + + + align:start position:0% +sexual desires and liveed together as +brother and sisters or as intimate + + align:start position:0% +brother and sisters or as intimate + + + align:start position:0% +brother and sisters or as intimate +friends uh within + + align:start position:0% +friends uh within + + + align:start position:0% +friends uh within +Christ the idea of filia therefore was + + align:start position:0% +Christ the idea of filia therefore was + + + align:start position:0% +Christ the idea of filia therefore was +being applied by them and it continued + + align:start position:0% +being applied by them and it continued + + + align:start position:0% +being applied by them and it continued +as an important element in Christian + + align:start position:0% +as an important element in Christian + + + align:start position:0% +as an important element in Christian +ideas + + align:start position:0% +ideas + + + align:start position:0% +ideas +about the nature of Love of religious + + align:start position:0% +about the nature of Love of religious + + + align:start position:0% +about the nature of Love of religious +Love um stos oh yeah so is that the + + align:start position:0% +Love um stos oh yeah so is that the + + + align:start position:0% +Love um stos oh yeah so is that the +reason why monasteries are all men and + + align:start position:0% +reason why monasteries are all men and + + + align:start position:0% +reason why monasteries are all men and +or did they originate from the + + align:start position:0% +or did they originate from the + + + align:start position:0% +or did they originate from the +I think the upshot of that conflict was + + align:start position:0% +I think the upshot of that conflict was + + + align:start position:0% +I think the upshot of that conflict was +the need to separate the sexes in order + + align:start position:0% +the need to separate the sexes in order + + + align:start position:0% +the need to separate the sexes in order +to keep The Devout Believers + + align:start position:0% +to keep The Devout Believers + + + align:start position:0% +to keep The Devout Believers +purified uh at the same time uh the + + align:start position:0% +purified uh at the same time uh the + + + align:start position:0% +purified uh at the same time uh the +Church of course recognized that there + + align:start position:0% +Church of course recognized that there + + + align:start position:0% +Church of course recognized that there +wouldn't be + + align:start position:0% +wouldn't be + + + align:start position:0% +wouldn't be +any uh future Generations unless + + align:start position:0% +any uh future Generations unless + + + align:start position:0% +any uh future Generations unless +something of that sort went on and so + + align:start position:0% +something of that sort went on and so + + + align:start position:0% +something of that sort went on and so +they made a big thing about the San + + align:start position:0% +they made a big thing about the San + + + align:start position:0% +they made a big thing about the San +sanctity um the sacrament of marriage so + + align:start position:0% +sanctity um the sacrament of marriage so + + + align:start position:0% +sanctity um the sacrament of marriage so +in + + align:start position:0% +in + + + align:start position:0% +in +marriage what you couldn't be could do + + align:start position:0% +marriage what you couldn't be could do + + + align:start position:0% +marriage what you couldn't be could do +out could not do outside was not only + + align:start position:0% +out could not do outside was not only + + + align:start position:0% +out could not do outside was not only +free and and uh um recommended it was + + align:start position:0% +free and and uh um recommended it was + + + align:start position:0% +free and and uh um recommended it was +triy to part of the beauty of marriage + + align:start position:0% +triy to part of the beauty of marriage + + + align:start position:0% +triy to part of the beauty of marriage +which is I always think is a very great + + align:start position:0% +which is I always think is a very great + + + align:start position:0% +which is I always think is a very great +anomaly particularly nowadays when + + align:start position:0% +anomaly particularly nowadays when + + + align:start position:0% +anomaly particularly nowadays when +marriage is crumbling all around um why + + align:start position:0% +marriage is crumbling all around um why + + + align:start position:0% +marriage is crumbling all around um why +can't you do outside of marriage what + + align:start position:0% +can't you do outside of marriage what + + + align:start position:0% +can't you do outside of marriage what +you're encouraged to do inside of + + align:start position:0% +you're encouraged to do inside of + + + align:start position:0% +you're encouraged to do inside of +marriage well this is something we can + + align:start position:0% +marriage well this is something we can + + + align:start position:0% +marriage well this is something we can +come back there um filia then is the + + align:start position:0% +come back there um filia then is the + + + align:start position:0% +come back there um filia then is the +second ingredient of the Catholic + + align:start position:0% +second ingredient of the Catholic + + + align:start position:0% +second ingredient of the Catholic +synthesis in the Middle Ages the third + + align:start position:0% +synthesis in the Middle Ages the third + + + align:start position:0% +synthesis in the Middle Ages the third +ingredient uh doesn't come from Greek + + align:start position:0% +ingredient uh doesn't come from Greek + + + align:start position:0% +ingredient uh doesn't come from Greek +philosophy it comes from the other + + align:start position:0% +philosophy it comes from the other + + + align:start position:0% +philosophy it comes from the other +parent of Christianity which is + + align:start position:0% +parent of Christianity which is + + + align:start position:0% +parent of Christianity which is +Judaism in the Old Testament there is + + align:start position:0% +Judaism in the Old Testament there is + + + align:start position:0% +Judaism in the Old Testament there is +the idea of God's law and uh man being + + align:start position:0% +the idea of God's law and uh man being + + + align:start position:0% +the idea of God's law and uh man being +ordained to be willing to submit to + + align:start position:0% +ordained to be willing to submit to + + + align:start position:0% +ordained to be willing to submit to +God's law not doing it grudging in L but + + align:start position:0% +God's law not doing it grudging in L but + + + align:start position:0% +God's law not doing it grudging in L but +doing it with a good will doing it + + align:start position:0% +doing it with a good will doing it + + + align:start position:0% +doing it with a good will doing it +lovingly and that there love would show + + align:start position:0% +lovingly and that there love would show + + + align:start position:0% +lovingly and that there love would show +itself in uh living up to God's + + align:start position:0% +itself in uh living up to God's + + + align:start position:0% +itself in uh living up to God's +Commandments and God's laws so uh that + + align:start position:0% +Commandments and God's laws so uh that + + + align:start position:0% +Commandments and God's laws so uh that +was the third ingredient the fourth + + align:start position:0% +was the third ingredient the fourth + + + align:start position:0% +was the third ingredient the fourth +ingredient is agape Agape is God because + + align:start position:0% +ingredient is agape Agape is God because + + + align:start position:0% +ingredient is agape Agape is God because +Agape is God's love and and God is + + align:start position:0% +Agape is God's love and and God is + + + align:start position:0% +Agape is God's love and and God is +defined as love and that involves what I + + align:start position:0% +defined as love and that involves what I + + + align:start position:0% +defined as love and that involves what I +call in the chapter in the first volume + + align:start position:0% +call in the chapter in the first volume + + + align:start position:0% +call in the chapter in the first volume +the Divine + + align:start position:0% +the Divine + + + align:start position:0% +the Divine +bestow God bestows love upon the world + + align:start position:0% +bestow God bestows love upon the world + + + align:start position:0% +bestow God bestows love upon the world +first in creating it out of nothing no + + align:start position:0% +first in creating it out of nothing no + + + align:start position:0% +first in creating it out of nothing no +reason why there had to be a world and + + align:start position:0% +reason why there had to be a world and + + + align:start position:0% +reason why there had to be a world and +no reason why there had to be human + + align:start position:0% +no reason why there had to be human + + + align:start position:0% +no reason why there had to be human +beings this was a bestow of God's + + align:start position:0% +beings this was a bestow of God's + + + align:start position:0% +beings this was a bestow of God's +goodness in creating this beautiful + + align:start position:0% +goodness in creating this beautiful + + + align:start position:0% +goodness in creating this beautiful +world as it used to be and allowing + + align:start position:0% +world as it used to be and allowing + + + align:start position:0% +world as it used to be and allowing +people to enjoy life as they sometimes + + align:start position:0% +people to enjoy life as they sometimes + + + align:start position:0% +people to enjoy life as they sometimes +still do try to do try to do + + align:start position:0% +still do try to do try to do + + + align:start position:0% +still do try to do try to do +um second bestow occurs when God seeing + + align:start position:0% +um second bestow occurs when God seeing + + + align:start position:0% +um second bestow occurs when God seeing +how weak and feeble morally and + + align:start position:0% +how weak and feeble morally and + + + align:start position:0% +how weak and feeble morally and +spiritually people are um how sinful + + align:start position:0% +spiritually people are um how sinful + + + align:start position:0% +spiritually people are um how sinful +they are he nevertheless instead of just + + align:start position:0% +they are he nevertheless instead of just + + + align:start position:0% +they are he nevertheless instead of just +wiping them off the face of the globe um + + align:start position:0% +wiping them off the face of the globe um + + + align:start position:0% +wiping them off the face of the globe um +he sends his own son and the meaning of + + align:start position:0% +he sends his own son and the meaning of + + + align:start position:0% +he sends his own son and the meaning of +the son word son is metaphoric it refers + + align:start position:0% +the son word son is metaphoric it refers + + + align:start position:0% +the son word son is metaphoric it refers +to the a second person as it's called + + align:start position:0% +to the a second person as it's called + + + align:start position:0% +to the a second person as it's called +now for me all of this language is very + + align:start position:0% +now for me all of this language is very + + + align:start position:0% +now for me all of this language is very +hard to understand and I'm not sure that + + align:start position:0% +hard to understand and I'm not sure that + + + align:start position:0% +hard to understand and I'm not sure that +it is really uh understandable um what + + align:start position:0% +it is really uh understandable um what + + + align:start position:0% +it is really uh understandable um what +sense is uh Christ something like a son + + align:start position:0% +sense is uh Christ something like a son + + + align:start position:0% +sense is uh Christ something like a son +uh and if Christ is the second person of + + align:start position:0% +uh and if Christ is the second person of + + + align:start position:0% +uh and if Christ is the second person of +God what is the meaning of person + + align:start position:0% +God what is the meaning of person + + + align:start position:0% +God what is the meaning of person +anymore you one doesn't one thinks of + + align:start position:0% +anymore you one doesn't one thinks of + + + align:start position:0% +anymore you one doesn't one thinks of +the Pagan image of Janice with the faces + + align:start position:0% +the Pagan image of Janice with the faces + + + align:start position:0% +the Pagan image of Janice with the faces +you know pointing in different + + align:start position:0% +you know pointing in different + + + align:start position:0% +you know pointing in different +directions two-faced creature but it's + + align:start position:0% +directions two-faced creature but it's + + + align:start position:0% +directions two-faced creature but it's +more more complicated than that um and + + align:start position:0% +more more complicated than that um and + + + align:start position:0% +more more complicated than that um and +then the third person is the Holy Ghost + + align:start position:0% +then the third person is the Holy Ghost + + + align:start position:0% +then the third person is the Holy Ghost +which sometimes is now called the Holy + + align:start position:0% +which sometimes is now called the Holy + + + align:start position:0% +which sometimes is now called the Holy +Spirit um now the point about the Holy + + align:start position:0% +Spirit um now the point about the Holy + + + align:start position:0% +Spirit um now the point about the Holy +Spirit is that it itself is defined in + + align:start position:0% +Spirit is that it itself is defined in + + + align:start position:0% +Spirit is that it itself is defined in +terms of God's Agape it itself is the + + align:start position:0% +terms of God's Agape it itself is the + + + align:start position:0% +terms of God's Agape it itself is the +purity of his besto upon the + + align:start position:0% +purity of his besto upon the + + + align:start position:0% +purity of his besto upon the +world however we interpret the three + + align:start position:0% +world however we interpret the three + + + align:start position:0% +world however we interpret the three +persons that God is since Catholicism is + + align:start position:0% +persons that God is since Catholicism is + + + align:start position:0% +persons that God is since Catholicism is +TR Arian and of course later prant sex + + align:start position:0% +TR Arian and of course later prant sex + + + align:start position:0% +TR Arian and of course later prant sex +sex will not be and Judaism was not um + + align:start position:0% +sex will not be and Judaism was not um + + + align:start position:0% +sex will not be and Judaism was not um +the second bestow of goodness upon the + + align:start position:0% +the second bestow of goodness upon the + + + align:start position:0% +the second bestow of goodness upon the +world occurs when he sends his own son + + align:start position:0% +world occurs when he sends his own son + + + align:start position:0% +world occurs when he sends his own son +for God hath sent his own son um to save + + align:start position:0% +for God hath sent his own son um to save + + + align:start position:0% +for God hath sent his own son um to save +the + + align:start position:0% +the + + + align:start position:0% +the +world um save the world from what from + + align:start position:0% +world um save the world from what from + + + align:start position:0% +world um save the world from what from +its own sinfulness so God so Christ dies + + align:start position:0% +its own sinfulness so God so Christ dies + + + align:start position:0% +its own sinfulness so God so Christ dies +as a way of taking away the sins of + + align:start position:0% +as a way of taking away the sins of + + + align:start position:0% +as a way of taking away the sins of +humanity one can always say why how does + + align:start position:0% +humanity one can always say why how does + + + align:start position:0% +humanity one can always say why how does +that happen why just just because Christ + + align:start position:0% +that happen why just just because Christ + + + align:start position:0% +that happen why just just because Christ +dies how are the sins taken away how can + + align:start position:0% +dies how are the sins taken away how can + + + align:start position:0% +dies how are the sins taken away how can +you erase + + align:start position:0% +you erase + + + align:start position:0% +you erase +reality what occurs is is infinite + + align:start position:0% +reality what occurs is is infinite + + + align:start position:0% +reality what occurs is is infinite +infinitely unerasable because it is what + + align:start position:0% +infinitely unerasable because it is what + + + align:start position:0% +infinitely unerasable because it is what +it is it happened that sin existed you + + align:start position:0% +it is it happened that sin existed you + + + align:start position:0% +it is it happened that sin existed you +know sort how can you erase it um all of + + align:start position:0% +know sort how can you erase it um all of + + + align:start position:0% +know sort how can you erase it um all of +this is is a mystery that the + + align:start position:0% +this is is a mystery that the + + + align:start position:0% +this is is a mystery that the +theologians uh agree cannot be fully + + align:start position:0% +theologians uh agree cannot be fully + + + align:start position:0% +theologians uh agree cannot be fully +understood to our feeble Minds + + align:start position:0% +understood to our feeble Minds + + + align:start position:0% +understood to our feeble Minds +but it's and it's part of the Dogma so I + + align:start position:0% +but it's and it's part of the Dogma so I + + + align:start position:0% +but it's and it's part of the Dogma so I +won't I won't try to make too much sense + + align:start position:0% +won't I won't try to make too much sense + + + align:start position:0% +won't I won't try to make too much sense +out of that uh for me the um oh and then + + align:start position:0% +out of that uh for me the um oh and then + + + align:start position:0% +out of that uh for me the um oh and then +finally uh the Third Kind of a sto is + + align:start position:0% +finally uh the Third Kind of a sto is + + + align:start position:0% +finally uh the Third Kind of a sto is +that when uh the Sinners die they aren't + + align:start position:0% +that when uh the Sinners die they aren't + + + align:start position:0% +that when uh the Sinners die they aren't +all thrown into hell uh that God tries + + align:start position:0% +all thrown into hell uh that God tries + + + align:start position:0% +all thrown into hell uh that God tries +his best to be merciful and to spare as + + align:start position:0% +his best to be merciful and to spare as + + + align:start position:0% +his best to be merciful and to spare as +many as possible and uh that uh is part + + align:start position:0% +many as possible and uh that uh is part + + + align:start position:0% +many as possible and uh that uh is part +of the function of Christ and he + + align:start position:0% +of the function of Christ and he + + + align:start position:0% +of the function of Christ and he +intervenes with his mother + + align:start position:0% +intervenes with his mother + + + align:start position:0% +intervenes with his mother +um but there can't be a spiritual mother + + align:start position:0% +um but there can't be a spiritual mother + + + align:start position:0% +um but there can't be a spiritual mother +God doesn't have a wife it's the mother + + align:start position:0% +God doesn't have a wife it's the mother + + + align:start position:0% +God doesn't have a wife it's the mother +of Jesus who to in whose person uh + + align:start position:0% +of Jesus who to in whose person uh + + + align:start position:0% +of Jesus who to in whose person uh +Christ appears and then somehow she + + align:start position:0% +Christ appears and then somehow she + + + align:start position:0% +Christ appears and then somehow she +becomes more than just a saint uh kind + + align:start position:0% +becomes more than just a saint uh kind + + + align:start position:0% +becomes more than just a saint uh kind +of goddess in fact um and he intervene + + align:start position:0% +of goddess in fact um and he intervene + + + align:start position:0% +of goddess in fact um and he intervene +people will inter can intervene with her + + align:start position:0% +people will inter can intervene with her + + + align:start position:0% +people will inter can intervene with her +to be spared to get favors to have + + align:start position:0% +to be spared to get favors to have + + + align:start position:0% +to be spared to get favors to have +mercies per formed and so will Christ + + align:start position:0% +mercies per formed and so will Christ + + + align:start position:0% +mercies per formed and so will Christ +all of this being a a third illustration + + align:start position:0% +all of this being a a third illustration + + + align:start position:0% +all of this being a a third illustration +of God's infinite bestow upon the + + align:start position:0% +of God's infinite bestow upon the + + + align:start position:0% +of God's infinite bestow upon the +world um I in the book I present all of + + align:start position:0% +world um I in the book I present all of + + + align:start position:0% +world um I in the book I present all of +this as sympathetically as I can because + + align:start position:0% +this as sympathetically as I can because + + + align:start position:0% +this as sympathetically as I can because +as I keep saying being a philosopher + + align:start position:0% +as I keep saying being a philosopher + + + align:start position:0% +as I keep saying being a philosopher +means trying to help people to make + + align:start position:0% +means trying to help people to make + + + align:start position:0% +means trying to help people to make +their ideas clear it's not uh going + + align:start position:0% +their ideas clear it's not uh going + + + align:start position:0% +their ideas clear it's not uh going +around with a uh kind of intellectual + + align:start position:0% +around with a uh kind of intellectual + + + align:start position:0% +around with a uh kind of intellectual +machete cutting down all of uh the + + align:start position:0% +machete cutting down all of uh the + + + align:start position:0% +machete cutting down all of uh the +people who don't agree with with you + + align:start position:0% +people who don't agree with with you + + + align:start position:0% +people who don't agree with with you +that's the way you can get to be a + + align:start position:0% +that's the way you can get to be a + + + align:start position:0% +that's the way you can get to be a +professor but it's not it's not the true + + align:start position:0% +professor but it's not it's not the true + + + align:start position:0% +professor but it's not it's not the true +to the spirit of philosophy uh what why + + align:start position:0% +to the spirit of philosophy uh what why + + + align:start position:0% +to the spirit of philosophy uh what why +then do I pay so much attention to this + + align:start position:0% +then do I pay so much attention to this + + + align:start position:0% +then do I pay so much attention to this +because for me it's all + + align:start position:0% +because for me it's all + + + align:start position:0% +because for me it's all +magnificent mythology it's all a + + align:start position:0% +magnificent mythology it's all a + + + align:start position:0% +magnificent mythology it's all a +beautiful picture of the world beautiful + + align:start position:0% +beautiful picture of the world beautiful + + + align:start position:0% +beautiful picture of the world beautiful +not in the sense that the world is shown + + align:start position:0% +not in the sense that the world is shown + + + align:start position:0% +not in the sense that the world is shown +to be beautiful but rather because the + + align:start position:0% +to be beautiful but rather because the + + + align:start position:0% +to be beautiful but rather because the +doing of it is beautiful the Act is D + + align:start position:0% +doing of it is beautiful the Act is D + + + align:start position:0% +doing of it is beautiful the Act is D +it's an artistic conceptual artistic + + align:start position:0% +it's an artistic conceptual artistic + + + align:start position:0% +it's an artistic conceptual artistic +feat to think of the world in terms of + + align:start position:0% +feat to think of the world in terms of + + + align:start position:0% +feat to think of the world in terms of +these categories and in terms of these + + align:start position:0% +these categories and in terms of these + + + align:start position:0% +these categories and in terms of these +different ingredients and I'm fascinated + + align:start position:0% +different ingredients and I'm fascinated + + + align:start position:0% +different ingredients and I'm fascinated +by that but I'm also fascinated being + + align:start position:0% +by that but I'm also fascinated being + + + align:start position:0% +by that but I'm also fascinated being +pluralistic uh and not you know I'm not + + align:start position:0% +pluralistic uh and not you know I'm not + + + align:start position:0% +pluralistic uh and not you know I'm not +faithful to any one religion uh I love + + align:start position:0% +faithful to any one religion uh I love + + + align:start position:0% +faithful to any one religion uh I love +them all and they're all different and + + align:start position:0% +them all and they're all different and + + + align:start position:0% +them all and they're all different and +there are many more that aren't + + align:start position:0% +there are many more that aren't + + + align:start position:0% +there are many more that aren't +religious at all and I feel the same way + + align:start position:0% +religious at all and I feel the same way + + + align:start position:0% +religious at all and I feel the same way +about it about them uh at least I + + align:start position:0% +about it about them uh at least I + + + align:start position:0% +about it about them uh at least I +aspired to that um we won't we later in + + align:start position:0% +aspired to that um we won't we later in + + + align:start position:0% +aspired to that um we won't we later in +the course we may get to that I'll just + + align:start position:0% +the course we may get to that I'll just + + + align:start position:0% +the course we may get to that I'll just +briefly mention that that's what I mean + + align:start position:0% +briefly mention that that's what I mean + + + align:start position:0% +briefly mention that that's what I mean +by having the love of Love or the love + + align:start position:0% +by having the love of Love or the love + + + align:start position:0% +by having the love of Love or the love +of the love in + + align:start position:0% +of the love in + + + align:start position:0% +of the love in +everything that that then becomes for me + + align:start position:0% +everything that that then becomes for me + + + align:start position:0% +everything that that then becomes for me +as it did for George santiana whom I + + align:start position:0% +as it did for George santiana whom I + + + align:start position:0% +as it did for George santiana whom I +mentioned to you and others becomes the + + align:start position:0% +mentioned to you and others becomes the + + + align:start position:0% +mentioned to you and others becomes the +basis of a humanistic uh non-theistic + + align:start position:0% +basis of a humanistic uh non-theistic + + + align:start position:0% +basis of a humanistic uh non-theistic +religion very different from the + + align:start position:0% +religion very different from the + + + align:start position:0% +religion very different from the +established religions but it's the + + align:start position:0% +established religions but it's the + + + align:start position:0% +established religions but it's the +equivalent of an of a + + align:start position:0% +equivalent of an of a + + + align:start position:0% +equivalent of an of a +religion + + align:start position:0% + + + + align:start position:0% + +um that being my + + align:start position:0% +um that being my + + + align:start position:0% +um that being my +motive what I want to do is to stand + + align:start position:0% +motive what I want to do is to stand + + + align:start position:0% +motive what I want to do is to stand +Christianity on its head or if I'm right + + align:start position:0% +Christianity on its head or if I'm right + + + align:start position:0% +Christianity on its head or if I'm right +stand it on its feet by saying these + + align:start position:0% +stand it on its feet by saying these + + + align:start position:0% +stand it on its feet by saying these +ideas of + + align:start position:0% +ideas of + + + align:start position:0% +ideas of +bestow are simply Expressions metaphoric + + align:start position:0% +bestow are simply Expressions metaphoric + + + align:start position:0% +bestow are simply Expressions metaphoric +versions of something that human beings + + align:start position:0% +versions of something that human beings + + + align:start position:0% +versions of something that human beings +do not just God the all of love can be + + align:start position:0% +do not just God the all of love can be + + + align:start position:0% +do not just God the all of love can be +understood in terms of a system of + + align:start position:0% +understood in terms of a system of + + + align:start position:0% +understood in terms of a system of +bestow and then having got that um I + + align:start position:0% +bestow and then having got that um I + + + align:start position:0% +bestow and then having got that um I +then contrast with sto with appraisal + + align:start position:0% +then contrast with sto with appraisal + + + align:start position:0% +then contrast with sto with appraisal +having made the contrast I then try to + + align:start position:0% +having made the contrast I then try to + + + align:start position:0% +having made the contrast I then try to +show the + + align:start position:0% +show the + + + align:start position:0% +show the +harmonization between Theo and appraisal + + align:start position:0% +harmonization between Theo and appraisal + + + align:start position:0% +harmonization between Theo and appraisal +and then after that there are other + + align:start position:0% +and then after that there are other + + + align:start position:0% +and then after that there are other +distinctions and the matter gets to be + + align:start position:0% +distinctions and the matter gets to be + + + align:start position:0% +distinctions and the matter gets to be +more and more complicated as you'll see + + align:start position:0% +more and more complicated as you'll see + + + align:start position:0% +more and more complicated as you'll see +when you get to the book called + + align:start position:0% +when you get to the book called + + + align:start position:0% +when you get to the book called +Explorations in love and sex + + align:start position:0% +Explorations in love and sex + + + align:start position:0% +Explorations in love and sex +um my first acquaintance with the idea + + align:start position:0% +um my first acquaintance with the idea + + + align:start position:0% +um my first acquaintance with the idea +of Agape of God's pistol came to me in + + align:start position:0% +of Agape of God's pistol came to me in + + + align:start position:0% +of Agape of God's pistol came to me in +the in a great work by a Protestant + + align:start position:0% +the in a great work by a Protestant + + + align:start position:0% +the in a great work by a Protestant +Bishop the bishop of Lun uh whose name + + align:start position:0% +Bishop the bishop of Lun uh whose name + + + align:start position:0% +Bishop the bishop of Lun uh whose name +was + + align:start position:0% +was + + + align:start position:0% +was +um + + align:start position:0% +um + + + align:start position:0% +um +nigr I forget now what his first name + + align:start position:0% + + + + align:start position:0% + +was and the n y g re n um and the book + + align:start position:0% +was and the n y g re n um and the book + + + align:start position:0% +was and the n y g re n um and the book +is called agape and + + align:start position:0% +is called agape and + + + align:start position:0% +is called agape and +and it's a marvelous history of Western + + align:start position:0% +and it's a marvelous history of Western + + + align:start position:0% +and it's a marvelous history of Western +philosop Christian Philosophy from the + + align:start position:0% +philosop Christian Philosophy from the + + + align:start position:0% +philosop Christian Philosophy from the +point of view of the um two ways of + + align:start position:0% +point of view of the um two ways of + + + align:start position:0% +point of view of the um two ways of +thinking entering into the thought of + + align:start position:0% +thinking entering into the thought of + + + align:start position:0% +thinking entering into the thought of +Christians that's where I got the idea + + align:start position:0% +Christians that's where I got the idea + + + align:start position:0% +Christians that's where I got the idea +the Christian idea of of bestow and then + + align:start position:0% +the Christian idea of of bestow and then + + + align:start position:0% +the Christian idea of of bestow and then +not being a devout believer like uh + + align:start position:0% +not being a devout believer like uh + + + align:start position:0% +not being a devout believer like uh +nigran uh I be I wanted to see how this + + align:start position:0% +nigran uh I be I wanted to see how this + + + align:start position:0% +nigran uh I be I wanted to see how this +could be an expression + + align:start position:0% +could be an expression + + + align:start position:0% +could be an expression +of the mythologizing idealizing aspect + + align:start position:0% +of the mythologizing idealizing aspect + + + align:start position:0% +of the mythologizing idealizing aspect +of human nature then I had to explain + + align:start position:0% +of human nature then I had to explain + + + align:start position:0% +of human nature then I had to explain +what it was to + + align:start position:0% +what it was to + + + align:start position:0% +what it was to +idealize what how imagination comes into + + align:start position:0% +idealize what how imagination comes into + + + align:start position:0% +idealize what how imagination comes into +it and so on all of that drives out of + + align:start position:0% +it and so on all of that drives out of + + + align:start position:0% +it and so on all of that drives out of +this early + + align:start position:0% +this early + + + align:start position:0% +this early +exploration uh for me all right so here + + align:start position:0% +exploration uh for me all right so here + + + align:start position:0% +exploration uh for me all right so here +we have the four Concepts I'm sorry this + + align:start position:0% +we have the four Concepts I'm sorry this + + + align:start position:0% +we have the four Concepts I'm sorry this +so lengthy Adriana you will have all the + + align:start position:0% +so lengthy Adriana you will have all the + + + align:start position:0% +so lengthy Adriana you will have all the +time you want very shortly um four four + + align:start position:0% +time you want very shortly um four four + + + align:start position:0% +time you want very shortly um four four +concepts of + + align:start position:0% +concepts of + + + align:start position:0% +concepts of +AOS filia nomos and + + align:start position:0% +AOS filia nomos and + + + align:start position:0% +AOS filia nomos and +Agape the great Genius of the Catholic + + align:start position:0% +Agape the great Genius of the Catholic + + + align:start position:0% +Agape the great Genius of the Catholic +world uh was St Thomas + + align:start position:0% +world uh was St Thomas + + + align:start position:0% +world uh was St Thomas +aquinus um in books in you know more I + + align:start position:0% +aquinus um in books in you know more I + + + align:start position:0% +aquinus um in books in you know more I +don't know if one call them books sort + + align:start position:0% +don't know if one call them books sort + + + align:start position:0% +don't know if one call them books sort +of monuments like uh + + align:start position:0% +of monuments like uh + + + align:start position:0% +of monuments like uh +sumica some the high highest summation + + align:start position:0% +sumica some the high highest summation + + + align:start position:0% +sumica some the high highest summation +of of theology um + + align:start position:0% +of of theology um + + + align:start position:0% +of of theology um +in the uh in the I guess the 14th + + align:start position:0% +in the uh in the I guess the 14th + + + align:start position:0% +in the uh in the I guess the 14th +century is when he lived right am I + + align:start position:0% +century is when he lived right am I + + + align:start position:0% +century is when he lived right am I +right or was it it wasn't the + + align:start position:0% +right or was it it wasn't the + + + align:start position:0% +right or was it it wasn't the +13th um he um formulated what became the + + align:start position:0% +13th um he um formulated what became the + + + align:start position:0% +13th um he um formulated what became the +basis of all subsequent Catholicism and + + align:start position:0% +basis of all subsequent Catholicism and + + + align:start position:0% +basis of all subsequent Catholicism and +Central in that was the idea that + + align:start position:0% +Central in that was the idea that + + + align:start position:0% +Central in that was the idea that +God is all of these that all of these + + align:start position:0% +God is all of these that all of these + + + align:start position:0% +God is all of these that all of these +are Christian Concepts and and they are + + align:start position:0% +are Christian Concepts and and they are + + + align:start position:0% +are Christian Concepts and and they are +entirely compatible they're they are + + align:start position:0% +entirely compatible they're they are + + + align:start position:0% +entirely compatible they're they are +synthesized and he he created a + + align:start position:0% +synthesized and he he created a + + + align:start position:0% +synthesized and he he created a +synthesis by welding them into each + + align:start position:0% +synthesis by welding them into each + + + align:start position:0% +synthesis by welding them into each +other right all right uh in the case of + + align:start position:0% +other right all right uh in the case of + + + align:start position:0% +other right all right uh in the case of +Luther now was jumping to the + + align:start position:0% +Luther now was jumping to the + + + align:start position:0% +Luther now was jumping to the +Reformation Luther um couldn't believe + + align:start position:0% +Reformation Luther um couldn't believe + + + align:start position:0% +Reformation Luther um couldn't believe +all four of them he thought that God was + + align:start position:0% +all four of them he thought that God was + + + align:start position:0% +all four of them he thought that God was +Agape for him that was the basis of + + align:start position:0% +Agape for him that was the basis of + + + align:start position:0% +Agape for him that was the basis of +Christianity but uh AOS he me means + + align:start position:0% +Christianity but uh AOS he me means + + + align:start position:0% +Christianity but uh AOS he me means +thought of no matter what St Augustine + + align:start position:0% +thought of no matter what St Augustine + + + align:start position:0% +thought of no matter what St Augustine +said uh is selfish it's somebody wanting + + align:start position:0% +said uh is selfish it's somebody wanting + + + align:start position:0% +said uh is selfish it's somebody wanting +to get better something better so given + + align:start position:0% +to get better something better so given + + + align:start position:0% +to get better something better so given +a choice between a lesser spiritual good + + align:start position:0% +a choice between a lesser spiritual good + + + align:start position:0% +a choice between a lesser spiritual good +which is what human beings would have + + align:start position:0% +which is what human beings would have + + + align:start position:0% +which is what human beings would have +and a better higher spiritual good which + + align:start position:0% +and a better higher spiritual good which + + + align:start position:0% +and a better higher spiritual good which +is what a Divinity would have God then + + align:start position:0% +is what a Divinity would have God then + + + align:start position:0% +is what a Divinity would have God then +uh a Lusty selfish man will try to make + + align:start position:0% +uh a Lusty selfish man will try to make + + + align:start position:0% +uh a Lusty selfish man will try to make +himself better so that he can get the + + align:start position:0% +himself better so that he can get the + + + align:start position:0% +himself better so that he can get the +best there is nobody wants an inferior + + align:start position:0% +best there is nobody wants an inferior + + + align:start position:0% +best there is nobody wants an inferior +thing but that's selfishness according + + align:start position:0% +thing but that's selfishness according + + + align:start position:0% +thing but that's selfishness according +uh to + + align:start position:0% +uh to + + + align:start position:0% +uh to +Luther uh in he was originally in his + + align:start position:0% +Luther uh in he was originally in his + + + align:start position:0% +Luther uh in he was originally in his +life in a a austinian + + align:start position:0% +life in a a austinian + + + align:start position:0% +life in a a austinian +monastery um and he lost his faith in + + align:start position:0% +monastery um and he lost his faith in + + + align:start position:0% +monastery um and he lost his faith in +Catholicism there um he went through all + + align:start position:0% +Catholicism there um he went through all + + + align:start position:0% +Catholicism there um he went through all +of the rituals self- flatulation and all + + align:start position:0% +of the rituals self- flatulation and all + + + align:start position:0% +of the rituals self- flatulation and all +of the very difficult hardships that + + align:start position:0% +of the very difficult hardships that + + + align:start position:0% +of the very difficult hardships that +were supposed to purify oneself of the + + align:start position:0% +were supposed to purify oneself of the + + + align:start position:0% +were supposed to purify oneself of the +longings of the flesh uh make one more + + align:start position:0% +longings of the flesh uh make one more + + + align:start position:0% +longings of the flesh uh make one more +and more spiritual and um you know he + + align:start position:0% +and more spiritual and um you know he + + + align:start position:0% +and more spiritual and um you know he +suffered in the proper manner but um he + + align:start position:0% +suffered in the proper manner but um he + + + align:start position:0% +suffered in the proper manner but um he +writes um the more I did that the more I + + align:start position:0% +writes um the more I did that the more I + + + align:start position:0% +writes um the more I did that the more I +realize that how sinful I was because of + + align:start position:0% +realize that how sinful I was because of + + + align:start position:0% +realize that how sinful I was because of +my desire to do that uh it I couldn't + + align:start position:0% +my desire to do that uh it I couldn't + + + align:start position:0% +my desire to do that uh it I couldn't +eliminate + + align:start position:0% +eliminate + + + align:start position:0% +eliminate +that uh and why well if I could if I did + + align:start position:0% +that uh and why well if I could if I did + + + align:start position:0% +that uh and why well if I could if I did +eliminate + + align:start position:0% +eliminate + + + align:start position:0% +eliminate +that I would if I did the job properly + + align:start position:0% +that I would if I did the job properly + + + align:start position:0% +that I would if I did the job properly +the way I'm being trained in the + + align:start position:0% +the way I'm being trained in the + + + align:start position:0% +the way I'm being trained in the +monastery I'd become a + + align:start position:0% +monastery I'd become a + + + align:start position:0% +monastery I'd become a +saint but + + align:start position:0% +saint but + + + align:start position:0% +saint but +uh for the wrong + + align:start position:0% +uh for the wrong + + + align:start position:0% +uh for the wrong +reasons and there's one line I've always + + align:start position:0% +reasons and there's one line I've always + + + align:start position:0% +reasons and there's one line I've always +remembered from his description of those + + align:start position:0% +remembered from his description of those + + + align:start position:0% +remembered from his description of those +days he said I + + align:start position:0% +days he said I + + + align:start position:0% +days he said I +concluded + + align:start position:0% +concluded + + + align:start position:0% +concluded +um uh oh devil the devil you'll make + + align:start position:0% +um uh oh devil the devil you'll make + + + align:start position:0% +um uh oh devil the devil you'll make +you'll you'll make a saint of me yet W + + align:start position:0% +you'll you'll make a saint of me yet W + + + align:start position:0% +you'll you'll make a saint of me yet W +you that there was something infinitely + + align:start position:0% +you that there was something infinitely + + + align:start position:0% +you that there was something infinitely +sinful and evil in the very idea of + + align:start position:0% +sinful and evil in the very idea of + + + align:start position:0% +sinful and evil in the very idea of +anybody wanting to make himself into his + + align:start position:0% +anybody wanting to make himself into his + + + align:start position:0% +anybody wanting to make himself into his +Saint if you become one it's not because + + align:start position:0% +Saint if you become one it's not because + + + align:start position:0% +Saint if you become one it's not because +of anything you do it's because of God's + + align:start position:0% +of anything you do it's because of God's + + + align:start position:0% +of anything you do it's because of God's +grace God's grace is outflowing from his + + align:start position:0% +grace God's grace is outflowing from his + + + align:start position:0% +grace God's grace is outflowing from his +um Agape his Theo of Love um and your + + align:start position:0% +um Agape his Theo of Love um and your + + + align:start position:0% +um Agape his Theo of Love um and your +striving to get it is no better than + + align:start position:0% +striving to get it is no better than + + + align:start position:0% +striving to get it is no better than +you're striving to make a fortune or um + + align:start position:0% +you're striving to make a fortune or um + + + align:start position:0% +you're striving to make a fortune or um +to make love to a very large number of + + align:start position:0% +to make love to a very large number of + + + align:start position:0% +to make love to a very large number of +women all of that is evil the spirit + + align:start position:0% +women all of that is evil the spirit + + + align:start position:0% +women all of that is evil the spirit +that's it's a kind of spiritual evil as + + align:start position:0% +that's it's a kind of spiritual evil as + + + align:start position:0% +that's it's a kind of spiritual evil as +opposed to more M material evils on that + + align:start position:0% +opposed to more M material evils on that + + + align:start position:0% +opposed to more M material evils on that +basis uh Luther began by separating AOS + + align:start position:0% +basis uh Luther began by separating AOS + + + align:start position:0% +basis uh Luther began by separating AOS +out of + + align:start position:0% +out of + + + align:start position:0% +out of +Christianity um and um the uh living up + + align:start position:0% +Christianity um and um the uh living up + + + align:start position:0% +Christianity um and um the uh living up +to the laws and he thought that was the + + align:start position:0% +to the laws and he thought that was the + + + align:start position:0% +to the laws and he thought that was the +the uh reason why the Jews U were + + align:start position:0% +the uh reason why the Jews U were + + + align:start position:0% +the uh reason why the Jews U were +finally uh dismissed by God and a new + + align:start position:0% +finally uh dismissed by God and a new + + + align:start position:0% +finally uh dismissed by God and a new +religion had to be created because you + + align:start position:0% +religion had to be created because you + + + align:start position:0% +religion had to be created because you +would live up to the law laws inevitably + + align:start position:0% +would live up to the law laws inevitably + + + align:start position:0% +would live up to the law laws inevitably +out of obedience not out of love so that + + align:start position:0% +out of obedience not out of love so that + + + align:start position:0% +out of obedience not out of love so that +took care of nomos filia uh was uh a + + align:start position:0% +took care of nomos filia uh was uh a + + + align:start position:0% +took care of nomos filia uh was uh a +little better but not much because you + + align:start position:0% +little better but not much because you + + + align:start position:0% +little better but not much because you +could have a society of robbers or + + align:start position:0% +could have a society of robbers or + + + align:start position:0% +could have a society of robbers or +murderers or Sinners so just the + + align:start position:0% +murderers or Sinners so just the + + + align:start position:0% +murderers or Sinners so just the +Friendship among people who are + + align:start position:0% +Friendship among people who are + + + align:start position:0% +Friendship among people who are +imperfect doesn't yet bring one into the + + align:start position:0% +imperfect doesn't yet bring one into the + + + align:start position:0% +imperfect doesn't yet bring one into the +religious condition one wants the only + + align:start position:0% +religious condition one wants the only + + + align:start position:0% +religious condition one wants the only +thing that would would be Agape but man + + align:start position:0% +thing that would would be Agape but man + + + align:start position:0% +thing that would would be Agape but man +can't have agape and therefore uh life + + align:start position:0% +can't have agape and therefore uh life + + + align:start position:0% +can't have agape and therefore uh life +on Earth human nature is evil inherently + + align:start position:0% +on Earth human nature is evil inherently + + + align:start position:0% +on Earth human nature is evil inherently +and the Lutheran nowadays really seem to + + align:start position:0% +and the Lutheran nowadays really seem to + + + align:start position:0% +and the Lutheran nowadays really seem to +believe that I don't know if any of you + + align:start position:0% +believe that I don't know if any of you + + + align:start position:0% +believe that I don't know if any of you +listen to + + align:start position:0% +listen to + + + align:start position:0% +listen to +um um + + align:start position:0% +um um + + + align:start position:0% +um um +Prairie Home Companion on + + align:start position:0% +Prairie Home Companion on + + + align:start position:0% +Prairie Home Companion on +radio do does that not popular thing to + + align:start position:0% +radio do does that not popular thing to + + + align:start position:0% +radio do does that not popular thing to +you for all of you it's on all the + + align:start position:0% +you for all of you it's on all the + + + align:start position:0% +you for all of you it's on all the +public broadcasting stations at the same + + align:start position:0% +public broadcasting stations at the same + + + align:start position:0% +public broadcasting stations at the same +time Saturday at 6 o00 when I'm in New + + align:start position:0% +time Saturday at 6 o00 when I'm in New + + + align:start position:0% +time Saturday at 6 o00 when I'm in New +Hampshire because where I happen to be + + align:start position:0% +Hampshire because where I happen to be + + + align:start position:0% +Hampshire because where I happen to be +located i' pick up about six or seven + + align:start position:0% +located i' pick up about six or seven + + + align:start position:0% +located i' pick up about six or seven +different public broadcasting stations + + align:start position:0% +different public broadcasting stations + + + align:start position:0% +different public broadcasting stations +Albany um uh ammer + + align:start position:0% + + + + align:start position:0% + +Boston and two in New Hampshire you know + + align:start position:0% +Boston and two in New Hampshire you know + + + align:start position:0% +Boston and two in New Hampshire you know +all of them and at 6:00 they all play + + align:start position:0% +all of them and at 6:00 they all play + + + align:start position:0% +all of them and at 6:00 they all play +this thing because it's so popular uh + + align:start position:0% +this thing because it's so popular uh + + + align:start position:0% +this thing because it's so popular uh +and the it uh the the um the master + + align:start position:0% +and the it uh the the um the master + + + align:start position:0% +and the it uh the the um the master +ceremonies who is very famous but whose + + align:start position:0% +ceremonies who is very famous but whose + + + align:start position:0% +ceremonies who is very famous but whose +name I've now forgot what is what is his + + align:start position:0% +name I've now forgot what is what is his + + + align:start position:0% +name I've now forgot what is what is his +name you don't know um + + align:start position:0% + + + + align:start position:0% + +in any event he has a a + + align:start position:0% +in any event he has a a + + + align:start position:0% +in any event he has a a +monologue about life in his hometown + + align:start position:0% +monologue about life in his hometown + + + align:start position:0% +monologue about life in his hometown +which is a fictional place somewhere in + + align:start position:0% +which is a fictional place somewhere in + + + align:start position:0% +which is a fictional place somewhere in +Minnesota uh called Lake wagon now the + + align:start position:0% +Minnesota uh called Lake wagon now the + + + align:start position:0% +Minnesota uh called Lake wagon now the +name itself and it's where everybody is + + align:start position:0% +name itself and it's where everybody is + + + align:start position:0% +name itself and it's where everybody is +a Lutheran and all being Lutheran + + align:start position:0% +a Lutheran and all being Lutheran + + + align:start position:0% +a Lutheran and all being Lutheran +they're all sure of their own their own + + align:start position:0% +they're all sure of their own their own + + + align:start position:0% +they're all sure of their own their own +sinfulness that everything they do is + + align:start position:0% +sinfulness that everything they do is + + + align:start position:0% +sinfulness that everything they do is +Tainted and uh since uh presumably he's + + align:start position:0% +Tainted and uh since uh presumably he's + + + align:start position:0% +Tainted and uh since uh presumably he's +a Lutheran and he's very comical uh it's + + align:start position:0% +a Lutheran and he's very comical uh it's + + + align:start position:0% +a Lutheran and he's very comical uh it's +done with a good spirit nobody seems to + + align:start position:0% +done with a good spirit nobody seems to + + + align:start position:0% +done with a good spirit nobody seems to +think this is a kind of Lutheran baiting + + align:start position:0% +think this is a kind of Lutheran baiting + + + align:start position:0% +think this is a kind of Lutheran baiting +uh but the point is that that goes back + + align:start position:0% +uh but the point is that that goes back + + + align:start position:0% +uh but the point is that that goes back +to Luther's belief that uh human nature + + align:start position:0% +to Luther's belief that uh human nature + + + align:start position:0% +to Luther's belief that uh human nature +is inherently evil he doesn't give up + + align:start position:0% +is inherently evil he doesn't give up + + + align:start position:0% +is inherently evil he doesn't give up +however because God being infinitely + + align:start position:0% +however because God being infinitely + + + align:start position:0% +however because God being infinitely +good bestows his love uh upon the world + + align:start position:0% +good bestows his love uh upon the world + + + align:start position:0% +good bestows his love uh upon the world +and + + align:start position:0% +and + + + align:start position:0% +and +uh give rewards those who have faith in + + align:start position:0% +uh give rewards those who have faith in + + + align:start position:0% +uh give rewards those who have faith in +him not for their Good Deeds because you + + align:start position:0% +him not for their Good Deeds because you + + + align:start position:0% +him not for their Good Deeds because you +do good deeds you're scheming um uh but + + align:start position:0% +do good deeds you're scheming um uh but + + + align:start position:0% +do good deeds you're scheming um uh but +rather uh + + align:start position:0% +rather uh + + + align:start position:0% +rather uh +because it's God's grace which can fall + + align:start position:0% +because it's God's grace which can fall + + + align:start position:0% +because it's God's grace which can fall +on anybody without the person knowing + + align:start position:0% +on anybody without the person knowing + + + align:start position:0% +on anybody without the person knowing +about it so you have a very different + + align:start position:0% +about it so you have a very different + + + align:start position:0% +about it so you have a very different +conception from St um uh Thomas aquinus + + align:start position:0% +conception from St um uh Thomas aquinus + + + align:start position:0% +conception from St um uh Thomas aquinus +is all right and that results in the + + align:start position:0% +is all right and that results in the + + + align:start position:0% +is all right and that results in the +splitting of the + + align:start position:0% +splitting of the + + + align:start position:0% +splitting of the +synthesis that's what those pages of + + align:start position:0% +synthesis that's what those pages of + + + align:start position:0% +synthesis that's what those pages of +mine are about the creation of the + + align:start position:0% +mine are about the creation of the + + + align:start position:0% +mine are about the creation of the +synthesis and the splitting of the + + align:start position:0% + + + + align:start position:0% + +synthesis when the uh first volume came + + align:start position:0% +synthesis when the uh first volume came + + + align:start position:0% +synthesis when the uh first volume came +out I thought you know I was doing a + + align:start position:0% +out I thought you know I was doing a + + + align:start position:0% +out I thought you know I was doing a +good philosophical job my colleagues the + + align:start position:0% +good philosophical job my colleagues the + + + align:start position:0% +good philosophical job my colleagues the +American philosophers would recognize + + align:start position:0% +American philosophers would recognize + + + align:start position:0% +American philosophers would recognize +the Brilliance of my analysis + + align:start position:0% +the Brilliance of my analysis + + + align:start position:0% +the Brilliance of my analysis +uh and the historian would see uh how + + align:start position:0% +uh and the historian would see uh how + + + align:start position:0% +uh and the historian would see uh how +insightful I was as a historian of ideas + + align:start position:0% +insightful I was as a historian of ideas + + + align:start position:0% +insightful I was as a historian of ideas +uh but I was afraid the religious people + + align:start position:0% +uh but I was afraid the religious people + + + align:start position:0% +uh but I was afraid the religious people +would be horrified at my standing their + + align:start position:0% +would be horrified at my standing their + + + align:start position:0% +would be horrified at my standing their +religion on its head and then chopping + + align:start position:0% +religion on its head and then chopping + + + align:start position:0% +religion on its head and then chopping +it up and for the sake of this argument + + align:start position:0% +it up and for the sake of this argument + + + align:start position:0% +it up and for the sake of this argument +that I was developing I was completely + + align:start position:0% +that I was developing I was completely + + + align:start position:0% +that I was developing I was completely +wrong the philosophers completely + + align:start position:0% +wrong the philosophers completely + + + align:start position:0% +wrong the philosophers completely +ignored it and the religious people + + align:start position:0% +ignored it and the religious people + + + align:start position:0% +ignored it and the religious people +thought there was something of interest + + align:start position:0% +thought there was something of interest + + + align:start position:0% +thought there was something of interest +and nowadays I think that's still the + + align:start position:0% +and nowadays I think that's still the + + + align:start position:0% +and nowadays I think that's still the +case that um is it has a great Fair + + align:start position:0% +case that um is it has a great Fair + + + align:start position:0% +case that um is it has a great Fair +reputation among my whereas other books + + align:start position:0% +reputation among my whereas other books + + + align:start position:0% +reputation among my whereas other books +of mine have been totally neglected but + + align:start position:0% +of mine have been totally neglected but + + + align:start position:0% +of mine have been totally neglected but +um I think mainly by by people who take + + align:start position:0% +um I think mainly by by people who take + + + align:start position:0% +um I think mainly by by people who take +religion seriously they didn't mind the + + align:start position:0% +religion seriously they didn't mind the + + + align:start position:0% +religion seriously they didn't mind the +fact that I was an outsider a humanist + + align:start position:0% +fact that I was an outsider a humanist + + + align:start position:0% +fact that I was an outsider a humanist +um so I'm very I'm happy to have been of + + align:start position:0% +um so I'm very I'm happy to have been of + + + align:start position:0% +um so I'm very I'm happy to have been of +service to that extent though I'm sorry + + align:start position:0% +service to that extent though I'm sorry + + + align:start position:0% +service to that extent though I'm sorry +that philosophy has gone off in its own + + align:start position:0% +that philosophy has gone off in its own + + + align:start position:0% +that philosophy has gone off in its own +in its own Wayward manner + + align:start position:0% +in its own Wayward manner + + + align:start position:0% +in its own Wayward manner +Adriana have you forgotten everything + + align:start position:0% +Adriana have you forgotten everything + + + align:start position:0% +Adriana have you forgotten everything +that you wanted to say um not not really + + align:start position:0% +that you wanted to say um not not really + + + align:start position:0% +that you wanted to say um not not really +have I I hope I haven't deterred you no + + align:start position:0% +have I I hope I haven't deterred you no + + + align:start position:0% +have I I hope I haven't deterred you no +then let's go back you were saying about + + align:start position:0% +then let's go back you were saying about + + + align:start position:0% +then let's go back you were saying about +RS filia yes and uh well you already + + align:start position:0% +RS filia yes and uh well you already + + + align:start position:0% +RS filia yes and uh well you already +talked about what I was going to say + + align:start position:0% +talked about what I was going to say + + + align:start position:0% +talked about what I was going to say +about how St Austine made the + + align:start position:0% +about how St Austine made the + + + align:start position:0% +about how St Austine made the +distinction between the body and soul + + align:start position:0% +distinction between the body and soul + + + align:start position:0% +distinction between the body and soul +based on Plato + + align:start position:0% +based on Plato + + + align:start position:0% +based on Plato +PL dous view of the + + align:start position:0% +PL dous view of the + + + align:start position:0% +PL dous view of the +world and he praised the soul and + + align:start position:0% +world and he praised the soul and + + + align:start position:0% +world and he praised the soul and +sustained the body so Christianity takes + + align:start position:0% +sustained the body so Christianity takes + + + align:start position:0% +sustained the body so Christianity takes +this and gives rise to to Christian and + + align:start position:0% +this and gives rise to to Christian and + + + align:start position:0% +this and gives rise to to Christian and +Catholic morals and deres the concept of + + align:start position:0% +Catholic morals and deres the concept of + + + align:start position:0% +Catholic morals and deres the concept of +Sin from uh disdaining the + + align:start position:0% +Sin from uh disdaining the + + + align:start position:0% +Sin from uh disdaining the +body and uh I just wanted to mention + + align:start position:0% +body and uh I just wanted to mention + + + align:start position:0% +body and uh I just wanted to mention +that because this is the reason why + + align:start position:0% +that because this is the reason why + + + align:start position:0% +that because this is the reason why +sometimes s sexuality is treated as as + + align:start position:0% +sometimes s sexuality is treated as as + + + align:start position:0% +sometimes s sexuality is treated as as +sort of a taboo + + align:start position:0% +sort of a taboo + + + align:start position:0% +sort of a taboo +topic um + + align:start position:0% +topic um + + + align:start position:0% +topic um +and it it wasn't very it wasn't + + align:start position:0% +and it it wasn't very it wasn't + + + align:start position:0% +and it it wasn't very it wasn't +mentioned on that chapter so I just + + align:start position:0% +mentioned on that chapter so I just + + + align:start position:0% +mentioned on that chapter so I just +wanted to no this is worth developing + + align:start position:0% +wanted to no this is worth developing + + + align:start position:0% +wanted to no this is worth developing +does anyone want to say anything about + + align:start position:0% +does anyone want to say anything about + + + align:start position:0% +does anyone want to say anything about +that uh St uh I think why sexuality is + + align:start position:0% +that uh St uh I think why sexuality is + + + align:start position:0% +that uh St uh I think why sexuality is +considered a taboo by Christians is + + align:start position:0% +considered a taboo by Christians is + + + align:start position:0% +considered a taboo by Christians is +because it was a pagan uh they wanted to + + align:start position:0% +because it was a pagan uh they wanted to + + + align:start position:0% +because it was a pagan uh they wanted to +you know make pagans they didn't want to + + align:start position:0% +you know make pagans they didn't want to + + + align:start position:0% +you know make pagans they didn't want to +have Pagan traits in their religion and + + align:start position:0% +have Pagan traits in their religion and + + + align:start position:0% +have Pagan traits in their religion and +pagans used to have I mean in ancient + + align:start position:0% +pagans used to have I mean in ancient + + + align:start position:0% +pagans used to have I mean in ancient +Greek these big ories and you know sex + + align:start position:0% +Greek these big ories and you know sex + + + align:start position:0% +Greek these big ories and you know sex +and you know loving of the woman was + + align:start position:0% +and you know loving of the woman was + + + align:start position:0% +and you know loving of the woman was +part of um the whole + + align:start position:0% +part of um the whole + + + align:start position:0% +part of um the whole +Pagan uh religion so Christians in their + + align:start position:0% +Pagan uh religion so Christians in their + + + align:start position:0% +Pagan uh religion so Christians in their +effort to try to you know shun paganism + + align:start position:0% +effort to try to you know shun paganism + + + align:start position:0% +effort to try to you know shun paganism +made sex a taboo and made the woman + + align:start position:0% +made sex a taboo and made the woman + + + align:start position:0% +made sex a taboo and made the woman +inferior to + + align:start position:0% +inferior to + + + align:start position:0% +inferior to +man um I think that may have been a + + align:start position:0% +man um I think that may have been a + + + align:start position:0% +man um I think that may have been a +second idea because even + + align:start position:0% +second idea because even + + + align:start position:0% +second idea because even +if um you shun sex doesn't make women + + align:start position:0% +if um you shun sex doesn't make women + + + align:start position:0% +if um you shun sex doesn't make women +inferior I was just there were there + + align:start position:0% +inferior I was just there were there + + + align:start position:0% +inferior I was just there were there +were goddesses F fertility goddesses + + align:start position:0% +were goddesses F fertility goddesses + + + align:start position:0% +were goddesses F fertility goddesses +among ancient people and maybe that was + + align:start position:0% +among ancient people and maybe that was + + + align:start position:0% +among ancient people and maybe that was +thought to be competitive with the one + + align:start position:0% +thought to be competitive with the one + + + align:start position:0% +thought to be competitive with the one +God that Christianity believed in but + + align:start position:0% +God that Christianity believed in but + + + align:start position:0% +God that Christianity believed in but +they could just as easily have said that + + align:start position:0% +they could just as easily have said that + + + align:start position:0% +they could just as easily have said that +um sex is bad + + align:start position:0% +um sex is bad + + + align:start position:0% +um sex is bad +because of the men as well as because of + + align:start position:0% +because of the men as well as because of + + + align:start position:0% +because of the men as well as because of +the + + align:start position:0% + + + + align:start position:0% + +women in terms of the history of the + + align:start position:0% +women in terms of the history of the + + + align:start position:0% +women in terms of the history of the +different versions of + + align:start position:0% +different versions of + + + align:start position:0% +different versions of +Christianity Catholicism has always been + + align:start position:0% +Christianity Catholicism has always been + + + align:start position:0% +Christianity Catholicism has always been +much friendlier to sexuality than + + align:start position:0% +much friendlier to sexuality than + + + align:start position:0% +much friendlier to sexuality than +Protestant protestantism until the 20th + + align:start position:0% +Protestant protestantism until the 20th + + + align:start position:0% +Protestant protestantism until the 20th +century I think uh in the last 100 years + + align:start position:0% +century I think uh in the last 100 years + + + align:start position:0% +century I think uh in the last 100 years +or maybe maybe that was part of the + + align:start position:0% +or maybe maybe that was part of the + + + align:start position:0% +or maybe maybe that was part of the +influence of 19th century + + align:start position:0% +influence of 19th century + + + align:start position:0% +influence of 19th century +Romanticism uh which we haven't got to + + align:start position:0% +Romanticism uh which we haven't got to + + + align:start position:0% +Romanticism uh which we haven't got to +yet um uh really I mean the + + align:start position:0% +yet um uh really I mean the + + + align:start position:0% +yet um uh really I mean the +analysis of um the origin of romantis 19 + + align:start position:0% +analysis of um the origin of romantis 19 + + + align:start position:0% +analysis of um the origin of romantis 19 +century Romanticism out of Christian + + align:start position:0% +century Romanticism out of Christian + + + align:start position:0% +century Romanticism out of Christian +religion I haven't touched on uh I don't + + align:start position:0% +religion I haven't touched on uh I don't + + + align:start position:0% +religion I haven't touched on uh I don't +think it I go into it much in this book + + align:start position:0% +think it I go into it much in this book + + + align:start position:0% +think it I go into it much in this book +that there are hundreds of pages on that + + align:start position:0% +that there are hundreds of pages on that + + + align:start position:0% +that there are hundreds of pages on that +in the second volume I'll spare you that + + align:start position:0% +in the second volume I'll spare you that + + + align:start position:0% +in the second volume I'll spare you that +today um we'll come back to it but uh in + + align:start position:0% +today um we'll come back to it but uh in + + + align:start position:0% +today um we'll come back to it but uh in +recent times there have been Protestant + + align:start position:0% +recent times there have been Protestant + + + align:start position:0% +recent times there have been Protestant +sects + + align:start position:0% +sects + + + align:start position:0% +sects +that say God is love and the U nature of + + align:start position:0% +that say God is love and the U nature of + + + align:start position:0% +that say God is love and the U nature of +our uh Christianity is to try to emulate + + align:start position:0% +our uh Christianity is to try to emulate + + + align:start position:0% +our uh Christianity is to try to emulate +God and to establish a loving communion + + align:start position:0% +God and to establish a loving communion + + + align:start position:0% +God and to establish a loving communion +uh with other people so there ideas of + + align:start position:0% +uh with other people so there ideas of + + + align:start position:0% +uh with other people so there ideas of +filia but + + align:start position:0% +filia but + + + align:start position:0% +filia but +um they don't say the way they did in + + align:start position:0% +um they don't say the way they did in + + + align:start position:0% +um they don't say the way they did in +the 17th century or or 16th century uh + + align:start position:0% +the 17th century or or 16th century uh + + + align:start position:0% +the 17th century or or 16th century uh +that uh sex + + align:start position:0% +that uh sex + + + align:start position:0% +that uh sex +itself is + + align:start position:0% +itself is + + + align:start position:0% +itself is +bad they say well maybe that's a way of + + align:start position:0% +bad they say well maybe that's a way of + + + align:start position:0% +bad they say well maybe that's a way of +loving other people and therefore + + align:start position:0% +loving other people and therefore + + + align:start position:0% +loving other people and therefore +emulating God whereas and in Catholicism + + align:start position:0% +emulating God whereas and in Catholicism + + + align:start position:0% +emulating God whereas and in Catholicism +which had ties to Pagan + + align:start position:0% +which had ties to Pagan + + + align:start position:0% +which had ties to Pagan +religion uh in many ways uh sex was not + + align:start position:0% +religion uh in many ways uh sex was not + + + align:start position:0% +religion uh in many ways uh sex was not +ruled out the gustiness the enjoyment of + + align:start position:0% +ruled out the gustiness the enjoyment of + + + align:start position:0% +ruled out the gustiness the enjoyment of +sex it had to be uh controlled by the + + align:start position:0% +sex it had to be uh controlled by the + + + align:start position:0% +sex it had to be uh controlled by the +church it had to occur in marriage it + + align:start position:0% +church it had to occur in marriage it + + + align:start position:0% +church it had to occur in marriage it +had to occur uh it had to be Sanctified + + align:start position:0% +had to occur uh it had to be Sanctified + + + align:start position:0% +had to occur uh it had to be Sanctified +uh but in itself it was simply um a way + + align:start position:0% +uh but in itself it was simply um a way + + + align:start position:0% +uh but in itself it was simply um a way +of propagating the race and what could + + align:start position:0% +of propagating the race and what could + + + align:start position:0% +of propagating the race and what could +be wrong with that in accordance with + + align:start position:0% +be wrong with that in accordance with + + + align:start position:0% +be wrong with that in accordance with +God's laws so you get this interesting + + align:start position:0% +God's laws so you get this interesting + + + align:start position:0% +God's laws so you get this interesting +reversal that um + + align:start position:0% +reversal that um + + + align:start position:0% +reversal that um +protestantism uh was reaction kind of + + align:start position:0% +protestantism uh was reaction kind of + + + align:start position:0% +protestantism uh was reaction kind of +often a puritanical reaction against + + align:start position:0% +often a puritanical reaction against + + + align:start position:0% +often a puritanical reaction against +that uh until recently when many pro + + align:start position:0% +that uh until recently when many pro + + + align:start position:0% +that uh until recently when many pro +Protestant beliefs sects are quite happy + + align:start position:0% +Protestant beliefs sects are quite happy + + + align:start position:0% +Protestant beliefs sects are quite happy +with the + + align:start position:0% +with the + + + align:start position:0% +with the +idea many pro sects I mean divisions + + align:start position:0% +idea many pro sects I mean divisions + + + align:start position:0% +idea many pro sects I mean divisions +within Protestant are happy with the + + align:start position:0% +within Protestant are happy with the + + + align:start position:0% +within Protestant are happy with the +idea of + + align:start position:0% +idea of + + + align:start position:0% +idea of +sex and in Pro and in Catholicism until + + align:start position:0% +sex and in Pro and in Catholicism until + + + align:start position:0% +sex and in Pro and in Catholicism until +re uh recently also uh often there was a + + align:start position:0% +re uh recently also uh often there was a + + + align:start position:0% +re uh recently also uh often there was a +kind of puritanism of a Catholic sort in + + align:start position:0% +kind of puritanism of a Catholic sort in + + + align:start position:0% +kind of puritanism of a Catholic sort in +Ireland for instance if I don't know any + + align:start position:0% +Ireland for instance if I don't know any + + + align:start position:0% +Ireland for instance if I don't know any +you know the work of the great novelist + + align:start position:0% +you know the work of the great novelist + + + align:start position:0% +you know the work of the great novelist +James Joyce he grew up in uh Catholic um + + align:start position:0% +James Joyce he grew up in uh Catholic um + + + align:start position:0% +James Joyce he grew up in uh Catholic um +uh Society in which sex was uh uh + + align:start position:0% +uh Society in which sex was uh uh + + + align:start position:0% +uh Society in which sex was uh uh +thought of the way the Puritans would + + align:start position:0% +thought of the way the Puritans would + + + align:start position:0% +thought of the way the Puritans would +have and he + + align:start position:0% +have and he + + + align:start position:0% +have and he +reacted and for that he was condemned + + align:start position:0% +reacted and for that he was condemned + + + align:start position:0% +reacted and for that he was condemned +and in fact his books were occasionally + + align:start position:0% +and in fact his books were occasionally + + + align:start position:0% +and in fact his books were occasionally +banned um maybe they I don't know if + + align:start position:0% +banned um maybe they I don't know if + + + align:start position:0% +banned um maybe they I don't know if +they still are in Ireland but for a long + + align:start position:0% +they still are in Ireland but for a long + + + align:start position:0% +they still are in Ireland but for a long +time they you couldn't read ulyses which + + align:start position:0% +time they you couldn't read ulyses which + + + align:start position:0% +time they you couldn't read ulyses which +has a lot of sex in it uh in Ireland uh + + align:start position:0% +has a lot of sex in it uh in Ireland uh + + + align:start position:0% +has a lot of sex in it uh in Ireland uh +and even could be U sold in the United + + align:start position:0% +and even could be U sold in the United + + + align:start position:0% +and even could be U sold in the United +States until uh about 12 years or so + + align:start position:0% +States until uh about 12 years or so + + + align:start position:0% +States until uh about 12 years or so +after was written it was banned it was + + align:start position:0% +after was written it was banned it was + + + align:start position:0% +after was written it was banned it was +seized by the uh by the immigration + + align:start position:0% +seized by the uh by the immigration + + + align:start position:0% +seized by the uh by the immigration +people and + + align:start position:0% + + + + align:start position:0% + +destroyed + + align:start position:0% + + + + align:start position:0% + +goad did you want to say something yeah + + align:start position:0% +goad did you want to say something yeah + + + align:start position:0% +goad did you want to say something yeah +I've thought about this a lot in terms + + align:start position:0% +I've thought about this a lot in terms + + + align:start position:0% +I've thought about this a lot in terms +of Plato and um there's kind of two key + + align:start position:0% +of Plato and um there's kind of two key + + + align:start position:0% +of Plato and um there's kind of two key +dialogues if you want to it's it's the + + align:start position:0% +dialogues if you want to it's it's the + + + align:start position:0% +dialogues if you want to it's it's the +Symposium in the Fus and uh the Fus is + + align:start position:0% +Symposium in the Fus and uh the Fus is + + + align:start position:0% +Symposium in the Fus and uh the Fus is +very strange because + + align:start position:0% +very strange because + + + align:start position:0% +very strange because +U um in in describing love he makes he + + align:start position:0% +U um in in describing love he makes he + + + align:start position:0% +U um in in describing love he makes he +makes this metaphor or he makes this + + align:start position:0% +makes this metaphor or he makes this + + + align:start position:0% +makes this metaphor or he makes this +metaphor of the soul that the soul is + + align:start position:0% +metaphor of the soul that the soul is + + + align:start position:0% +metaphor of the soul that the soul is +like a charioteer with two horses and + + align:start position:0% +like a charioteer with two horses and + + + align:start position:0% +like a charioteer with two horses and +that you mind if I get into this no if + + align:start position:0% +that you mind if I get into this no if + + + align:start position:0% +that you mind if I get into this no if +adri + + align:start position:0% +adri + + + align:start position:0% +adri +doesn't so one of the horses is uh Noble + + align:start position:0% +doesn't so one of the horses is uh Noble + + + align:start position:0% +doesn't so one of the horses is uh Noble +and well bred and well-mannered follows + + align:start position:0% +and well bred and well-mannered follows + + + align:start position:0% +and well bred and well-mannered follows +the lead of The Chariot here and the + + align:start position:0% +the lead of The Chariot here and the + + + align:start position:0% +the lead of The Chariot here and the +other one is unruly and wild and has its + + align:start position:0% +other one is unruly and wild and has its + + + align:start position:0% +other one is unruly and wild and has its +own kind of very chaotic nature and The + + align:start position:0% +own kind of very chaotic nature and The + + + align:start position:0% +own kind of very chaotic nature and The +Chariot here is supposed to be reason + + align:start position:0% +Chariot here is supposed to be reason + + + align:start position:0% +Chariot here is supposed to be reason +and I think the noble seed supposed to + + align:start position:0% +and I think the noble seed supposed to + + + align:start position:0% +and I think the noble seed supposed to +be something like the spirited element + + align:start position:0% +be something like the spirited element + + + align:start position:0% +be something like the spirited element +of the soul and the uh the wild SE is + + align:start position:0% +of the soul and the uh the wild SE is + + + align:start position:0% +of the soul and the uh the wild SE is +supposed to be um I don't know what it's + + align:start position:0% +supposed to be um I don't know what it's + + + align:start position:0% +supposed to be um I don't know what it's +called kind of Bas this oh no the white + + align:start position:0% +called kind of Bas this oh no the white + + + align:start position:0% +called kind of Bas this oh no the white +was spiritual and the black horse was + + align:start position:0% +was spiritual and the black horse was + + + align:start position:0% +was spiritual and the black horse was +Bas yeah some kind of and Chariot here + + align:start position:0% +Bas yeah some kind of and Chariot here + + + align:start position:0% +Bas yeah some kind of and Chariot here +would be reason trying to keep them in + + align:start position:0% +would be reason trying to keep them in + + + align:start position:0% +would be reason trying to keep them in +control yeah and so in in this in this + + align:start position:0% +control yeah and so in in this in this + + + align:start position:0% +control yeah and so in in this in this +metaphor when when when you come upon + + align:start position:0% +metaphor when when when you come upon + + + align:start position:0% +metaphor when when when you come upon +somebody that uh so first of all the + + align:start position:0% +somebody that uh so first of all the + + + align:start position:0% +somebody that uh so first of all the +idea of this soul is that this Chariot + + align:start position:0% +idea of this soul is that this Chariot + + + align:start position:0% +idea of this soul is that this Chariot +was wandering around in heaven around uh + + align:start position:0% +was wandering around in heaven around uh + + + align:start position:0% +was wandering around in heaven around uh +true beauty and truth and God and uh + + align:start position:0% +true beauty and truth and God and uh + + + align:start position:0% +true beauty and truth and God and uh +then it fell down into a body and so now + + align:start position:0% +then it fell down into a body and so now + + + align:start position:0% +then it fell down into a body and so now +when you uh see somebody who uh who has + + align:start position:0% +when you uh see somebody who uh who has + + + align:start position:0% +when you uh see somebody who uh who has +some of the a reflection of that truth + + align:start position:0% +some of the a reflection of that truth + + + align:start position:0% +some of the a reflection of that truth +that you saw there uh you're in awe and + + align:start position:0% +that you saw there uh you're in awe and + + + align:start position:0% +that you saw there uh you're in awe and +you try to uh spend time with them and + + align:start position:0% +you try to uh spend time with them and + + + align:start position:0% +you try to uh spend time with them and +to remember remember this beautiful + + align:start position:0% +to remember remember this beautiful + + + align:start position:0% +to remember remember this beautiful +world that you fell from but uh the + + align:start position:0% +world that you fell from but uh the + + + align:start position:0% +world that you fell from but uh the +point about sex is that this this wild + + align:start position:0% +point about sex is that this this wild + + + align:start position:0% +point about sex is that this this wild +Ste when you come to a person Plato + + align:start position:0% +Ste when you come to a person Plato + + + align:start position:0% +Ste when you come to a person Plato +thinks this wild Ste says you know + + align:start position:0% +thinks this wild Ste says you know + + + align:start position:0% +thinks this wild Ste says you know +forget about what's beautiful and true + + align:start position:0% +forget about what's beautiful and true + + + align:start position:0% +forget about what's beautiful and true +about them grab them jump onto them and + + align:start position:0% +about them grab them jump onto them and + + + align:start position:0% +about them grab them jump onto them and +this he thinks is the very base and and + + align:start position:0% +this he thinks is the very base and and + + + align:start position:0% +this he thinks is the very base and and +vulgar part of man so you should try to + + align:start position:0% +vulgar part of man so you should try to + + + align:start position:0% +vulgar part of man so you should try to +control this Ste and beat him keep him + + align:start position:0% +control this Ste and beat him keep him + + + align:start position:0% +control this Ste and beat him keep him +in + + align:start position:0% +in + + + align:start position:0% +in +check something like this okay more I + + align:start position:0% +check something like this okay more I + + + align:start position:0% +check something like this okay more I +anything about + + align:start position:0% +anything about + + + align:start position:0% +anything about +this so why to + + align:start position:0% + + + + align:start position:0% + +continue + + align:start position:0% +continue + + + align:start position:0% +continue +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um you define sexual love in terms of + + align:start position:0% +um you define sexual love in terms of + + + align:start position:0% +um you define sexual love in terms of +three concepts the libidinal the erotic + + align:start position:0% +three concepts the libidinal the erotic + + + align:start position:0% +three concepts the libidinal the erotic +and the + + align:start position:0% +and the + + + align:start position:0% +and the +Romantic uh the libidinal is the animal + + align:start position:0% +Romantic uh the libidinal is the animal + + + align:start position:0% +Romantic uh the libidinal is the animal +part the erotic is more of the + + align:start position:0% +part the erotic is more of the + + + align:start position:0% +part the erotic is more of the +imagination part and here I want to stop + + align:start position:0% +imagination part and here I want to stop + + + align:start position:0% +imagination part and here I want to stop +because + + align:start position:0% +because + + + align:start position:0% +because +at some point you say that with the + + align:start position:0% +at some point you say that with the + + + align:start position:0% +at some point you say that with the +erotic we can enjoy the presence of + + align:start position:0% +erotic we can enjoy the presence of + + + align:start position:0% +erotic we can enjoy the presence of +someone for whom we don't have Lial + + align:start position:0% +someone for whom we don't have Lial + + + align:start position:0% +someone for whom we don't have Lial +desire so I wanted to ask you if this + + align:start position:0% +desire so I wanted to ask you if this + + + align:start position:0% +desire so I wanted to ask you if this +means that erotism has two aspects the + + align:start position:0% +means that erotism has two aspects the + + + align:start position:0% +means that erotism has two aspects the +aspect of um when when the Beloved is + + align:start position:0% +aspect of um when when the Beloved is + + + align:start position:0% +aspect of um when when the Beloved is +not involved and you + + align:start position:0% +not involved and you + + + align:start position:0% +not involved and you +can um you can see someone + + align:start position:0% +can um you can see someone + + + align:start position:0% +can um you can see someone +who for whom you have no Lial desire and + + align:start position:0% +who for whom you have no Lial desire and + + + align:start position:0% +who for whom you have no Lial desire and +then the other aspect is when the erotic + + align:start position:0% +then the other aspect is when the erotic + + + align:start position:0% +then the other aspect is when the erotic +comes together with the theal and the + + align:start position:0% +comes together with the theal and the + + + align:start position:0% +comes together with the theal and the +Romantic to give rise to the meaning of + + align:start position:0% +Romantic to give rise to the meaning of + + + align:start position:0% +Romantic to give rise to the meaning of +life as you say and this only happens in + + align:start position:0% +life as you say and this only happens in + + + align:start position:0% +life as you say and this only happens in +the Beloved so right um the + + align:start position:0% +the Beloved so right um the + + + align:start position:0% +the Beloved so right um the +um the analysis you're referring to is + + align:start position:0% +um the analysis you're referring to is + + + align:start position:0% +um the analysis you're referring to is +between the libidinal the erotic and the + + align:start position:0% +between the libidinal the erotic and the + + + align:start position:0% +between the libidinal the erotic and the +Romantic you didn't say get to the + + align:start position:0% +Romantic you didn't say get to the + + + align:start position:0% +Romantic you didn't say get to the +Romantic yet + + align:start position:0% + + + + align:start position:0% + +um like all of my + + align:start position:0% +um like all of my + + + align:start position:0% +um like all of my +analyses these are conceptual + + align:start position:0% +analyses these are conceptual + + + align:start position:0% +analyses these are conceptual +tools and in terms of me as a thinker I + + align:start position:0% +tools and in terms of me as a thinker I + + + align:start position:0% +tools and in terms of me as a thinker I +I think of myself as a Craftsman or + + align:start position:0% +I think of myself as a Craftsman or + + + align:start position:0% +I think of myself as a Craftsman or +Carpenter uh in a shop and uh suddenly + + align:start position:0% +Carpenter uh in a shop and uh suddenly + + + align:start position:0% +Carpenter uh in a shop and uh suddenly +he + + align:start position:0% +he + + + align:start position:0% +he +needs something done and he grabs for a + + align:start position:0% +needs something done and he grabs for a + + + align:start position:0% +needs something done and he grabs for a +tool that'll do it uh um I don't lay any + + align:start position:0% +tool that'll do it uh um I don't lay any + + + align:start position:0% +tool that'll do it uh um I don't lay any +importance on the uh Concepts themselves + + align:start position:0% +importance on the uh Concepts themselves + + + align:start position:0% +importance on the uh Concepts themselves +they're just tools to help clarify some + + align:start position:0% +they're just tools to help clarify some + + + align:start position:0% +they're just tools to help clarify some +job that I want uh and that I think is + + align:start position:0% +job that I want uh and that I think is + + + align:start position:0% +job that I want uh and that I think is +relevant to what you were saying about + + align:start position:0% +relevant to what you were saying about + + + align:start position:0% +relevant to what you were saying about +there being two kinds one in which AOS + + align:start position:0% +there being two kinds one in which AOS + + + align:start position:0% +there being two kinds one in which AOS +is combined with the libidinal and the + + align:start position:0% +is combined with the libidinal and the + + + align:start position:0% +is combined with the libidinal and the +other in which it's purified and + + align:start position:0% +other in which it's purified and + + + align:start position:0% +other in which it's purified and +separated from the + + align:start position:0% +separated from the + + + align:start position:0% +separated from the +libidinal um in a sense one might say + + align:start position:0% +libidinal um in a sense one might say + + + align:start position:0% +libidinal um in a sense one might say +that um all three of them + + align:start position:0% +that um all three of them + + + align:start position:0% +that um all three of them +happen or can happen + + align:start position:0% +happen or can happen + + + align:start position:0% +happen or can happen +simultaneously you could have a + + align:start position:0% +simultaneously you could have a + + + align:start position:0% +simultaneously you could have a +relationship which + + align:start position:0% +relationship which + + + align:start position:0% +relationship which +is lital erotic and romantic and also + + align:start position:0% +is lital erotic and romantic and also + + + align:start position:0% +is lital erotic and romantic and also +spiritual so that one having made the + + align:start position:0% +spiritual so that one having made the + + + align:start position:0% +spiritual so that one having made the +artificial distinction I don't want to + + align:start position:0% +artificial distinction I don't want to + + + align:start position:0% +artificial distinction I don't want to +be a slave to it just that that will + + align:start position:0% +be a slave to it just that that will + + + align:start position:0% +be a slave to it just that that will +give me a certain Insight which I can + + align:start position:0% +give me a certain Insight which I can + + + align:start position:0% +give me a certain Insight which I can +then walk around in order to show the + + align:start position:0% +then walk around in order to show the + + + align:start position:0% +then walk around in order to show the +complexity of human nature + + align:start position:0% +complexity of human nature + + + align:start position:0% +complexity of human nature +um the uh also I'm not sure that they + + align:start position:0% +um the uh also I'm not sure that they + + + align:start position:0% +um the uh also I'm not sure that they +ever occur in any kind of + + align:start position:0% + + + + align:start position:0% + +Purity is there such a thing as a leidal + + align:start position:0% +Purity is there such a thing as a leidal + + + align:start position:0% +Purity is there such a thing as a leidal +interest devoid of other things like the + + align:start position:0% +interest devoid of other things like the + + + align:start position:0% +interest devoid of other things like the +erotic for instance see the point about + + align:start position:0% +erotic for instance see the point about + + + align:start position:0% +erotic for instance see the point about +Freud is that Freud came from a + + align:start position:0% +Freud is that Freud came from a + + + align:start position:0% +Freud is that Freud came from a +scientific + + align:start position:0% +scientific + + + align:start position:0% +scientific +tradition uh which you will all + + align:start position:0% +tradition uh which you will all + + + align:start position:0% +tradition uh which you will all +recognize uh that's called reductivism + + align:start position:0% +recognize uh that's called reductivism + + + align:start position:0% +recognize uh that's called reductivism +that is if you can well um Arthur you're + + align:start position:0% +that is if you can well um Arthur you're + + + align:start position:0% +that is if you can well um Arthur you're +nodding maybe you should explain it well + + align:start position:0% +nodding maybe you should explain it well + + + align:start position:0% +nodding maybe you should explain it well +something we were just talking about to + + align:start position:0% +something we were just talking about to + + + align:start position:0% +something we were just talking about to +talk so everything is is you take just + + align:start position:0% +talk so everything is is you take just + + + align:start position:0% +talk so everything is is you take just +an idea and break it down to a + + align:start position:0% +an idea and break it down to a + + + align:start position:0% +an idea and break it down to a +single set of unanalyzable Rock Bottom + + align:start position:0% +single set of unanalyzable Rock Bottom + + + align:start position:0% +single set of unanalyzable Rock Bottom +bases exactly then you can find out all + + align:start position:0% +bases exactly then you can find out all + + + align:start position:0% +bases exactly then you can find out all +there is to know about it or at least + + align:start position:0% +there is to know about it or at least + + + align:start position:0% +there is to know about it or at least +everything about it can be derived from + + align:start position:0% +everything about it can be derived from + + + align:start position:0% +everything about it can be derived from +those from that set of principles right + + align:start position:0% +those from that set of principles right + + + align:start position:0% +those from that set of principles right +now that's um a an attitude that has um + + align:start position:0% +now that's um a an attitude that has um + + + align:start position:0% +now that's um a an attitude that has um +intrigued me all my life and I finally + + align:start position:0% +intrigued me all my life and I finally + + + align:start position:0% +intrigued me all my life and I finally +came to grips with it in a book of M + + align:start position:0% +came to grips with it in a book of M + + + align:start position:0% +came to grips with it in a book of M +feeling and + + align:start position:0% +feeling and + + + align:start position:0% +feeling and +Imagination where I try to express my + + align:start position:0% +Imagination where I try to express my + + + align:start position:0% +Imagination where I try to express my +doubts about their + + align:start position:0% +doubts about their + + + align:start position:0% +doubts about their +being make if it making any sense what + + align:start position:0% +being make if it making any sense what + + + align:start position:0% +being make if it making any sense what +would it be like to get to the Rock + + align:start position:0% +would it be like to get to the Rock + + + align:start position:0% +would it be like to get to the Rock +Bottom about anything maybe there is no + + align:start position:0% +Bottom about anything maybe there is no + + + align:start position:0% +Bottom about anything maybe there is no +Rock Bottom you know who said that the + + align:start position:0% +Rock Bottom you know who said that the + + + align:start position:0% +Rock Bottom you know who said that the +world uh + + align:start position:0% +world uh + + + align:start position:0% +world uh +uh can be understood can be reduced to + + align:start position:0% +uh can be understood can be reduced to + + + align:start position:0% +uh can be understood can be reduced to +any principle that will enable us to + + align:start position:0% +any principle that will enable us to + + + align:start position:0% +any principle that will enable us to +know everything or know anything in fact + + align:start position:0% +know everything or know anything in fact + + + align:start position:0% +know everything or know anything in fact +um the search for the meaning of + + align:start position:0% +um the search for the meaning of + + + align:start position:0% +um the search for the meaning of +everything right uh and String Theory + + align:start position:0% +everything right uh and String Theory + + + align:start position:0% +everything right uh and String Theory +comes into this because maybe just as a + + align:start position:0% +comes into this because maybe just as a + + + align:start position:0% +comes into this because maybe just as a +matter of advertising but maybe it's + + align:start position:0% +matter of advertising but maybe it's + + + align:start position:0% +matter of advertising but maybe it's +fundamental in their concept there there + + align:start position:0% +fundamental in their concept there there + + + align:start position:0% +fundamental in their concept there there +it's they describe themselves is the + + align:start position:0% +it's they describe themselves is the + + + align:start position:0% +it's they describe themselves is the +theory of everything that they they want + + align:start position:0% +theory of everything that they they want + + + align:start position:0% +theory of everything that they they want +to find a rock bottom solution to the + + align:start position:0% +to find a rock bottom solution to the + + + align:start position:0% +to find a rock bottom solution to the +nature of the physical universe but + + align:start position:0% +nature of the physical universe but + + + align:start position:0% +nature of the physical universe but +maybe there isn't any Rock Bottom maybe + + align:start position:0% +maybe there isn't any Rock Bottom maybe + + + align:start position:0% +maybe there isn't any Rock Bottom maybe +we don't even know what we're looking + + align:start position:0% +we don't even know what we're looking + + + align:start position:0% +we don't even know what we're looking +for maybe uh we'll never be able to find + + align:start position:0% +for maybe uh we'll never be able to find + + + align:start position:0% +for maybe uh we'll never be able to find +it doesn't mean that we couldn't pick up + + align:start position:0% +it doesn't mean that we couldn't pick up + + + align:start position:0% +it doesn't mean that we couldn't pick up +some interesting facts and theories on + + align:start position:0% +some interesting facts and theories on + + + align:start position:0% +some interesting facts and theories on +the way and that's for scientists to + + align:start position:0% +the way and that's for scientists to + + + align:start position:0% +the way and that's for scientists to +determine um but often scientists are + + align:start position:0% +determine um but often scientists are + + + align:start position:0% +determine um but often scientists are +fooled by their own + + align:start position:0% +fooled by their own + + + align:start position:0% +fooled by their own +propaganda uh that is fundraising which + + align:start position:0% +propaganda uh that is fundraising which + + + align:start position:0% +propaganda uh that is fundraising which +is to say we're we've reached a very + + align:start position:0% +is to say we're we've reached a very + + + align:start position:0% +is to say we're we've reached a very +interesting uh conclusion here and if we + + align:start position:0% +interesting uh conclusion here and if we + + + align:start position:0% +interesting uh conclusion here and if we +only are given enough funds and allowed + + align:start position:0% +only are given enough funds and allowed + + + align:start position:0% +only are given enough funds and allowed +to continue maybe 10,000 50,000 years + + align:start position:0% +to continue maybe 10,000 50,000 years + + + align:start position:0% +to continue maybe 10,000 50,000 years +we'll get to the Bottom of Everything + + align:start position:0% +we'll get to the Bottom of Everything + + + align:start position:0% +we'll get to the Bottom of Everything +we'll find out what everything is like + + align:start position:0% +we'll find out what everything is like + + + align:start position:0% +we'll find out what everything is like +you know it's accelarating and some + + align:start position:0% +you know it's accelarating and some + + + align:start position:0% +you know it's accelarating and some +people will pay for that + + align:start position:0% +people will pay for that + + + align:start position:0% +people will pay for that +acceleration um but otherwise maybe + + align:start position:0% +acceleration um but otherwise maybe + + + align:start position:0% +acceleration um but otherwise maybe +simply a big mistake in scientific + + align:start position:0% +simply a big mistake in scientific + + + align:start position:0% +simply a big mistake in scientific +theory to assume that there is a rock + + align:start position:0% +theory to assume that there is a rock + + + align:start position:0% +theory to assume that there is a rock +bottom um Freud did that in 19th century + + align:start position:0% +bottom um Freud did that in 19th century + + + align:start position:0% +bottom um Freud did that in 19th century +people were very optimistic about the + + align:start position:0% +people were very optimistic about the + + + align:start position:0% +people were very optimistic about the +hard Sciences physics and chemistry in + + align:start position:0% +hard Sciences physics and chemistry in + + + align:start position:0% +hard Sciences physics and chemistry in +particular and his idea was to create a + + align:start position:0% +particular and his idea was to create a + + + align:start position:0% +particular and his idea was to create a +psychology on the model of that to make + + align:start position:0% +psychology on the model of that to make + + + align:start position:0% +psychology on the model of that to make +psychology into a hard science and to + + align:start position:0% +psychology into a hard science and to + + + align:start position:0% +psychology into a hard science and to +reduce all of the psychological + + align:start position:0% +reduce all of the psychological + + + align:start position:0% +reduce all of the psychological +appearances to some rock bottom + + align:start position:0% +appearances to some rock bottom + + + align:start position:0% +appearances to some rock bottom +ideas and one idea I don't want to go + + align:start position:0% +ideas and one idea I don't want to go + + + align:start position:0% +ideas and one idea I don't want to go +through the whole Freudian structure if + + align:start position:0% +through the whole Freudian structure if + + + align:start position:0% +through the whole Freudian structure if +you're interested I I keep I apologize + + align:start position:0% +you're interested I I keep I apologize + + + align:start position:0% +you're interested I I keep I apologize +but it's all I know I'm I'm so limited + + align:start position:0% +but it's all I know I'm I'm so limited + + + align:start position:0% +but it's all I know I'm I'm so limited +uh look at the third volum of the + + align:start position:0% +uh look at the third volum of the + + + align:start position:0% +uh look at the third volum of the +trilogy uh where I have a 70 page + + align:start position:0% +trilogy uh where I have a 70 page + + + align:start position:0% +trilogy uh where I have a 70 page +chapter on Freud as a + + align:start position:0% +chapter on Freud as a + + + align:start position:0% +chapter on Freud as a +philosopher uh and a philosopher of Love + + align:start position:0% +philosopher uh and a philosopher of Love + + + align:start position:0% +philosopher uh and a philosopher of Love +uh the one of the element El one of + + align:start position:0% +uh the one of the element El one of + + + align:start position:0% +uh the one of the element El one of +quite a number of these elements uh is + + align:start position:0% +quite a number of these elements uh is + + + align:start position:0% +quite a number of these elements uh is +the idea of + + align:start position:0% +the idea of + + + align:start position:0% +the idea of +libido uh and that's where why I use the + + align:start position:0% +libido uh and that's where why I use the + + + align:start position:0% +libido uh and that's where why I use the +word the + + align:start position:0% +word the + + + align:start position:0% +word the +libidol to separate myself from Freud + + align:start position:0% +libidol to separate myself from Freud + + + align:start position:0% +libidol to separate myself from Freud +while also talking about things similar + + align:start position:0% +while also talking about things similar + + + align:start position:0% +while also talking about things similar +to what he does when he talks about the + + align:start position:0% +to what he does when he talks about the + + + align:start position:0% +to what he does when he talks about the +libido his idea is that the the liido is + + align:start position:0% +libido his idea is that the the liido is + + + align:start position:0% +libido his idea is that the the liido is +a field of force which he gets from + + align:start position:0% +a field of force which he gets from + + + align:start position:0% +a field of force which he gets from +schopenhauer uh and as he admits and + + align:start position:0% +schopenhauer uh and as he admits and + + + align:start position:0% +schopenhauer uh and as he admits and +um it um is just sheer + + align:start position:0% +um it um is just sheer + + + align:start position:0% +um it um is just sheer +energy it explains the nature of + + align:start position:0% +energy it explains the nature of + + + align:start position:0% +energy it explains the nature of +passion why because people are uh laidly + + align:start position:0% +passion why because people are uh laidly + + + align:start position:0% +passion why because people are uh laidly +attracted to each other um it's mindless + + align:start position:0% +attracted to each other um it's mindless + + + align:start position:0% +attracted to each other um it's mindless +uh it's not civilized on the contrary it + + align:start position:0% +uh it's not civilized on the contrary it + + + align:start position:0% +uh it's not civilized on the contrary it +can be very dangerous to civilization + + align:start position:0% +can be very dangerous to civilization + + + align:start position:0% +can be very dangerous to civilization +when uh for reasons of leidal love + + align:start position:0% +when uh for reasons of leidal love + + + align:start position:0% +when uh for reasons of leidal love +people do foolish things and endanger + + align:start position:0% +people do foolish things and endanger + + + align:start position:0% +people do foolish things and endanger +the + + align:start position:0% +the + + + align:start position:0% +the +species who knows you know all sorts of + + align:start position:0% +species who knows you know all sorts of + + + align:start position:0% +species who knows you know all sorts of +examples uh but without it one wouldn't + + align:start position:0% +examples uh but without it one wouldn't + + + align:start position:0% +examples uh but without it one wouldn't +be able to explain human feelings affect + + align:start position:0% +be able to explain human feelings affect + + + align:start position:0% +be able to explain human feelings affect +uh or the way in which human beings are + + align:start position:0% +uh or the way in which human beings are + + + align:start position:0% +uh or the way in which human beings are +capable of + + align:start position:0% +capable of + + + align:start position:0% +capable of +loving now the reason I mentioned this + + align:start position:0% +loving now the reason I mentioned this + + + align:start position:0% +loving now the reason I mentioned this +is because uh I want to make sure that + + align:start position:0% +is because uh I want to make sure that + + + align:start position:0% +is because uh I want to make sure that +Adriana was right in her presentation of + + align:start position:0% +Adriana was right in her presentation of + + + align:start position:0% +Adriana was right in her presentation of +my analysis it isn't as if there is a + + align:start position:0% +my analysis it isn't as if there is a + + + align:start position:0% +my analysis it isn't as if there is a +separate thing which + + align:start position:0% +separate thing which + + + align:start position:0% +separate thing which +is the the leidal that would would be + + align:start position:0% +is the the leidal that would would be + + + align:start position:0% +is the the leidal that would would be +like saying that there is a rock bottom + + align:start position:0% +like saying that there is a rock bottom + + + align:start position:0% +like saying that there is a rock bottom +uh energy which + + align:start position:0% +uh energy which + + + align:start position:0% +uh energy which +is uh um uh liido is Freud reduces love + + align:start position:0% +is uh um uh liido is Freud reduces love + + + align:start position:0% +is uh um uh liido is Freud reduces love +to right um it's a useful concept it's a + + align:start position:0% +to right um it's a useful concept it's a + + + align:start position:0% +to right um it's a useful concept it's a +tool it enables me to set up the + + align:start position:0% +tool it enables me to set up the + + + align:start position:0% +tool it enables me to set up the +contrast enables me to make the + + align:start position:0% +contrast enables me to make the + + + align:start position:0% +contrast enables me to make the +analysis because in the process + + align:start position:0% +analysis because in the process + + + align:start position:0% +analysis because in the process +I think I can illuminate different + + align:start position:0% +I think I can illuminate different + + + align:start position:0% +I think I can illuminate different +aspects of human + + align:start position:0% +aspects of human + + + align:start position:0% +aspects of human +nature leidal the erotic and then later + + align:start position:0% +nature leidal the erotic and then later + + + align:start position:0% +nature leidal the erotic and then later +we'll get through the Romantic but if + + align:start position:0% +we'll get through the Romantic but if + + + align:start position:0% +we'll get through the Romantic but if +somebody said well why can't they all + + align:start position:0% +somebody said well why can't they all + + + align:start position:0% +somebody said well why can't they all +interact I'll would say that's fine + + align:start position:0% +interact I'll would say that's fine + + + align:start position:0% +interact I'll would say that's fine +let's try that out um and I make a few I + + align:start position:0% +let's try that out um and I make a few I + + + align:start position:0% +let's try that out um and I make a few I +have a couple of paragraphs on that I I + + align:start position:0% +have a couple of paragraphs on that I I + + + align:start position:0% +have a couple of paragraphs on that I I +don't know how far I can go well maybe + + align:start position:0% +don't know how far I can go well maybe + + + align:start position:0% +don't know how far I can go well maybe +in a sense I've skirting been skirting + + align:start position:0% +in a sense I've skirting been skirting + + + align:start position:0% +in a sense I've skirting been skirting +around that in many places uh or if + + align:start position:0% +around that in many places uh or if + + + align:start position:0% +around that in many places uh or if +someone says well you know these are so + + align:start position:0% +someone says well you know these are so + + + align:start position:0% +someone says well you know these are so +antagonistic um they're going to + + align:start position:0% +antagonistic um they're going to + + + align:start position:0% +antagonistic um they're going to +interfere with each other and certainly + + align:start position:0% +interfere with each other and certainly + + + align:start position:0% +interfere with each other and certainly +can find exam extreme examples um a man + + align:start position:0% +can find exam extreme examples um a man + + + align:start position:0% +can find exam extreme examples um a man +who for reasons of his own libidinal + + align:start position:0% +who for reasons of his own libidinal + + + align:start position:0% +who for reasons of his own libidinal +impulse rapes a + + align:start position:0% +impulse rapes a + + + align:start position:0% +impulse rapes a +woman can't just say well you know it's + + align:start position:0% +woman can't just say well you know it's + + + align:start position:0% +woman can't just say well you know it's +a part of love we all believe in love + + align:start position:0% +a part of love we all believe in love + + + align:start position:0% +a part of love we all believe in love +and this is my contribution to the + + align:start position:0% +and this is my contribution to the + + + align:start position:0% +and this is my contribution to the +cause uh in mozarts oper + + align:start position:0% +cause uh in mozarts oper + + + align:start position:0% +cause uh in mozarts oper +Donovan know you know about that at + + align:start position:0% +Donovan know you know about that at + + + align:start position:0% +Donovan know you know about that at +least right the greatest Opera many + + align:start position:0% +least right the greatest Opera many + + + align:start position:0% +least right the greatest Opera many +people say that was ever written he his + + align:start position:0% +people say that was ever written he his + + + align:start position:0% +people say that was ever written he his +servant + + align:start position:0% +servant + + + align:start position:0% +servant +lapello takes um Donavan aside at one + + align:start position:0% +lapello takes um Donavan aside at one + + + align:start position:0% +lapello takes um Donavan aside at one +point the beginning of the second act + + align:start position:0% +point the beginning of the second act + + + align:start position:0% +point the beginning of the second act +and says to him look what are you doing + + align:start position:0% +and says to him look what are you doing + + + align:start position:0% +and says to him look what are you doing +don't you realize you seduce all of + + align:start position:0% +don't you realize you seduce all of + + + align:start position:0% +don't you realize you seduce all of +these women and then you abandon them + + align:start position:0% +these women and then you abandon them + + + align:start position:0% +these women and then you abandon them +and some of them are in misery you know + + align:start position:0% +and some of them are in misery you know + + + align:start position:0% +and some of them are in misery you know +they're not all flirts they really treat + + align:start position:0% +they're not all flirts they really treat + + + align:start position:0% +they're not all flirts they really treat +love seriously and they fall in love + + align:start position:0% +love seriously and they fall in love + + + align:start position:0% +love seriously and they fall in love +with you and you just ditch them you do + + align:start position:0% +with you and you just ditch them you do + + + align:start position:0% +with you and you just ditch them you do +a great deal of + + align:start position:0% +a great deal of + + + align:start position:0% +a great deal of +harm + + align:start position:0% +harm + + + align:start position:0% +harm +right to which Donavan + + align:start position:0% +right to which Donavan + + + align:start position:0% +right to which Donavan +replies in Italian I'll translate it but + + align:start position:0% +replies in Italian I'll translate it but + + + align:start position:0% +replies in Italian I'll translate it but +you can figure it out he + + align:start position:0% + + + + align:start position:0% + +says you got the idea but it's all love + + align:start position:0% +says you got the idea but it's all love + + + align:start position:0% +says you got the idea but it's all love +right well the point is that uh love can + + align:start position:0% +right well the point is that uh love can + + + align:start position:0% +right well the point is that uh love can +do a great deal of harm and if you + + align:start position:0% +do a great deal of harm and if you + + + align:start position:0% +do a great deal of harm and if you +refuse to say it's just love you then + + align:start position:0% +refuse to say it's just love you then + + + align:start position:0% +refuse to say it's just love you then +are in the position to say that the LI + + align:start position:0% +are in the position to say that the LI + + + align:start position:0% +are in the position to say that the LI +libidinal at its worst can do a great + + align:start position:0% +libidinal at its worst can do a great + + + align:start position:0% +libidinal at its worst can do a great +deal of harm and can be evil and just + + align:start position:0% +deal of harm and can be evil and just + + + align:start position:0% +deal of harm and can be evil and just +because you have a libidinal interests + + align:start position:0% +because you have a libidinal interests + + + align:start position:0% +because you have a libidinal interests +uh which in Men in particular involves + + align:start position:0% +uh which in Men in particular involves + + + align:start position:0% +uh which in Men in particular involves +physical aggressiveness because both are + + align:start position:0% +physical aggressiveness because both are + + + align:start position:0% +physical aggressiveness because both are +based on St around uh and then you feel + + align:start position:0% +based on St around uh and then you feel + + + align:start position:0% +based on St around uh and then you feel +well you know I'm just uh doing what I + + align:start position:0% +well you know I'm just uh doing what I + + + align:start position:0% +well you know I'm just uh doing what I +was made to + + align:start position:0% +was made to + + + align:start position:0% +was made to +do that no justification that that's + + align:start position:0% +do that no justification that that's + + + align:start position:0% +do that no justification that that's +wrong that's + + align:start position:0% +wrong that's + + + align:start position:0% +wrong that's +evil the greatest evil in rape is not in + + align:start position:0% +evil the greatest evil in rape is not in + + + align:start position:0% +evil the greatest evil in rape is not in +um entering the body of a non willing + + align:start position:0% +um entering the body of a non willing + + + align:start position:0% +um entering the body of a non willing +woman uh it's + + align:start position:0% +woman uh it's + + + align:start position:0% +woman uh it's +violating + + align:start position:0% +violating + + + align:start position:0% +violating +her will it's it's violating her being + + align:start position:0% +her will it's it's violating her being + + + align:start position:0% +her will it's it's violating her being +by not doing what she wants you to do + + align:start position:0% +by not doing what she wants you to do + + + align:start position:0% +by not doing what she wants you to do +even if you con even if you convince + + align:start position:0% +even if you con even if you convince + + + align:start position:0% +even if you con even if you convince +yourself that's what she really wants + + align:start position:0% +yourself that's what she really wants + + + align:start position:0% +yourself that's what she really wants +that always comes up in rape cases where + + align:start position:0% +that always comes up in rape cases where + + + align:start position:0% +that always comes up in rape cases where +the uh defense of the U of the Raper + + align:start position:0% +the uh defense of the U of the Raper + + + align:start position:0% +the uh defense of the U of the Raper +tries to convince the court that the + + align:start position:0% +tries to convince the court that the + + + align:start position:0% +tries to convince the court that the +woman really wanted it that's a male + + align:start position:0% +woman really wanted it that's a male + + + align:start position:0% +woman really wanted it that's a male +myth both women + + align:start position:0% +myth both women + + + align:start position:0% +myth both women +probably great majority who are raped + + align:start position:0% +probably great majority who are raped + + + align:start position:0% +probably great majority who are raped +don't want it and the crime which + + align:start position:0% +don't want it and the crime which + + + align:start position:0% +don't want it and the crime which +doesn't enter into the Law Courts + + align:start position:0% +doesn't enter into the Law Courts + + + align:start position:0% +doesn't enter into the Law Courts +because it's such a an abstract + + align:start position:0% +because it's such a an abstract + + + align:start position:0% +because it's such a an abstract +philosophical crime uh is violating her + + align:start position:0% +philosophical crime uh is violating her + + + align:start position:0% +philosophical crime uh is violating her +will violating her personhood violating + + align:start position:0% +will violating her personhood violating + + + align:start position:0% +will violating her personhood violating +her + + align:start position:0% +her + + + align:start position:0% +her +autonomy but of course that's too much + + align:start position:0% +autonomy but of course that's too much + + + align:start position:0% +autonomy but of course that's too much +for the law court so they talk about her + + align:start position:0% +for the law court so they talk about her + + + align:start position:0% +for the law court so they talk about her +body being uh invaded without against + + align:start position:0% +body being uh invaded without against + + + align:start position:0% +body being uh invaded without against +her choice without her compliance + + align:start position:0% +her choice without her compliance + + + align:start position:0% +her choice without her compliance +non-consensual sex so physical but it's + + align:start position:0% +non-consensual sex so physical but it's + + + align:start position:0% +non-consensual sex so physical but it's +the idea of the of the consensuality and + + align:start position:0% +the idea of the of the consensuality and + + + align:start position:0% +the idea of the of the consensuality and +its destruction that seems to me to be + + align:start position:0% +its destruction that seems to me to be + + + align:start position:0% +its destruction that seems to me to be +the basic thing uh about the evil of + + align:start position:0% +the basic thing uh about the evil of + + + align:start position:0% +the basic thing uh about the evil of +rape so physical violence is exactly the + + align:start position:0% +rape so physical violence is exactly the + + + align:start position:0% +rape so physical violence is exactly the +same thing violence is what exactly the + + align:start position:0% +same thing violence is what exactly the + + + align:start position:0% +same thing violence is what exactly the +same kind of thing um robbery or + + align:start position:0% +same kind of thing um robbery or + + + align:start position:0% +same kind of thing um robbery or +anything well VI if by violence you mean + + align:start position:0% +anything well VI if by violence you mean + + + align:start position:0% +anything well VI if by violence you mean +uh + + align:start position:0% +uh + + + align:start position:0% +uh +nonconceptual harm done to another + + align:start position:0% +nonconceptual harm done to another + + + align:start position:0% +nonconceptual harm done to another +person mean no I mean there's a lot of + + align:start position:0% +person mean no I mean there's a lot of + + + align:start position:0% +person mean no I mean there's a lot of +violence in football and people are not + + align:start position:0% +violence in football and people are not + + + align:start position:0% +violence in football and people are not +to prison for that I me that's part of + + align:start position:0% +to prison for that I me that's part of + + + align:start position:0% +to prison for that I me that's part of +the game you run that risk so you see + + align:start position:0% +the game you run that risk so you see + + + align:start position:0% +the game you run that risk so you see +it's non non-consensual + + align:start position:0% + + + + align:start position:0% + +violence can the other types of Love + + align:start position:0% +violence can the other types of Love + + + align:start position:0% +violence can the other types of Love +have this kind of negative side to them + + align:start position:0% +have this kind of negative side to them + + + align:start position:0% +have this kind of negative side to them +as the I think I think that the the + + align:start position:0% +as the I think I think that the the + + + align:start position:0% +as the I think I think that the the +analysis is made in such a broad way + + align:start position:0% +analysis is made in such a broad way + + + align:start position:0% +analysis is made in such a broad way +because I want you to you know see what + + align:start position:0% +because I want you to you know see what + + + align:start position:0% +because I want you to you know see what +what you know it's like somebody with a + + align:start position:0% +what you know it's like somebody with a + + + align:start position:0% +what you know it's like somebody with a +with a net let's see what we'll pick up + + align:start position:0% +with a net let's see what we'll pick up + + + align:start position:0% +with a net let's see what we'll pick up +with it and so I want it to be a big net + + align:start position:0% +with it and so I want it to be a big net + + + align:start position:0% +with it and so I want it to be a big net +but I'm I don't think the mind works at + + align:start position:0% +but I'm I don't think the mind works at + + + align:start position:0% +but I'm I don't think the mind works at +least not my mind uh Works in such a way + + align:start position:0% +least not my mind uh Works in such a way + + + align:start position:0% +least not my mind uh Works in such a way +that um it can have necessary and + + align:start position:0% +that um it can have necessary and + + + align:start position:0% +that um it can have necessary and +sufficient conditions so that U there + + align:start position:0% +sufficient conditions so that U there + + + align:start position:0% +sufficient conditions so that U there +will be no overl overlap uh + + align:start position:0% +will be no overl overlap uh + + + align:start position:0% +will be no overl overlap uh +mathematics can do that logic is based + + align:start position:0% +mathematics can do that logic is based + + + align:start position:0% +mathematics can do that logic is based +on that and modern a lot of modern + + align:start position:0% +on that and modern a lot of modern + + + align:start position:0% +on that and modern a lot of modern +philosophy which I don't subscribe to is + + align:start position:0% +philosophy which I don't subscribe to is + + + align:start position:0% +philosophy which I don't subscribe to is +based on logic um but the world as I see + + align:start position:0% +based on logic um but the world as I see + + + align:start position:0% +based on logic um but the world as I see +it is a + + align:start position:0% +it is a + + + align:start position:0% +it is a +fluid mess it's uh well the subtitle is + + align:start position:0% +fluid mess it's uh well the subtitle is + + + align:start position:0% +fluid mess it's uh well the subtitle is +of the book feeling and Imagination + + align:start position:0% +of the book feeling and Imagination + + + align:start position:0% +of the book feeling and Imagination +is the vibrant flux of our existence + + align:start position:0% +is the vibrant flux of our existence + + + align:start position:0% +is the vibrant flux of our existence +life human life and the and reality is a + + align:start position:0% +life human life and the and reality is a + + + align:start position:0% +life human life and the and reality is a +flux but it can be vibrant because there + + align:start position:0% +flux but it can be vibrant because there + + + align:start position:0% +flux but it can be vibrant because there +are values and that's what the book is + + align:start position:0% +are values and that's what the book is + + + align:start position:0% +are values and that's what the book is +about um so that you're right + + align:start position:0% +about um so that you're right + + + align:start position:0% +about um so that you're right +um there would + + align:start position:0% +um there would + + + align:start position:0% +um there would +be more than just what is at the core of + + align:start position:0% +be more than just what is at the core of + + + align:start position:0% +be more than just what is at the core of +these Concepts and they can overlap in + + align:start position:0% +these Concepts and they can overlap in + + + align:start position:0% +these Concepts and they can overlap in +all sorts of various + + align:start position:0% + + + + align:start position:0% + +ways + + align:start position:0% + + + + align:start position:0% + +AR uh I had another question about the + + align:start position:0% +AR uh I had another question about the + + + align:start position:0% +AR uh I had another question about the +erotic before I move on remember but you + + align:start position:0% +erotic before I move on remember but you + + + align:start position:0% +erotic before I move on remember but you +haven't say anything about the erotic we + + align:start position:0% +haven't say anything about the erotic we + + + align:start position:0% +haven't say anything about the erotic we +hardly got started on the libidinal what + + align:start position:0% +hardly got started on the libidinal what + + + align:start position:0% +hardly got started on the libidinal what +what do you mean by erotic what do I how + + align:start position:0% +what do you mean by erotic what do I how + + + align:start position:0% +what do you mean by erotic what do I how +do you interpret my use of it since + + align:start position:0% +do you interpret my use of it since + + + align:start position:0% +do you interpret my use of it since +we're working out of my book I interpret + + align:start position:0% +we're working out of my book I interpret + + + align:start position:0% +we're working out of my book I interpret +it as the use of + + align:start position:0% +it as the use of + + + align:start position:0% +it as the use of +imagination + + align:start position:0% +imagination + + + align:start position:0% +imagination +to exalt the Beloved or to appreciate + + align:start position:0% +to exalt the Beloved or to appreciate + + + align:start position:0% +to exalt the Beloved or to appreciate +the beautiful of things that is the + + align:start position:0% +the beautiful of things that is the + + + align:start position:0% +the beautiful of things that is the +interpretation imagination comes into + + align:start position:0% +interpretation imagination comes into + + + align:start position:0% +interpretation imagination comes into +it but I give the + + align:start position:0% +it but I give the + + + align:start position:0% +it but I give the +analogy which is opening a enormous can + + align:start position:0% +analogy which is opening a enormous can + + + align:start position:0% +analogy which is opening a enormous can +of worms um with + + align:start position:0% +of worms um with + + + align:start position:0% +of worms um with +gravity gravity is a concept that Newton + + align:start position:0% +gravity gravity is a concept that Newton + + + align:start position:0% +gravity gravity is a concept that Newton +used that is still thought of as being + + align:start position:0% +used that is still thought of as being + + + align:start position:0% +used that is still thought of as being +one of the laws of nature but the whole + + align:start position:0% +one of the laws of nature but the whole + + + align:start position:0% +one of the laws of nature but the whole +trend of 20th and 21st century is to get + + align:start position:0% +trend of 20th and 21st century is to get + + + align:start position:0% +trend of 20th and 21st century is to get +far beyond the Reliance upon that + + align:start position:0% +far beyond the Reliance upon that + + + align:start position:0% +far beyond the Reliance upon that +concept of + + align:start position:0% +concept of + + + align:start position:0% +concept of +gravity what Newton observed was um the + + align:start position:0% +gravity what Newton observed was um the + + + align:start position:0% +gravity what Newton observed was um the +Apple falling on his head um the bodies + + align:start position:0% +Apple falling on his head um the bodies + + + align:start position:0% +Apple falling on his head um the bodies +seem to get attracted the Apple not + + align:start position:0% +seem to get attracted the Apple not + + + align:start position:0% +seem to get attracted the Apple not +aiming for him but aiming for the Earth + + align:start position:0% +aiming for him but aiming for the Earth + + + align:start position:0% +aiming for him but aiming for the Earth +that objects that are height are pulled + + align:start position:0% +that objects that are height are pulled + + + align:start position:0% +that objects that are height are pulled +to the Earth but it's it's it's a + + align:start position:0% +to the Earth but it's it's it's a + + + align:start position:0% +to the Earth but it's it's it's a +mystical sort of thing you don't see it + + align:start position:0% +mystical sort of thing you don't see it + + + align:start position:0% +mystical sort of thing you don't see it +have you ever seen gravity + + align:start position:0% +have you ever seen gravity + + + align:start position:0% +have you ever seen gravity +no um it's a force and yet without it + + align:start position:0% +no um it's a force and yet without it + + + align:start position:0% +no um it's a force and yet without it +Newton says we can't explain how the + + align:start position:0% +Newton says we can't explain how the + + + align:start position:0% +Newton says we can't explain how the +planets go around the Sun how the the + + align:start position:0% +planets go around the Sun how the the + + + align:start position:0% +planets go around the Sun how the the +Sun stays where it is or all the + + align:start position:0% +Sun stays where it is or all the + + + align:start position:0% +Sun stays where it is or all the +movement in the in the heavens + + align:start position:0% +movement in the in the heavens + + + align:start position:0% +movement in the in the heavens +um gravity therefore is a very + + align:start position:0% +um gravity therefore is a very + + + align:start position:0% +um gravity therefore is a very +important law of nature for him um now + + align:start position:0% +important law of nature for him um now + + + align:start position:0% +important law of nature for him um now +what intrigues me is that um it's a + + align:start position:0% +what intrigues me is that um it's a + + + align:start position:0% +what intrigues me is that um it's a +mysterious + + align:start position:0% +mysterious + + + align:start position:0% +mysterious +thing no matter how much scientists May + + align:start position:0% +thing no matter how much scientists May + + + align:start position:0% +thing no matter how much scientists May +dress it up it's a great mystery about + + align:start position:0% +dress it up it's a great mystery about + + + align:start position:0% +dress it up it's a great mystery about +why should things pull at each other why + + align:start position:0% +why should things pull at each other why + + + align:start position:0% +why should things pull at each other why +should there be Fe why should these + + align:start position:0% +should there be Fe why should these + + + align:start position:0% +should there be Fe why should these +fields of forces somehow be interrelated + + align:start position:0% +fields of forces somehow be interrelated + + + align:start position:0% +fields of forces somehow be interrelated +in a dynamic way of sort a gravitational + + align:start position:0% +in a dynamic way of sort a gravitational + + + align:start position:0% +in a dynamic way of sort a gravitational +sort of way and then I think about + + align:start position:0% +sort of way and then I think about + + + align:start position:0% +sort of way and then I think about +people I mean uh a man and a + + align:start position:0% +people I mean uh a man and a + + + align:start position:0% +people I mean uh a man and a +woman um they gravitate to each + + align:start position:0% +woman um they gravitate to each + + + align:start position:0% +woman um they gravitate to each +other and sometimes dramatically well + + align:start position:0% +other and sometimes dramatically well + + + align:start position:0% +other and sometimes dramatically well +this is so far be before your time um + + align:start position:0% +this is so far be before your time um + + + align:start position:0% +this is so far be before your time um +there was a a cartoon in my childhood um + + align:start position:0% +there was a a cartoon in my childhood um + + + align:start position:0% +there was a a cartoon in my childhood um +called + + align:start position:0% +called + + + align:start position:0% +called +uh Gerald MCB Bo and that sound it is + + align:start position:0% +uh Gerald MCB Bo and that sound it is + + + align:start position:0% +uh Gerald MCB Bo and that sound it is +Bo suddenly something will strike his + + align:start position:0% +Bo suddenly something will strike his + + + align:start position:0% +Bo suddenly something will strike his +mind or something like that you know you + + align:start position:0% +mind or something like that you know you + + + align:start position:0% +mind or something like that you know you +know get the idea of vibrations like + + align:start position:0% +know get the idea of vibrations like + + + align:start position:0% +know get the idea of vibrations like +that well but that's the way people + + align:start position:0% +that well but that's the way people + + + align:start position:0% +that well but that's the way people +often do relate to each other not always + + align:start position:0% +often do relate to each other not always + + + align:start position:0% +often do relate to each other not always +but sometimes man is walking down the + + align:start position:0% +but sometimes man is walking down the + + + align:start position:0% +but sometimes man is walking down the +street and then at least uh metaphoric I + + align:start position:0% +street and then at least uh metaphoric I + + + align:start position:0% +street and then at least uh metaphoric I +mean met metaphorically + + align:start position:0% +mean met metaphorically + + + align:start position:0% +mean met metaphorically +and also um + + align:start position:0% +and also um + + + align:start position:0% +and also um +mythologically + + align:start position:0% +mythologically + + + align:start position:0% +mythologically +uh it strikes him + + align:start position:0% +uh it strikes him + + + align:start position:0% +uh it strikes him +and and he's in love this is a constant + + align:start position:0% +and and he's in love this is a constant + + + align:start position:0% +and and he's in love this is a constant +theme in the movies you know no + + align:start position:0% +theme in the movies you know no + + + align:start position:0% +theme in the movies you know no +explanation no accounting for such + + align:start position:0% +explanation no accounting for such + + + align:start position:0% +explanation no accounting for such +things but it's such a force that he has + + align:start position:0% +things but it's such a force that he has + + + align:start position:0% +things but it's such a force that he has +to live live in it and it's more than + + align:start position:0% +to live live in it and it's more than + + + align:start position:0% +to live live in it and it's more than +just sexual + + align:start position:0% +just sexual + + + align:start position:0% +just sexual +libido which is a biological thing + + align:start position:0% +libido which is a biological thing + + + align:start position:0% +libido which is a biological thing +related to reproduction of the species + + align:start position:0% +related to reproduction of the species + + + align:start position:0% +related to reproduction of the species +and involves certain changes um in uh + + align:start position:0% +and involves certain changes um in uh + + + align:start position:0% +and involves certain changes um in uh +the body this is suddenly a feeling that + + align:start position:0% +the body this is suddenly a feeling that + + + align:start position:0% +the body this is suddenly a feeling that +this is my girl this is the one for + + align:start position:0% +this is my girl this is the one for + + + align:start position:0% +this is my girl this is the one for +me and it one it find it's very hard to + + align:start position:0% +me and it one it find it's very hard to + + + align:start position:0% +me and it one it find it's very hard to +know how it happens or why it happens + + align:start position:0% +know how it happens or why it happens + + + align:start position:0% +know how it happens or why it happens +could be because she looks like uh his + + align:start position:0% +could be because she looks like uh his + + + align:start position:0% +could be because she looks like uh his +mother Freud tended that way or it could + + align:start position:0% +mother Freud tended that way or it could + + + align:start position:0% +mother Freud tended that way or it could +be she doesn't look like his mother and + + align:start position:0% +be she doesn't look like his mother and + + + align:start position:0% +be she doesn't look like his mother and +he's reacting against his mother so it's + + align:start position:0% +he's reacting against his mother so it's + + + align:start position:0% +he's reacting against his mother so it's +always subject to some kind of + + align:start position:0% +always subject to some kind of + + + align:start position:0% +always subject to some kind of +interpretation + + align:start position:0% +interpretation + + + align:start position:0% +interpretation +but people do get attracted to to one + + align:start position:0% +but people do get attracted to to one + + + align:start position:0% +but people do get attracted to to one +another it usually doesn't end up being + + align:start position:0% +another it usually doesn't end up being + + + align:start position:0% +another it usually doesn't end up being +falling in love or being that dramatic + + align:start position:0% +falling in love or being that dramatic + + + align:start position:0% +falling in love or being that dramatic +you know but rather it could be + + align:start position:0% +you know but rather it could be + + + align:start position:0% +you know but rather it could be +friendship or you know somehow I can + + align:start position:0% +friendship or you know somehow I can + + + align:start position:0% +friendship or you know somehow I can +communicate with that person or we have + + align:start position:0% +communicate with that person or we have + + + align:start position:0% +communicate with that person or we have +something in common or I feel for him um + + align:start position:0% +something in common or I feel for him um + + + align:start position:0% +something in common or I feel for him um +you know and it varies it + + align:start position:0% +you know and it varies it + + + align:start position:0% +you know and it varies it +varies + + align:start position:0% +varies + + + align:start position:0% +varies +um the feeling can become be strong + + align:start position:0% +um the feeling can become be strong + + + align:start position:0% +um the feeling can become be strong +sometimes weak at other times can be + + align:start position:0% +sometimes weak at other times can be + + + align:start position:0% +sometimes weak at other times can be +disappointed this lead to + + align:start position:0% +disappointed this lead to + + + align:start position:0% +disappointed this lead to +disappointments it can lead to + + align:start position:0% +disappointments it can lead to + + + align:start position:0% +disappointments it can lead to +ecstasies the uh so for me the erotic is + + align:start position:0% +ecstasies the uh so for me the erotic is + + + align:start position:0% +ecstasies the uh so for me the erotic is +this sort of + + align:start position:0% + + + + align:start position:0% + +gravitational phenomenon in relation to + + align:start position:0% +gravitational phenomenon in relation to + + + align:start position:0% +gravitational phenomenon in relation to +somebody else but having said + + align:start position:0% +somebody else but having said + + + align:start position:0% +somebody else but having said +that I can see how this would also apply + + align:start position:0% +that I can see how this would also apply + + + align:start position:0% +that I can see how this would also apply +not just to other persons but to other + + align:start position:0% +not just to other persons but to other + + + align:start position:0% +not just to other persons but to other +um + + align:start position:0% +um + + + align:start position:0% +um +things um a work of + + align:start position:0% +things um a work of + + + align:start position:0% +things um a work of +art um a work of carpentry you know just + + align:start position:0% +art um a work of carpentry you know just + + + align:start position:0% +art um a work of carpentry you know just +the shape of that or um you know the + + align:start position:0% +the shape of that or um you know the + + + align:start position:0% +the shape of that or um you know the +smoothness of this the surface of a + + align:start position:0% +smoothness of this the surface of a + + + align:start position:0% +smoothness of this the surface of a +table you sort of gravitate towards that + + align:start position:0% +table you sort of gravitate towards that + + + align:start position:0% +table you sort of gravitate towards that +that you this is it's what you like it + + align:start position:0% +that you this is it's what you like it + + + align:start position:0% +that you this is it's what you like it +somehow comes down to the whole system + + align:start position:0% +somehow comes down to the whole system + + + align:start position:0% +somehow comes down to the whole system +of likings which seem to be very + + align:start position:0% +of likings which seem to be very + + + align:start position:0% +of likings which seem to be very +different from love but this Aros is + + align:start position:0% +different from love but this Aros is + + + align:start position:0% +different from love but this Aros is +only the erotic I mean is only one of + + align:start position:0% +only the erotic I mean is only one of + + + align:start position:0% +only the erotic I mean is only one of +the elements in love but it's the part + + align:start position:0% +the elements in love but it's the part + + + align:start position:0% +the elements in love but it's the part +of love that + + align:start position:0% +of love that + + + align:start position:0% +of love that +explains our attachment to various + + align:start position:0% + + + + align:start position:0% + +things um it can be the result of the + + align:start position:0% +things um it can be the result of the + + + align:start position:0% +things um it can be the result of the +passage of + + align:start position:0% +passage of + + + align:start position:0% +passage of +time um you the old people having lived + + align:start position:0% +time um you the old people having lived + + + align:start position:0% +time um you the old people having lived +together a long time become very + + align:start position:0% +together a long time become very + + + align:start position:0% +together a long time become very +attached they get used to each other + + align:start position:0% +attached they get used to each other + + + align:start position:0% +attached they get used to each other +they get + + align:start position:0% +they get + + + align:start position:0% +they get +habituated uh they become a habit for + + align:start position:0% +habituated uh they become a habit for + + + align:start position:0% +habituated uh they become a habit for +each other + + align:start position:0% +each other + + + align:start position:0% +each other +uh the line in My Fair Lady um I've + + align:start position:0% +uh the line in My Fair Lady um I've + + + align:start position:0% +uh the line in My Fair Lady um I've +become accustomed to her face her UPS or + + align:start position:0% +become accustomed to her face her UPS or + + + align:start position:0% +become accustomed to her face her UPS or +Downs or Smiles or frowns um that's + + align:start position:0% +Downs or Smiles or frowns um that's + + + align:start position:0% +Downs or Smiles or frowns um that's +seems to have nothing to do with libido + + align:start position:0% +seems to have nothing to do with libido + + + align:start position:0% +seems to have nothing to do with libido +but it and it looks as if one could say + + align:start position:0% +but it and it looks as if one could say + + + align:start position:0% +but it and it looks as if one could say +well but you know break the Habit why + + align:start position:0% +well but you know break the Habit why + + + align:start position:0% +well but you know break the Habit why +why do you call this love but there's + + align:start position:0% +why do you call this love but there's + + + align:start position:0% +why do you call this love but there's +something in the in an attachment to + + align:start position:0% +something in the in an attachment to + + + align:start position:0% +something in the in an attachment to +another person which is part of love and + + align:start position:0% +another person which is part of love and + + + align:start position:0% +another person which is part of love and +the attachment can come in this bizarre + + align:start position:0% +the attachment can come in this bizarre + + + align:start position:0% +the attachment can come in this bizarre +way that is comparable to gravity that I + + align:start position:0% +way that is comparable to gravity that I + + + align:start position:0% +way that is comparable to gravity that I +call the + + align:start position:0% + + + + align:start position:0% + +erotic yeah I guess it just I don't know + + align:start position:0% +erotic yeah I guess it just I don't know + + + align:start position:0% +erotic yeah I guess it just I don't know +if I really understand what you're + + align:start position:0% +if I really understand what you're + + + align:start position:0% +if I really understand what you're +saying by the I don't know whether I do + + align:start position:0% +saying by the I don't know whether I do + + + align:start position:0% +saying by the I don't know whether I do +either or the habituation really is a + + align:start position:0% +either or the habituation really is a + + + align:start position:0% +either or the habituation really is a +form of love because I guess even + + align:start position:0% +form of love because I guess even + + + align:start position:0% +form of love because I guess even +nowadays people seem to think more + + align:start position:0% +nowadays people seem to think more + + + align:start position:0% +nowadays people seem to think more +rather than in the past oh there is one + + align:start position:0% +rather than in the past oh there is one + + + align:start position:0% +rather than in the past oh there is one +person meant for me but now there's you + + align:start position:0% +person meant for me but now there's you + + + align:start position:0% +person meant for me but now there's you +know a lot of people that divorce and do + + align:start position:0% +know a lot of people that divorce and do + + + align:start position:0% +know a lot of people that divorce and do +those types of things and it seems that + + align:start position:0% +those types of things and it seems that + + + align:start position:0% +those types of things and it seems that +just because you + + align:start position:0% +just because you + + + align:start position:0% +just because you +are getting used to someone that doesn't + + align:start position:0% +are getting used to someone that doesn't + + + align:start position:0% +are getting used to someone that doesn't +mean that love really is there well but + + align:start position:0% +mean that love really is there well but + + + align:start position:0% +mean that love really is there well but +why could you say instead of gravitating + + align:start position:0% +why could you say instead of gravitating + + + align:start position:0% +why could you say instead of gravitating +toward your one and only you gravitate + + align:start position:0% +toward your one and only you gravitate + + + align:start position:0% +toward your one and only you gravitate +toward many + + align:start position:0% +toward many + + + align:start position:0% +toward many +people oh I guess so I mean uh the + + align:start position:0% +people oh I guess so I mean uh the + + + align:start position:0% +people oh I guess so I mean uh the +universe is infinite it goes off in all + + align:start position:0% +universe is infinite it goes off in all + + + align:start position:0% +universe is infinite it goes off in all +directions why does it have to be + + align:start position:0% +directions why does it have to be + + + align:start position:0% +directions why does it have to be +limited to a linear progression to what + + align:start position:0% +limited to a linear progression to what + + + align:start position:0% +limited to a linear progression to what +you were saying about the getting + + align:start position:0% +you were saying about the getting + + + align:start position:0% +you were saying about the getting +accustomed to someone that being a part + + align:start position:0% +accustomed to someone that being a part + + + align:start position:0% +accustomed to someone that being a part +of the uh of the erotic that's how we + + align:start position:0% +of the uh of the erotic that's how we + + + align:start position:0% +of the uh of the erotic that's how we +were like I just don't see how that's a + + align:start position:0% +were like I just don't see how that's a + + + align:start position:0% +were like I just don't see how that's a +part of that + + align:start position:0% +part of that + + + align:start position:0% +part of that +love well it works it works the way + + align:start position:0% +love well it works it works the way + + + align:start position:0% +love well it works it works the way +people have thought about love uh the uh + + align:start position:0% +people have thought about love uh the uh + + + align:start position:0% +people have thought about love uh the uh +line + + align:start position:0% +line + + + align:start position:0% +line +comes particularly the way I was badly + + align:start position:0% +comes particularly the way I was badly + + + align:start position:0% +comes particularly the way I was badly +mauling it uh comes from the musical My + + align:start position:0% +mauling it uh comes from the musical My + + + align:start position:0% +mauling it uh comes from the musical My +Fair Lady + + align:start position:0% +Fair Lady + + + align:start position:0% +Fair Lady +uh it doesn't uh exist in the same way + + align:start position:0% +uh it doesn't uh exist in the same way + + + align:start position:0% +uh it doesn't uh exist in the same way +in George Bernard Shaw's + + align:start position:0% +in George Bernard Shaw's + + + align:start position:0% +in George Bernard Shaw's +play which you're going to reading it + + align:start position:0% +play which you're going to reading it + + + align:start position:0% +play which you're going to reading it +occurred to me pig ban that's right um + + align:start position:0% +occurred to me pig ban that's right um + + + align:start position:0% +occurred to me pig ban that's right um +and in the case the difference between + + align:start position:0% +and in the case the difference between + + + align:start position:0% +and in the case the difference between +the play and the musical is + + align:start position:0% +the play and the musical is + + + align:start position:0% +the play and the musical is +that at the end of the musical there is + + align:start position:0% +that at the end of the musical there is + + + align:start position:0% +that at the end of the musical there is +a kind of romance a love that's + + align:start position:0% +a kind of romance a love that's + + + align:start position:0% +a kind of romance a love that's +developed between + + align:start position:0% +developed between + + + align:start position:0% +developed between +them and maybe um who knows they might + + align:start position:0% +them and maybe um who knows they might + + + align:start position:0% +them and maybe um who knows they might +even get married afterwards they don't + + align:start position:0% +even get married afterwards they don't + + + align:start position:0% +even get married afterwards they don't +nothing like that happens in any of the + + align:start position:0% +nothing like that happens in any of the + + + align:start position:0% +nothing like that happens in any of the +versions but uh it's much more romantic + + align:start position:0% +versions but uh it's much more romantic + + + align:start position:0% +versions but uh it's much more romantic +than the play + + align:start position:0% +than the play + + + align:start position:0% +than the play +was um so that um just for the there to + + align:start position:0% +was um so that um just for the there to + + + align:start position:0% +was um so that um just for the there to +be the erotic + + align:start position:0% +be the erotic + + + align:start position:0% +be the erotic +attachment doesn't mean it's going to + + align:start position:0% +attachment doesn't mean it's going to + + + align:start position:0% +attachment doesn't mean it's going to +be love of of a romantic sort or of a + + align:start position:0% +be love of of a romantic sort or of a + + + align:start position:0% +be love of of a romantic sort or of a +marital sort but it's a kind of love if + + align:start position:0% +marital sort but it's a kind of love if + + + align:start position:0% +marital sort but it's a kind of love if +you're gravitating towards somebody um + + align:start position:0% +you're gravitating towards somebody um + + + align:start position:0% +you're gravitating towards somebody um +that's not hostility hostility goes in + + align:start position:0% +that's not hostility hostility goes in + + + align:start position:0% +that's not hostility hostility goes in +the opposite direction or and it's not + + align:start position:0% +the opposite direction or and it's not + + + align:start position:0% +the opposite direction or and it's not +indifference which means you don't even + + align:start position:0% +indifference which means you don't even + + + align:start position:0% +indifference which means you don't even +feel anything for the other person don't + + align:start position:0% +feel anything for the other person don't + + + align:start position:0% +feel anything for the other person don't +even notice the other + + align:start position:0% + + + + align:start position:0% + +person but I don't want to you know + + align:start position:0% +person but I don't want to you know + + + align:start position:0% +person but I don't want to you know +create these artificial principalities I + + align:start position:0% +create these artificial principalities I + + + align:start position:0% +create these artificial principalities I +just want to make a concept which itself + + align:start position:0% +just want to make a concept which itself + + + align:start position:0% +just want to make a concept which itself +is analyzable into more uh fi refined uh + + align:start position:0% +is analyzable into more uh fi refined uh + + + align:start position:0% +is analyzable into more uh fi refined uh +Concepts that to the extent that they + + align:start position:0% +Concepts that to the extent that they + + + align:start position:0% +Concepts that to the extent that they +have help us to think + + align:start position:0% +have help us to think + + + align:start position:0% +have help us to think +better I think in various places in that + + align:start position:0% +better I think in various places in that + + + align:start position:0% +better I think in various places in that +book in particular I say that um of + + align:start position:0% +book in particular I say that um of + + + align:start position:0% +book in particular I say that um of +course they're going there will be + + align:start position:0% +course they're going there will be + + + align:start position:0% +course they're going there will be +subdivisions and and that it isn't if + + align:start position:0% +subdivisions and and that it isn't if + + + align:start position:0% +subdivisions and and that it isn't if +everything will be + + align:start position:0% +everything will be + + + align:start position:0% +everything will be +alike but that gives you an idea of a a + + align:start position:0% +alike but that gives you an idea of a a + + + align:start position:0% +alike but that gives you an idea of a a +fact a + + align:start position:0% +fact a + + + align:start position:0% +fact a +phenomenon related to + + align:start position:0% +phenomenon related to + + + align:start position:0% +phenomenon related to +love um that people might not have been + + align:start position:0% +love um that people might not have been + + + align:start position:0% +love um that people might not have been +able to think about as clearly without + + align:start position:0% +able to think about as clearly without + + + align:start position:0% +able to think about as clearly without +this kind of analysis and my hope is to + + align:start position:0% +this kind of analysis and my hope is to + + + align:start position:0% +this kind of analysis and my hope is to +help them to make these difficult ideas + + align:start position:0% +help them to make these difficult ideas + + + align:start position:0% +help them to make these difficult ideas +a little more + + align:start position:0% +a little more + + + align:start position:0% +a little more +clear thank your question was more like + + align:start position:0% +clear thank your question was more like + + + align:start position:0% +clear thank your question was more like +gravitation is part of like kind love at + + align:start position:0% +gravitation is part of like kind love at + + + align:start position:0% +gravitation is part of like kind love at +first sight + + align:start position:0% +first sight + + + align:start position:0% +first sight +no that's kind of what I was + + align:start position:0% +no that's kind of what I was + + + align:start position:0% +no that's kind of what I was +thinking the well like the gravitation + + align:start position:0% +thinking the well like the gravitation + + + align:start position:0% +thinking the well like the gravitation +pull towards someone is kind of like + + align:start position:0% +pull towards someone is kind of like + + + align:start position:0% +pull towards someone is kind of like +instantaneous almost as opposed to uh as + + align:start position:0% +instantaneous almost as opposed to uh as + + + align:start position:0% +instantaneous almost as opposed to uh as +if you're with someone for a long time + + align:start position:0% +if you're with someone for a long time + + + align:start position:0% +if you're with someone for a long time +it's not you know instant + + align:start position:0% +it's not you know instant + + + align:start position:0% +it's not you know instant +no let's let's get on to the Romantic + + align:start position:0% +no let's let's get on to the Romantic + + + align:start position:0% +no let's let's get on to the Romantic +was that there it's more relevant what + + align:start position:0% +was that there it's more relevant what + + + align:start position:0% +was that there it's more relevant what +you're saying I think um about the + + align:start position:0% +you're saying I think um about the + + + align:start position:0% +you're saying I think um about the +imagination I think of that as belonging + + align:start position:0% +imagination I think of that as belonging + + + align:start position:0% +imagination I think of that as belonging +to + + align:start position:0% +to + + + align:start position:0% +to +Eros and but it isn't as if that is + + align:start position:0% +Eros and but it isn't as if that is + + + align:start position:0% +Eros and but it isn't as if that is +enough for that defines AOS the erotic + + align:start position:0% +enough for that defines AOS the erotic + + + align:start position:0% +enough for that defines AOS the erotic +I'm sorry I shouldn't say AOS I mean the + + align:start position:0% +I'm sorry I shouldn't say AOS I mean the + + + align:start position:0% +I'm sorry I shouldn't say AOS I mean the +erotic I was very careful to call these + + align:start position:0% +erotic I was very careful to call these + + + align:start position:0% +erotic I was very careful to call these +with these adjectival forms not to get + + align:start position:0% +with these adjectival forms not to get + + + align:start position:0% +with these adjectival forms not to get +it confused with what Plato had said or + + align:start position:0% +it confused with what Plato had said or + + + align:start position:0% +it confused with what Plato had said or +what Freud had said uh when the book + + align:start position:0% +what Freud had said uh when the book + + + align:start position:0% +what Freud had said uh when the book +came out it got a very favorable review + + align:start position:0% +came out it got a very favorable review + + + align:start position:0% +came out it got a very favorable review +uh by someone who is a philosopher but a + + align:start position:0% +uh by someone who is a philosopher but a + + + align:start position:0% +uh by someone who is a philosopher but a +literary philosopher and in a literary + + align:start position:0% +literary philosopher and in a literary + + + align:start position:0% +literary philosopher and in a literary +journal and she sent me her review + + align:start position:0% +journal and she sent me her review + + + align:start position:0% +journal and she sent me her review +before it came out and I was horrified + + align:start position:0% +before it came out and I was horrified + + + align:start position:0% +before it came out and I was horrified +this she said sing a distinguishes + + align:start position:0% +this she said sing a distinguishes + + + align:start position:0% +this she said sing a distinguishes +between libido Eros and romance and so I + + align:start position:0% +between libido Eros and romance and so I + + + align:start position:0% +between libido Eros and romance and so I +quickly wrote is saying no no no that + + align:start position:0% +quickly wrote is saying no no no that + + + align:start position:0% +quickly wrote is saying no no no that +were liido is Freud Aros is Plato I'm + + align:start position:0% +were liido is Freud Aros is Plato I'm + + + align:start position:0% +were liido is Freud Aros is Plato I'm +talking about I call it the leidal the + + align:start position:0% +talking about I call it the leidal the + + + align:start position:0% +talking about I call it the leidal the +erotic rantic in order to indicate I'm + + align:start position:0% +erotic rantic in order to indicate I'm + + + align:start position:0% +erotic rantic in order to indicate I'm +saying something different and when the + + align:start position:0% +saying something different and when the + + + align:start position:0% +saying something different and when the +review was published she had it + + align:start position:0% +review was published she had it + + + align:start position:0% +review was published she had it +right so again here I keep saying erors + + align:start position:0% +right so again here I keep saying erors + + + align:start position:0% +right so again here I keep saying erors +but I mean the + + align:start position:0% + + + + align:start position:0% + +ironic an imagination I I think is + + align:start position:0% +ironic an imagination I I think is + + + align:start position:0% +ironic an imagination I I think is +important that does anybody want to say + + align:start position:0% +important that does anybody want to say + + + align:start position:0% +important that does anybody want to say +anything about that + + align:start position:0% + + + + align:start position:0% + +there's a chapter on imagination in + + align:start position:0% +there's a chapter on imagination in + + + align:start position:0% +there's a chapter on imagination in +feeling and Imagination but I I better + + align:start position:0% +feeling and Imagination but I I better + + + align:start position:0% +feeling and Imagination but I I better +not get into that how about Romance the + + align:start position:0% +not get into that how about Romance the + + + align:start position:0% +not get into that how about Romance the +third okay + + align:start position:0% +third okay + + + align:start position:0% +third okay +um be before we move on to romance I + + align:start position:0% +um be before we move on to romance I + + + align:start position:0% +um be before we move on to romance I +just wanted to ask you a question about + + align:start position:0% +just wanted to ask you a question about + + + align:start position:0% +just wanted to ask you a question about +the erotic you say that without the + + align:start position:0% +the erotic you say that without the + + + align:start position:0% +the erotic you say that without the +erotic there would be no civilization + + align:start position:0% +erotic there would be no civilization + + + align:start position:0% +erotic there would be no civilization +and no desecration of it and it wasn't + + align:start position:0% +and no desecration of it and it wasn't + + + align:start position:0% +and no desecration of it and it wasn't +clear to me why what you meant well I + + align:start position:0% +clear to me why what you meant well I + + + align:start position:0% +clear to me why what you meant well I +often see nowadays not as much but well + + align:start position:0% +often see nowadays not as much but well + + + align:start position:0% +often see nowadays not as much but well +you all know all of the graffiti that + + align:start position:0% +you all know all of the graffiti that + + + align:start position:0% +you all know all of the graffiti that +appears in public + + align:start position:0% +appears in public + + + align:start position:0% +appears in public +places um I live in the Back Bay and in + + align:start position:0% +places um I live in the Back Bay and in + + + align:start position:0% +places um I live in the Back Bay and in +a part of the U of Mass Avenue part + + align:start position:0% +a part of the U of Mass Avenue part + + + align:start position:0% +a part of the U of Mass Avenue part +south of u b Street I think it was they + + align:start position:0% +south of u b Street I think it was they + + + align:start position:0% +south of u b Street I think it was they +did a lot of resurfacing of the concrete + + align:start position:0% +did a lot of resurfacing of the concrete + + + align:start position:0% +did a lot of resurfacing of the concrete +sidewalks and I was horrified that + + align:start position:0% +sidewalks and I was horrified that + + + align:start position:0% +sidewalks and I was horrified that +everybody felt the need to put in his or + + align:start position:0% +everybody felt the need to put in his or + + + align:start position:0% +everybody felt the need to put in his or +her uh initials and sometimes with + + align:start position:0% +her uh initials and sometimes with + + + align:start position:0% +her uh initials and sometimes with +hearts and dates and it's got me + + align:start position:0% +hearts and dates and it's got me + + + align:start position:0% +hearts and dates and it's got me +thinking you know you know what's + + align:start position:0% +thinking you know you know what's + + + align:start position:0% +thinking you know you know what's +happening there they're using their + + align:start position:0% +happening there they're using their + + + align:start position:0% +happening there they're using their +imagination to imag so I think of a Time + + align:start position:0% +imagination to imag so I think of a Time + + + align:start position:0% +imagination to imag so I think of a Time +who knows 20 years I don't know how big + + align:start position:0% +who knows 20 years I don't know how big + + + align:start position:0% +who knows 20 years I don't know how big +an imagination they have 50 years + + align:start position:0% +an imagination they have 50 years + + + align:start position:0% +an imagination they have 50 years +when people are going to see that and + + align:start position:0% +when people are going to see that and + + + align:start position:0% +when people are going to see that and +it'll mean something to them of course + + align:start position:0% +it'll mean something to them of course + + + align:start position:0% +it'll mean something to them of course +people won't know what in the world was + + align:start position:0% +people won't know what in the world was + + + align:start position:0% +people won't know what in the world was +going on in those days or who these who + + align:start position:0% +going on in those days or who these who + + + align:start position:0% +going on in those days or who these who +JT and LW are nobody will know they + + align:start position:0% +JT and LW are nobody will know they + + + align:start position:0% +JT and LW are nobody will know they +themselves probably will fall fall out + + align:start position:0% +themselves probably will fall fall out + + + align:start position:0% +themselves probably will fall fall out +of love in two months and will regret it + + align:start position:0% +of love in two months and will regret it + + + align:start position:0% +of love in two months and will regret it +and it won't mean anything to them later + + align:start position:0% +and it won't mean anything to them later + + + align:start position:0% +and it won't mean anything to them later +on or might it might maybe they'll come + + align:start position:0% +on or might it might maybe they'll come + + + align:start position:0% +on or might it might maybe they'll come +back with their children and say this + + align:start position:0% +back with their children and say this + + + align:start position:0% +back with their children and say this +was what we were you know in play in in + + align:start position:0% +was what we were you know in play in in + + + align:start position:0% +was what we were you know in play in in +Shakespeare uh uh for instance + + align:start position:0% +Shakespeare uh uh for instance + + + align:start position:0% +Shakespeare uh uh for instance +in as you like + + align:start position:0% +in as you like + + + align:start position:0% +in as you like +it that play um there is the young man + + align:start position:0% +it that play um there is the young man + + + align:start position:0% +it that play um there is the young man +who's fallen in love with um the heroine + + align:start position:0% +who's fallen in love with um the heroine + + + align:start position:0% +who's fallen in love with um the heroine +rosalin and um he's very he feels + + align:start position:0% +rosalin and um he's very he feels + + + align:start position:0% +rosalin and um he's very he feels +worthless and carried away by his love + + align:start position:0% +worthless and carried away by his love + + + align:start position:0% +worthless and carried away by his love +and uh he takes it out on the trees when + + align:start position:0% +and uh he takes it out on the trees when + + + align:start position:0% +and uh he takes it out on the trees when +I talked about the innocent trees well + + align:start position:0% +I talked about the innocent trees well + + + align:start position:0% +I talked about the innocent trees well +he carves their initials in the trees + + align:start position:0% +he carves their initials in the trees + + + align:start position:0% +he carves their initials in the trees +and hearts probably and sort of + + align:start position:0% +and hearts probably and sort of + + + align:start position:0% +and hearts probably and sort of +desecrates the beauty of these natural + + align:start position:0% +desecrates the beauty of these natural + + + align:start position:0% +desecrates the beauty of these natural +entities um whom I love very much but + + align:start position:0% +entities um whom I love very much but + + + align:start position:0% +entities um whom I love very much but +you know it's as if + + align:start position:0% +you know it's as if + + + align:start position:0% +you know it's as if +somebody + + align:start position:0% +somebody + + + align:start position:0% +somebody +uh captured you and uh engraved on your + + align:start position:0% +uh captured you and uh engraved on your + + + align:start position:0% +uh captured you and uh engraved on your +farhead uh LW loves c c CM or something + + align:start position:0% +farhead uh LW loves c c CM or something + + + align:start position:0% +farhead uh LW loves c c CM or something +something has nothing to do with you so + + align:start position:0% +something has nothing to do with you so + + + align:start position:0% +something has nothing to do with you so +you could go through the world + + align:start position:0% +you could go through the world + + + align:start position:0% +you could go through the world +advertising This Love that he has um and + + align:start position:0% +advertising This Love that he has um and + + + align:start position:0% +advertising This Love that he has um and +why should the trees be forced into that + + align:start position:0% +why should the trees be forced into that + + + align:start position:0% +why should the trees be forced into that +condition well because they can't help + + align:start position:0% +condition well because they can't help + + + align:start position:0% +condition well because they can't help +it they're they're they're not mobile + + align:start position:0% +it they're they're they're not mobile + + + align:start position:0% +it they're they're they're not mobile +they're stabile people can just go up + + align:start position:0% +they're stabile people can just go up + + + align:start position:0% +they're stabile people can just go up +and do to them whatever they can get + + align:start position:0% +and do to them whatever they can get + + + align:start position:0% +and do to them whatever they can get +away with uh that it's an act of + + align:start position:0% +away with uh that it's an act of + + + align:start position:0% +away with uh that it's an act of +imagination in thinking that this is + + align:start position:0% +imagination in thinking that this is + + + align:start position:0% +imagination in thinking that this is +going to me anything it's like an artist + + align:start position:0% +going to me anything it's like an artist + + + align:start position:0% +going to me anything it's like an artist +who expresses himself in his + + align:start position:0% +who expresses himself in his + + + align:start position:0% +who expresses himself in his +painting uh it's an expression of him + + align:start position:0% +painting uh it's an expression of him + + + align:start position:0% +painting uh it's an expression of him +but also takes imagination to make it a + + align:start position:0% +but also takes imagination to make it a + + + align:start position:0% +but also takes imagination to make it a +good painting So this expresses what the + + align:start position:0% +good painting So this expresses what the + + + align:start position:0% +good painting So this expresses what the +young lovers feel and they have enough + + align:start position:0% +young lovers feel and they have enough + + + align:start position:0% +young lovers feel and they have enough +imagination to think it might matter to + + align:start position:0% +imagination to think it might matter to + + + align:start position:0% +imagination to think it might matter to +somebody else but they don't have enough + + align:start position:0% +somebody else but they don't have enough + + + align:start position:0% +somebody else but they don't have enough +imagination to to realize how ridiculous + + align:start position:0% +imagination to to realize how ridiculous + + + align:start position:0% +imagination to to realize how ridiculous +it makes them uh and how unfair it is to + + align:start position:0% +it makes them uh and how unfair it is to + + + align:start position:0% +it makes them uh and how unfair it is to +everybody else to have to be confronted + + align:start position:0% +everybody else to have to be confronted + + + align:start position:0% +everybody else to have to be confronted +with this it it's a a kind of + + align:start position:0% +with this it it's a a kind of + + + align:start position:0% +with this it it's a a kind of +exhibitionism which if it were with + + align:start position:0% +exhibitionism which if it were with + + + align:start position:0% +exhibitionism which if it were with +parts of the body would be + + align:start position:0% +parts of the body would be + + + align:start position:0% +parts of the body would be +criminal and I suppose it probably is + + align:start position:0% +criminal and I suppose it probably is + + + align:start position:0% +criminal and I suppose it probably is +Criminal to do it to the poor innocent + + align:start position:0% +Criminal to do it to the poor innocent + + + align:start position:0% +Criminal to do it to the poor innocent +side cement in the + + align:start position:0% +side cement in the + + + align:start position:0% +side cement in the +sidewalk but it takes imagination that's + + align:start position:0% +sidewalk but it takes imagination that's + + + align:start position:0% +sidewalk but it takes imagination that's +all I meant okay I guess I just feel + + align:start position:0% +all I meant okay I guess I just feel + + + align:start position:0% +all I meant okay I guess I just feel +that's still a very strong statement to + + align:start position:0% +that's still a very strong statement to + + + align:start position:0% +that's still a very strong statement to +say that without the erotic there would + + align:start position:0% +say that without the erotic there would + + + align:start position:0% +say that without the erotic there would +be no + + align:start position:0% +be no + + + align:start position:0% +be no +civilization yeah um I think so because + + align:start position:0% +civilization yeah um I think so because + + + align:start position:0% +civilization yeah um I think so because +the erotic is a way of I mean + + align:start position:0% +the erotic is a way of I mean + + + align:start position:0% +the erotic is a way of I mean +civilization is a way of creating + + align:start position:0% +civilization is a way of creating + + + align:start position:0% +civilization is a way of creating +objects that Express the interests of + + align:start position:0% +objects that Express the interests of + + + align:start position:0% +objects that Express the interests of +the creators for the enjoyment and and + + align:start position:0% +the creators for the enjoyment and and + + + align:start position:0% +the creators for the enjoyment and and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +glorification of what other people also + + align:start position:0% +glorification of what other people also + + + align:start position:0% +glorification of what other people also +care about so that the uh person the + + align:start position:0% +care about so that the uh person the + + + align:start position:0% +care about so that the uh person the +prince who built the Taj Mahal you know + + align:start position:0% +prince who built the Taj Mahal you know + + + align:start position:0% +prince who built the Taj Mahal you know +the story of that or why do you tell + + align:start position:0% +the story of that or why do you tell + + + align:start position:0% +the story of that or why do you tell +that he built it for his + + align:start position:0% +that he built it for his + + + align:start position:0% +that he built it for his +wife or his wife you know and who he had + + align:start position:0% +wife or his wife you know and who he had + + + align:start position:0% +wife or his wife you know and who he had +loved I don't really know much about the + + align:start position:0% +loved I don't really know much about the + + + align:start position:0% +loved I don't really know much about the +story actually but who died and he was + + align:start position:0% +story actually but who died and he was + + + align:start position:0% +story actually but who died and he was +so grief stricken uh he wanted to make + + align:start position:0% +so grief stricken uh he wanted to make + + + align:start position:0% +so grief stricken uh he wanted to make +some kind of Tomb or Temple but he also + + align:start position:0% +some kind of Tomb or Temple but he also + + + align:start position:0% +some kind of Tomb or Temple but he also +wanted it to be an expression of her + + align:start position:0% +wanted it to be an expression of her + + + align:start position:0% +wanted it to be an expression of her +goodness and Beauty and the great love + + align:start position:0% +goodness and Beauty and the great love + + + align:start position:0% +goodness and Beauty and the great love +that they had for each other and that's + + align:start position:0% +that they had for each other and that's + + + align:start position:0% +that they had for each other and that's +part of the account it all may be + + align:start position:0% +part of the account it all may be + + + align:start position:0% +part of the account it all may be +mythological but at least that's the + + align:start position:0% +mythological but at least that's the + + + align:start position:0% +mythological but at least that's the +account and so we made the This + + align:start position:0% +account and so we made the This + + + align:start position:0% +account and so we made the This +Magnificent U Muslim style or H what is + + align:start position:0% +Magnificent U Muslim style or H what is + + + align:start position:0% +Magnificent U Muslim style or H what is +it it must be Muslim because it's curved + + align:start position:0% +it it must be Muslim because it's curved + + + align:start position:0% +it it must be Muslim because it's curved +like Muslim uh in any event um Indian + + align:start position:0% +like Muslim uh in any event um Indian + + + align:start position:0% +like Muslim uh in any event um Indian +style u uh Palace it's not it's not a + + align:start position:0% +style u uh Palace it's not it's not a + + + align:start position:0% +style u uh Palace it's not it's not a +tomb uh it's not a mosum but it's a + + align:start position:0% +tomb uh it's not a mosum but it's a + + + align:start position:0% +tomb uh it's not a mosum but it's a +beautiful + + align:start position:0% +beautiful + + + align:start position:0% +beautiful +building that expresses what he felt for + + align:start position:0% +building that expresses what he felt for + + + align:start position:0% +building that expresses what he felt for +that woman and that adds to civilization + + align:start position:0% +that woman and that adds to civilization + + + align:start position:0% +that woman and that adds to civilization +I mean we stand there if we go there and + + align:start position:0% +I mean we stand there if we go there and + + + align:start position:0% +I mean we stand there if we go there and +uh watch it look at it with awe becomes + + align:start position:0% +uh watch it look at it with awe becomes + + + align:start position:0% +uh watch it look at it with awe becomes +a tourist attraction it makes life more + + align:start position:0% +a tourist attraction it makes life more + + + align:start position:0% +a tourist attraction it makes life more +interesting think of all the millions of + + align:start position:0% +interesting think of all the millions of + + + align:start position:0% +interesting think of all the millions of +people who spent money and time just to + + align:start position:0% +people who spent money and time just to + + + align:start position:0% +people who spent money and time just to +go see the Taj Maha well that's what + + align:start position:0% +go see the Taj Maha well that's what + + + align:start position:0% +go see the Taj Maha well that's what +civilization is like it's without + + align:start position:0% +civilization is like it's without + + + align:start position:0% +civilization is like it's without +imagination and without the + + align:start position:0% +imagination and without the + + + align:start position:0% +imagination and without the +erotic uh it wouldn't it wouldn't + + align:start position:0% +erotic uh it wouldn't it wouldn't + + + align:start position:0% +erotic uh it wouldn't it wouldn't +occur Sor I just I feel like there's so + + align:start position:0% +occur Sor I just I feel like there's so + + + align:start position:0% +occur Sor I just I feel like there's so +much more to civilization though than + + align:start position:0% +much more to civilization though than + + + align:start position:0% +much more to civilization though than +just those things so + + align:start position:0% +just those things so + + + align:start position:0% +just those things so +I just don't think that statement can + + align:start position:0% +I just don't think that statement can + + + align:start position:0% +I just don't think that statement can +really be the the U the graffiti the + + align:start position:0% +really be the the U the graffiti the + + + align:start position:0% +really be the the U the graffiti the +graffiti are a kind of uh vulgarization + + align:start position:0% +graffiti are a kind of uh vulgarization + + + align:start position:0% +graffiti are a kind of uh vulgarization +of civilization and they do it out in + + align:start position:0% +of civilization and they do it out in + + + align:start position:0% +of civilization and they do it out in +public they do it so everybody will see + + align:start position:0% +public they do it so everybody will see + + + align:start position:0% +public they do it so everybody will see +or the uh subway cars which uh used to + + align:start position:0% +or the uh subway cars which uh used to + + + align:start position:0% +or the uh subway cars which uh used to +in New York in particular and you don't + + align:start position:0% +in New York in particular and you don't + + + align:start position:0% +in New York in particular and you don't +see it so often nowadays but you've + + align:start position:0% +see it so often nowadays but you've + + + align:start position:0% +see it so often nowadays but you've +probably seen in the movies or heard of + + align:start position:0% +probably seen in the movies or heard of + + + align:start position:0% +probably seen in the movies or heard of +it the cars covered with graffiti well + + align:start position:0% +it the cars covered with graffiti well + + + align:start position:0% +it the cars covered with graffiti well +those graffiti are a kind of calligraphy + + align:start position:0% +those graffiti are a kind of calligraphy + + + align:start position:0% +those graffiti are a kind of calligraphy +very + + align:start position:0% +very + + + align:start position:0% +very +curved uh elaborate + + align:start position:0% +curved uh elaborate + + + align:start position:0% +curved uh elaborate +designs uh possibly with the initials of + + align:start position:0% +designs uh possibly with the initials of + + + align:start position:0% +designs uh possibly with the initials of +people that they know but nobody else + + align:start position:0% +people that they know but nobody else + + + align:start position:0% +people that they know but nobody else +could know uh it's and they do it as a + + align:start position:0% +could know uh it's and they do it as a + + + align:start position:0% +could know uh it's and they do it as a +kind of expression of their feelings or + + align:start position:0% +kind of expression of their feelings or + + + align:start position:0% +kind of expression of their feelings or +their love or even maybe the love of + + align:start position:0% +their love or even maybe the love of + + + align:start position:0% +their love or even maybe the love of +their life in New York for all to see + + align:start position:0% +their life in New York for all to see + + + align:start position:0% +their life in New York for all to see +well that's it may be varization but + + align:start position:0% +well that's it may be varization but + + + align:start position:0% +well that's it may be varization but +it's still a vulgarization of + + align:start position:0% +it's still a vulgarization of + + + align:start position:0% +it's still a vulgarization of +civilization civilization progresses + + align:start position:0% +civilization civilization progresses + + + align:start position:0% +civilization civilization progresses +that way and the parts that we cherish + + align:start position:0% +that way and the parts that we cherish + + + align:start position:0% +that way and the parts that we cherish +as great works of art um usually come + + align:start position:0% +as great works of art um usually come + + + align:start position:0% +as great works of art um usually come +out of + + align:start position:0% +out of + + + align:start position:0% +out of +that the way the way I inter it is I + + align:start position:0% +that the way the way I inter it is I + + + align:start position:0% +that the way the way I inter it is I +mean not so much civilization like you + + align:start position:0% +mean not so much civilization like you + + + align:start position:0% +mean not so much civilization like you +know organized government but it gives + + align:start position:0% +know organized government but it gives + + + align:start position:0% +know organized government but it gives +to culture and uh aesthetic Beauty which + + align:start position:0% +to culture and uh aesthetic Beauty which + + + align:start position:0% +to culture and uh aesthetic Beauty which +is essentially civilization in quotes + + align:start position:0% +is essentially civilization in quotes + + + align:start position:0% +is essentially civilization in quotes +like if there wasn't the era the ironic + + align:start position:0% +like if there wasn't the era the ironic + + + align:start position:0% +like if there wasn't the era the ironic +everything would just be very cold and + + align:start position:0% +everything would just be very cold and + + + align:start position:0% +everything would just be very cold and +there would be no aesthetic Beauty + + align:start position:0% +there would be no aesthetic Beauty + + + align:start position:0% +there would be no aesthetic Beauty +everybody would just be you know a the + + align:start position:0% +everybody would just be you know a the + + + align:start position:0% +everybody would just be you know a the +way I picture it at Le it would just be + + align:start position:0% +way I picture it at Le it would just be + + + align:start position:0% +way I picture it at Le it would just be +a robot just you know doing stuff and + + align:start position:0% +a robot just you know doing stuff and + + + align:start position:0% +a robot just you know doing stuff and +there would be no pleasure or art or any + + align:start position:0% +there would be no pleasure or art or any + + + align:start position:0% +there would be no pleasure or art or any +sorts of expression of human feeling + + align:start position:0% +sorts of expression of human feeling + + + align:start position:0% +sorts of expression of human feeling +that's what how I see me you're going to + + align:start position:0% +that's what how I see me you're going to + + + align:start position:0% +that's what how I see me you're going to +be reading + + align:start position:0% +be reading + + + align:start position:0% +be reading +about certain aspect of Freud's + + align:start position:0% +about certain aspect of Freud's + + + align:start position:0% +about certain aspect of Freud's +Philosophy for next time + + align:start position:0% +Philosophy for next time + + + align:start position:0% +Philosophy for next time +and my criticism of it I don't think I + + align:start position:0% +and my criticism of it I don't think I + + + align:start position:0% +and my criticism of it I don't think I +go into this but sudden it curs me from + + align:start position:0% +go into this but sudden it curs me from + + + align:start position:0% +go into this but sudden it curs me from +what suatu was saying that this it's + + align:start position:0% +what suatu was saying that this it's + + + align:start position:0% +what suatu was saying that this it's +worth telling you about it Freud wrote a + + align:start position:0% +worth telling you about it Freud wrote a + + + align:start position:0% +worth telling you about it Freud wrote a +couple of articles on + + align:start position:0% +couple of articles on + + + align:start position:0% +couple of articles on +Aesthetics except there the psychology + + align:start position:0% +Aesthetics except there the psychology + + + align:start position:0% +Aesthetics except there the psychology +of + + align:start position:0% +of + + + align:start position:0% +of +art uh and um he apologizes as I'm not a + + align:start position:0% +art uh and um he apologizes as I'm not a + + + align:start position:0% +art uh and um he apologizes as I'm not a +Phil excuse me I'm not a philosopher I'm + + align:start position:0% +Phil excuse me I'm not a philosopher I'm + + + align:start position:0% +Phil excuse me I'm not a philosopher I'm +just a psychologist but I have ideas + + align:start position:0% +just a psychologist but I have ideas + + + align:start position:0% +just a psychologist but I have ideas +about the psych olical development that + + align:start position:0% +about the psych olical development that + + + align:start position:0% +about the psych olical development that +goes into the being of art so he starts + + align:start position:0% +goes into the being of art so he starts + + + align:start position:0% +goes into the being of art so he starts +out with the fact that the artist is a + + align:start position:0% +out with the fact that the artist is a + + + align:start position:0% +out with the fact that the artist is a +biological entity like everyone else and + + align:start position:0% +biological entity like everyone else and + + + align:start position:0% +biological entity like everyone else and +that um he wants and it's always from + + align:start position:0% +that um he wants and it's always from + + + align:start position:0% +that um he wants and it's always from +the man's point of view that's what + + align:start position:0% +the man's point of view that's what + + + align:start position:0% +the man's point of view that's what +Freud is like uh he wants what everybody + + align:start position:0% +Freud is like uh he wants what everybody + + + align:start position:0% +Freud is like uh he wants what everybody +wants what is it that everybody wants + + align:start position:0% +wants what is it that everybody wants + + + align:start position:0% +wants what is it that everybody wants +they're all men what is it all men want + + align:start position:0% +they're all men what is it all men want + + + align:start position:0% +they're all men what is it all men want +they want money they want Power they + + align:start position:0% +they want money they want Power they + + + align:start position:0% +they want money they want Power they +want the love of + + align:start position:0% +want the love of + + + align:start position:0% +want the love of +women money power and the love of women + + align:start position:0% +women money power and the love of women + + + align:start position:0% +women money power and the love of women +right + + align:start position:0% +right + + + align:start position:0% +right +um the + + align:start position:0% +um the + + + align:start position:0% +um the +artist Freud says is you usually + + align:start position:0% +artist Freud says is you usually + + + align:start position:0% +artist Freud says is you usually +somebody who has a + + align:start position:0% +somebody who has a + + + align:start position:0% +somebody who has a +defect most people if you want money you + + align:start position:0% +defect most people if you want money you + + + align:start position:0% +defect most people if you want money you +want Power uh you go to school you + + align:start position:0% +want Power uh you go to school you + + + align:start position:0% +want Power uh you go to school you +become an accountant uh you work your + + align:start position:0% +become an accountant uh you work your + + + align:start position:0% +become an accountant uh you work your +way up up the hierarchy of the business + + align:start position:0% +way up up the hierarchy of the business + + + align:start position:0% +way up up the hierarchy of the business +and then you end up being the CEO and + + align:start position:0% +and then you end up being the CEO and + + + align:start position:0% +and then you end up being the CEO and +you got more money than you know what to + + align:start position:0% +you got more money than you know what to + + + align:start position:0% +you got more money than you know what to +do with lots of power and the love of + + align:start position:0% +do with lots of power and the love of + + + align:start position:0% +do with lots of power and the love of +women they the women flock around those + + align:start position:0% +women they the women flock around those + + + align:start position:0% +women they the women flock around those +who have money and power that's the + + align:start position:0% +who have money and power that's the + + + align:start position:0% +who have money and power that's the +normal + + align:start position:0% +normal + + + align:start position:0% +normal +healthy ordinary way of going about + + align:start position:0% +healthy ordinary way of going about + + + align:start position:0% +healthy ordinary way of going about +things according to Freud but uh if + + align:start position:0% +things according to Freud but uh if + + + align:start position:0% +things according to Freud but uh if +you're a little different for whatever + + align:start position:0% +you're a little different for whatever + + + align:start position:0% +you're a little different for whatever +reason um you um just can't compete on + + align:start position:0% +reason um you um just can't compete on + + + align:start position:0% +reason um you um just can't compete on +that level + + align:start position:0% +that level + + + align:start position:0% +that level +but if you are not and if you can't + + align:start position:0% +but if you are not and if you can't + + + align:start position:0% +but if you are not and if you can't +compete and that's the end of it then + + align:start position:0% +compete and that's the end of it then + + + align:start position:0% +compete and that's the end of it then +you're Misfit or you become sick or or a + + align:start position:0% +you're Misfit or you become sick or or a + + + align:start position:0% +you're Misfit or you become sick or or a +loser in life if however you're not + + align:start position:0% +loser in life if however you're not + + + align:start position:0% +loser in life if however you're not +only different in that respect but also + + align:start position:0% +only different in that respect but also + + + align:start position:0% +only different in that respect but also +you can do something that no one else + + align:start position:0% +you can do something that no one else + + + align:start position:0% +you can do something that no one else +can do you have a knack for instance for + + align:start position:0% +can do you have a knack for instance for + + + align:start position:0% +can do you have a knack for instance for +drawing for instance or you have perfect + + align:start position:0% +drawing for instance or you have perfect + + + align:start position:0% +drawing for instance or you have perfect +pitch or you have uh a certain kind of + + align:start position:0% +pitch or you have uh a certain kind of + + + align:start position:0% +pitch or you have uh a certain kind of +Acuity in your body I suppose this could + + align:start position:0% +Acuity in your body I suppose this could + + + align:start position:0% +Acuity in your body I suppose this could +apply to the athlete as well but he's + + align:start position:0% +apply to the athlete as well but he's + + + align:start position:0% +apply to the athlete as well but he's +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +artists and if you then are recognize + + align:start position:0% +artists and if you then are recognize + + + align:start position:0% +artists and if you then are recognize +for that and it's developed in + + align:start position:0% +for that and it's developed in + + + align:start position:0% +for that and it's developed in +you then you start making things that + + align:start position:0% +you then you start making things that + + + align:start position:0% +you then you start making things that +nobody else can + + align:start position:0% +nobody else can + + + align:start position:0% +nobody else can +make right and if you do it well + + align:start position:0% +make right and if you do it well + + + align:start position:0% +make right and if you do it well +enough people will pay attention to what + + align:start position:0% +enough people will pay attention to what + + + align:start position:0% +enough people will pay attention to what +your you've done and they'll give you + + align:start position:0% +your you've done and they'll give you + + + align:start position:0% +your you've done and they'll give you +money and if you're a good enough artist + + align:start position:0% +money and if you're a good enough artist + + + align:start position:0% +money and if you're a good enough artist +like a Picasso you get so much money + + align:start position:0% +like a Picasso you get so much money + + + align:start position:0% +like a Picasso you get so much money +you'll have power with + + align:start position:0% +you'll have power with + + + align:start position:0% +you'll have power with +it and with the money and the power + + align:start position:0% +it and with the money and the power + + + align:start position:0% +it and with the money and the power +there'll be the women who will throw + + align:start position:0% +there'll be the women who will throw + + + align:start position:0% +there'll be the women who will throw +themselves at your feet the way they did + + align:start position:0% +themselves at your feet the way they did + + + align:start position:0% +themselves at your feet the way they did +with great artists for instance in in + + align:start position:0% +with great artists for instance in in + + + align:start position:0% +with great artists for instance in in +the 19th century uh list and chopan + + align:start position:0% +the 19th century uh list and chopan + + + align:start position:0% +the 19th century uh list and chopan +other Heroes because they were such uh + + align:start position:0% +other Heroes because they were such uh + + + align:start position:0% +other Heroes because they were such uh +great + + align:start position:0% +great + + + align:start position:0% +great +musicians uh and even nowadays there are + + align:start position:0% +musicians uh and even nowadays there are + + + align:start position:0% +musicians uh and even nowadays there are +the rock singers that women Swoon over + + align:start position:0% +the rock singers that women Swoon over + + + align:start position:0% +the rock singers that women Swoon over +uh there are uh the musical Stars + + align:start position:0% +uh there are uh the musical Stars + + + align:start position:0% +uh there are uh the musical Stars +they're not similar to the ones in the + + align:start position:0% +they're not similar to the ones in the + + + align:start position:0% +they're not similar to the ones in the +20th century but they can have all the + + align:start position:0% +20th century but they can have all the + + + align:start position:0% +20th century but they can have all the +groupies and all the all the apperences + + align:start position:0% +groupies and all the all the apperences + + + align:start position:0% +groupies and all the all the apperences +of great wealth and + + align:start position:0% +of great wealth and + + + align:start position:0% +of great wealth and +power Freud Freud's solution is that + + align:start position:0% +power Freud Freud's solution is that + + + align:start position:0% +power Freud Freud's solution is that +what the artist can't get directly he + + align:start position:0% +what the artist can't get directly he + + + align:start position:0% +what the artist can't get directly he +gets + + align:start position:0% +gets + + + align:start position:0% +gets +indirectly that is he can't go up + + align:start position:0% +indirectly that is he can't go up + + + align:start position:0% +indirectly that is he can't go up +through the ladder of business but he + + align:start position:0% +through the ladder of business but he + + + align:start position:0% +through the ladder of business but he +gets it indirectly because by pursuing + + align:start position:0% +gets it indirectly because by pursuing + + + align:start position:0% +gets it indirectly because by pursuing +his Knack he creates things for which + + align:start position:0% +his Knack he creates things for which + + + align:start position:0% +his Knack he creates things for which +people will reward + + align:start position:0% +people will reward + + + align:start position:0% +people will reward +him um now the + + align:start position:0% +him um now the + + + align:start position:0% +him um now the +reason this this um is related to what + + align:start position:0% +reason this this um is related to what + + + align:start position:0% +reason this this um is related to what +stus was saying I think is because + + align:start position:0% +stus was saying I think is because + + + align:start position:0% +stus was saying I think is because +there's always this lust or love that + + align:start position:0% +there's always this lust or love that + + + align:start position:0% +there's always this lust or love that +Freud is talking about the Love of Money + + align:start position:0% +Freud is talking about the Love of Money + + + align:start position:0% +Freud is talking about the Love of Money +the love of power the love of women and + + align:start position:0% +the love of power the love of women and + + + align:start position:0% +the love of power the love of women and +if you can't get it + + align:start position:0% +if you can't get it + + + align:start position:0% +if you can't get it +directly you can you might get it + + align:start position:0% +directly you can you might get it + + + align:start position:0% +directly you can you might get it +indirectly but those are the people who + + align:start position:0% +indirectly but those are the people who + + + align:start position:0% +indirectly but those are the people who +create civilization + + align:start position:0% +create civilization + + + align:start position:0% +create civilization +civilization itself on Freud's view is + + align:start position:0% +civilization itself on Freud's view is + + + align:start position:0% +civilization itself on Freud's view is +an indirect accumulation of the love + + align:start position:0% +an indirect accumulation of the love + + + align:start position:0% +an indirect accumulation of the love +that everybody wants there's a book of + + align:start position:0% +that everybody wants there's a book of + + + align:start position:0% +that everybody wants there's a book of +his called one of his I think great + + align:start position:0% +his called one of his I think great + + + align:start position:0% +his called one of his I think great +books that everybody should be forced to + + align:start position:0% +books that everybody should be forced to + + + align:start position:0% +books that everybody should be forced to +read before graduating from college like + + align:start position:0% +read before graduating from college like + + + align:start position:0% +read before graduating from college like +the Republic everyone should be reading + + align:start position:0% +the Republic everyone should be reading + + + align:start position:0% +the Republic everyone should be reading +and that is civilization and its + + align:start position:0% +and that is civilization and its + + + align:start position:0% +and that is civilization and its +discontents I strongly recommend it you + + align:start position:0% +discontents I strongly recommend it you + + + align:start position:0% +discontents I strongly recommend it you +it's only about 800 pages long and in it + + align:start position:0% +it's only about 800 pages long and in it + + + align:start position:0% +it's only about 800 pages long and in it +he says that + + align:start position:0% +he says that + + + align:start position:0% +he says that +Civilization uh arises out out of the + + align:start position:0% +Civilization uh arises out out of the + + + align:start position:0% +Civilization uh arises out out of the +love of beauty but then uh it separates + + align:start position:0% +love of beauty but then uh it separates + + + align:start position:0% +love of beauty but then uh it separates +one from the satisfaction the in love + + align:start position:0% +one from the satisfaction the in love + + + align:start position:0% +one from the satisfaction the in love +and sex that one really wants so there's + + align:start position:0% +and sex that one really wants so there's + + + align:start position:0% +and sex that one really wants so there's +a conflict between civilization and + + align:start position:0% +a conflict between civilization and + + + align:start position:0% +a conflict between civilization and +sexuality that's the issue that Freud + + align:start position:0% +sexuality that's the issue that Freud + + + align:start position:0% +sexuality that's the issue that Freud +talks about I don't agree with the the + + align:start position:0% +talks about I don't agree with the the + + + align:start position:0% +talks about I don't agree with the the +basic argument but that doesn't matter + + align:start position:0% +basic argument but that doesn't matter + + + align:start position:0% +basic argument but that doesn't matter +uh my point is that whatever the outcome + + align:start position:0% +uh my point is that whatever the outcome + + + align:start position:0% +uh my point is that whatever the outcome +of civilization is it originates in a + + align:start position:0% +of civilization is it originates in a + + + align:start position:0% +of civilization is it originates in a +kind of love and that's what I try to + + align:start position:0% +kind of love and that's what I try to + + + align:start position:0% +kind of love and that's what I try to +explain through the erotic and through + + align:start position:0% +explain through the erotic and through + + + align:start position:0% +explain through the erotic and through +the idea of the imagination so that's + + align:start position:0% +the idea of the imagination so that's + + + align:start position:0% +the idea of the imagination so that's +where that comes + + align:start position:0% +where that comes + + + align:start position:0% +where that comes +in okay um it's must be getting on yeah + + align:start position:0% +in okay um it's must be getting on yeah + + + align:start position:0% +in okay um it's must be getting on yeah +it is should we take a break now or + + align:start position:0% +it is should we take a break now or + + + align:start position:0% +it is should we take a break now or +should we talk about the romantic + + align:start position:0% + + + + align:start position:0% + +we can talk about the what do you tell + + align:start position:0% +we can talk about the what do you tell + + + align:start position:0% +we can talk about the what do you tell +me what does class want do you want to + + align:start position:0% +me what does class want do you want to + + + align:start position:0% +me what does class want do you want to +take a break you want to talk about the + + align:start position:0% +take a break you want to talk about the + + + align:start position:0% +take a break you want to talk about the +Romantic all right let's go on to the + + align:start position:0% +Romantic all right let's go on to the + + + align:start position:0% +Romantic all right let's go on to the +Romantic there is Lial derotic in the + + align:start position:0% +Romantic there is Lial derotic in the + + + align:start position:0% +Romantic there is Lial derotic in the +Romantic the Romantic the way I perceive + + align:start position:0% +Romantic the Romantic the way I perceive + + + align:start position:0% +Romantic the Romantic the way I perceive +the Romantic is + + align:start position:0% +the Romantic is + + + align:start position:0% +the Romantic is +the it is what unifies the libidinal + + align:start position:0% +the it is what unifies the libidinal + + + align:start position:0% +the it is what unifies the libidinal +with the + + align:start position:0% +with the + + + align:start position:0% +with the +erotic but it also needs a sense of uh + + align:start position:0% +erotic but it also needs a sense of uh + + + align:start position:0% +erotic but it also needs a sense of uh +uh of + + align:start position:0% +uh of + + + align:start position:0% +uh of +Perpetual um of continuous love um and + + align:start position:0% +Perpetual um of continuous love um and + + + align:start position:0% +Perpetual um of continuous love um and +here give the example of of the Moon the + + align:start position:0% +here give the example of of the Moon the + + + align:start position:0% +here give the example of of the Moon the +Moon cycle and how um the lovers + + align:start position:0% +Moon cycle and how um the lovers + + + align:start position:0% +Moon cycle and how um the lovers +identify that the moon cycle and the + + align:start position:0% +identify that the moon cycle and the + + + align:start position:0% +identify that the moon cycle and the +appearance of the Moon with something + + align:start position:0% +appearance of the Moon with something + + + align:start position:0% +appearance of the Moon with something +that is constant and that they want to + + align:start position:0% +that is constant and that they want to + + + align:start position:0% +that is constant and that they want to +associate with their love okay does + + align:start position:0% +associate with their love okay does + + + align:start position:0% +associate with their love okay does +anyone else want to say anything about + + align:start position:0% +anyone else want to say anything about + + + align:start position:0% +anyone else want to say anything about +romantic I think Veronica was talking + + align:start position:0% +romantic I think Veronica was talking + + + align:start position:0% +romantic I think Veronica was talking +about the Romantic last time when you + + align:start position:0% +about the Romantic last time when you + + + align:start position:0% +about the Romantic last time when you +were talking about falling in + + align:start position:0% +were talking about falling in + + + align:start position:0% +were talking about falling in +love uh there are two principles that + + align:start position:0% +love uh there are two principles that + + + align:start position:0% +love uh there are two principles that +seem to me to be definitive for the + + align:start position:0% +seem to me to be definitive for the + + + align:start position:0% +seem to me to be definitive for the +Romantic one is this the well before I + + align:start position:0% +Romantic one is this the well before I + + + align:start position:0% +Romantic one is this the well before I +get to that um the one and only there's + + align:start position:0% +get to that um the one and only there's + + + align:start position:0% +get to that um the one and only there's +only it isn't something you can + + align:start position:0% +only it isn't something you can + + + align:start position:0% +only it isn't something you can +have with everybody at least not at the + + align:start position:0% +have with everybody at least not at the + + + align:start position:0% +have with everybody at least not at the +same time uh it's having an attachment + + align:start position:0% +same time uh it's having an attachment + + + align:start position:0% +same time uh it's having an attachment +to at least or let's say to one other + + align:start position:0% +to at least or let's say to one other + + + align:start position:0% +to at least or let's say to one other +person and the second principle is to + + align:start position:0% +person and the second principle is to + + + align:start position:0% +person and the second principle is to +have having that intimate relationship + + align:start position:0% +have having that intimate relationship + + + align:start position:0% +have having that intimate relationship +forever so the the idea of forever or as + + align:start position:0% +forever so the the idea of forever or as + + + align:start position:0% +forever so the the idea of forever or as +the religions say or The Poets say + + align:start position:0% +the religions say or The Poets say + + + align:start position:0% +the religions say or The Poets say +eternity whatever that means right um is + + align:start position:0% +eternity whatever that means right um is + + + align:start position:0% +eternity whatever that means right um is +built into the idea of the Romantic and + + align:start position:0% +built into the idea of the Romantic and + + + align:start position:0% +built into the idea of the Romantic and +also that there's something unique in + + align:start position:0% +also that there's something unique in + + + align:start position:0% +also that there's something unique in +the attachment into one and only + + align:start position:0% +the attachment into one and only + + + align:start position:0% +the attachment into one and only +person now this is also very enormous + + align:start position:0% +person now this is also very enormous + + + align:start position:0% +person now this is also very enormous +net because um why + + align:start position:0% +net because um why + + + align:start position:0% +net because um why +one I've thought an awful lot about that + + align:start position:0% +one I've thought an awful lot about that + + + align:start position:0% +one I've thought an awful lot about that +and it occurs to me that if you can find + + align:start position:0% +and it occurs to me that if you can find + + + align:start position:0% +and it occurs to me that if you can find +just + + align:start position:0% +just + + + align:start position:0% +just +one who really would be totally + + align:start position:0% +one who really would be totally + + + align:start position:0% +one who really would be totally +satisfying whom you can love as much as + + align:start position:0% +satisfying whom you can love as much as + + + align:start position:0% +satisfying whom you can love as much as +you're capable and who can love you as + + align:start position:0% +you're capable and who can love you as + + + align:start position:0% +you're capable and who can love you as +much as you're capable + + align:start position:0% +much as you're capable + + + align:start position:0% +much as you're capable +I think you wouldn't feel the need for + + align:start position:0% +I think you wouldn't feel the need for + + + align:start position:0% +I think you wouldn't feel the need for +anything + + align:start position:0% +anything + + + align:start position:0% +anything +more this was tested in the 1960s by the + + align:start position:0% +more this was tested in the 1960s by the + + + align:start position:0% +more this was tested in the 1960s by the +communes in which uh there would be um + + align:start position:0% +communes in which uh there would be um + + + align:start position:0% +communes in which uh there would be um +sharing of uh bed bed fellows + + align:start position:0% +sharing of uh bed bed fellows + + + align:start position:0% +sharing of uh bed bed fellows +of wife swapping but also with people + + align:start position:0% +of wife swapping but also with people + + + align:start position:0% +of wife swapping but also with people +who weren't married the idea that why be + + align:start position:0% +who weren't married the idea that why be + + + align:start position:0% +who weren't married the idea that why be +exclusive well I think most human beings + + align:start position:0% +exclusive well I think most human beings + + + align:start position:0% +exclusive well I think most human beings +at least seem to + + align:start position:0% +at least seem to + + + align:start position:0% +at least seem to +feel that one is + + align:start position:0% +feel that one is + + + align:start position:0% +feel that one is +enough because if it's done if it's an + + align:start position:0% +enough because if it's done if it's an + + + align:start position:0% +enough because if it's done if it's an +adequate one it'll satisfy all your + + align:start position:0% +adequate one it'll satisfy all your + + + align:start position:0% +adequate one it'll satisfy all your +needs and with democracy as I think I + + align:start position:0% +needs and with democracy as I think I + + + align:start position:0% +needs and with democracy as I think I +mentioned that there's a kind of + + align:start position:0% +mentioned that there's a kind of + + + align:start position:0% +mentioned that there's a kind of +democratization of love where one other + + align:start position:0% +democratization of love where one other + + + align:start position:0% +democratization of love where one other +person uh is expected to do everything + + align:start position:0% +person uh is expected to do everything + + + align:start position:0% +person uh is expected to do everything +it's a what do you call um an all uh + + align:start position:0% +it's a what do you call um an all uh + + + align:start position:0% +it's a what do you call um an all uh +what is it all all purpose an allpurpose + + align:start position:0% +what is it all all purpose an allpurpose + + + align:start position:0% +what is it all all purpose an allpurpose +solution to Life's problems + + align:start position:0% +solution to Life's problems + + + align:start position:0% +solution to Life's problems +um now as a matter of fact it it may be + + align:start position:0% +um now as a matter of fact it it may be + + + align:start position:0% +um now as a matter of fact it it may be +hard to Hope ever to find any one person + + align:start position:0% +hard to Hope ever to find any one person + + + align:start position:0% +hard to Hope ever to find any one person +who can do all of that and in in in a + + align:start position:0% +who can do all of that and in in in a + + + align:start position:0% +who can do all of that and in in in a +way that is not inconsistent with that + + align:start position:0% +way that is not inconsistent with that + + + align:start position:0% +way that is not inconsistent with that +most I think probably statistically most + + align:start position:0% +most I think probably statistically most + + + align:start position:0% +most I think probably statistically most +people have um sought for love with more + + align:start position:0% +people have um sought for love with more + + + align:start position:0% +people have um sought for love with more +than one other person one other partner + + align:start position:0% +than one other person one other partner + + + align:start position:0% +than one other person one other partner +whole cultures are built up out of the + + align:start position:0% +whole cultures are built up out of the + + + align:start position:0% +whole cultures are built up out of the +idea of polygamy for the men or polygyny + + align:start position:0% +idea of polygamy for the men or polygyny + + + align:start position:0% +idea of polygamy for the men or polygyny +even not too many but some for women + + align:start position:0% +even not too many but some for women + + + align:start position:0% +even not too many but some for women +that is men have polygamy is men having + + align:start position:0% +that is men have polygamy is men having + + + align:start position:0% +that is men have polygamy is men having +many wives women having many husbands or + + align:start position:0% +many wives women having many husbands or + + + align:start position:0% +many wives women having many husbands or +in monogamous + + align:start position:0% +in monogamous + + + align:start position:0% +in monogamous +societies um that um a man will have two + + align:start position:0% +societies um that um a man will have two + + + align:start position:0% +societies um that um a man will have two +establishments one for his wife and + + align:start position:0% +establishments one for his wife and + + + align:start position:0% +establishments one for his wife and +another for his mistress in France in + + align:start position:0% +another for his mistress in France in + + + align:start position:0% +another for his mistress in France in +the 19th and probably still in many ways + + align:start position:0% +the 19th and probably still in many ways + + + align:start position:0% +the 19th and probably still in many ways +it was common place that uh you would + + align:start position:0% +it was common place that uh you would + + + align:start position:0% +it was common place that uh you would +marry the right woman but then you would + + align:start position:0% +marry the right woman but then you would + + + align:start position:0% +marry the right woman but then you would +also satisfy your sexual needs with some + + align:start position:0% +also satisfy your sexual needs with some + + + align:start position:0% +also satisfy your sexual needs with some +other woman even having a second family + + align:start position:0% +other woman even having a second family + + + align:start position:0% +other woman even having a second family +and even sometimes with a wife knowing + + align:start position:0% +and even sometimes with a wife knowing + + + align:start position:0% +and even sometimes with a wife knowing +about it in other words adultery was + + align:start position:0% +about it in other words adultery was + + + align:start position:0% +about it in other words adultery was +built into the matrimonial system but + + align:start position:0% +built into the matrimonial system but + + + align:start position:0% +built into the matrimonial system but +whether or not it's that rigorously + + align:start position:0% +whether or not it's that rigorously + + + align:start position:0% +whether or not it's that rigorously +organized uh adultery is not uncommon uh + + align:start position:0% +organized uh adultery is not uncommon uh + + + align:start position:0% +organized uh adultery is not uncommon uh +and even if men don't indulge and are + + align:start position:0% +and even if men don't indulge and are + + + align:start position:0% +and even if men don't indulge and are +faithful to their wives there is the + + align:start position:0% +faithful to their wives there is the + + + align:start position:0% +faithful to their wives there is the +tradition um embodied in the saying I + + align:start position:0% +tradition um embodied in the saying I + + + align:start position:0% +tradition um embodied in the saying I +love my wife but oh you kid you know + + align:start position:0% +love my wife but oh you kid you know + + + align:start position:0% +love my wife but oh you kid you know +that you the night that comes from the + + align:start position:0% +that you the night that comes from the + + + align:start position:0% +that you the night that comes from the +1920s I loved my wife but oh you kid + + align:start position:0% +1920s I loved my wife but oh you kid + + + align:start position:0% +1920s I loved my wife but oh you kid +meaning there's a part of me that would + + align:start position:0% +meaning there's a part of me that would + + + align:start position:0% +meaning there's a part of me that would +like to indulge itself with you sexually + + align:start position:0% +like to indulge itself with you sexually + + + align:start position:0% +like to indulge itself with you sexually +um prostitute or girlfriend or a + + align:start position:0% +um prostitute or girlfriend or a + + + align:start position:0% +um prostitute or girlfriend or a +mistress or some beautiful woman I'm + + align:start position:0% +mistress or some beautiful woman I'm + + + align:start position:0% +mistress or some beautiful woman I'm +talking again it's always from the man's + + align:start position:0% +talking again it's always from the man's + + + align:start position:0% +talking again it's always from the man's +point of view um or the woman too you + + align:start position:0% +point of view um or the woman too you + + + align:start position:0% +point of view um or the woman too you +know I love my husband but there are all + + align:start position:0% +know I love my husband but there are all + + + align:start position:0% +know I love my husband but there are all +these beautiful boys lying around uh + + align:start position:0% +these beautiful boys lying around uh + + + align:start position:0% +these beautiful boys lying around uh +there is that sentiment which is very + + align:start position:0% +there is that sentiment which is very + + + align:start position:0% +there is that sentiment which is very +common so why does it have to be one and + + align:start position:0% +common so why does it have to be one and + + + align:start position:0% +common so why does it have to be one and +only well if you can find just one and + + align:start position:0% +only well if you can find just one and + + + align:start position:0% +only well if you can find just one and +it's perfect just right you you know for + + align:start position:0% +it's perfect just right you you know for + + + align:start position:0% +it's perfect just right you you know for +most people that might be enough also it + + align:start position:0% +most people that might be enough also it + + + align:start position:0% +most people that might be enough also it +gets to be a question of economics how + + align:start position:0% +gets to be a question of economics how + + + align:start position:0% +gets to be a question of economics how +many households can you support and how + + align:start position:0% +many households can you support and how + + + align:start position:0% +many households can you support and how +do you keep the wives from getting + + align:start position:0% +do you keep the wives from getting + + + align:start position:0% +do you keep the wives from getting +jealous jealousy is a very important + + align:start position:0% +jealous jealousy is a very important + + + align:start position:0% +jealous jealousy is a very important +phenomenon uh some people even try to + + align:start position:0% +phenomenon uh some people even try to + + + align:start position:0% +phenomenon uh some people even try to +Define love in terms of jealousy about + + align:start position:0% +Define love in terms of jealousy about + + + align:start position:0% +Define love in terms of jealousy about +competitors but if then if they're going + + align:start position:0% +competitors but if then if they're going + + + align:start position:0% +competitors but if then if they're going +to be jealous then the this multiple + + align:start position:0% +to be jealous then the this multiple + + + align:start position:0% +to be jealous then the this multiple +kind of arrangement isn't going to be a + + align:start position:0% +kind of arrangement isn't going to be a + + + align:start position:0% +kind of arrangement isn't going to be a +very happy one but that I + + align:start position:0% +very happy one but that I + + + align:start position:0% +very happy one but that I +think was part of what was going on in + + align:start position:0% +think was part of what was going on in + + + align:start position:0% +think was part of what was going on in +the 19th and 20th Century concepts of + + align:start position:0% +the 19th and 20th Century concepts of + + + align:start position:0% +the 19th and 20th Century concepts of +romantic love with the capital r right + + align:start position:0% +romantic love with the capital r right + + + align:start position:0% +romantic love with the capital r right +the + + align:start position:0% +the + + + align:start position:0% +the +Romantic the other princip + + align:start position:0% +Romantic the other princip + + + align:start position:0% +Romantic the other princip +of um + + align:start position:0% +of um + + + align:start position:0% +of um +perpetuity uh is explained by the fact + + align:start position:0% +perpetuity uh is explained by the fact + + + align:start position:0% +perpetuity uh is explained by the fact +that um you don't want to put in all the + + align:start position:0% +that um you don't want to put in all the + + + align:start position:0% +that um you don't want to put in all the +energy with somebody who's going to + + align:start position:0% +energy with somebody who's going to + + + align:start position:0% +energy with somebody who's going to +ditch you the next day or who you know + + align:start position:0% +ditch you the next day or who you know + + + align:start position:0% +ditch you the next day or who you know +you're going to be tired + + align:start position:0% +you're going to be tired + + + align:start position:0% +you're going to be tired +of uh men in particular we also women + + align:start position:0% +of uh men in particular we also women + + + align:start position:0% +of uh men in particular we also women +are notoriously faithless this idea of + + align:start position:0% +are notoriously faithless this idea of + + + align:start position:0% +are notoriously faithless this idea of +being permanent you know I'll be I'll + + align:start position:0% +being permanent you know I'll be I'll + + + align:start position:0% +being permanent you know I'll be I'll +that well that's right I I'm um C the + + align:start position:0% +that well that's right I I'm um C the + + + align:start position:0% +that well that's right I I'm um C the +cold porter songer but I'm always true + + align:start position:0% +cold porter songer but I'm always true + + + align:start position:0% +cold porter songer but I'm always true +to you darling right that's the dream + + align:start position:0% +to you darling right that's the dream + + + align:start position:0% +to you darling right that's the dream +but uh because it's cold porter was very + + align:start position:0% +but uh because it's cold porter was very + + + align:start position:0% +but uh because it's cold porter was very +humorously cynical uh the next part of + + align:start position:0% +humorously cynical uh the next part of + + + align:start position:0% +humorously cynical uh the next part of +it + + align:start position:0% +it + + + align:start position:0% +it +is um do you know + + align:start position:0% +is um do you know + + + align:start position:0% +is um do you know +it I'm I will I'll I'll be I will always + + align:start position:0% +it I'm I will I'll I'll be I will always + + + align:start position:0% +it I'm I will I'll I'll be I will always +be true to you darling in my + + align:start position:0% +be true to you darling in my + + + align:start position:0% +be true to you darling in my +fashion right + + align:start position:0% +fashion right + + + align:start position:0% +fashion right +so that that that is an escape Clause + + align:start position:0% +so that that that is an escape Clause + + + align:start position:0% +so that that that is an escape Clause +enabling the the person to uh uh the + + align:start position:0% +enabling the the person to uh uh the + + + align:start position:0% +enabling the the person to uh uh the +woman in particular to find what she + + align:start position:0% +woman in particular to find what she + + + align:start position:0% +woman in particular to find what she +wants in love with other people but that + + align:start position:0% +wants in love with other people but that + + + align:start position:0% +wants in love with other people but that +is that's very common uh at the same + + align:start position:0% +is that's very common uh at the same + + + align:start position:0% +is that's very common uh at the same +time there's something beautiful about + + align:start position:0% +time there's something beautiful about + + + align:start position:0% +time there's something beautiful about +the + + align:start position:0% +the + + + align:start position:0% +the +Romantic in the purple rose of Cairo do + + align:start position:0% +Romantic in the purple rose of Cairo do + + + align:start position:0% +Romantic in the purple rose of Cairo do +you know that movie of Woody Woody Allen + + align:start position:0% +you know that movie of Woody Woody Allen + + + align:start position:0% +you know that movie of Woody Woody Allen +uh I'll be showing it tomorrow from 2: + + align:start position:0% +uh I'll be showing it tomorrow from 2: + + + align:start position:0% +uh I'll be showing it tomorrow from 2: +to 5: in my film course + + align:start position:0% +to 5: in my film course + + + align:start position:0% +to 5: in my film course +uh uh which is about philosophy of film + + align:start position:0% +uh uh which is about philosophy of film + + + align:start position:0% +uh uh which is about philosophy of film +um and what I just thought of there's a + + align:start position:0% +um and what I just thought of there's a + + + align:start position:0% +um and what I just thought of there's a +scene in which the perfect man the actor + + align:start position:0% +scene in which the perfect man the actor + + + align:start position:0% +scene in which the perfect man the actor +who comes off the out of the screen + + align:start position:0% +who comes off the out of the screen + + + align:start position:0% +who comes off the out of the screen +descends into the movie audience it's a + + align:start position:0% +descends into the movie audience it's a + + + align:start position:0% +descends into the movie audience it's a +fantasy and falls in love with Cecilia + + align:start position:0% +fantasy and falls in love with Cecilia + + + align:start position:0% +fantasy and falls in love with Cecilia +who's just a plain ordinary + + align:start position:0% +who's just a plain ordinary + + + align:start position:0% +who's just a plain ordinary +um married woman um and um declares his + + align:start position:0% +um married woman um and um declares his + + + align:start position:0% +um married woman um and um declares his +complete romantic love for her and he's + + align:start position:0% +complete romantic love for her and he's + + + align:start position:0% +complete romantic love for her and he's +he's pure he's absolutely innocent he + + align:start position:0% +he's pure he's absolutely innocent he + + + align:start position:0% +he's pure he's absolutely innocent he +really believes it he feels it uh at one + + align:start position:0% +really believes it he feels it uh at one + + + align:start position:0% +really believes it he feels it uh at one +point he's separated in This Strange New + + align:start position:0% +point he's separated in This Strange New + + + align:start position:0% +point he's separated in This Strange New +World off the screen um and ends up uh + + align:start position:0% +World off the screen um and ends up uh + + + align:start position:0% +World off the screen um and ends up uh +being accosted by a very pleasant woman + + align:start position:0% +being accosted by a very pleasant woman + + + align:start position:0% +being accosted by a very pleasant woman +who is a prostitute and says would you + + align:start position:0% +who is a prostitute and says would you + + + align:start position:0% +who is a prostitute and says would you +like to see where I work and he's always + + align:start position:0% +like to see where I work and he's always + + + align:start position:0% +like to see where I work and he's always +oh yes that's interesting I really like + + align:start position:0% +oh yes that's interesting I really like + + + align:start position:0% +oh yes that's interesting I really like +to see where you work you look like such + + align:start position:0% +to see where you work you look like such + + + align:start position:0% +to see where you work you look like such +a fine person and so they go to brothel + + align:start position:0% +a fine person and so they go to brothel + + + align:start position:0% +a fine person and so they go to brothel +and there he meets other other girls and + + align:start position:0% +and there he meets other other girls and + + + align:start position:0% +and there he meets other other girls and +they all try to entice him and he he + + align:start position:0% +they all try to entice him and he he + + + align:start position:0% +they all try to entice him and he he +doesn't respond he it's not in his + + align:start position:0% +doesn't respond he it's not in his + + + align:start position:0% +doesn't respond he it's not in his +character it's not the way he was made + + align:start position:0% +character it's not the way he was made + + + align:start position:0% +character it's not the way he was made +it was made in the movie um and uh they + + align:start position:0% +it was made in the movie um and uh they + + + align:start position:0% +it was made in the movie um and uh they +try to explain to + + align:start position:0% +try to explain to + + + align:start position:0% +try to explain to +him and he he finally sort of gets a + + align:start position:0% +him and he he finally sort of gets a + + + align:start position:0% +him and he he finally sort of gets a +rough idea and says oh well no I I have + + align:start position:0% +rough idea and says oh well no I I have + + + align:start position:0% +rough idea and says oh well no I I have +to tell you fine ladies + + align:start position:0% +to tell you fine ladies + + + align:start position:0% +to tell you fine ladies +um I I love + + align:start position:0% +um I I love + + + align:start position:0% +um I I love +Celia and uh I couldn't do what you're + + align:start position:0% +Celia and uh I couldn't do what you're + + + align:start position:0% +Celia and uh I couldn't do what you're +saying and they say oh well we're not + + align:start position:0% +saying and they say oh well we're not + + + align:start position:0% +saying and they say oh well we're not +talking about love you can love Celia + + align:start position:0% +talking about love you can love Celia + + + align:start position:0% +talking about love you can love Celia +we're talking about making + + align:start position:0% +we're talking about making + + + align:start position:0% +we're talking about making +love and then he does really seem to + + align:start position:0% +love and then he does really seem to + + + align:start position:0% +love and then he does really seem to +understand where he is and what what's + + align:start position:0% +understand where he is and what what's + + + align:start position:0% +understand where he is and what what's +at stake and he says oh you don't + + align:start position:0% +at stake and he says oh you don't + + + align:start position:0% +at stake and he says oh you don't +understand Celia is for me everything + + align:start position:0% +understand Celia is for me everything + + + align:start position:0% +understand Celia is for me everything +she is all that I've ever wanted she is + + align:start position:0% +she is all that I've ever wanted she is + + + align:start position:0% +she is all that I've ever wanted she is +for me Perfection I wouldn't want to do + + align:start position:0% +for me Perfection I wouldn't want to do + + + align:start position:0% +for me Perfection I wouldn't want to do +any of those things with anybody + + align:start position:0% +any of those things with anybody + + + align:start position:0% +any of those things with anybody +else and the scene ends when the + + align:start position:0% +else and the scene ends when the + + + align:start position:0% +else and the scene ends when the +first very likable young woman who's uh + + align:start position:0% +first very likable young woman who's uh + + + align:start position:0% +first very likable young woman who's uh +taking him there uh looks in amazement + + align:start position:0% +taking him there uh looks in amazement + + + align:start position:0% +taking him there uh looks in amazement +and + + align:start position:0% +and + + + align:start position:0% +and +says are there any other men out there + + align:start position:0% +says are there any other men out there + + + align:start position:0% +says are there any other men out there +like that + + align:start position:0% + + + + align:start position:0% + +it's a very funny Woody Allen movie and + + align:start position:0% +it's a very funny Woody Allen movie and + + + align:start position:0% +it's a very funny Woody Allen movie and +I think it's one of his very best uh + + align:start position:0% +I think it's one of his very best uh + + + align:start position:0% +I think it's one of his very best uh +well that I think that's the point uh to + + align:start position:0% +well that I think that's the point uh to + + + align:start position:0% +well that I think that's the point uh to +get somebody who will be perfect and who + + align:start position:0% +get somebody who will be perfect and who + + + align:start position:0% +get somebody who will be perfect and who +will with whom you will be perfectly + + align:start position:0% +will with whom you will be perfectly + + + align:start position:0% +will with whom you will be perfectly +alied May really be unrealizable but + + align:start position:0% +alied May really be unrealizable but + + + align:start position:0% +alied May really be unrealizable but +it's that's part of the Romantic that's + + align:start position:0% +it's that's part of the Romantic that's + + + align:start position:0% +it's that's part of the Romantic that's +why I tell that story dur I each to + + align:start position:0% +why I tell that story dur I each to + + + align:start position:0% +why I tell that story dur I each to +repeat + + align:start position:0% +repeat + + + align:start position:0% +repeat +it oh wait a minute this is a good point + + align:start position:0% +it oh wait a minute this is a good point + + + align:start position:0% +it oh wait a minute this is a good point +for me to close my eyes Adriana could + + align:start position:0% +for me to close my eyes Adriana could + + + align:start position:0% +for me to close my eyes Adriana could +you take a hedg count of how many have + + align:start position:0% +you take a hedg count of how many have + + + align:start position:0% +you take a hedg count of how many have +done today's reading yes sir but I'm not + + align:start position:0% +done today's reading yes sir but I'm not + + + align:start position:0% +done today's reading yes sir but I'm not +interested in names I just want to know + + align:start position:0% +interested in names I just want to know + + + align:start position:0% +interested in names I just want to know +how + + align:start position:0% + + + + align:start position:0% + +many + + align:start position:0% +many + + + align:start position:0% +many +okay seven can I open how many seven + + align:start position:0% +okay seven can I open how many seven + + + align:start position:0% +okay seven can I open how many seven +that's pretty good um then possibly + + align:start position:0% +that's pretty good um then possibly + + + align:start position:0% +that's pretty good um then possibly +remember the George S calman remark to + + align:start position:0% +remember the George S calman remark to + + + align:start position:0% +remember the George S calman remark to +Irving Berlin calman was very famous + + align:start position:0% +Irving Berlin calman was very famous + + + align:start position:0% +Irving Berlin calman was very famous +playright uh wrote the uh screenplays + + align:start position:0% +playright uh wrote the uh screenplays + + + align:start position:0% +playright uh wrote the uh screenplays +for Groucho Mark for the gr the the + + align:start position:0% +for Groucho Mark for the gr the the + + + align:start position:0% +for Groucho Mark for the gr the the +Mark's Brother movies and um various uh + + align:start position:0% +Mark's Brother movies and um various uh + + + align:start position:0% +Mark's Brother movies and um various uh +successes on Broadway he and Irving + + align:start position:0% +successes on Broadway he and Irving + + + align:start position:0% +successes on Broadway he and Irving +Berlin wrote the song always and I + + align:start position:0% +Berlin wrote the song always and I + + + align:start position:0% +Berlin wrote the song always and I +mentioned that but do you know what the + + align:start position:0% +mentioned that but do you know what the + + + align:start position:0% +mentioned that but do you know what the +song sounds like I'll be loving you + + align:start position:0% +song sounds like I'll be loving you + + + align:start position:0% +song sounds like I'll be loving you +always very sentimental romantic song + + align:start position:0% +always very sentimental romantic song + + + align:start position:0% +always very sentimental romantic song +with a love that's true + + align:start position:0% +with a love that's true + + + align:start position:0% +with a love that's true +always right all right the wit and cynic + + align:start position:0% +always right all right the wit and cynic + + + align:start position:0% +always right all right the wit and cynic +calman says Irving I think you should + + align:start position:0% +calman says Irving I think you should + + + align:start position:0% +calman says Irving I think you should +change that title or change that song + + align:start position:0% +change that title or change that song + + + align:start position:0% +change that title or change that song +you ought to make it I'll be loving you + + align:start position:0% +you ought to make it I'll be loving you + + + align:start position:0% +you ought to make it I'll be loving you +Thursday well it's funny because it + + align:start position:0% +Thursday well it's funny because it + + + align:start position:0% +Thursday well it's funny because it +wouldn't be + + align:start position:0% +wouldn't be + + + align:start position:0% +wouldn't be +romantic right okay anything else about + + align:start position:0% +romantic right okay anything else about + + + align:start position:0% +romantic right okay anything else about +the + + align:start position:0% +the + + + align:start position:0% +the +Romantic um well I wanted to mention how + + align:start position:0% +Romantic um well I wanted to mention how + + + align:start position:0% +Romantic um well I wanted to mention how +this Rel reles to uh the myth you + + align:start position:0% +this Rel reles to uh the myth you + + + align:start position:0% +this Rel reles to uh the myth you +mention uh I mean the the speech uh by + + align:start position:0% +mention uh I mean the the speech uh by + + + align:start position:0% +mention uh I mean the the speech uh by +Socrates and + + align:start position:0% +Socrates and + + + align:start position:0% +Socrates and +Aristotle's + + align:start position:0% +Aristotle's + + + align:start position:0% +Aristotle's +um + + align:start position:0% +um + + + align:start position:0% +um +um I forgot the + + align:start position:0% + + + + align:start position:0% + +name um well in any case um where uh + + align:start position:0% +name um well in any case um where uh + + + align:start position:0% +name um well in any case um where uh +Socrates is asked to Define what love is + + align:start position:0% +Socrates is asked to Define what love is + + + align:start position:0% +Socrates is asked to Define what love is +and he says that it is + + align:start position:0% +and he says that it is + + + align:start position:0% +and he says that it is +the it it means the Perpetual possession + + align:start position:0% +the it it means the Perpetual possession + + + align:start position:0% +the it it means the Perpetual possession +of the good right and it also emphasizes + + align:start position:0% +of the good right and it also emphasizes + + + align:start position:0% +of the good right and it also emphasizes +that it has to be Perpetual uh like do + + align:start position:0% +that it has to be Perpetual uh like do + + + align:start position:0% +that it has to be Perpetual uh like do +here and that's what Christianity picks + + align:start position:0% +here and that's what Christianity picks + + + align:start position:0% +here and that's what Christianity picks +up out of platonism because God + + align:start position:0% +up out of platonism because God + + + align:start position:0% +up out of platonism because God +is perpetually good and has in a sense + + align:start position:0% +is perpetually good and has in a sense + + + align:start position:0% +is perpetually good and has in a sense +the Perpetual possession of the + + align:start position:0% +the Perpetual possession of the + + + align:start position:0% +the Perpetual possession of the +good without platonism and Greek + + align:start position:0% +good without platonism and Greek + + + align:start position:0% +good without platonism and Greek +philosophy wouldn't be any Christianity + + align:start position:0% +philosophy wouldn't be any Christianity + + + align:start position:0% +philosophy wouldn't be any Christianity +wouldn't have got any religion of that + + align:start position:0% +wouldn't have got any religion of that + + + align:start position:0% +wouldn't have got any religion of that +sort uh Judaism comes into it because of + + align:start position:0% +sort uh Judaism comes into it because of + + + align:start position:0% +sort uh Judaism comes into it because of +the Bible um but um the those + + align:start position:0% +the Bible um but um the those + + + align:start position:0% +the Bible um but um the those +Greek concepts are really very special + + align:start position:0% +Greek concepts are really very special + + + align:start position:0% +Greek concepts are really very special +they out of them the Christian religion + + align:start position:0% +they out of them the Christian religion + + + align:start position:0% +they out of them the Christian religion +generates and anyhow what do we mean by + + align:start position:0% +generates and anyhow what do we mean by + + + align:start position:0% +generates and anyhow what do we mean by +the Christian religion we mean the U + + align:start position:0% +the Christian religion we mean the U + + + align:start position:0% +the Christian religion we mean the U +religion of the western world and Greek + + align:start position:0% +religion of the western world and Greek + + + align:start position:0% +religion of the western world and Greek +philosophy is the beginning of the + + align:start position:0% +philosophy is the beginning of the + + + align:start position:0% +philosophy is the beginning of the +Western + + align:start position:0% + + + + align:start position:0% + +World all right we now could take a + + align:start position:0% +World all right we now could take a + + + align:start position:0% +World all right we now could take a +break or we can go on for another half + + align:start position:0% +break or we can go on for another half + + + align:start position:0% +break or we can go on for another half +hour we don't have to stay for the full + + align:start position:0% +hour we don't have to stay for the full + + + align:start position:0% +hour we don't have to stay for the full +three hours cuz in principle the course + + align:start position:0% +three hours cuz in principle the course + + + align:start position:0% +three hours cuz in principle the course +lasts for 50 minutes times three so you + + align:start position:0% +lasts for 50 minutes times three so you + + + align:start position:0% +lasts for 50 minutes times three so you +tell me what we what you would + + align:start position:0% +tell me what we what you would + + + align:start position:0% +tell me what we what you would +like I'm having a good time I yeah I may + + align:start position:0% +like I'm having a good time I yeah I may + + + align:start position:0% +like I'm having a good time I yeah I may +faint in any + + align:start position:0% +faint in any + + + align:start position:0% +faint in any +moment do you want to drink or do you + + align:start position:0% +moment do you want to drink or do you + + + align:start position:0% +moment do you want to drink or do you +want to go out anywhere to well then + + align:start position:0% +want to go out anywhere to well then + + + align:start position:0% +want to go out anywhere to well then +should we + + align:start position:0% + + + + align:start position:0% + +continue all right + + align:start position:0% + + + + align:start position:0% + +um anything anybody wants to say about + + align:start position:0% +um anything anybody wants to say about + + + align:start position:0% +um anything anybody wants to say about +that chapter on sexual love + + align:start position:0% + + + + align:start position:0% + +and should we go on to the one on stages + + align:start position:0% +and should we go on to the one on stages + + + align:start position:0% +and should we go on to the one on stages +of Love uh loving Society + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +um in in this chapter of love in society + + align:start position:0% +um in in this chapter of love in society + + + align:start position:0% +um in in this chapter of love in society +you define different kinds of + + align:start position:0% +you define different kinds of + + + align:start position:0% +you define different kinds of +relationships and how love is different + + align:start position:0% +relationships and how love is different + + + align:start position:0% +relationships and how love is different +in these relationships sh + + align:start position:0% +in these relationships sh + + + align:start position:0% +in these relationships sh +and um first of all I would like to say + + align:start position:0% +and um first of all I would like to say + + + align:start position:0% +and um first of all I would like to say +that uh you you talk a lot about + + align:start position:0% +that uh you you talk a lot about + + + align:start position:0% +that uh you you talk a lot about +friendship and you + + align:start position:0% +friendship and you + + + align:start position:0% +friendship and you +mention that you disagree with + + align:start position:0% +mention that you disagree with + + + align:start position:0% +mention that you disagree with +Aristotle's notion of friendship + + align:start position:0% +Aristotle's notion of friendship + + + align:start position:0% +Aristotle's notion of friendship +occurring only between two virtuous + + align:start position:0% +occurring only between two virtuous + + + align:start position:0% +occurring only between two virtuous +human beings true friendship true + + align:start position:0% +human beings true friendship true + + + align:start position:0% +human beings true friendship true +friendship because he talks about other + + align:start position:0% +friendship because he talks about other + + + align:start position:0% +friendship because he talks about other +kinds yes I don't do do I I don't go + + align:start position:0% +kinds yes I don't do do I I don't go + + + align:start position:0% +kinds yes I don't do do I I don't go +into them uh no but you just mentioned + + align:start position:0% +into them uh no but you just mentioned + + + align:start position:0% +into them uh no but you just mentioned +that um you don't agree with this notion + + align:start position:0% +that um you don't agree with this notion + + + align:start position:0% +that um you don't agree with this notion +because uh then we would be disregarding + + align:start position:0% +because uh then we would be disregarding + + + align:start position:0% +because uh then we would be disregarding +the capacity of love to treat someone + + align:start position:0% +the capacity of love to treat someone + + + align:start position:0% +the capacity of love to treat someone +better than he is and I wanted to + + align:start position:0% +better than he is and I wanted to + + + align:start position:0% +better than he is and I wanted to +mention that I don't agree with this you + + align:start position:0% +mention that I don't agree with this you + + + align:start position:0% +mention that I don't agree with this you +give the example of being friends with a + + align:start position:0% +give the example of being friends with a + + + align:start position:0% +give the example of being friends with a +criminal for example and sort of + + align:start position:0% +criminal for example and sort of + + + align:start position:0% +criminal for example and sort of +disregarding the The Faults of that + + align:start position:0% +disregarding the The Faults of that + + + align:start position:0% +disregarding the The Faults of that +person and still being able to achieve + + align:start position:0% +person and still being able to achieve + + + align:start position:0% +person and still being able to achieve +yeah do you think you can't be friends + + align:start position:0% +yeah do you think you can't be friends + + + align:start position:0% +yeah do you think you can't be friends +with a + + align:start position:0% +with a + + + align:start position:0% +with a +Criminal I think that having more or + + align:start position:0% +Criminal I think that having more or + + + align:start position:0% +Criminal I think that having more or +less the same morals and and the same + + align:start position:0% +less the same morals and and the same + + + align:start position:0% +less the same morals and and the same +values as someone else is very important + + align:start position:0% +values as someone else is very important + + + align:start position:0% +values as someone else is very important +for a friendship to if um you + + align:start position:0% +for a friendship to if um you + + + align:start position:0% +for a friendship to if um you +can quantify values I mean it's + + align:start position:0% +can quantify values I mean it's + + + align:start position:0% +can quantify values I mean it's +you is there anybody that you have the + + align:start position:0% +you is there anybody that you have the + + + align:start position:0% +you is there anybody that you have the +same values with we usually share values + + align:start position:0% +same values with we usually share values + + + align:start position:0% +same values with we usually share values +in some respects but not with others and + + align:start position:0% +in some respects but not with others and + + + align:start position:0% +in some respects but not with others and +uh if you feel friendly you ignore + + align:start position:0% +uh if you feel friendly you ignore + + + align:start position:0% +uh if you feel friendly you ignore +that + + align:start position:0% +that + + + align:start position:0% +that +um for instance I I in a very low at a + + align:start position:0% +um for instance I I in a very low at a + + + align:start position:0% +um for instance I I in a very low at a +very low level I find in my case I find + + align:start position:0% +very low level I find in my case I find + + + align:start position:0% +very low level I find in my case I find +it very easy to be friendly with people + + align:start position:0% +it very easy to be friendly with people + + + align:start position:0% +it very easy to be friendly with people +I talk with for couple of minutes on the + + align:start position:0% +I talk with for couple of minutes on the + + + align:start position:0% +I talk with for couple of minutes on the +the bus or in the street there's a kind + + align:start position:0% +the bus or in the street there's a kind + + + align:start position:0% +the bus or in the street there's a kind +of insipient friendliness that usually + + align:start position:0% +of insipient friendliness that usually + + + align:start position:0% +of insipient friendliness that usually +doesn't amount to + + align:start position:0% +doesn't amount to + + + align:start position:0% +doesn't amount to +anything um and it's because we have + + align:start position:0% +anything um and it's because we have + + + align:start position:0% +anything um and it's because we have +different values there there's a very + + align:start position:0% +different values there there's a very + + + align:start position:0% +different values there there's a very +limited number of people I could really + + align:start position:0% +limited number of people I could really + + + align:start position:0% +limited number of people I could really +spend much time with I get bored with + + align:start position:0% +spend much time with I get bored with + + + align:start position:0% +spend much time with I get bored with +them they get bored with me you know I + + align:start position:0% +them they get bored with me you know I + + + align:start position:0% +them they get bored with me you know I +don't um anymore I used to when I was + + align:start position:0% +don't um anymore I used to when I was + + + align:start position:0% +don't um anymore I used to when I was +young but nowadays I don't care about of + + align:start position:0% +young but nowadays I don't care about of + + + align:start position:0% +young but nowadays I don't care about of +football heroes or baseball uh players + + align:start position:0% +football heroes or baseball uh players + + + align:start position:0% +football heroes or baseball uh players +um basketball I never paid much + + align:start position:0% +um basketball I never paid much + + + align:start position:0% +um basketball I never paid much +attention to I'm not see I'm not I never + + align:start position:0% +attention to I'm not see I'm not I never + + + align:start position:0% +attention to I'm not see I'm not I never +I don't drink beer I'm I'm I'm not a + + align:start position:0% +I don't drink beer I'm I'm I'm not a + + + align:start position:0% +I don't drink beer I'm I'm I'm not a +regular guy in any of those ways so how + + align:start position:0% +regular guy in any of those ways so how + + + align:start position:0% +regular guy in any of those ways so how +could I + + align:start position:0% +could I + + + align:start position:0% +could I +expect those who are which is most + + align:start position:0% +expect those who are which is most + + + align:start position:0% +expect those who are which is most +people normal people um to be friends + + align:start position:0% +people normal people um to be friends + + + align:start position:0% +people normal people um to be friends +with me and yet in a casual incipient + + align:start position:0% +with me and yet in a casual incipient + + + align:start position:0% +with me and yet in a casual incipient +way I find I can be friends with a great + + align:start position:0% +way I find I can be friends with a great + + + align:start position:0% +way I find I can be friends with a great +great many it's by disregarding all of + + align:start position:0% +great many it's by disregarding all of + + + align:start position:0% +great many it's by disregarding all of +the other values that's one thing I + + align:start position:0% +the other values that's one thing I + + + align:start position:0% +the other values that's one thing I +wanted to say second thing if you think + + align:start position:0% +wanted to say second thing if you think + + + align:start position:0% +wanted to say second thing if you think +about Hollywood + + align:start position:0% +about Hollywood + + + align:start position:0% +about Hollywood +movies the uh the people in them are + + align:start position:0% +movies the uh the people in them are + + + align:start position:0% +movies the uh the people in them are +often either criminals or else they're + + align:start position:0% +often either criminals or else they're + + + align:start position:0% +often either criminals or else they're +robbers and and uh violent or + + align:start position:0% +robbers and and uh violent or + + + align:start position:0% +robbers and and uh violent or +troubled um they they + + align:start position:0% +troubled um they they + + + align:start position:0% +troubled um they they +um they fall in with somebody who might + + align:start position:0% +um they fall in with somebody who might + + + align:start position:0% +um they fall in with somebody who might +get them out of their troubles or + + align:start position:0% +get them out of their troubles or + + + align:start position:0% +get them out of their troubles or +they're thrown together in a a romantic + + align:start position:0% +they're thrown together in a a romantic + + + align:start position:0% +they're thrown together in a a romantic +P pattern that I discuss I think toward + + align:start position:0% +P pattern that I discuss I think toward + + + align:start position:0% +P pattern that I discuss I think toward +the end of the this book um which + + align:start position:0% +the end of the this book um which + + + align:start position:0% +the end of the this book um which +they're both caught in so that they have + + align:start position:0% +they're both caught in so that they have + + + align:start position:0% +they're both caught in so that they have +no interest in each other and sometimes + + align:start position:0% +no interest in each other and sometimes + + + align:start position:0% +no interest in each other and sometimes +a lot of hostility but but because + + align:start position:0% +a lot of hostility but but because + + + align:start position:0% +a lot of hostility but but because +they're in it together they have to + + align:start position:0% +they're in it together they have to + + + align:start position:0% +they're in it together they have to +escape by means of each other and so + + align:start position:0% +escape by means of each other and so + + + align:start position:0% +escape by means of each other and so +they become friends I mean you all can + + align:start position:0% +they become friends I mean you all can + + + align:start position:0% +they become friends I mean you all can +think of dozens of examples of this very + + align:start position:0% +think of dozens of examples of this very + + + align:start position:0% +think of dozens of examples of this very +common movie theme um now if in that + + align:start position:0% +common movie theme um now if in that + + + align:start position:0% +common movie theme um now if in that +event their values are not + + align:start position:0% +event their values are not + + + align:start position:0% +event their values are not +alike at the end they might if they're + + align:start position:0% +alike at the end they might if they're + + + align:start position:0% +alike at the end they might if they're +different Sexes they might uh get + + align:start position:0% +different Sexes they might uh get + + + align:start position:0% +different Sexes they might uh get +married or they might become lovers + + align:start position:0% +married or they might become lovers + + + align:start position:0% +married or they might become lovers +or well we'll be talking about this in + + align:start position:0% +or well we'll be talking about this in + + + align:start position:0% +or well we'll be talking about this in +case of pigan where they don't do either + + align:start position:0% +case of pigan where they don't do either + + + align:start position:0% +case of pigan where they don't do either +of those things but they become sort of + + align:start position:0% +of those things but they become sort of + + + align:start position:0% +of those things but they become sort of +comrades together um and that seems to + + align:start position:0% +comrades together um and that seems to + + + align:start position:0% +comrades together um and that seems to +me to be built into the structure of of + + align:start position:0% +me to be built into the structure of of + + + align:start position:0% +me to be built into the structure of of +friendship that you come to accept the + + align:start position:0% +friendship that you come to accept the + + + align:start position:0% +friendship that you come to accept the +other person for what that other person + + align:start position:0% +other person for what that other person + + + align:start position:0% +other person for what that other person +is in other words there's the idea of + + align:start position:0% +is in other words there's the idea of + + + align:start position:0% +is in other words there's the idea of +bestow uh even if that person is + + align:start position:0% +bestow uh even if that person is + + + align:start position:0% +bestow uh even if that person is +different from yourself you share some + + align:start position:0% +different from yourself you share some + + + align:start position:0% +different from yourself you share some +values but maybe not too many not as + + align:start position:0% +values but maybe not too many not as + + + align:start position:0% +values but maybe not too many not as +many as is needed to fall in love and to + + align:start position:0% +many as is needed to fall in love and to + + + align:start position:0% +many as is needed to fall in love and to +get married and to live in a happy + + align:start position:0% +get married and to live in a happy + + + align:start position:0% +get married and to live in a happy +married relationship loving relationship + + align:start position:0% +married relationship loving relationship + + + align:start position:0% +married relationship loving relationship +ever after that's is that what you don't + + align:start position:0% +ever after that's is that what you don't + + + align:start position:0% +ever after that's is that what you don't +agree with + + align:start position:0% +agree with + + + align:start position:0% +agree with +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um not exactly I I'm not saying that + + align:start position:0% +um not exactly I I'm not saying that + + + align:start position:0% +um not exactly I I'm not saying that +they need to be exactly the same but I + + align:start position:0% +they need to be exactly the same but I + + + align:start position:0% +they need to be exactly the same but I +think that there needs to be at least + + align:start position:0% +think that there needs to be at least + + + align:start position:0% +think that there needs to be at least +some sort of similarity between the + + align:start position:0% +some sort of similarity between the + + + align:start position:0% +some sort of similarity between the +concepts of good and bad + + align:start position:0% +concepts of good and bad + + + align:start position:0% +concepts of good and bad +because um these are important for trust + + align:start position:0% +because um these are important for trust + + + align:start position:0% +because um these are important for trust +to exist and I think that if trust + + align:start position:0% +to exist and I think that if trust + + + align:start position:0% +to exist and I think that if trust +doesn't exist between between two + + align:start position:0% +doesn't exist between between two + + + align:start position:0% +doesn't exist between between two +peoples and no true friendship can arise + + align:start position:0% +peoples and no true friendship can arise + + + align:start position:0% +peoples and no true friendship can arise +between now I see the truth in what + + align:start position:0% +between now I see the truth in what + + + align:start position:0% +between now I see the truth in what +you're saying uh I could never be + + align:start position:0% +you're saying uh I could never be + + + align:start position:0% +you're saying uh I could never be +friends with anybody who does that who + + align:start position:0% +friends with anybody who does that who + + + align:start position:0% +friends with anybody who does that who +uh you know goes out with a BB gun and + + align:start position:0% +uh you know goes out with a BB gun and + + + align:start position:0% +uh you know goes out with a BB gun and +shoots cats or you know something how + + align:start position:0% +shoots cats or you know something how + + + align:start position:0% +shoots cats or you know something how +can you be friends with a monster of + + align:start position:0% +can you be friends with a monster of + + + align:start position:0% +can you be friends with a monster of +that sort uh that you see in some + + align:start position:0% +that sort uh that you see in some + + + align:start position:0% +that sort uh that you see in some +respects so it's surely true that one + + align:start position:0% +respects so it's surely true that one + + + align:start position:0% +respects so it's surely true that one +can't imagine being + + align:start position:0% +can't imagine being + + + align:start position:0% +can't imagine being +friends on the other hand the U the the + + align:start position:0% +friends on the other hand the U the the + + + align:start position:0% +friends on the other hand the U the the +political + + align:start position:0% +political + + + align:start position:0% +political +Monsters of modern history people like + + align:start position:0% +Monsters of modern history people like + + + align:start position:0% +Monsters of modern history people like +Stalin and Hitler musolini Saddam + + align:start position:0% +Stalin and Hitler musolini Saddam + + + align:start position:0% +Stalin and Hitler musolini Saddam +Hussein they they were very friendly to + + align:start position:0% +Hussein they they were very friendly to + + + align:start position:0% +Hussein they they were very friendly to +people had friends who recognized what + + align:start position:0% +people had friends who recognized what + + + align:start position:0% +people had friends who recognized what +they were uh so that uh some people are + + align:start position:0% +they were uh so that uh some people are + + + align:start position:0% +they were uh so that uh some people are +able to overcome their horror at what + + align:start position:0% +able to overcome their horror at what + + + align:start position:0% +able to overcome their horror at what +they also + + align:start position:0% +they also + + + align:start position:0% +they also +do but do you think those were true + + align:start position:0% +do but do you think those were true + + + align:start position:0% +do but do you think those were true +friends cuz when someone has power many + + align:start position:0% +friends cuz when someone has power many + + + align:start position:0% +friends cuz when someone has power many +people can pretend I know to be friends + + align:start position:0% +people can pretend I know to be friends + + + align:start position:0% +people can pretend I know to be friends +but then that's true in any event that's + + align:start position:0% +but then that's true in any event that's + + + align:start position:0% +but then that's true in any event that's +true of any kind of friendship or any + + align:start position:0% +true of any kind of friendship or any + + + align:start position:0% +true of any kind of friendship or any +kind of relationship it doesn't + + align:start position:0% +kind of relationship it doesn't + + + align:start position:0% +kind of relationship it doesn't +necessarily follow from a sharing of the + + align:start position:0% +necessarily follow from a sharing of the + + + align:start position:0% +necessarily follow from a sharing of the +uh of the uh of the morals as you + + align:start position:0% +uh of the uh of the morals as you + + + align:start position:0% +uh of the uh of the morals as you +said but I see a point in + + align:start position:0% +said but I see a point in + + + align:start position:0% +said but I see a point in +Aristotle's idea of true friendship + + align:start position:0% +Aristotle's idea of true friendship + + + align:start position:0% +Aristotle's idea of true friendship +people are alike in virtue so they can + + align:start position:0% +people are alike in virtue so they can + + + align:start position:0% +people are alike in virtue so they can +really respect each + + align:start position:0% +really respect each + + + align:start position:0% +really respect each +other + + align:start position:0% +other + + + align:start position:0% +other +um but uh it also means you're going to + + align:start position:0% +um but uh it also means you're going to + + + align:start position:0% +um but uh it also means you're going to +limit the number of friends you're going + + align:start position:0% +limit the number of friends you're going + + + align:start position:0% +limit the number of friends you're going +to + + align:start position:0% +to + + + align:start position:0% +to +have you're not going to have too + + align:start position:0% +have you're not going to have too + + + align:start position:0% +have you're not going to have too +many well you're not going to have too + + align:start position:0% +many well you're not going to have too + + + align:start position:0% +many well you're not going to have too +many true friends you can have but + + align:start position:0% +many true friends you can have but + + + align:start position:0% +many true friends you can have but +that's by definition that's the + + align:start position:0% +that's by definition that's the + + + align:start position:0% +that's by definition that's the +definition of the word true oh no I'm + + align:start position:0% +definition of the word true oh no I'm + + + align:start position:0% +definition of the word true oh no I'm +I'm a true friend of uh + + align:start position:0% +I'm a true friend of uh + + + align:start position:0% +I'm a true friend of uh +a man I meet casually and you know we + + align:start position:0% +a man I meet casually and you know we + + + align:start position:0% +a man I meet casually and you know we +talk briefly and I'll never see him + + align:start position:0% +talk briefly and I'll never see him + + + align:start position:0% +talk briefly and I'll never see him +again uh it's a very limit it's not that + + align:start position:0% +again uh it's a very limit it's not that + + + align:start position:0% +again uh it's a very limit it's not that +I'm not a true friend that I'm trying to + + align:start position:0% +I'm not a true friend that I'm trying to + + + align:start position:0% +I'm not a true friend that I'm trying to +use him or trying to get him to please + + align:start position:0% +use him or trying to get him to please + + + align:start position:0% +use him or trying to get him to please +me and some way I may I'm within those + + align:start position:0% +me and some way I may I'm within those + + + align:start position:0% +me and some way I may I'm within those +very narrow limits it's a kind of true + + align:start position:0% +very narrow limits it's a kind of true + + + align:start position:0% +very narrow limits it's a kind of true +friendship it's not as broad as it is + + align:start position:0% +friendship it's not as broad as it is + + + align:start position:0% +friendship it's not as broad as it is +with the kind of people that Aristotle + + align:start position:0% +with the kind of people that Aristotle + + + align:start position:0% +with the kind of people that Aristotle +is talking about when one is how much + + align:start position:0% +is talking about when one is how much + + + align:start position:0% +is talking about when one is how much +how many people there are like that and + + align:start position:0% +how many people there are like that and + + + align:start position:0% +how many people there are like that and +really how much you get out of them + + align:start position:0% + + + + align:start position:0% + +um so when you when you say true friend + + align:start position:0% +um so when you when you say true friend + + + align:start position:0% +um so when you when you say true friend +you just mean a friend who has no other + + align:start position:0% +you just mean a friend who has no other + + + align:start position:0% +you just mean a friend who has no other +Shady purpose or a person when you the + + align:start position:0% +Shady purpose or a person when you the + + + align:start position:0% +Shady purpose or a person when you the +true friend I don't true friendship you + + align:start position:0% +true friend I don't true friendship you + + + align:start position:0% +true friend I don't true friendship you +mean somebody who is friendly to someone + + align:start position:0% +mean somebody who is friendly to someone + + + align:start position:0% +mean somebody who is friendly to someone +for no you know other reason except for + + align:start position:0% +for no you know other reason except for + + + align:start position:0% +for no you know other reason except for +the pleasure me of conversing with them + + align:start position:0% +the pleasure me of conversing with them + + + align:start position:0% +the pleasure me of conversing with them +or sharing ideas not let you know up but + + align:start position:0% +or sharing ideas not let you know up but + + + align:start position:0% +or sharing ideas not let you know up but +you know I this is very interesting um I + + align:start position:0% +you know I this is very interesting um I + + + align:start position:0% +you know I this is very interesting um I +was just thinking about true friends + + align:start position:0% +was just thinking about true friends + + + align:start position:0% +was just thinking about true friends +I've had while we were talking because + + align:start position:0% +I've had while we were talking because + + + align:start position:0% +I've had while we were talking because +as as I keep telling you I learned from + + align:start position:0% +as as I keep telling you I learned from + + + align:start position:0% +as as I keep telling you I learned from +being with you uh I may not be able to + + align:start position:0% +being with you uh I may not be able to + + + align:start position:0% +being with you uh I may not be able to +use it too well and I don't believe + + align:start position:0% +use it too well and I don't believe + + + align:start position:0% +use it too well and I don't believe +anything I've written is the last word + + align:start position:0% +anything I've written is the last word + + + align:start position:0% +anything I've written is the last word +of any sort I'm I think if anything with + + align:start position:0% +of any sort I'm I think if anything with + + + align:start position:0% +of any sort I'm I think if anything with +last word that would be wholly + + align:start position:0% +last word that would be wholly + + + align:start position:0% +last word that would be wholly +unphilosophical the world is not the + + align:start position:0% +unphilosophical the world is not the + + + align:start position:0% +unphilosophical the world is not the +last word there's no remember there's no + + align:start position:0% +last word there's no remember there's no + + + align:start position:0% +last word there's no remember there's no +mathematical it's not like a + + align:start position:0% +mathematical it's not like a + + + align:start position:0% +mathematical it's not like a +mathematical problem so there's no + + align:start position:0% +mathematical problem so there's no + + + align:start position:0% +mathematical problem so there's no +solution and the what I just thought of + + align:start position:0% +solution and the what I just thought of + + + align:start position:0% +solution and the what I just thought of +was um a man who is not was not much + + align:start position:0% +was um a man who is not was not much + + + align:start position:0% +was um a man who is not was not much +older than me who + + align:start position:0% +older than me who + + + align:start position:0% +older than me who +um I who was um a young faculty member + + align:start position:0% +um I who was um a young faculty member + + + align:start position:0% +um I who was um a young faculty member +Harvard When I Was An undergraduate and + + align:start position:0% +Harvard When I Was An undergraduate and + + + align:start position:0% +Harvard When I Was An undergraduate and +then graduate student and he became a + + align:start position:0% +then graduate student and he became a + + + align:start position:0% +then graduate student and he became a +mentor he was a mentor of + + align:start position:0% +mentor he was a mentor of + + + align:start position:0% +mentor he was a mentor of +mine and I knew him for the rest of his + + align:start position:0% +mine and I knew him for the rest of his + + + align:start position:0% +mine and I knew him for the rest of his +life he died about three years + + align:start position:0% +life he died about three years + + + align:start position:0% +life he died about three years +ago and I always thought of him and said + + align:start position:0% +ago and I always thought of him and said + + + align:start position:0% +ago and I always thought of him and said +about him + + align:start position:0% +about him + + + align:start position:0% +about him +he's maybe the only + + align:start position:0% +he's maybe the only + + + align:start position:0% +he's maybe the only +person who has never defeated any + + align:start position:0% +person who has never defeated any + + + align:start position:0% +person who has never defeated any +expectation of mine he's never betrayed + + align:start position:0% +expectation of mine he's never betrayed + + + align:start position:0% +expectation of mine he's never betrayed +me or let me me down um I always think + + align:start position:0% +me or let me me down um I always think + + + align:start position:0% +me or let me me down um I always think +of him as a true friend now it wasn't + + align:start position:0% +of him as a true friend now it wasn't + + + align:start position:0% +of him as a true friend now it wasn't +because and we also conversed and there + + align:start position:0% +because and we also conversed and there + + + align:start position:0% +because and we also conversed and there +were there were limits there were things + + align:start position:0% +were there were limits there were things + + + align:start position:0% +were there were limits there were things +I couldn't talk with him about and + + align:start position:0% +I couldn't talk with him about and + + + align:start position:0% +I couldn't talk with him about and +things he didn't talk to me about you + + align:start position:0% +things he didn't talk to me about you + + + align:start position:0% +things he didn't talk to me about you +know it wasn't as if it was a loving a + + align:start position:0% +know it wasn't as if it was a loving a + + + align:start position:0% +know it wasn't as if it was a loving a +romantic relationship you know the way + + align:start position:0% +romantic relationship you know the way + + + align:start position:0% +romantic relationship you know the way +it is would be between uh lovers or + + align:start position:0% +it is would be between uh lovers or + + + align:start position:0% +it is would be between uh lovers or +husband and wife there were definite + + align:start position:0% +husband and wife there were definite + + + align:start position:0% +husband and wife there were definite +limits um not arbitrarily imposed just + + align:start position:0% +limits um not arbitrarily imposed just + + + align:start position:0% +limits um not arbitrarily imposed just +the things I wouldn't ask him that I + + align:start position:0% +the things I wouldn't ask him that I + + + align:start position:0% +the things I wouldn't ask him that I +might ask my wife + + align:start position:0% +might ask my wife + + + align:start position:0% +might ask my wife +um but it seems to be the definition + + align:start position:0% +um but it seems to be the definition + + + align:start position:0% +um but it seems to be the definition +seems to be my he not never his never + + align:start position:0% +seems to be my he not never his never + + + align:start position:0% +seems to be my he not never his never +having let me + + align:start position:0% +having let me + + + align:start position:0% +having let me +down now was I using him or is this a + + align:start position:0% +down now was I using him or is this a + + + align:start position:0% +down now was I using him or is this a +testament to + + align:start position:0% +testament to + + + align:start position:0% +testament to +the true nature of or of the + + align:start position:0% +the true nature of or of the + + + align:start position:0% +the true nature of or of the +relationship from my point of view I + + align:start position:0% +relationship from my point of view I + + + align:start position:0% +relationship from my point of view I +might he might have said Irving has let + + align:start position:0% +might he might have said Irving has let + + + align:start position:0% +might he might have said Irving has let +me down uh he hasn't done this or that I + + align:start position:0% +me down uh he hasn't done this or that I + + + align:start position:0% +me down uh he hasn't done this or that I +don't know what uh he he never + + align:start position:0% +don't know what uh he he never + + + align:start position:0% +don't know what uh he he never +complained to me and I never really + + align:start position:0% +complained to me and I never really + + + align:start position:0% +complained to me and I never really +never complained to him I never felt + + align:start position:0% +never complained to him I never felt + + + align:start position:0% +never complained to him I never felt +there was anything I wanted to + + align:start position:0% +there was anything I wanted to + + + align:start position:0% +there was anything I wanted to +change but it was but the the Criterion + + align:start position:0% +change but it was but the the Criterion + + + align:start position:0% +change but it was but the the Criterion +that I seem to have used was that he + + align:start position:0% +that I seem to have used was that he + + + align:start position:0% +that I seem to have used was that he +never led me + + align:start position:0% +never led me + + + align:start position:0% +never led me +down I mean but so you're saying that + + align:start position:0% +down I mean but so you're saying that + + + align:start position:0% +down I mean but so you're saying that +you can't be a true friend with somebody + + align:start position:0% +you can't be a true friend with somebody + + + align:start position:0% +you can't be a true friend with somebody +if he if he let you down I mean letting + + align:start position:0% +if he if he let you down I mean letting + + + align:start position:0% +if he if he let you down I mean letting +you down you might have I don't know + + align:start position:0% +you down you might have I don't know + + + align:start position:0% +you down you might have I don't know +your first concert and you really wanted + + align:start position:0% +your first concert and you really wanted + + + align:start position:0% +your first concert and you really wanted +your friend to be there and uh he didn't + + align:start position:0% +your friend to be there and uh he didn't + + + align:start position:0% +your friend to be there and uh he didn't +come because I don't know he was snowed + + align:start position:0% +come because I don't know he was snowed + + + align:start position:0% +come because I don't know he was snowed +snowed in in Chicago or something I mean + + align:start position:0% +snowed in in Chicago or something I mean + + + align:start position:0% +snowed in in Chicago or something I mean +he'd let you down no not if he was + + align:start position:0% +he'd let you down no not if he was + + + align:start position:0% +he'd let you down no not if he was +snowed in or no if he forgot if he if he + + align:start position:0% +snowed in or no if he forgot if he if he + + + align:start position:0% +snowed in or no if he forgot if he if he +said I'll be there tomorrow night and + + align:start position:0% +said I'll be there tomorrow night and + + + align:start position:0% +said I'll be there tomorrow night and +then uh you know he met a a lovely young + + align:start position:0% +then uh you know he met a a lovely young + + + align:start position:0% +then uh you know he met a a lovely young +lady and said well he won't notice I'm + + align:start position:0% +lady and said well he won't notice I'm + + + align:start position:0% +lady and said well he won't notice I'm +not at this concert I he could have let + + align:start position:0% +not at this concert I he could have let + + + align:start position:0% +not at this concert I he could have let +me down but um + + align:start position:0% +me down but um + + + align:start position:0% +me down but um +if so if he did you what what's wrong + + align:start position:0% +if so if he did you what what's wrong + + + align:start position:0% +if so if he did you what what's wrong +with that that he never did let me down + + align:start position:0% +with that that he never did let me down + + + align:start position:0% +with that that he never did let me down +I'm not saying it's wrong I'm just + + align:start position:0% +I'm not saying it's wrong I'm just + + + align:start position:0% +I'm not saying it's wrong I'm just +saying is that defining what's makes it + + align:start position:0% +saying is that defining what's makes it + + + align:start position:0% +saying is that defining what's makes it +a true friendship no I'm asking you I'm + + align:start position:0% +a true friendship no I'm asking you I'm + + + align:start position:0% +a true friendship no I'm asking you I'm +asking so if somebody if somebody let + + align:start position:0% +asking so if somebody if somebody let + + + align:start position:0% +asking so if somebody if somebody let +you down he can't be a true friend of + + align:start position:0% +you down he can't be a true friend of + + + align:start position:0% +you down he can't be a true friend of +yours is that I would yeah yeah I think + + align:start position:0% +yours is that I would yeah yeah I think + + + align:start position:0% +yours is that I would yeah yeah I think +that's an element how big an element I'm + + align:start position:0% +that's an element how big an element I'm + + + align:start position:0% +that's an element how big an element I'm +not clear yet but let's say you do have + + align:start position:0% +not clear yet but let's say you do have + + + align:start position:0% +not clear yet but let's say you do have +a relationship with somebody who + + align:start position:0% +a relationship with somebody who + + + align:start position:0% +a relationship with somebody who +continually lets you down say he's not a + + align:start position:0% +continually lets you down say he's not a + + + align:start position:0% +continually lets you down say he's not a +true friend continually is different + + align:start position:0% +true friend continually is different + + + align:start position:0% +true friend continually is different +well continually is different from once + + align:start position:0% +well continually is different from once + + + align:start position:0% +well continually is different from once +or twice so cuz I mean you were saying + + align:start position:0% +or twice so cuz I mean you were saying + + + align:start position:0% +or twice so cuz I mean you were saying +that you're well everybody is is fine I + + align:start position:0% +that you're well everybody is is fine I + + + align:start position:0% +that you're well everybody is is fine I +mean we're all Immortal uh occasionally + + align:start position:0% +mean we're all Immortal uh occasionally + + + align:start position:0% +mean we're all Immortal uh occasionally +they might let you down in some + + align:start position:0% +they might let you down in some + + + align:start position:0% +they might let you down in some +unimportant way but the my image is that + + align:start position:0% +unimportant way but the my image is that + + + align:start position:0% +unimportant way but the my image is that +he didn't let me down and I'm but I hav + + align:start position:0% +he didn't let me down and I'm but I hav + + + align:start position:0% +he didn't let me down and I'm but I hav +improved it of somebody might have said + + align:start position:0% +improved it of somebody might have said + + + align:start position:0% +improved it of somebody might have said +oh but remember this or that but it + + align:start position:0% +oh but remember this or that but it + + + align:start position:0% +oh but remember this or that but it +couldn't have been too important or I + + align:start position:0% +couldn't have been too important or I + + + align:start position:0% +couldn't have been too important or I +would have remembered okay so not + + align:start position:0% +would have remembered okay so not + + + align:start position:0% +would have remembered okay so not +letting you doubt it it important way + + align:start position:0% +letting you doubt it it important way + + + align:start position:0% +letting you doubt it it important way +okay I'm just trying to see what you + + align:start position:0% +okay I'm just trying to see what you + + + align:start position:0% +okay I'm just trying to see what you +mean by true + + align:start position:0% + + + + align:start position:0% + +friend but U I don't know how far this + + align:start position:0% +friend but U I don't know how far this + + + align:start position:0% +friend but U I don't know how far this +is going to take us in terms of the + + align:start position:0% +is going to take us in terms of the + + + align:start position:0% +is going to take us in terms of the +concept of true + + align:start position:0% +concept of true + + + align:start position:0% +concept of true +friendship Adana Demetri would or Arthur + + align:start position:0% +friendship Adana Demetri would or Arthur + + + align:start position:0% +friendship Adana Demetri would or Arthur +would you say + + align:start position:0% + + + + align:start position:0% + +something uh you talked about this idea + + align:start position:0% +something uh you talked about this idea + + + align:start position:0% +something uh you talked about this idea +of the that uh somebody may be very God + + align:start position:0% +of the that uh somebody may be very God + + + align:start position:0% +of the that uh somebody may be very God +in various ways a criminal any number of + + align:start position:0% +in various ways a criminal any number of + + + align:start position:0% +in various ways a criminal any number of +things uh however you can just forgive + + align:start position:0% +things uh however you can just forgive + + + align:start position:0% +things uh however you can just forgive +that and love them as as they are + + align:start position:0% +that and love them as as they are + + + align:start position:0% +that and love them as as they are +something like this so my question is um + + align:start position:0% +something like this so my question is um + + + align:start position:0% +something like this so my question is um +I I had this had this sense that the + + align:start position:0% +I I had this had this sense that the + + + align:start position:0% +I I had this had this sense that the +reason that you are friends with + + align:start position:0% +reason that you are friends with + + + align:start position:0% +reason that you are friends with +somebody or you love them is because of + + align:start position:0% +somebody or you love them is because of + + + align:start position:0% +somebody or you love them is because of +some good in them that you wish to uh + + align:start position:0% +some good in them that you wish to uh + + + align:start position:0% +some good in them that you wish to uh +either be near or have some or or uh + + align:start position:0% +either be near or have some or or uh + + + align:start position:0% +either be near or have some or or uh +become like well so my question is can + + align:start position:0% +become like well so my question is can + + + align:start position:0% +become like well so my question is can +somebody be uh that's not my okay goad + + align:start position:0% +somebody be uh that's not my okay goad + + + align:start position:0% +somebody be uh that's not my okay goad +so can somebody lack uh all virtue + + align:start position:0% +so can somebody lack uh all virtue + + + align:start position:0% +so can somebody lack uh all virtue +whatsoever and can you still have this + + align:start position:0% +whatsoever and can you still have this + + + align:start position:0% +whatsoever and can you still have this +love of bestow in which you forgive them + + align:start position:0% +love of bestow in which you forgive them + + + align:start position:0% +love of bestow in which you forgive them +the fact that they have absolutely no + + align:start position:0% +the fact that they have absolutely no + + + align:start position:0% +the fact that they have absolutely no +beauty or virtue at all and yeah all + + align:start position:0% +beauty or virtue at all and yeah all + + + align:start position:0% +beauty or virtue at all and yeah all +these limiting cases are always hard for + + align:start position:0% +these limiting cases are always hard for + + + align:start position:0% +these limiting cases are always hard for +me to imagine because I never encounter + + align:start position:0% +me to imagine because I never encounter + + + align:start position:0% +me to imagine because I never encounter +them in the world have you ever met + + align:start position:0% +them in the world have you ever met + + + align:start position:0% +them in the world have you ever met +anybody who had + + align:start position:0% +anybody who had + + + align:start position:0% +anybody who had +no redeeming virtues + + align:start position:0% +no redeeming virtues + + + align:start position:0% +no redeeming virtues +whatsoever okay or somebody who who had + + align:start position:0% +whatsoever okay or somebody who who had + + + align:start position:0% +whatsoever okay or somebody who who had +uh nothing but redeeming virtues were + + align:start position:0% +uh nothing but redeeming virtues were + + + align:start position:0% +uh nothing but redeeming virtues were +all you know a little in between fair + + align:start position:0% + + + + align:start position:0% + +enough we're we're a mixture um if the + + align:start position:0% +enough we're we're a mixture um if the + + + align:start position:0% +enough we're we're a mixture um if the +if the um nastiness is too great we + + align:start position:0% +if the um nastiness is too great we + + + align:start position:0% +if the um nastiness is too great we +can't stand the person but a little + + align:start position:0% +can't stand the person but a little + + + align:start position:0% +can't stand the person but a little +nastiness we can put up with and even + + align:start position:0% +nastiness we can put up with and even + + + align:start position:0% +nastiness we can put up with and even +humor and even enjoy um so we're all mix + + align:start position:0% +humor and even enjoy um so we're all mix + + + align:start position:0% +humor and even enjoy um so we're all mix +thinking terms of the middle that way + + align:start position:0% +thinking terms of the middle that way + + + align:start position:0% +thinking terms of the middle that way +you get closer close to what the world + + align:start position:0% +you get closer close to what the world + + + align:start position:0% +you get closer close to what the world +is like I guess my real question is that + + align:start position:0% +is like I guess my real question is that + + + align:start position:0% +is like I guess my real question is that +when you have one of these let's suppose + + align:start position:0% +when you have one of these let's suppose + + + align:start position:0% +when you have one of these let's suppose +you have a friend who is very brave on + + align:start position:0% +you have a friend who is very brave on + + + align:start position:0% +you have a friend who is very brave on +the other hand he is uh terrible in + + align:start position:0% +the other hand he is uh terrible in + + + align:start position:0% +the other hand he is uh terrible in +every other way he's a Neo-Nazi you know + + align:start position:0% +every other way he's a Neo-Nazi you know + + + align:start position:0% +every other way he's a Neo-Nazi you know +any number of things but very brave so I + + align:start position:0% +any number of things but very brave so I + + + align:start position:0% +any number of things but very brave so I +could certainly see that you could love + + align:start position:0% +could certainly see that you could love + + + align:start position:0% +could certainly see that you could love +that aspect + + align:start position:0% +that aspect + + + align:start position:0% +that aspect +of love his his his courage in action + + align:start position:0% +of love his his his courage in action + + + align:start position:0% +of love his his his courage in action +and + + align:start position:0% +and + + + align:start position:0% +and +things like this but but you that take + + align:start position:0% +things like this but but you that take + + + align:start position:0% +things like this but but you that take +the think of um uh one of the Hitler + + align:start position:0% +the think of um uh one of the Hitler + + + align:start position:0% +the think of um uh one of the Hitler +Youth a young fellow who uh is a fanatic + + align:start position:0% +Youth a young fellow who uh is a fanatic + + + align:start position:0% +Youth a young fellow who uh is a fanatic +who is totally dedicated to the cause uh + + align:start position:0% +who is totally dedicated to the cause uh + + + align:start position:0% +who is totally dedicated to the cause uh +he knows that what it asks him to do is + + align:start position:0% +he knows that what it asks him to do is + + + align:start position:0% +he knows that what it asks him to do is +horrible to most people and it'll cause + + align:start position:0% +horrible to most people and it'll cause + + + align:start position:0% +horrible to most people and it'll cause +pain to a great many uh but uh for + + align:start position:0% +pain to a great many uh but uh for + + + align:start position:0% +pain to a great many uh but uh for +reasons of Duty he he will be + + align:start position:0% +reasons of Duty he he will be + + + align:start position:0% +reasons of Duty he he will be +unswerving and this is not only when he + + align:start position:0% +unswerving and this is not only when he + + + align:start position:0% +unswerving and this is not only when he +is in control but when he is asked to + + align:start position:0% +is in control but when he is asked to + + + align:start position:0% +is in control but when he is asked to +risk his life and he's prepared really + + align:start position:0% +risk his life and he's prepared really + + + align:start position:0% +risk his life and he's prepared really +prepared to die for that cause + + align:start position:0% +prepared to die for that cause + + + align:start position:0% +prepared to die for that cause +right + + align:start position:0% + + + + align:start position:0% + +um can you be a friend with such a + + align:start position:0% +um can you be a friend with such a + + + align:start position:0% +um can you be a friend with such a +person even though you admire his + + align:start position:0% +person even though you admire his + + + align:start position:0% +person even though you admire his +bravery and Fidelity to + + align:start position:0% +bravery and Fidelity to + + + align:start position:0% +bravery and Fidelity to +cause I would think probably not so it's + + align:start position:0% +cause I would think probably not so it's + + + align:start position:0% +cause I would think probably not so it's +matter of it's a matter of degree uh the + + align:start position:0% +matter of it's a matter of degree uh the + + + align:start position:0% +matter of it's a matter of degree uh the +um the more you are horrified by what he + + align:start position:0% +um the more you are horrified by what he + + + align:start position:0% +um the more you are horrified by what he +has turned + + align:start position:0% +has turned + + + align:start position:0% +has turned +into um the less likely it'll be for you + + align:start position:0% +into um the less likely it'll be for you + + + align:start position:0% +into um the less likely it'll be for you +to be a friend even though you admire + + align:start position:0% +to be a friend even though you admire + + + align:start position:0% +to be a friend even though you admire +some of his remaining + + align:start position:0% +some of his remaining + + + align:start position:0% +some of his remaining +virtues but but if you ask me how many + + align:start position:0% +virtues but but if you ask me how many + + + align:start position:0% +virtues but but if you ask me how many +you know or where do we draw the + + align:start position:0% +you know or where do we draw the + + + align:start position:0% +you know or where do we draw the +line I would say uh here I am + + align:start position:0% +line I would say uh here I am + + + align:start position:0% +line I would say uh here I am +Holding On by my fingertips s in the + + align:start position:0% +Holding On by my fingertips s in the + + + align:start position:0% +Holding On by my fingertips s in the +flux of existence you know swirling All + + align:start position:0% +flux of existence you know swirling All + + + align:start position:0% +flux of existence you know swirling All +Around Me With Me part of the stream and + + align:start position:0% +Around Me With Me part of the stream and + + + align:start position:0% +Around Me With Me part of the stream and +you ask me you know you got the idea + + align:start position:0% +you ask me you know you got the idea + + + align:start position:0% +you ask me you know you got the idea +yeah I can't answer that yeah this not + + align:start position:0% +yeah I can't answer that yeah this not + + + align:start position:0% +yeah I can't answer that yeah this not +what I mean my question is whether you + + align:start position:0% +what I mean my question is whether you + + + align:start position:0% +what I mean my question is whether you +can love anything but a good part of a + + align:start position:0% +can love anything but a good part of a + + + align:start position:0% +can love anything but a good part of a +person can you love any part of a person + + align:start position:0% +person can you love any part of a person + + + align:start position:0% +person can you love any part of a person +other than their virtue or their + + align:start position:0% +other than their virtue or their + + + align:start position:0% +other than their virtue or their +Excellence oh well I think um because + + align:start position:0% +Excellence oh well I think um because + + + align:start position:0% +Excellence oh well I think um because +you seem to say that you can you kind of + + align:start position:0% +you seem to say that you can you kind of + + + align:start position:0% +you seem to say that you can you kind of +forgive and you love them completely + + align:start position:0% +forgive and you love them completely + + + align:start position:0% +forgive and you love them completely +something like that I think yes you can + + align:start position:0% +something like that I think yes you can + + + align:start position:0% +something like that I think yes you can +love you can bestow love upon Him + + align:start position:0% +love you can bestow love upon Him + + + align:start position:0% +love you can bestow love upon Him +despite his lack of + + align:start position:0% +despite his lack of + + + align:start position:0% +despite his lack of +perfection I think in not not in this + + align:start position:0% +perfection I think in not not in this + + + align:start position:0% +perfection I think in not not in this +book in the other in volume one uh I + + align:start position:0% +book in the other in volume one uh I + + + align:start position:0% +book in the other in volume one uh I +give you example of the man who um loves + + align:start position:0% +give you example of the man who um loves + + + align:start position:0% +give you example of the man who um loves +the U blemish on the face of his + + align:start position:0% +the U blemish on the face of his + + + align:start position:0% +the U blemish on the face of his +beloved a mole or something like that + + align:start position:0% +beloved a mole or something like that + + + align:start position:0% +beloved a mole or something like that +it's not that it makes her more + + align:start position:0% +it's not that it makes her more + + + align:start position:0% +it's not that it makes her more +beautiful it's not that he uh goes + + align:start position:0% +beautiful it's not that he uh goes + + + align:start position:0% +beautiful it's not that he uh goes +through life looking for molds because + + align:start position:0% +through life looking for molds because + + + align:start position:0% +through life looking for molds because +he's a specialist in the in the in the + + align:start position:0% +he's a specialist in the in the in the + + + align:start position:0% +he's a specialist in the in the in the +beauty of them um or you know it's not + + align:start position:0% +beauty of them um or you know it's not + + + align:start position:0% +beauty of them um or you know it's not +that it applies to anybody else but it's + + align:start position:0% +that it applies to anybody else but it's + + + align:start position:0% +that it applies to anybody else but it's +her mole and though it's + + align:start position:0% +her mole and though it's + + + align:start position:0% +her mole and though it's +undesirable in general and he and if she + + align:start position:0% +undesirable in general and he and if she + + + align:start position:0% +undesirable in general and he and if she +wants to remove it he will encourage her + + align:start position:0% +wants to remove it he will encourage her + + + align:start position:0% +wants to remove it he will encourage her +to do it + + align:start position:0% +to do it + + + align:start position:0% +to do it +and let you know say he has lots of + + align:start position:0% +and let you know say he has lots of + + + align:start position:0% +and let you know say he has lots of +money give her money to get an operation + + align:start position:0% +money give her money to get an operation + + + align:start position:0% +money give her money to get an operation +because that's what she + + align:start position:0% +because that's what she + + + align:start position:0% +because that's what she +wants apart from that he may love that + + align:start position:0% +wants apart from that he may love that + + + align:start position:0% +wants apart from that he may love that +little mole just because it signifies + + align:start position:0% +little mole just because it signifies + + + align:start position:0% +little mole just because it signifies +her it indicates what she is but not + + align:start position:0% +her it indicates what she is but not + + + align:start position:0% +her it indicates what she is but not +because it's good in itself so could he + + align:start position:0% +because it's good in itself so could he + + + align:start position:0% +because it's good in itself so could he +love her + + align:start position:0% + + + + align:start position:0% + +cowardice I think he can love anything + + align:start position:0% +cowardice I think he can love anything + + + align:start position:0% +cowardice I think he can love anything +that sets her Apart Her cowardice no + + align:start position:0% +that sets her Apart Her cowardice no + + + align:start position:0% +that sets her Apart Her cowardice no +women are are often allowed to be + + align:start position:0% +women are are often allowed to be + + + align:start position:0% +women are are often allowed to be +cowardly when men are not that's not a + + align:start position:0% +cowardly when men are not that's not a + + + align:start position:0% +cowardly when men are not that's not a +good example would he love her uh uh uh + + align:start position:0% +good example would he love her uh uh uh + + + align:start position:0% +good example would he love her uh uh uh +snotty attitude + + align:start position:0% +snotty attitude + + + align:start position:0% +snotty attitude +or uh + + align:start position:0% +or uh + + + align:start position:0% +or uh +biting uh uh way of talking about people + + align:start position:0% +biting uh uh way of talking about people + + + align:start position:0% +biting uh uh way of talking about people +particularly himself can he love her + + align:start position:0% +particularly himself can he love her + + + align:start position:0% +particularly himself can he love her +enough to uh love her for her vicious + + align:start position:0% +enough to uh love her for her vicious + + + align:start position:0% +enough to uh love her for her vicious +attacks on him well vicious attacks + + align:start position:0% +attacks on him well vicious attacks + + + align:start position:0% +attacks on him well vicious attacks +might be good depending on whether + + align:start position:0% +might be good depending on whether + + + align:start position:0% +might be good depending on whether +they're philosophical well they may be + + align:start position:0% +they're philosophical well they may be + + + align:start position:0% +they're philosophical well they may be +well done but you mean good in what + + align:start position:0% +well done but you mean good in what + + + align:start position:0% +well done but you mean good in what +sense good for him or beneficial to him + + align:start position:0% +sense good for him or beneficial to him + + + align:start position:0% +sense good for him or beneficial to him +yeah I mean you know if it's a critique + + align:start position:0% +yeah I mean you know if it's a critique + + + align:start position:0% +yeah I mean you know if it's a critique +or if it's a critique or if it's a if + + align:start position:0% +or if it's a critique or if it's a if + + + align:start position:0% +or if it's a critique or if it's a if +it's not just it may be but what if it's + + align:start position:0% +it's not just it may be but what if it's + + + align:start position:0% +it's not just it may be but what if it's +just the fault of hers MH and uh does + + align:start position:0% +just the fault of hers MH and uh does + + + align:start position:0% +just the fault of hers MH and uh does +that make it impossible for him to love + + align:start position:0% +that make it impossible for him to love + + + align:start position:0% +that make it impossible for him to love +her probably not there'll be other I + + align:start position:0% +her probably not there'll be other I + + + align:start position:0% +her probably not there'll be other I +don't mean to love her I mean to love + + align:start position:0% +don't mean to love her I mean to love + + + align:start position:0% +don't mean to love her I mean to love +Arthur is shaking his head I I think if + + align:start position:0% +Arthur is shaking his head I I think if + + + align:start position:0% +Arthur is shaking his head I I think if +you if you love a person I mean it goes + + align:start position:0% +you if you love a person I mean it goes + + + align:start position:0% +you if you love a person I mean it goes +back to the the reading from last time + + align:start position:0% +back to the the reading from last time + + + align:start position:0% +back to the the reading from last time +if you love a person it's it might have + + align:start position:0% +if you love a person it's it might have + + + align:start position:0% +if you love a person it's it might have +been a quote in at this time it's + + align:start position:0% +been a quote in at this time it's + + + align:start position:0% +been a quote in at this time it's +acceptance of their + + align:start position:0% +acceptance of their + + + align:start position:0% +acceptance of their +entire person so what do you mean by + + align:start position:0% +entire person so what do you mean by + + + align:start position:0% +entire person so what do you mean by +acceptance the bad along with the good + + align:start position:0% +acceptance the bad along with the good + + + align:start position:0% +acceptance the bad along with the good +right even though you recognize the bad + + align:start position:0% +right even though you recognize the bad + + + align:start position:0% +right even though you recognize the bad +is bad and if there were some way of + + align:start position:0% +is bad and if there were some way of + + + align:start position:0% +is bad and if there were some way of +helping her to overcome that part of + + align:start position:0% +helping her to overcome that part of + + + align:start position:0% +helping her to overcome that part of +herself assuming she wants to you would + + align:start position:0% +herself assuming she wants to you would + + + align:start position:0% +herself assuming she wants to you would +be eager to + + align:start position:0% +be eager to + + + align:start position:0% +be eager to +cooperate I think yeah I think that's + + align:start position:0% +cooperate I think yeah I think that's + + + align:start position:0% +cooperate I think yeah I think that's +right that's at least that's part of my + + align:start position:0% +right that's at least that's part of my + + + align:start position:0% +right that's at least that's part of my +idea of Love um at times I think I'm I'm + + align:start position:0% +idea of Love um at times I think I'm I'm + + + align:start position:0% +idea of Love um at times I think I'm I'm +crazy but um it's + + align:start position:0% +crazy but um it's + + + align:start position:0% +crazy but um it's +seems to be the only view that I can + + align:start position:0% +seems to be the only view that I can + + + align:start position:0% +seems to be the only view that I can +take that if you love somebody you love + + align:start position:0% +take that if you love somebody you love + + + align:start position:0% +take that if you love somebody you love +that + + align:start position:0% +that + + + align:start position:0% +that +person even if that person is not good + + align:start position:0% +person even if that person is not good + + + align:start position:0% +person even if that person is not good +for you even if that person um does + + align:start position:0% +for you even if that person um does + + + align:start position:0% +for you even if that person um does +things that you wouldn't approve of um + + align:start position:0% +things that you wouldn't approve of um + + + align:start position:0% +things that you wouldn't approve of um +and even if um she doesn't love you as + + align:start position:0% +and even if um she doesn't love you as + + + align:start position:0% +and even if um she doesn't love you as +much as some she loves somebody else + + align:start position:0% +much as some she loves somebody else + + + align:start position:0% +much as some she loves somebody else +which is from your point of view a great + + align:start position:0% +which is from your point of view a great + + + align:start position:0% +which is from your point of view a great +fault on her her + + align:start position:0% +fault on her her + + + align:start position:0% +fault on her her +part but uh if that's if she's the + + align:start position:0% +part but uh if that's if she's the + + + align:start position:0% +part but uh if that's if she's the +person you love then you have to accept + + align:start position:0% +person you love then you have to accept + + + align:start position:0% +person you love then you have to accept +it because that's what she wants that's + + align:start position:0% +it because that's what she wants that's + + + align:start position:0% +it because that's what she wants that's +one reason why love is not always happy + + align:start position:0% +one reason why love is not always happy + + + align:start position:0% +one reason why love is not always happy +because just loving the other person + + align:start position:0% +because just loving the other person + + + align:start position:0% +because just loving the other person +there's no guarantee that both of you + + align:start position:0% +there's no guarantee that both of you + + + align:start position:0% +there's no guarantee that both of you +are going to be fully satisfied with + + align:start position:0% +are going to be fully satisfied with + + + align:start position:0% +are going to be fully satisfied with +what happens to each of you can can I + + align:start position:0% +what happens to each of you can can I + + + align:start position:0% +what happens to each of you can can I +just ask him one more question sure when + + align:start position:0% +just ask him one more question sure when + + + align:start position:0% +just ask him one more question sure when +you say that you accept these uh faults + + align:start position:0% +you say that you accept these uh faults + + + align:start position:0% +you say that you accept these uh faults +in a person uh what do you mean uh do + + align:start position:0% +in a person uh what do you mean uh do + + + align:start position:0% +in a person uh what do you mean uh do +you mean simply that you don't try to + + align:start position:0% +you mean simply that you don't try to + + + align:start position:0% +you mean simply that you don't try to +change to help improve this person or uh + + align:start position:0% +change to help improve this person or uh + + + align:start position:0% +change to help improve this person or uh +uh what would it mean not to accept them + + align:start position:0% + + + + align:start position:0% + +you not try to change them this was + + align:start position:0% +you not try to change them this was + + + align:start position:0% +you not try to change them this was +mentioned this was mentioned in in in + + align:start position:0% +mentioned this was mentioned in in in + + + align:start position:0% +mentioned this was mentioned in in in +the reading from this time you not try + + align:start position:0% +the reading from this time you not try + + + align:start position:0% +the reading from this time you not try +to change them unless they themselves + + align:start position:0% +to change them unless they themselves + + + align:start position:0% +to change them unless they themselves +wanted it + + align:start position:0% +wanted it + + + align:start position:0% +wanted it +changed if if that person thinks if that + + align:start position:0% +changed if if that person thinks if that + + + align:start position:0% +changed if if that person thinks if that +person thinks it's a flaw of theirs then + + align:start position:0% +person thinks it's a flaw of theirs then + + + align:start position:0% +person thinks it's a flaw of theirs then +and then they're trying to change it + + align:start position:0% +and then they're trying to change it + + + align:start position:0% +and then they're trying to change it +then you would support that let's say + + align:start position:0% +then you would support that let's say + + + align:start position:0% +then you would support that let's say +you had a friend who uh was very deluded + + align:start position:0% +you had a friend who uh was very deluded + + + align:start position:0% +you had a friend who uh was very deluded +in his way of thinking and uh you saw + + align:start position:0% +in his way of thinking and uh you saw + + + align:start position:0% +in his way of thinking and uh you saw +that he was going about something the + + align:start position:0% +that he was going about something the + + + align:start position:0% +that he was going about something the +wrong way would you attempt to improve + + align:start position:0% +wrong way would you attempt to improve + + + align:start position:0% +wrong way would you attempt to improve +him in this or would you wait him to + + align:start position:0% +him in this or would you wait him to + + + align:start position:0% +him in this or would you wait him to +choose no Arthur the real problem comes + + align:start position:0% +choose no Arthur the real problem comes + + + align:start position:0% +choose no Arthur the real problem comes +up if the person the object is this + + align:start position:0% +up if the person the object is this + + + align:start position:0% +up if the person the object is this +young + + align:start position:0% +young + + + align:start position:0% +young +fanatic you who kills people innocent + + align:start position:0% +fanatic you who kills people innocent + + + align:start position:0% +fanatic you who kills people innocent +people uh who is simp makes himself into + + align:start position:0% +people uh who is simp makes himself into + + + align:start position:0% +people uh who is simp makes himself into +a machine a thing to carry out the + + align:start position:0% +a machine a thing to carry out the + + + align:start position:0% +a machine a thing to carry out the +orders of those who um uh have power in + + align:start position:0% +orders of those who um uh have power in + + + align:start position:0% +orders of those who um uh have power in +the cause that he believes in can you + + align:start position:0% +the cause that he believes in can you + + + align:start position:0% +the cause that he believes in can you +really love that person I think if the + + align:start position:0% +really love that person I think if the + + + align:start position:0% +really love that person I think if the +person is such a polar opposite from the + + align:start position:0% +person is such a polar opposite from the + + + align:start position:0% +person is such a polar opposite from the +ideals that you hold no I didn't + + align:start position:0% +ideals that you hold no I didn't + + + align:start position:0% +ideals that you hold no I didn't +understand even even + + align:start position:0% +understand even even + + + align:start position:0% +understand even even +a an admirable quality such as The + + align:start position:0% +a an admirable quality such as The + + + align:start position:0% +a an admirable quality such as The +fanatic's Bravery you the person is such + + align:start position:0% +fanatic's Bravery you the person is such + + + align:start position:0% +fanatic's Bravery you the person is such +a such a bad person from your point of + + align:start position:0% +a such a bad person from your point of + + + align:start position:0% +a such a bad person from your point of +view that you would almost contrive The + + align:start position:0% +view that you would almost contrive The + + + align:start position:0% +view that you would almost contrive The +Bravery to be + + align:start position:0% +Bravery to be + + + align:start position:0% +Bravery to be +foolishness that + + align:start position:0% + + + + align:start position:0% + +um but can't you imagine that you're at + + align:start position:0% +um but can't you imagine that you're at + + + align:start position:0% +um but can't you imagine that you're at +a certain point you're saying I just + + align:start position:0% +a certain point you're saying I just + + + align:start position:0% +a certain point you're saying I just +can't + + align:start position:0% +can't + + + align:start position:0% +can't +tolerate being near this kind of person + + align:start position:0% +tolerate being near this kind of person + + + align:start position:0% +tolerate being near this kind of person +anymore I uh love why think I capable of + + align:start position:0% +anymore I uh love why think I capable of + + + align:start position:0% +anymore I uh love why think I capable of +loving that kind of monster but + + align:start position:0% +loving that kind of monster but + + + align:start position:0% +loving that kind of monster but +sometimes you might try to see why he + + align:start position:0% +sometimes you might try to see why he + + + align:start position:0% +sometimes you might try to see why he +became like that and in the case of the + + align:start position:0% +became like that and in the case of the + + + align:start position:0% +became like that and in the case of the +hler you might but then why should you + + align:start position:0% +hler you might but then why should you + + + align:start position:0% +hler you might but then why should you +because you see that I mean he's been + + align:start position:0% +because you see that I mean he's been + + + align:start position:0% +because you see that I mean he's been +been the case that we're talking about + + align:start position:0% +been the case that we're talking about + + + align:start position:0% +been the case that we're talking about +he's been brainwashed obviously because + + align:start position:0% +he's been brainwashed obviously because + + + align:start position:0% +he's been brainwashed obviously because +that's what they did from 7 years old + + align:start position:0% +that's what they did from 7 years old + + + align:start position:0% +that's what they did from 7 years old +they took them in and you know told them + + align:start position:0% +they took them in and you know told them + + + align:start position:0% +they took them in and you know told them +various things and you might see you + + align:start position:0% +various things and you might see you + + + align:start position:0% +various things and you might see you +know some traits that and if you you may + + align:start position:0% +know some traits that and if you you may + + + align:start position:0% +know some traits that and if you you may +make the connection that you see some + + align:start position:0% +make the connection that you see some + + + align:start position:0% +make the connection that you see some +traits in the person and you see that he + + align:start position:0% +traits in the person and you see that he + + + align:start position:0% +traits in the person and you see that he +kills a bunch of people in birds and I + + align:start position:0% +kills a bunch of people in birds and I + + + align:start position:0% +kills a bunch of people in birds and I +don't know does whatever but you see + + align:start position:0% +don't know does whatever but you see + + + align:start position:0% +don't know does whatever but you see +some traits in him that and then you + + align:start position:0% +some traits in him that and then you + + + align:start position:0% +some traits in him that and then you +might think well what would have + + align:start position:0% +might think well what would have + + + align:start position:0% +might think well what would have +happened if uh he didn't undergo this + + align:start position:0% +happened if uh he didn't undergo this + + + align:start position:0% +happened if uh he didn't undergo this +brainwashing and and I mean you may + + align:start position:0% +brainwashing and and I mean you may + + + align:start position:0% +brainwashing and and I mean you may +start to really you know love him for + + align:start position:0% +start to really you know love him for + + + align:start position:0% +start to really you know love him for +those traits and maybe love some an + + align:start position:0% +those traits and maybe love some an + + + align:start position:0% +those traits and maybe love some an +other an other image of him really and + + align:start position:0% +other an other image of him really and + + + align:start position:0% +other an other image of him really and +in your love try to maybe change him + + align:start position:0% +in your love try to maybe change him + + + align:start position:0% +in your love try to maybe change him +that's one scenario but there's also + + align:start position:0% +that's one scenario but there's also + + + align:start position:0% +that's one scenario but there's also +another scenario which is you see + + align:start position:0% +another scenario which is you see + + + align:start position:0% +another scenario which is you see +that eliminating him from reality would + + align:start position:0% +that eliminating him from reality would + + + align:start position:0% +that eliminating him from reality would +be a benefit to the + + align:start position:0% +be a benefit to the + + + align:start position:0% +be a benefit to the +universe and so you but that would mean + + align:start position:0% +universe and so you but that would mean + + + align:start position:0% +universe and so you but that would mean +so you take a revolver and shoot him and + + align:start position:0% +so you take a revolver and shoot him and + + + align:start position:0% +so you take a revolver and shoot him and +having done that somebody said why did + + align:start position:0% +having done that somebody said why did + + + align:start position:0% +having done that somebody said why did +you do that uh could you in good faith + + align:start position:0% +you do that uh could you in good faith + + + align:start position:0% +you do that uh could you in good faith +say it was because I loved him but the + + align:start position:0% +say it was because I loved him but the + + + align:start position:0% +say it was because I loved him but the +point is if you did that if you if you + + align:start position:0% +point is if you did that if you if you + + + align:start position:0% +point is if you did that if you if you +you believe that eliminating him is good + + align:start position:0% +you believe that eliminating him is good + + + align:start position:0% +you believe that eliminating him is good +for the universe that's your opinion he + + align:start position:0% +for the universe that's your opinion he + + + align:start position:0% +for the universe that's your opinion he +believes that eliminating other races is + + align:start position:0% +believes that eliminating other races is + + + align:start position:0% +believes that eliminating other races is +good for the universe therefore if you + + align:start position:0% +good for the universe therefore if you + + + align:start position:0% +good for the universe therefore if you +were inclined to do that that means that + + align:start position:0% +were inclined to do that that means that + + + align:start position:0% +were inclined to do that that means that +really your moral beliefs wouldn't + + align:start position:0% +really your moral beliefs wouldn't + + + align:start position:0% +really your moral beliefs wouldn't +differ so much + + align:start position:0% +differ so much + + + align:start position:0% +differ so much +my moral belief would what we're talking + + align:start position:0% +my moral belief would what we're talking + + + align:start position:0% +my moral belief would what we're talking +about the Hitler Youth and if you said + + align:start position:0% +about the Hitler Youth and if you said + + + align:start position:0% +about the Hitler Youth and if you said +well if you killed him yeah to make the + + align:start position:0% +well if you killed him yeah to make the + + + align:start position:0% +well if you killed him yeah to make the +world a better place according to your + + align:start position:0% +world a better place according to your + + + align:start position:0% +world a better place according to your +views your moral beliefs would be + + align:start position:0% +views your moral beliefs would be + + + align:start position:0% +views your moral beliefs would be +exactly the same as his would because no + + align:start position:0% +exactly the same as his would because no + + + align:start position:0% +exactly the same as his would because no +that's true no I agree with that so + + align:start position:0% +that's true no I agree with that so + + + align:start position:0% +that's true no I agree with that so +therefore you could be a friend with him + + align:start position:0% +therefore you could be a friend with him + + + align:start position:0% +therefore you could be a friend with him +because you had but that doesn't make + + align:start position:0% +because you had but that doesn't make + + + align:start position:0% +because you had but that doesn't make +you a friend because you're going to + + align:start position:0% +you a friend because you're going to + + + align:start position:0% +you a friend because you're going to +kill the guy that you murder him you you + + align:start position:0% +kill the guy that you murder him you you + + + align:start position:0% +kill the guy that you murder him you you +you execute him put it that way + + align:start position:0% +you execute him put it that way + + + align:start position:0% +you execute him put it that way +um I I mean as + + align:start position:0% +um I I mean as + + + align:start position:0% +um I I mean as +Hamlet + + align:start position:0% +Hamlet + + + align:start position:0% +Hamlet +says in in that play love does not that + + align:start position:0% +says in in that play love does not that + + + align:start position:0% +says in in that play love does not that +way + + align:start position:0% +way + + + align:start position:0% +way +tend or affections do her + + align:start position:0% +tend or affections do her + + + align:start position:0% +tend or affections do her +AFF + + align:start position:0% +AFF + + + align:start position:0% +AFF +orilia uh it's not ponus says that to + + align:start position:0% +orilia uh it's not ponus says that to + + + align:start position:0% +orilia uh it's not ponus says that to +the King after having overheard the + + align:start position:0% +the King after having overheard the + + + align:start position:0% +the King after having overheard the +conversation between Hamlet and ailia in + + align:start position:0% +conversation between Hamlet and ailia in + + + align:start position:0% +conversation between Hamlet and ailia in +which Hamlet berates her and tells her + + align:start position:0% +which Hamlet berates her and tells her + + + align:start position:0% +which Hamlet berates her and tells her +to go into a monastery and says she's + + align:start position:0% +to go into a monastery and says she's + + + align:start position:0% +to go into a monastery and says she's +worthless and uh Pon says his affections + + align:start position:0% +worthless and uh Pon says his affections + + + align:start position:0% +worthless and uh Pon says his affections +do not that way tend I think if you're + + align:start position:0% +do not that way tend I think if you're + + + align:start position:0% +do not that way tend I think if you're +going to murder somebody one could say + + align:start position:0% +going to murder somebody one could say + + + align:start position:0% +going to murder somebody one could say +well that's not the way to show your + + align:start position:0% +well that's not the way to show your + + + align:start position:0% +well that's not the way to show your +love that's affections do not that way + + align:start position:0% +love that's affections do not that way + + + align:start position:0% +love that's affections do not that way +tend uh even though it's true that it's + + align:start position:0% +tend uh even though it's true that it's + + + align:start position:0% +tend uh even though it's true that it's +because you have different moral systems + + align:start position:0% +because you have different moral systems + + + align:start position:0% +because you have different moral systems +it may be that the moral the moral + + align:start position:0% +it may be that the moral the moral + + + align:start position:0% +it may be that the moral the moral +difference in the Moral Moral systems + + align:start position:0% +difference in the Moral Moral systems + + + align:start position:0% +difference in the Moral Moral systems +causes the death of love love is a + + align:start position:0% +causes the death of love love is a + + + align:start position:0% +causes the death of love love is a +fragile thing and can be destroyed + + align:start position:0% +fragile thing and can be destroyed + + + align:start position:0% +fragile thing and can be destroyed +because of that kind of difference can + + align:start position:0% +because of that kind of difference can + + + align:start position:0% +because of that kind of difference can +be destroyed for all sorts of reasons + + align:start position:0% +be destroyed for all sorts of reasons + + + align:start position:0% +be destroyed for all sorts of reasons +but that would be one uh but the + + align:start position:0% +but that would be one uh but the + + + align:start position:0% +but that would be one uh but the +difficulty would be to say that you + + align:start position:0% +difficulty would be to say that you + + + align:start position:0% +difficulty would be to say that you +could remain a friend or have love for + + align:start position:0% +could remain a friend or have love for + + + align:start position:0% +could remain a friend or have love for +somebody who is so horrible that you + + align:start position:0% +somebody who is so horrible that you + + + align:start position:0% +somebody who is so horrible that you +really feel it's your obligation to um + + align:start position:0% +really feel it's your obligation to um + + + align:start position:0% +really feel it's your obligation to um +uh kill + + align:start position:0% +uh kill + + + align:start position:0% +uh kill +him I mean you may + + align:start position:0% + + + + align:start position:0% + +I don't I mean you wouldn't really feel + + align:start position:0% +I don't I mean you wouldn't really feel + + + align:start position:0% +I don't I mean you wouldn't really feel +the obligation to kill him if you loved + + align:start position:0% +the obligation to kill him if you loved + + + align:start position:0% +the obligation to kill him if you loved +him I mean I agree I mean I would feel + + align:start position:0% +him I mean I agree I mean I would feel + + + align:start position:0% +him I mean I agree I mean I would feel +the obligation to kill anyone it's the + + align:start position:0% +the obligation to kill anyone it's the + + + align:start position:0% +the obligation to kill anyone it's the +other way around you you wouldn't have + + align:start position:0% +other way around you you wouldn't have + + + align:start position:0% +other way around you you wouldn't have +um killed him if + + align:start position:0% +um killed him if + + + align:start position:0% +um killed him if +you if you killed him it means you + + align:start position:0% +you if you killed him it means you + + + align:start position:0% +you if you killed him it means you +didn't have love yes + + align:start position:0% +didn't have love yes + + + align:start position:0% +didn't have love yes +right in that case but uh what what if + + align:start position:0% +right in that case but uh what what if + + + align:start position:0% +right in that case but uh what what if +he was a a terminally ill patient and + + align:start position:0% +he was a a terminally ill patient and + + + align:start position:0% +he was a a terminally ill patient and +you pulled the plug you could kill him + + align:start position:0% +you pulled the plug you could kill him + + + align:start position:0% +you pulled the plug you could kill him +that's different now you're getting into + + align:start position:0% +that's different now you're getting into + + + align:start position:0% +that's different now you're getting into +the plot of U John Steinbeck's novel Of + + align:start position:0% +the plot of U John Steinbeck's novel Of + + + align:start position:0% +the plot of U John Steinbeck's novel Of +Mice and + + align:start position:0% +Mice and + + + align:start position:0% +Mice and +Men and the wonderful movie that was + + align:start position:0% +Men and the wonderful movie that was + + + align:start position:0% +Men and the wonderful movie that was +made out of that did you see the + + align:start position:0% +made out of that did you see the + + + align:start position:0% +made out of that did you see the +original oh there's been a recent + + align:start position:0% +original oh there's been a recent + + + align:start position:0% +original oh there's been a recent +remake where where the little guy who is + + align:start position:0% +remake where where the little guy who is + + + align:start position:0% +remake where where the little guy who is +is the close friend of this tall + + align:start position:0% +is the close friend of this tall + + + align:start position:0% +is the close friend of this tall +somewhat fellow Who U + + align:start position:0% +somewhat fellow Who U + + + align:start position:0% +somewhat fellow Who U +kills a a woman without knowing what he + + align:start position:0% +kills a a woman without knowing what he + + + align:start position:0% +kills a a woman without knowing what he +was doing he he just he was sort of + + align:start position:0% +was doing he he just he was sort of + + + align:start position:0% +was doing he he just he was sort of +stroking her and ended up ringing her + + align:start position:0% +stroking her and ended up ringing her + + + align:start position:0% +stroking her and ended up ringing her +neck and sort of didn't know what he was + + align:start position:0% +neck and sort of didn't know what he was + + + align:start position:0% +neck and sort of didn't know what he was +doing uh he was uh criminally in I don't + + align:start position:0% +doing uh he was uh criminally in I don't + + + align:start position:0% +doing uh he was uh criminally in I don't +know if you could call it criminally + + align:start position:0% +know if you could call it criminally + + + align:start position:0% +know if you could call it criminally +insan he was hardly uh aware of what he + + align:start position:0% +insan he was hardly uh aware of what he + + + align:start position:0% +insan he was hardly uh aware of what he +was doing but you get the his problem + + align:start position:0% +was doing but you get the his problem + + + align:start position:0% +was doing but you get the his problem +and the the um the local men are out + + align:start position:0% +and the the um the local men are out + + + align:start position:0% +and the the um the local men are out +ready to blinch the guy and and uh Mal + + align:start position:0% +ready to blinch the guy and and uh Mal + + + align:start position:0% +ready to blinch the guy and and uh Mal +treat him if they ever caught him and + + align:start position:0% +treat him if they ever caught him and + + + align:start position:0% +treat him if they ever caught him and +they're about to catch him and so his + + align:start position:0% +they're about to catch him and so his + + + align:start position:0% +they're about to catch him and so his +friend the little one um shoots + + align:start position:0% +friend the little one um shoots + + + align:start position:0% +friend the little one um shoots +him + + align:start position:0% +him + + + align:start position:0% +him +and one feels that that was an act of + + align:start position:0% +and one feels that that was an act of + + + align:start position:0% +and one feels that that was an act of +love that it was because he loved him + + align:start position:0% +love that it was because he loved him + + + align:start position:0% +love that it was because he loved him +that he could kill him rather than let + + align:start position:0% +that he could kill him rather than let + + + align:start position:0% +that he could kill him rather than let +him be caught by the people who would + + align:start position:0% +him be caught by the people who would + + + align:start position:0% +him be caught by the people who would +not understand and would would U do him + + align:start position:0% +not understand and would would U do him + + + align:start position:0% +not understand and would would U do him +harm it was a way not of doing allowing + + align:start position:0% +harm it was a way not of doing allowing + + + align:start position:0% +harm it was a way not of doing allowing +no harm to be done merely U killing him + + align:start position:0% +no harm to be done merely U killing him + + + align:start position:0% +no harm to be done merely U killing him +so that others cannot kill him now that + + align:start position:0% +so that others cannot kill him now that + + + align:start position:0% +so that others cannot kill him now that +that's an act of love but that's not + + align:start position:0% +that's an act of love but that's not + + + align:start position:0% +that's an act of love but that's not +what we were talking about + + align:start position:0% + + + + align:start position:0% + +before I think we're getting pretty far + + align:start position:0% +before I think we're getting pretty far + + + align:start position:0% +before I think we're getting pretty far +off the topic of + + align:start position:0% + + + + align:start position:0% + +friendship I don't get so I think we're + + align:start position:0% +friendship I don't get so I think we're + + + align:start position:0% +friendship I don't get so I think we're +getting pretty far off the topic of well + + align:start position:0% +getting pretty far off the topic of well + + + align:start position:0% +getting pretty far off the topic of well +maybe we are + + align:start position:0% +maybe we are + + + align:start position:0% +maybe we are +um Ariana you want to bring us back + + align:start position:0% +um Ariana you want to bring us back + + + align:start position:0% +um Ariana you want to bring us back +let's let's go into the next chapter + + align:start position:0% +let's let's go into the next chapter + + + align:start position:0% +let's let's go into the next chapter +which is uh more than you have which is + + align:start position:0% +which is uh more than you have which is + + + align:start position:0% +which is uh more than you have which is +um a stage Theory did you notice that do + + align:start position:0% +um a stage Theory did you notice that do + + + align:start position:0% +um a stage Theory did you notice that do +I call it that in the + + align:start position:0% +I call it that in the + + + align:start position:0% +I call it that in the +chapter it's a theory of different kinds + + align:start position:0% +chapter it's a theory of different kinds + + + align:start position:0% +chapter it's a theory of different kinds +of Love developing out of each other and + + align:start position:0% +of Love developing out of each other and + + + align:start position:0% +of Love developing out of each other and +some of the + + align:start position:0% +some of the + + + align:start position:0% +some of the +higher level is in the stage being + + align:start position:0% +higher level is in the stage being + + + align:start position:0% +higher level is in the stage being +impossible unless you've gone through an + + align:start position:0% +impossible unless you've gone through an + + + align:start position:0% +impossible unless you've gone through an +earlier + + align:start position:0% +earlier + + + align:start position:0% +earlier +stage I get the idea for that in the uh + + align:start position:0% +stage I get the idea for that in the uh + + + align:start position:0% +stage I get the idea for that in the uh +primatological research that I mentioned + + align:start position:0% +primatological research that I mentioned + + + align:start position:0% +primatological research that I mentioned +by Harry harlo Harry harlo was a + + align:start position:0% +by Harry harlo Harry harlo was a + + + align:start position:0% +by Harry harlo Harry harlo was a +biologist at the University of Wisconsin + + align:start position:0% +biologist at the University of Wisconsin + + + align:start position:0% +biologist at the University of Wisconsin +um about 50 years ago uh who uh did + + align:start position:0% +um about 50 years ago uh who uh did + + + align:start position:0% +um about 50 years ago uh who uh did +research on the feelings of primates and + + align:start position:0% +research on the feelings of primates and + + + align:start position:0% +research on the feelings of primates and +in a way that nobody else attempted + + align:start position:0% +in a way that nobody else attempted + + + align:start position:0% +in a way that nobody else attempted +anything like that particularly + + align:start position:0% +anything like that particularly + + + align:start position:0% +anything like that particularly +chimpanzees and + + align:start position:0% +chimpanzees and + + + align:start position:0% +chimpanzees and +Ms um and he put it into a a book of his + + align:start position:0% +Ms um and he put it into a a book of his + + + align:start position:0% +Ms um and he put it into a a book of his +called learning to love uh which is + + align:start position:0% +called learning to love uh which is + + + align:start position:0% +called learning to love uh which is +mainly about um these primates uh to and + + align:start position:0% +mainly about um these primates uh to and + + + align:start position:0% +mainly about um these primates uh to and +to some extent with the relevance to the + + align:start position:0% +to some extent with the relevance to the + + + align:start position:0% +to some extent with the relevance to the +primates that we are uh and in it he + + align:start position:0% +primates that we are uh and in it he + + + align:start position:0% +primates that we are uh and in it he +reached some conclusions one of which is + + align:start position:0% +reached some conclusions one of which is + + + align:start position:0% +reached some conclusions one of which is +that if a u juvenile hasn't gone through + + align:start position:0% +that if a u juvenile hasn't gone through + + + align:start position:0% +that if a u juvenile hasn't gone through +pure + + align:start position:0% +pure + + + align:start position:0% +pure +love he or she will find it very hard or + + align:start position:0% +love he or she will find it very hard or + + + align:start position:0% +love he or she will find it very hard or +impossible to have mature sexual + + align:start position:0% +impossible to have mature sexual + + + align:start position:0% +impossible to have mature sexual +love for you know for a mate or any + + align:start position:0% +love for you know for a mate or any + + + align:start position:0% +love for you know for a mate or any +other person that she might he might + + align:start position:0% +other person that she might he might + + + align:start position:0% +other person that she might he might +want to spend the rest of his life with + + align:start position:0% +want to spend the rest of his life with + + + align:start position:0% +want to spend the rest of his life with +they and some of them would be clearly + + align:start position:0% +they and some of them would be clearly + + + align:start position:0% +they and some of them would be clearly +schizophrenic so that there is a stage + + align:start position:0% +schizophrenic so that there is a stage + + + align:start position:0% +schizophrenic so that there is a stage +Theory built into analysis or comes out + + align:start position:0% +Theory built into analysis or comes out + + + align:start position:0% +Theory built into analysis or comes out +of his analysis which seem to me very + + align:start position:0% +of his analysis which seem to me very + + + align:start position:0% +of his analysis which seem to me very +suggestive and I play with the idea of + + align:start position:0% +suggestive and I play with the idea of + + + align:start position:0% +suggestive and I play with the idea of +there being stages like that among human + + align:start position:0% +there being stages like that among human + + + align:start position:0% +there being stages like that among human +beings so that if you want to have a + + align:start position:0% +beings so that if you want to have a + + + align:start position:0% +beings so that if you want to have a +happy marriage and being phous because + + align:start position:0% +happy marriage and being phous because + + + align:start position:0% +happy marriage and being phous because +it's not something you can just you know + + align:start position:0% +it's not something you can just you know + + + align:start position:0% +it's not something you can just you know +arrange see to it that you have uh lots + + align:start position:0% +arrange see to it that you have uh lots + + + align:start position:0% +arrange see to it that you have uh lots +of friends when you're young and that + + align:start position:0% +of friends when you're young and that + + + align:start position:0% +of friends when you're young and that +peer friends and that you develop out of + + align:start position:0% +peer friends and that you develop out of + + + align:start position:0% +peer friends and that you develop out of +that + + align:start position:0% +that + + + align:start position:0% +that +now this reminds me of + + align:start position:0% +now this reminds me of + + + align:start position:0% +now this reminds me of +another thing that's related in in + + align:start position:0% +another thing that's related in in + + + align:start position:0% +another thing that's related in in +Israel in the early days I don't know if + + align:start position:0% +Israel in the early days I don't know if + + + align:start position:0% +Israel in the early days I don't know if +there are many um of the kabas that + + align:start position:0% +there are many um of the kabas that + + + align:start position:0% +there are many um of the kabas that +existed then uh boys and girls were + + align:start position:0% +existed then uh boys and girls were + + + align:start position:0% +existed then uh boys and girls were +often brought up in a kind of commune + + align:start position:0% +often brought up in a kind of commune + + + align:start position:0% +often brought up in a kind of commune +and they would take showers together so + + align:start position:0% +and they would take showers together so + + + align:start position:0% +and they would take showers together so +that nudity was not a problem of any + + align:start position:0% +that nudity was not a problem of any + + + align:start position:0% +that nudity was not a problem of any +sort uh and they thought of each other + + align:start position:0% +sort uh and they thought of each other + + + align:start position:0% +sort uh and they thought of each other +uh the way little children do in in the + + align:start position:0% +uh the way little children do in in the + + + align:start position:0% +uh the way little children do in in the +family + + align:start position:0% +family + + + align:start position:0% +family +with their little brothers and little + + align:start position:0% +with their little brothers and little + + + align:start position:0% +with their little brothers and little +sisters what the sociologist discovered + + align:start position:0% +sisters what the sociologist discovered + + + align:start position:0% +sisters what the sociologist discovered +was that once they got through + + align:start position:0% +was that once they got through + + + align:start position:0% +was that once they got through +puberty and started looking for a mate + + align:start position:0% +puberty and started looking for a mate + + + align:start position:0% +puberty and started looking for a mate +and falling in love um they didn't fall + + align:start position:0% +and falling in love um they didn't fall + + + align:start position:0% +and falling in love um they didn't fall +in love with each other they had to go + + align:start position:0% +in love with each other they had to go + + + align:start position:0% +in love with each other they had to go +outside and fall in love with somebody + + align:start position:0% +outside and fall in love with somebody + + + align:start position:0% +outside and fall in love with somebody +else there was a kind of extension of + + align:start position:0% +else there was a kind of extension of + + + align:start position:0% +else there was a kind of extension of +the U in incest taboo uh about not only + + align:start position:0% +the U in incest taboo uh about not only + + + align:start position:0% +the U in incest taboo uh about not only +well I yes it is the incept had do with + + align:start position:0% +well I yes it is the incept had do with + + + align:start position:0% +well I yes it is the incept had do with +a a sibling the way the incest to do is + + align:start position:0% +a a sibling the way the incest to do is + + + align:start position:0% +a a sibling the way the incest to do is +usually with a parent and child uh so + + align:start position:0% +usually with a parent and child uh so + + + align:start position:0% +usually with a parent and child uh so +that + + align:start position:0% +that + + + align:start position:0% +that +um the pure love wouldn't + + align:start position:0% +um the pure love wouldn't + + + align:start position:0% +um the pure love wouldn't +automatically issue into the later phase + + align:start position:0% +automatically issue into the later phase + + + align:start position:0% +automatically issue into the later phase +of love that's that was why I thought of + + align:start position:0% +of love that's that was why I thought of + + + align:start position:0% +of love that's that was why I thought of +that because CH as children they might + + align:start position:0% +that because CH as children they might + + + align:start position:0% +that because CH as children they might +have had this pure love they just + + align:start position:0% +have had this pure love they just + + + align:start position:0% +have had this pure love they just +because they live together so intimately + + align:start position:0% +because they live together so intimately + + + align:start position:0% +because they live together so intimately +but that wouldn't necessarily wouldn't + + align:start position:0% +but that wouldn't necessarily wouldn't + + + align:start position:0% +but that wouldn't necessarily wouldn't +cause um statistically issue into their + + align:start position:0% +cause um statistically issue into their + + + align:start position:0% +cause um statistically issue into their +loving in in a more mature + + align:start position:0% +loving in in a more mature + + + align:start position:0% +loving in in a more mature +sense so so this is a complication in + + align:start position:0% +sense so so this is a complication in + + + align:start position:0% +sense so so this is a complication in +any stage Theory I don't think I'd take + + align:start position:0% +any stage Theory I don't think I'd take + + + align:start position:0% +any stage Theory I don't think I'd take +it very far + + align:start position:0% +it very far + + + align:start position:0% +it very far +incidentally did any of you who are more + + align:start position:0% +incidentally did any of you who are more + + + align:start position:0% +incidentally did any of you who are more +scientific than me get ideas about how + + align:start position:0% +scientific than me get ideas about how + + + align:start position:0% +scientific than me get ideas about how +you could do it better I'm sure you + + align:start position:0% +you could do it better I'm sure you + + + align:start position:0% +you could do it better I'm sure you +could well I understood it I I see it + + align:start position:0% +could well I understood it I I see it + + + align:start position:0% +could well I understood it I I see it +more as being that because you + + align:start position:0% +more as being that because you + + + align:start position:0% +more as being that because you +experience pure your love then you are + + align:start position:0% +experience pure your love then you are + + + align:start position:0% +experience pure your love then you are +able to move on to the next stage but + + align:start position:0% +able to move on to the next stage but + + + align:start position:0% +able to move on to the next stage but +not necessarily with the same person is + + align:start position:0% +not necessarily with the same person is + + + align:start position:0% +not necessarily with the same person is +that what you're saying or no you mean + + align:start position:0% +that what you're saying or no you mean + + + align:start position:0% +that what you're saying or no you mean +it's a necessary condition but not + + align:start position:0% +it's a necessary condition but not + + + align:start position:0% +it's a necessary condition but not +sufficient that may be that may be a way + + align:start position:0% +sufficient that may be that may be a way + + + align:start position:0% +sufficient that may be that may be a way +of handling it that without pure love + + align:start position:0% +of handling it that without pure love + + + align:start position:0% +of handling it that without pure love +you'll find it very hard to have mature + + align:start position:0% +you'll find it very hard to have mature + + + align:start position:0% +you'll find it very hard to have mature +love but it's no guarantee that you + + align:start position:0% +love but it's no guarantee that you + + + align:start position:0% +love but it's no guarantee that you +would or would + + align:start position:0% +would or would + + + align:start position:0% +would or would +not that's but it's just that it's a + + align:start position:0% +not that's but it's just that it's a + + + align:start position:0% +not that's but it's just that it's a +necessary condition for the mature love + + align:start position:0% +necessary condition for the mature love + + + align:start position:0% +necessary condition for the mature love +but might be well that's a + + align:start position:0% +but might be well that's a + + + align:start position:0% +but might be well that's a +weakly situation condition but that may + + align:start position:0% +weakly situation condition but that may + + + align:start position:0% +weakly situation condition but that may +be all the one can say of + + align:start position:0% + + + + align:start position:0% + +this so but the way I I read about those + + align:start position:0% +this so but the way I I read about those + + + align:start position:0% +this so but the way I I read about those +kabes they're called um k i BB u t I + + align:start position:0% +kabes they're called um k i BB u t I + + + align:start position:0% +kabes they're called um k i BB u t I +read them in the Contex of an article + + align:start position:0% +read them in the Contex of an article + + + align:start position:0% +read them in the Contex of an article +that that was actually talking about + + align:start position:0% +that that was actually talking about + + + align:start position:0% +that that was actually talking about +this phenomenon called genetic sexual + + align:start position:0% +this phenomenon called genetic sexual + + + align:start position:0% +this phenomenon called genetic sexual +attraction who was the author of that uh + + align:start position:0% +attraction who was the author of that uh + + + align:start position:0% +attraction who was the author of that uh +I I don't recall I I've been reading on + + align:start position:0% +I I don't recall I I've been reading on + + + align:start position:0% +I I don't recall I I've been reading on +the internet a couple months ago but + + align:start position:0% +the internet a couple months ago but + + + align:start position:0% +the internet a couple months ago but +it's just several by a man I I met I + + align:start position:0% +it's just several by a man I I met I + + + align:start position:0% +it's just several by a man I I met I +think they're classic now maybe + + align:start position:0% +think they're classic now maybe + + + align:start position:0% +think they're classic now maybe +phenomenon where um um a mother who + + align:start position:0% +phenomenon where um um a mother who + + + align:start position:0% +phenomenon where um um a mother who +separated from her son at Birth for + + align:start position:0% +separated from her son at Birth for + + + align:start position:0% +separated from her son at Birth for +example right um gave gave him up for + + align:start position:0% +example right um gave gave him up for + + + align:start position:0% +example right um gave gave him up for +adoption or something and they're + + align:start position:0% +adoption or something and they're + + + align:start position:0% +adoption or something and they're +they're reunited many years later um in + + align:start position:0% +they're reunited many years later um in + + + align:start position:0% +they're reunited many years later um in +in some sort of uh disturbingly High + + align:start position:0% +in some sort of uh disturbingly High + + + align:start position:0% +in some sort of uh disturbingly High +statistical sense like there's some kind + + align:start position:0% +statistical sense like there's some kind + + + align:start position:0% +statistical sense like there's some kind +of sexual attraction between them when + + align:start position:0% +of sexual attraction between them when + + + align:start position:0% +of sexual attraction between them when +they meet um and and so this this + + align:start position:0% +they meet um and and so this this + + + align:start position:0% +they meet um and and so this this +article was was talking about this from + + align:start position:0% +article was was talking about this from + + + align:start position:0% +article was was talking about this from +a psychological perspective that there + + align:start position:0% +a psychological perspective that there + + + align:start position:0% +a psychological perspective that there +seem that genetically there seems to be + + align:start position:0% +seem that genetically there seems to be + + + align:start position:0% +seem that genetically there seems to be +some kind of circuitry or something that + + align:start position:0% +some kind of circuitry or something that + + + align:start position:0% +some kind of circuitry or something that +that can sort of + + align:start position:0% +that can sort of + + + align:start position:0% +that can sort of +um like deactivate like the sexual + + align:start position:0% +um like deactivate like the sexual + + + align:start position:0% +um like deactivate like the sexual +attraction when when there're sort of + + align:start position:0% +attraction when when there're sort of + + + align:start position:0% +attraction when when there're sort of +that peer or that or that mother son + + align:start position:0% +that peer or that or that mother son + + + align:start position:0% +that peer or that or that mother son +relationship through through the that's + + align:start position:0% +relationship through through the that's + + + align:start position:0% +relationship through through the that's +interesting I didn't know about that + + align:start position:0% +interesting I didn't know about that + + + align:start position:0% +interesting I didn't know about that +research yeah that's related to my + + align:start position:0% +research yeah that's related to my + + + align:start position:0% +research yeah that's related to my +emphasis upon self-love as being the + + align:start position:0% +emphasis upon self-love as being the + + + align:start position:0% +emphasis upon self-love as being the +fundamental um stage of love that + + align:start position:0% +fundamental um stage of love that + + + align:start position:0% +fundamental um stage of love that +without that there is no + + align:start position:0% +without that there is no + + + align:start position:0% +without that there is no +love um it's my reaction against the uh + + align:start position:0% +love um it's my reaction against the uh + + + align:start position:0% +love um it's my reaction against the uh +what was Comon when I started out + + align:start position:0% +what was Comon when I started out + + + align:start position:0% +what was Comon when I started out +writing about love the idea that love + + align:start position:0% +writing about love the idea that love + + + align:start position:0% +writing about love the idea that love +means + + align:start position:0% +means + + + align:start position:0% +means +self-sacrifice the ability to sacrifice + + align:start position:0% +self-sacrifice the ability to sacrifice + + + align:start position:0% +self-sacrifice the ability to sacrifice +yourself for somebody else being um a + + align:start position:0% +yourself for somebody else being um a + + + align:start position:0% +yourself for somebody else being um a +definitive condition for there to be + + align:start position:0% +definitive condition for there to be + + + align:start position:0% +definitive condition for there to be +love and as again said it seemed to me + + align:start position:0% +love and as again said it seemed to me + + + align:start position:0% +love and as again said it seemed to me +that uh without + + align:start position:0% +that uh without + + + align:start position:0% +that uh without +selflove uh there won't be any kind of + + align:start position:0% +selflove uh there won't be any kind of + + + align:start position:0% +selflove uh there won't be any kind of +love and uh in a a complete + + align:start position:0% +love and uh in a a complete + + + align:start position:0% +love and uh in a a complete +mature harmonious + + align:start position:0% +mature harmonious + + + align:start position:0% +mature harmonious +happy you know very successful + + align:start position:0% +happy you know very successful + + + align:start position:0% +happy you know very successful +love there has to be a great deal of + + align:start position:0% +love there has to be a great deal of + + + align:start position:0% +love there has to be a great deal of +selfishness or it isn't going to + + align:start position:0% +selfishness or it isn't going to + + + align:start position:0% +selfishness or it isn't going to +work uh in the uh first volume of the + + align:start position:0% +work uh in the uh first volume of the + + + align:start position:0% +work uh in the uh first volume of the +trilogy uh I attack Freud all over the + + align:start position:0% +trilogy uh I attack Freud all over the + + + align:start position:0% +trilogy uh I attack Freud all over the +place uh he was the great man of into + + align:start position:0% +place uh he was the great man of into + + + align:start position:0% +place uh he was the great man of into +which I was born on these subjects uh + + align:start position:0% +which I was born on these subjects uh + + + align:start position:0% +which I was born on these subjects uh +and so it was natural for me to deal + + align:start position:0% +and so it was natural for me to deal + + + align:start position:0% +and so it was natural for me to deal +with him and and since my views are + + align:start position:0% +with him and and since my views are + + + align:start position:0% +with him and and since my views are +different to attack him what I attacked + + align:start position:0% +different to attack him what I attacked + + + align:start position:0% +different to attack him what I attacked +him for was his ignorance of the idea of + + align:start position:0% +him for was his ignorance of the idea of + + + align:start position:0% +him for was his ignorance of the idea of +bestow that he always seemed to + + align:start position:0% +bestow that he always seemed to + + + align:start position:0% +bestow that he always seemed to +emphasize appraisal as the method of + + align:start position:0% +emphasize appraisal as the method of + + + align:start position:0% +emphasize appraisal as the method of +analysis which made it all look very + + align:start position:0% +analysis which made it all look very + + + align:start position:0% +analysis which made it all look very +Mercantile and businesslike um as if um + + align:start position:0% +Mercantile and businesslike um as if um + + + align:start position:0% +Mercantile and businesslike um as if um +you know you sort of add up the + + align:start position:0% +you know you sort of add up the + + + align:start position:0% +you know you sort of add up the +attractions what can she bring into the + + align:start position:0% +attractions what can she bring into the + + + align:start position:0% +attractions what can she bring into the +relationship um uh if she doesn't have + + align:start position:0% +relationship um uh if she doesn't have + + + align:start position:0% +relationship um uh if she doesn't have +enough to offer she doesn't have he + + align:start position:0% +enough to offer she doesn't have he + + + align:start position:0% +enough to offer she doesn't have he +isn't beautiful enough smart enough + + align:start position:0% +isn't beautiful enough smart enough + + + align:start position:0% +isn't beautiful enough smart enough +clever enough I mean intelligent enough + + align:start position:0% +clever enough I mean intelligent enough + + + align:start position:0% +clever enough I mean intelligent enough +uh from a good family all that how can I + + align:start position:0% +uh from a good family all that how can I + + + align:start position:0% +uh from a good family all that how can I +love her right uh that I don't mean that + + align:start position:0% +love her right uh that I don't mean that + + + align:start position:0% +love her right uh that I don't mean that +in a sense does Freud in Injustice + + align:start position:0% +in a sense does Freud in Injustice + + + align:start position:0% +in a sense does Freud in Injustice +because this theory is far more + + align:start position:0% +because this theory is far more + + + align:start position:0% +because this theory is far more +sophisticated than that but uh the idea + + align:start position:0% +sophisticated than that but uh the idea + + + align:start position:0% +sophisticated than that but uh the idea +of bestow is a way of + + align:start position:0% +of bestow is a way of + + + align:start position:0% +of bestow is a way of +creating value through your attachment + + align:start position:0% +creating value through your attachment + + + align:start position:0% +creating value through your attachment +meaning being an important part of human + + align:start position:0% +meaning being an important part of human + + + align:start position:0% +meaning being an important part of human +nature that he didn't he didn't seem to + + align:start position:0% +nature that he didn't he didn't seem to + + + align:start position:0% +nature that he didn't he didn't seem to +me to get it um in by the time I got to + + align:start position:0% +me to get it um in by the time I got to + + + align:start position:0% +me to get it um in by the time I got to +the third volume which is on the 20th + + align:start position:0% +the third volume which is on the 20th + + + align:start position:0% +the third volume which is on the 20th +century in which there is a a 70 page + + align:start position:0% +century in which there is a a 70 page + + + align:start position:0% +century in which there is a a 70 page +chap that 7 70 page chapter I mentioned + + align:start position:0% +chap that 7 70 page chapter I mentioned + + + align:start position:0% +chap that 7 70 page chapter I mentioned +to you I had changed or I began to + + align:start position:0% +to you I had changed or I began to + + + align:start position:0% +to you I had changed or I began to +appreciate what I how much more Freud + + align:start position:0% +appreciate what I how much more Freud + + + align:start position:0% +appreciate what I how much more Freud +had done in the world than I had because + + align:start position:0% +had done in the world than I had because + + + align:start position:0% +had done in the world than I had because +I was some considered older and I began + + align:start position:0% +I was some considered older and I began + + + align:start position:0% +I was some considered older and I began +to see all of the ways in which there + + align:start position:0% +to see all of the ways in which there + + + align:start position:0% +to see all of the ways in which there +was a great deal of wisdom in his + + align:start position:0% +was a great deal of wisdom in his + + + align:start position:0% +was a great deal of wisdom in his +ability to show how important appraisal + + align:start position:0% +ability to show how important appraisal + + + align:start position:0% +ability to show how important appraisal +is in human + + align:start position:0% +is in human + + + align:start position:0% +is in human +relationship and that uh Med had an + + align:start position:0% +relationship and that uh Med had an + + + align:start position:0% +relationship and that uh Med had an +effect on that volume partly because the + + align:start position:0% +effect on that volume partly because the + + + align:start position:0% +effect on that volume partly because the +first volume had been misinterpreted by + + align:start position:0% +first volume had been misinterpreted by + + + align:start position:0% +first volume had been misinterpreted by +even friendly critics in in thinking + + align:start position:0% +even friendly critics in in thinking + + + align:start position:0% +even friendly critics in in thinking +that I defined love as witho which I + + align:start position:0% +that I defined love as witho which I + + + align:start position:0% +that I defined love as witho which I +don't of course I don't believe in + + align:start position:0% +don't of course I don't believe in + + + align:start position:0% +don't of course I don't believe in +defining words like love but I + + align:start position:0% +defining words like love but I + + + align:start position:0% +defining words like love but I +emphasized + + align:start position:0% +emphasized + + + align:start position:0% +emphasized +Bou less than appraisal in the third + + align:start position:0% +Bou less than appraisal in the third + + + align:start position:0% +Bou less than appraisal in the third +volume I wanted to remedy that and there + + align:start position:0% +volume I wanted to remedy that and there + + + align:start position:0% +volume I wanted to remedy that and there +was Freud who was so shrewd about all + + align:start position:0% +was Freud who was so shrewd about all + + + align:start position:0% +was Freud who was so shrewd about all +these different forms of appraisal so I + + align:start position:0% +these different forms of appraisal so I + + + align:start position:0% +these different forms of appraisal so I +balanced it better I think in that than + + align:start position:0% +balanced it better I think in that than + + + align:start position:0% +balanced it better I think in that than +I had before uh but also it fits in with + + align:start position:0% +I had before uh but also it fits in with + + + align:start position:0% +I had before uh but also it fits in with +this idea in the stage theory of + + align:start position:0% +this idea in the stage theory of + + + align:start position:0% +this idea in the stage theory of +self-love being fundamental at every + + align:start position:0% +self-love being fundamental at every + + + align:start position:0% +self-love being fundamental at every +stage because through self-love you are + + align:start position:0% +stage because through self-love you are + + + align:start position:0% +stage because through self-love you are +appraising it self-love of course is + + align:start position:0% +appraising it self-love of course is + + + align:start position:0% +appraising it self-love of course is +ambiguous do you want to get into that + + align:start position:0% +ambiguous do you want to get into that + + + align:start position:0% +ambiguous do you want to get into that +ambiguity well before that just one + + align:start position:0% +ambiguity well before that just one + + + align:start position:0% +ambiguity well before that just one +minute if I'm going to appraise another + + align:start position:0% +minute if I'm going to appraise another + + + align:start position:0% +minute if I'm going to appraise another +person I do it in terms of what she is + + align:start position:0% +person I do it in terms of what she is + + + align:start position:0% +person I do it in terms of what she is +worth to me so that's a form of + + align:start position:0% +worth to me so that's a form of + + + align:start position:0% +worth to me so that's a form of +self-love now let's get into the + + align:start position:0% +self-love now let's get into the + + + align:start position:0% +self-love now let's get into the +distinction + + align:start position:0% +distinction + + + align:start position:0% +distinction +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um I I didn't get the + + align:start position:0% +um I I didn't get the + + + align:start position:0% +um I I didn't get the +distinction from self love + + align:start position:0% +distinction from self love + + + align:start position:0% +distinction from self love +uh you mean is there does self love mean + + align:start position:0% +uh you mean is there does self love mean + + + align:start position:0% +uh you mean is there does self love mean +the same as selfishness on my view oh no + + align:start position:0% +the same as selfishness on my view oh no + + + align:start position:0% +the same as selfishness on my view oh no +no no that's my that was the ambiguity I + + align:start position:0% +no no that's my that was the ambiguity I + + + align:start position:0% +no no that's my that was the ambiguity I +okay okay um selflove is different from + + align:start position:0% +okay okay um selflove is different from + + + align:start position:0% +okay okay um selflove is different from +selfishness + + align:start position:0% +selfishness + + + align:start position:0% +selfishness +because through selflove we can love + + align:start position:0% +because through selflove we can love + + + align:start position:0% +because through selflove we can love +other people and with selfishness we are + + align:start position:0% +other people and with selfishness we are + + + align:start position:0% +other people and with selfishness we are +just looking for our own good and not + + align:start position:0% +just looking for our own good and not + + + align:start position:0% +just looking for our own good and not +for the for the good of the other person + + align:start position:0% +for the for the good of the other person + + + align:start position:0% +for the for the good of the other person +so so if by self-love you mean seeing + + align:start position:0% +so so if by self-love you mean seeing + + + align:start position:0% +so so if by self-love you mean seeing +things from your own point of view and + + align:start position:0% +things from your own point of view and + + + align:start position:0% +things from your own point of view and +accepting yourself and loving yourself + + align:start position:0% +accepting yourself and loving yourself + + + align:start position:0% +accepting yourself and loving yourself +which will involve some S I mean you you + + align:start position:0% +which will involve some S I mean you you + + + align:start position:0% +which will involve some S I mean you you +will get things that you need out of the + + align:start position:0% +will get things that you need out of the + + + align:start position:0% +will get things that you need out of the +other person through appraisal and + + align:start position:0% +other person through appraisal and + + + align:start position:0% +other person through appraisal and +through a kind of minimal selfishness at + + align:start position:0% +through a kind of minimal selfishness at + + + align:start position:0% +through a kind of minimal selfishness at +least um that seems to me to be a prime + + align:start position:0% +least um that seems to me to be a prime + + + align:start position:0% +least um that seems to me to be a prime +condition for there to be love so self- + + align:start position:0% +condition for there to be love so self- + + + align:start position:0% +condition for there to be love so self- +L I think is the foundation + + align:start position:0% +L I think is the foundation + + + align:start position:0% +L I think is the foundation +but it doesn't have to be + + align:start position:0% +but it doesn't have to be + + + align:start position:0% +but it doesn't have to be +selfishness right um because selfishness + + align:start position:0% +selfishness right um because selfishness + + + align:start position:0% +selfishness right um because selfishness +as you say is pajor to that's right it + + align:start position:0% +as you say is pajor to that's right it + + + align:start position:0% +as you say is pajor to that's right it +means getting more for yourself than for + + align:start position:0% +means getting more for yourself than for + + + align:start position:0% +means getting more for yourself than for +somebody else whereas as this is + + align:start position:0% +somebody else whereas as this is + + + align:start position:0% +somebody else whereas as this is +something Aristotle points out I don't + + align:start position:0% +something Aristotle points out I don't + + + align:start position:0% +something Aristotle points out I don't +know if I mentioned that he has the + + align:start position:0% +know if I mentioned that he has the + + + align:start position:0% +know if I mentioned that he has the +concept of the magnanimous man the man + + align:start position:0% +concept of the magnanimous man the man + + + align:start position:0% +concept of the magnanimous man the man +who is so sure of himself and so + + align:start position:0% +who is so sure of himself and so + + + align:start position:0% +who is so sure of himself and so +confident and so strong + + align:start position:0% +confident and so strong + + + align:start position:0% +confident and so strong +and right that um you know he can be + + align:start position:0% +and right that um you know he can be + + + align:start position:0% +and right that um you know he can be +gracious and he can tolerate all sorts + + align:start position:0% +gracious and he can tolerate all sorts + + + align:start position:0% +gracious and he can tolerate all sorts +of other people getting what they want + + align:start position:0% +of other people getting what they want + + + align:start position:0% +of other people getting what they want +but he does it because he loves himself + + align:start position:0% +but he does it because he loves himself + + + align:start position:0% +but he does it because he loves himself +with such completeness and with and with + + align:start position:0% +with such completeness and with and with + + + align:start position:0% +with such completeness and with and with +such good + + align:start position:0% +such good + + + align:start position:0% +such good +judgment now that that's the magnanimous + + align:start position:0% +judgment now that that's the magnanimous + + + align:start position:0% +judgment now that that's the magnanimous +man that's what I mean by the one who + + align:start position:0% +man that's what I mean by the one who + + + align:start position:0% +man that's what I mean by the one who +has true self-love and that that's + + align:start position:0% +has true self-love and that that's + + + align:start position:0% +has true self-love and that that's +fundamental because if you really hate + + align:start position:0% +fundamental because if you really hate + + + align:start position:0% +fundamental because if you really hate +yourself you won't be able to love + + align:start position:0% +yourself you won't be able to love + + + align:start position:0% +yourself you won't be able to love +anybody but I think that it's also + + align:start position:0% +anybody but I think that it's also + + + align:start position:0% +anybody but I think that it's also +important to + + align:start position:0% +important to + + + align:start position:0% +important to +distinguish uh that level of self-love + + align:start position:0% +distinguish uh that level of self-love + + + align:start position:0% +distinguish uh that level of self-love +with the selflove that makes us love + + align:start position:0% +with the selflove that makes us love + + + align:start position:0% +with the selflove that makes us love +ourselves and accept ourselves but also + + align:start position:0% +ourselves and accept ourselves but also + + + align:start position:0% +ourselves and accept ourselves but also +seek for the Improvement of ourselves + + align:start position:0% +seek for the Improvement of ourselves + + + align:start position:0% +seek for the Improvement of ourselves +and that way seek for love in other + + align:start position:0% +and that way seek for love in other + + + align:start position:0% +and that way seek for love in other +person as opposed to selfishness right + + align:start position:0% +person as opposed to selfishness right + + + align:start position:0% +person as opposed to selfishness right +no I think that's right in a sense + + align:start position:0% +no I think that's right in a sense + + + align:start position:0% +no I think that's right in a sense +that's also what Plato meant because + + align:start position:0% +that's also what Plato meant because + + + align:start position:0% +that's also what Plato meant because +Plato meant that if um the Republic a + + align:start position:0% +Plato meant that if um the Republic a + + + align:start position:0% +Plato meant that if um the Republic a +lot of Plato Plato on love comes out in + + align:start position:0% +lot of Plato Plato on love comes out in + + + align:start position:0% +lot of Plato Plato on love comes out in +the Republic as well as Symposium and + + align:start position:0% +the Republic as well as Symposium and + + + align:start position:0% +the Republic as well as Symposium and +the feedr since and the Republic is + + align:start position:0% +the feedr since and the Republic is + + + align:start position:0% +the feedr since and the Republic is +about the construction of a an ideal + + align:start position:0% +about the construction of a an ideal + + + align:start position:0% +about the construction of a an ideal +society and he his point is that um if + + align:start position:0% +society and he his point is that um if + + + align:start position:0% +society and he his point is that um if +you do the right + + align:start position:0% +you do the right + + + align:start position:0% +you do the right +thing then um you you won't care about + + align:start position:0% +thing then um you you won't care about + + + align:start position:0% +thing then um you you won't care about +being selfish in all the petty ways if + + align:start position:0% +being selfish in all the petty ways if + + + align:start position:0% +being selfish in all the petty ways if +you pursue the good you will be ready to + + align:start position:0% +you pursue the good you will be ready to + + + align:start position:0% +you pursue the good you will be ready to +sacrifice these so so everything you do + + align:start position:0% +sacrifice these so so everything you do + + + align:start position:0% +sacrifice these so so everything you do +is for your own self worth PL would say + + align:start position:0% +is for your own self worth PL would say + + + align:start position:0% +is for your own self worth PL would say +but that doesn't mean that you'll try to + + align:start position:0% +but that doesn't mean that you'll try to + + + align:start position:0% +but that doesn't mean that you'll try to +acquire more wealth you'll be selfish in + + align:start position:0% +acquire more wealth you'll be selfish in + + + align:start position:0% +acquire more wealth you'll be selfish in +other ways so that there is a a + + align:start position:0% +other ways so that there is a a + + + align:start position:0% +other ways so that there is a a +relationship between that idea in Plato + + align:start position:0% +relationship between that idea in Plato + + + align:start position:0% +relationship between that idea in Plato +and what I was trying to say uh more + + align:start position:0% +and what I was trying to say uh more + + + align:start position:0% +and what I was trying to say uh more +immediately however it's what I was + + align:start position:0% +immediately however it's what I was + + + align:start position:0% +immediately however it's what I was +trying to say had its roots in nich's + + align:start position:0% +trying to say had its roots in nich's + + + align:start position:0% +trying to say had its roots in nich's +idea of the Superman the Superman is so + + align:start position:0% +idea of the Superman the Superman is so + + + align:start position:0% +idea of the Superman the Superman is so +strong and confident and + + align:start position:0% +strong and confident and + + + align:start position:0% +strong and confident and +creative that um he doesn't have to be + + align:start position:0% +creative that um he doesn't have to be + + + align:start position:0% +creative that um he doesn't have to be +selfish he shows himself forth um uh + + align:start position:0% +selfish he shows himself forth um uh + + + align:start position:0% +selfish he shows himself forth um uh +what n was saying was not as we be + + align:start position:0% +what n was saying was not as we be + + + align:start position:0% +what n was saying was not as we be +you'll see when we get to talking about + + align:start position:0% +you'll see when we get to talking about + + + align:start position:0% +you'll see when we get to talking about +n not what the Nazis thought that the + + align:start position:0% +n not what the Nazis thought that the + + + align:start position:0% +n not what the Nazis thought that the +Superman is superior to everyone else so + + align:start position:0% +Superman is superior to everyone else so + + + align:start position:0% +Superman is superior to everyone else so +he trounces trounces them and and uh + + align:start position:0% +he trounces trounces them and and uh + + + align:start position:0% +he trounces trounces them and and uh +subjugates them and enslaves them and + + align:start position:0% +subjugates them and enslaves them and + + + align:start position:0% +subjugates them and enslaves them and +destroys them that's and they use the + + align:start position:0% +destroys them that's and they use the + + + align:start position:0% +destroys them that's and they use the +word Superman ubych uh because they + + align:start position:0% +word Superman ubych uh because they + + + align:start position:0% +word Superman ubych uh because they +wanted to use n as a kind of uh + + align:start position:0% +wanted to use n as a kind of uh + + + align:start position:0% +wanted to use n as a kind of uh +credentials for themselves but it was + + align:start position:0% +credentials for themselves but it was + + + align:start position:0% +credentials for themselves but it was +the opposite of what nature meant he + + align:start position:0% +the opposite of what nature meant he + + + align:start position:0% +the opposite of what nature meant he +meant by the superman the most creative + + align:start position:0% +meant by the superman the most creative + + + align:start position:0% +meant by the superman the most creative +person and that for Superman is not the + + align:start position:0% +person and that for Superman is not the + + + align:start position:0% +person and that for Superman is not the +military person but the + + align:start position:0% +military person but the + + + align:start position:0% +military person but the +artist so it's + + align:start position:0% +artist so it's + + + align:start position:0% +artist so it's +that the authentically nian idea that + + align:start position:0% +that the authentically nian idea that + + + align:start position:0% +that the authentically nian idea that +inspired me also I was inspired by um + + align:start position:0% +inspired me also I was inspired by um + + + align:start position:0% +inspired me also I was inspired by um +primatology which I was studying uh at + + align:start position:0% +primatology which I was studying uh at + + + align:start position:0% +primatology which I was studying uh at +that time along with my wife and + + align:start position:0% +that time along with my wife and + + + align:start position:0% +that time along with my wife and +um if I don't know if you've ever + + align:start position:0% +um if I don't know if you've ever + + + align:start position:0% +um if I don't know if you've ever +watched documentaries about a baboon + + align:start position:0% +watched documentaries about a baboon + + + align:start position:0% +watched documentaries about a baboon +Colony a tribe of bamboon well it's it + + align:start position:0% +Colony a tribe of bamboon well it's it + + + align:start position:0% +Colony a tribe of bamboon well it's it +it is run like a military dictatorship + + align:start position:0% +it is run like a military dictatorship + + + align:start position:0% +it is run like a military dictatorship +there is a an oligarchy of three + + align:start position:0% +there is a an oligarchy of three + + + align:start position:0% +there is a an oligarchy of three +powerful males who run everything and + + align:start position:0% +powerful males who run everything and + + + align:start position:0% +powerful males who run everything and +among the three there's one that is the + + align:start position:0% +among the three there's one that is the + + + align:start position:0% +among the three there's one that is the +dominant male for the whole troop which + + align:start position:0% +dominant male for the whole troop which + + + align:start position:0% +dominant male for the whole troop which +means that he gets the best food and the + + align:start position:0% +means that he gets the best food and the + + + align:start position:0% +means that he gets the best food and the +choice females in other words his genes + + align:start position:0% +choice females in other words his genes + + + align:start position:0% +choice females in other words his genes +go on and uh he is kept alive for that + + align:start position:0% +go on and uh he is kept alive for that + + + align:start position:0% +go on and uh he is kept alive for that +purpose as he gets weak the uh the other + + align:start position:0% +purpose as he gets weak the uh the other + + + align:start position:0% +purpose as he gets weak the uh the other +members of the oligarchy who are always + + align:start position:0% +members of the oligarchy who are always + + + align:start position:0% +members of the oligarchy who are always +snipping at him and attacking him like + + align:start position:0% +snipping at him and attacking him like + + + align:start position:0% +snipping at him and attacking him like +in Parliament or in Congress you know + + align:start position:0% +in Parliament or in Congress you know + + + align:start position:0% +in Parliament or in Congress you know +it's political situation um they once he + + align:start position:0% +it's political situation um they once he + + + align:start position:0% +it's political situation um they once he +gets weak enough they get rid of him + + align:start position:0% +gets weak enough they get rid of him + + + align:start position:0% +gets weak enough they get rid of him +they drive him away right but while he + + align:start position:0% +they drive him away right but while he + + + align:start position:0% +they drive him away right but while he +is dominant male and you see in these + + align:start position:0% +is dominant male and you see in these + + + align:start position:0% +is dominant male and you see in these +documentaries when he walks in front of + + align:start position:0% +documentaries when he walks in front of + + + align:start position:0% +documentaries when he walks in front of +the through the troop all the juveniles + + align:start position:0% +the through the troop all the juveniles + + + align:start position:0% +the through the troop all the juveniles +Scurry out of his way the women cower + + align:start position:0% +Scurry out of his way the women cower + + + align:start position:0% +Scurry out of his way the women cower +everybody makes room for him he is the + + align:start position:0% +everybody makes room for him he is the + + + align:start position:0% +everybody makes room for him he is the +creative person who shows forth his love + + align:start position:0% +creative person who shows forth his love + + + align:start position:0% +creative person who shows forth his love +and + + align:start position:0% +and + + + align:start position:0% +and +self-confidence and then of course if + + align:start position:0% +self-confidence and then of course if + + + align:start position:0% +self-confidence and then of course if +the troop is attacked he takes the lead + + align:start position:0% +the troop is attacked he takes the lead + + + align:start position:0% +the troop is attacked he takes the lead +and and he um fights and sometimes gets + + align:start position:0% +and and he um fights and sometimes gets + + + align:start position:0% +and and he um fights and sometimes gets +killed there's a he he he has a a + + align:start position:0% +killed there's a he he he has a a + + + align:start position:0% +killed there's a he he he has a a +function of that military sort so he has + + align:start position:0% +function of that military sort so he has + + + align:start position:0% +function of that military sort so he has +to pay for being so self-confident but + + align:start position:0% +to pay for being so self-confident but + + + align:start position:0% +to pay for being so self-confident but +in the meantime he shows forth this love + + align:start position:0% +in the meantime he shows forth this love + + + align:start position:0% +in the meantime he shows forth this love +of himself and I think it's I stand in + + align:start position:0% +of himself and I think it's I stand in + + + align:start position:0% +of himself and I think it's I stand in +admiration in all of that and think that + + align:start position:0% +admiration in all of that and think that + + + align:start position:0% +admiration in all of that and think that +that's what love involves not self + + align:start position:0% +that's what love involves not self + + + align:start position:0% +that's what love involves not self +sacrifice not + + align:start position:0% +sacrifice not + + + align:start position:0% +sacrifice not +the the um Christlike figure who dies + + align:start position:0% +the the um Christlike figure who dies + + + align:start position:0% +the the um Christlike figure who dies +for this to take the sins away from + + align:start position:0% +for this to take the sins away from + + + align:start position:0% +for this to take the sins away from +other people uh and the idea of + + align:start position:0% +other people uh and the idea of + + + align:start position:0% +other people uh and the idea of +sacrifice being not only Christian but + + align:start position:0% +sacrifice being not only Christian but + + + align:start position:0% +sacrifice being not only Christian but +also pervading U the Western World and + + align:start position:0% +also pervading U the Western World and + + + align:start position:0% +also pervading U the Western World and +in other cultures too as an Evidence of + + align:start position:0% +in other cultures too as an Evidence of + + + align:start position:0% +in other cultures too as an Evidence of +love for me that's not true for me love + + align:start position:0% +love for me that's not true for me love + + + align:start position:0% +love for me that's not true for me love +starts out as this love of self and then + + align:start position:0% +starts out as this love of self and then + + + align:start position:0% +starts out as this love of self and then +develops in all sorts of different ways + + align:start position:0% +develops in all sorts of different ways + + + align:start position:0% +develops in all sorts of different ways +one of which might involve s + + align:start position:0% +one of which might involve s + + + align:start position:0% +one of which might involve s +self-sacrifice if you love your + + align:start position:0% +self-sacrifice if you love your + + + align:start position:0% +self-sacrifice if you love your +country uh just out of a love of your + + align:start position:0% +country uh just out of a love of your + + + align:start position:0% +country uh just out of a love of your +own d and position in the society you + + align:start position:0% +own d and position in the society you + + + align:start position:0% +own d and position in the society you +may risk your life and or even give your + + align:start position:0% +may risk your life and or even give your + + + align:start position:0% +may risk your life and or even give your +life like PE men in in + + align:start position:0% +life like PE men in in + + + align:start position:0% +life like PE men in in +the um in the war in the in the world + + align:start position:0% +the um in the war in the in the world + + + align:start position:0% +the um in the war in the in the world +war who sometimes uh were in a group + + align:start position:0% +war who sometimes uh were in a group + + + align:start position:0% +war who sometimes uh were in a group +with their comrades and a grenade was + + align:start position:0% +with their comrades and a grenade was + + + align:start position:0% +with their comrades and a grenade was +thrown in and they the individual would + + align:start position:0% +thrown in and they the individual would + + + align:start position:0% +thrown in and they the individual would +throw himself on the grenade so he would + + align:start position:0% +throw himself on the grenade so he would + + + align:start position:0% +throw himself on the grenade so he would +got killed in order to prevent all the + + align:start position:0% +got killed in order to prevent all the + + + align:start position:0% +got killed in order to prevent all the +rest of them from getting killed that's + + align:start position:0% +rest of them from getting killed that's + + + align:start position:0% +rest of them from getting killed that's +a love that that I really think is great + + align:start position:0% +a love that that I really think is great + + + align:start position:0% +a love that that I really think is great +wonderful sign not only of heroism but + + align:start position:0% +wonderful sign not only of heroism but + + + align:start position:0% +wonderful sign not only of heroism but +of love the love of his people a love of + + align:start position:0% +of love the love of his people a love of + + + align:start position:0% +of love the love of his people a love of +everything um thinking of this speaking + + align:start position:0% +everything um thinking of this speaking + + + align:start position:0% +everything um thinking of this speaking +of this I just thought of suicide + + align:start position:0% +of this I just thought of suicide + + + align:start position:0% +of this I just thought of suicide +bombers maybe maybe what they do has to + + align:start position:0% +bombers maybe maybe what they do has to + + + align:start position:0% +bombers maybe maybe what they do has to +be thought of as love + + align:start position:0% + + + + align:start position:0% + +too you you also mentioned that we have + + align:start position:0% +too you you also mentioned that we have + + + align:start position:0% +too you you also mentioned that we have +to love ourselves before loving Humanity + + align:start position:0% +to love ourselves before loving Humanity + + + align:start position:0% +to love ourselves before loving Humanity +or for being able to love our country + + align:start position:0% +or for being able to love our country + + + align:start position:0% +or for being able to love our country +not necessarily temporally I mean this + + align:start position:0% +not necessarily temporally I mean this + + + align:start position:0% +not necessarily temporally I mean this +is a nanalysis + + align:start position:0% +is a nanalysis + + + align:start position:0% +is a nanalysis +but usually I mean you don't start the + + align:start position:0% +but usually I mean you don't start the + + + align:start position:0% +but usually I mean you don't start the +babies don't start out out loving + + align:start position:0% +babies don't start out out loving + + + align:start position:0% +babies don't start out out loving +anything so that so it might be temporal + + align:start position:0% +anything so that so it might be temporal + + + align:start position:0% +anything so that so it might be temporal +too but I I it was the use of the word + + align:start position:0% +too but I I it was the use of the word + + + align:start position:0% +too but I I it was the use of the word +before that I was wondering about any go + + align:start position:0% +before that I was wondering about any go + + + align:start position:0% +before that I was wondering about any go +on but for the suicide bombers I think + + align:start position:0% +on but for the suicide bombers I think + + + align:start position:0% +on but for the suicide bombers I think +that um I I wouldn't call it love + + align:start position:0% +that um I I wouldn't call it love + + + align:start position:0% +that um I I wouldn't call it love +because they get brainwashed + + align:start position:0% +because they get brainwashed + + + align:start position:0% +because they get brainwashed +from the beginning and I don't think + + align:start position:0% +from the beginning and I don't think + + + align:start position:0% +from the beginning and I don't think +that they really are doing it for For + + align:start position:0% +that they really are doing it for For + + + align:start position:0% +that they really are doing it for For +the Love of of an ideal I think they are + + align:start position:0% +the Love of of an ideal I think they are + + + align:start position:0% +the Love of of an ideal I think they are +just doing it because that is what is + + align:start position:0% +just doing it because that is what is + + + align:start position:0% +just doing it because that is what is +expected of them who knows I mean some + + align:start position:0% +expected of them who knows I mean some + + + align:start position:0% +expected of them who knows I mean some +probably it's a mixtures some some that + + align:start position:0% +probably it's a mixtures some some that + + + align:start position:0% +probably it's a mixtures some some that +way some others some of them may be + + align:start position:0% +way some others some of them may be + + + align:start position:0% +way some others some of them may be +psychotic who are s going to commit + + align:start position:0% +psychotic who are s going to commit + + + align:start position:0% +psychotic who are s going to commit +suicide anyhow and so they're in a sense + + align:start position:0% +suicide anyhow and so they're in a sense + + + align:start position:0% +suicide anyhow and so they're in a sense +they're told look you're going to kill + + align:start position:0% +they're told look you're going to kill + + + align:start position:0% +they're told look you're going to kill +yourself why do you do us to favor we + + align:start position:0% +yourself why do you do us to favor we + + + align:start position:0% +yourself why do you do us to favor we +can use you I mean it surely must + + align:start position:0% +can use you I mean it surely must + + + align:start position:0% +can use you I mean it surely must +include a great number of different + + align:start position:0% +include a great number of different + + + align:start position:0% +include a great number of different +elements but I don't want to rule out + + align:start position:0% +elements but I don't want to rule out + + + align:start position:0% +elements but I don't want to rule out +the possibility of a Jon of Arc who uh + + align:start position:0% +the possibility of a Jon of Arc who uh + + + align:start position:0% +the possibility of a Jon of Arc who uh +will give herself for her + + align:start position:0% +will give herself for her + + + align:start position:0% +will give herself for her +people well I mean I mean the myth of + + align:start position:0% +people well I mean I mean the myth of + + + align:start position:0% +people well I mean I mean the myth of +Jon ofar was that their reality is more + + align:start position:0% +Jon ofar was that their reality is more + + + align:start position:0% +Jon ofar was that their reality is more +complicated with her + + align:start position:0% +complicated with her + + + align:start position:0% +complicated with her +too agre + + align:start position:0% +too agre + + + align:start position:0% +too agre +on I feel you should be able to answer + + align:start position:0% +on I feel you should be able to answer + + + align:start position:0% +on I feel you should be able to answer +yes but it's different because she for + + align:start position:0% +yes but it's different because she for + + + align:start position:0% +yes but it's different because she for +example Jonah VAR had an idea an ideal + + align:start position:0% +example Jonah VAR had an idea an ideal + + + align:start position:0% +example Jonah VAR had an idea an ideal +and she fought for that ideal + + align:start position:0% +and she fought for that ideal + + + align:start position:0% +and she fought for that ideal +and um her love for that ideal made her + + align:start position:0% +and um her love for that ideal made her + + + align:start position:0% +and um her love for that ideal made her +sacrifice her life and give her life for + + align:start position:0% +sacrifice her life and give her life for + + + align:start position:0% +sacrifice her life and give her life for +it + + align:start position:0% +it + + + align:start position:0% +it +but I don't think that suicide bombers + + align:start position:0% +but I don't think that suicide bombers + + + align:start position:0% +but I don't think that suicide bombers +have such a clear idea of what they're + + align:start position:0% +have such a clear idea of what they're + + + align:start position:0% +have such a clear idea of what they're +doing + + align:start position:0% +doing + + + align:start position:0% +doing +I I've never known a suicide NE there + + align:start position:0% +I I've never known a suicide NE there + + + align:start position:0% +I I've never known a suicide NE there +must there must be some of them are + + align:start position:0% +must there must be some of them are + + + align:start position:0% +must there must be some of them are +idealistic well and their people you + + align:start position:0% +idealistic well and their people you + + + align:start position:0% +idealistic well and their people you +mean particularly in the present War + + align:start position:0% +mean particularly in the present War + + + align:start position:0% +mean particularly in the present War +have often suffered so much that they + + align:start position:0% +have often suffered so much that they + + + align:start position:0% +have often suffered so much that they +feel this is they should do their utmost + + align:start position:0% +feel this is they should do their utmost + + + align:start position:0% +feel this is they should do their utmost +and this is it the suicide bombers the + + align:start position:0% +and this is it the suicide bombers the + + + align:start position:0% +and this is it the suicide bombers the +great suicide bombers that I grew up + + align:start position:0% +great suicide bombers that I grew up + + + align:start position:0% +great suicide bombers that I grew up +with are the + + align:start position:0% +with are the + + + align:start position:0% +with are the +kamakazi aviators + + align:start position:0% +kamakazi aviators + + + align:start position:0% +kamakazi aviators +in the second world war you know the + + align:start position:0% +in the second world war you know the + + + align:start position:0% +in the second world war you know the +Japanese kamakazi you know what they + + align:start position:0% +Japanese kamakazi you know what they + + + align:start position:0% +Japanese kamakazi you know what they +they want to draw a distinction right + + align:start position:0% +they want to draw a distinction right + + + align:start position:0% +they want to draw a distinction right +between the suicide bombers who blow up + + align:start position:0% +between the suicide bombers who blow up + + + align:start position:0% +between the suicide bombers who blow up +a nightclub right and and the ones who + + align:start position:0% +a nightclub right and and the ones who + + + align:start position:0% +a nightclub right and and the ones who +will you know attack like a military and + + align:start position:0% +will you know attack like a military and + + + align:start position:0% +will you know attack like a military and +stuff like that I I think there's a + + align:start position:0% +stuff like that I I think there's a + + + align:start position:0% +stuff like that I I think there's a +distinction there oh no I'm not denying + + align:start position:0% +distinction there oh no I'm not denying + + + align:start position:0% +distinction there oh no I'm not denying +any distinction beyond the level of + + align:start position:0% +any distinction beyond the level of + + + align:start position:0% +any distinction beyond the level of +question of love I mean you might say + + align:start position:0% +question of love I mean you might say + + + align:start position:0% +question of love I mean you might say +that uh uh it's unwise or immoral love + + align:start position:0% +that uh uh it's unwise or immoral love + + + align:start position:0% +that uh uh it's unwise or immoral love +isn't always moral + + align:start position:0% +isn't always moral + + + align:start position:0% +isn't always moral +um you know that might be but again one + + align:start position:0% +um you know that might be but again one + + + align:start position:0% +um you know that might be but again one +doesn't know quite what's the motives + + align:start position:0% +doesn't know quite what's the motives + + + align:start position:0% +doesn't know quite what's the motives +are but in the case of the + + align:start position:0% +are but in the case of the + + + align:start position:0% +are but in the case of the +kamakazi Japanese there was no sympathy + + align:start position:0% +kamakazi Japanese there was no sympathy + + + align:start position:0% +kamakazi Japanese there was no sympathy +with them in America they were all said + + align:start position:0% +with them in America they were all said + + + align:start position:0% +with them in America they were all said +to be uh sort of bizarre creatures who + + align:start position:0% +to be uh sort of bizarre creatures who + + + align:start position:0% +to be uh sort of bizarre creatures who +were brainwashed and were out of their + + align:start position:0% +were brainwashed and were out of their + + + align:start position:0% +were brainwashed and were out of their +minds um I'm sure that in many cases + + align:start position:0% +minds um I'm sure that in many cases + + + align:start position:0% +minds um I'm sure that in many cases +they were just Heroes they're just + + align:start position:0% +they were just Heroes they're just + + + align:start position:0% +they were just Heroes they're just +heroic and if they had if they were the + + align:start position:0% +heroic and if they had if they were the + + + align:start position:0% +heroic and if they had if they were the +2000 had 2,000 who got killed that way + + align:start position:0% +2000 had 2,000 who got killed that way + + + align:start position:0% +2000 had 2,000 who got killed that way +and they nearly destroyed the American + + align:start position:0% +and they nearly destroyed the American + + + align:start position:0% +and they nearly destroyed the American +Fleet if they had had 10,000 the + + align:start position:0% +Fleet if they had had 10,000 the + + + align:start position:0% +Fleet if they had had 10,000 the +Japanese would have won the war so they + + align:start position:0% +Japanese would have won the war so they + + + align:start position:0% +Japanese would have won the war so they +were heroic if you relate that to the + + align:start position:0% +were heroic if you relate that to the + + + align:start position:0% +were heroic if you relate that to the +person who D who dives on the hand + + align:start position:0% +person who D who dives on the hand + + + align:start position:0% +person who D who dives on the hand +grenade the person who dives on the hand + + align:start position:0% +grenade the person who dives on the hand + + + align:start position:0% +grenade the person who dives on the hand +grenade does so to save the men around + + align:start position:0% +grenade does so to save the men around + + + align:start position:0% +grenade does so to save the men around +him which is just what the kamakazi + + align:start position:0% +him which is just what the kamakazi + + + align:start position:0% +him which is just what the kamakazi +fighters were doing because if you sink + + align:start position:0% +fighters were doing because if you sink + + + align:start position:0% +fighters were doing because if you sink +a battleship how many more lives of your + + align:start position:0% +a battleship how many more lives of your + + + align:start position:0% +a battleship how many more lives of your +men is that going to save yeah right + + align:start position:0% +men is that going to save yeah right + + + align:start position:0% +men is that going to save yeah right +those kind of same same mentality I was + + align:start position:0% +those kind of same same mentality I was + + + align:start position:0% +those kind of same same mentality I was +going to say about suicide bombers I I + + align:start position:0% +going to say about suicide bombers I I + + + align:start position:0% +going to say about suicide bombers I I +just I think that they do have have + + align:start position:0% +just I think that they do have have + + + align:start position:0% +just I think that they do have have +ideals I mean some of them most of them + + align:start position:0% +ideals I mean some of them most of them + + + align:start position:0% +ideals I mean some of them most of them +I think all of them have have the ideal + + align:start position:0% +I think all of them have have the ideal + + + align:start position:0% +I think all of them have have the ideal +I mean + + align:start position:0% +I mean + + + align:start position:0% +I mean +um which whichever ones you take the + + align:start position:0% +um which whichever ones you take the + + + align:start position:0% +um which whichever ones you take the +ones in Iraq or the ones in um I don't + + align:start position:0% +ones in Iraq or the ones in um I don't + + + align:start position:0% +ones in Iraq or the ones in um I don't +know in Israel or wherever they have an + + align:start position:0% +know in Israel or wherever they have an + + + align:start position:0% +know in Israel or wherever they have an +ideal of I guess they they see + + align:start position:0% +ideal of I guess they they see + + + align:start position:0% +ideal of I guess they they see +themselves as Freedom Fighters and they + + align:start position:0% +themselves as Freedom Fighters and they + + + align:start position:0% +themselves as Freedom Fighters and they +have an ideal of either you know um I + + align:start position:0% +have an ideal of either you know um I + + + align:start position:0% +have an ideal of either you know um I +don't know making a Palestinian state or + + align:start position:0% +don't know making a Palestinian state or + + + align:start position:0% +don't know making a Palestinian state or +making some sort of different Iraq than + + align:start position:0% +making some sort of different Iraq than + + + align:start position:0% +making some sort of different Iraq than +now so they don't they're not just + + align:start position:0% +now so they don't they're not just + + + align:start position:0% +now so they don't they're not just +brainwashed I mean you know they they've + + align:start position:0% +brainwashed I mean you know they they've + + + align:start position:0% +brainwashed I mean you know they they've +they've reached a point I mean it's been + + align:start position:0% +they've reached a point I mean it's been + + + align:start position:0% +they've reached a point I mean it's been +proven that most of them are just normal + + align:start position:0% +proven that most of them are just normal + + + align:start position:0% +proven that most of them are just normal +people they're not you know crazy people + + align:start position:0% +people they're not you know crazy people + + + align:start position:0% +people they're not you know crazy people +who are inal institutions who have + + align:start position:0% +who are inal institutions who have + + + align:start position:0% +who are inal institutions who have +measured the ground how do you know + + align:start position:0% +measured the ground how do you know + + + align:start position:0% +measured the ground how do you know +that well I mean hav I've seen lots of + + align:start position:0% +that well I mean hav I've seen lots of + + + align:start position:0% +that well I mean hav I've seen lots of +uh reports mostly on the uh Palestinian + + align:start position:0% +uh reports mostly on the uh Palestinian + + + align:start position:0% +uh reports mostly on the uh Palestinian +Israeli conflict that they've said that + + align:start position:0% +Israeli conflict that they've said that + + + align:start position:0% +Israeli conflict that they've said that +they're just you know uh family members + + align:start position:0% +they're just you know uh family members + + + align:start position:0% +they're just you know uh family members +uh you know like a father of a family + + align:start position:0% +uh you know like a father of a family + + + align:start position:0% +uh you know like a father of a family +and stuff um you know I mean they're not + + align:start position:0% +and stuff um you know I mean they're not + + + align:start position:0% +and stuff um you know I mean they're not +people who are in Asylum that's what I'm + + align:start position:0% +people who are in Asylum that's what I'm + + + align:start position:0% +people who are in Asylum that's what I'm +saying they're not they're not crazy + + align:start position:0% +saying they're not they're not crazy + + + align:start position:0% +saying they're not they're not crazy +officially but ad's idea of brainwashing + + align:start position:0% +officially but ad's idea of brainwashing + + + align:start position:0% +officially but ad's idea of brainwashing +didn't mean that they were + + align:start position:0% +didn't mean that they were + + + align:start position:0% +didn't mean that they were +psychotic they they had been brainwashed + + align:start position:0% +psychotic they they had been brainwashed + + + align:start position:0% +psychotic they they had been brainwashed +that's different from what I don't know + + align:start position:0% +that's different from what I don't know + + + align:start position:0% +that's different from what I don't know +I don't I just don't know what the + + align:start position:0% +I don't I just don't know what the + + + align:start position:0% +I don't I just don't know what the +figures are in this well I + + align:start position:0% +figures are in this well I + + + align:start position:0% +figures are in this well I +mean I + + align:start position:0% + + + + align:start position:0% + +I I don't I mean + + align:start position:0% +I I don't I mean + + + align:start position:0% +I I don't I mean +brainwashed brainwashed by somebody I I + + align:start position:0% +brainwashed brainwashed by somebody I I + + + align:start position:0% +brainwashed brainwashed by somebody I I +find it hard to believe brainwashed by + + align:start position:0% +find it hard to believe brainwashed by + + + align:start position:0% +find it hard to believe brainwashed by +what they see happening around them yes + + align:start position:0% +what they see happening around them yes + + + align:start position:0% +what they see happening around them yes +but brainwash there's some Authority + + align:start position:0% +but brainwash there's some Authority + + + align:start position:0% +but brainwash there's some Authority +that goes around and brainwashes people + + align:start position:0% +that goes around and brainwashes people + + + align:start position:0% +that goes around and brainwashes people +as uh they did to the Hitler Youth I + + align:start position:0% +as uh they did to the Hitler Youth I + + + align:start position:0% +as uh they did to the Hitler Youth I +don't think that really happens I just + + align:start position:0% +don't think that really happens I just + + + align:start position:0% +don't think that really happens I just +think they're brainwashed I mean when + + align:start position:0% +think they're brainwashed I mean when + + + align:start position:0% +think they're brainwashed I mean when +they see you know their brother killed + + align:start position:0% +they see you know their brother killed + + + align:start position:0% +they see you know their brother killed +or whatever they see a bunch of + + align:start position:0% +or whatever they see a bunch of + + + align:start position:0% +or whatever they see a bunch of +casualties that are related to them or + + align:start position:0% +casualties that are related to them or + + + align:start position:0% +casualties that are related to them or +they see that their dream of whichever + + align:start position:0% +they see that their dream of whichever + + + align:start position:0% +they see that their dream of whichever +whatever dream they have is just you + + align:start position:0% +whatever dream they have is just you + + + align:start position:0% +whatever dream they have is just you +know totally being stomped on and they + + align:start position:0% +know totally being stomped on and they + + + align:start position:0% +know totally being stomped on and they +see they that may be a sort of brainwash + + align:start position:0% +see they that may be a sort of brainwash + + + align:start position:0% +see they that may be a sort of brainwash +but I don't want to call it brainwash I + + align:start position:0% +but I don't want to call it brainwash I + + + align:start position:0% +but I don't want to call it brainwash I +want to call it more well I mean I guess + + align:start position:0% +want to call it more well I mean I guess + + + align:start position:0% +want to call it more well I mean I guess +you can't really call it braid wash it's + + align:start position:0% +you can't really call it braid wash it's + + + align:start position:0% +you can't really call it braid wash it's +more you're becoming desperate okay why + + align:start position:0% +more you're becoming desperate okay why + + + align:start position:0% +more you're becoming desperate okay why +don't we stop there um next week there + + align:start position:0% +don't we stop there um next week there + + + align:start position:0% +don't we stop there um next week there +is the chapter on religious Love and the + + align:start position:0% +is the chapter on religious Love and the + + + align:start position:0% +is the chapter on religious Love and the +concluding two chapters who would like + + align:start position:0% +concluding two chapters who would like + + + align:start position:0% +concluding two chapters who would like +to give the presentation I think + + align:start position:0% +to give the presentation I think + + + align:start position:0% +to give the presentation I think +uh Adriana like Veronica did a very good + + align:start position:0% +uh Adriana like Veronica did a very good + + + align:start position:0% +uh Adriana like Veronica did a very good +job and so who would like to continue + + align:start position:0% +job and so who would like to continue + + + align:start position:0% +job and so who would like to continue +the tradition + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um one thing that in the chapter + + align:start position:0% +um one thing that in the chapter + + + align:start position:0% +um one thing that in the chapter +on love in society we didn't get to is + + align:start position:0% +on love in society we didn't get to is + + + align:start position:0% +on love in society we didn't get to is +the distinction between of the analysis + + align:start position:0% +the distinction between of the analysis + + + align:start position:0% +the distinction between of the analysis +of + + align:start position:0% +of + + + align:start position:0% +of +compassion of U love of country we + + align:start position:0% +compassion of U love of country we + + + align:start position:0% +compassion of U love of country we +touched on beginning to touch on it here + + align:start position:0% +touched on beginning to touch on it here + + + align:start position:0% +touched on beginning to touch on it here +we might could begin there if you want + + align:start position:0% +we might could begin there if you want + + + align:start position:0% +we might could begin there if you want +and then that quickly enters into + + align:start position:0% +and then that quickly enters into + + + align:start position:0% +and then that quickly enters into +religious love as as as I mentioned at + + align:start position:0% +religious love as as as I mentioned at + + + align:start position:0% +religious love as as as I mentioned at +the end of the + + align:start position:0% +the end of the + + + align:start position:0% +the end of the +chapter um and that aspect of compassion + + align:start position:0% +chapter um and that aspect of compassion + + + align:start position:0% +chapter um and that aspect of compassion +of Buddhism uh I find very beautiful and + + align:start position:0% +of Buddhism uh I find very beautiful and + + + align:start position:0% +of Buddhism uh I find very beautiful and +attractive if anyone knows more about + + align:start position:0% +attractive if anyone knows more about + + + align:start position:0% +attractive if anyone knows more about +Buddhism this would be a good time to + + align:start position:0% +Buddhism this would be a good time to + + + align:start position:0% +Buddhism this would be a good time to +think about + + align:start position:0% +think about + + + align:start position:0% +think about +that so are we is it next do we we meet + + align:start position:0% +that so are we is it next do we we meet + + + align:start position:0% +that so are we is it next do we we meet +next week or when is the holiday the + + align:start position:0% +next week or when is the holiday the + + + align:start position:0% +next week or when is the holiday the +holiday is the week after the week after + + align:start position:0% +holiday is the week after the week after + + + align:start position:0% +holiday is the week after the week after +we so we do meet next week and then + + align:start position:0% +we so we do meet next week and then + + + align:start position:0% +we so we do meet next week and then +holidays after that all right so next + + align:start position:0% +holidays after that all right so next + + + align:start position:0% +holidays after that all right so next +week Columbus Day yeah yeah that's two + + align:start position:0% +week Columbus Day yeah yeah that's two + + + align:start position:0% +week Columbus Day yeah yeah that's two +apparently that's two weeks so good then + + align:start position:0% +apparently that's two weeks so good then + + + align:start position:0% +apparently that's two weeks so good then +I I'll see you there I'm + + align:start position:0% +I I'll see you there I'm + + + align:start position:0% +I I'll see you there I'm +delighted we had no suicide day on + + align:start position:0% +delighted we had no suicide day on + + + align:start position:0% +delighted we had no suicide day on +September I'm delighted with the work + + align:start position:0% +September I'm delighted with the work + + + align:start position:0% +September I'm delighted with the work +you're doing and the did reading the + + align:start position:0% +you're doing and the did reading the + + + align:start position:0% +you're doing and the did reading the +book so I'll see you then thank you + + align:start position:0% +book so I'll see you then thank you + + + align:start position:0% +book so I'll see you then thank you +thank you \ No newline at end of file diff --git a/Kk7cc15gWF8.txt b/Kk7cc15gWF8.txt new file mode 100644 index 0000000000000000000000000000000000000000..7b00288682ac42ecea16bc943fac9e04a3c059c9 --- /dev/null +++ b/Kk7cc15gWF8.txt @@ -0,0 +1,1515 @@ +align:start position:0% + +okay so our discussion at the beginning + + align:start position:0% +okay so our discussion at the beginning + + + align:start position:0% +okay so our discussion at the beginning +was based on just taking a state those + + align:start position:0% +was based on just taking a state those + + + align:start position:0% +was based on just taking a state those +energy instantaneous energy eigenstates + + align:start position:0% +energy instantaneous energy eigenstates + + + align:start position:0% +energy instantaneous energy eigenstates +and putting calculating what phases + + align:start position:0% +and putting calculating what phases + + + align:start position:0% +and putting calculating what phases +would make it satisfy the Schrodinger + + align:start position:0% +would make it satisfy the Schrodinger + + + align:start position:0% +would make it satisfy the Schrodinger +equation and we found those are the + + align:start position:0% +equation and we found those are the + + + align:start position:0% +equation and we found those are the +phases that came close to satisfying the + + align:start position:0% +phases that came close to satisfying the + + + align:start position:0% +phases that came close to satisfying the +Schrodinger equation but not quite so in + + align:start position:0% +Schrodinger equation but not quite so in + + + align:start position:0% +Schrodinger equation but not quite so in +order to do this a little more and there + + align:start position:0% +order to do this a little more and there + + + align:start position:0% +order to do this a little more and there +are more controlled approximation let's + + align:start position:0% +are more controlled approximation let's + + + align:start position:0% +are more controlled approximation let's +do a calculation where we put all the + + align:start position:0% +do a calculation where we put all the + + + align:start position:0% +do a calculation where we put all the +information in so if we have a stapes i + + align:start position:0% +information in so if we have a stapes i + + + align:start position:0% +information in so if we have a stapes i +of t will write it as a superposition of + + align:start position:0% +of t will write it as a superposition of + + + align:start position:0% +of t will write it as a superposition of +states of instantaneous eigenstates so + + align:start position:0% +states of instantaneous eigenstates so + + + align:start position:0% +states of instantaneous eigenstates so +this is a general solution maybe general + + align:start position:0% +this is a general solution maybe general + + + align:start position:0% +this is a general solution maybe general +answers for a solution the wave function + + align:start position:0% +answers for a solution the wave function + + + align:start position:0% +answers for a solution the wave function +since those instantaneous energy + + align:start position:0% +since those instantaneous energy + + + align:start position:0% +since those instantaneous energy +eigenstates are complete or for normal + + align:start position:0% +eigenstates are complete or for normal + + + align:start position:0% +eigenstates are complete or for normal +this former Oh n basis orthonormal basis + + align:start position:0% +this former Oh n basis orthonormal basis + + + align:start position:0% +this former Oh n basis orthonormal basis +at all times at any time it's an + + align:start position:0% +at all times at any time it's an + + + align:start position:0% +at all times at any time it's an +orthonormal set of states we should be + + align:start position:0% +orthonormal set of states we should be + + + align:start position:0% +orthonormal set of states we should be +able to write our state as that + + align:start position:0% +able to write our state as that + + + align:start position:0% +able to write our state as that +superposition so what we're gonna do is + + align:start position:0% +superposition so what we're gonna do is + + + align:start position:0% +superposition so what we're gonna do is +now kind of redo the analysis of the + + align:start position:0% +now kind of redo the analysis of the + + + align:start position:0% +now kind of redo the analysis of the +idea by take the approximation more + + align:start position:0% +idea by take the approximation more + + + align:start position:0% +idea by take the approximation more +generally so that we see in fact the + + align:start position:0% +generally so that we see in fact the + + + align:start position:0% +generally so that we see in fact the +equations that show up that you can + + align:start position:0% +equations that show up that you can + + + align:start position:0% +equations that show up that you can +solve in general so the Schrodinger + + align:start position:0% +solve in general so the Schrodinger + + + align:start position:0% +solve in general so the Schrodinger +equation is IH bar d DP of sy is equal + + align:start position:0% +equation is IH bar d DP of sy is equal + + + align:start position:0% +equation is IH bar d DP of sy is equal +to IH + + align:start position:0% +to IH + + + align:start position:0% +to IH +sy so let's look at what it gives us + + align:start position:0% +sy so let's look at what it gives us + + + align:start position:0% +sy so let's look at what it gives us +here so we'll have IH bar + + align:start position:0% + + + + align:start position:0% + +some over N and I have to differentiate + + align:start position:0% +some over N and I have to differentiate + + + align:start position:0% +some over N and I have to differentiate +this state so I get C and dot dot for + + align:start position:0% +this state so I get C and dot dot for + + + align:start position:0% +this state so I get C and dot dot for +time derivatives sigh and plus C and + + align:start position:0% +time derivatives sigh and plus C and + + + align:start position:0% +time derivatives sigh and plus C and +sorry and dot this is a time derivative + + align:start position:0% +sorry and dot this is a time derivative + + + align:start position:0% +sorry and dot this is a time derivative +of the state it is equal to HM sighs + + align:start position:0% +of the state it is equal to HM sighs + + + align:start position:0% +of the state it is equal to HM sighs +this is the sum over n CN of T H sy n is + + align:start position:0% +this is the sum over n CN of T H sy n is + + + align:start position:0% +this is the sum over n CN of T H sy n is +equal to e n of T sy n of T okay so + + align:start position:0% +equal to e n of T sy n of T okay so + + + align:start position:0% +equal to e n of T sy n of T okay so +that's your equation now let's see in + + align:start position:0% +that's your equation now let's see in + + + align:start position:0% +that's your equation now let's see in +various components what it gives you so + + align:start position:0% +various components what it gives you so + + + align:start position:0% +various components what it gives you so +to see the various components we form an + + align:start position:0% +to see the various components we form an + + + align:start position:0% +to see the various components we form an +overlap with up side K of T so bringing + + align:start position:0% +overlap with up side K of T so bringing + + + align:start position:0% +overlap with up side K of T so bringing +up side K of T and what do we get + + align:start position:0% +up side K of T and what do we get + + + align:start position:0% +up side K of T and what do we get +since these states are orthonormal side + + align:start position:0% +since these states are orthonormal side + + + align:start position:0% +since these states are orthonormal side +K when it comes here this is a function + + align:start position:0% +K when it comes here this is a function + + + align:start position:0% +K when it comes here this is a function +of time it doesn't care sorry K hit + + align:start position:0% +of time it doesn't care sorry K hit + + + align:start position:0% +of time it doesn't care sorry K hit +subside and that's a Kronecker Delta the + + align:start position:0% +subside and that's a Kronecker Delta the + + + align:start position:0% +subside and that's a Kronecker Delta the +some disappears and the only term that + + align:start position:0% +some disappears and the only term that + + + align:start position:0% +some disappears and the only term that +is left here is C k dot so we get IH bar + + align:start position:0% +is left here is C k dot so we get IH bar + + + align:start position:0% +is left here is C k dot so we get IH bar +CK dot from this term and let's put the + + align:start position:0% +CK dot from this term and let's put the + + + align:start position:0% +CK dot from this term and let's put the +second term to the right-hand side + + align:start position:0% +second term to the right-hand side + + + align:start position:0% +second term to the right-hand side +so let's just write what we get from the + + align:start position:0% +so let's just write what we get from the + + + align:start position:0% +so let's just write what we get from the +right hand side and from this term so + + align:start position:0% +right hand side and from this term so + + + align:start position:0% +right hand side and from this term so +from the right hand side we have the + + align:start position:0% +from the right hand side we have the + + + align:start position:0% +from the right hand side we have the +side K on that thing that is on the + + align:start position:0% +side K on that thing that is on the + + + align:start position:0% +side K on that thing that is on the +right that again + + align:start position:0% +right that again + + + align:start position:0% +right that again +fits the state and produces a chronicle + + align:start position:0% +fits the state and produces a chronicle + + + align:start position:0% +fits the state and produces a chronicle +Delta so we get CK + + align:start position:0% + + + + align:start position:0% + +Ek of tea from the term that wasn't the + + align:start position:0% +Ek of tea from the term that wasn't the + + + align:start position:0% +Ek of tea from the term that wasn't the +right hand side and here however we + + align:start position:0% +right hand side and here however we + + + align:start position:0% +right hand side and here however we +don't get rid of the sum because psyche + + align:start position:0% +don't get rid of the sum because psyche + + + align:start position:0% +don't get rid of the sum because psyche +is not orthogonal to psi n dot sine dot + + align:start position:0% +is not orthogonal to psi n dot sine dot + + + align:start position:0% +is not orthogonal to psi n dot sine dot +is more complicated so what do we get + + align:start position:0% +is more complicated so what do we get + + + align:start position:0% +is more complicated so what do we get +here minus I h-bar the sum over end sy k + + align:start position:0% +here minus I h-bar the sum over end sy k + + + align:start position:0% +here minus I h-bar the sum over end sy k +sy and dot inner product cm okay that's + + align:start position:0% +sy and dot inner product cm okay that's + + + align:start position:0% +sy and dot inner product cm okay that's +pretty close to what we want but let's + + align:start position:0% +pretty close to what we want but let's + + + align:start position:0% +pretty close to what we want but let's +write it still in a slightly different + + align:start position:0% +write it still in a slightly different + + + align:start position:0% +write it still in a slightly different +way I want to isolate the CK's so from + + align:start position:0% +way I want to isolate the CK's so from + + + align:start position:0% +way I want to isolate the CK's so from +that sum + + align:start position:0% +that sum + + + align:start position:0% +that sum +I will separate the CK part so we'll + + align:start position:0% +I will separate the CK part so we'll + + + align:start position:0% +I will separate the CK part so we'll +have EK of T and there's going to be a + + align:start position:0% +have EK of T and there's going to be a + + + align:start position:0% +have EK of T and there's going to be a +term here when we have n equal K so I'll + + align:start position:0% +term here when we have n equal K so I'll + + + align:start position:0% +term here when we have n equal K so I'll +bring it out there - I h-bar sy k sy k + + align:start position:0% +bring it out there - I h-bar sy k sy k + + + align:start position:0% +bring it out there - I h-bar sy k sy k +dot CK and the last term now becomes IH + + align:start position:0% +dot CK and the last term now becomes IH + + + align:start position:0% +dot CK and the last term now becomes IH +bar the sum over n different from k sy k + + align:start position:0% +bar the sum over n different from k sy k + + + align:start position:0% +bar the sum over n different from k sy k +sy n dot c n okay so this is the form of + + align:start position:0% +sy n dot c n okay so this is the form of + + + align:start position:0% +sy n dot c n okay so this is the form of +the equation that this nice and gives + + align:start position:0% +the equation that this nice and gives + + + align:start position:0% +the equation that this nice and gives +you a little understanding of what's + + align:start position:0% +you a little understanding of what's + + + align:start position:0% +you a little understanding of what's +going on that's a general treatment of + + align:start position:0% +going on that's a general treatment of + + + align:start position:0% +going on that's a general treatment of +trying to make a solution from energy + + align:start position:0% +trying to make a solution from energy + + + align:start position:0% +trying to make a solution from energy +instantaneous energy + + align:start position:0% +instantaneous energy + + + align:start position:0% +instantaneous energy +agon states here where your + + align:start position:0% +agon states here where your + + + align:start position:0% +agon states here where your +instantaneous energizer we try to make a + + align:start position:0% +instantaneous energizer we try to make a + + + align:start position:0% +instantaneous energizer we try to make a +solution that is the full equation what + + align:start position:0% +solution that is the full equation what + + + align:start position:0% +solution that is the full equation what +did we do before we used just one of + + align:start position:0% +did we do before we used just one of + + + align:start position:0% +did we do before we used just one of +them we took one instantaneous energy I + + align:start position:0% +them we took one instantaneous energy I + + + align:start position:0% +them we took one instantaneous energy I +can say that we try to make a solution + + align:start position:0% +can say that we try to make a solution + + + align:start position:0% +can say that we try to make a solution +by multiplying by one thing and then we + + align:start position:0% +by multiplying by one thing and then we + + + align:start position:0% +by multiplying by one thing and then we +tried but then it doesn't work because + + align:start position:0% +tried but then it doesn't work because + + + align:start position:0% +tried but then it doesn't work because +when you have just one coefficient say K + + align:start position:0% +when you have just one coefficient say K + + + align:start position:0% +when you have just one coefficient say K +with some fixed K you have this equation + + align:start position:0% +with some fixed K you have this equation + + + align:start position:0% +with some fixed K you have this equation +but then you couple to all other + + align:start position:0% +but then you couple to all other + + + align:start position:0% +but then you couple to all other +coefficients where n is different from + + align:start position:0% +coefficients where n is different from + + + align:start position:0% +coefficients where n is different from +okay so what we did before was + + align:start position:0% +okay so what we did before was + + + align:start position:0% +okay so what we did before was +essentially by claiming that this term + + align:start position:0% +essentially by claiming that this term + + + align:start position:0% +essentially by claiming that this term +is small just focus on this thing and + + align:start position:0% +is small just focus on this thing and + + + align:start position:0% +is small just focus on this thing and +this is an easily solvable equation that + + align:start position:0% +this is an easily solvable equation that + + + align:start position:0% +this is an easily solvable equation that +in fact gives the type of solution we + + align:start position:0% +in fact gives the type of solution we + + + align:start position:0% +in fact gives the type of solution we +have there when you have C dot equal to + + align:start position:0% +have there when you have C dot equal to + + + align:start position:0% +have there when you have C dot equal to +this I'll write it in our previous + + align:start position:0% +this I'll write it in our previous + + + align:start position:0% +this I'll write it in our previous +approximation so in the approximation + + align:start position:0% +approximation so in the approximation + + + align:start position:0% +approximation so in the approximation +where the last term is negligible and we + + align:start position:0% +where the last term is negligible and we + + + align:start position:0% +where the last term is negligible and we +would see why it could be negligible + + align:start position:0% +would see why it could be negligible + + + align:start position:0% +would see why it could be negligible +then we get just I h-bar C K dot equals + + align:start position:0% +then we get just I h-bar C K dot equals + + + align:start position:0% +then we get just I h-bar C K dot equals +e K of T minus I h-bar sorry + + align:start position:0% +e K of T minus I h-bar sorry + + + align:start position:0% +e K of T minus I h-bar sorry +Capeside K dot CK and this thing is + + align:start position:0% +Capeside K dot CK and this thing is + + + align:start position:0% +Capeside K dot CK and this thing is +solved by writing C K of P is equal to e + + align:start position:0% +solved by writing C K of P is equal to e + + + align:start position:0% +solved by writing C K of P is equal to e +to the 1 over I h-bar interval from 0 to + + align:start position:0% +to the 1 over I h-bar interval from 0 to + + + align:start position:0% +to the 1 over I h-bar interval from 0 to +T of this whole thing + + align:start position:0% +T of this whole thing + + + align:start position:0% +T of this whole thing +of T prime minus IH bar sy Cape psyche a + + align:start position:0% +of T prime minus IH bar sy Cape psyche a + + + align:start position:0% +of T prime minus IH bar sy Cape psyche a +dot of T prime DT prime x ck of 0 this + + align:start position:0% +dot of T prime DT prime x ck of 0 this + + + align:start position:0% +dot of T prime DT prime x ck of 0 this +is a differential equation so IH bar + + align:start position:0% +is a differential equation so IH bar + + + align:start position:0% +is a differential equation so IH bar +times the time derivative of this if you + + align:start position:0% +times the time derivative of this if you + + + align:start position:0% +times the time derivative of this if you +apply IH bar time derivative you + + align:start position:0% +apply IH bar time derivative you + + + align:start position:0% +apply IH bar time derivative you +differentiate with respect to time then + + align:start position:0% +differentiate with respect to time then + + + align:start position:0% +differentiate with respect to time then +exponent you get 1 over IH bar that + + align:start position:0% +exponent you get 1 over IH bar that + + + align:start position:0% +exponent you get 1 over IH bar that +cancels this IH bar and the derivative + + align:start position:0% +cancels this IH bar and the derivative + + + align:start position:0% +cancels this IH bar and the derivative +of the exponent is this factor just a + + align:start position:0% +of the exponent is this factor just a + + + align:start position:0% +of the exponent is this factor just a +standard first-order time-dependent + + align:start position:0% +standard first-order time-dependent + + + align:start position:0% +standard first-order time-dependent +differential equation so last time we + + align:start position:0% +differential equation so last time we + + + align:start position:0% +differential equation so last time we +said we Nord possible couplings between + + align:start position:0% +said we Nord possible couplings between + + + align:start position:0% +said we Nord possible couplings between +the different modes represented by this + + align:start position:0% +the different modes represented by this + + + align:start position:0% +the different modes represented by this +term and we just solved this equation + + align:start position:0% +term and we just solved this equation + + + align:start position:0% +term and we just solved this equation +which gave us this which is exactly what + + align:start position:0% +which gave us this which is exactly what + + + align:start position:0% +which gave us this which is exactly what +we've been writing here + + align:start position:0% +we've been writing here + + + align:start position:0% +we've been writing here +e to the I theta of K comes from the + + align:start position:0% +e to the I theta of K comes from the + + + align:start position:0% +e to the I theta of K comes from the +first term on that integral and e to the + + align:start position:0% +first term on that integral and e to the + + + align:start position:0% +first term on that integral and e to the +I gamma of K comes from the second term + + align:start position:0% +I gamma of K comes from the second term + + + align:start position:0% +I gamma of K comes from the second term +on that integral sorry the same things + + align:start position:0% +on that integral sorry the same things + + + align:start position:0% +on that integral sorry the same things +so what what this new here is that there + + align:start position:0% +so what what this new here is that there + + + align:start position:0% +so what what this new here is that there +is a coupling and you cannot assume that + + align:start position:0% +is a coupling and you cannot assume that + + + align:start position:0% +is a coupling and you cannot assume that +just CK evolves in time some particular + + align:start position:0% +just CK evolves in time some particular + + + align:start position:0% +just CK evolves in time some particular +K and the others don't the others with + + align:start position:0% +K and the others don't the others with + + + align:start position:0% +K and the others don't the others with +will get coupled in particular if you + + align:start position:0% +will get coupled in particular if you + + + align:start position:0% +will get coupled in particular if you +have + + align:start position:0% + + + + align:start position:0% + +if you have that at time equals zero P + + align:start position:0% +if you have that at time equals zero P + + + align:start position:0% +if you have that at time equals zero P +equals zero + + align:start position:0% +equals zero + + + align:start position:0% +equals zero +some see K of 0 is equal to 1 but all + + align:start position:0% +some see K of 0 is equal to 1 but all + + + align:start position:0% +some see K of 0 is equal to 1 but all +the other ones CK Prime's at 0 are equal + + align:start position:0% +the other ones CK Prime's at 0 are equal + + + align:start position:0% +the other ones CK Prime's at 0 are equal +to 0 for all K Prime different from K so + + align:start position:0% +to 0 for all K Prime different from K so + + + align:start position:0% +to 0 for all K Prime different from K so +your initial condition is you are in the + + align:start position:0% +your initial condition is you are in the + + + align:start position:0% +your initial condition is you are in the +state k at time equals 0 that's why you + + align:start position:0% +state k at time equals 0 that's why you + + + align:start position:0% +state k at time equals 0 that's why you +have CK at time equal 0 equal 1 and the + + align:start position:0% +have CK at time equal 0 equal 1 and the + + + align:start position:0% +have CK at time equal 0 equal 1 and the +others are 0 at different times if you + + align:start position:0% +others are 0 at different times if you + + + align:start position:0% +others are 0 at different times if you +look at your differential equation and + + align:start position:0% + + + + align:start position:0% + +and try to see what happens after a + + align:start position:0% +and try to see what happens after a + + + align:start position:0% +and try to see what happens after a +little time well we know CK dot is good + + align:start position:0% +little time well we know CK dot is good + + + align:start position:0% +little time well we know CK dot is good +a change it's gonna have a non-trivial + + align:start position:0% +a change it's gonna have a non-trivial + + + align:start position:0% +a change it's gonna have a non-trivial +value this happen but these things are + + align:start position:0% +value this happen but these things are + + + align:start position:0% +value this happen but these things are +not going to remain zero those other + + align:start position:0% +not going to remain zero those other + + + align:start position:0% +not going to remain zero those other +states are going to get populated the + + align:start position:0% +states are going to get populated the + + + align:start position:0% +states are going to get populated the +particular I h-bar see K prime dot look + + align:start position:0% +particular I h-bar see K prime dot look + + + align:start position:0% +particular I h-bar see K prime dot look +at the top equation applied for k equal + + align:start position:0% +at the top equation applied for k equal + + + align:start position:0% +at the top equation applied for k equal +to K Prime and look at time equals 0 + + align:start position:0% +to K Prime and look at time equals 0 + + + align:start position:0% +to K Prime and look at time equals 0 +what do you get at time equals 0 well + + align:start position:0% +what do you get at time equals 0 well + + + align:start position:0% +what do you get at time equals 0 well +you would get all this factor EK prime + + align:start position:0% +you would get all this factor EK prime + + + align:start position:0% +you would get all this factor EK prime +time CK prime at time equals 0 well + + align:start position:0% +time CK prime at time equals 0 well + + + align:start position:0% +time CK prime at time equals 0 well +that's 0 that's nothing but from the + + align:start position:0% +that's 0 that's nothing but from the + + + align:start position:0% +that's 0 that's nothing but from the +last term what would we get minus I + + align:start position:0% +last term what would we get minus I + + + align:start position:0% +last term what would we get minus I +h-bar sum over n different from K prime + + align:start position:0% +h-bar sum over n different from K prime + + + align:start position:0% +h-bar sum over n different from K prime +of psy K Prime sigh and dot C and at + + align:start position:0% +of psy K Prime sigh and dot C and at + + + align:start position:0% +of psy K Prime sigh and dot C and at +time equals 0 + + align:start position:0% + + + + align:start position:0% + +and here well the only one that is + + align:start position:0% +and here well the only one that is + + + align:start position:0% +and here well the only one that is +different from zero time equals zero is + + align:start position:0% +different from zero time equals zero is + + + align:start position:0% +different from zero time equals zero is +CK so an k when n is equal to K is + + align:start position:0% +CK so an k when n is equal to K is + + + align:start position:0% +CK so an k when n is equal to K is +allowed because we said K Prime is + + align:start position:0% +allowed because we said K Prime is + + + align:start position:0% +allowed because we said K Prime is +different from K so there is one term + + align:start position:0% +different from K so there is one term + + + align:start position:0% +different from K so there is one term +here this is minus IH bar psy K Prime + + align:start position:0% +here this is minus IH bar psy K Prime + + + align:start position:0% +here this is minus IH bar psy K Prime +psy K dot only when N equals to K you + + align:start position:0% +psy K dot only when N equals to K you + + + align:start position:0% +psy K dot only when N equals to K you +get something here because this is the + + align:start position:0% +get something here because this is the + + + align:start position:0% +get something here because this is the +only term that exists and it's equal to + + align:start position:0% +only term that exists and it's equal to + + + align:start position:0% +only term that exists and it's equal to +one so immediately at time equals zero + + align:start position:0% +one so immediately at time equals zero + + + align:start position:0% +one so immediately at time equals zero +the other coefficients start changing + + align:start position:0% +the other coefficients start changing + + + align:start position:0% +the other coefficients start changing +you start populating the other + + align:start position:0% +you start populating the other + + + align:start position:0% +you start populating the other +instantaneous energy eigenstates so this + + align:start position:0% +instantaneous energy eigenstates so this + + + align:start position:0% +instantaneous energy eigenstates so this +this is there's real mixing in this top + + align:start position:0% +this is there's real mixing in this top + + + align:start position:0% +this is there's real mixing in this top +thing that says it's not rigorous to + + align:start position:0% +thing that says it's not rigorous to + + + align:start position:0% +thing that says it's not rigorous to +claim that you stay in that energy + + align:start position:0% +claim that you stay in that energy + + + align:start position:0% +claim that you stay in that energy +eigenstate it starts to couple and if it + + align:start position:0% +eigenstate it starts to couple and if it + + + align:start position:0% +eigenstate it starts to couple and if it +starts to couple then eventually you + + align:start position:0% +starts to couple then eventually you + + + align:start position:0% +starts to couple then eventually you +make transitions the only hope of course + + align:start position:0% +make transitions the only hope of course + + + align:start position:0% +make transitions the only hope of course +is that that term is really small and + + align:start position:0% + + + + align:start position:0% + +basically we can argue how that term + + align:start position:0% +basically we can argue how that term + + + align:start position:0% +basically we can argue how that term +becomes a little small by doing a little + + align:start position:0% +becomes a little small by doing a little + + + align:start position:0% +becomes a little small by doing a little +calculation and then we could be + + align:start position:0% +calculation and then we could be + + + align:start position:0% +calculation and then we could be +rigorous and take a long time to get to + + align:start position:0% +rigorous and take a long time to get to + + + align:start position:0% +rigorous and take a long time to get to +the conclusion or we can just state it + + align:start position:0% +the conclusion or we can just state it + + + align:start position:0% +the conclusion or we can just state it +and that's what we're gonna do after + + align:start position:0% +and that's what we're gonna do after + + + align:start position:0% +and that's what we're gonna do after +analyzing that term a little more \ No newline at end of file diff --git a/Ksl0Vp4jhmA.txt b/Ksl0Vp4jhmA.txt new file mode 100644 index 0000000000000000000000000000000000000000..f821130df7fe66c6fddc7b7656b6f12c6af47d3d --- /dev/null +++ b/Ksl0Vp4jhmA.txt @@ -0,0 +1,763 @@ +align:start position:0% + +hi everyone so our project is called + + align:start position:0% +hi everyone so our project is called + + + align:start position:0% +hi everyone so our project is called +mini world so basically we want to build + + align:start position:0% +mini world so basically we want to build + + + align:start position:0% +mini world so basically we want to build +this video game where you can build a + + align:start position:0% +this video game where you can build a + + + align:start position:0% +this video game where you can build a +world with Kinect by just like grabbing + + align:start position:0% +world with Kinect by just like grabbing + + + align:start position:0% +world with Kinect by just like grabbing +things and filled them by dropping them + + align:start position:0% +things and filled them by dropping them + + + align:start position:0% +things and filled them by dropping them +so the idea is like you can go into the + + align:start position:0% +so the idea is like you can go into the + + + align:start position:0% +so the idea is like you can go into the +3d environment to design your own home + + align:start position:0% +3d environment to design your own home + + + align:start position:0% +3d environment to design your own home +and your own room and also my name is + + align:start position:0% +and your own room and also my name is + + + align:start position:0% +and your own room and also my name is +Jane + + align:start position:0% +Jane + + + align:start position:0% +Jane +so I'm from co3 and I'm a graduate + + align:start position:0% +so I'm from co3 and I'm a graduate + + + align:start position:0% +so I'm from co3 and I'm a graduate +student and I am Cattleya I am caustics + + align:start position:0% +student and I am Cattleya I am caustics + + + align:start position:0% +student and I am Cattleya I am caustics +undergrad student class of 2019 so we + + align:start position:0% +undergrad student class of 2019 so we + + + align:start position:0% +undergrad student class of 2019 so we +address this problem of when we try to + + align:start position:0% +address this problem of when we try to + + + align:start position:0% +address this problem of when we try to +create our own room as Jing has already + + align:start position:0% +create our own room as Jing has already + + + align:start position:0% +create our own room as Jing has already +introduced so we then come up with our + + align:start position:0% +introduced so we then come up with our + + + align:start position:0% +introduced so we then come up with our +game call meeting world and we will show + + align:start position:0% +game call meeting world and we will show + + + align:start position:0% +game call meeting world and we will show +you the our demo now I guess you don't + + align:start position:0% +you the our demo now I guess you don't + + + align:start position:0% +you the our demo now I guess you don't +turn that way + + align:start position:0% + + + + align:start position:0% + +yes so Cattleya will be controlling the + + align:start position:0% +yes so Cattleya will be controlling the + + + align:start position:0% +yes so Cattleya will be controlling the +game and I will be doing here + + align:start position:0% + + + + align:start position:0% + +should we go quickly + + align:start position:0% + + + + align:start position:0% + +yeah so I'm not sure if that's captured + + align:start position:0% + + + + align:start position:0% + +is that comeback + + align:start position:0% + + + + align:start position:0% + +okay yeah I know it's worked so I hope + + align:start position:0% +okay yeah I know it's worked so I hope + + + align:start position:0% +okay yeah I know it's worked so I hope +it's not okay so now we are trying to + + align:start position:0% +it's not okay so now we are trying to + + + align:start position:0% +it's not okay so now we are trying to +locate ourselves in our home + + align:start position:0% + + + + align:start position:0% + +Philippians country other people yeah I + + align:start position:0% +Philippians country other people yeah I + + + align:start position:0% +Philippians country other people yeah I +think it's not tracking do you have the + + align:start position:0% +think it's not tracking do you have the + + + align:start position:0% +think it's not tracking do you have the +SDK installed yes you should pull that + + align:start position:0% +SDK installed yes you should pull that + + + align:start position:0% +SDK installed yes you should pull that +up + + align:start position:0% +up + + + align:start position:0% +up +I don't know how you get away this isn't + + align:start position:0% +I don't know how you get away this isn't + + + align:start position:0% +I don't know how you get away this isn't +a nice nose yeah sure I think there's + + align:start position:0% +a nice nose yeah sure I think there's + + + align:start position:0% +a nice nose yeah sure I think there's +two because we people tested + + align:start position:0% + + + + align:start position:0% + +okay - so that's a good place + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +yep okay so somehow we just got indoor + + align:start position:0% +yep okay so somehow we just got indoor + + + align:start position:0% +yep okay so somehow we just got indoor +because I saw a house and we just went + + align:start position:0% +because I saw a house and we just went + + + align:start position:0% +because I saw a house and we just went +through that door to go into your room + + align:start position:0% +through that door to go into your room + + + align:start position:0% +through that door to go into your room +and then you are getting out of here to + + align:start position:0% +and then you are getting out of here to + + + align:start position:0% +and then you are getting out of here to +your yard + + align:start position:0% + + + + align:start position:0% + +yes and + + align:start position:0% + + + + align:start position:0% + +so how are you switching rooms we change + + align:start position:0% +so how are you switching rooms we change + + + align:start position:0% +so how are you switching rooms we change +the scene we can disable agree these are + + align:start position:0% +the scene we can disable agree these are + + + align:start position:0% +the scene we can disable agree these are +a wider problem + + align:start position:0% + + + + align:start position:0% + +okay so what we just did it's like + + align:start position:0% +okay so what we just did it's like + + + align:start position:0% +okay so what we just did it's like +that's the worst you cannot go indoor + + align:start position:0% +that's the worst you cannot go indoor + + + align:start position:0% +that's the worst you cannot go indoor +and now you come travel more freely in + + align:start position:0% +and now you come travel more freely in + + + align:start position:0% +and now you come travel more freely in +your yard now to just keep that the word + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +we can choose the material and then + + align:start position:0% +we can choose the material and then + + + align:start position:0% +we can choose the material and then +choose the object + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Laughter] + + align:start position:0% + + + + align:start position:0% + +oh we can also rotate being around + + align:start position:0% + + + + align:start position:0% + +so the only problem here is it's a + + align:start position:0% +so the only problem here is it's a + + + align:start position:0% +so the only problem here is it's a +little bit hard to control things from + + align:start position:0% +little bit hard to control things from + + + align:start position:0% +little bit hard to control things from +this for you so and then we just visit + + align:start position:0% +this for you so and then we just visit + + + align:start position:0% +this for you so and then we just visit +that yard and you want to locate + + align:start position:0% +that yard and you want to locate + + + align:start position:0% +that yard and you want to locate +yourself again + + align:start position:0% + + + + align:start position:0% + +no music oh yeah here good and there you + + align:start position:0% +no music oh yeah here good and there you + + + align:start position:0% +no music oh yeah here good and there you +can create that object + + align:start position:0% + + + + align:start position:0% + +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +if you want to + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +thank you establish a protocol if you + + align:start position:0% +thank you establish a protocol if you + + + align:start position:0% +thank you establish a protocol if you +were there for many Oh + + align:start position:0% +were there for many Oh + + + align:start position:0% +were there for many Oh +so for the connect our TA have already + + align:start position:0% +so for the connect our TA have already + + + align:start position:0% +so for the connect our TA have already +made the script that allow us to keep + + align:start position:0% +made the script that allow us to keep + + + align:start position:0% +made the script that allow us to keep +track of the code coordinate in 3d of + + align:start position:0% +track of the code coordinate in 3d of + + + align:start position:0% +track of the code coordinate in 3d of +our hands and the other joint like it + + align:start position:0% +our hands and the other joint like it + + + align:start position:0% +our hands and the other joint like it +and what I do is that we I implement for + + align:start position:0% +and what I do is that we I implement for + + + align:start position:0% +and what I do is that we I implement for +example the zoom in and zoom out I + + align:start position:0% +example the zoom in and zoom out I + + + align:start position:0% +example the zoom in and zoom out I +implement that if you are have if your + + align:start position:0% +implement that if you are have if your + + + align:start position:0% +implement that if you are have if your +right hand is built behind your right + + align:start position:0% +right hand is built behind your right + + + align:start position:0% +right hand is built behind your right +shoulder for certain amount you will cut + + align:start position:0% +shoulder for certain amount you will cut + + + align:start position:0% +shoulder for certain amount you will cut +zoom out and if it like there's I think + + align:start position:0% +zoom out and if it like there's I think + + + align:start position:0% +zoom out and if it like there's I think +it's the C direction C index if it more + + align:start position:0% +it's the C direction C index if it more + + + align:start position:0% +it's the C direction C index if it more +than your shoulder it will go to zoom in + + align:start position:0% +than your shoulder it will go to zoom in + + + align:start position:0% +than your shoulder it will go to zoom in +like that X Y Z coordinates like any + + align:start position:0% +like that X Y Z coordinates like any + + + align:start position:0% +like that X Y Z coordinates like any +gesture that she was doing she actually + + align:start position:0% +gesture that she was doing she actually + + + align:start position:0% +gesture that she was doing she actually +programs just based on like logical + + align:start position:0% +programs just based on like logical + + + align:start position:0% +programs just based on like logical +rules about where two points in space + + align:start position:0% +rules about where two points in space + + + align:start position:0% +rules about where two points in space +are + + align:start position:0% +are + + + align:start position:0% +are +so you traded before me and then I'm + + align:start position:0% +so you traded before me and then I'm + + + align:start position:0% +so you traded before me and then I'm +curious whether again another connected + + align:start position:0% +curious whether again another connected + + + align:start position:0% +curious whether again another connected +be more responsive get one in the front + + align:start position:0% +be more responsive get one in the front + + + align:start position:0% +be more responsive get one in the front +of the back long that really makes the + + align:start position:0% +of the back long that really makes the + + + align:start position:0% +of the back long that really makes the +sensor 21 people do yeah give me a lot + + align:start position:0% +sensor 21 people do yeah give me a lot + + + align:start position:0% +sensor 21 people do yeah give me a lot +of math because you to mess up also the + + align:start position:0% +of math because you to mess up also the + + + align:start position:0% +of math because you to mess up also the +very upright cameras probably inside + + align:start position:0% +very upright cameras probably inside + + + align:start position:0% +very upright cameras probably inside +each other okay + + align:start position:0% + + + + align:start position:0% + +I have a little bit but yes but learn + + align:start position:0% +I have a little bit but yes but learn + + + align:start position:0% +I have a little bit but yes but learn +from this car a lot yes + + align:start position:0% + + + + align:start position:0% + +no oh never happen yes \ No newline at end of file diff --git a/L27JVpZoz_Y.txt b/L27JVpZoz_Y.txt new file mode 100644 index 0000000000000000000000000000000000000000..06159b781202e30f40296b2946e03b04417a0c9f --- /dev/null +++ b/L27JVpZoz_Y.txt @@ -0,0 +1,2225 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Ladies and gentlemen, +welcome to this + +lecture on nonlinear finite +element analysis of solids and + +structures. + +In the previous lectures, we +talked about the general + +incremental continuum mechanics +equations that we're + +using in nonlinear finite +element analysis. + +In this lecture, I would like, +now, to talk about the finite + +element matrices that we're +using, actually, in static and + +dynamic analysis. + +You want to talk about these +in quite general terms. + +In the next lecture then, we +will talk more about the + +details of these matrices. + +You want to formulate these +finite element matrices. + +And we want to talk about the +numerical integration that we + +use to actually evaluate +the matrices. + +I've prepared some view graphs +regarding this material. + +And I'd like to share the +information on these view + +graphs now with you. + +The derivation of the finite +element matrices, of course, + +is based on the continuum +mechanics equations that we + +have developed earlier. + +And you have seen this equation +earlier when we + +talked about the total +Lagrangian formulation, the + +T.L. formulation. + +We talked about the terms +in this equation. + +We talked about their meaning, +what they stand for. + +And we have derived certain +terms here because they have + +been obtained by linearization +process. + +This was the governing equation +for the total + +Lagrangian formulation. + +The governing continuum +mechanics equation for the + +updated Lagrangian formulation +is shown here. + +Once again, we talked about +each of these terms. + +We talked about what +their meaning is. + +And, of course, we arrived +at this equation by + +linearization process. + +For the total Lagrangian and +the updated Lagrangian + +formulation, we recognized +because of the linearization + +process that was involved, we +need to iterate to obtain an + +accurate solution to the actual +problem of interest. + +And here on this view graph, +I've summarized the iterative + +equations that are used in the +total Lagrangian formulation. + +We, once again, have seen +this equation before. + +We should recognize, +now, these terms. + +The iteration count, of course, +being k, as shown here + +on the left-hand side +of the equation. + +And k minus one on the + +right-hand side of the equation. + +We also recognize this +equation here, now. + +Namely, the equation where we +update the displacements from + +the k minus first iteration +to the k iteration. + +For this iteration, of course, +we need initial conditions. + +And those initial conditions we +also talked about earlier. + +A similar equation is used +in the updated Lagrangian + +formulation. + +These are the terms that we +talked about earlier. + +And, of course, once again, we +are iterating with iteration + +count of k on the left-hand +side, iteration count of k + +minus one on the right-hand +side of the equation. + +The displacements are +updated, as shown + +here in this equation. + +And for this iteration, of +course, we need initial + +conditions, which +are given here. + +And all of these terms, really, +we discussed in some + +detail in the earlier +lectures. + +Well, assuming that loading is +deformation-independent, we + +also recognize that this here +is the expression for the + +external virtual work. + +t plus theta tR, the script +R that I talked + +about earlier already. + +And these are the terms that +we already defined earlier. + +Particularly the body force +term, the surface force term. + +Notice that, so far, we really +talked about static analysis. + +And I'd like to now, of course, +also introduce the + +term that we use in +dynamic analysis. + +This, of course, is +the inertia term. + +And in dynamic analysis, this +is the term that is really + +contained in this term here +as an effect of fV. + +Of the volume forces, the +forces per unit volume. + +Notice that this is really +here an integral over the + +volume at time t plus theta t of +the mass density at time t + +plus theta t times the +accelerations at time t plus + +theta t, the virtual +displacements, and, of course, + +the integrating over the +volume at time t plus + +[? theta, ?] + +t plus theta t, as +I said already. + +This is, of course, an +"inconvenient" interval. + +Inconvenient in quotes because +we don't know this volume. + +So we cannot really directly +evaluate this integral. + +Instead we'd rather like to work +with the original volume + +like we do in the total +Lagrangian formulation. + +And transformation of this +integral to an integral over + +the original volume is achieved +by this equation + +here, by this term here. + +Notice that, of course, 0 rho +times 0 dV for a particular + +set of mass particles must be +equal to t plus theta t rho + +times t plus theta tdV. + +And this is the reason why we +can directly write down this + +equation here. + +However, considering this +transformation for finite + +element analysis, it is +important to realize that we + +assume here that the +possibilities of the motion, + +of the material particles as +contained in the finite + +element interpolations +are the same in this + +volume as in that volume. + +This fortunately, is true +in isoparametric + +finite element analysis. + +And therefore, this +transformation from the volume + +t plus theta t to the volume +V 0 is a very convenient + +transformation to perform for +the evaluation of this term. + +We use that abundantly +in isoparametric + +finite element analysis. + +If the external loads are +deformation-dependent, then we + +have to recognize that +these forces here are + +deformation-dependent, and +therefore, we have to evaluate + +them in the iteration. + +And that is being shown +here in this equation. + +That we are always evaluating +this term new, depending on + +the iteration k minus 1, we +integrate this product here + +over the volume at time +t plus theta t in + +iteration k minus 1. + +Similarly, we update, also, +the surface forces. + +Since the surface area changes +of the body during the last + +information process, we evaluate +this part here as + +shown here. + +Of course, there is an +approximation involved. + +But if we keep on it iterating +t plus theta tVk minus one, + +we'll take on the volume +t plus theta tV. + +And of course then, we really +include here the term that we + +want to include, namely that +one in the analysis. + +Similarly here. + +The surface area, in iteration +k minus 1, as k goes larger + +and larger. + +If we converge, we'll actually +be equal to that surface area, + +meaning that this expression is +equal to that expression, + +which of course we +want to include. + +It's this expression that +we want to include + +in the force vector. + +We, in one of the very early +lectures, talked about the + +materially-nonlinear-only +analysis. + +And the equation that is used, +the continuum mechanics + +equation that is used in the +materially-nonlinear-only + +analysis is given here. + +Notice, here we have a stress +strain law tensor, an + +incremental strain tensor, +the virtual strain. + +The incremental strain +tensor is the real + +strain tensor here. + +All the components of that +tensor have a superscript k. + +The external virtual work. + +And here, we have the stress +tensor, components of the + +stress tensor. + +At time t plus theta t in +iteration k minus 1. + +And the virtual strains again. + +Notice here now, we do not have +anymore subscripts, 0 or + +t, on these components because +in materially-nonlinear-only + +analysis, we assume that the +deformations are very small. + +The displacements are +infinitesimal. + +And the stress, the second +Piola-Kirchhoff stress, which + +we defined in an earlier lecture +is actually equal to + +the Cauchy stress under those +conditions and is equal to the + +physical stress that we are +talking about here in the + +materially-nonlinear-only +analysis. + +In other words, both those +stress measures are equal to + +the physical stress that appears +here, which is, of + +course, the force +per unit area. + +The one that we are so familiar +with in infinitesimal + +displacement analysis. + +Let us look further at +dynamic analysis. + +Dynamic analysis is generally +performed in nonlinear + +analysis, using an implicit time +integration scheme or an + +explicit time integration +scheme. + +And in a later lecture, we +will discuss such time + +integration schemes. + +In implicit time integration, +we look at the equilibrium + +equation at time t plus theta +t to obtain the solution at + +time t plus theta t. + +And this means that we will +have to evaluate this + +left-hand side written here as +given on the right-hand side. + +This part here, this external +virtual work, comes from the + +external loads that +are not the mass + +of the inertia forces. + +The inertia forces are taken +care of via this part, via + +this integral here, +which I discussed + +already a bit earlier. + +In explicit time integration, +we are evaluating or we're + +looking at the equilibrium +equation at time t to obtain + +the solution at time +t plus theta t. + +Quite different from implicit +time integration. + +And the governing equations are +in the total Lagrangian + +formulation right here, in the +U.L., the updated Lagrangian + +formulation given here, and in +the materially-nonlinear-only + +analysis as given here. + +Notice, of course, that R will +involve the inertia forces + +evaluated at time t now. + +And that will, of course, enable +us to march forward + +with a solution as we +will discuss later + +on in another lecture. + +The finite element equations +corresponding to these + +continuum mechanics equations +look as follows. + +In materially-nonlinear-only +analysis, let's look first at + +static analysis. + +We have this basic equation. + +Notice a tension stiffness +matrix that does not carry any + +subscript 0 or t because we are +talking about the original + +volume, the displacements being +infinitesimally small, + +the physical stress, no Cauchy +stress really, no second + +Piola-Kirchhoff stress needs +to be introduced. + +We just talk about the physical +stress that we are so + +familiar with in infinitesimal +displacement analysis. + +And that, of course, goes into +the evaluation of the K matrix + +because the material law will +appear in here, the + +incremental displacement vector, +and on the right-hand + +side, the load vector, and the +nodal point forces that are + +equivalent in the sense of the +principle of virtual work to + +the current element stresses. + +By current, I mean F time t +plus theta t at the end of + +iteration i minus 1. + +This equation, of course, looks +very much alike of what + +we have seen in the updated +Lagrangian formulation and in + +the total Lagrangian +formulation. + +In dynamic analysis using +implicit time integration, + +this will be the governing +equation. + +Now, the mass matrix, the +acceleration vector with an + +iteration [? count of ?] i +because we are marching + +forward to a situation, to a +configuration which is still + +unknown, a tangent stiffness +matrix, the same tangent + +stiffness matrix that we see +here, by the way, the + +incremental displacement vector, +and on the right-hand + +side, the same quantities +that we have here. + +In dynamic analysis using +explicit time integration, we + +have the mass matrix, the same +mass matrix, generally, that + +we have here. + +Although in implicit time +integration, we will sometimes + +use a lump mass matrix, +sometimes a banded mass + +matrix, a consistent +mass matrix. + +With an explicit time +integration, we generally use + +only the lump mass matrix. + +But otherwise, the same +kind of matrix here. + +The acceleration vector. + +The force vector or the nodal +point forces, corresponding to + +time t that are externally +applied to the structure. + +And the tF vector, which is the +force vector corresponding + +to the stresses in the +elements at time t. + +Notice, we are looking here at +equilibrium at time t to + +obtain the solution at +time t plus theta t. + +We are looking here at +equilibrium, or I should say, + +we're iterating for equilibrium +at time + +t plus theta t. + +And thus, we will obtain +the solution for time + +t plus theta t. + +In the total Lagrangian +formulation, we have very + +similar equations. + +In static analysis, a tangent +stiffness matrix, and + +otherwise, the same kind of +vectors that I talked about + +earlier already. + +Notice now, of course, we +have the subscript 0. + +Notice also that the total +tangent stiffness matrix is + +made up of a part that we might +call a linear strain + +stiffness matrix and a part +that we may call nonlinear + +strain stiffness matrix. + +This is also called the +geometric stiffness matrix. + +We will talk about how +we construct these + +matrices just now. + +In dynamic analysis, we +proceed as in the + +material-nonlinear-only +formulation, of course. + +And in all the other +formulations, if we use + +implicit time integration, +we apply + +the equilibrium equation. + +We look for the equilibrium +at time t plus theta t, as + +expressed here. + +And we have vectors, matrices +very similar to what we have + +in the material-nonlinear-only +formulation except that once + +again, of course, we have now +introduced here the geometric + +stiffening affect, +the nonlinear + +strain stiffness matrix. + +In dynamic analysis using +explicit time integration, we + +don't use any K matrix. + +We will discuss that also +much more later on. + +And this is the governing +equation. + +Very much the same as in the +material-nonlinear-only + +formulation. + +Finally, in the updated +Lagrangian formulation, we + +also obtain similar equations +and static analysis. + +These are the equations +that we want to solve. + +Notice also, the nonlinear +strain to them there or the + +nonlinear strain stiffness +matrix. + +Otherwise, the matrices and +vectors are very much alike + +what we have seen before. + +Dynamic analysis implicit time +integration and in dynamic + +analysis using explicit +time integration. + +Notice that in each of these, we +are always cutting out the + +subscript t or t plus theta t +the way I have been talking + +about earlier already. + +We have seen this equation, +of course, before + +in our earlier lectures. + +What we now do is we introduce +the mass terms. + +And we are talking about +implicit time integration and + +explicit time integration. + +We should note that these +equations are valid for single + +finite element as +well as for an + +assemblage of finite elements. + +If we have a large number of +elements, then, of course, we + +would assemble these as we do it +in linear elastic analysis + +using the direct stiffness +method. + +Considering an assemblage of +elements, we will see that + +different formulations may be +used in different regions of + +the structure. + +In other words, schematically +here we may have some elements + +that are governed by the T.L., +the total Lagrangian + +formulation, some others by +the updated Lagrangian + +formulation, and some others by +the material-nonlinear-only + +formulation. + +Notice that compatibility +between these elements is, of + +course, perfectly preserved if +these are compatible elements + +as shown here. + +Then, there is nothing wrong +with using the U.L. + +formulation for certain elements +that are bordering + +elements with another +formulation such as this. + +It is not true, for example, +that due to the fact that + +you're using here different +kinds of formulations, you are + +getting an incompatibility +introduced here. + +I've heard that sometimes. + +That is certainly not +my understanding + +of the subject matter. + +It does not matter whether +you have the same kind of + +formulations or two different +kind of formulations. + +That will not effect the + +compatibility between two elements. + +Let us now concentrate on +the derivation or on the + +formulation of a single +element matrix. + +To obtain a single element +matrices, we have to + +introduce, of course, an +interpolation matrix. + +And this matrix interpolates +the internal element + +displacements via the nodal +point displacements. + +Here, I'm showing a full node +element with these nodal point + +displacements. + +Notice these are measured in +the Cartesian coordinate + +directions. + +Notice however, that these nodal +point displacements are + +measured into a skewed +direction, an a + +b coordinate system. + +There's nothing wrong with +introducing different systems + +because this is Q system at the +different nodal points. + +The nodal point vector, the +vector of nodal point degrees + +of freedom is listed here. + +Notice that vector carries a hat +to denote the fact that it + +contains this great nodal +point displacements. + +Notice also, that the subscripts +1, 2 refer to the + +Cartesian coordinate +directions for the + +superscripts referred +to the nodal point. + +Here 1, 2 again. + +3 denoting the nodal point. + +Notice up here, a b, of course +refer to the skewed + +directions. + +And the 1 refers to +the nodal point 1. + +We want to interpolate the +internal displacements in + +terms of the nodal point +displacements. + +And that is being achieved by +this relationship here. + +U, the internal particle +displacements are given via H, + +the displacement interpolation +matrix times U hat. + +U hat being this vector, the +one we just discussed. + +U being a vector of these +two displacements. + +Now, notice that these two +displacements, of course, + +depend on which particle +you are looking at. + +Here, a particular particle. + +This would be the displacement +you want. + +That's the displacement U2. + +And these displacements vary +over the element, which would + +be expressed by this H matrix. + +These are the nodal point +displacements. + +These are the varying, +continuously varying + +displacements of the particles +within the element. + +We will, of course, use this +kind of relationship now quite + +extensively. + +We have, of course, also already +encountered this + +relationship in linear +elastic analysis. + +Let us now see how we +are formulating + +the different matrices. + +For all analysis types, in +which we want to include + +inertia forces, we evaluate this +integral as shown here. + +Notice the displacements and +accelerations are interpolated + +via this relationship here. + +For the accelerations, of +course, we would have dots + +here, dots there denoting +second time derivatives. + +And we would have t plus theta +t as a superscript on each of + +these variables. + +Notice that we also use this +interpolation here for the + +virtual displacements. + +And the result is given right +here just like in linear + +elastic analysis. + +The right inside load vector +as evaluated is shown here. + +Once again, we introduce +interpolation for U or for the + +virtual displacements and the +virtual surface displacements. + +This interpolation here +gives us this H + +matrix, H transpose matrix. + +This here interpolated gives +us the HST matrix. + +Notice that HS is the +interpolation matrix for the + +surface displacements +as a function of-- + +or rather it gives the surface +displacements I should say as + +a function of the nodal +point displacements. + +So HS is really evaluated by +using H, the H matrix I just + +talked about, and evaluating +that H matrix on the surface + +of the element. + +That is how you get HS. + +And all of this expression +together + +gives us the load vector. + +As a matter of fact it is +really the same process + +followed that we are using +in linear infinitesimally + +displacement analysis. + +In material-nonlinear-only +analysis, considering an + +incremental displacement UI, we +evaluate this integral here + +as shown here. + +Notice here the virtual +displacements that are coming + +in because we have the virtual +strains there. + +Notice here the real +displacements, which are + +coming in from these +real strains. + +Of course, these are strain +increments and, + +correspondingly, displacement +increments. + +Nodal point displacement +increments always. + +These B matrices, BL matrices, +are obtained by evaluating the + +strains from the nodal +point displacements. + +And, of course, the +interpolation that is used for + +the element goes in here. + +The B matrix, of course, +contains derivatives of the + +elements of the H matrix. + +A vector containing components +of eIj is this one here. + +For example, in two dimensional +plane stress + +analysis, the entries in this +vector are listed right here. + +Notice that there is a 2 here +because e12 is equal to e21. + +And the sum of these two, +of course, gives us + +a total sheer strain. + +And therefore, we simply +put a 2 times e12 here. + +This evaluation is performed +much in the same way as in + +linear infinitesimal +displacement analysis. + +Except that we have to remember +this stress tensor, + +this stress strain tensor, +this considerative tensor + +varies in the incremental +solution because we have + +materially nonlinear +conditions. + +So the K matrix here +will change. + +And that is indicated, of +course, by the t up there. + +Notice the B matrix, in this +incremental analysis, using + +the material-nonlinear-only +formulations is constant. + +For the material-nonlinear-only + +formulation, we also want to +evaluate the F vector. + +And that F vector is a result +of this integral here. + +We take this integral, + +interpolate the virtual strains. + +And that is this part here, in +terms of the virtual nodal + +point displacements. + +And we assemble in this vector +here capital sigma at time t, + +the stresses t sigma ij. + +We assemble those +in this vector. + +Notice, in two dimensions +analysis, this vector is given + +down here as these components. + +By the way, no two here. + +You should think about that. + +There should be no two here. + +Total Lagrangian formulation. + +We have similarly an +integral as in the + +material-nonlinear-only +formulation. + +We interpolate, once again, +these real incremental + +strains, the virtual strains. + +And the result is directly +given here. + +With the B matrix, now, +defined via this + +equation down here. + +And, of course, this vector here +contains the components + +of the incremental +strain tensor. + +However, in the total Lagrangian +formulation, we + +know also have an additional +integral. + +And that integral is coming in +because of the geometric + +stiffening effect of the +nonlinear strain term effect. + +Here we have the integral. + +And the discretization +is given on the + +right-hand side here. + +Notice this is a BNL matrix, +nonlinear strain + +matrix, we call it. + +This here is a matrix of the +second Piola-Kirchhoff + +stresses at time t. + +And here we have, again, +the BNL matrix. + +This product together gives +us the KNL matrix. + +One might ask how do you +get these quantities? + +Well, actually we construct +this S matrix and the BNL + +matrix such that when you take +the product of this whole + +right-hand side, you get that. + +So these matrices are really +constructed such as to obtain + +what we need to get. + +And that is this part here. + +I will show you later +on specific + +examples in another lecture. + +Here we have the S +matrix containing + +components as I've mentioned. + +And this matrix here times +this vector contains the + +components of this displacement +derivative. + +The right-hand side, of +course, for the total + +Lagrangian formulation has the +evaluation of the F vector. + +And that one is obtained +from this integral. + +Notice we go over. + +We evaluate this integral by +this relationship here. + +The linear strain displacement +matrix goes in here. + +And a vector of the second +Piola-Kirchhoff + +stresses goes in here. + +Once again, this vector is +constructed in such a way that + +this right-hand side here is +equal to that integral. + +In the updated Lagrangian +formulation, we proceed much + +in the same way. + +Considering incremental +displacement UI, we have this + +integral to evaluate. + +We interpolate the strains via +the strain-displacement + +[? interpolation ?] matrix, and +the result is this here. + +This is here the linear strain +stiffness matrix. + +Here we have a relation very +much alike of what we have in + +the total Lagrangian +formulation for the + +incremental strains. + +The nonlinear strain stiffness +matrix in the updated + +Lagrangian formulation is also +very much evaluated like in + +the total Lagrangian +formulation. + +It is this integral that +we now have to capture. + +And we do so by constructing a +BNL matrix, a tall matrix, + +such that this total +product here is + +equal to this integral. + +And what's underlined here in +blue is the matrix that we're + +looking for. + +We should, of course, also +evaluate in the updated + +Lagrangian formulation +the F vector. + +And that F vector, which appears +on the right-hand side + +of the equation in the updated +Lagrangian formulation, is + +evaluated by calculating +this integral. + +Notice that this is obtained +by this right-hand side. + +The BL, of course, is +the linear strain + +displacement matrix. + +And here we have a vector, tall +hat, which contains the + +stresses, Cauchy the +stresses at time t. + +It's constructed such that this +integral here, with this + +part in front of it, gives +us exactly that integral. + +And what is underlined here in +blue is the actual F vector + +that we're looking for. + +So what we have seen then, is +that the finite element + +matrices for the +material-nonlinear-only, the + +total Lagrangian, and the +updated Lagrangian formulation + +are formulated by looking +at the individual volume + +integrals in these continuum +mechanics formulations. + +And by interpolating the +displacements and strains much + +in the same way as we are used +to in linear analysis. + +Once we have formulated these +matrices, we, of course, have + +to evaluate them. + +And that is done using numerical +integration, once + +again, just very similar +to what we're + +doing in linear analysis. + +We're using, primarily, Gauss +integration or Newton-Cotes + +integration. + +Schematically, in +two-dimensional analysis, the + +K matrix would be evaluated +as shown here. + +Notice that in isoparametric +finite element analysis, we + +are integrating from minus 1 +to plus 1 over the domain. + +Two-dimensional analysis, +of course, two + +integrations involved. + +That we have a B matrix +transposed, C matrix, B here, + +a determinant of a Jacobian +matrix, which comes in because + +we are transforming from the x1, +x2 space to the RS space. + +And we call that the G matrix's +total product. + +And the numerical integrations +then really involves nothing + +else but summing a product +of alpha ij, Gij over all + +numerical integration points. + +Notice the ij here now refers to +the ij's integration point. + +This is what we are doing also +in linear analysis and in + +nonlinear analysis as well. + +Similarly, we would evaluate +the F vector, which, of + +course, we have in the +material-nonlinear-only, total + +Lagrangian, or updated +Lagrangian formulation as + +shown here. + +Notice, once again, +integration from + +minus 1 to plus 1. + +And this part here is what +we might call G again. + +F then, is obtained +as shown here. + +Of course these are the +integration point weights that + +are given to us, which we +simply use in the finite + +element solution. + +The mass matrix is evaluated +as shown here. + +Mass density goes in there. + +H transpose H. H, of course, +being the displacement + +interpolation matrix. + +And this is our G here. + +With that G, we should put a bar +under that G here because + +it's a matrix. + +You put it in. + +And if we use that G here +in this formula, + +we get the M matrix. + +So the numerical integration +is really performed much in + +the way as we're doing it +in linear analysis. + +Frequently, we use Gauss +integration, + +as I mentioned earlier. + +And, as a typical example, 3x3 +into Gauss integration is + +schematically shown here. + +Here is our element. + +Here is the R coordinate axes. + +Here is the s coordinate axes. + +This would be the integration +point stations that we are + +using for 3x3 integration. + +The r and s values are +given as shown here. + +Same r and s values as +in linear analysis. + +And we notice that these +integration point stations are + +all within the element. + +That is, of course, one +feature off the Gauss + +integration. + +As I mentioned earlier they +use also Newton-Cotes + +integration, for example for +the integration through the + +shell's thickness. + +Here is the r direction, which +is a coordinate axis in the + +mid-surface of the shell. + +And s goes through +the thickness. + +Notice here we have five point +Newton-Cotes integration. + +And that some integration +points, as a matter of fact + +two here, are actually on the +surface of the element. + +Because we are including the +surface of the element, we use + +Newton-Cotes integration +quite frequently + +in nonlinear analysis. + +The reason being that if we do +an elasto-plastic analysis, we + +find that the larger stresses, +of course, are generally + +generated on the surfaces +of the element. + +And these are then also the +areas where plasticity sets in + +earliest, which means that +we want to pick up this + +elasto-plastic response as +quickly as possible. + +And integration point stations +on the surface of the element + +can be of benefit. + +If you compare Gauss with +Newton-Cotes integration, we + +recognize that with n Gauss +points, we integrate a + +polynomial of order 2n minus 1 +exactly, meaning, for example, + +with two Gauss points, you +integrate a cubic exactly and + +everything below +it, of course. + +Whereas with n Newton-Cotes +points, we integrate only a + +polynomial of n minus +1 exactly. + +So we need really many more +Newton-Cotes integration + +points to pick up the same +accuracy in the integration as + +you do with the Gauss +point integration. + +For this reason, we use, +primarily really, the Gauss + +integration, particularly in +the analysis of solids. + +Maybe a big, chunky bodies +where there is no need, + +really, to pick up the plastic +response say on the surface + +directly of the solid. + +Newton-Cotes integration +involves points on the + +boundaries. + +I mentioned that already. + +And therefore, this integration +scheme is + +effective for structural +elements for the reasons that + +I just gave. + +In principle, the integration +schemes I employed as in + +linear analysis. + +The integration order must be +high enough not to have any + +spurious energy modes +in the elements. + +We will get back to that in +later lectures, particularly + +when we talk about structural +elements, beam elements, and + +shell elements. + +This is a very important +point. + +The appropriate integration +order in nonlinear analysis + +can sometimes be higher than +in linear analysis, for + +example, to model the plasticity +accurately, once + +again, in a shell solution +or such type of analysis. + +On the other hand, a too high +integration order is also not + +of value because remember, that +the maximum displacement + +variation, therefore, the +maximum strain variation you + +can pick up, is of course, given +by the interpolation + +you're using. + +So it doesn't make much sense +to go up in very high + +integration order in order +to try to pick up a high + +variation in strains, plastic +strains, and the corresponding + +stresses, of course. + +It doesn't make sense to do that +when you are limited by + +the actual strain variation +anyway due to the + +interpolations on the + +displacements that you're using. + +Let me show you an example here +that demonstrates some of + +the points that I'm +trying to make. + +Here we have an eight node +element that models the + +response of a cantilever +and the bending moment. + +We measure the rotation +phi here. + +We have here the +material data. + +Notice we are talking about an +elasto-plastic material with + +yield stress. + +And we apply a bending +moment as shown here. + +In linear elastic analysis, +you would get the exact + +response to this problem using +one eight node element. + +You might have tried +it already. + +You may know that. + +The reason, of course, being +that this element contains a + +parabolic displacement +interpolation, which is the + +analytical solution +to this problem. + +And therefore, you get +the exact solution. + +In elasto-plastic analysis, +however, the solution depends + +on the integration order +we are using. + +And this is demonstrated +on this view graph. + +Here we show on the vertical +axis, the moment normalized to + +the moment at first yield. + +And on the horizontal axis, +the rotation of the beam + +normalized to the rotation at +first yield, respectively. + +Now, notice that the linear +elastic response, of course, + +would be simply this line here +going up vertically. + +In elasto-plastic analysis, +however, the + +element starts yielding. + +And the yield is picked up, +depending on the integration + +order you're using. + +With 2 by 2 integration, we +get this solution here. + +And this would be +the limit load. + +With 3 by 3 integration, we +get this solution for the + +limit load. + +And with 4 by 4 integration, +we get this solution as a + +limit load. + +So this solution very much +depends on the integration + +order that you're using. + +And it shows here that we need +enough integration point + +stations through the thickness +of the beam in order to + +approximate, appropriately, +the limit load + +that we want to calculate. + +Let me show you another +problem. + +And this is an interesting +problem in which we want to + +design a numerical experiment to +test whether an element can + +undergo properly large, +rigid body motions. + +Here we consider a single + +two-dimensional four node element. + +It could be plain stress +or plain strain. + +And we want to test by a +numerical experiment that you + +can perform on a computer +program, whether this element + +can actually perform +large, rigid body + +motions, of course, properly. + +And by properly, I mean there +should be no stresses + +generated in the element when it +is subjected to these rigid + +body motions. + +Well, there are for this element +three rigid body + +motions of interest. + +Two translations and +one rotation. + +It's a two-dimensional +element, so these two + +translations, of course, refer +to the horizontal translation + +and the vertical translation. + +The rotation, of course, refers +to the rotation in the + +two-dimensional plane. + +To test whether the element +can undergo properly the + +horizontal rigid body motion, +we designed this numerical + +experiment. + +We put here to truss elements. + +We call them M.N.O. trusses +because they do not include + +then any geometric +nonlinearalities. + +They are really just springs. + +And we put this element +on a roller here. + +Keep it otherwise free. + +And we put onto this degree of +freedom a load, R. And on that + +degree of freedom a +load, R, as well. + +The load is very large. + +So the element should move over +stress free by a very + +large amount. + +This is one rigid body movement +that the fall out + +element must, of course, +be able to undergo. + +And this test is passed for the +T.L., U.L., and the M.N.O, + +or linear analysis, of course. + +Similarly, we could perform +this test for + +the vertical direction. + +And we would find that, once +again, the T.L., U.L. + +formulation, and M.N.O. +formulation will pass a test + +for the vertical direction +as well. + +The interesting test is the +one for the rotation. + +Here we have our fall out +element supported at the + +left-hand side by a pin, and on +the right-hand side by an + +M.N.O. truss. + +Once again, a truss element +that does not model any + +geometric nonlinearalities. + +We are applying to this node +here a force, R, that would, + +of course, make this element +here go through the rotation. + +Since the force should be +taken in the spring, the + +element should rotate +stress free. + +Note that because this spring +is and M.N.O. spring, the + +force acting onto this node +here must always work + +vertically only. + +After the load is applied, the +element, originally here, must + +have rotated by a very +large amount. + +The area must have +not changed. + +In other words, the element +size must remain constant. + +And the element must +be stress free. + +This test is passed by the by +the U.L., and the T.L., the + +total Lagrangian formulations, +by the updated Lagrangian, and + +the total Lagrangian formations +properly. + +But if you were to use the +material-nonlinear-only + +formulation, you would see that +this element does not + +remain or keep its +original size. + +The reason being that this node +here will move up on this + +side here because of the +M.N.O. truss there. + +We move up here. + +And all of the element remain +stress free, the element + +actually grows in size. + +It's an interesting test that +you can actually perform on a + +computer program. + +Once again, the total Lagrangian +and the updated + +Lagrangian formulations, which, +of course, are designed + +to more large quotations and +large strains pass this test + +properly, whereas the M.N.O. +Formulation, which is not + +designed to model large +quotations, would not pass + +this test property. + +Well, in this lecture, I've +been trying to give you an + +overview of the general element +matrices that we need + +in the U.L., T.L., and +M.N.O. formulations. + +In the next lectures, we will +derive these element matrices + +in detail for different +types of elements. + +Thank you very much for +your attention. \ No newline at end of file diff --git a/LwSk9M5lJx4.txt b/LwSk9M5lJx4.txt new file mode 100644 index 0000000000000000000000000000000000000000..c1855608c6aa47bc2419c0841f8f52c4ac693f67 --- /dev/null +++ b/LwSk9M5lJx4.txt @@ -0,0 +1,2075 @@ +align:start position:0% + +okay uh we're still solving systems of + + align:start position:0% +okay uh we're still solving systems of + + + align:start position:0% +okay uh we're still solving systems of +differential equations with a matrix a + + align:start position:0% +differential equations with a matrix a + + + align:start position:0% +differential equations with a matrix a +in them uh and now I want to create the + + align:start position:0% +in them uh and now I want to create the + + + align:start position:0% +in them uh and now I want to create the +exponential it's just natural to to + + align:start position:0% +exponential it's just natural to to + + + align:start position:0% +exponential it's just natural to to +produce e to the a or e to the a t the + + align:start position:0% +produce e to the a or e to the a t the + + + align:start position:0% +produce e to the a or e to the a t the +exponential of a matrix so uh if we have + + align:start position:0% +exponential of a matrix so uh if we have + + + align:start position:0% +exponential of a matrix so uh if we have +one + + align:start position:0% +one + + + align:start position:0% +one +equation small a then we know the + + align:start position:0% +equation small a then we know the + + + align:start position:0% +equation small a then we know the +solution is an e to the a t times the + + align:start position:0% +solution is an e to the a t times the + + + align:start position:0% +solution is an e to the a t times the +starting value now we have n equations + + align:start position:0% +starting value now we have n equations + + + align:start position:0% +starting value now we have n equations +with a matrix a and a vector Y and the + + align:start position:0% +with a matrix a and a vector Y and the + + + align:start position:0% +with a matrix a and a vector Y and the +solution should be at time t e to the a + + align:start position:0% +solution should be at time t e to the a + + + align:start position:0% +solution should be at time t e to the a +t times the starting value it should be + + align:start position:0% +t times the starting value it should be + + + align:start position:0% +t times the starting value it should be +a perfect match with this one where this + + align:start position:0% +a perfect match with this one where this + + + align:start position:0% +a perfect match with this one where this +had a number in the exponent and this + + align:start position:0% +had a number in the exponent and this + + + align:start position:0% +had a number in the exponent and this +has a matrix in the exponent okay + + align:start position:0% +has a matrix in the exponent okay + + + align:start position:0% +has a matrix in the exponent okay +no problem we just use the series for e + + align:start position:0% +no problem we just use the series for e + + + align:start position:0% +no problem we just use the series for e +to the a t we plug in a matrix instead + + align:start position:0% +to the a t we plug in a matrix instead + + + align:start position:0% +to the a t we plug in a matrix instead +of a number so the identity plus + + align:start position:0% +of a number so the identity plus + + + align:start position:0% +of a number so the identity plus +a plus 12 a^ SAR plus 1 16 of a cubed + + align:start position:0% +a plus 12 a^ SAR plus 1 16 of a cubed + + + align:start position:0% +a plus 12 a^ SAR plus 1 16 of a cubed +forever it's the same it's the + + align:start position:0% +forever it's the same it's the + + + align:start position:0% +forever it's the same it's the +exponential series the most important + + align:start position:0% +exponential series the most important + + + align:start position:0% +exponential series the most important +series in mathematics I think and it + + align:start position:0% +series in mathematics I think and it + + + align:start position:0% +series in mathematics I think and it +gives us an answer and that answer is a + + align:start position:0% +gives us an answer and that answer is a + + + align:start position:0% +gives us an answer and that answer is a +matrix everything here every term is a + + align:start position:0% +matrix everything here every term is a + + + align:start position:0% +matrix everything here every term is a +matrix okay now is that the right answer + + align:start position:0% +matrix okay now is that the right answer + + + align:start position:0% +matrix okay now is that the right answer +we check that by putting it into the + + align:start position:0% +we check that by putting it into the + + + align:start position:0% +we check that by putting it into the +differential equation so I want to put + + align:start position:0% +differential equation so I want to put + + + align:start position:0% +differential equation so I want to put +that solution in to the equation so I + + align:start position:0% +that solution in to the equation so I + + + align:start position:0% +that solution in to the equation so I +need to take the derivative the + + align:start position:0% +need to take the derivative the + + + align:start position:0% +need to take the derivative the +derivative of this is the derivative + + align:start position:0% +derivative of this is the derivative + + + align:start position:0% +derivative of this is the derivative +that's a constant the derivative of that + + align:start position:0% +that's a constant the derivative of that + + + align:start position:0% +that's a constant the derivative of that +is a the derivative of this is 12 a I + + align:start position:0% +is a the derivative of this is 12 a I + + + align:start position:0% +is a the derivative of this is 12 a I +have an A + + align:start position:0% +have an A + + + align:start position:0% +have an A +squ and I have a t^2 the derivative of + + align:start position:0% +squ and I have a t^2 the derivative of + + + align:start position:0% +squ and I have a t^2 the derivative of +t^2 is 2T so that'll just be a t the two + + align:start position:0% +t^2 is 2T so that'll just be a t the two + + + align:start position:0% +t^2 is 2T so that'll just be a t the two +and the two cancel okay now I have a + + align:start position:0% +and the two cancel okay now I have a + + + align:start position:0% +and the two cancel okay now I have a +cubed + + align:start position:0% +cubed + + + align:start position:0% +cubed +here T cubed the derivative of of T + + align:start position:0% +here T cubed the derivative of of T + + + align:start position:0% +here T cubed the derivative of of T +cubed is 3 t^2 so I have a t^2 and the + + align:start position:0% +cubed is 3 t^2 so I have a t^2 and the + + + align:start position:0% +cubed is 3 t^2 so I have a t^2 and the +three cancels the three and the six and + + align:start position:0% +three cancels the three and the six and + + + align:start position:0% +three cancels the three and the six and +leave 1/ 2 factorial and so + + align:start position:0% +leave 1/ 2 factorial and so + + + align:start position:0% +leave 1/ 2 factorial and so +on and I look at that and I say it's + + align:start position:0% +on and I look at that and I say it's + + + align:start position:0% +on and I look at that and I say it's +very much like the one above look this + + align:start position:0% +very much like the one above look this + + + align:start position:0% +very much like the one above look this +series is just a * this one multiply + + align:start position:0% +series is just a * this one multiply + + + align:start position:0% +series is just a * this one multiply +this top one by a a * I is a a * a t is + + align:start position:0% +this top one by a a * I is a a * a t is + + + align:start position:0% +this top one by a a * I is a a * a t is +a 2 T term by term it just has a factor + + align:start position:0% +a 2 T term by term it just has a factor + + + align:start position:0% +a 2 T term by term it just has a factor +a so it's a e to the A a t is the + + align:start position:0% +a so it's a e to the A a t is the + + + align:start position:0% +a so it's a e to the A a t is the +derivative of my Matrix exponential it + + align:start position:0% +derivative of my Matrix exponential it + + + align:start position:0% +derivative of my Matrix exponential it +brings down an a just what we want just + + align:start position:0% +brings down an a just what we want just + + + align:start position:0% +brings down an a just what we want just +what we want so so then if I add a if I + + align:start position:0% +what we want so so then if I add a if I + + + align:start position:0% +what we want so so then if I add a if I +add a y of zero in here that's just a + + align:start position:0% +add a y of zero in here that's just a + + + align:start position:0% +add a y of zero in here that's just a +constant Vector I'll have a y of zero + + align:start position:0% +constant Vector I'll have a y of zero + + + align:start position:0% +constant Vector I'll have a y of zero +I'll have a y of zero here it it when I + + align:start position:0% +I'll have a y of zero here it it when I + + + align:start position:0% +I'll have a y of zero here it it when I +put this into the differential equation + + align:start position:0% +put this into the differential equation + + + align:start position:0% +put this into the differential equation +it works it works + + align:start position:0% +it works it works + + + align:start position:0% +it works it works +now is it better + + align:start position:0% +now is it better + + + align:start position:0% +now is it better +than what we had before which was using + + align:start position:0% +than what we had before which was using + + + align:start position:0% +than what we had before which was using +igen values and igen + + align:start position:0% +igen values and igen + + + align:start position:0% +igen values and igen +vectors it's better in one way it will + + align:start position:0% +vectors it's better in one way it will + + + align:start position:0% +vectors it's better in one way it will +this exponential this series is totally + + align:start position:0% +this exponential this series is totally + + + align:start position:0% +this exponential this series is totally +fine whether we have n independent IG + + align:start position:0% +fine whether we have n independent IG + + + align:start position:0% +fine whether we have n independent IG +vectors or not we could have repeated + + align:start position:0% +vectors or not we could have repeated + + + align:start position:0% +vectors or not we could have repeated +igen values I'll do an example so for + + align:start position:0% +igen values I'll do an example so for + + + align:start position:0% +igen values I'll do an example so for +with repeated igen values and missing + + align:start position:0% +with repeated igen values and missing + + + align:start position:0% +with repeated igen values and missing +igen vectors e to the a is still the + + align:start position:0% +igen vectors e to the a is still the + + + align:start position:0% +igen vectors e to the a is still the +correct answer + + align:start position:0% +correct answer + + + align:start position:0% +correct answer +still the correct answer but if we want + + align:start position:0% +still the correct answer but if we want + + + align:start position:0% +still the correct answer but if we want +to use igen values and igen vectors to + + align:start position:0% +to use igen values and igen vectors to + + + align:start position:0% +to use igen values and igen vectors to +to compute e to the a because we don't + + align:start position:0% +to compute e to the a because we don't + + + align:start position:0% +to compute e to the a because we don't +want to add up an infinite series very + + align:start position:0% +want to add up an infinite series very + + + align:start position:0% +want to add up an infinite series very +often uh then we would want an + + align:start position:0% +often uh then we would want an + + + align:start position:0% +often uh then we would want an +independent igen Vector so what am I + + align:start position:0% +independent igen Vector so what am I + + + align:start position:0% +independent igen Vector so what am I +saying I'm saying that this e to the + + align:start position:0% +saying I'm saying that this e to the + + + align:start position:0% +saying I'm saying that this e to the +a all right suppose we have n + + align:start position:0% +a all right suppose we have n + + + align:start position:0% +a all right suppose we have n +independent ion vectors + + align:start position:0% +independent ion vectors + + + align:start position:0% +independent ion vectors +and we know that that means in that case + + align:start position:0% +and we know that that means in that case + + + align:start position:0% +and we know that that means in that case +a is V * Lambda * V inverse and we can + + align:start position:0% +a is V * Lambda * V inverse and we can + + + align:start position:0% +a is V * Lambda * V inverse and we can +write V inverse because the Matrix V has + + align:start position:0% +write V inverse because the Matrix V has + + + align:start position:0% +write V inverse because the Matrix V has +the IG vectors this is the IG Vector + + align:start position:0% +the IG vectors this is the IG Vector + + + align:start position:0% +the IG vectors this is the IG Vector +Matrix if I have n independent ion + + align:start position:0% +Matrix if I have n independent ion + + + align:start position:0% +Matrix if I have n independent ion +vectors that Matrix is invertible I have + + align:start position:0% +vectors that Matrix is invertible I have + + + align:start position:0% +vectors that Matrix is invertible I have +that nice formula and now I can see what + + align:start position:0% +that nice formula and now I can see what + + + align:start position:0% +that nice formula and now I can see what +is e to the + + align:start position:0% +is e to the + + + align:start position:0% +is e to the +a is always + + align:start position:0% +a is always + + + align:start position:0% +a is always +identity plus a I'm now going to use the + + align:start position:0% +identity plus a I'm now going to use the + + + align:start position:0% +identity plus a I'm now going to use the +diagonalization the the IG vectors and + + align:start position:0% +diagonalization the the IG vectors and + + + align:start position:0% +diagonalization the the IG vectors and +the igon values for a with so I'm doing + + align:start position:0% +the igon values for a with so I'm doing + + + align:start position:0% +the igon values for a with so I'm doing +the good case now when there are in full + + align:start position:0% +the good case now when there are in full + + + align:start position:0% +the good case now when there are in full +set of independent ion vectors then the + + align:start position:0% +set of independent ion vectors then the + + + align:start position:0% +set of independent ion vectors then the +a is V Lambda V inverse T that's right + + align:start position:0% +a is V Lambda V inverse T that's right + + + align:start position:0% +a is V Lambda V inverse T that's right +that's I + a t + 12 a t^ sared right so + + align:start position:0% +that's I + a t + 12 a t^ sared right so + + + align:start position:0% +that's I + a t + 12 a t^ sared right so +I need a squ so everybody remembers what + + align:start position:0% +I need a squ so everybody remembers what + + + align:start position:0% +I need a squ so everybody remembers what +a squ + + align:start position:0% +a squ + + + align:start position:0% +a squ +is a s is V Lambda V inverse time V + + align:start position:0% +is a s is V Lambda V inverse time V + + + align:start position:0% +is a s is V Lambda V inverse time V +Lambda V inverse and those cancel out to + + align:start position:0% +Lambda V inverse and those cancel out to + + + align:start position:0% +Lambda V inverse and those cancel out to +give V Lambda + + align:start position:0% +give V Lambda + + + align:start position:0% +give V Lambda +squar V inverse + + align:start position:0% +squar V inverse + + + align:start position:0% +squar V inverse +time T ^2 and so + + align:start position:0% + + + + align:start position:0% + +on let + + align:start position:0% +on let + + + align:start position:0% +on let +me you you remember this a squ so I'll + + align:start position:0% +me you you remember this a squ so I'll + + + align:start position:0% +me you you remember this a squ so I'll +take that + + align:start position:0% +take that + + + align:start position:0% +take that +away and look at what I've got look what + + align:start position:0% +away and look at what I've got look what + + + align:start position:0% +away and look at what I've got look what +I've got yes Factor V out of the + + align:start position:0% +I've got yes Factor V out of the + + + align:start position:0% +I've got yes Factor V out of the +start and Factor V inverse out of the + + align:start position:0% +start and Factor V inverse out of the + + + align:start position:0% +start and Factor V inverse out of the +end and in here I + + align:start position:0% +end and in here I + + + align:start position:0% +end and in here I +have V * V inverse is I so that's fine V + + align:start position:0% +have V * V inverse is I so that's fine V + + + align:start position:0% +have V * V inverse is I so that's fine V +* V inverse I have a Lambda + + align:start position:0% +* V inverse I have a Lambda + + + align:start position:0% +* V inverse I have a Lambda +t v and the V inverse so I have a 1 + + align:start position:0% + + + + align:start position:0% + +12 Lambda squar + + align:start position:0% +12 Lambda squar + + + align:start position:0% +12 Lambda squar +t^2 and so + + align:start position:0% +t^2 and so + + + align:start position:0% +t^2 and so +on times V + + align:start position:0% +on times V + + + align:start position:0% +on times V +inverse th this is all just what we hope + + align:start position:0% +inverse th this is all just what we hope + + + align:start position:0% +inverse th this is all just what we hope +for we expect that a v goes out at the + + align:start position:0% +for we expect that a v goes out at the + + + align:start position:0% +for we expect that a v goes out at the +far left at the front this V inverse + + align:start position:0% +far left at the front this V inverse + + + align:start position:0% +far left at the front this V inverse +comes out at the far right and what do + + align:start position:0% +comes out at the far right and what do + + + align:start position:0% +comes out at the far right and what do +you see in the middle you see so this is + + align:start position:0% +you see in the middle you see so this is + + + align:start position:0% +you see in the middle you see so this is +now my formula for E to the a + + align:start position:0% +now my formula for E to the a + + + align:start position:0% +now my formula for E to the a +t is + + align:start position:0% +t is + + + align:start position:0% +t is +V and what do I have there I have the + + align:start position:0% +V and what do I have there I have the + + + align:start position:0% +V and what do I have there I have the +exponential series for Lambda T so it's + + align:start position:0% +exponential series for Lambda T so it's + + + align:start position:0% +exponential series for Lambda T so it's +e to the Lambda t v + + align:start position:0% +e to the Lambda t v + + + align:start position:0% +e to the Lambda t v +inverse and what is e to the Lambda T + + align:start position:0% +inverse and what is e to the Lambda T + + + align:start position:0% +inverse and what is e to the Lambda T +let's just understand The Matrix + + align:start position:0% +let's just understand The Matrix + + + align:start position:0% +let's just understand The Matrix +exponential when the Matrix is diagonal + + align:start position:0% +exponential when the Matrix is diagonal + + + align:start position:0% +exponential when the Matrix is diagonal +the best possible Matrix this will be V + + align:start position:0% +the best possible Matrix this will be V + + + align:start position:0% +the best possible Matrix this will be V +what is my Matrix look like V inverse if + + align:start position:0% +what is my Matrix look like V inverse if + + + align:start position:0% +what is my Matrix look like V inverse if +I'm looking at this looking at this + + align:start position:0% +I'm looking at this looking at this + + + align:start position:0% +I'm looking at this looking at this +lambda's diagonal all these matrices are + + align:start position:0% +lambda's diagonal all these matrices are + + + align:start position:0% +lambda's diagonal all these matrices are +diagonal the with lambdas so that'll be + + align:start position:0% +diagonal the with lambdas so that'll be + + + align:start position:0% +diagonal the with lambdas so that'll be +e to the Lambda 1 T down to e to the + + align:start position:0% +e to the Lambda 1 T down to e to the + + + align:start position:0% +e to the Lambda 1 T down to e to the +Lambda n + + align:start position:0% +Lambda n + + + align:start position:0% +Lambda n +t I'm not doing anything brilliant + + align:start position:0% +t I'm not doing anything brilliant + + + align:start position:0% +t I'm not doing anything brilliant +here I'm just using the standard + + align:start position:0% +here I'm just using the standard + + + align:start position:0% +here I'm just using the standard +diagonalization to represent our to to + + align:start position:0% +diagonalization to represent our to to + + + align:start position:0% +diagonalization to represent our to to +to produce our uh + + align:start position:0% +to produce our uh + + + align:start position:0% +to produce our uh +exponential from the igen vector Matrix + + align:start position:0% +exponential from the igen vector Matrix + + + align:start position:0% +exponential from the igen vector Matrix +and from the igen values so I'm I'm just + + align:start position:0% +and from the igen values so I'm I'm just + + + align:start position:0% +and from the igen values so I'm I'm just +taking the exponentials of the N + + align:start position:0% +taking the exponentials of the N + + + align:start position:0% +taking the exponentials of the N +different IG values so e to the + + align:start position:0% +different IG values so e to the + + + align:start position:0% +different IG values so e to the +at yeah it it's this this would lead to + + align:start position:0% +at yeah it it's this this would lead to + + + align:start position:0% +at yeah it it's this this would lead to +e to the A Y at + + align:start position:0% +e to the A Y at + + + align:start position:0% +e to the A Y at +Zer would be some y of Z is some + + align:start position:0% +Zer would be some y of Z is some + + + align:start position:0% +Zer would be some y of Z is some +combination and then there's an e to the + + align:start position:0% +combination and then there's an e to the + + + align:start position:0% +combination and then there's an e to the +Lambda 1 T coming from here and there's + + align:start position:0% +Lambda 1 T coming from here and there's + + + align:start position:0% +Lambda 1 T coming from here and there's +an + + align:start position:0% +an + + + align:start position:0% +an +X I can Vector X1 + C2 e the Lambda 2T + + align:start position:0% +X I can Vector X1 + C2 e the Lambda 2T + + + align:start position:0% +X I can Vector X1 + C2 e the Lambda 2T +X2 so on that's the solution that we had + + align:start position:0% +X2 so on that's the solution that we had + + + align:start position:0% +X2 so on that's the solution that we had +last time that's the solution that using + + align:start position:0% +last time that's the solution that using + + + align:start position:0% +last time that's the solution that using +igen values and igen vectors + + align:start position:0% +igen values and igen vectors + + + align:start position:0% +igen values and igen vectors +now can I get something new here + + align:start position:0% +now can I get something new here + + + align:start position:0% +now can I get something new here +something new will be Suppose there are + + align:start position:0% +something new will be Suppose there are + + + align:start position:0% +something new will be Suppose there are +not a full set of n independent I + + align:start position:0% +not a full set of n independent I + + + align:start position:0% +not a full set of n independent I +vectors e to the a is still + + align:start position:0% +vectors e to the a is still + + + align:start position:0% +vectors e to the a is still +okay but uh we can't but this formula is + + align:start position:0% +okay but uh we can't but this formula is + + + align:start position:0% +okay but uh we can't but this formula is +no good that formula depends on V and V + + align:start position:0% +no good that formula depends on V and V + + + align:start position:0% +no good that formula depends on V and V +inverse and I'm suppose we have an + + align:start position:0% +inverse and I'm suppose we have an + + + align:start position:0% +inverse and I'm suppose we have an +example so all that is very nice that's + + align:start position:0% +example so all that is very nice that's + + + align:start position:0% +example so all that is very nice that's +what we + + align:start position:0% +what we + + + align:start position:0% +what we +expect + + align:start position:0% +expect + + + align:start position:0% +expect +but we could have a matrix like this one + + align:start position:0% +but we could have a matrix like this one + + + align:start position:0% +but we could have a matrix like this one +a equals well here's an extreme + + align:start position:0% + + + + align:start position:0% + +case what are the IG values of that + + align:start position:0% +case what are the IG values of that + + + align:start position:0% +case what are the IG values of that +matrix it's a diagonal matrix the IG + + align:start position:0% +matrix it's a diagonal matrix the IG + + + align:start position:0% +matrix it's a diagonal matrix the IG +values are zero and zero the igon value + + align:start position:0% +values are zero and zero the igon value + + + align:start position:0% +values are zero and zero the igon value +zero is repeated it's a double I value + + align:start position:0% +zero is repeated it's a double I value + + + align:start position:0% +zero is repeated it's a double I value +and we hope for two I Val vectors but we + + align:start position:0% +and we hope for two I Val vectors but we + + + align:start position:0% +and we hope for two I Val vectors but we +don't find them that has only one line + + align:start position:0% +don't find them that has only one line + + + align:start position:0% +don't find them that has only one line +of I vectors it only has an X1 equals + + align:start position:0% +of I vectors it only has an X1 equals + + + align:start position:0% +of I vectors it only has an X1 equals +one Z I think if I multiply that a times + + align:start position:0% +one Z I think if I multiply that a times + + + align:start position:0% +one Z I think if I multiply that a times +that X1 gives me 0 * X1 that's an igen + + align:start position:0% +that X1 gives me 0 * X1 that's an igen + + + align:start position:0% +that X1 gives me 0 * X1 that's an igen +Vector but there well because the igen + + align:start position:0% +Vector but there well because the igen + + + align:start position:0% +Vector but there well because the igen +value is zero I'm looking for the null + + align:start position:0% +value is zero I'm looking for the null + + + align:start position:0% +value is zero I'm looking for the null +space there's in the null space but + + align:start position:0% +space there's in the null space but + + + align:start position:0% +space there's in the null space but +there's not a the null space is only one + + align:start position:0% +there's not a the null space is only one + + + align:start position:0% +there's not a the null space is only one +dimension dial only one igen vector + + align:start position:0% +dimension dial only one igen vector + + + align:start position:0% +dimension dial only one igen vector +missing an igen Vector + + align:start position:0% +missing an igen Vector + + + align:start position:0% +missing an igen Vector +Still Still I can do e to the a that's + + align:start position:0% +Still Still I can do e to the a that's + + + align:start position:0% +Still Still I can do e to the a that's +still completely correct that series + + align:start position:0% +still completely correct that series + + + align:start position:0% +still completely correct that series +will work so to do the series I need to + + align:start position:0% +will work so to do the series I need to + + + align:start position:0% +will work so to do the series I need to +know a + + align:start position:0% +know a + + + align:start position:0% +know a +squared so I'm actually going to use the + + align:start position:0% +squared so I'm actually going to use the + + + align:start position:0% +squared so I'm actually going to use the +series but you'll see that it cuts off + + align:start position:0% +series but you'll see that it cuts off + + + align:start position:0% +series but you'll see that it cuts off +very fast a s if if you work that out + + align:start position:0% +very fast a s if if you work that out + + + align:start position:0% +very fast a s if if you work that out +it's all zeros + + align:start position:0% + + + + align:start position:0% + +so our e to the a t is just I + a t plus + + align:start position:0% + + + + align:start position:0% + +stop a squar is all zeros a cubed is all + + align:start position:0% +stop a squar is all zeros a cubed is all + + + align:start position:0% +stop a squar is all zeros a cubed is all +zeros so the The Matrix e to the a t is + + align:start position:0% +zeros so the The Matrix e to the a t is + + + align:start position:0% +zeros so the The Matrix e to the a t is +identity a * t a is this times T is + + align:start position:0% +identity a * t a is this times T is + + + align:start position:0% +identity a * t a is this times T is +going to put a t there + + align:start position:0% + + + + align:start position:0% + +there you + + align:start position:0% +there you + + + align:start position:0% +there you +go that's a case of the Matrix + + align:start position:0% +go that's a case of the Matrix + + + align:start position:0% +go that's a case of the Matrix +exponential would which would lead us to + + align:start position:0% +exponential would which would lead us to + + + align:start position:0% +exponential would which would lead us to +the solution of the + + align:start position:0% +the solution of the + + + align:start position:0% +the solution of the +equations of course it's a pretty simple + + align:start position:0% + + + + align:start position:0% + +exponential but it comes from pretty + + align:start position:0% +exponential but it comes from pretty + + + align:start position:0% +exponential but it comes from pretty +simple equations the equations dydt that + + align:start position:0% +simple equations the equations dydt that + + + align:start position:0% +simple equations the equations dydt that +system of two equations with that Matrix + + align:start position:0% +system of two equations with that Matrix + + + align:start position:0% +system of two equations with that Matrix +in it is just our system of equations is + + align:start position:0% +in it is just our system of equations is + + + align:start position:0% +in it is just our system of equations is +just dy1 1 + + align:start position:0% +just dy1 1 + + + align:start position:0% +just dy1 1 +DT I have a one there so it would be a + + align:start position:0% +DT I have a one there so it would be a + + + align:start position:0% +DT I have a one there so it would be a +Y2 and dy2 + + align:start position:0% + + + + align:start position:0% + +DT is zero from the second row well + + align:start position:0% +DT is zero from the second row well + + + align:start position:0% +DT is zero from the second row well +that's pretty easy to solve in fact this + + align:start position:0% +that's pretty easy to solve in fact this + + + align:start position:0% +that's pretty easy to solve in fact this +tells you how to solve you you could + + align:start position:0% +tells you how to solve you you could + + + align:start position:0% +tells you how to solve you you could +naturally ask the question how do we + + align:start position:0% +naturally ask the question how do we + + + align:start position:0% +naturally ask the question how do we +solve differential equations when the + + align:start position:0% +solve differential equations when the + + + align:start position:0% +solve differential equations when the +Matrix doesn't have an vectors + + align:start position:0% +Matrix doesn't have an vectors + + + align:start position:0% +Matrix doesn't have an vectors +here's an example this Matrix has only + + align:start position:0% +here's an example this Matrix has only + + + align:start position:0% +here's an example this Matrix has only +one igen vector but the equation the we + + align:start position:0% +one igen vector but the equation the we + + + align:start position:0% +one igen vector but the equation the we +just solve by you could say back + + align:start position:0% +just solve by you could say back + + + align:start position:0% +just solve by you could say back +substitution this gives Y2 equal + + align:start position:0% + + + + align:start position:0% + +constant and + + align:start position:0% +constant and + + + align:start position:0% +constant and +then that equation dy1 DT equal that + + align:start position:0% +then that equation dy1 DT equal that + + + align:start position:0% +then that equation dy1 DT equal that +constant gives me y1 = T * + + align:start position:0% +constant gives me y1 = T * + + + align:start position:0% +constant gives me y1 = T * +constant and + + align:start position:0% + + + + align:start position:0% + +that's what I'm seeing oh + + align:start position:0% +that's what I'm seeing oh + + + align:start position:0% +that's what I'm seeing oh +yeah are you surprised to see a t show + + align:start position:0% +yeah are you surprised to see a t show + + + align:start position:0% +yeah are you surprised to see a t show +up here normally I don't see a t in + + align:start position:0% +up here normally I don't see a t in + + + align:start position:0% +up here normally I don't see a t in +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +exponentials but in this repeated case + + align:start position:0% +exponentials but in this repeated case + + + align:start position:0% +exponentials but in this repeated case +that's the T that we're always seeing + + align:start position:0% +that's the T that we're always seeing + + + align:start position:0% +that's the T that we're always seeing +when we have repeated Solutions + + align:start position:0% +when we have repeated Solutions + + + align:start position:0% +when we have repeated Solutions +everybody remembers that when we have + + align:start position:0% +everybody remembers that when we have + + + align:start position:0% +everybody remembers that when we have +second order equations and we have the + + align:start position:0% +second order equations and we have the + + + align:start position:0% +second order equations and we have the +two exponents are the same + + align:start position:0% +two exponents are the same + + + align:start position:0% +two exponents are the same +so we only get one solution of that e to + + align:start position:0% +so we only get one solution of that e to + + + align:start position:0% +so we only get one solution of that e to +the St and we have to look for another + + align:start position:0% +the St and we have to look for another + + + align:start position:0% +the St and we have to look for another +one and that other one is t e to the St + + align:start position:0% +one and that other one is t e to the St + + + align:start position:0% +one and that other one is t e to the St +it's that same T there okay that's + + align:start position:0% +it's that same T there okay that's + + + align:start position:0% +it's that same T there okay that's +there's an example of how a matrix with + + align:start position:0% +there's an example of how a matrix with + + + align:start position:0% +there's an example of how a matrix with +a missing igen + + align:start position:0% +a missing igen + + + align:start position:0% +a missing igen +Vector the + + align:start position:0% +Vector the + + + align:start position:0% +Vector the +exponential shows pops a t in the + + align:start position:0% +exponential shows pops a t in the + + + align:start position:0% +exponential shows pops a t in the +exponential pops a t in and if I had two + + align:start position:0% +exponential pops a t in and if I had two + + + align:start position:0% +exponential pops a t in and if I had two +missing I vectors + + align:start position:0% +missing I vectors + + + align:start position:0% +missing I vectors +then in the exponential shall I just + + align:start position:0% +then in the exponential shall I just + + + align:start position:0% +then in the exponential shall I just +show you an example with two missing + + align:start position:0% +show you an example with two missing + + + align:start position:0% +show you an example with two missing +igen vectors let that a b well here it + + align:start position:0% +igen vectors let that a b well here it + + + align:start position:0% +igen vectors let that a b well here it +would be z0 Z + + align:start position:0% +would be z0 Z + + + align:start position:0% +would be z0 Z +z0 triple + + align:start position:0% +z0 triple + + + align:start position:0% +z0 triple +0o with uh let's + + align:start position:0% + + + + align:start position:0% + +say there's a + + align:start position:0% +say there's a + + + align:start position:0% +say there's a +matrix with triple three zero igen + + align:start position:0% +matrix with triple three zero igen + + + align:start position:0% +matrix with triple three zero igen +values but only one igen vector so it's + + align:start position:0% +values but only one igen vector so it's + + + align:start position:0% +values but only one igen vector so it's +missing two two I vectors and I would in + + align:start position:0% +missing two two I vectors and I would in + + + align:start position:0% +missing two two I vectors and I would in +the end in e to the a here I would + + align:start position:0% +the end in e to the a here I would + + + align:start position:0% +the end in e to the a here I would +see probably one one one t t and + + align:start position:0% +see probably one one one t t and + + + align:start position:0% +see probably one one one t t and +probably I'll see a half T2 + + align:start position:0% +probably I'll see a half T2 + + + align:start position:0% +probably I'll see a half T2 +there a little bit like that but one + + align:start position:0% +there a little bit like that but one + + + align:start position:0% +there a little bit like that but one +step worse because the triple igen value + + align:start position:0% +step worse because the triple igen value + + + align:start position:0% +step worse because the triple igen value +well that's not going to happen very + + align:start position:0% +well that's not going to happen very + + + align:start position:0% +well that's not going to happen very +often in reality but we see what produ + + align:start position:0% +often in reality but we see what produ + + + align:start position:0% +often in reality but we see what produ +what it produces it produces a t sared + + align:start position:0% +what it produces it produces a t sared + + + align:start position:0% +what it produces it produces a t sared +as well as the t's okay so the ex Matrix + + align:start position:0% +as well as the t's okay so the ex Matrix + + + align:start position:0% +as well as the t's okay so the ex Matrix +exponential gives a beautiful concise + + align:start position:0% +exponential gives a beautiful concise + + + align:start position:0% +exponential gives a beautiful concise +short formula for the + + align:start position:0% +short formula for the + + + align:start position:0% +short formula for the +solution and it gives a formula that's + + align:start position:0% +solution and it gives a formula that's + + + align:start position:0% +solution and it gives a formula that's +correct and even in the case of missing + + align:start position:0% +correct and even in the case of missing + + + align:start position:0% +correct and even in the case of missing +nigen vectors thank you \ No newline at end of file diff --git a/N8gtnbJuMoo.txt b/N8gtnbJuMoo.txt new file mode 100644 index 0000000000000000000000000000000000000000..145995eebedb0c90c3f4b25b3187597855e5d253 --- /dev/null +++ b/N8gtnbJuMoo.txt @@ -0,0 +1,13995 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay uh what I'd like to do + + align:start position:0% +ocw.mit.edu okay uh what I'd like to do + + + align:start position:0% +ocw.mit.edu okay uh what I'd like to do +today is to continue where we left off + + align:start position:0% +today is to continue where we left off + + + align:start position:0% +today is to continue where we left off +last time in talking about this risk + + align:start position:0% +last time in talking about this risk + + + align:start position:0% +last time in talking about this risk +reward tradeoff uh which ultimately will + + align:start position:0% +reward tradeoff uh which ultimately will + + + align:start position:0% +reward tradeoff uh which ultimately will +allow us to be able to figure out how to + + align:start position:0% +allow us to be able to figure out how to + + + align:start position:0% +allow us to be able to figure out how to +calculate the proper discount rate for + + align:start position:0% +calculate the proper discount rate for + + + align:start position:0% +calculate the proper discount rate for +any project Under the Sun now where we + + align:start position:0% +any project Under the Sun now where we + + + align:start position:0% +any project Under the Sun now where we +left off last time was uh the this + + align:start position:0% +left off last time was uh the this + + + align:start position:0% +left off last time was uh the this +equation and the one after it this + + align:start position:0% +equation and the one after it this + + + align:start position:0% +equation and the one after it this +equation we actually derived I showed + + align:start position:0% +equation we actually derived I showed + + + align:start position:0% +equation we actually derived I showed +you how to get this equation from this + + align:start position:0% +you how to get this equation from this + + + align:start position:0% +you how to get this equation from this +particular uh bullet and the tangency + + align:start position:0% +particular uh bullet and the tangency + + + align:start position:0% +particular uh bullet and the tangency +line and today I'm going to give you + + align:start position:0% +line and today I'm going to give you + + + align:start position:0% +line and today I'm going to give you +names for them the bullet as we've said + + align:start position:0% +names for them the bullet as we've said + + + align:start position:0% +names for them the bullet as we've said +before is the frontier + + align:start position:0% +before is the frontier + + + align:start position:0% +before is the frontier +it's the set of Frontier portfolios and + + align:start position:0% +it's the set of Frontier portfolios and + + + align:start position:0% +it's the set of Frontier portfolios and +the upper Arc of that bullet is called + + align:start position:0% +the upper Arc of that bullet is called + + + align:start position:0% +the upper Arc of that bullet is called +the efficient Frontier now the tangency + + align:start position:0% +the efficient Frontier now the tangency + + + align:start position:0% +the efficient Frontier now the tangency +line has a special name too that + + align:start position:0% +line has a special name too that + + + align:start position:0% +line has a special name too that +tangency line is known as the Capital + + align:start position:0% +tangency line is known as the Capital + + + align:start position:0% +tangency line is known as the Capital +Market line uh because it represents + + align:start position:0% +Market line uh because it represents + + + align:start position:0% +Market line uh because it represents +what all efficient Capital markets + + align:start position:0% +what all efficient Capital markets + + + align:start position:0% +what all efficient Capital markets +should represent in terms of risk-reward + + align:start position:0% +should represent in terms of risk-reward + + + align:start position:0% +should represent in terms of risk-reward +trade-offs so if you are an efficient + + align:start position:0% +trade-offs so if you are an efficient + + + align:start position:0% +trade-offs so if you are an efficient +portfolio manager you want to be on that + + align:start position:0% +portfolio manager you want to be on that + + + align:start position:0% +portfolio manager you want to be on that +line okay so the Capital Market line the + + align:start position:0% +line okay so the Capital Market line the + + + align:start position:0% +line okay so the Capital Market line the +equation for that tangency line is given + + align:start position:0% +equation for that tangency line is given + + + align:start position:0% +equation for that tangency line is given +by this the expected rate of return is + + align:start position:0% +by this the expected rate of return is + + + align:start position:0% +by this the expected rate of return is +equal to the risk-free rate plus some + + align:start position:0% +equal to the risk-free rate plus some + + + align:start position:0% +equal to the risk-free rate plus some +kind of risk premium where the risk + + align:start position:0% +kind of risk premium where the risk + + + align:start position:0% +kind of risk premium where the risk +premium is given by a multiple of the + + align:start position:0% +premium is given by a multiple of the + + + align:start position:0% +premium is given by a multiple of the +markets risk premium or the market + + align:start position:0% +markets risk premium or the market + + + align:start position:0% +markets risk premium or the market +excess return okay and the multiple is + + align:start position:0% +excess return okay and the multiple is + + + align:start position:0% +excess return okay and the multiple is +simply the ratio of the riskiness of + + align:start position:0% +simply the ratio of the riskiness of + + + align:start position:0% +simply the ratio of the riskiness of +your efficient portfolio relative to the + + align:start position:0% +your efficient portfolio relative to the + + + align:start position:0% +your efficient portfolio relative to the +market portfolio or the tangency + + align:start position:0% +market portfolio or the tangency + + + align:start position:0% +market portfolio or the tangency +portfolio Okay if it's twice as risky + + align:start position:0% +portfolio Okay if it's twice as risky + + + align:start position:0% +portfolio Okay if it's twice as risky +you're going to get twice the risk + + align:start position:0% +you're going to get twice the risk + + + align:start position:0% +you're going to get twice the risk +premium if it's half as risky you're + + align:start position:0% +premium if it's half as risky you're + + + align:start position:0% +premium if it's half as risky you're +going to get half the risk premium and + + align:start position:0% +going to get half the risk premium and + + + align:start position:0% +going to get half the risk premium and +we said last time that while this is + + align:start position:0% +we said last time that while this is + + + align:start position:0% +we said last time that while this is +helpful and interesting and even + + align:start position:0% +helpful and interesting and even + + + align:start position:0% +helpful and interesting and even +possibly useful it's going to be of + + align:start position:0% +possibly useful it's going to be of + + + align:start position:0% +possibly useful it's going to be of +limited applicability because not + + align:start position:0% +limited applicability because not + + + align:start position:0% +limited applicability because not +everything is an efficient portfolio + + align:start position:0% +everything is an efficient portfolio + + + align:start position:0% +everything is an efficient portfolio +what we mean by an efficient portfolio + + align:start position:0% +what we mean by an efficient portfolio + + + align:start position:0% +what we mean by an efficient portfolio +the intuition for what an efficient + + align:start position:0% +the intuition for what an efficient + + + align:start position:0% +the intuition for what an efficient +portfolio is is a portfolio where you + + align:start position:0% +portfolio is is a portfolio where you + + + align:start position:0% +portfolio is is a portfolio where you +cannot do + + align:start position:0% +cannot do + + + align:start position:0% +cannot do +better by cannot do better I mean you + + align:start position:0% +better by cannot do better I mean you + + + align:start position:0% +better by cannot do better I mean you +can't get less risk for that same level + + align:start position:0% +can't get less risk for that same level + + + align:start position:0% +can't get less risk for that same level +of return or you can't get more expected + + align:start position:0% +of return or you can't get more expected + + + align:start position:0% +of return or you can't get more expected +return for that same level of risk okay + + align:start position:0% +return for that same level of risk okay + + + align:start position:0% +return for that same level of risk okay +that's what we mean by an efficient + + align:start position:0% +that's what we mean by an efficient + + + align:start position:0% +that's what we mean by an efficient +portfolio it's the best you can do now + + align:start position:0% +portfolio it's the best you can do now + + + align:start position:0% +portfolio it's the best you can do now +most Investments are frankly not + + align:start position:0% +most Investments are frankly not + + + align:start position:0% +most Investments are frankly not +efficient if you pick an arbitrary stock + + align:start position:0% +efficient if you pick an arbitrary stock + + + align:start position:0% +efficient if you pick an arbitrary stock +like IBM that's not an efficient + + align:start position:0% +like IBM that's not an efficient + + + align:start position:0% +like IBM that's not an efficient +portfolio it doesn't mean mean it's no + + align:start position:0% +portfolio it doesn't mean mean it's no + + + align:start position:0% +portfolio it doesn't mean mean it's no +good it doesn't mean you don't want to + + align:start position:0% +good it doesn't mean you don't want to + + + align:start position:0% +good it doesn't mean you don't want to +hold it but it means that you would + + align:start position:0% +hold it but it means that you would + + + align:start position:0% +hold it but it means that you would +never want to hold just + + align:start position:0% +never want to hold just + + + align:start position:0% +never want to hold just +IBM because if you mixed IBM with other + + align:start position:0% +IBM because if you mixed IBM with other + + + align:start position:0% +IBM because if you mixed IBM with other +stuff you can always do better by do + + align:start position:0% +stuff you can always do better by do + + + align:start position:0% +stuff you can always do better by do +better again I'm going to reiterate I + + align:start position:0% +better again I'm going to reiterate I + + + align:start position:0% +better again I'm going to reiterate I +mean you can have higher expected return + + align:start position:0% +mean you can have higher expected return + + + align:start position:0% +mean you can have higher expected return +for the same level of risk or lower risk + + align:start position:0% +for the same level of risk or lower risk + + + align:start position:0% +for the same level of risk or lower risk +for the same level of expected return + + align:start position:0% +for the same level of expected return + + + align:start position:0% +for the same level of expected return +that's what I mean by do better so you + + align:start position:0% +that's what I mean by do better so you + + + align:start position:0% +that's what I mean by do better so you +would never want to hold IBM just by + + align:start position:0% +would never want to hold IBM just by + + + align:start position:0% +would never want to hold IBM just by +itself because you can do better right + + align:start position:0% +itself because you can do better right + + + align:start position:0% +itself because you can do better right +you can do better in getting up to that + + align:start position:0% +you can do better in getting up to that + + + align:start position:0% +you can do better in getting up to that +Northwest Quadrant uh from the IBM + + align:start position:0% +Northwest Quadrant uh from the IBM + + + align:start position:0% +Northwest Quadrant uh from the IBM +point but even though IBM is not + + align:start position:0% +point but even though IBM is not + + + align:start position:0% +point but even though IBM is not +efficient you might still want to hold + + align:start position:0% +efficient you might still want to hold + + + align:start position:0% +efficient you might still want to hold +it and more importantly you might still + + align:start position:0% +it and more importantly you might still + + + align:start position:0% +it and more importantly you might still +want to know what the appropriate + + align:start position:0% +want to know what the appropriate + + + align:start position:0% +want to know what the appropriate +discount rate is for companies that are + + align:start position:0% +discount rate is for companies that are + + + align:start position:0% +discount rate is for companies that are +like IBM okay that's what we're going to + + align:start position:0% +like IBM okay that's what we're going to + + + align:start position:0% +like IBM okay that's what we're going to +do next where I left off last time was + + align:start position:0% +do next where I left off last time was + + + align:start position:0% +do next where I left off last time was +not the Capital Market line but this + + align:start position:0% +not the Capital Market line but this + + + align:start position:0% +not the Capital Market line but this +equation which I did not derive but + + align:start position:0% +equation which I did not derive but + + + align:start position:0% +equation which I did not derive but +which I argued comes from the + + align:start position:0% +which I argued comes from the + + + align:start position:0% +which I argued comes from the +equilibrium argument that Bill Sharp + + align:start position:0% +equilibrium argument that Bill Sharp + + + align:start position:0% +equilibrium argument that Bill Sharp +made 50 years + + align:start position:0% +made 50 years + + + align:start position:0% +made 50 years +ago uh and this really relies on the + + align:start position:0% +ago uh and this really relies on the + + + align:start position:0% +ago uh and this really relies on the +fact that if markets are in + + align:start position:0% +fact that if markets are in + + + align:start position:0% +fact that if markets are in +equilibrium there is a relationship + + align:start position:0% +equilibrium there is a relationship + + + align:start position:0% +equilibrium there is a relationship +between risk and expected return for all + + align:start position:0% +between risk and expected return for all + + + align:start position:0% +between risk and expected return for all +Securities not just efficient portfolios + + align:start position:0% +Securities not just efficient portfolios + + + align:start position:0% +Securities not just efficient portfolios +but any arbitrary security has to + + align:start position:0% +but any arbitrary security has to + + + align:start position:0% +but any arbitrary security has to +satisfy this equation if Supply equals + + align:start position:0% +satisfy this equation if Supply equals + + + align:start position:0% +satisfy this equation if Supply equals +demand if there's an equilibrium if + + align:start position:0% +demand if there's an equilibrium if + + + align:start position:0% +demand if there's an equilibrium if +everybody holds the tangency portfolio + + align:start position:0% +everybody holds the tangency portfolio + + + align:start position:0% +everybody holds the tangency portfolio +and the tangency portfolio therefore is + + align:start position:0% +and the tangency portfolio therefore is + + + align:start position:0% +and the tangency portfolio therefore is +the market portfolio in that situation + + align:start position:0% +the market portfolio in that situation + + + align:start position:0% +the market portfolio in that situation +this equation has to hold so where we + + align:start position:0% +this equation has to hold so where we + + + align:start position:0% +this equation has to hold so where we +left off was to try to interpret this + + align:start position:0% +left off was to try to interpret this + + + align:start position:0% +left off was to try to interpret this +equation this equation is almost + + align:start position:0% +equation this equation is almost + + + align:start position:0% +equation this equation is almost +identical to the Capital Market line + + align:start position:0% +identical to the Capital Market line + + + align:start position:0% +identical to the Capital Market line +there's only one difference the only + + align:start position:0% +there's only one difference the only + + + align:start position:0% +there's only one difference the only +difference is that the multiplier the + + align:start position:0% +difference is that the multiplier the + + + align:start position:0% +difference is that the multiplier the +thing that multiplies the market risk + + align:start position:0% +thing that multiplies the market risk + + + align:start position:0% +thing that multiplies the market risk +premium is not Sigma p over Sigma M it + + align:start position:0% +premium is not Sigma p over Sigma M it + + + align:start position:0% +premium is not Sigma p over Sigma M it +is beta and beta we said was the ratio + + align:start position:0% +is beta and beta we said was the ratio + + + align:start position:0% +is beta and beta we said was the ratio +of the co-variance of an asset with the + + align:start position:0% +of the co-variance of an asset with the + + + align:start position:0% +of the co-variance of an asset with the +market divided by the variance of the + + align:start position:0% +market divided by the variance of the + + + align:start position:0% +market divided by the variance of the +market it is a measure of that + + align:start position:0% +market it is a measure of that + + + align:start position:0% +market it is a measure of that +particular assets riskiness it's not + + align:start position:0% +particular assets riskiness it's not + + + align:start position:0% +particular assets riskiness it's not +variance anymore or standard deviation + + align:start position:0% +variance anymore or standard deviation + + + align:start position:0% +variance anymore or standard deviation +it's something else and so I want to + + align:start position:0% +it's something else and so I want to + + + align:start position:0% +it's something else and so I want to +spend this class talking about what that + + align:start position:0% +spend this class talking about what that + + + align:start position:0% +spend this class talking about what that +something else is and why it makes sense + + align:start position:0% +something else is and why it makes sense + + + align:start position:0% +something else is and why it makes sense +okay first of all let's make sure we + + align:start position:0% +okay first of all let's make sure we + + + align:start position:0% +okay first of all let's make sure we +understand the equation I want to do a + + align:start position:0% +understand the equation I want to do a + + + align:start position:0% +understand the equation I want to do a +few special cases and then I'm going to + + align:start position:0% +few special cases and then I'm going to + + + align:start position:0% +few special cases and then I'm going to +take apart this notion of beta as being + + align:start position:0% +take apart this notion of beta as being + + + align:start position:0% +take apart this notion of beta as being +the right measure of risk in all + + align:start position:0% +the right measure of risk in all + + + align:start position:0% +the right measure of risk in all +circumstances so the first thing I want + + align:start position:0% +circumstances so the first thing I want + + + align:start position:0% +circumstances so the first thing I want +to do is to look at some examples let's + + align:start position:0% +to do is to look at some examples let's + + + align:start position:0% +to do is to look at some examples let's +take an example where the beta is equal + + align:start position:0% +take an example where the beta is equal + + + align:start position:0% +take an example where the beta is equal +to one if the beta is equal to one what + + align:start position:0% +to one if the beta is equal to one what + + + align:start position:0% +to one if the beta is equal to one what +that's saying is that the + + align:start position:0% +that's saying is that the + + + align:start position:0% +that's saying is that the +co-variance between the asset and the + + align:start position:0% +co-variance between the asset and the + + + align:start position:0% +co-variance between the asset and the +market divided by the variance of the + + align:start position:0% +market divided by the variance of the + + + align:start position:0% +market divided by the variance of the +market that that number is equal to one + + align:start position:0% +market that that number is equal to one + + + align:start position:0% +market that that number is equal to one +okay if that's the case then it turns + + align:start position:0% +okay if that's the case then it turns + + + align:start position:0% +okay if that's the case then it turns +out that the expected rate of return of + + align:start position:0% +out that the expected rate of return of + + + align:start position:0% +out that the expected rate of return of +this asset with a beta of one is going + + align:start position:0% +this asset with a beta of one is going + + + align:start position:0% +this asset with a beta of one is going +to be just equal to the market risk + + align:start position:0% +to be just equal to the market risk + + + align:start position:0% +to be just equal to the market risk +premium or the expected return is equal + + align:start position:0% +premium or the expected return is equal + + + align:start position:0% +premium or the expected return is equal +to the Market's expected rate of return + + align:start position:0% +to the Market's expected rate of return + + + align:start position:0% +to the Market's expected rate of return +right when beta is equal to one the RFS + + align:start position:0% +right when beta is equal to one the RFS + + + align:start position:0% +right when beta is equal to one the RFS +cancel out and the expected rate of + + align:start position:0% +cancel out and the expected rate of + + + align:start position:0% +cancel out and the expected rate of +return of the asset is equal to the + + align:start position:0% +return of the asset is equal to the + + + align:start position:0% +return of the asset is equal to the +expected rate of return on the + + align:start position:0% +expected rate of return on the + + + align:start position:0% +expected rate of return on the +market now what about if the beta is + + align:start position:0% +market now what about if the beta is + + + align:start position:0% +market now what about if the beta is +equal to zero if the beta is equal to + + align:start position:0% +equal to zero if the beta is equal to + + + align:start position:0% +equal to zero if the beta is equal to +zero then you get the risk-free + + align:start position:0% +zero then you get the risk-free + + + align:start position:0% +zero then you get the risk-free +rate it's important to realize that if + + align:start position:0% +rate it's important to realize that if + + + align:start position:0% +rate it's important to realize that if +the beta of an asset is equal to zero it + + align:start position:0% +the beta of an asset is equal to zero it + + + align:start position:0% +the beta of an asset is equal to zero it +doesn't mean that the asset has no + + align:start position:0% +doesn't mean that the asset has no + + + align:start position:0% +doesn't mean that the asset has no +volatility in the past when we've looked + + align:start position:0% +volatility in the past when we've looked + + + align:start position:0% +volatility in the past when we've looked +at mixing the risk-free asset t- bills + + align:start position:0% +at mixing the risk-free asset t- bills + + + align:start position:0% +at mixing the risk-free asset t- bills +with the market we know that when the + + align:start position:0% +with the market we know that when the + + + align:start position:0% +with the market we know that when the +risk-free asset is included you get a + + align:start position:0% +risk-free asset is included you get a + + + align:start position:0% +risk-free asset is included you get a +that straight line and it's because the + + align:start position:0% +that straight line and it's because the + + + align:start position:0% +that straight line and it's because the +risk-free asset has no covariance it has + + align:start position:0% +risk-free asset has no covariance it has + + + align:start position:0% +risk-free asset has no covariance it has +no risk at all but now with an asset + + align:start position:0% +no risk at all but now with an asset + + + align:start position:0% +no risk at all but now with an asset +that has a beta of zero you're getting + + align:start position:0% +that has a beta of zero you're getting + + + align:start position:0% +that has a beta of zero you're getting +the risk-free return even though an + + align:start position:0% +the risk-free return even though an + + + align:start position:0% +the risk-free return even though an +asset with a beta of zero still may have + + align:start position:0% +asset with a beta of zero still may have + + + align:start position:0% +asset with a beta of zero still may have +some volatility there it's not the + + align:start position:0% +some volatility there it's not the + + + align:start position:0% +some volatility there it's not the +risk-free asset it's any asset with a + + align:start position:0% +risk-free asset it's any asset with a + + + align:start position:0% +risk-free asset it's any asset with a +zero + + align:start position:0% +zero + + + align:start position:0% +zero +beta and the third observation that I + + align:start position:0% +beta and the third observation that I + + + align:start position:0% +beta and the third observation that I +want to make is when a beta is + + align:start position:0% +want to make is when a beta is + + + align:start position:0% +want to make is when a beta is +negative with the beta that's negative + + align:start position:0% +negative with the beta that's negative + + + align:start position:0% +negative with the beta that's negative +the expected rate of return is actually + + align:start position:0% +the expected rate of return is actually + + + align:start position:0% +the expected rate of return is actually +less than the risk-free rate now that's + + align:start position:0% +less than the risk-free rate now that's + + + align:start position:0% +less than the risk-free rate now that's +really odd + + align:start position:0% +really odd + + + align:start position:0% +really odd +I've got an asset that is + + align:start position:0% +I've got an asset that is + + + align:start position:0% +I've got an asset that is +risky but just because it has a negative + + align:start position:0% +risky but just because it has a negative + + + align:start position:0% +risky but just because it has a negative +beta the expected rate of return is less + + align:start position:0% +beta the expected rate of return is less + + + align:start position:0% +beta the expected rate of return is less +than the risk-free rate that means that + + align:start position:0% +than the risk-free rate that means that + + + align:start position:0% +than the risk-free rate that means that +you are willing to take a lower expected + + align:start position:0% +you are willing to take a lower expected + + + align:start position:0% +you are willing to take a lower expected +rate of return than the risk-free rate + + align:start position:0% +rate of return than the risk-free rate + + + align:start position:0% +rate of return than the risk-free rate +for an asset that has this weird + + align:start position:0% +for an asset that has this weird + + + align:start position:0% +for an asset that has this weird +property of negative beta and the + + align:start position:0% +property of negative beta and the + + + align:start position:0% +property of negative beta and the +question I want to answer today is why + + align:start position:0% +question I want to answer today is why + + + align:start position:0% +question I want to answer today is why +is that why why why is it the case that + + align:start position:0% +is that why why why is it the case that + + + align:start position:0% +is that why why why is it the case that +you might be willing to take such a low + + align:start position:0% +you might be willing to take such a low + + + align:start position:0% +you might be willing to take such a low +rate of return and actually if the beta + + align:start position:0% +rate of return and actually if the beta + + + align:start position:0% +rate of return and actually if the beta +is negative enough if this beta is + + align:start position:0% +is negative enough if this beta is + + + align:start position:0% +is negative enough if this beta is +negative enough it could be the case + + align:start position:0% +negative enough it could be the case + + + align:start position:0% +negative enough it could be the case +that the expected rate of return is + + align:start position:0% +that the expected rate of return is + + + align:start position:0% +that the expected rate of return is +negative in other words you might be + + align:start position:0% +negative in other words you might be + + + align:start position:0% +negative in other words you might be +willing to pay somebody for the + + align:start position:0% +willing to pay somebody for the + + + align:start position:0% +willing to pay somebody for the +privilege of bearing that risk that that + + align:start position:0% +privilege of bearing that risk that that + + + align:start position:0% +privilege of bearing that risk that that +seems completely counterintuitive why + + align:start position:0% +seems completely counterintuitive why + + + align:start position:0% +seems completely counterintuitive why +would you be willing to + + align:start position:0% +would you be willing to + + + align:start position:0% +would you be willing to +pay to take risk you should be getting + + align:start position:0% +pay to take risk you should be getting + + + align:start position:0% +pay to take risk you should be getting +paid to take risk right that's the the + + align:start position:0% +paid to take risk right that's the the + + + align:start position:0% +paid to take risk right that's the the +the standard uh hypothesis that we come + + align:start position:0% +the standard uh hypothesis that we come + + + align:start position:0% +the standard uh hypothesis that we come +into the financial markets + + align:start position:0% +into the financial markets + + + align:start position:0% +into the financial markets +with so yeah + + align:start position:0% + + + + align:start position:0% + +Leah that's + + align:start position:0% + + + + align:start position:0% + +right exactly that's that's exactly the + + align:start position:0% +right exactly that's that's exactly the + + + align:start position:0% +right exactly that's that's exactly the +intuition for all three of these cases + + align:start position:0% +intuition for all three of these cases + + + align:start position:0% +intuition for all three of these cases +it turns out that the beta remember has + + align:start position:0% +it turns out that the beta remember has + + + align:start position:0% +it turns out that the beta remember has +this covariance term there in there and + + align:start position:0% +this covariance term there in there and + + + align:start position:0% +this covariance term there in there and +it is going to turn out that if you can + + align:start position:0% +it is going to turn out that if you can + + + align:start position:0% +it is going to turn out that if you can +find an asset that is + + align:start position:0% +find an asset that is + + + align:start position:0% +find an asset that is +negatively correlated to the tangency + + align:start position:0% +negatively correlated to the tangency + + + align:start position:0% +negatively correlated to the tangency +portfolio that is going to be of + + align:start position:0% +portfolio that is going to be of + + + align:start position:0% +portfolio that is going to be of +tremendous value to you it's very very + + align:start position:0% +tremendous value to you it's very very + + + align:start position:0% +tremendous value to you it's very very +valuable now okay let me try to explain + + align:start position:0% +valuable now okay let me try to explain + + + align:start position:0% +valuable now okay let me try to explain +the logic behind it now we're going to + + align:start position:0% +the logic behind it now we're going to + + + align:start position:0% +the logic behind it now we're going to +do a few examples so let's go through + + align:start position:0% +do a few examples so let's go through + + + align:start position:0% +do a few examples so let's go through +the basic logic of what's going on the + + align:start position:0% +the basic logic of what's going on the + + + align:start position:0% +the basic logic of what's going on the +tangency portfolio M plays a central + + align:start position:0% +tangency portfolio M plays a central + + + align:start position:0% +tangency portfolio M plays a central +role in that everybody in the world is + + align:start position:0% +role in that everybody in the world is + + + align:start position:0% +role in that everybody in the world is +going to want to have a portfolio that's + + align:start position:0% +going to want to have a portfolio that's + + + align:start position:0% +going to want to have a portfolio that's +a combination of the risk-free asset and + + align:start position:0% +a combination of the risk-free asset and + + + align:start position:0% +a combination of the risk-free asset and +the tangency + + align:start position:0% +the tangency + + + align:start position:0% +the tangency +portfolio that's fact number one fact + + align:start position:0% +portfolio that's fact number one fact + + + align:start position:0% +portfolio that's fact number one fact +number two the tangency + + align:start position:0% +number two the tangency + + + align:start position:0% +number two the tangency +portfolio is a portfolio that has the + + align:start position:0% +portfolio is a portfolio that has the + + + align:start position:0% +portfolio is a portfolio that has the +aggregate measure of the total amount of + + align:start position:0% +aggregate measure of the total amount of + + + align:start position:0% +aggregate measure of the total amount of +risk in the economy that cannot be + + align:start position:0% +risk in the economy that cannot be + + + align:start position:0% +risk in the economy that cannot be +Diversified beyond that point in other + + align:start position:0% +Diversified beyond that point in other + + + align:start position:0% +Diversified beyond that point in other +words uh in order to get lower risk than + + align:start position:0% +words uh in order to get lower risk than + + + align:start position:0% +words uh in order to get lower risk than +this particular portfolio you have to + + align:start position:0% +this particular portfolio you have to + + + align:start position:0% +this particular portfolio you have to +decrease your uh expected rate of return + + align:start position:0% +decrease your uh expected rate of return + + + align:start position:0% +decrease your uh expected rate of return +there's no way to get lower risk uh and + + align:start position:0% +there's no way to get lower risk uh and + + + align:start position:0% +there's no way to get lower risk uh and +keep that same level of expected return + + align:start position:0% +keep that same level of expected return + + + align:start position:0% +keep that same level of expected return +you can't go this way you have to go + + align:start position:0% +you can't go this way you have to go + + + align:start position:0% +you can't go this way you have to go +down this line okay so if you're going + + align:start position:0% +down this line okay so if you're going + + + align:start position:0% +down this line okay so if you're going +to hold a portfolio of purely risky + + align:start position:0% +to hold a portfolio of purely risky + + + align:start position:0% +to hold a portfolio of purely risky +Securities then basically this is the + + align:start position:0% +Securities then basically this is the + + + align:start position:0% +Securities then basically this is the +best that you can do this is the best + + align:start position:0% +best that you can do this is the best + + + align:start position:0% +best that you can do this is the best +tradeoff that you can get uh in ter + + align:start position:0% +tradeoff that you can get uh in ter + + + align:start position:0% +tradeoff that you can get uh in ter +terms of risk reward so right away you + + align:start position:0% +terms of risk reward so right away you + + + align:start position:0% +terms of risk reward so right away you +know that this Market portfolio plays a + + align:start position:0% +know that this Market portfolio plays a + + + align:start position:0% +know that this Market portfolio plays a +very special role right it is it is + + align:start position:0% +very special role right it is it is + + + align:start position:0% +very special role right it is it is +really the the representation of the + + align:start position:0% +really the the representation of the + + + align:start position:0% +really the the representation of the +aggregate risk in the stock market and + + align:start position:0% +aggregate risk in the stock market and + + + align:start position:0% +aggregate risk in the stock market and +that's why it can serve as a kind of a + + align:start position:0% +that's why it can serve as a kind of a + + + align:start position:0% +that's why it can serve as a kind of a +benchmark for what the stock market is + + align:start position:0% +benchmark for what the stock market is + + + align:start position:0% +benchmark for what the stock market is +doing so we'll going of come back to + + align:start position:0% +doing so we'll going of come back to + + + align:start position:0% +doing so we'll going of come back to +that Benchmark idea in a few minutes so + + align:start position:0% +that Benchmark idea in a few minutes so + + + align:start position:0% +that Benchmark idea in a few minutes so +if you have a a a security that is very + + align:start position:0% +if you have a a a security that is very + + + align:start position:0% +if you have a a a security that is very +highly correlated to that market return + + align:start position:0% +highly correlated to that market return + + + align:start position:0% +highly correlated to that market return +then that's not going to help you in + + align:start position:0% +then that's not going to help you in + + + align:start position:0% +then that's not going to help you in +terms of your own + + align:start position:0% +terms of your own + + + align:start position:0% +terms of your own +diversification if on the other hand you + + align:start position:0% +diversification if on the other hand you + + + align:start position:0% +diversification if on the other hand you +have a security that is negatively + + align:start position:0% +have a security that is negatively + + + align:start position:0% +have a security that is negatively +correlated with that market portfolio + + align:start position:0% +correlated with that market portfolio + + + align:start position:0% +correlated with that market portfolio +that's going to help you a + + align:start position:0% +that's going to help you a + + + align:start position:0% +that's going to help you a +lot and if it's going to help you a lot + + align:start position:0% +lot and if it's going to help you a lot + + + align:start position:0% +lot and if it's going to help you a lot +you're willing to pay for it when you're + + align:start position:0% +you're willing to pay for it when you're + + + align:start position:0% +you're willing to pay for it when you're +willing to pay for it what does that + + align:start position:0% +willing to pay for it what does that + + + align:start position:0% +willing to pay for it what does that +mean you drive the price today high and + + align:start position:0% +mean you drive the price today high and + + + align:start position:0% +mean you drive the price today high and +therefore the expected rate of return + + align:start position:0% +therefore the expected rate of return + + + align:start position:0% +therefore the expected rate of return +return which is the return between today + + align:start position:0% +return which is the return between today + + + align:start position:0% +return which is the return between today +and Next + + align:start position:0% +and Next + + + align:start position:0% +and Next +Period that becomes + + align:start position:0% +Period that becomes + + + align:start position:0% +Period that becomes +lower okay so an asset that helps you + + align:start position:0% +lower okay so an asset that helps you + + + align:start position:0% +lower okay so an asset that helps you +hedge what is essentially unhedgeable in + + align:start position:0% +hedge what is essentially unhedgeable in + + + align:start position:0% +hedge what is essentially unhedgeable in +other words the market portfolio that + + align:start position:0% +other words the market portfolio that + + + align:start position:0% +other words the market portfolio that +can benefit you a great deal as a result + + align:start position:0% +can benefit you a great deal as a result + + + align:start position:0% +can benefit you a great deal as a result +it's going to be very hard to find + + align:start position:0% +it's going to be very hard to find + + + align:start position:0% +it's going to be very hard to find +negative + + align:start position:0% +negative + + + align:start position:0% +negative +beta Securities or assets but in any + + align:start position:0% +beta Securities or assets but in any + + + align:start position:0% +beta Securities or assets but in any +case this relationship really really + + align:start position:0% +case this relationship really really + + + align:start position:0% +case this relationship really really +tells you that given a particular + + align:start position:0% +tells you that given a particular + + + align:start position:0% +tells you that given a particular +covariance you can measure the expected + + align:start position:0% +covariance you can measure the expected + + + align:start position:0% +covariance you can measure the expected +rate of return that you ought to be + + align:start position:0% +rate of return that you ought to be + + + align:start position:0% +rate of return that you ought to be +getting all right and this relationship + + align:start position:0% +getting all right and this relationship + + + align:start position:0% +getting all right and this relationship +is so important that we give it a + + align:start position:0% +is so important that we give it a + + + align:start position:0% +is so important that we give it a +separate name it's called the security + + align:start position:0% +separate name it's called the security + + + align:start position:0% +separate name it's called the security +Market line not the Capital Market line + + align:start position:0% +Market line not the Capital Market line + + + align:start position:0% +Market line not the Capital Market line +but the security Market line because + + align:start position:0% +but the security Market line because + + + align:start position:0% +but the security Market line because +this applies to every single security uh + + align:start position:0% +this applies to every single security uh + + + align:start position:0% +this applies to every single security uh +in your entire universe yeah Dennis you + + align:start position:0% +in your entire universe yeah Dennis you + + + align:start position:0% +in your entire universe yeah Dennis you +say it's hard to something ative yeah + + align:start position:0% +say it's hard to something ative yeah + + + align:start position:0% +say it's hard to something ative yeah +short something does that mean you're + + align:start position:0% +short something does that mean you're + + + align:start position:0% +short something does that mean you're +getting negative it is it is you you do + + align:start position:0% +getting negative it is it is you you do + + + align:start position:0% +getting negative it is it is you you do +but the problem with shorting something + + align:start position:0% +but the problem with shorting something + + + align:start position:0% +but the problem with shorting something +where you get a negative beta you also + + align:start position:0% +where you get a negative beta you also + + + align:start position:0% +where you get a negative beta you also +get a negative expected rate of return + + align:start position:0% +get a negative expected rate of return + + + align:start position:0% +get a negative expected rate of return +typically so what you want to have is an + + align:start position:0% +typically so what you want to have is an + + + align:start position:0% +typically so what you want to have is an +asset that's got a positive beta or + + align:start position:0% +asset that's got a positive beta or + + + align:start position:0% +asset that's got a positive beta or +negative beta but a positive expected + + align:start position:0% +negative beta but a positive expected + + + align:start position:0% +negative beta but a positive expected +rate of return that's what's very rare + + align:start position:0% +rate of return that's what's very rare + + + align:start position:0% +rate of return that's what's very rare +but you can manufacture a negative beta + + align:start position:0% +but you can manufacture a negative beta + + + align:start position:0% +but you can manufacture a negative beta +security very easily by just shorting it + + align:start position:0% +security very easily by just shorting it + + + align:start position:0% +security very easily by just shorting it +right the problem is that when you short + + align:start position:0% +right the problem is that when you short + + + align:start position:0% +right the problem is that when you short +a stock you're going to also get a very + + align:start position:0% +a stock you're going to also get a very + + + align:start position:0% +a stock you're going to also get a very +negative expected rate of return and + + align:start position:0% +negative expected rate of return and + + + align:start position:0% +negative expected rate of return and +that doesn't help you in terms of + + align:start position:0% +that doesn't help you in terms of + + + align:start position:0% +that doesn't help you in terms of +producing an attractive investment + + align:start position:0% +producing an attractive investment + + + align:start position:0% +producing an attractive investment +opportunity Ken + + align:start position:0% +opportunity Ken + + + align:start position:0% +opportunity Ken +question question so what's an example + + align:start position:0% +question question so what's an example + + + align:start position:0% +question question so what's an example +of security well uh it's very hard to + + align:start position:0% +of security well uh it's very hard to + + + align:start position:0% +of security well uh it's very hard to +come by but the closest thing that + + align:start position:0% +come by but the closest thing that + + + align:start position:0% +come by but the closest thing that +exists in markets today is uh stocks + + align:start position:0% +exists in markets today is uh stocks + + + align:start position:0% +exists in markets today is uh stocks +that are uh involved in uh gold uh + + align:start position:0% +that are uh involved in uh gold uh + + + align:start position:0% +that are uh involved in uh gold uh +production gold mining stocks that has a + + align:start position:0% +production gold mining stocks that has a + + + align:start position:0% +production gold mining stocks that has a +beta of around zero but sometimes it's + + align:start position:0% +beta of around zero but sometimes it's + + + align:start position:0% +beta of around zero but sometimes it's +negative sometimes it's positive but + + align:start position:0% +negative sometimes it's positive but + + + align:start position:0% +negative sometimes it's positive but +it's small so that's an example but + + align:start position:0% +it's small so that's an example but + + + align:start position:0% +it's small so that's an example but +that's about the only example that we + + align:start position:0% +that's about the only example that we + + + align:start position:0% +that's about the only example that we +can come up with in the data that looks + + align:start position:0% +can come up with in the data that looks + + + align:start position:0% +can come up with in the data that looks +slightly negative right by and large + + align:start position:0% +slightly negative right by and large + + + align:start position:0% +slightly negative right by and large +most of the betas uh in the data sets + + align:start position:0% +most of the betas uh in the data sets + + + align:start position:0% +most of the betas uh in the data sets +are positive and they're actually + + align:start position:0% +are positive and they're actually + + + align:start position:0% +are positive and they're actually +clustered around one so the typical beta + + align:start position:0% +clustered around one so the typical beta + + + align:start position:0% +clustered around one so the typical beta +is in in the neighborhood of 0.5 to + + align:start position:0% +is in in the neighborhood of 0.5 to + + + align:start position:0% +is in in the neighborhood of 0.5 to +1.5 all right now before we start + + align:start position:0% +1.5 all right now before we start + + + align:start position:0% +1.5 all right now before we start +looking at the data I'm going to show + + align:start position:0% +looking at the data I'm going to show + + + align:start position:0% +looking at the data I'm going to show +you some data in a minute I I want to + + align:start position:0% +you some data in a minute I I want to + + + align:start position:0% +you some data in a minute I I want to +take the security Market line and apply + + align:start position:0% +take the security Market line and apply + + + align:start position:0% +take the security Market line and apply +it so the security Market line I did not + + align:start position:0% +it so the security Market line I did not + + + align:start position:0% +it so the security Market line I did not +derive I want to make that clear and + + align:start position:0% +derive I want to make that clear and + + + align:start position:0% +derive I want to make that clear and +those of you who are interested in the + + align:start position:0% +those of you who are interested in the + + + align:start position:0% +those of you who are interested in the +derivation you can take a look at the + + align:start position:0% +derivation you can take a look at the + + + align:start position:0% +derivation you can take a look at the +appendix in the Brey Myers and Allen + + align:start position:0% +appendix in the Brey Myers and Allen + + + align:start position:0% +appendix in the Brey Myers and Allen +they provide the derivation it's a + + align:start position:0% +they provide the derivation it's a + + + align:start position:0% +they provide the derivation it's a +little bit messy but uh you know with a + + align:start position:0% +little bit messy but uh you know with a + + + align:start position:0% +little bit messy but uh you know with a +little bit of Matrix algebra uh you can + + align:start position:0% +little bit of Matrix algebra uh you can + + + align:start position:0% +little bit of Matrix algebra uh you can +work through it um but the implications + + align:start position:0% +work through it um but the implications + + + align:start position:0% +work through it um but the implications +are extremely important so I want all of + + align:start position:0% +are extremely important so I want all of + + + align:start position:0% +are extremely important so I want all of +you to know how to use it so it may look + + align:start position:0% +you to know how to use it so it may look + + + align:start position:0% +you to know how to use it so it may look +pretty simple but I'll show you a few + + align:start position:0% +pretty simple but I'll show you a few + + + align:start position:0% +pretty simple but I'll show you a few +applications that you might not have uh + + align:start position:0% +applications that you might not have uh + + + align:start position:0% +applications that you might not have uh +thought of for + + align:start position:0% +thought of for + + + align:start position:0% +thought of for +example suppose this is true for every + + align:start position:0% +example suppose this is true for every + + + align:start position:0% +example suppose this is true for every +single + + align:start position:0% +single + + + align:start position:0% +single +security well if it's true for every + + align:start position:0% +security well if it's true for every + + + align:start position:0% +security well if it's true for every +single security it turns out that this + + align:start position:0% +single security it turns out that this + + + align:start position:0% +single security it turns out that this +works for portfolios as well and let me + + align:start position:0% +works for portfolios as well and let me + + + align:start position:0% +works for portfolios as well and let me +show you why suppose we've got a + + align:start position:0% +show you why suppose we've got a + + + align:start position:0% +show you why suppose we've got a +portfolio that's a weighted average of + + align:start position:0% +portfolio that's a weighted average of + + + align:start position:0% +portfolio that's a weighted average of +the returns for the individual component + + align:start position:0% +the returns for the individual component + + + align:start position:0% +the returns for the individual component +Securities right then if I calculate the + + align:start position:0% +Securities right then if I calculate the + + + align:start position:0% +Securities right then if I calculate the +co-variance between the portfolio return + + align:start position:0% +co-variance between the portfolio return + + + align:start position:0% +co-variance between the portfolio return +and the tangency portfolio or the + + align:start position:0% +and the tangency portfolio or the + + + align:start position:0% +and the tangency portfolio or the +market the co-variance is going to look + + align:start position:0% +market the co-variance is going to look + + + align:start position:0% +market the co-variance is going to look +like this which is actually just going + + align:start position:0% +like this which is actually just going + + + align:start position:0% +like this which is actually just going +to look like a weighted average of the + + align:start position:0% +to look like a weighted average of the + + + align:start position:0% +to look like a weighted average of the +covariances + + align:start position:0% +covariances + + + align:start position:0% +covariances +okay this is a mathematical identity + + align:start position:0% +okay this is a mathematical identity + + + align:start position:0% +okay this is a mathematical identity +from here down to here and therefore + + align:start position:0% +from here down to here and therefore + + + align:start position:0% +from here down to here and therefore +when I divide both sides by the variance + + align:start position:0% +when I divide both sides by the variance + + + align:start position:0% +when I divide both sides by the variance +of the market I get something pretty + + align:start position:0% +of the market I get something pretty + + + align:start position:0% +of the market I get something pretty +neat which is that the beta of my + + align:start position:0% +neat which is that the beta of my + + + align:start position:0% +neat which is that the beta of my +portfolio + + align:start position:0% +portfolio + + + align:start position:0% +portfolio +where beta is defined as the co-variance + + align:start position:0% +where beta is defined as the co-variance + + + align:start position:0% +where beta is defined as the co-variance +between the portfolio and the market the + + align:start position:0% +between the portfolio and the market the + + + align:start position:0% +between the portfolio and the market the +ba divided by the variance the beta of + + align:start position:0% +ba divided by the variance the beta of + + + align:start position:0% +ba divided by the variance the beta of +the portfolio is just equal to the + + align:start position:0% +the portfolio is just equal to the + + + align:start position:0% +the portfolio is just equal to the +weighted average of the betas of my + + align:start position:0% +weighted average of the betas of my + + + align:start position:0% +weighted average of the betas of my +component + + align:start position:0% +component + + + align:start position:0% +component +Securities that's that's really neat + + align:start position:0% +Securities that's that's really neat + + + align:start position:0% +Securities that's that's really neat +because what that says is that when I + + align:start position:0% +because what that says is that when I + + + align:start position:0% +because what that says is that when I +want to measure the risk of a collection + + align:start position:0% +want to measure the risk of a collection + + + align:start position:0% +want to measure the risk of a collection +of Securities as long as I know the + + align:start position:0% +of Securities as long as I know the + + + align:start position:0% +of Securities as long as I know the +betas of each + + align:start position:0% +betas of each + + + align:start position:0% +betas of each +individual security I can calculate the + + align:start position:0% +individual security I can calculate the + + + align:start position:0% +individual security I can calculate the +weighted average of those betas and that + + align:start position:0% +weighted average of those betas and that + + + align:start position:0% +weighted average of those betas and that +is the beta of my + + align:start position:0% +is the beta of my + + + align:start position:0% +is the beta of my +portfolio so if you think of beta as a + + align:start position:0% +portfolio so if you think of beta as a + + + align:start position:0% +portfolio so if you think of beta as a +measure of + + align:start position:0% +measure of + + + align:start position:0% +measure of +risk this measure of + + align:start position:0% +risk this measure of + + + align:start position:0% +risk this measure of +risk is actually linear unlike + + align:start position:0% +risk is actually linear unlike + + + align:start position:0% +risk is actually linear unlike +volatility which is not linear right the + + align:start position:0% +volatility which is not linear right the + + + align:start position:0% +volatility which is not linear right the +variance of a portfolio is not simply + + align:start position:0% +variance of a portfolio is not simply + + + align:start position:0% +variance of a portfolio is not simply +equal to the sum of the variances + + align:start position:0% +equal to the sum of the variances + + + align:start position:0% +equal to the sum of the variances +weighted by their portfolio weights it's + + align:start position:0% +weighted by their portfolio weights it's + + + align:start position:0% +weighted by their portfolio weights it's +that complicated expression where you're + + align:start position:0% +that complicated expression where you're + + + align:start position:0% +that complicated expression where you're +adding up all of those cross products as + + align:start position:0% +adding up all of those cross products as + + + align:start position:0% +adding up all of those cross products as +well so we get an enormous + + align:start position:0% +well so we get an enormous + + + align:start position:0% +well so we get an enormous +simplification with the security Market + + align:start position:0% +simplification with the security Market + + + align:start position:0% +simplification with the security Market +line it says that we can measure the + + align:start position:0% +line it says that we can measure the + + + align:start position:0% +line it says that we can measure the +risk of a portfolio using this concept + + align:start position:0% +risk of a portfolio using this concept + + + align:start position:0% +risk of a portfolio using this concept +called beta and beta happens to be + + align:start position:0% +called beta and beta happens to be + + + align:start position:0% +called beta and beta happens to be +linear in the sense that when you take a + + align:start position:0% +linear in the sense that when you take a + + + align:start position:0% +linear in the sense that when you take a +weighted average the beta is equal to + + align:start position:0% +weighted average the beta is equal to + + + align:start position:0% +weighted average the beta is equal to +the weighted average of the individual + + align:start position:0% +the weighted average of the individual + + + align:start position:0% +the weighted average of the individual +asset betas okay so therefore if you + + align:start position:0% +asset betas okay so therefore if you + + + align:start position:0% +asset betas okay so therefore if you +know that the betas are going to be a + + align:start position:0% +know that the betas are going to be a + + + align:start position:0% +know that the betas are going to be a +weighted average then in fact fact the + + align:start position:0% +weighted average then in fact fact the + + + align:start position:0% +weighted average then in fact fact the +expected rate of return on the portfolio + + align:start position:0% +expected rate of return on the portfolio + + + align:start position:0% +expected rate of return on the portfolio +now is equal to the risk-free rate plus + + align:start position:0% +now is equal to the risk-free rate plus + + + align:start position:0% +now is equal to the risk-free rate plus +this weighted average beta times the + + align:start position:0% +this weighted average beta times the + + + align:start position:0% +this weighted average beta times the +market risk + + align:start position:0% +market risk + + + align:start position:0% +market risk +premium do you see the power of this + + align:start position:0% +premium do you see the power of this + + + align:start position:0% +premium do you see the power of this +this now allows you to analyze the + + align:start position:0% +this now allows you to analyze the + + + align:start position:0% +this now allows you to analyze the +expected return on anything any + + align:start position:0% +expected return on anything any + + + align:start position:0% +expected return on anything any +collection of assets if you know what + + align:start position:0% +collection of assets if you know what + + + align:start position:0% +collection of assets if you know what +the betas are for the individual + + align:start position:0% +the betas are for the individual + + + align:start position:0% +the betas are for the individual +components you know what the betas are + + align:start position:0% +components you know what the betas are + + + align:start position:0% +components you know what the betas are +for the whole + + align:start position:0% +for the whole + + + align:start position:0% +for the whole +thing right + + align:start position:0% +thing right + + + align:start position:0% +thing right +so now you can calculate the appropriate + + align:start position:0% +so now you can calculate the appropriate + + + align:start position:0% +so now you can calculate the appropriate +rate of return for virtually anything + + align:start position:0% +rate of return for virtually anything + + + align:start position:0% +rate of return for virtually anything +and this is not just limited to stocks + + align:start position:0% +and this is not just limited to stocks + + + align:start position:0% +and this is not just limited to stocks +you can apply this to projects for + + align:start position:0% +you can apply this to projects for + + + align:start position:0% +you can apply this to projects for +example if you want to know what the + + align:start position:0% +example if you want to know what the + + + align:start position:0% +example if you want to know what the +expected rate of return is on an oil + + align:start position:0% +expected rate of return is on an oil + + + align:start position:0% +expected rate of return is on an oil +drilling project well measure the beta + + align:start position:0% +drilling project well measure the beta + + + align:start position:0% +drilling project well measure the beta +of oil drilling stocks use that beta and + + align:start position:0% +of oil drilling stocks use that beta and + + + align:start position:0% +of oil drilling stocks use that beta and +that will be your appropriate discount + + align:start position:0% +that will be your appropriate discount + + + align:start position:0% +that will be your appropriate discount +rate for the particular oil drilling + + align:start position:0% +rate for the particular oil drilling + + + align:start position:0% +rate for the particular oil drilling +project right it's a really remarkable a + + align:start position:0% +project right it's a really remarkable a + + + align:start position:0% +project right it's a really remarkable a +remarkable uh result + + align:start position:0% +remarkable uh result + + + align:start position:0% +remarkable uh result +so we have an expression for the + + align:start position:0% +so we have an expression for the + + + align:start position:0% +so we have an expression for the +required rate of return opportunity cost + + align:start position:0% +required rate of return opportunity cost + + + align:start position:0% +required rate of return opportunity cost +of capital risk adjusted discount rate + + align:start position:0% +of capital risk adjusted discount rate + + + align:start position:0% +of capital risk adjusted discount rate +for all the various different kind of + + align:start position:0% +for all the various different kind of + + + align:start position:0% +for all the various different kind of +examples and cases that we looked at up + + align:start position:0% +examples and cases that we looked at up + + + align:start position:0% +examples and cases that we looked at up +until + + align:start position:0% +until + + + align:start position:0% +until +now and the last point I want to make + + align:start position:0% +now and the last point I want to make + + + align:start position:0% +now and the last point I want to make +about this equation is how do you + + align:start position:0% +about this equation is how do you + + + align:start position:0% +about this equation is how do you +actually take it out for a spin how do + + align:start position:0% +actually take it out for a spin how do + + + align:start position:0% +actually take it out for a spin how do +you estimate the expected rate of return + + align:start position:0% +you estimate the expected rate of return + + + align:start position:0% +you estimate the expected rate of return +on the market and the risk-free rate + + align:start position:0% +on the market and the risk-free rate + + + align:start position:0% +on the market and the risk-free rate +well that comes from the data that comes + + align:start position:0% +well that comes from the data that comes + + + align:start position:0% +well that comes from the data that comes +from the marketplace we observe it in + + align:start position:0% +from the marketplace we observe it in + + + align:start position:0% +from the marketplace we observe it in +the marketplace and we can actually see + + align:start position:0% +the marketplace and we can actually see + + + align:start position:0% +the marketplace and we can actually see +it okay so let's do some examples just + + align:start position:0% +it okay so let's do some examples just + + + align:start position:0% +it okay so let's do some examples just +to make sure that we all get this and + + align:start position:0% +to make sure that we all get this and + + + align:start position:0% +to make sure that we all get this and +know how to apply it using returns from + + align:start position:0% +know how to apply it using returns from + + + align:start position:0% +know how to apply it using returns from +1990 to 2001 we estimate that + + align:start position:0% +1990 to 2001 we estimate that + + + align:start position:0% +1990 to 2001 we estimate that +Microsoft's beta during that period of + + align:start position:0% +Microsoft's beta during that period of + + + align:start position:0% +Microsoft's beta during that period of +time is + + align:start position:0% +time is + + + align:start position:0% +time is +1.49 and uh if you do the same thing for + + align:start position:0% +1.49 and uh if you do the same thing for + + + align:start position:0% +1.49 and uh if you do the same thing for +Gillette you get that gillette's beta is + + align:start position:0% +Gillette you get that gillette's beta is + + + align:start position:0% +Gillette you get that gillette's beta is +081 now let's not even look at the next + + align:start position:0% +081 now let's not even look at the next + + + align:start position:0% +081 now let's not even look at the next +uh set of numbers for a moment just talk + + align:start position:0% +uh set of numbers for a moment just talk + + + align:start position:0% +uh set of numbers for a moment just talk +about those two numbers 1.49 and 081 + + align:start position:0% +about those two numbers 1.49 and 081 + + + align:start position:0% +about those two numbers 1.49 and 081 +does that make sense to you let's think + + align:start position:0% +does that make sense to you let's think + + + align:start position:0% +does that make sense to you let's think +about what that's saying + + align:start position:0% +about what that's saying + + + align:start position:0% +about what that's saying +1.49 says that the covariance between + + align:start position:0% +1.49 says that the covariance between + + + align:start position:0% +1.49 says that the covariance between +Microsoft and the market + + align:start position:0% +Microsoft and the market + + + align:start position:0% +Microsoft and the market +portfolio is actually a lot + + align:start position:0% +portfolio is actually a lot + + + align:start position:0% +portfolio is actually a lot +higher than the variance of the market + + align:start position:0% +higher than the variance of the market + + + align:start position:0% +higher than the variance of the market +itself so let me ask you to think about + + align:start position:0% +itself so let me ask you to think about + + + align:start position:0% +itself so let me ask you to think about +whether or not adding Microsoft to your + + align:start position:0% +whether or not adding Microsoft to your + + + align:start position:0% +whether or not adding Microsoft to your +portfolio is going to make it less risky + + align:start position:0% +portfolio is going to make it less risky + + + align:start position:0% +portfolio is going to make it less risky +or more more risky and and here's how I + + align:start position:0% +or more more risky and and here's how I + + + align:start position:0% +or more more risky and and here's how I +want you to think about it remember what + + align:start position:0% +want you to think about it remember what + + + align:start position:0% +want you to think about it remember what +we said about diversification when you + + align:start position:0% +we said about diversification when you + + + align:start position:0% +we said about diversification when you +hold a collection of Securities what + + align:start position:0% +hold a collection of Securities what + + + align:start position:0% +hold a collection of Securities what +matters more the variances or the + + align:start position:0% +matters more the variances or the + + + align:start position:0% +matters more the variances or the +co-variances + + align:start position:0% +co-variances + + + align:start position:0% +co-variances +right why is the co-variances more + + align:start position:0% + + + + align:start position:0% + +important what's a quick and dirty way + + align:start position:0% +important what's a quick and dirty way + + + align:start position:0% +important what's a quick and dirty way +of arguing that the co-variances matter + + align:start position:0% +of arguing that the co-variances matter + + + align:start position:0% +of arguing that the co-variances matter +more yeah + + align:start position:0% +more yeah + + + align:start position:0% +more yeah +word exactly there are heck of a lot + + align:start position:0% +word exactly there are heck of a lot + + + align:start position:0% +word exactly there are heck of a lot +more covariances than there are + + align:start position:0% +more covariances than there are + + + align:start position:0% +more covariances than there are +variances you got n variances to worry + + align:start position:0% +variances you got n variances to worry + + + align:start position:0% +variances you got n variances to worry +about but you got n^2 minus n + + align:start position:0% +about but you got n^2 minus n + + + align:start position:0% +about but you got n^2 minus n +co-variances and if they all line up in + + align:start position:0% +co-variances and if they all line up in + + + align:start position:0% +co-variances and if they all line up in +the same + + align:start position:0% +the same + + + align:start position:0% +the same +direction you get the subprime crisis + + align:start position:0% +direction you get the subprime crisis + + + align:start position:0% +direction you get the subprime crisis +problem right okay so co-variances + + align:start position:0% +problem right okay so co-variances + + + align:start position:0% +problem right okay so co-variances +matter more than variances well if + + align:start position:0% +matter more than variances well if + + + align:start position:0% +matter more than variances well if +that's the case then when we look at a + + align:start position:0% +that's the case then when we look at a + + + align:start position:0% +that's the case then when we look at a +stock and think about bringing it into + + align:start position:0% +stock and think about bringing it into + + + align:start position:0% +stock and think about bringing it into +our portfolio we want to ask the + + align:start position:0% +our portfolio we want to ask the + + + align:start position:0% +our portfolio we want to ask the +question what is it doing in terms of + + align:start position:0% +question what is it doing in terms of + + + align:start position:0% +question what is it doing in terms of +adding or subtracting covariances to our + + align:start position:0% +adding or subtracting covariances to our + + + align:start position:0% +adding or subtracting covariances to our +portfolio and one way to measure whether + + align:start position:0% +portfolio and one way to measure whether + + + align:start position:0% +portfolio and one way to measure whether +or not it's adding or subtracting is to + + align:start position:0% +or not it's adding or subtracting is to + + + align:start position:0% +or not it's adding or subtracting is to +ask the question what is the covariance + + align:start position:0% +ask the question what is the covariance + + + align:start position:0% +ask the question what is the covariance +between Microsoft and my my stockh + + align:start position:0% +between Microsoft and my my stockh + + + align:start position:0% +between Microsoft and my my stockh +Holdings now what are your stock + + align:start position:0% +Holdings now what are your stock + + + align:start position:0% +Holdings now what are your stock +Holdings if everybody is a rational + + align:start position:0% +Holdings if everybody is a rational + + + align:start position:0% +Holdings if everybody is a rational +investor by rational I mean you like + + align:start position:0% +investor by rational I mean you like + + + align:start position:0% +investor by rational I mean you like +return and you don't like Risk then you + + align:start position:0% +return and you don't like Risk then you + + + align:start position:0% +return and you don't like Risk then you +know you're going to be holding the + + align:start position:0% +know you're going to be holding the + + + align:start position:0% +know you're going to be holding the +risk-free rate and the market portfolio + + align:start position:0% +risk-free rate and the market portfolio + + + align:start position:0% +risk-free rate and the market portfolio +you're going to be on that c Capital + + align:start position:0% +you're going to be on that c Capital + + + align:start position:0% +you're going to be on that c Capital +Market line right so if you're a + + align:start position:0% +Market line right so if you're a + + + align:start position:0% +Market line right so if you're a +rational investor the only stock holding + + align:start position:0% +rational investor the only stock holding + + + align:start position:0% +rational investor the only stock holding +you have is that mutual fund M the + + align:start position:0% +you have is that mutual fund M the + + + align:start position:0% +you have is that mutual fund M the +tangency portfolio so therefore the most + + align:start position:0% +tangency portfolio so therefore the most + + + align:start position:0% +tangency portfolio so therefore the most +important thing in your mind is when you + + align:start position:0% +important thing in your mind is when you + + + align:start position:0% +important thing in your mind is when you +think about buying a new stock and + + align:start position:0% +think about buying a new stock and + + + align:start position:0% +think about buying a new stock and +putting into your portfolio is this + + align:start position:0% +putting into your portfolio is this + + + align:start position:0% +putting into your portfolio is this +going to be highly correlated with my + + align:start position:0% +going to be highly correlated with my + + + align:start position:0% +going to be highly correlated with my +market + + align:start position:0% +market + + + align:start position:0% +market +portfolio well that's what beta measures + + align:start position:0% +portfolio well that's what beta measures + + + align:start position:0% +portfolio well that's what beta measures +beta is a relative measure that says + + align:start position:0% +beta is a relative measure that says + + + align:start position:0% +beta is a relative measure that says +okay the total variance that you're + + align:start position:0% +okay the total variance that you're + + + align:start position:0% +okay the total variance that you're +holding in Risky Securities that's Sigma + + align:start position:0% +holding in Risky Securities that's Sigma + + + align:start position:0% +holding in Risky Securities that's Sigma +m s that's the variance of the market + + align:start position:0% +m s that's the variance of the market + + + align:start position:0% +m s that's the variance of the market +portfolio how does Microsoft + + align:start position:0% +portfolio how does Microsoft + + + align:start position:0% +portfolio how does Microsoft +compare to that in terms of what it will + + align:start position:0% +compare to that in terms of what it will + + + align:start position:0% +compare to that in terms of what it will +contribute in terms of its covariance + + align:start position:0% +contribute in terms of its covariance + + + align:start position:0% +contribute in terms of its covariance +with your holding so you're holding one + + align:start position:0% +with your holding so you're holding one + + + align:start position:0% +with your holding so you're holding one +mutual fund and you're thinking about + + align:start position:0% +mutual fund and you're thinking about + + + align:start position:0% +mutual fund and you're thinking about +adding Microsoft the only co-variance + + align:start position:0% +adding Microsoft the only co-variance + + + align:start position:0% +adding Microsoft the only co-variance +that you should care about is the + + align:start position:0% +that you should care about is the + + + align:start position:0% +that you should care about is the +co-variance between Microsoft and what + + align:start position:0% +co-variance between Microsoft and what + + + align:start position:0% +co-variance between Microsoft and what +you're + + align:start position:0% +you're + + + align:start position:0% +you're +holding well that's what beta measures + + align:start position:0% +holding well that's what beta measures + + + align:start position:0% +holding well that's what beta measures +if the number is greater than one what + + align:start position:0% +if the number is greater than one what + + + align:start position:0% +if the number is greater than one what +it's saying is is that when you bring + + align:start position:0% +it's saying is is that when you bring + + + align:start position:0% +it's saying is is that when you bring +Microsoft into your portfolio you're + + align:start position:0% +Microsoft into your portfolio you're + + + align:start position:0% +Microsoft into your portfolio you're +going to be increasing the variance + + align:start position:0% +going to be increasing the variance + + + align:start position:0% +going to be increasing the variance +because the co-variance which is what we + + align:start position:0% +because the co-variance which is what we + + + align:start position:0% +because the co-variance which is what we +care about is greater than the variance + + align:start position:0% +care about is greater than the variance + + + align:start position:0% +care about is greater than the variance +of what you're + + align:start position:0% +of what you're + + + align:start position:0% +of what you're +holding if on the other hand the beta is + + align:start position:0% +holding if on the other hand the beta is + + + align:start position:0% +holding if on the other hand the beta is +less than one then presumably that's + + align:start position:0% +less than one then presumably that's + + + align:start position:0% +less than one then presumably that's +helping you because that's lowering the + + align:start position:0% +helping you because that's lowering the + + + align:start position:0% +helping you because that's lowering the +variance relative to what you're holding + + align:start position:0% +variance relative to what you're holding + + + align:start position:0% +variance relative to what you're holding +but helping or hurting that only uh can + + align:start position:0% +but helping or hurting that only uh can + + + align:start position:0% +but helping or hurting that only uh can +be answered Direct directly if you + + align:start position:0% +be answered Direct directly if you + + + align:start position:0% +be answered Direct directly if you +explain what you're getting in terms of + + align:start position:0% +explain what you're getting in terms of + + + align:start position:0% +explain what you're getting in terms of +the expected rate of return so looking + + align:start position:0% +the expected rate of return so looking + + + align:start position:0% +the expected rate of return so looking +at beta by itself is not enough beta is + + align:start position:0% +at beta by itself is not enough beta is + + + align:start position:0% +at beta by itself is not enough beta is +a measure of risk right it measures this + + align:start position:0% +a measure of risk right it measures this + + + align:start position:0% +a measure of risk right it measures this +covariance divided by the variance or + + align:start position:0% +covariance divided by the variance or + + + align:start position:0% +covariance divided by the variance or +covariance per unit variance in the + + align:start position:0% +covariance per unit variance in the + + + align:start position:0% +covariance per unit variance in the +marketplace but you want to know what + + align:start position:0% +marketplace but you want to know what + + + align:start position:0% +marketplace but you want to know what +the expected rate of return is as well + + align:start position:0% +the expected rate of return is as well + + + align:start position:0% +the expected rate of return is as well +that's what the security Market line + + align:start position:0% +that's what the security Market line + + + align:start position:0% +that's what the security Market line +gives you okay so now let's get back to + + align:start position:0% +gives you okay so now let's get back to + + + align:start position:0% +gives you okay so now let's get back to +the example Microsoft is a lot more + + align:start position:0% +the example Microsoft is a lot more + + + align:start position:0% +the example Microsoft is a lot more +risky than the market it's about 49% + + align:start position:0% +risky than the market it's about 49% + + + align:start position:0% +risky than the market it's about 49% +more risky according to this measure on + + align:start position:0% +more risky according to this measure on + + + align:start position:0% +more risky according to this measure on +the other hand Gillette is actually less + + align:start position:0% +the other hand Gillette is actually less + + + align:start position:0% +the other hand Gillette is actually less +risky than the + + align:start position:0% +risky than the + + + align:start position:0% +risky than the +market now do you guys buy that does + + align:start position:0% +market now do you guys buy that does + + + align:start position:0% +market now do you guys buy that does +that does that pass the smell test does + + align:start position:0% +that does that pass the smell test does + + + align:start position:0% +that does that pass the smell test does +that make sense why what's what's what's + + align:start position:0% +that make sense why what's what's what's + + + align:start position:0% +that make sense why what's what's what's +the intuition for + + align:start position:0% +the intuition for + + + align:start position:0% +the intuition for +that Courtney well people don't + + align:start position:0% +that Courtney well people don't + + + align:start position:0% +that Courtney well people don't +necessarily need computers and the + + align:start position:0% +necessarily need computers and the + + + align:start position:0% +necessarily need computers and the +technology is variable but Gillette + + align:start position:0% +technology is variable but Gillette + + + align:start position:0% +technology is variable but Gillette +sells razor products and deodorant which + + align:start position:0% +sells razor products and deodorant which + + + align:start position:0% +sells razor products and deodorant which +is kind of a staple in a lot of people + + align:start position:0% +is kind of a staple in a lot of people + + + align:start position:0% +is kind of a staple in a lot of people +exactly that's right if you make the + + align:start position:0% +exactly that's right if you make the + + + align:start position:0% +exactly that's right if you make the +argument that from 1990 to + + align:start position:0% +argument that from 1990 to + + + align:start position:0% +argument that from 1990 to +2001 if there are economic downturns + + align:start position:0% +2001 if there are economic downturns + + + align:start position:0% +2001 if there are economic downturns +what's the first to go razor blades or + + align:start position:0% +what's the first to go razor blades or + + + align:start position:0% +what's the first to go razor blades or +Windows thankfully Windows uh nowadays I + + align:start position:0% +Windows thankfully Windows uh nowadays I + + + align:start position:0% +Windows thankfully Windows uh nowadays I +don't know the answer to that actually + + align:start position:0% +don't know the answer to that actually + + + align:start position:0% +don't know the answer to that actually +you know because nowadays we depend so + + align:start position:0% +you know because nowadays we depend so + + + align:start position:0% +you know because nowadays we depend so +much on the internet that actually it + + align:start position:0% +much on the internet that actually it + + + align:start position:0% +much on the internet that actually it +could be different so I haven't updated + + align:start position:0% +could be different so I haven't updated + + + align:start position:0% +could be different so I haven't updated +this analysis to see what the beta is + + align:start position:0% +this analysis to see what the beta is + + + align:start position:0% +this analysis to see what the beta is +from 2001 to 2008 but it could be + + align:start position:0% +from 2001 to 2008 but it could be + + + align:start position:0% +from 2001 to 2008 but it could be +different uh so now we may have unshaven + + align:start position:0% +different uh so now we may have unshaven + + + align:start position:0% +different uh so now we may have unshaven +Geeks that uh you know during downturns + + align:start position:0% +Geeks that uh you know during downturns + + + align:start position:0% +Geeks that uh you know during downturns +and uh maybe it's flipped around + + align:start position:0% +and uh maybe it's flipped around + + + align:start position:0% +and uh maybe it's flipped around +Edward could you give us an intuition + + align:start position:0% +Edward could you give us an intuition + + + align:start position:0% +Edward could you give us an intuition +because beta allows us to compute the + + align:start position:0% +because beta allows us to compute the + + + align:start position:0% +because beta allows us to compute the +appropriate for certain risk yes but + + align:start position:0% +appropriate for certain risk yes but + + + align:start position:0% +appropriate for certain risk yes but +what is the intuition of how far away am + + align:start position:0% +what is the intuition of how far away am + + + align:start position:0% +what is the intuition of how far away am +I from the efficient + + align:start position:0% +I from the efficient + + + align:start position:0% +I from the efficient +portfolio + + align:start position:0% +portfolio + + + align:start position:0% +portfolio +so how how how bad is this portfolio + + align:start position:0% +so how how how bad is this portfolio + + + align:start position:0% +so how how how bad is this portfolio +compared to the efficient one yeah so uh + + align:start position:0% +compared to the efficient one yeah so uh + + + align:start position:0% +compared to the efficient one yeah so uh +that's a good question let me go back to + + align:start position:0% +that's a good question let me go back to + + + align:start position:0% +that's a good question let me go back to +this equation and take a look at it and + + align:start position:0% +this equation and take a look at it and + + + align:start position:0% +this equation and take a look at it and +try to provide even more intuition for + + align:start position:0% +try to provide even more intuition for + + + align:start position:0% +try to provide even more intuition for +this before we go on so the idea behind + + align:start position:0% +this before we go on so the idea behind + + + align:start position:0% +this before we go on so the idea behind +this equation is that it tells you that + + align:start position:0% +this equation is that it tells you that + + + align:start position:0% +this equation is that it tells you that +this is the rate of return that you + + align:start position:0% +this is the rate of return that you + + + align:start position:0% +this is the rate of return that you +should have if you have a certain + + align:start position:0% +should have if you have a certain + + + align:start position:0% +should have if you have a certain +beta now you can actually measure the + + align:start position:0% +beta now you can actually measure the + + + align:start position:0% +beta now you can actually measure the +deviation from that very simply by + + align:start position:0% +deviation from that very simply by + + + align:start position:0% +deviation from that very simply by +asking the question for a portfolio + + align:start position:0% +asking the question for a portfolio + + + align:start position:0% +asking the question for a portfolio +manager or an investment project that + + align:start position:0% +manager or an investment project that + + + align:start position:0% +manager or an investment project that +yields an expected rate of return that's + + align:start position:0% +yields an expected rate of return that's + + + align:start position:0% +yields an expected rate of return that's +different from this + + align:start position:0% +different from this + + + align:start position:0% +different from this +that difference is actually what we call + + align:start position:0% +that difference is actually what we call + + + align:start position:0% +that difference is actually what we call +Alpha and Alpha could be positive or + + align:start position:0% +Alpha and Alpha could be positive or + + + align:start position:0% +Alpha and Alpha could be positive or +negative so when you say how far away + + align:start position:0% +negative so when you say how far away + + + align:start position:0% +negative so when you say how far away +are you from efficiency this gives you a + + align:start position:0% +are you from efficiency this gives you a + + + align:start position:0% +are you from efficiency this gives you a +direct measure of how far away you are + + align:start position:0% +direct measure of how far away you are + + + align:start position:0% +direct measure of how far away you are +it's basically the difference between + + align:start position:0% +it's basically the difference between + + + align:start position:0% +it's basically the difference between +the expected rate of return you have + + align:start position:0% +the expected rate of return you have + + + align:start position:0% +the expected rate of return you have +versus what you're supposed to have + + align:start position:0% +versus what you're supposed to have + + + align:start position:0% +versus what you're supposed to have +given the beta of the security but let + + align:start position:0% +given the beta of the security but let + + + align:start position:0% +given the beta of the security but let +me add one more thing to that which is + + align:start position:0% +me add one more thing to that which is + + + align:start position:0% +me add one more thing to that which is +that beta is a measure of a particular + + align:start position:0% +that beta is a measure of a particular + + + align:start position:0% +that beta is a measure of a particular +kind of risk that uh a particular + + align:start position:0% +kind of risk that uh a particular + + + align:start position:0% +kind of risk that uh a particular +security has and the kind of risk as I + + align:start position:0% +security has and the kind of risk as I + + + align:start position:0% +security has and the kind of risk as I +said before is this co-variance between + + align:start position:0% +said before is this co-variance between + + + align:start position:0% +said before is this co-variance between +the rate of return on a particular asset + + align:start position:0% +the rate of return on a particular asset + + + align:start position:0% +the rate of return on a particular asset +uh and the rate of return on the market + + align:start position:0% +uh and the rate of return on the market + + + align:start position:0% +uh and the rate of return on the market +portfolio this kind of risk is not the + + align:start position:0% +portfolio this kind of risk is not the + + + align:start position:0% +portfolio this kind of risk is not the +total risk of a particular Security in + + align:start position:0% +total risk of a particular Security in + + + align:start position:0% +total risk of a particular Security in +fact it is called the systematic risk + + align:start position:0% +fact it is called the systematic risk + + + align:start position:0% +fact it is called the systematic risk +the systematic risk is the portion of + + align:start position:0% +the systematic risk is the portion of + + + align:start position:0% +the systematic risk is the portion of +the risk that is related to the market + + align:start position:0% +the risk that is related to the market + + + align:start position:0% +the risk that is related to the market +portfolio so how far away you are from + + align:start position:0% +portfolio so how far away you are from + + + align:start position:0% +portfolio so how far away you are from +efficiency really depends upon how much + + align:start position:0% +efficiency really depends upon how much + + + align:start position:0% +efficiency really depends upon how much +risk you have that is not necessarily + + align:start position:0% +risk you have that is not necessarily + + + align:start position:0% +risk you have that is not necessarily +systematic risk now you I don't expect + + align:start position:0% +systematic risk now you I don't expect + + + align:start position:0% +systematic risk now you I don't expect +you to understand all of it yet because + + align:start position:0% +you to understand all of it yet because + + + align:start position:0% +you to understand all of it yet because +I need to develop a little bit more + + align:start position:0% +I need to develop a little bit more + + + align:start position:0% +I need to develop a little bit more +Machinery but I'm going to get back to + + align:start position:0% +Machinery but I'm going to get back to + + + align:start position:0% +Machinery but I'm going to get back to +that intuition in just a few minutes + + align:start position:0% +that intuition in just a few minutes + + + align:start position:0% +that intuition in just a few minutes +okay so I'm going to give you a better + + align:start position:0% +okay so I'm going to give you a better + + + align:start position:0% +okay so I'm going to give you a better +answer to your question than what I just + + align:start position:0% +answer to your question than what I just + + + align:start position:0% +answer to your question than what I just +did because I'll explain the difference + + align:start position:0% +did because I'll explain the difference + + + align:start position:0% +did because I'll explain the difference +between systematic risk and + + align:start position:0% +between systematic risk and + + + align:start position:0% +between systematic risk and +idiosyncratic risk and I think then + + align:start position:0% +idiosyncratic risk and I think then + + + align:start position:0% +idiosyncratic risk and I think then +it'll make this completely transparent + + align:start position:0% +it'll make this completely transparent + + + align:start position:0% +it'll make this completely transparent +so give me another 15 minutes yeah so + + align:start position:0% +so give me another 15 minutes yeah so + + + align:start position:0% +so give me another 15 minutes yeah so +you mentioned that gold stocks can + + align:start position:0% +you mentioned that gold stocks can + + + align:start position:0% +you mentioned that gold stocks can +reduce the I mean they may have + + align:start position:0% +reduce the I mean they may have + + + align:start position:0% +reduce the I mean they may have +historically it has yeah so uh there are + + align:start position:0% +historically it has yeah so uh there are + + + align:start position:0% +historically it has yeah so uh there are +some currencies that are uh indexed to + + align:start position:0% +some currencies that are uh indexed to + + + align:start position:0% +some currencies that are uh indexed to +gold prices yes so let's say you're a + + align:start position:0% +gold prices yes so let's say you're a + + + align:start position:0% +gold prices yes so let's say you're a +company X if you are listed in the Dow + + align:start position:0% +company X if you are listed in the Dow + + + align:start position:0% +company X if you are listed in the Dow +Jones versus this uh country which whose + + align:start position:0% +Jones versus this uh country which whose + + + align:start position:0% +Jones versus this uh country which whose +currency is indexed to Gold y do you + + align:start position:0% +currency is indexed to Gold y do you + + + align:start position:0% +currency is indexed to Gold y do you +expect the company that's listed in the + + align:start position:0% +expect the company that's listed in the + + + align:start position:0% +expect the company that's listed in the +gold index currency to have a lower beta + + align:start position:0% +gold index currency to have a lower beta + + + align:start position:0% +gold index currency to have a lower beta +uh well it could but on the other hand + + align:start position:0% +uh well it could but on the other hand + + + align:start position:0% +uh well it could but on the other hand +the question is you know what what are + + align:start position:0% +the question is you know what what are + + + align:start position:0% +the question is you know what what are +they doing to try to hedge that currency + + align:start position:0% +they doing to try to hedge that currency + + + align:start position:0% +they doing to try to hedge that currency +exposure in other words if they end up + + align:start position:0% +exposure in other words if they end up + + + align:start position:0% +exposure in other words if they end up +hedging all of that exposure then it + + align:start position:0% +hedging all of that exposure then it + + + align:start position:0% +hedging all of that exposure then it +doesn't matter anymore right so so it + + align:start position:0% +doesn't matter anymore right so so it + + + align:start position:0% +doesn't matter anymore right so so it +depends but the idea is that if it it + + align:start position:0% +depends but the idea is that if it it + + + align:start position:0% +depends but the idea is that if it it +has exposure to a zero beta asset then + + align:start position:0% +has exposure to a zero beta asset then + + + align:start position:0% +has exposure to a zero beta asset then +you will find that the ultimate + + align:start position:0% +you will find that the ultimate + + + align:start position:0% +you will find that the ultimate +fluctuations are going to have less + + align:start position:0% +fluctuations are going to have less + + + align:start position:0% +fluctuations are going to have less +correlation to the market portfolio Slow + + align:start position:0% +correlation to the market portfolio Slow + + + align:start position:0% +correlation to the market portfolio Slow +Me Maybe Microsoft has a bigger beta + + align:start position:0% +Me Maybe Microsoft has a bigger beta + + + align:start position:0% +Me Maybe Microsoft has a bigger beta +because during this period 10 years yeah + + align:start position:0% +because during this period 10 years yeah + + + align:start position:0% +because during this period 10 years yeah +Microsoft is a yeah and more return yeah + + align:start position:0% +Microsoft is a yeah and more return yeah + + + align:start position:0% +Microsoft is a yeah and more return yeah +this is the + + align:start position:0% +this is the + + + align:start position:0% +this is the +reason you know that's possible but + + align:start position:0% +reason you know that's possible but + + + align:start position:0% +reason you know that's possible but +remember that when we estimate the beta + + align:start position:0% +remember that when we estimate the beta + + + align:start position:0% +remember that when we estimate the beta +we're estimating it using monthly + + align:start position:0% +we're estimating it using monthly + + + align:start position:0% +we're estimating it using monthly +returns and so we're measuring the + + align:start position:0% +returns and so we're measuring the + + + align:start position:0% +returns and so we're measuring the +co-variance on a month-to-month basis + + align:start position:0% +co-variance on a month-to-month basis + + + align:start position:0% +co-variance on a month-to-month basis +not just the trend we're me measuring + + align:start position:0% +not just the trend we're me measuring + + + align:start position:0% +not just the trend we're me measuring +fluctuations around that Trend so the + + align:start position:0% +fluctuations around that Trend so the + + + align:start position:0% +fluctuations around that Trend so the +trend alone won't necessarily explain + + align:start position:0% +trend alone won't necessarily explain + + + align:start position:0% +trend alone won't necessarily explain +all of it it has to also be the + + align:start position:0% +all of it it has to also be the + + + align:start position:0% +all of it it has to also be the +fluctuations are actually going both up + + align:start position:0% +fluctuations are actually going both up + + + align:start position:0% +fluctuations are actually going both up +and down you know higher than the + + align:start position:0% +and down you know higher than the + + + align:start position:0% +and down you know higher than the +variability of the market portfolio all + + align:start position:0% +variability of the market portfolio all + + + align:start position:0% +variability of the market portfolio all +right let me continue on with the + + align:start position:0% +right let me continue on with the + + + align:start position:0% +right let me continue on with the +example and we're going to come back I'm + + align:start position:0% +example and we're going to come back I'm + + + align:start position:0% +example and we're going to come back I'm +going to show you how to estimate this + + align:start position:0% +going to show you how to estimate this + + + align:start position:0% +going to show you how to estimate this +and then you'll develop more intuition + + align:start position:0% +and then you'll develop more intuition + + + align:start position:0% +and then you'll develop more intuition +from it so you know this makes sense + + align:start position:0% +from it so you know this makes sense + + + align:start position:0% +from it so you know this makes sense +from the smell test in the sense that + + align:start position:0% +from the smell test in the sense that + + + align:start position:0% +from the smell test in the sense that +Microsoft at least during that period of + + align:start position:0% +Microsoft at least during that period of + + + align:start position:0% +Microsoft at least during that period of +time was not necessarily something that + + align:start position:0% +time was not necessarily something that + + + align:start position:0% +time was not necessarily something that +you would expect would do well in good + + align:start position:0% +you would expect would do well in good + + + align:start position:0% +you would expect would do well in good +times and bad but something like razor + + align:start position:0% +times and bad but something like razor + + + align:start position:0% +times and bad but something like razor +blades uh and shaving cream we need to + + align:start position:0% +blades uh and shaving cream we need to + + + align:start position:0% +blades uh and shaving cream we need to +use regardless so that that's sort of + + align:start position:0% +use regardless so that that's sort of + + + align:start position:0% +use regardless so that that's sort of +tells us that these betas look about + + align:start position:0% +tells us that these betas look about + + + align:start position:0% +tells us that these betas look about +right okay if you agree with the betas + + align:start position:0% +right okay if you agree with the betas + + + align:start position:0% +right okay if you agree with the betas +then it turns out that we can actually + + align:start position:0% +then it turns out that we can actually + + + align:start position:0% +then it turns out that we can actually +calculate the required rate of return + + align:start position:0% +calculate the required rate of return + + + align:start position:0% +calculate the required rate of return +for each of these two stocks so if you + + align:start position:0% +for each of these two stocks so if you + + + align:start position:0% +for each of these two stocks so if you +assume that the risk free rate is 5% + + align:start position:0% +assume that the risk free rate is 5% + + + align:start position:0% +assume that the risk free rate is 5% +which is what it was about in that + + align:start position:0% +which is what it was about in that + + + align:start position:0% +which is what it was about in that +period right not not today obviously but + + align:start position:0% +period right not not today obviously but + + + align:start position:0% +period right not not today obviously but +back in that period was about 5% and if + + align:start position:0% +back in that period was about 5% and if + + + align:start position:0% +back in that period was about 5% and if +historically the risk premium as I told + + align:start position:0% +historically the risk premium as I told + + + align:start position:0% +historically the risk premium as I told +you last time is about 6% then when you + + align:start position:0% +you last time is about 6% then when you + + + align:start position:0% +you last time is about 6% then when you +do the calculations us the security + + align:start position:0% +do the calculations us the security + + + align:start position:0% +do the calculations us the security +Market line you get a very sharp answer + + align:start position:0% +Market line you get a very sharp answer + + + align:start position:0% +Market line you get a very sharp answer +to the question what are the appropriate + + align:start position:0% +to the question what are the appropriate + + + align:start position:0% +to the question what are the appropriate +discount rates or cost of capital for + + align:start position:0% +discount rates or cost of capital for + + + align:start position:0% +discount rates or cost of capital for +these two companies the answer for + + align:start position:0% +these two companies the answer for + + + align:start position:0% +these two companies the answer for +Gillette it's about + + align:start position:0% +Gillette it's about + + + align:start position:0% +Gillette it's about +99.86% for Microsoft 13.94% + + align:start position:0% +99.86% for Microsoft 13.94% + + + align:start position:0% +99.86% for Microsoft 13.94% +so now if you're sitting in these in + + align:start position:0% +so now if you're sitting in these in + + + align:start position:0% +so now if you're sitting in these in +these companies and you're asking the + + align:start position:0% +these companies and you're asking the + + + align:start position:0% +these companies and you're asking the +question we're going to expand our + + align:start position:0% +question we're going to expand our + + + align:start position:0% +question we're going to expand our +operations but in order to do that we + + align:start position:0% +operations but in order to do that we + + + align:start position:0% +operations but in order to do that we +have to do an npv calculation to see + + align:start position:0% +have to do an npv calculation to see + + + align:start position:0% +have to do an npv calculation to see +whether it's worthwhile we have to + + align:start position:0% +whether it's worthwhile we have to + + + align:start position:0% +whether it's worthwhile we have to +compute the expected net present value + + align:start position:0% +compute the expected net present value + + + align:start position:0% +compute the expected net present value +of expansion and in order to do that + + align:start position:0% +of expansion and in order to do that + + + align:start position:0% +of expansion and in order to do that +we've got estimates of what our cash + + align:start position:0% +we've got estimates of what our cash + + + align:start position:0% +we've got estimates of what our cash +flows are going to be for our expansion + + align:start position:0% +flows are going to be for our expansion + + + align:start position:0% +flows are going to be for our expansion +but we don't know what the cost of + + align:start position:0% +but we don't know what the cost of + + + align:start position:0% +but we don't know what the cost of +capital is well here's the answer for + + align:start position:0% +capital is well here's the answer for + + + align:start position:0% +capital is well here's the answer for +you you've actually got hard numbers to + + align:start position:0% +you you've actually got hard numbers to + + + align:start position:0% +you you've actually got hard numbers to +plug in to your npv calculations + + align:start position:0% +plug in to your npv calculations + + + align:start position:0% +plug in to your npv calculations +now now there are a bunch of assumptions + + align:start position:0% +now now there are a bunch of assumptions + + + align:start position:0% +now now there are a bunch of assumptions +that we've made so we're going to have + + align:start position:0% +that we've made so we're going to have + + + align:start position:0% +that we've made so we're going to have +to go back and justify those assumptions + + align:start position:0% +to go back and justify those assumptions + + + align:start position:0% +to go back and justify those assumptions +each and every time you use this + + align:start position:0% +each and every time you use this + + + align:start position:0% +each and every time you use this +technology it's not it's not physics + + align:start position:0% +technology it's not it's not physics + + + align:start position:0% +technology it's not it's not physics +this is not mathema matics you're + + align:start position:0% +this is not mathema matics you're + + + align:start position:0% +this is not mathema matics you're +applying a set of theories and + + align:start position:0% +applying a set of theories and + + + align:start position:0% +applying a set of theories and +approximations to a much much more + + align:start position:0% +approximations to a much much more + + + align:start position:0% +approximations to a much much more +complex reality every time you apply it + + align:start position:0% +complex reality every time you apply it + + + align:start position:0% +complex reality every time you apply it +you got to go back and ask the question + + align:start position:0% +you got to go back and ask the question + + + align:start position:0% +you got to go back and ask the question +does it make sense do these assumptions + + align:start position:0% +does it make sense do these assumptions + + + align:start position:0% +does it make sense do these assumptions +hold and if so great go ahead and use it + + align:start position:0% +hold and if so great go ahead and use it + + + align:start position:0% +hold and if so great go ahead and use it +if not you've got to go back and + + align:start position:0% +if not you've got to go back and + + + align:start position:0% +if not you've got to go back and +rederive some of these + + align:start position:0% +rederive some of these + + + align:start position:0% +rederive some of these +analytics okay so the security Market + + align:start position:0% +analytics okay so the security Market + + + align:start position:0% +analytics okay so the security Market +Line is now a line that describes the + + align:start position:0% +Line is now a line that describes the + + + align:start position:0% +Line is now a line that describes the +expected return or required rate of + + align:start position:0% +expected return or required rate of + + + align:start position:0% +expected return or required rate of +return on an asset or a project as a + + align:start position:0% +return on an asset or a project as a + + + align:start position:0% +return on an asset or a project as a +function of the riskiness where the + + align:start position:0% +function of the riskiness where the + + + align:start position:0% +function of the riskiness where the +riskiness is now measured by Beta not by + + align:start position:0% +riskiness is now measured by Beta not by + + + align:start position:0% +riskiness is now measured by Beta not by +Sigma it's not variance or standard + + align:start position:0% +Sigma it's not variance or standard + + + align:start position:0% +Sigma it's not variance or standard +deviation that measures the appropriate + + align:start position:0% +deviation that measures the appropriate + + + align:start position:0% +deviation that measures the appropriate +risk for most + + align:start position:0% +risk for most + + + align:start position:0% +risk for most +projects most projects the way you + + align:start position:0% +projects most projects the way you + + + align:start position:0% +projects most projects the way you +measure their risk is not by + + align:start position:0% +measure their risk is not by + + + align:start position:0% +measure their risk is not by +Sigma it turns out that the way you + + align:start position:0% +Sigma it turns out that the way you + + + align:start position:0% +Sigma it turns out that the way you +measure their risk for the purposes of + + align:start position:0% +measure their risk for the purposes of + + + align:start position:0% +measure their risk for the purposes of +calculating the required rate of return + + align:start position:0% +calculating the required rate of return + + + align:start position:0% +calculating the required rate of return +you measure it by Beta + + align:start position:0% +you measure it by Beta + + + align:start position:0% +you measure it by Beta +okay that's a very deep Insight it + + align:start position:0% +okay that's a very deep Insight it + + + align:start position:0% +okay that's a very deep Insight it +changes the way we think about risk and + + align:start position:0% +changes the way we think about risk and + + + align:start position:0% +changes the way we think about risk and +expected rate of return it's not to say + + align:start position:0% +expected rate of return it's not to say + + + align:start position:0% +expected rate of return it's not to say +that risk in in terms of volatility + + align:start position:0% +that risk in in terms of volatility + + + align:start position:0% +that risk in in terms of volatility +doesn't matter of course it does that is + + align:start position:0% +doesn't matter of course it does that is + + + align:start position:0% +doesn't matter of course it does that is +the basis of this entire framework we + + align:start position:0% +the basis of this entire framework we + + + align:start position:0% +the basis of this entire framework we +started out by saying that people don't + + align:start position:0% +started out by saying that people don't + + + align:start position:0% +started out by saying that people don't +like Sigma and they do like mu right + + align:start position:0% +like Sigma and they do like mu right + + + align:start position:0% +like Sigma and they do like mu right +they don't like variance they do like + + align:start position:0% +they don't like variance they do like + + + align:start position:0% +they don't like variance they do like +expected rate of return that still holds + + align:start position:0% +expected rate of return that still holds + + + align:start position:0% +expected rate of return that still holds +but in doing so when we derive all of + + align:start position:0% +but in doing so when we derive all of + + + align:start position:0% +but in doing so when we derive all of +these implications what we find is that + + align:start position:0% +these implications what we find is that + + + align:start position:0% +these implications what we find is that +as an investor you don't get rewarded + + align:start position:0% +as an investor you don't get rewarded + + + align:start position:0% +as an investor you don't get rewarded +for taking larger and larger amounts of + + align:start position:0% +for taking larger and larger amounts of + + + align:start position:0% +for taking larger and larger amounts of +volatility necessarily you do get + + align:start position:0% +volatility necessarily you do get + + + align:start position:0% +volatility necessarily you do get +rewarded for taking larger and larger + + align:start position:0% +rewarded for taking larger and larger + + + align:start position:0% +rewarded for taking larger and larger +amounts of beta that's the sense in + + align:start position:0% +amounts of beta that's the sense in + + + align:start position:0% +amounts of beta that's the sense in +which beta is a better measure of risk + + align:start position:0% +which beta is a better measure of risk + + + align:start position:0% +which beta is a better measure of risk +for the purposes of computing the + + align:start position:0% +for the purposes of computing the + + + align:start position:0% +for the purposes of computing the +required rate of return beta is the + + align:start position:0% +required rate of return beta is the + + + align:start position:0% +required rate of return beta is the +right measurement not Sigma the only + + align:start position:0% +right measurement not Sigma the only + + + align:start position:0% +right measurement not Sigma the only +cases where Sigma is the right right + + align:start position:0% +cases where Sigma is the right right + + + align:start position:0% +cases where Sigma is the right right +measure of risk when I say right I mean + + align:start position:0% +measure of risk when I say right I mean + + + align:start position:0% +measure of risk when I say right I mean +where increases in Sigma must imply + + align:start position:0% +where increases in Sigma must imply + + + align:start position:0% +where increases in Sigma must imply +increases in the required rate of + + align:start position:0% +increases in the required rate of + + + align:start position:0% +increases in the required rate of +return is + + align:start position:0% +return is + + + align:start position:0% +return is +when when is Sigma the right measure of + + align:start position:0% +when when is Sigma the right measure of + + + align:start position:0% +when when is Sigma the right measure of +risk for the purposes of of computing + + align:start position:0% +risk for the purposes of of computing + + + align:start position:0% +risk for the purposes of of computing +the required rate of + + align:start position:0% +the required rate of + + + align:start position:0% +the required rate of +return for what kind of Securities or + + align:start position:0% + + + + align:start position:0% + +portfolios yeah go is it for efficient + + align:start position:0% +portfolios yeah go is it for efficient + + + align:start position:0% +portfolios yeah go is it for efficient +portfolio exactly for efficient + + align:start position:0% +portfolio exactly for efficient + + + align:start position:0% +portfolio exactly for efficient +portfolios only efficient portfolios + + align:start position:0% +portfolios only efficient portfolios + + + align:start position:0% +portfolios only efficient portfolios +meaning these guys meaning these guys + + align:start position:0% +meaning these guys meaning these guys + + + align:start position:0% +meaning these guys meaning these guys +anything on this line then Sigma is the + + align:start position:0% +anything on this line then Sigma is the + + + align:start position:0% +anything on this line then Sigma is the +right measure right Sigma p over Sigma M + + align:start position:0% +right measure right Sigma p over Sigma M + + + align:start position:0% +right measure right Sigma p over Sigma M +that is the right + + align:start position:0% + + + + align:start position:0% + +measure for any kind of portfolio that + + align:start position:0% +measure for any kind of portfolio that + + + align:start position:0% +measure for any kind of portfolio that +is efficient but we know that the + + align:start position:0% +is efficient but we know that the + + + align:start position:0% +is efficient but we know that the +typical security the typical project the + + align:start position:0% +typical security the typical project the + + + align:start position:0% +typical security the typical project the +typical division is not efficient + + align:start position:0% +typical division is not efficient + + + align:start position:0% +typical division is not efficient +efficient again meaning you can get the + + align:start position:0% +efficient again meaning you can get the + + + align:start position:0% +efficient again meaning you can get the +you can't get any better expected rate + + align:start position:0% +you can't get any better expected rate + + + align:start position:0% +you can't get any better expected rate +of return for the same risk or you can't + + align:start position:0% +of return for the same risk or you can't + + + align:start position:0% +of return for the same risk or you can't +get a lower amount of risk for the same + + align:start position:0% +get a lower amount of risk for the same + + + align:start position:0% +get a lower amount of risk for the same +expected rate of return so for all of + + align:start position:0% +expected rate of return so for all of + + + align:start position:0% +expected rate of return so for all of +the inefficient Securities portfolios or + + align:start position:0% +the inefficient Securities portfolios or + + + align:start position:0% +the inefficient Securities portfolios or +projects you got to use this + + align:start position:0% +projects you got to use this + + + align:start position:0% +projects you got to use this +relationship and this relationship tells + + align:start position:0% +relationship and this relationship tells + + + align:start position:0% +relationship and this relationship tells +you beta is what matters not Sigma Sigma + + align:start position:0% +you beta is what matters not Sigma Sigma + + + align:start position:0% +you beta is what matters not Sigma Sigma +is not the same as beta except if you + + align:start position:0% +is not the same as beta except if you + + + align:start position:0% +is not the same as beta except if you +happen to be an efficient + + align:start position:0% +happen to be an efficient + + + align:start position:0% +happen to be an efficient +portfolio Okay question an do you have a + + align:start position:0% +portfolio Okay question an do you have a + + + align:start position:0% +portfolio Okay question an do you have a +question no okay + + align:start position:0% +question no okay + + + align:start position:0% +question no okay +all right so here's an example of the + + align:start position:0% +all right so here's an example of the + + + align:start position:0% +all right so here's an example of the +security Market line at work and the + + align:start position:0% +security Market line at work and the + + + align:start position:0% +security Market line at work and the +slope of this security Market line is of + + align:start position:0% +slope of this security Market line is of + + + align:start position:0% +slope of this security Market line is of +course the expected rate of return on + + align:start position:0% +course the expected rate of return on + + + align:start position:0% +course the expected rate of return on +the market minus the risk-free rate and + + align:start position:0% +the market minus the risk-free rate and + + + align:start position:0% +the market minus the risk-free rate and +the idea behind the security Market line + + align:start position:0% +the idea behind the security Market line + + + align:start position:0% +the idea behind the security Market line +is that no matter what your beta is + + align:start position:0% +is that no matter what your beta is + + + align:start position:0% +is that no matter what your beta is +you've got a required rate of return + + align:start position:0% +you've got a required rate of return + + + align:start position:0% +you've got a required rate of return +that's determined by the slope and now + + align:start position:0% +that's determined by the slope and now + + + align:start position:0% +that's determined by the slope and now +to answer eduard's question about + + align:start position:0% +to answer eduard's question about + + + align:start position:0% +to answer eduard's question about +deviations and how far away you are from + + align:start position:0% +deviations and how far away you are from + + + align:start position:0% +deviations and how far away you are from +efficiency if you deviate from this line + + align:start position:0% +efficiency if you deviate from this line + + + align:start position:0% +efficiency if you deviate from this line +then the vertical distance is the + + align:start position:0% +then the vertical distance is the + + + align:start position:0% +then the vertical distance is the +alpha of your portfolio or project or + + align:start position:0% +alpha of your portfolio or project or + + + align:start position:0% +alpha of your portfolio or project or +investment + + align:start position:0% +investment + + + align:start position:0% +investment +opportunity if markets are working + + align:start position:0% +opportunity if markets are working + + + align:start position:0% +opportunity if markets are working +exactly the way they should then you're + + align:start position:0% +exactly the way they should then you're + + + align:start position:0% +exactly the way they should then you're +on this line you're always on this line + + align:start position:0% +on this line you're always on this line + + + align:start position:0% +on this line you're always on this line +and if you're Warren Buffett you're off + + align:start position:0% +and if you're Warren Buffett you're off + + + align:start position:0% +and if you're Warren Buffett you're off +of this line you've got a very large + + align:start position:0% +of this line you've got a very large + + + align:start position:0% +of this line you've got a very large +positive Alpha so if you've got skill if + + align:start position:0% +positive Alpha so if you've got skill if + + + align:start position:0% +positive Alpha so if you've got skill if +you can forecast markets then you will + + align:start position:0% +you can forecast markets then you will + + + align:start position:0% +you can forecast markets then you will +do better than this but what this + + align:start position:0% +do better than this but what this + + + align:start position:0% +do better than this but what this +framework tells you is that even if you + + align:start position:0% +framework tells you is that even if you + + + align:start position:0% +framework tells you is that even if you +cannot forecast markets even if you + + align:start position:0% +cannot forecast markets even if you + + + align:start position:0% +cannot forecast markets even if you +don't know what's going to happen next + + align:start position:0% +don't know what's going to happen next + + + align:start position:0% +don't know what's going to happen next +year to stock + + align:start position:0% +year to stock + + + align:start position:0% +year to stock +prices you should still do as well as + + align:start position:0% +prices you should still do as well as + + + align:start position:0% +prices you should still do as well as +what this line suggests that you can do + + align:start position:0% +what this line suggests that you can do + + + align:start position:0% +what this line suggests that you can do +okay on average this line should be + + align:start position:0% +okay on average this line should be + + + align:start position:0% +okay on average this line should be +achievable by everybody that understands + + align:start position:0% +achievable by everybody that understands + + + align:start position:0% +achievable by everybody that understands +the basics of portfolio Theory + + align:start position:0% +the basics of portfolio Theory + + + align:start position:0% +the basics of portfolio Theory +now as I said the performance evaluation + + align:start position:0% +now as I said the performance evaluation + + + align:start position:0% +now as I said the performance evaluation +uh approach to using the security Market + + align:start position:0% +uh approach to using the security Market + + + align:start position:0% +uh approach to using the security Market +line is just to measure the vertical + + align:start position:0% +line is just to measure the vertical + + + align:start position:0% +line is just to measure the vertical +distances and it can lead to some + + align:start position:0% +distances and it can lead to some + + + align:start position:0% +distances and it can lead to some +interesting uh results for example here + + align:start position:0% +interesting uh results for example here + + + align:start position:0% +interesting uh results for example here +are three managers all three of these + + align:start position:0% +are three managers all three of these + + + align:start position:0% +are three managers all three of these +managers have a 15% expected rate of + + align:start position:0% + + + + align:start position:0% + +return but they have different + + align:start position:0% +return but they have different + + + align:start position:0% +return but they have different +betas and so the question is if you had + + align:start position:0% +betas and so the question is if you had + + + align:start position:0% +betas and so the question is if you had +money to put into these managers which + + align:start position:0% +money to put into these managers which + + + align:start position:0% +money to put into these managers which +would you choose well clearly you would + + align:start position:0% +would you choose well clearly you would + + + align:start position:0% +would you choose well clearly you would +choose manager a because the manager is + + align:start position:0% +choose manager a because the manager is + + + align:start position:0% +choose manager a because the manager is +only supposed to have a 6% rate of + + align:start position:0% +only supposed to have a 6% rate of + + + align:start position:0% +only supposed to have a 6% rate of +return but in fact is offering 15 for + + align:start position:0% +return but in fact is offering 15 for + + + align:start position:0% +return but in fact is offering 15 for +that level of risk manager B is just + + align:start position:0% +that level of risk manager B is just + + + align:start position:0% +that level of risk manager B is just +basically doing uh what you would expect + + align:start position:0% +basically doing uh what you would expect + + + align:start position:0% +basically doing uh what you would expect +the manager should be doing and manager + + align:start position:0% +the manager should be doing and manager + + + align:start position:0% +the manager should be doing and manager +C is actually underperforming given the + + align:start position:0% +C is actually underperforming given the + + + align:start position:0% +C is actually underperforming given the +risk that manager C is exposing you to + + align:start position:0% +risk that manager C is exposing you to + + + align:start position:0% +risk that manager C is exposing you to +manager C should be doing much better + + align:start position:0% +manager C should be doing much better + + + align:start position:0% +manager C should be doing much better +than than he + + align:start position:0% +than than he + + + align:start position:0% +than than he +is + + align:start position:0% +is + + + align:start position:0% +is +okay and by the way notice that I've + + align:start position:0% +okay and by the way notice that I've + + + align:start position:0% +okay and by the way notice that I've +said that the same all three managers + + align:start position:0% +said that the same all three managers + + + align:start position:0% +said that the same all three managers +have the same volatility 20% you can + + align:start position:0% +have the same volatility 20% you can + + + align:start position:0% +have the same volatility 20% you can +have the same volatility but have + + align:start position:0% +have the same volatility but have + + + align:start position:0% +have the same volatility but have +different + + align:start position:0% +different + + + align:start position:0% +different +betas betas and volatilities do not + + align:start position:0% +betas betas and volatilities do not + + + align:start position:0% +betas betas and volatilities do not +necessarily go hand inand there is + + align:start position:0% +necessarily go hand inand there is + + + align:start position:0% +necessarily go hand inand there is +actually a relationship between beta and + + align:start position:0% +actually a relationship between beta and + + + align:start position:0% +actually a relationship between beta and +volatility we'll talk about that in a + + align:start position:0% +volatility we'll talk about that in a + + + align:start position:0% +volatility we'll talk about that in a +little while but that relationship is + + align:start position:0% +little while but that relationship is + + + align:start position:0% +little while but that relationship is +not near nearly uh as straightforward as + + align:start position:0% +not near nearly uh as straightforward as + + + align:start position:0% +not near nearly uh as straightforward as +you might think + + align:start position:0% + + + + align:start position:0% + +ingred Can you estimate the future + + align:start position:0% +ingred Can you estimate the future + + + align:start position:0% +ingred Can you estimate the future +return of mut fund byal return Ian I + + align:start position:0% +return of mut fund byal return Ian I + + + align:start position:0% +return of mut fund byal return Ian I +understand it's the best you can do but + + align:start position:0% +understand it's the best you can do but + + + align:start position:0% +understand it's the best you can do but +how really well so it depends on on who + + align:start position:0% +how really well so it depends on on who + + + align:start position:0% +how really well so it depends on on who +you are if you are a typical uh index + + align:start position:0% +you are if you are a typical uh index + + + align:start position:0% +you are if you are a typical uh index +fund manager you would argue that mutual + + align:start position:0% +fund manager you would argue that mutual + + + align:start position:0% +fund manager you would argue that mutual +funds are basically going to provide you + + align:start position:0% +funds are basically going to provide you + + + align:start position:0% +funds are basically going to provide you +with a relatively uh relatively stable + + align:start position:0% +with a relatively uh relatively stable + + + align:start position:0% +with a relatively uh relatively stable +expected rate of return over time so in + + align:start position:0% +expected rate of return over time so in + + + align:start position:0% +expected rate of return over time so in +other words it'll fluctuate up and down + + align:start position:0% +other words it'll fluctuate up and down + + + align:start position:0% +other words it'll fluctuate up and down +because it's got some variance but there + + align:start position:0% +because it's got some variance but there + + + align:start position:0% +because it's got some variance but there +is a baseline expected rate of return + + align:start position:0% +is a baseline expected rate of return + + + align:start position:0% +is a baseline expected rate of return +that a mutual fund offers you and that's + + align:start position:0% +that a mutual fund offers you and that's + + + align:start position:0% +that a mutual fund offers you and that's +what people are buying when you put your + + align:start position:0% +what people are buying when you put your + + + align:start position:0% +what people are buying when you put your +money in an Emerging Market uh Equity + + align:start position:0% +money in an Emerging Market uh Equity + + + align:start position:0% +money in an Emerging Market uh Equity +mutual fund you're going to have a + + align:start position:0% +mutual fund you're going to have a + + + align:start position:0% +mutual fund you're going to have a +higher return on average on average than + + align:start position:0% +higher return on average on average than + + + align:start position:0% +higher return on average on average than +if you put your money in a uh S&P 500 + + align:start position:0% +if you put your money in a uh S&P 500 + + + align:start position:0% +if you put your money in a uh S&P 500 +Index Fund why are you going to have a + + align:start position:0% +Index Fund why are you going to have a + + + align:start position:0% +Index Fund why are you going to have a +higher rate of return return on average + + align:start position:0% +higher rate of return return on average + + + align:start position:0% +higher rate of return return on average +because you're going to be bearing more + + align:start position:0% +because you're going to be bearing more + + + align:start position:0% +because you're going to be bearing more +risk on average the only way to convince + + align:start position:0% +risk on average the only way to convince + + + align:start position:0% +risk on average the only way to convince +you to put your money in an emerging + + align:start position:0% +you to put your money in an emerging + + + align:start position:0% +you to put your money in an emerging +market fund is if it does have that + + align:start position:0% +market fund is if it does have that + + + align:start position:0% +market fund is if it does have that +higher expected rate of return on + + align:start position:0% +higher expected rate of return on + + + align:start position:0% +higher expected rate of return on +average so what you're ba what you're + + align:start position:0% +average so what you're ba what you're + + + align:start position:0% +average so what you're ba what you're +basing these kinds of calculations on is + + align:start position:0% +basing these kinds of calculations on is + + + align:start position:0% +basing these kinds of calculations on is +not that I can forecast what mutual + + align:start position:0% +not that I can forecast what mutual + + + align:start position:0% +not that I can forecast what mutual +funds are going to do next year but + + align:start position:0% +funds are going to do next year but + + + align:start position:0% +funds are going to do next year but +rather mutual funds offer expected rate + + align:start position:0% +rather mutual funds offer expected rate + + + align:start position:0% +rather mutual funds offer expected rate +of returns that are stable over time so + + align:start position:0% +of returns that are stable over time so + + + align:start position:0% +of returns that are stable over time so +what happened last year and the year + + align:start position:0% +what happened last year and the year + + + align:start position:0% +what happened last year and the year +before and the year before that when you + + align:start position:0% +before and the year before that when you + + + align:start position:0% +before and the year before that when you +average it all together it's about what + + align:start position:0% +average it all together it's about what + + + align:start position:0% +average it all together it's about what +you're going to get over the next five + + align:start position:0% +you're going to get over the next five + + + align:start position:0% +you're going to get over the next five +years that's it that's the argument yes + + align:start position:0% +years that's it that's the argument yes + + + align:start position:0% +years that's it that's the argument yes +we don't know right exactly so so there + + align:start position:0% +we don't know right exactly so so there + + + align:start position:0% +we don't know right exactly so so there +is a very large idiosyncratic component + + align:start position:0% +is a very large idiosyncratic component + + + align:start position:0% +is a very large idiosyncratic component +you know that fluctuates year by year + + align:start position:0% +you know that fluctuates year by year + + + align:start position:0% +you know that fluctuates year by year +and who knows what that could + + align:start position:0% +and who knows what that could + + + align:start position:0% +and who knows what that could +be okay yes um last time when you were + + align:start position:0% +be okay yes um last time when you were + + + align:start position:0% +be okay yes um last time when you were +describing more yes you mentioned that + + align:start position:0% +describing more yes you mentioned that + + + align:start position:0% +describing more yes you mentioned that +for more risk + + align:start position:0% +for more risk + + + align:start position:0% +for more risk +um people will expect more return but + + align:start position:0% +um people will expect more return but + + + align:start position:0% +um people will expect more return but +not necessarily proportional to so so + + align:start position:0% +not necessarily proportional to so so + + + align:start position:0% +not necessarily proportional to so so +you end up having a line that just goes + + align:start position:0% +you end up having a line that just goes + + + align:start position:0% +you end up having a line that just goes +up + + align:start position:0% +up + + + align:start position:0% +up +exponentially right because I mean + + align:start position:0% +exponentially right because I mean + + + align:start position:0% +exponentially right because I mean +because you you given analogy that okay + + align:start position:0% +because you you given analogy that okay + + + align:start position:0% +because you you given analogy that okay +in order to get investors to Bear more + + align:start position:0% +in order to get investors to Bear more + + + align:start position:0% +in order to get investors to Bear more +risk to take on more risk you have to + + align:start position:0% +risk to take on more risk you have to + + + align:start position:0% +risk to take on more risk you have to +offer a lot more than + + align:start position:0% +offer a lot more than + + + align:start position:0% +offer a lot more than +right well you you may but the + + align:start position:0% +right well you you may but the + + + align:start position:0% +right well you you may but the +equilibrium Theory that we've argued uh + + align:start position:0% +equilibrium Theory that we've argued uh + + + align:start position:0% +equilibrium Theory that we've argued uh +has to hold actually says that the risk + + align:start position:0% +has to hold actually says that the risk + + + align:start position:0% +has to hold actually says that the risk +reward tradeoff is in fact linear for + + align:start position:0% +reward tradeoff is in fact linear for + + + align:start position:0% +reward tradeoff is in fact linear for +efficient portfolios if it's not for + + align:start position:0% +efficient portfolios if it's not for + + + align:start position:0% +efficient portfolios if it's not for +efficient portfolios then who + + align:start position:0% +efficient portfolios then who + + + align:start position:0% +efficient portfolios then who +knows but the theory of the capital + + align:start position:0% +knows but the theory of the capital + + + align:start position:0% +knows but the theory of the capital +asset pricing model or the security + + align:start position:0% +asset pricing model or the security + + + align:start position:0% +asset pricing model or the security +Market line which is what we derive what + + align:start position:0% +Market line which is what we derive what + + + align:start position:0% +Market line which is what we derive what +we what we talked about today this says + + align:start position:0% +we what we talked about today this says + + + align:start position:0% +we what we talked about today this says +that in fact it is linear so in other + + align:start position:0% +that in fact it is linear so in other + + + align:start position:0% +that in fact it is linear so in other +words this result as I told you we + + align:start position:0% +words this result as I told you we + + + align:start position:0% +words this result as I told you we +didn't derive it but it's a major result + + align:start position:0% +didn't derive it but it's a major result + + + align:start position:0% +didn't derive it but it's a major result +that show knows that the relationship + + align:start position:0% +that show knows that the relationship + + + align:start position:0% +that show knows that the relationship +between risk and expected return where + + align:start position:0% +between risk and expected return where + + + align:start position:0% +between risk and expected return where +risk is measured by Beta + + align:start position:0% +risk is measured by Beta + + + align:start position:0% +risk is measured by Beta +now is linear right this is a linear + + align:start position:0% +now is linear right this is a linear + + + align:start position:0% +now is linear right this is a linear +relationship so this is a major advance + + align:start position:0% +relationship so this is a major advance + + + align:start position:0% +relationship so this is a major advance +that we we didn't expect and in fact so + + align:start position:0% +that we we didn't expect and in fact so + + + align:start position:0% +that we we didn't expect and in fact so +what I showed before was the preferences + + align:start position:0% +what I showed before was the preferences + + + align:start position:0% +what I showed before was the preferences +the so in other words we talked last + + align:start position:0% +the so in other words we talked last + + + align:start position:0% +the so in other words we talked last +time about the situation where suppose + + align:start position:0% +time about the situation where suppose + + + align:start position:0% +time about the situation where suppose +that you're an investor and I start you + + align:start position:0% +that you're an investor and I start you + + + align:start position:0% +that you're an investor and I start you +off at a point like this + + align:start position:0% +off at a point like this + + + align:start position:0% +off at a point like this +and I asked the question if I want you + + align:start position:0% +and I asked the question if I want you + + + align:start position:0% +and I asked the question if I want you +to tell me where you're going to be uh + + align:start position:0% +to tell me where you're going to be uh + + + align:start position:0% +to tell me where you're going to be uh +such that you're just as well off you + + align:start position:0% +such that you're just as well off you + + + align:start position:0% +such that you're just as well off you +you have the same level of utility that + + align:start position:0% +you have the same level of utility that + + + align:start position:0% +you have the same level of utility that +curve that indifference curve is going + + align:start position:0% +curve that indifference curve is going + + + align:start position:0% +curve that indifference curve is going +to look something like this that's going + + align:start position:0% +to look something like this that's going + + + align:start position:0% +to look something like this that's going +to be curved right that's what you're + + align:start position:0% +to be curved right that's what you're + + + align:start position:0% +to be curved right that's what you're +talking about but that's the behavior of + + align:start position:0% +talking about but that's the behavior of + + + align:start position:0% +talking about but that's the behavior of +one + + align:start position:0% +one + + + align:start position:0% +one +individual the point about the capm is + + align:start position:0% +individual the point about the capm is + + + align:start position:0% +individual the point about the capm is +that if you aggregate all of the + + align:start position:0% +that if you aggregate all of the + + + align:start position:0% +that if you aggregate all of the +individuals together + + align:start position:0% +individuals together + + + align:start position:0% +individuals together +and ask the question what does the + + align:start position:0% +and ask the question what does the + + + align:start position:0% +and ask the question what does the +expected rate of return and volatility + + align:start position:0% +expected rate of return and volatility + + + align:start position:0% +expected rate of return and volatility +or expected rate of return and beta look + + align:start position:0% +or expected rate of return and beta look + + + align:start position:0% +or expected rate of return and beta look +like how are they related in fact it's + + align:start position:0% +like how are they related in fact it's + + + align:start position:0% +like how are they related in fact it's +it's magical that it actually is linear + + align:start position:0% +it's magical that it actually is linear + + + align:start position:0% +it's magical that it actually is linear +so it's exactly the the fact that we + + align:start position:0% +so it's exactly the the fact that we + + + align:start position:0% +so it's exactly the the fact that we +didn't expect linearity given that there + + align:start position:0% +didn't expect linearity given that there + + + align:start position:0% +didn't expect linearity given that there +are diminishing marginal returns to risk + + align:start position:0% +are diminishing marginal returns to risk + + + align:start position:0% +are diminishing marginal returns to risk +and reward you wouldn't expect linearity + + align:start position:0% +and reward you wouldn't expect linearity + + + align:start position:0% +and reward you wouldn't expect linearity +but in fact it it drops out I mean this + + align:start position:0% +but in fact it it drops out I mean this + + + align:start position:0% +but in fact it it drops out I mean this +drops out of this tangency portfolio + + align:start position:0% +drops out of this tangency portfolio + + + align:start position:0% +drops out of this tangency portfolio +argument right nothing up my sleeve this + + align:start position:0% +argument right nothing up my sleeve this + + + align:start position:0% +argument right nothing up my sleeve this +was an argument that we all did together + + align:start position:0% +was an argument that we all did together + + + align:start position:0% +was an argument that we all did together +and we derived this curve right from + + align:start position:0% +and we derived this curve right from + + + align:start position:0% +and we derived this curve right from +first principles so this is really an + + align:start position:0% +first principles so this is really an + + + align:start position:0% +first principles so this is really an +astounding result but it's even more + + align:start position:0% +astounding result but it's even more + + + align:start position:0% +astounding result but it's even more +astonishing that you get this result for + + align:start position:0% +astonishing that you get this result for + + + align:start position:0% +astonishing that you get this result for +all Securities not just for efficient + + align:start position:0% +all Securities not just for efficient + + + align:start position:0% +all Securities not just for efficient +portfolios okay other + + align:start position:0% +portfolios okay other + + + align:start position:0% +portfolios okay other +questions all right let's do another + + align:start position:0% +questions all right let's do another + + + align:start position:0% +questions all right let's do another +example so here I want to show you how + + align:start position:0% +example so here I want to show you how + + + align:start position:0% +example so here I want to show you how +you can use the security Market + + align:start position:0% +you can use the security Market + + + align:start position:0% +you can use the security Market +line also called the capm capm for + + align:start position:0% +line also called the capm capm for + + + align:start position:0% +line also called the capm capm for +Capital asset pricing + + align:start position:0% +Capital asset pricing + + + align:start position:0% +Capital asset pricing +model I want to show you how you could + + align:start position:0% +model I want to show you how you could + + + align:start position:0% +model I want to show you how you could +use it to do performance attribution + + align:start position:0% +use it to do performance attribution + + + align:start position:0% +use it to do performance attribution +this is uh the data from a real live + + align:start position:0% +this is uh the data from a real live + + + align:start position:0% +this is uh the data from a real live +hedge fund manager who will go nameless + + align:start position:0% +hedge fund manager who will go nameless + + + align:start position:0% +hedge fund manager who will go nameless +since I don't want to get sued by him uh + + align:start position:0% +since I don't want to get sued by him uh + + + align:start position:0% +since I don't want to get sued by him uh +for any reason hedge fund managers are + + align:start position:0% +for any reason hedge fund managers are + + + align:start position:0% +for any reason hedge fund managers are +both very wealthy typically and also uh + + align:start position:0% +both very wealthy typically and also uh + + + align:start position:0% +both very wealthy typically and also uh +very litigious so you want to be careful + + align:start position:0% +very litigious so you want to be careful + + + align:start position:0% +very litigious so you want to be careful +when you talk about them in public uh + + align:start position:0% +when you talk about them in public uh + + + align:start position:0% +when you talk about them in public uh +hedge fund XYZ had an average annualized + + align:start position:0% +hedge fund XYZ had an average annualized + + + align:start position:0% +hedge fund XYZ had an average annualized +return of 12 1.5% and a return standard + + align:start position:0% +return of 12 1.5% and a return standard + + + align:start position:0% +return of 12 1.5% and a return standard +deviation of 5.2% from January 885 to + + align:start position:0% +deviation of 5.2% from January 885 to + + + align:start position:0% +deviation of 5.2% from January 885 to +December 2002 and the estimated beta + + align:start position:0% +December 2002 and the estimated beta + + + align:start position:0% +December 2002 and the estimated beta +over this period was minus 028 now + + align:start position:0% +over this period was minus 028 now + + + align:start position:0% +over this period was minus 028 now +somebody asked about a negative beta + + align:start position:0% +somebody asked about a negative beta + + + align:start position:0% +somebody asked about a negative beta +well here's an example of a negative + + align:start position:0% +well here's an example of a negative + + + align:start position:0% +well here's an example of a negative +beta + + align:start position:0% +beta + + + align:start position:0% +beta +asset positive expected rate of return + + align:start position:0% +asset positive expected rate of return + + + align:start position:0% +asset positive expected rate of return +negative beta so if it's got a positive + + align:start position:0% +negative beta so if it's got a positive + + + align:start position:0% +negative beta so if it's got a positive +expected rate return on a negative beta + + align:start position:0% +expected rate return on a negative beta + + + align:start position:0% +expected rate return on a negative beta +you know something can't exactly be + + align:start position:0% +you know something can't exactly be + + + align:start position:0% +you know something can't exactly be +right because that doesn't sound like it + + align:start position:0% +right because that doesn't sound like it + + + align:start position:0% +right because that doesn't sound like it +makes sense in terms of the capm + + align:start position:0% +makes sense in terms of the capm + + + align:start position:0% +makes sense in terms of the capm +framework and in fact it doesn't it + + align:start position:0% +framework and in fact it doesn't it + + + align:start position:0% +framework and in fact it doesn't it +doesn't make sense well let's do the + + align:start position:0% +doesn't make sense well let's do the + + + align:start position:0% +doesn't make sense well let's do the +math the expected rate of return is + + align:start position:0% +math the expected rate of return is + + + align:start position:0% +math the expected rate of return is +equal to RF plus beta times the market + + align:start position:0% +equal to RF plus beta times the market + + + align:start position:0% +equal to RF plus beta times the market +risk premium Market risk premium of 6% + + align:start position:0% +risk premium Market risk premium of 6% + + + align:start position:0% +risk premium Market risk premium of 6% +risk free rate of 5% plug that in with + + align:start position:0% +risk free rate of 5% plug that in with + + + align:start position:0% +risk free rate of 5% plug that in with +the beta of minus 028 and you get that + + align:start position:0% +the beta of minus 028 and you get that + + + align:start position:0% +the beta of minus 028 and you get that +this manager should have earned + + align:start position:0% +this manager should have earned + + + align:start position:0% +this manager should have earned +4.83% per year + + align:start position:0% +4.83% per year + + + align:start position:0% +4.83% per year +that's what the manager should have + + align:start position:0% +that's what the manager should have + + + align:start position:0% +that's what the manager should have +earned in fact the manager earned a rate + + align:start position:0% +earned in fact the manager earned a rate + + + align:start position:0% +earned in fact the manager earned a rate +of return of 12 a half% per year so + + align:start position:0% +of return of 12 a half% per year so + + + align:start position:0% +of return of 12 a half% per year so +that's an alpha if you define the alpha + + align:start position:0% +that's an alpha if you define the alpha + + + align:start position:0% +that's an alpha if you define the alpha +as what the manager did earn minus what + + align:start position:0% +as what the manager did earn minus what + + + align:start position:0% +as what the manager did earn minus what +the manager should have earned you got + + align:start position:0% +the manager should have earned you got + + + align:start position:0% +the manager should have earned you got +an + + align:start position:0% +an + + + align:start position:0% +an +alpha of 771 basis points per year + + align:start position:0% +alpha of 771 basis points per year + + + align:start position:0% +alpha of 771 basis points per year +that's a humongous + + align:start position:0% +that's a humongous + + + align:start position:0% +that's a humongous +Alpha very very very big amount of + + align:start position:0% +Alpha very very very big amount of + + + align:start position:0% +Alpha very very very big amount of +excess performance this is why people + + align:start position:0% +excess performance this is why people + + + align:start position:0% +excess performance this is why people +are excited about hedge funds now we + + align:start position:0% +are excited about hedge funds now we + + + align:start position:0% +are excited about hedge funds now we +we're not going to talk in great detail + + align:start position:0% +we're not going to talk in great detail + + + align:start position:0% +we're not going to talk in great detail +about it in this course because it goes + + align:start position:0% +about it in this course because it goes + + + align:start position:0% +about it in this course because it goes +beyond the scope of Finance uh 401 uh + + align:start position:0% +beyond the scope of Finance uh 401 uh + + + align:start position:0% +beyond the scope of Finance uh 401 uh +but in an Investments course the next + + align:start position:0% +but in an Investments course the next + + + align:start position:0% +but in an Investments course the next +level of sophistication would be to take + + align:start position:0% +level of sophistication would be to take + + + align:start position:0% +level of sophistication would be to take +a look at this and say okay is this + + align:start position:0% +a look at this and say okay is this + + + align:start position:0% +a look at this and say okay is this +Alpha really alpha or is it due to other + + align:start position:0% +Alpha really alpha or is it due to other + + + align:start position:0% +Alpha really alpha or is it due to other +factors other risks that were we're not + + align:start position:0% +factors other risks that were we're not + + + align:start position:0% +factors other risks that were we're not +measuring right now the only risk we're + + align:start position:0% +measuring right now the only risk we're + + + align:start position:0% +measuring right now the only risk we're +measuring is this tangency + + align:start position:0% +measuring is this tangency + + + align:start position:0% +measuring is this tangency +portfolio risk this beta risk but maybe + + align:start position:0% +portfolio risk this beta risk but maybe + + + align:start position:0% +portfolio risk this beta risk but maybe +there are multiple betas out there we're + + align:start position:0% +there are multiple betas out there we're + + + align:start position:0% +there are multiple betas out there we're +not going to talk about it in this + + align:start position:0% +not going to talk about it in this + + + align:start position:0% +not going to talk about it in this +course but in 433 you will discuss it + + align:start position:0% +course but in 433 you will discuss it + + + align:start position:0% +course but in 433 you will discuss it +and it will turn out that hedge funds + + align:start position:0% +and it will turn out that hedge funds + + + align:start position:0% +and it will turn out that hedge funds +actually do have multiple betas so you + + align:start position:0% +actually do have multiple betas so you + + + align:start position:0% +actually do have multiple betas so you +shouldn't go out and put all your money + + align:start position:0% +shouldn't go out and put all your money + + + align:start position:0% +shouldn't go out and put all your money +in hedge funds right away because this + + align:start position:0% +in hedge funds right away because this + + + align:start position:0% +in hedge funds right away because this +extra performance some of it is due to + + align:start position:0% +extra performance some of it is due to + + + align:start position:0% +extra performance some of it is due to +true genius and uh uh insight and unique + + align:start position:0% +true genius and uh uh insight and unique + + + align:start position:0% +true genius and uh uh insight and unique +skill + + align:start position:0% +skill + + + align:start position:0% +skill +but part of it is also due to the fact + + align:start position:0% +but part of it is also due to the fact + + + align:start position:0% +but part of it is also due to the fact +that you're bearing risks that you had + + align:start position:0% +that you're bearing risks that you had + + + align:start position:0% +that you're bearing risks that you had +no idea you're bearing and so you got to + + align:start position:0% +no idea you're bearing and so you got to + + + align:start position:0% +no idea you're bearing and so you got to +be careful about getting on the + + align:start position:0% +be careful about getting on the + + + align:start position:0% +be careful about getting on the +bandwagon and saying yeah give me some + + align:start position:0% +bandwagon and saying yeah give me some + + + align:start position:0% +bandwagon and saying yeah give me some +hedge funds I want some of this Alpha + + align:start position:0% +hedge funds I want some of this Alpha + + + align:start position:0% +hedge funds I want some of this Alpha +and + + align:start position:0% + + + + align:start position:0% + +on you know gotten a huge Al but how do + + align:start position:0% +on you know gotten a huge Al but how do + + + align:start position:0% +on you know gotten a huge Al but how do +we know this is good for the investor + + align:start position:0% +we know this is good for the investor + + + align:start position:0% +we know this is good for the investor +because they could have invested in the + + align:start position:0% +because they could have invested in the + + + align:start position:0% +because they could have invested in the +S&P and probably got + + align:start position:0% +S&P and probably got + + + align:start position:0% +S&P and probably got +more so the question is how do we know + + align:start position:0% +more so the question is how do we know + + + align:start position:0% +more so the question is how do we know +that this is actually good for the + + align:start position:0% +that this is actually good for the + + + align:start position:0% +that this is actually good for the +investor because the they could have got + + align:start position:0% +investor because the they could have got + + + align:start position:0% +investor because the they could have got +gotten uh some return for the + + align:start position:0% +gotten uh some return for the + + + align:start position:0% +gotten uh some return for the +S&P the way we know that is because + + align:start position:0% +S&P the way we know that is because + + + align:start position:0% +S&P the way we know that is because +we're measuring the expected rate of + + align:start position:0% +we're measuring the expected rate of + + + align:start position:0% +we're measuring the expected rate of +return relative to the S&P so in other + + align:start position:0% +return relative to the S&P so in other + + + align:start position:0% +return relative to the S&P so in other +words the way I got this number this is + + align:start position:0% +words the way I got this number this is + + + align:start position:0% +words the way I got this number this is +the excess return on the S&P that's what + + align:start position:0% +the excess return on the S&P that's what + + + align:start position:0% +the excess return on the S&P that's what +the market risk premium is so in fact + + align:start position:0% +the market risk premium is so in fact + + + align:start position:0% +the market risk premium is so in fact +given the beta of this + + align:start position:0% +given the beta of this + + + align:start position:0% +given the beta of this +manager it should have only given you + + align:start position:0% +manager it should have only given you + + + align:start position:0% +manager it should have only given you +4.83% return relative to what the S&P + + align:start position:0% +4.83% return relative to what the S&P + + + align:start position:0% +4.83% return relative to what the S&P +would have given you which is a 6% + + align:start position:0% +would have given you which is a 6% + + + align:start position:0% +would have given you which is a 6% +excess rate of return and in fact what + + align:start position:0% +excess rate of return and in fact what + + + align:start position:0% +excess rate of return and in fact what +we see is that you know this manager + + align:start position:0% +we see is that you know this manager + + + align:start position:0% +we see is that you know this manager +produced a 12% rate of return or 7% + + align:start position:0% +produced a 12% rate of return or 7% + + + align:start position:0% +produced a 12% rate of return or 7% +above and beyond what it was supposed to + + align:start position:0% +above and beyond what it was supposed to + + + align:start position:0% +above and beyond what it was supposed to +have done okay so this takes that into + + align:start position:0% +have done okay so this takes that into + + + align:start position:0% +have done okay so this takes that into +account what it doesn't take into + + align:start position:0% +account what it doesn't take into + + + align:start position:0% +account what it doesn't take into +account is how much liquidity risk the + + align:start position:0% +account is how much liquidity risk the + + + align:start position:0% +account is how much liquidity risk the +hedge fund manager was taking how much + + align:start position:0% +hedge fund manager was taking how much + + + align:start position:0% +hedge fund manager was taking how much +currency risk how much commodity risk + + align:start position:0% +currency risk how much commodity risk + + + align:start position:0% +currency risk how much commodity risk +and a bunch of other risks that are not + + align:start position:0% +and a bunch of other risks that are not + + + align:start position:0% +and a bunch of other risks that are not +represented by the tangency portfolio + + align:start position:0% + + + + align:start position:0% + +Megan dress as it's really because mple + + align:start position:0% +Megan dress as it's really because mple + + + align:start position:0% +Megan dress as it's really because mple +that AR + + align:start position:0% +that AR + + + align:start position:0% +that AR +getting exactly that's exactly right + + align:start position:0% +getting exactly that's exactly right + + + align:start position:0% +getting exactly that's exactly right +recently a lot of institutional + + align:start position:0% +recently a lot of institutional + + + align:start position:0% +recently a lot of institutional +investors have become skeptical of hedge + + align:start position:0% +investors have become skeptical of hedge + + + align:start position:0% +investors have become skeptical of hedge +funds because they say hedge funds Alpha + + align:start position:0% +funds because they say hedge funds Alpha + + + align:start position:0% +funds because they say hedge funds Alpha +uh is really dressed up beta in other + + align:start position:0% +uh is really dressed up beta in other + + + align:start position:0% +uh is really dressed up beta in other +words hedge fund managers are taking + + align:start position:0% +words hedge fund managers are taking + + + align:start position:0% +words hedge fund managers are taking +risks that that are not captured by this + + align:start position:0% +risks that that are not captured by this + + + align:start position:0% +risks that that are not captured by this +very simple framework and so when you + + align:start position:0% +very simple framework and so when you + + + align:start position:0% +very simple framework and so when you +run these kind of regressions and do + + align:start position:0% +run these kind of regressions and do + + + align:start position:0% +run these kind of regressions and do +this analysis you're getting tremendous + + align:start position:0% +this analysis you're getting tremendous + + + align:start position:0% +this analysis you're getting tremendous +Alpha but in fact it's not all Alpha + + align:start position:0% +Alpha but in fact it's not all Alpha + + + align:start position:0% +Alpha but in fact it's not all Alpha +there's other kinds of betas in there + + align:start position:0% +there's other kinds of betas in there + + + align:start position:0% +there's other kinds of betas in there +and so there's a whole literature that + + align:start position:0% +and so there's a whole literature that + + + align:start position:0% +and so there's a whole literature that +has developed about multiple what are + + align:start position:0% +has developed about multiple what are + + + align:start position:0% +has developed about multiple what are +called exotic betas or alternative betas + + align:start position:0% +called exotic betas or alternative betas + + + align:start position:0% +called exotic betas or alternative betas +again not part of the scope of + + align:start position:0% +again not part of the scope of + + + align:start position:0% +again not part of the scope of +introductory Finance but it is something + + align:start position:0% +introductory Finance but it is something + + + align:start position:0% +introductory Finance but it is something +that's covered in uh + + align:start position:0% +that's covered in uh + + + align:start position:0% +that's covered in uh +Investments okay + + align:start position:0% +Investments okay + + + align:start position:0% +Investments okay +just uh another illustration of what + + align:start position:0% +just uh another illustration of what + + + align:start position:0% +just uh another illustration of what +this hedge fund has done take a look at + + align:start position:0% +this hedge fund has done take a look at + + + align:start position:0% +this hedge fund has done take a look at +the the growth of a dollar invested in + + align:start position:0% +the the growth of a dollar invested in + + + align:start position:0% +the the growth of a dollar invested in +the hedge fund over the last uh 20 years + + align:start position:0% +the hedge fund over the last uh 20 years + + + align:start position:0% +the hedge fund over the last uh 20 years +and you'll see that the blue line is the + + align:start position:0% +and you'll see that the blue line is the + + + align:start position:0% +and you'll see that the blue line is the +hedge fund the red line is the S&P 500 + + align:start position:0% +hedge fund the red line is the S&P 500 + + + align:start position:0% +hedge fund the red line is the S&P 500 +so to your point Anand the S&P 500 gave + + align:start position:0% +so to your point Anand the S&P 500 gave + + + align:start position:0% +so to your point Anand the S&P 500 gave +you a wild ride and so for a while you + + align:start position:0% +you a wild ride and so for a while you + + + align:start position:0% +you a wild ride and so for a while you +were doing better than the hedge fund + + align:start position:0% +were doing better than the hedge fund + + + align:start position:0% +were doing better than the hedge fund +but in fact now this hedge fund has done + + align:start position:0% +but in fact now this hedge fund has done + + + align:start position:0% +but in fact now this hedge fund has done +quite a bit better now this ends in 2002 + + align:start position:0% +quite a bit better now this ends in 2002 + + + align:start position:0% +quite a bit better now this ends in 2002 +I'll give you a little bit of an update + + align:start position:0% +I'll give you a little bit of an update + + + align:start position:0% +I'll give you a little bit of an update +uh I don't have it here in in the graph + + align:start position:0% +uh I don't have it here in in the graph + + + align:start position:0% +uh I don't have it here in in the graph +but you can use your + + align:start position:0% +but you can use your + + + align:start position:0% +but you can use your +imagination it turns out that up to 2007 + + align:start position:0% +imagination it turns out that up to 2007 + + + align:start position:0% +imagination it turns out that up to 2007 +the blue line is way ahead of the red + + align:start position:0% +the blue line is way ahead of the red + + + align:start position:0% +the blue line is way ahead of the red +line okay that's actually changed in + + align:start position:0% +line okay that's actually changed in + + + align:start position:0% +line okay that's actually changed in +2008 this this hedge fund has done very + + align:start position:0% +2008 this this hedge fund has done very + + + align:start position:0% +2008 this this hedge fund has done very +badly this year uh of course the S&P has + + align:start position:0% +badly this year uh of course the S&P has + + + align:start position:0% +badly this year uh of course the S&P has +done even worse so the Gap is not as + + align:start position:0% +done even worse so the Gap is not as + + + align:start position:0% +done even worse so the Gap is not as +wide as it used to be there's still a + + align:start position:0% +wide as it used to be there's still a + + + align:start position:0% +wide as it used to be there's still a +gap but the Gap is actually narrowed a + + align:start position:0% +gap but the Gap is actually narrowed a + + + align:start position:0% +gap but the Gap is actually narrowed a +bit + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +isang no in fact everything is changing + + align:start position:0% +isang no in fact everything is changing + + + align:start position:0% +isang no in fact everything is changing +so if you want to take seriously change + + align:start position:0% +so if you want to take seriously change + + + align:start position:0% +so if you want to take seriously change +you've basically got to figure out how + + align:start position:0% +you've basically got to figure out how + + + align:start position:0% +you've basically got to figure out how +the risk-free rate is changing the + + align:start position:0% +the risk-free rate is changing the + + + align:start position:0% +the risk-free rate is changing the +expected rate of return is changing and + + align:start position:0% +expected rate of return is changing and + + + align:start position:0% +expected rate of return is changing and +the betas actually are also changing but + + align:start position:0% +the betas actually are also changing but + + + align:start position:0% +the betas actually are also changing but +what I'm trying to do with the simple + + align:start position:0% +what I'm trying to do with the simple + + + align:start position:0% +what I'm trying to do with the simple +illustration is use a long period and + + align:start position:0% +illustration is use a long period and + + + align:start position:0% +illustration is use a long period and +say over that entire period let's + + align:start position:0% +say over that entire period let's + + + align:start position:0% +say over that entire period let's +average across all of these changes + + align:start position:0% + + + + align:start position:0% + +Justin at the graph and it seems like + + align:start position:0% +Justin at the graph and it seems like + + + align:start position:0% +Justin at the graph and it seems like +the differences of the graph is just + + align:start position:0% +the differences of the graph is just + + + align:start position:0% +the differences of the graph is just +higher with the market it is but you + + align:start position:0% +higher with the market it is but you + + + align:start position:0% +higher with the market it is but you +don't just for the + + align:start position:0% +don't just for the + + + align:start position:0% +don't just for the +beta that's the key right the S&P has a + + align:start position:0% +beta that's the key right the S&P has a + + + align:start position:0% +beta that's the key right the S&P has a +beta of one this guy this hedge fund + + align:start position:0% +beta of one this guy this hedge fund + + + align:start position:0% +beta of one this guy this hedge fund +manager has a beta of zero or slightly + + align:start position:0% +manager has a beta of zero or slightly + + + align:start position:0% +manager has a beta of zero or slightly +negative that's the difference you see + + align:start position:0% +negative that's the difference you see + + + align:start position:0% +negative that's the difference you see +that's why looking at volatility can be + + align:start position:0% +that's why looking at volatility can be + + + align:start position:0% +that's why looking at volatility can be +misleading if you look at volatility + + align:start position:0% +misleading if you look at volatility + + + align:start position:0% +misleading if you look at volatility +you'd say well you know obviously the + + align:start position:0% +you'd say well you know obviously the + + + align:start position:0% +you'd say well you know obviously the +S&P is done better but keep in mind that + + align:start position:0% +S&P is done better but keep in mind that + + + align:start position:0% +S&P is done better but keep in mind that +look how smooth the blue line is and the + + align:start position:0% +look how smooth the blue line is and the + + + align:start position:0% +look how smooth the blue line is and the +the lesson of the capm is that investors + + align:start position:0% +the lesson of the capm is that investors + + + align:start position:0% +the lesson of the capm is that investors +pay for smoothness but only a certain + + align:start position:0% +pay for smoothness but only a certain + + + align:start position:0% +pay for smoothness but only a certain +kind of smoothness in other words + + align:start position:0% +kind of smoothness in other words + + + align:start position:0% +kind of smoothness in other words +smoothness means low volatility right + + align:start position:0% +smoothness means low volatility right + + + align:start position:0% +smoothness means low volatility right +the smoothest line of course is t- bills + + align:start position:0% +the smoothest line of course is t- bills + + + align:start position:0% +the smoothest line of course is t- bills +that that that's a straight line right + + align:start position:0% +that that that's a straight line right + + + align:start position:0% +that that that's a straight line right +that'll go sort of like this + + align:start position:0% +that'll go sort of like this + + + align:start position:0% +that'll go sort of like this +and investors not going to pay a lot for + + align:start position:0% +and investors not going to pay a lot for + + + align:start position:0% +and investors not going to pay a lot for +that because there that doesn't really + + align:start position:0% +that because there that doesn't really + + + align:start position:0% +that because there that doesn't really +help them generate expected rate of + + align:start position:0% +help them generate expected rate of + + + align:start position:0% +help them generate expected rate of +return if you've got expected rate of + + align:start position:0% +return if you've got expected rate of + + + align:start position:0% +return if you've got expected rate of +return and smoothness together you get a + + align:start position:0% +return and smoothness together you get a + + + align:start position:0% +return and smoothness together you get a +really big big Alpha and that's exactly + + align:start position:0% +really big big Alpha and that's exactly + + + align:start position:0% +really big big Alpha and that's exactly +what we see here an alpha of 771 basis + + align:start position:0% +what we see here an alpha of 771 basis + + + align:start position:0% +what we see here an alpha of 771 basis +points okay now here I talk about these + + align:start position:0% +points okay now here I talk about these + + + align:start position:0% +points okay now here I talk about these +multiple sources of systematic risk I + + align:start position:0% +multiple sources of systematic risk I + + + align:start position:0% +multiple sources of systematic risk I +don't want to focus on that for this + + align:start position:0% +don't want to focus on that for this + + + align:start position:0% +don't want to focus on that for this +course because as I said it's going to + + align:start position:0% +course because as I said it's going to + + + align:start position:0% +course because as I said it's going to +be much more complicated and requires + + align:start position:0% +be much more complicated and requires + + + align:start position:0% +be much more complicated and requires +more Machinery but the basic intuition + + align:start position:0% +more Machinery but the basic intuition + + + align:start position:0% +more Machinery but the basic intuition +is the same instead of just one source + + align:start position:0% +is the same instead of just one source + + + align:start position:0% +is the same instead of just one source +of of systematic risk you may have + + align:start position:0% +of of systematic risk you may have + + + align:start position:0% +of of systematic risk you may have +multiple sources and so therefore you're + + align:start position:0% +multiple sources and so therefore you're + + + align:start position:0% +multiple sources and so therefore you're +going to have multiple risk Premia as + + align:start position:0% +going to have multiple risk Premia as + + + align:start position:0% +going to have multiple risk Premia as +opposed to just one but for now let's + + align:start position:0% +opposed to just one but for now let's + + + align:start position:0% +opposed to just one but for now let's +not focus on that and we're going to + + align:start position:0% +not focus on that and we're going to + + + align:start position:0% +not focus on that and we're going to +focus our attention just on this simple + + align:start position:0% +focus our attention just on this simple + + + align:start position:0% +focus our attention just on this simple +equation and make sure we understand it + + align:start position:0% +equation and make sure we understand it + + + align:start position:0% +equation and make sure we understand it +and know how to apply + + align:start position:0% +and know how to apply + + + align:start position:0% +and know how to apply +it + + align:start position:0% +it + + + align:start position:0% +it +okay now I want to go with I want to + + align:start position:0% +okay now I want to go with I want to + + + align:start position:0% +okay now I want to go with I want to +give you one more + + align:start position:0% +give you one more + + + align:start position:0% +give you one more +intuition for why it is that + + align:start position:0% +intuition for why it is that + + + align:start position:0% +intuition for why it is that +beta is the appropriate measure of risk + + align:start position:0% +beta is the appropriate measure of risk + + + align:start position:0% +beta is the appropriate measure of risk +and not Sigma for arbitrary inefficient + + align:start position:0% +and not Sigma for arbitrary inefficient + + + align:start position:0% +and not Sigma for arbitrary inefficient +portfolios and the idea is actually + + align:start position:0% +portfolios and the idea is actually + + + align:start position:0% +portfolios and the idea is actually +pretty simple when you think of an + + align:start position:0% +pretty simple when you think of an + + + align:start position:0% +pretty simple when you think of an +investment like Microsoft or like + + align:start position:0% +investment like Microsoft or like + + + align:start position:0% +investment like Microsoft or like +Gillette you can think of the risk of + + align:start position:0% +Gillette you can think of the risk of + + + align:start position:0% +Gillette you can think of the risk of +that portfolio as being uh the risk of + + align:start position:0% +that portfolio as being uh the risk of + + + align:start position:0% +that portfolio as being uh the risk of +that investment in those individual + + align:start position:0% +that investment in those individual + + + align:start position:0% +that investment in those individual +Securities as having two two components + + align:start position:0% +Securities as having two two components + + + align:start position:0% +Securities as having two two components +so when you think of the the volatility + + align:start position:0% +so when you think of the the volatility + + + align:start position:0% +so when you think of the the volatility +of Gillette you can think of the + + align:start position:0% +of Gillette you can think of the + + + align:start position:0% +of Gillette you can think of the +volatility of Gillette coming from two + + align:start position:0% +volatility of Gillette coming from two + + + align:start position:0% +volatility of Gillette coming from two +sources One Source is the aggregate risk + + align:start position:0% +sources One Source is the aggregate risk + + + align:start position:0% +sources One Source is the aggregate risk +that affects all + + align:start position:0% +that affects all + + + align:start position:0% +that affects all +companies and the second source of risk + + align:start position:0% +companies and the second source of risk + + + align:start position:0% +companies and the second source of risk +is the risk unique to Gillette you know + + align:start position:0% +is the risk unique to Gillette you know + + + align:start position:0% +is the risk unique to Gillette you know +the fact that they've got a particular + + align:start position:0% +the fact that they've got a particular + + + align:start position:0% +the fact that they've got a particular +manufacturing plant in a particular + + align:start position:0% +manufacturing plant in a particular + + + align:start position:0% +manufacturing plant in a particular +location of the country the fact that + + align:start position:0% +location of the country the fact that + + + align:start position:0% +location of the country the fact that +they've got a specific set of managers + + align:start position:0% +they've got a specific set of managers + + + align:start position:0% +they've got a specific set of managers +that are either good or bad the fact + + align:start position:0% +that are either good or bad the fact + + + align:start position:0% +that are either good or bad the fact +that they are subject to a very specific + + align:start position:0% +that they are subject to a very specific + + + align:start position:0% +that they are subject to a very specific +set of requirements uh for producing + + align:start position:0% +set of requirements uh for producing + + + align:start position:0% +set of requirements uh for producing +their blades who knows but very specific + + align:start position:0% +their blades who knows but very specific + + + align:start position:0% +their blades who knows but very specific +to that company when you think about + + align:start position:0% +to that company when you think about + + + align:start position:0% +to that company when you think about +that kind of + + align:start position:0% +that kind of + + + align:start position:0% +that kind of +risk let me ask you a question from a + + align:start position:0% +risk let me ask you a question from a + + + align:start position:0% +risk let me ask you a question from a +purely business perspective you're the + + align:start position:0% +purely business perspective you're the + + + align:start position:0% +purely business perspective you're the +investor I'm a representative Gillette + + align:start position:0% +investor I'm a representative Gillette + + + align:start position:0% +investor I'm a representative Gillette +I'm trying to sell you my company's + + align:start position:0% +I'm trying to sell you my company's + + + align:start position:0% +I'm trying to sell you my company's +stock I want you to invest in my + + align:start position:0% +stock I want you to invest in my + + + align:start position:0% +stock I want you to invest in my +company and therefore I have to pay you + + align:start position:0% +company and therefore I have to pay you + + + align:start position:0% +company and therefore I have to pay you +to take the risk of + + align:start position:0% +to take the risk of + + + align:start position:0% +to take the risk of +Gillette if I tell you that Gillette has + + align:start position:0% +Gillette if I tell you that Gillette has + + + align:start position:0% +Gillette if I tell you that Gillette has +these two pieces of risk so I'm the + + align:start position:0% +these two pieces of risk so I'm the + + + align:start position:0% +these two pieces of risk so I'm the +representative from Gillette and I tell + + align:start position:0% +representative from Gillette and I tell + + + align:start position:0% +representative from Gillette and I tell +you that our company is subject to + + align:start position:0% +you that our company is subject to + + + align:start position:0% +you that our company is subject to +economy-wide fluctuations that will help + + align:start position:0% +economy-wide fluctuations that will help + + + align:start position:0% +economy-wide fluctuations that will help +or hurt our business and unique + + align:start position:0% +or hurt our business and unique + + + align:start position:0% +or hurt our business and unique +fluctuations that are spe specific and + + align:start position:0% +fluctuations that are spe specific and + + + align:start position:0% +fluctuations that are spe specific and +special to + + align:start position:0% +special to + + + align:start position:0% +special to +Gillette which of these two risks are + + align:start position:0% +Gillette which of these two risks are + + + align:start position:0% +Gillette which of these two risks are +you going to be more concerned about + + align:start position:0% +you going to be more concerned about + + + align:start position:0% +you going to be more concerned about +from your Investment Portfolio + + align:start position:0% +from your Investment Portfolio + + + align:start position:0% +from your Investment Portfolio +perspective + + align:start position:0% + + + + align:start position:0% + +Ry as a as think + + align:start position:0% + + + + align:start position:0% + +this okay but I want to I want you you + + align:start position:0% +this okay but I want to I want you you + + + align:start position:0% +this okay but I want to I want you you +hurried through the first point and I + + align:start position:0% +hurried through the first point and I + + + align:start position:0% +hurried through the first point and I +want you to expand on that a little bit + + align:start position:0% +want you to expand on that a little bit + + + align:start position:0% +want you to expand on that a little bit +you said that if you're worried about + + align:start position:0% +you said that if you're worried about + + + align:start position:0% +you said that if you're worried about +your portfolio then obviously the + + align:start position:0% +your portfolio then obviously the + + + align:start position:0% +your portfolio then obviously the +economy wide risk absolutely if you're + + align:start position:0% +economy wide risk absolutely if you're + + + align:start position:0% +economy wide risk absolutely if you're +if you're worried about you know the + + align:start position:0% +if you're worried about you know the + + + align:start position:0% +if you're worried about you know the +economy wide r you know for example the + + align:start position:0% +economy wide r you know for example the + + + align:start position:0% +economy wide r you know for example the +next two three years you don't think the + + align:start position:0% +next two three years you don't think the + + + align:start position:0% +next two three years you don't think the +economy is to recover yeah then you're + + align:start position:0% +economy is to recover yeah then you're + + + align:start position:0% +economy is to recover yeah then you're +to just avoid that type of investment as + + align:start position:0% +to just avoid that type of investment as + + + align:start position:0% +to just avoid that type of investment as +a okay might just go for the risk okay + + align:start position:0% +a okay might just go for the risk okay + + + align:start position:0% +a okay might just go for the risk okay +fine so but but on the other hand you + + align:start position:0% +fine so but but on the other hand you + + + align:start position:0% +fine so but but on the other hand you +also said something else which is that + + align:start position:0% +also said something else which is that + + + align:start position:0% +also said something else which is that +if you're comparing between two stocks + + align:start position:0% +if you're comparing between two stocks + + + align:start position:0% +if you're comparing between two stocks +then what you're focusing on is the + + align:start position:0% +then what you're focusing on is the + + + align:start position:0% +then what you're focusing on is the +risks that are unique to Gillette you + + align:start position:0% +risks that are unique to Gillette you + + + align:start position:0% +risks that are unique to Gillette you +also might look at how how much Ecom + + align:start position:0% +also might look at how how much Ecom + + + align:start position:0% +also might look at how how much Ecom +down would affect right + + align:start position:0% +down would affect right + + + align:start position:0% +down would affect right +rights Microsoft uhhuh than obiously you + + align:start position:0% +rights Microsoft uhhuh than obiously you + + + align:start position:0% +rights Microsoft uhhuh than obiously you +something go forette if on the other + + align:start position:0% +something go forette if on the other + + + align:start position:0% +something go forette if on the other +didn't that might go okay but but let's + + align:start position:0% +didn't that might go okay but but let's + + + align:start position:0% +didn't that might go okay but but let's +now talk about the negotiations between + + align:start position:0% +now talk about the negotiations between + + + align:start position:0% +now talk about the negotiations between +you and me I'm a representative Gillette + + align:start position:0% +you and me I'm a representative Gillette + + + align:start position:0% +you and me I'm a representative Gillette +I'm trying to get you to invest with us + + align:start position:0% +I'm trying to get you to invest with us + + + align:start position:0% +I'm trying to get you to invest with us +and I've got two sources of risk that + + align:start position:0% +and I've got two sources of risk that + + + align:start position:0% +and I've got two sources of risk that +you might be concerned about Market + + align:start position:0% +you might be concerned about Market + + + align:start position:0% +you might be concerned about Market +risk or Gillette specific risk from your + + align:start position:0% +risk or Gillette specific risk from your + + + align:start position:0% +risk or Gillette specific risk from your +portfolio perspective since you just + + align:start position:0% +portfolio perspective since you just + + + align:start position:0% +portfolio perspective since you just +care about maximizing the value of your + + align:start position:0% +care about maximizing the value of your + + + align:start position:0% +care about maximizing the value of your +portfolio right you're not worried about + + align:start position:0% +portfolio right you're not worried about + + + align:start position:0% +portfolio right you're not worried about +Gillette in particular you're not + + align:start position:0% +Gillette in particular you're not + + + align:start position:0% +Gillette in particular you're not +management you're an investor I'm + + align:start position:0% +management you're an investor I'm + + + align:start position:0% +management you're an investor I'm +management I'm worried about Gillette I + + align:start position:0% +management I'm worried about Gillette I + + + align:start position:0% +management I'm worried about Gillette I +I couldn't care less about your + + align:start position:0% +I couldn't care less about your + + + align:start position:0% +I couldn't care less about your +portfolio I'm sorry to say what I care + + align:start position:0% +portfolio I'm sorry to say what I care + + + align:start position:0% +portfolio I'm sorry to say what I care +about is my company but what you care + + align:start position:0% +about is my company but what you care + + + align:start position:0% +about is my company but what you care +about is your portfolio from your + + align:start position:0% +about is your portfolio from your + + + align:start position:0% +about is your portfolio from your +portfolio perspective what are you going + + align:start position:0% +portfolio perspective what are you going + + + align:start position:0% +portfolio perspective what are you going +to care more about Gillette specific + + align:start position:0% +to care more about Gillette specific + + + align:start position:0% +to care more about Gillette specific +risk or the the the the macroeconomic + + align:start position:0% +risk or the the the the macroeconomic + + + align:start position:0% +risk or the the the the macroeconomic +risk that I represent to your portfolio + + align:start position:0% +risk that I represent to your portfolio + + + align:start position:0% +risk that I represent to your portfolio +I'm talking to you I more about yourf + + align:start position:0% +I'm talking to you I more about yourf + + + align:start position:0% +I'm talking to you I more about yourf +well what when I'm I'm asking a question + + align:start position:0% +well what when I'm I'm asking a question + + + align:start position:0% +well what when I'm I'm asking a question +though about your portfolio what you + + align:start position:0% +though about your portfolio what you + + + align:start position:0% +though about your portfolio what you +care about is your portfolio I + + align:start position:0% +care about is your portfolio I + + + align:start position:0% +care about is your portfolio I +understand that when you're talking to + + align:start position:0% +understand that when you're talking to + + + align:start position:0% +understand that when you're talking to +me you're going to be asking me about my + + align:start position:0% +me you're going to be asking me about my + + + align:start position:0% +me you're going to be asking me about my +company specific risk to try to get a + + align:start position:0% +company specific risk to try to get a + + + align:start position:0% +company specific risk to try to get a +handle on it but is that what you + + align:start position:0% +handle on it but is that what you + + + align:start position:0% +handle on it but is that what you +ultimately are going to be concerned + + align:start position:0% +ultimately are going to be concerned + + + align:start position:0% +ultimately are going to be concerned +about I'm be concerned about obviously + + align:start position:0% +about I'm be concerned about obviously + + + align:start position:0% +about I'm be concerned about obviously +the + + align:start position:0% +the + + + align:start position:0% +the +macro of it how you fit into that look + + align:start position:0% +macro of it how you fit into that look + + + align:start position:0% +macro of it how you fit into that look +at your data and see I you don't know + + align:start position:0% +at your data and see I you don't know + + + align:start position:0% +at your data and see I you don't know +the capm though okay so you know now now + + align:start position:0% +the capm though okay so you know now now + + + align:start position:0% +the capm though okay so you know now now +you're cheating because you now know you + + align:start position:0% +you're cheating because you now know you + + + align:start position:0% +you're cheating because you now know you +now know the capm but suppose you didn't + + align:start position:0% +now know the capm but suppose you didn't + + + align:start position:0% +now know the capm but suppose you didn't +what I'm trying to get at is the + + align:start position:0% +what I'm trying to get at is the + + + align:start position:0% +what I'm trying to get at is the +intuition a businessman's intuition for + + align:start position:0% +intuition a businessman's intuition for + + + align:start position:0% +intuition a businessman's intuition for +what you would care about more in terms + + align:start position:0% +what you would care about more in terms + + + align:start position:0% +what you would care about more in terms +of what I do to your + + align:start position:0% +of what I do to your + + + align:start position:0% +of what I do to your +portfolio right yeah s didn't say few + + align:start position:0% +portfolio right yeah s didn't say few + + + align:start position:0% +portfolio right yeah s didn't say few +ago that the risk isable yes so + + align:start position:0% +ago that the risk isable yes so + + + align:start position:0% +ago that the risk isable yes so +more can that's exactly right the idea + + align:start position:0% +more can that's exactly right the idea + + + align:start position:0% +more can that's exactly right the idea +is that if it's Gillette specific risk + + align:start position:0% +is that if it's Gillette specific risk + + + align:start position:0% +is that if it's Gillette specific risk +then by definition if you're holding a + + align:start position:0% +then by definition if you're holding a + + + align:start position:0% +then by definition if you're holding a +well Diversified + + align:start position:0% +well Diversified + + + align:start position:0% +well Diversified +portfolio then you're not going to care + + align:start position:0% +portfolio then you're not going to care + + + align:start position:0% +portfolio then you're not going to care +about that because that's going to + + align:start position:0% +about that because that's going to + + + align:start position:0% +about that because that's going to +average out to nothing now of course we + + align:start position:0% +average out to nothing now of course we + + + align:start position:0% +average out to nothing now of course we +have to think about the case where + + align:start position:0% +have to think about the case where + + + align:start position:0% +have to think about the case where +you're not holding a diversified + + align:start position:0% +you're not holding a diversified + + + align:start position:0% +you're not holding a diversified +portfolio but let me get back to that in + + align:start position:0% +portfolio but let me get back to that in + + + align:start position:0% +portfolio but let me get back to that in +a minute I'm assuming that all of you + + align:start position:0% +a minute I'm assuming that all of you + + + align:start position:0% +a minute I'm assuming that all of you +are good business folks which means that + + align:start position:0% +are good business folks which means that + + + align:start position:0% +are good business folks which means that +you're going to be holding a diversified + + align:start position:0% +you're going to be holding a diversified + + + align:start position:0% +you're going to be holding a diversified +portfolio you're not going to + + align:start position:0% +portfolio you're not going to + + + align:start position:0% +portfolio you're not going to +concentrate all your bets on one + + align:start position:0% +concentrate all your bets on one + + + align:start position:0% +concentrate all your bets on one +particular uh kind of investment right + + align:start position:0% +particular uh kind of investment right + + + align:start position:0% +particular uh kind of investment right +so if you are already holding a well- + + align:start position:0% +so if you are already holding a well- + + + align:start position:0% +so if you are already holding a well- +diversified portfolio then when you + + align:start position:0% +diversified portfolio then when you + + + align:start position:0% +diversified portfolio then when you +interview me as a potential investment + + align:start position:0% +interview me as a potential investment + + + align:start position:0% +interview me as a potential investment +opportunity do you really care about the + + align:start position:0% +opportunity do you really care about the + + + align:start position:0% +opportunity do you really care about the +idiosyncratic risk because that risk is + + align:start position:0% +idiosyncratic risk because that risk is + + + align:start position:0% +idiosyncratic risk because that risk is +going to be Diversified away what you + + align:start position:0% +going to be Diversified away what you + + + align:start position:0% +going to be Diversified away what you +care about from a portfolio perspective + + align:start position:0% +care about from a portfolio perspective + + + align:start position:0% +care about from a portfolio perspective +is how much am I going to be + + align:start position:0% +is how much am I going to be + + + align:start position:0% +is how much am I going to be +contributing to your overall risk and + + align:start position:0% +contributing to your overall risk and + + + align:start position:0% +contributing to your overall risk and +now now that you know the capm you + + align:start position:0% +now now that you know the capm you + + + align:start position:0% +now now that you know the capm you +understand the logic of it right it says + + align:start position:0% +understand the logic of it right it says + + + align:start position:0% +understand the logic of it right it says +you care about my Beta because my Beta + + align:start position:0% +you care about my Beta because my Beta + + + align:start position:0% +you care about my Beta because my Beta +is a measure of the amount of risk I'm + + align:start position:0% +is a measure of the amount of risk I'm + + + align:start position:0% +is a measure of the amount of risk I'm +going to be adding to your portfolio + + align:start position:0% +going to be adding to your portfolio + + + align:start position:0% +going to be adding to your portfolio +that you cannot get rid of how do you + + align:start position:0% +that you cannot get rid of how do you + + + align:start position:0% +that you cannot get rid of how do you +know you cannot get rid of it well by + + align:start position:0% +know you cannot get rid of it well by + + + align:start position:0% +know you cannot get rid of it well by +definition it's the market portfolio + + align:start position:0% +definition it's the market portfolio + + + align:start position:0% +definition it's the market portfolio +everybody's holding it nobody wants to + + align:start position:0% +everybody's holding it nobody wants to + + + align:start position:0% +everybody's holding it nobody wants to +get rid of it completely you're on the + + align:start position:0% +get rid of it completely you're on the + + + align:start position:0% +get rid of it completely you're on the +capital markets line right that's the + + align:start position:0% +capital markets line right that's the + + + align:start position:0% +capital markets line right that's the +best you can do so this notion of firm + + align:start position:0% +best you can do so this notion of firm + + + align:start position:0% +best you can do so this notion of firm +specific + + align:start position:0% +specific + + + align:start position:0% +specific +risk versus economy-wide risk that + + align:start position:0% +risk versus economy-wide risk that + + + align:start position:0% +risk versus economy-wide risk that +distinction is a really important one + + align:start position:0% +distinction is a really important one + + + align:start position:0% +distinction is a really important one +and I'll show you the mathematics of it + + align:start position:0% +and I'll show you the mathematics of it + + + align:start position:0% +and I'll show you the mathematics of it +in a minute but I want to give you the + + align:start position:0% +in a minute but I want to give you the + + + align:start position:0% +in a minute but I want to give you the +intuition + + align:start position:0% +intuition + + + align:start position:0% +intuition +as a + + align:start position:0% +as a + + + align:start position:0% +as a +result think about this conversation + + align:start position:0% +result think about this conversation + + + align:start position:0% +result think about this conversation +happening not just for Gillette for Ev + + align:start position:0% +happening not just for Gillette for Ev + + + align:start position:0% +happening not just for Gillette for Ev +but for every company in the economy if + + align:start position:0% +but for every company in the economy if + + + align:start position:0% +but for every company in the economy if +it's the case that portfolio managers + + align:start position:0% +it's the case that portfolio managers + + + align:start position:0% +it's the case that portfolio managers +that are buying stocks only care about + + align:start position:0% +that are buying stocks only care about + + + align:start position:0% +that are buying stocks only care about +the systematic risk about the market + + align:start position:0% +the systematic risk about the market + + + align:start position:0% +the systematic risk about the market +risk about the risk that they cannot get + + align:start position:0% +risk about the risk that they cannot get + + + align:start position:0% +risk about the risk that they cannot get +rid of and they then you have to reward + + align:start position:0% +rid of and they then you have to reward + + + align:start position:0% +rid of and they then you have to reward +them for that then what that means is + + align:start position:0% +them for that then what that means is + + + align:start position:0% +them for that then what that means is +that you don't have to reward + + align:start position:0% +that you don't have to reward + + + align:start position:0% +that you don't have to reward +them for idiosyncratic risk why because + + align:start position:0% +them for idiosyncratic risk why because + + + align:start position:0% +them for idiosyncratic risk why because +that's not risk that you are to Bear + + align:start position:0% +that's not risk that you are to Bear + + + align:start position:0% +that's not risk that you are to Bear +there's nothing that says you have to + + align:start position:0% +there's nothing that says you have to + + + align:start position:0% +there's nothing that says you have to +bear idiosyncratic risk how do you get + + align:start position:0% +bear idiosyncratic risk how do you get + + + align:start position:0% +bear idiosyncratic risk how do you get +rid of idiosyncratic risk if you don't + + align:start position:0% +rid of idiosyncratic risk if you don't + + + align:start position:0% +rid of idiosyncratic risk if you don't +want to Bear + + align:start position:0% +want to Bear + + + align:start position:0% +want to Bear +it diversify exactly just buy 10 stocks + + align:start position:0% +it diversify exactly just buy 10 stocks + + + align:start position:0% +it diversify exactly just buy 10 stocks +instead of one and then you're + + align:start position:0% +instead of one and then you're + + + align:start position:0% +instead of one and then you're +Diversified 20 stocks is better than 10 + + align:start position:0% +Diversified 20 stocks is better than 10 + + + align:start position:0% +Diversified 20 stocks is better than 10 +and mathematically after 50 stocks + + align:start position:0% +and mathematically after 50 stocks + + + align:start position:0% +and mathematically after 50 stocks +you're basically Diversified you're + + align:start position:0% +you're basically Diversified you're + + + align:start position:0% +you're basically Diversified you're +you're done so nobody should be holding + + align:start position:0% +you're done so nobody should be holding + + + align:start position:0% +you're done so nobody should be holding +two or three stocks or if they do they + + align:start position:0% +two or three stocks or if they do they + + + align:start position:0% +two or three stocks or if they do they +are bearing risk that they need not bear + + align:start position:0% +are bearing risk that they need not bear + + + align:start position:0% +are bearing risk that they need not bear +and they may want to do it for other + + align:start position:0% +and they may want to do it for other + + + align:start position:0% +and they may want to do it for other +reasons for example as a manager of + + align:start position:0% +reasons for example as a manager of + + + align:start position:0% +reasons for example as a manager of +Gillette I believe in the company I want + + align:start position:0% +Gillette I believe in the company I want + + + align:start position:0% +Gillette I believe in the company I want +to demonstrate to my shareholders that + + align:start position:0% +to demonstrate to my shareholders that + + + align:start position:0% +to demonstrate to my shareholders that +I'm tied to the company so I'm going to + + align:start position:0% +I'm tied to the company so I'm going to + + + align:start position:0% +I'm tied to the company so I'm going to +hold a lot of my wealth in Gillette + + align:start position:0% +hold a lot of my wealth in Gillette + + + align:start position:0% +hold a lot of my wealth in Gillette +stock that's not well Diversified I'm + + align:start position:0% +stock that's not well Diversified I'm + + + align:start position:0% +stock that's not well Diversified I'm +holding a lot of Gillette specific risk + + align:start position:0% +holding a lot of Gillette specific risk + + + align:start position:0% +holding a lot of Gillette specific risk +that's not a smart thing to do from an + + align:start position:0% +that's not a smart thing to do from an + + + align:start position:0% +that's not a smart thing to do from an +investment's point of view but that is a + + align:start position:0% +investment's point of view but that is a + + + align:start position:0% +investment's point of view but that is a +smart thing to do from a management + + align:start position:0% +smart thing to do from a management + + + align:start position:0% +smart thing to do from a management +point of view because I'm tying my fate + + align:start position:0% +point of view because I'm tying my fate + + + align:start position:0% +point of view because I'm tying my fate +to the the fate of the company okay it's + + align:start position:0% +to the the fate of the company okay it's + + + align:start position:0% +to the the fate of the company okay it's +not it's definitely not a smart thing + + align:start position:0% +not it's definitely not a smart thing + + + align:start position:0% +not it's definitely not a smart thing +from an investment's perspective if + + align:start position:0% +from an investment's perspective if + + + align:start position:0% +from an investment's perspective if +you're in a financial services sector + + align:start position:0% +you're in a financial services sector + + + align:start position:0% +you're in a financial services sector +you should not be buying Financial + + align:start position:0% +you should not be buying Financial + + + align:start position:0% +you should not be buying Financial +Services stocks if you're in the + + align:start position:0% +Services stocks if you're in the + + + align:start position:0% +Services stocks if you're in the +pharmaceutical sector you should not be + + align:start position:0% +pharmaceutical sector you should not be + + + align:start position:0% +pharmaceutical sector you should not be +buying biotech stocks and yet we do that + + align:start position:0% +buying biotech stocks and yet we do that + + + align:start position:0% +buying biotech stocks and yet we do that +for reasons other than portfolio + + align:start position:0% +for reasons other than portfolio + + + align:start position:0% +for reasons other than portfolio +management but given that I'm teaching + + align:start position:0% +management but given that I'm teaching + + + align:start position:0% +management but given that I'm teaching +you about portfolio management I'm not + + align:start position:0% +you about portfolio management I'm not + + + align:start position:0% +you about portfolio management I'm not +going to focus on those other reasons If + + align:start position:0% +going to focus on those other reasons If + + + align:start position:0% +going to focus on those other reasons If +This Were an organizational studies + + align:start position:0% +This Were an organizational studies + + + align:start position:0% +This Were an organizational studies +course you'd be getting a different + + align:start position:0% +course you'd be getting a different + + + align:start position:0% +course you'd be getting a different +perspective and you should get a + + align:start position:0% +perspective and you should get a + + + align:start position:0% +perspective and you should get a +different perspective but for the + + align:start position:0% +different perspective but for the + + + align:start position:0% +different perspective but for the +purposes of building Financial wealth + + align:start position:0% +purposes of building Financial wealth + + + align:start position:0% +purposes of building Financial wealth +what you want to do is to focus on how + + align:start position:0% +what you want to do is to focus on how + + + align:start position:0% +what you want to do is to focus on how +much the systematic component is + + align:start position:0% +much the systematic component is + + + align:start position:0% +much the systematic component is +contributing to your risk because the + + align:start position:0% +contributing to your risk because the + + + align:start position:0% +contributing to your risk because the +idiosyncratic component you don't have + + align:start position:0% +idiosyncratic component you don't have + + + align:start position:0% +idiosyncratic component you don't have +to bear + + align:start position:0% + + + + align:start position:0% + +yeah yes yes not that well I recommend + + align:start position:0% +yeah yes yes not that well I recommend + + + align:start position:0% +yeah yes yes not that well I recommend +not doing it from the financial + + align:start position:0% +not doing it from the financial + + + align:start position:0% +not doing it from the financial +perspective but I may recommend doing it + + align:start position:0% +perspective but I may recommend doing it + + + align:start position:0% +perspective but I may recommend doing it +from the management or managerial + + align:start position:0% +from the management or managerial + + + align:start position:0% +from the management or managerial +incentives perspective the reason that + + align:start position:0% +incentives perspective the reason that + + + align:start position:0% +incentives perspective the reason that +companies do that is very simple they're + + align:start position:0% +companies do that is very simple they're + + + align:start position:0% +companies do that is very simple they're +trying to suck you in they're trying to + + align:start position:0% +trying to suck you in they're trying to + + + align:start position:0% +trying to suck you in they're trying to +get you to be more intimately tied to + + align:start position:0% +get you to be more intimately tied to + + + align:start position:0% +get you to be more intimately tied to +the company so you'll act like an owner + + align:start position:0% +the company so you'll act like an owner + + + align:start position:0% +the company so you'll act like an owner +of the company as opposed to an + + align:start position:0% +of the company as opposed to an + + + align:start position:0% +of the company as opposed to an +employee and if you act like an owner + + align:start position:0% +employee and if you act like an owner + + + align:start position:0% +employee and if you act like an owner +you will engage in behavior that is much + + align:start position:0% +you will engage in behavior that is much + + + align:start position:0% +you will engage in behavior that is much +more productive for building the + + align:start position:0% +more productive for building the + + + align:start position:0% +more productive for building the +company's wealth rather than as an + + align:start position:0% +company's wealth rather than as an + + + align:start position:0% +company's wealth rather than as an +employee but from your personal + + align:start position:0% +employee but from your personal + + + align:start position:0% +employee but from your personal +perspective you're bearing risk + + align:start position:0% +perspective you're bearing risk + + + align:start position:0% +perspective you're bearing risk +that you you don't need to so you know + + align:start position:0% +that you you don't need to so you know + + + align:start position:0% +that you you don't need to so you know +the analogy that I give I've given + + align:start position:0% +the analogy that I give I've given + + + align:start position:0% +the analogy that I give I've given +before it may work for some of you it + + align:start position:0% +before it may work for some of you it + + + align:start position:0% +before it may work for some of you it +may not let me explain uh anybody know + + align:start position:0% +may not let me explain uh anybody know + + + align:start position:0% +may not let me explain uh anybody know +um how much window washers in Midtown + + align:start position:0% +um how much window washers in Midtown + + + align:start position:0% +um how much window washers in Midtown +Manhattan get paid on an annual basis + + align:start position:0% +Manhattan get paid on an annual basis + + + align:start position:0% +Manhattan get paid on an annual basis +you know what I'm talking about the + + align:start position:0% +you know what I'm talking about the + + + align:start position:0% +you know what I'm talking about the +these are the folks that climb up on + + align:start position:0% +these are the folks that climb up on + + + align:start position:0% +these are the folks that climb up on +these you know twoof foot catwalks that + + align:start position:0% +these you know twoof foot catwalks that + + + align:start position:0% +these you know twoof foot catwalks that +are 40 stories high and they wash the + + align:start position:0% +are 40 stories high and they wash the + + + align:start position:0% +are 40 stories high and they wash the +windows of these skyscrapers that's a + + align:start position:0% +windows of these skyscrapers that's a + + + align:start position:0% +windows of these skyscrapers that's a +pretty risky job anybody know what their + + align:start position:0% +pretty risky job anybody know what their + + + align:start position:0% +pretty risky job anybody know what their +annual salary is when you annualize it I + + align:start position:0% +annual salary is when you annualize it I + + + align:start position:0% +annual salary is when you annualize it I +I actually decided to find out one one + + align:start position:0% +I actually decided to find out one one + + + align:start position:0% +I actually decided to find out one one +day was kind of curious about that + + align:start position:0% +day was kind of curious about that + + + align:start position:0% +day was kind of curious about that +because you know there's a trade offing + + align:start position:0% +because you know there's a trade offing + + + align:start position:0% +because you know there's a trade offing +risk and return and that's really risky + + align:start position:0% +risk and return and that's really risky + + + align:start position:0% +risk and return and that's really risky +you know there was one day where I was + + align:start position:0% +you know there was one day where I was + + + align:start position:0% +you know there was one day where I was +staying at a hotel it was I think it was + + align:start position:0% +staying at a hotel it was I think it was + + + align:start position:0% +staying at a hotel it was I think it was +the Millennium and I was on the you know + + align:start position:0% +the Millennium and I was on the you know + + + align:start position:0% +the Millennium and I was on the you know +30th floor and it was a windy winter day + + align:start position:0% +30th floor and it was a windy winter day + + + align:start position:0% +30th floor and it was a windy winter day +and sure enough there was somebody there + + align:start position:0% +and sure enough there was somebody there + + + align:start position:0% +and sure enough there was somebody there +you know pulling up the thing you know + + align:start position:0% +you know pulling up the thing you know + + + align:start position:0% +you know pulling up the thing you know +cleaning the window and looked happy as + + align:start position:0% +cleaning the window and looked happy as + + + align:start position:0% +cleaning the window and looked happy as +can be you know no problem and I was + + align:start position:0% +can be you know no problem and I was + + + align:start position:0% +can be you know no problem and I was +thinking boy this this guy's taking a + + align:start position:0% +thinking boy this this guy's taking a + + + align:start position:0% +thinking boy this this guy's taking a +lot of risk you know and I hope he's + + align:start position:0% +lot of risk you know and I hope he's + + + align:start position:0% +lot of risk you know and I hope he's +getting paid for it um and you know it's + + align:start position:0% +getting paid for it um and you know it's + + + align:start position:0% +getting paid for it um and you know it's +that these these salaries are determined + + align:start position:0% +that these these salaries are determined + + + align:start position:0% +that these these salaries are determined +by supply and demand so what do you + + align:start position:0% +by supply and demand so what do you + + + align:start position:0% +by supply and demand so what do you +think it would be anybody have a guess + + align:start position:0% +think it would be anybody have a guess + + + align:start position:0% +think it would be anybody have a guess +yeah about 70,000 + + align:start position:0% +yeah about 70,000 + + + align:start position:0% +yeah about 70,000 +$70,000 okay anybody else + + align:start position:0% +$70,000 okay anybody else + + + align:start position:0% +$70,000 okay anybody else +Justin + + align:start position:0% +Justin + + + align:start position:0% +Justin +125 that's higher than some NBA starting + + align:start position:0% +125 that's higher than some NBA starting + + + align:start position:0% +125 that's higher than some NBA starting +salar okay + + align:start position:0% +salar okay + + + align:start position:0% +salar okay +Leah 30,000 do they take interest + + align:start position:0% +Leah 30,000 do they take interest + + + align:start position:0% +Leah 30,000 do they take interest +Insurance interns interns I don't know + + align:start position:0% +Insurance interns interns I don't know + + + align:start position:0% +Insurance interns interns I don't know +about that + + align:start position:0% +about that + + + align:start position:0% +about that +well so when I looked last time which + + align:start position:0% +well so when I looked last time which + + + align:start position:0% +well so when I looked last time which +was about four years ago it turns out + + align:start position:0% +was about four years ago it turns out + + + align:start position:0% +was about four years ago it turns out +that the typical window washer uh for + + align:start position:0% +that the typical window washer uh for + + + align:start position:0% +that the typical window washer uh for +these skyscrapers get paid about $60,000 + + align:start position:0% +these skyscrapers get paid about $60,000 + + + align:start position:0% +these skyscrapers get paid about $60,000 +a year annual salary $660,000 + + align:start position:0% +a year annual salary $660,000 + + + align:start position:0% +a year annual salary $660,000 +now you know I don't know I don't know + + align:start position:0% +now you know I don't know I don't know + + + align:start position:0% +now you know I don't know I don't know +whether you think that's a lot or a + + align:start position:0% +whether you think that's a lot or a + + + align:start position:0% +whether you think that's a lot or a +little but seems to me that uh you know + + align:start position:0% +little but seems to me that uh you know + + + align:start position:0% +little but seems to me that uh you know +that compensation reflects the kind of + + align:start position:0% +that compensation reflects the kind of + + + align:start position:0% +that compensation reflects the kind of +risk that we're talking about okay and + + align:start position:0% +risk that we're talking about okay and + + + align:start position:0% +risk that we're talking about okay and +you know you have no educational + + align:start position:0% +you know you have no educational + + + align:start position:0% +you know you have no educational +requirement ments no no degrees no + + align:start position:0% +requirement ments no no degrees no + + + align:start position:0% +requirement ments no no degrees no +certifications you just show up and you + + align:start position:0% +certifications you just show up and you + + + align:start position:0% +certifications you just show up and you +know up you + + align:start position:0% +know up you + + + align:start position:0% +know up you +go now let me ask you a question suppose + + align:start position:0% +go now let me ask you a question suppose + + + align:start position:0% +go now let me ask you a question suppose +that + + align:start position:0% +that + + + align:start position:0% +that +uh a window washer comes to the job who + + align:start position:0% +uh a window washer comes to the job who + + + align:start position:0% +uh a window washer comes to the job who +happens to really enjoy dancing while he + + align:start position:0% +happens to really enjoy dancing while he + + + align:start position:0% +happens to really enjoy dancing while he +washes windows in particular he dances + + align:start position:0% +washes windows in particular he dances + + + align:start position:0% +washes windows in particular he dances +that you know the Irish jig or whatever + + align:start position:0% +that you know the Irish jig or whatever + + + align:start position:0% +that you know the Irish jig or whatever +the uh you know the uh you know what I'm + + align:start position:0% +the uh you know the uh you know what I'm + + + align:start position:0% +the uh you know the uh you know what I'm +talking about that you know that dancing + + align:start position:0% +talking about that you know that dancing + + + align:start position:0% +talking about that you know that dancing +they're very you know and he just likes + + align:start position:0% +they're very you know and he just likes + + + align:start position:0% +they're very you know and he just likes +to do that while he's washing windows on + + align:start position:0% +to do that while he's washing windows on + + + align:start position:0% +to do that while he's washing windows on +the 40th + + align:start position:0% +the 40th + + + align:start position:0% +the 40th +floor you you agree that that's more + + align:start position:0% +floor you you agree that that's more + + + align:start position:0% +floor you you agree that that's more +risky right do you think that that + + align:start position:0% +risky right do you think that that + + + align:start position:0% +risky right do you think that that +particular individual gets paid more + + align:start position:0% +particular individual gets paid more + + + align:start position:0% +particular individual gets paid more +than 60,000 a + + align:start position:0% +than 60,000 a + + + align:start position:0% +than 60,000 a +year why he's taking more + + align:start position:0% +year why he's taking more + + + align:start position:0% +year why he's taking more +risk why not why is he get to pay + + align:start position:0% + + + + align:start position:0% + +more exactly he doesn't have to take + + align:start position:0% +more exactly he doesn't have to take + + + align:start position:0% +more exactly he doesn't have to take +that risk that's not part of the job he + + align:start position:0% +that risk that's not part of the job he + + + align:start position:0% +that risk that's not part of the job he +can choose to take that risk but he's + + align:start position:0% +can choose to take that risk but he's + + + align:start position:0% +can choose to take that risk but he's +not going to get compensated for it + + align:start position:0% +not going to get compensated for it + + + align:start position:0% +not going to get compensated for it +because it's not necessary and there are + + align:start position:0% +because it's not necessary and there are + + + align:start position:0% +because it's not necessary and there are +a 100,000 people behind him waiting in + + align:start position:0% +a 100,000 people behind him waiting in + + + align:start position:0% +a 100,000 people behind him waiting in +line to get that job that won't + + align:start position:0% +line to get that job that won't + + + align:start position:0% +line to get that job that won't +necessarily need to take that risk yeah + + align:start position:0% +necessarily need to take that risk yeah + + + align:start position:0% +necessarily need to take that risk yeah +I thought of it differently um so like + + align:start position:0% +I thought of it differently um so like + + + align:start position:0% +I thought of it differently um so like +if you had a long short portfolio would + + align:start position:0% +if you had a long short portfolio would + + + align:start position:0% +if you had a long short portfolio would +it be the other way around because you + + align:start position:0% +it be the other way around because you + + + align:start position:0% +it be the other way around because you +wouldn't care about the market risk you + + align:start position:0% +wouldn't care about the market risk you + + + align:start position:0% +wouldn't care about the market risk you +can hedge that out you're thinking only + + align:start position:0% +can hedge that out you're thinking only + + + align:start position:0% +can hedge that out you're thinking only +about the specific risk so like in that + + align:start position:0% +about the specific risk so like in that + + + align:start position:0% +about the specific risk so like in that +case I would short the guy who likes The + + align:start position:0% +case I would short the guy who likes The + + + align:start position:0% +case I would short the guy who likes The +Jig and I would invest in the guy who + + align:start position:0% +Jig and I would invest in the guy who + + + align:start position:0% +Jig and I would invest in the guy who +didn't well that depends on whether or + + align:start position:0% +didn't well that depends on whether or + + + align:start position:0% +didn't well that depends on whether or +not you know doing the Irish jig + + align:start position:0% +not you know doing the Irish jig + + + align:start position:0% +not you know doing the Irish jig +actually makes you wash windows better + + align:start position:0% +actually makes you wash windows better + + + align:start position:0% +actually makes you wash windows better +or worse in other words where there's an + + align:start position:0% +or worse in other words where there's an + + + align:start position:0% +or worse in other words where there's an +alpha to that risk all right it may be + + align:start position:0% +alpha to that risk all right it may be + + + align:start position:0% +alpha to that risk all right it may be +the case that dancing the IR jig + + align:start position:0% +the case that dancing the IR jig + + + align:start position:0% +the case that dancing the IR jig +actually helps you scrape off dirt that + + align:start position:0% +actually helps you scrape off dirt that + + + align:start position:0% +actually helps you scrape off dirt that +much more effectively in which case you + + align:start position:0% +much more effectively in which case you + + + align:start position:0% +much more effectively in which case you +may not want to short him because then + + align:start position:0% +may not want to short him because then + + + align:start position:0% +may not want to short him because then +he will earn a premium in certain + + align:start position:0% +he will earn a premium in certain + + + align:start position:0% +he will earn a premium in certain +markets right those with lots of uh you + + align:start position:0% +markets right those with lots of uh you + + + align:start position:0% +markets right those with lots of uh you +know pigeon poop on the + + align:start position:0% +know pigeon poop on the + + + align:start position:0% +know pigeon poop on the +windows so we can get into this analogy + + align:start position:0% +windows so we can get into this analogy + + + align:start position:0% +windows so we can get into this analogy +more deeply than we should but the point + + align:start position:0% +more deeply than we should but the point + + + align:start position:0% +more deeply than we should but the point +is that when you think about the capm + + align:start position:0% +is that when you think about the capm + + + align:start position:0% +is that when you think about the capm +all it's saying is that you get what you + + align:start position:0% +all it's saying is that you get what you + + + align:start position:0% +all it's saying is that you get what you +pay for and you pay for what you get in + + align:start position:0% +pay for and you pay for what you get in + + + align:start position:0% +pay for and you pay for what you get in +other words if there's a certain amount + + align:start position:0% +other words if there's a certain amount + + + align:start position:0% +other words if there's a certain amount +of risk in a in a particular investment + + align:start position:0% +of risk in a in a particular investment + + + align:start position:0% +of risk in a in a particular investment +that that is risk that nobody can get + + align:start position:0% +that that is risk that nobody can get + + + align:start position:0% +that that is risk that nobody can get +rid of easily in other words you have to + + align:start position:0% +rid of easily in other words you have to + + + align:start position:0% +rid of easily in other words you have to +bear it then you have to pay for it + + align:start position:0% +bear it then you have to pay for it + + + align:start position:0% +bear it then you have to pay for it +because otherwise people aren't going to + + align:start position:0% +because otherwise people aren't going to + + + align:start position:0% +because otherwise people aren't going to +do it however if there's risk in a + + align:start position:0% +do it however if there's risk in a + + + align:start position:0% +do it however if there's risk in a +particular company that you don't have + + align:start position:0% +particular company that you don't have + + + align:start position:0% +particular company that you don't have +to pay for if if that you don't have to + + align:start position:0% +to pay for if if that you don't have to + + + align:start position:0% +to pay for if if that you don't have to +take then you don't have to pay for it + + align:start position:0% +take then you don't have to pay for it + + + align:start position:0% +take then you don't have to pay for it +that's all that the capm is saying beta + + align:start position:0% +that's all that the capm is saying beta + + + align:start position:0% +that's all that the capm is saying beta +is a measure of that hard little pellet + + align:start position:0% +is a measure of that hard little pellet + + + align:start position:0% +is a measure of that hard little pellet +of risk that you can't get rid of and + + align:start position:0% +of risk that you can't get rid of and + + + align:start position:0% +of risk that you can't get rid of and +the variance is the measure of the + + align:start position:0% +the variance is the measure of the + + + align:start position:0% +the variance is the measure of the +entire risk in a particular + + align:start position:0% +entire risk in a particular + + + align:start position:0% +entire risk in a particular +portfolio the only case where variance + + align:start position:0% +portfolio the only case where variance + + + align:start position:0% +portfolio the only case where variance +and beta are the + + align:start position:0% +and beta are the + + + align:start position:0% +and beta are the +same is for what kind of + + align:start position:0% +same is for what kind of + + + align:start position:0% +same is for what kind of +portfolio an efficient portfolio what is + + align:start position:0% +portfolio an efficient portfolio what is + + + align:start position:0% +portfolio an efficient portfolio what is +an efficient portfolio it's one that is + + align:start position:0% +an efficient portfolio it's one that is + + + align:start position:0% +an efficient portfolio it's one that is +already maximally Diversified by adding + + align:start position:0% +already maximally Diversified by adding + + + align:start position:0% +already maximally Diversified by adding +more Securities you are not going to do + + align:start position:0% +more Securities you are not going to do + + + align:start position:0% +more Securities you are not going to do +any better than that straight line right + + align:start position:0% +any better than that straight line right + + + align:start position:0% +any better than that straight line right +all of these + + align:start position:0% +all of these + + + align:start position:0% +all of these +portfolios have been completely + + align:start position:0% +portfolios have been completely + + + align:start position:0% +portfolios have been completely +Diversified how do I know that because + + align:start position:0% +Diversified how do I know that because + + + align:start position:0% +Diversified how do I know that because +you're at the tangency portfolio there + + align:start position:0% +you're at the tangency portfolio there + + + align:start position:0% +you're at the tangency portfolio there +is nowh to go in the northwest region + + align:start position:0% +is nowh to go in the northwest region + + + align:start position:0% +is nowh to go in the northwest region +off of that line so for all of these + + align:start position:0% +off of that line so for all of these + + + align:start position:0% +off of that line so for all of these +Securities the sigma and the beta are + + align:start position:0% +Securities the sigma and the beta are + + + align:start position:0% +Securities the sigma and the beta are +literally numerically identical because + + align:start position:0% +literally numerically identical because + + + align:start position:0% +literally numerically identical because +there is no more extra risk in the + + align:start position:0% +there is no more extra risk in the + + + align:start position:0% +there is no more extra risk in the +portfolio it's been Diversified away but + + align:start position:0% +portfolio it's been Diversified away but + + + align:start position:0% +portfolio it's been Diversified away but +for Gillette for Microsoft for IBM + + align:start position:0% +for Gillette for Microsoft for IBM + + + align:start position:0% +for Gillette for Microsoft for IBM +General Motors and Motorola each of + + align:start position:0% +General Motors and Motorola each of + + + align:start position:0% +General Motors and Motorola each of +these contain both beta risk and non + + align:start position:0% +these contain both beta risk and non + + + align:start position:0% +these contain both beta risk and non +beta risk the non-ba risk is that Iris + + align:start position:0% +beta risk the non-ba risk is that Iris + + + align:start position:0% +beta risk the non-ba risk is that Iris +jig that you don't have to do while + + align:start position:0% +jig that you don't have to do while + + + align:start position:0% +jig that you don't have to do while +you're washing windows and you're not + + align:start position:0% +you're washing windows and you're not + + + align:start position:0% +you're washing windows and you're not +going to get paid for I'm sorry to say + + align:start position:0% +going to get paid for I'm sorry to say + + + align:start position:0% +going to get paid for I'm sorry to say +so the relationship that you want to + + align:start position:0% +so the relationship that you want to + + + align:start position:0% +so the relationship that you want to +focus on is the capital asset pricing + + align:start position:0% +focus on is the capital asset pricing + + + align:start position:0% +focus on is the capital asset pricing +models security Market line measure the + + align:start position:0% +models security Market line measure the + + + align:start position:0% +models security Market line measure the +stuff that you're going to get paid for + + align:start position:0% +stuff that you're going to get paid for + + + align:start position:0% +stuff that you're going to get paid for +and this is what you're going to get + + align:start position:0% +and this is what you're going to get + + + align:start position:0% +and this is what you're going to get +paid for it okay + + align:start position:0% +paid for it okay + + + align:start position:0% +paid for it okay +yeah uh when you go back into of the + + align:start position:0% +yeah uh when you go back into of the + + + align:start position:0% +yeah uh when you go back into of the +real world include transaction costs how + + align:start position:0% +real world include transaction costs how + + + align:start position:0% +real world include transaction costs how +do they enter here well so there have + + align:start position:0% +do they enter here well so there have + + + align:start position:0% +do they enter here well so there have +been vers of the capm with transactions + + align:start position:0% +been vers of the capm with transactions + + + align:start position:0% +been vers of the capm with transactions +cost and it turns out that it doesn't + + align:start position:0% +cost and it turns out that it doesn't + + + align:start position:0% +cost and it turns out that it doesn't +change things too much if you impose + + align:start position:0% +change things too much if you impose + + + align:start position:0% +change things too much if you impose +transactions cost on all Securities uh + + align:start position:0% +transactions cost on all Securities uh + + + align:start position:0% +transactions cost on all Securities uh +you know and say that there's a + + align:start position:0% +you know and say that there's a + + + align:start position:0% +you know and say that there's a +percentage uh cost for going in and out + + align:start position:0% +percentage uh cost for going in and out + + + align:start position:0% +percentage uh cost for going in and out +you can derive a Neta fee transactions + + align:start position:0% +you can derive a Neta fee transactions + + + align:start position:0% +you can derive a Neta fee transactions +cost it won't affect the pricing + + align:start position:0% +cost it won't affect the pricing + + + align:start position:0% +cost it won't affect the pricing +necessarily what it will affect is the + + align:start position:0% +necessarily what it will affect is the + + + align:start position:0% +necessarily what it will affect is the +Dynamics the trading what it'll mean is + + align:start position:0% +Dynamics the trading what it'll mean is + + + align:start position:0% +Dynamics the trading what it'll mean is +that you will rebalance your portfolios + + align:start position:0% +that you will rebalance your portfolios + + + align:start position:0% +that you will rebalance your portfolios +less frequently than you otherwise might + + align:start position:0% +less frequently than you otherwise might + + + align:start position:0% +less frequently than you otherwise might +but there is still going to be a + + align:start position:0% +but there is still going to be a + + + align:start position:0% +but there is still going to be a +relationship between the net of fee uh + + align:start position:0% +relationship between the net of fee uh + + + align:start position:0% +relationship between the net of fee uh +transactions costs of these Securities + + align:start position:0% +transactions costs of these Securities + + + align:start position:0% +transactions costs of these Securities +so you can actually look at the + + align:start position:0% +so you can actually look at the + + + align:start position:0% +so you can actually look at the +transactions cost as a a way to deduct + + align:start position:0% +transactions cost as a a way to deduct + + + align:start position:0% +transactions cost as a a way to deduct +the expected rate of return from each of + + align:start position:0% +the expected rate of return from each of + + + align:start position:0% +the expected rate of return from each of +these + + align:start position:0% +these + + + align:start position:0% +these +Securities so transactions cost is not a + + align:start position:0% +Securities so transactions cost is not a + + + align:start position:0% +Securities so transactions cost is not a +big issue but there are other issues + + align:start position:0% +big issue but there are other issues + + + align:start position:0% +big issue but there are other issues +that I'll come to that will be a problem + + align:start position:0% +that I'll come to that will be a problem + + + align:start position:0% +that I'll come to that will be a problem +for + + align:start position:0% +for + + + align:start position:0% +for +this looking at this we understand that + + align:start position:0% +this looking at this we understand that + + + align:start position:0% +this looking at this we understand that +the best efficient my portfolio I can + + align:start position:0% +the best efficient my portfolio I can + + + align:start position:0% +the best efficient my portfolio I can +have is basically the index if I want to + + align:start position:0% +have is basically the index if I want to + + + align:start position:0% +have is basically the index if I want to +allocate my money globally yes should I + + align:start position:0% +allocate my money globally yes should I + + + align:start position:0% +allocate my money globally yes should I +buy index according to the market cap of + + align:start position:0% +buy index according to the market cap of + + + align:start position:0% +buy index according to the market cap of +the markets yeah this is the most + + align:start position:0% +the markets yeah this is the most + + + align:start position:0% +the markets yeah this is the most +efficient glal portfolio right so that's + + align:start position:0% +efficient glal portfolio right so that's + + + align:start position:0% +efficient glal portfolio right so that's +a great question and we actually have a + + align:start position:0% +a great question and we actually have a + + + align:start position:0% +a great question and we actually have a +separate course on international finance + + align:start position:0% +separate course on international finance + + + align:start position:0% +separate course on international finance +that deals just with those kind of + + align:start position:0% +that deals just with those kind of + + + align:start position:0% +that deals just with those kind of +issues because they're so tricky but + + align:start position:0% +issues because they're so tricky but + + + align:start position:0% +issues because they're so tricky but +I'll give you the short answer according + + align:start position:0% +I'll give you the short answer according + + + align:start position:0% +I'll give you the short answer according +to the theory this tangency portfolio is + + align:start position:0% +to the theory this tangency portfolio is + + + align:start position:0% +to the theory this tangency portfolio is +not just for the US Stock Market it + + align:start position:0% +not just for the US Stock Market it + + + align:start position:0% +not just for the US Stock Market it +should be for the world stock market + + align:start position:0% +should be for the world stock market + + + align:start position:0% +should be for the world stock market +exactly everything so this tangency + + align:start position:0% +exactly everything so this tangency + + + align:start position:0% +exactly everything so this tangency +portfolio should not be the S&P 500 or + + align:start position:0% +portfolio should not be the S&P 500 or + + + align:start position:0% +portfolio should not be the S&P 500 or +the Russell 2000 it should be the msci + + align:start position:0% +the Russell 2000 it should be the msci + + + align:start position:0% +the Russell 2000 it should be the msci +or epha index that has all of the Assets + + align:start position:0% +or epha index that has all of the Assets + + + align:start position:0% +or epha index that has all of the Assets +in the world weighted relative to their + + align:start position:0% +in the world weighted relative to their + + + align:start position:0% +in the world weighted relative to their +market cap in the particular currency of + + align:start position:0% +market cap in the particular currency of + + + align:start position:0% +market cap in the particular currency of +the investor that you're ha that you + + align:start position:0% +the investor that you're ha that you + + + align:start position:0% +the investor that you're ha that you +happen to be so if uh you're a US + + align:start position:0% +happen to be so if uh you're a US + + + align:start position:0% +happen to be so if uh you're a US +investor it'll be in dollars if you're a + + align:start position:0% +investor it'll be in dollars if you're a + + + align:start position:0% +investor it'll be in dollars if you're a +Brazilian investor it'll be in real + + align:start position:0% +Brazilian investor it'll be in real + + + align:start position:0% +Brazilian investor it'll be in real +it'll be in whatever currency you trade + + align:start position:0% +it'll be in whatever currency you trade + + + align:start position:0% +it'll be in whatever currency you trade +in but that + + align:start position:0% +in but that + + + align:start position:0% +in but that +presupposes that there's Capital Market + + align:start position:0% +presupposes that there's Capital Market + + + align:start position:0% +presupposes that there's Capital Market +inter migration throughout the world so + + align:start position:0% +inter migration throughout the world so + + + align:start position:0% +inter migration throughout the world so +in other words if I call this the world + + align:start position:0% +in other words if I call this the world + + + align:start position:0% +in other words if I call this the world +portfolio implicitly I'm assuming that + + align:start position:0% +portfolio implicitly I'm assuming that + + + align:start position:0% +portfolio implicitly I'm assuming that +you can you're free to trade stocks in + + align:start position:0% +you can you're free to trade stocks in + + + align:start position:0% +you can you're free to trade stocks in +any part of the world freely there's no + + align:start position:0% +any part of the world freely there's no + + + align:start position:0% +any part of the world freely there's no +barriers to trading and we know that + + align:start position:0% +barriers to trading and we know that + + + align:start position:0% +barriers to trading and we know that +that's not the case there are barriers + + align:start position:0% +that's not the case there are barriers + + + align:start position:0% +that's not the case there are barriers +in fact so what that means is the capm + + align:start position:0% +in fact so what that means is the capm + + + align:start position:0% +in fact so what that means is the capm +applied to International stocks is an + + align:start position:0% +applied to International stocks is an + + + align:start position:0% +applied to International stocks is an +approximation that may actually be worse + + align:start position:0% +approximation that may actually be worse + + + align:start position:0% +approximation that may actually be worse +than applying it country by country and + + align:start position:0% +than applying it country by country and + + + align:start position:0% +than applying it country by country and +then looking to see whether there are + + align:start position:0% +then looking to see whether there are + + + align:start position:0% +then looking to see whether there are +any kind of distances or discrepancies + + align:start position:0% +any kind of distances or discrepancies + + + align:start position:0% +any kind of distances or discrepancies +across those different countries but + + align:start position:0% +across those different countries but + + + align:start position:0% +across those different countries but +people have come up with International + + align:start position:0% +people have come up with International + + + align:start position:0% +people have come up with International +versions of the capm and they don't work + + align:start position:0% +versions of the capm and they don't work + + + align:start position:0% +versions of the capm and they don't work +very well at least they didn't as of 10 + + align:start position:0% +very well at least they didn't as of 10 + + + align:start position:0% +very well at least they didn't as of 10 +years ago within the last 10 years A lot + + align:start position:0% +years ago within the last 10 years A lot + + + align:start position:0% +years ago within the last 10 years A lot +has changed so it could be that Capital + + align:start position:0% +has changed so it could be that Capital + + + align:start position:0% +has changed so it could be that Capital +Market integration has made the world + + align:start position:0% +Market integration has made the world + + + align:start position:0% +Market integration has made the world +capm look a lot better uh in terms of + + align:start position:0% +capm look a lot better uh in terms of + + + align:start position:0% +capm look a lot better uh in terms of +the + + align:start position:0% +the + + + align:start position:0% +the +data okay other other + + align:start position:0% +data okay other other + + + align:start position:0% +data okay other other +questions all right so now um I'm going + + align:start position:0% +questions all right so now um I'm going + + + align:start position:0% +questions all right so now um I'm going +to talk about implementing it and we're + + align:start position:0% +to talk about implementing it and we're + + + align:start position:0% +to talk about implementing it and we're +going to deal with all of the the messy + + align:start position:0% +going to deal with all of the the messy + + + align:start position:0% +going to deal with all of the the messy +issues that I tried to put off uh a + + align:start position:0% +issues that I tried to put off uh a + + + align:start position:0% +issues that I tried to put off uh a +lecture ago how do you take this thing + + align:start position:0% +lecture ago how do you take this thing + + + align:start position:0% +lecture ago how do you take this thing +out for a spin well one thing you could + + align:start position:0% +out for a spin well one thing you could + + + align:start position:0% +out for a spin well one thing you could +do is to try to test the capm to see if + + align:start position:0% +do is to try to test the capm to see if + + + align:start position:0% +do is to try to test the capm to see if +it works and one way to test it is to + + align:start position:0% +it works and one way to test it is to + + + align:start position:0% +it works and one way to test it is to +ask the question if we assume that all + + align:start position:0% +ask the question if we assume that all + + + align:start position:0% +ask the question if we assume that all +Securities are priced according to this + + align:start position:0% +Securities are priced according to this + + + align:start position:0% +Securities are priced according to this +equation + + align:start position:0% +equation + + + align:start position:0% +equation +then another way to write the equation + + align:start position:0% +then another way to write the equation + + + align:start position:0% +then another way to write the equation +that doesn't rely on expected returns + + align:start position:0% +that doesn't rely on expected returns + + + align:start position:0% +that doesn't rely on expected returns +but REI relies on realized returns is to + + align:start position:0% +but REI relies on realized returns is to + + + align:start position:0% +but REI relies on realized returns is to +write it as a regression equation as you + + align:start position:0% +write it as a regression equation as you + + + align:start position:0% +write it as a regression equation as you +did in DMD right the regression equation + + align:start position:0% +did in DMD right the regression equation + + + align:start position:0% +did in DMD right the regression equation +is the return the actual realized + + align:start position:0% +is the return the actual realized + + + align:start position:0% +is the return the actual realized +return on security I is given by the + + align:start position:0% +return on security I is given by the + + + align:start position:0% +return on security I is given by the +risk-free rate plus beta times the + + align:start position:0% +risk-free rate plus beta times the + + + align:start position:0% +risk-free rate plus beta times the +realized return on the market minus the + + align:start position:0% +realized return on the market minus the + + + align:start position:0% +realized return on the market minus the +risk-free rate + + align:start position:0% +risk-free rate + + + align:start position:0% +risk-free rate +plus + + align:start position:0% +plus + + + align:start position:0% +plus +Epsilon Epsilon is + + align:start position:0% +Epsilon Epsilon is + + + align:start position:0% +Epsilon Epsilon is +the error term the disturbance the + + align:start position:0% +the error term the disturbance the + + + align:start position:0% +the error term the disturbance the +residual that is giving you the + + align:start position:0% +residual that is giving you the + + + align:start position:0% +residual that is giving you the +fluctuations around the expected value + + align:start position:0% +fluctuations around the expected value + + + align:start position:0% +fluctuations around the expected value +so when we remove the expected values + + align:start position:0% +so when we remove the expected values + + + align:start position:0% +so when we remove the expected values +from this equation we have to stick in + + align:start position:0% +from this equation we have to stick in + + + align:start position:0% +from this equation we have to stick in +this Epsilon term that sort of bounces + + align:start position:0% +this Epsilon term that sort of bounces + + + align:start position:0% +this Epsilon term that sort of bounces +around + + align:start position:0% +around + + + align:start position:0% +around +right by the way when you look at this + + align:start position:0% +right by the way when you look at this + + + align:start position:0% +right by the way when you look at this +equation you now have an explicit + + align:start position:0% +equation you now have an explicit + + + align:start position:0% +equation you now have an explicit +representation for systematic risk and + + align:start position:0% +representation for systematic risk and + + + align:start position:0% +representation for systematic risk and +idiosyn ratic risk right for a given + + align:start position:0% +idiosyn ratic risk right for a given + + + align:start position:0% +idiosyn ratic risk right for a given +return it's comprised of three pieces + + align:start position:0% +return it's comprised of three pieces + + + align:start position:0% +return it's comprised of three pieces +the risk-free + + align:start position:0% +the risk-free + + + align:start position:0% +the risk-free +rate beta times the market return that + + align:start position:0% +rate beta times the market return that + + + align:start position:0% +rate beta times the market return that +bounces + + align:start position:0% +bounces + + + align:start position:0% +bounces +around and this Epsilon is the Irish jig + + align:start position:0% +around and this Epsilon is the Irish jig + + + align:start position:0% +around and this Epsilon is the Irish jig +that is the idiosyncratic bouncing + + align:start position:0% +that is the idiosyncratic bouncing + + + align:start position:0% +that is the idiosyncratic bouncing +around that you don't get any reward for + + align:start position:0% +around that you don't get any reward for + + + align:start position:0% +around that you don't get any reward for +how do you know you don't get any reward + + align:start position:0% +how do you know you don't get any reward + + + align:start position:0% +how do you know you don't get any reward +for it because on average the expected + + align:start position:0% +for it because on average the expected + + + align:start position:0% +for it because on average the expected +value of this is equal to zero how do I + + align:start position:0% +value of this is equal to zero how do I + + + align:start position:0% +value of this is equal to zero how do I +know that by definition + + align:start position:0% +know that by definition + + + align:start position:0% +know that by definition +that's how I got from this equation down + + align:start position:0% +that's how I got from this equation down + + + align:start position:0% +that's how I got from this equation down +here if you take the expected value of + + align:start position:0% +here if you take the expected value of + + + align:start position:0% +here if you take the expected value of +this equation the only way that the + + align:start position:0% +this equation the only way that the + + + align:start position:0% +this equation the only way that the +expected value of this gives you this + + align:start position:0% +expected value of this gives you this + + + align:start position:0% +expected value of this gives you this +equation on the top is if that Epsilon + + align:start position:0% +equation on the top is if that Epsilon + + + align:start position:0% +equation on the top is if that Epsilon +has a zero mean so you don't get paid + + align:start position:0% +has a zero mean so you don't get paid + + + align:start position:0% +has a zero mean so you don't get paid +for bearing Epsilon + + align:start position:0% +for bearing Epsilon + + + align:start position:0% +for bearing Epsilon +risk it's there it's Def and for some + + align:start position:0% +risk it's there it's Def and for some + + + align:start position:0% +risk it's there it's Def and for some +stocks it's + + align:start position:0% +stocks it's + + + align:start position:0% +stocks it's +huge but you don't get paid for it + + align:start position:0% +huge but you don't get paid for it + + + align:start position:0% +huge but you don't get paid for it +because you don't have to bear it and + + align:start position:0% +because you don't have to bear it and + + + align:start position:0% +because you don't have to bear it and +the reason you don't have to bear it is + + align:start position:0% +the reason you don't have to bear it is + + + align:start position:0% +the reason you don't have to bear it is +if you take 50 of these stocks and stick + + align:start position:0% +if you take 50 of these stocks and stick + + + align:start position:0% +if you take 50 of these stocks and stick +them in a portfolio the epsilons average + + align:start position:0% +them in a portfolio the epsilons average + + + align:start position:0% +them in a portfolio the epsilons average +out to zero how do I know that well this + + align:start position:0% +out to zero how do I know that well this + + + align:start position:0% +out to zero how do I know that well this +relies on a piece of mathematics that's + + align:start position:0% +relies on a piece of mathematics that's + + + align:start position:0% +relies on a piece of mathematics that's +known as the law of large numbers you + + align:start position:0% +known as the law of large numbers you + + + align:start position:0% +known as the law of large numbers you +may have heard that term used in casual + + align:start position:0% +may have heard that term used in casual + + + align:start position:0% +may have heard that term used in casual +conversation but it's actually a real + + align:start position:0% +conversation but it's actually a real + + + align:start position:0% +conversation but it's actually a real +theorem what it says is that when you + + align:start position:0% +theorem what it says is that when you + + + align:start position:0% +theorem what it says is that when you +have large large numbers of fluctuations + + align:start position:0% +have large large numbers of fluctuations + + + align:start position:0% +have large large numbers of fluctuations +that are not correlated with each other + + align:start position:0% +that are not correlated with each other + + + align:start position:0% +that are not correlated with each other +and by definition idiosyncratic risks + + align:start position:0% +and by definition idiosyncratic risks + + + align:start position:0% +and by definition idiosyncratic risks +for Gillette and Microsoft and other + + align:start position:0% +for Gillette and Microsoft and other + + + align:start position:0% +for Gillette and Microsoft and other +companies are not correlated because + + align:start position:0% +companies are not correlated because + + + align:start position:0% +companies are not correlated because +they're idiosyncratic they're unique to + + align:start position:0% +they're idiosyncratic they're unique to + + + align:start position:0% +they're idiosyncratic they're unique to +those firms that when you get a large + + align:start position:0% +those firms that when you get a large + + + align:start position:0% +those firms that when you get a large +number of these uncorrelated + + align:start position:0% +number of these uncorrelated + + + align:start position:0% +number of these uncorrelated +fluctuations that in the limit they + + align:start position:0% +fluctuations that in the limit they + + + align:start position:0% +fluctuations that in the limit they +actually go to zero you can disregard + + align:start position:0% +actually go to zero you can disregard + + + align:start position:0% +actually go to zero you can disregard +them okay so the law of large numbers is + + align:start position:0% +them okay so the law of large numbers is + + + align:start position:0% +them okay so the law of large numbers is +what tells you that this idiosyncratic + + align:start position:0% +what tells you that this idiosyncratic + + + align:start position:0% +what tells you that this idiosyncratic +risk is not going to be something you + + align:start position:0% +risk is not going to be something you + + + align:start position:0% +risk is not going to be something you +will get paid for okay so this is the + + align:start position:0% +will get paid for okay so this is the + + + align:start position:0% +will get paid for okay so this is the +capm relationship using actual data and + + align:start position:0% +capm relationship using actual data and + + + align:start position:0% +capm relationship using actual data and +if we stick in an alpha term to + + align:start position:0% +if we stick in an alpha term to + + + align:start position:0% +if we stick in an alpha term to +represent deviations from the cap M and + + align:start position:0% +represent deviations from the cap M and + + + align:start position:0% +represent deviations from the cap M and +I subtract the free rate from both sides + + align:start position:0% +I subtract the free rate from both sides + + + align:start position:0% +I subtract the free rate from both sides +just to have everything in excess + + align:start position:0% +just to have everything in excess + + + align:start position:0% +just to have everything in excess +returns then the capm reduces to the + + align:start position:0% +returns then the capm reduces to the + + + align:start position:0% +returns then the capm reduces to the +hypothesis that the alpha across all + + align:start position:0% +hypothesis that the alpha across all + + + align:start position:0% +hypothesis that the alpha across all +stocks all managers all projects the + + align:start position:0% +stocks all managers all projects the + + + align:start position:0% +stocks all managers all projects the +alpha is equal to + + align:start position:0% +alpha is equal to + + + align:start position:0% +alpha is equal to +zero that's what the capb + + align:start position:0% +zero that's what the capb + + + align:start position:0% +zero that's what the capb +says and if you want to formulate it + + align:start position:0% +says and if you want to formulate it + + + align:start position:0% +says and if you want to formulate it +strictly in terms of uh total rates of + + align:start position:0% +strictly in terms of uh total rates of + + + align:start position:0% +strictly in terms of uh total rates of +return it says that the alpha has to be + + align:start position:0% +return it says that the alpha has to be + + + align:start position:0% +return it says that the alpha has to be +equal to the risk-free rate Time 1 us + + align:start position:0% +equal to the risk-free rate Time 1 us + + + align:start position:0% +equal to the risk-free rate Time 1 us +beta this is a different Alpha than this + + align:start position:0% +beta this is a different Alpha than this + + + align:start position:0% +beta this is a different Alpha than this +Alpha this Alpha represents the excess + + align:start position:0% +Alpha this Alpha represents the excess + + + align:start position:0% +Alpha this Alpha represents the excess +rate of + + align:start position:0% +rate of + + + align:start position:0% +rate of +right okay so let's uh let's do it let's + + align:start position:0% +right okay so let's uh let's do it let's + + + align:start position:0% +right okay so let's uh let's do it let's +let's see whether or not it's true let's + + align:start position:0% +let's see whether or not it's true let's + + + align:start position:0% +let's see whether or not it's true let's +take a bunch of stocks subtract the + + align:start position:0% +take a bunch of stocks subtract the + + + align:start position:0% +take a bunch of stocks subtract the +risk-free rate from the stock returns + + align:start position:0% +risk-free rate from the stock returns + + + align:start position:0% +risk-free rate from the stock returns +run a regression of that Stock's return + + align:start position:0% +run a regression of that Stock's return + + + align:start position:0% +run a regression of that Stock's return +on a constant and the market excess + + align:start position:0% +on a constant and the market excess + + + align:start position:0% +on a constant and the market excess +return and let's see whether the + + align:start position:0% +return and let's see whether the + + + align:start position:0% +return and let's see whether the +intercept is equal to zero + + align:start position:0% +intercept is equal to zero + + + align:start position:0% +intercept is equal to zero +well if you do this for two stocks + + align:start position:0% +well if you do this for two stocks + + + align:start position:0% +well if you do this for two stocks +Biogen and Motorola I've done this from + + align:start position:0% +Biogen and Motorola I've done this from + + + align:start position:0% +Biogen and Motorola I've done this from +uh 1988 to uh the I think + + align:start position:0% +uh 1988 to uh the I think + + + align:start position:0% +uh 1988 to uh the I think +2006 um when you run that + + align:start position:0% +2006 um when you run that + + + align:start position:0% +2006 um when you run that +regression here's what you get for + + align:start position:0% +regression here's what you get for + + + align:start position:0% +regression here's what you get for +Biogen the beta is + + align:start position:0% +Biogen the beta is + + + align:start position:0% +Biogen the beta is +1.43 the + + align:start position:0% +1.43 the + + + align:start position:0% +1.43 the +intercept + + align:start position:0% +intercept + + + align:start position:0% +intercept +1.61% and the standard error is 1.1% and + + align:start position:0% +1.61% and the standard error is 1.1% and + + + align:start position:0% +1.61% and the standard error is 1.1% and +then RF * 1 minus beta is - + + align:start position:0% +then RF * 1 minus beta is - + + + align:start position:0% +then RF * 1 minus beta is - +2.1% this should be equal to the alpha + + align:start position:0% +2.1% this should be equal to the alpha + + + align:start position:0% +2.1% this should be equal to the alpha +uh in that previous uh equation that I + + align:start position:0% +uh in that previous uh equation that I + + + align:start position:0% +uh in that previous uh equation that I +gave you okay so in other words the + + align:start position:0% +gave you okay so in other words the + + + align:start position:0% +gave you okay so in other words the +alpha that we've estimated for a Biogen + + align:start position:0% +alpha that we've estimated for a Biogen + + + align:start position:0% +alpha that we've estimated for a Biogen +using this capm regression is + + align:start position:0% +using this capm regression is + + + align:start position:0% +using this capm regression is +3.77% or on a monthly basis 45% + + align:start position:0% +3.77% or on a monthly basis 45% + + + align:start position:0% +3.77% or on a monthly basis 45% +Alpha by Biogen is an incredibly good + + align:start position:0% +Alpha by Biogen is an incredibly good + + + align:start position:0% +Alpha by Biogen is an incredibly good +buy according to the capm if you believe + + align:start position:0% +buy according to the capm if you believe + + + align:start position:0% +buy according to the capm if you believe +the capm all right now that's Biogen + + align:start position:0% +the capm all right now that's Biogen + + + align:start position:0% +the capm all right now that's Biogen +what about Motorola during the same + + align:start position:0% +what about Motorola during the same + + + align:start position:0% +what about Motorola during the same +period when you estimate Motorola it's + + align:start position:0% +period when you estimate Motorola it's + + + align:start position:0% +period when you estimate Motorola it's +got a beta of + + align:start position:0% +got a beta of + + + align:start position:0% +got a beta of +1.42 and we're estimating an alpha not + + align:start position:0% +1.42 and we're estimating an alpha not + + + align:start position:0% +1.42 and we're estimating an alpha not +quite as big but + + align:start position:0% +quite as big but + + + align:start position:0% +quite as big but +23.5% on an annualized basis that's + + align:start position:0% +23.5% on an annualized basis that's + + + align:start position:0% +23.5% on an annualized basis that's +still pretty + + align:start position:0% +still pretty + + + align:start position:0% +still pretty +big so if you run this regression and + + align:start position:0% +big so if you run this regression and + + + align:start position:0% +big so if you run this regression and +analyze it this is what you would + + align:start position:0% +analyze it this is what you would + + + align:start position:0% +analyze it this is what you would +conclude that um these two stocks are + + align:start position:0% +conclude that um these two stocks are + + + align:start position:0% +conclude that um these two stocks are +wonderful buys what we're going to talk + + align:start position:0% +wonderful buys what we're going to talk + + + align:start position:0% +wonderful buys what we're going to talk +about next time is whether this + + align:start position:0% +about next time is whether this + + + align:start position:0% +about next time is whether this +interpretation really makes sense or + + align:start position:0% +interpretation really makes sense or + + + align:start position:0% +interpretation really makes sense or +whether we've got some missing factors + + align:start position:0% +whether we've got some missing factors + + + align:start position:0% +whether we've got some missing factors +or whether we're measuring things + + align:start position:0% +or whether we're measuring things + + + align:start position:0% +or whether we're measuring things +improperly we're going to need to do a + + align:start position:0% +improperly we're going to need to do a + + + align:start position:0% +improperly we're going to need to do a +bit more work but we're very close to + + align:start position:0% +bit more work but we're very close to + + + align:start position:0% +bit more work but we're very close to +being able to figure out exactly how all + + align:start position:0% +being able to figure out exactly how all + + + align:start position:0% +being able to figure out exactly how all +of these pricing models work in tandem + + align:start position:0% +of these pricing models work in tandem + + + align:start position:0% +of these pricing models work in tandem +with the kinds of uh risk budgeting + + align:start position:0% +with the kinds of uh risk budgeting + + + align:start position:0% +with the kinds of uh risk budgeting +calculations that we're going to need to + + align:start position:0% +calculations that we're going to need to + + + align:start position:0% +calculations that we're going to need to +do for the rest of the course so see you + + align:start position:0% +do for the rest of the course so see you + + + align:start position:0% +do for the rest of the course so see you +on Monday \ No newline at end of file diff --git a/NE2UztTuZ8A.txt b/NE2UztTuZ8A.txt new file mode 100644 index 0000000000000000000000000000000000000000..ff6555d7ea407518e47b546dafa829f24c780e79 --- /dev/null +++ b/NE2UztTuZ8A.txt @@ -0,0 +1,14115 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu hello everyone and good + + align:start position:0% +ocw.mit.edu hello everyone and good + + + align:start position:0% +ocw.mit.edu hello everyone and good +afternoon + + align:start position:0% + + + + align:start position:0% + +thank you for coming to our third forum + + align:start position:0% +thank you for coming to our third forum + + + align:start position:0% +thank you for coming to our third forum +and concert I hope within our winter + + align:start position:0% +and concert I hope within our winter + + + align:start position:0% +and concert I hope within our winter +festival series uh it's a pleasure to + + align:start position:0% +festival series uh it's a pleasure to + + + align:start position:0% +festival series uh it's a pleasure to +see so many of you who've been here + + align:start position:0% +see so many of you who've been here + + + align:start position:0% +see so many of you who've been here +before and we hope to do this again + + align:start position:0% +before and we hope to do this again + + + align:start position:0% +before and we hope to do this again +sometime + + align:start position:0% +sometime + + + align:start position:0% +sometime +um I would like to uh introduce our + + align:start position:0% +um I would like to uh introduce our + + + align:start position:0% +um I would like to uh introduce our +moderator for today she is Ellen Harris + + align:start position:0% +moderator for today she is Ellen Harris + + + align:start position:0% +moderator for today she is Ellen Harris +the class of 49 professor of Music in + + align:start position:0% +the class of 49 professor of Music in + + + align:start position:0% +the class of 49 professor of Music in +our music and theater Department thank + + align:start position:0% +our music and theater Department thank + + + align:start position:0% +our music and theater Department thank +you very + + align:start position:0% + + + + align:start position:0% + +much welcome + + align:start position:0% +much welcome + + + align:start position:0% +much welcome +welcome yes yes uh welcome to the final + + align:start position:0% +welcome yes yes uh welcome to the final + + + align:start position:0% +welcome yes yes uh welcome to the final +forum in the winter festival on musical + + align:start position:0% +forum in the winter festival on musical + + + align:start position:0% +forum in the winter festival on musical +time sponsored by the Boston chamber + + align:start position:0% +time sponsored by the Boston chamber + + + align:start position:0% +time sponsored by the Boston chamber +music society and the faculty of music + + align:start position:0% +music society and the faculty of music + + + align:start position:0% +music society and the faculty of music +and Theater Arts at MIT I want to say + + align:start position:0% +and Theater Arts at MIT I want to say + + + align:start position:0% +and Theater Arts at MIT I want to say +thank you to our funders without whom of + + align:start position:0% +thank you to our funders without whom of + + + align:start position:0% +thank you to our funders without whom of +course this would not have been possible + + align:start position:0% +course this would not have been possible + + + align:start position:0% +course this would not have been possible +to the Nea program on American + + align:start position:0% +to the Nea program on American + + + align:start position:0% +to the Nea program on American +masterpieces the Massachusetts + + align:start position:0% +masterpieces the Massachusetts + + + align:start position:0% +masterpieces the Massachusetts +Humanities Council and the council for + + align:start position:0% +Humanities Council and the council for + + + align:start position:0% +Humanities Council and the council for +the Arts at MIT you if you've been here + + align:start position:0% +the Arts at MIT you if you've been here + + + align:start position:0% +the Arts at MIT you if you've been here +before you will know that at the end of + + align:start position:0% +before you will know that at the end of + + + align:start position:0% +before you will know that at the end of +The Forum that they pass out you will + + align:start position:0% +The Forum that they pass out you will + + + align:start position:0% +The Forum that they pass out you will +have for uh forms handed out to you to + + align:start position:0% +have for uh forms handed out to you to + + + align:start position:0% +have for uh forms handed out to you to +fill out which go back to the mass + + align:start position:0% +fill out which go back to the mass + + + align:start position:0% +fill out which go back to the mass +Council on the Arts and uh especially if + + align:start position:0% +Council on the Arts and uh especially if + + + align:start position:0% +Council on the Arts and uh especially if +you think that this is a good use of + + align:start position:0% +you think that this is a good use of + + + align:start position:0% +you think that this is a good use of +your tax dollars please fill it out + + align:start position:0% +your tax dollars please fill it out + + + align:start position:0% +your tax dollars please fill it out +that's one of the questions actually + + align:start position:0% +that's one of the questions actually + + + align:start position:0% +that's one of the questions actually +it's why I say uh the previous panels + + align:start position:0% +it's why I say uh the previous panels + + + align:start position:0% +it's why I say uh the previous panels +have been on time as shape and time as + + align:start position:0% +have been on time as shape and time as + + + align:start position:0% +have been on time as shape and time as +memory and today we're going to be + + align:start position:0% +memory and today we're going to be + + + align:start position:0% +memory and today we're going to be +talking about time as the subject and + + align:start position:0% +talking about time as the subject and + + + align:start position:0% +talking about time as the subject and +substance of Art and we have uh together + + align:start position:0% +substance of Art and we have uh together + + + align:start position:0% +substance of Art and we have uh together +we have uh three panelists in addition + + align:start position:0% +we have uh three panelists in addition + + + align:start position:0% +we have uh three panelists in addition +to me and let me introduce them to you + + align:start position:0% +to me and let me introduce them to you + + + align:start position:0% +to me and let me introduce them to you +first on my right LS Lockwood professor + + align:start position:0% +first on my right LS Lockwood professor + + + align:start position:0% +first on my right LS Lockwood professor +ameritus of Music at Harvard University + + align:start position:0% +ameritus of Music at Harvard University + + + align:start position:0% +ameritus of Music at Harvard University +and a renowned Authority on both music + + align:start position:0% +and a renowned Authority on both music + + + align:start position:0% +and a renowned Authority on both music +of the Renaissance and on Beethoven his + + align:start position:0% +of the Renaissance and on Beethoven his + + + align:start position:0% +of the Renaissance and on Beethoven his +pathbreaking book on music in + + align:start position:0% +pathbreaking book on music in + + + align:start position:0% +pathbreaking book on music in +Renaissance fora 1400 to 155 was + + align:start position:0% +Renaissance fora 1400 to 155 was + + + align:start position:0% +Renaissance fora 1400 to 155 was +published in + + align:start position:0% +published in + + + align:start position:0% +published in +1984 and was released last year 2009 in + + align:start position:0% +1984 and was released last year 2009 in + + + align:start position:0% +1984 and was released last year 2009 in +paperback the longevity of this book + + align:start position:0% +paperback the longevity of this book + + + align:start position:0% +paperback the longevity of this book +giving an indication of its important to + + align:start position:0% +giving an indication of its important to + + + align:start position:0% +giving an indication of its important to +schol of its importance to scholarship + + align:start position:0% +schol of its importance to scholarship + + + align:start position:0% +schol of its importance to scholarship +probably many of you are more familiar + + align:start position:0% +probably many of you are more familiar + + + align:start position:0% +probably many of you are more familiar +with his more recent Publications on + + align:start position:0% +with his more recent Publications on + + + align:start position:0% +with his more recent Publications on +Beethoven Beethoven the music and the + + align:start position:0% +Beethoven Beethoven the music and the + + + align:start position:0% +Beethoven Beethoven the music and the +life which was a pullit surprise + + align:start position:0% +life which was a pullit surprise + + + align:start position:0% +life which was a pullit surprise +finalist in 2003 and inside Beethoven's + + align:start position:0% +finalist in 2003 and inside Beethoven's + + + align:start position:0% +finalist in 2003 and inside Beethoven's +quartets in 2009 which he co- which he + + align:start position:0% +quartets in 2009 which he co- which he + + + align:start position:0% +quartets in 2009 which he co- which he +co-authored with the juliard + + align:start position:0% +co-authored with the juliard + + + align:start position:0% +co-authored with the juliard +portet today he will be speaking on the + + align:start position:0% +portet today he will be speaking on the + + + align:start position:0% +portet today he will be speaking on the +development of the metronome and its + + align:start position:0% +development of the metronome and its + + + align:start position:0% +development of the metronome and its +impact on Beethoven I'm going to do all + + align:start position:0% +impact on Beethoven I'm going to do all + + + align:start position:0% +impact on Beethoven I'm going to do all +the introductions uh sitting next to uh + + align:start position:0% +the introductions uh sitting next to uh + + + align:start position:0% +the introductions uh sitting next to uh +to Lewis is Steven Tapscott professor of + + align:start position:0% +to Lewis is Steven Tapscott professor of + + + align:start position:0% +to Lewis is Steven Tapscott professor of +literature at MIT poet and author of + + align:start position:0% +literature at MIT poet and author of + + + align:start position:0% +literature at MIT poet and author of +five books of poems among which his + + align:start position:0% +five books of poems among which his + + + align:start position:0% +five books of poems among which his +translations of Pablo nuda sonets 100 + + align:start position:0% +translations of Pablo nuda sonets 100 + + + align:start position:0% +translations of Pablo nuda sonets 100 +Love sonets is particularly well known + + align:start position:0% +Love sonets is particularly well known + + + align:start position:0% +Love sonets is particularly well known +back in 1991 when I was associate + + align:start position:0% +back in 1991 when I was associate + + + align:start position:0% +back in 1991 when I was associate +Provost for the Arts at MIT I + + align:start position:0% +Provost for the Arts at MIT I + + + align:start position:0% +Provost for the Arts at MIT I +commissioned Steve to write a poem for + + align:start position:0% +commissioned Steve to write a poem for + + + align:start position:0% +commissioned Steve to write a poem for +the inauguration of Chuck vest as + + align:start position:0% +the inauguration of Chuck vest as + + + align:start position:0% +the inauguration of Chuck vest as +president of Mi and his poem his poem of + + align:start position:0% +president of Mi and his poem his poem of + + + align:start position:0% +president of Mi and his poem his poem of +Welcome which he read at the + + align:start position:0% +Welcome which he read at the + + + align:start position:0% +Welcome which he read at the +inauguration ceremony stole the + + align:start position:0% +inauguration ceremony stole the + + + align:start position:0% +inauguration ceremony stole the +show and I suppose we are faced with the + + align:start position:0% +show and I suppose we are faced with the + + + align:start position:0% +show and I suppose we are faced with the +same threat + + align:start position:0% +same threat + + + align:start position:0% +same threat +today uh as he will be reading from his + + align:start position:0% +today uh as he will be reading from his + + + align:start position:0% +today uh as he will be reading from his +newest collection a book of poems that + + align:start position:0% +newest collection a book of poems that + + + align:start position:0% +newest collection a book of poems that +he has completed on the 19th century + + align:start position:0% +he has completed on the 19th century + + + align:start position:0% +he has completed on the 19th century +Pioneer of stop time photography Edward + + align:start position:0% +Pioneer of stop time photography Edward + + + align:start position:0% +Pioneer of stop time photography Edward +mbridge + + align:start position:0% +mbridge + + + align:start position:0% +mbridge +and finally Paul matis artist and + + align:start position:0% +and finally Paul matis artist and + + + align:start position:0% +and finally Paul matis artist and +inventor one of whose abiding interests + + align:start position:0% +inventor one of whose abiding interests + + + align:start position:0% +inventor one of whose abiding interests +in the creation of his public art + + align:start position:0% +in the creation of his public art + + + align:start position:0% +in the creation of his public art +sculptures is the use of bells some of + + align:start position:0% +sculptures is the use of bells some of + + + align:start position:0% +sculptures is the use of bells some of +which he will be talking about + + align:start position:0% +which he will be talking about + + + align:start position:0% +which he will be talking about +today I think he may be best known in + + align:start position:0% +today I think he may be best known in + + + align:start position:0% +today I think he may be best known in +Cambridge for the Kendall band which is + + align:start position:0% +Cambridge for the Kendall band which is + + + align:start position:0% +Cambridge for the Kendall band which is +his sculpture in the Kendall Square t- + + align:start position:0% +his sculpture in the Kendall Square t- + + + align:start position:0% +his sculpture in the Kendall Square t- +stop which permits passengers waiting on + + align:start position:0% +stop which permits passengers waiting on + + + align:start position:0% +stop which permits passengers waiting on +the platform to buy their time by + + align:start position:0% +the platform to buy their time by + + + align:start position:0% +the platform to buy their time by +playing hand operated music sculptures + + align:start position:0% +playing hand operated music sculptures + + + align:start position:0% +playing hand operated music sculptures +including Chimes a Gong and what I would + + align:start position:0% +including Chimes a Gong and what I would + + + align:start position:0% +including Chimes a Gong and what I would +call a Thunders + + align:start position:0% +call a Thunders + + + align:start position:0% +call a Thunders +sheet uh alas rather overzealous or + + align:start position:0% +sheet uh alas rather overzealous or + + + align:start position:0% +sheet uh alas rather overzealous or +impatient commuters frequently fail to + + align:start position:0% +impatient commuters frequently fail to + + + align:start position:0% +impatient commuters frequently fail to +understand how these mechanisms work and + + align:start position:0% +understand how these mechanisms work and + + + align:start position:0% +understand how these mechanisms work and +as a result the handles have frequently + + align:start position:0% +as a result the handles have frequently + + + align:start position:0% +as a result the handles have frequently +broken and I'm happy to report that the + + align:start position:0% +broken and I'm happy to report that the + + + align:start position:0% +broken and I'm happy to report that the +music and Theater Arts at MIT in + + align:start position:0% +music and Theater Arts at MIT in + + + align:start position:0% +music and Theater Arts at MIT in +conjunction with engineering is now in + + align:start position:0% +conjunction with engineering is now in + + + align:start position:0% +conjunction with engineering is now in +the process of setting up a student + + align:start position:0% +the process of setting up a student + + + align:start position:0% +the process of setting up a student +Group which is called the Kendall band + + align:start position:0% +Group which is called the Kendall band + + + align:start position:0% +Group which is called the Kendall band +preservation + + align:start position:0% +preservation + + + align:start position:0% +preservation +society which sounds to me like a cross + + align:start position:0% +society which sounds to me like a cross + + + align:start position:0% +society which sounds to me like a cross +between a 19th century town band and the + + align:start position:0% +between a 19th century town band and the + + + align:start position:0% +between a 19th century town band and the +Salvation + + align:start position:0% +Salvation + + + align:start position:0% +Salvation +Army uh and the goal of the Kendall band + + align:start position:0% +Army uh and the goal of the Kendall band + + + align:start position:0% +Army uh and the goal of the Kendall band +preservation Society will be nothing + + align:start position:0% +preservation Society will be nothing + + + align:start position:0% +preservation Society will be nothing +less than to Monitor and maintain the + + align:start position:0% +less than to Monitor and maintain the + + + align:start position:0% +less than to Monitor and maintain the +Kendall band in the Kendall Square TV + + align:start position:0% +Kendall band in the Kendall Square TV + + + align:start position:0% +Kendall band in the Kendall Square TV +stop in + + align:start position:0% +stop in + + + align:start position:0% +stop in +perpetuity so we look forward to + + align:start position:0% + + + + align:start position:0% + +that the order of our speakers today is + + align:start position:0% +that the order of our speakers today is + + + align:start position:0% +that the order of our speakers today is +in a semblance of chronological order we + + align:start position:0% +in a semblance of chronological order we + + + align:start position:0% +in a semblance of chronological order we +will first have Lewis Lockwood bringing + + align:start position:0% +will first have Lewis Lockwood bringing + + + align:start position:0% +will first have Lewis Lockwood bringing +us out of the 18th century then we will + + align:start position:0% +us out of the 18th century then we will + + + align:start position:0% +us out of the 18th century then we will +have Steve tabscott immersing Us in the + + align:start position:0% +have Steve tabscott immersing Us in the + + + align:start position:0% +have Steve tabscott immersing Us in the +19th century Paul matis will take us + + align:start position:0% +19th century Paul matis will take us + + + align:start position:0% +19th century Paul matis will take us +through the 20th century and then I like + + align:start position:0% +through the 20th century and then I like + + + align:start position:0% +through the 20th century and then I like +to say I will talk about about the + + align:start position:0% +to say I will talk about about the + + + align:start position:0% +to say I will talk about about the +future because I'll be talking about the + + align:start position:0% +future because I'll be talking about the + + + align:start position:0% +future because I'll be talking about the +concert we'll hear after dinner thank + + align:start position:0% + + + + align:start position:0% + +you yes uh first may I ask can I be + + align:start position:0% +you yes uh first may I ask can I be + + + align:start position:0% +you yes uh first may I ask can I be +heard if I speak at this + + align:start position:0% +heard if I speak at this + + + align:start position:0% +heard if I speak at this +level thank you + + align:start position:0% +level thank you + + + align:start position:0% +level thank you +um I'd like to say first that um I'm + + align:start position:0% +um I'd like to say first that um I'm + + + align:start position:0% +um I'd like to say first that um I'm +going to play for you uh two contrasting + + align:start position:0% +going to play for you uh two contrasting + + + align:start position:0% +going to play for you uh two contrasting +excerpts of the same movement the first + + align:start position:0% +excerpts of the same movement the first + + + align:start position:0% +excerpts of the same movement the first +18 measures of the slow movement of + + align:start position:0% +18 measures of the slow movement of + + + align:start position:0% +18 measures of the slow movement of +Beethoven's Ninth Symphony and for this + + align:start position:0% +Beethoven's Ninth Symphony and for this + + + align:start position:0% +Beethoven's Ninth Symphony and for this +purpose to make the difference in + + align:start position:0% +purpose to make the difference in + + + align:start position:0% +purpose to make the difference in +interpretation as clear as could be I + + align:start position:0% +interpretation as clear as could be I + + + align:start position:0% +interpretation as clear as could be I +had a special disc made for the purpose + + align:start position:0% +had a special disc made for the purpose + + + align:start position:0% +had a special disc made for the purpose +which had recordings by two extremely + + align:start position:0% +which had recordings by two extremely + + + align:start position:0% +which had recordings by two extremely +different conductors with two extremely + + align:start position:0% +different conductors with two extremely + + + align:start position:0% +different conductors with two extremely +different approaches bhel F Wangler and + + align:start position:0% +different approaches bhel F Wangler and + + + align:start position:0% +different approaches bhel F Wangler and +Roger + + align:start position:0% +Roger + + + align:start position:0% +Roger +Norrington now in the abstract which my + + align:start position:0% +Norrington now in the abstract which my + + + align:start position:0% +Norrington now in the abstract which my +colleagues here kindly asked me to + + align:start position:0% +colleagues here kindly asked me to + + + align:start position:0% +colleagues here kindly asked me to +supply I offered some general remarks + + align:start position:0% +supply I offered some general remarks + + + align:start position:0% +supply I offered some general remarks +about music and time and you will find + + align:start position:0% +about music and time and you will find + + + align:start position:0% +about music and time and you will find +those somewhere in the in the program uh + + align:start position:0% +those somewhere in the in the program uh + + + align:start position:0% +those somewhere in the in the program uh +I certainly want to stand by them and + + align:start position:0% +I certainly want to stand by them and + + + align:start position:0% +I certainly want to stand by them and +one of the most important things I want + + align:start position:0% +one of the most important things I want + + + align:start position:0% +one of the most important things I want +to emphasize is the opaqueness of + + align:start position:0% +to emphasize is the opaqueness of + + + align:start position:0% +to emphasize is the opaqueness of +problem that we're dealing + + align:start position:0% +problem that we're dealing + + + align:start position:0% +problem that we're dealing +with my favorite remark on the entire + + align:start position:0% +with my favorite remark on the entire + + + align:start position:0% +with my favorite remark on the entire +subject of time is found in book 11 of + + align:start position:0% +subject of time is found in book 11 of + + + align:start position:0% +subject of time is found in book 11 of +the confessions of St Augustine probably + + align:start position:0% +the confessions of St Augustine probably + + + align:start position:0% +the confessions of St Augustine probably +known to many here + + align:start position:0% +known to many here + + + align:start position:0% +known to many here +in which he asks the question what is + + align:start position:0% +in which he asks the question what is + + + align:start position:0% +in which he asks the question what is +time now needless to say this extremely + + align:start position:0% +time now needless to say this extremely + + + align:start position:0% +time now needless to say this extremely +uh this religious Church Father believed + + align:start position:0% +uh this religious Church Father believed + + + align:start position:0% +uh this religious Church Father believed +the time was a creation of God uh a fact + + align:start position:0% +the time was a creation of God uh a fact + + + align:start position:0% +the time was a creation of God uh a fact +which is not open to uh controversion by + + align:start position:0% +which is not open to uh controversion by + + + align:start position:0% +which is not open to uh controversion by +me I can assure + + align:start position:0% +me I can assure + + + align:start position:0% +me I can assure +you but he wants to relate it to Human + + align:start position:0% +you but he wants to relate it to Human + + + align:start position:0% +you but he wants to relate it to Human +Experience so what St Augustine says + + align:start position:0% +Experience so what St Augustine says + + + align:start position:0% +Experience so what St Augustine says +about it in in a nutshell comes out + + align:start position:0% +about it in in a nutshell comes out + + + align:start position:0% +about it in in a nutshell comes out +something like this if someone asks me + + align:start position:0% +something like this if someone asks me + + + align:start position:0% +something like this if someone asks me +what time is I know + + align:start position:0% +what time is I know + + + align:start position:0% +what time is I know +but if I try to explain it to somebody + + align:start position:0% +but if I try to explain it to somebody + + + align:start position:0% +but if I try to explain it to somebody +else I don't I am not able to do so and + + align:start position:0% +else I don't I am not able to do so and + + + align:start position:0% +else I don't I am not able to do so and +this sense of the intuitive character of + + align:start position:0% +this sense of the intuitive character of + + + align:start position:0% +this sense of the intuitive character of +time in Human Experience absolutely + + align:start position:0% +time in Human Experience absolutely + + + align:start position:0% +time in Human Experience absolutely +underlies my feeling about how the + + align:start position:0% +underlies my feeling about how the + + + align:start position:0% +underlies my feeling about how the +larger issues of time and experience + + align:start position:0% +larger issues of time and experience + + + align:start position:0% +larger issues of time and experience +affect our perceptions of Music + + align:start position:0% +affect our perceptions of Music + + + align:start position:0% +affect our perceptions of Music +certainly serious music and music that + + align:start position:0% +certainly serious music and music that + + + align:start position:0% +certainly serious music and music that +makes demands upon our perceptions of a + + align:start position:0% +makes demands upon our perceptions of a + + + align:start position:0% +makes demands upon our perceptions of a +high order that is certainly the case + + align:start position:0% +high order that is certainly the case + + + align:start position:0% +high order that is certainly the case +with the music I'm dealing with today + + align:start position:0% +with the music I'm dealing with today + + + align:start position:0% +with the music I'm dealing with today +and in general the music uh we all deal + + align:start position:0% +and in general the music uh we all deal + + + align:start position:0% +and in general the music uh we all deal +with I think for the most + + align:start position:0% +with I think for the most + + + align:start position:0% +with I think for the most +part now the question of time in music + + align:start position:0% +part now the question of time in music + + + align:start position:0% +part now the question of time in music +is of such enormous scope that it has to + + align:start position:0% +is of such enormous scope that it has to + + + align:start position:0% +is of such enormous scope that it has to +be broken down to make sense and in my + + align:start position:0% +be broken down to make sense and in my + + + align:start position:0% +be broken down to make sense and in my +case what I'm principally going to talk + + align:start position:0% +case what I'm principally going to talk + + + align:start position:0% +case what I'm principally going to talk +about and illustrate for you for the + + align:start position:0% +about and illustrate for you for the + + + align:start position:0% +about and illustrate for you for the +next maybe 17 minutes to accommodate to + + align:start position:0% +next maybe 17 minutes to accommodate to + + + align:start position:0% +next maybe 17 minutes to accommodate to +my rigorous colleagues + + align:start position:0% +my rigorous colleagues + + + align:start position:0% +my rigorous colleagues +20 is the question of tempo and how + + align:start position:0% +20 is the question of tempo and how + + + align:start position:0% +20 is the question of tempo and how +Tempo was conceived and to some extent + + align:start position:0% +Tempo was conceived and to some extent + + + align:start position:0% +Tempo was conceived and to some extent +controlled in the classical Western + + align:start position:0% + + + + align:start position:0% + +tradition in Broad terms it the + + align:start position:0% +tradition in Broad terms it the + + + align:start position:0% +tradition in Broad terms it the +situation of tempo at the time of + + align:start position:0% +situation of tempo at the time of + + + align:start position:0% +situation of tempo at the time of +Beethoven's life and career looked + + align:start position:0% +Beethoven's life and career looked + + + align:start position:0% +Beethoven's life and career looked +something like this he's born into the + + align:start position:0% +something like this he's born into the + + + align:start position:0% +something like this he's born into the +late 18th century scene bovin was 10 + + align:start position:0% +late 18th century scene bovin was 10 + + + align:start position:0% +late 18th century scene bovin was 10 +years old in 1780 he was 20 years old in + + align:start position:0% +years old in 1780 he was 20 years old in + + + align:start position:0% +years old in 1780 he was 20 years old in +1791 when mozar died he is obviously the + + align:start position:0% +1791 when mozar died he is obviously the + + + align:start position:0% +1791 when mozar died he is obviously the +Contemporary of early Mo of in early + + align:start position:0% +Contemporary of early Mo of in early + + + align:start position:0% +Contemporary of early Mo of in early +years of mozard but only as a child and + + align:start position:0% +years of mozard but only as a child and + + + align:start position:0% +years of mozard but only as a child and +later the Contemporary of heyen much + + align:start position:0% +later the Contemporary of heyen much + + + align:start position:0% +later the Contemporary of heyen much +much older than he and of many other + + align:start position:0% +much older than he and of many other + + + align:start position:0% +much older than he and of many other +composers who are living through a + + align:start position:0% +composers who are living through a + + + align:start position:0% +composers who are living through a +period of enormous historical + + align:start position:0% +period of enormous historical + + + align:start position:0% +period of enormous historical +transformation I remind you to come to + + align:start position:0% +transformation I remind you to come to + + + align:start position:0% +transformation I remind you to come to +the end of my remarks just to Telegraph + + align:start position:0% +the end of my remarks just to Telegraph + + + align:start position:0% +the end of my remarks just to Telegraph +it we are dealing here not only with the + + align:start position:0% +it we are dealing here not only with the + + + align:start position:0% +it we are dealing here not only with the +period of the French Revolution and the + + align:start position:0% +period of the French Revolution and the + + + align:start position:0% +period of the French Revolution and the +vast political change of Europe and of + + align:start position:0% +vast political change of Europe and of + + + align:start position:0% +vast political change of Europe and of +the world but also with the industri + + align:start position:0% +the world but also with the industri + + + align:start position:0% +the world but also with the industri +oncoming Industrial Revolution the + + align:start position:0% +oncoming Industrial Revolution the + + + align:start position:0% +oncoming Industrial Revolution the +consequence es of both of these + + align:start position:0% +consequence es of both of these + + + align:start position:0% +consequence es of both of these +developments for the awareness of time + + align:start position:0% +developments for the awareness of time + + + align:start position:0% +developments for the awareness of time +is very much to think about with regard + + align:start position:0% +is very much to think about with regard + + + align:start position:0% +is very much to think about with regard +to how music was conceived and + + align:start position:0% +to how music was conceived and + + + align:start position:0% +to how music was conceived and +transmitted and received by audiences in + + align:start position:0% +transmitted and received by audiences in + + + align:start position:0% +transmitted and received by audiences in +this time but I'm considering here + + align:start position:0% +this time but I'm considering here + + + align:start position:0% +this time but I'm considering here +primarily at the production and a + + align:start position:0% +primarily at the production and a + + + align:start position:0% +primarily at the production and a +composer's way of dealing with Tempo and + + align:start position:0% +composer's way of dealing with Tempo and + + + align:start position:0% +composer's way of dealing with Tempo and +the + + align:start position:0% +the + + + align:start position:0% +the +time now devices for measuring Tempo in + + align:start position:0% +time now devices for measuring Tempo in + + + align:start position:0% +time now devices for measuring Tempo in +music had been oncoming for about about + + align:start position:0% +music had been oncoming for about about + + + align:start position:0% +music had been oncoming for about about +100 years gradually by the time the + + align:start position:0% +100 years gradually by the time the + + + align:start position:0% +100 years gradually by the time the +first chronometer was perfected just + + align:start position:0% +first chronometer was perfected just + + + align:start position:0% +first chronometer was perfected just +about the turn of the 19th century by + + align:start position:0% +about the turn of the 19th century by + + + align:start position:0% +about the turn of the 19th century by +about 185 or 6 it was known that there + + align:start position:0% +about 185 or 6 it was known that there + + + align:start position:0% +about 185 or 6 it was known that there +were chronome Metra as the French called + + align:start position:0% +were chronome Metra as the French called + + + align:start position:0% +were chronome Metra as the French called +them which could be used to measure time + + align:start position:0% +them which could be used to measure time + + + align:start position:0% +them which could be used to measure time +and 18th century theorists tell us about + + align:start position:0% +and 18th century theorists tell us about + + + align:start position:0% +and 18th century theorists tell us about +measure the ways of measuring Tempo so + + align:start position:0% +measure the ways of measuring Tempo so + + + align:start position:0% +measure the ways of measuring Tempo so +that words like Allegro Andante Presto + + align:start position:0% +that words like Allegro Andante Presto + + + align:start position:0% +that words like Allegro Andante Presto +Adagio presumably had meanings for late + + align:start position:0% +Adagio presumably had meanings for late + + + align:start position:0% +Adagio presumably had meanings for late +18th century musicians that can be + + align:start position:0% +18th century musicians that can be + + + align:start position:0% +18th century musicians that can be +deduced from a variety of factors some + + align:start position:0% +deduced from a variety of factors some + + + align:start position:0% +deduced from a variety of factors some +very good scholarly work on this has + + align:start position:0% +very good scholarly work on this has + + + align:start position:0% +very good scholarly work on this has +been done by various Scholars one I'll + + align:start position:0% +been done by various Scholars one I'll + + + align:start position:0% +been done by various Scholars one I'll +just mention is the Mozart scholar Neil + + align:start position:0% +just mention is the Mozart scholar Neil + + + align:start position:0% +just mention is the Mozart scholar Neil +zaso working on Mozart's Tempo + + align:start position:0% +zaso working on Mozart's Tempo + + + align:start position:0% +zaso working on Mozart's Tempo +conventions what Neil is able to find + + align:start position:0% +conventions what Neil is able to find + + + align:start position:0% +conventions what Neil is able to find +out is that it's extremely probable not + + align:start position:0% +out is that it's extremely probable not + + + align:start position:0% +out is that it's extremely probable not +certain but probable that musicians + + align:start position:0% +certain but probable that musicians + + + align:start position:0% +certain but probable that musicians +around 1780 could look at a piece of + + align:start position:0% +around 1780 could look at a piece of + + + align:start position:0% +around 1780 could look at a piece of +music and know about how fast it should + + align:start position:0% +music and know about how fast it should + + + align:start position:0% +music and know about how fast it should +go + + align:start position:0% +go + + + align:start position:0% +go +by seeing the meter in which it was + + align:start position:0% +by seeing the meter in which it was + + + align:start position:0% +by seeing the meter in which it was +written + + align:start position:0% +written + + + align:start position:0% +written +3444 or various other + + align:start position:0% +3444 or various other + + + align:start position:0% +3444 or various other +options the tempo marking the usual at + + align:start position:0% +options the tempo marking the usual at + + + align:start position:0% +options the tempo marking the usual at +that time Italian + + align:start position:0% +that time Italian + + + align:start position:0% +that time Italian +term the ones that we're accustomed to + + align:start position:0% +term the ones that we're accustomed to + + + align:start position:0% +term the ones that we're accustomed to +from Doo at the slow end to presto at + + align:start position:0% +from Doo at the slow end to presto at + + + align:start position:0% +from Doo at the slow end to presto at +the fast end and the note values which + + align:start position:0% +the fast end and the note values which + + + align:start position:0% +the fast end and the note values which +were prevalent in the notation of the + + align:start position:0% +were prevalent in the notation of the + + + align:start position:0% +were prevalent in the notation of the +composition itself but all this is at + + align:start position:0% +composition itself but all this is at + + + align:start position:0% +composition itself but all this is at +the at best probably ility hypothesis + + align:start position:0% +the at best probably ility hypothesis + + + align:start position:0% +the at best probably ility hypothesis +although it's a very good one with + + align:start position:0% +although it's a very good one with + + + align:start position:0% +although it's a very good one with +regard to how musicians felt about the + + align:start position:0% +regard to how musicians felt about the + + + align:start position:0% +regard to how musicians felt about the +matter though we have no particular + + align:start position:0% +matter though we have no particular + + + align:start position:0% +matter though we have no particular +evidence showing impatience on the part + + align:start position:0% +evidence showing impatience on the part + + + align:start position:0% +evidence showing impatience on the part +of composers when it comes to fixing + + align:start position:0% +of composers when it comes to fixing + + + align:start position:0% +of composers when it comes to fixing +Tempo absolutely but there may have been + + align:start position:0% +Tempo absolutely but there may have been + + + align:start position:0% +Tempo absolutely but there may have been +a kind of ongoing sense that it was + + align:start position:0% +a kind of ongoing sense that it was + + + align:start position:0% +a kind of ongoing sense that it was +about time if it were possible for + + align:start position:0% +about time if it were possible for + + + align:start position:0% +about time if it were possible for +technology to catch up with + + align:start position:0% +technology to catch up with + + + align:start position:0% +technology to catch up with +Aesthetics and there were people working + + align:start position:0% +Aesthetics and there were people working + + + align:start position:0% +Aesthetics and there were people working +on metronomes as they came to be called + + align:start position:0% +on metronomes as they came to be called + + + align:start position:0% +on metronomes as they came to be called +through the late 18th century and + + align:start position:0% +through the late 18th century and + + + align:start position:0% +through the late 18th century and +particularly in the early 19 + + align:start position:0% +particularly in the early 19 + + + align:start position:0% +particularly in the early 19 +19 now before I get to my example I just + + align:start position:0% +19 now before I get to my example I just + + + align:start position:0% +19 now before I get to my example I just +want to frame a little bit for you about + + align:start position:0% +want to frame a little bit for you about + + + align:start position:0% +want to frame a little bit for you about +the two more minutes worth of + + align:start position:0% +the two more minutes worth of + + + align:start position:0% +the two more minutes worth of +discussion one of the very best + + align:start position:0% +discussion one of the very best + + + align:start position:0% +discussion one of the very best +solutions to the problem of a good + + align:start position:0% +solutions to the problem of a good + + + align:start position:0% +solutions to the problem of a good +metronome was developed by a Dutch + + align:start position:0% +metronome was developed by a Dutch + + + align:start position:0% +metronome was developed by a Dutch +inventor and technician named dri vinko + + align:start position:0% +inventor and technician named dri vinko + + + align:start position:0% +inventor and technician named dri vinko +working in Amsterdam he seems to have + + align:start position:0% +working in Amsterdam he seems to have + + + align:start position:0% +working in Amsterdam he seems to have +been the first to figure out that a + + align:start position:0% +been the first to figure out that a + + + align:start position:0% +been the first to figure out that a +double weighted pendulum on a small uh + + align:start position:0% +double weighted pendulum on a small uh + + + align:start position:0% +double weighted pendulum on a small uh +conical shaped object would be able to + + align:start position:0% +conical shaped object would be able to + + + align:start position:0% +conical shaped object would be able to +click back and forth clearly I would + + align:start position:0% +click back and forth clearly I would + + + align:start position:0% +click back and forth clearly I would +have brought our own example from home + + align:start position:0% +have brought our own example from home + + + align:start position:0% +have brought our own example from home +but it wasn't working very well today so + + align:start position:0% +but it wasn't working very well today so + + + align:start position:0% +but it wasn't working very well today so +if you'll spare me I brought along this + + align:start position:0% +if you'll spare me I brought along this + + + align:start position:0% +if you'll spare me I brought along this +electronic substitute which we'll have + + align:start position:0% +electronic substitute which we'll have + + + align:start position:0% +electronic substitute which we'll have +to do and it's very important to + + align:start position:0% +to do and it's very important to + + + align:start position:0% +to do and it's very important to +understand that this is the level of dis + + align:start position:0% +understand that this is the level of dis + + + align:start position:0% +understand that this is the level of dis +of uh perception which people have once + + align:start position:0% +of uh perception which people have once + + + align:start position:0% +of uh perception which people have once +a metronome was started something that + + align:start position:0% +a metronome was started something that + + + align:start position:0% +a metronome was started something that +would simply register beats per minute + + align:start position:0% + + + + align:start position:0% + +that's a deliberate by the way + + align:start position:0% +that's a deliberate by the way + + + align:start position:0% +that's a deliberate by the way +deliberately set at the number 60 which + + align:start position:0% +deliberately set at the number 60 which + + + align:start position:0% +deliberately set at the number 60 which +means 60 beats per minute and that + + align:start position:0% +means 60 beats per minute and that + + + align:start position:0% +means 60 beats per minute and that +vinkle thought he had a very good thing + + align:start position:0% +vinkle thought he had a very good thing + + + align:start position:0% +vinkle thought he had a very good thing +going and was uh deed had a genuine + + align:start position:0% +going and was uh deed had a genuine + + + align:start position:0% +going and was uh deed had a genuine +right to inventorship of a working + + align:start position:0% +right to inventorship of a working + + + align:start position:0% +right to inventorship of a working +simple device that musicians could have + + align:start position:0% +simple device that musicians could have + + + align:start position:0% +simple device that musicians could have +used had it been the case that he could + + align:start position:0% +used had it been the case that he could + + + align:start position:0% +used had it been the case that he could +have developed it we could have had vle + + align:start position:0% +have developed it we could have had vle + + + align:start position:0% +have developed it we could have had vle +metronome from all time since then but + + align:start position:0% +metronome from all time since then but + + + align:start position:0% +metronome from all time since then but +something happened to vinl namely a came + + align:start position:0% +something happened to vinl namely a came + + + align:start position:0% +something happened to vinl namely a came +a German inventor and one of the great + + align:start position:0% +a German inventor and one of the great + + + align:start position:0% +a German inventor and one of the great +and flamboyant entrepreneurs of the + + align:start position:0% +and flamboyant entrepreneurs of the + + + align:start position:0% +and flamboyant entrepreneurs of the +early 19th century a certain Johan + + align:start position:0% +early 19th century a certain Johan + + + align:start position:0% +early 19th century a certain Johan +nepomuk meltel m a l + + align:start position:0% +nepomuk meltel m a l + + + align:start position:0% +nepomuk meltel m a l +zel who uh is a kind of PT Barnum of the + + align:start position:0% +zel who uh is a kind of PT Barnum of the + + + align:start position:0% +zel who uh is a kind of PT Barnum of the +world of Music in that period and who + + align:start position:0% +world of Music in that period and who + + + align:start position:0% +world of Music in that period and who +immediately saw that vingle had done + + align:start position:0% +immediately saw that vingle had done + + + align:start position:0% +immediately saw that vingle had done +something extraordinary so what did + + align:start position:0% +something extraordinary so what did + + + align:start position:0% +something extraordinary so what did +melel do but copy B vink's invention + + align:start position:0% +melel do but copy B vink's invention + + + align:start position:0% +melel do but copy B vink's invention +patent it himself take it around to as + + align:start position:0% +patent it himself take it around to as + + + align:start position:0% +patent it himself take it around to as +many composers as he could could find + + align:start position:0% +many composers as he could could find + + + align:start position:0% +many composers as he could could find +who had Authority and get them to + + align:start position:0% +who had Authority and get them to + + + align:start position:0% +who had Authority and get them to +endorse his new invention which should + + align:start position:0% +endorse his new invention which should + + + align:start position:0% +endorse his new invention which should +now be called male SS metronome for all + + align:start position:0% +now be called male SS metronome for all + + + align:start position:0% +now be called male SS metronome for all +time to come as it has indeed thus been + + align:start position:0% +time to come as it has indeed thus been + + + align:start position:0% +time to come as it has indeed thus been +known anybody who has played let's say + + align:start position:0% +known anybody who has played let's say + + + align:start position:0% +known anybody who has played let's say +mozar orov and piano sonaras from an old + + align:start position:0% +mozar orov and piano sonaras from an old + + + align:start position:0% +mozar orov and piano sonaras from an old +Shermer Edition would have seen mm at + + align:start position:0% +Shermer Edition would have seen mm at + + + align:start position:0% +Shermer Edition would have seen mm at +the top of the page mm is Ms + + align:start position:0% +the top of the page mm is Ms + + + align:start position:0% +the top of the page mm is Ms +metronome an astonishing feed of + + align:start position:0% +metronome an astonishing feed of + + + align:start position:0% +metronome an astonishing feed of +salesmanship and must have been one of + + align:start position:0% +salesmanship and must have been one of + + + align:start position:0% +salesmanship and must have been one of +the most remarkable characters that the + + align:start position:0% +the most remarkable characters that the + + + align:start position:0% +the most remarkable characters that the +world could see in musical + + align:start position:0% +world could see in musical + + + align:start position:0% +world could see in musical +Vienna now + + align:start position:0% +Vienna now + + + align:start position:0% +Vienna now +Beethoven ever anxious to exert some + + align:start position:0% +Beethoven ever anxious to exert some + + + align:start position:0% +Beethoven ever anxious to exert some +kind of control over the expanding + + align:start position:0% +kind of control over the expanding + + + align:start position:0% +kind of control over the expanding +musical world that he's + + align:start position:0% +musical world that he's + + + align:start position:0% +musical world that he's +conceiving falls in love with the idea + + align:start position:0% +conceiving falls in love with the idea + + + align:start position:0% +conceiving falls in love with the idea +of the metronome as soon as belil brings + + align:start position:0% +of the metronome as soon as belil brings + + + align:start position:0% +of the metronome as soon as belil brings +it to him and shows him what it can do + + align:start position:0% +it to him and shows him what it can do + + + align:start position:0% +it to him and shows him what it can do +but much more than this there are two + + align:start position:0% +but much more than this there are two + + + align:start position:0% +but much more than this there are two +other factors one factor is that Boven + + align:start position:0% +other factors one factor is that Boven + + + align:start position:0% +other factors one factor is that Boven +is becoming by the time the metronome is + + align:start position:0% +is becoming by the time the metronome is + + + align:start position:0% +is becoming by the time the metronome is +truly perfected if not invented + + align:start position:0% +truly perfected if not invented + + + align:start position:0% +truly perfected if not invented +perfected by about 185 + + align:start position:0% +perfected by about 185 + + + align:start position:0% +perfected by about 185 +bethoven is functionally + + align:start position:0% +bethoven is functionally + + + align:start position:0% +bethoven is functionally +deaf he can see the thing ticking going + + align:start position:0% +deaf he can see the thing ticking going + + + align:start position:0% +deaf he can see the thing ticking going +back and forth the pendulum but he can't + + align:start position:0% +back and forth the pendulum but he can't + + + align:start position:0% +back and forth the pendulum but he can't +hear it certainly not at the level at + + align:start position:0% +hear it certainly not at the level at + + + align:start position:0% +hear it certainly not at the level at +which Tick Tock were audible at the time + + align:start position:0% +which Tick Tock were audible at the time + + + align:start position:0% +which Tick Tock were audible at the time +furthermore we have plenty of evidence + + align:start position:0% +furthermore we have plenty of evidence + + + align:start position:0% +furthermore we have plenty of evidence +including recent studies and quotations + + align:start position:0% +including recent studies and quotations + + + align:start position:0% +including recent studies and quotations +from from citations from contemporaries + + align:start position:0% +from from citations from contemporaries + + + align:start position:0% +from from citations from contemporaries +that his own ability to perform with + + align:start position:0% +that his own ability to perform with + + + align:start position:0% +that his own ability to perform with +other musicians was increasingly uh + + align:start position:0% +other musicians was increasingly uh + + + align:start position:0% +other musicians was increasingly uh +difficult and subject to P discrepancies + + align:start position:0% +difficult and subject to P discrepancies + + + align:start position:0% +difficult and subject to P discrepancies +between what was desired and what + + align:start position:0% +between what was desired and what + + + align:start position:0% +between what was desired and what +happened Louis schore describes + + align:start position:0% +happened Louis schore describes + + + align:start position:0% +happened Louis schore describes +Beethoven conducting for example the + + align:start position:0% +Beethoven conducting for example the + + + align:start position:0% +Beethoven conducting for example the +seventh Symphony and says in the soft + + align:start position:0% +seventh Symphony and says in the soft + + + align:start position:0% +seventh Symphony and says in the soft +passages he was 10 or 12 measures behind + + align:start position:0% +passages he was 10 or 12 measures behind + + + align:start position:0% +passages he was 10 or 12 measures behind +the + + align:start position:0% +the + + + align:start position:0% +the +performers it is an incredibly difficult + + align:start position:0% +performers it is an incredibly difficult + + + align:start position:0% +performers it is an incredibly difficult +and almost poignant situation it's not + + align:start position:0% +and almost poignant situation it's not + + + align:start position:0% +and almost poignant situation it's not +almost poignant it is poignant to think + + align:start position:0% +almost poignant it is poignant to think + + + align:start position:0% +almost poignant it is poignant to think +of this musical mind increasingly + + align:start position:0% +of this musical mind increasingly + + + align:start position:0% +of this musical mind increasingly +isolated from The Real World of music + + align:start position:0% +isolated from The Real World of music + + + align:start position:0% +isolated from The Real World of music +making for which he is producing the + + align:start position:0% +making for which he is producing the + + + align:start position:0% +making for which he is producing the +greatest music of his time time and when + + align:start position:0% +greatest music of his time time and when + + + align:start position:0% +greatest music of his time time and when +it comes to the metronome story I think + + align:start position:0% +it comes to the metronome story I think + + + align:start position:0% +it comes to the metronome story I think +what we see in Beethoven is a kind of + + align:start position:0% +what we see in Beethoven is a kind of + + + align:start position:0% +what we see in Beethoven is a kind of +strong reaction towards making something + + align:start position:0% +strong reaction towards making something + + + align:start position:0% +strong reaction towards making something +happen ideally in the world uh Imagining + + align:start position:0% +happen ideally in the world uh Imagining + + + align:start position:0% +happen ideally in the world uh Imagining +the possibility of it becoming a very + + align:start position:0% +the possibility of it becoming a very + + + align:start position:0% +the possibility of it becoming a very +important fact that everybody uh device + + align:start position:0% +important fact that everybody uh device + + + align:start position:0% +important fact that everybody uh device +that everybody could share in all + + align:start position:0% +that everybody could share in all + + + align:start position:0% +that everybody could share in all +right what did bovin do about all this + + align:start position:0% +right what did bovin do about all this + + + align:start position:0% +right what did bovin do about all this +first of all one thing he did was + + align:start position:0% +first of all one thing he did was + + + align:start position:0% +first of all one thing he did was +to publish a whole set of metronome + + align:start position:0% +to publish a whole set of metronome + + + align:start position:0% +to publish a whole set of metronome +marking + + align:start position:0% +marking + + + align:start position:0% +marking +according to mael for in + + align:start position:0% +according to mael for in + + + align:start position:0% +according to mael for in +1817 for all the Symphonies he' written + + align:start position:0% +1817 for all the Symphonies he' written + + + align:start position:0% +1817 for all the Symphonies he' written +up to that time that's all the first + + align:start position:0% +up to that time that's all the first + + + align:start position:0% +up to that time that's all the first +eight the ninth isn't written until + + align:start position:0% +eight the ninth isn't written until + + + align:start position:0% +eight the ninth isn't written until +several years later and all the string + + align:start position:0% +several years later and all the string + + + align:start position:0% +several years later and all the string +quartets up to that time that is Opus 18 + + align:start position:0% +quartets up to that time that is Opus 18 + + + align:start position:0% +quartets up to that time that is Opus 18 +5974 and + + align:start position:0% +5974 and + + + align:start position:0% +5974 and +95 the lake cortet is another story by + + align:start position:0% +95 the lake cortet is another story by + + + align:start position:0% +95 the lake cortet is another story by +that time he's in another world and we + + align:start position:0% +that time he's in another world and we + + + align:start position:0% +that time he's in another world and we +don't have his own authentic metronome + + align:start position:0% +don't have his own authentic metronome + + + align:start position:0% +don't have his own authentic metronome +markings we do have some from his + + align:start position:0% +markings we do have some from his + + + align:start position:0% +markings we do have some from his +performers however but for the 18 17 + + align:start position:0% +performers however but for the 18 17 + + + align:start position:0% +performers however but for the 18 17 +group he publishes a whole set of + + align:start position:0% +group he publishes a whole set of + + + align:start position:0% +group he publishes a whole set of +metronome markings that's where the + + align:start position:0% +metronome markings that's where the + + + align:start position:0% +metronome markings that's where the +trouble + + align:start position:0% +trouble + + + align:start position:0% +trouble +started these markings are extremely + + align:start position:0% +started these markings are extremely + + + align:start position:0% +started these markings are extremely +controversial because many of them are + + align:start position:0% +controversial because many of them are + + + align:start position:0% +controversial because many of them are +much much faster than anybody at the + + align:start position:0% +much much faster than anybody at the + + + align:start position:0% +much much faster than anybody at the +time presumably could play and certainly + + align:start position:0% +time presumably could play and certainly + + + align:start position:0% +time presumably could play and certainly +much faster than most conductors wished + + align:start position:0% +much faster than most conductors wished + + + align:start position:0% +much faster than most conductors wished +to play until the early music movement + + align:start position:0% +to play until the early music movement + + + align:start position:0% +to play until the early music movement +came along about 30 years ago and said + + align:start position:0% +came along about 30 years ago and said + + + align:start position:0% +came along about 30 years ago and said +no we can do it but what has happened is + + align:start position:0% +no we can do it but what has happened is + + + align:start position:0% +no we can do it but what has happened is +that there are two enormously + + align:start position:0% +that there are two enormously + + + align:start position:0% +that there are two enormously +conflicting or sides here one are the + + align:start position:0% +conflicting or sides here one are the + + + align:start position:0% +conflicting or sides here one are the +traditionalists you might say who feel + + align:start position:0% +traditionalists you might say who feel + + + align:start position:0% +traditionalists you might say who feel +that the tempo comes from the content + + align:start position:0% +that the tempo comes from the content + + + align:start position:0% +that the tempo comes from the content +and the other are the performers of + + align:start position:0% +and the other are the performers of + + + align:start position:0% +and the other are the performers of +early music certain ones like Norrington + + align:start position:0% +early music certain ones like Norrington + + + align:start position:0% +early music certain ones like Norrington +and Gardner who wish to stick to the + + align:start position:0% +and Gardner who wish to stick to the + + + align:start position:0% +and Gardner who wish to stick to the +letter of the published metronome + + align:start position:0% +letter of the published metronome + + + align:start position:0% +letter of the published metronome +markings of + + align:start position:0% +markings of + + + align:start position:0% +markings of +1817 and if they're too if they're too + + align:start position:0% +1817 and if they're too if they're too + + + align:start position:0% +1817 and if they're too if they're too +fast there's some + + align:start position:0% +fast there's some + + + align:start position:0% +fast there's some +modifications but basically there are + + align:start position:0% +modifications but basically there are + + + align:start position:0% +modifications but basically there are +two schools of thought okay enough for + + align:start position:0% +two schools of thought okay enough for + + + align:start position:0% +two schools of thought okay enough for +now let's hear some music + + align:start position:0% +now let's hear some music + + + align:start position:0% +now let's hear some music +let us hear not ft bengler who is as so + + align:start position:0% +let us hear not ft bengler who is as so + + + align:start position:0% +let us hear not ft bengler who is as so +slow that in his performance an eighth + + align:start position:0% +slow that in his performance an eighth + + + align:start position:0% +slow that in his performance an eighth +note equals + + align:start position:0% +note equals + + + align:start position:0% +note equals +Beethoven's bov's original marking for + + align:start position:0% +Beethoven's bov's original marking for + + + align:start position:0% +Beethoven's bov's original marking for +this movement instead of a quarter note + + align:start position:0% +this movement instead of a quarter note + + + align:start position:0% +this movement instead of a quarter note +Boven wrote for the Adagio of the Ninth + + align:start position:0% +Boven wrote for the Adagio of the Ninth + + + align:start position:0% +Boven wrote for the Adagio of the Ninth +Symphony quarter note equals + + align:start position:0% + + + + align:start position:0% + +60 that's a qu Note 1 2 3 4 you believe + + align:start position:0% +60 that's a qu Note 1 2 3 4 you believe + + + align:start position:0% +60 that's a qu Note 1 2 3 4 you believe +it not many people + + align:start position:0% +it not many people + + + align:start position:0% +it not many people +do let me make sure I've got it on 60 + + align:start position:0% +do let me make sure I've got it on 60 + + + align:start position:0% +do let me make sure I've got it on 60 +yes I + + align:start position:0% +yes I + + + align:start position:0% +yes I +do + + align:start position:0% + + + + align:start position:0% + +whoops did not have it on 60 apologies + + align:start position:0% +whoops did not have it on 60 apologies + + + align:start position:0% +whoops did not have it on 60 apologies +correction + + align:start position:0% + + + + align:start position:0% + +60 if you hear the Ninth Symphony slow + + align:start position:0% +60 if you hear the Ninth Symphony slow + + + align:start position:0% +60 if you hear the Ninth Symphony slow +movement in your head right now and + + align:start position:0% +movement in your head right now and + + + align:start position:0% +movement in your head right now and +think it at this tempo + + align:start position:0% +think it at this tempo + + + align:start position:0% +think it at this tempo +then you're on one side of the room F + + align:start position:0% +then you're on one side of the room F + + + align:start position:0% +then you're on one side of the room F +bangler and Kion are on the other side + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +of + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and one thing it reinforces is that we + + align:start position:0% +and one thing it reinforces is that we + + + align:start position:0% +and one thing it reinforces is that we +are not simply talking about a + + align:start position:0% +are not simply talking about a + + + align:start position:0% +are not simply talking about a +difference in speed or duration or time + + align:start position:0% +difference in speed or duration or time + + + align:start position:0% +difference in speed or duration or time +elapsed we're talking about a difference + + align:start position:0% +elapsed we're talking about a difference + + + align:start position:0% +elapsed we're talking about a difference +in + + align:start position:0% +in + + + align:start position:0% +in +character and now the great question is + + align:start position:0% +character and now the great question is + + + align:start position:0% +character and now the great question is +what did bovin really think about the + + align:start position:0% +what did bovin really think about the + + + align:start position:0% +what did bovin really think about the +character of these movements and what + + align:start position:0% +character of these movements and what + + + align:start position:0% +character of these movements and what +did character in music mean to him that + + align:start position:0% +did character in music mean to him that + + + align:start position:0% +did character in music mean to him that +is the source of a large amount of + + align:start position:0% +is the source of a large amount of + + + align:start position:0% +is the source of a large amount of +discourse and discussion and scholarship + + align:start position:0% +discourse and discussion and scholarship + + + align:start position:0% +discourse and discussion and scholarship +on the whole question of the right temp + + align:start position:0% +on the whole question of the right temp + + + align:start position:0% +on the whole question of the right temp +Tempo and the right interpretation of + + align:start position:0% +Tempo and the right interpretation of + + + align:start position:0% +Tempo and the right interpretation of +his very controversial metronome + + align:start position:0% +his very controversial metronome + + + align:start position:0% +his very controversial metronome +markings which I'll just tell you exists + + align:start position:0% +markings which I'll just tell you exists + + + align:start position:0% +markings which I'll just tell you exists +without trying even to summarize the + + align:start position:0% +without trying even to summarize the + + + align:start position:0% +without trying even to summarize the +viewpoints the viewpoints do however + + align:start position:0% +viewpoints the viewpoints do however + + + align:start position:0% +viewpoints the viewpoints do however +include some some material some + + align:start position:0% +include some some material some + + + align:start position:0% +include some some material some +documentary evidence from bov's own life + + align:start position:0% +documentary evidence from bov's own life + + + align:start position:0% +documentary evidence from bov's own life +time including his own enthusiastic + + align:start position:0% +time including his own enthusiastic + + + align:start position:0% +time including his own enthusiastic +statements about the importance of the + + align:start position:0% +statements about the importance of the + + + align:start position:0% +statements about the importance of the +metronome for musical life I'm going to + + align:start position:0% +metronome for musical life I'm going to + + + align:start position:0% +metronome for musical life I'm going to +read you a couple of very brief excerpts + + align:start position:0% +read you a couple of very brief excerpts + + + align:start position:0% +read you a couple of very brief excerpts +from such a letter that he wrote in + + align:start position:0% +from such a letter that he wrote in + + + align:start position:0% +from such a letter that he wrote in +1817 just at the time that he was uh + + align:start position:0% +1817 just at the time that he was uh + + + align:start position:0% +1817 just at the time that he was uh +indeed endorsing the uh the metronome + + align:start position:0% +indeed endorsing the uh the metronome + + + align:start position:0% +indeed endorsing the uh the metronome +and Publishing these markings for his up + + align:start position:0% +and Publishing these markings for his up + + + align:start position:0% +and Publishing these markings for his up +to then Symphonies and up to then string + + align:start position:0% +to then Symphonies and up to then string + + + align:start position:0% +to then Symphonies and up to then string +cour TXS the first thing he says is that + + align:start position:0% +cour TXS the first thing he says is that + + + align:start position:0% +cour TXS the first thing he says is that +the old words of doio algro and Dante + + align:start position:0% +the old words of doio algro and Dante + + + align:start position:0% +the old words of doio algro and Dante +Presto originated in the barbarous ages + + align:start position:0% +Presto originated in the barbarous ages + + + align:start position:0% +Presto originated in the barbarous ages +of + + align:start position:0% +of + + + align:start position:0% +of +music and I he claims in this letter to + + align:start position:0% +music and I he claims in this letter to + + + align:start position:0% +music and I he claims in this letter to +somebody that he's planning to give them + + align:start position:0% +somebody that he's planning to give them + + + align:start position:0% +somebody that he's planning to give them +up by the way B has not yet written The + + align:start position:0% +up by the way B has not yet written The + + + align:start position:0% +up by the way B has not yet written The +Late Late piano sonatas the D variations + + align:start position:0% +Late Late piano sonatas the D variations + + + align:start position:0% +Late Late piano sonatas the D variations +the late Court that's the N Symphony the + + align:start position:0% +the late Court that's the N Symphony the + + + align:start position:0% +the late Court that's the N Symphony the +memus but he says he's planning to give + + align:start position:0% +memus but he says he's planning to give + + + align:start position:0% +memus but he says he's planning to give +up these words nothing like that in fact + + align:start position:0% +up these words nothing like that in fact + + + align:start position:0% +up these words nothing like that in fact +ever happened but he goes on in this + + align:start position:0% +ever happened but he goes on in this + + + align:start position:0% +ever happened but he goes on in this +letter to say something important he + + align:start position:0% +letter to say something important he + + + align:start position:0% +letter to say something important he +says that these words although they do + + align:start position:0% +says that these words although they do + + + align:start position:0% +says that these words although they do +not they are not adequate substitutes + + align:start position:0% +not they are not adequate substitutes + + + align:start position:0% +not they are not adequate substitutes +for determining Tempo nevertheless they + + align:start position:0% +for determining Tempo nevertheless they + + + align:start position:0% +for determining Tempo nevertheless they +describe the character of the + + align:start position:0% +describe the character of the + + + align:start position:0% +describe the character of the +composition quote we cannot give these + + align:start position:0% +composition quote we cannot give these + + + align:start position:0% +composition quote we cannot give these +up the tempo is more like the body but + + align:start position:0% +up the tempo is more like the body but + + + align:start position:0% +up the tempo is more like the body but +these certainly refer to the spirit of + + align:start position:0% +these certainly refer to the spirit of + + + align:start position:0% +these certainly refer to the spirit of +the composition so the character and the + + align:start position:0% +the composition so the character and the + + + align:start position:0% +the composition so the character and the +spirit are what he is after and those + + align:start position:0% +spirit are what he is after and those + + + align:start position:0% +spirit are what he is after and those +who are on the conservative side of this + + align:start position:0% +who are on the conservative side of this + + + align:start position:0% +who are on the conservative side of this +issues who do not believe that his very + + align:start position:0% +issues who do not believe that his very + + + align:start position:0% +issues who do not believe that his very +very fast Tempe which may be aberrations + + align:start position:0% +very fast Tempe which may be aberrations + + + align:start position:0% +very fast Tempe which may be aberrations +of his + + align:start position:0% +of his + + + align:start position:0% +of his +deafness those who do not believe in + + align:start position:0% +deafness those who do not believe in + + + align:start position:0% +deafness those who do not believe in +that claim that indeed Tempo arises from + + align:start position:0% +that claim that indeed Tempo arises from + + + align:start position:0% +that claim that indeed Tempo arises from +content and not from the application of + + align:start position:0% +content and not from the application of + + + align:start position:0% +content and not from the application of +a strict metronomic beat back to B's + + align:start position:0% +a strict metronomic beat back to B's + + + align:start position:0% +a strict metronomic beat back to B's +letter for a + + align:start position:0% +letter for a + + + align:start position:0% +letter for a +moment I fancy he said says quote and + + align:start position:0% +moment I fancy he said says quote and + + + align:start position:0% +moment I fancy he said says quote and +this is really wonderful that the best + + align:start position:0% +this is really wonderful that the best + + + align:start position:0% +this is really wonderful that the best +solution would + + align:start position:0% +solution would + + + align:start position:0% +solution would +be particularly for our country where + + align:start position:0% +be particularly for our country where + + + align:start position:0% +be particularly for our country where +music is now become a national need and + + align:start position:0% +music is now become a national need and + + + align:start position:0% +music is now become a national need and +where every Village School Master will + + align:start position:0% +where every Village School Master will + + + align:start position:0% +where every Village School Master will +be expected to use the + + align:start position:0% +be expected to use the + + + align:start position:0% +be expected to use the +metronome that Mel should try to sell a + + align:start position:0% +metronome that Mel should try to sell a + + + align:start position:0% +metronome that Mel should try to sell a +certain number of metronomes by + + align:start position:0% +certain number of metronomes by + + + align:start position:0% +certain number of metronomes by +subscription at a very high price then + + align:start position:0% +subscription at a very high price then + + + align:start position:0% +subscription at a very high price then +as soon as he has been covered + + align:start position:0% +as soon as he has been covered + + + align:start position:0% +as soon as he has been covered +financially by this number he'll be able + + align:start position:0% +financially by this number he'll be able + + + align:start position:0% +financially by this number he'll be able +to dispose of the other necessary + + align:start position:0% +to dispose of the other necessary + + + align:start position:0% +to dispose of the other necessary +metronomes for the musical need of the + + align:start position:0% +metronomes for the musical need of the + + + align:start position:0% +metronomes for the musical need of the +nation so cheap + + align:start position:0% +nation so cheap + + + align:start position:0% +nation so cheap +that we can certainly expect to see the + + align:start position:0% +that we can certainly expect to see the + + + align:start position:0% +that we can certainly expect to see the +greatest Universal use and distri and + + align:start position:0% +greatest Universal use and distri and + + + align:start position:0% +greatest Universal use and distri and +distribution of this commodity and + + align:start position:0% +distribution of this commodity and + + + align:start position:0% +distribution of this commodity and +quote I leave it with you that it is + + align:start position:0% +quote I leave it with you that it is + + + align:start position:0% +quote I leave it with you that it is +wonderful to think about a time in + + align:start position:0% +wonderful to think about a time in + + + align:start position:0% +wonderful to think about a time in +Western history when a great composer + + align:start position:0% +Western history when a great composer + + + align:start position:0% +Western history when a great composer +could think that the musical need of the + + align:start position:0% +could think that the musical need of the + + + align:start position:0% +could think that the musical need of the +country was something so important that + + align:start position:0% +country was something so important that + + + align:start position:0% +country was something so important that +a timekeeping device should be in every + + align:start position:0% +a timekeeping device should be in every + + + align:start position:0% +a timekeeping device should be in every +school everybody should use it and the + + align:start position:0% +school everybody should use it and the + + + align:start position:0% +school everybody should use it and the +world would be a better place to live in + + align:start position:0% +world would be a better place to live in + + + align:start position:0% +world would be a better place to live in +I by the way honestly believe believe + + align:start position:0% +I by the way honestly believe believe + + + align:start position:0% +I by the way honestly believe believe +that it + + align:start position:0% +that it + + + align:start position:0% +that it +would so I'm just going to leave that on + + align:start position:0% +would so I'm just going to leave that on + + + align:start position:0% +would so I'm just going to leave that on +the table and that's my my contribution + + align:start position:0% +the table and that's my my contribution + + + align:start position:0% +the table and that's my my contribution +for the moment thank + + align:start position:0% +for the moment thank + + + align:start position:0% +for the moment thank +[Applause] + + align:start position:0% + + + + align:start position:0% + +you before we start + + align:start position:0% +you before we start + + + align:start position:0% +you before we start +um I would like to thank the uh the + + align:start position:0% +um I would like to thank the uh the + + + align:start position:0% +um I would like to thank the uh the +organizers of this event um specifically + + align:start position:0% +organizers of this event um specifically + + + align:start position:0% +organizers of this event um specifically +W and Marcus and thank you for + + align:start position:0% +W and Marcus and thank you for + + + align:start position:0% +W and Marcus and thank you for +chairing I I was skeptical um + + align:start position:0% +chairing I I was skeptical um + + + align:start position:0% +chairing I I was skeptical um +I this has turned out to be great fun I + + align:start position:0% +I this has turned out to be great fun I + + + align:start position:0% +I this has turned out to be great fun I +was I wasn't sure uh will an audience + + align:start position:0% +was I wasn't sure uh will an audience + + + align:start position:0% +was I wasn't sure uh will an audience +sustain effectively a lecture series for + + align:start position:0% +sustain effectively a lecture series for + + + align:start position:0% +sustain effectively a lecture series for +all these afternoons this has been great + + align:start position:0% +all these afternoons this has been great + + + align:start position:0% +all these afternoons this has been great +fun it's s Beyond expectations thanks + + align:start position:0% +fun it's s Beyond expectations thanks + + + align:start position:0% +fun it's s Beyond expectations thanks +you + + align:start position:0% + + + + align:start position:0% + +guys I want to read to you some some + + align:start position:0% +guys I want to read to you some some + + + align:start position:0% +guys I want to read to you some some +sections of a poem um I've been working + + align:start position:0% +sections of a poem um I've been working + + + align:start position:0% +sections of a poem um I've been working +on for the Last 5 Years about the + + align:start position:0% +on for the Last 5 Years about the + + + align:start position:0% +on for the Last 5 Years about the +photographer Edward mybridge um you know + + align:start position:0% +photographer Edward mybridge um you know + + + align:start position:0% +photographer Edward mybridge um you know +him but you don't know you know him + + align:start position:0% +him but you don't know you know him + + + align:start position:0% +him but you don't know you know him +here's how you know him + + align:start position:0% + + + + align:start position:0% + +um do you recognize these that stop + + align:start position:0% +um do you recognize these that stop + + + align:start position:0% +um do you recognize these that stop +action photographs from the + + align:start position:0% +action photographs from the + + + align:start position:0% +action photographs from the +1870s uh they originated they originated + + align:start position:0% +1870s uh they originated they originated + + + align:start position:0% +1870s uh they originated they originated +in a bet Leland Stanford the former + + align:start position:0% +in a bet Leland Stanford the former + + + align:start position:0% +in a bet Leland Stanford the former +govern governor of + + align:start position:0% + + + + align:start position:0% + +California Leland Stanford the former + + align:start position:0% +California Leland Stanford the former + + + align:start position:0% +California Leland Stanford the former +Governor of California got into a uh bet + + align:start position:0% +Governor of California got into a uh bet + + + align:start position:0% +Governor of California got into a uh bet +at the racetrack and the BET was + + align:start position:0% +at the racetrack and the BET was + + + align:start position:0% +at the racetrack and the BET was +Stanford wagered $25,000 which is almost + + align:start position:0% +Stanford wagered $25,000 which is almost + + + align:start position:0% +Stanford wagered $25,000 which is almost +half a million dollars by contemporary + + align:start position:0% +half a million dollars by contemporary + + + align:start position:0% +half a million dollars by contemporary +currency bet + + align:start position:0% +currency bet + + + align:start position:0% +currency bet +$25,000 in 1870 + + align:start position:0% +$25,000 in 1870 + + + align:start position:0% +$25,000 in 1870 +currency that all four Hooves of a horse + + align:start position:0% +currency that all four Hooves of a horse + + + align:start position:0% +currency that all four Hooves of a horse +in gate at any moment are off the ground + + align:start position:0% + + + + align:start position:0% + +right the eye can't register such a + + align:start position:0% +right the eye can't register such a + + + align:start position:0% +right the eye can't register such a +moment empirically so Stanford having + + align:start position:0% +moment empirically so Stanford having + + + align:start position:0% +moment empirically so Stanford having +laid $25,000 on this on this wager then + + align:start position:0% +laid $25,000 on this on this wager then + + + align:start position:0% +laid $25,000 on this on this wager then +engaged mbridge who who up until then + + align:start position:0% +engaged mbridge who who up until then + + + align:start position:0% +engaged mbridge who who up until then +had been a landscape photographer in the + + align:start position:0% +had been a landscape photographer in the + + + align:start position:0% +had been a landscape photographer in the +west um engag mybridge to solve this + + align:start position:0% +west um engag mybridge to solve this + + + align:start position:0% +west um engag mybridge to solve this +problem + + align:start position:0% +problem + + + align:start position:0% +problem +photographically mybridge uh brooded + + align:start position:0% +photographically mybridge uh brooded + + + align:start position:0% +photographically mybridge uh brooded +about the question for about a year and + + align:start position:0% +about the question for about a year and + + + align:start position:0% +about the question for about a year and +then then he laid + + align:start position:0% +then then he laid + + + align:start position:0% +then then he laid +out uh at first 4 and then 12 and then + + align:start position:0% +out uh at first 4 and then 12 and then + + + align:start position:0% +out uh at first 4 and then 12 and then +16 cameras with thin copper trip wires + + align:start position:0% +16 cameras with thin copper trip wires + + + align:start position:0% +16 cameras with thin copper trip wires +on the racetrack and sent a racehorse + + align:start position:0% +on the racetrack and sent a racehorse + + + align:start position:0% +on the racetrack and sent a racehorse +pulling a a + + align:start position:0% +pulling a a + + + align:start position:0% +pulling a a +sulky down the line of trip wires each + + align:start position:0% +sulky down the line of trip wires each + + + align:start position:0% +sulky down the line of trip wires each +trip wire tripped the shutter to a + + align:start position:0% +trip wire tripped the shutter to a + + + align:start position:0% +trip wire tripped the shutter to a +camera with a fast uh emulsified plate + + align:start position:0% +camera with a fast uh emulsified plate + + + align:start position:0% +camera with a fast uh emulsified plate +in it um so that in sequence as the + + align:start position:0% +in it um so that in sequence as the + + + align:start position:0% +in it um so that in sequence as the +horse ran down the the racetrack the + + align:start position:0% +horse ran down the the racetrack the + + + align:start position:0% +horse ran down the the racetrack the +horse in effect photographed itself in + + align:start position:0% +horse in effect photographed itself in + + + align:start position:0% +horse in effect photographed itself in +serot photographs which register the + + align:start position:0% +serot photographs which register the + + + align:start position:0% +serot photographs which register the +deconstruction of a continuous motion + + align:start position:0% +deconstruction of a continuous motion + + + align:start position:0% +deconstruction of a continuous motion +right so what mbridge is responsible for + + align:start position:0% +right so what mbridge is responsible for + + + align:start position:0% +right so what mbridge is responsible for +is breaking the moment of a continuous + + align:start position:0% +is breaking the moment of a continuous + + + align:start position:0% +is breaking the moment of a continuous +motion into discrete pieces + + align:start position:0% +motion into discrete pieces + + + align:start position:0% +motion into discrete pieces +uh he won for uh Stanford won the won + + align:start position:0% +uh he won for uh Stanford won the won + + + align:start position:0% +uh he won for uh Stanford won the won +the bed right um and Stanford + + align:start position:0% +the bed right um and Stanford + + + align:start position:0% +the bed right um and Stanford +immediately wanted to do more because he + + align:start position:0% +immediately wanted to do more because he + + + align:start position:0% +immediately wanted to do more because he +thought it would help in uh his horse + + align:start position:0% +thought it would help in uh his horse + + + align:start position:0% +thought it would help in uh his horse +breeding business and we said I think + + align:start position:0% +breeding business and we said I think + + + align:start position:0% +breeding business and we said I think +there are different applications for + + align:start position:0% +there are different applications for + + + align:start position:0% +there are different applications for +this this technology mbridge immediately + + align:start position:0% +this this technology mbridge immediately + + + align:start position:0% +this this technology mbridge immediately +began to see the the effects in uh uh + + align:start position:0% +began to see the the effects in uh uh + + + align:start position:0% +began to see the the effects in uh uh +aesthetic the possible ramifications for + + align:start position:0% +aesthetic the possible ramifications for + + + align:start position:0% +aesthetic the possible ramifications for +philosophy of Mo motion and kinesthetic + + align:start position:0% +philosophy of Mo motion and kinesthetic + + + align:start position:0% +philosophy of Mo motion and kinesthetic +studies in skeletal muscular studies um + + align:start position:0% +studies in skeletal muscular studies um + + + align:start position:0% +studies in skeletal muscular studies um +in Veterinary studies in uh artistic + + align:start position:0% +in Veterinary studies in uh artistic + + + align:start position:0% +in Veterinary studies in uh artistic +representation + + align:start position:0% +representation + + + align:start position:0% +representation +of motions specifically mbridge was + + align:start position:0% +of motions specifically mbridge was + + + align:start position:0% +of motions specifically mbridge was +interested in + + align:start position:0% + + + + align:start position:0% + +uh how awkward an animal looks in a in + + align:start position:0% +uh how awkward an animal looks in a in + + + align:start position:0% +uh how awkward an animal looks in a in +in these moments of odd Grace and + + align:start position:0% +in these moments of odd Grace and + + + align:start position:0% +in these moments of odd Grace and +perilousness in the sequence of a + + align:start position:0% +perilousness in the sequence of a + + + align:start position:0% +perilousness in the sequence of a +continuous motion which the eye + + align:start position:0% +continuous motion which the eye + + + align:start position:0% +continuous motion which the eye +registers as graceful there are these + + align:start position:0% +registers as graceful there are these + + + align:start position:0% +registers as graceful there are these +these oddly + + align:start position:0% +these oddly + + + align:start position:0% +these oddly +discontinuous moments which we see but + + align:start position:0% +discontinuous moments which we see but + + + align:start position:0% +discontinuous moments which we see but +don't know that we are seeing it's the + + align:start position:0% +don't know that we are seeing it's the + + + align:start position:0% +don't know that we are seeing it's the +the doc Edon phenomenon isn't + + align:start position:0% + + + + align:start position:0% + +it uh eventually he + + align:start position:0% +it uh eventually he + + + align:start position:0% +it uh eventually he +uh mounted the cameras on different + + align:start position:0% +uh mounted the cameras on different + + + align:start position:0% +uh mounted the cameras on different +angles so that you can see the motion + + align:start position:0% +angles so that you can see the motion + + + align:start position:0% +angles so that you can see the motion +laterally horizontally and and front + + align:start position:0% +laterally horizontally and and front + + + align:start position:0% +laterally horizontally and and front +on + + align:start position:0% +on + + + align:start position:0% +on +uh eventually he was he was lured to the + + align:start position:0% +uh eventually he was he was lured to the + + + align:start position:0% +uh eventually he was he was lured to the +University of Pennsylvania with the + + align:start position:0% +University of Pennsylvania with the + + + align:start position:0% +University of Pennsylvania with the +promised that he could use uh naked + + align:start position:0% +promised that he could use uh naked + + + align:start position:0% +promised that he could use uh naked +models from the art school for human uh + + align:start position:0% +models from the art school for human uh + + + align:start position:0% +models from the art school for human uh +subjects and that he would have uh free + + align:start position:0% +subjects and that he would have uh free + + + align:start position:0% +subjects and that he would have uh free +access to the Philadelphia Zoo so he he + + align:start position:0% +access to the Philadelphia Zoo so he he + + + align:start position:0% +access to the Philadelphia Zoo so he he +prodded the baboon to walk down walk + + align:start position:0% +prodded the baboon to walk down walk + + + align:start position:0% +prodded the baboon to walk down walk +down the aisle right um he also + + align:start position:0% +down the aisle right um he also + + + align:start position:0% +down the aisle right um he also +photographed Walt Whitman naked if + + align:start position:0% +photographed Walt Whitman naked if + + + align:start position:0% +photographed Walt Whitman naked if +you're if you're interested but I'm not + + align:start position:0% +you're if you're interested but I'm not + + + align:start position:0% +you're if you're interested but I'm not +going to show you the + + align:start position:0% + + + + align:start position:0% + +picture wridge recognized that uh having + + align:start position:0% +picture wridge recognized that uh having + + + align:start position:0% +picture wridge recognized that uh having +deconstructed the moment he had also the + + align:start position:0% +deconstructed the moment he had also the + + + align:start position:0% +deconstructed the moment he had also the +option + + align:start position:0% +option + + + align:start position:0% +option +or the the further challenge would be to + + align:start position:0% +or the the further challenge would be to + + + align:start position:0% +or the the further challenge would be to +reconstruct the motion in such a way as + + align:start position:0% +reconstruct the motion in such a way as + + + align:start position:0% +reconstruct the motion in such a way as +to have a fully moving picture right um + + align:start position:0% +to have a fully moving picture right um + + + align:start position:0% +to have a fully moving picture right um +that the the secret of the motion + + align:start position:0% +that the the secret of the motion + + + align:start position:0% +that the the secret of the motion +in uh film what became film was going to + + align:start position:0% +in uh film what became film was going to + + + align:start position:0% +in uh film what became film was going to +be the Reconstruction of motion on the + + align:start position:0% +be the Reconstruction of motion on the + + + align:start position:0% +be the Reconstruction of motion on the +basis of this this deconstruction + + align:start position:0% +basis of this this deconstruction + + + align:start position:0% +basis of this this deconstruction +um he tried various uh + + align:start position:0% +um he tried various uh + + + align:start position:0% +um he tried various uh +technological attempts he kept inventing + + align:start position:0% +technological attempts he kept inventing + + + align:start position:0% +technological attempts he kept inventing +these machines for um representing + + align:start position:0% +these machines for um representing + + + align:start position:0% +these machines for um representing +simultaneity and then representing the + + align:start position:0% +simultaneity and then representing the + + + align:start position:0% +simultaneity and then representing the +Reconstruction of the motion into a into + + align:start position:0% +Reconstruction of the motion into a into + + + align:start position:0% +Reconstruction of the motion into a into +a single fluid motion + + align:start position:0% +a single fluid motion + + + align:start position:0% +a single fluid motion +um because here's where here's where the + + align:start position:0% +um because here's where here's where the + + + align:start position:0% +um because here's where here's where the +story gets complicated can you still + + align:start position:0% +story gets complicated can you still + + + align:start position:0% +story gets complicated can you still +hear me in 1875 in the middle of these + + align:start position:0% +hear me in 1875 in the middle of these + + + align:start position:0% +hear me in 1875 in the middle of these +uh initial experiments running the + + align:start position:0% +uh initial experiments running the + + + align:start position:0% +uh initial experiments running the +racehorse oxident down the down the + + align:start position:0% +racehorse oxident down the down the + + + align:start position:0% +racehorse oxident down the down the +track to stop the motion stop the visual + + align:start position:0% +track to stop the motion stop the visual + + + align:start position:0% +track to stop the motion stop the visual +represent to have a visual + + align:start position:0% +represent to have a visual + + + align:start position:0% +represent to have a visual +representation of the stopped motion uh + + align:start position:0% +representation of the stopped motion uh + + + align:start position:0% +representation of the stopped motion uh +mbridge began to worry whether his only + + align:start position:0% +mbridge began to worry whether his only + + + align:start position:0% +mbridge began to worry whether his only +child with his wife who was 23 years + + align:start position:0% +child with his wife who was 23 years + + + align:start position:0% +child with his wife who was 23 years +younger than he whether his only child + + align:start position:0% +younger than he whether his only child + + + align:start position:0% +younger than he whether his only child +in fact resembled + + align:start position:0% +in fact resembled + + + align:start position:0% +in fact resembled +him he came to the conclusion that the + + align:start position:0% +him he came to the conclusion that the + + + align:start position:0% +him he came to the conclusion that the +child resembled the family's best friend + + align:start position:0% +child resembled the family's best friend + + + align:start position:0% +child resembled the family's best friend +a English journalist and drama + + align:start position:0% +a English journalist and drama + + + align:start position:0% +a English journalist and drama +critic and part-time professional G + + align:start position:0% +critic and part-time professional G + + + align:start position:0% +critic and part-time professional G +he bought a pistol he took the the stage + + align:start position:0% +he bought a pistol he took the the stage + + + align:start position:0% +he bought a pistol he took the the stage +coach to Sacramento he shot the man once + + align:start position:0% +coach to Sacramento he shot the man once + + + align:start position:0% +coach to Sacramento he shot the man once +through the heart and waited beside the + + align:start position:0% +through the heart and waited beside the + + + align:start position:0% +through the heart and waited beside the +body to be + + align:start position:0% +body to be + + + align:start position:0% +body to be +arrested I'm interested in this K and + + align:start position:0% +arrested I'm interested in this K and + + + align:start position:0% +arrested I'm interested in this K and +was found not + + align:start position:0% +was found not + + + align:start position:0% +was found not +guilty this is California in the + + align:start position:0% + + + + align:start position:0% + +1870s but there's a there's a Nexus of + + align:start position:0% +1870s but there's a there's a Nexus of + + + align:start position:0% +1870s but there's a there's a Nexus of +ideas here that that has to do with um + + align:start position:0% +ideas here that that has to do with um + + + align:start position:0% +ideas here that that has to do with um +has the Nexus has has to do with uh not + + align:start position:0% +has the Nexus has has to do with uh not + + + align:start position:0% +has the Nexus has has to do with uh not +only with with time in the visual arts + + align:start position:0% +only with with time in the visual arts + + + align:start position:0% +only with with time in the visual arts +but with a relationship between stopping + + align:start position:0% +but with a relationship between stopping + + + align:start position:0% +but with a relationship between stopping +time and the American propensity to + + align:start position:0% +time and the American propensity to + + + align:start position:0% +time and the American propensity to +solve problems with violence which is + + align:start position:0% +solve problems with violence which is + + + align:start position:0% +solve problems with violence which is +related also to something that's going + + align:start position:0% +related also to something that's going + + + align:start position:0% +related also to something that's going +on in the American West with the the + + align:start position:0% +on in the American West with the the + + + align:start position:0% +on in the American West with the the +spatialization of time right think how + + align:start position:0% +spatialization of time right think how + + + align:start position:0% +spatialization of time right think how +often the + + align:start position:0% +often the + + + align:start position:0% +often the +um geological studies are part of the + + align:start position:0% +um geological studies are part of the + + + align:start position:0% +um geological studies are part of the +philosophic philosophical movements of + + align:start position:0% +philosophic philosophical movements of + + + align:start position:0% +philosophic philosophical movements of +the late 19th century think Darwin right + + align:start position:0% +the late 19th century think Darwin right + + + align:start position:0% +the late 19th century think Darwin right +um uh I think the question of fossils um + + align:start position:0% +um uh I think the question of fossils um + + + align:start position:0% +um uh I think the question of fossils um +and how the uh the stunning + + align:start position:0% +and how the uh the stunning + + + align:start position:0% +and how the uh the stunning +spatialization of time in the American + + align:start position:0% +spatialization of time in the American + + + align:start position:0% +spatialization of time in the American +West changed Americans concepts of + + align:start position:0% +West changed Americans concepts of + + + align:start position:0% +West changed Americans concepts of +personal time and duration right so um I + + align:start position:0% +personal time and duration right so um I + + + align:start position:0% +personal time and duration right so um I +didn't know I was going to spend four + + align:start position:0% +didn't know I was going to spend four + + + align:start position:0% +didn't know I was going to spend four +years writing about a man who in fact um + + align:start position:0% +years writing about a man who in fact um + + + align:start position:0% +years writing about a man who in fact um +murdered out of jealousy + + align:start position:0% +murdered out of jealousy + + + align:start position:0% +murdered out of jealousy +but I want to read you some some uh + + align:start position:0% +but I want to read you some some uh + + + align:start position:0% +but I want to read you some some uh +sections of this + + align:start position:0% +sections of this + + + align:start position:0% +sections of this +poem it begins in the mid 186s when he + + align:start position:0% +poem it begins in the mid 186s when he + + + align:start position:0% +poem it begins in the mid 186s when he +first encounters the American + + align:start position:0% + + + + align:start position:0% + +landscape time was where the Nations + + align:start position:0% +landscape time was where the Nations + + + align:start position:0% +landscape time was where the Nations +wandered time was the cavern Lake the + + align:start position:0% +wandered time was the cavern Lake the + + + align:start position:0% +wandered time was the cavern Lake the +gold unmodified bodies danced + + align:start position:0% +gold unmodified bodies danced + + + align:start position:0% +gold unmodified bodies danced +beside time was the Buffalo his for scar + + align:start position:0% +beside time was the Buffalo his for scar + + + align:start position:0% +beside time was the Buffalo his for scar +strength and range the kindness of his + + align:start position:0% +strength and range the kindness of his + + + align:start position:0% +strength and range the kindness of his +usage jerky tent boot cloak sack Powder + + align:start position:0% +usage jerky tent boot cloak sack Powder + + + align:start position:0% +usage jerky tent boot cloak sack Powder +Horn beads even his severed tail a + + align:start position:0% +Horn beads even his severed tail a + + + align:start position:0% +Horn beads even his severed tail a +switch to flick the pesky green veined + + align:start position:0% +switch to flick the pesky green veined + + + align:start position:0% +switch to flick the pesky green veined +flies time was the musical staff of the + + align:start position:0% +flies time was the musical staff of the + + + align:start position:0% +flies time was the musical staff of the +plane where feral Pony Grace treble to + + align:start position:0% +plane where feral Pony Grace treble to + + + align:start position:0% +plane where feral Pony Grace treble to +the ironline base the hymn that Kansas + + align:start position:0% +the ironline base the hymn that Kansas + + + align:start position:0% +the ironline base the hymn that Kansas +hummed bleeding unsure of the words time + + align:start position:0% +hummed bleeding unsure of the words time + + + align:start position:0% +hummed bleeding unsure of the words time +was one may lifted her head on her + + align:start position:0% +was one may lifted her head on her + + + align:start position:0% +was one may lifted her head on her +thunderc colored neck watching through + + align:start position:0% +thunderc colored neck watching through + + + align:start position:0% +thunderc colored neck watching through +the cleft West where the rail line + + align:start position:0% +the cleft West where the rail line + + + align:start position:0% +the cleft West where the rail line +sutured the field was the history of new + + align:start position:0% +sutured the field was the history of new + + + align:start position:0% +sutured the field was the history of new +light swollen between the hills and + + align:start position:0% +light swollen between the hills and + + + align:start position:0% +light swollen between the hills and +passed into her eye dissolving back + + align:start position:0% +passed into her eye dissolving back + + + align:start position:0% +passed into her eye dissolving back +through her dark Gold Body and she + + align:start position:0% +through her dark Gold Body and she + + + align:start position:0% +through her dark Gold Body and she +contained it and moved off she she slow + + align:start position:0% +contained it and moved off she she slow + + + align:start position:0% +contained it and moved off she she slow +cantered in Poise and + + align:start position:0% + + + + align:start position:0% + +silhouette he moves to yosity to to + + align:start position:0% +silhouette he moves to yosity to to + + + align:start position:0% +silhouette he moves to yosity to to +photograph the the uh Park the + + align:start position:0% +photograph the the uh Park the + + + align:start position:0% +photograph the the uh Park the +landscape High blue miles above the sea + + align:start position:0% +landscape High blue miles above the sea + + + align:start position:0% +landscape High blue miles above the sea +men sank like + + align:start position:0% +men sank like + + + align:start position:0% +men sank like +fish pant silked and drank lied at night + + align:start position:0% +fish pant silked and drank lied at night + + + align:start position:0% +fish pant silked and drank lied at night +like gospel + + align:start position:0% +like gospel + + + align:start position:0% +like gospel +Paradise none bar his cabin door there + + align:start position:0% +Paradise none bar his cabin door there + + + align:start position:0% +Paradise none bar his cabin door there +being little enough to hoard but hope + + align:start position:0% +being little enough to hoard but hope + + + align:start position:0% +being little enough to hoard but hope +and old + + align:start position:0% +and old + + + align:start position:0% +and old +jokes or locked in slow Stone her ages + + align:start position:0% +jokes or locked in slow Stone her ages + + + align:start position:0% +jokes or locked in slow Stone her ages +piled and folded + + align:start position:0% +piled and folded + + + align:start position:0% +piled and folded +waiting from Sky to ground and lower + + align:start position:0% +waiting from Sky to ground and lower + + + align:start position:0% +waiting from Sky to ground and lower +through mineral water dropping slowly + + align:start position:0% +through mineral water dropping slowly + + + align:start position:0% +through mineral water dropping slowly +carved the caves filled them with + + align:start position:0% +carved the caves filled them with + + + align:start position:0% +carved the caves filled them with +Rift what I learned from the mountain + + align:start position:0% +Rift what I learned from the mountain + + + align:start position:0% +Rift what I learned from the mountain +was formalism watching quietly while + + align:start position:0% +was formalism watching quietly while + + + align:start position:0% +was formalism watching quietly while +what fell + + align:start position:0% +what fell + + + align:start position:0% +what fell +fell I was patient I sifted the light + + align:start position:0% +fell I was patient I sifted the light + + + align:start position:0% +fell I was patient I sifted the light +for a dust it was bright golden + + align:start position:0% +for a dust it was bright golden + + + align:start position:0% +for a dust it was bright golden +momentary passive and cold it was free + + align:start position:0% +momentary passive and cold it was free + + + align:start position:0% +momentary passive and cold it was free +for the work of taking hey America + + align:start position:0% +for the work of taking hey America + + + align:start position:0% +for the work of taking hey America +suited me just + + align:start position:0% + + + + align:start position:0% + +fine something about those photographs + + align:start position:0% +fine something about those photographs + + + align:start position:0% +fine something about those photographs +has always always reminded me of riding + + align:start position:0% +has always always reminded me of riding + + + align:start position:0% +has always always reminded me of riding +in a train right the the the way the + + align:start position:0% +in a train right the the the way the + + + align:start position:0% +in a train right the the the way the +train window frames the dis frames The + + align:start position:0% +train window frames the dis frames The + + + align:start position:0% +train window frames the dis frames The +Continuous landscape making it seem a + + align:start position:0% +Continuous landscape making it seem a + + + align:start position:0% +Continuous landscape making it seem a +series of discontinuous shots + + align:start position:0% +series of discontinuous shots + + + align:start position:0% +series of discontinuous shots +right in the railway Carriage window a + + align:start position:0% +right in the railway Carriage window a + + + align:start position:0% +right in the railway Carriage window a +continent slid past serial discontinuous + + align:start position:0% +continent slid past serial discontinuous + + + align:start position:0% +continent slid past serial discontinuous +framed Chief Joseph Trails through the + + align:start position:0% +framed Chief Joseph Trails through the + + + align:start position:0% +framed Chief Joseph Trails through the +Black Hills honoring his defeat the clan + + align:start position:0% +Black Hills honoring his defeat the clan + + + align:start position:0% +Black Hills honoring his defeat the clan +reassembles the South Sitting Bull joins + + align:start position:0% +reassembles the South Sitting Bull joins + + + align:start position:0% +reassembles the South Sitting Bull joins +the traveling circus a barrel of whale + + align:start position:0% +the traveling circus a barrel of whale + + + align:start position:0% +the traveling circus a barrel of whale +oil smolders on the + + align:start position:0% +oil smolders on the + + + align:start position:0% +oil smolders on the +warf each of us now was simultaneous now + + align:start position:0% +warf each of us now was simultaneous now + + + align:start position:0% +warf each of us now was simultaneous now +no need to wait no longer idle now even + + align:start position:0% +no need to wait no longer idle now even + + + align:start position:0% +no need to wait no longer idle now even +American Leisure was eager and Americans + + align:start position:0% +American Leisure was eager and Americans + + + align:start position:0% +American Leisure was eager and Americans +adore that sort of thing the high futin + + align:start position:0% +adore that sort of thing the high futin + + + align:start position:0% +adore that sort of thing the high futin +slurry of pragmatism civic virtue and + + align:start position:0% +slurry of pragmatism civic virtue and + + + align:start position:0% +slurry of pragmatism civic virtue and +greed that lays the track towards + + align:start position:0% +greed that lays the track towards + + + align:start position:0% +greed that lays the track towards +metaphor that is a violence against the + + align:start position:0% +metaphor that is a violence against the + + + align:start position:0% +metaphor that is a violence against the +particular Stanford the iron iron yard + + align:start position:0% +particular Stanford the iron iron yard + + + align:start position:0% +particular Stanford the iron iron yard +millionaire the Big Shot Gas bag craved + + align:start position:0% +millionaire the Big Shot Gas bag craved + + + align:start position:0% +millionaire the Big Shot Gas bag craved +admiration and called it science he + + align:start position:0% +admiration and called it science he + + + align:start position:0% +admiration and called it science he +loved that Beast me I felt half at home + + align:start position:0% +loved that Beast me I felt half at home + + + align:start position:0% +loved that Beast me I felt half at home +California Big Empty I had time on my + + align:start position:0% +California Big Empty I had time on my + + + align:start position:0% +California Big Empty I had time on my +hands imagining a new mode of seeing + + align:start position:0% +hands imagining a new mode of seeing + + + align:start position:0% +hands imagining a new mode of seeing +time as form relieved of matter the + + align:start position:0% +time as form relieved of matter the + + + align:start position:0% +time as form relieved of matter the +visible object of Interest as glassy + + align:start position:0% +visible object of Interest as glassy + + + align:start position:0% +visible object of Interest as glassy +surface real itself and not what the + + align:start position:0% +surface real itself and not what the + + + align:start position:0% +surface real itself and not what the +shape contained + + align:start position:0% +shape contained + + + align:start position:0% +shape contained +well that was a big pile of thinking the + + align:start position:0% +well that was a big pile of thinking the + + + align:start position:0% +well that was a big pile of thinking the +two of us in the Big Bay geling we made + + align:start position:0% +two of us in the Big Bay geling we made + + + align:start position:0% +two of us in the Big Bay geling we made +a hell of the + + align:start position:0% + + + + align:start position:0% + +team he meets Stanford to and is hired + + align:start position:0% +team he meets Stanford to and is hired + + + align:start position:0% +team he meets Stanford to and is hired +to test the theory of unsupported + + align:start position:0% + + + + align:start position:0% + +motion I practiced on the mountain + + align:start position:0% +motion I practiced on the mountain + + + align:start position:0% +motion I practiced on the mountain +because it mused slowly in its skin of + + align:start position:0% +because it mused slowly in its skin of + + + align:start position:0% +because it mused slowly in its skin of +forms I practiced on the Autumn I knew + + align:start position:0% +forms I practiced on the Autumn I knew + + + align:start position:0% +forms I practiced on the Autumn I knew +from the inside the Cadence of the great + + align:start position:0% +from the inside the Cadence of the great + + + align:start position:0% +from the inside the Cadence of the great +waste I practiced on the city because it + + align:start position:0% +waste I practiced on the city because it + + + align:start position:0% +waste I practiced on the city because it +hid within itself growing by folding + + align:start position:0% +hid within itself growing by folding + + + align:start position:0% +hid within itself growing by folding +back like a girl's growing + + align:start position:0% +back like a girl's growing + + + align:start position:0% +back like a girl's growing +body I married a woman because I had + + align:start position:0% +body I married a woman because I had + + + align:start position:0% +body I married a woman because I had +penetrated her when I saw the horse the + + align:start position:0% +penetrated her when I saw the horse the + + + align:start position:0% +penetrated her when I saw the horse the +one of its body complete in the field + + align:start position:0% +one of its body complete in the field + + + align:start position:0% +one of its body complete in the field +the question was already familiar + + align:start position:0% + + + + align:start position:0% + +the answer to uh Stanford's question is + + align:start position:0% +the answer to uh Stanford's question is + + + align:start position:0% +the answer to uh Stanford's question is +yes at first the negative was slow + + align:start position:0% +yes at first the negative was slow + + + align:start position:0% +yes at first the negative was slow +admitting too much necessary light the + + align:start position:0% +admitting too much necessary light the + + + align:start position:0% +admitting too much necessary light the +body of the animal entered a blur when I + + align:start position:0% +body of the animal entered a blur when I + + + align:start position:0% +body of the animal entered a blur when I +rinsed the plate dry with silver salt + + align:start position:0% +rinsed the plate dry with silver salt + + + align:start position:0% +rinsed the plate dry with silver salt +the the ordinary spil it broke open it + + align:start position:0% +the the ordinary spil it broke open it + + + align:start position:0% +the the ordinary spil it broke open it +stopped to happen through stations of + + align:start position:0% +stopped to happen through stations of + + + align:start position:0% +stopped to happen through stations of +blunder The Arc of the lyric motion + + align:start position:0% +blunder The Arc of the lyric motion + + + align:start position:0% +blunder The Arc of the lyric motion +poised from me light spelled its genus + + align:start position:0% +poised from me light spelled its genus + + + align:start position:0% +poised from me light spelled its genus +ology in the continuous a posture had + + align:start position:0% +ology in the continuous a posture had + + + align:start position:0% +ology in the continuous a posture had +told where the body had been + + align:start position:0% +told where the body had been + + + align:start position:0% +told where the body had been +splice and that was until then site the + + align:start position:0% +splice and that was until then site the + + + align:start position:0% +splice and that was until then site the +art of + + align:start position:0% +art of + + + align:start position:0% +art of +Elegy I tighten the eye my line detailed + + align:start position:0% +Elegy I tighten the eye my line detailed + + + align:start position:0% +Elegy I tighten the eye my line detailed +a lessness of form so clean the eye + + align:start position:0% +a lessness of form so clean the eye + + + align:start position:0% +a lessness of form so clean the eye +could lick it look I developed a new + + align:start position:0% +could lick it look I developed a new + + + align:start position:0% +could lick it look I developed a new +world grammar all verb writing the + + align:start position:0% +world grammar all verb writing the + + + align:start position:0% +world grammar all verb writing the +moment in salted light this is how to + + align:start position:0% +moment in salted light this is how to + + + align:start position:0% +moment in salted light this is how to +this is how to count one one one one + + align:start position:0% + + + + align:start position:0% + +one just one poem for the murder and + + align:start position:0% +one just one poem for the murder and + + + align:start position:0% +one just one poem for the murder and +then one poem for the for the for the + + align:start position:0% + + + + align:start position:0% + +conclusion out of kindness she lied she + + align:start position:0% +conclusion out of kindness she lied she + + + align:start position:0% +conclusion out of kindness she lied she +that is you my warm + + align:start position:0% +that is you my warm + + + align:start position:0% +that is you my warm +particular in the Flinch of the false + + align:start position:0% +particular in the Flinch of the false + + + align:start position:0% +particular in the Flinch of the false +word a ripping slice in the the fabric + + align:start position:0% +word a ripping slice in the the fabric + + + align:start position:0% +word a ripping slice in the the fabric +wall of the other world what was it + + align:start position:0% +wall of the other world what was it + + + align:start position:0% +wall of the other world what was it +leaked + + align:start position:0% +leaked + + + align:start position:0% +leaked +through it seemed like error + + align:start position:0% +through it seemed like error + + + align:start position:0% +through it seemed like error +ballooning it seemed like trouble a + + align:start position:0% +ballooning it seemed like trouble a + + + align:start position:0% +ballooning it seemed like trouble a +doubleness changing texture turning blue + + align:start position:0% +doubleness changing texture turning blue + + + align:start position:0% +doubleness changing texture turning blue +seemed she + + align:start position:0% +seemed she + + + align:start position:0% +seemed she +seemed I heard only change Lial between + + align:start position:0% +seemed I heard only change Lial between + + + align:start position:0% +seemed I heard only change Lial between +us a pure apparent seeming a pounding as + + align:start position:0% +us a pure apparent seeming a pounding as + + + align:start position:0% +us a pure apparent seeming a pounding as +of hooves some strain trust failed + + align:start position:0% +of hooves some strain trust failed + + + align:start position:0% +of hooves some strain trust failed +dropping from the wh lit single world + + align:start position:0% +dropping from the wh lit single world + + + align:start position:0% +dropping from the wh lit single world +into common history can a seeming be + + align:start position:0% +into common history can a seeming be + + + align:start position:0% +into common history can a seeming be +pure you seem like a she if only for + + align:start position:0% +pure you seem like a she if only for + + + align:start position:0% +pure you seem like a she if only for +that I needed to kill him poor thing + + align:start position:0% +that I needed to kill him poor thing + + + align:start position:0% +that I needed to kill him poor thing +poor depleted thing no wonder it was + + align:start position:0% +poor depleted thing no wonder it was + + + align:start position:0% +poor depleted thing no wonder it was +pressured urgent to escape being in this + + align:start position:0% +pressured urgent to escape being in this + + + align:start position:0% +pressured urgent to escape being in this +way divided from itself made many and + + align:start position:0% +way divided from itself made many and + + + align:start position:0% +way divided from itself made many and +Wishful as swedenberg says of the + + align:start position:0% +Wishful as swedenberg says of the + + + align:start position:0% +Wishful as swedenberg says of the +angels I focused I aligned I aimed High + + align:start position:0% +angels I focused I aligned I aimed High + + + align:start position:0% +angels I focused I aligned I aimed High +like any other man I aspired to an + + align:start position:0% +like any other man I aspired to an + + + align:start position:0% +like any other man I aspired to an +accurate damage I almost pied him but I + + align:start position:0% +accurate damage I almost pied him but I + + + align:start position:0% +accurate damage I almost pied him but I +took my + + align:start position:0% + + + + align:start position:0% + +time he died in 194 back in England uh + + align:start position:0% +time he died in 194 back in England uh + + + align:start position:0% +time he died in 194 back in England uh +his birthplace where he had uh been + + align:start position:0% +his birthplace where he had uh been + + + align:start position:0% +his birthplace where he had uh been +digging in his back Garden uh uh + + align:start position:0% +digging in his back Garden uh uh + + + align:start position:0% +digging in his back Garden uh uh +representation of the continental United + + align:start position:0% +representation of the continental United + + + align:start position:0% +representation of the continental United +States um he tripped and fell and Dred + + align:start position:0% +States um he tripped and fell and Dred + + + align:start position:0% +States um he tripped and fell and Dred +Lake + + align:start position:0% + + + + align:start position:0% + +Michigan I try not to dream much it + + align:start position:0% +Michigan I try not to dream much it + + + align:start position:0% +Michigan I try not to dream much it +cries the night open and it bothers the + + align:start position:0% +cries the night open and it bothers the + + + align:start position:0% +cries the night open and it bothers the +dogs but some days on a broken day when + + align:start position:0% +dogs but some days on a broken day when + + + align:start position:0% +dogs but some days on a broken day when +it turns hard to tell the difference + + align:start position:0% +it turns hard to tell the difference + + + align:start position:0% +it turns hard to tell the difference +between cloud and stone I lie down on + + align:start position:0% +between cloud and stone I lie down on + + + align:start position:0% +between cloud and stone I lie down on +the ground and the black dog comes and + + align:start position:0% +the ground and the black dog comes and + + + align:start position:0% +the ground and the black dog comes and +lies down beside me settling her moist + + align:start position:0% +lies down beside me settling her moist + + + align:start position:0% +lies down beside me settling her moist +snout in the hollow of my shoulder and + + align:start position:0% +snout in the hollow of my shoulder and + + + align:start position:0% +snout in the hollow of my shoulder and +snoring eventually + + align:start position:0% +snoring eventually + + + align:start position:0% +snoring eventually +lightly and then because I can because + + align:start position:0% +lightly and then because I can because + + + align:start position:0% +lightly and then because I can because +she breathes so evenly we both are + + align:start position:0% +she breathes so evenly we both are + + + align:start position:0% +she breathes so evenly we both are +saved I am still and gradually I am in a + + align:start position:0% +saved I am still and gradually I am in a + + + align:start position:0% +saved I am still and gradually I am in a +room and there I am brought forward in a + + align:start position:0% +room and there I am brought forward in a + + + align:start position:0% +room and there I am brought forward in a +body convergent as the whittel end of a + + align:start position:0% +body convergent as the whittel end of a + + + align:start position:0% +body convergent as the whittel end of a +stub pencil though it does not feel + + align:start position:0% +stub pencil though it does not feel + + + align:start position:0% +stub pencil though it does not feel +exactly like my life it is so + + align:start position:0% +exactly like my life it is so + + + align:start position:0% +exactly like my life it is so +teen the light kind and lacking a source + + align:start position:0% +teen the light kind and lacking a source + + + align:start position:0% +teen the light kind and lacking a source +and it is a kind of relief this white + + align:start position:0% +and it is a kind of relief this white + + + align:start position:0% +and it is a kind of relief this white +expansiveness a silence after + + align:start position:0% +expansiveness a silence after + + + align:start position:0% +expansiveness a silence after +Bells not to be seen not to burn inside + + align:start position:0% +Bells not to be seen not to burn inside + + + align:start position:0% +Bells not to be seen not to burn inside +and justify not to play that red ukulele + + align:start position:0% +and justify not to play that red ukulele + + + align:start position:0% +and justify not to play that red ukulele +it sparkling River of fleas not to harm + + align:start position:0% +it sparkling River of fleas not to harm + + + align:start position:0% +it sparkling River of fleas not to harm +in a dailiness not to work not to make + + align:start position:0% +in a dailiness not to work not to make + + + align:start position:0% +in a dailiness not to work not to make +art left and right beyond the blind + + align:start position:0% +art left and right beyond the blind + + + align:start position:0% +art left and right beyond the blind +walls there may be actions animated + + align:start position:0% +walls there may be actions animated + + + align:start position:0% +walls there may be actions animated +things but I am this composure + + align:start position:0% +things but I am this composure + + + align:start position:0% +things but I am this composure +sometimes an animal is waiting and I + + align:start position:0% +sometimes an animal is waiting and I + + + align:start position:0% +sometimes an animal is waiting and I +know I do not need to avoid + + align:start position:0% +know I do not need to avoid + + + align:start position:0% +know I do not need to avoid +her of course she's some sort of Doubt + + align:start position:0% +her of course she's some sort of Doubt + + + align:start position:0% +her of course she's some sort of Doubt +or death some animal neutrality I can + + align:start position:0% +or death some animal neutrality I can + + + align:start position:0% +or death some animal neutrality I can +interpret but still in the room she + + align:start position:0% +interpret but still in the room she + + + align:start position:0% +interpret but still in the room she +watches uncurling her righteous + + align:start position:0% +watches uncurling her righteous + + + align:start position:0% +watches uncurling her righteous +improbable tail she prows she knows me + + align:start position:0% +improbable tail she prows she knows me + + + align:start position:0% +improbable tail she prows she knows me +her teeth raggedy with + + align:start position:0% +her teeth raggedy with + + + align:start position:0% +her teeth raggedy with +glint my skin anticipates the pounce + + align:start position:0% +glint my skin anticipates the pounce + + + align:start position:0% +glint my skin anticipates the pounce +noisess the claws the + + align:start position:0% +noisess the claws the + + + align:start position:0% +noisess the claws the +slashing her Lush Whispers tick I find + + align:start position:0% +slashing her Lush Whispers tick I find + + + align:start position:0% +slashing her Lush Whispers tick I find +it easy to + + align:start position:0% +it easy to + + + align:start position:0% +it easy to +acques she's not + + align:start position:0% +acques she's not + + + align:start position:0% +acques she's not +angry she's + + align:start position:0% + + + + align:start position:0% + +hungry well I think you see a burial + + align:start position:0% +hungry well I think you see a burial + + + align:start position:0% +hungry well I think you see a burial +ground it's in + + align:start position:0% +ground it's in + + + align:start position:0% +ground it's in +gr it's um very close to my + + align:start position:0% +gr it's um very close to my + + + align:start position:0% +gr it's um very close to my +house and in this burial ground last + + align:start position:0% +house and in this burial ground last + + + align:start position:0% +house and in this burial ground last +summer a man was + + align:start position:0% +summer a man was + + + align:start position:0% +summer a man was +was photographing the stones and he + + align:start position:0% +was photographing the stones and he + + + align:start position:0% +was photographing the stones and he +turned around and saw the church that + + align:start position:0% +turned around and saw the church that + + + align:start position:0% +turned around and saw the church that +was up opposite and he photographed the + + align:start position:0% +was up opposite and he photographed the + + + align:start position:0% +was up opposite and he photographed the +church and then he came to the door of + + align:start position:0% +church and then he came to the door of + + + align:start position:0% +church and then he came to the door of +the church and he + + align:start position:0% +the church and he + + + align:start position:0% +the church and he +said could I'd see the clock and so I + + align:start position:0% +said could I'd see the clock and so I + + + align:start position:0% +said could I'd see the clock and so I +said of course cuz I love the clock and + + align:start position:0% +said of course cuz I love the clock and + + + align:start position:0% +said of course cuz I love the clock and +I'm delighted to show anybody the clock + + align:start position:0% +I'm delighted to show anybody the clock + + + align:start position:0% +I'm delighted to show anybody the clock +and so he came in and he was + + align:start position:0% +and so he came in and he was + + + align:start position:0% +and so he came in and he was +photographing all this time he's a + + align:start position:0% +photographing all this time he's a + + + align:start position:0% +photographing all this time he's a +videographer ER which um was very + + align:start position:0% +videographer ER which um was very + + + align:start position:0% +videographer ER which um was very +recently retired and he um was using and + + align:start position:0% +recently retired and he um was using and + + + align:start position:0% +recently retired and he um was using and +now doing it for himself instead of U + + align:start position:0% +now doing it for himself instead of U + + + align:start position:0% +now doing it for himself instead of U +following other people's instructions so + + align:start position:0% +following other people's instructions so + + + align:start position:0% +following other people's instructions so +we + + align:start position:0% +we + + + align:start position:0% +we +um came into the church and he + + align:start position:0% +um came into the church and he + + + align:start position:0% +um came into the church and he +photographed and I took him up to the + + align:start position:0% +photographed and I took him up to the + + + align:start position:0% +photographed and I took him up to the +clock now this just this little tiny um + + align:start position:0% +clock now this just this little tiny um + + + align:start position:0% +clock now this just this little tiny um +piece of the clock is um just an opening + + align:start position:0% +piece of the clock is um just an opening + + + align:start position:0% +piece of the clock is um just an opening +to this uh movie that he made now if I + + align:start position:0% +to this uh movie that he made now if I + + + align:start position:0% +to this uh movie that he made now if I +go a little further we'll start the + + align:start position:0% +go a little further we'll start the + + + align:start position:0% +go a little further we'll start the +movie as he did you do we hear + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +yet do we hear + + align:start position:0% + + + + align:start position:0% + +it when I got the invitation to talk + + align:start position:0% +it when I got the invitation to talk + + + align:start position:0% +it when I got the invitation to talk +here I really thought that I was + + align:start position:0% +here I really thought that I was + + + align:start position:0% +here I really thought that I was +completely + + align:start position:0% +completely + + + align:start position:0% +completely +unprofessional knew loved musical time + + align:start position:0% +unprofessional knew loved musical time + + + align:start position:0% +unprofessional knew loved musical time +of course but knew nothing whatsoever + + align:start position:0% +of course but knew nothing whatsoever + + + align:start position:0% +of course but knew nothing whatsoever +about it except to experience + + align:start position:0% +about it except to experience + + + align:start position:0% +about it except to experience +it and thought it was really a + + align:start position:0% +it and thought it was really a + + + align:start position:0% +it and thought it was really a +mistake I'm Paul MTI I'm an artist and I + + align:start position:0% +mistake I'm Paul MTI I'm an artist and I + + + align:start position:0% +mistake I'm Paul MTI I'm an artist and I +live in this church and have lived in + + align:start position:0% +live in this church and have lived in + + + align:start position:0% +live in this church and have lived in +this church since about + + align:start position:0% + + + + align:start position:0% + +1981 so I was taking him upstairs + + align:start position:0% +1981 so I was taking him upstairs + + + align:start position:0% +1981 so I was taking him upstairs +to and we're going to turn down the + + align:start position:0% +to and we're going to turn down the + + + align:start position:0% +to and we're going to turn down the +sound up there um because I found myself + + align:start position:0% +sound up there um because I found myself + + + align:start position:0% +sound up there um because I found myself +explaining to him the clock and showing + + align:start position:0% +explaining to him the clock and showing + + + align:start position:0% +explaining to him the clock and showing +him uh all the different parts of it and + + align:start position:0% +him uh all the different parts of it and + + + align:start position:0% +him uh all the different parts of it and +realizing that this clock is a very + + align:start position:0% +realizing that this clock is a very + + + align:start position:0% +realizing that this clock is a very +central part of the church for me I love + + align:start position:0% +central part of the church for me I love + + + align:start position:0% +central part of the church for me I love +mechanisms and as you'll see the way + + align:start position:0% +mechanisms and as you'll see the way + + + align:start position:0% +mechanisms and as you'll see the way +they fit together these um beautiful + + align:start position:0% +they fit together these um beautiful + + + align:start position:0% +they fit together these um beautiful +Wheels the escapement The Arc there that + + align:start position:0% +Wheels the escapement The Arc there that + + + align:start position:0% +Wheels the escapement The Arc there that +is attached to the pendulum the pendulum + + align:start position:0% +is attached to the pendulum the pendulum + + + align:start position:0% +is attached to the pendulum the pendulum +moves back and forth the teeth come in + + align:start position:0% +moves back and forth the teeth come in + + + align:start position:0% +moves back and forth the teeth come in +and out of the escapement wheel and as + + align:start position:0% +and out of the escapement wheel and as + + + align:start position:0% +and out of the escapement wheel and as +the + + align:start position:0% +the + + + align:start position:0% +the +wheel leaves the the ark it gives a + + align:start position:0% +wheel leaves the the ark it gives a + + + align:start position:0% +wheel leaves the the ark it gives a +little bit of energy to the ark it it's + + align:start position:0% +little bit of energy to the ark it it's + + + align:start position:0% +little bit of energy to the ark it it's +what keeps the pendulum going it's so + + align:start position:0% +what keeps the pendulum going it's so + + + align:start position:0% +what keeps the pendulum going it's so +beautiful because if the if the + + align:start position:0% +beautiful because if the if the + + + align:start position:0% +beautiful because if the if the +escapement wheel were not there the + + align:start position:0% +escapement wheel were not there the + + + align:start position:0% +escapement wheel were not there the +whole thing would run out and the clock + + align:start position:0% +whole thing would run out and the clock + + + align:start position:0% +whole thing would run out and the clock +would go down down down anyway this is a + + align:start position:0% +would go down down down anyway this is a + + + align:start position:0% +would go down down down anyway this is a +clock that I have kept wound um for the + + align:start position:0% +clock that I have kept wound um for the + + + align:start position:0% +clock that I have kept wound um for the +last 20 years and it's been there since + + align:start position:0% +last 20 years and it's been there since + + + align:start position:0% +last 20 years and it's been there since +1893 it uh needs no repairs it just + + align:start position:0% +1893 it uh needs no repairs it just + + + align:start position:0% +1893 it uh needs no repairs it just +needs oil and um it's the I just love + + align:start position:0% +needs oil and um it's the I just love + + + align:start position:0% +needs oil and um it's the I just love +the the way + + align:start position:0% +the the way + + + align:start position:0% +the the way +the the mechanics work and work together + + align:start position:0% +the the mechanics work and work together + + + align:start position:0% +the the mechanics work and work together +now this um film I showed because the + + align:start position:0% +now this um film I showed because the + + + align:start position:0% +now this um film I showed because the +first site was musical time that is to + + align:start position:0% +first site was musical time that is to + + + align:start position:0% +first site was musical time that is to +say you saw the clock and you heard the + + align:start position:0% +say you saw the clock and you heard the + + + align:start position:0% +say you saw the clock and you heard the +music and I thought well maybe I've got + + align:start position:0% +music and I thought well maybe I've got + + + align:start position:0% +music and I thought well maybe I've got +some qualifications for coming here + + align:start position:0% +some qualifications for coming here + + + align:start position:0% +some qualifications for coming here +after all and I looked into my other uh + + align:start position:0% +after all and I looked into my other uh + + + align:start position:0% +after all and I looked into my other uh +work and I thought well um I could I + + align:start position:0% +work and I thought well um I could I + + + align:start position:0% +work and I thought well um I could I +could think in terms of the time um of + + align:start position:0% +could think in terms of the time um of + + + align:start position:0% +could think in terms of the time um of +one of my pieces which I would think of + + align:start position:0% +one of my pieces which I would think of + + + align:start position:0% +one of my pieces which I would think of +is having endless time this is going to + + align:start position:0% +is having endless time this is going to + + + align:start position:0% +is having endless time this is going to +interrupt and I just want you to um I + + align:start position:0% +interrupt and I just want you to um I + + + align:start position:0% +interrupt and I just want you to um I +mean I will stop talking um but we go to + + align:start position:0% +mean I will stop talking um but we go to + + + align:start position:0% +mean I will stop talking um but we go to +winding the clock and then we go + + align:start position:0% +winding the clock and then we go + + + align:start position:0% +winding the clock and then we go +upstairs to seeing the Bell here's the + + align:start position:0% +upstairs to seeing the Bell here's the + + + align:start position:0% +upstairs to seeing the Bell here's the +winding and the + + align:start position:0% +winding and the + + + align:start position:0% +winding and the +this this is a ratchet you're lifting up + + align:start position:0% +this this is a ratchet you're lifting up + + + align:start position:0% +this this is a ratchet you're lifting up +about 700 lb of + + align:start position:0% +about 700 lb of + + + align:start position:0% +about 700 lb of +stone first we wind the strip side which + + align:start position:0% +stone first we wind the strip side which + + + align:start position:0% +stone first we wind the strip side which +is raises the ham strike the Bell + + align:start position:0% + + + + align:start position:0% + +I love + + align:start position:0% + + + + align:start position:0% + +ratchet so the Wade is pulling this big + + align:start position:0% +ratchet so the Wade is pulling this big + + + align:start position:0% +ratchet so the Wade is pulling this big +drum with the wire the drum has teeth on + + align:start position:0% +drum with the wire the drum has teeth on + + + align:start position:0% +drum with the wire the drum has teeth on +the edge it's lifting the lever + + align:start position:0% + + + + align:start position:0% + +everything else is taking place as + + align:start position:0% +everything else is taking place as + + + align:start position:0% +everything else is taking place as +necessary there's the wire that goes up + + align:start position:0% +necessary there's the wire that goes up + + + align:start position:0% +necessary there's the wire that goes up +to the + + align:start position:0% +to the + + + align:start position:0% +to the +steeple that is being pulled down by + + align:start position:0% +steeple that is being pulled down by + + + align:start position:0% +steeple that is being pulled down by +that lever through the + + align:start position:0% + + + + align:start position:0% + +ceiling up to the + + align:start position:0% + + + + align:start position:0% + +Bell the hammer falling on the Bell + + align:start position:0% +Bell the hammer falling on the Bell + + + align:start position:0% +Bell the hammer falling on the Bell +it's called clocking the Bell by the way + + align:start position:0% +it's called clocking the Bell by the way + + + align:start position:0% +it's called clocking the Bell by the way +not that that's very + + align:start position:0% +not that that's very + + + align:start position:0% +not that that's very +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +important and so um with this little + + align:start position:0% +important and so um with this little + + + align:start position:0% +important and so um with this little +film I thought we could we could get get + + align:start position:0% +film I thought we could we could get get + + + align:start position:0% +film I thought we could we could get get +started um so I I found five other times + + align:start position:0% +started um so I I found five other times + + + align:start position:0% +started um so I I found five other times +if that we call that musical time I + + align:start position:0% +if that we call that musical time I + + + align:start position:0% +if that we call that musical time I +would find five others to to talk about + + align:start position:0% +would find five others to to talk about + + + align:start position:0% +would find five others to to talk about +and the + + align:start position:0% +and the + + + align:start position:0% +and the +first it really does work better with + + align:start position:0% +first it really does work better with + + + align:start position:0% +first it really does work better with +glasses + + align:start position:0% + + + + align:start position:0% + +the first from one of my early + + align:start position:0% +the first from one of my early + + + align:start position:0% +the first from one of my early +inventions is endless time and so I + + align:start position:0% +inventions is endless time and so I + + + align:start position:0% +inventions is endless time and so I +believe that we can see this object + + align:start position:0% +believe that we can see this object + + + align:start position:0% +believe that we can see this object +which is called + + align:start position:0% +which is called + + + align:start position:0% +which is called +aeroscope it's um the result of somebody + + align:start position:0% +aeroscope it's um the result of somebody + + + align:start position:0% +aeroscope it's um the result of somebody +having given me at some point a um liter + + align:start position:0% +having given me at some point a um liter + + + align:start position:0% +having given me at some point a um liter +bottle of kerosene with aluminum flakes + + align:start position:0% +bottle of kerosene with aluminum flakes + + + align:start position:0% +bottle of kerosene with aluminum flakes +in it which left a a sense of what the + + align:start position:0% +in it which left a a sense of what the + + + align:start position:0% +in it which left a a sense of what the +currents were and I worked on that out + + align:start position:0% +currents were and I worked on that out + + + align:start position:0% +currents were and I worked on that out +of sheer enthusiasm and made ccops in a + + align:start position:0% +of sheer enthusiasm and made ccops in a + + + align:start position:0% +of sheer enthusiasm and made ccops in a +variety of ways this is a circular one + + align:start position:0% +variety of ways this is a circular one + + + align:start position:0% +variety of ways this is a circular one +and it rotates and of course none of + + align:start position:0% +and it rotates and of course none of + + + align:start position:0% +and it rotates and of course none of +them are supposed to be photographed + + align:start position:0% +them are supposed to be photographed + + + align:start position:0% +them are supposed to be photographed +still because they're objects in + + align:start position:0% +still because they're objects in + + + align:start position:0% +still because they're objects in +motion this is just a moment of the um + + align:start position:0% +motion this is just a moment of the um + + + align:start position:0% +motion this is just a moment of the um +of the + + align:start position:0% +of the + + + align:start position:0% +of the +uh the moving ccope which will about to + + align:start position:0% +uh the moving ccope which will about to + + + align:start position:0% +uh the moving ccope which will about to +see now thanks to a film that somebody + + align:start position:0% +see now thanks to a film that somebody + + + align:start position:0% +see now thanks to a film that somebody +made haphazardly and left with + + align:start position:0% +made haphazardly and left with + + + align:start position:0% +made haphazardly and left with +me + + align:start position:0% +me + + + align:start position:0% +me +um and it it shows the why I would call + + align:start position:0% +um and it it shows the why I would call + + + align:start position:0% +um and it it shows the why I would call +it endless time primarily + + align:start position:0% +it endless time primarily + + + align:start position:0% +it endless time primarily +because there is no + + align:start position:0% +because there is no + + + align:start position:0% +because there is no +scale in this + + align:start position:0% +scale in this + + + align:start position:0% +scale in this +object and there are no + + align:start position:0% +object and there are no + + + align:start position:0% +object and there are no +boundaries in this this could be the + + align:start position:0% +boundaries in this this could be the + + + align:start position:0% +boundaries in this this could be the +universe + + align:start position:0% +universe + + + align:start position:0% +universe +it could be a + + align:start position:0% + + + + align:start position:0% + +microscopic and it really to me was an + + align:start position:0% +microscopic and it really to me was an + + + align:start position:0% +microscopic and it really to me was an +image of Eternity this constant motion + + align:start position:0% +image of Eternity this constant motion + + + align:start position:0% +image of Eternity this constant motion +and the chaotic + + align:start position:0% +and the chaotic + + + align:start position:0% +and the chaotic +flux all the fluid dynamist would + + align:start position:0% +flux all the fluid dynamist would + + + align:start position:0% +flux all the fluid dynamist would +question that um but for me it was it + + align:start position:0% +question that um but for me it was it + + + align:start position:0% +question that um but for me it was it +was a piece of great Beauty and one that + + align:start position:0% +was a piece of great Beauty and one that + + + align:start position:0% +was a piece of great Beauty and one that +just took time out of the question + + align:start position:0% + + + + align:start position:0% + +this is the same ccope after it's been + + align:start position:0% +this is the same ccope after it's been + + + align:start position:0% +this is the same ccope after it's been +still for a long long time it is still + + align:start position:0% +still for a long long time it is still + + + align:start position:0% +still for a long long time it is still +showing in the in the liquid a remnant + + align:start position:0% +showing in the in the liquid a remnant + + + align:start position:0% +showing in the in the liquid a remnant +of where it was this is very close to a + + align:start position:0% +of where it was this is very close to a + + + align:start position:0% +of where it was this is very close to a +yinyang and of course there are + + align:start position:0% +yinyang and of course there are + + + align:start position:0% +yinyang and of course there are +thousands and thousands of other images + + align:start position:0% +thousands and thousands of other images + + + align:start position:0% +thousands and thousands of other images +that come from this piece + + align:start position:0% + + + + align:start position:0% + +my next um one which I call ordered and + + align:start position:0% +my next um one which I call ordered and + + + align:start position:0% +my next um one which I call ordered and +chaotic time there's a little bit of a + + align:start position:0% +chaotic time there's a little bit of a + + + align:start position:0% +chaotic time there's a little bit of a +story + + align:start position:0% +story + + + align:start position:0% +story +here in + + align:start position:0% +here in + + + align:start position:0% +here in +1680 a man by the name of Johan bestler + + align:start position:0% +1680 a man by the name of Johan bestler + + + align:start position:0% +1680 a man by the name of Johan bestler +a boy a child a baby was born and + + align:start position:0% +a boy a child a baby was born and + + + align:start position:0% +a boy a child a baby was born and +bestler became a person who did OD jobs + + align:start position:0% +bestler became a person who did OD jobs + + + align:start position:0% +bestler became a person who did OD jobs +who studied different ways of making + + align:start position:0% +who studied different ways of making + + + align:start position:0% +who studied different ways of making +things and worked for different people + + align:start position:0% +things and worked for different people + + + align:start position:0% +things and worked for different people +he was extremely difficult to work with + + align:start position:0% +he was extremely difficult to work with + + + align:start position:0% +he was extremely difficult to work with +he found other people extremely + + align:start position:0% +he found other people extremely + + + align:start position:0% +he found other people extremely +difficult to work with he changed his + + align:start position:0% +difficult to work with he changed his + + + align:start position:0% +difficult to work with he changed his +name to or ferious to make it a little + + align:start position:0% +name to or ferious to make it a little + + + align:start position:0% +name to or ferious to make it a little +bit more + + align:start position:0% +bit more + + + align:start position:0% +bit more +interesting he had made an invention + + align:start position:0% +interesting he had made an invention + + + align:start position:0% +interesting he had made an invention +which he wanted to sell he tried to find + + align:start position:0% +which he wanted to sell he tried to find + + + align:start position:0% +which he wanted to sell he tried to find +people to sell it he made four wheels + + align:start position:0% +people to sell it he made four wheels + + + align:start position:0% +people to sell it he made four wheels +which were + + align:start position:0% +which were + + + align:start position:0% +which were +theoretically um and for all intents and + + align:start position:0% +theoretically um and for all intents and + + + align:start position:0% +theoretically um and for all intents and +purposes um uh perpetuum Mobil which + + align:start position:0% +purposes um uh perpetuum Mobil which + + + align:start position:0% +purposes um uh perpetuum Mobil which +even then they knew you could not do and + + align:start position:0% +even then they knew you could not do and + + + align:start position:0% +even then they knew you could not do and +you could not make however he did show + + align:start position:0% +you could not make however he did show + + + align:start position:0% +you could not make however he did show +these wheels in four different towns in + + align:start position:0% +these wheels in four different towns in + + + align:start position:0% +these wheels in four different towns in +uh larger and larger forms the first one + + align:start position:0% +uh larger and larger forms the first one + + + align:start position:0% +uh larger and larger forms the first one +was only about 3T the last one was about + + align:start position:0% +was only about 3T the last one was about + + + align:start position:0% +was only about 3T the last one was about +11 ft in + + align:start position:0% +11 ft in + + + align:start position:0% +11 ft in +diameter they started turning when you + + align:start position:0% +diameter they started turning when you + + + align:start position:0% +diameter they started turning when you +let them go the first two um and + + align:start position:0% +let them go the first two um and + + + align:start position:0% +let them go the first two um and +continued turning he covered their + + align:start position:0% +continued turning he covered their + + + align:start position:0% +continued turning he covered their +innards so nobody could + + align:start position:0% +innards so nobody could + + + align:start position:0% +innards so nobody could +see well it's a crazy story + + align:start position:0% +see well it's a crazy story + + + align:start position:0% +see well it's a crazy story +and um it's even crazier to even mention + + align:start position:0% +and um it's even crazier to even mention + + + align:start position:0% +and um it's even crazier to even mention +it at MIT where everybody knows the um + + align:start position:0% +it at MIT where everybody knows the um + + + align:start position:0% +it at MIT where everybody knows the um +the laws I went to Harvard but I I even + + align:start position:0% +the laws I went to Harvard but I I even + + + align:start position:0% +the laws I went to Harvard but I I even +knew that this is impossible + + align:start position:0% +knew that this is impossible + + + align:start position:0% +knew that this is impossible +so I loved this story I read it in a + + align:start position:0% +so I loved this story I read it in a + + + align:start position:0% +so I loved this story I read it in a +book called Oddities published in + + align:start position:0% +book called Oddities published in + + + align:start position:0% +book called Oddities published in +1928 written by Lieutenant uh Commander + + align:start position:0% +1928 written by Lieutenant uh Commander + + + align:start position:0% +1928 written by Lieutenant uh Commander +rert Thomas Gould a brilliant um and + + align:start position:0% +rert Thomas Gould a brilliant um and + + + align:start position:0% +rert Thomas Gould a brilliant um and +very gifted historian in the English + + align:start position:0% +very gifted historian in the English + + + align:start position:0% +very gifted historian in the English +Royal Navy and he was um so gifted that + + align:start position:0% +Royal Navy and he was um so gifted that + + + align:start position:0% +Royal Navy and he was um so gifted that +in fact he was given the honor of + + align:start position:0% +in fact he was given the honor of + + + align:start position:0% +in fact he was given the honor of +cleaning and repairing Harrison's number + + align:start position:0% +cleaning and repairing Harrison's number + + + align:start position:0% +cleaning and repairing Harrison's number +four the most famous clock in England + + align:start position:0% +four the most famous clock in England + + + align:start position:0% +four the most famous clock in England +for those who know their clocks I can't + + align:start position:0% +for those who know their clocks I can't + + + align:start position:0% +for those who know their clocks I can't +get into it now but it's extraordinary + + align:start position:0% + + + + align:start position:0% + +that what are we + + align:start position:0% +that what are we + + + align:start position:0% +that what are we +missing did they not hear any of the the + + align:start position:0% +missing did they not hear any of the the + + + align:start position:0% +missing did they not hear any of the the +bells before they catch + + align:start position:0% +bells before they catch + + + align:start position:0% +bells before they catch +I see okay well I'm sorry for what you + + align:start position:0% +I see okay well I'm sorry for what you + + + align:start position:0% +I see okay well I'm sorry for what you +missed I got it right up here and I + + align:start position:0% +missed I got it right up here and I + + + align:start position:0% +missed I got it right up here and I +couldn't tell whether you were really + + align:start position:0% +couldn't tell whether you were really + + + align:start position:0% +couldn't tell whether you were really +hearing it but that was the the clock on + + align:start position:0% +hearing it but that was the the clock on + + + align:start position:0% +hearing it but that was the the clock on +the + + align:start position:0% +the + + + align:start position:0% +the +steeple and the mechanism in any case um + + align:start position:0% +steeple and the mechanism in any case um + + + align:start position:0% +steeple and the mechanism in any case um +G read this + + align:start position:0% +G read this + + + align:start position:0% +G read this +because this + + align:start position:0% +because this + + + align:start position:0% +because this +looks oh no that's all right G read this + + align:start position:0% +looks oh no that's all right G read this + + + align:start position:0% +looks oh no that's all right G read this +uh because he was interested in Oni + + align:start position:0% +uh because he was interested in Oni + + + align:start position:0% +uh because he was interested in Oni +these and he was and so he wrote about + + align:start position:0% +these and he was and so he wrote about + + + align:start position:0% +these and he was and so he wrote about +them and he wrote this wonderful story + + align:start position:0% +them and he wrote this wonderful story + + + align:start position:0% +them and he wrote this wonderful story +which was as true as he could make it um + + align:start position:0% +which was as true as he could make it um + + + align:start position:0% +which was as true as he could make it um +from the literature of the + + align:start position:0% +from the literature of the + + + align:start position:0% +from the literature of the +times or ferious himself was a failure + + align:start position:0% +times or ferious himself was a failure + + + align:start position:0% +times or ferious himself was a failure +he failed to find anybody who could um + + align:start position:0% +he failed to find anybody who could um + + + align:start position:0% +he failed to find anybody who could um +who would buy his invention he failed to + + align:start position:0% +who would buy his invention he failed to + + + align:start position:0% +who would buy his invention he failed to +um he failed to live uh too long he died + + align:start position:0% +um he failed to live uh too long he died + + + align:start position:0% +um he failed to live uh too long he died +in 1745 he was not a success uh a lot of + + align:start position:0% +in 1745 he was not a success uh a lot of + + + align:start position:0% +in 1745 he was not a success uh a lot of +people knew about him and um had seen + + align:start position:0% +people knew about him and um had seen + + + align:start position:0% +people knew about him and um had seen +the wheel wheels at one form or another + + align:start position:0% +the wheel wheels at one form or another + + + align:start position:0% +the wheel wheels at one form or another +or Furious destroyed the wheels every + + align:start position:0% +or Furious destroyed the wheels every + + + align:start position:0% +or Furious destroyed the wheels every +time he moved so nothing was left there + + align:start position:0% +time he moved so nothing was left there + + + align:start position:0% +time he moved so nothing was left there +was no other protection but it was clear + + align:start position:0% +was no other protection but it was clear + + + align:start position:0% +was no other protection but it was clear +that the last wheel which ran for some + + align:start position:0% +that the last wheel which ran for some + + + align:start position:0% +that the last wheel which ran for some +54 days inside a locked room in the + + align:start position:0% +54 days inside a locked room in the + + + align:start position:0% +54 days inside a locked room in the +viernstein castle in + + align:start position:0% +viernstein castle in + + + align:start position:0% +viernstein castle in +escaso um was working continuously and + + align:start position:0% +escaso um was working continuously and + + + align:start position:0% +escaso um was working continuously and +there was nobody inside it and there + + align:start position:0% +there was nobody inside it and there + + + align:start position:0% +there was nobody inside it and there +were no wires going to it and this was + + align:start position:0% +were no wires going to it and this was + + + align:start position:0% +were no wires going to it and this was +documented by physicists of the + + align:start position:0% +documented by physicists of the + + + align:start position:0% +documented by physicists of the +time however it all came to an end but + + align:start position:0% +time however it all came to an end but + + + align:start position:0% +time however it all came to an end but +the story was wonderful I loved it I + + align:start position:0% +the story was wonderful I loved it I + + + align:start position:0% +the story was wonderful I loved it I +felt I had to make something just some + + align:start position:0% +felt I had to make something just some + + + align:start position:0% +felt I had to make something just some +kind of an answer for this and so I made + + align:start position:0% +kind of an answer for this and so I made + + + align:start position:0% +kind of an answer for this and so I made +a wheel and I put pendulum on it and I + + align:start position:0% +a wheel and I put pendulum on it and I + + + align:start position:0% +a wheel and I put pendulum on it and I +put handles on it which you can see and + + align:start position:0% +put handles on it which you can see and + + + align:start position:0% +put handles on it which you can see and +then um I also what you can't see from + + align:start position:0% +then um I also what you can't see from + + + align:start position:0% +then um I also what you can't see from +here is that I put lights in the ends of + + align:start position:0% +here is that I put lights in the ends of + + + align:start position:0% +here is that I put lights in the ends of +the pendulums and then I could spin it + + align:start position:0% +the pendulums and then I could spin it + + + align:start position:0% +the pendulums and then I could spin it +and so so there you get to sense of what + + align:start position:0% +and so so there you get to sense of what + + + align:start position:0% +and so so there you get to sense of what +was going on and it was + + align:start position:0% +was going on and it was + + + align:start position:0% +was going on and it was +glorious it's just marvelous now these + + align:start position:0% +glorious it's just marvelous now these + + + align:start position:0% +glorious it's just marvelous now these +are just you know 1 second + + align:start position:0% +are just you know 1 second + + + align:start position:0% +are just you know 1 second +exposures now here is four or five + + align:start position:0% +exposures now here is four or five + + + align:start position:0% +exposures now here is four or five +seconds exposure so uh you get this + + align:start position:0% +seconds exposure so uh you get this + + + align:start position:0% +seconds exposure so uh you get this +crazy and yet it's exactly right + + align:start position:0% +crazy and yet it's exactly right + + + align:start position:0% +crazy and yet it's exactly right +movement that's the thing that I loved + + align:start position:0% +movement that's the thing that I loved + + + align:start position:0% +movement that's the thing that I loved +about it there's it's not as if I was + + align:start position:0% +about it there's it's not as if I was + + + align:start position:0% +about it there's it's not as if I was +drawing a picture of what the the + + align:start position:0% +drawing a picture of what the the + + + align:start position:0% +drawing a picture of what the the +pendulum would do um they were doing + + align:start position:0% +pendulum would do um they were doing + + + align:start position:0% +pendulum would do um they were doing +their stuff exactly right given the the + + align:start position:0% +their stuff exactly right given the the + + + align:start position:0% +their stuff exactly right given the the +the turning that I had put three or four + + align:start position:0% +the turning that I had put three or four + + + align:start position:0% +the turning that I had put three or four +turns into it and as you can see they + + align:start position:0% +turns into it and as you can see they + + + align:start position:0% +turns into it and as you can see they +are uh beautiful I wish you could see + + align:start position:0% +are uh beautiful I wish you could see + + + align:start position:0% +are uh beautiful I wish you could see +them now look at this one every once in + + align:start position:0% +them now look at this one every once in + + + align:start position:0% +them now look at this one every once in +a while the pendulum for some crazy + + align:start position:0% +a while the pendulum for some crazy + + + align:start position:0% +a while the pendulum for some crazy +reason decide to just do their own thing + + align:start position:0% +reason decide to just do their own thing + + + align:start position:0% +reason decide to just do their own thing +and not go mad about it and + + align:start position:0% +and not go mad about it and + + + align:start position:0% +and not go mad about it and +so this is 1 2 3 4 five + + align:start position:0% +so this is 1 2 3 4 five + + + align:start position:0% +so this is 1 2 3 4 five +six um + + align:start position:0% +six um + + + align:start position:0% +six um +revolutions and here the pendulums are + + align:start position:0% +revolutions and here the pendulums are + + + align:start position:0% +revolutions and here the pendulums are +showing that they are Discerning a sort + + align:start position:0% +showing that they are Discerning a sort + + + align:start position:0% +showing that they are Discerning a sort +of uh + + align:start position:0% +of uh + + + align:start position:0% +of uh +attractor and this is the picture that I + + align:start position:0% +attractor and this is the picture that I + + + align:start position:0% +attractor and this is the picture that I +love + + align:start position:0% +love + + + align:start position:0% +love +because at the bottom the pendulum is at + + align:start position:0% +because at the bottom the pendulum is at + + + align:start position:0% +because at the bottom the pendulum is at +the bottom of it it does two swings + + align:start position:0% +the bottom of it it does two swings + + + align:start position:0% +the bottom of it it does two swings +around the wheel and makes this + + align:start position:0% +around the wheel and makes this + + + align:start position:0% +around the wheel and makes this +beautiful form + + align:start position:0% +beautiful form + + + align:start position:0% +beautiful form +well I thought that was lovely but I had + + align:start position:0% +well I thought that was lovely but I had + + + align:start position:0% +well I thought that was lovely but I had +other things to do I knew that um this + + align:start position:0% +other things to do I knew that um this + + + align:start position:0% +other things to do I knew that um this +could go on forever here at the at the + + align:start position:0% +could go on forever here at the at the + + + align:start position:0% +could go on forever here at the at the +end of the the the term the pendulums + + align:start position:0% +end of the the the term the pendulums + + + align:start position:0% +end of the the the term the pendulums +are just going back and + + align:start position:0% +are just going back and + + + align:start position:0% +are just going back and +forth here it's another + + align:start position:0% +forth here it's another + + + align:start position:0% +forth here it's another +Madness and yet with a certain + + align:start position:0% +Madness and yet with a certain + + + align:start position:0% +Madness and yet with a certain +Beauty and here at the very end they're + + align:start position:0% +Beauty and here at the very end they're + + + align:start position:0% +Beauty and here at the very end they're +just kind of waving around a little + + align:start position:0% +just kind of waving around a little + + + align:start position:0% +just kind of waving around a little +bit looking pretty much like + + align:start position:0% +bit looking pretty much like + + + align:start position:0% +bit looking pretty much like +that + + align:start position:0% +that + + + align:start position:0% +that +so that was my um my ordered and chaotic + + align:start position:0% +so that was my um my ordered and chaotic + + + align:start position:0% +so that was my um my ordered and chaotic +time story + + align:start position:0% +time story + + + align:start position:0% +time story +and oh there is one there's one other + + align:start position:0% +and oh there is one there's one other + + + align:start position:0% +and oh there is one there's one other +thing which I have to throw in here in + + align:start position:0% +thing which I have to throw in here in + + + align:start position:0% +thing which I have to throw in here in +1978 I asked aopa who was a friend and + + align:start position:0% +1978 I asked aopa who was a friend and + + + align:start position:0% +1978 I asked aopa who was a friend and +an artist who was at cabs at the time + + align:start position:0% +an artist who was at cabs at the time + + + align:start position:0% +an artist who was at cabs at the time +how I could see the wheel done with a + + align:start position:0% +how I could see the wheel done with a + + + align:start position:0% +how I could see the wheel done with a +computer and so he said just join cabs + + align:start position:0% +computer and so he said just join cabs + + + align:start position:0% +computer and so he said just join cabs +and then I can give you some graduate + + align:start position:0% +and then I can give you some graduate + + + align:start position:0% +and then I can give you some graduate +students so I joined C I said what do I + + align:start position:0% +students so I joined C I said what do I + + + align:start position:0% +students so I joined C I said what do I +have to do he said nothing I joined cabs + + align:start position:0% +have to do he said nothing I joined cabs + + + align:start position:0% +have to do he said nothing I joined cabs +and um he sent me over to Nicholas neup + + align:start position:0% +and um he sent me over to Nicholas neup + + + align:start position:0% +and um he sent me over to Nicholas neup +who found me a couple of graduate + + align:start position:0% +who found me a couple of graduate + + + align:start position:0% +who found me a couple of graduate +students who + + align:start position:0% +students who + + + align:start position:0% +students who +made after a while a um a program where + + align:start position:0% +made after a while a um a program where + + + align:start position:0% +made after a while a um a program where +I could say what the pendulums how long + + align:start position:0% +I could say what the pendulums how long + + + align:start position:0% +I could say what the pendulums how long +they were how much they weighed how much + + align:start position:0% +they were how much they weighed how much + + + align:start position:0% +they were how much they weighed how much +the wheel weighed how big it was what + + align:start position:0% +the wheel weighed how big it was what + + + align:start position:0% +the wheel weighed how big it was what +the initial speed was what the initial + + align:start position:0% +the initial speed was what the initial + + + align:start position:0% +the initial speed was what the initial +uh positions were and then I could let + + align:start position:0% +uh positions were and then I could let + + + align:start position:0% +uh positions were and then I could let +it go and see what + + align:start position:0% +it go and see what + + + align:start position:0% +it go and see what +happened and I did that and I one of the + + align:start position:0% +happened and I did that and I one of the + + + align:start position:0% +happened and I did that and I one of the +ones I liked the M best was I put both + + align:start position:0% +ones I liked the M best was I put both + + + align:start position:0% +ones I liked the M best was I put both +pendulums straight up and then I just + + align:start position:0% +pendulums straight up and then I just + + + align:start position:0% +pendulums straight up and then I just +let go and sooner or you know the + + align:start position:0% +let go and sooner or you know the + + + align:start position:0% +let go and sooner or you know the +pendulums fall down and then they fall + + align:start position:0% +pendulums fall down and then they fall + + + align:start position:0% +pendulums fall down and then they fall +down and and then they shake and then + + align:start position:0% +down and and then they shake and then + + + align:start position:0% +down and and then they shake and then +the wheel starts to move and then the + + align:start position:0% +the wheel starts to move and then the + + + align:start position:0% +the wheel starts to move and then the +they go quite a little bit faster and + + align:start position:0% +they go quite a little bit faster and + + + align:start position:0% +they go quite a little bit faster and +and they keep on going fat I said my God + + align:start position:0% +and they keep on going fat I said my God + + + align:start position:0% +and they keep on going fat I said my God +this thing is behaving like a Perpetual + + align:start position:0% +this thing is behaving like a Perpetual + + + align:start position:0% +this thing is behaving like a Perpetual +emotion machine and it's from MIT this + + align:start position:0% +emotion machine and it's from MIT this + + + align:start position:0% +emotion machine and it's from MIT this +is + + align:start position:0% +is + + + align:start position:0% +is +ridiculous and um I just thought it was + + align:start position:0% +ridiculous and um I just thought it was + + + align:start position:0% +ridiculous and um I just thought it was +so beautiful that uh I didn't take it + + align:start position:0% +so beautiful that uh I didn't take it + + + align:start position:0% +so beautiful that uh I didn't take it +seriously and I did get an explanation + + align:start position:0% +seriously and I did get an explanation + + + align:start position:0% +seriously and I did get an explanation +that this was due to rounding + + align:start position:0% +that this was due to rounding + + + align:start position:0% +that this was due to rounding +errors so there's always something one + + align:start position:0% +errors so there's always something one + + + align:start position:0% +errors so there's always something one +can say it was just wonderful to have it + + align:start position:0% +can say it was just wonderful to have it + + + align:start position:0% +can say it was just wonderful to have it +happen that way though I also felt very + + align:start position:0% +happen that way though I also felt very + + + align:start position:0% +happen that way though I also felt very +strongly that it was a deep mistake on + + align:start position:0% +strongly that it was a deep mistake on + + + align:start position:0% +strongly that it was a deep mistake on +my part to go to the computer to see + + align:start position:0% +my part to go to the computer to see + + + align:start position:0% +my part to go to the computer to see +something + + align:start position:0% +something + + + align:start position:0% +something +happen because I really like things when + + align:start position:0% +happen because I really like things when + + + align:start position:0% +happen because I really like things when +um they come by mistake my mistake and + + align:start position:0% +um they come by mistake my mistake and + + + align:start position:0% +um they come by mistake my mistake and +I've got a couple of um + + align:start position:0% +I've got a couple of um + + + align:start position:0% +I've got a couple of um +uh examples of that at the very end this + + align:start position:0% +uh examples of that at the very end this + + + align:start position:0% +uh examples of that at the very end this +is the Kendall band as you as some of + + align:start position:0% +is the Kendall band as you as some of + + + align:start position:0% +is the Kendall band as you as some of +you know now if you always drive your + + align:start position:0% +you know now if you always drive your + + + align:start position:0% +you know now if you always drive your +car the chances are that you might never + + align:start position:0% +car the chances are that you might never + + + align:start position:0% +car the chances are that you might never +have been down to the Kendall subway + + align:start position:0% +have been down to the Kendall subway + + + align:start position:0% +have been down to the Kendall subway +station certainly that was true for me + + align:start position:0% +station certainly that was true for me + + + align:start position:0% +station certainly that was true for me +and I even lived in Kendall Square at + + align:start position:0% +and I even lived in Kendall Square at + + + align:start position:0% +and I even lived in Kendall Square at +one point but I did nothing but drive + + align:start position:0% +one point but I did nothing but drive + + + align:start position:0% +one point but I did nothing but drive +drive and I saw the Kendall station for + + align:start position:0% +drive and I saw the Kendall station for + + + align:start position:0% +drive and I saw the Kendall station for +the first time when the commission came + + align:start position:0% +the first time when the commission came + + + align:start position:0% +the first time when the commission came +up for a piece to um put it in and let's + + align:start position:0% +up for a piece to um put it in and let's + + + align:start position:0% +up for a piece to um put it in and let's +see this piece I + + align:start position:0% +see this piece I + + + align:start position:0% +see this piece I +Call untimed Music because as it turned + + align:start position:0% +Call untimed Music because as it turned + + + align:start position:0% +Call untimed Music because as it turned +out what I wanted I I wanted the sound I + + align:start position:0% +out what I wanted I I wanted the sound I + + + align:start position:0% +out what I wanted I I wanted the sound I +figured I have tubes they make a + + align:start position:0% +figured I have tubes they make a + + + align:start position:0% +figured I have tubes they make a +beautiful sound I would have pendulums + + align:start position:0% +beautiful sound I would have pendulums + + + align:start position:0% +beautiful sound I would have pendulums +between them we could make the pendulums + + align:start position:0% +between them we could make the pendulums + + + align:start position:0% +between them we could make the pendulums +go back and forth by rocking them a + + align:start position:0% +go back and forth by rocking them a + + + align:start position:0% +go back and forth by rocking them a +little bit with a hang them from a beam + + align:start position:0% +little bit with a hang them from a beam + + + align:start position:0% +little bit with a hang them from a beam +that would be attached to the wall and + + align:start position:0% +that would be attached to the wall and + + + align:start position:0% +that would be attached to the wall and +um then everything would be just just + + align:start position:0% +um then everything would be just just + + + align:start position:0% +um then everything would be just just +fine well I found out that first of all + + align:start position:0% +fine well I found out that first of all + + + align:start position:0% +fine well I found out that first of all +tubs like that do not make a nice sound + + align:start position:0% +tubs like that do not make a nice sound + + + align:start position:0% +tubs like that do not make a nice sound +uh at all + + align:start position:0% +uh at all + + + align:start position:0% +uh at all +and I had already gotten the commission + + align:start position:0% +and I had already gotten the commission + + + align:start position:0% +and I had already gotten the commission +so I couldn't stop making it and I + + align:start position:0% +so I couldn't stop making it and I + + + align:start position:0% +so I couldn't stop making it and I +wasn't going to make it awful and so I + + align:start position:0% +wasn't going to make it awful and so I + + + align:start position:0% +wasn't going to make it awful and so I +had to go back to my first Physics + + align:start position:0% +had to go back to my first Physics + + + align:start position:0% +had to go back to my first Physics +course which I had taken at Harvard and + + align:start position:0% +course which I had taken at Harvard and + + + align:start position:0% +course which I had taken at Harvard and +barely + + align:start position:0% +barely + + + align:start position:0% +barely +passed and I found out where how they + + align:start position:0% +passed and I found out where how they + + + align:start position:0% +passed and I found out where how they +were bending and what I could do about + + align:start position:0% +were bending and what I could do about + + + align:start position:0% +were bending and what I could do about +it and so I doctored them up a little + + align:start position:0% +it and so I doctored them up a little + + + align:start position:0% +it and so I doctored them up a little +bit and got the two overtones that they + + align:start position:0% +bit and got the two overtones that they + + + align:start position:0% +bit and got the two overtones that they +were producing to be just an optimal + + align:start position:0% +were producing to be just an optimal + + + align:start position:0% +were producing to be just an optimal +part so that they are beautiful sounding + + align:start position:0% +part so that they are beautiful sounding + + + align:start position:0% +part so that they are beautiful sounding +now I think that here is another little + + align:start position:0% +now I think that here is another little + + + align:start position:0% +now I think that here is another little +film that somebody u a a professor in + + align:start position:0% +film that somebody u a a professor in + + + align:start position:0% +film that somebody u a a professor in +Japan made for me but for himself of + + align:start position:0% +Japan made for me but for himself of + + + align:start position:0% +Japan made for me but for himself of +course and left your copy + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so some of you know this and some of you + + align:start position:0% +so some of you know this and some of you + + + align:start position:0% +so some of you know this and some of you +also know how often the poor piece was + + align:start position:0% +also know how often the poor piece was + + + align:start position:0% +also know how often the poor piece was +in disarray having been broken because + + align:start position:0% +in disarray having been broken because + + + align:start position:0% +in disarray having been broken because +some joint failed or something that that + + align:start position:0% +some joint failed or something that that + + + align:start position:0% +some joint failed or something that that +was my mistake for going to Harvard + + align:start position:0% +was my mistake for going to Harvard + + + align:start position:0% +was my mistake for going to Harvard +really but um I don't know if I'd come + + align:start position:0% +really but um I don't know if I'd come + + + align:start position:0% +really but um I don't know if I'd come +here if I would have become somebody + + align:start position:0% +here if I would have become somebody + + + align:start position:0% +here if I would have become somebody +totally different um okay well I can + + align:start position:0% +totally different um okay well I can + + + align:start position:0% +totally different um okay well I can +skip the last section I'll just show you + + align:start position:0% +skip the last section I'll just show you + + + align:start position:0% +skip the last section I'll just show you +a couple of notes when I was fixing the + + align:start position:0% +a couple of notes when I was fixing the + + + align:start position:0% +a couple of notes when I was fixing the +the the Kendall band here's the first + + align:start position:0% +the the Kendall band here's the first + + + align:start position:0% +the the Kendall band here's the first +note I I left it saying something had + + align:start position:0% +note I I left it saying something had + + + align:start position:0% +note I I left it saying something had +broken I was fixing it and when I came + + align:start position:0% +broken I was fixing it and when I came + + + align:start position:0% +broken I was fixing it and when I came +back with the fixed part the person had + + align:start position:0% +back with the fixed part the person had + + + align:start position:0% +back with the fixed part the person had +written one person had written if you if + + align:start position:0% +written one person had written if you if + + + align:start position:0% +written one person had written if you if +you spent my tax dollars on this then + + align:start position:0% +you spent my tax dollars on this then + + + align:start position:0% +you spent my tax dollars on this then +may you die + + align:start position:0% +may you die + + + align:start position:0% +may you die +slowly and then underneath somebody else + + align:start position:0% +slowly and then underneath somebody else + + + align:start position:0% +slowly and then underneath somebody else +had written in not as dark if you spent + + align:start position:0% +had written in not as dark if you spent + + + align:start position:0% +had written in not as dark if you spent +my tax dollars on this may you live long + + align:start position:0% +my tax dollars on this may you live long + + + align:start position:0% +my tax dollars on this may you live long +and + + align:start position:0% +and + + + align:start position:0% +and +happily and after that every time I had + + align:start position:0% +happily and after that every time I had + + + align:start position:0% +happily and after that every time I had +to go in and fix it more notes would + + align:start position:0% +to go in and fix it more notes would + + + align:start position:0% +to go in and fix it more notes would +appear I have 50 pages of notes and I'm + + align:start position:0% +appear I have 50 pages of notes and I'm + + + align:start position:0% +appear I have 50 pages of notes and I'm +going to show you two in Rapid order + + align:start position:0% +going to show you two in Rapid order + + + align:start position:0% +going to show you two in Rapid order +here's one I give my explanation at the + + align:start position:0% +here's one I give my explanation at the + + + align:start position:0% +here's one I give my explanation at the +top they put in everything they they've + + align:start position:0% +top they put in everything they they've + + + align:start position:0% +top they put in everything they they've +got to say and some go against it some + + align:start position:0% +got to say and some go against it some + + + align:start position:0% +got to say and some go against it some +say you know this you should have spent + + align:start position:0% +say you know this you should have spent + + + align:start position:0% +say you know this you should have spent +the money on the trains making them come + + align:start position:0% +the money on the trains making them come + + + align:start position:0% +the money on the trains making them come +in time and some somebody else says on + + align:start position:0% +in time and some somebody else says on + + + align:start position:0% +in time and some somebody else says on +the contrary they always are coming too + + align:start position:0% +the contrary they always are coming too + + + align:start position:0% +the contrary they always are coming too +fast for + + align:start position:0% +fast for + + + align:start position:0% +fast for +me and + + align:start position:0% +me and + + + align:start position:0% +me and +so this is the larger Bell and it's I + + align:start position:0% +so this is the larger Bell and it's I + + + align:start position:0% +so this is the larger Bell and it's I +call this extended time I made this for + + align:start position:0% +call this extended time I made this for + + + align:start position:0% +call this extended time I made this for +a um uh the a memorial in Japanese + + align:start position:0% +a um uh the a memorial in Japanese + + + align:start position:0% +a um uh the a memorial in Japanese +American Memorial in Washington and what + + align:start position:0% +American Memorial in Washington and what + + + align:start position:0% +American Memorial in Washington and what +I found out by making a large Bell like + + align:start position:0% +I found out by making a large Bell like + + + align:start position:0% +I found out by making a large Bell like +this which makes a deep and wonderful + + align:start position:0% +this which makes a deep and wonderful + + + align:start position:0% +this which makes a deep and wonderful +sound was + + align:start position:0% +sound was + + + align:start position:0% +sound was +that the sound you have expectations + + align:start position:0% +that the sound you have expectations + + + align:start position:0% +that the sound you have expectations +that the sound is going to + + align:start position:0% +that the sound is going to + + + align:start position:0% +that the sound is going to +drop and it + + align:start position:0% +drop and it + + + align:start position:0% +drop and it +doesn't and here we'll hear a little + + align:start position:0% +doesn't and here we'll hear a little + + + align:start position:0% +doesn't and here we'll hear a little +bit that um of course + + align:start position:0% +bit that um of course + + + align:start position:0% +bit that um of course +it's you won't we won't hear the bells + + align:start position:0% +it's you won't we won't hear the bells + + + align:start position:0% +it's you won't we won't hear the bells +as strongly as I would like + + align:start position:0% + + + + align:start position:0% + +but but when you're standing there + + align:start position:0% +but but when you're standing there + + + align:start position:0% +but but when you're standing there +you're wrapped up in the sound this is a + + align:start position:0% +you're wrapped up in the sound this is a + + + align:start position:0% +you're wrapped up in the sound this is a +very low frequency sound it doesn't come + + align:start position:0% +very low frequency sound it doesn't come + + + align:start position:0% +very low frequency sound it doesn't come +up in the in the um + + align:start position:0% +up in the in the um + + + align:start position:0% +up in the in the um +microphones and uh but there it is now + + align:start position:0% +microphones and uh but there it is now + + + align:start position:0% +microphones and uh but there it is now +we could stop right + + align:start position:0% + + + + align:start position:0% + +there H + + align:start position:0% + + + + align:start position:0% + +that thank you I'm going to try to do a + + align:start position:0% +that thank you I'm going to try to do a + + + align:start position:0% +that thank you I'm going to try to do a +little bit about um our concert + + align:start position:0% +little bit about um our concert + + + align:start position:0% +little bit about um our concert +tonight uh music has I believe a very + + align:start position:0% +tonight uh music has I believe a very + + + align:start position:0% +tonight uh music has I believe a very +special ability to depict + + align:start position:0% +special ability to depict + + + align:start position:0% +special ability to depict +simultaneity in the class on music and + + align:start position:0% +simultaneity in the class on music and + + + align:start position:0% +simultaneity in the class on music and +time offered at MIT this January in + + align:start position:0% +time offered at MIT this January in + + + align:start position:0% +time offered at MIT this January in +conjunction with the festival Steve tcot + + align:start position:0% +conjunction with the festival Steve tcot + + + align:start position:0% +conjunction with the festival Steve tcot +spoke on Thursday about how language how + + align:start position:0% +spoke on Thursday about how language how + + + align:start position:0% +spoke on Thursday about how language how +in language metaphor serves that + + align:start position:0% +in language metaphor serves that + + + align:start position:0% +in language metaphor serves that +function of allowing two connotation + + align:start position:0% +function of allowing two connotation + + + align:start position:0% +function of allowing two connotation +simultaneously I had not really thought + + align:start position:0% +simultaneously I had not really thought + + + align:start position:0% +simultaneously I had not really thought +sufficiently about that before hearing + + align:start position:0% +sufficiently about that before hearing + + + align:start position:0% +sufficiently about that before hearing +him talk about it and obviously cubism + + align:start position:0% +him talk about it and obviously cubism + + + align:start position:0% +him talk about it and obviously cubism +in art particularly in its use of mri's + + align:start position:0% +in art particularly in its use of mri's + + + align:start position:0% +in art particularly in its use of mri's +images um one is Marshal duchamp's uh + + align:start position:0% +images um one is Marshal duchamp's uh + + + align:start position:0% +images um one is Marshal duchamp's uh +new descending stairs is very much + + align:start position:0% +new descending stairs is very much + + + align:start position:0% +new descending stairs is very much +influenced by muybridge's + + align:start position:0% +influenced by muybridge's + + + align:start position:0% +influenced by muybridge's +images um provides multiple views + + align:start position:0% +images um provides multiple views + + + align:start position:0% +images um provides multiple views +simultaneously and in theater it + + align:start position:0% +simultaneously and in theater it + + + align:start position:0% +simultaneously and in theater it +certainly possible to show two scenes + + align:start position:0% +certainly possible to show two scenes + + + align:start position:0% +certainly possible to show two scenes +simultaneously but harder to have two + + align:start position:0% +simultaneously but harder to have two + + + align:start position:0% +simultaneously but harder to have two +conversations running at the same time + + align:start position:0% +conversations running at the same time + + + align:start position:0% +conversations running at the same time +time although Robert Alton does do this + + align:start position:0% +time although Robert Alton does do this + + + align:start position:0% +time although Robert Alton does do this +sometimes in his films but it does make + + align:start position:0% +sometimes in his films but it does make + + + align:start position:0% +sometimes in his films but it does make +it difficult to hear what anyone is + + align:start position:0% +it difficult to hear what anyone is + + + align:start position:0% +it difficult to hear what anyone is +saying so allowing that all great art + + align:start position:0% +saying so allowing that all great art + + + align:start position:0% +saying so allowing that all great art +makes use of Multiplicity to some degree + + align:start position:0% +makes use of Multiplicity to some degree + + + align:start position:0% +makes use of Multiplicity to some degree +I still feel music is privileged in this + + align:start position:0% +I still feel music is privileged in this + + + align:start position:0% +I still feel music is privileged in this +regard as it typically layers different + + align:start position:0% +regard as it typically layers different + + + align:start position:0% +regard as it typically layers different +kinds of events and we hear and listen + + align:start position:0% +kinds of events and we hear and listen + + + align:start position:0% +kinds of events and we hear and listen +to and understand these simultaneities + + align:start position:0% +to and understand these simultaneities + + + align:start position:0% +to and understand these simultaneities +as part of musical + + align:start position:0% +as part of musical + + + align:start position:0% +as part of musical +substance the main except ition to this + + align:start position:0% +substance the main except ition to this + + + align:start position:0% +substance the main except ition to this +situation occurs in religious music or + + align:start position:0% +situation occurs in religious music or + + + align:start position:0% +situation occurs in religious music or +nationalistic music where the purpose is + + align:start position:0% +nationalistic music where the purpose is + + + align:start position:0% +nationalistic music where the purpose is +rather to create a sense of unity or + + align:start position:0% +rather to create a sense of unity or + + + align:start position:0% +rather to create a sense of unity or +even Conformity so that when at + + align:start position:0% +even Conformity so that when at + + + align:start position:0% +even Conformity so that when at +Thanksgiving we sing We Gather together + + align:start position:0% +Thanksgiving we sing We Gather together + + + align:start position:0% +Thanksgiving we sing We Gather together +to ask the Lord's blessing or at a + + align:start position:0% +to ask the Lord's blessing or at a + + + align:start position:0% +to ask the Lord's blessing or at a +political event we stand and Sing + + align:start position:0% +political event we stand and Sing + + + align:start position:0% +political event we stand and Sing +America the Beautiful we either sing the + + align:start position:0% +America the Beautiful we either sing the + + + align:start position:0% +America the Beautiful we either sing the +melody all together or we sing it in + + align:start position:0% +melody all together or we sing it in + + + align:start position:0% +melody all together or we sing it in +harmony with all the parts moving + + align:start position:0% +harmony with all the parts moving + + + align:start position:0% +harmony with all the parts moving +together in rhythmic lock step what is + + align:start position:0% +together in rhythmic lock step what is + + + align:start position:0% +together in rhythmic lock step what is +called homophony in music but that is + + align:start position:0% +called homophony in music but that is + + + align:start position:0% +called homophony in music but that is +not the most typical texture in + + align:start position:0% +not the most typical texture in + + + align:start position:0% +not the most typical texture in +classical or popular music which + + align:start position:0% +classical or popular music which + + + align:start position:0% +classical or popular music which +typically has multiple things going on + + align:start position:0% +typically has multiple things going on + + + align:start position:0% +typically has multiple things going on +at the same time even in music which is + + align:start position:0% +at the same time even in music which is + + + align:start position:0% +at the same time even in music which is +largely Melody and accompaniment we can + + align:start position:0% +largely Melody and accompaniment we can + + + align:start position:0% +largely Melody and accompaniment we can +separate out the accompaniment which + + align:start position:0% +separate out the accompaniment which + + + align:start position:0% +separate out the accompaniment which +typically provides a beat pattern from + + align:start position:0% +typically provides a beat pattern from + + + align:start position:0% +typically provides a beat pattern from +the melody which floats over the top and + + align:start position:0% +the melody which floats over the top and + + + align:start position:0% +the melody which floats over the top and +this is certainly true in popular music + + align:start position:0% +this is certainly true in popular music + + + align:start position:0% +this is certainly true in popular music +where you hear you know the Rhythm + + align:start position:0% +where you hear you know the Rhythm + + + align:start position:0% +where you hear you know the Rhythm +Section is doing one thing and the lead + + align:start position:0% +Section is doing one thing and the lead + + + align:start position:0% +Section is doing one thing and the lead +vocalist is doing something else and you + + align:start position:0% +vocalist is doing something else and you + + + align:start position:0% +vocalist is doing something else and you +hear how those things work together but + + align:start position:0% +hear how those things work together but + + + align:start position:0% +hear how those things work together but +it works just as well in a Mozart Sonata + + align:start position:0% +it works just as well in a Mozart Sonata + + + align:start position:0% +it works just as well in a Mozart Sonata +where the alberty bass is going + + align:start position:0% + + + + align:start position:0% + +on and you have the melody over the + + align:start position:0% +on and you have the melody over the + + + align:start position:0% +on and you have the melody over the +top and we hear differences in tamber + + align:start position:0% +top and we hear differences in tamber + + + align:start position:0% +top and we hear differences in tamber +that is um who is playing whether it's a + + align:start position:0% +that is um who is playing whether it's a + + + align:start position:0% +that is um who is playing whether it's a +voice or a solo instrument and we hear + + align:start position:0% +voice or a solo instrument and we hear + + + align:start position:0% +voice or a solo instrument and we hear +the accompaniment on a keyboard or a + + align:start position:0% +the accompaniment on a keyboard or a + + + align:start position:0% +the accompaniment on a keyboard or a +guitar combined forces and these + + align:start position:0% +guitar combined forces and these + + + align:start position:0% +guitar combined forces and these +differences in rhythm in tamber and in + + align:start position:0% +differences in rhythm in tamber and in + + + align:start position:0% +differences in rhythm in tamber and in +melodiousness create different textures + + align:start position:0% +melodiousness create different textures + + + align:start position:0% +melodiousness create different textures +that we as listeners can separate or we + + align:start position:0% +that we as listeners can separate or we + + + align:start position:0% +that we as listeners can separate or we +can combine at our pleasure while we + + align:start position:0% +can combine at our pleasure while we + + + align:start position:0% +can combine at our pleasure while we +listen the first movement of Mozart's + + align:start position:0% +listen the first movement of Mozart's + + + align:start position:0% +listen the first movement of Mozart's +OBO cartet which we will hear this + + align:start position:0% +OBO cartet which we will hear this + + + align:start position:0% +OBO cartet which we will hear this +evening provides a very good example of + + align:start position:0% +evening provides a very good example of + + + align:start position:0% +evening provides a very good example of +how this works in a more standard + + align:start position:0% +how this works in a more standard + + + align:start position:0% +how this works in a more standard +operation than I will talk about um and + + align:start position:0% +operation than I will talk about um and + + + align:start position:0% +operation than I will talk about um and +so if we could have a well I'm going to + + align:start position:0% +so if we could have a well I'm going to + + + align:start position:0% +so if we could have a well I'm going to +show you a video of an animation of this + + align:start position:0% +show you a video of an animation of this + + + align:start position:0% +show you a video of an animation of this +movement and this animation has been + + align:start position:0% +movement and this animation has been + + + align:start position:0% +movement and this animation has been +made by Steven melanowski and the + + align:start position:0% +made by Steven melanowski and the + + + align:start position:0% +made by Steven melanowski and the +performance is actually by American + + align:start position:0% +performance is actually by American + + + align:start position:0% +performance is actually by American +Baroque and Gonzalo Ruiz is playing the + + align:start position:0% +Baroque and Gonzalo Ruiz is playing the + + + align:start position:0% +Baroque and Gonzalo Ruiz is playing the +OBO in the animation you can just see + + align:start position:0% +OBO in the animation you can just see + + + align:start position:0% +OBO in the animation you can just see +the beginning of it the OBO is red the + + align:start position:0% +the beginning of it the OBO is red the + + + align:start position:0% +the beginning of it the OBO is red the +violin and the viola are green and blue + + align:start position:0% +violin and the viola are green and blue + + + align:start position:0% +violin and the viola are green and blue +and the cello is blue it's very clear + + align:start position:0% +and the cello is blue it's very clear + + + align:start position:0% +and the cello is blue it's very clear +who's doing what and you will see that + + align:start position:0% +who's doing what and you will see that + + + align:start position:0% +who's doing what and you will see that +by and large the OBO has a certain + + align:start position:0% +by and large the OBO has a certain + + + align:start position:0% +by and large the OBO has a certain +amount of Precedence here it's not only + + align:start position:0% +amount of Precedence here it's not only + + + align:start position:0% +amount of Precedence here it's not only +high but it's a different tamber than + + align:start position:0% +high but it's a different tamber than + + + align:start position:0% +high but it's a different tamber than +the other instruments and it by and + + align:start position:0% +the other instruments and it by and + + + align:start position:0% +the other instruments and it by and +large plays faster than the other + + align:start position:0% +large plays faster than the other + + + align:start position:0% +large plays faster than the other +instruments smaller notes so there are + + align:start position:0% +instruments smaller notes so there are + + + align:start position:0% +instruments smaller notes so there are +all sorts of ways in which which the OBO + + align:start position:0% +all sorts of ways in which which the OBO + + + align:start position:0% +all sorts of ways in which which the OBO +is distinguished from the strings so + + align:start position:0% +is distinguished from the strings so + + + align:start position:0% +is distinguished from the strings so +this is what it is looks like animated + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so we stop if we see right here you can + + align:start position:0% +so we stop if we see right here you can + + + align:start position:0% +so we stop if we see right here you can +actually see it very very clearly that + + align:start position:0% +actually see it very very clearly that + + + align:start position:0% +actually see it very very clearly that +you have the dump bum + + align:start position:0% +you have the dump bum + + + align:start position:0% +you have the dump bum +bum in the strings it's very clearly + + align:start position:0% +bum in the strings it's very clearly + + + align:start position:0% +bum in the strings it's very clearly +laid out you can see the violin the uh + + align:start position:0% +laid out you can see the violin the uh + + + align:start position:0% +laid out you can see the violin the uh +the violin and the viola playing that in + + align:start position:0% +the violin and the viola playing that in + + + align:start position:0% +the violin and the viola playing that in +green you see that the cello is giving + + align:start position:0% +green you see that the cello is giving + + + align:start position:0% +green you see that the cello is giving +you the harmonic bases and you see that + + align:start position:0% +you the harmonic bases and you see that + + + align:start position:0% +you the harmonic bases and you see that +the OBO is really just off in another + + align:start position:0% +the OBO is really just off in another + + + align:start position:0% +the OBO is really just off in another +world um I love this animation which you + + align:start position:0% +world um I love this animation which you + + + align:start position:0% +world um I love this animation which you +can actually find on YouTube we just go + + align:start position:0% +can actually find on YouTube we just go + + + align:start position:0% +can actually find on YouTube we just go +for another 10 + + align:start position:0% + + + + align:start position:0% + +seconds that's + + align:start position:0% + + + + align:start position:0% + +fine so and what you're seeing there is + + align:start position:0% +fine so and what you're seeing there is + + + align:start position:0% +fine so and what you're seeing there is +um of course at a Cadence where the + + align:start position:0% +um of course at a Cadence where the + + + align:start position:0% +um of course at a Cadence where the +strings really broaden out that the OBO + + align:start position:0% +strings really broaden out that the OBO + + + align:start position:0% +strings really broaden out that the OBO +in fact gets more + + align:start position:0% +in fact gets more + + + align:start position:0% +in fact gets more +excited um very interesting to watch now + + align:start position:0% +excited um very interesting to watch now + + + align:start position:0% +excited um very interesting to watch now +in these kinds of differences in + + align:start position:0% +in these kinds of differences in + + + align:start position:0% +in these kinds of differences in +layerings in music sometimes composers + + align:start position:0% +layerings in music sometimes composers + + + align:start position:0% +layerings in music sometimes composers +specifically use the organiz time + + align:start position:0% +specifically use the organiz time + + + align:start position:0% +specifically use the organiz time +organization to make the difference and + + align:start position:0% +organization to make the difference and + + + align:start position:0% +organization to make the difference and +to make the difference um clearer uh and + + align:start position:0% +to make the difference um clearer uh and + + + align:start position:0% +to make the difference um clearer uh and +they will layer things on top of one + + align:start position:0% +they will layer things on top of one + + + align:start position:0% +they will layer things on top of one +another simultaneously in drama so that + + align:start position:0% +another simultaneously in drama so that + + + align:start position:0% +another simultaneously in drama so that +in fact people are singing different + + align:start position:0% +in fact people are singing different + + + align:start position:0% +in fact people are singing different +words doing different things and you can + + align:start position:0% +words doing different things and you can + + + align:start position:0% +words doing different things and you can +tell it apart uh you probably know the + + align:start position:0% +tell it apart uh you probably know the + + + align:start position:0% +tell it apart uh you probably know the +operatic ensembles from mozarts operas + + align:start position:0% +operatic ensembles from mozarts operas + + + align:start position:0% +operatic ensembles from mozarts operas +but this happen in popular music as well + + align:start position:0% +but this happen in popular music as well + + + align:start position:0% +but this happen in popular music as well +and a really good example is in + + align:start position:0% +and a really good example is in + + + align:start position:0% +and a really good example is in +burnstein's Westside Story where at one + + align:start position:0% +burnstein's Westside Story where at one + + + align:start position:0% +burnstein's Westside Story where at one +point all the characters are thinking + + align:start position:0% +point all the characters are thinking + + + align:start position:0% +point all the characters are thinking +about what's going to happen that night + + align:start position:0% +about what's going to happen that night + + + align:start position:0% +about what's going to happen that night +tonight and the two gangs the Jets and + + align:start position:0% +tonight and the two gangs the Jets and + + + align:start position:0% +tonight and the two gangs the Jets and +the sharks are talking about how they're + + align:start position:0% +the sharks are talking about how they're + + + align:start position:0% +the sharks are talking about how they're +going to rumble and Anita is talking + + align:start position:0% +going to rumble and Anita is talking + + + align:start position:0% +going to rumble and Anita is talking +about how much he's looking forward to + + align:start position:0% +about how much he's looking forward to + + + align:start position:0% +about how much he's looking forward to +Bernardo coming back because they're + + align:start position:0% +Bernardo coming back because they're + + + align:start position:0% +Bernardo coming back because they're +really going to have a hot + + align:start position:0% +really going to have a hot + + + align:start position:0% +really going to have a hot +time and then we have Maria and ton + + align:start position:0% +time and then we have Maria and ton + + + align:start position:0% +time and then we have Maria and ton +looking forward to Simply seeing one + + align:start position:0% +looking forward to Simply seeing one + + + align:start position:0% +looking forward to Simply seeing one +another again and Bernstein gives it to + + align:start position:0% +another again and Bernstein gives it to + + + align:start position:0% +another again and Bernstein gives it to +you serially one thing after another so + + align:start position:0% +you serially one thing after another so + + + align:start position:0% +you serially one thing after another so +that you get we're going to rock it + + align:start position:0% +that you get we're going to rock it + + + align:start position:0% +that you get we're going to rock it +tonight we're going to Jazz it up and + + align:start position:0% +tonight we're going to Jazz it up and + + + align:start position:0% +tonight we're going to Jazz it up and +have us a ball they're going to get it + + align:start position:0% +have us a ball they're going to get it + + + align:start position:0% +have us a ball they're going to get it +tonight the more they turn it on the + + align:start position:0% +tonight the more they turn it on the + + + align:start position:0% +tonight the more they turn it on the +harder they'll fall well they began it + + align:start position:0% +harder they'll fall well they began it + + + align:start position:0% +harder they'll fall well they began it +well they began it and we're the ones to + + align:start position:0% +well they began it and we're the ones to + + + align:start position:0% +well they began it and we're the ones to +stop it once and for all + + align:start position:0% +stop it once and for all + + + align:start position:0% +stop it once and for all +tonight Anita is going to have her fun + + align:start position:0% +tonight Anita is going to have her fun + + + align:start position:0% +tonight Anita is going to have her fun +tonight + + align:start position:0% +tonight + + + align:start position:0% +tonight +she's going to have her little BX F + + align:start position:0% +she's going to have her little BX F + + + align:start position:0% +she's going to have her little BX F +tonight he'll come in hot and tired so + + align:start position:0% +tonight he'll come in hot and tired so + + + align:start position:0% +tonight he'll come in hot and tired so +what and so forth and then + + align:start position:0% +what and so forth and then + + + align:start position:0% +what and so forth and then +tonight tonight won't be so you have all + + align:start position:0% +tonight tonight won't be so you have all + + + align:start position:0% +tonight tonight won't be so you have all +of those things one at a time and then + + align:start position:0% +of those things one at a time and then + + + align:start position:0% +of those things one at a time and then +Burnstein of course does what is + + align:start position:0% +Burnstein of course does what is + + + align:start position:0% +Burnstein of course does what is +miraculous in music you hear them all at + + align:start position:0% +miraculous in music you hear them all at + + + align:start position:0% +miraculous in music you hear them all at +the same + + align:start position:0% +the same + + + align:start position:0% +the same +time and so you not only know when you + + align:start position:0% +time and so you not only know when you + + + align:start position:0% +time and so you not only know when you +hear them serially that it's happening + + align:start position:0% +hear them serially that it's happening + + + align:start position:0% +hear them serially that it's happening +at the same time because you can + + align:start position:0% +at the same time because you can + + + align:start position:0% +at the same time because you can +understand that dramatically but then + + align:start position:0% +understand that dramatically but then + + + align:start position:0% +understand that dramatically but then +music gives you the opportunity to + + align:start position:0% +music gives you the opportunity to + + + align:start position:0% +music gives you the opportunity to +actually experience it simultaneously + + align:start position:0% +actually experience it simultaneously + + + align:start position:0% +actually experience it simultaneously +and not just understand that it's + + align:start position:0% +and not just understand that it's + + + align:start position:0% +and not just understand that it's +simultaneous sometimes composers will + + align:start position:0% +simultaneous sometimes composers will + + + align:start position:0% +simultaneous sometimes composers will +take the extra step and will actually + + align:start position:0% +take the extra step and will actually + + + align:start position:0% +take the extra step and will actually +set the pieces in different as I said + + align:start position:0% +set the pieces in different as I said + + + align:start position:0% +set the pieces in different as I said +time organizations and there's a + + align:start position:0% +time organizations and there's a + + + align:start position:0% +time organizations and there's a +wonderful example that I can't resist + + align:start position:0% +wonderful example that I can't resist + + + align:start position:0% +wonderful example that I can't resist +showing you from Gilbert and civan + + align:start position:0% +showing you from Gilbert and civan + + + align:start position:0% +showing you from Gilbert and civan +Pirates of Penzance when Mabel and + + align:start position:0% +Pirates of Penzance when Mabel and + + + align:start position:0% +Pirates of Penzance when Mabel and +Frederick uh first see one another and + + align:start position:0% +Frederick uh first see one another and + + + align:start position:0% +Frederick uh first see one another and +they're going off to one side of the + + align:start position:0% +they're going off to one side of the + + + align:start position:0% +they're going off to one side of the +stage and the sisters of Mabel are + + align:start position:0% +stage and the sisters of Mabel are + + + align:start position:0% +stage and the sisters of Mabel are +trying to decide whether to stay or they + + align:start position:0% +trying to decide whether to stay or they + + + align:start position:0% +trying to decide whether to stay or they +it would be more appropriate for them to + + align:start position:0% +it would be more appropriate for them to + + + align:start position:0% +it would be more appropriate for them to +leave and they finally say well no we'll + + align:start position:0% +leave and they finally say well no we'll + + + align:start position:0% +leave and they finally say well no we'll +stay but we'll talk about the + + align:start position:0% +stay but we'll talk about the + + + align:start position:0% +stay but we'll talk about the +weather and in this version from + + align:start position:0% +weather and in this version from + + + align:start position:0% +weather and in this version from +Australia which is wonderful the singers + + align:start position:0% +Australia which is wonderful the singers + + + align:start position:0% +Australia which is wonderful the singers +are sung by a trio a woman's Trio called + + align:start position:0% +are sung by a trio a woman's Trio called + + + align:start position:0% +are sung by a trio a woman's Trio called +The Fabulous + + align:start position:0% +The Fabulous + + + align:start position:0% +The Fabulous +singlets who are known for their Camp + + align:start position:0% +singlets who are known for their Camp + + + align:start position:0% +singlets who are known for their Camp +Renditions of pop songs this is a very + + align:start position:0% +Renditions of pop songs this is a very + + + align:start position:0% +Renditions of pop songs this is a very +Camp rendition of Gilbert and Sol + + align:start position:0% +Camp rendition of Gilbert and Sol + + + align:start position:0% +Camp rendition of Gilbert and Sol +um and the Frederick is sung by Simon + + align:start position:0% +um and the Frederick is sung by Simon + + + align:start position:0% +um and the Frederick is sung by Simon +Gallagher and Mabel by Helen Donaldson + + align:start position:0% +Gallagher and Mabel by Helen Donaldson + + + align:start position:0% +Gallagher and Mabel by Helen Donaldson +and what happens is the sisters are + + align:start position:0% +and what happens is the sisters are + + + align:start position:0% +and what happens is the sisters are +singing in 44 time how beautifully the + + align:start position:0% +singing in 44 time how beautifully the + + + align:start position:0% +singing in 44 time how beautifully the +sky the glass is rising very + + align:start position:0% +sky the glass is rising very + + + align:start position:0% +sky the glass is rising very +high and it's faster than that and then + + align:start position:0% +high and it's faster than that and then + + + align:start position:0% +high and it's faster than that and then +in 68 we have the love + + align:start position:0% + + + + align:start position:0% + +song and then you get these two + + align:start position:0% +song and then you get these two + + + align:start position:0% +song and then you get these two +different time organizations overlaid on + + align:start position:0% +different time organizations overlaid on + + + align:start position:0% +different time organizations overlaid on +one another we'll hear a little + + align:start position:0% +one another we'll hear a little + + + align:start position:0% +one another we'll hear a little +[Music] + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% +this + + + align:start position:0% +this +[Music] + + align:start position:0% + + + + align:start position:0% + +Andor I country people say I know not + + align:start position:0% +Andor I country people say I know not + + + align:start position:0% +Andor I country people say I know not +why that we shall have a ju like + + align:start position:0% +why that we shall have a ju like + + + align:start position:0% +why that we shall have a ju like +tomorrow + + align:start position:0% +tomorrow + + + align:start position:0% +tomorrow +[Music] + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Beauty + + align:start position:0% +Beauty + + + align:start position:0% +Beauty +eyes + + align:start position:0% +eyes + + + align:start position:0% +eyes +sadness + + align:start position:0% +sadness + + + align:start position:0% +sadness +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Dre + + align:start position:0% + + + + align:start position:0% + +s i + + align:start position:0% +s i + + + align:start position:0% +s i +yes this is + + align:start position:0% +yes this is + + + align:start position:0% +yes this is +exceeding + + align:start position:0% +exceeding + + + align:start position:0% +exceeding +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +gladness and ultimately you get much + + align:start position:0% +gladness and ultimately you get much + + + align:start position:0% +gladness and ultimately you get much +more overlap and so they actually sing + + align:start position:0% +more overlap and so they actually sing + + + align:start position:0% +more overlap and so they actually sing +the whole thing on top of one another + + align:start position:0% +the whole thing on top of one another + + + align:start position:0% +the whole thing on top of one another +simultaneously choruses inevitably have + + align:start position:0% +simultaneously choruses inevitably have + + + align:start position:0% +simultaneously choruses inevitably have +trouble with this moment um so now + + align:start position:0% +trouble with this moment um so now + + + align:start position:0% +trouble with this moment um so now +returning and perhaps unexpectedly to + + align:start position:0% +returning and perhaps unexpectedly to + + + align:start position:0% +returning and perhaps unexpectedly to +the OBO + + align:start position:0% +the OBO + + + align:start position:0% +the OBO +quartet we find that Mozart does just + + align:start position:0% +quartet we find that Mozart does just + + + align:start position:0% +quartet we find that Mozart does just +this well not quite exactly that but + + align:start position:0% +this well not quite exactly that but + + + align:start position:0% +this well not quite exactly that but +something very very similar if we could + + align:start position:0% +something very very similar if we could + + + align:start position:0% +something very very similar if we could +have the obok we can hear this in the + + align:start position:0% +have the obok we can hear this in the + + + align:start position:0% +have the obok we can hear this in the +last movement which is a Rondo horo is a + + align:start position:0% +last movement which is a Rondo horo is a + + + align:start position:0% +last movement which is a Rondo horo is a +movement in which you have a refrain + + align:start position:0% +movement in which you have a refrain + + + align:start position:0% +movement in which you have a refrain +that comes back and in between the + + align:start position:0% +that comes back and in between the + + + align:start position:0% +that comes back and in between the +refrain you get episodes of much more um + + align:start position:0% +refrain you get episodes of much more um + + + align:start position:0% +refrain you get episodes of much more um +well less structured music much more + + align:start position:0% +well less structured music much more + + + align:start position:0% +well less structured music much more +improvisatory music a more developmental + + align:start position:0% +improvisatory music a more developmental + + + align:start position:0% +improvisatory music a more developmental +music uh where the music is not as + + align:start position:0% +music uh where the music is not as + + + align:start position:0% +music uh where the music is not as +stable + + align:start position:0% +stable + + + align:start position:0% +stable +um in the refrain the OBO and the violin + + align:start position:0% +um in the refrain the OBO and the violin + + + align:start position:0% +um in the refrain the OBO and the violin +play very nicely together um except for + + align:start position:0% +play very nicely together um except for + + + align:start position:0% +play very nicely together um except for +the fact that the OBO takes the lead the + + align:start position:0% +the fact that the OBO takes the lead the + + + align:start position:0% +the fact that the OBO takes the lead the +OBO there is a sense of still dominance + + align:start position:0% +OBO there is a sense of still dominance + + + align:start position:0% +OBO there is a sense of still dominance +by the OBO here the OBO takes the lead + + align:start position:0% +by the OBO here the OBO takes the lead + + + align:start position:0% +by the OBO here the OBO takes the lead +the violent follows it's all very nice + + align:start position:0% +the violent follows it's all very nice + + + align:start position:0% +the violent follows it's all very nice +you know nice playing and in the first + + align:start position:0% +you know nice playing and in the first + + + align:start position:0% +you know nice playing and in the first +episode The OBO asserts its dominance by + + align:start position:0% +episode The OBO asserts its dominance by + + + align:start position:0% +episode The OBO asserts its dominance by +playing much faster than everyone else + + align:start position:0% +playing much faster than everyone else + + + align:start position:0% +playing much faster than everyone else +and much more virtuosic music than + + align:start position:0% +and much more virtuosic music than + + + align:start position:0% +and much more virtuosic music than +everyone else and then the refrain comes + + align:start position:0% +everyone else and then the refrain comes + + + align:start position:0% +everyone else and then the refrain comes +back and then in the second + + align:start position:0% +back and then in the second + + + align:start position:0% +back and then in the second +episode what the OBO does is different + + align:start position:0% +episode what the OBO does is different + + + align:start position:0% +episode what the OBO does is different +not just asserting it's indep it's its + + align:start position:0% +not just asserting it's indep it's its + + + align:start position:0% +not just asserting it's indep it's its +dominance but its independence that is + + align:start position:0% +dominance but its independence that is + + + align:start position:0% +dominance but its independence that is +okay you can play whatever you want but + + align:start position:0% +okay you can play whatever you want but + + + align:start position:0% +okay you can play whatever you want but +I'm going to play in my own time my time + + align:start position:0% +I'm going to play in my own time my time + + + align:start position:0% +I'm going to play in my own time my time +and your time aren't necessarily the + + align:start position:0% +and your time aren't necessarily the + + + align:start position:0% +and your time aren't necessarily the +same time so the strings continue + + align:start position:0% +same time so the strings continue + + + align:start position:0% +same time so the strings continue +playing in + + align:start position:0% + + + + align:start position:0% + +68 and the elbow moves into four FL and + + align:start position:0% +68 and the elbow moves into four FL and + + + align:start position:0% +68 and the elbow moves into four FL and +it's an extraordinary moment throughout + + align:start position:0% +it's an extraordinary moment throughout + + + align:start position:0% +it's an extraordinary moment throughout +this entire episode and we can hear this + + align:start position:0% +this entire episode and we can hear this + + + align:start position:0% +this entire episode and we can hear this +um and we'll hear it again tonight but + + align:start position:0% +um and we'll hear it again tonight but + + + align:start position:0% +um and we'll hear it again tonight but +let's hear it + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +now again + + align:start position:0% +now again + + + align:start position:0% +now again +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +is that + + align:start position:0% + + + + align:start position:0% + +wonderful thank you very + + align:start position:0% + + + + align:start position:0% + +much they have waited a long time to + + align:start position:0% +much they have waited a long time to + + + align:start position:0% +much they have waited a long time to +um what we have you know I want to say a + + align:start position:0% +um what we have you know I want to say a + + + align:start position:0% +um what we have you know I want to say a +few words about the Lucas F time time + + align:start position:0% +few words about the Lucas F time time + + + align:start position:0% +few words about the Lucas F time time +cycle which will be the last piece on + + align:start position:0% +cycle which will be the last piece on + + + align:start position:0% +cycle which will be the last piece on +the + + align:start position:0% +the + + + align:start position:0% +the +program um and without a doubt in that + + align:start position:0% +program um and without a doubt in that + + + align:start position:0% +program um and without a doubt in that +piece time is the subject and substance + + align:start position:0% +piece time is the subject and substance + + + align:start position:0% +piece time is the subject and substance +of the work each of the movements + + align:start position:0% +of the work each of the movements + + + align:start position:0% +of the work each of the movements +that'ss a text that deals with time + + align:start position:0% +that'ss a text that deals with time + + + align:start position:0% +that'ss a text that deals with time +there are poems by Ain and AE Housman + + align:start position:0% +there are poems by Ain and AE Housman + + + align:start position:0% +there are poems by Ain and AE Housman +and a Pros passage by Kafka and a + + align:start position:0% +and a Pros passage by Kafka and a + + + align:start position:0% +and a Pros passage by Kafka and a +passage from Alo zarra by + + align:start position:0% +passage from Alo zarra by + + + align:start position:0% +passage from Alo zarra by +n all of the these texts deal with + + align:start position:0% +n all of the these texts deal with + + + align:start position:0% +n all of the these texts deal with +clocks or bells and the whole cycle is + + align:start position:0% +clocks or bells and the whole cycle is + + + align:start position:0% +clocks or bells and the whole cycle is +imbued with the relationship between + + align:start position:0% +imbued with the relationship between + + + align:start position:0% +imbued with the relationship between +time and + + align:start position:0% +time and + + + align:start position:0% +time and +death no matter how fast he runs the + + align:start position:0% +death no matter how fast he runs the + + + align:start position:0% +death no matter how fast he runs the +human always loses in his Race Against + + align:start position:0% +human always loses in his Race Against + + + align:start position:0% +human always loses in his Race Against +Time which continues in its inexurable + + align:start position:0% +Time which continues in its inexurable + + + align:start position:0% +Time which continues in its inexurable +March forward measured in drops of sand + + align:start position:0% +March forward measured in drops of sand + + + align:start position:0% +March forward measured in drops of sand +ticks of clocks tolling Bells coffee + + align:start position:0% +ticks of clocks tolling Bells coffee + + + align:start position:0% +ticks of clocks tolling Bells coffee +spoons if you + + align:start position:0% +spoons if you + + + align:start position:0% +spoons if you +may in the text of the third movement + + align:start position:0% +may in the text of the third movement + + + align:start position:0% +may in the text of the third movement +kofka writes the clocks do not + + align:start position:0% + + + + align:start position:0% + +synchronized the inner one chases in a + + align:start position:0% +synchronized the inner one chases in a + + + align:start position:0% +synchronized the inner one chases in a +devilish or demonic or in any rate + + align:start position:0% +devilish or demonic or in any rate + + + align:start position:0% +devilish or demonic or in any rate +inhuman Manner and the outer one goes + + align:start position:0% +inhuman Manner and the outer one goes + + + align:start position:0% +inhuman Manner and the outer one goes +haltingly at its usual + + align:start position:0% +haltingly at its usual + + + align:start position:0% +haltingly at its usual +Pace F at least seems to me uses this + + align:start position:0% +Pace F at least seems to me uses this + + + align:start position:0% +Pace F at least seems to me uses this +idea in his setting of zarathustra's + + align:start position:0% +idea in his setting of zarathustra's + + + align:start position:0% +idea in his setting of zarathustra's +round delay also set by Mal in the + + align:start position:0% +round delay also set by Mal in the + + + align:start position:0% +round delay also set by Mal in the +Fourth Movement of his third Symphony + + align:start position:0% +Fourth Movement of his third Symphony + + + align:start position:0% +Fourth Movement of his third Symphony +and here's a translation of that + + align:start position:0% +and here's a translation of that + + + align:start position:0% +and here's a translation of that +movement this is the Fourth Movement of + + align:start position:0% +movement this is the Fourth Movement of + + + align:start position:0% +movement this is the Fourth Movement of +the Lucas boss and this is the text + + align:start position:0% +the Lucas boss and this is the text + + + align:start position:0% +the Lucas boss and this is the text +uh again a translation by Walter calman + + align:start position:0% +uh again a translation by Walter calman + + + align:start position:0% +uh again a translation by Walter calman +oh man take care what does the Deep + + align:start position:0% +oh man take care what does the Deep + + + align:start position:0% +oh man take care what does the Deep +midnight + + align:start position:0% +midnight + + + align:start position:0% +midnight +declare I was asleep from a dream I + + align:start position:0% +declare I was asleep from a dream I + + + align:start position:0% +declare I was asleep from a dream I +awoke and swear the world is + + align:start position:0% +awoke and swear the world is + + + align:start position:0% +awoke and swear the world is +deep deeper than day has been aware deep + + align:start position:0% +deep deeper than day has been aware deep + + + align:start position:0% +deep deeper than day has been aware deep +is its woe Joy deeper yet than Agony woe + + align:start position:0% +is its woe Joy deeper yet than Agony woe + + + align:start position:0% +is its woe Joy deeper yet than Agony woe +implores go but all joy wants eternity + + align:start position:0% +implores go but all joy wants eternity + + + align:start position:0% +implores go but all joy wants eternity +wants deep deep + + align:start position:0% +wants deep deep + + + align:start position:0% +wants deep deep +eternity now we're having + + align:start position:0% + + + + align:start position:0% + +apparently um + + align:start position:0% + + + + align:start position:0% + +is I'm not getting the light + + align:start position:0% + + + + align:start position:0% + +so okay um I think I'm just going to go + + align:start position:0% +so okay um I think I'm just going to go + + + align:start position:0% +so okay um I think I'm just going to go +ahead without it for now um this + + align:start position:0% +ahead without it for now um this + + + align:start position:0% +ahead without it for now um this +movement um has many things just toos + + align:start position:0% +movement um has many things just toos + + + align:start position:0% +movement um has many things just toos +posed uh there are 11 lines to the poem + + align:start position:0% +posed uh there are 11 lines to the poem + + + align:start position:0% +posed uh there are 11 lines to the poem +and what F does is before each line + + align:start position:0% +and what F does is before each line + + + align:start position:0% +and what F does is before each line +gives you a stroke of the clock so you + + align:start position:0% +gives you a stroke of the clock so you + + + align:start position:0% +gives you a stroke of the clock so you +move from one to 2 to 3 to 4 and + + align:start position:0% +move from one to 2 to 3 to 4 and + + + align:start position:0% +move from one to 2 to 3 to 4 and +ultimately to + + align:start position:0% +ultimately to + + + align:start position:0% +ultimately to +midnight um each of the 11 lines is set + + align:start position:0% +midnight um each of the 11 lines is set + + + align:start position:0% +midnight um each of the 11 lines is set +to 1 through 11 midnight of course ends + + align:start position:0% +to 1 through 11 midnight of course ends + + + align:start position:0% +to 1 through 11 midnight of course ends +um yeah uh without a line and so the + + align:start position:0% +um yeah uh without a line and so the + + + align:start position:0% +um yeah uh without a line and so the +voice is silenced at midnight + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% + + + + align:start position:0% + +um the clocks are set in a very um + + align:start position:0% +um the clocks are set in a very um + + + align:start position:0% +um the clocks are set in a very um +particular Way by + + align:start position:0% +particular Way by + + + align:start position:0% +particular Way by +F and you can see the one four at the + + align:start position:0% +F and you can see the one four at the + + + align:start position:0% +F and you can see the one four at the +bottom which is circled in in pink and + + align:start position:0% +bottom which is circled in in pink and + + + align:start position:0% +bottom which is circled in in pink and +then you see two four he is actually has + + align:start position:0% +then you see two four he is actually has + + + align:start position:0% +then you see two four he is actually has +a nominal meter going of 32 but every + + align:start position:0% +a nominal meter going of 32 but every + + + align:start position:0% +a nominal meter going of 32 but every +time the clock strikes it's as if time + + align:start position:0% +time the clock strikes it's as if time + + + align:start position:0% +time the clock strikes it's as if time +stops so that the normative pulse which + + align:start position:0% +stops so that the normative pulse which + + + align:start position:0% +stops so that the normative pulse which +is faster than they'll play it say it's + + align:start position:0% +is faster than they'll play it say it's + + + align:start position:0% +is faster than they'll play it say it's +one and two and three and one and two + + align:start position:0% +one and two and three and one and two + + + align:start position:0% +one and two and three and one and two +and three and one one and two and three + + align:start position:0% +and three and one one and two and three + + + align:start position:0% +and three and one one and two and three +and one two one and two and three and + + align:start position:0% +and one two one and two and three and + + + align:start position:0% +and one two one and two and three and +one 2 three and each time you get to one + + align:start position:0% +one 2 three and each time you get to one + + + align:start position:0% +one 2 three and each time you get to one +of those funny measures the clock begins + + align:start position:0% +of those funny measures the clock begins + + + align:start position:0% +of those funny measures the clock begins +striking on the final beat + + align:start position:0% +striking on the final beat + + + align:start position:0% +striking on the final beat +so that when it's 3:00 the clock starts + + align:start position:0% +so that when it's 3:00 the clock starts + + + align:start position:0% +so that when it's 3:00 the clock starts +on beat three of that interpolated + + align:start position:0% +on beat three of that interpolated + + + align:start position:0% +on beat three of that interpolated +measure and when it's 11:00 starts + + align:start position:0% +measure and when it's 11:00 starts + + + align:start position:0% +measure and when it's 11:00 starts +beating on the + + align:start position:0% +beating on the + + + align:start position:0% +beating on the +11th count of the interpolated measure + + align:start position:0% +11th count of the interpolated measure + + + align:start position:0% +11th count of the interpolated measure +this is very funny things at the speed + + align:start position:0% +this is very funny things at the speed + + + align:start position:0% +this is very funny things at the speed +at which this goes I think you have no + + align:start position:0% +at which this goes I think you have no + + + align:start position:0% +at which this goes I think you have no +perception really of time or beat or + + align:start position:0% +perception really of time or beat or + + + align:start position:0% +perception really of time or beat or +pulse and there is that sense of + + align:start position:0% +pulse and there is that sense of + + + align:start position:0% +pulse and there is that sense of +Eternity which is in the text throughout + + align:start position:0% +Eternity which is in the text throughout + + + align:start position:0% +Eternity which is in the text throughout +in the center of the p we have a canonic + + align:start position:0% +in the center of the p we have a canonic + + + align:start position:0% +in the center of the p we have a canonic +thing going on with some of the + + align:start position:0% +thing going on with some of the + + + align:start position:0% +thing going on with some of the +instruments and I've highlighted some + + align:start position:0% +instruments and I've highlighted some + + + align:start position:0% +instruments and I've highlighted some +notes in blue this is sort of to make it + + align:start position:0% +notes in blue this is sort of to make it + + + align:start position:0% +notes in blue this is sort of to make it +look like the animation um and this + + align:start position:0% +look like the animation um and this + + + align:start position:0% +look like the animation um and this +continues throughout most of the piece + + align:start position:0% +continues throughout most of the piece + + + align:start position:0% +continues throughout most of the piece +and this kind of canonic cycling which + + align:start position:0% +and this kind of canonic cycling which + + + align:start position:0% +and this kind of canonic cycling which +I've been thinking about very much in + + align:start position:0% +I've been thinking about very much in + + + align:start position:0% +I've been thinking about very much in +terms of the Fates and the spinning of + + align:start position:0% +terms of the Fates and the spinning of + + + align:start position:0% +terms of the Fates and the spinning of +the wheel and the spinning out of the + + align:start position:0% +the wheel and the spinning out of the + + + align:start position:0% +the wheel and the spinning out of the +life thread at the center of this + + align:start position:0% +life thread at the center of this + + + align:start position:0% +life thread at the center of this +movement have a colleague who said to me + + align:start position:0% +movement have a colleague who said to me + + + align:start position:0% +movement have a colleague who said to me +well it could just be DNA I mean it's + + align:start position:0% +well it could just be DNA I mean it's + + + align:start position:0% +well it could just be DNA I mean it's +the same spin + + align:start position:0% +the same spin + + + align:start position:0% +the same spin +in fact uh and so whatever it is it is + + align:start position:0% +in fact uh and so whatever it is it is + + + align:start position:0% +in fact uh and so whatever it is it is +the life force of the peace and I want + + align:start position:0% +the life force of the peace and I want + + + align:start position:0% +the life force of the peace and I want +to give you a sense of that because you + + align:start position:0% +to give you a sense of that because you + + + align:start position:0% +to give you a sense of that because you +have the clocks going on you have the + + align:start position:0% +have the clocks going on you have the + + + align:start position:0% +have the clocks going on you have the +voice who's giving you the poem which is + + align:start position:0% +voice who's giving you the poem which is + + + align:start position:0% +voice who's giving you the poem which is +nche you have um the life force so you + + align:start position:0% +nche you have um the life force so you + + + align:start position:0% +nche you have um the life force so you +have three very distinct things being + + align:start position:0% +have three very distinct things being + + + align:start position:0% +have three very distinct things being +layered the clock going from 1 to 12 the + + align:start position:0% +layered the clock going from 1 to 12 the + + + align:start position:0% +layered the clock going from 1 to 12 the +life force which continues and the poem + + align:start position:0% +life force which continues and the poem + + + align:start position:0% +life force which continues and the poem +which goes through the 11th hour and + + align:start position:0% +which goes through the 11th hour and + + + align:start position:0% +which goes through the 11th hour and +then not Beyond so here's a little bit + + align:start position:0% +then not Beyond so here's a little bit + + + align:start position:0% +then not Beyond so here's a little bit +of the of the cannon if we could hear + + align:start position:0% +of the of the cannon if we could hear + + + align:start position:0% +of the of the cannon if we could hear +first um the vione play measure two and + + align:start position:0% +first um the vione play measure two and + + + align:start position:0% +first um the vione play measure two and +then let's hear the clarinet play + + align:start position:0% +then let's hear the clarinet play + + + align:start position:0% +then let's hear the clarinet play +measure + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +two and then similarly the vione this is + + align:start position:0% +two and then similarly the vione this is + + + align:start position:0% +two and then similarly the vione this is +the third line down if you could play + + align:start position:0% +the third line down if you could play + + + align:start position:0% +the third line down if you could play +measures three and four and then the + + align:start position:0% +measures three and four and then the + + + align:start position:0% +measures three and four and then the +clarinet play measures three and four + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so I hope you can hear how similar these + + align:start position:0% +so I hope you can hear how similar these + + + align:start position:0% +so I hope you can hear how similar these +lines are because when they're overlaid + + align:start position:0% +lines are because when they're overlaid + + + align:start position:0% +lines are because when they're overlaid +on one another it's very hard to hear + + align:start position:0% +on one another it's very hard to hear + + + align:start position:0% +on one another it's very hard to hear +the canonic + + align:start position:0% +the canonic + + + align:start position:0% +the canonic +force um but that continues through the + + align:start position:0% +force um but that continues through the + + + align:start position:0% +force um but that continues through the +movement and we'll see if the movement + + align:start position:0% +movement and we'll see if the movement + + + align:start position:0% +movement and we'll see if the movement +continues how the cannon shifts from + + align:start position:0% +continues how the cannon shifts from + + + align:start position:0% +continues how the cannon shifts from +part to part by the end of the page the + + align:start position:0% +part to part by the end of the page the + + + align:start position:0% +part to part by the end of the page the +cannon is between the piano and the + + align:start position:0% +cannon is between the piano and the + + + align:start position:0% +cannon is between the piano and the +clarinet and if we can just get a little + + align:start position:0% +clarinet and if we can just get a little + + + align:start position:0% +clarinet and if we can just get a little +bit of the piano + + align:start position:0% +bit of the piano + + + align:start position:0% +bit of the piano +and then after it clear the clarinet + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +line okay and now the clarinet The + + align:start position:0% + + + + align:start position:0% + +Vibes sorry + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +we also oops we can also see in this + + align:start position:0% +we also oops we can also see in this + + + align:start position:0% +we also oops we can also see in this +image where you get to + + align:start position:0% +image where you get to + + + align:start position:0% +image where you get to +44 and then at the end of the page where + + align:start position:0% +44 and then at the end of the page where + + + align:start position:0% +44 and then at the end of the page where +you get to + + align:start position:0% +you get to + + + align:start position:0% +you get to +54 this is that continues throughout the + + align:start position:0% +54 this is that continues throughout the + + + align:start position:0% +54 this is that continues throughout the +piece what I'd like them to do is for + + align:start position:0% +piece what I'd like them to do is for + + + align:start position:0% +piece what I'd like them to do is for +you you to hear the beginning of this + + align:start position:0% +you you to hear the beginning of this + + + align:start position:0% +you you to hear the beginning of this +piece um just what did we say the first + + align:start position:0% +piece um just what did we say the first + + + align:start position:0% +piece um just what did we say the first +16 measures + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +men + + align:start position:0% +men + + + align:start position:0% +men +keep heart + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +F deep + + align:start position:0% + + + + align:start position:0% + +te m + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +the end of this Movement we keep going I + + align:start position:0% +the end of this Movement we keep going I + + + align:start position:0% +the end of this Movement we keep going I +can just show you here how we get to uh + + align:start position:0% +can just show you here how we get to uh + + + align:start position:0% +can just show you here how we get to uh +74 there's + + align:start position:0% +74 there's + + + align:start position:0% +74 there's +84 there's your 94 + + align:start position:0% +84 there's your 94 + + + align:start position:0% +84 there's your 94 +here it's the sort of thing I think + + align:start position:0% +here it's the sort of thing I think + + + align:start position:0% +here it's the sort of thing I think +could drive you crazy I I'm glad I'm + + align:start position:0% +could drive you crazy I I'm glad I'm + + + align:start position:0% +could drive you crazy I I'm glad I'm +talking about it not playing it um + + align:start position:0% +talking about it not playing it um + + + align:start position:0% +talking about it not playing it um +here's + + align:start position:0% +here's + + + align:start position:0% +here's +114 and finally we get to 124 and what's + + align:start position:0% +114 and finally we get to 124 and what's + + + align:start position:0% +114 and finally we get to 124 and what's +uh striking I it's the right word is + + align:start position:0% +uh striking I it's the right word is + + + align:start position:0% +uh striking I it's the right word is +that um midnight is the only hour we + + align:start position:0% +that um midnight is the only hour we + + + align:start position:0% +that um midnight is the only hour we +actually he struck in any kind of + + align:start position:0% +actually he struck in any kind of + + + align:start position:0% +actually he struck in any kind of +audible way and it is struck by + + align:start position:0% +audible way and it is struck by + + + align:start position:0% +audible way and it is struck by +uh an antique symbol being played by a + + align:start position:0% +uh an antique symbol being played by a + + + align:start position:0% +uh an antique symbol being played by a +thimble correct that's correct okay and + + align:start position:0% +thimble correct that's correct okay and + + + align:start position:0% +thimble correct that's correct okay and +we get all 12 Strokes of midnight and of + + align:start position:0% +we get all 12 Strokes of midnight and of + + + align:start position:0% +we get all 12 Strokes of midnight and of +course after we get Midnight the voice + + align:start position:0% +course after we get Midnight the voice + + + align:start position:0% +course after we get Midnight the voice +is + + align:start position:0% +is + + + align:start position:0% +is +silenced and just before 12 the cannon + + align:start position:0% +silenced and just before 12 the cannon + + + align:start position:0% +silenced and just before 12 the cannon +is cut off and the sense is very much at + + align:start position:0% +is cut off and the sense is very much at + + + align:start position:0% +is cut off and the sense is very much at +the end of this piece which Fades the + + align:start position:0% +the end of this piece which Fades the + + + align:start position:0% +the end of this piece which Fades the +the last stroke of midnight is played + + align:start position:0% +the last stroke of midnight is played + + + align:start position:0% +the last stroke of midnight is played +Pian + + align:start position:0% +Pian + + + align:start position:0% +Pian +and in fact it's not regularly to the + + align:start position:0% +and in fact it's not regularly to the + + + align:start position:0% +and in fact it's not regularly to the +way a clock would toll but in fact + + align:start position:0% +way a clock would toll but in fact + + + align:start position:0% +way a clock would toll but in fact +pretty much although not regularly slows + + align:start position:0% +pretty much although not regularly slows + + + align:start position:0% +pretty much although not regularly slows +down so that it's almost as if the clock + + align:start position:0% +down so that it's almost as if the clock + + + align:start position:0% +down so that it's almost as if the clock +itself is running out at the end of the + + align:start position:0% +itself is running out at the end of the + + + align:start position:0% +itself is running out at the end of the +piece and at the very end of the piece + + align:start position:0% +piece and at the very end of the piece + + + align:start position:0% +piece and at the very end of the piece +you get that last 12th panimo + + align:start position:0% +you get that last 12th panimo + + + align:start position:0% +you get that last 12th panimo +stroke The Voice has been + + align:start position:0% +stroke The Voice has been + + + align:start position:0% +stroke The Voice has been +stilled the canonic life force has been + + align:start position:0% +stilled the canonic life force has been + + + align:start position:0% +stilled the canonic life force has been +stop the peace comes to an end almost + + align:start position:0% +stop the peace comes to an end almost + + + align:start position:0% +stop the peace comes to an end almost +into nothingness the work ends and with + + align:start position:0% +into nothingness the work ends and with + + + align:start position:0% +into nothingness the work ends and with +that moment of course the winter + + align:start position:0% +that moment of course the winter + + + align:start position:0% +that moment of course the winter +festival will + + align:start position:0% +festival will + + + align:start position:0% +festival will +end + + align:start position:0% +end + + + align:start position:0% +end +so just let's hear that last section + + align:start position:0% +so just let's hear that last section + + + align:start position:0% +so just let's hear that last section +through the 124 we're actually going to + + align:start position:0% +through the 124 we're actually going to + + + align:start position:0% +through the 124 we're actually going to +start on the 124 r or just before first + + align:start position:0% + + + + align:start position:0% + +starting pick up to Bar 48 + + align:start position:0% +starting pick up to Bar 48 + + + align:start position:0% +starting pick up to Bar 48 +all right there we go up here y mhm fine + + align:start position:0% +all right there we go up here y mhm fine + + + align:start position:0% +all right there we go up here y mhm fine +so we're going to be starting here + + align:start position:0% +so we're going to be starting here + + + align:start position:0% +so we're going to be starting here +people want to follow + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +come + + align:start position:0% +come + + + align:start position:0% +come +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +for + + align:start position:0% + + + + align:start position:0% + +thank + + align:start position:0% +thank + + + align:start position:0% +thank +[Applause] + + align:start position:0% + + + + align:start position:0% + +you for \ No newline at end of file diff --git a/Ne2lmAZI4-I.txt b/Ne2lmAZI4-I.txt new file mode 100644 index 0000000000000000000000000000000000000000..86c1fba919e7d802ec7bc18f77deb3eeb2ece365 --- /dev/null +++ b/Ne2lmAZI4-I.txt @@ -0,0 +1,1747 @@ +align:start position:0% + +in this last video we illustrate how to + + align:start position:0% +in this last video we illustrate how to + + + align:start position:0% +in this last video we illustrate how to +use the techniques we have recently + + align:start position:0% +use the techniques we have recently + + + align:start position:0% +use the techniques we have recently +learned in order to answer some + + align:start position:0% +learned in order to answer some + + + align:start position:0% +learned in order to answer some +questions about the following classical + + align:start position:0% +questions about the following classical + + + align:start position:0% +questions about the following classical +problem consider a gambler putting a bet + + align:start position:0% +problem consider a gambler putting a bet + + + align:start position:0% +problem consider a gambler putting a bet +of $1 in a game that has a payoff of $1 + + align:start position:0% +of $1 in a game that has a payoff of $1 + + + align:start position:0% +of $1 in a game that has a payoff of $1 +if she wins we assume that this is a + + align:start position:0% +if she wins we assume that this is a + + + align:start position:0% +if she wins we assume that this is a +fair game so that the probability of + + align:start position:0% +fair game so that the probability of + + + align:start position:0% +fair game so that the probability of +winning $1 on each play of the game is + + align:start position:0% +winning $1 on each play of the game is + + + align:start position:0% +winning $1 on each play of the game is +one-half and so the priority of losing + + align:start position:0% +one-half and so the priority of losing + + + align:start position:0% +one-half and so the priority of losing +the bet is also one-half suppose that + + align:start position:0% +the bet is also one-half suppose that + + + align:start position:0% +the bet is also one-half suppose that +she starts with I dollars and continues + + align:start position:0% +she starts with I dollars and continues + + + align:start position:0% +she starts with I dollars and continues +to play the game until either she + + align:start position:0% +to play the game until either she + + + align:start position:0% +to play the game until either she +reaches a goal of n dollars or she has + + align:start position:0% +reaches a goal of n dollars or she has + + + align:start position:0% +reaches a goal of n dollars or she has +no money left whatever come first let us + + align:start position:0% +no money left whatever come first let us + + + align:start position:0% +no money left whatever come first let us +consider a first question which is the + + align:start position:0% +consider a first question which is the + + + align:start position:0% +consider a first question which is the +following what is the probability that + + align:start position:0% +following what is the probability that + + + align:start position:0% +following what is the probability that +she ends up with having her goal of n + + align:start position:0% +she ends up with having her goal of n + + + align:start position:0% +she ends up with having her goal of n +dollars now how to go about solving this + + align:start position:0% +dollars now how to go about solving this + + + align:start position:0% +dollars now how to go about solving this +problem can we think of a Markov chain + + align:start position:0% +problem can we think of a Markov chain + + + align:start position:0% +problem can we think of a Markov chain +representation for this problem but in + + align:start position:0% +representation for this problem but in + + + align:start position:0% +representation for this problem but in +that case what would be good choices for + + align:start position:0% +that case what would be good choices for + + + align:start position:0% +that case what would be good choices for +the definition of the state let us think + + align:start position:0% +the definition of the state let us think + + + align:start position:0% +the definition of the state let us think +at any point in time the only relevant + + align:start position:0% +at any point in time the only relevant + + + align:start position:0% +at any point in time the only relevant +information is the amount of money the + + align:start position:0% +information is the amount of money the + + + align:start position:0% +information is the amount of money the +gambler as available how she got to that + + align:start position:0% +gambler as available how she got to that + + + align:start position:0% +gambler as available how she got to that +amount in the past is irrelevant and if + + align:start position:0% +amount in the past is irrelevant and if + + + align:start position:0% +amount in the past is irrelevant and if +this amount is neither 0 nor n then she + + align:start position:0% +this amount is neither 0 nor n then she + + + align:start position:0% +this amount is neither 0 nor n then she +will play again and the next state will + + align:start position:0% +will play again and the next state will + + + align:start position:0% +will play again and the next state will +be a number which will be increased or + + align:start position:0% +be a number which will be increased or + + + align:start position:0% +be a number which will be increased or +decreased by one unit depending on + + align:start position:0% +decreased by one unit depending on + + + align:start position:0% +decreased by one unit depending on +winning or losing the next bet so we can + + align:start position:0% +winning or losing the next bet so we can + + + align:start position:0% +winning or losing the next bet so we can +represent the possible evolution of this + + align:start position:0% +represent the possible evolution of this + + + align:start position:0% +represent the possible evolution of this +game with the following probability + + align:start position:0% +game with the following probability + + + align:start position:0% +game with the following probability +transition graph so we have n plus 1 + + align:start position:0% +transition graph so we have n plus 1 + + + align:start position:0% +transition graph so we have n plus 1 +States this is the state where she loses + + align:start position:0% +States this is the state where she loses + + + align:start position:0% +States this is the state where she loses +all the money this is the state where + + align:start position:0% +all the money this is the state where + + + align:start position:0% +all the money this is the state where +she has AI amount of money before the + + align:start position:0% +she has AI amount of money before the + + + align:start position:0% +she has AI amount of money before the +next betting and here this is the state + + align:start position:0% +next betting and here this is the state + + + align:start position:0% +next betting and here this is the state +and where she reaches her goal and she + + align:start position:0% +and where she reaches her goal and she + + + align:start position:0% +and where she reaches her goal and she +can lead in terms of the transition + + align:start position:0% +can lead in terms of the transition + + + align:start position:0% +can lead in terms of the transition +probability assuming that you are at the + + align:start position:0% +probability assuming that you are at the + + + align:start position:0% +probability assuming that you are at the +given time + + align:start position:0% +given time + + + align:start position:0% +given time +in that state that means that you have + + align:start position:0% +in that state that means that you have + + + align:start position:0% +in that state that means that you have +I'm money in your pocket and you play + + align:start position:0% +I'm money in your pocket and you play + + + align:start position:0% +I'm money in your pocket and you play +the next bet with a perky 1/2 you will + + align:start position:0% +the next bet with a perky 1/2 you will + + + align:start position:0% +the next bet with a perky 1/2 you will +gain or win and so your amount of money + + align:start position:0% +gain or win and so your amount of money + + + align:start position:0% +gain or win and so your amount of money +is I plus 1 or you lose and your money + + align:start position:0% +is I plus 1 or you lose and your money + + + align:start position:0% +is I plus 1 or you lose and your money +is I minus 1 and you keep repeating + + align:start position:0% +is I minus 1 and you keep repeating + + + align:start position:0% +is I minus 1 and you keep repeating +until you reach either n or 0 and then + + align:start position:0% +until you reach either n or 0 and then + + + align:start position:0% +until you reach either n or 0 and then +you stop so this is a Markov chain and + + align:start position:0% +you stop so this is a Markov chain and + + + align:start position:0% +you stop so this is a Markov chain and +that state 0 and that state and are + + align:start position:0% +that state 0 and that state and are + + + align:start position:0% +that state 0 and that state and are +absorbing states once you reach them + + align:start position:0% +absorbing states once you reach them + + + align:start position:0% +absorbing states once you reach them +you stay there forever so what this + + align:start position:0% +you stay there forever so what this + + + align:start position:0% +you stay there forever so what this +question is asking is the probability a + + align:start position:0% +question is asking is the probability a + + + align:start position:0% +question is asking is the probability a +of I of starting from hi what is the + + align:start position:0% +of I of starting from hi what is the + + + align:start position:0% +of I of starting from hi what is the +probability that you will end up in that + + align:start position:0% +probability that you will end up in that + + + align:start position:0% +probability that you will end up in that +absorbing state and we have done this + + align:start position:0% +absorbing state and we have done this + + + align:start position:0% +absorbing state and we have done this +calculation previously so let us repeat + + align:start position:0% +calculation previously so let us repeat + + + align:start position:0% +calculation previously so let us repeat +the technique very briefly clearly here + + align:start position:0% +the technique very briefly clearly here + + + align:start position:0% +the technique very briefly clearly here +if you start with $0 you will never + + align:start position:0% +if you start with $0 you will never + + + align:start position:0% +if you start with $0 you will never +reach that so it's going to be 0 on the + + align:start position:0% +reach that so it's going to be 0 on the + + + align:start position:0% +reach that so it's going to be 0 on the +other hand if you start with your + + align:start position:0% +other hand if you start with your + + + align:start position:0% +other hand if you start with your +desired goal you don't play anymore so + + align:start position:0% +desired goal you don't play anymore so + + + align:start position:0% +desired goal you don't play anymore so +your prodigy is 1 now of course what is + + align:start position:0% +your prodigy is 1 now of course what is + + + align:start position:0% +your prodigy is 1 now of course what is +of interest is if I is strictly between + + align:start position:0% +of interest is if I is strictly between + + + align:start position:0% +of interest is if I is strictly between +0 and n and now the question is how to + + align:start position:0% +0 and n and now the question is how to + + + align:start position:0% +0 and n and now the question is how to +calculate that probability and we have + + align:start position:0% +calculate that probability and we have + + + align:start position:0% +calculate that probability and we have +seen that the way to do that is to look + + align:start position:0% +seen that the way to do that is to look + + + align:start position:0% +seen that the way to do that is to look +at the situation and say well let's + + align:start position:0% +at the situation and say well let's + + + align:start position:0% +at the situation and say well let's +assume that you are in that state I and + + align:start position:0% +assume that you are in that state I and + + + align:start position:0% +assume that you are in that state I and +what will happen next well with a pie + + align:start position:0% +what will happen next well with a pie + + + align:start position:0% +what will happen next well with a pie +which is 0.5 you will move to that state + + align:start position:0% +which is 0.5 you will move to that state + + + align:start position:0% +which is 0.5 you will move to that state +and now you are in that level with I + + align:start position:0% +and now you are in that level with I + + + align:start position:0% +and now you are in that level with I +plus 1 amount of money and what is the + + align:start position:0% +plus 1 amount of money and what is the + + + align:start position:0% +plus 1 amount of money and what is the +probability that given that you are here + + align:start position:0% +probability that given that you are here + + + align:start position:0% +probability that given that you are here +you're gonna end up in n is going to be + + align:start position:0% +you're gonna end up in n is going to be + + + align:start position:0% +you're gonna end up in n is going to be +AI plus 1 so it's 8 I plus 1 plus the + + align:start position:0% +AI plus 1 so it's 8 I plus 1 plus the + + + align:start position:0% +AI plus 1 so it's 8 I plus 1 plus the +other alternative is that you are going + + align:start position:0% +other alternative is that you are going + + + align:start position:0% +other alternative is that you are going +to lose money and end up in that state + + align:start position:0% +to lose money and end up in that state + + + align:start position:0% +to lose money and end up in that state +and there the remaining probability to + + align:start position:0% +and there the remaining probability to + + + align:start position:0% +and there the remaining probability to +reach the time and is AI minus 1 so you + + align:start position:0% +reach the time and is AI minus 1 so you + + + align:start position:0% +reach the time and is AI minus 1 so you +have this kind of equation this is valid + + align:start position:0% +have this kind of equation this is valid + + + align:start position:0% +have this kind of equation this is valid +for all I between 0 and n and + + align:start position:0% +for all I between 0 and n and + + + align:start position:0% +for all I between 0 and n and +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +this is a system of equation that you + + align:start position:0% +this is a system of equation that you + + + align:start position:0% +this is a system of equation that you +can solve it's not very difficult to + + align:start position:0% +can solve it's not very difficult to + + + align:start position:0% +can solve it's not very difficult to +solve actually you can look in a + + align:start position:0% +solve actually you can look in a + + + align:start position:0% +solve actually you can look in a +textbook there will be some trick to do + + align:start position:0% +textbook there will be some trick to do + + + align:start position:0% +textbook there will be some trick to do +that there are many many ways to do that + + align:start position:0% +that there are many many ways to do that + + + align:start position:0% +that there are many many ways to do that +when I can spend our time explain going + + align:start position:0% +when I can spend our time explain going + + + align:start position:0% +when I can spend our time explain going +that in details but essentially if you + + align:start position:0% +that in details but essentially if you + + + align:start position:0% +that in details but essentially if you +solve that system you will see that the + + align:start position:0% +solve that system you will see that the + + + align:start position:0% +solve that system you will see that the +answer will be that a of I is I over N + + align:start position:0% +answer will be that a of I is I over N + + + align:start position:0% +answer will be that a of I is I over N +so if you start with I amount of money + + align:start position:0% +so if you start with I amount of money + + + align:start position:0% +so if you start with I amount of money +the probability that you're going to + + align:start position:0% +the probability that you're going to + + + align:start position:0% +the probability that you're going to +reach your goal and here is I over N so + + align:start position:0% +reach your goal and here is I over N so + + + align:start position:0% +reach your goal and here is I over N so +here clearly if you're extremely greedy + + align:start position:0% +here clearly if you're extremely greedy + + + align:start position:0% +here clearly if you're extremely greedy +and you had a very very very high goal + + align:start position:0% +and you had a very very very high goal + + + align:start position:0% +and you had a very very very high goal +that means n is very very loud so large + + align:start position:0% +that means n is very very loud so large + + + align:start position:0% +that means n is very very loud so large +that compared to your initial amount I + + align:start position:0% +that compared to your initial amount I + + + align:start position:0% +that compared to your initial amount I +and can be considered to be infinity + + align:start position:0% +and can be considered to be infinity + + + align:start position:0% +and can be considered to be infinity +then the probability that you can reach + + align:start position:0% +then the probability that you can reach + + + align:start position:0% +then the probability that you can reach +your high goal will go to 0 where n get + + align:start position:0% +your high goal will go to 0 where n get + + + align:start position:0% +your high goal will go to 0 where n get +goes to infinity so again if you're + + align:start position:0% +goes to infinity so again if you're + + + align:start position:0% +goes to infinity so again if you're +extremely greedy + + align:start position:0% +extremely greedy + + + align:start position:0% +extremely greedy +nobody are much your fixed amount of + + align:start position:0% +nobody are much your fixed amount of + + + align:start position:0% +nobody are much your fixed amount of +initial money is the probability that + + align:start position:0% +initial money is the probability that + + + align:start position:0% +initial money is the probability that +you will stop the game reaching your + + align:start position:0% +you will stop the game reaching your + + + align:start position:0% +you will stop the game reaching your +goal is going to be increasingly small + + align:start position:0% +goal is going to be increasingly small + + + align:start position:0% +goal is going to be increasingly small +and since the author state is 1 minus + + align:start position:0% +and since the author state is 1 minus + + + align:start position:0% +and since the author state is 1 minus +this one the priority that you're going + + align:start position:0% +this one the priority that you're going + + + align:start position:0% +this one the priority that you're going +to get ruined is going to be closer to 1 + + align:start position:0% +to get ruined is going to be closer to 1 + + + align:start position:0% +to get ruined is going to be closer to 1 +all right so we have that answer here + + align:start position:0% +all right so we have that answer here + + + align:start position:0% +all right so we have that answer here +what about the next question next + + align:start position:0% +what about the next question next + + + align:start position:0% +what about the next question next +question is the following what would be + + align:start position:0% +question is the following what would be + + + align:start position:0% +question is the following what would be +the expected wealth at the end again + + align:start position:0% +the expected wealth at the end again + + + align:start position:0% +the expected wealth at the end again +this is a Markov chain where there are + + align:start position:0% +this is a Markov chain where there are + + + align:start position:0% +this is a Markov chain where there are +two absorbing States all the others are + + align:start position:0% +two absorbing States all the others are + + + align:start position:0% +two absorbing States all the others are +transient you are guaranteed with + + align:start position:0% +transient you are guaranteed with + + + align:start position:0% +transient you are guaranteed with +priority one that you will reach either + + align:start position:0% +priority one that you will reach either + + + align:start position:0% +priority one that you will reach either +0 or n so it's a valid question to know + + align:start position:0% +0 or n so it's a valid question to know + + + align:start position:0% +0 or n so it's a valid question to know +once you reach either 0 or n what is the + + align:start position:0% +once you reach either 0 or n what is the + + + align:start position:0% +once you reach either 0 or n what is the +expected wealth at the end well it's + + align:start position:0% +expected wealth at the end well it's + + + align:start position:0% +expected wealth at the end well it's +going to be if you arrive here it's + + align:start position:0% +going to be if you arrive here it's + + + align:start position:0% +going to be if you arrive here it's +going to be 0 and if you arrive here + + align:start position:0% +going to be 0 and if you arrive here + + + align:start position:0% +going to be 0 and if you arrive here +it's gonna be n so the expected value of + + align:start position:0% +it's gonna be n so the expected value of + + + align:start position:0% +it's gonna be n so the expected value of +that wealth will be 0 times the priority + + align:start position:0% +that wealth will be 0 times the priority + + + align:start position:0% +that wealth will be 0 times the priority +of running in that plus n times the + + align:start position:0% +of running in that plus n times the + + + align:start position:0% +of running in that plus n times the +gravity of the game there so it's going + + align:start position:0% +gravity of the game there so it's going + + + align:start position:0% +gravity of the game there so it's going +to be that expression 0 times 1 minus a + + align:start position:0% +to be that expression 0 times 1 minus a + + + align:start position:0% +to be that expression 0 times 1 minus a +of I plus n times a of I and here what + + align:start position:0% +of I plus n times a of I and here what + + + align:start position:0% +of I plus n times a of I and here what +we then + + align:start position:0% +we then + + + align:start position:0% +we then +it is n times I over N which is I which + + align:start position:0% +it is n times I over N which is I which + + + align:start position:0% +it is n times I over N which is I which +is quite interesting this is exactly how + + align:start position:0% +is quite interesting this is exactly how + + + align:start position:0% +is quite interesting this is exactly how +you started + + align:start position:0% +you started + + + align:start position:0% +you started +so in some sense in expectation there is + + align:start position:0% +so in some sense in expectation there is + + + align:start position:0% +so in some sense in expectation there is +no free lunch here the next question is + + align:start position:0% +no free lunch here the next question is + + + align:start position:0% +no free lunch here the next question is +how long does a gambler expect to stay + + align:start position:0% +how long does a gambler expect to stay + + + align:start position:0% +how long does a gambler expect to stay +in the game we know that eventually you + + align:start position:0% +in the game we know that eventually you + + + align:start position:0% +in the game we know that eventually you +will either reach zero or n with + + align:start position:0% +will either reach zero or n with + + + align:start position:0% +will either reach zero or n with +property one the question is how long is + + align:start position:0% +property one the question is how long is + + + align:start position:0% +property one the question is how long is +it going to take and again we have seen + + align:start position:0% +it going to take and again we have seen + + + align:start position:0% +it going to take and again we have seen +in a previous video that this is + + align:start position:0% +in a previous video that this is + + + align:start position:0% +in a previous video that this is +essentially calculating the expectation + + align:start position:0% +essentially calculating the expectation + + + align:start position:0% +essentially calculating the expectation +to absorption and we know how to do that + + align:start position:0% +to absorption and we know how to do that + + + align:start position:0% +to absorption and we know how to do that +so let's recap what we had said if you + + align:start position:0% +so let's recap what we had said if you + + + align:start position:0% +so let's recap what we had said if you +define mu of I to be the expected number + + align:start position:0% +define mu of I to be the expected number + + + align:start position:0% +define mu of I to be the expected number +of plays starting from I what do you + + align:start position:0% +of plays starting from I what do you + + + align:start position:0% +of plays starting from I what do you +have well for I equals zero + + align:start position:0% +have well for I equals zero + + + align:start position:0% +have well for I equals zero +or I equals n either way if you start + + align:start position:0% +or I equals n either way if you start + + + align:start position:0% +or I equals n either way if you start +from here or you start from here the + + align:start position:0% +from here or you start from here the + + + align:start position:0% +from here or you start from here the +expected number of play is zero right + + align:start position:0% +expected number of play is zero right + + + align:start position:0% +expected number of play is zero right +because you're done and otherwise you + + align:start position:0% +because you're done and otherwise you + + + align:start position:0% +because you're done and otherwise you +use the same kind of derivation that we + + align:start position:0% +use the same kind of derivation that we + + + align:start position:0% +use the same kind of derivation that we +had if you start at I between 1 and n + + align:start position:0% +had if you start at I between 1 and n + + + align:start position:0% +had if you start at I between 1 and n +then you will see that mu of I after one + + align:start position:0% +then you will see that mu of I after one + + + align:start position:0% +then you will see that mu of I after one +transition plus 1 you will either be in + + align:start position:0% +transition plus 1 you will either be in + + + align:start position:0% +transition plus 1 you will either be in +state I plus 1 and in that case this + + align:start position:0% +state I plus 1 and in that case this + + + align:start position:0% +state I plus 1 and in that case this +expectation will be mu I plus 1 or you + + align:start position:0% +expectation will be mu I plus 1 or you + + + align:start position:0% +expectation will be mu I plus 1 or you +will be in state I minus 1 and that case + + align:start position:0% +will be in state I minus 1 and that case + + + align:start position:0% +will be in state I minus 1 and that case +the expectation is mu I minus 1 so this + + align:start position:0% +the expectation is mu I minus 1 so this + + + align:start position:0% +the expectation is mu I minus 1 so this +is an equation that you have which is + + align:start position:0% +is an equation that you have which is + + + align:start position:0% +is an equation that you have which is +almost the same as this one except that + + align:start position:0% +almost the same as this one except that + + + align:start position:0% +almost the same as this one except that +you have a plus 1 in it and as we had + + align:start position:0% +you have a plus 1 in it and as we had + + + align:start position:0% +you have a plus 1 in it and as we had +discussed before in general this is the + + align:start position:0% +discussed before in general this is the + + + align:start position:0% +discussed before in general this is the +kind of formula that you have now you + + align:start position:0% +kind of formula that you have now you + + + align:start position:0% +kind of formula that you have now you +can solve the system I will let you do + + align:start position:0% +can solve the system I will let you do + + + align:start position:0% +can solve the system I will let you do +that there are many ways to do this but + + align:start position:0% +that there are many ways to do this but + + + align:start position:0% +that there are many ways to do this but +the solution that you're going to have + + align:start position:0% +the solution that you're going to have + + + align:start position:0% +the solution that you're going to have +is that mu I will be equals to I times n + + align:start position:0% +is that mu I will be equals to I times n + + + align:start position:0% +is that mu I will be equals to I times n +minus 1 this is the result + + align:start position:0% + + + + align:start position:0% + +family what would be the case if you + + align:start position:0% +family what would be the case if you + + + align:start position:0% +family what would be the case if you +didn't have a fair game for example and + + align:start position:0% +didn't have a fair game for example and + + + align:start position:0% +didn't have a fair game for example and +fair to the gambler or unfair to the + + align:start position:0% +fair to the gambler or unfair to the + + + align:start position:0% +fair to the gambler or unfair to the +casino so what we mean here is that the + + align:start position:0% +casino so what we mean here is that the + + + align:start position:0% +casino so what we mean here is that the +probability P is different from 0.5 so + + align:start position:0% +probability P is different from 0.5 so + + + align:start position:0% +probability P is different from 0.5 so +here instead of 0.5 you have P + + align:start position:0% +here instead of 0.5 you have P + + + align:start position:0% +here instead of 0.5 you have P +everywhere and here of course you have 1 + + align:start position:0% +everywhere and here of course you have 1 + + + align:start position:0% +everywhere and here of course you have 1 +minus P everywhere on this side so you + + align:start position:0% +minus P everywhere on this side so you + + + align:start position:0% +minus P everywhere on this side so you +have a priority P of winning and + + align:start position:0% +have a priority P of winning and + + + align:start position:0% +have a priority P of winning and +priority 1 minus P of losing each bet so + + align:start position:0% +priority 1 minus P of losing each bet so + + + align:start position:0% +priority 1 minus P of losing each bet so +you might ask the same question well for + + align:start position:0% +you might ask the same question well for + + + align:start position:0% +you might ask the same question well for +the probability of AI you still have + + align:start position:0% +the probability of AI you still have + + + align:start position:0% +the probability of AI you still have +zero here you still have 1 here the + + align:start position:0% +zero here you still have 1 here the + + + align:start position:0% +zero here you still have 1 here the +formula that you would write here + + align:start position:0% +formula that you would write here + + + align:start position:0% +formula that you would write here +instead of writing it this way it would + + align:start position:0% +instead of writing it this way it would + + + align:start position:0% +instead of writing it this way it would +be you start from here with a very P you + + align:start position:0% +be you start from here with a very P you + + + align:start position:0% +be you start from here with a very P you +might appear and with a priority 1 minus + + align:start position:0% +might appear and with a priority 1 minus + + + align:start position:0% +might appear and with a priority 1 minus +P you end up there + + align:start position:0% +P you end up there + + + align:start position:0% +P you end up there +and the expression that you get for a of + + align:start position:0% +and the expression that you get for a of + + + align:start position:0% +and the expression that you get for a of +AI if you define R to be 1 minus P over + + align:start position:0% +AI if you define R to be 1 minus P over + + + align:start position:0% +AI if you define R to be 1 minus P over +P you will see that a of I is going to + + align:start position:0% +P you will see that a of I is going to + + + align:start position:0% +P you will see that a of I is going to +be 1 minus R at the power I over 1 minus + + align:start position:0% +be 1 minus R at the power I over 1 minus + + + align:start position:0% +be 1 minus R at the power I over 1 minus +R at the power n and what would be the + + align:start position:0% +R at the power n and what would be the + + + align:start position:0% +R at the power n and what would be the +expected amount of time she will play + + align:start position:0% +expected amount of time she will play + + + align:start position:0% +expected amount of time she will play +instead of that equation if you solve it + + align:start position:0% +instead of that equation if you solve it + + + align:start position:0% +instead of that equation if you solve it +you would have mu of I equals R plus 1 + + align:start position:0% +you would have mu of I equals R plus 1 + + + align:start position:0% +you would have mu of I equals R plus 1 +divided by R minus 1 times I minus n + + align:start position:0% +divided by R minus 1 times I minus n + + + align:start position:0% +divided by R minus 1 times I minus n +times 1 minus R I divided by 1 minus R + + align:start position:0% +times 1 minus R I divided by 1 minus R + + + align:start position:0% +times 1 minus R I divided by 1 minus R +at the power n + + align:start position:0% +at the power n + + + align:start position:0% +at the power n +because you would have here again P and + + align:start position:0% +because you would have here again P and + + + align:start position:0% +because you would have here again P and +1 minus P here and you can see that when + + align:start position:0% +1 minus P here and you can see that when + + + align:start position:0% +1 minus P here and you can see that when +P is strictly less than 1/2 in other + + align:start position:0% +P is strictly less than 1/2 in other + + + align:start position:0% +P is strictly less than 1/2 in other +words it's even worse for this gambler + + align:start position:0% +words it's even worse for this gambler + + + align:start position:0% +words it's even worse for this gambler +then a of I which is the priority of + + align:start position:0% +then a of I which is the priority of + + + align:start position:0% +then a of I which is the priority of +getting to this favorable state will + + align:start position:0% +getting to this favorable state will + + + align:start position:0% +getting to this favorable state will +also go to 0 when n goes to infinity and + + align:start position:0% +also go to 0 when n goes to infinity and + + + align:start position:0% +also go to 0 when n goes to infinity and +in the case where P is strictly greater + + align:start position:0% +in the case where P is strictly greater + + + align:start position:0% +in the case where P is strictly greater +than alpha that means that she has some + + align:start position:0% +than alpha that means that she has some + + + align:start position:0% +than alpha that means that she has some +favored odd on her favor then in that + + align:start position:0% +favored odd on her favor then in that + + + align:start position:0% +favored odd on her favor then in that +case this number are at the power n will + + align:start position:0% +case this number are at the power n will + + + align:start position:0% +case this number are at the power n will +go to 0 and 1 minus R of I will + + align:start position:0% +go to 0 and 1 minus R of I will + + + align:start position:0% +go to 0 and 1 minus R of I will +represent the probability that she would + + align:start position:0% +represent the probability that she would + + + align:start position:0% +represent the probability that she would +become infinitely rich in other words a + + align:start position:0% +become infinitely rich in other words a + + + align:start position:0% +become infinitely rich in other words a +being very greedy and going to infinity + + align:start position:0% +being very greedy and going to infinity + + + align:start position:0% +being very greedy and going to infinity +this will go to 0 and 1 minus R the + + align:start position:0% +this will go to 0 and 1 minus R the + + + align:start position:0% +this will go to 0 and 1 minus R the +power R is the priority that she would + + align:start position:0% +power R is the priority that she would + + + align:start position:0% +power R is the priority that she would +get infinitely rich \ No newline at end of file diff --git a/Nx76XS_4FRE.txt b/Nx76XS_4FRE.txt new file mode 100644 index 0000000000000000000000000000000000000000..86593da38318137e5a5f2734c128cf9a16139eb1 --- /dev/null +++ b/Nx76XS_4FRE.txt @@ -0,0 +1,6587 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu some good questions let's + + align:start position:0% +ocw.mit.edu some good questions let's + + + align:start position:0% +ocw.mit.edu some good questions let's +zip through quickly why can't initial + + align:start position:0% +zip through quickly why can't initial + + + align:start position:0% +zip through quickly why can't initial +depolarization travel along the length + + align:start position:0% +depolarization travel along the length + + + align:start position:0% +depolarization travel along the length +of the axon last time we went through in + + align:start position:0% +of the axon last time we went through in + + + align:start position:0% +of the axon last time we went through in +detail how a signal is + + align:start position:0% +detail how a signal is + + + align:start position:0% +detail how a signal is +transmitted from the outside to the + + align:start position:0% +transmitted from the outside to the + + + align:start position:0% +transmitted from the outside to the +inside of the cell by ion flux across + + align:start position:0% +inside of the cell by ion flux across + + + align:start position:0% +inside of the cell by ion flux across +the membrane and then how that ion flux + + align:start position:0% +the membrane and then how that ion flux + + + align:start position:0% +the membrane and then how that ion flux +is transmitted down the + + align:start position:0% +is transmitted down the + + + align:start position:0% +is transmitted down the +neuron remember that the ions entering + + align:start position:0% +neuron remember that the ions entering + + + align:start position:0% +neuron remember that the ions entering +the cell are just ions they'll diffuse + + align:start position:0% +the cell are just ions they'll diffuse + + + align:start position:0% +the cell are just ions they'll diffuse +away and so the depolarization kind of + + align:start position:0% +away and so the depolarization kind of + + + align:start position:0% +away and so the depolarization kind of +dissipates and it then needs to be + + align:start position:0% +dissipates and it then needs to be + + + align:start position:0% +dissipates and it then needs to be +regenerated + + align:start position:0% +regenerated + + + align:start position:0% +regenerated +the action potential each small + + align:start position:0% +the action potential each small + + + align:start position:0% +the action potential each small +depolarization or the whole signal each + + align:start position:0% +depolarization or the whole signal each + + + align:start position:0% +depolarization or the whole signal each +small + + align:start position:0% +small + + + align:start position:0% +small +depolarization with a specific magnitude + + align:start position:0% +depolarization with a specific magnitude + + + align:start position:0% +depolarization with a specific magnitude +the com the reversal of membrane + + align:start position:0% +the com the reversal of membrane + + + align:start position:0% +the com the reversal of membrane +potential going from aboutus 60 molts + + align:start position:0% +potential going from aboutus 60 molts + + + align:start position:0% +potential going from aboutus 60 molts +negative inside to plus 55 or 60 M volts + + align:start position:0% +negative inside to plus 55 or 60 M volts + + + align:start position:0% +negative inside to plus 55 or 60 M volts +positive Insight each of those is an + + align:start position:0% +positive Insight each of those is an + + + align:start position:0% +positive Insight each of those is an +action potential and here is an + + align:start position:0% +action potential and here is an + + + align:start position:0% +action potential and here is an +interesting one why doesn't the membrane + + align:start position:0% +interesting one why doesn't the membrane + + + align:start position:0% +interesting one why doesn't the membrane +potential stop at zero when sodium + + align:start position:0% +potential stop at zero when sodium + + + align:start position:0% +potential stop at zero when sodium +rushes into the cell during an action + + align:start position:0% +rushes into the cell during an action + + + align:start position:0% +rushes into the cell during an action +potential which is is what you'd expect + + align:start position:0% +potential which is is what you'd expect + + + align:start position:0% +potential which is is what you'd expect +if sodium was just moving along its + + align:start position:0% +if sodium was just moving along its + + + align:start position:0% +if sodium was just moving along its +concentration radiant because the + + align:start position:0% +concentration radiant because the + + + align:start position:0% +concentration radiant because the +potential is not only governed by sodium + + align:start position:0% +potential is not only governed by sodium + + + align:start position:0% +potential is not only governed by sodium +influx the chloride ions outside the + + align:start position:0% +influx the chloride ions outside the + + + align:start position:0% +influx the chloride ions outside the +cell and potassium ions inside over the + + align:start position:0% +cell and potassium ions inside over the + + + align:start position:0% +cell and potassium ions inside over the +duration of the potential and as we'll + + align:start position:0% +duration of the potential and as we'll + + + align:start position:0% +duration of the potential and as we'll +discuss briefly in a moment it's during + + align:start position:0% +discuss briefly in a moment it's during + + + align:start position:0% +discuss briefly in a moment it's during +the rectification process that you go + + align:start position:0% +the rectification process that you go + + + align:start position:0% +the rectification process that you go +back to zero and then you reverse + + align:start position:0% +back to zero and then you reverse + + + align:start position:0% +back to zero and then you reverse +membrane potential + + align:start position:0% +membrane potential + + + align:start position:0% +membrane potential +again let's move on to nervous system + + align:start position:0% +again let's move on to nervous system + + + align:start position:0% +again let's move on to nervous system +two + + align:start position:0% +two + + + align:start position:0% +two +and I want to cover two things + + align:start position:0% + + + + align:start position:0% + +today both of + + align:start position:0% +today both of + + + align:start position:0% +today both of +which connect with last lecture and then + + align:start position:0% +which connect with last lecture and then + + + align:start position:0% +which connect with last lecture and then +move on to our topic + + align:start position:0% +move on to our topic + + + align:start position:0% +move on to our topic +today we've drawn the analogy of the + + align:start position:0% +today we've drawn the analogy of the + + + align:start position:0% +today we've drawn the analogy of the +nervous system as a communication system + + align:start position:0% +nervous system as a communication system + + + align:start position:0% +nervous system as a communication system +through the body where there are wires + + align:start position:0% +through the body where there are wires + + + align:start position:0% +through the body where there are wires +there connections between the wires and + + align:start position:0% +there connections between the wires and + + + align:start position:0% +there connections between the wires and +there circuits that need to be laid down + + align:start position:0% +there circuits that need to be laid down + + + align:start position:0% +there circuits that need to be laid down +today we're mostly going to talk about + + align:start position:0% +today we're mostly going to talk about + + + align:start position:0% +today we're mostly going to talk about +the + + align:start position:0% +the + + + align:start position:0% +the +connections + + align:start position:0% + + + + align:start position:0% + +but I want to talk a little more about + + align:start position:0% +but I want to talk a little more about + + + align:start position:0% +but I want to talk a little more about +pumps and + + align:start position:0% + + + + align:start position:0% + +channels and then we're going to talk + + align:start position:0% +channels and then we're going to talk + + + align:start position:0% +channels and then we're going to talk +about the connections between + + align:start position:0% + + + + align:start position:0% + +neurons which is also called + + align:start position:0% + + + + align:start position:0% + +synapses let's begin + + align:start position:0% +synapses let's begin + + + align:start position:0% +synapses let's begin +with a little more about pumps and + + align:start position:0% +with a little more about pumps and + + + align:start position:0% +with a little more about pumps and +channels and I want + + align:start position:0% +channels and I want + + + align:start position:0% +channels and I want +to Briefly summarize where we were with + + align:start position:0% +to Briefly summarize where we were with + + + align:start position:0% +to Briefly summarize where we were with +talking about an action potential and + + align:start position:0% +talking about an action potential and + + + align:start position:0% +talking about an action potential and +introduce one last kind of Chan of pump + + align:start position:0% +introduce one last kind of Chan of pump + + + align:start position:0% +introduce one last kind of Chan of pump +of Channel excuse me that we didn't + + align:start position:0% +of Channel excuse me that we didn't + + + align:start position:0% +of Channel excuse me that we didn't +quite get to at the end of last lecture + + align:start position:0% +quite get to at the end of last lecture + + + align:start position:0% +quite get to at the end of last lecture +and then we'll talk about the pumps and + + align:start position:0% +and then we'll talk about the pumps and + + + align:start position:0% +and then we'll talk about the pumps and +channels involved in synapses so in an + + align:start position:0% +channels involved in synapses so in an + + + align:start position:0% +channels involved in synapses so in an +action + + align:start position:0% + + + + align:start position:0% + +potential and the sequence of an AC + + align:start position:0% +potential and the sequence of an AC + + + align:start position:0% +potential and the sequence of an AC +action + + align:start position:0% + + + + align:start position:0% + +potential we Define three + + align:start position:0% +potential we Define three + + + align:start position:0% +potential we Define three +phases along the length of the axon with + + align:start position:0% +phases along the length of the axon with + + + align:start position:0% +phases along the length of the axon with +regard to the membrane potential that + + align:start position:0% +regard to the membrane potential that + + + align:start position:0% +regard to the membrane potential that +was involved in transmitting the signal + + align:start position:0% +was involved in transmitting the signal + + + align:start position:0% +was involved in transmitting the signal +along the very long axon + + align:start position:0% +along the very long axon + + + align:start position:0% +along the very long axon +intracellular + + align:start position:0% +intracellular + + + align:start position:0% +intracellular +signaling those with a resting potential + + align:start position:0% + + + + align:start position:0% + +the threshold or the action potential + + align:start position:0% +the threshold or the action potential + + + align:start position:0% +the threshold or the action potential +the threshold leading to the action + + align:start position:0% +the threshold leading to the action + + + align:start position:0% +the threshold leading to the action +potential and then the question of + + align:start position:0% +potential and then the question of + + + align:start position:0% +potential and then the question of +repolarization resetting the membrane + + align:start position:0% +repolarization resetting the membrane + + + align:start position:0% +repolarization resetting the membrane +potential which is + + align:start position:0% +potential which is + + + align:start position:0% +potential which is +pivotal otherwise the cell can't fire + + align:start position:0% + + + + align:start position:0% + +again and we talked about one pump which + + align:start position:0% +again and we talked about one pump which + + + align:start position:0% +again and we talked about one pump which +is really pivotal for life we study it + + align:start position:0% +is really pivotal for life we study it + + + align:start position:0% +is really pivotal for life we study it +in my own laboratory but one pump P + + align:start position:0% +in my own laboratory but one pump P + + + align:start position:0% +in my own laboratory but one pump P +which is on all the time and which is + + align:start position:0% +which is on all the time and which is + + + align:start position:0% +which is on all the time and which is +involved primarily in the resting + + align:start position:0% +involved primarily in the resting + + + align:start position:0% +involved primarily in the resting +potential and the + + align:start position:0% +potential and the + + + align:start position:0% +potential and the +repolarization this is the + + align:start position:0% +repolarization this is the + + + align:start position:0% +repolarization this is the +sodium pottassium + + align:start position:0% +sodium pottassium + + + align:start position:0% +sodium pottassium +Pump It pumps sodium + + align:start position:0% +Pump It pumps sodium + + + align:start position:0% +Pump It pumps sodium +out and potassium in but less sodium out + + align:start position:0% +out and potassium in but less sodium out + + + align:start position:0% +out and potassium in but less sodium out +and potassium in and it is on all the + + align:start position:0% +and potassium in and it is on all the + + + align:start position:0% +and potassium in and it is on all the +time there are other channels that are + + align:start position:0% +time there are other channels that are + + + align:start position:0% +time there are other channels that are +open all the time + + align:start position:0% +open all the time + + + align:start position:0% +open all the time +the key one are pottassium + + align:start position:0% +the key one are pottassium + + + align:start position:0% +the key one are pottassium +channels but there are also open + + align:start position:0% +channels but there are also open + + + align:start position:0% +channels but there are also open +chloride and sodium channels and those + + align:start position:0% +chloride and sodium channels and those + + + align:start position:0% +chloride and sodium channels and those +are open all the time and depending on + + align:start position:0% +are open all the time and depending on + + + align:start position:0% +are open all the time and depending on +the concentration of the ions and also + + align:start position:0% +the concentration of the ions and also + + + align:start position:0% +the concentration of the ions and also +electrostatic repulsion which will + + align:start position:0% +electrostatic repulsion which will + + + align:start position:0% +electrostatic repulsion which will +counter sometimes movement along a + + align:start position:0% +counter sometimes movement along a + + + align:start position:0% +counter sometimes movement along a +concentration gradient those are + + align:start position:0% +concentration gradient those are + + + align:start position:0% +concentration gradient those are +involved in everything but primarily + + align:start position:0% +involved in everything but primarily + + + align:start position:0% +involved in everything but primarily +they're open all the time but they are + + align:start position:0% +they're open all the time but they are + + + align:start position:0% +they're open all the time but they are +primarily involved in setting up resting + + align:start position:0% +primarily involved in setting up resting + + + align:start position:0% +primarily involved in setting up resting +potential and repolarization so we'll + + align:start position:0% +potential and repolarization so we'll + + + align:start position:0% +potential and repolarization so we'll +put some + + align:start position:0% +put some + + + align:start position:0% +put some +dots I'm going to dash the + + align:start position:0% +dots I'm going to dash the + + + align:start position:0% +dots I'm going to dash the +line in the action + + align:start position:0% +line in the action + + + align:start position:0% +line in the action +potential area which indicates that + + align:start position:0% +potential area which indicates that + + + align:start position:0% +potential area which indicates that +those pumps and channel that pump and + + align:start position:0% +those pumps and channel that pump and + + + align:start position:0% +those pumps and channel that pump and +channel are being used and active but + + align:start position:0% +channel are being used and active but + + + align:start position:0% +channel are being used and active but +they're not pivotal in those processes + + align:start position:0% +they're not pivotal in those processes + + + align:start position:0% +they're not pivotal in those processes +the one that's really pivotal in the + + align:start position:0% +the one that's really pivotal in the + + + align:start position:0% +the one that's really pivotal in the +action potential is the voltage gated + + align:start position:0% +action potential is the voltage gated + + + align:start position:0% +action potential is the voltage gated +sodium + + align:start position:0% + + + + align:start position:0% + +Channel we talked about this last time + + align:start position:0% +Channel we talked about this last time + + + align:start position:0% +Channel we talked about this last time +you can look a bit more on the slides + + align:start position:0% +you can look a bit more on the slides + + + align:start position:0% +you can look a bit more on the slides +that I posted with regard to the ideas + + align:start position:0% +that I posted with regard to the ideas + + + align:start position:0% +that I posted with regard to the ideas +behind how this channel is closed at + + align:start position:0% +behind how this channel is closed at + + + align:start position:0% +behind how this channel is closed at +certain membrane potential how if the + + align:start position:0% +certain membrane potential how if the + + + align:start position:0% +certain membrane potential how if the +membrane potential changes slightly + + align:start position:0% +membrane potential changes slightly + + + align:start position:0% +membrane potential changes slightly +there's a confirmational change in the + + align:start position:0% +there's a confirmational change in the + + + align:start position:0% +there's a confirmational change in the +protein and a pore opens that allows + + align:start position:0% +protein and a pore opens that allows + + + align:start position:0% +protein and a pore opens that allows +sodium to rush + + align:start position:0% +sodium to rush + + + align:start position:0% +sodium to rush +down its concentration gradient over a + + align:start position:0% +down its concentration gradient over a + + + align:start position:0% +down its concentration gradient over a +very small area of membrane so the + + align:start position:0% +very small area of membrane so the + + + align:start position:0% +very small area of membrane so the +voltage gated sodium Channel allows + + align:start position:0% +voltage gated sodium Channel allows + + + align:start position:0% +voltage gated sodium Channel allows +sodium in and it is closed if we look at + + align:start position:0% +sodium in and it is closed if we look at + + + align:start position:0% +sodium in and it is closed if we look at +this it's open during an action + + align:start position:0% +this it's open during an action + + + align:start position:0% +this it's open during an action +potential it is closed at resting but is + + align:start position:0% +potential it is closed at resting but is + + + align:start position:0% +potential it is closed at resting but is +ready to be open and then subsequent ly + + align:start position:0% +ready to be open and then subsequent ly + + + align:start position:0% +ready to be open and then subsequent ly +it is + + align:start position:0% +it is + + + align:start position:0% +it is +closed during repolarization when the + + align:start position:0% +closed during repolarization when the + + + align:start position:0% +closed during repolarization when the +membrane potential is reset and it's not + + align:start position:0% +membrane potential is reset and it's not + + + align:start position:0% +membrane potential is reset and it's not +openable it's not actually clear why + + align:start position:0% +openable it's not actually clear why + + + align:start position:0% +openable it's not actually clear why +there's some funny + + align:start position:0% +there's some funny + + + align:start position:0% +there's some funny +confirmation and that pump is not ready + + align:start position:0% +confirmation and that pump is not ready + + + align:start position:0% +confirmation and that pump is not ready +to be opened for some period of time + + align:start position:0% +to be opened for some period of time + + + align:start position:0% +to be opened for some period of time +until the protein structure resets + + align:start position:0% +until the protein structure resets + + + align:start position:0% +until the protein structure resets +itself and then it's openable so it's + + align:start position:0% +itself and then it's openable so it's + + + align:start position:0% +itself and then it's openable so it's +closed and it's not ready to be opened + + align:start position:0% +closed and it's not ready to be opened + + + align:start position:0% +closed and it's not ready to be opened +and this is really pivotal in making + + align:start position:0% +and this is really pivotal in making + + + align:start position:0% +and this is really pivotal in making +making sure that an action potential + + align:start position:0% +making sure that an action potential + + + align:start position:0% +making sure that an action potential +traverses in One Direction along the + + align:start position:0% +traverses in One Direction along the + + + align:start position:0% +traverses in One Direction along the +axon and doesn't go backwards as the + + align:start position:0% +axon and doesn't go backwards as the + + + align:start position:0% +axon and doesn't go backwards as the +ions diffuse backwards and then finally + + align:start position:0% +ions diffuse backwards and then finally + + + align:start position:0% +ions diffuse backwards and then finally +I want to mention or I want to tell you + + align:start position:0% +I want to mention or I want to tell you + + + align:start position:0% +I want to mention or I want to tell you +that there is a voltage + + align:start position:0% +that there is a voltage + + + align:start position:0% +that there is a voltage +gated potassium + + align:start position:0% +gated potassium + + + align:start position:0% +gated potassium +channel that opens up after the action + + align:start position:0% +channel that opens up after the action + + + align:start position:0% +channel that opens up after the action +potential and that is one of the things + + align:start position:0% +potential and that is one of the things + + + align:start position:0% +potential and that is one of the things +that is pivotal in resetting the + + align:start position:0% +that is pivotal in resetting the + + + align:start position:0% +that is pivotal in resetting the +membrane potential during repolarization + + align:start position:0% +membrane potential during repolarization + + + align:start position:0% +membrane potential during repolarization +the other thing that is really pivotal + + align:start position:0% +the other thing that is really pivotal + + + align:start position:0% +the other thing that is really pivotal +is this sodium potassium pump so the + + align:start position:0% +is this sodium potassium pump so the + + + align:start position:0% +is this sodium potassium pump so the +voltage gated potassium + + align:start position:0% +voltage gated potassium + + + align:start position:0% +voltage gated potassium +channel gets pottassium out of the + + align:start position:0% +channel gets pottassium out of the + + + align:start position:0% +channel gets pottassium out of the +cell in the area where there's been + + align:start position:0% +cell in the area where there's been + + + align:start position:0% +cell in the area where there's been +depolarization you're very positive + + align:start position:0% +depolarization you're very positive + + + align:start position:0% +depolarization you're very positive +inside ions go out along their + + align:start position:0% +inside ions go out along their + + + align:start position:0% +inside ions go out along their +concentration gradient or along um an + + align:start position:0% +concentration gradient or along um an + + + align:start position:0% +concentration gradient or along um an +electrostatic gradient and so potassium + + align:start position:0% +electrostatic gradient and so potassium + + + align:start position:0% +electrostatic gradient and so potassium +goes out both in this case and so it is + + align:start position:0% +goes out both in this case and so it is + + + align:start position:0% +goes out both in this case and so it is +open during + + align:start position:0% +open during + + + align:start position:0% +open during +repolarization and it is + + align:start position:0% +repolarization and it is + + + align:start position:0% +repolarization and it is +closed for the rest of the + + align:start position:0% + + + + align:start position:0% + +time okay the thing you're going to have + + align:start position:0% +time okay the thing you're going to have + + + align:start position:0% +time okay the thing you're going to have +to do with these channels that you will + + align:start position:0% +to do with these channels that you will + + + align:start position:0% +to do with these channels that you will +do in section and with your problem set + + align:start position:0% +do in section and with your problem set + + + align:start position:0% +do in section and with your problem set +is to really work through the kind of + + align:start position:0% +is to really work through the kind of + + + align:start position:0% +is to really work through the kind of +logic behind what pump and channel is + + align:start position:0% +logic behind what pump and channel is + + + align:start position:0% +logic behind what pump and channel is +doing what at what stage of the action + + align:start position:0% +doing what at what stage of the action + + + align:start position:0% +doing what at what stage of the action +potential and then it will start to make + + align:start position:0% +potential and then it will start to make + + + align:start position:0% +potential and then it will start to make +sense sense + + align:start position:0% + + + + align:start position:0% + +okay so we're going to move on in a + + align:start position:0% +okay so we're going to move on in a + + + align:start position:0% +okay so we're going to move on in a +moment and talk about the synapse but + + align:start position:0% +moment and talk about the synapse but + + + align:start position:0% +moment and talk about the synapse but +I'm going to talk about the pumps and + + align:start position:0% +I'm going to talk about the pumps and + + + align:start position:0% +I'm going to talk about the pumps and +channels during a + + align:start position:0% +channels during a + + + align:start position:0% +channels during a +synapse and point out to you that these + + align:start position:0% +synapse and point out to you that these + + + align:start position:0% +synapse and point out to you that these +pumps and channels are being used but + + align:start position:0% +pumps and channels are being used but + + + align:start position:0% +pumps and channels are being used but +there are others which are really + + align:start position:0% +there are others which are really + + + align:start position:0% +there are others which are really +crucial one of them is a voltage gated + + align:start position:0% +crucial one of them is a voltage gated + + + align:start position:0% +crucial one of them is a voltage gated +VG voltage gated + + align:start position:0% +VG voltage gated + + + align:start position:0% +VG voltage gated +calcium + + align:start position:0% + + + + align:start position:0% + +channel and the other are a series of + + align:start position:0% +channel and the other are a series of + + + align:start position:0% +channel and the other are a series of +liand + + align:start position:0% + + + + align:start position:0% + +gated or second messenger + + align:start position:0% + + + + align:start position:0% + +gated second messenger regulated let's + + align:start position:0% +gated second messenger regulated let's + + + align:start position:0% +gated second messenger regulated let's +say not + + align:start position:0% + + + + align:start position:0% + +gated ion channels + + align:start position:0% + + + + align:start position:0% + +and these Lian gated or voltage gated + + align:start position:0% +and these Lian gated or voltage gated + + + align:start position:0% +and these Lian gated or voltage gated +second messenger regulated channels + + align:start position:0% +second messenger regulated channels + + + align:start position:0% +second messenger regulated channels +these things are specific to the synapse + + align:start position:0% +these things are specific to the synapse + + + align:start position:0% +these things are specific to the synapse +and are specific to the connections + + align:start position:0% +and are specific to the connections + + + align:start position:0% +and are specific to the connections +between cells + + align:start position:0% + + + + align:start position:0% + +good so let's move on to the major topic + + align:start position:0% +good so let's move on to the major topic + + + align:start position:0% +good so let's move on to the major topic +today which is this question of the + + align:start position:0% + + + + align:start position:0% + +synapse the connection between + + align:start position:0% + + + + align:start position:0% + +cells and let me throw out some facts + + align:start position:0% +cells and let me throw out some facts + + + align:start position:0% +cells and let me throw out some facts +and then I'll show you kind of a cool + + align:start position:0% +and then I'll show you kind of a cool + + + align:start position:0% +and then I'll show you kind of a cool +picture neurons connect with one another + + align:start position:0% +picture neurons connect with one another + + + align:start position:0% +picture neurons connect with one another +to make circuits that's the deal that's + + align:start position:0% +to make circuits that's the deal that's + + + align:start position:0% +to make circuits that's the deal that's +the wiring so how complex is this wiring + + align:start position:0% +the wiring so how complex is this wiring + + + align:start position:0% +the wiring so how complex is this wiring +I showed you a very cool 3D + + align:start position:0% +I showed you a very cool 3D + + + align:start position:0% +I showed you a very cool 3D +reconstruction of the brain that showed + + align:start position:0% +reconstruction of the brain that showed + + + align:start position:0% +reconstruction of the brain that showed +you the packing of the neurons in the + + align:start position:0% +you the packing of the neurons in the + + + align:start position:0% +you the packing of the neurons in the +brain but quantitatively what does that + + align:start position:0% +brain but quantitatively what does that + + + align:start position:0% +brain but quantitatively what does that +mean one + + align:start position:0% +mean one + + + align:start position:0% +mean one +neuron can connect with can synapse with + + align:start position:0% +neuron can connect with can synapse with + + + align:start position:0% +neuron can connect with can synapse with +up to 100,000 other neurons + + align:start position:0% + + + + align:start position:0% + +in the brain alone there are at least 10 + + align:start position:0% +in the brain alone there are at least 10 + + + align:start position:0% +in the brain alone there are at least 10 +to the 10th + + align:start position:0% + + + + align:start position:0% + +neurons it's not clear really to anyone + + align:start position:0% +neurons it's not clear really to anyone + + + align:start position:0% +neurons it's not clear really to anyone +how you put those two numbers together + + align:start position:0% +how you put those two numbers together + + + align:start position:0% +how you put those two numbers together +whether you can multiply them and + + align:start position:0% +whether you can multiply them and + + + align:start position:0% +whether you can multiply them and +whether that's + + align:start position:0% +whether that's + + + align:start position:0% +whether that's +fair but whatever you come out with with + + align:start position:0% +fair but whatever you come out with with + + + align:start position:0% +fair but whatever you come out with with +that's a lot of connections just in the + + align:start position:0% +that's a lot of connections just in the + + + align:start position:0% +that's a lot of connections just in the +brain + + align:start position:0% +brain + + + align:start position:0% +brain +okay the number of synapses therefore is + + align:start position:0% +okay the number of synapses therefore is + + + align:start position:0% +okay the number of synapses therefore is +huge so what kinds of connections are + + align:start position:0% +huge so what kinds of connections are + + + align:start position:0% +huge so what kinds of connections are +there let's just write this I'm not + + align:start position:0% +there let's just write this I'm not + + + align:start position:0% +there let's just write this I'm not +going to try + + align:start position:0% +going to try + + + align:start position:0% +going to try +to huge number of synapses there you go + + align:start position:0% +to huge number of synapses there you go + + + align:start position:0% +to huge number of synapses there you go +that's + + align:start position:0% + + + + align:start position:0% + +quantitative what are these connections + + align:start position:0% +quantitative what are these connections + + + align:start position:0% +quantitative what are these connections +we've talked a lot about an electrical + + align:start position:0% +we've talked a lot about an electrical + + + align:start position:0% +we've talked a lot about an electrical +signal moving down the Axon but now we + + align:start position:0% +signal moving down the Axon but now we + + + align:start position:0% +signal moving down the Axon but now we +I'm going to tell you that most + + align:start position:0% +I'm going to tell you that most + + + align:start position:0% +I'm going to tell you that most +connections between cells are not + + align:start position:0% +connections between cells are not + + + align:start position:0% +connections between cells are not +electrical they're chemical and I told + + align:start position:0% +electrical they're chemical and I told + + + align:start position:0% +electrical they're chemical and I told +you last time when we explored the + + align:start position:0% +you last time when we explored the + + + align:start position:0% +you last time when we explored the +reason that you have these long axons + + align:start position:0% +reason that you have these long axons + + + align:start position:0% +reason that you have these long axons +and intracellular signaling rather than + + align:start position:0% +and intracellular signaling rather than + + + align:start position:0% +and intracellular signaling rather than +cells all piled up next to one another + + align:start position:0% +cells all piled up next to one another + + + align:start position:0% +cells all piled up next to one another +doing intercellular + + align:start position:0% +doing intercellular + + + align:start position:0% +doing intercellular +signaling that's slow I told you that + + align:start position:0% +signaling that's slow I told you that + + + align:start position:0% +signaling that's slow I told you that +last time and that's still true in a + + align:start position:0% +last time and that's still true in a + + + align:start position:0% +last time and that's still true in a +synaps the connections between the cells + + align:start position:0% +synaps the connections between the cells + + + align:start position:0% +synaps the connections between the cells +is the slow point of neural trans + + align:start position:0% +is the slow point of neural trans + + + align:start position:0% +is the slow point of neural trans +transmission there are electrical + + align:start position:0% + + + + align:start position:0% + +synapses and they are used sometimes but + + align:start position:0% +synapses and they are used sometimes but + + + align:start position:0% +synapses and they are used sometimes but +rarely they're + + align:start position:0% +rarely they're + + + align:start position:0% +rarely they're +fast because they're connected by Gap + + align:start position:0% +fast because they're connected by Gap + + + align:start position:0% +fast because they're connected by Gap +Junctions one neuron to + + align:start position:0% +Junctions one neuron to + + + align:start position:0% +Junctions one neuron to +another and that + + align:start position:0% +another and that + + + align:start position:0% +another and that +allows ion + + align:start position:0% + + + + align:start position:0% + +flow but the thing about + + align:start position:0% +flow but the thing about + + + align:start position:0% +flow but the thing about +electrical synapses is that they're + + align:start position:0% +electrical synapses is that they're + + + align:start position:0% +electrical synapses is that they're +always open the cells are always + + align:start position:0% +always open the cells are always + + + align:start position:0% +always open the cells are always +connected they're + + align:start position:0% + + + + align:start position:0% + +unregulated and the thing about the + + align:start position:0% +unregulated and the thing about the + + + align:start position:0% +unregulated and the thing about the +nervous system is that it is exquisitly + + align:start position:0% +nervous system is that it is exquisitly + + + align:start position:0% +nervous system is that it is exquisitly +regulated it is fine-tuned to respond to + + align:start position:0% +regulated it is fine-tuned to respond to + + + align:start position:0% +regulated it is fine-tuned to respond to +the smallest stimula both from within + + align:start position:0% +the smallest stimula both from within + + + align:start position:0% +the smallest stimula both from within +your body and from without and + + align:start position:0% +your body and from without and + + + align:start position:0% +your body and from without and +unregulated synapses will not do that + + align:start position:0% +unregulated synapses will not do that + + + align:start position:0% +unregulated synapses will not do that +for you so the flip of those are + + align:start position:0% +for you so the flip of those are + + + align:start position:0% +for you so the flip of those are +chemical + + align:start position:0% + + + + align:start position:0% + +synapses they are + + align:start position:0% +synapses they are + + + align:start position:0% +synapses they are +slow they diffusion + + align:start position:0% + + + + align:start position:0% + +limited and they're diffusion limited of + + align:start position:0% +limited and they're diffusion limited of + + + align:start position:0% +limited and they're diffusion limited of +chemicals that we'll discuss in detail + + align:start position:0% +chemicals that we'll discuss in detail + + + align:start position:0% +chemicals that we'll discuss in detail +that are called neurotransmitters + + align:start position:0% + + + + align:start position:0% + +but they have the wonderful property of + + align:start position:0% +but they have the wonderful property of + + + align:start position:0% +but they have the wonderful property of +being highly + + align:start position:0% + + + + align:start position:0% + +regulatable and so the majority of + + align:start position:0% +regulatable and so the majority of + + + align:start position:0% +regulatable and so the majority of +synapses in higher animals are these + + align:start position:0% +synapses in higher animals are these + + + align:start position:0% +synapses in higher animals are these +chemical synapses and that's what we'll + + align:start position:0% +chemical synapses and that's what we'll + + + align:start position:0% +chemical synapses and that's what we'll +talk about today + + align:start position:0% + + + + align:start position:0% + +this is a picture which I really like + + align:start position:0% +this is a picture which I really like + + + align:start position:0% +this is a picture which I really like +it's a neuron where and these are the + + align:start position:0% +it's a neuron where and these are the + + + align:start position:0% +it's a neuron where and these are the +dendrites and here's a cell body and the + + align:start position:0% +dendrites and here's a cell body and the + + + align:start position:0% +dendrites and here's a cell body and the +axon coming out and each of these dots + + align:start position:0% +axon coming out and each of these dots + + + align:start position:0% +axon coming out and each of these dots +represents a synapse what doesn't + + align:start position:0% +represents a synapse what doesn't + + + align:start position:0% +represents a synapse what doesn't +represent a synapse it's is it's stained + + align:start position:0% +represent a synapse it's is it's stained + + + align:start position:0% +represent a synapse it's is it's stained +for a protein that's only found at + + align:start position:0% +for a protein that's only found at + + + align:start position:0% +for a protein that's only found at +synapses and you can see this tremendous + + align:start position:0% +synapses and you can see this tremendous + + + align:start position:0% +synapses and you can see this tremendous +studing of the dendrites with synapses + + align:start position:0% +studing of the dendrites with synapses + + + align:start position:0% +studing of the dendrites with synapses +which gives you a sense of the + + align:start position:0% +which gives you a sense of the + + + align:start position:0% +which gives you a sense of the +complexity + + align:start position:0% + + + + align:start position:0% + +okay it's really pivotal when we talk + + align:start position:0% +okay it's really pivotal when we talk + + + align:start position:0% +okay it's really pivotal when we talk +about the connections so we get some of + + align:start position:0% +about the connections so we get some of + + + align:start position:0% +about the connections so we get some of +the principles correct so I want to + + align:start position:0% +the principles correct so I want to + + + align:start position:0% +the principles correct so I want to +spend a board going through some of the + + align:start position:0% +spend a board going through some of the + + + align:start position:0% +spend a board going through some of the +principles that we have to bear in mind + + align:start position:0% +principles that we have to bear in mind + + + align:start position:0% +principles that we have to bear in mind +in thinking about the + + align:start position:0% + + + + align:start position:0% + +connections so let's think about this + + align:start position:0% +connections so let's think about this + + + align:start position:0% +connections so let's think about this +here in neurons + + align:start position:0% + + + + align:start position:0% + +well let's have neuron + + align:start position:0% +well let's have neuron + + + align:start position:0% +well let's have neuron +one but we could actually have neuron + + align:start position:0% +one but we could actually have neuron + + + align:start position:0% +one but we could actually have neuron +one to n it doesn't matter it could be a + + align:start position:0% +one to n it doesn't matter it could be a + + + align:start position:0% +one to n it doesn't matter it could be a +whole bunch of neuron one and along that + + align:start position:0% +whole bunch of neuron one and along that + + + align:start position:0% +whole bunch of neuron one and along that +one neuron or those Bunches of neurons + + align:start position:0% +one neuron or those Bunches of neurons + + + align:start position:0% +one neuron or those Bunches of neurons +is coming an action + + align:start position:0% + + + + align:start position:0% + +potential and over + + align:start position:0% +potential and over + + + align:start position:0% +potential and over +here is Neuron + + align:start position:0% + + + + align:start position:0% + +2 and between + + align:start position:0% +2 and between + + + align:start position:0% +2 and between +them is a connection is a + + align:start position:0% + + + + align:start position:0% + +synapse and the thing that neuron 2 has + + align:start position:0% +synapse and the thing that neuron 2 has + + + align:start position:0% +synapse and the thing that neuron 2 has +to decide when it connects with neuron + + align:start position:0% +to decide when it connects with neuron + + + align:start position:0% +to decide when it connects with neuron +one is whether it's going to make an + + align:start position:0% +one is whether it's going to make an + + + align:start position:0% +one is whether it's going to make an +action potential whether it's going to + + align:start position:0% +action potential whether it's going to + + + align:start position:0% +action potential whether it's going to +send a + + align:start position:0% +send a + + + align:start position:0% +send a +signal that is the big decision that + + align:start position:0% +signal that is the big decision that + + + align:start position:0% +signal that is the big decision that +this neuron has to make so neuron 2 must + + align:start position:0% + + + + align:start position:0% + +decide to make an action + + align:start position:0% +decide to make an action + + + align:start position:0% +decide to make an action +potential and it is a yes no decision + + align:start position:0% +potential and it is a yes no decision + + + align:start position:0% +potential and it is a yes no decision +it's it's not a sort of an action + + align:start position:0% +it's it's not a sort of an action + + + align:start position:0% +it's it's not a sort of an action +potential or a half an action potential + + align:start position:0% +potential or a half an action potential + + + align:start position:0% +potential or a half an action potential +and so we need to remember action + + align:start position:0% +and so we need to remember action + + + align:start position:0% +and so we need to remember action +potential + + align:start position:0% + + + + align:start position:0% + +facts all or none you either get an + + align:start position:0% +facts all or none you either get an + + + align:start position:0% +facts all or none you either get an +action potential or you + + align:start position:0% +action potential or you + + + align:start position:0% +action potential or you +don't that means you get complete + + align:start position:0% +don't that means you get complete + + + align:start position:0% +don't that means you get complete +depolarization or + + align:start position:0% + + + + align:start position:0% + +nothing and if you have a lot of action + + align:start position:0% +nothing and if you have a lot of action + + + align:start position:0% +nothing and if you have a lot of action +potential + + align:start position:0% +potential + + + align:start position:0% +potential +coming along neuron one the way neuron 2 + + align:start position:0% +coming along neuron one the way neuron 2 + + + align:start position:0% +coming along neuron one the way neuron 2 +can respond is not to make a big action + + align:start position:0% +can respond is not to make a big action + + + align:start position:0% +can respond is not to make a big action +potential obviously but it can make a + + align:start position:0% +potential obviously but it can make a + + + align:start position:0% +potential obviously but it can make a +lot of action potentials so a + + align:start position:0% +lot of action potentials so a + + + align:start position:0% +lot of action potentials so a +change in + + align:start position:0% + + + + align:start position:0% + +input where we can + + align:start position:0% +input where we can + + + align:start position:0% +input where we can +call this action potential from neuron + + align:start position:0% +call this action potential from neuron + + + align:start position:0% +call this action potential from neuron +one the input a change in input + + align:start position:0% +one the input a change in input + + + align:start position:0% +one the input a change in input +results in an increase or change let's + + align:start position:0% +results in an increase or change let's + + + align:start position:0% +results in an increase or change let's +just say + + align:start position:0% +just say + + + align:start position:0% +just say +a change in the number of action + + align:start position:0% +a change in the number of action + + + align:start position:0% +a change in the number of action +potentials per time or the + + align:start position:0% +potentials per time or the + + + align:start position:0% +potentials per time or the +frequency of action + + align:start position:0% + + + + align:start position:0% + +potentials in neuron + + align:start position:0% + + + + align:start position:0% + +2 other + + align:start position:0% +2 other + + + align:start position:0% +2 other +facts other really key + + align:start position:0% + + + + align:start position:0% + +facts resting potential can change + + align:start position:0% + + + + align:start position:0% + +threshold potential and the action + + align:start position:0% +threshold potential and the action + + + align:start position:0% +threshold potential and the action +potential as I've been belaboring do not + + align:start position:0% + + + + align:start position:0% + +change and you can see that nicely in + + align:start position:0% +change and you can see that nicely in + + + align:start position:0% +change and you can see that nicely in +this slide + + align:start position:0% +this slide + + + align:start position:0% +this slide +where here's a neuron firing and this is + + align:start position:0% +where here's a neuron firing and this is + + + align:start position:0% +where here's a neuron firing and this is +a different way of showing the neuron + + align:start position:0% +a different way of showing the neuron + + + align:start position:0% +a different way of showing the neuron +firing here's the action potential + + align:start position:0% +firing here's the action potential + + + align:start position:0% +firing here's the action potential +showing as a spike of + + align:start position:0% +showing as a spike of + + + align:start position:0% +showing as a spike of +depolarization and then there's a time + + align:start position:0% +depolarization and then there's a time + + + align:start position:0% +depolarization and then there's a time +another Spike another action potential + + align:start position:0% +another Spike another action potential + + + align:start position:0% +another Spike another action potential +weight another Spike and so on here is a + + align:start position:0% +weight another Spike and so on here is a + + + align:start position:0% +weight another Spike and so on here is a +neuron that's gotten a lot of input and + + align:start position:0% +neuron that's gotten a lot of input and + + + align:start position:0% +neuron that's gotten a lot of input and +look at it it's Spike Spike Spike Spike + + align:start position:0% +look at it it's Spike Spike Spike Spike + + + align:start position:0% +look at it it's Spike Spike Spike Spike +spike but if you look at the height of + + align:start position:0% +spike but if you look at the height of + + + align:start position:0% +spike but if you look at the height of +that Spike that is the depolarization + + align:start position:0% +that Spike that is the depolarization + + + align:start position:0% +that Spike that is the depolarization +height it's the same within the + + align:start position:0% +height it's the same within the + + + align:start position:0% +height it's the same within the +sensitivity of the recording device for + + align:start position:0% +sensitivity of the recording device for + + + align:start position:0% +sensitivity of the recording device for +each of these Action potentials so I + + align:start position:0% +each of these Action potentials so I + + + align:start position:0% +each of these Action potentials so I +really like that slide to + + align:start position:0% +really like that slide to + + + align:start position:0% +really like that slide to +exemplify these principles that I've + + align:start position:0% +exemplify these principles that I've + + + align:start position:0% +exemplify these principles that I've +just put on this + + align:start position:0% +just put on this + + + align:start position:0% +just put on this +board + + align:start position:0% + + + + align:start position:0% + +okay there are the principles how does + + align:start position:0% +okay there are the principles how does + + + align:start position:0% +okay there are the principles how does +it work very cool this is really + + align:start position:0% +it work very cool this is really + + + align:start position:0% +it work very cool this is really +amazing let's again have X on + + align:start position:0% +amazing let's again have X on + + + align:start position:0% +amazing let's again have X on +one we're going to have X on one here + + align:start position:0% +one we're going to have X on one here + + + align:start position:0% +one we're going to have X on one here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +axon well let's have axon derived from + + align:start position:0% +axon well let's have axon derived from + + + align:start position:0% +axon well let's have axon derived from +neuron + + align:start position:0% + + + + align:start position:0% + +one and now we got to distinguish two + + align:start position:0% +one and now we got to distinguish two + + + align:start position:0% +one and now we got to distinguish two +different parts of the + + align:start position:0% + + + + align:start position:0% + +axon and I'm going to draw this on the + + align:start position:0% +axon and I'm going to draw this on the + + + align:start position:0% +axon and I'm going to draw this on the +board and then I'm going to go through + + align:start position:0% +board and then I'm going to go through + + + align:start position:0% +board and then I'm going to go through +it with you on a handout because it's + + align:start position:0% +it with you on a handout because it's + + + align:start position:0% +it with you on a handout because it's +important there's an electrical signal + + align:start position:0% +important there's an electrical signal + + + align:start position:0% +important there's an electrical signal +coming along xon + + align:start position:0% + + + + align:start position:0% + +one and you know that it involves action + + align:start position:0% +one and you know that it involves action + + + align:start position:0% +one and you know that it involves action +potential via the voltage gated sodium + + align:start position:0% + + + + align:start position:0% + +channels as that signal nears the end of + + align:start position:0% +channels as that signal nears the end of + + + align:start position:0% +channels as that signal nears the end of +the axon the axon kind of bulges out + + align:start position:0% +the axon the axon kind of bulges out + + + align:start position:0% +the axon the axon kind of bulges out +into a terminal and the voltage gated + + align:start position:0% +into a terminal and the voltage gated + + + align:start position:0% +into a terminal and the voltage gated +channels change from sodium to + + align:start position:0% + + + + align:start position:0% + +calcium so here's the end of the axon + + align:start position:0% +calcium so here's the end of the axon + + + align:start position:0% +calcium so here's the end of the axon +and here you change to voltage + + align:start position:0% +and here you change to voltage + + + align:start position:0% +and here you change to voltage +gated calcium + + align:start position:0% +gated calcium + + + align:start position:0% +gated calcium +channels that are + + align:start position:0% + + + + align:start position:0% + +activated + + align:start position:0% +activated + + + align:start position:0% +activated +okay these voltage GED calcium channels + + align:start position:0% +okay these voltage GED calcium channels + + + align:start position:0% +okay these voltage GED calcium channels +this is called actually let's put some + + align:start position:0% +this is called actually let's put some + + + align:start position:0% +this is called actually let's put some +terminology this is called the + + align:start position:0% +terminology this is called the + + + align:start position:0% +terminology this is called the +preoptic + + align:start position:0% +preoptic + + + align:start position:0% +preoptic +neuron and the voltage gated calcium + + align:start position:0% +neuron and the voltage gated calcium + + + align:start position:0% +neuron and the voltage gated calcium +channels are at the preoptic terminus + + align:start position:0% + + + + align:start position:0% + +now the thing about + + align:start position:0% +now the thing about + + + align:start position:0% +now the thing about +calcium that we've mentioned before is + + align:start position:0% +calcium that we've mentioned before is + + + align:start position:0% +calcium that we've mentioned before is +that it is a mediator of + + align:start position:0% +that it is a mediator of + + + align:start position:0% +that it is a mediator of +exocytosis of having little vesicles + + align:start position:0% +exocytosis of having little vesicles + + + align:start position:0% +exocytosis of having little vesicles +containing proteins or other molecules + + align:start position:0% +containing proteins or other molecules + + + align:start position:0% +containing proteins or other molecules +released from the cell these voltage + + align:start position:0% +released from the cell these voltage + + + align:start position:0% +released from the cell these voltage +gated calcium channels increase + + align:start position:0% +gated calcium channels increase + + + align:start position:0% +gated calcium channels increase +intracellular calcium + + align:start position:0% + + + + align:start position:0% + +and lead to the + + align:start position:0% +and lead to the + + + align:start position:0% +and lead to the +exocytosis the release of chemicals that + + align:start position:0% +exocytosis the release of chemicals that + + + align:start position:0% +exocytosis the release of chemicals that +are contained in vesicles at the end at + + align:start position:0% +are contained in vesicles at the end at + + + align:start position:0% +are contained in vesicles at the end at +the prapti Terminus so the pratic + + align:start position:0% +the prapti Terminus so the pratic + + + align:start position:0% +the prapti Terminus so the pratic +Terminus contains + + align:start position:0% + + + + align:start position:0% + +vesicles with + + align:start position:0% +vesicles with + + + align:start position:0% +vesicles with +neurotransmitter we'll talk about this + + align:start position:0% +neurotransmitter we'll talk about this + + + align:start position:0% +neurotransmitter we'll talk about this +in detail + + align:start position:0% + + + + align:start position:0% + +the voltage gated calcium channels which + + align:start position:0% +the voltage gated calcium channels which + + + align:start position:0% +the voltage gated calcium channels which +increase intracellular + + align:start position:0% +increase intracellular + + + align:start position:0% +increase intracellular +calcium lead to + + align:start position:0% +calcium lead to + + + align:start position:0% +calcium lead to +exocytosis + + align:start position:0% +exocytosis + + + align:start position:0% +exocytosis +release of the + + align:start position:0% +release of the + + + align:start position:0% +release of the +neurotransmitter which is released + + align:start position:0% +neurotransmitter which is released + + + align:start position:0% +neurotransmitter which is released +outside the + + align:start position:0% +outside the + + + align:start position:0% +outside the +cell and that + + align:start position:0% +cell and that + + + align:start position:0% +cell and that +neurotransmitter diffuses across the + + align:start position:0% +neurotransmitter diffuses across the + + + align:start position:0% +neurotransmitter diffuses across the +space between neuron one and neuron 2 + + align:start position:0% +space between neuron one and neuron 2 + + + align:start position:0% +space between neuron one and neuron 2 +it's about 30 nanometers and it diffuses + + align:start position:0% +it's about 30 nanometers and it diffuses + + + align:start position:0% +it's about 30 nanometers and it diffuses +across the space and when it gets to the + + align:start position:0% +across the space and when it gets to the + + + align:start position:0% +across the space and when it gets to the +other side + + align:start position:0% +other side + + + align:start position:0% +other side +two here's neuron + + align:start position:0% +two here's neuron + + + align:start position:0% +two here's neuron +2 called the post synaptic + + align:start position:0% + + + + align:start position:0% + +neuron when it gets to the other side + + align:start position:0% +neuron when it gets to the other side + + + align:start position:0% +neuron when it gets to the other side +and it'll get to either the + + align:start position:0% +and it'll get to either the + + + align:start position:0% +and it'll get to either the +dendrites or the cell body + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% + + + + align:start position:0% + +neurotransmitter binds + + align:start position:0% +neurotransmitter binds + + + align:start position:0% +neurotransmitter binds +to things that we've talked about a lot + + align:start position:0% +to things that we've talked about a lot + + + align:start position:0% +to things that we've talked about a lot +it binds to + + align:start position:0% +it binds to + + + align:start position:0% +it binds to +receptors those receptors plus Lian do + + align:start position:0% +receptors those receptors plus Lian do + + + align:start position:0% +receptors those receptors plus Lian do +all the things we've talked about in + + align:start position:0% +all the things we've talked about in + + + align:start position:0% +all the things we've talked about in +many lectures they do something in this + + align:start position:0% +many lectures they do something in this + + + align:start position:0% +many lectures they do something in this +case they can do one of two things as + + align:start position:0% +case they can do one of two things as + + + align:start position:0% +case they can do one of two things as +we'll talk about but it all culminates + + align:start position:0% +we'll talk about but it all culminates + + + align:start position:0% +we'll talk about but it all culminates +in changing ing ion flux across the post + + align:start position:0% +in changing ing ion flux across the post + + + align:start position:0% +in changing ing ion flux across the post +synaptic membrane so the + + align:start position:0% +synaptic membrane so the + + + align:start position:0% +synaptic membrane so the +neurotransmitter diffuses it hits the + + align:start position:0% +neurotransmitter diffuses it hits the + + + align:start position:0% +neurotransmitter diffuses it hits the +dendrit so cell body it binds + + align:start position:0% + + + + align:start position:0% + +receptors to + + align:start position:0% + + + + align:start position:0% + +change ion flux or ion + + align:start position:0% + + + + align:start position:0% + +movement and this + + align:start position:0% +movement and this + + + align:start position:0% +movement and this +eventually gets turned + + align:start position:0% +eventually gets turned + + + align:start position:0% +eventually gets turned +into the action potential + + align:start position:0% + + + + align:start position:0% + +decision okay so let's put some more on + + align:start position:0% +decision okay so let's put some more on + + + align:start position:0% +decision okay so let's put some more on +here here's an electrical signal from + + align:start position:0% +here here's an electrical signal from + + + align:start position:0% +here here's an electrical signal from +neuron + + align:start position:0% +neuron + + + align:start position:0% +neuron +one here this neurotransmitter diffusion + + align:start position:0% +one here this neurotransmitter diffusion + + + align:start position:0% +one here this neurotransmitter diffusion +is a chemical + + align:start position:0% + + + + align:start position:0% + +signal across what is called the + + align:start position:0% +signal across what is called the + + + align:start position:0% +signal across what is called the +synaptic Clift which is the space + + align:start position:0% +synaptic Clift which is the space + + + align:start position:0% +synaptic Clift which is the space +between + + align:start position:0% +between + + + align:start position:0% +between +neurons and the signal in neuron + + align:start position:0% +neurons and the signal in neuron + + + align:start position:0% +neurons and the signal in neuron +2 becomes electrical + + align:start position:0% +2 becomes electrical + + + align:start position:0% +2 becomes electrical +again so there's a conversion device + + align:start position:0% +again so there's a conversion device + + + align:start position:0% +again so there's a conversion device +which converts electrical to chemical to + + align:start position:0% +which converts electrical to chemical to + + + align:start position:0% +which converts electrical to chemical to +electrical signals all right let's look + + align:start position:0% +electrical signals all right let's look + + + align:start position:0% +electrical signals all right let's look +at your first handout and we'll Hammer + + align:start position:0% +at your first handout and we'll Hammer + + + align:start position:0% +at your first handout and we'll Hammer +this in in more detail + + align:start position:0% + + + + align:start position:0% + +here's the action + + align:start position:0% +here's the action + + + align:start position:0% +here's the action +potential let me stand here in case + + align:start position:0% +potential let me stand here in case + + + align:start position:0% +potential let me stand here in case +you're they don't like me doing that + + align:start position:0% +you're they don't like me doing that + + + align:start position:0% +you're they don't like me doing that +okay let me stand here here's the action + + align:start position:0% +okay let me stand here here's the action + + + align:start position:0% +okay let me stand here here's the action +potential coming along neuron + + align:start position:0% +potential coming along neuron + + + align:start position:0% +potential coming along neuron +one voltage gated sodium channels until + + align:start position:0% +one voltage gated sodium channels until + + + align:start position:0% +one voltage gated sodium channels until +you get near the end when you switch to + + align:start position:0% +you get near the end when you switch to + + + align:start position:0% +you get near the end when you switch to +these voltage gated calcium channels + + align:start position:0% +these voltage gated calcium channels + + + align:start position:0% +these voltage gated calcium channels +calcium Flows + + align:start position:0% +calcium Flows + + + align:start position:0% +calcium Flows +In leads to + + align:start position:0% +In leads to + + + align:start position:0% +In leads to +exocytosis of vesicles containing + + align:start position:0% +exocytosis of vesicles containing + + + align:start position:0% +exocytosis of vesicles containing +neurotransmitter the neurotransmitter + + align:start position:0% +neurotransmitter the neurotransmitter + + + align:start position:0% +neurotransmitter the neurotransmitter +diffuses across the synaptic Clift binds + + align:start position:0% +diffuses across the synaptic Clift binds + + + align:start position:0% +diffuses across the synaptic Clift binds +two receptors on either side which + + align:start position:0% +two receptors on either side which + + + align:start position:0% +two receptors on either side which +changes the ion flux into neuron + + align:start position:0% +changes the ion flux into neuron + + + align:start position:0% +changes the ion flux into neuron +2 and there is an action potential + + align:start position:0% +2 and there is an action potential + + + align:start position:0% +2 and there is an action potential +decision it's on your P it's on your + + align:start position:0% +decision it's on your P it's on your + + + align:start position:0% +decision it's on your P it's on your +sheet an action potential decision that + + align:start position:0% +sheet an action potential decision that + + + align:start position:0% +sheet an action potential decision that +eventually as we'll discuss involves + + align:start position:0% +eventually as we'll discuss involves + + + align:start position:0% +eventually as we'll discuss involves +voltage gated sodium channels so that + + align:start position:0% +voltage gated sodium channels so that + + + align:start position:0% +voltage gated sodium channels so that +the cell decides whether or not it's + + align:start position:0% +the cell decides whether or not it's + + + align:start position:0% +the cell decides whether or not it's +going to high fire an action potential + + align:start position:0% +going to high fire an action potential + + + align:start position:0% +going to high fire an action potential +okay we'll talk about the + + align:start position:0% +okay we'll talk about the + + + align:start position:0% +okay we'll talk about the +neurotransmitters and The receptors in + + align:start position:0% +neurotransmitters and The receptors in + + + align:start position:0% +neurotransmitters and The receptors in +more detail in a moment but I want to + + align:start position:0% +more detail in a moment but I want to + + + align:start position:0% +more detail in a moment but I want to +introduce you + + align:start position:0% +introduce you + + + align:start position:0% +introduce you +to three concepts of the synapse which + + align:start position:0% +to three concepts of the synapse which + + + align:start position:0% +to three concepts of the synapse which +are really very important the first is + + align:start position:0% +are really very important the first is + + + align:start position:0% +are really very important the first is +the concept of + + align:start position:0% + + + + align:start position:0% + +summation and now we go back to the + + align:start position:0% +summation and now we go back to the + + + align:start position:0% +summation and now we go back to the +notion that many neurons can give + + align:start position:0% +notion that many neurons can give + + + align:start position:0% +notion that many neurons can give +signals to another + + align:start position:0% +signals to another + + + align:start position:0% +signals to another +neuron such that that other neuron is + + align:start position:0% +neuron such that that other neuron is + + + align:start position:0% +neuron such that that other neuron is +deciding yes no I'm going to fire an + + align:start position:0% +deciding yes no I'm going to fire an + + + align:start position:0% +deciding yes no I'm going to fire an +action potential and transmit the signal + + align:start position:0% +action potential and transmit the signal + + + align:start position:0% +action potential and transmit the signal +the neuron that's receiving all of that + + align:start position:0% +the neuron that's receiving all of that + + + align:start position:0% +the neuron that's receiving all of that +signaling has to add up its inputs and + + align:start position:0% +signaling has to add up its inputs and + + + align:start position:0% +signaling has to add up its inputs and +say what's the sum of the input + + align:start position:0% +say what's the sum of the input + + + align:start position:0% +say what's the sum of the input +literally it has to add up the inputs so + + align:start position:0% +literally it has to add up the inputs so + + + align:start position:0% +literally it has to add up the inputs so +summation is the + + align:start position:0% + + + + align:start position:0% + +addition of all synaptic input + + align:start position:0% + + + + align:start position:0% + +which is change in membrane + + align:start position:0% + + + + align:start position:0% + +potential governed + + align:start position:0% +potential governed + + + align:start position:0% +potential governed +by change in ion + + align:start position:0% + + + + align:start position:0% + +movement on a recipient neuron + + align:start position:0% + + + + align:start position:0% + +okay so the addition of all synaptic + + align:start position:0% +okay so the addition of all synaptic + + + align:start position:0% +okay so the addition of all synaptic +input on a recipient neuron or by a + + align:start position:0% +input on a recipient neuron or by a + + + align:start position:0% +input on a recipient neuron or by a +recipient neuron if you like there's two + + align:start position:0% +recipient neuron if you like there's two + + + align:start position:0% +recipient neuron if you like there's two +kinds there's spatial + + align:start position:0% + + + + align:start position:0% + +summation which has to do where the + + align:start position:0% +summation which has to do where the + + + align:start position:0% +summation which has to do where the +signal is + + align:start position:0% + + + + align:start position:0% + +received and so those synapses that I + + align:start position:0% +received and so those synapses that I + + + align:start position:0% +received and so those synapses that I +showed you in that picture of the cell + + align:start position:0% +showed you in that picture of the cell + + + align:start position:0% +showed you in that picture of the cell +with all its dendrites and all of those + + align:start position:0% +with all its dendrites and all of those + + + align:start position:0% +with all its dendrites and all of those +little dots we're all over the place + + align:start position:0% +little dots we're all over the place + + + align:start position:0% +little dots we're all over the place +each of those little dots is getting a + + align:start position:0% +each of those little dots is getting a + + + align:start position:0% +each of those little dots is getting a +signal on the dendrites on the ends of + + align:start position:0% +signal on the dendrites on the ends of + + + align:start position:0% +signal on the dendrites on the ends of +the dendrites near the cell body in the + + align:start position:0% +the dendrites near the cell body in the + + + align:start position:0% +the dendrites near the cell body in the +cell body all of those inputs have to be + + align:start position:0% +cell body all of those inputs have to be + + + align:start position:0% +cell body all of those inputs have to be +added up so where the signal receive + + align:start position:0% +added up so where the signal receive + + + align:start position:0% +added up so where the signal receive +ised cell body plus + + align:start position:0% + + + + align:start position:0% + +dendrites that would be spatial + + align:start position:0% +dendrites that would be spatial + + + align:start position:0% +dendrites that would be spatial +summation and then temporal + + align:start position:0% +summation and then temporal + + + align:start position:0% +summation and then temporal +summation means over + + align:start position:0% +summation means over + + + align:start position:0% +summation means over +time when the signal is + + align:start position:0% + + + + align:start position:0% + +received over a period of a millisecond + + align:start position:0% +received over a period of a millisecond + + + align:start position:0% +received over a period of a millisecond +or so all of those inputs to the neuron + + align:start position:0% +or so all of those inputs to the neuron + + + align:start position:0% +or so all of those inputs to the neuron +are added up and the addition is + + align:start position:0% +are added up and the addition is + + + align:start position:0% +are added up and the addition is +actually a simple one the addition is + + align:start position:0% +actually a simple one the addition is + + + align:start position:0% +actually a simple one the addition is +how much has the membrane potential + + align:start position:0% +how much has the membrane potential + + + align:start position:0% +how much has the membrane potential +changed and overall have you brought the + + align:start position:0% +changed and overall have you brought the + + + align:start position:0% +changed and overall have you brought the +membrane potential of the recipient + + align:start position:0% +membrane potential of the recipient + + + align:start position:0% +membrane potential of the recipient +neuron up to threshold if you have that + + align:start position:0% +neuron up to threshold if you have that + + + align:start position:0% +neuron up to threshold if you have that +recipient neuron fires and if you + + align:start position:0% +recipient neuron fires and if you + + + align:start position:0% +recipient neuron fires and if you +haven't it doesn't so the total membrane + + align:start position:0% +haven't it doesn't so the total membrane + + + align:start position:0% +haven't it doesn't so the total membrane +potential so the + + align:start position:0% +potential so the + + + align:start position:0% +potential so the +answer of whether to fire or not is the + + align:start position:0% + + + + align:start position:0% + +total membrane + + align:start position:0% + + + + align:start position:0% + +potential which is a decision + + align:start position:0% +potential which is a decision + + + align:start position:0% +potential which is a decision +and if it's threshold + + align:start position:0% + + + + align:start position:0% + +potential out of that an action + + align:start position:0% +potential out of that an action + + + align:start position:0% +potential out of that an action +potential + + align:start position:0% + + + + align:start position:0% + +results the addition the summation is + + align:start position:0% +results the addition the summation is + + + align:start position:0% +results the addition the summation is +done in the dendrites and the cell body + + align:start position:0% +done in the dendrites and the cell body + + + align:start position:0% +done in the dendrites and the cell body +and the answer is read at the place + + align:start position:0% +and the answer is read at the place + + + align:start position:0% +and the answer is read at the place +where the axon comes off the cell body + + align:start position:0% +where the axon comes off the cell body + + + align:start position:0% +where the axon comes off the cell body +which is called the axon + + align:start position:0% +which is called the axon + + + align:start position:0% +which is called the axon +hiloc so the sum + + align:start position:0% +hiloc so the sum + + + align:start position:0% +hiloc so the sum +is + + align:start position:0% + + + + align:start position:0% + +calculated over all of the + + align:start position:0% + + + + align:start position:0% + +dendrites plus the cell + + align:start position:0% +dendrites plus the cell + + + align:start position:0% +dendrites plus the cell +body but it is + + align:start position:0% +body but it is + + + align:start position:0% +body but it is +red at this thing called the axon + + align:start position:0% + + + + align:start position:0% + +hillock and the only read the X on + + align:start position:0% +hillock and the only read the X on + + + align:start position:0% +hillock and the only read the X on +hilock + + align:start position:0% + + + + align:start position:0% + +is where the + + align:start position:0% +is where the + + + align:start position:0% +is where the +axon leaves the cell body or originates + + align:start position:0% +axon leaves the cell body or originates + + + align:start position:0% +axon leaves the cell body or originates +from the cell + + align:start position:0% + + + + align:start position:0% + +body and the reason that that is + + align:start position:0% +body and the reason that that is + + + align:start position:0% +body and the reason that that is +a important place is that that is where + + align:start position:0% +a important place is that that is where + + + align:start position:0% +a important place is that that is where +the voltage gated sodium channels are + + align:start position:0% +the voltage gated sodium channels are + + + align:start position:0% +the voltage gated sodium channels are +found it's only there they start at the + + align:start position:0% +found it's only there they start at the + + + align:start position:0% +found it's only there they start at the +axon hillock and they are present all + + align:start position:0% +axon hillock and they are present all + + + align:start position:0% +axon hillock and they are present all +the way down the axon there are no and + + align:start position:0% +the way down the axon there are no and + + + align:start position:0% +the way down the axon there are no and +you can look at your diagram for this + + align:start position:0% +you can look at your diagram for this + + + align:start position:0% +you can look at your diagram for this +there are no voltage G sodium channels + + align:start position:0% +there are no voltage G sodium channels + + + align:start position:0% +there are no voltage G sodium channels +in the cell body or the dendrites so + + align:start position:0% +in the cell body or the dendrites so + + + align:start position:0% +in the cell body or the dendrites so +they can't fire an action potential they + + align:start position:0% +they can't fire an action potential they + + + align:start position:0% +they can't fire an action potential they +can add up how membrane potentials + + align:start position:0% +can add up how membrane potentials + + + align:start position:0% +can add up how membrane potentials +changed but they can't do anything about + + align:start position:0% +changed but they can't do anything about + + + align:start position:0% +changed but they can't do anything about +it so the hillock is where the axon + + align:start position:0% +it so the hillock is where the axon + + + align:start position:0% +it so the hillock is where the axon +leaves the cell body and where the + + align:start position:0% +leaves the cell body and where the + + + align:start position:0% +leaves the cell body and where the +voltage + + align:start position:0% +voltage + + + align:start position:0% +voltage +gated sodium + + align:start position:0% +gated sodium + + + align:start position:0% +gated sodium +channels begin + + align:start position:0% + + + + align:start position:0% + +begin and to where and where an action + + align:start position:0% +begin and to where and where an action + + + align:start position:0% +begin and to where and where an action +potential can therefore come out that's + + align:start position:0% +potential can therefore come out that's + + + align:start position:0% +potential can therefore come out that's +a bunch of + + align:start position:0% + + + + align:start position:0% + +sentences + + align:start position:0% + + + + align:start position:0% + +okay couple more terms excitatory and + + align:start position:0% +okay couple more terms excitatory and + + + align:start position:0% +okay couple more terms excitatory and +inhibitory synapses + + align:start position:0% +inhibitory synapses + + + align:start position:0% +inhibitory synapses +excitatory and inhibitory + + align:start position:0% + + + + align:start position:0% + +it's kind of like a simple math problem + + align:start position:0% +it's kind of like a simple math problem + + + align:start position:0% +it's kind of like a simple math problem +where you're adding positive numbers or + + align:start position:0% +where you're adding positive numbers or + + + align:start position:0% +where you're adding positive numbers or +negative numbers you know you come out + + align:start position:0% +negative numbers you know you come out + + + align:start position:0% +negative numbers you know you come out +with something that's either zero + + align:start position:0% +with something that's either zero + + + align:start position:0% +with something that's either zero +negative or positive same idea here when + + align:start position:0% +negative or positive same idea here when + + + align:start position:0% +negative or positive same idea here when +you add all these inputs that a neuron + + align:start position:0% +you add all these inputs that a neuron + + + align:start position:0% +you add all these inputs that a neuron +gets it figures out what it's going to + + align:start position:0% +gets it figures out what it's going to + + + align:start position:0% +gets it figures out what it's going to +do and the inputs can be either pushing + + align:start position:0% +do and the inputs can be either pushing + + + align:start position:0% +do and the inputs can be either pushing +a neuron closer towards an action + + align:start position:0% +a neuron closer towards an action + + + align:start position:0% +a neuron closer towards an action +potential closer towards threshold or + + align:start position:0% +potential closer towards threshold or + + + align:start position:0% +potential closer towards threshold or +pushing a neuron away from being able to + + align:start position:0% +pushing a neuron away from being able to + + + align:start position:0% +pushing a neuron away from being able to +make an action potential further away + + align:start position:0% +make an action potential further away + + + align:start position:0% +make an action potential further away +from threshold excitatory + + align:start position:0% +from threshold excitatory + + + align:start position:0% +from threshold excitatory +synapses bring the resting + + align:start position:0% + + + + align:start position:0% + +potential closer to threshold + + align:start position:0% + + + + align:start position:0% + +whereas + + align:start position:0% +whereas + + + align:start position:0% +whereas +inhibitory bring the resting + + align:start position:0% +inhibitory bring the resting + + + align:start position:0% +inhibitory bring the resting +potential further from fresh + + align:start position:0% + + + + align:start position:0% + +threshold all right here's where it gets + + align:start position:0% +threshold all right here's where it gets + + + align:start position:0% +threshold all right here's where it gets +even more complicated one neuron can be + + align:start position:0% +even more complicated one neuron can be + + + align:start position:0% +even more complicated one neuron can be +making both excitatory and inhibitory + + align:start position:0% +making both excitatory and inhibitory + + + align:start position:0% +making both excitatory and inhibitory +synapses and depending on which + + align:start position:0% +synapses and depending on which + + + align:start position:0% +synapses and depending on which +predominant + + align:start position:0% +predominant + + + align:start position:0% +predominant +the recipient neuron will either be told + + align:start position:0% +the recipient neuron will either be told + + + align:start position:0% +the recipient neuron will either be told +to fire or not to fire to make an action + + align:start position:0% +to fire or not to fire to make an action + + + align:start position:0% +to fire or not to fire to make an action +potential or not so one + + align:start position:0% + + + + align:start position:0% + +neuron can make + + align:start position:0% +neuron can make + + + align:start position:0% +neuron can make +both + + align:start position:0% +both + + + align:start position:0% +both +excitatory and + + align:start position:0% +excitatory and + + + align:start position:0% +excitatory and +inhibitory + + align:start position:0% +inhibitory + + + align:start position:0% +inhibitory +synapses how does this work you ask well + + align:start position:0% +synapses how does this work you ask well + + + align:start position:0% +synapses how does this work you ask well +you you have all the tools to know it's + + align:start position:0% +you you have all the tools to know it's + + + align:start position:0% +you you have all the tools to know it's +all got to do with iron flux and which + + align:start position:0% +all got to do with iron flux and which + + + align:start position:0% +all got to do with iron flux and which +irons are flowing in and which irons are + + align:start position:0% +irons are flowing in and which irons are + + + align:start position:0% +irons are flowing in and which irons are +flowing out and we can answer that by + + align:start position:0% +flowing out and we can answer that by + + + align:start position:0% +flowing out and we can answer that by +looking at your next + + align:start position:0% + + + + align:start position:0% + +handouts in number two of your handouts + + align:start position:0% +handouts in number two of your handouts + + + align:start position:0% +handouts in number two of your handouts +I've shown you the synaptic Clift here's + + align:start position:0% +I've shown you the synaptic Clift here's + + + align:start position:0% +I've shown you the synaptic Clift here's +a synaptic Clift and here are the + + align:start position:0% +a synaptic Clift and here are the + + + align:start position:0% +a synaptic Clift and here are the +voltage gated calcium channels opening + + align:start position:0% +voltage gated calcium channels opening + + + align:start position:0% +voltage gated calcium channels opening +to allow calcium in and neurotrans MIT a + + align:start position:0% +to allow calcium in and neurotrans MIT a + + + align:start position:0% +to allow calcium in and neurotrans MIT a +vesical + + align:start position:0% + + + + align:start position:0% + +exocytosis here is an excitatory synapse + + align:start position:0% +exocytosis here is an excitatory synapse + + + align:start position:0% +exocytosis here is an excitatory synapse +bringing the resting potential closer to + + align:start position:0% +bringing the resting potential closer to + + + align:start position:0% +bringing the resting potential closer to +threshold let's think about that you + + align:start position:0% +threshold let's think about that you + + + align:start position:0% +threshold let's think about that you +want positive ions to come in from the + + align:start position:0% +want positive ions to come in from the + + + align:start position:0% +want positive ions to come in from the +outside that would help bring your + + align:start position:0% +outside that would help bring your + + + align:start position:0% +outside that would help bring your +resting potential closer to threshold so + + align:start position:0% +resting potential closer to threshold so + + + align:start position:0% +resting potential closer to threshold so +there are some sodium channels that can + + align:start position:0% +there are some sodium channels that can + + + align:start position:0% +there are some sodium channels that can +open maybe calcium channels that can + + align:start position:0% +open maybe calcium channels that can + + + align:start position:0% +open maybe calcium channels that can +open not the voltage gated ones and that + + align:start position:0% +open not the voltage gated ones and that + + + align:start position:0% +open not the voltage gated ones and that +would increase the resting potential + + align:start position:0% +would increase the resting potential + + + align:start position:0% +would increase the resting potential +that would increase the potential inside + + align:start position:0% +that would increase the potential inside + + + align:start position:0% +that would increase the potential inside +the cell bring it more positive closer + + align:start position:0% +the cell bring it more positive closer + + + align:start position:0% +the cell bring it more positive closer +to + + align:start position:0% +to + + + align:start position:0% +to +threshold + + align:start position:0% +threshold + + + align:start position:0% +threshold +conversely in an inhibitory synapse + + align:start position:0% +conversely in an inhibitory synapse + + + align:start position:0% +conversely in an inhibitory synapse +you'd get a net inflow of negative + + align:start position:0% +you'd get a net inflow of negative + + + align:start position:0% +you'd get a net inflow of negative +charges the Chlor chloride ions might + + align:start position:0% +charges the Chlor chloride ions might + + + align:start position:0% +charges the Chlor chloride ions might +move from the outside in that would take + + align:start position:0% +move from the outside in that would take + + + align:start position:0% +move from the outside in that would take +make your inside of your cell more + + align:start position:0% +make your inside of your cell more + + + align:start position:0% +make your inside of your cell more +negative and further away from threshold + + align:start position:0% +negative and further away from threshold + + + align:start position:0% +negative and further away from threshold +you could also get potassium out and + + align:start position:0% +you could also get potassium out and + + + align:start position:0% +you could also get potassium out and +that would again make the inside of the + + align:start position:0% +that would again make the inside of the + + + align:start position:0% +that would again make the inside of the +cell more negative and further from + + align:start position:0% +cell more negative and further from + + + align:start position:0% +cell more negative and further from +threshold so you can see already I've + + align:start position:0% +threshold so you can see already I've + + + align:start position:0% +threshold so you can see already I've +got four different channels they're not + + align:start position:0% +got four different channels they're not + + + align:start position:0% +got four different channels they're not +the ones we've talked about before the + + align:start position:0% +the ones we've talked about before the + + + align:start position:0% +the ones we've talked about before the +different ones four different channels + + align:start position:0% +different ones four different channels + + + align:start position:0% +different ones four different channels +which can modulate the membrane + + align:start position:0% +which can modulate the membrane + + + align:start position:0% +which can modulate the membrane +potential on the recipient + + align:start position:0% + + + + align:start position:0% + +cell all + + align:start position:0% +cell all + + + align:start position:0% +cell all +right let us move on + + align:start position:0% +right let us move on + + + align:start position:0% +right let us move on +now to those + + align:start position:0% +now to those + + + align:start position:0% +now to those +neurotransmitters and their receptors + + align:start position:0% + + + + align:start position:0% + +neurotransmitters and neurotransmitter + + align:start position:0% +neurotransmitters and neurotransmitter + + + align:start position:0% +neurotransmitters and neurotransmitter +receptors are very cool because they are + + align:start position:0% +receptors are very cool because they are + + + align:start position:0% +receptors are very cool because they are +probably what makes us who we are in + + align:start position:0% +probably what makes us who we are in + + + align:start position:0% +probably what makes us who we are in +terms of personality in terms of ability + + align:start position:0% +terms of personality in terms of ability + + + align:start position:0% +terms of personality in terms of ability +in terms of our interface with the world + + align:start position:0% +in terms of our interface with the world + + + align:start position:0% +in terms of our interface with the world +in terms of whether we're an + + align:start position:0% +in terms of whether we're an + + + align:start position:0% +in terms of whether we're an +intrinsically happy happy or not so + + align:start position:0% +intrinsically happy happy or not so + + + align:start position:0% +intrinsically happy happy or not so +happy person Etc neurotransmitters + + align:start position:0% +happy person Etc neurotransmitters + + + align:start position:0% +happy person Etc neurotransmitters +however are a class of molecule we have + + align:start position:0% +however are a class of molecule we have + + + align:start position:0% +however are a class of molecule we have +previously encountered they are + + align:start position:0% +previously encountered they are + + + align:start position:0% +previously encountered they are +lians but they're different lians when + + align:start position:0% +lians but they're different lians when + + + align:start position:0% +lians but they're different lians when +we talked about lians previously we've + + align:start position:0% +we talked about lians previously we've + + + align:start position:0% +we talked about lians previously we've +largely been talking not not entirely + + align:start position:0% +largely been talking not not entirely + + + align:start position:0% +largely been talking not not entirely +we've largely been talking about + + align:start position:0% +we've largely been talking about + + + align:start position:0% +we've largely been talking about +peptides + + align:start position:0% +peptides + + + align:start position:0% +peptides +or molecules that are are sort of of a a + + align:start position:0% +or molecules that are are sort of of a a + + + align:start position:0% +or molecules that are are sort of of a a +reasonable size not always the steroid + + align:start position:0% +reasonable size not always the steroid + + + align:start position:0% +reasonable size not always the steroid +the steroid hormones are very tiny + + align:start position:0% +the steroid hormones are very tiny + + + align:start position:0% +the steroid hormones are very tiny +neurotransmitters are pretty much all + + align:start position:0% +neurotransmitters are pretty much all + + + align:start position:0% +neurotransmitters are pretty much all +very tiny and the thing that you should + + align:start position:0% +very tiny and the thing that you should + + + align:start position:0% +very tiny and the thing that you should +know is that you can have one or + + align:start position:0% + + + + align:start position:0% + +many types of + + align:start position:0% +many types of + + + align:start position:0% +many types of +neurotransmitter per + + align:start position:0% +neurotransmitter per + + + align:start position:0% +neurotransmitter per +synapse here's another + + align:start position:0% + + + + align:start position:0% + +complication they can + + align:start position:0% +complication they can + + + align:start position:0% +complication they can +be am neurotransmitters can be + + align:start position:0% +be am neurotransmitters can be + + + align:start position:0% +be am neurotransmitters can be +tiddes + + align:start position:0% +tiddes + + + align:start position:0% +tiddes +sometimes but they are very largely + + align:start position:0% +sometimes but they are very largely + + + align:start position:0% +sometimes but they are very largely +amino acids the same amino acids that + + align:start position:0% +amino acids the same amino acids that + + + align:start position:0% +amino acids the same amino acids that +you build proteins with + + align:start position:0% + + + + align:start position:0% + +nucleotides or other small + + align:start position:0% + + + + align:start position:0% + +molecules like the C of synapses + + align:start position:0% +molecules like the C of synapses + + + align:start position:0% +molecules like the C of synapses +synapses are excitatory or inhibitory + + align:start position:0% +synapses are excitatory or inhibitory + + + align:start position:0% +synapses are excitatory or inhibitory +because of the kinds of + + align:start position:0% +because of the kinds of + + + align:start position:0% +because of the kinds of +neurotransmitters that they're making so + + align:start position:0% +neurotransmitters that they're making so + + + align:start position:0% +neurotransmitters that they're making so +there are + + align:start position:0% +there are + + + align:start position:0% +there are +excitatory + + align:start position:0% + + + + align:start position:0% + +neurotransmitters + + align:start position:0% +neurotransmitters + + + align:start position:0% +neurotransmitters +glutamate + + align:start position:0% +glutamate + + + align:start position:0% +glutamate +glut glutamate glutamic acid okay the + + align:start position:0% +glut glutamate glutamic acid okay the + + + align:start position:0% +glut glutamate glutamic acid okay the +same one we've talked about before and + + align:start position:0% +same one we've talked about before and + + + align:start position:0% +same one we've talked about before and +adenine are both examples of excitatory + + align:start position:0% +adenine are both examples of excitatory + + + align:start position:0% +adenine are both examples of excitatory +Adine are examples of excitatory + + align:start position:0% +Adine are examples of excitatory + + + align:start position:0% +Adine are examples of excitatory +neurotransmitters glutamate is involved + + align:start position:0% +neurotransmitters glutamate is involved + + + align:start position:0% +neurotransmitters glutamate is involved +involed in being + + align:start position:0% + + + + align:start position:0% + +alert adenine is involved in being + + align:start position:0% +alert adenine is involved in being + + + align:start position:0% +alert adenine is involved in being +sleepy and one of the things that + + align:start position:0% +sleepy and one of the things that + + + align:start position:0% +sleepy and one of the things that +caffeine does is to counteract the + + align:start position:0% +caffeine does is to counteract the + + + align:start position:0% +caffeine does is to counteract the +effects of adenine so that it kind of + + align:start position:0% +effects of adenine so that it kind of + + + align:start position:0% +effects of adenine so that it kind of +competit it's thought to + + align:start position:0% +competit it's thought to + + + align:start position:0% +competit it's thought to +competitively interact or competitively + + align:start position:0% +competitively interact or competitively + + + align:start position:0% +competitively interact or competitively +inhibit adenine + + align:start position:0% +inhibit adenine + + + align:start position:0% +inhibit adenine +function inhibitory neurotransmitters + + align:start position:0% + + + + align:start position:0% + +something called Gaba gamma amino butc + + align:start position:0% +something called Gaba gamma amino butc + + + align:start position:0% +something called Gaba gamma amino butc +acid and glycine are the two major CNS + + align:start position:0% +acid and glycine are the two major CNS + + + align:start position:0% +acid and glycine are the two major CNS +central nervous system + + align:start position:0% +central nervous system + + + align:start position:0% +central nervous system +neurotransmitters Gaba particularly is + + align:start position:0% +neurotransmitters Gaba particularly is + + + align:start position:0% +neurotransmitters Gaba particularly is +an anti-anxiety + + align:start position:0% + + + + align:start position:0% + +neurotransmitter and things like Xanax + + align:start position:0% +neurotransmitter and things like Xanax + + + align:start position:0% +neurotransmitter and things like Xanax +which I will get to today or Friday are + + align:start position:0% +which I will get to today or Friday are + + + align:start position:0% +which I will get to today or Friday are +things which will be agonists of Gaba + + align:start position:0% +things which will be agonists of Gaba + + + align:start position:0% +things which will be agonists of Gaba +function and sometimes neurotransmitters + + align:start position:0% +function and sometimes neurotransmitters + + + align:start position:0% +function and sometimes neurotransmitters +can be both excitatory and + + align:start position:0% +can be both excitatory and + + + align:start position:0% +can be both excitatory and +inhibitory acet choline for + + align:start position:0% + + + + align:start position:0% + +example which is involved in connections + + align:start position:0% +example which is involved in connections + + + align:start position:0% +example which is involved in connections +between nerves and muscles neuromuscular + + align:start position:0% +between nerves and muscles neuromuscular + + + align:start position:0% +between nerves and muscles neuromuscular +connections and also found in the CNS + + align:start position:0% +connections and also found in the CNS + + + align:start position:0% +connections and also found in the CNS +can be both excitatory and + + align:start position:0% +can be both excitatory and + + + align:start position:0% +can be both excitatory and +inhibitory and + + align:start position:0% + + + + align:start position:0% + +serotonin and I'll put dopamine on the + + align:start position:0% +serotonin and I'll put dopamine on the + + + align:start position:0% +serotonin and I'll put dopamine on the +same line for space + + align:start position:0% +same line for space + + + align:start position:0% +same line for space +serotonin and + + align:start position:0% +serotonin and + + + align:start position:0% +serotonin and +dopamine both of which are kind of + + align:start position:0% + + + + align:start position:0% + +Feelgood + + align:start position:0% +Feelgood + + + align:start position:0% +Feelgood +neurotransmitters also involved in + + align:start position:0% +neurotransmitters also involved in + + + align:start position:0% +neurotransmitters also involved in +alertness + + align:start position:0% + + + + align:start position:0% + +and other things for dopamine locomotive + + align:start position:0% +and other things for dopamine locomotive + + + align:start position:0% +and other things for dopamine locomotive +activity + + align:start position:0% +activity + + + align:start position:0% +activity +movement they can be either excitatory + + align:start position:0% +movement they can be either excitatory + + + align:start position:0% +movement they can be either excitatory +or + + align:start position:0% + + + + align:start position:0% + +inhibitory what do they look like let me + + align:start position:0% +inhibitory what do they look like let me + + + align:start position:0% +inhibitory what do they look like let me +go on and then I'll show you some + + align:start position:0% +go on and then I'll show you some + + + align:start position:0% +go on and then I'll show you some +pictures in a moment all right so how + + align:start position:0% +pictures in a moment all right so how + + + align:start position:0% +pictures in a moment all right so how +can something be excitatory and + + align:start position:0% + + + + align:start position:0% + +inhibitory what's Downstream of these + + align:start position:0% +inhibitory what's Downstream of these + + + align:start position:0% +inhibitory what's Downstream of these +neurotransmitters + + align:start position:0% + + + + align:start position:0% + +The + + align:start position:0% +The + + + align:start position:0% +The +receptors good job okay all right + + align:start position:0% +receptors good job okay all right + + + align:start position:0% +receptors good job okay all right +neurotransmitters lians bind receptors + + align:start position:0% +neurotransmitters lians bind receptors + + + align:start position:0% +neurotransmitters lians bind receptors +and the way the neurotransmitters affect + + align:start position:0% +and the way the neurotransmitters affect + + + align:start position:0% +and the way the neurotransmitters affect +what they're going to do is by binding + + align:start position:0% +what they're going to do is by binding + + + align:start position:0% +what they're going to do is by binding +the appropriate receptor so here are the + + align:start position:0% +the appropriate receptor so here are the + + + align:start position:0% +the appropriate receptor so here are the +receptors for the + + align:start position:0% + + + + align:start position:0% + +neurotransmitters and + + align:start position:0% +neurotransmitters and + + + align:start position:0% +neurotransmitters and +like the neurotransmitters there can be + + align:start position:0% +like the neurotransmitters there can be + + + align:start position:0% +like the neurotransmitters there can be +many many different kinds per + + align:start position:0% + + + + align:start position:0% + +synapse there are two classes of + + align:start position:0% +synapse there are two classes of + + + align:start position:0% +synapse there are two classes of +receptors that you should know one are + + align:start position:0% +receptors that you should know one are + + + align:start position:0% +receptors that you should know one are +ion channels they are receptors which + + align:start position:0% +ion channels they are receptors which + + + align:start position:0% +ion channels they are receptors which +bind the + + align:start position:0% +bind the + + + align:start position:0% +bind the +neurotransmitter and they open up + + align:start position:0% +neurotransmitter and they open up + + + align:start position:0% +neurotransmitter and they open up +they're liand gated ion channels but the + + align:start position:0% +they're liand gated ion channels but the + + + align:start position:0% +they're liand gated ion channels but the +other kind are not ion channels they + + align:start position:0% +other kind are not ion channels they + + + align:start position:0% +other kind are not ion channels they +bind the receptor and then they activate + + align:start position:0% +bind the receptor and then they activate + + + align:start position:0% +bind the receptor and then they activate +a second messenger system as we talked + + align:start position:0% +a second messenger system as we talked + + + align:start position:0% +a second messenger system as we talked +about before and it's the second + + align:start position:0% +about before and it's the second + + + align:start position:0% +about before and it's the second +messenger system that later on opens an + + align:start position:0% +messenger system that later on opens an + + + align:start position:0% +messenger system that later on opens an +ion Channel they have + + align:start position:0% +ion Channel they have + + + align:start position:0% +ion Channel they have +names so two + + align:start position:0% + + + + align:start position:0% + +classes one are the iron + + align:start position:0% + + + + align:start position:0% + +channels they're called + + align:start position:0% +channels they're called + + + align:start position:0% +channels they're called +ionotropic receptors + + align:start position:0% + + + + align:start position:0% + +so they're liand gated ion + + align:start position:0% + + + + align:start position:0% + +channels and the thing about these is + + align:start position:0% +channels and the thing about these is + + + align:start position:0% +channels and the thing about these is +that they response is very + + align:start position:0% + + + + align:start position:0% + +rapid in the millisecond + + align:start position:0% + + + + align:start position:0% + +range there's in the other class + + align:start position:0% +range there's in the other class + + + align:start position:0% +range there's in the other class +although those receptors which + + align:start position:0% +although those receptors which + + + align:start position:0% +although those receptors which +activate ion + + align:start position:0% + + + + align:start position:0% + +channels they are called + + align:start position:0% + + + + align:start position:0% + +metabotropic it's the concept that's + + align:start position:0% +metabotropic it's the concept that's + + + align:start position:0% +metabotropic it's the concept that's +more important than the term but I'm + + align:start position:0% +more important than the term but I'm + + + align:start position:0% +more important than the term but I'm +giving you the term for completeness and + + align:start position:0% +giving you the term for completeness and + + + align:start position:0% +giving you the term for completeness and +they act + + align:start position:0% + + + + align:start position:0% + +via a second messenger system + + align:start position:0% + + + + align:start position:0% + +that almost always involves G + + align:start position:0% + + + + align:start position:0% + +proteins and these are + + align:start position:0% + + + + align:start position:0% + +slow their + + align:start position:0% +slow their + + + align:start position:0% +slow their +response is at least a second often much + + align:start position:0% +response is at least a second often much + + + align:start position:0% +response is at least a second often much +greater than a + + align:start position:0% + + + + align:start position:0% + +second okay and let + + align:start position:0% +second okay and let + + + align:start position:0% +second okay and let +me as the last thing I'll tell you today + + align:start position:0% +me as the last thing I'll tell you today + + + align:start position:0% +me as the last thing I'll tell you today +I'll show you if we have a moment I'll + + align:start position:0% +I'll show you if we have a moment I'll + + + align:start position:0% +I'll show you if we have a moment I'll +show you some pictures but I want to + + align:start position:0% +show you some pictures but I want to + + + align:start position:0% +show you some pictures but I want to +tell you that one neurotransmitter can + + align:start position:0% +tell you that one neurotransmitter can + + + align:start position:0% +tell you that one neurotransmitter can +activate different kinds of the receptor + + align:start position:0% +activate different kinds of the receptor + + + align:start position:0% +activate different kinds of the receptor +so one + + align:start position:0% +so one + + + align:start position:0% +so one +[Music] + + align:start position:0% + + + + align:start position:0% + +neurotransmitter can + + align:start position:0% +neurotransmitter can + + + align:start position:0% +neurotransmitter can +activate greater than one type of + + align:start position:0% + + + + align:start position:0% + +receptor and this was implicit in the + + align:start position:0% +receptor and this was implicit in the + + + align:start position:0% +receptor and this was implicit in the +notion that neurotransmitters could be + + align:start position:0% +notion that neurotransmitters could be + + + align:start position:0% +notion that neurotransmitters could be +both excitatory and hibitory for + + align:start position:0% +both excitatory and hibitory for + + + align:start position:0% +both excitatory and hibitory for +example + + align:start position:0% + + + + align:start position:0% + +serotonin binds to no fewer than 14 + + align:start position:0% +serotonin binds to no fewer than 14 + + + align:start position:0% +serotonin binds to no fewer than 14 +different + + align:start position:0% +different + + + align:start position:0% +different +receptors and one neuron can express + + align:start position:0% +receptors and one neuron can express + + + align:start position:0% +receptors and one neuron can express +probably not all 14 but it could + + align:start position:0% +probably not all 14 but it could + + + align:start position:0% +probably not all 14 but it could +probably Express five different + + align:start position:0% +probably Express five different + + + align:start position:0% +probably Express five different +serotonin receptors and they do + + align:start position:0% +serotonin receptors and they do + + + align:start position:0% +serotonin receptors and they do +different things one of them is a liand + + align:start position:0% +different things one of them is a liand + + + align:start position:0% +different things one of them is a liand +gated sodium ch + + align:start position:0% + + + + align:start position:0% + +Channel another type is G protein + + align:start position:0% + + + + align:start position:0% + +coupled so including both metabotropic + + align:start position:0% +coupled so including both metabotropic + + + align:start position:0% +coupled so including both metabotropic +and ionotropic + + align:start position:0% + + + + align:start position:0% + +receptors and to throw out at you the + + align:start position:0% +receptors and to throw out at you the + + + align:start position:0% +receptors and to throw out at you the +last couple of slides + + align:start position:0% +last couple of slides + + + align:start position:0% +last couple of slides +here are some of these amino acids and + + align:start position:0% +here are some of these amino acids and + + + align:start position:0% +here are some of these amino acids and +small molecules that are + + align:start position:0% + + + + align:start position:0% + +neurotransmitters and this really + + align:start position:0% +neurotransmitters and this really + + + align:start position:0% +neurotransmitters and this really +exemplifies what I've said on the board + + align:start position:0% +exemplifies what I've said on the board + + + align:start position:0% +exemplifies what I've said on the board +so I'm going to stop here now \ No newline at end of file diff --git a/OyZbj4_P7JM.txt b/OyZbj4_P7JM.txt new file mode 100644 index 0000000000000000000000000000000000000000..3c74ee5bc96c2b1e29355faca3facadec3924fe4 --- /dev/null +++ b/OyZbj4_P7JM.txt @@ -0,0 +1,1995 @@ +align:start position:0% + +today let's catch up with what we were + + align:start position:0% +today let's catch up with what we were + + + align:start position:0% +today let's catch up with what we were +doing before and last time we're talking + + align:start position:0% +doing before and last time we're talking + + + align:start position:0% +doing before and last time we're talking +about hydrogen ionization and we went + + align:start position:0% +about hydrogen ionization and we went + + + align:start position:0% +about hydrogen ionization and we went +through a whole discussion of how it + + align:start position:0% +through a whole discussion of how it + + + align:start position:0% +through a whole discussion of how it +would happen + + align:start position:0% +would happen + + + align:start position:0% +would happen +it was ionized because there would be an + + align:start position:0% +it was ionized because there would be an + + + align:start position:0% +it was ionized because there would be an +electromagnetic wave hitting the + + align:start position:0% +electromagnetic wave hitting the + + + align:start position:0% +electromagnetic wave hitting the +hydrogen atom the initial state was the + + align:start position:0% +hydrogen atom the initial state was the + + + align:start position:0% +hydrogen atom the initial state was the +ground state of the hydrogen atom the + + align:start position:0% +ground state of the hydrogen atom the + + + align:start position:0% +ground state of the hydrogen atom the +final state was a plane wave our main + + align:start position:0% +final state was a plane wave our main + + + align:start position:0% +final state was a plane wave our main +work was computing this matrix element + + align:start position:0% +work was computing this matrix element + + + align:start position:0% +work was computing this matrix element +and that's what we did last time it took + + align:start position:0% +and that's what we did last time it took + + + align:start position:0% +and that's what we did last time it took +us some work because there's a spatial + + align:start position:0% +us some work because there's a spatial + + + align:start position:0% +us some work because there's a spatial +integral here that was quite complicated + + align:start position:0% +integral here that was quite complicated + + + align:start position:0% +integral here that was quite complicated +given the various directions that are + + align:start position:0% +given the various directions that are + + + align:start position:0% +given the various directions that are +going on but that was our result here is + + align:start position:0% +going on but that was our result here is + + + align:start position:0% +going on but that was our result here is +the formula and a few things to notice + + align:start position:0% +the formula and a few things to notice + + + align:start position:0% +the formula and a few things to notice +here were that there's an angle theta + + align:start position:0% +here were that there's an angle theta + + + align:start position:0% +here were that there's an angle theta +that we recognized as the angle between + + align:start position:0% +that we recognized as the angle between + + + align:start position:0% +that we recognized as the angle between +the electric field polarization and the + + align:start position:0% +the electric field polarization and the + + + align:start position:0% +the electric field polarization and the +momentum of the electron so K is the + + align:start position:0% +momentum of the electron so K is the + + + align:start position:0% +momentum of the electron so K is the +momentum of the electron and when K + + align:start position:0% +momentum of the electron and when K + + + align:start position:0% +momentum of the electron and when K +doesn't have an arrow is a magnitude of + + align:start position:0% +doesn't have an arrow is a magnitude of + + + align:start position:0% +doesn't have an arrow is a magnitude of +the electron momenta as any K well it's + + align:start position:0% +the electron momenta as any K well it's + + + align:start position:0% +the electron momenta as any K well it's +a little bit of an exaggerated h-bar K + + align:start position:0% +a little bit of an exaggerated h-bar K + + + align:start position:0% +a little bit of an exaggerated h-bar K +is a momentum but we understand when we + + align:start position:0% +is a momentum but we understand when we + + + align:start position:0% +is a momentum but we understand when we +say that case a momentum K times a it + + align:start position:0% +say that case a momentum K times a it + + + align:start position:0% +say that case a momentum K times a it +has no units which is appropriate of the + + align:start position:0% +has no units which is appropriate of the + + + align:start position:0% +has no units which is appropriate of the +units of this quantity R units of energy + + align:start position:0% +units of this quantity R units of energy + + + align:start position:0% +units of this quantity R units of energy +and then another quantity here in naught + + align:start position:0% +and then another quantity here in naught + + + align:start position:0% +and then another quantity here in naught +is the magnitude of the electric field + + align:start position:0% +is the magnitude of the electric field + + + align:start position:0% +is the magnitude of the electric field +defined by this formula with a 2 in not + + align:start position:0% +defined by this formula with a 2 in not + + + align:start position:0% +defined by this formula with a 2 in not +here we discuss that the alleged the + + align:start position:0% +here we discuss that the alleged the + + + align:start position:0% +here we discuss that the alleged the +photon had to have an energy that it was + + align:start position:0% +photon had to have an energy that it was + + + align:start position:0% +photon had to have an energy that it was +not supposed to be too big so that the + + align:start position:0% +not supposed to be too big so that the + + + align:start position:0% +not supposed to be too big so that the +wavelength of the photon would be + + align:start position:0% +wavelength of the photon would be + + + align:start position:0% +wavelength of the photon would be +smaller or much smaller than the atom in + + align:start position:0% +smaller or much smaller than the atom in + + + align:start position:0% +smaller or much smaller than the atom in +which case the spatial dependence of the + + align:start position:0% +which case the spatial dependence of the + + + align:start position:0% +which case the spatial dependence of the +electromagnetic field would be relevant + + align:start position:0% +electromagnetic field would be relevant + + + align:start position:0% +electromagnetic field would be relevant +so for simplicity we + + align:start position:0% +so for simplicity we + + + align:start position:0% +so for simplicity we +two photos not to be too energetic and + + align:start position:0% +two photos not to be too energetic and + + + align:start position:0% +two photos not to be too energetic and +we also took photos to be energetic + + align:start position:0% +we also took photos to be energetic + + + align:start position:0% +we also took photos to be energetic +enough that when they would ionize the + + align:start position:0% +enough that when they would ionize the + + + align:start position:0% +enough that when they would ionize the +atom the electron that would go out + + align:start position:0% +atom the electron that would go out + + + align:start position:0% +atom the electron that would go out +would not be too affected by the Coulomb + + align:start position:0% +would not be too affected by the Coulomb + + + align:start position:0% +would not be too affected by the Coulomb +potential and we could treat it like a + + align:start position:0% +potential and we could treat it like a + + + align:start position:0% +potential and we could treat it like a +plane wave to a good approximation a + + align:start position:0% +plane wave to a good approximation a + + + align:start position:0% +plane wave to a good approximation a +free plane wave otherwise you would have + + align:start position:0% +free plane wave otherwise you would have + + + align:start position:0% +free plane wave otherwise you would have +to use more complicated plane waves + + align:start position:0% +to use more complicated plane waves + + + align:start position:0% +to use more complicated plane waves +associated with a hydrogen atom so under + + align:start position:0% +associated with a hydrogen atom so under + + + align:start position:0% +associated with a hydrogen atom so under +this ranges this range is translate to + + align:start position:0% +this ranges this range is translate to + + + align:start position:0% +this ranges this range is translate to +this ranges for the momentum of the + + align:start position:0% +this ranges for the momentum of the + + + align:start position:0% +this ranges for the momentum of the +electron and if the as required the + + align:start position:0% +electron and if the as required the + + + align:start position:0% +electron and if the as required the +energy of the photon is significantly + + align:start position:0% +energy of the photon is significantly + + + align:start position:0% +energy of the photon is significantly +bigger than a red bird which is that + + align:start position:0% +bigger than a red bird which is that + + + align:start position:0% +bigger than a red bird which is that +thirteen point six V's this is like ten + + align:start position:0% +thirteen point six V's this is like ten + + + align:start position:0% +thirteen point six V's this is like ten +red birds in here then the momentum of + + align:start position:0% +red birds in here then the momentum of + + + align:start position:0% +red birds in here then the momentum of +the electron is given by this formula to + + align:start position:0% +the electron is given by this formula to + + + align:start position:0% +the electron is given by this formula to +a good approximation it's essentially + + align:start position:0% +a good approximation it's essentially + + + align:start position:0% +a good approximation it's essentially +the energy of the photon the square root + + align:start position:0% +the energy of the photon the square root + + + align:start position:0% +the energy of the photon the square root +of that + + align:start position:0% +of that + + + align:start position:0% +of that +the last ingredient in our computation + + align:start position:0% +the last ingredient in our computation + + + align:start position:0% +the last ingredient in our computation +is the density of states this was + + align:start position:0% +is the density of states this was + + + align:start position:0% +is the density of states this was +calculated and also a couple of weeks + + align:start position:0% +calculated and also a couple of weeks + + + align:start position:0% +calculated and also a couple of weeks +ago so have to keep track of some + + align:start position:0% +ago so have to keep track of some + + + align:start position:0% +ago so have to keep track of some +formulas here there are some formulas + + align:start position:0% +formulas here there are some formulas + + + align:start position:0% +formulas here there are some formulas +that are a little complicated but we'll + + align:start position:0% +that are a little complicated but we'll + + + align:start position:0% +that are a little complicated but we'll +have to box them and just be ready to + + align:start position:0% +have to box them and just be ready to + + + align:start position:0% +have to box them and just be ready to +use them or to spend five minutes Reed + + align:start position:0% +use them or to spend five minutes Reed + + + align:start position:0% +use them or to spend five minutes Reed +arriving them and this was the formula + + align:start position:0% +arriving them and this was the formula + + + align:start position:0% +arriving them and this was the formula +for a density of states with some energy + + align:start position:0% +for a density of states with some energy + + + align:start position:0% +for a density of states with some energy +e with that energy e this were free + + align:start position:0% +e with that energy e this were free + + + align:start position:0% +e with that energy e this were free +plane wave States energy e momentum K + + align:start position:0% +plane wave States energy e momentum K + + + align:start position:0% +plane wave States energy e momentum K +associated with E and being shot into + + align:start position:0% +associated with E and being shot into + + + align:start position:0% +associated with E and being shot into +some solid angle in space and this is + + align:start position:0% +some solid angle in space and this is + + + align:start position:0% +some solid angle in space and this is +the solid angle so I wrote it as a solid + + align:start position:0% +the solid angle so I wrote it as a solid + + + align:start position:0% +the solid angle so I wrote it as a solid +angle in here so this is basically where + + align:start position:0% +angle in here so this is basically where + + + align:start position:0% +angle in here so this is basically where +we stood and at this moment + + align:start position:0% +we stood and at this moment + + + align:start position:0% +we stood and at this moment +I want to complete the discussion and + + align:start position:0% +I want to complete the discussion and + + + align:start position:0% +I want to complete the discussion and +get a simple expression and simplify it + + align:start position:0% +get a simple expression and simplify it + + + align:start position:0% +get a simple expression and simplify it +and get what we need to have for the + + align:start position:0% +and get what we need to have for the + + + align:start position:0% +and get what we need to have for the +rate so if you remember Fermi's golden + + align:start position:0% +rate so if you remember Fermi's golden + + + align:start position:0% +rate so if you remember Fermi's golden +rule expresses a rate Omega in terms of + + align:start position:0% +rule expresses a rate Omega in terms of + + + align:start position:0% +rule expresses a rate Omega in terms of +Q PI over H bar robot e times H F I + + align:start position:0% +Q PI over H bar robot e times H F I + + + align:start position:0% +Q PI over H bar robot e times H F I +squared so that's Fermi's golden rule + + align:start position:0% +squared so that's Fermi's golden rule + + + align:start position:0% +squared so that's Fermi's golden rule +and this is what we want to apply + + align:start position:0% +and this is what we want to apply + + + align:start position:0% +and this is what we want to apply +well we've calculated the matrix element + + align:start position:0% + + + + align:start position:0% + +this will be h fi prime here that's what + + align:start position:0% +this will be h fi prime here that's what + + + align:start position:0% +this will be h fi prime here that's what +we have up there + + align:start position:0% +we have up there + + + align:start position:0% +we have up there +we have row would have this quantity 2 + + align:start position:0% +we have row would have this quantity 2 + + + align:start position:0% +we have row would have this quantity 2 +PI over H bar is just a constant so we + + align:start position:0% +PI over H bar is just a constant so we + + + align:start position:0% +PI over H bar is just a constant so we +can simply plug this here square that + + align:start position:0% +can simply plug this here square that + + + align:start position:0% +can simply plug this here square that +there's lots of H bars and things that I + + align:start position:0% +there's lots of H bars and things that I + + + align:start position:0% +there's lots of H bars and things that I +don't think you'll benefit if I go + + align:start position:0% +don't think you'll benefit if I go + + + align:start position:0% +don't think you'll benefit if I go +through them in front of your eyes so + + align:start position:0% +through them in front of your eyes so + + + align:start position:0% +through them in front of your eyes so +I'll write the answer but in writing the + + align:start position:0% +I'll write the answer but in writing the + + + align:start position:0% +I'll write the answer but in writing the +answer remember this row it's a + + align:start position:0% +answer remember this row it's a + + + align:start position:0% +answer remember this row it's a +differential in some sense some people + + align:start position:0% +differential in some sense some people + + + align:start position:0% +differential in some sense some people +might put even a dual role here because + + align:start position:0% +might put even a dual role here because + + + align:start position:0% +might put even a dual role here because +there's a do meiga so think of this when + + align:start position:0% +there's a do meiga so think of this when + + + align:start position:0% +there's a do meiga so think of this when +I substitute row I have the B Omega and + + align:start position:0% +I substitute row I have the B Omega and + + + align:start position:0% +I substitute row I have the B Omega and +I think of this as the V W a little rate + + align:start position:0% +I think of this as the V W a little rate + + + align:start position:0% +I think of this as the V W a little rate +so BW D Omega so I simply pass from W to + + align:start position:0% +so BW D Omega so I simply pass from W to + + + align:start position:0% +so BW D Omega so I simply pass from W to +I called it DW and substituted the row + + align:start position:0% +I called it DW and substituted the row + + + align:start position:0% +I called it DW and substituted the row +here for the Omega and here's what we + + align:start position:0% +here for the Omega and here's what we + + + align:start position:0% +here for the Omega and here's what we +get 256 over PI et not a naught square + + align:start position:0% +get 256 over PI et not a naught square + + + align:start position:0% +get 256 over PI et not a naught square +over H bar m a naught squared over H bar + + align:start position:0% +over H bar m a naught squared over H bar + + + align:start position:0% +over H bar m a naught squared over H bar +squared K a naught cube over 1 plus K + + align:start position:0% +squared K a naught cube over 1 plus K + + + align:start position:0% +squared K a naught cube over 1 plus K +a not squared to the six times six times + + align:start position:0% +a not squared to the six times six times + + + align:start position:0% +a not squared to the six times six times +cosine squared theta okay + + align:start position:0% +cosine squared theta okay + + + align:start position:0% +cosine squared theta okay +still a little complicated but mainly + + align:start position:0% +still a little complicated but mainly + + + align:start position:0% +still a little complicated but mainly +complicated because of constants that + + align:start position:0% +complicated because of constants that + + + align:start position:0% +complicated because of constants that +have been grouped in the best possible + + align:start position:0% +have been grouped in the best possible + + + align:start position:0% +have been grouped in the best possible +way in my opinion to make it + + align:start position:0% +way in my opinion to make it + + + align:start position:0% +way in my opinion to make it +understandable this is an energy and + + align:start position:0% +understandable this is an energy and + + + align:start position:0% +understandable this is an energy and +this is an H bar this is actually a red + + align:start position:0% +this is an H bar this is actually a red + + + align:start position:0% +this is an H bar this is actually a red +burg with a factor of two so in a second + + align:start position:0% +burg with a factor of two so in a second + + + align:start position:0% +burg with a factor of two so in a second +you can see that this thing has units of + + align:start position:0% +you can see that this thing has units of + + + align:start position:0% +you can see that this thing has units of +one over time this also an important + + align:start position:0% +one over time this also an important + + + align:start position:0% +one over time this also an important +factor here and that's an intuitively + + align:start position:0% +factor here and that's an intuitively + + + align:start position:0% +factor here and that's an intuitively +interesting fact that the emission of + + align:start position:0% +interesting fact that the emission of + + + align:start position:0% +interesting fact that the emission of +the electron is preferential in the + + align:start position:0% +the electron is preferential in the + + + align:start position:0% +the electron is preferential in the +direction that the electric field is + + align:start position:0% +direction that the electric field is + + + align:start position:0% +direction that the electric field is +polarized the cosine squared theta with + + align:start position:0% +polarized the cosine squared theta with + + + align:start position:0% +polarized the cosine squared theta with +no electrons emitted orthogonal e to the + + align:start position:0% +no electrons emitted orthogonal e to the + + + align:start position:0% +no electrons emitted orthogonal e to the +electric field and that's kind of into + + align:start position:0% +electric field and that's kind of into + + + align:start position:0% +electric field and that's kind of into +it if it's almost like the electric + + align:start position:0% +it if it's almost like the electric + + + align:start position:0% +it if it's almost like the electric +fields shaking the letter it kicks it + + align:start position:0% +fields shaking the letter it kicks it + + + align:start position:0% +fields shaking the letter it kicks it +out + + align:start position:0% +out + + + align:start position:0% +out +so okay this is a differential rate so + + align:start position:0% +so okay this is a differential rate so + + + align:start position:0% +so okay this is a differential rate so +the total rate W is the integral of this + + align:start position:0% +the total rate W is the integral of this + + + align:start position:0% +the total rate W is the integral of this +differential rate over solid angle and + + align:start position:0% +differential rate over solid angle and + + + align:start position:0% +differential rate over solid angle and +for that you need to know that the + + align:start position:0% +for that you need to know that the + + + align:start position:0% +for that you need to know that the +integral over solid angle of cosine + + align:start position:0% +integral over solid angle of cosine + + + align:start position:0% +integral over solid angle of cosine +squared theta is 4 pi that if you don't + + align:start position:0% +squared theta is 4 pi that if you don't + + + align:start position:0% +squared theta is 4 pi that if you don't +have the cosine squared you would have + + align:start position:0% +have the cosine squared you would have + + + align:start position:0% +have the cosine squared you would have +the 4pi but due to the cosine squared + + align:start position:0% +the 4pi but due to the cosine squared + + + align:start position:0% +the 4pi but due to the cosine squared +the this is multiplied by one-third you + + align:start position:0% +the this is multiplied by one-third you + + + align:start position:0% +the this is multiplied by one-third you +can do + + align:start position:0% +can do + + + align:start position:0% +can do +calculation just doesn't take any real + + align:start position:0% +calculation just doesn't take any real + + + align:start position:0% +calculation just doesn't take any real +time but many people remember this by + + align:start position:0% +time but many people remember this by + + + align:start position:0% +time but many people remember this by +thinking of the sphere or planet Earth + + align:start position:0% +thinking of the sphere or planet Earth + + + align:start position:0% +thinking of the sphere or planet Earth +cosine squared theta is large near the + + align:start position:0% +cosine squared theta is large near the + + + align:start position:0% +cosine squared theta is large near the +North Pole is large near the South Pole + + align:start position:0% +North Pole is large near the South Pole + + + align:start position:0% +North Pole is large near the South Pole +that doesn't amount to much as opposed + + align:start position:0% +that doesn't amount to much as opposed + + + align:start position:0% +that doesn't amount to much as opposed +to sine squared theta which is large all + + align:start position:0% +to sine squared theta which is large all + + + align:start position:0% +to sine squared theta which is large all +over the bigot auriol region so it's a + + align:start position:0% +over the bigot auriol region so it's a + + + align:start position:0% +over the bigot auriol region so it's a +little bigger and it turns out cosine + + align:start position:0% +little bigger and it turns out cosine + + + align:start position:0% +little bigger and it turns out cosine +squared the average over the sphere is + + align:start position:0% +squared the average over the sphere is + + + align:start position:0% +squared the average over the sphere is +1/3 and sine squared the average of + + align:start position:0% +1/3 and sine squared the average of + + + align:start position:0% +1/3 and sine squared the average of +earth sphere is 2/3 so it's kind of an + + align:start position:0% +earth sphere is 2/3 so it's kind of an + + + align:start position:0% +earth sphere is 2/3 so it's kind of an +not a bad thing to know how because + + align:start position:0% +not a bad thing to know how because + + + align:start position:0% +not a bad thing to know how because +saves you a minute or two from doing + + align:start position:0% +saves you a minute or two from doing + + + align:start position:0% +saves you a minute or two from doing +this integral and now I'm also going to + + align:start position:0% +this integral and now I'm also going to + + + align:start position:0% +this integral and now I'm also going to +apply something that basically you know + + align:start position:0% +apply something that basically you know + + + align:start position:0% +apply something that basically you know +a formula sometimes gives you more + + align:start position:0% +a formula sometimes gives you more + + + align:start position:0% +a formula sometimes gives you more +things that you should really trust and + + align:start position:0% +things that you should really trust and + + + align:start position:0% +things that you should really trust and +I would say here this one is not to be + + align:start position:0% +I would say here this one is not to be + + + align:start position:0% +I would say here this one is not to be +trusted + + align:start position:0% +trusted + + + align:start position:0% +trusted +basically because K a naught must be + + align:start position:0% +basically because K a naught must be + + + align:start position:0% +basically because K a naught must be +significantly bigger than this number + + align:start position:0% +significantly bigger than this number + + + align:start position:0% +significantly bigger than this number +probably for this to be accurate so + + align:start position:0% +probably for this to be accurate so + + + align:start position:0% +probably for this to be accurate so +under most circumstances this one it's + + align:start position:0% +under most circumstances this one it's + + + align:start position:0% +under most circumstances this one it's +not worth it in fact if you calculate + + align:start position:0% +not worth it in fact if you calculate + + + align:start position:0% +not worth it in fact if you calculate +this thing using different + + align:start position:0% +this thing using different + + + align:start position:0% +this thing using different +approximations people sometimes don't + + align:start position:0% +approximations people sometimes don't + + + align:start position:0% +approximations people sometimes don't +get this one and you may see that in + + align:start position:0% +get this one and you may see that in + + + align:start position:0% +get this one and you may see that in +books so let's ignore this one and then + + align:start position:0% +books so let's ignore this one and then + + + align:start position:0% +books so let's ignore this one and then +this answer is 512 over 3 e e naught a + + align:start position:0% +this answer is 512 over 3 e e naught a + + + align:start position:0% +this answer is 512 over 3 e e naught a +naught squared over H bar + + align:start position:0% +naught squared over H bar + + + align:start position:0% +naught squared over H bar +Redbird 1 over K a naught to the 9th + + align:start position:0% +Redbird 1 over K a naught to the 9th + + + align:start position:0% +Redbird 1 over K a naught to the 9th +pretty high power and the answer starts + + align:start position:0% +pretty high power and the answer starts + + + align:start position:0% +pretty high power and the answer starts +to be reasonably simple this 9 arises + + align:start position:0% +to be reasonably simple this 9 arises + + + align:start position:0% +to be reasonably simple this 9 arises +because of 12 minus 3 here + + align:start position:0% + + + + align:start position:0% + +this is still probably not ideal if you + + align:start position:0% +this is still probably not ideal if you + + + align:start position:0% +this is still probably not ideal if you +want to have intuition about what's + + align:start position:0% +want to have intuition about what's + + + align:start position:0% +want to have intuition about what's +going on and the scale of the effects + + align:start position:0% +going on and the scale of the effects + + + align:start position:0% +going on and the scale of the effects +you know once you have a formula and + + align:start position:0% +you know once you have a formula and + + + align:start position:0% +you know once you have a formula and +you've worked so hard to get it this + + align:start position:0% +you've worked so hard to get it this + + + align:start position:0% +you've worked so hard to get it this +calculation is doing it reliably so + + align:start position:0% +calculation is doing it reliably so + + + align:start position:0% +calculation is doing it reliably so +couple of hours of work and you might as + + align:start position:0% +couple of hours of work and you might as + + + align:start position:0% +couple of hours of work and you might as +well manipulate it and try to make it + + align:start position:0% +well manipulate it and try to make it + + + align:start position:0% +well manipulate it and try to make it +look a reasonably nice and this is what + + align:start position:0% +look a reasonably nice and this is what + + + align:start position:0% +look a reasonably nice and this is what +people are doing on ik physics do with + + align:start position:0% +people are doing on ik physics do with + + + align:start position:0% +people are doing on ik physics do with +this rate so they write it in the + + align:start position:0% +this rate so they write it in the + + + align:start position:0% +this rate so they write it in the +following way again a short calculation + + align:start position:0% +following way again a short calculation + + + align:start position:0% +following way again a short calculation +to get this 256 over three and they put + + align:start position:0% +to get this 256 over three and they put + + + align:start position:0% +to get this 256 over three and they put +in atomic units EP over e star I will + + align:start position:0% +in atomic units EP over e star I will + + + align:start position:0% +in atomic units EP over e star I will +explain what these numbers are squared 1 + + align:start position:0% +explain what these numbers are squared 1 + + + align:start position:0% +explain what these numbers are squared 1 +over T star 1 over K a naught to the 9th + + align:start position:0% +over T star 1 over K a naught to the 9th + + + align:start position:0% +over T star 1 over K a naught to the 9th +I think it's important to notice as well + + align:start position:0% +I think it's important to notice as well + + + align:start position:0% +I think it's important to notice as well +that you could say okay so how did the + + align:start position:0% +that you could say okay so how did the + + + align:start position:0% +that you could say okay so how did the +photon energy or photon frequency affect + + align:start position:0% +photon energy or photon frequency affect + + + align:start position:0% +photon energy or photon frequency affect +this result + + align:start position:0% +this result + + + align:start position:0% +this result +well actually the photon Omega doesn't + + align:start position:0% +well actually the photon Omega doesn't + + + align:start position:0% +well actually the photon Omega doesn't +seem to be anywhere here it has + + align:start position:0% +seem to be anywhere here it has + + + align:start position:0% +seem to be anywhere here it has +disappeared but it is implicit in the + + align:start position:0% +disappeared but it is implicit in the + + + align:start position:0% +disappeared but it is implicit in the +electron momentum because basically the + + align:start position:0% +electron momentum because basically the + + + align:start position:0% +electron momentum because basically the +momentum of the electron is what is + + align:start position:0% +momentum of the electron is what is + + + align:start position:0% +momentum of the electron is what is +obtained from using the energy of the + + align:start position:0% +obtained from using the energy of the + + + align:start position:0% +obtained from using the energy of the +photon that ionizes the electron + + align:start position:0% +photon that ionizes the electron + + + align:start position:0% +photon that ionizes the electron +liberate selector and then gives it some + + align:start position:0% +liberate selector and then gives it some + + + align:start position:0% +liberate selector and then gives it some +kinetic energy and roughly K goes like + + align:start position:0% +kinetic energy and roughly K goes like + + + align:start position:0% +kinetic energy and roughly K goes like +square root of Omega so there is an + + align:start position:0% +square root of Omega so there is an + + + align:start position:0% +square root of Omega so there is an +Omega dependence here now what are these + + align:start position:0% +Omega dependence here now what are these + + + align:start position:0% +Omega dependence here now what are these +other quantities of these quantities are + + align:start position:0% +other quantities of these quantities are + + + align:start position:0% +other quantities of these quantities are +simple EP is the peak electric field + + align:start position:0% +simple EP is the peak electric field + + + align:start position:0% +simple EP is the peak electric field +this peak electric + + align:start position:0% + + + + align:start position:0% + +in the wave that you've sent in so it's + + align:start position:0% +in the wave that you've sent in so it's + + + align:start position:0% +in the wave that you've sent in so it's +true he not East our is the atomic + + align:start position:0% +true he not East our is the atomic + + + align:start position:0% +true he not East our is the atomic +electric field and that's defined as the + + align:start position:0% +electric field and that's defined as the + + + align:start position:0% +electric field and that's defined as the +electric field that the proton creates + + align:start position:0% +electric field that the proton creates + + + align:start position:0% +electric field that the proton creates +at the electrode so is equal to e over a + + align:start position:0% +at the electrode so is equal to e over a + + + align:start position:0% +at the electrode so is equal to e over a +zero squared that's a definition or if + + align:start position:0% +zero squared that's a definition or if + + + align:start position:0% +zero squared that's a definition or if +you want in terms of read Burke's to + + align:start position:0% +you want in terms of read Burke's to + + + align:start position:0% +you want in terms of read Burke's to +read birds over e a not and it's about + + align:start position:0% +read birds over e a not and it's about + + + align:start position:0% +read birds over e a not and it's about +five point fourteen times 10 to the 11 + + align:start position:0% +five point fourteen times 10 to the 11 + + + align:start position:0% +five point fourteen times 10 to the 11 +volts per meter so it's a nice quantity + + align:start position:0% + + + + align:start position:0% + +it's an L and you're comparing your + + align:start position:0% +it's an L and you're comparing your + + + align:start position:0% +it's an L and you're comparing your +electric field from your laser to the + + align:start position:0% +electric field from your laser to the + + + align:start position:0% +electric field from your laser to the +typical electric field in the atom and + + align:start position:0% +typical electric field in the atom and + + + align:start position:0% +typical electric field in the atom and +that ratio is meaningful and then T star + + align:start position:0% +that ratio is meaningful and then T star + + + align:start position:0% +that ratio is meaningful and then T star +is the time the electron takes to travel + + align:start position:0% +is the time the electron takes to travel + + + align:start position:0% +is the time the electron takes to travel +a distance a knot so it's a knot over + + align:start position:0% +a distance a knot so it's a knot over + + + align:start position:0% +a distance a knot so it's a knot over +the velocity of the electron which is + + align:start position:0% +the velocity of the electron which is + + + align:start position:0% +the velocity of the electron which is +roughly the fine-structure constant MC + + align:start position:0% +roughly the fine-structure constant MC + + + align:start position:0% +roughly the fine-structure constant MC +you remember the lectern is roughly as a + + align:start position:0% +you remember the lectern is roughly as a + + + align:start position:0% +you remember the lectern is roughly as a +beta parameter equal to 1 over 137 this + + align:start position:0% +beta parameter equal to 1 over 137 this + + + align:start position:0% +beta parameter equal to 1 over 137 this +is a chancre says alpha equal beta + + align:start position:0% +is a chancre says alpha equal beta + + + align:start position:0% +is a chancre says alpha equal beta +meaning the fine-structure constant + + align:start position:0% +meaning the fine-structure constant + + + align:start position:0% +meaning the fine-structure constant +alpha is the beta of the electron so + + align:start position:0% +alpha is the beta of the electron so + + + align:start position:0% +alpha is the beta of the electron so +this is T star and it's actually two + + align:start position:0% +this is T star and it's actually two + + + align:start position:0% +this is T star and it's actually two +Redbird over H bar and it's 2.42 that's + + align:start position:0% +Redbird over H bar and it's 2.42 that's + + + align:start position:0% +Redbird over H bar and it's 2.42 that's +10 to the minus 17 seconds + + align:start position:0% + + + + align:start position:0% + +it's a time the electron which is not + + align:start position:0% +it's a time the electron which is not + + + align:start position:0% +it's a time the electron which is not +moving that fast thanks to move a bore + + align:start position:0% +moving that fast thanks to move a bore + + + align:start position:0% +moving that fast thanks to move a bore +radius so this is the last form will + + align:start position:0% +radius so this is the last form will + + + align:start position:0% +radius so this is the last form will +take atomic physics books would consider + + align:start position:0% +take atomic physics books would consider + + + align:start position:0% +take atomic physics books would consider +that the best way to describe the + + align:start position:0% +that the best way to describe the + + + align:start position:0% +that the best way to describe the +physics of the problem and and this is + + align:start position:0% +physics of the problem and and this is + + + align:start position:0% +physics of the problem and and this is +really all we're gonna say about + + align:start position:0% +really all we're gonna say about + + + align:start position:0% +really all we're gonna say about +ionization it's kind of a precursor of + + align:start position:0% +ionization it's kind of a precursor of + + + align:start position:0% +ionization it's kind of a precursor of +field theory calculations you will do + + align:start position:0% +field theory calculations you will do + + + align:start position:0% +field theory calculations you will do +soon not in 806 in which you do + + align:start position:0% +soon not in 806 in which you do + + + align:start position:0% +soon not in 806 in which you do +reasonably complicated calculations + + align:start position:0% +reasonably complicated calculations + + + align:start position:0% +reasonably complicated calculations +matrix elements Fineman diagrams and at + + align:start position:0% +matrix elements Fineman diagrams and at + + + align:start position:0% +matrix elements Fineman diagrams and at +the end of the day by the time you're + + align:start position:0% +the end of the day by the time you're + + + align:start position:0% +the end of the day by the time you're +all done the answer simplifies to + + align:start position:0% +all done the answer simplifies to + + + align:start position:0% +all done the answer simplifies to +something rather reasonable and not + + align:start position:0% +something rather reasonable and not + + + align:start position:0% +something rather reasonable and not +complicated \ No newline at end of file diff --git a/PptQgy89cN8.txt b/PptQgy89cN8.txt new file mode 100644 index 0000000000000000000000000000000000000000..16f2b8d2b51c53384b981b2bd84e60bf7022fea6 --- /dev/null +++ b/PptQgy89cN8.txt @@ -0,0 +1,3209 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation, or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: So we're going +to do a problem that + +looks like the guitar problem. + +But it's a bit cooler. + +At the same time, +there are fewer states, + +so I think it's +easier to manage. + +How many people know +how to play DDR? + +AUDIENCE: Well. + +PROFESSOR: Yeah. + +OK. + +How many people know the +rules of playing DDR? + +Because otherwise I won't +be able to lift my hand up. + +OK. + +OK, so let's go through +an algorithmic model. + +So, you have a board that +basically looks like this. + +And you have four +touch sensitive pads. + +Up, down, left, right. + +And then you have +a center position. + +You also have a sheet of notes +that looks something like this. + +Say, up, up down, down, up +down, up, up down, left right, + +left, left right, right. + +So on and so forth. + +So when you see an +arrow of up, that's + +a constraint that +says one of your feet + +has to be on the up arrow. + +Has to tap the up +arrow, actually. + +There's no constraint +for the other foot. + +So your other foot can be +anywhere else on the board. + +It doesn't matter. + +You are also allowed to tap +the board some extra times. + +So if you don't have +a note showing up, + +you can still hit the board. + +And there's no penalty. + +So you can hop around as +many times as you want, + +or as many times as you can, +until you run out of breath. + +So up basically means, it's +actually one foot has to be up. + +The other one center. + +Also, of course, because +of the design of the board, + +it doesn't matter +what foot is where. + +So what are possible +goals for this game? + +AUDIENCE: Not to get an F. + +PROFESSOR: OK. + +AUDIENCE: Hit all +the arrows when + +they line up with the top row. + +PROFESSOR: OK. + +So there are two different +ways of doing it. + +One, you said, +"not to get an F." + +So I would say, given some +limited set of skills. + +So given a set of skills, +or your skill level + +maximizes your score. right? + +AUDIENCE: Yeah. + +PROFESSOR: This is +dynamic programming, + +so we always want to +maximize something. + +Now, if you're really good, +then another possible goal + +is hit all the notes with +a minimum amount of effort. + +If you're going to +be in a competition, + +and you're going to +be doing 10 songs, + +you don't want to die after +the first song, right? + +So, assuming you can do +everything reasonably well, + +this is another possible goal. + +Any other goals? + +So we're brainstorming here. + +This isn't set in stone. + +We've already seen the formal +solution for this problem. + +So I want to play with it +for a little bit, right? + +We brought a DDR pad, so +I want to play with it. + +What else could you hope +to maximize or minimize + +for with dynamic programming? + +AUDIENCE: Not look ridiculous. + +PROFESSOR: OK. + +AUDIENCE: I guess we're looking +at the cost of each move, + +right? + +PROFESSOR: So, +hit all the notes. + +Minimum effort, or otherwise +say best appearance. + +So every move looks somewhat +good or somewhat bad. + +And you want to do the moves +that look as good as possible. + +So this maximizes +entertainment, right? + +if you're on TV, you +probably want this. + +Now suppose you are +in a competition + +and you only have +one track to play. + +AUDIENCE: Well, you know +where all the notes are. + +PROFESSOR: Sure. + +Like, we assume that we +know this ahead of time. + +So you've memorized this. + +And you're trying to +compute the best strategy, + +so you can memorize that. + +Then when you go and +play, you dominate. + +AUDIENCE: Yeah. + +PROFESSOR: So, if +you have one track, + +then I would say that +what you'd want to do + +is minimize your +probability of failure. + +Right? + +So given the probability of +failure for each possible move. + +You want to minimize the +overall probability of failure + +so your teammates +won't hate you. + +So, hit all the +notes and minimize. + +So this one's a little bit +different from the other ones + +because all the other +ones are already + +set up as a nice problem +where you add up things. + +So you can solve +them with graphs + +or with dynamic programming. + +If you want to minimize +the probability of failure, + +then you want to maximize +the probability of success. + +The probability of +succeeding on all your moves + +is the product of +the probability + +of succeeding on each move. + +All right? + +So if you have five +moves, then you + +have five individual +probabilities. + +You multiply them up. + +And that's the probability that +you execute the whole sequence + +correctly, and not stumble. + +So we have products +instead of sums. + +Yes? + +AUDIENCE: Isn't it related +to the maximizing score goal? + +PROFESSOR: You can. + +Well, not necessarily +because this one + +says that you only have +some possible moves. + +I think in the end, all of +them, except for this last one, + +can be solved using the +recursion depth we have for it. + +The last one, you have +to do a bit of massaging. + +And we're going +over that right now. + +So, you have products +instead of sums. + +How do you turn +products into sums? + +AUDIENCE: Logs? + +PROFESSOR: Yep. + +So, for this one, I +would want to use logs, + +so that I can say that +I want to maximize + +the log probability of success. + +Which is just the sum of the +log probabilities for each move. + +And then it looks like +dynamic programming, as usual. + +Now, if I wouldn't +want to use logs, + +if I'm using the DP formulation, +where I'm doing recursion, + +I can incorporate +products there. + +But it turns out, +I didn't practice. + +If you have a lot of +numbers that are close to 1, + +or that are close to 0, +so all the easy moves + +are going to be really +close to 1, for example. + +If you have a lot of numbers +that are close to 1 or close + +to 0, if you +multiply them up, you + +get numerical instabilities. + +So we get the number +that's really close to 1. + +So for example, if I'm choosing +whether to do, say I'm here, + +and I'm thinking, do I +want to move like this? + +Or do I want to move like +this, and then like this? + +These are both +pretty easy moves. + +So, in both cases, we're +looking at probabilities + +of success of 99.991%. + +And maybe 99.992%. + +So if you have numbers +with probabilities + +that are really close to 1, +and if you have a lot of them + +and you try to +multiply them, you're + +going to get a bad result. + +So all the products are going +to start looking the same. + +So we're going to get +a random solution, + +instead of what you want. + +This is a practical thing. + +It's called numerical +instability. + +And it's a practical +reason why you'd + +want to use logs, instead +of multiplying things up. + +So it's not just a +theoretical thing. + +It also makes life +nice in practice. + +OK. + +So we have a goal +that looks like this. + +Say, let's go for this one. + +Hit all the notes, +minimize the effort. + +And all the other ones can +be reduced to this one. + +We need to define effort, right? + +Let's say that we have a +function called delta, that + +takes two foot locations-- +so, where both of my feet + +are-- from and to. + +And it gives me a number from +0 to 1, where 0 is really easy. + +And 1 is really hard. + +So from would look something +like, my left foot is up. + +My right foot is centered. + +To would look something like, +my left foot is centered + +and my right foot is up. + +So basically going +from here to here. + +So from left foot up. + +Right foot center. + +To here. + +So there is some +difficulty there, right? + +We have to jump, so it's not 0. + +I'm burning some calories here. + +So any move that I make +has some difficulty. + +And I want to solve the +game so that overall I + +have a reasonably +small total difficulty. + +OK, are we understanding +the problem? + +So we have three +possible avenues here. + +We can start solving it +using dynamic programming. + +We can start solving +it using graphs. + +Or we can have someone else +play the DDR again so that we + +can get more hands +on experience, + +and look at what a good strategy +or a bad strategy looks like. + +So you guys get to vote. + +Who wants to solve this using +the dynamic programming? + +Who wants to solve +this using graphs? + +Who wants to get more +hands on experience? + +Damn. + +I was hoping that DDR would win. + +You guys are boring. + +So, graphs, right? + +We're going to have notes. + +Notes represent states, right? + +So a state is where you are +at some point in the game. + +And we'll have to define +what where you are means. + +And then, when you +jump, you make a move. + +So moves go between states. + +So in any game, you +have states and moves. + +A state is very +hard to put in time. + +And then you make a move. + +Like in chess. + +Your state is your +board position. + +And whether you're +moving, or your opponent + +is the next to move. + +And the move is when you take a +piece and put it from one place + +to another. + +So your vertices are states. + +And your edges are moves. + +So what's in a state? + +This is our problem. + +Whether we're solving +it with graphs + +or with dynamic +programming, this + +is what everything +comes down to. + +What's in the state? + +AUDIENCE: So your current +state is how much difficulty + +have you-- what is the problem? + +Are those representing +the probabilities, + +the difficulties? + +Or. + +PROFESSOR: So this is the +difficulty for one move. + +Does it depend on +previous moves? + +AUDIENCE: No, but. + +PROFESSOR: No. + +So it's a nice thing to +note that the difficulties + +for each move are independent. + +AUDIENCE: Would it be +dependent in real life? + +You'll get tired at the end. + +And he's able to +have less energy. + +PROFESSOR: Yep. + +So, in real life, we might +want to say that this actually + +depends on how much energy +you've expended so far. + +And if we have time, +let's solve that problem. + +So the nice thing +about this problem + +is there are many directions +in which we can take it. + +This is one of them. + +I'm fine. + +And I think we'll learn +a lot by doing that. + +So back to the original problem. + +Suppose that it doesn't +matter how tired you are. + +You're pretty +good, so you're not + +going to be tired +enough to go [GASP]. + +So, mostly independent +difficulties for each move. + +What's in a state? + +AUDIENCE: The sum of the +difficulties up to that point. + +PROFESSOR: OK. + +So. + +AUDIENCE: Your +appearance factor, + +if we're including that. + +Or are we only doing-- + +PROFESSOR: So we're doing this. + +AUDIENCE: Oh, I was just. + +Oh, effort. + +OK, we're minimizing effort. + +PROFESSOR: So the way +I like to think of this + +is, what is does a +solution look like? + +It's made up of +decisions, right? + +What are the decisions? + +AUDIENCE: To make that move +or don't make that move? + +PROFESSOR: We'll see. + +But once you know what +the decisions are, + +then you have to think, what +do I need to make a decision? + +AUDIENCE: The note. + +PROFESSOR: So, a +note is one of these. + +For some reason, +they're called notes. + +AUDIENCE: So you +know that somehow you + +have to hit all of them? + +Like, you can have +steps in between. + +PROFESSOR: Yep. + +AUDIENCE: Moves in between. + +You have to hit all of them. + +PROFESSOR: OK, so I like this. + +So, every one of these is going +to have to generate a move. + +And there might be +some moves in between. + +Well, each move is going +to map to some edge. + +And I'm going to need vertices. + +So, as an algorithms program +where when I hear that, oh. + +I can have some moves in +between, I get really uneasy. + +Like, what is this? + +How many moves am +I going to have? + +Is this going to +become really huge? + +And am I not going to be able +to run any algorithm on it? + +So let's think about that. + +How many moves would +I have in between? + +And, what would I +achieve with them? + +AUDIENCE: I guess you'd have +a max of, like, four, right? + +I mean, you can put your +right leg someplace, + +and you can put your +left leg someplace. + +That's like a max of two. + +Right? + +Or no? + +PROFESSOR: So, let's +think of an example. + +You want to go, say, +I want to go, what? + +From here to here, right? + +AUDIENCE: Um-hmm. + +PROFESSOR: And +you're thinking what? + +They can do this, oh sorry. + +So I can do this as one move. + +And this is one move. + +AUDIENCE: Yeah. + +Or you can just do +one jump, right? + +So it's-- oh, yeah. + +I guess that's more than one. + +PROFESSOR: OK. + +So looking at this, +if I'm considering + +whether to go from here to here. + +If I want to go either this way, +or if I want to go this way. + +So let's write this +down on the board. + +So I'm going from up +down to left right. + +And I'm considering, do +I want to go directly + +or do I want to +go up right first. + +And then left right. + +Let's not do these arrows +because they're confusing. + +So, do I want to +transition like this? + +Or do I want to +transition like this? + +Well, I claim that, since +my moves are independent, + +going from here to here, +if it's beneficial to go + +this way instead of +this way, I would + +want to go this +way all the time. + +So I would just say that, look. + +Inside my delta here, I +would say that, actually, + +if you know what you're +doing, whenever you have + +to go from here to here, +you're going to go like this. + +And the delta is going to report +to the total delta for this. + +So, if the problem is +that they have one note, + +and then I have my next note +like this, between these two + +notes, I can always +go in one move. + +AUDIENCE: So you're +saying 1 would + +like, including in our +difficulty function, + +it'll also tell +us, like, what move + +we should make to get there? + +PROFESSOR: How to get there. + +The best way to get from +one state to another. + +Well, like when +you're learning DDR, + +these are the +basic steps, right? + +Like, you practice until you +know how to get from one place + +to another. + +There is something else where +you need intermediate steps. + +AUDIENCE: Or if +you're holding one + +and then you've got +to move to another. + +Right? + +PROFESSOR: So, let's +not worry about holds. + +Let's say that we +would just represent + +holds as-- so if you have +a hold in a game, then + +we're just going to +represent it like this. + +We're going to cheat. + +So we don't have +to deal with it. + +In real life, you would +have to deal with it. + +Like if you're actually writing +a program that trains people. + +AUDIENCE: What happens if you +have, like, right, left, up + +or something. + +So let's say you start off +hitting your right foot + +on the top, and then you have +to hit the right one again. + +And then you have +to hit up again + +and then you have to transfer. + +So I guess anytime you +have to through the middle. + +You have move your foot. + +PROFESSOR: So I like the idea +of going through the middle. + +Why or how do you, why would +you go through the middle? + +AUDIENCE: To avoid crossing +your leg over or something. + +PROFESSOR: Well, what if I +have something like this? + +If there are DDR experts, I +know this isn't the right way + +to do it. + +But one way of doing it is +left, right, left, right, left, + +right. + +So then, I have some states +that account for the fact + +that I'm centering. + +So, some people like +to do this, right? + +Some people like to go to the +center as much as possible, + +if they have time +between the moves. + +So then, I would need +at least one state + +in between where I'm +allowed to center, right? + +In order to represent +what I just did there, + +I need one move. + +So, one way I could meet +this is I have left center. + +And then left right. + +And then left right, +left right, left right. + +So on and so forth. + +But this would mean that +instead of doing this, which + +is reasonably easy, I +would have to do this. + +This. + +And then jump, jump, +jump, jump every time. + +Harder. + +Not good. + +Not good for my knees. + +Not good for my score. + +So I don't want to do this. + +I want to have an intermediate +state so I can say, + +I start here and +then I get back here. + +Then I do this. + +Then I get back here. + +Then I go here. + +And then I go back here. + +And then go back. + +Do guys see how this works? + +AUDIENCE: You could +also rock back and forth + +to because they don't require +both feet to be on the ground + +the entire time. + +PROFESSOR: Rock back and forth. + +Hold that thought. + +That might come in handy. + +Assuming we have enough time. + +So, if we only do one move +every time we see a note, + +we're stuck with this. + +In our to allow +re-centering, we have + +to add states between the notes. + +We need to add an +intermediary state. + +And you can either think about +it, or take my word for it, + +but if you represent the notes +using the trick that I said + +above, and you want to represent +centering, then all you need + +is one extra state. + +So one extra move +between every two states. + +Between two notes. + +And that's enough. + +Because that one extra +state allows you to center. + +And it allows you to do pretty +much everything a beginner + +like me would know how to do. + +AUDIENCE: So you only need one +extra state between each note? + +PROFESSOR: Yep. + +That is the inside. + +That is where I'm +thinking, right? + +So I have to do both +this trick, to see + +that I don't need an +infinite number of steps. + +And come up with the +need for centering + +to see why I need one +intermediate step. + +By the way, does +anyone know what's + +the right way of doing that? + +What's the right way +of doing this move? + +You said, rock back and forth. + +So I wouldn't rock back and +forth in this case, right? + +Because that +wouldn't be helpful. + +How would I rock? + +AUDIENCE: Well, +you hold down one + +and then you go +to the other one. + +PROFESSOR: Yeah, so +rock left and right. + +OK. + +AUDIENCE: I said back and +forth, I meant rocking-- + +PROFESSOR: Sorry. + +I thought back, forth. + +So, the optimal +way of doing this + +is left, right, left, +right, left, right. + +So what am I doing? + +AUDIENCE: You have another move. + +You have, like, one +state for your foot where + +it's not touching the ground. + +PROFESSOR: OK. + +It's an interesting, and +important, distinction. + +So if I wanted to hit +both of them, if I'm here, + +and I need to hit both of +them, I need to hit them. + +If I only need to hit +one of them, if I'm here, + +I can hit it like this. + +If I'm here, though, +and I want to hit it, + +I have to lift myself up. + +So the difference is +whether I'm like this. + +Or like this. + +Where is my weight? + +So if I want to allow +for these moves, + +if I want to go past the +stage of very beginner, + +aside from keeping track +of where my feet are, + +I have to keep track of whether +my weight is on my left foot + +or on my right foot. + +So, I would actually +have l, r, and W, + +where W is either l or r. + +AUDIENCE: So your state now +has what you're currently + +putting more weight on. + +PROFESSOR: And where +each of the feet are. + +AUDIENCE: Yeah. + +Where your two feet are. + +And then also, the +song difficulty. + +So it's everything +in your state, right? + +PROFESSOR: Ah, yes. + +I didn't think about it. + +I was just talking +about foot position. + +But we need to get back +to the state thing. + +So that's a good point. + +So before we get to that, how +many feet positions do we have? + +If we don't include where +do I have my weight, + +how many possible positions +for both of my feet do I have? + +So I have two feet. + +Each of them can be in any +of these five squares, right? + +So how many total positions? + +AUDIENCE: 5 choose 2. + +Using 2. + +PROFESSOR: So I can do this. + +AUDIENCE: Sure. + +Why not? + +PROFESSOR: Well, if I have +5 choose 2, then you-- + +AUDIENCE: Oh, then that +doesn't quite work. + +PROFESSOR: Yeah. + +AUDIENCE: Yeah, no. + +PROFESSOR: So flip. + +AUDIENCE: Times 2. + +PROFESSOR: Yeah. + +So you have two feet. + +Each foot, five possibilities. + +Now, what if we have weight? + +If we are tracking on +where I keep my weight. + +How many possible positions? + +AUDIENCE: [INAUDIBLE]? + +Oh no, because there's only two. + +PROFESSOR: So, +for each of these, + +there's two possibilities now. + +So 50. + +AUDIENCE: You also have to be +so your weight is like this. + +PROFESSOR: In the middle? + +AUDIENCE: Yeah. + +PROFESSOR: You can. + +Based on that what I've been +reading, you never want to. + +Because if you're +weight is in the middle, + +then you're extending a lot +of effort to move either foot. + +So you always want to have +your weight somewhere. + +So that, at least +for one of your feet, + +it's easy to move it. + +AUDIENCE: Could it be the back? + +PROFESSOR: If that's +not true, then yeah. + +We'd need to have a center. + +Oh, so, like, whether I'm +like this or like this? + +AUDIENCE: Yeah. + +If you were, like, +doing the same thing. + +Rocking back and forth. + +PROFESSOR: So, if +I have two feet, + +then this says my weight +is on my left foot. + +My weight is on my right foot. + +So l and r is which foot, +not where on the board. + +AUDIENCE: So, did you not do +center because it was optimal? + +PROFESSOR: Because I claim +that, in an optimal strategy, + +you wouldn't have it. + +But you don't have to +take my word for it. + +If you don't believe +me, then you add center. + +And you just have +more possibilities. + +And if it happens to +not be an optimal thing, + +then the dynamic +programming will ignore it. + +So how many positions do +I have if I add center? + +So if I have left, center, +right for each position. + +AUDIENCE: 75. + +PROFESSOR: Cool. + +Yes. + +AUDIENCE: So why is it 25? + +You wouldn't actually have +both of your feet on the right. + +PROFESSOR: Why? + +Maybe, well especially, for +maximizing this one actually. + +Especially for +maximizing entertainment. + +Then it's way cooler +to do this, right? + +[LAUGHTER] + +You get the point. + +AUDIENCE: --possible weight. + +Like combinations +for like, where is + +you should have your +feet at one time. + +Like, not necessarily what +the game is asking you to do. + +PROFESSOR: Yeah. + +So this is where my feet are. + +The game will always +ask something like this. + +So the game won't always +care about both of my feet. + +Sometimes it'll only +care about one foot. + +So, yeah. + +There are two different +concepts, right? + +There's the position of my feet. + +And then there's the +note on the screen. + +And my feet have to match +the note on the screen. + +And we'll have to +capture that somehow. + +So what's in a state? + +What are my decisions? + +Come on, now. + +We should be in a good shape +to know what my decisions are. + +What do I decide every time? + +AUDIENCE: What move to make? + +PROFESSOR: Yeah. + +How am I going to jump, right? + +Where my feet are going +to be in the new position. + +So every time, I'm deciding +what's the new foot position. + +AUDIENCE: Aren't you also +deciding weight position, + +where you're going +to hold to, right? + +PROFESSOR: OK. + +So when I say foot position, +it's a cheat for everything. + +So yeah. + +Good observation. + +OK. + +What do I need to know, in +order to make this decision? + +OK. + +I would need to know +where I was before + +if I want to compute +the difficulties. + +But aside from that-- what? + +AUDIENCE: Sir, it came +up with this polynomial. + +PROFESSOR: All right. + +AUDIENCE: Is that a hint to what +the run time of this will be? + +PROFESSOR: It's not on purpose. + +But yes. + +So, yeah. + +That makes sense. + +Probably not good. + +I should probably not have +my screen up without me + +looking at it. + +OK, so. + +Back to decisions. + +I think I want to know what's +going to be on the screen + +when I land, right? + +Because if the screen says, +yo, you need to go up and down. + +Then maybe I shouldn't +do this, right? + +That would not be good. + +So I need to know what the note +is going to be when I land. + +Note. + +AUDIENCE: Is that +the same as the next? + +PROFESSOR: Yep. + +Next note. + +Yes. + +So the next note +here on the screen. + +So, my position in +this list, basically. + +AUDIENCE: So it's kind of like +the knapsack problem, where + +it's like which thing we're +considering picking up. + +But in this case, it's +coming [INAUDIBLE]. + +PROFESSOR: So it's +close to knapsack. + +But the difference +is, in knapsack, I + +have to decide, do I choose +this or do I ignore it. + +So, if I'd be like, if I +can only do a few things + +and I want to maximize +my score, then + +maybe I would choose, all right. + +This is easy. + +I'm going to do it. + +This is hard. + +Screw it. + +This is easy. + +I'm going to do it. + +So then my decisions are 0, 1. + +Pick or not pick. + +In this case, every +time my decision + +is a new state of my feet. + +So it's not 0, 1. + +AUDIENCE: OK. + +PROFESSOR: That's +the difference. + +And then, because +of that, the state + +is going to look different. + +And the recursion's will +look a bit different. + +OK. + +So I want to know the +note that I'm landing at. + +I want to know +the sum of-- well, + +we'll see if I want to know +the sum of difficulties + +up to this point. + +And I want to know +one more thing, so. + +If this is going +to be my new state, + +and I know what note I'm landing +at, I'm making a decision. + +The decision tells me where +my feet are going to be. + +Right? + +The move decides where +my feet are going to be. + +What do I need to do? + +What else do I need to +know for my total solution? + +So what do I need to know to +consider between decisions? + +So say I'm considering the +state of-- I'm at note two. + +Note two says, left right. + +And I'm considering +of coming here + +from note one, where my +foot position was up down. + +Or come here from +note one, where + +my foot position was left right. + +I need to know where +my foot position was, + +to choose between these, right? + +If I don't know that, +then I can't choose. + +AUDIENCE: That's not +from your state, though? + +PROFESSOR: Not yet. + +It's not here, so it's +not part of my state. + +We've been talking about it a +lot, but we didn't put it here. + +So let's say that +the state is going + +to have the note +that I'm landing at. + +And my foot position +after landing. + +So, if I know that I'm +going to land like this, + +then I know where +I was here. l r. + +Say, l r. + +I can compute the +costs here, right? + +This is delta of going +from this to this. + +And this is the delta for +going from this to this. + +Can you see? + +Is that too small? + +Delta wants to know where +my feet were before. + +And where they're +going to be now. + +So when I call it, I need +to know where I was before. + +And I need to know where +I'm going to be now. + +So this should be +part of my state. + +So our decision says, what's +my new position going to be? + +So when I make a move, I +influence my new foot position. + +They're going to +be in someplace. + +And independently of that, +the note-- the position here-- + +the position of the note, +increases all the time, right? + +Because time can +only go forwards. + +How are we going to account +for these extra moves? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: So, we said that +between every two notes, + +we might want to +make one extra move. + +AUDIENCE: Like, a +potential new note + +in between your +destination note? + +PROFESSOR: Yep. + +AUDIENCE: And then just fill +in the difficulties for that + +and see which ones-- + +PROFESSOR: So, if I want to use +the algorithm that I already + +have, that compares my +landing position to my note, + +to see whether I can go +there or not, what note would + +I want to put in that +intermediate note? + +So, you're basically saying +that between every two notes, + +I'm going to have one more note. + +And my feet can +be wherever here. + +AUDIENCE: Oh. + +I mean, you'll also +have the edge originally + +connecting them. + +So, you'd have it going +to the intermediate note, + +but also from the destination. + +Yeah, like that. + +You'd have to-- + +PROFESSOR: So, what +note would I have here? + +AUDIENCE: It makes +you go to the center. + +PROFESSOR: Do I have +to be at the center? + +AUDIENCE: Well, you +can be anywhere. + +PROFESSOR: Yeah. + +So I'm going to +invent the blank note. + +That's a big O. That means +you can do whatever you want. + +There are no constraints. + +So that is just an +intermediary state. + +So then I'm going +to take this input, + +and I'm going to add +these blank notes here. + +And these map to adding +notes in the graph. + +AUDIENCE: Well, +then, when you just + +run through your difficulty +function between each two notes + +and see if, for all the +potential moves, which + +one minimizes that path. + +PROFESSOR: Yep. + +So basically, I'm assuming +I don't need this. + +I'm assuming that. + +This is going to +be where there's + +at least one choice +where this is going + +to have the same cost +as a direct note. + +And then I'm going +to say that instead + +of having more complex +shapes in the graph, + +I'm going to insert +extra moves here. + +AUDIENCE: OK. + +I would think that, if you +have an intermediate move that + +might be less expensive, +you should, like, just + +hop to that new +position than to have + +an intermediate move, right? + +PROFESSOR: Yeah. + +And I'm going to assume that +either that's not the case, + +or that I can always find +an intermediate move that + +makes my life better. + +AUDIENCE: Every case? + +PROFESSOR: Yeah. + +PROFESSOR: These +results do work. + +You'll have to take my word +for it that this works. + +And this makes your +dynamic programming easy. + +And it makes your +graph building easy. + +So the advantage of this is +you're changing the input. + +And then, when you're +building your graph + +or when you're doing +the DP, you only + +worry about an input +that looks like this. + +You don't care about +any intermediate stuff. + +You have notes, and you have to +transition between the notes. + +Period. + +So we reduce the +complexity of the problem. + +So whenever you can get away +with that, it's really nice. + +We can do that for centering. + +We might not be able to do +it for other more complicated + +stuff. + +OK. + +So, we sort of know +what we want in a state. + +Now we want to build a +graph, so that the path + +from some source +to some destination + +has a cost that's equivalent to +the sum of these difficulties. + +Right? + +Because then I can +run the shortest path. + +And my solution +will be right there. + +I know. + +You guys seem awfully sad. + +Do you want to take a break +and play for a little bit more? + +Yes? + +How many people want +to play, instead of. + +You don't have to play yourself. + +You can just rest for +these two or three minutes. + +And you can watch +someone else play. + +And get more intuition about +how you're supposed to play. + +OK. + +So one person wants +to take a break. + +Everyone else wants +to keep going? + +Or are you guys +passed out already? + +AUDIENCE: Can we get out early? + +PROFESSOR: Sort of. + +Yeah. + +You'll get out +three minutes early, + +if we don't do another round. + +So who wants to keep going? + +AUDIENCE: No. + +Let's play. + +PROFESSOR: OK. + +So who wants to keep going? + +You can only vote on one thing. + +Who wants to play? + +AUDIENCE: OK. + +AUDIENCE: Five. + +AUDIENCE: Four. + +AUDIENCE: Victor, go. + +PROFESSOR: OK. + +Who wants to go? + +So we decided what we're +going to have in notes. + +And we're going to +build a graph, where + +the notes are the states. + +And the edges are the moves. + +Right? + +So a note tells me, just +like there, what note I'm at. + +Say I'm at note two. + +And where my feet are on. + +So, left foot left. + +Right foot right. + +So, given a state, what +outgoing edges do I build? + +Where can I go to? + +So let's say I have a state +that says I'm at note n + +and my left foot is +in some position. + +My right foot is +in some position. + +What are my outgoing +edges from here? + +AUDIENCE: Is there an +outgoing edge to every move? + +Because there's a point. + +PROFESSOR: OK. + +Well, actually, the +blank is a note, right? + +So if the next note, if +note three's a blank, + +then the note is a blank. + +And then I can have. + +AUDIENCE: I guess, +isn't the difficulty + +of the move dependent on what +note that blank actually is? + +PROFESSOR: So, it doesn't +depend on what the screen says. + +It depends on where my feet are. + +AUDIENCE: Oh, OK. + +I see. + +PROFESSOR: So I +have a number that + +tells me what's on my screen. + +This number is +enough for me to know + +what's going to be on my screen +from now on until forever. + +Because I have the +list ahead of time. + +And then I have the +position of my feet. + +So these are both +part of the state. + +So I have notes +for all the notes. + +And all the positions +of the feet. + +AUDIENCE: Right. + +But the blank note is +just one position of feet? + +PROFESSOR: No. + +AUDIENCE: Or, it's +all positions. + +PROFESSOR: Yeah. + +AUDIENCE: Isn't the +difficulty dependent + +on what position +your feet end up? + +PROFESSOR: Yeah. + +So it's from where I +start to where I land. + +So, if I decide to start +from here, and go here, + +the difficulty of this move +is-- so it doesn't depend on + +whether I have a blank there. + +And this was OK. + +Or, if I had an up down, +then I just missed the note. + +But the difficulty, the effort +I'm expending, is the same. + +AUDIENCE: OK. + +But if you start from that +other move and go to a different + +position, that's-- + +PROFESSOR: If I go +from this to this, + +then that's a +different difficulty. + +AUDIENCE: But it still +could be a blank note? + +PROFESSOR: Yeah. + +So, a blank note will let +me go wherever I want. + +AUDIENCE: I see. + +But there are different kinds +of blank notes, with different-- + +I guess I'm confused +as to what-- + +PROFESSOR: OK. + +So let's go through them again. + +AUDIENCE: Is it kind of +like it's, like, spreading, + +so really when you +have your source note, + +it's actually connecting +to every possible move. + +And every possible move is +connecting to your next-- + +so it's kind of like a +diamond shaped thing? + +PROFESSOR: Not quite. + +Not quite. + +So, let's go through +the notes again. + +And then let's go through that. + +So the source move will be +connected to some notes. + +And then those notes will +be connected to other notes. + +And it looks more like you +have a big, outgoing degree. + +Then you have a big network. + +Then the big, incoming degree. + +It looks like a messed +up sorting network. + +So, notes are constraints. + +This accepts any possible +feet combination, right? + +So this accepts this. + +AUDIENCE: Is the +first combination + +contained in that note? + +In that blank note? + +PROFESSOR: No. + +The blank is a constraint. + +So, if I have a note that +looks like this, then + +if one of my feet is here and +the other one is in the center, + +then that's fine. + +The constraint is met. + +If one of my feet is up +and the other one is down, + +then the constraint is met. + +AUDIENCE: But the edge +running into that blank note, + +depending on how your feet +land, is different difficulty. + +Is that right? + +PROFESSOR: Yep. + +But when I compute +the edge width, + +I need to know where +I'm landing exactly. + +Not just where the note +is because the note might + +admit multiple positions. + +AUDIENCE: I see. + +PROFESSOR: So this guy +admits all positions. + +AUDIENCE: OK. + +PROFESSOR: This guy admits +some positions, right? + +These are l r, l r. + +If I have up down, how many +feet positions does it admit? + +AUDIENCE: Just one. + +PROFESSOR: Not great. + +AUDIENCE: No. + +PROFESSOR: How many? + +AUDIENCE: As an intermediate? + +PROFESSOR: If it's up down, +then it's on the screen. + +My intermediates are all blank. + +AUDIENCE: Oh, oh. + +I thought you were +saying start with that. + +PROFESSOR: So up down. + +If you see up down +on the screen, + +how many feet positions? + +AUDIENCE: Left to right +what it could have. + +PROFESSOR: Yep. + +So, if the screen says up +down, the only two ways + +I can do that is this. + +Or this. + +Right? + +So, two positions. + +AUDIENCE: I see. + +AUDIENCE: Well, I mean, but +you could have intermediate + +where you step in the +first one, then back. + +PROFESSOR: But I don't +care because I've + +added these blank notes. + +And they take care of +my intermediates for me. + +AUDIENCE: But so, +we're saying where + +the feet land aren't +part of the note. + +PROFESSOR: Nope. + +They're just states. + +So they're a +decision I'm making. + +AUDIENCE: So, do we +have the multiple-- no, + +we don't because they're +not part of the-- + +PROFESSOR: For each +note position here, + +for every position +in the screen thing, + +I have multiple feet +positions that I could be in. + +AUDIENCE: Right. + +Right. + +But then, are there multiple +moves to get to those? + +PROFESSOR: Yep. + +AUDIENCE: OK. + +So there's multiple +moves connecting each. + +PROFESSOR: Yeah. + +So for example, if I want +to get to l r, up down here, + +I can go from l r, +up down in the blank. + +Or, I could have +l r be like this. + +And then transition. + +So I can have a lot of +possible foot positions + +that I'm transitioning +from in order to get here. + +AUDIENCE: But those +aren't actually + +separate notes on the graph. + +PROFESSOR: They are. + +They have to be. + +So these all have to +be separate notes. + +Because the edges are going +to have separate weights. + +Right? + +This edge is going +to have one weight. + +This edge is going to +have another weight. + +AUDIENCE: OK. + +That's what I thought. + +But then you said there +was only one blank. + +Don't there have to be multiple +blank notes for every foot + +thing. + +If you're approaching +a note from different-- + +PROFESSOR: So, I'm not +sure what you're asking. + +So, if you want to +care about centering, + +if you want to have +intermediate moves, + +you need one blank note +between every real note. + +So that you're allowed to make +one intermediate move between. + +AUDIENCE: Right. + +I get that that's talking +about the on the screen. + +PROFESSOR: Yeah. + +That's the screen. + +AUDIENCE: That's the screen. + +PROFESSOR: Yep. + +AUDIENCE: OK. + +So, that's not +the graph, though. + +Here, we're talking about +the screen on the graph. + +PROFESSOR: Here, we're +talking about the graph. + +So two tells me that the +screen is at note two. + +Whatever that happens to be. + +And my feet are +in this position. + +OK. + +So that's very important. + +Thanks for asking because +that's very important. + +So, a state has the note +that I'm landing at. + +So, where the screen is. + +And where my feet are. + +AUDIENCE: OK. + +PROFESSOR: OK. + +AUDIENCE: The state corresponds +to the nodes that you're on. + +PROFESSOR: A note. + +A note is a state. + +So, a note is a state. + +And a move goes +between two states. + +This is how we represent +all the graph problems. + +OK. + +AUDIENCE: So, you +need multiple blank. + +PROFESSOR: Yeah. + +So here, I'm just +drawing one example. + +Yeah. + +Yeah. + +So for example, here +I would need-- sorry. + +Oh, OK. + +I get your confusion now. + +So, yeah. + +This would be one move. + +This would be another move. + +AUDIENCE: That's all for a +single thing on the screen. + +PROFESSOR: Yep. + +AUDIENCE: OK. + +OK. + +That makes sense. + +AUDIENCE: So the next note +would have a really large end + +degree, right? + +I guess they always have-- + +AUDIENCE: Well, no. + +It'd have lots of-- + +PROFESSOR: So, this note +has a huge out degree. + +AUDIENCE: Yeah. + +But I'm saying the ones that all +those intermediates connect to. + +PROFESSOR: Yeah. + +AUDIENCE: So, then, +they would connect + +with some note that have, +like, really large degree. + +PROFESSOR: Yep. + +AUDIENCE: But there's two +of them after that, right? + +Because there would +be two different-- + +PROFESSOR: So, what's next? + +Next, is position, hmm. + +How did U number them? + +I guess, crap. + +No. + +It's not going to +match that, so. + +Whatever we do, it's +not going to match that. + +Say the next note, +4, is just an up. + +4 is up down. + +And then I have two +notes for it, right? + +Wild One note, l r. + +So this is note 4. + +That happens to be up down. + +And then I have this. + +And every one of these +connects to every one of these. + +AUDIENCE: If the +next move is up down, + +how can notes have down up? + +Oh, because you can +switch the feet. + +PROFESSOR: Yep. + +AUDIENCE: Oh. + +PROFESSOR: Yeah. + +So, I aimed to ask you guys, how +am I going to draw the edges? + +But you guys made me +do it with questions. + +So, suppose I met note n, l, r. + +What edges do I draw +going out of it? + +So, note n, left foot +at some position. + +Right foot at some position. + +What are my outgoing edges? + +AUDIENCE: This is a +note on the screen. + +Or-- + +PROFESSOR: In the graph. + +AUDIENCE: --the new one +or intermediate one? + +PROFESSOR: Doesn't matter. + +So, intermediate notes +have a note blank. + +AUDIENCE: That's +just everything. + +PROFESSOR: It doesn't matter. + +Yeah, we're looking at all +of them at the same time. + +AUDIENCE: Wait, so +you're asking what are-- + +PROFESSOR: So, given this note, +who am I connecting it to? + +Let's draw the outgoing edges. + +So, if you're solving +this as a graph problem, + +you build the notes. + +You draw the edges. + +You're on some algorithm. + +So let's draw the edges. + +AUDIENCE: I think it depends +if you're an intermediate note + +or not. + +PROFESSOR: Nope. + +So the note tells you +what your constraints are. + +And that covers +intermediate notes. + +If you're note is a blank, then, +well, there's no constraints. + +If the note is not a blank, +then there are constraints. + +AUDIENCE: Oh, note. + +I thought that was referring +to the note, not the-- + +PROFESSOR: No. + +So this is a note. + +Maybe n is not good. + +Let's use i, instead, then. + +If n is hard. + +So, i is the position +here, in this guy. + +Right? + +Say for example, +i equals 1 here. + +I equals 2 here. + +I equals 3 here. + +So and so forth. + +And that doesn't match this, so. + +AUDIENCE: We're +talking about note-- + +PROFESSOR: Yep. + +AUDIENCE: --not-- + +PROFESSOR: If one +note is represented + +by these three numbers, right? + +Each note has this tuple in it. + +AUDIENCE: Then i is the note. + +PROFESSOR: Yep. + +AUDIENCE: So i +connects to i plus 1. + +And then all +possibilities known. + +PROFESSOR: OK. + +So this connects to i plus 1. + +And then all possible +destinations, right? + +So I'm going to say left. + +This is after the jump. + +So, left after the jump, +and right after the jump. + +And this is for all +possible left after a jump, + +right after the jump. + +And lost a weight on this edge. + +AUDIENCE: The way +that it's from-- + +AUDIENCE: l r to + +AUDIENCE: --l r to l r. + +AUDIENCE: l j-- l sub j r. + +AUDIENCE: l r. + +PROFESSOR: So you want to +say from l r to l j, r j. + +But what? + +AUDIENCE: Difficulty level? + +PROFESSOR: Yeah. + +Where is that? + +AUDIENCE: Your +difficulty function. + +PROFESSOR: Which is? + +AUDIENCE: Delta. + +PROFESSOR: Delta. + +So, yeah. + +The weight is delta. + +I drew d. + +Delta of these two +foot positions. + +Almost. + +If I want to minimize the +difficulty, then this is right. + +If I want to maximize +a score, then I + +would have to add a minus sign. + +But if you're minimizing +the difficulty, + +this is exactly the way because +it maps the shortest path. + +Usually, in dynamic programming, +things are maximized. + +AUDIENCE: Wait, why would +you add a minus if it's-- + +PROFESSOR: So, if we're +maximizing something, + +we have to flip-- we have to +add a minus to the edge costs + +because-- + +AUDIENCE: Right. + +PROFESSOR: Yeah. + +But this time we're +minimizing something. + +AUDIENCE: Oh. + +Right, right, right. + +PROFESSOR: I promised you +that we'll maximize something + +all the time. + +Well, I guess I lied. + +AUDIENCE: OK. + +Right, right, right. + +AUDIENCE: You don't +want to maximize d. + +Then you're dead. + +PROFESSOR: No. + +You want to maximize show offs. + +So if we have the +entertainment thing, + +then that would be maximized. + +And then you'd have minus. + +AUDIENCE: Then you'd +have everything you need. + +PROFESSOR: Yep. + +AUDIENCE: OK. + +PROFESSOR: OK, so +we're almost good. + +Source notes and +destination notes. + +AUDIENCE: Well, I +guess source, we + +know that means +start in the middle. + +Right? + +Like, you would start off with-- + +PROFESSOR: What's the source? + +You want to start at +the first note, right? + +AUDIENCE: Yeah. + +PROFESSOR: But in +which position? + +AUDIENCE: Well, in +the center, right? + +I mean, the [INAUDIBLE] start. + +Or, I guess you could start-- + +AUDIENCE: Wherever you want. + +AUDIENCE: Could you +add a source note + +going to a bunch of +intermediate notes? + +PROFESSOR: Yeah. + +Yeah. + +So what I'm going to do is I'm +going to say there is a note 0. + +That let's me choose +how I'm going to start. + +AUDIENCE: Oh, it +could be any position. + +It's like an +intermediate note itself. + +PROFESSOR: Yep. + +So I'm going to have a note +0, with all possible foot + +positions. + +And then this is going to +be connected to a source, + +by edges of weight 0. + +So the intuition is that I get +to choose my starting position, + +right? + +Starting position. + +I see the first note. + +I make a move. + +So I want to be able to +choose the starting position. + +That's why I have +all those notes. + +And then make a move to +touch the first note. + +AUDIENCE: The starting +position is also a note. + +PROFESSOR: Yep. + +Because, if the +first note is here, + +I don't necessarily +want to start like this + +because maybe this +is harder than this. + +All right. + +What's the destination? + +AUDIENCE: The last note. + +PROFESSOR: OK. + +So, all the notes that are at +note n, and have any position, + +would be connected to +a destination note, + +using an edge of weight 0. + +Or I can consider +them as destinations. + +And then choose the destination +that has the shortest path. + +AUDIENCE: Oh, I see. + +The final destination is +going to be, like, two notes. + +Right? + +It's going to be that +last position, and then-- + +PROFESSOR: Or it +might be more than two + +if the note is +just a simple note. + +Because that wouldn't +constrain my feet too much. + +OK. + +And last, last question. + +Dijkstra or Bellman-Ford? + +AUDIENCE: Bellman-Ford, +because you + +have negative edges, +negative weight, + +as if you were going +to maximize to death. + +PROFESSOR: So, this is always +going to be from 0 to 1. + +So I could possibly +use Dijkstra. + +The answer is neither. + +The answer is, we're +building a DAG, so. + +AUDIENCE: Dijkstra. + +AUDIENCE: We don't use that. + +PROFESSOR: DAG, shortest path. + +Every time we have +dynamic programming, DAG, + +shortest path. + +OK? + +AUDIENCE: Question. + +PROFESSOR: Yeah. + +Come on, last question. + +You can't get away that easily. + +OK, so. + +Who wants to play? \ No newline at end of file diff --git a/RBPcKbEvK3U.txt b/RBPcKbEvK3U.txt new file mode 100644 index 0000000000000000000000000000000000000000..42e20460ce0b9f65b1bf3869d236b0181d2069dd --- /dev/null +++ b/RBPcKbEvK3U.txt @@ -0,0 +1,5305 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Going to +finish up a little bit + +from last time on gene +regulatory networks + +and see how the different +methods that we looked at + +compared, and then we'll +dive into protein interaction + +networks. + +Were there any questions +from last time? + +OK. + +Very good. + +So recall that we start off with +this dream challenge in which + +they provided unlabeled data +representing gene expression + +data for either in a completely +synthetic case, in silico data, + +or for three different +actual experiments-- + +one in E. coli, one in S. +cerevisiae, and one in aureus. + +For some of those, it was +straight expression data + +under different conditions. + +In other cases, there were +actual knock-down experiments + +or other kinds of perturbations. + +And then they gave that +data out to the community + +and asked people to use +whatever methods they wanted + +to try to rediscover +automatically the gene + +regulatory networks. + +So with some +preliminary analysis, + +we saw that there were a couple +of main clusters of kinds + +of analyses that all had similar +properties across these data + +sets. + +There were the +Bayesian networks, + +that we've discussed now +in two separate contexts. + +And then we looked at +regression-based techniques + +and mutual information +based techniques. + +And there were a bunch of +other kinds of approaches. + +And some of them actually +combine multiple predictors + +from different kinds +of algorithms together. + +And some of them, they +evaluated how well each of these + +did on all the +different data sets. + +So first the results +on the in silico data, + +and they're showing +this as an area + +under the +precision-recall curve. + +Obviously, higher numbers +are going to be better here. + +So in this first +group over here are + +the regression-based +techniques, mutual information, + +correlation, Bayesian networks. + +Things didn't fall into any of +those particular categories. + +Meta were techniques that +use more than one class + +of prediction and then develop +their own prediction based + +on those individual techniques. + +Then they defined something +that they call the community + +definition, which +they combine data + +from many of the +different techniques + +together with their own +algorithms to kind of come up + +with what they call the +"wisdom of the crowds." + +And then R represents +a random collection + +of other predictions. + +And you can see that on +these in silico data, + +the performances +don't dramatically + +differ one from the other. + +Within each class, if you +look at the best performer + +in each class, they're all +sort of in the same league. + +Obviously, some of the classes +do better consistently. + +Now their point +in their analysis + +is about the wisdom +of the crowds, that + +taking all these data +together, even including + +some of the bad +ones, is beneficial. + +That's not the main +thing that I wanted + +to get out of these +data for our purposes. + +So these E. coli data, +notice though that the errant + +to the curve, it's about +30 something percent. + +Now this is, oh, sorry, +this is in silico data. + +Now this is the first +real experimental data + +we'll look at, so +this is E. coli data. + +And notice the change of scale, +that the best performer's only + +doing under less than 10% of +the possible objective optimal + +results. + +So you can see that the real +data are much, much harder + +than the in silico data. + +And here the performance +varies quite a lot. + +You can see that the Bayesian +networks are struggling, + +compared to some of +the other techniques. + +The best of those +doesn't really get + +close to the best of some +of these other approaches. + +So what they did next, was they +took some of the predictions + +from their community +predictions that were built off + +of all these other data, and +they went and actually tested + +some of these. + +So they built regulatory +networks for E. coli + +and for aureus. + +And then they actually did +some experiments to test them. + +I think the results +overall are kind + +of encouraging, in the +sense that if you focus + +on the top pie chart +here, of all the things + +that they tested, +about half of them, + +they could get some support. + +In some cases, it was +very strong support. + +In other cases, it +wasn't quite as good. + +So the glass is half +empty or half full. + +But also, one of the +interesting things + +is that the data +are quite variable + +over the different +predictions that they make. + +So each one of these circles +represents a regulator, + +and the things that they claim +are targets of that regulator. + +And things that are +in blue are things + +that were confirmed +by their experiments. + +The things with black outlines +and blue are the controls. + +So they knew that +these would be right. + +So you could see that for +pure R, they do very well. + +For some of these +others, they do mediocre. + +But there are some, which +they're honest enough to admit, + +they do very poorly on. + +So they didn't get any +of their predictions + +right for this regulator. + +And this probably reflects the +kind of data that they had, + +in terms of what conditions +were being tested. + +So, so far, things +look reasonable. + +I think the real +shocker of this paper + +does not appear in the +abstract or the title. + +But it is in one of the main +figures, if you pay attention. + +So these were the results +for in silico data. + +Everything looked pretty good. + +Change of scale to E. coli, +there's some variation. + +But you can make arguments. + +These are the results for +Saccharomyces cerevisiae. + +So this is the organism, +yeast, on which + +most of the gene +regulatory algorithms + +were originally developed. + +And people actually +built careers + +off of saying how great +their algorithms were + +in reconstructing these +regulatory networks. + +And we look at these +completely blinded data, + +where people don't know +what they're looking for. + +You could see that the actual +results are rather terrible. + +So the area under the curve +is in the single digits + +of percentage. + +And it doesn't seem to matter +what algorithm they're using. + +They're all doing very badly. + +And the community predictions +are no better-- in some cases, + +worse-- than the +individual ones. + +So this is really +a stunning result. + +It's there in the data. + +And if you dig into +the supplement, + +they actually explain +what's going on, I think, + +pretty clearly. + +Remember that all +of these predictions + +are being made by looking for a +transcriptional regulator that + +increases in its own +expression or decreases + +in its own expression. + +And that change in +its own expression + +is predictive of its targets. + +So the hypothesis is when you +have more of an activator, + +you'll have more of +its targets coming on. + +If you have less +of an activator, + +you'll have less of the targets. + +And you look through +all the data, + +whether it's by Bayesian +networks or regression, + +to find those kinds +of relationships. + +Now what if those +relationships don't actually + +exist in the data? + +And that's what +this chart shows. + +So the green are genes +that have no relationship + +with each other. + +And they're measuring here the +correlation across all the data + +sets, between two +pairs of genes, + +for which have no known +regulatory relationship. + +The purple are ones +that are targets + +of the same +transcription factor. + +And the orange +are ones where one + +is the activator or +repressor of the other. + +And in the in silico data, +they give a very nice spread + +between the green, the +orange, and the purple. + +So the co-regulator are +very highly correlated + +with each other. + +The ones that are parent-child +relationships-- a regulator + +and its target-- have a +pretty good correlation, + +much, much different +from the distribution + +that you see for the things +that are not interacting. + +And on these data, the +algorithms do their best. + +Then you look at +the E. coli data, + +and you can see that in +E. Coli, the curves are + +much closer to each other, +but there's still some spread. + +But when you look +at yeast-- again, + +this is where a lot +of these algorithms + +were developed-- you +could see there's + +almost no difference between the +correlation between the things + +that have no relationship +to each other, + +things that are co-regulated +by the same regulatory protein, + +or those parent-child +relationships. + +They're all quite similar. + +And it doesn't +matter whether you + +use correlation analysis +or mutual information. + +Over here and in this +right-hand panel, + +they've blown up the +bottom part of this curve, + +and you can see how +similar these are. + +So again, this is a +mutual information + +spread for in silico data for +E. coli and then for yeast. + +OK. + +So what I think we can say +about the expression analysis + +is that expression data +are very, very powerful + +for some things and +are going to be rather + +poor for some +other applications. + +So they're very powerful for +classification and clustering. + +We saw that earlier. + +Now what those +clusters mean, that's + +this inference problem +they're trying to solve now. + +And the expression data are +not sufficient to figure out + +what the regulatory proteins +are that are causing + +those sets of genes to be +co-expressed-- at least + +not in yeast. + +And I think there's +every expectation + +that if you did the +same thing in humans, + +you would have the same result. + +So the critical +question then is if you + +do want to build models of +how regulation is taking place + +in organisms, what do you do? + +And the answer is that you +need some other kind of data. + +So one thing you might +think, if we go back + +to this core analysis, +like what's wrong? + +Why is it that these gene +expression levels cannot be + +used to predict the +regulatory networks? + +And it comes down to +whether gene levels are + +predictive approaching levels. + +And a couple of groups +have looked into this. + +One of the earlier studies +was this one, now 2009, + +where they used microarray data +and looked at mRNA expression + +levels versus protein levels. + +And what do you see in this? + +You see that there is a trend. + +Right there, R +squared is around 0.2, + +but that there's a huge spread. + +So that for any +position on the x-axis, + +a particular level of mRNA, you +can have 1,000-fold variation + +in the protein levels. + +So a lot of people +saw this and said, + +well, we know there are +problems with microarrays. + +They're not really great +at predicting mRNA levels + +or low in protein levels. + +So maybe this will all get +better if we use mRNA-Seq. + +Now that turns out +not to be the case. + +So there was a very careful +study published in 2012, + +where the group used +microarray data, RNA-Seq data, + +and a number of different ways +of calling the proteomics data. + +So you might say, well, +maybe some of the problem + +is that you're not doing a very +good job of inferring protein + +levels from mass spec data. + +And so they try a whole +bunch of these different ways + +of pulling mass spec data. + +And then they look, +you should focus + +on the numbers in these +columns for the average + +and the best correlations +between the RNA + +data in these columns and the +proteomic data in the rows. + +And you could see the +best case scenario-- + +you can get these up to 0.54 +correlation, still pretty weak. + +So what's going on? + +What we've been focusing +on now is the idea + +that the RNA levels are going +to be very well correlated + +with protein levels. + +And I think a lot +of literature is + +based on hypotheses that +are almost identical. + +But in reality, of +course, there are + +a lot of processes involved. + +There's the process +of translation, + +which has a rate +associated with it. + +It has regulatory steps +associated with it. + +And then there are +degradatory pathways. + +So the RNA gets +degraded at some rate, + +and the protein gets +degraded at some rate. + +And sometimes those +rates are regulated, + +sometimes they're not. + +Sometimes it depends +on the sequence. + +So what would happen +if you actually + +measured what's going on? + +And that was done recently +in this paper in 2011, + +where the group used a +labeling technique for proteins + +to [INAUDIBLE] and measure +steady state levels of proteins + +and then label the +proteins at specific times + +and see how much +newly synthesized + +their protein was +at various times. + +And similarly, for RNA, using +a technology that allowed them + +to separate newly synthesized +transcripts from the bulk RNA. + +And once you have +those data, then you + +can find out what the spread is +in the half lives of proteins + +and the abundance of proteins. + +So if you focus on +the left-hand side, + +these are the +determined half lives + +for various RNAs in blue +and proteins in red. + +If you look at the +spread in the red ones, + +you've got at least three +orders of magnitude of range + +in stability in half +lives for proteins. + +So that's really at the +heart of why RNA levels are + +very poorly predictive +approaching levels, + +because there's such a range +of the stability proteins. + +And the RNAs also, they +spread over probably + +about one or two orders of +magnitude in the RNA stability. + +And then here are +the abundances. + +So you can see that +the range of abundance + +for average copies +per cell of proteins + +is extremely large, +from 100 to 10 + +to the eighth copies per cell. + +Now if you look at the +degradation rates for protein + +half lives and RNA +half lives, you + +can see there's no correlation. + +So these are completely +independent processes + +that determine whether an +RNA is degraded or a protein + +is degraded. + +So then when you try to figure +out what the relationship is + +between RNA levels +and protein levels, + +you really have to resort to a +set of differential equations + +to map out what +all the rates are. + +And if you know all +those rates, then you + +can estimate what the +relationships will be. + +And so they did exactly that. + +And these charts show +what they inferred + +to be the contribution of +each of these components + +to protein levels. + +So on the left-hand +side, these are + +from cells which +had the most data. + +And they build a model +on the same cells + +from which they +collected the data. + +And in these cells, the RNA +levels account for about 40% + +of the protein +levels, the variance. + +And the biggest +thing that affects + +the abundance of proteins +is rates of translation. + +And then they took the data +built from one set of cells + +and tried to use it +to predict outcomes + +in another set of +cells in replicate. + +And the results are +kind of similar. + +They also did it for an entirely +different kind of cell types. + +In all of these cases, +the precise amounts + +are going to vary. + +But you can see that +the red bars, which + +represent the amount of +information content in the RNA, + +is less than about half of what +you can get from other sources. + +So this gets back +to why it's so hard + +to infer regulatory networks +solely from RNA levels. + +So this is the +plot that they get + +when they compare +protein levels and RNA + +levels at the +experimental level. + +And again, you see +that big spread and R + +squared at about 0.4, +which at the time, + +they were very proud of. + +They write several +times in the article, + +this is the best anyone +has seen to date. + +But if you incorporate all these +other pieces of information + +about RNA stability +and protein stability, + +you can actually get a +very, very good correlation. + +So once you know the variation +in the protein stability + +and the RNA stability for each +and every protein and RNA, + +then you can do a good job +of predicting protein levels + +from RNA levels. + +But without all that +data, you can't. + +Any questions on this? + +So what are we going to do then? + +So we really have two primary +things that we can do. + +We can try to explicitly model +all of these regulatory steps + +and include those in +our predictive models + +and try to build up gene +regulatory networks, protein + +models that actually include all +those different kinds of data. + +And we'll see that +in just a minute. + +And the other thing we +can try to do is actually, + +rather than try +to focus on what's + +downstream of RNA synthesis, +the protein levels, + +we can try to focus on what's +upstream of RNA synthesis + +and look at what the production +of RNAs-- which RNAs are + +getting turned on +and off-- tell us + +about the signaling pathways +and the transcription factors. + +And that's going to be a +topic of one of the upcoming + +lectures in which Professor +Gifford will look at variations + +in epigenomic data and +using those variations + +in epigenomic data to identify +sequences that represent which + +regulatory proteins are bound +under certain conditions + +and not others. + +Questions? + +Yeah? + +AUDIENCE: In a +typical experiment, + +the rate constants for how +many mRNAs or proteins can + +be estimated? + +PROFESSOR: So the question was +how many rate constants can you + +estimate in a +typical experiment? + +So I should say, +first of all, they're + +not typical experiments. + +Very few people do +this kind of analysis. + +It's actually very time +consuming, very expensive. + +So I think in this one, it was-- +I'll get the numbers roughly + +wrong-- but it was thousands. + +It was some decent fraction +of the proteome, but not + +the entire one. + +But most of the data +set's papers you'll read + +do not include any analysis of +stability rates, degradation + +rates. + +They only look at the bulk +abundance of the RNAs. + +Other questions? + +OK. + +So this is an +upcoming lecture where + +we're going to actually +try to go backwards. + +We're going to say, we +see these changes in RNA. + +What does that +tell us about what + +regulatory regions of the +genome were active or not? + +And then you could +go upstream from that + +and try to figure out +the signaling pathways. + +So if I know +changes in RNA, I'll + +deduce, as we'll see in +that upcoming lecture-- + +the sequences-- the identity +of the DNA binding proteins. + +And then I could +try to figure out + +what the signaling +pathways were that drove + +those changes in +gene expression. + +Now later in this lecture, we'll +talk about the network modeling + +problem. + +If assuming you knew these +transcription factors, + +what could you do to +infer this network? + +But before we go +to that, I'd like + +to talk about an interesting +modeling approach that + +tries to take into account +all these degradatory pathways + +and look specifically at +each kind of regulation + +as an explicit step in +the model and see how that + +copes with some of these issues. + +So this is work +from Josh Stewart. + +And one of the first +papers is here. + +We'll look at some +later ones as well. + +And the idea here is to +explicitly, as I said, + +deal with many, many +different steps in regulation + +and try to be quite specific +about what kinds of data + +are informing about what +step in the process. + +So we measure the +things in the bottom + +here-- arrays that tell us +how many copies of a gene + +there are in the genome, +especially in cancer. + +And you can get +big changes of what + +are called copy number, +amplifications, or deletions + +of large chunks of chromosomes. + +You need to take +that into account. + +All the RNA-Seq and microarrays +that we were talking about + +in measuring +transcription levels-- + +what do they actually tell us? + +Well, they give us +some information + +about what they're +directly connected to. + +So the transcriptomic data tells +something about the expression + +state. + +But notice they have explicitly +separated the expression + +state of the RNA from +the protein level. + +And they separated +the protein level + +from the protein activity. + +And they have these +little black boxes in here + +that represent the different +kinds of regulations. + +So however many copies of a +gene you have in the genome, + +there's some regulatory event, +transcriptional regulation, + +that determines how +much expression you + +get at the mRNA level. + +There's another +regulatory event here + +that determines at what +rate those RNAs are + +turned into proteins. + +And there are other +regulatory steps here + +that have to do with +signaling pathways, + +for example, that determine +whether those proteins are + +active or not. + +So we're going to treat each +of those as separate variables + +in our model that +are going to be + +connected by these black boxes. + +So they call their +algorithm "Paradigm," + +and they developed +it in the context + +of looking at cancer data. + +In cancer data, the two primary +kinds of information they had + +were the RNA levels from either +microarray or RNA-Seq and then + +these copy number +variations, again, + +representing +amplifications or deletions + +of chunks of the genome. + +And what they're trying +to infer from that + +is how active different +components are of + +known signaling pathways. + +Now the approach that +they used that involved + +all of those little +black boxes is something + +called a factor graph. + +And factor graphs can be +thought of in the same context + +as Bayesian networks. + +In fact, Bayesian networks +are a type of factor graph. + +So if I have a +Bayesian network that + +represents these three +variables, where they're + +directly connected by +edges, in a factor graph, + +there would be this extra +kind of node-- this black box + +or red box-- that's the factor +that's going to connect them. + +So what do these things do? + +Well, again, they're +bipartite graphs. + +They always have these +two different kinds + +of nodes-- the random +variables and the factors. + +And the reason they're +called factor graphs is they + +describe how the global +function-- in our case, + +it's going to be the global +probability distribution-- + +can be broken down into +factorable components. + +It can be combined +in a product to look + +at what the global +probability function is. + +So if I have some +global function over all + +the variables, you can think +of this again, specifically, + +as the probability function-- +the joint probability for all + +the variables in my system-- +I want to be able to divide it + +into a product of +individual terms, + +where I don't have all the +variables in each of these f's. + +They're just some +subset of variables. + +And each of these represents +one of these terms + +in that global product. + +The only things that +are in this function, + +are things to which +it's directly connected. + +So these edges exist +solely between a factor + +and the variables that are +terms in that equation. + +Is that clear? + +So in this context, +the variables + +are going to be nodes. + +And their allowed +values are going + +to be whether they're +activated or not activated. + +The factors are going to +describe the relationships + +among those variables. + +We previously saw those as +being cases of regulation. + +Is the RNA turned into protein? + +Is the protein activated? + +And what we'd like +to be able do is + +compute marginal probabilities. + +So we've got some +big network that + +represents our understanding +of all the signaling pathways + +and all the transcriptional +regulatory networks in a cancer + +cell. + +And we want to ask about +a particular pathway + +or a particular protein, +what's the probability + +that this protein or this +pathway is activated, + +marginalized over all +the other variables? + +So that's our goal. + +Our goal is to find +a way to compute + +these marginal +probabilities efficiently. + +And how do you +compute a marginal? + +Well, obviously you need to +sum over all the configurations + +of all the variables that +have your particular variable + +at its value. + +So if I want to know if +MYC and MAX are active, + +I set MYC and MAX +equal to active. + +And then I sum over +all the configurations + +that are consistent with that. + +And in general, that +would be hard to do. + +But the factor graph +gives us an efficient way + +of figuring out how to do that. + +I'll show you in a second. + +So I have some global function. + +In this case, this little +factor graph over here, + +this is the global function. + +Now remember, these +represent the factors, + +and they only have +edges to things + +that are terms in +their equations. + +So over here, is a +function of x3 and x5. + +And so it has edges to x3 and +x5, and so on for all of them. + +And if I want to explicitly +compute the marginal + +with respect to a +particular variable, + +so the marginal +with respect to x1 + +set equal to a, so I'd +have this function with x1 + +equal to a times the sum over +all possible states of x2, + +the sum over all possible +states of x3, x4, and x5. + +Is that clear? + +That's just the +definition of a marginal. + +They introduced a notation in +factor graphs that's called + +a "not-sum." + +It's rather terrible, but +the not-sum or summary. + +So I like this term, +summary, better. + +The summary over +all the variables. + +So if I want to figure +out the summary for x1, + +that's the sum over +all the other variables + +of all their +possible states when + +I set x1 equal to +a, in this case. + +So it's purely a definition. + +So then I can rewrite-- and you +can work this through by hand + +after class-- but +I can rewrite this, + +which is this intuitive way +of thinking of the marginal, + +in terms of these not-sums, +where each one of these + +is over all the other +variables that are not + +the one that's in the brackets. + +So that's just the definition. + +OK, this hasn't really +helped us very much, + +if we don't have +some efficient way + +of computing these marginals. + +And that's what the +factor graph does. + +So we've got some factor graph. + +We have this +representation, either + +in terms of graph or equation, +of how the global function can + +be partitioned. + +Now if I take any one +of these factor graphs, + +and I want to compute +a marginal over a node, + +I can re-draw the factor graph +so that variable of interest + +is the root node. + +Right? + +Everyone see that these +two representations + +are completely equivalent? + +I've just yanked +x1 up to the top. + +So now this is a tree structure. + +So this is that factor +graph that we just + +saw drawn as a tree. + +And this is what's called +an expression tree, which + +is going to tell +us how to compute + +the marginal over the +structure of the graph. + +So this is just copied +from the previous picture. + +And now we're going to come up +with a program for computing + +these marginals, using +this tree structure. + +So first I'm going to compute +that summary function-- + +the sum over all sets of the +other variables for everything + +below this point, starting with +the lowest point in the graph. + +And we can compute the +summary function there. + +And that's this term, the +summary for x3 of just this fE. + +I do the same thing for +fD, the summary for it. + +And then I go up a +level in the tree, + +and I multiply the summary +for everything below it. + +So I'm going to compute +the product of the summary + +functions. + +And I always compute the summary +with respect to the parent. + +So here the parent was +x3, for both of these. + +So these are summaries +with respect to x3. + +Here who's the parent? + +x1. + +And so the summary is to x1. + +Yes? + +AUDIENCE: Are there +directed edges? + +In the sense that in f, in +the example on the right, + +is fD just relating +how x4 relates to x3? + +PROFESSOR: That's exactly right. + +So the edges represent which +factor you're related to. + +So that's why I can +redraw it in any way. + +I'm always going to +go from the leaves up. + +I don't have to worry about any +directed edges in the graph. + +Other questions. + +So what this does +is it gives us a way + +to officially, overall a +complicated graph structure, + +compute marginals. + +And they're typically +thought of in terms + +of messages that are being sent +from the bottom of the graph up + +to the top. + +And you can have a rule from +computing these marginals. + +And the rule is as follows. + +Each vertex waits +for the messages + +from all of its +children, until it + +gets its-- the messages are +accumulating their way up + +the graph. + +And every node is +waiting until it + +hears from all of its progeny +about what's going on. + +And then it sends the signal +up above it to its parent, + +based on the following rules. + +A variable node just takes +the product of the children. + +And a factor node-- one of +those little black boxes-- + +computes the summary +for the children + +and sends that up to the parent. + +And it's the summary with +respect to the parent, + +just like in the +examples before. + +So this is a formula for +computing single marginals. + +Now it turns out-- I'm not going +to go into details of this. + +It's kind of complicated. + +But you actually can, +based on this core idea, + +come up with an efficient way of +computing all of the marginals + +without having to +do this separately + +for every single one. + +And that's called a +message passing algorithm. + +And if you're really +interested, you + +can look into the citation +for how that's done. + +So the core idea is that we +can take a representation + +of our belief of how this +global function-- in our case, + +it's going to be the joint +probability-- factors in terms + +of particular +biological processes. + +We can encode what we know about +the regulation in that factor + +graph, the structure +of the graph. + +And then we could +have an efficient way + +of computing the marginals, +which will tell us, + +given the data, +what's the probability + +that this particular +pathway is active? + +So in this particular case, +in this paradigm model, + +the variables can +take three states-- + +activated, deactivated, +or unchanged. + +And this is, in a tumor +setting, for example, + +you might say the tumor is +just like the wild type cell, + +or the tumor has activation +with respect to the wild type, + +or it has a repression with +respect to the wild type. + +Again, this is the structure of +the factor graph that they're + +using and the different kinds +of information that they have. + +The primary experimental +data are just + +these arrays that tell us about +SNiPs and copy number variation + +and then arrays or RNA-Seq to +tell us about the transcript + +levels. + +But now they can +encode all sorts + +of rather complicated +biological functions + +in the graph structure itself. + +So transcription +regulation is shown here. + +Why is the edge from +activity to here? + +Because we don't +want to just infer + +that if there's more of the +protein, there's more activity. + +So we're actually, +explicitly computing + +the activity of each protein. + +So if an RNA gets +transcribed, it's + +because some transcription +factor was active. + +And the transcription +factor might not + +be active, even if the levels +of the transcription factor + +are high. + +That's one of the +pieces that's not + +encoded in all of those +things that were in the dream + +challenge, that are really +critical for representing + +the regulatory structure. + +Similarly, protein +activation-- I + +can have protein that goes from +being present to being active. + +So think of a +kinase, that itself + +needs to be phosphorylated +to be active. + +So that would be +that transition. + +Some other kinase comes in. + +And if that other +kinase1 is active, + +then it can +phosphorylate kinase2 + +and make that one active. + +And so it's pretty +straightforward. + +You can also represent the +formation of a complex. + +So the fact that all the +proteins are in the cell + +doesn't necessarily mean they're +forming an active complex. + +So the next step +then can be here. + +Only when I have +all of them, would I + +have activity of the complex. + +We'll talk about how AND-like +connections are formed. + +And then they also +can incorporate OR. + +So what does that mean? + +So if I know that all +members of the gene family + +can do something, I might +want to explicitly represent + +that gene family as an element +to the graph-- a variable. + +Is any member of +this family active? + +And so that would be +done this way, where + +if you have an OR-like +function here, then + +this factor would make this gene +active if any of the parents + +are active. + +So there, they +give a toy example, + +where they're trying to figure +out if the P53 pathway is + +active, so MDM2 is +an inhibitor of P53. + +P53 can be an +activator-related apoptosis. + +And so for separately, +for MDM2 and for P53, + +they have the factor graphs +that show the relationship + +between copy number +variation and transcript + +level and protein +level and activity. + +And those relate to each other. + +And then those relate to +the apoptotic pathway. + +So what they want to do +then is take the data + +that they have, in +terms of these pathways, + +and they want to compute +the likelihood ratios. + +What's the probability +of observing + +the data, given a hypothesis +that this pathway is active + +and all my other settings +of the parameters? + +And compare that +to the probability + +of the data, given that +that pathway is not active. + +So this is the kinds +of likelihood ratios + +we've been seeing now +in a couple of lectures. + +So now it gets into the details +of how you actually do this. + +So there's a lot of manual +steps involved here. + +So if I want to encode a +regulatory pathway as a factor + +graph, it's currently done in a +manual way or semi-manual way. + +You convert what's +in the databases + +into the structure +or factor graph. + +And you make a +series of decisions + +about exactly how +you want to do that. + +You can argue with the +particular decisions + +they made, but the +reasonable ones. + +People could do +things differently. + +So they convert the regulatory +networks into graphs. + +And then they have to +define some of the functions + +on this graph. + +So they define the expected +state of a variable, + +based on the state +of its parents. + +And they take a majority +vote of the parents. + +So a parent that's connected by +a positive edge, meaning it's + +an activator, if the +parent is active, + +then it contributes a +plus 1 to the child. + +If it's connected by +a repressive edge, + +then the parenting active +would make a vote of minus 1 + +for the child. + +And you take the majority +vote of all those votes. + +So that's what this says. + +But the nice thing is that you +can also incorporate logic. + +So for example, when +we said, is any member + +of this pathway active? + +And you have a +family member node. + +So that can be done +with an OR function. + +And there, it's +these same factors + +that will determine-- +so some of these edges + +are going to get +labeled "maximum" + +or "minimum," that +tell you what's + +the expected value of the +child, based on the parent. + +So if it's an OR, then if any +of the parents are active, + +then the child is active. + +And if it's AND, you +need all of them. + +So you could have described +all of these networks + +by Bayesian networks. + +But the advantage +of a factor graph + +is that your explicitly +able to include + +all these steps to describe this +regulation in an intuitive way. + +So you can go back +to your models + +and understand what +you've done, and change it + +in an obvious way. + +Now critically, we're +not trying to learn + +the structure of the +graph from the data. + +We're imposing the +structure of the graph. + +We still need to learn +a lot of variables, + +and that's done using +expectation maximization, + +as we saw in the +Bayesian networks. + +And then, again, +it's a factor graph, + +which primarily means that we +can factor the global function + +into all of these factor nodes. + +So the total probability +is normalized, + +but it's the product +of these factors which + +have to do with just the +variables that are connected + +to that factor +node in the graph. + +And this notation +that you'll see + +if you look through +this, this notation + +means the setting +of all the variables + +consistent with something. + +So let's see that-- here we go. + +So this here, this is the +setting of all the variables + +X, consistent with the data +that we have-- so the data + +being the arrays, the +RNA-Seq, if you had it. + +And so we want to compute +the marginal probability + +of some particular variable +being at a particular setting, + +given the fully +specified factor graph. + +And we just take the product +of all of these marginals. + +Is that clear? + +Consistent with all +the settings where + +that variable is +set to x equals a. + +Questions? + +OK. + +And we can compute the +likelihood function + +in the same way. + +So then what actually happens +when you try to do this? + +So they give an example here in +this more recent paper, where + +it's basically a toy example. + +But they're modeling all +of these different states + +in the cells. + +So G are the number +of genomic copies, + +T, the level of transcripts. + +Those are connected by a factor +to what you actually measure. + +So there is some true +change in the number + +of copies in the cell. + +And then there's what +appears in your array. + +There's some true number of +copies of RNA in the cell. + +And then there's what you +get out of your RNA-Seq. + +So that's what these +factors are present-- + +and then these are +regulatory terms. + +So how much transcript you get +depends on these two variables, + +the epigenetic state +of the promoter + +and the regulatory proteins +that interact with it. + +How much transcript +gets turned into protein + +depends on regulatory proteins. + +And those are determined by +upstream signaling events. + +And how much protein +becomes active, + +again, is determined by the +upstream signaling events. + +And then those can have effects +on downstream pathways as well. + +So then in this toy example, +they're looking at MYC/MAX. + +They're trying to figure out +whether it's active or not. + +So we've got this pathway. + +PAK2 represses MYC/MAX. + +MYC/MAX activates these two +genes and represses this one. + +And so if these were +the data that we + +had coming from copy number +variation, DNA methylation, + +and RNA expression, then I'd +see that the following states + +of the downstream genes-- +this one's active. + +This one's repressed. + +This one's active. + +This one's repressed. + +They infer that +MYC/MAX is active. + +Oh, but what about the fact +that this one should also + +be activated? + +That can be explained +away by the fact + +that there's a difference in the +epigenetic state between ENO1 + +and the other two. + +And then the belief +propagation allows + +us to transfer that information +upward through the graph + +to figure out, OK, so now we've +decided that MYC/MAX is active. + +And that gives us information +about the state of the proteins + +upstream of it and the +activity then of PAK2, + +which is a repressor of MYC/MAX. + +Questions on the factor +graphs specifically + +or anything's that +come up until now? + +So this has all been +reasoning on known pathways. + +One of the big promises of +these systematic approaches + +is the hope that we can +discover new pathways. + +Can we discover things we +don't already know about? + +And for this, we're going to +look at interactome graphs, + +so graphs that are +built primarily + +from high throughput +protein-protein interaction + +data, but could also +be built, as we'll see, + +from other kinds of +large-scale connections. + +And we're going to look +at what the underlying + +structure of these +networks could be. + +And so they could +arise from a graph + +where you put an edge +between two nodes + +if their co-expressed, if they +have high mutual information. + +That's what we saw +in say, ARACHNE, + +which we talked +about a lecture ago. + +Or, if say, the two hybrids +and affinity capture mass spec + +indicated direct +physical interaction + +or say a high throughput +genetic screen + +indicated a genetic interaction. + +These are going to be +very, very large graphs. + +And we're going to look at some +of the algorithmic problems + +that we have dealing +with huge graphs + +and how to compress the +information down so we get + +some piece of the network +that's quite interpretable. + +And we'll look at +various kinds of ways + +of analyzing these graphs +that are listed here. + +So one of the advantages of +dealing with data in the graph + +formulation is that we can +leverage the fact that computer + +science has dealt with large +graphs for quite a while + +now, often in the context +of telecommunications. + +Now big data, Facebook, +Google-- they're always + +dealing with things in +a graph formulation. + +So there are a lot of algorithms +that we can take advantage of. + +We're going to look at +how to use quick distance + +calculations on graphs. + +And we'll look at that +specifically in an example + +of how to find the kinase +target relationships. + +Then we'll look at how +to cluster large graphs + +to find subgraphs +that either represents + +an interesting +topological feature + +of the inherent +structure of the graph + +or perhaps to represent +active pieces of the network. + +And then we'll look at +other kinds of optimization + +techniques to help us find +the part of the network that's + +most relevant to our particular +experimental setting. + +So let's start with +ostensibly a simple problem. + +I know a lot about-- I have a +lot of protein phosphorylation + +data. + +I'd like to figure +out what kinase + +was that phosphorylated +a particular protein. + +So let's say I have +this protein that's + +involved in cancer +signaling, Rad50. + +And I know it's phosphorylated +these two sites. + +And I have the sequences +of those sites. + +So what kinds of tools do +we have at our disposal + +if I have a set of +sequences that I believe + +are phosphorylated, +that would help + +me try to figure out what +kinase did the phosphorylation? + +Any ideas? + +So if I know the specificity of +the kinases, what could I do? + +I could look for +a sequence match + +between the specificity +of the kinase + +and the sequence of +the protein, right? + +In the same way that +we can look for a match + +between the specificity +of a transcription factor + +and the region of the +genome to which it binds. + +So if I have a library +of specificity motifs + +for different kinases, +where every position here + +represents a piece of +the recognition element, + +and the height of the letters +represent the information + +content, I can scan those. + +And I can see what +family of kinases + +are most likely to be +responsible for phosphorylating + +these sites. + +But again, those are +families of kinases. + +There are many +individual members + +of each of those families. + +So how to I find +the specific member + +of that family that's +most likely to carry out + +the regulation? + +So here, what happens +in this paper. + +It's called [? "Network." ?] +And as they say, well, + +let's use the graph properties. + +Let's try to figure out which +proteins are physically linked + +relatively closely in the +network to the target. + +So in this case, they've +got Rad50 over here. + +And they're trying to figure out +which kinase is regulating it. + +So here are two kinases that +have similar specificity. + +But this one's +directly connected + +in the interaction +that works so it's + +more likely to be responsible. + +And here's the member +of the kinase that + +seems to be consistent with the +sequence being phosphorylated + +over here. + +It's not directly connected, +but it's relatively close. + +And so that's also a +highly probable member, + +compared to one that's +more distantly related. + +So in general, if I've +got a set of kinases + +that are all of equally good +sequence matches to the target + +sequence, represented by these +dash lines, but one of them + +is physically linked as well, +perhaps directly and perhaps + +indirectly, I have +higher confidence + +in this kinase because +of its physical links + +than I do in these. + +So that's fine if you want +to look at things one by one. + +But if you want to look +at this at a global scale, + +we need very +efficient algorithms + +for figuring out what the +distance is in this interaction + +network between any +kinase and any target. + +So how do you go about +officially computing distances? + +Well that's where converting +things into a graph structure + +is helpful. + +So when we talk +about graphs here, + +we mean sets of vertices and +the edges that connect them. + +The vertices, in our case, +are going to be proteins. + +The edges are going +to perhaps represent + +physical interactions or some +of these other kinds of graphs + +we talked about. + +These graphs can be directed, +or they can the undirected. + +Undirected would be what? + +For example, say two hybrid. + +I don't know which one's +doing what to which. + +I just know that two +proteins can come together. + +Whereas a directed edge +might be this kinase + +phosphorylates this target. + +And so it's a directed edge. + +I can have weights +associated with these edges. + +We'll see in a +second how we can use + +that to encode our confidence +that the edge represents + +a true physical interaction. + +We can also talk about the +degree, the number of edges + +that come into a +node or leave a node. + +And for our point, +it's rather important + +to talk about the path, +the set of vertices + +that can get me from one +node to another node, + +without ever retracing my steps. + +And we're going to +talk about path length, + +so if my graph is +unweighted, that's + +just the number of +edges along the path. + +But if my graph +has edge weights, + +it's going to be the sum of the +edge weights along that path. + +Is that clear? + +And then we're going to +use an adjacency matrix + +to represent the graphs. + +So I have two completely +equivalent formulations + +of the graph. + +One is the picture on +the left-hand side, + +and the other one is the matrix +on the right-hand side, where + +a 1 between any row +and column represents + +the presence of an edge. + +So the only edge connecting +node 1 goes to node 2. + +Whereas, node 2 is connected +both to node 1 and to node 3. + +Hopefully, that agrees. + +OK. + +Is that clear? + +And if I have a weighted +graph, then instead + +of putting zeros or +ones in the matrix, + +I'll put the actual edge +weights in the matrix. + +So there are algorithms that +exist for officially finding + +shortest paths in large graphs. + +So we can very +rapidly, for example, + +compute the shortest path +between any two nodes, + +based solely on that +adjacency matrix. + +Now why are we going to +look at weighted graphs? + +Because that gives us the +way to encode our confidence + +in the underlying data. + +So because the total +distance in network + +is the sum of the edge weights, +if I set my edge weights + +to be negative log +of a probability, + +then if I sum all +the edge weights, + +I'm taking the product of +all those probabilities. + +And so the shortest +path is going + +to be the most probable +path as well, because it's + +going to be the minimum of +the sum of the negative log. + +So it's going to be the maximum +of the joint probability. + +Is that clear? + +OK. + +Very good. + +So by encoding our network as a +weighted graph, where the edge + +weights are minus log +of the probability, + +then when I use these standard +algorithms for finding + +the shortest path +between any two nodes, + +I'm also getting the most +probable path between these two + +proteins. + +So where these edge +weights come from? + +So if my network consists +say of affinity capture mass + +spec and two hybrid +interactions, + +how would I compute the edge +of weights for that network? + +We actually explicitly +talked about this + +just a lecture or two ago. + +So I have all this +affinity capture mass spec, + +two hybrid data. + +And I want to +assign a probability + +to every edge that tells me how +confident I am that it's real. + +So we already saw that in +the context of this paper + +where we use Bayesian networks +and gold standards to compute + +the probability for every +single edge in the interactome. + +OK. + +So that works pretty well if you +can define the gold standards. + +It turns out that that has +not been the most popular way + +of dealing with mammalian data. + +It works pretty well +for yeast, but it's not + +what's used primarily +in mammalian data. + +So in mammalian data, the +databases are much larger. + +The number of gold +standards are fewer. + +People rely on more +ad hoc methods. + +One of the big advances, +technically, for the field + +was the development of a common +way for all these databases + +of protein-protein interactions +to report their data, + +to be able to interchange them. + +There's something called +PSICQUIC and PSISCORE, that + +allow a client to +pull information + +from all the different +databases of protein-protein + +interactions. + +And because you can get all +the data in a common format + +where it's traceable back to +the underlying experiment, + +then you can start +computing confidence scores + +based on these +properties, what we + +know about where the data came +from in a high throughput way. + +Different people have +different approaches + +to computing those scores. + +So there's a common +format for that + +as well, which is +this PSISCORE where + +you can build your interaction +database from whichever + +one of these underlying +databases you want, + +filter it however you want. + +And then send your database to +one of these scoring servers. + +And they'll send +you back the scores + +according to their algorithm. + +One that I kind of like this +is this Miscore algorithm. + +It digs down into +the underlying data + +of what kind of +experiments were done + +and how many +experiments were done. + +Again, they make all sorts +of arbitrary decisions + +in how they do that. + +But the arbitrary +decisions seem reasonable + +in the absence of +any other data. + +So their scores are based on +these three kinds of terms-- + +how many publications +there are associated + +with any interaction, what +experimental method was used, + +and then also, if there's an +annotation in the database + +saying that we know that this +is a genetic interaction, + +or we know that it's a +physical interaction. + +And then they put weights +on all of these things. + +So people can argue +about what the best + +way of approaching this is. + +The fundamental point +is that we can now + +have a very, very +large database of known + +interactions as weighted. + +So by last count, +there are about 250,000 + +protein-protein interactions +for humans in these databases. + +So you have that +giant interactome. + +It's got all these scores +associated with it. + +And now we can dive +into that and say, + +these data are somewhat largely +unbiased by our prior notions + +about what's important. + +They're built up from +high throughput data. + +So unlike the carefully +curated pathways + +that are what everybody's +been studying for decades, + +there might be information +here about pathways + +no one knows about. + +Can we find those pathways +in different contexts? + +What can we learn from that? + +So one early thing +people can do is just + +try to find pieces +of the network that + +seem to be modular, +where there are + +more interactions among the +components of that module + +than they are to other +pieces of the network. + +And you can find those +modules in two different ways. + +One is just based on +the underlying network. + +And one is based on the +network, plus some external data + +you have. + +So one would be +to say, are there + +proteins that fundamentally +interact with each other + +under all possible settings? + +And then we would say, in +my particular patient sample + +or my disease or +my microorganism, + +which proteins seem +to be functioning + +in this particular condition? + +So one is the topological model. + +That's just the network itself. + +And one is the functional model, +where I layer onto information + +that the dark nodes are active +in my particular condition. + +So an early use of +this kind of approach + +was to try to annotate +nodes-- a large fraction + +of even well studied +genomes that we don't know + +the function of +any of those genes. + +So what if I use the +structure of the network + +to infer that if some protein +is close to another protein + +in this interaction +network, it is + +likely to have similar function? + +And statistically, +that's definitely true. + +So this graph shows, for things +for where we know the function, + +the semantic similarity +in the y-axis, + +the distance in the +network in the x-axis, + +things that are close to +each other in the network + +of interactions, are +also more likely to be + +similar in terms of function. + +So how do we go +about doing that? + +So let's say we +have got this graph. + +We've got some unknown +node labeled u. + +And we've got two +known nodes in black. + +And we want to systematically +deduce for every example + +like this, every u, what +its annotation should be. + +So I could just look +at its neighbors, + +and depending on how I +set the window around it, + +do I look at the +immediate neighbors? + +Do I go two out? + +Do I go three out? + +I could get different answers. + +So if I set K equal to 1, +I've got the unknown node, + +but all the neighbors +are also unknown. + +If I go two steps out, +then I pick up two knowns. + +Now there's a fundamental +assumption going on here + +that the node has the same +function as its neighbors, + +which is fine when the +neighbors are homogeneous. + +But what do you do when the +neighbors are heterogeneous? + +So in this case, I've +got two unknowns u and v. + +And if I just were to take +the K nearest neighbors, + +they would have the same +neighborhood, right? + +But I might have a prior +expectation that u is more like + +the black nodes, and v is +more like the grey nodes. + +So how do you choose +the best annotation? + +The K nearest neighbors is +OK, but it's not the optimal. + +So here's one approach, +which says the following. + +I'm going to go through +for every function, + +every annotation in my +database, separately. + +And for each annotation, +I'll set all the nodes that + +have that annotation to +plus 1 and every node + +that doesn't have that +annotation, either it's unknown + +or it's got some other +annotation, to minus 1. + +And then for every +unknown, I'm going + +to try to find the +setting which is going + +to maximize the sum of products. + +So we're going to take the +sum of the products of u + +and all of its neighbors. + +So in this setting, +if I set u to plus 1, + +then I do better than if I +set it to minus 1, right? + +Because I'll get plus +1 plus 1 minus 1. + +So that will be better +than setting it to minus 1. + +Yes. + +AUDIENCE: Are we ignoring +all the end weights? + +PROFESSOR: In this case, we're +ignoring the end weights. + +We'll come back to using +the end weights later. + +But this was done with +an unweighted graph. + +AUDIENCE: [INAUDIBLE] +[? nearest neighborhood ?] + +they're using it then? + +PROFESSOR: So here they're +using the nearest neighbors. + +That's right, with +no cutoff, right? + +So any interaction. + +So then we could iterate +this into convergence. + +That's one problem with this. + +But maybe a more +fundamental problem + +is that you're never going to +get the best overall solution + +by this local +optimization procedure. + +So consider a setting like this. + +Remember, I'm trying +to maximize the sum + +of the product of the +settings for neighbors. + +So how could I ever-- it seems +plausible that all A, B, and C + +here, should have the +red annotation, right? + +But if I set C to red, +that doesn't help me. + +If I set A to red, +that doesn't help me. + +If I set B to red, it +makes things worse. + +So no local change is going +to get me where I want to go. + +So let's think for a second. + +What algorithms +have we already seen + +that could help us get +to the right answer? + +We can't get here by +local optimization. + +We need to find the global +minimum, not the local minimum. + +So what algorithms +have we seen that + +help us find that +global minimum? + +Yeah, sorry, so a video +simulated annealing. + +So the simulated annealing +version in this setting + +is as follows. + +I initialize the graph. + +I pick a neighboring node, +v, that I'm going to add. + +Say we'll turn one of these red. + +I check the value of that sum of +the products for this new one. + +And if it's improving +things, I keep it. + +But the critical thing +is, if it doesn't improve, + +if it makes things +worse, I still + +keep it with some probability. + +It's based on how bad +things have gotten. + +And by doing this, +we can climb the hill + +and get over to +some global optimum. + +So we saw simulating before. + +In what context? + +When in the side chain +placement problem. + +Here we're seeing it again. + +It's quite broad. + +Any time you've got a +local optimization that + +doesn't get you +where you need to go, + +you need global optimization. + +You can think +simulated annealing. + +It's quite often the +plausible way to go. + +All right. + +So this is one approach +for annotation. + +We also wanted to see +whether we could discover + +inherent structure +in these graphs. + +So often, we'll be +interested in trying + +to find clusters in a graph. + +Some graphs have obvious +structures in them. + +Other graphs, it's a +little less obvious. + +What algorithms exist +for trying to do this? + +We're going to look at two +relatively straightforward + +ways. + +One is called edge +betweenness clustering + +and the other one +is a Markov process. + +Edge betweenness, I think, +is the most intuitive. + +So I look at each +edge, and I ask + +for all pairs of +nodes in the graph, + +does the shortest path +between those nodes + +pass through this edge? + +So if I look at this edge, +very few shortest paths + +go through this edge, right? + +Just the shortest path +for those two nodes. + +But if I look at this edge, +all of the shortest paths + +between any node on this side +and any node on this side + +have to pass through there. + +So that has a high betweenness. + +So if I want a cluster, I +can go through my graph. + +I can compute betweenness. + +I take the edge that has +the highest betweenness, + +and I remove it from my graph. + +And then I repeat. + +And I'll be slowly +breaking my graph down + +into chunks that are relatively +more connected internally + +than they are to +things in other pieces. + +Any questions? + +So that's an entire +edge betweenness + +clustering algorithm. + +Pretty straightforward. + +Now an alternative is a +Markov clustering method. + +And the Markov +clustering method is + +based on the idea of +random walks in the graph. + +So again, let's try to +develop some intuition here. + +If I start at some +node over here, + +and I randomly wander +across this graph, + +I'm more likely to stay +on the left-hand side + +than I am to move all the way +across to the right-hand side, + +correct? + +So can I formalize that +and actually come up + +with a measure of how +often any node will visit + +any other and then use +that to cluster the graph? + +So remember our +adjacency matrix, + +which just represented which +nodes were connected to which. + +And what happens if I multiply +the adjacency matrix by itself? + +So I raise it to some power. + +Well, if I multiply the +adjacency matrix by itself + +just once, the squared adjacency +matrix of the property, + +that it tells me how +many paths of length 2 + +exists between any two nodes. + +So the adjacency matrix told +me how many paths of length 1 + +exist. + +Right? + +You're directly connected. + +If I squared the +adjacency matrix, + +it tells me how many +paths of length 2 exist. + +N-th power tells me how many +paths of length N exist. + +So let's see if that works. + +This claims that +there are exactly + +two paths that connect +node 2 to node 2. + +What are those two paths? + +Connect node 2 to node 2. + +I go here, and I go back. + +That's the path of length 2, and +this is the path of length 2. + +And there are zero +paths of length 2 + +that connect node 2 to +node three, because 1, 2. + +I'm not back at 3. + +So that's from general +A to the N equals m, + +if there exists exactly m paths +of length N between those two + +nodes. + +So how does this help me? + +Well, when you take that idea of +the N-th power of the adjacency + +matrix and convert it to a +transition probability matrix, + +simply by normalizing. + +So if I were to do a +random walk in this graph, + +what's the probability +that I'll move from node i + +to node j in a certain +number of steps? + +That's what I want to compute. + +So I need to have a +stochastic matrix, + +where the sum of +the probabilities + +for any transition is 1. + +I have to end up somewhere. + +I either end up back +in myself, or I end up + +at some other nodes. + +I'm just going to take +that adjacency matrix + +and normalize the columns. + +And then that gives me +the stochastic matrix. + +And then I can exponentiate +the stochastic matrix + +to figure out my probability +of moving from any node + +to any other in a +certain number of steps. + +Any questions on that? + +OK. + +So if we simply keep multiplying +this stochasticity matrix, + +we'll get the probability of +increasing numbers of moves. + +But it doesn't give us sharp +partitions of the matrix. + +So to do a Markov clustering, +we do an exponentiation + +of this matrix with +what's called an inflation + +operator, which +is the following. + +This inflation operator +takes the r-th power + +of the adjacency matrix +and puts a denominator, + +the sum of the powers +of the transition. + +So here's an example. + +Let's say I've got two +probabilities-- 0.9 and 0.1. + +When I inflate it, I +square the numerator, + +and I square each element +of the denominator. + +Now I've gone from 0.9 +to 0.99 and 0.1 to 0.01. + +So this inflation +operator exaggerates + +all my probabilities and makes +the higher probabilities more + +probable and makes the lower +probabilities even less + +probable. + +So I take this +adjacency matrix that + +represents the number +of steps in my matrix, + +and I exaggerate it with +the inflation operator. + +And that takes the +basic clustering, + +and it makes it more compact. + +So the algorithm for this +Markov clustering is as follows. + +I start with a graph. + +I add loops to the graph. + +Why do I add loops? + +Because I need some probability +that I stay in the same place, + +right? + +And in a normal +adjacency matrix, + +you can't stay in +the same place. + +You have to go somewhere. + +So I add a loop. + +So there's always a self loop. + +Then I set the inflation +parameter to some value. + +M_1 is the matrix of random +walks in the original graph. + +I multiply that. + +I inflate it. + +And then I find the difference. + +And I do that until the +difference in this-- + +because this matrix +gets below some value. + +And what I end up with then +are relatively sharp partitions + +of the overall structure. + +So I'll show you an +example of how that works. + +So in this case, +the authors were + +using a matrix where the +nodes represented proteins. + +The edges represented +BLAST hits. + +And what they wanted +to do was find + +families of proteins +that had similar sequence + +similarity to each other. + +But they didn't want it to be +entirely dominated by domains. + +So they figured that this graph +structure would be helpful, + +because you'd get-- +for any protein, + +there'd be edges, +not just things + +that had similar common +domains, but also things that + +had edges connecting it +to other proteins as well. + +So in the original graph, the +edges are these BLAST values. + +They come up with the +transition matrix. + +They convert into +the Markov matrix, + +and they carry out +that exponentiation. + +And what they end +up with are clusters + +where any individual domain +can appear multiple clusters. + +The domains are dominated not +just by the highest BLAST hit, + +but by the whole network +property of what other proteins + +they're connected to. + +And it's also been done with a +network, where the underlying + +network represents +gene expression, + +and edges between two +genes represent the degree + +of correlation of the expression +across a very large data + +set for 61 mouse tissues. + +And once again, you +take the overall graph, + +and you can break it +down into clusters, + +where you can find +functional annotations + +for specific clusters. + +Any questions then on +the Markov clustering? + +So these are two +separate ways of looking + +at the underlying +structure of a graph. + +We had the edge betweenness +clustering and the Markov + +clustering. + +Now when you do this, you +have to make some decision, + +as I found this cluster. + +Now how do I decide +what it's doing? + +So you need to do some +sort of annotation. + +So once I have a +cluster, how am I + +going to assign a +function to that cluster? + +So one thing I could +do would be to look + +at things that already +have an annotation. + +So I got some cluster. + +Maybe two members +of this cluster + +have an annotation and +two members of this one. + +And that's fine. + +But what do I do +when a cluster has + +a whole bunch of +different annotations? + +So I could be arbitrary. + +I could just take the one +that's the most common. + +But a nice way to do it is by +the hypergeometric distribution + +that you saw in the earlier +part of the semester. + +So these are all ways of +clustering the underlying graph + +without any reference +to specific data + +for a particular condition +that you're interested in. + +A slightly harder +problem is when + +I do have those +specific data, and I'd + +like to find a piece +of the network that's + +most relevant to +those specific data. + +So it could be different +in different settings. + +Maybe the part of +the network that's + +relevant in the +cancer setting is not + +the part of the network that's +relevant in the diabetes + +setting. + +So one way to think about this +is that I have the network, + +and I paint onto +it my expression + +data or my proteomic data. + +And then I want to find +chunks of the network that + +are enriched in activity. + +So this is sometimes called +the active subgraph problem. + +And how do we find +the active subgraph? + +Well, it's not that +different from the problem + +that we just looked at. + +So if I want to figure out a +piece of the network that's + +active, I could just take the +things that are immediately + +connected to each other. + +That doesn't give me +the global picture. + +So instead why +don't I try to find + +larger chunks of +the network where + +I can include some +nodes for which I do not + +have specific data? + +And one way that's +been done for that + +is, again, the simulated +annealing approach. + +So you can try to find +pieces of the network that + +maximize the +probability that all + +the things in the +subnetwork are active. + +Another formulation +of this problem + +is something that's called +the Steiner tree problem. + +And in the Steiner tree, +I want to find trees + +in the network that consist of +all the nodes that are active, + +plus some nodes that are not, +for which I have no data. + +And those nodes for +which I have no data + +are called Steiner nodes. + +And this was a problem that +was looked at extensively + +in telecommunications. + +So if I want to wire up +a bunch of buildings-- + +back when people used wires-- +say to give telephone service, + +so I need to figure out +what the minimum cost is + +for wiring them all up. + +And sometimes, that involves +sticking a pole in the ground, + +then having everybody +communicate to that pole. + +So if I've got paying +customers over here, + +and I want to wire +them to each other, + +I could run wires +between everybody. + +But I don't have to. + +If I stick a pole over here, +then I don't need this wire, + +and I don't need this wire, +and I don't need this wire. + +So this is what's +called a Steiner node. + +And so in graph theory, there +are pretty efficient algorithms + +for finding a Steiner graph-- +the Steiner tree-- the smallest + +tree that connects +all of the nodes. + +Now the problem in our setting +is that we don't necessarily + +want to connect every +node, because we're + +going to have in our +data some things that + +are false positives. + +And if we connect too +many things in our graph, + +we end up with what are +lovingly called "hairballs." + +So I'll give you a +specific example of that. + +Here's some data that +we were working with. + +We had a relatively small +number of experimental hits that + +were detected as +changing in a cancer + +setting and the +interactome graph. + +And if you simply look +for the shortest path, + +I should say, between +the experimental hits + +across the +interactome, you end up + +with something that looks very +similar to the interactome. + +So you start off with a +relatively small set of nodes, + +and you try to find +the subnetwork that + +includes everything. + +And you get a giant graph. + +And it's very hard +to figure out what + +to do with a graph +that's this big. + +I mean, there may be +some information here, + +but you've taken a +relatively simple problem + +to try to understand the +relationship among these hits. + +And you've turned it +into a problem that + +now involves hundreds +and hundreds of nodes. + +So these kinds of +problems arise, as I said, + +in part, because of +noise in the data. + +So some of these +hits are not real. + +And incorporating +those, obviously, + +makes me take very long +paths in the interactome, + +but also arises because of +the noise in the interactome-- + +both false positives +and false negatives. + +So I have two proteins +that I'm trying to connect, + +and there's a false +positive in the interactome. + +It's going to draw +a line between them. + +If there's a false negative +in the interactome, + +maybe these things really do +interact, but there's no edge. + +If I force the algorithm +to find a connection, + +it probably can, because +most of the interactome + +is one giant +connected component. + +But it could be a +very, very long edge. + +It goes through +many other proteins. + +And so in the process of +trying to connect all my data, + +I can get extremely +large graphs. + +So to avoid having +giant networks-- + +so on this projector, +unfortunately, you + +can't see this very well. + +But there are a lot of edges +among all the nodes here. + +Most of you have your computers. + +You can look at it there. + +So in a Steiner tree +approach, if my data + +are the ones that are yellow, +they're called terminals. + +And the grey ones, +I have no data. + +And I ask to try to solve +the Steiner tree problem, + +it's going to have to find a +way to connect this node up + +to the rest of the network. + +But if this one's +a false positive, + +that's not the desired outcome. + +So there are +optimization techniques + +that actually allow me to +tell the algorithm that it's + +OK to leave out some of the data +to get a more compact network. + +So one of those approaches +is called a prize + +collecting Steiner tree problem. + +And the idea here +is the following. + +For every node for which +I have experimental data, + +I associate with +that node a prize. + +The prize is larger, +the more confident + +I am that that node is +relevant in the experiment. + +And for every edge, +I take the edge away, + +and I convert it into a cost. + +If I have a high confidence +edge, there's a low cost. + +It's cheap. + +Low confidence edges are +going to be very expensive. + +And now I ask the +algorithm to try + +to connect up all +the things it can. + +Every time it includes a +node for which the zeta keeps + +the prize, but it had to add +an edge, so it pays the cost. + +So there's a trade-off +for every node. + +So if the algorithm wants +to include this node, + +then it's going to pay the +price for all the edges, + +but it gets to keep the node. + +So the optimization +function is the following. + +For every vertex that's not in +the tree, there's a penalty. + +And for every edge in +the tree, there's a cost. + +And you want to minimize +the sum of these two terms. + +You want to minimize the number +of edge costs you pay for. + +And you want to +minimize the number + +of prizes you leave behind. + +Is that clear? + +So then the algorithm then can, +depending on the optimization + +terms, figure out is it more of +a benefit to include this node, + +keep the prize, and pay all +the edge costs or the opposite? + +Throw it out. + +You don't get to keep +the prize, but you + +don't have to pay +the edge costs. + +And so that turns these +very, very large networks + +into relatively compact ones. + +Now solving this problem is +actually rather computationally + +challenging. + +You can do it with integer +linear programming. + +It takes a huge +amount of memory. + +There's also signal and +message passing approach. + +If you're interested in +the underlying algorithms, + +you can look at some +of these papers. + +So what happens when +you actually do this? + +So that hairball that +I showed you before + +consisted of a very +small initial data set. + +If you do a shortest path +search across the network, + +you get thousands +of edges shown here. + +But the prize collecting Steiner +tree solution to this problem + +is actually extremely compact, +and it consists of subnetworks. + +You can cluster +it automatically. + +This was clustered by hand, +but you get more or less + +the same results. + +It's just not quite as pretty. + +If you cluster by hand or by +say, edge betweenness, then + +you get subnetworks +that are enriched + +in various reasonable +cellular processes. + +This was a network +built from cancer data. + +And you can see things that are +highly relevant to cancer-- DNA + +damage, cell cycle, and so on. + +And the really nice +thing about this + +then is it gives you +a very focused way + +to then go and do experiments. + +So you can take the networks +that come out of it. + +And now you're not +operating on a network that + +consists of tens of +thousands of edges. + +You're working on a +network that consists + +of very small sets of proteins. + +So in this particular +case, we actually + +were able to go in and test +the number of the nodes that + +were not detected by +the experimental data, + +but were inferred by the +algorithms of the Steiner + +nodes, which had no +direct experimental data. + +We will test whether blocking +the activities of these nodes + +had any effect on the +growth of these tumor cells. + +We will show that +nodes that were + +very central to the +network that were included + +in the prize collecting +Steiner tree solution, + +had a high probability +of being cancer targets. + +Whereas the ones that were +just slightly more removed + +were much lower in probability. + +So one of the advantages of +these large interaction graphs + +is they give us a +natural way to integrate + +many different kinds of data. + +So we already saw that the +protein levels and the mRNA + +levels agreed very +poorly with each other. + +And we talked about +the fact that one thing + +you could do with +those data would + +be to try to find the +connections between not + +the RNAs and the proteins, +but the connections + +between the RNAs +and the things that + +drove the expression of the RNA. + +And so as I said, we'll see +in one of Professor Gifford's + +lectures, precisely +how to do that. + +But once you are able to do +that, you take epigenetic data, + +look at the regions that are +regulatory around the sites + +of genes that are +changing in transcription. + +You can infer DNA +binding proteins. + +And then you can +pile all those data + +onto an interaction +graph, where you've + +got different kinds of edges. + +So you've got RNA nodes that +represent the transcript + +levels. + +You've got the +transcription factors + +that infer from the +epigenetic data. + +And then you've got the +protein-protein interaction + +data that came from +the two hybrid, + +the affinity capture mass spec. + +And now you can put all +those different kinds + +of data in the same graph. + +And even though +there's no correlation + +between what happens in an RNA +and what happens in the protein + +level-- or very +low correlation-- + +there's this +physical process that + +links that RNA up +to the signaling + +pathways that are above it. + +And by using the prize +collecting Steiner tree + +approaches, you can rediscover. + +And these kinds +of networks can be + +very valuable for other kinds +of data that don't agree. + +So it's not unique to transcript +data and proteome data. + +Turns out there are many +different kinds of omic data, + +when looked at individually, +give you very different views + +of what's going on in a cell. + +So if you take knockout data, +so which genes when knocked out, + +affect the phenotype? + +And which genes, in +the same condition, + +change an expression? + +Those give you two +completely different answers + +about which genes are important +in a particular setting. + +So here we're looking at +which genes are differentially + +expressed when you put +cells under a whole bunch + +of these different conditions. + +And which genes +when knocked out, + +affect viability +in that condition. + +And then the right-hand +column shows the overlap + +in the number of genes. + +And you can see the +overlap is small. + +In fact, it's less +than you would + +expect by chance +for most of these. + +So just to drill that home, if +I do two separate experiments + +on exactly the same +experimental system, + +say yeast responding +to DNA damage. + +And in one case, +I read out which + +genes are important by +looking at RNA levels. + +And the other one, +I read out which + +genes are important by knocking +every gene out and seeing + +whether it affects viability. + +We'll get two completely +different sets of genes. + +And we'll also have two +completely different sets + +of gene ontology categories. + +But there is some underlying +biological process + +that gives rise to that, right? + +And one of the +reasons for this is + +different assays are +measuring different things. + +So it turns out, if you +look-- at least in yeast-- + +over 156 different +experiments, for which there's + +both transcriptional +data and genetic data, + +the things that come +out in genetic screens + +seem to be master regulators. + +Things that were knocked out +have a big effect in phenotype. + +Whereas the things that +change in expression + +tend to be effector molecules. + +And so in say, the +DNA damage case, + +the proteins that +were knocked out + +and have a big +effect on phenotype + +are ones that detect DNA damage +and signal to the nucleus + +that there's been +changes in DNA damage + +that then goes on and +blocks the cell cycle, + +initiates DNA +response to repair. + +Those things show +up as genetic hits, + +but they don't show up as +differentially expressed. + +The things that do show up +as differentially expressed, + +the repair enzymes. + +Those, when you +knock them out, don't + +have a big effect on +phenotype, because they're + +highly redundant. + +But there are these +underlying pathways. + +And so the idea is well, you +could reconstruct these by, + +again, using the +epigenetic data, + +the tough stuff +Professor Gifford + +will talk about in +upcoming lectures. + +And for the transcription +factors and then the network + +properties, to try to build +up a full network of how those + +relate to upstream +signaling pathways + +that would then include +some of the genetic hits. + +I think I'll skip to +the punchline here. + +So we've looked at a number of +different modeling approaches + +for these large interactomes. + +We've also looked at +ways of identifying + +transcriptional +regulatory networks using + +mutual information, +regression, Bayesian networks. + +And how do all these +things fit together? + +And when would you want to +use one of these techniques, + +and when would you +want to use another? + +So I like to think about the +problem along these two axes. + +On one dimension, +we're thinking about + +whether we have systems of +known components or unknown + +components. + +And the other one +is whether we want + +to identify physical +relationships + +or statistical relationships. + +So clustering, regression, +mutual information-- those + +are very, very +powerful for looking + +at the entire genome, +the entire proteome. + +What they give you are +statistical relationships. + +There's no guarantee of +a functional link, right? + +We saw that in the prediction +that postprandial laughter + +predicts breast cancer +outcome, that there's + +no causal link between those. + +Ultimately, you can +find some reason + +why it's not totally random. + +But it's not as if +that's going to lead you + +to new drug targets. + +But those can be on a +completely hypothesis-free way, + +with no external data. + +Bayesian networks are +somewhat more causal. + +But depending on how +much data you have, + +they may not be +perfectly causal. + +You need a lot of +intervention data. + +We also saw that they did +not perform particularly + +well in discovering +gene regulatory networks + +in the dream challenge. + +These interactome +models that we've just + +been talking about work very +well across giant omic data + +sets. + +And they require +this external data. + +They need the interactome. + +So it works well in +organisms for which + +you have all that +interactome data. + +It's not going to work in an +organism for which you don't. + +What they give you +at the end, though, + +is a graph that tells +you relationships + +among the proteins. + +But it doesn't tell +you what's going + +to happen if you start to +perturb those networks. + +So if I give you the +active subgraph that + +has all the proteins and genes +that are changing expression + +in my tumor sample, now +the question is, OK, + +should you inhibit the +nodes in that graph? + +Or should you activate +the nodes in that graph? + +And the interactome +model doesn't tell you + +the answer to that. + +And so what you're going to +hear about in the next lecture + +from Professor +Lauffenburger are models + +that live up in this space. + +Once you've defined a relatively +small piece of the network, + +you can use other kinds +of approaches-- logic + +based models, differential +equation based models, decision + +trees, and other techniques +that will actually + +make very quantitative +processions. + +What happens if I inhibit +a particular node? + +Does it activate the process, +or does it repress the process? + +And so what you could +think about then + +is going from a completely +unbiased view of what's + +going in a cell, collect all +the various kinds of omic data, + +and go through these +kinds of modeling + +approaches to identify a +subnetwork that's of interest. + +And then use the techniques +that we'll [? be hearing ?] + +about in the next lecture +to figure out quantitatively + +what would happen if I were +to inhibit individual nodes + +or inhibit combinations of +nodes or activate, and so on. + +Any questions on anything +we've talked about so far? + +Yes. + +AUDIENCE: Can you say again +the fundamental difference + +between why you get those two +different results if you're + +just weeding out the gene +expression versus the proteins? + +PROFESSOR: Oh, sure. + +Right. + +So we talked about the fact that +if you look at genetic hits, + +and you look at +differential expression, + +you get two completely different +views of what's going in cells. + +So why is that? + +So the genetic hits to tend to +hit master regulators, things + +that when you knock +out a single gene, + +you have a global +effect on the response. + +So in the case of +DNA damage, those + +are things that +detect the DNA damage. + +Those genes tend often not +to be changing very much + +in expression. + +So transcription factors +are very low abundance. + +They usually don't +change very much. + +A lot of signaling proteins +are kept at a constant level, + +and they're regulated +post-transcriptionally. + +So those don't show up in +the differential expression. + +The things that are +changing in expression-- + +say the response regulators, +the DNA damage response-- + +those often are redundant. + +So one good analogy is to +think about a smoke detector. + +A smoke detector +is on all the time. + +You don't wait until the fire. + +So that's not going to be +changing in expression, + +if you will. + +But if you knock it out, +you've got a big problem. + +The effectors, say +the sprinklers-- + +the sprinklers only come +on when there's a fire. + +So that's like the +response genes. + +They come on only in +certain circumstances, + +but they're highly redundant. + +Any room will have +multiple sprinklers, + +so if one gets +damaged or is blocked, + +you still get a response. + +So that's why you get this +discrepancy between the two + +different kinds of data. + +But again, in both +cases, there's + +an underlying physical process +that gives rise to both. + +And if you do this +properly, you can + +detect that on these +interactome models. + +Other questions? + +OK. + +Very good. \ No newline at end of file diff --git a/S8FDEtLNjz4.txt b/S8FDEtLNjz4.txt new file mode 100644 index 0000000000000000000000000000000000000000..f53eebf3acc0e551c5cd24f947eea15153e76c40 --- /dev/null +++ b/S8FDEtLNjz4.txt @@ -0,0 +1,731 @@ +align:start position:0% + +surface currents induced in a ground + + align:start position:0% +surface currents induced in a ground + + + align:start position:0% +surface currents induced in a ground +plane by an overhead conductor + + align:start position:0% +plane by an overhead conductor + + + align:start position:0% +plane by an overhead conductor +illustrate the method of images also + + align:start position:0% +illustrate the method of images also + + + align:start position:0% +illustrate the method of images also +Illustrated is the superposition of + + align:start position:0% +Illustrated is the superposition of + + + align:start position:0% +Illustrated is the superposition of +fields due to line currents to satisfy + + align:start position:0% +fields due to line currents to satisfy + + + align:start position:0% +fields due to line currents to satisfy +boundary + + align:start position:0% +boundary + + + align:start position:0% +boundary +conditions now the situation is Magneto + + align:start position:0% +conditions now the situation is Magneto + + + align:start position:0% +conditions now the situation is Magneto +quasy static + + align:start position:0% +quasy static + + + align:start position:0% +quasy static +mqs here's the metal cylinder mounted + + align:start position:0% +mqs here's the metal cylinder mounted + + + align:start position:0% +mqs here's the metal cylinder mounted +over the metal ground plane the cylinder + + align:start position:0% +over the metal ground plane the cylinder + + + align:start position:0% +over the metal ground plane the cylinder +is driven by a current Source at one end + + align:start position:0% +is driven by a current Source at one end + + + align:start position:0% +is driven by a current Source at one end +and is shorted to the ground plane at + + align:start position:0% +and is shorted to the ground plane at + + + align:start position:0% +and is shorted to the ground plane at +the other + + align:start position:0% + + + + align:start position:0% + +end the ground plane consists of an + + align:start position:0% +end the ground plane consists of an + + + align:start position:0% +end the ground plane consists of an +aluminum sheet having a thickness of + + align:start position:0% +aluminum sheet having a thickness of + + + align:start position:0% +aluminum sheet having a thickness of +about 1 mm it's resting on a plywood + + align:start position:0% + + + + align:start position:0% + +base our magnetic field is the same as + + align:start position:0% +base our magnetic field is the same as + + + align:start position:0% +base our magnetic field is the same as +that due to a line current here just + + align:start position:0% +that due to a line current here just + + + align:start position:0% +that due to a line current here just +below the center of the conductor and + + align:start position:0% +below the center of the conductor and + + + align:start position:0% +below the center of the conductor and +its image here below the ground plane + + align:start position:0% + + + + align:start position:0% + +when we drive a current from a 3 KZ + + align:start position:0% +when we drive a current from a 3 KZ + + + align:start position:0% +when we drive a current from a 3 KZ +Source through the circular conductor + + align:start position:0% +Source through the circular conductor + + + align:start position:0% +Source through the circular conductor +the actual currents are in the metal + + align:start position:0% +the actual currents are in the metal + + + align:start position:0% +the actual currents are in the metal +conductor walls distributed in just such + + align:start position:0% +conductor walls distributed in just such + + + align:start position:0% +conductor walls distributed in just such +a way that there is no magnetic flux + + align:start position:0% +a way that there is no magnetic flux + + + align:start position:0% +a way that there is no magnetic flux +normal to every point on a given + + align:start position:0% +normal to every point on a given + + + align:start position:0% +normal to every point on a given +conductor + + align:start position:0% +conductor + + + align:start position:0% +conductor +surface similarly these currents are + + align:start position:0% +surface similarly these currents are + + + align:start position:0% +surface similarly these currents are +returned in the ground plane in just + + align:start position:0% +returned in the ground plane in just + + + align:start position:0% +returned in the ground plane in just +such a way that there is essentially no + + align:start position:0% +such a way that there is essentially no + + + align:start position:0% +such a way that there is essentially no +magnetic flux density normal to the + + align:start position:0% +magnetic flux density normal to the + + + align:start position:0% +magnetic flux density normal to the +ground plane either we can measure the + + align:start position:0% +ground plane either we can measure the + + + align:start position:0% +ground plane either we can measure the +maget magnetic field using this + + align:start position:0% +maget magnetic field using this + + + align:start position:0% +maget magnetic field using this +induction + + align:start position:0% + + + + align:start position:0% + +coil the induced voltage is related + + align:start position:0% +coil the induced voltage is related + + + align:start position:0% +coil the induced voltage is related +through Faraday's law to the time rate + + align:start position:0% +through Faraday's law to the time rate + + + align:start position:0% +through Faraday's law to the time rate +of change of the link magnetic + + align:start position:0% + + + + align:start position:0% + +flux with the coil oriented this way the + + align:start position:0% +flux with the coil oriented this way the + + + align:start position:0% +flux with the coil oriented this way the +vertical field component is + + align:start position:0% +vertical field component is + + + align:start position:0% +vertical field component is +recorded when oriented this way the + + align:start position:0% +recorded when oriented this way the + + + align:start position:0% +recorded when oriented this way the +horizontal field component is measured + + align:start position:0% + + + + align:start position:0% + +here at the center line the tangential + + align:start position:0% +here at the center line the tangential + + + align:start position:0% +here at the center line the tangential +field is horizontal just because of + + align:start position:0% +field is horizontal just because of + + + align:start position:0% +field is horizontal just because of +symmetry let's see if the flux density + + align:start position:0% +symmetry let's see if the flux density + + + align:start position:0% +symmetry let's see if the flux density +normal to the conducting sheet does tend + + align:start position:0% +normal to the conducting sheet does tend + + + align:start position:0% +normal to the conducting sheet does tend +to be zero off the center + + align:start position:0% +to be zero off the center + + + align:start position:0% +to be zero off the center +line here to the side the normal flux + + align:start position:0% +line here to the side the normal flux + + + align:start position:0% +line here to the side the normal flux +density appears to remain small compared + + align:start position:0% +density appears to remain small compared + + + align:start position:0% +density appears to remain small compared +to that + + align:start position:0% + + + + align:start position:0% + +tangential so the current is returned in + + align:start position:0% +tangential so the current is returned in + + + align:start position:0% +tangential so the current is returned in +the sheet with just that distribution + + align:start position:0% +the sheet with just that distribution + + + align:start position:0% +the sheet with just that distribution +required to make the normal flux density + + align:start position:0% + + + + align:start position:0% + +small as the sensing coil is moved out + + align:start position:0% +small as the sensing coil is moved out + + + align:start position:0% +small as the sensing coil is moved out +from under the conductor the tangential + + align:start position:0% +from under the conductor the tangential + + + align:start position:0% +from under the conductor the tangential +flux density + + align:start position:0% +flux density + + + align:start position:0% +flux density +decreases because there is little normal + + align:start position:0% +decreases because there is little normal + + + align:start position:0% +decreases because there is little normal +flux density just above the sheet there + + align:start position:0% +flux density just above the sheet there + + + align:start position:0% +flux density just above the sheet there +is little of either of the components of + + align:start position:0% +is little of either of the components of + + + align:start position:0% +is little of either of the components of +magnetic field below the sheet so so + + align:start position:0% +magnetic field below the sheet so so + + + align:start position:0% +magnetic field below the sheet so so +what we see is the distribution of + + align:start position:0% +what we see is the distribution of + + + align:start position:0% +what we see is the distribution of +surface current density returning in the + + align:start position:0% +surface current density returning in the + + + align:start position:0% +surface current density returning in the +sheet at high frequency the current + + align:start position:0% +sheet at high frequency the current + + + align:start position:0% +sheet at high frequency the current +distributes itself in the sheet in just + + align:start position:0% +distributes itself in the sheet in just + + + align:start position:0% +distributes itself in the sheet in just +such a way as to make the normal flux + + align:start position:0% +such a way as to make the normal flux + + + align:start position:0% +such a way as to make the normal flux +density near + + align:start position:0% + + + + align:start position:0% + +zero our experiments have shown that the + + align:start position:0% +zero our experiments have shown that the + + + align:start position:0% +zero our experiments have shown that the +perpendicular field at the surface of + + align:start position:0% +perpendicular field at the surface of + + + align:start position:0% +perpendicular field at the surface of +the ground plane is much smaller than + + align:start position:0% +the ground plane is much smaller than + + + align:start position:0% +the ground plane is much smaller than +the tangential + + align:start position:0% +the tangential + + + align:start position:0% +the tangential +field this is true because the frequency + + align:start position:0% +field this is true because the frequency + + + align:start position:0% +field this is true because the frequency +of 3 khz is high enough that the ground + + align:start position:0% +of 3 khz is high enough that the ground + + + align:start position:0% +of 3 khz is high enough that the ground +plane behaves as a perfect conductor + + align:start position:0% +plane behaves as a perfect conductor + + + align:start position:0% +plane behaves as a perfect conductor +let's see what happens if we lower the + + align:start position:0% + + + + align:start position:0% + +frequency if we reduce the frequency by + + align:start position:0% +frequency if we reduce the frequency by + + + align:start position:0% +frequency if we reduce the frequency by +10 to 300 Hertz the induced volage + + align:start position:0% +10 to 300 Hertz the induced volage + + + align:start position:0% +10 to 300 Hertz the induced volage +decreases by 10 that's just because of + + align:start position:0% +decreases by 10 that's just because of + + + align:start position:0% +decreases by 10 that's just because of +Faraday's law so let's compensate by + + align:start position:0% +Faraday's law so let's compensate by + + + align:start position:0% +Faraday's law so let's compensate by +turning up the scope gain by 10 + + align:start position:0% + + + + align:start position:0% + +at this lower frequency we see that the + + align:start position:0% +at this lower frequency we see that the + + + align:start position:0% +at this lower frequency we see that the +ratio of normal component to tangential + + align:start position:0% +ratio of normal component to tangential + + + align:start position:0% +ratio of normal component to tangential +component is larger than a 3 + + align:start position:0% +component is larger than a 3 + + + align:start position:0% +component is larger than a 3 +khz at 300 Hertz here's the tangential + + align:start position:0% +khz at 300 Hertz here's the tangential + + + align:start position:0% +khz at 300 Hertz here's the tangential +component and here's the normal + + align:start position:0% +component and here's the normal + + + align:start position:0% +component and here's the normal +component at 3 + + align:start position:0% + + + + align:start position:0% + +khz here's the normal component and and + + align:start position:0% +khz here's the normal component and and + + + align:start position:0% +khz here's the normal component and and +here's the tangential + + align:start position:0% + + + + align:start position:0% + +component at 3 khz the ground plane is + + align:start position:0% +component at 3 khz the ground plane is + + + align:start position:0% +component at 3 khz the ground plane is +thick enough to act as a perfect + + align:start position:0% +thick enough to act as a perfect + + + align:start position:0% +thick enough to act as a perfect +conductor + + align:start position:0% +conductor + + + align:start position:0% +conductor +giving the tangential field predicted + + align:start position:0% +giving the tangential field predicted + + + align:start position:0% +giving the tangential field predicted +using the fields of a line current and + + align:start position:0% +using the fields of a line current and + + + align:start position:0% +using the fields of a line current and +its image \ No newline at end of file diff --git a/SBWns1XNcuY.txt b/SBWns1XNcuY.txt new file mode 100644 index 0000000000000000000000000000000000000000..0df99ec3cf93f00c53eb7cd1fa7006e767e7bf21 --- /dev/null +++ b/SBWns1XNcuY.txt @@ -0,0 +1,1315 @@ +align:start position:0% + +in this video we will do some basic data + + align:start position:0% +in this video we will do some basic data + + + align:start position:0% +in this video we will do some basic data +analysis all that I've done since our + + align:start position:0% +analysis all that I've done since our + + + align:start position:0% +analysis all that I've done since our +previous video is clear the console but + + align:start position:0% +previous video is clear the console but + + + align:start position:0% +previous video is clear the console but +our still has all the information stored + + align:start position:0% +our still has all the information stored + + + align:start position:0% +our still has all the information stored +in fact if we use the up arrow on our + + align:start position:0% +in fact if we use the up arrow on our + + + align:start position:0% +in fact if we use the up arrow on our +keyboard we retrieve the last command we + + align:start position:0% +keyboard we retrieve the last command we + + + align:start position:0% +keyboard we retrieve the last command we +typed which was the summary of the USDA + + align:start position:0% +typed which was the summary of the USDA + + + align:start position:0% +typed which was the summary of the USDA +data frame and as a quick reminder at + + align:start position:0% +data frame and as a quick reminder at + + + align:start position:0% +data frame and as a quick reminder at +the end of our last video we realize + + align:start position:0% +the end of our last video we realize + + + align:start position:0% +the end of our last video we realize +that the maximum level of sodium was 38 + + align:start position:0% +that the maximum level of sodium was 38 + + + align:start position:0% +that the maximum level of sodium was 38 +thousand seven hundred and fifty eight + + align:start position:0% +thousand seven hundred and fifty eight + + + align:start position:0% +thousand seven hundred and fifty eight +milligrams which is very high we would + + align:start position:0% +milligrams which is very high we would + + + align:start position:0% +milligrams which is very high we would +like to see which food this corresponds + + align:start position:0% +like to see which food this corresponds + + + align:start position:0% +like to see which food this corresponds +to well to check the values of sodium + + align:start position:0% +to well to check the values of sodium + + + align:start position:0% +to well to check the values of sodium +levels and the foods within the data set + + align:start position:0% +levels and the foods within the data set + + + align:start position:0% +levels and the foods within the data set +we can type USDA dollar signs + + align:start position:0% +we can type USDA dollar signs + + + align:start position:0% +we can type USDA dollar signs +sodium this gives us a series of numbers + + align:start position:0% +sodium this gives us a series of numbers + + + align:start position:0% +sodium this gives us a series of numbers +associated with the amount of sodium and + + align:start position:0% +associated with the amount of sodium and + + + align:start position:0% +associated with the amount of sodium and +all the foods in our data set remember + + align:start position:0% +all the foods in our data set remember + + + align:start position:0% +all the foods in our data set remember +from the lecture that this is called a + + align:start position:0% +from the lecture that this is called a + + + align:start position:0% +from the lecture that this is called a +vector and it is associated with the + + align:start position:0% +vector and it is associated with the + + + align:start position:0% +vector and it is associated with the +variable sodium for instance the sodium + + align:start position:0% +variable sodium for instance the sodium + + + align:start position:0% +variable sodium for instance the sodium +level of the last food in our data set + + align:start position:0% +level of the last food in our data set + + + align:start position:0% +level of the last food in our data set +is 68 milligrams + + align:start position:0% +is 68 milligrams + + + align:start position:0% +is 68 milligrams +now to find which food has the highest + + align:start position:0% +now to find which food has the highest + + + align:start position:0% +now to find which food has the highest +level of sodium we can simply use the + + align:start position:0% +level of sodium we can simply use the + + + align:start position:0% +level of sodium we can simply use the +function which dot max which takes as an + + align:start position:0% +function which dot max which takes as an + + + align:start position:0% +function which dot max which takes as an +input the sodium vector and it gives us + + align:start position:0% +input the sodium vector and it gives us + + + align:start position:0% +input the sodium vector and it gives us +the index of the food with the highest + + align:start position:0% +the index of the food with the highest + + + align:start position:0% +the index of the food with the highest +sodium level in this case the 264 food + + align:start position:0% +sodium level in this case the 264 food + + + align:start position:0% +sodium level in this case the 264 food +in our data set has the maximum sodium + + align:start position:0% +in our data set has the maximum sodium + + + align:start position:0% +in our data set has the maximum sodium +content now to know which food that is + + align:start position:0% +content now to know which food that is + + + align:start position:0% +content now to know which food that is +we need to take a look at the vector + + align:start position:0% +we need to take a look at the vector + + + align:start position:0% +we need to take a look at the vector +corresponding to the text description of + + align:start position:0% +corresponding to the text description of + + + align:start position:0% +corresponding to the text description of +the foods however I cannot remember the + + align:start position:0% +the foods however I cannot remember the + + + align:start position:0% +the foods however I cannot remember the +exact name of that variable on top of my + + align:start position:0% +exact name of that variable on top of my + + + align:start position:0% +exact name of that variable on top of my +hat to be able to call it an R but we + + align:start position:0% +hat to be able to call it an R but we + + + align:start position:0% +hat to be able to call it an R but we +can use the function names which takes + + align:start position:0% +can use the function names which takes + + + align:start position:0% +can use the function names which takes +as an input the USDA data frame and + + align:start position:0% +as an input the USDA data frame and + + + align:start position:0% +as an input the USDA data frame and +gives us the exact names of all the + + align:start position:0% +gives us the exact names of all the + + + align:start position:0% +gives us the exact names of all the +variables are stored in the USDA data + + align:start position:0% +variables are stored in the USDA data + + + align:start position:0% +variables are stored in the USDA data +frame and now we know that the name of + + align:start position:0% +frame and now we know that the name of + + + align:start position:0% +frame and now we know that the name of +the variable we're looking at is + + align:start position:0% +the variable we're looking at is + + + align:start position:0% +the variable we're looking at is +description so now to get the name of + + align:start position:0% +description so now to get the name of + + + align:start position:0% +description so now to get the name of +the 265th food we simply need to ask R + + align:start position:0% +the 265th food we simply need to ask R + + + align:start position:0% +the 265th food we simply need to ask R +to pick the 260 fifth element from the + + align:start position:0% +to pick the 260 fifth element from the + + + align:start position:0% +to pick the 260 fifth element from the +vector description so using our dollar + + align:start position:0% +vector description so using our dollar + + + align:start position:0% +vector description so using our dollar +notation to call the description vector + + align:start position:0% +notation to call the description vector + + + align:start position:0% +notation to call the description vector +and then the square brackets around + + align:start position:0% +and then the square brackets around + + + align:start position:0% +and then the square brackets around +index 265 and the winner is table salt + + align:start position:0% +index 265 and the winner is table salt + + + align:start position:0% +index 265 and the winner is table salt +well having thirty eight thousand seven + + align:start position:0% +well having thirty eight thousand seven + + + align:start position:0% +well having thirty eight thousand seven +hundred and fifty eight milligrams of + + align:start position:0% +hundred and fifty eight milligrams of + + + align:start position:0% +hundred and fifty eight milligrams of +sodium in 100 grams of table salt sort + + align:start position:0% +sodium in 100 grams of table salt sort + + + align:start position:0% +sodium in 100 grams of table salt sort +of makes sense but none of us will eat + + align:start position:0% +of makes sense but none of us will eat + + + align:start position:0% +of makes sense but none of us will eat +100 grams of salt in one sitting so it + + align:start position:0% +100 grams of salt in one sitting so it + + + align:start position:0% +100 grams of salt in one sitting so it +might be more interesting to find out + + align:start position:0% +might be more interesting to find out + + + align:start position:0% +might be more interesting to find out +which foods for instance contain more + + align:start position:0% +which foods for instance contain more + + + align:start position:0% +which foods for instance contain more +than say ten thousand milligrams of + + align:start position:0% +than say ten thousand milligrams of + + + align:start position:0% +than say ten thousand milligrams of +sodium to do so we can create a new data + + align:start position:0% +sodium to do so we can create a new data + + + align:start position:0% +sodium to do so we can create a new data +frame and let's call it high sodium and + + align:start position:0% +frame and let's call it high sodium and + + + align:start position:0% +frame and let's call it high sodium and +this is going to be a subset of our + + align:start position:0% +this is going to be a subset of our + + + align:start position:0% +this is going to be a subset of our +original data frame USDA with only the + + align:start position:0% +original data frame USDA with only the + + + align:start position:0% +original data frame USDA with only the +foods that have sodium content that + + align:start position:0% +foods that have sodium content that + + + align:start position:0% +foods that have sodium content that +exceeds ten thousand and now we created + + align:start position:0% +exceeds ten thousand and now we created + + + align:start position:0% +exceeds ten thousand and now we created +this new data frame and to see how many + + align:start position:0% +this new data frame and to see how many + + + align:start position:0% +this new data frame and to see how many +foods there exist in this new data frame + + align:start position:0% +foods there exist in this new data frame + + + align:start position:0% +foods there exist in this new data frame +we need to see how many observations + + align:start position:0% +we need to see how many observations + + + align:start position:0% +we need to see how many observations +this data frame has and this can be done + + align:start position:0% +this data frame has and this can be done + + + align:start position:0% +this data frame has and this can be done +by using the function n row which + + align:start position:0% +by using the function n row which + + + align:start position:0% +by using the function n row which +computes the number of rows in the data + + align:start position:0% +computes the number of rows in the data + + + align:start position:0% +computes the number of rows in the data +frame high sodium and then we obtain ten + + align:start position:0% +frame high sodium and then we obtain ten + + + align:start position:0% +frame high sodium and then we obtain ten +foods for sodium levels above ten + + align:start position:0% +foods for sodium levels above ten + + + align:start position:0% +foods for sodium levels above ten +thousand milligrams since they're not + + align:start position:0% +thousand milligrams since they're not + + + align:start position:0% +thousand milligrams since they're not +many we can output the names of these + + align:start position:0% +many we can output the names of these + + + align:start position:0% +many we can output the names of these +foods by looking at their description + + align:start position:0% +foods by looking at their description + + + align:start position:0% +foods by looking at their description +vector but this time the description + + align:start position:0% +vector but this time the description + + + align:start position:0% +vector but this time the description +vector is not associated with the USDA + + align:start position:0% +vector is not associated with the USDA + + + align:start position:0% +vector is not associated with the USDA +data frame but with the high sodium data + + align:start position:0% +data frame but with the high sodium data + + + align:start position:0% +data frame but with the high sodium data +frame so high sodium dollar-sign + + align:start position:0% +frame so high sodium dollar-sign + + + align:start position:0% +frame so high sodium dollar-sign +description and now pressing enter we + + align:start position:0% +description and now pressing enter we + + + align:start position:0% +description and now pressing enter we +obtained the names of these ten foods so + + align:start position:0% +obtained the names of these ten foods so + + + align:start position:0% +obtained the names of these ten foods so +definitely table salt is one of them we + + align:start position:0% +definitely table salt is one of them we + + + align:start position:0% +definitely table salt is one of them we +also have dry soup gravy some leavening + + align:start position:0% +also have dry soup gravy some leavening + + + align:start position:0% +also have dry soup gravy some leavening +agents but I thought caviar is well + + align:start position:0% +agents but I thought caviar is well + + + align:start position:0% +agents but I thought caviar is well +known to be among the top 10 foods with + + align:start position:0% +known to be among the top 10 foods with + + + align:start position:0% +known to be among the top 10 foods with +highest levels of sodium but it doesn't + + align:start position:0% +highest levels of sodium but it doesn't + + + align:start position:0% +highest levels of sodium but it doesn't +appear in this list + + align:start position:0% +appear in this list + + + align:start position:0% +appear in this list +let's find how much sodium it has in 100 + + align:start position:0% +let's find how much sodium it has in 100 + + + align:start position:0% +let's find how much sodium it has in 100 +grams now obviously this task would have + + align:start position:0% +grams now obviously this task would have + + + align:start position:0% +grams now obviously this task would have +been very easy if we knew the index of + + align:start position:0% +been very easy if we knew the index of + + + align:start position:0% +been very easy if we knew the index of +caviar in our data set and we simply + + align:start position:0% +caviar in our data set and we simply + + + align:start position:0% +caviar in our data set and we simply +feed it into the vector sodium however + + align:start position:0% +feed it into the vector sodium however + + + align:start position:0% +feed it into the vector sodium however +we need to get the index of caviar and + + align:start position:0% +we need to get the index of caviar and + + + align:start position:0% +we need to get the index of caviar and +to do this we need to track down the + + align:start position:0% +to do this we need to track down the + + + align:start position:0% +to do this we need to track down the +word caviar + + align:start position:0% +word caviar + + + align:start position:0% +word caviar +the text description to do this we can + + align:start position:0% +the text description to do this we can + + + align:start position:0% +the text description to do this we can +use the mash function and ask our to dig + + align:start position:0% +use the mash function and ask our to dig + + + align:start position:0% +use the mash function and ask our to dig +the word caviar in the description + + align:start position:0% +the word caviar in the description + + + align:start position:0% +the word caviar in the description +vector so USD a dollar sign description + + align:start position:0% +vector so USD a dollar sign description + + + align:start position:0% +vector so USD a dollar sign description +a now pressing enter we obtain that + + align:start position:0% +a now pressing enter we obtain that + + + align:start position:0% +a now pressing enter we obtain that +caviar is the 4150 for food in our + + align:start position:0% +caviar is the 4150 for food in our + + + align:start position:0% +caviar is the 4150 for food in our +dataset + + align:start position:0% +dataset + + + align:start position:0% +dataset +so now finding the sodium level of + + align:start position:0% +so now finding the sodium level of + + + align:start position:0% +so now finding the sodium level of +caviar is a piece of cake we just type + + align:start position:0% +caviar is a piece of cake we just type + + + align:start position:0% +caviar is a piece of cake we just type +USD a dollar sign sodium and using the + + align:start position:0% +USD a dollar sign sodium and using the + + + align:start position:0% +USD a dollar sign sodium and using the +square brackets with the index 4154 ask + + align:start position:0% +square brackets with the index 4154 ask + + + align:start position:0% +square brackets with the index 4154 ask +art to pick the sodium level of caviar + + align:start position:0% +art to pick the sodium level of caviar + + + align:start position:0% +art to pick the sodium level of caviar +for us in this is 1500 milligrams now to + + align:start position:0% +for us in this is 1500 milligrams now to + + + align:start position:0% +for us in this is 1500 milligrams now to +find the level of sodium in caviar we + + align:start position:0% +find the level of sodium in caviar we + + + align:start position:0% +find the level of sodium in caviar we +use 2 steps but we can actually lock + + align:start position:0% +use 2 steps but we can actually lock + + + align:start position:0% +use 2 steps but we can actually lock +them all in one single step so let's use + + align:start position:0% +them all in one single step so let's use + + + align:start position:0% +them all in one single step so let's use +the up arrow twice to go back to the + + align:start position:0% +the up arrow twice to go back to the + + + align:start position:0% +the up arrow twice to go back to the +match function and we know that this + + align:start position:0% +match function and we know that this + + + align:start position:0% +match function and we know that this +match function gives us an index that + + align:start position:0% +match function gives us an index that + + + align:start position:0% +match function gives us an index that +then should be fed into the sodium + + align:start position:0% +then should be fed into the sodium + + + align:start position:0% +then should be fed into the sodium +vector using square brackets so let's + + align:start position:0% +vector using square brackets so let's + + + align:start position:0% +vector using square brackets so let's +enclose it in square bracket and then at + + align:start position:0% +enclose it in square bracket and then at + + + align:start position:0% +enclose it in square bracket and then at +the beginning we're going to just write + + align:start position:0% +the beginning we're going to just write + + + align:start position:0% +the beginning we're going to just write +USD a dollar sign sodium and again of + + align:start position:0% +USD a dollar sign sodium and again of + + + align:start position:0% +USD a dollar sign sodium and again of +course this gives us 1500 milligrams of + + align:start position:0% +course this gives us 1500 milligrams of + + + align:start position:0% +course this gives us 1500 milligrams of +sodium in 100 grams of caviar now the + + align:start position:0% +sodium in 100 grams of caviar now the + + + align:start position:0% +sodium in 100 grams of caviar now the +value 1500 milligrams seems to be very + + align:start position:0% +value 1500 milligrams seems to be very + + + align:start position:0% +value 1500 milligrams seems to be very +small compared to ten thousand + + align:start position:0% +small compared to ten thousand + + + align:start position:0% +small compared to ten thousand +milligrams or thirty-eight thousand + + align:start position:0% +milligrams or thirty-eight thousand + + + align:start position:0% +milligrams or thirty-eight thousand +milligrams which are the values that we + + align:start position:0% +milligrams which are the values that we + + + align:start position:0% +milligrams which are the values that we +worked with so far with respect to + + align:start position:0% +worked with so far with respect to + + + align:start position:0% +worked with so far with respect to +sodium levels but this doesn't seem to + + align:start position:0% +sodium levels but this doesn't seem to + + + align:start position:0% +sodium levels but this doesn't seem to +be a fair comparison maybe the best way + + align:start position:0% +be a fair comparison maybe the best way + + + align:start position:0% +be a fair comparison maybe the best way +to figure out how big this value is is + + align:start position:0% +to figure out how big this value is is + + + align:start position:0% +to figure out how big this value is is +by comparing it to the mean and the + + align:start position:0% +by comparing it to the mean and the + + + align:start position:0% +by comparing it to the mean and the +standard deviation of the sodium levels + + align:start position:0% +standard deviation of the sodium levels + + + align:start position:0% +standard deviation of the sodium levels +across the data set to find the mean we + + align:start position:0% +across the data set to find the mean we + + + align:start position:0% +across the data set to find the mean we +know that this information is given to + + align:start position:0% +know that this information is given to + + + align:start position:0% +know that this information is given to +us using the summary function so let's + + align:start position:0% +us using the summary function so let's + + + align:start position:0% +us using the summary function so let's +use the summary function and this time + + align:start position:0% +use the summary function and this time + + + align:start position:0% +use the summary function and this time +give it the input the sodium vector + + align:start position:0% +give it the input the sodium vector + + + align:start position:0% +give it the input the sodium vector +instead of the whole USDA data frame and + + align:start position:0% +instead of the whole USDA data frame and + + + align:start position:0% +instead of the whole USDA data frame and +we can see that the mean sodium value is + + align:start position:0% +we can see that the mean sodium value is + + + align:start position:0% +we can see that the mean sodium value is +322 milligrams + + align:start position:0% +322 milligrams + + + align:start position:0% +322 milligrams +however the summary function does not + + align:start position:0% +however the summary function does not + + + align:start position:0% +however the summary function does not +give us standard deviation information + + align:start position:0% +give us standard deviation information + + + align:start position:0% +give us standard deviation information +but we can do this using the function SD + + align:start position:0% +but we can do this using the function SD + + + align:start position:0% +but we can do this using the function SD +which stands for standard deviation give + + align:start position:0% +which stands for standard deviation give + + + align:start position:0% +which stands for standard deviation give +it as an input the sodium + + align:start position:0% +it as an input the sodium + + + align:start position:0% +it as an input the sodium +and oh we obtained none available well + + align:start position:0% +and oh we obtained none available well + + + align:start position:0% +and oh we obtained none available well +we got an a because we forgot to remove + + align:start position:0% +we got an a because we forgot to remove + + + align:start position:0% +we got an a because we forgot to remove +the non available entries before + + align:start position:0% +the non available entries before + + + align:start position:0% +the non available entries before +computing our statistical measure so + + align:start position:0% +computing our statistical measure so + + + align:start position:0% +computing our statistical measure so +let's use the up arrow to go back to the + + align:start position:0% +let's use the up arrow to go back to the + + + align:start position:0% +let's use the up arrow to go back to the +standard deviation function and now we + + align:start position:0% +standard deviation function and now we + + + align:start position:0% +standard deviation function and now we +have to explicitly tell our to remove + + align:start position:0% +have to explicitly tell our to remove + + + align:start position:0% +have to explicitly tell our to remove +these non available entries by typing a + + align:start position:0% +these non available entries by typing a + + + align:start position:0% +these non available entries by typing a +dot RM equal true and now the standard + + align:start position:0% +dot RM equal true and now the standard + + + align:start position:0% +dot RM equal true and now the standard +deviation is 1045 milligrams + + align:start position:0% +deviation is 1045 milligrams + + + align:start position:0% +deviation is 1045 milligrams +note that if we sum the mean and the + + align:start position:0% +note that if we sum the mean and the + + + align:start position:0% +note that if we sum the mean and the +standard deviation we obtain around + + align:start position:0% +standard deviation we obtain around + + + align:start position:0% +standard deviation we obtain around +1,400 milligrams which is still smaller + + align:start position:0% +1,400 milligrams which is still smaller + + + align:start position:0% +1,400 milligrams which is still smaller +than the amount of sodium in 100 grams + + align:start position:0% +than the amount of sodium in 100 grams + + + align:start position:0% +than the amount of sodium in 100 grams +of caviar well this means that caviar is + + align:start position:0% +of caviar well this means that caviar is + + + align:start position:0% +of caviar well this means that caviar is +pretty rich in sodium compared to most + + align:start position:0% +pretty rich in sodium compared to most + + + align:start position:0% +pretty rich in sodium compared to most +of the foods in our data set now that we + + align:start position:0% +of the foods in our data set now that we + + + align:start position:0% +of the foods in our data set now that we +know how to do a basic analysis of our + + align:start position:0% +know how to do a basic analysis of our + + + align:start position:0% +know how to do a basic analysis of our +data let's look at the plotting + + align:start position:0% +data let's look at the plotting + + + align:start position:0% +data let's look at the plotting +functionality in our in our next video + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/SSnV-2uWG9w.txt b/SSnV-2uWG9w.txt new file mode 100644 index 0000000000000000000000000000000000000000..49e462e0f481a4f1618cec7e44e05800780be89e --- /dev/null +++ b/SSnV-2uWG9w.txt @@ -0,0 +1,12747 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu otherwise class + + align:start position:0% +ocw.mit.edu otherwise class + + + align:start position:0% +ocw.mit.edu otherwise class +announcements um Sprint task list do + + align:start position:0% +announcements um Sprint task list do + + + align:start position:0% +announcements um Sprint task list do +today hopefully youall turned them in um + + align:start position:0% +today hopefully youall turned them in um + + + align:start position:0% +today hopefully youall turned them in um +PL is going to check that out um and + + align:start position:0% +PL is going to check that out um and + + + align:start position:0% +PL is going to check that out um and +make sure that we have each team has a + + align:start position:0% +make sure that we have each team has a + + + align:start position:0% +make sure that we have each team has a +new Sprint test that's turned in we're + + align:start position:0% +new Sprint test that's turned in we're + + + align:start position:0% +new Sprint test that's turned in we're +asking for one of those once a week + + align:start position:0% +asking for one of those once a week + + + align:start position:0% +asking for one of those once a week +because we want to know the state of + + align:start position:0% +because we want to know the state of + + + align:start position:0% +because we want to know the state of +your game as it is right now um it's a + + align:start position:0% +your game as it is right now um it's a + + + align:start position:0% +your game as it is right now um it's a +lot of it is is for our use to kind of + + align:start position:0% +lot of it is is for our use to kind of + + + align:start position:0% +lot of it is is for our use to kind of +track where your game is going and how + + align:start position:0% +track where your game is going and how + + + align:start position:0% +track where your game is going and how +your game is going the actual format + + align:start position:0% +your game is going the actual format + + + align:start position:0% +your game is going the actual format +you're using isn't as important to us + + align:start position:0% +you're using isn't as important to us + + + align:start position:0% +you're using isn't as important to us +for this last project um again if you're + + align:start position:0% +for this last project um again if you're + + + align:start position:0% +for this last project um again if you're +using a non-standard format um once we + + align:start position:0% +using a non-standard format um once we + + + align:start position:0% +using a non-standard format um once we +get to the next um product backlog um + + align:start position:0% +get to the next um product backlog um + + + align:start position:0% +get to the next um product backlog um +presentation which I believe is next + + align:start position:0% +presentation which I believe is next + + + align:start position:0% +presentation which I believe is next +week but could be wrong about that um + + align:start position:0% +week but could be wrong about that um + + + align:start position:0% +week but could be wrong about that um +it's in Stellar um we'll be asking you + + align:start position:0% +it's in Stellar um we'll be asking you + + + align:start position:0% +it's in Stellar um we'll be asking you +about your project management process + + align:start position:0% +about your project management process + + + align:start position:0% +about your project management process +what you've been using how it's been + + align:start position:0% +what you've been using how it's been + + + align:start position:0% +what you've been using how it's been +working what changes you've made stuff + + align:start position:0% +working what changes you've made stuff + + + align:start position:0% +working what changes you've made stuff +like that to know how you're tracking + + align:start position:0% +like that to know how you're tracking + + + align:start position:0% +like that to know how you're tracking +what you're doing and when you're doing + + align:start position:0% +what you're doing and when you're doing + + + align:start position:0% +what you're doing and when you're doing +it + + align:start position:0% +it + + + align:start position:0% +it +um yeah so today um I got another minute + + align:start position:0% +um yeah so today um I got another minute + + + align:start position:0% +um yeah so today um I got another minute +um but today we're going to talk about + + align:start position:0% +um but today we're going to talk about + + + align:start position:0% +um but today we're going to talk about +story and video games um then you have + + align:start position:0% +story and video games um then you have + + + align:start position:0% +story and video games um then you have +time to work in your class and then at + + align:start position:0% +time to work in your class and then at + + + align:start position:0% +time to work in your class and then at +3M Ed Barrett's class is coming in we've + + align:start position:0% +3M Ed Barrett's class is coming in we've + + + align:start position:0% +3M Ed Barrett's class is coming in we've +got 18 folks coming in to play test your + + align:start position:0% +got 18 folks coming in to play test your + + + align:start position:0% +got 18 folks coming in to play test your +games um remember we did require you to + + align:start position:0% +games um remember we did require you to + + + align:start position:0% +games um remember we did require you to +have a playable digital build today um + + align:start position:0% +have a playable digital build today um + + + align:start position:0% +have a playable digital build today um +please test that build if that build + + align:start position:0% +please test that build if that build + + + align:start position:0% +please test that build if that build +does not get you the test data you need + + align:start position:0% +does not get you the test data you need + + + align:start position:0% +does not get you the test data you need +also test another one so if you if you + + align:start position:0% +also test another one so if you if you + + + align:start position:0% +also test another one so if you if you +have a paper prototype and you want to + + align:start position:0% +have a paper prototype and you want to + + + align:start position:0% +have a paper prototype and you want to +test that you can test that concurrently + + align:start position:0% +test that you can test that concurrently + + + align:start position:0% +test that you can test that concurrently +um again just like before um having + + align:start position:0% +um again just like before um having + + + align:start position:0% +um again just like before um having +three workstations open at each team + + align:start position:0% +three workstations open at each team + + + align:start position:0% +three workstations open at each team +would be awesome it means everybody gets + + align:start position:0% +would be awesome it means everybody gets + + + align:start position:0% +would be awesome it means everybody gets +to play the games quickly and get out + + align:start position:0% +to play the games quickly and get out + + + align:start position:0% +to play the games quickly and get out +quickly so that you can then finish up + + align:start position:0% +quickly so that you can then finish up + + + align:start position:0% +quickly so that you can then finish up +working um and you don't need to test + + align:start position:0% +working um and you don't need to test + + + align:start position:0% +working um and you don't need to test +each other's games so um and actually + + align:start position:0% +each other's games so um and actually + + + align:start position:0% +each other's games so um and actually +allow Our Guest to test GES first before + + align:start position:0% +allow Our Guest to test GES first before + + + align:start position:0% +allow Our Guest to test GES first before +you start testing each's GES + + align:start position:0% + + + + align:start position:0% + +today questions about procedures and + + align:start position:0% +today questions about procedures and + + + align:start position:0% +today questions about procedures and +whatnots all right so we're going to + + align:start position:0% +whatnots all right so we're going to + + + align:start position:0% +whatnots all right so we're going to +talk about stories and games um this is + + align:start position:0% +talk about stories and games um this is + + + align:start position:0% +talk about stories and games um this is +a lecture that I've adapted from a + + align:start position:0% +a lecture that I've adapted from a + + + align:start position:0% +a lecture that I've adapted from a +previous colleague of ours Clara + + align:start position:0% +previous colleague of ours Clara + + + align:start position:0% +previous colleague of ours Clara +Fernandes Vera um she studies um she + + align:start position:0% +Fernandes Vera um she studies um she + + + align:start position:0% +Fernandes Vera um she studies um she +studies adventure games she studies + + align:start position:0% +studies adventure games she studies + + + align:start position:0% +studies adventure games she studies +games through the lens of theater um so + + align:start position:0% +games through the lens of theater um so + + + align:start position:0% +games through the lens of theater um so +she's got a really interesting um view + + align:start position:0% +she's got a really interesting um view + + + align:start position:0% +she's got a really interesting um view +on on play as performance but this is + + align:start position:0% +on on play as performance but this is + + + align:start position:0% +on on play as performance but this is +much more of a talk about what is usable + + align:start position:0% +much more of a talk about what is usable + + + align:start position:0% +much more of a talk about what is usable +for you right now in the games you're + + align:start position:0% +for you right now in the games you're + + + align:start position:0% +for you right now in the games you're +making uh in this class uh I'll start + + align:start position:0% +making uh in this class uh I'll start + + + align:start position:0% +making uh in this class uh I'll start +out with talking a little bit about um + + align:start position:0% +out with talking a little bit about um + + + align:start position:0% +out with talking a little bit about um +bigger games but then I'm going to move + + align:start position:0% +bigger games but then I'm going to move + + + align:start position:0% +bigger games but then I'm going to move +quickly into talking about things that + + align:start position:0% +quickly into talking about things that + + + align:start position:0% +quickly into talking about things that +are more useful for you all right now so + + align:start position:0% +are more useful for you all right now so + + + align:start position:0% +are more useful for you all right now so +um just a question for you do games tell + + align:start position:0% +um just a question for you do games tell + + + align:start position:0% +um just a question for you do games tell +stories yes I see you nodded why how + + align:start position:0% + + + + align:start position:0% + +well I mean obviously there are the + + align:start position:0% +well I mean obviously there are the + + + align:start position:0% +well I mean obviously there are the +games that are more narrative heavy with + + align:start position:0% +games that are more narrative heavy with + + + align:start position:0% +games that are more narrative heavy with +like cut scenes and words and people + + align:start position:0% +like cut scenes and words and people + + + align:start position:0% +like cut scenes and words and people +happening but I feel like you can also + + align:start position:0% +happening but I feel like you can also + + + align:start position:0% +happening but I feel like you can also +easily convey stories just like with the + + align:start position:0% +easily convey stories just like with the + + + align:start position:0% +easily convey stories just like with the +images and the way the player interacts + + align:start position:0% +images and the way the player interacts + + + align:start position:0% +images and the way the player interacts +with the game itself you kind of create + + align:start position:0% +with the game itself you kind of create + + + align:start position:0% +with the game itself you kind of create +a narrative within it great you did my + + align:start position:0% +a narrative within it great you did my + + + align:start position:0% +a narrative within it great you did my +lecture I'm done thank you uh any other + + align:start position:0% +lecture I'm done thank you uh any other + + + align:start position:0% +lecture I'm done thank you uh any other +ways games tell + + align:start position:0% + + + + align:start position:0% + +stories so we heard cut scenes we heard + + align:start position:0% +stories so we heard cut scenes we heard + + + align:start position:0% +stories so we heard cut scenes we heard +narrative we heard words we heard + + align:start position:0% +narrative we heard words we heard + + + align:start position:0% +narrative we heard words we heard +pictures um + + align:start position:0% +pictures um + + + align:start position:0% +pictures um +yeah oh yeah one more hand where + + align:start position:0% + + + + align:start position:0% + +yes Game books can also tell stories yes + + align:start position:0% +yes Game books can also tell stories yes + + + align:start position:0% +yes Game books can also tell stories yes +Game books the the physical things + + align:start position:0% +Game books the the physical things + + + align:start position:0% +Game books the the physical things +around games it's also really rare and + + align:start position:0% +around games it's also really rare and + + + align:start position:0% +around games it's also really rare and +hard to do it's really great when games + + align:start position:0% +hard to do it's really great when games + + + align:start position:0% +hard to do it's really great when games +can actually tell the story through the + + align:start position:0% +can actually tell the story through the + + + align:start position:0% +can actually tell the story through the +mechanics yes absolutely telling the + + align:start position:0% +mechanics yes absolutely telling the + + + align:start position:0% +mechanics yes absolutely telling the +story through the mechanics uh which + + align:start position:0% +story through the mechanics uh which + + + align:start position:0% +story through the mechanics uh which +game did you mention papers please I + + align:start position:0% +game did you mention papers please I + + + align:start position:0% +game did you mention papers please I +think + + align:start position:0% +think + + + align:start position:0% +think +really excellent um so when we talk + + align:start position:0% +really excellent um so when we talk + + + align:start position:0% +really excellent um so when we talk +about games and stories sometimes we + + align:start position:0% +about games and stories sometimes we + + + align:start position:0% +about games and stories sometimes we +think about these you actually you're + + align:start position:0% +think about these you actually you're + + + align:start position:0% +think about these you actually you're +you're good you mentioned some other + + align:start position:0% +you're good you mentioned some other + + + align:start position:0% +you're good you mentioned some other +types of games um Final Fantasy 13 Metal + + align:start position:0% +types of games um Final Fantasy 13 Metal + + + align:start position:0% +types of games um Final Fantasy 13 Metal +Gear Solid 4 both games uh kind of + + align:start position:0% +Gear Solid 4 both games uh kind of + + + align:start position:0% +Gear Solid 4 both games uh kind of +derided for um in certain circles for + + align:start position:0% +derided for um in certain circles for + + + align:start position:0% +derided for um in certain circles for +the linear of their games um you start + + align:start position:0% +the linear of their games um you start + + + align:start position:0% +the linear of their games um you start +the game you watch the movie you hit + + align:start position:0% +the game you watch the movie you hit + + + align:start position:0% +the game you watch the movie you hit +some buttons you watch the next movie + + align:start position:0% +some buttons you watch the next movie + + + align:start position:0% +some buttons you watch the next movie +you hit some buttons some people like + + align:start position:0% +you hit some buttons some people like + + + align:start position:0% +you hit some buttons some people like +that that's a that's a one way to play + + align:start position:0% +that that's a that's a one way to play + + + align:start position:0% +that that's a that's a one way to play +games it's one games one kind of game + + align:start position:0% +games it's one games one kind of game + + + align:start position:0% +games it's one games one kind of game +that is out there um not exactly the + + align:start position:0% +that is out there um not exactly the + + + align:start position:0% +that is out there um not exactly the +kind of games that we're making in this + + align:start position:0% +kind of games that we're making in this + + + align:start position:0% +kind of games that we're making in this +class um but also not exactly the kind + + align:start position:0% +class um but also not exactly the kind + + + align:start position:0% +class um but also not exactly the kind +of games um not the only way to tell + + align:start position:0% +of games um not the only way to tell + + + align:start position:0% +of games um not the only way to tell +stories and games as you just + + align:start position:0% +stories and games as you just + + + align:start position:0% +stories and games as you just +mentioned um to make those kind of games + + align:start position:0% +mentioned um to make those kind of games + + + align:start position:0% +mentioned um to make those kind of games +like in those what we're calling call + + align:start position:0% +like in those what we're calling call + + + align:start position:0% +like in those what we're calling call +them AAA games if anybody's heard that + + align:start position:0% +them AAA games if anybody's heard that + + + align:start position:0% +them AAA games if anybody's heard that +that phrase before AAA does meaning + + align:start position:0% +that phrase before AAA does meaning + + + align:start position:0% +that phrase before AAA does meaning +expensive um Blockbuster um the Marvel + + align:start position:0% +expensive um Blockbuster um the Marvel + + + align:start position:0% +expensive um Blockbuster um the Marvel +blockbuster movies or basically what's + + align:start position:0% +blockbuster movies or basically what's + + + align:start position:0% +blockbuster movies or basically what's +happened to film Call of Duty is the is + + align:start position:0% +happened to film Call of Duty is the is + + + align:start position:0% +happened to film Call of Duty is the is +the game version of that um so they + + align:start position:0% +the game version of that um so they + + + align:start position:0% +the game version of that um so they +require many expensive art resources + + align:start position:0% +require many expensive art resources + + + align:start position:0% +require many expensive art resources +artists sound designers we we heard an + + align:start position:0% +artists sound designers we we heard an + + + align:start position:0% +artists sound designers we we heard an +artist talk in talk earlier this week + + align:start position:0% +artist talk in talk earlier this week + + + align:start position:0% +artist talk in talk earlier this week +about how Art's important and why art is + + align:start position:0% +about how Art's important and why art is + + + align:start position:0% +about how Art's important and why art is +important um and how difficult it is for + + align:start position:0% +important um and how difficult it is for + + + align:start position:0% +important um and how difficult it is for +one person to do all s all those + + align:start position:0% +one person to do all s all those + + + align:start position:0% +one person to do all s all those +different kinds of tasks that are + + align:start position:0% +different kinds of tasks that are + + + align:start position:0% +different kinds of tasks that are +required for a complicated game um also + + align:start position:0% +required for a complicated game um also + + + align:start position:0% +required for a complicated game um also +just to note that um those two games + + align:start position:0% +just to note that um those two games + + + align:start position:0% +just to note that um those two games +that I mentioned previously um usually + + align:start position:0% +that I mentioned previously um usually + + + align:start position:0% +that I mentioned previously um usually +borrow techniques from Cinema so things + + align:start position:0% +borrow techniques from Cinema so things + + + align:start position:0% +borrow techniques from Cinema so things +like camera placement lighting visual + + align:start position:0% +like camera placement lighting visual + + + align:start position:0% +like camera placement lighting visual +effects and sound effects a lot of those + + align:start position:0% +effects and sound effects a lot of those + + + align:start position:0% +effects and sound effects a lot of those +things are they're borrowing Concepts + + align:start position:0% +things are they're borrowing Concepts + + + align:start position:0% +things are they're borrowing Concepts +from Cinema that have been proven to + + align:start position:0% +from Cinema that have been proven to + + + align:start position:0% +from Cinema that have been proven to +work in cinema and then just throwing + + align:start position:0% +work in cinema and then just throwing + + + align:start position:0% +work in cinema and then just throwing +them in the game because they know they + + align:start position:0% +them in the game because they know they + + + align:start position:0% +them in the game because they know they +work so one way a AAA Studio might think + + align:start position:0% +work so one way a AAA Studio might think + + + align:start position:0% +work so one way a AAA Studio might think +about making a game with story is All + + align:start position:0% +about making a game with story is All + + + align:start position:0% +about making a game with story is All +right so it's this balance between + + align:start position:0% +right so it's this balance between + + + align:start position:0% +right so it's this balance between +interactivity and narrative right um and + + align:start position:0% +interactivity and narrative right um and + + + align:start position:0% +interactivity and narrative right um and +there's just cost so think of that + + align:start position:0% +there's just cost so think of that + + + align:start position:0% +there's just cost so think of that +triangle as the cost um cost money to + + align:start position:0% +triangle as the cost um cost money to + + + align:start position:0% +triangle as the cost um cost money to +make these games and that money is + + align:start position:0% +make these games and that money is + + + align:start position:0% +make these games and that money is +generally either spent on people or it's + + align:start position:0% +generally either spent on people or it's + + + align:start position:0% +generally either spent on people or it's +spent on people or time so people times + + align:start position:0% +spent on people or time so people times + + + align:start position:0% +spent on people or time so people times +time basically um and the idea is that + + align:start position:0% +time basically um and the idea is that + + + align:start position:0% +time basically um and the idea is that +all right so we've got this interactive + + align:start position:0% +all right so we've got this interactive + + + align:start position:0% +all right so we've got this interactive +stuff going on right here the player + + align:start position:0% +stuff going on right here the player + + + align:start position:0% +stuff going on right here the player +presses buttons great we've got this + + align:start position:0% +presses buttons great we've got this + + + align:start position:0% +presses buttons great we've got this +narrative stuff here and I'm borrowing + + align:start position:0% +narrative stuff here and I'm borrowing + + + align:start position:0% +narrative stuff here and I'm borrowing +comedy and tragedy um this is when I + + align:start position:0% +comedy and tragedy um this is when I + + + align:start position:0% +comedy and tragedy um this is when I +when I say narrative um think back to + + align:start position:0% +when I say narrative um think back to + + + align:start position:0% +when I say narrative um think back to +your Aristotle so plot comedy tragedy + + align:start position:0% +your Aristotle so plot comedy tragedy + + + align:start position:0% +your Aristotle so plot comedy tragedy +melodrama a lot of the Tria games tend + + align:start position:0% +melodrama a lot of the Tria games tend + + + align:start position:0% +melodrama a lot of the Tria games tend +to just basically be big melodrama + + align:start position:0% +to just basically be big melodrama + + + align:start position:0% +to just basically be big melodrama +pieces um but it could be folk tales + + align:start position:0% +pieces um but it could be folk tales + + + align:start position:0% +pieces um but it could be folk tales +that narrative could be sometimes it has + + align:start position:0% +that narrative could be sometimes it has + + + align:start position:0% +that narrative could be sometimes it has +conflict sometimes there's not conflict + + align:start position:0% +conflict sometimes there's not conflict + + + align:start position:0% +conflict sometimes there's not conflict +sometimes there's a dramatic Arc or + + align:start position:0% +sometimes there's a dramatic Arc or + + + align:start position:0% +sometimes there's a dramatic Arc or +not um but yeah so they say all right so + + align:start position:0% +not um but yeah so they say all right so + + + align:start position:0% +not um but yeah so they say all right so +we've got to balance the two and how do + + align:start position:0% +we've got to balance the two and how do + + + align:start position:0% +we've got to balance the two and how do +we do that uh state-of-the-art triaa + + align:start position:0% +we do that uh state-of-the-art triaa + + + align:start position:0% +we do that uh state-of-the-art triaa +2011 this is Arkham City that's Batman + + align:start position:0% +2011 this is Arkham City that's Batman + + + align:start position:0% +2011 this is Arkham City that's Batman +his parents are dead press X to pay your + + align:start position:0% +his parents are dead press X to pay your + + + align:start position:0% +his parents are dead press X to pay your +respects you press the X button he + + align:start position:0% +respects you press the X button he + + + align:start position:0% +respects you press the X button he +places down the rows you get a nice + + align:start position:0% +places down the rows you get a nice + + + align:start position:0% +places down the rows you get a nice +little cut scene reward Award with + + align:start position:0% +little cut scene reward Award with + + + align:start position:0% +little cut scene reward Award with +reward with it so you can see a little + + align:start position:0% +reward with it so you can see a little + + + align:start position:0% +reward with it so you can see a little +bit of a movie going on of him you know + + align:start position:0% +bit of a movie going on of him you know + + + align:start position:0% +bit of a movie going on of him you know +being grim and putting down the rows um + + align:start position:0% +being grim and putting down the rows um + + + align:start position:0% +being grim and putting down the rows um +but you also get a little achievement so + + align:start position:0% +but you also get a little achievement so + + + align:start position:0% +but you also get a little achievement so +it's a reward it's an Easter egg um but + + align:start position:0% +it's a reward it's an Easter egg um but + + + align:start position:0% +it's a reward it's an Easter egg um but +it's a it's a crucial backstory to the + + align:start position:0% +it's a it's a crucial backstory to the + + + align:start position:0% +it's a it's a crucial backstory to the +character they put it in the game um + + align:start position:0% +character they put it in the game um + + + align:start position:0% +character they put it in the game um +they spent a lot of money making that + + align:start position:0% +they spent a lot of money making that + + + align:start position:0% +they spent a lot of money making that +animation um not all players are going + + align:start position:0% +animation um not all players are going + + + align:start position:0% +animation um not all players are going +to see it and when they do see it it + + align:start position:0% +to see it and when they do see it it + + + align:start position:0% +to see it and when they do see it it +only lasts for a very short period of + + align:start position:0% +only lasts for a very short period of + + + align:start position:0% +only lasts for a very short period of +time all right so that was 2011 let's + + align:start position:0% +time all right so that was 2011 let's + + + align:start position:0% +time all right so that was 2011 let's +it's 2014 we're we're we've got really + + align:start position:0% +it's 2014 we're we're we've got really + + + align:start position:0% +it's 2014 we're we're we've got really +cool computers we've got X one PS4 + + align:start position:0% +cool computers we've got X one PS4 + + + align:start position:0% +cool computers we've got X one PS4 +here's state-of-the-art AAA 2014 Call of + + align:start position:0% +here's state-of-the-art AAA 2014 Call of + + + align:start position:0% +here's state-of-the-art AAA 2014 Call of +Duty Advanced Warfare we've got an + + align:start position:0% +Duty Advanced Warfare we've got an + + + align:start position:0% +Duty Advanced Warfare we've got an +upgrade hold X to pay + + align:start position:0% +upgrade hold X to pay + + + align:start position:0% +upgrade hold X to pay +respects basically it's a QuickTime + + align:start position:0% +respects basically it's a QuickTime + + + align:start position:0% +respects basically it's a QuickTime +event um we've seen QuickTime events + + align:start position:0% +event um we've seen QuickTime events + + + align:start position:0% +event um we've seen QuickTime events +with with other games before if + + align:start position:0% +with with other games before if + + + align:start position:0% +with with other games before if +anybody's played uh Heavy Rain um if + + align:start position:0% +anybody's played uh Heavy Rain um if + + + align:start position:0% +anybody's played uh Heavy Rain um if +anybody's played the shenmu games um + + align:start position:0% +anybody's played the shenmu games um + + + align:start position:0% +anybody's played the shenmu games um +Resident Evil games things like that + + align:start position:0% +Resident Evil games things like that + + + align:start position:0% +Resident Evil games things like that +basically you've got a video footage + + align:start position:0% +basically you've got a video footage + + + align:start position:0% +basically you've got a video footage +going on and you can press a button and + + align:start position:0% +going on and you can press a button and + + + align:start position:0% +going on and you can press a button and +it'll give you a new set of video + + align:start position:0% +it'll give you a new set of video + + + align:start position:0% +it'll give you a new set of video +footage um so there's a lot of Animation + + align:start position:0% +footage um so there's a lot of Animation + + + align:start position:0% +footage um so there's a lot of Animation +going on there's a lot of Co cost going + + align:start position:0% +going on there's a lot of Co cost going + + + align:start position:0% +going on there's a lot of Co cost going +into this um I think the hope for this + + align:start position:0% +into this um I think the hope for this + + + align:start position:0% +into this um I think the hope for this +kind of thing why it's hold X instead of + + align:start position:0% +kind of thing why it's hold X instead of + + + align:start position:0% +kind of thing why it's hold X instead of +press x is by holding X you're embodying + + align:start position:0% +press x is by holding X you're embodying + + + align:start position:0% +press x is by holding X you're embodying +that action um you know maybe you're + + align:start position:0% +that action um you know maybe you're + + + align:start position:0% +that action um you know maybe you're +grieving maybe it's praying maybe it's + + align:start position:0% +grieving maybe it's praying maybe it's + + + align:start position:0% +grieving maybe it's praying maybe it's +holding the button um maybe the longer + + align:start position:0% +holding the button um maybe the longer + + + align:start position:0% +holding the button um maybe the longer +you hold it the more you grieve so maybe + + align:start position:0% +you hold it the more you grieve so maybe + + + align:start position:0% +you hold it the more you grieve so maybe +there should have been a score that was + + align:start position:0% +there should have been a score that was + + + align:start position:0% +there should have been a score that was +counting down how much grief you got um + + align:start position:0% +counting down how much grief you got um + + + align:start position:0% +counting down how much grief you got um +but if you've read the internet about + + align:start position:0% +but if you've read the internet about + + + align:start position:0% +but if you've read the internet about +about the game you notice that yeah it's + + align:start position:0% +about the game you notice that yeah it's + + + align:start position:0% +about the game you notice that yeah it's +hasn't quite worked out to the way that + + align:start position:0% +hasn't quite worked out to the way that + + + align:start position:0% +hasn't quite worked out to the way that +they might have thought it + + align:start position:0% +they might have thought it + + + align:start position:0% +they might have thought it +worked all right so you don't have AAA + + align:start position:0% +worked all right so you don't have AAA + + + align:start position:0% +worked all right so you don't have AAA +resources so why did I talk about all + + align:start position:0% +resources so why did I talk about all + + + align:start position:0% +resources so why did I talk about all +that and you should probably just give + + align:start position:0% +that and you should probably just give + + + align:start position:0% +that and you should probably just give +up on stories + + align:start position:0% +up on stories + + + align:start position:0% +up on stories +right I'm GNA say no of course that's + + align:start position:0% +right I'm GNA say no of course that's + + + align:start position:0% +right I'm GNA say no of course that's +why I'm talking about this for about + + align:start position:0% +why I'm talking about this for about + + + align:start position:0% +why I'm talking about this for about +another 45 minutes um but some games + + align:start position:0% +another 45 minutes um but some games + + + align:start position:0% +another 45 minutes um but some games +don't need stories to be fun or have a + + align:start position:0% +don't need stories to be fun or have a + + + align:start position:0% +don't need stories to be fun or have a +meaning anybody recognize the pieces on + + align:start position:0% +meaning anybody recognize the pieces on + + + align:start position:0% +meaning anybody recognize the pieces on +the + + align:start position:0% +the + + + align:start position:0% +the +screen Tetris the tetos of Tetris is + + align:start position:0% +screen Tetris the tetos of Tetris is + + + align:start position:0% +screen Tetris the tetos of Tetris is +there a story to Tetris + + align:start position:0% +there a story to Tetris + + + align:start position:0% +there a story to Tetris +some people say there + + align:start position:0% +some people say there + + + align:start position:0% +some people say there +is and I'm talking about this Tetris too + + align:start position:0% +is and I'm talking about this Tetris too + + + align:start position:0% +is and I'm talking about this Tetris too +there's not even color in that you can't + + align:start position:0% +there's not even color in that you can't + + + align:start position:0% +there's not even color in that you can't +even tell what the touchs are once they + + align:start position:0% +even tell what the touchs are once they + + + align:start position:0% +even tell what the touchs are once they +hit the hit the the pile they're just + + align:start position:0% +hit the hit the the pile they're just + + + align:start position:0% +hit the hit the the pile they're just +there um and actually that might be that + + align:start position:0% +there um and actually that might be that + + + align:start position:0% +there um and actually that might be that +I don't know I think no that bottom of + + align:start position:0% +I don't know I think no that bottom of + + + align:start position:0% +I don't know I think no that bottom of +the that bottom row is the the bottom of + + align:start position:0% +the that bottom row is the the bottom of + + + align:start position:0% +the that bottom row is the the bottom of +the the bucket that's holding it so R + + align:start position:0% +the the bucket that's holding it so R + + + align:start position:0% +the the bucket that's holding it so R +mit's media lab um Janet Murray would + + align:start position:0% +mit's media lab um Janet Murray would + + + align:start position:0% +mit's media lab um Janet Murray would +say that Tetris is the monotony of the + + align:start position:0% +say that Tetris is the monotony of the + + + align:start position:0% +say that Tetris is the monotony of the +workday of putting things in the in + + align:start position:0% +workday of putting things in the in + + + align:start position:0% +workday of putting things in the in +their places um uh another professor Jim + + align:start position:0% +their places um uh another professor Jim + + + align:start position:0% +their places um uh another professor Jim +G over at University of Wisconsin + + align:start position:0% +G over at University of Wisconsin + + + align:start position:0% +G over at University of Wisconsin +Madison um he says Tetris is an escape + + align:start position:0% +Madison um he says Tetris is an escape + + + align:start position:0% +Madison um he says Tetris is an escape +into the very desire for order control + + align:start position:0% +into the very desire for order control + + + align:start position:0% +into the very desire for order control +and workable solutions that we have all + + align:start position:0% +and workable solutions that we have all + + + align:start position:0% +and workable solutions that we have all +the + + align:start position:0% +the + + + align:start position:0% +the +time um some other less notable but + + align:start position:0% +time um some other less notable but + + + align:start position:0% +time um some other less notable but +equally valid people on the internet say + + align:start position:0% +equally valid people on the internet say + + + align:start position:0% +equally valid people on the internet say +that you know it's the story of life um + + align:start position:0% +that you know it's the story of life um + + + align:start position:0% +that you know it's the story of life um +it's never one it always has an ending + + align:start position:0% +it's never one it always has an ending + + + align:start position:0% +it's never one it always has an ending +and that ending is your death or the + + align:start position:0% +and that ending is your death or the + + + align:start position:0% +and that ending is your death or the +everything just piling up to not um to + + align:start position:0% +everything just piling up to not um to + + + align:start position:0% +everything just piling up to not um to +the top um because it was made in Russia + + align:start position:0% +the top um because it was made in Russia + + + align:start position:0% +the top um because it was made in Russia +some people might say that it's a + + align:start position:0% +some people might say that it's a + + + align:start position:0% +some people might say that it's a +critique of communism maybe or of + + align:start position:0% +critique of communism maybe or of + + + align:start position:0% +critique of communism maybe or of +sameness or of bureaucracy although the + + align:start position:0% +sameness or of bureaucracy although the + + + align:start position:0% +sameness or of bureaucracy although the +Creator the Russian Creator Alexia pinov + + align:start position:0% +Creator the Russian Creator Alexia pinov + + + align:start position:0% +Creator the Russian Creator Alexia pinov +would say he does say that that for him + + align:start position:0% +would say he does say that that for him + + + align:start position:0% +would say he does say that that for him +it's about playing on the edge of your + + align:start position:0% +it's about playing on the edge of your + + + align:start position:0% +it's about playing on the edge of your +abilities and about playing to a life + + align:start position:0% +abilities and about playing to a life + + + align:start position:0% +abilities and about playing to a life +well lived so the point of all this + + align:start position:0% +well lived so the point of all this + + + align:start position:0% +well lived so the point of all this +stuff is people read patterns in the + + align:start position:0% +stuff is people read patterns in the + + + align:start position:0% +stuff is people read patterns in the +most abstract things so maybe you don't + + align:start position:0% +most abstract things so maybe you don't + + + align:start position:0% +most abstract things so maybe you don't +need story maybe you just give some give + + align:start position:0% +need story maybe you just give some give + + + align:start position:0% +need story maybe you just give some give +them some abstractness and and then move + + align:start position:0% +them some abstractness and and then move + + + align:start position:0% +them some abstractness and and then move +on uh Tetris was made + + align:start position:0% +on uh Tetris was made + + + align:start position:0% +on uh Tetris was made +1981 thereabouts on that one 1983 I + + align:start position:0% +1981 thereabouts on that one 1983 I + + + align:start position:0% +1981 thereabouts on that one 1983 I +should have put that in the slide um so + + align:start position:0% +should have put that in the slide um so + + + align:start position:0% +should have put that in the slide um so +that was you know 30 something odd years + + align:start position:0% +that was you know 30 something odd years + + + align:start position:0% +that was you know 30 something odd years +ago what if they made Tetris today + + align:start position:0% +ago what if they made Tetris today + + + align:start position:0% +ago what if they made Tetris today +here's Tetris today or one version of + + align:start position:0% +here's Tetris today or one version of + + + align:start position:0% +here's Tetris today or one version of +Tetris today um why would somebody make + + align:start position:0% +Tetris today um why would somebody make + + + align:start position:0% +Tetris today um why would somebody make +a Tetris game with story this is the + + align:start position:0% +a Tetris game with story this is the + + + align:start position:0% +a Tetris game with story this is the +Japanese only puyo PUO Tetris so it's + + align:start position:0% +Japanese only puyo PUO Tetris so it's + + + align:start position:0% +Japanese only puyo PUO Tetris so it's +taking two different game mechanics and + + align:start position:0% +taking two different game mechanics and + + + align:start position:0% +taking two different game mechanics and +splice them together why would they put + + align:start position:0% +splice them together why would they put + + + align:start position:0% +splice them together why would they put +characters in The Tetris + + align:start position:0% + + + + align:start position:0% + +game what's + + align:start position:0% +game what's + + + align:start position:0% +game what's +up it might yeah and people are used to + + align:start position:0% +up it might yeah and people are used to + + + align:start position:0% +up it might yeah and people are used to +seeing + + align:start position:0% +seeing + + + align:start position:0% +seeing +characters possibly yeah any others any + + align:start position:0% +characters possibly yeah any others any + + + align:start position:0% +characters possibly yeah any others any +other + + align:start position:0% +other + + + align:start position:0% +other +ideas yeah exists need make something + + align:start position:0% +ideas yeah exists need make something + + + align:start position:0% +ideas yeah exists need make something +slightly different absolutely yeah um + + align:start position:0% +slightly different absolutely yeah um + + + align:start position:0% +slightly different absolutely yeah um +actually we were just talking about this + + align:start position:0% +actually we were just talking about this + + + align:start position:0% +actually we were just talking about this +um before class um would Tetris be able + + align:start position:0% +um before class um would Tetris be able + + + align:start position:0% +um before class um would Tetris be able +to would would you be able to sell this + + align:start position:0% +to would would you be able to sell this + + + align:start position:0% +to would would you be able to sell this +today do you think this could sell + + align:start position:0% +today do you think this could sell + + + align:start position:0% +today do you think this could sell +today you never seen Tetris before it's + + align:start position:0% +today you never seen Tetris before it's + + + align:start position:0% +today you never seen Tetris before it's +a brand new thing you look it out maybe + + align:start position:0% +a brand new thing you look it out maybe + + + align:start position:0% +a brand new thing you look it out maybe +maybe it would maybe it wouldn't has + + align:start position:0% +maybe it would maybe it wouldn't has + + + align:start position:0% +maybe it would maybe it wouldn't has +anybody played the game hexagon or Super + + align:start position:0% +anybody played the game hexagon or Super + + + align:start position:0% +anybody played the game hexagon or Super +Hexagon yes does hexagon Super Hexagon + + align:start position:0% +Hexagon yes does hexagon Super Hexagon + + + align:start position:0% +Hexagon yes does hexagon Super Hexagon +have a story + + align:start position:0% +have a story + + + align:start position:0% +have a story +no okay then why is there a narrator and + + align:start position:0% +no okay then why is there a narrator and + + + align:start position:0% +no okay then why is there a narrator and +a + + align:start position:0% +a + + + align:start position:0% +a +voice why is she telling you like I feel + + align:start position:0% +voice why is she telling you like I feel + + + align:start position:0% +voice why is she telling you like I feel +like it's partially toer know where they + + align:start position:0% +like it's partially toer know where they + + + align:start position:0% +like it's partially toer know where they +are in the game how does she + + align:start position:0% +are in the game how does she + + + align:start position:0% +are in the game how does she +talk kind of robotic it's Robo but also + + align:start position:0% +talk kind of robotic it's Robo but also + + + align:start position:0% +talk kind of robotic it's Robo but also +there's a woman's voice there's a little + + align:start position:0% +there's a woman's voice there's a little + + + align:start position:0% +there's a woman's voice there's a little +bit of St is the the the character a + + align:start position:0% +bit of St is the the the character a + + + align:start position:0% +bit of St is the the the character a +triangle why is the character a triangle + + align:start position:0% +triangle why is the character a triangle + + + align:start position:0% +triangle why is the character a triangle +the the the the thing that you're moving + + align:start position:0% +the the the the thing that you're moving + + + align:start position:0% +the the the the thing that you're moving +on the screen why a triangle not a + + align:start position:0% +on the screen why a triangle not a + + + align:start position:0% +on the screen why a triangle not a +square or + + align:start position:0% +square or + + + align:start position:0% +square or +Circle + + align:start position:0% +Circle + + + align:start position:0% +Circle +maybe I'm gonna argue that there's a + + align:start position:0% +maybe I'm gonna argue that there's a + + + align:start position:0% +maybe I'm gonna argue that there's a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +of's what's that they're more sturdy + + align:start position:0% +of's what's that they're more sturdy + + + align:start position:0% +of's what's that they're more sturdy +than squares if you a square it turns + + align:start position:0% +than squares if you a square it turns + + + align:start position:0% +than squares if you a square it turns +into like weird Square there you + + align:start position:0% +into like weird Square there you + + + align:start position:0% +into like weird Square there you +go there's little little hints story + + align:start position:0% +go there's little little hints story + + + align:start position:0% +go there's little little hints story +there character as the triangle + + align:start position:0% +there character as the triangle + + + align:start position:0% +there character as the triangle +I think yeah what are the reason for + + align:start position:0% +I think yeah what are the reason for + + + align:start position:0% +I think yeah what are the reason for +characters merch merchandise actually + + align:start position:0% +characters merch merchandise actually + + + align:start position:0% +characters merch merchandise actually +yeah especially with this one um the + + align:start position:0% +yeah especially with this one um the + + + align:start position:0% +yeah especially with this one um the +what do they call the the characters + + align:start position:0% +what do they call the the characters + + + align:start position:0% +what do they call the the characters +when they make like Internet Explorer is + + align:start position:0% +when they make like Internet Explorer is + + + align:start position:0% +when they make like Internet Explorer is +a character is it Mo or is it a Tomo + + align:start position:0% +a character is it Mo or is it a Tomo + + + align:start position:0% +a character is it Mo or is it a Tomo +like something something T something + + align:start position:0% +like something something T something + + + align:start position:0% +like something something T something +yeah so Elon and and other Elon maybe + + align:start position:0% +yeah so Elon and and other Elon maybe + + + align:start position:0% +yeah so Elon and and other Elon maybe +all right so that's story that's they're + + align:start position:0% +all right so that's story that's they're + + + align:start position:0% +all right so that's story that's they're +bringing this story to that um even + + align:start position:0% +bringing this story to that um even + + + align:start position:0% +bringing this story to that um even +better story can serve a gameplay + + align:start position:0% +better story can serve a gameplay + + + align:start position:0% +better story can serve a gameplay +purpose um I'm going to argue that + + align:start position:0% +purpose um I'm going to argue that + + + align:start position:0% +purpose um I'm going to argue that +Pac-Man has a + + align:start position:0% + + + + align:start position:0% + +story a noticeable story right there's + + align:start position:0% +story a noticeable story right there's + + + align:start position:0% +story a noticeable story right there's +cut scenes in this Pac-Man but what's + + align:start position:0% +cut scenes in this Pac-Man but what's + + + align:start position:0% +cut scenes in this Pac-Man but what's +the story of + + align:start position:0% +the story of + + + align:start position:0% +the story of +Pacman where like where are the hints of + + align:start position:0% +Pacman where like where are the hints of + + + align:start position:0% +Pacman where like where are the hints of +story + + align:start position:0% +story + + + align:start position:0% +story +there I guess it be enem yeah only + + align:start position:0% +there I guess it be enem yeah only + + + align:start position:0% +there I guess it be enem yeah only +absolutely and why why did they give the + + align:start position:0% +absolutely and why why did they give the + + + align:start position:0% +absolutely and why why did they give the +characters + + align:start position:0% +characters + + + align:start position:0% +characters +names why did do the why do why is + + align:start position:0% +names why did do the why do why is + + + align:start position:0% +names why did do the why do why is +Blinky Blinky and or his and his + + align:start position:0% +Blinky Blinky and or his and his + + + align:start position:0% +Blinky Blinky and or his and his +character his personality Shadow I think + + align:start position:0% +character his personality Shadow I think + + + align:start position:0% +character his personality Shadow I think +as far as I remember like that's a + + align:start position:0% +as far as I remember like that's a + + + align:start position:0% +as far as I remember like that's a +really translations really poor like + + align:start position:0% +really translations really poor like + + + align:start position:0% +really translations really poor like +translation of it in the original it's + + align:start position:0% +translation of it in the original it's + + + align:start position:0% +translation of it in the original it's +like very clear as to like their names + + align:start position:0% +like very clear as to like their names + + + align:start position:0% +like very clear as to like their names +gives a hint as how they'll act + + align:start position:0% +gives a hint as how they'll act + + + align:start position:0% +gives a hint as how they'll act +absolutely they have they have + + align:start position:0% +absolutely they have they have + + + align:start position:0% +absolutely they have they have +deterministic actions um so I've given + + align:start position:0% +deterministic actions um so I've given + + + align:start position:0% +deterministic actions um so I've given +them a little bit of character but + + align:start position:0% +them a little bit of character but + + + align:start position:0% +them a little bit of character but +that's going to help you to identify one + + align:start position:0% +that's going to help you to identify one + + + align:start position:0% +that's going to help you to identify one +before the other like if anybody's + + align:start position:0% +before the other like if anybody's + + + align:start position:0% +before the other like if anybody's +played the Atari 2600 version of Pac-Man + + align:start position:0% +played the Atari 2600 version of Pac-Man + + + align:start position:0% +played the Atari 2600 version of Pac-Man +my first experience with it all the all + + align:start position:0% +my first experience with it all the all + + + align:start position:0% +my first experience with it all the all +the ghosts had the same image um you + + align:start position:0% +the ghosts had the same image um you + + + align:start position:0% +the ghosts had the same image um you +couldn't tell which one had which act + + align:start position:0% +couldn't tell which one had which act + + + align:start position:0% +couldn't tell which one had which act +type of action they probably actually + + align:start position:0% +type of action they probably actually + + + align:start position:0% +type of action they probably actually +didn't have a different AI those was a + + align:start position:0% +didn't have a different AI those was a + + + align:start position:0% +didn't have a different AI those was a +really difficult games for them to make + + align:start position:0% +really difficult games for them to make + + + align:start position:0% +really difficult games for them to make +they had to make it in like a two or + + align:start position:0% +they had to make it in like a two or + + + align:start position:0% +they had to make it in like a two or +three weeks I believe all right so what + + align:start position:0% +three weeks I believe all right so what + + + align:start position:0% +three weeks I believe all right so what +do we gain from story this is why this + + align:start position:0% +do we gain from story this is why this + + + align:start position:0% +do we gain from story this is why this +is where I come in and say this is what + + align:start position:0% +is where I come in and say this is what + + + align:start position:0% +is where I come in and say this is what +I think story is going to give to your + + align:start position:0% +I think story is going to give to your + + + align:start position:0% +I think story is going to give to your +games even if you're making a strategy + + align:start position:0% +games even if you're making a strategy + + + align:start position:0% +games even if you're making a strategy +game doesn't matter what kind of game + + align:start position:0% +game doesn't matter what kind of game + + + align:start position:0% +game doesn't matter what kind of game +you make you're going to get something + + align:start position:0% +you make you're going to get something + + + align:start position:0% +you make you're going to get something +out of a + + align:start position:0% +out of a + + + align:start position:0% +out of a +story um we understand our lived + + align:start position:0% +story um we understand our lived + + + align:start position:0% +story um we understand our lived +experiences of stories uh so providing a + + align:start position:0% +experiences of stories uh so providing a + + + align:start position:0% +experiences of stories uh so providing a +story is going to help a player like + + align:start position:0% +story is going to help a player like + + + align:start position:0% +story is going to help a player like +understand what's going on in the game + + align:start position:0% +understand what's going on in the game + + + align:start position:0% +understand what's going on in the game +uh if you think about you know what + + align:start position:0% +uh if you think about you know what + + + align:start position:0% +uh if you think about you know what +you've ever done in the past you're + + align:start position:0% +you've ever done in the past you're + + + align:start position:0% +you've ever done in the past you're +always telling it to another person as a + + align:start position:0% +always telling it to another person as a + + + align:start position:0% +always telling it to another person as a +story uh the way you do the way you're + + align:start position:0% +story uh the way you do the way you're + + + align:start position:0% +story uh the way you do the way you're +able to memorize things often is you're + + align:start position:0% +able to memorize things often is you're + + + align:start position:0% +able to memorize things often is you're +constructing stories in your head of + + align:start position:0% +constructing stories in your head of + + + align:start position:0% +constructing stories in your head of +things that you've done uh it's events + + align:start position:0% +things that you've done uh it's events + + + align:start position:0% +things that you've done uh it's events +with causes you're placing together + + align:start position:0% +with causes you're placing together + + + align:start position:0% +with causes you're placing together +you're finding patterns and you're + + align:start position:0% +you're finding patterns and you're + + + align:start position:0% +you're finding patterns and you're +putting the story in there and it helps + + align:start position:0% +putting the story in there and it helps + + + align:start position:0% +putting the story in there and it helps +you understand what's going on around + + align:start position:0% +you understand what's going on around + + + align:start position:0% +you understand what's going on around +you um a story can help you explain the + + align:start position:0% +you um a story can help you explain the + + + align:start position:0% +you um a story can help you explain the +world to the player it can also + + align:start position:0% +world to the player it can also + + + align:start position:0% +world to the player it can also +encourage the player to explore it so if + + align:start position:0% +encourage the player to explore it so if + + + align:start position:0% +encourage the player to explore it so if +you've got something in the game that's + + align:start position:0% +you've got something in the game that's + + + align:start position:0% +you've got something in the game that's +that's hidden later on you want them to + + align:start position:0% +that's hidden later on you want them to + + + align:start position:0% +that's hidden later on you want them to +find it you can use story to to to give + + align:start position:0% +find it you can use story to to to give + + + align:start position:0% +find it you can use story to to to give +them hints towards this is there's this + + align:start position:0% +them hints towards this is there's this + + + align:start position:0% +them hints towards this is there's this +cool thing coming up that you might want + + align:start position:0% +cool thing coming up that you might want + + + align:start position:0% +cool thing coming up that you might want +to check out um on a parallel level to + + align:start position:0% +to check out um on a parallel level to + + + align:start position:0% +to check out um on a parallel level to +explanation stories provide consistency + + align:start position:0% +explanation stories provide consistency + + + align:start position:0% +explanation stories provide consistency +to the world so if you've got various + + align:start position:0% +to the world so if you've got various + + + align:start position:0% +to the world so if you've got various +things going on within your game the way + + align:start position:0% +things going on within your game the way + + + align:start position:0% +things going on within your game the way +you can kind of massage the the + + align:start position:0% +you can kind of massage the the + + + align:start position:0% +you can kind of massage the the +differences between things going on + + align:start position:0% +differences between things going on + + + align:start position:0% +differences between things going on +between the mechanics is by covering + + align:start position:0% +between the mechanics is by covering + + + align:start position:0% +between the mechanics is by covering +that up with story or rather + + align:start position:0% +that up with story or rather + + + align:start position:0% +that up with story or rather +embellishing and and supporting it with + + align:start position:0% +embellishing and and supporting it with + + + align:start position:0% +embellishing and and supporting it with +story rather than covering it + + align:start position:0% +story rather than covering it + + + align:start position:0% +story rather than covering it +up all right so a couple quick videos um + + align:start position:0% +up all right so a couple quick videos um + + + align:start position:0% +up all right so a couple quick videos um +when I'm talking about story games + + align:start position:0% +when I'm talking about story games + + + align:start position:0% +when I'm talking about story games +especially in this lecture I'm mainly + + align:start position:0% +especially in this lecture I'm mainly + + + align:start position:0% +especially in this lecture I'm mainly +talking about games with story not story + + align:start position:0% +talking about games with story not story + + + align:start position:0% +talking about games with story not story +driven games the games we talked about + + align:start position:0% +driven games the games we talked about + + + align:start position:0% +driven games the games we talked about +earlier those were story driven games + + align:start position:0% +earlier those were story driven games + + + align:start position:0% +earlier those were story driven games +this is a game with a + + align:start position:0% + + + + align:start position:0% + +story on the left we got on the right we + + align:start position:0% +story on the left we got on the right we + + + align:start position:0% +story on the left we got on the right we +got + + align:start position:0% +got + + + align:start position:0% +got +Cassandra I'm sorry but I can't back + + align:start position:0% +Cassandra I'm sorry but I can't back + + + align:start position:0% +Cassandra I'm sorry but I can't back +down what do you + + align:start position:0% +down what do you + + + align:start position:0% +down what do you +want battle one + + align:start position:0% +want battle one + + + align:start position:0% +want battle one +fight recognize + + align:start position:0% +fight recognize + + + align:start position:0% +fight recognize +game so Cali yeah it's I think it's + + align:start position:0% +game so Cali yeah it's I think it's + + + align:start position:0% +game so Cali yeah it's I think it's +three + + align:start position:0% + + + + align:start position:0% + +it's from + + align:start position:0% +it's from + + + align:start position:0% +it's from +2008 or 2010 I think this video is + + align:start position:0% + + + + align:start position:0% + +from youbody catch what she said don't + + align:start position:0% +from youbody catch what she said don't + + + align:start position:0% +from youbody catch what she said don't +try to confuse me don't try to confuse + + align:start position:0% +try to confuse me don't try to confuse + + + align:start position:0% +try to confuse me don't try to confuse +me so KO we get to the + + align:start position:0% +me so KO we get to the + + + align:start position:0% +me so KO we get to the +end God please forgive me God please + + align:start position:0% +end God please forgive me God please + + + align:start position:0% +end God please forgive me God please +forgive me what is she talking about + + align:start position:0% +forgive me what is she talking about + + + align:start position:0% +forgive me what is she talking about +does anybody know what what she's what + + align:start position:0% +does anybody know what what she's what + + + align:start position:0% +does anybody know what what she's what +she's saying there and why she's saying + + align:start position:0% +she's saying there and why she's saying + + + align:start position:0% +she's saying there and why she's saying +it you might only know this if you ever + + align:start position:0% +it you might only know this if you ever + + + align:start position:0% +it you might only know this if you ever +played if you played the game before and + + align:start position:0% +played if you played the game before and + + + align:start position:0% +played if you played the game before and +you're really really into the game so + + align:start position:0% +you're really really into the game so + + + align:start position:0% +you're really really into the game so +Matt yeah yeah so Cassandra is sua's + + align:start position:0% +Matt yeah yeah so Cassandra is sua's + + + align:start position:0% +Matt yeah yeah so Cassandra is sua's +sister and they're fighting for the soul + + align:start position:0% +sister and they're fighting for the soul + + + align:start position:0% +sister and they're fighting for the soul +Edge for this demonic sword that's going + + align:start position:0% +Edge for this demonic sword that's going + + + align:start position:0% +Edge for this demonic sword that's going +to destroy the world and she has to to + + align:start position:0% +to destroy the world and she has to to + + + align:start position:0% +to destroy the world and she has to to +fight her sister and kill her sister to + + align:start position:0% +fight her sister and kill her sister to + + + align:start position:0% +fight her sister and kill her sister to +get to the sword in order to either I + + align:start position:0% +get to the sword in order to either I + + + align:start position:0% +get to the sword in order to either I +think for sopa's version It's to save + + align:start position:0% +think for sopa's version It's to save + + + align:start position:0% +think for sopa's version It's to save +the world um why didn't she work with + + align:start position:0% +the world um why didn't she work with + + + align:start position:0% +the world um why didn't she work with +her sister it's a fighting game who + + align:start position:0% +her sister it's a fighting game who + + + align:start position:0% +her sister it's a fighting game who +knows um if I were I I meant to update + + align:start position:0% +knows um if I were I I meant to update + + + align:start position:0% +knows um if I were I I meant to update +the slides see something a more modern + + align:start position:0% +the slides see something a more modern + + + align:start position:0% +the slides see something a more modern +audience might understand hand um in + + align:start position:0% +audience might understand hand um in + + + align:start position:0% +audience might understand hand um in +particular League of Legend does this + + align:start position:0% +particular League of Legend does this + + + align:start position:0% +particular League of Legend does this +kind of thing a lot right there's story + + align:start position:0% +kind of thing a lot right there's story + + + align:start position:0% +kind of thing a lot right there's story +moments going on in games you mention um + + align:start position:0% +moments going on in games you mention um + + + align:start position:0% +moments going on in games you mention um +a moment in the game certain characters + + align:start position:0% +a moment in the game certain characters + + + align:start position:0% +a moment in the game certain characters +on the same team I believe they they + + align:start position:0% +on the same team I believe they they + + + align:start position:0% +on the same team I believe they they +have different voice promps or different + + align:start position:0% +have different voice promps or different + + + align:start position:0% +have different voice promps or different +vocal lines that it would say to + + align:start position:0% +vocal lines that it would say to + + + align:start position:0% +vocal lines that it would say to +acknowledge that they have a history um + + align:start position:0% +acknowledge that they have a history um + + + align:start position:0% +acknowledge that they have a history um +so does that help you play the game + + align:start position:0% +so does that help you play the game + + + align:start position:0% +so does that help you play the game +better no game play no it's a valid use + + align:start position:0% +better no game play no it's a valid use + + + align:start position:0% +better no game play no it's a valid use +of story but it's not an efficient use + + align:start position:0% +of story but it's not an efficient use + + + align:start position:0% +of story but it's not an efficient use +of story especially for your kinds of + + align:start position:0% +of story especially for your kinds of + + + align:start position:0% +of story especially for your kinds of +games right it doesn't directly connect + + align:start position:0% +games right it doesn't directly connect + + + align:start position:0% +games right it doesn't directly connect +this the story doesn't directly connect + + align:start position:0% +this the story doesn't directly connect + + + align:start position:0% +this the story doesn't directly connect +to the players experience of the game + + align:start position:0% +to the players experience of the game + + + align:start position:0% +to the players experience of the game +but it is something players like like we + + align:start position:0% +but it is something players like like we + + + align:start position:0% +but it is something players like like we +talked about with characters like we + + align:start position:0% +talked about with characters like we + + + align:start position:0% +talked about with characters like we +talked with the merchandise and in + + align:start position:0% +talked with the merchandise and in + + + align:start position:0% +talked with the merchandise and in +particular in particular for this game + + align:start position:0% +particular in particular for this game + + + align:start position:0% +particular in particular for this game +for Soulcalibur why is soulcaliber doing + + align:start position:0% +for Soulcalibur why is soulcaliber doing + + + align:start position:0% +for Soulcalibur why is soulcaliber doing +this but Street Fighter isn't doing this + + align:start position:0% +this but Street Fighter isn't doing this + + + align:start position:0% +this but Street Fighter isn't doing this +um soulcaliber stands itself stands + + align:start position:0% +um soulcaliber stands itself stands + + + align:start position:0% +um soulcaliber stands itself stands +apart from the other fighting games um + + align:start position:0% +apart from the other fighting games um + + + align:start position:0% +apart from the other fighting games um +by having these complex story lines um + + align:start position:0% +by having these complex story lines um + + + align:start position:0% +by having these complex story lines um +that are actually visible to the player + + align:start position:0% +that are actually visible to the player + + + align:start position:0% +that are actually visible to the player +within the game Street Fighter does have + + align:start position:0% +within the game Street Fighter does have + + + align:start position:0% +within the game Street Fighter does have +complex story lines but they're like + + align:start position:0% +complex story lines but they're like + + + align:start position:0% +complex story lines but they're like +large largely um fan service or outside + + align:start position:0% +large largely um fan service or outside + + + align:start position:0% +large largely um fan service or outside +of the game merchandise books things + + align:start position:0% +of the game merchandise books things + + + align:start position:0% +of the game merchandise books things +like that you don't see you maybe see a + + align:start position:0% +like that you don't see you maybe see a + + + align:start position:0% +like that you don't see you maybe see a +little cut scene or two at the end of + + align:start position:0% +little cut scene or two at the end of + + + align:start position:0% +little cut scene or two at the end of +the game but not while you're playing it + + align:start position:0% +the game but not while you're playing it + + + align:start position:0% +the game but not while you're playing it +and also to really enhance the single + + align:start position:0% +and also to really enhance the single + + + align:start position:0% +and also to really enhance the single +player experience of the game that's + + align:start position:0% +player experience of the game that's + + + align:start position:0% +player experience of the game that's +that's actually how I know the + + align:start position:0% +that's actually how I know the + + + align:start position:0% +that's actually how I know the +Soulcalibur series is I played it single + + align:start position:0% +Soulcalibur series is I played it single + + + align:start position:0% +Soulcalibur series is I played it single +player um because they they added an RPG + + align:start position:0% +player um because they they added an RPG + + + align:start position:0% +player um because they they added an RPG +to it that was really basic and stupid + + align:start position:0% +to it that was really basic and stupid + + + align:start position:0% +to it that was really basic and stupid +um but it made the story a little bit + + align:start position:0% +um but it made the story a little bit + + + align:start position:0% +um but it made the story a little bit +more more uh concrete they took the RPG + + align:start position:0% +more more uh concrete they took the RPG + + + align:start position:0% +more more uh concrete they took the RPG +out that's when I stopped playing the + + align:start position:0% +out that's when I stopped playing the + + + align:start position:0% +out that's when I stopped playing the +game because that story didn't have any + + align:start position:0% +game because that story didn't have any + + + align:start position:0% +game because that story didn't have any +any there was no reason for that story + + align:start position:0% +any there was no reason for that story + + + align:start position:0% +any there was no reason for that story +in the gameplay anymore + + align:start position:0% +in the gameplay anymore + + + align:start position:0% +in the gameplay anymore +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so uh all right so I asking you about + + align:start position:0% +so uh all right so I asking you about + + + align:start position:0% +so uh all right so I asking you about +games telling stories and how how do + + align:start position:0% +games telling stories and how how do + + + align:start position:0% +games telling stories and how how do +games tell tell stories and what I'm + + align:start position:0% +games tell tell stories and what I'm + + + align:start position:0% +games tell tell stories and what I'm +going to say now is technically games + + align:start position:0% +going to say now is technically games + + + align:start position:0% +going to say now is technically games +don't exactly tell stories if you think + + align:start position:0% +don't exactly tell stories if you think + + + align:start position:0% +don't exactly tell stories if you think +about it like who is a Storyteller in a + + align:start position:0% + + + + align:start position:0% + +game you so it's not storytelling it's + + align:start position:0% +game you so it's not storytelling it's + + + align:start position:0% +game you so it's not storytelling it's +story building the the player the the + + align:start position:0% +story building the the player the the + + + align:start position:0% +story building the the player the the +game the designer the developer is + + align:start position:0% +game the designer the developer is + + + align:start position:0% +game the designer the developer is +giving you the tools to build a story of + + align:start position:0% +giving you the tools to build a story of + + + align:start position:0% +giving you the tools to build a story of +your own uh why we why we say they're + + align:start position:0% +your own uh why we why we say they're + + + align:start position:0% +your own uh why we why we say they're +different um so just to to to compare + + align:start position:0% +different um so just to to to compare + + + align:start position:0% +different um so just to to to compare +and contrast storytelling is continuous + + align:start position:0% +and contrast storytelling is continuous + + + align:start position:0% +and contrast storytelling is continuous +there's a one-way communication it is + + align:start position:0% +there's a one-way communication it is + + + align:start position:0% +there's a one-way communication it is +from atour and author to the player um + + align:start position:0% +from atour and author to the player um + + + align:start position:0% +from atour and author to the player um +the order and in one in particular the + + align:start position:0% +the order and in one in particular the + + + align:start position:0% +the order and in one in particular the +order of events and disclosure of + + align:start position:0% +order of events and disclosure of + + + align:start position:0% +order of events and disclosure of +information is determined by the author + + align:start position:0% +information is determined by the author + + + align:start position:0% +information is determined by the author +of the game I'm going to show you this + + align:start position:0% +of the game I'm going to show you this + + + align:start position:0% +of the game I'm going to show you this +and I'm going to show you this and I'm + + align:start position:0% +and I'm going to show you this and I'm + + + align:start position:0% +and I'm going to show you this and I'm +going to show you that uh story building + + align:start position:0% +going to show you that uh story building + + + align:start position:0% +going to show you that uh story building +is more fragmented and it could be a + + align:start position:0% +is more fragmented and it could be a + + + align:start position:0% +is more fragmented and it could be a +simple as I'm going to show you this now + + align:start position:0% +simple as I'm going to show you this now + + + align:start position:0% +simple as I'm going to show you this now +you can go see all these other things + + align:start position:0% +you can go see all these other things + + + align:start position:0% +you can go see all these other things +but you know I'm going to pull you back + + align:start position:0% +but you know I'm going to pull you back + + + align:start position:0% +but you know I'm going to pull you back +and I'm going to show you this next + + align:start position:0% +and I'm going to show you this next + + + align:start position:0% +and I'm going to show you this next +thing and you have to see those two + + align:start position:0% +thing and you have to see those two + + + align:start position:0% +thing and you have to see those two +things in order I'm in a more o Open + + align:start position:0% +things in order I'm in a more o Open + + + align:start position:0% +things in order I'm in a more o Open +oriented game you could see everything + + align:start position:0% +oriented game you could see everything + + + align:start position:0% +oriented game you could see everything +all when at any point of time depending + + align:start position:0% +all when at any point of time depending + + + align:start position:0% +all when at any point of time depending +on when you like it um rather than a + + align:start position:0% +on when you like it um rather than a + + + align:start position:0% +on when you like it um rather than a +one-way communication there's + + align:start position:0% +one-way communication there's + + + align:start position:0% +one-way communication there's +collaboration between narrative design + + align:start position:0% +collaboration between narrative design + + + align:start position:0% +collaboration between narrative design +and and the players anybody heard the + + align:start position:0% +and and the players anybody heard the + + + align:start position:0% +and and the players anybody heard the +term narrative design + + align:start position:0% +term narrative design + + + align:start position:0% +term narrative design +before or the ter or the title the job + + align:start position:0% +before or the ter or the title the job + + + align:start position:0% +before or the ter or the title the job +title narrative + + align:start position:0% +title narrative + + + align:start position:0% +title narrative +designer what do you think that is on a + + align:start position:0% +designer what do you think that is on a + + + align:start position:0% +designer what do you think that is on a +company and let's say rational rational + + align:start position:0% +company and let's say rational rational + + + align:start position:0% +company and let's say rational rational +has narrative designers um she was + + align:start position:0% +has narrative designers um she was + + + align:start position:0% +has narrative designers um she was +actually a a CMS student uh for for + + align:start position:0% +actually a a CMS student uh for for + + + align:start position:0% +actually a a CMS student uh for for +infinite what would a narrative designer + + align:start position:0% +infinite what would a narrative designer + + + align:start position:0% +infinite what would a narrative designer +do in in BioShock + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Infinite you a little + + align:start position:0% +Infinite you a little + + + align:start position:0% +Infinite you a little +bit I think Ken wrote A lot of that Ken + + align:start position:0% +bit I think Ken wrote A lot of that Ken + + + align:start position:0% +bit I think Ken wrote A lot of that Ken +uh the the director wrote A lot of that + + align:start position:0% +uh the the director wrote A lot of that + + + align:start position:0% +uh the the director wrote A lot of that +but they they they touch that though + + align:start position:0% + + + + align:start position:0% + +yeah yep they touch that + + align:start position:0% +yeah yep they touch that + + + align:start position:0% +yeah yep they touch that +too the other thing they do is you've + + align:start position:0% +too the other thing they do is you've + + + align:start position:0% +too the other thing they do is you've +got a level designer and you've got a + + align:start position:0% +got a level designer and you've got a + + + align:start position:0% +got a level designer and you've got a +writer and right in between you've got + + align:start position:0% +writer and right in between you've got + + + align:start position:0% +writer and right in between you've got +the narrative designer on some companies + + align:start position:0% +the narrative designer on some companies + + + align:start position:0% +the narrative designer on some companies +this isn't this isn't for all companies + + align:start position:0% +this isn't this isn't for all companies + + + align:start position:0% +this isn't this isn't for all companies +this is just for some um and in + + align:start position:0% +this is just for some um and in + + + align:start position:0% +this is just for some um and in +particular this is how I understand how + + align:start position:0% +particular this is how I understand how + + + align:start position:0% +particular this is how I understand how +IR rational works right is level + + align:start position:0% +IR rational works right is level + + + align:start position:0% +IR rational works right is level +designer creates a level based on how a + + align:start position:0% +designer creates a level based on how a + + + align:start position:0% +designer creates a level based on how a +person's going to play it um how they're + + align:start position:0% +person's going to play it um how they're + + + align:start position:0% +person's going to play it um how they're +going to get through it how they're + + align:start position:0% +going to get through it how they're + + + align:start position:0% +going to get through it how they're +going to get from point A to point B + + align:start position:0% +going to get from point A to point B + + + align:start position:0% +going to get from point A to point B +writer says here's the story I need + + align:start position:0% +writer says here's the story I need + + + align:start position:0% +writer says here's the story I need +everybody to see and here's all the + + align:start position:0% +everybody to see and here's all the + + + align:start position:0% +everybody to see and here's all the +elements I need them to see narrative + + align:start position:0% +elements I need them to see narrative + + + align:start position:0% +elements I need them to see narrative +designer figures out where within the + + align:start position:0% +designer figures out where within the + + + align:start position:0% +designer figures out where within the +level those things are going to exist + + align:start position:0% +level those things are going to exist + + + align:start position:0% +level those things are going to exist +and we'll talk about that when we're + + align:start position:0% +and we'll talk about that when we're + + + align:start position:0% +and we'll talk about that when we're +talking about envir environmental design + + align:start position:0% +talking about envir environmental design + + + align:start position:0% +talking about envir environmental design +um point I'll point out a couple places + + align:start position:0% +um point I'll point out a couple places + + + align:start position:0% +um point I'll point out a couple places +where a narrative designer had an active + + align:start position:0% +where a narrative designer had an active + + + align:start position:0% +where a narrative designer had an active +role in that + + align:start position:0% + + + + align:start position:0% + +game all right so I'm going to say that + + align:start position:0% +game all right so I'm going to say that + + + align:start position:0% +game all right so I'm going to say that +we don't need expensive cutcenes to tell + + align:start position:0% +we don't need expensive cutcenes to tell + + + align:start position:0% +we don't need expensive cutcenes to tell +stories I know we've we've come up with + + align:start position:0% +stories I know we've we've come up with + + + align:start position:0% +stories I know we've we've come up with +a few we've kind of touched on this a + + align:start position:0% +a few we've kind of touched on this a + + + align:start position:0% +a few we've kind of touched on this a +little bit instead I'm going to say is + + align:start position:0% +little bit instead I'm going to say is + + + align:start position:0% +little bit instead I'm going to say is +let's reduce the cost of the game but + + align:start position:0% +let's reduce the cost of the game but + + + align:start position:0% +let's reduce the cost of the game but +let's keep interactivity and narrative + + align:start position:0% +let's keep interactivity and narrative + + + align:start position:0% +let's keep interactivity and narrative +so things a player does and the the + + align:start position:0% +so things a player does and the the + + + align:start position:0% +so things a player does and the the +story that the player experiences about + + align:start position:0% +story that the player experiences about + + + align:start position:0% +story that the player experiences about +s similar so what tools are we going to + + align:start position:0% +s similar so what tools are we going to + + + align:start position:0% +s similar so what tools are we going to +give the player to build their story and + + align:start position:0% +give the player to build their story and + + + align:start position:0% +give the player to build their story and +the where we give them the tools depends + + align:start position:0% +the where we give them the tools depends + + + align:start position:0% +the where we give them the tools depends +on the type of story we're we're giving + + align:start position:0% +on the type of story we're we're giving + + + align:start position:0% +on the type of story we're we're giving +them so there's two stories to to games + + align:start position:0% +them so there's two stories to to games + + + align:start position:0% +them so there's two stories to to games +that that the player that the player + + align:start position:0% +that that the player that the player + + + align:start position:0% +that that the player that the player +builds there's the story of the world + + align:start position:0% +builds there's the story of the world + + + align:start position:0% +builds there's the story of the world +which largely is seen and heard and it's + + align:start position:0% +which largely is seen and heard and it's + + + align:start position:0% +which largely is seen and heard and it's +interpreted by the player and there's + + align:start position:0% +interpreted by the player and there's + + + align:start position:0% +interpreted by the player and there's +the story of the player the actions that + + align:start position:0% +the story of the player the actions that + + + align:start position:0% +the story of the player the actions that +the player does and when I say told + + align:start position:0% +the player does and when I say told + + + align:start position:0% +the player does and when I say told +there I kind of mean built as well the + + align:start position:0% +there I kind of mean built as well the + + + align:start position:0% +there I kind of mean built as well the +told is in that the player is telling it + + align:start position:0% +told is in that the player is telling it + + + align:start position:0% +told is in that the player is telling it +not the so the world might be something + + align:start position:0% +not the so the world might be something + + + align:start position:0% +not the so the world might be something +that the the game is telling the player + + align:start position:0% +that the the game is telling the player + + + align:start position:0% +that the the game is telling the player +but the story of the players is + + align:start position:0% +but the story of the players is + + + align:start position:0% +but the story of the players is +something that the player is telling + + align:start position:0% +something that the player is telling + + + align:start position:0% +something that the player is telling +back to the game or back to their + + align:start position:0% +back to the game or back to their + + + align:start position:0% +back to the game or back to their +friends or or in their own + + align:start position:0% +friends or or in their own + + + align:start position:0% +friends or or in their own +head so story of the world it's the + + align:start position:0% +head so story of the world it's the + + + align:start position:0% +head so story of the world it's the +world's history right it's the events + + align:start position:0% +world's history right it's the events + + + align:start position:0% +world's history right it's the events +that happen in the fictional world + + align:start position:0% +that happen in the fictional world + + + align:start position:0% +that happen in the fictional world +before the game starts you've got a lot + + align:start position:0% +before the game starts you've got a lot + + + align:start position:0% +before the game starts you've got a lot +of control over all this um you're as a + + align:start position:0% +of control over all this um you're as a + + + align:start position:0% +of control over all this um you're as a +developer you're writing all of this um + + align:start position:0% +developer you're writing all of this um + + + align:start position:0% +developer you're writing all of this um +for the player they're discovering it + + align:start position:0% +for the player they're discovering it + + + align:start position:0% +for the player they're discovering it +and they're discovering it peace mail + + align:start position:0% +and they're discovering it peace mail + + + align:start position:0% +and they're discovering it peace mail +they're discovering it through the + + align:start position:0% +they're discovering it through the + + + align:start position:0% +they're discovering it through the +gameplay so that story with with a great + + align:start position:0% +gameplay so that story with with a great + + + align:start position:0% +gameplay so that story with with a great +world that story becomes a puzzle for + + align:start position:0% +world that story becomes a puzzle for + + + align:start position:0% +world that story becomes a puzzle for +the player to to to want to to to + + align:start position:0% +the player to to to want to to to + + + align:start position:0% +the player to to to want to to to +explore it could be as literal as in + + align:start position:0% +explore it could be as literal as in + + + align:start position:0% +explore it could be as literal as in +Mist where it literally is a a puzzle + + align:start position:0% +Mist where it literally is a a puzzle + + + align:start position:0% +Mist where it literally is a a puzzle +that you were going around and solving + + align:start position:0% +that you were going around and solving + + + align:start position:0% +that you were going around and solving +puzzle here and solving puzzle there + + align:start position:0% +puzzle here and solving puzzle there + + + align:start position:0% +puzzle here and solving puzzle there +getting little Snippets of background + + align:start position:0% +getting little Snippets of background + + + align:start position:0% +getting little Snippets of background +and putting them together in your head + + align:start position:0% +and putting them together in your head + + + align:start position:0% +and putting them together in your head +to come up with a whole view of what the + + align:start position:0% +to come up with a whole view of what the + + + align:start position:0% +to come up with a whole view of what the +the world is um or it could be things + + align:start position:0% +the world is um or it could be things + + + align:start position:0% +the world is um or it could be things +like I'm going to show you with um with + + align:start position:0% +like I'm going to show you with um with + + + align:start position:0% +like I'm going to show you with um with +environmental yeah sort of ideally too + + align:start position:0% +environmental yeah sort of ideally too + + + align:start position:0% +environmental yeah sort of ideally too +if your story is becoming a puzzle it + + align:start position:0% +if your story is becoming a puzzle it + + + align:start position:0% +if your story is becoming a puzzle it +would be really really cool if it was + + align:start position:0% +would be really really cool if it was + + + align:start position:0% +would be really really cool if it was +useful to have solved it right so maybe + + align:start position:0% +useful to have solved it right so maybe + + + align:start position:0% +useful to have solved it right so maybe +as a player if you can figure out + + align:start position:0% +as a player if you can figure out + + + align:start position:0% +as a player if you can figure out +something cool about the world so that + + align:start position:0% +something cool about the world so that + + + align:start position:0% +something cool about the world so that +can be useful to you back in your game + + align:start position:0% +can be useful to you back in your game + + + align:start position:0% +can be useful to you back in your game +again that's sort of the Holy + + align:start position:0% + + + + align:start position:0% + +Grail so the tools you're giving the + + align:start position:0% +Grail so the tools you're giving the + + + align:start position:0% +Grail so the tools you're giving the +player to do that to do exactly that um + + align:start position:0% +player to do that to do exactly that um + + + align:start position:0% +player to do that to do exactly that um +and these are these are three tools that + + align:start position:0% +and these are these are three tools that + + + align:start position:0% +and these are these are three tools that +you have at your disposal in your games + + align:start position:0% +you have at your disposal in your games + + + align:start position:0% +you have at your disposal in your games +right now they're really simple and easy + + align:start position:0% +right now they're really simple and easy + + + align:start position:0% +right now they're really simple and easy +to use at least the top two + + align:start position:0% +to use at least the top two + + + align:start position:0% +to use at least the top two +are Title Character design and your + + align:start position:0% +are Title Character design and your + + + align:start position:0% +are Title Character design and your +environmental + + align:start position:0% +environmental + + + align:start position:0% +environmental +design so we're going to go through + + align:start position:0% +design so we're going to go through + + + align:start position:0% +design so we're going to go through +about four titles um I'm going to give + + align:start position:0% +about four titles um I'm going to give + + + align:start position:0% +about four titles um I'm going to give +you the name of the the game I'm + + align:start position:0% +you the name of the the game I'm + + + align:start position:0% +you the name of the the game I'm +cheating a little bit because I'm + + align:start position:0% +cheating a little bit because I'm + + + align:start position:0% +cheating a little bit because I'm +actually giving you the cover art for + + align:start position:0% +actually giving you the cover art for + + + align:start position:0% +actually giving you the cover art for +the game I'd like to know what the story + + align:start position:0% +the game I'd like to know what the story + + + align:start position:0% +the game I'd like to know what the story +is for the game so Zombies Ate My + + align:start position:0% +is for the game so Zombies Ate My + + + align:start position:0% +is for the game so Zombies Ate My +Neighbors what is the story of Zombies + + align:start position:0% +Neighbors what is the story of Zombies + + + align:start position:0% +Neighbors what is the story of Zombies +Ate My + + align:start position:0% + + + + align:start position:0% + +Neighbors about zombies what are the + + align:start position:0% +Neighbors about zombies what are the + + + align:start position:0% +Neighbors about zombies what are the +zombies + + align:start position:0% +zombies + + + align:start position:0% +zombies +doing they're eating neighbors where + + align:start position:0% +doing they're eating neighbors where + + + align:start position:0% +doing they're eating neighbors where +does it take + + align:start position:0% +does it take + + + align:start position:0% +does it take +place neighborhood in your neighborhood + + align:start position:0% +place neighborhood in your neighborhood + + + align:start position:0% +place neighborhood in your neighborhood +all right anything else they're coming + + align:start position:0% +all right anything else they're coming + + + align:start position:0% +all right anything else they're coming +for you they're coming for + + align:start position:0% +for you they're coming for + + + align:start position:0% +for you they're coming for +you damn right yeah in the back appears + + align:start position:0% +you damn right yeah in the back appears + + + align:start position:0% +you damn right yeah in the back appears +that it's in like a kind of campy style + + align:start position:0% +that it's in like a kind of campy style + + + align:start position:0% +that it's in like a kind of campy style +absolutely + + align:start position:0% +absolutely + + + align:start position:0% +absolutely +May + + align:start position:0% +May + + + align:start position:0% +May +mhm you get the the kind of distressed + + align:start position:0% +mhm you get the the kind of distressed + + + align:start position:0% +mhm you get the the kind of distressed +woman in the front she's being chased by + + align:start position:0% +woman in the front she's being chased by + + + align:start position:0% +woman in the front she's being chased by +very are they slow they're slow zombies + + align:start position:0% +very are they slow they're slow zombies + + + align:start position:0% +very are they slow they're slow zombies +right so these days we have to kind of + + align:start position:0% +right so these days we have to kind of + + + align:start position:0% +right so these days we have to kind of +specify back in the day they were always + + align:start position:0% +specify back in the day they were always + + + align:start position:0% +specify back in the day they were always +slow all right next one the Earth dies + + align:start position:0% +slow all right next one the Earth dies + + + align:start position:0% +slow all right next one the Earth dies +screaming + + align:start position:0% +screaming + + + align:start position:0% +screaming +what's it + + align:start position:0% +what's it + + + align:start position:0% +what's it +about what's that space anything + + align:start position:0% +about what's that space anything + + + align:start position:0% +about what's that space anything +else what's + + align:start position:0% +else what's + + + align:start position:0% +else what's +that war did I hear + + align:start position:0% +that war did I hear + + + align:start position:0% +that war did I hear +aliens something yeah anybody recognize + + align:start position:0% +aliens something yeah anybody recognize + + + align:start position:0% +aliens something yeah anybody recognize +the + + align:start position:0% +the + + + align:start position:0% +the +title was a movie yeah do you think the + + align:start position:0% +title was a movie yeah do you think the + + + align:start position:0% +title was a movie yeah do you think the +game is based on the + + align:start position:0% +game is based on the + + + align:start position:0% +game is based on the +movie I don't it actually isn't so the + + align:start position:0% +movie I don't it actually isn't so the + + + align:start position:0% +movie I don't it actually isn't so the +movie is from 55 57 + + align:start position:0% +movie is from 55 57 + + + align:start position:0% +movie is from 55 57 +um I don't even remember if it's a if + + align:start position:0% +um I don't even remember if it's a if + + + align:start position:0% +um I don't even remember if it's a if +it's an alien invasion movie it's just + + align:start position:0% +it's an alien invasion movie it's just + + + align:start position:0% +it's an alien invasion movie it's just +one of those things where in the 50s you + + align:start position:0% +one of those things where in the 50s you + + + align:start position:0% +one of those things where in the 50s you +made a movie and then somebody came and + + align:start position:0% +made a movie and then somebody came and + + + align:start position:0% +made a movie and then somebody came and +put a title on it based on what titles + + align:start position:0% +put a title on it based on what titles + + + align:start position:0% +put a title on it based on what titles +were working that day um but they + + align:start position:0% +were working that day um but they + + + align:start position:0% +were working that day um but they +licensed it from 20th Century + + align:start position:0% +licensed it from 20th Century + + + align:start position:0% +licensed it from 20th Century +Fox but there's these spaceships these + + align:start position:0% +Fox but there's these spaceships these + + + align:start position:0% +Fox but there's these spaceships these +these very 80s looking spaceships this + + align:start position:0% +these very 80s looking spaceships this + + + align:start position:0% +these very 80s looking spaceships this +is actually a cartridge for the 2600 + + align:start position:0% +is actually a cartridge for the 2600 + + + align:start position:0% +is actually a cartridge for the 2600 +looks awful um but um yeah the Earth + + align:start position:0% +looks awful um but um yeah the Earth + + + align:start position:0% +looks awful um but um yeah the Earth +dies screaming at the what happens at + + align:start position:0% +dies screaming at the what happens at + + + align:start position:0% +dies screaming at the what happens at +the end of the + + align:start position:0% +the end of the + + + align:start position:0% +the end of the +game yeah arcade games back in the day + + align:start position:0% +game yeah arcade games back in the day + + + align:start position:0% +game yeah arcade games back in the day +they how did they end they always ended + + align:start position:0% +they how did they end they always ended + + + align:start position:0% +they how did they end they always ended +with you dying it was always about + + align:start position:0% +with you dying it was always about + + + align:start position:0% +with you dying it was always about +throwing in another quarter playing it + + align:start position:0% +throwing in another quarter playing it + + + align:start position:0% +throwing in another quarter playing it +some more getting more time that + + align:start position:0% +some more getting more time that + + + align:start position:0% +some more getting more time that +actually came back over to the consoles + + align:start position:0% +actually came back over to the consoles + + + align:start position:0% +actually came back over to the consoles +especially the 2600 days um we've moved + + align:start position:0% +especially the 2600 days um we've moved + + + align:start position:0% +especially the 2600 days um we've moved +beyond that for the most part um in some + + align:start position:0% +beyond that for the most part um in some + + + align:start position:0% +beyond that for the most part um in some +cases it's actually brought back in iOS + + align:start position:0% +cases it's actually brought back in iOS + + + align:start position:0% +cases it's actually brought back in iOS +but yeah Earth th screaming all right + + align:start position:0% +but yeah Earth th screaming all right + + + align:start position:0% +but yeah Earth th screaming all right +next one this is harder a mind forever + + align:start position:0% +next one this is harder a mind forever + + + align:start position:0% +next one this is harder a mind forever +voyaging o what's going on + + align:start position:0% +voyaging o what's going on + + + align:start position:0% +voyaging o what's going on +there Discovery Discovery yeah so allow + + align:start position:0% +there Discovery Discovery yeah so allow + + + align:start position:0% +there Discovery Discovery yeah so allow +to at + + align:start position:0% + + + + align:start position:0% + +absolutely expor all world and maybe + + align:start position:0% +absolutely expor all world and maybe + + + align:start position:0% +absolutely expor all world and maybe +have you played + + align:start position:0% +have you played + + + align:start position:0% +have you played +this I just looked at the image the + + align:start position:0% +this I just looked at the image the + + + align:start position:0% +this I just looked at the image the +title image and that really helps it + + align:start position:0% +title image and that really helps it + + + align:start position:0% +title image and that really helps it +does it does help a lot but yeah that's + + align:start position:0% +does it does help a lot but yeah that's + + + align:start position:0% +does it does help a lot but yeah that's +exactly right except you're you're wrong + + align:start position:0% +exactly right except you're you're wrong + + + align:start position:0% +exactly right except you're you're wrong +you're not a guy right you're not a guy + + align:start position:0% +you're not a guy right you're not a guy + + + align:start position:0% +you're not a guy right you're not a guy +you're an AI right yeah I probably + + align:start position:0% +you're an AI right yeah I probably + + + align:start position:0% +you're an AI right yeah I probably +spoiled it for you it's okay it's an + + align:start position:0% +spoiled it for you it's okay it's an + + + align:start position:0% +spoiled it for you it's okay it's an +infocom game uh it's a text Adventure + + align:start position:0% +infocom game uh it's a text Adventure + + + align:start position:0% +infocom game uh it's a text Adventure +from 1988 uh so you're exploring text + + align:start position:0% +from 1988 uh so you're exploring text + + + align:start position:0% +from 1988 uh so you're exploring text +Adventures were open door go right open + + align:start position:0% +Adventures were open door go right open + + + align:start position:0% +Adventures were open door go right open +mailbox die from grw um and in this case + + align:start position:0% +mailbox die from grw um and in this case + + + align:start position:0% +mailbox die from grw um and in this case +it's it's you're going to these you are + + align:start position:0% +it's it's you're going to these you are + + + align:start position:0% +it's it's you're going to these you are +going to all these different worlds and + + align:start position:0% +going to all these different worlds and + + + align:start position:0% +going to all these different worlds and +it's the mind so that it had to do with + + align:start position:0% +it's the mind so that it had to do with + + + align:start position:0% +it's the mind so that it had to do with +an the AI attaining sence and figuring + + align:start position:0% +an the AI attaining sence and figuring + + + align:start position:0% +an the AI attaining sence and figuring +out what was going on and what's around + + align:start position:0% +out what was going on and what's around + + + align:start position:0% +out what was going on and what's around +it what this the world was like at the + + align:start position:0% +it what this the world was like at the + + + align:start position:0% +it what this the world was like at the +time really great game cool little bit + + align:start position:0% +time really great game cool little bit + + + align:start position:0% +time really great game cool little bit +of of tidbit of info for these kind of + + align:start position:0% +of of tidbit of info for these kind of + + + align:start position:0% +of of tidbit of info for these kind of +games they came with these things called + + align:start position:0% +games they came with these things called + + + align:start position:0% +games they came with these things called +fies so elements like physical elements + + align:start position:0% +fies so elements like physical elements + + + align:start position:0% +fies so elements like physical elements +that were shipped with the game box that + + align:start position:0% +that were shipped with the game box that + + + align:start position:0% +that were shipped with the game box that +kind of added a little bit to the game + + align:start position:0% +kind of added a little bit to the game + + + align:start position:0% +kind of added a little bit to the game +because they didn't have Graphics to + + align:start position:0% +because they didn't have Graphics to + + + align:start position:0% +because they didn't have Graphics to +show you everything um so in this case + + align:start position:0% +show you everything um so in this case + + + align:start position:0% +show you everything um so in this case +it was a file folder a pen I think it + + align:start position:0% +it was a file folder a pen I think it + + + align:start position:0% +it was a file folder a pen I think it +was related to a company um that you + + align:start position:0% +was related to a company um that you + + + align:start position:0% +was related to a company um that you +that you that you thought you worked for + + align:start position:0% +that you that you thought you worked for + + + align:start position:0% +that you that you thought you worked for +all right here's a more recent game 868 + + align:start position:0% +all right here's a more recent game 868 + + + align:start position:0% +all right here's a more recent game 868 +hack what's it about + + align:start position:0% + + + + align:start position:0% + +what is 868 + + align:start position:0% + + + + align:start position:0% + +DH yes it's a phone number there's no + + align:start position:0% +DH yes it's a phone number there's no + + + align:start position:0% +DH yes it's a phone number there's no +area code right normally we'd have an + + align:start position:0% +area code right normally we'd have an + + + align:start position:0% +area code right normally we'd have an +area code there so it's kind of + + align:start position:0% +area code there so it's kind of + + + align:start position:0% +area code there so it's kind of +referencing back to maybe the 80s you + + align:start position:0% +referencing back to maybe the 80s you + + + align:start position:0% +referencing back to maybe the 80s you +hacker maybe + + align:start position:0% +hacker maybe + + + align:start position:0% +hacker maybe +probably anything else we can get from + + align:start position:0% +probably anything else we can get from + + + align:start position:0% +probably anything else we can get from +the + + align:start position:0% +the + + + align:start position:0% +the +title all right we're going to come back + + align:start position:0% +title all right we're going to come back + + + align:start position:0% +title all right we're going to come back +I'm G to use this example again because + + align:start position:0% +I'm G to use this example again because + + + align:start position:0% +I'm G to use this example again because +I love this game um so titles provide + + align:start position:0% +I love this game um so titles provide + + + align:start position:0% +I love this game um so titles provide +clues towards setting character action + + align:start position:0% +clues towards setting character action + + + align:start position:0% +clues towards setting character action +even better while you're thinking of + + align:start position:0% +even better while you're thinking of + + + align:start position:0% +even better while you're thinking of +your charact your title think about what + + align:start position:0% +your charact your title think about what + + + align:start position:0% +your charact your title think about what +it's like on Google think about + + align:start position:0% +it's like on Google think about + + + align:start position:0% +it's like on Google think about +marketing right now if you're making a + + align:start position:0% +marketing right now if you're making a + + + align:start position:0% +marketing right now if you're making a +game that's going to be marketed + + align:start position:0% +game that's going to be marketed + + + align:start position:0% +game that's going to be marketed +somewhere can you Google the title and + + align:start position:0% +somewhere can you Google the title and + + + align:start position:0% +somewhere can you Google the title and +come up with your game if you can you + + align:start position:0% +come up with your game if you can you + + + align:start position:0% +come up with your game if you can you +win um it's very hard for some other + + align:start position:0% +win um it's very hard for some other + + + align:start position:0% +win um it's very hard for some other +games unless you add a ton of money into + + align:start position:0% +games unless you add a ton of money into + + + align:start position:0% +games unless you add a ton of money into +it all right next up is character design + + align:start position:0% +it all right next up is character design + + + align:start position:0% +it all right next up is character design +who's + + align:start position:0% +who's + + + align:start position:0% +who's +that Sonic what does Sonic do he runs + + align:start position:0% +that Sonic what does Sonic do he runs + + + align:start position:0% +that Sonic what does Sonic do he runs +fast what's he doing + + align:start position:0% +fast what's he doing + + + align:start position:0% +fast what's he doing +here yeah yeah why because you're not + + align:start position:0% +here yeah yeah why because you're not + + + align:start position:0% +here yeah yeah why because you're not +running exactly right wow I could have + + align:start position:0% +running exactly right wow I could have + + + align:start position:0% +running exactly right wow I could have +written this out yeah he's pissed he's + + align:start position:0% +written this out yeah he's pissed he's + + + align:start position:0% +written this out yeah he's pissed he's +like what the hell make me move you're + + align:start position:0% +like what the hell make me move you're + + + align:start position:0% +like what the hell make me move you're +not moving them on the controller this + + align:start position:0% +not moving them on the controller this + + + align:start position:0% +not moving them on the controller this +is is Idol animation there a ton of + + align:start position:0% +is is Idol animation there a ton of + + + align:start position:0% +is is Idol animation there a ton of +expressive expressiveness in this Idol + + align:start position:0% +expressive expressiveness in this Idol + + + align:start position:0% +expressive expressiveness in this Idol +animation it's maybe three or four + + align:start position:0% +animation it's maybe three or four + + + align:start position:0% +animation it's maybe three or four +frames of animation of just him tapping + + align:start position:0% +frames of animation of just him tapping + + + align:start position:0% +frames of animation of just him tapping +his feet looking at you breaking the + + align:start position:0% +his feet looking at you breaking the + + + align:start position:0% +his feet looking at you breaking the +fourth wall um some really great stuff + + align:start position:0% +fourth wall um some really great stuff + + + align:start position:0% +fourth wall um some really great stuff +you can do you can do with characters on + + align:start position:0% +you can do you can do with characters on + + + align:start position:0% +you can do you can do with characters on +in that way um and yeah like why do we + + align:start position:0% +in that way um and yeah like why do we + + + align:start position:0% +in that way um and yeah like why do we +know he runs if we were if this were + + align:start position:0% +know he runs if we were if this were + + + align:start position:0% +know he runs if we were if this were +like the first time we saw this and this + + align:start position:0% +like the first time we saw this and this + + + align:start position:0% +like the first time we saw this and this +was Christmas day back in the time when + + align:start position:0% +was Christmas day back in the time when + + + align:start position:0% +was Christmas day back in the time when +we didn't find out about games three + + align:start position:0% +we didn't find out about games three + + + align:start position:0% +we didn't find out about games three +years before they came out um you get + + align:start position:0% +years before they came out um you get + + + align:start position:0% +years before they came out um you get +this spiky haired dude with big feet + + align:start position:0% +this spiky haired dude with big feet + + + align:start position:0% +this spiky haired dude with big feet +right he's fast and he runs so + + align:start position:0% +right he's fast and he runs so + + + align:start position:0% +right he's fast and he runs so +yeah all right back to 868 hack because + + align:start position:0% +yeah all right back to 868 hack because + + + align:start position:0% +yeah all right back to 868 hack because +I said I love this game where what is + + align:start position:0% +I said I love this game where what is + + + align:start position:0% +I said I love this game where what is +the player on the screen what what + + align:start position:0% +the player on the screen what what + + + align:start position:0% +the player on the screen what what +element of the screen is is the + + align:start position:0% +element of the screen is is the + + + align:start position:0% +element of the screen is is the +player yes which + + align:start position:0% +player yes which + + + align:start position:0% +player yes which +one yeah the top one right what are you + + align:start position:0% +one yeah the top one right what are you + + + align:start position:0% +one yeah the top one right what are you +like what like what is it doing there + + align:start position:0% +like what like what is it doing there + + + align:start position:0% +like what like what is it doing there +how do you think it interacts within the + + align:start position:0% + + + + align:start position:0% + +system + + align:start position:0% +system + + + align:start position:0% +system +yeah basically yeah do you see you see I + + align:start position:0% +yeah basically yeah do you see you see I + + + align:start position:0% +yeah basically yeah do you see you see I +I kind of said there's other smiley + + align:start position:0% +I kind of said there's other smiley + + + align:start position:0% +I kind of said there's other smiley +faces there right what do they + + align:start position:0% + + + + align:start position:0% + +do okay + + align:start position:0% + + + + align:start position:0% + +so yeah yeah so those the the purple one + + align:start position:0% +so yeah yeah so those the the purple one + + + align:start position:0% +so yeah yeah so those the the purple one +the magenta one the purple one the red + + align:start position:0% +the magenta one the purple one the red + + + align:start position:0% +the magenta one the purple one the red +one those are bad guys coming to get you + + align:start position:0% +one those are bad guys coming to get you + + + align:start position:0% +one those are bad guys coming to get you +um there's these little ones in the + + align:start position:0% +um there's these little ones in the + + + align:start position:0% +um there's these little ones in the +bottom left and right and there's a + + align:start position:0% +bottom left and right and there's a + + + align:start position:0% +bottom left and right and there's a +couple in the in the top right that say + + align:start position:0% +couple in the in the top right that say + + + align:start position:0% +couple in the in the top right that say +data data siphon that's something you + + align:start position:0% +data data siphon that's something you + + + align:start position:0% +data data siphon that's something you +leave behind so you're leaving behind a + + align:start position:0% +leave behind so you're leaving behind a + + + align:start position:0% +leave behind so you're leaving behind a +piece of yourself in order to claim + + align:start position:0% +piece of yourself in order to claim + + + align:start position:0% +piece of yourself in order to claim +space it's a territory um control game + + align:start position:0% +space it's a territory um control game + + + align:start position:0% +space it's a territory um control game +where you drop a piece of yourself to + + align:start position:0% +where you drop a piece of yourself to + + + align:start position:0% +where you drop a piece of yourself to +consume the things around it you can + + align:start position:0% +consume the things around it you can + + + align:start position:0% +consume the things around it you can +consume the programs there and you can + + align:start position:0% +consume the programs there and you can + + + align:start position:0% +consume the programs there and you can +use the programs there uh but I really + + align:start position:0% +use the programs there uh but I really + + + align:start position:0% +use the programs there uh but I really +like it for this why do you think I like + + align:start position:0% +like it for this why do you think I like + + + align:start position:0% +like it for this why do you think I like +it for this what do you when I'm talking + + align:start position:0% +it for this what do you when I'm talking + + + align:start position:0% +it for this what do you when I'm talking +about hackers and I'm talking about the + + align:start position:0% +about hackers and I'm talking about the + + + align:start position:0% +about hackers and I'm talking about the +smiley face what does that what does + + align:start position:0% +smiley face what does that what does + + + align:start position:0% +smiley face what does that what does +that connote to you + + align:start position:0% + + + + align:start position:0% + +what I hear it's fun + + align:start position:0% +what I hear it's fun + + + align:start position:0% +what I hear it's fun +yeah yeah + + align:start position:0% +yeah yeah + + + align:start position:0% +yeah yeah +Matt your identity list right you're + + align:start position:0% +Matt your identity list right you're + + + align:start position:0% +Matt your identity list right you're +anonymous I I just kind of like that all + + align:start position:0% +anonymous I I just kind of like that all + + + align:start position:0% +anonymous I I just kind of like that all +right so moving on character design it + + align:start position:0% +right so moving on character design it + + + align:start position:0% +right so moving on character design it +provides Clues towards your actions and + + align:start position:0% +provides Clues towards your actions and + + + align:start position:0% +provides Clues towards your actions and +your verbs although in that last example + + align:start position:0% +your verbs although in that last example + + + align:start position:0% +your verbs although in that last example +it was actually not very good at that + + align:start position:0% +it was actually not very good at that + + + align:start position:0% +it was actually not very good at that +part but it does give Clues towards your + + align:start position:0% +part but it does give Clues towards your + + + align:start position:0% +part but it does give Clues towards your +background who you are what you are why + + align:start position:0% +background who you are what you are why + + + align:start position:0% +background who you are what you are why +you are and then the feel what's the + + align:start position:0% +you are and then the feel what's the + + + align:start position:0% +you are and then the feel what's the +feel of that game supposed to be what + + align:start position:0% +feel of that game supposed to be what + + + align:start position:0% +feel of that game supposed to be what +like what's the feel you're supposed to + + align:start position:0% +like what's the feel you're supposed to + + + align:start position:0% +like what's the feel you're supposed to +have when you're playing the game + + align:start position:0% +have when you're playing the game + + + align:start position:0% +have when you're playing the game +question okay cool all right + + align:start position:0% +question okay cool all right + + + align:start position:0% +question okay cool all right +environmental design is that third thing + + align:start position:0% +environmental design is that third thing + + + align:start position:0% +environmental design is that third thing +I talked about uh this is Portal this is + + align:start position:0% +I talked about uh this is Portal this is + + + align:start position:0% +I talked about uh this is Portal this is +when you first start portal it's very + + align:start position:0% +when you first start portal it's very + + + align:start position:0% +when you first start portal it's very +clean it's very spacious except for that + + align:start position:0% +clean it's very spacious except for that + + + align:start position:0% +clean it's very spacious except for that +little box that you're stuck in you + + align:start position:0% +little box that you're stuck in you + + + align:start position:0% +little box that you're stuck in you +eventually get out um but something + + align:start position:0% +eventually get out um but something + + + align:start position:0% +eventually get out um but something +happens and you see something later in + + align:start position:0% +happens and you see something later in + + + align:start position:0% +happens and you see something later in +the game does anybody remember where + + align:start position:0% +the game does anybody remember where + + + align:start position:0% +the game does anybody remember where +this + + align:start position:0% +this + + + align:start position:0% +this +is oh not played it the middle what + + align:start position:0% +is oh not played it the middle what + + + align:start position:0% +is oh not played it the middle what +which which + + align:start position:0% +which which + + + align:start position:0% +which which +level like three or four or five or six + + align:start position:0% +level like three or four or five or six + + + align:start position:0% +level like three or four or five or six +or have you seen a turret yet have I + + align:start position:0% +or have you seen a turret yet have I + + + align:start position:0% +or have you seen a turret yet have I +seen a turret yeah oh no okay all right + + align:start position:0% +seen a turret yeah oh no okay all right + + + align:start position:0% +seen a turret yeah oh no okay all right +close your eyes sh + + align:start position:0% +close your eyes sh + + + align:start position:0% +close your eyes sh +ears it's it's 2014 come + + align:start position:0% +ears it's it's 2014 come + + + align:start position:0% +ears it's it's 2014 come +on um yeah so this is the cake is a + + align:start position:0% +on um yeah so this is the cake is a + + + align:start position:0% +on um yeah so this is the cake is a +lieat it's later in the game um it's + + align:start position:0% +lieat it's later in the game um it's + + + align:start position:0% +lieat it's later in the game um it's +actually in a part of the game where + + align:start position:0% +actually in a part of the game where + + + align:start position:0% +actually in a part of the game where +everything's still looks really clean + + align:start position:0% +everything's still looks really clean + + + align:start position:0% +everything's still looks really clean +and that's as far as I'm going to go um + + align:start position:0% +and that's as far as I'm going to go um + + + align:start position:0% +and that's as far as I'm going to go um +somebody left stuff back there and this + + align:start position:0% +somebody left stuff back there and this + + + align:start position:0% +somebody left stuff back there and this +this is actually something that not a + + align:start position:0% +this is actually something that not a + + + align:start position:0% +this is actually something that not a +lot of players saw when it first came + + align:start position:0% +lot of players saw when it first came + + + align:start position:0% +lot of players saw when it first came +out and then a lot of people other + + align:start position:0% +out and then a lot of people other + + + align:start position:0% +out and then a lot of people other +players told each other about it later + + align:start position:0% +players told each other about it later + + + align:start position:0% +players told each other about it later +on so it's also a game event which I'm + + align:start position:0% +on so it's also a game event which I'm + + + align:start position:0% +on so it's also a game event which I'm +going to talk about later um we're + + align:start position:0% +going to talk about later um we're + + + align:start position:0% +going to talk about later um we're +talking about the story of the player + + align:start position:0% +talking about the story of the player + + + align:start position:0% +talking about the story of the player +but this is where level design and + + align:start position:0% +but this is where level design and + + + align:start position:0% +but this is where level design and +narrative design meet so the level was + + align:start position:0% +narrative design meet so the level was + + + align:start position:0% +narrative design meet so the level was +created there was a story moment that + + align:start position:0% +created there was a story moment that + + + align:start position:0% +created there was a story moment that +had to be placed somewhere The Narrative + + align:start position:0% +had to be placed somewhere The Narrative + + + align:start position:0% +had to be placed somewhere The Narrative +designer placed it in in a spot that was + + align:start position:0% +designer placed it in in a spot that was + + + align:start position:0% +designer placed it in in a spot that was +hidden that was hard to get to but still + + align:start position:0% +hidden that was hard to get to but still + + + align:start position:0% +hidden that was hard to get to but still +reachable and when we talk about + + align:start position:0% +reachable and when we talk about + + + align:start position:0% +reachable and when we talk about +environmental storytelling we often talk + + align:start position:0% +environmental storytelling we often talk + + + align:start position:0% +environmental storytelling we often talk +about there's been some articles about + + align:start position:0% +about there's been some articles about + + + align:start position:0% +about there's been some articles about +bad graffiti in games and just how how + + align:start position:0% +bad graffiti in games and just how how + + + align:start position:0% +bad graffiti in games and just how how +TR this this has been used and trying to + + align:start position:0% +TR this this has been used and trying to + + + align:start position:0% +TR this this has been used and trying to +use other we're trying to find new ways + + align:start position:0% +use other we're trying to find new ways + + + align:start position:0% +use other we're trying to find new ways +of doing the same thing but it's + + align:start position:0% +of doing the same thing but it's + + + align:start position:0% +of doing the same thing but it's +basically there was someone in there + + align:start position:0% +basically there was someone in there + + + align:start position:0% +basically there was someone in there +before you is what happened there and + + align:start position:0% +before you is what happened there and + + + align:start position:0% +before you is what happened there and +that's as far as I'm going to get all + + align:start position:0% +that's as far as I'm going to get all + + + align:start position:0% +that's as far as I'm going to get all +right so environment provides Clues + + align:start position:0% +right so environment provides Clues + + + align:start position:0% +right so environment provides Clues +towards what happened in the past but + + align:start position:0% +towards what happened in the past but + + + align:start position:0% +towards what happened in the past but +also what's going to happen in the + + align:start position:0% +also what's going to happen in the + + + align:start position:0% +also what's going to happen in the +future and it provides Clues towards the + + align:start position:0% +future and it provides Clues towards the + + + align:start position:0% +future and it provides Clues towards the +feel so again what's what's the game + + align:start position:0% +feel so again what's what's the game + + + align:start position:0% +feel so again what's what's the game +supposed to feel + + align:start position:0% +supposed to feel + + + align:start position:0% +supposed to feel +like all right so moving on we've got + + align:start position:0% +like all right so moving on we've got + + + align:start position:0% +like all right so moving on we've got +the story of the player so there's the + + align:start position:0% +the story of the player so there's the + + + align:start position:0% +the story of the player so there's the +embedded story of the player and what I + + align:start position:0% +embedded story of the player and what I + + + align:start position:0% +embedded story of the player and what I +mean by that is that's the story of the + + align:start position:0% +mean by that is that's the story of the + + + align:start position:0% +mean by that is that's the story of the +player that's pre-established by the + + align:start position:0% +player that's pre-established by the + + + align:start position:0% +player that's pre-established by the +game so everybody played oakarina of + + align:start position:0% +game so everybody played oakarina of + + + align:start position:0% +game so everybody played oakarina of +time or heard of it or seen it + + align:start position:0% +time or heard of it or seen it + + + align:start position:0% +time or heard of it or seen it +yeah okay um so you're a link you start + + align:start position:0% +yeah okay um so you're a link you start + + + align:start position:0% +yeah okay um so you're a link you start +out not knowing a lot about the world + + align:start position:0% +out not knowing a lot about the world + + + align:start position:0% +out not knowing a lot about the world +and slowly the game lets you know more + + align:start position:0% +and slowly the game lets you know more + + + align:start position:0% +and slowly the game lets you know more +about what what happened in the World + + align:start position:0% +about what what happened in the World + + + align:start position:0% +about what what happened in the World +Behind you um you don't get to choose to + + align:start position:0% +Behind you um you don't get to choose to + + + align:start position:0% +Behind you um you don't get to choose to +have this friend I don't think right um + + align:start position:0% +have this friend I don't think right um + + + align:start position:0% +have this friend I don't think right um +what's her name sarla Saria the game + + align:start position:0% +what's her name sarla Saria the game + + + align:start position:0% +what's her name sarla Saria the game +gave you this friend um and actually + + align:start position:0% +gave you this friend um and actually + + + align:start position:0% +gave you this friend um and actually +later on the other friends you give you + + align:start position:0% +later on the other friends you give you + + + align:start position:0% +later on the other friends you give you +get the game's going to give you those + + align:start position:0% +get the game's going to give you those + + + align:start position:0% +get the game's going to give you those +too you don't get to choose to have them + + align:start position:0% +too you don't get to choose to have them + + + align:start position:0% +too you don't get to choose to have them +or not and she gives you this okarina + + align:start position:0% +or not and she gives you this okarina + + + align:start position:0% +or not and she gives you this okarina +the oar is a very important aspect of + + align:start position:0% +the oar is a very important aspect of + + + align:start position:0% +the oar is a very important aspect of +the game so in this case it's this + + align:start position:0% +the game so in this case it's this + + + align:start position:0% +the game so in this case it's this +embedded story of here's this object + + align:start position:0% +embedded story of here's this object + + + align:start position:0% +embedded story of here's this object +that you're going to use it's going to + + align:start position:0% +that you're going to use it's going to + + + align:start position:0% +that you're going to use it's going to +be incredibly useful for you in later in + + align:start position:0% +be incredibly useful for you in later in + + + align:start position:0% +be incredibly useful for you in later in +the game to the point where you're going + + align:start position:0% +the game to the point where you're going + + + align:start position:0% +the game to the point where you're going +to get really annoyed by having to bring + + align:start position:0% +to get really annoyed by having to bring + + + align:start position:0% +to get really annoyed by having to bring +it up all the time um and play the same + + align:start position:0% +it up all the time um and play the same + + + align:start position:0% +it up all the time um and play the same +song all the time but it's also part of + + align:start position:0% +song all the time but it's also part of + + + align:start position:0% +song all the time but it's also part of +the character design it's giving you + + align:start position:0% +the character design it's giving you + + + align:start position:0% +the character design it's giving you +what your capabilities like what are you + + align:start position:0% +what your capabilities like what are you + + + align:start position:0% +what your capabilities like what are you +capable of doing in this case you're + + align:start position:0% +capable of doing in this case you're + + + align:start position:0% +capable of doing in this case you're +capable of singing songs on the oena or + + align:start position:0% +capable of singing songs on the oena or + + + align:start position:0% +capable of singing songs on the oena or +playing songs on the o Arena that do + + align:start position:0% +playing songs on the o Arena that do + + + align:start position:0% +playing songs on the o Arena that do +magical effects within the game there's + + align:start position:0% +magical effects within the game there's + + + align:start position:0% +magical effects within the game there's +also emergent and this is the cooler + + align:start position:0% +also emergent and this is the cooler + + + align:start position:0% +also emergent and this is the cooler +thing this is I'm going to spend more + + align:start position:0% +thing this is I'm going to spend more + + + align:start position:0% +thing this is I'm going to spend more +time on this is the result of the player + + align:start position:0% +time on this is the result of the player + + + align:start position:0% +time on this is the result of the player +interacting with the system in this case + + align:start position:0% +interacting with the system in this case + + + align:start position:0% +interacting with the system in this case +it's Sims 3 um and much of the systems + + align:start position:0% +it's Sims 3 um and much of the systems + + + align:start position:0% +it's Sims 3 um and much of the systems +of at least Sims 1 I I think still in + + align:start position:0% +of at least Sims 1 I I think still in + + + align:start position:0% +of at least Sims 1 I I think still in +Sim Sims 3 it's the entire game is + + align:start position:0% +Sim Sims 3 it's the entire game is + + + align:start position:0% +Sim Sims 3 it's the entire game is +basically based on maso's um hierarchy + + align:start position:0% +basically based on maso's um hierarchy + + + align:start position:0% +basically based on maso's um hierarchy +of needs which I'll I'll bring up the + + align:start position:0% +of needs which I'll I'll bring up the + + + align:start position:0% +of needs which I'll I'll bring up the +slide I think I bring that up in a later + + align:start position:0% +slide I think I bring that up in a later + + + align:start position:0% +slide I think I bring that up in a later +version but basically it is there's + + align:start position:0% +version but basically it is there's + + + align:start position:0% +version but basically it is there's +things going it's a Sandbox game there + + align:start position:0% +things going it's a Sandbox game there + + + align:start position:0% +things going it's a Sandbox game there +are things you can do in the game and + + align:start position:0% +are things you can do in the game and + + + align:start position:0% +are things you can do in the game and +the story that's being told is the the + + align:start position:0% +the story that's being told is the the + + + align:start position:0% +the story that's being told is the the +events and things that happen to the + + align:start position:0% +events and things that happen to the + + + align:start position:0% +events and things that happen to the +characters based on changes you make in + + align:start position:0% +characters based on changes you make in + + + align:start position:0% +characters based on changes you make in +the environment you're not always you're + + align:start position:0% +the environment you're not always you're + + + align:start position:0% +the environment you're not always you're +not going to get the same story over and + + align:start position:0% +not going to get the same story over and + + + align:start position:0% +not going to get the same story over and +over again you're going to get new new + + align:start position:0% +over again you're going to get new new + + + align:start position:0% +over again you're going to get new new +stories um some big some like this case + + align:start position:0% +stories um some big some like this case + + + align:start position:0% +stories um some big some like this case +the entire game is that kind of thing in + + align:start position:0% +the entire game is that kind of thing in + + + align:start position:0% +the entire game is that kind of thing in +other games it's a it's more of a + + align:start position:0% +other games it's a it's more of a + + + align:start position:0% +other games it's a it's more of a +smaller aspect of the game it's a it's + + align:start position:0% +smaller aspect of the game it's a it's + + + align:start position:0% +smaller aspect of the game it's a it's +an added bonus to the + + align:start position:0% +an added bonus to the + + + align:start position:0% +an added bonus to the +game so the story of this player in + + align:start position:0% +game so the story of this player in + + + align:start position:0% +game so the story of this player in +either of those cases usually told + + align:start position:0% +either of those cases usually told + + + align:start position:0% +either of those cases usually told +through three things and these are three + + align:start position:0% +through three things and these are three + + + align:start position:0% +through three things and these are three +things you can use in your games right + + align:start position:0% +things you can use in your games right + + + align:start position:0% +things you can use in your games right +now uh game premise or the goal of the + + align:start position:0% +now uh game premise or the goal of the + + + align:start position:0% +now uh game premise or the goal of the +game is your story right why are you + + align:start position:0% +game is your story right why are you + + + align:start position:0% +game is your story right why are you +going where are you going uh game events + + align:start position:0% +going where are you going uh game events + + + align:start position:0% +going where are you going uh game events +so things that happen within the game + + align:start position:0% +so things that happen within the game + + + align:start position:0% +so things that happen within the game +either predetermined or emergent and + + align:start position:0% +either predetermined or emergent and + + + align:start position:0% +either predetermined or emergent and +then micro narratives which I'll explain + + align:start position:0% +then micro narratives which I'll explain + + + align:start position:0% +then micro narratives which I'll explain +what that is um at the end so here is a + + align:start position:0% +what that is um at the end so here is a + + + align:start position:0% +what that is um at the end so here is a +Prem + + align:start position:0% +Prem + + + align:start position:0% +Prem +again we're at MIT so we talk about + + align:start position:0% +again we're at MIT so we talk about + + + align:start position:0% +again we're at MIT so we talk about +hacking + + align:start position:0% +hacking + + + align:start position:0% +hacking +righten + + align:start position:0% +righten + + + align:start position:0% +righten +genius a true original from introversion + + align:start position:0% +genius a true original from introversion + + + align:start position:0% +genius a true original from introversion +software the award winning ladies of + + align:start position:0% +software the award winning ladies of + + + align:start position:0% +software the award winning ladies of +doia a futuristic Hightech computer chme + + align:start position:0% +doia a futuristic Hightech computer chme + + + align:start position:0% +doia a futuristic Hightech computer chme +game for the ha + + align:start position:0% +game for the ha + + + align:start position:0% +game for the ha +up you're an uping agent a freelance + + align:start position:0% +up you're an uping agent a freelance + + + align:start position:0% +up you're an uping agent a freelance +hacker your client Global multinationals + + align:start position:0% +hacker your client Global multinationals + + + align:start position:0% +hacker your client Global multinationals +you happen to R computer systems steal + + align:start position:0% +you happen to R computer systems steal + + + align:start position:0% +you happen to R computer systems steal +research data sabotage other companies + + align:start position:0% +research data sabotage other companies + + + align:start position:0% +research data sabotage other companies +Lo money the evidence even inent people + + align:start position:0% +Lo money the evidence even inent people + + + align:start position:0% +Lo money the evidence even inent people +that all from the comt of your own home + + align:start position:0% +that all from the comt of your own home + + + align:start position:0% +that all from the comt of your own home +in up you are the hacker Elite one more + + align:start position:0% +in up you are the hacker Elite one more + + + align:start position:0% +in up you are the hacker Elite one more +dangerous and profitable missions change + + align:start position:0% +dangerous and profitable missions change + + + align:start position:0% +dangerous and profitable missions change +people's academic and even criminal + + align:start position:0% +people's academic and even criminal + + + align:start position:0% +people's academic and even criminal +records and enph money by out into yours + + align:start position:0% +records and enph money by out into yours + + + align:start position:0% +records and enph money by out into yours +and why not construct the most deadly + + align:start position:0% +and why not construct the most deadly + + + align:start position:0% +and why not construct the most deadly +computer virus ever designed but watch + + align:start position:0% +computer virus ever designed but watch + + + align:start position:0% +computer virus ever designed but watch +out when you're online you're being + + align:start position:0% + + + + align:start position:0% + +traced again for the corrupted heart + + align:start position:0% +traced again for the corrupted heart + + + align:start position:0% +traced again for the corrupted heart +where Trust + + align:start position:0% + + + + align:start position:0% + +G yeah + + align:start position:0% +G yeah + + + align:start position:0% +G yeah +so threw a lot of words at you but + + align:start position:0% +so threw a lot of words at you but + + + align:start position:0% +so threw a lot of words at you but +basically every single thing inside of + + align:start position:0% +basically every single thing inside of + + + align:start position:0% +basically every single thing inside of +that game is something you can do in the + + align:start position:0% +that game is something you can do in the + + + align:start position:0% +that game is something you can do in the +game you can hack another person you can + + align:start position:0% +game you can hack another person you can + + + align:start position:0% +game you can hack another person you can +create a virus you can download their + + align:start position:0% +create a virus you can download their + + + align:start position:0% +create a virus you can download their +personal records you can change their + + align:start position:0% +personal records you can change their + + + align:start position:0% +personal records you can change their +personal records everything single + + align:start position:0% +personal records everything single + + + align:start position:0% +personal records everything single +single one of those things mentioned in + + align:start position:0% +single one of those things mentioned in + + + align:start position:0% +single one of those things mentioned in +the in the premise in the trailer is a + + align:start position:0% +the in the premise in the trailer is a + + + align:start position:0% +the in the premise in the trailer is a +mechanic that is usable within the game + + align:start position:0% +mechanic that is usable within the game + + + align:start position:0% +mechanic that is usable within the game +in some form and it's large it's like a + + align:start position:0% +in some form and it's large it's like a + + + align:start position:0% +in some form and it's large it's like a +lot of it is a a user interface that + + align:start position:0% +lot of it is a a user interface that + + + align:start position:0% +lot of it is a a user interface that +kind of looks like a futuristic uh + + align:start position:0% +kind of looks like a futuristic uh + + + align:start position:0% +kind of looks like a futuristic uh +computer terminal or an interface + + align:start position:0% +computer terminal or an interface + + + align:start position:0% +computer terminal or an interface +terminal made by the same people if you + + align:start position:0% +terminal made by the same people if you + + + align:start position:0% +terminal made by the same people if you +remember we showed Defcon earlier in the + + align:start position:0% +remember we showed Defcon earlier in the + + + align:start position:0% +remember we showed Defcon earlier in the +semester uh same folks they're really + + align:start position:0% +semester uh same folks they're really + + + align:start position:0% +semester uh same folks they're really +good at that kind of atmosphere and + + align:start position:0% +good at that kind of atmosphere and + + + align:start position:0% +good at that kind of atmosphere and +building + + align:start position:0% +building + + + align:start position:0% +building +atmosphere futuristic from the 90s point + + align:start position:0% +atmosphere futuristic from the 90s point + + + align:start position:0% +atmosphere futuristic from the 90s point +of view yeah it's still + + align:start position:0% +of view yeah it's still + + + align:start position:0% +of view yeah it's still +futuristic um all right so game PR + + align:start position:0% +futuristic um all right so game PR + + + align:start position:0% +futuristic um all right so game PR +that's an easy one to get across + + align:start position:0% +that's an easy one to get across + + + align:start position:0% +that's an easy one to get across +basically it's just think about all the + + align:start position:0% +basically it's just think about all the + + + align:start position:0% +basically it's just think about all the +things that you do in the game all those + + align:start position:0% +things that you do in the game all those + + + align:start position:0% +things that you do in the game all those +things when when you put them together + + align:start position:0% +things when when you put them together + + + align:start position:0% +things when when you put them together +one by one that is the story that the + + align:start position:0% +one by one that is the story that the + + + align:start position:0% +one by one that is the story that the +player is going to be telling when they + + align:start position:0% +player is going to be telling when they + + + align:start position:0% +player is going to be telling when they +play your game um so think of it in in + + align:start position:0% +play your game um so think of it in in + + + align:start position:0% +play your game um so think of it in in +in that case what they're doing is + + align:start position:0% +in that case what they're doing is + + + align:start position:0% +in that case what they're doing is +they're they're using a genre convention + + align:start position:0% +they're they're using a genre convention + + + align:start position:0% +they're they're using a genre convention +and they're using some tropes that you + + align:start position:0% +and they're using some tropes that you + + + align:start position:0% +and they're using some tropes that you +might already know tropes can be useful + + align:start position:0% +might already know tropes can be useful + + + align:start position:0% +might already know tropes can be useful +tropes can be baggage tropes are usually + + align:start position:0% +tropes can be baggage tropes are usually + + + align:start position:0% +tropes can be baggage tropes are usually +baggage um but genre conventions are + + align:start position:0% +baggage um but genre conventions are + + + align:start position:0% +baggage um but genre conventions are +great um especially when it's just I + + align:start position:0% +great um especially when it's just I + + + align:start position:0% +great um especially when it's just I +want to get this theme across to you I + + align:start position:0% +want to get this theme across to you I + + + align:start position:0% +want to get this theme across to you I +want to get this like Hard Punch of you + + align:start position:0% +want to get this like Hard Punch of you + + + align:start position:0% +want to get this like Hard Punch of you +know exactly what you need to do I don't + + align:start position:0% +know exactly what you need to do I don't + + + align:start position:0% +know exactly what you need to do I don't +need to explain the game to you because + + align:start position:0% +need to explain the game to you because + + + align:start position:0% +need to explain the game to you because +you know what a hacker is supposed to do + + align:start position:0% +you know what a hacker is supposed to do + + + align:start position:0% +you know what a hacker is supposed to do +that's where those things are incredibly + + align:start position:0% +that's where those things are incredibly + + + align:start position:0% +that's where those things are incredibly +useful + + align:start position:0% +useful + + + align:start position:0% +useful +oops give me my slides all right game + + align:start position:0% +oops give me my slides all right game + + + align:start position:0% +oops give me my slides all right game +events has anybody played Final Fantasy + + align:start position:0% +events has anybody played Final Fantasy + + + align:start position:0% +events has anybody played Final Fantasy +4 or two if you played the original or + + align:start position:0% +4 or two if you played the original or + + + align:start position:0% +4 or two if you played the original or +the US version I mean so there is a + + align:start position:0% +the US version I mean so there is a + + + align:start position:0% +the US version I mean so there is a +character called Ria the sumoner that is + + align:start position:0% +character called Ria the sumoner that is + + + align:start position:0% +character called Ria the sumoner that is +not what she looked like in the game + + align:start position:0% +not what she looked like in the game + + + align:start position:0% +not what she looked like in the game +that was the the illustration that that + + align:start position:0% +that was the the illustration that that + + + align:start position:0% +that was the the illustration that that +she looked like she looked like a very + + align:start position:0% +she looked like she looked like a very + + + align:start position:0% +she looked like she looked like a very +small uh green-haired + + align:start position:0% +small uh green-haired + + + align:start position:0% +small uh green-haired +person um she is a Summoner she has + + align:start position:0% +person um she is a Summoner she has + + + align:start position:0% +person um she is a Summoner she has +magic powers what kind of magic powers + + align:start position:0% +magic powers what kind of magic powers + + + align:start position:0% +magic powers what kind of magic powers +are common in the Final Fantasy series + + align:start position:0% +are common in the Final Fantasy series + + + align:start position:0% +are common in the Final Fantasy series +what's the three + + align:start position:0% + + + + align:start position:0% + +Basics ice and thunder yeah or or or + + align:start position:0% +Basics ice and thunder yeah or or or + + + align:start position:0% +Basics ice and thunder yeah or or or +yeah fire ice and thunder yeah exactly + + align:start position:0% +yeah fire ice and thunder yeah exactly + + + align:start position:0% +yeah fire ice and thunder yeah exactly +right + + align:start position:0% +right + + + align:start position:0% +right +um Mo and I think so she is a Summoner + + align:start position:0% +um Mo and I think so she is a Summoner + + + align:start position:0% +um Mo and I think so she is a Summoner +but she has those are Black Mage Powers + + align:start position:0% +but she has those are Black Mage Powers + + + align:start position:0% +but she has those are Black Mage Powers +pretty common most characters would have + + align:start position:0% +pretty common most characters would have + + + align:start position:0% +pretty common most characters would have +those three those three powers except + + align:start position:0% +those three those three powers except + + + align:start position:0% +those three those three powers except +for her she hates fire and you don't + + align:start position:0% +for her she hates fire and you don't + + + align:start position:0% +for her she hates fire and you don't +have fire for for a good part of the + + align:start position:0% +have fire for for a good part of the + + + align:start position:0% +have fire for for a good part of the +game there's a moment in the game you're + + align:start position:0% +game there's a moment in the game you're + + + align:start position:0% +game there's a moment in the game you're +at Mount hob there's it's an Ice + + align:start position:0% +at Mount hob there's it's an Ice + + + align:start position:0% +at Mount hob there's it's an Ice +Mountain you need to get + + align:start position:0% +Mountain you need to get + + + align:start position:0% +Mountain you need to get +through yeah you can kind of see ice in + + align:start position:0% +through yeah you can kind of see ice in + + + align:start position:0% +through yeah you can kind of see ice in +the background there um you need to get + + align:start position:0% +the background there um you need to get + + + align:start position:0% +the background there um you need to get +through the the the cave and there's a + + align:start position:0% +through the the the cave and there's a + + + align:start position:0% +through the the the cave and there's a +story moment one of the characters Cecil + + align:start position:0% +story moment one of the characters Cecil + + + align:start position:0% +story moment one of the characters Cecil +on the left there says she's afraid of + + align:start position:0% +on the left there says she's afraid of + + + align:start position:0% +on the left there says she's afraid of +fire because her Village was destroyed + + align:start position:0% +fire because her Village was destroyed + + + align:start position:0% +fire because her Village was destroyed +in a fire and you and you see the a + + align:start position:0% +in a fire and you and you see the a + + + align:start position:0% +in a fire and you and you see the a +snippet of this early in the game and + + align:start position:0% +snippet of this early in the game and + + + align:start position:0% +snippet of this early in the game and +you get moments that you she's got this + + align:start position:0% +you get moments that you she's got this + + + align:start position:0% +you get moments that you she's got this +back story where trumatic ped it's + + align:start position:0% +back story where trumatic ped it's + + + align:start position:0% +back story where trumatic ped it's +preventing her from doing a thing again + + align:start position:0% +preventing her from doing a thing again + + + align:start position:0% +preventing her from doing a thing again +this is a Trope that's pretty common uh + + align:start position:0% +this is a Trope that's pretty common uh + + + align:start position:0% +this is a Trope that's pretty common uh +after this point they're all like yeah + + align:start position:0% +after this point they're all like yeah + + + align:start position:0% +after this point they're all like yeah +you can do it you're awesome you're + + align:start position:0% +you can do it you're awesome you're + + + align:start position:0% +you can do it you're awesome you're +great and then she gets fire and now all + + align:start position:0% +great and then she gets fire and now all + + + align:start position:0% +great and then she gets fire and now all +of a sudden you've got the fire skill + + align:start position:0% +of a sudden you've got the fire skill + + + align:start position:0% +of a sudden you've got the fire skill +for this character for the rest of the + + align:start position:0% +for this character for the rest of the + + + align:start position:0% +for this character for the rest of the +game um anytime you play the game after + + align:start position:0% +game um anytime you play the game after + + + align:start position:0% +game um anytime you play the game after +that and you're using fire there's some + + align:start position:0% +that and you're using fire there's some + + + align:start position:0% +that and you're using fire there's some +part of you that might be remembering + + align:start position:0% +part of you that might be remembering + + + align:start position:0% +part of you that might be remembering +this story moment and how important the + + align:start position:0% +this story moment and how important the + + + align:start position:0% +this story moment and how important the +story moment was it's being linked back + + align:start position:0% +story moment was it's being linked back + + + align:start position:0% +story moment was it's being linked back +into the game mechanics really really + + align:start position:0% +into the game mechanics really really + + + align:start position:0% +into the game mechanics really really +well well but it always happens every + + align:start position:0% +well well but it always happens every + + + align:start position:0% +well well but it always happens every +time you play the game that's embedded + + align:start position:0% +time you play the game that's embedded + + + align:start position:0% +time you play the game that's embedded +that's always going to happen one more + + align:start position:0% +that's always going to happen one more + + + align:start position:0% +that's always going to happen one more +video here is an emergent event has + + align:start position:0% +video here is an emergent event has + + + align:start position:0% +video here is an emergent event has +anybody seen this + + align:start position:0% +anybody seen this + + + align:start position:0% +anybody seen this +video everybody recognizes the game + + align:start position:0% +video everybody recognizes the game + + + align:start position:0% +video everybody recognizes the game +though + + align:start position:0% + + + + align:start position:0% + +yeah hi guys and just here I've been + + align:start position:0% +yeah hi guys and just here I've been + + + align:start position:0% +yeah hi guys and just here I've been +getting some questions on how to um + + align:start position:0% +getting some questions on how to um + + + align:start position:0% +getting some questions on how to um +make indefinite Fire and Fire that's + + align:start position:0% +make indefinite Fire and Fire that's + + + align:start position:0% +make indefinite Fire and Fire that's +cool castle whatever it is is currently + + align:start position:0% +cool castle whatever it is is currently + + + align:start position:0% +cool castle whatever it is is currently +not + + align:start position:0% +not + + + align:start position:0% +not +avable into the room something maybe so + + align:start position:0% +avable into the room something maybe so + + + align:start position:0% +avable into the room something maybe so +he gave me of this just before I and see + + align:start position:0% +he gave me of this just before I and see + + + align:start position:0% +he gave me of this just before I and see +well we team can need fire as well and + + align:start position:0% +well we team can need fire as well and + + + align:start position:0% +well we team can need fire as well and +so let's go ahead and just make like a a + + align:start position:0% +so let's go ahead and just make like a a + + + align:start position:0% +so let's go ahead and just make like a a +fireplace and we've already made it as + + align:start position:0% +fireplace and we've already made it as + + + align:start position:0% +fireplace and we've already made it as +you see it's inact here and that's + + align:start position:0% +you see it's inact here and that's + + + align:start position:0% +you see it's inact here and that's +cool so + + align:start position:0% +cool so + + + align:start position:0% +cool so +yeah apparently all need is some Fint + + align:start position:0% +yeah apparently all need is some Fint + + + align:start position:0% +yeah apparently all need is some Fint +and a log um just a chop down Tre bit + + align:start position:0% +and a log um just a chop down Tre bit + + + align:start position:0% +and a log um just a chop down Tre bit +log and all you do is you put it in the + + align:start position:0% +log and all you do is you put it in the + + + align:start position:0% +log and all you do is you put it in the +center here like this and then set far + + align:start position:0% +center here like this and then set far + + + align:start position:0% +center here like this and then set far +and not always well most + + align:start position:0% + + + + align:start position:0% + +of I didn't knew that was going to + + align:start position:0% +of I didn't knew that was going to + + + align:start position:0% +of I didn't knew that was going to +happen yeah a little little + + align:start position:0% + + + + align:start position:0% + +transparent okay he had some water he + + align:start position:0% +transparent okay he had some water he + + + align:start position:0% +transparent okay he had some water he +[Music] + + align:start position:0% + + + + align:start position:0% + +tried sorry sorry guys and not suppos to + + align:start position:0% +tried sorry sorry guys and not suppos to + + + align:start position:0% +tried sorry sorry guys and not suppos to +happen + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +yeah what the hell is + + align:start position:0% + + + + align:start position:0% + +happening so there's system going on got + + align:start position:0% +happening so there's system going on got + + + align:start position:0% +happening so there's system going on got +to + + align:start position:0% + + + + align:start position:0% + +be there's a system within the game that + + align:start position:0% +be there's a system within the game that + + + align:start position:0% +be there's a system within the game that +fire burns pretty much anything it + + align:start position:0% +fire burns pretty much anything it + + + align:start position:0% +fire burns pretty much anything it +touches that's wood and it just travels + + align:start position:0% +touches that's wood and it just travels + + + align:start position:0% +touches that's wood and it just travels +right um you set this little system up + + align:start position:0% +right um you set this little system up + + + align:start position:0% +right um you set this little system up +you use it the way you use it and in + + align:start position:0% +you use it the way you use it and in + + + align:start position:0% +you use it the way you use it and in +this case he tried to tell a story of + + align:start position:0% +this case he tried to tell a story of + + + align:start position:0% +this case he tried to tell a story of +building a fire and it turned out he + + align:start position:0% +building a fire and it turned out he + + + align:start position:0% +building a fire and it turned out he +burned his house down um you also see + + align:start position:0% +burned his house down um you also see + + + align:start position:0% +burned his house down um you also see +this Minecraft uh the the creepers when + + align:start position:0% +this Minecraft uh the the creepers when + + + align:start position:0% +this Minecraft uh the the creepers when +if everybody hears that hiss of a + + align:start position:0% +if everybody hears that hiss of a + + + align:start position:0% +if everybody hears that hiss of a +creeper especially after you after + + align:start position:0% +creeper especially after you after + + + align:start position:0% +creeper especially after you after +you've built something you've got this + + align:start position:0% +you've built something you've got this + + + align:start position:0% +you've built something you've got this +tension you got this moment of panic + + align:start position:0% +tension you got this moment of panic + + + align:start position:0% +tension you got this moment of panic +that's a that's a memorable game event + + align:start position:0% +that's a that's a memorable game event + + + align:start position:0% +that's a that's a memorable game event +that you're going to tell another person + + align:start position:0% +that you're going to tell another person + + + align:start position:0% +that you're going to tell another person +after you've played the game um and + + align:start position:0% +after you've played the game um and + + + align:start position:0% +after you've played the game um and +especially these days you might you're + + align:start position:0% +especially these days you might you're + + + align:start position:0% +especially these days you might you're +going to record it onto YouTube and put + + align:start position:0% +going to record it onto YouTube and put + + + align:start position:0% +going to record it onto YouTube and put +it on online this was I think from 2010 + + align:start position:0% +it on online this was I think from 2010 + + + align:start position:0% +it on online this was I think from 2010 +because it's an alpha build of Minecraft + + align:start position:0% +because it's an alpha build of Minecraft + + + align:start position:0% +because it's an alpha build of Minecraft +all right continuing on the + + align:start position:0% +all right continuing on the + + + align:start position:0% +all right continuing on the +theme here's the Sims has anybody had + + align:start position:0% +theme here's the Sims has anybody had + + + align:start position:0% +theme here's the Sims has anybody had +this happen to them in The + + align:start position:0% +this happen to them in The + + + align:start position:0% +this happen to them in The +Sims they're just trying to have a party + + align:start position:0% +Sims they're just trying to have a party + + + align:start position:0% +Sims they're just trying to have a party +they're trying to meet their M's + + align:start position:0% +they're trying to meet their M's + + + align:start position:0% +they're trying to meet their M's +hierarchy of needs right they're trying + + align:start position:0% +hierarchy of needs right they're trying + + + align:start position:0% +hierarchy of needs right they're trying +to love and belong to each other and + + align:start position:0% +to love and belong to each other and + + + align:start position:0% +to love and belong to each other and +build some esteem and self-actualized + + align:start position:0% +build some esteem and self-actualized + + + align:start position:0% +build some esteem and self-actualized +himself but they forgot about the safety + + align:start position:0% +himself but they forgot about the safety + + + align:start position:0% +himself but they forgot about the safety +part of it and so the event the oven + + align:start position:0% +part of it and so the event the oven + + + align:start position:0% +part of it and so the event the oven +blew up and their fire happened and they + + align:start position:0% +blew up and their fire happened and they + + + align:start position:0% +blew up and their fire happened and they +all burned and died um common common + + align:start position:0% +all burned and died um common common + + + align:start position:0% +all burned and died um common common +Trope with with the Sims + + align:start position:0% +Trope with with the Sims + + + align:start position:0% +Trope with with the Sims +so another example I love um anybody + + align:start position:0% +so another example I love um anybody + + + align:start position:0% +so another example I love um anybody +play fir Cry 2 yeah um You' so fire + + align:start position:0% +play fir Cry 2 yeah um You' so fire + + + align:start position:0% +play fir Cry 2 yeah um You' so fire +existing fire Cry 2 I love fire um Far + + align:start position:0% +existing fire Cry 2 I love fire um Far + + + align:start position:0% +existing fire Cry 2 I love fire um Far +Cry 2 takes place in Africa you're a + + align:start position:0% +Cry 2 takes place in Africa you're a + + + align:start position:0% +Cry 2 takes place in Africa you're a +mercenary um you're going to um find a + + align:start position:0% +mercenary um you're going to um find a + + + align:start position:0% +mercenary um you're going to um find a +warlord and kill him at the end of the + + align:start position:0% +warlord and kill him at the end of the + + + align:start position:0% +warlord and kill him at the end of the +game it's basically what you're trying + + align:start position:0% +game it's basically what you're trying + + + align:start position:0% +game it's basically what you're trying +to do um you have different ways of + + align:start position:0% +to do um you have different ways of + + + align:start position:0% +to do um you have different ways of +doing that different means of doing that + + align:start position:0% +doing that different means of doing that + + + align:start position:0% +doing that different means of doing that +um you are in a savannah it's very dry + + align:start position:0% +um you are in a savannah it's very dry + + + align:start position:0% +um you are in a savannah it's very dry +you can burn the savan it's great um and + + align:start position:0% +you can burn the savan it's great um and + + + align:start position:0% +you can burn the savan it's great um and +you can use that to get past like a um a + + align:start position:0% +you can use that to get past like a um a + + + align:start position:0% +you can use that to get past like a um a +machine gun in place or set a trap for + + align:start position:0% +machine gun in place or set a trap for + + + align:start position:0% +machine gun in place or set a trap for +somebody um in-game character not not + + align:start position:0% +somebody um in-game character not not + + + align:start position:0% +somebody um in-game character not not +another PC but in game um in an early + + align:start position:0% +another PC but in game um in an early + + + align:start position:0% +another PC but in game um in an early +version of + + align:start position:0% +version of + + + align:start position:0% +version of +this an early test play testers Set Fire + + align:start position:0% +this an early test play testers Set Fire + + + align:start position:0% +this an early test play testers Set Fire +To The Savannah and then a few 10 15 20 + + align:start position:0% +To The Savannah and then a few 10 15 20 + + + align:start position:0% +To The Savannah and then a few 10 15 20 +minutes later it said okay you won the + + align:start position:0% +minutes later it said okay you won the + + + align:start position:0% +minutes later it said okay you won the +game what + + align:start position:0% +game what + + + align:start position:0% +game what +happened fire spread the boss was set in + + align:start position:0% +happened fire spread the boss was set in + + + align:start position:0% +happened fire spread the boss was set in +the fire in in the in the in dry grass + + align:start position:0% +the fire in in the in the in dry grass + + + align:start position:0% +the fire in in the in the in dry grass +the fire spread all the way through the + + align:start position:0% +the fire spread all the way through the + + + align:start position:0% +the fire spread all the way through the +the the game the the many many miles + + align:start position:0% +the the game the the many many miles + + + align:start position:0% +the the game the the many many miles +Square miles of gameplay and it killed + + align:start position:0% +Square miles of gameplay and it killed + + + align:start position:0% +Square miles of gameplay and it killed +the boss and ended the game I really + + align:start position:0% +the boss and ended the game I really + + + align:start position:0% +the boss and ended the game I really +wish they kept that in or a version of + + align:start position:0% +wish they kept that in or a version of + + + align:start position:0% +wish they kept that in or a version of +that they ended up um reducing the the + + align:start position:0% +that they ended up um reducing the the + + + align:start position:0% +that they ended up um reducing the the +the spread of fire because of that and + + align:start position:0% +the spread of fire because of that and + + + align:start position:0% +the spread of fire because of that and +they moved the character from the but + + align:start position:0% +they moved the character from the but + + + align:start position:0% +they moved the character from the but +that's a that's a game event they could + + align:start position:0% +that's a that's a game event they could + + + align:start position:0% +that's a that's a game event they could +have capitalized on that's an eer that's + + align:start position:0% +have capitalized on that's an eer that's + + + align:start position:0% +have capitalized on that's an eer that's +a piece of emergent storytelling that's + + align:start position:0% +a piece of emergent storytelling that's + + + align:start position:0% +a piece of emergent storytelling that's +going on that people tell the story to + + align:start position:0% +going on that people tell the story to + + + align:start position:0% +going on that people tell the story to +each other in developer circles I heard + + align:start position:0% +each other in developer circles I heard + + + align:start position:0% +each other in developer circles I heard +about this in GDC um the year after this + + align:start position:0% +about this in GDC um the year after this + + + align:start position:0% +about this in GDC um the year after this +came out that's a great one so that's + + align:start position:0% +came out that's a great one so that's + + + align:start position:0% +came out that's a great one so that's +game events um next up micro narratives + + align:start position:0% +game events um next up micro narratives + + + align:start position:0% +game events um next up micro narratives +um these are similar but different + + align:start position:0% +um these are similar but different + + + align:start position:0% +um these are similar but different +Micron narrative is basically a little + + align:start position:0% +Micron narrative is basically a little + + + align:start position:0% +Micron narrative is basically a little +bit of Storytelling inside of the game + + align:start position:0% +bit of Storytelling inside of the game + + + align:start position:0% +bit of Storytelling inside of the game +that's again really really small so + + align:start position:0% +that's again really really small so + + + align:start position:0% +that's again really really small so +maybe it's an animation in this case + + align:start position:0% +maybe it's an animation in this case + + + align:start position:0% +maybe it's an animation in this case +this is jetset Willie um and jetset + + align:start position:0% +this is jetset Willie um and jetset + + + align:start position:0% +this is jetset Willie um and jetset +Willie you are a rich guy you made all + + align:start position:0% +Willie you are a rich guy you made all + + + align:start position:0% +Willie you are a rich guy you made all +your money in the previous game uh by + + align:start position:0% +your money in the previous game uh by + + + align:start position:0% +your money in the previous game uh by +Mining and you came home and you invited + + align:start position:0% +Mining and you came home and you invited + + + align:start position:0% +Mining and you came home and you invited +a bunch of friends to your house and you + + align:start position:0% +a bunch of friends to your house and you + + + align:start position:0% +a bunch of friends to your house and you +had this awesome rockus party and you + + align:start position:0% +had this awesome rockus party and you + + + align:start position:0% +had this awesome rockus party and you +trashed the place and unfortunately you + + align:start position:0% +trashed the place and unfortunately you + + + align:start position:0% +trashed the place and unfortunately you +rent you rent a mansion instead of + + align:start position:0% +rent you rent a mansion instead of + + + align:start position:0% +rent you rent a mansion instead of +buying the mansion and you're you're + + align:start position:0% +buying the mansion and you're you're + + + align:start position:0% +buying the mansion and you're you're +trying to go to bed and your landl is + + align:start position:0% +trying to go to bed and your landl is + + + align:start position:0% +trying to go to bed and your landl is +just like no + + align:start position:0% +just like no + + + align:start position:0% +just like no +you don't get to go to bed you don't get + + align:start position:0% +you don't get to go to bed you don't get + + + align:start position:0% +you don't get to go to bed you don't get +to sleep you got to clean all this stuff + + align:start position:0% +to sleep you got to clean all this stuff + + + align:start position:0% +to sleep you got to clean all this stuff +up she doesn't say any of that though + + align:start position:0% +up she doesn't say any of that though + + + align:start position:0% +up she doesn't say any of that though +this is all she does just she's standing + + align:start position:0% +this is all she does just she's standing + + + align:start position:0% +this is all she does just she's standing +in front of the bed she's going that + + align:start position:0% +in front of the bed she's going that + + + align:start position:0% +in front of the bed she's going that +very this is for the ZX Spectrum so a + + align:start position:0% +very this is for the ZX Spectrum so a + + + align:start position:0% +very this is for the ZX Spectrum so a +really um I think it had 64k of ram + + align:start position:0% +really um I think it had 64k of ram + + + align:start position:0% +really um I think it had 64k of ram +maybe you could look that up maybe it's + + align:start position:0% +maybe you could look that up maybe it's + + + align:start position:0% +maybe you could look that up maybe it's +8K it's really small um really bad Keys + + align:start position:0% +8K it's really small um really bad Keys + + + align:start position:0% +8K it's really small um really bad Keys +really bad uh keyboard um not a lot of + + align:start position:0% +really bad uh keyboard um not a lot of + + + align:start position:0% +really bad uh keyboard um not a lot of +Graphics but that that version is + + align:start position:0% +Graphics but that that version is + + + align:start position:0% +Graphics but that that version is +actually a later version I couldn't find + + align:start position:0% +actually a later version I couldn't find + + + align:start position:0% +actually a later version I couldn't find +um this is the closest thing we found + + align:start position:0% +um this is the closest thing we found + + + align:start position:0% +um this is the closest thing we found +for what what it originally looked like + + align:start position:0% +for what what it originally looked like + + + align:start position:0% +for what what it originally looked like +but you can really there's character + + align:start position:0% +but you can really there's character + + + align:start position:0% +but you can really there's character +design there but it's also just saying + + align:start position:0% +design there but it's also just saying + + + align:start position:0% +design there but it's also just saying +you know no you you can't come back here + + align:start position:0% +you know no you you can't come back here + + + align:start position:0% +you know no you you can't come back here +16k go 128 + + align:start position:0% +16k go 128 + + + align:start position:0% +16k go 128 +okay all right + + align:start position:0% +okay all right + + + align:start position:0% +okay all right +so now I've spewed all this out what can + + align:start position:0% +so now I've spewed all this out what can + + + align:start position:0% +so now I've spewed all this out what can +you do with all this and so the next I'm + + align:start position:0% +you do with all this and so the next I'm + + + align:start position:0% +you do with all this and so the next I'm +going to show an example of a game + + align:start position:0% +going to show an example of a game + + + align:start position:0% +going to show an example of a game +created last semester by a team in this + + align:start position:0% +created last semester by a team in this + + + align:start position:0% +created last semester by a team in this +class uh for the final project um + + align:start position:0% +class uh for the final project um + + + align:start position:0% +class uh for the final project um +they made a game called Sugar Rush + + align:start position:0% +they made a game called Sugar Rush + + + align:start position:0% +they made a game called Sugar Rush +what's the game about first what's the + + align:start position:0% +what's the game about first what's the + + + align:start position:0% +what's the game about first what's the +well I sold the title Sugar Rush what's + + align:start position:0% +well I sold the title Sugar Rush what's + + + align:start position:0% +well I sold the title Sugar Rush what's +the game + + align:start position:0% + + + + align:start position:0% + +about yeah candy candy candy candy candy + + align:start position:0% +about yeah candy candy candy candy candy + + + align:start position:0% +about yeah candy candy candy candy candy +look at him all that candy and it's a + + align:start position:0% +look at him all that candy and it's a + + + align:start position:0% +look at him all that candy and it's a +kid so Title Character design all + + align:start position:0% +kid so Title Character design all + + + align:start position:0% +kid so Title Character design all +working really well right + + align:start position:0% +working really well right + + + align:start position:0% +working really well right +there here's the game + + align:start position:0% +there here's the game + + + align:start position:0% +there here's the game +premise one day strange leafy beasts + + align:start position:0% +premise one day strange leafy beasts + + + align:start position:0% +premise one day strange leafy beasts +Spawn from four mysterious portals and + + align:start position:0% +Spawn from four mysterious portals and + + + align:start position:0% +Spawn from four mysterious portals and +they plundered The Villages terrorizing + + align:start position:0% +they plundered The Villages terrorizing + + + align:start position:0% +they plundered The Villages terrorizing +Candyland what do you think you're going + + align:start position:0% +Candyland what do you think you're going + + + align:start position:0% +Candyland what do you think you're going +to have to do kill the vegetables um and + + align:start position:0% +to have to do kill the vegetables um and + + + align:start position:0% +to have to do kill the vegetables um and +they're mean because look at them so + + align:start position:0% +they're mean because look at them so + + + align:start position:0% +they're mean because look at them so +mean um now when we say like we said + + align:start position:0% +mean um now when we say like we said + + + align:start position:0% +mean um now when we say like we said +don't use cut scenes that doesn't mean + + align:start position:0% +don't use cut scenes that doesn't mean + + + align:start position:0% +don't use cut scenes that doesn't mean +we say don't use Exposition um a simple + + align:start position:0% +we say don't use Exposition um a simple + + + align:start position:0% +we say don't use Exposition um a simple +screen with a little bit of instructions + + align:start position:0% +screen with a little bit of instructions + + + align:start position:0% +screen with a little bit of instructions +like basically this is like we told them + + align:start position:0% +like basically this is like we told them + + + align:start position:0% +like basically this is like we told them +have an instruction screen this was part + + align:start position:0% +have an instruction screen this was part + + + align:start position:0% +have an instruction screen this was part +of their instruction screen they had the + + align:start position:0% +of their instruction screen they had the + + + align:start position:0% +of their instruction screen they had the +screen that says these are the keys but + + align:start position:0% +screen that says these are the keys but + + + align:start position:0% +screen that says these are the keys but +they also this is what you do um really + + align:start position:0% +they also this is what you do um really + + + align:start position:0% +they also this is what you do um really +really useful we want something that + + align:start position:0% +really useful we want something that + + + align:start position:0% +really useful we want something that +fulfills that for your game the way it's + + align:start position:0% +fulfills that for your game the way it's + + + align:start position:0% +fulfills that for your game the way it's +NE necessary for your game um the + + align:start position:0% +NE necessary for your game um the + + + align:start position:0% +NE necessary for your game um the +difference between a game that has + + align:start position:0% +difference between a game that has + + + align:start position:0% +difference between a game that has +something like this and doesn't have + + align:start position:0% +something like this and doesn't have + + + align:start position:0% +something like this and doesn't have +something like this is basically it's a + + align:start position:0% +something like this is basically it's a + + + align:start position:0% +something like this is basically it's a +level of Polish a game that has a little + + align:start position:0% +level of Polish a game that has a little + + + align:start position:0% +level of Polish a game that has a little +bit of exposition like this feels a + + align:start position:0% +bit of exposition like this feels a + + + align:start position:0% +bit of exposition like this feels a +little bit more concrete um there's it + + align:start position:0% +little bit more concrete um there's it + + + align:start position:0% +little bit more concrete um there's it +just feels like there's there's more + + align:start position:0% +just feels like there's there's more + + + align:start position:0% +just feels like there's there's more +it's more complete there's more thought + + align:start position:0% +it's more complete there's more thought + + + align:start position:0% +it's more complete there's more thought +put into it um it just feels a little + + align:start position:0% +put into it um it just feels a little + + + align:start position:0% +put into it um it just feels a little +bit richer um it's still playable + + align:start position:0% +bit richer um it's still playable + + + align:start position:0% +bit richer um it's still playable +without it it doesn't need this screen + + align:start position:0% +without it it doesn't need this screen + + + align:start position:0% +without it it doesn't need this screen +but the screen's really really helpful + + align:start position:0% +but the screen's really really helpful + + + align:start position:0% +but the screen's really really helpful +and the gameplay itself it has mechanics + + align:start position:0% +and the gameplay itself it has mechanics + + + align:start position:0% +and the gameplay itself it has mechanics +that are consistent with the design um + + align:start position:0% +that are consistent with the design um + + + align:start position:0% +that are consistent with the design um +you are a kid you are fighting a tomato + + align:start position:0% +you are a kid you are fighting a tomato + + + align:start position:0% +you are a kid you are fighting a tomato +what do you fight with you have weapons + + align:start position:0% +what do you fight with you have weapons + + + align:start position:0% +what do you fight with you have weapons +what are your weapons made out of candy + + align:start position:0% +what are your weapons made out of candy + + + align:start position:0% +what are your weapons made out of candy +how do you heal yourself you eat candy + + align:start position:0% +how do you heal yourself you eat candy + + + align:start position:0% +how do you heal yourself you eat candy +how do you make new weapons you combine + + align:start position:0% +how do you make new weapons you combine + + + align:start position:0% +how do you make new weapons you combine +and craft candy everything's revolving + + align:start position:0% +and craft candy everything's revolving + + + align:start position:0% +and craft candy everything's revolving +around that that premise of candy is is + + align:start position:0% +around that that premise of candy is is + + + align:start position:0% +around that that premise of candy is is +the world you are the lone human being + + align:start position:0% +the world you are the lone human being + + + align:start position:0% +the world you are the lone human being +in this world that we see um and so it's + + align:start position:0% +in this world that we see um and so it's + + + align:start position:0% +in this world that we see um and so it's +not like Adventure Time you're not + + align:start position:0% +not like Adventure Time you're not + + + align:start position:0% +not like Adventure Time you're not +harvesting candy from candy people um + + align:start position:0% +harvesting candy from candy people um + + + align:start position:0% +harvesting candy from candy people um +but and you're and the weird thing about + + align:start position:0% +but and you're and the weird thing about + + + align:start position:0% +but and you're and the weird thing about +it I think you when you kill vegetables + + align:start position:0% +it I think you when you kill vegetables + + + align:start position:0% +it I think you when you kill vegetables +you take the candy from them maybe + + align:start position:0% +you take the candy from them maybe + + + align:start position:0% +you take the candy from them maybe +they're stealing your candy yeah you are + + align:start position:0% +they're stealing your candy yeah you are + + + align:start position:0% +they're stealing your candy yeah you are +stealing your candy it says plundering + + align:start position:0% +stealing your candy it says plundering + + + align:start position:0% +stealing your candy it says plundering +aha they thought ahead + + align:start position:0% +aha they thought ahead + + + align:start position:0% +aha they thought ahead +um and yeah the health points what are + + align:start position:0% +um and yeah the health points what are + + + align:start position:0% +um and yeah the health points what are +the health points called if you can read + + align:start position:0% +the health points called if you can read + + + align:start position:0% +the health points called if you can read +it yeah really simple stuff really + + align:start position:0% +it yeah really simple stuff really + + + align:start position:0% +it yeah really simple stuff really +really simple just theming it thinking + + align:start position:0% +really simple just theming it thinking + + + align:start position:0% +really simple just theming it thinking +about what you call things how you call + + align:start position:0% +about what you call things how you call + + + align:start position:0% +about what you call things how you call +things where you place things what your + + align:start position:0% +things where you place things what your + + + align:start position:0% +things where you place things what your +verbs you're using all that ties into + + align:start position:0% +verbs you're using all that ties into + + + align:start position:0% +verbs you're using all that ties into +into the + + align:start position:0% +into the + + + align:start position:0% +into the +game all right so um another here's + + align:start position:0% +game all right so um another here's + + + align:start position:0% +game all right so um another here's +another student made game it's actually + + align:start position:0% +another student made game it's actually + + + align:start position:0% +another student made game it's actually +made um by a larger team over the course + + align:start position:0% +made um by a larger team over the course + + + align:start position:0% +made um by a larger team over the course +of a summer so they actually had nine + + align:start position:0% +of a summer so they actually had nine + + + align:start position:0% +of a summer so they actually had nine +weeks to make the make the game and they + + align:start position:0% +weeks to make the make the game and they + + + align:start position:0% +weeks to make the make the game and they +had dedicated artists um on this game um + + align:start position:0% +had dedicated artists um on this game um + + + align:start position:0% +had dedicated artists um on this game um +but there's a game called gum beat which + + align:start position:0% +but there's a game called gum beat which + + + align:start position:0% +but there's a game called gum beat which +we have on our website there um you are + + align:start position:0% +we have on our website there um you are + + + align:start position:0% +we have on our website there um you are +a little girl going around chewing + + align:start position:0% +a little girl going around chewing + + + align:start position:0% +a little girl going around chewing +bubblegum in this idelic land and that I + + align:start position:0% +bubblegum in this idelic land and that I + + + align:start position:0% +bubblegum in this idelic land and that I +don't think there's no there's an + + align:start position:0% +don't think there's no there's an + + + align:start position:0% +don't think there's no there's an +information sign up there if it said it' + + align:start position:0% +information sign up there if it said it' + + + align:start position:0% +information sign up there if it said it' +say keep the place clean basically gum's + + align:start position:0% +say keep the place clean basically gum's + + + align:start position:0% +say keep the place clean basically gum's +not allowed it's not clean um but you go + + align:start position:0% +not allowed it's not clean um but you go + + + align:start position:0% +not allowed it's not clean um but you go +around you recruit people you blow + + align:start position:0% +around you recruit people you blow + + + align:start position:0% +around you recruit people you blow +bubble gum in front of them they say pop + + align:start position:0% +bubble gum in front of them they say pop + + + align:start position:0% +bubble gum in front of them they say pop +the bubble you pop it they're like sweet + + align:start position:0% +the bubble you pop it they're like sweet + + + align:start position:0% +the bubble you pop it they're like sweet +I'm joining you and then they travel + + align:start position:0% +I'm joining you and then they travel + + + align:start position:0% +I'm joining you and then they travel +they trail behind you and you see on the + + align:start position:0% +they trail behind you and you see on the + + + align:start position:0% +they trail behind you and you see on the +right there a little guard melar solid + + align:start position:0% +right there a little guard melar solid + + + align:start position:0% +right there a little guard melar solid +style he's got a zone of of sight line + + align:start position:0% +style he's got a zone of of sight line + + + align:start position:0% +style he's got a zone of of sight line +of sight if he sees you he's going to + + align:start position:0% +of sight if he sees you he's going to + + + align:start position:0% +of sight if he sees you he's going to +chase you down and hit you early in the + + align:start position:0% +chase you down and hit you early in the + + + align:start position:0% +chase you down and hit you early in the +development someone so if you um put if + + align:start position:0% +development someone so if you um put if + + + align:start position:0% +development someone so if you um put if +you pop the bubble on somebody like on + + align:start position:0% +you pop the bubble on somebody like on + + + align:start position:0% +you pop the bubble on somebody like on +your on your friend they'll get stuck + + align:start position:0% +your on your friend they'll get stuck + + + align:start position:0% +your on your friend they'll get stuck +with gum if you pop the bubble on the + + align:start position:0% +with gum if you pop the bubble on the + + + align:start position:0% +with gum if you pop the bubble on the +guard they'll get stuck with gum and + + align:start position:0% +guard they'll get stuck with gum and + + + align:start position:0% +guard they'll get stuck with gum and +they'll they'll not be able to move but + + align:start position:0% +they'll they'll not be able to move but + + + align:start position:0% +they'll they'll not be able to move but +we found if you put the bubble the gum + + align:start position:0% +we found if you put the bubble the gum + + + align:start position:0% +we found if you put the bubble the gum +on the on the guard and you have a guard + + align:start position:0% +on the on the guard and you have a guard + + + align:start position:0% +on the on the guard and you have a guard +basically look another a second guard + + align:start position:0% +basically look another a second guard + + + align:start position:0% +basically look another a second guard +looking for that guard for for people + + align:start position:0% +looking for that guard for for people + + + align:start position:0% +looking for that guard for for people +all the guard that all the AI was was if + + align:start position:0% +all the guard that all the AI was was if + + + align:start position:0% +all the guard that all the AI was was if +gum attack guard with gum found the + + align:start position:0% +gum attack guard with gum found the + + + align:start position:0% +gum attack guard with gum found the +guard attacked not they didn't even + + align:start position:0% +guard attacked not they didn't even + + + align:start position:0% +guard attacked not they didn't even +think about this this wasn't a feature + + align:start position:0% +think about this this wasn't a feature + + + align:start position:0% +think about this this wasn't a feature +they were they were planning it just + + align:start position:0% +they were they were planning it just + + + align:start position:0% +they were they were planning it just +happened and it happened in the space of + + align:start position:0% +happened and it happened in the space of + + + align:start position:0% +happened and it happened in the space of +gameplay and play testing just like that + + align:start position:0% +gameplay and play testing just like that + + + align:start position:0% +gameplay and play testing just like that +fire in in Far Cry to except in this + + align:start position:0% +fire in in Far Cry to except in this + + + align:start position:0% +fire in in Far Cry to except in this +case they're like that's really freaking + + align:start position:0% +case they're like that's really freaking + + + align:start position:0% +case they're like that's really freaking +awesome we're going to polish the crap + + align:start position:0% +awesome we're going to polish the crap + + + align:start position:0% +awesome we're going to polish the crap +out of that and make that a key feature + + align:start position:0% +out of that and make that a key feature + + + align:start position:0% +out of that and make that a key feature +or a really interesting feature in the + + align:start position:0% +or a really interesting feature in the + + + align:start position:0% +or a really interesting feature in the +game we're not going to tell the player + + align:start position:0% +game we're not going to tell the player + + + align:start position:0% +game we're not going to tell the player +how to do that but we are going to + + align:start position:0% +how to do that but we are going to + + + align:start position:0% +how to do that but we are going to +create a level design that encourages + + align:start position:0% +create a level design that encourages + + + align:start position:0% +create a level design that encourages +the player to experiment with that um so + + align:start position:0% +the player to experiment with that um so + + + align:start position:0% +the player to experiment with that um so +that's where you get that kind of + + align:start position:0% +that's where you get that kind of + + + align:start position:0% +that's where you get that kind of +gameplay so play testing is a way to + + align:start position:0% +gameplay so play testing is a way to + + + align:start position:0% +gameplay so play testing is a way to +discover emergent game events so that's + + align:start position:0% +discover emergent game events so that's + + + align:start position:0% +discover emergent game events so that's +why we're asking a play test your game + + align:start position:0% +why we're asking a play test your game + + + align:start position:0% +why we're asking a play test your game +especially people who are not you is to + + align:start position:0% +especially people who are not you is to + + + align:start position:0% +especially people who are not you is to +see what you've you've created this + + align:start position:0% +see what you've you've created this + + + align:start position:0% +see what you've you've created this +amazing possibility space you can't + + align:start position:0% +amazing possibility space you can't + + + align:start position:0% +amazing possibility space you can't +explore the entire thing on your own + + align:start position:0% +explore the entire thing on your own + + + align:start position:0% +explore the entire thing on your own +they might see something and they might + + align:start position:0% +they might see something and they might + + + align:start position:0% +they might see something and they might +and not knowing what the game is + + align:start position:0% +and not knowing what the game is + + + align:start position:0% +and not knowing what the game is +possible to do and what you should be + + align:start position:0% +possible to do and what you should be + + + align:start position:0% +possible to do and what you should be +doing in the game they might come up + + align:start position:0% +doing in the game they might come up + + + align:start position:0% +doing in the game they might come up +with some cool things to do in the game + + align:start position:0% +with some cool things to do in the game + + + align:start position:0% +with some cool things to do in the game +so play testing is + + align:start position:0% +so play testing is + + + align:start position:0% +so play testing is +key lastly um not a student game but um + + align:start position:0% +key lastly um not a student game but um + + + align:start position:0% +key lastly um not a student game but um +another favorite game of mine FTL um + + align:start position:0% +another favorite game of mine FTL um + + + align:start position:0% +another favorite game of mine FTL um +there is a story to FTL that's really + + align:start position:0% +there is a story to FTL that's really + + + align:start position:0% +there is a story to FTL that's really +complicated and I'm not asking you to + + align:start position:0% +complicated and I'm not asking you to + + + align:start position:0% +complicated and I'm not asking you to +try to to emulate that sort of thing + + align:start position:0% +try to to emulate that sort of thing + + + align:start position:0% +try to to emulate that sort of thing +it's really hard it's a lot of detail + + align:start position:0% +it's really hard it's a lot of detail + + + align:start position:0% +it's really hard it's a lot of detail +it's a lot of writing it's a lot of + + align:start position:0% +it's a lot of writing it's a lot of + + + align:start position:0% +it's a lot of writing it's a lot of +thought being put into this randomized + + align:start position:0% +thought being put into this randomized + + + align:start position:0% +thought being put into this randomized +event thing but there's a feature in the + + align:start position:0% +event thing but there's a feature in the + + + align:start position:0% +event thing but there's a feature in the +game that I'm showing here right now + + align:start position:0% +game that I'm showing here right now + + + align:start position:0% +game that I'm showing here right now +that is only used on this screen that's + + align:start position:0% +that is only used on this screen that's + + + align:start position:0% +that is only used on this screen that's +probably kind of it was it was probably + + align:start position:0% +probably kind of it was it was probably + + + align:start position:0% +probably kind of it was it was probably +a high price for them to put the feature + + align:start position:0% +a high price for them to put the feature + + + align:start position:0% +a high price for them to put the feature +in can you maybe you can't read it + + align:start position:0% +in can you maybe you can't read it + + + align:start position:0% +in can you maybe you can't read it +actually you can't read it that well + + align:start position:0% +actually you can't read it that well + + + align:start position:0% +actually you can't read it that well +basically you can change the name of the + + align:start position:0% +basically you can change the name of the + + + align:start position:0% +basically you can change the name of the +characters this is something that + + align:start position:0% +characters this is something that + + + align:start position:0% +characters this is something that +strategy games have had for a long + + align:start position:0% +strategy games have had for a long + + + align:start position:0% +strategy games have had for a long +period of time um I think we remember it + + align:start position:0% +period of time um I think we remember it + + + align:start position:0% +period of time um I think we remember it +through XCOM um back in 9394 + + align:start position:0% +through XCOM um back in 9394 + + + align:start position:0% +through XCOM um back in 9394 +um or earlier no 94 um basically you + + align:start position:0% +um or earlier no 94 um basically you + + + align:start position:0% +um or earlier no 94 um basically you +name your characters if you name your + + align:start position:0% +name your characters if you name your + + + align:start position:0% +name your characters if you name your +characters you might be more inclined to + + align:start position:0% +characters you might be more inclined to + + + align:start position:0% +characters you might be more inclined to +make stories of their gameplay so I've + + align:start position:0% +make stories of their gameplay so I've + + + align:start position:0% +make stories of their gameplay so I've +got my ship is the good ship game lab + + align:start position:0% +got my ship is the good ship game lab + + + align:start position:0% +got my ship is the good ship game lab +with my buddies Andrew Philip and Sarah + + align:start position:0% +with my buddies Andrew Philip and Sarah + + + align:start position:0% +with my buddies Andrew Philip and Sarah +and we're going to be awesome and take + + align:start position:0% +and we're going to be awesome and take + + + align:start position:0% +and we're going to be awesome and take +down are you taking down the Empire I + + align:start position:0% +down are you taking down the Empire I + + + align:start position:0% +down are you taking down the Empire I +never remember Empire or Rebel are you a + + align:start position:0% +never remember Empire or Rebel are you a + + + align:start position:0% +never remember Empire or Rebel are you a +rebel or are you the Empire you are a + + align:start position:0% +rebel or are you the Empire you are a + + + align:start position:0% +rebel or are you the Empire you are a +rebel you are the rebel + + align:start position:0% +rebel you are the rebel + + + align:start position:0% +rebel you are the rebel +okay actually think yeah you're the + + align:start position:0% +okay actually think yeah you're the + + + align:start position:0% +okay actually think yeah you're the +Empire you're trying to take down the + + align:start position:0% +Empire you're trying to take down the + + + align:start position:0% +Empire you're trying to take down the +run + + align:start position:0% +run + + + align:start position:0% +run +yeah okay cool um so one thing that + + align:start position:0% +yeah okay cool um so one thing that + + + align:start position:0% +yeah okay cool um so one thing that +sometimes happens with this game though + + align:start position:0% +sometimes happens with this game though + + + align:start position:0% +sometimes happens with this game though +some players are going to optimize it + + align:start position:0% +some players are going to optimize it + + + align:start position:0% +some players are going to optimize it +what do they name their + + align:start position:0% + + + + align:start position:0% + +characters pilot Shields engines who's + + align:start position:0% +characters pilot Shields engines who's + + + align:start position:0% +characters pilot Shields engines who's +dying looks like the Pilot's dying how + + align:start position:0% +dying looks like the Pilot's dying how + + + align:start position:0% +dying looks like the Pilot's dying how +do you know it's named + + align:start position:0% +do you know it's named + + + align:start position:0% +do you know it's named +pilot um I forget if you can I don't + + align:start position:0% +pilot um I forget if you can I don't + + + align:start position:0% +pilot um I forget if you can I don't +think you can rename characters when you + + align:start position:0% +think you can rename characters when you + + + align:start position:0% +think you can rename characters when you +bring when you when you bring them back + + align:start position:0% +bring when you when you bring them back + + + align:start position:0% +bring when you when you bring them back +onto your ship I should have looked that + + align:start position:0% +onto your ship I should have looked that + + + align:start position:0% +onto your ship I should have looked that +up if anybody plays take a look at that + + align:start position:0% +up if anybody plays take a look at that + + + align:start position:0% +up if anybody plays take a look at that +but you can bring it you can get new + + align:start position:0% +but you can bring it you can get new + + + align:start position:0% +but you can bring it you can get new +characters later on um whether or not + + align:start position:0% +characters later on um whether or not + + + align:start position:0% +characters later on um whether or not +you can name them or not you might name + + align:start position:0% +you can name them or not you might name + + + align:start position:0% +you can name them or not you might name +them you might not name them but either + + align:start position:0% +them you might not name them but either + + + align:start position:0% +them you might not name them but either +way even if you give they they've spent + + align:start position:0% +way even if you give they they've spent + + + align:start position:0% +way even if you give they they've spent +a lot of time and money putting this + + align:start position:0% +a lot of time and money putting this + + + align:start position:0% +a lot of time and money putting this +feature in some players aren't going to + + align:start position:0% +feature in some players aren't going to + + + align:start position:0% +feature in some players aren't going to +use it so what do you do you blow + + align:start position:0% +use it so what do you do you blow + + + align:start position:0% +use it so what do you do you blow +up um the the game is is basically about + + align:start position:0% +up um the the game is is basically about + + + align:start position:0% +up um the the game is is basically about +um traveling the ship things catch on + + align:start position:0% +um traveling the ship things catch on + + + align:start position:0% +um traveling the ship things catch on +fire and hopefully maybe they're not + + align:start position:0% +fire and hopefully maybe they're not + + + align:start position:0% +fire and hopefully maybe they're not +concerned about pilot but they are + + align:start position:0% +concerned about pilot but they are + + + align:start position:0% +concerned about pilot but they are +concerned about their ship so give them + + align:start position:0% +concerned about their ship so give them + + + align:start position:0% +concerned about their ship so give them +these these cool little game events to + + align:start position:0% +these these cool little game events to + + + align:start position:0% +these these cool little game events to +to keep them + + align:start position:0% +to keep them + + + align:start position:0% +to keep them +going so one of the interesting things + + align:start position:0% +going so one of the interesting things + + + align:start position:0% +going so one of the interesting things +about this kind of story is that it's + + align:start position:0% +about this kind of story is that it's + + + align:start position:0% +about this kind of story is that it's +actually it's for all that you're + + align:start position:0% +actually it's for all that you're + + + align:start position:0% +actually it's for all that you're +talking about it does take time and + + align:start position:0% +talking about it does take time and + + + align:start position:0% +talking about it does take time and +money and stuff to create it but it's + + align:start position:0% +money and stuff to create it but it's + + + align:start position:0% +money and stuff to create it but it's +actually pretty cheap to be able to let + + align:start position:0% +actually pretty cheap to be able to let + + + align:start position:0% +actually pretty cheap to be able to let +players name their characters but it's + + align:start position:0% +players name their characters but it's + + + align:start position:0% +players name their characters but it's +even cheaper to do what FTL did at the + + align:start position:0% +even cheaper to do what FTL did at the + + + align:start position:0% +even cheaper to do what FTL did at the +beginning where they automatically name + + align:start position:0% +beginning where they automatically name + + + align:start position:0% +beginning where they automatically name +all your characters like when when you + + align:start position:0% +all your characters like when when you + + + align:start position:0% +all your characters like when when you +get a random human the character isn't + + align:start position:0% +get a random human the character isn't + + + align:start position:0% +get a random human the character isn't +named human number 38 the character is + + align:start position:0% +named human number 38 the character is + + + align:start position:0% +named human number 38 the character is +named Fred or or or something and that + + align:start position:0% +named Fred or or or something and that + + + align:start position:0% +named Fred or or or something and that +was actually originally from their + + align:start position:0% +was actually originally from their + + + align:start position:0% +was actually originally from their +Kickstarter backers got to have their + + align:start position:0% +Kickstarter backers got to have their + + + align:start position:0% +Kickstarter backers got to have their +names in which is kind of cool but it's + + align:start position:0% +names in which is kind of cool but it's + + + align:start position:0% +names in which is kind of cool but it's +actually worth doing because there are + + align:start position:0% +actually worth doing because there are + + + align:start position:0% +actually worth doing because there are +certain kinds of players who will really + + align:start position:0% +certain kinds of players who will really + + + align:start position:0% +certain kinds of players who will really +get into those names in a way that you + + align:start position:0% +get into those names in a way that you + + + align:start position:0% +get into those names in a way that you +don't expect I got two friends who + + align:start position:0% +don't expect I got two friends who + + + align:start position:0% +don't expect I got two friends who +really get into their games um one Mark + + align:start position:0% +really get into their games um one Mark + + + align:start position:0% +really get into their games um one Mark +LeBlanc was playing XCOM and I you + + align:start position:0% +LeBlanc was playing XCOM and I you + + + align:start position:0% +LeBlanc was playing XCOM and I you +probably some of you seen the more + + align:start position:0% +probably some of you seen the more + + + align:start position:0% +probably some of you seen the more +recent XCOM I assume but maybe not the + + align:start position:0% +recent XCOM I assume but maybe not the + + + align:start position:0% +recent XCOM I assume but maybe not the +old one so you can name your characters + + align:start position:0% +old one so you can name your characters + + + align:start position:0% +old one so you can name your characters +or whatnot and it gives gives you some + + align:start position:0% +or whatnot and it gives gives you some + + + align:start position:0% +or whatnot and it gives gives you some +names that you can use um he had went + + align:start position:0% +names that you can use um he had went + + + align:start position:0% +names that you can use um he had went +through the entire game and this is you + + align:start position:0% +through the entire game and this is you + + + align:start position:0% +through the entire game and this is you +know back when the games were hard um so + + align:start position:0% +know back when the games were hard um so + + + align:start position:0% +know back when the games were hard um so +40 to 60 hours of gam play and he had a + + align:start position:0% +40 to 60 hours of gam play and he had a + + + align:start position:0% +40 to 60 hours of gam play and he had a +squad of super uber soldiers and they + + align:start position:0% +squad of super uber soldiers and they + + + align:start position:0% +squad of super uber soldiers and they +all had names and he didn't quite have + + align:start position:0% +all had names and he didn't quite have + + + align:start position:0% +all had names and he didn't quite have +personalities for them but they were + + align:start position:0% +personalities for them but they were + + + align:start position:0% +personalities for them but they were +kind of heck personalities and the final + + align:start position:0% +kind of heck personalities and the final + + + align:start position:0% +kind of heck personalities and the final +second to final battle one of his top a + + align:start position:0% +second to final battle one of his top a + + + align:start position:0% +second to final battle one of his top a +squad people was got a broken leg or + + align:start position:0% +squad people was got a broken leg or + + + align:start position:0% +squad people was got a broken leg or +something and he was like oh that's + + align:start position:0% +something and he was like oh that's + + + align:start position:0% +something and he was like oh that's +really annoying because I'm going to + + align:start position:0% +really annoying because I'm going to + + + align:start position:0% +really annoying because I'm going to +Mars tomorrow well all of my guys that + + align:start position:0% +Mars tomorrow well all of my guys that + + + align:start position:0% +Mars tomorrow well all of my guys that +are high level are gone but I've got + + align:start position:0% +are high level are gone but I've got + + + align:start position:0% +are high level are gone but I've got +this guy's really cool equipment like he + + align:start position:0% +this guy's really cool equipment like he + + + align:start position:0% +this guy's really cool equipment like he +got the laser rful of Doom and the super + + align:start position:0% +got the laser rful of Doom and the super + + + align:start position:0% +got the laser rful of Doom and the super +uber armor and so he went to his second + + align:start position:0% +uber armor and so he went to his second + + + align:start position:0% +uber armor and so he went to his second +string Squad you know the guys who are + + align:start position:0% +string Squad you know the guys who are + + + align:start position:0% +string Squad you know the guys who are +second level and like you suit up son + + align:start position:0% +second level and like you suit up son + + + align:start position:0% +second level and like you suit up son +you're going to Mars which for him was a + + align:start position:0% +you're going to Mars which for him was a + + + align:start position:0% +you're going to Mars which for him was a +story and it was all inside his head the + + align:start position:0% +story and it was all inside his head the + + + align:start position:0% +story and it was all inside his head the +game didn't make that the game did not + + align:start position:0% +game didn't make that the game did not + + + align:start position:0% +game didn't make that the game did not +make that story The designers could not + + align:start position:0% +make that story The designers could not + + + align:start position:0% +make that story The designers could not +have anticipated that story but in his + + align:start position:0% +have anticipated that story but in his + + + align:start position:0% +have anticipated that story but in his +head because he was the kind of player + + align:start position:0% +head because he was the kind of player + + + align:start position:0% +head because he was the kind of player +who really tried to personify his + + align:start position:0% +who really tried to personify his + + + align:start position:0% +who really tried to personify his +characters a little bit it was actually + + align:start position:0% +characters a little bit it was actually + + + align:start position:0% +characters a little bit it was actually +a really big thing for him similarly + + align:start position:0% +a really big thing for him similarly + + + align:start position:0% +a really big thing for him similarly +another one of my friends who um will + + align:start position:0% +another one of my friends who um will + + + align:start position:0% +another one of my friends who um will +probably come in for a lecture later + + align:start position:0% +probably come in for a lecture later + + + align:start position:0% +probably come in for a lecture later +Laura Baldwin is playing XCOM as well + + align:start position:0% +Laura Baldwin is playing XCOM as well + + + align:start position:0% +Laura Baldwin is playing XCOM as well +basically the same game she in her head + + align:start position:0% +basically the same game she in her head + + + align:start position:0% +basically the same game she in her head +kept all the default names the default + + align:start position:0% +kept all the default names the default + + + align:start position:0% +kept all the default names the default +names was a randomized first name and a + + align:start position:0% +names was a randomized first name and a + + + align:start position:0% +names was a randomized first name and a +randomized last name and in her head + + align:start position:0% +randomized last name and in her head + + + align:start position:0% +randomized last name and in her head +when she saw the same last name she + + align:start position:0% +when she saw the same last name she + + + align:start position:0% +when she saw the same last name she +assumed that meant the characters were + + align:start position:0% +assumed that meant the characters were + + + align:start position:0% +assumed that meant the characters were +related now of course this meant nothing + + align:start position:0% +related now of course this meant nothing + + + align:start position:0% +related now of course this meant nothing +in the game the game didn't care but + + align:start position:0% +in the game the game didn't care but + + + align:start position:0% +in the game the game didn't care but +here are the two brothers here are the + + align:start position:0% +here are the two brothers here are the + + + align:start position:0% +here are the two brothers here are the +two sisters here's the married couple + + align:start position:0% +two sisters here's the married couple + + + align:start position:0% +two sisters here's the married couple +and so apparently in the final final + + align:start position:0% +and so apparently in the final final + + + align:start position:0% +and so apparently in the final final +battle you've got you're going in to + + align:start position:0% +battle you've got you're going in to + + + align:start position:0% +battle you've got you're going in to +destroy the big bad thing and the big + + align:start position:0% +destroy the big bad thing and the big + + + align:start position:0% +destroy the big bad thing and the big +bad thing does horrible psychic damage + + align:start position:0% +bad thing does horrible psychic damage + + + align:start position:0% +bad thing does horrible psychic damage +to all of your soldiers on the map every + + align:start position:0% +to all of your soldiers on the map every + + + align:start position:0% +to all of your soldiers on the map every +turn and she was losing horribly and the + + align:start position:0% +turn and she was losing horribly and the + + + align:start position:0% +turn and she was losing horribly and the +husband and wife team made it into the + + align:start position:0% +husband and wife team made it into the + + + align:start position:0% +husband and wife team made it into the +final room with a big brain alien and + + align:start position:0% +final room with a big brain alien and + + + align:start position:0% +final room with a big brain alien and +the wife runs in to and discovers the + + align:start position:0% +the wife runs in to and discovers the + + + align:start position:0% +the wife runs in to and discovers the +final bat + + align:start position:0% +final bat + + + align:start position:0% +final bat +boss and in XCOM it didn't you had + + align:start position:0% +boss and in XCOM it didn't you had + + + align:start position:0% +boss and in XCOM it didn't you had +movement points so she went in and + + align:start position:0% +movement points so she went in and + + + align:start position:0% +movement points so she went in and +revealed the fog of War here's the bad + + align:start position:0% +revealed the fog of War here's the bad + + + align:start position:0% +revealed the fog of War here's the bad +guy she has not enough movement points + + align:start position:0% +guy she has not enough movement points + + + align:start position:0% +guy she has not enough movement points +to to get to run away and the husband + + align:start position:0% +to to get to run away and the husband + + + align:start position:0% +to to get to run away and the husband +meanwhile is out the doorway with a + + align:start position:0% +meanwhile is out the doorway with a + + + align:start position:0% +meanwhile is out the doorway with a +rocket + + align:start position:0% +rocket + + + align:start position:0% +rocket +launcher and so apparently Laura the way + + align:start position:0% +launcher and so apparently Laura the way + + + align:start position:0% +launcher and so apparently Laura the way +she tells it she spent about 15 minutes + + align:start position:0% +she tells it she spent about 15 minutes + + + align:start position:0% +she tells it she spent about 15 minutes +having a conversation between these two + + align:start position:0% +having a conversation between these two + + + align:start position:0% +having a conversation between these two +characters as the husband's like I've a + + align:start position:0% +characters as the husband's like I've a + + + align:start position:0% +characters as the husband's like I've a +rocket launcher get out of the way honey + + align:start position:0% +rocket launcher get out of the way honey + + + align:start position:0% +rocket launcher get out of the way honey +and she's like I don't have enough + + align:start position:0% +and she's like I don't have enough + + + align:start position:0% +and she's like I don't have enough +movement points fire the + + align:start position:0% +movement points fire the + + + align:start position:0% +movement points fire the +rocket I can't I'll kill you I'm going + + align:start position:0% +rocket I can't I'll kill you I'm going + + + align:start position:0% +rocket I can't I'll kill you I'm going +to die anyway fire the rocket and this + + align:start position:0% +to die anyway fire the rocket and this + + + align:start position:0% +to die anyway fire the rocket and this +goes back and forth until finally she + + align:start position:0% +goes back and forth until finally she + + + align:start position:0% +goes back and forth until finally she +decides all right boom fires the rocket + + align:start position:0% +decides all right boom fires the rocket + + + align:start position:0% +decides all right boom fires the rocket +kills the person next to the big bad guy + + align:start position:0% +kills the person next to the big bad guy + + + align:start position:0% +kills the person next to the big bad guy +and wins the game but again this is + + align:start position:0% +and wins the game but again this is + + + align:start position:0% +and wins the game but again this is +because you had a player who's very + + align:start position:0% +because you had a player who's very + + + align:start position:0% +because you had a player who's very +Cooperative something as simple as the + + align:start position:0% +Cooperative something as simple as the + + + align:start position:0% +Cooperative something as simple as the +names actually helped now you can't + + align:start position:0% +names actually helped now you can't + + + align:start position:0% +names actually helped now you can't +guarantee you're going to get players + + align:start position:0% +guarantee you're going to get players + + + align:start position:0% +guarantee you're going to get players +like that but those players do exist and + + align:start position:0% +like that but those players do exist and + + + align:start position:0% +like that but those players do exist and +if it's easy to give them the + + align:start position:0% +if it's easy to give them the + + + align:start position:0% +if it's easy to give them the +opportunity to have that awesome + + align:start position:0% +opportunity to have that awesome + + + align:start position:0% +opportunity to have that awesome +experience that she + + align:start position:0% +experience that she + + + align:start position:0% +experience that she +tells 20 years + + align:start position:0% +tells 20 years + + + align:start position:0% +tells 20 years +later do it it's relatively + + align:start position:0% + + + + align:start position:0% + +cheap all right that's it for lecture + + align:start position:0% +cheap all right that's it for lecture + + + align:start position:0% +cheap all right that's it for lecture +any questions about any of this stuff + + align:start position:0% +any questions about any of this stuff + + + align:start position:0% +any questions about any of this stuff +and how it applies to your + + align:start position:0% +and how it applies to your + + + align:start position:0% +and how it applies to your +games we have an idea what they can do + + align:start position:0% +games we have an idea what they can do + + + align:start position:0% +games we have an idea what they can do +in their game right now just thinking + + align:start position:0% +in their game right now just thinking + + + align:start position:0% +in their game right now just thinking +about any of this has anybody thought + + align:start position:0% +about any of this has anybody thought + + + align:start position:0% +about any of this has anybody thought +about their title at least + + align:start position:0% +about their title at least + + + align:start position:0% +about their title at least +yeah + + align:start position:0% + + + + align:start position:0% + +snap okay all right so take a couple + + align:start position:0% +snap okay all right so take a couple + + + align:start position:0% +snap okay all right so take a couple +minutes um it's 203 right now Break um + + align:start position:0% +minutes um it's 203 right now Break um + + + align:start position:0% +minutes um it's 203 right now Break um +work in your teams whatever that might + + align:start position:0% +work in your teams whatever that might + + + align:start position:0% +work in your teams whatever that might +be we've got a test coming in at 3 so be + + align:start position:0% +be we've got a test coming in at 3 so be + + + align:start position:0% +be we've got a test coming in at 3 so be +ready for the test at 3 I'll remind you + + align:start position:0% +ready for the test at 3 I'll remind you + + + align:start position:0% +ready for the test at 3 I'll remind you +maybe five minutes or beforehand + + align:start position:0% + + + + align:start position:0% + +so everyone raise your hand if you are + + align:start position:0% +so everyone raise your hand if you are + + + align:start position:0% +so everyone raise your hand if you are +ready to test if at a workstation if you + + align:start position:0% +ready to test if at a workstation if you + + + align:start position:0% +ready to test if at a workstation if you +are ready to test so I can count off two + + align:start position:0% +are ready to test so I can count off two + + + align:start position:0% +are ready to test so I can count off two +three four one two one two kind of all + + align:start position:0% +three four one two one two kind of all + + + align:start position:0% +three four one two one two kind of all +right we'll take you get two more + + align:start position:0% +right we'll take you get two more + + + align:start position:0% +right we'll take you get two more +minutes Philip you want to talk + + align:start position:0% +minutes Philip you want to talk + + + align:start position:0% +minutes Philip you want to talk +to um can I speak to to ed students I + + align:start position:0% +to um can I speak to to ed students I + + + align:start position:0% +to um can I speak to to ed students I +don't know if you're like scattered + + align:start position:0% +don't know if you're like scattered + + + align:start position:0% +don't know if you're like scattered +around but it will help if uh you could + + align:start position:0% +around but it will help if uh you could + + + align:start position:0% +around but it will help if uh you could +meet up here you want of them yeah yeah + + align:start position:0% +meet up here you want of them yeah yeah + + + align:start position:0% +meet up here you want of them yeah yeah +you yeah so so I just want the first + + align:start position:0% +you yeah so so I just want the first + + + align:start position:0% +you yeah so so I just want the first +thing I want to say is thank you so much + + align:start position:0% +thing I want to say is thank you so much + + + align:start position:0% +thing I want to say is thank you so much +for coming and uh you may have overheard + + align:start position:0% +for coming and uh you may have overheard + + + align:start position:0% +for coming and uh you may have overheard +what Rick was saying earlier this is + + align:start position:0% +what Rick was saying earlier this is + + + align:start position:0% +what Rick was saying earlier this is +going to be our first Digital Play test + + align:start position:0% +going to be our first Digital Play test + + + align:start position:0% +going to be our first Digital Play test +for the games then there are five games + + align:start position:0% +for the games then there are five games + + + align:start position:0% +for the games then there are five games +some of the teams have multiple uh uh + + align:start position:0% +some of the teams have multiple uh uh + + + align:start position:0% +some of the teams have multiple uh uh +stations and uh there's probably not + + align:start position:0% +stations and uh there's probably not + + + align:start position:0% +stations and uh there's probably not +going to be enough computer for every + + align:start position:0% +going to be enough computer for every + + + align:start position:0% +going to be enough computer for every +single one of you who are here so some + + align:start position:0% +single one of you who are here so some + + + align:start position:0% +single one of you who are here so some +of you may be waiting in line but you + + align:start position:0% +of you may be waiting in line but you + + + align:start position:0% +of you may be waiting in line but you +know um please be patient with with us + + align:start position:0% +know um please be patient with with us + + + align:start position:0% +know um please be patient with with us +and we'll hope to get your feedback on + + align:start position:0% +and we'll hope to get your feedback on + + + align:start position:0% +and we'll hope to get your feedback on +Le one or two games um if not more um + + align:start position:0% +Le one or two games um if not more um + + + align:start position:0% +Le one or two games um if not more um +it's good uh for you to give us uh uh + + align:start position:0% +it's good uh for you to give us uh uh + + + align:start position:0% +it's good uh for you to give us uh uh +feedback while you are playing the game + + align:start position:0% +feedback while you are playing the game + + + align:start position:0% +feedback while you are playing the game +so if you are uh the the students will + + align:start position:0% +so if you are uh the the students will + + + align:start position:0% +so if you are uh the the students will +get more specific about the kind of + + align:start position:0% +get more specific about the kind of + + + align:start position:0% +get more specific about the kind of +feedback that they need but you know if + + align:start position:0% +feedback that they need but you know if + + + align:start position:0% +feedback that they need but you know if +something's frustrating if something's + + align:start position:0% +something's frustrating if something's + + + align:start position:0% +something's frustrating if something's +confusing if something's intriguing or + + align:start position:0% +confusing if something's intriguing or + + + align:start position:0% +confusing if something's intriguing or +some or you're really you you really + + align:start position:0% +some or you're really you you really + + + align:start position:0% +some or you're really you you really +think something look look looks cool or + + align:start position:0% +think something look look looks cool or + + + align:start position:0% +think something look look looks cool or +or or is an interesting decision try to + + align:start position:0% +or or is an interesting decision try to + + + align:start position:0% +or or is an interesting decision try to +verbalize it so that we can actually + + align:start position:0% +verbalize it so that we can actually + + + align:start position:0% +verbalize it so that we can actually +realize that something's working or + + align:start position:0% +realize that something's working or + + + align:start position:0% +realize that something's working or +something's not working um don't worry + + align:start position:0% +something's not working um don't worry + + + align:start position:0% +something's not working um don't worry +about our egos at this point we + + align:start position:0% +about our egos at this point we + + + align:start position:0% +about our egos at this point we +absolutely need um the harshest + + align:start position:0% +absolutely need um the harshest + + + align:start position:0% +absolutely need um the harshest +criticism that you can possibly give us + + align:start position:0% +criticism that you can possibly give us + + + align:start position:0% +criticism that you can possibly give us +at this point because it's easy for us + + align:start position:0% +at this point because it's easy for us + + + align:start position:0% +at this point because it's easy for us +to change things at this point of our + + align:start position:0% +to change things at this point of our + + + align:start position:0% +to change things at this point of our +project if you if we learned about the + + align:start position:0% +project if you if we learned about the + + + align:start position:0% +project if you if we learned about the +same things that bother you two weeks + + align:start position:0% +same things that bother you two weeks + + + align:start position:0% +same things that bother you two weeks +from now U reversing all of those + + align:start position:0% +from now U reversing all of those + + + align:start position:0% +from now U reversing all of those +changes is going to be harder so please + + align:start position:0% +changes is going to be harder so please + + + align:start position:0% +changes is going to be harder so please +please be harsh now um other than that + + align:start position:0% +please be harsh now um other than that + + + align:start position:0% +please be harsh now um other than that +um yeah if anything is confusing do of + + align:start position:0% +um yeah if anything is confusing do of + + + align:start position:0% +um yeah if anything is confusing do of +course vocalize it um but uh the people + + align:start position:0% +course vocalize it um but uh the people + + + align:start position:0% +course vocalize it um but uh the people +who are uh the the people who are making + + align:start position:0% +who are uh the the people who are making + + + align:start position:0% +who are uh the the people who are making +the game may not tell you what to do + + align:start position:0% +the game may not tell you what to do + + + align:start position:0% +the game may not tell you what to do +next because they want to see if you can + + align:start position:0% +next because they want to see if you can + + + align:start position:0% +next because they want to see if you can +figure it out uh now if if you can't + + align:start position:0% +figure it out uh now if if you can't + + + align:start position:0% +figure it out uh now if if you can't +figure it out that's not a problem with + + align:start position:0% +figure it out that's not a problem with + + + align:start position:0% +figure it out that's not a problem with +you that's a problem with the G but they + + align:start position:0% +you that's a problem with the G but they + + + align:start position:0% +you that's a problem with the G but they +need to be able to see you sort of like + + align:start position:0% +need to be able to see you sort of like + + + align:start position:0% +need to be able to see you sort of like +muddle through what already there uh in + + align:start position:0% +muddle through what already there uh in + + + align:start position:0% +muddle through what already there uh in +order to figure out how to fix it later + + align:start position:0% +order to figure out how to fix it later + + + align:start position:0% +order to figure out how to fix it later +so if you do start getting frustrated of + + align:start position:0% +so if you do start getting frustrated of + + + align:start position:0% +so if you do start getting frustrated of +course you can always say I'm done with + + align:start position:0% +course you can always say I'm done with + + + align:start position:0% +course you can always say I'm done with +this game and move on to another uh to + + align:start position:0% +this game and move on to another uh to + + + align:start position:0% +this game and move on to another uh to +another + + align:start position:0% +another + + + align:start position:0% +another +game huh that's a very valid data yeah + + align:start position:0% +game huh that's a very valid data yeah + + + align:start position:0% +game huh that's a very valid data yeah +that's that's very valid data it's like + + align:start position:0% +that's that's very valid data it's like + + + align:start position:0% +that's that's very valid data it's like +I'm done no no more uh that's and that's + + align:start position:0% +I'm done no no more uh that's and that's + + + align:start position:0% +I'm done no no more uh that's and that's +absolutely fine it'll be great to be + + align:start position:0% +absolutely fine it'll be great to be + + + align:start position:0% +absolutely fine it'll be great to be +able to then tell the other uh the + + align:start position:0% +able to then tell the other uh the + + + align:start position:0% +able to then tell the other uh the +students why why you're done right um + + align:start position:0% +students why why you're done right um + + + align:start position:0% +students why why you're done right um +maybe it's because you you you feel like + + align:start position:0% +maybe it's because you you you feel like + + + align:start position:0% +maybe it's because you you you feel like +you've seen everything that there is to + + align:start position:0% +you've seen everything that there is to + + + align:start position:0% +you've seen everything that there is to +see to a game and that's very different + + align:start position:0% +see to a game and that's very different + + + align:start position:0% +see to a game and that's very different +from I have no idea what's going on + + align:start position:0% +from I have no idea what's going on + + + align:start position:0% +from I have no idea what's going on +that's two different reasons to leave a + + align:start position:0% +that's two different reasons to leave a + + + align:start position:0% +that's two different reasons to leave a +game and they need to know what that + + align:start position:0% +game and they need to know what that + + + align:start position:0% +game and they need to know what that +reason is um otherwise uh this by the + + align:start position:0% +reason is um otherwise uh this by the + + + align:start position:0% +reason is um otherwise uh this by the +way is uh creating video games uh it is + + align:start position:0% +way is uh creating video games uh it is + + + align:start position:0% +way is uh creating video games uh it is +six what's the course number 6 60773 or + + align:start position:0% +six what's the course number 6 60773 or + + + align:start position:0% +six what's the course number 6 60773 or +CMS 611 uh it is a so the course says + + align:start position:0% +CMS 611 uh it is a so the course says + + + align:start position:0% +CMS 611 uh it is a so the course says +joint Humanities and uh computer science + + align:start position:0% +joint Humanities and uh computer science + + + align:start position:0% +joint Humanities and uh computer science +and it runs for this full semester + + align:start position:0% +and it runs for this full semester + + + align:start position:0% +and it runs for this full semester +students actually work on four project + + align:start position:0% +students actually work on four project + + + align:start position:0% +students actually work on four project +projects for the entire semester but the + + align:start position:0% +projects for the entire semester but the + + + align:start position:0% +projects for the entire semester but the +first three are really really short like + + align:start position:0% +first three are really really short like + + + align:start position:0% +first three are really really short like +two we projects and this is kind of like + + align:start position:0% +two we projects and this is kind of like + + + align:start position:0% +two we projects and this is kind of like +the mega big project so um yeah if you + + align:start position:0% +the mega big project so um yeah if you + + + align:start position:0% +the mega big project so um yeah if you +have questions about the class feel free + + align:start position:0% +have questions about the class feel free + + + align:start position:0% +have questions about the class feel free +to grab us for the instructors we can + + align:start position:0% +to grab us for the instructors we can + + + align:start position:0% +to grab us for the instructors we can +answer those questions for you Yep this + + align:start position:0% +answer those questions for you Yep this + + + align:start position:0% +answer those questions for you Yep this +is Rick I'm Phillip you all know Ed and + + align:start position:0% +is Rick I'm Phillip you all know Ed and + + + align:start position:0% +is Rick I'm Phillip you all know Ed and +uh and and Sarah and Pina are over there + + align:start position:0% +uh and and Sarah and Pina are over there + + + align:start position:0% +uh and and Sarah and Pina are over there +um just look forward any one of us and + + align:start position:0% +um just look forward any one of us and + + + align:start position:0% +um just look forward any one of us and +we'll be happy to help okay so play test + + align:start position:0% +we'll be happy to help okay so play test + + + align:start position:0% +we'll be happy to help okay so play test +H workstation stand up if you are a + + align:start position:0% +H workstation stand up if you are a + + + align:start position:0% +H workstation stand up if you are a +computer that someone can come to to + + align:start position:0% +computer that someone can come to to + + + align:start position:0% +computer that someone can come to to +play your game and testers in the back + + align:start position:0% +play your game and testers in the back + + + align:start position:0% +play your game and testers in the back +stand up if you are a test station and + + align:start position:0% +stand up if you are a test station and + + + align:start position:0% +stand up if you are a test station and +testers please go find a standing person + + align:start position:0% +testers please go find a standing person + + + align:start position:0% +testers please go find a standing person +and play their game see what's currently + + align:start position:0% +and play their game see what's currently + + + align:start position:0% +and play their game see what's currently +active on this side okay it's going to + + align:start position:0% +active on this side okay it's going to + + + align:start position:0% +active on this side okay it's going to +come up + + align:start position:0% + + + + align:start position:0% + +uh yeah so for improvements it's like I + + align:start position:0% +uh yeah so for improvements it's like I + + + align:start position:0% +uh yeah so for improvements it's like I +figured out what to do I think the + + align:start position:0% +figured out what to do I think the + + + align:start position:0% +figured out what to do I think the +instructions are clear this time \ No newline at end of file diff --git a/SSzcvj2biAQ.txt b/SSzcvj2biAQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..73826eb30600c7a962838afcdfe687ba0f5df506 --- /dev/null +++ b/SSzcvj2biAQ.txt @@ -0,0 +1,1035 @@ +align:start position:0% + +in this recitation we'll discuss + + align:start position:0% +in this recitation we'll discuss + + + align:start position:0% +in this recitation we'll discuss +operating room scheduling that is how + + align:start position:0% +operating room scheduling that is how + + + align:start position:0% +operating room scheduling that is how +hospitals can be made to run smoothly in + + align:start position:0% +hospitals can be made to run smoothly in + + + align:start position:0% +hospitals can be made to run smoothly in +particular we'll discuss how an + + align:start position:0% +particular we'll discuss how an + + + align:start position:0% +particular we'll discuss how an +operating room manager can use integer + + align:start position:0% +operating room manager can use integer + + + align:start position:0% +operating room manager can use integer +optimization to make sure the hospital + + align:start position:0% +optimization to make sure the hospital + + + align:start position:0% +optimization to make sure the hospital +runs smoothly so hospitals have a + + align:start position:0% +runs smoothly so hospitals have a + + + align:start position:0% +runs smoothly so hospitals have a +limited number of operating rooms or ORS + + align:start position:0% +limited number of operating rooms or ORS + + + align:start position:0% +limited number of operating rooms or ORS +and operating room managers must + + align:start position:0% +and operating room managers must + + + align:start position:0% +and operating room managers must +determine a weekly schedule assigning + + align:start position:0% +determine a weekly schedule assigning + + + align:start position:0% +determine a weekly schedule assigning +ORS to different departments in the + + align:start position:0% +ORS to different departments in the + + + align:start position:0% +ORS to different departments in the +hospital if you look on the right you'll + + align:start position:0% +hospital if you look on the right you'll + + + align:start position:0% +hospital if you look on the right you'll +see a picture of an operating room you + + align:start position:0% +see a picture of an operating room you + + + align:start position:0% +see a picture of an operating room you +can see immediately how much specialized + + align:start position:0% +can see immediately how much specialized + + + align:start position:0% +can see immediately how much specialized +in fancy equipment there is and you have + + align:start position:0% +in fancy equipment there is and you have + + + align:start position:0% +in fancy equipment there is and you have +to remember that for any surgery + + align:start position:0% +to remember that for any surgery + + + align:start position:0% +to remember that for any surgery +staffing the o.r doesn't just involve + + align:start position:0% +staffing the o.r doesn't just involve + + + align:start position:0% +staffing the o.r doesn't just involve +the surgeon performing the surgery but + + align:start position:0% +the surgeon performing the surgery but + + + align:start position:0% +the surgeon performing the surgery but +also other doctors nurses residents and + + align:start position:0% +also other doctors nurses residents and + + + align:start position:0% +also other doctors nurses residents and +fellows there is usually an entire + + align:start position:0% +fellows there is usually an entire + + + align:start position:0% +fellows there is usually an entire +surgery team so due to the specialized + + align:start position:0% +surgery team so due to the specialized + + + align:start position:0% +surgery team so due to the specialized +equipment in an O are as well as the + + align:start position:0% +equipment in an O are as well as the + + + align:start position:0% +equipment in an O are as well as the +specialized staff members it's been + + align:start position:0% +specialized staff members it's been + + + align:start position:0% +specialized staff members it's been +estimated that staffing and operating + + align:start position:0% +estimated that staffing and operating + + + align:start position:0% +estimated that staffing and operating +room costs over $100 a minute therefore + + align:start position:0% +room costs over $100 a minute therefore + + + align:start position:0% +room costs over $100 a minute therefore +for a hospital to run on a budget it's + + align:start position:0% +for a hospital to run on a budget it's + + + align:start position:0% +for a hospital to run on a budget it's +very critical for the operating room + + align:start position:0% +very critical for the operating room + + + align:start position:0% +very critical for the operating room +manager to create a good schedule + + align:start position:0% +manager to create a good schedule + + + align:start position:0% +manager to create a good schedule +however this isn't without difficulties + + align:start position:0% +however this isn't without difficulties + + + align:start position:0% +however this isn't without difficulties +creating an acceptable schedule is a + + align:start position:0% +creating an acceptable schedule is a + + + align:start position:0% +creating an acceptable schedule is a +highly political process within the + + align:start position:0% +highly political process within the + + + align:start position:0% +highly political process within the +hospital surgeons are frequently paid on + + align:start position:0% +hospital surgeons are frequently paid on + + + align:start position:0% +hospital surgeons are frequently paid on +a fee-for-service basis which means they + + align:start position:0% +a fee-for-service basis which means they + + + align:start position:0% +a fee-for-service basis which means they +get paid for every surgery they perform + + align:start position:0% +get paid for every surgery they perform + + + align:start position:0% +get paid for every surgery they perform +that means that when you change their + + align:start position:0% +that means that when you change their + + + align:start position:0% +that means that when you change their +allocated number of operating room hours + + align:start position:0% +allocated number of operating room hours + + + align:start position:0% +allocated number of operating room hours +it directly affects their income + + align:start position:0% +it directly affects their income + + + align:start position:0% +it directly affects their income +therefore the operating room managers + + align:start position:0% +therefore the operating room managers + + + align:start position:0% +therefore the operating room managers +proposed schedule must strike a delicate + + align:start position:0% +proposed schedule must strike a delicate + + + align:start position:0% +proposed schedule must strike a delicate +balance between all the surgical + + align:start position:0% +balance between all the surgical + + + align:start position:0% +balance between all the surgical +departments in the hospital however + + align:start position:0% +departments in the hospital however + + + align:start position:0% +departments in the hospital however +there are many logistical issues for the + + align:start position:0% +there are many logistical issues for the + + + align:start position:0% +there are many logistical issues for the +operating room manager to consider when + + align:start position:0% +operating room manager to consider when + + + align:start position:0% +operating room manager to consider when +designing the scheduled operating rooms + + align:start position:0% +designing the scheduled operating rooms + + + align:start position:0% +designing the scheduled operating rooms +are staffed in a tower blocks each + + align:start position:0% +are staffed in a tower blocks each + + + align:start position:0% +are staffed in a tower blocks each +department sets their own target number + + align:start position:0% +department sets their own target number + + + align:start position:0% +department sets their own target number +of allocation hours which may not be + + align:start position:0% +of allocation hours which may not be + + + align:start position:0% +of allocation hours which may not be +integer + + align:start position:0% +integer + + + align:start position:0% +integer +in addition departments may have daily + + align:start position:0% +in addition departments may have daily + + + align:start position:0% +in addition departments may have daily +and weekly requirements for example + + align:start position:0% +and weekly requirements for example + + + align:start position:0% +and weekly requirements for example +gynecology might need at least 100 are + + align:start position:0% +gynecology might need at least 100 are + + + align:start position:0% +gynecology might need at least 100 are +per day + + align:start position:0% + + + + align:start position:0% + +ophthalmology might need at least two + + align:start position:0% +ophthalmology might need at least two + + + align:start position:0% +ophthalmology might need at least two +ORS per week + + align:start position:0% +ORS per week + + + align:start position:0% +ORS per week +and for example the oral surgeon might + + align:start position:0% +and for example the oral surgeon might + + + align:start position:0% +and for example the oral surgeon might +only be present on Tuesdays and + + align:start position:0% +only be present on Tuesdays and + + + align:start position:0% +only be present on Tuesdays and +Thursdays the operating room manager + + align:start position:0% +Thursdays the operating room manager + + + align:start position:0% +Thursdays the operating room manager +needs to take into account all of these + + align:start position:0% +needs to take into account all of these + + + align:start position:0% +needs to take into account all of these +logistical issues when designing a + + align:start position:0% +logistical issues when designing a + + + align:start position:0% +logistical issues when designing a +feasible schedule in this recitation + + align:start position:0% +feasible schedule in this recitation + + + align:start position:0% +feasible schedule in this recitation +we'll consider a case study of Mount + + align:start position:0% +we'll consider a case study of Mount + + + align:start position:0% +we'll consider a case study of Mount +Sinai Hospital in Toronto there are 10 + + align:start position:0% +Sinai Hospital in Toronto there are 10 + + + align:start position:0% +Sinai Hospital in Toronto there are 10 +operating rooms at Mount Sinai which are + + align:start position:0% +operating rooms at Mount Sinai which are + + + align:start position:0% +operating rooms at Mount Sinai which are +staffed from Monday through Friday + + align:start position:0% +staffed from Monday through Friday + + + align:start position:0% +staffed from Monday through Friday +so 1000rs times 5 days times 8 hours per + + align:start position:0% +so 1000rs times 5 days times 8 hours per + + + align:start position:0% +so 1000rs times 5 days times 8 hours per +day means that they have four hundred + + align:start position:0% +day means that they have four hundred + + + align:start position:0% +day means that they have four hundred +hours to assign between five different + + align:start position:0% +hours to assign between five different + + + align:start position:0% +hours to assign between five different +surgical departments the departments + + align:start position:0% +surgical departments the departments + + + align:start position:0% +surgical departments the departments +they're assigning our ophthalmology + + align:start position:0% +they're assigning our ophthalmology + + + align:start position:0% +they're assigning our ophthalmology +gynecology oral surgery Otolaryngology + + align:start position:0% +gynecology oral surgery Otolaryngology + + + align:start position:0% +gynecology oral surgery Otolaryngology +and general surgery each of these + + align:start position:0% +and general surgery each of these + + + align:start position:0% +and general surgery each of these +departments has come up with a weekly + + align:start position:0% +departments has come up with a weekly + + + align:start position:0% +departments has come up with a weekly +number of target allocation hours for + + align:start position:0% +number of target allocation hours for + + + align:start position:0% +number of target allocation hours for +example ophthalmology requests thirty + + align:start position:0% +example ophthalmology requests thirty + + + align:start position:0% +example ophthalmology requests thirty +nine point four hours of operating room + + align:start position:0% +nine point four hours of operating room + + + align:start position:0% +nine point four hours of operating room +time and Otolaryngology requests twenty + + align:start position:0% +time and Otolaryngology requests twenty + + + align:start position:0% +time and Otolaryngology requests twenty +six point three hours of operating room + + align:start position:0% +six point three hours of operating room + + + align:start position:0% +six point three hours of operating room +time now it's very clear that just by + + align:start position:0% +time now it's very clear that just by + + + align:start position:0% +time now it's very clear that just by +looking at these numbers they are not + + align:start position:0% +looking at these numbers they are not + + + align:start position:0% +looking at these numbers they are not +integer and they are certainly not + + align:start position:0% +integer and they are certainly not + + + align:start position:0% +integer and they are certainly not +multiples of eight hours this means that + + align:start position:0% +multiples of eight hours this means that + + + align:start position:0% +multiples of eight hours this means that +it's impossible for the operating room + + align:start position:0% +it's impossible for the operating room + + + align:start position:0% +it's impossible for the operating room +manager to give any department exactly + + align:start position:0% +manager to give any department exactly + + + align:start position:0% +manager to give any department exactly +their weekly number of target allocation + + align:start position:0% +their weekly number of target allocation + + + align:start position:0% +their weekly number of target allocation +hours + + align:start position:0% +hours + + + align:start position:0% +hours +however the operating room manager would + + align:start position:0% +however the operating room manager would + + + align:start position:0% +however the operating room manager would +like to try to give as many hours to + + align:start position:0% +like to try to give as many hours to + + + align:start position:0% +like to try to give as many hours to +each department as possible up to their + + align:start position:0% +each department as possible up to their + + + align:start position:0% +each department as possible up to their +target allocation number we'll see how + + align:start position:0% +target allocation number we'll see how + + + align:start position:0% +target allocation number we'll see how +to solve this with integer optimization + + align:start position:0% +to solve this with integer optimization + + + align:start position:0% +to solve this with integer optimization +let's consider the rest of the problem + + align:start position:0% +let's consider the rest of the problem + + + align:start position:0% +let's consider the rest of the problem +data for example we need to consider the + + align:start position:0% +data for example we need to consider the + + + align:start position:0% +data for example we need to consider the +number of surgery teams from each + + align:start position:0% +number of surgery teams from each + + + align:start position:0% +number of surgery teams from each +department that is available each day we + + align:start position:0% +department that is available each day we + + + align:start position:0% +department that is available each day we +also need to consider the maximum number + + align:start position:0% +also need to consider the maximum number + + + align:start position:0% +also need to consider the maximum number +of operating rooms required by each + + align:start position:0% +of operating rooms required by each + + + align:start position:0% +of operating rooms required by each +department each day frequently these + + align:start position:0% +department each day frequently these + + + align:start position:0% +department each day frequently these +numbers are the same + + align:start position:0% +numbers are the same + + + align:start position:0% +numbers are the same +for example ophthalmology requires at + + align:start position:0% +for example ophthalmology requires at + + + align:start position:0% +for example ophthalmology requires at +most two operating rooms every day + + align:start position:0% + + + + align:start position:0% + +and we see that they have to surgery + + align:start position:0% +and we see that they have to surgery + + + align:start position:0% +and we see that they have to surgery +teams available every day however let's + + align:start position:0% +teams available every day however let's + + + align:start position:0% +teams available every day however let's +look at the case of oral surgery they + + align:start position:0% +look at the case of oral surgery they + + + align:start position:0% +look at the case of oral surgery they +require at most one operating room every + + align:start position:0% +require at most one operating room every + + + align:start position:0% +require at most one operating room every +day however the oral surgeon is only + + align:start position:0% +day however the oral surgeon is only + + + align:start position:0% +day however the oral surgeon is only +present on Tuesdays and Thursdays + + align:start position:0% + + + + align:start position:0% + +additionally each department has weekly + + align:start position:0% +additionally each department has weekly + + + align:start position:0% +additionally each department has weekly +requirements on the number of operating + + align:start position:0% +requirements on the number of operating + + + align:start position:0% +requirements on the number of operating +rooms they need for example gynecology + + align:start position:0% +rooms they need for example gynecology + + + align:start position:0% +rooms they need for example gynecology +needs to have at least 12 operating + + align:start position:0% +needs to have at least 12 operating + + + align:start position:0% +needs to have at least 12 operating +rooms in a given week and at most 18 the + + align:start position:0% +rooms in a given week and at most 18 the + + + align:start position:0% +rooms in a given week and at most 18 the +traditional way of doing this was not by + + align:start position:0% +traditional way of doing this was not by + + + align:start position:0% +traditional way of doing this was not by +using integer optimization before + + align:start position:0% +using integer optimization before + + + align:start position:0% +using integer optimization before +integer optimization was implemented at + + align:start position:0% +integer optimization was implemented at + + + align:start position:0% +integer optimization was implemented at +Mount Sinai in 1999 the operating room + + align:start position:0% +Mount Sinai in 1999 the operating room + + + align:start position:0% +Mount Sinai in 1999 the operating room +manager used graph paper and a large + + align:start position:0% +manager used graph paper and a large + + + align:start position:0% +manager used graph paper and a large +eraser to try to assign the operating + + align:start position:0% +eraser to try to assign the operating + + + align:start position:0% +eraser to try to assign the operating +room blocks any changes that were + + align:start position:0% +room blocks any changes that were + + + align:start position:0% +room blocks any changes that were +necessary were incorporated by trial and + + align:start position:0% +necessary were incorporated by trial and + + + align:start position:0% +necessary were incorporated by trial and +error the operating room manager made a + + align:start position:0% +error the operating room manager made a + + + align:start position:0% +error the operating room manager made a +draft and this schedule was circulated + + align:start position:0% +draft and this schedule was circulated + + + align:start position:0% +draft and this schedule was circulated +to all of the surgical groups however + + align:start position:0% +to all of the surgical groups however + + + align:start position:0% +to all of the surgical groups however +incorporating feedback from one + + align:start position:0% +incorporating feedback from one + + + align:start position:0% +incorporating feedback from one +department usually met altering another + + align:start position:0% +department usually met altering another + + + align:start position:0% +department usually met altering another +groups schedule leading to many + + align:start position:0% +groups schedule leading to many + + + align:start position:0% +groups schedule leading to many +iterations of this process in the next + + align:start position:0% +iterations of this process in the next + + + align:start position:0% +iterations of this process in the next +video we'll design an integer + + align:start position:0% +video we'll design an integer + + + align:start position:0% +video we'll design an integer +optimization formulation for this + + align:start position:0% +optimization formulation for this + + + align:start position:0% +optimization formulation for this +problem + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/SXBG3RGr_Rc.txt b/SXBG3RGr_Rc.txt new file mode 100644 index 0000000000000000000000000000000000000000..31f6187605d36c89dd5dd5d32c02f5916ae28860 --- /dev/null +++ b/SXBG3RGr_Rc.txt @@ -0,0 +1,2507 @@ +PATRICK WINSTON: Ladies and +gentlemen, the Romanian + +national anthem. + +I did not ask you to stand, +because I didn't play it as a + +symbol of Romanian national +identity. + +But rather, to celebrate the +end of the Cold War, which + +occurred about the time +that you were born. + +Before that, no one came to +MIT from Eastern Europe. + +But since that time, we've been +blessed by having in our + +midst Lithuanians, Estonians, +Poles, Czecs, Slovaks, + +Bulgarians, Romanians, +Slovenians, Serbs, and all + +sorts of people from regions +of the world + +formally excluded to us. + +Believe me, you are all +welcome in our house. + +Almost all, that is to say. + +Because you may recall that +Romania is the traditional + +home of vampires. + +And since the end of the Cold +War, vampires have had new + +vectors for emerging from their +traditional places and + +penetrating into the +world at large. + +You may have vampire in your +suite, or on your floor. + +And it's important to know how +to recognize them, and take + +the necessary precautions. + +So if you have this concern, I +would expect that the first + +thing you would do would be to +look at some data concerning + +the characteristics +of vampires. + +So there's a little database of +samples of individuals who + +have been determined to be +vampires and not vampires. + +And our task today-- + +and what you'll understand how +to do by the end of the hour-- + +is to use data like this to +build a recognition mechanism + +that would help you to identify +whether someone is a + +vampire or an ordinary person. + +So this is a little different +from the kind of problem we + +worked with neural nets. + +Right? + +So what's the most conspicuous +difference between this data + +set and anything you could think +to work on with nearest + +neighbors, which we +studied last time. + +Katie, do you have any thoughts +about why it would be + +difficult to use nearest +neighbors with data like this? + +The question mark is there +because this is MIT, and a lot + +of people are completely +nocturnal. + +So you can't tell whether they +cast a shadow or not. + +We want to take that +into account. + +So what's different about +this from the + +electrical cover data set? + +STUDENT: [INAUDIBLE] + +PATRICK WINSTON: Could you use +the nearest neighbor technique + +to identify vampires +with this data? + +STUDENT: [INAUDIBLE] + +PATRICK WINSTON: +So obviously-- + +Yes, Lana? + +STUDENT: [INAUDIBLE] + +STUDENT: You cannot +really quantify-- + +PATRICK WINSTON: Oh, +that's the problem. + +This is not numerical data. + +This is symbolic. + +So we're not saying that +your ability to + +cast a shadow is 0.7. + +You either cast a shadow, +down cast a + +shadow, or we can't tell. + +It's a symbolic result. + +So problem number one we have to +face with data of this kind + +is that it's not numeric. + +And there are other +characteristics, as well. + +For example, it's not clear +that all of these + +characteristics actually +matter. + +So some characteristics +don't matter. + +And a corollary to that is that +some characteristics do + +matter, but they only matter +part of the time. + +And finally, there's +the matter of cost. + +Some of these tests may +be more expensive to + +perform than others. + +For example, if you wanted to +determine whether someone + +casts a shadow, you'd have to +go to the trouble of getting + +up during daylight. + +That might be an expensive +operation for you. + +You'd have to go find some +garlic and ask them to eat it. + +That might be expensive. + +So some of these tests +might be expensive + +relative to other tests. + +But once you realize that we are +talking in terms of tests, + +and not a vector of +real values, then + +what you do is clear. + +You build yourself a little +tree of tests. + +So who knows how this problem +will turn out? + +But you can imagine a situation +where you have one + +test up here which might +have three outcomes. + +And one but only one of those +outcomes might require you to + +perform another test. + +And only when you've created +the tree of tests that look + +like this are you finished. + +So given this set of tests and a +set of samples, the question + +becomes, how do you arrange the +tests in a tree like that + +so as to do the identification +that you want to do? + +So since we're talking about +identification, it's not + +surprising that this kind +of tree is called an + +identification tree. + +And there's a tendency-- and I +may slip into it myself-- to + +call this a decision tree. + +But a decision tree is a label +for something else. + +This is an identification +tree. + +And the task is to create +a good one. + +So what is a good one versus +a not so good one? + +What characteristic would you +like for a decision tree-- + +for an identification trade to +have, if you're going to call + +it good identification tree? + +What do you think, Krishna? + +What would be a good +characteristic? + +STUDENT: Maybe the minimum +number of levels? + +PATRICK WINSTON: Yeah. + +He said minimum number +of levels. + +What's another way you could +say what a good one is? + +Each test costs something, +right? + +So what's another way of +thinking about what a good + +tree would look like? + +STUDENT: Minimum cost. + +PATRICK WINSTON: The +minimum cost. + +And if they all have the +same cost, then it's + +the number of tests. + +So overall, what you like +is a small tree + +rather than a big one. + +So you might be able to take +your sample data and divide it + +up, so that at the bottom of the +tree, at the leaves, all + +of the sets that are produced +by the tests are uniform, + +homogeneous. + +We'd like that tree to be the +simplest possible tree you can + +find, not some big complicated +one that also divides up all + +the data into uniform subsets. + +By uniform subset-- + +at the bottom of the tree, you +have all of the vampires + +together, and all the +non-vampires together. + +So you'd like a small tree. + +So why not just go all the way +and do British Museum, and + +calculate all possible trees? + +Well, you can do that, but it's +one of those NP problems. + +And as you know, NP problems +suck in general. + +And so you don't want +to do that. + +You want to have some kind of +heuristic mechanism for + +building a small tree. + +And we want a small +tree because-- + +Why do we want a small tree? + +Because of the cost. + +but there's another, more +important reason why we want a + +small tree. + +Let me give you a hint. + +It's Occam's Razor. + +The simplest explanation is +often the best explanation. + +So if you have a big, +complicated explanation, + +that's probably less good than +a simple, small explanation. + +Occam's Razor. + +Spelled so many ways it doesn't +matter how I spell it. + +And that's good, because +I can't spell. + +So how are we going to go +about finding the best + +possible arrangement +of those four tests + +in a tree like that? + +Well, step one will be +to see what each test + +does with the data. + +And by the way, before I go a +step further, you know and I + +know that this is a sample data +set that's very small, + +suitable for classroom +manipulation. + +You'd never bet your life on +a data set this small. + +We use it only for classroom +illustration. + +But imagine that these rows +are multiplied by 10. + +So instead of eight samples, +you've got 80. + +Then you might begin +to believe the + +results that are produced. + +So I'm just going to pretend +that each one of those + +represents 10 other +samples that I + +haven't bothered to show. + +But we can work with this one in +the classroom, because it's + +pretty small. + +And we can say, well, what +does this shadow test do? + +Well, the shadow test divides +the sample population into + +three groups. + +There's the I Don't Know group +of people who are nocturnal. + +There are the people +who do cast the + +shadow, the Yes people. + +And the people who do not cast +a shadow, the No people. + +So if I look at those rows up +there and see which ones are + +vampires, it looks to me that +if there's no shadow cast-- + +there's only one that doesn't +cast a shadow-- + +and that is a vampire. + +So that's a plus over there. + +Vampire. + +Now, if we look at the ones +who do cast a shadow, all + +those are not vampires. + +They're all OK. + +And now there're 8. + +Three are vampires. + +So that means that two of +these must be vampires. + +And I've got three, four, +five, six so far. + +So there must be two left. + +So that's the way the shadow +test divides up the data. + +Now let's do garlic. + +Vampires traditionally +don't eat garlic. + +I don't know why. + +So we look at the garlic +test, and we see + +that all of the Nos-- + +well, there're three +Yeses, and they all + +produce a No answer. + +So if somebody eats garlic, +they're not vampires. + +That means the three vampires +must be over here. + +Then there are two left. + +So that's what the +garlic test does. + +See what we're trying to do? + +We're trying to look at all +these tests to see which one + +we like best on the basis of +how it divides up the data. + +So now we've got complexion. + +And there are three +choices for this. + +You can have an average +complexion. + +But a lot of vampires, in my +experience, are rather pale. + +So pale is a possibility. + +And then the other option is +that just after gorging + +themselves with blood, +they tend to get a + +little red in the face. + +So we'll have a ruddy +over here. + +Once again, we have to go back +to our data set to see how + +this test divides things up. + +So there are three ruddies, and +one's a No, one's a No, + +and one's a Yes. + +So two Nos and a Yes. + +Two Nos and a Yes. + +Now we can try for pale +complexion people. + +There are only two of those. + +A No and a No. + +That must mean that there are +two pluses over here, because + +there are three vampires +altogether. + +Two, four, six, seven, +eight, nine. + +Eight, sorry. + +Eight. + +Only eight. + +Just one more to go, and +that's the accent. + +Historically, vampires go to +great length to protect their + +accent and not betray +their origins. + +But nevertheless, we +can expect that if + +they've just arrived-- + +if they're just in from + +Transylvania, part of Romania-- + +they may still have an accent. + +So there's a normal, some still +have a heavy accent, and + +some persist in having +odd accents. + +So let's see. + +Accent. + +Four of them, right at the +top, have no accent. + +Two Nos and a Yes. + +Heavy accent. + +Three of those. + +A Yes and two Nos. + +That means we must +have a plus here. + +3, 6, plus and a minus. + +So we can look at this data and +say, well, what will be + +the best test to use? + +And the best test to use would +surely be the one that + +produces sets here, at the +bottom of the branches, that + +correspond to the outcomes +of the test. + +We're looking for a test that +produces homogeneous groups. + +So just for the sake of +illustration, I'm going to + +suppose that we're going to +judge the quality of the test + +by how many sample individuals +it put into a homogeneous set. + +So ideally, we'd like a test +that will put all the vampires + +in one group and all the +ordinary people in another + +group right off the bat. + +But there are no such tests. + +But we can add up the number of +sample individuals who are + +put in to at least +homogeneous sets. + +So when we do that, this +guy has 3 in a + +homogeneous set here. + +A fourth. + +But these are not a +homogeneous set. + +So the overall score for +this guy will be 4. + +This one, well, not +quite as good. + +It only puts 3 individuals +in a homogeneous set. + +This one here, 2 individuals +into a homogeneous set. + +Everybody else is all +mixed up with some + +other kind of person. + +And over here, how many +samples are in + +a homogeneous set? + +0. + +So on the basis of this +analysis, you would conclude + +that the ordering of the test +with respect to their quality + +is left to right. + +So the best test must +be the shadow test. + +So let's pick the shadow +test first, see what + +we can do with that. + +If we pick the shadow test +first, then we have this + +arrangement. + +We have question mark, and we +have Yes, casts a shadow, and + +No, doesn't. + +We have 3 minuses here. + +We have a plus here. + +And unfortunately, over +here, we have plus, + +plus, minus, minus. + +So we need another test to +divide that group up. + +Yes. + +STUDENT: How did you get the +4 on the shadow test again? + +Why was it 4? + +PATRICK WINSTON: Well, +if I look at the + +data and I see who-- + +the question is, what about +that shadow test? + +If you look at the shadow test, +and you say, well, there + +are 4 question marks. + +And if we look and see what kind +of people belong to those + +4 question marks, there are 2 +vampires and 2 non-vampires. + +That's why it's 2 pluses +and 2 minuses. + +STUDENT: No, I understand +that. + +The question is, how did you +get to the score of 4? + +PATRICK WINSTON: Oh, yeah. + +The question is how did +I get this number 4? + +It has nothing to do this, +because this is a mixed set. + +In fact, I've got three guys in +a homogeneous set here, and + +one guy in a homogeneous +set here, and I'm + +just adding them up. + +STUDENT: OK. + +PATRICK WINSTON: So very simple +classroom illustration. + +Wouldn't work in practice. + +Yes. + +STUDENT: How do you adjust +this for larger data sets + +where it's unlikely you're going +to have any [INAUDIBLE]? + +PATRICK WINSTON: The question +is, how do I adjust this for + +larger data sets? + +You're one step ahead. + +Trust me, I'll be doing large +data sets in a moment. + +I just want to get +the idea across. + +And I don't want there to be any +thought that the method we + +use for larger data sets has got +anything magic about it. + +OK, so we're off and running. + +And now we have to pick a +test that will divide + +those four guys up. + +So we're going to have to work +this a little harder, and + +repeat the analysis +we did there. + +But at least it'll be simpler, +because now we're only + +considering 4 samples, not 8. + +Just the 4 samples that we still +have to divide up that + +have come down that +left branch. + +So I have the shadow test. + +It has 3 outcomes. + +We have the garlic test. + +It has 2 outcomes. + +Yes and No. + +We have the complexion test. + +There's 3 outcomes. + +Average, pale, and ruddy. + +And we have finally +the accent test. + +And that comes out to be either +normal, heavy, or odd. + +And now, it's a little awkward +to figure out what the results + +are for this data +set as shown. + +So let me just strike out. + +The ones that we're no longer +concerned with, and limit our + +analysis to the samples for +which the outcome of the + +shadow test is a +question mark. + +This is exactly the four +people we still need to + +separate, right? + +So switching colors, keeping +the color the same. + +We actually don't want +to do the shadow + +test anymore, right? + +Because we've already +done that. + +There's no point in +doing that again. + +We don't have to look at that. + +It's already done all the +division of data that it can. + +So the garlic test. + +Well, let's see. + +Garlic. + +2 Yeses, 2 Nos. + +The Yeses produce Nos and +the Nos produce Yeses. + +So if the person does eat +garlic, they're OK. + +And if they don't eat garlic, +bad news-- they're vampires. + +Well, that looks like +a pretty good test. + +But just for the sake of working +it all out, let's try + +the others. + +Complexion. + +2 Ruddies, a Yes, and a No. + +1 pale, and that's a No. + +1 pale, and that's a No. + +And we must have 1 average, and +sure enough, that's a Yes. + +Now we can do accent, the one on +the far right, and look at + +how that measures up against the +people who are still under + +consideration as samples. + +Accent. + +Let's see. + +2 Nones, a Yes and a No. + +No Heavies. + +2 Odds, a Yes and a No. + +All right. + +So now we can do the same thing +we did before, and just + +say, for sake of classroom +illustration, how many + +individuals are put into +a homogeneous sets. + +And here we have 4. + +And here we have 2. + +And here we have 0. + +So plainly, the garlic test +is the test of choice. + +So we go back over here, and +we've completed the work that + +we needed to do. + +So that's the garlic test. + +And that produces 2 pluses. + +Let's see. + +Eats garlic, Yes. + +Eats garlic, No. + +I guess the pluses go +over here like so. + +And these are the two +ordinary people. + +And we're done with our task. + +And now you can quickly run +off and put this into your + +PDA, and forever be protected +against the possibility that + +one of those vampires got out +in the flood of people that + +came in from Eastern Europe. + +Except what do we do +a large data set? + +Well, the trouble is, +a large data set's + +not likely to produce-- + +if you have a large data set, +no test is likely to put + +together any homogeneous +set right off. + +So you never get started. + +Everything would be 0. + +Every test would say, oh it +doesn't put anybody into + +homogeneous sets. + +So you're screwed. + +You need some other, more +sophisticated way of measuring + +how disordered this data is. + +Or how disordered these sets +are that you find at the + +bottom of the tree branches. + +That's what you need. + +You need a way of measuring +disorder of these sets that + +you find at the bottom of these +branches, so you can + +find a kind of overall quality +to the test based on your + +measurement of disorder. + +Now, the first heuristic of a +good life is, when you have a + +problem to solve, ask somebody +who knows the answer. + +It's the least amount of work. + +It's not even as hard +going to Google. + +So who would you ask +about ways of + +measuring disorder in sets? + +There are two possible +answers. + +STUDENT: You could +just do entropy. + +PATRICK WINSTON: What? + +STUDENT: Find the entropy +of the set. + +PATRICK WINSTON: Who +studies entropy? + +STUDENT: Probability. + +PATRICK WINSTON: What +kind of classes? + +STUDENT: Physics. + +STUDENT: Thermodynamics. + +PATRICK WINSTON: +Thermodynamics! + +The thermodynamicists are good +at measuring disorder, because + +that's what thermodynamics +is all about. + +Entropy increasing over time, +and all that sort of stuff. + +There's another equally +good answer. + +STUDENT: Statisticians? + +PATRICK WINSTON: +Statisticians. + +Perhaps, but it's not the +second best answer. + +It's actually not even +the best answer. + +That's the best answer. + +What's your name? + +STUDENT: Leo. + +PATRICK WINSTON: Oh, yeah. + +[LAUGHTER] + +PATRICK WINSTON: Leonardo has +got his finger on it. + +The information theorists are +pretty good at measuring + +disorder, because that's what +information is all about, too. + +So we might as well borrow a +mechanism for measuring the + +disorder of a set from those +information theory guys. + +So what we're going to +do is exactly that. + +Let's put it over here, so we'll +have it handy when we + +want to try to measure +those things. + +The gospel according to +information theorists is that + +the disorder, D, or some set +is equal to-- now let's + +suppose that this is a +set of binary values. + +So we have positives and +then we have negatives. + +Pluses and minuses. + +But pluses, they don't go very +well in an algebraic equation, + +because they might be confused +with adding. + +So I'm going to say P and N. And +then it'll be the total, + +which is P plus N. We only +have two choices, + +positive and negative. + +So the disorder of set, +according those guys, is equal + +to minus the number of positives +over the total + +number, times the log to the +base 2 of the positives over + +the total, minus the negatives +over the total, times the log + +2 of the negatives +over the total. + +Those negatives look a little +worrisome, because you think, + +well, maybe this thing +can go negative. + +But that's not going +to be true, right? + +Because these ratios are all +less than 1, and the logarithm + +of something that's less +than 1 is negative. + +So we're OK. + +So that's a lovely way of +measuring disorder. + +And then we ought to draw +a graph of what + +that curve looks like. + +And what we're going to graph +it against is the ratio of + +positives to the total number. + +So that's going to be an axis +where we go from 0 to 1. + +So let's just find a couple +of useful values. + +And by the way, it pays to pay +attention to these curves, + +because if you pay attention +to this stuff, you can work + +the quiz questions on +this very rapidly. + +Otherwise, we see people getting +out their calculators + +and quickly becoming both +lost and screwed. + +OK so let's see. + +Let's suppose that the number +of positives is equal to the + +number of negatives. + +So we've got a completely +mixed-up set. + +It has no bias in either +direction. + +So in that case, if P over T is +equal to 1/2, then this is + +equal to minus 1/2, times +the logarithm of 1/2. + +And I guess, since they're +both the same, we + +can multiply by two. + +And what's that value? + +[INAUDIBLE], what does that +calculate out to? + +STUDENT: Minus [INAUDIBLE] + +PATRICK WINSTON: Minus +[INAUDIBLE]. + +Well, with a minus sign, you +just turn the argument upside + +down, so it's log(2). + +So what's log(2)? + +Logarithm of base 2 of 2? + +1! + +So this whole thing is-- + +STUDENT: 1. + +PATRICK WINSTON: 1. + +So [INAUDIBLE], in her soft way, +says, well, let's see. + +2 times 1/2. + +That cancels out. + +The minus, that flips the +arguments so it's log to the + +base 2 of 2, and that's 1. + +So this whole thing, You +work out the algebra, + +it gives you 1. + +So that's cool. + +So right here in the middle +where they're equal, we get a + +value of 1. + +Next thing we need to do is +let's calculate what happens + +if P over T is equal to 1. + +That is to say, everything +is a positive. + +Any guesses? + +Maybe 10, 20, minus 15? + +Let's work it out. + +So if P over T equal 1, that +would be minus 1 times the log + +to the base 2 of 1. + +What's that? + +STUDENT: [INAUDIBLE] + +PATRICK WINSTON: A 0? + +Oh, yeah. + +Because 2 raise to +the 0 is one. + +So this part is 0. + +Now, what about this +other part? + +If everything's a P, then +nothing's an N. + +So we've got 0. + +And we can quit already. + +Well, not quite. + +We ought to work it out. + +Log 2 to the base 2 of 0. + +What's that? + +STUDENT: [INAUDIBLE] + +PATRICK WINSTON: Who? + +Minus infinity? + +Uh oh. + +0 times minus infinity is What +I didn't get that when I was + +in high school. + +Finally, 1801 makes +a difference. + +Finally. + +What's the answer. + +We're interested in the limit as +N over T goes to 0, right? + +And when you have a deal like +this, what do you do? + +You use that famous rule, that +we all mispronounce when we + +see it written, right? + +We use the good old El +Hospital's rule. + +OK, it's L'Hopital. + +L'Hopital's Rule. + +You have to differentiate +the-- + +I guess we differentiate this +guy as a ratio or something, + +and see what happens +when it goes to 0. + +And what we get when we use +L'Hopital's Rule is that, oh + +thank God, this is still zero. + +So now we know that we have a +point up there and a point + +down there. + +So now we've got three +points on the curve, + +and we can draw it. + +It goes like that. + +No, it doesn't go like that. + +It's obviously a Gaussian, +right? + +Because everything in a +nature is a Gaussian. + +Can you put that laptop +away, please? + +Everything in nature +is a Gaussian, so + +it looks like this. + +That right? + +No, actually, not everything +in nature is a Gaussian. + +And in particular, this one +isn't a Gaussian either. + +It looks more like one of those +metal things they used + +to call quonset huts. + +That's what it looks like. + +Boom, like so. + +So that is the curve +of interest. + +Now, did God say that using this +way of measuring disorder + +was the best way? + +No, Got has not indicated +any choice here. + +We use this because it's a +convenient mechanism, it seems + +to make sense, but in contrast +to the reason it's used + +information theory, it's not +the result of some elegant + +mathematics. + +It's just a borrowing of +something that seems to work + +pretty well. + +Any of those curves would work +just about the same, because + +all we're doing with +it is measuring how + +disordered a set is. + +So one thing to note here is +that in this situation, where + +we're dealing with +two choices-- + +P and N, positives +and negatives-- + +we get a curve that +maxes out at one. + +And notice that it kind of gets +up there pretty fast. + +In fact, if you're down here +at 2/3, are you're up here, + +this is about 0.9. + +So it gives you a large number +for quite a bit of that area + +in the middle. + +So that, unfortunately, still +doesn't tell us everything we + +need to know. + +That tells us how to measure a +disorder in one of these sets. + +But we want to know how to +measure the quality of the + +test overall. + +So we need some mechanism that +says, OK, given that this test + +produces three different sets, +and we now have a measure of + +the disorder in each of these +sets, how do we measure the + +overall quality of the test? + +Well, you could just add +up the disorder. + +Let's write that down, because +that sounds good. + +So you can say that the quality +of a test is equal to + +some sum over the +sets produced. + +And what we're going to do is +we're going to add up the + +disorder of each +of those sets. + +I'm almost home, except that +this means we're going to give + +equal weight to a branch that +has almost nothing down it-- + +we're going to give the same +weight to that as a branch + +that has almost everything +going down it. + +So that doesn't seem +that make sense. + +So one final flourish is we're +going to weight this sum + +according to the fraction of the +samples that end up down + +that branch. + +So it's, as usual, easier to +write it down than to say it. + +So we're going to multiply +that times the number of + +samples in the set, divided +by the number of + +samples handled by test. + +So if half the samples go down +a branch, and if that branch + +has a certain disorder, then +we're going to multiply that + +disorder times 1/2. + +All right. + +So now let's see how it works +with our sample problem. + +Well, here is our sample data. + +And we didn't need anything +fancy for it. + +But let's pretend it was +a large data set. + +Well, let's see. + +What would we do? + +Well, go down this +way, there are 4 + +samples down that direction. + +That's half of the total +number of samples. + +So whatever we find down +there, we're going + +to multiply by 1/2. + +This one we're going +to multiply by 3/8. + +And this one we're going +to multiply by 1/8. + +Now, what do we actually find at +the bottom of these things? + +Well, here's a homogeneous +set. + +Everything's the same. + +So we go to that curve and say, +what is the disorder of a + +homogeneous set? + +It's zero. + +Let's see, they're +all the same. + +I guess that means it's +0 over there. + +So the disorder of this set +of three samples is zero. + +The disorder of this set +of one sample, all + +the same, is zero. + +The disorder of this set-- +well, let's see. + +Half of the samples there are +plus, and half are minus, so + +we go over to our curve, and we +say, what's the disorder of + +something with equal mixture +of pluses and minuses? + +And that's one. + +So the disorder of +this guy is one. + +So now we've got 1/2 times 1, +and 3/8 times 0, 1/8 times 0. + +So the quality of this +particular test, as determined + +by the disorder of the sets +it produces, is 1/5. + +0.5. + +Let's do this one. + +So we have 3/8 coming +down this way, 5/8 + +coming down this way. + +3/8 is multiplied by +the disorder of a + +set of uniform things. + +That's disorder 0. + +So this guy over here, +let's see. + +That's 2/5 and 3/5 +multiplied-- + +You know, this is one of those +deals where if you look at the + +curve, you're pretty close +to the middle. + +And that curve goes all the +way up to about 0.9 there. + +So you can kind of just look at +this, and eyeball it, and + +say, well, whatever it is, the +overall, this is going to be + +something multiplied +times 5/8. + +Something like 0.9 times 5/8. + +So let's just say, for the +sake of discussion, that + +that's going to be about 0.6, +which is within a hundredth, I + +think, of being right. + +Just kind of guessing. + +OK, well now we're on a roll. + +Here, we have 3/8 coming down +this branch, 3/8 coming down + +this branch, 1/4 coming +down this branch. + +This is 0. + +And this is one of those deals +where these two are about 0.9. + +So it looks like it's going +to be 3/8 plus 3/8 is 3/4. + +Times about 0.9. + +So that's going to turn +out to be about 0.7. + +So one last go here. + +3/8, 3/8, and 1/4. + +Oh, that's interesting. + +Because these two +are what we got + +contributed up to that 0.7. + +This one is 0.4 times-- + +this is evenly divided, +so that's going to + +have disorder of 1. + +So that's going to be +0.25 bigger than the + +number we got over here. + +So that's going to end +up being about 0.95. + +So thanks god our answer is the +same as we got with our + +simple classroom measurement +of disorder. + +Except this is measuring how +disordered stuff is, we want + +the small number, not +the big number. + +So once again, based on this +analysis, you'll be sure to + +pick the shadow cast, because +0.5 is less than 0.6, which is + +less than 0.7, which +is less than 0.95. + +So that accent test is +really horrible. + +Don't use it. + +Just because somebody has a +heavy accent doesn't mean + +they're a vampire. + +In fact, most vampires have +worked very hard on their + +accent, as I mentioned before. + +All right, so now we know that +we're still going to pick the + +shadow test as our first go. + +So that's good. + +Now, let's see if we can repeat +the exercise with our + +second selection, the one we +have to have to pick those + +guys apart. + +And this is going to be easier, +because there are + +fewer things to work with. + +Ooh, wow, look. + +That's 0. + +That's 0. + +That's 1/2. + +That's 1/2. + +So the disorder of +this guy is 0.0. + +So this is 1/4, 1/4, +1/2, 0, 0. + +1/2 times 1. + +Ooh, that's 0.5. + +That was easy. + +How about this one? + +Oh, he says 1. + +Let's see. + +That's 1. + +That's 1. + +That's 1/2. + +That's 1/2. + +Yeah, it is one. + +So sure enough, the answer also +comes out to be the same + +as before, when we did our just + +simple intuition exercise. + +So I don't know. + +Christopher, is this all about +using information theory? + +STUDENT: No. + +PATRICK WINSTON: No, no, no. + +See, it's not about the math. + +It's about the intuition. + +And the intuition is that you +want to build a tree that's as + +simple as possible. + +And you can build a tree that's +as simple as possible + +if you look at the data, and +say, well, which test does the + +best job of splitting +things up? + +Which test does the best job of +building subsets underneath + +it that are as homogeneous +as possible? + +So all this information theory, +all this entropy + +stuff, is just a convenient +mechanism for doing something + +that is intuitionally sound. + +OK? + +It's not about information +theory. + +It's about a sound intuition. + +Oh, by the way. + +Does this kind of stuff ever +get used in practice? + +10s of thousands of times. + +This is a winning mechanism +that's used over and over + +again, even when the +data is numeric. + +How would it work if +it's numeric data? + +Well, let's think about +that for a little bit. + +So let's suppose that we +have an opportunity. + +We're an EMT or something, +we work in the infirmary. + +What do they call +it these days? + +Something else. + +But anyhow, you work in that +kind of area, and you have the + +opportunity to take people's +temperature. + +And so over time, you've +accumulated some data on the + +temperature of people. + +And maybe you've found that +there's a vampire + +here at about 102. + +There's a normal person +here, about 98.6. + +But then they're scattered +around. + +Some people have fevers +when they come in. + +So the question is, is there a +way of using numerical data-- + +things that you can +put real numbers-- + +is there a way of using that +with this mechanism? + +And the answer is yes. + +You just say, is the temperature +greater than or + +less than some threshold? + +And that gives you a test, a +binary test, just like any of + +these other tests. + +[? Krishna? ?] + +Right? + +But where would I put +the threshold? + +I suppose I could just put +it at the average value. + +But that might not be the place +that does the best job + +of splitting the samples into +homogeneous groups. + +Christopher? + +STUDENT: So you run this +numerical analysis on + +different places with different +thresholds. + +PATRICK WINSTON: So you try +different places, he says. + +And he's right. + +Because this is a computer, +this is our slave. + +We don't care how much +it works to figure + +out the right threshold. + +So what we do is we say, well, +maybe the threshold's halfway + +between those two guys, or +halfway between those two + +guys, or those two guys, +or those two guys, + +or those two guys. + +So we can try one +less threshold + +than we have samples. + +And we don't care if there are +10,000 samples, because this + +is a computer, and we don't care +if it works all night. + +So that's how you find the +threshold for a numeric test. + +By the way, I assured you +earlier on you would never use + +the same test twice. + +Is that true for this? + +Yes, you would still never +use the same test twice. + +But what you might do is you +might use a different + +threshold on the same +measurement + +the next time around. + +So when you start having +numerical data, you may find + +yourself using the same test +with the same axis but with a + +different value. + +All right. + +So now that we have this, then +we can go back and compare how + +this method would look when we +put it up against the sort of + +stuff we were talking about +last time, with + +the electrical covers. + +So with the electrical covers, +we had a situation like this. + +I don't know. + +We had samples that were places +like this, and we had a + +division of the space that look +pretty much like that. + +Not quite exactly in the right +spots, but pretty close. + +So these are the decision +boundaries for the situation + +where we are using nearest +neighbors to + +divide up the data. + +What would the decision +boundaries look like if these + +were four different kinds of +things, and we were using this + +kind of mechanism? + +And maybe there's a lot of +samples all clustered around + +places like that. + +What would the decision +boundaries look like? + +Would they be the +same as this? + +god, I hope not. + +Why? + +Because what we're going to +do is we're going to use a + +threshold on each axis. + +So therefore, the decision +boundaries are going to be + +parallel to one axis +or the other. + +So we might decide, +for example-- + +Oh, shoot. + +I think I'll draw it again, +because it'll get confused if + +I draw it over the other one. + +So it looks like this. + +And that's how nearest +neighbors does it. + +But a identification tree +approach will pick a threshold + +along one axis or the other. + +Let's say it's this axis. + +It's only got one +choice there. + +So it's going to put +a line there. + +And now, what's the next +thing it does? + +Well, it still has these +two different kinds + +of things to separate. + +We're going to assume +we've got four + +different kinds of things. + +So it's going to say, oh! + +I've Come down the negative +side, so I need a threshold on + +the remaining data. + +And these are the only two +things that are now remaining. + +So my only choice is to put +a threshold in there. + +Now I guarantee this, absolutely +guaranteed-- + +on the quiz, somebody-- + +presumably somebody who doesn't +go to lectures-- + +will draw that line all +the way across. + +And that's desperately wrong. + +Because we've already divided +this data set in half. + +Now the choice of what we do +over here is governed only by + +the remaining samples that +we see, these two. + +And so the threshold is going +to go in there like that. + +So that's what happens +when you go back. + +This is used 10s of thousands +of times. + +Always used. + +What are the virtues of it? + +Number one, you don't +use all the tests. + +You use only the test that seem +to be doing some useful + +work for you. + +So that means that you do a +better job, because your + +measurement technique +is simpler. + +And it costs less, because +you're not going to the + +expense of doing all +of the testing. + +So it's a real winner. + +But you know what? + +Some classes of people-- + +not scientists, but I mean +people like doctors and stuff. + +They don't like to look +at these tress. + +They're kind of rule-oriented. + +So they look a tree like this +for determining what kind of + +thyroid disease you have, and +it would have maybe 20 or so + +tests in it of various kinds +of hormones, like thyroxine + +and this and that. + +And they say, ah, we can't +deal with that. + +So we have to work with them. + +So what we do is we convert the +tree into a set of rules. + +How do we convert the tree +into a set of rules? + +Oops, wrong one. + +Go away, go away. + +Here's what I want. + +Yeah, good. + +How would we convert this tree +into a set of rules? + +It's straightforward. + +[INAUDIBLE], what do we do? + +STUDENT: You'd basically just +look down each branch-- + +PATRICK WINSTON: You'd basically +just go down each + +branch to a leaf. + +So you say, for example, +here's one rule. + +If shadow equals question mark, +and garlic equals oh, + +[INAUDIBLE] + +want to choose No. + +Doesn't eat garlic. + +No. + +I think I'll say Yes. + +Yes. + +That changes the answer. + +Then if it eats garlic, it's +not a vampire, right? + +That's one of four possible +rules, because there are four + +leaf nodes. + +Now, almost done. + +We are done, except +for one thing. + +We can actually take these four +rules, and start thinking + +about how to simplify them. + +You can ask questions like, if +I have a rule that tests both + +the shadow and the garlic, do I +actually need both of those + +antecedents? + +And the answer is, in +many cases, no. + +And in particular, +in this case, no. + +Because if we look at our data +set, what we discover is that + +in the event that we're +talking about a shadow + +question mark-- + +oh, I guess I had a better +choice the other way. + +Oh, no. + +If you look at the garlic, +all the garlics-- + +Yes, Yes, and Yes-- + +it turns out that the answer is +no, independent of what the + +shadow condition is. + +So we can look at the rules, +and in some cases, we'll + +discover that our tree is a +little bit more complicated + +than it needs to be. + +We can actually get rid of +some of the clauses. + +So in the end, we can develop a +very simple mechanism based + +on good old fashioned rule-based +behavior, like you + +saw almost in the beginning +of the subject, + +that does the job. + +And now, without any royalty, +you're all free to put this in + +your PDA and use it to protect +yourself in the days to com, + +especially since Halloween's +just around the corner. \ No newline at end of file diff --git a/SchmVoc5NzY.txt b/SchmVoc5NzY.txt new file mode 100644 index 0000000000000000000000000000000000000000..4925f072f50fee7394075c3d1ff28fde0344dd0d --- /dev/null +++ b/SchmVoc5NzY.txt @@ -0,0 +1,20203 @@ +align:start position:0% + +before we get on to the topic for today + + align:start position:0% +before we get on to the topic for today + + + align:start position:0% +before we get on to the topic for today +i felt like last + + align:start position:0% +i felt like last + + + align:start position:0% +i felt like last +monday's lecture was not my best i don't + + align:start position:0% +monday's lecture was not my best i don't + + + align:start position:0% +monday's lecture was not my best i don't +know why it's not that i didn't put time + + align:start position:0% +know why it's not that i didn't put time + + + align:start position:0% +know why it's not that i didn't put time +on it i looked and i had the + + align:start position:0% +on it i looked and i had the + + + align:start position:0% +on it i looked and i had the +wrong + + align:start position:0% +wrong + + + align:start position:0% +wrong +lecture numbers on slides it was all + + align:start position:0% +lecture numbers on slides it was all + + + align:start position:0% +lecture numbers on slides it was all +kind of chaos i'm sorry about that + + align:start position:0% +kind of chaos i'm sorry about that + + + align:start position:0% +kind of chaos i'm sorry about that +sometimes you put in a lot of effort and + + align:start position:0% +sometimes you put in a lot of effort and + + + align:start position:0% +sometimes you put in a lot of effort and +you still give a lecture that isn't all + + align:start position:0% +you still give a lecture that isn't all + + + align:start position:0% +you still give a lecture that isn't all +that clear so let me try to tell you + + align:start position:0% +that clear so let me try to tell you + + + align:start position:0% +that clear so let me try to tell you +what i thought were the main points + + align:start position:0% +what i thought were the main points + + + align:start position:0% +what i thought were the main points +i started off by saying why it's really + + align:start position:0% +i started off by saying why it's really + + + align:start position:0% +i started off by saying why it's really +fundamentally important to be able to + + align:start position:0% +fundamentally important to be able to + + + align:start position:0% +fundamentally important to be able to +understand not just what people look + + align:start position:0% +understand not just what people look + + + align:start position:0% +understand not just what people look +like for from the outside but what we + + align:start position:0% +like for from the outside but what we + + + align:start position:0% +like for from the outside but what we +really care about people is what's going + + align:start position:0% +really care about people is what's going + + + align:start position:0% +really care about people is what's going +on on the inside about their thoughts + + align:start position:0% +on on the inside about their thoughts + + + align:start position:0% +on on the inside about their thoughts +and their beliefs and we are constantly + + align:start position:0% +and their beliefs and we are constantly + + + align:start position:0% +and their beliefs and we are constantly +making inferences about what people + + align:start position:0% +making inferences about what people + + + align:start position:0% +making inferences about what people +know and believe and want and think + + align:start position:0% +know and believe and want and think + + + align:start position:0% +know and believe and want and think +uh and we do that all the time to + + align:start position:0% +uh and we do that all the time to + + + align:start position:0% +uh and we do that all the time to +understand why they're doing something + + align:start position:0% +understand why they're doing something + + + align:start position:0% +understand why they're doing something +and to predict what they'll do next and + + align:start position:0% +and to predict what they'll do next and + + + align:start position:0% +and to predict what they'll do next and +so it's fundamentally important it's + + align:start position:0% +so it's fundamentally important it's + + + align:start position:0% +so it's fundamentally important it's +kind of the essence of being a human + + align:start position:0% +kind of the essence of being a human + + + align:start position:0% +kind of the essence of being a human +being in many ways it's the essence of + + align:start position:0% +being in many ways it's the essence of + + + align:start position:0% +being in many ways it's the essence of +literature + + align:start position:0% +literature + + + align:start position:0% +literature +and + + align:start position:0% +and + + + align:start position:0% +and +and we do it all the time + + align:start position:0% +and we do it all the time + + + align:start position:0% +and we do it all the time +and a classic way that people have + + align:start position:0% +and a classic way that people have + + + align:start position:0% +and a classic way that people have +studied false beliefs is + + align:start position:0% +studied false beliefs is + + + align:start position:0% +studied false beliefs is +thinking about other people's thoughts + + align:start position:0% +thinking about other people's thoughts + + + align:start position:0% +thinking about other people's thoughts +is with the false belief task the sally + + align:start position:0% +is with the false belief task the sally + + + align:start position:0% +is with the false belief task the sally +ann task that i described and the reason + + align:start position:0% +ann task that i described and the reason + + + align:start position:0% +ann task that i described and the reason +people use the false belief task rather + + align:start position:0% +people use the false belief task rather + + + align:start position:0% +people use the false belief task rather +than just a belief task is if the + + align:start position:0% +than just a belief task is if the + + + align:start position:0% +than just a belief task is if the +beliefs are true you can answer what + + align:start position:0% +beliefs are true you can answer what + + + align:start position:0% +beliefs are true you can answer what +somebody will do based on the world not + + align:start position:0% +somebody will do based on the world not + + + align:start position:0% +somebody will do based on the world not +based on their mind and so to unconfound + + align:start position:0% +based on their mind and so to unconfound + + + align:start position:0% +based on their mind and so to unconfound +the two we use a false belief that's + + align:start position:0% +the two we use a false belief that's + + + align:start position:0% +the two we use a false belief that's +different than the state of the world so + + align:start position:0% +different than the state of the world so + + + align:start position:0% +different than the state of the world so +we can be sure we're asking people uh + + align:start position:0% +we can be sure we're asking people uh + + + align:start position:0% +we can be sure we're asking people uh +what will happen next based on what that + + align:start position:0% +what will happen next based on what that + + + align:start position:0% +what will happen next based on what that +person believes + + align:start position:0% +person believes + + + align:start position:0% +person believes +and + + align:start position:0% +and + + + align:start position:0% +and +uh through decades of use of the um the + + align:start position:0% +uh through decades of use of the um the + + + align:start position:0% +uh through decades of use of the um the +sally anne false belief task and + + align:start position:0% +sally anne false belief task and + + + align:start position:0% +sally anne false belief task and +variations of it + + align:start position:0% +variations of it + + + align:start position:0% +variations of it +it's clear that there's a very + + align:start position:0% +it's clear that there's a very + + + align:start position:0% +it's clear that there's a very +distinctive developmental time course uh + + align:start position:0% +distinctive developmental time course uh + + + align:start position:0% +distinctive developmental time course uh +an ability to solve this problem + + align:start position:0% +an ability to solve this problem + + + align:start position:0% +an ability to solve this problem +five-year-olds solve it no problem + + align:start position:0% +five-year-olds solve it no problem + + + align:start position:0% +five-year-olds solve it no problem +three-year-olds systematically fail + + align:start position:0% +three-year-olds systematically fail + + + align:start position:0% +three-year-olds systematically fail +and people with autism + + align:start position:0% +and people with autism + + + align:start position:0% +and people with autism +typically get + + align:start position:0% +typically get + + + align:start position:0% +typically get +past this task late or not at all + + align:start position:0% +past this task late or not at all + + + align:start position:0% +past this task late or not at all +high functioning people with autism uh + + align:start position:0% +high functioning people with autism uh + + + align:start position:0% +high functioning people with autism uh +pass the task just later like seven + + align:start position:0% +pass the task just later like seven + + + align:start position:0% +pass the task just later like seven +eight nine years not five years old okay + + align:start position:0% +eight nine years not five years old okay + + + align:start position:0% +eight nine years not five years old okay +so that's the kind of behavioral + + align:start position:0% +so that's the kind of behavioral + + + align:start position:0% +so that's the kind of behavioral +background evidence that there's you + + align:start position:0% +background evidence that there's you + + + align:start position:0% +background evidence that there's you +know something distinctive about + + align:start position:0% +know something distinctive about + + + align:start position:0% +know something distinctive about +thinking about other people's minds + + align:start position:0% +thinking about other people's minds + + + align:start position:0% +thinking about other people's minds +then we considered whether they're + + align:start position:0% +then we considered whether they're + + + align:start position:0% +then we considered whether they're +special brain mechanisms uh and i argued + + align:start position:0% +special brain mechanisms uh and i argued + + + align:start position:0% +special brain mechanisms uh and i argued +that yes there are there's a bunch of + + align:start position:0% +that yes there are there's a bunch of + + + align:start position:0% +that yes there are there's a bunch of +them but the most impressively selective + + align:start position:0% +them but the most impressively selective + + + align:start position:0% +them but the most impressively selective +one is the tbj shown up there + + align:start position:0% +one is the tbj shown up there + + + align:start position:0% +one is the tbj shown up there +and evidence that it's specifically + + align:start position:0% +and evidence that it's specifically + + + align:start position:0% +and evidence that it's specifically +involved in thinking about other + + align:start position:0% +involved in thinking about other + + + align:start position:0% +involved in thinking about other +people's thoughts comes from the fact + + align:start position:0% +people's thoughts comes from the fact + + + align:start position:0% +people's thoughts comes from the fact +that that activation is a greater + + align:start position:0% +that that activation is a greater + + + align:start position:0% +that that activation is a greater +activation when you think about when you + + align:start position:0% +activation when you think about when you + + + align:start position:0% +activation when you think about when you +solve the false belief type problems + + align:start position:0% +solve the false belief type problems + + + align:start position:0% +solve the false belief type problems +when you think about another person's + + align:start position:0% +when you think about another person's + + + align:start position:0% +when you think about another person's +thoughts compared to when you think + + align:start position:0% +thoughts compared to when you think + + + align:start position:0% +thoughts compared to when you think +about a representation of physical + + align:start position:0% +about a representation of physical + + + align:start position:0% +about a representation of physical +representation like a photograph or a + + align:start position:0% +representation like a photograph or a + + + align:start position:0% +representation like a photograph or a +map okay so those are sort of logically + + align:start position:0% +map okay so those are sort of logically + + + align:start position:0% +map okay so those are sort of logically +isomorphic + + align:start position:0% +isomorphic + + + align:start position:0% +isomorphic +problems where you have to + + align:start position:0% +problems where you have to + + + align:start position:0% +problems where you have to +always answer a question about a + + align:start position:0% +always answer a question about a + + + align:start position:0% +always answer a question about a +representation it's just a + + align:start position:0% +representation it's just a + + + align:start position:0% +representation it's just a +representation is in somebody's head or + + align:start position:0% +representation is in somebody's head or + + + align:start position:0% +representation is in somebody's head or +it's a physical representation in the + + align:start position:0% +it's a physical representation in the + + + align:start position:0% +it's a physical representation in the +world and in that difference you get + + align:start position:0% +world and in that difference you get + + + align:start position:0% +world and in that difference you get +that region of the brain + + align:start position:0% +that region of the brain + + + align:start position:0% +that region of the brain +okay so that's cool because it's a very + + align:start position:0% +okay so that's cool because it's a very + + + align:start position:0% +okay so that's cool because it's a very +kind of um + + align:start position:0% +kind of um + + + align:start position:0% +kind of um +nicely nicely designed kind of it's not + + align:start position:0% +nicely nicely designed kind of it's not + + + align:start position:0% +nicely nicely designed kind of it's not +quite nothing's a minimal pair but it's + + align:start position:0% +quite nothing's a minimal pair but it's + + + align:start position:0% +quite nothing's a minimal pair but it's +a minimal pair in some respects right it + + align:start position:0% +a minimal pair in some respects right it + + + align:start position:0% +a minimal pair in some respects right it +carves out uh whether the representation + + align:start position:0% +carves out uh whether the representation + + + align:start position:0% +carves out uh whether the representation +is mental or physical + + align:start position:0% +is mental or physical + + + align:start position:0% +is mental or physical +um + + align:start position:0% +um + + + align:start position:0% +um +but it doesn't solve everything and a + + align:start position:0% +but it doesn't solve everything and a + + + align:start position:0% +but it doesn't solve everything and a +suite of other tasks have shown that + + align:start position:0% +suite of other tasks have shown that + + + align:start position:0% +suite of other tasks have shown that +that region is actually specific in a + + align:start position:0% +that region is actually specific in a + + + align:start position:0% +that region is actually specific in a +whole bunch of other respects + + align:start position:0% +whole bunch of other respects + + + align:start position:0% +whole bunch of other respects +it doesn't respond just whenever you + + align:start position:0% +it doesn't respond just whenever you + + + align:start position:0% +it doesn't respond just whenever you +think about a person their external + + align:start position:0% +think about a person their external + + + align:start position:0% +think about a person their external +properties + + align:start position:0% +properties + + + align:start position:0% +properties +and most impressively it does not even + + align:start position:0% +and most impressively it does not even + + + align:start position:0% +and most impressively it does not even +respond when you think about their + + align:start position:0% +respond when you think about their + + + align:start position:0% +respond when you think about their +visceral body sensations like thirst and + + align:start position:0% +visceral body sensations like thirst and + + + align:start position:0% +visceral body sensations like thirst and +hunger and pain + + align:start position:0% +hunger and pain + + + align:start position:0% +hunger and pain +so the tpga doesn't respond to just any + + align:start position:0% +so the tpga doesn't respond to just any + + + align:start position:0% +so the tpga doesn't respond to just any +thinking about any any mental states of + + align:start position:0% +thinking about any any mental states of + + + align:start position:0% +thinking about any any mental states of +another person it's specifically + + align:start position:0% +another person it's specifically + + + align:start position:0% +another person it's specifically +thinking about their thoughts and + + align:start position:0% +thinking about their thoughts and + + + align:start position:0% +thinking about their thoughts and +beliefs and that's pretty damn + + align:start position:0% +beliefs and that's pretty damn + + + align:start position:0% +beliefs and that's pretty damn +remarkable right it's how abstract can + + align:start position:0% +remarkable right it's how abstract can + + + align:start position:0% +remarkable right it's how abstract can +you get and yet here's a specific brain + + align:start position:0% +you get and yet here's a specific brain + + + align:start position:0% +you get and yet here's a specific brain +region for that very abstract very + + align:start position:0% +region for that very abstract very + + + align:start position:0% +region for that very abstract very +specific thing + + align:start position:0% +specific thing + + + align:start position:0% +specific thing +um and the final little bit of evidence + + align:start position:0% +um and the final little bit of evidence + + + align:start position:0% +um and the final little bit of evidence +i showed you is that it also generalizes + + align:start position:0% +i showed you is that it also generalizes + + + align:start position:0% +i showed you is that it also generalizes +it's not just about language because you + + align:start position:0% +it's not just about language because you + + + align:start position:0% +it's not just about language because you +can show people um movies that have no + + align:start position:0% +can show people um movies that have no + + + align:start position:0% +can show people um movies that have no +words in them + + align:start position:0% +words in them + + + align:start position:0% +words in them +but that clearly show characters who + + align:start position:0% +but that clearly show characters who + + + align:start position:0% +but that clearly show characters who +must be thinking about each other's + + align:start position:0% +must be thinking about each other's + + + align:start position:0% +must be thinking about each other's +thoughts and in those moments when the + + align:start position:0% +thoughts and in those moments when the + + + align:start position:0% +thoughts and in those moments when the +characters are thinking about each + + align:start position:0% +characters are thinking about each + + + align:start position:0% +characters are thinking about each +other's thoughts that region turns on + + align:start position:0% +other's thoughts that region turns on + + + align:start position:0% +other's thoughts that region turns on +more for example than uh when they're + + align:start position:0% +more for example than uh when they're + + + align:start position:0% +more for example than uh when they're +thinking about each other's pain okay + + align:start position:0% +thinking about each other's pain okay + + + align:start position:0% +thinking about each other's pain okay +yeah and did somebody look into + + align:start position:0% +yeah and did somebody look into + + + align:start position:0% +yeah and did somebody look into +what happens if other people think about + + align:start position:0% +what happens if other people think about + + + align:start position:0% +what happens if other people think about +me or if i think there's me thinking + + align:start position:0% +me or if i think there's me thinking + + + align:start position:0% +me or if i think there's me thinking +about me + + align:start position:0% +about me + + + align:start position:0% +about me +if other people you mean if you're + + align:start position:0% +if other people you mean if you're + + + align:start position:0% +if other people you mean if you're +thinking about other people thinking + + align:start position:0% +thinking about other people thinking + + + align:start position:0% +thinking about other people thinking +about you or yeah exciting um yeah i + + align:start position:0% +about you or yeah exciting um yeah i + + + align:start position:0% +about you or yeah exciting um yeah i +would assume that that region would be + + align:start position:0% +would assume that that region would be + + + align:start position:0% +would assume that that region would be +engaged i'm sure there's studies on that + + align:start position:0% +engaged i'm sure there's studies on that + + + align:start position:0% +engaged i'm sure there's studies on that +because because you're thinking about + + align:start position:0% +because because you're thinking about + + + align:start position:0% +because because you're thinking about +their thoughts right but more + + align:start position:0% +their thoughts right but more + + + align:start position:0% +their thoughts right but more +is it more interesting probably just + + align:start position:0% +is it more interesting probably just + + + align:start position:0% +is it more interesting probably just +because it's more salient + + align:start position:0% +because it's more salient + + + align:start position:0% +because it's more salient +right i mean i actually oddly in this + + align:start position:0% +right i mean i actually oddly in this + + + align:start position:0% +right i mean i actually oddly in this +class i talk about attention at the end + + align:start position:0% +class i talk about attention at the end + + + align:start position:0% +class i talk about attention at the end +which is weird because attention is a + + align:start position:0% +which is weird because attention is a + + + align:start position:0% +which is weird because attention is a +an issue with every study but most of + + align:start position:0% +an issue with every study but most of + + + align:start position:0% +an issue with every study but most of +the brain regions we've talked about + + align:start position:0% +the brain regions we've talked about + + + align:start position:0% +the brain regions we've talked about +surely including this one are modulable + + align:start position:0% +surely including this one are modulable + + + align:start position:0% +surely including this one are modulable +by how strongly you're attending to + + align:start position:0% +by how strongly you're attending to + + + align:start position:0% +by how strongly you're attending to +something + + align:start position:0% +something + + + align:start position:0% +something +so if something's really salient or + + align:start position:0% +so if something's really salient or + + + align:start position:0% +so if something's really salient or +important or + + align:start position:0% +important or + + + align:start position:0% +important or +you know uh you're really paying a lot + + align:start position:0% +you know uh you're really paying a lot + + + align:start position:0% +you know uh you're really paying a lot +of attention to it you're gonna get more + + align:start position:0% +of attention to it you're gonna get more + + + align:start position:0% +of attention to it you're gonna get more +activation and if it's more interesting + + align:start position:0% +activation and if it's more interesting + + + align:start position:0% +activation and if it's more interesting +to think about what other people think + + align:start position:0% +to think about what other people think + + + align:start position:0% +to think about what other people think +about me + + align:start position:0% +about me + + + align:start position:0% +about me +than to think about what other people + + align:start position:0% +than to think about what other people + + + align:start position:0% +than to think about what other people +think about each other + + align:start position:0% +think about each other + + + align:start position:0% +think about each other +you'll you'll find some modulation in + + align:start position:0% +you'll you'll find some modulation in + + + align:start position:0% +you'll you'll find some modulation in +here i'm sure + + align:start position:0% +here i'm sure + + + align:start position:0% +here i'm sure +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then finally i talked about moral + + align:start position:0% +and then finally i talked about moral + + + align:start position:0% +and then finally i talked about moral +reasoning as a test case it's not that + + align:start position:0% +reasoning as a test case it's not that + + + align:start position:0% +reasoning as a test case it's not that +the tpj is selectively involved in moral + + align:start position:0% +the tpj is selectively involved in moral + + + align:start position:0% +the tpj is selectively involved in moral +reasoning it's that many of the critical + + align:start position:0% +reasoning it's that many of the critical + + + align:start position:0% +reasoning it's that many of the critical +aspects of moral reasoning depend on + + align:start position:0% +aspects of moral reasoning depend on + + + align:start position:0% +aspects of moral reasoning depend on +what a person knew at the time + + align:start position:0% +what a person knew at the time + + + align:start position:0% +what a person knew at the time +and so to use that information in moral + + align:start position:0% +and so to use that information in moral + + + align:start position:0% +and so to use that information in moral +reasoning you need to pull that region + + align:start position:0% +reasoning you need to pull that region + + + align:start position:0% +reasoning you need to pull that region +in so i realized i wrote that question + + align:start position:0% +in so i realized i wrote that question + + + align:start position:0% +in so i realized i wrote that question +ambiguously on the quiz i meant to ask + + align:start position:0% +ambiguously on the quiz i meant to ask + + + align:start position:0% +ambiguously on the quiz i meant to ask +is the tpj engaged specifically or only + + align:start position:0% +is the tpj engaged specifically or only + + + align:start position:0% +is the tpj engaged specifically or only +in moral reasoning to which the answer + + align:start position:0% +in moral reasoning to which the answer + + + align:start position:0% +in moral reasoning to which the answer +the correct answer would be no + + align:start position:0% +the correct answer would be no + + + align:start position:0% +the correct answer would be no +but i didn't put the only in there and i + + align:start position:0% +but i didn't put the only in there and i + + + align:start position:0% +but i didn't put the only in there and i +decided it was ambiguous so if you said + + align:start position:0% +decided it was ambiguous so if you said + + + align:start position:0% +decided it was ambiguous so if you said +yes you got the points + + align:start position:0% + + + + align:start position:0% + +anyway i gave several bits of evidence + + align:start position:0% +anyway i gave several bits of evidence + + + align:start position:0% +anyway i gave several bits of evidence +that um + + align:start position:0% +that um + + + align:start position:0% +that um +using the moral reasoning case + + align:start position:0% +using the moral reasoning case + + + align:start position:0% +using the moral reasoning case +that the tbj is + + align:start position:0% +that the tbj is + + + align:start position:0% +that the tbj is +is + + align:start position:0% +is + + + align:start position:0% +is +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +stronger evidence that's involved in + + align:start position:0% +stronger evidence that's involved in + + + align:start position:0% +stronger evidence that's involved in +thinking about other people's thoughts + + align:start position:0% +thinking about other people's thoughts + + + align:start position:0% +thinking about other people's thoughts +first that we showed that in people with + + align:start position:0% +first that we showed that in people with + + + align:start position:0% +first that we showed that in people with +autism who have this difficulty in + + align:start position:0% +autism who have this difficulty in + + + align:start position:0% +autism who have this difficulty in +thinking about each other's thoughts + + align:start position:0% +thinking about each other's thoughts + + + align:start position:0% +thinking about each other's thoughts +even once they can pass the false belief + + align:start position:0% +even once they can pass the false belief + + + align:start position:0% +even once they can pass the false belief +task they put less emphasis less weight + + align:start position:0% +task they put less emphasis less weight + + + align:start position:0% +task they put less emphasis less weight +on what the person knew at the time when + + align:start position:0% +on what the person knew at the time when + + + align:start position:0% +on what the person knew at the time when +evaluating the moral status of their + + align:start position:0% +evaluating the moral status of their + + + align:start position:0% +evaluating the moral status of their +actions + + align:start position:0% +actions + + + align:start position:0% +actions +okay it's not that they make a mistake + + align:start position:0% +okay it's not that they make a mistake + + + align:start position:0% +okay it's not that they make a mistake +or that they're unable to morally reason + + align:start position:0% +or that they're unable to morally reason + + + align:start position:0% +or that they're unable to morally reason +it's a pretty subtle thing is just a + + align:start position:0% +it's a pretty subtle thing is just a + + + align:start position:0% +it's a pretty subtle thing is just a +small difference in how much they weigh + + align:start position:0% +small difference in how much they weigh + + + align:start position:0% +small difference in how much they weigh +what another person knew at the time + + align:start position:0% +what another person knew at the time + + + align:start position:0% +what another person knew at the time +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that was that's also known as less + + align:start position:0% +so that was that's also known as less + + + align:start position:0% +so that was that's also known as less +forgiveness or less exoneration for + + align:start position:0% +forgiveness or less exoneration for + + + align:start position:0% +forgiveness or less exoneration for +accidental harm + + align:start position:0% +accidental harm + + + align:start position:0% +accidental harm +right you kick somebody by accident and + + align:start position:0% +right you kick somebody by accident and + + + align:start position:0% +right you kick somebody by accident and +they go ouch + + align:start position:0% +they go ouch + + + align:start position:0% +they go ouch +well maybe you get a little bit of blame + + align:start position:0% +well maybe you get a little bit of blame + + + align:start position:0% +well maybe you get a little bit of blame +because you were a klutz and you should + + align:start position:0% +because you were a klutz and you should + + + align:start position:0% +because you were a klutz and you should +have thought or something but it was an + + align:start position:0% +have thought or something but it was an + + + align:start position:0% +have thought or something but it was an +accident so you should be exonerated + + align:start position:0% +accident so you should be exonerated + + + align:start position:0% +accident so you should be exonerated +people with autism exonerate slightly + + align:start position:0% +people with autism exonerate slightly + + + align:start position:0% +people with autism exonerate slightly +less right + + align:start position:0% +less right + + + align:start position:0% +less right +um + + align:start position:0% +um + + + align:start position:0% +um +okay so we then talked about the the + + align:start position:0% +okay so we then talked about the the + + + align:start position:0% +okay so we then talked about the the +fact that if you zap the tbj with tms + + align:start position:0% +fact that if you zap the tbj with tms + + + align:start position:0% +fact that if you zap the tbj with tms +stick a coil there right you do the same + + align:start position:0% +stick a coil there right you do the same + + + align:start position:0% +stick a coil there right you do the same +thing you slightly reduce the weight + + align:start position:0% +thing you slightly reduce the weight + + + align:start position:0% +thing you slightly reduce the weight +people put on what the person knew at + + align:start position:0% +people put on what the person knew at + + + align:start position:0% +people put on what the person knew at +the time in their moral evaluation of + + align:start position:0% +the time in their moral evaluation of + + + align:start position:0% +the time in their moral evaluation of +the person's + + align:start position:0% +the person's + + + align:start position:0% +the person's +actions + + align:start position:0% +actions + + + align:start position:0% +actions +um and then i showed this bizarre fact + + align:start position:0% +um and then i showed this bizarre fact + + + align:start position:0% +um and then i showed this bizarre fact +that as i think gisela asked + + align:start position:0% +that as i think gisela asked + + + align:start position:0% +that as i think gisela asked +shouldn't the tbj be different in people + + align:start position:0% +shouldn't the tbj be different in people + + + align:start position:0% +shouldn't the tbj be different in people +with autism yes absolutely according to + + align:start position:0% +with autism yes absolutely according to + + + align:start position:0% +with autism yes absolutely according to +all of this it should be but the basic + + align:start position:0% +all of this it should be but the basic + + + align:start position:0% +all of this it should be but the basic +univariate measures how big it is how + + align:start position:0% +univariate measures how big it is how + + + align:start position:0% +univariate measures how big it is how +selective it is where it is do not find + + align:start position:0% +selective it is where it is do not find + + + align:start position:0% +selective it is where it is do not find +a difference in that region with that + + align:start position:0% +a difference in that region with that + + + align:start position:0% +a difference in that region with that +contrast in high functioning people with + + align:start position:0% +contrast in high functioning people with + + + align:start position:0% +contrast in high functioning people with +autism that's surprising + + align:start position:0% +autism that's surprising + + + align:start position:0% +autism that's surprising +but one possible answer to that is even + + align:start position:0% +but one possible answer to that is even + + + align:start position:0% +but one possible answer to that is even +though it's there and it's just as big + + align:start position:0% +though it's there and it's just as big + + + align:start position:0% +though it's there and it's just as big +and strong and all of that + + align:start position:0% +and strong and all of that + + + align:start position:0% +and strong and all of that +it's um + + align:start position:0% +it's um + + + align:start position:0% +it's um +that doesn't mean it doesn't represent + + align:start position:0% +that doesn't mean it doesn't represent + + + align:start position:0% +that doesn't mean it doesn't represent +different information and i showed you + + align:start position:0% +different information and i showed you + + + align:start position:0% +different information and i showed you +an example that in + + align:start position:0% +an example that in + + + align:start position:0% +an example that in +typical people you can decode from the + + align:start position:0% +typical people you can decode from the + + + align:start position:0% +typical people you can decode from the +tpj whether the person is reading about + + align:start position:0% +tpj whether the person is reading about + + + align:start position:0% +tpj whether the person is reading about +another person's intentional harm or + + align:start position:0% +another person's intentional harm or + + + align:start position:0% +another person's intentional harm or +accidental harm + + align:start position:0% +accidental harm + + + align:start position:0% +accidental harm +and you can't in people with asd + + align:start position:0% +and you can't in people with asd + + + align:start position:0% +and you can't in people with asd +okay so that's my + + align:start position:0% +okay so that's my + + + align:start position:0% +okay so that's my +summary of last time uh and then all of + + align:start position:0% +summary of last time uh and then all of + + + align:start position:0% +summary of last time uh and then all of +that was focusing very particularly on + + align:start position:0% +that was focusing very particularly on + + + align:start position:0% +that was focusing very particularly on +the kind of most fancy quintessentially + + align:start position:0% +the kind of most fancy quintessentially + + + align:start position:0% +the kind of most fancy quintessentially +human aspect of social cognition which + + align:start position:0% +human aspect of social cognition which + + + align:start position:0% +human aspect of social cognition which +is this business of representing each + + align:start position:0% +is this business of representing each + + + align:start position:0% +is this business of representing each +other's thoughts and beliefs + + align:start position:0% +other's thoughts and beliefs + + + align:start position:0% +other's thoughts and beliefs +but i pointed out at the end that all + + align:start position:0% +but i pointed out at the end that all + + + align:start position:0% +but i pointed out at the end that all +right that there are also lots and lots + + align:start position:0% +right that there are also lots and lots + + + align:start position:0% +right that there are also lots and lots +of other facets of social perception and + + align:start position:0% +of other facets of social perception and + + + align:start position:0% +of other facets of social perception and +social cognition many of which have + + align:start position:0% +social cognition many of which have + + + align:start position:0% +social cognition many of which have +somewhat selective brain regions lots of + + align:start position:0% +somewhat selective brain regions lots of + + + align:start position:0% +somewhat selective brain regions lots of +them other parts of the brain and we + + align:start position:0% +them other parts of the brain and we + + + align:start position:0% +them other parts of the brain and we +just didn't have time to for full + + align:start position:0% +just didn't have time to for full + + + align:start position:0% +just didn't have time to for full +treatment + + align:start position:0% +treatment + + + align:start position:0% +treatment +okay + + align:start position:0% +okay + + + align:start position:0% +okay +hopefully that was a little bit clearer + + align:start position:0% +hopefully that was a little bit clearer + + + align:start position:0% +hopefully that was a little bit clearer +than i was last time + + align:start position:0% +than i was last time + + + align:start position:0% +than i was last time +okay so so far in this course we've been + + align:start position:0% +okay so so far in this course we've been + + + align:start position:0% +okay so so far in this course we've been +focusing on all these bits of brain that + + align:start position:0% +focusing on all these bits of brain that + + + align:start position:0% +focusing on all these bits of brain that +seem to do very distinctive often very + + align:start position:0% +seem to do very distinctive often very + + + align:start position:0% +seem to do very distinctive often very +selective things okay so the one we've + + align:start position:0% +selective things okay so the one we've + + + align:start position:0% +selective things okay so the one we've +just been talking about is that little + + align:start position:0% +just been talking about is that little + + + align:start position:0% +just been talking about is that little +guy right there + + align:start position:0% +guy right there + + + align:start position:0% +guy right there +but we've talked about a lot of these + + align:start position:0% +but we've talked about a lot of these + + + align:start position:0% +but we've talked about a lot of these +things in here + + align:start position:0% +things in here + + + align:start position:0% +things in here +and + + align:start position:0% +and + + + align:start position:0% +and +the field of human cognitive + + align:start position:0% +the field of human cognitive + + + align:start position:0% +the field of human cognitive +neuroscience has invested lots of effort + + align:start position:0% +neuroscience has invested lots of effort + + + align:start position:0% +neuroscience has invested lots of effort +to find these things and try to + + align:start position:0% +to find these things and try to + + + align:start position:0% +to find these things and try to +characterize what each of them does + + align:start position:0% +characterize what each of them does + + + align:start position:0% +characterize what each of them does +and that's pretty cool right this is all + + align:start position:0% +and that's pretty cool right this is all + + + align:start position:0% +and that's pretty cool right this is all +stuff we didn't know 20 years ago and + + align:start position:0% +stuff we didn't know 20 years ago and + + + align:start position:0% +stuff we didn't know 20 years ago and +it's nice and it's like counts as real + + align:start position:0% +it's nice and it's like counts as real + + + align:start position:0% +it's nice and it's like counts as real +progress i think + + align:start position:0% +progress i think + + + align:start position:0% +progress i think +um but it + + align:start position:0% +um but it + + + align:start position:0% +um but it +leaves lots of things woefully + + align:start position:0% +leaves lots of things woefully + + + align:start position:0% +leaves lots of things woefully +unanswered + + align:start position:0% +unanswered + + + align:start position:0% +unanswered +these none of these regions can act + + align:start position:0% +these none of these regions can act + + + align:start position:0% +these none of these regions can act +alone even though i've depicted them + + align:start position:0% +alone even though i've depicted them + + + align:start position:0% +alone even though i've depicted them +somewhat + + align:start position:0% +somewhat + + + align:start position:0% +somewhat +in a somewhat silly fashion as nice + + align:start position:0% +in a somewhat silly fashion as nice + + + align:start position:0% +in a somewhat silly fashion as nice +little you know m m's on the brain + + align:start position:0% +little you know m m's on the brain + + + align:start position:0% +little you know m m's on the brain +none of them act alone none of them + + align:start position:0% +none of them act alone none of them + + + align:start position:0% +none of them act alone none of them +could act alone they need information to + + align:start position:0% +could act alone they need information to + + + align:start position:0% +could act alone they need information to +process so there has to be input to each + + align:start position:0% +process so there has to be input to each + + + align:start position:0% +process so there has to be input to each +region they need to be able to tell + + align:start position:0% +region they need to be able to tell + + + align:start position:0% +region they need to be able to tell +other regions what they figured out or + + align:start position:0% +other regions what they figured out or + + + align:start position:0% +other regions what they figured out or +there's no point + + align:start position:0% +there's no point + + + align:start position:0% +there's no point +and probably as they solve a problem as + + align:start position:0% +and probably as they solve a problem as + + + align:start position:0% +and probably as they solve a problem as +they conduct their computations they're + + align:start position:0% +they conduct their computations they're + + + align:start position:0% +they conduct their computations they're +probably interacting all the time with + + align:start position:0% +probably interacting all the time with + + + align:start position:0% +probably interacting all the time with +lots of other regions + + align:start position:0% +lots of other regions + + + align:start position:0% +lots of other regions +so we desperately need to understand not + + align:start position:0% +so we desperately need to understand not + + + align:start position:0% +so we desperately need to understand not +just that you know this patch does faces + + align:start position:0% +just that you know this patch does faces + + + align:start position:0% +just that you know this patch does faces +there's lots more we need to know one of + + align:start position:0% +there's lots more we need to know one of + + + align:start position:0% +there's lots more we need to know one of +the things we really need to know is + + align:start position:0% +the things we really need to know is + + + align:start position:0% +the things we really need to know is +what is it connected to and who is it + + align:start position:0% +what is it connected to and who is it + + + align:start position:0% +what is it connected to and who is it +interacting with + + align:start position:0% +interacting with + + + align:start position:0% +interacting with +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's what i just said and so that + + align:start position:0% +so that's what i just said and so that + + + align:start position:0% +so that's what i just said and so that +means looking at not just the cortex + + align:start position:0% +means looking at not just the cortex + + + align:start position:0% +means looking at not just the cortex +that we've been focusing on through this + + align:start position:0% +that we've been focusing on through this + + + align:start position:0% +that we've been focusing on through this +whole course this dark matter that's on + + align:start position:0% +whole course this dark matter that's on + + + align:start position:0% +whole course this dark matter that's on +the surface of the brain up there + + align:start position:0% +the surface of the brain up there + + + align:start position:0% +the surface of the brain up there +uh but today we're gonna do a kind of + + align:start position:0% +uh but today we're gonna do a kind of + + + align:start position:0% +uh but today we're gonna do a kind of +figure ground flip on the brain and + + align:start position:0% +figure ground flip on the brain and + + + align:start position:0% +figure ground flip on the brain and +we're going to start paying attention to + + align:start position:0% +we're going to start paying attention to + + + align:start position:0% +we're going to start paying attention to +all that stuff that used to be + + align:start position:0% +all that stuff that used to be + + + align:start position:0% +all that stuff that used to be +background down there + + align:start position:0% +background down there + + + align:start position:0% +background down there +all that white matter underneath which + + align:start position:0% +all that white matter underneath which + + + align:start position:0% +all that white matter underneath which +is like a big heap of myelinated fibers + + align:start position:0% +is like a big heap of myelinated fibers + + + align:start position:0% +is like a big heap of myelinated fibers +that connect long-range regions of the + + align:start position:0% +that connect long-range regions of the + + + align:start position:0% +that connect long-range regions of the +brain to each other okay + + align:start position:0% +brain to each other okay + + + align:start position:0% +brain to each other okay +so you might say okay just wires who + + align:start position:0% +so you might say okay just wires who + + + align:start position:0% +so you might say okay just wires who +cares about the wires that was my + + align:start position:0% +cares about the wires that was my + + + align:start position:0% +cares about the wires that was my +attitude for a long time i've gotten + + align:start position:0% +attitude for a long time i've gotten + + + align:start position:0% +attitude for a long time i've gotten +over it + + align:start position:0% +over it + + + align:start position:0% +over it +we desperately need to know about the + + align:start position:0% +we desperately need to know about the + + + align:start position:0% +we desperately need to know about the +wires for all kinds of reasons so i'm + + align:start position:0% +wires for all kinds of reasons so i'm + + + align:start position:0% +wires for all kinds of reasons so i'm +going to go through a whole bunch of + + align:start position:0% +going to go through a whole bunch of + + + align:start position:0% +going to go through a whole bunch of +reasons and there's a lot of little + + align:start position:0% +reasons and there's a lot of little + + + align:start position:0% +reasons and there's a lot of little +details and i don't want you to panic i + + align:start position:0% +details and i don't want you to panic i + + + align:start position:0% +details and i don't want you to panic i +just want to give you the gist of + + align:start position:0% +just want to give you the gist of + + + align:start position:0% +just want to give you the gist of +why this is worth paying attention to + + align:start position:0% +why this is worth paying attention to + + + align:start position:0% +why this is worth paying attention to +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so first of all + + align:start position:0% +so first of all + + + align:start position:0% +so first of all +white matter makes up 45 of the human + + align:start position:0% +white matter makes up 45 of the human + + + align:start position:0% +white matter makes up 45 of the human +brain + + align:start position:0% +brain + + + align:start position:0% +brain +so that alone tells you it's not like + + align:start position:0% +so that alone tells you it's not like + + + align:start position:0% +so that alone tells you it's not like +some trivial thing as a big part of your + + align:start position:0% +some trivial thing as a big part of your + + + align:start position:0% +some trivial thing as a big part of your +brain + + align:start position:0% +brain + + + align:start position:0% +brain +this is all the more interesting + + align:start position:0% +this is all the more interesting + + + align:start position:0% +this is all the more interesting +because that's not true in other animals + + align:start position:0% +because that's not true in other animals + + + align:start position:0% +because that's not true in other animals +so um i think white matter makes up a + + align:start position:0% +so um i think white matter makes up a + + + align:start position:0% +so um i think white matter makes up a +higher percent of the human brain than + + align:start position:0% +higher percent of the human brain than + + + align:start position:0% +higher percent of the human brain than +any other animal or at least we're way + + align:start position:0% +any other animal or at least we're way + + + align:start position:0% +any other animal or at least we're way +up there in mice it's only 10 percent + + align:start position:0% +up there in mice it's only 10 percent + + + align:start position:0% +up there in mice it's only 10 percent +and maybe that's a relatively + + align:start position:0% +and maybe that's a relatively + + + align:start position:0% +and maybe that's a relatively +uninteresting thing about scaling with + + align:start position:0% +uninteresting thing about scaling with + + + align:start position:0% +uninteresting thing about scaling with +brain's highs but maybe it's something + + align:start position:0% +brain's highs but maybe it's something + + + align:start position:0% +brain's highs but maybe it's something +deeper about human brain what's special + + align:start position:0% +deeper about human brain what's special + + + align:start position:0% +deeper about human brain what's special +about the human brain and nobody knows + + align:start position:0% +about the human brain and nobody knows + + + align:start position:0% +about the human brain and nobody knows +and here's a fun fact if you took all + + align:start position:0% +and here's a fun fact if you took all + + + align:start position:0% +and here's a fun fact if you took all +the myelinated fibers in the human brain + + align:start position:0% +the myelinated fibers in the human brain + + + align:start position:0% +the myelinated fibers in the human brain +and you laid them out end to end you + + align:start position:0% +and you laid them out end to end you + + + align:start position:0% +and you laid them out end to end you +could go around the world three times so + + align:start position:0% +could go around the world three times so + + + align:start position:0% +could go around the world three times so +we've got lots of cableage sitting in + + align:start position:0% +we've got lots of cableage sitting in + + + align:start position:0% +we've got lots of cableage sitting in +here + + align:start position:0% +here + + + align:start position:0% +here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +i briefly argued before that you simply + + align:start position:0% +i briefly argued before that you simply + + + align:start position:0% +i briefly argued before that you simply +cannot understand the cortex without + + align:start position:0% +cannot understand the cortex without + + + align:start position:0% +cannot understand the cortex without +understanding uh its connections of one + + align:start position:0% +understanding uh its connections of one + + + align:start position:0% +understanding uh its connections of one +region to another it's just + + align:start position:0% +region to another it's just + + + align:start position:0% +region to another it's just +crazy to study one little patch of the + + align:start position:0% +crazy to study one little patch of the + + + align:start position:0% +crazy to study one little patch of the +brain and not know who it's talking to + + align:start position:0% +brain and not know who it's talking to + + + align:start position:0% +brain and not know who it's talking to +and where it gets its inputs from + + align:start position:0% +and where it gets its inputs from + + + align:start position:0% +and where it gets its inputs from +and as i just said that the the um + + align:start position:0% +and as i just said that the the um + + + align:start position:0% +and as i just said that the the um +pressing need for that knowledge is + + align:start position:0% +pressing need for that knowledge is + + + align:start position:0% +pressing need for that knowledge is +heightened by the presence of this map + + align:start position:0% +heightened by the presence of this map + + + align:start position:0% +heightened by the presence of this map +which we didn't used to have now that we + + align:start position:0% +which we didn't used to have now that we + + + align:start position:0% +which we didn't used to have now that we +have this map it's all the more + + align:start position:0% +have this map it's all the more + + + align:start position:0% +have this map it's all the more +important and pressing to know what the + + align:start position:0% +important and pressing to know what the + + + align:start position:0% +important and pressing to know what the +connections of those regions are + + align:start position:0% +connections of those regions are + + + align:start position:0% +connections of those regions are +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so here's a nice quote making this point + + align:start position:0% +so here's a nice quote making this point + + + align:start position:0% +so here's a nice quote making this point +this is heidi johnson berg and matt + + align:start position:0% +this is heidi johnson berg and matt + + + align:start position:0% +this is heidi johnson berg and matt +rushworth they say + + align:start position:0% +rushworth they say + + + align:start position:0% +rushworth they say +connectivity patterns define functional + + align:start position:0% +connectivity patterns define functional + + + align:start position:0% +connectivity patterns define functional +networks the inputs to a brain region + + align:start position:0% +networks the inputs to a brain region + + + align:start position:0% +networks the inputs to a brain region +determine the information available to + + align:start position:0% +determine the information available to + + + align:start position:0% +determine the information available to +it + + align:start position:0% +it + + + align:start position:0% +it +whereas its outputs dictate the + + align:start position:0% +whereas its outputs dictate the + + + align:start position:0% +whereas its outputs dictate the +influence that brain region have on + + align:start position:0% +influence that brain region have on + + + align:start position:0% +influence that brain region have on +other areas + + align:start position:0% +other areas + + + align:start position:0% +other areas +therefore simply by knowing the pattern + + align:start position:0% +therefore simply by knowing the pattern + + + align:start position:0% +therefore simply by knowing the pattern +of inputs and outputs of a brain region + + align:start position:0% +of inputs and outputs of a brain region + + + align:start position:0% +of inputs and outputs of a brain region +we can begin to make inferences about + + align:start position:0% +we can begin to make inferences about + + + align:start position:0% +we can begin to make inferences about +its likely functional specialization so + + align:start position:0% +its likely functional specialization so + + + align:start position:0% +its likely functional specialization so +i think that's a nice quote it makes the + + align:start position:0% +i think that's a nice quote it makes the + + + align:start position:0% +i think that's a nice quote it makes the +point that + + align:start position:0% +point that + + + align:start position:0% +point that +that it's not just that we need to know + + align:start position:0% +that it's not just that we need to know + + + align:start position:0% +that it's not just that we need to know +the connections but the connections and + + align:start position:0% +the connections but the connections and + + + align:start position:0% +the connections but the connections and +the function are bound to be deeply + + align:start position:0% +the function are bound to be deeply + + + align:start position:0% +the function are bound to be deeply +enmeshed one constrains the other + + align:start position:0% +enmeshed one constrains the other + + + align:start position:0% +enmeshed one constrains the other +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay + + align:start position:0% + + + + align:start position:0% + +further recall way back which will quite + + align:start position:0% +further recall way back which will quite + + + align:start position:0% +further recall way back which will quite +possibly return on the final exam how do + + align:start position:0% +possibly return on the final exam how do + + + align:start position:0% +possibly return on the final exam how do +we define a cortical area i gave you + + align:start position:0% +we define a cortical area i gave you + + + align:start position:0% +we define a cortical area i gave you +criteria for a cortical area and one of + + align:start position:0% +criteria for a cortical area and one of + + + align:start position:0% +criteria for a cortical area and one of +the criteria was a distinctive pattern + + align:start position:0% +the criteria was a distinctive pattern + + + align:start position:0% +the criteria was a distinctive pattern +of connectivity right so it's part of + + align:start position:0% +of connectivity right so it's part of + + + align:start position:0% +of connectivity right so it's part of +the identifying + + align:start position:0% +the identifying + + + align:start position:0% +the identifying +properties of a cortical area is is what + + align:start position:0% +properties of a cortical area is is what + + + align:start position:0% +properties of a cortical area is is what +it's connected to + + align:start position:0% +it's connected to + + + align:start position:0% +it's connected to +and + + align:start position:0% +and + + + align:start position:0% +and +so that's another reason we should care + + align:start position:0% + + + + align:start position:0% + +a third reason is if we knew of a given + + align:start position:0% +a third reason is if we knew of a given + + + align:start position:0% +a third reason is if we knew of a given +cortical area what its long-range + + align:start position:0% +cortical area what its long-range + + + align:start position:0% +cortical area what its long-range +connections were to lots of other + + align:start position:0% +connections were to lots of other + + + align:start position:0% +connections were to lots of other +regions + + align:start position:0% +regions + + + align:start position:0% +regions +that connectivity fingerprint remember + + align:start position:0% +that connectivity fingerprint remember + + + align:start position:0% +that connectivity fingerprint remember +we talked briefly about connectivity + + align:start position:0% +we talked briefly about connectivity + + + align:start position:0% +we talked briefly about connectivity +fingerprints a month or so ago + + align:start position:0% +fingerprints a month or so ago + + + align:start position:0% +fingerprints a month or so ago +that fingerprint this distinctive set of + + align:start position:0% +that fingerprint this distinctive set of + + + align:start position:0% +that fingerprint this distinctive set of +connections of that region + + align:start position:0% +connections of that region + + + align:start position:0% +connections of that region +you can think of it as a signature of + + align:start position:0% +you can think of it as a signature of + + + align:start position:0% +you can think of it as a signature of +not not just how that region differs + + align:start position:0% +not not just how that region differs + + + align:start position:0% +not not just how that region differs +from other regions in that same + + align:start position:0% +from other regions in that same + + + align:start position:0% +from other regions in that same +individual brain + + align:start position:0% +individual brain + + + align:start position:0% +individual brain +but + + align:start position:0% +but + + + align:start position:0% +but +how we might find a homolog of that + + align:start position:0% +how we might find a homolog of that + + + align:start position:0% +how we might find a homolog of that +region in another species + + align:start position:0% +region in another species + + + align:start position:0% +region in another species +and that would be a very interesting + + align:start position:0% +and that would be a very interesting + + + align:start position:0% +and that would be a very interesting +thing to do + + align:start position:0% +thing to do + + + align:start position:0% +thing to do +like wouldn't it be cool to know + + align:start position:0% +like wouldn't it be cool to know + + + align:start position:0% +like wouldn't it be cool to know +is there a tpj + + align:start position:0% +is there a tpj + + + align:start position:0% +is there a tpj +in macaques + + align:start position:0% +in macaques + + + align:start position:0% +in macaques +well macaques can't solve an analog of + + align:start position:0% +well macaques can't solve an analog of + + + align:start position:0% +well macaques can't solve an analog of +the + + align:start position:0% +the + + + align:start position:0% +the +theory of mind task + + align:start position:0% +theory of mind task + + + align:start position:0% +theory of mind task +chimps we could debate a little bit in + + align:start position:0% +chimps we could debate a little bit in + + + align:start position:0% +chimps we could debate a little bit in +narrow domains kind of sort of a little + + align:start position:0% +narrow domains kind of sort of a little + + + align:start position:0% +narrow domains kind of sort of a little +bit not really + + align:start position:0% +bit not really + + + align:start position:0% +bit not really +macaques no okay + + align:start position:0% +macaques no okay + + + align:start position:0% +macaques no okay +um so + + align:start position:0% +um so + + + align:start position:0% +um so +do is there a homolog is there a + + align:start position:0% +do is there a homolog is there a + + + align:start position:0% +do is there a homolog is there a +corresponding region that maybe + + align:start position:0% +corresponding region that maybe + + + align:start position:0% +corresponding region that maybe +you know + + align:start position:0% +you know + + + align:start position:0% +you know +we took that region and we adapted it + + align:start position:0% +we took that region and we adapted it + + + align:start position:0% +we took that region and we adapted it +and made it work better so we could do + + align:start position:0% +and made it work better so we could do + + + align:start position:0% +and made it work better so we could do +better things with it and if so what is + + align:start position:0% +better things with it and if so what is + + + align:start position:0% +better things with it and if so what is +it doing in macaques right i mean i + + align:start position:0% +it doing in macaques right i mean i + + + align:start position:0% +it doing in macaques right i mean i +think that's just a totally cool + + align:start position:0% +think that's just a totally cool + + + align:start position:0% +think that's just a totally cool +question and in principle + + align:start position:0% +question and in principle + + + align:start position:0% +question and in principle +one way to say what counts as the same + + align:start position:0% +one way to say what counts as the same + + + align:start position:0% +one way to say what counts as the same +region across species which is kind of a + + align:start position:0% +region across species which is kind of a + + + align:start position:0% +region across species which is kind of a +weird question they're different species + + align:start position:0% +weird question they're different species + + + align:start position:0% +weird question they're different species +so what would the same region mean + + align:start position:0% +so what would the same region mean + + + align:start position:0% +so what would the same region mean +one way to say what the same region + + align:start position:0% +one way to say what the same region + + + align:start position:0% +one way to say what the same region +means is to have a similar connectivity + + align:start position:0% +means is to have a similar connectivity + + + align:start position:0% +means is to have a similar connectivity +fingerprint + + align:start position:0% +fingerprint + + + align:start position:0% +fingerprint +okay so there's several studies that try + + align:start position:0% +okay so there's several studies that try + + + align:start position:0% +okay so there's several studies that try +to do that i couldn't cram them into + + align:start position:0% +to do that i couldn't cram them into + + + align:start position:0% +to do that i couldn't cram them into +this lecture but if you're interested in + + align:start position:0% +this lecture but if you're interested in + + + align:start position:0% +this lecture but if you're interested in +reading on it reading about it shoot me + + align:start position:0% +reading on it reading about it shoot me + + + align:start position:0% +reading on it reading about it shoot me +an email i'll send you some papers + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +i also mentioned that the specific set + + align:start position:0% +i also mentioned that the specific set + + + align:start position:0% +i also mentioned that the specific set +of connections of a cortical region + + align:start position:0% +of connections of a cortical region + + + align:start position:0% +of connections of a cortical region +particularly its inputs play an + + align:start position:0% +particularly its inputs play an + + + align:start position:0% +particularly its inputs play an +important role in development remember + + align:start position:0% +important role in development remember + + + align:start position:0% +important role in development remember +the rewired ferrets if you redirect the + + align:start position:0% +the rewired ferrets if you redirect the + + + align:start position:0% +the rewired ferrets if you redirect the +input to what would have been primary + + align:start position:0% +input to what would have been primary + + + align:start position:0% +input to what would have been primary +auditory cortex in a ferret + + align:start position:0% +auditory cortex in a ferret + + + align:start position:0% +auditory cortex in a ferret +and you have it have that input come in + + align:start position:0% +and you have it have that input come in + + + align:start position:0% +and you have it have that input come in +from the eyes + + align:start position:0% +from the eyes + + + align:start position:0% +from the eyes +you can get what would have been primary + + align:start position:0% +you can get what would have been primary + + + align:start position:0% +you can get what would have been primary +auditory cortex to become a lot like + + align:start position:0% +auditory cortex to become a lot like + + + align:start position:0% +auditory cortex to become a lot like +primary visual cortex + + align:start position:0% +primary visual cortex + + + align:start position:0% +primary visual cortex +so connectivity is important not just in + + align:start position:0% +so connectivity is important not just in + + + align:start position:0% +so connectivity is important not just in +how a region functions and how we say + + align:start position:0% +how a region functions and how we say + + + align:start position:0% +how a region functions and how we say +what counts as the same across species + + align:start position:0% +what counts as the same across species + + + align:start position:0% +what counts as the same across species +but is probably also crucially important + + align:start position:0% +but is probably also crucially important + + + align:start position:0% +but is probably also crucially important +in the development of regions + + align:start position:0% +in the development of regions + + + align:start position:0% +in the development of regions +okay i also showed you evidence that the + + align:start position:0% +okay i also showed you evidence that the + + + align:start position:0% +okay i also showed you evidence that the +visual word form area we can pick out + + align:start position:0% +visual word form area we can pick out + + + align:start position:0% +visual word form area we can pick out +exactly where it's going to land in an + + align:start position:0% +exactly where it's going to land in an + + + align:start position:0% +exactly where it's going to land in an +individual brain by the connectivity + + align:start position:0% +individual brain by the connectivity + + + align:start position:0% +individual brain by the connectivity +fingerprint of that region before kids + + align:start position:0% +fingerprint of that region before kids + + + align:start position:0% +fingerprint of that region before kids +learn to read + + align:start position:0% +learn to read + + + align:start position:0% +learn to read +further evidence that connectivity + + align:start position:0% +further evidence that connectivity + + + align:start position:0% +further evidence that connectivity +determines later function + + align:start position:0% +determines later function + + + align:start position:0% +determines later function +okay if as if this is not enough other + + align:start position:0% +okay if as if this is not enough other + + + align:start position:0% +okay if as if this is not enough other +reasons to care about white matter + + align:start position:0% +reasons to care about white matter + + + align:start position:0% +reasons to care about white matter +is that disruptions of white matter are + + align:start position:0% +is that disruptions of white matter are + + + align:start position:0% +is that disruptions of white matter are +at the root of many clinical disorders + + align:start position:0% +at the root of many clinical disorders + + + align:start position:0% +at the root of many clinical disorders +dyslexia autism + + align:start position:0% +dyslexia autism + + + align:start position:0% +dyslexia autism +developmental prosopagnosia amusia all + + align:start position:0% +developmental prosopagnosia amusia all + + + align:start position:0% +developmental prosopagnosia amusia all +of these things + + align:start position:0% +of these things + + + align:start position:0% +of these things +and others for all of them + + align:start position:0% +and others for all of them + + + align:start position:0% +and others for all of them +disruptions in long-range + + align:start position:0% +disruptions in long-range + + + align:start position:0% +disruptions in long-range +white matter connections have been + + align:start position:0% +white matter connections have been + + + align:start position:0% +white matter connections have been +implicated as possibly playing + + align:start position:0% +implicated as possibly playing + + + align:start position:0% +implicated as possibly playing +an important role + + align:start position:0% +an important role + + + align:start position:0% +an important role +in the + + align:start position:0% +in the + + + align:start position:0% +in the +in the + + align:start position:0% +in the + + + align:start position:0% +in the +etiology of that disease + + align:start position:0% +etiology of that disease + + + align:start position:0% +etiology of that disease +aging most definitely + + align:start position:0% +aging most definitely + + + align:start position:0% +aging most definitely +decline in white matter is prominent in + + align:start position:0% +decline in white matter is prominent in + + + align:start position:0% +decline in white matter is prominent in +aging + + align:start position:0% +aging + + + align:start position:0% +aging +sorry to say there's a 10 decrease in + + align:start position:0% +sorry to say there's a 10 decrease in + + + align:start position:0% +sorry to say there's a 10 decrease in +white matter fibers per decade starting + + align:start position:0% +white matter fibers per decade starting + + + align:start position:0% +white matter fibers per decade starting +at age 20. use yours now while you have + + align:start position:0% +at age 20. use yours now while you have + + + align:start position:0% +at age 20. use yours now while you have +them + + align:start position:0% +them + + + align:start position:0% +them +let's change the topic + + align:start position:0% +let's change the topic + + + align:start position:0% +let's change the topic +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um there's a lot of talk about how white + + align:start position:0% +um there's a lot of talk about how white + + + align:start position:0% +um there's a lot of talk about how white +matter connections may change with + + align:start position:0% +matter connections may change with + + + align:start position:0% +matter connections may change with +experience and learning and plasticity + + align:start position:0% +experience and learning and plasticity + + + align:start position:0% +experience and learning and plasticity +and um that's a pretty patchy literature + + align:start position:0% +and um that's a pretty patchy literature + + + align:start position:0% +and um that's a pretty patchy literature +and um it's not a very impressive + + align:start position:0% +and um it's not a very impressive + + + align:start position:0% +and um it's not a very impressive +literature the classic thing you + + align:start position:0% +literature the classic thing you + + + align:start position:0% +literature the classic thing you +probably learned in 900 that when you + + align:start position:0% +probably learned in 900 that when you + + + align:start position:0% +probably learned in 900 that when you +juggle you get changes in white matter + + align:start position:0% +juggle you get changes in white matter + + + align:start position:0% +juggle you get changes in white matter +connections from juggling expertise + + align:start position:0% +connections from juggling expertise + + + align:start position:0% +connections from juggling expertise +maybe maybe not there's problems with a + + align:start position:0% +maybe maybe not there's problems with a + + + align:start position:0% +maybe maybe not there's problems with a +lot of that literature so it's an + + align:start position:0% +lot of that literature so it's an + + + align:start position:0% +lot of that literature so it's an +interesting question but it's not clear + + align:start position:0% +interesting question but it's not clear + + + align:start position:0% +interesting question but it's not clear +what the strong answers are + + align:start position:0% +what the strong answers are + + + align:start position:0% +what the strong answers are +and finally + + align:start position:0% +and finally + + + align:start position:0% +and finally +i don't know about circuit design + + align:start position:0% +i don't know about circuit design + + + align:start position:0% +i don't know about circuit design +probably some of you do but i gather + + align:start position:0% +probably some of you do but i gather + + + align:start position:0% +probably some of you do but i gather +that people who think a lot about + + align:start position:0% +that people who think a lot about + + + align:start position:0% +that people who think a lot about +circuit design one of the key features + + align:start position:0% +circuit design one of the key features + + + align:start position:0% +circuit design one of the key features +you need to take into account is wiring + + align:start position:0% +you need to take into account is wiring + + + align:start position:0% +you need to take into account is wiring +length you want to keep wiring lengths + + align:start position:0% +length you want to keep wiring lengths + + + align:start position:0% +length you want to keep wiring lengths +short + + align:start position:0% +short + + + align:start position:0% +short +right you have conduction delays you + + align:start position:0% +right you have conduction delays you + + + align:start position:0% +right you have conduction delays you +have heating you have space taken up in + + align:start position:0% +have heating you have space taken up in + + + align:start position:0% +have heating you have space taken up in +circuits all of those things + + align:start position:0% +circuits all of those things + + + align:start position:0% +circuits all of those things +are bad in circuit design and they're + + align:start position:0% +are bad in circuit design and they're + + + align:start position:0% +are bad in circuit design and they're +bad in brain design too there's a lot of + + align:start position:0% +bad in brain design too there's a lot of + + + align:start position:0% +bad in brain design too there's a lot of +reason to think that a major + + align:start position:0% +reason to think that a major + + + align:start position:0% +reason to think that a major +factor in the design of of brains + + align:start position:0% +factor in the design of of brains + + + align:start position:0% +factor in the design of of brains +especially human brains is minimizing + + align:start position:0% +especially human brains is minimizing + + + align:start position:0% +especially human brains is minimizing +wiring length because wiring length is + + align:start position:0% +wiring length because wiring length is + + + align:start position:0% +wiring length because wiring length is +very expensive metabolically you got to + + align:start position:0% +very expensive metabolically you got to + + + align:start position:0% +very expensive metabolically you got to +maintain ion gradient gradients across + + align:start position:0% +maintain ion gradient gradients across + + + align:start position:0% +maintain ion gradient gradients across +across cell membranes + + align:start position:0% +across cell membranes + + + align:start position:0% +across cell membranes +it's expensive developmentally these + + align:start position:0% +it's expensive developmentally these + + + align:start position:0% +it's expensive developmentally these +damn things need to figure out where to + + align:start position:0% +damn things need to figure out where to + + + align:start position:0% +damn things need to figure out where to +go and if they don't go to the right + + align:start position:0% +go and if they don't go to the right + + + align:start position:0% +go and if they don't go to the right +place you have a developmental disorder + + align:start position:0% +place you have a developmental disorder + + + align:start position:0% +place you have a developmental disorder +and um so it's probably a real cons + + align:start position:0% +and um so it's probably a real cons + + + align:start position:0% +and um so it's probably a real cons +constraint on designs of brains + + align:start position:0% +constraint on designs of brains + + + align:start position:0% +constraint on designs of brains +okay so that was a whirlwind lots of + + align:start position:0% +okay so that was a whirlwind lots of + + + align:start position:0% +okay so that was a whirlwind lots of +reasons to care about white matter and + + align:start position:0% +reasons to care about white matter and + + + align:start position:0% +reasons to care about white matter and +connectivity + + align:start position:0% +connectivity + + + align:start position:0% +connectivity +oh plus at least in animal research + + align:start position:0% +oh plus at least in animal research + + + align:start position:0% +oh plus at least in animal research +there's a whole suite of amazing new + + align:start position:0% +there's a whole suite of amazing new + + + align:start position:0% +there's a whole suite of amazing new +methods for looking at + + align:start position:0% +methods for looking at + + + align:start position:0% +methods for looking at +connectivity in animal brains + + align:start position:0% +connectivity in animal brains + + + align:start position:0% +connectivity in animal brains +and min young could tell us more about + + align:start position:0% +and min young could tell us more about + + + align:start position:0% +and min young could tell us more about +that than i could + + align:start position:0% +that than i could + + + align:start position:0% +that than i could +because she's working in a lab that's + + align:start position:0% +because she's working in a lab that's + + + align:start position:0% +because she's working in a lab that's +right at the forefront of developing + + align:start position:0% +right at the forefront of developing + + + align:start position:0% +right at the forefront of developing +those methods someday we're going to + + align:start position:0% +those methods someday we're going to + + + align:start position:0% +those methods someday we're going to +apply those methods to a human brain i + + align:start position:0% +apply those methods to a human brain i + + + align:start position:0% +apply those methods to a human brain i +can't wait to get the whole + + align:start position:0% +can't wait to get the whole + + + align:start position:0% +can't wait to get the whole +wiring diagram okay + + align:start position:0% +wiring diagram okay + + + align:start position:0% +wiring diagram okay +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +so what do we know about the + + align:start position:0% +so what do we know about the + + + align:start position:0% +so what do we know about the +connectivity of these regions + + align:start position:0% +connectivity of these regions + + + align:start position:0% +connectivity of these regions +well you may be thinking don't we + + align:start position:0% +well you may be thinking don't we + + + align:start position:0% +well you may be thinking don't we +already know all this stuff after all i + + align:start position:0% +already know all this stuff after all i + + + align:start position:0% +already know all this stuff after all i +showed you this diagram way back and + + align:start position:0% +showed you this diagram way back and + + + align:start position:0% +showed you this diagram way back and +you've probably seen it in every damn + + align:start position:0% +you've probably seen it in every damn + + + align:start position:0% +you've probably seen it in every damn +course you take in this department + + align:start position:0% +course you take in this department + + + align:start position:0% +course you take in this department +it's in most textbooks in the field + + align:start position:0% +it's in most textbooks in the field + + + align:start position:0% +it's in most textbooks in the field +the whole wiring diagram of the visual + + align:start position:0% +the whole wiring diagram of the visual + + + align:start position:0% +the whole wiring diagram of the visual +system so don't we already know all this + + align:start position:0% +system so don't we already know all this + + + align:start position:0% +system so don't we already know all this +stuff so what's the big deal + + align:start position:0% +stuff so what's the big deal + + + align:start position:0% +stuff so what's the big deal +well here's the big deal + + align:start position:0% +well here's the big deal + + + align:start position:0% +well here's the big deal +that's i'm a cac brain + + align:start position:0% +that's i'm a cac brain + + + align:start position:0% +that's i'm a cac brain +and in macaque brain you can get the + + align:start position:0% +and in macaque brain you can get the + + + align:start position:0% +and in macaque brain you can get the +actual answer to what is the actual + + align:start position:0% +actual answer to what is the actual + + + align:start position:0% +actual answer to what is the actual +structural connectivity of this patch of + + align:start position:0% +structural connectivity of this patch of + + + align:start position:0% +structural connectivity of this patch of +cortex to that patch of cortex + + align:start position:0% +cortex to that patch of cortex + + + align:start position:0% +cortex to that patch of cortex +you do there's a whole bunch of methods + + align:start position:0% +you do there's a whole bunch of methods + + + align:start position:0% +you do there's a whole bunch of methods +but traditionally you inject some dye + + align:start position:0% +but traditionally you inject some dye + + + align:start position:0% +but traditionally you inject some dye +here that's uptaken by neurons that + + align:start position:0% +here that's uptaken by neurons that + + + align:start position:0% +here that's uptaken by neurons that +travels along axons that goes here you + + align:start position:0% +travels along axons that goes here you + + + align:start position:0% +travels along axons that goes here you +kill the animal slice up the brain and + + align:start position:0% +kill the animal slice up the brain and + + + align:start position:0% +kill the animal slice up the brain and +find that tracer over here and then you + + align:start position:0% +find that tracer over here and then you + + + align:start position:0% +find that tracer over here and then you +know those two things are absolutely + + align:start position:0% +know those two things are absolutely + + + align:start position:0% +know those two things are absolutely +connected that's the gold standard and + + align:start position:0% +connected that's the gold standard and + + + align:start position:0% +connected that's the gold standard and +that's the basis of most of those + + align:start position:0% +that's the basis of most of those + + + align:start position:0% +that's the basis of most of those +studies that method and variations + + align:start position:0% +studies that method and variations + + + align:start position:0% +studies that method and variations +thereof + + align:start position:0% +thereof + + + align:start position:0% +thereof +but we can't do that in human brains + + align:start position:0% +but we can't do that in human brains + + + align:start position:0% +but we can't do that in human brains +and so we do not have anything like this + + align:start position:0% +and so we do not have anything like this + + + align:start position:0% +and so we do not have anything like this +information in human brains yes whether + + align:start position:0% +information in human brains yes whether + + + align:start position:0% +information in human brains yes whether +it was a stone + + align:start position:0% +it was a stone + + + align:start position:0% +it was a stone +oh that is a compilation this was + + align:start position:0% +oh that is a compilation this was + + + align:start position:0% +oh that is a compilation this was +published in i think 1991 + + align:start position:0% +published in i think 1991 + + + align:start position:0% +published in i think 1991 +um but that was a compilation of heaps + + align:start position:0% +um but that was a compilation of heaps + + + align:start position:0% +um but that was a compilation of heaps +of studies that have been done before + + align:start position:0% +of studies that have been done before + + + align:start position:0% +of studies that have been done before +that it was a big review article looking + + align:start position:0% +that it was a big review article looking + + + align:start position:0% +that it was a big review article looking +at all of this literature + + align:start position:0% +at all of this literature + + + align:start position:0% +at all of this literature +where lots of classic neuroanatomy + + align:start position:0% +where lots of classic neuroanatomy + + + align:start position:0% +where lots of classic neuroanatomy +people would do these things where they + + align:start position:0% +people would do these things where they + + + align:start position:0% +people would do these things where they +would inject tracers and slice up brains + + align:start position:0% +would inject tracers and slice up brains + + + align:start position:0% +would inject tracers and slice up brains +and look in other places and it was just + + align:start position:0% +and look in other places and it was just + + + align:start position:0% +and look in other places and it was just +a vast amount of literature that did + + align:start position:0% +a vast amount of literature that did + + + align:start position:0% +a vast amount of literature that did +that for many decades it's sort of + + align:start position:0% +that for many decades it's sort of + + + align:start position:0% +that for many decades it's sort of +fallen out of favor even though these + + align:start position:0% +fallen out of favor even though these + + + align:start position:0% +fallen out of favor even though these +things are at least + + align:start position:0% +things are at least + + + align:start position:0% +things are at least +i don't know + + align:start position:0% +i don't know + + + align:start position:0% +i don't know +these are really crucial questions now + + align:start position:0% +these are really crucial questions now + + + align:start position:0% +these are really crucial questions now +people use other methods to do that you + + align:start position:0% +people use other methods to do that you + + + align:start position:0% +people use other methods to do that you +can use all kinds of optogenetic and + + align:start position:0% +can use all kinds of optogenetic and + + + align:start position:0% +can use all kinds of optogenetic and +other methods to map connectivity in + + align:start position:0% +other methods to map connectivity in + + + align:start position:0% +other methods to map connectivity in +animals yeah + + align:start position:0% + + + + align:start position:0% + +in here + + align:start position:0% +in here + + + align:start position:0% +in here +oh that's a good question uh i oh it's + + align:start position:0% +oh that's a good question uh i oh it's + + + align:start position:0% +oh that's a good question uh i oh it's +probably dorsal and ventral pathways let + + align:start position:0% +probably dorsal and ventral pathways let + + + align:start position:0% +probably dorsal and ventral pathways let +me see here + + align:start position:0% +me see here + + + align:start position:0% +me see here +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah the red ones + + align:start position:0% +yeah the red ones + + + align:start position:0% +yeah the red ones +this is another thing i didn't even + + align:start position:0% +this is another thing i didn't even + + + align:start position:0% +this is another thing i didn't even +really + + align:start position:0% +really + + + align:start position:0% +really +mention probably let alone give short + + align:start position:0% +mention probably let alone give short + + + align:start position:0% +mention probably let alone give short +drift that was lame but anyway + + align:start position:0% +drift that was lame but anyway + + + align:start position:0% +drift that was lame but anyway +the visual high levels of the visual + + align:start position:0% +the visual high levels of the visual + + + align:start position:0% +the visual high levels of the visual +system we focused on the ventral visual + + align:start position:0% +system we focused on the ventral visual + + + align:start position:0% +system we focused on the ventral visual +pathway coming down the bottom of the + + align:start position:0% +pathway coming down the bottom of the + + + align:start position:0% +pathway coming down the bottom of the +temporal lobe but there's a whole other + + align:start position:0% +temporal lobe but there's a whole other + + + align:start position:0% +temporal lobe but there's a whole other +visual pathway that goes up into the + + align:start position:0% +visual pathway that goes up into the + + + align:start position:0% +visual pathway that goes up into the +parietal lobe did i talk about that a + + align:start position:0% +parietal lobe did i talk about that a + + + align:start position:0% +parietal lobe did i talk about that a +little bit reaching and grasping no i + + align:start position:0% +little bit reaching and grasping no i + + + align:start position:0% +little bit reaching and grasping no i +didn't lame + + align:start position:0% +didn't lame + + + align:start position:0% +didn't lame +lame lamely anyway + + align:start position:0% +lame lamely anyway + + + align:start position:0% +lame lamely anyway +um major part of the field i didn't get + + align:start position:0% +um major part of the field i didn't get + + + align:start position:0% +um major part of the field i didn't get +to + + align:start position:0% +to + + + align:start position:0% +to +anyway it's a whole other part of the + + align:start position:0% +anyway it's a whole other part of the + + + align:start position:0% +anyway it's a whole other part of the +visual system that seems to be more + + align:start position:0% +visual system that seems to be more + + + align:start position:0% +visual system that seems to be more +involved in visually guided action + + align:start position:0% +involved in visually guided action + + + align:start position:0% +involved in visually guided action +and + + align:start position:0% +and + + + align:start position:0% +and +they're very they're actually very + + align:start position:0% +they're very they're actually very + + + align:start position:0% +they're very they're actually very +interconnected but they're trying to + + align:start position:0% +interconnected but they're trying to + + + align:start position:0% +interconnected but they're trying to +emphasize that the dorsal pathway is at + + align:start position:0% +emphasize that the dorsal pathway is at + + + align:start position:0% +emphasize that the dorsal pathway is at +least somewhat separable + + align:start position:0% +least somewhat separable + + + align:start position:0% +least somewhat separable +in monkeys + + align:start position:0% +in monkeys + + + align:start position:0% +in monkeys +but my point is this is monkeys where + + align:start position:0% +but my point is this is monkeys where + + + align:start position:0% +but my point is this is monkeys where +they have the gold standard methods and + + align:start position:0% +they have the gold standard methods and + + + align:start position:0% +they have the gold standard methods and +they can actually discover the real + + align:start position:0% +they can actually discover the real + + + align:start position:0% +they can actually discover the real +connectivity + + align:start position:0% +connectivity + + + align:start position:0% +connectivity +um sadly we can't do those things in + + align:start position:0% +um sadly we can't do those things in + + + align:start position:0% +um sadly we can't do those things in +humans + + align:start position:0% +humans + + + align:start position:0% +humans +um and in humans we have only three + + align:start position:0% +um and in humans we have only three + + + align:start position:0% +um and in humans we have only three +methods + + align:start position:0% +methods + + + align:start position:0% +methods +and none of them are very good so we'll + + align:start position:0% +and none of them are very good so we'll + + + align:start position:0% +and none of them are very good so we'll +talk about them today anyway because + + align:start position:0% +talk about them today anyway because + + + align:start position:0% +talk about them today anyway because +this is such an important question + + align:start position:0% +this is such an important question + + + align:start position:0% +this is such an important question +but the bottom line is this drives me + + align:start position:0% +but the bottom line is this drives me + + + align:start position:0% +but the bottom line is this drives me +out of my mind we basically don't know + + align:start position:0% +out of my mind we basically don't know + + + align:start position:0% +out of my mind we basically don't know +the connectivity of any of those regions + + align:start position:0% +the connectivity of any of those regions + + + align:start position:0% +the connectivity of any of those regions +for sure in human brains + + align:start position:0% +for sure in human brains + + + align:start position:0% +for sure in human brains +and um somebody's got to solve that + + align:start position:0% +and um somebody's got to solve that + + + align:start position:0% +and um somebody's got to solve that +maybe one of you will go invent a method + + align:start position:0% +maybe one of you will go invent a method + + + align:start position:0% +maybe one of you will go invent a method +that works in humans that helps us solve + + align:start position:0% +that works in humans that helps us solve + + + align:start position:0% +that works in humans that helps us solve +that problem because it's actually + + align:start position:0% +that problem because it's actually + + + align:start position:0% +that problem because it's actually +um i think really paralyzing to our + + align:start position:0% +um i think really paralyzing to our + + + align:start position:0% +um i think really paralyzing to our +field but so i'll tell you what we do + + align:start position:0% +field but so i'll tell you what we do + + + align:start position:0% +field but so i'll tell you what we do +know which isn't much but you know + + align:start position:0% +know which isn't much but you know + + + align:start position:0% +know which isn't much but you know +beggars can't be choosers okay first + + align:start position:0% +beggars can't be choosers okay first + + + align:start position:0% +beggars can't be choosers okay first +method has been around for a few hundred + + align:start position:0% +method has been around for a few hundred + + + align:start position:0% +method has been around for a few hundred +years + + align:start position:0% +years + + + align:start position:0% +years +and that's gross dissection and i mean + + align:start position:0% +and that's gross dissection and i mean + + + align:start position:0% +and that's gross dissection and i mean +gross + + align:start position:0% +gross + + + align:start position:0% +gross +i like that kind of gross + + align:start position:0% +i like that kind of gross + + + align:start position:0% +i like that kind of gross +so only good for postmortem brains but + + align:start position:0% +so only good for postmortem brains but + + + align:start position:0% +so only good for postmortem brains but +it's really quite amazing this is a + + align:start position:0% +it's really quite amazing this is a + + + align:start position:0% +it's really quite amazing this is a +bottom view of the brain back in front + + align:start position:0% +bottom view of the brain back in front + + + align:start position:0% +bottom view of the brain back in front +um and you can actually this is actually + + align:start position:0% +um and you can actually this is actually + + + align:start position:0% +um and you can actually this is actually +a physically dissected brain like it + + align:start position:0% +a physically dissected brain like it + + + align:start position:0% +a physically dissected brain like it +takes a real serious neuroanatomist you + + align:start position:0% +takes a real serious neuroanatomist you + + + align:start position:0% +takes a real serious neuroanatomist you +know and lots of fancy methods i mean + + align:start position:0% +know and lots of fancy methods i mean + + + align:start position:0% +know and lots of fancy methods i mean +not fancy methods but lots of careful + + align:start position:0% +not fancy methods but lots of careful + + + align:start position:0% +not fancy methods but lots of careful +precise teasing apart of bits of brain + + align:start position:0% +precise teasing apart of bits of brain + + + align:start position:0% +precise teasing apart of bits of brain +and you can actually see + + align:start position:0% +and you can actually see + + + align:start position:0% +and you can actually see +these big fibers coming up here so if + + align:start position:0% +these big fibers coming up here so if + + + align:start position:0% +these big fibers coming up here so if +this is the back of the brain and we're + + align:start position:0% +this is the back of the brain and we're + + + align:start position:0% +this is the back of the brain and we're +looking up like this what do you think + + align:start position:0% +looking up like this what do you think + + + align:start position:0% +looking up like this what do you think +those fibers are connecting right there + + align:start position:0% +those fibers are connecting right there + + + align:start position:0% +those fibers are connecting right there +big fiber bundle + + align:start position:0% +big fiber bundle + + + align:start position:0% +big fiber bundle +coming from deep down in the brain + + align:start position:0% +coming from deep down in the brain + + + align:start position:0% +coming from deep down in the brain +up to + + align:start position:0% +up to + + + align:start position:0% +up to +right in there is that that was the + + align:start position:0% +right in there is that that was the + + + align:start position:0% +right in there is that that was the +primary weight report bingo exactly + + align:start position:0% +primary weight report bingo exactly + + + align:start position:0% +primary weight report bingo exactly +okay so that's the lgn right there and + + align:start position:0% +okay so that's the lgn right there and + + + align:start position:0% +okay so that's the lgn right there and +this is called the optic radiation it's + + align:start position:0% +this is called the optic radiation it's + + + align:start position:0% +this is called the optic radiation it's +this huge cable of fibers that come up + + align:start position:0% +this huge cable of fibers that come up + + + align:start position:0% +this huge cable of fibers that come up +okay first here's the um optic track + + align:start position:0% +okay first here's the um optic track + + + align:start position:0% +okay first here's the um optic track +actually i forget that's not i think + + align:start position:0% +actually i forget that's not i think + + + align:start position:0% +actually i forget that's not i think +this is the optic track that's been + + align:start position:0% +this is the optic track that's been + + + align:start position:0% +this is the optic track that's been +snipped there then it comes up in here + + align:start position:0% +snipped there then it comes up in here + + + align:start position:0% +snipped there then it comes up in here +makes a stop in the lgn and then this + + align:start position:0% +makes a stop in the lgn and then this + + + align:start position:0% +makes a stop in the lgn and then this +big batch of fibers comes up right there + + align:start position:0% +big batch of fibers comes up right there + + + align:start position:0% +big batch of fibers comes up right there +to primary official cortex okay + + align:start position:0% +to primary official cortex okay + + + align:start position:0% +to primary official cortex okay +everybody got that + + align:start position:0% +everybody got that + + + align:start position:0% +everybody got that +um okay so you can actually see it in + + align:start position:0% +um okay so you can actually see it in + + + align:start position:0% +um okay so you can actually see it in +dissecting a dead brain + + align:start position:0% +dissecting a dead brain + + + align:start position:0% +dissecting a dead brain +okay that's pretty cool + + align:start position:0% +okay that's pretty cool + + + align:start position:0% +okay that's pretty cool +um + + align:start position:0% +um + + + align:start position:0% +um +but what if we don't want to wait for + + align:start position:0% +but what if we don't want to wait for + + + align:start position:0% +but what if we don't want to wait for +people to die + + align:start position:0% +people to die + + + align:start position:0% +people to die +often we want to ask questions about a + + align:start position:0% +often we want to ask questions about a + + + align:start position:0% +often we want to ask questions about a +person right now in their brain do they + + align:start position:0% +person right now in their brain do they + + + align:start position:0% +person right now in their brain do they +have this disorder are they at risk of + + align:start position:0% +have this disorder are they at risk of + + + align:start position:0% +have this disorder are they at risk of +that disorder + + align:start position:0% +that disorder + + + align:start position:0% +that disorder +you know what is what is their + + align:start position:0% +you know what is what is their + + + align:start position:0% +you know what is what is their +connectivity + + align:start position:0% +connectivity + + + align:start position:0% +connectivity +so for that we have two methods and i'll + + align:start position:0% +so for that we have two methods and i'll + + + align:start position:0% +so for that we have two methods and i'll +talk about these two methods in the rest + + align:start position:0% +talk about these two methods in the rest + + + align:start position:0% +talk about these two methods in the rest +of the lecture the first one is + + align:start position:0% +of the lecture the first one is + + + align:start position:0% +of the lecture the first one is +diffusion imaging + + align:start position:0% +diffusion imaging + + + align:start position:0% +diffusion imaging +okay so i talked about this briefly + + align:start position:0% +okay so i talked about this briefly + + + align:start position:0% +okay so i talked about this briefly +before but let me remind you of what the + + align:start position:0% +before but let me remind you of what the + + + align:start position:0% +before but let me remind you of what the +basic principles are + + align:start position:0% +basic principles are + + + align:start position:0% +basic principles are +so + + align:start position:0% +so + + + align:start position:0% +so +uh here is a picture of the optic nerve + + align:start position:0% +uh here is a picture of the optic nerve + + + align:start position:0% +uh here is a picture of the optic nerve +with a bunch of axons oriented like that + + align:start position:0% +with a bunch of axons oriented like that + + + align:start position:0% +with a bunch of axons oriented like that +it's a big + + align:start position:0% +it's a big + + + align:start position:0% +it's a big +cable with a whole bunch of little + + align:start position:0% +cable with a whole bunch of little + + + align:start position:0% +cable with a whole bunch of little +fibers in there + + align:start position:0% +fibers in there + + + align:start position:0% +fibers in there +and the basic kind of biophysics is that + + align:start position:0% +and the basic kind of biophysics is that + + + align:start position:0% +and the basic kind of biophysics is that +water wants to fuse more along this + + align:start position:0% +water wants to fuse more along this + + + align:start position:0% +water wants to fuse more along this +length + + align:start position:0% +length + + + align:start position:0% +length +following the orientation of the fibers + + align:start position:0% +following the orientation of the fibers + + + align:start position:0% +following the orientation of the fibers +then it wants to diffuse this way + + align:start position:0% +then it wants to diffuse this way + + + align:start position:0% +then it wants to diffuse this way +okay and diffusion imaging i'm not + + align:start position:0% +okay and diffusion imaging i'm not + + + align:start position:0% +okay and diffusion imaging i'm not +explaining any of the physics but just + + align:start position:0% +explaining any of the physics but just + + + align:start position:0% +explaining any of the physics but just +take it for my word that what diffusion + + align:start position:0% +take it for my word that what diffusion + + + align:start position:0% +take it for my word that what diffusion +imaging does is give you a picture of + + align:start position:0% +imaging does is give you a picture of + + + align:start position:0% +imaging does is give you a picture of +the direction of water diffusion + + align:start position:0% +the direction of water diffusion + + + align:start position:0% +the direction of water diffusion +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so you get a picture of a piece of brain + + align:start position:0% +so you get a picture of a piece of brain + + + align:start position:0% +so you get a picture of a piece of brain +and it'll show you for example that + + align:start position:0% +and it'll show you for example that + + + align:start position:0% +and it'll show you for example that +right in there all the fibers well the + + align:start position:0% +right in there all the fibers well the + + + align:start position:0% +right in there all the fibers well the +water is diffusing this way and over + + align:start position:0% +water is diffusing this way and over + + + align:start position:0% +water is diffusing this way and over +here the water's diffusing that way + + align:start position:0% +here the water's diffusing that way + + + align:start position:0% +here the water's diffusing that way +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and that's just what you see in a + + align:start position:0% +and that's just what you see in a + + + align:start position:0% +and that's just what you see in a +diffusion image + + align:start position:0% +diffusion image + + + align:start position:0% +diffusion image +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so that the inference people make is + + align:start position:0% +and so that the inference people make is + + + align:start position:0% +and so that the inference people make is +if you have all those parallel lines + + align:start position:0% +if you have all those parallel lines + + + align:start position:0% +if you have all those parallel lines +telling you there's lots of diffusion + + align:start position:0% +telling you there's lots of diffusion + + + align:start position:0% +telling you there's lots of diffusion +like this there's probably a big fiber + + align:start position:0% +like this there's probably a big fiber + + + align:start position:0% +like this there's probably a big fiber +bundle going like that and there is that + + align:start position:0% +bundle going like that and there is that + + + align:start position:0% +bundle going like that and there is that +would be the corpus callosum + + align:start position:0% +would be the corpus callosum + + + align:start position:0% +would be the corpus callosum +okay + + align:start position:0% + + + + align:start position:0% + +all right so um this method works great + + align:start position:0% +all right so um this method works great + + + align:start position:0% +all right so um this method works great +for finding the big fiber bundles + + align:start position:0% +for finding the big fiber bundles + + + align:start position:0% +for finding the big fiber bundles +okay i'm gonna disc diffusion imaging in + + align:start position:0% +okay i'm gonna disc diffusion imaging in + + + align:start position:0% +okay i'm gonna disc diffusion imaging in +a bunch of ways but it is great for + + align:start position:0% +a bunch of ways but it is great for + + + align:start position:0% +a bunch of ways but it is great for +finding + + align:start position:0% +finding + + + align:start position:0% +finding +the big fiber bundles because in those + + align:start position:0% +the big fiber bundles because in those + + + align:start position:0% +the big fiber bundles because in those +big fiber bundles the axons are very + + align:start position:0% +big fiber bundles the axons are very + + + align:start position:0% +big fiber bundles the axons are very +parallel there's a whole bunch of them + + align:start position:0% +parallel there's a whole bunch of them + + + align:start position:0% +parallel there's a whole bunch of them +and you can really see it + + align:start position:0% +and you can really see it + + + align:start position:0% +and you can really see it +okay and so people have been using this + + align:start position:0% +okay and so people have been using this + + + align:start position:0% +okay and so people have been using this +for + + align:start position:0% +for + + + align:start position:0% +for +over a decade to find some of the major + + align:start position:0% +over a decade to find some of the major + + + align:start position:0% +over a decade to find some of the major +fiber bundles in the brain + + align:start position:0% +fiber bundles in the brain + + + align:start position:0% +fiber bundles in the brain +so you may have heard of the arcuate + + align:start position:0% +so you may have heard of the arcuate + + + align:start position:0% +so you may have heard of the arcuate +fasciculus that basically connects + + align:start position:0% +fasciculus that basically connects + + + align:start position:0% +fasciculus that basically connects +language regions in the temporal lobe + + align:start position:0% +language regions in the temporal lobe + + + align:start position:0% +language regions in the temporal lobe +up to um broca's area in the frontal + + align:start position:0% +up to um broca's area in the frontal + + + align:start position:0% +up to um broca's area in the frontal +lobe okay it's a big bunch of fibers + + align:start position:0% +lobe okay it's a big bunch of fibers + + + align:start position:0% +lobe okay it's a big bunch of fibers +that go i guess in me they go like this + + align:start position:0% +that go i guess in me they go like this + + + align:start position:0% +that go i guess in me they go like this +boom + + align:start position:0% +boom + + + align:start position:0% +boom +right pretty oriented + + align:start position:0% +right pretty oriented + + + align:start position:0% +right pretty oriented +and you can see those guys with this is + + align:start position:0% +and you can see those guys with this is + + + align:start position:0% +and you can see those guys with this is +a + + align:start position:0% +a + + + align:start position:0% +a +distant reconstruction but you can see + + align:start position:0% +distant reconstruction but you can see + + + align:start position:0% +distant reconstruction but you can see +those with diffusion imaging + + align:start position:0% +those with diffusion imaging + + + align:start position:0% +those with diffusion imaging +um another one the unsonic goes from the + + align:start position:0% +um another one the unsonic goes from the + + + align:start position:0% +um another one the unsonic goes from the +front of the temporal lobe up to the + + align:start position:0% +front of the temporal lobe up to the + + + align:start position:0% +front of the temporal lobe up to the +frontal lobe you don't need to memorize + + align:start position:0% +frontal lobe you don't need to memorize + + + align:start position:0% +frontal lobe you don't need to memorize +these i don't care about that i just + + align:start position:0% +these i don't care about that i just + + + align:start position:0% +these i don't care about that i just +want you to give get the idea of what + + align:start position:0% +want you to give get the idea of what + + + align:start position:0% +want you to give get the idea of what +you can see yeah question so these are + + align:start position:0% +you can see yeah question so these are + + + align:start position:0% +you can see yeah question so these are +the struggling good without the person + + align:start position:0% +the struggling good without the person + + + align:start position:0% +the struggling good without the person +having to do anything i mean yes yes + + align:start position:0% +having to do anything i mean yes yes + + + align:start position:0% +having to do anything i mean yes yes +these are anatomical images so in + + align:start position:0% +these are anatomical images so in + + + align:start position:0% +these are anatomical images so in +diffusion imaging you don't do anything + + align:start position:0% +diffusion imaging you don't do anything + + + align:start position:0% +diffusion imaging you don't do anything +you can sleep actually that's ideal + + align:start position:0% +you can sleep actually that's ideal + + + align:start position:0% +you can sleep actually that's ideal +because it's long and boring + + align:start position:0% +because it's long and boring + + + align:start position:0% +because it's long and boring +actually it's not boring the scanner + + align:start position:0% +actually it's not boring the scanner + + + align:start position:0% +actually it's not boring the scanner +shakes like hell in a diffusion imaging + + align:start position:0% +shakes like hell in a diffusion imaging + + + align:start position:0% +shakes like hell in a diffusion imaging +scan + + align:start position:0% +scan + + + align:start position:0% +scan +it's pretty wild + + align:start position:0% +it's pretty wild + + + align:start position:0% +it's pretty wild +we could charge admission for it + + align:start position:0% + + + + align:start position:0% + +and um + + align:start position:0% +and um + + + align:start position:0% +and um +i don't know i find it quite + + align:start position:0% +i don't know i find it quite + + + align:start position:0% +i don't know i find it quite +quite wild + + align:start position:0% +quite wild + + + align:start position:0% +quite wild +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +this is the inferior longitudinal + + align:start position:0% +this is the inferior longitudinal + + + align:start position:0% +this is the inferior longitudinal +fasciculus it goes down the temporal + + align:start position:0% +fasciculus it goes down the temporal + + + align:start position:0% +fasciculus it goes down the temporal +lobe so we talk about the ventral visual + + align:start position:0% +lobe so we talk about the ventral visual + + + align:start position:0% +lobe so we talk about the ventral visual +pathway face areas place areas all that + + align:start position:0% +pathway face areas place areas all that + + + align:start position:0% +pathway face areas place areas all that +stuff + + align:start position:0% +stuff + + + align:start position:0% +stuff +this is the big fiber highway that sits + + align:start position:0% +this is the big fiber highway that sits + + + align:start position:0% +this is the big fiber highway that sits +right on top of that whole + + align:start position:0% +right on top of that whole + + + align:start position:0% +right on top of that whole +chunk of gray matter that does all the + + align:start position:0% +chunk of gray matter that does all the + + + align:start position:0% +chunk of gray matter that does all the +processing and it's a big pile of fibers + + align:start position:0% +processing and it's a big pile of fibers + + + align:start position:0% +processing and it's a big pile of fibers +that go straight down the temporal lobe + + align:start position:0% +that go straight down the temporal lobe + + + align:start position:0% +that go straight down the temporal lobe +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +and so um here's a more recent data this + + align:start position:0% +and so um here's a more recent data this + + + align:start position:0% +and so um here's a more recent data this +is from anastasia yendiki over at um mgh + + align:start position:0% +is from anastasia yendiki over at um mgh + + + align:start position:0% +is from anastasia yendiki over at um mgh +charlestown over there and she's + + align:start position:0% +charlestown over there and she's + + + align:start position:0% +charlestown over there and she's +developed this lovely piece of software + + align:start position:0% +developed this lovely piece of software + + + align:start position:0% +developed this lovely piece of software +that enables you to take diffusion + + align:start position:0% +that enables you to take diffusion + + + align:start position:0% +that enables you to take diffusion +images and identify based on an atlas + + align:start position:0% +images and identify based on an atlas + + + align:start position:0% +images and identify based on an atlas +she's put together 18 of the major fiber + + align:start position:0% +she's put together 18 of the major fiber + + + align:start position:0% +she's put together 18 of the major fiber +tracks in the human brain + + align:start position:0% +tracks in the human brain + + + align:start position:0% +tracks in the human brain +okay so nine per hemisphere and this is + + align:start position:0% +okay so nine per hemisphere and this is + + + align:start position:0% +okay so nine per hemisphere and this is +just showing you some of the big ones + + align:start position:0% +just showing you some of the big ones + + + align:start position:0% +just showing you some of the big ones +this is the inferior longitudinal + + align:start position:0% +this is the inferior longitudinal + + + align:start position:0% +this is the inferior longitudinal +fasciculus i just showed you and so + + align:start position:0% +fasciculus i just showed you and so + + + align:start position:0% +fasciculus i just showed you and so +forth yeah + + align:start position:0% +forth yeah + + + align:start position:0% +forth yeah +um so how does this compare to just like + + align:start position:0% +um so how does this compare to just like + + + align:start position:0% +um so how does this compare to just like +the most important dissection like could + + align:start position:0% +the most important dissection like could + + + align:start position:0% +the most important dissection like could +you see it's a good question it's a good + + align:start position:0% +you see it's a good question it's a good + + + align:start position:0% +you see it's a good question it's a good +question i don't exactly know it + + align:start position:0% +question i don't exactly know it + + + align:start position:0% +question i don't exactly know it +wouldn't be easy like a lot of those + + align:start position:0% +wouldn't be easy like a lot of those + + + align:start position:0% +wouldn't be easy like a lot of those +things + + align:start position:0% +things + + + align:start position:0% +things +you know that thing i showed you works + + align:start position:0% +you know that thing i showed you works + + + align:start position:0% +you know that thing i showed you works +because you take the stuff off the top + + align:start position:0% +because you take the stuff off the top + + + align:start position:0% +because you take the stuff off the top +and it's just kind of sitting there + + align:start position:0% +and it's just kind of sitting there + + + align:start position:0% +and it's just kind of sitting there +but then you would have taken a lot of + + align:start position:0% +but then you would have taken a lot of + + + align:start position:0% +but then you would have taken a lot of +other stuff out and you wouldn't be able + + align:start position:0% +other stuff out and you wouldn't be able + + + align:start position:0% +other stuff out and you wouldn't be able +to see that other stuff you had to take + + align:start position:0% +to see that other stuff you had to take + + + align:start position:0% +to see that other stuff you had to take +out you know what i mean so + + align:start position:0% +out you know what i mean so + + + align:start position:0% +out you know what i mean so +here you can surf through and pick out + + align:start position:0% +here you can surf through and pick out + + + align:start position:0% +here you can surf through and pick out +any of these so it's definitely going to + + align:start position:0% +any of these so it's definitely going to + + + align:start position:0% +any of these so it's definitely going to +be better but + + align:start position:0% +be better but + + + align:start position:0% +be better but +which of these you can see with + + align:start position:0% +which of these you can see with + + + align:start position:0% +which of these you can see with +postmortem dissection i'm not sure some + + align:start position:0% +postmortem dissection i'm not sure some + + + align:start position:0% +postmortem dissection i'm not sure some +of them some of the bigger ones but + + align:start position:0% +of them some of the bigger ones but + + + align:start position:0% +of them some of the bigger ones but +probably not all of them + + align:start position:0% + + + + align:start position:0% + +okay so here are some of the major + + align:start position:0% +okay so here are some of the major + + + align:start position:0% +okay so here are some of the major +tracks + + align:start position:0% +tracks + + + align:start position:0% +tracks +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but you can do a little bit more than + + align:start position:0% +but you can do a little bit more than + + + align:start position:0% +but you can do a little bit more than +just find them with diffusion imaging + + align:start position:0% +just find them with diffusion imaging + + + align:start position:0% +just find them with diffusion imaging +you can also characterize them a little + + align:start position:0% +you can also characterize them a little + + + align:start position:0% +you can also characterize them a little +bit + + align:start position:0% +bit + + + align:start position:0% +bit +and this is a whole universe there's + + align:start position:0% +and this is a whole universe there's + + + align:start position:0% +and this is a whole universe there's +people who spend their lives with all + + align:start position:0% +people who spend their lives with all + + + align:start position:0% +people who spend their lives with all +kinds of fancy measures and i'm just + + align:start position:0% +kinds of fancy measures and i'm just + + + align:start position:0% +kinds of fancy measures and i'm just +going to tell you about the most common + + align:start position:0% +going to tell you about the most common + + + align:start position:0% +going to tell you about the most common +one + + align:start position:0% +one + + + align:start position:0% +one +so recall that the whole deal with + + align:start position:0% +so recall that the whole deal with + + + align:start position:0% +so recall that the whole deal with +diffusion imaging is it's looking for + + align:start position:0% +diffusion imaging is it's looking for + + + align:start position:0% +diffusion imaging is it's looking for +orientations of maximum water diffusion + + align:start position:0% +orientations of maximum water diffusion + + + align:start position:0% +orientations of maximum water diffusion +so some parts of the brain have a + + align:start position:0% +so some parts of the brain have a + + + align:start position:0% +so some parts of the brain have a +systematic set of directions of water + + align:start position:0% +systematic set of directions of water + + + align:start position:0% +systematic set of directions of water +diffusion and other ones don't right + + align:start position:0% +diffusion and other ones don't right + + + align:start position:0% +diffusion and other ones don't right +inside a ventricle the water can go any + + align:start position:0% +inside a ventricle the water can go any + + + align:start position:0% +inside a ventricle the water can go any +which way there's nothing determining + + align:start position:0% +which way there's nothing determining + + + align:start position:0% +which way there's nothing determining +which way it goes so this is called + + align:start position:0% +which way it goes so this is called + + + align:start position:0% +which way it goes so this is called +isotropic because you have diffusion + + align:start position:0% +isotropic because you have diffusion + + + align:start position:0% +isotropic because you have diffusion +equally going equally in equal amounts + + align:start position:0% +equally going equally in equal amounts + + + align:start position:0% +equally going equally in equal amounts +in all directions and anisotropic right + + align:start position:0% +in all directions and anisotropic right + + + align:start position:0% +in all directions and anisotropic right +so it goes systematically more in one + + align:start position:0% +so it goes systematically more in one + + + align:start position:0% +so it goes systematically more in one +direction + + align:start position:0% +direction + + + align:start position:0% +direction +one axis than others okay diffusion + + align:start position:0% +one axis than others okay diffusion + + + align:start position:0% +one axis than others okay diffusion +can't see the actual direction like left + + align:start position:0% +can't see the actual direction like left + + + align:start position:0% +can't see the actual direction like left +to right versus right to left it can + + align:start position:0% +to right versus right to left it can + + + align:start position:0% +to right versus right to left it can +just see that this axis is more + + align:start position:0% +just see that this axis is more + + + align:start position:0% +just see that this axis is more +prominent than this one or this one or + + align:start position:0% +prominent than this one or this one or + + + align:start position:0% +prominent than this one or this one or +this one + + align:start position:0% +this one + + + align:start position:0% +this one +okay so you're not actually seeing it + + align:start position:0% +okay so you're not actually seeing it + + + align:start position:0% +okay so you're not actually seeing it +move in a systematic direction + + align:start position:0% +move in a systematic direction + + + align:start position:0% +move in a systematic direction +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's the basic signal + + align:start position:0% +so that's the basic signal + + + align:start position:0% +so that's the basic signal +so what you can do is in a little patch + + align:start position:0% +so what you can do is in a little patch + + + align:start position:0% +so what you can do is in a little patch +of brain you can ask not just + + align:start position:0% +of brain you can ask not just + + + align:start position:0% +of brain you can ask not just +what direction has maximum diffusion + + align:start position:0% +what direction has maximum diffusion + + + align:start position:0% +what direction has maximum diffusion +which is what i've been talking about so + + align:start position:0% +which is what i've been talking about so + + + align:start position:0% +which is what i've been talking about so +far + + align:start position:0% +far + + + align:start position:0% +far +you can say + + align:start position:0% +you can say + + + align:start position:0% +you can say +how much more does it go in that maximum + + align:start position:0% +how much more does it go in that maximum + + + align:start position:0% +how much more does it go in that maximum +direction than any of the others is it + + align:start position:0% +direction than any of the others is it + + + align:start position:0% +direction than any of the others is it +more like this or more like that and you + + align:start position:0% +more like this or more like that and you + + + align:start position:0% +more like this or more like that and you +can imagine a whole spectrum in between + + align:start position:0% +can imagine a whole spectrum in between + + + align:start position:0% +can imagine a whole spectrum in between +okay so you're just asking how oriented + + align:start position:0% +okay so you're just asking how oriented + + + align:start position:0% +okay so you're just asking how oriented +is it is it like totally oriented or + + align:start position:0% +is it is it like totally oriented or + + + align:start position:0% +is it is it like totally oriented or +just partially + + align:start position:0% +just partially + + + align:start position:0% +just partially +and that measure is called fractional + + align:start position:0% +and that measure is called fractional + + + align:start position:0% +and that measure is called fractional +anisotropy or fa + + align:start position:0% +anisotropy or fa + + + align:start position:0% +anisotropy or fa +it's prominent enough in the field you + + align:start position:0% +it's prominent enough in the field you + + + align:start position:0% +it's prominent enough in the field you +should just learn this phrase you will + + align:start position:0% +should just learn this phrase you will + + + align:start position:0% +should just learn this phrase you will +if you read any articles especially any + + align:start position:0% +if you read any articles especially any + + + align:start position:0% +if you read any articles especially any +clinical articles this is the first + + align:start position:0% +clinical articles this is the first + + + align:start position:0% +clinical articles this is the first +thing you'll see + + align:start position:0% +thing you'll see + + + align:start position:0% +thing you'll see +in any clinical papers on um that use + + align:start position:0% +in any clinical papers on um that use + + + align:start position:0% +in any clinical papers on um that use +diffusion imaging + + align:start position:0% +diffusion imaging + + + align:start position:0% +diffusion imaging +okay and so fractional and isotropy + + align:start position:0% +okay and so fractional and isotropy + + + align:start position:0% +okay and so fractional and isotropy +there's a bunch of fancy definitions so + + align:start position:0% +there's a bunch of fancy definitions so + + + align:start position:0% +there's a bunch of fancy definitions so +we don't care we just want the idea it's + + align:start position:0% +we don't care we just want the idea it's + + + align:start position:0% +we don't care we just want the idea it's +just it's just + + align:start position:0% +just it's just + + + align:start position:0% +just it's just +to what degree is that little patch of + + align:start position:0% +to what degree is that little patch of + + + align:start position:0% +to what degree is that little patch of +brain in this little part of a tract + + align:start position:0% +brain in this little part of a tract + + + align:start position:0% +brain in this little part of a tract +that you've identified more like this or + + align:start position:0% +that you've identified more like this or + + + align:start position:0% +that you've identified more like this or +more like that + + align:start position:0% +more like that + + + align:start position:0% +more like that +okay is it more + + align:start position:0% +okay is it more + + + align:start position:0% +okay is it more +is it anisotropic or isotropic + + align:start position:0% +is it anisotropic or isotropic + + + align:start position:0% +is it anisotropic or isotropic +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so this has been used a lot + + align:start position:0% +and so this has been used a lot + + + align:start position:0% +and so this has been used a lot +to try to ask about the nature of fiber + + align:start position:0% +to try to ask about the nature of fiber + + + align:start position:0% +to try to ask about the nature of fiber +tracks in different groups + + align:start position:0% +tracks in different groups + + + align:start position:0% +tracks in different groups +young versus old + + align:start position:0% +young versus old + + + align:start position:0% +young versus old +different clinical groups autism versus + + align:start position:0% +different clinical groups autism versus + + + align:start position:0% +different clinical groups autism versus +typical schizophrenia you name it + + align:start position:0% +typical schizophrenia you name it + + + align:start position:0% +typical schizophrenia you name it +experience you train people up on a task + + align:start position:0% +experience you train people up on a task + + + align:start position:0% +experience you train people up on a task +do you change the fa the fractional + + align:start position:0% +do you change the fa the fractional + + + align:start position:0% +do you change the fa the fractional +anisotropy of some particular tract + + align:start position:0% +anisotropy of some particular tract + + + align:start position:0% +anisotropy of some particular tract +okay so it's just a characteristic of a + + align:start position:0% +okay so it's just a characteristic of a + + + align:start position:0% +okay so it's just a characteristic of a +tract is how + + align:start position:0% +tract is how + + + align:start position:0% +tract is how +kind of oriented is it along the way is + + align:start position:0% +kind of oriented is it along the way is + + + align:start position:0% +kind of oriented is it along the way is +it + + align:start position:0% +it + + + align:start position:0% +it +super clean you know totally oriented or + + align:start position:0% +super clean you know totally oriented or + + + align:start position:0% +super clean you know totally oriented or +does it have some + + align:start position:0% +does it have some + + + align:start position:0% +does it have some +you know + + align:start position:0% +you know + + + align:start position:0% +you know +some isotropy mixed in + + align:start position:0% +some isotropy mixed in + + + align:start position:0% +some isotropy mixed in +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so this is all over the + + align:start position:0% +all right so this is all over the + + + align:start position:0% +all right so this is all over the +literature let me give you one kind of + + align:start position:0% +literature let me give you one kind of + + + align:start position:0% +literature let me give you one kind of +cool example from gabrielli lab that + + align:start position:0% +cool example from gabrielli lab that + + + align:start position:0% +cool example from gabrielli lab that +came out recently + + align:start position:0% +came out recently + + + align:start position:0% +came out recently +so they identified the um + + align:start position:0% +so they identified the um + + + align:start position:0% +so they identified the um +arcuate fasciculus that i showed you + + align:start position:0% +arcuate fasciculus that i showed you + + + align:start position:0% +arcuate fasciculus that i showed you +before going from the basically + + align:start position:0% +before going from the basically + + + align:start position:0% +before going from the basically +wernicke's area curving around up to + + align:start position:0% +wernicke's area curving around up to + + + align:start position:0% +wernicke's area curving around up to +broca's area up there okay so that you + + align:start position:0% +broca's area up there okay so that you + + + align:start position:0% +broca's area up there okay so that you +can identify it anatomically in each + + align:start position:0% +can identify it anatomically in each + + + align:start position:0% +can identify it anatomically in each +subject individually okay now you've got + + align:start position:0% +subject individually okay now you've got + + + align:start position:0% +subject individually okay now you've got +it you've identified which voxels are + + align:start position:0% +it you've identified which voxels are + + + align:start position:0% +it you've identified which voxels are +part of the arcuate fasciculus + + align:start position:0% +part of the arcuate fasciculus + + + align:start position:0% +part of the arcuate fasciculus +and then what they want to ask what they + + align:start position:0% +and then what they want to ask what they + + + align:start position:0% +and then what they want to ask what they +wanted to ask is + + align:start position:0% +wanted to ask is + + + align:start position:0% +wanted to ask is +is the integrity or the characteristics + + align:start position:0% +is the integrity or the characteristics + + + align:start position:0% +is the integrity or the characteristics +of the arcuate fasciculus is that + + align:start position:0% +of the arcuate fasciculus is that + + + align:start position:0% +of the arcuate fasciculus is that +important + + align:start position:0% +important + + + align:start position:0% +important +for language process for dyslexia right + + align:start position:0% +for language process for dyslexia right + + + align:start position:0% +for language process for dyslexia right +so they measured the fa along this tract + + align:start position:0% +so they measured the fa along this tract + + + align:start position:0% +so they measured the fa along this tract +how oriented is it all the way along + + align:start position:0% +how oriented is it all the way along + + + align:start position:0% +how oriented is it all the way along +here and then you get some kind of + + align:start position:0% +here and then you get some kind of + + + align:start position:0% +here and then you get some kind of +average + + align:start position:0% +average + + + align:start position:0% +average +and they measure that in a bunch of kids + + align:start position:0% +and they measure that in a bunch of kids + + + align:start position:0% +and they measure that in a bunch of kids +with dyslexia and in a bunch of kids + + align:start position:0% +with dyslexia and in a bunch of kids + + + align:start position:0% +with dyslexia and in a bunch of kids +with no reading disability who are + + align:start position:0% +with no reading disability who are + + + align:start position:0% +with no reading disability who are +matched in other dimensions of + + align:start position:0% +matched in other dimensions of + + + align:start position:0% +matched in other dimensions of +non-verbal cognitive ability + + align:start position:0% +non-verbal cognitive ability + + + align:start position:0% +non-verbal cognitive ability +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and what they found is the fractional + + align:start position:0% +and what they found is the fractional + + + align:start position:0% +and what they found is the fractional +and isotropy was higher in the typical + + align:start position:0% +and isotropy was higher in the typical + + + align:start position:0% +and isotropy was higher in the typical +kids than the kids with reading + + align:start position:0% +kids than the kids with reading + + + align:start position:0% +kids than the kids with reading +disability with dyslexia + + align:start position:0% +disability with dyslexia + + + align:start position:0% +disability with dyslexia +okay and from that they implicated that + + align:start position:0% +okay and from that they implicated that + + + align:start position:0% +okay and from that they implicated that +this connection may play some role + + align:start position:0% +this connection may play some role + + + align:start position:0% +this connection may play some role +in dyslexia + + align:start position:0% +in dyslexia + + + align:start position:0% +in dyslexia +okay it's not totally obvious because + + align:start position:0% +okay it's not totally obvious because + + + align:start position:0% +okay it's not totally obvious because +one would think this region is connected + + align:start position:0% +one would think this region is connected + + + align:start position:0% +one would think this region is connected +to that region those are those are sort + + align:start position:0% +to that region those are those are sort + + + align:start position:0% +to that region those are those are sort +of languagey regions right it's not + + align:start position:0% +of languagey regions right it's not + + + align:start position:0% +of languagey regions right it's not +visual regions you think of dyslexia's + + align:start position:0% +visual regions you think of dyslexia's + + + align:start position:0% +visual regions you think of dyslexia's +problem seeing the letters and which + + align:start position:0% +problem seeing the letters and which + + + align:start position:0% +problem seeing the letters and which +ones are oriented which way and this + + align:start position:0% +ones are oriented which way and this + + + align:start position:0% +ones are oriented which way and this +suggests that at least higher level + + align:start position:0% +suggests that at least higher level + + + align:start position:0% +suggests that at least higher level +connectivity between language regions + + align:start position:0% +connectivity between language regions + + + align:start position:0% +connectivity between language regions +may be implicated okay yeah so so this + + align:start position:0% +may be implicated okay yeah so so this + + + align:start position:0% +may be implicated okay yeah so so this +just talks about the architecture and + + align:start position:0% +just talks about the architecture and + + + align:start position:0% +just talks about the architecture and +not the sort of per unit information + + align:start position:0% +not the sort of per unit information + + + align:start position:0% +not the sort of per unit information +that's right there's no information + + align:start position:0% +that's right there's no information + + + align:start position:0% +that's right there's no information +that's right it's just saying where are + + align:start position:0% +that's right it's just saying where are + + + align:start position:0% +that's right it's just saying where are +the wires and how organized are the + + align:start position:0% +the wires and how organized are the + + + align:start position:0% +the wires and how organized are the +wires period + + align:start position:0% +wires period + + + align:start position:0% +wires period +yeah so if the water flow + + align:start position:0% +yeah so if the water flow + + + align:start position:0% +yeah so if the water flow +through some technique is sort of i can + + align:start position:0% +through some technique is sort of i can + + + align:start position:0% +through some technique is sort of i can +mess with it + + align:start position:0% +mess with it + + + align:start position:0% +mess with it +like how i'm measuring it if there's + + align:start position:0% +like how i'm measuring it if there's + + + align:start position:0% +like how i'm measuring it if there's +some means to sort of miss the + + align:start position:0% +some means to sort of miss the + + + align:start position:0% +some means to sort of miss the +fusion without have any effect + + align:start position:0% +fusion without have any effect + + + align:start position:0% +fusion without have any effect +i didn't quite get that say it again so + + align:start position:0% +i didn't quite get that say it again so + + + align:start position:0% +i didn't quite get that say it again so +there's this water diffusion that's + + align:start position:0% +there's this water diffusion that's + + + align:start position:0% +there's this water diffusion that's +happening that i'm trying to measure but + + align:start position:0% +happening that i'm trying to measure but + + + align:start position:0% +happening that i'm trying to measure but +what if i have some way to intervene and + + align:start position:0% +what if i have some way to intervene and + + + align:start position:0% +what if i have some way to intervene and +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +change the rate of diffusion + + align:start position:0% +change the rate of diffusion + + + align:start position:0% +change the rate of diffusion +i don't know how you do that i mean it's + + align:start position:0% +i don't know how you do that i mean it's + + + align:start position:0% +i don't know how you do that i mean it's +a pretty basic physical property + + align:start position:0% +a pretty basic physical property + + + align:start position:0% +a pretty basic physical property +diffusion of water and how it's + + align:start position:0% +diffusion of water and how it's + + + align:start position:0% +diffusion of water and how it's +constrained by lipids right + + align:start position:0% +constrained by lipids right + + + align:start position:0% +constrained by lipids right +but that shouldn't have + + align:start position:0% +but that shouldn't have + + + align:start position:0% +but that shouldn't have +uh + + align:start position:0% +uh + + + align:start position:0% +uh +like the functional sort of information + + align:start position:0% +like the functional sort of information + + + align:start position:0% +like the functional sort of information +flow + + align:start position:0% +flow + + + align:start position:0% +flow +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i have no idea i mean that's a + + align:start position:0% +i have no idea i mean that's a + + + align:start position:0% +i have no idea i mean that's a +biophysical question i don't know about + + align:start position:0% +biophysical question i don't know about + + + align:start position:0% +biophysical question i don't know about +right but but notice this is this is a + + align:start position:0% +right but but notice this is this is a + + + align:start position:0% +right but but notice this is this is a +pretty distant proxy you're mostly + + align:start position:0% +pretty distant proxy you're mostly + + + align:start position:0% +pretty distant proxy you're mostly +looking at water between axons not even + + align:start position:0% +looking at water between axons not even + + + align:start position:0% +looking at water between axons not even +within them + + align:start position:0% +within them + + + align:start position:0% +within them +and so it's just a proxy for how well + + align:start position:0% +and so it's just a proxy for how well + + + align:start position:0% +and so it's just a proxy for how well +can we see those fibers and how they're + + align:start position:0% +can we see those fibers and how they're + + + align:start position:0% +can we see those fibers and how they're +oriented + + align:start position:0% +oriented + + + align:start position:0% +oriented +okay it's pretty yeah it's pretty + + align:start position:0% +okay it's pretty yeah it's pretty + + + align:start position:0% +okay it's pretty yeah it's pretty +removed from actual + + align:start position:0% +removed from actual + + + align:start position:0% +removed from actual +signals going along the wires + + align:start position:0% +signals going along the wires + + + align:start position:0% +signals going along the wires +um + + align:start position:0% +um + + + align:start position:0% +um +anyway does everybody get the sense that + + align:start position:0% +anyway does everybody get the sense that + + + align:start position:0% +anyway does everybody get the sense that +you know it's it's one little finding + + align:start position:0% +you know it's it's one little finding + + + align:start position:0% +you know it's it's one little finding +but it's it it implicates something + + align:start position:0% +but it's it it implicates something + + + align:start position:0% +but it's it it implicates something +about that tract uh in dyslexia + + align:start position:0% +about that tract uh in dyslexia + + + align:start position:0% +about that tract uh in dyslexia +okay so that's interesting um but first + + align:start position:0% +okay so that's interesting um but first + + + align:start position:0% +okay so that's interesting um but first +it's just correlational lots of things + + align:start position:0% +it's just correlational lots of things + + + align:start position:0% +it's just correlational lots of things +are just correlational most of the stuff + + align:start position:0% +are just correlational most of the stuff + + + align:start position:0% +are just correlational most of the stuff +in this class is just correlational same + + align:start position:0% +in this class is just correlational same + + + align:start position:0% +in this class is just correlational same +is true here + + align:start position:0% +is true here + + + align:start position:0% +is true here +um but a little more seriously it's not + + align:start position:0% +um but a little more seriously it's not + + + align:start position:0% +um but a little more seriously it's not +totally clear what fractional anisotropy + + align:start position:0% +totally clear what fractional anisotropy + + + align:start position:0% +totally clear what fractional anisotropy +means okay so there's a + + align:start position:0% +means okay so there's a + + + align:start position:0% +means okay so there's a +real tradition of treating high + + align:start position:0% +real tradition of treating high + + + align:start position:0% +real tradition of treating high +fractional anisotropy as if that's good + + align:start position:0% +fractional anisotropy as if that's good + + + align:start position:0% +fractional anisotropy as if that's good +after all we're in a fiber bundle + + align:start position:0% +after all we're in a fiber bundle + + + align:start position:0% +after all we're in a fiber bundle +shouldn't all the axons be oriented + + align:start position:0% +shouldn't all the axons be oriented + + + align:start position:0% +shouldn't all the axons be oriented +nicely in there and not all scrambled + + align:start position:0% +nicely in there and not all scrambled + + + align:start position:0% +nicely in there and not all scrambled +surely oriented as good and scrambled is + + align:start position:0% +surely oriented as good and scrambled is + + + align:start position:0% +surely oriented as good and scrambled is +bad + + align:start position:0% +bad + + + align:start position:0% +bad +well maybe but sometimes fibers cross a + + align:start position:0% +well maybe but sometimes fibers cross a + + + align:start position:0% +well maybe but sometimes fibers cross a +fiber bundle so you can have a fiber + + align:start position:0% +fiber bundle so you can have a fiber + + + align:start position:0% +fiber bundle so you can have a fiber +bundle like this with other fibers + + align:start position:0% +bundle like this with other fibers + + + align:start position:0% +bundle like this with other fibers +crossing it and so when that happens + + align:start position:0% +crossing it and so when that happens + + + align:start position:0% +crossing it and so when that happens +maybe that's good and so people use faa + + align:start position:0% +maybe that's good and so people use faa + + + align:start position:0% +maybe that's good and so people use faa +as a proxy for you know good fiber you + + align:start position:0% +as a proxy for you know good fiber you + + + align:start position:0% +as a proxy for you know good fiber you +know people say fiber integrity even + + align:start position:0% +know people say fiber integrity even + + + align:start position:0% +know people say fiber integrity even +but there's a whole question about what + + align:start position:0% +but there's a whole question about what + + + align:start position:0% +but there's a whole question about what +exactly it means and there are people + + align:start position:0% +exactly it means and there are people + + + align:start position:0% +exactly it means and there are people +who spend their lives looking at the + + align:start position:0% +who spend their lives looking at the + + + align:start position:0% +who spend their lives looking at the +biophysics of fibers and all the + + align:start position:0% +biophysics of fibers and all the + + + align:start position:0% +biophysics of fibers and all the +different things that fractional + + align:start position:0% +different things that fractional + + + align:start position:0% +different things that fractional +anisotropy and the other measures might + + align:start position:0% +anisotropy and the other measures might + + + align:start position:0% +anisotropy and the other measures might +mean + + align:start position:0% +mean + + + align:start position:0% +mean +and it's actually pretty complicated and + + align:start position:0% +and it's actually pretty complicated and + + + align:start position:0% +and it's actually pretty complicated and +unresolved + + align:start position:0% + + + + align:start position:0% + +another challenge with fractional + + align:start position:0% +another challenge with fractional + + + align:start position:0% +another challenge with fractional +anisotropy + + align:start position:0% +anisotropy + + + align:start position:0% +anisotropy +is it's extremely vulnerable to + + align:start position:0% +is it's extremely vulnerable to + + + align:start position:0% +is it's extremely vulnerable to +artifacts all of diffusion imaging is + + align:start position:0% +artifacts all of diffusion imaging is + + + align:start position:0% +artifacts all of diffusion imaging is +extremely vulnerable to artifacts + + align:start position:0% +extremely vulnerable to artifacts + + + align:start position:0% +extremely vulnerable to artifacts +okay and i'm going to give you an + + align:start position:0% +okay and i'm going to give you an + + + align:start position:0% +okay and i'm going to give you an +example of a study we did a few years + + align:start position:0% +example of a study we did a few years + + + align:start position:0% +example of a study we did a few years +ago + + align:start position:0% +ago + + + align:start position:0% +ago +so i was for a while trying to work on + + align:start position:0% +so i was for a while trying to work on + + + align:start position:0% +so i was for a while trying to work on +autism i've more or less given up + + align:start position:0% +autism i've more or less given up + + + align:start position:0% +autism i've more or less given up +because it's as far as i can tell + + align:start position:0% +because it's as far as i can tell + + + align:start position:0% +because it's as far as i can tell +impossible + + align:start position:0% +impossible + + + align:start position:0% +impossible +but back while i was still trying + + align:start position:0% +but back while i was still trying + + + align:start position:0% +but back while i was still trying +we scanned a whole bunch of kids with + + align:start position:0% +we scanned a whole bunch of kids with + + + align:start position:0% +we scanned a whole bunch of kids with +and without autism with diffusion + + align:start position:0% +and without autism with diffusion + + + align:start position:0% +and without autism with diffusion +imaging okay + + align:start position:0% +imaging okay + + + align:start position:0% +imaging okay +and at the time there were about 50 + + align:start position:0% +and at the time there were about 50 + + + align:start position:0% +and at the time there were about 50 +published papers almost all of which + + align:start position:0% +published papers almost all of which + + + align:start position:0% +published papers almost all of which +said + + align:start position:0% +said + + + align:start position:0% +said +one of the things you find with autism + + align:start position:0% +one of the things you find with autism + + + align:start position:0% +one of the things you find with autism +is that there's an underdevelopment of + + align:start position:0% +is that there's an underdevelopment of + + + align:start position:0% +is that there's an underdevelopment of +long-range connectivity and an + + align:start position:0% +long-range connectivity and an + + + align:start position:0% +long-range connectivity and an +over-development of short-range + + align:start position:0% +over-development of short-range + + + align:start position:0% +over-development of short-range +connectivity and so then people would + + align:start position:0% +connectivity and so then people would + + + align:start position:0% +connectivity and so then people would +kind of free associate with all kinds of + + align:start position:0% +kind of free associate with all kinds of + + + align:start position:0% +kind of free associate with all kinds of +speculations about okay this explains + + align:start position:0% +speculations about okay this explains + + + align:start position:0% +speculations about okay this explains +aspects of the autism phenotype they + + align:start position:0% +aspects of the autism phenotype they + + + align:start position:0% +aspects of the autism phenotype they +can't put different ideas together + + align:start position:0% +can't put different ideas together + + + align:start position:0% +can't put different ideas together +because their connections across the + + align:start position:0% +because their connections across the + + + align:start position:0% +because their connections across the +brain aren't as good and they're + + align:start position:0% +brain aren't as good and they're + + + align:start position:0% +brain aren't as good and they're +obsessed with little details because + + align:start position:0% +obsessed with little details because + + + align:start position:0% +obsessed with little details because +they have too many local connections and + + align:start position:0% +they have too many local connections and + + + align:start position:0% +they have too many local connections and +all kinds of you know + + align:start position:0% +all kinds of you know + + + align:start position:0% +all kinds of you know +suggestive but very very fuzzy ideas + + align:start position:0% +suggestive but very very fuzzy ideas + + + align:start position:0% +suggestive but very very fuzzy ideas +like that so 50 papers pretty much all + + align:start position:0% +like that so 50 papers pretty much all + + + align:start position:0% +like that so 50 papers pretty much all +found + + align:start position:0% +found + + + align:start position:0% +found +underdeveloped lower fractional + + align:start position:0% +underdeveloped lower fractional + + + align:start position:0% +underdeveloped lower fractional +anisotropy and long-range connections + + align:start position:0% +anisotropy and long-range connections + + + align:start position:0% +anisotropy and long-range connections +long-range tracks in autism okay a very + + align:start position:0% +long-range tracks in autism okay a very + + + align:start position:0% +long-range tracks in autism okay a very +established finding + + align:start position:0% +established finding + + + align:start position:0% +established finding +so we went in not to raise hell but just + + align:start position:0% +so we went in not to raise hell but just + + + align:start position:0% +so we went in not to raise hell but just +to kind of replicate some of those basic + + align:start position:0% +to kind of replicate some of those basic + + + align:start position:0% +to kind of replicate some of those basic +findings while studying some other + + align:start position:0% +findings while studying some other + + + align:start position:0% +findings while studying some other +things + + align:start position:0% +things + + + align:start position:0% +things +and in fact when we did what everyone + + align:start position:0% +and in fact when we did what everyone + + + align:start position:0% +and in fact when we did what everyone +else does + + align:start position:0% +else does + + + align:start position:0% +else does +that is standard analysis + + align:start position:0% +that is standard analysis + + + align:start position:0% +that is standard analysis +you collect your diffusion imaging data + + align:start position:0% +you collect your diffusion imaging data + + + align:start position:0% +you collect your diffusion imaging data +and you kind of eyeball it loosely and + + align:start position:0% +and you kind of eyeball it loosely and + + + align:start position:0% +and you kind of eyeball it loosely and +if it really looks terribly tainted with + + align:start position:0% +if it really looks terribly tainted with + + + align:start position:0% +if it really looks terribly tainted with +artifact you throw that subject out and + + align:start position:0% +artifact you throw that subject out and + + + align:start position:0% +artifact you throw that subject out and +otherwise you keep it + + align:start position:0% +otherwise you keep it + + + align:start position:0% +otherwise you keep it +and you analyze your data + + align:start position:0% +and you analyze your data + + + align:start position:0% +and you analyze your data +and you look at here are the 18 fiber + + align:start position:0% +and you look at here are the 18 fiber + + + align:start position:0% +and you look at here are the 18 fiber +tracks that i showed you before + + align:start position:0% +tracks that i showed you before + + + align:start position:0% +tracks that i showed you before +and you ask which of those + + align:start position:0% +and you ask which of those + + + align:start position:0% +and you ask which of those +have higher or lower fractional + + align:start position:0% +have higher or lower fractional + + + align:start position:0% +have higher or lower fractional +anisotropy in kids with autism compared + + align:start position:0% +anisotropy in kids with autism compared + + + align:start position:0% +anisotropy in kids with autism compared +to typical kids + + align:start position:0% +to typical kids + + + align:start position:0% +to typical kids +and the basic finding we replicated the + + align:start position:0% +and the basic finding we replicated the + + + align:start position:0% +and the basic finding we replicated the +usual finding and that is overall this + + align:start position:0% +usual finding and that is overall this + + + align:start position:0% +usual finding and that is overall this +is column a most of those tracks + + align:start position:0% +is column a most of those tracks + + + align:start position:0% +is column a most of those tracks +showed lower fractional anisotropy in + + align:start position:0% +showed lower fractional anisotropy in + + + align:start position:0% +showed lower fractional anisotropy in +the kids with autism than the typical + + align:start position:0% +the kids with autism than the typical + + + align:start position:0% +the kids with autism than the typical +kids + + align:start position:0% +kids + + + align:start position:0% +kids +okay + + align:start position:0% +okay + + + align:start position:0% +okay +many of those differences were + + align:start position:0% +many of those differences were + + + align:start position:0% +many of those differences were +individually significant in individual + + align:start position:0% +individually significant in individual + + + align:start position:0% +individually significant in individual +trans tracts those are the ones with + + align:start position:0% +trans tracts those are the ones with + + + align:start position:0% +trans tracts those are the ones with +asterisks + + align:start position:0% +asterisks + + + align:start position:0% +asterisks +okay so that's the standard finding in + + align:start position:0% +okay so that's the standard finding in + + + align:start position:0% +okay so that's the standard finding in +the literature and we replicated it + + align:start position:0% +the literature and we replicated it + + + align:start position:0% +the literature and we replicated it +however + + align:start position:0% +however + + + align:start position:0% +however +we noticed + + align:start position:0% +we noticed + + + align:start position:0% +we noticed +that a lot of the data + + align:start position:0% +that a lot of the data + + + align:start position:0% +that a lot of the data +like + + align:start position:0% +like + + + align:start position:0% +like +really seemed suspect and we started + + align:start position:0% +really seemed suspect and we started + + + align:start position:0% +really seemed suspect and we started +measuring the amount of head motion + + align:start position:0% +measuring the amount of head motion + + + align:start position:0% +measuring the amount of head motion +between the kids with autism and the + + align:start position:0% +between the kids with autism and the + + + align:start position:0% +between the kids with autism and the +kids without + + align:start position:0% +kids without + + + align:start position:0% +kids without +and guess what kids with autism move in + + align:start position:0% +and guess what kids with autism move in + + + align:start position:0% +and guess what kids with autism move in +the scanner more than kids without + + align:start position:0% +the scanner more than kids without + + + align:start position:0% +the scanner more than kids without +and guess what + + align:start position:0% +and guess what + + + align:start position:0% +and guess what +diffusion imaging and fractional + + align:start position:0% +diffusion imaging and fractional + + + align:start position:0% +diffusion imaging and fractional +anisotropy in particular are highly + + align:start position:0% +anisotropy in particular are highly + + + align:start position:0% +anisotropy in particular are highly +influenced by head motion + + align:start position:0% +influenced by head motion + + + align:start position:0% +influenced by head motion +so then we said okay let's get a little + + align:start position:0% +so then we said okay let's get a little + + + align:start position:0% +so then we said okay let's get a little +more careful and so we did a more + + align:start position:0% +more careful and so we did a more + + + align:start position:0% +more careful and so we did a more +stringent analysis and we looked at the + + align:start position:0% +stringent analysis and we looked at the + + + align:start position:0% +stringent analysis and we looked at the +kids we had quite a few of them in + + align:start position:0% +kids we had quite a few of them in + + + align:start position:0% +kids we had quite a few of them in +each group and we took the subset of + + align:start position:0% +each group and we took the subset of + + + align:start position:0% +each group and we took the subset of +kids who we could match for head motion + + align:start position:0% +kids who we could match for head motion + + + align:start position:0% +kids who we could match for head motion +okay so now we've got the kids with + + align:start position:0% +okay so now we've got the kids with + + + align:start position:0% +okay so now we've got the kids with +autism and the typical kids but we've + + align:start position:0% +autism and the typical kids but we've + + + align:start position:0% +autism and the typical kids but we've +now got the subset we have to choose + + align:start position:0% +now got the subset we have to choose + + + align:start position:0% +now got the subset we have to choose +to match for head motion okay it usually + + align:start position:0% +to match for head motion okay it usually + + + align:start position:0% +to match for head motion okay it usually +means the typical kids who move a little + + align:start position:0% +means the typical kids who move a little + + + align:start position:0% +means the typical kids who move a little +more and the autistic kids who had + + align:start position:0% +more and the autistic kids who had + + + align:start position:0% +more and the autistic kids who had +slightly less head motion that's what + + align:start position:0% +slightly less head motion that's what + + + align:start position:0% +slightly less head motion that's what +you need to do to match them + + align:start position:0% +you need to do to match them + + + align:start position:0% +you need to do to match them +and when we do that the usual pattern + + align:start position:0% +and when we do that the usual pattern + + + align:start position:0% +and when we do that the usual pattern +disappears now there's only a single + + align:start position:0% +disappears now there's only a single + + + align:start position:0% +disappears now there's only a single +tract that shows lower fractional + + align:start position:0% +tract that shows lower fractional + + + align:start position:0% +tract that shows lower fractional +anisotropy and the kids would with + + align:start position:0% +anisotropy and the kids would with + + + align:start position:0% +anisotropy and the kids would with +autism than the typical kids + + align:start position:0% +autism than the typical kids + + + align:start position:0% +autism than the typical kids +okay the inferior longitudinal + + align:start position:0% +okay the inferior longitudinal + + + align:start position:0% +okay the inferior longitudinal +fasciculus + + align:start position:0% +fasciculus + + + align:start position:0% +fasciculus +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +that's worrying + + align:start position:0% +that's worrying + + + align:start position:0% +that's worrying +um but then further we thought okay + + align:start position:0% +um but then further we thought okay + + + align:start position:0% +um but then further we thought okay +since many of those kids we had + + align:start position:0% +since many of those kids we had + + + align:start position:0% +since many of those kids we had +especially the typical kids many of them + + align:start position:0% +especially the typical kids many of them + + + align:start position:0% +especially the typical kids many of them +we had scanned twice + + align:start position:0% +we had scanned twice + + + align:start position:0% +we had scanned twice +so we thought okay let's really make + + align:start position:0% +so we thought okay let's really make + + + align:start position:0% +so we thought okay let's really make +this case this is clearly a problem in + + align:start position:0% +this case this is clearly a problem in + + + align:start position:0% +this case this is clearly a problem in +the field in fact it's a broader problem + + align:start position:0% +the field in fact it's a broader problem + + + align:start position:0% +the field in fact it's a broader problem +pretty much any comparison across age + + align:start position:0% +pretty much any comparison across age + + + align:start position:0% +pretty much any comparison across age +groups or clinical groups one group + + align:start position:0% +groups or clinical groups one group + + + align:start position:0% +groups or clinical groups one group +moves more than the other group + + align:start position:0% +moves more than the other group + + + align:start position:0% +moves more than the other group +uh-oh + + align:start position:0% +uh-oh + + + align:start position:0% +uh-oh +what about the entire literature + + align:start position:0% +what about the entire literature + + + align:start position:0% +what about the entire literature +hundreds probably thousands of published + + align:start position:0% +hundreds probably thousands of published + + + align:start position:0% +hundreds probably thousands of published +papers essentially none of which pay + + align:start position:0% +papers essentially none of which pay + + + align:start position:0% +papers essentially none of which pay +attention to this this is 2014. people + + align:start position:0% +attention to this this is 2014. people + + + align:start position:0% +attention to this this is 2014. people +have cleaned up their accents but up + + align:start position:0% +have cleaned up their accents but up + + + align:start position:0% +have cleaned up their accents but up +until 2014 almost none of them paid any + + align:start position:0% +until 2014 almost none of them paid any + + + align:start position:0% +until 2014 almost none of them paid any +attention to this whopping problem + + align:start position:0% +attention to this whopping problem + + + align:start position:0% +attention to this whopping problem +so we figured we better make this point + + align:start position:0% +so we figured we better make this point + + + align:start position:0% +so we figured we better make this point +salient because there's a lot of money + + align:start position:0% +salient because there's a lot of money + + + align:start position:0% +salient because there's a lot of money +and time being wasted + + align:start position:0% +and time being wasted + + + align:start position:0% +and time being wasted +publishing garbage + + align:start position:0% +publishing garbage + + + align:start position:0% +publishing garbage +and we want to make the point saliently + + align:start position:0% +and we want to make the point saliently + + + align:start position:0% +and we want to make the point saliently +so we took the typical kids who he had + + align:start position:0% +so we took the typical kids who he had + + + align:start position:0% +so we took the typical kids who he had +scanned we had scanned twice + + align:start position:0% +scanned we had scanned twice + + + align:start position:0% +scanned we had scanned twice +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and sometimes a kid will the same kid + + align:start position:0% +and sometimes a kid will the same kid + + + align:start position:0% +and sometimes a kid will the same kid +will move more in one session than + + align:start position:0% +will move more in one session than + + + align:start position:0% +will move more in one session than +another session + + align:start position:0% +another session + + + align:start position:0% +another session +so we said okay let's compare the very + + align:start position:0% +so we said okay let's compare the very + + + align:start position:0% +so we said okay let's compare the very +same kids on the session where they + + align:start position:0% +same kids on the session where they + + + align:start position:0% +same kids on the session where they +moved more than the session where they + + align:start position:0% +moved more than the session where they + + + align:start position:0% +moved more than the session where they +moved less and you know what + + align:start position:0% +moved less and you know what + + + align:start position:0% +moved less and you know what +we replicated the autism phenotype + + align:start position:0% +we replicated the autism phenotype + + + align:start position:0% +we replicated the autism phenotype +those were typical kids not autistic + + align:start position:0% +those were typical kids not autistic + + + align:start position:0% +those were typical kids not autistic +kids + + align:start position:0% +kids + + + align:start position:0% +kids +the point is head motion alone + + align:start position:0% +the point is head motion alone + + + align:start position:0% +the point is head motion alone +will reduce fractional anisotropy and + + align:start position:0% +will reduce fractional anisotropy and + + + align:start position:0% +will reduce fractional anisotropy and +will look a whole lot like a clinical + + align:start position:0% +will look a whole lot like a clinical + + + align:start position:0% +will look a whole lot like a clinical +disorder and so every time you see that + + align:start position:0% +disorder and so every time you see that + + + align:start position:0% +disorder and so every time you see that +a clinical disorder is marked by some + + align:start position:0% +a clinical disorder is marked by some + + + align:start position:0% +a clinical disorder is marked by some +anatomical difference your first thought + + align:start position:0% +anatomical difference your first thought + + + align:start position:0% +anatomical difference your first thought +should be how carefully do they deal + + align:start position:0% +should be how carefully do they deal + + + align:start position:0% +should be how carefully do they deal +with head motion and other artifacts + + align:start position:0% +with head motion and other artifacts + + + align:start position:0% +with head motion and other artifacts +that are going to differ between groups + + align:start position:0% +that are going to differ between groups + + + align:start position:0% +that are going to differ between groups +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so i say that not to diss the entire + + align:start position:0% +so i say that not to diss the entire + + + align:start position:0% +so i say that not to diss the entire +literature but just to alert you that + + align:start position:0% +literature but just to alert you that + + + align:start position:0% +literature but just to alert you that +these things can really matter + + align:start position:0% +these things can really matter + + + align:start position:0% +these things can really matter +the paper from gabrielli lab that i just + + align:start position:0% +the paper from gabrielli lab that i just + + + align:start position:0% +the paper from gabrielli lab that i just +described i looked of course before i + + align:start position:0% +described i looked of course before i + + + align:start position:0% +described i looked of course before i +presented in here and they cited us and + + align:start position:0% +presented in here and they cited us and + + + align:start position:0% +presented in here and they cited us and +they used our methods for matching head + + align:start position:0% +they used our methods for matching head + + + align:start position:0% +they used our methods for matching head +motion good for them so these things are + + align:start position:0% +motion good for them so these things are + + + align:start position:0% +motion good for them so these things are +changing and um i think you know the + + align:start position:0% +changing and um i think you know the + + + align:start position:0% +changing and um i think you know the +field will start cleaning up its act but + + align:start position:0% +field will start cleaning up its act but + + + align:start position:0% +field will start cleaning up its act but +it's amazing it took this long + + align:start position:0% +it's amazing it took this long + + + align:start position:0% +it's amazing it took this long +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so + + align:start position:0% +all right so + + + align:start position:0% +all right so +finding fiber tracks and characterizing + + align:start position:0% +finding fiber tracks and characterizing + + + align:start position:0% +finding fiber tracks and characterizing +them with fractal fractional and + + align:start position:0% +them with fractal fractional and + + + align:start position:0% +them with fractal fractional and +isotropy are nice but really what we + + align:start position:0% +isotropy are nice but really what we + + + align:start position:0% +isotropy are nice but really what we +want to know is what's connected to what + + align:start position:0% +want to know is what's connected to what + + + align:start position:0% +want to know is what's connected to what +okay + + align:start position:0% +okay + + + align:start position:0% +okay +which of these things are connected to + + align:start position:0% +which of these things are connected to + + + align:start position:0% +which of these things are connected to +each other which other brain regions are + + align:start position:0% +each other which other brain regions are + + + align:start position:0% +each other which other brain regions are +they connected to + + align:start position:0% +they connected to + + + align:start position:0% +they connected to +and so to find that out + + align:start position:0% +and so to find that out + + + align:start position:0% +and so to find that out +we need to + + align:start position:0% +we need to + + + align:start position:0% +we need to +not just study white matter itself and + + align:start position:0% +not just study white matter itself and + + + align:start position:0% +not just study white matter itself and +the tracks but we have to get out of the + + align:start position:0% +the tracks but we have to get out of the + + + align:start position:0% +the tracks but we have to get out of the +tracks and into the gray matter + + align:start position:0% +tracks and into the gray matter + + + align:start position:0% +tracks and into the gray matter +right so we need to start in a patch of + + align:start position:0% +right so we need to start in a patch of + + + align:start position:0% +right so we need to start in a patch of +gray matter and figure out where we can + + align:start position:0% +gray matter and figure out where we can + + + align:start position:0% +gray matter and figure out where we can +go by following those axons + + align:start position:0% +go by following those axons + + + align:start position:0% +go by following those axons +okay and so the method for doing that is + + align:start position:0% +okay and so the method for doing that is + + + align:start position:0% +okay and so the method for doing that is +called tractography + + align:start position:0% +called tractography + + + align:start position:0% +called tractography +so there are many versions of this i + + align:start position:0% +so there are many versions of this i + + + align:start position:0% +so there are many versions of this i +showed brief you briefly this pictures + + align:start position:0% +showed brief you briefly this pictures + + + align:start position:0% +showed brief you briefly this pictures +before i'm sure you've seen these + + align:start position:0% +before i'm sure you've seen these + + + align:start position:0% +before i'm sure you've seen these +um the the simplest idea of what you do + + align:start position:0% +um the the simplest idea of what you do + + + align:start position:0% +um the the simplest idea of what you do +leaving out all the + + align:start position:0% +leaving out all the + + + align:start position:0% +leaving out all the +you know + + align:start position:0% +you know + + + align:start position:0% +you know +details is you start in some gray matter + + align:start position:0% +details is you start in some gray matter + + + align:start position:0% +details is you start in some gray matter +region + + align:start position:0% +region + + + align:start position:0% +region +some voxel in the gray matter you want + + align:start position:0% +some voxel in the gray matter you want + + + align:start position:0% +some voxel in the gray matter you want +to know what it's connected to + + align:start position:0% +to know what it's connected to + + + align:start position:0% +to know what it's connected to +you just follow those little + + align:start position:0% +you just follow those little + + + align:start position:0% +you just follow those little +orientations and you can you see where + + align:start position:0% +orientations and you can you see where + + + align:start position:0% +orientations and you can you see where +you can go + + align:start position:0% +you can go + + + align:start position:0% +you can go +okay and so that's basically how you + + align:start position:0% +okay and so that's basically how you + + + align:start position:0% +okay and so that's basically how you +make this diagram + + align:start position:0% +make this diagram + + + align:start position:0% +make this diagram +okay you're just following those you + + align:start position:0% +okay you're just following those you + + + align:start position:0% +okay you're just following those you +start over here you follow the + + align:start position:0% +start over here you follow the + + + align:start position:0% +start over here you follow the +orientation + + align:start position:0% +orientation + + + align:start position:0% +orientation +right okay + + align:start position:0% +right okay + + + align:start position:0% +right okay +i mean you do that in a computer right + + align:start position:0% +i mean you do that in a computer right + + + align:start position:0% +i mean you do that in a computer right +an algorithm does that follows along + + align:start position:0% +an algorithm does that follows along + + + align:start position:0% +an algorithm does that follows along +okay okay so that's called tractography + + align:start position:0% +okay okay so that's called tractography + + + align:start position:0% +okay okay so that's called tractography +and the idea is awesome how great to be + + align:start position:0% +and the idea is awesome how great to be + + + align:start position:0% +and the idea is awesome how great to be +able to see + + align:start position:0% +able to see + + + align:start position:0% +able to see +what's connected to what + + align:start position:0% +what's connected to what + + + align:start position:0% +what's connected to what +and there are many many thousands of + + align:start position:0% +and there are many many thousands of + + + align:start position:0% +and there are many many thousands of +papers that do this + + align:start position:0% +papers that do this + + + align:start position:0% +papers that do this +for good reason we need to know what's + + align:start position:0% +for good reason we need to know what's + + + align:start position:0% +for good reason we need to know what's +connected to what + + align:start position:0% +connected to what + + + align:start position:0% +connected to what +this is our currently best method for + + align:start position:0% +this is our currently best method for + + + align:start position:0% +this is our currently best method for +looking at the structural connectivity + + align:start position:0% +looking at the structural connectivity + + + align:start position:0% +looking at the structural connectivity +of different gray matter regions to each + + align:start position:0% +of different gray matter regions to each + + + align:start position:0% +of different gray matter regions to each +other + + align:start position:0% +other + + + align:start position:0% +other +and so you can ask for example okay + + align:start position:0% +and so you can ask for example okay + + + align:start position:0% +and so you can ask for example okay +let's put a seed in the fusiform face + + align:start position:0% +let's put a seed in the fusiform face + + + align:start position:0% +let's put a seed in the fusiform face +area and see where it goes wouldn't that + + align:start position:0% +area and see where it goes wouldn't that + + + align:start position:0% +area and see where it goes wouldn't that +be cool + + align:start position:0% +be cool + + + align:start position:0% +be cool +right + + align:start position:0% +right + + + align:start position:0% +right +wouldn't it be cool + + align:start position:0% +wouldn't it be cool + + + align:start position:0% +wouldn't it be cool +unfortunately + + align:start position:0% +unfortunately + + + align:start position:0% +unfortunately +it doesn't work + + align:start position:0% +it doesn't work + + + align:start position:0% +it doesn't work +so i have to tell you that i don't know + + align:start position:0% +so i have to tell you that i don't know + + + align:start position:0% +so i have to tell you that i don't know +if i'm a the best person to report to + + align:start position:0% +if i'm a the best person to report to + + + align:start position:0% +if i'm a the best person to report to +this but because i'm not you know i've + + align:start position:0% +this but because i'm not you know i've + + + align:start position:0% +this but because i'm not you know i've +only been trying to do this for a few + + align:start position:0% +only been trying to do this for a few + + + align:start position:0% +only been trying to do this for a few +years but i've been collaborating with + + align:start position:0% +years but i've been collaborating with + + + align:start position:0% +years but i've been collaborating with +the best people in the world over there + + align:start position:0% +the best people in the world over there + + + align:start position:0% +the best people in the world over there +at mgh charlestown who are working + + align:start position:0% +at mgh charlestown who are working + + + align:start position:0% +at mgh charlestown who are working +closely with us and we can't get this + + align:start position:0% +closely with us and we can't get this + + + align:start position:0% +closely with us and we can't get this +thing to work worth a damn + + align:start position:0% +thing to work worth a damn + + + align:start position:0% +thing to work worth a damn +and so now i'm actually confused whether + + align:start position:0% +and so now i'm actually confused whether + + + align:start position:0% +and so now i'm actually confused whether +the entire literature is garbage i don't + + align:start position:0% +the entire literature is garbage i don't + + + align:start position:0% +the entire literature is garbage i don't +think it's entirely garbage but i think + + align:start position:0% +think it's entirely garbage but i think + + + align:start position:0% +think it's entirely garbage but i think +it's full of + + align:start position:0% +it's full of + + + align:start position:0% +it's full of +over-optimistic evaluations of what you + + align:start position:0% +over-optimistic evaluations of what you + + + align:start position:0% +over-optimistic evaluations of what you +can tell + + align:start position:0% +can tell + + + align:start position:0% +can tell +from tractography um because in in our + + align:start position:0% +from tractography um because in in our + + + align:start position:0% +from tractography um because in in our +hands we started with reality checks put + + align:start position:0% +hands we started with reality checks put + + + align:start position:0% +hands we started with reality checks put +a seed in the lateral geniculate nucleus + + align:start position:0% +a seed in the lateral geniculate nucleus + + + align:start position:0% +a seed in the lateral geniculate nucleus +let's make damn sure we can get up to v1 + + align:start position:0% +let's make damn sure we can get up to v1 + + + align:start position:0% +let's make damn sure we can get up to v1 +well you can get up to v1 + + align:start position:0% +well you can get up to v1 + + + align:start position:0% +well you can get up to v1 +but you can get up to v2 and v3 and v4 + + align:start position:0% +but you can get up to v2 and v3 and v4 + + + align:start position:0% +but you can get up to v2 and v3 and v4 +as well which which are all wrong right + + align:start position:0% +as well which which are all wrong right + + + align:start position:0% +as well which which are all wrong right +lgn only goes to v1 + + align:start position:0% +lgn only goes to v1 + + + align:start position:0% +lgn only goes to v1 +worse + + align:start position:0% +worse + + + align:start position:0% +worse +you stick a seed next door in the medial + + align:start position:0% +you stick a seed next door in the medial + + + align:start position:0% +you stick a seed next door in the medial +geniculate nucleus which is the part of + + align:start position:0% +geniculate nucleus which is the part of + + + align:start position:0% +geniculate nucleus which is the part of +the thalamus that goes up to auditory + + align:start position:0% +the thalamus that goes up to auditory + + + align:start position:0% +the thalamus that goes up to auditory +cortex + + align:start position:0% +cortex + + + align:start position:0% +cortex +you also end up in v1 wrong wrong wrong + + align:start position:0% +you also end up in v1 wrong wrong wrong + + + align:start position:0% +you also end up in v1 wrong wrong wrong +wrong + + align:start position:0% +wrong + + + align:start position:0% +wrong +there's not very many anatomical connect + + align:start position:0% +there's not very many anatomical connect + + + align:start position:0% +there's not very many anatomical connect +anatomical connections in the human + + align:start position:0% +anatomical connections in the human + + + align:start position:0% +anatomical connections in the human +brain where we actually know the right + + align:start position:0% +brain where we actually know the right + + + align:start position:0% +brain where we actually know the right +answer where we can do these reality + + align:start position:0% +answer where we can do these reality + + + align:start position:0% +answer where we can do these reality +checks but of the ones we know that + + align:start position:0% +checks but of the ones we know that + + + align:start position:0% +checks but of the ones we know that +we've tried doesn't work + + align:start position:0% +we've tried doesn't work + + + align:start position:0% +we've tried doesn't work +and we're using the best diffusion + + align:start position:0% +and we're using the best diffusion + + + align:start position:0% +and we're using the best diffusion +imaging scanner in the world it's right + + align:start position:0% +imaging scanner in the world it's right + + + align:start position:0% +imaging scanner in the world it's right +over there + + align:start position:0% +over there + + + align:start position:0% +over there +so maybe i'm doing everything wrong but + + align:start position:0% +so maybe i'm doing everything wrong but + + + align:start position:0% +so maybe i'm doing everything wrong but +at the very least i think um there are a + + align:start position:0% +at the very least i think um there are a + + + align:start position:0% +at the very least i think um there are a +lot of problems with this method + + align:start position:0% +lot of problems with this method + + + align:start position:0% +lot of problems with this method +um + + align:start position:0% +um + + + align:start position:0% +um +so and and many of these have this is + + align:start position:0% +so and and many of these have this is + + + align:start position:0% +so and and many of these have this is +not just me worrying about this so many + + align:start position:0% +not just me worrying about this so many + + + align:start position:0% +not just me worrying about this so many +people have been worrying about this for + + align:start position:0% +people have been worrying about this for + + + align:start position:0% +people have been worrying about this for +the whole 15 20 year life of diffusion + + align:start position:0% +the whole 15 20 year life of diffusion + + + align:start position:0% +the whole 15 20 year life of diffusion +tractography and some of the challenges + + align:start position:0% +tractography and some of the challenges + + + align:start position:0% +tractography and some of the challenges +are like famous so to follow those + + align:start position:0% +are like famous so to follow those + + + align:start position:0% +are like famous so to follow those +little orientations you need to you can + + align:start position:0% +little orientations you need to you can + + + align:start position:0% +little orientations you need to you can +see like there'd be lots of places where + + align:start position:0% +see like there'd be lots of places where + + + align:start position:0% +see like there'd be lots of places where +okay there's a bunch of different ways + + align:start position:0% +okay there's a bunch of different ways + + + align:start position:0% +okay there's a bunch of different ways +you could go so people use it's + + align:start position:0% +you could go so people use it's + + + align:start position:0% +you could go so people use it's +ill-posed right so people use heuristics + + align:start position:0% +ill-posed right so people use heuristics + + + align:start position:0% +ill-posed right so people use heuristics +to constrain those solutions and those + + align:start position:0% +to constrain those solutions and those + + + align:start position:0% +to constrain those solutions and those +heuristics are based on assumptions + + align:start position:0% +heuristics are based on assumptions + + + align:start position:0% +heuristics are based on assumptions +about how fibers bend in the brain + + align:start position:0% +about how fibers bend in the brain + + + align:start position:0% +about how fibers bend in the brain +namely that they don't make really sharp + + align:start position:0% +namely that they don't make really sharp + + + align:start position:0% +namely that they don't make really sharp +angles + + align:start position:0% +angles + + + align:start position:0% +angles +right that's reasonable most of the time + + align:start position:0% +right that's reasonable most of the time + + + align:start position:0% +right that's reasonable most of the time +they don't + + align:start position:0% +they don't + + + align:start position:0% +they don't +but sometimes they do and in particular + + align:start position:0% +but sometimes they do and in particular + + + align:start position:0% +but sometimes they do and in particular +when you're going from white matter to + + align:start position:0% +when you're going from white matter to + + + align:start position:0% +when you're going from white matter to +cortex often you make a very sharp turn + + align:start position:0% +cortex often you make a very sharp turn + + + align:start position:0% +cortex often you make a very sharp turn +and so it's very very difficult to + + align:start position:0% +and so it's very very difficult to + + + align:start position:0% +and so it's very very difficult to +figure out how to get from a given gray + + align:start position:0% +figure out how to get from a given gray + + + align:start position:0% +figure out how to get from a given gray +matter patch + + align:start position:0% +matter patch + + + align:start position:0% +matter patch +into the underlying white matter exactly + + align:start position:0% +into the underlying white matter exactly + + + align:start position:0% +into the underlying white matter exactly +what the connectivity is + + align:start position:0% +what the connectivity is + + + align:start position:0% +what the connectivity is +so that's one problem + + align:start position:0% +so that's one problem + + + align:start position:0% +so that's one problem +another famous problem with tractography + + align:start position:0% +another famous problem with tractography + + + align:start position:0% +another famous problem with tractography +is called the crossing fiber problem + + align:start position:0% +is called the crossing fiber problem + + + align:start position:0% +is called the crossing fiber problem +so imagine a bunch of axons somewhere in + + align:start position:0% +so imagine a bunch of axons somewhere in + + + align:start position:0% +so imagine a bunch of axons somewhere in +the brain that cross like this + + align:start position:0% +the brain that cross like this + + + align:start position:0% +the brain that cross like this +versus imagine a bunch of fibers in the + + align:start position:0% +versus imagine a bunch of fibers in the + + + align:start position:0% +versus imagine a bunch of fibers in the +brain that come up to each other and + + align:start position:0% +brain that come up to each other and + + + align:start position:0% +brain that come up to each other and +then go apart + + align:start position:0% +then go apart + + + align:start position:0% +then go apart +okay everybody get this the connectivity + + align:start position:0% +okay everybody get this the connectivity + + + align:start position:0% +okay everybody get this the connectivity +is totally different here + + align:start position:0% +is totally different here + + + align:start position:0% +is totally different here +no way you're ever going to distinguish + + align:start position:0% +no way you're ever going to distinguish + + + align:start position:0% +no way you're ever going to distinguish +those with diffusion tractography + + align:start position:0% +those with diffusion tractography + + + align:start position:0% +those with diffusion tractography +i mean so people try to get higher and + + align:start position:0% +i mean so people try to get higher and + + + align:start position:0% +i mean so people try to get higher and +higher resolution to kind of see down + + align:start position:0% +higher resolution to kind of see down + + + align:start position:0% +higher resolution to kind of see down +those individual things but + + align:start position:0% +those individual things but + + + align:start position:0% +those individual things but +you know they're not there yeah why why + + align:start position:0% +you know they're not there yeah why why + + + align:start position:0% +you know they're not there yeah why why +wouldn't something like that happen + + align:start position:0% +wouldn't something like that happen + + + align:start position:0% +wouldn't something like that happen +um it's not yeah why would they do that + + align:start position:0% +um it's not yeah why would they do that + + + align:start position:0% +um it's not yeah why would they do that +weird stuff happens in the brain + + align:start position:0% +weird stuff happens in the brain + + + align:start position:0% +weird stuff happens in the brain +um so it's not incredibly common but + + align:start position:0% +um so it's not incredibly common but + + + align:start position:0% +um so it's not incredibly common but +it's not unheard of + + align:start position:0% +it's not unheard of + + + align:start position:0% +it's not unheard of +yeah i mean remember + + align:start position:0% +yeah i mean remember + + + align:start position:0% +yeah i mean remember +you know the brain wasn't dissolved + + align:start position:0% +you know the brain wasn't dissolved + + + align:start position:0% +you know the brain wasn't dissolved +designed you know now optimally to solve + + align:start position:0% +designed you know now optimally to solve + + + align:start position:0% +designed you know now optimally to solve +all the problems it needs to solve with + + align:start position:0% +all the problems it needs to solve with + + + align:start position:0% +all the problems it needs to solve with +the optimal solution + + align:start position:0% +the optimal solution + + + align:start position:0% +the optimal solution +from scratch + + align:start position:0% +from scratch + + + align:start position:0% +from scratch +it evolved gradually over time and so + + align:start position:0% +it evolved gradually over time and so + + + align:start position:0% +it evolved gradually over time and so +there are all kinds of weird things that + + align:start position:0% +there are all kinds of weird things that + + + align:start position:0% +there are all kinds of weird things that +are workarounds for pre-existing + + align:start position:0% +are workarounds for pre-existing + + + align:start position:0% +are workarounds for pre-existing +decisions that evolution made earlier + + align:start position:0% +decisions that evolution made earlier + + + align:start position:0% +decisions that evolution made earlier +and so both brain and body have lots of + + align:start position:0% +and so both brain and body have lots of + + + align:start position:0% +and so both brain and body have lots of +bizarre + + align:start position:0% +bizarre + + + align:start position:0% +bizarre +attributes that aren't how you would + + align:start position:0% +attributes that aren't how you would + + + align:start position:0% +attributes that aren't how you would +design it from scratch they're just + + align:start position:0% +design it from scratch they're just + + + align:start position:0% +design it from scratch they're just +you know the fix that evolution made at + + align:start position:0% +you know the fix that evolution made at + + + align:start position:0% +you know the fix that evolution made at +that point + + align:start position:0% +that point + + + align:start position:0% +that point +given what had already been fixed right + + align:start position:0% +given what had already been fixed right + + + align:start position:0% +given what had already been fixed right +and so this weird stuff like that + + align:start position:0% +and so this weird stuff like that + + + align:start position:0% +and so this weird stuff like that +anyway i mentioned this to say i'm more + + align:start position:0% +anyway i mentioned this to say i'm more + + + align:start position:0% +anyway i mentioned this to say i'm more +negative about diffusion cractography + + align:start position:0% +negative about diffusion cractography + + + align:start position:0% +negative about diffusion cractography +than probably anyone else because i've + + align:start position:0% +than probably anyone else because i've + + + align:start position:0% +than probably anyone else because i've +spent a lot of the last few years trying + + align:start position:0% +spent a lot of the last few years trying + + + align:start position:0% +spent a lot of the last few years trying +to do it and it's big bust and i'm + + align:start position:0% +to do it and it's big bust and i'm + + + align:start position:0% +to do it and it's big bust and i'm +cranky + + align:start position:0% +cranky + + + align:start position:0% +cranky +so it's probably not as bad as i'm + + align:start position:0% +so it's probably not as bad as i'm + + + align:start position:0% +so it's probably not as bad as i'm +laying out plenty of people do it they + + align:start position:0% +laying out plenty of people do it they + + + align:start position:0% +laying out plenty of people do it they +get some kind of answers out of it but + + align:start position:0% +get some kind of answers out of it but + + + align:start position:0% +get some kind of answers out of it but +it's some problematic at least + + align:start position:0% +it's some problematic at least + + + align:start position:0% +it's some problematic at least +my best guess is that it is okay for + + align:start position:0% +my best guess is that it is okay for + + + align:start position:0% +my best guess is that it is okay for +fingerprints right if you're asking okay + + align:start position:0% +fingerprints right if you're asking okay + + + align:start position:0% +fingerprints right if you're asking okay +here's some patch of brain how much does + + align:start position:0% +here's some patch of brain how much does + + + align:start position:0% +here's some patch of brain how much does +it connect to say these 85 other regions + + align:start position:0% +it connect to say these 85 other regions + + + align:start position:0% +it connect to say these 85 other regions +and is that different than the + + align:start position:0% +and is that different than the + + + align:start position:0% +and is that different than the +fingerprint for this region that's + + align:start position:0% +fingerprint for this region that's + + + align:start position:0% +fingerprint for this region that's +probably okay because a lot of those + + align:start position:0% +probably okay because a lot of those + + + align:start position:0% +probably okay because a lot of those +individual solutions might be wrong and + + align:start position:0% +individual solutions might be wrong and + + + align:start position:0% +individual solutions might be wrong and +there's still enough left over to see a + + align:start position:0% +there's still enough left over to see a + + + align:start position:0% +there's still enough left over to see a +kind of difference + + align:start position:0% +kind of difference + + + align:start position:0% +kind of difference +so i feel like you can connectivity + + align:start position:0% +so i feel like you can connectivity + + + align:start position:0% +so i feel like you can connectivity +fingerprints are probably worth doing + + align:start position:0% +fingerprints are probably worth doing + + + align:start position:0% +fingerprints are probably worth doing +but actually just answering the question + + align:start position:0% +but actually just answering the question + + + align:start position:0% +but actually just answering the question +of is there a structural connection from + + align:start position:0% +of is there a structural connection from + + + align:start position:0% +of is there a structural connection from +a to b + + align:start position:0% +a to b + + + align:start position:0% +a to b +i don't know i can't get it to work + + align:start position:0% +i don't know i can't get it to work + + + align:start position:0% +i don't know i can't get it to work +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so um i think i did all this before + + align:start position:0% +okay so um i think i did all this before + + + align:start position:0% +okay so um i think i did all this before +just + + align:start position:0% +just + + + align:start position:0% +just +connectivity fingerprints do you + + align:start position:0% +connectivity fingerprints do you + + + align:start position:0% +connectivity fingerprints do you +remember this you start with one place + + align:start position:0% +remember this you start with one place + + + align:start position:0% +remember this you start with one place +and you + + align:start position:0% +and you + + + align:start position:0% +and you +you know you measure how well you can + + align:start position:0% +you know you measure how well you can + + + align:start position:0% +you know you measure how well you can +get from each location to each of these + + align:start position:0% +get from each location to each of these + + + align:start position:0% +get from each location to each of these +other ones + + align:start position:0% +other ones + + + align:start position:0% +other ones +and i showed you before that um + + align:start position:0% +and i showed you before that um + + + align:start position:0% +and i showed you before that um +the work of zanub sagan and a bunch of + + align:start position:0% +the work of zanub sagan and a bunch of + + + align:start position:0% +the work of zanub sagan and a bunch of +other people + + align:start position:0% +other people + + + align:start position:0% +other people +has shown that you can actually in an + + align:start position:0% +has shown that you can actually in an + + + align:start position:0% +has shown that you can actually in an +adult you can predict + + align:start position:0% +adult you can predict + + + align:start position:0% +adult you can predict +where that + + align:start position:0% +where that + + + align:start position:0% +where that +adult's fusiform face area is just from + + align:start position:0% +adult's fusiform face area is just from + + + align:start position:0% +adult's fusiform face area is just from +their diffusion tractography data alone + + align:start position:0% +their diffusion tractography data alone + + + align:start position:0% +their diffusion tractography data alone +okay because it has a distinctive + + align:start position:0% +okay because it has a distinctive + + + align:start position:0% +okay because it has a distinctive +connectivity fingerprint + + align:start position:0% +connectivity fingerprint + + + align:start position:0% +connectivity fingerprint +okay + + align:start position:0% +okay + + + align:start position:0% +okay +i don't want to go through all that + + align:start position:0% +i don't want to go through all that + + + align:start position:0% +i don't want to go through all that +again do you guys remember that more or + + align:start position:0% +again do you guys remember that more or + + + align:start position:0% +again do you guys remember that more or +less than just okay so that just tells + + align:start position:0% +less than just okay so that just tells + + + align:start position:0% +less than just okay so that just tells +you that there is this + + align:start position:0% +you that there is this + + + align:start position:0% +you that there is this +systematic mapping between uh the + + align:start position:0% +systematic mapping between uh the + + + align:start position:0% +systematic mapping between uh the +connectivity of a region and its + + align:start position:0% +connectivity of a region and its + + + align:start position:0% +connectivity of a region and its +function + + align:start position:0% +function + + + align:start position:0% +function +and + + align:start position:0% +and + + + align:start position:0% +and +connectivity fingerprints despite all + + align:start position:0% +connectivity fingerprints despite all + + + align:start position:0% +connectivity fingerprints despite all +these problems i've been carrying on + + align:start position:0% +these problems i've been carrying on + + + align:start position:0% +these problems i've been carrying on +about have enough signal left in there + + align:start position:0% +about have enough signal left in there + + + align:start position:0% +about have enough signal left in there +to + + align:start position:0% +to + + + align:start position:0% +to +predict the function of a region + + align:start position:0% +predict the function of a region + + + align:start position:0% +predict the function of a region +okay and maybe + + align:start position:0% +okay and maybe + + + align:start position:0% +okay and maybe +to say something about homologies across + + align:start position:0% +to say something about homologies across + + + align:start position:0% +to say something about homologies across +species + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +blah blah right okay so where do we get + + align:start position:0% +blah blah right okay so where do we get + + + align:start position:0% +blah blah right okay so where do we get +you can find the major fiber bundles + + align:start position:0% +you can find the major fiber bundles + + + align:start position:0% +you can find the major fiber bundles +with the fusion imaging that's + + align:start position:0% +with the fusion imaging that's + + + align:start position:0% +with the fusion imaging that's +worthwhile you can characterize + + align:start position:0% +worthwhile you can characterize + + + align:start position:0% +worthwhile you can characterize +fractional anisotropy i don't really + + align:start position:0% +fractional anisotropy i don't really + + + align:start position:0% +fractional anisotropy i don't really +know what it means but it means + + align:start position:0% +know what it means but it means + + + align:start position:0% +know what it means but it means +something + + align:start position:0% +something + + + align:start position:0% +something +and you can find very approximate + + align:start position:0% +and you can find very approximate + + + align:start position:0% +and you can find very approximate +connectivity fingerprints + + align:start position:0% +connectivity fingerprints + + + align:start position:0% +connectivity fingerprints +good enough to predict function + + align:start position:0% +good enough to predict function + + + align:start position:0% +good enough to predict function +okay so that's worthwhile + + align:start position:0% +okay so that's worthwhile + + + align:start position:0% +okay so that's worthwhile +um but actual structural connections of + + align:start position:0% +um but actual structural connections of + + + align:start position:0% +um but actual structural connections of +one particular cortical area uh + + align:start position:0% +one particular cortical area uh + + + align:start position:0% +one particular cortical area uh +not very good at best it's a weak signal + + align:start position:0% +not very good at best it's a weak signal + + + align:start position:0% +not very good at best it's a weak signal +so that's drag + + align:start position:0% +so that's drag + + + align:start position:0% +so that's drag +so let's consider the other method + + align:start position:0% +so let's consider the other method + + + align:start position:0% +so let's consider the other method +people have used to try to work these + + align:start position:0% +people have used to try to work these + + + align:start position:0% +people have used to try to work these +things out + + align:start position:0% +things out + + + align:start position:0% +things out +and that's resting functional + + align:start position:0% +and that's resting functional + + + align:start position:0% +and that's resting functional +correlations + + align:start position:0% +correlations + + + align:start position:0% +correlations +so let me + + align:start position:0% +so let me + + + align:start position:0% +so let me +describe where this story starts this + + align:start position:0% +describe where this story starts this + + + align:start position:0% +describe where this story starts this +story starts with a paper in 1995 by + + align:start position:0% +story starts with a paper in 1995 by + + + align:start position:0% +story starts with a paper in 1995 by +biswal + + align:start position:0% +biswal + + + align:start position:0% +biswal +and this is the figure from his paper so + + align:start position:0% +and this is the figure from his paper so + + + align:start position:0% +and this is the figure from his paper so +first he had people move they had he had + + align:start position:0% +first he had people move they had he had + + + align:start position:0% +first he had people move they had he had +people in the scanner doing finger + + align:start position:0% +people in the scanner doing finger + + + align:start position:0% +people in the scanner doing finger +tapping so they're lying in the scanner + + align:start position:0% +tapping so they're lying in the scanner + + + align:start position:0% +tapping so they're lying in the scanner +he's skating their brains while they tap + + align:start position:0% +he's skating their brains while they tap + + + align:start position:0% +he's skating their brains while they tap +both fingers or not + + align:start position:0% +both fingers or not + + + align:start position:0% +both fingers or not +or tap both fingers or not + + align:start position:0% +or tap both fingers or not + + + align:start position:0% +or tap both fingers or not +and you get these it's hard to see these + + align:start position:0% +and you get these it's hard to see these + + + align:start position:0% +and you get these it's hard to see these +two little bits of motor cortex + + align:start position:0% +two little bits of motor cortex + + + align:start position:0% +two little bits of motor cortex +corresponding to the finger motor region + + align:start position:0% +corresponding to the finger motor region + + + align:start position:0% +corresponding to the finger motor region +okay no surprise there we're just + + align:start position:0% +okay no surprise there we're just + + + align:start position:0% +okay no surprise there we're just +mapping a little bit of motor cortex + + align:start position:0% +mapping a little bit of motor cortex + + + align:start position:0% +mapping a little bit of motor cortex +but then he does something cool + + align:start position:0% +but then he does something cool + + + align:start position:0% +but then he does something cool +he puts + + align:start position:0% +he puts + + + align:start position:0% +he puts +he looks at the time course + + align:start position:0% +he looks at the time course + + + align:start position:0% +he looks at the time course +over that experiment in one of those + + align:start position:0% +over that experiment in one of those + + + align:start position:0% +over that experiment in one of those +motor regions in one hemisphere + + align:start position:0% + + + + align:start position:0% + +and he looks at the time course in the + + align:start position:0% +and he looks at the time course in the + + + align:start position:0% +and he looks at the time course in the +other hemisphere + + align:start position:0% +other hemisphere + + + align:start position:0% +other hemisphere +when the subject is at rest not doing + + align:start position:0% +when the subject is at rest not doing + + + align:start position:0% +when the subject is at rest not doing +anything okay sorry left this out you + + align:start position:0% +anything okay sorry left this out you + + + align:start position:0% +anything okay sorry left this out you +scan them doing this and then you scan + + align:start position:0% +scan them doing this and then you scan + + + align:start position:0% +scan them doing this and then you scan +them just lying there + + align:start position:0% +them just lying there + + + align:start position:0% +them just lying there +going dum dum dee dum or whatever you do + + align:start position:0% +going dum dum dee dum or whatever you do + + + align:start position:0% +going dum dum dee dum or whatever you do +when you don't have a task okay + + align:start position:0% +when you don't have a task okay + + + align:start position:0% +when you don't have a task okay +and he finds that these very far apart + + align:start position:0% +and he finds that these very far apart + + + align:start position:0% +and he finds that these very far apart +regions + + align:start position:0% +regions + + + align:start position:0% +regions +at rest when the subject is not tapping + + align:start position:0% +at rest when the subject is not tapping + + + align:start position:0% +at rest when the subject is not tapping +their fingers + + align:start position:0% +their fingers + + + align:start position:0% +their fingers +are extremely correlated + + align:start position:0% + + + + align:start position:0% + +so that's very non-obvious + + align:start position:0% +so that's very non-obvious + + + align:start position:0% +so that's very non-obvious +these things are centimeters apart + + align:start position:0% +these things are centimeters apart + + + align:start position:0% +these things are centimeters apart +the subject isn't doing anything in + + align:start position:0% +the subject isn't doing anything in + + + align:start position:0% +the subject isn't doing anything in +particular you're not telling them what + + align:start position:0% +particular you're not telling them what + + + align:start position:0% +particular you're not telling them what +to do and they certainly aren't tapping + + align:start position:0% +to do and they certainly aren't tapping + + + align:start position:0% +to do and they certainly aren't tapping +their fingers + + align:start position:0% +their fingers + + + align:start position:0% +their fingers +so why are these two bits of finger + + align:start position:0% +so why are these two bits of finger + + + align:start position:0% +so why are these two bits of finger +motor cortex going up and down in lock + + align:start position:0% +motor cortex going up and down in lock + + + align:start position:0% +motor cortex going up and down in lock +step like that + + align:start position:0% + + + + align:start position:0% + +well nobody knows actually + + align:start position:0% +well nobody knows actually + + + align:start position:0% +well nobody knows actually +i mean this was + + align:start position:0% +i mean this was + + + align:start position:0% +i mean this was +however 20 some years ago right um + + align:start position:0% +however 20 some years ago right um + + + align:start position:0% +however 20 some years ago right um +still nobody really knows why those damn + + align:start position:0% +still nobody really knows why those damn + + + align:start position:0% +still nobody really knows why those damn +things are going up in lockstep like + + align:start position:0% +things are going up in lockstep like + + + align:start position:0% +things are going up in lockstep like +that + + align:start position:0% +that + + + align:start position:0% +that +but it's systematic it's tantalizing + + align:start position:0% +but it's systematic it's tantalizing + + + align:start position:0% +but it's systematic it's tantalizing +it makes you want to play more and many + + align:start position:0% +it makes you want to play more and many + + + align:start position:0% +it makes you want to play more and many +people have + + align:start position:0% +people have + + + align:start position:0% +people have +okay so i would say we still don't know + + align:start position:0% +okay so i would say we still don't know + + + align:start position:0% +okay so i would say we still don't know +exactly why those things are going up + + align:start position:0% +exactly why those things are going up + + + align:start position:0% +exactly why those things are going up +and down together + + align:start position:0% +and down together + + + align:start position:0% +and down together +but the pattern of brain regions that go + + align:start position:0% +but the pattern of brain regions that go + + + align:start position:0% +but the pattern of brain regions that go +up and down together has proven to be a + + align:start position:0% +up and down together has proven to be a + + + align:start position:0% +up and down together has proven to be a +whole fascinating window into the brain + + align:start position:0% +whole fascinating window into the brain + + + align:start position:0% +whole fascinating window into the brain +okay so that's our next topic here + + align:start position:0% +okay so that's our next topic here + + + align:start position:0% +okay so that's our next topic here +um + + align:start position:0% +um + + + align:start position:0% +um +so um + + align:start position:0% +so um + + + align:start position:0% +so um +okay so here's another depiction of more + + align:start position:0% +okay so here's another depiction of more + + + align:start position:0% +okay so here's another depiction of more +exactly what you do + + align:start position:0% +exactly what you do + + + align:start position:0% +exactly what you do +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you okay so step one + + align:start position:0% +you okay so step one + + + align:start position:0% +you okay so step one +um you find a seed region it's in here + + align:start position:0% +um you find a seed region it's in here + + + align:start position:0% +um you find a seed region it's in here +and left somatosensory motor cortex + + align:start position:0% +and left somatosensory motor cortex + + + align:start position:0% +and left somatosensory motor cortex +okay so that's that region there you get + + align:start position:0% +okay so that's that region there you get + + + align:start position:0% +okay so that's that region there you get +its time course + + align:start position:0% +its time course + + + align:start position:0% +its time course +okay + + align:start position:0% +okay + + + align:start position:0% +okay +sorry at rest + + align:start position:0% +sorry at rest + + + align:start position:0% +sorry at rest +you find that region and then you scan + + align:start position:0% +you find that region and then you scan + + + align:start position:0% +you find that region and then you scan +the person well they're just told to do + + align:start position:0% +the person well they're just told to do + + + align:start position:0% +the person well they're just told to do +nothing in particular + + align:start position:0% +nothing in particular + + + align:start position:0% +nothing in particular +you get the time course averaged over + + align:start position:0% +you get the time course averaged over + + + align:start position:0% +you get the time course averaged over +all those voxels at rest there it is + + align:start position:0% +all those voxels at rest there it is + + + align:start position:0% +all those voxels at rest there it is +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now you take that time course + + align:start position:0% +now you take that time course + + + align:start position:0% +now you take that time course +and you correlate it with the time + + align:start position:0% +and you correlate it with the time + + + align:start position:0% +and you correlate it with the time +course of every other voxel in the brain + + align:start position:0% +course of every other voxel in the brain + + + align:start position:0% +course of every other voxel in the brain +you say show me all the voxels that are + + align:start position:0% +you say show me all the voxels that are + + + align:start position:0% +you say show me all the voxels that are +correlated with this region at rest + + align:start position:0% +correlated with this region at rest + + + align:start position:0% +correlated with this region at rest +and you get this + + align:start position:0% +and you get this + + + align:start position:0% +and you get this +lots of systematic brain regions that + + align:start position:0% +lots of systematic brain regions that + + + align:start position:0% +lots of systematic brain regions that +are highly correlated at rest with that + + align:start position:0% +are highly correlated at rest with that + + + align:start position:0% +are highly correlated at rest with that +region you started with + + align:start position:0% +region you started with + + + align:start position:0% +region you started with +everybody get what we just did + + align:start position:0% + + + + align:start position:0% + +okay totally not obvious well you might + + align:start position:0% +okay totally not obvious well you might + + + align:start position:0% +okay totally not obvious well you might +say okay fine this is finger motor + + align:start position:0% +say okay fine this is finger motor + + + align:start position:0% +say okay fine this is finger motor +cortex this is the other one that's what + + align:start position:0% +cortex this is the other one that's what + + + align:start position:0% +cortex this is the other one that's what +i showed you from biswal before + + align:start position:0% +i showed you from biswal before + + + align:start position:0% +i showed you from biswal before +but why this thing why this thing way + + align:start position:0% +but why this thing why this thing way + + + align:start position:0% +but why this thing why this thing way +down deep in the brain why that thing + + align:start position:0% +down deep in the brain why that thing + + + align:start position:0% +down deep in the brain why that thing +down in the cerebellum miles away in the + + align:start position:0% +down in the cerebellum miles away in the + + + align:start position:0% +down in the cerebellum miles away in the +brain + + align:start position:0% +brain + + + align:start position:0% +brain +why are they all kind of in cahoots with + + align:start position:0% +why are they all kind of in cahoots with + + + align:start position:0% +why are they all kind of in cahoots with +each other + + align:start position:0% +each other + + + align:start position:0% +each other +i like using in cahoots when talking + + align:start position:0% +i like using in cahoots when talking + + + align:start position:0% +i like using in cahoots when talking +about correlations because nobody knows + + align:start position:0% +about correlations because nobody knows + + + align:start position:0% +about correlations because nobody knows +what the correlations mean so in cahoots + + align:start position:0% +what the correlations mean so in cahoots + + + align:start position:0% +what the correlations mean so in cahoots +is like as technical as i think we + + align:start position:0% +is like as technical as i think we + + + align:start position:0% +is like as technical as i think we +should get + + align:start position:0% +should get + + + align:start position:0% +should get +court + + align:start position:0% +court + + + align:start position:0% +court +solutions without a time shift just + + align:start position:0% +solutions without a time shift just + + + align:start position:0% +solutions without a time shift just +exactly uh good question good question + + align:start position:0% +exactly uh good question good question + + + align:start position:0% +exactly uh good question good question +wouldn't we love to know about the time + + align:start position:0% +wouldn't we love to know about the time + + + align:start position:0% +wouldn't we love to know about the time +shift but here's the problem + + align:start position:0% +shift but here's the problem + + + align:start position:0% +shift but here's the problem +there should be a time shift because it + + align:start position:0% +there should be a time shift because it + + + align:start position:0% +there should be a time shift because it +takes a while to conduct + + align:start position:0% +takes a while to conduct + + + align:start position:0% +takes a while to conduct +down axons from here to here + + align:start position:0% +down axons from here to here + + + align:start position:0% +down axons from here to here +probably a few milliseconds + + align:start position:0% +probably a few milliseconds + + + align:start position:0% +probably a few milliseconds +but a few milliseconds we are never + + align:start position:0% +but a few milliseconds we are never + + + align:start position:0% +but a few milliseconds we are never +going to see with functional mri + + align:start position:0% +going to see with functional mri + + + align:start position:0% +going to see with functional mri +so surely there is a time shift but this + + align:start position:0% +so surely there is a time shift but this + + + align:start position:0% +so surely there is a time shift but this +method can't exploit it + + align:start position:0% +method can't exploit it + + + align:start position:0% +method can't exploit it +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and yeah i'll just leave it at that okay + + align:start position:0% +and yeah i'll just leave it at that okay + + + align:start position:0% +and yeah i'll just leave it at that okay +but does everybody get what this map is + + align:start position:0% +but does everybody get what this map is + + + align:start position:0% +but does everybody get what this map is +we've just chosen a seed region a + + align:start position:0% +we've just chosen a seed region a + + + align:start position:0% +we've just chosen a seed region a +starting point just for the hell of it + + align:start position:0% +starting point just for the hell of it + + + align:start position:0% +starting point just for the hell of it +and we've asked what other bits of the + + align:start position:0% +and we've asked what other bits of the + + + align:start position:0% +and we've asked what other bits of the +brain are correlated with that region at + + align:start position:0% +brain are correlated with that region at + + + align:start position:0% +brain are correlated with that region at +rest it's a pretty weird thing to do + + align:start position:0% +rest it's a pretty weird thing to do + + + align:start position:0% +rest it's a pretty weird thing to do +and you wouldn't do it if you didn't + + align:start position:0% +and you wouldn't do it if you didn't + + + align:start position:0% +and you wouldn't do it if you didn't +find systematically replicable answers + + align:start position:0% +find systematically replicable answers + + + align:start position:0% +find systematically replicable answers +that are repeatable across subjects and + + align:start position:0% +that are repeatable across subjects and + + + align:start position:0% +that are repeatable across subjects and +when that happens you kind of go okay i + + align:start position:0% +when that happens you kind of go okay i + + + align:start position:0% +when that happens you kind of go okay i +don't know what this means but it's + + align:start position:0% +don't know what this means but it's + + + align:start position:0% +don't know what this means but it's +pretty systematic let's keep following + + align:start position:0% +pretty systematic let's keep following + + + align:start position:0% +pretty systematic let's keep following +the thread okay that's a question + + align:start position:0% +the thread okay that's a question + + + align:start position:0% +the thread okay that's a question +uh what do you like for the addresses + + align:start position:0% +uh what do you like for the addresses + + + align:start position:0% +uh what do you like for the addresses +that + + align:start position:0% +that + + + align:start position:0% +that +i mean that returns + + align:start position:0% +i mean that returns + + + align:start position:0% +i mean that returns +okay so let's do this again you've you + + align:start position:0% +okay so let's do this again you've you + + + align:start position:0% +okay so let's do this again you've you +scan people moving their fingers you + + align:start position:0% +scan people moving their fingers you + + + align:start position:0% +scan people moving their fingers you +find little finger region here + + align:start position:0% +find little finger region here + + + align:start position:0% +find little finger region here +now you scan the same person just in the + + align:start position:0% +now you scan the same person just in the + + + align:start position:0% +now you scan the same person just in the +scanner you say i'm going to scan you + + align:start position:0% +scanner you say i'm going to scan you + + + align:start position:0% +scanner you say i'm going to scan you +for five minutes just close your eyes + + align:start position:0% +for five minutes just close your eyes + + + align:start position:0% +for five minutes just close your eyes +and don't do anything in particular you + + align:start position:0% +and don't do anything in particular you + + + align:start position:0% +and don't do anything in particular you +lie there i scan your brain + + align:start position:0% +lie there i scan your brain + + + align:start position:0% +lie there i scan your brain +now i take that region which i found + + align:start position:0% +now i take that region which i found + + + align:start position:0% +now i take that region which i found +before + + align:start position:0% +before + + + align:start position:0% +before +and i take the time course of that + + align:start position:0% +and i take the time course of that + + + align:start position:0% +and i take the time course of that +region while you were just lying in the + + align:start position:0% +region while you were just lying in the + + + align:start position:0% +region while you were just lying in the +scanner doing nothing and i get some + + align:start position:0% +scanner doing nothing and i get some + + + align:start position:0% +scanner doing nothing and i get some +randomish looking thing like this + + align:start position:0% +randomish looking thing like this + + + align:start position:0% +randomish looking thing like this +now i take that time course + + align:start position:0% +now i take that time course + + + align:start position:0% +now i take that time course +and i say let's see if there are any + + align:start position:0% +and i say let's see if there are any + + + align:start position:0% +and i say let's see if there are any +other voxels in your brain that were + + align:start position:0% +other voxels in your brain that were + + + align:start position:0% +other voxels in your brain that were +correlated when you were lying there + + align:start position:0% +correlated when you were lying there + + + align:start position:0% +correlated when you were lying there +with that time course + + align:start position:0% +with that time course + + + align:start position:0% +with that time course +and i color them in and there are lots + + align:start position:0% +and i color them in and there are lots + + + align:start position:0% +and i color them in and there are lots +of them + + align:start position:0% +of them + + + align:start position:0% +of them +even regions that are far away + + align:start position:0% + + + + align:start position:0% + +okay it's really not obvious like you + + align:start position:0% +okay it's really not obvious like you + + + align:start position:0% +okay it's really not obvious like you +wouldn't have predicted this would + + align:start position:0% +wouldn't have predicted this would + + + align:start position:0% +wouldn't have predicted this would +happen yeah + + align:start position:0% +happen yeah + + + align:start position:0% +happen yeah +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so okay what if the brain just has like + + align:start position:0% +so okay what if the brain just has like + + + align:start position:0% +so okay what if the brain just has like +some + + align:start position:0% +some + + + align:start position:0% +some +underlying like resting rhythm and like + + align:start position:0% +underlying like resting rhythm and like + + + align:start position:0% +underlying like resting rhythm and like +just always just the brain just have + + align:start position:0% +just always just the brain just have + + + align:start position:0% +just always just the brain just have +something like resting with them + + align:start position:0% +something like resting with them + + + align:start position:0% +something like resting with them +wouldn't they just always be quality + + align:start position:0% +wouldn't they just always be quality + + + align:start position:0% +wouldn't they just always be quality +yeah okay so there's been a whole suite + + align:start position:0% +yeah okay so there's been a whole suite + + + align:start position:0% +yeah okay so there's been a whole suite +of speculations of exactly that kind are + + align:start position:0% +of speculations of exactly that kind are + + + align:start position:0% +of speculations of exactly that kind are +there endogenous rigid + + align:start position:0% +there endogenous rigid + + + align:start position:0% +there endogenous rigid +rhythms that are characteristic of + + align:start position:0% +rhythms that are characteristic of + + + align:start position:0% +rhythms that are characteristic of +particular brain regions and so those + + align:start position:0% +particular brain regions and so those + + + align:start position:0% +particular brain regions and so those +things go together + + align:start position:0% +things go together + + + align:start position:0% +things go together +maybe but so far that doesn't seem to be + + align:start position:0% +maybe but so far that doesn't seem to be + + + align:start position:0% +maybe but so far that doesn't seem to be +the main answer for a long time people + + align:start position:0% +the main answer for a long time people + + + align:start position:0% +the main answer for a long time people +thought okay is it just blood flow + + align:start position:0% +thought okay is it just blood flow + + + align:start position:0% +thought okay is it just blood flow +supply maybe the blood supply to the + + align:start position:0% +supply maybe the blood supply to the + + + align:start position:0% +supply maybe the blood supply to the +brain branches and feeds those regions + + align:start position:0% +brain branches and feeds those regions + + + align:start position:0% +brain branches and feeds those regions +and that somehow regulates the gold + + align:start position:0% +and that somehow regulates the gold + + + align:start position:0% +and that somehow regulates the gold +response in those regions there have + + align:start position:0% +response in those regions there have + + + align:start position:0% +response in those regions there have +been many accounts like this and none of + + align:start position:0% +been many accounts like this and none of + + + align:start position:0% +been many accounts like this and none of +those seem to really capture it it + + align:start position:0% +those seem to really capture it it + + + align:start position:0% +those seem to really capture it it +really seems like probably those neurons + + align:start position:0% +really seems like probably those neurons + + + align:start position:0% +really seems like probably those neurons +are firing kind of in sync with each + + align:start position:0% +are firing kind of in sync with each + + + align:start position:0% +are firing kind of in sync with each +other right um + + align:start position:0% +other right um + + + align:start position:0% +other right um +yeah question nava um + + align:start position:0% +yeah question nava um + + + align:start position:0% +yeah question nava um +yes before a question direction um if + + align:start position:0% +yes before a question direction um if + + + align:start position:0% +yes before a question direction um if +you have a time delay yeah and i guess + + align:start position:0% +you have a time delay yeah and i guess + + + align:start position:0% +you have a time delay yeah and i guess +the question was because if you would + + align:start position:0% +the question was because if you would + + + align:start position:0% +the question was because if you would +have the time delay you could see what's + + align:start position:0% +have the time delay you could see what's + + + align:start position:0% +have the time delay you could see what's +further right can you instead of a time + + align:start position:0% +further right can you instead of a time + + + align:start position:0% +further right can you instead of a time +delay c + + align:start position:0% +delay c + + + align:start position:0% +delay c +if you measure in one of the regions + + align:start position:0% +if you measure in one of the regions + + + align:start position:0% +if you measure in one of the regions +that seems to be + + align:start position:0% +that seems to be + + + align:start position:0% +that seems to be +seems to be correlated if you measure + + align:start position:0% +seems to be correlated if you measure + + + align:start position:0% +seems to be correlated if you measure +from one of those if you could estimate + + align:start position:0% +from one of those if you could estimate + + + align:start position:0% +from one of those if you could estimate +the distance based on how strong your + + align:start position:0% +the distance based on how strong your + + + align:start position:0% +the distance based on how strong your +correlator is + + align:start position:0% +correlator is + + + align:start position:0% +correlator is +oh with the thought of that maybe + + align:start position:0% +oh with the thought of that maybe + + + align:start position:0% +oh with the thought of that maybe +there's not a time delay but maybe you + + align:start position:0% +there's not a time delay but maybe you + + + align:start position:0% +there's not a time delay but maybe you +lose some of your correlation with + + align:start position:0% +lose some of your correlation with + + + align:start position:0% +lose some of your correlation with +distance + + align:start position:0% +distance + + + align:start position:0% +distance +you could but just looking at this these + + align:start position:0% +you could but just looking at this these + + + align:start position:0% +you could but just looking at this these +guys are pretty far apart + + align:start position:0% +guys are pretty far apart + + + align:start position:0% +guys are pretty far apart +so it's certainly not + + align:start position:0% +so it's certainly not + + + align:start position:0% +so it's certainly not +that there's just things are you know + + align:start position:0% +that there's just things are you know + + + align:start position:0% +that there's just things are you know +that the nearby things have a similar + + align:start position:0% +that the nearby things have a similar + + + align:start position:0% +that the nearby things have a similar +i don't know but i'm i mean um to if you + + align:start position:0% +i don't know but i'm i mean um to if you + + + align:start position:0% +i don't know but i'm i mean um to if you +would say those are five different + + align:start position:0% +would say those are five different + + + align:start position:0% +would say those are five different +reaches that you measure from reaching + + align:start position:0% +reaches that you measure from reaching + + + align:start position:0% +reaches that you measure from reaching +one yeah yeah i got you yeah + + align:start position:0% +one yeah yeah i got you yeah + + + align:start position:0% +one yeah yeah i got you yeah +yeah yeah you could i think that's not + + align:start position:0% +yeah yeah you could i think that's not + + + align:start position:0% +yeah yeah you could i think that's not +going to work because there are big big + + align:start position:0% +going to work because there are big big + + + align:start position:0% +going to work because there are big big +correlations that people find between + + align:start position:0% +correlations that people find between + + + align:start position:0% +correlations that people find between +very distant regions + + align:start position:0% +very distant regions + + + align:start position:0% +very distant regions +i'll show you more yeah i mean you could + + align:start position:0% +i'll show you more yeah i mean you could + + + align:start position:0% +i'll show you more yeah i mean you could +try that and i i'm sure people have done + + align:start position:0% +try that and i i'm sure people have done + + + align:start position:0% +try that and i i'm sure people have done +that i can't tell you exactly where + + align:start position:0% +that i can't tell you exactly where + + + align:start position:0% +that i can't tell you exactly where +actually actually they do it as part of + + align:start position:0% +actually actually they do it as part of + + + align:start position:0% +actually actually they do it as part of +their one of the common ways you + + align:start position:0% +their one of the common ways you + + + align:start position:0% +their one of the common ways you +normalize your data + + align:start position:0% +normalize your data + + + align:start position:0% +normalize your data +is to take this and normalize it for + + align:start position:0% +is to take this and normalize it for + + + align:start position:0% +is to take this and normalize it for +distance from the seed region + + align:start position:0% +distance from the seed region + + + align:start position:0% +distance from the seed region +which would be a way to kind of build + + align:start position:0% +which would be a way to kind of build + + + align:start position:0% +which would be a way to kind of build +that factor in and once you do that you + + align:start position:0% +that factor in and once you do that you + + + align:start position:0% +that factor in and once you do that you +still get lots of stuff they take the + + align:start position:0% +still get lots of stuff they take the + + + align:start position:0% +still get lots of stuff they take the +distance into the image space for that + + align:start position:0% +distance into the image space for that + + + align:start position:0% +distance into the image space for that +you can do it different ways there's an + + align:start position:0% +you can do it different ways there's an + + + align:start position:0% +you can do it different ways there's an +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +that somebody at mgh wrote that is + + align:start position:0% +that somebody at mgh wrote that is + + + align:start position:0% +that somebody at mgh wrote that is +distance by the most likely uh white + + align:start position:0% +distance by the most likely uh white + + + align:start position:0% +distance by the most likely uh white +matter path + + align:start position:0% +matter path + + + align:start position:0% +matter path +uh or as the crow flies not that the + + align:start position:0% +uh or as the crow flies not that the + + + align:start position:0% +uh or as the crow flies not that the +crow can fly straight through the brain + + align:start position:0% +crow can fly straight through the brain + + + align:start position:0% +crow can fly straight through the brain +but you see what i mean + + align:start position:0% +but you see what i mean + + + align:start position:0% +but you see what i mean +um + + align:start position:0% +um + + + align:start position:0% +um +okay i'm gonna + + align:start position:0% +okay i'm gonna + + + align:start position:0% +okay i'm gonna +yeah sorry go ahead is it both different + + align:start position:0% +yeah sorry go ahead is it both different + + + align:start position:0% +yeah sorry go ahead is it both different +if you measure the correlation when + + align:start position:0% +if you measure the correlation when + + + align:start position:0% +if you measure the correlation when +they're doing the figure tapping action + + align:start position:0% +they're doing the figure tapping action + + + align:start position:0% +they're doing the figure tapping action +versus + + align:start position:0% +versus + + + align:start position:0% +versus +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay so this is a really important + + align:start position:0% +okay so this is a really important + + + align:start position:0% +okay so this is a really important +question and it's a whole part of this + + align:start position:0% +question and it's a whole part of this + + + align:start position:0% +question and it's a whole part of this +field that i'm leaving out of this + + align:start position:0% +field that i'm leaving out of this + + + align:start position:0% +field that i'm leaving out of this +lecture because i'm sort of suspicious + + align:start position:0% +lecture because i'm sort of suspicious + + + align:start position:0% +lecture because i'm sort of suspicious +of it but your but your question is a + + align:start position:0% +of it but your but your question is a + + + align:start position:0% +of it but your but your question is a +good one + + align:start position:0% +good one + + + align:start position:0% +good one +um so you're saying would they be + + align:start position:0% +um so you're saying would they be + + + align:start position:0% +um so you're saying would they be +correlated while you're finger tapping + + align:start position:0% +correlated while you're finger tapping + + + align:start position:0% +correlated while you're finger tapping +well certainly + + align:start position:0% +well certainly + + + align:start position:0% +well certainly +if we did the paradigm while they're + + align:start position:0% +if we did the paradigm while they're + + + align:start position:0% +if we did the paradigm while they're +tapping both fingers they're going to be + + align:start position:0% +tapping both fingers they're going to be + + + align:start position:0% +tapping both fingers they're going to be +correlated because we built the + + align:start position:0% +correlated because we built the + + + align:start position:0% +correlated because we built the +correlation into the task we said while + + align:start position:0% +correlation into the task we said while + + + align:start position:0% +correlation into the task we said while +you're doing this do that and so they + + align:start position:0% +you're doing this do that and so they + + + align:start position:0% +you're doing this do that and so they +will surely be correlated + + align:start position:0% +will surely be correlated + + + align:start position:0% +will surely be correlated +and so there's a whole enterprise where + + align:start position:0% +and so there's a whole enterprise where + + + align:start position:0% +and so there's a whole enterprise where +people try to factor out those things + + align:start position:0% +people try to factor out those things + + + align:start position:0% +people try to factor out those things +and ask even after you account for the + + align:start position:0% +and ask even after you account for the + + + align:start position:0% +and ask even after you account for the +activation of the task are there changes + + align:start position:0% +activation of the task are there changes + + + align:start position:0% +activation of the task are there changes +in these patterns of correlation with + + align:start position:0% +in these patterns of correlation with + + + align:start position:0% +in these patterns of correlation with +the task you're doing + + align:start position:0% +the task you're doing + + + align:start position:0% +the task you're doing +and that's called ppi for + + align:start position:0% +and that's called ppi for + + + align:start position:0% +and that's called ppi for +psychophysiological interactions and + + align:start position:0% +psychophysiological interactions and + + + align:start position:0% +psychophysiological interactions and +lots and lots of people do it hundreds + + align:start position:0% +lots and lots of people do it hundreds + + + align:start position:0% +lots and lots of people do it hundreds +thousands of papers it's probably pretty + + align:start position:0% +thousands of papers it's probably pretty + + + align:start position:0% +thousands of papers it's probably pretty +respectable but it drives me nuts + + align:start position:0% +respectable but it drives me nuts + + + align:start position:0% +respectable but it drives me nuts +because i don't feel like there's any + + align:start position:0% +because i don't feel like there's any + + + align:start position:0% +because i don't feel like there's any +way you could know that you're fully + + align:start position:0% +way you could know that you're fully + + + align:start position:0% +way you could know that you're fully +accounting for the task and so i think + + align:start position:0% +accounting for the task and so i think + + + align:start position:0% +accounting for the task and so i think +those correlations may be largely + + align:start position:0% +those correlations may be largely + + + align:start position:0% +those correlations may be largely +reflecting regions commonly activated by + + align:start position:0% +reflecting regions commonly activated by + + + align:start position:0% +reflecting regions commonly activated by +the task and that's why i didn't put + + align:start position:0% +the task and that's why i didn't put + + + align:start position:0% +the task and that's why i didn't put +that in this lecture + + align:start position:0% +that in this lecture + + + align:start position:0% +that in this lecture +but surely task will also produce + + align:start position:0% +but surely task will also produce + + + align:start position:0% +but surely task will also produce +correlations right i mean let me just + + align:start position:0% +correlations right i mean let me just + + + align:start position:0% +correlations right i mean let me just +put another way + + align:start position:0% +put another way + + + align:start position:0% +put another way +if i ask if i flash up a bunch of faces + + align:start position:0% +if i ask if i flash up a bunch of faces + + + align:start position:0% +if i ask if i flash up a bunch of faces +versus you know it's like faces versus + + align:start position:0% +versus you know it's like faces versus + + + align:start position:0% +versus you know it's like faces versus +nothing + + align:start position:0% +nothing + + + align:start position:0% +nothing +and then we look at your correlations + + align:start position:0% +and then we look at your correlations + + + align:start position:0% +and then we look at your correlations +during that period well you'll find + + align:start position:0% +during that period well you'll find + + + align:start position:0% +during that period well you'll find +correlations between v1 and the ffa + + align:start position:0% +correlations between v1 and the ffa + + + align:start position:0% +correlations between v1 and the ffa +because when their face is on both v1 + + align:start position:0% +because when their face is on both v1 + + + align:start position:0% +because when their face is on both v1 +and f8 turn on and when there aren't + + align:start position:0% +and f8 turn on and when there aren't + + + align:start position:0% +and f8 turn on and when there aren't +they both turn off + + align:start position:0% +they both turn off + + + align:start position:0% +they both turn off +that's just a task response + + align:start position:0% +that's just a task response + + + align:start position:0% +that's just a task response +right so to be able to look at how + + align:start position:0% +right so to be able to look at how + + + align:start position:0% +right so to be able to look at how +these kind of endogenous correlations + + align:start position:0% +these kind of endogenous correlations + + + align:start position:0% +these kind of endogenous correlations +are affected by task we would have to be + + align:start position:0% +are affected by task we would have to be + + + align:start position:0% +are affected by task we would have to be +certain we could siphon off the entire + + align:start position:0% +certain we could siphon off the entire + + + align:start position:0% +certain we could siphon off the entire +task effect so that we could look at + + align:start position:0% +task effect so that we could look at + + + align:start position:0% +task effect so that we could look at +just the residual and i don't think any + + align:start position:0% +just the residual and i don't think any + + + align:start position:0% +just the residual and i don't think any +of our analyses are good enough to + + align:start position:0% +of our analyses are good enough to + + + align:start position:0% +of our analyses are good enough to +siphon off an entire task effect and + + align:start position:0% +siphon off an entire task effect and + + + align:start position:0% +siphon off an entire task effect and +that's why i just don't go there with + + align:start position:0% +that's why i just don't go there with + + + align:start position:0% +that's why i just don't go there with +ppi even though everyone else does + + align:start position:0% +ppi even though everyone else does + + + align:start position:0% +ppi even though everyone else does +if you didn't follow that doesn't matter + + align:start position:0% +if you didn't follow that doesn't matter + + + align:start position:0% +if you didn't follow that doesn't matter +i'm just trying to give you an answer + + align:start position:0% +i'm just trying to give you an answer + + + align:start position:0% +i'm just trying to give you an answer +i'm going to take just questions of + + align:start position:0% +i'm going to take just questions of + + + align:start position:0% +i'm going to take just questions of +clarification now because there's a + + align:start position:0% +clarification now because there's a + + + align:start position:0% +clarification now because there's a +couple things i really want to get to + + align:start position:0% +couple things i really want to get to + + + align:start position:0% +couple things i really want to get to +and i'm + + align:start position:0% +and i'm + + + align:start position:0% +and i'm +running out of time + + align:start position:0% +running out of time + + + align:start position:0% +running out of time +um + + align:start position:0% +um + + + align:start position:0% +um +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um but but but everybody should + + align:start position:0% +um but but but everybody should + + + align:start position:0% +um but but but everybody should +understand this right an activation map + + align:start position:0% +understand this right an activation map + + + align:start position:0% +understand this right an activation map +that's made by asking which brain + + align:start position:0% +that's made by asking which brain + + + align:start position:0% +that's made by asking which brain +regions are correlated at rest with a + + align:start position:0% +regions are correlated at rest with a + + + align:start position:0% +regions are correlated at rest with a +given region i choose + + align:start position:0% +given region i choose + + + align:start position:0% +given region i choose +okay + + align:start position:0% +okay + + + align:start position:0% +okay +a seed region i choose okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +important caveat + + align:start position:0% +important caveat + + + align:start position:0% +important caveat +even though people call this resting + + align:start position:0% +even though people call this resting + + + align:start position:0% +even though people call this resting +functional connectivity + + align:start position:0% +functional connectivity + + + align:start position:0% +functional connectivity +we will not be using that phrase in this + + align:start position:0% +we will not be using that phrase in this + + + align:start position:0% +we will not be using that phrase in this +class because we do not know that it's + + align:start position:0% +class because we do not know that it's + + + align:start position:0% +class because we do not know that it's +connectivity in the structural sense + + align:start position:0% +connectivity in the structural sense + + + align:start position:0% +connectivity in the structural sense +it's just a correlation + + align:start position:0% +it's just a correlation + + + align:start position:0% +it's just a correlation +okay and i'll say more about that later + + align:start position:0% +okay and i'll say more about that later + + + align:start position:0% +okay and i'll say more about that later +but if you read about resting functional + + align:start position:0% +but if you read about resting functional + + + align:start position:0% +but if you read about resting functional +connectivity it's the same thing it's + + align:start position:0% +connectivity it's the same thing it's + + + align:start position:0% +connectivity it's the same thing it's +just i think people are making a mistake + + align:start position:0% +just i think people are making a mistake + + + align:start position:0% +just i think people are making a mistake +using that word + + align:start position:0% +using that word + + + align:start position:0% +using that word +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +let me get this idea across here + + align:start position:0% +let me get this idea across here + + + align:start position:0% +let me get this idea across here +you may have heard of the default mode + + align:start position:0% +you may have heard of the default mode + + + align:start position:0% +you may have heard of the default mode +network it's there's heaps of papers on + + align:start position:0% +network it's there's heaps of papers on + + + align:start position:0% +network it's there's heaps of papers on +this it's a thing there's a lot of + + align:start position:0% +this it's a thing there's a lot of + + + align:start position:0% +this it's a thing there's a lot of +discussion of it and it's bizarre it has + + align:start position:0% +discussion of it and it's bizarre it has + + + align:start position:0% +discussion of it and it's bizarre it has +arisen from two kind of independent + + align:start position:0% +arisen from two kind of independent + + + align:start position:0% +arisen from two kind of independent +findings okay so let's do these findings + + align:start position:0% +findings okay so let's do these findings + + + align:start position:0% +findings okay so let's do these findings +one at a time + + align:start position:0% +one at a time + + + align:start position:0% +one at a time +the first one is people started noticing + + align:start position:0% +the first one is people started noticing + + + align:start position:0% +the first one is people started noticing +around 15 years ago that across lots of + + align:start position:0% +around 15 years ago that across lots of + + + align:start position:0% +around 15 years ago that across lots of +different kinds of tasks + + align:start position:0% +different kinds of tasks + + + align:start position:0% +different kinds of tasks +if you looked at not the + + align:start position:0% +if you looked at not the + + + align:start position:0% +if you looked at not the +intended direction like say + + align:start position:0% +intended direction like say + + + align:start position:0% +intended direction like say +reading sentences versus staring at a + + align:start position:0% +reading sentences versus staring at a + + + align:start position:0% +reading sentences versus staring at a +dot or + + align:start position:0% +dot or + + + align:start position:0% +dot or +you know + + align:start position:0% +you know + + + align:start position:0% +you know +doing a demanding working memory task + + align:start position:0% +doing a demanding working memory task + + + align:start position:0% +doing a demanding working memory task +versus a really you know passive viewing + + align:start position:0% +versus a really you know passive viewing + + + align:start position:0% +versus a really you know passive viewing +task anything where there's a you know + + align:start position:0% +task anything where there's a you know + + + align:start position:0% +task anything where there's a you know +in a really engaging task versus an easy + + align:start position:0% +in a really engaging task versus an easy + + + align:start position:0% +in a really engaging task versus an easy +task + + align:start position:0% +task + + + align:start position:0% +task +you would find a bunch of regions that + + align:start position:0% +you would find a bunch of regions that + + + align:start position:0% +you would find a bunch of regions that +were activated in the reverse contrast + + align:start position:0% +were activated in the reverse contrast + + + align:start position:0% +were activated in the reverse contrast +regions that are more activated when + + align:start position:0% +regions that are more activated when + + + align:start position:0% +regions that are more activated when +you're doing less mental activity + + align:start position:0% +you're doing less mental activity + + + align:start position:0% +you're doing less mental activity +typically regions that are active when + + align:start position:0% +typically regions that are active when + + + align:start position:0% +typically regions that are active when +you're just lying there at rest compared + + align:start position:0% +you're just lying there at rest compared + + + align:start position:0% +you're just lying there at rest compared +to doing something difficult + + align:start position:0% +to doing something difficult + + + align:start position:0% +to doing something difficult +and so originally people were like + + align:start position:0% +and so originally people were like + + + align:start position:0% +and so originally people were like +what's up with that like how can that be + + align:start position:0% +what's up with that like how can that be + + + align:start position:0% +what's up with that like how can that be +it seemed like paradoxical impossible + + align:start position:0% +it seemed like paradoxical impossible + + + align:start position:0% +it seemed like paradoxical impossible +um but in fact it's not impossible right + + align:start position:0% +um but in fact it's not impossible right + + + align:start position:0% +um but in fact it's not impossible right +consider suppose i had you do a bunch of + + align:start position:0% +consider suppose i had you do a bunch of + + + align:start position:0% +consider suppose i had you do a bunch of +mental arithmetic tasks + + align:start position:0% +mental arithmetic tasks + + + align:start position:0% +mental arithmetic tasks +and they're pretty demanding and i + + align:start position:0% +and they're pretty demanding and i + + + align:start position:0% +and they're pretty demanding and i +compared that to just having you lie + + align:start position:0% +compared that to just having you lie + + + align:start position:0% +compared that to just having you lie +there in the scanner doing nothing it's + + align:start position:0% +there in the scanner doing nothing it's + + + align:start position:0% +there in the scanner doing nothing it's +like okay do mental arithmetic for 20 + + align:start position:0% +like okay do mental arithmetic for 20 + + + align:start position:0% +like okay do mental arithmetic for 20 +seconds + + align:start position:0% +seconds + + + align:start position:0% +seconds +you know rest 20 seconds mental + + align:start position:0% +you know rest 20 seconds mental + + + align:start position:0% +you know rest 20 seconds mental +arithmetic for 20 seconds rest for 20 + + align:start position:0% +arithmetic for 20 seconds rest for 20 + + + align:start position:0% +arithmetic for 20 seconds rest for 20 +seconds + + align:start position:0% +seconds + + + align:start position:0% +seconds +now imagine we find parts of your brain + + align:start position:0% +now imagine we find parts of your brain + + + align:start position:0% +now imagine we find parts of your brain +systematic ones that are more engaged at + + align:start position:0% +systematic ones that are more engaged at + + + align:start position:0% +systematic ones that are more engaged at +rest + + align:start position:0% +rest + + + align:start position:0% +rest +what might that mean + + align:start position:0% + + + + align:start position:0% + +david that part of the brain could be + + align:start position:0% +david that part of the brain could be + + + align:start position:0% +david that part of the brain could be +anything like daydreaming daydreaming + + align:start position:0% +anything like daydreaming daydreaming + + + align:start position:0% +anything like daydreaming daydreaming +exactly yeah you can't turn your brain + + align:start position:0% +exactly yeah you can't turn your brain + + + align:start position:0% +exactly yeah you can't turn your brain +off you don't turn your brain off at + + align:start position:0% +off you don't turn your brain off at + + + align:start position:0% +off you don't turn your brain off at +rest + + align:start position:0% +rest + + + align:start position:0% +rest +you daydream + + align:start position:0% +you daydream + + + align:start position:0% +you daydream +absolutely + + align:start position:0% +absolutely + + + align:start position:0% +absolutely +what else what are the things some of + + align:start position:0% +what else what are the things some of + + + align:start position:0% +what else what are the things some of +the things you do when you daydream + + align:start position:0% + + + + align:start position:0% + +what are the typical contents of + + align:start position:0% +what are the typical contents of + + + align:start position:0% +what are the typical contents of +daydreaming i guess it depends who it is + + align:start position:0% +daydreaming i guess it depends who it is + + + align:start position:0% +daydreaming i guess it depends who it is +and what you're daydreaming about but + + align:start position:0% +and what you're daydreaming about but + + + align:start position:0% +and what you're daydreaming about but +they're very systematic things people do + + align:start position:0% +they're very systematic things people do + + + align:start position:0% +they're very systematic things people do +they recall episodic memories it's like + + align:start position:0% +they recall episodic memories it's like + + + align:start position:0% +they recall episodic memories it's like +oh yeah like before i got in here you + + align:start position:0% +oh yeah like before i got in here you + + + align:start position:0% +oh yeah like before i got in here you +really replay things that were happening + + align:start position:0% +really replay things that were happening + + + align:start position:0% +really replay things that were happening +and what else do you do you think about + + align:start position:0% +and what else do you do you think about + + + align:start position:0% +and what else do you do you think about +people + + align:start position:0% +people + + + align:start position:0% +people +why because we're social primates and + + align:start position:0% +why because we're social primates and + + + align:start position:0% +why because we're social primates and +that's what we care a lot about you + + align:start position:0% +that's what we care a lot about you + + + align:start position:0% +that's what we care a lot about you +don't think only about people you might + + align:start position:0% +don't think only about people you might + + + align:start position:0% +don't think only about people you might +some of you guys might be trying to + + align:start position:0% +some of you guys might be trying to + + + align:start position:0% +some of you guys might be trying to +solve a math problem that you couldn't + + align:start position:0% +solve a math problem that you couldn't + + + align:start position:0% +solve a math problem that you couldn't +solve before + + align:start position:0% +solve before + + + align:start position:0% +solve before +but most people in the scanner asked to + + align:start position:0% +but most people in the scanner asked to + + + align:start position:0% +but most people in the scanner asked to +do nothing are recalling events which + + align:start position:0% +do nothing are recalling events which + + + align:start position:0% +do nothing are recalling events which +usually involve people or thinking about + + align:start position:0% +usually involve people or thinking about + + + align:start position:0% +usually involve people or thinking about +people + + align:start position:0% +people + + + align:start position:0% +people +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this whole suite of brain regions was + + align:start position:0% +so this whole suite of brain regions was + + + align:start position:0% +so this whole suite of brain regions was +called the default mode network is just + + align:start position:0% +called the default mode network is just + + + align:start position:0% +called the default mode network is just +the regions that are more engaged when + + align:start position:0% +the regions that are more engaged when + + + align:start position:0% +the regions that are more engaged when +nobody tells you what to do + + align:start position:0% +nobody tells you what to do + + + align:start position:0% +nobody tells you what to do +than for a whole bunch of things when + + align:start position:0% +than for a whole bunch of things when + + + align:start position:0% +than for a whole bunch of things when +they tell you what to do and so it's + + align:start position:0% +they tell you what to do and so it's + + + align:start position:0% +they tell you what to do and so it's +some weird mix of daydreaming and other + + align:start position:0% +some weird mix of daydreaming and other + + + align:start position:0% +some weird mix of daydreaming and other +stuff + + align:start position:0% +stuff + + + align:start position:0% +stuff +and the interesting thing about it is + + align:start position:0% +and the interesting thing about it is + + + align:start position:0% +and the interesting thing about it is +they're reasonably systematic so those + + align:start position:0% +they're reasonably systematic so those + + + align:start position:0% +they're reasonably systematic so those +are the um + + align:start position:0% +are the um + + + align:start position:0% +are the um +i keep getting confused here hang on let + + align:start position:0% +i keep getting confused here hang on let + + + align:start position:0% +i keep getting confused here hang on let +me get this right + + align:start position:0% +me get this right + + + align:start position:0% +me get this right +um + + align:start position:0% +um + + + align:start position:0% +um +did i label this backwards + + align:start position:0% +did i label this backwards + + + align:start position:0% +did i label this backwards +uh all right they're the green guys + + align:start position:0% +uh all right they're the green guys + + + align:start position:0% +uh all right they're the green guys +yeah deactivated during the + + align:start position:0% +yeah deactivated during the + + + align:start position:0% +yeah deactivated during the +demanding tasks yeah there's too many + + align:start position:0% +demanding tasks yeah there's too many + + + align:start position:0% +demanding tasks yeah there's too many +negatives for me here the green guys + + align:start position:0% +negatives for me here the green guys + + + align:start position:0% +negatives for me here the green guys +here does that look familiar + + align:start position:0% + + + + align:start position:0% + +that patch + + align:start position:0% +that patch + + + align:start position:0% +that patch +what does that look like + + align:start position:0% +what does that look like + + + align:start position:0% +what does that look like +kind of not exactly but kind of + + align:start position:0% +kind of not exactly but kind of + + + align:start position:0% +kind of not exactly but kind of +sorry + + align:start position:0% + + + + align:start position:0% + +it's sort of near the visual system yeah + + align:start position:0% +it's sort of near the visual system yeah + + + align:start position:0% +it's sort of near the visual system yeah +it is but it's also like something else + + align:start position:0% +it is but it's also like something else + + + align:start position:0% +it is but it's also like something else +we've been talking about recently + + align:start position:0% +we've been talking about recently + + + align:start position:0% +we've been talking about recently +our tpj + + align:start position:0% +our tpj + + + align:start position:0% +our tpj +it's a little further back but it's + + align:start position:0% +it's a little further back but it's + + + align:start position:0% +it's a little further back but it's +right in the same region okay + + align:start position:0% +right in the same region okay + + + align:start position:0% +right in the same region okay +and so and here are these medial regions + + align:start position:0% +and so and here are these medial regions + + + align:start position:0% +and so and here are these medial regions +this is like there's a medial view of + + align:start position:0% +this is like there's a medial view of + + + align:start position:0% +this is like there's a medial view of +the left hemisphere like take my right + + align:start position:0% +the left hemisphere like take my right + + + align:start position:0% +the left hemisphere like take my right +hemisphere out and look at the inside + + align:start position:0% +hemisphere out and look at the inside + + + align:start position:0% +hemisphere out and look at the inside +view that's this calcarine sulcus right + + align:start position:0% +view that's this calcarine sulcus right + + + align:start position:0% +view that's this calcarine sulcus right +all these medial regions + + align:start position:0% +all these medial regions + + + align:start position:0% +all these medial regions +it looks a whole lot like the social + + align:start position:0% +it looks a whole lot like the social + + + align:start position:0% +it looks a whole lot like the social +cognition network that i talked about + + align:start position:0% +cognition network that i talked about + + + align:start position:0% +cognition network that i talked about +last time + + align:start position:0% +last time + + + align:start position:0% +last time +that you identify with the contrast of + + align:start position:0% +that you identify with the contrast of + + + align:start position:0% +that you identify with the contrast of +belief tasks versus the false belief + + align:start position:0% +belief tasks versus the false belief + + + align:start position:0% +belief tasks versus the false belief +test versus the false photo tests + + align:start position:0% +test versus the false photo tests + + + align:start position:0% +test versus the false photo tests +so that's weird weird finding number one + + align:start position:0% +so that's weird weird finding number one + + + align:start position:0% +so that's weird weird finding number one +that there's a systematic set of regions + + align:start position:0% +that there's a systematic set of regions + + + align:start position:0% +that there's a systematic set of regions +that are engaged at rest they're called + + align:start position:0% +that are engaged at rest they're called + + + align:start position:0% +that are engaged at rest they're called +the default mode network + + align:start position:0% +the default mode network + + + align:start position:0% +the default mode network +because they're sort of what you do by + + align:start position:0% +because they're sort of what you do by + + + align:start position:0% +because they're sort of what you do by +default when nobody's controlling you + + align:start position:0% +default when nobody's controlling you + + + align:start position:0% +default when nobody's controlling you +externally so that's finding number one + + align:start position:0% +externally so that's finding number one + + + align:start position:0% +externally so that's finding number one +and there's finding number two but first + + align:start position:0% +and there's finding number two but first + + + align:start position:0% +and there's finding number two but first +jack did you have a question yeah i was + + align:start position:0% +jack did you have a question yeah i was + + + align:start position:0% +jack did you have a question yeah i was +just wondering does deactivated during + + align:start position:0% +just wondering does deactivated during + + + align:start position:0% +just wondering does deactivated during +demanding tasks necessarily imply that + + align:start position:0% +demanding tasks necessarily imply that + + + align:start position:0% +demanding tasks necessarily imply that +it is activated during not demanding + + align:start position:0% +it is activated during not demanding + + + align:start position:0% +it is activated during not demanding +tasks we're not distinguishing between + + align:start position:0% +tasks we're not distinguishing between + + + align:start position:0% +tasks we're not distinguishing between +those we're just taking those two + + align:start position:0% +those we're just taking those two + + + align:start position:0% +those we're just taking those two +conditions you'd have to have some third + + align:start position:0% +conditions you'd have to have some third + + + align:start position:0% +conditions you'd have to have some third +base line to figure out whether those + + align:start position:0% +base line to figure out whether those + + + align:start position:0% +base line to figure out whether those +two were different and that's very + + align:start position:0% +two were different and that's very + + + align:start position:0% +two were different and that's very +problematic because we're already having + + align:start position:0% +problematic because we're already having + + + align:start position:0% +problematic because we're already having +a problem saying what counts as a + + align:start position:0% +a problem saying what counts as a + + + align:start position:0% +a problem saying what counts as a +baseline right so we'll just compare + + align:start position:0% +baseline right so we'll just compare + + + align:start position:0% +baseline right so we'll just compare +those two okay + + align:start position:0% +those two okay + + + align:start position:0% +those two okay +um so that's weird finding number one + + align:start position:0% +um so that's weird finding number one + + + align:start position:0% +um so that's weird finding number one +and it's not that weird when you think + + align:start position:0% +and it's not that weird when you think + + + align:start position:0% +and it's not that weird when you think +about it further because of course + + align:start position:0% +about it further because of course + + + align:start position:0% +about it further because of course +you're doing stuff when you're lying + + align:start position:0% +you're doing stuff when you're lying + + + align:start position:0% +you're doing stuff when you're lying +there right + + align:start position:0% +there right + + + align:start position:0% +there right +um but the further finding that really + + align:start position:0% +um but the further finding that really + + + align:start position:0% +um but the further finding that really +put the default mode network on the map + + align:start position:0% +put the default mode network on the map + + + align:start position:0% +put the default mode network on the map +was when people started putting seeds in + + align:start position:0% +was when people started putting seeds in + + + align:start position:0% +was when people started putting seeds in +parts of that default mode network + + align:start position:0% +parts of that default mode network + + + align:start position:0% +parts of that default mode network +up here + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +finding that they got the whole rest of + + align:start position:0% +finding that they got the whole rest of + + + align:start position:0% +finding that they got the whole rest of +the network at rest + + align:start position:0% +the network at rest + + + align:start position:0% +the network at rest +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so all of those things are correlated at + + align:start position:0% +so all of those things are correlated at + + + align:start position:0% +so all of those things are correlated at +rest + + align:start position:0% +rest + + + align:start position:0% +rest +it's not just that they're all activated + + align:start position:0% +it's not just that they're all activated + + + align:start position:0% +it's not just that they're all activated +at rest their time courses are + + align:start position:0% +at rest their time courses are + + + align:start position:0% +at rest their time courses are +correlated at rest + + align:start position:0% +correlated at rest + + + align:start position:0% +correlated at rest +so actually what people mean by default + + align:start position:0% +so actually what people mean by default + + + align:start position:0% +so actually what people mean by default +mode network now + + align:start position:0% +mode network now + + + align:start position:0% +mode network now +is not + + align:start position:0% +is not + + + align:start position:0% +is not +i took the reverse contrast and all the + + align:start position:0% +i took the reverse contrast and all the + + + align:start position:0% +i took the reverse contrast and all the +stuff that activated more for rest than + + align:start position:0% +stuff that activated more for rest than + + + align:start position:0% +stuff that activated more for rest than +task i called that default mode actually + + align:start position:0% +task i called that default mode actually + + + align:start position:0% +task i called that default mode actually +what they mean is i stuck a seed in + + align:start position:0% +what they mean is i stuck a seed in + + + align:start position:0% +what they mean is i stuck a seed in +there during my rest scans and i took + + align:start position:0% +there during my rest scans and i took + + + align:start position:0% +there during my rest scans and i took +all the stuff that was correlated with + + align:start position:0% +all the stuff that was correlated with + + + align:start position:0% +all the stuff that was correlated with +that position + + align:start position:0% +that position + + + align:start position:0% +that position +because those pick out more or less the + + align:start position:0% +because those pick out more or less the + + + align:start position:0% +because those pick out more or less the +same thing + + align:start position:0% +same thing + + + align:start position:0% +same thing +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's led to a whole lot of + + align:start position:0% +so that's led to a whole lot of + + + align:start position:0% +so that's led to a whole lot of +discussion about what the default mode + + align:start position:0% +discussion about what the default mode + + + align:start position:0% +discussion about what the default mode +network is and what it means and what we + + align:start position:0% +network is and what it means and what we + + + align:start position:0% +network is and what it means and what we +can learn from it + + align:start position:0% +can learn from it + + + align:start position:0% +can learn from it +um that's what all this says + + align:start position:0% +um that's what all this says + + + align:start position:0% +um that's what all this says +um + + align:start position:0% +um + + + align:start position:0% +um +i'm just trying to figure out how i'm + + align:start position:0% +i'm just trying to figure out how i'm + + + align:start position:0% +i'm just trying to figure out how i'm +going to do this because i'm going to + + align:start position:0% +going to do this because i'm going to + + + align:start position:0% +going to do this because i'm going to +run out of time maybe i won't run out of + + align:start position:0% +run out of time maybe i won't run out of + + + align:start position:0% +run out of time maybe i won't run out of +time we'll just go for it + + align:start position:0% +time we'll just go for it + + + align:start position:0% +time we'll just go for it +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +people started messing around with these + + align:start position:0% +people started messing around with these + + + align:start position:0% +people started messing around with these +correlations at rest + + align:start position:0% +correlations at rest + + + align:start position:0% +correlations at rest +and they found that you could find other + + align:start position:0% +and they found that you could find other + + + align:start position:0% +and they found that you could find other +systematic sets of regions if you stuck + + align:start position:0% +systematic sets of regions if you stuck + + + align:start position:0% +systematic sets of regions if you stuck +seeds elsewhere and so another + + align:start position:0% +seeds elsewhere and so another + + + align:start position:0% +seeds elsewhere and so another +systematic region a set of regions + + align:start position:0% +systematic region a set of regions + + + align:start position:0% +systematic region a set of regions +is all the kind of hot color ones the + + align:start position:0% +is all the kind of hot color ones the + + + align:start position:0% +is all the kind of hot color ones the +yellow and red ones here + + align:start position:0% +yellow and red ones here + + + align:start position:0% +yellow and red ones here +and so if you look in there you see + + align:start position:0% +and so if you look in there you see + + + align:start position:0% +and so if you look in there you see +various things interpretable sulcus a + + align:start position:0% +various things interpretable sulcus a + + + align:start position:0% +various things interpretable sulcus a +bunch of frontal regions + + align:start position:0% +bunch of frontal regions + + + align:start position:0% +bunch of frontal regions +visual motion area mt or other visual + + align:start position:0% +visual motion area mt or other visual + + + align:start position:0% +visual motion area mt or other visual +regions down there + + align:start position:0% +regions down there + + + align:start position:0% +regions down there +um and they found that that set of + + align:start position:0% +um and they found that that set of + + + align:start position:0% +um and they found that that set of +regions was strongly correlated with + + align:start position:0% +regions was strongly correlated with + + + align:start position:0% +regions was strongly correlated with +each other at rest you stick a seed in + + align:start position:0% +each other at rest you stick a seed in + + + align:start position:0% +each other at rest you stick a seed in +here and you get all that yellow stuff + + align:start position:0% +here and you get all that yellow stuff + + + align:start position:0% +here and you get all that yellow stuff +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then they looked at it and they said + + align:start position:0% +and then they looked at it and they said + + + align:start position:0% +and then they looked at it and they said +yeah right + + align:start position:0% +yeah right + + + align:start position:0% +yeah right +we've seen those regions engaged + + align:start position:0% +we've seen those regions engaged + + + align:start position:0% +we've seen those regions engaged +whenever people do demanding potentially + + align:start position:0% +whenever people do demanding potentially + + + align:start position:0% +whenever people do demanding potentially +demanding tasks + + align:start position:0% +demanding tasks + + + align:start position:0% +demanding tasks +they've seen that before in other kind + + align:start position:0% +they've seen that before in other kind + + + align:start position:0% +they've seen that before in other kind +of task contrast so all those things + + align:start position:0% +of task contrast so all those things + + + align:start position:0% +of task contrast so all those things +that turn on + + align:start position:0% +that turn on + + + align:start position:0% +that turn on +when you really have to pay a lot of + + align:start position:0% +when you really have to pay a lot of + + + align:start position:0% +when you really have to pay a lot of +attention you're doing a really hard + + align:start position:0% +attention you're doing a really hard + + + align:start position:0% +attention you're doing a really hard +task all those regions do that + + align:start position:0% +task all those regions do that + + + align:start position:0% +task all those regions do that +um and they're also correlated with each + + align:start position:0% +um and they're also correlated with each + + + align:start position:0% +um and they're also correlated with each +other at rest + + align:start position:0% +other at rest + + + align:start position:0% +other at rest +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so there's this convergence of these + + align:start position:0% +and so there's this convergence of these + + + align:start position:0% +and so there's this convergence of these +two different lines of work + + align:start position:0% +two different lines of work + + + align:start position:0% +two different lines of work +uh task contrasts that just say what + + align:start position:0% +uh task contrasts that just say what + + + align:start position:0% +uh task contrasts that just say what +makes a given set of regions turn on or + + align:start position:0% +makes a given set of regions turn on or + + + align:start position:0% +makes a given set of regions turn on or +off + + align:start position:0% +off + + + align:start position:0% +off +and correlations which things are + + align:start position:0% +and correlations which things are + + + align:start position:0% +and correlations which things are +correlated at rest + + align:start position:0% +correlated at rest + + + align:start position:0% +correlated at rest +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so they're both converging here with + + align:start position:0% +and so they're both converging here with + + + align:start position:0% +and so they're both converging here with +these two different networks + + align:start position:0% +these two different networks + + + align:start position:0% +these two different networks +okay so i need to do a little sidebar on + + align:start position:0% +okay so i need to do a little sidebar on + + + align:start position:0% +okay so i need to do a little sidebar on +this other hot color network okay not + + align:start position:0% +this other hot color network okay not + + + align:start position:0% +this other hot color network okay not +the default mode network but this other + + align:start position:0% +the default mode network but this other + + + align:start position:0% +the default mode network but this other +one it was originally called task + + align:start position:0% +one it was originally called task + + + align:start position:0% +one it was originally called task +positive because it turns on more when + + align:start position:0% +positive because it turns on more when + + + align:start position:0% +positive because it turns on more when +you do tasks than rest i mean that's a + + align:start position:0% +you do tasks than rest i mean that's a + + + align:start position:0% +you do tasks than rest i mean that's a +really vague statement okay + + align:start position:0% +really vague statement okay + + + align:start position:0% +really vague statement okay +but it also has lots of other names + + align:start position:0% +but it also has lots of other names + + + align:start position:0% +but it also has lots of other names +and the name that we're going to refer + + align:start position:0% +and the name that we're going to refer + + + align:start position:0% +and the name that we're going to refer +to here is the multiple demand regions + + align:start position:0% +to here is the multiple demand regions + + + align:start position:0% +to here is the multiple demand regions +okay + + align:start position:0% +okay + + + align:start position:0% +okay +multiple demand comes out from another + + align:start position:0% +multiple demand comes out from another + + + align:start position:0% +multiple demand comes out from another +line of work that just kind of converged + + align:start position:0% +line of work that just kind of converged + + + align:start position:0% +line of work that just kind of converged +with us they're picking up pretty much + + align:start position:0% +with us they're picking up pretty much + + + align:start position:0% +with us they're picking up pretty much +the same set of brain regions but + + align:start position:0% +the same set of brain regions but + + + align:start position:0% +the same set of brain regions but +multiple demand means lots of different + + align:start position:0% +multiple demand means lots of different + + + align:start position:0% +multiple demand means lots of different +kinds of cognitive demand + + align:start position:0% +kinds of cognitive demand + + + align:start position:0% +kinds of cognitive demand +activate those same regions + + align:start position:0% +activate those same regions + + + align:start position:0% +activate those same regions +okay so i can give you a difficult + + align:start position:0% +okay so i can give you a difficult + + + align:start position:0% +okay so i can give you a difficult +spatial working memory task i can give + + align:start position:0% +spatial working memory task i can give + + + align:start position:0% +spatial working memory task i can give +you a difficult perceptual orientation + + align:start position:0% +you a difficult perceptual orientation + + + align:start position:0% +you a difficult perceptual orientation +judgment task a difficult arithmetic + + align:start position:0% +judgment task a difficult arithmetic + + + align:start position:0% +judgment task a difficult arithmetic +task in each of those cases i can + + align:start position:0% +task in each of those cases i can + + + align:start position:0% +task in each of those cases i can +compare them to an easy version of the + + align:start position:0% +compare them to an easy version of the + + + align:start position:0% +compare them to an easy version of the +same task + + align:start position:0% +same task + + + align:start position:0% +same task +and i'll get more or less those regions + + align:start position:0% +and i'll get more or less those regions + + + align:start position:0% +and i'll get more or less those regions +there + + align:start position:0% +there + + + align:start position:0% +there +okay which are + + align:start position:0% +okay which are + + + align:start position:0% +okay which are +that's getting a little vague here but + + align:start position:0% +that's getting a little vague here but + + + align:start position:0% +that's getting a little vague here but +they're pretty similar to the + + align:start position:0% +they're pretty similar to the + + + align:start position:0% +they're pretty similar to the +task positive ones okay + + align:start position:0% +task positive ones okay + + + align:start position:0% +task positive ones okay +so + + align:start position:0% +so + + + align:start position:0% +so +this is both interesting and scandalous + + align:start position:0% +this is both interesting and scandalous + + + align:start position:0% +this is both interesting and scandalous +it's scandalous because to me only not + + align:start position:0% +it's scandalous because to me only not + + + align:start position:0% +it's scandalous because to me only not +to anyone else because unlike all the + + align:start position:0% +to anyone else because unlike all the + + + align:start position:0% +to anyone else because unlike all the +regions we've been talking about so far + + align:start position:0% +regions we've been talking about so far + + + align:start position:0% +regions we've been talking about so far +that have these very specific functions + + align:start position:0% +that have these very specific functions + + + align:start position:0% +that have these very specific functions +they just do face recognition or just + + align:start position:0% +they just do face recognition or just + + + align:start position:0% +they just do face recognition or just +theory of mind right + + align:start position:0% +theory of mind right + + + align:start position:0% +theory of mind right +these ones will do anything almost + + align:start position:0% +these ones will do anything almost + + + align:start position:0% +these ones will do anything almost +anything difficult okay + + align:start position:0% +anything difficult okay + + + align:start position:0% +anything difficult okay +so whenever you engage in a difficult + + align:start position:0% +so whenever you engage in a difficult + + + align:start position:0% +so whenever you engage in a difficult +task i'm skipping over a whole + + align:start position:0% +task i'm skipping over a whole + + + align:start position:0% +task i'm skipping over a whole +literature it's big literature on this + + align:start position:0% +literature it's big literature on this + + + align:start position:0% +literature it's big literature on this +but lots and lots of totally different + + align:start position:0% +but lots and lots of totally different + + + align:start position:0% +but lots and lots of totally different +kinds of tasks that have nothing in + + align:start position:0% +kinds of tasks that have nothing in + + + align:start position:0% +kinds of tasks that have nothing in +common other than they're very demanding + + align:start position:0% +common other than they're very demanding + + + align:start position:0% +common other than they're very demanding +you engage those regions + + align:start position:0% +you engage those regions + + + align:start position:0% +you engage those regions +and in some ways that's an even more + + align:start position:0% +and in some ways that's an even more + + + align:start position:0% +and in some ways that's an even more +fascinating puzzle like what the hell + + align:start position:0% +fascinating puzzle like what the hell + + + align:start position:0% +fascinating puzzle like what the hell +would those operations be what is in + + align:start position:0% +would those operations be what is in + + + align:start position:0% +would those operations be what is in +common between you know spatial working + + align:start position:0% +common between you know spatial working + + + align:start position:0% +common between you know spatial working +memory and arithmetic and + + align:start position:0% +memory and arithmetic and + + + align:start position:0% +memory and arithmetic and +you know line orientation judgment and + + align:start position:0% +you know line orientation judgment and + + + align:start position:0% +you know line orientation judgment and +all the other things that have been + + align:start position:0% +all the other things that have been + + + align:start position:0% +all the other things that have been +shown to activate these regions when + + align:start position:0% +shown to activate these regions when + + + align:start position:0% +shown to activate these regions when +they're demanding nobody knows i think + + align:start position:0% +they're demanding nobody knows i think + + + align:start position:0% +they're demanding nobody knows i think +it's a big fascinating puzzle someday + + align:start position:0% +it's a big fascinating puzzle someday + + + align:start position:0% +it's a big fascinating puzzle someday +we'll have a computational story about + + align:start position:0% +we'll have a computational story about + + + align:start position:0% +we'll have a computational story about +what's actually computed in those + + align:start position:0% +what's actually computed in those + + + align:start position:0% +what's actually computed in those +regions but we don't yet + + align:start position:0% +regions but we don't yet + + + align:start position:0% +regions but we don't yet +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um so the i'll skip more there's a lot + + align:start position:0% +um so the i'll skip more there's a lot + + + align:start position:0% +um so the i'll skip more there's a lot +of stuff on the multiple demand regions + + align:start position:0% +of stuff on the multiple demand regions + + + align:start position:0% +of stuff on the multiple demand regions +and they're interesting but + + align:start position:0% +and they're interesting but + + + align:start position:0% +and they're interesting but +okay i can't resist one little thing all + + align:start position:0% +okay i can't resist one little thing all + + + align:start position:0% +okay i can't resist one little thing all +right i can't i have no self-control + + align:start position:0% +right i can't i have no self-control + + + align:start position:0% +right i can't i have no self-control +because i'm not i don't have enough + + align:start position:0% +because i'm not i don't have enough + + + align:start position:0% +because i'm not i don't have enough +multiple man activity right now so i'm + + align:start position:0% +multiple man activity right now so i'm + + + align:start position:0% +multiple man activity right now so i'm +gonna have to just tell you these things + + align:start position:0% +gonna have to just tell you these things + + + align:start position:0% +gonna have to just tell you these things +because they're cool okay so + + align:start position:0% +because they're cool okay so + + + align:start position:0% +because they're cool okay so +um + + align:start position:0% +um + + + align:start position:0% +um +uh a guy named john duncan has spent the + + align:start position:0% +uh a guy named john duncan has spent the + + + align:start position:0% +uh a guy named john duncan has spent the +last 15 years arguing that the multiple + + align:start position:0% +last 15 years arguing that the multiple + + + align:start position:0% +last 15 years arguing that the multiple +demand regions first are really truly + + align:start position:0% +demand regions first are really truly + + + align:start position:0% +demand regions first are really truly +multiple demand and they are like he's + + align:start position:0% +multiple demand and they are like he's + + + align:start position:0% +multiple demand and they are like he's +tested lots and lots of different tasks + + align:start position:0% +tested lots and lots of different tasks + + + align:start position:0% +tested lots and lots of different tasks +and they're very very + + align:start position:0% +and they're very very + + + align:start position:0% +and they're very very +domain general + + align:start position:0% +domain general + + + align:start position:0% +domain general +but second he thinks they're implicated + + align:start position:0% +but second he thinks they're implicated + + + align:start position:0% +but second he thinks they're implicated +in fluid intelligence + + align:start position:0% +in fluid intelligence + + + align:start position:0% +in fluid intelligence +okay fluid intelligence differs from + + align:start position:0% +okay fluid intelligence differs from + + + align:start position:0% +okay fluid intelligence differs from +crystallized intelligence crystallized + + align:start position:0% +crystallized intelligence crystallized + + + align:start position:0% +crystallized intelligence crystallized +intelligence is stuff like + + align:start position:0% +intelligence is stuff like + + + align:start position:0% +intelligence is stuff like +your vocabulary just stuff you've + + align:start position:0% +your vocabulary just stuff you've + + + align:start position:0% +your vocabulary just stuff you've +learned and cached away and facts you've + + align:start position:0% +learned and cached away and facts you've + + + align:start position:0% +learned and cached away and facts you've +stored and abilities you've specific + + align:start position:0% +stored and abilities you've specific + + + align:start position:0% +stored and abilities you've specific +abilities you've stored + + align:start position:0% +abilities you've stored + + + align:start position:0% +abilities you've stored +fluid intelligence you measure with + + align:start position:0% +fluid intelligence you measure with + + + align:start position:0% +fluid intelligence you measure with +stuff like raven's matrices where + + align:start position:0% +stuff like raven's matrices where + + + align:start position:0% +stuff like raven's matrices where +nothing you know is going to help you do + + align:start position:0% +nothing you know is going to help you do + + + align:start position:0% +nothing you know is going to help you do +it you just have to be smart and see + + align:start position:0% +it you just have to be smart and see + + + align:start position:0% +it you just have to be smart and see +some abstract pattern or something like + + align:start position:0% +some abstract pattern or something like + + + align:start position:0% +some abstract pattern or something like +that + + align:start position:0% +that + + + align:start position:0% +that +and so duncan thinks that these regions + + align:start position:0% +and so duncan thinks that these regions + + + align:start position:0% +and so duncan thinks that these regions +are related to fluid intelligence + + align:start position:0% +are related to fluid intelligence + + + align:start position:0% +are related to fluid intelligence +and one of his measures of that is if + + align:start position:0% +and one of his measures of that is if + + + align:start position:0% +and one of his measures of that is if +you find people with brain damage he had + + align:start position:0% +you find people with brain damage he had + + + align:start position:0% +you find people with brain damage he had +a big set of around 80 people who had + + align:start position:0% +a big set of around 80 people who had + + + align:start position:0% +a big set of around 80 people who had +brain damage who had been studying + + align:start position:0% +brain damage who had been studying + + + align:start position:0% +brain damage who had been studying +in all different parts of the brain + + align:start position:0% +in all different parts of the brain + + + align:start position:0% +in all different parts of the brain +and what he found is if you have brain + + align:start position:0% +and what he found is if you have brain + + + align:start position:0% +and what he found is if you have brain +damage in those regions + + align:start position:0% +damage in those regions + + + align:start position:0% +damage in those regions +your iq goes down as a result of the + + align:start position:0% +your iq goes down as a result of the + + + align:start position:0% +your iq goes down as a result of the +damage in proportion to the amount of + + align:start position:0% +damage in proportion to the amount of + + + align:start position:0% +damage in proportion to the amount of +cortical volume + + align:start position:0% +cortical volume + + + align:start position:0% +cortical volume +destroyed by the damage + + align:start position:0% +destroyed by the damage + + + align:start position:0% +destroyed by the damage +if you have damage anywhere else in the + + align:start position:0% +if you have damage anywhere else in the + + + align:start position:0% +if you have damage anywhere else in the +brain your iq is unaffected + + align:start position:0% +brain your iq is unaffected + + + align:start position:0% +brain your iq is unaffected +you may become paralyzed or aphasic or + + align:start position:0% +you may become paralyzed or aphasic or + + + align:start position:0% +you may become paralyzed or aphasic or +prosopagnosic or akinatopsic + + align:start position:0% +prosopagnosic or akinatopsic + + + align:start position:0% +prosopagnosic or akinatopsic +right you may have any of these very + + align:start position:0% +right you may have any of these very + + + align:start position:0% +right you may have any of these very +specific deficits according to where it + + align:start position:0% +specific deficits according to where it + + + align:start position:0% +specific deficits according to where it +lands but it won't affect your iq + + align:start position:0% +lands but it won't affect your iq + + + align:start position:0% +lands but it won't affect your iq +and so the picture here is that in + + align:start position:0% +and so the picture here is that in + + + align:start position:0% +and so the picture here is that in +addition to all these special purpose + + align:start position:0% +addition to all these special purpose + + + align:start position:0% +addition to all these special purpose +processors that this course has been + + align:start position:0% +processors that this course has been + + + align:start position:0% +processors that this course has been +focusing on we have this thing that's + + align:start position:0% +focusing on we have this thing that's + + + align:start position:0% +focusing on we have this thing that's +kind of like the brain cpu or something + + align:start position:0% +kind of like the brain cpu or something + + + align:start position:0% +kind of like the brain cpu or something +like that + + align:start position:0% +like that + + + align:start position:0% +like that +um and um and it seems to live in + + align:start position:0% +um and um and it seems to live in + + + align:start position:0% +um and um and it seems to live in +approximately those regions and it seems + + align:start position:0% +approximately those regions and it seems + + + align:start position:0% +approximately those regions and it seems +to under you know it seems to be + + align:start position:0% +to under you know it seems to be + + + align:start position:0% +to under you know it seems to be +essential for fluid intelligence + + align:start position:0% +essential for fluid intelligence + + + align:start position:0% +essential for fluid intelligence +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so i'm skipping over lots of literature + + align:start position:0% +so i'm skipping over lots of literature + + + align:start position:0% +so i'm skipping over lots of literature +just to heighten that this is a + + align:start position:0% +just to heighten that this is a + + + align:start position:0% +just to heighten that this is a +particularly interesting set of regions + + align:start position:0% +particularly interesting set of regions + + + align:start position:0% +particularly interesting set of regions +here + + align:start position:0% +here + + + align:start position:0% +here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +do people study novelty + + align:start position:0% +do people study novelty + + + align:start position:0% +do people study novelty +yeah their regions are specialized these + + align:start position:0% +yeah their regions are specialized these + + + align:start position:0% +yeah their regions are specialized these +guys these guys will be interested in + + align:start position:0% +guys these guys will be interested in + + + align:start position:0% +guys these guys will be interested in +novelty + + align:start position:0% + + + + align:start position:0% + +these guys will be interested in novelty + + align:start position:0% +these guys will be interested in novelty + + + align:start position:0% +these guys will be interested in novelty +but not only you can do the same boring + + align:start position:0% +but not only you can do the same boring + + + align:start position:0% +but not only you can do the same boring +but difficult task on and on and they'll + + align:start position:0% +but difficult task on and on and they'll + + + align:start position:0% +but difficult task on and on and they'll +keep going + + align:start position:0% + + + + align:start position:0% + +okay so now the reason i went on that + + align:start position:0% +okay so now the reason i went on that + + + align:start position:0% +okay so now the reason i went on that +sidebar + + align:start position:0% +sidebar + + + align:start position:0% +sidebar +is that you can identify these regions + + align:start position:0% +is that you can identify these regions + + + align:start position:0% +is that you can identify these regions +not just by scanning people while + + align:start position:0% +not just by scanning people while + + + align:start position:0% +not just by scanning people while +they're doing difficult tasks + + align:start position:0% +they're doing difficult tasks + + + align:start position:0% +they're doing difficult tasks +but by sticking a seed in any of those + + align:start position:0% +but by sticking a seed in any of those + + + align:start position:0% +but by sticking a seed in any of those +regions and getting the others + + align:start position:0% +regions and getting the others + + + align:start position:0% +regions and getting the others +okay that's the task positive network + + align:start position:0% +okay that's the task positive network + + + align:start position:0% +okay that's the task positive network +pretty much + + align:start position:0% +pretty much + + + align:start position:0% +pretty much +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we're getting this convergence + + align:start position:0% +so we're getting this convergence + + + align:start position:0% +so we're getting this convergence +between + + align:start position:0% +between + + + align:start position:0% +between +sets of brain regions that we find with + + align:start position:0% +sets of brain regions that we find with + + + align:start position:0% +sets of brain regions that we find with +a task contrast and sets of brain + + align:start position:0% +a task contrast and sets of brain + + + align:start position:0% +a task contrast and sets of brain +regions we find by finding what's + + align:start position:0% +regions we find by finding what's + + + align:start position:0% +regions we find by finding what's +correlated with what + + align:start position:0% +correlated with what + + + align:start position:0% +correlated with what +and the bigger picture of this whole + + align:start position:0% +and the bigger picture of this whole + + + align:start position:0% +and the bigger picture of this whole +thing is that i've been focusing on + + align:start position:0% +thing is that i've been focusing on + + + align:start position:0% +thing is that i've been focusing on +individual regions of what they do + + align:start position:0% +individual regions of what they do + + + align:start position:0% +individual regions of what they do +and the gist of this whole resting + + align:start position:0% +and the gist of this whole resting + + + align:start position:0% +and the gist of this whole resting +functional correlation literature is + + align:start position:0% +functional correlation literature is + + + align:start position:0% +functional correlation literature is +a very relevant level of organization of + + align:start position:0% +a very relevant level of organization of + + + align:start position:0% +a very relevant level of organization of +the brain is not just an individual + + align:start position:0% +the brain is not just an individual + + + align:start position:0% +the brain is not just an individual +cortical region but a set of cortical + + align:start position:0% +cortical region but a set of cortical + + + align:start position:0% +cortical region but a set of cortical +regions that seem to be + + align:start position:0% +regions that seem to be + + + align:start position:0% +regions that seem to be +in cahoots + + align:start position:0% +in cahoots + + + align:start position:0% +in cahoots +and again we don't know what that means + + align:start position:0% +and again we don't know what that means + + + align:start position:0% +and again we don't know what that means +exactly but they're correlated at rest + + align:start position:0% +exactly but they're correlated at rest + + + align:start position:0% +exactly but they're correlated at rest +and they have something to do with each + + align:start position:0% +and they have something to do with each + + + align:start position:0% +and they have something to do with each +other okay so we're finding this kind of + + align:start position:0% +other okay so we're finding this kind of + + + align:start position:0% +other okay so we're finding this kind of +higher level organization and the + + align:start position:0% +higher level organization and the + + + align:start position:0% +higher level organization and the +multiple demand system is part of it + + align:start position:0% +multiple demand system is part of it + + + align:start position:0% +multiple demand system is part of it +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +how are we going to look at this + + align:start position:0% +how are we going to look at this + + + align:start position:0% +how are we going to look at this +um so there's a bunch of these i've + + align:start position:0% +um so there's a bunch of these i've + + + align:start position:0% +um so there's a bunch of these i've +talked only about the default mode + + align:start position:0% +talked only about the default mode + + + align:start position:0% +talked only about the default mode +network and + + align:start position:0% +network and + + + align:start position:0% +network and +it's another name for the same thing + + align:start position:0% +it's another name for the same thing + + + align:start position:0% +it's another name for the same thing +executive control don't worry about it + + align:start position:0% +executive control don't worry about it + + + align:start position:0% +executive control don't worry about it +could think of that as multiple demand + + align:start position:0% +could think of that as multiple demand + + + align:start position:0% +could think of that as multiple demand +doesn't matter + + align:start position:0% +doesn't matter + + + align:start position:0% +doesn't matter +but there's a bunch of them that you can + + align:start position:0% +but there's a bunch of them that you can + + + align:start position:0% +but there's a bunch of them that you can +find by sticking seeds in different + + align:start position:0% +find by sticking seeds in different + + + align:start position:0% +find by sticking seeds in different +places + + align:start position:0% +places + + + align:start position:0% +places +and so yeah as i just said the big idea + + align:start position:0% +and so yeah as i just said the big idea + + + align:start position:0% +and so yeah as i just said the big idea +here is that networks are an interesting + + align:start position:0% +here is that networks are an interesting + + + align:start position:0% +here is that networks are an interesting +level + + align:start position:0% +level + + + align:start position:0% +level +an interesting kind of unit in thinking + + align:start position:0% +an interesting kind of unit in thinking + + + align:start position:0% +an interesting kind of unit in thinking +about brain organization + + align:start position:0% +about brain organization + + + align:start position:0% +about brain organization +bigger than an individual region it's a + + align:start position:0% +bigger than an individual region it's a + + + align:start position:0% +bigger than an individual region it's a +set of regions that have something in + + align:start position:0% +set of regions that have something in + + + align:start position:0% +set of regions that have something in +common + + align:start position:0% +common + + + align:start position:0% +common +okay + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +i've sort of backed into this in this + + align:start position:0% +i've sort of backed into this in this + + + align:start position:0% +i've sort of backed into this in this +awkward way of kind of saying okay here + + align:start position:0% +awkward way of kind of saying okay here + + + align:start position:0% +awkward way of kind of saying okay here +things are correlated with each other + + align:start position:0% +things are correlated with each other + + + align:start position:0% +things are correlated with each other +and here's what we know about the same + + align:start position:0% +and here's what we know about the same + + + align:start position:0% +and here's what we know about the same +regions from previous task analyses + + align:start position:0% +regions from previous task analyses + + + align:start position:0% +regions from previous task analyses +most of the literature on resting + + align:start position:0% +most of the literature on resting + + + align:start position:0% +most of the literature on resting +functional correlation just looks at + + align:start position:0% +functional correlation just looks at + + + align:start position:0% +functional correlation just looks at +correlations + + align:start position:0% +correlations + + + align:start position:0% +correlations +and doesn't try to put it together with + + align:start position:0% +and doesn't try to put it together with + + + align:start position:0% +and doesn't try to put it together with +what we know about those regions and + + align:start position:0% +what we know about those regions and + + + align:start position:0% +what we know about those regions and +that just seems deeply weird to me + + align:start position:0% +that just seems deeply weird to me + + + align:start position:0% +that just seems deeply weird to me +so um so for years i ignored this whole + + align:start position:0% +so um so for years i ignored this whole + + + align:start position:0% +so um so for years i ignored this whole +thing because i says like i don't know + + align:start position:0% +thing because i says like i don't know + + + align:start position:0% +thing because i says like i don't know +what these resting correlations are if i + + align:start position:0% +what these resting correlations are if i + + + align:start position:0% +what these resting correlations are if i +don't know what they are + + align:start position:0% +don't know what they are + + + align:start position:0% +don't know what they are +i'm not going to work on them + + align:start position:0% +i'm not going to work on them + + + align:start position:0% +i'm not going to work on them +and then um edon blank came along and + + align:start position:0% +and then um edon blank came along and + + + align:start position:0% +and then um edon blank came along and +when he was a first year grad student at + + align:start position:0% +when he was a first year grad student at + + + align:start position:0% +when he was a first year grad student at +federenco said hey we have all these + + align:start position:0% +federenco said hey we have all these + + + align:start position:0% +federenco said hey we have all these +resting functional data let's have you + + align:start position:0% +resting functional data let's have you + + + align:start position:0% +resting functional data let's have you +don + + align:start position:0% +don + + + align:start position:0% +don +for his rotation for a month analyze the + + align:start position:0% +for his rotation for a month analyze the + + + align:start position:0% +for his rotation for a month analyze the +resting functional data i said oh + + align:start position:0% +resting functional data i said oh + + + align:start position:0% +resting functional data i said oh +arresting functional we don't know what + + align:start position:0% +arresting functional we don't know what + + + align:start position:0% +arresting functional we don't know what +the hell it means let's not bother she's + + align:start position:0% +the hell it means let's not bother she's + + + align:start position:0% +the hell it means let's not bother she's +like get over yourself + + align:start position:0% +like get over yourself + + + align:start position:0% +like get over yourself +let's let him play with it + + align:start position:0% +let's let him play with it + + + align:start position:0% +let's let him play with it +well thank god she's not as stuck in her + + align:start position:0% +well thank god she's not as stuck in her + + + align:start position:0% +well thank god she's not as stuck in her +ways as i am because edon spent just a + + align:start position:0% +ways as i am because edon spent just a + + + align:start position:0% +ways as i am because edon spent just a +month playing with some of our data and + + align:start position:0% +month playing with some of our data and + + + align:start position:0% +month playing with some of our data and +what he found blew me away + + align:start position:0% +what he found blew me away + + + align:start position:0% +what he found blew me away +so um here's what he did he said okay + + align:start position:0% +so um here's what he did he said okay + + + align:start position:0% +so um here's what he did he said okay +let's start with + + align:start position:0% +let's start with + + + align:start position:0% +let's start with +actually identified regions of brain + + align:start position:0% +actually identified regions of brain + + + align:start position:0% +actually identified regions of brain +where we know something about what they + + align:start position:0% +where we know something about what they + + + align:start position:0% +where we know something about what they +do + + align:start position:0% +do + + + align:start position:0% +do +like the language system and the + + align:start position:0% +like the language system and the + + + align:start position:0% +like the language system and the +multiple demand system okay + + align:start position:0% +multiple demand system okay + + + align:start position:0% +multiple demand system okay +let's identify those regions in each + + align:start position:0% +let's identify those regions in each + + + align:start position:0% +let's identify those regions in each +subject individually + + align:start position:0% +subject individually + + + align:start position:0% +subject individually +and then let's scan subjects at rest + + align:start position:0% +and then let's scan subjects at rest + + + align:start position:0% +and then let's scan subjects at rest +okay so first + + align:start position:0% +okay so first + + + align:start position:0% +okay so first +you know first you scan subjects with + + align:start position:0% +you know first you scan subjects with + + + align:start position:0% +you know first you scan subjects with +sentences versus non-words you find the + + align:start position:0% +sentences versus non-words you find the + + + align:start position:0% +sentences versus non-words you find the +language regions then you scan them with + + align:start position:0% +language regions then you scan them with + + + align:start position:0% +language regions then you scan them with +a difficult versus easy spatial working + + align:start position:0% +a difficult versus easy spatial working + + + align:start position:0% +a difficult versus easy spatial working +memory task you find the multiple demand + + align:start position:0% +memory task you find the multiple demand + + + align:start position:0% +memory task you find the multiple demand +regions + + align:start position:0% +regions + + + align:start position:0% +regions +then you scan them at rest + + align:start position:0% +then you scan them at rest + + + align:start position:0% +then you scan them at rest +and you get the average time course + + align:start position:0% +and you get the average time course + + + align:start position:0% +and you get the average time course +from each of those regions at rest these + + align:start position:0% +from each of those regions at rest these + + + align:start position:0% +from each of those regions at rest these +are fake data just to give you the gist + + align:start position:0% +are fake data just to give you the gist + + + align:start position:0% +are fake data just to give you the gist +make sense are you with me now + + align:start position:0% +make sense are you with me now + + + align:start position:0% +make sense are you with me now +now you can ask okay which of these + + align:start position:0% +now you can ask okay which of these + + + align:start position:0% +now you can ask okay which of these +things are correlated with each other at + + align:start position:0% +things are correlated with each other at + + + align:start position:0% +things are correlated with each other at +rest + + align:start position:0% +rest + + + align:start position:0% +rest +and this is now a more interesting thing + + align:start position:0% +and this is now a more interesting thing + + + align:start position:0% +and this is now a more interesting thing +to do because we're asking this + + align:start position:0% +to do because we're asking this + + + align:start position:0% +to do because we're asking this +principled question of reasons we know + + align:start position:0% +principled question of reasons we know + + + align:start position:0% +principled question of reasons we know +something about rather than random seeds + + align:start position:0% +something about rather than random seeds + + + align:start position:0% +something about rather than random seeds +in some random location right + + align:start position:0% +in some random location right + + + align:start position:0% +in some random location right +okay so now + + align:start position:0% +okay so now + + + align:start position:0% +okay so now +what we do is we examine those + + align:start position:0% +what we do is we examine those + + + align:start position:0% +what we do is we examine those +correlations and we just ask for example + + align:start position:0% +correlations and we just ask for example + + + align:start position:0% +correlations and we just ask for example +how correlated are those time courses of + + align:start position:0% +how correlated are those time courses of + + + align:start position:0% +how correlated are those time courses of +two different language regions + + align:start position:0% +two different language regions + + + align:start position:0% +two different language regions +or those two different parts of the + + align:start position:0% +or those two different parts of the + + + align:start position:0% +or those two different parts of the +multiple demand system + + align:start position:0% +multiple demand system + + + align:start position:0% +multiple demand system +and + + align:start position:0% +and + + + align:start position:0% +and +how how strong are the correlations + + align:start position:0% +how how strong are the correlations + + + align:start position:0% +how how strong are the correlations +between the systems + + align:start position:0% +between the systems + + + align:start position:0% +between the systems +some little piece of the language system + + align:start position:0% +some little piece of the language system + + + align:start position:0% +some little piece of the language system +and some little piece of the multiple + + align:start position:0% +and some little piece of the multiple + + + align:start position:0% +and some little piece of the multiple +demand system + + align:start position:0% +demand system + + + align:start position:0% +demand system +makes sense + + align:start position:0% +makes sense + + + align:start position:0% +makes sense +so that's a cool question to ask + + align:start position:0% +so that's a cool question to ask + + + align:start position:0% +so that's a cool question to ask +and that's what edon did + + align:start position:0% +and that's what edon did + + + align:start position:0% +and that's what edon did +and here's what he found let me first + + align:start position:0% +and here's what he found let me first + + + align:start position:0% +and here's what he found let me first +orient you + + align:start position:0% +orient you + + + align:start position:0% +orient you +so here are lots and lots of regions of + + align:start position:0% +so here are lots and lots of regions of + + + align:start position:0% +so here are lots and lots of regions of +interest that were identified + + align:start position:0% +interest that were identified + + + align:start position:0% +interest that were identified +functionally a whole bunch of language + + align:start position:0% +functionally a whole bunch of language + + + align:start position:0% +functionally a whole bunch of language +regions up here a whole bunch of + + align:start position:0% +regions up here a whole bunch of + + + align:start position:0% +regions up here a whole bunch of +multiple demand regions down here the + + align:start position:0% +multiple demand regions down here the + + + align:start position:0% +multiple demand regions down here the +details don't matter okay + + align:start position:0% +details don't matter okay + + + align:start position:0% +details don't matter okay +but what i'm going to show you is in + + align:start position:0% +but what i'm going to show you is in + + + align:start position:0% +but what i'm going to show you is in +each cell we're going to have a + + align:start position:0% +each cell we're going to have a + + + align:start position:0% +each cell we're going to have a +correlation + + align:start position:0% +correlation + + + align:start position:0% +correlation +between a given so this would be a given + + align:start position:0% +between a given so this would be a given + + + align:start position:0% +between a given so this would be a given +part a cell over here given part of the + + align:start position:0% +part a cell over here given part of the + + + align:start position:0% +part a cell over here given part of the +multiple demand system and + + align:start position:0% +multiple demand system and + + + align:start position:0% +multiple demand system and +you know + + align:start position:0% +you know + + + align:start position:0% +you know +sorry given part of the multiple demand + + align:start position:0% +sorry given part of the multiple demand + + + align:start position:0% +sorry given part of the multiple demand +system and some other part of the + + align:start position:0% +system and some other part of the + + + align:start position:0% +system and some other part of the +multiple demand system + + align:start position:0% +multiple demand system + + + align:start position:0% +multiple demand system +or + + align:start position:0% +or + + + align:start position:0% +or +um over here a cell would be some part + + align:start position:0% +um over here a cell would be some part + + + align:start position:0% +um over here a cell would be some part +of the language system and some part the + + align:start position:0% +of the language system and some part the + + + align:start position:0% +of the language system and some part the +multiple demand system okay + + align:start position:0% +multiple demand system okay + + + align:start position:0% +multiple demand system okay +so + + align:start position:0% +so + + + align:start position:0% +so +when you do that here's what you see + + align:start position:0% +when you do that here's what you see + + + align:start position:0% +when you do that here's what you see +here are the correlations at rest + + align:start position:0% +here are the correlations at rest + + + align:start position:0% +here are the correlations at rest +between all of these pairs of conditions + + align:start position:0% +between all of these pairs of conditions + + + align:start position:0% +between all of these pairs of conditions +and if you squint a little you don't + + align:start position:0% +and if you squint a little you don't + + + align:start position:0% +and if you squint a little you don't +even have to squint much but the black + + align:start position:0% +even have to squint much but the black + + + align:start position:0% +even have to squint much but the black +ones are the ones that are not + + align:start position:0% +ones are the ones that are not + + + align:start position:0% +ones are the ones that are not +significantly correlated at all blue + + align:start position:0% +significantly correlated at all blue + + + align:start position:0% +significantly correlated at all blue +means a negative correlation and hot + + align:start position:0% +means a negative correlation and hot + + + align:start position:0% +means a negative correlation and hot +colors mean a positive correlation + + align:start position:0% +colors mean a positive correlation + + + align:start position:0% +colors mean a positive correlation +and so what you see is + + align:start position:0% +and so what you see is + + + align:start position:0% +and so what you see is +here are all the language regions + + align:start position:0% +here are all the language regions + + + align:start position:0% +here are all the language regions +these are the right hemisphere language + + align:start position:0% +these are the right hemisphere language + + + align:start position:0% +these are the right hemisphere language +regions which barely even count they're + + align:start position:0% +regions which barely even count they're + + + align:start position:0% +regions which barely even count they're +not they're just there for the hell of + + align:start position:0% +not they're just there for the hell of + + + align:start position:0% +not they're just there for the hell of +it + + align:start position:0% +it + + + align:start position:0% +it +this is really the core language regions + + align:start position:0% +this is really the core language regions + + + align:start position:0% +this is really the core language regions +and you can see they're all correlated + + align:start position:0% +and you can see they're all correlated + + + align:start position:0% +and you can see they're all correlated +with each other + + align:start position:0% +with each other + + + align:start position:0% +with each other +even ones that are really far apart + + align:start position:0% +even ones that are really far apart + + + align:start position:0% +even ones that are really far apart +broca's area and wernicke's area 10 12 + + align:start position:0% +broca's area and wernicke's area 10 12 + + + align:start position:0% +broca's area and wernicke's area 10 12 +centimeters apart strongly correlated at + + align:start position:0% +centimeters apart strongly correlated at + + + align:start position:0% +centimeters apart strongly correlated at +rest + + align:start position:0% +rest + + + align:start position:0% +rest +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and if you look at different parts of + + align:start position:0% +and if you look at different parts of + + + align:start position:0% +and if you look at different parts of +the multiple demand system + + align:start position:0% +the multiple demand system + + + align:start position:0% +the multiple demand system +they're all strongly correlated at rest + + align:start position:0% +they're all strongly correlated at rest + + + align:start position:0% +they're all strongly correlated at rest +even regions that are far apart + + align:start position:0% +even regions that are far apart + + + align:start position:0% +even regions that are far apart +something way up in the frontal lobe + + align:start position:0% +something way up in the frontal lobe + + + align:start position:0% +something way up in the frontal lobe +something way back in the parietal lobe + + align:start position:0% +something way back in the parietal lobe + + + align:start position:0% +something way back in the parietal lobe +strongly correlated at rest + + align:start position:0% +strongly correlated at rest + + + align:start position:0% +strongly correlated at rest +and so + + align:start position:0% +and so + + + align:start position:0% +and so +um + + align:start position:0% +um + + + align:start position:0% +um +and so yeah if you zoom in here + + align:start position:0% +and so yeah if you zoom in here + + + align:start position:0% +and so yeah if you zoom in here +so what this is really + + align:start position:0% +so what this is really + + + align:start position:0% +so what this is really +does everybody see that this is really + + align:start position:0% +does everybody see that this is really + + + align:start position:0% +does everybody see that this is really +revealing a lot of structure yeah + + align:start position:0% +revealing a lot of structure yeah + + + align:start position:0% +revealing a lot of structure yeah +question so the diagonal should be like + + align:start position:0% +question so the diagonal should be like + + + align:start position:0% +question so the diagonal should be like +self-correlation green yeah that's why + + align:start position:0% +self-correlation green yeah that's why + + + align:start position:0% +self-correlation green yeah that's why +it's black + + align:start position:0% +it's black + + + align:start position:0% +it's black +i don't i black + + align:start position:0% +i don't i black + + + align:start position:0% +i don't i black +uh + + align:start position:0% +uh + + + align:start position:0% +uh +actually what is it oh you know what it + + align:start position:0% +actually what is it oh you know what it + + + align:start position:0% +actually what is it oh you know what it +split half a split half + + align:start position:0% +split half a split half + + + align:start position:0% +split half a split half +it's actually a better way to do it you + + align:start position:0% +it's actually a better way to do it you + + + align:start position:0% +it's actually a better way to do it you +take your data and you have two + + align:start position:0% +take your data and you have two + + + align:start position:0% +take your data and you have two +different halves of the data and so it + + align:start position:0% +different halves of the data and so it + + + align:start position:0% +different halves of the data and so it +gives you a baseline for for the no that + + align:start position:0% +gives you a baseline for for the no that + + + align:start position:0% +gives you a baseline for for the no that +doesn't make any sense does it never + + align:start position:0% +doesn't make any sense does it never + + + align:start position:0% +doesn't make any sense does it never +mind yeah + + align:start position:0% +mind yeah + + + align:start position:0% +mind yeah +it's dark red + + align:start position:0% + + + + align:start position:0% + +it is maroon + + align:start position:0% +it is maroon + + + align:start position:0% +it is maroon +um + + align:start position:0% +um + + + align:start position:0% +um +if you look at the spectrum on the + + align:start position:0% +if you look at the spectrum on the + + + align:start position:0% +if you look at the spectrum on the +bottom + + align:start position:0% + + + + align:start position:0% + +all right i'm gonna have to solve this + + align:start position:0% +all right i'm gonna have to solve this + + + align:start position:0% +all right i'm gonna have to solve this +offline because i'm now confused unless + + align:start position:0% +offline because i'm now confused unless + + + align:start position:0% +offline because i'm now confused unless +anya can figure it out right now and + + align:start position:0% +anya can figure it out right now and + + + align:start position:0% +anya can figure it out right now and +bail us out + + align:start position:0% +bail us out + + + align:start position:0% +bail us out +yeah but as they're pointing out it's + + align:start position:0% +yeah but as they're pointing out it's + + + align:start position:0% +yeah but as they're pointing out it's +not black it's some other okay + + align:start position:0% +not black it's some other okay + + + align:start position:0% +not black it's some other okay +i'm saying it should be high that's what + + align:start position:0% +i'm saying it should be high that's what + + + align:start position:0% +i'm saying it should be high that's what +i was just wondering why oh it's a + + align:start position:0% +i was just wondering why oh it's a + + + align:start position:0% +i was just wondering why oh it's a +correlation of one is that what it is + + align:start position:0% +correlation of one is that what it is + + + align:start position:0% +correlation of one is that what it is +okay because it's correlated with itself + + align:start position:0% +okay because it's correlated with itself + + + align:start position:0% +okay because it's correlated with itself +all right okay thank you + + align:start position:0% +all right okay thank you + + + align:start position:0% +all right okay thank you +uh anyway does everybody get the pat the + + align:start position:0% +uh anyway does everybody get the pat the + + + align:start position:0% +uh anyway does everybody get the pat the +the gist that all of these different + + align:start position:0% +the gist that all of these different + + + align:start position:0% +the gist that all of these different +pieces of the multiple demand system + + align:start position:0% +pieces of the multiple demand system + + + align:start position:0% +pieces of the multiple demand system +that we identified individually + + align:start position:0% +that we identified individually + + + align:start position:0% +that we identified individually +they're all correlated with each other + + align:start position:0% +they're all correlated with each other + + + align:start position:0% +they're all correlated with each other +at rest + + align:start position:0% +at rest + + + align:start position:0% +at rest +all these different pieces of the + + align:start position:0% +all these different pieces of the + + + align:start position:0% +all these different pieces of the +language system are correlated with each + + align:start position:0% +language system are correlated with each + + + align:start position:0% +language system are correlated with each +other at rest + + align:start position:0% +other at rest + + + align:start position:0% +other at rest +and there's no correlation at all + + align:start position:0% +and there's no correlation at all + + + align:start position:0% +and there's no correlation at all +between any part of the language system + + align:start position:0% +between any part of the language system + + + align:start position:0% +between any part of the language system +and any part of the multiple man system + + align:start position:0% +and any part of the multiple man system + + + align:start position:0% +and any part of the multiple man system +at rest + + align:start position:0% +at rest + + + align:start position:0% +at rest +all of these can maybe a couple + + align:start position:0% +all of these can maybe a couple + + + align:start position:0% +all of these can maybe a couple +these cells are all either black for not + + align:start position:0% +these cells are all either black for not + + + align:start position:0% +these cells are all either black for not +significant or inversely correlated + + align:start position:0% +significant or inversely correlated + + + align:start position:0% +significant or inversely correlated +that's the cool colors + + align:start position:0% +that's the cool colors + + + align:start position:0% +that's the cool colors +so do you see how this gives us + + align:start position:0% +so do you see how this gives us + + + align:start position:0% +so do you see how this gives us +a totally cool way aside from just the + + align:start position:0% +a totally cool way aside from just the + + + align:start position:0% +a totally cool way aside from just the +functional localizers we ran to identify + + align:start position:0% +functional localizers we ran to identify + + + align:start position:0% +functional localizers we ran to identify +these regions + + align:start position:0% +these regions + + + align:start position:0% +these regions +to show us that these things are + + align:start position:0% +to show us that these things are + + + align:start position:0% +to show us that these things are +functioning as a system + + align:start position:0% +functioning as a system + + + align:start position:0% +functioning as a system +right it's not just that broca's area is + + align:start position:0% +right it's not just that broca's area is + + + align:start position:0% +right it's not just that broca's area is +a cool little thing that does a piece of + + align:start position:0% +a cool little thing that does a piece of + + + align:start position:0% +a cool little thing that does a piece of +language + + align:start position:0% +language + + + align:start position:0% +language +and some bit of the temporal lobe is a + + align:start position:0% +and some bit of the temporal lobe is a + + + align:start position:0% +and some bit of the temporal lobe is a +cool thing that does some piece of + + align:start position:0% +cool thing that does some piece of + + + align:start position:0% +cool thing that does some piece of +language but those guys are part of a + + align:start position:0% +language but those guys are part of a + + + align:start position:0% +language but those guys are part of a +broader system and these resting + + align:start position:0% +broader system and these resting + + + align:start position:0% +broader system and these resting +functional correlations are revealing + + align:start position:0% +functional correlations are revealing + + + align:start position:0% +functional correlations are revealing +this broader system and the integrity of + + align:start position:0% +this broader system and the integrity of + + + align:start position:0% +this broader system and the integrity of +the parts within it as well as the + + align:start position:0% +the parts within it as well as the + + + align:start position:0% +the parts within it as well as the +distinction between those parts and + + align:start position:0% +distinction between those parts and + + + align:start position:0% +distinction between those parts and +parts of another system or network does + + align:start position:0% +parts of another system or network does + + + align:start position:0% +parts of another system or network does +everybody get that idea + + align:start position:0% +everybody get that idea + + + align:start position:0% +everybody get that idea +good that's a big idea for this lecture + + align:start position:0% +good that's a big idea for this lecture + + + align:start position:0% +good that's a big idea for this lecture +i think what i'll do + + align:start position:0% +i think what i'll do + + + align:start position:0% +i think what i'll do +so you can + + align:start position:0% +so you can + + + align:start position:0% +so you can +skip that you can do this you can also + + align:start position:0% +skip that you can do this you can also + + + align:start position:0% +skip that you can do this you can also +so this is basically the correlation + + align:start position:0% +so this is basically the correlation + + + align:start position:0% +so this is basically the correlation +between all of the cells within the + + align:start position:0% +between all of the cells within the + + + align:start position:0% +between all of the cells within the +language system + + align:start position:0% +language system + + + align:start position:0% +language system +all of the cells within the multiple + + align:start position:0% +all of the cells within the multiple + + + align:start position:0% +all of the cells within the multiple +demand system and any pair of cells + + align:start position:0% +demand system and any pair of cells + + + align:start position:0% +demand system and any pair of cells +between systems here so that's just + + align:start position:0% +between systems here so that's just + + + align:start position:0% +between systems here so that's just +averaging over the matrix i showed you + + align:start position:0% +averaging over the matrix i showed you + + + align:start position:0% +averaging over the matrix i showed you +before + + align:start position:0% +before + + + align:start position:0% +before +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so + + align:start position:0% +and so + + + align:start position:0% +and so +this is a cool way to ask about broader + + align:start position:0% +this is a cool way to ask about broader + + + align:start position:0% +this is a cool way to ask about broader +systems in the brain + + align:start position:0% +systems in the brain + + + align:start position:0% +systems in the brain +and i was going to show you some data + + align:start position:0% +and i was going to show you some data + + + align:start position:0% +and i was going to show you some data +published just a month ago that asked + + align:start position:0% +published just a month ago that asked + + + align:start position:0% +published just a month ago that asked +this question not just about the + + align:start position:0% +this question not just about the + + + align:start position:0% +this question not just about the +language and multiple demand systems but + + align:start position:0% +language and multiple demand systems but + + + align:start position:0% +language and multiple demand systems but +also about the + + align:start position:0% +also about the + + + align:start position:0% +also about the +the theory of mind + + align:start position:0% +the theory of mind + + + align:start position:0% +the theory of mind +network which is basically really + + align:start position:0% +network which is basically really + + + align:start position:0% +network which is basically really +similar to the fault mode network but + + align:start position:0% +similar to the fault mode network but + + + align:start position:0% +similar to the fault mode network but +the theory of mind network we can + + align:start position:0% +the theory of mind network we can + + + align:start position:0% +the theory of mind network we can +identify that we talked about last time + + align:start position:0% +identify that we talked about last time + + + align:start position:0% +identify that we talked about last time +and you can go think offline actually + + align:start position:0% +and you can go think offline actually + + + align:start position:0% +and you can go think offline actually +i'll take a suggestion what do you think + + align:start position:0% +i'll take a suggestion what do you think + + + align:start position:0% +i'll take a suggestion what do you think +should the theory of mind network + + align:start position:0% +should the theory of mind network + + + align:start position:0% +should the theory of mind network +be correlated with the language system + + align:start position:0% +be correlated with the language system + + + align:start position:0% +be correlated with the language system +with the multiple demand system both or + + align:start position:0% +with the multiple demand system both or + + + align:start position:0% +with the multiple demand system both or +neither + + align:start position:0% +neither + + + align:start position:0% +neither +either neither + + align:start position:0% +either neither + + + align:start position:0% +either neither +why + + align:start position:0% +why + + + align:start position:0% +why +something different okay that's a + + align:start position:0% +something different okay that's a + + + align:start position:0% +something different okay that's a +totally reasonable answer and that's + + align:start position:0% +totally reasonable answer and that's + + + align:start position:0% +totally reasonable answer and that's +largely true but not 100 true what else + + align:start position:0% +largely true but not 100 true what else + + + align:start position:0% +largely true but not 100 true what else +might you think it is a different system + + align:start position:0% +might you think it is a different system + + + align:start position:0% +might you think it is a different system +and it does function + + align:start position:0% +and it does function + + + align:start position:0% +and it does function +quite independently but not perfectly + + align:start position:0% +quite independently but not perfectly + + + align:start position:0% +quite independently but not perfectly +yeah + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +all right that's a lovely a lovely + + align:start position:0% +all right that's a lovely a lovely + + + align:start position:0% +all right that's a lovely a lovely +speculation and an intelligent one and + + align:start position:0% +speculation and an intelligent one and + + + align:start position:0% +speculation and an intelligent one and +it's half true i'll just skip to the + + align:start position:0% +it's half true i'll just skip to the + + + align:start position:0% +it's half true i'll just skip to the +data + + align:start position:0% +data + + + align:start position:0% +data +so in this very recently published paper + + align:start position:0% +so in this very recently published paper + + + align:start position:0% +so in this very recently published paper +um + + align:start position:0% +um + + + align:start position:0% +um +uh alex poundoff and edom blanket of + + align:start position:0% +uh alex poundoff and edom blanket of + + + align:start position:0% +uh alex poundoff and edom blanket of +federenko looked at the language system + + align:start position:0% +federenko looked at the language system + + + align:start position:0% +federenko looked at the language system +the theory of mind network which is not + + align:start position:0% +the theory of mind network which is not + + + align:start position:0% +the theory of mind network which is not +just a tbj but these other regions that + + align:start position:0% +just a tbj but these other regions that + + + align:start position:0% +just a tbj but these other regions that +i mentioned briefly that you also get in + + align:start position:0% +i mentioned briefly that you also get in + + + align:start position:0% +i mentioned briefly that you also get in +the contrast of the false belief task + + align:start position:0% +the contrast of the false belief task + + + align:start position:0% +the contrast of the false belief task +versus a false photo task and the + + align:start position:0% +versus a false photo task and the + + + align:start position:0% +versus a false photo task and the +multiple demand network same deal + + align:start position:0% +multiple demand network same deal + + + align:start position:0% +multiple demand network same deal +identify each of those regions in each + + align:start position:0% +identify each of those regions in each + + + align:start position:0% +identify each of those regions in each +subject individually + + align:start position:0% +subject individually + + + align:start position:0% +subject individually +then scan the subject at rest and see + + align:start position:0% +then scan the subject at rest and see + + + align:start position:0% +then scan the subject at rest and see +what's correlated with what + + align:start position:0% +what's correlated with what + + + align:start position:0% +what's correlated with what +and + + align:start position:0% +and + + + align:start position:0% +and +here's the answer you see again + + align:start position:0% +here's the answer you see again + + + align:start position:0% +here's the answer you see again +replicate the language system especially + + align:start position:0% +replicate the language system especially + + + align:start position:0% +replicate the language system especially +in the left hemisphere + + align:start position:0% +in the left hemisphere + + + align:start position:0% +in the left hemisphere +the theory of mind system is all a + + align:start position:0% +the theory of mind system is all a + + + align:start position:0% +the theory of mind system is all a +system + + align:start position:0% +system + + + align:start position:0% +system +and the multiple demand system is a + + align:start position:0% +and the multiple demand system is a + + + align:start position:0% +and the multiple demand system is a +system separate system + + align:start position:0% +system separate system + + + align:start position:0% +system separate system +but if you look in at the cell where you + + align:start position:0% +but if you look in at the cell where you + + + align:start position:0% +but if you look in at the cell where you +have + + align:start position:0% +have + + + align:start position:0% +have +theory of mind and + + align:start position:0% +theory of mind and + + + align:start position:0% +theory of mind and +language + + align:start position:0% +language + + + align:start position:0% +language +it's slightly above chance + + align:start position:0% +it's slightly above chance + + + align:start position:0% +it's slightly above chance +not theory of mind and multiple demand + + align:start position:0% +not theory of mind and multiple demand + + + align:start position:0% +not theory of mind and multiple demand +the theory of mind and language probably + + align:start position:0% +the theory of mind and language probably + + + align:start position:0% +the theory of mind and language probably +for just the reason you said the whole + + align:start position:0% +for just the reason you said the whole + + + align:start position:0% +for just the reason you said the whole +essence of language even though it's a + + align:start position:0% +essence of language even though it's a + + + align:start position:0% +essence of language even though it's a +different thing than thinking about the + + align:start position:0% +different thing than thinking about the + + + align:start position:0% +different thing than thinking about the +contents of someone else's thoughts they + + align:start position:0% +contents of someone else's thoughts they + + + align:start position:0% +contents of someone else's thoughts they +are so enmeshed in each other the reason + + align:start position:0% +are so enmeshed in each other the reason + + + align:start position:0% +are so enmeshed in each other the reason +we have language is to take our thoughts + + align:start position:0% +we have language is to take our thoughts + + + align:start position:0% +we have language is to take our thoughts +and put them in your head and take your + + align:start position:0% +and put them in your head and take your + + + align:start position:0% +and put them in your head and take your +thoughts and put them in our head + + align:start position:0% +thoughts and put them in our head + + + align:start position:0% +thoughts and put them in our head +and so + + align:start position:0% +and so + + + align:start position:0% +and so +it makes sense that those things are a + + align:start position:0% +it makes sense that those things are a + + + align:start position:0% +it makes sense that those things are a +little bit correlated + + align:start position:0% + + + + align:start position:0% + +language yeah yeah + + align:start position:0% +language yeah yeah + + + align:start position:0% +language yeah yeah +but neither of them is correlated with + + align:start position:0% +but neither of them is correlated with + + + align:start position:0% +but neither of them is correlated with +multiple demand + + align:start position:0% +multiple demand + + + align:start position:0% +multiple demand +it's 126 so + + align:start position:0% +it's 126 so + + + align:start position:0% +it's 126 so +wait one point whatever am i reading the + + align:start position:0% +wait one point whatever am i reading the + + + align:start position:0% +wait one point whatever am i reading the +wrong yeah oh 12 28 sorry + + align:start position:0% +wrong yeah oh 12 28 sorry + + + align:start position:0% +wrong yeah oh 12 28 sorry +uh it's like there's a number here + + align:start position:0% +uh it's like there's a number here + + + align:start position:0% +uh it's like there's a number here +that's how long i've been talking so um + + align:start position:0% +that's how long i've been talking so um + + + align:start position:0% +that's how long i've been talking so um +12 28 so if you need to go that's fine + + align:start position:0% +12 28 so if you need to go that's fine + + + align:start position:0% +12 28 so if you need to go that's fine +but i'm happy to answer questions so go + + align:start position:0% +but i'm happy to answer questions so go + + + align:start position:0% +but i'm happy to answer questions so go +ahead + + align:start position:0% +ahead + + + align:start position:0% +ahead +there was a review speaker by like + + align:start position:0% +there was a review speaker by like + + + align:start position:0% +there was a review speaker by like +science and bear and growing talk about + + align:start position:0% +science and bear and growing talk about + + + align:start position:0% +science and bear and growing talk about +how there was like a behavioral + + align:start position:0% +how there was like a behavioral + + + align:start position:0% +how there was like a behavioral +dimension between their mind and like + + align:start position:0% +dimension between their mind and like + + + align:start position:0% +dimension between their mind and like +when children started to learn + + align:start position:0% +when children started to learn + + + align:start position:0% +when children started to learn +lots of links especially developmentally + + align:start position:0% +lots of links especially developmentally + + + align:start position:0% +lots of links especially developmentally +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah did you have a by an extension of + + align:start position:0% +yeah did you have a by an extension of + + + align:start position:0% +yeah did you have a by an extension of +that hypothesis + + align:start position:0% + + + + align:start position:0% + +okay should be coordinated with the + + align:start position:0% +okay should be coordinated with the + + + align:start position:0% +okay should be coordinated with the +theory of mind + + align:start position:0% +theory of mind + + + align:start position:0% +theory of mind +yes wouldn't you think + + align:start position:0% +yes wouldn't you think + + + align:start position:0% +yes wouldn't you think +not + + align:start position:0% +not + + + align:start position:0% +not +really ffa is irritating it's not + + align:start position:0% +really ffa is irritating it's not + + + align:start position:0% +really ffa is irritating it's not +strongly correlated with the things that + + align:start position:0% +strongly correlated with the things that + + + align:start position:0% +strongly correlated with the things that +ought to be correlated with + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/So_UGo4dSJs.txt b/So_UGo4dSJs.txt new file mode 100644 index 0000000000000000000000000000000000000000..e5d8363ca275564a8c21268983b3e8dee8c0f7dc --- /dev/null +++ b/So_UGo4dSJs.txt @@ -0,0 +1,8432 @@ +align:start position:0% + +okay why don't we get + + align:start position:0% +okay why don't we get + + + align:start position:0% +okay why don't we get +started we're going to switch topics + + align:start position:0% +started we're going to switch topics + + + align:start position:0% +started we're going to switch topics +today and we're going to talk about a + + align:start position:0% +today and we're going to talk about a + + + align:start position:0% +today and we're going to talk about a +different class of power converter + + align:start position:0% +different class of power converter + + + align:start position:0% +different class of power converter +circuit uh called an inverter so + + align:start position:0% + + + + align:start position:0% + +inverters or DC to AC + + align:start position:0% + + + + align:start position:0% + +converters uh are important for a lot of + + align:start position:0% +converters uh are important for a lot of + + + align:start position:0% +converters uh are important for a lot of +applications right so if you're going to + + align:start position:0% +applications right so if you're going to + + + align:start position:0% +applications right so if you're going to +build a motor drive a lot of motors need + + align:start position:0% +build a motor drive a lot of motors need + + + align:start position:0% +build a motor drive a lot of motors need +to run off AC if you're going to have an + + align:start position:0% +to run off AC if you're going to have an + + + align:start position:0% +to run off AC if you're going to have an +uninterruptible power supply to power + + align:start position:0% +uninterruptible power supply to power + + + align:start position:0% +uninterruptible power supply to power +your AC powered devices when the grid + + align:start position:0% +your AC powered devices when the grid + + + align:start position:0% +your AC powered devices when the grid +goes out you need it if you're getting + + align:start position:0% +goes out you need it if you're getting + + + align:start position:0% +goes out you need it if you're getting +power from a a wind turbine or or for + + align:start position:0% +power from a a wind turbine or or for + + + align:start position:0% +power from a a wind turbine or or for +example a DC solar panel you need to + + align:start position:0% +example a DC solar panel you need to + + + align:start position:0% +example a DC solar panel you need to +take that and convert it into AC in + + align:start position:0% +take that and convert it into AC in + + + align:start position:0% +take that and convert it into AC in +order to feed the power into the grid so + + align:start position:0% +order to feed the power into the grid so + + + align:start position:0% +order to feed the power into the grid so +there's a lot of where you need to come + + align:start position:0% +there's a lot of where you need to come + + + align:start position:0% +there's a lot of where you need to come +from + + align:start position:0% +from + + + align:start position:0% +from +DC input input out AC output um this is + + align:start position:0% +DC input input out AC output um this is + + + align:start position:0% +DC input input out AC output um this is +the topic of + + align:start position:0% +the topic of + + + align:start position:0% +the topic of +kpvs chapter + + align:start position:0% + + + + align:start position:0% + +8 and we're going to spend the next few + + align:start position:0% +8 and we're going to spend the next few + + + align:start position:0% +8 and we're going to spend the next few +lectures talking about some of the the + + align:start position:0% +lectures talking about some of the the + + + align:start position:0% +lectures talking about some of the the +issues associated with DC AC + + align:start position:0% +issues associated with DC AC + + + align:start position:0% +issues associated with DC AC +conversion now before we jump into that + + align:start position:0% +conversion now before we jump into that + + + align:start position:0% +conversion now before we jump into that +let's just have a really Brief Review of + + align:start position:0% +let's just have a really Brief Review of + + + align:start position:0% +let's just have a really Brief Review of +expressing waveforms the periodic + + align:start position:0% +expressing waveforms the periodic + + + align:start position:0% +expressing waveforms the periodic +waveforms in terms of 4A series just + + align:start position:0% +waveforms in terms of 4A series just + + + align:start position:0% +waveforms in terms of 4A series just +because it's going to be really useful + + align:start position:0% +because it's going to be really useful + + + align:start position:0% +because it's going to be really useful +in thinking about what kinds of AC + + align:start position:0% +in thinking about what kinds of AC + + + align:start position:0% +in thinking about what kinds of AC +waveforms might we want to Sy synthesize + + align:start position:0% +waveforms might we want to Sy synthesize + + + align:start position:0% +waveforms might we want to Sy synthesize +right so if I have a periodic waveform F + + align:start position:0% +right so if I have a periodic waveform F + + + align:start position:0% +right so if I have a periodic waveform F +of + + align:start position:0% +of + + + align:start position:0% +of +T right I might Express that as some DC + + align:start position:0% +T right I might Express that as some DC + + + align:start position:0% +T right I might Express that as some DC +term + + align:start position:0% +term + + + align:start position:0% +term +plus um Nal 1 to Infinity of a subn sin + + align:start position:0% +plus um Nal 1 to Infinity of a subn sin + + + align:start position:0% +plus um Nal 1 to Infinity of a subn sin +of n Omega + + align:start position:0% +of n Omega + + + align:start position:0% +of n Omega +t plus b subn + + align:start position:0% +t plus b subn + + + align:start position:0% +t plus b subn +cosine of n Omega T where the this is + + align:start position:0% +cosine of n Omega T where the this is + + + align:start position:0% +cosine of n Omega T where the this is +the angular frequency associated with + + align:start position:0% +the angular frequency associated with + + + align:start position:0% +the angular frequency associated with +the fundamental period capital T So + + align:start position:0% +the fundamental period capital T So + + + align:start position:0% +the fundamental period capital T So +Omega KN is equal to 2 pi over the + + align:start position:0% +Omega KN is equal to 2 pi over the + + + align:start position:0% +Omega KN is equal to 2 pi over the +period and then we can go find using + + align:start position:0% +period and then we can go find using + + + align:start position:0% +period and then we can go find using +orthogonality the expression to uh get + + align:start position:0% +orthogonality the expression to uh get + + + align:start position:0% +orthogonality the expression to uh get +the 4 a series coefficients so a subn + + align:start position:0% +the 4 a series coefficients so a subn + + + align:start position:0% +the 4 a series coefficients so a subn +would be equal to 2 over T the integral + + align:start position:0% +would be equal to 2 over T the integral + + + align:start position:0% +would be equal to 2 over T the integral +over T of f of t + + align:start position:0% +over T of f of t + + + align:start position:0% +over T of f of t +s of n Omega T DT and B subn would + + align:start position:0% +s of n Omega T DT and B subn would + + + align:start position:0% +s of n Omega T DT and B subn would +simply be 2 over T integral over + + align:start position:0% +simply be 2 over T integral over + + + align:start position:0% +simply be 2 over T integral over +t f of T cosine of n Omega T DT okay so + + align:start position:0% +t f of T cosine of n Omega T DT okay so + + + align:start position:0% +t f of T cosine of n Omega T DT okay so +I can take any periodic waveform break + + align:start position:0% +I can take any periodic waveform break + + + align:start position:0% +I can take any periodic waveform break +it down into uh some Harmon fundamental + + align:start position:0% +it down into uh some Harmon fundamental + + + align:start position:0% +it down into uh some Harmon fundamental +and Har DC fundamental and harmonic + + align:start position:0% +and Har DC fundamental and harmonic + + + align:start position:0% +and Har DC fundamental and harmonic +description and one way to do that is in + + align:start position:0% +description and one way to do that is in + + + align:start position:0% +description and one way to do that is in +terms of s and cosine components and + + align:start position:0% +terms of s and cosine components and + + + align:start position:0% +terms of s and cosine components and +we'll see why we picked this particular + + align:start position:0% +we'll see why we picked this particular + + + align:start position:0% +we'll see why we picked this particular +representation + + align:start position:0% +representation + + + align:start position:0% +representation +shortly okay so it turns out that + + align:start position:0% +shortly okay so it turns out that + + + align:start position:0% +shortly okay so it turns out that +different + + align:start position:0% +different + + + align:start position:0% +different +waveforms have um different special + + align:start position:0% +waveforms have um different special + + + align:start position:0% +waveforms have um different special +characteristics all right so I'd like to + + align:start position:0% +characteristics all right so I'd like to + + + align:start position:0% +characteristics all right so I'd like to +think about a + + align:start position:0% +think about a + + + align:start position:0% +think about a +few uh different kinds of waveforms and + + align:start position:0% +few uh different kinds of waveforms and + + + align:start position:0% +few uh different kinds of waveforms and +some of this you've seen some of this um + + align:start position:0% +some of this you've seen some of this um + + + align:start position:0% +some of this you've seen some of this um +maybe will be a little bit less familiar + + align:start position:0% +maybe will be a little bit less familiar + + + align:start position:0% +maybe will be a little bit less familiar +the first kind of waveform we might + + align:start position:0% +the first kind of waveform we might + + + align:start position:0% +the first kind of waveform we might +think of is an even + + align:start position:0% +think of is an even + + + align:start position:0% +think of is an even +waveform right what does it mean for a + + align:start position:0% +waveform right what does it mean for a + + + align:start position:0% +waveform right what does it mean for a +waveform to be even um if I have t in + + align:start position:0% +waveform to be even um if I have t in + + + align:start position:0% +waveform to be even um if I have t in +even waveform looks symmetric about t + + align:start position:0% +even waveform looks symmetric about t + + + align:start position:0% +even waveform looks symmetric about t +equals z okay so it flips about t equal + + align:start position:0% +equals z okay so it flips about t equal + + + align:start position:0% +equals z okay so it flips about t equal +Z so maybe I have a waveform that looks + + align:start position:0% +Z so maybe I have a waveform that looks + + + align:start position:0% +Z so maybe I have a waveform that looks +like this say this is T over2 and this + + align:start position:0% +like this say this is T over2 and this + + + align:start position:0% +like this say this is T over2 and this +is minus t + + align:start position:0% +is minus t + + + align:start position:0% +is minus t +over2 okay and it might look like this + + align:start position:0% +over2 okay and it might look like this + + + align:start position:0% +over2 okay and it might look like this +for example okay so if I just flip it + + align:start position:0% +for example okay so if I just flip it + + + align:start position:0% +for example okay so if I just flip it +about T equals z nothing + + align:start position:0% +about T equals z nothing + + + align:start position:0% +about T equals z nothing +changes + + align:start position:0% +changes + + + align:start position:0% +changes +okay well why might I care about an even + + align:start position:0% +okay well why might I care about an even + + + align:start position:0% +okay well why might I care about an even +waveform um because all the a subn + + align:start position:0% +waveform um because all the a subn + + + align:start position:0% +waveform um because all the a subn +terms are zero in that case right uh one + + align:start position:0% +terms are zero in that case right uh one + + + align:start position:0% +terms are zero in that case right uh one +way to think about that is how do I find + + align:start position:0% +way to think about that is how do I find + + + align:start position:0% +way to think about that is how do I find +the a subn terms I + + align:start position:0% +the a subn terms I + + + align:start position:0% +the a subn terms I +take F of T if this is f of + + align:start position:0% +take F of T if this is f of + + + align:start position:0% +take F of T if this is f of +T and I multip multiply it by sin n + + align:start position:0% +T and I multip multiply it by sin n + + + align:start position:0% +T and I multip multiply it by sin n +Omega T So if I multip it by sin Omega T + + align:start position:0% +Omega T So if I multip it by sin Omega T + + + align:start position:0% +Omega T So if I multip it by sin Omega T +maybe I'd be multiplying it by something + + align:start position:0% +maybe I'd be multiplying it by something + + + align:start position:0% +maybe I'd be multiplying it by something +like looks like this + + align:start position:0% +like looks like this + + + align:start position:0% +like looks like this +um and then i' take the White and the + + align:start position:0% +um and then i' take the White and the + + + align:start position:0% +um and then i' take the White and the +orange and multiply them and integrate + + align:start position:0% +orange and multiply them and integrate + + + align:start position:0% +orange and multiply them and integrate +them and whatever's over + + align:start position:0% +them and whatever's over + + + align:start position:0% +them and whatever's over +here exactly is the negative of what's + + align:start position:0% +here exactly is the negative of what's + + + align:start position:0% +here exactly is the negative of what's +over here and I get + + align:start position:0% +over here and I get + + + align:start position:0% +over here and I get +zero okay in the integral when I + + align:start position:0% +zero okay in the integral when I + + + align:start position:0% +zero okay in the integral when I +integrate it out right so one way to + + align:start position:0% +integrate it out right so one way to + + + align:start position:0% +integrate it out right so one way to +think about it is that uh an even times + + align:start position:0% +think about it is that uh an even times + + + align:start position:0% +think about it is that uh an even times +an odd is odd and then when I take the + + align:start position:0% +an odd is odd and then when I take the + + + align:start position:0% +an odd is odd and then when I take the +integral or of an odd waveform I get + + align:start position:0% +integral or of an odd waveform I get + + + align:start position:0% +integral or of an odd waveform I get +zero okay another way to think about it + + align:start position:0% +zero okay another way to think about it + + + align:start position:0% +zero okay another way to think about it +is signs are odd + + align:start position:0% +is signs are odd + + + align:start position:0% +is signs are odd +waveforms and this is an even waveform + + align:start position:0% +waveforms and this is an even waveform + + + align:start position:0% +waveforms and this is an even waveform +so it makes sense that I ought to build + + align:start position:0% +so it makes sense that I ought to build + + + align:start position:0% +so it makes sense that I ought to build +an even waveform out of even components + + align:start position:0% +an even waveform out of even components + + + align:start position:0% +an even waveform out of even components +right and the cosine terms are the even + + align:start position:0% +right and the cosine terms are the even + + + align:start position:0% +right and the cosine terms are the even +components of my 4A Series so an even + + align:start position:0% +components of my 4A Series so an even + + + align:start position:0% +components of my 4A Series so an even +waveform will only have B subn ter B + + align:start position:0% +waveform will only have B subn ter B + + + align:start position:0% +waveform will only have B subn ter B +subn terms right only cosines and DC + + align:start position:0% +subn terms right only cosines and DC + + + align:start position:0% +subn terms right only cosines and DC +okay uh of course we can also have an + + align:start position:0% +okay uh of course we can also have an + + + align:start position:0% +okay uh of course we can also have an +odd + + align:start position:0% +odd + + + align:start position:0% +odd +waveform right uh even is X of T is + + align:start position:0% +waveform right uh even is X of T is + + + align:start position:0% +waveform right uh even is X of T is +equal to X of minus t right it flips + + align:start position:0% +equal to X of minus t right it flips + + + align:start position:0% +equal to X of minus t right it flips +about the T equals z axis odd is X of T + + align:start position:0% +about the T equals z axis odd is X of T + + + align:start position:0% +about the T equals z axis odd is X of T +is equal to Min - x of minus t okay so + + align:start position:0% +is equal to Min - x of minus t okay so + + + align:start position:0% +is equal to Min - x of minus t okay so +what does that + + align:start position:0% +what does that + + + align:start position:0% +what does that +mean an odd waveform would mean um if I + + align:start position:0% +mean an odd waveform would mean um if I + + + align:start position:0% +mean an odd waveform would mean um if I +had this + + align:start position:0% +had this + + + align:start position:0% +had this +then I should have uh + + align:start position:0% +then I should have uh + + + align:start position:0% +then I should have uh +this okay and then I could + + align:start position:0% +this okay and then I could + + + align:start position:0% +this okay and then I could +um can you I could I could replicate + + align:start position:0% +um can you I could I could replicate + + + align:start position:0% +um can you I could I could replicate +this cycle to cycle something like this + + align:start position:0% +this cycle to cycle something like this + + + align:start position:0% +this cycle to cycle something like this +for example okay where this is minus t + + align:start position:0% +for example okay where this is minus t + + + align:start position:0% +for example okay where this is minus t +over2 and this is T + + align:start position:0% +over2 and this is T + + + align:start position:0% +over2 and this is T +over2 okay so basically I go across the + + align:start position:0% +over2 okay so basically I go across the + + + align:start position:0% +over2 okay so basically I go across the +axis and then flip down I flip both this + + align:start position:0% +axis and then flip down I flip both this + + + align:start position:0% +axis and then flip down I flip both this +way and this way and I get some + + align:start position:0% +way and this way and I get some + + + align:start position:0% +way and this way and I get some +symmetry okay + + align:start position:0% +symmetry okay + + + align:start position:0% +symmetry okay +and so that's a + + align:start position:0% +and so that's a + + + align:start position:0% +and so that's a +uh that characteristic what what do I + + align:start position:0% +uh that characteristic what what do I + + + align:start position:0% +uh that characteristic what what do I +have about that well here right this is + + align:start position:0% +have about that well here right this is + + + align:start position:0% +have about that well here right this is +composed of only odd waveforms I could + + align:start position:0% +composed of only odd waveforms I could + + + align:start position:0% +composed of only odd waveforms I could +make the same kind of argument and say + + align:start position:0% +make the same kind of argument and say + + + align:start position:0% +make the same kind of argument and say +that b subn ought to equal + + align:start position:0% +that b subn ought to equal + + + align:start position:0% +that b subn ought to equal +zero okay so I only build an odd + + align:start position:0% +zero okay so I only build an odd + + + align:start position:0% +zero okay so I only build an odd +waveform out of sine waves why because + + align:start position:0% +waveform out of sine waves why because + + + align:start position:0% +waveform out of sine waves why because +signs are odd and hence those are the + + align:start position:0% +signs are odd and hence those are the + + + align:start position:0% +signs are odd and hence those are the +subcomponents that I get okay any + + align:start position:0% +subcomponents that I get okay any + + + align:start position:0% +subcomponents that I get okay any +questions about + + align:start position:0% + + + + align:start position:0% + +that so many way many people will be + + align:start position:0% +that so many way many people will be + + + align:start position:0% +that so many way many people will be +familiar with even and odd there's + + align:start position:0% +familiar with even and odd there's + + + align:start position:0% +familiar with even and odd there's +another + + align:start position:0% +another + + + align:start position:0% +another +decomposition that we can think + + align:start position:0% +decomposition that we can think + + + align:start position:0% +decomposition that we can think +of which is um one where we talk about + + align:start position:0% +of which is um one where we talk about + + + align:start position:0% +of which is um one where we talk about +something that's halfwave + + align:start position:0% + + + + align:start position:0% + +symmetric and what does halfway of + + align:start position:0% +symmetric and what does halfway of + + + align:start position:0% +symmetric and what does halfway of +symmetric means that means X of T is + + align:start position:0% +symmetric means that means X of T is + + + align:start position:0% +symmetric means that means X of T is +equal to minus X of tus capital T / 2 + + align:start position:0% +equal to minus X of tus capital T / 2 + + + align:start position:0% +equal to minus X of tus capital T / 2 +okay so what is a halfwave symmetric + + align:start position:0% +okay so what is a halfwave symmetric + + + align:start position:0% +okay so what is a halfwave symmetric +waveform look like a half wave symmetric + + align:start position:0% +waveform look like a half wave symmetric + + + align:start position:0% +waveform look like a half wave symmetric +waveform looks like um looks like this + + align:start position:0% +waveform looks like um looks like this + + + align:start position:0% +waveform looks like um looks like this +suppose I have + + align:start position:0% + + + + align:start position:0% + +something that looks like this between 0 + + align:start position:0% +something that looks like this between 0 + + + align:start position:0% +something that looks like this between 0 +and T + + align:start position:0% +and T + + + align:start position:0% +and T +over2 okay if I go back half a cycle I + + align:start position:0% +over2 okay if I go back half a cycle I + + + align:start position:0% +over2 okay if I go back half a cycle I +flip it all right so here I'll slide + + align:start position:0% +flip it all right so here I'll slide + + + align:start position:0% +flip it all right so here I'll slide +back half a cycle and I flip it and I'll + + align:start position:0% +back half a cycle and I flip it and I'll + + + align:start position:0% +back half a cycle and I flip it and I'll +get a waveform that looks like this okay + + align:start position:0% +get a waveform that looks like this okay + + + align:start position:0% +get a waveform that looks like this okay +so um here's what my halfwave symmetric + + align:start position:0% +so um here's what my halfwave symmetric + + + align:start position:0% +so um here's what my halfwave symmetric +waveform would look like and so forth + + align:start position:0% +waveform would look like and so forth + + + align:start position:0% +waveform would look like and so forth +okay where this is minus t over2 right + + align:start position:0% +okay where this is minus t over2 right + + + align:start position:0% +okay where this is minus t over2 right +so if I if I go at any point in the + + align:start position:0% +so if I if I go at any point in the + + + align:start position:0% +so if I if I go at any point in the +waveform and I go back half a + + align:start position:0% +waveform and I go back half a + + + align:start position:0% +waveform and I go back half a +cycle I + + align:start position:0% +cycle I + + + align:start position:0% +cycle I +flip + + align:start position:0% +flip + + + align:start position:0% +flip +okay well why might I be + + align:start position:0% +okay well why might I be + + + align:start position:0% +okay well why might I be +interested um in halfwave symmetry + + align:start position:0% +interested um in halfwave symmetry + + + align:start position:0% +interested um in halfwave symmetry +well that's because all of the a sub + + align:start position:0% +well that's because all of the a sub + + + align:start position:0% +well that's because all of the a sub +2ks and B sub 2ks are equal to + + align:start position:0% +2ks and B sub 2ks are equal to + + + align:start position:0% +2ks and B sub 2ks are equal to +zero okay all the even harmonic terms + + align:start position:0% +zero okay all the even harmonic terms + + + align:start position:0% +zero okay all the even harmonic terms +are equal to + + align:start position:0% +are equal to + + + align:start position:0% +are equal to +zero okay why would that be the case + + align:start position:0% +zero okay why would that be the case + + + align:start position:0% +zero okay why would that be the case +well how would I find uh say the second + + align:start position:0% +well how would I find uh say the second + + + align:start position:0% +well how would I find uh say the second +harmonic component of this thing I would + + align:start position:0% +harmonic component of this thing I would + + + align:start position:0% +harmonic component of this thing I would +multiply it for for example suppose I + + align:start position:0% +multiply it for for example suppose I + + + align:start position:0% +multiply it for for example suppose I +wanted the + + align:start position:0% +wanted the + + + align:start position:0% +wanted the +2A the the the a sub 2 component I would + + align:start position:0% +2A the the the a sub 2 component I would + + + align:start position:0% +2A the the the a sub 2 component I would +multiply it by S of 2 Omega T which be + + align:start position:0% +multiply it by S of 2 Omega T which be + + + align:start position:0% +multiply it by S of 2 Omega T which be +multiplying it by this and multiplying + + align:start position:0% +multiplying it by this and multiplying + + + align:start position:0% +multiplying it by this and multiplying +it by this and then integrating over the + + align:start position:0% +it by this and then integrating over the + + + align:start position:0% +it by this and then integrating over the +full cycle and you can see that the + + align:start position:0% +full cycle and you can see that the + + + align:start position:0% +full cycle and you can see that the +product of orange and white here this + + align:start position:0% +product of orange and white here this + + + align:start position:0% +product of orange and white here this +half of the waveform is exactly the + + align:start position:0% +half of the waveform is exactly the + + + align:start position:0% +half of the waveform is exactly the +complement of the product the orange and + + align:start position:0% +complement of the product the orange and + + + align:start position:0% +complement of the product the orange and +white in this half of the waveform when + + align:start position:0% +white in this half of the waveform when + + + align:start position:0% +white in this half of the waveform when +I integrate them I get + + align:start position:0% +I integrate them I get + + + align:start position:0% +I integrate them I get +zero okay the same thing would have been + + align:start position:0% +zero okay the same thing would have been + + + align:start position:0% +zero okay the same thing would have been +true had I had a cosine wave okay so the + + align:start position:0% +true had I had a cosine wave okay so the + + + align:start position:0% +true had I had a cosine wave okay so the +point of being half wve symmetric is + + align:start position:0% +point of being half wve symmetric is + + + align:start position:0% +point of being half wve symmetric is +that because of the orthogonality + + align:start position:0% +that because of the orthogonality + + + align:start position:0% +that because of the orthogonality +involved all of the even terms are + + align:start position:0% +involved all of the even terms are + + + align:start position:0% +involved all of the even terms are +zero okay so it has no even + + align:start position:0% +zero okay so it has no even + + + align:start position:0% +zero okay so it has no even +harmonic now the complement to this is + + align:start position:0% +harmonic now the complement to this is + + + align:start position:0% +harmonic now the complement to this is +something I would call a halfwave + + align:start position:0% +something I would call a halfwave + + + align:start position:0% +something I would call a halfwave +[Music] + + align:start position:0% + + + + align:start position:0% + +repeating okay and it looks like + + align:start position:0% +repeating okay and it looks like + + + align:start position:0% +repeating okay and it looks like +this if I had something that was doing + + align:start position:0% +this if I had something that was doing + + + align:start position:0% +this if I had something that was doing +this this in one half of the waveform + + align:start position:0% +this this in one half of the waveform + + + align:start position:0% +this this in one half of the waveform +for t/2 to zero it would just repeat + + align:start position:0% +for t/2 to zero it would just repeat + + + align:start position:0% +for t/2 to zero it would just repeat +half a cycle back that is X of T is + + align:start position:0% +half a cycle back that is X of T is + + + align:start position:0% +half a cycle back that is X of T is +equal to X of T minus capital T / 2 okay + + align:start position:0% +equal to X of T minus capital T / 2 okay + + + align:start position:0% +equal to X of T minus capital T / 2 okay +so if I have defined a period capital T + + align:start position:0% +so if I have defined a period capital T + + + align:start position:0% +so if I have defined a period capital T +that just means the waveform repeats + + align:start position:0% +that just means the waveform repeats + + + align:start position:0% +that just means the waveform repeats +twice in that Capital period + + align:start position:0% +twice in that Capital period + + + align:start position:0% +twice in that Capital period +T okay or another way to think about it + + align:start position:0% +T okay or another way to think about it + + + align:start position:0% +T okay or another way to think about it +is um the fundamental period of this + + align:start position:0% +is um the fundamental period of this + + + align:start position:0% +is um the fundamental period of this +waveform is actually + + align:start position:0% +waveform is actually + + + align:start position:0% +waveform is actually +t/2 okay but if we Define if we're + + align:start position:0% +t/2 okay but if we Define if we're + + + align:start position:0% +t/2 okay but if we Define if we're +looking at across some period T this + + align:start position:0% +looking at across some period T this + + + align:start position:0% +looking at across some period T this +comprises + + align:start position:0% +comprises + + + align:start position:0% +comprises +only a sub + + align:start position:0% + + + + align:start position:0% + +2ks and B sub + + align:start position:0% +2ks and B sub + + + align:start position:0% +2ks and B sub +2ks that is a sub 2N + 1 and B sub 2N + + + align:start position:0% +2ks that is a sub 2N + 1 and B sub 2N + + + + align:start position:0% +2ks that is a sub 2N + 1 and B sub 2N + +1 is equal to 0 right so this has no + + align:start position:0% +1 is equal to 0 right so this has no + + + align:start position:0% +1 is equal to 0 right so this has no +even + + align:start position:0% +even + + + align:start position:0% +even +harmonics this kind of waveform only has + + align:start position:0% +harmonics this kind of waveform only has + + + align:start position:0% +harmonics this kind of waveform only has +even harmonics it has no odd harmonics + + align:start position:0% +even harmonics it has no odd harmonics + + + align:start position:0% +even harmonics it has no odd harmonics +or + + align:start position:0% +or + + + align:start position:0% +or +fundamental + + align:start position:0% +fundamental + + + align:start position:0% +fundamental +okay any questions about + + align:start position:0% + + + + align:start position:0% + +that yeah is that only the case if we + + align:start position:0% +that yeah is that only the case if we + + + align:start position:0% +that yeah is that only the case if we +Define the period to be T yes right now + + align:start position:0% +Define the period to be T yes right now + + + align:start position:0% +Define the period to be T yes right now +why might I do + + align:start position:0% +why might I do + + + align:start position:0% +why might I do +that because firstly we can um sometimes + + align:start position:0% +that because firstly we can um sometimes + + + align:start position:0% +that because firstly we can um sometimes +decompose waveforms right I could say + + align:start position:0% +decompose waveforms right I could say + + + align:start position:0% +decompose waveforms right I could say +that okay I could come up with some + + align:start position:0% +that okay I could come up with some + + + align:start position:0% +that okay I could come up with some +waveform f of t + + align:start position:0% +waveform f of t + + + align:start position:0% +waveform f of t +okay and I could say you know so so I + + align:start position:0% +okay and I could say you know so so I + + + align:start position:0% +okay and I could say you know so so I +could take some arbitrary F of T and + + align:start position:0% +could take some arbitrary F of T and + + + align:start position:0% +could take some arbitrary F of T and +come up with f of + + align:start position:0% +come up with f of + + + align:start position:0% +come up with f of +T is equal to some even + + align:start position:0% +T is equal to some even + + + align:start position:0% +T is equal to some even +component plus some odd + + align:start position:0% +component plus some odd + + + align:start position:0% +component plus some odd +component okay and decompose that into + + align:start position:0% +component okay and decompose that into + + + align:start position:0% +component okay and decompose that into +different parts where F + + align:start position:0% +different parts where F + + + align:start position:0% +different parts where F +even is equal to X of t plus x ofus t / + + align:start position:0% +even is equal to X of t plus x ofus t / + + + align:start position:0% +even is equal to X of t plus x ofus t / +2 and F OD is equal to X of T minus x + + align:start position:0% +2 and F OD is equal to X of T minus x + + + align:start position:0% +2 and F OD is equal to X of T minus x +ofus t / 2 okay so essentially I can + + align:start position:0% +ofus t / 2 okay so essentially I can + + + align:start position:0% +ofus t / 2 okay so essentially I can +decompose a waveform into one term that + + align:start position:0% +decompose a waveform into one term that + + + align:start position:0% +decompose a waveform into one term that +basically is all the cosine components + + align:start position:0% +basically is all the cosine components + + + align:start position:0% +basically is all the cosine components +in DC and one element that is only the + + align:start position:0% +in DC and one element that is only the + + + align:start position:0% +in DC and one element that is only the +sign + + align:start position:0% +sign + + + align:start position:0% +sign +terms okay so I get this decomposition + + align:start position:0% +terms okay so I get this decomposition + + + align:start position:0% +terms okay so I get this decomposition +and because it signs and cosiness split + + align:start position:0% +and because it signs and cosiness split + + + align:start position:0% +and because it signs and cosiness split +the even and odd components of the the + + align:start position:0% +the even and odd components of the the + + + align:start position:0% +the even and odd components of the the +waveform happen to be + + align:start position:0% +waveform happen to be + + + align:start position:0% +waveform happen to be +orthogonal okay + + align:start position:0% +orthogonal okay + + + align:start position:0% +orthogonal okay +likewise I could make a + + align:start position:0% +likewise I could make a + + + align:start position:0% +likewise I could make a +decomposition of f of T any waveform F + + align:start position:0% +decomposition of f of T any waveform F + + + align:start position:0% +decomposition of f of T any waveform F +of T to have a f of halfwave + + align:start position:0% +of T to have a f of halfwave + + + align:start position:0% +of T to have a f of halfwave +symmetric element plus a half of f of + + align:start position:0% +symmetric element plus a half of f of + + + align:start position:0% +symmetric element plus a half of f of +halfwave + + align:start position:0% +halfwave + + + align:start position:0% +halfwave +repeating component and again this is + + align:start position:0% +repeating component and again this is + + + align:start position:0% +repeating component and again this is +going to be the fundamental and odd + + align:start position:0% +going to be the fundamental and odd + + + align:start position:0% +going to be the fundamental and odd +harmonics this is going to be DC and + + align:start position:0% +harmonics this is going to be DC and + + + align:start position:0% +harmonics this is going to be DC and +even harmonics + + align:start position:0% +even harmonics + + + align:start position:0% +even harmonics +okay and those are sort of time waveform + + align:start position:0% +okay and those are sort of time waveform + + + align:start position:0% +okay and those are sort of time waveform +decompositions but they're into + + align:start position:0% +decompositions but they're into + + + align:start position:0% +decompositions but they're into +different parts of the um of the 4A + + align:start position:0% +different parts of the um of the 4A + + + align:start position:0% +different parts of the um of the 4A +components okay any questions about + + align:start position:0% + + + + align:start position:0% + +that okay so that's just a little kind + + align:start position:0% +that okay so that's just a little kind + + + align:start position:0% +that okay so that's just a little kind +of review and perhaps an extension of + + align:start position:0% +of review and perhaps an extension of + + + align:start position:0% +of review and perhaps an extension of +different ways we might um think of + + align:start position:0% +different ways we might um think of + + + align:start position:0% +different ways we might um think of +getting the components we'll see in a + + align:start position:0% +getting the components we'll see in a + + + align:start position:0% +getting the components we'll see in a +while why we might think of decomposing + + align:start position:0% +while why we might think of decomposing + + + align:start position:0% +while why we might think of decomposing +things that way or think carefully about + + align:start position:0% +things that way or think carefully about + + + align:start position:0% +things that way or think carefully about +whether my waveform is even or odd or + + align:start position:0% +whether my waveform is even or odd or + + + align:start position:0% +whether my waveform is even or odd or +halfwave symmetric or or not + + align:start position:0% +halfwave symmetric or or not + + + align:start position:0% +halfwave symmetric or or not +okay but let's start talking about um an + + align:start position:0% +okay but let's start talking about um an + + + align:start position:0% +okay but let's start talking about um an +inverter what would be the basic + + align:start position:0% +inverter what would be the basic + + + align:start position:0% +inverter what would be the basic +structure of a three-phase inverter well + + align:start position:0% +structure of a three-phase inverter well + + + align:start position:0% +structure of a three-phase inverter well +one basic structure might be to have + + align:start position:0% +one basic structure might be to have + + + align:start position:0% +one basic structure might be to have +some DC waveform and of course by the + + align:start position:0% +some DC waveform and of course by the + + + align:start position:0% +some DC waveform and of course by the +way whether I talk about something this + + align:start position:0% +way whether I talk about something this + + + align:start position:0% +way whether I talk about something this +structure as an inverter going flowing + + align:start position:0% +structure as an inverter going flowing + + + align:start position:0% +structure as an inverter going flowing +power DC to AC or is a rectifier flowing + + align:start position:0% +power DC to AC or is a rectifier flowing + + + align:start position:0% +power DC to AC or is a rectifier flowing +power AC to DC it really just depends + + align:start position:0% +power AC to DC it really just depends + + + align:start position:0% +power AC to DC it really just depends +upon the power flow Direction and in + + align:start position:0% +upon the power flow Direction and in + + + align:start position:0% +upon the power flow Direction and in +fact um the same circuit structure can + + align:start position:0% +fact um the same circuit structure can + + + align:start position:0% +fact um the same circuit structure can +do either thing okay uh how you + + align:start position:0% +do either thing okay uh how you + + + align:start position:0% +do either thing okay uh how you +implement the switches however may be + + align:start position:0% +implement the switches however may be + + + align:start position:0% +implement the switches however may be +different okay and in fact where did the + + align:start position:0% +different okay and in fact where did the + + + align:start position:0% +different okay and in fact where did the +term inverter come from it came from the + + align:start position:0% +term inverter come from it came from the + + + align:start position:0% +term inverter come from it came from the +notion of inverting rectifier the + + align:start position:0% +notion of inverting rectifier the + + + align:start position:0% +notion of inverting rectifier the +first kind of power electronic solid + + align:start position:0% +first kind of power electronic solid + + + align:start position:0% +first kind of power electronic solid +state or actually wasn't even solid + + align:start position:0% +state or actually wasn't even solid + + + align:start position:0% +state or actually wasn't even solid +state it was tube power electronic + + align:start position:0% +state it was tube power electronic + + + align:start position:0% +state it was tube power electronic +component that people were able to build + + align:start position:0% +component that people were able to build + + + align:start position:0% +component that people were able to build +was a rectifier and they eventually + + align:start position:0% +was a rectifier and they eventually + + + align:start position:0% +was a rectifier and they eventually +figured out that with certain kinds of + + align:start position:0% +figured out that with certain kinds of + + + align:start position:0% +figured out that with certain kinds of +controlled rectifiers they could go DC + + align:start position:0% +controlled rectifiers they could go DC + + + align:start position:0% +controlled rectifiers they could go DC +power to AC power so they called that an + + align:start position:0% +power to AC power so they called that an + + + align:start position:0% +power to AC power so they called that an +inverting rectifier and then they + + align:start position:0% +inverting rectifier and then they + + + align:start position:0% +inverting rectifier and then they +eventually just started calling it an + + align:start position:0% +eventually just started calling it an + + + align:start position:0% +eventually just started calling it an +inverter okay so that's where the term + + align:start position:0% +inverter okay so that's where the term + + + align:start position:0% +inverter okay so that's where the term +comes from but here's a basic + + align:start position:0% +comes from but here's a basic + + + align:start position:0% +comes from but here's a basic +structure okay maybe I would have uh + + align:start position:0% +structure okay maybe I would have uh + + + align:start position:0% +structure okay maybe I would have uh +four + + align:start position:0% + + + + align:start position:0% + +switches S1 + + align:start position:0% + + + + align:start position:0% + +uh let me get my switch numberings right + + align:start position:0% +uh let me get my switch numberings right + + + align:start position:0% +uh let me get my switch numberings right +S2 + + align:start position:0% +S2 + + + align:start position:0% +S2 +S3 and S4 and we'll see why we number + + align:start position:0% +S3 and S4 and we'll see why we number + + + align:start position:0% +S3 and S4 and we'll see why we number +them this way and here is + + align:start position:0% +them this way and here is + + + align:start position:0% +them this way and here is +my load in this case if I'm going to go + + align:start position:0% +my load in this case if I'm going to go + + + align:start position:0% +my load in this case if I'm going to go +from DC to power to AC power and let me + + align:start position:0% +from DC to power to AC power and let me + + + align:start position:0% +from DC to power to AC power and let me +call the output here + + align:start position:0% +call the output here + + + align:start position:0% +call the output here +VX okay so I'm going to come from some + + align:start position:0% +VX okay so I'm going to come from some + + + align:start position:0% +VX okay so I'm going to come from some +DC voltage and I'm going to deliver + + align:start position:0% +DC voltage and I'm going to deliver + + + align:start position:0% +DC voltage and I'm going to deliver +power at AC into some voltage VX + + align:start position:0% +power at AC into some voltage VX + + + align:start position:0% +power at AC into some voltage VX +okay um what + + align:start position:0% +okay um what + + + align:start position:0% +okay um what +voltages VX can I synthesize with this + + align:start position:0% +voltages VX can I synthesize with this + + + align:start position:0% +voltages VX can I synthesize with this +structure um well let's think about this + + align:start position:0% +structure um well let's think about this + + + align:start position:0% +structure um well let's think about this +if I have um switches + + align:start position:0% + + + + align:start position:0% + +on what voltage VX do I get well if S1 + + align:start position:0% +on what voltage VX do I get well if S1 + + + align:start position:0% +on what voltage VX do I get well if S1 +and S2 are + + align:start position:0% + + + + align:start position:0% + +on I get plus + + align:start position:0% +on I get plus + + + align:start position:0% +on I get plus +VDC if S2 and S3 are + + align:start position:0% +VDC if S2 and S3 are + + + align:start position:0% +VDC if S2 and S3 are +on I get zero right because I've just + + align:start position:0% +on I get zero right because I've just + + + align:start position:0% +on I get zero right because I've just +shorted out the load on the bottom if S3 + + align:start position:0% +shorted out the load on the bottom if S3 + + + align:start position:0% +shorted out the load on the bottom if S3 +and S4 are on well then VX becomes minus + + align:start position:0% + + + + align:start position:0% + +VDC and if S4 and S1 are on top two + + align:start position:0% +VDC and if S4 and S1 are on top two + + + align:start position:0% +VDC and if S4 and S1 are on top two +switches I again get zero right so I + + align:start position:0% +switches I again get zero right so I + + + align:start position:0% +switches I again get zero right so I +sort of have two ways I can apply a zero + + align:start position:0% +sort of have two ways I can apply a zero + + + align:start position:0% +sort of have two ways I can apply a zero +voltage across the load I can apply a + + align:start position:0% +voltage across the load I can apply a + + + align:start position:0% +voltage across the load I can apply a +positive voltage and I can apply a + + align:start position:0% +positive voltage and I can apply a + + + align:start position:0% +positive voltage and I can apply a +negative voltage all right so I can sort + + align:start position:0% +negative voltage all right so I can sort + + + align:start position:0% +negative voltage all right so I can sort +of go one way the other way and two ways + + align:start position:0% +of go one way the other way and two ways + + + align:start position:0% +of go one way the other way and two ways +I can get zero okay and what we're going + + align:start position:0% +I can get zero okay and what we're going + + + align:start position:0% +I can get zero okay and what we're going +to see is that means given a DC voltage + + align:start position:0% +to see is that means given a DC voltage + + + align:start position:0% +to see is that means given a DC voltage +I can put AC on the load okay and this + + align:start position:0% +I can put AC on the load okay and this + + + align:start position:0% +I can put AC on the load okay and this +is a very + + align:start position:0% +is a very + + + align:start position:0% +is a very +common singlephase inverter + + align:start position:0% +common singlephase inverter + + + align:start position:0% +common singlephase inverter +structure if I have say a typical thing + + align:start position:0% +structure if I have say a typical thing + + + align:start position:0% +structure if I have say a typical thing +is if I have an inductive and resistive + + align:start position:0% +is if I have an inductive and resistive + + + align:start position:0% +is if I have an inductive and resistive +load right maybe I would implement it + + align:start position:0% +load right maybe I would implement it + + + align:start position:0% +load right maybe I would implement it +this + + align:start position:0% + + + + align:start position:0% + +way okay I would have say a mosfet here + + align:start position:0% +way okay I would have say a mosfet here + + + align:start position:0% +way okay I would have say a mosfet here +and a mosfet here for my + + align:start position:0% +and a mosfet here for my + + + align:start position:0% +and a mosfet here for my +switches and keep in mind these guys + + align:start position:0% +switches and keep in mind these guys + + + align:start position:0% +switches and keep in mind these guys +well I don't usually draw it they have + + align:start position:0% +well I don't usually draw it they have + + + align:start position:0% +well I don't usually draw it they have +internal body diodes like this + + align:start position:0% + + + + align:start position:0% + +okay so this would be a typical + + align:start position:0% + + + + align:start position:0% + +structure where internally I have these + + align:start position:0% +structure where internally I have these + + + align:start position:0% +structure where internally I have these +diodes okay and here's VX + + align:start position:0% + + + + align:start position:0% + +again okay just to illustrate you know + + align:start position:0% +again okay just to illustrate you know + + + align:start position:0% +again okay just to illustrate you know +this kind of structure being very common + + align:start position:0% +this kind of structure being very common + + + align:start position:0% +this kind of structure being very common +what I have here is um sort of one of + + align:start position:0% +what I have here is um sort of one of + + + align:start position:0% +what I have here is um sort of one of +these things you plug into the cigarette + + align:start position:0% +these things you plug into the cigarette + + + align:start position:0% +these things you plug into the cigarette +lighter in your car to generate AC from + + align:start position:0% +lighter in your car to generate AC from + + + align:start position:0% +lighter in your car to generate AC from +uh you know to power your laptop or + + align:start position:0% +uh you know to power your laptop or + + + align:start position:0% +uh you know to power your laptop or +something when you're on a trip or + + align:start position:0% +something when you're on a trip or + + + align:start position:0% +something when you're on a trip or +something and you know as is all D + + align:start position:0% +something and you know as is all D + + + align:start position:0% +something and you know as is all D +always dangerous give me a power + + align:start position:0% +always dangerous give me a power + + + align:start position:0% +always dangerous give me a power +converter because usually I'll just take + + align:start position:0% +converter because usually I'll just take + + + align:start position:0% +converter because usually I'll just take +it apart um but what you'll see + + align:start position:0% +it apart um but what you'll see + + + align:start position:0% +it apart um but what you'll see +is on one side of this thing there's + + align:start position:0% +is on one side of this thing there's + + + align:start position:0% +is on one side of this thing there's +kind of four switches and you'll see the + + align:start position:0% +kind of four switches and you'll see the + + + align:start position:0% +kind of four switches and you'll see the +in fact you we were talking about + + align:start position:0% +in fact you we were talking about + + + align:start position:0% +in fact you we were talking about +insulation pads last time I'll pass this + + align:start position:0% +insulation pads last time I'll pass this + + + align:start position:0% +insulation pads last time I'll pass this +around you can see the insulation pad + + align:start position:0% +around you can see the insulation pad + + + align:start position:0% +around you can see the insulation pad +here and then you'll see this + + align:start position:0% +here and then you'll see this + + + align:start position:0% +here and then you'll see this +Transformer and you'll see a set of + + align:start position:0% +Transformer and you'll see a set of + + + align:start position:0% +Transformer and you'll see a set of +diodes here which are right here that's + + align:start position:0% +diodes here which are right here that's + + + align:start position:0% +diodes here which are right here that's +an isolated dcdc converter so that takes + + align:start position:0% +an isolated dcdc converter so that takes + + + align:start position:0% +an isolated dcdc converter so that takes +the 12 volts or 14 volts from your car + + align:start position:0% +the 12 volts or 14 volts from your car + + + align:start position:0% +the 12 volts or 14 volts from your car +battery and generates a higher voltage + + align:start position:0% +battery and generates a higher voltage + + + align:start position:0% +battery and generates a higher voltage +and then there's four more switches + + align:start position:0% +and then there's four more switches + + + align:start position:0% +and then there's four more switches +which are the ones + + align:start position:0% +which are the ones + + + align:start position:0% +which are the ones +here those are your four + + align:start position:0% +here those are your four + + + align:start position:0% +here those are your four +mosfets and those are going to generate + + align:start position:0% +mosfets and those are going to generate + + + align:start position:0% +mosfets and those are going to generate +a + + align:start position:0% +a + + + align:start position:0% +a +and it goes to two plugs so you can plug + + align:start position:0% +and it goes to two plugs so you can plug + + + align:start position:0% +and it goes to two plugs so you can plug +in your toys and you know play your + + align:start position:0% +in your toys and you know play your + + + align:start position:0% +in your toys and you know play your +gaming system or whatever you want so um + + align:start position:0% +gaming system or whatever you want so um + + + align:start position:0% +gaming system or whatever you want so um +this is just to illustrate you know one + + align:start position:0% +this is just to illustrate you know one + + + align:start position:0% +this is just to illustrate you know one +very simple example of an + + align:start position:0% +very simple example of an + + + align:start position:0% +very simple example of an +inverter okay and it'll have exactly + + align:start position:0% +inverter okay and it'll have exactly + + + align:start position:0% +inverter okay and it'll have exactly +this structure right so we have an + + align:start position:0% +this structure right so we have an + + + align:start position:0% +this structure right so we have an +isolated DCd converter to get get us + + align:start position:0% +isolated DCd converter to get get us + + + align:start position:0% +isolated DCd converter to get get us +voltage gain and then this + + align:start position:0% +voltage gain and then this + + + align:start position:0% +voltage gain and then this +inverter + + align:start position:0% +inverter + + + align:start position:0% +inverter +okay um what would this when I'm drawing + + align:start position:0% +okay um what would this when I'm drawing + + + align:start position:0% +okay um what would this when I'm drawing +this load VX what am I meaning well it + + align:start position:0% +this load VX what am I meaning well it + + + align:start position:0% +this load VX what am I meaning well it +depends what my load is but I could + + align:start position:0% +depends what my load is but I could + + + align:start position:0% +depends what my load is but I could +imagine maybe I would have an + + align:start position:0% +imagine maybe I would have an + + + align:start position:0% +imagine maybe I would have an +inductor and a capacitor and + + align:start position:0% + + + + align:start position:0% + +some you know resistor that's getting my + + align:start position:0% +some you know resistor that's getting my + + + align:start position:0% +some you know resistor that's getting my +AC load um right so this filters out + + align:start position:0% +AC load um right so this filters out + + + align:start position:0% +AC load um right so this filters out +higher harmonics or this could be a + + align:start position:0% +higher harmonics or this could be a + + + align:start position:0% +higher harmonics or this could be a +machine winding where there's a you know + + align:start position:0% +machine winding where there's a you know + + + align:start position:0% +machine winding where there's a you know +sort of phase inductance from the + + align:start position:0% +sort of phase inductance from the + + + align:start position:0% +sort of phase inductance from the +machine winding and a resistor it just + + align:start position:0% +machine winding and a resistor it just + + + align:start position:0% +machine winding and a resistor it just +sort of depends on what you're driving + + align:start position:0% +sort of depends on what you're driving + + + align:start position:0% +sort of depends on what you're driving +for a load okay or it could be an induct + + align:start position:0% +for a load okay or it could be an induct + + + align:start position:0% +for a load okay or it could be an induct +filter and that could run into the grid + + align:start position:0% +filter and that could run into the grid + + + align:start position:0% +filter and that could run into the grid +right so that's the basic notion of what + + align:start position:0% +right so that's the basic notion of what + + + align:start position:0% +right so that's the basic notion of what +the structure of an inverter + + align:start position:0% +the structure of an inverter + + + align:start position:0% +the structure of an inverter +is why don't we think about how could we + + align:start position:0% +is why don't we think about how could we + + + align:start position:0% +is why don't we think about how could we +well approximate a sinusoid by + + align:start position:0% +well approximate a sinusoid by + + + align:start position:0% +well approximate a sinusoid by +switching these transistors S1 to S4 and + + align:start position:0% +switching these transistors S1 to S4 and + + + align:start position:0% +switching these transistors S1 to S4 and +the case I'd like to start with is + + align:start position:0% +the case I'd like to start with is + + + align:start position:0% +the case I'd like to start with is +perhaps the simplest one I'd like to + + align:start position:0% +perhaps the simplest one I'd like to + + + align:start position:0% +perhaps the simplest one I'd like to +switch each switch on and off only once + + align:start position:0% +switch each switch on and off only once + + + align:start position:0% +switch each switch on and off only once +per AC output cycle and let's imagine + + align:start position:0% +per AC output cycle and let's imagine + + + align:start position:0% +per AC output cycle and let's imagine +for the moment that what I want is + + align:start position:0% +for the moment that what I want is + + + align:start position:0% +for the moment that what I want is +something that approximates a sine wave + + align:start position:0% +something that approximates a sine wave + + + align:start position:0% +something that approximates a sine wave +at the output or crudely approximates a + + align:start position:0% +at the output or crudely approximates a + + + align:start position:0% +at the output or crudely approximates a +sine wave at the output okay why am I + + align:start position:0% +sine wave at the output okay why am I + + + align:start position:0% +sine wave at the output okay why am I +focusing on Switching only once per + + align:start position:0% +focusing on Switching only once per + + + align:start position:0% +focusing on Switching only once per +cycle well the number of times I switch + + align:start position:0% +cycle well the number of times I switch + + + align:start position:0% +cycle well the number of times I switch +per cycle is going to have to do with my + + align:start position:0% +per cycle is going to have to do with my + + + align:start position:0% +per cycle is going to have to do with my +switching losses right we talked about + + align:start position:0% +switching losses right we talked about + + + align:start position:0% +switching losses right we talked about +switching + + align:start position:0% +switching + + + align:start position:0% +switching +losses and so especially at very high + + align:start position:0% +losses and so especially at very high + + + align:start position:0% +losses and so especially at very high +power levels I really want to minimize + + align:start position:0% +power levels I really want to minimize + + + align:start position:0% +power levels I really want to minimize +the number of times I switch per cycle + + align:start position:0% +the number of times I switch per cycle + + + align:start position:0% +the number of times I switch per cycle +um in order to reduce those switching + + align:start position:0% +um in order to reduce those switching + + + align:start position:0% +um in order to reduce those switching +losses okay + + align:start position:0% +losses okay + + + align:start position:0% +losses okay +so the obsession with not switching very + + align:start position:0% +so the obsession with not switching very + + + align:start position:0% +so the obsession with not switching very +often comes from mitigating those losses + + align:start position:0% +often comes from mitigating those losses + + + align:start position:0% +often comes from mitigating those losses +and so I want to just treat the simplest + + align:start position:0% +and so I want to just treat the simplest + + + align:start position:0% +and so I want to just treat the simplest +case and this is actually what one might + + align:start position:0% +case and this is actually what one might + + + align:start position:0% +case and this is actually what one might +do at very high power levels where you + + align:start position:0% +do at very high power levels where you + + + align:start position:0% +do at very high power levels where you +really don't want to switch very often + + align:start position:0% +really don't want to switch very often + + + align:start position:0% +really don't want to switch very often +okay um or very high frequency levels I + + align:start position:0% +okay um or very high frequency levels I + + + align:start position:0% +okay um or very high frequency levels I +should say Okay so let's think about + + align:start position:0% +should say Okay so let's think about + + + align:start position:0% +should say Okay so let's think about +what we might do let me plot things in + + align:start position:0% +what we might do let me plot things in + + + align:start position:0% +what we might do let me plot things in +terms of electrical angle + + align:start position:0% + + + + align:start position:0% + +okay so here is + + align:start position:0% + + + + align:start position:0% + +um here is you know so it's two pi and 2 + + align:start position:0% +um here is you know so it's two pi and 2 + + + align:start position:0% +um here is you know so it's two pi and 2 +pi this is Omega T this is electrical + + align:start position:0% +pi this is Omega T this is electrical + + + align:start position:0% +pi this is Omega T this is electrical +angle and what I was hoping to + + align:start position:0% +angle and what I was hoping to + + + align:start position:0% +angle and what I was hoping to +synthesize is you know some sine wave + + align:start position:0% +synthesize is you know some sine wave + + + align:start position:0% +synthesize is you know some sine wave +right so maybe it would look like + + align:start position:0% + + + + align:start position:0% + +this an ideal S Wave if I could synth it + + align:start position:0% +this an ideal S Wave if I could synth it + + + align:start position:0% +this an ideal S Wave if I could synth it +would look like this okay now I clearly + + align:start position:0% +would look like this okay now I clearly + + + align:start position:0% +would look like this okay now I clearly +can't synthesize that with my inverter + + align:start position:0% +can't synthesize that with my inverter + + + align:start position:0% +can't synthesize that with my inverter +but what could I do well I can generate + + align:start position:0% +but what could I do well I can generate + + + align:start position:0% +but what could I do well I can generate +a positive voltage right so maybe what I + + align:start position:0% +a positive voltage right so maybe what I + + + align:start position:0% +a positive voltage right so maybe what I +would do is let's just + + align:start position:0% +would do is let's just + + + align:start position:0% +would do is let's just +suppose um so starting sometime here I + + align:start position:0% +suppose um so starting sometime here I + + + align:start position:0% +suppose um so starting sometime here I +will have I will apply plus VDC maybe + + align:start position:0% +will have I will apply plus VDC maybe + + + align:start position:0% +will have I will apply plus VDC maybe +I'll do that at some electrical angle + + align:start position:0% +I'll do that at some electrical angle + + + align:start position:0% +I'll do that at some electrical angle +Delta okay so in this time period I will + + align:start position:0% +Delta okay so in this time period I will + + + align:start position:0% +Delta okay so in this time period I will +Sy the size plus + + align:start position:0% +Sy the size plus + + + align:start position:0% +Sy the size plus +VDC and what I'm going to do is I'm + + align:start position:0% +VDC and what I'm going to do is I'm + + + align:start position:0% +VDC and what I'm going to do is I'm +going to do this I'm going to do this + + align:start position:0% +going to do this I'm going to do this + + + align:start position:0% +going to do this I'm going to do this +between Delta and Pi minus + + align:start position:0% +between Delta and Pi minus + + + align:start position:0% +between Delta and Pi minus +Delta okay and how would I do that in + + align:start position:0% +Delta okay and how would I do that in + + + align:start position:0% +Delta okay and how would I do that in +this time period what what switch + + align:start position:0% +this time period what what switch + + + align:start position:0% +this time period what what switch +pattern would let me synthesize plus + + align:start position:0% +pattern would let me synthesize plus + + + align:start position:0% +pattern would let me synthesize plus +VDC S12 S1 S2 will give + + align:start position:0% +VDC S12 S1 S2 will give + + + align:start position:0% +VDC S12 S1 S2 will give +me plus VDC now I want to synthesize + + align:start position:0% +me plus VDC now I want to synthesize + + + align:start position:0% +me plus VDC now I want to synthesize +zero okay in this time period and I'm + + align:start position:0% +zero okay in this time period and I'm + + + align:start position:0% +zero okay in this time period and I'm +going to do that between Pius Delta and + + align:start position:0% +going to do that between Pius Delta and + + + align:start position:0% +going to do that between Pius Delta and +Pi + + + align:start position:0% + + + + align:start position:0% + +Delta okay I can get zero just by + + align:start position:0% +Delta okay I can get zero just by + + + align:start position:0% +Delta okay I can get zero just by +leaving switch S2 on and going to switch + + align:start position:0% +leaving switch S2 on and going to switch + + + align:start position:0% +leaving switch S2 on and going to switch +S3 so I can have S2 + + align:start position:0% +S3 so I can have S2 + + + align:start position:0% +S3 so I can have S2 +S3 okay now I'm in the negative half of + + align:start position:0% +S3 okay now I'm in the negative half of + + + align:start position:0% +S3 okay now I'm in the negative half of +the cycle so maybe I want to syn maybe I + + align:start position:0% +the cycle so maybe I want to syn maybe I + + + align:start position:0% +the cycle so maybe I want to syn maybe I +want to make this minus + + align:start position:0% + + + + align:start position:0% + +VDC right so I will + + align:start position:0% +VDC right so I will + + + align:start position:0% +VDC right so I will +then switch here and for from Pi + Delta + + align:start position:0% +then switch here and for from Pi + Delta + + + align:start position:0% +then switch here and for from Pi + Delta +to 2 pi minus + + align:start position:0% +to 2 pi minus + + + align:start position:0% +to 2 pi minus +Delta I will + + align:start position:0% +Delta I will + + + align:start position:0% +Delta I will +have minus VDC and I get that with what + + align:start position:0% +have minus VDC and I get that with what + + + align:start position:0% +have minus VDC and I get that with what +switch + + align:start position:0% +switch + + + align:start position:0% +switch +pattern S3 S4 so I've turned off S2 and + + align:start position:0% +pattern S3 S4 so I've turned off S2 and + + + align:start position:0% +pattern S3 S4 so I've turned off S2 and +now I've turned on + + align:start position:0% +now I've turned on + + + align:start position:0% +now I've turned on +S4 and then I can get back to + + align:start position:0% +S4 and then I can get back to + + + align:start position:0% +S4 and then I can get back to +synthesizing zero with S4 + + align:start position:0% +synthesizing zero with S4 + + + align:start position:0% +synthesizing zero with S4 +S1 so right so here's my + + align:start position:0% +S1 so right so here's my + + + align:start position:0% +S1 so right so here's my +pattern okay + + align:start position:0% + + + + align:start position:0% + +and it looks like + + align:start position:0% +and it looks like + + + align:start position:0% +and it looks like +this okay does that make sense + + align:start position:0% +this okay does that make sense + + + align:start position:0% +this okay does that make sense +everybody so what have I done each + + align:start position:0% +everybody so what have I done each + + + align:start position:0% +everybody so what have I done each +switch turns on if I look over two Pi + + align:start position:0% +switch turns on if I look over two Pi + + + align:start position:0% +switch turns on if I look over two Pi +one AC cycle each switch turns on once + + align:start position:0% +one AC cycle each switch turns on once + + + align:start position:0% +one AC cycle each switch turns on once +per cycle each switch turns off once per + + align:start position:0% +per cycle each switch turns off once per + + + align:start position:0% +per cycle each switch turns off once per +cycle okay so that's the minimum I can + + align:start position:0% +cycle okay so that's the minimum I can + + + align:start position:0% +cycle okay so that's the minimum I can +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +do um and synthesize this kind of + + align:start position:0% +do um and synthesize this kind of + + + align:start position:0% +do um and synthesize this kind of +waveform now what can you tell me I I + + align:start position:0% +waveform now what can you tell me I I + + + align:start position:0% +waveform now what can you tell me I I +drew a sine + + align:start position:0% +drew a sine + + + align:start position:0% +drew a sine +wave here right + + align:start position:0% + + + + align:start position:0% + +um and I want in some measure for my + + align:start position:0% +um and I want in some measure for my + + + align:start position:0% +um and I want in some measure for my +synthesized AC output voltage of my + + align:start position:0% +synthesized AC output voltage of my + + + align:start position:0% +synthesized AC output voltage of my +inverter this + + align:start position:0% +inverter this + + + align:start position:0% +inverter this +VX right this is + + align:start position:0% +VX right this is + + + align:start position:0% +VX right this is +vx to try to approximate that sine wave + + align:start position:0% +vx to try to approximate that sine wave + + + align:start position:0% +vx to try to approximate that sine wave +in some + + align:start position:0% + + + + align:start position:0% + +fashion this is you know V sin Omega T + + align:start position:0% +fashion this is you know V sin Omega T + + + align:start position:0% +fashion this is you know V sin Omega T +well s Omega T is odd right so if I want + + align:start position:0% +well s Omega T is odd right so if I want + + + align:start position:0% +well s Omega T is odd right so if I want +to do a good job with as least kind of + + align:start position:0% +to do a good job with as least kind of + + + align:start position:0% +to do a good job with as least kind of +unwanted harmonic content as I can it + + align:start position:0% +unwanted harmonic content as I can it + + + align:start position:0% +unwanted harmonic content as I can it +makes sense that because sign is odd I + + align:start position:0% +makes sense that because sign is odd I + + + align:start position:0% +makes sense that because sign is odd I +also ought to use only odd components + + align:start position:0% +also ought to use only odd components + + + align:start position:0% +also ought to use only odd components +right so I ought to synthesize it with + + align:start position:0% +right so I ought to synthesize it with + + + align:start position:0% +right so I ought to synthesize it with +an odd waveform and what do I know about + + align:start position:0% +an odd waveform and what do I know about + + + align:start position:0% +an odd waveform and what do I know about +this waveform this waveforms odd and I + + align:start position:0% +this waveform this waveforms odd and I + + + align:start position:0% +this waveform this waveforms odd and I +should maybe I'll just draw it out here + + align:start position:0% +should maybe I'll just draw it out here + + + align:start position:0% +should maybe I'll just draw it out here +right it is indeed this is minus Delta + + align:start position:0% +right it is indeed this is minus Delta + + + align:start position:0% +right it is indeed this is minus Delta +this white waveform here VX is indeed + + align:start position:0% +this white waveform here VX is indeed + + + align:start position:0% +this white waveform here VX is indeed +odd right it reflects if I flip it + + align:start position:0% +odd right it reflects if I flip it + + + align:start position:0% +odd right it reflects if I flip it +across tal 0 and I flip it I get the + + align:start position:0% +across tal 0 and I flip it I get the + + + align:start position:0% +across tal 0 and I flip it I get the +same thing right so what I know is this + + align:start position:0% +same thing right so what I know is this + + + align:start position:0% +same thing right so what I know is this +white waveform it's odd it's comprising + + align:start position:0% +white waveform it's odd it's comprising + + + align:start position:0% +white waveform it's odd it's comprising +only s components so it comprises only + + align:start position:0% +only s components so it comprises only + + + align:start position:0% +only s components so it comprises only +you know s Omega T some amount of s of 3 + + align:start position:0% +you know s Omega T some amount of s of 3 + + + align:start position:0% +you know s Omega T some amount of s of 3 +omega T some amount of s I'm sorry it + + align:start position:0% +omega T some amount of s I'm sorry it + + + align:start position:0% +omega T some amount of s I'm sorry it +has only sign terms as far as I have + + align:start position:0% +has only sign terms as far as I have + + + align:start position:0% +has only sign terms as far as I have +told you so far okay there's no cosine + + align:start position:0% +told you so far okay there's no cosine + + + align:start position:0% +told you so far okay there's no cosine +terms in this thing so that means it's + + align:start position:0% +terms in this thing so that means it's + + + align:start position:0% +terms in this thing so that means it's +good because I'm kind of building it out + + align:start position:0% +good because I'm kind of building it out + + + align:start position:0% +good because I'm kind of building it out +of its the things I would want to build + + align:start position:0% +of its the things I would want to build + + + align:start position:0% +of its the things I would want to build +it up any questions about that + + align:start position:0% + + + + align:start position:0% + +what else did I do in this waveform + + align:start position:0% +what else did I do in this waveform + + + align:start position:0% +what else did I do in this waveform +well you notice that this half of the + + align:start position:0% +well you notice that this half of the + + + align:start position:0% +well you notice that this half of the +waveform for the negative + + align:start position:0% +waveform for the negative + + + align:start position:0% +waveform for the negative +sign is exactly the + + align:start position:0% +sign is exactly the + + + align:start position:0% +sign is exactly the +flip I come back half cycle and I flip + + align:start position:0% +flip I come back half cycle and I flip + + + align:start position:0% +flip I come back half cycle and I flip +it for the first half of the cycle right + + align:start position:0% +it for the first half of the cycle right + + + align:start position:0% +it for the first half of the cycle right +what characteristic has + + align:start position:0% + + + + align:start position:0% + +that it's halfwave + + align:start position:0% +that it's halfwave + + + align:start position:0% +that it's halfwave +symmetric so what that means is that + + align:start position:0% +symmetric so what that means is that + + + align:start position:0% +symmetric so what that means is that +this white waveform that I've + + align:start position:0% +this white waveform that I've + + + align:start position:0% +this white waveform that I've +synthesized has no even + + align:start position:0% +synthesized has no even + + + align:start position:0% +synthesized has no even +harmonics right so if I did a forier + + align:start position:0% +harmonics right so if I did a forier + + + align:start position:0% +harmonics right so if I did a forier +decomposition on this white waveform + + align:start position:0% +decomposition on this white waveform + + + align:start position:0% +decomposition on this white waveform +what I know is it has well it has no DC + + align:start position:0% +what I know is it has well it has no DC + + + align:start position:0% +what I know is it has well it has no DC +it has no cosine terms and it has no + + align:start position:0% +it has no cosine terms and it has no + + + align:start position:0% +it has no cosine terms and it has no +even harmonics right so the lowest + + align:start position:0% +even harmonics right so the lowest + + + align:start position:0% +even harmonics right so the lowest +harmonic component can only be the third + + align:start position:0% +harmonic component can only be the third + + + align:start position:0% +harmonic component can only be the third +right and then the fifth and the seventh + + align:start position:0% +right and then the fifth and the seventh + + + align:start position:0% +right and then the fifth and the seventh +and so forth Okay so + + align:start position:0% +and so forth Okay so + + + align:start position:0% +and so forth Okay so +um the reason I chose this pattern just + + align:start position:0% +um the reason I chose this pattern just + + + align:start position:0% +um the reason I chose this pattern just +this way for both being odd because I + + align:start position:0% +this way for both being odd because I + + + align:start position:0% +this way for both being odd because I +was trying to happen to be trying to + + align:start position:0% +was trying to happen to be trying to + + + align:start position:0% +was trying to happen to be trying to +match a sine wave but more importantly + + align:start position:0% +match a sine wave but more importantly + + + align:start position:0% +match a sine wave but more importantly +that I made it halfwave symmetric I've + + align:start position:0% +that I made it halfwave symmetric I've + + + align:start position:0% +that I made it halfwave symmetric I've +gotten rid of even harmonic components + + align:start position:0% +gotten rid of even harmonic components + + + align:start position:0% +gotten rid of even harmonic components +and if I imagined that I was going to + + align:start position:0% +and if I imagined that I was going to + + + align:start position:0% +and if I imagined that I was going to +come up here and say oh + + align:start position:0% +come up here and say oh + + + align:start position:0% +come up here and say oh +um you know I'm going to take this VX + + align:start position:0% +um you know I'm going to take this VX + + + align:start position:0% +um you know I'm going to take this VX +here and try to synthesize some output + + align:start position:0% +here and try to synthesize some output + + + align:start position:0% +here and try to synthesize some output +voltage vac by filtering it if I can get + + align:start position:0% +voltage vac by filtering it if I can get + + + align:start position:0% +voltage vac by filtering it if I can get +rid of my even harmonics I can more + + align:start position:0% +rid of my even harmonics I can more + + + align:start position:0% +rid of my even harmonics I can more +easily filter that waveform right when + + align:start position:0% +easily filter that waveform right when + + + align:start position:0% +easily filter that waveform right when +we thought about sort of DC to DC + + align:start position:0% +we thought about sort of DC to DC + + + align:start position:0% +we thought about sort of DC to DC +converters I'm trying to separate out DC + + align:start position:0% +converters I'm trying to separate out DC + + + align:start position:0% +converters I'm trying to separate out DC +from any AC stuff that's kind of easy + + align:start position:0% +from any AC stuff that's kind of easy + + + align:start position:0% +from any AC stuff that's kind of easy +right because they're kind of infinitely + + align:start position:0% +right because they're kind of infinitely + + + align:start position:0% +right because they're kind of infinitely +separated in frequency or at least on a + + align:start position:0% +separated in frequency or at least on a + + + align:start position:0% +separated in frequency or at least on a +log scale um if I'm trying to separate + + align:start position:0% +log scale um if I'm trying to separate + + + align:start position:0% +log scale um if I'm trying to separate +out some fundamental that I want to + + align:start position:0% +out some fundamental that I want to + + + align:start position:0% +out some fundamental that I want to +create and I want to get my fundamental + + align:start position:0% +create and I want to get my fundamental + + + align:start position:0% +create and I want to get my fundamental +here but I've got second harmonic here I + + align:start position:0% +here but I've got second harmonic here I + + + align:start position:0% +here but I've got second harmonic here I +need a very good filter to you know keep + + align:start position:0% +need a very good filter to you know keep + + + align:start position:0% +need a very good filter to you know keep +one Omega T and kill 2 Omega T right + + align:start position:0% +one Omega T and kill 2 Omega T right + + + align:start position:0% +one Omega T and kill 2 Omega T right +well by making it halfway symmetric I + + align:start position:0% +well by making it halfway symmetric I + + + align:start position:0% +well by making it halfway symmetric I +don't need to kill 2 omega-3 I just need + + align:start position:0% +don't need to kill 2 omega-3 I just need + + + align:start position:0% +don't need to kill 2 omega-3 I just need +to kill three Omega T all right so + + align:start position:0% +to kill three Omega T all right so + + + align:start position:0% +to kill three Omega T all right so +there's a large motivation to control + + align:start position:0% +there's a large motivation to control + + + align:start position:0% +there's a large motivation to control +the harmonic content of your waveforms + + align:start position:0% +the harmonic content of your waveforms + + + align:start position:0% +the harmonic content of your waveforms +by picking waveform symmetries and hence + + align:start position:0% +by picking waveform symmetries and hence + + + align:start position:0% +by picking waveform symmetries and hence +the interest in halfwave symmetric + + align:start position:0% +the interest in halfwave symmetric + + + align:start position:0% +the interest in halfwave symmetric +waveforms + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% +questions + + + align:start position:0% +questions +okay why did I bother and by the way I + + align:start position:0% +okay why did I bother and by the way I + + + align:start position:0% +okay why did I bother and by the way I +should have said you know if I had made + + align:start position:0% +should have said you know if I had made + + + align:start position:0% +should have said you know if I had made +my angle Delta equals + + align:start position:0% +my angle Delta equals + + + align:start position:0% +my angle Delta equals +z okay at Delta equals 0 this would just + + align:start position:0% +z okay at Delta equals 0 this would just + + + align:start position:0% +z okay at Delta equals 0 this would just +be a sine wave right so at Delta equals + + align:start position:0% +be a sine wave right so at Delta equals + + + align:start position:0% +be a sine wave right so at Delta equals +0 what I would get is um I would get U + + align:start position:0% +0 what I would get is um I would get U + + + align:start position:0% +0 what I would get is um I would get U +my voltage VX would simply equal + + align:start position:0% +my voltage VX would simply equal + + + align:start position:0% +my voltage VX would simply equal +VDC + + align:start position:0% +VDC + + + align:start position:0% +VDC +times + + align:start position:0% +times + + + align:start position:0% +times +uh summation n = 1 to Infinity + + align:start position:0% +uh summation n = 1 to Infinity + + + align:start position:0% +uh summation n = 1 to Infinity +of 4 Pi + + align:start position:0% +of 4 Pi + + + align:start position:0% +of 4 Pi +n sin of n Omega + + align:start position:0% +n sin of n Omega + + + align:start position:0% +n sin of n Omega +T right where did I get that from that + + align:start position:0% +T right where did I get that from that + + + align:start position:0% +T right where did I get that from that +is just the 4A series for a square wave + + align:start position:0% +is just the 4A series for a square wave + + + align:start position:0% +is just the 4A series for a square wave +okay you can look it up in any book and + + align:start position:0% +okay you can look it up in any book and + + + align:start position:0% +okay you can look it up in any book and +so what that says is that first of all + + align:start position:0% +so what that says is that first of all + + + align:start position:0% +so what that says is that first of all +it's a sine wave series because it's odd + + align:start position:0% +it's a sine wave series because it's odd + + + align:start position:0% +it's a sine wave series because it's odd +right so I knew all the even terms went + + align:start position:0% +right so I knew all the even terms went + + + align:start position:0% +right so I knew all the even terms went +away it because it's halfwave symmetric + + align:start position:0% +away it because it's halfwave symmetric + + + align:start position:0% +away it because it's halfwave symmetric +a square wave is halfwave symmetric + + align:start position:0% +a square wave is halfwave symmetric + + + align:start position:0% +a square wave is halfwave symmetric +then or 50% Dy cycle square waves + + align:start position:0% +then or 50% Dy cycle square waves + + + align:start position:0% +then or 50% Dy cycle square waves +halfway symmetric then it doesn't have + + align:start position:0% +halfway symmetric then it doesn't have + + + align:start position:0% +halfway symmetric then it doesn't have +any this is n odd + + align:start position:0% +any this is n odd + + + align:start position:0% +any this is n odd +only uh summation and that means it's 4 + + align:start position:0% +only uh summation and that means it's 4 + + + align:start position:0% +only uh summation and that means it's 4 +over Pi sin of Omega t plus 4 over 3 Pi + + align:start position:0% +over Pi sin of Omega t plus 4 over 3 Pi + + + align:start position:0% +over Pi sin of Omega t plus 4 over 3 Pi +sin 3 omega T and so forth it has + + align:start position:0% +sin 3 omega T and so forth it has + + + align:start position:0% +sin 3 omega T and so forth it has +harmonics that sort of fall off as one + + align:start position:0% +harmonics that sort of fall off as one + + + align:start position:0% +harmonics that sort of fall off as one +over n but only odd + + align:start position:0% +over n but only odd + + + align:start position:0% +over n but only odd +components does that make sense + + align:start position:0% +components does that make sense + + + align:start position:0% +components does that make sense +everybody + + align:start position:0% +everybody + + + align:start position:0% +everybody +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +I came in and I introduced this angle + + align:start position:0% +I came in and I introduced this angle + + + align:start position:0% +I came in and I introduced this angle +Delta right and I I said what you could + + align:start position:0% +Delta right and I I said what you could + + + align:start position:0% +Delta right and I I said what you could +do for Delta equals z and so forth um + + align:start position:0% +do for Delta equals z and so forth um + + + align:start position:0% +do for Delta equals z and so forth um +why do I have it there what can I do + + align:start position:0% +why do I have it there what can I do + + + align:start position:0% +why do I have it there what can I do +with my angle Delta right I have my one + + align:start position:0% +with my angle Delta right I have my one + + + align:start position:0% +with my angle Delta right I have my one +control variable that I can use and I'm + + align:start position:0% +control variable that I can use and I'm + + + align:start position:0% +control variable that I can use and I'm +still switching each switch only once + + align:start position:0% +still switching each switch only once + + + align:start position:0% +still switching each switch only once +per + + align:start position:0% +per + + + align:start position:0% +per +cycle okay what can I do I can basically + + align:start position:0% +cycle okay what can I do I can basically + + + align:start position:0% +cycle okay what can I do I can basically +vary Delta between zero that's my + + align:start position:0% +vary Delta between zero that's my + + + align:start position:0% +vary Delta between zero that's my +perfect square wave and you know + + align:start position:0% +perfect square wave and you know + + + align:start position:0% +perfect square wave and you know +something less than Pi / 2 + + align:start position:0% +something less than Pi / 2 + + + align:start position:0% +something less than Pi / 2 +okay and I can really use + + align:start position:0% + + + + align:start position:0% + +Delta to do kind of two things one I can + + align:start position:0% +Delta to do kind of two things one I can + + + align:start position:0% +Delta to do kind of two things one I can +vary the + + align:start position:0% + + + + align:start position:0% + +fundamental and two I can control + + align:start position:0% + + + + align:start position:0% + +harmonics I can't do both at the same + + align:start position:0% +harmonics I can't do both at the same + + + align:start position:0% +harmonics I can't do both at the same +time but I can use that as a control + + align:start position:0% +time but I can use that as a control + + + align:start position:0% +time but I can use that as a control +variable without switching more times + + align:start position:0% +variable without switching more times + + + align:start position:0% +variable without switching more times +per cycle + + align:start position:0% +per cycle + + + align:start position:0% +per cycle +okay what would I do in terms of varying + + align:start position:0% +okay what would I do in terms of varying + + + align:start position:0% +okay what would I do in terms of varying +the fundamental very often you know if + + align:start position:0% +the fundamental very often you know if + + + align:start position:0% +the fundamental very often you know if +I'm driving a motor or something right + + align:start position:0% +I'm driving a motor or something right + + + align:start position:0% +I'm driving a motor or something right +um how hard I'm driving the motor kind + + align:start position:0% +um how hard I'm driving the motor kind + + + align:start position:0% +um how hard I'm driving the motor kind +of has to do with the amplitude of the + + align:start position:0% +of has to do with the amplitude of the + + + align:start position:0% +of has to do with the amplitude of the +waveform I'm driving it with right so if + + align:start position:0% +waveform I'm driving it with right so if + + + align:start position:0% +waveform I'm driving it with right so if +I can have some means of amplitude + + align:start position:0% +I can have some means of amplitude + + + align:start position:0% +I can have some means of amplitude +control that's a good thing okay let's + + align:start position:0% +control that's a good thing okay let's + + + align:start position:0% +control that's a good thing okay let's +just think about what is the fundamental + + align:start position:0% +just think about what is the fundamental + + + align:start position:0% +just think about what is the fundamental +of VX here look like right so + + align:start position:0% +of VX here look like right so + + + align:start position:0% +of VX here look like right so +VX I said we can you know we can express + + align:start position:0% +VX I said we can you know we can express + + + align:start position:0% +VX I said we can you know we can express +uh + + align:start position:0% + + + + align:start position:0% + +VX uh as the sum of odd harmonics only + + align:start position:0% +VX uh as the sum of odd harmonics only + + + align:start position:0% +VX uh as the sum of odd harmonics only +right as odd harmonic sign terms only + + align:start position:0% +right as odd harmonic sign terms only + + + align:start position:0% +right as odd harmonic sign terms only +what is + + align:start position:0% +what is + + + align:start position:0% +what is +V1 right so so you know VX of t i could + + align:start position:0% +V1 right so so you know VX of t i could + + + align:start position:0% +V1 right so so you know VX of t i could +express as being V1 s of Omega + + align:start position:0% +express as being V1 s of Omega + + + align:start position:0% +express as being V1 s of Omega +t plus V3 sin of 3 omega t + + align:start position:0% +t plus V3 sin of 3 omega t + + + align:start position:0% +t plus V3 sin of 3 omega t +plus V5 sin 5 Omega + + align:start position:0% +plus V5 sin 5 Omega + + + align:start position:0% +plus V5 sin 5 Omega +T and so forth + + align:start position:0% +T and so forth + + + align:start position:0% +T and so forth +right but if what I'm mainly interested + + align:start position:0% +right but if what I'm mainly interested + + + align:start position:0% +right but if what I'm mainly interested +in is controlling the fundamental is the + + align:start position:0% +in is controlling the fundamental is the + + + align:start position:0% +in is controlling the fundamental is the +the thing I'm driving what is that + + align:start position:0% +the thing I'm driving what is that + + + align:start position:0% +the thing I'm driving what is that +fundamental well we come back you know + + align:start position:0% +fundamental well we come back you know + + + align:start position:0% +fundamental well we come back you know +basically we come back to this + + align:start position:0% +basically we come back to this + + + align:start position:0% +basically we come back to this +expression + + align:start position:0% +expression + + + align:start position:0% +expression +here okay to figure out + + align:start position:0% +here okay to figure out + + + align:start position:0% +here okay to figure out +what V1 is so why don't we write V1 V1 + + align:start position:0% +what V1 is so why don't we write V1 V1 + + + align:start position:0% +what V1 is so why don't we write V1 V1 +in this expression would simply be equal + + align:start position:0% +in this expression would simply be equal + + + align:start position:0% +in this expression would simply be equal +to 2 over T in this case I'm doing it in + + align:start position:0% +to 2 over T in this case I'm doing it in + + + align:start position:0% +to 2 over T in this case I'm doing it in +electrical angle 2 pi integral from + + align:start position:0% +electrical angle 2 pi integral from + + + align:start position:0% +electrical angle 2 pi integral from +integral over 0 to 2 + + align:start position:0% +integral over 0 to 2 + + + align:start position:0% +integral over 0 to 2 +pi uh + + align:start position:0% +pi uh + + + align:start position:0% +pi uh +VX s of Omega not t d Omega + + align:start position:0% +VX s of Omega not t d Omega + + + align:start position:0% +VX s of Omega not t d Omega +T right because I have this so I'm going + + align:start position:0% +T right because I have this so I'm going + + + align:start position:0% +T right because I have this so I'm going +to multiply that by the sine wave + + align:start position:0% +to multiply that by the sine wave + + + align:start position:0% +to multiply that by the sine wave +actually conveniently I've drawn the + + align:start position:0% +actually conveniently I've drawn the + + + align:start position:0% +actually conveniently I've drawn the +sine wave up there right I can I could + + align:start position:0% +sine wave up there right I can I could + + + align:start position:0% +sine wave up there right I can I could +just say that's going to be equal to uh + + align:start position:0% +just say that's going to be equal to uh + + + align:start position:0% +just say that's going to be equal to uh +this is one over Pi but I can do it over + + align:start position:0% +this is one over Pi but I can do it over + + + align:start position:0% +this is one over Pi but I can do it over +only half the cycle and I can get 2 over + + align:start position:0% +only half the cycle and I can get 2 over + + + align:start position:0% +only half the cycle and I can get 2 over +Pi um the integral from Delta to Pi + + align:start position:0% +Pi um the integral from Delta to Pi + + + align:start position:0% +Pi um the integral from Delta to Pi +minus + + align:start position:0% +minus + + + align:start position:0% +minus +Delta of + + align:start position:0% +Delta of + + + align:start position:0% +Delta of +VDC + + align:start position:0% +VDC + + + align:start position:0% +VDC +s of Omega t d Omega + + align:start position:0% +s of Omega t d Omega + + + align:start position:0% +s of Omega t d Omega +T + + align:start position:0% +T + + + align:start position:0% +T +right all I'm doing is I'm multiplying + + align:start position:0% + + + + align:start position:0% + +essentially I'm multiplying this green + + align:start position:0% +essentially I'm multiplying this green + + + align:start position:0% +essentially I'm multiplying this green +waveform or a unit height version of + + align:start position:0% +waveform or a unit height version of + + + align:start position:0% +waveform or a unit height version of +this green + + align:start position:0% + + + + align:start position:0% + +waveform by the white waveform and + + align:start position:0% +waveform by the white waveform and + + + align:start position:0% +waveform by the white waveform and +integrating it to find V1 and because + + align:start position:0% +integrating it to find V1 and because + + + align:start position:0% +integrating it to find V1 and because +the two halves of the integral are the + + align:start position:0% +the two halves of the integral are the + + + align:start position:0% +the two halves of the integral are the +same I can just do it over half a cycle + + align:start position:0% +same I can just do it over half a cycle + + + align:start position:0% +same I can just do it over half a cycle +and double it + + align:start position:0% +and double it + + + align:start position:0% +and double it +okay and if I do that that becomes very + + align:start position:0% +okay and if I do that that becomes very + + + align:start position:0% +okay and if I do that that becomes very +convenient because this just becomes + + align:start position:0% +convenient because this just becomes + + + align:start position:0% +convenient because this just becomes +minus cosine so what I get is I get uh 2 + + align:start position:0% +minus cosine so what I get is I get uh 2 + + + align:start position:0% +minus cosine so what I get is I get uh 2 +over + + align:start position:0% +over + + + align:start position:0% +over +Pi + + align:start position:0% +Pi + + + align:start position:0% +Pi +VDC + + align:start position:0% +VDC + + + align:start position:0% +VDC +uh + + align:start position:0% + + + + align:start position:0% + +cosine of Delta minus cosine of Pius + + align:start position:0% +cosine of Delta minus cosine of Pius + + + align:start position:0% +cosine of Delta minus cosine of Pius +Delta right which just gives + + align:start position:0% +Delta right which just gives + + + align:start position:0% +Delta right which just gives +me I could rewrite this as being equal + + align:start position:0% +me I could rewrite this as being equal + + + align:start position:0% +me I could rewrite this as being equal +to 4 VDC over Pi cosine of Delta + + align:start position:0% +to 4 VDC over Pi cosine of Delta + + + align:start position:0% +to 4 VDC over Pi cosine of Delta +that make sense + + align:start position:0% + + + + align:start position:0% + +everybody so what am I + + align:start position:0% +everybody so what am I + + + align:start position:0% +everybody so what am I +saying if I made Delta equals zero + + align:start position:0% +saying if I made Delta equals zero + + + align:start position:0% +saying if I made Delta equals zero +that's my Square wave case right I just + + align:start position:0% +that's my Square wave case right I just + + + align:start position:0% +that's my Square wave case right I just +get a fundamental that's four over Pi + + align:start position:0% +get a fundamental that's four over Pi + + + align:start position:0% +get a fundamental that's four over Pi +VDC right that's exactly what I said + + align:start position:0% +VDC right that's exactly what I said + + + align:start position:0% +VDC right that's exactly what I said +before for the square wave case as I + + align:start position:0% +before for the square wave case as I + + + align:start position:0% +before for the square wave case as I +keep increasing Delta I you know make it + + align:start position:0% +keep increasing Delta I you know make it + + + align:start position:0% +keep increasing Delta I you know make it +nonzero further into the cycle this way + + align:start position:0% +nonzero further into the cycle this way + + + align:start position:0% +nonzero further into the cycle this way +and further into the cycle that + + align:start position:0% +and further into the cycle that + + + align:start position:0% +and further into the cycle that +way I reduce my fundamental why because + + align:start position:0% +way I reduce my fundamental why because + + + align:start position:0% +way I reduce my fundamental why because +basically as Delta becomes bigger I'm + + align:start position:0% +basically as Delta becomes bigger I'm + + + align:start position:0% +basically as Delta becomes bigger I'm +reducing the amount of overlap between + + align:start position:0% +reducing the amount of overlap between + + + align:start position:0% +reducing the amount of overlap between +the White waveform and the green + + align:start position:0% +the White waveform and the green + + + align:start position:0% +the White waveform and the green +waveform and when I multiply and + + align:start position:0% +waveform and when I multiply and + + + align:start position:0% +waveform and when I multiply and +integrate I get a smaller number and + + align:start position:0% +integrate I get a smaller number and + + + align:start position:0% +integrate I get a smaller number and +that goes as a cosine of + + align:start position:0% +that goes as a cosine of + + + align:start position:0% +that goes as a cosine of +Delta okay so what I can do is if what I + + align:start position:0% +Delta okay so what I can do is if what I + + + align:start position:0% +Delta okay so what I can do is if what I +cared about + + align:start position:0% +cared about + + + align:start position:0% +cared about +mainly was the fundamental amplitude of + + align:start position:0% +mainly was the fundamental amplitude of + + + align:start position:0% +mainly was the fundamental amplitude of +my output I can modulate that for a + + align:start position:0% +my output I can modulate that for a + + + align:start position:0% +my output I can modulate that for a +fixed DC voltage by modulating + + align:start position:0% +fixed DC voltage by modulating + + + align:start position:0% +fixed DC voltage by modulating +Delta okay I have a means of controlling + + align:start position:0% +Delta okay I have a means of controlling + + + align:start position:0% +Delta okay I have a means of controlling +the fundamental + + align:start position:0% +the fundamental + + + align:start position:0% +the fundamental +amplitude does that make sense + + align:start position:0% +amplitude does that make sense + + + align:start position:0% +amplitude does that make sense +everybody I want to drive my motor + + align:start position:0% +everybody I want to drive my motor + + + align:start position:0% +everybody I want to drive my motor +easier I use a bigger Delta I you know I + + align:start position:0% +easier I use a bigger Delta I you know I + + + align:start position:0% +easier I use a bigger Delta I you know I +drive it with less fundamental amplitude + + align:start position:0% +drive it with less fundamental amplitude + + + align:start position:0% +drive it with less fundamental amplitude +if I want more fundamental amplitude I + + align:start position:0% +if I want more fundamental amplitude I + + + align:start position:0% +if I want more fundamental amplitude I +use a smaller Delta and the most I can + + align:start position:0% +use a smaller Delta and the most I can + + + align:start position:0% +use a smaller Delta and the most I can +do is a square wave where I get a + + align:start position:0% +do is a square wave where I get a + + + align:start position:0% +do is a square wave where I get a +fundamental as four over Pi * + + align:start position:0% + + + + align:start position:0% + +VDC questions + + align:start position:0% + + + + align:start position:0% + +what else could I do with this thing + + align:start position:0% +what else could I do with this thing + + + align:start position:0% +what else could I do with this thing +well I can pick Delta to control the + + align:start position:0% +well I can pick Delta to control the + + + align:start position:0% +well I can pick Delta to control the +fundamental another way to control the + + align:start position:0% +fundamental another way to control the + + + align:start position:0% +fundamental another way to control the +fundamental would be to directly control + + align:start position:0% +fundamental would be to directly control + + + align:start position:0% +fundamental would be to directly control +VDC right so in that inverter I'm + + align:start position:0% +VDC right so in that inverter I'm + + + align:start position:0% +VDC right so in that inverter I'm +passing around right they have a they + + align:start position:0% +passing around right they have a they + + + align:start position:0% +passing around right they have a they +have an isolated DCd converter well + + align:start position:0% +have an isolated DCd converter well + + + align:start position:0% +have an isolated DCd converter well +guess what they can use that if they + + align:start position:0% +guess what they can use that if they + + + align:start position:0% +guess what they can use that if they +want to control the VDC that they get + + align:start position:0% +want to control the VDC that they get + + + align:start position:0% +want to control the VDC that they get +right so if you have a dcdc converter + + align:start position:0% +right so if you have a dcdc converter + + + align:start position:0% +right so if you have a dcdc converter +before your inverter you get to control + + align:start position:0% +before your inverter you get to control + + + align:start position:0% +before your inverter you get to control +this because you have a converter that + + align:start position:0% +this because you have a converter that + + + align:start position:0% +this because you have a converter that +can control it all right so maybe I + + align:start position:0% +can control it all right so maybe I + + + align:start position:0% +can control it all right so maybe I +don't need to use Delta to control the + + align:start position:0% +don't need to use Delta to control the + + + align:start position:0% +don't need to use Delta to control the +fundamental maybe I can do something + + align:start position:0% +fundamental maybe I can do something + + + align:start position:0% +fundamental maybe I can do something +else with + + align:start position:0% +else with + + + align:start position:0% +else with +it well the other thing I can do is + + align:start position:0% +it well the other thing I can do is + + + align:start position:0% +it well the other thing I can do is +harmonic + + align:start position:0% +harmonic + + + align:start position:0% +harmonic +control let's ask the + + align:start position:0% +control let's ask the + + + align:start position:0% +control let's ask the +question um what + + align:start position:0% +question um what + + + align:start position:0% +question um what +does what does V3 look + + align:start position:0% +does what does V3 look + + + align:start position:0% +does what does V3 look +like well + + align:start position:0% +like well + + + align:start position:0% +like well +V3 is equal to 2 over 2 pi + + align:start position:0% +V3 is equal to 2 over 2 pi + + + align:start position:0% +V3 is equal to 2 over 2 pi +integral from 0 to 2 pi of uh of VX of + + align:start position:0% +integral from 0 to 2 pi of uh of VX of + + + align:start position:0% +integral from 0 to 2 pi of uh of VX of +T Time s of 3 omega T 3 omega t d Omega + + align:start position:0% +T Time s of 3 omega T 3 omega t d Omega + + + align:start position:0% +T Time s of 3 omega T 3 omega t d Omega +not + + align:start position:0% +not + + + align:start position:0% +not +t right and likewise so what I'm doing + + align:start position:0% +t right and likewise so what I'm doing + + + align:start position:0% +t right and likewise so what I'm doing +in this + + align:start position:0% +in this + + + align:start position:0% +in this +case is I'm going to + + align:start position:0% +case is I'm going to + + + align:start position:0% +case is I'm going to +multiply this waveform by sin 3 omega T + + align:start position:0% +multiply this waveform by sin 3 omega T + + + align:start position:0% +multiply this waveform by sin 3 omega T +right so I'm going to mly it by + + align:start position:0% +right so I'm going to mly it by + + + align:start position:0% +right so I'm going to mly it by +something that looks like + + align:start position:0% + + + + align:start position:0% + +this right and then I'm going to that's + + align:start position:0% +this right and then I'm going to that's + + + align:start position:0% +this right and then I'm going to that's +a that's horribly asymmetric but I'm + + align:start position:0% +a that's horribly asymmetric but I'm + + + align:start position:0% +a that's horribly asymmetric but I'm +going to multiply it by sin3 Omega T not + + align:start position:0% +going to multiply it by sin3 Omega T not + + + align:start position:0% +going to multiply it by sin3 Omega T not +t and then integrate it right well okay + + align:start position:0% +t and then integrate it right well okay + + + align:start position:0% +t and then integrate it right well okay +because that's again halfwave symmetric + + align:start position:0% +because that's again halfwave symmetric + + + align:start position:0% +because that's again halfwave symmetric +I can write that as simply being equal + + align:start position:0% +I can write that as simply being equal + + + align:start position:0% +I can write that as simply being equal +to this is 1 over Pi but then I can + + align:start position:0% +to this is 1 over Pi but then I can + + + align:start position:0% +to this is 1 over Pi but then I can +double it and only do it over half the + + align:start position:0% +double it and only do it over half the + + + align:start position:0% +double it and only do it over half the +cycle and I get uh 2 over Pi the + + align:start position:0% +cycle and I get uh 2 over Pi the + + + align:start position:0% +cycle and I get uh 2 over Pi the +integral from Delta to Pi minus Delta + + align:start position:0% +integral from Delta to Pi minus Delta + + + align:start position:0% +integral from Delta to Pi minus Delta +VDC s of 3 3 omega t d Omega + + align:start position:0% +VDC s of 3 3 omega t d Omega + + + align:start position:0% +VDC s of 3 3 omega t d Omega +T + + align:start position:0% +T + + + align:start position:0% +T +okay it's the same game all over again + + align:start position:0% +okay it's the same game all over again + + + align:start position:0% +okay it's the same game all over again +but what I get is + + align:start position:0% +but what I get is + + + align:start position:0% +but what I get is +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh four + + align:start position:0% +uh four + + + align:start position:0% +uh four +BDC over + + align:start position:0% +BDC over + + + align:start position:0% +BDC over + + align:start position:0% + + + align:start position:0% +Pi um times the cosine of 3 + + align:start position:0% + + + + align:start position:0% + +Delta okay that's just the result of + + align:start position:0% +Delta okay that's just the result of + + + align:start position:0% +Delta okay that's just the result of +that + + align:start position:0% +that + + + align:start position:0% +that +integral okay so I can + + align:start position:0% +integral okay so I can + + + align:start position:0% +integral okay so I can +again you know if I can only you know + + align:start position:0% +again you know if I can only you know + + + align:start position:0% +again you know if I can only you know +once I've determined Delta I determine + + align:start position:0% +once I've determined Delta I determine + + + align:start position:0% +once I've determined Delta I determine +the fundamental and I determine the + + align:start position:0% +the fundamental and I determine the + + + align:start position:0% +the fundamental and I determine the +third + + align:start position:0% +third + + + align:start position:0% +third +harmonic right but what can I do with + + align:start position:0% +harmonic right but what can I do with + + + align:start position:0% +harmonic right but what can I do with +this + + align:start position:0% + + + + align:start position:0% + +well if Delta was 30° or pi/ 6 what + + align:start position:0% +well if Delta was 30° or pi/ 6 what + + + align:start position:0% +well if Delta was 30° or pi/ 6 what +would be the cosine of 3 + + align:start position:0% +would be the cosine of 3 + + + align:start position:0% +would be the cosine of 3 +Delta what's the cosine of 90 + + align:start position:0% +Delta what's the cosine of 90 + + + align:start position:0% +Delta what's the cosine of 90 +degrees zip right so if I pick Delta is + + align:start position:0% +degrees zip right so if I pick Delta is + + + align:start position:0% +degrees zip right so if I pick Delta is +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +30° V3 goes to + + align:start position:0% + + + + align:start position:0% + +zero that's kind of + + align:start position:0% +zero that's kind of + + + align:start position:0% +zero that's kind of +nice right why is that nice I'm trying + + align:start position:0% +nice right why is that nice I'm trying + + + align:start position:0% +nice right why is that nice I'm trying +to make something that looks like a sine + + align:start position:0% +to make something that looks like a sine + + + align:start position:0% +to make something that looks like a sine +wave and has kind of limit the harmonic + + align:start position:0% +wave and has kind of limit the harmonic + + + align:start position:0% +wave and has kind of limit the harmonic +content so that I can filter it right I + + align:start position:0% +content so that I can filter it right I + + + align:start position:0% +content so that I can filter it right I +can by picking Delta is 30 Dees I can + + align:start position:0% +can by picking Delta is 30 Dees I can + + + align:start position:0% +can by picking Delta is 30 Dees I can +make V3 to go to zero what am I doing + + align:start position:0% +make V3 to go to zero what am I doing + + + align:start position:0% +make V3 to go to zero what am I doing +there if I come back here to this + + align:start position:0% +there if I come back here to this + + + align:start position:0% +there if I come back here to this +picture I said I'm multiplying the white + + align:start position:0% +picture I said I'm multiplying the white + + + align:start position:0% +picture I said I'm multiplying the white +waveform by the blue waveform but notice + + align:start position:0% +waveform by the blue waveform but notice + + + align:start position:0% +waveform by the blue waveform but notice +I drew actually Delta is exactly 30° + + align:start position:0% +I drew actually Delta is exactly 30° + + + align:start position:0% +I drew actually Delta is exactly 30° +what happens when it's 30 deges is this + + align:start position:0% +what happens when it's 30 deges is this + + + align:start position:0% +what happens when it's 30 deges is this +positive area in the + + align:start position:0% +positive area in the + + + align:start position:0% +positive area in the +multiplication is sort of a half sign + + align:start position:0% +multiplication is sort of a half sign + + + align:start position:0% +multiplication is sort of a half sign +bump and half sign bump exactly cancels + + align:start position:0% +bump and half sign bump exactly cancels + + + align:start position:0% +bump and half sign bump exactly cancels +this in each half in each half + + align:start position:0% +this in each half in each half + + + align:start position:0% +this in each half in each half +cycle and when I do that boom the third + + align:start position:0% +cycle and when I do that boom the third + + + align:start position:0% +cycle and when I do that boom the third +harmonic goes + + align:start position:0% +harmonic goes + + + align:start position:0% +harmonic goes +away all + + align:start position:0% +away all + + + align:start position:0% +away all +right so what am I left with if I do + + align:start position:0% +right so what am I left with if I do + + + align:start position:0% +right so what am I left with if I do +that + + align:start position:0% +that + + + align:start position:0% +that +um right if I thought about my + + align:start position:0% +um right if I thought about my + + + align:start position:0% +um right if I thought about my +system right suppose I put up um some + + align:start position:0% +system right suppose I put up um some + + + align:start position:0% +system right suppose I put up um some +filter like here's some filter + + align:start position:0% + + + + align:start position:0% + +and here's some you know vac that I want + + align:start position:0% +and here's some you know vac that I want + + + align:start position:0% +and here's some you know vac that I want +for example so here's + + align:start position:0% +for example so here's + + + align:start position:0% +for example so here's +VX and here is you know some vac that's + + align:start position:0% +VX and here is you know some vac that's + + + align:start position:0% +VX and here is you know some vac that's +filtered that I might care about or in + + align:start position:0% +filtered that I might care about or in + + + align:start position:0% +filtered that I might care about or in +some cases I might care about iix which + + align:start position:0% +some cases I might care about iix which + + + align:start position:0% +some cases I might care about iix which +is also related to VX by some filtering + + align:start position:0% +is also related to VX by some filtering + + + align:start position:0% +is also related to VX by some filtering +okay depends what I'm interested in but + + align:start position:0% +okay depends what I'm interested in but + + + align:start position:0% +okay depends what I'm interested in but +what I can think about that is taking + + align:start position:0% +what I can think about that is taking + + + align:start position:0% +what I can think about that is taking +some values of VX and then running + + align:start position:0% +some values of VX and then running + + + align:start position:0% +some values of VX and then running +running it through a filter transfer + + align:start position:0% +running it through a filter transfer + + + align:start position:0% +running it through a filter transfer +function that might be vac over VX and + + align:start position:0% +function that might be vac over VX and + + + align:start position:0% +function that might be vac over VX and +maybe I can make it look like some cut + + align:start position:0% +maybe I can make it look like some cut + + + align:start position:0% +maybe I can make it look like some cut +off right well what do I generally get I + + align:start position:0% +off right well what do I generally get I + + + align:start position:0% +off right well what do I generally get I +get um a + + align:start position:0% +get um a + + + align:start position:0% +get um a +fundamental then I get a second harmonic + + align:start position:0% +fundamental then I get a second harmonic + + + align:start position:0% +fundamental then I get a second harmonic +and a third harmonic and a fourth + + align:start position:0% +and a third harmonic and a fourth + + + align:start position:0% +and a third harmonic and a fourth +harmonic and a fifth harmonic and a + + align:start position:0% +harmonic and a fifth harmonic and a + + + align:start position:0% +harmonic and a fifth harmonic and a +sixth harmonic right so one two three + + align:start position:0% +sixth harmonic right so one two three + + + align:start position:0% +sixth harmonic right so one two three +four five six right I want to put the + + align:start position:0% +four five six right I want to put the + + + align:start position:0% +four five six right I want to put the +fundamental you know within the cut off + + align:start position:0% +fundamental you know within the cut off + + + align:start position:0% +fundamental you know within the cut off +of my filter because I'm trying to get + + align:start position:0% +of my filter because I'm trying to get + + + align:start position:0% +of my filter because I'm trying to get +fundamental of the output but I don't + + align:start position:0% +fundamental of the output but I don't + + + align:start position:0% +fundamental of the output but I don't +want I want to filter off all the + + align:start position:0% +want I want to filter off all the + + + align:start position:0% +want I want to filter off all the +harmonics right well I naturally by + + align:start position:0% +harmonics right well I naturally by + + + align:start position:0% +harmonics right well I naturally by +halfway + + align:start position:0% +halfway + + + align:start position:0% +halfway +symmetry I've gotten rid of two four and + + align:start position:0% +symmetry I've gotten rid of two four and + + + align:start position:0% +symmetry I've gotten rid of two four and +six so I've killed these just by how + + align:start position:0% +six so I've killed these just by how + + + align:start position:0% +six so I've killed these just by how +I've picked the pattern of the waveform + + align:start position:0% +I've picked the pattern of the waveform + + + align:start position:0% +I've picked the pattern of the waveform +to be halfway + + align:start position:0% +to be halfway + + + align:start position:0% +to be halfway +symmetric okay now if I magically go + + align:start position:0% +symmetric okay now if I magically go + + + align:start position:0% +symmetric okay now if I magically go +pick a Delta of + + align:start position:0% +pick a Delta of + + + align:start position:0% +pick a Delta of +30 then I kill off this guy + + align:start position:0% + + + + align:start position:0% + +okay by picking Delta exactly 30 I kill + + align:start position:0% +okay by picking Delta exactly 30 I kill + + + align:start position:0% +okay by picking Delta exactly 30 I kill +off the third and so the lowest Contents + + align:start position:0% +off the third and so the lowest Contents + + + align:start position:0% +off the third and so the lowest Contents +I have to deal with are the fifth and + + align:start position:0% +I have to deal with are the fifth and + + + align:start position:0% +I have to deal with are the fifth and +the + + align:start position:0% +the + + + align:start position:0% +the +seventh it's a heck of a lot easier to + + align:start position:0% +seventh it's a heck of a lot easier to + + + align:start position:0% +seventh it's a heck of a lot easier to +filter the fifth than it is the second + + align:start position:0% +filter the fifth than it is the second + + + align:start position:0% +filter the fifth than it is the second +or + + align:start position:0% +or + + + align:start position:0% +or +third okay so I can get much cleaner + + align:start position:0% +third okay so I can get much cleaner + + + align:start position:0% +third okay so I can get much cleaner +output voltage waveforms even though I'm + + align:start position:0% +output voltage waveforms even though I'm + + + align:start position:0% +output voltage waveforms even though I'm +not switching very often by being very + + align:start position:0% +not switching very often by being very + + + align:start position:0% +not switching very often by being very +clever in how I picked my switching + + align:start position:0% +clever in how I picked my switching + + + align:start position:0% +clever in how I picked my switching +angles + + align:start position:0% + + + + align:start position:0% + +any questions about + + align:start position:0% + + + + align:start position:0% + +that and we are going to see and and + + align:start position:0% +that and we are going to see and and + + + align:start position:0% +that and we are going to see and and +this can all be related back to um some + + align:start position:0% +this can all be related back to um some + + + align:start position:0% +this can all be related back to um some +games about + + align:start position:0% +games about + + + align:start position:0% +games about +um how I'm picking the W precise wave or + + align:start position:0% +um how I'm picking the W precise wave or + + + align:start position:0% +um how I'm picking the W precise wave or +I + + align:start position:0% +I + + + align:start position:0% +I +synthesize with the states I have which + + align:start position:0% +synthesize with the states I have which + + + align:start position:0% +synthesize with the states I have which +are basically plus VDC minus VDC and + + align:start position:0% +are basically plus VDC minus VDC and + + + align:start position:0% +are basically plus VDC minus VDC and +zero okay + + align:start position:0% + + + + align:start position:0% + +let me just give you a little bit of + + align:start position:0% +let me just give you a little bit of + + + align:start position:0% +let me just give you a little bit of +extra um kind of color about inverters + + align:start position:0% +extra um kind of color about inverters + + + align:start position:0% +extra um kind of color about inverters +and we're going to talk about expanding + + align:start position:0% +and we're going to talk about expanding + + + align:start position:0% +and we're going to talk about expanding +out on this in a lot of different + + align:start position:0% +out on this in a lot of different + + + align:start position:0% +out on this in a lot of different +dimensions as we move forward but I + + align:start position:0% +dimensions as we move forward but I + + + align:start position:0% +dimensions as we move forward but I +wanted to give you sort of an idea of + + align:start position:0% +wanted to give you sort of an idea of + + + align:start position:0% +wanted to give you sort of an idea of +like what's the the + + align:start position:0% +like what's the the + + + align:start position:0% +like what's the the +fundamental no pun intended smallest + + align:start position:0% +fundamental no pun intended smallest + + + align:start position:0% +fundamental no pun intended smallest +thing I can do to to get nice waveforms + + align:start position:0% +thing I can do to to get nice waveforms + + + align:start position:0% +thing I can do to to get nice waveforms +okay one thing relates to um how I + + align:start position:0% +okay one thing relates to um how I + + + align:start position:0% +okay one thing relates to um how I +control these switches in the real world + + align:start position:0% +control these switches in the real world + + + align:start position:0% +control these switches in the real world +and I mentioned this because there's the + + align:start position:0% +and I mentioned this because there's the + + + align:start position:0% +and I mentioned this because there's the +theoretically controlling the switches + + align:start position:0% +theoretically controlling the switches + + + align:start position:0% +theoretically controlling the switches +and then there's the Practical + + align:start position:0% +and then there's the Practical + + + align:start position:0% +and then there's the Practical +considerations okay if I come to this + + align:start position:0% +considerations okay if I come to this + + + align:start position:0% +considerations okay if I come to this +thing suppose I put this kind of filter + + align:start position:0% +thing suppose I put this kind of filter + + + align:start position:0% +thing suppose I put this kind of filter +in here right so suppose you know this + + align:start position:0% +in here right so suppose you know this + + + align:start position:0% +in here right so suppose you know this +is equal to this box that I'm drawing + + align:start position:0% +is equal to this box that I'm drawing + + + align:start position:0% +is equal to this box that I'm drawing +right so basically I've got an inductive + + align:start position:0% +right so basically I've got an inductive + + + align:start position:0% +right so basically I've got an inductive +load right so if this load is somewhat + + align:start position:0% +load right so if this load is somewhat + + + align:start position:0% +load right so if this load is somewhat +inductive or maybe it's resistive this + + align:start position:0% +inductive or maybe it's resistive this + + + align:start position:0% +inductive or maybe it's resistive this +is what a motor winding might look like + + align:start position:0% +is what a motor winding might look like + + + align:start position:0% +is what a motor winding might look like +right + + align:start position:0% +right + + + align:start position:0% +right +um I've got to be careful never to open + + align:start position:0% +um I've got to be careful never to open + + + align:start position:0% +um I've got to be careful never to open +circuit that winding right so suppose I + + align:start position:0% +circuit that winding right so suppose I + + + align:start position:0% +circuit that winding right so suppose I +have um S1 and S2 + + align:start position:0% +have um S1 and S2 + + + align:start position:0% +have um S1 and S2 +on right and I wanted to do that + + align:start position:0% +on right and I wanted to do that + + + align:start position:0% +on right and I wanted to do that +switching pattern what's the next thing + + align:start position:0% +switching pattern what's the next thing + + + align:start position:0% +switching pattern what's the next thing +I'm going to + + align:start position:0% + + + + align:start position:0% + +do what would be my next state after S1 + + align:start position:0% +do what would be my next state after S1 + + + align:start position:0% +do what would be my next state after S1 +and S2 is + + align:start position:0% +and S2 is + + + align:start position:0% +and S2 is +on S2 S3 right so I'm going to turn off + + align:start position:0% +on S2 S3 right so I'm going to turn off + + + align:start position:0% +on S2 S3 right so I'm going to turn off +S1 and turn on + + align:start position:0% +S1 and turn on + + + align:start position:0% +S1 and turn on +S3 okay now when you think about doing + + align:start position:0% +S3 okay now when you think about doing + + + align:start position:0% +S3 okay now when you think about doing +that in the real world you got to be a + + align:start position:0% +that in the real world you got to be a + + + align:start position:0% +that in the real world you got to be a +little bit careful right if I ever + + align:start position:0% +little bit careful right if I ever + + + align:start position:0% +little bit careful right if I ever +turned on S1 and S3 together unfortunate + + align:start position:0% +turned on S1 and S3 together unfortunate + + + align:start position:0% +turned on S1 and S3 together unfortunate +things would happen right that's called + + align:start position:0% +things would happen right that's called + + + align:start position:0% +things would happen right that's called +a shoot through and you know if you do + + align:start position:0% +a shoot through and you know if you do + + + align:start position:0% +a shoot through and you know if you do +it too long you will kill the switches + + align:start position:0% +it too long you will kill the switches + + + align:start position:0% +it too long you will kill the switches +right because you'll Short Circuit the + + align:start position:0% +right because you'll Short Circuit the + + + align:start position:0% +right because you'll Short Circuit the +DC bus and he can Source a lot of + + align:start position:0% +DC bus and he can Source a lot of + + + align:start position:0% +DC bus and he can Source a lot of +current into that so you got to make + + align:start position:0% +current into that so you got to make + + + align:start position:0% +current into that so you got to make +sure S1 and S3 are never on together and + + align:start position:0% +sure S1 and S3 are never on together and + + + align:start position:0% +sure S1 and S3 are never on together and +S2 and S4 are never on together at the + + align:start position:0% +S2 and S4 are never on together at the + + + align:start position:0% +S2 and S4 are never on together at the +same time you really really don't want + + align:start position:0% +same time you really really don't want + + + align:start position:0% +same time you really really don't want +to open circuit that load but the nice + + align:start position:0% +to open circuit that load but the nice + + + align:start position:0% +to open circuit that load but the nice +thing about this structure and by the + + align:start position:0% +thing about this structure and by the + + + align:start position:0% +thing about this structure and by the +way this is sometimes called a quote + + align:start position:0% +way this is sometimes called a quote + + + align:start position:0% +way this is sometimes called a quote +unquote vsi or voltage source inverter + + align:start position:0% +unquote vsi or voltage source inverter + + + align:start position:0% +unquote vsi or voltage source inverter +because you're coming from a DC voltage + + align:start position:0% +because you're coming from a DC voltage + + + align:start position:0% +because you're coming from a DC voltage +okay and generating + + align:start position:0% +okay and generating + + + align:start position:0% +okay and generating +AC is that I can have S1 and S2 on first + + align:start position:0% +AC is that I can have S1 and S2 on first + + + align:start position:0% +AC is that I can have S1 and S2 on first +I turn off + + align:start position:0% +I turn off + + + align:start position:0% +I turn off +S1 if I turn on off S1 say this + + align:start position:0% +S1 if I turn on off S1 say this + + + align:start position:0% +S1 if I turn on off S1 say this +current's + + align:start position:0% +current's + + + align:start position:0% +current's +positive um he still has to flow + + align:start position:0% +positive um he still has to flow + + + align:start position:0% +positive um he still has to flow +somewhere but he can just commutate from + + align:start position:0% +somewhere but he can just commutate from + + + align:start position:0% +somewhere but he can just commutate from +S1 into this diode + + align:start position:0% +S1 into this diode + + + align:start position:0% +S1 into this diode +right and so I don't have to + + align:start position:0% +right and so I don't have to + + + align:start position:0% +right and so I don't have to +worry and then once the diode's on I can + + align:start position:0% +worry and then once the diode's on I can + + + align:start position:0% +worry and then once the diode's on I can +turn on + + align:start position:0% +turn on + + + align:start position:0% +turn on +S3 right so basically I will have my Q + + align:start position:0% +S3 right so basically I will have my Q + + + align:start position:0% +S3 right so basically I will have my Q +of T of q1 of T I'll turn the switch one + + align:start position:0% +of T of q1 of T I'll turn the switch one + + + align:start position:0% +of T of q1 of T I'll turn the switch one +off and then I'll have Q3 of T and I'll + + align:start position:0% +off and then I'll have Q3 of T and I'll + + + align:start position:0% +off and then I'll have Q3 of T and I'll +turn him on after some so-called + + align:start position:0% +turn him on after some so-called + + + align:start position:0% +turn him on after some so-called +Deadtime delay between the two + + align:start position:0% +Deadtime delay between the two + + + align:start position:0% +Deadtime delay between the two +switches okay or even if the current was + + align:start position:0% +switches okay or even if the current was + + + align:start position:0% +switches okay or even if the current was +coming this way if I turn on + + align:start position:0% +coming this way if I turn on + + + align:start position:0% +coming this way if I turn on +off S1 the diode's on and then I can + + align:start position:0% +off S1 the diode's on and then I can + + + align:start position:0% +off S1 the diode's on and then I can +turn on S3 and it'll just turn off this + + align:start position:0% +turn on S3 and it'll just turn off this + + + align:start position:0% +turn on S3 and it'll just turn off this +diode naturally right so one thing I + + align:start position:0% +diode naturally right so one thing I + + + align:start position:0% +diode naturally right so one thing I +want to emphasize is in the real world + + align:start position:0% +want to emphasize is in the real world + + + align:start position:0% +want to emphasize is in the real world +you're always having some you know + + align:start position:0% +you're always having some you know + + + align:start position:0% +you're always having some you know +controls to make sure you're not + + align:start position:0% +controls to make sure you're not + + + align:start position:0% +controls to make sure you're not +shooting through your switches + + align:start position:0% +shooting through your switches + + + align:start position:0% +shooting through your switches +okay that's just a practical detail that + + align:start position:0% +okay that's just a practical detail that + + + align:start position:0% +okay that's just a practical detail that +you take care of when you lay out the + + align:start position:0% +you take care of when you lay out the + + + align:start position:0% +you take care of when you lay out the +controls for your inverter any questions + + align:start position:0% +controls for your inverter any questions + + + align:start position:0% +controls for your inverter any questions +about + + align:start position:0% + + + + align:start position:0% + +that what about other switches that + + align:start position:0% +that what about other switches that + + + align:start position:0% +that what about other switches that +uh well then you could get unhappy + + align:start position:0% +uh well then you could get unhappy + + + align:start position:0% +uh well then you could get unhappy +really quick right so if I had igbts and + + align:start position:0% +really quick right so if I had igbts and + + + align:start position:0% +really quick right so if I had igbts and +by the way igbts are very common for + + align:start position:0% +by the way igbts are very common for + + + align:start position:0% +by the way igbts are very common for +driving inverters what they will do is + + align:start position:0% +driving inverters what they will do is + + + align:start position:0% +driving inverters what they will do is +they will go put external diodes across + + align:start position:0% +they will go put external diodes across + + + align:start position:0% +they will go put external diodes across +them because otherwise you will blow + + align:start position:0% +them because otherwise you will blow + + + align:start position:0% +them because otherwise you will blow +them up right so in fact I later I'll + + align:start position:0% +them up right so in fact I later I'll + + + align:start position:0% +them up right so in fact I later I'll +bring in a an inverter module for Prius + + align:start position:0% +bring in a an inverter module for Prius + + + align:start position:0% +bring in a an inverter module for Prius +and you can actually see the the igbts + + align:start position:0% +and you can actually see the the igbts + + + align:start position:0% +and you can actually see the the igbts +and right next to them are the diodes + + align:start position:0% +and right next to them are the diodes + + + align:start position:0% +and right next to them are the diodes +that they put in to do it that's an old + + align:start position:0% +that they put in to do it that's an old + + + align:start position:0% +that they put in to do it that's an old +Prius inverter new Prius inverter uses + + align:start position:0% +Prius inverter new Prius inverter uses + + + align:start position:0% +Prius inverter new Prius inverter uses +silicon carbide fets I think + + align:start position:0% +silicon carbide fets I think + + + align:start position:0% +silicon carbide fets I think +um so that's one way to do this and as I + + align:start position:0% +um so that's one way to do this and as I + + + align:start position:0% +um so that's one way to do this and as I +said this is called a voltage source + + align:start position:0% +said this is called a voltage source + + + align:start position:0% +said this is called a voltage source +inverter it's not the only way you can + + align:start position:0% +inverter it's not the only way you can + + + align:start position:0% +inverter it's not the only way you can +build an inverter okay what would be + + align:start position:0% +build an inverter okay what would be + + + align:start position:0% +build an inverter okay what would be +another way + + align:start position:0% +another way + + + align:start position:0% +another way +well here's another trick suppose I took + + align:start position:0% +well here's another trick suppose I took + + + align:start position:0% +well here's another trick suppose I took +a DC voltage + + align:start position:0% +a DC voltage + + + align:start position:0% +a DC voltage +source and I put it in series with L + + align:start position:0% +source and I put it in series with L + + + align:start position:0% +source and I put it in series with L +big and I'll make this inductor so big + + align:start position:0% +big and I'll make this inductor so big + + + align:start position:0% +big and I'll make this inductor so big +that that this I becomes approximately + + align:start position:0% +that that this I becomes approximately + + + align:start position:0% +that that this I becomes approximately +equal to IDC right if I have a huge + + align:start position:0% +equal to IDC right if I have a huge + + + align:start position:0% +equal to IDC right if I have a huge +inductor here I can sort of make a + + align:start position:0% +inductor here I can sort of make a + + + align:start position:0% +inductor here I can sort of make a +voltage source and series with an + + align:start position:0% +voltage source and series with an + + + align:start position:0% +voltage source and series with an +inductor look at least on a short time + + align:start position:0% +inductor look at least on a short time + + + align:start position:0% +inductor look at least on a short time +scale like a current Source right so I + + align:start position:0% +scale like a current Source right so I + + + align:start position:0% +scale like a current Source right so I +might think of this thing as being a + + align:start position:0% +might think of this thing as being a + + + align:start position:0% +might think of this thing as being a +current Source now right so here I have + + align:start position:0% +current Source now right so here I have + + + align:start position:0% +current Source now right so here I have +some current + + align:start position:0% + + + + align:start position:0% + +IDC and now I might want to create an + + align:start position:0% +IDC and now I might want to create an + + + align:start position:0% +IDC and now I might want to create an +AC current from that + + align:start position:0% +AC current from that + + + align:start position:0% +AC current from that +I could do that again with a set of + + align:start position:0% +I could do that again with a set of + + + align:start position:0% +I could do that again with a set of +switches okay maybe however what I would + + align:start position:0% +switches okay maybe however what I would + + + align:start position:0% +switches okay maybe however what I would +want is switches that do + + align:start position:0% +want is switches that do + + + align:start position:0% +want is switches that do +this + + align:start position:0% + + + + align:start position:0% + +um I'm picking a different switch type + + align:start position:0% +um I'm picking a different switch type + + + align:start position:0% +um I'm picking a different switch type +just for + + align:start position:0% + + + + align:start position:0% + +fun okay these + + align:start position:0% +fun okay these + + + align:start position:0% +fun okay these +switches can carry unidirectional + + align:start position:0% +switches can carry unidirectional + + + align:start position:0% +switches can carry unidirectional +current but they can block voltage in + + align:start position:0% +current but they can block voltage in + + + align:start position:0% +current but they can block voltage in +both directions right because they will + + align:start position:0% +both directions right because they will + + + align:start position:0% +both directions right because they will +not car ever carry current that way and + + align:start position:0% +not car ever carry current that way and + + + align:start position:0% +not car ever carry current that way and +if I try to put a reverse voltage on + + align:start position:0% +if I try to put a reverse voltage on + + + align:start position:0% +if I try to put a reverse voltage on +them this diode will block and + + align:start position:0% +them this diode will block and + + + align:start position:0% +them this diode will block and +everything will be happy okay so then I + + align:start position:0% +everything will be happy okay so then I + + + align:start position:0% +everything will be happy okay so then I +could have a current Source essentially + + align:start position:0% +could have a current Source essentially + + + align:start position:0% +could have a current Source essentially +going in and then instead of having a + + align:start position:0% +going in and then instead of having a + + + align:start position:0% +going in and then instead of having a +filter that looks inductive maybe I will + + align:start position:0% +filter that looks inductive maybe I will + + + align:start position:0% +filter that looks inductive maybe I will +have a filter that looks capacitive + + align:start position:0% + + + + align:start position:0% + +something like this + + align:start position:0% +something like this + + + align:start position:0% +something like this +um and here I can have IAC or I or vac + + align:start position:0% +um and here I can have IAC or I or vac + + + align:start position:0% +um and here I can have IAC or I or vac +or an + + align:start position:0% +or an + + + align:start position:0% +or an +IAC okay so what I'm going to do is I + + align:start position:0% +IAC okay so what I'm going to do is I + + + align:start position:0% +IAC okay so what I'm going to do is I +can switch this DC current into the load + + align:start position:0% +can switch this DC current into the load + + + align:start position:0% +can switch this DC current into the load +this way by having these two switches + + align:start position:0% +this way by having these two switches + + + align:start position:0% +this way by having these two switches +on I can switch this current into the + + align:start position:0% +on I can switch this current into the + + + align:start position:0% +on I can switch this current into the +load the other way by having these two + + align:start position:0% +load the other way by having these two + + + align:start position:0% +load the other way by having these two +switches on + + align:start position:0% +switches on + + + align:start position:0% +switches on +or if I turn these two switches on the + + align:start position:0% +or if I turn these two switches on the + + + align:start position:0% +or if I turn these two switches on the +load gets no + + align:start position:0% +load gets no + + + align:start position:0% +load gets no +current or if I switch these two + + align:start position:0% +current or if I switch these two + + + align:start position:0% +current or if I switch these two +switches on the load gets no + + align:start position:0% +switches on the load gets no + + + align:start position:0% +switches on the load gets no +current that make sense so instead of + + align:start position:0% +current that make sense so instead of + + + align:start position:0% +current that make sense so instead of +synthesizing some pulsed DC voltage + + align:start position:0% +synthesizing some pulsed DC voltage + + + align:start position:0% +synthesizing some pulsed DC voltage +that's positive and negative I can + + align:start position:0% +that's positive and negative I can + + + align:start position:0% +that's positive and negative I can +synthesize a pulse AC current that's + + align:start position:0% +synthesize a pulse AC current that's + + + align:start position:0% +synthesize a pulse AC current that's +positive and negative this would be + + align:start position:0% +positive and negative this would be + + + align:start position:0% +positive and negative this would be +called a current Source + + align:start position:0% +called a current Source + + + align:start position:0% +called a current Source +inverter um now in Practical + + align:start position:0% +inverter um now in Practical + + + align:start position:0% +inverter um now in Practical +applications voltage source inverters + + align:start position:0% +applications voltage source inverters + + + align:start position:0% +applications voltage source inverters +especially at low Powers tend to be much + + align:start position:0% +especially at low Powers tend to be much + + + align:start position:0% +especially at low Powers tend to be much +more common because they're simpler to + + align:start position:0% +more common because they're simpler to + + + align:start position:0% +more common because they're simpler to +realize you don't need a big inductor + + align:start position:0% +realize you don't need a big inductor + + + align:start position:0% +realize you don't need a big inductor +and everything else people do however at + + align:start position:0% +and everything else people do however at + + + align:start position:0% +and everything else people do however at +high power sometimes like current Source + + align:start position:0% +high power sometimes like current Source + + + align:start position:0% +high power sometimes like current Source +inverters because if these switches fail + + align:start position:0% +inverters because if these switches fail + + + align:start position:0% +inverters because if these switches fail +you don't IM immediately short + + align:start position:0% +you don't IM immediately short + + + align:start position:0% +you don't IM immediately short +everything out like from a DC voltage + + align:start position:0% +everything out like from a DC voltage + + + align:start position:0% +everything out like from a DC voltage +source and get a huge pulse of current + + align:start position:0% +source and get a huge pulse of current + + + align:start position:0% +source and get a huge pulse of current +things take time to ramp up through this + + align:start position:0% +things take time to ramp up through this + + + align:start position:0% +things take time to ramp up through this +current which lets you blow fuses or + + align:start position:0% +current which lets you blow fuses or + + + align:start position:0% +current which lets you blow fuses or +shut things down or whatever so at high + + align:start position:0% +shut things down or whatever so at high + + + align:start position:0% +shut things down or whatever so at high +power sometimes people like versions of + + align:start position:0% +power sometimes people like versions of + + + align:start position:0% +power sometimes people like versions of +current Source inverters but more + + align:start position:0% +current Source inverters but more + + + align:start position:0% +current Source inverters but more +frequently people use voltage source + + align:start position:0% +frequently people use voltage source + + + align:start position:0% +frequently people use voltage source +inverters and interestingly by the way I + + align:start position:0% +inverters and interestingly by the way I + + + align:start position:0% +inverters and interestingly by the way I +talked about Deadtime where these two + + align:start position:0% +talked about Deadtime where these two + + + align:start position:0% +talked about Deadtime where these two +switches have to be off at the same time + + align:start position:0% +switches have to be off at the same time + + + align:start position:0% +switches have to be off at the same time +for a little while and we let current go + + align:start position:0% +for a little while and we let current go + + + align:start position:0% +for a little while and we let current go +through the diodes + + align:start position:0% +through the diodes + + + align:start position:0% +through the diodes +here I better never have a time when all + + align:start position:0% +here I better never have a time when all + + + align:start position:0% +here I better never have a time when all +four switches are off because then I'd + + align:start position:0% +four switches are off because then I'd + + + align:start position:0% +four switches are off because then I'd +be open circuiting this guy right so + + align:start position:0% +be open circuiting this guy right so + + + align:start position:0% +be open circuiting this guy right so +what I might do is you know if this + + align:start position:0% +what I might do is you know if this + + + align:start position:0% +what I might do is you know if this +switch and this switch were on I will + + align:start position:0% +switch and this switch were on I will + + + align:start position:0% +switch and this switch were on I will +then briefly turn this one on + + align:start position:0% +then briefly turn this one on + + + align:start position:0% +then briefly turn this one on +also and then I can turn this one off + + align:start position:0% +also and then I can turn this one off + + + align:start position:0% +also and then I can turn this one off +right so I have overlap in my switch on + + align:start position:0% +right so I have overlap in my switch on + + + align:start position:0% +right so I have overlap in my switch on +times instead of dead time in my switch + + align:start position:0% +times instead of dead time in my switch + + + align:start position:0% +times instead of dead time in my switch +on times okay but you can use apply all + + align:start position:0% +on times okay but you can use apply all + + + align:start position:0% +on times okay but you can use apply all +the same Concepts I talked about about + + align:start position:0% +the same Concepts I talked about about + + + align:start position:0% +the same Concepts I talked about about +synthesizing pulse voltage waveforms to + + align:start position:0% +synthesizing pulse voltage waveforms to + + + align:start position:0% +synthesizing pulse voltage waveforms to +synthesize pulse current waveforms we'll + + align:start position:0% +synthesize pulse current waveforms we'll + + + align:start position:0% +synthesize pulse current waveforms we'll +spend most of our talk time talking + + align:start position:0% +spend most of our talk time talking + + + align:start position:0% +spend most of our talk time talking +about voltage source inverters but I + + align:start position:0% +about voltage source inverters but I + + + align:start position:0% +about voltage source inverters but I +just wanted you to know there are other + + align:start position:0% +just wanted you to know there are other + + + align:start position:0% +just wanted you to know there are other +ways to play these + + align:start position:0% +ways to play these + + + align:start position:0% +ways to play these +games any final questions before wrap up + + align:start position:0% +games any final questions before wrap up + + + align:start position:0% +games any final questions before wrap up +for the + + align:start position:0% + + + + align:start position:0% + +day okay we'll pick this up tomorrow + + align:start position:0% +day okay we'll pick this up tomorrow + + + align:start position:0% +day okay we'll pick this up tomorrow +have a great day \ No newline at end of file diff --git a/TJUXTASd0g0.txt b/TJUXTASd0g0.txt new file mode 100644 index 0000000000000000000000000000000000000000..36d47d83a0eadb0880e4215ef05e06480095bab1 --- /dev/null +++ b/TJUXTASd0g0.txt @@ -0,0 +1,3622 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: OK. + +Now, before we start with +the prepared questions, + +I have another question for you. + +It's sort of taking a straw +poll before and after discussing + +something. + +And the question for +you, I want to ask + +you is, what is the +nature of shot noise? + +The whole set of +questions will build up + +to teach you something +about what is shot noise. + +In other words, when +you measure in photons, + +you start with coherent +beams, you always + +have sort of square root n. + +And the question +I want you to ask + +is, when we measure square +root n fluctuations, + +when we detect n +photons, is this + +caused by the nature of +the measurement process-- + +sort of how we detect +photons-- or is it + +an intrinsic quantity +of the quantum fields? + +So I just want to get your +intuition, your gut feeling, + +with the shot noise-- it's +maybe not black and white, + +but if you think it's more +related to the measurement-- + +Well, let me write it down. + +Shot noise. + +OK, so the question +is, shot noise, + +is it caused by the quantum +measurement process, projection + +of whatever you know about it? + +Second part, is it a property +of the quantum fields? + +For instance, if you +don't make a measurement, + +if you run the quantum fields +through a beam splitter, + +we can split it. + +We can split the shot noise +even before we measure it. + +That would mean quantum fields. + +And maybe then, third is both. + +And the fourth is +none of the above. + +So let's just take an opinion. + +And I'm not discussing +the answer at this point. + +I will come back to that at the +end of those 10 or 15 minutes + +and ask you the question again. + +So I just want to see what your +intuitive understanding is when + +you measure the number +of photons in a laser + +beam in an optical field +and you see fluctuations. + +Quantum measurement versus +properties of a quantum field. + +Quantum measurement +means mainly it + +caused the moment you detected. + +And quantum fields means +it's there already before, + +and it can be, +whatever, modified. + +Quantum fields or both. + +All right. + +Good. + +Fine. + +Let's now go through +the question. + +We first have to make sure +that we use the same definition + +and measure things +in the same unit. + +We want to talk about +coherent states. + +So the first is just +little, quick checks. + +Coherent states are +eigenstates of the Hamiltonians + +of a or a dagger? + +For the easy question, I will +just give you 10 seconds. + +All right. + +Stop. + +Display. + +Yes. + +OK. + +That's good. + +Next question. + +Which states realize the +minimum quantum uncertainty + +with delta p delta q +equals h-bar over 2? + +I give you five +different states. + +And in order to use +the clicker, you + +should just answer how many of +them are minimum uncertainty + +states. + +Ready, set, go. + +So three or two. + +Let's just go through them. + +The vacuum, definitely. + +The coherent state, definitely. + +The thermal state, +definitely not. + +Now, number states, +they are eigenstates. + +But let's just take +a big number state. + +It's a big lean in +the quasi-probability. + +It has a huge delta +x and a huge delta p. + +It's definitely-- it's a +very quantum like state, + +very nonclassical. + +But it doesn't have +minimum uncertainty. + +Final question. + +x and p, are those minimum +uncertainty states? + +x and p are a +little bit cryptic, + +because one is infinite, +the other one is 0. + +And infinite times 0 +is h-bar over 2, yes. + +So it's a minimum uncertainty +state, because we discussed it. + +It is the limit of squeezing, +when we perform the limit + +that the squeezing +parameter goes to infinity. + +You can send me +your lawyer, and I + +may have to step back from it. + +But the way I present it, +this is one correct answer. + +It's a limit of an +infinitely squeezed state. + +So if the squeezed vacuum-- +which I forgot actually + +to ask-- if the squeezed vacuum +is a minimum uncertainty state, + +then the x and p state +are the limiting case. + +By the way, your clicks +are getting recorded, + +and the clicks are responsible +for half of your semester + +grade. + +This was a joke. + +You can actually use +clickers and record them, + +but then each student +would have a clicker + +with an already set number. + +But as you see, you just take +a random clicker out of the box + +and put it back in. + +So I have no idea what +your clicker number is. + +And to use the clicker is solely +for our joint entertainment + +here. + +OK, next question. + +What features are unique +to nonclassical light? + +And nonclassical +light means-- well, + +we have discussed +nonclassical lights + +but their different aspects. + +One is that the roots +of the two quadrature + +components-- the uncertainty of +the two quadrature components-- + +the cosine and sine quadrature +components are unequal; + +negative cosine probabilities; +a correlation function, which + +is smaller than 1; and +sub-Poissonian statistics. + +So I've given you four criteria. + +How many of those four are +features which we will not + +associate with classical light, +only with nonclassical light? + +OK. + +Stop. + +Display. + +So there's a wide distribution. + +Let's quickly +discuss the answer. + +Negative cosine +probabilities, well, + +if you use w distribution +and p distribution, + +negative probabilities +are always + +associated with +nonclassical light. + +You can also say +it's the definition + +of nonclassical light. + +g 2 function of-- maybe, I +should not say smaller or equal + +-- smaller than 1 is only +possible for nonclassical + +light. + +Sub-Poissonian +statistics is also + +only possible for +nonclassical light. + +Now, the fact that the two +quadrature components are + +different, you +can just use some, + +and you can choose +classical states + +and prepare them, that +you have more certainty + +in the sine quadrature than +in the cosine quadrature, + +so definitely not. + +OK, now, we really +need prominently + +to discuss quantum noise and +shot noise, the coherent state. + +So just to make sure +that we relate-- + +I will relate later +everything to photon number. + +Because photon +number is intuitive. + +You can count, you can feel +the photons fluctuation + +of square root n and +immediately tell you Poissonian, + +if it's less, +sub-Poisson, all that. + +So I want to make sure we are +correctly associating photon + +number with coherent states. + +So, therefore, +the first question + +is if you have a +coherent state, alpha, + +and we detect all the +photons with a photodiode + +of 100% efficiency, +is the number + +of detected photons +alpha or alpha squared? + +Yes. + +Alpha is, so to +speak, the field. + +And alpha squared +is the intensity. + +So, therefore, form +now one, I will always + +use units for the +photocurrent in such a way + +that the photocurrent, or +the integrated photocurrent, + +is the number of photons. + +So when I say, what is +the current associated + +with a coherent state, +it's just alpha squared. + +Just one side remark. + +If you use a laser +beam, you sort of + +have a stream of +photons, but you + +have a time constant +in your detector, + +and every millisecond +you do a measurement. + +And then, what I mean by +alpha or alpha squared + +is the number of photons +which arrive during the time + +constant. + +So that's sort of the mapping. + +We all usually talk +about coherent state + +in an isolated system. + +But if you have a beam, you +just chop the beam into pieces + +and associate that with +your coherent state. + +OK. + +So now, we are talking about the +measurement of coherent beams. + +We will have now lots +of coherent beams, + +running through beam splitters, +being mixed at beam splitters + +and such. + +And we will always +characterize the strength + +of the coherent beam +by alpha squared. + +And that means in photons. + +So now, the next +question is-- again, + +just to make sure we +are all on the same-- + +we have the same basis, +what is now the variance? + +If I measure the fluctuating +current, I measure the current, + +I have a coherent state, and I +repeatedly measure the current, + +it will show fluctuations. + +And the question is, what is +not the standard deviation + +of the current, what +is the variance, which + +is the standard +deviation squared? + +Yes, the standard +deviation is square root n. + +The variance is n. + +OK. + +Stop. + +Hide. + +OK, now finally, now we can +have fun with beam splitters. + +So, so far, we have +really just repeated + +a little bit of definitions +of classical and nonclassical + +light at coherent states. + +We measured current. + +We know now in what units we +need to measure the current. + +And we characterized the +fluctuations in variance + +not in standard deviation +for the rest of this unit. + +But now, we run the coherent +state through a beam splitter. + +And we have two photodiodes, +one i1 and one i2. + +And we measure the current, i1. + +What is the variance now +in the current you measure? + +OK. + +It is A. It's n/2. + +The way how you +think about what it + +is, when you split a laser +beam with a beam splitter, + +you get two laser beams. + +Each is half the intensity. + +So therefore, each creates a +photocurrent, which is n/2. + +And since one laser beam, +which is a coherent state, + +gives two laser beams, which +are two coherent states, + +each of them has +a variance which + +is equal to the photon number. + +And this means, we have +Poissonian statistics. + +So we have n/2 +photons in each beam. + +The standard deviation is +the square root of n/2. + +And the variance is n/2. + +Ask me, if there +are any questions. + +I mean, this is still +the preliminaries. + +We are not yet bringing +in squeezed light. + +Then, it gets +really interesting. + +OK, we will always +refer to that situation. + +We have a laser beam. + +We split it. + +We create-- and that's actually +your homework assignment. + +We'll actually show +wonderful operator algebra. + +If you split a coherent beam, +you get two coherent beams. + +And they are simply +characterized + +that the alpha value is +now down by square root 2. + +The number is down by 2. + +And if the number is down by 2 +and you have a coherent beam, + +the variance is down by 2. + +Poissonian statistics. + +OK, next question is we +have a beam splitter. + +We have two photodiodes, +i1 and i2, and now + +we measure-- it's important +for balanced homodyne + +detection-- we can now +take the two currents, + +and we can add them or +we can subtract them. + +So the question is, if we add +the two currents, what is now + +the variance in +the two currents? + +Remember, each current +had a variance of n/2. + +So now, you are asked, when +you sum the currents of the two + +photodetectors, what happens +to the two variances? + +Do they sum up? + +Do they--? + +I don't know. + +Do people want +to-- does somebody + +want to defend +his or her choice? + +What do you think +is the variance? + +AUDIENCE: It should be +the answer, you just + +measure before +the beam splitter. + +PROFESSOR: You said it should be +as if I measure before the beam + +splitter, and then it would be +n, because we have n photons. + +Well, you can also see if +you put in a mirror here, + +and you shine the two beams +on the same photodiode. + +And then you would say +you have n photons. + +And if there are Poissonian +fluctuations, you would get n. + +But there is one thing +you should keep in mind. + +Since we have the +beam splitter here-- + +this is the correct answer. + +But I want to point out +one subtlety for you, which + +will become important later. + +The beam splitter has an +open part with the vacuum. + +And so when you said we can +measure before or by sort + +of just combining the two +beams with a big photodiode, + +we can measure after, that's +now a question for you-- which, + +maybe hold the thought +and ask me later, + +if it doesn't become clear +with the following question. + +Hasn't the vacuum entered here, +and hasn't the vacuum, which + +has entered here +added fluctuations? + +So if you put in +a beam splitter, + +and we mix in the vacuum +with our coherent states, + +shouldn't that possibly +mean that if you + +use a big photodiode and +measure everything together, + +that we measure the +variance we had before. + +But isn't that +possibly a contribution + +of the vacuum, because we were +opening the door to the vacuum? + +Please hold the thought. + +OK. + +The next thing is now, you can't +have the solution that we take + +sort of a big photodiode +and combine the two beams, + +because I'm asking +you now is, what + +is the variance in i1 minus i2? + +So you subtract +the two currents. + +So the question is, if +you have technical noise, + +the two beams would +be fluctuating, + +and you would form i1 minus i2. + +All the technical noise +would cancel away. + +But what is shot noise? + +Is shot noise technical noise? + +Is shot noise that every +time you prepare an ensemble, + +there is a hiccup, and you +can split it and subtract it? + +So now, it's getting +really interesting. + +To what extent does a +beam splitter-- does + +a split coherent state, +which has shot noise, + +and you now perform the +difference of the measurement, + +can you get rid of some +of the shot noise or not? + +You vote, please. + +Yes. + +So it doesn't matter +whether we measure + +the sum or the difference. + +So it seems, we have two beams. + +And it seems that the +noise in i1 and i2 + +is completely uncorrelated. + +And whether we perform +the sum or the difference, + +it doesn't matter. + +As long as you think +about classical states + +and coherent states, you can +get away with this notion. + +But now I'm going to +add some squeezed light. + +And now, it's +getting more subtle. + +So we have exactly +the same situation. + +We have our beam splitter. + +We split our coherent beam into +two beams, exactly as before. + +But now, I'm playing +with a vacuum. + +I'm playing with the open +part of the beam splitter, + +and I put in squeezed vacuum. + +And just to be specific, +I've squeezed the vacuum + +in such a way that +what is narrow now + +is the quadrature component +of the coherent state. + +In other words, the coherent +state is cosine omega t. + +In sine omega t, we haven't +been put in any photons. + +Our coherent state has really +a classical oscillation + +in cosine omega t. + +And what I have squeezed +here with the vacuum + +is the noise in the cosine +omega t quadrature component. + +So in other words, the coherent +state and the short axis + +of the ellipse are the +same quadrature component, + +which means, they +can now interfere. + +So the question is +now the following. + +We split the beam. + +We have n/2 photons here. + +We have n/2 photons there. + +And what is now the +result for the variance? + +I formulated a +condition up there, + +which is the strong local +oscillator condition. + +You should assume, +if you get confused, + +that the local oscillator +is very, very strong. + +And if you have any doubts +about some smaller terms, + +just crank up the +power and make sure + +that it's really the local +oscillator which dominates, + +which is the biggest +number in all equations. + +OK. + +So the reference is +without squeezing, + +the noise, or the +variance, in i1 was n/2. + +With n/2 photons, Poissonian +statistics was n/2. + +The question is now, when +we use squeezed light, + +does the variance stay the same? + +Does it go up? + +Does it go down? + +Or does it go to 0? + +By the way, at the end +of the clicker question, + +if you come to me after +class and honestly declare + +you got 100% on all +questions, I buy you a lunch. + +OK, you're done? + +What have you learned? + +It's almost random. + +I will give you a little bit +formalism later, but I mean, + +let me say one thing. + +I had a few discussion +with students after class, + +and I came to the +conclusion after last class + +that I could teach today about +the Deutsch-Jozsa algorithms' + +wonderful applications +of all that, + +but I came to the conclusion, +you can go to the Wikipedia + +and read about yourself. + +Because this is simply +using beam splitters, + +homodyne detection. + +It's just using kind +of all the tools. + +But what I said instead is, +I'd rather spend half the class + +today in trying to give you, +with very simple examples, + +an intuitive understanding. + +I mean, everything +I'm saying you + +can do with operator algebra. + +But to some extent, I feel +when we learn physics, + +we use operators, we use +equations, but in the end, + +we want to shape our intuition. + +And what I try to sort of +challenge you today is, + +what happens to noise? + +So what I have to tell you +now is-- OK, got to hide this. + +The way you should look +at it very soon, I hope, + +is the following, that when +you split the coherent beam, + +you also split the noise. + +In other words, your +little uncertainty circle + +goes down in the amplitude +by square root of 2. + +It is split-- the reflection +coefficient of the beam spit + +and transmission coefficient +is 1 over square root 2. + +But what happens is, you +let in the vacuum here. + +And so, the vacuum comes into +the transmission coefficient + +of 1 over square root 2. + +So what I want to teach you +is that when we think back + +to this example and we had +this situation with a vacuum, + +yes, it looked to +us that we had n/2-- + +so this was i1 plus +i2-- we had n/2 photons + +and the variance was n/2, it +looked completely Poissonian + +as if nothing has happened. + +But what you should understand +is, that the beam splitter + +has taken out-- in amplitude, +1 over square root 2, + +when I square it-- +half of the noise out + +of the coherent state. + +But half of the vacuum +state was added. + +And half of the vacuum state +and half of the intrinsic noise + +of the coherent state give +you back this circle of unity. + +And you can pretty much +neglect all subtleties + +of the quantum field. + +But now, by messing +up with a vacuum, + +by squeezing the vacuum, +half of the shot noise + +comes from the beam splitter. + +It's a 50-50 beam splitter. + +But the other half comes +from the open part. + +But if you squeeze it strongly, +it's on the order epsilon. + +That means, it +doesn't contribute. + +And the correct answer is +now, we have-- just a second. + +It is linear or quadratic? + +Variance is quadratic. + +The correct answer is here, +because this is epsilon; + +this is small. + +We only get half of the +noise we had before. + +We had n/2, and +now, we have n/4. + +OK. + +Now, we take exactly +the same situation. + +So the thought is that you +measure the fluctuation here + +and you have only half of them, +because this squeezed vacuum, + +you've squeezed out the +noise from the vacuum part. + +And since you have a +strong coherent state, + +everything which is sine +omega t doesn't matter. + +Cosine omega t is homodyned, +everything fluctuation + +and cosine omega t. + +When we measure, the intensity +is the square of phi, + +or it's a dagger a. + +And so if you measure +a quadratic quantity + +and we have a very +strong local oscillator, + +everything is projected +on cosine omega t. + +This is why only the +cosine omega t fluctuations + +of discrete statement are here. + +It's a strong local +oscillator limit. + +OK. + +Now, I hope you've +learned something. + +Next question is now, we +do exactly the same thing, + +but now we have +the two currents, + +and the question is, what +is the variance in i-plus? + +I add the two currents. + +What do I get? + +And I give you the +same choices as before. + +Just as a reminder, +when we did not squeeze, + +the variance was n. + +So the question is now, has +this squeezing done nothing, + +or has it reduced the variance? + +What is happening? + +The correct answer is C. It's n. + +And I will show you-- I owe +you a little bit of math now. + +But the way how you should +feel is the following. + +The noise of the coherent +oscillator is equally split. + +But the amplitude-- I mean, +you can say 50% go through, 50% + +go through here. + +And if you add the +two currents, you + +get back the full noise of +the original coherent state. + +You would say what +about the squeezing? + +Well, the issue +is the following. + +The squeezed light, +the squeezed vacuum, + +is reflected with a reflection +coefficient, which is minus 1 + +over square root of 2. + +You know when you have two +beams reflected, by unitarity, + +it's necessary that +one has a negative, + +the other one has a positive +reflection coefficient. + +So therefore, you have +this squeezed vacuum + +appears in this arm +with a minus sign + +and this arm with a plus sign. + +And if you sum up +the two currents, + +you lose everything which is +related to the vacuum part. + +So when you measure +i1 plus i2, what + +came from the vacuum part +entered here with a minus sign, + +here with a plus sign. + +And therefore, you +[INAUDIBLE] what you've + +done at the vacuum part. + +This is when I told you +earlier, you measure i1 plus i2, + +and we all agreed, +the variance was n. + +And I said, well, this +is exactly the same + +if you put a photodiode-- big +photodiode-- behind the beam + +splitter or before +the beam splitter. + +The vacuum has not contributed. + +That's what it seems. + +But even if you squeeze +the vacuum, it cancels out. + +OK. + +Now, the obvious +next question-- but I + +think I've given +you the answer-- + +is what happens when we +now measure the difference, + +i1 minus i2? + +Again, without squeezing, +the variance was n. + +So now, we measure i1 +minus i2, and what happens? + +OK. + +The correct answer is this. + +Well, when I say 0, it's +always epsilon squared terms + +which I neglect. + +I just assume strong squeezing. + +I mean, I just want to give you +the most conceptional problem. + +What happens is the following. + +And I will show +you the equation. + +The noise of the coherent +state is split equally. + +So we have a delta a-- +a is the field operator, + +or the quadrature operator +here-- and a delta a here. + +And therefore, the +original shot noise + +is common mode, because the +reflection and transmission + +coefficients are the same. + +And if you subtract the +current, you completely + +get rid of all noise, +which was originally + +associated with +your coherent state. + +Now, what happens is +the small noise we get, + +but now, we have to +consider the vacuum part. + +But what comes in on the +same quadrature component + +point on the vacuum +tube is strongly split. + +And because the beam +splitter has different signs + +for reflection and transmission, +the noise is anti-correlated. + +And if you take +the difference, you + +will actually measure the noise +of the input of the open part + +of the beam splitter, which +would mean, in terms of order + +epsilon-- I didn't work it out. + +I think it's epsilon squared. + +But it's a power of epsilon. + +So anyway, it seems your +intuition fails here. + +So let me try to give you a few +equations which explain that. + +In your homework and +in most of the course, + +we really want to +work with operators. + +We do transformation +of operators and such. + +But I've found-- for +shaping my intuition-- + +I found a simplified +approach very helpful. + +And I've posted two +references for you. + +One is the article +by Schumacher, + +and one are some +older lecture notes, + +where I summarize some +results of this article. + +And this goes as follows. + +When you have a +coherent input, you + +can say you have a +deterministic classical field. + +And then, you have some noise +in one quadrature component, + +which is cosine omega t. + +And the i is a reminder +that there's also + +noise in sine omega t. + +So you can really say +the electric field has + +a sharp value, +but then, there is + +some fluctuation in the +coefficient of cosine omega t + +and a little bit fluctuation in +the coefficient of sine omega + +t. + +And what is important now is, if +you shine that on a photodiode, + +this is sort of the field. + +The current is proportional +to the square of it. + +You have to be a little +bit careful where + +you put complex conjugation, +but it is the square of it. + +And now, if we use the strong +local oscillator assumption, + +we only take alpha +squared, which + +gives us a number of photons. + +But then, those +fluctuations are homodyned. + +We only take-- we +don't consider that + +the square of the fluctuation. + +We only homodyne it. + +We use, at the cross term, +where we multiply with alpha. + +So if I now put in +photon numbers for alpha, + +we get n photons. + +Yes, OK. + +And now, we get some noise. + +Well, the noise is +the current squared. + +The noise is-- we take the +average of the current squared + +and subtract the average +of the current squared. + +So if you do that-- +this is the current + +squared-- the current +squared average, + +and the average current +squared takes that away. + +So we get this here +as the variance. + +And now, I have to tell you that +in the units I'm using here, + +this delta a1 squared +for coherent state-- + +so if I show the +standard circle-- + +the standard +Heisenberg uncertainty + +circle-- this quantity is 1/4. + +I've just kept track +of my constant. + +So therefore, we obtain in this +picture that the variance is n. + +And this is Poissonian +light with a coherent state. + +And the fluctuation +squared of the current, n, + +this is Poissonian +statistics, square root + +in fluctuations of the current. + +The variance is n. + +But what you should +realize is one thing. + +The moment I have a +strong coherent state, + +the sign quadrature component +doesn't matter at all. + +Because if you multiply +cosine with sine and average, + +you get 0. + +So we only consider the +quadrature component, + +which is given by +the coherent state. + +This is a principle of homodyne. + +You set your +quadrature component + +with your local oscillator. + +OK. + +But now, I have a beam splitter. + +And the way you +can think about it + +is, you can get everything +in operator algebra, + +but just take my word or +follow the procedure now + +that we are saying, +we can always + +think about a +quantum field that it + +has an average value +and some fluctuations. + +And if you pass it through +an optical element or a beam + +splitter, we have a +transmission coefficient, + +but it multiplies the +mean value of the field. + +But it also multiplies the +fluctuations of the field. + +So that's why I'm saying the +beam splitter is actually + +splitting the +fluctuations of the field. + +And therefore, you get reduced +fluctuations in either beam. + +But we have to consider +that there may be vacuum, + +and the vacuum has +also some fluctuations + +and will reflect in or transmit +through parts of the vacuum. + +So now, we want to +understand photocurrents. + +For photocurrents, we take those +quantities and square them. + +So which one should I take? + +Well, let me take +the first line. + +So this is i1. + +So if I calculate now i1, I +obtain t squared alpha squared, + +plus the cross product +between the first two terms + +is 2 times t alpha +times t delta a1. + +And then, I get a second +term from the vacuum, + +which is 2tr alpha delta b2. + +And let me assume that we have +a balanced beam splitter, 50-50. + +So t squared is simply 1/2. + +Alpha squared is the +number of photons. + +So this term becomes n/2. + +t squared is 1/2. + +It cancels with the 2. + +We are left with alpha. + +And this is shot noise. + +Here, appears our square root n. + +So you can say the +shot noise comes + +because we have homodyned +the quantum noise. + +The quantum noise, which is the +same for all coherent states, + +has now been multiplied +with square root n + +through the homodyne process. + +OK. + +So I lost my line. + +That's delta a2. + +And then-- and +this is important-- + +because of the mixing +at the beam splitter, + +the quantum noise off the +vacuum gets also homodyned + +by a factor of square root n. + +So now, I think you see +what I told you before. + +The transmitted beam has +half of its noise coming + +from the coherent state, +and half of the noise + +comes from the vacuum. + +So if I would now +take the current, + +square it, calculate +the variance, + +I would find that I have n/2 +photons with a variance of n/2. + +But an identical +contribution of the noise + +will come from the +original coherent state + +and from the vacuum. + +So therefore, when +I replace the vacuum + +by a strongly squeezed vacuum, +the beam, the current i1, + +lost half of its shot noise. + +We had n/2 photons +with a noise-- + +with a variance, which was n/4. + +Any questions? + +Yes. + +AUDIENCE: Why are the subscripts +on the delta operator of + +[INAUDIBLE]? + +PROFESSOR: Because I should +have dropped them all together, + +saying we are only using +the quadrature component + +of the local oscillator now. + +Everything else is orthogonal +to it and cancels out. + +But if you want me to put them +back, they should all be equal. + +I compiled this writeup from +different lecture notes, which + +one had the cosine, one +had the sine component. + +I just made a +[? stitching error. ?] + +OK. + +So this was i1. + +If I would now look at-- +let me change the color-- + +at the current, i2, the only +anything which changes is + +that because the quantum +noise is transmitted + +with a positive +coefficient, that I + +have to put a plus sign here. + +And now, you realize the magic. + +When you form i1 +plus i2, whatever + +came through the vacuum part, +or through the open part, + +cancels out. + +Therefore, when we calculated-- +or when I asked you + +for the variance +in i1 plus i2, it + +was independent, whether +there was squeezing, + +whether whatever was +at the vacuum part. + +And therefore, it doesn't matter +whether I put my power meter, + +measuring both currents-- +both beams-- before the beam + +splitter or after +the beam splitter. + +But-- yes, a question? + +AUDIENCE: This +last really depends + +on the convention +of where we put + +the negative sign in reflection? + +Because if I had put +the negative sign here + +and a positive there, then +I would have been canceling + +my delta a's instead of b's? + +[INAUDIBLE] the process? + +PROFESSOR: Yes. + +Well, so you should +[INAUDIBLE] conventions here. + +It's clear that you +have to be careful. + +We're talking about +[? face-sensitive ?] detection. + +So what happens +is-- number one is-- + +there is really +physics associated. + +When you have a +beam splitter, one, + +let's assume you have +a piece of glass, + +which has some coating on it. + +One beam is reflected when +it goes from the vacuum + +to material interface. + +The other one is reflected +from the material + +to vacuum interface. + +AUDIENCE: So then, it depends +on which face of the beam + +that will be put which--? + +PROFESSOR: But one thing +is absolutely clear. + +The two reflected beams, one +of them has a minus sign. + +So therefore, when I do i1 minus +i2, the contribution of the-- + +AUDIENCE: --If a's will cancel. + +PROFESSOR: Oh. + +It is clear that +in i1-- OK, yes. + +But the question +is whether we have + +to perform i1 minus +i2 or i1 plus i2. + +Well, I don't know +if it helps you, + +but what happens is we have +a propagating laser beam. + +If you would simply move your +mirror by half a wavelength, + +you get a minus sign. + +So eventually, all of the +phases-- the beam splitter + +phase, the propagating +phase-- all the phases + +have to be controlled. + +And in essence, what you do is +you put an experiment together, + +you measure some noise, and +then you move your mirror + +or you change your phase. + +And then, you really figure out +which noise is now subtracting + +and which noise is +constructively interfering. + +Other questions? + +OK. + +But the other thing +is now obvious. + +When we measure i1 +minus i2, everything + +related to the coherent +input, to the original noise + +of the beam, cancels out. + +And what we are +measuring is only + +the noise which came in +through the other part. + +So this is the reason why, if +you have interesting light you + +want to measure it, you +use a local oscillator. + +But then, you do i1 minus i2. + +And this is what I presented to +you at the end of last class, + +is the way how +people have measured + +the signature of squeezing. + +Any questions? + +And finally, I think this is +one of the coolest things. + +Now, we want to talk about +the displaced squeezed vacuum. + +Now, we put everything together. + +Remember, we have +learned by applying + +the squeezing operator, how +we can squeeze the vacuum. + +And then, with the +displacement operator, + +I can move the displaced vacuum, +that there is an expectation + +value, alpha, for the field. + +So it now looks like a +squeezed coherent state. + +So this is now the +state we have generated. + +And I explained to +you that such a state + +can be generated by using a +beam splitter in the limit where + +the transmission +coefficient goes to 1. + +So the squeezed vacuum is pretty +much transmitted without loss. + +But now, we have a very +strong local oscillator. + +Also, the reflection +coefficient goes to 0. + +We can just crank up the +power in alpha in such a way + +that r alpha squared-- the +number of photons which get + +reflected-- is n. + +So the limit we are looking at +it is small n and large alpha. + +But what we keep constant-- +throughout actually + +all those questions-- is that +we have n photons in that beam. + +And I explained +to you in class-- + +and I showed it to +you with operators-- + +that this setup +is really creating + +the displeased squeezed vacuum. + +OK. + +Now, we have one +laser beam, which + +has an average value +of the field, alpha. + +It has certain properties. + +And now, I want to ask you, what +is the variance of this beam? + +We measure the +photocurrent of this beam. + +We measure-- of course, the +photocurrent is n photons. + +But what is this variance? + +So the choices are +we have n photons. + +Is the variance n? + +We learned before, with +the 50-50 beam splitter, + +that we were able, by +squeezing the vacuum, + +to eliminate half +of the shot noise. + +Maybe what I've done +is wrong, and we get 2 + +and we increase the noise? + +Or does the noise +really go to 0, + +which means it's on the order +of epsilon, whatever I define + +for the squeezing for the short +axis of this squeezed vacuum. + +So now, we are not +subtracting currents. + +No i1 minus i2. + +We have one beam hitting +straight the photodiode. + +There are n photons +per unit time. + +And the question is, what are +the fluctuations of this beam? + +What is the variance? + +Well, the correct +answer is this one. + +What happens is the following. + +In terms of fields-- +you should go + +through that again +a little bit more + +slowly-- but what happens +is the coherent state is + +sort of this disk. + +But when we make alpha +larger and larger, + +the disk of the coherent +state is the same. + +But now, we have of a +reflection coefficient, + +which goes to 0, such that +the product of r alpha + +stays the same. + +But that means the +reflected beam, + +we have divided the disk by +the reflection coefficient-- + +multiplied with the +reflection coefficient-- + +so therefore, the original +noise of the coherent beam + +has been completely eliminated +because of the small reflection + +coefficient. + +So the only noise which is +there, is from the other part. + +But we have strongly +squeezed the noise + +in this quadrature component. + +And therefore, the +noise goes really down + +to 0 or to I think it's +epsilon squared when epsilon + +is the normalized widths of +the narrow part of the ellipse. + +I've written down the +math for you here, + +which is the following. + +We have a reflection coefficient +for the coherent beam + +and the reflection coefficient +for the fluctuating fields. + +Whereas, the squeezed +fluctuations, + +they are fully transmitted. + +And what I'm +completely neglecting + +is-- and you'll realize it +already-- the other quadrature + +component. + +Because the moment I square +it to obtain the current, + +I'm only considering +parts, which + +are in the right +quadrature component, + +that they get enhanced by alpha. + +So if I square that and +neglect all terms which do not + +get multiplied with +alpha, I get this line. + +And now, you see that +this term here-- the one + +which had the fluctuations +of the coherent beam-- + +is what I just said. + +r times alpha is n. + +So this is n. + +It would be the normal variance. + +But now, we have +another power of r. + +So therefore, delta a1 +really got diminished. + +I mean, you see that +actually already better + +in the previous line. + +So therefore, in the limit of +r, in the limit considered, + +there is no contribution +from the fluctuations + +of the coherent beam. + +The only fluctuations +come from the squeezing. + +And therefore, the variance +is, well, 0 or epsilon squared. + +So you can create a beam, which +has no fluctuations-- or almost + +no fluctuation-- in +the photon number + +by mixing a strong local +oscillator with a squeeze + +vacuum. + +And that would mean now, +if you take this beam + +and send it through +a cesium cell + +and do spectroscopy of cesium, +you have reduced noise, + +and you are more sensitive +to obtain, to observe, + +a small quantity of cesium. + +I've posted it actually-- +this is exactly what + +I described here, how +the first spectroscopy + +with squeezed light was done. + +And I've posted the paper +of Jeff Kimble's group + +on our website. + +So I'm wondering, by going +through these examples, + +if I would ask you that the +shot noise, which is square root + +n in the fields and +n in the variance, + +after looking at the beam +splitter and the modes which + +are involved, how would you +now answer this question? + +Is the shot noise related +to quantum measurement, + +is it related to quantum +fields, both, or none? + +That's interpretation +of physics; + +I think there is +no right and wrong. + +I would actually very +strongly-- my opinion is, + +it's B. It's really +the quantum fields. + +The quantum fields +which are split. + +If the noise were done +in the measurement, + +you cannot have constructive +and destructive interference due + +to the positive and negative +reflection coefficient. + +So for me, the noise, which +is responsible for shot noise, + +is a field which +can be split where + +you have constructive and +destructive interference + +even before the measurement +process takes place. + +But this is sort of +my interpretation. + +And let me maybe point out why +I think that for those cases, + +the quantum measurement +process is not relevant. + +Here, we've always talked +about square root n + +fluctuations, where n is big. + +So the fluctuations of +the coherent field-- + +all of the fluctuations +we were discussing here-- + +had many, many photons. + +So to some extent that we have +maybe just a single photon, + +and we can only get one +click and not two clicks, + +doesn't measure it. + +That doesn't matter here. + +All the fluctuations +we considered + +here were fluctuations +in the field, where + +many, many photons +were involved. + +So, therefore, I think +the quantum character + +of the measurement process +does not really show up. + +If I would construct +something-- other examples-- + +where we wouldn't always have +this strong local oscillator, + +this strong homodyning. + +Then I think we +would find quantum + +noise of a single photon, +and then I would say, + +we're getting closer, that's +really quantum measurement. + +But here, I would say +the short noise related + +to a strong local +oscillator-- at least, + +I find it easier for go +through those questions + +if I think about it as a quantum +field, which can be split, + +added up. + +Constructive and +destructive interference. + +Good. + +Questions? + +Yes? + +AUDIENCE: So, when we're talking +about [INAUDIBLE], can we + +actually talk about it +without referring to i, + +because that makes me +think of measurements. + +PROFESSOR: You mean +i, as the current? + +AUDIENCE: Yeah. + +PROFESSOR: But we +have to do something. + +OK, what happens is +i was nothing else + +than the expectation +value of a dagger a. + +In other words, whenever we +had a photodiode-- I mean, + +we learn how to +transform modes, and i + +was synonymous to +performing a measurement, + +and the measurement +is a dagger a. + +And when we talked +about i squared, + +in order to get the noise, +the operator involved + +was a a dagger, a a dagger. + +I think I will ask you +something about the displaced. + +Yeah, it's too nice a problem. + +I should ask about the +displaced squeezed vacuum + +in the next problem set. + +I really want you to calculate, +maybe with a higher order + +term-- it's a three-liner-- in +operators, what is the noise? + +And in your calculation, +photodiode will not appear. + +What will appear is +"Calculate the expectation + +value of a dagger a. + +If you call it a +measurement process, + +it's [? inobservable ?] and +it's an expectation value + +of an emission operator. + +Other questions? + +AUDIENCE: [INAUDIBLE] +understand the [INAUDIBLE] + +for a stream of particles, +which [INAUDIBLE] + +with a constant +probability per unit time? + +[INAUDIBLE] The detector +is also [INAUDIBLE]. + +I think you also +get the square root. + +PROFESSOR: Well, a lot of +classical counting statistics + +needs to short noise. + +If you have +independent particles + +with a certain probability, +then you get short noise. + +But I would sort of +press you hard to make + +a classical explanation for +the last example I gave you, + +where we had a strong +local oscillator. + +We reflected it and superimposed +it with squeezed vacuum. + +At that point, all the +short noise has disappeared. + +So therefore, I would be +hard-pressed to connect it + +with the classical probability +of detecting a photon. + +Of course, classically +speaking, the empty part + +of a beam splitter is +empty, and squeezed + +vacuum doesn't +exist classically. + +Yes, [INAUDIBLE]. + +AUDIENCE: So it might be +kind of a silly question, + +but we say we have a +minimum uncertainty + +state when delta x delta p is 0. + +But a lot of times, +we talk about + +the number-phase uncertainty. + +So, I'm just curious, +because the coherent state + +has the same circle +of-- the area + +of the circle is +the same, right? + +I know this is +wrong, but can't you + +always make the delta +m delta phi uncertainty + +very small by having +a very large n? + +Delta n stays the same, but +the angular spread always + +goes down as you make the circle +farther away from the origin? + +PROFESSOR: So you're talking +about an uncertainty relation + +we have not discussed. + +In the last homework, +you looked at it. + +So what happens is if you +have a coherent state, + +you would say the phase angle +phi has this uncertainty. + +And then there's an +uncertainty relation. + +AUDIENCE: Maybe you should +have talked about this problem + +yesterday. + +I think the uncertainty +and the size of the disc + +is constant, +[INAUDIBLE] in alpha. + +But alpha is proportional not +to n, but the square root of n. + +[INAUDIBLE] an arrow propagation +[INAUDIBLE] square root of n. + +If we move the +circle further away, + +the uncertainty alpha stays the +same, but the uncertainty of n + +goes actually up. + +But we don't see +this [INAUDIBLE], + +because we only have +alpha, not [INAUDIBLE]. + +PROFESSOR: Yes, you +have to be careful. + +That's another comment +I wanted to make, + +but thanks for +reminding of that. + +When we have coherent states, +it looks that the uncertainty + +is always the same, +because it's a disk. + +But we learned today, +and in the last class + +that the uncertainty of the +coherent state when you measure + +the photocurrent +is square root n. + +What happens is the following: +the uncertainty-- and this is + +what I was referring +to-- the uncertainty, + +let's say delta a in one +[? quadrature ?] component, is + +constant for the coherent +state, independent of n. + +But that would mean +what you really + +calculate, when you +calculate the photocurrent, + +is alpha plus delta +a which is constant. + +But then you square it. + +In the limit of a +strong coherent state, + +you get alpha squared, which +is the number of photons, + +plus 2 alpha times delta a. + +So the delta a, +which is constant, + +gets multiplied with +square root n here. + +So therefore when you go +to launch a coherent state, + +you increase the +number uncertainty, + +but by the same factor, you +reduce the phase uncertainty. + +Well, I thought this +would take half an hour. + +It took an hour, but I hope +it was time well spent. + +So let's get started +on the next unit, which + +is fully dedicated +to single photons. + +So after learning +about different aspects + +of the electromagnetic +field, we now + +want to focus on +the purest quantum + +states, which are +single photons. + +And this unit it is +definitely motivated + +by quantum information +processing. + +We want to use control +over single photos + +to realize interesting devices. + +We talk about beam splitters +and phase shifters, + +but then we put beam splitters +and phase shifters together + +to make Mach-Zehnder +interferometers. + +And then eventually +I can show you + +how Mach-Zehnder interferometers +with a non-linearity + +can be used to +realize quantum gates. + +But let me make maybe +one general comment here. + +This unit here on single photons +has actually two purposes. + +It tries to give you some +fundamentals, which are really + +necessary to follow recently +literature in quantum + +information science, so +we introduce some concepts + +of gates and truth +tables and such. + +But for those of +you who are maybe + +less interested in quantum +information science, + +I have to say that as a more +traditional atomic physicist, + +I've never worked in quantum +information science myself. + +I started with atomic +molecular spectroscopy, + +and advanced from laser +cooling to quantum gases. + +I feel that using the +quantum logic formalism + +is a very elegant way of +organizing your thoughts. + +So I do feel even for the +rest of the world, who is not + +doing kind quantum +information process, which + +is a pretty big +fraction of AMO science + +these days, even +for the rest of us, + +to use concepts of quantum +logic and quantum information + +is very, very powerful. + +So in other words, I +would say right now + +every atomic physicist should +have some knowledge in what + +happens to beam splitters, what +happens to singular photons + +when they're manipulating, +and the way, the approach, + +how we formulate it using +concepts of quantum information + +processing is +extremely powerful. + +Like in quantum +mechanics, you need + +to know the Schrodinger +representation + +and the Heisenberg +interpretation. + +You can't get away with one. + +Similarly, for some aspects +of the propagation of quantum + +states, you should just use the +language of quantum information + +processing. + +Just sort of to give you +already an outlook where + +I think everything +comes together, + +I've taught for 15 +years, 20 years, + +about decoherence +and master equation. + +And I know how to derive it +from general quantum physics, + +and I will show you that +later in this course. + +But then I learned from +Professor Ike Chuang, + +when I co-taught +the course with him, + +that he could actually make +a model for decoherence + +by just passing light through +many, many beams splitters. + +So there is a beam +splitter model + +for decoherence, which +is just beautiful. + +You can give derive a master +equation by just sending light + +through many, many +beams splitters. + +So that taught me something, +that actually those + +was elementary devices for +quantum information science can + +really act as conceptual +models for more complicated, + +more general things. + +So I've decided now, +over the last few years, + +to make quantum +information language + +an essential ingredient +of this course. + +But I should say over +the last couple of years, + +I've de-emphasized some of the +more formal algorithmic things, + +but I'm focusing +on the concepts. + +And I think some +concepts are really + +highlighted by using +quantum information aspects. + +So with that +introduction, we want + +to talk about single photons. + +And I want to introduce for +you the single photon qubit. + +Now, [INAUDIBLE] would think, if +you talk about single photons, + +you automatically +have one qubit. + +0 is no photon. + +One is the single photon state. + +We make in addition +later on, this + +is not the most +robust qubit, because + +if, due to unavoidable losses +or limited quantum efficiency, + +you have one photon, +and you lose it, + +you think the bit +has been flipped. + +So you don't want +to really use that, + +but we will use, in a +moment, a single photon + +in two different quantum states. + +And then, if you detect zero, +you know you've lost it. + +We will talk about one photon, +which is either here or there. + +And this is zero of +our qubit, and this + +would be one of our qubit. + +But we will come to that later. + +I first need the Hilbert +space of zero one + +to introduce a few +things, and then we'll + +use what we've learned to define +the dual-rail single photon + +state. + +But for now we don't have +to make this distinction. + +The question we +want to answer is + +what happens when +those states pass + +through optical components. + +I want to show you how +beam splitters and phase + +shifters can be used-- very +simple optical components-- + +they can be used to realize +an arbitrary single qubit + +operation. + +And then we introduce +non-linear interferometers, + +and we get two qubit operations. + +So let's start out very simple +and talk about phase shifters + +and beam splitters. + +And this is pretty +much how far we + +will get today in this chapter. + +Well, if you have a single +photon and time passes on, + +the single photon +gets phase shifted. + +If you pass it through +a dispersive medium, + +it will have +another phase shift. + +So this is how phase +shifts can be realized. + +But there is one caveat, and +that immediately tells us + +we can't get away with just +a single photon in one fiber + +and phase shifting it, +because everything phase + +shifts a photon. + +Time and everything which +is in the beam path. + +So whenever we talk about the +phase, we need a reference. + +So therefore, we're +immediately drawn + +that one mode and one +photon is not enough, + +even if you're interested +in one-photon gates, + +we need two modes. + +Just think about two wave +guides or two optical fibers. + +We call them mode A and B. +If you put one photon in-- + +and this is now the symbol for +a phase shifter, a little box + +with the letter +phi-- then we get + +a phase shift of the state one. + +And the second mode A +acts as a reference mode + +to detect the shift +of phase, let's say + +by interfering the two photons. + +So in general, we +have an input state, + +and we obtain an output state, +which has a phase shift. + +We'll come back to +phase shifters later. + +So we'll have two modes. + +The next thing we can do +is we can combine modes, + +and this is done +with a beam splitter. + +So we've talked +about beam splitters + +in the context of +homodyne detection. + +We've talked about +beams splitters most + +of the first hour with +a clicker question, + +and I was mainly referring +to the beam splitter + +before in a rather +non-formal way. + +If you've a 50:50 beam splitter, +and you have two inputs, + +you get a symmetric and +antisymmetric combination + +of the two, if it's a +50:50 beam splitter. + +What else can you get? + +Or, I used the concept of just +reflection and transmission + +coefficients. + +I think that's all important +to get an intuitive + +feel for the beam splitter. + +But now I use a more +rigorous approach. + +I have a beam splitter, +which is characterized + +by an angle theta. + +We will later find +out what theta is. + +And we have an input mode A +and a second input mode B, + +and those modes get mixed now. + +We have output modes B prime +and output modes A prime. + +And we can use the +Schrodinger picture + +and talk about the photon +states in those modes, + +but I prefer to use +the Heisenberg picture, + +so when I put A, A +prime, B and B prime in, + +just think about +annihilation operators which + +annihilate photons +in those modes. + +So what I postulate +is that this system + +is described by the +following Hamiltonian. + +And I'm sort of telling +you, this Hamiltonian + +describes this beam splitter. + +You will say, why and how? + +Well, I will tell you what this +Hamiltonian does to the modes, + +and then we have the +quantum description + +of the beams splitter, and you +will then see in your homework + +that this quantum description +of the beam splitter + +does exactly what it is expected +to do to coherent states. + +It just splits a +laser beam into two, + +with a reflection and +transmission coefficient + +which are cosine squared +theta and sine squared theta. + +And I will also show you that +this beam splitter is doing + +the same, splitting +with cosine squared + +and sine squared theta +probabilities, a single photon. + +So in essence, I give +you the Hamiltonian, + +I discuss that the +transfer matrix, which + +is built upon this Hamiltonian, +does everything you ever + +wanted a beam splitter to do, +and therefore you can say, + +this defines the beam splitter. + +OK, if you have a +Hamiltonian, that + +means after propagating +through the Hamiltonian, + +we have the following transfer. + +You may be familiar with +putting the unitary time + +evolution here, and the +time which has elapsed, + +but we are always +using a fixed time + +after the light has +transformed the beam splitter. + +So you can see the +time t is absorbed + +in the definition of +h, the Hamiltonian, + +and b is really the unitary +time evolution from [? being ?] + +before and [? being ?] +after the beam splitter. + +So the transformation, +which transforms the modes + +at this beam splitter, has now +the following unitary operator. + +And we have modes a, +b, mode one and two, + +before the beam splitter. + +After the beam +splitter, they have + +been transformed to +a prime and b prime. + +And we obtain that by +taking the input modes + +and doing unitary +time evolution. + +You do simply the +operator transformation + +for unitary transformation. + +So we can now transform +the operators a and b. + +I'm not going with you +through the exercise + +how you transform an operator. + +I think in undergraduate +quantum mechanics classes, + +you do the +Baker-Campbell-Hausdorff + +formula, how to use with +operators in the exponent. + +And if you do with that, +you find-- not surprisingly, + +a beam splitter is a linear +element-- that what you get + +is a linear +combination of a and b. + +So if you don't like me +postulating an operator + +and saying, "Believe me, +this is a beam splitter," + +you can reverse engineer. + +You can say, this really looks +like the modes, the operators + +a b get linearly superposed +with cosine and sine. + +This is what a beam splitter +does, is it mixes two modes. + +And then you can reverse +engineer and figure out + +that it's exactly the +Hamiltonian above which + +does it. + +So your homework will show +that this happens exactly + +for coherent states. + +So if you've a coherent +state with alpha, + +you get a coherent state with +alpha cosine theta in one arm, + +and alpha sine theta +in the other arm, + +and you will see that +everything works beautifully. + +I have to use one convention +now for a 50:50 beam splitter. + +And I use a convention +that I chose theta + +to be pi over 2 +b and 90 degrees. + +And we want to use +symbolic language, + +because we want to draw +diagrams of multiple beam + +splitters and such. + +So this tilted square is the +symbol for beam splitter. + +We have input ports a +and b on the left side. + +We have output ports, which +are now b prime and a prime. + +And for the 50:50 beam +splitter, the modes + +are symmetric and +antisymmetric superpositions. + +So this is the symbol for +the unitary transformation b. + +And since one output port has a +minus sign, it's antisymmetric, + +and one is positive. + +We usually put a dot there +which distinguishes the two + +different ports. + +So this is the operator B. + +We have already used, for +the unitary transformation, + +the operator b dagger. + +So for the operator b dagger, +using the equations above, + +we have input modes a +b, but what happens now + +is for the operator b +dagger, the output modes + +are interchanged. + +So we have a plus b over +square root a, a minus b + +over square root 2, and +therefore the symbol + +for b dagger has the dot here. + +I just want to warn you +that there are other phase + +conventions in the literature +which are equivalent. + +But sometimes if you read a +paper and all of the minus + +signs appear somewhere +else, well, people + +have a different +phase convention. + +You can postulate that +you have a beam splitter + +without having the i here. + +And everything works similarly. + +It's just that, for +instance, in this equation, + +you get an i here. + +So imaginary units +and plus-minus signs + +and that busyness are +phase conversations. + +If you'd say, hey, but if +you another definition, + +don't you have +another beam splitter? + +Yes, it is another +beam splitter, + +but I can always get it out +of my beam splitter-- which + +now is our beam splitter-- +by putting a phase + +shifter afterwards. + +So it doesn't limit the +generality of the discussion + +by defining our beam +splitter in this way. + +OK, time is over. + +Reminder, we have another +class this week on Friday, + +and finally, your +graded homework is here. + +Have a good afternoon. \ No newline at end of file diff --git a/TcNXre5Ea6Y.txt b/TcNXre5Ea6Y.txt new file mode 100644 index 0000000000000000000000000000000000000000..5d3de36263592fede957e6458bc61dc4e5ac19ab --- /dev/null +++ b/TcNXre5Ea6Y.txt @@ -0,0 +1,3674 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +IAIN STEWART: All right, so this +is where we got to last time. + +So we were on the road to +deriving the leading order SCET + +Lagrangian. + +We said that there +were some things + +that we had to deal with, +in particular expanding it. + +And we started out, +as a first step, + +getting rid of two of the +components of the field + +that we said are not going +to be ones that we project + +onto in the high energy limit. + +And that led us to this +Lagrangian right here, + +but we haven't yet expanded it. + +We haven't yet separated +the ultra soft and collinear + +momenta or the ultra soft +and collinear gauge fields. + +And so in order to +do that, I argued + +that you have to make +multipole expansion. + +And I talked a +little bit about what + +the multipole expansion would +look like in position space. + +And then I said, it's better for +us to do it in momentum space. + +And we started to do that. + +And we're going to +continue to do that today. + +So first of all, let's +just go to momentum space. + +So I've called the field here-- +since it's not the final field + +that we want, I introduced a +crummy notation for it, Cn hat. + +And once we get to the final +field, it won't have a hat. + +And that'll be the one that +we keep using from then on. + +So let's take this hatted guy, +which is not the final guy, + +Fourier transform him and +talk about doing things + +in momentum space. + +In momentum space, I'm +going to make an analogy + +with what we did in HQET. + +In HQET, we split the +momentum into two pieces. + +We had a piece that was large +and a piece that was small. + +And then we could expand. + +I'm going to do the +same thing here, + +split it into a large +piece and a small piece + +where I'll call the +large pieces the one + +in the lambda components. + +And then the small +piece will just + +be all the pieces that are +of order lambda squared. + +So if you draw a picture for +this, it looks as follows. + +How should I think about +what I'm doing here? + +Here's how I want you +to think about it. + +So let's draw a two-dimensional +picture in minus perp space. + +In plus space, there's no split +because there's no plus here. + +So it's really in the +minus and the perp space + +that we have to make a split. + +Yeah, let's see. + +All right, so I'm +going to draw a grid. + +And the way I want to +make this split precise + +is I'm going to think-- + +OK, so I should have maybe made +my axes in a different color + +to distinguish +them from the grid. + +Let's make them orange. + +So the way I want to think +about these two types of momenta + +is I'm going to think about +these Pl's as discrete + +and the Pr's as continuous. + +So let's think about +the Pl's as labeling + +these points at +the center of each + +of these boxes in the grid. + +This one was supposed to be-- + +that's fine. + +My squares are +not the same size, + +but they roughly should be. + +And so then we can think +about, if we specify + +some momentum in the space-- + +let's say we specify momentum +that points to this point right + +here. + +The way that I can +point to that point + +is I take one vector that +points to the center. + +And then I take +another small vector + +that points to that point. + +The large vector is the Pl. + +The small vector is the Pr. + +OK, so this guy here is Pl. + +Maybe I should make the other +one a different color, Pr. + +And so the way that we +should think about this + +is in the following sense. + +We should think about +the average spacing + +in between these +grid points here + +is something that gets +a power counting that + +makes it of order Q lambda. + +And the average spacing between +grid points in this direction + +is something that +makes it order 1. + +But if I ask about +distances inside a box, + +if I ask about a +distance like this one, + +that's of order lambda squared. + +So to get between +boxes, you need + +to make a big jump to +the larger momentum. + +But to move around in a box, +that's only small momenta. + +AUDIENCE: So why can't +you have order lambda + +basically inside the box +in the P minus dimension? + +IAIN STEWART: Yeah. + +So you could. + +So you can ask, where is in +order lambda momentum in the P + +minus? + +AUDIENCE: Yeah. + +IAIN STEWART: And +it's in a nether land. + +Either way, you +can think about it + +as being part of +this one or that one. + +It doesn't matter. + +Because technically, if I +just talked about minus, + +I'd only be interested +in separating a 1 + +and a lambda squared. + +And whether I call this +lambda squared or I call it + +lambda or I call it eta-- + +let eta equal lambda squared-- + +I'm only trying to +separate two things. + +So if you talk about some +momentum that's in between, + +you could ask the same +question actually about, + +what about a lambda to the 3/2 +momentum in the perp space? + +And that's the same question +you just asked about the minus + +space, right? + +And that's something +that we don't really + +care about because there's +not going to be momenta + +that are scaling like that. + +So we don't really care +about separating it. + +OK, so Pl are +discrete grid points. + +And Pr-- continuous. + +And this picture also makes +clear that, if you take any P, + +it uniquely is given +by some Pl and some Pr. + +If I point at any +place in this grid, + +you can tell me exactly +which Pl I should pick + +and then what Pr I should pick. + +This is, in some ways, +just going to be a tool. + +And in the end of the +day, we can kind of + +dispense with this picture. + +But it'll be a useful way of +thinking about what's going on + +and getting to sort of the +final results that allow us + +to dispense with this picture. + +So what about integration? + +So if I integrate over +all P and P is collinear, + +what does that mean? + +So it corresponds to summing +over all the grid points + +and then integrating +over all the residuals + +except for one location. + +And that's the special box +here that has label equal 0 + +because we know that the power +counting of the collinear + +momentum is such that it +always has to have a non-0 Pl. + +And so the one box where +Pl is equal to 0, 0, + +that particular box doesn't +have a collinear momentum. + +And actually, that +box is exactly what + +you think of as the +ultra soft momentum. + +So if you have an integral +d4P and P is ultra soft, + +there's no sum. + +And you just have interval d4Pr. + +And that's like integrating over +the 0, 0 location in the grid. + +OK, so you can see +that together we + +cover all possible places +for an integration. + +And we actually don't +do any double counting + +with this setup. + +What am I going to +do with my fields? + +Well, because of this split +into two different pieces, + +I'm going to say that my fields +actually can be labeled by Pl + +and carry Pr also as an +index or as a function of Pr. + +So in order to +make this explicit, + +we're going to write +our Fourier transform + +guy with a label Pl and +an argument Pr like that. + +So the name label comes from +the fact that we do this. + +And there will be some +analogies with why + +we called this a label in HQET. + +We'll see to what extent +that analogy carries through + +in a minute. + +Another thing you should +note from this grid picture + +is that you have separate +momentum conservation + +in the label and the residual. + +So if you think about some +integral d4x of something + +that you split between label +pieces and residual pieces, + +then the right way of +thinking about this + +is that you have a discrete +[INAUDIBLE] delta for the label + +and then a continuous +Dirac delta + +for the continuous variables. + +And there's some 2 pis. + +And so this is what +would be meant by-- + +if you have two +momenta that are equal, + +you know that they're +in the same grid square. + +And then they have the same +little green arrow as well. + +That's what that's saying. + +So when we talked +about what happens + +with the multipole +expansion in position space, + +we said that +effectively you have + +a non-conservation of momenta. + +OK. + +We had a field at 0. + +We worked through +what that meant. + +And it meant, basically, +that the momenta + +was conserved on the other +line, but not on the one + +that you were doing +the expansion on. + +The nice thing about +this type of setup + +is that we have +conservation of momenta, + +but we actually have two +conservations of momenta. + +So we don't give up +momentum conservation. + +It's just that we go +over to a picture where + +we have two of them. + +So let me show you +how that works. + +Let's say we have an +ultra soft particle, + +and it's hitting +a collinear quark. + +The collinear quark, +because it's collinear, + +carries two types of momentum. + +It carries a label +P and a residual. + +But the ultra soft guy, +it's only residual. + +So let's just call +that k residual. + +There's no label to +that ultra soft guy. + +So if I just look then what +this guy's momentum is, + +it's P label for the large +piece because that is not + +affected by the ultra soft guy. + +And then it's P residual +plus k residual. + +OK, so we have a conservation +in the residual space, + +which is the standard one. + +And we have a conservation +in the label space, + +but the ultra soft particles +just don't contribute to that. + +So we have two +conservation laws. + +And we just know that certain +fields can carry these label + +momentum and other fields can't. + +All right, well, +since Pr here and kr, + +the residual components, is just +standard quantum field theory-- + +the only thing that's +special is the Pl. + +For the Pr, what we're going to +do for the residual momenta is + +we're going to transform +back to position space. + +And that's kind of what we +do in HQET as well, right? + +We treat this guy in momentum +space as a label and this guy + +as a position space +for the residual. + +And the reason we really want to +do that is related to locality. + +And I'll say some +more words about that. + +AUDIENCE: [INAUDIBLE] + +IAIN STEWART: Yeah. + +AUDIENCE: I have a question. + +IAIN STEWART: Sure. + +AUDIENCE: So this top equation-- + +IAIN STEWART: Yeah. + +AUDIENCE: So are you bounding +the d4Pr by lambda squared, + +or is there some reason why +the integral should fall off + +before you get +there or something? + +IAIN STEWART: Yeah, we're +going to talk about that. + +So, so far, this +is just notation. + +If you think about it +from this grid picture, + +you'd think some +hard walls put in. + +That's not quite the right +way of thinking about it. + +It's actually not right +for several reasons. + +And we will come back +and talk much more + +about what the right way +of thinking about it is. + +But the physical picture +that you're in this box + +is the right way of +thinking about it. + +The tricky thing is that +these boxes are infinite. + +Each of these boxes is infinite. + +And we'll have to +see why that is. + +In what I've told +you so far, you'd + +think that the d4Pr would really +be a box with some fixed edges. + +And it's going to turn +out that the d4Pr-- + +we're going to use dimensional +regularization-- it's + +going to be an infinite box. + +But we're still going +to be able to do + +exactly what I'm telling you. + +And it's going to make sense. + +We're going to +want infinite boxes + +to avoid breaking symmetries, +like gauge symmetry and Lorentz + +symmetry. + +And we'll come back +and see how that works. + +So in some sense, what I've +told you is a Wilsonian story. + +And we're going to have +to make it into a more + +continuum friendly story. + +But the moral of +the story, the way + +you think about where +these momentum modes live, + +what kind of momentum they +carry, that is just true. + +So that part of the +story, which you + +can think of so far +as Wilsonian, is true. + +And it's OK to think like that. + +So we'll see actually what we do +in practice a little later on. + +Where this will +really come in is + +when we start wanting to +think about doing loops, + +but we won't get there +for a little while yet. + +So the conservation +law in the residual + +just corresponds to locality. + +We learned all about +locality yesterday + +in [INAUDIBLE] seminar. + +And so we can make things +local by just going back + +to the x base for +the residual momenta. + +OK, so we go back +to the x base, which + +is the Fourier transform +conjugate variable + +to the residual momenta. + +So the fields we're +actually going to use + +are these ones, where we +Fourier transform back + +in the residual, +these guys here. + +So it's kind of +like HQET, where you + +think about this part +as momentum space + +and that part in position space. + +OK, so if you talk about +ultra soft interactions-- + +you can see it from over there-- + +they conserve the labels. + +So there's label +conservation of a field + +for ultra soft interactions. + +The label of the +field here is the same + +as the label of the field there, +so that ultra soft guys do not + +change labels. + +So this is Pl. + +This is Pl. + +And if this is ultra soft, +it's still labeled by Pl. + +And the thing that can change +is the residual momenta. + +And that's now +encoded in locality + +in saying these fields all +sit at the same point x. + +On the other hand, the +collinear gluons cause us + +to hop between boxes. + +So the collinear gluons +are label changing. + +And that's what's +different than HQET. + +In HQET, we don't +really have interactions + +in the theory in the Lagrangian +that do that, but here we do. + +So if we have a +collinear gluon come in, + +the collinear gluon, +again, carries both labels + +and residuals if I +just draw the labels. + +And this is some Ql coming in. + +And this will be Pl plus Ql. + +And so the label of the +outgoing field has changed. + +There's one more label. + +And that's this n, right? + +We also label these +guys by a direction. + +And that is unchanged also by +the collinear interactions. + +So it's preserved by both +ultra soft and collinear + +interactions. + +It can only be changed +by hard interactions + +where you would have +some hard production that + +could produce, say, two guys +in two different directions. + +And those type of +interactions are typically + +only going to occur once in +your quantum field theory, + +kind of like a decay, a weak +decay where it occurs once. + +And then you do perturbation +theory around that. + +Hard interactions +are that way, too. + +So as far as dynamics +is concerned, + +this label n is +something that you + +can think of as being +conserved for the field. + +It's not going to be +changed by the Lagrangian, + +for example, all right? + +OK, so, now, we have +kind of what we want. + +And now, I want to +write the action + +that we had before +in terms of this guy + +and see what it looks like. + +This split of these guys +into a Pl and Pr or Pl and x + +allows us to expand +very easily in momenta. + +It's allowing us to do the +multipole expansion because we + +have two things to talk about. + +And we just can compare them. + +So let's put the +pieces together. + +So Cn hat of x is the +full Fourier transform + +of this Cn twiddle. + +And that can be split +for a collinear guy. + +We can split the measure, +and we can split the phase. + +And we can write the +field in this way. + +And then we decided that we +wanted to use this field. + +Let me see, [INAUDIBLE] +two pis here. + +So that means we take this +measure, we take this phase, + +we take this guy, and we write +it back in terms of that field. + +So that leaves, if we +want to relate the field + +that their Lagrangian was in +terms of in terms of this field + +that I told you we're going to +use, it's this equation, OK? + +All right-- a little +bit more formalism. + +So we're going to actually want +to have two different types + +of derivatives, derivatives +that can talk to the momentum + +conjugate to x and +derivatives that give this Pl. + +So we define two types +of derivative operators. + +One is just, if you like, +a standard derivative + +in the x base of this guy, +acts only on that coordinate. + +And that derivative scales +like lambda squared. + +So that's residual, picking out +talking to residual momenta. + +Then we need something that +can give us the labels. + +So we define an +operator that does + +that, which we'll call curly p. + +It doesn't care about x. + +And it's just defined +to give the Pl + +mu of the field it acts on. + +So there's no plus +component to this. + +There's an order +1 minus component. + +And then perp is order lambda. + +I want to say how +big that guy is. + +So then we have a power counting +that tells us how big the p is + +and how big the partial is. + +And we can compare them, and +we can expand in them, OK? + +So the bottom line +is that we now + +can just say that, like we had a +comparison for the gauge field, + +we have a comparison +for derivatives. + +And so this is exactly +analogous to what + +we said before where we +had M bar dot A ultra soft + +is much less than N bar dot +A collinear and A perp ultra + +soft being much less +than A perp collinear. + +And in fact, the way +we're setting things up + +is going to make the +gauge symmetry also easy. + +Because by gauge symmetry, these +derivatives and these fields + +should go together. + +They are the same size +in the power counting. + +And these guys should +go with those guys. + +So we're kind of doing this same +thing we thought of for fields + +we're doing for momenta here. + +So when we talk +about gauge symmetry, + +this will make gauge +symmetry easier, + +this homogeneity between the +derivatives and the fields. + +So that's one of the powers +of thinking like this. + +OK, so let's see that +this notation is actually + +kind of friendly. + +So let me try to +convince you of that. + +It looks kind of daunting, but +maybe it's not so daunting. + +So let's look at this guy, +which was equal to this. + +So what I can do is I can +take this and replace it + +by e to the minus i label +operator dot x, right? + +But the label operator then +doesn't care about the sum. + +So I can push it through. + +So as an operator, it +goes through the sum. + +I have that. + +And for a lot of purposes, in +a sense of suppressing indices, + +we can just use a +simplified notation + +for this guy where +we suppress the sum. + +So we were thinking about +this as a discrete sum. + +And we can always write out +that sum if we get confused. + +But we could also +adopt a notation + +where we suppress the sum. + +And for many +manipulations, just like + +you might suppress some +indices in a quantum field + +theory, that's perfectly fine. + +And having this label operator +makes it easy to do that. + +So if you have, for +example, field products, + +say I had two fermions, we +try to make the notation work + +for us as nice as possible. + +Well, if you have +a sum of momenta + +and then it's exponentiated, +if you have a product + +and it's a product +of exponentials, + +then it just becomes the +sum in the exponential. + +So this is true if we do +it for two fields, right? + +I'd have the label +operator acting + +on this guy and that guy. + +And if I were to write out +this twice with two sums, + +then because the product +of those two exponentials + +can be just written as a single +exponential, this is true. + +So this guy acts on both fields. + +So in this sense, the +notation is friendly. + +And what this phase factor +here is really doing for you, + +if you think about it, +if you think about it + +in a whole product +of fields, it's + +just when you Fourier transform +giving the label conservation, + +OK? + +So there's going to be this +kind of overall e to the minus + +i p dot x. + +And it's just sitting +there to conserve momentum + +in the label space. + +So that's its purpose. + +OK, so there's one +more step that we + +have to do before we start +talking about the Lagrangian. + +And that's this +little caveat that I + +had right at the +beginning where I said, + +let's consider only quarks. + +So far, we've only considered +the quark part, not + +the antiquark part. + +So let's see what we want +to do about antiquarks. + +Technically, the way that the +field theory wants to work + +is that the quarks +and the antiquarks + +kind of want to be +different fields, + +but that's very cumbersome. + +And so we're not +going to do that. + +And we're going to find, again, +sneaky notation to treat them + +as one field even though +they want to be two. + +The reason that +they want to be two + +is because, if you look at the +phase factor for the quarks + +in the antiquarks in the kind +of standard mode decomposition, + +it has the opposite sign. + +So look at the mode +expansion in QCD. + +I can write it in a covariant +type notation or with a d4p p + +if I put in the +proper projection. + +And then we have the quark +part with the e to the minus ip + +dot x. + +And then we have antiquark +part, our b daggers, + +and the e to the +plus ip dot x, OK? + +So let me think of that as +a psi plus plus a psi minus. + +And we've so far only +talked about psi plus. + +So for psi plus of x, +we have a sum over Pl + +not equal to 0 e to +the minus i Pl dot + +x of sort of a Cn Pl plus of x. + +So this is the case we did. + +If we were to repeat everything +we did for this case, then what + +we would get for psi minus-- + +and this is why I say that +they want to kind of look + +like separate fields-- + +is we'd get a plus i Pl dot x. + +And in this notation, if +you think about the P0, + +the P0 is the sum of the +P minus and the P plus. + +So saying that, in this +mode decomposition, + +P0 is greater than 0 +for these two equations + +and when we go over to sort +of a collinear scaling, + +it becomes that Pl +minus is greater than 0 + +in these equations. + +OK, so that's the sense in +which these are different. + +With a positive Pl minus, we +have an opposite phase factor + +for these two guys. + +And in both of these +cases, it's true + +that just as kind of a way of +remark, we still have this. + +That didn't change, remember. + +OK, but talking about minus +and plus fields would just + +make our life really +difficult. Actually, + +when we first derived SCET, +sometimes you're bone-headed. + +And we went through everything +in a much more detailed way + +that I'm going to +present it to you now, + +wrote out everything in terms +of plus fields and minus + +fields because of +this little issue. + +Then we noticed +the following thing + +that I'm going to tell you, that +we could just put everything + +back together with +a simple definition. + +And that's because really the +only difference is this sign. + +So if we want a kind +of convenient notation, + +we can do the following. + +So far, if you like, we +have this guy with Pl's + +not equal to 0, but the Pl +minus should be greater than 0. + +So we can make use of +kind of negative labels + +by the following trick. + +Just define a +composite field that + +looks like this where I put +the minuses and the pluses + +back together. + +If I have a positive +Pl minus here, + +then that's giving the pluses. + +If I have a negative +Pl minus here, + +then that's giving +the minuses because + +of what I just told you. + +We don't just think about this +guy as having plus Pl minus. + +We allow it to have negative. + +And we take the +negative Pl minuses + +as a way of encoding what's +going on with this guy. + +So we have different +possibilities for M bar dot Pl. + +And if you like, what +the plus guy is doing + +is destroying particles. + +And so let's say +this is for the-- + +if I think about Cn of-- + +let me make my chart like this. + +If I think about what +Cn of Pl is doing, + +it's destroying particles and +the antiparticles are created. + +But the antiparticles +are going to be + +created for the +opposite sign of the Pl. + +And then if I think about +what the barred field would + +be doing with this +notation, if the M + +bar dot Pl is greater than 0, +then the particles are created. + +So this guy is +really just the field + +we were talking about before +if Pl is greater than 0. + +And if Pl is less +than 0, it just + +repeats the whole story +for the antiparticles. + +OK, so I could +write everything out + +in terms of this +plus and minus field. + +But if I just make +this simple definition, + +I could put everything +back together + +and just work in terms of +one field, which kind of does + +what we're used to. + +And it's just a sign convention +to remember for this Pl. + +And that sign convention +is also easy to remember + +because the Pl is really +following the fermion flow. + +If you think about +the fermion, then + +if you think about the physical +momentum of that fermion, + +then the physical momentum +follows the fermion + +in the case of the fermion. + +And it's opposite to the fermion +in the case of the antifermion. + +So here's a fermion +coming into some vertex. + +There's a antiparticle +coming into the vertex. + +And the Pl goes this way. + +It follows the fermion flow, +whereas the physical momentum + +is going this way. + +And that's the sign we're +just keeping track of. + +And so the P labels are +always following the arrows + +of the fermion lines. + +They're always along the fermion +number with the conventions + +we've set up. + +OK, so with that little +piece of notation, + +we take into account the +antiparticles as well. + +There's no real +additional complications + +since any way you +draw a picture it's + +completely clear +what's an antiparticle + +and what's a particle. + +And it just follows +your intuition. + +And furthermore, because the +only difference in the mode + +decomposition was that +sign and we've now + +accounted for it by just +making the labels negative, + +we have this equation, +too, for both particles + +and antiparticles. + +So we get the +opposite phase here + +because this guy has +the opposite sign. + +So there's really no +additional complications + +from adding the antiparticles +once we set up this notation. + +OK, any questions so far? + +What about collinear gluons? + +So the gluon field is +Hermitian, the original one. + +And what does that +translate into? + +Well, it translates into +the B's and the A's, right? + +They're both appearing in the +decomposition of the field. + +There's no B's. + +There are just A's. + +And if you work out, using +the type of body decomposition + +that we're doing and +using the type of notation + +that we're doing, +what that means, + +it means that the star of +this guy just flips the sign. + +So that's what Hermiticity +of the original field + +becomes for this notation. + +And again, because of +the theta functions + +that show up in the +mode decomposition, + +you can think of associating +ql minus greater than 0 + +as sort of destruction and +then ql minus less than 0 + +as creation. + +If you want, although it's +not absolutely necessary, + +you could adopt this convention. + +And then that would just be +putting a particular direction + +to your gluons. + +And everything that we +said before goes through. + +And in particular, if +we think of decomposing + +sort of the hatted version +of the fields, then this-- + +just like before. + +And we can just also, +again as before, + +if we like, adopt the notation +where we suppress the labels + +if we don't need them. + +So the gluons really, +in some sense, + +it's just simpler +because we don't + +have to worry about the +particles and the antiparticles + +because of their Hermiticity. + +It's sort of they're +all the same thing. + +And for most purposes, there's +no sense in even keeping + +track of this convention. + +So that's why I went +through it quickly + +because the convention +is always kind + +of obvious from the context. + +If you're really talking about +production of a real gluon + +or annihilation of a +real gluon, then you + +can keep track of +the signs that way. + +The fermions are a +little different. + +So because any starred field is +just the negative of this guy, + +we could always write everything +in terms of fields that + +have no daggers for the gluons. + +But for the fermions, +some of the fields + +are barred or daggered. + +OK, so what would be the form +of having a general label + +operator act on some +combination of daggered fields + +and some combination +of undaggered fields + +where the gluons are +always undaggered? + +Well, it just gives the +sum of these momenta. + +And the way it does it-- so +sum of the label of momenta. + +So I'm thinking of all these +denominators as label momenta. + +I'll maybe not put the l. + +And the way that +the convention works + +is that we get a minus +sign for the daggered guys. + +That's our sign convention. + +And the reason for that sign +convention is effectively that, + +if you think about +e to the minus i + +curly p dot x on sum +5 p1 and then you + +take the dagger of that, then +it becomes 5 p1 dagger of e + +top the plus i kind +of p dagger dot x. + +And basically, I'm +saying that I want to be + +able to write that like this. + +And that convention is useful. + +So if I want to act forward +on this field, which + +is a daggered field, +then I'm going + +to take the opposite side. + +And if I have a daggered p, then +it would take the plus sign. + +And that convention +is the useful one + +for keeping track of +momentum conservation + +because then every field +has the same convention. + +We just have e to the minus i +p dot x for every single field. + +All right, so if we started +with some partial derivative-- + +I mean some regular derivative. + +And it was acting on one +of our hatted fields. + +So if I write it out in +terms of the labels-- + +put a Pl on it if you like-- + +we'd have that. + +And so there's two contributions +from this derivative. + +It either hits the phase +or it hits the field. + +And so we can write it like-- + +if we go over to +the label operator, + +we can write it that +this partial derivative + +is the sum of two +derivatives, which then we + +can take the sum over Pl +inside and write it as-- + +so every derivative for the +purposes of this exercise + +is to convince you of the +sanity of the notation. + +Every regular derivative acting +on one of these hatted fields + +where we hadn't yet +decomposed momenta + +just becomes a sum of +these two derivatives. + +And that's just like the fact +that we split the full momentum + +into the sum of the label +in the residual piece. + +OK, this is the field version +of P mu equals Pl mu plus P + +residual mu. + +OK, but the advantage +of this notation + +is that we can then drop the +partials if they're smaller. + +That's the whole +reason for this setup. + +So now, we can +expand because we've + +split up both the +fields and the momentum. + +So we're able to expand. + +So let's go back to the +thing we wanted to expand. + +So we had this guy. + +And we wanted to expand it. + +And now, we know +how to expand it. + +We've set up a nice way of +doing the multipole expansion + +by introducing some +additional notation. + +So because of what I just +said and because of what I + +said last night for +the gauge field, + +we have a very +simple decomposition + +for the covariant derivative. + +It's the sum of a +collinear kind of piece + +and an ultra soft kind of piece. + +So this P mu plus i +partial mu is just this. + +And the split of the gauge +field into these two pieces + +is what we talked +about last time. + +And that split of +the gauge field + +actually led to some things +that we didn't talk about + +that we'll talk about later. + +So if we now look at +the components that + +are appearing in here, +we can figure out + +what to keep in each case. + +And it's pretty simple. + +Well, for the plus, +there's nothing to drop. + +We just keep everything. + +And there's also only +one type of derivative, + +so we just keep this. + +This is exact. + +All terms here are +order lambda squared. + +For the perp, we just +keep the collinear parts. + +So if I write out +the other part, + +just for completeness +we can drop those terms + +relative to these terms. + +Because these terms +here are lambda, + +and these terms here are +order lambda squared. + +So we drop these guys from +the leading order and then, + +similarly, for the minus. + +So here, this guy is +order lambda squared. + +And this guy is order lambda 0. + +So we drop this guy. + +OK. + +So now, just plug those +things into our Lagrangian. + +And then we get the +leading order Lagrangian. + +All of these phase factors can +be encoded in an overall phase + +factor. + +We get the full n +dot D derivative. + +But for the collinear +parts, we only + +get these piece, this piece, +and the piece over there. + +And so you can think of that +as a collinear covariant + +derivative. + +No. + +So sort of in the +obvious notation, + +we take the two pieces that +are collinear and put them + +into a collinear D and likewise +in the n bar direction. + +OK, so this Lagrangian here is +the leading order Lagrangian + +with this additional notation. + +And if you like, we +have this kind of D + +that has both pieces in it +for that n dot direction. + +And then for the other two, we +just have the collinear pieces. + +And that's the +leading order action. + +Where we've carried out +the multipole expansion, + +after we introduced notation, +it became something trivial. + +So the power of the notation is +that, once you've swallowed it, + +everything else is simple. + +If I want to go to +higher order, I just + +work out what these terms are. + +Then I should also +worry about these terms. + +And we'll do that later on. + +OK, so what can we +note about this? + +Well, one thing that +we worked out earlier + +was that this should +be of order lambda. + +And that actually implies +that, our new field, + +we were just pulling out phases. + +And that doesn't change +the overall power counting. + +So our new field is of +order lambda as well. + +And likewise, before +we sort of had a power + +counting for the +measure, which you + +can think of in our +new notation as a power + +counting for this +thing, and that just + +scales like lambda to +the minus 4 as before. + +So all the power +counting that we + +were doing even before +we sort of figured out + +what the right field to use, +that all carries through. + +And that's why I did it earlier. + +OK, so what's going on +here, which I didn't really + +spell out, but I +can spell out now, + +is since this phase is +order 1, the power counting + +from momenta induces a +power counting on the x. + +And it's kind of the larger +momentum that dominates. + +So x minus scales like +1 over p plus x plus-- + +remember in the +dot product, it's + +always plus times +minus, a confusing thing + +about light cone coordinates. + +And so if you count up +the powers of lambda, + +you get minus 4 of +them because you + +get 2 here, none here, +and then 2 there. + +So that's all going +through as before. + +And then if you ask, what's +the order of the Lagrangian, + +the Lagrangian density here +is order lambda to the 4. + +Because we have two +fields, and then + +we have a lambda squared +here and then a lambda here, + +a lambda 0 here, +and a lambda there. + +And our power counting +made that explicit. + +So the whole thing +is lambda to the 4. + +This lambda to the 4 +of the Lagrange density + +cancels the lambda to the +minus 4 of the measure. + +And you get that, +when you integrate, + +this is lambda to the 0. + +And that's what we wanted. + +That was our convention for +the leading order term, OK? + +So the power counting, +nothing really changes. + +We had a power +counting for momenta. + +We just now have a power +counting for all these objects + +that we're talking about. + +What about locality? + +Well, all the fields in +this Lagrangian are at x. + +So it is local in +residual momenta. + +We said that already when we +were drawing Feynman diagrams. + +And that's just +true of the action. + +And so what that +means is the action + +is local at the smallest +momentum scale in our problem. + +And we would have been +surprised if we'd encountered + +anything different than that. + +The action is actually also +local at the scale lambda. + +Even though we adopted +this label convention just + +to separate the momenta, there's +no inverse perp derivatives + +in this action. + +And so the perp derivatives +appear in the numerator. + +And so it's actually +local at that scale, too. + +And so if you like +this, we've just + +written something that's +in momentum space. + +And it's the momentum +space version + +of locality at the scale lambda. + +And we've hidden all +the momentum space + +so it even looks local. + +But if we were to write +out the indices again, + +we would see that it's +the momentum space + +version of locality. + +And so the only scale +that it's non-local at + +is actually scale that +we want to integrate out, + +the hard scale. + +And that's due to sort of the +presence of this kind of 1 + +over M bar dot Pl type factor. + +So that we already +sort of saw earlier + +when we were talking about +building up the Wilson line, + +right? + +We said, well, there's +some off-shell fields. + +Let's start +integrating them out. + +And we got inverse powers +of this M bar dot Pl, + +but that was at the hard scale. + +So we had no choice but +to integrate them out. + +And you can think +about this factor here. + +If it bothers you, you can +think about it in the same way + +that it's not any worse +than what we already did. + +OK, let's see if this +Lagrangian does what we want. + +Let's look at propagators. + +If we have a collinear +propagator with a collinear + +gluon, say, coming in, +let's look at this diagram. + +These are fields +in the n direction. + +This is some guy that's Pl Pr. + +And let me just take it to +be Pr plus for convenience. + +Then if you look +at this guy and you + +ask what that propagator +is, it comes out exactly how + +we want it to come out. + +So there's nothing +that gets dropped + +in the denominator in +particular in the sense + +that all components of the +momentum are showing up. + +We're still dropping residuals. + +But if we're just talking +about collinear particles, + +then the residuals +are kind of redundant. + +The purpose of the +residual's momenta + +is when we're talking +about both collinear + +and ultra soft particles. + +So the other case +that we need to treat + +is when we have an +ultra soft particle. + +We could, of course, have +both of them at the same time, + +but let's treat this case. + +So we have Pl, Pl plus some +k, which is purely residual. + +And now, this guy, because +of the derivatives, + +these derivatives +don't see the k. + +None of these +derivatives see the k. + +So in the n bar in the +perp, we don't see the k. + +It would look like that. + +If you like, if you want to +make it kind of look more + +like the Lagrangian, +convince yourself + +that this is the inverse, +just divide by this factor. + +Divide by this factor, +then it puts it under here. + +And that's exactly what +this is doing if you + +ignore the Dirac structure. + +It's not playing a role +really for the propagator. + +And same here, if you take +this factor, divide it out, + +then you got the plus piece +which is this derivative. + +And then you get perp +squared over minus. + +And that's what happens if +you put this down stairs, OK? + +For linear, all the +components show up + +because we didn't drop anything. + +For ultra soft, only +the plus shows up + +because it only changes the +plus momentum of the collinear + +field. + +So the Lagrangian is smart. + +It knows how to +deal with the fact + +that the propagator should +be different for these two + +situations. + +And that was one of the +things that we wanted, + +and we achieved it. + +So even though the +Lagrangian doesn't + +know what's going +to happen, it's + +smart enough to deal with +any possible thing that + +could happen and give +the right propagator. + +So we don't have to +expand any further. + +The Lagrangian knows how to give +the leading order propagator + +for any situation that +we might be interested + +in at leading order, which +are these two situations. + +What about Feynman +rules for interactions? + +So that's also interesting. + +So if we have an +ultra soft gluon, + +and let's say it +has an index mu, + +there's only one +term that comes in + +because it's only the n dot D +that had an ultra soft field. + +All the other ultra +soft fields got dropped. + +So there's only n dot A +ultra soft in the Lcc0. + +And so there's only one term. + +Things are a little more +complicated for the collinear. + +And this is kind of +the price that we + +pay for setting up the notation +that we did the way we did. + +So this guy here has all terms. + +Just by pulling a gluon field +out of any one of the terms + +it can couple to any +component of the gluon field + +just like in QCD, +but our Feynman rule + +is a little more complicated +because of the way + +we set things up. + +And in some ways, +what's happened + +is that we've made +the propagator simpler + +for the collinear fields at +the expense of complicating + +the interaction. + +OK, so we couple +to all components-- + +the perp component, +the n component, + +and the n bar component if +this is a collinear field. + +So these are all +collinear fields. + +So one way of thinking about +why that kind of had to happen + +is the following. + +What if we didn't +have ultra softs? + +Imagine that we were going +through this whole story, + +but we just had collinears. + +Then you wouldn't +really need to go + +through this multipole expansion +because there would never be + +two momentum of different size. + +And you could actually, just +for the collinears, use QCD. + +The purpose of having +this multipole expansion + +is really because we want to +talk about both of these things + +at the same time. + +In fact, if you +only had collinears, + +you just boost to the +frame where they're not + +having this boosted scaling. + +It's really relative scalings +that the effective theory + +is trying to encode, relative +scaling between collinear + +and ultra soft or between, +say, two collinears going off + +back to back. + +That's where the power of +the effective theory is, + +in relative thing. + +So it's only when you have +two things at the same time + +and you want to +describe both of them + +that you get into the +kind of complications + +we're talking about. + +If you just have one thing, +then things are simple. + +You could just use QCD. + +But if you just had QCD +for the collinear sector, + +you'd know that you have a very +simple Feynman rule, igTA gamma + +mu, and a more +complicated propagator + +because you'd have a P slash. + +Well, here we don't +have any P slash. + +The propagator, if you +write out the spin, + +is simply n slash over 2. + +But the P slash has to +come back somewhere. + +And it's coming +back because it gets + +encoded in the way we set +things up in this vertex. + +So these factors of P slash here +are just reproducing P slashes. + +Then in the full QCD context, +it would be in the propagator. + +You can actually +work out, if you + +start writing down Feynman +diagrams, that that's + +exactly what's going on, OK? + +So that's kind of +the price that we + +paid for sort of making +a Lagrangian that + +dealt with both things +at the same time + +and made this part +really simple. + +That part became slightly +more complicated. + +But once we know +what I just told you, + +we can oftentimes, you know, +carry out calculations here + +by making correspondences +with the full QCD Lagrangian. + +Sometimes that's done anyway. + +They couple to all four +components of the field. + +Actually, once +you start learning + +how to deal with +numerators like this, + +it's different than +what you're used to, + +but it's just, in some +sense, as complicated + +using this Lagrangian. + +It's just that you're +writing things out + +in components, which you +might not want to do, right? + +Why decompose things +into components, + +which we're doing here? + +Why do that if you don't +have sort of something that's + +projecting onto a component? + +That's, in some sense, +the only complication. + +OK. + +And there's one other +thing, of course, + +which is that the Lagrangian +also had terms like this. + +So it's not simply just +one gluon interaction. + +We could have, for example, +two covariant derivatives, + +two of these perp covariant +derivatives, for example. + +And there's a Feynman +rule for that, too, + +which comes out of the +action that we wrote down. + +OK, questions? + +AUDIENCE: So I +guess this, I mean, + +the effective theory is +reproducing the collinear + +[INAUDIBLE] divergences of QCD? + +IAIN STEWART: It is, yeah. + +AUDIENCE: So in [INAUDIBLE] +QCD, the higher divergence + +cancel with interference +[INAUDIBLE]?? + +IAIN STEWART: And +that'll happen here, too. + +AUDIENCE: And you have to loops? + +Or it's happening like a +leading order [INAUDIBLE]?? + +IAIN STEWART: No, you have +to look at loops, too. + +So, yeah, there can +be cancellations + +between real and virtual graphs. + +And there actually can +be such cancellations + +separately for ultra soft +gluons and for collinear gluons. + +So we'll talk about what +you're talking about a little + +later on. + +But there is an important +point that I'll emphasize + +since you ask the question. + +If you ask about +the divergences, + +the infrared divergences +of an ultra soft gluon, so + +the ultra soft gluon, if we go +back to sort of where it was + +living, it was littered here. + +Collinear gluon was living here. + +And if you ask +about divergences, + +what the divergences +are coming from + +are momenta going to 0 or +momentum going collinear. + +And this guy here that +lives kind of here + +can go both collinear, +and it can go soft. + +So the names collinear +and soft, which + +correspond to the names +collinear and soft divergences, + +are not a one-to-one +correspondence. + +An ultra soft +particle can actually + +have both collinear +and soft divergences. + +The collinear particle +can also actually + +have both types of divergences. + +And so the names are +associated to where + +they live in momentum space, +not the type of divergences + +that they're encoding. + +If I wanted to do something +along the lines of setting up + +the field theory to just exactly +correspond to the divergences, + +well, first of +all, no one's ever + +figured out how to do that. + +But you could imagine +how it would be + +different than what I'm doing. + +Because if I wanted to +do that, then somehow + +my collinear field would sort of +be sort of sensitive to angles. + +It should be like +an angular variable + +because the divergences are +coming from angles going to 0. + +And it's not an +angular variable. + +It's just a regular field. + +So setting things +up in this way is + +kind of how we usually think +of an effective field theory. + +We're just talking about +momenta small or big. + +And that's what we're doing, +but it comes in the sense + +that you don't have a +direct correspondence + +with the divergences. + +AUDIENCE: So you have more +divergences [INAUDIBLE]?? + +IAIN STEWART: The +way of saying it + +is that you have more +divergences in a way, + +but they're the +same divergences-- + +yeah. + +Yeah. + +So you don't have +more divergences, + +but really what's happening is-- + +so if you look at +this kind of picture, + +if you look at the kind +of infrared divergences + +that you could have, +so let's regulate them + +with an off-shellness. + +You could have +infrared divergences + +that would be like that. + +But when you do some +diagrams, there's + +kind of infrared divergences +that could look like this, OK? + +I'm just telling you something +that you have to trust me. + +And this is coming from +an ultra soft scale. + +P squared over P minus, +that's this hyperbola. + +That's the scale +of this hyperbola. + +And the P squared here is +the scale of this hyperbola. + +What the effective theory does +is, any ultra soft diagram, + +that'll give all these logs. + +Any collinear diagram +will give all these logs. + +You could say, well, P +minus is a hard scale. + +So really the only the IR +divergences are just P squared, + +but the effective theory +is kind of dividing it up + +into these two types of logs. + +And that's actually going +to be useful for us. + +We'll see that that +allows us to do + +some things that are +not so obvious how + +to do in the full theory. + +So, yes, it is kind of splitting +and IR divergence in these two + +different types of terms, +but that's actually going + +to be something that's useful. + +Because in some sense, +there's two physical scales + +in the infrared. + +There's a sort of +collinear hyperbola + +and the ultra soft hyperbola. + +And the effective theory +is making that explicit. + +Other questions? + +All questions have +been good so far. + +Keep asking them. + +AUDIENCE: Could you try +using two different lambdas + +for the ultra soft +and the collinear? + +IAIN STEWART: Yeah. + +So you could if there +was a physical reason why + +you wanted to. + +And the thing is that, if +the lambdas order each other, + +then there's no point. + +If there's a hierarchy, +then what that would change + +would be that the n dot D +should get expanded, too. + +But if the n dot +D gets expanded, + +then kind of what is +happening is you're really + +decoupling everything. + +AUDIENCE: [INAUDIBLE] + +IAIN STEWART: Yeah. + +And so you're kind of losing +the dynamical connection that we + +have so far in this theory. + +So I think it's +not so interesting, + +but it's worth thinking about. + +OK. + +We're going to erase this. + +OK. + +So now, that we have a +leading order Lagrangian, + +it does everything +that we want it to do. + +We can use it to calculate +Feynman diagrams. + +It defines the leading +order collinear + +sector in the effective theory. + +There's one more +thing I want to do. + +And that's come back to the +fact that I told you before, + +but now that we can +actually make more explicit. + +And that fact was, when we +were talking about currents + +and integrating that +off-shell particles, + +we saw that you start +with these guys. + +You start attaching them. + +And you end up +with a Wilson line. + +I'd now like to make it obvious +that that kind of manipulation + +always is true, that we can +always get rid of this field + +and put it in terms +of a Wilson line. + +And the notations +that we've introduced + +are going to allow +us to do that. + +So let's have a little +aside on that fact. + +So if you are in momentum +space, the Wilson line + +has an equation of motion, or a +defining equation if you like, + +that's this. + +This defines the direction, +that the Wilson line is + +long n bar dot n bar direction. + +And the x and the minus +infinity are telling you + +what the end points are. + +So this is the +defining equation. + +You can look back +at Peskin if you + +want to see how that all works. + +And that's the defining +equation in position space. + +But we've just advocated +for a kind of momentum space + +notation. + +So what's the corresponding +equation to momentum space? + +It's pretty simple. + +If we go over to our +momentum space Wilson line, + +we just go over to our momentum +space covariant derivative. + +And the defining +equation is this. + +So the notation, in some +sense, is pretty simple. + +We just have to switch objects. + +If we write out what +that derivative is, + +then it's that, OK? + +So now, consider +the following thing. + +Consider this +combination, but let + +me think about it as +an operator equation. + +So let me think about +it as if there could + +be something to the right. + +If there's something to +the right, than the P bar + +can act on that thing, too. + +So I get 0 if the P +bar acts on this thing. + +But if the P bar +acts through, then I + +get just P bar on the operator. + +So as an operator +equation, I can + +trace the O. This +is true for any O. + +And we have this +operator equation. + +But I know something else I +know that the Wilson line is + +at e to the i something. + +And actually, it's unitary. + +So W dagger W is 1. + +And again, in momentum +space notation, + +that's kind of +the obvious thing. + +W dagger W is 1. + +And that means I can +multiply this equation here + +on the left or the +right by W daggers. + +And so if I do that, let +me multiply it by W dagger. + +And I can write i n bar dot +Dn is Wn P bar Wn dagger. + +So the gauge field, g n bar dot +An, because of gauge symmetry, + +it's always going to show up +in the covariant derivative. + +So it's always going to +show up in this combination. + +And this equation +is telling me I + +can switch that for Wilson lines +in this P bar if I want to. + +I could have also multiplied +things the other way around + +and written it P bar. + +So sort of by way +of completeness, + +I could have written +that as well. + +It's also easy to convince +yourself of the following. + +1 over P bar is Wn dagger +1 over i n bar dot D W. + +And 1 over i n bar dot D-- + +I'll check that I got the +daggers in the right place. + +But these two equations +are true, kind + +of the inverse of +those equations. + +So how do we check that? + +Well, just multiply +this times this. + +You should get 1, right? + +And if I multiply, +say, on the right here, + +then the W dagger here +kills the W dagger. + +Then the P bar kills the P bar. + +And then the W +kills the W dagger. + +So those are true. + +And so we can put this into +the Lagrangian if we want. + +And we can do what I said, +that we can actually, + +if we want to, get +rid of the n bar + +dot A field for the collinears +in terms of Wilson lines. + +And we'll use this from time +to time when it's convenient. + +If we use the D Lagrangian, the +Lagrangian becomes this thing. + +So that 1 over i n bar +dot D becomes this thing. + +And in some sense, +you might think + +that this is easier +to expand if you + +know the expansion +of the Wilson line. + +And we just have to +let a 1 over P bar act + +on this full +combination of fields. + +And it just gives +the total n bar + +dot P momentum of that +full combination of fields. + +I claimed this was true. + +And now, I show you in a +kind of non-trivial case + +how, with these +operator manipulations, + +we could just quickly +go back and forth. + +And it's related +to the fact that it + +appears in this combination. + +We'll talk more about +gauge symmetry later on. + +I'm alluding to it +from time to time, + +but we'll talk about it +more precisely later on. + +We have to do this story for +the collinear gluon Lagrangian. + +And much of this +is just repeating + +what we've said for the +quarks for the gluons. + +And once we know how to write +down the covariant derivatives, + +then it's actually +not so complicated. + +And there's just one +little complication + +that we should be +careful about, which + +I want to emphasize to you. + +And so we'll go through it. + +Let me write the Lagrangian +in QCD in terms of traces. + +And let me use a +general covariant gauge. + +So this is a general +covariant gauge fixing term. + +That should be called +the gauge parameter tau. + +Then we have some +ghost fields as well. + +And of course, g mu nu is +the usual g mu nu A TA. + +And that's my sign convention +commutator of two derivatives + +with the pi over g. + +So we do the same +steps to get SCET. + +And so really, if you +think about writing + +all the g's in terms +of D's, we already + +know how to split +the D's in terms + +of ultra soft and +collinear parts. + +And so that's what we do. + +Let me write out a D, which +is kind of a leading order D. + +And we'll just set +up some notation. + +And then I can just basically +write down the answer. + +So let's set up a curly D that +has all the sort of pieces that + +will survive at leading order. + +So all the pieces that survived +were the collinear pieces + +and perp in n bar and then, in +the n direction, both pieces. + +And effectively, I'm just +changing all the regular Roman + +D's in my gluon action +into these curly D's. + +And that's almost +the entire story. + +So from a kind of power +counting perspective, once + +you take into account +that, when you dot things, + +n's are always dotting +with the n bars, + +so it's this times this. + +So this is lambda squared. + +This is order lambda 0. + +This guy dots into himself. + +So you get lambda +squared there as well. + +So for power counting purposes, +when you start squaring things, + +they're all going to be +homogeneous with this setup. + +So basically, that's +what I'm saying here. + +And then there's +one complication, + +and that's this +partial derivative. + +Well, there's two +partial derivatives. + +There's one there, +and there's one there. + +So this is in the +gauge fixing term. + +These terms are both +related to the gauge fixing. + +And then those terms, actually, +I want to make them covariant. + +So let me define one more thing. + +I want to make them +covariant, but I + +want to make them only covariant +under the ultra soft part + +of the action. + +So here is just +pulling out the pieces + +that would have the +ultra soft field making + +a derivative that I'll +call curly D ultra soft. + +So one way of +thinking about that + +is that it would be like +background field gauge. + +In background field gauge, +you'd make this partial view + +into the D mu of the background +involving the background field. + +And that would be a +background field gauge. + +So from the point of view +of the ultra soft field + +being a background +field, it's very natural + +to have a replacement +that looks like this. + +And that's one way of arguing. + +Really what's going on +in the effective theory + +is that this is general +covariant gauge for A n. + +That's what we want +it to be for A n mu. + +This should be the gauge fixing +term for the collinear gluons. + +And it shouldn't be +breaking any gauge + +symmetry of ultra soft gluons. + +So we'd actually +like the Lagrangian + +to both have gauge symmetry +for collinear gluons + +and a separate gauge symmetry +for the ultra soft gluons. + +Since this guy is supposed to be +gauge fixing for the collinear + +gluons, we don't want +it to be doing anything + +to the ultra soft gluons. + +And that's accomplished if +we make this replacement + +that i partial goes to +i curly D, all right? + +So we could write +out what Lcg0 is, + +but it's just these +two replacements. + +Since we're out of +time, I'll just say that + +and, you know, sort of write +out the fields and the notation + +that we developed, OK? + +So we'll talk more next time. + +What we'll do next time is +we'll talk about symmetries. + +We'll finally talk +about gauge symmetry. + +And we'll talk about +other symmetries. + +And in particular, +symmetries are + +going to be important +for understanding + +how much of this story that I've +told you really carries through + +once you start doing loops. + +Symmetries protect you from +certain loop corrections. + +Gauge symmetry, for +example, connects terms + +to all orders in +perturbation theory. + +And we'll see how those +things kind of work next time. + +Really, the story I've told +you so far is all tree level. + +We haven't done any loops. + +One way of handling +what loops can do + +is by looking at +symmetries and saying, + +once we impose those +symmetries, what's + +the most general possible +things that loops could do. + +And we'll do that next time. \ No newline at end of file diff --git a/TluTv5V0RmE.txt b/TluTv5V0RmE.txt new file mode 100644 index 0000000000000000000000000000000000000000..1e14566d62284ba82e0140ace8bf53fb33accdca --- /dev/null +++ b/TluTv5V0RmE.txt @@ -0,0 +1,2587 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu + +JOHN TSISIKLIS: So here's +the agenda for today. + +We're going to do a +very quick review. + +And then we're going +to introduce some + +very important concepts. + +The idea is that all +information is-- + +Information is always partial. + +And the question is what do we +do to probabilities if we have + +some partial information about +the random experiments. + +We're going to introduce the +important concept of + +conditional probability. + +And then we will see three +very useful ways + +in which it is used. + +And these ways basically +correspond to divide and + +conquer methods for breaking +up problems + +into simpler pieces. + +And also one more fundamental +tool which allows us to use + +conditional probabilities to do +inference, that is, if we + +get a little bit of information +about some + +phenomenon, what can we +infer about the things + +that we have not seen? + +So our quick review. + +In setting up a model of a +random experiment, the first + +thing to do is to come up with +a list of all the possible + +outcomes of the experiment. + +So that list is what we +call the sample space. + +It's a set. + +And the elements of the +sample space are all + +the possible outcomes. + +Those possible outcomes must be + +distinguishable from each other. + +They're mutually exclusive. + +Either one happens or the other +happens, but not both. + +And they are collectively +exhaustive, that is no matter + +what the outcome of the +experiment is going to be an + +element of the sample space. + +And then we discussed last +time that there's also an + +element of art in how to choose +your sample space, + +depending on how much detail +you want to capture. + +This is usually the easy part. + +Then the more interesting part +is to assign probabilities to + +our model, that is to make some +statements about what we + +believe to be likely and what +we believe to be unlikely. + +The way we do that is by +assigning probabilities to + +subsets of the sample space. + +So as we have our sample space +here, we may have a subset A. + +And we assign a number to that +subset P(A), which is the + +probability that this +event happens. + +Or this is the probability that +when we do the experiment + +and we get an outcome it's the +probability that the outcome + +happens to fall inside +that event. + +We have certain rules that +probabilities should satisfy. + +They're non-negative. + +The probability of the overall +sample space is equal to one, + +which expresses the fact that +we're are certain, no matter + +what, the outcome is going +to be an element + +of the sample space. + +Well, if we set the top right +so that it exhausts all + +possibilities, this should +be the case. + +And then there's another +interesting property of + +probabilities that says that, +if we have two events or two + +subsets that are disjoint, and +we're interested in the + +probability, that one or the +other happens, that is the + +outcome belongs to A or belongs +to B. For disjoint + +events the total probability of +these two, taken together, + +is just the sum of their +individual probabilities. + +So probabilities behave +like masses. + +The mass of the object +consisting of A and B is the + +sum of the masses of +these two objects. + +Or you can think of +probabilities as areas. + +They have, again, the +same property. + +The area of A together with B is +the area of A plus the area + +B. + +But as we discussed at the end +of last lecture, it's useful + +to have in our hands a more +general version of this + +additivity property, which says +the following, if we take + +a sequence of sets-- + +A1, A2, A3, A4, and so on. + +And we put all of those +sets together. + +It's an infinite sequence. + +And we ask for the probability +that the outcome falls + +somewhere in this infinite +union, that is we are asking + +for the probability that the +outcome belongs to one of + +these sets, and assuming that +the sets are disjoint, we can + +again find the probability for +the overall set by adding up + +the probabilities of the +individual sets. + +So this is a nice and +simple property. + +But it's a little more subtle +than you might think. + +And let's see what's going +on by considering + +the following example. + +We had an example last time +where we take our sample space + +to be the unit square. + +And we said let's consider a +probability law that says that + +the probability of a subset is +just the area of that subset. + +So let's consider this +probability law. + +OK. + +Now the unit square is +the set --let me just + +draw it this way-- + +the unit square is the union of +one element set consisting + +all of the points. + +So the unit square is made up +by the union of the various + +points inside the square. + +So union over all x's and y's. + +OK? + +So the square is made +up out of all the + +points that this contains. + +And now let's do +a calculation. + +One is the probability of our +overall sample space, which is + +the unit square. + +Now the unit square is the union +of these things, which, + +according to our additivity +axiom, is the sum of the + +probabilities of all of these +one element sets. + +Now what is the probability +of a one element set? + +What is the probability of +this one element set? + +What's the probability that our +outcome is exactly that + +particular point? + +Well, it's the area of that +set, which is zero. + +So it's just the sum of zeros. + +And by any reasonable +definition the + +sum of zeros is zero. + +So we just proved that +one is equal to zero. + +OK. + +Either probability theory is +dead or there is some mistake + +in the derivation that I did. + +OK, the mistake is quite +subtle and it + +comes at this step. + +We're sort of applied the +additivity axiom by saying + +that the unit square is the +union of all those sets. + +Can we really apply our +additivity axiom. + +Here's the catch. + +The additivity axiom applies +to the case where we have a + +sequence of disjoint events +and we take their union. + +Is this a sequence of sets? + +Can you make up the whole unit +square by taking a sequence of + +elements inside it and cover +the whole unit square? + +Well if you try, if you start +looking at the sequence of one + +element points, that sequence +will never be able to exhaust + +the whole unit square. + +So there's a deeper reason +behind that. + +And the reason is that infinite +sets are not all of + +the same size. + +The integers are an +infinite set. + +And you can arrange the integers +in a sequence. + +But the continuous set +like the units + +square is a bigger set. + +It's so-called uncountable. + +It has more elements than +any sequence could have. + +So this union here is not of +this kind, where we would have + +a sequence of events. + +It's a different +kind of union. + +It's a Union that involves a +union of many, many more sets. + +So the countable additivity +axiom does not + +apply in this case. + +Because, we're not dealing +with a sequence of sets. + +And so this is the +incorrect step. + +So at some level you might think +that this is puzzling + +and awfully confusing. + +On the other hand, if you think +about areas of the way + +you're used to them from +calculus, there's nothing + +mysterious about it. + +Every point on the unit +square has zero area. + +When you put all the points +together, they make up + +something that has +finite area. + +So there shouldn't be any +mystery behind it. + +Now, one interesting thing that +this discussion tells us, + +especially the fact that the +single elements set has zero + +area, is the following-- + +Individual points have +zero probability. + +After you do the experiment and +you observe the outcome, + +it's going to be an +individual point. + +So what happened in that +experiment is something that + +initially you thought had zero +probability of occurring. + +So if you happen to get some +particular numbers and you + +say, "Well, in the beginning, +what did I think about those + +specific numbers? + +I thought they had +zero probability. + +But yet those particular +numbers did occur." + +So one moral from this is that +zero probability does not mean + +impossible. + +It just means extremely, +extremely unlikely by itself. + +So zero probability +things do happen. + +In such continuous models, +actually zero probability + +outcomes are everything +that happens. + +And the bumper sticker version +of this is to always expect + +the unexpected. + +Yes? + +AUDIENCE: [INAUDIBLE]. + +JOHN TSISIKLIS: Well, +probability is supposed to be + +a real number. + +So it's either zero or it's +a positive number. + +So you can think of the +probability of things just + +close to that point and those +probabilities are tiny and + +close to zero. + +So that's how we're going to +interpret probabilities in + +continuous models. + +But this is two chapters +ahead. + +Yeah? + +AUDIENCE: How do we interpret +probability of zero? + +If we can use models that +way, then how about + +probability of one? + +That it it's extremely +likely but not + +necessarily for certain? + +JOHN TSISIKLIS: That's +also the case. + +For example, if you ask in this +continuous model, if you + +ask me for the probability that +x, y, is different than + +the zero, zero this is +the whole square, + +except for one point. + +So the area of this is +going to be one. + +But this event is not entirely +certain because the zero, zero + +outcome is also possible. + +So again, probability of one +means essential certainty. + +But it still allows the +possibility that the outcome + +might be outside that set. + +So these are some of the weird +things that are happening when + +you have continuous models. + +And that's why we start to +this class with discrete + +models, on which would +be spending the + +next couple of weeks. + +OK. + +So now once we have set up our +probability model and we have + +a legitimate probability law +that has these properties, + +then the rest is +usually simple. + +Somebody asks you a question of +calculating the probability + +of some event. + +While you were told something +about the probability law, + +such as for example the +probabilities are equal to + +areas, and then you just +need to calculate. + +In these type of examples +somebody would give you a set + +and you would have +to calculate the + +area of that set. + +So the rest is just calculation +and simple. + +Alright, so now it's time +to start with our main + +business for today. + +And the starting point +is the following-- + +You know something +about the world. + +And based on what you know when +you set up a probability + +model and you write down +probabilities for the + +different outcomes. + +Then something happens, and +somebody tells you a little + +more about the world, gives +you some new information. + +This new information, in +general, should change your + +beliefs about what happened +or what may happen. + +So whenever we're given new +information, some partial + +information about the outcome +of the experiment, we should + +revise our beliefs. + +And conditional probabilities +are just the probabilities + +that apply after the revision +of our beliefs, when we're + +given some information. + +So lets make this into +a numerical example. + +So inside the sample space, this +part of the sample space, + +let's say has probability 3/6, +this part has 2/6, and that + +part has 1/6. + +I guess that means that out here +we have zero probability. + +So these were our initial +beliefs about the outcome of + +the experiment. + +Suppose now that someone +comes and tells you + +that event B occurred. + +So they don't tell you the +full outcome with the + +experiment. + +But they just tell you that the +outcome is known to lie + +inside this set B. + +Well then, you should certainly +change your beliefs + +in some way. + +And your new beliefs about what +is likely to occur and + +what is not is going to be +denoted by this notation. + +This is the conditional +probability that the event A + +is going to occur, the +probability that the outcome + +is going to fall inside the set +A given that we are told + +and we're sure that the event +lies inside the event B Now + +once you're told that the +outcome lies inside the event + +B, then our old sample space +in some ways is irrelevant. + +We have then you sample space, +which is just the set B. We + +are certain that the outcome +is going to be inside B. + +For example, what is this +conditional probability? + +It should be one. + +Given that I told you that B +occurred, you're certain that + +B occurred, so this has +unit probability. + +So here we see an instance of +revision of our beliefs. + +Initially, event B had the +probability of (2+1)/6 -- + +that's 1/2. + +Initially, we thought B +had probability 1/2. + +Once we're told that B occurred, +the new probability + +of B is equal to one. + +OK. + +How do we revise the probability +that A occurs? + +So we are going to have the +outcome of the experiment. + +We know that it's inside B. So +we will either get something + +here, and A does not occur. + +Or something inside here, +and A does occur. + +What's the likelihood that, +given that we're inside B, the + +outcome is inside here? + +Here's how we're going +to think about. + +This part of this set B, in +which A also occurs, in our + +initial model was twice as +likely as that part of B. So + +outcomes inside here +collectively were twice as + +likely as outcomes out there. + +So we're going to keep the same +proportions and say, that + +given that we are inside the set +B, we still want outcomes + +inside here to be twice as +likely outcomes there. + +So the proportion of the +probabilities should be two + +versus one. + +And these probabilities should +add up to one because together + +they make the conditional +probability of B. So the + +conditional probabilities should +be 2/3 probability of + +being here and 1/3 probability +of being there. + +That's how we revise +our probabilities. + +That's a reasonable, intuitively +reasonable, way of + +doing this revision. + +Let's translate what we +did into a definition. + +The definition says the +following, that the + +conditional probability of A +given that B occurred is + +calculated as follows. + +We look at the total probability +of B. And out of + +that probability that was inside +here, what fraction of + +that probability is assigned to +points for which the event + +A also occurs? + +Does it give us the same numbers +as we got with this + +heuristic argument? + +Well in this example, +probability of A intersection + +B is 2/6, divided by total +probability of B, which is + +3/6, and so it's 2/3, which +agrees with this answer that's + +we got before. + +So the former indeed matches +what we were trying to do. + +One little technical detail. + +If the event B has zero +probability, and then here we + +have a ratio that doesn't +make sense. + +So in this case, we say that +conditional probabilities are + +not defined. + +Now you can take this definition +and unravel it and + +write it in this form. + +The probability of A +intersection B is the + +probability of B times the +conditional probability. + +So this is just consequence of +the definition but it has a + +nice interpretation. + +Think of probabilities +as frequencies. + +If I do the experiment over and +over, what fraction of the + +time is it going to be the case +that both A and B occur? + +Well, there's going to be a +certain fraction of the time + +at which B occurs. + +And out of those times when B +occurs, there's going to be a + +further fraction of +the experiments in + +which A also occurs. + +So interpret the conditional +probability as follows. + +You only look at those +experiments at which + +B happens to occur. + +And look at what fraction of +those experiments where B + +already occurred, event +A also occurs. + +And there's a symmetrical +version of this equality. + +There's symmetry between the +events B and A. So you also + +have this relation that +goes the other way. + +OK, so what do we use these +conditional probabilities for? + +First, one comment. + +Conditional probabilities +are just like ordinary + +probabilities. + +They're the new probabilities +that apply in a new universe + +where event B is known +to have occurred. + +So we had an original +probability model. + +We are told that B occurs. + +We revise our model. + +Our new model should still be +legitimate probability model. + +So it should satisfy all sorts +of properties that ordinary + +probabilities do satisfy. + +So for example, if A and B are +disjoint events, then we know + +that the probability of A +union B is equal to the + +probability of A plus +probability of B. And now if I + +tell you that a certain event C +occurred, we're placed in a + +new universe where +event C occurred. + +We have new probabilities +for that universe. + +These are the conditional +probabilities. + +And conditional probabilities +also satisfy + +this kind of property. + +So this is just our usual +additivity axiom but the + +applied in a new model, in which +we were told that event + +C occurred. + +So conditional probabilities +do not taste or smell any + +different than ordinary +probabilities do. + +Conditional probabilities, given +a specific event B, just + +form a probability law +on our sample space. + +It's a different probability +law but it's still a + +probability law that has all +of the desired properties. + +OK, so where do conditional +probabilities come up? + +They do come up in quizzes +and they do + +come up in silly problems. + +So let's start with this. + +We have this example +from last time. + +Two rolls of a die, all possible +pairs of roles are + +equally likely, so every element +in this square has + +probability of 1/16. + +So all elements are +equally likely. + +That's our original model. + +Then somebody comes and tells us +that the minimum of the two + +rolls is equal to zero. + +What's that event? + +The minimum equal to zero can +happen in many ways, if we get + +two zeros or if we +get a zero and-- + +sorry, if we get two +two's, or get a two + +and something larger. + +And so the is our new event B. +The red event is the event B. + +And now we want to calculate +probabilities + +inside this new universe. + +For example, you may be +interested in the question, + +questions about the maximum +of the two rolls. + +In the new universe, what's +the probability that the + +maximum is equal to one? + +The maximum being equal to +one is this black event. + +And given that we're told that +B occurred, this black events + +cannot happen. + +So this probability +is equal to zero. + +How about the maximum +being equal to two, + +given that event B? + +OK, we can use the +definition here. + +It's going to be the probability +that the maximum + +is equal to two and B occurs +divided by the probability of + +B. The probability that the +maximum is equal to two. + +OK, what's the event that the +maximum is equal to two? + +Let's draw it. + +This is going to be +the blue event. + +The maximum is equal to +two if we get any + +of those blue points. + +So the intersection of the two +events is the intersection of + +the red event and +the blue event. + +There's only one point in +their intersection. + +So the probability of +that intersection + +happening is 1/16. + +That's the numerator. + +How about the denominator? + +The event B consists of five +elements, each one of which + +had probability of 1/16. + +So that's 5/16. + +And so the answer is 1/5. + +Could we have gotten this +answer in a faster way? + +Yes. + +Here's how it goes. + +We're trying to find the +conditional probability that + +we get this point, given +that B occurred. + +B consist of five elements. + +All of those five elements were +equally likely when we + +started, so they remain equally +likely afterwards. + +Because when we define +conditional probabilities, we + +keep the same proportions +inside the set. + +So the five red elements +were equally likely. + +They remain equally likely +in the conditional world. + +So conditional event B having +happened, each one of these + +five elements has the +same probability. + +So the probability that we +actually get this point is + +going to be 1/5. + +And so that's the shortcut. + +More generally, whenever you +have a uniform distribution on + +your initial sample space, +when you condition on an + +event, your new distribution is +still going to be uniform, + +but on the smaller events +of that we considered. + +So we started with a uniform +distribution on the big square + +and we ended up with a +uniform distribution + +just on the red point. + +Now besides silly problems, +however, conditional + +probabilities show up in real +and interesting situations. + +And this example is going +to give you some + +idea of how that happens. + +OK. + +Actually, in this example, +instead of starting with a + +probability model in terms of +regular probabilities, I'm + +actually going to define the +model in terms of conditional + +probabilities. + +And we'll see how +this is done. + +So here's the story. + +There may be an airplane flying +up in the sky, in a + +particular sector of the sky +that you're watching. + +Sometimes there is one sometimes +there isn't. + +And from experience you know +that when you look up, there's + +five percent probability that +the plane is flying above + +there and 95% probability that +there's no plane up there. + +So event A is the event that the +plane is flying out there. + +Now you bought this wonderful +radar that's looks up. + +And you're told in the +manufacturer's specs that, if + +there is a plane out there, +your radar is going to + +register something, a +blip on the screen + +with probability 99%. + +And it will not register +anything with + +probability one percent. + +So this particular part of the +picture is a self-contained + +probability model of what your +radar does in a world where a + +plane is out there. + +So I'm telling you that the +plane is out there. + +So we're now dealing with +conditional probabilities + +because I gave you some +particular information. + +Given this information that the +plane is out there, that's + +how your radar is going to +behave with probability 99% is + +going to detect it, with +probability one percent is + +going to miss it. + +So this piece of the picture +is a self-contained + +probability model. + +The probabilities +add up to one. + +But it's a piece of +a larger model. + +Similarly, there's the +other possibility. + +Maybe a plane is not up there +and the manufacturer specs + +tell you something about +false alarms. + +A false alarm is the situation +where the plane is not there, + +but for some reason your radar +picked up some noise or + +whatever and shows a +blip on the screen. + +And suppose that this happens +with probability ten percent. + +Whereas with probability +90% your radar + +gives the correct answer. + +So this is sort of a model of +what's going to happen with + +respect to both the plane -- +we're given probabilities + +about this -- and we're given +probabilities about how the + +radar behaves. + +So here I have indirectly +specified the probability law + +in our model by starting with +conditional probabilities as + +opposed to starting with +ordinary probabilities. + +Can we derive ordinary +probabilities starting from + +the conditional number ones? + +Yeah, we certainly can. + +Let's look at this event, A +intersection B, which is the + +event up here, that there +is a plane and our + +radar picks it up. + +How can we calculate +this probability? + +Well we use the definition of +conditional probabilities and + +this is the probability of +A times the conditional + +probability of B given A. +So it's 0.05 times 0.99. + +And the answer, in +case you care-- + +It's 0.0495. + +OK. + +So we can calculate the +probabilities of final + +outcomes, which are the leaves +of the tree, by using the + +probabilities that +we have along the + +branches of the tree. + +So essentially, what we ended +up doing was to multiply the + +probability of this +branch times the + +probability of that branch. + +Now, how about the answer +to this question. + +What is the probability +that our radar is + +going to register something? + +OK, this is an event that can +happen in multiple ways. + +It's the event that consists +of this outcome. + +There is a plane and the radar +registers something together + +with this outcome, there is no +plane but the radar still + +registers something. + +So to find the probability of +this event, we need the + +individual probabilities +of the two outcomes. + +For the first outcome, we +already calculated it. + +For the second outcome, the +probability that this happens + +is going to be this probability +95% times 0.10, + +which is the conditional +probability for taking this + +branch, given that there +was no plane out there. + +So we just add the numbers. + +0.05 times 0.99 plus 0.95 +times 0.1 and the + +final answer is 0.1445. + +OK. + +And now here's the interesting +question. + +Given that your radar recorded +something, how likely is it + +that there is an airplane +up there? + +Your radar registering +something -- + +that can be caused +by two things. + +Either there's a plane there, +and your radar did its job. + +Or there was nothing, but your +radar fired a false alarm. + +What's the probability that this +is the case as opposed to + +that being the case? + +OK. + +The intuitive shortcut would +be that it should be the + +probability-- + +you look at their relative odds +of these two elements and + +you use them to find out how +much more likely it is to be + +there as opposed +to being there. + +But instead of doing this, +let's just write down the + +definition and just use it. + +It's the probability of A and +B happening, divided by the + +probability of B. This is just +our definition of conditional + +probabilities. + +Now we have already found +the numerator. + +We have already calculated +the denominator. + +So we take the ratio of these +two numbers and we find the + +final answer -- + +which is 0.34. + +OK. + +There's this slightly +curious thing that's + +happened in this example. + +Doesn't this number feel +a little too low? + +My radar -- + +So this is a conditional +probability, given that my + +radar said there is something +out there, that there is + +indeed something there. + +So it's sort of the probability +that our radar + +gave the correct answer. + +Now, the specs of our radar +we're pretty good. + +In this situation, it gives +you the correct + +answer 99% of the time. + +In this situation, it gives +you the correct + +answer 90% of the time. + +So you would think +that your radar + +there is really reliable. + +But yet here the radar recorded +something, but the + +chance that the answer that +you get out of this is the + +right one, given that it +recorded something, the chance + +that there is an airplane +out there is only 30%. + +So you cannot really rely on +the measurements from your + +radar, even though the specs of +the radar were really good. + +What's the reason for this? + +Well, the reason is that false +alarms are pretty common. + +Most of the time there's +nothing. + +And there's a ten percent +probability of false alarms. + +So there's roughly a ten percent +probability that in + +any given experiment, you +have a false alarm. + +And there is about the five +percent probability that + +something out there and +your radar gets it. + +So when your radar records +something, it's actually more + +likely to be a false +alarm rather than + +being an actual airplane. + +This has probability ten +percent roughly. + +This has probability roughly +five percent + +So conditional probabilities +are sometimes + +counter-intuitive in terms of +the answers that they get. + +And you can make similar +stories about doctors + +interpreting the results +of tests. + +So you tested positive for +a certain disease. + +Does it mean that you have +the disease necessarily? + +Well if that disease has been +eradicated from the face of + +the earth, testing positive +doesn't mean that you have the + +disease, even if the test +was designed to be + +a pretty good one. + +So unfortunately, doctors do get +it wrong also sometimes. + +And the reasoning that +comes in such + +situations is pretty subtle. + +Now for the rest of the lecture, +what we're going to + +do is to take this example where +we did three things and + +abstract them. + +These three trivial calculations +that's we just + +did are three very important, +very basic tools that you use + +to solve more general +probability problems. + +So what's the first one? + +We find the probability of a +composite event, two things + +happening, by multiplying +probabilities and conditional + +probabilities. + +More general version of this, +look at any situation, maybe + +involving lots and +lots of events. + +So here's a story that event A +may happen or may not happen. + +Given that A occurred, it's +possible that B happens or + +that B does not happen. + +Given that B also happens, it's +possible that the event C + +also happens or that event +C does not happen. + +And somebody specifies for you +a model by giving you all + +these conditional probabilities +along the way. + +Notice what we move along +the branches as the tree + +progresses. + +Any point in the tree +corresponds to certain events + +having happened. + +And then, given that this +has happened, we specify + +conditional probabilities. + +Given that this has happened, +how likely is it for that C + +also occurs? + +Given a model of this kind, how +do we find the probability + +or for this event? + +The answer is extremely +simple. + +All that you do is move along +with the tree and multiply + +conditional probabilities +along the way. + +So in terms of frequencies, how +often do all three things + +happen, A, B, and C? + +You first see how often +does A occur. + +Out of the times that +A occurs, how + +often does B occur? + +And out of the times where both +A and B have occurred, + +how often does C occur? + +And you can just multiply those +three frequencies with + +each other. + +What is the formal +proof of this? + +Well, the only thing we have in +our hands is the definition + +of conditional probabilities. + +So let's just use this. + +And-- + +OK. + +Now, the definition of +conditional probabilities + +tells us that the probability +of two things is the + +probability of one of them +times a conditional + +probability. + +Unfortunately, here we have the + +probability of three things. + +What can I do? + +I can put a parenthesis in here +and think of this as the + +probability of this and that +and apply our definition of + +conditional probabilities +here. + +The probability of two things +happening is the probability + +that the first happens times +the conditional probability + +that the second happens, given +A and B, given that the first + +one happened. + +So this is just the definition +of the conditional probability + +of an event, given +another event. + +That other event is a +composite one, but + +that's not an issue. + +It's just an event. + +And then we use the definition +of conditional probabilities + +once more to break this apart +and make it P(A), P(B given A) + +and then finally, +the last term. + +OK. + +So this proves the formula +that I have up + +there on the slides. + +And if you wish to calculate +any other + +probability in this diagram. + +For example, if you want to +calculate this probability, + +you would still multiply the +conditional probabilities + +along the different branches +of the tree. + +In particular, here in this +branch, you would have the + +conditional probability of +C complement, given A + +intersection B complement, +and so on. + +So you write down probabilities +along all those + +tree branches and just multiply +them as you go. + +So this was the first skill +that we are covering. + +What was the second one? + +What we did was to calculate +the total probability of a + +certain event B that +consisted of-- + +was made up from different +possibilities, which + +corresponded to different +scenarios. + +So we wanted to calculate the +probability of this event B + +that consisted of those +two elements. + +Let's generalize. + +So we have our big model. + +And this sample space +is partitioned + +in a number of sets. + +In our radar example, we had +a partition in two sets. + +Either a plane is there, or +a plane is not there. + +Since we're trying to +generalize, now I'm going to + +give you a picture for the case +of three possibilities or + +three possible scenarios. + +So whatever happens in the +world, there are three + +possible scenarios, +A1, A2, A3. + +So think of these as there's +nothing in the air, there's an + +airplane in the air, or there's +a flock of geese + +flying in the air. + +So there's three possible +scenarios. + +And then there's a certain event +B of interest, such as a + +radar records something or +doesn't record something. + +We specify this model by giving + +probabilities for the Ai's-- + +That's the probability of +the different scenarios. + +And somebody also gives us the +probabilities that this event + +B is going to occur, given +that the Ai-th + +scenario has occurred. + +Think of the Ai's +as scenarios. + +And we want to calculate the +overall probability of the + +event B. What's happening +in this example? + +Perhaps, instead of this +picture, it's easier to + +visualize if I go back to the +picture I was using before. + +We have three possible +scenarios, A1, A2, A3. + +And under each scenario, B may +happen or B may not happen. + +And so on. + +So here we have A2 intersection +B. And here we + +have A3 intersection B. In the +previous slide, we found how + +to calculate the probability +of any event of this kind, + +which is done by multiplying +probabilities here and + +conditional probabilities +there. + +Now we are asked to calculate +the total probability of the + +event B. The event B can happen +in three possible ways. + +It can happen here. + +It can happen there. + +And it can happen here. + +So this is our event B. It +consists of three elements. + +To calculate the total +probability of our event B, + +all we need to do is to add +these three probabilities. + +So B is an event that consists +of these three elements. + +There are three ways +that B can happen. + +Either B happens together with +A1, or B happens together with + +A2, or B happens together +with A3. + +So we need to add the +probabilities of these three + +contingencies. + +For each one of those +contingencies, we can + +calculate its probability by +using the multiplication rule. + +So the probability of A1 and +B happening is this-- + +It's the probability of A1 +and then B happening + +given that A1 happens. + +The probability of this +contingency is found by taking + +the probability that A2 happens +times the conditional + +probability of A2, given +that B happened. + +And similarly for +the third one. + +So this is the general rule +that we have here. + +The rule is written for the +case of three scenarios. + +But obviously, it has a +generalization for the case of + +four or five or more +scenarios. + +It gives you a way of breaking +up the calculation of an event + +that can happen in multiple ways +by considering individual + +probabilities for the different +ways that the event + +can happen. + +OK. + +So-- + +Yes? + +AUDIENCE: Does this +have to change for + +infinite sample space? + +JOHN TSISIKLIS: No. + +This is true whether +your sample space + +is infinite or finite. + +What I'm using in this argument +that we have a + +partition into just three +scenarios, three events. + +So it's a partition to a finite +number of events. + +It's also true if it's a +partition into an infinite + +sequence of events. + +But that's, I think, one of the +theoretical problems at + +the end of the chapter. + +You probably may not +need it for now. + +OK, going back to +the story here. + +There are three possible +scenarios about what could + +happen in the world that +are captured here. + +Event, under each scenario, +event B may or may not happen. + +And so these probabilities tell +us the likelihoods of the + +different scenarios. + +These conditional probabilities +tell us how + +likely is it for B to happen +under one scenario, or the + +other scenario, or the +other scenario. + +The overall probability of +B is found by taking some + +combination of the probabilities +of B in the + +different possible +worlds, in the + +different possible scenarios. + +Under some scenario, B +may be very likely. + +Under another scenario, it +may be very unlikely. + +We take all of these into +account and weigh them + +according to the likelihood +of the scenarios. + +Now notice that since A1, A2, +and three form a partition, + +these three probabilities +have what property? + +Add to what? + +They add to one. + +So it's the probability of this +branch, plus this branch, + +plus this branch. + +So what we have here is a +weighted average of the + +probabilities of the B's into +the different worlds, or in + +the different scenarios. + +Special case. + +Suppose the three scenarios +are equally likely. + +So P of A1 equals 1/3, equals +to P of A2, P of A3. + +what are we saying here? + +In that case of equally likely +scenarios, the probability of + +B is the average of the +probabilities of B in the + +three different words, or in the +three different scenarios. + +OK. + +So to finally, the last step. + +If we go back again two slides, +the last thing that we + +did was to calculate a +conditional probability of + +this kind, probability of +A given B, which is a + +probability associated +essentially with + +an inference problem. + +Given that our radar recorded +something, how likely is it + +that the plane was up there? + +So we're trying to infer whether +a plane was up there + +or not, based on the information +that we've got. + +So let's generalize once more. + +And we're just going to rewrite +what we did in that + +example, but in terms of general +symbols instead of the + +specific numbers. + +So once more, the model that we +have involves probabilities + +of the different scenarios. + +These we call them prior +probabilities. + +They're are our initial beliefs +about how likely each + +scenario is to occur. + +We also have a model of our +measuring device that tells us + +under that scenario how likely +is it that our radar will + +register something or not. + +So we're given again these +conditional probabilities. + +We're given the conditional + +probabilities for these branches. + +Then we are told that +event B occurred. + +And on the basis of this new +information, we want to form + +some new beliefs about the +relative likelihood of the + +different scenarios. + +Going back again to our radar +example, an airplane was + +present with probability 5%. + +Given that the radar recorded +something, we're going to + +change our beliefs. + +Now, a plane is present +with probability 34%. + +The radar, since we saw +something, we are going to + +revise our beliefs as to whether +the plane is out there + +or is not there. + +And so what we need to do is to +calculate the conditional + +probabilities of the different +scenarios, given the + +information that we got. + +So initially, we have these +probabilities for the + +different scenarios. + +Once we get the information, +we update them and we + +calculate our revised +probabilities or conditional + +probabilities given the +observation that we made. + +OK. + +So what do we do? + +We just use the definition +of conditional + +probabilities twice. + +By definition the conditional +probability is the probability + +of two things happening divided +by the probability of + +the conditioning event. + +Now, I'm using the definition +of conditional probabilities + +once more, or rather I use +the multiplication rule. + +The probability of two things +happening is the probability + +of the first and the second. + +So these are things that +are given to us. + +They're the probabilities of +the different scenarios. + +And it's the model of our +measuring device, which we + +assume to be available. + +And how about the denominator? + +This is total probability of the +event B. But we just found + +that's it's easy to calculate +using the formula in the + +previous slide. + +To find the overall probability +of event B + +occurring, we look at the +probabilities of B occurring + +under the different scenario +and weigh them according to + +the probabilities of +all the scenarios. + +So in the end, we have a formula +for the conditional + +probability, A's given B, +based on the data of the + +problem, which were +probabilities of the different + +scenarios and conditional +probabilities of + +B, given the A's. + +So what this calculation does +is, basically, it reverses the + +order of conditioning. + +We are given conditional +probabilities of these kind, + +where it's B given A and we +produce new conditional + +probabilities, where things +go the other way. + +So schematically, what's +happening here is that we have + +model of cause and +effect and-- + +So a scenario occurs and that +may cause B to happen or may + +not cause it to happen. + +So this is a cause/effect +model. + +And it's modeled using +probabilities, such as + +probability of B given Ai. + +And what we want to do is +inference where we are told + +that B occurs, and we want +to infer whether Ai + +also occurred or not. + +And the appropriate +probabilities for that are the + +conditional probabilities +that A occurred, + +given that B occurred. + +So we're starting with a causal +model of our situation. + +It models from a given cause how +likely is a certain effect + +to be observed. + +And then we do inference, which +answers the question, + +given that the effect was +observed, how likely is it + +that the world was in this +particular situation or state + +or scenario. + +So the name of the Bayes rule +comes from Thomas Bayes, a + +British theologian back +in the 1700s. + +It actually-- + +This calculation addresses +a basic problem, a basic + +philosophical problem, how one +can learn from experience or + +from experimental data and +some systematic way. + +So the British at that time +were preoccupied with this + +type of question. + +Is there a basic theory that +about how we can incorporate + +new knowledge to previous +knowledge. + +And this calculation made an +argument that, yes, it is + +possible to do that in +a systematic way. + +So the philosophical +underpinnings of this have a + +very long history and a lot +of discussion around them. + +But for our purposes, it's just +an extremely useful tool. + +And it's the foundation of +almost everything that gets + +done when you try to do +inference based on partial + +observations. + +Very well. + +Till next time. \ No newline at end of file diff --git a/TmbsF5HkhnU.txt b/TmbsF5HkhnU.txt new file mode 100644 index 0000000000000000000000000000000000000000..f81ccb5af9c4c5970c56098f246f16ff3a077ef3 --- /dev/null +++ b/TmbsF5HkhnU.txt @@ -0,0 +1,5499 @@ +align:start position:0% + +ocw is definitely something which I + + align:start position:0% +ocw is definitely something which I + + + align:start position:0% +ocw is definitely something which I +would identify as like an extra work + + align:start position:0% +would identify as like an extra work + + + align:start position:0% +would identify as like an extra work +which I had taken for myself because I + + align:start position:0% +which I had taken for myself because I + + + align:start position:0% +which I had taken for myself because I +want to think differently I want I I + + align:start position:0% +want to think differently I want I I + + + align:start position:0% +want to think differently I want I I +always sort of had this um repulsion + + align:start position:0% +always sort of had this um repulsion + + + align:start position:0% +always sort of had this um repulsion +against group thing repulsion are very + + align:start position:0% +against group thing repulsion are very + + + align:start position:0% +against group thing repulsion are very +quite strong words so I'll just say very + + align:start position:0% +quite strong words so I'll just say very + + + align:start position:0% +quite strong words so I'll just say very +very cautious probably because I follow + + align:start position:0% +very cautious probably because I follow + + + align:start position:0% +very cautious probably because I follow +the market every day and I Tred to be + + align:start position:0% +the market every day and I Tred to be + + + align:start position:0% +the market every day and I Tred to be +very very cautious about group think + + align:start position:0% +very very cautious about group think + + + align:start position:0% +very very cautious about group think +well how can I think different how can I + + align:start position:0% +well how can I think different how can I + + + align:start position:0% +well how can I think different how can I +think logically + + align:start position:0% +think logically + + + align:start position:0% +think logically +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +welcome to open Learners a podcast that + + align:start position:0% +welcome to open Learners a podcast that + + + align:start position:0% +welcome to open Learners a podcast that +tells the stories of Learners all over + + align:start position:0% +tells the stories of Learners all over + + + align:start position:0% +tells the stories of Learners all over +the world who use mit's open courseware + + align:start position:0% +the world who use mit's open courseware + + + align:start position:0% +the world who use mit's open courseware +I'm Emmanuel Li kasigi an open learner + + align:start position:0% +I'm Emmanuel Li kasigi an open learner + + + align:start position:0% +I'm Emmanuel Li kasigi an open learner +myself from campala Uganda in East + + align:start position:0% +myself from campala Uganda in East + + + align:start position:0% +myself from campala Uganda in East +Africa and I'm Michael Jordan pilra an + + align:start position:0% +Africa and I'm Michael Jordan pilra an + + + align:start position:0% +Africa and I'm Michael Jordan pilra an +open learner from Memphis + + align:start position:0% + + + + align:start position:0% + +Tennessee we're back episode two Michael + + align:start position:0% +Tennessee we're back episode two Michael + + + align:start position:0% +Tennessee we're back episode two Michael +hey Emanuel uh do you want to introduce + + align:start position:0% +hey Emanuel uh do you want to introduce + + + align:start position:0% +hey Emanuel uh do you want to introduce +today's open lner today we will hear + + align:start position:0% +today's open lner today we will hear + + + align:start position:0% +today's open lner today we will hear +from J mean Hong an open learner + + align:start position:0% +from J mean Hong an open learner + + + align:start position:0% +from J mean Hong an open learner +currently living in Soul South Korea I + + align:start position:0% +currently living in Soul South Korea I + + + align:start position:0% +currently living in Soul South Korea I +met J mean about two years ago after my + + align:start position:0% +met J mean about two years ago after my + + + align:start position:0% +met J mean about two years ago after my +MIT news article came out she reached + + align:start position:0% +MIT news article came out she reached + + + align:start position:0% +MIT news article came out she reached +out to me via LinkedIn and I got on a + + align:start position:0% +out to me via LinkedIn and I got on a + + + align:start position:0% +out to me via LinkedIn and I got on a +zoom call with her for about an hour + + align:start position:0% +zoom call with her for about an hour + + + align:start position:0% +zoom call with her for about an hour +while she was studying at the University + + align:start position:0% +while she was studying at the University + + + align:start position:0% +while she was studying at the University +of Wisconsin well for me this interview + + align:start position:0% +of Wisconsin well for me this interview + + + align:start position:0% +of Wisconsin well for me this interview +was the first time I met J me face to + + align:start position:0% +was the first time I met J me face to + + + align:start position:0% +was the first time I met J me face to +face but we're actually in the same AI + + align:start position:0% +face but we're actually in the same AI + + + align:start position:0% +face but we're actually in the same AI +study group on ledin which is + + align:start position:0% +study group on ledin which is + + + align:start position:0% +study group on ledin which is +interesting so it was really cool for + + align:start position:0% +interesting so it was really cool for + + + align:start position:0% +interesting so it was really cool for +both of us to put faces to our names + + align:start position:0% +both of us to put faces to our names + + + align:start position:0% +both of us to put faces to our names +that's awesome Emanuel I know you + + align:start position:0% +that's awesome Emanuel I know you + + + align:start position:0% +that's awesome Emanuel I know you +started the AI learning group on + + align:start position:0% +started the AI learning group on + + + align:start position:0% +started the AI learning group on +LinkedIn and you were really excited to + + align:start position:0% +LinkedIn and you were really excited to + + + align:start position:0% +LinkedIn and you were really excited to +start building a community of AI + + align:start position:0% +start building a community of AI + + + align:start position:0% +start building a community of AI +Learners all over the world one reason + + align:start position:0% +Learners all over the world one reason + + + align:start position:0% +Learners all over the world one reason +we really wanted to interview jam mean + + align:start position:0% +we really wanted to interview jam mean + + + align:start position:0% +we really wanted to interview jam mean +for open Learners was because her + + align:start position:0% +for open Learners was because her + + + align:start position:0% +for open Learners was because her +educational path is so unique one she + + align:start position:0% +educational path is so unique one she + + + align:start position:0% +educational path is so unique one she +started her open course s Journey as an + + align:start position:0% +started her open course s Journey as an + + + align:start position:0% +started her open course s Journey as an +undergrad student with a course in + + align:start position:0% +undergrad student with a course in + + + align:start position:0% +undergrad student with a course in +thermodynamics to supplement her dual + + align:start position:0% +thermodynamics to supplement her dual + + + align:start position:0% +thermodynamics to supplement her dual +degree program in chemistry and finance + + align:start position:0% +degree program in chemistry and finance + + + align:start position:0% +degree program in chemistry and finance +and two Jam has lived and learned all + + align:start position:0% +and two Jam has lived and learned all + + + align:start position:0% +and two Jam has lived and learned all +over the world she left Korea at 14 to + + align:start position:0% +over the world she left Korea at 14 to + + + align:start position:0% +over the world she left Korea at 14 to +attend high school in New Zealand and + + align:start position:0% +attend high school in New Zealand and + + + align:start position:0% +attend high school in New Zealand and +she attended the University of Wisconsin + + align:start position:0% +she attended the University of Wisconsin + + + align:start position:0% +she attended the University of Wisconsin +for a year in the middle of the pandemic + + align:start position:0% +for a year in the middle of the pandemic + + + align:start position:0% +for a year in the middle of the pandemic +before returning to Korea to finish her + + align:start position:0% +before returning to Korea to finish her + + + align:start position:0% +before returning to Korea to finish her +economic degree that's really cool Jam + + align:start position:0% +economic degree that's really cool Jam + + + align:start position:0% +economic degree that's really cool Jam +is really he a really driven person + + align:start position:0% +is really he a really driven person + + + align:start position:0% +is really he a really driven person +because most people don't usually start + + align:start position:0% +because most people don't usually start + + + align:start position:0% +because most people don't usually start +these paths during their underground but + + align:start position:0% +these paths during their underground but + + + align:start position:0% +these paths during their underground but +she did and she shared with us her + + align:start position:0% +she did and she shared with us her + + + align:start position:0% +she did and she shared with us her +perspective on how education defers + + align:start position:0% +perspective on how education defers + + + align:start position:0% +perspective on how education defers +around the world her ocw gave her new + + align:start position:0% +around the world her ocw gave her new + + + align:start position:0% +around the world her ocw gave her new +ways of thinking about herself and her + + align:start position:0% +ways of thinking about herself and her + + + align:start position:0% +ways of thinking about herself and her +career path which is really interesting + + align:start position:0% +career path which is really interesting + + + align:start position:0% +career path which is really interesting +and I'm excited to hear all about that + + align:start position:0% +and I'm excited to hear all about that + + + align:start position:0% +and I'm excited to hear all about that +so let's get to it here is our + + align:start position:0% +so let's get to it here is our + + + align:start position:0% +so let's get to it here is our +conversation with Jam Hong of Soul South + + align:start position:0% +conversation with Jam Hong of Soul South + + + align:start position:0% +conversation with Jam Hong of Soul South +Korea + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +hi my name is Jamon Hong and I'm a final + + align:start position:0% +hi my name is Jamon Hong and I'm a final + + + align:start position:0% +hi my name is Jamon Hong and I'm a final +year economics student studying um at + + align:start position:0% +year economics student studying um at + + + align:start position:0% +year economics student studying um at +yon University and I was born and raised + + align:start position:0% +yon University and I was born and raised + + + align:start position:0% +yon University and I was born and raised +in Korea for the most part of my life + + align:start position:0% +in Korea for the most part of my life + + + align:start position:0% +in Korea for the most part of my life +but I also had some very exciting + + align:start position:0% +but I also had some very exciting + + + align:start position:0% +but I also had some very exciting +Journeys in America and New Zealand late + + align:start position:0% +Journeys in America and New Zealand late + + + align:start position:0% +Journeys in America and New Zealand late +2022 so I finished the first semester of + + align:start position:0% +2022 so I finished the first semester of + + + align:start position:0% +2022 so I finished the first semester of +my sophomore year but then that was + + align:start position:0% +my sophomore year but then that was + + + align:start position:0% +my sophomore year but then that was +still when covid was still around and + + align:start position:0% +still when covid was still around and + + + align:start position:0% +still when covid was still around and +all the campus lectures they were all + + align:start position:0% +all the campus lectures they were all + + + align:start position:0% +all the campus lectures they were all +shut down so all the classes were done + + align:start position:0% +shut down so all the classes were done + + + align:start position:0% +shut down so all the classes were done +online but then as a very social and + + align:start position:0% +online but then as a very social and + + + align:start position:0% +online but then as a very social and +active human interaction driven person I + + align:start position:0% +active human interaction driven person I + + + align:start position:0% +active human interaction driven person I +wanted to go out there but there was no + + align:start position:0% +wanted to go out there but there was no + + + align:start position:0% +wanted to go out there but there was no +chance of having any campus lectur so I + + align:start position:0% +chance of having any campus lectur so I + + + align:start position:0% +chance of having any campus lectur so I +went to + + align:start position:0% +went to + + + align:start position:0% +went to +America I went to America where inperson + + align:start position:0% +America I went to America where inperson + + + align:start position:0% +America I went to America where inperson +lectures were um permitted and I went to + + align:start position:0% +lectures were um permitted and I went to + + + align:start position:0% +lectures were um permitted and I went to +W Madison and then this was the time + + align:start position:0% +W Madison and then this was the time + + + align:start position:0% +W Madison and then this was the time +when I was trying to explore more + + align:start position:0% +when I was trying to explore more + + + align:start position:0% +when I was trying to explore more +subjects and yeah really establish my + + align:start position:0% +subjects and yeah really establish my + + + align:start position:0% +subjects and yeah really establish my +perspective of the world and how I would + + align:start position:0% +perspective of the world and how I would + + + align:start position:0% +perspective of the world and how I would +like to apply this this the knowledge + + align:start position:0% +like to apply this this the knowledge + + + align:start position:0% +like to apply this this the knowledge +that I really wanted to learn while + + align:start position:0% +that I really wanted to learn while + + + align:start position:0% +that I really wanted to learn while +while I was at University I was studying + + align:start position:0% +while I was at University I was studying + + + align:start position:0% +while I was at University I was studying +chemistry when I was at W Madison which + + align:start position:0% +chemistry when I was at W Madison which + + + align:start position:0% +chemistry when I was at W Madison which +is up north very very cold but I studied + + align:start position:0% +is up north very very cold but I studied + + + align:start position:0% +is up north very very cold but I studied +chemistry Finance data science and + + align:start position:0% +chemistry Finance data science and + + + align:start position:0% +chemistry Finance data science and +computer science all sorts of subjects + + align:start position:0% +computer science all sorts of subjects + + + align:start position:0% +computer science all sorts of subjects +there but chemistry was very exciting + + align:start position:0% +there but chemistry was very exciting + + + align:start position:0% +there but chemistry was very exciting +but challenging so I was sort of trying + + align:start position:0% +but challenging so I was sort of trying + + + align:start position:0% +but challenging so I was sort of trying +to seek out and gather around more + + align:start position:0% +to seek out and gather around more + + + align:start position:0% +to seek out and gather around more +information so that I can improve my + + align:start position:0% +information so that I can improve my + + + align:start position:0% +information so that I can improve my +understanding and I and then I came + + align:start position:0% +understanding and I and then I came + + + align:start position:0% +understanding and I and then I came +across + + align:start position:0% +across + + + align:start position:0% +across +mitw videos and then the first course + + align:start position:0% +mitw videos and then the first course + + + align:start position:0% +mitw videos and then the first course +that I took was called thermodynamics + + align:start position:0% +that I took was called thermodynamics + + + align:start position:0% +that I took was called thermodynamics +and kinetics and this was the most + + align:start position:0% +and kinetics and this was the most + + + align:start position:0% +and kinetics and this was the most +difficult subject within chemistry but I + + align:start position:0% +difficult subject within chemistry but I + + + align:start position:0% +difficult subject within chemistry but I +loved it how was it like like first of + + align:start position:0% +loved it how was it like like first of + + + align:start position:0% +loved it how was it like like first of +all meeting all these online resources + + align:start position:0% +all meeting all these online resources + + + align:start position:0% +all meeting all these online resources +maybe compared to your former education + + align:start position:0% +maybe compared to your former education + + + align:start position:0% +maybe compared to your former education +experiences from New Zealand from South + + align:start position:0% +experiences from New Zealand from South + + + align:start position:0% +experiences from New Zealand from South +Korea how was the difference when you + + align:start position:0% +Korea how was the difference when you + + + align:start position:0% +Korea how was the difference when you +finally met ocw and MIT and uh how is it + + align:start position:0% +finally met ocw and MIT and uh how is it + + + align:start position:0% +finally met ocw and MIT and uh how is it +for you + + align:start position:0% +for you + + + align:start position:0% +for you +personally well I think the major + + align:start position:0% +personally well I think the major + + + align:start position:0% +personally well I think the major +difference was about flexibility because + + align:start position:0% +difference was about flexibility because + + + align:start position:0% +difference was about flexibility because +when you're taking a lecture and you're + + align:start position:0% +when you're taking a lecture and you're + + + align:start position:0% +when you're taking a lecture and you're +in a lecture hall filled with 300 + + align:start position:0% +in a lecture hall filled with 300 + + + align:start position:0% +in a lecture hall filled with 300 +different students you cannot just sort + + align:start position:0% +different students you cannot just sort + + + align:start position:0% +different students you cannot just sort +of actively try to find out information + + align:start position:0% +of actively try to find out information + + + align:start position:0% +of actively try to find out information +or like areas of interest you can you + + align:start position:0% +or like areas of interest you can you + + + align:start position:0% +or like areas of interest you can you +can't directly ask the professor but + + align:start position:0% +can't directly ask the professor but + + + align:start position:0% +can't directly ask the professor but +then or + + align:start position:0% +then or + + + align:start position:0% +then or +rewind it's a bit difficult to do that + + align:start position:0% +rewind it's a bit difficult to do that + + + align:start position:0% +rewind it's a bit difficult to do that +and so because I'm I'm quite a proactive + + align:start position:0% +and so because I'm I'm quite a proactive + + + align:start position:0% +and so because I'm I'm quite a proactive +learner and so I want to find out more + + align:start position:0% +learner and so I want to find out more + + + align:start position:0% +learner and so I want to find out more +information for myself but with a more + + align:start position:0% +information for myself but with a more + + + align:start position:0% +information for myself but with a more +structured learning program that is more + + align:start position:0% +structured learning program that is more + + + align:start position:0% +structured learning program that is more +conventionally offered at universities + + align:start position:0% +conventionally offered at universities + + + align:start position:0% +conventionally offered at universities +was quite difficult to do and so with + + align:start position:0% +was quite difficult to do and so with + + + align:start position:0% +was quite difficult to do and so with +MIT ocw I was able to sometimes pick out + + align:start position:0% +MIT ocw I was able to sometimes pick out + + + align:start position:0% +MIT ocw I was able to sometimes pick out +topics that that Drew me the most and + + align:start position:0% +topics that that Drew me the most and + + + align:start position:0% +topics that that Drew me the most and +that was entropy for me thermodynamics + + align:start position:0% +that was entropy for me thermodynamics + + + align:start position:0% +that was entropy for me thermodynamics +and then I wanted to learn more about + + align:start position:0% +and then I wanted to learn more about + + + align:start position:0% +and then I wanted to learn more about +that instead of you know just trying to + + align:start position:0% +that instead of you know just trying to + + + align:start position:0% +that instead of you know just trying to +rely on very structured course learning + + align:start position:0% +rely on very structured course learning + + + align:start position:0% +rely on very structured course learning +at um conventional you know traditional + + align:start position:0% +at um conventional you know traditional + + + align:start position:0% +at um conventional you know traditional +University Systems Mark Twain once + + align:start position:0% +University Systems Mark Twain once + + + align:start position:0% +University Systems Mark Twain once +famously said that I never let my school + + align:start position:0% +famously said that I never let my school + + + align:start position:0% +famously said that I never let my school +institutional learning interfere with my + + align:start position:0% +institutional learning interfere with my + + + align:start position:0% +institutional learning interfere with my +education and that is the sort of phrase + + align:start position:0% +education and that is the sort of phrase + + + align:start position:0% +education and that is the sort of phrase +that swept me away at that time this is + + align:start position:0% +that swept me away at that time this is + + + align:start position:0% +that swept me away at that time this is +education like this is what learning + + align:start position:0% +education like this is what learning + + + align:start position:0% +education like this is what learning +actually means I was going to ask a + + align:start position:0% +actually means I was going to ask a + + + align:start position:0% +actually means I was going to ask a +quick question here when you have this + + align:start position:0% +quick question here when you have this + + + align:start position:0% +quick question here when you have this +breakthrough moment when you start + + align:start position:0% +breakthrough moment when you start + + + align:start position:0% +breakthrough moment when you start +actually learning from open educ + + align:start position:0% +actually learning from open educ + + + align:start position:0% +actually learning from open educ +materials and not you know waiting for a + + align:start position:0% +materials and not you know waiting for a + + + align:start position:0% +materials and not you know waiting for a +teacher to prod you like what did it + + align:start position:0% +teacher to prod you like what did it + + + align:start position:0% +teacher to prod you like what did it +change in your life the first change is + + align:start position:0% +change in your life the first change is + + + align:start position:0% +change in your life the first change is +that okay like I'm actually learning + + align:start position:0% +that okay like I'm actually learning + + + align:start position:0% +that okay like I'm actually learning +this so in terms of the finance Theory + + align:start position:0% +this so in terms of the finance Theory + + + align:start position:0% +this so in terms of the finance Theory +which I know you also took as part of + + align:start position:0% +which I know you also took as part of + + + align:start position:0% +which I know you also took as part of +your MIT ocw Journey when I was taking + + align:start position:0% +your MIT ocw Journey when I was taking + + + align:start position:0% +your MIT ocw Journey when I was taking +the finance Theory course taught by + + align:start position:0% +the finance Theory course taught by + + + align:start position:0% +the finance Theory course taught by +Professor Andrew low I was taking a more + + align:start position:0% +Professor Andrew low I was taking a more + + + align:start position:0% +Professor Andrew low I was taking a more +or less equivalent course at W Madison + + align:start position:0% +or less equivalent course at W Madison + + + align:start position:0% +or less equivalent course at W Madison +it was called money and Market we were + + align:start position:0% +it was called money and Market we were + + + align:start position:0% +it was called money and Market we were +learning about the impact of monetary + + align:start position:0% +learning about the impact of monetary + + + align:start position:0% +learning about the impact of monetary +policies conducted by Federal Reserve + + align:start position:0% +policies conducted by Federal Reserve + + + align:start position:0% +policies conducted by Federal Reserve +but then what was really interesting was + + align:start position:0% +but then what was really interesting was + + + align:start position:0% +but then what was really interesting was +that in this course Finance the the MIT + + align:start position:0% +that in this course Finance the the MIT + + + align:start position:0% +that in this course Finance the the MIT +ocw course this was actually filmed when + + align:start position:0% +ocw course this was actually filmed when + + + align:start position:0% +ocw course this was actually filmed when +G um when GFC the global financial + + align:start position:0% +G um when GFC the global financial + + + align:start position:0% +G um when GFC the global financial +crisis was happening and so it was more + + align:start position:0% +crisis was happening and so it was more + + + align:start position:0% +crisis was happening and so it was more +like I'm actually learning about these + + align:start position:0% +like I'm actually learning about these + + + align:start position:0% +like I'm actually learning about these +theories but I'm actually also seeing + + align:start position:0% +theories but I'm actually also seeing + + + align:start position:0% +theories but I'm actually also seeing +how these theories were like happening + + align:start position:0% +how these theories were like happening + + + align:start position:0% +how these theories were like happening +in real life and how they actually apply + + align:start position:0% +in real life and how they actually apply + + + align:start position:0% +in real life and how they actually apply +to R scenarios like fixed income + + align:start position:0% +to R scenarios like fixed income + + + align:start position:0% +to R scenarios like fixed income +security products went a bit too complex + + align:start position:0% +security products went a bit too complex + + + align:start position:0% +security products went a bit too complex +and the leverage ratio went a bit crazy + + align:start position:0% +and the leverage ratio went a bit crazy + + + align:start position:0% +and the leverage ratio went a bit crazy +these were the sort of knowledge that I + + align:start position:0% +these were the sort of knowledge that I + + + align:start position:0% +these were the sort of knowledge that I +was learning theoretically at University + + align:start position:0% +was learning theoretically at University + + + align:start position:0% +was learning theoretically at University +and sure I was like watching videos and + + align:start position:0% +and sure I was like watching videos and + + + align:start position:0% +and sure I was like watching videos and +learning theoretically but then actually + + align:start position:0% +learning theoretically but then actually + + + align:start position:0% +learning theoretically but then actually +I was able to see the real impact of it + + align:start position:0% +I was able to see the real impact of it + + + align:start position:0% +I was able to see the real impact of it +like through the video that was actually + + align:start position:0% +like through the video that was actually + + + align:start position:0% +like through the video that was actually +recorded at the time of GFC and so it + + align:start position:0% +recorded at the time of GFC and so it + + + align:start position:0% +recorded at the time of GFC and so it +was more like a reward for my proactive + + align:start position:0% +was more like a reward for my proactive + + + align:start position:0% +was more like a reward for my proactive +learning because it was genuinely quite + + align:start position:0% +learning because it was genuinely quite + + + align:start position:0% +learning because it was genuinely quite +interesting and yeah I was able to draw + + align:start position:0% +interesting and yeah I was able to draw + + + align:start position:0% +interesting and yeah I was able to draw +parallels in many different angles and + + align:start position:0% +parallels in many different angles and + + + align:start position:0% +parallels in many different angles and +it was yeah it make my life more + + align:start position:0% + + + + align:start position:0% + +fun I like when you mentioned it was + + align:start position:0% +fun I like when you mentioned it was + + + align:start position:0% +fun I like when you mentioned it was +like in real time I experienced that CU + + align:start position:0% +like in real time I experienced that CU + + + align:start position:0% +like in real time I experienced that CU +I took the computer science courses 61 + + align:start position:0% +I took the computer science courses 61 + + + align:start position:0% +I took the computer science courses 61 +and 62 and also what stood out for me + + align:start position:0% +and 62 and also what stood out for me + + + align:start position:0% +and 62 and also what stood out for me +was the time they recorded those was the + + align:start position:0% +was the time they recorded those was the + + + align:start position:0% +was the time they recorded those was the +time I was in university so it was like + + align:start position:0% +time I was in university so it was like + + + align:start position:0% +time I was in university so it was like +I was in + + align:start position:0% +I was in + + + align:start position:0% +I was in +learning some other things and these + + align:start position:0% +learning some other things and these + + + align:start position:0% +learning some other things and these +people are learning like these things + + align:start position:0% +people are learning like these things + + + align:start position:0% +people are learning like these things +like we on the same timeline if I'm + + align:start position:0% +like we on the same timeline if I'm + + + align:start position:0% +like we on the same timeline if I'm +remember to meet those people in the + + align:start position:0% +remember to meet those people in the + + + align:start position:0% +remember to meet those people in the +class in the real world like oh we're in + + align:start position:0% +class in the real world like oh we're in + + + align:start position:0% +class in the real world like oh we're in +University at the same time but it felt + + align:start position:0% +University at the same time but it felt + + + align:start position:0% +University at the same time but it felt +like we're learning like two different + + align:start position:0% +like we're learning like two different + + + align:start position:0% +like we're learning like two different +things yes you're both learning computer + + align:start position:0% +things yes you're both learning computer + + + align:start position:0% +things yes you're both learning computer +science related things but it's like a + + align:start position:0% +science related things but it's like a + + + align:start position:0% +science related things but it's like a +different difference so I understand you + + align:start position:0% +different difference so I understand you + + + align:start position:0% +different difference so I understand you +on that you mentioned something about + + align:start position:0% +on that you mentioned something about + + + align:start position:0% +on that you mentioned something about +you know the need to find people moving + + align:start position:0% +you know the need to find people moving + + + align:start position:0% +you know the need to find people moving +the US and finding + + align:start position:0% +the US and finding + + + align:start position:0% +the US and finding +ocw was the impact more in like you and + + align:start position:0% +ocw was the impact more in like you and + + + align:start position:0% +ocw was the impact more in like you and +yourself and identity as a person when + + align:start position:0% +yourself and identity as a person when + + + align:start position:0% +yourself and identity as a person when +you start taking ocw you mention you've + + align:start position:0% +you start taking ocw you mention you've + + + align:start position:0% +you start taking ocw you mention you've +taken Finance Theory thermodynamics how + + align:start position:0% +taken Finance Theory thermodynamics how + + + align:start position:0% +taken Finance Theory thermodynamics how +was the impact in your evolving identity + + align:start position:0% +was the impact in your evolving identity + + + align:start position:0% +was the impact in your evolving identity +how did you start to see yourself as a + + align:start position:0% +how did you start to see yourself as a + + + align:start position:0% +how did you start to see yourself as a +person who now has all this knowledge + + align:start position:0% +person who now has all this knowledge + + + align:start position:0% +person who now has all this knowledge +did it have any real life applications + + align:start position:0% +did it have any real life applications + + + align:start position:0% +did it have any real life applications +or any real life effects or impact when + + align:start position:0% +or any real life effects or impact when + + + align:start position:0% +or any real life effects or impact when +you studying these + + align:start position:0% +you studying these + + + align:start position:0% +you studying these +things maybe you could shed some light + + align:start position:0% +things maybe you could shed some light + + + align:start position:0% +things maybe you could shed some light +on that yeah that's such an excellent + + align:start position:0% +on that yeah that's such an excellent + + + align:start position:0% +on that yeah that's such an excellent +question because I genuinely feel that + + align:start position:0% +question because I genuinely feel that + + + align:start position:0% +question because I genuinely feel that +I'm more like an + + align:start position:0% +I'm more like an + + + align:start position:0% +I'm more like an +Explorer I'm never satisfied with just + + align:start position:0% +Explorer I'm never satisfied with just + + + align:start position:0% +Explorer I'm never satisfied with just +like one path I have to just like look + + align:start position:0% +like one path I have to just like look + + + align:start position:0% +like one path I have to just like look +around and they okay like this is some + + align:start position:0% +around and they okay like this is some + + + align:start position:0% +around and they okay like this is some +this is something else which I can + + align:start position:0% +this is something else which I can + + + align:start position:0% +this is something else which I can +integrate with this past or this might + + align:start position:0% +integrate with this past or this might + + + align:start position:0% +integrate with this past or this might +be some other Branch from this past with + + align:start position:0% +be some other Branch from this past with + + + align:start position:0% +be some other Branch from this past with +which I'm trotting upon while I was + + align:start position:0% +which I'm trotting upon while I was + + + align:start position:0% +which I'm trotting upon while I was +listening to your question I actually + + align:start position:0% +listening to your question I actually + + + align:start position:0% +listening to your question I actually +had something that I wanted to ask you + + align:start position:0% +had something that I wanted to ask you + + + align:start position:0% +had something that I wanted to ask you +Emanual if that's right you said that + + align:start position:0% +Emanual if that's right you said that + + + align:start position:0% +Emanual if that's right you said that +you were taking the ocw courses while + + align:start position:0% +you were taking the ocw courses while + + + align:start position:0% +you were taking the ocw courses while +you were at University am I correct no I + + align:start position:0% +you were at University am I correct no I + + + align:start position:0% +you were at University am I correct no I +I took + + align:start position:0% +I took + + + align:start position:0% +I took +them I took them in 2020 + + align:start position:0% +them I took them in 2020 + + + align:start position:0% +them I took them in 2020 +2021 but the courses were recorded in + + align:start position:0% +2021 but the courses were recorded in + + + align:start position:0% +2021 but the courses were recorded in +2020 is it 2013 2011 2013 and that was + + align:start position:0% +2020 is it 2013 2011 2013 and that was + + + align:start position:0% +2020 is it 2013 2011 2013 and that was +the time I was in university so they + + align:start position:0% +the time I was in university so they + + + align:start position:0% +the time I was in university so they +recorded their courses while I was also + + align:start position:0% +recorded their courses while I was also + + + align:start position:0% +recorded their courses while I was also +in University I watched them like way + + align:start position:0% +in University I watched them like way + + + align:start position:0% +in University I watched them like way +later right that's so cool so I was + + align:start position:0% +later right that's so cool so I was + + + align:start position:0% +later right that's so cool so I was +wondering what your major was and like + + align:start position:0% +wondering what your major was and like + + + align:start position:0% +wondering what your major was and like +what your favorite course of ocw was and + + align:start position:0% +what your favorite course of ocw was and + + + align:start position:0% +what your favorite course of ocw was and +like how you came came across ocw like + + align:start position:0% +like how you came came across ocw like + + + align:start position:0% +like how you came came across ocw like +basically like your story too I was + + align:start position:0% +basically like your story too I was + + + align:start position:0% +basically like your story too I was +actually about to ask you the same + + align:start position:0% +actually about to ask you the same + + + align:start position:0% +actually about to ask you the same +question about how you came across ocw + + align:start position:0% +question about how you came across ocw + + + align:start position:0% +question about how you came across ocw +so I like this um my major was also + + align:start position:0% +so I like this um my major was also + + + align:start position:0% +so I like this um my major was also +actually in computer science but + + align:start position:0% +actually in computer science but + + + align:start position:0% +actually in computer science but +Information Systems it was a new course + + align:start position:0% +Information Systems it was a new course + + + align:start position:0% +Information Systems it was a new course +in the country I think they only did + + align:start position:0% +in the country I think they only did + + + align:start position:0% +in the country I think they only did +like three years of it then they + + align:start position:0% +like three years of it then they + + + align:start position:0% +like three years of it then they +absorbed it back into the information + + align:start position:0% +absorbed it back into the information + + + align:start position:0% +absorbed it back into the information +technology course so I've been in this + + align:start position:0% +technology course so I've been in this + + + align:start position:0% +technology course so I've been in this +computer science world for a while + + align:start position:0% +computer science world for a while + + + align:start position:0% +computer science world for a while +started out front end didn't like it I + + align:start position:0% +started out front end didn't like it I + + + align:start position:0% +started out front end didn't like it I +went to more graphics design so I + + align:start position:0% +went to more graphics design so I + + + align:start position:0% +went to more graphics design so I +discovered ocw in lockdown when I wanted + + align:start position:0% +discovered ocw in lockdown when I wanted + + + align:start position:0% +discovered ocw in lockdown when I wanted +now to learn backend I went to Dubai and + + align:start position:0% +now to learn backend I went to Dubai and + + + align:start position:0% +now to learn backend I went to Dubai and +saw they had a World Expo so most of the + + align:start position:0% +saw they had a World Expo so most of the + + + align:start position:0% +saw they had a World Expo so most of the +Pavilions most of the countries were + + align:start position:0% +Pavilions most of the countries were + + + align:start position:0% +Pavilions most of the countries were +showcasing things to do with ai ai so I + + align:start position:0% +showcasing things to do with ai ai so I + + + align:start position:0% +showcasing things to do with ai ai so I +was I realized this is the future it's + + align:start position:0% +was I realized this is the future it's + + + align:start position:0% +was I realized this is the future it's +coming this was like in 2020 so when I + + align:start position:0% +coming this was like in 2020 so when I + + + align:start position:0% +coming this was like in 2020 so when I +came back home I wanted to look up you + + align:start position:0% +came back home I wanted to look up you + + + align:start position:0% +came back home I wanted to look up you +know to learn more about a I get into + + align:start position:0% +know to learn more about a I get into + + + align:start position:0% +know to learn more about a I get into +the backend and that's how I came across + + align:start position:0% +the backend and that's how I came across + + + align:start position:0% +the backend and that's how I came across +ocw + + align:start position:0% +ocw + + + align:start position:0% +ocw +actually how did you come across W I was + + align:start position:0% +actually how did you come across W I was + + + align:start position:0% +actually how did you come across W I was +on YouTube actually cuz I've been doing + + align:start position:0% +on YouTube actually cuz I've been doing + + + align:start position:0% +on YouTube actually cuz I've been doing +a lot of YouTube learning for like 10 + + align:start position:0% +a lot of YouTube learning for like 10 + + + align:start position:0% +a lot of YouTube learning for like 10 +years now yeah um so my first + + align:start position:0% +years now yeah um so my first + + + align:start position:0% +years now yeah um so my first +convergence with ocw was through that + + align:start position:0% +convergence with ocw was through that + + + align:start position:0% +convergence with ocw was through that +course that I talked about the + + align:start position:0% +course that I talked about the + + + align:start position:0% +course that I talked about the +thermodynamics and kinetics course I was + + align:start position:0% +thermodynamics and kinetics course I was + + + align:start position:0% +thermodynamics and kinetics course I was +just trying to search up what video + + align:start position:0% +just trying to search up what video + + + align:start position:0% +just trying to search up what video +lectures I was seeking for lectures not + + align:start position:0% +lectures I was seeking for lectures not + + + align:start position:0% +lectures I was seeking for lectures not +like 10 minutes explanation video I did + + align:start position:0% +like 10 minutes explanation video I did + + + align:start position:0% +like 10 minutes explanation video I did +not want that although condensed + + align:start position:0% +not want that although condensed + + + align:start position:0% +not want that although condensed +explanation on summary videos they help + + align:start position:0% +explanation on summary videos they help + + + align:start position:0% +explanation on summary videos they help +but when you're actually trying to ro + + align:start position:0% +but when you're actually trying to ro + + + align:start position:0% +but when you're actually trying to ro +really understand and absorb the + + align:start position:0% +really understand and absorb the + + + align:start position:0% +really understand and absorb the +material and topic or um studies which + + align:start position:0% +material and topic or um studies which + + + align:start position:0% +material and topic or um studies which +you're interested in 10 minutes can + + align:start position:0% +you're interested in 10 minutes can + + + align:start position:0% +you're interested in 10 minutes can +never satisfy you and it never answers + + align:start position:0% +never satisfy you and it never answers + + + align:start position:0% +never satisfy you and it never answers +your question you often have to do + + align:start position:0% +your question you often have to do + + + align:start position:0% +your question you often have to do +additional yeah searching and then you + + align:start position:0% +additional yeah searching and then you + + + align:start position:0% +additional yeah searching and then you +actually have to do okay which textbook + + align:start position:0% +actually have to do okay which textbook + + + align:start position:0% +actually have to do okay which textbook +or like materials are they basing their + + align:start position:0% +or like materials are they basing their + + + align:start position:0% +or like materials are they basing their +argument upon like I'm sort of like this + + align:start position:0% +argument upon like I'm sort of like this + + + align:start position:0% +argument upon like I'm sort of like this +fact Checker and so if I watch a video I + + align:start position:0% +fact Checker and so if I watch a video I + + + align:start position:0% +fact Checker and so if I watch a video I +first of all check the profile of that + + align:start position:0% +first of all check the profile of that + + + align:start position:0% +first of all check the profile of that +person who's explaining okay this this + + align:start position:0% +person who's explaining okay this this + + + align:start position:0% +person who's explaining okay this this +is this person that qualified to teach + + align:start position:0% +is this person that qualified to teach + + + align:start position:0% +is this person that qualified to teach +me this and so you never you never ask + + align:start position:0% +me this and so you never you never ask + + + align:start position:0% +me this and so you never you never ask +those questions when it comes to MIT + + align:start position:0% +those questions when it comes to MIT + + + align:start position:0% +those questions when it comes to MIT +course materials and so yeah so it + + align:start position:0% +course materials and so yeah so it + + + align:start position:0% +course materials and so yeah so it +ticked off every box on my + + align:start position:0% + + + + align:start position:0% + +checklist I'm kind of interested in the + + align:start position:0% +checklist I'm kind of interested in the + + + align:start position:0% +checklist I'm kind of interested in the +impact it had you know in your life + + align:start position:0% +impact it had you know in your life + + + align:start position:0% +impact it had you know in your life +outside of your academic studies what do + + align:start position:0% +outside of your academic studies what do + + + align:start position:0% +outside of your academic studies what do +your friends think do you share with + + align:start position:0% +your friends think do you share with + + + align:start position:0% +your friends think do you share with +your friends this open course where + + align:start position:0% +your friends this open course where + + + align:start position:0% +your friends this open course where +Journey what did your family think and + + align:start position:0% +Journey what did your family think and + + + align:start position:0% +Journey what did your family think and +you know did it Ripple into your + + align:start position:0% +you know did it Ripple into your + + + align:start position:0% +you know did it Ripple into your +community as well or yeah I think I + + align:start position:0% +community as well or yeah I think I + + + align:start position:0% +community as well or yeah I think I +would have actively shared these + + align:start position:0% +would have actively shared these + + + align:start position:0% +would have actively shared these +materials MIT ocw materials with my + + align:start position:0% +materials MIT ocw materials with my + + + align:start position:0% +materials MIT ocw materials with my +friends um if they spoke + + align:start position:0% +friends um if they spoke + + + align:start position:0% +friends um if they spoke +English but yeah I + + align:start position:0% +English but yeah I + + + align:start position:0% +English but yeah I +think yeah I do have um friends who are + + align:start position:0% +think yeah I do have um friends who are + + + align:start position:0% +think yeah I do have um friends who are +living in America and they are Americans + + align:start position:0% +living in America and they are Americans + + + align:start position:0% +living in America and they are Americans +cuz you've lived in like several + + align:start position:0% +cuz you've lived in like several + + + align:start position:0% +cuz you've lived in like several +countries how was that yeah definitely + + align:start position:0% +countries how was that yeah definitely + + + align:start position:0% +countries how was that yeah definitely +um my lifestyle has been quite + + align:start position:0% +um my lifestyle has been quite + + + align:start position:0% +um my lifestyle has been quite +paretic I've basically been being like a + + align:start position:0% +paretic I've basically been being like a + + + align:start position:0% +paretic I've basically been being like a +nomad my mom is an English teacher half + + align:start position:0% +nomad my mom is an English teacher half + + + align:start position:0% +nomad my mom is an English teacher half +of my mom's family so my aunties and my + + align:start position:0% +of my mom's family so my aunties and my + + + align:start position:0% +of my mom's family so my aunties and my +uncles they all live in America and yeah + + align:start position:0% +uncles they all live in America and yeah + + + align:start position:0% +uncles they all live in America and yeah +we've got quite mixed family backgrounds + + align:start position:0% +we've got quite mixed family backgrounds + + + align:start position:0% +we've got quite mixed family backgrounds +happening on my mom's side my dad's + + align:start position:0% +happening on my mom's side my dad's + + + align:start position:0% +happening on my mom's side my dad's +side's very much yeah rooted in Korea so + + align:start position:0% +side's very much yeah rooted in Korea so + + + align:start position:0% +side's very much yeah rooted in Korea so +it's quite an interesting um family and + + align:start position:0% +it's quite an interesting um family and + + + align:start position:0% +it's quite an interesting um family and +cultural Dynamic so then this sort of + + align:start position:0% +cultural Dynamic so then this sort of + + + align:start position:0% +cultural Dynamic so then this sort of +epiphany did not really click through + + align:start position:0% +epiphany did not really click through + + + align:start position:0% +epiphany did not really click through +until I entered middle school so when I + + align:start position:0% +until I entered middle school so when I + + + align:start position:0% +until I entered middle school so when I +became School junior I realized that I + + align:start position:0% +became School junior I realized that I + + + align:start position:0% +became School junior I realized that I +just did not want to stick with this + + align:start position:0% +just did not want to stick with this + + + align:start position:0% +just did not want to stick with this +very regimented school system that is + + align:start position:0% +very regimented school system that is + + + align:start position:0% +very regimented school system that is +very much prominent in Korea so my + + align:start position:0% +very much prominent in Korea so my + + + align:start position:0% +very much prominent in Korea so my +parents also shared the same view they + + align:start position:0% +parents also shared the same view they + + + align:start position:0% +parents also shared the same view they +wanted me to explore the wider pool um + + align:start position:0% +wanted me to explore the wider pool um + + + align:start position:0% +wanted me to explore the wider pool um +overseas they so I moved to New Zealand + + align:start position:0% +overseas they so I moved to New Zealand + + + align:start position:0% +overseas they so I moved to New Zealand +when I was 14 and I had no one there I + + align:start position:0% +when I was 14 and I had no one there I + + + align:start position:0% +when I was 14 and I had no one there I +had no family relations so spent my + + align:start position:0% +had no family relations so spent my + + + align:start position:0% +had no family relations so spent my +Junior and senior years there so middle + + align:start position:0% +Junior and senior years there so middle + + + align:start position:0% +Junior and senior years there so middle +school high school and then I was going + + align:start position:0% +school high school and then I was going + + + align:start position:0% +school high school and then I was going +to take my tertiary ation in London + + align:start position:0% +to take my tertiary ation in London + + + align:start position:0% +to take my tertiary ation in London +there's a universal University College + + align:start position:0% +there's a universal University College + + + align:start position:0% +there's a universal University College +London I was going to study economics + + align:start position:0% +London I was going to study economics + + + align:start position:0% +London I was going to study economics +there but then that was also the year + + align:start position:0% +there but then that was also the year + + + align:start position:0% +there but then that was also the year +when covid broke out and I couldn't pay + + align:start position:0% +when covid broke out and I couldn't pay + + + align:start position:0% +when covid broke out and I couldn't pay +like a million dollars + + align:start position:0% +like a million dollars + + + align:start position:0% +like a million dollars +for for for this education which I had + + align:start position:0% +for for for this education which I had + + + align:start position:0% +for for for this education which I had +no real access to and so I quickly + + align:start position:0% +no real access to and so I quickly + + + align:start position:0% +no real access to and so I quickly +changed my plan came back to Korea but I + + align:start position:0% +changed my plan came back to Korea but I + + + align:start position:0% +changed my plan came back to Korea but I +always had this yearning for broader + + align:start position:0% +always had this yearning for broader + + + align:start position:0% +always had this yearning for broader +learning something else that I can do + + align:start position:0% +learning something else that I can do + + + align:start position:0% +learning something else that I can do +okay like I'm working on this but what + + align:start position:0% +okay like I'm working on this but what + + + align:start position:0% +okay like I'm working on this but what +else can I do more + + align:start position:0% +else can I do more + + + align:start position:0% +else can I do more +amazing you moved to New Zealand at 14 + + align:start position:0% +amazing you moved to New Zealand at 14 + + + align:start position:0% +amazing you moved to New Zealand at 14 +when you knew no one that's + + align:start position:0% +when you knew no one that's + + + align:start position:0% +when you knew no one that's +courageous on the same point we can + + align:start position:0% +courageous on the same point we can + + + align:start position:0% +courageous on the same point we can +highlight how was the difference in + + align:start position:0% +highlight how was the difference in + + + align:start position:0% +highlight how was the difference in +traditional learnings I going to call + + align:start position:0% +traditional learnings I going to call + + + align:start position:0% +traditional learnings I going to call +them several CU you've taken classes + + align:start position:0% +them several CU you've taken classes + + + align:start position:0% +them several CU you've taken classes +from different countries how was the + + align:start position:0% +from different countries how was the + + + align:start position:0% +from different countries how was the +difference in those places traditional + + align:start position:0% +difference in those places traditional + + + align:start position:0% +difference in those places traditional +learnings versus open + + align:start position:0% +learnings versus open + + + align:start position:0% +learnings versus open +learning I'd say that they're both + + align:start position:0% +learning I'd say that they're both + + + align:start position:0% +learning I'd say that they're both +strengths and sometimes a bit weaknesses + + align:start position:0% +strengths and sometimes a bit weaknesses + + + align:start position:0% +strengths and sometimes a bit weaknesses +so strengths when it comes to + + align:start position:0% +so strengths when it comes to + + + align:start position:0% +so strengths when it comes to +Conventional education the main strength + + align:start position:0% +Conventional education the main strength + + + align:start position:0% +Conventional education the main strength +I would say is that you're able to + + align:start position:0% +I would say is that you're able to + + + align:start position:0% +I would say is that you're able to +directly interact with professors and + + align:start position:0% +directly interact with professors and + + + align:start position:0% +directly interact with professors and +ask questions to Tas if you have them + + align:start position:0% +ask questions to Tas if you have them + + + align:start position:0% +ask questions to Tas if you have them +when it comes to open learning although + + align:start position:0% +when it comes to open learning although + + + align:start position:0% +when it comes to open learning although +you're able to really search out for + + align:start position:0% +you're able to really search out for + + + align:start position:0% +you're able to really search out for +information and dig out those extra + + align:start position:0% +information and dig out those extra + + + align:start position:0% +information and dig out those extra +learning materials that you wanted for + + align:start position:0% +learning materials that you wanted for + + + align:start position:0% +learning materials that you wanted for +yourself um let's say you've got your + + align:start position:0% +yourself um let's say you've got your + + + align:start position:0% +yourself um let's say you've got your +answer sheet and then the quiz materials + + align:start position:0% +answer sheet and then the quiz materials + + + align:start position:0% +answer sheet and then the quiz materials +the quiz um question sheet you're able + + align:start position:0% +the quiz um question sheet you're able + + + align:start position:0% +the quiz um question sheet you're able +to check that you've got this question + + align:start position:0% +to check that you've got this question + + + align:start position:0% +to check that you've got this question +wrong but sometimes when you trip over + + align:start position:0% +wrong but sometimes when you trip over + + + align:start position:0% +wrong but sometimes when you trip over +to this question and not able to really + + align:start position:0% +to this question and not able to really + + + align:start position:0% +to this question and not able to really +figure out what's like why I have gotten + + align:start position:0% +figure out what's like why I have gotten + + + align:start position:0% +figure out what's like why I have gotten +this question wrong I I needed some + + align:start position:0% +this question wrong I I needed some + + + align:start position:0% +this question wrong I I needed some +external help and so I would be asking + + align:start position:0% +external help and so I would be asking + + + align:start position:0% +external help and so I would be asking +my friends whose major is chemistry and + + align:start position:0% +my friends whose major is chemistry and + + + align:start position:0% +my friends whose major is chemistry and +then they would help me um in in that + + align:start position:0% +then they would help me um in in that + + + align:start position:0% +then they would help me um in in that +but then there's sort of like this Cross + + align:start position:0% +but then there's sort of like this Cross + + + align:start position:0% +but then there's sort of like this Cross +transation of what I am learning here + + align:start position:0% +transation of what I am learning here + + + align:start position:0% +transation of what I am learning here +and then they are trying to figure out + + align:start position:0% +and then they are trying to figure out + + + align:start position:0% +and then they are trying to figure out +put their fingers on what what is this + + align:start position:0% +put their fingers on what what is this + + + align:start position:0% +put their fingers on what what is this +context like why are you doing this and + + align:start position:0% +context like why are you doing this and + + + align:start position:0% +context like why are you doing this and +then I often find myself having to + + align:start position:0% +then I often find myself having to + + + align:start position:0% +then I often find myself having to +explain oh I'm actually an economics + + align:start position:0% +explain oh I'm actually an economics + + + align:start position:0% +explain oh I'm actually an economics +student just interested in chemist CH + + align:start position:0% +student just interested in chemist CH + + + align:start position:0% +student just interested in chemist CH +istry and so like learning about this + + align:start position:0% +istry and so like learning about this + + + align:start position:0% +istry and so like learning about this +and then they are trying to diagnose my + + align:start position:0% +and then they are trying to diagnose my + + + align:start position:0% +and then they are trying to diagnose my +prior knowledge in chemistry and then + + align:start position:0% +prior knowledge in chemistry and then + + + align:start position:0% +prior knowledge in chemistry and then +they realize that okay you should + + align:start position:0% +they realize that okay you should + + + align:start position:0% +they realize that okay you should +probably like start with this and this + + align:start position:0% +probably like start with this and this + + + align:start position:0% +probably like start with this and this +and this and so sort of like that + + align:start position:0% +and this and so sort of like that + + + align:start position:0% +and this and so sort of like that +structured guidance it might become a + + align:start position:0% +structured guidance it might become a + + + align:start position:0% +structured guidance it might become a +sort of impediment in some way um when + + align:start position:0% +sort of impediment in some way um when + + + align:start position:0% +sort of impediment in some way um when +it comes to Conventional traditional + + align:start position:0% +it comes to Conventional traditional + + + align:start position:0% +it comes to Conventional traditional +education system but it also works + + align:start position:0% +education system but it also works + + + align:start position:0% +education system but it also works +enormously well for students who aren't + + align:start position:0% +enormously well for students who aren't + + + align:start position:0% +enormously well for students who aren't +quite sure like where they're lost in + + align:start position:0% +quite sure like where they're lost in + + + align:start position:0% +quite sure like where they're lost in +but um but also at the same time um as + + align:start position:0% +but um but also at the same time um as + + + align:start position:0% +but um but also at the same time um as +I've mentioned the flexibility comes in + + align:start position:0% +I've mentioned the flexibility comes in + + + align:start position:0% +I've mentioned the flexibility comes in +just just very very encouraging and it's + + align:start position:0% +just just very very encouraging and it's + + + align:start position:0% +just just very very encouraging and it's +it's it's highly invigorating if you're + + align:start position:0% +it's it's highly invigorating if you're + + + align:start position:0% +it's it's highly invigorating if you're +if you feel if you derive satisfaction + + align:start position:0% +if you feel if you derive satisfaction + + + align:start position:0% +if you feel if you derive satisfaction +from taking on the initiative and then + + align:start position:0% +from taking on the initiative and then + + + align:start position:0% +from taking on the initiative and then +actually executing those initiatives if + + align:start position:0% +actually executing those initiatives if + + + align:start position:0% +actually executing those initiatives if +you're like very action taker like me so + + align:start position:0% +you're like very action taker like me so + + + align:start position:0% +you're like very action taker like me so +I just did not want to form a plan okay + + align:start position:0% +I just did not want to form a plan okay + + + align:start position:0% +I just did not want to form a plan okay +I want to learn more about chemistry but + + align:start position:0% +I want to learn more about chemistry but + + + align:start position:0% +I want to learn more about chemistry but +then I'll just put that aside for a week + + align:start position:0% +then I'll just put that aside for a week + + + align:start position:0% +then I'll just put that aside for a week +or so but then if you actually want to + + align:start position:0% +or so but then if you actually want to + + + align:start position:0% +or so but then if you actually want to +get down to it immediately and then seek + + align:start position:0% +get down to it immediately and then seek + + + align:start position:0% +get down to it immediately and then seek +out an all available resource which you + + align:start position:0% +out an all available resource which you + + + align:start position:0% +out an all available resource which you +can learn more about than like ocw is + + align:start position:0% +can learn more about than like ocw is + + + align:start position:0% +can learn more about than like ocw is +definitely a cutout like + + align:start position:0% +definitely a cutout like + + + align:start position:0% +definitely a cutout like +prototype you talk about self-learning + + align:start position:0% +prototype you talk about self-learning + + + align:start position:0% +prototype you talk about self-learning +you know a lot of people think of + + align:start position:0% +you know a lot of people think of + + + align:start position:0% +you know a lot of people think of +self-learning as you know running a + + align:start position:0% +self-learning as you know running a + + + align:start position:0% +self-learning as you know running a +marathon like they think it's the same + + align:start position:0% +marathon like they think it's the same + + + align:start position:0% +marathon like they think it's the same +thing right like that's just this + + align:start position:0% +thing right like that's just this + + + align:start position:0% +thing right like that's just this +impossible task but but oddly enough you + + align:start position:0% +impossible task but but oddly enough you + + + align:start position:0% +impossible task but but oddly enough you +know you you talk about it and you're + + align:start position:0% +know you you talk about it and you're + + + align:start position:0% +know you you talk about it and you're +like I'm invigorated I'm inspired to do + + align:start position:0% +like I'm invigorated I'm inspired to do + + + align:start position:0% +like I'm invigorated I'm inspired to do +more I I think bigger you know what are + + align:start position:0% +more I I think bigger you know what are + + + align:start position:0% +more I I think bigger you know what are +some ways maybe even now like entering + + align:start position:0% +some ways maybe even now like entering + + + align:start position:0% +some ways maybe even now like entering +your last last year of University what + + align:start position:0% +your last last year of University what + + + align:start position:0% +your last last year of University what +are you thinking about like what does + + align:start position:0% +are you thinking about like what does + + + align:start position:0% +are you thinking about like what does +your Mor look like now I think this goes + + align:start position:0% +your Mor look like now I think this goes + + + align:start position:0% +your Mor look like now I think this goes +back to the cultural background so sort + + align:start position:0% +back to the cultural background so sort + + + align:start position:0% +back to the cultural background so sort +of like the sort of Mantra that I grew + + align:start position:0% +of like the sort of Mantra that I grew + + + align:start position:0% +of like the sort of Mantra that I grew +up with so you mentioned that I try to + + align:start position:0% +up with so you mentioned that I try to + + + align:start position:0% +up with so you mentioned that I try to +think bigger and like expand what I have + + align:start position:0% +think bigger and like expand what I have + + + align:start position:0% +think bigger and like expand what I have +right now and I think that comes from my + + align:start position:0% +right now and I think that comes from my + + + align:start position:0% +right now and I think that comes from my +background where I was constantly + + align:start position:0% +background where I was constantly + + + align:start position:0% +background where I was constantly +shuffling between America um Korea and + + align:start position:0% +shuffling between America um Korea and + + + align:start position:0% +shuffling between America um Korea and +then New Zealand and because I know that + + align:start position:0% +then New Zealand and because I know that + + + align:start position:0% +then New Zealand and because I know that +your degree was poetry and my favorite + + align:start position:0% +your degree was poetry and my favorite + + + align:start position:0% +your degree was poetry and my favorite +poet was Emily Dickinson she wrote this + + align:start position:0% +poet was Emily Dickinson she wrote this + + + align:start position:0% +poet was Emily Dickinson she wrote this +um really famous verse called I'm like a + + align:start position:0% +um really famous verse called I'm like a + + + align:start position:0% +um really famous verse called I'm like a +flower that cannot take its roots + + align:start position:0% +flower that cannot take its roots + + + align:start position:0% +flower that cannot take its roots +anywhere and that was the sort of thing + + align:start position:0% +anywhere and that was the sort of thing + + + align:start position:0% +anywhere and that was the sort of thing +that I was feeling for myself but I + + align:start position:0% +that I was feeling for myself but I + + + align:start position:0% +that I was feeling for myself but I +tried to translate that into my own + + align:start position:0% +tried to translate that into my own + + + align:start position:0% +tried to translate that into my own +Advantage I attend y University but I + + align:start position:0% +Advantage I attend y University but I + + + align:start position:0% +Advantage I attend y University but I +don't always follow the crowd I always + + align:start position:0% +don't always follow the crowd I always + + + align:start position:0% +don't always follow the crowd I always +think about what can I do differently so + + align:start position:0% +think about what can I do differently so + + + align:start position:0% +think about what can I do differently so +actually like I'm trying to enter + + align:start position:0% +actually like I'm trying to enter + + + align:start position:0% +actually like I'm trying to enter +Investment Banking right now and then + + align:start position:0% +Investment Banking right now and then + + + align:start position:0% +Investment Banking right now and then +there is a group of University clubs and + + align:start position:0% +there is a group of University clubs and + + + align:start position:0% +there is a group of University clubs and +societies where they are working + + align:start position:0% +societies where they are working + + + align:start position:0% +societies where they are working +Investment Banking entry roles by doing + + align:start position:0% +Investment Banking entry roles by doing + + + align:start position:0% +Investment Banking entry roles by doing +case studies together and then getting + + align:start position:0% +case studies together and then getting + + + align:start position:0% +case studies together and then getting +feedback with the ultimate goal being + + align:start position:0% +feedback with the ultimate goal being + + + align:start position:0% +feedback with the ultimate goal being +trying to get a place at an investment + + align:start position:0% +trying to get a place at an investment + + + align:start position:0% +trying to get a place at an investment +Bank in Korea but then when I look at + + align:start position:0% +Bank in Korea but then when I look at + + + align:start position:0% +Bank in Korea but then when I look at +them like they all qualified to apply + + align:start position:0% +them like they all qualified to apply + + + align:start position:0% +them like they all qualified to apply +for a role in like basically like Wall + + align:start position:0% +for a role in like basically like Wall + + + align:start position:0% +for a role in like basically like Wall +Street they're so talented but then they + + align:start position:0% +Street they're so talented but then they + + + align:start position:0% +Street they're so talented but then they +never sort of think outsides their + + align:start position:0% +never sort of think outsides their + + + align:start position:0% +never sort of think outsides their +institution and then think okay if I if + + align:start position:0% +institution and then think okay if I if + + + align:start position:0% +institution and then think okay if I if +I sort of Leverage this resource let's + + align:start position:0% +I sort of Leverage this resource let's + + + align:start position:0% +I sort of Leverage this resource let's +say this external resource communities + + align:start position:0% +say this external resource communities + + + align:start position:0% +say this external resource communities +like 100 women in finance I'll be able + + align:start position:0% +like 100 women in finance I'll be able + + + align:start position:0% +like 100 women in finance I'll be able +to probably reach out to different + + align:start position:0% +to probably reach out to different + + + align:start position:0% +to probably reach out to different +people and then um put my paws on that + + align:start position:0% +people and then um put my paws on that + + + align:start position:0% +people and then um put my paws on that +opportunity as well and so just sort of + + align:start position:0% +opportunity as well and so just sort of + + + align:start position:0% +opportunity as well and so just sort of +like reaching out for different + + align:start position:0% +like reaching out for different + + + align:start position:0% +like reaching out for different +opportunities and seeing what I can do + + align:start position:0% +opportunities and seeing what I can do + + + align:start position:0% +opportunities and seeing what I can do +differently is basically something that + + align:start position:0% +differently is basically something that + + + align:start position:0% +differently is basically something that +shapes me and has been this sort of + + align:start position:0% +shapes me and has been this sort of + + + align:start position:0% +shapes me and has been this sort of +identified of me and ocw is definitely + + align:start position:0% +identified of me and ocw is definitely + + + align:start position:0% +identified of me and ocw is definitely +something which I would identify as like + + align:start position:0% +something which I would identify as like + + + align:start position:0% +something which I would identify as like +an extra work which I had taken for + + align:start position:0% +an extra work which I had taken for + + + align:start position:0% +an extra work which I had taken for +myself because I want to think + + align:start position:0% +myself because I want to think + + + align:start position:0% +myself because I want to think +differently I always sort of had this + + align:start position:0% +differently I always sort of had this + + + align:start position:0% +differently I always sort of had this +repulsion against group thing repulsion + + align:start position:0% +repulsion against group thing repulsion + + + align:start position:0% +repulsion against group thing repulsion +is a very quite strong word so I'll just + + align:start position:0% +is a very quite strong word so I'll just + + + align:start position:0% +is a very quite strong word so I'll just +say very very cautious probably because + + align:start position:0% +say very very cautious probably because + + + align:start position:0% +say very very cautious probably because +I follow the market every day and I + + align:start position:0% +I follow the market every day and I + + + align:start position:0% +I follow the market every day and I +tried to very very cautious about this + + align:start position:0% +tried to very very cautious about this + + + align:start position:0% +tried to very very cautious about this +group think how can I think logically + + align:start position:0% +group think how can I think logically + + + align:start position:0% +group think how can I think logically +it's very very long response sorry like + + align:start position:0% +it's very very long response sorry like + + + align:start position:0% +it's very very long response sorry like +yeah it was a big question it was you + + align:start position:0% +yeah it was a big question it was you + + + align:start position:0% +yeah it was a big question it was you +know you could go anywhere with it um + + align:start position:0% +know you could go anywhere with it um + + + align:start position:0% +know you could go anywhere with it um +the director of MIT open course where + + align:start position:0% +the director of MIT open course where + + + align:start position:0% +the director of MIT open course where +Curt Newton this is a question from him + + align:start position:0% +Curt Newton this is a question from him + + + align:start position:0% +Curt Newton this is a question from him +you know when you think about the impact + + align:start position:0% +you know when you think about the impact + + + align:start position:0% +you know when you think about the impact +of open educational resources that + + align:start position:0% +of open educational resources that + + + align:start position:0% +of open educational resources that +they've had on your life and people that + + align:start position:0% +they've had on your life and people that + + + align:start position:0% +they've had on your life and people that +you know when you look into the future + + align:start position:0% +you know when you look into the future + + + align:start position:0% +you know when you look into the future +with all the newly acquired knowledge + + align:start position:0% +with all the newly acquired knowledge + + + align:start position:0% +with all the newly acquired knowledge +you have is is there anything that if + + align:start position:0% +you have is is there anything that if + + + align:start position:0% +you have is is there anything that if +you had a magic wand that you would want + + align:start position:0% +you had a magic wand that you would want + + + align:start position:0% +you had a magic wand that you would want +for a free open educational resource + + align:start position:0% +for a free open educational resource + + + align:start position:0% +for a free open educational resource +available for the world can I be very + + align:start position:0% +available for the world can I be very + + + align:start position:0% +available for the world can I be very +very specific because I was I I'm in + + align:start position:0% +very specific because I was I I'm in + + + align:start position:0% +very specific because I was I I'm in +preparation for certain as I've said I'm + + align:start position:0% +preparation for certain as I've said I'm + + + align:start position:0% +preparation for certain as I've said I'm +preparing to become like um investment + + align:start position:0% +preparing to become like um investment + + + align:start position:0% +preparing to become like um investment +banker um um as like my um entry role in + + align:start position:0% +banker um um as like my um entry role in + + + align:start position:0% +banker um um as like my um entry role in +my career in my very early career stage + + align:start position:0% +my career in my very early career stage + + + align:start position:0% +my career in my very early career stage +and then I was trying to seek out for + + align:start position:0% +and then I was trying to seek out for + + + align:start position:0% +and then I was trying to seek out for +MIT ocw courses that are relate to this + + align:start position:0% +MIT ocw courses that are relate to this + + + align:start position:0% +MIT ocw courses that are relate to this +subject but I had somewhat difficulty + + align:start position:0% +subject but I had somewhat difficulty + + + align:start position:0% +subject but I had somewhat difficulty +finding it and the subject is + + align:start position:0% +finding it and the subject is + + + align:start position:0% +finding it and the subject is +accounting I realized that MCW um + + align:start position:0% +accounting I realized that MCW um + + + align:start position:0% +accounting I realized that MCW um +actually has phenomenal finance-based + + align:start position:0% +actually has phenomenal finance-based + + + align:start position:0% +actually has phenomenal finance-based +courses but then when it comes to + + align:start position:0% +courses but then when it comes to + + + align:start position:0% +courses but then when it comes to +accounting I had some difficulties + + align:start position:0% +accounting I had some difficulties + + + align:start position:0% +accounting I had some difficulties +trying to find related resources and so + + align:start position:0% +trying to find related resources and so + + + align:start position:0% +trying to find related resources and so +that is very very specific answer mean + + align:start position:0% +that is very very specific answer mean + + + align:start position:0% +that is very very specific answer mean +what happens when you finish all those + + align:start position:0% +what happens when you finish all those + + + align:start position:0% +what happens when you finish all those +accounting + + align:start position:0% +accounting + + + align:start position:0% +accounting +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +courses what's next what's next + + align:start position:0% +courses what's next what's next + + + align:start position:0% +courses what's next what's next +but you + + align:start position:0% +but you + + + align:start position:0% +but you +know every open learner we've talked to + + align:start position:0% +know every open learner we've talked to + + + align:start position:0% +know every open learner we've talked to +so far has said the same exact answer + + align:start position:0% +so far has said the same exact answer + + + align:start position:0% +so far has said the same exact answer +which is like more courses yeah it's + + align:start position:0% +which is like more courses yeah it's + + + align:start position:0% +which is like more courses yeah it's +it's kind of weird + + align:start position:0% +it's kind of weird + + + align:start position:0% +it's kind of weird +actually more courses maybe I'll ask you + + align:start position:0% +actually more courses maybe I'll ask you + + + align:start position:0% +actually more courses maybe I'll ask you +something extra because I'm seeing + + align:start position:0% +something extra because I'm seeing + + + align:start position:0% +something extra because I'm seeing +you've taken mainly accounting and + + align:start position:0% +you've taken mainly accounting and + + + align:start position:0% +you've taken mainly accounting and +economics and finance related coures + + align:start position:0% +economics and finance related coures + + + align:start position:0% +economics and finance related coures +have you taken anything outside like + + align:start position:0% +have you taken anything outside like + + + align:start position:0% +have you taken anything outside like +those fields anything outside accounting + + align:start position:0% +those fields anything outside accounting + + + align:start position:0% +those fields anything outside accounting +and economics on ocw um yeah that's + + align:start position:0% +and economics on ocw um yeah that's + + + align:start position:0% +and economics on ocw um yeah that's +that's another great question so the + + align:start position:0% +that's another great question so the + + + align:start position:0% +that's another great question so the +courses I sort of like dabbled in many + + align:start position:0% +courses I sort of like dabbled in many + + + align:start position:0% +courses I sort of like dabbled in many +different courses as in there were some + + align:start position:0% +different courses as in there were some + + + align:start position:0% +different courses as in there were some +courses which I did not watch to their + + align:start position:0% +courses which I did not watch to their + + + align:start position:0% +courses which I did not watch to their +full length but then there were some + + align:start position:0% +full length but then there were some + + + align:start position:0% +full length but then there were some +courses where I just sort of like + + align:start position:0% +courses where I just sort of like + + + align:start position:0% +courses where I just sort of like +watched one or two videos on the + + align:start position:0% +watched one or two videos on the + + + align:start position:0% +watched one or two videos on the +playlist and the reason being I was + + align:start position:0% +playlist and the reason being I was + + + align:start position:0% +playlist and the reason being I was +often finding myself in a quite + + align:start position:0% +often finding myself in a quite + + + align:start position:0% +often finding myself in a quite +difficult time management situation and + + align:start position:0% +difficult time management situation and + + + align:start position:0% +difficult time management situation and +so I was trying to maximize the + + align:start position:0% +so I was trying to maximize the + + + align:start position:0% +so I was trying to maximize the +efficiency of learning by watching the + + align:start position:0% +efficiency of learning by watching the + + + align:start position:0% +efficiency of learning by watching the +videos that are most relevant to the + + align:start position:0% +videos that are most relevant to the + + + align:start position:0% +videos that are most relevant to the +questions that I have inside my head or + + align:start position:0% +questions that I have inside my head or + + + align:start position:0% +questions that I have inside my head or +the difficulties that I'm facing at my + + align:start position:0% +the difficulties that I'm facing at my + + + align:start position:0% +the difficulties that I'm facing at my +like actual University the courses that + + align:start position:0% +like actual University the courses that + + + align:start position:0% +like actual University the courses that +I've taken so chemistry the thermod + + align:start position:0% +I've taken so chemistry the thermod + + + align:start position:0% +I've taken so chemistry the thermod +Dynamics and connectic one and I've also + + align:start position:0% +Dynamics and connectic one and I've also + + + align:start position:0% +Dynamics and connectic one and I've also +taken of course Professor Gilbert + + align:start position:0% +taken of course Professor Gilbert + + + align:start position:0% +taken of course Professor Gilbert +strang's linear algebra course which has + + align:start position:0% +strang's linear algebra course which has + + + align:start position:0% +strang's linear algebra course which has +come in very very handy when I was + + align:start position:0% +come in very very handy when I was + + + align:start position:0% +come in very very handy when I was +studying convolutional neural + + align:start position:0% +studying convolutional neural + + + align:start position:0% +studying convolutional neural +networks um I was I was going to say we + + align:start position:0% +networks um I was I was going to say we + + + align:start position:0% +networks um I was I was going to say we +need to come back to gilver + + align:start position:0% +need to come back to gilver + + + align:start position:0% +need to come back to gilver +strange yeah we deserve yeah a whole + + align:start position:0% +strange yeah we deserve yeah a whole + + + align:start position:0% +strange yeah we deserve yeah a whole +separate conversation like what a legend + + align:start position:0% +separate conversation like what a legend + + + align:start position:0% +separate conversation like what a legend +what brings you back to your career I + + align:start position:0% +what brings you back to your career I + + + align:start position:0% +what brings you back to your career I +know you're in University now like has + + align:start position:0% +know you're in University now like has + + + align:start position:0% +know you're in University now like has +this always been a drive for you or is + + align:start position:0% +this always been a drive for you or is + + + align:start position:0% +this always been a drive for you or is +it just in University you're feeling the + + align:start position:0% +it just in University you're feeling the + + + align:start position:0% +it just in University you're feeling the +pressure now that like I got to figure + + align:start position:0% +pressure now that like I got to figure + + + align:start position:0% +pressure now that like I got to figure +out what I'm going to do to make money + + align:start position:0% +out what I'm going to do to make money + + + align:start position:0% +out what I'm going to do to make money +you know after this or what what are you + + align:start position:0% +you know after this or what what are you + + + align:start position:0% +you know after this or what what are you +thinking very very + + align:start position:0% +thinking very very + + + align:start position:0% +thinking very very +realistically half and half of each so + + align:start position:0% +realistically half and half of each so + + + align:start position:0% +realistically half and half of each so +half being I generally enjoy learning + + align:start position:0% +half being I generally enjoy learning + + + align:start position:0% +half being I generally enjoy learning +and so there was absolutely no reason + + align:start position:0% +and so there was absolutely no reason + + + align:start position:0% +and so there was absolutely no reason +just no modom reason for me to take + + align:start position:0% +just no modom reason for me to take + + + align:start position:0% +just no modom reason for me to take +chemistry courses but I took it because + + align:start position:0% +chemistry courses but I took it because + + + align:start position:0% +chemistry courses but I took it because +I really enjoyed it chemistry learning + + align:start position:0% +I really enjoyed it chemistry learning + + + align:start position:0% +I really enjoyed it chemistry learning +chemistry really pushed forwards my + + align:start position:0% +chemistry really pushed forwards my + + + align:start position:0% +chemistry really pushed forwards my +drive to learn more and then expands my + + align:start position:0% +drive to learn more and then expands my + + + align:start position:0% +drive to learn more and then expands my +Horizon like you have rightly pointed + + align:start position:0% +Horizon like you have rightly pointed + + + align:start position:0% +Horizon like you have rightly pointed +out I'm also a final year student and I + + align:start position:0% +out I'm also a final year student and I + + + align:start position:0% +out I'm also a final year student and I +think I have dabbled in all the areas + + align:start position:0% +think I have dabbled in all the areas + + + align:start position:0% +think I have dabbled in all the areas +which drew me in so like chemistry + + align:start position:0% +which drew me in so like chemistry + + + align:start position:0% +which drew me in so like chemistry +Finance data science and then economics + + align:start position:0% +Finance data science and then economics + + + align:start position:0% +Finance data science and then economics +I tried them all and now I think it's + + align:start position:0% +I tried them all and now I think it's + + + align:start position:0% +I tried them all and now I think it's +probably the time where I have to yes + + align:start position:0% +probably the time where I have to yes + + + align:start position:0% +probably the time where I have to yes +basically root myself in specific + + align:start position:0% +basically root myself in specific + + + align:start position:0% +basically root myself in specific +grounds and then even if they don't work + + align:start position:0% +grounds and then even if they don't work + + + align:start position:0% +grounds and then even if they don't work +out you know they say like it doesn't + + align:start position:0% +out you know they say like it doesn't + + + align:start position:0% +out you know they say like it doesn't +matter in 5 + + align:start position:0% +matter in 5 + + + align:start position:0% +matter in 5 +years probably I can like change my + + align:start position:0% +years probably I can like change my + + + align:start position:0% +years probably I can like change my +career plan after 5 years but as of the + + align:start position:0% +career plan after 5 years but as of the + + + align:start position:0% +career plan after 5 years but as of the +moment I'm trying to solidify and + + align:start position:0% +moment I'm trying to solidify and + + + align:start position:0% +moment I'm trying to solidify and +consolidate one specific goal and really + + align:start position:0% +consolidate one specific goal and really + + + align:start position:0% +consolidate one specific goal and really +gear towards that goal so using all the + + align:start position:0% +gear towards that goal so using all the + + + align:start position:0% +gear towards that goal so using all the +resources and the learnings that I've + + align:start position:0% +resources and the learnings that I've + + + align:start position:0% +resources and the learnings that I've +had to achieve a specific goal you know + + align:start position:0% +had to achieve a specific goal you know + + + align:start position:0% +had to achieve a specific goal you know +me in my journey too like when you get a + + align:start position:0% +me in my journey too like when you get a + + + align:start position:0% +me in my journey too like when you get a +specific goal you can always line up + + align:start position:0% +specific goal you can always line up + + + align:start position:0% +specific goal you can always line up +another one you can always make another + + align:start position:0% +another one you can always make another + + + align:start position:0% +another one you can always make another +one you can always change that's your + + align:start position:0% +one you can always change that's your + + + align:start position:0% +one you can always change that's your +right as a human being right completely + + align:start position:0% +right as a human being right completely + + + align:start position:0% +right as a human being right completely +agree with you yeah this has been + + align:start position:0% +agree with you yeah this has been + + + align:start position:0% +agree with you yeah this has been +amazing uh I just have one more thing + + align:start position:0% +amazing uh I just have one more thing + + + align:start position:0% +amazing uh I just have one more thing +maybe to ask you're an amazing character + + align:start position:0% +maybe to ask you're an amazing character + + + align:start position:0% +maybe to ask you're an amazing character +you've gone from Finance to sances to + + align:start position:0% +you've gone from Finance to sances to + + + align:start position:0% +you've gone from Finance to sances to +fch you're now in Investment Banking + + align:start position:0% +fch you're now in Investment Banking + + + align:start position:0% +fch you're now in Investment Banking +amazing amazing journey any advice for + + align:start position:0% +amazing amazing journey any advice for + + + align:start position:0% +amazing amazing journey any advice for +anyone listen listening who may want to + + align:start position:0% +anyone listen listening who may want to + + + align:start position:0% +anyone listen listening who may want to +take your path or maybe learn a few + + align:start position:0% +take your path or maybe learn a few + + + align:start position:0% +take your path or maybe learn a few +things from you for future ocw Learners + + align:start position:0% +things from you for future ocw Learners + + + align:start position:0% +things from you for future ocw Learners +or listeners to this podcast I would say + + align:start position:0% +or listeners to this podcast I would say + + + align:start position:0% +or listeners to this podcast I would say +that my path up to this point has been + + align:start position:0% +that my path up to this point has been + + + align:start position:0% +that my path up to this point has been +incredibly + + align:start position:0% +incredibly + + + align:start position:0% +incredibly +unpredictable but I always tried to + + align:start position:0% +unpredictable but I always tried to + + + align:start position:0% +unpredictable but I always tried to +follow what I'm interested in and being + + align:start position:0% +follow what I'm interested in and being + + + align:start position:0% +follow what I'm interested in and being +able to search the resources I'm wanting + + align:start position:0% +able to search the resources I'm wanting + + + align:start position:0% +able to search the resources I'm wanting +to learn more for your advantage these + + align:start position:0% +to learn more for your advantage these + + + align:start position:0% +to learn more for your advantage these +are like very very important qualities + + align:start position:0% +are like very very important qualities + + + align:start position:0% +are like very very important qualities +that will eventually lead you up to a + + align:start position:0% +that will eventually lead you up to a + + + align:start position:0% +that will eventually lead you up to a +certain point and for me that is + + align:start position:0% +certain point and for me that is + + + align:start position:0% +certain point and for me that is +investment banking at this point I'm not + + align:start position:0% +investment banking at this point I'm not + + + align:start position:0% +investment banking at this point I'm not +sure if what what I will say after like + + align:start position:0% +sure if what what I will say after like + + + align:start position:0% +sure if what what I will say after like +five years but that is my current career + + align:start position:0% +five years but that is my current career + + + align:start position:0% +five years but that is my current career +goal the 5-year plan and up to this + + align:start position:0% +goal the 5-year plan and up to this + + + align:start position:0% +goal the 5-year plan and up to this +point there's been so many different + + align:start position:0% +point there's been so many different + + + align:start position:0% +point there's been so many different +Explorations where I went from economics + + align:start position:0% +Explorations where I went from economics + + + align:start position:0% +Explorations where I went from economics +chemistry Finance fintech data science + + align:start position:0% +chemistry Finance fintech data science + + + align:start position:0% +chemistry Finance fintech data science +but then at every Point what I can say + + align:start position:0% +but then at every Point what I can say + + + align:start position:0% +but then at every Point what I can say +for sure is I did not just rely on my + + align:start position:0% +for sure is I did not just rely on my + + + align:start position:0% +for sure is I did not just rely on my +conventional education I Tred to do more + + align:start position:0% +conventional education I Tred to do more + + + align:start position:0% +conventional education I Tred to do more +and then I try to actively seek out what + + align:start position:0% +and then I try to actively seek out what + + + align:start position:0% +and then I try to actively seek out what +I'm like truly passionate about and in + + align:start position:0% +I'm like truly passionate about and in + + + align:start position:0% +I'm like truly passionate about and in +order to have that gauge for yourself + + align:start position:0% +order to have that gauge for yourself + + + align:start position:0% +order to have that gauge for yourself +being a very very active learner will + + align:start position:0% +being a very very active learner will + + + align:start position:0% +being a very very active learner will +come into to Great advantage and then + + align:start position:0% +come into to Great advantage and then + + + align:start position:0% +come into to Great advantage and then +having this all available accessible + + align:start position:0% +having this all available accessible + + + align:start position:0% +having this all available accessible +resource like ocw will be something that + + align:start position:0% +resource like ocw will be something that + + + align:start position:0% +resource like ocw will be something that +will meet all your expectations and then + + align:start position:0% +will meet all your expectations and then + + + align:start position:0% +will meet all your expectations and then +meet the requirements that you have for + + align:start position:0% +meet the requirements that you have for + + + align:start position:0% +meet the requirements that you have for +yourself but then I feel like ocw is a + + align:start position:0% +yourself but then I feel like ocw is a + + + align:start position:0% +yourself but then I feel like ocw is a +great pool of resources where people can + + align:start position:0% +great pool of resources where people can + + + align:start position:0% +great pool of resources where people can +sort of dream about one career pathway + + align:start position:0% +sort of dream about one career pathway + + + align:start position:0% +sort of dream about one career pathway +but if that doesn't work out there's + + align:start position:0% +but if that doesn't work out there's + + + align:start position:0% +but if that doesn't work out there's +always like different courses that they + + align:start position:0% +always like different courses that they + + + align:start position:0% +always like different courses that they +can come back to and then explore + + align:start position:0% + + + + align:start position:0% + +further that was such a cool + + align:start position:0% +further that was such a cool + + + align:start position:0% +further that was such a cool +conversation cool cool conversation I + + align:start position:0% +conversation cool cool conversation I + + + align:start position:0% +conversation cool cool conversation I +haven't stopped thinking about it what's + + align:start position:0% +haven't stopped thinking about it what's + + + align:start position:0% +haven't stopped thinking about it what's +your biggest take away from J's + + align:start position:0% +your biggest take away from J's + + + align:start position:0% +your biggest take away from J's +conversation Michael I love the + + align:start position:0% +conversation Michael I love the + + + align:start position:0% +conversation Michael I love the +conversation with Jam because I think it + + align:start position:0% +conversation with Jam because I think it + + + align:start position:0% +conversation with Jam because I think it +shows + + align:start position:0% +shows + + + align:start position:0% +shows +the ability to be curious and to still + + align:start position:0% +the ability to be curious and to still + + + align:start position:0% +the ability to be curious and to still +explore as an undergrad when I first met + + align:start position:0% +explore as an undergrad when I first met + + + align:start position:0% +explore as an undergrad when I first met +Jam she was primarily focused on just + + align:start position:0% +Jam she was primarily focused on just + + + align:start position:0% +Jam she was primarily focused on just +getting her chemistry degree and through + + align:start position:0% +getting her chemistry degree and through + + + align:start position:0% +getting her chemistry degree and through +the conversation I had with her but also + + align:start position:0% +the conversation I had with her but also + + + align:start position:0% +the conversation I had with her but also +with her leveraging open educational + + align:start position:0% +with her leveraging open educational + + + align:start position:0% +with her leveraging open educational +resources she was able to expand her + + align:start position:0% +resources she was able to expand her + + + align:start position:0% +resources she was able to expand her +view expand her Consciousness and + + align:start position:0% +view expand her Consciousness and + + + align:start position:0% +view expand her Consciousness and +ultimately changed what she was studying + + align:start position:0% +ultimately changed what she was studying + + + align:start position:0% +ultimately changed what she was studying +in her undergraduate program so I + + align:start position:0% +in her undergraduate program so I + + + align:start position:0% +in her undergraduate program so I +thought that was very fascinating how + + align:start position:0% +thought that was very fascinating how + + + align:start position:0% +thought that was very fascinating how +she went from just being focused on + + align:start position:0% +she went from just being focused on + + + align:start position:0% +she went from just being focused on +chemistry to start looking at the whole + + align:start position:0% +chemistry to start looking at the whole + + + align:start position:0% +chemistry to start looking at the whole +world and then studying economics as + + align:start position:0% +world and then studying economics as + + + align:start position:0% +world and then studying economics as +well I personally loved how she has + + align:start position:0% +well I personally loved how she has + + + align:start position:0% +well I personally loved how she has +experienced learning from all across the + + align:start position:0% +experienced learning from all across the + + + align:start position:0% +experienced learning from all across the +world you know we've heard from her + + align:start position:0% +world you know we've heard from her + + + align:start position:0% +world you know we've heard from her +story she was in New Zealand at some + + align:start position:0% +story she was in New Zealand at some + + + align:start position:0% +story she was in New Zealand at some +point she's been to Korea and she found + + align:start position:0% +point she's been to Korea and she found + + + align:start position:0% +point she's been to Korea and she found +open learning with this whole background + + align:start position:0% +open learning with this whole background + + + align:start position:0% +open learning with this whole background +from all these different places and all + + align:start position:0% +from all these different places and all + + + align:start position:0% +from all these different places and all +these different types of education and + + align:start position:0% +these different types of education and + + + align:start position:0% +these different types of education and +still opcw was something and open + + align:start position:0% +still opcw was something and open + + + align:start position:0% +still opcw was something and open +learning was something that could still + + align:start position:0% +learning was something that could still + + + align:start position:0% +learning was something that could still +add to that and to such a person with + + align:start position:0% +add to that and to such a person with + + + align:start position:0% +add to that and to such a person with +such experience and such diverse range + + align:start position:0% +such experience and such diverse range + + + align:start position:0% +such experience and such diverse range +from and still she comes open learning + + align:start position:0% +from and still she comes open learning + + + align:start position:0% +from and still she comes open learning +and still has something to add her value + + align:start position:0% +and still has something to add her value + + + align:start position:0% +and still has something to add her value +I like that aspect of it in that this is + + align:start position:0% +I like that aspect of it in that this is + + + align:start position:0% +I like that aspect of it in that this is +something that can touch anyone from + + align:start position:0% +something that can touch anyone from + + + align:start position:0% +something that can touch anyone from +whatever background from whatever + + align:start position:0% +whatever background from whatever + + + align:start position:0% +whatever background from whatever +experience you have it can still add + + align:start position:0% +experience you have it can still add + + + align:start position:0% +experience you have it can still add +value to you thanks to everyone for + + align:start position:0% +value to you thanks to everyone for + + + align:start position:0% +value to you thanks to everyone for +tuning into our conversation with J mean + + align:start position:0% +tuning into our conversation with J mean + + + align:start position:0% +tuning into our conversation with J mean +Hong of Soul South Korea we will be back + + align:start position:0% +Hong of Soul South Korea we will be back + + + align:start position:0% +Hong of Soul South Korea we will be back +in two weeks with another story from a + + align:start position:0% +in two weeks with another story from a + + + align:start position:0% +in two weeks with another story from a +different Learner in the global ocw + + align:start position:0% +different Learner in the global ocw + + + align:start position:0% +different Learner in the global ocw +Community see you + + align:start position:0% +Community see you + + + align:start position:0% +Community see you +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +then open L produced by Alexis hot + + align:start position:0% +then open L produced by Alexis hot + + + align:start position:0% +then open L produced by Alexis hot +special thanks to the supporters and + + align:start position:0% +special thanks to the supporters and + + + align:start position:0% +special thanks to the supporters and +donors who make ocw possible to learn + + align:start position:0% +donors who make ocw possible to learn + + + align:start position:0% +donors who make ocw possible to learn +more about mit's Open courseware and to + + align:start position:0% +more about mit's Open courseware and to + + + align:start position:0% +more about mit's Open courseware and to +check out the courses mentioned in this + + align:start position:0% +check out the courses mentioned in this + + + align:start position:0% +check out the courses mentioned in this +episode visit the open courseware + + align:start position:0% +episode visit the open courseware + + + align:start position:0% +episode visit the open courseware +website at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +a \ No newline at end of file diff --git a/TxG1iPXznBs.txt b/TxG1iPXznBs.txt new file mode 100644 index 0000000000000000000000000000000000000000..9f57282503dfcffaed62708815b04689ad41e06a --- /dev/null +++ b/TxG1iPXznBs.txt @@ -0,0 +1,1787 @@ +align:start position:0% + +the isoclines applet lets us explore + + align:start position:0% +the isoclines applet lets us explore + + + align:start position:0% +the isoclines applet lets us explore +graphs of solutions of differential + + align:start position:0% +graphs of solutions of differential + + + align:start position:0% +graphs of solutions of differential +equations using Direction fields and + + align:start position:0% +equations using Direction fields and + + + align:start position:0% +equations using Direction fields and +iines the first thing to do is to choose + + align:start position:0% +iines the first thing to do is to choose + + + align:start position:0% +iines the first thing to do is to choose +an equation from the pul down menu + + align:start position:0% +an equation from the pul down menu + + + align:start position:0% +an equation from the pul down menu +here and for this demonstration I will + + align:start position:0% +here and for this demonstration I will + + + align:start position:0% +here and for this demonstration I will +choose the differential equation Y Prime + + align:start position:0% +choose the differential equation Y Prime + + + align:start position:0% +choose the differential equation Y Prime += y^2 - + + align:start position:0% += y^2 - + + + align:start position:0% += y^2 - +x in the window at left you can see the + + align:start position:0% +x in the window at left you can see the + + + align:start position:0% +x in the window at left you can see the +direction or slope field + + align:start position:0% +direction or slope field + + + align:start position:0% +direction or slope field +drawn this is a representation of the + + align:start position:0% +drawn this is a representation of the + + + align:start position:0% +drawn this is a representation of the +differential equation when I M move the + + align:start position:0% +differential equation when I M move the + + + align:start position:0% +differential equation when I M move the +cursor over this window a readout of the + + align:start position:0% +cursor over this window a readout of the + + + align:start position:0% +cursor over this window a readout of the +X and Y coordinates shows up on the + + align:start position:0% +X and Y coordinates shows up on the + + + align:start position:0% +X and Y coordinates shows up on the +right hand side of the screen this is + + align:start position:0% +right hand side of the screen this is + + + align:start position:0% +right hand side of the screen this is +very useful in making + + align:start position:0% +very useful in making + + + align:start position:0% +very useful in making +measurements if I click on the graphing + + align:start position:0% +measurements if I click on the graphing + + + align:start position:0% +measurements if I click on the graphing +window the solution through the point + + align:start position:0% +window the solution through the point + + + align:start position:0% +window the solution through the point +that I've clicked on is + + align:start position:0% +that I've clicked on is + + + align:start position:0% +that I've clicked on is +drawn this is an interesting function + + align:start position:0% +drawn this is an interesting function + + + align:start position:0% +drawn this is an interesting function +probably one you've never seen before + + align:start position:0% +probably one you've never seen before + + + align:start position:0% +probably one you've never seen before +certainly it's not an elementary + + align:start position:0% +certainly it's not an elementary + + + align:start position:0% +certainly it's not an elementary +function + + align:start position:0% +function + + + align:start position:0% +function +clicking some more points makes more + + align:start position:0% +clicking some more points makes more + + + align:start position:0% +clicking some more points makes more +solutions + + align:start position:0% + + + + align:start position:0% + +appear in fact every point on this plane + + align:start position:0% +appear in fact every point on this plane + + + align:start position:0% +appear in fact every point on this plane +has exactly one solution through it this + + align:start position:0% +has exactly one solution through it this + + + align:start position:0% +has exactly one solution through it this +is the meaning of the existence and + + align:start position:0% +is the meaning of the existence and + + + align:start position:0% +is the meaning of the existence and +uniqueness theorem for differential + + align:start position:0% +uniqueness theorem for differential + + + align:start position:0% +uniqueness theorem for differential +equations now let's clear the solutions + + align:start position:0% +equations now let's clear the solutions + + + align:start position:0% +equations now let's clear the solutions +using this button down here Clear + + align:start position:0% +using this button down here Clear + + + align:start position:0% +using this button down here Clear +Solutions button you see a blank screen + + align:start position:0% +Solutions button you see a blank screen + + + align:start position:0% +Solutions button you see a blank screen +again you can control how the slope + + align:start position:0% +again you can control how the slope + + + align:start position:0% +again you can control how the slope +field looks by using this slope field + + align:start position:0% +field looks by using this slope field + + + align:start position:0% +field looks by using this slope field +toggle here you can make them blank or + + align:start position:0% +toggle here you can make them blank or + + + align:start position:0% +toggle here you can make them blank or +bright for a display for example or the + + align:start position:0% +bright for a display for example or the + + + align:start position:0% +bright for a display for example or the +way it was originally and I think I'm + + align:start position:0% +way it was originally and I think I'm + + + align:start position:0% +way it was originally and I think I'm +going to turn it off altogether so now + + align:start position:0% +going to turn it off altogether so now + + + align:start position:0% +going to turn it off altogether so now +we're faced with a blank screen now how + + align:start position:0% +we're faced with a blank screen now how + + + align:start position:0% +we're faced with a blank screen now how +would you go about drawing some + + align:start position:0% +would you go about drawing some + + + align:start position:0% +would you go about drawing some +solutions to this differential equation + + align:start position:0% +solutions to this differential equation + + + align:start position:0% +solutions to this differential equation +by hand just knowing the differential + + align:start position:0% +by hand just knowing the differential + + + align:start position:0% +by hand just knowing the differential +equations equation and this blank + + align:start position:0% +equations equation and this blank + + + align:start position:0% +equations equation and this blank +screen well isolines give you a good way + + align:start position:0% +screen well isolines give you a good way + + + align:start position:0% +screen well isolines give you a good way +of doing this and they reveal things + + align:start position:0% +of doing this and they reveal things + + + align:start position:0% +of doing this and they reveal things +about the qualitative behavior of the + + align:start position:0% +about the qualitative behavior of the + + + align:start position:0% +about the qualitative behavior of the +differential equation as well an isine + + align:start position:0% +differential equation as well an isine + + + align:start position:0% +differential equation as well an isine +is the subset of the plane where the + + align:start position:0% +is the subset of the plane where the + + + align:start position:0% +is the subset of the plane where the +slope field takes on a given value I can + + align:start position:0% +slope field takes on a given value I can + + + align:start position:0% +slope field takes on a given value I can +choose that value M using this slider + + align:start position:0% +choose that value M using this slider + + + align:start position:0% +choose that value M using this slider +here and when I click here and move this + + align:start position:0% +here and when I click here and move this + + + align:start position:0% +here and when I click here and move this +the isine with the given value of M is + + align:start position:0% +the isine with the given value of M is + + + align:start position:0% +the isine with the given value of M is +drawn in yellow on the screen and you + + align:start position:0% +drawn in yellow on the screen and you + + + align:start position:0% +drawn in yellow on the screen and you +can see the value of the slope field + + align:start position:0% +can see the value of the slope field + + + align:start position:0% +can see the value of the slope field +drawn as well so here the value is is + + align:start position:0% +drawn as well so here the value is is + + + align:start position:0% +drawn as well so here the value is is +one and the slope field has is given by + + align:start position:0% +one and the slope field has is given by + + + align:start position:0% +one and the slope field has is given by +little intervals of value one of slope + + align:start position:0% +little intervals of value one of slope + + + align:start position:0% +little intervals of value one of slope +one I can choose that value using the + + align:start position:0% +one I can choose that value using the + + + align:start position:0% +one I can choose that value using the +slider marked M if I click on the handle + + align:start position:0% +slider marked M if I click on the handle + + + align:start position:0% +slider marked M if I click on the handle +and drag it you see the isine for the + + align:start position:0% +and drag it you see the isine for the + + + align:start position:0% +and drag it you see the isine for the +corresponding value of M drawn on the + + align:start position:0% +corresponding value of M drawn on the + + + align:start position:0% +corresponding value of M drawn on the +screen and on the isocline is also drawn + + align:start position:0% +screen and on the isocline is also drawn + + + align:start position:0% +screen and on the isocline is also drawn +the direction field so when m is two the + + align:start position:0% +the direction field so when m is two the + + + align:start position:0% +the direction field so when m is two the +direction field has slope two and when I + + align:start position:0% +direction field has slope two and when I + + + align:start position:0% +direction field has slope two and when I +drag the slider back down to Zer the + + align:start position:0% +drag the slider back down to Zer the + + + align:start position:0% +drag the slider back down to Zer the +isine with value zero has a horizontal + + align:start position:0% +isine with value zero has a horizontal + + + align:start position:0% +isine with value zero has a horizontal +uh Direction field marked along it each + + align:start position:0% +uh Direction field marked along it each + + + align:start position:0% +uh Direction field marked along it each +one of these is a curve where y^2 - x = + + align:start position:0% +one of these is a curve where y^2 - x = + + + align:start position:0% +one of these is a curve where y^2 - x = +m or x = y^2 minus M this is a parabola + + align:start position:0% +m or x = y^2 minus M this is a parabola + + + align:start position:0% +m or x = y^2 minus M this is a parabola +lying on its side with a Vertex at xals + + align:start position:0% +lying on its side with a Vertex at xals + + + align:start position:0% +lying on its side with a Vertex at xals +minus + + align:start position:0% +minus + + + align:start position:0% +minus +M let's draw the V the the isine for + + align:start position:0% +M let's draw the V the the isine for + + + align:start position:0% +M let's draw the V the the isine for +Value one for example I've now released + + align:start position:0% +Value one for example I've now released + + + align:start position:0% +Value one for example I've now released +the mouse key and the isine is Left + + align:start position:0% +the mouse key and the isine is Left + + + align:start position:0% +the mouse key and the isine is Left +Behind and I can easily draw in some + + align:start position:0% +Behind and I can easily draw in some + + + align:start position:0% +Behind and I can easily draw in some +other isoclines as well by clicking on + + align:start position:0% +other isoclines as well by clicking on + + + align:start position:0% +other isoclines as well by clicking on +different values of M and releasing the + + align:start position:0% +different values of M and releasing the + + + align:start position:0% +different values of M and releasing the +mouse + + align:start position:0% + + + + align:start position:0% + +key so once you've drawn several of + + align:start position:0% +key so once you've drawn several of + + + align:start position:0% +key so once you've drawn several of +these iines in the on the plane it's + + align:start position:0% +these iines in the on the plane it's + + + align:start position:0% +these iines in the on the plane it's +pretty easy to Envision what + + align:start position:0% +pretty easy to Envision what + + + align:start position:0% +pretty easy to Envision what +the solution field what the solutions + + align:start position:0% +the solution field what the solutions + + + align:start position:0% +the solution field what the solutions +will look like to this curve you just + + align:start position:0% +will look like to this curve you just + + + align:start position:0% +will look like to this curve you just +have to thread your way along the part + + align:start position:0% +have to thread your way along the part + + + align:start position:0% +have to thread your way along the part +of the direction field that you've + + align:start position:0% +of the direction field that you've + + + align:start position:0% +of the direction field that you've +drawn I can check that by clicking on + + align:start position:0% +drawn I can check that by clicking on + + + align:start position:0% +drawn I can check that by clicking on +the screen and drawing a solution in + + align:start position:0% +the screen and drawing a solution in + + + align:start position:0% +the screen and drawing a solution in +this is quite easy to do by hand it's + + align:start position:0% +this is quite easy to do by hand it's + + + align:start position:0% +this is quite easy to do by hand it's +easy to draw the isons and then sketch a + + align:start position:0% +easy to draw the isons and then sketch a + + + align:start position:0% +easy to draw the isons and then sketch a +solution + + align:start position:0% +solution + + + align:start position:0% +solution +accordingly but you can see other things + + align:start position:0% +accordingly but you can see other things + + + align:start position:0% +accordingly but you can see other things +as well from ISAC clines I'm going to + + align:start position:0% +as well from ISAC clines I'm going to + + + align:start position:0% +as well from ISAC clines I'm going to +clear all of these and redraw the Mal + + align:start position:0% +clear all of these and redraw the Mal + + + align:start position:0% +clear all of these and redraw the Mal +equals z isocline on the + + align:start position:0% +equals z isocline on the + + + align:start position:0% +equals z isocline on the +screen and I think I'm going to draw the + + align:start position:0% +screen and I think I'm going to draw the + + + align:start position:0% +screen and I think I'm going to draw the +redraw the slope field as + + align:start position:0% +redraw the slope field as + + + align:start position:0% +redraw the slope field as +well + + align:start position:0% +well + + + align:start position:0% +well +now critical points of a function occur + + align:start position:0% +now critical points of a function occur + + + align:start position:0% +now critical points of a function occur +where the derivative is equal to zero + + align:start position:0% +where the derivative is equal to zero + + + align:start position:0% +where the derivative is equal to zero +and the derivative is exactly what we + + align:start position:0% +and the derivative is exactly what we + + + align:start position:0% +and the derivative is exactly what we +know about the solution to a + + align:start position:0% +know about the solution to a + + + align:start position:0% +know about the solution to a +differential equation so the critical + + align:start position:0% +differential equation so the critical + + + align:start position:0% +differential equation so the critical +points the Minima or Maxima of solutions + + align:start position:0% +points the Minima or Maxima of solutions + + + align:start position:0% +points the Minima or Maxima of solutions +to this differential equation occur when + + align:start position:0% +to this differential equation occur when + + + align:start position:0% +to this differential equation occur when +the solution crosses the Mal equals zero + + align:start position:0% +the solution crosses the Mal equals zero + + + align:start position:0% +the solution crosses the Mal equals zero +isocline also known as the + + align:start position:0% +isocline also known as the + + + align:start position:0% +isocline also known as the +nullcline all Maxima and Minima of + + align:start position:0% +nullcline all Maxima and Minima of + + + align:start position:0% +nullcline all Maxima and Minima of +solutions to this differential equation + + align:start position:0% +solutions to this differential equation + + + align:start position:0% +solutions to this differential equation +occur along this particular yellow + + align:start position:0% +occur along this particular yellow + + + align:start position:0% +occur along this particular yellow +Parabola I can check that by drawing in + + align:start position:0% +Parabola I can check that by drawing in + + + align:start position:0% +Parabola I can check that by drawing in +some solutions and you can see that + + align:start position:0% +some solutions and you can see that + + + align:start position:0% +some solutions and you can see that +these functions have Maxima that which + + align:start position:0% +these functions have Maxima that which + + + align:start position:0% +these functions have Maxima that which +occur just along that Parabola if the + + align:start position:0% +occur just along that Parabola if the + + + align:start position:0% +occur just along that Parabola if the +solutions miss the parabola they don't + + align:start position:0% +solutions miss the parabola they don't + + + align:start position:0% +solutions miss the parabola they don't +have any critical + + align:start position:0% + + + + align:start position:0% + +points another thing you can + + align:start position:0% +points another thing you can + + + align:start position:0% +points another thing you can +see from this picture is that apparently + + align:start position:0% +see from this picture is that apparently + + + align:start position:0% +see from this picture is that apparently +many of the solutions to this + + align:start position:0% +many of the solutions to this + + + align:start position:0% +many of the solutions to this +differential equation cluster near to + + align:start position:0% +differential equation cluster near to + + + align:start position:0% +differential equation cluster near to +this branch of the nullcline and maybe + + align:start position:0% +this branch of the nullcline and maybe + + + align:start position:0% +this branch of the nullcline and maybe +we can see why this is using the isine + + align:start position:0% +we can see why this is using the isine + + + align:start position:0% +we can see why this is using the isine +picture I'm going to clear CLE the + + align:start position:0% +picture I'm going to clear CLE the + + + align:start position:0% +picture I'm going to clear CLE the +solutions now to make the picture + + align:start position:0% +solutions now to make the picture + + + align:start position:0% +solutions now to make the picture +clearer and draw in one more + + align:start position:0% +clearer and draw in one more + + + align:start position:0% +clearer and draw in one more +nullcline one more isocline namely the m + + align:start position:0% +nullcline one more isocline namely the m + + + align:start position:0% +nullcline one more isocline namely the m +equal minus1 + + align:start position:0% + + + + align:start position:0% + +isine now suppose that a solution finds + + align:start position:0% +isine now suppose that a solution finds + + + align:start position:0% +isine now suppose that a solution finds +itself below the m equals minus1 isine + + align:start position:0% +itself below the m equals minus1 isine + + + align:start position:0% +itself below the m equals minus1 isine +so it's in here + + align:start position:0% +so it's in here + + + align:start position:0% +so it's in here +somewhere can it ever cross the malal + + align:start position:0% +somewhere can it ever cross the malal + + + align:start position:0% +somewhere can it ever cross the malal +minus1 isine once it's below it can it + + align:start position:0% +minus1 isine once it's below it can it + + + align:start position:0% +minus1 isine once it's below it can it +ever cross it + + align:start position:0% +ever cross it + + + align:start position:0% +ever cross it +well it's below it so if it crosses the + + align:start position:0% +well it's below it so if it crosses the + + + align:start position:0% +well it's below it so if it crosses the +malal minus1 ISAC line it must cross it + + align:start position:0% +malal minus1 ISAC line it must cross it + + + align:start position:0% +malal minus1 ISAC line it must cross it +with a slope which is bigger than the + + align:start position:0% +with a slope which is bigger than the + + + align:start position:0% +with a slope which is bigger than the +slope of that yellow + + align:start position:0% +slope of that yellow + + + align:start position:0% +slope of that yellow +curve but when it crosses it it also has + + align:start position:0% +curve but when it crosses it it also has + + + align:start position:0% +curve but when it crosses it it also has +to cross it with slope minus one because + + align:start position:0% +to cross it with slope minus one because + + + align:start position:0% +to cross it with slope minus one because +that's because this is the m equals + + align:start position:0% +that's because this is the m equals + + + align:start position:0% +that's because this is the m equals +minus1 + + align:start position:0% +minus1 + + + align:start position:0% +minus1 +isine but the slope of this yellow + + align:start position:0% +isine but the slope of this yellow + + + align:start position:0% +isine but the slope of this yellow +Parabola is bigger than minus1 along + + align:start position:0% +Parabola is bigger than minus1 along + + + align:start position:0% +Parabola is bigger than minus1 along +here and so the solution curve can never + + align:start position:0% +here and so the solution curve can never + + + align:start position:0% +here and so the solution curve can never +cross + + align:start position:0% +cross + + + align:start position:0% +cross +it similarly suppose that you have a + + align:start position:0% +it similarly suppose that you have a + + + align:start position:0% +it similarly suppose that you have a +solution which is above the + + align:start position:0% +solution which is above the + + + align:start position:0% +solution which is above the +nullcline can it ever cross the + + align:start position:0% +nullcline can it ever cross the + + + align:start position:0% +nullcline can it ever cross the +nullcline well if it crosses the + + align:start position:0% +nullcline well if it crosses the + + + align:start position:0% +nullcline well if it crosses the +nullcline it must cross it from + + align:start position:0% +nullcline it must cross it from + + + align:start position:0% +nullcline it must cross it from +above so when it crosses it its slope + + align:start position:0% +above so when it crosses it its slope + + + align:start position:0% +above so when it crosses it its slope +must be less than the slope of the null + + align:start position:0% +must be less than the slope of the null + + + align:start position:0% +must be less than the slope of the null +Cline which is negative as you can see + + align:start position:0% +Cline which is negative as you can see + + + align:start position:0% +Cline which is negative as you can see +but when the solution crosses the nine + + align:start position:0% +but when the solution crosses the nine + + + align:start position:0% +but when the solution crosses the nine +it must cross it with slope + + align:start position:0% +it must cross it with slope + + + align:start position:0% +it must cross it with slope +zero and so that can't happen and so you + + align:start position:0% +zero and so that can't happen and so you + + + align:start position:0% +zero and so that can't happen and so you +see if if a solution is between those + + align:start position:0% +see if if a solution is between those + + + align:start position:0% +see if if a solution is between those +two iines then it stays between them + + align:start position:0% +two iines then it stays between them + + + align:start position:0% +two iines then it stays between them +forever more it's trapped between them + + align:start position:0% +forever more it's trapped between them + + + align:start position:0% +forever more it's trapped between them +this is called a + + align:start position:0% +this is called a + + + align:start position:0% +this is called a +funnel it's trapped between these two + + align:start position:0% +funnel it's trapped between these two + + + align:start position:0% +funnel it's trapped between these two +things and gets closer and closer + + align:start position:0% +things and gets closer and closer + + + align:start position:0% +things and gets closer and closer +because these two isoclines become as + + align:start position:0% +because these two isoclines become as + + + align:start position:0% +because these two isoclines become as +totic as X gets + + align:start position:0% +totic as X gets + + + align:start position:0% +totic as X gets +large it's also called These are called + + align:start position:0% +large it's also called These are called + + + align:start position:0% +large it's also called These are called +fences as well once uh solution is in + + align:start position:0% +fences as well once uh solution is in + + + align:start position:0% +fences as well once uh solution is in +here it can't cross either of these two + + align:start position:0% +here it can't cross either of these two + + + align:start position:0% +here it can't cross either of these two +fences this lets us estimate the value + + align:start position:0% +fences this lets us estimate the value + + + align:start position:0% +fences this lets us estimate the value +of solutions for large x these Solutions + + align:start position:0% +of solutions for large x these Solutions + + + align:start position:0% +of solutions for large x these Solutions +anyway for large + + align:start position:0% +anyway for large + + + align:start position:0% +anyway for large +x and all these Sol for example if x is + + align:start position:0% +x and all these Sol for example if x is + + + align:start position:0% +x and all these Sol for example if x is +equal to 100 the solution has to be + + align:start position:0% +equal to 100 the solution has to be + + + align:start position:0% +equal to 100 the solution has to be +bigger than the value of this Parabola + + align:start position:0% +bigger than the value of this Parabola + + + align:start position:0% +bigger than the value of this Parabola +which is minus 10 and less than the + + align:start position:0% +which is minus 10 and less than the + + + align:start position:0% +which is minus 10 and less than the +value along this Parabola which is minus + + align:start position:0% +value along this Parabola which is minus + + + align:start position:0% +value along this Parabola which is minus +the square root of 99 so you get a very + + align:start position:0% +the square root of 99 so you get a very + + + align:start position:0% +the square root of 99 so you get a very +good estimate for the value of solutions + + align:start position:0% +good estimate for the value of solutions + + + align:start position:0% +good estimate for the value of solutions +for large x from these kinds of + + align:start position:0% +for large x from these kinds of + + + align:start position:0% +for large x from these kinds of +considerations more thing you can see + + align:start position:0% +considerations more thing you can see + + + align:start position:0% +considerations more thing you can see +from this applet is this if a solution + + align:start position:0% +from this applet is this if a solution + + + align:start position:0% +from this applet is this if a solution +is above well above the nullcline it + + align:start position:0% +is above well above the nullcline it + + + align:start position:0% +is above well above the nullcline it +gets caught in this powerful up draft + + align:start position:0% +gets caught in this powerful up draft + + + align:start position:0% +gets caught in this powerful up draft +and goes off to Infinity in fact all + + align:start position:0% +and goes off to Infinity in fact all + + + align:start position:0% +and goes off to Infinity in fact all +these Solutions become tangent to + + align:start position:0% +these Solutions become tangent to + + + align:start position:0% +these Solutions become tangent to +vertical lines they don't continue for + + align:start position:0% +vertical lines they don't continue for + + + align:start position:0% +vertical lines they don't continue for +all large + + align:start position:0% +all large + + + align:start position:0% +all large +x they blow up in finite time on the + + align:start position:0% +x they blow up in finite time on the + + + align:start position:0% +x they blow up in finite time on the +other hand if you're just a little bit + + align:start position:0% +other hand if you're just a little bit + + + align:start position:0% +other hand if you're just a little bit +smaller than these Solutions then you + + align:start position:0% +smaller than these Solutions then you + + + align:start position:0% +smaller than these Solutions then you +get Solutions which cross the nullcline + + align:start position:0% +get Solutions which cross the nullcline + + + align:start position:0% +get Solutions which cross the nullcline +get trapped into this parabolic region + + align:start position:0% +get trapped into this parabolic region + + + align:start position:0% +get trapped into this parabolic region +and fall down in between our funnel down + + align:start position:0% +and fall down in between our funnel down + + + align:start position:0% +and fall down in between our funnel down +here and so become ASM totic to minus + + align:start position:0% +here and so become ASM totic to minus + + + align:start position:0% +here and so become ASM totic to minus +the root of x when time when X gets + + align:start position:0% +the root of x when time when X gets + + + align:start position:0% +the root of x when time when X gets +large there's just one solution which + + align:start position:0% +large there's just one solution which + + + align:start position:0% +large there's just one solution which +doesn't do either of these very + + align:start position:0% +doesn't do either of these very + + + align:start position:0% +doesn't do either of these very +different behaviors and it's right along + + align:start position:0% +different behaviors and it's right along + + + align:start position:0% +different behaviors and it's right along +here it becomes ASM totic to the + + align:start position:0% +here it becomes ASM totic to the + + + align:start position:0% +here it becomes ASM totic to the +positive branch of the parabola and + + align:start position:0% +positive branch of the parabola and + + + align:start position:0% +positive branch of the parabola and +every solution above it blows up in + + align:start position:0% +every solution above it blows up in + + + align:start position:0% +every solution above it blows up in +finite time and every solution below it + + align:start position:0% +finite time and every solution below it + + + align:start position:0% +finite time and every solution below it +falls down and becomes ASM totic to + + align:start position:0% +falls down and becomes ASM totic to + + + align:start position:0% +falls down and becomes ASM totic to +minus theare < TK of X this special + + align:start position:0% +minus theare < TK of X this special + + + align:start position:0% +minus theare < TK of X this special +solution which doesn't do either of + + align:start position:0% +solution which doesn't do either of + + + align:start position:0% +solution which doesn't do either of +those two behaviors but continues to + + align:start position:0% +those two behaviors but continues to + + + align:start position:0% +those two behaviors but continues to +exist for all positive values of X and + + align:start position:0% +exist for all positive values of X and + + + align:start position:0% +exist for all positive values of X and +become ASM totic to the square root of x + + align:start position:0% +become ASM totic to the square root of x + + + align:start position:0% +become ASM totic to the square root of x +this is called the + + align:start position:0% +this is called the + + + align:start position:0% +this is called the +separatrix it separates Solutions + + align:start position:0% +separatrix it separates Solutions + + + align:start position:0% +separatrix it separates Solutions +showing two very different types of + + align:start position:0% +showing two very different types of + + + align:start position:0% +showing two very different types of +behavior the ones that fall down and the + + align:start position:0% +behavior the ones that fall down and the + + + align:start position:0% +behavior the ones that fall down and the +ones that blow + + align:start position:0% +ones that blow + + + align:start position:0% +ones that blow +up well these are just a few of the + + align:start position:0% +up well these are just a few of the + + + align:start position:0% +up well these are just a few of the +things you can understand using this + + align:start position:0% +things you can understand using this + + + align:start position:0% +things you can understand using this +applet play with items play with + + align:start position:0% +applet play with items play with + + + align:start position:0% +applet play with items play with +different menu items open a copy of this + + align:start position:0% +different menu items open a copy of this + + + align:start position:0% +different menu items open a copy of this +applet in your browser window play with + + align:start position:0% +applet in your browser window play with + + + align:start position:0% +applet in your browser window play with +some other menu items maybe the default + + align:start position:0% +some other menu items maybe the default + + + align:start position:0% +some other menu items maybe the default +item at the bottom of the of of this + + align:start position:0% +item at the bottom of the of of this + + + align:start position:0% +item at the bottom of the of of this +pull down menu down + + align:start position:0% +pull down menu down + + + align:start position:0% +pull down menu down +here are there funnels are there + + align:start position:0% +here are there funnels are there + + + align:start position:0% +here are there funnels are there +separatrices what happens to Solutions + + align:start position:0% +separatrices what happens to Solutions + + + align:start position:0% +separatrices what happens to Solutions +as X goes to minus infinity rather than + + align:start position:0% +as X goes to minus infinity rather than + + + align:start position:0% +as X goes to minus infinity rather than +xal plus infinity where are the critical + + align:start position:0% +xal plus infinity where are the critical + + + align:start position:0% +xal plus infinity where are the critical +points of solutions of this equation \ No newline at end of file diff --git a/U3ebQ5Z4Jt8.txt b/U3ebQ5Z4Jt8.txt new file mode 100644 index 0000000000000000000000000000000000000000..dc56f9997434ea8e9520af6a3e222c23e5c5ed4a --- /dev/null +++ b/U3ebQ5Z4Jt8.txt @@ -0,0 +1,1539 @@ +align:start position:0% + +hi welcome back to recitation we've been + + align:start position:0% +hi welcome back to recitation we've been + + + align:start position:0% +hi welcome back to recitation we've been +talking in lecture about various + + align:start position:0% +talking in lecture about various + + + align:start position:0% +talking in lecture about various +different applications of of definite + + align:start position:0% +different applications of of definite + + + align:start position:0% +different applications of of definite +integrals and one of them has been that + + align:start position:0% +integrals and one of them has been that + + + align:start position:0% +integrals and one of them has been that +we can use definite integrals to find + + align:start position:0% +we can use definite integrals to find + + + align:start position:0% +we can use definite integrals to find +areas of regions that that previously we + + align:start position:0% +areas of regions that that previously we + + + align:start position:0% +areas of regions that that previously we +wouldn't have been able to so one simple + + align:start position:0% +wouldn't have been able to so one simple + + + align:start position:0% +wouldn't have been able to so one simple +example of that is that we can use a + + align:start position:0% +example of that is that we can use a + + + align:start position:0% +example of that is that we can use a +definite integral to find the area of a + + align:start position:0% +definite integral to find the area of a + + + align:start position:0% +definite integral to find the area of a +region bounded between two curves so I + + align:start position:0% +region bounded between two curves so I + + + align:start position:0% +region bounded between two curves so I +have an example of such a question right + + align:start position:0% +have an example of such a question right + + + align:start position:0% +have an example of such a question right +here so the question is to compute the + + align:start position:0% +here so the question is to compute the + + + align:start position:0% +here so the question is to compute the +area of the region that's bounded + + align:start position:0% +area of the region that's bounded + + + align:start position:0% +area of the region that's bounded +between the curves y = x cubed and y = + + align:start position:0% +between the curves y = x cubed and y = + + + align:start position:0% +between the curves y = x cubed and y = +3x - 2 so one thing you'll notice is + + align:start position:0% +3x - 2 so one thing you'll notice is + + + align:start position:0% +3x - 2 so one thing you'll notice is +that I haven't given you end points for + + align:start position:0% +that I haven't given you end points for + + + align:start position:0% +that I haven't given you end points for +this region so I've just given you the + + align:start position:0% +this region so I've just given you the + + + align:start position:0% +this region so I've just given you the +bounding curves so one thing you're + + align:start position:0% +bounding curves so one thing you're + + + align:start position:0% +bounding curves so one thing you're +going to have to do right at the + + align:start position:0% +going to have to do right at the + + + align:start position:0% +going to have to do right at the +beginning is to is to figure out what + + align:start position:0% +beginning is to is to figure out what + + + align:start position:0% +beginning is to is to figure out what +this looks like and what it's what the + + align:start position:0% +this looks like and what it's what the + + + align:start position:0% +this looks like and what it's what the +what region you're going to be + + align:start position:0% +what region you're going to be + + + align:start position:0% +what region you're going to be +integrating over what what interval + + align:start position:0% +integrating over what what interval + + + align:start position:0% +integrating over what what interval +you're going to be integrating over so + + align:start position:0% +you're going to be integrating over so + + + align:start position:0% +you're going to be integrating over so +this is a kind of tricky one why don't + + align:start position:0% +this is a kind of tricky one why don't + + + align:start position:0% +this is a kind of tricky one why don't +you pause the video think about it for a + + align:start position:0% +you pause the video think about it for a + + + align:start position:0% +you pause the video think about it for a +few minutes um try and work it out + + align:start position:0% +few minutes um try and work it out + + + align:start position:0% +few minutes um try and work it out +yourself and you can come back and we + + align:start position:0% +yourself and you can come back and we + + + align:start position:0% +yourself and you can come back and we +can try and work it out + + align:start position:0% + + + + align:start position:0% + +together all right welcome back so + + align:start position:0% +together all right welcome back so + + + align:start position:0% +together all right welcome back so +hopefully you've you've had some some + + align:start position:0% +hopefully you've you've had some some + + + align:start position:0% +hopefully you've you've had some some +luck figuring out what this situation + + align:start position:0% +luck figuring out what this situation + + + align:start position:0% +luck figuring out what this situation +looks like and then Computing the the + + align:start position:0% +looks like and then Computing the the + + + align:start position:0% +looks like and then Computing the the +integral so let's let's talk about it + + align:start position:0% +integral so let's let's talk about it + + + align:start position:0% +integral so let's let's talk about it +for a minute um so we have these two + + align:start position:0% +for a minute um so we have these two + + + align:start position:0% +for a minute um so we have these two +curves and so somewhere I'm I'm asking + + align:start position:0% +curves and so somewhere I'm I'm asking + + + align:start position:0% +curves and so somewhere I'm I'm asking +about about the region bounded by them + + align:start position:0% +about about the region bounded by them + + + align:start position:0% +about about the region bounded by them +so what what I'm telling you is + + align:start position:0% +so what what I'm telling you is + + + align:start position:0% +so what what I'm telling you is +somewhere these curves intersect and + + align:start position:0% +somewhere these curves intersect and + + + align:start position:0% +somewhere these curves intersect and +they they surround some bounded region + + align:start position:0% +they they surround some bounded region + + + align:start position:0% +they they surround some bounded region +um and and so I'm asking you for what + + align:start position:0% +um and and so I'm asking you for what + + + align:start position:0% +um and and so I'm asking you for what +the area of that region is so so in + + align:start position:0% +the area of that region is so so in + + + align:start position:0% +the area of that region is so so in +order to figure that out we should we + + align:start position:0% +order to figure that out we should we + + + align:start position:0% +order to figure that out we should we +should figure out where these curves + + align:start position:0% +should figure out where these curves + + + align:start position:0% +should figure out where these curves +intersect so to find the in other words + + align:start position:0% +intersect so to find the in other words + + + align:start position:0% +intersect so to find the in other words +we need to find the end points of the + + align:start position:0% +we need to find the end points of the + + + align:start position:0% +we need to find the end points of the +interval over which we're going to + + align:start position:0% +interval over which we're going to + + + align:start position:0% +interval over which we're going to +integrate um so in order to do that we + + align:start position:0% +integrate um so in order to do that we + + + align:start position:0% +integrate um so in order to do that we +have to we have to solve for where we + + align:start position:0% +have to we have to solve for where we + + + align:start position:0% +have to we have to solve for where we +have the intersection between y = X cub + + align:start position:0% +have the intersection between y = X cub + + + align:start position:0% +have the intersection between y = X cub +and y = 3x - 2 so we have to solve the + + align:start position:0% +and y = 3x - 2 so we have to solve the + + + align:start position:0% +and y = 3x - 2 so we have to solve the +equation um so we + + align:start position:0% + + + + align:start position:0% + +need to solve the + + align:start position:0% +need to solve the + + + align:start position:0% +need to solve the +equation x cubed = 3x - 2 or X Cub - 3x + + align:start position:0% +equation x cubed = 3x - 2 or X Cub - 3x + + + align:start position:0% +equation x cubed = 3x - 2 or X Cub - 3x ++ 2 equal 0 so this is a polinomial + + align:start position:0% ++ 2 equal 0 so this is a polinomial + + + align:start position:0% ++ 2 equal 0 so this is a polinomial +equation it's not quadratic right it's a + + align:start position:0% +equation it's not quadratic right it's a + + + align:start position:0% +equation it's not quadratic right it's a +cubic equation so that that means it's + + align:start position:0% +cubic equation so that that means it's + + + align:start position:0% +cubic equation so that that means it's +hard to solve in general um luckily in + + align:start position:0% +hard to solve in general um luckily in + + + align:start position:0% +hard to solve in general um luckily in +this case it's it's there are some + + align:start position:0% +this case it's it's there are some + + + align:start position:0% +this case it's it's there are some +there's a root we can recognize fairly + + align:start position:0% +there's a root we can recognize fairly + + + align:start position:0% +there's a root we can recognize fairly +easily which is it's it's pretty you + + align:start position:0% +easily which is it's it's pretty you + + + align:start position:0% +easily which is it's it's pretty you +know one thing you can always do is + + align:start position:0% +know one thing you can always do is + + + align:start position:0% +know one thing you can always do is +check small positive integers or use the + + align:start position:0% +check small positive integers or use the + + + align:start position:0% +check small positive integers or use the +rational root theorem if you remember + + align:start position:0% +rational root theorem if you remember + + + align:start position:0% +rational root theorem if you remember +that from from high school math so in + + align:start position:0% +that from from high school math so in + + + align:start position:0% +that from from high school math so in +this in this case if you check x equals + + align:start position:0% +this in this case if you check x equals + + + align:start position:0% +this in this case if you check x equals +one it's fairly easy to see that x + + align:start position:0% +one it's fairly easy to see that x + + + align:start position:0% +one it's fairly easy to see that x +equals 1 is a is a root of this equation + + align:start position:0% +equals 1 is a is a root of this equation + + + align:start position:0% +equals 1 is a is a root of this equation +so in other words we can Factor the left + + align:start position:0% +so in other words we can Factor the left + + + align:start position:0% +so in other words we can Factor the left +hand side we can divide it divide out a + + align:start position:0% +hand side we can divide it divide out a + + + align:start position:0% +hand side we can divide it divide out a +factor of xus one okay and so now we + + align:start position:0% +factor of xus one okay and so now we + + + align:start position:0% +factor of xus one okay and so now we +have to do you know long division or or + + align:start position:0% +have to do you know long division or or + + + align:start position:0% +have to do you know long division or or +synthetic division whatever uh kind of + + align:start position:0% +synthetic division whatever uh kind of + + + align:start position:0% +synthetic division whatever uh kind of +division you want to to divide through + + align:start position:0% +division you want to to divide through + + + align:start position:0% +division you want to to divide through +here so we get + + align:start position:0% + + + + align:start position:0% + +x² minus so we've got uh nope I lied + + align:start position:0% +x² minus so we've got uh nope I lied + + + align:start position:0% +x² minus so we've got uh nope I lied +plus + + align:start position:0% +plus + + + align:start position:0% +plus +x minus 2 after you divide how's that + + align:start position:0% +x minus 2 after you divide how's that + + + align:start position:0% +x minus 2 after you divide how's that +look we can just double check you know + + align:start position:0% +look we can just double check you know + + + align:start position:0% +look we can just double check you know +we get an X cubed - x^2 plus x^2 - 2x - + + align:start position:0% +we get an X cubed - x^2 plus x^2 - 2x - + + + align:start position:0% +we get an X cubed - x^2 plus x^2 - 2x - +x + 2 okay so that adds up to the right + + align:start position:0% +x + 2 okay so that adds up to the right + + + align:start position:0% +x + 2 okay so that adds up to the right +thing okay so so we either have that one + + align:start position:0% +thing okay so so we either have that one + + + align:start position:0% +thing okay so so we either have that one +is a root or that uh X2 you know rather + + align:start position:0% +is a root or that uh X2 you know rather + + + align:start position:0% +is a root or that uh X2 you know rather +for for the for the places where this is + + align:start position:0% +for for the for the places where this is + + + align:start position:0% +for for the for the places where this is +intersection where these intersect we + + align:start position:0% +intersection where these intersect we + + + align:start position:0% +intersection where these intersect we +have either x equals 1 or x^2 + x - 2 + + align:start position:0% +have either x equals 1 or x^2 + x - 2 + + + align:start position:0% +have either x equals 1 or x^2 + x - 2 +equal 0 and now here you can you know + + align:start position:0% +equal 0 and now here you can you know + + + align:start position:0% +equal 0 and now here you can you know +again factor or uh or use the quadratic + + align:start position:0% +again factor or uh or use the quadratic + + + align:start position:0% +again factor or uh or use the quadratic +equation or or what have you and you can + + align:start position:0% +equation or or what have you and you can + + + align:start position:0% +equation or or what have you and you can +see so so we have that this actually + + align:start position:0% +see so so we have that this actually + + + align:start position:0% +see so so we have that this actually +fully factors as X - 1 2 * x + 2 = 0 + + align:start position:0% +fully factors as X - 1 2 * x + 2 = 0 + + + align:start position:0% +fully factors as X - 1 2 * x + 2 = 0 +which means that we + + align:start position:0% + + + + align:start position:0% + +have + + align:start position:0% +have + + + align:start position:0% +have +intersections when either x - one is z + + align:start position:0% +intersections when either x - one is z + + + align:start position:0% +intersections when either x - one is z +or when X+ 2 is zero so intersections at + + align:start position:0% +or when X+ 2 is zero so intersections at + + + align:start position:0% +or when X+ 2 is zero so intersections at +x = + + align:start position:0% +x = + + + align:start position:0% +x = +1 and x = + + align:start position:0% +1 and x = + + + align:start position:0% +1 and x = +-2 all right so you can take that + + align:start position:0% +-2 all right so you can take that + + + align:start position:0% +-2 all right so you can take that +information and you can you know put it + + align:start position:0% +information and you can you know put it + + + align:start position:0% +information and you can you know put it +together and you can make a nice picture + + align:start position:0% +together and you can make a nice picture + + + align:start position:0% +together and you can make a nice picture +like this or I suppose you could have + + align:start position:0% +like this or I suppose you could have + + + align:start position:0% +like this or I suppose you could have +made the nice picture before you had + + align:start position:0% +made the nice picture before you had + + + align:start position:0% +made the nice picture before you had +that information um and so we see that + + align:start position:0% +that information um and so we see that + + + align:start position:0% +that information um and so we see that +we've got this line yal 3x - 2 here and + + align:start position:0% +we've got this line yal 3x - 2 here and + + + align:start position:0% +we've got this line yal 3x - 2 here and +we have the curve y = x cubed and they + + align:start position:0% +we have the curve y = x cubed and they + + + align:start position:0% +we have the curve y = x cubed and they +have two intersection points they + + align:start position:0% +have two intersection points they + + + align:start position:0% +have two intersection points they +intersect once down at x = -2 yal - 8 + + align:start position:0% +intersect once down at x = -2 yal - 8 + + + align:start position:0% +intersect once down at x = -2 yal - 8 +and they intersect again up at uh the0 1 + + align:start position:0% +and they intersect again up at uh the0 1 + + + align:start position:0% +and they intersect again up at uh the0 1 +one and they're actually tangent there + + align:start position:0% +one and they're actually tangent there + + + align:start position:0% +one and they're actually tangent there +so so X cubed the the curve yal X Cub + + align:start position:0% +so so X cubed the the curve yal X Cub + + + align:start position:0% +so so X cubed the the curve yal X Cub +stays above the line at this point so so + + align:start position:0% +stays above the line at this point so so + + + align:start position:0% +stays above the line at this point so so +one way you can read that off is is here + + align:start position:0% +one way you can read that off is is here + + + align:start position:0% +one way you can read that off is is here +you had a double root at at minus one if + + align:start position:0% +you had a double root at at minus one if + + + align:start position:0% +you had a double root at at minus one if +you like but okay so so then the region + + align:start position:0% +you like but okay so so then the region + + + align:start position:0% +you like but okay so so then the region +in + + align:start position:0% + + + + align:start position:0% + +question is this region here so it's the + + align:start position:0% +question is this region here so it's the + + + align:start position:0% +question is this region here so it's the +region + + align:start position:0% +region + + + align:start position:0% +region +bounded between those two curves that + + align:start position:0% +bounded between those two curves that + + + align:start position:0% +bounded between those two curves that +we're trying to compute the area of so + + align:start position:0% +we're trying to compute the area of so + + + align:start position:0% +we're trying to compute the area of so +now that we have the end points this + + align:start position:0% +now that we have the end points this + + + align:start position:0% +now that we have the end points this +isn't such a tricky problem at all right + + align:start position:0% +isn't such a tricky problem at all right + + + align:start position:0% +isn't such a tricky problem at all right +so we've got the end points and we know + + align:start position:0% +so we've got the end points and we know + + + align:start position:0% +so we've got the end points and we know +now now that we've we've drawn this + + align:start position:0% +now now that we've we've drawn this + + + align:start position:0% +now now that we've we've drawn this +picture we know which curve is is on top + + align:start position:0% +picture we know which curve is is on top + + + align:start position:0% +picture we know which curve is is on top +and which curve is on bottom right so + + align:start position:0% +and which curve is on bottom right so + + + align:start position:0% +and which curve is on bottom right so +the height of our when we when we + + align:start position:0% +the height of our when we when we + + + align:start position:0% +the height of our when we when we +imagine cutting this region into lots of + + align:start position:0% +imagine cutting this region into lots of + + + align:start position:0% +imagine cutting this region into lots of +little rectangles or or approximate + + align:start position:0% +little rectangles or or approximate + + + align:start position:0% +little rectangles or or approximate +rectangles the height is going to be X + + align:start position:0% +rectangles the height is going to be X + + + align:start position:0% +rectangles the height is going to be X +cubed minus 3x - 2 minus the quantity 3x + + align:start position:0% +cubed minus 3x - 2 minus the quantity 3x + + + align:start position:0% +cubed minus 3x - 2 minus the quantity 3x +- 2 right the the X cubed is on top and + + align:start position:0% +- 2 right the the X cubed is on top and + + + align:start position:0% +- 2 right the the X cubed is on top and +3X -2 is on the bottom so the + + align:start position:0% + + + + align:start position:0% + +area is equal to the integral okay and + + align:start position:0% +area is equal to the integral okay and + + + align:start position:0% +area is equal to the integral okay and +now we we know where we have to + + align:start position:0% +now we we know where we have to + + + align:start position:0% +now we we know where we have to +integrate from and two so we're + + align:start position:0% +integrate from and two so we're + + + align:start position:0% +integrate from and two so we're +integrating from X = - 2 to 1 to get + + align:start position:0% +integrating from X = - 2 to 1 to get + + + align:start position:0% +integrating from X = - 2 to 1 to get +this whole region + + align:start position:0% +this whole region + + + align:start position:0% +this whole region +of X cubus the 3x - + + align:start position:0% +of X cubus the 3x - + + + align:start position:0% +of X cubus the 3x - +2 DX okay because X the yal X Cub is the + + align:start position:0% +2 DX okay because X the yal X Cub is the + + + align:start position:0% +2 DX okay because X the yal X Cub is the +top curve and y equal 3x - 2 is the + + align:start position:0% +top curve and y equal 3x - 2 is the + + + align:start position:0% +top curve and y equal 3x - 2 is the +bottom curve so this is the the height + + align:start position:0% +bottom curve so this is the the height + + + align:start position:0% +bottom curve so this is the the height +of those rectangles which is positive + + align:start position:0% +of those rectangles which is positive + + + align:start position:0% +of those rectangles which is positive +okay and so now okay well now this is + + align:start position:0% +okay and so now okay well now this is + + + align:start position:0% +okay and so now okay well now this is +pretty straightforward we're integrating + + align:start position:0% +pretty straightforward we're integrating + + + align:start position:0% +pretty straightforward we're integrating +a polinomial at this point so so this is + + align:start position:0% +a polinomial at this point so so this is + + + align:start position:0% +a polinomial at this point so so this is +the integral well okay so so integrating + + align:start position:0% +the integral well okay so so integrating + + + align:start position:0% +the integral well okay so so integrating +X cubed that gives me X 4th over 4 + + align:start position:0% +X cubed that gives me X 4th over 4 + + + align:start position:0% +X cubed that gives me X 4th over 4 +integrating - 3x gives me - 3 x^2 over 2 + + align:start position:0% +integrating - 3x gives me - 3 x^2 over 2 + + + align:start position:0% +integrating - 3x gives me - 3 x^2 over 2 +and integrating plus 2 gives me + 2x + + align:start position:0% +and integrating plus 2 gives me + 2x + + + align:start position:0% +and integrating plus 2 gives me + 2x +between x = -2 and 1 so okay so now I + + align:start position:0% +between x = -2 and 1 so okay so now I + + + align:start position:0% +between x = -2 and 1 so okay so now I +just do this difference so this is equal + + align:start position:0% +just do this difference so this is equal + + + align:start position:0% +just do this difference so this is equal +to 1 14 + + align:start position:0% +to 1 14 + + + align:start position:0% +to 1 14 +- 3es + + + align:start position:0% +- 3es + + + + align:start position:0% +- 3es + +2 minus okay now I put in minus 2 I get + + align:start position:0% +2 minus okay now I put in minus 2 I get + + + align:start position:0% +2 minus okay now I put in minus 2 I get +2 to the 4th sorry minus 2 to the 4th is + + align:start position:0% +2 to the 4th sorry minus 2 to the 4th is + + + align:start position:0% +2 to the 4th sorry minus 2 to the 4th is +16 over 4 so that's - + + align:start position:0% +16 over 4 so that's - + + + align:start position:0% +16 over 4 so that's - +4 okay + + align:start position:0% +4 okay + + + align:start position:0% +4 okay +minus 3 * 4 over 2 is 6 and then + 2 * + + align:start position:0% +minus 3 * 4 over 2 is 6 and then + 2 * + + + align:start position:0% +minus 3 * 4 over 2 is 6 and then + 2 * +-2 is min - 4 again okay and now we've + + align:start position:0% +-2 is min - 4 again okay and now we've + + + align:start position:0% +-2 is min - 4 again okay and now we've +just got some arithmetic so this is this + + align:start position:0% +just got some arithmetic so this is this + + + align:start position:0% +just got some arithmetic so this is this +all becomes a plus six and oh I have to + + align:start position:0% +all becomes a plus six and oh I have to + + + align:start position:0% +all becomes a plus six and oh I have to +add everything together so that's + + align:start position:0% +add everything together so that's + + + align:start position:0% +add everything together so that's +something like well I've got a + + align:start position:0% +something like well I've got a + + + align:start position:0% +something like well I've got a +denominator four so + + align:start position:0% +denominator four so + + + align:start position:0% +denominator four so +it's yeah all right so there's a a + + align:start position:0% +it's yeah all right so there's a a + + + align:start position:0% +it's yeah all right so there's a a +secret I should tell you which is that + + align:start position:0% +secret I should tell you which is that + + + align:start position:0% +secret I should tell you which is that +which is that mathematicians are not + + align:start position:0% +which is that mathematicians are not + + + align:start position:0% +which is that mathematicians are not +actually very good at arithmetic usually + + align:start position:0% +actually very good at arithmetic usually + + + align:start position:0% +actually very good at arithmetic usually +so so this is min - + + align:start position:0% +so so this is min - + + + align:start position:0% +so so this is min - +64 + 2 + 6 so Plus 8 so this is 8 - + + align:start position:0% +64 + 2 + 6 so Plus 8 so this is 8 - + + + align:start position:0% +64 + 2 + 6 so Plus 8 so this is 8 - +54s which is + + align:start position:0% +54s which is + + + align:start position:0% +54s which is +six and 3/4 + + align:start position:0% +six and 3/4 + + + align:start position:0% +six and 3/4 +okay that's 6 plus 3/4 okay so six and + + align:start position:0% +okay that's 6 plus 3/4 okay so six and + + + align:start position:0% +okay that's 6 plus 3/4 okay so six and +3/4 all right this was just arithmetic + + align:start position:0% +3/4 all right this was just arithmetic + + + align:start position:0% +3/4 all right this was just arithmetic +um here was here was the calculus part + + align:start position:0% +um here was here was the calculus part + + + align:start position:0% +um here was here was the calculus part +and in fact you know one one feature of + + align:start position:0% +and in fact you know one one feature of + + + align:start position:0% +and in fact you know one one feature of +a problem like this is that you have a + + align:start position:0% +a problem like this is that you have a + + + align:start position:0% +a problem like this is that you have a +fair amount of work sometimes to see the + + align:start position:0% +fair amount of work sometimes to see the + + + align:start position:0% +fair amount of work sometimes to see the +the picture of what you're you're + + align:start position:0% +the picture of what you're you're + + + align:start position:0% +the picture of what you're you're +working with then the integration here + + align:start position:0% +working with then the integration here + + + align:start position:0% +working with then the integration here +was was pretty straightforward right + + align:start position:0% +was was pretty straightforward right + + + align:start position:0% +was was pretty straightforward right +this this was a fairly easy integral to + + align:start position:0% +this this was a fairly easy integral to + + + align:start position:0% +this this was a fairly easy integral to +compute if if if you're say better at + + align:start position:0% +compute if if if you're say better at + + + align:start position:0% +compute if if if you're say better at +fraction arithmetic than I am at least + + align:start position:0% +fraction arithmetic than I am at least + + + align:start position:0% +fraction arithmetic than I am at least +um okay so so there you go so we had + + align:start position:0% +um okay so so there you go so we had + + + align:start position:0% +um okay so so there you go so we had +this region so we found actually the end + + align:start position:0% +this region so we found actually the end + + + align:start position:0% +this region so we found actually the end +points of the interval we found which + + align:start position:0% +points of the interval we found which + + + align:start position:0% +points of the interval we found which +was the top curve and which was the + + align:start position:0% +was the top curve and which was the + + + align:start position:0% +was the top curve and which was the +bottom curve and that let us write down + + align:start position:0% +bottom curve and that let us write down + + + align:start position:0% +bottom curve and that let us write down +this integral and then that integral was + + align:start position:0% +this integral and then that integral was + + + align:start position:0% +this integral and then that integral was +fairly easy to compute from that point + + align:start position:0% +fairly easy to compute from that point + + + align:start position:0% +fairly easy to compute from that point +out and we ended up with this as our + + align:start position:0% +out and we ended up with this as our + + + align:start position:0% +out and we ended up with this as our +final area so I'll end there \ No newline at end of file diff --git a/Uk5DUtHY7LM.txt b/Uk5DUtHY7LM.txt new file mode 100644 index 0000000000000000000000000000000000000000..aa4fa6435deab36d569942ccd7644dcf09dc7026 --- /dev/null +++ b/Uk5DUtHY7LM.txt @@ -0,0 +1,12531 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay so I want to start out by reviewing + + align:start position:0% +okay so I want to start out by reviewing + + + align:start position:0% +okay so I want to start out by reviewing +a few things and putting putting some + + align:start position:0% +a few things and putting putting some + + + align:start position:0% +a few things and putting putting some +machinery together + + align:start position:0% +machinery together + + + align:start position:0% +machinery together +unfortunately this thing is sort of + + align:start position:0% +unfortunately this thing is sort of + + + align:start position:0% +unfortunately this thing is sort of +stuck we're going to need it later so I + + align:start position:0% +stuck we're going to need it later so I + + + align:start position:0% +stuck we're going to need it later so I +don't know I'll put it up for now so + + align:start position:0% +don't know I'll put it up for now so + + + align:start position:0% +don't know I'll put it up for now so +first just a bit of notation this symbol + + align:start position:0% +first just a bit of notation this symbol + + + align:start position:0% +first just a bit of notation this symbol +you should think of it like the dot + + align:start position:0% +you should think of it like the dot + + + align:start position:0% +you should think of it like the dot +product or the inner product it's just + + align:start position:0% +product or the inner product it's just + + + align:start position:0% +product or the inner product it's just +saying that bracket FG is the integral + + align:start position:0% +saying that bracket FG is the integral + + + align:start position:0% +saying that bracket FG is the integral +it's a number that you get so this is a + + align:start position:0% +it's a number that you get so this is a + + + align:start position:0% +it's a number that you get so this is a +number that you get from the function f + + align:start position:0% +number that you get from the function f + + + align:start position:0% +number that you get from the function f +in the function G by taking F taking its + + align:start position:0% +in the function G by taking F taking its + + + align:start position:0% +in the function G by taking F taking its +complex conjugate multiplying it by G + + align:start position:0% +complex conjugate multiplying it by G + + + align:start position:0% +complex conjugate multiplying it by G +and then integrating over all positions + + align:start position:0% +and then integrating over all positions + + + align:start position:0% +and then integrating over all positions +right so it's a way to get a number and + + align:start position:0% +right so it's a way to get a number and + + + align:start position:0% +right so it's a way to get a number and +you should think about it as the analog + + align:start position:0% +you should think about it as the analog + + + align:start position:0% +you should think about it as the analog +for functions of the dot product for + + align:start position:0% +for functions of the dot product for + + + align:start position:0% +for functions of the dot product for +vectors it's a way to get a number out + + align:start position:0% +vectors it's a way to get a number out + + + align:start position:0% +vectors it's a way to get a number out +of two vectors and so for example with + + align:start position:0% +of two vectors and so for example with + + + align:start position:0% +of two vectors and so for example with +vectors we could do V dot W and this is + + align:start position:0% +vectors we could do V dot W and this is + + + align:start position:0% +vectors we could do V dot W and this is +some number and it has a nice property + + align:start position:0% +some number and it has a nice property + + + align:start position:0% +some number and it has a nice property +that V dot V we can think of as V + + align:start position:0% +that V dot V we can think of as V + + + align:start position:0% +that V dot V we can think of as V +squared it's something like a length + + align:start position:0% +squared it's something like a length + + + align:start position:0% +squared it's something like a length +it's strictly positive and it's + + align:start position:0% +it's strictly positive and it's + + + align:start position:0% +it's strictly positive and it's +something like the length of a vector + + align:start position:0% +something like the length of a vector + + + align:start position:0% +something like the length of a vector +similarly if I take F and take its + + align:start position:0% +similarly if I take F and take its + + + align:start position:0% +similarly if I take F and take its +bracket with F this is equal to the + + align:start position:0% +bracket with F this is equal to the + + + align:start position:0% +bracket with F this is equal to the +integral DX of F squared and in + + align:start position:0% +integral DX of F squared and in + + + align:start position:0% +integral DX of F squared and in +particular F could be complex so f norm + + align:start position:0% +particular F could be complex so f norm + + + align:start position:0% +particular F could be complex so f norm +squared this is strictly non-negative it + + align:start position:0% +squared this is strictly non-negative it + + + align:start position:0% +squared this is strictly non-negative it +could vanish but it's not zero at a pole + + align:start position:0% +could vanish but it's not zero at a pole + + + align:start position:0% +could vanish but it's not zero at a pole +it's not negative at a point it's the + + align:start position:0% +it's not negative at a point it's the + + + align:start position:0% +it's not negative at a point it's the +norm squared so this will be zero if and + + align:start position:0% +norm squared so this will be zero if and + + + align:start position:0% +norm squared so this will be zero if and +only if what F is zero F is the zero + + align:start position:0% +only if what F is zero F is the zero + + + align:start position:0% +only if what F is zero F is the zero +function right so same way that the + + align:start position:0% +function right so same way that the + + + align:start position:0% +function right so same way that the +vector if you take a vector and you take + + align:start position:0% +vector if you take a vector and you take + + + align:start position:0% +vector if you take a vector and you take +its dot product with itself take it the + + align:start position:0% +its dot product with itself take it the + + + align:start position:0% +its dot product with itself take it the +norm it's zero if and only if the vector + + align:start position:0% +norm it's zero if and only if the vector + + + align:start position:0% +norm it's zero if and only if the vector +is zero so this beast satisfies a lot of + + align:start position:0% +is zero so this beast satisfies a lot of + + + align:start position:0% +is zero so this beast satisfies a lot of +the properties of a dot product you + + align:start position:0% +the properties of a dot product you + + + align:start position:0% +the properties of a dot product you +should think about it is morally + + align:start position:0% +should think about it is morally + + + align:start position:0% +should think about it is morally +equivalent we'll talk about that in more + + align:start position:0% +equivalent we'll talk about that in more + + + align:start position:0% +equivalent we'll talk about that in more +detail later second basic postulate of + + align:start position:0% +detail later second basic postulate of + + + align:start position:0% +detail later second basic postulate of +quantum mechanics to every observable is + + align:start position:0% +quantum mechanics to every observable is + + + align:start position:0% +quantum mechanics to every observable is +associated an operator and it's an + + align:start position:0% +associated an operator and it's an + + + align:start position:0% +associated an operator and it's an +operator acting on the space of + + align:start position:0% +operator acting on the space of + + + align:start position:0% +operator acting on the space of +functions are on the space of wave + + align:start position:0% +functions are on the space of wave + + + align:start position:0% +functions are on the space of wave +functions and to every operator + + align:start position:0% +functions and to every operator + + + align:start position:0% +functions and to every operator +corresponding to an observable in + + align:start position:0% +corresponding to an observable in + + + align:start position:0% +corresponding to an observable in +quantum mechanics are associated a + + align:start position:0% +quantum mechanics are associated a + + + align:start position:0% +quantum mechanics are associated a +special set of functions called the + + align:start position:0% +special set of functions called the + + + align:start position:0% +special set of functions called the +eigen functions such that when the + + align:start position:0% +eigen functions such that when the + + + align:start position:0% +eigen functions such that when the +operator acts on that function it gives + + align:start position:0% +operator acts on that function it gives + + + align:start position:0% +operator acts on that function it gives +you the same function back times a + + align:start position:0% +you the same function back times a + + + align:start position:0% +you the same function back times a +constant what these functions mean + + align:start position:0% +constant what these functions mean + + + align:start position:0% +constant what these functions mean +physically is they are the wave + + align:start position:0% +physically is they are the wave + + + align:start position:0% +physically is they are the wave +functions describing configurations with + + align:start position:0% +functions describing configurations with + + + align:start position:0% +functions describing configurations with +a definite value of the corresponding + + align:start position:0% +a definite value of the corresponding + + + align:start position:0% +a definite value of the corresponding +observable if I'm in an eigen + + align:start position:0% +observable if I'm in an eigen + + + align:start position:0% +observable if I'm in an eigen +function of position with eigenvalue x + + align:start position:0% +function of position with eigenvalue x + + + align:start position:0% +function of position with eigenvalue x +not awesome thank you AV person thank + + align:start position:0% +not awesome thank you AV person thank + + + align:start position:0% +not awesome thank you AV person thank +you so if if if your system is described + + align:start position:0% +you so if if if your system is described + + + align:start position:0% +you so if if if your system is described +by a wave function which is an + + align:start position:0% +by a wave function which is an + + + align:start position:0% +by a wave function which is an +eigenfunction of the position operator + + align:start position:0% +eigenfunction of the position operator + + + align:start position:0% +eigenfunction of the position operator +with eigenvalue X naught that means you + + align:start position:0% +with eigenvalue X naught that means you + + + align:start position:0% +with eigenvalue X naught that means you +can be confident that the system isn't + + align:start position:0% +can be confident that the system isn't + + + align:start position:0% +can be confident that the system isn't +the configuration corresponding to + + align:start position:0% +the configuration corresponding to + + + align:start position:0% +the configuration corresponding to +having a definite position X naught + + align:start position:0% +having a definite position X naught + + + align:start position:0% +having a definite position X naught +right it's not a superposition of + + align:start position:0% +right it's not a superposition of + + + align:start position:0% +right it's not a superposition of +different positions it is at X naught + + align:start position:0% +different positions it is at X naught + + + align:start position:0% +different positions it is at X naught +similarly momentum momentum has + + align:start position:0% +similarly momentum momentum has + + + align:start position:0% +similarly momentum momentum has +eigenfunctions and we know what these + + align:start position:0% +eigenfunctions and we know what these + + + align:start position:0% +eigenfunctions and we know what these +guys are these are the Exponential's e + + align:start position:0% +guys are these are the Exponential's e + + + align:start position:0% +guys are these are the Exponential's e +to the ikx s they're the eigenfunctions + + align:start position:0% +to the ikx s they're the eigenfunctions + + + align:start position:0% +to the ikx s they're the eigenfunctions +and those are the wave functions + + align:start position:0% +and those are the wave functions + + + align:start position:0% +and those are the wave functions +describing states with definite value of + + align:start position:0% +describing states with definite value of + + + align:start position:0% +describing states with definite value of +the of the momentum of the Associated + + align:start position:0% +the of the momentum of the Associated + + + align:start position:0% +the of the momentum of the Associated +observable energy as an operator energy + + align:start position:0% +observable energy as an operator energy + + + align:start position:0% +observable energy as an operator energy +is an as described by an operator which + + align:start position:0% +is an as described by an operator which + + + align:start position:0% +is an as described by an operator which +has good which has eigenfunctions which + + align:start position:0% +has good which has eigenfunctions which + + + align:start position:0% +has good which has eigenfunctions which +I'll call Phi sub n with energy Z sub n + + align:start position:0% +I'll call Phi sub n with energy Z sub n + + + align:start position:0% +I'll call Phi sub n with energy Z sub n +those are the eigenvalues and if I tell + + align:start position:0% +those are the eigenvalues and if I tell + + + align:start position:0% +those are the eigenvalues and if I tell +you that your wave function is the state + + align:start position:0% +you that your wave function is the state + + + align:start position:0% +you that your wave function is the state +Phi sub 2 what that tells you is that + + align:start position:0% +Phi sub 2 what that tells you is that + + + align:start position:0% +Phi sub 2 what that tells you is that +the system has a definite energy e sub 2 + + align:start position:0% +the system has a definite energy e sub 2 + + + align:start position:0% +the system has a definite energy e sub 2 +corresponding to that eigenvalue cool + + align:start position:0% +corresponding to that eigenvalue cool + + + align:start position:0% +corresponding to that eigenvalue cool +and this is true for any physical + + align:start position:0% +and this is true for any physical + + + align:start position:0% +and this is true for any physical +observable but these are sort of the + + align:start position:0% +observable but these are sort of the + + + align:start position:0% +observable but these are sort of the +basic ones that we'll keep focusing on + + align:start position:0% +basic ones that we'll keep focusing on + + + align:start position:0% +basic ones that we'll keep focusing on +position momentum and energy for the + + align:start position:0% +position momentum and energy for the + + + align:start position:0% +position momentum and energy for the +next while okay now a nice property + + align:start position:0% +next while okay now a nice property + + + align:start position:0% +next while okay now a nice property +about these eigenfunctions is that for + + align:start position:0% +about these eigenfunctions is that for + + + align:start position:0% +about these eigenfunctions is that for +different eigenvalues the Associated + + align:start position:0% +different eigenvalues the Associated + + + align:start position:0% +different eigenvalues the Associated +wave functions are different functions + + align:start position:0% +wave functions are different functions + + + align:start position:0% +wave functions are different functions +and what I mean by saying there are + + align:start position:0% +and what I mean by saying there are + + + align:start position:0% +and what I mean by saying there are +different functions that they're + + align:start position:0% +different functions that they're + + + align:start position:0% +different functions that they're +actually orthogonal functions in the + + align:start position:0% +actually orthogonal functions in the + + + align:start position:0% +actually orthogonal functions in the +sense of this dot product if I have a + + align:start position:0% +sense of this dot product if I have a + + + align:start position:0% +sense of this dot product if I have a +state corresponding to be it at X 0 + + align:start position:0% +state corresponding to be it at X 0 + + + align:start position:0% +state corresponding to be it at X 0 +definite position X 0 that means I'm an + + align:start position:0% +definite position X 0 that means I'm an + + + align:start position:0% +definite position X 0 that means I'm an +eigenfunction of position with + + align:start position:0% +eigenfunction of position with + + + align:start position:0% +eigenfunction of position with +eigenvalue X 0 and I have another that + + align:start position:0% +eigenvalue X 0 and I have another that + + + align:start position:0% +eigenvalue X 0 and I have another that +corresponds to being at X 1 an eigen + + align:start position:0% +corresponds to being at X 1 an eigen + + + align:start position:0% +corresponds to being at X 1 an eigen +function of the position operator the + + align:start position:0% +function of the position operator the + + + align:start position:0% +function of the position operator the +eigenvalue x 1 then these wave functions + + align:start position:0% +eigenvalue x 1 then these wave functions + + + align:start position:0% +eigenvalue x 1 then these wave functions +are orthogonal to each other ie we get 0 + + align:start position:0% +are orthogonal to each other ie we get 0 + + + align:start position:0% +are orthogonal to each other ie we get 0 +if X naught is not equal to X 1 let me + + align:start position:0% +if X naught is not equal to X 1 let me + + + align:start position:0% +if X naught is not equal to X 1 let me +call that now meanwhile not only are + + align:start position:0% +call that now meanwhile not only are + + + align:start position:0% +call that now meanwhile not only are +they orthogonal but they're normalized + + align:start position:0% +they orthogonal but they're normalized + + + align:start position:0% +they orthogonal but they're normalized +in a particular way the inner product + + align:start position:0% +in a particular way the inner product + + + align:start position:0% +in a particular way the inner product +gives me a delta function which goes + + align:start position:0% +gives me a delta function which goes + + + align:start position:0% +gives me a delta function which goes +beep once so that if I integrate against + + align:start position:0% +beep once so that if I integrate against + + + align:start position:0% +beep once so that if I integrate against +it I get a 1 + + align:start position:0% +it I get a 1 + + + align:start position:0% +it I get a 1 +same thing with momentum and you do this + + align:start position:0% +same thing with momentum and you do this + + + align:start position:0% +same thing with momentum and you do this +this you're checking on the problem set + + align:start position:0% +this you're checking on the problem set + + + align:start position:0% +this you're checking on the problem set +I don't know if it was last one or this + + align:start position:0% +I don't know if it was last one or this + + + align:start position:0% +I don't know if it was last one or this +one + + align:start position:0% +one + + + align:start position:0% +one +and for the energies and energy one if I + + align:start position:0% +and for the energies and energy one if I + + + align:start position:0% +and for the energies and energy one if I +know the system is in state energy one + + align:start position:0% +know the system is in state energy one + + + align:start position:0% +know the system is in state energy one +and one let's say energy sub N and E sub + + align:start position:0% +and one let's say energy sub N and E sub + + + align:start position:0% +and one let's say energy sub N and E sub +m those are different states if N and M + + align:start position:0% +m those are different states if N and M + + + align:start position:0% +m those are different states if N and M +are not equal to each other and this + + align:start position:0% +are not equal to each other and this + + + align:start position:0% +are not equal to each other and this +inner product is 0 if n and M are not + + align:start position:0% +inner product is 0 if n and M are not + + + align:start position:0% +inner product is 0 if n and M are not +equal to each other and 1 if they are + + align:start position:0% +equal to each other and 1 if they are + + + align:start position:0% +equal to each other and 1 if they are +the properly normalized I recall that + + align:start position:0% +the properly normalized I recall that + + + align:start position:0% +the properly normalized I recall that +yeah absolutely it is absolutely + + align:start position:0% +yeah absolutely it is absolutely + + + align:start position:0% +yeah absolutely it is absolutely +possible for two eigenfunctions to have + + align:start position:0% +possible for two eigenfunctions to have + + + align:start position:0% +possible for two eigenfunctions to have +the same eigenvalue that is certainly + + align:start position:0% +the same eigenvalue that is certainly + + + align:start position:0% +the same eigenvalue that is certainly +possible yeah good so um + + align:start position:0% +possible yeah good so um + + + align:start position:0% +possible yeah good so um +so here's a crude thank you this is a + + align:start position:0% +so here's a crude thank you this is a + + + align:start position:0% +so here's a crude thank you this is a +good technicality that I didn't want to + + align:start position:0% +good technicality that I didn't want to + + + align:start position:0% +good technicality that I didn't want to +get into but I'll go ahead and get into + + align:start position:0% +get into but I'll go ahead and get into + + + align:start position:0% +get into but I'll go ahead and get into +it it's a very good question so the + + align:start position:0% +it it's a very good question so the + + + align:start position:0% +it it's a very good question so the +question is is it possible for two + + align:start position:0% +question is is it possible for two + + + align:start position:0% +question is is it possible for two +different eigenfunctions to have the + + align:start position:0% +different eigenfunctions to have the + + + align:start position:0% +different eigenfunctions to have the +same eigenvalue could there be two + + align:start position:0% +same eigenvalue could there be two + + + align:start position:0% +same eigenvalue could there be two +states with the same energy different + + align:start position:0% +states with the same energy different + + + align:start position:0% +states with the same energy different +states same energy yeah that's + + align:start position:0% +states same energy yeah that's + + + align:start position:0% +states same energy yeah that's +absolutely possible and we'll run into + + align:start position:0% +absolutely possible and we'll run into + + + align:start position:0% +absolutely possible and we'll run into +that and there's nice physics encoded in + + align:start position:0% +that and there's nice physics encoded in + + + align:start position:0% +that and there's nice physics encoded in +it but let's think about what that means + + align:start position:0% +it but let's think about what that means + + + align:start position:0% +it but let's think about what that means +that the subsequent question is well if + + align:start position:0% +that the subsequent question is well if + + + align:start position:0% +that the subsequent question is well if +that's the case are they really still + + align:start position:0% +that's the case are they really still + + + align:start position:0% +that's the case are they really still +orthogonal and here's the crucial thing + + align:start position:0% +orthogonal and here's the crucial thing + + + align:start position:0% +orthogonal and here's the crucial thing +the crucial thing is let's say take a 1 + + align:start position:0% +the crucial thing is let's say take a 1 + + + align:start position:0% +the crucial thing is let's say take a 1 +function I'll call the function f 1 or + + align:start position:0% +function I'll call the function f 1 or + + + align:start position:0% +function I'll call the function f 1 or +Phi 1 consider Phi 1 and let it have + + align:start position:0% +Phi 1 consider Phi 1 and let it have + + + align:start position:0% +Phi 1 consider Phi 1 and let it have +energy e 1 so that e acting on Phi 1 is + + align:start position:0% +energy e 1 so that e acting on Phi 1 is + + + align:start position:0% +energy e 1 so that e acting on Phi 1 is +equal to e 1 Phi 1 ok and let there be + + align:start position:0% +equal to e 1 Phi 1 ok and let there be + + + align:start position:0% +equal to e 1 Phi 1 ok and let there be +another function Phi 2 such that the + + align:start position:0% +another function Phi 2 such that the + + + align:start position:0% +another function Phi 2 such that the +energy operator acting on Phi 2 is also + + align:start position:0% +energy operator acting on Phi 2 is also + + + align:start position:0% +energy operator acting on Phi 2 is also +equal to e 1 Phi 2 these are set to be + + align:start position:0% +equal to e 1 Phi 2 these are set to be + + + align:start position:0% +equal to e 1 Phi 2 these are set to be +degenerate degenerate doesn't mean you + + align:start position:0% +degenerate degenerate doesn't mean you + + + align:start position:0% +degenerate degenerate doesn't mean you +go out and trash your card degenerate + + align:start position:0% +go out and trash your card degenerate + + + align:start position:0% +go out and trash your card degenerate +means that the energies are the same + + align:start position:0% +means that the energies are the same + + + align:start position:0% +means that the energies are the same +there is yeah okay so what does this + + align:start position:0% +there is yeah okay so what does this + + + align:start position:0% +there is yeah okay so what does this +tell me this tells me a cool fact if I + + align:start position:0% +tell me this tells me a cool fact if I + + + align:start position:0% +tell me this tells me a cool fact if I +take a wave function Phi and I will call + + align:start position:0% +take a wave function Phi and I will call + + + align:start position:0% +take a wave function Phi and I will call +this Phi star in on R Street kulkarni so + + align:start position:0% +this Phi star in on R Street kulkarni so + + + align:start position:0% +this Phi star in on R Street kulkarni so +I've got this Phi star which is a linear + + align:start position:0% +I've got this Phi star which is a linear + + + align:start position:0% +I've got this Phi star which is a linear +combination alpha Phi 1 plus beta fi 2 a + + align:start position:0% +combination alpha Phi 1 plus beta fi 2 a + + + align:start position:0% +combination alpha Phi 1 plus beta fi 2 a +linear combination of them a + + align:start position:0% +linear combination of them a + + + align:start position:0% +linear combination of them a +superposition of those two states is + + align:start position:0% +superposition of those two states is + + + align:start position:0% +superposition of those two states is +this also an energy eigenfunction yeah + + align:start position:0% +this also an energy eigenfunction yeah + + + align:start position:0% +this also an energy eigenfunction yeah +because if I act on e on Phi star with E + + align:start position:0% +because if I act on e on Phi star with E + + + align:start position:0% +because if I act on e on Phi star with E +then that's its linear so e acting on + + align:start position:0% +then that's its linear so e acting on + + + align:start position:0% +then that's its linear so e acting on +Phi star is e acting on Alpha Phi 1 + + align:start position:0% +Phi star is e acting on Alpha Phi 1 + + + align:start position:0% +Phi star is e acting on Alpha Phi 1 +alpha Z constant doesn't care + + align:start position:0% +alpha Z constant doesn't care + + + align:start position:0% +alpha Z constant doesn't care +Phi 1 gives me an e 1 similarly e acting + + align:start position:0% +Phi 1 gives me an e 1 similarly e acting + + + align:start position:0% +Phi 1 gives me an e 1 similarly e acting +on Phi 2 gives me an e 1 so this is + + align:start position:0% +on Phi 2 gives me an e 1 so this is + + + align:start position:0% +on Phi 2 gives me an e 1 so this is +equal to if I act + + align:start position:0% +equal to if I act + + + align:start position:0% +equal to if I act +II on this guy this is equal to from + + align:start position:0% +II on this guy this is equal to from + + + align:start position:0% +II on this guy this is equal to from +both of these I get an overall factor of + + align:start position:0% +both of these I get an overall factor of + + + align:start position:0% +both of these I get an overall factor of +u1 so notice that we get the same vector + + align:start position:0% +u1 so notice that we get the same vector + + + align:start position:0% +u1 so notice that we get the same vector +back times a constant a common constant + + align:start position:0% +back times a constant a common constant + + + align:start position:0% +back times a constant a common constant +so when we have degenerate eigen + + align:start position:0% +so when we have degenerate eigen + + + align:start position:0% +so when we have degenerate eigen +functions we can take arbitrary linear + + align:start position:0% +functions we can take arbitrary linear + + + align:start position:0% +functions we can take arbitrary linear +combinations to them get another + + align:start position:0% +combinations to them get another + + + align:start position:0% +combinations to them get another +degenerate eigen function cool so this + + align:start position:0% +degenerate eigen function cool so this + + + align:start position:0% +degenerate eigen function cool so this +is like imagine I have a vector and I + + align:start position:0% +is like imagine I have a vector and I + + + align:start position:0% +is like imagine I have a vector and I +have another vector and they share the + + align:start position:0% +have another vector and they share the + + + align:start position:0% +have another vector and they share the +property that they're both + + align:start position:0% +property that they're both + + + align:start position:0% +property that they're both +eigenfunctions of some operator that + + align:start position:0% +eigenfunctions of some operator that + + + align:start position:0% +eigenfunctions of some operator that +means any linear combination of them is + + align:start position:0% +means any linear combination of them is + + + align:start position:0% +means any linear combination of them is +also right so there's a whole vector + + align:start position:0% +also right so there's a whole vector + + + align:start position:0% +also right so there's a whole vector +space there's a whole space of possible + + align:start position:0% +space there's a whole space of possible + + + align:start position:0% +space there's a whole space of possible +functions that all have the same eigen + + align:start position:0% +functions that all have the same eigen + + + align:start position:0% +functions that all have the same eigen +value so now you say well look are these + + align:start position:0% +value so now you say well look are these + + + align:start position:0% +value so now you say well look are these +two orthogonal to each other no these + + align:start position:0% +two orthogonal to each other no these + + + align:start position:0% +two orthogonal to each other no these +two no but here's the thing if you have + + align:start position:0% +two no but here's the thing if you have + + + align:start position:0% +two no but here's the thing if you have +a vector space if you have a space you + + align:start position:0% +a vector space if you have a space you + + + align:start position:0% +a vector space if you have a space you +can always find or THOG '''l guys and a + + align:start position:0% +can always find or THOG '''l guys and a + + + align:start position:0% +can always find or THOG '''l guys and a +basis for that space yes so while it's + + align:start position:0% +basis for that space yes so while it's + + + align:start position:0% +basis for that space yes so while it's +not true that they the eigenfunctions + + align:start position:0% +not true that they the eigenfunctions + + + align:start position:0% +not true that they the eigenfunctions +are always orthogonal it is true we will + + align:start position:0% +are always orthogonal it is true we will + + + align:start position:0% +are always orthogonal it is true we will +not prove this but we will discuss the + + align:start position:0% +not prove this but we will discuss the + + + align:start position:0% +not prove this but we will discuss the +proof of it later by pulling the + + align:start position:0% +proof of it later by pulling the + + + align:start position:0% +proof of it later by pulling the +mathematician out of the closet the + + align:start position:0% +mathematician out of the closet the + + + align:start position:0% +mathematician out of the closet the +proof will say that it is possible to + + align:start position:0% +proof will say that it is possible to + + + align:start position:0% +proof will say that it is possible to +find a set of eigenfunctions which are + + align:start position:0% +find a set of eigenfunctions which are + + + align:start position:0% +find a set of eigenfunctions which are +orthogonal in precisely this fashion + + align:start position:0% +orthogonal in precisely this fashion + + + align:start position:0% +orthogonal in precisely this fashion +even if there are degeneracies okay that + + align:start position:0% +even if there are degeneracies okay that + + + align:start position:0% +even if there are degeneracies okay that +theorem is called the spectral theorem + + align:start position:0% +theorem is called the spectral theorem + + + align:start position:0% +theorem is called the spectral theorem +and we'll discuss it later + + align:start position:0% +and we'll discuss it later + + + align:start position:0% +and we'll discuss it later +so it is always possible to do so but + + align:start position:0% +so it is always possible to do so but + + + align:start position:0% +so it is always possible to do so but +you must be alert that there may be + + align:start position:0% +you must be alert that there may be + + + align:start position:0% +you must be alert that there may be +degeneracies there aren't always + + align:start position:0% +degeneracies there aren't always + + + align:start position:0% +degeneracies there aren't always +degeneracies in fact degeneracies are + + align:start position:0% +degeneracies in fact degeneracies are + + + align:start position:0% +degeneracies in fact degeneracies are +very special why should two numbers + + align:start position:0% +very special why should two numbers + + + align:start position:0% +very special why should two numbers +happen to be the same something has to + + align:start position:0% +happen to be the same something has to + + + align:start position:0% +happen to be the same something has to +be forcing them to be the same and then + + align:start position:0% +be forcing them to be the same and then + + + align:start position:0% +be forcing them to be the same and then +that that's going to an important theme + + align:start position:0% +that that's going to an important theme + + + align:start position:0% +that that's going to an important theme +for us but but it certainly is possible + + align:start position:0% +for us but but it certainly is possible + + + align:start position:0% +for us but but it certainly is possible +good question other questions yeah + + align:start position:0% + + + + align:start position:0% + +yeah so using the triangular brackets it + + align:start position:0% +yeah so using the triangular brackets it + + + align:start position:0% +yeah so using the triangular brackets it +is al is a there's another notation for + + align:start position:0% +is al is a there's another notation for + + + align:start position:0% +is al is a there's another notation for +the same thing which is FG but this + + align:start position:0% +the same thing which is FG but this + + + align:start position:0% +the same thing which is FG but this +carries some slightly different weight + + align:start position:0% +carries some slightly different weight + + + align:start position:0% +carries some slightly different weight +it means something slightly you'll see + + align:start position:0% +it means something slightly you'll see + + + align:start position:0% +it means something slightly you'll see +this in books and this means something + + align:start position:0% +this in books and this means something + + + align:start position:0% +this in books and this means something +very similar to this + + align:start position:0% +very similar to this + + + align:start position:0% +very similar to this +but I'm not going to use this notation + + align:start position:0% +but I'm not going to use this notation + + + align:start position:0% +but I'm not going to use this notation +it's called Dirac notation we'll talk + + align:start position:0% +it's called Dirac notation we'll talk + + + align:start position:0% +it's called Dirac notation we'll talk +about it later in the semester but we're + + align:start position:0% +about it later in the semester but we're + + + align:start position:0% +about it later in the semester but we're +not going to talk about it just yet + + align:start position:0% +not going to talk about it just yet + + + align:start position:0% +not going to talk about it just yet +but you see this it means effectively it + + align:start position:0% +but you see this it means effectively it + + + align:start position:0% +but you see this it means effectively it +means the same thing as this this is + + align:start position:0% +means the same thing as this this is + + + align:start position:0% +means the same thing as this this is +sort of like dialect + + align:start position:0% +sort of like dialect + + + align:start position:0% +sort of like dialect +you know it's like French and québécois + + align:start position:0% +you know it's like French and québécois + + + align:start position:0% +you know it's like French and québécois +other questions + + align:start position:0% +other questions + + + align:start position:0% +other questions +my wife's Canadians other questions okay + + align:start position:0% +my wife's Canadians other questions okay + + + align:start position:0% +my wife's Canadians other questions okay +so given this fact given the fact that + + align:start position:0% +so given this fact given the fact that + + + align:start position:0% +so given this fact given the fact that +we can associate observables to + + align:start position:0% +we can associate observables to + + + align:start position:0% +we can associate observables to +operators operators come with special + + align:start position:0% +operators operators come with special + + + align:start position:0% +operators operators come with special +functions the eigenfunctions those + + align:start position:0% +functions the eigenfunctions those + + + align:start position:0% +functions the eigenfunctions those +eigenfunctions corresponding to have a + + align:start position:0% +eigenfunctions corresponding to have a + + + align:start position:0% +eigenfunctions corresponding to have a +definite value of the observable and + + align:start position:0% +definite value of the observable and + + + align:start position:0% +definite value of the observable and +they're orthonormal this tells us and + + align:start position:0% +they're orthonormal this tells us and + + + align:start position:0% +they're orthonormal this tells us and +this is really the statement of the + + align:start position:0% +this is really the statement of the + + + align:start position:0% +this is really the statement of the +spectral theorem that any function can + + align:start position:0% +spectral theorem that any function can + + + align:start position:0% +spectral theorem that any function can +be expanded in a basis of states with + + align:start position:0% +be expanded in a basis of states with + + + align:start position:0% +be expanded in a basis of states with +definite values of some observable so + + align:start position:0% +definite values of some observable so + + + align:start position:0% +definite values of some observable so +for example consider position I claim + + align:start position:0% +for example consider position I claim + + + align:start position:0% +for example consider position I claim +that any wave function can be expanded + + align:start position:0% +that any wave function can be expanded + + + align:start position:0% +that any wave function can be expanded +as a superposition of states with + + align:start position:0% +as a superposition of states with + + + align:start position:0% +as a superposition of states with +definite position so here is an + + align:start position:0% +definite position so here is an + + + align:start position:0% +definite position so here is an +arbitrary function here's a set of + + align:start position:0% +arbitrary function here's a set of + + + align:start position:0% +arbitrary function here's a set of +states with definite position the Delta + + align:start position:0% +states with definite position the Delta + + + align:start position:0% +states with definite position the Delta +functions and I can write any function + + align:start position:0% +functions and I can write any function + + + align:start position:0% +functions and I can write any function +as a superposition with some + + align:start position:0% +as a superposition with some + + + align:start position:0% +as a superposition with some +coefficients of states with definite + + align:start position:0% +coefficients of states with definite + + + align:start position:0% +coefficients of states with definite +position integrating over all possible + + align:start position:0% +position integrating over all possible + + + align:start position:0% +position integrating over all possible +positions X not yeah and this is also + + align:start position:0% +positions X not yeah and this is also + + + align:start position:0% +positions X not yeah and this is also +sort of trivially true because e in it + + align:start position:0% +sort of trivially true because e in it + + + align:start position:0% +sort of trivially true because e in it +what's this integral well it's an + + align:start position:0% +what's this integral well it's an + + + align:start position:0% +what's this integral well it's an +integral DX not over all possible + + align:start position:0% +integral DX not over all possible + + + align:start position:0% +integral DX not over all possible +positions of this Delta function but + + align:start position:0% +positions of this Delta function but + + + align:start position:0% +positions of this Delta function but +we're evaluating at X so this only this + + align:start position:0% +we're evaluating at X so this only this + + + align:start position:0% +we're evaluating at X so this only this +is 0 unless X is equal to X naught so I + + align:start position:0% +is 0 unless X is equal to X naught so I + + + align:start position:0% +is 0 unless X is equal to X naught so I +just put in X instead of X naught and + + align:start position:0% +just put in X instead of X naught and + + + align:start position:0% +just put in X instead of X naught and +that gives me 5x sort of tautological we + + align:start position:0% +that gives me 5x sort of tautological we + + + align:start position:0% +that gives me 5x sort of tautological we +can do the same thing for momentum + + align:start position:0% +can do the same thing for momentum + + + align:start position:0% +can do the same thing for momentum +eigenfunctions I claim that any function + + align:start position:0% +eigenfunctions I claim that any function + + + align:start position:0% +eigenfunctions I claim that any function +can be expanded in a superposition of + + align:start position:0% +can be expanded in a superposition of + + + align:start position:0% +can be expanded in a superposition of +momentum eigenfunctions where I sum over + + align:start position:0% +momentum eigenfunctions where I sum over + + + align:start position:0% +momentum eigenfunctions where I sum over +all possible values in the momentum with + + align:start position:0% +all possible values in the momentum with + + + align:start position:0% +all possible values in the momentum with +some weight right where this side tilde + + align:start position:0% +some weight right where this side tilde + + + align:start position:0% +some weight right where this side tilde +of K is just telling me how much + + align:start position:0% +of K is just telling me how much + + + align:start position:0% +of K is just telling me how much +amplitude there is at that wave number + + align:start position:0% +amplitude there is at that wave number + + + align:start position:0% +amplitude there is at that wave number +cool but this is the Fourier theorem + + align:start position:0% +cool but this is the Fourier theorem + + + align:start position:0% +cool but this is the Fourier theorem +it's a Fourier expansion so purely + + align:start position:0% +it's a Fourier expansion so purely + + + align:start position:0% +it's a Fourier expansion so purely +mathematically we know that this is true + + align:start position:0% +mathematically we know that this is true + + + align:start position:0% +mathematically we know that this is true +ok but there's also the physical + + align:start position:0% +ok but there's also the physical + + + align:start position:0% +ok but there's also the physical +statement any state can be expressed as + + align:start position:0% +statement any state can be expressed as + + + align:start position:0% +statement any state can be expressed as +a superposition of states with definite + + align:start position:0% +a superposition of states with definite + + + align:start position:0% +a superposition of states with definite +momentum there's math in here but + + align:start position:0% +momentum there's math in here but + + + align:start position:0% +momentum there's math in here but +there's also physics in finally this is + + align:start position:0% +there's also physics in finally this is + + + align:start position:0% +there's also physics in finally this is +less obvious from a mathematical point + + align:start position:0% +less obvious from a mathematical point + + + align:start position:0% +less obvious from a mathematical point +of view because Evan even told you what + + align:start position:0% +of view because Evan even told you what + + + align:start position:0% +of view because Evan even told you what +energy is any wave function can be + + align:start position:0% +energy is any wave function can be + + + align:start position:0% +energy is any wave function can be +banded in states with definite energy so + + align:start position:0% +banded in states with definite energy so + + + align:start position:0% +banded in states with definite energy so +this is a state my state en with + + align:start position:0% +this is a state my state en with + + + align:start position:0% +this is a state my state en with +definite energy with some coefficient + + align:start position:0% +definite energy with some coefficient + + + align:start position:0% +definite energy with some coefficient +summed over all possible values of the + + align:start position:0% +summed over all possible values of the + + + align:start position:0% +summed over all possible values of the +energy okay given any physical + + align:start position:0% +energy okay given any physical + + + align:start position:0% +energy okay given any physical +observable any physical observable + + align:start position:0% +observable any physical observable + + + align:start position:0% +observable any physical observable +momentum position angular momentum + + align:start position:0% +momentum position angular momentum + + + align:start position:0% +momentum position angular momentum +whatever + + align:start position:0% +whatever + + + align:start position:0% +whatever +given any physical observable a given + + align:start position:0% +given any physical observable a given + + + align:start position:0% +given any physical observable a given +wave function can be expanded as some + + align:start position:0% +wave function can be expanded as some + + + align:start position:0% +wave function can be expanded as some +superposition of having definite values + + align:start position:0% +superposition of having definite values + + + align:start position:0% +superposition of having definite values +of that will it in general have definite + + align:start position:0% +of that will it in general have definite + + + align:start position:0% +of that will it in general have definite +values of the observable will a general + + align:start position:0% +values of the observable will a general + + + align:start position:0% +values of the observable will a general +state be an energy eigenfunction no but + + align:start position:0% +state be an energy eigenfunction no but + + + align:start position:0% +state be an energy eigenfunction no but +any state is a superposition of energy + + align:start position:0% +any state is a superposition of energy + + + align:start position:0% +any state is a superposition of energy +eigenfunctions will a definite state or + + align:start position:0% +eigenfunctions will a definite state or + + + align:start position:0% +eigenfunctions will a definite state or +a random state have a definite position + + align:start position:0% +a random state have a definite position + + + align:start position:0% +a random state have a definite position +certainly not you could have this wave + + align:start position:0% +certainly not you could have this wave + + + align:start position:0% +certainly not you could have this wave +function write superposition yeah such + + align:start position:0% +function write superposition yeah such + + + align:start position:0% +function write superposition yeah such +that you can make an arbitrary state + + align:start position:0% +that you can make an arbitrary state + + + align:start position:0% +that you can make an arbitrary state +with a countable number of energy + + align:start position:0% +with a countable number of energy + + + align:start position:0% +with a countable number of energy +eigenfunctions rather than having to do + + align:start position:0% +eigenfunctions rather than having to do + + + align:start position:0% +eigenfunctions rather than having to do +a continuous excellent question so i + + align:start position:0% +a continuous excellent question so i + + + align:start position:0% +a continuous excellent question so i +mean a phrase that slightly differently + + align:start position:0% +mean a phrase that slightly differently + + + align:start position:0% +mean a phrase that slightly differently +it's an excellent question we'll come to + + align:start position:0% +it's an excellent question we'll come to + + + align:start position:0% +it's an excellent question we'll come to +that at the end of today's lecture so + + align:start position:0% +that at the end of today's lecture so + + + align:start position:0% +that at the end of today's lecture so +the question is this those are integrals + + align:start position:0% +the question is this those are integrals + + + align:start position:0% +the question is this those are integrals +that is a sum over discrete things why + + align:start position:0% +that is a sum over discrete things why + + + align:start position:0% +that is a sum over discrete things why +why is the possible values of position + + align:start position:0% +why is the possible values of position + + + align:start position:0% +why is the possible values of position +continuous possible values momentum + + align:start position:0% +continuous possible values momentum + + + align:start position:0% +continuous possible values momentum +continuous the possible values of energy + + align:start position:0% +continuous the possible values of energy + + + align:start position:0% +continuous the possible values of energy +discrete the answer to this will will + + align:start position:0% +discrete the answer to this will will + + + align:start position:0% +discrete the answer to this will will +become apparent over the course of your + + align:start position:0% +become apparent over the course of your + + + align:start position:0% +become apparent over the course of your +next few problem sets you have to do + + align:start position:0% +next few problem sets you have to do + + + align:start position:0% +next few problem sets you have to do +some problems to get your fingers dirty + + align:start position:0% +some problems to get your fingers dirty + + + align:start position:0% +some problems to get your fingers dirty +you to really understand this but here's + + align:start position:0% +you to really understand this but here's + + + align:start position:0% +you to really understand this but here's +the statement and we'll see the first + + align:start position:0% +the statement and we'll see the first + + + align:start position:0% +the statement and we'll see the first +version of this at the end of today's + + align:start position:0% +version of this at the end of today's + + + align:start position:0% +version of this at the end of today's +lecture + + align:start position:0% +lecture + + + align:start position:0% +lecture +sometimes the allowed energies of a + + align:start position:0% +sometimes the allowed energies of a + + + align:start position:0% +sometimes the allowed energies of a +system the energy eigenvalues are + + align:start position:0% +system the energy eigenvalues are + + + align:start position:0% +system the energy eigenvalues are +discrete sometimes they are continuous + + align:start position:0% +discrete sometimes they are continuous + + + align:start position:0% +discrete sometimes they are continuous +they will be discrete when you have + + align:start position:0% +they will be discrete when you have + + + align:start position:0% +they will be discrete when you have +bound States states that are trapped in + + align:start position:0% +bound States states that are trapped in + + + align:start position:0% +bound States states that are trapped in +some region and aren't allowed to get + + align:start position:0% +some region and aren't allowed to get + + + align:start position:0% +some region and aren't allowed to get +arbitrarily far away they will be + + align:start position:0% +arbitrarily far away they will be + + + align:start position:0% +arbitrarily far away they will be +continuous when you have states that + + align:start position:0% +continuous when you have states that + + + align:start position:0% +continuous when you have states that +that it can get arbitrarily far away + + align:start position:0% +that it can get arbitrarily far away + + + align:start position:0% +that it can get arbitrarily far away +sometimes the momentum will be allowed + + align:start position:0% +sometimes the momentum will be allowed + + + align:start position:0% +sometimes the momentum will be allowed +to be a discrete value sometimes it will + + align:start position:0% +to be a discrete value sometimes it will + + + align:start position:0% +to be a discrete value sometimes it will +be allowed to be continuous values and + + align:start position:0% +be allowed to be continuous values and + + + align:start position:0% +be allowed to be continuous values and +we'll see exactly why subsequently but + + align:start position:0% +we'll see exactly why subsequently but + + + align:start position:0% +we'll see exactly why subsequently but +the thing I one emphasize is that I'm + + align:start position:0% +the thing I one emphasize is that I'm + + + align:start position:0% +the thing I one emphasize is that I'm +writing this to emphasize that it's + + align:start position:0% +writing this to emphasize that it's + + + align:start position:0% +writing this to emphasize that it's +possible that each of these can be + + align:start position:0% +possible that each of these can be + + + align:start position:0% +possible that each of these can be +discrete or continuous the important + + align:start position:0% +discrete or continuous the important + + + align:start position:0% +discrete or continuous the important +thing is that once you pick your + + align:start position:0% +thing is that once you pick your + + + align:start position:0% +thing is that once you pick your +physical system you ask + + align:start position:0% +physical system you ask + + + align:start position:0% +physical system you ask +what are the allowed values of position + + align:start position:0% +what are the allowed values of position + + + align:start position:0% +what are the allowed values of position +what are the allowed values of momentum + + align:start position:0% +what are the allowed values of momentum + + + align:start position:0% +what are the allowed values of momentum +and what are the allowed values of + + align:start position:0% +and what are the allowed values of + + + align:start position:0% +and what are the allowed values of +energy and then you sum over all + + align:start position:0% +energy and then you sum over all + + + align:start position:0% +energy and then you sum over all +possible values now in the examples we + + align:start position:0% +possible values now in the examples we + + + align:start position:0% +possible values now in the examples we +looked at yesterday or last lecture the + + align:start position:0% +looked at yesterday or last lecture the + + + align:start position:0% +looked at yesterday or last lecture the +energy could have been discrete as in + + align:start position:0% +energy could have been discrete as in + + + align:start position:0% +energy could have been discrete as in +the case of the infinite well or + + align:start position:0% +the case of the infinite well or + + + align:start position:0% +the case of the infinite well or +continuous as in the case of the free + + align:start position:0% +continuous as in the case of the free + + + align:start position:0% +continuous as in the case of the free +particle in the case of a continuous + + align:start position:0% +particle in the case of a continuous + + + align:start position:0% +particle in the case of a continuous +particle this would have been an + + align:start position:0% +particle this would have been an + + + align:start position:0% +particle this would have been an +integral in the Katyn sorry in the case + + align:start position:0% +integral in the Katyn sorry in the case + + + align:start position:0% +integral in the Katyn sorry in the case +of a system such as a free particle + + align:start position:0% +of a system such as a free particle + + + align:start position:0% +of a system such as a free particle +where the energy could take any of a + + align:start position:0% +where the energy could take any of a + + + align:start position:0% +where the energy could take any of a +continuous number of possible values + + align:start position:0% +continuous number of possible values + + + align:start position:0% +continuous number of possible values +this would be a continuous integral to + + align:start position:0% +this would be a continuous integral to + + + align:start position:0% +this would be a continuous integral to +deal with that I'm often going to use + + align:start position:0% +deal with that I'm often going to use + + + align:start position:0% +deal with that I'm often going to use +the notation just shorthand integral sum + + align:start position:0% +the notation just shorthand integral sum + + + align:start position:0% +the notation just shorthand integral sum +because I which I know is a horrible + + align:start position:0% +because I which I know is a horrible + + + align:start position:0% +because I which I know is a horrible +bastardization of all that's good and + + align:start position:0% +bastardization of all that's good and + + + align:start position:0% +bastardization of all that's good and +just but on the other hand emphasizes + + align:start position:0% +just but on the other hand emphasizes + + + align:start position:0% +just but on the other hand emphasizes +the fact that it's a in some systems you + + align:start position:0% +the fact that it's a in some systems you + + + align:start position:0% +the fact that it's a in some systems you +will get continuous in some systems + + align:start position:0% +will get continuous in some systems + + + align:start position:0% +will get continuous in some systems +discrete and sometimes you'll have both + + align:start position:0% +discrete and sometimes you'll have both + + + align:start position:0% +discrete and sometimes you'll have both +continuous and discrete for example in a + + align:start position:0% +continuous and discrete for example in a + + + align:start position:0% +continuous and discrete for example in a +hydrogen in hydrogen we will find that + + align:start position:0% +hydrogen in hydrogen we will find that + + + align:start position:0% +hydrogen in hydrogen we will find that +there are bound states where the + + align:start position:0% +there are bound states where the + + + align:start position:0% +there are bound states where the +electron is stuck to the hydrogen + + align:start position:0% +electron is stuck to the hydrogen + + + align:start position:0% +electron is stuck to the hydrogen +nucleus to the proton and there are + + align:start position:0% +nucleus to the proton and there are + + + align:start position:0% +nucleus to the proton and there are +discrete allowed energy levels for that + + align:start position:0% +discrete allowed energy levels for that + + + align:start position:0% +discrete allowed energy levels for that +configuration however once you I + + align:start position:0% +configuration however once you I + + + align:start position:0% +configuration however once you I +envision the electron can have any + + align:start position:0% +envision the electron can have any + + + align:start position:0% +envision the electron can have any +energy you want it's no longer bound it + + align:start position:0% +energy you want it's no longer bound it + + + align:start position:0% +energy you want it's no longer bound it +can just get arbitrarily far away and + + align:start position:0% +can just get arbitrarily far away and + + + align:start position:0% +can just get arbitrarily far away and +there are an uncountable infinity a + + align:start position:0% +there are an uncountable infinity a + + + align:start position:0% +there are an uncountable infinity a +continuous Vout set of possible States + + align:start position:0% +continuous Vout set of possible States + + + align:start position:0% +continuous Vout set of possible States +so in that situation we'll find that we + + align:start position:0% +so in that situation we'll find that we + + + align:start position:0% +so in that situation we'll find that we +have both the discrete and a continuous + + align:start position:0% +have both the discrete and a continuous + + + align:start position:0% +have both the discrete and a continuous +series of possible States + + align:start position:0% +series of possible States + + + align:start position:0% +series of possible States +yeah yeah sure if you work on a lattice + + align:start position:0% +yeah yeah sure if you work on a lattice + + + align:start position:0% +yeah yeah sure if you work on a lattice +so for example consider the following + + align:start position:0% +so for example consider the following + + + align:start position:0% +so for example consider the following +quantum system I have an undergraduate + + align:start position:0% +quantum system I have an undergraduate + + + align:start position:0% +quantum system I have an undergraduate +and that undergraduate has been placed + + align:start position:0% +and that undergraduate has been placed + + + align:start position:0% +and that undergraduate has been placed +in one of 12 boxes ok now what's the + + align:start position:0% +in one of 12 boxes ok now what's the + + + align:start position:0% +in one of 12 boxes ok now what's the +state of the undergraduate I don't know + + align:start position:0% +state of the undergraduate I don't know + + + align:start position:0% +state of the undergraduate I don't know +is it a definite position state it might + + align:start position:0% +is it a definite position state it might + + + align:start position:0% +is it a definite position state it might +be but probably it's a superposition of + + align:start position:0% +be but probably it's a superposition of + + + align:start position:0% +be but probably it's a superposition of +an arbitrary superposition right + + align:start position:0% +an arbitrary superposition right + + + align:start position:0% +an arbitrary superposition right +a very impressive undergraduates at MIT + + align:start position:0% +a very impressive undergraduates at MIT + + + align:start position:0% +a very impressive undergraduates at MIT +so ok other questions yeah this is hole + + align:start position:0% +so ok other questions yeah this is hole + + + align:start position:0% +so ok other questions yeah this is hole +even + + align:start position:0% +even + + + align:start position:0% +even +changes overtime excellent question + + align:start position:0% +changes overtime excellent question + + + align:start position:0% +changes overtime excellent question +we'll come back to that very good + + align:start position:0% +we'll come back to that very good + + + align:start position:0% +we'll come back to that very good +question leading question okay so we + + align:start position:0% +question leading question okay so we + + + align:start position:0% +question leading question okay so we +have this the next thing is that energy + + align:start position:0% +have this the next thing is that energy + + + align:start position:0% +have this the next thing is that energy +eigenfunctions satisfy some very special + + align:start position:0% +eigenfunctions satisfy some very special + + + align:start position:0% +eigenfunctions satisfy some very special +properties right and in particular + + align:start position:0% +properties right and in particular + + + align:start position:0% +properties right and in particular +energy eigenfunctions have the property + + align:start position:0% +energy eigenfunctions have the property + + + align:start position:0% +energy eigenfunctions have the property +from the straining equation I h-bar + + align:start position:0% +from the straining equation I h-bar + + + align:start position:0% +from the straining equation I h-bar +DT on sigh of X and T is equal to the + + align:start position:0% +DT on sigh of X and T is equal to the + + + align:start position:0% +DT on sigh of X and T is equal to the +energy operator acting on sine of X and + + align:start position:0% +energy operator acting on sine of X and + + + align:start position:0% +energy operator acting on sine of X and +T this tells us that if we have sine X + + align:start position:0% +T this tells us that if we have sine X + + + align:start position:0% +T this tells us that if we have sine X +naught time t0 is equal to Phi n of X as + + align:start position:0% +naught time t0 is equal to Phi n of X as + + + align:start position:0% +naught time t0 is equal to Phi n of X as +we saw last time then the wave function + + align:start position:0% +we saw last time then the wave function + + + align:start position:0% +we saw last time then the wave function +sine at X at time T is equal to Phi n of + + align:start position:0% +sine at X at time T is equal to Phi n of + + + align:start position:0% +sine at X at time T is equal to Phi n of +X and it only changes by an overall + + align:start position:0% +X and it only changes by an overall + + + align:start position:0% +X and it only changes by an overall +phase e to the minus I en T over H bar + + align:start position:0% +phase e to the minus I en T over H bar + + + align:start position:0% +phase e to the minus I en T over H bar +and this ratio en upon H bar will often + + align:start position:0% +and this ratio en upon H bar will often + + + align:start position:0% +and this ratio en upon H bar will often +be written Omega n is equal to en over H + + align:start position:0% +be written Omega n is equal to en over H + + + align:start position:0% +be written Omega n is equal to en over H +bar this is just the de briare relations + + align:start position:0% +bar this is just the de briare relations + + + align:start position:0% +bar this is just the de briare relations +okay I recall that so our energy + + align:start position:0% +okay I recall that so our energy + + + align:start position:0% +okay I recall that so our energy +eigenfunctions you know are how to say + + align:start position:0% +eigenfunctions you know are how to say + + + align:start position:0% +eigenfunctions you know are how to say +no to possible wave functions are no + + align:start position:0% +no to possible wave functions are no + + + align:start position:0% +no to possible wave functions are no +wave which is more morally good than + + align:start position:0% +wave which is more morally good than + + + align:start position:0% +wave which is more morally good than +another but some are particularly + + align:start position:0% +another but some are particularly + + + align:start position:0% +another but some are particularly +convenient energy eigenfunctions have + + align:start position:0% +convenient energy eigenfunctions have + + + align:start position:0% +convenient energy eigenfunctions have +the nice property that while they're not + + align:start position:0% +the nice property that while they're not + + + align:start position:0% +the nice property that while they're not +a definite position they don't + + align:start position:0% +a definite position they don't + + + align:start position:0% +a definite position they don't +necessarily have a definite momentum + + align:start position:0% +necessarily have a definite momentum + + + align:start position:0% +necessarily have a definite momentum +they do evolve over time in a + + align:start position:0% +they do evolve over time in a + + + align:start position:0% +they do evolve over time in a +particularly simple way okay and that + + align:start position:0% +particularly simple way okay and that + + + align:start position:0% +particularly simple way okay and that +allows me that and the superposition + + align:start position:0% +allows me that and the superposition + + + align:start position:0% +allows me that and the superposition +principle allow me to write the + + align:start position:0% +principle allow me to write the + + + align:start position:0% +principle allow me to write the +following if I know that this is my wave + + align:start position:0% +following if I know that this is my wave + + + align:start position:0% +following if I know that this is my wave +function at sy at x times 0 okay so + + align:start position:0% +function at sy at x times 0 okay so + + + align:start position:0% +function at sy at x times 0 okay so +let's say in all these cases this is + + align:start position:0% +let's say in all these cases this is + + + align:start position:0% +let's say in all these cases this is +sine of X at time 0 how does this state + + align:start position:0% +sine of X at time 0 how does this state + + + align:start position:0% +sine of X at time 0 how does this state +evolve forward in time it's kind of + + align:start position:0% +evolve forward in time it's kind of + + + align:start position:0% +evolve forward in time it's kind of +complicated how does this description + + align:start position:0% +complicated how does this description + + + align:start position:0% +complicated how does this description +how does sy tilde of K evolve for it in + + align:start position:0% +how does sy tilde of K evolve for it in + + + align:start position:0% +how does sy tilde of K evolve for it in +time again kind of complicated but when + + align:start position:0% +time again kind of complicated but when + + + align:start position:0% +time again kind of complicated but when +I express in terms of the energy + + align:start position:0% +I express in terms of the energy + + + align:start position:0% +I express in terms of the energy +eigenstates the answer to how it evolved + + align:start position:0% +eigenstates the answer to how it evolved + + + align:start position:0% +eigenstates the answer to how it evolved +forward in time is very simple because I + + align:start position:0% +forward in time is very simple because I + + + align:start position:0% +forward in time is very simple because I +know that this is a superposition a + + align:start position:0% +know that this is a superposition a + + + align:start position:0% +know that this is a superposition a +linear combination of states with + + align:start position:0% +linear combination of states with + + + align:start position:0% +linear combination of states with +definite energy states with definite + + align:start position:0% +definite energy states with definite + + + align:start position:0% +definite energy states with definite +energy involved with a phase and the + + align:start position:0% +energy involved with a phase and the + + + align:start position:0% +energy involved with a phase and the +Schrodinger equation is linear so + + align:start position:0% +Schrodinger equation is linear so + + + align:start position:0% +Schrodinger equation is linear so +solutions of the Schrodinger equation ad + + align:start position:0% +solutions of the Schrodinger equation ad + + + align:start position:0% +solutions of the Schrodinger equation ad +to become solutions of the Schrodinger + + align:start position:0% +to become solutions of the Schrodinger + + + align:start position:0% +to become solutions of the Schrodinger +equation so how does this state of all + + align:start position:0% +equation so how does this state of all + + + align:start position:0% +equation so how does this state of all +for it in time it involves forward + + align:start position:0% +for it in time it involves forward + + + align:start position:0% +for it in time it involves forward +the phase minus I Omega NT one for every + + align:start position:0% +the phase minus I Omega NT one for every + + + align:start position:0% +the phase minus I Omega NT one for every +different term in this some cool so we + + align:start position:0% +different term in this some cool so we + + + align:start position:0% +different term in this some cool so we +are going to harp on energy + + align:start position:0% +are going to harp on energy + + + align:start position:0% +are going to harp on energy +eigenfunctions not because they're more + + align:start position:0% +eigenfunctions not because they're more + + + align:start position:0% +eigenfunctions not because they're more +moral or more just or more good but + + align:start position:0% +moral or more just or more good but + + + align:start position:0% +moral or more just or more good but +because they're more convenient for + + align:start position:0% +because they're more convenient for + + + align:start position:0% +because they're more convenient for +solving the time evolution problem in + + align:start position:0% +solving the time evolution problem in + + + align:start position:0% +solving the time evolution problem in +quantum mechanics so most of today is + + align:start position:0% +quantum mechanics so most of today is + + + align:start position:0% +quantum mechanics so most of today is +going to be about this expansion and + + align:start position:0% +going to be about this expansion and + + + align:start position:0% +going to be about this expansion and +qualitative features of energy + + align:start position:0% +qualitative features of energy + + + align:start position:0% +qualitative features of energy +eigenfunctions cool okay and just to + + align:start position:0% +eigenfunctions cool okay and just to + + + align:start position:0% +eigenfunctions cool okay and just to +close that out let's think of I just + + align:start position:0% +close that out let's think of I just + + + align:start position:0% +close that out let's think of I just +want to remind you of a couple of + + align:start position:0% +want to remind you of a couple of + + + align:start position:0% +want to remind you of a couple of +examples that we did that we did last + + align:start position:0% +examples that we did that we did last + + + align:start position:0% +examples that we did that we did last +time just get them on the board so the + + align:start position:0% +time just get them on the board so the + + + align:start position:0% +time just get them on the board so the +first is a free particle so for a free + + align:start position:0% +first is a free particle so for a free + + + align:start position:0% +first is a free particle so for a free +particle we have that our wave functions + + align:start position:0% +particle we have that our wave functions + + + align:start position:0% +particle we have that our wave functions +F Phi n are equal to ei well actually + + align:start position:0% +F Phi n are equal to ei well actually + + + align:start position:0% +F Phi n are equal to ei well actually +let me not write that down like so let + + align:start position:0% +let me not write that down like so let + + + align:start position:0% +let me not write that down like so let +me skip over the free particle because + + align:start position:0% +me skip over the free particle because + + + align:start position:0% +me skip over the free particle because +it's so trivial let me just talk about + + align:start position:0% +it's so trivial let me just talk about + + + align:start position:0% +it's so trivial let me just talk about +the infinite well okay so the potential + + align:start position:0% +the infinite well okay so the potential + + + align:start position:0% +the infinite well okay so the potential +is infinite out here and it's zero + + align:start position:0% +is infinite out here and it's zero + + + align:start position:0% +is infinite out here and it's zero +inside the well and it goes from zero to + + align:start position:0% +inside the well and it goes from zero to + + + align:start position:0% +inside the well and it goes from zero to +L this is just my choice of notation and + + align:start position:0% +L this is just my choice of notation and + + + align:start position:0% +L this is just my choice of notation and +the energy operator as usual is P + + align:start position:0% +the energy operator as usual is P + + + align:start position:0% +the energy operator as usual is P +squared upon 2m plus U of X you might + + align:start position:0% +squared upon 2m plus U of X you might + + + align:start position:0% +squared upon 2m plus U of X you might +say where did I Drive this and the + + align:start position:0% +say where did I Drive this and the + + + align:start position:0% +say where did I Drive this and the +answer is I didn't derive this I just + + align:start position:0% +answer is I didn't derive this I just + + + align:start position:0% +answer is I didn't derive this I just +wrote it down it's like force in + + align:start position:0% +wrote it down it's like force in + + + align:start position:0% +wrote it down it's like force in +Newton's equations you just declare some + + align:start position:0% +Newton's equations you just declare some + + + align:start position:0% +Newton's equations you just declare some +force and then you ask what system + + align:start position:0% +force and then you ask what system + + + align:start position:0% +force and then you ask what system +doesn't model so here's my system it has + + align:start position:0% +doesn't model so here's my system it has + + + align:start position:0% +doesn't model so here's my system it has +what looks like a classical kind of of + + align:start position:0% +what looks like a classical kind of of + + + align:start position:0% +what looks like a classical kind of of +energy except these are all operators + + align:start position:0% +energy except these are all operators + + + align:start position:0% +energy except these are all operators +and the potential here is this guy it's + + align:start position:0% +and the potential here is this guy it's + + + align:start position:0% +and the potential here is this guy it's +zero out between zero and L and it's + + align:start position:0% +zero out between zero and L and it's + + + align:start position:0% +zero out between zero and L and it's +infinite elsewhere and as we saw last + + align:start position:0% +infinite elsewhere and as we saw last + + + align:start position:0% +infinite elsewhere and as we saw last +time the solutions to the energy + + align:start position:0% +time the solutions to the energy + + + align:start position:0% +time the solutions to the energy +eigenvalue equation aren't particularly + + align:start position:0% +eigenvalue equation aren't particularly + + + align:start position:0% +eigenvalue equation aren't particularly +simple Phi sub n of X is equal to root + + align:start position:0% +simple Phi sub n of X is equal to root + + + align:start position:0% +simple Phi sub n of X is equal to root +properly normalized to upon L sine of KX + + align:start position:0% +properly normalized to upon L sine of KX + + + align:start position:0% +properly normalized to upon L sine of KX +where kin is equal to n plus 1 pi where + + align:start position:0% +where kin is equal to n plus 1 pi where + + + align:start position:0% +where kin is equal to n plus 1 pi where +n is an integer upon L and these were + + align:start position:0% +n is an integer upon L and these were + + + align:start position:0% +n is an integer upon L and these were +chosen to satisfy our boundary + + align:start position:0% +chosen to satisfy our boundary + + + align:start position:0% +chosen to satisfy our boundary +conditions that the wave function must + + align:start position:0% +conditions that the wave function must + + + align:start position:0% +conditions that the wave function must +vanish here hence a sign and K was + + align:start position:0% +vanish here hence a sign and K was + + + align:start position:0% +vanish here hence a sign and K was +chosen so that it turned over and just + + align:start position:0% +chosen so that it turned over and just + + + align:start position:0% +chosen so that it turned over and just +hit 0 as we got to L and that gave us + + align:start position:0% +hit 0 as we got to L and that gave us + + + align:start position:0% +hit 0 as we got to L and that gave us +that the allowed energies were discrete + + align:start position:0% +that the allowed energies were discrete + + + align:start position:0% +that the allowed energies were discrete +because the e and which you can get by + + align:start position:0% +because the e and which you can get by + + + align:start position:0% +because the e and which you can get by +just plugging + + align:start position:0% +just plugging + + + align:start position:0% +just plugging +to the energy eigenvalue equation was + + align:start position:0% +to the energy eigenvalue equation was + + + align:start position:0% +to the energy eigenvalue equation was +equal to H bar squared K n squared upon + + align:start position:0% +equal to H bar squared K n squared upon + + + align:start position:0% +equal to H bar squared K n squared upon +2m so this tells us a nice thing first + + align:start position:0% +2m so this tells us a nice thing first + + + align:start position:0% +2m so this tells us a nice thing first +off in this system if I take a particle + + align:start position:0% +off in this system if I take a particle + + + align:start position:0% +off in this system if I take a particle +and I throw it in here in some arbitrary + + align:start position:0% +and I throw it in here in some arbitrary + + + align:start position:0% +and I throw it in here in some arbitrary +state at so that at time T equals zero + + align:start position:0% +state at so that at time T equals zero + + + align:start position:0% +state at so that at time T equals zero +the wave function x0 is equal to sum + + align:start position:0% +the wave function x0 is equal to sum + + + align:start position:0% +the wave function x0 is equal to sum +over n CN oh sorry let me write this as + + align:start position:0% +over n CN oh sorry let me write this as + + + align:start position:0% +over n CN oh sorry let me write this as +Phi n of X CN okay can I do this can I + + align:start position:0% +Phi n of X CN okay can I do this can I + + + align:start position:0% +Phi n of X CN okay can I do this can I +just pick some arbitrary function which + + align:start position:0% +just pick some arbitrary function which + + + align:start position:0% +just pick some arbitrary function which +is a superposition of energy eigenstates + + align:start position:0% +is a superposition of energy eigenstates + + + align:start position:0% +is a superposition of energy eigenstates +sure because any function is any + + align:start position:0% +sure because any function is any + + + align:start position:0% +sure because any function is any +function can be described as a + + align:start position:0% +function can be described as a + + + align:start position:0% +function can be described as a +superposition energy eigenfunctions and + + align:start position:0% +superposition energy eigenfunctions and + + + align:start position:0% +superposition energy eigenfunctions and +if I build the energy eigenfunctions + + align:start position:0% +if I build the energy eigenfunctions + + + align:start position:0% +if I build the energy eigenfunctions +jagan functions will automatically + + align:start position:0% +jagan functions will automatically + + + align:start position:0% +jagan functions will automatically +satisfy the boundary conditions all the + + align:start position:0% +satisfy the boundary conditions all the + + + align:start position:0% +satisfy the boundary conditions all the +good things will happen so this is + + align:start position:0% +good things will happen so this is + + + align:start position:0% +good things will happen so this is +perfectly fine an initial condition what + + align:start position:0% +perfectly fine an initial condition what + + + align:start position:0% +perfectly fine an initial condition what +is the system at time T yeah we just + + align:start position:0% +is the system at time T yeah we just + + + align:start position:0% +is the system at time T yeah we just +pick up the faces in what faces this guy + + align:start position:0% +pick up the faces in what faces this guy + + + align:start position:0% +pick up the faces in what faces this guy +it's this e to the minus I Omega n T and + + align:start position:0% +it's this e to the minus I Omega n T and + + + align:start position:0% +it's this e to the minus I Omega n T and +when I write Omega n let me be more + + align:start position:0% +when I write Omega n let me be more + + + align:start position:0% +when I write Omega n let me be more +explicit about that that's en over h-bar + + align:start position:0% +explicit about that that's en over h-bar + + + align:start position:0% +explicit about that that's en over h-bar +so that's h-bar K n squared upon 2m T + + align:start position:0% + + + + align:start position:0% + +cool so there is our solution for + + align:start position:0% +cool so there is our solution for + + + align:start position:0% +cool so there is our solution for +arbitrary initial conditions to the + + align:start position:0% +arbitrary initial conditions to the + + + align:start position:0% +arbitrary initial conditions to the +infinite square well problem in quantum + + align:start position:0% +infinite square well problem in quantum + + + align:start position:0% +infinite square well problem in quantum +mechanics and you're going to study this + + align:start position:0% +mechanics and you're going to study this + + + align:start position:0% +mechanics and you're going to study this +in some detail on your problem set but + + align:start position:0% +in some detail on your problem set but + + + align:start position:0% +in some detail on your problem set but +just to start with a little bit of + + align:start position:0% +just to start with a little bit of + + + align:start position:0% +just to start with a little bit of +intuition let's look at the wave + + align:start position:0% +intuition let's look at the wave + + + align:start position:0% +intuition let's look at the wave +functions and the probability + + align:start position:0% +functions and the probability + + + align:start position:0% +functions and the probability +distributions for the lowest lying + + align:start position:0% +distributions for the lowest lying + + + align:start position:0% +distributions for the lowest lying +States so for example let's look at the + + align:start position:0% +States so for example let's look at the + + + align:start position:0% +States so for example let's look at the +wave function for the ground state what + + align:start position:0% +wave function for the ground state what + + + align:start position:0% +wave function for the ground state what +I will call sy Sub Zero and this is from + + align:start position:0% +I will call sy Sub Zero and this is from + + + align:start position:0% +I will call sy Sub Zero and this is from +0 to L ok and I put these bars here not + + align:start position:0% +0 to L ok and I put these bars here not + + + align:start position:0% +0 to L ok and I put these bars here not +because we're looking at the potential + + align:start position:0% +because we're looking at the potential + + + align:start position:0% +because we're looking at the potential +I'm going to be plotting the real part + + align:start position:0% +I'm going to be plotting the real part + + + align:start position:0% +I'm going to be plotting the real part +of the wave function but I put these + + align:start position:0% +of the wave function but I put these + + + align:start position:0% +of the wave function but I put these +balls Wells here just to emphasize that + + align:start position:0% +balls Wells here just to emphasize that + + + align:start position:0% +balls Wells here just to emphasize that +that's where the walls are at x equals 0 + + align:start position:0% +that's where the walls are at x equals 0 + + + align:start position:0% +that's where the walls are at x equals 0 +and x equals L so what does it look like + + align:start position:0% +and x equals L so what does it look like + + + align:start position:0% +and x equals L so what does it look like +well the first one is going to be sine + + align:start position:0% +well the first one is going to be sine + + + align:start position:0% +well the first one is going to be sine +of KX and a 0 KN is going to be PI upon + + align:start position:0% +of KX and a 0 KN is going to be PI upon + + + align:start position:0% +of KX and a 0 KN is going to be PI upon +L so that's again just this guy now + + align:start position:0% +L so that's again just this guy now + + + align:start position:0% +L so that's again just this guy now +what's the probability distribution + + align:start position:0% +what's the probability distribution + + + align:start position:0% +what's the probability distribution +associated with sy 0 + + align:start position:0% +associated with sy 0 + + + align:start position:0% +associated with sy 0 +where do you find the particle so we + + align:start position:0% +where do you find the particle so we + + + align:start position:0% +where do you find the particle so we +know that it's just the norm squared of + + align:start position:0% +know that it's just the norm squared of + + + align:start position:0% +know that it's just the norm squared of +this wave function and the norm squared + + align:start position:0% +this wave function and the norm squared + + + align:start position:0% +this wave function and the norm squared +here it's zero so it's quadratic SERO + + align:start position:0% +here it's zero so it's quadratic SERO + + + align:start position:0% +here it's zero so it's quadratic SERO +and it rises linearly cosine is linear + + align:start position:0% +and it rises linearly cosine is linear + + + align:start position:0% +and it rises linearly cosine is linear +small values that makes this quadratic + + align:start position:0% +small values that makes this quadratic + + + align:start position:0% +small values that makes this quadratic +the maximum and then quadratic so + + align:start position:0% +the maximum and then quadratic so + + + align:start position:0% +the maximum and then quadratic so +there's our probability distribution now + + align:start position:0% +there's our probability distribution now + + + align:start position:0% +there's our probability distribution now +here's a funny thing imagine I take a + + align:start position:0% +here's a funny thing imagine I take a + + + align:start position:0% +here's a funny thing imagine I take a +particle classical particle and I put it + + align:start position:0% +particle classical particle and I put it + + + align:start position:0% +particle classical particle and I put it +in a box okay and you put it in the box + + align:start position:0% +in a box okay and you put it in the box + + + align:start position:0% +in a box okay and you put it in the box +and you tell it okay it's got some + + align:start position:0% +and you tell it okay it's got some + + + align:start position:0% +and you tell it okay it's got some +energy so classically it's got some + + align:start position:0% +energy so classically it's got some + + + align:start position:0% +energy so classically it's got some +momentum so it's sort of bouncing back + + align:start position:0% +momentum so it's sort of bouncing back + + + align:start position:0% +momentum so it's sort of bouncing back +and forth and it just bounces off the + + align:start position:0% +and forth and it just bounces off the + + + align:start position:0% +and forth and it just bounces off the +arbitrarily hard walls and moves around + + align:start position:0% +arbitrarily hard walls and moves around + + + align:start position:0% +arbitrarily hard walls and moves around +where are you most likely to find that + + align:start position:0% +where are you most likely to find that + + + align:start position:0% +where are you most likely to find that +particle where does it spend most of its + + align:start position:0% +particle where does it spend most of its + + + align:start position:0% +particle where does it spend most of its +time it spends the same amount of time + + align:start position:0% +time it spends the same amount of time + + + align:start position:0% +time it spends the same amount of time +in any point it's got moving at constant + + align:start position:0% +in any point it's got moving at constant + + + align:start position:0% +in any point it's got moving at constant +velocity goes boom boom boom right so + + align:start position:0% +velocity goes boom boom boom right so + + + align:start position:0% +velocity goes boom boom boom right so +what's the probability distribution for + + align:start position:0% +what's the probability distribution for + + + align:start position:0% +what's the probability distribution for +finding it at any point inside + + align:start position:0% +finding it at any point inside + + + align:start position:0% +finding it at any point inside +classically constant classically the + + align:start position:0% +classically constant classically the + + + align:start position:0% +classically constant classically the +probability distribution is constant or + + align:start position:0% +probability distribution is constant or + + + align:start position:0% +probability distribution is constant or +just as likely to find it near the wall + + align:start position:0% +just as likely to find it near the wall + + + align:start position:0% +just as likely to find it near the wall +as not near the wall okay however + + align:start position:0% +as not near the wall okay however + + + align:start position:0% +as not near the wall okay however +quantum mechanically for the lowest + + align:start position:0% +quantum mechanically for the lowest + + + align:start position:0% +quantum mechanically for the lowest +lying state that is clearly not true + + align:start position:0% +lying state that is clearly not true + + + align:start position:0% +lying state that is clearly not true +you're really unlikely to find it near + + align:start position:0% +you're really unlikely to find it near + + + align:start position:0% +you're really unlikely to find it near +the wall what's up with that so that's a + + align:start position:0% +the wall what's up with that so that's a + + + align:start position:0% +the wall what's up with that so that's a +question that I want to put in your head + + align:start position:0% +question that I want to put in your head + + + align:start position:0% +question that I want to put in your head +and have you think about I'm we're going + + align:start position:0% +and have you think about I'm we're going + + + align:start position:0% +and have you think about I'm we're going +to you're going to see a similar effect + + align:start position:0% +to you're going to see a similar effect + + + align:start position:0% +to you're going to see a similar effect +arising over and over and we're going to + + align:start position:0% +arising over and over and we're going to + + + align:start position:0% +arising over and over and we're going to +see at the very end that that is + + align:start position:0% +see at the very end that that is + + + align:start position:0% +see at the very end that that is +directly related the fact that this goes + + align:start position:0% +directly related the fact that this goes + + + align:start position:0% +directly related the fact that this goes +to zero is directly related and I'm not + + align:start position:0% +to zero is directly related and I'm not + + + align:start position:0% +to zero is directly related and I'm not +kidding + + align:start position:0% +kidding + + + align:start position:0% +kidding +to the transparency of Dimond not good + + align:start position:0% +to the transparency of Dimond not good + + + align:start position:0% +to the transparency of Dimond not good +okay I think it's pretty cool okay so + + align:start position:0% +okay I think it's pretty cool okay so + + + align:start position:0% +okay I think it's pretty cool okay so +look they're they're expensive + + align:start position:0% + + + + align:start position:0% + +it's also related to the transparency of + + align:start position:0% +it's also related to the transparency of + + + align:start position:0% +it's also related to the transparency of +cubic zirconium which I guess is less + + align:start position:0% +cubic zirconium which I guess is less + + + align:start position:0% +cubic zirconium which I guess is less +impressive but so so the first state + + align:start position:0% +impressive but so so the first state + + + align:start position:0% +impressive but so so the first state +again let's look at the real part of sy + + align:start position:0% +again let's look at the real part of sy + + + align:start position:0% +again let's look at the real part of sy +one the first excited state well this is + + align:start position:0% +one the first excited state well this is + + + align:start position:0% +one the first excited state well this is +now a sign with one extra with a two + + align:start position:0% +now a sign with one extra with a two + + + align:start position:0% +now a sign with one extra with a two +here two pi so it goes through zero okay + + align:start position:0% +here two pi so it goes through zero okay + + + align:start position:0% +here two pi so it goes through zero okay +so the probability distribution + + align:start position:0% +so the probability distribution + + + align:start position:0% +so the probability distribution +associated with sy one and I should say + + align:start position:0% +associated with sy one and I should say + + + align:start position:0% +associated with sy one and I should say +right this is the function of X looks + + align:start position:0% +right this is the function of X looks + + + align:start position:0% +right this is the function of X looks +like well again it's quadratic but it + + align:start position:0% +like well again it's quadratic but it + + + align:start position:0% +like well again it's quadratic but it +has a zero again in the middle so it's + + align:start position:0% +has a zero again in the middle so it's + + + align:start position:0% +has a zero again in the middle so it's +going to look like oops my bad art + + align:start position:0% +going to look like oops my bad art + + + align:start position:0% +going to look like oops my bad art +defeats me okay + + align:start position:0% +defeats me okay + + + align:start position:0% +defeats me okay +there we go so now it's even worse not + + align:start position:0% +there we go so now it's even worse not + + + align:start position:0% +there we go so now it's even worse not +only is it unlikely to be out here it's + + align:start position:0% +only is it unlikely to be out here it's + + + align:start position:0% +only is it unlikely to be out here it's +also very unlikely to be found the + + align:start position:0% +also very unlikely to be found the + + + align:start position:0% +also very unlikely to be found the +middle in fact there are zero + + align:start position:0% +middle in fact there are zero + + + align:start position:0% +middle in fact there are zero +probability you'll find in the middle + + align:start position:0% +probability you'll find in the middle + + + align:start position:0% +probability you'll find in the middle +that's sort of surprising but you can + + align:start position:0% +that's sort of surprising but you can + + + align:start position:0% +that's sort of surprising but you can +quickly guess what happens as you go to + + align:start position:0% +quickly guess what happens as you go to + + + align:start position:0% +quickly guess what happens as you go to +very high energies the real part of sy + + align:start position:0% +very high energies the real part of sy + + + align:start position:0% +very high energies the real part of sy +and let's say you know ten thousand ten + + align:start position:0% +and let's say you know ten thousand ten + + + align:start position:0% +and let's say you know ten thousand ten +to the four what is that going to look + + align:start position:0% +to the four what is that going to look + + + align:start position:0% +to the four what is that going to look +like well this had no zeros this had one + + align:start position:0% +like well this had no zeros this had one + + + align:start position:0% +like well this had no zeros this had one +zeros and every time you increase n by + + align:start position:0% +zeros and every time you increase n by + + + align:start position:0% +zeros and every time you increase n by +one you're just going to add one more + + align:start position:0% +one you're just going to add one more + + + align:start position:0% +one you're just going to add one more +zero to the sign that's an interesting + + align:start position:0% +zero to the sign that's an interesting + + + align:start position:0% +zero to the sign that's an interesting +and suggestive factor fact so if it's + + align:start position:0% +and suggestive factor fact so if it's + + + align:start position:0% +and suggestive factor fact so if it's +size of 10,000 how many nodes are there + + align:start position:0% +size of 10,000 how many nodes are there + + + align:start position:0% +size of 10,000 how many nodes are there +going to be in the middle of the domain + + align:start position:0% +going to be in the middle of the domain + + + align:start position:0% +going to be in the middle of the domain +10,000 and the amplitude is going to be + + align:start position:0% +10,000 and the amplitude is going to be + + + align:start position:0% +10,000 and the amplitude is going to be +the same okay I'm not going to be able + + align:start position:0% +the same okay I'm not going to be able + + + align:start position:0% +the same okay I'm not going to be able +to do this but you get the idea and now + + align:start position:0% +to do this but you get the idea and now + + + align:start position:0% +to do this but you get the idea and now +if I construct the probability + + align:start position:0% +if I construct the probability + + + align:start position:0% +if I construct the probability +distribution what's the probability + + align:start position:0% +distribution what's the probability + + + align:start position:0% +distribution what's the probability +distribution going to be probability of + + align:start position:0% +distribution going to be probability of + + + align:start position:0% +distribution going to be probability of +the 10,000th psy sub 10 to the 4 of X + + align:start position:0% +the 10,000th psy sub 10 to the 4 of X + + + align:start position:0% +the 10,000th psy sub 10 to the 4 of X +well it's again going to be strictly + + align:start position:0% +well it's again going to be strictly + + + align:start position:0% +well it's again going to be strictly +positive and if you are not able to make + + align:start position:0% +positive and if you are not able to make + + + align:start position:0% +positive and if you are not able to make +measurements on the scale of L upon + + align:start position:0% +measurements on the scale of L upon + + + align:start position:0% +measurements on the scale of L upon +10,000 let's just say like L over 3 + + align:start position:0% +10,000 let's just say like L over 3 + + + align:start position:0% +10,000 let's just say like L over 3 +because you know you have a thumb and + + align:start position:0% +because you know you have a thumb and + + + align:start position:0% +because you know you have a thumb and +you don't have an infinitely accurate + + align:start position:0% +you don't have an infinitely accurate + + + align:start position:0% +you don't have an infinitely accurate +meter what do you see you see + + align:start position:0% +meter what do you see you see + + + align:start position:0% +meter what do you see you see +effectively a constant probability + + align:start position:0% +effectively a constant probability + + + align:start position:0% +effectively a constant probability +distribution and actually shouldn't draw + + align:start position:0% +distribution and actually shouldn't draw + + + align:start position:0% +distribution and actually shouldn't draw +out there I should draw through the half + + align:start position:0% +out there I should draw through the half + + + align:start position:0% +out there I should draw through the half +because sine squared over two averages + + align:start position:0% +because sine squared over two averages + + + align:start position:0% +because sine squared over two averages +to one half + + align:start position:0% +to one half + + + align:start position:0% +to one half +Arcite sine squared averages to one half + + align:start position:0% +Arcite sine squared averages to one half + + + align:start position:0% +Arcite sine squared averages to one half +over many periods so what we see is that + + align:start position:0% +over many periods so what we see is that + + + align:start position:0% +over many periods so what we see is that +the classical probability distribution + + align:start position:0% +the classical probability distribution + + + align:start position:0% +the classical probability distribution +constant does arise when we look at very + + align:start position:0% +constant does arise when we look at very + + + align:start position:0% +constant does arise when we look at very +high energy states + + align:start position:0% + + + + align:start position:0% + +cool but it is manifestly not a good + + align:start position:0% +cool but it is manifestly not a good + + + align:start position:0% +cool but it is manifestly not a good +description the classical description is + + align:start position:0% +description the classical description is + + + align:start position:0% +description the classical description is +not a good description your intuition is + + align:start position:0% +not a good description your intuition is + + + align:start position:0% +not a good description your intuition is +crappy at low energies near the ground + + align:start position:0% +crappy at low energies near the ground + + + align:start position:0% +crappy at low energies near the ground +state where quantum effects are + + align:start position:0% +state where quantum effects are + + + align:start position:0% +state where quantum effects are +dominating because indeed classically + + align:start position:0% +dominating because indeed classically + + + align:start position:0% +dominating because indeed classically +there was no minimum energy quantum + + align:start position:0% +there was no minimum energy quantum + + + align:start position:0% +there was no minimum energy quantum +effects have to be dominating there and + + align:start position:0% +effects have to be dominating there and + + + align:start position:0% +effects have to be dominating there and +here we see that even the probability + + align:start position:0% +here we see that even the probability + + + align:start position:0% +here we see that even the probability +distribution is radically different than + + align:start position:0% +distribution is radically different than + + + align:start position:0% +distribution is radically different than +our intuition yeah + + align:start position:0% + + + + align:start position:0% + +we keep working on it so so I want you + + align:start position:0% +we keep working on it so so I want you + + + align:start position:0% +we keep working on it so so I want you +all to think about what you're not gonna + + align:start position:0% +all to think about what you're not gonna + + + align:start position:0% +all to think about what you're not gonna +promise you unless you've already seen + + align:start position:0% +promise you unless you've already seen + + + align:start position:0% +promise you unless you've already seen +some quantum mechanics you're not gonna + + align:start position:0% +some quantum mechanics you're not gonna + + + align:start position:0% +some quantum mechanics you're not gonna +be able to answer this question now but + + align:start position:0% +be able to answer this question now but + + + align:start position:0% +be able to answer this question now but +I want you to have it as an + + align:start position:0% +I want you to have it as an + + + align:start position:0% +I want you to have it as an +uncomfortable little piece of sand in + + align:start position:0% +uncomfortable little piece of sand in + + + align:start position:0% +uncomfortable little piece of sand in +the back of your oyster mind you know + + align:start position:0% +the back of your oyster mind you know + + + align:start position:0% +the back of your oyster mind you know +what no offense + + align:start position:0% +what no offense + + + align:start position:0% +what no offense +what what what what is causing that zero + + align:start position:0% +what what what what is causing that zero + + + align:start position:0% +what what what what is causing that zero +why are we getting zero and I'll give + + align:start position:0% +why are we getting zero and I'll give + + + align:start position:0% +why are we getting zero and I'll give +you a hint in quantum mechanics any time + + align:start position:0% +you a hint in quantum mechanics any time + + + align:start position:0% +you a hint in quantum mechanics any time +something interesting happens it's + + align:start position:0% +something interesting happens it's + + + align:start position:0% +something interesting happens it's +because of superposition and + + align:start position:0% +because of superposition and + + + align:start position:0% +because of superposition and +interference all right so with all that + + align:start position:0% +interference all right so with all that + + + align:start position:0% +interference all right so with all that +said so any questions now over this + + align:start position:0% +said so any questions now over this + + + align:start position:0% +said so any questions now over this +story about energy eigenfunctions + + align:start position:0% +story about energy eigenfunctions + + + align:start position:0% +story about energy eigenfunctions +expanding into bases etc before we get + + align:start position:0% +expanding into bases etc before we get + + + align:start position:0% +expanding into bases etc before we get +moving + + align:start position:0% +moving + + + align:start position:0% +moving +no okay in that case get out your + + align:start position:0% +no okay in that case get out your + + + align:start position:0% +no okay in that case get out your +clickers we're going to test your + + align:start position:0% +clickers we're going to test your + + + align:start position:0% +clickers we're going to test your +knowledge Oh + + align:start position:0% + + + + align:start position:0% + +channel 41 for those of you who have to + + align:start position:0% +channel 41 for those of you who have to + + + align:start position:0% +channel 41 for those of you who have to +adjust it + + align:start position:0% + + + + align:start position:0% + +Wow + + align:start position:0% + + + + align:start position:0% + +that's kind of worrying + + align:start position:0% + + + + align:start position:0% + +aha + + align:start position:0% + + + + align:start position:0% + +okay ready + + align:start position:0% +okay ready + + + align:start position:0% +okay ready +okay channel 41 and here we go oops + + align:start position:0% + + + + align:start position:0% + +okay so go ahead and start now sorry + + align:start position:0% +okay so go ahead and start now sorry + + + align:start position:0% +okay so go ahead and start now sorry +there was a little technical glitch + + align:start position:0% +there was a little technical glitch + + + align:start position:0% +there was a little technical glitch +there so so I'm going to cite or + + align:start position:0% +there so so I'm going to cite or + + + align:start position:0% +there so so I'm going to cite or +eigenstates they're non degenerate + + align:start position:0% +eigenstates they're non degenerate + + + align:start position:0% +eigenstates they're non degenerate +meaning the energies are different is a + + align:start position:0% +meaning the energies are different is a + + + align:start position:0% +meaning the energies are different is a +superposition so i1 plus i2 also an + + align:start position:0% +superposition so i1 plus i2 also an + + + align:start position:0% +superposition so i1 plus i2 also an +eigenstate + + align:start position:0% + + + + align:start position:0% + +all right four more seconds all right I + + align:start position:0% +all right four more seconds all right I + + + align:start position:0% +all right four more seconds all right I +want everyone to turn to the person next + + align:start position:0% +want everyone to turn to the person next + + + align:start position:0% +want everyone to turn to the person next +to you and discuss this you've got about + + align:start position:0% +to you and discuss this you've got about + + + align:start position:0% +to you and discuss this you've got about +30 seconds to discuss or a minute + + align:start position:0% + + + + align:start position:0% + +possibly yet + + align:start position:0% + + + + align:start position:0% + +this is it + + align:start position:0% + + + + align:start position:0% + +I'm not sure the + + align:start position:0% + + + + align:start position:0% + +all right yeah all right now I want + + align:start position:0% +all right yeah all right now I want + + + align:start position:0% +all right yeah all right now I want +everyone now that you've got an answer + + align:start position:0% +everyone now that you've got an answer + + + align:start position:0% +everyone now that you've got an answer +click again put in your current best + + align:start position:0% +click again put in your current best + + + align:start position:0% +click again put in your current best +guess oh wait sorry for some reason it's + + align:start position:0% +guess oh wait sorry for some reason it's + + + align:start position:0% +guess oh wait sorry for some reason it's +I have to start over again okay now + + align:start position:0% +I have to start over again okay now + + + align:start position:0% +I have to start over again okay now +click + + align:start position:0% + + + + align:start position:0% + +this is the best I'm such a convert to + + align:start position:0% +this is the best I'm such a convert to + + + align:start position:0% +this is the best I'm such a convert to +clickers this is just fantastic so you + + align:start position:0% +clickers this is just fantastic so you + + + align:start position:0% +clickers this is just fantastic so you +guys went from okay so roughly y'all + + align:start position:0% +guys went from okay so roughly y'all + + + align:start position:0% +guys went from okay so roughly y'all +went from about thirty sixty ten to what + + align:start position:0% +went from about thirty sixty ten to what + + + align:start position:0% +went from about thirty sixty ten to what +are we now eight eight and end + + align:start position:0% +are we now eight eight and end + + + align:start position:0% +are we now eight eight and end +eighty-two and ten so it sounds like you + + align:start position:0% +eighty-two and ten so it sounds like you + + + align:start position:0% +eighty-two and ten so it sounds like you +guys are predicting answer B and the + + align:start position:0% +guys are predicting answer B and the + + + align:start position:0% +guys are predicting answer B and the +answer is I like the suspense there we + + align:start position:0% +answer is I like the suspense there we + + + align:start position:0% +answer is I like the suspense there we +go + + align:start position:0% +go + + + align:start position:0% +go +be good so so here's a quick question so + + align:start position:0% +be good so so here's a quick question so + + + align:start position:0% +be good so so here's a quick question so +it does anyone want to defend so why and + + align:start position:0% +it does anyone want to defend so why and + + + align:start position:0% +it does anyone want to defend so why and +the reason why is that if we have e on + + align:start position:0% +the reason why is that if we have e on + + + align:start position:0% +the reason why is that if we have e on +psy 1 plus I 2 this is equal to e on psy + + align:start position:0% +psy 1 plus I 2 this is equal to e on psy + + + align:start position:0% +psy 1 plus I 2 this is equal to e on psy +1 + E on sigh - operator operator + + align:start position:0% +1 + E on sigh - operator operator + + + align:start position:0% +1 + E on sigh - operator operator +operator but this is equal to e 1 sy 1 + + align:start position:0% +operator but this is equal to e 1 sy 1 + + + align:start position:0% +operator but this is equal to e 1 sy 1 +plus E - psy - which is not if you want + + align:start position:0% +plus E - psy - which is not if you want + + + align:start position:0% +plus E - psy - which is not if you want +to need two are not equal which is not + + align:start position:0% +to need two are not equal which is not + + + align:start position:0% +to need two are not equal which is not +equal to e times so I want plus I 2 + + align:start position:0% +equal to e times so I want plus I 2 + + + align:start position:0% +equal to e times so I want plus I 2 +right not equal to e anything times I 1 + + align:start position:0% +right not equal to e anything times I 1 + + + align:start position:0% +right not equal to e anything times I 1 +plus I 2 and it needs to be in order to + + align:start position:0% +plus I 2 and it needs to be in order to + + + align:start position:0% +plus I 2 and it needs to be in order to +be an eigenfunction an eigenfunction of + + align:start position:0% +be an eigenfunction an eigenfunction of + + + align:start position:0% +be an eigenfunction an eigenfunction of +the energy operator so yeah does this + + align:start position:0% +the energy operator so yeah does this + + + align:start position:0% +the energy operator so yeah does this +only happen + + align:start position:0% +only happen + + + align:start position:0% +only happen +yeah okay that's a really good question + + align:start position:0% +yeah okay that's a really good question + + + align:start position:0% +yeah okay that's a really good question +so first off how do you measure an + + align:start position:0% +so first off how do you measure an + + + align:start position:0% +so first off how do you measure an +energy do you ever measure an energy let + + align:start position:0% +energy do you ever measure an energy let + + + align:start position:0% +energy do you ever measure an energy let +me more feel like do you ever measure a + + align:start position:0% +me more feel like do you ever measure a + + + align:start position:0% +me more feel like do you ever measure a +voltage the actual value of the scalar + + align:start position:0% +voltage the actual value of the scalar + + + align:start position:0% +voltage the actual value of the scalar +potential the electromagnetic scalar + + align:start position:0% +potential the electromagnetic scalar + + + align:start position:0% +potential the electromagnetic scalar +potential no you measure a difference do + + align:start position:0% +potential no you measure a difference do + + + align:start position:0% +potential no you measure a difference do +you ever measure the energy no you + + align:start position:0% +you ever measure the energy no you + + + align:start position:0% +you ever measure the energy no you +measure a difference in energy so the + + align:start position:0% +measure a difference in energy so the + + + align:start position:0% +measure a difference in energy so the +absolute value of energy is sort of a + + align:start position:0% +absolute value of energy is sort of a + + + align:start position:0% +absolute value of energy is sort of a +silly thing do you but we always talk + + align:start position:0% +silly thing do you but we always talk + + + align:start position:0% +silly thing do you but we always talk +about it as if it's not we said it's got + + align:start position:0% +about it as if it's not we said it's got + + + align:start position:0% +about it as if it's not we said it's got +energy 14 it's a little bit suspicious + + align:start position:0% +energy 14 it's a little bit suspicious + + + align:start position:0% +energy 14 it's a little bit suspicious +so to answer your question + + align:start position:0% +so to answer your question + + + align:start position:0% +so to answer your question +there's nothing hallowed about the + + align:start position:0% +there's nothing hallowed about the + + + align:start position:0% +there's nothing hallowed about the +number zero although we will often refer + + align:start position:0% +number zero although we will often refer + + + align:start position:0% +number zero although we will often refer +to zero energy with a very specific + + align:start position:0% +to zero energy with a very specific + + + align:start position:0% +to zero energy with a very specific +meaning what we really mean in that case + + align:start position:0% +meaning what we really mean in that case + + + align:start position:0% +meaning what we really mean in that case +is the value of the potential energy at + + align:start position:0% +is the value of the potential energy at + + + align:start position:0% +is the value of the potential energy at +infinity okay so when I say like energy + + align:start position:0% +infinity okay so when I say like energy + + + align:start position:0% +infinity okay so when I say like energy +usually what I mean is relative to the + + align:start position:0% +usually what I mean is relative to the + + + align:start position:0% +usually what I mean is relative to the +value infinity so then let me ask your + + align:start position:0% +value infinity so then let me ask your + + + align:start position:0% +value infinity so then let me ask your +question again your question is is it + + align:start position:0% +question again your question is is it + + + align:start position:0% +question again your question is is it +possible to have energy 0 absolutely and + + align:start position:0% +possible to have energy 0 absolutely and + + + align:start position:0% +possible to have energy 0 absolutely and +we'll see that and it's actually gonna + + align:start position:0% +we'll see that and it's actually gonna + + + align:start position:0% +we'll see that and it's actually gonna +be really interesting what's true of + + align:start position:0% +be really interesting what's true of + + + align:start position:0% +be really interesting what's true of +states with energy 0 in that sense + + align:start position:0% +states with energy 0 in that sense + + + align:start position:0% +states with energy 0 in that sense +second part of your question though is + + align:start position:0% +second part of your question though is + + + align:start position:0% +second part of your question though is +how does energy being 0 fit into this + + align:start position:0% +how does energy being 0 fit into this + + + align:start position:0% +how does energy being 0 fit into this +well does that save us suppose one of + + align:start position:0% +well does that save us suppose one of + + + align:start position:0% +well does that save us suppose one of +the energies is zero then that says the + + align:start position:0% +the energies is zero then that says the + + + align:start position:0% +the energies is zero then that says the +EON sign 1 plus I 2 is equal to let's + + align:start position:0% +EON sign 1 plus I 2 is equal to let's + + + align:start position:0% +EON sign 1 plus I 2 is equal to let's +say e 2 is 0 well that term is gone so + + align:start position:0% +say e 2 is 0 well that term is gone so + + + align:start position:0% +say e 2 is 0 well that term is gone so +there's just the 1 e 1 are we an energy + + align:start position:0% +there's just the 1 e 1 are we an energy + + + align:start position:0% +there's just the 1 e 1 are we an energy +eigenstate no because it's still not + + align:start position:0% +eigenstate no because it's still not + + + align:start position:0% +eigenstate no because it's still not +over the form e times I 1 plus I 2 so it + + align:start position:0% +over the form e times I 1 plus I 2 so it + + + align:start position:0% +over the form e times I 1 plus I 2 so it +doesn't save us but it's an interesting + + align:start position:0% +doesn't save us but it's an interesting + + + align:start position:0% +doesn't save us but it's an interesting +question for the future all right next + + align:start position:0% +question for the future all right next + + + align:start position:0% +question for the future all right next +question for parts + + align:start position:0% + + + + align:start position:0% + +so the question says X and P can you tie + + align:start position:0% +so the question says X and P can you tie + + + align:start position:0% +so the question says X and P can you tie +h-bar we've shown this is px equal to IH + + align:start position:0% +h-bar we've shown this is px equal to IH + + + align:start position:0% +h-bar we've shown this is px equal to IH +bar and is IP plus CX the same as CX + + align:start position:0% +bar and is IP plus CX the same as CX + + + align:start position:0% +bar and is IP plus CX the same as CX +plus IP + + align:start position:0% + + + + align:start position:0% + +okay if you're really unsure you can ask + + align:start position:0% +okay if you're really unsure you can ask + + + align:start position:0% +okay if you're really unsure you can ask +the person next to you but you don't + + align:start position:0% +the person next to you but you don't + + + align:start position:0% +the person next to you but you don't +have to okay + + align:start position:0% +have to okay + + + align:start position:0% +have to okay +so this is looking good so everyone have + + align:start position:0% +so this is looking good so everyone have + + + align:start position:0% +so this is looking good so everyone have +an answer in you know okay five four + + align:start position:0% +an answer in you know okay five four + + + align:start position:0% +an answer in you know okay five four +three two one okay good so ah the answer + + align:start position:0% +three two one okay good so ah the answer + + + align:start position:0% +three two one okay good so ah the answer +is C which most of you got but not + + align:start position:0% +is C which most of you got but not + + + align:start position:0% +is C which most of you got but not +everyone a bunch of you put D so let's + + align:start position:0% +everyone a bunch of you put D so let's + + + align:start position:0% +everyone a bunch of you put D so let's +talk through it + + align:start position:0% +talk through it + + + align:start position:0% +talk through it +so if X so remember what the definition + + align:start position:0% +so if X so remember what the definition + + + align:start position:0% +so if X so remember what the definition +of the commutator is X with P by + + align:start position:0% +of the commutator is X with P by + + + align:start position:0% +of the commutator is X with P by +definition is equal to X P minus P X if + + align:start position:0% +definition is equal to X P minus P X if + + + align:start position:0% +definition is equal to X P minus P X if +we change the order here P X is equal to + + align:start position:0% +we change the order here P X is equal to + + + align:start position:0% +we change the order here P X is equal to +minus this px minus X P okay it's just + + align:start position:0% +minus this px minus X P okay it's just + + + align:start position:0% +minus this px minus X P okay it's just +the definition of the commutator so on + + align:start position:0% +the definition of the commutator so on + + + align:start position:0% +the definition of the commutator so on +the other hand if you add things does 7 + + align:start position:0% +the other hand if you add things does 7 + + + align:start position:0% +the other hand if you add things does 7 +plus 6 equals 6 plus 7 yeah well of + + align:start position:0% +plus 6 equals 6 plus 7 yeah well of + + + align:start position:0% +plus 6 equals 6 plus 7 yeah well of +course 6 times 7 is 7 times 6 so that's + + align:start position:0% +course 6 times 7 is 7 times 6 so that's + + + align:start position:0% +course 6 times 7 is 7 times 6 so that's +not a terribly good analogy do operators + + align:start position:0% +not a terribly good analogy do operators + + + align:start position:0% +not a terribly good analogy do operators +do that do they does the map this is the + + align:start position:0% +do that do they does the map this is the + + + align:start position:0% +do that do they does the map this is the +order of addition of operators matter no + + align:start position:0% +order of addition of operators matter no + + + align:start position:0% +order of addition of operators matter no +so yeah yeah exactly exactly so it's + + align:start position:0% +so yeah yeah exactly exactly so it's + + + align:start position:0% +so yeah yeah exactly exactly so it's +slightly sneaky ok next question okay + + align:start position:0% +slightly sneaky ok next question okay + + + align:start position:0% +slightly sneaky ok next question okay +this one has five ok F and G are both + + align:start position:0% +this one has five ok F and G are both + + + align:start position:0% +this one has five ok F and G are both +wave functions C is a constant then if + + align:start position:0% +wave functions C is a constant then if + + + align:start position:0% +wave functions C is a constant then if +we take the inner product C times F with + + align:start position:0% +we take the inner product C times F with + + + align:start position:0% +we take the inner product C times F with +G this is equal to what + + align:start position:0% + + + + align:start position:0% + +three two one okay so the answer is so + + align:start position:0% +three two one okay so the answer is so + + + align:start position:0% +three two one okay so the answer is so +this one there's okay this one + + align:start position:0% +this one there's okay this one + + + align:start position:0% +this one there's okay this one +definitely discuss discuss with the + + align:start position:0% +definitely discuss discuss with the + + + align:start position:0% +definitely discuss discuss with the +person next year + + align:start position:0% + + + + align:start position:0% + +all right and okay go ahead and enter + + align:start position:0% +all right and okay go ahead and enter + + + align:start position:0% +all right and okay go ahead and enter +your guess again or your answer again + + align:start position:0% +your guess again or your answer again + + + align:start position:0% +your guess again or your answer again +let it not be a guess okay ten seconds + + align:start position:0% +let it not be a guess okay ten seconds + + + align:start position:0% +let it not be a guess okay ten seconds +Wow + + align:start position:0% +Wow + + + align:start position:0% +Wow +okay fantastic that worked like a champ + + align:start position:0% +okay fantastic that worked like a champ + + + align:start position:0% +okay fantastic that worked like a champ +so what's the answer yes complex + + align:start position:0% +so what's the answer yes complex + + + align:start position:0% +so what's the answer yes complex +conjugation don't screw that one out + + align:start position:0% +conjugation don't screw that one out + + + align:start position:0% +conjugation don't screw that one out +it's very easy to forget but it matters + + align:start position:0% +it's very easy to forget but it matters + + + align:start position:0% +it's very easy to forget but it matters +a lot okay cursor keeps disappearing + + align:start position:0% +a lot okay cursor keeps disappearing + + + align:start position:0% +a lot okay cursor keeps disappearing +okay next one a wavefunction sorry a + + align:start position:0% + + + + align:start position:0% + +wavefunction has been expressed as sum + + align:start position:0% +wavefunction has been expressed as sum + + + align:start position:0% +wavefunction has been expressed as sum +of energy eigenfunctions here I'm + + align:start position:0% +of energy eigenfunctions here I'm + + + align:start position:0% +of energy eigenfunctions here I'm +calling the EU rather than Phi but same + + align:start position:0% +calling the EU rather than Phi but same + + + align:start position:0% +calling the EU rather than Phi but same +thing compared to the original wave + + align:start position:0% +thing compared to the original wave + + + align:start position:0% +thing compared to the original wave +function the set of coefficients given + + align:start position:0% +function the set of coefficients given + + + align:start position:0% +function the set of coefficients given +that we're using the energy basis the + + align:start position:0% +that we're using the energy basis the + + + align:start position:0% +that we're using the energy basis the +set of coefficients contains more or + + align:start position:0% +set of coefficients contains more or + + + align:start position:0% +set of coefficients contains more or +less the same information or it can be + + align:start position:0% +less the same information or it can be + + + align:start position:0% +less the same information or it can be +determined okay five seconds + + align:start position:0% + + + + align:start position:0% + +all right and the answer is C great okay + + align:start position:0% +all right and the answer is C great okay + + + align:start position:0% +all right and the answer is C great okay +next one so right now we're normalizing + + align:start position:0% + + + + align:start position:0% + +okay all stationary states are all + + align:start position:0% +okay all stationary states are all + + + align:start position:0% +okay all stationary states are all +energy eigenstates have the form that + + align:start position:0% +energy eigenstates have the form that + + + align:start position:0% +energy eigenstates have the form that +spatial and time dependence is a spatial + + align:start position:0% +spatial and time dependence is a spatial + + + align:start position:0% +spatial and time dependence is a spatial +dependence the energy eigenfunction + + align:start position:0% +dependence the energy eigenfunction + + + align:start position:0% +dependence the energy eigenfunction +times the phase so that the norm squared + + align:start position:0% +times the phase so that the norm squared + + + align:start position:0% +times the phase so that the norm squared +is time independent consider the sum of + + align:start position:0% +is time independent consider the sum of + + + align:start position:0% +is time independent consider the sum of +two non degenerate energy eigenstates so + + align:start position:0% +two non degenerate energy eigenstates so + + + align:start position:0% +two non degenerate energy eigenstates so +I went in situ + + align:start position:0% +I went in situ + + + align:start position:0% +I went in situ +non degenerate means they're not energy + + align:start position:0% +non degenerate means they're not energy + + + align:start position:0% +non degenerate means they're not energy +they have different energies is the + + align:start position:0% +they have different energies is the + + + align:start position:0% +they have different energies is the +wavefunction stationary is a probability + + align:start position:0% +wavefunction stationary is a probability + + + align:start position:0% +wavefunction stationary is a probability +distribution time independent or is it + + align:start position:0% +distribution time independent or is it + + + align:start position:0% +distribution time independent or is it +time dependent + + align:start position:0% + + + + align:start position:0% + +this one's this one's not trivial oh + + align:start position:0% +this one's this one's not trivial oh + + + align:start position:0% +this one's this one's not trivial oh +shoot I forgot to get it started + + align:start position:0% +shoot I forgot to get it started + + + align:start position:0% +shoot I forgot to get it started +sorry it's particularly untrue you can + + align:start position:0% +sorry it's particularly untrue you can + + + align:start position:0% +sorry it's particularly untrue you can +tend to your answer right so go ahead + + align:start position:0% +tend to your answer right so go ahead + + + align:start position:0% +tend to your answer right so go ahead +and enter your enter your answer + + align:start position:0% + + + + align:start position:0% + +yeah this one always kills people + + align:start position:0% + + + + align:start position:0% + +no chatting just yeah test yourself not + + align:start position:0% +no chatting just yeah test yourself not + + + align:start position:0% +no chatting just yeah test yourself not +your neighbor you know it's fine to look + + align:start position:0% +your neighbor you know it's fine to look + + + align:start position:0% +your neighbor you know it's fine to look +deep into your soul don't look deep into + + align:start position:0% +deep into your soul don't look deep into + + + align:start position:0% +deep into your soul don't look deep into +the soul of the person sitting next to + + align:start position:0% +the soul of the person sitting next to + + + align:start position:0% +the soul of the person sitting next to +you all right so at this point chat with + + align:start position:0% +you all right so at this point chat with + + + align:start position:0% +you all right so at this point chat with +your neighbor okay let me just let me + + align:start position:0% +your neighbor okay let me just let me + + + align:start position:0% +your neighbor okay let me just let me +just give you some presage the the + + align:start position:0% +just give you some presage the the + + + align:start position:0% +just give you some presage the the +pairwise strategy is probably not so + + align:start position:0% +pairwise strategy is probably not so + + + align:start position:0% +pairwise strategy is probably not so +good because about half of you got it + + align:start position:0% +good because about half of you got it + + + align:start position:0% +good because about half of you got it +right in about a half of you got it + + align:start position:0% +right in about a half of you got it + + + align:start position:0% +right in about a half of you got it +wrong so + + align:start position:0% + + + + align:start position:0% + +all right let's uh let's vote again + + align:start position:0% +all right let's uh let's vote again + + + align:start position:0% +all right let's uh let's vote again +woods and hold on starting now + + align:start position:0% +woods and hold on starting now + + + align:start position:0% +woods and hold on starting now +okay vote again you've got ten seconds + + align:start position:0% +okay vote again you've got ten seconds + + + align:start position:0% +okay vote again you've got ten seconds +to enter a vote Wow okay two seconds + + align:start position:0% +to enter a vote Wow okay two seconds + + + align:start position:0% +to enter a vote Wow okay two seconds +good so the distribution on this one + + align:start position:0% +good so the distribution on this one + + + align:start position:0% +good so the distribution on this one +went from thirty fifty twenty initially + + align:start position:0% +went from thirty fifty twenty initially + + + align:start position:0% +went from thirty fifty twenty initially +to now it is 1080 and ten amazingly you + + align:start position:0% +to now it is 1080 and ten amazingly you + + + align:start position:0% +to now it is 1080 and ten amazingly you +guys got worse the answer is C and I + + align:start position:0% +guys got worse the answer is C and I + + + align:start position:0% +guys got worse the answer is C and I +want you two to discuss with each other + + align:start position:0% +want you two to discuss with each other + + + align:start position:0% +want you two to discuss with each other +why it's C + + align:start position:0% + + + + align:start position:0% + +all right so so let me talk you through + + align:start position:0% +all right so so let me talk you through + + + align:start position:0% +all right so so let me talk you through +it so the wavefunction we've said sine X + + align:start position:0% +it so the wavefunction we've said sine X + + + align:start position:0% +it so the wavefunction we've said sine X +and T is equal to u sine 1 or Phi 1 at X + + align:start position:0% +and T is equal to u sine 1 or Phi 1 at X + + + align:start position:0% +and T is equal to u sine 1 or Phi 1 at X +e to the minus I Omega 1 T and plus Phi + + align:start position:0% +e to the minus I Omega 1 T and plus Phi + + + align:start position:0% +e to the minus I Omega 1 T and plus Phi +2 of X e to the minus I Omega 2 T all + + align:start position:0% +2 of X e to the minus I Omega 2 T all + + + align:start position:0% +2 of X e to the minus I Omega 2 T all +right so great we take the norm squared + + align:start position:0% +right so great we take the norm squared + + + align:start position:0% +right so great we take the norm squared +what's the probability to find it at X + + align:start position:0% +what's the probability to find it at X + + + align:start position:0% +what's the probability to find it at X +at time T the probability density the + + align:start position:0% +at time T the probability density the + + + align:start position:0% +at time T the probability density the +norm squared of this guy size squared + + align:start position:0% +norm squared of this guy size squared + + + align:start position:0% +norm squared of this guy size squared +which is equal to Phi 1 complex + + align:start position:0% +which is equal to Phi 1 complex + + + align:start position:0% +which is equal to Phi 1 complex +conjugate e to the plus I Omega 1 T plus + + align:start position:0% +conjugate e to the plus I Omega 1 T plus + + + align:start position:0% +conjugate e to the plus I Omega 1 T plus +Phi 2 complex conjugate e to the plus I + + align:start position:0% +Phi 2 complex conjugate e to the plus I + + + align:start position:0% +Phi 2 complex conjugate e to the plus I +Omega 2 T times the thing itself Phi 1 + + align:start position:0% +Omega 2 T times the thing itself Phi 1 + + + align:start position:0% +Omega 2 T times the thing itself Phi 1 +of X e to the minus I Omega 1 T plus Phi + + align:start position:0% +of X e to the minus I Omega 1 T plus Phi + + + align:start position:0% +of X e to the minus I Omega 1 T plus Phi +2 of X e to the minus I Omega 2 T right + + align:start position:0% +2 of X e to the minus I Omega 2 T right + + + align:start position:0% +2 of X e to the minus I Omega 2 T right +and so this has four terms the first + + align:start position:0% +and so this has four terms the first + + + align:start position:0% +and so this has four terms the first +term is sy 1 norm squared the phases + + align:start position:0% +term is sy 1 norm squared the phases + + + align:start position:0% +term is sy 1 norm squared the phases +cancel right you're going to see this + + align:start position:0% +cancel right you're going to see this + + + align:start position:0% +cancel right you're going to see this +happen a billion times in 804 the first + + align:start position:0% +happen a billion times in 804 the first + + + align:start position:0% +happen a billion times in 804 the first +term is going to be fine one norm + + align:start position:0% +term is going to be fine one norm + + + align:start position:0% +term is going to be fine one norm +squared there's another term which is + + align:start position:0% +squared there's another term which is + + + align:start position:0% +squared there's another term which is +Phi 2 norm squared again the phase is + + align:start position:0% +Phi 2 norm squared again the phase is + + + align:start position:0% +Phi 2 norm squared again the phase is +exactly cancel you do the minus I Omega + + align:start position:0% +exactly cancel you do the minus I Omega + + + align:start position:0% +exactly cancel you do the minus I Omega +2 T to the plus I Omega 2 T plus Phi 2 + + align:start position:0% +2 T to the plus I Omega 2 T plus Phi 2 + + + align:start position:0% +2 T to the plus I Omega 2 T plus Phi 2 +squared but then there are two cross + + align:start position:0% +squared but then there are two cross + + + align:start position:0% +squared but then there are two cross +terms the interference terms plus Phi + + align:start position:0% +terms the interference terms plus Phi + + + align:start position:0% +terms the interference terms plus Phi +one complex conjugate Phi 2 e to the I + + align:start position:0% +one complex conjugate Phi 2 e to the I + + + align:start position:0% +one complex conjugate Phi 2 e to the I +Omega 1t e to the plus I Omega 1t I + + align:start position:0% +Omega 1t e to the plus I Omega 1t I + + + align:start position:0% +Omega 1t e to the plus I Omega 1t I +Omega 1 T and e to the minus I Omega 2 t + + align:start position:0% +Omega 1 T and e to the minus I Omega 2 t + + + align:start position:0% +Omega 1 T and e to the minus I Omega 2 t +minus Omega 2 so we have a cross term + + align:start position:0% +minus Omega 2 so we have a cross term + + + align:start position:0% +minus Omega 2 so we have a cross term +which depends on the difference in + + align:start position:0% +which depends on the difference in + + + align:start position:0% +which depends on the difference in +frequencies frequencies are like + + align:start position:0% +frequencies frequencies are like + + + align:start position:0% +frequencies frequencies are like +energies module and h-bar so it's the + + align:start position:0% +energies module and h-bar so it's the + + + align:start position:0% +energies module and h-bar so it's the +difference in energies and then there's + + align:start position:0% +difference in energies and then there's + + + align:start position:0% +difference in energies and then there's +another term which is the complex + + align:start position:0% +another term which is the complex + + + align:start position:0% +another term which is the complex +conjugate of this guy Phi 2 star times + + align:start position:0% +conjugate of this guy Phi 2 star times + + + align:start position:0% +conjugate of this guy Phi 2 star times +Phi 1 Phi 2 complex conjugate Phi 1 and + + align:start position:0% +Phi 1 Phi 2 complex conjugate Phi 1 and + + + align:start position:0% +Phi 1 Phi 2 complex conjugate Phi 1 and +the phases are also the Comets conjugate + + align:start position:0% +the phases are also the Comets conjugate + + + align:start position:0% +the phases are also the Comets conjugate +to the minus I Omega 1 minus Omega 2 T + + align:start position:0% +to the minus I Omega 1 minus Omega 2 T + + + align:start position:0% +to the minus I Omega 1 minus Omega 2 T +of X of X of X of X so is there time + + align:start position:0% +of X of X of X of X so is there time + + + align:start position:0% +of X of X of X of X so is there time +dependence in this in principle yeah + + align:start position:0% +dependence in this in principle yeah + + + align:start position:0% +dependence in this in principle yeah +absolutely from the interference terms + + align:start position:0% +absolutely from the interference terms + + + align:start position:0% +absolutely from the interference terms +were we not in the superposition we + + align:start position:0% +were we not in the superposition we + + + align:start position:0% +were we not in the superposition we +would not have the interference terms + + align:start position:0% +would not have the interference terms + + + align:start position:0% +would not have the interference terms +time dependence comes from interference + + align:start position:0% +time dependence comes from interference + + + align:start position:0% +time dependence comes from interference +when we expand in energy + + align:start position:0% +when we expand in energy + + + align:start position:0% +when we expand in energy +functions cool however can these vanish + + align:start position:0% +functions cool however can these vanish + + + align:start position:0% +functions cool however can these vanish +when sorry Sagan great so when Omega 1 + + align:start position:0% +when sorry Sagan great so when Omega 1 + + + align:start position:0% +when sorry Sagan great so when Omega 1 +equals Omega 2 what happens time + + align:start position:0% +equals Omega 2 what happens time + + + align:start position:0% +equals Omega 2 what happens time +dependence goes away but eat obey + + align:start position:0% +dependence goes away but eat obey + + + align:start position:0% +dependence goes away but eat obey +gowanni is e 1 over H bar Omega 2 is e 2 + + align:start position:0% +gowanni is e 1 over H bar Omega 2 is e 2 + + + align:start position:0% +gowanni is e 1 over H bar Omega 2 is e 2 +over H bar we started out by saying + + align:start position:0% +over H bar we started out by saying + + + align:start position:0% +over H bar we started out by saying +these are non degenerate so if they're + + align:start position:0% +these are non degenerate so if they're + + + align:start position:0% +these are non degenerate so if they're +non degenerate the energy is a + + align:start position:0% +non degenerate the energy is a + + + align:start position:0% +non degenerate the energy is a +difference the frequencies are different + + align:start position:0% +difference the frequencies are different + + + align:start position:0% +difference the frequencies are different +so that doesn't help us how do we kill + + align:start position:0% +so that doesn't help us how do we kill + + + align:start position:0% +so that doesn't help us how do we kill +this time dependence yes if the two + + align:start position:0% +this time dependence yes if the two + + + align:start position:0% +this time dependence yes if the two +functions aren't just orthogonal in a + + align:start position:0% +functions aren't just orthogonal in a + + + align:start position:0% +functions aren't just orthogonal in a +functional sense but if we have the + + align:start position:0% +functional sense but if we have the + + + align:start position:0% +functional sense but if we have the +following suppose Phi 1 is like this + + align:start position:0% +following suppose Phi 1 is like this + + + align:start position:0% +following suppose Phi 1 is like this +it's zero everywhere except for in some + + align:start position:0% +it's zero everywhere except for in some + + + align:start position:0% +it's zero everywhere except for in some +lump that's by 1 and Phi 2 is zero + + align:start position:0% +lump that's by 1 and Phi 2 is zero + + + align:start position:0% +lump that's by 1 and Phi 2 is zero +everywhere except here then any where + + align:start position:0% +everywhere except here then any where + + + align:start position:0% +everywhere except here then any where +Phi 1 is a nonzero Phi 2 is zero and + + align:start position:0% +Phi 1 is a nonzero Phi 2 is zero and + + + align:start position:0% +Phi 1 is a nonzero Phi 2 is zero and +anywhere where Phi 2 is nonzero Phi 1 is + + align:start position:0% +anywhere where Phi 2 is nonzero Phi 1 is + + + align:start position:0% +anywhere where Phi 2 is nonzero Phi 1 is +zero so this can point-wise vanish do + + align:start position:0% +zero so this can point-wise vanish do + + + align:start position:0% +zero so this can point-wise vanish do +you expect this to happen generically + + align:start position:0% +you expect this to happen generically + + + align:start position:0% +you expect this to happen generically +does it happen for the energy + + align:start position:0% +does it happen for the energy + + + align:start position:0% +does it happen for the energy +eigenfunctions in the infinite square + + align:start position:0% +eigenfunctions in the infinite square + + + align:start position:0% +eigenfunctions in the infinite square +well + + align:start position:0% + + + + align:start position:0% + +sine waves now some of the Rodino they + + align:start position:0% +sine waves now some of the Rodino they + + + align:start position:0% +sine waves now some of the Rodino they +have zero it isolated points right there + + align:start position:0% +have zero it isolated points right there + + + align:start position:0% +have zero it isolated points right there +nonzero generically yeah so it doesn't + + align:start position:0% +nonzero generically yeah so it doesn't + + + align:start position:0% +nonzero generically yeah so it doesn't +work there what about for the free + + align:start position:0% +work there what about for the free + + + align:start position:0% +work there what about for the free +particle well those are just plain waves + + align:start position:0% +particle well those are just plain waves + + + align:start position:0% +particle well those are just plain waves +does that ever happen no okay so this is + + align:start position:0% +does that ever happen no okay so this is + + + align:start position:0% +does that ever happen no okay so this is +an incredibly special case we'll + + align:start position:0% +an incredibly special case we'll + + + align:start position:0% +an incredibly special case we'll +actually see it in one problem on a + + align:start position:0% +actually see it in one problem on a + + + align:start position:0% +actually see it in one problem on a +problem set later on a very special case + + align:start position:0% +problem set later on a very special case + + + align:start position:0% +problem set later on a very special case +so technically the answer is C and I + + align:start position:0% +so technically the answer is C and I + + + align:start position:0% +so technically the answer is C and I +want you guys keep your minds open on + + align:start position:0% +want you guys keep your minds open on + + + align:start position:0% +want you guys keep your minds open on +these sorts of questions + + align:start position:0% +these sorts of questions + + + align:start position:0% +these sorts of questions +when does the spatial dependence matter + + align:start position:0% +when does the spatial dependence matter + + + align:start position:0% +when does the spatial dependence matter +and when are there interference terms is + + align:start position:0% +and when are there interference terms is + + + align:start position:0% +and when are there interference terms is +there two different questions I want you + + align:start position:0% +there two different questions I want you + + + align:start position:0% +there two different questions I want you +to tease them apart okay cool yeah + + align:start position:0% + + + + align:start position:0% + +that's a very good way to think about it + + align:start position:0% +that's a very good way to think about it + + + align:start position:0% +that's a very good way to think about it +that's exactly right so you've got an + + align:start position:0% +that's exactly right so you've got an + + + align:start position:0% +that's exactly right so you've got an +overall fit so let me that's a very very + + align:start position:0% +overall fit so let me that's a very very + + + align:start position:0% +overall fit so let me that's a very very +good question so the question can you + + align:start position:0% +good question so the question can you + + + align:start position:0% +good question so the question can you +let me let me say that subtly + + align:start position:0% +let me let me say that subtly + + + align:start position:0% +let me let me say that subtly +differently and tell me if this agrees + + align:start position:0% +differently and tell me if this agrees + + + align:start position:0% +differently and tell me if this agrees +with what you were just saying so look I + + align:start position:0% +with what you were just saying so look I + + + align:start position:0% +with what you were just saying so look I +can look at this wavefunction and I + + align:start position:0% +can look at this wavefunction and I + + + align:start position:0% +can look at this wavefunction and I +already know that the overall phase of + + align:start position:0% +already know that the overall phase of + + + align:start position:0% +already know that the overall phase of +wave function doesn't matter that's what + + align:start position:0% +wave function doesn't matter that's what + + + align:start position:0% +wave function doesn't matter that's what +it is to say stationary state is + + align:start position:0% +it is to say stationary state is + + + align:start position:0% +it is to say stationary state is +stationary is got an overall phase + + align:start position:0% +stationary is got an overall phase + + + align:start position:0% +stationary is got an overall phase +that's the only thing that norm squared + + align:start position:0% +that's the only thing that norm squared + + + align:start position:0% +that's the only thing that norm squared +it goes away so I can write this as e to + + align:start position:0% +it goes away so I can write this as e to + + + align:start position:0% +it goes away so I can write this as e to +the minus I Omega 1 T times Phi 1 of X + + align:start position:0% +the minus I Omega 1 T times Phi 1 of X + + + align:start position:0% +the minus I Omega 1 T times Phi 1 of X +plus Phi 2 of X e to the minus I Omega 2 + + align:start position:0% +plus Phi 2 of X e to the minus I Omega 2 + + + align:start position:0% +plus Phi 2 of X e to the minus I Omega 2 +minus Omega 1t is that what you mean so + + align:start position:0% +minus Omega 1t is that what you mean so + + + align:start position:0% +minus Omega 1t is that what you mean so +that's one way we could do this we could + + align:start position:0% +that's one way we could do this we could + + + align:start position:0% +that's one way we could do this we could +also do something else where you do e to + + align:start position:0% +also do something else where you do e to + + + align:start position:0% +also do something else where you do e to +the minus I Omega 1 plus Omega 2 upon 2 + + align:start position:0% +the minus I Omega 1 plus Omega 2 upon 2 + + + align:start position:0% +the minus I Omega 1 plus Omega 2 upon 2 +T this is more I think what you were + + align:start position:0% +T this is more I think what you were + + + align:start position:0% +T this is more I think what you were +thinking of a sort of average frequency + + align:start position:0% +thinking of a sort of average frequency + + + align:start position:0% +thinking of a sort of average frequency +and then a relative frequency and then + + align:start position:0% +and then a relative frequency and then + + + align:start position:0% +and then a relative frequency and then +the change in the frequencies on these + + align:start position:0% +the change in the frequencies on these + + + align:start position:0% +the change in the frequencies on these +two terms absolutely so you can organize + + align:start position:0% +two terms absolutely so you can organize + + + align:start position:0% +two terms absolutely so you can organize +this in many many ways but the important + + align:start position:0% +this in many many ways but the important + + + align:start position:0% +this in many many ways but the important +thing is that your question gets at a + + align:start position:0% +thing is that your question gets at a + + + align:start position:0% +thing is that your question gets at a +very important point which is that the + + align:start position:0% +very important point which is that the + + + align:start position:0% +very important point which is that the +overall phase doesn't matter but + + align:start position:0% +overall phase doesn't matter but + + + align:start position:0% +overall phase doesn't matter but +relative phases in a superposition do + + align:start position:0% +relative phases in a superposition do + + + align:start position:0% +relative phases in a superposition do +matter so when does a phase matter in a + + align:start position:0% +matter so when does a phase matter in a + + + align:start position:0% +matter so when does a phase matter in a +wave function it does not matter if it's + + align:start position:0% +wave function it does not matter if it's + + + align:start position:0% +wave function it does not matter if it's +an overall phase but it does matter if + + align:start position:0% +an overall phase but it does matter if + + + align:start position:0% +an overall phase but it does matter if +it's a relative phase between terms in a + + align:start position:0% +it's a relative phase between terms in a + + + align:start position:0% +it's a relative phase between terms in a +superposition cool very good question + + align:start position:0% +superposition cool very good question + + + align:start position:0% +superposition cool very good question +other questions if not then I have some + + align:start position:0% +other questions if not then I have some + + + align:start position:0% +other questions if not then I have some +so consider a system which is in the + + align:start position:0% +so consider a system which is in the + + + align:start position:0% +so consider a system which is in the +state oh so I should give you five + + align:start position:0% +state oh so I should give you five + + + align:start position:0% +state oh so I should give you five +system is in a state which is a linear + + align:start position:0% +system is in a state which is a linear + + + align:start position:0% +system is in a state which is a linear +combination of N equals 1 and N equals 2 + + align:start position:0% +combination of N equals 1 and N equals 2 + + + align:start position:0% +combination of N equals 1 and N equals 2 +eigen States what's the probability that + + align:start position:0% +eigen States what's the probability that + + + align:start position:0% +eigen States what's the probability that +measurement will give us energy e1 and + + align:start position:0% +measurement will give us energy e1 and + + + align:start position:0% +measurement will give us energy e1 and +it's in this superposition + + align:start position:0% + + + + align:start position:0% + +okay five seconds okay fantastic what's + + align:start position:0% +okay five seconds okay fantastic what's + + + align:start position:0% +okay five seconds okay fantastic what's +the answer yes see great okay everyone + + align:start position:0% +the answer yes see great okay everyone + + + align:start position:0% +the answer yes see great okay everyone +got that one so this one's a slightly + + align:start position:0% +got that one so this one's a slightly + + + align:start position:0% +got that one so this one's a slightly +this one's a more interesting question + + align:start position:0% + + + + align:start position:0% + +suppose I have an infinite well with + + align:start position:0% +suppose I have an infinite well with + + + align:start position:0% +suppose I have an infinite well with +width L how does the energy the ground + + align:start position:0% +width L how does the energy the ground + + + align:start position:0% +width L how does the energy the ground +state energy compared to that of a + + align:start position:0% +state energy compared to that of a + + + align:start position:0% +state energy compared to that of a +system with a wider well + + align:start position:0% + + + + align:start position:0% + +so L versus a larger L okay four seconds + + align:start position:0% + + + + align:start position:0% + +okay quickly discuss it amongst + + align:start position:0% +okay quickly discuss it amongst + + + align:start position:0% +okay quickly discuss it amongst +yourselves wait ten seconds + + align:start position:0% + + + + align:start position:0% + +all right now click again yeah all right + + align:start position:0% +all right now click again yeah all right + + + align:start position:0% +all right now click again yeah all right +5 seconds 1 2 3 4 5 great + + align:start position:0% +5 seconds 1 2 3 4 5 great + + + align:start position:0% +5 seconds 1 2 3 4 5 great +ok the answer is a-ok great you because + + align:start position:0% +ok the answer is a-ok great you because + + + align:start position:0% +ok the answer is a-ok great you because +the energy of the infinite well goes + + align:start position:0% +the energy of the infinite well goes + + + align:start position:0% +the energy of the infinite well goes +like K squared K goes like 1 over L ok + + align:start position:0% +like K squared K goes like 1 over L ok + + + align:start position:0% +like K squared K goes like 1 over L ok +so the energy is if we make it wider the + + align:start position:0% +so the energy is if we make it wider the + + + align:start position:0% +so the energy is if we make it wider the +energy if we make it wider is going to + + align:start position:0% +energy if we make it wider is going to + + + align:start position:0% +energy if we make it wider is going to +be lower and last couple of questions ok + + align:start position:0% +be lower and last couple of questions ok + + + align:start position:0% +be lower and last couple of questions ok +so at t equals 0 could the wave function + + align:start position:0% +so at t equals 0 could the wave function + + + align:start position:0% +so at t equals 0 could the wave function +for an electron in an infinite square + + align:start position:0% +for an electron in an infinite square + + + align:start position:0% +for an electron in an infinite square +well of with a rather than L be a sine + + align:start position:0% +well of with a rather than L be a sine + + + align:start position:0% +well of with a rather than L be a sine +squared of pi X upon a where a suitably + + align:start position:0% +squared of pi X upon a where a suitably + + + align:start position:0% +squared of pi X upon a where a suitably +chosen to be normalized + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +we've got about 5 seconds left and ok we + + align:start position:0% +we've got about 5 seconds left and ok we + + + align:start position:0% +we've got about 5 seconds left and ok we +are at chance we are even odds and the + + align:start position:0% +are at chance we are even odds and the + + + align:start position:0% +are at chance we are even odds and the +answer is not a superposition of a and B + + align:start position:0% +answer is not a superposition of a and B + + + align:start position:0% +answer is not a superposition of a and B +so I encourage you to discuss with the + + align:start position:0% +so I encourage you to discuss with the + + + align:start position:0% +so I encourage you to discuss with the +people around you + + align:start position:0% + + + + align:start position:0% + +yeah great what properties had it better + + align:start position:0% +yeah great what properties had it better + + + align:start position:0% +yeah great what properties had it better +satisfy in order to you know be a viable + + align:start position:0% +satisfy in order to you know be a viable + + + align:start position:0% +satisfy in order to you know be a viable +way functional what properties should + + align:start position:0% +way functional what properties should + + + align:start position:0% +way functional what properties should +the wavefunction have so that it's + + align:start position:0% +the wavefunction have so that it's + + + align:start position:0% +the wavefunction have so that it's +reasonable yeah is is your at the ends + + align:start position:0% +reasonable yeah is is your at the ends + + + align:start position:0% +reasonable yeah is is your at the ends +good is it smooth yeah exactly and so + + align:start position:0% +good is it smooth yeah exactly and so + + + align:start position:0% +good is it smooth yeah exactly and so +you can write it as a superposition + + align:start position:0% +you can write it as a superposition + + + align:start position:0% +you can write it as a superposition +excellent so the answer is yeah + + align:start position:0% + + + + align:start position:0% + +all right um vote again + + align:start position:0% + + + + align:start position:0% + +okay go I might have missed a few people + + align:start position:0% +okay go I might have missed a few people + + + align:start position:0% +okay go I might have missed a few people +so go ahead and start yeah okay five + + align:start position:0% +so go ahead and start yeah okay five + + + align:start position:0% +so go ahead and start yeah okay five +more seconds all right so we went from + + align:start position:0% +more seconds all right so we went from + + + align:start position:0% +more seconds all right so we went from +fifty fifty to seventy seven twenty + + align:start position:0% +fifty fifty to seventy seven twenty + + + align:start position:0% +fifty fifty to seventy seven twenty +three that's pretty good + + align:start position:0% +three that's pretty good + + + align:start position:0% +three that's pretty good +what's the answer eh why is this an + + align:start position:0% +what's the answer eh why is this an + + + align:start position:0% +what's the answer eh why is this an +energy eigenstate does that matter + + align:start position:0% +energy eigenstate does that matter + + + align:start position:0% +energy eigenstate does that matter +no what properties had this wave + + align:start position:0% +no what properties had this wave + + + align:start position:0% +no what properties had this wave +function better satisfied to be a + + align:start position:0% +function better satisfied to be a + + + align:start position:0% +function better satisfied to be a +reasonable wave function in this + + align:start position:0% +reasonable wave function in this + + + align:start position:0% +reasonable wave function in this +potential say again it's got to vanish + + align:start position:0% +potential say again it's got to vanish + + + align:start position:0% +potential say again it's got to vanish +at the walls it's got to satisfy the + + align:start position:0% +at the walls it's got to satisfy the + + + align:start position:0% +at the walls it's got to satisfy the +boundary conditions what else must be + + align:start position:0% +boundary conditions what else must be + + + align:start position:0% +boundary conditions what else must be +true of this wave function normalizable + + align:start position:0% +true of this wave function normalizable + + + align:start position:0% +true of this wave function normalizable +isn't normalizable yeah what else + + align:start position:0% +isn't normalizable yeah what else + + + align:start position:0% +isn't normalizable yeah what else +continuous is better not have any + + align:start position:0% +continuous is better not have any + + + align:start position:0% +continuous is better not have any +discontinuities is it continuous + + align:start position:0% +discontinuities is it continuous + + + align:start position:0% +discontinuities is it continuous +great okay is there any reason that this + + align:start position:0% +great okay is there any reason that this + + + align:start position:0% +great okay is there any reason that this +is a stupid wave function no it's + + align:start position:0% +is a stupid wave function no it's + + + align:start position:0% +is a stupid wave function no it's +perfectly reasonable it's not you know + + align:start position:0% +perfectly reasonable it's not you know + + + align:start position:0% +perfectly reasonable it's not you know +an energy eigenfunction but yeah cool + + align:start position:0% +an energy eigenfunction but yeah cool + + + align:start position:0% +an energy eigenfunction but yeah cool +yeah so right it is a superposition + + align:start position:0% +yeah so right it is a superposition + + + align:start position:0% +yeah so right it is a superposition +answer is like a ship or a time series + + align:start position:0% +answer is like a ship or a time series + + + align:start position:0% +answer is like a ship or a time series +yep + + align:start position:0% + + + + align:start position:0% + +on this domain these are that and the + + align:start position:0% +on this domain these are that and the + + + align:start position:0% +on this domain these are that and the +signs are even right so this is actually + + align:start position:0% +signs are even right so this is actually + + + align:start position:0% +signs are even right so this is actually +odd but we're only looking at from zero + + align:start position:0% +odd but we're only looking at from zero + + + align:start position:0% +odd but we're only looking at from zero +to L right + + align:start position:0% +to L right + + + align:start position:0% +to L right +so I mean that half of it the signs are + + align:start position:0% +so I mean that half of it the signs are + + + align:start position:0% +so I mean that half of it the signs are +odd but we're only looking at the first + + align:start position:0% +odd but we're only looking at the first + + + align:start position:0% +odd but we're only looking at the first +peak so if you're just a well written + + align:start position:0% +peak so if you're just a well written + + + align:start position:0% +peak so if you're just a well written +that as cosine of the midpoint plus the + + align:start position:0% +that as cosine of the midpoint plus the + + + align:start position:0% +that as cosine of the midpoint plus the +distance for the midpoint cool this + + align:start position:0% +distance for the midpoint cool this + + + align:start position:0% +distance for the midpoint cool this +actually let me say that again because + + align:start position:0% +actually let me say that again because + + + align:start position:0% +actually let me say that again because +it's a it's a much better question than + + align:start position:0% +it's a it's a much better question than + + + align:start position:0% +it's a it's a much better question than +I just gave it shre if for so so here's + + align:start position:0% +I just gave it shre if for so so here's + + + align:start position:0% +I just gave it shre if for so so here's +the question the question is look um + + align:start position:0% +the question the question is look um + + + align:start position:0% +the question the question is look um +this function in this business so sine + + align:start position:0% +this function in this business so sine + + + align:start position:0% +this function in this business so sine +is an odd function but sine squared is + + align:start position:0% +is an odd function but sine squared is + + + align:start position:0% +is an odd function but sine squared is +an even function so how can you expand + + align:start position:0% +an even function so how can you expand + + + align:start position:0% +an even function so how can you expand +sine squared and even function in terms + + align:start position:0% +sine squared and even function in terms + + + align:start position:0% +sine squared and even function in terms +of sines an odd function but this is we + + align:start position:0% +of sines an odd function but this is we + + + align:start position:0% +of sines an odd function but this is we +think about this physically here's sine + + align:start position:0% +think about this physically here's sine + + + align:start position:0% +think about this physically here's sine +squared in our domain and here's sine + + align:start position:0% +squared in our domain and here's sine + + + align:start position:0% +squared in our domain and here's sine +now what do you mean by even usually by + + align:start position:0% +now what do you mean by even usually by + + + align:start position:0% +now what do you mean by even usually by +even we mean reflection around zero but + + align:start position:0% +even we mean reflection around zero but + + + align:start position:0% +even we mean reflection around zero but +I could just as well have said + + align:start position:0% +I could just as well have said + + + align:start position:0% +I could just as well have said +reflection around the origin this + + align:start position:0% +reflection around the origin this + + + align:start position:0% +reflection around the origin this +potential is symmetric and the energy + + align:start position:0% +potential is symmetric and the energy + + + align:start position:0% +potential is symmetric and the energy +eigenfunctions are symmetric about the + + align:start position:0% +eigenfunctions are symmetric about the + + + align:start position:0% +eigenfunctions are symmetric about the +origin + + align:start position:0% +origin + + + align:start position:0% +origin +they're not symmetric about reflection + + align:start position:0% +they're not symmetric about reflection + + + align:start position:0% +they're not symmetric about reflection +around this point but they are symmetric + + align:start position:0% +around this point but they are symmetric + + + align:start position:0% +around this point but they are symmetric +about reflection around this point + + align:start position:0% +about reflection around this point + + + align:start position:0% +about reflection around this point +that's particularly natural place to + + align:start position:0% +that's particularly natural place to + + + align:start position:0% +that's particularly natural place to +call it zero so I was calling them + + align:start position:0% +call it zero so I was calling them + + + align:start position:0% +call it zero so I was calling them +signing so I was calling this here but I + + align:start position:0% +signing so I was calling this here but I + + + align:start position:0% +signing so I was calling this here but I +could have called a cosine if I called + + align:start position:0% +could have called a cosine if I called + + + align:start position:0% +could have called a cosine if I called +this zero cool for the same KX okay + + align:start position:0% +this zero cool for the same KX okay + + + align:start position:0% +this zero cool for the same KX okay +and indeed can we expand this sine + + align:start position:0% +and indeed can we expand this sine + + + align:start position:0% +and indeed can we expand this sine +squared function in terms of a basis of + + align:start position:0% +squared function in terms of a basis of + + + align:start position:0% +squared function in terms of a basis of +these signs on the domain 0 to L + + align:start position:0% +these signs on the domain 0 to L + + + align:start position:0% +these signs on the domain 0 to L +absolutely very good question okay + + align:start position:0% +absolutely very good question okay + + + align:start position:0% +absolutely very good question okay +and lastly last clicker question oops + + align:start position:0% +and lastly last clicker question oops + + + align:start position:0% +and lastly last clicker question oops +River okay at equal 0 the particle is + + align:start position:0% +River okay at equal 0 the particle is + + + align:start position:0% +River okay at equal 0 the particle is +described by the wave function we just + + align:start position:0% +described by the wave function we just + + + align:start position:0% +described by the wave function we just +saw which is true the following which + + align:start position:0% +saw which is true the following which + + + align:start position:0% +saw which is true the following which +the Phong is true about the wave + + align:start position:0% +the Phong is true about the wave + + + align:start position:0% +the Phong is true about the wave +function at subsequent times + + align:start position:0% + + + + align:start position:0% + +five seconds + + align:start position:0% + + + + align:start position:0% + +oh okay in the last few seconds we had + + align:start position:0% +oh okay in the last few seconds we had + + + align:start position:0% +oh okay in the last few seconds we had +an explosive burst for a B and C so our + + align:start position:0% +an explosive burst for a B and C so our + + + align:start position:0% +an explosive burst for a B and C so our +current dissipation is eight sixteen ten + + align:start position:0% +current dissipation is eight sixteen ten + + + align:start position:0% +current dissipation is eight sixteen ten +and sixty-seven sounds like 67 is + + align:start position:0% +and sixty-seven sounds like 67 is + + + align:start position:0% +and sixty-seven sounds like 67 is +popular uh discuss quickly very quickly + + align:start position:0% +popular uh discuss quickly very quickly + + + align:start position:0% +popular uh discuss quickly very quickly +with the person next + + align:start position:0% + + + + align:start position:0% + +okay and vote again okay five seconds + + align:start position:0% +okay and vote again okay five seconds + + + align:start position:0% +okay and vote again okay five seconds +get your last vote in all right and the + + align:start position:0% +get your last vote in all right and the + + + align:start position:0% +get your last vote in all right and the +answer is D yeah okay and the reason is + + align:start position:0% +answer is D yeah okay and the reason is + + + align:start position:0% +answer is D yeah okay and the reason is +so let's think about the logic let's go + + align:start position:0% +so let's think about the logic let's go + + + align:start position:0% +so let's think about the logic let's go +through the logic here so as was pointed + + align:start position:0% +through the logic here so as was pointed + + + align:start position:0% +through the logic here so as was pointed +out by student up here earlier the wave + + align:start position:0% +out by student up here earlier the wave + + + align:start position:0% +out by student up here earlier the wave +function sine squared of PI X can be + + align:start position:0% +function sine squared of PI X can be + + + align:start position:0% +function sine squared of PI X can be +expanded in terms of the energy + + align:start position:0% +expanded in terms of the energy + + + align:start position:0% +expanded in terms of the energy +eigenfunction any reasonable function + + align:start position:0% +eigenfunction any reasonable function + + + align:start position:0% +eigenfunction any reasonable function +can be expanded in terms of a + + align:start position:0% +can be expanded in terms of a + + + align:start position:0% +can be expanded in terms of a +superposition of definite energy states + + align:start position:0% +superposition of definite energy states + + + align:start position:0% +superposition of definite energy states +of energy eigenfunctions so that means + + align:start position:0% +of energy eigenfunctions so that means + + + align:start position:0% +of energy eigenfunctions so that means +we can write sy at some time as a + + align:start position:0% +we can write sy at some time as a + + + align:start position:0% +we can write sy at some time as a +superposition CN sine of n PI X upon ei + + align:start position:0% +superposition CN sine of n PI X upon ei + + + align:start position:0% +superposition CN sine of n PI X upon ei +e to the minus I en T on H bar since + + align:start position:0% +e to the minus I en T on H bar since + + + align:start position:0% +e to the minus I en T on H bar since +those are in fact the eigenfunctions + + align:start position:0% +those are in fact the eigenfunctions + + + align:start position:0% +those are in fact the eigenfunctions +okay so we can do that now when we look + + align:start position:0% +okay so we can do that now when we look + + + align:start position:0% +okay so we can do that now when we look +at the time evolution we know that each + + align:start position:0% +at the time evolution we know that each + + + align:start position:0% +at the time evolution we know that each +term in that superposition involves with + + align:start position:0% +term in that superposition involves with + + + align:start position:0% +term in that superposition involves with +a phase the overall wave function does + + align:start position:0% +a phase the overall wave function does + + + align:start position:0% +a phase the overall wave function does +not evolve with a phase it is not an + + align:start position:0% +not evolve with a phase it is not an + + + align:start position:0% +not evolve with a phase it is not an +energy eigenstate there are going to be + + align:start position:0% +energy eigenstate there are going to be + + + align:start position:0% +energy eigenstate there are going to be +interference terms due to the fact that + + align:start position:0% +interference terms due to the fact that + + + align:start position:0% +interference terms due to the fact that +it's a superposition so it's probability + + align:start position:0% +it's a superposition so it's probability + + + align:start position:0% +it's a superposition so it's probability +distribution is not time independent it + + align:start position:0% +distribution is not time independent it + + + align:start position:0% +distribution is not time independent it +is a superposition and so the wave + + align:start position:0% +is a superposition and so the wave + + + align:start position:0% +is a superposition and so the wave +function doesn't rotate by an overall + + align:start position:0% +function doesn't rotate by an overall + + + align:start position:0% +function doesn't rotate by an overall +phase however we can solve the + + align:start position:0% +phase however we can solve the + + + align:start position:0% +phase however we can solve the +Schrodinger equation as we did before + + align:start position:0% +Schrodinger equation as we did before + + + align:start position:0% +Schrodinger equation as we did before +the wave function is expanded at time 0 + + align:start position:0% +the wave function is expanded at time 0 + + + align:start position:0% +the wave function is expanded at time 0 +as the energy eigenfunctions time some + + align:start position:0% +as the energy eigenfunctions time some + + + align:start position:0% +as the energy eigenfunctions time some +set of coefficients and the time + + align:start position:0% +set of coefficients and the time + + + align:start position:0% +set of coefficients and the time +evolution corresponds to adding to each + + align:start position:0% +evolution corresponds to adding to each + + + align:start position:0% +evolution corresponds to adding to each +independent term in the superposition + + align:start position:0% +independent term in the superposition + + + align:start position:0% +independent term in the superposition +the appropriate phase for that energy + + align:start position:0% +the appropriate phase for that energy + + + align:start position:0% +the appropriate phase for that energy +eigenstate cool alright so the answer is + + align:start position:0% +eigenstate cool alright so the answer is + + + align:start position:0% +eigenstate cool alright so the answer is +D + + align:start position:0% + + + + align:start position:0% + +and that's it for the clicker questions + + align:start position:0% +and that's it for the clicker questions + + + align:start position:0% +and that's it for the clicker questions +okay so any questions on the clicker + + align:start position:0% +okay so any questions on the clicker + + + align:start position:0% +okay so any questions on the clicker +aggression so far okay those are going + + align:start position:0% +aggression so far okay those are going + + + align:start position:0% +aggression so far okay those are going +to be posted on the website you can go + + align:start position:0% +to be posted on the website you can go + + + align:start position:0% +to be posted on the website you can go +over them and now back to energy + + align:start position:0% +over them and now back to energy + + + align:start position:0% +over them and now back to energy +eigenfunctions okay so what I want to + + align:start position:0% +eigenfunctions okay so what I want to + + + align:start position:0% +eigenfunctions okay so what I want to +talk about now is the qualitative + + align:start position:0% +talk about now is the qualitative + + + align:start position:0% +talk about now is the qualitative +behavior of energy eigenfunctions + + align:start position:0% +behavior of energy eigenfunctions + + + align:start position:0% +behavior of energy eigenfunctions +suppose I know I have an energy + + align:start position:0% +suppose I know I have an energy + + + align:start position:0% +suppose I know I have an energy +eigenfunction what can I say generally + + align:start position:0% +eigenfunction what can I say generally + + + align:start position:0% +eigenfunction what can I say generally +about its structure so let me ask the + + align:start position:0% +about its structure so let me ask the + + + align:start position:0% +about its structure so let me ask the +question qualitative behavior so suppose + + align:start position:0% +question qualitative behavior so suppose + + + align:start position:0% +question qualitative behavior so suppose +that one hands you a potential U of X + + align:start position:0% +that one hands you a potential U of X + + + align:start position:0% +that one hands you a potential U of X +someone hands you some protection + + align:start position:0% +someone hands you some protection + + + align:start position:0% +someone hands you some protection +potential U of X and says you know look + + align:start position:0% +potential U of X and says you know look + + + align:start position:0% +potential U of X and says you know look +I've got this potential and maybe I'll + + align:start position:0% +I've got this potential and maybe I'll + + + align:start position:0% +I've got this potential and maybe I'll +draw it for you it's got some Wiggles + + align:start position:0% +draw it for you it's got some Wiggles + + + align:start position:0% +draw it for you it's got some Wiggles +and then a big wiggle and then it's got + + align:start position:0% +and then a big wiggle and then it's got + + + align:start position:0% +and then a big wiggle and then it's got +a big wiggle and then we won't do that + + align:start position:0% +a big wiggle and then we won't do that + + + align:start position:0% +a big wiggle and then we won't do that +yeah let's do that and the big wiggle + + align:start position:0% +yeah let's do that and the big wiggle + + + align:start position:0% +yeah let's do that and the big wiggle +and something like this and someone + + align:start position:0% +and something like this and someone + + + align:start position:0% +and something like this and someone +shows you this potential and they say + + align:start position:0% +shows you this potential and they say + + + align:start position:0% +shows you this potential and they say +look what are the energy eigenfunctions + + align:start position:0% +look what are the energy eigenfunctions + + + align:start position:0% +look what are the energy eigenfunctions +right well okay free particle was easy + + align:start position:0% +right well okay free particle was easy + + + align:start position:0% +right well okay free particle was easy +the infinite square well is easy we + + align:start position:0% +the infinite square well is easy we + + + align:start position:0% +the infinite square well is easy we +could solve that analytically but nets + + align:start position:0% +could solve that analytically but nets + + + align:start position:0% +could solve that analytically but nets +involve solving a differential equation + + align:start position:0% +involve solving a differential equation + + + align:start position:0% +involve solving a differential equation +so what differential equation is this + + align:start position:0% +so what differential equation is this + + + align:start position:0% +so what differential equation is this +going to lead us to well we know that + + align:start position:0% +going to lead us to well we know that + + + align:start position:0% +going to lead us to well we know that +the energy eigenvalue equation is minus + + align:start position:0% +the energy eigenvalue equation is minus + + + align:start position:0% +the energy eigenvalue equation is minus +H bar squared upon 2m v prime prime of X + + align:start position:0% +H bar squared upon 2m v prime prime of X + + + align:start position:0% +H bar squared upon 2m v prime prime of X +plus U of X 5x so that's the energy + + align:start position:0% +plus U of X 5x so that's the energy + + + align:start position:0% +plus U of X 5x so that's the energy +operator acting on Phi is equal to + + align:start position:0% +operator acting on Phi is equal to + + + align:start position:0% +operator acting on Phi is equal to +saying that it's an energy eigenvalue + + align:start position:0% +saying that it's an energy eigenvalue + + + align:start position:0% +saying that it's an energy eigenvalue +says that started that it's an energy + + align:start position:0% +says that started that it's an energy + + + align:start position:0% +says that started that it's an energy +eigenfunction phi sub e says that it's + + align:start position:0% +eigenfunction phi sub e says that it's + + + align:start position:0% +eigenfunction phi sub e says that it's +equal to the energy operator acting on + + align:start position:0% +equal to the energy operator acting on + + + align:start position:0% +equal to the energy operator acting on +this eigenfunction is just a constant e + + align:start position:0% +this eigenfunction is just a constant e + + + align:start position:0% +this eigenfunction is just a constant e +phi so P of X and I'm going to work at + + align:start position:0% +phi so P of X and I'm going to work at + + + align:start position:0% +phi so P of X and I'm going to work at +moment in time so we're not going to + + align:start position:0% +moment in time so we're not going to + + + align:start position:0% +moment in time so we're not going to +drop all the T dependence for the moment + + align:start position:0% +drop all the T dependence for the moment + + + align:start position:0% +drop all the T dependence for the moment +so this is a differential equation we + + align:start position:0% +so this is a differential equation we + + + align:start position:0% +so this is a differential equation we +need to solve where u of X is this + + align:start position:0% +need to solve where u of X is this + + + align:start position:0% +need to solve where u of X is this +god-awful function right do you think + + align:start position:0% +god-awful function right do you think + + + align:start position:0% +god-awful function right do you think +it's very likely that you're going to be + + align:start position:0% +it's very likely that you're going to be + + + align:start position:0% +it's very likely that you're going to be +able to solve this analytically yeah + + align:start position:0% +able to solve this analytically yeah + + + align:start position:0% +able to solve this analytically yeah +probably not + + align:start position:0% +probably not + + + align:start position:0% +probably not +however some basic some basic ideas will + + align:start position:0% +however some basic some basic ideas will + + + align:start position:0% +however some basic some basic ideas will +help you get an intuition for what the + + align:start position:0% +help you get an intuition for what the + + + align:start position:0% +help you get an intuition for what the +wave function should look like and so + + align:start position:0% +wave function should look like and so + + + align:start position:0% +wave function should look like and so +and this is I cannot overstate the + + align:start position:0% +and this is I cannot overstate the + + + align:start position:0% +and this is I cannot overstate the +importance of being able to eyeball a + + align:start position:0% +importance of being able to eyeball a + + + align:start position:0% +importance of being able to eyeball a +system and guess the qualitative + + align:start position:0% +system and guess the qualitative + + + align:start position:0% +system and guess the qualitative +features of its wave functions because + + align:start position:0% +features of its wave functions because + + + align:start position:0% +features of its wave functions because +they that that intuition that ability to + + align:start position:0% +they that that intuition that ability to + + + align:start position:0% +they that that intuition that ability to +estimate is going to contain an awful + + align:start position:0% +estimate is going to contain an awful + + + align:start position:0% +estimate is going to contain an awful +lot of physics so let's try to extract + + align:start position:0% +lot of physics so let's try to extract + + + align:start position:0% +lot of physics so let's try to extract +it so in order to do so I want to start + + align:start position:0% +it so in order to do so I want to start + + + align:start position:0% +it so in order to do so I want to start +by massaging this equation into a form + + align:start position:0% +by massaging this equation into a form + + + align:start position:0% +by massaging this equation into a form +which is particularly convenient so + + align:start position:0% +which is particularly convenient so + + + align:start position:0% +which is particularly convenient so +meticulous equation as Phi sub e prime + + align:start position:0% +meticulous equation as Phi sub e prime + + + align:start position:0% +meticulous equation as Phi sub e prime +prime so what I'm going to do is I'm + + align:start position:0% +prime so what I'm going to do is I'm + + + align:start position:0% +prime so what I'm going to do is I'm +going to take this term I'm going to + + align:start position:0% +going to take this term I'm going to + + + align:start position:0% +going to take this term I'm going to +notice this is two derivatives this has + + align:start position:0% +notice this is two derivatives this has + + + align:start position:0% +notice this is two derivatives this has +no derivatives S has no derivatives and + + align:start position:0% +no derivatives S has no derivatives and + + + align:start position:0% +no derivatives S has no derivatives and +I mean a move these this term over here + + align:start position:0% +I mean a move these this term over here + + + align:start position:0% +I mean a move these this term over here +and combine these terms into E minus U + + align:start position:0% +and combine these terms into E minus U + + + align:start position:0% +and combine these terms into E minus U +of X and I'm going to divide each side + + align:start position:0% +of X and I'm going to divide each side + + + align:start position:0% +of X and I'm going to divide each side +by 2m upon H bar squared with a minus + + align:start position:0% +by 2m upon H bar squared with a minus + + + align:start position:0% +by 2m upon H bar squared with a minus +sign giving me that v prime prime of e + + align:start position:0% +sign giving me that v prime prime of e + + + align:start position:0% +sign giving me that v prime prime of e +of X upon Phi e of X dividing through by + + align:start position:0% +of X upon Phi e of X dividing through by + + + align:start position:0% +of X upon Phi e of X dividing through by +this phi e is equal to minus 2m over H + + align:start position:0% +this phi e is equal to minus 2m over H + + + align:start position:0% +this phi e is equal to minus 2m over H +bar squared and let's just get our signs + + align:start position:0% +bar squared and let's just get our signs + + + align:start position:0% +bar squared and let's just get our signs +right we've got the minus from here so + + align:start position:0% +right we've got the minus from here so + + + align:start position:0% +right we've got the minus from here so +this is going to be e minus U of X okay + + align:start position:0% +this is going to be e minus U of X okay + + + align:start position:0% +this is going to be e minus U of X okay +so you might look at that and think well + + align:start position:0% +so you might look at that and think well + + + align:start position:0% +so you might look at that and think well +why is that any better than what I've + + align:start position:0% +why is that any better than what I've + + + align:start position:0% +why is that any better than what I've +just written down but what is the second + + align:start position:0% +just written down but what is the second + + + align:start position:0% +just written down but what is the second +derivative of a function it's telling + + align:start position:0% +derivative of a function it's telling + + + align:start position:0% +derivative of a function it's telling +you not its slope but it's telling you + + align:start position:0% +you not its slope but it's telling you + + + align:start position:0% +you not its slope but it's telling you +how the slope changes right it's telling + + align:start position:0% +how the slope changes right it's telling + + + align:start position:0% +how the slope changes right it's telling +you about the curvature of the function + + align:start position:0% +you about the curvature of the function + + + align:start position:0% +you about the curvature of the function +and what this is telling me is something + + align:start position:0% +and what this is telling me is something + + + align:start position:0% +and what this is telling me is something +very very useful if I know so for + + align:start position:0% +very very useful if I know so for + + + align:start position:0% +very very useful if I know so for +example let's look at the function let's + + align:start position:0% +example let's look at the function let's + + + align:start position:0% +example let's look at the function let's +assume that the function is real + + align:start position:0% +assume that the function is real + + + align:start position:0% +assume that the function is real +although we know in general it's not + + align:start position:0% +although we know in general it's not + + + align:start position:0% +although we know in general it's not +well let's assume that the function is + + align:start position:0% +well let's assume that the function is + + + align:start position:0% +well let's assume that the function is +real for simplicity so we're going to + + align:start position:0% +real for simplicity so we're going to + + + align:start position:0% +real for simplicity so we're going to +plot the real part of Phi okay the + + align:start position:0% +plot the real part of Phi okay the + + + align:start position:0% +plot the real part of Phi okay the +vertical axis and this is X suppose the + + align:start position:0% +vertical axis and this is X suppose the + + + align:start position:0% +vertical axis and this is X suppose the +real part of Phi is positive okay at + + align:start position:0% +real part of Phi is positive okay at + + + align:start position:0% +real part of Phi is positive okay at +some point Phi prime prime if it's + + align:start position:0% +some point Phi prime prime if it's + + + align:start position:0% +some point Phi prime prime if it's +positive tells us that not only is the + + align:start position:0% +positive tells us that not only is the + + + align:start position:0% +positive tells us that not only is the +slope positive its increasing or no it + + align:start position:0% +slope positive its increasing or no it + + + align:start position:0% +slope positive its increasing or no it +doesn't tell us anything about somebody + + align:start position:0% +doesn't tell us anything about somebody + + + align:start position:0% +doesn't tell us anything about somebody +tell us whatever the slope it's + + align:start position:0% +tell us whatever the slope it's + + + align:start position:0% +tell us whatever the slope it's +increasing if it's negative the slope is + + align:start position:0% +increasing if it's negative the slope is + + + align:start position:0% +increasing if it's negative the slope is +increasing as we increase X if it's + + align:start position:0% +increasing as we increase X if it's + + + align:start position:0% +increasing as we increase X if it's +positive its increasing as we increase X + + align:start position:0% +positive its increasing as we increase X + + + align:start position:0% +positive its increasing as we increase X +so it's telling us that the wave + + align:start position:0% +so it's telling us that the wave + + + align:start position:0% +so it's telling us that the wave +function looks like this locally yeah + + align:start position:0% +function looks like this locally yeah + + + align:start position:0% +function looks like this locally yeah +something like that + + align:start position:0% +something like that + + + align:start position:0% +something like that +if Phi is negative okay if I is negative + + align:start position:0% +if Phi is negative okay if I is negative + + + align:start position:0% +if Phi is negative okay if I is negative +then if this quantity is positive then + + align:start position:0% +then if this quantity is positive then + + + align:start position:0% +then if this quantity is positive then +Phi prime problem has to be negative but + + align:start position:0% +Phi prime problem has to be negative but + + + align:start position:0% +Phi prime problem has to be negative but +negative is curving down so if this + + align:start position:0% +negative is curving down so if this + + + align:start position:0% +negative is curving down so if this +quantity which I will call the curvature + + align:start position:0% +quantity which I will call the curvature + + + align:start position:0% +quantity which I will call the curvature +if this quantity is positive it curves + + align:start position:0% +if this quantity is positive it curves + + + align:start position:0% +if this quantity is positive it curves +away from the axis so this is Phi prime + + align:start position:0% +away from the axis so this is Phi prime + + + align:start position:0% +away from the axis so this is Phi prime +prime over Phi greater than zero if this + + align:start position:0% +prime over Phi greater than zero if this + + + align:start position:0% +prime over Phi greater than zero if this +quantity is positive the wave function + + align:start position:0% +quantity is positive the wave function + + + align:start position:0% +quantity is positive the wave function +or the function curves away from the + + align:start position:0% +or the function curves away from the + + + align:start position:0% +or the function curves away from the +axis cool if this quantity is negative + + align:start position:0% +axis cool if this quantity is negative + + + align:start position:0% +axis cool if this quantity is negative +five prime prime upon Phi less than zero + + align:start position:0% +five prime prime upon Phi less than zero + + + align:start position:0% +five prime prime upon Phi less than zero +exactly the opposite this has to be + + align:start position:0% +exactly the opposite this has to be + + + align:start position:0% +exactly the opposite this has to be +negative if Phi is positive then Phi + + align:start position:0% +negative if Phi is positive then Phi + + + align:start position:0% +negative if Phi is positive then Phi +prime prime has to be negative it has to + + align:start position:0% +prime prime has to be negative it has to + + + align:start position:0% +prime prime has to be negative it has to +be curving down yeah + + align:start position:0% +be curving down yeah + + + align:start position:0% +be curving down yeah +and similarly if we're if Phi is + + align:start position:0% +and similarly if we're if Phi is + + + align:start position:0% +and similarly if we're if Phi is +negative then Phi prime prime has to be + + align:start position:0% +negative then Phi prime prime has to be + + + align:start position:0% +negative then Phi prime prime has to be +positive and it has to curve up so if + + align:start position:0% +positive and it has to curve up so if + + + align:start position:0% +positive and it has to curve up so if +this quantity is positive if the + + align:start position:0% +this quantity is positive if the + + + align:start position:0% +this quantity is positive if the +curvature is positive it curves away + + align:start position:0% +curvature is positive it curves away + + + align:start position:0% +curvature is positive it curves away +from the axis if the curvature is + + align:start position:0% +from the axis if the curvature is + + + align:start position:0% +from the axis if the curvature is +negative if this quantity is negative it + + align:start position:0% +negative if this quantity is negative it + + + align:start position:0% +negative if this quantity is negative it +curves towards the axis so what does + + align:start position:0% +curves towards the axis so what does + + + align:start position:0% +curves towards the axis so what does +that tell you about solution + + align:start position:0% +that tell you about solution + + + align:start position:0% +that tell you about solution +when the curvature is positive or + + align:start position:0% +when the curvature is positive or + + + align:start position:0% +when the curvature is positive or +negative tells you the following it + + align:start position:0% +negative tells you the following it + + + align:start position:0% +negative tells you the following it +tells you that imagine we have a + + align:start position:0% +tells you that imagine we have a + + + align:start position:0% +tells you that imagine we have a +function where Phi prime prime over Phi + + align:start position:0% +function where Phi prime prime over Phi + + + align:start position:0% +function where Phi prime prime over Phi +is constant okay and in particular let's + + align:start position:0% +is constant okay and in particular let's + + + align:start position:0% +is constant okay and in particular let's +let Phi prime prime over Phi be a + + align:start position:0% +let Phi prime prime over Phi be a + + + align:start position:0% +let Phi prime prime over Phi be a +constant which is positive or sorry yeah + + align:start position:0% +constant which is positive or sorry yeah + + + align:start position:0% +constant which is positive or sorry yeah +let's say positive and I'll call that + + align:start position:0% +let's say positive and I'll call that + + + align:start position:0% +let's say positive and I'll call that +positive constant a constant Kappa + + align:start position:0% +positive constant a constant Kappa + + + align:start position:0% +positive constant a constant Kappa +squared and to emphasize that it's + + align:start position:0% +squared and to emphasize that it's + + + align:start position:0% +squared and to emphasize that it's +positive I'm going to call it Kappa + + align:start position:0% +positive I'm going to call it Kappa + + + align:start position:0% +positive I'm going to call it Kappa +squared this is a positive thing it's a + + align:start position:0% +squared this is a positive thing it's a + + + align:start position:0% +squared this is a positive thing it's a +real number squared okay what does the + + align:start position:0% +real number squared okay what does the + + + align:start position:0% +real number squared okay what does the +solution look like + + align:start position:0% + + + + align:start position:0% + +well this quantity is positive if it's + + align:start position:0% +well this quantity is positive if it's + + + align:start position:0% +well this quantity is positive if it's +always give me curving away so we have + + align:start position:0% +always give me curving away so we have + + + align:start position:0% +always give me curving away so we have +solutions that look like this or + + align:start position:0% +solutions that look like this or + + + align:start position:0% +solutions that look like this or +solutions that look like this can it + + align:start position:0% +solutions that look like this can it + + + align:start position:0% +solutions that look like this can it +ever be zero yeah sure it could be an + + align:start position:0% +ever be zero yeah sure it could be an + + + align:start position:0% +ever be zero yeah sure it could be an +inflection point so for example here the + + align:start position:0% +inflection point so for example here the + + + align:start position:0% +inflection point so for example here the +curvature is positive but at this point + + align:start position:0% +curvature is positive but at this point + + + align:start position:0% +curvature is positive but at this point +the curvature has to switch to be like + + align:start position:0% +the curvature has to switch to be like + + + align:start position:0% +the curvature has to switch to be like +this what functions are of this form let + + align:start position:0% +this what functions are of this form let + + + align:start position:0% +this what functions are of this form let +me give you another hint here's one is + + align:start position:0% +me give you another hint here's one is + + + align:start position:0% +me give you another hint here's one is +this curvature positive yes what about + + align:start position:0% +this curvature positive yes what about + + + align:start position:0% +this curvature positive yes what about +this one yep those are all positive + + align:start position:0% +this one yep those are all positive + + + align:start position:0% +this one yep those are all positive +curvature and these are Exponential's + + align:start position:0% +curvature and these are Exponential's + + + align:start position:0% +curvature and these are Exponential's +and the solution to this differential + + align:start position:0% +and the solution to this differential + + + align:start position:0% +and the solution to this differential +equation is e to the plus e to the plus + + align:start position:0% +equation is e to the plus e to the plus + + + align:start position:0% +equation is e to the plus e to the plus +Kappa X or e to the minus Kappa X and an + + align:start position:0% +Kappa X or e to the minus Kappa X and an + + + align:start position:0% +Kappa X or e to the minus Kappa X and an +arbitrary solution of this equation is a + + align:start position:0% +arbitrary solution of this equation is a + + + align:start position:0% +arbitrary solution of this equation is a +superposition a e to the Kappa X plus B + + align:start position:0% +superposition a e to the Kappa X plus B + + + align:start position:0% +superposition a e to the Kappa X plus B +e to the minus capex everyone call that + + align:start position:0% +e to the minus capex everyone call that + + + align:start position:0% +e to the minus capex everyone call that +when this quantity is positive we get + + align:start position:0% +when this quantity is positive we get + + + align:start position:0% +when this quantity is positive we get +growing and collapsing Exponential's + + align:start position:0% +growing and collapsing Exponential's + + + align:start position:0% +growing and collapsing Exponential's +yeah on the other hand if Phi prime + + align:start position:0% +yeah on the other hand if Phi prime + + + align:start position:0% +yeah on the other hand if Phi prime +prime over Phi is negative number ie - + + align:start position:0% +prime over Phi is negative number ie - + + + align:start position:0% +prime over Phi is negative number ie - +what I'll call K squared then the + + align:start position:0% +what I'll call K squared then the + + + align:start position:0% +what I'll call K squared then the +curvature has to be negative and what + + align:start position:0% +curvature has to be negative and what + + + align:start position:0% +curvature has to be negative and what +functions have everywhere negative + + align:start position:0% +functions have everywhere negative + + + align:start position:0% +functions have everywhere negative +curvature sinusoidal z-- + + align:start position:0% + + + + align:start position:0% + +cool and the general solution is a e to + + align:start position:0% +cool and the general solution is a e to + + + align:start position:0% +cool and the general solution is a e to +the I KX plus B e to the minus ikx so + + align:start position:0% +the I KX plus B e to the minus ikx so + + + align:start position:0% +the I KX plus B e to the minus ikx so +that differential equation also we're + + align:start position:0% +that differential equation also we're + + + align:start position:0% +that differential equation also we're +going to sign in co-sign cool so putting + + align:start position:0% +going to sign in co-sign cool so putting + + + align:start position:0% +going to sign in co-sign cool so putting +that together with our original function + + align:start position:0% +that together with our original function + + + align:start position:0% +that together with our original function +let's bring this up so you want to think + + align:start position:0% +let's bring this up so you want to think + + + align:start position:0% +let's bring this up so you want to think +about the wave functions here but in + + align:start position:0% +about the wave functions here but in + + + align:start position:0% +about the wave functions here but in +order to think about the energy + + align:start position:0% +order to think about the energy + + + align:start position:0% +order to think about the energy +eigenstates we need to decide on an + + align:start position:0% +eigenstates we need to decide on an + + + align:start position:0% +eigenstates we need to decide on an +energy we need to pick an energy because + + align:start position:0% +energy we need to pick an energy because + + + align:start position:0% +energy we need to pick an energy because +you can't find the solution without fit + + align:start position:0% +you can't find the solution without fit + + + align:start position:0% +you can't find the solution without fit +in the Ender but notice something nice + + align:start position:0% +in the Ender but notice something nice + + + align:start position:0% +in the Ender but notice something nice +here so suppose the energy is e and let + + align:start position:0% +here so suppose the energy is e and let + + + align:start position:0% +here so suppose the energy is e and let +me just draw e this is a constant the + + align:start position:0% +me just draw e this is a constant the + + + align:start position:0% +me just draw e this is a constant the +energy is this this is a value here were + + align:start position:0% +energy is this this is a value here were + + + align:start position:0% +energy is this this is a value here were +drawing potential the function value + + align:start position:0% +drawing potential the function value + + + align:start position:0% +drawing potential the function value +potential this is the value of the + + align:start position:0% +potential this is the value of the + + + align:start position:0% +potential this is the value of the +energy just a constant it's just a + + align:start position:0% +energy just a constant it's just a + + + align:start position:0% +energy just a constant it's just a +number if you had a classical particle + + align:start position:0% +number if you had a classical particle + + + align:start position:0% +number if you had a classical particle +moving in this potential what would + + align:start position:0% +moving in this potential what would + + + align:start position:0% +moving in this potential what would +happen it would roll around so for + + align:start position:0% +happen it would roll around so for + + + align:start position:0% +happen it would roll around so for +example say you gave it this energy by + + align:start position:0% +example say you gave it this energy by + + + align:start position:0% +example say you gave it this energy by +putting it here and think of this as a + + align:start position:0% +putting it here and think of this as a + + + align:start position:0% +putting it here and think of this as a +gravitational potential you put it here + + align:start position:0% +gravitational potential you put it here + + + align:start position:0% +gravitational potential you put it here +you let go and it falls down it'll keep + + align:start position:0% +you let go and it falls down it'll keep + + + align:start position:0% +you let go and it falls down it'll keep +rolling until it gets up here to the + + align:start position:0% +rolling until it gets up here to the + + + align:start position:0% +rolling until it gets up here to the +classical turning point and at that + + align:start position:0% +classical turning point and at that + + + align:start position:0% +classical turning point and at that +point its kinetic energy must be zero + + align:start position:0% +point its kinetic energy must be zero + + + align:start position:0% +point its kinetic energy must be zero +because potential energy is a total + + align:start position:0% +because potential energy is a total + + + align:start position:0% +because potential energy is a total +energy at which point it will turn + + align:start position:0% +energy at which point it will turn + + + align:start position:0% +energy at which point it will turn +around and fall back yes if you take + + align:start position:0% +around and fall back yes if you take + + + align:start position:0% +around and fall back yes if you take +your ball and you put it here you let it + + align:start position:0% +your ball and you put it here you let it + + + align:start position:0% +your ball and you put it here you let it +roll does it ever get here to this + + align:start position:0% +roll does it ever get here to this + + + align:start position:0% +roll does it ever get here to this +position + + align:start position:0% +position + + + align:start position:0% +position +no because doesn't have enough energy + + align:start position:0% +no because doesn't have enough energy + + + align:start position:0% +no because doesn't have enough energy +right classically this is a forbidden + + align:start position:0% +right classically this is a forbidden + + + align:start position:0% +right classically this is a forbidden +position so given an energy and given a + + align:start position:0% +position so given an energy and given a + + + align:start position:0% +position so given an energy and given a +potential we can break the system up + + align:start position:0% +potential we can break the system up + + + align:start position:0% +potential we can break the system up +into classically allowed zones and + + align:start position:0% +into classically allowed zones and + + + align:start position:0% +into classically allowed zones and +classically forbidden zones cool now in + + align:start position:0% +classically forbidden zones cool now in + + + align:start position:0% +classically forbidden zones cool now in +a classically allowed zone the energy is + + align:start position:0% +a classically allowed zone the energy is + + + align:start position:0% +a classically allowed zone the energy is +greater than the potential and + + align:start position:0% +greater than the potential and + + + align:start position:0% +greater than the potential and +classically forbidden zone the energy is + + align:start position:0% +classically forbidden zone the energy is + + + align:start position:0% +classically forbidden zone the energy is +less than the potential let me call that + + align:start position:0% +less than the potential let me call that + + + align:start position:0% +less than the potential let me call that +but this tells us something really nice + + align:start position:0% +but this tells us something really nice + + + align:start position:0% +but this tells us something really nice +if the energy is greater than the + + align:start position:0% +if the energy is greater than the + + + align:start position:0% +if the energy is greater than the +potential what do you know about the + + align:start position:0% +potential what do you know about the + + + align:start position:0% +potential what do you know about the +curvature yeah if we're in a classically + + align:start position:0% +curvature yeah if we're in a classically + + + align:start position:0% +curvature yeah if we're in a classically +allowed zone so the energy is greater + + align:start position:0% +allowed zone so the energy is greater + + + align:start position:0% +allowed zone so the energy is greater +than the potential then this quantity is + + align:start position:0% +than the potential then this quantity is + + + align:start position:0% +than the potential then this quantity is +positive there's a minus sign here so + + align:start position:0% +positive there's a minus sign here so + + + align:start position:0% +positive there's a minus sign here so +this is negative so the curvature is + + align:start position:0% +this is negative so the curvature is + + + align:start position:0% +this is negative so the curvature is +negative + + align:start position:0% + + + + align:start position:0% + +remember curvature is negative means + + align:start position:0% +remember curvature is negative means + + + align:start position:0% +remember curvature is negative means +that we curve towards the axis so in a + + align:start position:0% +that we curve towards the axis so in a + + + align:start position:0% +that we curve towards the axis so in a +classically allowed reason the wave + + align:start position:0% +classically allowed reason the wave + + + align:start position:0% +classically allowed reason the wave +function should be sinusoidal what about + + align:start position:0% +function should be sinusoidal what about + + + align:start position:0% +function should be sinusoidal what about +in the classically forbidden regions in + + align:start position:0% +in the classically forbidden regions in + + + align:start position:0% +in the classically forbidden regions in +the classically forbidden regions the + + align:start position:0% +the classically forbidden regions the + + + align:start position:0% +the classically forbidden regions the +energy is less than the potential that + + align:start position:0% +energy is less than the potential that + + + align:start position:0% +energy is less than the potential that +means a magnitude this is less than this + + align:start position:0% +means a magnitude this is less than this + + + align:start position:0% +means a magnitude this is less than this +this is negative number minus sign the + + align:start position:0% +this is negative number minus sign the + + + align:start position:0% +this is negative number minus sign the +curvature is going to be minus times the + + align:start position:0% +curvature is going to be minus times the + + + align:start position:0% +curvature is going to be minus times the +- as a positive so the curvature is + + align:start position:0% +- as a positive so the curvature is + + + align:start position:0% +- as a positive so the curvature is +positive so the solutions are either + + align:start position:0% +positive so the solutions are either + + + align:start position:0% +positive so the solutions are either +growing Exponential's or shrinking + + align:start position:0% +growing Exponential's or shrinking + + + align:start position:0% +growing Exponential's or shrinking +Exponential's or superpositions of them + + align:start position:0% +Exponential's or superpositions of them + + + align:start position:0% +Exponential's or superpositions of them +and recall that so let's think about a + + align:start position:0% +and recall that so let's think about a + + + align:start position:0% +and recall that so let's think about a +simple example let's work through this + + align:start position:0% +simple example let's work through this + + + align:start position:0% +simple example let's work through this +in a simple example now let me give you + + align:start position:0% +in a simple example now let me give you + + + align:start position:0% +in a simple example now let me give you +a little bit more board space simple + + align:start position:0% +a little bit more board space simple + + + align:start position:0% +a little bit more board space simple +example would be a potential that looks + + align:start position:0% +example would be a potential that looks + + + align:start position:0% +example would be a potential that looks +like this okay and let's just suppose + + align:start position:0% +like this okay and let's just suppose + + + align:start position:0% +like this okay and let's just suppose +that we want to find an energy + + align:start position:0% +that we want to find an energy + + + align:start position:0% +that we want to find an energy +eigenfunction with energy that's e well + + align:start position:0% +eigenfunction with energy that's e well + + + align:start position:0% +eigenfunction with energy that's e well +this is a classically allowed zone and + + align:start position:0% +this is a classically allowed zone and + + + align:start position:0% +this is a classically allowed zone and +these are the classically forbidden + + align:start position:0% +these are the classically forbidden + + + align:start position:0% +these are the classically forbidden +regions now I want to ask what is the + + align:start position:0% +regions now I want to ask what is the + + + align:start position:0% +regions now I want to ask what is the +wave function look like and I don't want + + align:start position:0% +wave function look like and I don't want + + + align:start position:0% +wave function look like and I don't want +to draw it on top of the energy diagram + + align:start position:0% +to draw it on top of the energy diagram + + + align:start position:0% +to draw it on top of the energy diagram +because wave function is not an energy + + align:start position:0% +because wave function is not an energy + + + align:start position:0% +because wave function is not an energy +wave function is a different quantity so + + align:start position:0% +wave function is a different quantity so + + + align:start position:0% +wave function is a different quantity so +it's got different axes and it one draw + + align:start position:0% +it's got different axes and it one draw + + + align:start position:0% +it's got different axes and it one draw +in a different plot so but as a function + + align:start position:0% +in a different plot so but as a function + + + align:start position:0% +in a different plot so but as a function +of X so just to get the position + + align:start position:0% +of X so just to get the position + + + align:start position:0% +of X so just to get the position +straight there is these are the bounds + + align:start position:0% +straight there is these are the bounds + + + align:start position:0% +straight there is these are the bounds +of the classically allowed and forbidden + + align:start position:0% +of the classically allowed and forbidden + + + align:start position:0% +of the classically allowed and forbidden +regions what do we expect well we expect + + align:start position:0% +regions what do we expect well we expect + + + align:start position:0% +regions what do we expect well we expect +that it's going to be sinusoidal in here + + align:start position:0% + + + + align:start position:0% + +we expected it's going to be exponential + + align:start position:0% +we expected it's going to be exponential + + + align:start position:0% +we expected it's going to be exponential +growing or converging out here X right + + align:start position:0% +growing or converging out here X right + + + align:start position:0% +growing or converging out here X right +but one last important thing is that not + + align:start position:0% +but one last important thing is that not + + + align:start position:0% +but one last important thing is that not +only is the curvature negative in here + + align:start position:0% +only is the curvature negative in here + + + align:start position:0% +only is the curvature negative in here +in these classically allowed region but + + align:start position:0% +in these classically allowed region but + + + align:start position:0% +in these classically allowed region but +the the magnitude of the curvature how + + align:start position:0% +the the magnitude of the curvature how + + + align:start position:0% +the the magnitude of the curvature how +rapidly it's turning over how big that + + align:start position:0% +rapidly it's turning over how big that + + + align:start position:0% +rapidly it's turning over how big that +second derivative is depends on the + + align:start position:0% +second derivative is depends on the + + + align:start position:0% +second derivative is depends on the +difference between the energy and the + + align:start position:0% +difference between the energy and the + + + align:start position:0% +difference between the energy and the +potential the greater the difference the + + align:start position:0% +potential the greater the difference the + + + align:start position:0% +potential the greater the difference the +more rapid the curvature the more rapid + + align:start position:0% +more rapid the curvature the more rapid + + + align:start position:0% +more rapid the curvature the more rapid +de turning over and fluctuation if the + + align:start position:0% +de turning over and fluctuation if the + + + align:start position:0% +de turning over and fluctuation if the +difference in between the potential and + + align:start position:0% +difference in between the potential and + + + align:start position:0% +difference in between the potential and +the true energy the total energy is + + align:start position:0% +the true energy the total energy is + + + align:start position:0% +the true energy the total energy is +small then the curvature is very small + + align:start position:0% +small then the curvature is very small + + + align:start position:0% +small then the curvature is very small +so the derivative changes very gradually + + align:start position:0% +so the derivative changes very gradually + + + align:start position:0% +so the derivative changes very gradually +what does that tell us that tells us + + align:start position:0% +what does that tell us that tells us + + + align:start position:0% +what does that tell us that tells us +that in here the wave function is + + align:start position:0% +that in here the wave function is + + + align:start position:0% +that in here the wave function is +oscillating rapidly because of curvature + + align:start position:0% +oscillating rapidly because of curvature + + + align:start position:0% +oscillating rapidly because of curvature +the difference between e energy in the + + align:start position:0% +the difference between e energy in the + + + align:start position:0% +the difference between e energy in the +potential is large and so the wave + + align:start position:0% +potential is large and so the wave + + + align:start position:0% +potential is large and so the wave +function is oscillating rapidly as we + + align:start position:0% +function is oscillating rapidly as we + + + align:start position:0% +function is oscillating rapidly as we +get out towards the classical turning + + align:start position:0% +get out towards the classical turning + + + align:start position:0% +get out towards the classical turning +point the wave function will be + + align:start position:0% +point the wave function will be + + + align:start position:0% +point the wave function will be +oscillating less rapidly the slope will + + align:start position:0% +oscillating less rapidly the slope will + + + align:start position:0% +oscillating less rapidly the slope will +be changing more gradually and as a + + align:start position:0% +be changing more gradually and as a + + + align:start position:0% +be changing more gradually and as a +consequence two things happen we + + align:start position:0% +consequence two things happen we + + + align:start position:0% +consequence two things happen we +actually draw this slowly differently so + + align:start position:0% +actually draw this slowly differently so + + + align:start position:0% +actually draw this slowly differently so +as a consequence two things happen one + + align:start position:0% +as a consequence two things happen one + + + align:start position:0% +as a consequence two things happen one +is the wavelength gets longer because + + align:start position:0% +is the wavelength gets longer because + + + align:start position:0% +is the wavelength gets longer because +the curvature is smaller and the second + + align:start position:0% +the curvature is smaller and the second + + + align:start position:0% +the curvature is smaller and the second +is the amplitude gets larger because it + + align:start position:0% +is the amplitude gets larger because it + + + align:start position:0% +is the amplitude gets larger because it +keeps on having a positive slope for + + align:start position:0% +keeps on having a positive slope for + + + align:start position:0% +keeps on having a positive slope for +longer and longer and it takes longer to + + align:start position:0% +longer and longer and it takes longer to + + + align:start position:0% +longer and longer and it takes longer to +curve back down so here we have rapid + + align:start position:0% +curve back down so here we have rapid + + + align:start position:0% +curve back down so here we have rapid +oscillations and then the oscillations + + align:start position:0% +oscillations and then the oscillations + + + align:start position:0% +oscillations and then the oscillations +get longer and longer wavelengths until + + align:start position:0% +get longer and longer wavelengths until + + + align:start position:0% +get longer and longer wavelengths until +we get out to the classical turning + + align:start position:0% +we get out to the classical turning + + + align:start position:0% +we get out to the classical turning +point and at this point what happens + + align:start position:0% +point and at this point what happens + + + align:start position:0% +point and at this point what happens +yeah it's got to be exponential is now + + align:start position:0% +yeah it's got to be exponential is now + + + align:start position:0% +yeah it's got to be exponential is now +here we have some sign at some super + + align:start position:0% +here we have some sign at some super + + + align:start position:0% +here we have some sign at some super +positions of sine and cosines + + align:start position:0% +positions of sine and cosines + + + align:start position:0% +positions of sine and cosines +Exponential's and a particular it + + align:start position:0% +Exponential's and a particular it + + + align:start position:0% +Exponential's and a particular it +arrives here with some slope and with + + align:start position:0% +arrives here with some slope and with + + + align:start position:0% +arrives here with some slope and with +some value we know on this side we've + + align:start position:0% +some value we know on this side we've + + + align:start position:0% +some value we know on this side we've +got to get Exponential's and so this sum + + align:start position:0% +got to get Exponential's and so this sum + + + align:start position:0% +got to get Exponential's and so this sum +of sines and cosines at this point must + + align:start position:0% +of sines and cosines at this point must + + + align:start position:0% +of sines and cosines at this point must +match that sum of Exponential's how must + + align:start position:0% +match that sum of Exponential's how must + + + align:start position:0% +match that sum of Exponential's how must +it do so what must be true of the wave + + align:start position:0% +it do so what must be true of the wave + + + align:start position:0% +it do so what must be true of the wave +function at this point + + align:start position:0% + + + + align:start position:0% + +can it be discontinuous can its + + align:start position:0% +can it be discontinuous can its + + + align:start position:0% +can it be discontinuous can its +derivative be discontinuous no so it's + + align:start position:0% +derivative be discontinuous no so it's + + + align:start position:0% +derivative be discontinuous no so it's +do it the value and the derivative must + + align:start position:0% +do it the value and the derivative must + + + align:start position:0% +do it the value and the derivative must +be continuous so that tells us precisely + + align:start position:0% +be continuous so that tells us precisely + + + align:start position:0% +be continuous so that tells us precisely +which linear combination of positive + + align:start position:0% +which linear combination of positive + + + align:start position:0% +which linear combination of positive +growing and shrinking Exponential's we + + align:start position:0% +growing and shrinking Exponential's we + + + align:start position:0% +growing and shrinking Exponential's we +get so we'll get some linear combination + + align:start position:0% +get so we'll get some linear combination + + + align:start position:0% +get so we'll get some linear combination +which may do this for a while but since + + align:start position:0% +which may do this for a while but since + + + align:start position:0% +which may do this for a while but since +it's got some contribution of positive + + align:start position:0% +it's got some contribution of positive + + + align:start position:0% +it's got some contribution of positive +exponential it'll just grow + + align:start position:0% +exponential it'll just grow + + + align:start position:0% +exponential it'll just grow +exponentially off to infinity and as the + + align:start position:0% +exponentially off to infinity and as the + + + align:start position:0% +exponentially off to infinity and as the +energy gets further and further away + + align:start position:0% +energy gets further and further away + + + align:start position:0% +energy gets further and further away +from the potential now in the negative + + align:start position:0% +from the potential now in the negative + + + align:start position:0% +from the potential now in the negative +sign what happens to the rate of growth + + align:start position:0% +sign what happens to the rate of growth + + + align:start position:0% +sign what happens to the rate of growth +it gets more and more rapid so this just + + align:start position:0% +it gets more and more rapid so this just + + + align:start position:0% +it gets more and more rapid so this just +diverges more and more rapidly + + align:start position:0% +diverges more and more rapidly + + + align:start position:0% +diverges more and more rapidly +similarly out here we have to match the + + align:start position:0% +similarly out here we have to match the + + + align:start position:0% +similarly out here we have to match the +slope and we know that the curvature has + + align:start position:0% +slope and we know that the curvature has + + + align:start position:0% +slope and we know that the curvature has +to be now positive so it has to do this + + align:start position:0% + + + + align:start position:0% + +so two questions first off is this + + align:start position:0% +so two questions first off is this + + + align:start position:0% +so two questions first off is this +sketch of the wave function a reasonable + + align:start position:0% +sketch of the wave function a reasonable + + + align:start position:0% +sketch of the wave function a reasonable +sketch given what we know about + + align:start position:0% +sketch given what we know about + + + align:start position:0% +sketch given what we know about +curvature and this potential of a wave + + align:start position:0% +curvature and this potential of a wave + + + align:start position:0% +curvature and this potential of a wave +function with that energy are there ways + + align:start position:0% +function with that energy are there ways + + + align:start position:0% +function with that energy are there ways +in which it's a bad estimate bed okay + + align:start position:0% +in which it's a bad estimate bed okay + + + align:start position:0% +in which it's a bad estimate bed okay +excellent absolutely could have crossed + + align:start position:0% +excellent absolutely could have crossed + + + align:start position:0% +excellent absolutely could have crossed +zero so I may have drawn this badly it + + align:start position:0% +zero so I may have drawn this badly it + + + align:start position:0% +zero so I may have drawn this badly it +turned out it was little subtle it's not + + align:start position:0% +turned out it was little subtle it's not + + + align:start position:0% +turned out it was little subtle it's not +obvious maybe it actually punched all + + align:start position:0% +obvious maybe it actually punched all + + + align:start position:0% +obvious maybe it actually punched all +the way through zero and then I diverge + + align:start position:0% +the way through zero and then I diverge + + + align:start position:0% +the way through zero and then I diverge +down negative that's absolutely positive + + align:start position:0% +down negative that's absolutely positive + + + align:start position:0% +down negative that's absolutely positive +so that was one of the quibbles you + + align:start position:0% +so that was one of the quibbles you + + + align:start position:0% +so that was one of the quibbles you +could have another quibble you could + + align:start position:0% +could have another quibble you could + + + align:start position:0% +could have another quibble you could +have is that it looks like I have + + align:start position:0% +have is that it looks like I have + + + align:start position:0% +have is that it looks like I have +constant wavelength in here but the + + align:start position:0% +constant wavelength in here but the + + + align:start position:0% +constant wavelength in here but the +potential is actually changing and the + + align:start position:0% +potential is actually changing and the + + + align:start position:0% +potential is actually changing and the +what you should chalk this up to if + + align:start position:0% +what you should chalk this up to if + + + align:start position:0% +what you should chalk this up to if +you'll pardon the pun is my artistic + + align:start position:0% +you'll pardon the pun is my artistic + + + align:start position:0% +you'll pardon the pun is my artistic +skills are limited okay so this is + + align:start position:0% +skills are limited okay so this is + + + align:start position:0% +skills are limited okay so this is +always going to be sort of inescapable + + align:start position:0% +always going to be sort of inescapable + + + align:start position:0% +always going to be sort of inescapable +that it's when you qualitatively draw + + align:start position:0% +that it's when you qualitatively draw + + + align:start position:0% +that it's when you qualitatively draw +something you know on a test I'm not + + align:start position:0% +something you know on a test I'm not + + + align:start position:0% +something you know on a test I'm not +going to value points on things like + + align:start position:0% +going to value points on things like + + + align:start position:0% +going to value points on things like +that that's what I want to emphasize but + + align:start position:0% +that that's what I want to emphasize but + + + align:start position:0% +that that's what I want to emphasize but +the second thing is there something bad + + align:start position:0% +the second thing is there something bad + + + align:start position:0% +the second thing is there something bad +about this wavefunction yes you've + + align:start position:0% +about this wavefunction yes you've + + + align:start position:0% +about this wavefunction yes you've +already named it what's bad about this + + align:start position:0% +already named it what's bad about this + + + align:start position:0% +already named it what's bad about this +wavefunction it's badly non-normalizable + + align:start position:0% +wavefunction it's badly non-normalizable + + + align:start position:0% +wavefunction it's badly non-normalizable +right it diverges off to infinity out + + align:start position:0% +right it diverges off to infinity out + + + align:start position:0% +right it diverges off to infinity out +here and out here what does that tell + + align:start position:0% +here and out here what does that tell + + + align:start position:0% +here and out here what does that tell +you + + align:start position:0% +you + + + align:start position:0% +you +it's not physical good what else does it + + align:start position:0% +it's not physical good what else does it + + + align:start position:0% +it's not physical good what else does it +tell you about the system + + align:start position:0% + + + + align:start position:0% + +sorry excellent is this an allowable + + align:start position:0% +sorry excellent is this an allowable + + + align:start position:0% +sorry excellent is this an allowable +energy no if the wavefunction has this + + align:start position:0% +energy no if the wavefunction has this + + + align:start position:0% +energy no if the wavefunction has this +energy it is impossible to make it + + align:start position:0% +energy it is impossible to make it + + + align:start position:0% +energy it is impossible to make it +continuous assuming that I drew it + + align:start position:0% +continuous assuming that I drew it + + + align:start position:0% +continuous assuming that I drew it +correctly and have it converge is this + + align:start position:0% +correctly and have it converge is this + + + align:start position:0% +correctly and have it converge is this +wavefunction allowable no because it + + align:start position:0% +wavefunction allowable no because it + + + align:start position:0% +wavefunction allowable no because it +does not satisfy our boundary conditions + + align:start position:0% +does not satisfy our boundary conditions + + + align:start position:0% +does not satisfy our boundary conditions +our boundary conditions are that the + + align:start position:0% +our boundary conditions are that the + + + align:start position:0% +our boundary conditions are that the +wave function must vanish out here and + + align:start position:0% +wave function must vanish out here and + + + align:start position:0% +wave function must vanish out here and +it must vanish out here at infinity in + + align:start position:0% +it must vanish out here at infinity in + + + align:start position:0% +it must vanish out here at infinity in +order to be normalizable here we failed + + align:start position:0% + + + + align:start position:0% + +now you can imagine that so let's + + align:start position:0% +now you can imagine that so let's + + + align:start position:0% +now you can imagine that so let's +decrease the energy a little bit if we + + align:start position:0% +decrease the energy a little bit if we + + + align:start position:0% +decrease the energy a little bit if we +decrease the energy that we are trial + + align:start position:0% +decrease the energy that we are trial + + + align:start position:0% +decrease the energy that we are trial +energy just a little tiny bit what + + align:start position:0% +energy just a little tiny bit what + + + align:start position:0% +energy just a little tiny bit what +happens well that's going to decrease + + align:start position:0% +happens well that's going to decrease + + + align:start position:0% +happens well that's going to decrease +the curvature in here right we decrease + + align:start position:0% +the curvature in here right we decrease + + + align:start position:0% +the curvature in here right we decrease +bring the energy in just a little tiny + + align:start position:0% +bring the energy in just a little tiny + + + align:start position:0% +bring the energy in just a little tiny +bit that means this is a little bit + + align:start position:0% +bit that means this is a little bit + + + align:start position:0% +bit that means this is a little bit +smaller the potential stays the same so + + align:start position:0% +smaller the potential stays the same so + + + align:start position:0% +smaller the potential stays the same so +the curvature in the allowed region is + + align:start position:0% +the curvature in the allowed region is + + + align:start position:0% +the curvature in the allowed region is +just a little tiny bit smaller and + + align:start position:0% +just a little tiny bit smaller and + + + align:start position:0% +just a little tiny bit smaller and +meanwhile the allowed region has got + + align:start position:0% +meanwhile the allowed region has got + + + align:start position:0% +meanwhile the allowed region has got +just a little bit thinner and what that + + align:start position:0% +just a little bit thinner and what that + + + align:start position:0% +just a little bit thinner and what that +will do is the curvature is a little + + align:start position:0% +will do is the curvature is a little + + + align:start position:0% +will do is the curvature is a little +less the region is a little less so now + + align:start position:0% +less the region is a little less so now + + + align:start position:0% +less the region is a little less so now +we have + + align:start position:0% + + + + align:start position:0% + +oops sorry get excited and if we if we + + align:start position:0% +oops sorry get excited and if we if we + + + align:start position:0% +oops sorry get excited and if we if we +tweak the energy what's going to happen + + align:start position:0% +tweak the energy what's going to happen + + + align:start position:0% +tweak the energy what's going to happen +what's going to right here a little bit + + align:start position:0% +what's going to right here a little bit + + + align:start position:0% +what's going to right here a little bit +sooner and let's imagine it's something + + align:start position:0% +sooner and let's imagine it's something + + + align:start position:0% +sooner and let's imagine it's something +like this and if we chose the energy + + align:start position:0% +like this and if we chose the energy + + + align:start position:0% +like this and if we chose the energy +just right we would get it to match to a + + align:start position:0% +just right we would get it to match to a + + + align:start position:0% +just right we would get it to match to a +linear combination of collapsing and + + align:start position:0% +linear combination of collapsing and + + + align:start position:0% +linear combination of collapsing and +growing Exponential's where the + + align:start position:0% +growing Exponential's where the + + + align:start position:0% +growing Exponential's where the +contribution from the growing + + align:start position:0% +contribution from the growing + + + align:start position:0% +contribution from the growing +exponential in this direction vanishes + + align:start position:0% +exponential in this direction vanishes + + + align:start position:0% +exponential in this direction vanishes +right there's precisely one value of the + + align:start position:0% +right there's precisely one value of the + + + align:start position:0% +right there's precisely one value of the +energy that lets me do that with this + + align:start position:0% +energy that lets me do that with this + + + align:start position:0% +energy that lets me do that with this +number of wiggles and so then it goes + + align:start position:0% +number of wiggles and so then it goes + + + align:start position:0% +number of wiggles and so then it goes +through and does its thing and we need + + align:start position:0% +through and does its thing and we need + + + align:start position:0% +through and does its thing and we need +it to happen on both sides now if I take + + align:start position:0% +it to happen on both sides now if I take + + + align:start position:0% +it to happen on both sides now if I take +that solution so that it achieves + + align:start position:0% +that solution so that it achieves + + + align:start position:0% +that solution so that it achieves +convergence out here and it achieves + + align:start position:0% +convergence out here and it achieves + + + align:start position:0% +convergence out here and it achieves +convergence out here and I take that + + align:start position:0% +convergence out here and I take that + + + align:start position:0% +convergence out here and I take that +energy and they increase it by epsilon + + align:start position:0% +energy and they increase it by epsilon + + + align:start position:0% +energy and they increase it by epsilon +by just the tiniest little bit what will + + align:start position:0% +by just the tiniest little bit what will + + + align:start position:0% +by just the tiniest little bit what will +happen to this wave function it will + + align:start position:0% +happen to this wave function it will + + + align:start position:0% +happen to this wave function it will +diverge it will no longer be + + align:start position:0% +diverge it will no longer be + + + align:start position:0% +diverge it will no longer be +normalizable when you have classically + + align:start position:0% +normalizable when you have classically + + + align:start position:0% +normalizable when you have classically +forbidden regions are the allowed + + align:start position:0% +forbidden regions are the allowed + + + align:start position:0% +forbidden regions are the allowed +energies continuous or discrete and that + + align:start position:0% +energies continuous or discrete and that + + + align:start position:0% +energies continuous or discrete and that +answers a question from earlier in the + + align:start position:0% +answers a question from earlier in the + + + align:start position:0% +answers a question from earlier in the +semester Murli ER in the class and it + + align:start position:0% +semester Murli ER in the class and it + + + align:start position:0% +semester Murli ER in the class and it +also is going to be the beginning of the + + align:start position:0% +also is going to be the beginning of the + + + align:start position:0% +also is going to be the beginning of the +answer to the question why is this + + align:start position:0% +answer to the question why is this + + + align:start position:0% +answer to the question why is this +spectrum of hydrogen discrete see you + + align:start position:0% +spectrum of hydrogen discrete see you + + + align:start position:0% +spectrum of hydrogen discrete see you +next time + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/V4xOdtqic3o.txt b/V4xOdtqic3o.txt new file mode 100644 index 0000000000000000000000000000000000000000..2deab08848ab0b7ddd6acdac870302a795c6d9fc --- /dev/null +++ b/V4xOdtqic3o.txt @@ -0,0 +1,12960 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so uh yes before we start uh + + align:start position:0% +ocw.mit.edu so uh yes before we start uh + + + align:start position:0% +ocw.mit.edu so uh yes before we start uh +there are the this chapter will not be + + align:start position:0% +there are the this chapter will not be + + + align:start position:0% +there are the this chapter will not be +part of the midterm uh everything else + + align:start position:0% +part of the midterm uh everything else + + + align:start position:0% +part of the midterm uh everything else +will be and uh uh so all the way up to + + align:start position:0% +will be and uh uh so all the way up to + + + align:start position:0% +will be and uh uh so all the way up to +goodness of fit tests and um there will + + align:start position:0% +goodness of fit tests and um there will + + + align:start position:0% +goodness of fit tests and um there will +be a some practice exams that will be + + align:start position:0% +be a some practice exams that will be + + + align:start position:0% +be a some practice exams that will be +posted in the recitation section of the + + align:start position:0% +posted in the recitation section of the + + + align:start position:0% +posted in the recitation section of the +course and that will be you will be + + align:start position:0% +course and that will be you will be + + + align:start position:0% +course and that will be you will be +working on so the recitation tomorrow + + align:start position:0% +working on so the recitation tomorrow + + + align:start position:0% +working on so the recitation tomorrow +will be a review session for the + + align:start position:0% +will be a review session for the + + + align:start position:0% +will be a review session for the +midterm I'll send an announcement by + + align:start position:0% +midterm I'll send an announcement by + + + align:start position:0% +midterm I'll send an announcement by +email okay + + align:start position:0% +email okay + + + align:start position:0% +email okay +so uh going back to our + + align:start position:0% +so uh going back to our + + + align:start position:0% +so uh going back to our +estimator uh we showed that the Le + + align:start position:0% +estimator uh we showed that the Le + + + align:start position:0% +estimator uh we showed that the Le +course estimator in the case where we + + align:start position:0% +course estimator in the case where we + + + align:start position:0% +course estimator in the case where we +had some uh Gap calcian observation so + + align:start position:0% +had some uh Gap calcian observation so + + + align:start position:0% +had some uh Gap calcian observation so +we had something that looked like this y + + align:start position:0% +we had something that looked like this y + + + align:start position:0% +we had something that looked like this y +was equal to some Matrix x * beta plus + + align:start position:0% +was equal to some Matrix x * beta plus + + + align:start position:0% +was equal to some Matrix x * beta plus +some Epsilon this was an equation that + + align:start position:0% +some Epsilon this was an equation that + + + align:start position:0% +some Epsilon this was an equation that +was happening in R to the N for n + + align:start position:0% +was happening in R to the N for n + + + align:start position:0% +was happening in R to the N for n +observations and then we wrote the Le + + align:start position:0% +observations and then we wrote the Le + + + align:start position:0% +observations and then we wrote the Le +squares estimator beta + + align:start position:0% + + + + align:start position:0% + +hat okay and for uh the purpose from + + align:start position:0% +hat okay and for uh the purpose from + + + align:start position:0% +hat okay and for uh the purpose from +here on WE you see that you have this + + align:start position:0% +here on WE you see that you have this + + + align:start position:0% +here on WE you see that you have this +normal distribution this gaussian P VAR + + align:start position:0% +normal distribution this gaussian P VAR + + + align:start position:0% +normal distribution this gaussian P VAR +distribution that means that at some + + align:start position:0% +distribution that means that at some + + + align:start position:0% +distribution that means that at some +point we've made the the assumption that + + align:start position:0% +point we've made the the assumption that + + + align:start position:0% +point we've made the the assumption that +epsilons were n and dimensional zero + + align:start position:0% +epsilons were n and dimensional zero + + + align:start position:0% +epsilons were n and dimensional zero +identity of our n times the time Sigma + + align:start position:0% +identity of our n times the time Sigma + + + align:start position:0% +identity of our n times the time Sigma +Square which I kept on forgetting about + + align:start position:0% +Square which I kept on forgetting about + + + align:start position:0% +Square which I kept on forgetting about +last time all right I will try not to do + + align:start position:0% +last time all right I will try not to do + + + align:start position:0% +last time all right I will try not to do +that this time and so from this we + + align:start position:0% +that this time and so from this we + + + align:start position:0% +that this time and so from this we +derived a bunch of properties of uh this + + align:start position:0% +derived a bunch of properties of uh this + + + align:start position:0% +derived a bunch of properties of uh this +Le squares estimator beta hat and in + + align:start position:0% +Le squares estimator beta hat and in + + + align:start position:0% +Le squares estimator beta hat and in +particular one the the key thing that + + align:start position:0% +particular one the the key thing that + + + align:start position:0% +particular one the the key thing that +everything was built on was that we + + align:start position:0% +everything was built on was that we + + + align:start position:0% +everything was built on was that we +could write beta hat as the true unknown + + align:start position:0% +could write beta hat as the true unknown + + + align:start position:0% +could write beta hat as the true unknown +beta plus some multivariate gaussian + + align:start position:0% +beta plus some multivariate gaussian + + + align:start position:0% +beta plus some multivariate gaussian +that was centered but had a weird cient + + align:start position:0% +that was centered but had a weird cient + + + align:start position:0% +that was centered but had a weird cient +structure so that was definitely P + + align:start position:0% +structure so that was definitely P + + + align:start position:0% +structure so that was definitely P +dimensional and it was Sigma squ time + + align:start position:0% +dimensional and it was Sigma squ time + + + align:start position:0% +dimensional and it was Sigma squ time +x x uh so that's X transpose X and + + align:start position:0% +x x uh so that's X transpose X and + + + align:start position:0% +x x uh so that's X transpose X and +that's inverse right + + align:start position:0% +that's inverse right + + + align:start position:0% +that's inverse right +yeah and the way we derived that was by + + align:start position:0% +yeah and the way we derived that was by + + + align:start position:0% +yeah and the way we derived that was by +having a lot of at least one + + align:start position:0% +having a lot of at least one + + + align:start position:0% +having a lot of at least one +cancellation between X transpose x and x + + align:start position:0% +cancellation between X transpose x and x + + + align:start position:0% +cancellation between X transpose x and x +transpose X inverse okay so this is + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% + + + + align:start position:0% + +basis for + + align:start position:0% + + + + align:start position:0% + +inference in uh uh uh linear uh in + + align:start position:0% +inference in uh uh uh linear uh in + + + align:start position:0% +inference in uh uh uh linear uh in +linear + + align:start position:0% + + + + align:start position:0% + +regression so in a way that's correct + + align:start position:0% +regression so in a way that's correct + + + align:start position:0% +regression so in a way that's correct +because what happened is that we use the + + align:start position:0% +because what happened is that we use the + + + align:start position:0% +because what happened is that we use the +fact that X beta hat once we have this + + align:start position:0% +fact that X beta hat once we have this + + + align:start position:0% +fact that X beta hat once we have this +beta X beta hat is really just the + + align:start position:0% +beta X beta hat is really just the + + + align:start position:0% +beta X beta hat is really just the +projection of Y onto the linear span of + + align:start position:0% +projection of Y onto the linear span of + + + align:start position:0% +projection of Y onto the linear span of +The Columns of X right or the column + + align:start position:0% +The Columns of X right or the column + + + align:start position:0% +The Columns of X right or the column +span of X and so in particular those + + align:start position:0% +span of X and so in particular those + + + align:start position:0% +span of X and so in particular those +things y minus X beta hats are called + + align:start position:0% + + + + align:start position:0% + +residuals so that's the vector of + + align:start position:0% + + + + align:start position:0% + +residuals what's the dimension of this + + align:start position:0% +residuals what's the dimension of this + + + align:start position:0% +residuals what's the dimension of this +uh of this + + align:start position:0% +uh of this + + + align:start position:0% +uh of this +uh + + align:start position:0% + + + + align:start position:0% + +Vector n by one right so those things we + + align:start position:0% +Vector n by one right so those things we + + + align:start position:0% +Vector n by one right so those things we +can sort of write as Epsilon hat right + + align:start position:0% +can sort of write as Epsilon hat right + + + align:start position:0% +can sort of write as Epsilon hat right +there's sort of an estimate for this + + align:start position:0% +there's sort of an estimate for this + + + align:start position:0% +there's sort of an estimate for this +Epsilon because we just put a hat on on + + align:start position:0% +Epsilon because we just put a hat on on + + + align:start position:0% +Epsilon because we just put a hat on on +beta and from this one we could actually + + align:start position:0% +beta and from this one we could actually + + + align:start position:0% +beta and from this one we could actually +build an unbiased estimator of Sigma hat + + align:start position:0% +build an unbiased estimator of Sigma hat + + + align:start position:0% +build an unbiased estimator of Sigma hat +squar and that was this guy okay and we + + align:start position:0% +squar and that was this guy okay and we + + + align:start position:0% +squar and that was this guy okay and we +showed that the indeed the right + + align:start position:0% +showed that the indeed the right + + + align:start position:0% +showed that the indeed the right +normalization for this was n us P + + align:start position:0% +normalization for this was n us P + + + align:start position:0% +normalization for this was n us P +because + + align:start position:0% +because + + + align:start position:0% +because +Yus X beta hat to Norm is actually a k + + align:start position:0% +Yus X beta hat to Norm is actually a k + + + align:start position:0% +Yus X beta hat to Norm is actually a k +Square within minus P degrees of freedom + + align:start position:0% +Square within minus P degrees of freedom + + + align:start position:0% +Square within minus P degrees of freedom +and so that's is uh up to the scaling by + + align:start position:0% +and so that's is uh up to the scaling by + + + align:start position:0% +and so that's is uh up to the scaling by +Sigma Square so that's what we came up + + align:start position:0% +Sigma Square so that's what we came up + + + align:start position:0% +Sigma Square so that's what we came up +with and something I told you which + + align:start position:0% +with and something I told you which + + + align:start position:0% +with and something I told you which +follows from cockran theorem we did not + + align:start position:0% +follows from cockran theorem we did not + + + align:start position:0% +follows from cockran theorem we did not +go into details about this but + + align:start position:0% +go into details about this but + + + align:start position:0% +go into details about this but +essentially since one of them + + align:start position:0% +essentially since one of them + + + align:start position:0% +essentially since one of them +corresponds to projection onto the + + align:start position:0% +corresponds to projection onto the + + + align:start position:0% +corresponds to projection onto the +linear span of The Columns of X and the + + align:start position:0% +linear span of The Columns of X and the + + + align:start position:0% +linear span of The Columns of X and the +other one corresponds to projection onto + + align:start position:0% +other one corresponds to projection onto + + + align:start position:0% +other one corresponds to projection onto +the orthogonal of this guy and we're in + + align:start position:0% +the orthogonal of this guy and we're in + + + align:start position:0% +the orthogonal of this guy and we're in +a gan case things that are orthogonal + + align:start position:0% +a gan case things that are orthogonal + + + align:start position:0% +a gan case things that are orthogonal +are actually independent in a gaan case + + align:start position:0% +are actually independent in a gaan case + + + align:start position:0% +are actually independent in a gaan case +so from a geometric point of view you + + align:start position:0% +so from a geometric point of view you + + + align:start position:0% +so from a geometric point of view you +can sort of understand everything you + + align:start position:0% +can sort of understand everything you + + + align:start position:0% +can sort of understand everything you +think of your Subspace of the linear + + align:start position:0% +think of your Subspace of the linear + + + align:start position:0% +think of your Subspace of the linear +span of the X's sometimes you project + + align:start position:0% +span of the X's sometimes you project + + + align:start position:0% +span of the X's sometimes you project +onto this guy sometimes you project onto + + align:start position:0% +onto this guy sometimes you project onto + + + align:start position:0% +onto this guy sometimes you project onto +its orthogonal beta hats corresponds to + + align:start position:0% +its orthogonal beta hats corresponds to + + + align:start position:0% +its orthogonal beta hats corresponds to +projection onto the linear span Epsilon + + align:start position:0% +projection onto the linear span Epsilon + + + align:start position:0% +projection onto the linear span Epsilon +hats correspond to a projection onto the + + align:start position:0% +hats correspond to a projection onto the + + + align:start position:0% +hats correspond to a projection onto the +orthogonal and those things tend to be + + align:start position:0% +orthogonal and those things tend to be + + + align:start position:0% +orthogonal and those things tend to be +independent and that's why you have that + + align:start position:0% +independent and that's why you have that + + + align:start position:0% +independent and that's why you have that +beta hat is independent of Sigma square + + align:start position:0% +beta hat is independent of Sigma square + + + align:start position:0% +beta hat is independent of Sigma square +of Sigma hat Square okay so it's really + + align:start position:0% +of Sigma hat Square okay so it's really + + + align:start position:0% +of Sigma hat Square okay so it's really +just a statement about two linear spaces + + align:start position:0% +just a statement about two linear spaces + + + align:start position:0% +just a statement about two linear spaces +being orthogonal with respect to each + + align:start position:0% +being orthogonal with respect to each + + + align:start position:0% +being orthogonal with respect to each +other + + align:start position:0% +other + + + align:start position:0% +other +so we uh we left at this um on this + + align:start position:0% +so we uh we left at this um on this + + + align:start position:0% +so we uh we left at this um on this +slide last time and what I claim is that + + align:start position:0% +slide last time and what I claim is that + + + align:start position:0% +slide last time and what I claim is that +this thing here is actually oh yeah the + + align:start position:0% +this thing here is actually oh yeah the + + + align:start position:0% +this thing here is actually oh yeah the +other thing we want to use so that's + + align:start position:0% +other thing we want to use so that's + + + align:start position:0% +other thing we want to use so that's +good for beta hats but since we don't + + align:start position:0% +good for beta hats but since we don't + + + align:start position:0% +good for beta hats but since we don't +know what Sigma square is if we knew + + align:start position:0% +know what Sigma square is if we knew + + + align:start position:0% +know what Sigma square is if we knew +what Sigma square is that would totally + + align:start position:0% +what Sigma square is that would totally + + + align:start position:0% +what Sigma square is that would totally +be enough for us but we also need this + + align:start position:0% +be enough for us but we also need this + + + align:start position:0% +be enough for us but we also need this +extra thing that Sigma Square hat + + align:start position:0% +extra thing that Sigma Square hat + + + align:start position:0% +extra thing that Sigma Square hat +Square uh over Sigma squ follows and + + align:start position:0% +Square uh over Sigma squ follows and + + + align:start position:0% +Square uh over Sigma squ follows and +there's n minus P this follows a k^ squ + + align:start position:0% +there's n minus P this follows a k^ squ + + + align:start position:0% +there's n minus P this follows a k^ squ +with n minus P degrees of freedom and + + align:start position:0% +with n minus P degrees of freedom and + + + align:start position:0% +with n minus P degrees of freedom and +sigma hat squ is independent of beta hat + + align:start position:0% +sigma hat squ is independent of beta hat + + + align:start position:0% +sigma hat squ is independent of beta hat +right + + align:start position:0% +right + + + align:start position:0% +right +so that's going to be something we need + + align:start position:0% +so that's going to be something we need + + + align:start position:0% +so that's going to be something we need +so that's + + align:start position:0% + + + + align:start position:0% + +useful if Sigma squ is + + align:start position:0% + + + + align:start position:0% + +unnown and again sometimes it might be + + align:start position:0% +unnown and again sometimes it might be + + + align:start position:0% +unnown and again sometimes it might be +known if you're using some sort of you + + align:start position:0% +known if you're using some sort of you + + + align:start position:0% +known if you're using some sort of you +know measurement device for which is + + align:start position:0% +know measurement device for which is + + + align:start position:0% +know measurement device for which is +written on the side of the box + + align:start position:0% + + + + align:start position:0% + +okay so from these two things we're + + align:start position:0% +okay so from these two things we're + + + align:start position:0% +okay so from these two things we're +going to be able to do inference and + + align:start position:0% +going to be able to do inference and + + + align:start position:0% +going to be able to do inference and +inference right we said there's I mean + + align:start position:0% +inference right we said there's I mean + + + align:start position:0% +inference right we said there's I mean +there's three pillars to inference the + + align:start position:0% +there's three pillars to inference the + + + align:start position:0% +there's three pillars to inference the +first one is estimation and we've been + + align:start position:0% +first one is estimation and we've been + + + align:start position:0% +first one is estimation and we've been +doing that so far right we've + + align:start position:0% +doing that so far right we've + + + align:start position:0% +doing that so far right we've +constructed this Le squares estimator + + align:start position:0% +constructed this Le squares estimator + + + align:start position:0% +constructed this Le squares estimator +which happens to be the maximum + + align:start position:0% +which happens to be the maximum + + + align:start position:0% +which happens to be the maximum +likelihood estimator in the gum case the + + align:start position:0% +likelihood estimator in the gum case the + + + align:start position:0% +likelihood estimator in the gum case the +two other things we do in in inference + + align:start position:0% +two other things we do in in inference + + + align:start position:0% +two other things we do in in inference +are confidence intervals and we can do + + align:start position:0% +are confidence intervals and we can do + + + align:start position:0% +are confidence intervals and we can do +confidence intervals we're not going to + + align:start position:0% +confidence intervals we're not going to + + + align:start position:0% +confidence intervals we're not going to +do much because we're going to talk + + align:start position:0% +do much because we're going to talk + + + align:start position:0% +do much because we're going to talk +about their sort of cousin which are + + align:start position:0% +about their sort of cousin which are + + + align:start position:0% +about their sort of cousin which are +tests okay and that's really where the + + align:start position:0% +tests okay and that's really where the + + + align:start position:0% +tests okay and that's really where the +statistical inference comes into and + + align:start position:0% +statistical inference comes into and + + + align:start position:0% +statistical inference comes into and +here we're going to be interested in a + + align:start position:0% +here we're going to be interested in a + + + align:start position:0% +here we're going to be interested in a +very specific kind of test for linear + + align:start position:0% +very specific kind of test for linear + + + align:start position:0% +very specific kind of test for linear +regression and those are tests of the + + align:start position:0% + + + + align:start position:0% + +form beta J so the J coefficient of beta + + align:start position:0% +form beta J so the J coefficient of beta + + + align:start position:0% +form beta J so the J coefficient of beta +is equal to zero and that's going to be + + align:start position:0% +is equal to zero and that's going to be + + + align:start position:0% +is equal to zero and that's going to be +our null hypothesis versus + + align:start position:0% +our null hypothesis versus + + + align:start position:0% +our null hypothesis versus +H1 where beta J is say not equal to zero + + align:start position:0% +H1 where beta J is say not equal to zero + + + align:start position:0% +H1 where beta J is say not equal to zero +and for the purpose of regression unless + + align:start position:0% +and for the purpose of regression unless + + + align:start position:0% +and for the purpose of regression unless +you have lots of domain specific a + + align:start position:0% +you have lots of domain specific a + + + align:start position:0% +you have lots of domain specific a +knowledge it won't be beta G positive or + + align:start position:0% +knowledge it won't be beta G positive or + + + align:start position:0% +knowledge it won't be beta G positive or +beta G negative it's really not not non + + align:start position:0% +beta G negative it's really not not non + + + align:start position:0% +beta G negative it's really not not non +zero that's interesting to you okay so + + align:start position:0% +zero that's interesting to you okay so + + + align:start position:0% +zero that's interesting to you okay so +why would I want to do this + + align:start position:0% +why would I want to do this + + + align:start position:0% +why would I want to do this +test well if I expand this thing where I + + align:start position:0% +test well if I expand this thing where I + + + align:start position:0% +test well if I expand this thing where I +have + + align:start position:0% +have + + + align:start position:0% +have +y uh is equal to uh X + + align:start position:0% +y uh is equal to uh X + + + align:start position:0% +y uh is equal to uh X +beta plus + + align:start position:0% +beta plus + + + align:start position:0% +beta plus +Epsilon so what happens if I look for + + align:start position:0% +Epsilon so what happens if I look for + + + align:start position:0% +Epsilon so what happens if I look for +example at uh the first coordinate so so + + align:start position:0% +example at uh the first coordinate so so + + + align:start position:0% +example at uh the first coordinate so so +I have that Y is actually so say + + align:start position:0% +I have that Y is actually so say + + + align:start position:0% +I have that Y is actually so say +y1 is equal to + + align:start position:0% +y1 is equal to + + + align:start position:0% +y1 is equal to +beta + + align:start position:0% +beta + + + align:start position:0% +beta + + align:start position:0% + + + align:start position:0% +plus beta + + align:start position:0% +plus beta + + + align:start position:0% +plus beta +2x1 well that's actually complicated let + + align:start position:0% +2x1 well that's actually complicated let + + + align:start position:0% +2x1 well that's actually complicated let +me write it like + + align:start position:0% +me write it like + + + align:start position:0% +me write it like +this beta 0 plus beta 1 + + align:start position:0% +this beta 0 plus beta 1 + + + align:start position:0% +this beta 0 plus beta 1 +X1 plus beta P minus one x p minus + + align:start position:0% + + + + align:start position:0% + +one plus uh Epsilon and that's true for + + align:start position:0% +one plus uh Epsilon and that's true for + + + align:start position:0% +one plus uh Epsilon and that's true for +all eyes + + align:start position:0% +all eyes + + + align:start position:0% +all eyes +right okay and this is right so this is + + align:start position:0% +right okay and this is right so this is + + + align:start position:0% +right okay and this is right so this is +beta 1 Time 1 that was our first + + align:start position:0% +beta 1 Time 1 that was our first + + + align:start position:0% +beta 1 Time 1 that was our first +coordinate okay so that's just expanding + + align:start position:0% +coordinate okay so that's just expanding + + + align:start position:0% +coordinate okay so that's just expanding +this going back to the to the the scalar + + align:start position:0% +this going back to the to the the scalar + + + align:start position:0% +this going back to the to the the scalar +form rather than going to the Matrix + + align:start position:0% +form rather than going to the Matrix + + + align:start position:0% +form rather than going to the Matrix +Vector form okay that's what we're doing + + align:start position:0% +Vector form okay that's what we're doing + + + align:start position:0% +Vector form okay that's what we're doing +when I write Y is equal to X beta plus + + align:start position:0% +when I write Y is equal to X beta plus + + + align:start position:0% +when I write Y is equal to X beta plus +Epsilon I I assume that each of my y's + + align:start position:0% +Epsilon I I assume that each of my y's + + + align:start position:0% +Epsilon I I assume that each of my y's +can be represented as a linear + + align:start position:0% +can be represented as a linear + + + align:start position:0% +can be represented as a linear +combination of the X's uh the first one + + align:start position:0% +combination of the X's uh the first one + + + align:start position:0% +combination of the X's uh the first one +being one plus M Epsilon I everybody + + align:start position:0% +being one plus M Epsilon I everybody + + + align:start position:0% +being one plus M Epsilon I everybody +agrees with this + + align:start position:0% +agrees with this + + + align:start position:0% +agrees with this +what does it mean for beta J to be equal + + align:start position:0% +what does it mean for beta J to be equal + + + align:start position:0% +what does it mean for beta J to be equal +to + + align:start position:0% + + + + align:start position:0% + +zero + + align:start position:0% + + + + align:start position:0% + +yeah yeah that XJ doesn't even show up + + align:start position:0% +yeah yeah that XJ doesn't even show up + + + align:start position:0% +yeah yeah that XJ doesn't even show up +in this thing right so if beta J is + + align:start position:0% +in this thing right so if beta J is + + + align:start position:0% +in this thing right so if beta J is +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +zero that means that essentially we can + + align:start position:0% + + + + align:start position:0% + +remove the J coordinate + + align:start position:0% + + + + align:start position:0% + +XJ from all + + align:start position:0% + + + + align:start position:0% + +observations okay so for example I'm a + + align:start position:0% +observations okay so for example I'm a + + + align:start position:0% +observations okay so for example I'm a +banker and I'm trying to + + align:start position:0% +banker and I'm trying to + + + align:start position:0% +banker and I'm trying to +predict some score let's call it why uh + + align:start position:0% +predict some score let's call it why uh + + + align:start position:0% +predict some score let's call it why uh +without the noise right so I'm trying to + + align:start position:0% +without the noise right so I'm trying to + + + align:start position:0% +without the noise right so I'm trying to +predict uh um what is going to be your + + align:start position:0% +predict uh um what is going to be your + + + align:start position:0% +predict uh um what is going to be your +score and that's something that should + + align:start position:0% +score and that's something that should + + + align:start position:0% +score and that's something that should +be sort of telling me how likely you are + + align:start position:0% +be sort of telling me how likely you are + + + align:start position:0% +be sort of telling me how likely you are +to uh reimburse your loan on time right + + align:start position:0% +to uh reimburse your loan on time right + + + align:start position:0% +to uh reimburse your loan on time right +or to have late payments or actually + + align:start position:0% +or to have late payments or actually + + + align:start position:0% +or to have late payments or actually +maybe this day's Bankers are actually + + align:start position:0% +maybe this day's Bankers are actually + + + align:start position:0% +maybe this day's Bankers are actually +looking at how much late fees can I will + + align:start position:0% +looking at how much late fees can I will + + + align:start position:0% +looking at how much late fees can I will +I be collecting from you right maybe + + align:start position:0% +I be collecting from you right maybe + + + align:start position:0% +I be collecting from you right maybe +that's what they're more after rather + + align:start position:0% +that's what they're more after rather + + + align:start position:0% +that's what they're more after rather +than making sure that you reimburse + + align:start position:0% +than making sure that you reimburse + + + align:start position:0% +than making sure that you reimburse +everything they're trying to maximize + + align:start position:0% +everything they're trying to maximize + + + align:start position:0% +everything they're trying to maximize +this number of late fees and they + + align:start position:0% +this number of late fees and they + + + align:start position:0% +this number of late fees and they +collect a bunch of things about you + + align:start position:0% +collect a bunch of things about you + + + align:start position:0% +collect a bunch of things about you +definitely your credit score but maybe + + align:start position:0% +definitely your credit score but maybe + + + align:start position:0% +definitely your credit score but maybe +your ZIP code profession years of + + align:start position:0% +your ZIP code profession years of + + + align:start position:0% +your ZIP code profession years of +education family status a bunch of + + align:start position:0% +education family status a bunch of + + + align:start position:0% +education family status a bunch of +things right one might be your shoe size + + align:start position:0% +things right one might be your shoe size + + + align:start position:0% +things right one might be your shoe size +okay and they want to know maybe shoe + + align:start position:0% +okay and they want to know maybe shoe + + + align:start position:0% +okay and they want to know maybe shoe +size is actually a good explanation for + + align:start position:0% +size is actually a good explanation for + + + align:start position:0% +size is actually a good explanation for +uh how much fees they're going to be + + align:start position:0% +uh how much fees they're going to be + + + align:start position:0% +uh how much fees they're going to be +collecting from you but as you can + + align:start position:0% +collecting from you but as you can + + + align:start position:0% +collecting from you but as you can +imagine this would be a controversial + + align:start position:0% +imagine this would be a controversial + + + align:start position:0% +imagine this would be a controversial +thing to bring and people might want to + + align:start position:0% +thing to bring and people might want to + + + align:start position:0% +thing to bring and people might want to +test whether shoe size is a good idea + + align:start position:0% +test whether shoe size is a good idea + + + align:start position:0% +test whether shoe size is a good idea +and so they would just look at the J + + align:start position:0% +and so they would just look at the J + + + align:start position:0% +and so they would just look at the J +corresponding to shoe size and test + + align:start position:0% +corresponding to shoe size and test + + + align:start position:0% +corresponding to shoe size and test +whether shoe size should appear or not + + align:start position:0% +whether shoe size should appear or not + + + align:start position:0% +whether shoe size should appear or not +in this formula okay and that's + + align:start position:0% +in this formula okay and that's + + + align:start position:0% +in this formula okay and that's +essentially the kind of thing that + + align:start position:0% +essentially the kind of thing that + + + align:start position:0% +essentially the kind of thing that +people are going to do now if I do + + align:start position:0% +people are going to do now if I do + + + align:start position:0% +people are going to do now if I do +genomics and I'm trying to predict the + + align:start position:0% +genomics and I'm trying to predict the + + + align:start position:0% +genomics and I'm trying to predict the +the size the girth of a pumpkin for + + align:start position:0% +the size the girth of a pumpkin for + + + align:start position:0% +the size the girth of a pumpkin for +competition based on some genomic + + align:start position:0% +competition based on some genomic + + + align:start position:0% +competition based on some genomic +available data of available genomic data + + align:start position:0% +available data of available genomic data + + + align:start position:0% +available data of available genomic data +then I can test whether Gan J which is + + align:start position:0% +then I can test whether Gan J which is + + + align:start position:0% +then I can test whether Gan J which is +called I don't know P snap 24 they + + align:start position:0% +called I don't know P snap 24 they + + + align:start position:0% +called I don't know P snap 24 they +always have these crazy names appears or + + align:start position:0% +always have these crazy names appears or + + + align:start position:0% +always have these crazy names appears or +not in this formula is that is the gene + + align:start position:0% +not in this formula is that is the gene + + + align:start position:0% +not in this formula is that is the gene +pnap 24 going to be important or not for + + align:start position:0% +pnap 24 going to be important or not for + + + align:start position:0% +pnap 24 going to be important or not for +the size of the final pumpkin so those + + align:start position:0% +the size of the final pumpkin so those + + + align:start position:0% +the size of the final pumpkin so those +are definitely the important things and + + align:start position:0% +are definitely the important things and + + + align:start position:0% +are definitely the important things and +definitely we want to put beta J not + + align:start position:0% +definitely we want to put beta J not + + + align:start position:0% +definitely we want to put beta J not +equal to zero as the alternative because + + align:start position:0% +equal to zero as the alternative because + + + align:start position:0% +equal to zero as the alternative because +that's where scientific discovery shows + + align:start position:0% +that's where scientific discovery shows + + + align:start position:0% +that's where scientific discovery shows +up okay and so to do that well we're in + + align:start position:0% +up okay and so to do that well we're in + + + align:start position:0% +up okay and so to do that well we're in +a gaussian setup so we know that even if + + align:start position:0% +a gaussian setup so we know that even if + + + align:start position:0% +a gaussian setup so we know that even if +we don't know what Sigma hat is we can + + align:start position:0% +we don't know what Sigma hat is we can + + + align:start position:0% +we don't know what Sigma hat is we can +actually call for a T Test okay so how + + align:start position:0% +actually call for a T Test okay so how + + + align:start position:0% +actually call for a T Test okay so how +did we build the T Test in general well + + align:start position:0% +did we build the T Test in general well + + + align:start position:0% +did we build the T Test in general well +we had something that looked like so + + align:start position:0% + + + + align:start position:0% + +before what we had was something that + + align:start position:0% +before what we had was something that + + + align:start position:0% +before what we had was something that +looked like Theta hat follows was equal + + align:start position:0% +looked like Theta hat follows was equal + + + align:start position:0% +looked like Theta hat follows was equal +to theta plus some n z and something + + align:start position:0% +to theta plus some n z and something + + + align:start position:0% +to theta plus some n z and something +that depended on N maybe right something + + align:start position:0% +that depended on N maybe right something + + + align:start position:0% +that depended on N maybe right something +like this Sigma Square Over N right so + + align:start position:0% +like this Sigma Square Over N right so + + + align:start position:0% +like this Sigma Square Over N right so +that's what it looked like + + align:start position:0% +that's what it looked like + + + align:start position:0% +that's what it looked like +now what we have is that beta hat is + + align:start position:0% +now what we have is that beta hat is + + + align:start position:0% +now what we have is that beta hat is +equal to Beta plus some n but this time + + align:start position:0% +equal to Beta plus some n but this time + + + align:start position:0% +equal to Beta plus some n but this time +it's p variat and then X transpose + + align:start position:0% +it's p variat and then X transpose + + + align:start position:0% +it's p variat and then X transpose +X inverse Sigma + + align:start position:0% +X inverse Sigma + + + align:start position:0% +X inverse Sigma +squ so it's actually very similar except + + align:start position:0% +squ so it's actually very similar except + + + align:start position:0% +squ so it's actually very similar except +that the Matrix + + align:start position:0% +that the Matrix + + + align:start position:0% +that the Matrix +uh X transpose X inverse is now + + align:start position:0% +uh X transpose X inverse is now + + + align:start position:0% +uh X transpose X inverse is now +replacing just this number one/ n but + + align:start position:0% +replacing just this number one/ n but + + + align:start position:0% +replacing just this number one/ n but +it's playing the same role so in + + align:start position:0% +it's playing the same role so in + + + align:start position:0% +it's playing the same role so in +particular this + + align:start position:0% +particular this + + + align:start position:0% +particular this +implies that's for for every J from one + + align:start position:0% +implies that's for for every J from one + + + align:start position:0% +implies that's for for every J from one +to P what is the distribution of beta + + align:start position:0% +to P what is the distribution of beta + + + align:start position:0% +to P what is the distribution of beta +had + + align:start position:0% +had + + + align:start position:0% +had +J well Beta had J is actually equal to + + align:start position:0% +J well Beta had J is actually equal to + + + align:start position:0% +J well Beta had J is actually equal to +so all I have to do so this is a system + + align:start position:0% +so all I have to do so this is a system + + + align:start position:0% +so all I have to do so this is a system +of P equations and all I have to do is + + align:start position:0% +of P equations and all I have to do is + + + align:start position:0% +of P equations and all I have to do is +to read The The J throw right so it's + + align:start position:0% +to read The The J throw right so it's + + + align:start position:0% +to read The The J throw right so it's +telling me here I'm going to read beta + + align:start position:0% +telling me here I'm going to read beta + + + align:start position:0% +telling me here I'm going to read beta +hat J here I'm going to read beta J and + + align:start position:0% +hat J here I'm going to read beta J and + + + align:start position:0% +hat J here I'm going to read beta J and +here I need to read what is the + + align:start position:0% +here I need to read what is the + + + align:start position:0% +here I need to read what is the +distribution of the J coordinate of this + + align:start position:0% +distribution of the J coordinate of this + + + align:start position:0% +distribution of the J coordinate of this +guy right so this is a gussan vector so + + align:start position:0% +guy right so this is a gussan vector so + + + align:start position:0% +guy right so this is a gussan vector so +I need to understand what this + + align:start position:0% +I need to understand what this + + + align:start position:0% +I need to understand what this +definition + + align:start position:0% + + + + align:start position:0% + +is okay + + align:start position:0% +is okay + + + align:start position:0% +is okay +so how do I do this well the observation + + align:start position:0% +so how do I do this well the observation + + + align:start position:0% +so how do I do this well the observation +that that's actually useful for this + + align:start position:0% +that that's actually useful for this + + + align:start position:0% +that that's actually useful for this +maybe I shouldn't use the word + + align:start position:0% +maybe I shouldn't use the word + + + align:start position:0% +maybe I shouldn't use the word +observation in a stats class um so let's + + align:start position:0% +observation in a stats class um so let's + + + align:start position:0% +observation in a stats class um so let's +call it + + align:start position:0% + + + + align:start position:0% + +claim the interesting claim is that if I + + align:start position:0% +claim the interesting claim is that if I + + + align:start position:0% +claim the interesting claim is that if I +want if I if I'm interest if I have a + + align:start position:0% +want if I if I'm interest if I have a + + + align:start position:0% +want if I if I'm interest if I have a +vector let's call it uh + + align:start position:0% +vector let's call it uh + + + align:start position:0% +vector let's call it uh +V then + + align:start position:0% +V then + + + align:start position:0% +V then +VJ is equal to V transpose + + align:start position:0% +VJ is equal to V transpose + + + align:start position:0% +VJ is equal to V transpose +EJ where + + align:start position:0% + + + + align:start position:0% + +EJ is the vector with 0 0 0 and then the + + align:start position:0% +EJ is the vector with 0 0 0 and then the + + + align:start position:0% +EJ is the vector with 0 0 0 and then the +one on the jth coordinate and then zero + + align:start position:0% +one on the jth coordinate and then zero + + + align:start position:0% +one on the jth coordinate and then zero +elsewhere that's the J + + align:start position:0% + + + + align:start position:0% + +coordinate okay so that's the J Vector + + align:start position:0% +coordinate okay so that's the J Vector + + + align:start position:0% +coordinate okay so that's the J Vector +of the canonical basis of + + align:start position:0% +of the canonical basis of + + + align:start position:0% +of the canonical basis of +RP + + align:start position:0% +RP + + + align:start position:0% +RP +right so now that I have this form I can + + align:start position:0% +right so now that I have this form I can + + + align:start position:0% +right so now that I have this form I can +see that essentially Beta had J is just + + align:start position:0% +see that essentially Beta had J is just + + + align:start position:0% +see that essentially Beta had J is just +EJ transpose this + + align:start position:0% +EJ transpose this + + + align:start position:0% +EJ transpose this +np0 Sigma s x + + align:start position:0% +np0 Sigma s x + + + align:start position:0% +np0 Sigma s x +transpose X inverse right + + align:start position:0% + + + + align:start position:0% + +and now I know what the distribution of + + align:start position:0% +and now I know what the distribution of + + + align:start position:0% +and now I know what the distribution of +the inner product between a gan and a ve + + align:start position:0% +the inner product between a gan and a ve + + + align:start position:0% +the inner product between a gan and a ve +deterministic Vector is what is + + align:start position:0% + + + + align:start position:0% + +it it's a gon right so all I have to + + align:start position:0% +it it's a gon right so all I have to + + + align:start position:0% +it it's a gon right so all I have to +check is that EJ transpose + + align:start position:0% +check is that EJ transpose + + + align:start position:0% +check is that EJ transpose +NP + + align:start position:0% +NP + + + align:start position:0% +NP +Z Sigma 2 x transpose X inverse well + + align:start position:0% +Z Sigma 2 x transpose X inverse well + + + align:start position:0% +Z Sigma 2 x transpose X inverse well +this is equal in distribution to what + + align:start position:0% +this is equal in distribution to what + + + align:start position:0% +this is equal in distribution to what +well this is going to be a + + align:start position:0% +well this is going to be a + + + align:start position:0% +well this is going to be a +one-dimensional thing right an in + + align:start position:0% +one-dimensional thing right an in + + + align:start position:0% +one-dimensional thing right an in +product is just a real + + align:start position:0% +product is just a real + + + align:start position:0% +product is just a real +number okay so it's going to be some + + align:start position:0% +number okay so it's going to be some + + + align:start position:0% +number okay so it's going to be some +gussan the mean is going to be zero in a + + align:start position:0% +gussan the mean is going to be zero in a + + + align:start position:0% +gussan the mean is going to be zero in a +product with EJ which + + align:start position:0% +product with EJ which + + + align:start position:0% +product with EJ which +is + + align:start position:0% +is + + + align:start position:0% +is +zero what is the variance of this + + align:start position:0% +zero what is the variance of this + + + align:start position:0% +zero what is the variance of this +guy we're actually used this except that + + align:start position:0% +guy we're actually used this except that + + + align:start position:0% +guy we're actually used this except that +EJ was not a vector but it was a matrix + + align:start position:0% +EJ was not a vector but it was a matrix + + + align:start position:0% +EJ was not a vector but it was a matrix +right so what we do is we to to C so the + + align:start position:0% +right so what we do is we to to C so the + + + align:start position:0% +right so what we do is we to to C so the +rule is that V + + align:start position:0% +rule is that V + + + align:start position:0% +rule is that V +transpose say n mu + + align:start position:0% +transpose say n mu + + + align:start position:0% +transpose say n mu +Sigma is equal is + + align:start position:0% +Sigma is equal is + + + align:start position:0% +Sigma is equal is +some + + align:start position:0% +some + + + align:start position:0% +some +n mu V transpose mu and then V transpose + + align:start position:0% +n mu V transpose mu and then V transpose + + + align:start position:0% +n mu V transpose mu and then V transpose +Sigma V + + align:start position:0% +Sigma V + + + align:start position:0% +Sigma V +right that's the rule for gussan vectors + + align:start position:0% +right that's the rule for gussan vectors + + + align:start position:0% +right that's the rule for gussan vectors +that's just the property of Gan + + align:start position:0% +that's just the property of Gan + + + align:start position:0% +that's just the property of Gan +vectors so what do we have here well e + + align:start position:0% +vectors so what do we have here well e + + + align:start position:0% +vectors so what do we have here well e +plays the role of uh V and sigma Square + + align:start position:0% +plays the role of uh V and sigma Square + + + align:start position:0% +plays the role of uh V and sigma Square +X transpose X inverse is the role of + + align:start position:0% +X transpose X inverse is the role of + + + align:start position:0% +X transpose X inverse is the role of +Sigma so here I'm left with EJ + + align:start position:0% +Sigma so here I'm left with EJ + + + align:start position:0% +Sigma so here I'm left with EJ +transpose let me pull out the sigma + + align:start position:0% +transpose let me pull out the sigma + + + align:start position:0% +transpose let me pull out the sigma +Square + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +okay but this thing is what happens if I + + align:start position:0% +okay but this thing is what happens if I + + + align:start position:0% +okay but this thing is what happens if I +take a matrix I pre-multiply it by this + + align:start position:0% +take a matrix I pre-multiply it by this + + + align:start position:0% +take a matrix I pre-multiply it by this +Vector EJ and I post multiply it by this + + align:start position:0% +Vector EJ and I post multiply it by this + + + align:start position:0% +Vector EJ and I post multiply it by this +Vector + + align:start position:0% + + + + align:start position:0% + +EJ I'm claiming that I'm actually this + + align:start position:0% +EJ I'm claiming that I'm actually this + + + align:start position:0% +EJ I'm claiming that I'm actually this +corresponds to only one single element + + align:start position:0% +corresponds to only one single element + + + align:start position:0% +corresponds to only one single element +of this Matrix which one is + + align:start position:0% +of this Matrix which one is + + + align:start position:0% +of this Matrix which one is +it J diagonal element right so this + + align:start position:0% +it J diagonal element right so this + + + align:start position:0% +it J diagonal element right so this +thing + + align:start position:0% +thing + + + align:start position:0% +thing +here is nothing but X transpose X + + align:start position:0% +here is nothing but X transpose X + + + align:start position:0% +here is nothing but X transpose X +inverse inverse and then the J diagonal + + align:start position:0% +inverse inverse and then the J diagonal + + + align:start position:0% +inverse inverse and then the J diagonal +element is + + align:start position:0% + + + + align:start position:0% + +JJ now I cannot go go any further right + + align:start position:0% +JJ now I cannot go go any further right + + + align:start position:0% +JJ now I cannot go go any further right +X transpose X inverse can be a + + align:start position:0% +X transpose X inverse can be a + + + align:start position:0% +X transpose X inverse can be a +complicated Matrix and I do not know how + + align:start position:0% +complicated Matrix and I do not know how + + + align:start position:0% +complicated Matrix and I do not know how +to express it's j j diagonal element uh + + align:start position:0% +to express it's j j diagonal element uh + + + align:start position:0% +to express it's j j diagonal element uh +much better than this + + align:start position:0% +much better than this + + + align:start position:0% +much better than this +actually uh + + align:start position:0% +actually uh + + + align:start position:0% +actually uh +well no actually I don't right it + + align:start position:0% +well no actually I don't right it + + + align:start position:0% +well no actually I don't right it +involves basically all the coefficients + + align:start position:0% + + + + align:start position:0% + +Yeah + + align:start position:0% +Yeah + + + align:start position:0% +Yeah +Yeah from this rule + + align:start position:0% +Yeah from this rule + + + align:start position:0% +Yeah from this rule +so you always pre and post multiply when + + align:start position:0% +so you always pre and post multiply when + + + align:start position:0% +so you always pre and post multiply when +you talk about the coant because if you + + align:start position:0% +you talk about the coant because if you + + + align:start position:0% +you talk about the coant because if you +did not it would be a vector and not a + + align:start position:0% +did not it would be a vector and not a + + + align:start position:0% +did not it would be a vector and not a +scalar for one uh but in general think + + align:start position:0% +scalar for one uh but in general think + + + align:start position:0% +scalar for one uh but in general think +of v as a matrix it's still true even if + + align:start position:0% +of v as a matrix it's still true even if + + + align:start position:0% +of v as a matrix it's still true even if +V is a matrix that's compatible with + + align:start position:0% +V is a matrix that's compatible with + + + align:start position:0% +V is a matrix that's compatible with +premultiplying by some + + align:start position:0% + + + + align:start position:0% + +gum + + align:start position:0% +gum + + + align:start position:0% +gum +okay any other + + align:start position:0% +okay any other + + + align:start position:0% +okay any other +question + + align:start position:0% + + + + align:start position:0% + +yeah uh so for any vector + + align:start position:0% + + + + align:start position:0% + +v any other + + align:start position:0% +v any other + + + align:start position:0% +v any other +question all right so now we've sort of + + align:start position:0% +question all right so now we've sort of + + + align:start position:0% +question all right so now we've sort of +identified that this the J coefficient + + align:start position:0% +identified that this the J coefficient + + + align:start position:0% +identified that this the J coefficient +of this Gan which I can represent from + + align:start position:0% +of this Gan which I can represent from + + + align:start position:0% +of this Gan which I can represent from +the claim as EJ transport this guy is + + align:start position:0% +the claim as EJ transport this guy is + + + align:start position:0% +the claim as EJ transport this guy is +also a gussan it's centered and its + + align:start position:0% +also a gussan it's centered and its + + + align:start position:0% +also a gussan it's centered and its +ciance its variance now is Sigma squ + + align:start position:0% +ciance its variance now is Sigma squ + + + align:start position:0% +ciance its variance now is Sigma squ +time the J diagonal element of X + + align:start position:0% +time the J diagonal element of X + + + align:start position:0% +time the J diagonal element of X +transpose X inverse so + + align:start position:0% +transpose X inverse so + + + align:start position:0% +transpose X inverse so +so the + + align:start position:0% +so the + + + align:start position:0% +so the +conclusion is that Beta had J is equal + + align:start position:0% +conclusion is that Beta had J is equal + + + align:start position:0% +conclusion is that Beta had J is equal +to Beta + + align:start position:0% +to Beta + + + align:start position:0% +to Beta +J plus some n and I'm going to emphasize + + align:start position:0% +J plus some n and I'm going to emphasize + + + align:start position:0% +J plus some n and I'm going to emphasize +the fact that now it's onedimensional + + align:start position:0% +the fact that now it's onedimensional + + + align:start position:0% +the fact that now it's onedimensional +with mean zero and coari sigma squ X + + align:start position:0% +with mean zero and coari sigma squ X + + + align:start position:0% +with mean zero and coari sigma squ X +transpose X inverse inverse + + align:start position:0% + + + + align:start position:0% + +JJ now if you look at the last line of + + align:start position:0% +JJ now if you look at the last line of + + + align:start position:0% +JJ now if you look at the last line of +the second board and the first line on + + align:start position:0% +the second board and the first line on + + + align:start position:0% +the second board and the first line on +the first + + align:start position:0% +the first + + + align:start position:0% +the first +board those are basically the same + + align:start position:0% +board those are basically the same + + + align:start position:0% +board those are basically the same +thing + + align:start position:0% +thing + + + align:start position:0% +thing +right beta hat J is my Theta hat beta J + + align:start position:0% +right beta hat J is my Theta hat beta J + + + align:start position:0% +right beta hat J is my Theta hat beta J +is my Theta and the variance Sigma + + align:start position:0% +is my Theta and the variance Sigma + + + align:start position:0% +is my Theta and the variance Sigma +Square Over N is now Sigma Square times + + align:start position:0% +Square Over N is now Sigma Square times + + + align:start position:0% +Square Over N is now Sigma Square times +this JJ element now the inverse sort of + + align:start position:0% +this JJ element now the inverse sort of + + + align:start position:0% +this JJ element now the inverse sort of +suggests that it looks like the inverse + + align:start position:0% +suggests that it looks like the inverse + + + align:start position:0% +suggests that it looks like the inverse +of n so those things are going to we're + + align:start position:0% +of n so those things are going to we're + + + align:start position:0% +of n so those things are going to we're +going to want to think of those guys as + + align:start position:0% +going to want to think of those guys as + + + align:start position:0% +going to want to think of those guys as +being some sort of one over n kind of of + + align:start position:0% +being some sort of one over n kind of of + + + align:start position:0% +being some sort of one over n kind of of +of of + + align:start position:0% +of of + + + align:start position:0% +of of +statement + + align:start position:0% + + + + align:start position:0% + +okay so from this the fact that those + + align:start position:0% +okay so from this the fact that those + + + align:start position:0% +okay so from this the fact that those +two things are the + + align:start position:0% +two things are the + + + align:start position:0% +two things are the +same leads us to believe that we are now + + align:start position:0% +same leads us to believe that we are now + + + align:start position:0% +same leads us to believe that we are now +equipped to perform the test that we're + + align:start position:0% +equipped to perform the test that we're + + + align:start position:0% +equipped to perform the test that we're +trying to do because under the null + + align:start position:0% +trying to do because under the null + + + align:start position:0% +trying to do because under the null +hypothesis beta J is known is is known + + align:start position:0% +hypothesis beta J is known is is known + + + align:start position:0% +hypothesis beta J is known is is known +it's equal to zero so I can remove it + + align:start position:0% +it's equal to zero so I can remove it + + + align:start position:0% +it's equal to zero so I can remove it +and I have to deal with the sigma square + + align:start position:0% +and I have to deal with the sigma square + + + align:start position:0% +and I have to deal with the sigma square +if Sigma square is known then I can just + + align:start position:0% +if Sigma square is known then I can just + + + align:start position:0% +if Sigma square is known then I can just +perform a regular G gon test using Gan + + align:start position:0% +perform a regular G gon test using Gan + + + align:start position:0% +perform a regular G gon test using Gan +quentel and if Sigma square is unknown + + align:start position:0% +quentel and if Sigma square is unknown + + + align:start position:0% +quentel and if Sigma square is unknown +I'm going to just divide by Sigma squar + + align:start position:0% +I'm going to just divide by Sigma squar + + + align:start position:0% +I'm going to just divide by Sigma squar +and multiply by Sigma hat and uh and + + align:start position:0% +and multiply by Sigma hat and uh and + + + align:start position:0% +and multiply by Sigma hat and uh and +then I'm going to basically get my T + + align:start position:0% +then I'm going to basically get my T + + + align:start position:0% +then I'm going to basically get my T +Test + + align:start position:0% + + + + align:start position:0% + +Okay so + + align:start position:0% + + + + align:start position:0% + +actually for the purpose of your uh exam + + align:start position:0% +actually for the purpose of your uh exam + + + align:start position:0% +actually for the purpose of your uh exam +I really suggest that you understand + + align:start position:0% +I really suggest that you understand + + + align:start position:0% +I really suggest that you understand +every single word I'm going to be saying + + align:start position:0% +every single word I'm going to be saying + + + align:start position:0% +every single word I'm going to be saying +now because this is exactly the same + + align:start position:0% +now because this is exactly the same + + + align:start position:0% +now because this is exactly the same +thing that you're expected to know from + + align:start position:0% +thing that you're expected to know from + + + align:start position:0% +thing that you're expected to know from +other courses right because right now + + align:start position:0% +other courses right because right now + + + align:start position:0% +other courses right because right now +I'm just going to apply exactly the same + + align:start position:0% +I'm just going to apply exactly the same + + + align:start position:0% +I'm just going to apply exactly the same +technique that we did for the single + + align:start position:0% +technique that we did for the single + + + align:start position:0% +technique that we did for the single +parameter estimation okay so what we + + align:start position:0% +parameter estimation okay so what we + + + align:start position:0% +parameter estimation okay so what we +have now is that under age + + align:start position:0% + + + + align:start position:0% + +zero beta J is equal to + + align:start position:0% +zero beta J is equal to + + + align:start position:0% +zero beta J is equal to +zero therefore + + align:start position:0% + + + + align:start position:0% + +beta head J follows some + + align:start position:0% +beta head J follows some + + + align:start position:0% +beta head J follows some +n zero Sigma squar and I'm going to call + + align:start position:0% +n zero Sigma squar and I'm going to call + + + align:start position:0% +n zero Sigma squar and I'm going to call +this just like I do in the slide I'm + + align:start position:0% +this just like I do in the slide I'm + + + align:start position:0% +this just like I do in the slide I'm +going to call this gamma + + align:start position:0% + + + + align:start position:0% + +J so gamma J is this x transpose X + + align:start position:0% +J so gamma J is this x transpose X + + + align:start position:0% +J so gamma J is this x transpose X +inverse JJ J diagonal + + align:start position:0% +inverse JJ J diagonal + + + align:start position:0% +inverse JJ J diagonal +element okay okay so that implies that + + align:start position:0% +element okay okay so that implies that + + + align:start position:0% +element okay okay so that implies that +beta hat J over Sigma oh was it a square + + align:start position:0% +beta hat J over Sigma oh was it a square + + + align:start position:0% +beta hat J over Sigma oh was it a square +root yeah Sigma square root of gamma J + + align:start position:0% +root yeah Sigma square root of gamma J + + + align:start position:0% +root yeah Sigma square root of gamma J +follows some + + align:start position:0% +follows some + + + align:start position:0% +follows some +n01 so I can form my test + + align:start position:0% + + + + align:start position:0% + +statistic which to be + + align:start position:0% + + + + align:start position:0% + +reject if the absolute value + + align:start position:0% +reject if the absolute value + + + align:start position:0% +reject if the absolute value +of beta had J divided by Sigma square + + align:start position:0% +of beta had J divided by Sigma square + + + align:start position:0% +of beta had J divided by Sigma square +root gamma + + align:start position:0% +root gamma + + + align:start position:0% +root gamma +J is larger than what can somebody tell + + align:start position:0% +J is larger than what can somebody tell + + + align:start position:0% +J is larger than what can somebody tell +me what I want this to be larger than to + + align:start position:0% + + + + align:start position:0% + +reject Q + + align:start position:0% + + + + align:start position:0% + +Alpha everybody agrees of what of of + + align:start position:0% +Alpha everybody agrees of what of of + + + align:start position:0% +Alpha everybody agrees of what of of +this guy + + align:start position:0% + + + + align:start position:0% + +right with the standard notation that + + align:start position:0% +right with the standard notation that + + + align:start position:0% +right with the standard notation that +this is the quantal do everybody + + align:start position:0% + + + + align:start position:0% + +agrees Alpha over two right so not + + align:start position:0% +agrees Alpha over two right so not + + + align:start position:0% +agrees Alpha over two right so not +everybody should be agreeing thank you + + align:start position:0% +everybody should be agreeing thank you + + + align:start position:0% +everybody should be agreeing thank you +you're the first one to disagree with + + align:start position:0% +you're the first one to disagree with + + + align:start position:0% +you're the first one to disagree with +yourself which is probably good uh it's + + align:start position:0% +yourself which is probably good uh it's + + + align:start position:0% +yourself which is probably good uh it's +half over two because of the absolute + + align:start position:0% +half over two because of the absolute + + + align:start position:0% +half over two because of the absolute +value right I want to just be away from + + align:start position:0% +value right I want to just be away from + + + align:start position:0% +value right I want to just be away from +this guy and that's because I have right + + align:start position:0% +this guy and that's because I have right + + + align:start position:0% +this guy and that's because I have right +so the alpha over two the the the sanity + + align:start position:0% +so the alpha over two the the the sanity + + + align:start position:0% +so the alpha over two the the the sanity +check should be that H1 is beta J not + + align:start position:0% +check should be that H1 is beta J not + + + align:start position:0% +check should be that H1 is beta J not +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +zero so that works if + + align:start position:0% +zero so that works if + + + align:start position:0% +zero so that works if +Sigma is + + align:start position:0% +Sigma is + + + align:start position:0% +Sigma is +known right because I need to know Sigma + + align:start position:0% +known right because I need to know Sigma + + + align:start position:0% +known right because I need to know Sigma +to be able to build my test so if Sigma + + align:start position:0% +to be able to build my test so if Sigma + + + align:start position:0% +to be able to build my test so if Sigma +is unknown well I can tell you use this + + align:start position:0% +is unknown well I can tell you use this + + + align:start position:0% +is unknown well I can tell you use this +test but you're going to be like okay + + align:start position:0% +test but you're going to be like okay + + + align:start position:0% +test but you're going to be like okay +when I'm going to have to plug in some + + align:start position:0% +when I'm going to have to plug in some + + + align:start position:0% +when I'm going to have to plug in some +numbers I'm going to be I'm going to be + + align:start position:0% + + + + align:start position:0% + +stuck but if + + align:start position:0% + + + + align:start position:0% + +Sigma is + + align:start position:0% + + + + align:start position:0% + +unnown we have + + align:start position:0% +unnown we have + + + align:start position:0% +unnown we have +Sigma hat squ as an estimator right let + + align:start position:0% +Sigma hat squ as an estimator right let + + + align:start position:0% +Sigma hat squ as an estimator right let +me write Sigma Square + + align:start position:0% +me write Sigma Square + + + align:start position:0% +me write Sigma Square +here so in particular beta + + align:start position:0% +here so in particular beta + + + align:start position:0% +here so in particular beta +hat divided by Sigma hat + + align:start position:0% +hat divided by Sigma hat + + + align:start position:0% +hat divided by Sigma hat +squ times R root gamma J is something I + + align:start position:0% +squ times R root gamma J is something I + + + align:start position:0% +squ times R root gamma J is something I +can compute right sorry that's beta hat + + align:start position:0% +can compute right sorry that's beta hat + + + align:start position:0% +can compute right sorry that's beta hat +J + + align:start position:0% +J + + + align:start position:0% +J +right right I can compute that thing + + align:start position:0% +right right I can compute that thing + + + align:start position:0% +right right I can compute that thing +agreed now I have Sigma J what I need to + + align:start position:0% +agreed now I have Sigma J what I need to + + + align:start position:0% +agreed now I have Sigma J what I need to +do is to be able to compute the + + align:start position:0% +do is to be able to compute the + + + align:start position:0% +do is to be able to compute the +distribution of this + + align:start position:0% +distribution of this + + + align:start position:0% +distribution of this +thing + + align:start position:0% +thing + + + align:start position:0% +thing +so I know the distribution of beta head + + align:start position:0% +so I know the distribution of beta head + + + align:start position:0% +so I know the distribution of beta head +J over square root of gamma J that's + + align:start position:0% +J over square root of gamma J that's + + + align:start position:0% +J over square root of gamma J that's +some gaussian 01 I don't know exactly + + align:start position:0% +some gaussian 01 I don't know exactly + + + align:start position:0% +some gaussian 01 I don't know exactly +what the distribution of Sigma hat J + + align:start position:0% +what the distribution of Sigma hat J + + + align:start position:0% +what the distribution of Sigma hat J +squar is but what I know is that that + + align:start position:0% +squar is but what I know is that that + + + align:start position:0% +squar is but what I know is that that +was actually written maybe here is that + + align:start position:0% +was actually written maybe here is that + + + align:start position:0% +was actually written maybe here is that +n minus + + align:start position:0% +n minus + + + align:start position:0% +n minus +P Sigma hat J Square Sigma hat over + + align:start position:0% +P Sigma hat J Square Sigma hat over + + + align:start position:0% +P Sigma hat J Square Sigma hat over +Sigma Sigma hat Square over Sigma Square + + align:start position:0% +Sigma Sigma hat Square over Sigma Square + + + align:start position:0% +Sigma Sigma hat Square over Sigma Square +follows some k^ + + align:start position:0% +follows some k^ + + + align:start position:0% +follows some k^ +squ with and minus P degrees of freedom + + align:start position:0% +squ with and minus P degrees of freedom + + + align:start position:0% +squ with and minus P degrees of freedom +and that it's actually + + align:start position:0% + + + + align:start position:0% + +independent of beta hat J it's + + align:start position:0% +independent of beta hat J it's + + + align:start position:0% +independent of beta hat J it's +independent of beta hat so it's + + align:start position:0% +independent of beta hat so it's + + + align:start position:0% +independent of beta hat so it's +independent of each of its coordinates + + align:start position:0% +independent of each of its coordinates + + + align:start position:0% +independent of each of its coordinates +right that was part of your homework uh + + align:start position:0% +right that was part of your homework uh + + + align:start position:0% +right that was part of your homework uh +where you had to some of you were + + align:start position:0% +where you had to some of you were + + + align:start position:0% +where you had to some of you were +confused by the fact that I mean if + + align:start position:0% +confused by the fact that I mean if + + + align:start position:0% +confused by the fact that I mean if +you're independent of some some big + + align:start position:0% +you're independent of some some big + + + align:start position:0% +you're independent of some some big +thing you're independent of all the + + align:start position:0% +thing you're independent of all the + + + align:start position:0% +thing you're independent of all the +smaller components of this big thing + + align:start position:0% +smaller components of this big thing + + + align:start position:0% +smaller components of this big thing +that's basically uh what you need to + + align:start position:0% +that's basically uh what you need to + + + align:start position:0% +that's basically uh what you need to +okay and so now I can just write this as + + align:start position:0% + + + + align:start position:0% + +this is beta head + + align:start position:0% +this is beta head + + + align:start position:0% +this is beta head +J divided by + + align:start position:0% +J divided by + + + align:start position:0% +J divided by +um so now I want to make this guy appear + + align:start position:0% +um so now I want to make this guy appear + + + align:start position:0% +um so now I want to make this guy appear +so it's uh beta head J Sigma s over + + align:start position:0% +so it's uh beta head J Sigma s over + + + align:start position:0% +so it's uh beta head J Sigma s over +Sigma s Sigma head squ over Sigma + + align:start position:0% +Sigma s Sigma head squ over Sigma + + + align:start position:0% +Sigma s Sigma head squ over Sigma +squ time n minus + + align:start position:0% +squ time n minus + + + align:start position:0% +squ time n minus +P divided by root gamma J so that's what + + align:start position:0% +P divided by root gamma J so that's what + + + align:start position:0% +P divided by root gamma J so that's what +I want to see right + + align:start position:0% + + + + align:start position:0% + +yeah yeah so I write this + + align:start position:0% +yeah yeah so I write this + + + align:start position:0% +yeah yeah so I write this +I decide to write this I could have put + + align:start position:0% +I decide to write this I could have put + + + align:start position:0% +I decide to write this I could have put +a a Mickey Mouse here it just wouldn't + + align:start position:0% +a a Mickey Mouse here it just wouldn't + + + align:start position:0% +a a Mickey Mouse here it just wouldn't +make sense I just decide to take this + + align:start position:0% +make sense I just decide to take this + + + align:start position:0% +make sense I just decide to take this +thing right okay so you know + + align:start position:0% +thing right okay so you know + + + align:start position:0% +thing right okay so you know +let okay so I take this guy and now I'm + + align:start position:0% +let okay so I take this guy and now I'm + + + align:start position:0% +let okay so I take this guy and now I'm +going to rewrite it as something I want + + align:start position:0% +going to rewrite it as something I want + + + align:start position:0% +going to rewrite it as something I want +because right if you don't know what + + align:start position:0% +because right if you don't know what + + + align:start position:0% +because right if you don't know what +Sigma is sorry that's not Sig you mean + + align:start position:0% +Sigma is sorry that's not Sig you mean + + + align:start position:0% +Sigma is sorry that's not Sig you mean +the square oh thank you yes that's + + align:start position:0% +the square oh thank you yes that's + + + align:start position:0% +the square oh thank you yes that's +correct okay so you don't know what + + align:start position:0% +correct okay so you don't know what + + + align:start position:0% +correct okay so you don't know what +Sigma is you replace it by Sigma hat + + align:start position:0% +Sigma is you replace it by Sigma hat + + + align:start position:0% +Sigma is you replace it by Sigma hat +that's the most natural thing to do you + + align:start position:0% +that's the most natural thing to do you + + + align:start position:0% +that's the most natural thing to do you +just now want to find out what the uh + + align:start position:0% +just now want to find out what the uh + + + align:start position:0% +just now want to find out what the uh +what the distribution of this guy is so + + align:start position:0% +what the distribution of this guy is so + + + align:start position:0% +what the distribution of this guy is so +this is not exactly what I had to be + + align:start position:0% +this is not exactly what I had to be + + + align:start position:0% +this is not exactly what I had to be +able to get this I need to divide by + + align:start position:0% +able to get this I need to divide by + + + align:start position:0% +able to get this I need to divide by +Sigma + + align:start position:0% +Sigma + + + align:start position:0% +Sigma +squar uh sorry I need + + align:start position:0% +squar uh sorry I need + + + align:start position:0% +squar uh sorry I need +to I'm + + align:start position:0% + + + + align:start position:0% + +sorry that's correct + + align:start position:0% +sorry that's correct + + + align:start position:0% +sorry that's correct +now + + align:start position:0% + + + + align:start position:0% + +uh okay and now I have that uh sorry I + + align:start position:0% +uh okay and now I have that uh sorry I + + + align:start position:0% +uh okay and now I have that uh sorry I +should not write it like that + + align:start position:0% +should not write it like that + + + align:start position:0% +should not write it like that +it's not what I + + align:start position:0% +it's not what I + + + align:start position:0% +it's not what I +want what I want + + align:start position:0% +want what I want + + + align:start position:0% +want what I want +is + + align:start position:0% + + + + align:start position:0% + +this and to be able to get this guy what + + align:start position:0% +this and to be able to get this guy what + + + align:start position:0% +this and to be able to get this guy what +I need is + + align:start position:0% + + + + align:start position:0% + +um Sigma hat Sigma over Sigma + + align:start position:0% + + + + align:start position:0% + +hat square root and then I need to have + + align:start position:0% +hat square root and then I need to have + + + align:start position:0% +hat square root and then I need to have +to make this thing show up right so I + + align:start position:0% +to make this thing show up right so I + + + align:start position:0% +to make this thing show up right so I +need to have this n minus P show up and + + align:start position:0% +need to have this n minus P show up and + + + align:start position:0% +need to have this n minus P show up and +the + + align:start position:0% +the + + + align:start position:0% +the +denominator so to be able to get it I + + align:start position:0% +denominator so to be able to get it I + + + align:start position:0% +denominator so to be able to get it I +need to multiply the entire thing by + + align:start position:0% +need to multiply the entire thing by + + + align:start position:0% +need to multiply the entire thing by +square root of n minus + + align:start position:0% + + + + align:start position:0% + +P okay so this is just a toy I just + + align:start position:0% +P okay so this is just a toy I just + + + align:start position:0% +P okay so this is just a toy I just +squeezed in what I + + align:start position:0% +squeezed in what I + + + align:start position:0% +squeezed in what I +wanted but now this whole thing + + align:start position:0% +wanted but now this whole thing + + + align:start position:0% +wanted but now this whole thing +here this is actually of the + + align:start position:0% +here this is actually of the + + + align:start position:0% +here this is actually of the +form beta J divid by Sigma over root + + align:start position:0% +form beta J divid by Sigma over root + + + align:start position:0% +form beta J divid by Sigma over root +gamma J and then divided by by sare root + + align:start position:0% +gamma J and then divided by by sare root + + + align:start position:0% +gamma J and then divided by by sare root +of Sigma hat squ + + align:start position:0% +of Sigma hat squ + + + align:start position:0% +of Sigma hat squ +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +over Sigma + + align:start position:0% + + + + align:start position:0% + +s oh no I don't want to divide it by + + align:start position:0% +s oh no I don't want to divide it by + + + align:start position:0% +s oh no I don't want to divide it by +square root minus P + + align:start position:0% + + + + align:start position:0% + +sorry and now it's uh times n minus + + align:start position:0% +sorry and now it's uh times n minus + + + align:start position:0% +sorry and now it's uh times n minus +p divid n minus + + align:start position:0% + + + + align:start position:0% + +P + + align:start position:0% +P + + + align:start position:0% +P +okay and what is the distribution of + + align:start position:0% +okay and what is the distribution of + + + align:start position:0% +okay and what is the distribution of +this thing + + align:start position:0% + + + + align:start position:0% + +here so I'm going to I'm going to keep + + align:start position:0% +here so I'm going to I'm going to keep + + + align:start position:0% +here so I'm going to I'm going to keep +going here so the distribution of this + + align:start position:0% +going here so the distribution of this + + + align:start position:0% +going here so the distribution of this +thing here is what well this + + align:start position:0% + + + + align:start position:0% + +numerator what is this distribution + + align:start position:0% + + + + align:start position:0% + +yeah n01 it's actually still R over + + align:start position:0% + + + + align:start position:0% + +there right so that's our + + align:start position:0% +there right so that's our + + + align:start position:0% +there right so that's our +n01 what is the distribution of this + + align:start position:0% + + + + align:start position:0% + +guy sorry I don't think I have callar + + align:start position:0% +guy sorry I don't think I have callar + + + align:start position:0% +guy sorry I don't think I have callar +again okay so uh what is the + + align:start position:0% +again okay so uh what is the + + + align:start position:0% +again okay so uh what is the +distribution of this + + align:start position:0% +distribution of this + + + align:start position:0% +distribution of this +guy this is still written on the board + + align:start position:0% +guy this is still written on the board + + + align:start position:0% +guy this is still written on the board +it's the K square that I have right here + + align:start position:0% + + + + align:start position:0% + +so that's a k squ n minus P divid by n + + align:start position:0% +so that's a k squ n minus P divid by n + + + align:start position:0% +so that's a k squ n minus P divid by n +minus P degrees of freedom the only + + align:start position:0% +minus P degrees of freedom the only + + + align:start position:0% +minus P degrees of freedom the only +thing I need to check is that those two + + align:start position:0% +thing I need to check is that those two + + + align:start position:0% +thing I need to check is that those two +guys are independent which is also what + + align:start position:0% +guys are independent which is also what + + + align:start position:0% +guys are independent which is also what +I have from + + align:start position:0% +I have from + + + align:start position:0% +I have from +here and so that + + align:start position:0% +here and so that + + + align:start position:0% +here and so that +implies that beta hat J divided by Sigma + + align:start position:0% +implies that beta hat J divided by Sigma + + + align:start position:0% +implies that beta hat J divided by Sigma +hat square root of gamma J what is the + + align:start position:0% +hat square root of gamma J what is the + + + align:start position:0% +hat square root of gamma J what is the +distribution of this guy + + align:start position:0% + + + + align:start position:0% + +n minus + + align:start position:0% +n minus + + + align:start position:0% +n minus +P was that crystal clear for everyone + + align:start position:0% +P was that crystal clear for everyone + + + align:start position:0% +P was that crystal clear for everyone +was that so simple that it was boring to + + align:start position:0% +was that so simple that it was boring to + + + align:start position:0% +was that so simple that it was boring to +everyone okay good that's where the + + align:start position:0% +everyone okay good that's where the + + + align:start position:0% +everyone okay good that's where the +point at which you should be at this all + + align:start position:0% +point at which you should be at this all + + + align:start position:0% +point at which you should be at this all +right so + + align:start position:0% +right so + + + align:start position:0% +right so +now I have this I can read the quintales + + align:start position:0% +now I have this I can read the quintales + + + align:start position:0% +now I have this I can read the quintales +of this guy so my test + + align:start position:0% + + + + align:start position:0% + +statistic becomes + + align:start position:0% +statistic becomes + + + align:start position:0% +statistic becomes +well my rejection region I reject if the + + align:start position:0% +well my rejection region I reject if the + + + align:start position:0% +well my rejection region I reject if the +absolute value of this new + + align:start position:0% + + + + align:start position:0% + +guy + + align:start position:0% +guy + + + align:start position:0% +guy +exceeds the quental of order Alpha over + + align:start position:0% +exceeds the quental of order Alpha over + + + align:start position:0% +exceeds the quental of order Alpha over +two but this time of a TN minus + + align:start position:0% +two but this time of a TN minus + + + align:start position:0% +two but this time of a TN minus +p and now you can actually see that the + + align:start position:0% +p and now you can actually see that the + + + align:start position:0% +p and now you can actually see that the +only difference between this test and + + align:start position:0% +only difference between this test and + + + align:start position:0% +only difference between this test and +that test apart from replacing Sigma by + + align:start position:0% +that test apart from replacing Sigma by + + + align:start position:0% +that test apart from replacing Sigma by +Sigma hat is that now I've moved from + + align:start position:0% +Sigma hat is that now I've moved from + + + align:start position:0% +Sigma hat is that now I've moved from +the quantiles of a gan to the quenes of + + align:start position:0% +the quantiles of a gan to the quenes of + + + align:start position:0% +the quantiles of a gan to the quenes of +a t and minus p and what's actually + + align:start position:0% +a t and minus p and what's actually + + + align:start position:0% +a t and minus p and what's actually +somewhat interesting from this + + align:start position:0% + + + + align:start position:0% + +perspective what's actually interesting + + align:start position:0% +perspective what's actually interesting + + + align:start position:0% +perspective what's actually interesting +from this perspective is + + align:start position:0% +from this perspective is + + + align:start position:0% +from this perspective is +that the TN minus P we know has heavier + + align:start position:0% +that the TN minus P we know has heavier + + + align:start position:0% +that the TN minus P we know has heavier +Tales than the Gan but if the number of + + align:start position:0% +Tales than the Gan but if the number of + + + align:start position:0% +Tales than the Gan but if the number of +degrees of freedom reaches maybe 30 or + + align:start position:0% +degrees of freedom reaches maybe 30 or + + + align:start position:0% +degrees of freedom reaches maybe 30 or +40 it's they're virtually the same and + + align:start position:0% +40 it's they're virtually the same and + + + align:start position:0% +40 it's they're virtually the same and +here the number of degrees of freedom is + + align:start position:0% +here the number of degrees of freedom is + + + align:start position:0% +here the number of degrees of freedom is +not given only by n but it's n minus P + + align:start position:0% +not given only by n but it's n minus P + + + align:start position:0% +not given only by n but it's n minus P +so if I have more and more parameters to + + align:start position:0% +so if I have more and more parameters to + + + align:start position:0% +so if I have more and more parameters to +estimate this will result in some + + align:start position:0% +estimate this will result in some + + + align:start position:0% +estimate this will result in some +heavier heavier tales and that's just to + + align:start position:0% +heavier heavier tales and that's just to + + + align:start position:0% +heavier heavier tales and that's just to +account for the fact that it's harder + + align:start position:0% +account for the fact that it's harder + + + align:start position:0% +account for the fact that it's harder +and harder to estimate the uh variance + + align:start position:0% +and harder to estimate the uh variance + + + align:start position:0% +and harder to estimate the uh variance +uh when I have a lot of parameters okay + + align:start position:0% +uh when I have a lot of parameters okay + + + align:start position:0% +uh when I have a lot of parameters okay +that's basically where it's coming from + + align:start position:0% +that's basically where it's coming from + + + align:start position:0% +that's basically where it's coming from +so now uh let's move on to uh uh uh + + align:start position:0% +so now uh let's move on to uh uh uh + + + align:start position:0% +so now uh let's move on to uh uh uh +let's move on to uh well I don't know + + align:start position:0% +let's move on to uh well I don't know + + + align:start position:0% +let's move on to uh well I don't know +what because this is not working anymore + + align:start position:0% +what because this is not working anymore + + + align:start position:0% +what because this is not working anymore +okay so this is the simplest test and + + align:start position:0% +okay so this is the simplest test and + + + align:start position:0% +okay so this is the simplest test and +actually if you run any statistical + + align:start position:0% +actually if you run any statistical + + + align:start position:0% +actually if you run any statistical +software for Le squares the output in + + align:start position:0% +software for Le squares the output in + + + align:start position:0% +software for Le squares the output in +any of them will look like + + align:start position:0% +any of them will look like + + + align:start position:0% +any of them will look like +this you will have a a sequence of rows + + align:start position:0% +this you will have a a sequence of rows + + + align:start position:0% +this you will have a a sequence of rows +and you're going to have an estimate for + + align:start position:0% +and you're going to have an estimate for + + + align:start position:0% +and you're going to have an estimate for +beta + + align:start position:0% +beta + + + align:start position:0% +beta +zero uh an estimate for beta one Etc + + align:start position:0% +zero uh an estimate for beta one Etc + + + align:start position:0% +zero uh an estimate for beta one Etc +here you're going to have a bunch of + + align:start position:0% +here you're going to have a bunch of + + + align:start position:0% +here you're going to have a bunch of +things and on this row you're going to + + align:start position:0% +things and on this row you're going to + + + align:start position:0% +things and on this row you're going to +have like the value here so that's going + + align:start position:0% +have like the value here so that's going + + + align:start position:0% +have like the value here so that's going +to be what's estimated by Le squares and + + align:start position:0% +to be what's estimated by Le squares and + + + align:start position:0% +to be what's estimated by Le squares and +then the second line immediately + + align:start position:0% +then the second line immediately + + + align:start position:0% +then the second line immediately +is the the is going to be well either + + align:start position:0% +is the the is going to be well either + + + align:start position:0% +is the the is going to be well either +the value of this + + align:start position:0% + + + + align:start position:0% + +thing so let's call it t and then + + align:start position:0% +thing so let's call it t and then + + + align:start position:0% +thing so let's call it t and then +there's going to be the P value + + align:start position:0% +there's going to be the P value + + + align:start position:0% +there's going to be the P value +corresponding to this T this is + + align:start position:0% +corresponding to this T this is + + + align:start position:0% +corresponding to this T this is +something that's just routinely coming + + align:start position:0% +something that's just routinely coming + + + align:start position:0% +something that's just routinely coming +out because and then there's of course + + align:start position:0% +out because and then there's of course + + + align:start position:0% +out because and then there's of course +the last line for people who cannot read + + align:start position:0% +the last line for people who cannot read + + + align:start position:0% +the last line for people who cannot read +numbers that's really just giving you + + align:start position:0% +numbers that's really just giving you + + + align:start position:0% +numbers that's really just giving you +little + + align:start position:0% + + + + align:start position:0% + +stars they're not stickers but that's + + align:start position:0% +stars they're not stickers but that's + + + align:start position:0% +stars they're not stickers but that's +close to it and uh and that's just + + align:start position:0% +close to it and uh and that's just + + + align:start position:0% +close to it and uh and that's just +saying I have three stars I'm very + + align:start position:0% +saying I have three stars I'm very + + + align:start position:0% +saying I have three stars I'm very +significantly different from zeros if I + + align:start position:0% +significantly different from zeros if I + + + align:start position:0% +significantly different from zeros if I +have two star I'm moderately differently + + align:start position:0% +have two star I'm moderately differently + + + align:start position:0% +have two star I'm moderately differently +from zero and if I have one star it + + align:start position:0% +from zero and if I have one star it + + + align:start position:0% +from zero and if I have one star it +means well just give me another thousand + + align:start position:0% +means well just give me another thousand + + + align:start position:0% +means well just give me another thousand +dollars and I will sign that it's + + align:start position:0% +dollars and I will sign that it's + + + align:start position:0% +dollars and I will sign that it's +actually different from zero okay so + + align:start position:0% +actually different from zero okay so + + + align:start position:0% +actually different from zero okay so +that's basically uh the kind of outputs + + align:start position:0% +that's basically uh the kind of outputs + + + align:start position:0% +that's basically uh the kind of outputs +everybody sees what I mean by that so + + align:start position:0% +everybody sees what I mean by that so + + + align:start position:0% +everybody sees what I mean by that so +what I mean what I'm trying to emphasize + + align:start position:0% +what I mean what I'm trying to emphasize + + + align:start position:0% +what I mean what I'm trying to emphasize +here is that those things are so routine + + align:start position:0% +here is that those things are so routine + + + align:start position:0% +here is that those things are so routine +when you run linear aggression because + + align:start position:0% +when you run linear aggression because + + + align:start position:0% +when you run linear aggression because +people stuffen maybe even if you have + + align:start position:0% +people stuffen maybe even if you have + + + align:start position:0% +people stuffen maybe even if you have +200 observations you're going to stuffen + + align:start position:0% +200 observations you're going to stuffen + + + align:start position:0% +200 observations you're going to stuffen +maybe 20 variables P equals 20 that's + + align:start position:0% +maybe 20 variables P equals 20 that's + + + align:start position:0% +maybe 20 variables P equals 20 that's +still a big number to interpret what's + + align:start position:0% +still a big number to interpret what's + + + align:start position:0% +still a big number to interpret what's +going on and it's nice for you if you + + align:start position:0% +going on and it's nice for you if you + + + align:start position:0% +going on and it's nice for you if you +can actually trim some fat out okay and + + align:start position:0% +can actually trim some fat out okay and + + + align:start position:0% +can actually trim some fat out okay and +so the problem is that when you start + + align:start position:0% +so the problem is that when you start + + + align:start position:0% +so the problem is that when you start +doing + + align:start position:0% +doing + + + align:start position:0% +doing +this and then this and then this and + + align:start position:0% +this and then this and then this and + + + align:start position:0% +this and then this and then this and +then this the + + align:start position:0% +then this the + + + align:start position:0% +then this the +probability that you make a mistake in + + align:start position:0% +probability that you make a mistake in + + + align:start position:0% +probability that you make a mistake in +your test right the probability that you + + align:start position:0% +your test right the probability that you + + + align:start position:0% +your test right the probability that you +erroneously reject the null here is + + align:start position:0% +erroneously reject the null here is + + + align:start position:0% +erroneously reject the null here is +5% here it's 5% here it's 5% + + align:start position:0% +5% here it's 5% here it's 5% + + + align:start position:0% +5% here it's 5% here it's 5% +there it's 5% and at some point you know + + align:start position:0% +there it's 5% and at some point you know + + + align:start position:0% +there it's 5% and at some point you know +if things happen with 5% chances and you + + align:start position:0% +if things happen with 5% chances and you + + + align:start position:0% +if things happen with 5% chances and you +keep on doing them over and over again + + align:start position:0% +keep on doing them over and over again + + + align:start position:0% +keep on doing them over and over again +they're going to start to happen so you + + align:start position:0% +they're going to start to happen so you + + + align:start position:0% +they're going to start to happen so you +can see that basically what's happening + + align:start position:0% +can see that basically what's happening + + + align:start position:0% +can see that basically what's happening +is that you actually have an issue is + + align:start position:0% +is that you actually have an issue is + + + align:start position:0% +is that you actually have an issue is +that you might not if you start + + align:start position:0% +that you might not if you start + + + align:start position:0% +that you might not if you start +repeating those tests you might not be + + align:start position:0% +repeating those tests you might not be + + + align:start position:0% +repeating those tests you might not be +at 5% error at some + + align:start position:0% +at 5% error at some + + + align:start position:0% +at 5% error at some +point and so what you do to prevent from + + align:start position:0% +point and so what you do to prevent from + + + align:start position:0% +point and so what you do to prevent from +that if you want to test all those beta + + align:start position:0% +that if you want to test all those beta + + + align:start position:0% +that if you want to test all those beta +J simultaneously you have to do what's + + align:start position:0% +J simultaneously you have to do what's + + + align:start position:0% +J simultaneously you have to do what's +called a bonferoni + + align:start position:0% +called a bonferoni + + + align:start position:0% +called a bonferoni +correction okay and the Bon fonic + + align:start position:0% +correction okay and the Bon fonic + + + align:start position:0% +correction okay and the Bon fonic +correction follows from what's called a + + align:start position:0% +correction follows from what's called a + + + align:start position:0% +correction follows from what's called a +union bound a union bound is actually so + + align:start position:0% +union bound a union bound is actually so + + + align:start position:0% +union bound a union bound is actually so +if you're a computer scientist you're + + align:start position:0% +if you're a computer scientist you're + + + align:start position:0% +if you're a computer scientist you're +very familiar with it if you're a + + align:start position:0% +very familiar with it if you're a + + + align:start position:0% +very familiar with it if you're a +mathematician that's just essentially + + align:start position:0% +mathematician that's just essentially + + + align:start position:0% +mathematician that's just essentially +the third axium of probability that you + + align:start position:0% +the third axium of probability that you + + + align:start position:0% +the third axium of probability that you +see that the probability of the Union is + + align:start position:0% +see that the probability of the Union is + + + align:start position:0% +see that the probability of the Union is +less than the sum of the probabilities + + align:start position:0% + + + + align:start position:0% + +right that's the union + + align:start position:0% +right that's the union + + + align:start position:0% +right that's the union +bound and you of course can generalize + + align:start position:0% +bound and you of course can generalize + + + align:start position:0% +bound and you of course can generalize +that to more than two and that's exactly + + align:start position:0% +that to more than two and that's exactly + + + align:start position:0% +that to more than two and that's exactly +what you're doing here okay so let's see + + align:start position:0% +what you're doing here okay so let's see + + + align:start position:0% +what you're doing here okay so let's see +how we would want to perform Bon fani + + align:start position:0% + + + + align:start position:0% + +correction to control the probability + + align:start position:0% +correction to control the probability + + + align:start position:0% +correction to control the probability +that they're all equal to zero at the + + align:start position:0% +that they're all equal to zero at the + + + align:start position:0% +that they're all equal to zero at the +same time + + align:start position:0% + + + + align:start position:0% + +right so recall so if I I want to + + align:start position:0% +right so recall so if I I want to + + + align:start position:0% +right so recall so if I I want to +perform this test over there where I + + align:start position:0% +perform this test over there where I + + + align:start position:0% +perform this test over there where I +want to test + + align:start position:0% +want to test + + + align:start position:0% +want to test +h0 that beta J is equal to Zer for all J + + align:start position:0% +h0 that beta J is equal to Zer for all J + + + align:start position:0% +h0 that beta J is equal to Zer for all J +in some subset + + align:start position:0% +in some subset + + + align:start position:0% +in some subset +s uh so right so think of s included in + + align:start position:0% +s uh so right so think of s included in + + + align:start position:0% +s uh so right so think of s included in +uh one p you can think of it as being + + align:start position:0% +uh one p you can think of it as being + + + align:start position:0% +uh one p you can think of it as being +all of one of P if you want right it + + align:start position:0% +all of one of P if you want right it + + + align:start position:0% +all of one of P if you want right it +really doesn't matter s is something + + align:start position:0% +really doesn't matter s is something + + + align:start position:0% +really doesn't matter s is something +that's given to you maybe you want to + + align:start position:0% +that's given to you maybe you want to + + + align:start position:0% +that's given to you maybe you want to +test just the subset of them but maybe + + align:start position:0% +test just the subset of them but maybe + + + align:start position:0% +test just the subset of them but maybe +you want to test all of them versus + + align:start position:0% +you want to test all of them versus + + + align:start position:0% +you want to test all of them versus +H1 beta J is not equal to zero for some + + align:start position:0% +H1 beta J is not equal to zero for some + + + align:start position:0% +H1 beta J is not equal to zero for some +J in + + align:start position:0% +J in + + + align:start position:0% +J in +s right that's a test that test all + + align:start position:0% +s right that's a test that test all + + + align:start position:0% +s right that's a test that test all +these things at once and if you actually + + align:start position:0% +these things at once and if you actually + + + align:start position:0% +these things at once and if you actually +look at this table all at once + + align:start position:0% +look at this table all at once + + + align:start position:0% +look at this table all at once +implicitly you're performing this test + + align:start position:0% +implicitly you're performing this test + + + align:start position:0% +implicitly you're performing this test +for all of the rows for S equal 1 to P + + align:start position:0% +for all of the rows for S equal 1 to P + + + align:start position:0% +for all of the rows for S equal 1 to P +you will do that whether you like it or + + align:start position:0% +you will do that whether you like it or + + + align:start position:0% +you will do that whether you like it or +not you + + align:start position:0% +not you + + + align:start position:0% +not you +will so now let's look at what the + + align:start position:0% +will so now let's look at what the + + + align:start position:0% +will so now let's look at what the +probability of type one error looks like + + align:start position:0% +probability of type one error looks like + + + align:start position:0% +probability of type one error looks like +okay so I want the probability of type + + align:start position:0% +okay so I want the probability of type + + + align:start position:0% +okay so I want the probability of type +one error so that's the probability when + + align:start position:0% +one error so that's the probability when + + + align:start position:0% +one error so that's the probability when +h0 is + + align:start position:0% +h0 is + + + align:start position:0% +h0 is +true that well so let me call P J the + + align:start position:0% +true that well so let me call P J the + + + align:start position:0% +true that well so let me call P J the +indicator that uh say beta J hat over uh + + align:start position:0% +indicator that uh say beta J hat over uh + + + align:start position:0% +indicator that uh say beta J hat over uh +Sigma + + align:start position:0% +Sigma + + + align:start position:0% +Sigma +hat square root gamma J exceeds Q Alpha + + align:start position:0% +hat square root gamma J exceeds Q Alpha + + + align:start position:0% +hat square root gamma J exceeds Q Alpha +over 2 of TN minus + + align:start position:0% +over 2 of TN minus + + + align:start position:0% +over 2 of TN minus +P right so we know that those are the + + align:start position:0% +P right so we know that those are the + + + align:start position:0% +P right so we know that those are the +tests that I perform here I just add + + align:start position:0% +tests that I perform here I just add + + + align:start position:0% +tests that I perform here I just add +this extra index J to tell me that I'm + + align:start position:0% +this extra index J to tell me that I'm + + + align:start position:0% +this extra index J to tell me that I'm +actually testing the J coefficient okay + + align:start position:0% +actually testing the J coefficient okay + + + align:start position:0% +actually testing the J coefficient okay +so what I want is the probability that + + align:start position:0% +so what I want is the probability that + + + align:start position:0% +so what I want is the probability that +under the null so that those are all + + align:start position:0% +under the null so that those are all + + + align:start position:0% +under the null so that those are all +equal to zero that I maybe that beta J + + align:start position:0% +equal to zero that I maybe that beta J + + + align:start position:0% +equal to zero that I maybe that beta J +is that I will reject to the alternative + + align:start position:0% +is that I will reject to the alternative + + + align:start position:0% +is that I will reject to the alternative +for one of them right so + + align:start position:0% +for one of them right so + + + align:start position:0% +for one of them right so +that's SI 1 is equal to + + align:start position:0% +that's SI 1 is equal to + + + align:start position:0% +that's SI 1 is equal to +one or 2 is equal to one all the way to + + align:start position:0% +one or 2 is equal to one all the way to + + + align:start position:0% +one or 2 is equal to one all the way to +P well let's just say that this is the + + align:start position:0% +P well let's just say that this is the + + + align:start position:0% +P well let's just say that this is the +entire thing because it's annoying + + align:start position:0% + + + + align:start position:0% + +okay I mean you can check the slide if + + align:start position:0% +okay I mean you can check the slide if + + + align:start position:0% +okay I mean you can check the slide if +you want to do it more generally but uh + + align:start position:0% +you want to do it more generally but uh + + + align:start position:0% +you want to do it more generally but uh +say uh p is is equal + + align:start position:0% +say uh p is is equal + + + align:start position:0% +say uh p is is equal +to okay or + + align:start position:0% +to okay or + + + align:start position:0% +to okay or +or everybody agrees that this is the + + align:start position:0% +or everybody agrees that this is the + + + align:start position:0% +or everybody agrees that this is the +probability of type one + + align:start position:0% +probability of type one + + + align:start position:0% +probability of type one +error right so either I reject this one + + align:start position:0% +error right so either I reject this one + + + align:start position:0% +error right so either I reject this one +or this one or this one or this one or + + align:start position:0% +or this one or this one or this one or + + + align:start position:0% +or this one or this one or this one or +this one and that's exactly what I'm + + align:start position:0% +this one and that's exactly what I'm + + + align:start position:0% +this one and that's exactly what I'm +going to reject at least one of them + + align:start position:0% +going to reject at least one of them + + + align:start position:0% +going to reject at least one of them +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +this is the + + align:start position:0% + + + + align:start position:0% + +probability of type one + + align:start position:0% +probability of type one + + + align:start position:0% +probability of type one +error and what I want is to keep this + + align:start position:0% +error and what I want is to keep this + + + align:start position:0% +error and what I want is to keep this +guy less than + + align:start position:0% +guy less than + + + align:start position:0% +guy less than +Alpha okay but what I know is to control + + align:start position:0% +Alpha okay but what I know is to control + + + align:start position:0% +Alpha okay but what I know is to control +the probability that this guy is less + + align:start position:0% +the probability that this guy is less + + + align:start position:0% +the probability that this guy is less +than Alpha that this guy is less than + + align:start position:0% +than Alpha that this guy is less than + + + align:start position:0% +than Alpha that this guy is less than +Alpha that this guy is less than Alpha + + align:start position:0% +Alpha that this guy is less than Alpha + + + align:start position:0% +Alpha that this guy is less than Alpha +in particular if all these guys are + + align:start position:0% +in particular if all these guys are + + + align:start position:0% +in particular if all these guys are +disjoint then this could really be the + + align:start position:0% +disjoint then this could really be the + + + align:start position:0% +disjoint then this could really be the +sum of all these probabilities so in the + + align:start position:0% +sum of all these probabilities so in the + + + align:start position:0% +sum of all these probabilities so in the +worst + + align:start position:0% + + + + align:start position:0% + +case if s j equal 1 intersected with s k + + align:start position:0% +case if s j equal 1 intersected with s k + + + align:start position:0% +case if s j equal 1 intersected with s k +equal 1 is the empty set so that means + + align:start position:0% +equal 1 is the empty set so that means + + + align:start position:0% +equal 1 is the empty set so that means +those are called this joint + + align:start position:0% + + + + align:start position:0% + +sets you've seen this terminology in + + align:start position:0% +sets you've seen this terminology in + + + align:start position:0% +sets you've seen this terminology in +probability right so if those sets are + + align:start position:0% +probability right so if those sets are + + + align:start position:0% +probability right so if those sets are +disjoint for all of them + + align:start position:0% + + + + align:start position:0% + +right for all J different from K then + + align:start position:0% +right for all J different from K then + + + align:start position:0% +right for all J different from K then +this + + align:start position:0% + + + + align:start position:0% + +probability well let me write it + + align:start position:0% +probability well let me write it + + + align:start position:0% +probability well let me write it +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +as + + align:start position:0% +as + + + align:start position:0% +as +star Then + + align:start position:0% +star Then + + + align:start position:0% +star Then +star is equal to well the probability + + align:start position:0% +star is equal to well the probability + + + align:start position:0% +star is equal to well the probability +under H zero that s + + align:start position:0% +under H zero that s + + + align:start position:0% +under H zero that s +one is equal to um One Plus + + align:start position:0% +one is equal to um One Plus + + + align:start position:0% +one is equal to um One Plus +the probability under zero that's like P + + align:start position:0% +the probability under zero that's like P + + + align:start position:0% +the probability under zero that's like P +is equal to one now if I use this test + + align:start position:0% +is equal to one now if I use this test + + + align:start position:0% +is equal to one now if I use this test +with this Alpha here then this + + align:start position:0% +with this Alpha here then this + + + align:start position:0% +with this Alpha here then this +probability is equal to Alpha this + + align:start position:0% +probability is equal to Alpha this + + + align:start position:0% +probability is equal to Alpha this +probability is also equal to Alpha so + + align:start position:0% +probability is also equal to Alpha so + + + align:start position:0% +probability is also equal to Alpha so +the probability of type one error is + + align:start position:0% +the probability of type one error is + + + align:start position:0% +the probability of type one error is +actually not equal to Alpha it's equal + + align:start position:0% +actually not equal to Alpha it's equal + + + align:start position:0% +actually not equal to Alpha it's equal +to P + + align:start position:0% + + + + align:start position:0% + +Alpha so what is the solution here well + + align:start position:0% +Alpha so what is the solution here well + + + align:start position:0% +Alpha so what is the solution here well +is to run those guys with not with Alpha + + align:start position:0% +is to run those guys with not with Alpha + + + align:start position:0% +is to run those guys with not with Alpha +but with Alpha over + + align:start position:0% +but with Alpha over + + + align:start position:0% +but with Alpha over +p and if I do this then this guy is + + align:start position:0% +p and if I do this then this guy is + + + align:start position:0% +p and if I do this then this guy is +equal to Alpha over P this guy is equal + + align:start position:0% +equal to Alpha over P this guy is equal + + + align:start position:0% +equal to Alpha over P this guy is equal +to Alpha over p and so when I get those + + align:start position:0% +to Alpha over p and so when I get those + + + align:start position:0% +to Alpha over p and so when I get those +things I get P * Alpha over P which is + + align:start position:0% +things I get P * Alpha over P which is + + + align:start position:0% +things I get P * Alpha over P which is +just + + align:start position:0% +just + + + align:start position:0% +just +Alpha + + align:start position:0% +Alpha + + + align:start position:0% +Alpha +okay so all I do is rather than running + + align:start position:0% +okay so all I do is rather than running + + + align:start position:0% +okay so all I do is rather than running +each of the tests with probability of + + align:start position:0% +each of the tests with probability of + + + align:start position:0% +each of the tests with probability of +error so that's a test at level + + align:start position:0% +error so that's a test at level + + + align:start position:0% +error so that's a test at level +Alpha over + + align:start position:0% +Alpha over + + + align:start position:0% +Alpha over +P okay that's actually very stringent if + + align:start position:0% +P okay that's actually very stringent if + + + align:start position:0% +P okay that's actually very stringent if +you think about it for one second even + + align:start position:0% +you think about it for one second even + + + align:start position:0% +you think about it for one second even +if you have only five obser five + + align:start position:0% +if you have only five obser five + + + align:start position:0% +if you have only five obser five +variables P + + align:start position:0% +variables P + + + align:start position:0% +variables P +equals + + align:start position:0% +equals + + + align:start position:0% +equals +five and you started with a test you + + align:start position:0% +five and you started with a test you + + + align:start position:0% +five and you started with a test you +wanted to do your test at + + align:start position:0% +wanted to do your test at + + + align:start position:0% +wanted to do your test at +5% it forces you to do the test at 1% + + align:start position:0% +5% it forces you to do the test at 1% + + + align:start position:0% +5% it forces you to do the test at 1% +for each of those + + align:start position:0% +for each of those + + + align:start position:0% +for each of those +variables if you have 10 variables I + + align:start position:0% +variables if you have 10 variables I + + + align:start position:0% +variables if you have 10 variables I +mean you know that starts to be very + + align:start position:0% +mean you know that starts to be very + + + align:start position:0% +mean you know that starts to be very +stringent so it's going to be harder and + + align:start position:0% +stringent so it's going to be harder and + + + align:start position:0% +stringent so it's going to be harder and +harder for you to make uh um to conclude + + align:start position:0% +harder for you to make uh um to conclude + + + align:start position:0% +harder for you to make uh um to conclude +to the alternative now one thing I need + + align:start position:0% +to the alternative now one thing I need + + + align:start position:0% +to the alternative now one thing I need +to tell you is that here I said if they + + align:start position:0% +to tell you is that here I said if they + + + align:start position:0% +to tell you is that here I said if they +are disjoined then those probabilities + + align:start position:0% +are disjoined then those probabilities + + + align:start position:0% +are disjoined then those probabilities +are equal but if they're not + + align:start position:0% + + + + align:start position:0% + +disjoint the union bound tells me that + + align:start position:0% +disjoint the union bound tells me that + + + align:start position:0% +disjoint the union bound tells me that +the probability of the Union is less + + align:start position:0% +the probability of the Union is less + + + align:start position:0% +the probability of the Union is less +than the sum of the probabilities and so + + align:start position:0% +than the sum of the probabilities and so + + + align:start position:0% +than the sum of the probabilities and so +now I'm not exactly equal to Alpha but + + align:start position:0% +now I'm not exactly equal to Alpha but + + + align:start position:0% +now I'm not exactly equal to Alpha but +I'm bounded by + + align:start position:0% +I'm bounded by + + + align:start position:0% +I'm bounded by +Alpha all right and that's where that's + + align:start position:0% +Alpha all right and that's where that's + + + align:start position:0% +Alpha all right and that's where that's +why Bon fonic correction people are not + + align:start position:0% +why Bon fonic correction people are not + + + align:start position:0% +why Bon fonic correction people are not +super comfortable with this because in + + align:start position:0% +super comfortable with this because in + + + align:start position:0% +super comfortable with this because in +reality you never think that those tests + + align:start position:0% +reality you never think that those tests + + + align:start position:0% +reality you never think that those tests +are going to be completely giving you + + align:start position:0% +are going to be completely giving you + + + align:start position:0% +are going to be completely giving you +completely disjoint things right I mean + + align:start position:0% +completely disjoint things right I mean + + + align:start position:0% +completely disjoint things right I mean +why would it be why would it be that if + + align:start position:0% +why would it be why would it be that if + + + align:start position:0% +why would it be why would it be that if +this guy is equal to one then all the + + align:start position:0% +this guy is equal to one then all the + + + align:start position:0% +this guy is equal to one then all the +other ones are equal to zero why would + + align:start position:0% +other ones are equal to zero why would + + + align:start position:0% +other ones are equal to zero why would +it make any sense right so this is + + align:start position:0% +it make any sense right so this is + + + align:start position:0% +it make any sense right so this is +definitely conservative but the problem + + align:start position:0% +definitely conservative but the problem + + + align:start position:0% +definitely conservative but the problem +is that we don't know how to do much + + align:start position:0% +is that we don't know how to do much + + + align:start position:0% +is that we don't know how to do much +better I mean we have a formula that + + align:start position:0% +better I mean we have a formula that + + + align:start position:0% +better I mean we have a formula that +tells you the probability of the Union + + align:start position:0% +tells you the probability of the Union + + + align:start position:0% +tells you the probability of the Union +as some crazy sum that looks at all the + + align:start position:0% +as some crazy sum that looks at all the + + + align:start position:0% +as some crazy sum that looks at all the +intersection and all these little things + + align:start position:0% +intersection and all these little things + + + align:start position:0% +intersection and all these little things +right I mean it's the generalization of + + align:start position:0% +right I mean it's the generalization of + + + align:start position:0% +right I mean it's the generalization of +P of A or B is equal to P of a plus P of + + align:start position:0% +P of A or B is equal to P of a plus P of + + + align:start position:0% +P of A or B is equal to P of a plus P of +B minus probability of the intersection + + align:start position:0% +B minus probability of the intersection + + + align:start position:0% +B minus probability of the intersection +right but if you start doing this for + + align:start position:0% +right but if you start doing this for + + + align:start position:0% +right but if you start doing this for +more than two it's super complicated the + + align:start position:0% +more than two it's super complicated the + + + align:start position:0% +more than two it's super complicated the +number of terms grows really fast but + + align:start position:0% +number of terms grows really fast but + + + align:start position:0% +number of terms grows really fast but +most importantly even if you go here you + + align:start position:0% +most importantly even if you go here you + + + align:start position:0% +most importantly even if you go here you +still need to control the probability of + + align:start position:0% +still need to control the probability of + + + align:start position:0% +still need to control the probability of +the intersection and those tests are not + + align:start position:0% +the intersection and those tests are not + + + align:start position:0% +the intersection and those tests are not +necessarily independent if they were + + align:start position:0% +necessarily independent if they were + + + align:start position:0% +necessarily independent if they were +independent that would be easy the + + align:start position:0% +independent that would be easy the + + + align:start position:0% +independent that would be easy the +probability of the intersection would be + + align:start position:0% +probability of the intersection would be + + + align:start position:0% +probability of the intersection would be +the product of the probabilities + + align:start position:0% +the product of the probabilities + + + align:start position:0% +the product of the probabilities +but those things are super + + align:start position:0% +but those things are super + + + align:start position:0% +but those things are super +correlated and so it doesn't really help + + align:start position:0% +correlated and so it doesn't really help + + + align:start position:0% +correlated and so it doesn't really help +and so we'll see when we talk about high + + align:start position:0% +and so we'll see when we talk about high + + + align:start position:0% +and so we'll see when we talk about high +dimensional stats towards the end that + + align:start position:0% +dimensional stats towards the end that + + + align:start position:0% +dimensional stats towards the end that +there's something called false Discovery + + align:start position:0% +there's something called false Discovery + + + align:start position:0% +there's something called false Discovery +rate which is essentially saying listen + + align:start position:0% +rate which is essentially saying listen + + + align:start position:0% +rate which is essentially saying listen +if I want to control this thing if I + + align:start position:0% +if I want to control this thing if I + + + align:start position:0% +if I want to control this thing if I +really Define my probability of type one + + align:start position:0% +really Define my probability of type one + + + align:start position:0% +really Define my probability of type one +error as this I want to make sure that I + + align:start position:0% +error as this I want to make sure that I + + + align:start position:0% +error as this I want to make sure that I +never make this kind of error I'm doomed + + align:start position:0% +never make this kind of error I'm doomed + + + align:start position:0% +never make this kind of error I'm doomed +this is just not going to happen but I + + align:start position:0% +this is just not going to happen but I + + + align:start position:0% +this is just not going to happen but I +can sort of revise what my goals are in + + align:start position:0% +can sort of revise what my goals are in + + + align:start position:0% +can sort of revise what my goals are in +terms of of errors that I make and then + + align:start position:0% +terms of of errors that I make and then + + + align:start position:0% +terms of of errors that I make and then +I will actually be able to do and that + + align:start position:0% +I will actually be able to do and that + + + align:start position:0% +I will actually be able to do and that +what people are looking at is false + + align:start position:0% +what people are looking at is false + + + align:start position:0% +what people are looking at is false +Discovery rate and this is called + + align:start position:0% +Discovery rate and this is called + + + align:start position:0% +Discovery rate and this is called +familywise error rate which is a + + align:start position:0% +familywise error rate which is a + + + align:start position:0% +familywise error rate which is a +stronger uh thing to control right so + + align:start position:0% +stronger uh thing to control right so + + + align:start position:0% +stronger uh thing to control right so +this trick that consists in replacing + + align:start position:0% +this trick that consists in replacing + + + align:start position:0% +this trick that consists in replacing +Alpha by Alpha over the number of times + + align:start position:0% +Alpha by Alpha over the number of times + + + align:start position:0% +Alpha by Alpha over the number of times +you're going to be performing your test + + align:start position:0% +you're going to be performing your test + + + align:start position:0% +you're going to be performing your test +or Alpha over the number of terms in + + align:start position:0% +or Alpha over the number of terms in + + + align:start position:0% +or Alpha over the number of terms in +your union is actually called the Bon + + align:start position:0% +your union is actually called the Bon + + + align:start position:0% +your union is actually called the Bon +feron correction + + align:start position:0% + + + + align:start position:0% + +okay and that's something you use when + + align:start position:0% +okay and that's something you use when + + + align:start position:0% +okay and that's something you use when +you have what's called another key word + + align:start position:0% +you have what's called another key word + + + align:start position:0% +you have what's called another key word +here is multiple + + align:start position:0% + + + + align:start position:0% + +testing right when you're trying to do + + align:start position:0% +testing right when you're trying to do + + + align:start position:0% +testing right when you're trying to do +multiple tests + + align:start position:0% + + + + align:start position:0% + +simultaneously okay and if s is not all + + align:start position:0% +simultaneously okay and if s is not all + + + align:start position:0% +simultaneously okay and if s is not all +of P well you just divide by the number + + align:start position:0% +of P well you just divide by the number + + + align:start position:0% +of P well you just divide by the number +of test that you're actually making + + align:start position:0% +of test that you're actually making + + + align:start position:0% +of test that you're actually making +right so if s is of size k for some K + + align:start position:0% +right so if s is of size k for some K + + + align:start position:0% +right so if s is of size k for some K +less than P you just divide Alpha by K + + align:start position:0% +less than P you just divide Alpha by K + + + align:start position:0% +less than P you just divide Alpha by K +and not by P of course you can always + + align:start position:0% +and not by P of course you can always + + + align:start position:0% +and not by P of course you can always +divide by P but it's you're going to + + align:start position:0% +divide by P but it's you're going to + + + align:start position:0% +divide by P but it's you're going to +make your life harder for no + + align:start position:0% + + + + align:start position:0% + +reason + + align:start position:0% +reason + + + align:start position:0% +reason +okay any question about bueron + + align:start position:0% +okay any question about bueron + + + align:start position:0% +okay any question about bueron +correction all + + align:start position:0% + + + + align:start position:0% + +right so one thing that + + align:start position:0% +right so one thing that + + + align:start position:0% +right so one thing that +uh is maybe not as obvious as the test + + align:start position:0% +uh is maybe not as obvious as the test + + + align:start position:0% +uh is maybe not as obvious as the test +beta J equal to Z versus beta G not + + align:start position:0% +beta J equal to Z versus beta G not + + + align:start position:0% +beta J equal to Z versus beta G not +equal to zero and in particular what it + + align:start position:0% +equal to zero and in particular what it + + + align:start position:0% +equal to zero and in particular what it +means is that it's not going to come up + + align:start position:0% +means is that it's not going to come up + + + align:start position:0% +means is that it's not going to come up +as a software output without even you + + align:start position:0% +as a software output without even you + + + align:start position:0% +as a software output without even you +requesting it because this is so + + align:start position:0% +requesting it because this is so + + + align:start position:0% +requesting it because this is so +standard that is just coming out but + + align:start position:0% +standard that is just coming out but + + + align:start position:0% +standard that is just coming out but +there's other tests that you might think + + align:start position:0% +there's other tests that you might think + + + align:start position:0% +there's other tests that you might think +of that might be more complicated and + + align:start position:0% +of that might be more complicated and + + + align:start position:0% +of that might be more complicated and +more tailored to your particular problem + + align:start position:0% +more tailored to your particular problem + + + align:start position:0% +more tailored to your particular problem +and those tests are of the + + align:start position:0% +and those tests are of the + + + align:start position:0% +and those tests are of the +form G * beta is equal to some Lambda + + align:start position:0% +form G * beta is equal to some Lambda + + + align:start position:0% +form G * beta is equal to some Lambda +all right so + + align:start position:0% + + + + align:start position:0% + +let's + + align:start position:0% +let's + + + align:start position:0% +let's +see the test we've just + + align:start position:0% + + + + align:start position:0% + +done beta J equal + + align:start position:0% +done beta J equal + + + align:start position:0% +done beta J equal +Z versus beta J not equal to + + align:start position:0% +Z versus beta J not equal to + + + align:start position:0% +Z versus beta J not equal to +zero is actually + + align:start position:0% +zero is actually + + + align:start position:0% +zero is actually +equivalent + + align:start position:0% +equivalent + + + align:start position:0% +equivalent +to V uh + + align:start position:0% +to V uh + + + align:start position:0% +to V uh +EJ transpose beta equals Z versus EJ + + align:start position:0% +EJ transpose beta equals Z versus EJ + + + align:start position:0% +EJ transpose beta equals Z versus EJ +transpose beta not equal to zero right + + align:start position:0% +transpose beta not equal to zero right + + + align:start position:0% +transpose beta not equal to zero right +that was our + + align:start position:0% +that was our + + + align:start position:0% +that was our +claim but now I don't have to stop here + + align:start position:0% +claim but now I don't have to stop here + + + align:start position:0% +claim but now I don't have to stop here +I don't have to multiply by a vector and + + align:start position:0% +I don't have to multiply by a vector and + + + align:start position:0% +I don't have to multiply by a vector and +test if it's equal to zero I can + + align:start position:0% +test if it's equal to zero I can + + + align:start position:0% +test if it's equal to zero I can +actually replace this by some general + + align:start position:0% + + + + align:start position:0% + +Matrix G and replace this guy by some + + align:start position:0% +Matrix G and replace this guy by some + + + align:start position:0% +Matrix G and replace this guy by some +general + + align:start position:0% + + + + align:start position:0% + +Vector + + align:start position:0% +Vector + + + align:start position:0% +Vector +Lambda and I'm not telling you what the + + align:start position:0% +Lambda and I'm not telling you what the + + + align:start position:0% +Lambda and I'm not telling you what the +dimensions are because they're + + align:start position:0% +dimensions are because they're + + + align:start position:0% +dimensions are because they're +generalized I can take whatever I want + + align:start position:0% +generalized I can take whatever I want + + + align:start position:0% +generalized I can take whatever I want +take your favorite Matrix as long as the + + align:start position:0% +take your favorite Matrix as long as the + + + align:start position:0% +take your favorite Matrix as long as the +right side of the Matrix can be + + align:start position:0% +right side of the Matrix can be + + + align:start position:0% +right side of the Matrix can be +multiplying b a beta and Lambda take it + + align:start position:0% +multiplying b a beta and Lambda take it + + + align:start position:0% +multiplying b a beta and Lambda take it +as the as the number of rows of G and + + align:start position:0% +as the as the number of rows of G and + + + align:start position:0% +as the as the number of rows of G and +then you can do that right I can always + + align:start position:0% +then you can do that right I can always + + + align:start position:0% +then you can do that right I can always +for formulate this test what will this + + align:start position:0% +for formulate this test what will this + + + align:start position:0% +for formulate this test what will this +test Encompass well those are kind of + + align:start position:0% +test Encompass well those are kind of + + + align:start position:0% +test Encompass well those are kind of +weird tests right so you can think of + + align:start position:0% +weird tests right so you can think of + + + align:start position:0% +weird tests right so you can think of +things + + align:start position:0% +things + + + align:start position:0% +things +like I want to test if beta 2 plus beta + + align:start position:0% +like I want to test if beta 2 plus beta + + + align:start position:0% +like I want to test if beta 2 plus beta +3 are equal to zero for + + align:start position:0% +3 are equal to zero for + + + align:start position:0% +3 are equal to zero for +example maybe I want to test if beta 5 + + align:start position:0% +example maybe I want to test if beta 5 + + + align:start position:0% +example maybe I want to test if beta 5 +minus 2 Beta 6 is equal to + + align:start position:0% +minus 2 Beta 6 is equal to + + + align:start position:0% +minus 2 Beta 6 is equal to +23 well that's weird but why would you + + align:start position:0% +23 well that's weird but why would you + + + align:start position:0% +23 well that's weird but why would you +want to test if beta 2 plus beta 3 is + + align:start position:0% +want to test if beta 2 plus beta 3 is + + + align:start position:0% +want to test if beta 2 plus beta 3 is +equal to zero maybe you want to know + + align:start position:0% +equal to zero maybe you want to know + + + align:start position:0% +equal to zero maybe you want to know +maybe you don't want to know if the you + + align:start position:0% +maybe you don't want to know if the you + + + align:start position:0% +maybe you don't want to know if the you +know that the effect of some Gene is not + + align:start position:0% +know that the effect of some Gene is not + + + align:start position:0% +know that the effect of some Gene is not +zero maybe you know that this Gene + + align:start position:0% +zero maybe you know that this Gene + + + align:start position:0% +zero maybe you know that this Gene +affects this trait but you want to know + + align:start position:0% +affects this trait but you want to know + + + align:start position:0% +affects this trait but you want to know +if the effect of this Gene is canel by + + align:start position:0% +if the effect of this Gene is canel by + + + align:start position:0% +if the effect of this Gene is canel by +the effect of that gen and this is the + + align:start position:0% +the effect of that gen and this is the + + + align:start position:0% +the effect of that gen and this is the +kind of stuff that you're going to be + + align:start position:0% +kind of stuff that you're going to be + + + align:start position:0% +kind of stuff that you're going to be +testing for + + align:start position:0% +testing for + + + align:start position:0% +testing for +that okay now this guy is much more + + align:start position:0% +that okay now this guy is much more + + + align:start position:0% +that okay now this guy is much more +artificial and I don't have a btime + + align:start position:0% +artificial and I don't have a btime + + + align:start position:0% +artificial and I don't have a btime +story to tell you around this right so + + align:start position:0% +story to tell you around this right so + + + align:start position:0% +story to tell you around this right so +it's just you know those things can + + align:start position:0% +it's just you know those things can + + + align:start position:0% +it's just you know those things can +happen and can be much more complicated + + align:start position:0% +happen and can be much more complicated + + + align:start position:0% +happen and can be much more complicated +now here notice that the Matrix G has + + align:start position:0% +now here notice that the Matrix G has + + + align:start position:0% +now here notice that the Matrix G has +one row every for both of the examples + + align:start position:0% +one row every for both of the examples + + + align:start position:0% +one row every for both of the examples +but if I want to test if those two + + align:start position:0% +but if I want to test if those two + + + align:start position:0% +but if I want to test if those two +things happen at the same time then I + + align:start position:0% +things happen at the same time then I + + + align:start position:0% +things happen at the same time then I +actually can take a + + align:start position:0% +actually can take a + + + align:start position:0% +actually can take a +matrix right another Matrix that can be + + align:start position:0% +matrix right another Matrix that can be + + + align:start position:0% +matrix right another Matrix that can be +useful + + align:start position:0% +useful + + + align:start position:0% +useful +is g equals the identity of RP and + + align:start position:0% +is g equals the identity of RP and + + + align:start position:0% +is g equals the identity of RP and +Lambda is equal to + + align:start position:0% +Lambda is equal to + + + align:start position:0% +Lambda is equal to +zero what am I doing + + align:start position:0% + + + + align:start position:0% + +here in this case what is this test + + align:start position:0% +here in this case what is this test + + + align:start position:0% +here in this case what is this test +testing sorry this + + align:start position:0% + + + + align:start position:0% + +test + + align:start position:0% +test + + + align:start position:0% +test +yeah yeah we're testing if the entire + + align:start position:0% +yeah yeah we're testing if the entire + + + align:start position:0% +yeah yeah we're testing if the entire +Vector beta is equal to zero because G + + align:start position:0% +Vector beta is equal to zero because G + + + align:start position:0% +Vector beta is equal to zero because G +times + + align:start position:0% +times + + + align:start position:0% +times +beta is equal to Beta and we're asking + + align:start position:0% +beta is equal to Beta and we're asking + + + align:start position:0% +beta is equal to Beta and we're asking +whether it's equal to zero + + align:start position:0% + + + + align:start position:0% + +so the thing is when you want to + + align:start position:0% +so the thing is when you want to + + + align:start position:0% +so the thing is when you want to +actually test if a beta is equal to zero + + align:start position:0% +actually test if a beta is equal to zero + + + align:start position:0% +actually test if a beta is equal to zero +you're actually testing if your entire + + align:start position:0% +you're actually testing if your entire + + + align:start position:0% +you're actually testing if your entire +model everything you're doing in life is + + align:start position:0% +model everything you're doing in life is + + + align:start position:0% +model everything you're doing in life is +just junk right it's just telling you + + align:start position:0% +just junk right it's just telling you + + + align:start position:0% +just junk right it's just telling you +actually forget about this Y is X beta + + align:start position:0% +actually forget about this Y is X beta + + + align:start position:0% +actually forget about this Y is X beta +plus Epsilon why is really just Epsilon + + align:start position:0% +plus Epsilon why is really just Epsilon + + + align:start position:0% +plus Epsilon why is really just Epsilon +there's nothing there's just some big + + align:start position:0% +there's nothing there's just some big + + + align:start position:0% +there's nothing there's just some big +noise with some big variant and there's + + align:start position:0% +noise with some big variant and there's + + + align:start position:0% +noise with some big variant and there's +nothing else all right so turns out that + + align:start position:0% +nothing else all right so turns out that + + + align:start position:0% +nothing else all right so turns out that +the statistical software output that I + + align:start position:0% +the statistical software output that I + + + align:start position:0% +the statistical software output that I +wrote here spits out an answer to this + + align:start position:0% +wrote here spits out an answer to this + + + align:start position:0% +wrote here spits out an answer to this +question just the last line usually is + + align:start position:0% +question just the last line usually is + + + align:start position:0% +question just the last line usually is +doing this test does your model even + + align:start position:0% +doing this test does your model even + + + align:start position:0% +doing this test does your model even +makes sense you know it's probably for + + align:start position:0% +makes sense you know it's probably for + + + align:start position:0% +makes sense you know it's probably for +people to check whether they actually + + align:start position:0% +people to check whether they actually + + + align:start position:0% +people to check whether they actually +just mix their two data sets right maybe + + align:start position:0% +just mix their two data sets right maybe + + + align:start position:0% +just mix their two data sets right maybe +they're actually trying to predict I + + align:start position:0% +they're actually trying to predict I + + + align:start position:0% +they're actually trying to predict I +don't know uh uh some credit score from + + align:start position:0% +don't know uh uh some credit score from + + + align:start position:0% +don't know uh uh some credit score from +genomic data and so just want to make + + align:start position:0% +genomic data and so just want to make + + + align:start position:0% +genomic data and so just want to make +sure maybe that's not the right thing + + align:start position:0% +sure maybe that's not the right thing + + + align:start position:0% +sure maybe that's not the right thing +all right so it turns out that the + + align:start position:0% +all right so it turns out that the + + + align:start position:0% +all right so it turns out that the +Machinery is exactly the same as the one + + align:start position:0% +Machinery is exactly the same as the one + + + align:start position:0% +Machinery is exactly the same as the one +we've just taken all right so we + + align:start position:0% +we've just taken all right so we + + + align:start position:0% +we've just taken all right so we +actually start from + + align:start position:0% + + + + align:start position:0% + +here so let me pull this + + align:start position:0% + + + + align:start position:0% + +up right so we start from here beta hat + + align:start position:0% +up right so we start from here beta hat + + + align:start position:0% +up right so we start from here beta hat +was equal to Beta plus this guy + + align:start position:0% +was equal to Beta plus this guy + + + align:start position:0% +was equal to Beta plus this guy +okay and the first thing we did was to + + align:start position:0% +okay and the first thing we did was to + + + align:start position:0% +okay and the first thing we did was to +say well beta J is equal to this thing + + align:start position:0% +say well beta J is equal to this thing + + + align:start position:0% +say well beta J is equal to this thing +because well beta J was just EJ Time + + align:start position:0% +because well beta J was just EJ Time + + + align:start position:0% +because well beta J was just EJ Time +beta right so rather than taking EJ here + + align:start position:0% +beta right so rather than taking EJ here + + + align:start position:0% +beta right so rather than taking EJ here +let me just take + + align:start position:0% + + + + align:start position:0% + +G now we said that for any + + align:start position:0% +G now we said that for any + + + align:start position:0% +G now we said that for any +Vector well that was + + align:start position:0% +Vector well that was + + + align:start position:0% +Vector well that was +trivial so the thing we need to know is + + align:start position:0% +trivial so the thing we need to know is + + + align:start position:0% +trivial so the thing we need to know is +what is this thing well this thing + + align:start position:0% +what is this thing well this thing + + + align:start position:0% +what is this thing well this thing +here what is what is this guy it's also + + align:start position:0% +here what is what is this guy it's also + + + align:start position:0% +here what is what is this guy it's also +normal + + align:start position:0% +normal + + + align:start position:0% +normal +the mean is zero again that's just using + + align:start position:0% +the mean is zero again that's just using + + + align:start position:0% +the mean is zero again that's just using +properties of GA and vectors and what is + + align:start position:0% +properties of GA and vectors and what is + + + align:start position:0% +properties of GA and vectors and what is +the ciance + + align:start position:0% +the ciance + + + align:start position:0% +the ciance +Matrix let's call this guy Sigma so that + + align:start position:0% +Matrix let's call this guy Sigma so that + + + align:start position:0% +Matrix let's call this guy Sigma so that +you can make an answer you can formulate + + align:start position:0% +you can make an answer you can formulate + + + align:start position:0% +you can make an answer you can formulate +an + + align:start position:0% +an + + + align:start position:0% +an +answer so if what is the distribution of + + align:start position:0% +answer so if what is the distribution of + + + align:start position:0% +answer so if what is the distribution of +what is the cience of G times some Gan Z + + align:start position:0% +what is the cience of G times some Gan Z + + + align:start position:0% +what is the cience of G times some Gan Z +Sigma G Sigma G transpose right so + + align:start position:0% +Sigma G Sigma G transpose right so + + + align:start position:0% +Sigma G Sigma G transpose right so +that's + + align:start position:0% + + + + align:start position:0% + +G X transpose X inverse + + align:start position:0% +G X transpose X inverse + + + align:start position:0% +G X transpose X inverse +G + + align:start position:0% +G + + + align:start position:0% +G +transpose + + align:start position:0% + + + + align:start position:0% + +okay now I'm not going to be able to go + + align:start position:0% +okay now I'm not going to be able to go + + + align:start position:0% +okay now I'm not going to be able to go +much further right I mean I made this + + align:start position:0% +much further right I mean I made this + + + align:start position:0% +much further right I mean I made this +very uh cute observation that EJ + + align:start position:0% +very uh cute observation that EJ + + + align:start position:0% +very uh cute observation that EJ +transposer Matrix times EJ is the J + + align:start position:0% +transposer Matrix times EJ is the J + + + align:start position:0% +transposer Matrix times EJ is the J +diagonal element now if I have a general + + align:start position:0% +diagonal element now if I have a general + + + align:start position:0% +diagonal element now if I have a general +Matrix the price to pce that I cannot + + align:start position:0% +Matrix the price to pce that I cannot + + + align:start position:0% +Matrix the price to pce that I cannot +just shrink this thing any further + + align:start position:0% +just shrink this thing any further + + + align:start position:0% +just shrink this thing any further +because I'm trying to be abstract okay + + align:start position:0% +because I'm trying to be abstract okay + + + align:start position:0% +because I'm trying to be abstract okay +and so I'm almost there the only thing + + align:start position:0% +and so I'm almost there the only thing + + + align:start position:0% +and so I'm almost there the only thing +that happened last time is that when + + align:start position:0% +that happened last time is that when + + + align:start position:0% +that happened last time is that when +this was EJ under h0 we knew that this + + align:start position:0% +this was EJ under h0 we knew that this + + + align:start position:0% +this was EJ under h0 we knew that this +was equal to zero under the null but + + align:start position:0% +was equal to zero under the null but + + + align:start position:0% +was equal to zero under the null but +under the + + align:start position:0% + + + + align:start position:0% + +null what is this equal + + align:start position:0% + + + + align:start position:0% + +to Lambda which I know right I mean I + + align:start position:0% +to Lambda which I know right I mean I + + + align:start position:0% +to Lambda which I know right I mean I +wrote my uh thing and in the couple + + align:start position:0% +wrote my uh thing and in the couple + + + align:start position:0% +wrote my uh thing and in the couple +instances I just showed you including uh + + align:start position:0% +instances I just showed you including uh + + + align:start position:0% +instances I just showed you including uh +this one over there on top Lambda was + + align:start position:0% +this one over there on top Lambda was + + + align:start position:0% +this one over there on top Lambda was +equal to zero but in general it can be + + align:start position:0% +equal to zero but in general it can be + + + align:start position:0% +equal to zero but in general it can be +any Lambda but what's key about this + + align:start position:0% +any Lambda but what's key about this + + + align:start position:0% +any Lambda but what's key about this +Lambda is that I actually know it that's + + align:start position:0% +Lambda is that I actually know it that's + + + align:start position:0% +Lambda is that I actually know it that's +the formul that's the hypothesis I'm + + align:start position:0% +the formul that's the hypothesis I'm + + + align:start position:0% +the formul that's the hypothesis I'm +formulating so now I'm going to have to + + align:start position:0% +formulating so now I'm going to have to + + + align:start position:0% +formulating so now I'm going to have to +be a little more careful when I want to + + align:start position:0% +be a little more careful when I want to + + + align:start position:0% +be a little more careful when I want to +build the distribution of G beta hat I + + align:start position:0% +build the distribution of G beta hat I + + + align:start position:0% +build the distribution of G beta hat I +need to actually subtract this Lambda + + align:start position:0% +need to actually subtract this Lambda + + + align:start position:0% +need to actually subtract this Lambda +okay so now we go from this and we say + + align:start position:0% +okay so now we go from this and we say + + + align:start position:0% +okay so now we go from this and we say +well + + align:start position:0% +well + + + align:start position:0% +well +G beta hat minus Lambda follows some + + align:start position:0% + + + + align:start position:0% + +np0 Sigma Square uh + + align:start position:0% +np0 Sigma Square uh + + + align:start position:0% +np0 Sigma Square uh +g x transpose X + + align:start position:0% +g x transpose X + + + align:start position:0% +g x transpose X +inverse G + + align:start position:0% + + + + align:start position:0% + +transpose right so that's true let's + + align:start position:0% +transpose right so that's true let's + + + align:start position:0% +transpose right so that's true let's +assume let's go straight to the case + + align:start position:0% +assume let's go straight to the case + + + align:start position:0% +assume let's go straight to the case +when we don't know what Sigma is so what + + align:start position:0% +when we don't know what Sigma is so what + + + align:start position:0% +when we don't know what Sigma is so what +I'm going to be interested in is is + + align:start position:0% +I'm going to be interested in is is + + + align:start position:0% +I'm going to be interested in is is +G beta + + align:start position:0% +G beta + + + align:start position:0% +G beta +hat + + align:start position:0% +hat + + + align:start position:0% +hat +minus + + align:start position:0% +minus + + + align:start position:0% +minus +Lambda uh divided + + align:start position:0% +Lambda uh divided + + + align:start position:0% +Lambda uh divided +by Sigma hat and that going to follow + + align:start position:0% +by Sigma hat and that going to follow + + + align:start position:0% +by Sigma hat and that going to follow +some gussan that has this thing G Xpose + + align:start position:0% +some gussan that has this thing G Xpose + + + align:start position:0% +some gussan that has this thing G Xpose +X inverse G + + align:start position:0% + + + + align:start position:0% + +transpose so now what I what did I do + + align:start position:0% +transpose so now what I what did I do + + + align:start position:0% +transpose so now what I what did I do +last time right so clearly the quals of + + align:start position:0% +last time right so clearly the quals of + + + align:start position:0% +last time right so clearly the quals of +this distribution is well okay what is + + align:start position:0% +this distribution is well okay what is + + + align:start position:0% +this distribution is well okay what is +the SI what is the size of this + + align:start position:0% +the SI what is the size of this + + + align:start position:0% +the SI what is the size of this +distribution well I need to tell you + + align:start position:0% +distribution well I need to tell you + + + align:start position:0% +distribution well I need to tell you +that + + align:start position:0% +that + + + align:start position:0% +that +g is + + align:start position:0% +g is + + + align:start position:0% +g is +an what did I take here + + align:start position:0% + + + + align:start position:0% + +oh yeah you're right so let me write it + + align:start position:0% +oh yeah you're right so let me write it + + + align:start position:0% +oh yeah you're right so let me write it +like this + + align:start position:0% + + + + align:start position:0% + +so well + + align:start position:0% + + + + align:start position:0% + +um let me write it like + + align:start position:0% +um let me write it like + + + align:start position:0% +um let me write it like +this a sigma Square over + + align:start position:0% + + + + align:start position:0% + +Sigma okay so let's forget about the + + align:start position:0% +Sigma okay so let's forget about the + + + align:start position:0% +Sigma okay so let's forget about the +size of G now let's just think of any + + align:start position:0% +size of G now let's just think of any + + + align:start position:0% +size of G now let's just think of any +general G + + align:start position:0% +general G + + + align:start position:0% +general G +when G was a vector what was nice is + + align:start position:0% +when G was a vector what was nice is + + + align:start position:0% +when G was a vector what was nice is +that this guy was just a scalar number + + align:start position:0% +that this guy was just a scalar number + + + align:start position:0% +that this guy was just a scalar number +just one number and so if I wanted to + + align:start position:0% +just one number and so if I wanted to + + + align:start position:0% +just one number and so if I wanted to +get rid of the of this in the right hand + + align:start position:0% +get rid of the of this in the right hand + + + align:start position:0% +get rid of the of this in the right hand +side all I had to do was to divide by + + align:start position:0% +side all I had to do was to divide by + + + align:start position:0% +side all I had to do was to divide by +this thing we called it gamma J and we + + align:start position:0% +this thing we called it gamma J and we + + + align:start position:0% +this thing we called it gamma J and we +just had to divide by square root of + + align:start position:0% +just had to divide by square root of + + + align:start position:0% +just had to divide by square root of +gamma J and that would be + + align:start position:0% +gamma J and that would be + + + align:start position:0% +gamma J and that would be +gone now I have a matrix right so I need + + align:start position:0% +gone now I have a matrix right so I need + + + align:start position:0% +gone now I have a matrix right so I need +to get rid of this Matrix somehow + + align:start position:0% +to get rid of this Matrix somehow + + + align:start position:0% +to get rid of this Matrix somehow +because clearly the quantales of this + + align:start position:0% +because clearly the quantales of this + + + align:start position:0% +because clearly the quantales of this +distribution are not going to be written + + align:start position:0% +distribution are not going to be written + + + align:start position:0% +distribution are not going to be written +at the of a book for any value of G and + + align:start position:0% +at the of a book for any value of G and + + + align:start position:0% +at the of a book for any value of G and +any value of x so I need to standardize + + align:start position:0% +any value of x so I need to standardize + + + align:start position:0% +any value of x so I need to standardize +before I can read anything out of a + + align:start position:0% +before I can read anything out of a + + + align:start position:0% +before I can read anything out of a +table so how do we do it + + align:start position:0% +table so how do we do it + + + align:start position:0% +table so how do we do it +well we + + align:start position:0% + + + + align:start position:0% + +just form this this guy here okay so + + align:start position:0% +just form this this guy here okay so + + + align:start position:0% +just form this this guy here okay so +what we know is that + + align:start position:0% +what we know is that + + + align:start position:0% +what we know is that +if so here's the claim again that + + align:start position:0% +if so here's the claim again that + + + align:start position:0% +if so here's the claim again that +another Claim about gon Vector if x + + align:start position:0% +another Claim about gon Vector if x + + + align:start position:0% +another Claim about gon Vector if x +follows some + + align:start position:0% +follows some + + + align:start position:0% +follows some +n0 + + align:start position:0% + + + + align:start position:0% + +Sigma then + + align:start position:0% +Sigma then + + + align:start position:0% +Sigma then +X transpose Sigma + + align:start position:0% +X transpose Sigma + + + align:start position:0% +X transpose Sigma +inverse + + align:start position:0% + + + + align:start position:0% + +X follows some K + + align:start position:0% + + + + align:start position:0% + +squ and here it's going to depend on how + + align:start position:0% +squ and here it's going to depend on how + + + align:start position:0% +squ and here it's going to depend on how +many what is the dimension here if I + + align:start position:0% +many what is the dimension here if I + + + align:start position:0% +many what is the dimension here if I +make this a k by K A K dimensional + + align:start position:0% +make this a k by K A K dimensional + + + align:start position:0% +make this a k by K A K dimensional +gaussin Vector this is a x sare k + + align:start position:0% + + + + align:start position:0% + +okay where have we used that + + align:start position:0% + + + + align:start position:0% + +before + + align:start position:0% +before + + + align:start position:0% +before +yeah W test that's exactly what we Ed + + align:start position:0% +yeah W test that's exactly what we Ed + + + align:start position:0% +yeah W test that's exactly what we Ed +right wad had a Kai square that was + + align:start position:0% +right wad had a Kai square that was + + + align:start position:0% +right wad had a Kai square that was +showing up and the way we made it show + + align:start position:0% +showing up and the way we made it show + + + align:start position:0% +showing up and the way we made it show +up was by taking the ASM totic variance + + align:start position:0% +up was by taking the ASM totic variance + + + align:start position:0% +up was by taking the ASM totic variance +taking its inverse which in this + + align:start position:0% +taking its inverse which in this + + + align:start position:0% +taking its inverse which in this +framework was + + align:start position:0% +framework was + + + align:start position:0% +framework was +called Fisher information + + align:start position:0% +called Fisher information + + + align:start position:0% +called Fisher information +and then we pre and post multiply by + + align:start position:0% +and then we pre and post multiply by + + + align:start position:0% +and then we pre and post multiply by +this + + align:start position:0% +this + + + align:start position:0% +this +thing okay so this is the key and so now + + align:start position:0% +thing okay so this is the key and so now + + + align:start position:0% +thing okay so this is the key and so now +it tells me exactly when I start from + + align:start position:0% +it tells me exactly when I start from + + + align:start position:0% +it tells me exactly when I start from +this guy that has this multivaried + + align:start position:0% +this guy that has this multivaried + + + align:start position:0% +this guy that has this multivaried +gussan it tells me how to turn it into + + align:start position:0% +gussan it tells me how to turn it into + + + align:start position:0% +gussan it tells me how to turn it into +something that has a distribution which + + align:start position:0% +something that has a distribution which + + + align:start position:0% +something that has a distribution which +is pivotal right K Square K is + + align:start position:0% +is pivotal right K Square K is + + + align:start position:0% +is pivotal right K Square K is +completely pivotal does not depend on + + align:start position:0% +completely pivotal does not depend on + + + align:start position:0% +completely pivotal does not depend on +anything I don't know and so the way I + + align:start position:0% +anything I don't know and so the way I + + + align:start position:0% +anything I don't know and so the way I +go from here + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +the way I go from here is by saying well + + align:start position:0% +the way I go from here is by saying well + + + align:start position:0% +the way I go from here is by saying well +now if I look at G beta hat minus + + align:start position:0% + + + + align:start position:0% + +Lambda transpose and now I need I need + + align:start position:0% +Lambda transpose and now I need I need + + + align:start position:0% +Lambda transpose and now I need I need +to look at the inverse of the Matrix + + align:start position:0% +to look at the inverse of the Matrix + + + align:start position:0% +to look at the inverse of the Matrix +over there so it's + + align:start position:0% +over there so it's + + + align:start position:0% +over there so it's +g x transpose X inverse + + align:start position:0% +g x transpose X inverse + + + align:start position:0% +g x transpose X inverse +G inverse + + align:start position:0% + + + + align:start position:0% + +G beta hat + + align:start position:0% +G beta hat + + + align:start position:0% +G beta hat +minus + + align:start position:0% + + + + align:start position:0% + +Lambda this guy is going to + + align:start position:0% +Lambda this guy is going to + + + align:start position:0% +Lambda this guy is going to +follow uh well here I need to actually + + align:start position:0% +follow uh well here I need to actually + + + align:start position:0% +follow uh well here I need to actually +divide by Sigma in this case + + align:start position:0% + + + + align:start position:0% + +if G is K * + + align:start position:0% +if G is K * + + + align:start position:0% +if G is K * +P right so that's what I mean here is + + align:start position:0% +P right so that's what I mean here is + + + align:start position:0% +P right so that's what I mean here is +just the that's the same K the K that + + align:start position:0% +just the that's the same K the K that + + + align:start position:0% +just the that's the same K the K that +shows up is the number of constraints + + align:start position:0% +shows up is the number of constraints + + + align:start position:0% +shows up is the number of constraints +that I have in my test + + align:start position:0% +that I have in my test + + + align:start position:0% +that I have in my test +right okay + + align:start position:0% +right okay + + + align:start position:0% +right okay +so now if I go from here to using Sigma + + align:start position:0% +so now if I go from here to using Sigma + + + align:start position:0% +so now if I go from here to using Sigma +hat the key thing to observe is that + + align:start position:0% +hat the key thing to observe is that + + + align:start position:0% +hat the key thing to observe is that +this guy is actually not a gaussian + + align:start position:0% +this guy is actually not a gaussian + + + align:start position:0% +this guy is actually not a gaussian +right I'm not going to have a student + + align:start position:0% +right I'm not going to have a student + + + align:start position:0% +right I'm not going to have a student +distribution that shows + + align:start position:0% + + + + align:start position:0% + +up + + align:start position:0% + + + + align:start position:0% + +so that implies that if I take the same + + align:start position:0% +so that implies that if I take the same + + + align:start position:0% +so that implies that if I take the same +thing + + align:start position:0% + + + + align:start position:0% + +okay so now I just go from Sigma to + + align:start position:0% +okay so now I just go from Sigma to + + + align:start position:0% +okay so now I just go from Sigma to +Sigma hat then this thing is of the + + align:start position:0% + + + + align:start position:0% + +form well this K Square + + align:start position:0% +form well this K Square + + + align:start position:0% +form well this K Square +K divided by the K square that shows up + + align:start position:0% +K divided by the K square that shows up + + + align:start position:0% +K divided by the K square that shows up +in the denominator of uh the T + + align:start position:0% +in the denominator of uh the T + + + align:start position:0% +in the denominator of uh the T +distribution which is square + + align:start position:0% + + + + align:start position:0% + +root of + + align:start position:0% +root of + + + align:start position:0% +root of +uh oh I should not divide by Sigma so + + align:start position:0% +uh oh I should not divide by Sigma so + + + align:start position:0% +uh oh I should not divide by Sigma so +this is Sigma square right so this is + + align:start position:0% +this is Sigma square right so this is + + + align:start position:0% +this is Sigma square right so this is +Sigma Square so this is of the + + align:start position:0% +Sigma Square so this is of the + + + align:start position:0% +Sigma Square so this is of the +form divided + + align:start position:0% +form divided + + + align:start position:0% +form divided +by k^ 2 N minus P divided by and minus P + + align:start position:0% +by k^ 2 N minus P divided by and minus P + + + align:start position:0% +by k^ 2 N minus P divided by and minus P +right so that's the same determinator + + align:start position:0% +right so that's the same determinator + + + align:start position:0% +right so that's the same determinator +that I saw in my T Test the numerator + + align:start position:0% +that I saw in my T Test the numerator + + + align:start position:0% +that I saw in my T Test the numerator +has changed though right the numerator + + align:start position:0% +has changed though right the numerator + + + align:start position:0% +has changed though right the numerator +is now this Cas Square no longer a + + align:start position:0% +is now this Cas Square no longer a + + + align:start position:0% +is now this Cas Square no longer a +gaan + + align:start position:0% +gaan + + + align:start position:0% +gaan +okay but this + + align:start position:0% +okay but this + + + align:start position:0% +okay but this +distribution is actually pivotal as long + + align:start position:0% +distribution is actually pivotal as long + + + align:start position:0% +distribution is actually pivotal as long +as we can guarantee that there's no + + align:start position:0% +as we can guarantee that there's no + + + align:start position:0% +as we can guarantee that there's no +hidden parameter in the in the + + align:start position:0% +hidden parameter in the in the + + + align:start position:0% +hidden parameter in the in the +correlation between the two k squares + + align:start position:0% +correlation between the two k squares + + + align:start position:0% +correlation between the two k squares +right so + + align:start position:0% +right so + + + align:start position:0% +right so +again as all statements of Independence + + align:start position:0% +again as all statements of Independence + + + align:start position:0% +again as all statements of Independence +in this class I will just give it to you + + align:start position:0% +in this class I will just give it to you + + + align:start position:0% +in this class I will just give it to you +for free those two + + align:start position:0% +for free those two + + + align:start position:0% +for free those two +things I + + align:start position:0% +things I + + + align:start position:0% +things I +claim so okay let's say admit + + align:start position:0% + + + + align:start position:0% + +these are + + align:start position:0% + + + + align:start position:0% + +independent + + align:start position:0% +independent + + + align:start position:0% +independent +okay we're almost there this could be a + + align:start position:0% +okay we're almost there this could be a + + + align:start position:0% +okay we're almost there this could be a +distribution that's pivotal but there's + + align:start position:0% +distribution that's pivotal but there's + + + align:start position:0% +distribution that's pivotal but there's +something that's a little imbalan with + + align:start position:0% +something that's a little imbalan with + + + align:start position:0% +something that's a little imbalan with +it is that this guy is divided by its + + align:start position:0% +it is that this guy is divided by its + + + align:start position:0% +it is that this guy is divided by its +number of degrees of freedom but this + + align:start position:0% +number of degrees of freedom but this + + + align:start position:0% +number of degrees of freedom but this +guy is not divided by its number of + + align:start position:0% +guy is not divided by its number of + + + align:start position:0% +guy is not divided by its number of +degrees of freedom and so we just have + + align:start position:0% +degrees of freedom and so we just have + + + align:start position:0% +degrees of freedom and so we just have +to make the extra step that if I divide + + align:start position:0% +to make the extra step that if I divide + + + align:start position:0% +to make the extra step that if I divide +this guy by K then this guy is a k + + align:start position:0% +this guy by K then this guy is a k + + + align:start position:0% +this guy by K then this guy is a k +Square divided by K if I divide this guy + + align:start position:0% +Square divided by K if I divide this guy + + + align:start position:0% +Square divided by K if I divide this guy +by K then I get this guy divided by + + align:start position:0% +by K then I get this guy divided by + + + align:start position:0% +by K then I get this guy divided by +K okay and now it looks I mean it + + align:start position:0% +K okay and now it looks I mean it + + + align:start position:0% +K okay and now it looks I mean it +doesn't change anything right I've just + + align:start position:0% +doesn't change anything right I've just + + + align:start position:0% +doesn't change anything right I've just +divided by a fixed number but it just + + align:start position:0% +divided by a fixed number but it just + + + align:start position:0% +divided by a fixed number but it just +look more elegant it's the ratio of two + + align:start position:0% +look more elegant it's the ratio of two + + + align:start position:0% +look more elegant it's the ratio of two +independent K square that are + + align:start position:0% +independent K square that are + + + align:start position:0% +independent K square that are +individually divided by the number of + + align:start position:0% +individually divided by the number of + + + align:start position:0% +individually divided by the number of +degrees of + + align:start position:0% +degrees of + + + align:start position:0% +degrees of +freedom + + align:start position:0% +freedom + + + align:start position:0% +freedom +okay and this has a name + + align:start position:0% + + + + align:start position:0% + +and it's called a Fisher or F + + align:start position:0% +and it's called a Fisher or F + + + align:start position:0% +and it's called a Fisher or F +distribution so + + align:start position:0% +distribution so + + + align:start position:0% +distribution so +unlike uh William Shan William goset who + + align:start position:0% +unlike uh William Shan William goset who + + + align:start position:0% +unlike uh William Shan William goset who +was not allowed to use his own name and + + align:start position:0% +was not allowed to use his own name and + + + align:start position:0% +was not allowed to use his own name and +use the name student Fisher was allowed + + align:start position:0% +use the name student Fisher was allowed + + + align:start position:0% +use the name student Fisher was allowed +to use his own name and that's called + + align:start position:0% +to use his own name and that's called + + + align:start position:0% +to use his own name and that's called +the Fisher distribution and the Fisher + + align:start position:0% +the Fisher distribution and the Fisher + + + align:start position:0% +the Fisher distribution and the Fisher +distribution has now two + + align:start position:0% +distribution has now two + + + align:start position:0% +distribution has now two +parameters two sets a set of two degrees + + align:start position:0% +parameters two sets a set of two degrees + + + align:start position:0% +parameters two sets a set of two degrees +of freedom one for the numerator and one + + align:start position:0% +of freedom one for the numerator and one + + + align:start position:0% +of freedom one for the numerator and one +for the denominator + + align:start position:0% +for the denominator + + + align:start position:0% +for the denominator +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so F or Fisher + + align:start position:0% + + + + align:start position:0% + +distribution so f is equal to the ratio + + align:start position:0% +distribution so f is equal to the ratio + + + align:start position:0% +distribution so f is equal to the ratio +of a k Square p over p and a k Square Q + + align:start position:0% +of a k Square p over p and a k Square Q + + + align:start position:0% +of a k Square p over p and a k Square Q +over + + align:start position:0% +over + + + align:start position:0% +over +Q so that's uh + + align:start position:0% + + + + align:start position:0% + +fpq where the 2K + + align:start position:0% +fpq where the 2K + + + align:start position:0% +fpq where the 2K +Square are + + align:start position:0% + + + + align:start position:0% + +independent okay is that clear what I'm + + align:start position:0% +independent okay is that clear what I'm + + + align:start position:0% +independent okay is that clear what I'm +defining here so this is basically what + + align:start position:0% +defining here so this is basically what + + + align:start position:0% +defining here so this is basically what +plays the role of T + + align:start position:0% +plays the role of T + + + align:start position:0% +plays the role of T +distributions when you're testing more + + align:start position:0% +distributions when you're testing more + + + align:start position:0% +distributions when you're testing more +than one parameter at a time so you + + align:start position:0% +than one parameter at a time so you + + + align:start position:0% +than one parameter at a time so you +basically replace the the normal that + + align:start position:0% +basically replace the the normal that + + + align:start position:0% +basically replace the the normal that +was in the numerator you replace it by K + + align:start position:0% +was in the numerator you replace it by K + + + align:start position:0% +was in the numerator you replace it by K +Square because you're testing if two + + align:start position:0% +Square because you're testing if two + + + align:start position:0% +Square because you're testing if two +vectors are simultaneously close and the + + align:start position:0% +vectors are simultaneously close and the + + + align:start position:0% +vectors are simultaneously close and the +way you do it is by looking at their + + align:start position:0% +way you do it is by looking at their + + + align:start position:0% +way you do it is by looking at their +squared norm and that's how is the + + align:start position:0% +squared norm and that's how is the + + + align:start position:0% +squared norm and that's how is the +that's how the K Square shows + + align:start position:0% + + + + align:start position:0% + +up quick + + align:start position:0% + + + + align:start position:0% + +remark are those things really very + + align:start position:0% +remark are those things really very + + + align:start position:0% +remark are those things really very +different right how can I relate a k + + align:start position:0% +different right how can I relate a k + + + align:start position:0% +different right how can I relate a k +square with a t distribution well + + align:start position:0% +square with a t distribution well + + + align:start position:0% +square with a t distribution well +if T follows say a + + align:start position:0% +if T follows say a + + + align:start position:0% +if T follows say a +t uh I don't know let's call it + + align:start position:0% +t uh I don't know let's call it + + + align:start position:0% +t uh I don't know let's call it +Q okay so that means that t + + align:start position:0% +Q okay so that means that t + + + align:start position:0% +Q okay so that means that t +let me look at abs look T is some + + align:start position:0% + + + + align:start position:0% + +n01 divided by the square root of a k + + align:start position:0% +n01 divided by the square root of a k + + + align:start position:0% +n01 divided by the square root of a k +squ q divided by Q + + align:start position:0% +squ q divided by Q + + + align:start position:0% +squ q divided by Q +right and dist that that's the + + align:start position:0% +right and dist that that's the + + + align:start position:0% +right and dist that that's the +distribution of of + + align:start position:0% +distribution of of + + + align:start position:0% +distribution of of +T So if I look at the square of the + + align:start position:0% +T So if I look at the square of the + + + align:start position:0% +T So if I look at the square of the +distribution of T + + align:start position:0% + + + + align:start position:0% + +squ put it here + + align:start position:0% + + + + align:start position:0% + +well that's the square of su + + align:start position:0% + + + + align:start position:0% + +n01 divided by k^2 Q over + + align:start position:0% + + + + align:start position:0% + +Q + + align:start position:0% +Q + + + align:start position:0% +Q +agreed I just removed the square root + + align:start position:0% +agreed I just removed the square root + + + align:start position:0% +agreed I just removed the square root +here and I took the square of the Gan + + align:start position:0% +here and I took the square of the Gan + + + align:start position:0% +here and I took the square of the Gan +but what is the distribution of a square + + align:start position:0% +but what is the distribution of a square + + + align:start position:0% +but what is the distribution of a square +of a + + align:start position:0% + + + + align:start position:0% + +gaan k squ with one degree of Freedom + + align:start position:0% +gaan k squ with one degree of Freedom + + + align:start position:0% +gaan k squ with one degree of Freedom +right so this is a K square with one + + align:start position:0% +right so this is a K square with one + + + align:start position:0% +right so this is a K square with one +degree of freedom and in particular it's + + align:start position:0% +degree of freedom and in particular it's + + + align:start position:0% +degree of freedom and in particular it's +also a k square with one degree of + + align:start position:0% +also a k square with one degree of + + + align:start position:0% +also a k square with one degree of +Freedom divided by + + align:start position:0% +Freedom divided by + + + align:start position:0% +Freedom divided by +one so T sare in the + + align:start position:0% + + + + align:start position:0% + +end has an F distribution with one and Q + + align:start position:0% +end has an F distribution with one and Q + + + align:start position:0% +end has an F distribution with one and Q +degrees of freedom so those two things + + align:start position:0% +degrees of freedom so those two things + + + align:start position:0% +degrees of freedom so those two things +are actually very similar the only thing + + align:start position:0% +are actually very similar the only thing + + + align:start position:0% +are actually very similar the only thing +that's going to change is that since + + align:start position:0% +that's going to change is that since + + + align:start position:0% +that's going to change is that since +we're actually looking at typically + + align:start position:0% +we're actually looking at typically + + + align:start position:0% +we're actually looking at typically +absolute values of T when we do our + + align:start position:0% +absolute values of T when we do our + + + align:start position:0% +absolute values of T when we do our +tests it's going to be exactly the same + + align:start position:0% +tests it's going to be exactly the same + + + align:start position:0% +tests it's going to be exactly the same +thing the quentes of one guy are going + + align:start position:0% +thing the quentes of one guy are going + + + align:start position:0% +thing the quentes of one guy are going +to be essentially square root of the + + align:start position:0% +to be essentially square root of the + + + align:start position:0% +to be essentially square root of the +quental of the other guy that's all it's + + align:start position:0% +quental of the other guy that's all it's + + + align:start position:0% +quental of the other guy that's all it's +going to + + align:start position:0% +going to + + + align:start position:0% +going to +be right so my if my test + + align:start position:0% +be right so my if my test + + + align:start position:0% +be right so my if my test +is Si is equal to the + + align:start position:0% +is Si is equal to the + + + align:start position:0% +is Si is equal to the +indicator that t exceeds Q Alpha over + + align:start position:0% +indicator that t exceeds Q Alpha over + + + align:start position:0% +indicator that t exceeds Q Alpha over +two of TQ for + + align:start position:0% +two of TQ for + + + align:start position:0% +two of TQ for +example then it's equal to the indicator + + align:start position:0% +example then it's equal to the indicator + + + align:start position:0% +example then it's equal to the indicator +that + + align:start position:0% +that + + + align:start position:0% +that +t^2 ex see + + align:start position:0% +t^2 ex see + + + align:start position:0% +t^2 ex see +q^2 Alpha over 2 TQ + + align:start position:0% +q^2 Alpha over 2 TQ + + + align:start position:0% +q^2 Alpha over 2 TQ +because I had the absolute value here + + align:start position:0% +because I had the absolute value here + + + align:start position:0% +because I had the absolute value here +which is equal to the indicator that t^2 + + align:start position:0% +which is equal to the indicator that t^2 + + + align:start position:0% +which is equal to the indicator that t^2 +is greater than Q Alpha over two and now + + align:start position:0% +is greater than Q Alpha over two and now + + + align:start position:0% +is greater than Q Alpha over two and now +this time it's an F1 + + align:start position:0% +this time it's an F1 + + + align:start position:0% +this time it's an F1 +Q so in a way those two things belong to + + align:start position:0% +Q so in a way those two things belong to + + + align:start position:0% +Q so in a way those two things belong to +the same family they really are a + + align:start position:0% +the same family they really are a + + + align:start position:0% +the same family they really are a +natural generalization of each other I + + align:start position:0% +natural generalization of each other I + + + align:start position:0% +natural generalization of each other I +mean at least the F test is a + + align:start position:0% +mean at least the F test is a + + + align:start position:0% +mean at least the F test is a +generalization of the T Test + + align:start position:0% +generalization of the T Test + + + align:start position:0% +generalization of the T Test +okay and so now I can perform my test + + align:start position:0% +okay and so now I can perform my test + + + align:start position:0% +okay and so now I can perform my test +just like it's written here I just + + align:start position:0% +just like it's written here I just + + + align:start position:0% +just like it's written here I just +formed this guy and then I perform + + align:start position:0% +formed this guy and then I perform + + + align:start position:0% +formed this guy and then I perform +against the quental of an F test notice + + align:start position:0% +against the quental of an F test notice + + + align:start position:0% +against the quental of an F test notice +there's no absolute value oh yeah I + + align:start position:0% +there's no absolute value oh yeah I + + + align:start position:0% +there's no absolute value oh yeah I +forgot uh this is + + align:start position:0% +forgot uh this is + + + align:start position:0% +forgot uh this is +actually Q Alpha because T the F test + + align:start position:0% +actually Q Alpha because T the F test + + + align:start position:0% +actually Q Alpha because T the F test +the F statistic is already positive so + + align:start position:0% +the F statistic is already positive so + + + align:start position:0% +the F statistic is already positive so +I'm not going to look between left and + + align:start position:0% +I'm not going to look between left and + + + align:start position:0% +I'm not going to look between left and +right I'm just going to look whether + + align:start position:0% +right I'm just going to look whether + + + align:start position:0% +right I'm just going to look whether +it's too large or + + align:start position:0% +it's too large or + + + align:start position:0% +it's too large or +not okay so that's by + + align:start position:0% +not okay so that's by + + + align:start position:0% +not okay so that's by +definition so you can check if you look + + align:start position:0% +definition so you can check if you look + + + align:start position:0% +definition so you can check if you look +at a table for student and you look at a + + align:start position:0% +at a table for student and you look at a + + + align:start position:0% +at a table for student and you look at a +table for f1q one is just you're going + + align:start position:0% +table for f1q one is just you're going + + + align:start position:0% +table for f1q one is just you're going +to have to move from one column to to + + align:start position:0% +to have to move from one column to to + + + align:start position:0% +to have to move from one column to to +the other because you're going to have + + align:start position:0% +the other because you're going to have + + + align:start position:0% +the other because you're going to have +to move from alpha over two to Alpha but + + align:start position:0% +to move from alpha over two to Alpha but + + + align:start position:0% +to move from alpha over two to Alpha but +one is going to be square root of the + + align:start position:0% +one is going to be square root of the + + + align:start position:0% +one is going to be square root of the +other + + align:start position:0% +other + + + align:start position:0% +other +one just like the K square is the square + + align:start position:0% +one just like the K square is the square + + + align:start position:0% +one just like the K square is the square +of the of the Gan I mean if you look at + + align:start position:0% +of the of the Gan I mean if you look at + + + align:start position:0% +of the of the Gan I mean if you look at +the K Square 1 degree of Freedom you + + align:start position:0% +the K Square 1 degree of Freedom you + + + align:start position:0% +the K Square 1 degree of Freedom you +will see the same thing as the as the + + align:start position:0% +will see the same thing as the as the + + + align:start position:0% +will see the same thing as the as the +Gans all + + align:start position:0% + + + + align:start position:0% + +right so uh + + align:start position:0% +right so uh + + + align:start position:0% +right so uh +okay I'm actually going to I'm actually + + align:start position:0% +okay I'm actually going to I'm actually + + + align:start position:0% +okay I'm actually going to I'm actually +going to start with the last one because + + align:start position:0% +going to start with the last one because + + + align:start position:0% +going to start with the last one because +you've been asking me a few questions + + align:start position:0% +you've been asking me a few questions + + + align:start position:0% +you've been asking me a few questions +about why is my design + + align:start position:0% +about why is my design + + + align:start position:0% +about why is my design +deterministic so there's many answers + + align:start position:0% +deterministic so there's many answers + + + align:start position:0% +deterministic so there's many answers +some are pH + + align:start position:0% +some are pH + + + align:start position:0% +some are pH +philosophical but one that's actually + + align:start position:0% +philosophical but one that's actually + + + align:start position:0% +philosophical but one that's actually +well there's the one that says + + align:start position:0% +well there's the one that says + + + align:start position:0% +well there's the one that says +everything you cannot do if if you don't + + align:start position:0% +everything you cannot do if if you don't + + + align:start position:0% +everything you cannot do if if you don't +have a condition if you don't have X + + align:start position:0% +have a condition if you don't have X + + + align:start position:0% +have a condition if you don't have X +because all the statements that we made + + align:start position:0% +because all the statements that we made + + + align:start position:0% +because all the statements that we made +here for example just the fact that this + + align:start position:0% +here for example just the fact that this + + + align:start position:0% +here for example just the fact that this +is K square if those starts those guys + + align:start position:0% +is K square if those starts those guys + + + align:start position:0% +is K square if those starts those guys +start to be random variables then it's + + align:start position:0% +start to be random variables then it's + + + align:start position:0% +start to be random variables then it's +clearly not going to be a k Square it + + align:start position:0% +clearly not going to be a k Square it + + + align:start position:0% +clearly not going to be a k Square it +cannot be a k Square when those guys are + + align:start position:0% +cannot be a k Square when those guys are + + + align:start position:0% +cannot be a k Square when those guys are +deterministic and when they are random I + + align:start position:0% +deterministic and when they are random I + + + align:start position:0% +deterministic and when they are random I +mean things change so that's just maybe + + align:start position:0% +mean things change so that's just maybe + + + align:start position:0% +mean things change so that's just maybe +one s is check statement but I think the + + align:start position:0% +one s is check statement but I think the + + + align:start position:0% +one s is check statement but I think the +one that really matters is that remember + + align:start position:0% +one that really matters is that remember + + + align:start position:0% +one that really matters is that remember +when we did the T Test we had this gamma + + align:start position:0% +when we did the T Test we had this gamma + + + align:start position:0% +when we did the T Test we had this gamma +J that showed up gamma J was playing the + + align:start position:0% +J that showed up gamma J was playing the + + + align:start position:0% +J that showed up gamma J was playing the +role of the variance so here the + + align:start position:0% +role of the variance so here the + + + align:start position:0% +role of the variance so here the +variance you never think of the I mean + + align:start position:0% +variance you never think of the I mean + + + align:start position:0% +variance you never think of the I mean +we'll talk about this in the beian setup + + align:start position:0% +we'll talk about this in the beian setup + + + align:start position:0% +we'll talk about this in the beian setup +but so far we haven't thought of the + + align:start position:0% +but so far we haven't thought of the + + + align:start position:0% +but so far we haven't thought of the +variance as a random variable and so + + align:start position:0% +variance as a random variable and so + + + align:start position:0% +variance as a random variable and so +here your X's really are the parameters + + align:start position:0% +here your X's really are the parameters + + + align:start position:0% +here your X's really are the parameters +of your data and the diagonal elements + + align:start position:0% +of your data and the diagonal elements + + + align:start position:0% +of your data and the diagonal elements +of X transpose X inverse actually tell + + align:start position:0% +of X transpose X inverse actually tell + + + align:start position:0% +of X transpose X inverse actually tell +you what the variance is so that's also + + align:start position:0% +you what the variance is so that's also + + + align:start position:0% +you what the variance is so that's also +one reason why you should think of your + + align:start position:0% +one reason why you should think of your + + + align:start position:0% +one reason why you should think of your +X as being deterministic number there + + align:start position:0% +X as being deterministic number there + + + align:start position:0% +X as being deterministic number there +are in a way things that change the G + + align:start position:0% +are in a way things that change the G + + + align:start position:0% +are in a way things that change the G +geometry of your problem they just say + + align:start position:0% +geometry of your problem they just say + + + align:start position:0% +geometry of your problem they just say +oh let me look at it from the + + align:start position:0% +oh let me look at it from the + + + align:start position:0% +oh let me look at it from the +perspective the perspective of X + + align:start position:0% +perspective the perspective of X + + + align:start position:0% +perspective the perspective of X +actually for that matter we didn't + + align:start position:0% +actually for that matter we didn't + + + align:start position:0% +actually for that matter we didn't +really spend much time commenting on + + align:start position:0% +really spend much time commenting on + + + align:start position:0% +really spend much time commenting on +what is the effect of X onto gamma right + + align:start position:0% +what is the effect of X onto gamma right + + + align:start position:0% +what is the effect of X onto gamma right +so remember gamma + + align:start position:0% + + + + align:start position:0% + +J right so that was the variance + + align:start position:0% +J right so that was the variance + + + align:start position:0% +J right so that was the variance +parameter so we should try to understand + + align:start position:0% +parameter so we should try to understand + + + align:start position:0% +parameter so we should try to understand +what X's lead to Big variance and what + + align:start position:0% +what X's lead to Big variance and what + + + align:start position:0% +what X's lead to Big variance and what +X's lead to small variant right that + + align:start position:0% +X's lead to small variant right that + + + align:start position:0% +X's lead to small variant right that +would be + + align:start position:0% +would be + + + align:start position:0% +would be +nice well if this is the identity Matrix + + align:start position:0% +nice well if this is the identity Matrix + + + align:start position:0% +nice well if this is the identity Matrix +let's say identity Over N which is the + + align:start position:0% +let's say identity Over N which is the + + + align:start position:0% +let's say identity Over N which is the +natural thing to look at because we want + + align:start position:0% +natural thing to look at because we want + + + align:start position:0% +natural thing to look at because we want +this thing to scale like one over n then + + align:start position:0% +this thing to scale like one over n then + + + align:start position:0% +this thing to scale like one over n then +this is just one over n we're back to + + align:start position:0% +this is just one over n we're back to + + + align:start position:0% +this is just one over n we're back to +the original case + + align:start position:0% +the original case + + + align:start position:0% +the original case +yes oh yeah thank you X inverse yes so + + align:start position:0% +yes oh yeah thank you X inverse yes so + + + align:start position:0% +yes oh yeah thank you X inverse yes so +if this is the identity then well the + + align:start position:0% +if this is the identity then well the + + + align:start position:0% +if this is the identity then well the +inverse is let's say just this guy here + + align:start position:0% +inverse is let's say just this guy here + + + align:start position:0% +inverse is let's say just this guy here +is n times this + + align:start position:0% +is n times this + + + align:start position:0% +is n times this +guy so then the inverse is one over n + + align:start position:0% +guy so then the inverse is one over n + + + align:start position:0% +guy so then the inverse is one over n +right so in this case that means that + + align:start position:0% +right so in this case that means that + + + align:start position:0% +right so in this case that means that +gamma J is equal to one/ n and we're + + align:start position:0% +gamma J is equal to one/ n and we're + + + align:start position:0% +gamma J is equal to one/ n and we're +back to the Theta hat Theta case right + + align:start position:0% +back to the Theta hat Theta case right + + + align:start position:0% +back to the Theta hat Theta case right +the basic onedimensional + + align:start position:0% +the basic onedimensional + + + align:start position:0% +the basic onedimensional +thing what does it mean for a matrix for + + align:start position:0% +thing what does it mean for a matrix for + + + align:start position:0% +thing what does it mean for a matrix for +when I take it's + + align:start position:0% +when I take it's + + + align:start position:0% +when I take it's +uh yeah so that's of Dimension P right + + align:start position:0% +uh yeah so that's of Dimension P right + + + align:start position:0% +uh yeah so that's of Dimension P right +when I take its transpose so forget + + align:start position:0% +when I take its transpose so forget + + + align:start position:0% +when I take its transpose so forget +about the scaling by n right now this is + + align:start position:0% +about the scaling by n right now this is + + + align:start position:0% +about the scaling by n right now this is +just a matter of scaling things right I + + align:start position:0% +just a matter of scaling things right I + + + align:start position:0% +just a matter of scaling things right I +can always multiply my exes so that I + + align:start position:0% +can always multiply my exes so that I + + + align:start position:0% +can always multiply my exes so that I +have this thing that shows up but when I + + align:start position:0% +have this thing that shows up but when I + + + align:start position:0% +have this thing that shows up but when I +have a matrix if I look at X transpose X + + align:start position:0% +have a matrix if I look at X transpose X + + + align:start position:0% +have a matrix if I look at X transpose X +and I get something which is is the + + align:start position:0% +and I get something which is is the + + + align:start position:0% +and I get something which is is the +identity how do I call this + + align:start position:0% + + + + align:start position:0% + +Matrix orthogonal yeah orthal or + + align:start position:0% +Matrix orthogonal yeah orthal or + + + align:start position:0% +Matrix orthogonal yeah orthal or +orthogonal so you you call this thing an + + align:start position:0% +orthogonal so you you call this thing an + + + align:start position:0% +orthogonal so you you call this thing an +orthogonal Matrix and when it's an + + align:start position:0% +orthogonal Matrix and when it's an + + + align:start position:0% +orthogonal Matrix and when it's an +orthogonal Matrix what it means is that + + align:start position:0% +orthogonal Matrix what it means is that + + + align:start position:0% +orthogonal Matrix what it means is that +the the the so this Matrix here if you + + align:start position:0% +the the the so this Matrix here if you + + + align:start position:0% +the the the so this Matrix here if you +look at the Matrix XX transpose the + + align:start position:0% +look at the Matrix XX transpose the + + + align:start position:0% +look at the Matrix XX transpose the +entries of this Matrix are the inner + + align:start position:0% +entries of this Matrix are the inner + + + align:start position:0% +entries of this Matrix are the inner +products between The Columns of X that's + + align:start position:0% +products between The Columns of X that's + + + align:start position:0% +products between The Columns of X that's +what's happening right you can write it + + align:start position:0% +what's happening right you can write it + + + align:start position:0% +what's happening right you can write it +and you will see that the the entries of + + align:start position:0% +and you will see that the the entries of + + + align:start position:0% +and you will see that the the entries of +this Matrix are the inner product if + + align:start position:0% +this Matrix are the inner product if + + + align:start position:0% +this Matrix are the inner product if +it's the + + align:start position:0% +it's the + + + align:start position:0% +it's the +identity that means that you get some + + align:start position:0% +identity that means that you get some + + + align:start position:0% +identity that means that you get some +ones and a bunch of zero it means that + + align:start position:0% +ones and a bunch of zero it means that + + + align:start position:0% +ones and a bunch of zero it means that +all the the inner product between two + + align:start position:0% +all the the inner product between two + + + align:start position:0% +all the the inner product between two +different columns is actually zero what + + align:start position:0% +different columns is actually zero what + + + align:start position:0% +different columns is actually zero what +it means is that this Matrix X is an + + align:start position:0% +it means is that this Matrix X is an + + + align:start position:0% +it means is that this Matrix X is an +orthonormal basis for your space The + + align:start position:0% +orthonormal basis for your space The + + + align:start position:0% +orthonormal basis for your space The +Columns form an orthonormal basis so + + align:start position:0% +Columns form an orthonormal basis so + + + align:start position:0% +Columns form an orthonormal basis so +they're basically as far from each other + + align:start position:0% +they're basically as far from each other + + + align:start position:0% +they're basically as far from each other +as they can now if I start making those + + align:start position:0% +as they can now if I start making those + + + align:start position:0% +as they can now if I start making those +guys closer and closer then I'm starting + + align:start position:0% +guys closer and closer then I'm starting + + + align:start position:0% +guys closer and closer then I'm starting +to have some issues right X transpose X + + align:start position:0% +to have some issues right X transpose X + + + align:start position:0% +to have some issues right X transpose X +is not going to be the identity I'm + + align:start position:0% +is not going to be the identity I'm + + + align:start position:0% +is not going to be the identity I'm +going to start to have some nonzero + + align:start position:0% +going to start to have some nonzero + + + align:start position:0% +going to start to have some nonzero +entries but if they all remain of Norm + + align:start position:0% +entries but if they all remain of Norm + + + align:start position:0% +entries but if they all remain of Norm +one then uh uh um oh sorry so that's for + + align:start position:0% +one then uh uh um oh sorry so that's for + + + align:start position:0% +one then uh uh um oh sorry so that's for +the inverse right so I first start + + align:start position:0% +the inverse right so I first start + + + align:start position:0% +the inverse right so I first start +putting some stuff here which is non + + align:start position:0% +putting some stuff here which is non + + + align:start position:0% +putting some stuff here which is non +zero by taking my x's rather than having + + align:start position:0% +zero by taking my x's rather than having + + + align:start position:0% +zero by taking my x's rather than having +this I move to + + align:start position:0% +this I move to + + + align:start position:0% +this I move to +this right now I'm going to start seeing + + align:start position:0% +this right now I'm going to start seeing + + + align:start position:0% +this right now I'm going to start seeing +some nonzero entries and when I'm going + + align:start position:0% +some nonzero entries and when I'm going + + + align:start position:0% +some nonzero entries and when I'm going +to take the inverse of this Matrix the + + align:start position:0% +to take the inverse of this Matrix the + + + align:start position:0% +to take the inverse of this Matrix the +diagonal elements are going to start to + + align:start position:0% +diagonal elements are going to start to + + + align:start position:0% +diagonal elements are going to start to +blow + + align:start position:0% +blow + + + align:start position:0% +blow +up sorry the are going to start to + + align:start position:0% +up sorry the are going to start to + + + align:start position:0% +up sorry the are going to start to +become smaller and smaller so when I + + align:start position:0% +become smaller and smaller so when I + + + align:start position:0% +become smaller and smaller so when I +take the inverse no sorry the the + + align:start position:0% +take the inverse no sorry the the + + + align:start position:0% +take the inverse no sorry the the +diagonal elements are going to blow up + + align:start position:0% +diagonal elements are going to blow up + + + align:start position:0% +diagonal elements are going to blow up +and so what it means is that the + + align:start position:0% +and so what it means is that the + + + align:start position:0% +and so what it means is that the +variance is going to blow up and that's + + align:start position:0% +variance is going to blow up and that's + + + align:start position:0% +variance is going to blow up and that's +essentially is telling you that if you + + align:start position:0% +essentially is telling you that if you + + + align:start position:0% +essentially is telling you that if you +if you get to choose your X's you want + + align:start position:0% +if you get to choose your X's you want + + + align:start position:0% +if you get to choose your X's you want +to take them as orthogonal as you can + + align:start position:0% +to take them as orthogonal as you can + + + align:start position:0% +to take them as orthogonal as you can +but if you don't then you just have to + + align:start position:0% +but if you don't then you just have to + + + align:start position:0% +but if you don't then you just have to +deal with it and it will have a + + align:start position:0% +deal with it and it will have a + + + align:start position:0% +deal with it and it will have a +significant impact on your uh on your + + align:start position:0% +significant impact on your uh on your + + + align:start position:0% +significant impact on your uh on your +estimation performance and that's what + + align:start position:0% +estimation performance and that's what + + + align:start position:0% +estimation performance and that's what +also routinely uh uh software + + align:start position:0% +also routinely uh uh software + + + align:start position:0% +also routinely uh uh software +statistical software is going to spit + + align:start position:0% +statistical software is going to spit + + + align:start position:0% +statistical software is going to spit +out this value here for you and you're + + align:start position:0% +out this value here for you and you're + + + align:start position:0% +out this value here for you and you're +going to have well actually square root + + align:start position:0% +going to have well actually square root + + + align:start position:0% +going to have well actually square root +of this value and it's going to tell you + + align:start position:0% +of this value and it's going to tell you + + + align:start position:0% +of this value and it's going to tell you +essentially you're going to know how + + align:start position:0% +essentially you're going to know how + + + align:start position:0% +essentially you're going to know how +much Randomness how much variation you + + align:start position:0% +much Randomness how much variation you + + + align:start position:0% +much Randomness how much variation you +have in this particular parameter that + + align:start position:0% +have in this particular parameter that + + + align:start position:0% +have in this particular parameter that +you're estimating so if gamma J is large + + align:start position:0% +you're estimating so if gamma J is large + + + align:start position:0% +you're estimating so if gamma J is large +then you know you're going to have wide + + align:start position:0% +then you know you're going to have wide + + + align:start position:0% +then you know you're going to have wide +confidence intervals and your tests are + + align:start position:0% +confidence intervals and your tests are + + + align:start position:0% +confidence intervals and your tests are +not going to reject very much and that's + + align:start position:0% +not going to reject very much and that's + + + align:start position:0% +not going to reject very much and that's +all captured by X that's what's + + align:start position:0% +all captured by X that's what's + + + align:start position:0% +all captured by X that's what's +important everything all of this is + + align:start position:0% +important everything all of this is + + + align:start position:0% +important everything all of this is +completely captured by X then of course + + align:start position:0% +completely captured by X then of course + + + align:start position:0% +completely captured by X then of course +there was the sigma square that showed + + align:start position:0% +there was the sigma square that showed + + + align:start position:0% +there was the sigma square that showed +up here right actually it was or even in + + align:start position:0% +up here right actually it was or even in + + + align:start position:0% +up here right actually it was or even in +the definition of gamma J I forgot it + + align:start position:0% +the definition of gamma J I forgot it + + + align:start position:0% +the definition of gamma J I forgot it +what is the sigma Square police doing + + align:start position:0% +what is the sigma Square police doing + + + align:start position:0% +what is the sigma Square police doing +and uh so this thing was here as well + + align:start position:0% +and uh so this thing was here as well + + + align:start position:0% +and uh so this thing was here as well +and that's just sort of exogenous it + + align:start position:0% +and that's just sort of exogenous it + + + align:start position:0% +and that's just sort of exogenous it +comes from the noise itself but there + + align:start position:0% +comes from the noise itself but there + + + align:start position:0% +comes from the noise itself but there +was this huge factor that came from the + + align:start position:0% +was this huge factor that came from the + + + align:start position:0% +was this huge factor that came from the +ex's + + align:start position:0% +ex's + + + align:start position:0% +ex's +itself okay so let's go back now to uh + + align:start position:0% +itself okay so let's go back now to uh + + + align:start position:0% +itself okay so let's go back now to uh +reading those this list in a linear + + align:start position:0% +reading those this list in a linear + + + align:start position:0% +reading those this list in a linear +fashion + + align:start position:0% +fashion + + + align:start position:0% +fashion +so I + + align:start position:0% +so I + + + align:start position:0% +so I +mean your MIT students you've probably + + align:start position:0% +mean your MIT students you've probably + + + align:start position:0% +mean your MIT students you've probably +heard that correlation does not imply + + align:start position:0% +heard that correlation does not imply + + + align:start position:0% +heard that correlation does not imply +cation many times maybe you don't know + + align:start position:0% +cation many times maybe you don't know + + + align:start position:0% +cation many times maybe you don't know +what it means uh if you don't that's + + align:start position:0% +what it means uh if you don't that's + + + align:start position:0% +what it means uh if you don't that's +okay you just have to know the sentence + + align:start position:0% +okay you just have to know the sentence + + + align:start position:0% +okay you just have to know the sentence +uh no what it means is that it's not + + align:start position:0% +uh no what it means is that it's not + + + align:start position:0% +uh no what it means is that it's not +because I decided that something was + + align:start position:0% +because I decided that something was + + + align:start position:0% +because I decided that something was +going to be the X and that something + + align:start position:0% +going to be the X and that something + + + align:start position:0% +going to be the X and that something +else was going to be the Y that whatever + + align:start position:0% +else was going to be the Y that whatever + + + align:start position:0% +else was going to be the Y that whatever +thing I'm getting it means that X + + align:start position:0% +thing I'm getting it means that X + + + align:start position:0% +thing I'm getting it means that X +implies y right for example even if I do + + align:start position:0% +implies y right for example even if I do + + + align:start position:0% +implies y right for example even if I do +genetics genomics or whatever I mean I + + align:start position:0% +genetics genomics or whatever I mean I + + + align:start position:0% +genetics genomics or whatever I mean I +sort of implicitly assume that the my + + align:start position:0% +sort of implicitly assume that the my + + + align:start position:0% +sort of implicitly assume that the my +genes are going to have an effect on my + + align:start position:0% +genes are going to have an effect on my + + + align:start position:0% +genes are going to have an effect on my +outside look it could be the opposite + + align:start position:0% +outside look it could be the opposite + + + align:start position:0% +outside look it could be the opposite +right I mean who am I to say I'm not a + + align:start position:0% +right I mean who am I to say I'm not a + + + align:start position:0% +right I mean who am I to say I'm not a +biologist I don't know I didn't open a + + align:start position:0% +biologist I don't know I didn't open a + + + align:start position:0% +biologist I don't know I didn't open a +Biology book in 20 years so maybe you + + align:start position:0% +Biology book in 20 years so maybe you + + + align:start position:0% +Biology book in 20 years so maybe you +know if I start hitting my head with a + + align:start position:0% +know if I start hitting my head with a + + + align:start position:0% +know if I start hitting my head with a +hammer I'm going to have changing my + + align:start position:0% +hammer I'm going to have changing my + + + align:start position:0% +hammer I'm going to have changing my +genetic material right probably not but + + align:start position:0% +genetic material right probably not but + + + align:start position:0% +genetic material right probably not but +you know that's why ca but causation + + align:start position:0% +you know that's why ca but causation + + + align:start position:0% +you know that's why ca but causation +definitely does not come from statistics + + align:start position:0% +definitely does not come from statistics + + + align:start position:0% +definitely does not come from statistics +if you know that that's the different + + align:start position:0% +if you know that that's the different + + + align:start position:0% +if you know that that's the different +thing it's actually gonna uh it's not + + align:start position:0% +thing it's actually gonna uh it's not + + + align:start position:0% +thing it's actually gonna uh it's not +coming from there so actually I remember + + align:start position:0% +coming from there so actually I remember + + + align:start position:0% +coming from there so actually I remember +once I put an exam to students in uh + + align:start position:0% +once I put an exam to students in uh + + + align:start position:0% +once I put an exam to students in uh +there was an old data set from polist + + align:start position:0% +there was an old data set from polist + + + align:start position:0% +there was an old data set from polist +expenditures I think in Chicago in the + + align:start position:0% +expenditures I think in Chicago in the + + + align:start position:0% +expenditures I think in Chicago in the +60s and it was they're trying to + + align:start position:0% +60s and it was they're trying to + + + align:start position:0% +60s and it was they're trying to +understand uh I mean no it was on crime + + align:start position:0% +understand uh I mean no it was on crime + + + align:start position:0% +understand uh I mean no it was on crime +it was the crime data set and they were + + align:start position:0% +it was the crime data set and they were + + + align:start position:0% +it was the crime data set and they were +trying so the Y variable was just the + + align:start position:0% +trying so the Y variable was just the + + + align:start position:0% +trying so the Y variable was just the +rate of crime and the X's were a bunch + + align:start position:0% +rate of crime and the X's were a bunch + + + align:start position:0% +rate of crime and the X's were a bunch +of things and one of them was polic + + align:start position:0% +of things and one of them was polic + + + align:start position:0% +of things and one of them was polic +expenditures and if you ran the + + align:start position:0% +expenditures and if you ran the + + + align:start position:0% +expenditures and if you ran the +regression you would find that the + + align:start position:0% +regression you would find that the + + + align:start position:0% +regression you would find that the +coefficient in front of police + + align:start position:0% +coefficient in front of police + + + align:start position:0% +coefficient in front of police +expenditure was a positive number which + + align:start position:0% +expenditure was a positive number which + + + align:start position:0% +expenditure was a positive number which +means that if you increase police + + align:start position:0% +means that if you increase police + + + align:start position:0% +means that if you increase police +expenditure that increases the + + align:start position:0% +expenditure that increases the + + + align:start position:0% +expenditure that increases the +crime right I mean that's what it means + + align:start position:0% +crime right I mean that's what it means + + + align:start position:0% +crime right I mean that's what it means +to have a positive + + align:start position:0% +to have a positive + + + align:start position:0% +to have a positive +coefficient everybody agrees with this + + align:start position:0% +coefficient everybody agrees with this + + + align:start position:0% +coefficient everybody agrees with this +fact right beta if bet J is 10 then it + + align:start position:0% +fact right beta if bet J is 10 then it + + + align:start position:0% +fact right beta if bet J is 10 then it +means that if I increase by $1 my PO + + align:start position:0% +means that if I increase by $1 my PO + + + align:start position:0% +means that if I increase by $1 my PO +expenditure I I by 10 my crime + + align:start position:0% +expenditure I I by 10 my crime + + + align:start position:0% +expenditure I I by 10 my crime +everything else being kept equal well + + align:start position:0% +everything else being kept equal well + + + align:start position:0% +everything else being kept equal well +you know there were I think about 80% of + + align:start position:0% +you know there were I think about 80% of + + + align:start position:0% +you know there were I think about 80% of +the students that were able to explain + + align:start position:0% +the students that were able to explain + + + align:start position:0% +the students that were able to explain +to me that if you give more money to the + + align:start position:0% +to me that if you give more money to the + + + align:start position:0% +to me that if you give more money to the +police then the crime is going to raise + + align:start position:0% +police then the crime is going to raise + + + align:start position:0% +police then the crime is going to raise +some people are like well you know + + align:start position:0% +some people are like well you know + + + align:start position:0% +some people are like well you know +police is making too much money and they + + align:start position:0% +police is making too much money and they + + + align:start position:0% +police is making too much money and they +don't think about their work and they + + align:start position:0% +don't think about their work and they + + + align:start position:0% +don't think about their work and they +become lazy and I mean people were + + align:start position:0% +become lazy and I mean people were + + + align:start position:0% +become lazy and I mean people were +really coming up with some crazy things + + align:start position:0% +really coming up with some crazy things + + + align:start position:0% +really coming up with some crazy things +and what it just meant is that no it's + + align:start position:0% +and what it just meant is that no it's + + + align:start position:0% +and what it just meant is that no it's +not correl it's not causation right it's + + align:start position:0% +not correl it's not causation right it's + + + align:start position:0% +not correl it's not causation right it's +just if you have more crime you give + + align:start position:0% +just if you have more crime you give + + + align:start position:0% +just if you have more crime you give +more money to your police that's what's + + align:start position:0% +more money to your police that's what's + + + align:start position:0% +more money to your police that's what's +happening right and uh that's all there + + align:start position:0% +happening right and uh that's all there + + + align:start position:0% +happening right and uh that's all there +is so just be careful when you actually + + align:start position:0% +is so just be careful when you actually + + + align:start position:0% +is so just be careful when you actually +draw some conclusions that causation is + + align:start position:0% +draw some conclusions that causation is + + + align:start position:0% +draw some conclusions that causation is +a very important thing to keep in mind + + align:start position:0% +a very important thing to keep in mind + + + align:start position:0% +a very important thing to keep in mind +and in practice unless you have external + + align:start position:0% +and in practice unless you have external + + + align:start position:0% +and in practice unless you have external +sources of reason for causality for + + align:start position:0% +sources of reason for causality for + + + align:start position:0% +sources of reason for causality for +example genetic material and and and + + align:start position:0% +example genetic material and and and + + + align:start position:0% +example genetic material and and and +physical traits we sort of you know + + align:start position:0% +physical traits we sort of you know + + + align:start position:0% +physical traits we sort of you know +agree upon what the arrow of causality + + align:start position:0% +agree upon what the arrow of causality + + + align:start position:0% +agree upon what the arrow of causality +what the direction of the arrow of + + align:start position:0% +what the direction of the arrow of + + + align:start position:0% +what the direction of the arrow of +causality is here uh there's places + + align:start position:0% +causality is here uh there's places + + + align:start position:0% +causality is here uh there's places +where you might + + align:start position:0% +where you might + + + align:start position:0% +where you might +not now finally the normality on the + + align:start position:0% +not now finally the normality on the + + + align:start position:0% +not now finally the normality on the +noise everything we did today required + + align:start position:0% +noise everything we did today required + + + align:start position:0% +noise everything we did today required +normal gussan distribution on the noise + + align:start position:0% +normal gussan distribution on the noise + + + align:start position:0% +normal gussan distribution on the noise +right I mean it's everywhere there's + + align:start position:0% +right I mean it's everywhere there's + + + align:start position:0% +right I mean it's everywhere there's +some gussan there's some K Square + + align:start position:0% +some gussan there's some K Square + + + align:start position:0% +some gussan there's some K Square +everything came out of gussan and for + + align:start position:0% +everything came out of gussan and for + + + align:start position:0% +everything came out of gussan and for +that we needed this basic formula for + + align:start position:0% +that we needed this basic formula for + + + align:start position:0% +that we needed this basic formula for +inference which we derive from the fact + + align:start position:0% +inference which we derive from the fact + + + align:start position:0% +inference which we derive from the fact +that the noise was gaussian itself if we + + align:start position:0% +that the noise was gaussian itself if we + + + align:start position:0% +that the noise was gaussian itself if we +did not have that the only thing we + + align:start position:0% +did not have that the only thing we + + + align:start position:0% +did not have that the only thing we +could write is beta hat is this number + + align:start position:0% +could write is beta hat is this number + + + align:start position:0% +could write is beta hat is this number +or this Vector we would not be able to + + align:start position:0% +or this Vector we would not be able to + + + align:start position:0% +or this Vector we would not be able to +say the fluctuations of beta hat are + + align:start position:0% +say the fluctuations of beta hat are + + + align:start position:0% +say the fluctuations of beta hat are +this guy we not be able to to do tests + + align:start position:0% +this guy we not be able to to do tests + + + align:start position:0% +this guy we not be able to to do tests +we not be able to build say conference + + align:start position:0% +we not be able to build say conference + + + align:start position:0% +we not be able to build say conference +regions or anything and + + align:start position:0% +regions or anything and + + + align:start position:0% +regions or anything and +so this is an important condition that + + align:start position:0% +so this is an important condition that + + + align:start position:0% +so this is an important condition that +we need and that's what statistical + + align:start position:0% +we need and that's what statistical + + + align:start position:0% +we need and that's what statistical +software assumes by default but we now + + align:start position:0% +software assumes by default but we now + + + align:start position:0% +software assumes by default but we now +have a recipe on how to do those tests + + align:start position:0% +have a recipe on how to do those tests + + + align:start position:0% +have a recipe on how to do those tests +right we can do it either visually if we + + align:start position:0% +right we can do it either visually if we + + + align:start position:0% +right we can do it either visually if we +really want to conclude that yes it's + + align:start position:0% +really want to conclude that yes it's + + + align:start position:0% +really want to conclude that yes it's +scalan uh using our normal QQ plots and + + align:start position:0% +scalan uh using our normal QQ plots and + + + align:start position:0% +scalan uh using our normal QQ plots and +we can also do it using our favorite + + align:start position:0% +we can also do it using our favorite + + + align:start position:0% +we can also do it using our favorite +test what test should I be using to test + + align:start position:0% + + + + align:start position:0% + +that would like two + + align:start position:0% +that would like two + + + align:start position:0% +that would like two +names + + align:start position:0% + + + + align:start position:0% + +yeah not the two Russians I want a + + align:start position:0% +yeah not the two Russians I want a + + + align:start position:0% +yeah not the two Russians I want a +Russian and a Scandinavian person for + + align:start position:0% +Russian and a Scandinavian person for + + + align:start position:0% +Russian and a Scandinavian person for +this + + align:start position:0% +this + + + align:start position:0% +this +one what's that yeah Lily something so K + + align:start position:0% +one what's that yeah Lily something so K + + + align:start position:0% +one what's that yeah Lily something so K +ly something test and + + align:start position:0% +ly something test and + + + align:start position:0% +ly something test and +uh so it's the kogas Le force test okay + + align:start position:0% +uh so it's the kogas Le force test okay + + + align:start position:0% +uh so it's the kogas Le force test okay +and uh because I'm testing they're + + align:start position:0% +and uh because I'm testing they're + + + align:start position:0% +and uh because I'm testing they're +gussan and I'm actually not really + + align:start position:0% +gussan and I'm actually not really + + + align:start position:0% +gussan and I'm actually not really +making any I don't need to know what the + + align:start position:0% +making any I don't need to know what the + + + align:start position:0% +making any I don't need to know what the +variance is right the mean is zero we + + align:start position:0% +variance is right the mean is zero we + + + align:start position:0% +variance is right the mean is zero we +saw that at the beginning it's zero by + + align:start position:0% +saw that at the beginning it's zero by + + + align:start position:0% +saw that at the beginning it's zero by +construction so we actually don't need + + align:start position:0% +construction so we actually don't need + + + align:start position:0% +construction so we actually don't need +to think about the mean being zero + + align:start position:0% +to think about the mean being zero + + + align:start position:0% +to think about the mean being zero +itself this just happens to be zero so + + align:start position:0% +itself this just happens to be zero so + + + align:start position:0% +itself this just happens to be zero so +we know that it's zero but the variance + + align:start position:0% +we know that it's zero but the variance + + + align:start position:0% +we know that it's zero but the variance +we don't know so we just want to know if + + align:start position:0% +we don't know so we just want to know if + + + align:start position:0% +we don't know so we just want to know if +it belongs to the family of Gans and so + + align:start position:0% +it belongs to the family of Gans and so + + + align:start position:0% +it belongs to the family of Gans and so +we need chog Le for for that and that's + + align:start position:0% +we need chog Le for for that and that's + + + align:start position:0% +we need chog Le for for that and that's +also one of the thing that's spit out by + + align:start position:0% +also one of the thing that's spit out by + + + align:start position:0% +also one of the thing that's spit out by +statistical software by default when you + + align:start position:0% +statistical software by default when you + + + align:start position:0% +statistical software by default when you +run a linear regression actually it + + align:start position:0% +run a linear regression actually it + + + align:start position:0% +run a linear regression actually it +spits out both ksme and off and L for + + align:start position:0% +spits out both ksme and off and L for + + + align:start position:0% +spits out both ksme and off and L for +probably contributing to the uh to the + + align:start position:0% +probably contributing to the uh to the + + + align:start position:0% +probably contributing to the uh to the +widespread use of KS enough when you + + align:start position:0% +widespread use of KS enough when you + + + align:start position:0% +widespread use of KS enough when you +really should it all right so next time + + align:start position:0% +really should it all right so next time + + + align:start position:0% +really should it all right so next time +uh we will talk about more advanced + + align:start position:0% +uh we will talk about more advanced + + + align:start position:0% +uh we will talk about more advanced +topics on regression but I think I'm + + align:start position:0% +topics on regression but I think I'm + + + align:start position:0% +topics on regression but I think I'm +going to stop here for today so again uh + + align:start position:0% +going to stop here for today so again uh + + + align:start position:0% +going to stop here for today so again uh +tomorrow sometime during the day at + + align:start position:0% +tomorrow sometime during the day at + + + align:start position:0% +tomorrow sometime during the day at +least before the recitation you will + + align:start position:0% +least before the recitation you will + + + align:start position:0% +least before the recitation you will +have a list of practice exercises that + + align:start position:0% +have a list of practice exercises that + + + align:start position:0% +have a list of practice exercises that +will be posted and if you go to the + + align:start position:0% +will be posted and if you go to the + + + align:start position:0% +will be posted and if you go to the +optional recitation you will have + + align:start position:0% +optional recitation you will have + + + align:start position:0% +optional recitation you will have +someone solving for you \ No newline at end of file diff --git a/VZm6mxu2xlk.txt b/VZm6mxu2xlk.txt new file mode 100644 index 0000000000000000000000000000000000000000..a8f83453c7b20cf21260f917043abd084d926fa8 --- /dev/null +++ b/VZm6mxu2xlk.txt @@ -0,0 +1,251 @@ +align:start position:0% + +vectors can be represented through their + + align:start position:0% +vectors can be represented through their + + + align:start position:0% +vectors can be represented through their +components if we have a vector a we can + + align:start position:0% +components if we have a vector a we can + + + align:start position:0% +components if we have a vector a we can +decompose it into its components in the + + align:start position:0% +decompose it into its components in the + + + align:start position:0% +decompose it into its components in the +X and Y directions by finding the + + align:start position:0% +X and Y directions by finding the + + + align:start position:0% +X and Y directions by finding the +vectors one along X and one along y that + + align:start position:0% +vectors one along X and one along y that + + + align:start position:0% +vectors one along X and one along y that +add up to the vector + + align:start position:0% +add up to the vector + + + align:start position:0% +add up to the vector +a this is the same thing as finding the + + align:start position:0% +a this is the same thing as finding the + + + align:start position:0% +a this is the same thing as finding the +projections of the vector a along the X + + align:start position:0% +projections of the vector a along the X + + + align:start position:0% +projections of the vector a along the X +and Y + + align:start position:0% +and Y + + + align:start position:0% +and Y +axes here is the projection of the + + align:start position:0% +axes here is the projection of the + + + align:start position:0% +axes here is the projection of the +vector onto the x- axis it's X + + align:start position:0% +vector onto the x- axis it's X + + + align:start position:0% +vector onto the x- axis it's X +component and here is the projection + + align:start position:0% +component and here is the projection + + + align:start position:0% +component and here is the projection +onto the Y AIS the Y + + align:start position:0% +onto the Y AIS the Y + + + align:start position:0% +onto the Y AIS the Y +component this particular Vector can be + + align:start position:0% +component this particular Vector can be + + + align:start position:0% +component this particular Vector can be +written as a is equal to - 2 I hat + - 2 + + align:start position:0% +written as a is equal to - 2 I hat + - 2 + + + align:start position:0% +written as a is equal to - 2 I hat + - 2 +J + + align:start position:0% +J + + + align:start position:0% +J +hat a generic Vector in two Dimensions + + align:start position:0% +hat a generic Vector in two Dimensions + + + align:start position:0% +hat a generic Vector in two Dimensions +can be written as a is equal to ax the X + + align:start position:0% +can be written as a is equal to ax the X + + + align:start position:0% +can be written as a is equal to ax the X +component of a Time IAT the unit Vector + + align:start position:0% +component of a Time IAT the unit Vector + + + align:start position:0% +component of a Time IAT the unit Vector +along X plus a y the Y component time J + + align:start position:0% +along X plus a y the Y component time J + + + align:start position:0% +along X plus a y the Y component time J +hat the unit Vector along + + align:start position:0% +hat the unit Vector along + + + align:start position:0% +hat the unit Vector along +y if the vector is in three dimensions + + align:start position:0% +y if the vector is in three dimensions + + + align:start position:0% +y if the vector is in three dimensions +we will also have an A Z * K + + align:start position:0% + + + + align:start position:0% + +hat what if we have the vector minus 3 I + + align:start position:0% +hat what if we have the vector minus 3 I + + + align:start position:0% +hat what if we have the vector minus 3 I +hat plus 2 J + + align:start position:0% +hat plus 2 J + + + align:start position:0% +hat plus 2 J +hat first we find the vector minus 3 * + + align:start position:0% +hat first we find the vector minus 3 * + + + align:start position:0% +hat first we find the vector minus 3 * +the unit vector ihat and add this to the + + align:start position:0% +the unit vector ihat and add this to the + + + align:start position:0% +the unit vector ihat and add this to the +the vector 2 + + align:start position:0% +the vector 2 + + + align:start position:0% +the vector 2 +* J + + align:start position:0% +* J + + + align:start position:0% +* J +hat we can draw this Vector anywhere it + + align:start position:0% +hat we can draw this Vector anywhere it + + + align:start position:0% +hat we can draw this Vector anywhere it +doesn't have to start start at the + + align:start position:0% +doesn't have to start start at the + + + align:start position:0% +doesn't have to start start at the +origin \ No newline at end of file diff --git a/XvNrcWQCAxQ.txt b/XvNrcWQCAxQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..715fe59eb439eada8ac46a5e639e287645dd4b29 --- /dev/null +++ b/XvNrcWQCAxQ.txt @@ -0,0 +1,15883 @@ +align:start position:0% + +okay um as I said so like you know + + align:start position:0% +okay um as I said so like you know + + + align:start position:0% +okay um as I said so like you know +classic example here American reparatory + + align:start position:0% +classic example here American reparatory + + + align:start position:0% +classic example here American reparatory +Theater in Cambridge you know players + + align:start position:0% +Theater in Cambridge you know players + + + align:start position:0% +Theater in Cambridge you know players +that are going to go to Broadway they + + align:start position:0% +that are going to go to Broadway they + + + align:start position:0% +that are going to go to Broadway they +try them out there also sort of avant + + align:start position:0% +try them out there also sort of avant + + + align:start position:0% +try them out there also sort of avant +guard stuff um if I buy a ticket there + + align:start position:0% +guard stuff um if I buy a ticket there + + + align:start position:0% +guard stuff um if I buy a ticket there +it's like $72 to sit in the back corner + + align:start position:0% +it's like $72 to sit in the back corner + + + align:start position:0% +it's like $72 to sit in the back corner +of the theater um you as students they + + align:start position:0% +of the theater um you as students they + + + align:start position:0% +of the theater um you as students they +actually if you're on their website they + + align:start position:0% +actually if you're on their website they + + + align:start position:0% +actually if you're on their website they +have a tremendous number of students + + align:start position:0% +have a tremendous number of students + + + align:start position:0% +have a tremendous number of students +basically everyone except me um and Stu + + align:start position:0% +basically everyone except me um and Stu + + + align:start position:0% +basically everyone except me um and Stu +the student discount there it's like you + + align:start position:0% +the student discount there it's like you + + + align:start position:0% +the student discount there it's like you +can go see plays that cost me $72 and + + align:start position:0% +can go see plays that cost me $72 and + + + align:start position:0% +can go see plays that cost me $72 and +you pay like 10 it's like less than + + align:start position:0% +you pay like 10 it's like less than + + + align:start position:0% +you pay like 10 it's like less than +going to a movie I would say you know + + align:start position:0% +going to a movie I would say you know + + + align:start position:0% +going to a movie I would say you know +it's a great thing to see that it is + + align:start position:0% +it's a great thing to see that it is + + + align:start position:0% +it's a great thing to see that it is +typical though that like you might buy a + + align:start position:0% +typical though that like you might buy a + + + align:start position:0% +typical though that like you might buy a +ticket to see Hamlet and find that like + + align:start position:0% +ticket to see Hamlet and find that like + + + align:start position:0% +ticket to see Hamlet and find that like +you've got guys stand in Kitty bathtubs + + align:start position:0% +you've got guys stand in Kitty bathtubs + + + align:start position:0% +you've got guys stand in Kitty bathtubs +wearing shorts playing guitars or + + align:start position:0% +wearing shorts playing guitars or + + + align:start position:0% +wearing shorts playing guitars or +whatever so it it is you know you have + + align:start position:0% +whatever so it it is you know you have + + + align:start position:0% +whatever so it it is you know you have +to be aware that you may not get what + + align:start position:0% +to be aware that you may not get what + + + align:start position:0% +to be aware that you may not get what +you think you're getting when you see + + align:start position:0% +you think you're getting when you see + + + align:start position:0% +you think you're getting when you see +the title of the play but you know great + + align:start position:0% +the title of the play but you know great + + + align:start position:0% +the title of the play but you know great +thing to go but anyway example of the + + align:start position:0% +thing to go but anyway example of the + + + align:start position:0% +thing to go but anyway example of the +you know they're selling the same ticket + + align:start position:0% +you know they're selling the same ticket + + + align:start position:0% +you know they're selling the same ticket +to you for $10 they would charge me $72 + + align:start position:0% +to you for $10 they would charge me $72 + + + align:start position:0% +to you for $10 they would charge me $72 +for um people often also think about + + align:start position:0% +for um people often also think about + + + align:start position:0% +for um people often also think about +this when you have nonlinear prices + + align:start position:0% +this when you have nonlinear prices + + + align:start position:0% +this when you have nonlinear prices +you'll go to the supermarket and it's + + align:start position:0% +you'll go to the supermarket and it's + + + align:start position:0% +you'll go to the supermarket and it's +like buy one get one half off it's like + + align:start position:0% +like buy one get one half off it's like + + + align:start position:0% +like buy one get one half off it's like +the first good is being sold at a + + align:start position:0% +the first good is being sold at a + + + align:start position:0% +the first good is being sold at a +different price from the second good and + + align:start position:0% +different price from the second good and + + + align:start position:0% +different price from the second good and +again the you know first thing a + + align:start position:0% +again the you know first thing a + + + align:start position:0% +again the you know first thing a +strawberries you buy and the second + + align:start position:0% +strawberries you buy and the second + + + align:start position:0% +strawberries you buy and the second +thing strawberries buy they're identical + + align:start position:0% +thing strawberries buy they're identical + + + align:start position:0% +thing strawberries buy they're identical +except they're selling them to you at + + align:start position:0% +except they're selling them to you at + + + align:start position:0% +except they're selling them to you at +different prices + + align:start position:0% +different prices + + + align:start position:0% +different prices +um we also talk about price + + align:start position:0% +um we also talk about price + + + align:start position:0% +um we also talk about price +discrimination when firms are + + align:start position:0% +discrimination when firms are + + + align:start position:0% +discrimination when firms are +selling uh similar Goods at very + + align:start position:0% +selling uh similar Goods at very + + + align:start position:0% +selling uh similar Goods at very +different prices uh so for instance I + + align:start position:0% +different prices uh so for instance I + + + align:start position:0% +different prices uh so for instance I +put the iPhone 14 down there you know + + align:start position:0% +put the iPhone 14 down there you know + + + align:start position:0% +put the iPhone 14 down there you know +the iPhone 14 128 gigabyte version + + align:start position:0% +the iPhone 14 128 gigabyte version + + + align:start position:0% +the iPhone 14 128 gigabyte version +is uh + + align:start position:0% +is uh + + + align:start position:0% +is uh +$799 the 512 GB version is $1,000 99 so + + align:start position:0% +$799 the 512 GB version is $1,000 99 so + + + align:start position:0% +$799 the 512 GB version is $1,000 99 so +it's $300 extra for the more expensive + + align:start position:0% +it's $300 extra for the more expensive + + + align:start position:0% +it's $300 extra for the more expensive +iPhone you know you might think to + + align:start position:0% +iPhone you know you might think to + + + align:start position:0% +iPhone you know you might think to +yourself wait I can buy a 512 gigabyte + + align:start position:0% +yourself wait I can buy a 512 gigabyte + + + align:start position:0% +yourself wait I can buy a 512 gigabyte +flash drive for 50 bucks why does it + + align:start position:0% +flash drive for 50 bucks why does it + + + align:start position:0% +flash drive for 50 bucks why does it +cost $300 more to put it in the phone is + + align:start position:0% +cost $300 more to put it in the phone is + + + align:start position:0% +cost $300 more to put it in the phone is +it better memory no it's it's exactly + + align:start position:0% +it better memory no it's it's exactly + + + align:start position:0% +it better memory no it's it's exactly +the same memory that's in the $50 flash + + align:start position:0% +the same memory that's in the $50 flash + + + align:start position:0% +the same memory that's in the $50 flash +drive that someone's making a profit on + + align:start position:0% +drive that someone's making a profit on + + + align:start position:0% +drive that someone's making a profit on +but it's you know somehow it's two + + align:start position:0% +but it's you know somehow it's two + + + align:start position:0% +but it's you know somehow it's two +similar Goods that are just being sold + + align:start position:0% +similar Goods that are just being sold + + + align:start position:0% +similar Goods that are just being sold +at very different markups just like you + + align:start position:0% +at very different markups just like you + + + align:start position:0% +at very different markups just like you +know + + align:start position:0% +know + + + align:start position:0% +know +um you know uh again you know + + align:start position:0% +um you know uh again you know + + + align:start position:0% +um you know uh again you know +it's whether we think of something as + + align:start position:0% +it's whether we think of something as + + + align:start position:0% +it's whether we think of something as +price discrimination when the goods are + + align:start position:0% +price discrimination when the goods are + + + align:start position:0% +price discrimination when the goods are +differ you know do you talk about a + + align:start position:0% +differ you know do you talk about a + + + align:start position:0% +differ you know do you talk about a +discrimination if it's like the ratio of + + align:start position:0% +discrimination if it's like the ratio of + + + align:start position:0% +discrimination if it's like the ratio of +the prices to costs are different or if + + align:start position:0% +the prices to costs are different or if + + + align:start position:0% +the prices to costs are different or if +the dollar value of price to cost is + + align:start position:0% +the dollar value of price to cost is + + + align:start position:0% +the dollar value of price to cost is +different but it just often in these + + align:start position:0% +different but it just often in these + + + align:start position:0% +different but it just often in these +examples it's very very clear that + + align:start position:0% +examples it's very very clear that + + + align:start position:0% +examples it's very very clear that +however you think about the adjusting + + align:start position:0% +however you think about the adjusting + + + align:start position:0% +however you think about the adjusting +for the cost something is just much more + + align:start position:0% +for the cost something is just much more + + + align:start position:0% +for the cost something is just much more +expensive than the others we'll call + + align:start position:0% +expensive than the others we'll call + + + align:start position:0% +expensive than the others we'll call +that price discrimination you know like + + align:start position:0% +that price discrimination you know like + + + align:start position:0% +that price discrimination you know like +the business class seat is $112,000 when + + align:start position:0% +the business class seat is $112,000 when + + + align:start position:0% +the business class seat is $112,000 when +the coach seat is $600 or whatever it's + + align:start position:0% +the coach seat is $600 or whatever it's + + + align:start position:0% +the coach seat is $600 or whatever it's +like I don't know whether I'm kind of + + align:start position:0% +like I don't know whether I'm kind of + + + align:start position:0% +like I don't know whether I'm kind of +cubic inches or whatever but one is just + + align:start position:0% +cubic inches or whatever but one is just + + + align:start position:0% +cubic inches or whatever but one is just +much more + + align:start position:0% +much more + + + align:start position:0% +much more +expensive um also sometimes you can + + align:start position:0% +expensive um also sometimes you can + + + align:start position:0% +expensive um also sometimes you can +think about it as being price + + align:start position:0% +think about it as being price + + + align:start position:0% +think about it as being price +discrimination when when costs differ + + align:start position:0% +discrimination when when costs differ + + + align:start position:0% +discrimination when when costs differ +and you don't discriminate in prices so + + align:start position:0% +and you don't discriminate in prices so + + + align:start position:0% +and you don't discriminate in prices so +for instance there are places that offer + + align:start position:0% +for instance there are places that offer + + + align:start position:0% +for instance there are places that offer +free delivery and the free delivery + + align:start position:0% +free delivery and the free delivery + + + align:start position:0% +free delivery and the free delivery +doesn't depend on how far it is to get + + align:start position:0% +doesn't depend on how far it is to get + + + align:start position:0% +doesn't depend on how far it is to get +to you so you might think that there in + + align:start position:0% +to you so you might think that there in + + + align:start position:0% +to you so you might think that there in +some sense the when the firm is + + align:start position:0% +some sense the when the firm is + + + align:start position:0% +some sense the when the firm is +incurring a large delivery cost to get + + align:start position:0% +incurring a large delivery cost to get + + + align:start position:0% +incurring a large delivery cost to get +it to you they're giving you a discount + + align:start position:0% +it to you they're giving you a discount + + + align:start position:0% +it to you they're giving you a discount +relative the people for whom they're + + align:start position:0% +relative the people for whom they're + + + align:start position:0% +relative the people for whom they're +getting spending a small amount of money + + align:start position:0% +getting spending a small amount of money + + + align:start position:0% +getting spending a small amount of money +to get it to you and so I would again I + + align:start position:0% +to get it to you and so I would again I + + + align:start position:0% +to get it to you and so I would again I +would think of that as charging the same + + align:start position:0% +would think of that as charging the same + + + align:start position:0% +would think of that as charging the same +price can actually be price + + align:start position:0% +price can actually be price + + + align:start position:0% +price can actually be price +discrimination if the costs are very + + align:start position:0% +discrimination if the costs are very + + + align:start position:0% +discrimination if the costs are very +different of serving the different + + align:start position:0% +different of serving the different + + + align:start position:0% +different of serving the different +consumers okay obviously uh price + + align:start position:0% +consumers okay obviously uh price + + + align:start position:0% +consumers okay obviously uh price +discrimination requires Market power + + align:start position:0% +discrimination requires Market power + + + align:start position:0% +discrimination requires Market power +this was actually one of my favorite + + align:start position:0% +this was actually one of my favorite + + + align:start position:0% +this was actually one of my favorite +signs I found at the uh Whole Foods once + + align:start position:0% +signs I found at the uh Whole Foods once + + + align:start position:0% +signs I found at the uh Whole Foods once +which was uh Cranberries for sale + + align:start position:0% +which was uh Cranberries for sale + + + align:start position:0% +which was uh Cranberries for sale +regularly $2 now two for $ four dollars + + align:start position:0% +regularly $2 now two for $ four dollars + + + align:start position:0% +regularly $2 now two for $ four dollars +which I didn't quite know what was going + + align:start position:0% +which I didn't quite know what was going + + + align:start position:0% +which I didn't quite know what was going +on there um + + align:start position:0% +on there um + + + align:start position:0% +on there um +uh okay so um theory of price + + align:start position:0% +uh okay so um theory of price + + + align:start position:0% +uh okay so um theory of price +discrimination goes back to pagu in the + + align:start position:0% +discrimination goes back to pagu in the + + + align:start position:0% +discrimination goes back to pagu in the +1920s U pagu made up three names for + + align:start position:0% +1920s U pagu made up three names for + + + align:start position:0% +1920s U pagu made up three names for +three different types of price + + align:start position:0% +three different types of price + + + align:start position:0% +three different types of price +discrimination these names are terrible + + align:start position:0% +discrimination these names are terrible + + + align:start position:0% +discrimination these names are terrible +names but they've survived um so first + + align:start position:0% +names but they've survived um so first + + + align:start position:0% +names but they've survived um so first +one he called first-degree price + + align:start position:0% +one he called first-degree price + + + align:start position:0% +one he called first-degree price +discrimination which some people also + + align:start position:0% +discrimination which some people also + + + align:start position:0% +discrimination which some people also +refer to as perfect price discrimination + + align:start position:0% +refer to as perfect price discrimination + + + align:start position:0% +refer to as perfect price discrimination +this is the you know ideal of a theorist + + align:start position:0% +this is the you know ideal of a theorist + + + align:start position:0% +this is the you know ideal of a theorist +where the firm knows everything they + + align:start position:0% +where the firm knows everything they + + + align:start position:0% +where the firm knows everything they +need to know they have all the power + + align:start position:0% +need to know they have all the power + + + align:start position:0% +need to know they have all the power +they would want they can price + + align:start position:0% +they would want they can price + + + align:start position:0% +they would want they can price +separately to every consumer it's really + + align:start position:0% +separately to every consumer it's really + + + align:start position:0% +separately to every consumer it's really +a theoretical ideal because firms are + + align:start position:0% +a theoretical ideal because firms are + + + align:start position:0% +a theoretical ideal because firms are +never in the situation of exactly + + align:start position:0% +never in the situation of exactly + + + align:start position:0% +never in the situation of exactly +knowing the consumer's utility + + align:start position:0% +knowing the consumer's utility + + + align:start position:0% +knowing the consumer's utility +function um second degree price + + align:start position:0% +function um second degree price + + + align:start position:0% +function um second degree price +discrimination um is price + + align:start position:0% +discrimination um is price + + + align:start position:0% +discrimination um is price +discrimination based on self- selection + + align:start position:0% +discrimination based on self- selection + + + align:start position:0% +discrimination based on self- selection +so this would be the offering an iPhone + + align:start position:0% +so this would be the offering an iPhone + + + align:start position:0% +so this would be the offering an iPhone +14 in two different quality levels and + + align:start position:0% +14 in two different quality levels and + + + align:start position:0% +14 in two different quality levels and +relying on the consumers to sort + + align:start position:0% +relying on the consumers to sort + + + align:start position:0% +relying on the consumers to sort +themselves between do they buy the the + + align:start position:0% +themselves between do they buy the the + + + align:start position:0% +themselves between do they buy the the +cheap iPhone 14 or the expensive iPhone + + align:start position:0% +cheap iPhone 14 or the expensive iPhone + + + align:start position:0% +cheap iPhone 14 or the expensive iPhone +14 um and you know you see lots of other + + align:start position:0% +14 um and you know you see lots of other + + + align:start position:0% +14 um and you know you see lots of other +examples of this you know cell phone + + align:start position:0% +examples of this you know cell phone + + + align:start position:0% +examples of this you know cell phone +plans health insurance contracts whether + + align:start position:0% +plans health insurance contracts whether + + + align:start position:0% +plans health insurance contracts whether +you buy regular premium gasoline um + + align:start position:0% +you buy regular premium gasoline um + + + align:start position:0% +you buy regular premium gasoline um +firms are selling these prices at + + align:start position:0% +firms are selling these prices at + + + align:start position:0% +firms are selling these prices at +relying entirely on the consumers to + + align:start position:0% +relying entirely on the consumers to + + + align:start position:0% +relying entirely on the consumers to +self- select among them and then third + + align:start position:0% +self- select among them and then third + + + align:start position:0% +self- select among them and then third +degree price + + align:start position:0% +degree price + + + align:start position:0% +degree price +discrimination is the examples like the + + align:start position:0% +discrimination is the examples like the + + + align:start position:0% +discrimination is the examples like the +art student tickets or uh military + + align:start position:0% +art student tickets or uh military + + + align:start position:0% +art student tickets or uh military +discount or senior citizen discount or + + align:start position:0% +discount or senior citizen discount or + + + align:start position:0% +discount or senior citizen discount or +whatever where the there are some + + align:start position:0% +whatever where the there are some + + + align:start position:0% +whatever where the there are some +observable characteristics of the + + align:start position:0% +observable characteristics of the + + + align:start position:0% +observable characteristics of the +consumers and then the firms can set + + align:start position:0% +consumers and then the firms can set + + + align:start position:0% +consumers and then the firms can set +different prices based on the different + + align:start position:0% +different prices based on the different + + + align:start position:0% +different prices based on the different +characteristics of the consumers um + + align:start position:0% +characteristics of the consumers um + + + align:start position:0% +characteristics of the consumers um +another one you'd see here classic third + + align:start position:0% +another one you'd see here classic third + + + align:start position:0% +another one you'd see here classic third +degree discrimination is is geographic + + align:start position:0% +degree discrimination is is geographic + + + align:start position:0% +degree discrimination is is geographic +location you know firms will set + + align:start position:0% +location you know firms will set + + + align:start position:0% +location you know firms will set +different prices in different countries + + align:start position:0% +different prices in different countries + + + align:start position:0% +different prices in different countries +because the they can observe in which + + align:start position:0% +because the they can observe in which + + + align:start position:0% +because the they can observe in which +country the the someone is buying the + + align:start position:0% +country the the someone is buying the + + + align:start position:0% +country the the someone is buying the +good okay um I would say you know it's + + align:start position:0% +good okay um I would say you know it's + + + align:start position:0% +good okay um I would say you know it's +why is this a bad nomenclature you know + + align:start position:0% +why is this a bad nomenclature you know + + + align:start position:0% +why is this a bad nomenclature you know +one is names first second and third + + align:start position:0% +one is names first second and third + + + align:start position:0% +one is names first second and third +degree don't really have any meaning um + + align:start position:0% +degree don't really have any meaning um + + + align:start position:0% +degree don't really have any meaning um +and then besides not really having any + + align:start position:0% +and then besides not really having any + + + align:start position:0% +and then besides not really having any +meaning the order is wrong in some sense + + align:start position:0% +meaning the order is wrong in some sense + + + align:start position:0% +meaning the order is wrong in some sense +you know first degree is when you know + + align:start position:0% +you know first degree is when you know + + + align:start position:0% +you know first degree is when you know +everything about the consumer third + + align:start position:0% +everything about the consumer third + + + align:start position:0% +everything about the consumer third +degree is when you know something about + + align:start position:0% +degree is when you know something about + + + align:start position:0% +degree is when you know something about +the consumer second degree is when you + + align:start position:0% +the consumer second degree is when you + + + align:start position:0% +the consumer second degree is when you +know nothing about the consumer so they + + align:start position:0% +know nothing about the consumer so they + + + align:start position:0% +know nothing about the consumer so they +really ought to be in this order but + + align:start position:0% +really ought to be in this order but + + + align:start position:0% +really ought to be in this order but +anyway that's the order pagu described + + align:start position:0% +anyway that's the order pagu described + + + align:start position:0% +anyway that's the order pagu described +them in people sort of still talk about + + align:start position:0% +them in people sort of still talk about + + + align:start position:0% +them in people sort of still talk about +second deegree price discrimination so + + align:start position:0% +second deegree price discrimination so + + + align:start position:0% +second deegree price discrimination so +anyway I'm G to continue to use those + + align:start position:0% +anyway I'm G to continue to use those + + + align:start position:0% +anyway I'm G to continue to use those +names because that's what everyone else + + align:start position:0% +names because that's what everyone else + + + align:start position:0% +names because that's what everyone else +uses um okay so let me start with first + + align:start position:0% +uses um okay so let me start with first + + + align:start position:0% +uses um okay so let me start with first +deegree price discrimination so first + + align:start position:0% +deegree price discrimination so first + + + align:start position:0% +deegree price discrimination so first +degree is the simplest so + + align:start position:0% +degree is the simplest so + + + align:start position:0% +degree is the simplest so +you know suppose this is the omniscient + + align:start position:0% +you know suppose this is the omniscient + + + align:start position:0% +you know suppose this is the omniscient +monopolis the monopolis and and om + + align:start position:0% +monopolis the monopolis and and om + + + align:start position:0% +monopolis the monopolis and and om +powerful whatever so you know monopolist + + align:start position:0% +powerful whatever so you know monopolist + + + align:start position:0% +powerful whatever so you know monopolist +every different consumer who walks into + + align:start position:0% +every different consumer who walks into + + + align:start position:0% +every different consumer who walks into +the + + align:start position:0% +the + + + align:start position:0% +the +store um you know the monopolist knows + + align:start position:0% +store um you know the monopolist knows + + + align:start position:0% +store um you know the monopolist knows +this is P1 of X this is P2 of X so if + + align:start position:0% +this is P1 of X this is P2 of X so if + + + align:start position:0% +this is P1 of X this is P2 of X so if +you know if customer one walks into the + + align:start position:0% +you know if customer one walks into the + + + align:start position:0% +you know if customer one walks into the +store the monopolis knows okay I'm + + align:start position:0% +store the monopolis knows okay I'm + + + align:start position:0% +store the monopolis knows okay I'm +facing customer one this is customer + + align:start position:0% +facing customer one this is customer + + + align:start position:0% +facing customer one this is customer +one's willingness to pay for X units for + + align:start position:0% +one's willingness to pay for X units for + + + align:start position:0% +one's willingness to pay for X units for +any number X and then uh customer 2 + + align:start position:0% +any number X and then uh customer 2 + + + align:start position:0% +any number X and then uh customer 2 +walks in the store this is customer 2 is + + align:start position:0% +walks in the store this is customer 2 is + + + align:start position:0% +walks in the store this is customer 2 is +willingness to pay for any number of + + align:start position:0% +willingness to pay for any number of + + + align:start position:0% +willingness to pay for any number of +units X + + align:start position:0% +units X + + + align:start position:0% +units X +um so I'm going to suppose this + + align:start position:0% +um so I'm going to suppose this + + + align:start position:0% +um so I'm going to suppose this +monopolist is powerful it can set + + align:start position:0% +monopolist is powerful it can set + + + align:start position:0% +monopolist is powerful it can set +customer specific nonlinear prices and + + align:start position:0% +customer specific nonlinear prices and + + + align:start position:0% +customer specific nonlinear prices and +it can prevent resale across the + + align:start position:0% +it can prevent resale across the + + + align:start position:0% +it can prevent resale across the +consumers so you know what's going to + + align:start position:0% +consumers so you know what's going to + + + align:start position:0% +consumers so you know what's going to +happen you could set up some imagine + + align:start position:0% +happen you could set up some imagine + + + align:start position:0% +happen you could set up some imagine +some very complicated menu of prices you + + align:start position:0% +some very complicated menu of prices you + + + align:start position:0% +some very complicated menu of prices you +set to Consumers you have them play some + + align:start position:0% +set to Consumers you have them play some + + + align:start position:0% +set to Consumers you have them play some +game you have them do something or other + + align:start position:0% +game you have them do something or other + + + align:start position:0% +game you have them do something or other +but at the end of the day you know + + align:start position:0% +but at the end of the day you know + + + align:start position:0% +but at the end of the day you know +suppose in equilibrium this consumer + + align:start position:0% +suppose in equilibrium this consumer + + + align:start position:0% +suppose in equilibrium this consumer +buys X1 units ends up paying + + align:start position:0% +buys X1 units ends up paying + + + align:start position:0% +buys X1 units ends up paying +X2 and sorry ends up paying T1 and this + + align:start position:0% +X2 and sorry ends up paying T1 and this + + + align:start position:0% +X2 and sorry ends up paying T1 and this +consumer buys X2 units and end up paying + + align:start position:0% +consumer buys X2 units and end up paying + + + align:start position:0% +consumer buys X2 units and end up paying +T2 if this is what's going to happen in + + align:start position:0% +T2 if this is what's going to happen in + + + align:start position:0% +T2 if this is what's going to happen in +equilibrium under some very complicated + + align:start position:0% +equilibrium under some very complicated + + + align:start position:0% +equilibrium under some very complicated +scheme you might as well just make a + + align:start position:0% +scheme you might as well just make a + + + align:start position:0% +scheme you might as well just make a +direct take it or leave it offer to each + + align:start position:0% +direct take it or leave it offer to each + + + align:start position:0% +direct take it or leave it offer to each +consumer so just offer consumer one + + align:start position:0% +consumer so just offer consumer one + + + align:start position:0% +consumer so just offer consumer one +either you buy X1 units at Price T1 or + + align:start position:0% +either you buy X1 units at Price T1 or + + + align:start position:0% +either you buy X1 units at Price T1 or +you get nothing at all you go to consum + + align:start position:0% +you get nothing at all you go to consum + + + align:start position:0% +you get nothing at all you go to consum +number two either you get x2 units at a + + align:start position:0% +number two either you get x2 units at a + + + align:start position:0% +number two either you get x2 units at a +price of T2 or you get nothing at all + + align:start position:0% +price of T2 or you get nothing at all + + + align:start position:0% +price of T2 or you get nothing at all +and so anything you can achieve with a + + align:start position:0% +and so anything you can achieve with a + + + align:start position:0% +and so anything you can achieve with a +more complicated scheme you can achieve + + align:start position:0% +more complicated scheme you can achieve + + + align:start position:0% +more complicated scheme you can achieve +with these simple take it or leave it + + align:start position:0% +with these simple take it or leave it + + + align:start position:0% +with these simple take it or leave it +customer by customer take it or leave it + + align:start position:0% +customer by customer take it or leave it + + + align:start position:0% +customer by customer take it or leave it +schemes okay so that's what we're going + + align:start position:0% +schemes okay so that's what we're going + + + align:start position:0% +schemes okay so that's what we're going +to think about doing is just offering + + align:start position:0% +to think about doing is just offering + + + align:start position:0% +to think about doing is just offering +these customer specific take it or leave + + align:start position:0% +these customer specific take it or leave + + + align:start position:0% +these customer specific take it or leave +it schemes um when is customer one going + + align:start position:0% +it schemes um when is customer one going + + + align:start position:0% +it schemes um when is customer one going +to an accept an offer that involves X1 + + align:start position:0% +to an accept an offer that involves X1 + + + align:start position:0% +to an accept an offer that involves X1 +units at a price of T1 + + align:start position:0% + + + + align:start position:0% + +if that's my + + align:start position:0% +if that's my + + + align:start position:0% +if that's my +offer you know this is the maximum + + align:start position:0% +offer you know this is the maximum + + + align:start position:0% +offer you know this is the maximum +amount that the customer is willing to + + align:start position:0% +amount that the customer is willing to + + + align:start position:0% +amount that the customer is willing to +pay for X1 units they're willing to pay + + align:start position:0% +pay for X1 units they're willing to pay + + + align:start position:0% +pay for X1 units they're willing to pay +this for the first unit this for the + + align:start position:0% +this for the first unit this for the + + + align:start position:0% +this for the first unit this for the +second unit this for the third unit and + + align:start position:0% +second unit this for the third unit and + + + align:start position:0% +second unit this for the third unit and +so on so the maximum they'll pay for X1 + + align:start position:0% +so on so the maximum they'll pay for X1 + + + align:start position:0% +so on so the maximum they'll pay for X1 +units is just the integral from zero to + + align:start position:0% +units is just the integral from zero to + + + align:start position:0% +units is just the integral from zero to +X of Pi of + + align:start position:0% +X of Pi of + + + align:start position:0% +X of Pi of +SDS um given that the customer is going + + align:start position:0% +SDS um given that the customer is going + + + align:start position:0% +SDS um given that the customer is going +to offer accept that offer if and only + + align:start position:0% +to offer accept that offer if and only + + + align:start position:0% +to offer accept that offer if and only +if TI is less than this clearly the best + + align:start position:0% +if TI is less than this clearly the best + + + align:start position:0% +if TI is less than this clearly the best +thing to do is to set the price as high + + align:start position:0% +thing to do is to set the price as high + + + align:start position:0% +thing to do is to set the price as high +as the consumer is willing this to pay + + align:start position:0% +as the consumer is willing this to pay + + + align:start position:0% +as the consumer is willing this to pay +so you set TI equals the integral from 0 + + align:start position:0% +so you set TI equals the integral from 0 + + + align:start position:0% +so you set TI equals the integral from 0 +to x Pi of + + align:start position:0% +to x Pi of + + + align:start position:0% +to x Pi of +SDS okay and so thinking about the + + align:start position:0% +SDS okay and so thinking about the + + + align:start position:0% +SDS okay and so thinking about the +Monopoly problem you're just trying to + + align:start position:0% +Monopoly problem you're just trying to + + + align:start position:0% +Monopoly problem you're just trying to +maximize uh the total amount you know + + align:start position:0% +maximize uh the total amount you know + + + align:start position:0% +maximize uh the total amount you know +you pick the number of units XI to sell + + align:start position:0% +you pick the number of units XI to sell + + + align:start position:0% +you pick the number of units XI to sell +that consumer this is the price you're + + align:start position:0% +that consumer this is the price you're + + + align:start position:0% +that consumer this is the price you're +going to charge when you sell X units + + align:start position:0% +going to charge when you sell X units + + + align:start position:0% +going to charge when you sell X units +and then this is the cost of producing + + align:start position:0% +and then this is the cost of producing + + + align:start position:0% +and then this is the cost of producing +the + + align:start position:0% +the + + + align:start position:0% +the +units so clearly you know I + + align:start position:0% +units so clearly you know I + + + align:start position:0% +units so clearly you know I +differentiate that with respect to + + align:start position:0% +differentiate that with respect to + + + align:start position:0% +differentiate that with respect to +XI uh the derivative of this with with + + align:start position:0% +XI uh the derivative of this with with + + + align:start position:0% +XI uh the derivative of this with with +respect to XI is just Pi of XI the + + align:start position:0% +respect to XI is just Pi of XI the + + + align:start position:0% +respect to XI is just Pi of XI the +derivative of this with respect to XI is + + align:start position:0% +derivative of this with respect to XI is + + + align:start position:0% +derivative of this with respect to XI is +C so the first order condition is just + + align:start position:0% +C so the first order condition is just + + + align:start position:0% +C so the first order condition is just +set XI star such that Pi of XI star + + align:start position:0% +set XI star such that Pi of XI star + + + align:start position:0% +set XI star such that Pi of XI star +equals c okay so this is just in some + + align:start position:0% +equals c okay so this is just in some + + + align:start position:0% +equals c okay so this is just in some +sense it becomes the optimal solution + + align:start position:0% +sense it becomes the optimal solution + + + align:start position:0% +sense it becomes the optimal solution +is do exactly what would happen with + + align:start position:0% +is do exactly what would happen with + + + align:start position:0% +is do exactly what would happen with +perfect competition so if this is my + + align:start position:0% +perfect competition so if this is my + + + align:start position:0% +perfect competition so if this is my +constant marginal + + align:start position:0% +constant marginal + + + align:start position:0% +constant marginal +cost for every + + align:start position:0% +cost for every + + + align:start position:0% +cost for every +consumer I just figure out how many + + align:start position:0% +consumer I just figure out how many + + + align:start position:0% +consumer I just figure out how many +units + + align:start position:0% +units + + + align:start position:0% +units +would they buy if I + + align:start position:0% +would they buy if I + + + align:start position:0% +would they buy if I +was setting the price at equal to C and + + align:start position:0% +was setting the price at equal to C and + + + align:start position:0% +was setting the price at equal to C and +I do this is X1 + + align:start position:0% +I do this is X1 + + + align:start position:0% +I do this is X1 +star I do this as X2 + + align:start position:0% +star I do this as X2 + + + align:start position:0% +star I do this as X2 +star and then the total amount that + + align:start position:0% +star and then the total amount that + + + align:start position:0% +star and then the total amount that +I charge them is just their + + align:start position:0% +I charge them is just their + + + align:start position:0% +I charge them is just their +total uh utility they get from buying + + align:start position:0% +total uh utility they get from buying + + + align:start position:0% +total uh utility they get from buying +the number of units that I sell + + align:start position:0% + + + + align:start position:0% + +them okay so comments you know um + + align:start position:0% +them okay so comments you know um + + + align:start position:0% +them okay so comments you know um +quantities are exact ex actly the same + + align:start position:0% +quantities are exact ex actly the same + + + align:start position:0% +quantities are exact ex actly the same +as with perfect + + align:start position:0% +as with perfect + + + align:start position:0% +as with perfect +competition first-degree discrimination + + align:start position:0% +competition first-degree discrimination + + + align:start position:0% +competition first-degree discrimination +is socially optimal again I'm ignoring + + align:start position:0% +is socially optimal again I'm ignoring + + + align:start position:0% +is socially optimal again I'm ignoring +distributional effects but it's just + + align:start position:0% +distributional effects but it's just + + + align:start position:0% +distributional effects but it's just +like you know there there's no failure + + align:start position:0% +like you know there there's no failure + + + align:start position:0% +like you know there there's no failure +to realize gains from trade every unit + + align:start position:0% +to realize gains from trade every unit + + + align:start position:0% +to realize gains from trade every unit +that is worth see get sold to somebody + + align:start position:0% +that is worth see get sold to somebody + + + align:start position:0% +that is worth see get sold to somebody +um notice also that rather than having + + align:start position:0% +um notice also that rather than having + + + align:start position:0% +um notice also that rather than having +this sort of take it or leave it + + align:start position:0% +this sort of take it or leave it + + + align:start position:0% +this sort of take it or leave it +offer bundle the monopolis could also do + + align:start position:0% +offer bundle the monopolis could also do + + + align:start position:0% +offer bundle the monopolis could also do +this by + + align:start position:0% +this by + + + align:start position:0% +this by +just offering the good at a price of c + + align:start position:0% +just offering the good at a price of c + + + align:start position:0% +just offering the good at a price of c +and then having a fixed fee that they + + align:start position:0% +and then having a fixed fee that they + + + align:start position:0% +and then having a fixed fee that they +add on top of that so in this case for + + align:start position:0% +add on top of that so in this case for + + + align:start position:0% +add on top of that so in this case for +this consumer what I can do is say you + + align:start position:0% +this consumer what I can do is say you + + + align:start position:0% +this consumer what I can do is say you +know you can buy as many you have to pay + + align:start position:0% +know you can buy as many you have to pay + + + align:start position:0% +know you can buy as many you have to pay +me this fixed + + align:start position:0% +me this fixed + + + align:start position:0% +me this fixed +fee which is equal to the area of this + + align:start position:0% +fee which is equal to the area of this + + + align:start position:0% +fee which is equal to the area of this +region and then you can buy as many + + align:start position:0% +region and then you can buy as many + + + align:start position:0% +region and then you can buy as many +units as you want at a a cost of c and + + align:start position:0% +units as you want at a a cost of c and + + + align:start position:0% +units as you want at a a cost of c and +so for this + + align:start position:0% +so for this + + + align:start position:0% +so for this +consumer again you have to pay me this + + align:start position:0% +consumer again you have to pay me this + + + align:start position:0% +consumer again you have to pay me this +fixed fee and then you can buy as many + + align:start position:0% +fixed fee and then you can buy as many + + + align:start position:0% +fixed fee and then you can buy as many +units as you want at a cost of C you + + align:start position:0% +units as you want at a cost of C you + + + align:start position:0% +units as you want at a cost of C you +know so for instance suppose you know + + align:start position:0% +know so for instance suppose you know + + + align:start position:0% +know so for instance suppose you know +you're a cloud computing provider and + + align:start position:0% +you're a cloud computing provider and + + + align:start position:0% +you're a cloud computing provider and +you're going You're you you have + + align:start position:0% +you're going You're you you have + + + align:start position:0% +you're going You're you you have +customers who are going to be doing a + + align:start position:0% +customers who are going to be doing a + + + align:start position:0% +customers who are going to be doing a +lot of calculations on your platform + + align:start position:0% +lot of calculations on your platform + + + align:start position:0% +lot of calculations on your platform +what you just have to do is you know you + + align:start position:0% +what you just have to do is you know you + + + align:start position:0% +what you just have to do is you know you +want to sort of charge all the cores + + align:start position:0% +want to sort of charge all the cores + + + align:start position:0% +want to sort of charge all the cores +that they that they rent from you and + + align:start position:0% +that they that they rent from you and + + + align:start position:0% +that they that they rent from you and +all the memory they rent from you at + + align:start position:0% +all the memory they rent from you at + + + align:start position:0% +all the memory they rent from you at +your marginal cost of providing cores + + align:start position:0% +your marginal cost of providing cores + + + align:start position:0% +your marginal cost of providing cores +and rent to avoid distorting what they + + align:start position:0% +and rent to avoid distorting what they + + + align:start position:0% +and rent to avoid distorting what they +do and make the service as valuable as + + align:start position:0% +do and make the service as valuable as + + + align:start position:0% +do and make the service as valuable as +possible for them and then you make the + + align:start position:0% +possible for them and then you make the + + + align:start position:0% +possible for them and then you make the +service as valuable as possible and then + + align:start position:0% +service as valuable as possible and then + + + align:start position:0% +service as valuable as possible and then +you extract all of the Surplus they + + align:start position:0% +you extract all of the Surplus they + + + align:start position:0% +you extract all of the Surplus they +would have gotten using the service in a + + align:start position:0% +would have gotten using the service in a + + + align:start position:0% +would have gotten using the service in a +fixed fee up front so it costs you + + align:start position:0% +fixed fee up front so it costs you + + + align:start position:0% +fixed fee up front so it costs you +2,743 th000 to join my platform and then + + align:start position:0% +2,743 th000 to join my platform and then + + + align:start position:0% +2,743 th000 to join my platform and then +you can rent Computing costs at a + + align:start position:0% +you can rent Computing costs at a + + + align:start position:0% +you can rent Computing costs at a +marginal cost cost you 4.7 million you + + align:start position:0% +marginal cost cost you 4.7 million you + + + align:start position:0% +marginal cost cost you 4.7 million you +just have a different price for every + + align:start position:0% +just have a different price for every + + + align:start position:0% +just have a different price for every +consumer to join and then once they're + + align:start position:0% +consumer to join and then once they're + + + align:start position:0% +consumer to join and then once they're +there you set a price equal to + + align:start position:0% + + + + align:start position:0% + +C you in some sense you could sort of + + align:start position:0% +C you in some sense you could sort of + + + align:start position:0% +C you in some sense you could sort of +think of that as maybe that's sort of + + align:start position:0% +think of that as maybe that's sort of + + + align:start position:0% +think of that as maybe that's sort of +what happens at Disneyland you know + + align:start position:0% +what happens at Disneyland you know + + + align:start position:0% +what happens at Disneyland you know +Disneyland you pay $135 to get into the + + align:start position:0% +Disneyland you pay $135 to get into the + + + align:start position:0% +Disneyland you pay $135 to get into the +into the park and then the rides are + + align:start position:0% +into the park and then the rides are + + + align:start position:0% +into the park and then the rides are +free and the rides are free because the + + align:start position:0% +free and the rides are free because the + + + align:start position:0% +free and the rides are free because the +marginal cost of providing a ride is + + align:start position:0% +marginal cost of providing a ride is + + + align:start position:0% +marginal cost of providing a ride is +essentially zero so what you want to do + + align:start position:0% +essentially zero so what you want to do + + + align:start position:0% +essentially zero so what you want to do +is make the rides free make the park as + + align:start position:0% +is make the rides free make the park as + + + align:start position:0% +is make the rides free make the park as +valuable as possible and then extract it + + align:start position:0% +valuable as possible and then extract it + + + align:start position:0% +valuable as possible and then extract it +all with these fixed fees okay the the + + align:start position:0% +all with these fixed fees okay the the + + + align:start position:0% +all with these fixed fees okay the the +difference between Disneyland and and + + align:start position:0% +difference between Disneyland and and + + + align:start position:0% +difference between Disneyland and and +this example is you know Disneyland + + align:start position:0% +this example is you know Disneyland + + + align:start position:0% +this example is you know Disneyland +tends to charge everyone the same price + + align:start position:0% +tends to charge everyone the same price + + + align:start position:0% +tends to charge everyone the same price +uh here you would have a customer + + align:start position:0% +uh here you would have a customer + + + align:start position:0% +uh here you would have a customer +specific price you know every family + + align:start position:0% +specific price you know every family + + + align:start position:0% +specific price you know every family +that walks in you'd be like oh for you + + align:start position:0% +that walks in you'd be like oh for you + + + align:start position:0% +that walks in you'd be like oh for you +$833 to get into the park for you $445 + + align:start position:0% +$833 to get into the park for you $445 + + + align:start position:0% +$833 to get into the park for you $445 +to get into the park and every customer + + align:start position:0% +to get into the park and every customer + + + align:start position:0% +to get into the park and every customer +would have a different price but other + + align:start position:0% +would have a different price but other + + + align:start position:0% +would have a different price but other +than that you know the rides are + + align:start position:0% + + + + align:start position:0% + +free okay questions on first-degree + + align:start position:0% + + + + align:start position:0% + +discrimination okay um you know in + + align:start position:0% +discrimination okay um you know in + + + align:start position:0% +discrimination okay um you know in +reality there number reasons why we + + align:start position:0% +reality there number reasons why we + + + align:start position:0% +reality there number reasons why we +don't do this um one is at least before + + align:start position:0% +don't do this um one is at least before + + + align:start position:0% +don't do this um one is at least before +there were these omnicient internet + + align:start position:0% +there were these omnicient internet + + + align:start position:0% +there were these omnicient internet +firms consumer preferences are typically + + align:start position:0% +firms consumer preferences are typically + + + align:start position:0% +firms consumer preferences are typically +not observable we don't know what the + + align:start position:0% +not observable we don't know what the + + + align:start position:0% +not observable we don't know what the +goods are worth to the consumers + + align:start position:0% +goods are worth to the consumers + + + align:start position:0% +goods are worth to the consumers +therefore we can't do these individual + + align:start position:0% +therefore we can't do these individual + + + align:start position:0% +therefore we can't do these individual +person personalized + + align:start position:0% +person personalized + + + align:start position:0% +person personalized +prices + + align:start position:0% +prices + + + align:start position:0% +prices +uh another constraint is ARB is + + align:start position:0% +uh another constraint is ARB is + + + align:start position:0% +uh another constraint is ARB is +arbitrage or resale across consumers um + + align:start position:0% +arbitrage or resale across consumers um + + + align:start position:0% +arbitrage or resale across consumers um +so you know for imagine you did the um + + align:start position:0% +so you know for imagine you did the um + + + align:start position:0% +so you know for imagine you did the um +you know Netflix is uh Netflix is 12295 + + align:start position:0% +you know Netflix is uh Netflix is 12295 + + + align:start position:0% +you know Netflix is uh Netflix is 12295 +a month and you get to watch an + + align:start position:0% +a month and you get to watch an + + + align:start position:0% +a month and you get to watch an +unlimited number of movies you have the + + align:start position:0% +unlimited number of movies you have the + + + align:start position:0% +unlimited number of movies you have the +problem that the instead of the one + + align:start position:0% +problem that the instead of the one + + + align:start position:0% +problem that the instead of the one +person watching an unlimited number of + + align:start position:0% +person watching an unlimited number of + + + align:start position:0% +person watching an unlimited number of +movies for 1295 a month all their + + align:start position:0% +movies for 1295 a month all their + + + align:start position:0% +movies for 1295 a month all their +friends and their relatives can all use + + align:start position:0% +friends and their relatives can all use + + + align:start position:0% +friends and their relatives can all use +the same password and all log into + + align:start position:0% +the same password and all log into + + + align:start position:0% +the same password and all log into +Netflix and all watch an unlimited + + align:start position:0% +Netflix and all watch an unlimited + + + align:start position:0% +Netflix and all watch an unlimited +number of movies per month so you need + + align:start position:0% +number of movies per month so you need + + + align:start position:0% +number of movies per month so you need +to be able to sort of prevent people + + align:start position:0% +to be able to sort of prevent people + + + align:start position:0% +to be able to sort of prevent people +from reselling the good across consumers + + align:start position:0% +from reselling the good across consumers + + + align:start position:0% +from reselling the good across consumers +and having different people consuming + + align:start position:0% +and having different people consuming + + + align:start position:0% +and having different people consuming +off the same uh pattern you could also + + align:start position:0% +off the same uh pattern you could also + + + align:start position:0% +off the same uh pattern you could also +Imagine you know you might want to have + + align:start position:0% +Imagine you know you might want to have + + + align:start position:0% +Imagine you know you might want to have +something like it seems like with with + + align:start position:0% +something like it seems like with with + + + align:start position:0% +something like it seems like with with +these um like statistical packages it's + + align:start position:0% +these um like statistical packages it's + + + align:start position:0% +these um like statistical packages it's +like you can get this much power for a + + align:start position:0% +like you can get this much power for a + + + align:start position:0% +like you can get this much power for a +very low price and then you want have a + + align:start position:0% +very low price and then you want have a + + + align:start position:0% +very low price and then you want have a +higher you know like you have a low + + align:start position:0% +higher you know like you have a low + + + align:start position:0% +higher you know like you have a low +price you can get a a low number of + + align:start position:0% +price you can get a a low number of + + + align:start position:0% +price you can get a a low number of +units and then for a high price you can + + align:start position:0% +units and then for a high price you can + + + align:start position:0% +units and then for a high price you can +get many more units you don't want + + align:start position:0% +get many more units you don't want + + + align:start position:0% +get many more units you don't want +someone to coming up to you twice and + + align:start position:0% +someone to coming up to you twice and + + + align:start position:0% +someone to coming up to you twice and +sort of buying the good and then showing + + align:start position:0% +sort of buying the good and then showing + + + align:start position:0% +sort of buying the good and then showing +up again half an hour later and say okay + + align:start position:0% +up again half an hour later and say okay + + + align:start position:0% +up again half an hour later and say okay +now I like more units also at the low + + align:start position:0% +now I like more units also at the low + + + align:start position:0% +now I like more units also at the low +price um and then administrative costs + + align:start position:0% +price um and then administrative costs + + + align:start position:0% +price um and then administrative costs +if you think about where does price + + align:start position:0% +if you think about where does price + + + align:start position:0% +if you think about where does price +discrimination occur you know like um in + + align:start position:0% +discrimination occur you know like um in + + + align:start position:0% +discrimination occur you know like um in +the United + + align:start position:0% +the United + + + align:start position:0% +the United +States many many goods are sold in + + align:start position:0% +States many many goods are sold in + + + align:start position:0% +States many many goods are sold in +stores that have prices printed on them + + align:start position:0% +stores that have prices printed on them + + + align:start position:0% +stores that have prices printed on them +and you walk in and you buy the good and + + align:start position:0% +and you walk in and you buy the good and + + + align:start position:0% +and you walk in and you buy the good and +you and you go home with it um you go to + + align:start position:0% +you and you go home with it um you go to + + + align:start position:0% +you and you go home with it um you go to +many developing countries that's not the + + align:start position:0% +many developing countries that's not the + + + align:start position:0% +many developing countries that's not the +way stores work you walk into a store or + + align:start position:0% +way stores work you walk into a store or + + + align:start position:0% +way stores work you walk into a store or +a guy's shop and he starts you want to + + align:start position:0% +a guy's shop and he starts you want to + + + align:start position:0% +a guy's shop and he starts you want to +buy something especially if you're a + + align:start position:0% +buy something especially if you're a + + + align:start position:0% +buy something especially if you're a +tourist and they just start + + align:start position:0% +tourist and they just start + + + align:start position:0% +tourist and they just start +discussing the what the price will be + + align:start position:0% +discussing the what the price will be + + + align:start position:0% +discussing the what the price will be +and there's a long haggling time and + + align:start position:0% +and there's a long haggling time and + + + align:start position:0% +and there's a long haggling time and +then at the end of haggling you + + align:start position:0% +then at the end of haggling you + + + align:start position:0% +then at the end of haggling you +eventually get to buy what you want to + + align:start position:0% +eventually get to buy what you want to + + + align:start position:0% +eventually get to buy what you want to +buy you know why does that happen you + + align:start position:0% +buy you know why does that happen you + + + align:start position:0% +buy you know why does that happen you +know I would say it it probably it's the + + align:start position:0% +know I would say it it probably it's the + + + align:start position:0% +know I would say it it probably it's the +low cost of Labor in in developing + + align:start position:0% +low cost of Labor in in developing + + + align:start position:0% +low cost of Labor in in developing +country retail there's just tremendous + + align:start position:0% +country retail there's just tremendous + + + align:start position:0% +country retail there's just tremendous +excess uh employees there you have these + + align:start position:0% +excess uh employees there you have these + + + align:start position:0% +excess uh employees there you have these +excess employees whose time is worth + + align:start position:0% +excess employees whose time is worth + + + align:start position:0% +excess employees whose time is worth +almost zero they can sort of do the hard + + align:start position:0% +almost zero they can sort of do the hard + + + align:start position:0% +almost zero they can sort of do the hard +work of trying to price discrimin figure + + align:start position:0% +work of trying to price discrimin figure + + + align:start position:0% +work of trying to price discrimin figure +out what it's worth you make some extra + + align:start position:0% +out what it's worth you make some extra + + + align:start position:0% +out what it's worth you make some extra +money I'm like you know in the US we + + align:start position:0% +money I'm like you know in the US we + + + align:start position:0% +money I'm like you know in the US we +actually we do this for um you know we + + align:start position:0% +actually we do this for um you know we + + + align:start position:0% +actually we do this for um you know we +we do haggle over cars and over houses + + align:start position:0% +we do haggle over cars and over houses + + + align:start position:0% +we do haggle over cars and over houses +and things where it's like it's a car + + align:start position:0% +and things where it's like it's a car + + + align:start position:0% +and things where it's like it's a car +the car is $30,000 that's enough of a + + align:start position:0% +the car is $30,000 that's enough of a + + + align:start position:0% +the car is $30,000 that's enough of a +difference that it makes sense to have a + + align:start position:0% +difference that it makes sense to have a + + + align:start position:0% +difference that it makes sense to have a +salesperson who's trained in negotiating + + align:start position:0% +salesperson who's trained in negotiating + + + align:start position:0% +salesperson who's trained in negotiating +and figuring out how much the customer's + + align:start position:0% +and figuring out how much the customer's + + + align:start position:0% +and figuring out how much the customer's +willingness to pay and trying to get + + align:start position:0% +willingness to pay and trying to get + + + align:start position:0% +willingness to pay and trying to get +them to pay a little bit more or pay + + align:start position:0% +them to pay a little bit more or pay + + + align:start position:0% +them to pay a little bit more or pay +them a little less or get them to pay a + + align:start position:0% +them a little less or get them to pay a + + + align:start position:0% +them a little less or get them to pay a +little less if they need to but you know + + align:start position:0% +little less if they need to but you know + + + align:start position:0% +little less if they need to but you know +normally most Goods it's not it's not + + align:start position:0% +normally most Goods it's not it's not + + + align:start position:0% +normally most Goods it's not it's not +worth it um you know I think there's a + + align:start position:0% +worth it um you know I think there's a + + + align:start position:0% +worth it um you know I think there's a +thought that price discrimination may + + align:start position:0% +thought that price discrimination may + + + align:start position:0% +thought that price discrimination may +have gone up with the rise of the + + align:start position:0% +have gone up with the rise of the + + + align:start position:0% +have gone up with the rise of the +internet because a a bot that prices + + align:start position:0% +internet because a a bot that prices + + + align:start position:0% +internet because a a bot that prices +things in a discriminatory way doesn't + + align:start position:0% +things in a discriminatory way doesn't + + + align:start position:0% +things in a discriminatory way doesn't +charge by the hour for its work trying + + align:start position:0% +charge by the hour for its work trying + + + align:start position:0% +charge by the hour for its work trying +to sort of figure out how to price + + align:start position:0% +to sort of figure out how to price + + + align:start position:0% +to sort of figure out how to price +discriminate among + + align:start position:0% +discriminate among + + + align:start position:0% +discriminate among +people um obviously there you can come + + align:start position:0% +people um obviously there you can come + + + align:start position:0% +people um obviously there you can come +up with several examples where if these + + align:start position:0% +up with several examples where if these + + + align:start position:0% +up with several examples where if these +problems are severe price discrimination + + align:start position:0% +problems are severe price discrimination + + + align:start position:0% +problems are severe price discrimination +impossible so for instance simplest + + align:start position:0% +impossible so for instance simplest + + + align:start position:0% +impossible so for instance simplest +example here you know suppose customers + + align:start position:0% +example here you know suppose customers + + + align:start position:0% +example here you know suppose customers +have unit demand + + align:start position:0% +have unit demand + + + align:start position:0% +have unit demand +and there's a competitive resale + + align:start position:0% +and there's a competitive resale + + + align:start position:0% +and there's a competitive resale +Market if if there's a competitive + + align:start position:0% +Market if if there's a competitive + + + align:start position:0% +Market if if there's a competitive +resale market then in that resale Market + + align:start position:0% +resale market then in that resale Market + + + align:start position:0% +resale market then in that resale Market +the price of the good is going to end up + + align:start position:0% +the price of the good is going to end up + + + align:start position:0% +the price of the good is going to end up +being capital P where p is you know + + align:start position:0% +being capital P where p is you know + + + align:start position:0% +being capital P where p is you know +inverse the uh inverse uh demand for + + align:start position:0% +inverse the uh inverse uh demand for + + + align:start position:0% +inverse the uh inverse uh demand for +aggregate demand it's going to be P of + + align:start position:0% +aggregate demand it's going to be P of + + + align:start position:0% +aggregate demand it's going to be P of +the total number of units that got sold + + align:start position:0% +the total number of units that got sold + + + align:start position:0% +the total number of units that got sold +in + + align:start position:0% +in + + + align:start position:0% +in +equilibrium and so given that consumers + + align:start position:0% +equilibrium and so given that consumers + + + align:start position:0% +equilibrium and so given that consumers +can always buy this good at P star in + + align:start position:0% +can always buy this good at P star in + + + align:start position:0% +can always buy this good at P star in +the resale Market they're going to buy + + align:start position:0% +the resale Market they're going to buy + + + align:start position:0% +the resale Market they're going to buy +from the monopolist if and only if the + + align:start position:0% +from the monopolist if and only if the + + + align:start position:0% +from the monopolist if and only if the +number of units the monopolist is + + align:start position:0% +number of units the monopolist is + + + align:start position:0% +number of units the monopolist is +selling them is less than P star uh + + align:start position:0% +selling them is less than P star uh + + + align:start position:0% +selling them is less than P star uh +times the number of units they get if + + align:start position:0% +times the number of units they get if + + + align:start position:0% +times the number of units they get if +that's the price therefore you might as + + align:start position:0% +that's the price therefore you might as + + + align:start position:0% +that's the price therefore you might as +well just directly sell it for p star + + align:start position:0% +well just directly sell it for p star + + + align:start position:0% +well just directly sell it for p star +and there's nothing you can + + align:start position:0% +and there's nothing you can + + + align:start position:0% +and there's nothing you can +do + + align:start position:0% +do + + + align:start position:0% +do +uh anyway I put a couple other examples + + align:start position:0% +uh anyway I put a couple other examples + + + align:start position:0% +uh anyway I put a couple other examples +on there um here are I + + align:start position:0% +on there um here are I + + + align:start position:0% +on there um here are I +found always like finding examples of + + align:start position:0% +found always like finding examples of + + + align:start position:0% +found always like finding examples of +factors limiting price discrimination + + align:start position:0% +factors limiting price discrimination + + + align:start position:0% +factors limiting price discrimination +and how sometimes it's harder to price + + align:start position:0% +and how sometimes it's harder to price + + + align:start position:0% +and how sometimes it's harder to price +discriminate than you think and + + align:start position:0% +discriminate than you think and + + + align:start position:0% +discriminate than you think and +sometimes it's easier so here's the it's + + align:start position:0% +sometimes it's easier so here's the it's + + + align:start position:0% +sometimes it's easier so here's the it's +harder than you think there's a story of + + align:start position:0% +harder than you think there's a story of + + + align:start position:0% +harder than you think there's a story of +a Italian Supermarket that had a 20% + + align:start position:0% +a Italian Supermarket that had a 20% + + + align:start position:0% +a Italian Supermarket that had a 20% +discount on groceries for anyone over 60 + + align:start position:0% +discount on groceries for anyone over 60 + + + align:start position:0% +discount on groceries for anyone over 60 +and they thought that this was going to + + align:start position:0% +and they thought that this was going to + + + align:start position:0% +and they thought that this was going to +be a + + align:start position:0% +be a + + + align:start position:0% +be a +fantastic uh plan because you know + + align:start position:0% +fantastic uh plan because you know + + + align:start position:0% +fantastic uh plan because you know +senior citizens are more price sensitive + + align:start position:0% +senior citizens are more price sensitive + + + align:start position:0% +senior citizens are more price sensitive +they're willing to shop around more they + + align:start position:0% +they're willing to shop around more they + + + align:start position:0% +they're willing to shop around more they +may go to multiple stores we'll just + + align:start position:0% +may go to multiple stores we'll just + + + align:start position:0% +may go to multiple stores we'll just +offer them all a discount and they will + + align:start position:0% +offer them all a discount and they will + + + align:start position:0% +offer them all a discount and they will +buy the goods and then what they + + align:start position:0% +buy the goods and then what they + + + align:start position:0% +buy the goods and then what they +realized apparently only after a year + + align:start position:0% +realized apparently only after a year + + + align:start position:0% +realized apparently only after a year +was that a number of seniors in that + + align:start position:0% +was that a number of seniors in that + + + align:start position:0% +was that a number of seniors in that +town had started businesses of shop + + align:start position:0% +town had started businesses of shop + + + align:start position:0% +town had started businesses of shop +shopping for other people and they were + + align:start position:0% +shopping for other people and they were + + + align:start position:0% +shopping for other people and they were +sort of they had become professional + + align:start position:0% +sort of they had become professional + + + align:start position:0% +sort of they had become professional +Shoppers you would go hand them your + + align:start position:0% +Shoppers you would go hand them your + + + align:start position:0% +Shoppers you would go hand them your +grocery list they would walk into the + + align:start position:0% +grocery list they would walk into the + + + align:start position:0% +grocery list they would walk into the +store buy all the goods get the 20% + + align:start position:0% +store buy all the goods get the 20% + + + align:start position:0% +store buy all the goods get the 20% +discount and then split the money with + + align:start position:0% +discount and then split the money with + + + align:start position:0% +discount and then split the money with +the customers who were you know happy to + + align:start position:0% +the customers who were you know happy to + + + align:start position:0% +the customers who were you know happy to +Ser you know some sense it was like a + + align:start position:0% +Ser you know some sense it was like a + + + align:start position:0% +Ser you know some sense it was like a +forerunner to instacart or whatever it's + + align:start position:0% +forerunner to instacart or whatever it's + + + align:start position:0% +forerunner to instacart or whatever it's +like they would take the discount they + + align:start position:0% +like they would take the discount they + + + align:start position:0% +like they would take the discount they +would sort of give you the stuff and + + align:start position:0% +would sort of give you the stuff and + + + align:start position:0% +would sort of give you the stuff and +then and then everyone was everyone was + + align:start position:0% +then and then everyone was everyone was + + + align:start position:0% +then and then everyone was everyone was +better off uh and and I guess when the + + align:start position:0% +better off uh and and I guess when the + + + align:start position:0% +better off uh and and I guess when the +firm realized that they decided they + + align:start position:0% +firm realized that they decided they + + + align:start position:0% +firm realized that they decided they +maybe this wasn't such a good price + + align:start position:0% +maybe this wasn't such a good price + + + align:start position:0% +maybe this wasn't such a good price +discrimination scheme after all um + + align:start position:0% +discrimination scheme after all um + + + align:start position:0% +discrimination scheme after all um +second example a sort of classic photo + + align:start position:0% +second example a sort of classic photo + + + align:start position:0% +second example a sort of classic photo +uh it doesn't come up so well at these + + align:start position:0% +uh it doesn't come up so well at these + + + align:start position:0% +uh it doesn't come up so well at these +if I turn off these lights you'll see it + + align:start position:0% +if I turn off these lights you'll see it + + + align:start position:0% +if I turn off these lights you'll see it +better but you know for those of you who + + align:start position:0% +better but you know for those of you who + + + align:start position:0% +better but you know for those of you who +um you know familiar with the Dutch and + + align:start position:0% +um you know familiar with the Dutch and + + + align:start position:0% +um you know familiar with the Dutch and +French flags you know the Dutch and + + align:start position:0% +French flags you know the Dutch and + + + align:start position:0% +French flags you know the Dutch and +French flags are very similar although + + align:start position:0% +French flags are very similar although + + + align:start position:0% +French flags are very similar although +one is like the stripes are vertical and + + align:start position:0% +one is like the stripes are vertical and + + + align:start position:0% +one is like the stripes are vertical and +the other is the stripes are horizontal + + align:start position:0% +the other is the stripes are horizontal + + + align:start position:0% +the other is the stripes are horizontal +but if you're a company that decides to + + align:start position:0% +but if you're a company that decides to + + + align:start position:0% +but if you're a company that decides to +sell sort of pillows online and you want + + align:start position:0% +sell sort of pillows online and you want + + + align:start position:0% +sell sort of pillows online and you want +to make a Dutch flag pillow uh it would + + align:start position:0% +to make a Dutch flag pillow uh it would + + + align:start position:0% +to make a Dutch flag pillow uh it would +look kind of like this you know a red + + align:start position:0% +look kind of like this you know a red + + + align:start position:0% +look kind of like this you know a red +stripe a white stripe and a blue stripe + + align:start position:0% +stripe a white stripe and a blue stripe + + + align:start position:0% +stripe a white stripe and a blue stripe +you want to make a French flag pillow + + align:start position:0% +you want to make a French flag pillow + + + align:start position:0% +you want to make a French flag pillow +would look like a blue stripe a white + + align:start position:0% +would look like a blue stripe a white + + + align:start position:0% +would look like a blue stripe a white +stripe and a red + + align:start position:0% +stripe and a red + + + align:start position:0% +stripe and a red +stripe you know obviously at some point + + align:start position:0% +stripe you know obviously at some point + + + align:start position:0% +stripe you know obviously at some point +they realize well look you know it's + + align:start position:0% +they realize well look you know it's + + + align:start position:0% +they realize well look you know it's +it's you know it's the same pillow just + + align:start position:0% +it's you know it's the same pillow just + + + align:start position:0% +it's you know it's the same pillow just +turned on its side uh but somehow on + + align:start position:0% +turned on its side uh but somehow on + + + align:start position:0% +turned on its side uh but somehow on +their website you know the website had + + align:start position:0% +their website you know the website had + + + align:start position:0% +their website you know the website had +the two of them there I don't know if if + + align:start position:0% +the two of them there I don't know if if + + + align:start position:0% +the two of them there I don't know if if +Dutch people pay less for pillows than + + align:start position:0% +Dutch people pay less for pillows than + + + align:start position:0% +Dutch people pay less for pillows than +French people do but they had the Dutch + + align:start position:0% +French people do but they had the Dutch + + + align:start position:0% +French people do but they had the Dutch +pillow was $9.99 the French pillow was + + align:start position:0% +pillow was $9.99 the French pillow was + + + align:start position:0% +pillow was $9.99 the French pillow was +$15.99 and you know I guess you had to + + align:start position:0% +$15.99 and you know I guess you had to + + + align:start position:0% +$15.99 and you know I guess you had to +count on people not realizing they could + + align:start position:0% +count on people not realizing they could + + + align:start position:0% +count on people not realizing they could +buy the wrong pillow and just turn it + + align:start position:0% +buy the wrong pillow and just turn it + + + align:start position:0% +buy the wrong pillow and just turn it +sideways to get the pillow that they + + align:start position:0% +sideways to get the pillow that they + + + align:start position:0% +sideways to get the pillow that they +pillow more and the French people get + + align:start position:0% +pillow more and the French people get + + + align:start position:0% +pillow more and the French people get +the could get the Dutch pillow and turn + + align:start position:0% +the could get the Dutch pillow and turn + + + align:start position:0% +the could get the Dutch pillow and turn +it on inside and get it more cheaply I + + align:start position:0% +it on inside and get it more cheaply I + + + align:start position:0% +it on inside and get it more cheaply I +mean the you know the Reds and the blues + + align:start position:0% +mean the you know the Reds and the blues + + + align:start position:0% +mean the you know the Reds and the blues +are not exactly the same on the three + + align:start position:0% +are not exactly the same on the three + + + align:start position:0% +are not exactly the same on the three +pillows but I'm sure if you on the flags + + align:start position:0% +pillows but I'm sure if you on the flags + + + align:start position:0% +pillows but I'm sure if you on the flags +themselves but I'm sure if you bought + + align:start position:0% +themselves but I'm sure if you bought + + + align:start position:0% +themselves but I'm sure if you bought +those pillows they're the same pillow + + align:start position:0% +those pillows they're the same pillow + + + align:start position:0% +those pillows they're the same pillow +just turned sideways um and you know + + align:start position:0% +just turned sideways um and you know + + + align:start position:0% +just turned sideways um and you know +apparently Arbitrage was not enough to + + align:start position:0% +apparently Arbitrage was not enough to + + + align:start position:0% +apparently Arbitrage was not enough to +prevent that scheme from working to some + + align:start position:0% +prevent that scheme from working to some + + + align:start position:0% +prevent that scheme from working to some +degree + + align:start position:0% + + + + align:start position:0% + +um okay so + + align:start position:0% +um okay so + + + align:start position:0% +um okay so +um uh Next Step uh third degree + + align:start position:0% +um uh Next Step uh third degree + + + align:start position:0% +um uh Next Step uh third degree +discrimination + + align:start position:0% +discrimination + + + align:start position:0% +discrimination +um so you know suppose the monopolis now + + align:start position:0% +um so you know suppose the monopolis now + + + align:start position:0% +um so you know suppose the monopolis now +can distinguish between classes of + + align:start position:0% +can distinguish between classes of + + + align:start position:0% +can distinguish between classes of +consumers uh but is limited to using + + align:start position:0% +consumers uh but is limited to using + + + align:start position:0% +consumers uh but is limited to using +simple linear pricing within each group + + align:start position:0% +simple linear pricing within each group + + + align:start position:0% +simple linear pricing within each group +so for instance maybe this sort of + + align:start position:0% +so for instance maybe this sort of + + + align:start position:0% +so for instance maybe this sort of +pillow retailer actually has two + + align:start position:0% +pillow retailer actually has two + + + align:start position:0% +pillow retailer actually has two +different websites they have a Dutch + + align:start position:0% +different websites they have a Dutch + + + align:start position:0% +different websites they have a Dutch +website that's only in Dutch and a + + align:start position:0% +website that's only in Dutch and a + + + align:start position:0% +website that's only in Dutch and a +French website that's only in French and + + align:start position:0% +French website that's only in French and + + + align:start position:0% +French website that's only in French and +so they can just set different prices in + + align:start position:0% +so they can just set different prices in + + + align:start position:0% +so they can just set different prices in +different countries and consumers can't + + align:start position:0% +different countries and consumers can't + + + align:start position:0% +different countries and consumers can't +see the see the other + + align:start position:0% +see the see the other + + + align:start position:0% +see the see the other +website um + + align:start position:0% +website um + + + align:start position:0% +website um +so anyway so I'm going to have two + + align:start position:0% +so anyway so I'm going to have two + + + align:start position:0% +so anyway so I'm going to have two +groups I equals 1 and two this will also + + align:start position:0% +groups I equals 1 and two this will also + + + align:start position:0% +groups I equals 1 and two this will also +be students and non- students uh each + + align:start position:0% +be students and non- students uh each + + + align:start position:0% +be students and non- students uh each +group has a demand XI of + + align:start position:0% +group has a demand XI of + + + align:start position:0% +group has a demand XI of +p uh and then again I'm going to go with + + align:start position:0% +p uh and then again I'm going to go with + + + align:start position:0% +p uh and then again I'm going to go with +the constant marginal cost of + + align:start position:0% +the constant marginal cost of + + + align:start position:0% +the constant marginal cost of +c um you know here I think what I'm + + align:start position:0% +c um you know here I think what I'm + + + align:start position:0% +c um you know here I think what I'm +going to do is think about group one as + + align:start position:0% +going to do is think about group one as + + + align:start position:0% +going to do is think about group one as +being sort of the students or the low + + align:start position:0% +being sort of the students or the low + + + align:start position:0% +being sort of the students or the low +demand + + align:start position:0% +demand + + + align:start position:0% +demand +consumers and group two as being + + align:start position:0% +consumers and group two as being + + + align:start position:0% +consumers and group two as being +the uh higher demand + + align:start position:0% +the uh higher demand + + + align:start position:0% +the uh higher demand +consumers okay so this is uh population + + align:start position:0% +consumers okay so this is uh population + + + align:start position:0% +consumers okay so this is uh population +two am I doing I did I put price in this + + align:start position:0% +two am I doing I did I put price in this + + + align:start position:0% +two am I doing I did I put price in this +axis I guess I switched so this is X1 of + + align:start position:0% +axis I guess I switched so this is X1 of + + + align:start position:0% +axis I guess I switched so this is X1 of +P this is X2 of P so at at any price the + + align:start position:0% +P this is X2 of P so at at any price the + + + align:start position:0% +P this is X2 of P so at at any price the +students are willing to pay less than + + align:start position:0% +students are willing to pay less than + + + align:start position:0% +students are willing to pay less than +the non- students because you presum + + align:start position:0% +the non- students because you presum + + + align:start position:0% +the non- students because you presum +they have less money um so anyway with + + align:start position:0% +they have less money um so anyway with + + + align:start position:0% +they have less money um so anyway with +discrimination uh what are you going to + + align:start position:0% +discrimination uh what are you going to + + + align:start position:0% +discrimination uh what are you going to +do within each population I you're just + + align:start position:0% +do within each population I you're just + + + align:start position:0% +do within each population I you're just +going to maximize Pi minus C * XI of Pi + + align:start position:0% +going to maximize Pi minus C * XI of Pi + + + align:start position:0% +going to maximize Pi minus C * XI of Pi +this is just the Monopoly pricing + + align:start position:0% +this is just the Monopoly pricing + + + align:start position:0% +this is just the Monopoly pricing +problem right so the Monopoly pricing + + align:start position:0% +problem right so the Monopoly pricing + + + align:start position:0% +problem right so the Monopoly pricing +problem has the marginal revenue equals + + align:start position:0% +problem has the marginal revenue equals + + + align:start position:0% +problem has the marginal revenue equals +marginal cost vers doar condition price + + align:start position:0% +marginal cost vers doar condition price + + + align:start position:0% +marginal cost vers doar condition price +Minus cost over price is one over the + + align:start position:0% +Minus cost over price is one over the + + + align:start position:0% +Minus cost over price is one over the +negative one over the elasticity of + + align:start position:0% +negative one over the elasticity of + + + align:start position:0% +negative one over the elasticity of +demand just like it was last week okay + + align:start position:0% +demand just like it was last week okay + + + align:start position:0% +demand just like it was last week okay +and so let me just say + + align:start position:0% +and so let me just say + + + align:start position:0% +and so let me just say +here + + align:start position:0% +here + + + align:start position:0% +here +um you know what supposed we would cost + + align:start position:0% +um you know what supposed we would cost + + + align:start position:0% +um you know what supposed we would cost +here so this is P1 + + align:start position:0% +here so this is P1 + + + align:start position:0% +here so this is P1 +star and then if this is + + align:start position:0% +star and then if this is + + + align:start position:0% +star and then if this is +cost this is P2 star + + align:start position:0% +cost this is P2 star + + + align:start position:0% +cost this is P2 star +so I'm going to assume that label the + + align:start position:0% +so I'm going to assume that label the + + + align:start position:0% +so I'm going to assume that label the +markets that the Monopoly price in + + align:start position:0% +markets that the Monopoly price in + + + align:start position:0% +markets that the Monopoly price in +Market one is smaller than the Monopoly + + align:start position:0% +Market one is smaller than the Monopoly + + + align:start position:0% +Market one is smaller than the Monopoly +price in Market + + align:start position:0% + + + + align:start position:0% + +to okay so you know third degree + + align:start position:0% +to okay so you know third degree + + + align:start position:0% +to okay so you know third degree +discrimination if you're allowed to + + align:start position:0% +discrimination if you're allowed to + + + align:start position:0% +discrimination if you're allowed to +practice it is just Monopoly pricing + + align:start position:0% +practice it is just Monopoly pricing + + + align:start position:0% +practice it is just Monopoly pricing +Market by + + align:start position:0% + + + + align:start position:0% + +market interesting questions that come + + align:start position:0% +market interesting questions that come + + + align:start position:0% +market interesting questions that come +up in third deegree discrimination is + + align:start position:0% +up in third deegree discrimination is + + + align:start position:0% +up in third deegree discrimination is +what if you decide that discrimination + + align:start position:0% +what if you decide that discrimination + + + align:start position:0% +what if you decide that discrimination +should not be allowed and we want to ban + + align:start position:0% +should not be allowed and we want to ban + + + align:start position:0% +should not be allowed and we want to ban +um price + + align:start position:0% +um price + + + align:start position:0% +um price +discrimination + + align:start position:0% + + + + align:start position:0% + +um you know let me say and generally + + align:start position:0% +um you know let me say and generally + + + align:start position:0% +um you know let me say and generally +it's it's we have this sort of funny + + align:start position:0% +it's it's we have this sort of funny + + + align:start position:0% +it's it's we have this sort of funny +relationship with price discrimination + + align:start position:0% +relationship with price discrimination + + + align:start position:0% +relationship with price discrimination +in the US so there is something called + + align:start position:0% +in the US so there is something called + + + align:start position:0% +in the US so there is something called +the Robinson Patman act which is dates + + align:start position:0% +the Robinson Patman act which is dates + + + align:start position:0% +the Robinson Patman act which is dates +to the early 20th century Robinson + + align:start position:0% +to the early 20th century Robinson + + + align:start position:0% +to the early 20th century Robinson +Patman act bans price discrimination but + + align:start position:0% +Patman act bans price discrimination but + + + align:start position:0% +Patman act bans price discrimination but +it bans price discrimination to the + + align:start position:0% +it bans price discrimination to the + + + align:start position:0% +it bans price discrimination to the +extent that it harms competition and so + + align:start position:0% +extent that it harms competition and so + + + align:start position:0% +extent that it harms competition and so +you know it was originally developed for + + align:start position:0% +you know it was originally developed for + + + align:start position:0% +you know it was originally developed for +things like not allowing the railroads + + align:start position:0% +things like not allowing the railroads + + + align:start position:0% +things like not allowing the railroads +to um charge one firm more for shipping + + align:start position:0% +to um charge one firm more for shipping + + + align:start position:0% +to um charge one firm more for shipping +oil than another firm for shipping oil + + align:start position:0% +oil than another firm for shipping oil + + + align:start position:0% +oil than another firm for shipping oil +in order to create an oil Monopoly on + + align:start position:0% +in order to create an oil Monopoly on + + + align:start position:0% +in order to create an oil Monopoly on +the east coast of the us or something + + align:start position:0% +the east coast of the us or something + + + align:start position:0% +the east coast of the us or something +like that um it's typically not applied + + align:start position:0% +like that um it's typically not applied + + + align:start position:0% +like that um it's typically not applied +to retail price discrimination or price + + align:start position:0% +to retail price discrimination or price + + + align:start position:0% +to retail price discrimination or price +discrimination that isn't sort of going + + align:start position:0% +discrimination that isn't sort of going + + + align:start position:0% +discrimination that isn't sort of going +to be harming competition of some where + + align:start position:0% +to be harming competition of some where + + + align:start position:0% +to be harming competition of some where +you're providing an intermediate input + + align:start position:0% +you're providing an intermediate input + + + align:start position:0% +you're providing an intermediate input +to some Downstream firms um but you know + + align:start position:0% +to some Downstream firms um but you know + + + align:start position:0% +to some Downstream firms um but you know +there's sometimes when we think that + + align:start position:0% +there's sometimes when we think that + + + align:start position:0% +there's sometimes when we think that +like price discrimination is okay like + + align:start position:0% +like price discrimination is okay like + + + align:start position:0% +like price discrimination is okay like +you know somehow it's okay to give + + align:start position:0% +you know somehow it's okay to give + + + align:start position:0% +you know somehow it's okay to give +senior citizen discounts it's okay to um + + align:start position:0% +senior citizen discounts it's okay to um + + + align:start position:0% +senior citizen discounts it's okay to um +it's okay to give student discounts but + + align:start position:0% +it's okay to give student discounts but + + + align:start position:0% +it's okay to give student discounts but +it's not okay to charge people extra so + + align:start position:0% +it's not okay to charge people extra so + + + align:start position:0% +it's not okay to charge people extra so +I I don't quite know how it is it's like + + align:start position:0% +I I don't quite know how it is it's like + + + align:start position:0% +I I don't quite know how it is it's like +discounts are okay charging someone more + + align:start position:0% +discounts are okay charging someone more + + + align:start position:0% +discounts are okay charging someone more +would be would be totally inappropriate + + align:start position:0% +would be would be totally inappropriate + + + align:start position:0% +would be would be totally inappropriate +right like if you had a you know a + + align:start position:0% +right like if you had a you know a + + + align:start position:0% +right like if you had a you know a +women's sirch charge that is like you + + align:start position:0% +women's sirch charge that is like you + + + align:start position:0% +women's sirch charge that is like you +know we have a price in our restaurant + + align:start position:0% +know we have a price in our restaurant + + + align:start position:0% +know we have a price in our restaurant +and women have to pay 10% more that + + align:start position:0% +and women have to pay 10% more that + + + align:start position:0% +and women have to pay 10% more that +would be considered completely + + align:start position:0% +would be considered completely + + + align:start position:0% +would be considered completely +inappropriate + + align:start position:0% +inappropriate + + + align:start position:0% +inappropriate +um and um you know or if there's a you + + align:start position:0% +um and um you know or if there's a you + + + align:start position:0% +um and um you know or if there's a you +know there's a whatever there's a big + + align:start position:0% +know there's a whatever there's a big + + + align:start position:0% +know there's a whatever there's a big +storm we have a a Sarge on gasoline or + + align:start position:0% +storm we have a a Sarge on gasoline or + + + align:start position:0% +storm we have a a Sarge on gasoline or +firewood or whatever because there's + + align:start position:0% +firewood or whatever because there's + + + align:start position:0% +firewood or whatever because there's +been some natural disaster you know + + align:start position:0% +been some natural disaster you know + + + align:start position:0% +been some natural disaster you know +discrimination there is just completely + + align:start position:0% +discrimination there is just completely + + + align:start position:0% +discrimination there is just completely +inappropriate and there there are sort + + align:start position:0% +inappropriate and there there are sort + + + align:start position:0% +inappropriate and there there are sort +of anti-price gouging laws that prevent + + align:start position:0% +of anti-price gouging laws that prevent + + + align:start position:0% +of anti-price gouging laws that prevent +that um so anyway what are we going to + + align:start position:0% +that um so anyway what are we going to + + + align:start position:0% +that um so anyway what are we going to +do in this market if you decide to ban + + align:start position:0% +do in this market if you decide to ban + + + align:start position:0% +do in this market if you decide to ban +price + + align:start position:0% +price + + + align:start position:0% +price +discrimination um we just going to + + align:start position:0% +discrimination um we just going to + + + align:start position:0% +discrimination um we just going to +maximize over single Price p p minus C + + align:start position:0% +maximize over single Price p p minus C + + + align:start position:0% +maximize over single Price p p minus C +X1 of p plus P minus C X2 of + + align:start position:0% + + + + align:start position:0% + +p uh if you want to think about what the + + align:start position:0% +p uh if you want to think about what the + + + align:start position:0% +p uh if you want to think about what the +first order condition looks like you + + align:start position:0% +first order condition looks like you + + + align:start position:0% +first order condition looks like you +know you just have DP D you know the + + align:start position:0% +know you just have DP D you know the + + + align:start position:0% +know you just have DP D you know the +single good case we had this was DPI + + align:start position:0% +single good case we had this was DPI + + + align:start position:0% +single good case we had this was DPI +DP you just are adding that up across + + align:start position:0% +DP you just are adding that up across + + + align:start position:0% +DP you just are adding that up across +the two markets and getting the + + align:start position:0% +the two markets and getting the + + + align:start position:0% +the two markets and getting the +derivative of profit with respect to p + + align:start position:0% +derivative of profit with respect to p + + + align:start position:0% +derivative of profit with respect to p +and Market one plus DP DP Market 2 + + align:start position:0% +and Market one plus DP DP Market 2 + + + align:start position:0% +and Market one plus DP DP Market 2 +equals + + align:start position:0% +equals + + + align:start position:0% +equals +z um what's that going to do you know + + align:start position:0% +z um what's that going to do you know + + + align:start position:0% +z um what's that going to do you know +most standard result is that if demand + + align:start position:0% +most standard result is that if demand + + + align:start position:0% +most standard result is that if demand +is well behaved by which I mean two + + align:start position:0% +is well behaved by which I mean two + + + align:start position:0% +is well behaved by which I mean two +things demand is single peaked and it's + + align:start position:0% +things demand is single peaked and it's + + + align:start position:0% +things demand is single peaked and it's +concave in P when p is less than P2 star + + align:start position:0% +concave in P when p is less than P2 star + + + align:start position:0% +concave in P when p is less than P2 star +then what the firm does is when you ban + + align:start position:0% +then what the firm does is when you ban + + + align:start position:0% +then what the firm does is when you ban +discrimination they just choose an + + align:start position:0% +discrimination they just choose an + + + align:start position:0% +discrimination they just choose an +intermediate price the consumers the + + align:start position:0% +intermediate price the consumers the + + + align:start position:0% +intermediate price the consumers the +students are hurt uh by the price going + + align:start position:0% +students are hurt uh by the price going + + + align:start position:0% +students are hurt uh by the price going +up the non students are helped by the + + align:start position:0% +up the non students are helped by the + + + align:start position:0% +up the non students are helped by the +price going down okay and why is that + + align:start position:0% +price going down okay and why is that + + + align:start position:0% +price going down okay and why is that +going to happen you know if you think + + align:start position:0% +going to happen you know if you think + + + align:start position:0% +going to happen you know if you think +about it + + align:start position:0% +about it + + + align:start position:0% +about it +[Applause] + + align:start position:0% + + + + align:start position:0% + +um okay + + align:start position:0% +um okay + + + align:start position:0% +um okay +so you know this thing has a has a uh + + align:start position:0% +so you know this thing has a has a uh + + + align:start position:0% +so you know this thing has a has a uh +this was the Monopoly price here so if I + + align:start position:0% +this was the Monopoly price here so if I + + + align:start position:0% +this was the Monopoly price here so if I +look + + align:start position:0% +look + + + align:start position:0% +look +at uh DP 1 + + align:start position:0% +at uh DP 1 + + + align:start position:0% +at uh DP 1 +DP uh that's what it looks like it's you + + align:start position:0% +DP uh that's what it looks like it's you + + + align:start position:0% +DP uh that's what it looks like it's you +know DP DP if if profit is concave then + + align:start position:0% +know DP DP if if profit is concave then + + + align:start position:0% +know DP DP if if profit is concave then +DP DP is downward sloping it crosses + + align:start position:0% +DP DP is downward sloping it crosses + + + align:start position:0% +DP DP is downward sloping it crosses +zero at P1 + + align:start position:0% +zero at P1 + + + align:start position:0% +zero at P1 +star and in this example if I + + align:start position:0% +star and in this example if I + + + align:start position:0% +star and in this example if I +graph uh D Pi + + align:start position:0% +graph uh D Pi + + + align:start position:0% +graph uh D Pi +2dp again it's downward sloping it + + align:start position:0% +2dp again it's downward sloping it + + + align:start position:0% +2dp again it's downward sloping it +crosses zero at P2 + + align:start position:0% + + + + align:start position:0% + +star so then if you ask well what if I + + align:start position:0% +star so then if you ask well what if I + + + align:start position:0% +star so then if you ask well what if I +just add this one and this + + align:start position:0% +just add this one and this + + + align:start position:0% +just add this one and this +one you know I have one function that's + + align:start position:0% +one you know I have one function that's + + + align:start position:0% +one you know I have one function that's +going negative here I have another + + align:start position:0% +going negative here I have another + + + align:start position:0% +going negative here I have another +function that's going negative here you + + align:start position:0% +function that's going negative here you + + + align:start position:0% +function that's going negative here you +know the optimal Price p star is just + + align:start position:0% +know the optimal Price p star is just + + + align:start position:0% +know the optimal Price p star is just +where the amount by which this one is + + align:start position:0% +where the amount by which this one is + + + align:start position:0% +where the amount by which this one is +negative equals the amount by this one + + align:start position:0% +negative equals the amount by this one + + + align:start position:0% +negative equals the amount by this one +is positive so that the sum of the two + + align:start position:0% +is positive so that the sum of the two + + + align:start position:0% +is positive so that the sum of the two +first order conditions is zero and as + + align:start position:0% +first order conditions is zero and as + + + align:start position:0% +first order conditions is zero and as +I've drawn it you know here this one's + + align:start position:0% +I've drawn it you know here this one's + + + align:start position:0% +I've drawn it you know here this one's +positive and this one's zero here this + + align:start position:0% +positive and this one's zero here this + + + align:start position:0% +positive and this one's zero here this +one's positive and this one's negative + + align:start position:0% +one's positive and this one's negative + + + align:start position:0% +one's positive and this one's negative +so obviously the P star is going to be + + align:start position:0% +so obviously the P star is going to be + + + align:start position:0% +so obviously the P star is going to be +in + + align:start position:0% +in + + + align:start position:0% +in +between and you know what I needed to do + + align:start position:0% +between and you know what I needed to do + + + align:start position:0% +between and you know what I needed to do +to say that is that um you know the if + + align:start position:0% +to say that is that um you know the if + + + align:start position:0% +to say that is that um you know the if +these things are if these things are + + align:start position:0% +these things are if these things are + + + align:start position:0% +these things are if these things are +concave then the those first order + + align:start position:0% +concave then the those first order + + + align:start position:0% +concave then the those first order +conditions are both downward sloping and + + align:start position:0% +conditions are both downward sloping and + + + align:start position:0% +conditions are both downward sloping and +so when they're downward sloping this + + align:start position:0% + + + + align:start position:0% + +happens + + align:start position:0% +happens + + + align:start position:0% +happens +um just one uh comment on elasticity you + + align:start position:0% +um just one uh comment on elasticity you + + + align:start position:0% +um just one uh comment on elasticity you +know still you know we just have this + + align:start position:0% +know still you know we just have this + + + align:start position:0% +know still you know we just have this +new demand X of + + align:start position:0% +new demand X of + + + align:start position:0% +new demand X of +p uh which is equal to X1 of p plus X2 + + align:start position:0% +p uh which is equal to X1 of p plus X2 + + + align:start position:0% +p uh which is equal to X1 of p plus X2 +of + + align:start position:0% +of + + + align:start position:0% +of +P right you you're inverse elasticity + + align:start position:0% +P right you you're inverse elasticity + + + align:start position:0% +P right you you're inverse elasticity +pricing based on this aggregate demand + + align:start position:0% +pricing based on this aggregate demand + + + align:start position:0% +pricing based on this aggregate demand +and just a note when you look at an + + align:start position:0% +and just a note when you look at an + + + align:start position:0% +and just a note when you look at an +aggregate demand uh the elasticity in a + + align:start position:0% +aggregate demand uh the elasticity in a + + + align:start position:0% +aggregate demand uh the elasticity in a +market that's a component of two + + align:start position:0% +market that's a component of two + + + align:start position:0% +market that's a component of two +submarkets is just a weighted average of + + align:start position:0% +submarkets is just a weighted average of + + + align:start position:0% +submarkets is just a weighted average of +the elasticities in the individual + + align:start position:0% +the elasticities in the individual + + + align:start position:0% +the elasticities in the individual +markets okay and it's a weighted average + + align:start position:0% +markets okay and it's a weighted average + + + align:start position:0% +markets okay and it's a weighted average +of the elasticities in the individual + + align:start position:0% +of the elasticities in the individual + + + align:start position:0% +of the elasticities in the individual +markets but where you're waiting by the + + align:start position:0% +markets but where you're waiting by the + + + align:start position:0% +markets but where you're waiting by the +share of the market so if there's a + + align:start position:0% +share of the market so if there's a + + + align:start position:0% +share of the market so if there's a +market that has more customers buying at + + align:start position:0% +market that has more customers buying at + + + align:start position:0% +market that has more customers buying at +that price it gets a larger weight than + + align:start position:0% +that price it gets a larger weight than + + + align:start position:0% +that price it gets a larger weight than +one that's + + align:start position:0% +one that's + + + align:start position:0% +one that's +smaller um but so it is the case that + + align:start position:0% +smaller um but so it is the case that + + + align:start position:0% +smaller um but so it is the case that +you know this is again another to think + + align:start position:0% +you know this is again another to think + + + align:start position:0% +you know this is again another to think +about why it's intermediate is you have + + align:start position:0% +about why it's intermediate is you have + + + align:start position:0% +about why it's intermediate is you have +the high elasticity Market you have the + + align:start position:0% +the high elasticity Market you have the + + + align:start position:0% +the high elasticity Market you have the +low elasticity Market the combined + + align:start position:0% +low elasticity Market the combined + + + align:start position:0% +low elasticity Market the combined +Market has an intermediate elasticity + + align:start position:0% +Market has an intermediate elasticity + + + align:start position:0% +Market has an intermediate elasticity +which is a weighted average of the other + + align:start position:0% +which is a weighted average of the other + + + align:start position:0% +which is a weighted average of the other +two so therefore it's in + + align:start position:0% +two so therefore it's in + + + align:start position:0% +two so therefore it's in +between okay + + align:start position:0% +between okay + + + align:start position:0% +between okay +um you know while this is what we think + + align:start position:0% +um you know while this is what we think + + + align:start position:0% +um you know while this is what we think +of as the normal case + + align:start position:0% +of as the normal case + + + align:start position:0% +of as the normal case +um you know I was assuming that Pi star + + align:start position:0% +um you know I was assuming that Pi star + + + align:start position:0% +um you know I was assuming that Pi star +is + + align:start position:0% +is + + + align:start position:0% +is +concave um profit functions are never + + align:start position:0% +concave um profit functions are never + + + align:start position:0% +concave um profit functions are never +concave pretty much um you know what are + + align:start position:0% +concave pretty much um you know what are + + + align:start position:0% +concave pretty much um you know what are +profit functions look like you know we + + align:start position:0% +profit functions look like you know we + + + align:start position:0% +profit functions look like you know we +normally you know draw them like + + align:start position:0% +normally you know draw them like + + + align:start position:0% +normally you know draw them like +this uh but we ignore the fact that + + align:start position:0% +this uh but we ignore the fact that + + + align:start position:0% +this uh but we ignore the fact that +profits don't go to negative Infinity as + + align:start position:0% +profits don't go to negative Infinity as + + + align:start position:0% +profits don't go to negative Infinity as +p goes to Infinity as p goes to Infinity + + align:start position:0% +p goes to Infinity as p goes to Infinity + + + align:start position:0% +p goes to Infinity as p goes to Infinity +people stop buying your product so what + + align:start position:0% +people stop buying your product so what + + + align:start position:0% +people stop buying your product so what +profit functions look like in practice + + align:start position:0% +profit functions look like in practice + + + align:start position:0% +profit functions look like in practice +is they go like this and then they ASM + + align:start position:0% +is they go like this and then they ASM + + + align:start position:0% +is they go like this and then they ASM +toote to zero as p goes to Infinity so + + align:start position:0% +toote to zero as p goes to Infinity so + + + align:start position:0% +toote to zero as p goes to Infinity so +they're concave part of the time and + + align:start position:0% +they're concave part of the time and + + + align:start position:0% +they're concave part of the time and +then they become + + align:start position:0% +then they become + + + align:start position:0% +then they become +as P gets + + align:start position:0% + + + + align:start position:0% + +large and so if you think about what + + align:start position:0% +large and so if you think about what + + + align:start position:0% +large and so if you think about what +happens when you when this is what + + align:start position:0% +happens when you when this is what + + + align:start position:0% +happens when you when this is what +profits look like um imagine what I have + + align:start position:0% +profits look like um imagine what I have + + + align:start position:0% +profits look like um imagine what I have +is the profit in the low demand Market + + align:start position:0% +is the profit in the low demand Market + + + align:start position:0% +is the profit in the low demand Market +looks like + + align:start position:0% +looks like + + + align:start position:0% +looks like +this and the profit in the high demand + + align:start position:0% +this and the profit in the high demand + + + align:start position:0% +this and the profit in the high demand +Market uh looks like this okay what do I + + align:start position:0% +Market uh looks like this okay what do I + + + align:start position:0% +Market uh looks like this okay what do I +get when I add those two together I get + + align:start position:0% +get when I add those two together I get + + + align:start position:0% +get when I add those two together I get +something that goes like this + + align:start position:0% + + + + align:start position:0% + +right you know some sense + + align:start position:0% + + + + align:start position:0% + +after after some point when this one + + align:start position:0% +after after some point when this one + + + align:start position:0% +after after some point when this one +becomes essentially zero this curve just + + align:start position:0% +becomes essentially zero this curve just + + + align:start position:0% +becomes essentially zero this curve just +coincides with this + + align:start position:0% +coincides with this + + + align:start position:0% +coincides with this +curve so if I'm adding together one + + align:start position:0% +curve so if I'm adding together one + + + align:start position:0% +curve so if I'm adding together one +profit that looks like this and one + + align:start position:0% +profit that looks like this and one + + + align:start position:0% +profit that looks like this and one +profit that looks like this there may be + + align:start position:0% +profit that looks like this there may be + + + align:start position:0% +profit that looks like this there may be +this bump over here on the left side or + + align:start position:0% +this bump over here on the left side or + + + align:start position:0% +this bump over here on the left side or +maybe there isn't even a bump on the + + align:start position:0% +maybe there isn't even a bump on the + + + align:start position:0% +maybe there isn't even a bump on the +left side + + align:start position:0% +left side + + + align:start position:0% +left side +but the maximize ER here can just coin + + align:start position:0% +but the maximize ER here can just coin + + + align:start position:0% +but the maximize ER here can just coin +like if this one imagine no student is + + align:start position:0% +like if this one imagine no student is + + + align:start position:0% +like if this one imagine no student is +willing to pay more than $100 for a + + align:start position:0% +willing to pay more than $100 for a + + + align:start position:0% +willing to pay more than $100 for a +ticket to the art or something like that + + align:start position:0% +ticket to the art or something like that + + + align:start position:0% +ticket to the art or something like that +then this just hits zero when this hits + + align:start position:0% +then this just hits zero when this hits + + + align:start position:0% +then this just hits zero when this hits +zero these things coincide and what you + + align:start position:0% +zero these things coincide and what you + + + align:start position:0% +zero these things coincide and what you +do is you just abandon Market one and + + align:start position:0% +do is you just abandon Market one and + + + align:start position:0% +do is you just abandon Market one and +Monopoly price in Market + + align:start position:0% + + + + align:start position:0% + +to so you know if you have that case + + align:start position:0% +to so you know if you have that case + + + align:start position:0% +to so you know if you have that case +where the the concavity is not applying + + align:start position:0% +where the the concavity is not applying + + + align:start position:0% +where the the concavity is not applying +in the relevant region you don't + + align:start position:0% +in the relevant region you don't + + + align:start position:0% +in the relevant region you don't +necessarily get the intermediate pricing + + align:start position:0% +necessarily get the intermediate pricing + + + align:start position:0% +necessarily get the intermediate pricing +result you can get the just price to + + align:start position:0% +result you can get the just price to + + + align:start position:0% +result you can get the just price to +Market 2 result uh if you just price to + + align:start position:0% +Market 2 result uh if you just price to + + + align:start position:0% +Market 2 result uh if you just price to +Market two then clearly if if if when + + align:start position:0% +Market two then clearly if if if when + + + align:start position:0% +Market two then clearly if if if when +you price discriminate you just price to + + align:start position:0% +you price discriminate you just price to + + + align:start position:0% +you price discriminate you just price to +Market two and you eliminate the student + + align:start position:0% +Market two and you eliminate the student + + + align:start position:0% +Market two and you eliminate the student +discount then clearly everybody is worse + + align:start position:0% +discount then clearly everybody is worse + + + align:start position:0% +discount then clearly everybody is worse +off right the monopolist makes less + + align:start position:0% +off right the monopolist makes less + + + align:start position:0% +off right the monopolist makes less +money because it's now no longer selling + + align:start position:0% +money because it's now no longer selling + + + align:start position:0% +money because it's now no longer selling +to any students the students are worse + + align:start position:0% +to any students the students are worse + + + align:start position:0% +to any students the students are worse +off because they're not buying any + + align:start position:0% +off because they're not buying any + + + align:start position:0% +off because they're not buying any +tickets they get zero Surplus instead of + + align:start position:0% +tickets they get zero Surplus instead of + + + align:start position:0% +tickets they get zero Surplus instead of +getting positive Surplus so that's a + + align:start position:0% +getting positive Surplus so that's a + + + align:start position:0% +getting positive Surplus so that's a +case + + align:start position:0% +case + + + align:start position:0% +case +where you know there's a clear sort of + + align:start position:0% +where you know there's a clear sort of + + + align:start position:0% +where you know there's a clear sort of +uh profit and profit and social welfare + + align:start position:0% +uh profit and profit and social welfare + + + align:start position:0% +uh profit and profit and social welfare +and consumer surplus advantage to + + align:start position:0% +and consumer surplus advantage to + + + align:start position:0% +and consumer surplus advantage to +allowing price + + align:start position:0% +allowing price + + + align:start position:0% +allowing price +discrimination + + align:start position:0% + + + + align:start position:0% + +okay you know in general the Monopoly + + align:start position:0% +okay you know in general the Monopoly + + + align:start position:0% +okay you know in general the Monopoly +result is fully General right monopolies + + align:start position:0% +result is fully General right monopolies + + + align:start position:0% +result is fully General right monopolies +always benefit from Price discriminating + + align:start position:0% +always benefit from Price discriminating + + + align:start position:0% +always benefit from Price discriminating +because they could always choose not to + + align:start position:0% +because they could always choose not to + + + align:start position:0% +because they could always choose not to +you know like the monopolis could be + + align:start position:0% +you know like the monopolis could be + + + align:start position:0% +you know like the monopolis could be +told okay you know this customer's in + + align:start position:0% +told okay you know this customer's in + + + align:start position:0% +told okay you know this customer's in +France this customer in in the + + align:start position:0% +France this customer in in the + + + align:start position:0% +France this customer in in the +Netherlands they could just ignore that + + align:start position:0% +Netherlands they could just ignore that + + + align:start position:0% +Netherlands they could just ignore that +and set the same price so the the fact + + align:start position:0% +and set the same price so the the fact + + + align:start position:0% +and set the same price so the the fact +that they choose to set different prices + + align:start position:0% +that they choose to set different prices + + + align:start position:0% +that they choose to set different prices +means they're always better off + + align:start position:0% +means they're always better off + + + align:start position:0% +means they're always better off +discriminating um but whether consumer + + align:start position:0% +discriminating um but whether consumer + + + align:start position:0% +discriminating um but whether consumer +surplus and social welfare change that + + align:start position:0% +surplus and social welfare change that + + + align:start position:0% +surplus and social welfare change that +that sort of a different story okay you + + align:start position:0% +that sort of a different story okay you + + + align:start position:0% +that sort of a different story okay you +know this nor normal case we have the + + align:start position:0% +know this nor normal case we have the + + + align:start position:0% +know this nor normal case we have the +sense that some consumers would like you + + align:start position:0% +sense that some consumers would like you + + + align:start position:0% +sense that some consumers would like you +to stop discriminating some don't want + + align:start position:0% +to stop discriminating some don't want + + + align:start position:0% +to stop discriminating some don't want +you stop discriminating um but that's + + align:start position:0% +you stop discriminating um but that's + + + align:start position:0% +you stop discriminating um but that's +not always + + align:start position:0% + + + + align:start position:0% + +true okay um a little more about welfare + + align:start position:0% +true okay um a little more about welfare + + + align:start position:0% +true okay um a little more about welfare +so to think about sort of aggregate + + align:start position:0% +so to think about sort of aggregate + + + align:start position:0% +so to think about sort of aggregate +social welfare of price + + align:start position:0% +social welfare of price + + + align:start position:0% +social welfare of price +discrimination you have to think about + + align:start position:0% +discrimination you have to think about + + + align:start position:0% +discrimination you have to think about +two different welfare effects so one + + align:start position:0% +two different welfare effects so one + + + align:start position:0% +two different welfare effects so one +welfare effect of price discrimination + + align:start position:0% +welfare effect of price discrimination + + + align:start position:0% +welfare effect of price discrimination +or not allowing price discrimination is + + align:start position:0% +or not allowing price discrimination is + + + align:start position:0% +or not allowing price discrimination is +dead weight loss how many consumers are + + align:start position:0% +dead weight loss how many consumers are + + + align:start position:0% +dead weight loss how many consumers are +there who would be willing to pay what a + + align:start position:0% +there who would be willing to pay what a + + + align:start position:0% +there who would be willing to pay what a +c who would like to buy the good at Cost + + align:start position:0% +c who would like to buy the good at Cost + + + align:start position:0% +c who would like to buy the good at Cost +who don't get + + align:start position:0% +who don't get + + + align:start position:0% +who don't get +served uh and then the new + + align:start position:0% +served uh and then the new + + + align:start position:0% +served uh and then the new +dis new problem we get in price + + align:start position:0% +dis new problem we get in price + + + align:start position:0% +dis new problem we get in price +discrimination is misallocation of goods + + align:start position:0% +discrimination is misallocation of goods + + + align:start position:0% +discrimination is misallocation of goods +sold that when you sell the goods at + + align:start position:0% +sold that when you sell the goods at + + + align:start position:0% +sold that when you sell the goods at +different prices there are high value + + align:start position:0% +different prices there are high value + + + align:start position:0% +different prices there are high value +people who are not buying the good and + + align:start position:0% +people who are not buying the good and + + + align:start position:0% +people who are not buying the good and +there are people who are with lower + + align:start position:0% +there are people who are with lower + + + align:start position:0% +there are people who are with lower +values who are getting the good um so + + align:start position:0% +values who are getting the good um so + + + align:start position:0% +values who are getting the good um so +you know for instance let me think about + + align:start position:0% +you know for instance let me think about + + + align:start position:0% +you know for instance let me think about +um uh you know let's think of a + + align:start position:0% +um uh you know let's think of a + + + align:start position:0% +um uh you know let's think of a +hypothetical world where somehow um + + align:start position:0% +hypothetical world where somehow um + + + align:start position:0% +hypothetical world where somehow um +Apple has two markets to which they sell + + align:start position:0% +Apple has two markets to which they sell + + + align:start position:0% +Apple has two markets to which they sell +iPhones um they sell iPhones to people + + align:start position:0% +iPhones um they sell iPhones to people + + + align:start position:0% +iPhones um they sell iPhones to people +who want to use them as phones and they + + align:start position:0% +who want to use them as phones and they + + + align:start position:0% +who want to use them as phones and they +also sell iPhones people who want to use + + align:start position:0% +also sell iPhones people who want to use + + + align:start position:0% +also sell iPhones people who want to use +them as paper + + align:start position:0% +them as paper + + + align:start position:0% +them as paper +weights and somehow they have this sort + + align:start position:0% +weights and somehow they have this sort + + + align:start position:0% +weights and somehow they have this sort +of ability to sort of restrict you when + + align:start position:0% +of ability to sort of restrict you when + + + align:start position:0% +of ability to sort of restrict you when +you buy it like I'm I'm in the paper + + align:start position:0% +you buy it like I'm I'm in the paper + + + align:start position:0% +you buy it like I'm I'm in the paper +weight Market or I'm in the phone market + + align:start position:0% +weight Market or I'm in the phone market + + + align:start position:0% +weight Market or I'm in the phone market +and if you only buy in the paperweight + + align:start position:0% +and if you only buy in the paperweight + + + align:start position:0% +and if you only buy in the paperweight +Market they ensure that the phone + + align:start position:0% +Market they ensure that the phone + + + align:start position:0% +Market they ensure that the phone +actually won't won't ever work um it's + + align:start position:0% +actually won't won't ever work um it's + + + align:start position:0% +actually won't won't ever work um it's +still a working phone they just you know + + align:start position:0% +still a working phone they just you know + + + align:start position:0% +still a working phone they just you know +somehow manage to block you from Ever + + align:start position:0% +somehow manage to block you from Ever + + + align:start position:0% +somehow manage to block you from Ever +Getting service on it okay if you + + align:start position:0% +Getting service on it okay if you + + + align:start position:0% +Getting service on it okay if you +imagine that world it would be a funny + + align:start position:0% +imagine that world it would be a funny + + + align:start position:0% +imagine that world it would be a funny +world where you have you know some + + align:start position:0% +world where you have you know some + + + align:start position:0% +world where you have you know some +people who would like to pay $700 for an + + align:start position:0% +people who would like to pay $700 for an + + + align:start position:0% +people who would like to pay $700 for an +iPhone and who don't get to have an + + align:start position:0% +iPhone and who don't get to have an + + + align:start position:0% +iPhone and who don't get to have an +iPhone because like the price is + + align:start position:0% +iPhone because like the price is + + + align:start position:0% +iPhone because like the price is +$7.99 and then you have other people or + + align:start position:0% +$7.99 and then you have other people or + + + align:start position:0% +$7.99 and then you have other people or +maybe it's a kid's toy it's like you + + align:start position:0% +maybe it's a kid's toy it's like you + + + align:start position:0% +maybe it's a kid's toy it's like you +know iPhone kids toy that's actually a + + align:start position:0% +know iPhone kids toy that's actually a + + + align:start position:0% +know iPhone kids toy that's actually a +functioning iPhone and that they get to + + align:start position:0% +functioning iPhone and that they get to + + + align:start position:0% +functioning iPhone and that they get to +buy it for + + align:start position:0% +buy it for + + + align:start position:0% +buy it for +$50 and then so the you know you have + + align:start position:0% +$50 and then so the you know you have + + + align:start position:0% +$50 and then so the you know you have +this someone who has this value for $50 + + align:start position:0% +this someone who has this value for $50 + + + align:start position:0% +this someone who has this value for $50 +for this toy who's en who's enjoying the + + align:start position:0% +for this toy who's en who's enjoying the + + + align:start position:0% +for this toy who's en who's enjoying the +who who's getting to use the toy someone + + align:start position:0% +who who's getting to use the toy someone + + + align:start position:0% +who who's getting to use the toy someone +El who's value home at $700 isn't + + align:start position:0% +El who's value home at $700 isn't + + + align:start position:0% +El who's value home at $700 isn't +getting it there's this gain from trade + + align:start position:0% +getting it there's this gain from trade + + + align:start position:0% +getting it there's this gain from trade +where for if the person owning the toy + + align:start position:0% +where for if the person owning the toy + + + align:start position:0% +where for if the person owning the toy +phone could hand it to the person who + + align:start position:0% +phone could hand it to the person who + + + align:start position:0% +phone could hand it to the person who +wants to use it a phone there' be this + + align:start position:0% +wants to use it a phone there' be this + + + align:start position:0% +wants to use it a phone there' be this +big gain in social surplus um you know + + align:start position:0% +big gain in social surplus um you know + + + align:start position:0% +big gain in social surplus um you know +it's but you know you're going to get + + align:start position:0% +it's but you know you're going to get + + + align:start position:0% +it's but you know you're going to get +that anytime you you have uh you know + + align:start position:0% +that anytime you you have uh you know + + + align:start position:0% +that anytime you you have uh you know +you have a senior citizen discount you + + align:start position:0% +you have a senior citizen discount you + + + align:start position:0% +you have a senior citizen discount you +have a senior citizen discount someone + + align:start position:0% +have a senior citizen discount someone + + + align:start position:0% +have a senior citizen discount someone +who doesn't even really want to go to + + align:start position:0% +who doesn't even really want to go to + + + align:start position:0% +who doesn't even really want to go to +the play is there and paying because + + align:start position:0% +the play is there and paying because + + + align:start position:0% +the play is there and paying because +it's only $15 and it was cheaper than + + align:start position:0% +it's only $15 and it was cheaper than + + + align:start position:0% +it's only $15 and it was cheaper than +going to the movie they would have + + align:start position:0% +going to the movie they would have + + + align:start position:0% +going to the movie they would have +rather seen and then you have someone + + align:start position:0% +rather seen and then you have someone + + + align:start position:0% +rather seen and then you have someone +else who would have liked to go who pay + + align:start position:0% +else who would have liked to go who pay + + + align:start position:0% +else who would have liked to go who pay +$60 but isn't there and there would be + + align:start position:0% +$60 but isn't there and there would be + + + align:start position:0% +$60 but isn't there and there would be +this like if you could just make this + + align:start position:0% +this like if you could just make this + + + align:start position:0% +this like if you could just make this +swap of I'll trade you my plan my play + + align:start position:0% +swap of I'll trade you my plan my play + + + align:start position:0% +swap of I'll trade you my plan my play +ticket and I'll give you a ticket to the + + align:start position:0% +ticket and I'll give you a ticket to the + + + align:start position:0% +ticket and I'll give you a ticket to the +movie in the in the theater next door + + align:start position:0% +movie in the in the theater next door + + + align:start position:0% +movie in the in the theater next door +we're both better off um and anyway that + + align:start position:0% +we're both better off um and anyway that + + + align:start position:0% +we're both better off um and anyway that +so that there's that misallocation of + + align:start position:0% +so that there's that misallocation of + + + align:start position:0% +so that there's that misallocation of +goods utility um proposition just + + align:start position:0% +goods utility um proposition just + + + align:start position:0% +goods utility um proposition just +highlighting this second effect is if + + align:start position:0% +highlighting this second effect is if + + + align:start position:0% +highlighting this second effect is if +third degree discrimination doesn't + + align:start position:0% +third degree discrimination doesn't + + + align:start position:0% +third degree discrimination doesn't +increase total output relative to + + align:start position:0% +increase total output relative to + + + align:start position:0% +increase total output relative to +uniform pricing then it reduces social + + align:start position:0% +uniform pricing then it reduces social + + + align:start position:0% +uniform pricing then it reduces social +welfare and this is going to be because + + align:start position:0% +welfare and this is going to be because + + + align:start position:0% +welfare and this is going to be because +if it doesn't increase output it's not + + align:start position:0% +if it doesn't increase output it's not + + + align:start position:0% +if it doesn't increase output it's not +helping with dead weight loss and so if + + align:start position:0% +helping with dead weight loss and so if + + + align:start position:0% +helping with dead weight loss and so if +it's not helping with dead weight loss + + align:start position:0% +it's not helping with dead weight loss + + + align:start position:0% +it's not helping with dead weight loss +it creates misallocation therefore + + align:start position:0% +it creates misallocation therefore + + + align:start position:0% +it creates misallocation therefore +people are worse off um so here's a a + + align:start position:0% +people are worse off um so here's a a + + + align:start position:0% +people are worse off um so here's a a +proof so imagine we start from a + + align:start position:0% +proof so imagine we start from a + + + align:start position:0% +proof so imagine we start from a +situation uh where we have uniform + + align:start position:0% +situation uh where we have uniform + + + align:start position:0% +situation uh where we have uniform +pricing and then we switch to um switch + + align:start position:0% +pricing and then we switch to um switch + + + align:start position:0% +pricing and then we switch to um switch +to discriminatory pricing and I'm going + + align:start position:0% +to discriminatory pricing and I'm going + + + align:start position:0% +to discriminatory pricing and I'm going +to write Delta X1 and Delta + + align:start position:0% +to write Delta X1 and Delta + + + align:start position:0% +to write Delta X1 and Delta +X2 for how does demand + + align:start position:0% +X2 for how does demand + + + align:start position:0% +X2 for how does demand +change uh so I'm going to write you know + + align:start position:0% +change uh so I'm going to write you know + + + align:start position:0% +change uh so I'm going to write you know +Delta XI to be XI under um + + align:start position:0% +Delta XI to be XI under um + + + align:start position:0% +Delta XI to be XI under um +discriminatory pricing minus so under + + align:start position:0% +discriminatory pricing minus so under + + + align:start position:0% +discriminatory pricing minus so under +discriminatory pricing minus the XI + + align:start position:0% +discriminatory pricing minus the XI + + + align:start position:0% +discriminatory pricing minus the XI +under uniform + + align:start position:0% +under uniform + + + align:start position:0% +under uniform +pricing + + align:start position:0% +pricing + + + align:start position:0% +pricing +okay so here's a picture here I guess + + align:start position:0% +okay so here's a picture here I guess + + + align:start position:0% +okay so here's a picture here I guess +I'll use this one instead of drawing a + + align:start position:0% +I'll use this one instead of drawing a + + + align:start position:0% +I'll use this one instead of drawing a +new one on the board so um if we had + + align:start position:0% +new one on the board so um if we had + + + align:start position:0% +new one on the board so um if we had +uniform + + align:start position:0% +uniform + + + align:start position:0% +uniform +pricing um this was going to be the + + align:start position:0% +pricing um this was going to be the + + + align:start position:0% +pricing um this was going to be the +price P star this was be the number of + + align:start position:0% +price P star this was be the number of + + + align:start position:0% +price P star this was be the number of +units sold + + align:start position:0% +units sold + + + align:start position:0% +units sold +xstar and then so this is the student + + align:start position:0% +xstar and then so this is the student + + + align:start position:0% +xstar and then so this is the student +Market these are the loow lower value + + align:start position:0% +Market these are the loow lower value + + + align:start position:0% +Market these are the loow lower value +consumers when you start discriminating + + align:start position:0% +consumers when you start discriminating + + + align:start position:0% +consumers when you start discriminating +you give them a price cut you cut their + + align:start position:0% +you give them a price cut you cut their + + + align:start position:0% +you give them a price cut you cut their +price from P to P star we get a positive + + align:start position:0% +price from P to P star we get a positive + + + align:start position:0% +price from P to P star we get a positive +Delta XI they buy this many units + + align:start position:0% +Delta XI they buy this many units + + + align:start position:0% +Delta XI they buy this many units +instead of this many + + align:start position:0% + + + + align:start position:0% + +units okay so comment is if I think + + align:start position:0% +units okay so comment is if I think + + + align:start position:0% +units okay so comment is if I think +about what is the welfare gain in this + + align:start position:0% +about what is the welfare gain in this + + + align:start position:0% +about what is the welfare gain in this +market the welfare gain in this market + + align:start position:0% +market the welfare gain in this market + + + align:start position:0% +market the welfare gain in this market +is I've reduced dead weight loss by this + + align:start position:0% +is I've reduced dead weight loss by this + + + align:start position:0% +is I've reduced dead weight loss by this +much uh this trapezoid + + align:start position:0% +much uh this trapezoid + + + align:start position:0% +much uh this trapezoid +here okay because all of these units + + align:start position:0% +here okay because all of these units + + + align:start position:0% +here okay because all of these units +that were not formerly getting purchased + + align:start position:0% +that were not formerly getting purchased + + + align:start position:0% +that were not formerly getting purchased +are now getting purchased at the lower + + align:start position:0% +are now getting purchased at the lower + + + align:start position:0% +are now getting purchased at the lower +price and then this is the amount of + + align:start position:0% +price and then this is the amount of + + + align:start position:0% +price and then this is the amount of +surplus that's being + + align:start position:0% +surplus that's being + + + align:start position:0% +surplus that's being +generated uh on each of those units as + + align:start position:0% +generated uh on each of those units as + + + align:start position:0% +generated uh on each of those units as +being purchased so what I get is if you + + align:start position:0% +being purchased so what I get is if you + + + align:start position:0% +being purchased so what I get is if you +think about this trapezoid it's bounded + + align:start position:0% +think about this trapezoid it's bounded + + + align:start position:0% +think about this trapezoid it's bounded +by the big rectangle and the little + + align:start position:0% +by the big rectangle and the little + + + align:start position:0% +by the big rectangle and the little +rectangle and so it tells me that P star + + align:start position:0% +rectangle and so it tells me that P star + + + align:start position:0% +rectangle and so it tells me that P star +minus C time Delta XI that's the big + + align:start position:0% +minus C time Delta XI that's the big + + + align:start position:0% +minus C time Delta XI that's the big +rectangle is bigger than Delta wi is + + align:start position:0% +rectangle is bigger than Delta wi is + + + align:start position:0% +rectangle is bigger than Delta wi is +bigger than P star minus C time Delta XI + + align:start position:0% +bigger than P star minus C time Delta XI + + + align:start position:0% +bigger than P star minus C time Delta XI +so P star minus C is the area of this + + align:start position:0% +so P star minus C is the area of this + + + align:start position:0% +so P star minus C is the area of this +little rectangle well that doesn't quite + + align:start position:0% +little rectangle well that doesn't quite + + + align:start position:0% +little rectangle well that doesn't quite +line up but underneath and then P star + + align:start position:0% +line up but underneath and then P star + + + align:start position:0% +line up but underneath and then P star +minus C is the height of the big + + align:start position:0% +minus C is the height of the big + + + align:start position:0% +minus C is the height of the big +rectangle so the change in welfare is + + align:start position:0% +rectangle so the change in welfare is + + + align:start position:0% +rectangle so the change in welfare is +bounded between those two um notice the + + align:start position:0% +bounded between those two um notice the + + + align:start position:0% +bounded between those two um notice the +same is true like if if there's another + + align:start position:0% +same is true like if if there's another + + + align:start position:0% +same is true like if if there's another +Market where I reduce uh I I raise the + + align:start position:0% +Market where I reduce uh I I raise the + + + align:start position:0% +Market where I reduce uh I I raise the +price and I reduce the demand again the + + align:start position:0% +price and I reduce the demand again the + + + align:start position:0% +price and I reduce the demand again the +loss uh in is going to be this trapezoid + + align:start position:0% +loss uh in is going to be this trapezoid + + + align:start position:0% +loss uh in is going to be this trapezoid +over + + align:start position:0% +over + + + align:start position:0% +over +here and the loss with that trapezoid is + + align:start position:0% +here and the loss with that trapezoid is + + + align:start position:0% +here and the loss with that trapezoid is +going to be bounded between two + + align:start position:0% +going to be bounded between two + + + align:start position:0% +going to be bounded between two +rectangles one being the P star minus C + + align:start position:0% +rectangles one being the P star minus C + + + align:start position:0% +rectangles one being the P star minus C +which is now negative the other being + + align:start position:0% +which is now negative the other being + + + align:start position:0% +which is now negative the other being +the P star minus C which is here and + + align:start position:0% +the P star minus C which is here and + + + align:start position:0% +the P star minus C which is here and +with the negative numbers the same + + align:start position:0% +with the negative numbers the same + + + align:start position:0% +with the negative numbers the same +inequality is still + + align:start position:0% +inequality is still + + + align:start position:0% +inequality is still +true okay you know it's now Pi star + + align:start position:0% +true okay you know it's now Pi star + + + align:start position:0% +true okay you know it's now Pi star +minus C is the big negative number this + + align:start position:0% +minus C is the big negative number this + + + align:start position:0% +minus C is the big negative number this +is the small negative number that it is + + align:start position:0% +is the small negative number that it is + + + align:start position:0% +is the small negative number that it is +in between the big negative number and + + align:start position:0% +in between the big negative number and + + + align:start position:0% +in between the big negative number and +the small negative + + align:start position:0% +the small negative + + + align:start position:0% +the small negative +number + + align:start position:0% +number + + + align:start position:0% +number +okay so if I just now add that across + + align:start position:0% +okay so if I just now add that across + + + align:start position:0% +okay so if I just now add that across +markets summing over I I sum this over + + align:start position:0% +markets summing over I I sum this over + + + align:start position:0% +markets summing over I I sum this over +markets I I get P star minus C * the sum + + align:start position:0% +markets I I get P star minus C * the sum + + + align:start position:0% +markets I I get P star minus C * the sum +of Delta x i is bigger than the change + + align:start position:0% +of Delta x i is bigger than the change + + + align:start position:0% +of Delta x i is bigger than the change +in welfare which is bigger than the sum + + align:start position:0% +in welfare which is bigger than the sum + + + align:start position:0% +in welfare which is bigger than the sum +over I of p i star minus C Delta + + align:start position:0% +over I of p i star minus C Delta + + + align:start position:0% +over I of p i star minus C Delta +XI and the left one is the one that's + + align:start position:0% +XI and the left one is the one that's + + + align:start position:0% +XI and the left one is the one that's +really involved in proving the + + align:start position:0% +really involved in proving the + + + align:start position:0% +really involved in proving the +proposition if the sum of the Delta XI + + align:start position:0% +proposition if the sum of the Delta XI + + + align:start position:0% +proposition if the sum of the Delta XI +star if the sum of the Delta XI is zero + + align:start position:0% +star if the sum of the Delta XI is zero + + + align:start position:0% +star if the sum of the Delta XI is zero +or negative then this is zero or a + + align:start position:0% +or negative then this is zero or a + + + align:start position:0% +or negative then this is zero or a +negative number and it's bigger than the + + align:start position:0% +negative number and it's bigger than the + + + align:start position:0% +negative number and it's bigger than the +change in welfare so the change in + + align:start position:0% +change in welfare so the change in + + + align:start position:0% +change in welfare so the change in +welfare is negative if output hasn't + + align:start position:0% +welfare is negative if output hasn't + + + align:start position:0% +welfare is negative if output hasn't +gone up + + align:start position:0% + + + + align:start position:0% + +okay okay so um some comments on + + align:start position:0% +okay okay so um some comments on + + + align:start position:0% +okay okay so um some comments on +here you + + align:start position:0% +here you + + + align:start position:0% +here you +know you know this is a result about + + align:start position:0% +know you know this is a result about + + + align:start position:0% +know you know this is a result about +welfare it's highlighting that there's + + align:start position:0% +welfare it's highlighting that there's + + + align:start position:0% +welfare it's highlighting that there's +that misallocation of goods sold + + align:start position:0% +that misallocation of goods sold + + + align:start position:0% +that misallocation of goods sold +obviously output can go up if output + + align:start position:0% +obviously output can go up if output + + + align:start position:0% +obviously output can go up if output +goes up and output goes up by enough + + align:start position:0% +goes up and output goes up by enough + + + align:start position:0% +goes up and output goes up by enough +then welfare can be higher with price + + align:start position:0% +then welfare can be higher with price + + + align:start position:0% +then welfare can be higher with price +discrimination um + + align:start position:0% +discrimination um + + + align:start position:0% +discrimination um +one example of that would be uh you know + + align:start position:0% +one example of that would be uh you know + + + align:start position:0% +one example of that would be uh you know +in the model where the you only serve + + align:start position:0% +in the model where the you only serve + + + align:start position:0% +in the model where the you only serve +One Market when you're discriminating + + align:start position:0% +One Market when you're discriminating + + + align:start position:0% +One Market when you're discriminating +then obviously output has gone up by the + + align:start position:0% +then obviously output has gone up by the + + + align:start position:0% +then obviously output has gone up by the +amount at which the students are buying + + align:start position:0% +amount at which the students are buying + + + align:start position:0% +amount at which the students are buying +things um Equity concerns can go either + + align:start position:0% +things um Equity concerns can go either + + + align:start position:0% +things um Equity concerns can go either +way you know we think about you know + + align:start position:0% +way you know we think about you know + + + align:start position:0% +way you know we think about you know +price discrimination also I said is a + + align:start position:0% +price discrimination also I said is a + + + align:start position:0% +price discrimination also I said is a +transfer between groups uh between the + + align:start position:0% +transfer between groups uh between the + + + align:start position:0% +transfer between groups uh between the +high demand group to the low demand + + align:start position:0% +high demand group to the low demand + + + align:start position:0% +high demand group to the low demand +group what we think about that um you + + align:start position:0% +group what we think about that um you + + + align:start position:0% +group what we think about that um you +know depends on on on what on the + + align:start position:0% +know depends on on on what on the + + + align:start position:0% +know depends on on on what on the +example so for instance one one case + + align:start position:0% +example so for instance one one case + + + align:start position:0% +example so for instance one one case +where we might think Equity says we + + align:start position:0% +where we might think Equity says we + + + align:start position:0% +where we might think Equity says we +should discriminate is financial aid for + + align:start position:0% +should discriminate is financial aid for + + + align:start position:0% +should discriminate is financial aid for +your undergraduate colleges in the US + + align:start position:0% +your undergraduate colleges in the US + + + align:start position:0% +your undergraduate colleges in the US +you know colleges charge very very + + align:start position:0% +you know colleges charge very very + + + align:start position:0% +you know colleges charge very very +different prices to different students + + align:start position:0% +different prices to different students + + + align:start position:0% +different prices to different students +they charge much less to low-income + + align:start position:0% +they charge much less to low-income + + + align:start position:0% +they charge much less to low-income +students than they charge to high income + + align:start position:0% +students than they charge to high income + + + align:start position:0% +students than they charge to high income +students we tend to think of like + + align:start position:0% +students we tend to think of like + + + align:start position:0% +students we tend to think of like +Banning price discrimination there would + + align:start position:0% +Banning price discrimination there would + + + align:start position:0% +Banning price discrimination there would +be a bad thing because it would be sort + + align:start position:0% +be a bad thing because it would be sort + + + align:start position:0% +be a bad thing because it would be sort +of raising the prices paid by all the + + align:start position:0% +of raising the prices paid by all the + + + align:start position:0% +of raising the prices paid by all the +low-income students uh and have you know + + align:start position:0% +low-income students uh and have you know + + + align:start position:0% +low-income students uh and have you know +who perhaps have a higher marginal + + align:start position:0% +who perhaps have a higher marginal + + + align:start position:0% +who perhaps have a higher marginal +utility of income uh another example + + align:start position:0% +utility of income uh another example + + + align:start position:0% +utility of income uh another example +though that goes the opposite direction + + align:start position:0% +though that goes the opposite direction + + + align:start position:0% +though that goes the opposite direction +is health insurance if you allow insur + + align:start position:0% +is health insurance if you allow insur + + + align:start position:0% +is health insurance if you allow insur +health insurance companies to + + align:start position:0% +health insurance companies to + + + align:start position:0% +health insurance companies to +discriminate the people who should pay + + align:start position:0% +discriminate the people who should pay + + + align:start position:0% +discriminate the people who should pay +the high price are the sick people and + + align:start position:0% +the high price are the sick people and + + + align:start position:0% +the high price are the sick people and +so if you you know if you um ban + + align:start position:0% +so if you you know if you um ban + + + align:start position:0% +so if you you know if you um ban +discrimination if you allow + + align:start position:0% +discrimination if you allow + + + align:start position:0% +discrimination if you allow +discrimination for health insurance + + align:start position:0% +discrimination for health insurance + + + align:start position:0% +discrimination for health insurance +they're like the health insurance you + + align:start position:0% +they're like the health insurance you + + + align:start position:0% +they're like the health insurance you +know the Discrimination allowing + + align:start position:0% +know the Discrimination allowing + + + align:start position:0% +know the Discrimination allowing +discrimination will be charging high + + align:start position:0% +discrimination will be charging high + + + align:start position:0% +discrimination will be charging high +prices to sick people maybe we don't + + align:start position:0% +prices to sick people maybe we don't + + + align:start position:0% +prices to sick people maybe we don't +want to allow you to charge high prices + + align:start position:0% +want to allow you to charge high prices + + + align:start position:0% +want to allow you to charge high prices +to sick people for Equity + + align:start position:0% + + + + align:start position:0% + +reasons okay um + + align:start position:0% +reasons okay um + + + align:start position:0% +reasons okay um +um here is a Corel the previous theorem + + align:start position:0% +um here is a Corel the previous theorem + + + align:start position:0% +um here is a Corel the previous theorem +which I think is important to know um + + align:start position:0% +which I think is important to know um + + + align:start position:0% +which I think is important to know um +suppose that demands in the Mar in all + + align:start position:0% +suppose that demands in the Mar in all + + + align:start position:0% +suppose that demands in the Mar in all +these submarkets are linear and that all + + align:start position:0% +these submarkets are linear and that all + + + align:start position:0% +these submarkets are linear and that all +markets are served under uniform pricing + + align:start position:0% +markets are served under uniform pricing + + + align:start position:0% +markets are served under uniform pricing +then third degree price discrimination + + align:start position:0% +then third degree price discrimination + + + align:start position:0% +then third degree price discrimination +always reduces + + align:start position:0% +always reduces + + + align:start position:0% +always reduces +welfare so again it why demand should be + + align:start position:0% +welfare so again it why demand should be + + + align:start position:0% +welfare so again it why demand should be +linear I don't know but it's a common + + align:start position:0% +linear I don't know but it's a common + + + align:start position:0% +linear I don't know but it's a common +Benchmark that you might use if you're + + align:start position:0% +Benchmark that you might use if you're + + + align:start position:0% +Benchmark that you might use if you're +first thought of you're studying a + + align:start position:0% +first thought of you're studying a + + + align:start position:0% +first thought of you're studying a +market and this theorem says says that + + align:start position:0% +market and this theorem says says that + + + align:start position:0% +market and this theorem says says that +if the demands are linear then third + + align:start position:0% +if the demands are linear then third + + + align:start position:0% +if the demands are linear then third +degree price discrimination reduces + + align:start position:0% +degree price discrimination reduces + + + align:start position:0% +degree price discrimination reduces +social + + align:start position:0% +social + + + align:start position:0% +social +welfare okay uh what's the argument for + + align:start position:0% +welfare okay uh what's the argument for + + + align:start position:0% +welfare okay uh what's the argument for +that the argument for this is going to + + align:start position:0% +that the argument for this is going to + + + align:start position:0% +that the argument for this is going to +be that uh the sum in the linear model + + align:start position:0% +be that uh the sum in the linear model + + + align:start position:0% +be that uh the sum in the linear model +the sum of the Delta XI is always equal + + align:start position:0% +the sum of the Delta XI is always equal + + + align:start position:0% +the sum of the Delta XI is always equal +to zero and because the sort of output + + align:start position:0% +to zero and because the sort of output + + + align:start position:0% +to zero and because the sort of output +is unchanged then discrimination hurts + + align:start position:0% +is unchanged then discrimination hurts + + + align:start position:0% +is unchanged then discrimination hurts +social welfare okay um how do I show + + align:start position:0% +social welfare okay um how do I show + + + align:start position:0% +social welfare okay um how do I show +that this is just this is algebra so I + + align:start position:0% +that this is just this is algebra so I + + + align:start position:0% +that this is just this is algebra so I +won't go through it but um you know this + + align:start position:0% +won't go through it but um you know this + + + align:start position:0% +won't go through it but um you know this +was something I think I've shown you + + align:start position:0% +was something I think I've shown you + + + align:start position:0% +was something I think I've shown you +over and over again when I've been + + align:start position:0% +over and over again when I've been + + + align:start position:0% +over and over again when I've been +drawing pictures on the board suppose + + align:start position:0% +drawing pictures on the board suppose + + + align:start position:0% +drawing pictures on the board suppose +you have a linear demand + + align:start position:0% +you have a linear demand + + + align:start position:0% +you have a linear demand +curve okay so this is my um uh X of + + align:start position:0% +curve okay so this is my um uh X of + + + align:start position:0% +curve okay so this is my um uh X of +p and this is p on this axis I draw uh + + align:start position:0% +p and this is p on this axis I draw uh + + + align:start position:0% +p and this is p on this axis I draw uh +my cost in here and then I ask what's + + align:start position:0% +my cost in here and then I ask what's + + + align:start position:0% +my cost in here and then I ask what's +the Monopoly price when I set uh what's + + align:start position:0% +the Monopoly price when I set uh what's + + + align:start position:0% +the Monopoly price when I set uh what's +the Monopoly price when I set uh when I + + align:start position:0% +the Monopoly price when I set uh when I + + + align:start position:0% +the Monopoly price when I set uh when I +have cost of c and I have a linear + + align:start position:0% +have cost of c and I have a linear + + + align:start position:0% +have cost of c and I have a linear +demand curve uh it's exactly in the + + align:start position:0% +demand curve uh it's exactly in the + + + align:start position:0% +demand curve uh it's exactly in the +middle so you always the rectangle that + + align:start position:0% +middle so you always the rectangle that + + + align:start position:0% +middle so you always the rectangle that +maximizes this is to set P halfway in + + align:start position:0% +maximizes this is to set P halfway in + + + align:start position:0% +maximizes this is to set P halfway in +between the price that's competitive uh + + align:start position:0% +between the price that's competitive uh + + + align:start position:0% +between the price that's competitive uh +oops what am I doing wrong here um sorry + + align:start position:0% +oops what am I doing wrong here um sorry + + + align:start position:0% +oops what am I doing wrong here um sorry +that's uh that's not what I wanted I + + align:start position:0% +that's uh that's not what I wanted I + + + align:start position:0% +that's uh that's not what I wanted I +wanted X here and P + + align:start position:0% +wanted X here and P + + + align:start position:0% +wanted X here and P +here so um if I set price equal to cost + + align:start position:0% +here so um if I set price equal to cost + + + align:start position:0% +here so um if I set price equal to cost +uh then this is the X in a competitive + + align:start position:0% +uh then this is the X in a competitive + + + align:start position:0% +uh then this is the X in a competitive +market this is the uh + + align:start position:0% +market this is the uh + + + align:start position:0% +market this is the uh +zero X Monopoly equals 12 x + + align:start position:0% +zero X Monopoly equals 12 x + + + align:start position:0% +zero X Monopoly equals 12 x +competitive okay so in a and then this + + align:start position:0% +competitive okay so in a and then this + + + align:start position:0% +competitive okay so in a and then this +is the Monopoly price here so in a if I + + align:start position:0% +is the Monopoly price here so in a if I + + + align:start position:0% +is the Monopoly price here so in a if I +put X on this on the x- axis I'm trying + + align:start position:0% +put X on this on the x- axis I'm trying + + + align:start position:0% +put X on this on the x- axis I'm trying +to figure out the Monopoly price it's + + align:start position:0% +to figure out the Monopoly price it's + + + align:start position:0% +to figure out the Monopoly price it's +always halfway in between zero and what + + align:start position:0% +always halfway in between zero and what + + + align:start position:0% +always halfway in between zero and what +what a competitive firm would charge + + align:start position:0% +what a competitive firm would charge + + + align:start position:0% +what a competitive firm would charge +would would produce okay um so that's so + + align:start position:0% +would would produce okay um so that's so + + + align:start position:0% +would would produce okay um so that's so +you know XI star is just 1/2 of the + + align:start position:0% +you know XI star is just 1/2 of the + + + align:start position:0% +you know XI star is just 1/2 of the +competitive + + align:start position:0% +competitive + + + align:start position:0% +competitive +output so if you sum across markets what + + align:start position:0% +output so if you sum across markets what + + + align:start position:0% +output so if you sum across markets what +you just find is + + align:start position:0% +you just find is + + + align:start position:0% +you just find is +that you know the sum of the XIs is just + + align:start position:0% +that you know the sum of the XIs is just + + + align:start position:0% +that you know the sum of the XIs is just +one/ half of the sum of what you'd get + + align:start position:0% +one/ half of the sum of what you'd get + + + align:start position:0% +one/ half of the sum of what you'd get +under perfect competition in in each + + align:start position:0% +under perfect competition in in each + + + align:start position:0% +under perfect competition in in each +market together and if you think about + + align:start position:0% +market together and if you think about + + + align:start position:0% +market together and if you think about +perfect competition with all the markets + + align:start position:0% +perfect competition with all the markets + + + align:start position:0% +perfect competition with all the markets +combined you set p will see that's still + + align:start position:0% +combined you set p will see that's still + + + align:start position:0% +combined you set p will see that's still +one half of what you get with perfect + + align:start position:0% +one half of what you get with perfect + + + align:start position:0% +one half of what you get with perfect +competition in all + + align:start position:0% +competition in all + + + align:start position:0% +competition in all +markets so if I combine the markets + + align:start position:0% +markets so if I combine the markets + + + align:start position:0% +markets so if I combine the markets +together I get one half of the + + align:start position:0% +together I get one half of the + + + align:start position:0% +together I get one half of the +competitive market as a total output and + + align:start position:0% +competitive market as a total output and + + + align:start position:0% +competitive market as a total output and +if I separate the markets I get one half + + align:start position:0% +if I separate the markets I get one half + + + align:start position:0% +if I separate the markets I get one half +of the competitive output in Market one + + align:start position:0% +of the competitive output in Market one + + + align:start position:0% +of the competitive output in Market one +plus one half of the competitive output + + align:start position:0% +plus one half of the competitive output + + + align:start position:0% +plus one half of the competitive output +in Market two plus one half of the + + align:start position:0% +in Market two plus one half of the + + + align:start position:0% +in Market two plus one half of the +competitive output in Market n that's + + align:start position:0% +competitive output in Market n that's + + + align:start position:0% +competitive output in Market n that's +just you know because the competitive + + align:start position:0% +just you know because the competitive + + + align:start position:0% +just you know because the competitive +output is always the demand at Price + + align:start position:0% +output is always the demand at Price + + + align:start position:0% +output is always the demand at Price +equal to C those two things are equal + + align:start position:0% +equal to C those two things are equal + + + align:start position:0% +equal to C those two things are equal +right so the sum of one/ half of the + + align:start position:0% +right so the sum of one/ half of the + + + align:start position:0% +right so the sum of one/ half of the +competitive outputs Market by market is + + align:start position:0% +competitive outputs Market by market is + + + align:start position:0% +competitive outputs Market by market is +1/ half of the competitive output in all + + align:start position:0% +1/ half of the competitive output in all + + + align:start position:0% +1/ half of the competitive output in all +the markets + + align:start position:0% +the markets + + + align:start position:0% +the markets +together so with linear demand curves + + align:start position:0% +together so with linear demand curves + + + align:start position:0% +together so with linear demand curves +because of this feature that you sell + + align:start position:0% +because of this feature that you sell + + + align:start position:0% +because of this feature that you sell +exactly half the competitive + + align:start position:0% +exactly half the competitive + + + align:start position:0% +exactly half the competitive +output output is unchanged under under + + align:start position:0% +output output is unchanged under under + + + align:start position:0% +output output is unchanged under under +um uh output is unchanged if you allow + + align:start position:0% +um uh output is unchanged if you allow + + + align:start position:0% +um uh output is unchanged if you allow +discrimination therefore discrimination + + align:start position:0% +discrimination therefore discrimination + + + align:start position:0% +discrimination therefore discrimination +reduces social + + align:start position:0% +reduces social + + + align:start position:0% +reduces social +welfare okay + + align:start position:0% +welfare okay + + + align:start position:0% +welfare okay +um I I I cover this theorem because I + + align:start position:0% +um I I I cover this theorem because I + + + align:start position:0% +um I I I cover this theorem because I +think it highlights a very general + + align:start position:0% +think it highlights a very general + + + align:start position:0% +think it highlights a very general +concern which is you know often people + + align:start position:0% +concern which is you know often people + + + align:start position:0% +concern which is you know often people +when they're doing structural estimation + + align:start position:0% +when they're doing structural estimation + + + align:start position:0% +when they're doing structural estimation +of models they assume some theoretical + + align:start position:0% +of models they assume some theoretical + + + align:start position:0% +of models they assume some theoretical +structure whether on the demand curves + + align:start position:0% +structure whether on the demand curves + + + align:start position:0% +structure whether on the demand curves +or on the utility functions and then + + align:start position:0% +or on the utility functions and then + + + align:start position:0% +or on the utility functions and then +they estimate some number of parameters + + align:start position:0% +they estimate some number of parameters + + + align:start position:0% +they estimate some number of parameters +and then they comment on something of + + align:start position:0% +and then they comment on something of + + + align:start position:0% +and then they comment on something of +Interest so you know this gives you an + + align:start position:0% +Interest so you know this gives you an + + + align:start position:0% +Interest so you know this gives you an +example you know suppose someone comes + + align:start position:0% +example you know suppose someone comes + + + align:start position:0% +example you know suppose someone comes +in and say okay I'm going to write a + + align:start position:0% +in and say okay I'm going to write a + + + align:start position:0% +in and say okay I'm going to write a +paper I'm concerned about uh price + + align:start position:0% +paper I'm concerned about uh price + + + align:start position:0% +paper I'm concerned about uh price +discrimination in uh health Insurance + + align:start position:0% +discrimination in uh health Insurance + + + align:start position:0% +discrimination in uh health Insurance +markets I'm going to imagine that + + align:start position:0% +markets I'm going to imagine that + + + align:start position:0% +markets I'm going to imagine that +instead of being allowed to discriminate + + align:start position:0% +instead of being allowed to discriminate + + + align:start position:0% +instead of being allowed to discriminate +and charge different Health rated prices + + align:start position:0% +and charge different Health rated prices + + + align:start position:0% +and charge different Health rated prices +I'm going to charge equal prices in all + + align:start position:0% +I'm going to charge equal prices in all + + + align:start position:0% +I'm going to charge equal prices in all +market and I'm going to see what's the + + align:start position:0% +market and I'm going to see what's the + + + align:start position:0% +market and I'm going to see what's the +effect on social welfare of forcing The + + align:start position:0% +effect on social welfare of forcing The + + + align:start position:0% +effect on social welfare of forcing The +Firm to charge a uniform price across + + align:start position:0% +Firm to charge a uniform price across + + + align:start position:0% +Firm to charge a uniform price across +all classes of consumers instead of + + align:start position:0% +all classes of consumers instead of + + + align:start position:0% +all classes of consumers instead of +discriminating by consumers and then the + + align:start position:0% +discriminating by consumers and then the + + + align:start position:0% +discriminating by consumers and then the +student tells me oh and I'm going to + + align:start position:0% +student tells me oh and I'm going to + + + align:start position:0% +student tells me oh and I'm going to +just for Simplicity I'm going to assume + + align:start position:0% +just for Simplicity I'm going to assume + + + align:start position:0% +just for Simplicity I'm going to assume +that demand curves are linear in every + + align:start position:0% +that demand curves are linear in every + + + align:start position:0% +that demand curves are linear in every +Market well then I already know what the + + align:start position:0% +Market well then I already know what the + + + align:start position:0% +Market well then I already know what the +results of the paper are right I know + + align:start position:0% +results of the paper are right I know + + + align:start position:0% +results of the paper are right I know +that the paper is going to say that + + align:start position:0% +that the paper is going to say that + + + align:start position:0% +that the paper is going to say that +charging a uniform price has increased + + align:start position:0% +charging a uniform price has increased + + + align:start position:0% +charging a uniform price has increased +social welfare and it's increased social + + align:start position:0% +social welfare and it's increased social + + + align:start position:0% +social welfare and it's increased social +welfare because it's implicit in this + + align:start position:0% +welfare because it's implicit in this + + + align:start position:0% +welfare because it's implicit in this +demand specification that + + align:start position:0% +demand specification that + + + align:start position:0% +demand specification that +um you increase social welfare when when + + align:start position:0% +um you increase social welfare when when + + + align:start position:0% +um you increase social welfare when when +you discriminate you when you when you + + align:start position:0% +you discriminate you when you when you + + + align:start position:0% +you discriminate you when you when you +ban discrimination uh and I think it's + + align:start position:0% +ban discrimination uh and I think it's + + + align:start position:0% +ban discrimination uh and I think it's +just it's it's you it's a very important + + align:start position:0% +just it's it's you it's a very important + + + align:start position:0% +just it's it's you it's a very important +thing to know that if you're thinking + + align:start position:0% +thing to know that if you're thinking + + + align:start position:0% +thing to know that if you're thinking +about writing down a model investigate + + align:start position:0% +about writing down a model investigate + + + align:start position:0% +about writing down a model investigate +some question you have to know whether + + align:start position:0% +some question you have to know whether + + + align:start position:0% +some question you have to know whether +the answer is already determined by this + + align:start position:0% +the answer is already determined by this + + + align:start position:0% +the answer is already determined by this +functional form you've chosen you know + + align:start position:0% +functional form you've chosen you know + + + align:start position:0% +functional form you've chosen you know +and again why is linear demand curves + + align:start position:0% +and again why is linear demand curves + + + align:start position:0% +and again why is linear demand curves +not right you know + + align:start position:0% +not right you know + + + align:start position:0% +not right you know +in part you know social welfare is about + + align:start position:0% +in part you know social welfare is about + + + align:start position:0% +in part you know social welfare is about +how much you know utility people are + + align:start position:0% +how much you know utility people are + + + align:start position:0% +how much you know utility people are +getting Beyond you know what what's the + + align:start position:0% +getting Beyond you know what what's the + + + align:start position:0% +getting Beyond you know what what's the +consumer surplus that people are + + align:start position:0% +consumer surplus that people are + + + align:start position:0% +consumer surplus that people are +getting you know that's very different + + align:start position:0% +getting you know that's very different + + + align:start position:0% +getting you know that's very different +if demand looks like this and there's + + align:start position:0% +if demand looks like this and there's + + + align:start position:0% +if demand looks like this and there's +some people who really like the product + + align:start position:0% +some people who really like the product + + + align:start position:0% +some people who really like the product +or if it goes like that and there's + + align:start position:0% +or if it goes like that and there's + + + align:start position:0% +or if it goes like that and there's +nobody who likes it very much you + + align:start position:0% +nobody who likes it very much you + + + align:start position:0% +nobody who likes it very much you +know some sense prices are determined by + + align:start position:0% +know some sense prices are determined by + + + align:start position:0% +know some sense prices are determined by +elasticities which are just determine + + align:start position:0% +elasticities which are just determine + + + align:start position:0% +elasticities which are just determine +these slopes here if you actually want + + align:start position:0% +these slopes here if you actually want + + + align:start position:0% +these slopes here if you actually want +to understand whether it's increasing or + + align:start position:0% +to understand whether it's increasing or + + + align:start position:0% +to understand whether it's increasing or +decreasing well welfare you'd have to be + + align:start position:0% +decreasing well welfare you'd have to be + + + align:start position:0% +decreasing well welfare you'd have to be +able to think about can I estimate these + + align:start position:0% +able to think about can I estimate these + + + align:start position:0% +able to think about can I estimate these +things like what's this how much + + align:start position:0% +things like what's this how much + + + align:start position:0% +things like what's this how much +consumer surplus is here relative to + + align:start position:0% +consumer surplus is here relative to + + + align:start position:0% +consumer surplus is here relative to +what the monopolis Dodge which is based + + align:start position:0% +what the monopolis Dodge which is based + + + align:start position:0% +what the monopolis Dodge which is based +on the elasticity at this one point the + + align:start position:0% +on the elasticity at this one point the + + + align:start position:0% +on the elasticity at this one point the +monopolist is choosing um and and you + + align:start position:0% +monopolist is choosing um and and you + + + align:start position:0% +monopolist is choosing um and and you +know you need to be aware that this + + align:start position:0% +know you need to be aware that this + + + align:start position:0% +know you need to be aware that this +assumption is is sort of picking the + + align:start position:0% +assumption is is sort of picking the + + + align:start position:0% +assumption is is sort of picking the +answer for + + align:start position:0% +answer for + + + align:start position:0% +answer for +you I mean I don't know that it's not a + + align:start position:0% +you I mean I don't know that it's not a + + + align:start position:0% +you I mean I don't know that it's not a +you know it's it um it may be a useful + + align:start position:0% +you know it's it um it may be a useful + + + align:start position:0% +you know it's it um it may be a useful +sort of rule I'm just to keep in mind if + + align:start position:0% +sort of rule I'm just to keep in mind if + + + align:start position:0% +sort of rule I'm just to keep in mind if +like if linear model there's no effect + + align:start position:0% +like if linear model there's no effect + + + align:start position:0% +like if linear model there's no effect +on aggregate output maybe we'd think + + align:start position:0% +on aggregate output maybe we'd think + + + align:start position:0% +on aggregate output maybe we'd think +that aggregate output effects typically + + align:start position:0% +that aggregate output effects typically + + + align:start position:0% +that aggregate output effects typically +are small uh but again it it's all based + + align:start position:0% +are small uh but again it it's all based + + + align:start position:0% +are small uh but again it it's all based +in the linearity + + align:start position:0% + + + + align:start position:0% + +there okay uh what is general um so + + align:start position:0% +there okay uh what is general um so + + + align:start position:0% +there okay uh what is general um so +there's a recent paper by uh Bergman + + align:start position:0% +there's a recent paper by uh Bergman + + + align:start position:0% +there's a recent paper by uh Bergman +Brooks and Morris that asked this + + align:start position:0% +Brooks and Morris that asked this + + + align:start position:0% +Brooks and Morris that asked this +question what happen you know what can + + align:start position:0% +question what happen you know what can + + + align:start position:0% +question what happen you know what can +we say generally about when you allow a + + align:start position:0% +we say generally about when you allow a + + + align:start position:0% +we say generally about when you allow a +monopolis to discriminate will welfare + + align:start position:0% +monopolis to discriminate will welfare + + + align:start position:0% +monopolis to discriminate will welfare +you know we know that you allow a + + align:start position:0% +you know we know that you allow a + + + align:start position:0% +you know we know that you allow a +monopolis discriminate profits go up + + align:start position:0% +monopolis discriminate profits go up + + + align:start position:0% +monopolis discriminate profits go up +will social welfare go up will consumer + + align:start position:0% +will social welfare go up will consumer + + + align:start position:0% +will social welfare go up will consumer +surplus go up or down what are the + + align:start position:0% +surplus go up or down what are the + + + align:start position:0% +surplus go up or down what are the +tradeoffs and what Bergman Brooks and + + align:start position:0% +tradeoffs and what Bergman Brooks and + + + align:start position:0% +tradeoffs and what Bergman Brooks and +Morris note is that it depends on what + + align:start position:0% +Morris note is that it depends on what + + + align:start position:0% +Morris note is that it depends on what +information the monopolist has about the + + align:start position:0% +information the monopolist has about the + + + align:start position:0% +information the monopolist has about the +consumers so let's think about sort of + + align:start position:0% +consumers so let's think about sort of + + + align:start position:0% +consumers so let's think about sort of +standard example where the consumer's + + align:start position:0% +standard example where the consumer's + + + align:start position:0% +standard example where the consumer's +values are uniform 01 C equals + + align:start position:0% +values are uniform 01 C equals + + + align:start position:0% +values are uniform 01 C equals +0 if the monopolist has no information + + align:start position:0% +0 if the monopolist has no information + + + align:start position:0% +0 if the monopolist has no information +about the + + align:start position:0% +about the + + + align:start position:0% +about the +consumers then doesn't matter if you + + align:start position:0% +consumers then doesn't matter if you + + + align:start position:0% +consumers then doesn't matter if you +allow them to discriminate he has no + + align:start position:0% +allow them to discriminate he has no + + + align:start position:0% +allow them to discriminate he has no +information on which to discriminate + + align:start position:0% +information on which to discriminate + + + align:start position:0% +information on which to discriminate +what's the monopolis going to + + align:start position:0% +what's the monopolis going to + + + align:start position:0% +what's the monopolis going to +do is going your standard Monopoly + + align:start position:0% +do is going your standard Monopoly + + + align:start position:0% +do is going your standard Monopoly +pricing P equals a half profit is a + + align:start position:0% +pricing P equals a half profit is a + + + align:start position:0% +pricing P equals a half profit is a +quarter consumer surplus is + + align:start position:0% +quarter consumer surplus is + + + align:start position:0% +quarter consumer surplus is +1/8 in their figure that's this point + + align:start position:0% +1/8 in their figure that's this point + + + align:start position:0% +1/8 in their figure that's this point +here consumer surplus is 1/8 uh producer + + align:start position:0% +here consumer surplus is 1/8 uh producer + + + align:start position:0% +here consumer surplus is 1/8 uh producer +Surplus is uh one + + align:start position:0% +Surplus is uh one + + + align:start position:0% +Surplus is uh one +quarter okay + + align:start position:0% +quarter okay + + + align:start position:0% +quarter okay +um one extreme is what if the monopolist + + align:start position:0% +um one extreme is what if the monopolist + + + align:start position:0% +um one extreme is what if the monopolist +can perform first-degree price + + align:start position:0% +can perform first-degree price + + + align:start position:0% +can perform first-degree price +discrimination the monopolist know know + + align:start position:0% +discrimination the monopolist know know + + + align:start position:0% +discrimination the monopolist know know +everything if monopolis knows everything + + align:start position:0% +everything if monopolis knows everything + + + align:start position:0% +everything if monopolis knows everything +then the monopolis charges each consumer + + align:start position:0% +then the monopolis charges each consumer + + + align:start position:0% +then the monopolis charges each consumer +their full value we know there that the + + align:start position:0% +their full value we know there that the + + + align:start position:0% +their full value we know there that the +monopolis profit has gone up + + align:start position:0% +monopolis profit has gone up + + + align:start position:0% +monopolis profit has gone up +tremendously uh and we know that the + + align:start position:0% +tremendously uh and we know that the + + + align:start position:0% +tremendously uh and we know that the +consumer surplus has been driven to zero + + align:start position:0% +consumer surplus has been driven to zero + + + align:start position:0% +consumer surplus has been driven to zero +so here if the monopolis knows + + align:start position:0% +so here if the monopolis knows + + + align:start position:0% +so here if the monopolis knows +everything about the consumers then the + + align:start position:0% +everything about the consumers then the + + + align:start position:0% +everything about the consumers then the +answer to what happens if you allow + + align:start position:0% +answer to what happens if you allow + + + align:start position:0% +answer to what happens if you allow +discrimination is profit goes up uh + + align:start position:0% +discrimination is profit goes up uh + + + align:start position:0% +discrimination is profit goes up uh +profit goes up consumer surplus goes + + align:start position:0% +profit goes up consumer surplus goes + + + align:start position:0% +profit goes up consumer surplus goes +down social welfare goes up because + + align:start position:0% +down social welfare goes up because + + + align:start position:0% +down social welfare goes up because +we're above the 45 Dee line okay um but + + align:start position:0% +we're above the 45 Dee line okay um but + + + align:start position:0% +we're above the 45 Dee line okay um but +they not in the paper you know thinking + + align:start position:0% +they not in the paper you know thinking + + + align:start position:0% +they not in the paper you know thinking +like same kind of reasoning as russler + + align:start position:0% +like same kind of reasoning as russler + + + align:start position:0% +like same kind of reasoning as russler +and Zenus there are other situations + + align:start position:0% +and Zenus there are other situations + + + align:start position:0% +and Zenus there are other situations +where consumer surplus and profit will + + align:start position:0% +where consumer surplus and profit will + + + align:start position:0% +where consumer surplus and profit will +also go up if you allow the monopolis to + + align:start position:0% +also go up if you allow the monopolis to + + + align:start position:0% +also go up if you allow the monopolis to +discriminate they both go up here's + + align:start position:0% +discriminate they both go up here's + + + align:start position:0% +discriminate they both go up here's +their sort of interesting and clever + + align:start position:0% +their sort of interesting and clever + + + align:start position:0% +their sort of interesting and clever +example so suppose what we have is you + + align:start position:0% +example so suppose what we have is you + + + align:start position:0% +example so suppose what we have is you +know we have this sort of demand curve + + align:start position:0% +know we have this sort of demand curve + + + align:start position:0% +know we have this sort of demand curve +that comes from there + + align:start position:0% +that comes from there + + + align:start position:0% +that comes from there +being consumers with every different you + + align:start position:0% +being consumers with every different you + + + align:start position:0% +being consumers with every different you +know these sort of subpopulations of + + align:start position:0% +know these sort of subpopulations of + + + align:start position:0% +know these sort of subpopulations of +consumers with every different + + align:start position:0% +consumers with every different + + + align:start position:0% +consumers with every different +value suppose what the monopolis gets is + + align:start position:0% +value suppose what the monopolis gets is + + + align:start position:0% +value suppose what the monopolis gets is +this signal that says one of two things + + align:start position:0% +this signal that says one of two things + + + align:start position:0% +this signal that says one of two things +is true + + align:start position:0% +is true + + + align:start position:0% +is true +either uh the consumer is uh someone + + align:start position:0% +either uh the consumer is uh someone + + + align:start position:0% +either uh the consumer is uh someone +whose + + align:start position:0% +whose + + + align:start position:0% +whose +value so this is going to be my um f of + + align:start position:0% +value so this is going to be my um f of + + + align:start position:0% +value so this is going to be my um f of +the given my signal the consumer either + + align:start position:0% +the given my signal the consumer either + + + align:start position:0% +the given my signal the consumer either +has a value between 01 and + + align:start position:0% +has a value between 01 and + + + align:start position:0% +has a value between 01 and +02 or the consumer's value is with small + + align:start position:0% +02 or the consumer's value is with small + + + align:start position:0% +02 or the consumer's value is with small +probability drwn from a uniform + + align:start position:0% +probability drwn from a uniform + + + align:start position:0% +probability drwn from a uniform +Distribution on + + align:start position:0% +Distribution on + + + align:start position:0% +Distribution on +0.02 up to + + align:start position:0% +0.02 up to + + + align:start position:0% +0.02 up to +one so this signal means there's no way + + align:start position:0% +one so this signal means there's no way + + + align:start position:0% +one so this signal means there's no way +their value is between 0 and .01 very + + align:start position:0% +their value is between 0 and .01 very + + + align:start position:0% +their value is between 0 and .01 very +likely it's between you know all + + align:start position:0% +likely it's between you know all + + + align:start position:0% +likely it's between you know all +consumers with values in this range will + + align:start position:0% +consumers with values in this range will + + + align:start position:0% +consumers with values in this range will +have that signal and then there's some + + align:start position:0% +have that signal and then there's some + + + align:start position:0% +have that signal and then there's some +small POS possibility of a false + + align:start position:0% +small POS possibility of a false + + + align:start position:0% +small POS possibility of a false +positive and it's actually a consumer + + align:start position:0% +positive and it's actually a consumer + + + align:start position:0% +positive and it's actually a consumer +the value drawn from here + + align:start position:0% +the value drawn from here + + + align:start position:0% +the value drawn from here +okay um what does your profit look + + align:start position:0% +okay um what does your profit look + + + align:start position:0% +okay um what does your profit look +like well your profit uh + + align:start position:0% +like well your profit uh + + + align:start position:0% +like well your profit uh +is increasing in price until you get to + + align:start position:0% + + + + align:start position:0% + +0.01 as you drop your price from 0.01 to + + align:start position:0% +0.01 as you drop your price from 0.01 to + + + align:start position:0% +0.01 as you drop your price from 0.01 to +0.02 per consumer prop you lose many + + align:start position:0% +0.02 per consumer prop you lose many + + + align:start position:0% +0.02 per consumer prop you lose many +customers + + align:start position:0% + + + + align:start position:0% + +um but then once you're you raise your + + align:start position:0% +um but then once you're you raise your + + + align:start position:0% +um but then once you're you raise your +price you then are just making more + + align:start position:0% +price you then are just making more + + + align:start position:0% +price you then are just making more +money now now all these consumers have + + align:start position:0% +money now now all these consumers have + + + align:start position:0% +money now now all these consumers have +gone away you're making more money off + + align:start position:0% +gone away you're making more money off + + + align:start position:0% +gone away you're making more money off +these consumers as you raise your price + + align:start position:0% +these consumers as you raise your price + + + align:start position:0% +these consumers as you raise your price +and you have you know something that + + align:start position:0% +and you have you know something that + + + align:start position:0% +and you have you know something that +looks like this right it's something + + align:start position:0% +looks like this right it's something + + + align:start position:0% +looks like this right it's something +like in this subp population it's like + + align:start position:0% +like in this subp population it's like + + + align:start position:0% +like in this subp population it's like +your standard Monopoly + + align:start position:0% +your standard Monopoly + + + align:start position:0% +your standard Monopoly +pricing and what they note is that by + + align:start position:0% +pricing and what they note is that by + + + align:start position:0% +pricing and what they note is that by +very clever choice of how many people to + + align:start position:0% +very clever choice of how many people to + + + align:start position:0% +very clever choice of how many people to +put in this + + align:start position:0% +put in this + + + align:start position:0% +put in this +band I can make it so that this profit + + align:start position:0% +band I can make it so that this profit + + + align:start position:0% +band I can make it so that this profit +level + + align:start position:0% +level + + + align:start position:0% +level +and this profit level + + align:start position:0% +and this profit level + + + align:start position:0% +and this profit level +coincide so I'm exactly in difference + + align:start position:0% +coincide so I'm exactly in difference + + + align:start position:0% +coincide so I'm exactly in difference +between two prices + + align:start position:0% +between two prices + + + align:start position:0% +between two prices +01 or my standard 0.5 + + align:start position:0% + + + + align:start position:0% + +price and so if you give the monopolis + + align:start position:0% +price and so if you give the monopolis + + + align:start position:0% +price and so if you give the monopolis +to signal that says there's a little a + + align:start position:0% +to signal that says there's a little a + + + align:start position:0% +to signal that says there's a little a +few consumers with this you know few + + align:start position:0% +few consumers with this you know few + + + align:start position:0% +few consumers with this you know few +consu there's some you know here's this + + align:start position:0% +consu there's some you know here's this + + + align:start position:0% +consu there's some you know here's this +signal you get this signal or you you + + align:start position:0% +signal you get this signal or you you + + + align:start position:0% +signal you get this signal or you you +like you get this signal occasionally + + align:start position:0% +like you get this signal occasionally + + + align:start position:0% +like you get this signal occasionally +and then the rest of time you just get + + align:start position:0% +and then the rest of time you just get + + + align:start position:0% +and then the rest of time you just get +the regular signal it's a regular + + align:start position:0% +the regular signal it's a regular + + + align:start position:0% +the regular signal it's a regular +customer then when you get this + + align:start position:0% +customer then when you get this + + + align:start position:0% +customer then when you get this +signal uh you know and then you have the + + align:start position:0% +signal uh you know and then you have the + + + align:start position:0% +signal uh you know and then you have the +other signal that tells you the + + align:start position:0% +other signal that tells you the + + + align:start position:0% +other signal that tells you the +complimentary signal would tell me that + + align:start position:0% +complimentary signal would tell me that + + + align:start position:0% +complimentary signal would tell me that +you know the consumer might have a value + + align:start position:0% +you know the consumer might have a value + + + align:start position:0% +you know the consumer might have a value +here uh uh no chance to have a value + + align:start position:0% +here uh uh no chance to have a value + + + align:start position:0% +here uh uh no chance to have a value +here and then they may have a value like + + align:start position:0% +here and then they may have a value like + + + align:start position:0% +here and then they may have a value like +that so that's my complimentary signal + + align:start position:0% +that so that's my complimentary signal + + + align:start position:0% +that so that's my complimentary signal +it's either this signal or this signal + + align:start position:0% +it's either this signal or this signal + + + align:start position:0% +it's either this signal or this signal +okay well when I get this + + align:start position:0% +okay well when I get this + + + align:start position:0% +okay well when I get this +signal my optimal price is p equal + + align:start position:0% +signal my optimal price is p equal + + + align:start position:0% +signal my optimal price is p equal +.5 when I get this signal I'm in + + align:start position:0% +.5 when I get this signal I'm in + + + align:start position:0% +.5 when I get this signal I'm in +different between 0.01 and 0.5 so if I + + align:start position:0% +different between 0.01 and 0.5 so if I + + + align:start position:0% +different between 0.01 and 0.5 so if I +charge 0.01 when I get this signal I've + + align:start position:0% +charge 0.01 when I get this signal I've + + + align:start position:0% +charge 0.01 when I get this signal I've +just created consumer surplus and I + + align:start position:0% +just created consumer surplus and I + + + align:start position:0% +just created consumer surplus and I +haven't affected profits at all so what + + align:start position:0% +haven't affected profits at all so what + + + align:start position:0% +haven't affected profits at all so what +I'm able to do is move along this line + + align:start position:0% +I'm able to do is move along this line + + + align:start position:0% +I'm able to do is move along this line +and just keep profits exactly at Point + + align:start position:0% +and just keep profits exactly at Point + + + align:start position:0% +and just keep profits exactly at Point +at the same thing I get charging 0.5 to + + align:start position:0% +at the same thing I get charging 0.5 to + + + align:start position:0% +at the same thing I get charging 0.5 to +everyone and give consumers + + align:start position:0% +everyone and give consumers + + + align:start position:0% +everyone and give consumers +Surplus and then you could think about + + align:start position:0% +Surplus and then you could think about + + + align:start position:0% +Surplus and then you could think about +this I could do the same argument adding + + align:start position:0% +this I could do the same argument adding + + + align:start position:0% +this I could do the same argument adding +more and more such signals I can do a + + align:start position:0% +more and more such signals I can do a + + + align:start position:0% +more and more such signals I can do a +0.02 to 0.03 signal a 03 to 04 4 04 to + + align:start position:0% +0.02 to 0.03 signal a 03 to 04 4 04 to + + + align:start position:0% +0.02 to 0.03 signal a 03 to 04 4 04 to +05 I can give the monopolis many many + + align:start position:0% +05 I can give the monopolis many many + + + align:start position:0% +05 I can give the monopolis many many +many signals and just by doing that give + + align:start position:0% +many signals and just by doing that give + + + align:start position:0% +many signals and just by doing that give +the monopolis to have more and more + + align:start position:0% +the monopolis to have more and more + + + align:start position:0% +the monopolis to have more and more +groups to which it offers a + + align:start position:0% +groups to which it offers a + + + align:start position:0% +groups to which it offers a +discount uh and increase consumer + + align:start position:0% +discount uh and increase consumer + + + align:start position:0% +discount uh and increase consumer +surplus up to some point + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +um you know it turns out I can also so + + align:start position:0% +um you know it turns out I can also so + + + align:start position:0% +um you know it turns out I can also so +this is you know that's their cover + + align:start position:0% +this is you know that's their cover + + + align:start position:0% +this is you know that's their cover +constructure for how I get from here out + + align:start position:0% +constructure for how I get from here out + + + align:start position:0% +constructure for how I get from here out +going in this direction turns I can also + + align:start position:0% +going in this direction turns I can also + + + align:start position:0% +going in this direction turns I can also +do the same kind of cever construction + + align:start position:0% +do the same kind of cever construction + + + align:start position:0% +do the same kind of cever construction +and go in that direction I can make the + + align:start position:0% +and go in that direction I can make the + + + align:start position:0% +and go in that direction I can make the +monopolist indifferent between 0.5 and a + + align:start position:0% +monopolist indifferent between 0.5 and a + + + align:start position:0% +monopolist indifferent between 0.5 and a +very high price and then once the + + align:start position:0% +very high price and then once the + + + align:start position:0% +very high price and then once the +anopolis difference between 0.5 and a + + align:start position:0% +anopolis difference between 0.5 and a + + + align:start position:0% +anopolis difference between 0.5 and a +very high price they start charging the + + align:start position:0% +very high price they start charging the + + + align:start position:0% +very high price they start charging the +high price to all these sign like + + align:start position:0% +high price to all these sign like + + + align:start position:0% +high price to all these sign like +there's a special signal that tells you + + align:start position:0% +there's a special signal that tells you + + + align:start position:0% +there's a special signal that tells you +that um there's some chance there's this + + align:start position:0% +that um there's some chance there's this + + + align:start position:0% +that um there's some chance there's this +excess probability that the value is up + + align:start position:0% +excess probability that the value is up + + + align:start position:0% +excess probability that the value is up +here and otherwise it's uniform when you + + align:start position:0% +here and otherwise it's uniform when you + + + align:start position:0% +here and otherwise it's uniform when you +get those signals people some sometimes + + align:start position:0% +get those signals people some sometimes + + + align:start position:0% +get those signals people some sometimes +you know they're in charging the very + + align:start position:0% +you know they're in charging the very + + + align:start position:0% +you know they're in charging the very +high price and selling to these + + align:start position:0% +high price and selling to these + + + align:start position:0% +high price and selling to these +consumers only or setting the 0. five + + align:start position:0% +consumers only or setting the 0. five + + + align:start position:0% +consumers only or setting the 0. five +price and so by using other signals I + + align:start position:0% +price and so by using other signals I + + + align:start position:0% +price and so by using other signals I +can you know keep the profit you know + + align:start position:0% +can you know keep the profit you know + + + align:start position:0% +can you know keep the profit you know +here the profit went up as consumer + + align:start position:0% +here the profit went up as consumer + + + align:start position:0% +here the profit went up as consumer +service went to zero here I can sort of + + align:start position:0% +service went to zero here I can sort of + + + align:start position:0% +service went to zero here I can sort of +have the monopolis profit go up go stay + + align:start position:0% +have the monopolis profit go up go stay + + + align:start position:0% +have the monopolis profit go up go stay +the same and drive consumer surplus to + + align:start position:0% +the same and drive consumer surplus to + + + align:start position:0% +the same and drive consumer surplus to +zero uh and their you know their General + + align:start position:0% +zero uh and their you know their General + + + align:start position:0% +zero uh and their you know their General +result is by this choice of clever + + align:start position:0% +result is by this choice of clever + + + align:start position:0% +result is by this choice of clever +distributions of signals what they show + + align:start position:0% +distributions of signals what they show + + + align:start position:0% +distributions of signals what they show +is that really what Monopoly price what + + align:start position:0% +is that really what Monopoly price what + + + align:start position:0% +is that really what Monopoly price what +price discrimination does to consumer + + align:start position:0% +price discrimination does to consumer + + + align:start position:0% +price discrimination does to consumer +surplus and to social welfare is just + + align:start position:0% +surplus and to social welfare is just + + + align:start position:0% +surplus and to social welfare is just +totally + + align:start position:0% +totally + + + align:start position:0% +totally +indeterminate if the monopolist has some + + align:start position:0% +indeterminate if the monopolist has some + + + align:start position:0% +indeterminate if the monopolist has some +types of information + + align:start position:0% +types of information + + + align:start position:0% +types of information +structures um you know it always raises + + align:start position:0% +structures um you know it always raises + + + align:start position:0% +structures um you know it always raises +the Monopoly profit but it can raise or + + align:start position:0% +the Monopoly profit but it can raise or + + + align:start position:0% +the Monopoly profit but it can raise or +lower consumer surplus and because it + + align:start position:0% +lower consumer surplus and because it + + + align:start position:0% +lower consumer surplus and because it +can go above or below this 45 degree + + align:start position:0% +can go above or below this 45 degree + + + align:start position:0% +can go above or below this 45 degree +line it can raise or lower total social + + align:start position:0% +line it can raise or lower total social + + + align:start position:0% +line it can raise or lower total social +welfare and it's all a function of what + + align:start position:0% +welfare and it's all a function of what + + + align:start position:0% +welfare and it's all a function of what +information does the monopolist have and + + align:start position:0% +information does the monopolist have and + + + align:start position:0% +information does the monopolist have and +is it the type of information that makes + + align:start position:0% +is it the type of information that makes + + + align:start position:0% +is it the type of information that makes +the monopolist want to charge low prices + + align:start position:0% +the monopolist want to charge low prices + + + align:start position:0% +the monopolist want to charge low prices +or is the type of information that wants + + align:start position:0% +or is the type of information that wants + + + align:start position:0% +or is the type of information that wants +the monopolis to charge high + + align:start position:0% +the monopolis to charge high + + + align:start position:0% +the monopolis to charge high +prices + + align:start position:0% +prices + + + align:start position:0% +prices +okay so this this resultz kind of goes + + align:start position:0% +okay so this this resultz kind of goes + + + align:start position:0% +okay so this this resultz kind of goes +away if monopolis is allowed to design + + align:start position:0% +away if monopolis is allowed to design + + + align:start position:0% +away if monopolis is allowed to design +their own information scheme that's + + align:start position:0% +their own information scheme that's + + + align:start position:0% +their own information scheme that's +right so this is thinking this is very + + align:start position:0% +right so this is thinking this is very + + + align:start position:0% +right so this is thinking this is very +much thinking about the you know the + + align:start position:0% +much thinking about the you know the + + + align:start position:0% +much thinking about the you know the +monopolist is given a scheme that is + + align:start position:0% +monopolist is given a scheme that is + + + align:start position:0% +monopolist is given a scheme that is +it's given a scheme like you either know + + align:start position:0% +it's given a scheme like you either know + + + align:start position:0% +it's given a scheme like you either know +that the person is a stud you know + + align:start position:0% +that the person is a stud you know + + + align:start position:0% +that the person is a stud you know +because it's third degree discrimination + + align:start position:0% +because it's third degree discrimination + + + align:start position:0% +because it's third degree discrimination +you need a you need to be able to price + + align:start position:0% +you need a you need to be able to price + + + align:start position:0% +you need a you need to be able to price +based on the signal so you're given + + align:start position:0% +based on the signal so you're given + + + align:start position:0% +based on the signal so you're given +you've got demand in in Mississippi + + align:start position:0% +you've got demand in in Mississippi + + + align:start position:0% +you've got demand in in Mississippi +demand in in Kansas demand in Boston + + align:start position:0% +demand in in Kansas demand in Boston + + + align:start position:0% +demand in in Kansas demand in Boston +that's all you know or you've got + + align:start position:0% +that's all you know or you've got + + + align:start position:0% +that's all you know or you've got +student demand you've got non-student + + align:start position:0% +student demand you've got non-student + + + align:start position:0% +student demand you've got non-student +demand so um you know obviously if the + + align:start position:0% +demand so um you know obviously if the + + + align:start position:0% +demand so um you know obviously if the +monopolist has you know the monopolist + + align:start position:0% +monopolist has you know the monopolist + + + align:start position:0% +monopolist has you know the monopolist +wants perfect information and wants to + + align:start position:0% +wants perfect information and wants to + + + align:start position:0% +wants perfect information and wants to +go here and so the more useful + + align:start position:0% +go here and so the more useful + + + align:start position:0% +go here and so the more useful +information the monopolis has the higher + + align:start position:0% +information the monopolis has the higher + + + align:start position:0% +information the monopolis has the higher +it's going to get up here but if it's + + align:start position:0% +it's going to get up here but if it's + + + align:start position:0% +it's going to get up here but if it's +just if the subpopulations are what they + + align:start position:0% +just if the subpopulations are what they + + + align:start position:0% +just if the subpopulations are what they +are it it can go either way yeah + + align:start position:0% + + + + align:start position:0% + +yeah because I I think on the monopo + + align:start position:0% +yeah because I I think on the monopo + + + align:start position:0% +yeah because I I think on the monopo +side the real intuition is you just you + + align:start position:0% +side the real intuition is you just you + + + align:start position:0% +side the real intuition is you just you +want to know everything and do first + + align:start position:0% +want to know everything and do first + + + align:start position:0% +want to know everything and do first +degree and if you can do that that's + + align:start position:0% +degree and if you can do that that's + + + align:start position:0% +degree and if you can do that that's +that's what you're going to do but it's + + align:start position:0% +that's what you're going to do but it's + + + align:start position:0% +that's what you're going to do but it's +as you're getting + + align:start position:0% +as you're getting + + + align:start position:0% +as you're getting +there you know it's possible you're + + align:start position:0% +there you know it's possible you're + + + align:start position:0% +there you know it's possible you're +going there this way or this way and + + align:start position:0% +going there this way or this way and + + + align:start position:0% +going there this way or this way and +reducing welfare it could be you're + + align:start position:0% +reducing welfare it could be you're + + + align:start position:0% +reducing welfare it could be you're +going there this way and increasing + + align:start position:0% +going there this way and increasing + + + align:start position:0% +going there this way and increasing +welfare on the path + + align:start position:0% + + + + align:start position:0% + +there okay um so final thing I'm going + + align:start position:0% +there okay um so final thing I'm going + + + align:start position:0% +there okay um so final thing I'm going +to do today well actually next to last + + align:start position:0% +to do today well actually next to last + + + align:start position:0% +to do today well actually next to last +thing uh second degree + + align:start position:0% +thing uh second degree + + + align:start position:0% +thing uh second degree +discrimination so now we're back in the + + align:start position:0% +discrimination so now we're back in the + + + align:start position:0% +discrimination so now we're back in the +sort of case of the iPhone 128 and the + + align:start position:0% +sort of case of the iPhone 128 and the + + + align:start position:0% +sort of case of the iPhone 128 and the +iPhone 512 where the monopolist can't + + align:start position:0% +iPhone 512 where the monopolist can't + + + align:start position:0% +iPhone 512 where the monopolist can't +observe the consumer preferences and is + + align:start position:0% +observe the consumer preferences and is + + + align:start position:0% +observe the consumer preferences and is +relying on the self selection to let the + + align:start position:0% +relying on the self selection to let the + + + align:start position:0% +relying on the self selection to let the +high value consumers buy the high + + align:start position:0% +high value consumers buy the high + + + align:start position:0% +high value consumers buy the high +high-end good okay so I'm going to have + + align:start position:0% +high-end good okay so I'm going to have + + + align:start position:0% +high-end good okay so I'm going to have +consumers have some unknown type Theta + + align:start position:0% +consumers have some unknown type Theta + + + align:start position:0% +consumers have some unknown type Theta +that's unobserved by the monopolist they + + align:start position:0% +that's unobserved by the monopolist they + + + align:start position:0% +that's unobserved by the monopolist they +get utility V of Q Theta + + align:start position:0% +get utility V of Q Theta + + + align:start position:0% +get utility V of Q Theta +uh if they buy a a type a quality Q good + + align:start position:0% +uh if they buy a a type a quality Q good + + + align:start position:0% +uh if they buy a a type a quality Q good +and their typ is data and they pay a + + align:start position:0% +and their typ is data and they pay a + + + align:start position:0% +and their typ is data and they pay a +total price of + + align:start position:0% +total price of + + + align:start position:0% +total price of +t I'm going to assume that the utilities + + align:start position:0% +t I'm going to assume that the utilities + + + align:start position:0% +t I'm going to assume that the utilities +that everyone agrees that quality is + + align:start position:0% +that everyone agrees that quality is + + + align:start position:0% +that everyone agrees that quality is +good um the higher Theta consumers have + + align:start position:0% +good um the higher Theta consumers have + + + align:start position:0% +good um the higher Theta consumers have +a higher willingness to pay for any good + + align:start position:0% +a higher willingness to pay for any good + + + align:start position:0% +a higher willingness to pay for any good +um cross partial of uh V with respect to + + align:start position:0% +um cross partial of uh V with respect to + + + align:start position:0% +um cross partial of uh V with respect to +q and Theta is positive so the higher + + align:start position:0% +q and Theta is positive so the higher + + + align:start position:0% +q and Theta is positive so the higher +Theta people have a higher valuation and + + align:start position:0% +Theta people have a higher valuation and + + + align:start position:0% +Theta people have a higher valuation and +a higher margin valuation for + + align:start position:0% +a higher margin valuation for + + + align:start position:0% +a higher margin valuation for +Quality uh and I'm going to assume that + + align:start position:0% +Quality uh and I'm going to assume that + + + align:start position:0% +Quality uh and I'm going to assume that +you know they're diminishing returns to + + align:start position:0% +you know they're diminishing returns to + + + align:start position:0% +you know they're diminishing returns to +Quality so uh second with spect Q is + + align:start position:0% +Quality so uh second with spect Q is + + + align:start position:0% +Quality so uh second with spect Q is +negative uh I'm going to and this is + + align:start position:0% +negative uh I'm going to and this is + + + align:start position:0% +negative uh I'm going to and this is +really sort of a labeling of quality um + + align:start position:0% +really sort of a labeling of quality um + + + align:start position:0% +really sort of a labeling of quality um +I'm going to assume that the cost of + + align:start position:0% +I'm going to assume that the cost of + + + align:start position:0% +I'm going to assume that the cost of +producing a quality Q good is C * Q so + + align:start position:0% +producing a quality Q good is C * Q so + + + align:start position:0% +producing a quality Q good is C * Q so +you can think of that as just + + align:start position:0% +you can think of that as just + + + align:start position:0% +you can think of that as just +determining how we call you know how do + + align:start position:0% +determining how we call you know how do + + + align:start position:0% +determining how we call you know how do +we call we don't want to call a 128 + + align:start position:0% +we call we don't want to call a 128 + + + align:start position:0% +we call we don't want to call a 128 +versus 512 four times as good the what Q + + align:start position:0% +versus 512 four times as good the what Q + + + align:start position:0% +versus 512 four times as good the what Q +is defined in terms of how much the cost + + align:start position:0% +is defined in terms of how much the cost + + + align:start position:0% +is defined in terms of how much the cost +of producing that quality is okay um for + + align:start position:0% +of producing that quality is okay um for + + + align:start position:0% +of producing that quality is okay um for +now I'm just going to assume there are + + align:start position:0% +now I'm just going to assume there are + + + align:start position:0% +now I'm just going to assume there are +two types um and I'm going to write VI + + align:start position:0% +two types um and I'm going to write VI + + + align:start position:0% +two types um and I'm going to write VI +of Q for the uh so I'm write V1 of Q and + + align:start position:0% +of Q for the uh so I'm write V1 of Q and + + + align:start position:0% +of Q for the uh so I'm write V1 of Q and +V2 of Q for what the utility function is + + align:start position:0% +V2 of Q for what the utility function is + + + align:start position:0% +V2 of Q for what the utility function is +for the low types and the high + + align:start position:0% + + + + align:start position:0% + +types again you know if the thetas were + + align:start position:0% +types again you know if the thetas were + + + align:start position:0% +types again you know if the thetas were +observable uh this would be the first + + align:start position:0% +observable uh this would be the first + + + align:start position:0% +observable uh this would be the first +disc first um you know this would be + + align:start position:0% +disc first um you know this would be + + + align:start position:0% +disc first um you know this would be +first-degree discrimination model I + + align:start position:0% +first-degree discrimination model I + + + align:start position:0% +first-degree discrimination model I +would just for every consumer sell them + + align:start position:0% +would just for every consumer sell them + + + align:start position:0% +would just for every consumer sell them +the efficient quality for them and + + align:start position:0% +the efficient quality for them and + + + align:start position:0% +the efficient quality for them and +charge them their full Surplus they get + + align:start position:0% +charge them their full Surplus they get + + + align:start position:0% +charge them their full Surplus they get +from + + align:start position:0% +from + + + align:start position:0% +from +it okay um you know with Theta + + align:start position:0% +it okay um you know with Theta + + + align:start position:0% +it okay um you know with Theta +unobserved this isn't going to work um + + align:start position:0% +unobserved this isn't going to work um + + + align:start position:0% +unobserved this isn't going to work um +you know in the perfect price + + align:start position:0% +you know in the perfect price + + + align:start position:0% +you know in the perfect price +discrimination scheme the type theta + + align:start position:0% +discrimination scheme the type theta + + + align:start position:0% +discrimination scheme the type theta +equals 2 consumers get zero utility when + + align:start position:0% +equals 2 consumers get zero utility when + + + align:start position:0% +equals 2 consumers get zero utility when +they buy Q2 star at a price of T2 Star + + align:start position:0% +they buy Q2 star at a price of T2 Star + + + align:start position:0% +they buy Q2 star at a price of T2 Star +right these were the first degree levels + + align:start position:0% +right these were the first degree levels + + + align:start position:0% +right these were the first degree levels +so they get zero utility from buying the + + align:start position:0% +so they get zero utility from buying the + + + align:start position:0% +so they get zero utility from buying the +sort of first-degree package aim for + + align:start position:0% +sort of first-degree package aim for + + + align:start position:0% +sort of first-degree package aim for +them but they're going to get positive + + align:start position:0% +them but they're going to get positive + + + align:start position:0% +them but they're going to get positive +utility from buying q1 star at a price + + align:start position:0% +utility from buying q1 star at a price + + + align:start position:0% +utility from buying q1 star at a price +of T1 star because you know the low + + align:start position:0% +of T1 star because you know the low + + + align:start position:0% +of T1 star because you know the low +types get non- Negative utility from + + align:start position:0% +types get non- Negative utility from + + + align:start position:0% +types get non- Negative utility from +buying q a quality q1 star good at Price + + align:start position:0% +buying q a quality q1 star good at Price + + + align:start position:0% +buying q a quality q1 star good at Price +T1 star the Theta 2 types always get + + align:start position:0% +T1 star the Theta 2 types always get + + + align:start position:0% +T1 star the Theta 2 types always get +more utility than the Theta 1 from get + + align:start position:0% +more utility than the Theta 1 from get + + + align:start position:0% +more utility than the Theta 1 from get +from any utility therefore the Theta 1 + + align:start position:0% +from any utility therefore the Theta 1 + + + align:start position:0% +from any utility therefore the Theta 1 +type Theta 2 types would would be better + + align:start position:0% +type Theta 2 types would would be better + + + align:start position:0% +type Theta 2 types would would be better +off not buying the package designed for + + align:start position:0% +off not buying the package designed for + + + align:start position:0% +off not buying the package designed for +them and instead you know like right so + + align:start position:0% +them and instead you know like right so + + + align:start position:0% +them and instead you know like right so +some the businessman would fly and if if + + align:start position:0% +some the businessman would fly and if if + + + align:start position:0% +some the businessman would fly and if if +the coach price if the business class + + align:start position:0% +the coach price if the business class + + + align:start position:0% +the coach price if the business class +tickets were the full willingness to pay + + align:start position:0% +tickets were the full willingness to pay + + + align:start position:0% +tickets were the full willingness to pay +of the businessman they would sort of go + + align:start position:0% +of the businessman they would sort of go + + + align:start position:0% +of the businessman they would sort of go +to fly and coach and get positive + + align:start position:0% +to fly and coach and get positive + + + align:start position:0% +to fly and coach and get positive +Surplus from sitting in a coach seat by + + align:start position:0% +Surplus from sitting in a coach seat by + + + align:start position:0% +Surplus from sitting in a coach seat by +the coach + + align:start position:0% + + + + align:start position:0% + +price okay um so what do you want to do + + align:start position:0% +price okay um so what do you want to do + + + align:start position:0% +price okay um so what do you want to do +with Theta unobservable this is your + + align:start position:0% +with Theta unobservable this is your + + + align:start position:0% +with Theta unobservable this is your +standard screening problem you have two + + align:start position:0% +standard screening problem you have two + + + align:start position:0% +standard screening problem you have two +you have um two types you offer a menu + + align:start position:0% +you have um two types you offer a menu + + + align:start position:0% +you have um two types you offer a menu +that has two options and you the + + align:start position:0% +that has two options and you the + + + align:start position:0% +that has two options and you the +consumers choose between those two + + align:start position:0% +consumers choose between those two + + + align:start position:0% +consumers choose between those two +options so consumers can are given the + + align:start position:0% +options so consumers can are given the + + + align:start position:0% +options so consumers can are given the +option you can either buy a quality q1 + + align:start position:0% +option you can either buy a quality q1 + + + align:start position:0% +option you can either buy a quality q1 +good at a price of T1 or quality Q2 good + + align:start position:0% +good at a price of T1 or quality Q2 good + + + align:start position:0% +good at a price of T1 or quality Q2 good +at a price of + + align:start position:0% +at a price of + + + align:start position:0% +at a price of +T2 um monopolis maximization problem I'm + + align:start position:0% +T2 um monopolis maximization problem I'm + + + align:start position:0% +T2 um monopolis maximization problem I'm +maximizing so I have you know equal + + align:start position:0% +maximizing so I have you know equal + + + align:start position:0% +maximizing so I have you know equal +masses of consumers of each type here + + align:start position:0% +masses of consumers of each type here + + + align:start position:0% +masses of consumers of each type here +I'm getting the PRI price I get from the + + align:start position:0% +I'm getting the PRI price I get from the + + + align:start position:0% +I'm getting the PRI price I get from the +low types plus the price I get from the + + align:start position:0% +low types plus the price I get from the + + + align:start position:0% +low types plus the price I get from the +high types minus the cost of producing + + align:start position:0% +high types minus the cost of producing + + + align:start position:0% +high types minus the cost of producing +all the goods and then I have these sort + + align:start position:0% +all the goods and then I have these sort + + + align:start position:0% +all the goods and then I have these sort +of four standard constraints like you're + + align:start position:0% +of four standard constraints like you're + + + align:start position:0% +of four standard constraints like you're +used to seeing in mechanism sign + + align:start position:0% +used to seeing in mechanism sign + + + align:start position:0% +used to seeing in mechanism sign +problems um the IR constraints you know + + align:start position:0% +problems um the IR constraints you know + + + align:start position:0% +problems um the IR constraints you know +that stands for individual + + align:start position:0% +that stands for individual + + + align:start position:0% +that stands for individual +[Applause] + + align:start position:0% + + + + align:start position:0% + +rationality the IR constraints say that + + align:start position:0% +rationality the IR constraints say that + + + align:start position:0% +rationality the IR constraints say that +the low type consumers have to be + + align:start position:0% +the low type consumers have to be + + + align:start position:0% +the low type consumers have to be +getting at least as much utility from + + align:start position:0% +getting at least as much utility from + + + align:start position:0% +getting at least as much utility from +the good they're buying as what they're + + align:start position:0% +the good they're buying as what they're + + + align:start position:0% +the good they're buying as what they're +paying for it as do the high types and + + align:start position:0% +paying for it as do the high types and + + + align:start position:0% +paying for it as do the high types and +then the IC constraints the incentive + + align:start position:0% +then the IC constraints the incentive + + + align:start position:0% +then the IC constraints the incentive +compatibility um + + align:start position:0% + + + + align:start position:0% + +the incentive compatibility constraints + + align:start position:0% +the incentive compatibility constraints + + + align:start position:0% +the incentive compatibility constraints +say that the um utility that the low + + align:start position:0% +say that the um utility that the low + + + align:start position:0% +say that the um utility that the low +types get from buying the package + + align:start position:0% +types get from buying the package + + + align:start position:0% +types get from buying the package +designed for them is at least as good as + + align:start position:0% +designed for them is at least as good as + + + align:start position:0% +designed for them is at least as good as +the utility they would get if they + + align:start position:0% +the utility they would get if they + + + align:start position:0% +the utility they would get if they +bought the package that was instead + + align:start position:0% +bought the package that was instead + + + align:start position:0% +bought the package that was instead +designed for the high types at the high + + align:start position:0% +designed for the high types at the high + + + align:start position:0% +designed for the high types at the high +and paid the high type price and + + align:start position:0% +and paid the high type price and + + + align:start position:0% +and paid the high type price and +similarly the high types the you know + + align:start position:0% +similarly the high types the you know + + + align:start position:0% +similarly the high types the you know +the businessmen have to be getting at + + align:start position:0% +the businessmen have to be getting at + + + align:start position:0% +the businessmen have to be getting at +least as much utility from sitting in + + align:start position:0% +least as much utility from sitting in + + + align:start position:0% +least as much utility from sitting in +business class as they would get if they + + align:start position:0% +business class as they would get if they + + + align:start position:0% +business class as they would get if they +instead sat in coach got the coach + + align:start position:0% +instead sat in coach got the coach + + + align:start position:0% +instead sat in coach got the coach +quality and paid the coach price so each + + align:start position:0% +quality and paid the coach price so each + + + align:start position:0% +quality and paid the coach price so each +group has to be willing to buy the + + align:start position:0% +group has to be willing to buy the + + + align:start position:0% +group has to be willing to buy the +package that you're selling to them in + + align:start position:0% +package that you're selling to them in + + + align:start position:0% +package that you're selling to them in +equilibrium relative to the other + + align:start position:0% +equilibrium relative to the other + + + align:start position:0% +equilibrium relative to the other +group's + + align:start position:0% + + + + align:start position:0% + +package okay um you know the first step + + align:start position:0% +package okay um you know the first step + + + align:start position:0% +package okay um you know the first step +in solving problems like this is always + + align:start position:0% +in solving problems like this is always + + + align:start position:0% +in solving problems like this is always +to figure out which constraints are + + align:start position:0% +to figure out which constraints are + + + align:start position:0% +to figure out which constraints are +binding and which constraints are not + + align:start position:0% +binding and which constraints are not + + + align:start position:0% +binding and which constraints are not +binding here um one observation is that + + align:start position:0% +binding here um one observation is that + + + align:start position:0% +binding here um one observation is that +the R2 constraint is not going to be + + align:start position:0% +the R2 constraint is not going to be + + + align:start position:0% +the R2 constraint is not going to be +binding um and the argument here is + + align:start position:0% +binding um and the argument here is + + + align:start position:0% +binding um and the argument here is +simply that you know the students are + + align:start position:0% +simply that you know the students are + + + align:start position:0% +simply that you know the students are +willing to fly on the on the plane and + + align:start position:0% +willing to fly on the on the plane and + + + align:start position:0% +willing to fly on the on the plane and +Coach um the IC constraint says the + + align:start position:0% +Coach um the IC constraint says the + + + align:start position:0% +Coach um the IC constraint says the +businessmen have to prefer what they're + + align:start position:0% +businessmen have to prefer what they're + + + align:start position:0% +businessmen have to prefer what they're +getting to flying in coach they have + + align:start position:0% +getting to flying in coach they have + + + align:start position:0% +getting to flying in coach they have +positive utility from that so therefore + + align:start position:0% +positive utility from that so therefore + + + align:start position:0% +positive utility from that so therefore +the they're automatically willing to buy + + align:start position:0% +the they're automatically willing to buy + + + align:start position:0% +the they're automatically willing to buy +because they would get more utility from + + align:start position:0% +because they would get more utility from + + + align:start position:0% +because they would get more utility from +the coach class seat um and then I would + + align:start position:0% +the coach class seat um and then I would + + + align:start position:0% +the coach class seat um and then I would +say the second thing is just sort of a + + align:start position:0% +say the second thing is just sort of a + + + align:start position:0% +say the second thing is just sort of a +guess although I'll show you it's true + + align:start position:0% +guess although I'll show you it's true + + + align:start position:0% +guess although I'll show you it's true +ic1 seems unlikely to bind um you know + + align:start position:0% +ic1 seems unlikely to bind um you know + + + align:start position:0% +ic1 seems unlikely to bind um you know +like if you're thinking about what's the + + align:start position:0% +like if you're thinking about what's the + + + align:start position:0% +like if you're thinking about what's the +airlines pricing problem you never have + + align:start position:0% +airlines pricing problem you never have + + + align:start position:0% +airlines pricing problem you never have +the problem of the students are going to + + align:start position:0% +the problem of the students are going to + + + align:start position:0% +the problem of the students are going to +buy the $3,000 ticket if you're not + + align:start position:0% +buy the $3,000 ticket if you're not + + + align:start position:0% +buy the $3,000 ticket if you're not +careful um it's it's the sort of the + + align:start position:0% +careful um it's it's the sort of the + + + align:start position:0% +careful um it's it's the sort of the +problem is keeping the wealthy people + + align:start position:0% +problem is keeping the wealthy people + + + align:start position:0% +problem is keeping the wealthy people +from buying the cheap product not + + align:start position:0% +from buying the cheap product not + + + align:start position:0% +from buying the cheap product not +keeping the poor people from buying the + + align:start position:0% +keeping the poor people from buying the + + + align:start position:0% +keeping the poor people from buying the +expensive product + + align:start position:0% +expensive product + + + align:start position:0% +expensive product +um so once I eliminate those two um you + + align:start position:0% +um so once I eliminate those two um you + + + align:start position:0% +um so once I eliminate those two um you +know simplified problem is I'm + + align:start position:0% +know simplified problem is I'm + + + align:start position:0% +know simplified problem is I'm +maximizing + + align:start position:0% +maximizing + + + align:start position:0% +maximizing +my profits subject to just two + + align:start position:0% +my profits subject to just two + + + align:start position:0% +my profits subject to just two +constraints uh the low types have to be + + align:start position:0% +constraints uh the low types have to be + + + align:start position:0% +constraints uh the low types have to be +willing to buy the product I'm I'm + + align:start position:0% +willing to buy the product I'm I'm + + + align:start position:0% +willing to buy the product I'm I'm +selling them and the high types have to + + align:start position:0% +selling them and the high types have to + + + align:start position:0% +selling them and the high types have to +prefer the product I'm TR the expensive + + align:start position:0% +prefer the product I'm TR the expensive + + + align:start position:0% +prefer the product I'm TR the expensive +product I'm trying to sell them to the + + align:start position:0% +product I'm trying to sell them to the + + + align:start position:0% +product I'm trying to sell them to the +cheaper product I'm selling to the low + + align:start position:0% + + + + align:start position:0% + +types so if you look at this problem now + + align:start position:0% +types so if you look at this problem now + + + align:start position:0% +types so if you look at this problem now +so I'm doing this constrained + + align:start position:0% +so I'm doing this constrained + + + align:start position:0% +so I'm doing this constrained +optimization I I want to make the t's as + + align:start position:0% +optimization I I want to make the t's as + + + align:start position:0% +optimization I I want to make the t's as +big as I can uh what are the constraints + + align:start position:0% +big as I can uh what are the constraints + + + align:start position:0% +big as I can uh what are the constraints +on making the t's as big as I can so for + + align:start position:0% +on making the t's as big as I can so for + + + align:start position:0% +on making the t's as big as I can so for +T1 if I raise it that's good it makes + + align:start position:0% +T1 if I raise it that's good it makes + + + align:start position:0% +T1 if I raise it that's good it makes +this constraint easier to satisfy so the + + align:start position:0% +this constraint easier to satisfy so the + + + align:start position:0% +this constraint easier to satisfy so the +only reason not to raise T1 is because + + align:start position:0% +only reason not to raise T1 is because + + + align:start position:0% +only reason not to raise T1 is because +this constraint is going to be violated + + align:start position:0% +this constraint is going to be violated + + + align:start position:0% +this constraint is going to be violated +so clearly in equilibrium I'm going to + + align:start position:0% +so clearly in equilibrium I'm going to + + + align:start position:0% +so clearly in equilibrium I'm going to +set T1 equal to V1 of q1 and have this + + align:start position:0% +set T1 equal to V1 of q1 and have this + + + align:start position:0% +set T1 equal to V1 of q1 and have this +constraint be + + align:start position:0% + + + + align:start position:0% + +binding and then also I'm going to want + + align:start position:0% +binding and then also I'm going to want + + + align:start position:0% +binding and then also I'm going to want +to raise the price to the high types as + + align:start position:0% +to raise the price to the high types as + + + align:start position:0% +to raise the price to the high types as +much as I can what prevents me from + + align:start position:0% +much as I can what prevents me from + + + align:start position:0% +much as I can what prevents me from +doing that it's only that T2 appears in + + align:start position:0% +doing that it's only that T2 appears in + + + align:start position:0% +doing that it's only that T2 appears in +this constraint and so I'm going to make + + align:start position:0% +this constraint and so I'm going to make + + + align:start position:0% +this constraint and so I'm going to make +T2 as large as I can before this + + align:start position:0% +T2 as large as I can before this + + + align:start position:0% +T2 as large as I can before this +constraint is violated and so this is + + align:start position:0% +constraint is violated and so this is + + + align:start position:0% +constraint is violated and so this is +going to also hold with equality and + + align:start position:0% +going to also hold with equality and + + + align:start position:0% +going to also hold with equality and +that means by bring it over to this side + + align:start position:0% +that means by bring it over to this side + + + align:start position:0% +that means by bring it over to this side +T2 equals T1 plus V2 of Q2 minus V2 of + + align:start position:0% +T2 equals T1 plus V2 of Q2 minus V2 of + + + align:start position:0% +T2 equals T1 plus V2 of Q2 minus V2 of +q1 so you know in some sense this is + + align:start position:0% +q1 so you know in some sense this is + + + align:start position:0% +q1 so you know in some sense this is +just like in the durable goods problem + + align:start position:0% +just like in the durable goods problem + + + align:start position:0% +just like in the durable goods problem +where people could buy the good in the + + align:start position:0% +where people could buy the good in the + + + align:start position:0% +where people could buy the good in the +second period so what I can charge them + + align:start position:0% +second period so what I can charge them + + + align:start position:0% +second period so what I can charge them +for getting the good in the first period + + align:start position:0% +for getting the good in the first period + + + align:start position:0% +for getting the good in the first period +instead is our incremental utility for + + align:start position:0% +instead is our incremental utility for + + + align:start position:0% +instead is our incremental utility for +getting it one period earlier again what + + align:start position:0% +getting it one period earlier again what + + + align:start position:0% +getting it one period earlier again what +I can get from selling them the higher + + align:start position:0% +I can get from selling them the higher + + + align:start position:0% +I can get from selling them the higher +quality good is what I'm they would pay + + align:start position:0% +quality good is what I'm they would pay + + + align:start position:0% +quality good is what I'm they would pay +for the low quality good plus the + + align:start position:0% +for the low quality good plus the + + + align:start position:0% +for the low quality good plus the +incremental utility that they get from + + align:start position:0% +incremental utility that they get from + + + align:start position:0% +incremental utility that they get from +the quality upgrade that's the most + + align:start position:0% +the quality upgrade that's the most + + + align:start position:0% +the quality upgrade that's the most +they're going to be able to pay and so + + align:start position:0% +they're going to be able to pay and so + + + align:start position:0% +they're going to be able to pay and so +that's V1 of q1 plus V2 of Q2 minus V2 + + align:start position:0% +that's V1 of q1 plus V2 of Q2 minus V2 + + + align:start position:0% +that's V1 of q1 plus V2 of Q2 minus V2 +of + + align:start position:0% +of + + + align:start position:0% +of +q1 + + align:start position:0% +q1 + + + align:start position:0% +q1 +okay and so once I've made these two + + align:start position:0% +okay and so once I've made these two + + + align:start position:0% +okay and so once I've made these two +substitutions this for T1 and this for + + align:start position:0% +substitutions this for T1 and this for + + + align:start position:0% +substitutions this for T1 and this for +T2 I now just have an unconstrained + + align:start position:0% +T2 I now just have an unconstrained + + + align:start position:0% +T2 I now just have an unconstrained +maximization problem + + align:start position:0% +maximization problem + + + align:start position:0% +maximization problem +what's the answer to that um so I just + + align:start position:0% +what's the answer to that um so I just + + + align:start position:0% +what's the answer to that um so I just +you know take assuming the v's are are + + align:start position:0% +you know take assuming the v's are are + + + align:start position:0% +you know take assuming the v's are are +concave functions I just take the first + + align:start position:0% +concave functions I just take the first + + + align:start position:0% +concave functions I just take the first +order conditions for this to + + align:start position:0% +order conditions for this to + + + align:start position:0% +order conditions for this to +maximize um first let me differentiate + + align:start position:0% +maximize um first let me differentiate + + + align:start position:0% +maximize um first let me differentiate +with respect to Q2 which only appears + + align:start position:0% +with respect to Q2 which only appears + + + align:start position:0% +with respect to Q2 which only appears +here and here I differentiate with + + align:start position:0% +here and here I differentiate with + + + align:start position:0% +here and here I differentiate with +respect to Q2 and I get DVD dv2 + + align:start position:0% +respect to Q2 and I get DVD dv2 + + + align:start position:0% +respect to Q2 and I get DVD dv2 +DQ uh equals + + align:start position:0% + + + + align:start position:0% + +c so that just tells me that the Q2 with + + align:start position:0% +c so that just tells me that the Q2 with + + + align:start position:0% +c so that just tells me that the Q2 with +second degree discrimination is equal to + + align:start position:0% +second degree discrimination is equal to + + + align:start position:0% +second degree discrimination is equal to +the Q2 star that you do with first + + align:start position:0% +the Q2 star that you do with first + + + align:start position:0% +the Q2 star that you do with first +degree discrimination or with a M + + align:start position:0% +degree discrimination or with a M + + + align:start position:0% +degree discrimination or with a M +Monopoly optimal quality theorem the + + align:start position:0% +Monopoly optimal quality theorem the + + + align:start position:0% +Monopoly optimal quality theorem the +high types get the optimal product okay + + align:start position:0% +high types get the optimal product okay + + + align:start position:0% +high types get the optimal product okay +and you know I think this a good thing + + align:start position:0% +and you know I think this a good thing + + + align:start position:0% +and you know I think this a good thing +sens to it like you know sometimes I + + align:start position:0% +sens to it like you know sometimes I + + + align:start position:0% +sens to it like you know sometimes I +know people have this sense that like + + align:start position:0% +know people have this sense that like + + + align:start position:0% +know people have this sense that like +there's excess consumption in the OR + + align:start position:0% +there's excess consumption in the OR + + + align:start position:0% +there's excess consumption in the OR +excess quality like you know I walk + + align:start position:0% +excess quality like you know I walk + + + align:start position:0% +excess quality like you know I walk +through that first class cabin on the + + align:start position:0% +through that first class cabin on the + + + align:start position:0% +through that first class cabin on the +airplane isn't that obscene that these + + align:start position:0% +airplane isn't that obscene that these + + + align:start position:0% +airplane isn't that obscene that these +people are + + align:start position:0% +people are + + + align:start position:0% +people are +drinking drinks from Glass glasses and + + align:start position:0% +drinking drinks from Glass glasses and + + + align:start position:0% +drinking drinks from Glass glasses and +using metal Silver Weare or whatever and + + align:start position:0% +using metal Silver Weare or whatever and + + + align:start position:0% +using metal Silver Weare or whatever and +you just have to think to yourself wait + + align:start position:0% +you just have to think to yourself wait + + + align:start position:0% +you just have to think to yourself wait +no actually you know I'm relatively low + + align:start position:0% +no actually you know I'm relatively low + + + align:start position:0% +no actually you know I'm relatively low +in the income distribution and I have + + align:start position:0% +in the income distribution and I have + + + align:start position:0% +in the income distribution and I have +metal silverware at my house and I drink + + align:start position:0% +metal silverware at my house and I drink + + + align:start position:0% +metal silverware at my house and I drink +out of glass cups instead of paper cups + + align:start position:0% +out of glass cups instead of paper cups + + + align:start position:0% +out of glass cups instead of paper cups +you know there's it's just that is sort + + align:start position:0% +you know there's it's just that is sort + + + align:start position:0% +you know there's it's just that is sort +of given the cost of providing metal it + + align:start position:0% +of given the cost of providing metal it + + + align:start position:0% +of given the cost of providing metal it +seems like that's a totally reasonable + + align:start position:0% +seems like that's a totally reasonable + + + align:start position:0% +seems like that's a totally reasonable +price to be paying for people or + + align:start position:0% +price to be paying for people or + + + align:start position:0% +price to be paying for people or +whatever so you you give them the + + align:start position:0% +whatever so you you give them the + + + align:start position:0% +whatever so you you give them the +optimal quality product and and charge + + align:start position:0% +optimal quality product and and charge + + + align:start position:0% +optimal quality product and and charge +them for it um and then what about q1 I + + align:start position:0% +them for it um and then what about q1 I + + + align:start position:0% +them for it um and then what about q1 I +differentiate this with respect to q1 + + align:start position:0% +differentiate this with respect to q1 + + + align:start position:0% +differentiate this with respect to q1 +you know I get a DVD + + align:start position:0% +you know I get a DVD + + + align:start position:0% +you know I get a DVD +q1 again it's equal to C but then I'm + + align:start position:0% +q1 again it's equal to C but then I'm + + + align:start position:0% +q1 again it's equal to C but then I'm +going to have two other + + align:start position:0% +going to have two other + + + align:start position:0% +going to have two other +terms derivatives a d dv1 dq1 and dv2 + + align:start position:0% +terms derivatives a d dv1 dq1 and dv2 + + + align:start position:0% +terms derivatives a d dv1 dq1 and dv2 +dq1 and so what you get is dv1 dq1 + + align:start position:0% +dq1 and so what you get is dv1 dq1 + + + align:start position:0% +dq1 and so what you get is dv1 dq1 +moving everything to the other side + + align:start position:0% +moving everything to the other side + + + align:start position:0% +moving everything to the other side +equals c plus partial of V2 with respect + + align:start position:0% +equals c plus partial of V2 with respect + + + align:start position:0% +equals c plus partial of V2 with respect +to Q minus partial of V1 with respect to + + align:start position:0% +to Q minus partial of V1 with respect to + + + align:start position:0% +to Q minus partial of V1 with respect to +Q + + align:start position:0% + + + + align:start position:0% + +remember the higher types have a higher + + align:start position:0% +remember the higher types have a higher + + + align:start position:0% +remember the higher types have a higher +incremental willingness to pay for + + align:start position:0% +incremental willingness to pay for + + + align:start position:0% +incremental willingness to pay for +Quality at the same quality level so + + align:start position:0% +Quality at the same quality level so + + + align:start position:0% +Quality at the same quality level so +this is greater than C so the Distortion + + align:start position:0% +this is greater than C so the Distortion + + + align:start position:0% +this is greater than C so the Distortion +is I distort quality down for the low + + align:start position:0% +is I distort quality down for the low + + + align:start position:0% +is I distort quality down for the low +for the low types uh and provide them + + align:start position:0% +for the low types uh and provide them + + + align:start position:0% +for the low types uh and provide them +with a suboptimal quality you know so + + align:start position:0% +with a suboptimal quality you know so + + + align:start position:0% +with a suboptimal quality you know so +right if you've done that calculation on + + align:start position:0% +right if you've done that calculation on + + + align:start position:0% +right if you've done that calculation on +the airplane I can't believe I'm sitting + + align:start position:0% +the airplane I can't believe I'm sitting + + + align:start position:0% +the airplane I can't believe I'm sitting +here and coach and like I I can't open + + align:start position:0% +here and coach and like I I can't open + + + align:start position:0% +here and coach and like I I can't open +my laptop whatsoever and my knees are + + align:start position:0% +my laptop whatsoever and my knees are + + + align:start position:0% +my laptop whatsoever and my knees are +pressed in the seat in front of me + + align:start position:0% +pressed in the seat in front of me + + + align:start position:0% +pressed in the seat in front of me +couldn't we just have like moved the + + align:start position:0% +couldn't we just have like moved the + + + align:start position:0% +couldn't we just have like moved the +seats one inch further apart take one + + align:start position:0% +seats one inch further apart take one + + + align:start position:0% +seats one inch further apart take one +seat out of the plane I would be willing + + align:start position:0% +seat out of the plane I would be willing + + + align:start position:0% +seat out of the plane I would be willing +to pay this much more they would make + + align:start position:0% +to pay this much more they would make + + + align:start position:0% +to pay this much more they would make +more money why don't they do that well + + align:start position:0% +more money why don't they do that well + + + align:start position:0% +more money why don't they do that well +the answer is yes they they could make + + align:start position:0% +the answer is yes they they could make + + + align:start position:0% +the answer is yes they they could make +more money in the coach cabin doing that + + align:start position:0% +more money in the coach cabin doing that + + + align:start position:0% +more money in the coach cabin doing that +and making the seats more comfortable + + align:start position:0% +and making the seats more comfortable + + + align:start position:0% +and making the seats more comfortable +but then the businessman would be + + align:start position:0% +but then the businessman would be + + + align:start position:0% +but then the businessman would be +willing to sit and Coach you know so you + + align:start position:0% +willing to sit and Coach you know so you + + + align:start position:0% +willing to sit and Coach you know so you +have to make those coach seats + + align:start position:0% +have to make those coach seats + + + align:start position:0% +have to make those coach seats +uncomfortable enough that the + + align:start position:0% +uncomfortable enough that the + + + align:start position:0% +uncomfortable enough that the +businessmen will not sit in them your + + align:start position:0% +businessmen will not sit in them your + + + align:start position:0% +businessmen will not sit in them your +seats are the ones that are distorted + + align:start position:0% +seats are the ones that are distorted + + + align:start position:0% +seats are the ones that are distorted +theirs where your knees don't bang into + + align:start position:0% +theirs where your knees don't bang into + + + align:start position:0% +theirs where your knees don't bang into +the seat in front of you that's optimal + + align:start position:0% +the seat in front of you that's optimal + + + align:start position:0% +the seat in front of you that's optimal +quality okay and so what we do is we + + align:start position:0% +quality okay and so what we do is we + + + align:start position:0% +quality okay and so what we do is we +distort quality down for the low types + + align:start position:0% +distort quality down for the low types + + + align:start position:0% +distort quality down for the low types +uh and so this is a you know this is a + + align:start position:0% +uh and so this is a you know this is a + + + align:start position:0% +uh and so this is a you know this is a +new inefficiency of second degree price + + align:start position:0% +new inefficiency of second degree price + + + align:start position:0% +new inefficiency of second degree price +discrimination we have all the old + + align:start position:0% +discrimination we have all the old + + + align:start position:0% +discrimination we have all the old +efficiencies inefficiencies our new + + align:start position:0% +efficiencies inefficiencies our new + + + align:start position:0% +efficiencies inefficiencies our new +inefficiency again is suboptimal product + + align:start position:0% +inefficiency again is suboptimal product + + + align:start position:0% +inefficiency again is suboptimal product +quality and the sub product quality is + + align:start position:0% +quality and the sub product quality is + + + align:start position:0% +quality and the sub product quality is +done because we have that you know it's + + align:start position:0% +done because we have that you know it's + + + align:start position:0% +done because we have that you know it's +it's because they don't have the ID to + + align:start position:0% +it's because they don't have the ID to + + + align:start position:0% +it's because they don't have the ID to +say I'm rich or I'm poor which seat I'm + + align:start position:0% +say I'm rich or I'm poor which seat I'm + + + align:start position:0% +say I'm rich or I'm poor which seat I'm +going to sit in we have to have this + + align:start position:0% +going to sit in we have to have this + + + align:start position:0% +going to sit in we have to have this +extra Distortion to allow them to screen + + align:start position:0% +extra Distortion to allow them to screen + + + align:start position:0% +extra Distortion to allow them to screen +without that + + align:start position:0% +without that + + + align:start position:0% +without that +signal okay + + align:start position:0% +signal okay + + + align:start position:0% +signal okay +um let's see other comments you know so + + align:start position:0% +um let's see other comments you know so + + + align:start position:0% +um let's see other comments you know so +the high types are getting positive + + align:start position:0% +the high types are getting positive + + + align:start position:0% +the high types are getting positive +Surplus the low types are not we + + align:start position:0% +Surplus the low types are not we + + + align:start position:0% +Surplus the low types are not we +sometimes call that an information rent + + align:start position:0% +sometimes call that an information rent + + + align:start position:0% +sometimes call that an information rent +um you know welfare is worse than + + align:start position:0% +um you know welfare is worse than + + + align:start position:0% +um you know welfare is worse than +first-degree discrimination um if if we + + align:start position:0% +first-degree discrimination um if if we + + + align:start position:0% +first-degree discrimination um if if we +could give the students their optimal + + align:start position:0% +could give the students their optimal + + + align:start position:0% +could give the students their optimal +seat pitch and charge them the optimal + + align:start position:0% +seat pitch and charge them the optimal + + + align:start position:0% +seat pitch and charge them the optimal +price they would be better off um but + + align:start position:0% +price they would be better off um but + + + align:start position:0% +price they would be better off um but +the comparison with what would happen + + align:start position:0% +the comparison with what would happen + + + align:start position:0% +the comparison with what would happen +for instance if we have uh uh require + + align:start position:0% +for instance if we have uh uh require + + + align:start position:0% +for instance if we have uh uh require +you to have only a single good and not + + align:start position:0% +you to have only a single good and not + + + align:start position:0% +you to have only a single good and not +have two different coach classes that's + + align:start position:0% +have two different coach classes that's + + + align:start position:0% +have two different coach classes that's +an ambiguous uh + + align:start position:0% +an ambiguous uh + + + align:start position:0% +an ambiguous uh +distinction so again you the fact that + + align:start position:0% +distinction so again you the fact that + + + align:start position:0% +distinction so again you the fact that +you may be able to create these + + align:start position:0% +you may be able to create these + + + align:start position:0% +you may be able to create these +lowquality seats and serve people who + + align:start position:0% +lowquality seats and serve people who + + + align:start position:0% +lowquality seats and serve people who +would not be in the market if there were + + align:start position:0% +would not be in the market if there were + + + align:start position:0% +would not be in the market if there were +no lowquality seats social welfare can + + align:start position:0% +no lowquality seats social welfare can + + + align:start position:0% +no lowquality seats social welfare can +be better than if you had the only first + + align:start position:0% +be better than if you had the only first + + + align:start position:0% +be better than if you had the only first +class plane for + + align:start position:0% +class plane for + + + align:start position:0% +class plane for +instance which is what you might get if + + align:start position:0% +instance which is what you might get if + + + align:start position:0% +instance which is what you might get if +you didn't allow + + align:start position:0% +you didn't allow + + + align:start position:0% +you didn't allow +discrimination okay um I would say you + + align:start position:0% +discrimination okay um I would say you + + + align:start position:0% +discrimination okay um I would say you +know modern IO Theory papers tend to + + align:start position:0% +know modern IO Theory papers tend to + + + align:start position:0% +know modern IO Theory papers tend to +work with a continu of types model + + align:start position:0% +work with a continu of types model + + + align:start position:0% +work with a continu of types model +instead of a uh discret type model you + + align:start position:0% +instead of a uh discret type model you + + + align:start position:0% +instead of a uh discret type model you +know these days I have this awkward + + align:start position:0% +know these days I have this awkward + + + align:start position:0% +know these days I have this awkward +thing that like uh Alex when he teaches + + align:start position:0% +thing that like uh Alex when he teaches + + + align:start position:0% +thing that like uh Alex when he teaches +124 does a really good job on the + + align:start position:0% +124 does a really good job on the + + + align:start position:0% +124 does a really good job on the +continu type screening models so I I'm + + align:start position:0% +continu type screening models so I I'm + + + align:start position:0% +continu type screening models so I I'm +not going to cover Contin type screening + + align:start position:0% +not going to cover Contin type screening + + + align:start position:0% +not going to cover Contin type screening +models it's in the slides that I have + + align:start position:0% +models it's in the slides that I have + + + align:start position:0% +models it's in the slides that I have +here um uh rowy is going to covered in + + align:start position:0% +here um uh rowy is going to covered in + + + align:start position:0% +here um uh rowy is going to covered in +recitation on Friday I think I haven't + + align:start position:0% +recitation on Friday I think I haven't + + + align:start position:0% +recitation on Friday I think I haven't +looked at it this morning but I think + + align:start position:0% +looked at it this morning but I think + + + align:start position:0% +looked at it this morning but I think +there's also a uh 2020 me discussing + + align:start position:0% +there's also a uh 2020 me discussing + + + align:start position:0% +there's also a uh 2020 me discussing +this material on Zoom video if you want + + align:start position:0% +this material on Zoom video if you want + + + align:start position:0% +this material on Zoom video if you want +to if if you can't make recitation on + + align:start position:0% +to if if you can't make recitation on + + + align:start position:0% +to if if you can't make recitation on +Friday and see me discussing the Contin + + align:start position:0% +Friday and see me discussing the Contin + + + align:start position:0% +Friday and see me discussing the Contin +of types price discrimination in a Coy + + align:start position:0% +of types price discrimination in a Coy + + + align:start position:0% +of types price discrimination in a Coy +world uh I think that's on the website + + align:start position:0% +world uh I think that's on the website + + + align:start position:0% +world uh I think that's on the website +too + + align:start position:0% +too + + + align:start position:0% +too +um but you know I mean the general + + align:start position:0% +um but you know I mean the general + + + align:start position:0% +um but you know I mean the general +intuitions are just that you know if you + + align:start position:0% +intuitions are just that you know if you + + + align:start position:0% +intuitions are just that you know if you +have three or four or five types instead + + align:start position:0% +have three or four or five types instead + + + align:start position:0% +have three or four or five types instead +of or Contin of types instead of two + + align:start position:0% +of or Contin of types instead of two + + + align:start position:0% +of or Contin of types instead of two +types you need to stop these guys from + + align:start position:0% +types you need to stop these guys from + + + align:start position:0% +types you need to stop these guys from +copying these guy by buying the product + + align:start position:0% +copying these guy by buying the product + + + align:start position:0% +copying these guy by buying the product +intended for these guys you need to + + align:start position:0% +intended for these guys you need to + + + align:start position:0% +intended for these guys you need to +these people from buying this product + + align:start position:0% +these people from buying this product + + + align:start position:0% +these people from buying this product +you need to stop these people from + + align:start position:0% +you need to stop these people from + + + align:start position:0% +you need to stop these people from +buying this product and so some you get + + align:start position:0% +buying this product and so some you get + + + align:start position:0% +buying this product and so some you get +this cascading distortions + + align:start position:0% +this cascading distortions + + + align:start position:0% +this cascading distortions +where anytime I give something to the + + align:start position:0% +where anytime I give something to the + + + align:start position:0% +where anytime I give something to the +lowest type the next lowest type gets + + align:start position:0% +lowest type the next lowest type gets + + + align:start position:0% +lowest type the next lowest type gets +more utility because have to be given + + align:start position:0% +more utility because have to be given + + + align:start position:0% +more utility because have to be given +utility so they won't copy the lowest + + align:start position:0% +utility so they won't copy the lowest + + + align:start position:0% +utility so they won't copy the lowest +type and then because they're getting a + + align:start position:0% +type and then because they're getting a + + + align:start position:0% +type and then because they're getting a +better product the next type up have to + + align:start position:0% +better product the next type up have to + + + align:start position:0% +better product the next type up have to +get a better product and so on so you + + align:start position:0% +get a better product and so on so you + + + align:start position:0% +get a better product and so on so you +get these sort of places where you have + + align:start position:0% +get these sort of places where you have + + + align:start position:0% +get these sort of places where you have +very severe distortions which is at the + + align:start position:0% +very severe distortions which is at the + + + align:start position:0% +very severe distortions which is at the +the further you go down in the + + align:start position:0% +the further you go down in the + + + align:start position:0% +the further you go down in the +distribution the more reasons you have + + align:start position:0% +distribution the more reasons you have + + + align:start position:0% +distribution the more reasons you have +to distort the package being getting by + + align:start position:0% +to distort the package being getting by + + + align:start position:0% +to distort the package being getting by +the low low types because you're giving + + align:start position:0% +the low low types because you're giving + + + align:start position:0% +the low low types because you're giving +money to every higher type when you give + + align:start position:0% +money to every higher type when you give + + + align:start position:0% +money to every higher type when you give +them something uh and then a second + + align:start position:0% +them something uh and then a second + + + align:start position:0% +them something uh and then a second +intuition is if there are types that + + align:start position:0% +intuition is if there are types that + + + align:start position:0% +intuition is if there are types that +there aren't a lot of you want to give + + align:start position:0% +there aren't a lot of you want to give + + + align:start position:0% +there aren't a lot of you want to give +them a very bad deal + + align:start position:0% +them a very bad deal + + + align:start position:0% +them a very bad deal +because you know anything you give them + + align:start position:0% +because you know anything you give them + + + align:start position:0% +because you know anything you give them +the fact that it's available raises the + + align:start position:0% +the fact that it's available raises the + + + align:start position:0% +the fact that it's available raises the +utility of the higher types if there + + align:start position:0% +utility of the higher types if there + + + align:start position:0% +utility of the higher types if there +aren't very many people in that group + + align:start position:0% +aren't very many people in that group + + + align:start position:0% +aren't very many people in that group +then you really want to discriminate you + + align:start position:0% +then you really want to discriminate you + + + align:start position:0% +then you really want to discriminate you +want to give them a terrible product + + align:start position:0% +want to give them a terrible product + + + align:start position:0% +want to give them a terrible product +because the profit you get from giving + + align:start position:0% +because the profit you get from giving + + + align:start position:0% +because the profit you get from giving +them off opal quality is Tiny when there + + align:start position:0% +them off opal quality is Tiny when there + + + align:start position:0% +them off opal quality is Tiny when there +aren't many people there so people who + + align:start position:0% +aren't many people there so people who + + + align:start position:0% +aren't many people there so people who +are in a small fraction of the + + align:start position:0% +are in a small fraction of the + + + align:start position:0% +are in a small fraction of the +population they also get really bad + + align:start position:0% +population they also get really bad + + + align:start position:0% +population they also get really bad +service on + + align:start position:0% +service on + + + align:start position:0% +service on +quality um but anyway so there's a video + + align:start position:0% +quality um but anyway so there's a video + + + align:start position:0% +quality um but anyway so there's a video +on the website I think what I want to do + + align:start position:0% +on the website I think what I want to do + + + align:start position:0% +on the website I think what I want to do +to jump ahead is the end is let me just + + align:start position:0% +to jump ahead is the end is let me just + + + align:start position:0% +to jump ahead is the end is let me just +talk about um + + align:start position:0% +talk about um + + + align:start position:0% +talk about um +bundling + + align:start position:0% + + + + align:start position:0% + +so you + + align:start position:0% +so you + + + align:start position:0% +so you +know let's think about you have a firm + + align:start position:0% +know let's think about you have a firm + + + align:start position:0% +know let's think about you have a firm +um that's selling multiple + + align:start position:0% +um that's selling multiple + + + align:start position:0% +um that's selling multiple +products + + align:start position:0% +products + + + align:start position:0% +products +um what's the best way to sell multiple + + align:start position:0% +um what's the best way to sell multiple + + + align:start position:0% +um what's the best way to sell multiple +Goods instead of a single good so for + + align:start position:0% +Goods instead of a single good so for + + + align:start position:0% +Goods instead of a single good so for +instance you know like apple doesn't + + align:start position:0% +instance you know like apple doesn't + + + align:start position:0% +instance you know like apple doesn't +just sell phones they sell phones and + + align:start position:0% +just sell phones they sell phones and + + + align:start position:0% +just sell phones they sell phones and +chargers and earbuds and uh apps for the + + align:start position:0% +chargers and earbuds and uh apps for the + + + align:start position:0% +chargers and earbuds and uh apps for the +phones + + align:start position:0% + + + + align:start position:0% + +um Netflix doesn't just sell movie by + + align:start position:0% +um Netflix doesn't just sell movie by + + + align:start position:0% +um Netflix doesn't just sell movie by +movie Netflix sells whole big bundles of + + align:start position:0% +movie Netflix sells whole big bundles of + + + align:start position:0% +movie Netflix sells whole big bundles of +movies um so + + align:start position:0% +movies um so + + + align:start position:0% +movies um so +observation from this literature is that + + align:start position:0% +observation from this literature is that + + + align:start position:0% +observation from this literature is that +often if a firm sells multiple products + + align:start position:0% +often if a firm sells multiple products + + + align:start position:0% +often if a firm sells multiple products +that are used together they're better + + align:start position:0% +that are used together they're better + + + align:start position:0% +that are used together they're better +off doing some kind of bundled pricing + + align:start position:0% +off doing some kind of bundled pricing + + + align:start position:0% +off doing some kind of bundled pricing +um why do you do some some kind of + + align:start position:0% +um why do you do some some kind of + + + align:start position:0% +um why do you do some some kind of +bundled pricing I put in this lecture + + align:start position:0% +bundled pricing I put in this lecture + + + align:start position:0% +bundled pricing I put in this lecture +because often the reasons why you want + + align:start position:0% +because often the reasons why you want + + + align:start position:0% +because often the reasons why you want +to bundle Goods together have something + + align:start position:0% +to bundle Goods together have something + + + align:start position:0% +to bundle Goods together have something +to do with price + + align:start position:0% +to do with price + + + align:start position:0% +to do with price +discrimination um so first example um + + align:start position:0% +discrimination um so first example um + + + align:start position:0% +discrimination um so first example um +due to Stigler is imagine you have + + align:start position:0% +due to Stigler is imagine you have + + + align:start position:0% +due to Stigler is imagine you have +consumers who have values for the two + + align:start position:0% +consumers who have values for the two + + + align:start position:0% +consumers who have values for the two +Goods that you sell which are negatively + + align:start position:0% +Goods that you sell which are negatively + + + align:start position:0% +Goods that you sell which are negatively +correlated um so you know the example + + align:start position:0% +correlated um so you know the example + + + align:start position:0% +correlated um so you know the example +that Stigler gave um is you know suppose + + align:start position:0% +that Stigler gave um is you know suppose + + + align:start position:0% +that Stigler gave um is you know suppose +you have these types Theta that are + + align:start position:0% +you have these types Theta that are + + + align:start position:0% +you have these types Theta that are +uniformly distributed on 01 and these + + align:start position:0% +uniformly distributed on 01 and these + + + align:start position:0% +uniformly distributed on 01 and these +are about their preferences over + + align:start position:0% +are about their preferences over + + + align:start position:0% +are about their preferences over +movies and so a type Theta consumer gets + + align:start position:0% +movies and so a type Theta consumer gets + + + align:start position:0% +movies and so a type Theta consumer gets +utility Theta from watching some kind of + + align:start position:0% +utility Theta from watching some kind of + + + align:start position:0% +utility Theta from watching some kind of +superhero action movie and gets utility + + align:start position:0% +superhero action movie and gets utility + + + align:start position:0% +superhero action movie and gets utility +one minus Theta from watching romantic + + align:start position:0% +one minus Theta from watching romantic + + + align:start position:0% +one minus Theta from watching romantic +comedy + + align:start position:0% +comedy + + + align:start position:0% +comedy +and people's preference over these + + align:start position:0% +and people's preference over these + + + align:start position:0% +and people's preference over these +things are just exactly negatively + + align:start position:0% +things are just exactly negatively + + + align:start position:0% +things are just exactly negatively +correlated so if I'm the far right + + align:start position:0% +correlated so if I'm the far right + + + align:start position:0% +correlated so if I'm the far right +superhero movie person I'm also the + + align:start position:0% +superhero movie person I'm also the + + + align:start position:0% +superhero movie person I'm also the +farle romantic comedy utility and if I'm + + align:start position:0% +farle romantic comedy utility and if I'm + + + align:start position:0% +farle romantic comedy utility and if I'm +the far right romantic comedy utility + + align:start position:0% +the far right romantic comedy utility + + + align:start position:0% +the far right romantic comedy utility +I'm the far left superhero quality okay + + align:start position:0% +I'm the far left superhero quality okay + + + align:start position:0% +I'm the far left superhero quality okay +um you know if Netflix had to sort of + + align:start position:0% +um you know if Netflix had to sort of + + + align:start position:0% +um you know if Netflix had to sort of +price these things separately and have + + align:start position:0% +price these things separately and have + + + align:start position:0% +price these things separately and have +we have Netflix action adventure movies + + align:start position:0% +we have Netflix action adventure movies + + + align:start position:0% +we have Netflix action adventure movies +and Netflix romantic comedy movies um + + align:start position:0% +and Netflix romantic comedy movies um + + + align:start position:0% +and Netflix romantic comedy movies um +what's going to happen well if it's if + + align:start position:0% +what's going to happen well if it's if + + + align:start position:0% +what's going to happen well if it's if +these are the values it's going to set + + align:start position:0% +these are the values it's going to set + + + align:start position:0% +these are the values it's going to set +piece star equals 1/2 for each + + align:start position:0% +piece star equals 1/2 for each + + + align:start position:0% +piece star equals 1/2 for each +service um every consumer is going to + + align:start position:0% +service um every consumer is going to + + + align:start position:0% +service um every consumer is going to +buy exactly one of the two + + align:start position:0% +buy exactly one of the two + + + align:start position:0% +buy exactly one of the two +Services um and + + align:start position:0% +Services um and + + + align:start position:0% +Services um and +so + + align:start position:0% +so + + + align:start position:0% +so +uh Netflix ends up earning profit one + + align:start position:0% +uh Netflix ends up earning profit one + + + align:start position:0% +uh Netflix ends up earning profit one +quarter on each I set a price of a half + + align:start position:0% +quarter on each I set a price of a half + + + align:start position:0% +quarter on each I set a price of a half +I sell a half the + + align:start position:0% +I sell a half the + + + align:start position:0% +I sell a half the +consumers uh and that's the profits that + + align:start position:0% +consumers uh and that's the profits that + + + align:start position:0% +consumers uh and that's the profits that +I + + align:start position:0% +I + + + align:start position:0% +I +get suppose they instead follow this + + align:start position:0% +get suppose they instead follow this + + + align:start position:0% +get suppose they instead follow this +pure bundling thing where we'll have + + align:start position:0% +pure bundling thing where we'll have + + + align:start position:0% +pure bundling thing where we'll have +both the action adventure movies and the + + align:start position:0% +both the action adventure movies and the + + + align:start position:0% +both the action adventure movies and the +romantic comedy + + align:start position:0% +romantic comedy + + + align:start position:0% +romantic comedy +on the same + + align:start position:0% +on the same + + + align:start position:0% +on the same +service well then what everybody can do + + align:start position:0% +service well then what everybody can do + + + align:start position:0% +service well then what everybody can do +is they can both watch their superhero + + align:start position:0% +is they can both watch their superhero + + + align:start position:0% +is they can both watch their superhero +movies and they can watch romantic + + align:start position:0% +movies and they can watch romantic + + + align:start position:0% +movies and they can watch romantic +comedies because they're both available + + align:start position:0% +comedies because they're both available + + + align:start position:0% +comedies because they're both available +free on the service what utility do they + + align:start position:0% +free on the service what utility do they + + + align:start position:0% +free on the service what utility do they +get from doing that they get utility + + align:start position:0% +get from doing that they get utility + + + align:start position:0% +get from doing that they get utility +theta plus one minus theta equals + + align:start position:0% +theta plus one minus theta equals + + + align:start position:0% +theta plus one minus theta equals +one um and + + align:start position:0% +one um and + + + align:start position:0% +one um and +so because they get utility one you can + + align:start position:0% +so because they get utility one you can + + + align:start position:0% +so because they get utility one you can +just set the price of the bundle equals + + align:start position:0% +just set the price of the bundle equals + + + align:start position:0% +just set the price of the bundle equals +one it's fully socially efficient we + + align:start position:0% +one it's fully socially efficient we + + + align:start position:0% +one it's fully socially efficient we +extract all the social surplus um but + + align:start position:0% +extract all the social surplus um but + + + align:start position:0% +extract all the social surplus um but +one way to think about sort of this + + align:start position:0% +one way to think about sort of this + + + align:start position:0% +one way to think about sort of this +bundle of one of what we're doing is we + + align:start position:0% +bundle of one of what we're doing is we + + + align:start position:0% +bundle of one of what we're doing is we +just have the people you know we have we + + align:start position:0% +just have the people you know we have we + + + align:start position:0% +just have the people you know we have we +know the people who are buying the + + align:start position:0% +know the people who are buying the + + + align:start position:0% +know the people who are buying the +superhero movie channel have low values + + align:start position:0% +superhero movie channel have low values + + + align:start position:0% +superhero movie channel have low values +for the Romantic Movie romantic movies + + align:start position:0% +for the Romantic Movie romantic movies + + + align:start position:0% +for the Romantic Movie romantic movies +so we just want to charge them a lower + + align:start position:0% +so we just want to charge them a lower + + + align:start position:0% +so we just want to charge them a lower +price for that and one this sort of + + align:start position:0% +price for that and one this sort of + + + align:start position:0% +price for that and one this sort of +combination of charging them a high + + align:start position:0% +combination of charging them a high + + + align:start position:0% +combination of charging them a high +price for one and a low price for one + + align:start position:0% +price for one and a low price for one + + + align:start position:0% +price for one and a low price for one +ends up being something you can do + + align:start position:0% +ends up being something you can do + + + align:start position:0% +ends up being something you can do +perfectly by bundling products + + align:start position:0% + + + + align:start position:0% + +together so that would be one argument + + align:start position:0% +together so that would be one argument + + + align:start position:0% +together so that would be one argument +for bundling + + align:start position:0% + + + + align:start position:0% + +um you know there's a very nice paper by + + align:start position:0% +um you know there's a very nice paper by + + + align:start position:0% +um you know there's a very nice paper by +McAfee McMillan and Winston that notes + + align:start position:0% +McAfee McMillan and Winston that notes + + + align:start position:0% +McAfee McMillan and Winston that notes +that you know this Stigler gave this + + align:start position:0% +that you know this Stigler gave this + + + align:start position:0% +that you know this Stigler gave this +example making you think negative + + align:start position:0% +example making you think negative + + + align:start position:0% +example making you think negative +correlation is important + + align:start position:0% +correlation is important + + + align:start position:0% +correlation is important +actually the same thing works with um uh + + align:start position:0% +actually the same thing works with um uh + + + align:start position:0% +actually the same thing works with um uh +independent valuations so suppose your + + align:start position:0% +independent valuations so suppose your + + + align:start position:0% +independent valuations so suppose your +values for romantic comedies and + + align:start position:0% +values for romantic comedies and + + + align:start position:0% +values for romantic comedies and +for uh romantic comedies and for + + align:start position:0% +for uh romantic comedies and for + + + align:start position:0% +for uh romantic comedies and for +superhero movies are are completely + + align:start position:0% +superhero movies are are completely + + + align:start position:0% +superhero movies are are completely +independent draws then it's still the + + align:start position:0% +independent draws then it's still the + + + align:start position:0% +independent draws then it's still the +case The Firm would be better off + + align:start position:0% +case The Firm would be better off + + + align:start position:0% +case The Firm would be better off +bundling not pure bundling like in + + align:start position:0% +bundling not pure bundling like in + + + align:start position:0% +bundling not pure bundling like in +Stigler but with mixed bundling you have + + align:start position:0% +Stigler but with mixed bundling you have + + + align:start position:0% +Stigler but with mixed bundling you have +offer three packages you offer the + + align:start position:0% +offer three packages you offer the + + + align:start position:0% +offer three packages you offer the +superhero movie channel the romantic + + align:start position:0% +superhero movie channel the romantic + + + align:start position:0% +superhero movie channel the romantic +comedy Channel or Netflix total um and + + align:start position:0% +comedy Channel or Netflix total um and + + + align:start position:0% +comedy Channel or Netflix total um and +this sort of mixed bundling scheme of + + align:start position:0% +this sort of mixed bundling scheme of + + + align:start position:0% +this sort of mixed bundling scheme of +offering the bundle and the two products + + align:start position:0% +offering the bundle and the two products + + + align:start position:0% +offering the bundle and the two products +separately strictly + + align:start position:0% +separately strictly + + + align:start position:0% +separately strictly +dominates uh offering the product + + align:start position:0% +dominates uh offering the product + + + align:start position:0% +dominates uh offering the product +separately when you have uh when you + + align:start position:0% +separately when you have uh when you + + + align:start position:0% +separately when you have uh when you +have independent value + + align:start position:0% +have independent value + + + align:start position:0% +have independent value +valuations um you in some sense it's + + align:start position:0% +valuations um you in some sense it's + + + align:start position:0% +valuations um you in some sense it's +it's an obvious statement that the mixed + + align:start position:0% +it's an obvious statement that the mixed + + + align:start position:0% +it's an obvious statement that the mixed +bundling strategy this offer you know P1 + + align:start position:0% +bundling strategy this offer you know P1 + + + align:start position:0% +bundling strategy this offer you know P1 +P2 and P bundle is at least weekly + + align:start position:0% +P2 and P bundle is at least weekly + + + align:start position:0% +P2 and P bundle is at least weekly +better because you could always offer + + align:start position:0% +better because you could always offer + + + align:start position:0% +better because you could always offer +good one at P1 star good to at P2 star + + align:start position:0% +good one at P1 star good to at P2 star + + + align:start position:0% +good one at P1 star good to at P2 star +and price the bundle at P1 Star Plus P2 + + align:start position:0% +and price the bundle at P1 Star Plus P2 + + + align:start position:0% +and price the bundle at P1 Star Plus P2 +star the bundle is some sense + + align:start position:0% +star the bundle is some sense + + + align:start position:0% +star the bundle is some sense +Superfluous but it doesn't hurt the + + align:start position:0% +Superfluous but it doesn't hurt the + + + align:start position:0% +Superfluous but it doesn't hurt the +monopolis profits um but what mc mc + + align:start position:0% +monopolis profits um but what mc mc + + + align:start position:0% +monopolis profits um but what mc mc +Winston Show is that in act um it it + + align:start position:0% +Winston Show is that in act um it it + + + align:start position:0% +Winston Show is that in act um it it +strictly raises profits and so let me + + align:start position:0% +strictly raises profits and so let me + + + align:start position:0% +strictly raises profits and so let me +I'll just sort of go through this as + + align:start position:0% +I'll just sort of go through this as + + + align:start position:0% +I'll just sort of go through this as +quickly as I can so you know start from + + align:start position:0% +quickly as I can so you know start from + + + align:start position:0% +quickly as I can so you know start from +the situation where you have P1 star P2 + + align:start position:0% +the situation where you have P1 star P2 + + + align:start position:0% +the situation where you have P1 star P2 +star and the price of the + + align:start position:0% +star and the price of the + + + align:start position:0% +star and the price of the +bundle + + align:start position:0% +bundle + + + align:start position:0% +bundle +okay then what's going to happen is + + align:start position:0% +okay then what's going to happen is + + + align:start position:0% +okay then what's going to happen is +these consumers with for which P1 for + + align:start position:0% +these consumers with for which P1 for + + + align:start position:0% +these consumers with for which P1 for +which V1 is large are going to buy good + + align:start position:0% +which V1 is large are going to buy good + + + align:start position:0% +which V1 is large are going to buy good +one these for whom V2 is large are going + + align:start position:0% +one these for whom V2 is large are going + + + align:start position:0% +one these for whom V2 is large are going +to buy good two and then people here are + + align:start position:0% +to buy good two and then people here are + + + align:start position:0% +to buy good two and then people here are +going to buy the + + align:start position:0% + + + + align:start position:0% + +bundle um um imagine that what the + + align:start position:0% +bundle um um imagine that what the + + + align:start position:0% +bundle um um imagine that what the +monopolis does now is it raises the + + align:start position:0% +monopolis does now is it raises the + + + align:start position:0% +monopolis does now is it raises the +price of good 2 by Epsilon and leaves + + align:start position:0% +price of good 2 by Epsilon and leaves + + + align:start position:0% +price of good 2 by Epsilon and leaves +the bundle price + + align:start position:0% +the bundle price + + + align:start position:0% +the bundle price +unchanged who is going to react when you + + align:start position:0% +unchanged who is going to react when you + + + align:start position:0% +unchanged who is going to react when you +raise the price of good two and you + + align:start position:0% +raise the price of good two and you + + + align:start position:0% +raise the price of good two and you +leave the bundle price + + align:start position:0% +leave the bundle price + + + align:start position:0% +leave the bundle price +unchanged + + align:start position:0% +unchanged + + + align:start position:0% +unchanged +well these consumers who would have + + align:start position:0% +well these consumers who would have + + + align:start position:0% +well these consumers who would have +bought formerly bought just good to now + + align:start position:0% +bought formerly bought just good to now + + + align:start position:0% +bought formerly bought just good to now +that good two has gone up in price + + align:start position:0% +that good two has gone up in price + + + align:start position:0% +that good two has gone up in price +they're going to switch from buying good + + align:start position:0% +they're going to switch from buying good + + + align:start position:0% +they're going to switch from buying good +two to buying the bundle + + align:start position:0% +two to buying the bundle + + + align:start position:0% +two to buying the bundle +and so we get this first Order gain and + + align:start position:0% +and so we get this first Order gain and + + + align:start position:0% +and so we get this first Order gain and +profits from all these people who were + + align:start position:0% +profits from all these people who were + + + align:start position:0% +profits from all these people who were +buying just good too now also buying + + align:start position:0% +buying just good too now also buying + + + align:start position:0% +buying just good too now also buying +good one from me which has a positive + + align:start position:0% +good one from me which has a positive + + + align:start position:0% +good one from me which has a positive +markup okay what do I lose I lose these + + align:start position:0% +markup okay what do I lose I lose these + + + align:start position:0% +markup okay what do I lose I lose these +people who would have bought good to at + + align:start position:0% +people who would have bought good to at + + + align:start position:0% +people who would have bought good to at +P2 star but now don't want to pay P2 + + align:start position:0% +P2 star but now don't want to pay P2 + + + align:start position:0% +P2 star but now don't want to pay P2 +Star Plus Epsilon because it's not worth + + align:start position:0% +Star Plus Epsilon because it's not worth + + + align:start position:0% +Star Plus Epsilon because it's not worth +it to them but you know we know that dpy + + align:start position:0% +it to them but you know we know that dpy + + + align:start position:0% +it to them but you know we know that dpy +2 dp2 to evaluated P2 + + align:start position:0% +2 dp2 to evaluated P2 + + + align:start position:0% +2 dp2 to evaluated P2 +star equals + + align:start position:0% +star equals + + + align:start position:0% +star equals +zero so the fact that I lose these + + align:start position:0% +zero so the fact that I lose these + + + align:start position:0% +zero so the fact that I lose these +customers and charge the price here I + + align:start position:0% +customers and charge the price here I + + + align:start position:0% +customers and charge the price here I +was to first order indiffer between this + + align:start position:0% +was to first order indiffer between this + + + align:start position:0% +was to first order indiffer between this +price and this price anyway in this + + align:start position:0% +price and this price anyway in this + + + align:start position:0% +price and this price anyway in this +market so I've got a second order loss + + align:start position:0% +market so I've got a second order loss + + + align:start position:0% +market so I've got a second order loss +from raising the price A first order + + align:start position:0% +from raising the price A first order + + + align:start position:0% +from raising the price A first order +benefit uh from cutting the price sorry + + align:start position:0% +benefit uh from cutting the price sorry + + + align:start position:0% +benefit uh from cutting the price sorry +from raising the price and getting them + + align:start position:0% +from raising the price and getting them + + + align:start position:0% +from raising the price and getting them +to buy the bundle instead and therefore + + align:start position:0% +to buy the bundle instead and therefore + + + align:start position:0% +to buy the bundle instead and therefore +uh I'm strictly better off by bundling + + align:start position:0% +uh I'm strictly better off by bundling + + + align:start position:0% +uh I'm strictly better off by bundling +and so that's the basic argument in M + + align:start position:0% +and so that's the basic argument in M + + + align:start position:0% +and so that's the basic argument in M +Winston is that sort of mixed bundling + + align:start position:0% +Winston is that sort of mixed bundling + + + align:start position:0% +Winston is that sort of mixed bundling +is obviously weekly optimal and if you + + align:start position:0% +is obviously weekly optimal and if you + + + align:start position:0% +is obviously weekly optimal and if you +just think about starting from that + + align:start position:0% +just think about starting from that + + + align:start position:0% +just think about starting from that +Weekly optimal thing and then just + + align:start position:0% +Weekly optimal thing and then just + + + align:start position:0% +Weekly optimal thing and then just +raising the price of the two goods + + align:start position:0% +raising the price of the two goods + + + align:start position:0% +raising the price of the two goods +individually that's always better for + + align:start position:0% +individually that's always better for + + + align:start position:0% +individually that's always better for +you so the fact that you can bundle and + + align:start position:0% +you so the fact that you can bundle and + + + align:start position:0% +you so the fact that you can bundle and +have people have this option to switch + + align:start position:0% +have people have this option to switch + + + align:start position:0% +have people have this option to switch +to the bundle which lets you sell extra + + align:start position:0% +to the bundle which lets you sell extra + + + align:start position:0% +to the bundle which lets you sell extra +Goods is good for you and so you do + + align:start position:0% +Goods is good for you and so you do + + + align:start position:0% +Goods is good for you and so you do +generally want to bundle if you're in + + align:start position:0% +generally want to bundle if you're in + + + align:start position:0% +generally want to bundle if you're in +this case where sort of values for the + + align:start position:0% +this case where sort of values for the + + + align:start position:0% +this case where sort of values for the +two goods are + + align:start position:0% +two goods are + + + align:start position:0% +two goods are +independent + + align:start position:0% +independent + + + align:start position:0% +independent +okay okay so I am out of time so why + + align:start position:0% +okay okay so I am out of time so why + + + align:start position:0% +okay okay so I am out of time so why +don't I just sort of stop there \ No newline at end of file diff --git a/Y-muIQlmKiE.txt b/Y-muIQlmKiE.txt new file mode 100644 index 0000000000000000000000000000000000000000..ff12c6a01996cd49eba8296cde3b591a290e6a80 --- /dev/null +++ b/Y-muIQlmKiE.txt @@ -0,0 +1,8619 @@ +align:start position:0% + +okay these are what i call the primitive + + align:start position:0% +okay these are what i call the primitive + + + align:start position:0% +okay these are what i call the primitive +cellular mechanisms irritability that is + + align:start position:0% +cellular mechanisms irritability that is + + + align:start position:0% +cellular mechanisms irritability that is +response to something in the environment + + align:start position:0% +response to something in the environment + + + align:start position:0% +response to something in the environment +conduction the other parts of the cell + + align:start position:0% +conduction the other parts of the cell + + + align:start position:0% +conduction the other parts of the cell +movement of the cell secretion + + align:start position:0% +movement of the cell secretion + + + align:start position:0% +movement of the cell secretion +we should probably add that's exocytosis + + align:start position:0% +we should probably add that's exocytosis + + + align:start position:0% +we should probably add that's exocytosis +we should probably add endocytosis + + align:start position:0% +we should probably add endocytosis + + + align:start position:0% +we should probably add endocytosis +define those terms + + align:start position:0% +define those terms + + + align:start position:0% +define those terms +taking in as well as + + align:start position:0% +taking in as well as + + + align:start position:0% +taking in as well as +secreting + + align:start position:0% +secreting + + + align:start position:0% +secreting +and we'll talk about membrane + + align:start position:0% +and we'll talk about membrane + + + align:start position:0% +and we'll talk about membrane +specializations + + align:start position:0% +specializations + + + align:start position:0% +specializations +transduction mechanisms and a little bit + + align:start position:0% +transduction mechanisms and a little bit + + + align:start position:0% +transduction mechanisms and a little bit +about endogenous activity before we + + align:start position:0% +about endogenous activity before we + + + align:start position:0% +about endogenous activity before we +go to the multicellular structures + + align:start position:0% + + + + align:start position:0% + +now movement of cells + + align:start position:0% +now movement of cells + + + align:start position:0% +now movement of cells +what's what what cells are we usually + + align:start position:0% +what's what what cells are we usually + + + align:start position:0% +what's what what cells are we usually +talking about when we talk about + + align:start position:0% +talking about when we talk about + + + align:start position:0% +talking about when we talk about +movement + + align:start position:0% + + + + align:start position:0% + +what cells move the most + + align:start position:0% +what cells move the most + + + align:start position:0% +what cells move the most +muscle cells and what does it require + + align:start position:0% + + + + align:start position:0% + +it requires contractual proteins and + + align:start position:0% +it requires contractual proteins and + + + align:start position:0% +it requires contractual proteins and +energy + + align:start position:0% +energy + + + align:start position:0% +energy +now are there any contractual proteins + + align:start position:0% +now are there any contractual proteins + + + align:start position:0% +now are there any contractual proteins +in neurons + + align:start position:0% + + + + align:start position:0% + +well especially in development there's a + + align:start position:0% +well especially in development there's a + + + align:start position:0% +well especially in development there's a +lot of actin many actin filaments + + align:start position:0% +lot of actin many actin filaments + + + align:start position:0% +lot of actin many actin filaments +okay especially in the part of the + + align:start position:0% +okay especially in the part of the + + + align:start position:0% +okay especially in the part of the +neuron changing the most during + + align:start position:0% +neuron changing the most during + + + align:start position:0% +neuron changing the most during +development + + align:start position:0% + + + + align:start position:0% + +and that occurs in migration of the + + align:start position:0% +and that occurs in migration of the + + + align:start position:0% +and that occurs in migration of the +whole cell + + align:start position:0% +whole cell + + + align:start position:0% +whole cell +as well as in the growth of the + + align:start position:0% +as well as in the growth of the + + + align:start position:0% +as well as in the growth of the +processes + + align:start position:0% +processes + + + align:start position:0% +processes +process + + align:start position:0% +process + + + align:start position:0% +process +is used in anatomy to mean the little + + align:start position:0% +is used in anatomy to mean the little + + + align:start position:0% +is used in anatomy to mean the little +extensions of neurons it's not the way + + align:start position:0% +extensions of neurons it's not the way + + + align:start position:0% +extensions of neurons it's not the way +you usually term use the term process + + align:start position:0% +you usually term use the term process + + + align:start position:0% +you usually term use the term process +so cellular processes are the little + + align:start position:0% +so cellular processes are the little + + + align:start position:0% +so cellular processes are the little +extensions + + align:start position:0% +extensions + + + align:start position:0% +extensions +of the neurons + + align:start position:0% +of the neurons + + + align:start position:0% +of the neurons +okay i'll try to stop myself in defined + + align:start position:0% +okay i'll try to stop myself in defined + + + align:start position:0% +okay i'll try to stop myself in defined +terms if i don't you should stop me and + + align:start position:0% +terms if i don't you should stop me and + + + align:start position:0% +terms if i don't you should stop me and +ask me + + align:start position:0% + + + + align:start position:0% + +you also of course get movement and + + align:start position:0% +you also of course get movement and + + + align:start position:0% +you also of course get movement and +regeneration + + align:start position:0% +regeneration + + + align:start position:0% +regeneration +and i'm going to talk a little bit about + + align:start position:0% +and i'm going to talk a little bit about + + + align:start position:0% +and i'm going to talk a little bit about +regeneration which is a topic i do + + align:start position:0% +regeneration which is a topic i do + + + align:start position:0% +regeneration which is a topic i do +research on + + align:start position:0% +research on + + + align:start position:0% +research on +when we talk about development + + align:start position:0% +when we talk about development + + + align:start position:0% +when we talk about development +a little bit later + + align:start position:0% +a little bit later + + + align:start position:0% +a little bit later +and there's + + align:start position:0% +and there's + + + align:start position:0% +and there's +more generally there's various kinds of + + align:start position:0% +more generally there's various kinds of + + + align:start position:0% +more generally there's various kinds of +plasticity not only in developing but + + align:start position:0% +plasticity not only in developing but + + + align:start position:0% +plasticity not only in developing but +even in adult brains yes even your brain + + align:start position:0% +even in adult brains yes even your brain + + + align:start position:0% +even in adult brains yes even your brain +is changing in its structure and its + + align:start position:0% +is changing in its structure and its + + + align:start position:0% +is changing in its structure and its +connections + + align:start position:0% + + + + align:start position:0% + +today we're more concerned with how + + align:start position:0% +today we're more concerned with how + + + align:start position:0% +today we're more concerned with how +activity spreads within a cell some of + + align:start position:0% +activity spreads within a cell some of + + + align:start position:0% +activity spreads within a cell some of +it's mechanical + + align:start position:0% +it's mechanical + + + align:start position:0% +it's mechanical +if the cell is + + align:start position:0% +if the cell is + + + align:start position:0% +if the cell is +mechanically moved you get changes that + + align:start position:0% +mechanically moved you get changes that + + + align:start position:0% +mechanically moved you get changes that +are communicated to the rest of the cell + + align:start position:0% +are communicated to the rest of the cell + + + align:start position:0% +are communicated to the rest of the cell +through the cytoskeleton + + align:start position:0% +through the cytoskeleton + + + align:start position:0% +through the cytoskeleton +it's been a particular topic of research + + align:start position:0% +it's been a particular topic of research + + + align:start position:0% +it's been a particular topic of research +of dying amber at harvard + + align:start position:0% +of dying amber at harvard + + + align:start position:0% +of dying amber at harvard +but usually we're dealing with these + + align:start position:0% +but usually we're dealing with these + + + align:start position:0% +but usually we're dealing with these +other things diffusion of molecules + + align:start position:0% + + + + align:start position:0% + +chains of reactions molecular cascades + + align:start position:0% +chains of reactions molecular cascades + + + align:start position:0% +chains of reactions molecular cascades +within the cell + + align:start position:0% +within the cell + + + align:start position:0% +within the cell +we also have in neurons specialized + + align:start position:0% +we also have in neurons specialized + + + align:start position:0% +we also have in neurons specialized +mechanisms that we call active transport + + align:start position:0% +mechanisms that we call active transport + + + align:start position:0% +mechanisms that we call active transport +mechanisms involving these molecules + + align:start position:0% +mechanisms involving these molecules + + + align:start position:0% +mechanisms involving these molecules +kinesin and dynein + + align:start position:0% +kinesin and dynein + + + align:start position:0% +kinesin and dynein +for moving organelles + + align:start position:0% +for moving organelles + + + align:start position:0% +for moving organelles +and molecules from one part of the cell + + align:start position:0% +and molecules from one part of the cell + + + align:start position:0% +and molecules from one part of the cell +to another usually from the cell body + + align:start position:0% +to another usually from the cell body + + + align:start position:0% +to another usually from the cell body +down to the endings of the axon or back + + align:start position:0% +down to the endings of the axon or back + + + align:start position:0% +down to the endings of the axon or back +from the accent ending back to the cell + + align:start position:0% +from the accent ending back to the cell + + + align:start position:0% +from the accent ending back to the cell +body + + align:start position:0% +body + + + align:start position:0% +body +okay and we'll mention this again + + align:start position:0% +okay and we'll mention this again + + + align:start position:0% +okay and we'll mention this again +and then the topic we'll talk most about + + align:start position:0% +and then the topic we'll talk most about + + + align:start position:0% +and then the topic we'll talk most about +today electrical changes in the membrane + + align:start position:0% +today electrical changes in the membrane + + + align:start position:0% +today electrical changes in the membrane +so mechanical stimulus or chemical + + align:start position:0% +so mechanical stimulus or chemical + + + align:start position:0% +so mechanical stimulus or chemical +stimulus or an electrical stimulus to + + align:start position:0% +stimulus or an electrical stimulus to + + + align:start position:0% +stimulus or an electrical stimulus to +the cell membrane + + align:start position:0% +the cell membrane + + + align:start position:0% +the cell membrane +will lead to a depolarization of the + + align:start position:0% +will lead to a depolarization of the + + + align:start position:0% +will lead to a depolarization of the +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +some cases hyperpolarization + + align:start position:0% +some cases hyperpolarization + + + align:start position:0% +some cases hyperpolarization +but if it's a mechanical nudge it's + + align:start position:0% +but if it's a mechanical nudge it's + + + align:start position:0% +but if it's a mechanical nudge it's +always depolarization and then that + + align:start position:0% +always depolarization and then that + + + align:start position:0% +always depolarization and then that +change is conducted away from the point + + align:start position:0% +change is conducted away from the point + + + align:start position:0% +change is conducted away from the point +of origin + + align:start position:0% +of origin + + + align:start position:0% +of origin +okay + + align:start position:0% + + + + align:start position:0% + +so that's how activity spreads within a + + align:start position:0% +so that's how activity spreads within a + + + align:start position:0% +so that's how activity spreads within a +cell + + align:start position:0% + + + + align:start position:0% + +and when we talk about irritability and + + align:start position:0% +and when we talk about irritability and + + + align:start position:0% +and when we talk about irritability and +conduction in neurons + + align:start position:0% +conduction in neurons + + + align:start position:0% +conduction in neurons +these are the terms + + align:start position:0% +these are the terms + + + align:start position:0% +these are the terms +at the left + + align:start position:0% + + + + align:start position:0% + +we're usually talking about polarization + + align:start position:0% +we're usually talking about polarization + + + align:start position:0% +we're usually talking about polarization +of the membrane + + align:start position:0% + + + + align:start position:0% + +either a graded or non-response + + align:start position:0% +either a graded or non-response + + + align:start position:0% +either a graded or non-response +conduction that can be decremental or + + align:start position:0% +conduction that can be decremental or + + + align:start position:0% +conduction that can be decremental or +non-decremental + + align:start position:0% +non-decremental + + + align:start position:0% +non-decremental +depending on whether we're talking about + + align:start position:0% +depending on whether we're talking about + + + align:start position:0% +depending on whether we're talking about +action potentials or not and after + + align:start position:0% +action potentials or not and after + + + align:start position:0% +action potentials or not and after +potentials + + align:start position:0% +potentials + + + align:start position:0% +potentials +okay and the terms on the right refer to + + align:start position:0% + + + + align:start position:0% + +synaptic action we'll talk about that + + align:start position:0% +synaptic action we'll talk about that + + + align:start position:0% +synaptic action we'll talk about that +afterwards + + align:start position:0% +afterwards + + + align:start position:0% +afterwards +this is i'm not sure i can't remember + + align:start position:0% +this is i'm not sure i can't remember + + + align:start position:0% +this is i'm not sure i can't remember +now which version of the text + + align:start position:0% +now which version of the text + + + align:start position:0% +now which version of the text +whether this picture is in your text or + + align:start position:0% +whether this picture is in your text or + + + align:start position:0% +whether this picture is in your text or +not but it was in an earlier version + + align:start position:0% +not but it was in an earlier version + + + align:start position:0% +not but it was in an earlier version +and i haven't changed the pictures + + align:start position:0% +and i haven't changed the pictures + + + align:start position:0% +and i haven't changed the pictures +i just want to note that these + + align:start position:0% +i just want to note that these + + + align:start position:0% +i just want to note that these +he puts these up as classification + + align:start position:0% +he puts these up as classification + + + align:start position:0% +he puts these up as classification +neurons into three principal types + + align:start position:0% +neurons into three principal types + + + align:start position:0% +neurons into three principal types +it actually means only three + + align:start position:0% +it actually means only three + + + align:start position:0% +it actually means only three +principal types of long axon neuron okay + + align:start position:0% +principal types of long axon neuron okay + + + align:start position:0% +principal types of long axon neuron okay +in fact there's probably more short acts + + align:start position:0% +in fact there's probably more short acts + + + align:start position:0% +in fact there's probably more short acts +on neurons in the nervous system than + + align:start position:0% +on neurons in the nervous system than + + + align:start position:0% +on neurons in the nervous system than +there are long axon neurons + + align:start position:0% +there are long axon neurons + + + align:start position:0% +there are long axon neurons +but these are + + align:start position:0% +but these are + + + align:start position:0% +but these are +when you see + + align:start position:0% + + + + align:start position:0% + +people talking about neurons they + + align:start position:0% +people talking about neurons they + + + align:start position:0% +people talking about neurons they +usually draw something that looks like + + align:start position:0% +usually draw something that looks like + + + align:start position:0% +usually draw something that looks like +that one on the left + + align:start position:0% +that one on the left + + + align:start position:0% +that one on the left +that would be like a motor neuron in the + + align:start position:0% +that would be like a motor neuron in the + + + align:start position:0% +that would be like a motor neuron in the +spinal cord + + align:start position:0% + + + + align:start position:0% + +with the cell body in the central + + align:start position:0% +with the cell body in the central + + + align:start position:0% +with the cell body in the central +nervous system and the axon going to a + + align:start position:0% +nervous system and the axon going to a + + + align:start position:0% +nervous system and the axon going to a +muscle + + align:start position:0% + + + + align:start position:0% + +the middle cell type is like + + align:start position:0% + + + + align:start position:0% + +the cell with its axon coming in through + + align:start position:0% +the cell with its axon coming in through + + + align:start position:0% +the cell with its axon coming in through +a dorsal root so the cell bodies outside + + align:start position:0% +a dorsal root so the cell bodies outside + + + align:start position:0% +a dorsal root so the cell bodies outside +the cns + + align:start position:0% +the cns + + + align:start position:0% +the cns +and what we call a dorsal root gang and + + align:start position:0% +and what we call a dorsal root gang and + + + align:start position:0% +and what we call a dorsal root gang and +that would be the cell type furthest to + + align:start position:0% +that would be the cell type furthest to + + + align:start position:0% +that would be the cell type furthest to +the right whereas in the middle one that + + align:start position:0% +the right whereas in the middle one that + + + align:start position:0% +the right whereas in the middle one that +would be like a cell in your + + align:start position:0% + + + + align:start position:0% + +connected to your + + align:start position:0% +connected to your + + + align:start position:0% +connected to your +vestibular or auditory apparatus the + + align:start position:0% +vestibular or auditory apparatus the + + + align:start position:0% +vestibular or auditory apparatus the +cochlea in the inner ear these are + + align:start position:0% +cochlea in the inner ear these are + + + align:start position:0% +cochlea in the inner ear these are +bipolar neurons + + align:start position:0% +bipolar neurons + + + align:start position:0% +bipolar neurons +a little bit more primitive in nature + + align:start position:0% +a little bit more primitive in nature + + + align:start position:0% +a little bit more primitive in nature +because all the neurons and + + align:start position:0% +because all the neurons and + + + align:start position:0% +because all the neurons and +lower creatures look like that + + align:start position:0% + + + + align:start position:0% + +so these are the types of long axon + + align:start position:0% +so these are the types of long axon + + + align:start position:0% +so these are the types of long axon +neurons and we can all in any neuron + + align:start position:0% +neurons and we can all in any neuron + + + align:start position:0% +neurons and we can all in any neuron +we can + + align:start position:0% +we can + + + align:start position:0% +we can +divide up the neuron into functional + + align:start position:0% +divide up the neuron into functional + + + align:start position:0% +divide up the neuron into functional +divisions an input area or input zone in + + align:start position:0% +divisions an input area or input zone in + + + align:start position:0% +divisions an input area or input zone in +the picture here + + align:start position:0% +the picture here + + + align:start position:0% +the picture here +a zone of transmission or conduction + + align:start position:0% +a zone of transmission or conduction + + + align:start position:0% +a zone of transmission or conduction +which is mostly the axon and then + + align:start position:0% +which is mostly the axon and then + + + align:start position:0% +which is mostly the axon and then +finally an output area + + align:start position:0% +finally an output area + + + align:start position:0% +finally an output area +where the activity is affects other + + align:start position:0% +where the activity is affects other + + + align:start position:0% +where the activity is affects other +cells + + align:start position:0% +cells + + + align:start position:0% +cells +the exon terminals + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +say we're going to record from a cell + + align:start position:0% + + + + align:start position:0% + +and i'm just indicating the cell here + + align:start position:0% +and i'm just indicating the cell here + + + align:start position:0% +and i'm just indicating the cell here +with a circle + + align:start position:0% +with a circle + + + align:start position:0% +with a circle +which is the + + align:start position:0% +which is the + + + align:start position:0% +which is the +lipid binomial lipid bilayer + + align:start position:0% + + + + align:start position:0% + +and i've indicated there that if we take + + align:start position:0% +and i've indicated there that if we take + + + align:start position:0% +and i've indicated there that if we take +an electrode + + align:start position:0% +an electrode + + + align:start position:0% +an electrode +here + + align:start position:0% + + + + align:start position:0% + +shown here in red + + align:start position:0% +shown here in red + + + align:start position:0% +shown here in red +okay i'm taking a little microelectrode + + align:start position:0% +okay i'm taking a little microelectrode + + + align:start position:0% +okay i'm taking a little microelectrode +and i'm advancing it toward the cell + + align:start position:0% +and i'm advancing it toward the cell + + + align:start position:0% +and i'm advancing it toward the cell +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and i'm recording against the + + align:start position:0% +and i'm recording against the + + + align:start position:0% +and i'm recording against the +extracellular fluid as soon as i poke + + align:start position:0% +extracellular fluid as soon as i poke + + + align:start position:0% +extracellular fluid as soon as i poke +through the membrane the potential + + align:start position:0% +through the membrane the potential + + + align:start position:0% +through the membrane the potential +changes to + + align:start position:0% +changes to + + + align:start position:0% +changes to +about minus 70 millivolts okay negative + + align:start position:0% +about minus 70 millivolts okay negative + + + align:start position:0% +about minus 70 millivolts okay negative +on the inside of the cell with respect + + align:start position:0% +on the inside of the cell with respect + + + align:start position:0% +on the inside of the cell with respect +to the outside okay + + align:start position:0% +to the outside okay + + + align:start position:0% +to the outside okay +because the membrane + + align:start position:0% +because the membrane + + + align:start position:0% +because the membrane +of neurons like the membrane of many + + align:start position:0% +of neurons like the membrane of many + + + align:start position:0% +of neurons like the membrane of many +other cells too is polarized + + align:start position:0% +other cells too is polarized + + + align:start position:0% +other cells too is polarized +okay it's an electrical potential across + + align:start position:0% +okay it's an electrical potential across + + + align:start position:0% +okay it's an electrical potential across +the membrane + + align:start position:0% + + + + align:start position:0% + +it's not only true of neurons it's even + + align:start position:0% +it's not only true of neurons it's even + + + align:start position:0% +it's not only true of neurons it's even +true leaf cells + + align:start position:0% +true leaf cells + + + align:start position:0% +true leaf cells +okay + + align:start position:0% + + + + align:start position:0% + +but the neuron is specialized in several + + align:start position:0% +but the neuron is specialized in several + + + align:start position:0% +but the neuron is specialized in several +ways + + align:start position:0% + + + + align:start position:0% + +and if we + + align:start position:0% +and if we + + + align:start position:0% +and if we +if we nudge the neuron a little bit as + + align:start position:0% +if we nudge the neuron a little bit as + + + align:start position:0% +if we nudge the neuron a little bit as +i'm showing there i poked around a + + align:start position:0% +i'm showing there i poked around a + + + align:start position:0% +i'm showing there i poked around a +little bit there's a depolarization of + + align:start position:0% +little bit there's a depolarization of + + + align:start position:0% +little bit there's a depolarization of +the membrane that that's the response + + align:start position:0% +the membrane that that's the response + + + align:start position:0% +the membrane that that's the response +primary response of that neural membrane + + align:start position:0% +primary response of that neural membrane + + + align:start position:0% +primary response of that neural membrane +to be stimulated even mechanically okay + + align:start position:0% + + + + align:start position:0% + +now i've indicated here that + + align:start position:0% +now i've indicated here that + + + align:start position:0% +now i've indicated here that +there's a differential distribution of + + align:start position:0% +there's a differential distribution of + + + align:start position:0% +there's a differential distribution of +ions on either side of the membrane + + align:start position:0% + + + + align:start position:0% + +first of all there are negatively + + align:start position:0% +first of all there are negatively + + + align:start position:0% +first of all there are negatively +charged anions + + align:start position:0% +charged anions + + + align:start position:0% +charged anions +inside the cell + + align:start position:0% + + + + align:start position:0% + +very few on the outside + + align:start position:0% +very few on the outside + + + align:start position:0% +very few on the outside +and the membrane is impermeable to them + + align:start position:0% +and the membrane is impermeable to them + + + align:start position:0% +and the membrane is impermeable to them +okay so they can't get through + + align:start position:0% + + + + align:start position:0% + +we call this membrane of the neuron a + + align:start position:0% +we call this membrane of the neuron a + + + align:start position:0% +we call this membrane of the neuron a +semi-permeable membrane because it's + + align:start position:0% +semi-permeable membrane because it's + + + align:start position:0% +semi-permeable membrane because it's +impermeable to some things it's + + align:start position:0% +impermeable to some things it's + + + align:start position:0% +impermeable to some things it's +permeable to other ions and it's + + align:start position:0% + + + + align:start position:0% + +semi-permeable to others + + align:start position:0% +semi-permeable to others + + + align:start position:0% +semi-permeable to others +so for example + + align:start position:0% +so for example + + + align:start position:0% +so for example +when the neurons in the resting state + + align:start position:0% +when the neurons in the resting state + + + align:start position:0% +when the neurons in the resting state +it's pretty impermeable to sodium ions + + align:start position:0% +it's pretty impermeable to sodium ions + + + align:start position:0% +it's pretty impermeable to sodium ions +there's many more sodium ions on the + + align:start position:0% +there's many more sodium ions on the + + + align:start position:0% +there's many more sodium ions on the +outside than there are on the inside + + align:start position:0% + + + + align:start position:0% + +there's also many more chloride ions on + + align:start position:0% +there's also many more chloride ions on + + + align:start position:0% +there's also many more chloride ions on +the outside on the inside besides those + + align:start position:0% +the outside on the inside besides those + + + align:start position:0% +the outside on the inside besides those +negatively charged anions you have the + + align:start position:0% +negatively charged anions you have the + + + align:start position:0% +negatively charged anions you have the +potassium ions now the membrane + + align:start position:0% +potassium ions now the membrane + + + align:start position:0% +potassium ions now the membrane +does have some + + align:start position:0% +does have some + + + align:start position:0% +does have some +potassium channels that are open others + + align:start position:0% +potassium channels that are open others + + + align:start position:0% +potassium channels that are open others +that are closed so the permeability the + + align:start position:0% +that are closed so the permeability the + + + align:start position:0% +that are closed so the permeability the +potassium can change depending on how + + align:start position:0% +potassium can change depending on how + + + align:start position:0% +potassium can change depending on how +many channels are open okay + + align:start position:0% + + + + align:start position:0% + +so the + + align:start position:0% +so the + + + align:start position:0% +so the +membrane potential then is a result of + + align:start position:0% +membrane potential then is a result of + + + align:start position:0% +membrane potential then is a result of +this + + align:start position:0% + + + + align:start position:0% + +distribution of ions on either side of + + align:start position:0% +distribution of ions on either side of + + + align:start position:0% +distribution of ions on either side of +the membrane + + align:start position:0% +the membrane + + + align:start position:0% +the membrane +as well as + + align:start position:0% + + + + align:start position:0% + +of course + + align:start position:0% +of course + + + align:start position:0% +of course +on electrostatic forces and one other + + align:start position:0% +on electrostatic forces and one other + + + align:start position:0% +on electrostatic forces and one other +thing + + align:start position:0% +thing + + + align:start position:0% +thing +i've indicated there at the bottom + + align:start position:0% +i've indicated there at the bottom + + + align:start position:0% +i've indicated there at the bottom +there's a little active + + align:start position:0% +there's a little active + + + align:start position:0% +there's a little active +protein engine in the membrane + + align:start position:0% +protein engine in the membrane + + + align:start position:0% +protein engine in the membrane +we call the sodium pump + + align:start position:0% +we call the sodium pump + + + align:start position:0% +we call the sodium pump +okay + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +using a little energy + + align:start position:0% +using a little energy + + + align:start position:0% +using a little energy +it moves three sodiums out and brings + + align:start position:0% +it moves three sodiums out and brings + + + align:start position:0% +it moves three sodiums out and brings +two potassiums in with every cycle + + align:start position:0% +two potassiums in with every cycle + + + align:start position:0% +two potassiums in with every cycle +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and that's important in order to + + align:start position:0% +and that's important in order to + + + align:start position:0% +and that's important in order to +maintain + + align:start position:0% +maintain + + + align:start position:0% +maintain +the + + align:start position:0% +the + + + align:start position:0% +the +high concentration of sodium on the + + align:start position:0% +high concentration of sodium on the + + + align:start position:0% +high concentration of sodium on the +outside but why would you have to + + align:start position:0% +outside but why would you have to + + + align:start position:0% +outside but why would you have to +maintain it what's happening to it well + + align:start position:0% +maintain it what's happening to it well + + + align:start position:0% +maintain it what's happening to it well +whenever you get an action potential + + align:start position:0% +whenever you get an action potential + + + align:start position:0% +whenever you get an action potential +there's an implosion of sodium ions and + + align:start position:0% +there's an implosion of sodium ions and + + + align:start position:0% +there's an implosion of sodium ions and +we will talk about that + + align:start position:0% +we will talk about that + + + align:start position:0% +we will talk about that +now first say a little bit about the + + align:start position:0% +now first say a little bit about the + + + align:start position:0% +now first say a little bit about the +factors determining a resting potential + + align:start position:0% +factors determining a resting potential + + + align:start position:0% +factors determining a resting potential +if you look at this picture it shows a + + align:start position:0% +if you look at this picture it shows a + + + align:start position:0% +if you look at this picture it shows a +picture of the lipid bilayer with + + align:start position:0% +picture of the lipid bilayer with + + + align:start position:0% +picture of the lipid bilayer with +proteins embedded in it + + align:start position:0% +proteins embedded in it + + + align:start position:0% +proteins embedded in it +proteins + + align:start position:0% +proteins + + + align:start position:0% +proteins +transmembrane proteins + + align:start position:0% +transmembrane proteins + + + align:start position:0% +transmembrane proteins +and these are the ion channels + + align:start position:0% +and these are the ion channels + + + align:start position:0% +and these are the ion channels +and it's showing + + align:start position:0% +and it's showing + + + align:start position:0% +and it's showing +potassium channels + + align:start position:0% +potassium channels + + + align:start position:0% +potassium channels +that are open + + align:start position:0% +that are open + + + align:start position:0% +that are open +so potassium can move in either + + align:start position:0% +so potassium can move in either + + + align:start position:0% +so potassium can move in either +direction + + align:start position:0% +direction + + + align:start position:0% +direction +but the sodium channels + + align:start position:0% +but the sodium channels + + + align:start position:0% +but the sodium channels +are closed + + align:start position:0% + + + + align:start position:0% + +well then why would potassium end up + + align:start position:0% +well then why would potassium end up + + + align:start position:0% +well then why would potassium end up +distributed differently on the two sides + + align:start position:0% +distributed differently on the two sides + + + align:start position:0% +distributed differently on the two sides +of the membrane + + align:start position:0% +of the membrane + + + align:start position:0% +of the membrane +if the channels are open + + align:start position:0% +if the channels are open + + + align:start position:0% +if the channels are open +anybody + + align:start position:0% + + + + align:start position:0% + +well remember + + align:start position:0% +well remember + + + align:start position:0% +well remember +you've got those big anions inside + + align:start position:0% +you've got those big anions inside + + + align:start position:0% +you've got those big anions inside +you've got the sodium ions in the + + align:start position:0% +you've got the sodium ions in the + + + align:start position:0% +you've got the sodium ions in the +outside + + align:start position:0% +outside + + + align:start position:0% +outside +so the way the other ions distribute + + align:start position:0% +so the way the other ions distribute + + + align:start position:0% +so the way the other ions distribute +even if they can get through the + + align:start position:0% +even if they can get through the + + + align:start position:0% +even if they can get through the +membrane will depend on + + align:start position:0% +membrane will depend on + + + align:start position:0% +membrane will depend on +what two kinds of forces + + align:start position:0% +what two kinds of forces + + + align:start position:0% +what two kinds of forces +electrostatic forces and concentration + + align:start position:0% +electrostatic forces and concentration + + + align:start position:0% +electrostatic forces and concentration +gradients + + align:start position:0% +gradients + + + align:start position:0% +gradients +okay + + align:start position:0% + + + + align:start position:0% + +diffusion forces okay + + align:start position:0% + + + + align:start position:0% + +let's talk a little more now about + + align:start position:0% +let's talk a little more now about + + + align:start position:0% +let's talk a little more now about +what happens if we poke an electrode + + align:start position:0% +what happens if we poke an electrode + + + align:start position:0% +what happens if we poke an electrode +inside the axon of the cell you see over + + align:start position:0% +inside the axon of the cell you see over + + + align:start position:0% +inside the axon of the cell you see over +there at the left they show + + align:start position:0% +there at the left they show + + + align:start position:0% +there at the left they show +they show a neuron + + align:start position:0% +they show a neuron + + + align:start position:0% +they show a neuron +in a petri dish + + align:start position:0% + + + + align:start position:0% + +and there's a + + align:start position:0% +and there's a + + + align:start position:0% +and there's a +recording electrode in the axon + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% +here + + + align:start position:0% +here +stimulating electrode + + align:start position:0% +stimulating electrode + + + align:start position:0% +stimulating electrode +okay and it's showing two kinds of + + align:start position:0% +okay and it's showing two kinds of + + + align:start position:0% +okay and it's showing two kinds of +stimulation here + + align:start position:0% +stimulation here + + + align:start position:0% +stimulation here +a hyperpolarizing stimulus + + align:start position:0% +a hyperpolarizing stimulus + + + align:start position:0% +a hyperpolarizing stimulus +that's + + align:start position:0% +that's + + + align:start position:0% +that's +making the axon more + + align:start position:0% +making the axon more + + + align:start position:0% +making the axon more +negative on the inside + + align:start position:0% +negative on the inside + + + align:start position:0% +negative on the inside +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and depolarizing stimuli + + align:start position:0% +and depolarizing stimuli + + + align:start position:0% +and depolarizing stimuli +which reduce that membrane polarity + + align:start position:0% +which reduce that membrane polarity + + + align:start position:0% +which reduce that membrane polarity +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +this shows what you will record just a + + align:start position:0% +this shows what you will record just a + + + align:start position:0% +this shows what you will record just a +little ways down the membrane + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% +because + + + align:start position:0% +because +those little changes in polarity are + + align:start position:0% +those little changes in polarity are + + + align:start position:0% +those little changes in polarity are +being conducted + + align:start position:0% +being conducted + + + align:start position:0% +being conducted +hyperpolarization you can see here + + align:start position:0% +hyperpolarization you can see here + + + align:start position:0% +hyperpolarization you can see here +it's a little weaker than the point of + + align:start position:0% +it's a little weaker than the point of + + + align:start position:0% +it's a little weaker than the point of +stimulation it would be weaker yet if + + align:start position:0% +stimulation it would be weaker yet if + + + align:start position:0% +stimulation it would be weaker yet if +you were further away + + align:start position:0% +you were further away + + + align:start position:0% +you were further away +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and here + + align:start position:0% +and here + + + align:start position:0% +and here +same thing but for depolarization + + align:start position:0% +same thing but for depolarization + + + align:start position:0% +same thing but for depolarization +but when the stimulus reaches a certain + + align:start position:0% +but when the stimulus reaches a certain + + + align:start position:0% +but when the stimulus reaches a certain +threshold + + align:start position:0% +threshold + + + align:start position:0% +threshold +and here they're indicating the + + align:start position:0% +and here they're indicating the + + + align:start position:0% +and here they're indicating the +threshold depolarization you trigger + + align:start position:0% +threshold depolarization you trigger + + + align:start position:0% +threshold depolarization you trigger +a much larger response that's called the + + align:start position:0% +a much larger response that's called the + + + align:start position:0% +a much larger response that's called the +action potential + + align:start position:0% +action potential + + + align:start position:0% +action potential +it's due to a sudden opening + + align:start position:0% +it's due to a sudden opening + + + align:start position:0% +it's due to a sudden opening +of voltage-gated ion channels the sodium + + align:start position:0% +of voltage-gated ion channels the sodium + + + align:start position:0% +of voltage-gated ion channels the sodium +channels are voltage-gated so when they + + align:start position:0% +channels are voltage-gated so when they + + + align:start position:0% +channels are voltage-gated so when they +reach a certain threshold level of + + align:start position:0% +reach a certain threshold level of + + + align:start position:0% +reach a certain threshold level of +depolarization they will open up sodium + + align:start position:0% +depolarization they will open up sodium + + + align:start position:0% +depolarization they will open up sodium +ions will rush in so there's an + + align:start position:0% +ions will rush in so there's an + + + align:start position:0% +ions will rush in so there's an +implosion of sodium ions + + align:start position:0% +implosion of sodium ions + + + align:start position:0% +implosion of sodium ions +and that's what causes the action + + align:start position:0% +and that's what causes the action + + + align:start position:0% +and that's what causes the action +potential and it's overshoot the + + align:start position:0% +potential and it's overshoot the + + + align:start position:0% +potential and it's overshoot the +membrane actually becomes positive on + + align:start position:0% +membrane actually becomes positive on + + + align:start position:0% +membrane actually becomes positive on +the inside very briefly and then there's + + align:start position:0% +the inside very briefly and then there's + + + align:start position:0% +the inside very briefly and then there's +a recovery of the membrane + + align:start position:0% +a recovery of the membrane + + + align:start position:0% +a recovery of the membrane +as the channels change + + align:start position:0% + + + + align:start position:0% + +okay so now we've talked about different + + align:start position:0% +okay so now we've talked about different + + + align:start position:0% +okay so now we've talked about different +kinds of responses different regions of + + align:start position:0% +kinds of responses different regions of + + + align:start position:0% +kinds of responses different regions of +the cell let's just review that + + align:start position:0% +the cell let's just review that + + + align:start position:0% +the cell let's just review that +relating the structural parts to the + + align:start position:0% +relating the structural parts to the + + + align:start position:0% +relating the structural parts to the +functional parts of the neuron to + + align:start position:0% +functional parts of the neuron to + + + align:start position:0% +functional parts of the neuron to +structural parts of the neuron then + + align:start position:0% +structural parts of the neuron then + + + align:start position:0% +structural parts of the neuron then +we'll look more carefully at a couple of + + align:start position:0% +we'll look more carefully at a couple of + + + align:start position:0% +we'll look more carefully at a couple of +neurons first of all the receptive + + align:start position:0% +neurons first of all the receptive + + + align:start position:0% +neurons first of all the receptive +region that's the dendrites in the cell + + align:start position:0% +region that's the dendrites in the cell + + + align:start position:0% +region that's the dendrites in the cell +body primarily + + align:start position:0% +body primarily + + + align:start position:0% +body primarily +and when that those areas are stimulated + + align:start position:0% +and when that those areas are stimulated + + + align:start position:0% +and when that those areas are stimulated +whether it be mechanically or with a + + align:start position:0% +whether it be mechanically or with a + + + align:start position:0% +whether it be mechanically or with a +electrode + + align:start position:0% +electrode + + + align:start position:0% +electrode +or + + align:start position:0% +or + + + align:start position:0% +or +physiologically with a + + align:start position:0% +physiologically with a + + + align:start position:0% +physiologically with a +synaptic input + + align:start position:0% +synaptic input + + + align:start position:0% +synaptic input +you get a graded response + + align:start position:0% +you get a graded response + + + align:start position:0% +you get a graded response +graded means the response depends on the + + align:start position:0% +graded means the response depends on the + + + align:start position:0% +graded means the response depends on the +strength of the stimulus you get a + + align:start position:0% +strength of the stimulus you get a + + + align:start position:0% +strength of the stimulus you get a +greater response for a greater stimulus + + align:start position:0% +greater response for a greater stimulus + + + align:start position:0% +greater response for a greater stimulus +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that's a graded response the conduction + + align:start position:0% +that's a graded response the conduction + + + align:start position:0% +that's a graded response the conduction +is decremental + + align:start position:0% +is decremental + + + align:start position:0% +is decremental +in most dendrites cell bodies there's a + + align:start position:0% +in most dendrites cell bodies there's a + + + align:start position:0% +in most dendrites cell bodies there's a +few exceptions to that + + align:start position:0% + + + + align:start position:0% + +that just means that the further away + + align:start position:0% +that just means that the further away + + + align:start position:0% +that just means that the further away +from the point of stimulation you get + + align:start position:0% +from the point of stimulation you get + + + align:start position:0% +from the point of stimulation you get +the weaker the effect is + + align:start position:0% +the weaker the effect is + + + align:start position:0% +the weaker the effect is +okay so if you've got very long + + align:start position:0% +okay so if you've got very long + + + align:start position:0% +okay so if you've got very long +dendrites and the stimulus is way out at + + align:start position:0% +dendrites and the stimulus is way out at + + + align:start position:0% +dendrites and the stimulus is way out at +the end the effects on the cell body + + align:start position:0% +the end the effects on the cell body + + + align:start position:0% +the end the effects on the cell body +will be a lot less and if you're much + + align:start position:0% +will be a lot less and if you're much + + + align:start position:0% +will be a lot less and if you're much +closer + + align:start position:0% +closer + + + align:start position:0% +closer +okay then you have the region of rapid + + align:start position:0% +okay then you have the region of rapid + + + align:start position:0% +okay then you have the region of rapid +conduction that's the axon that's where + + align:start position:0% +conduction that's the axon that's where + + + align:start position:0% +conduction that's the axon that's where +the membrane is specialized to give you + + align:start position:0% +the membrane is specialized to give you + + + align:start position:0% +the membrane is specialized to give you +that all or none response the action + + align:start position:0% +that all or none response the action + + + align:start position:0% +that all or none response the action +potential it's non-detrimental it's like + + align:start position:0% +potential it's non-detrimental it's like + + + align:start position:0% +potential it's non-detrimental it's like +a row of dominoes going down once you + + align:start position:0% +a row of dominoes going down once you + + + align:start position:0% +a row of dominoes going down once you +tip the first one the whole + + align:start position:0% +tip the first one the whole + + + align:start position:0% +tip the first one the whole +it goes right down the axon as a wave of + + align:start position:0% +it goes right down the axon as a wave of + + + align:start position:0% +it goes right down the axon as a wave of +depolarization reaching the accent + + align:start position:0% +depolarization reaching the accent + + + align:start position:0% +depolarization reaching the accent +terminals + + align:start position:0% + + + + align:start position:0% + +and then after certain after potentials + + align:start position:0% +and then after certain after potentials + + + align:start position:0% +and then after certain after potentials +it recovers to the resting potential + + align:start position:0% +it recovers to the resting potential + + + align:start position:0% +it recovers to the resting potential +until you get another action potential + + align:start position:0% +until you get another action potential + + + align:start position:0% +until you get another action potential +and finally + + align:start position:0% +and finally + + + align:start position:0% +and finally +you the region of transmission other + + align:start position:0% +you the region of transmission other + + + align:start position:0% +you the region of transmission other +cells these are the axon and arbors + + align:start position:0% +cells these are the axon and arbors + + + align:start position:0% +cells these are the axon and arbors +the enlargements are called + + align:start position:0% +the enlargements are called + + + align:start position:0% +the enlargements are called +boutons + + align:start position:0% +boutons + + + align:start position:0% +boutons +we always like the french term for + + align:start position:0% +we always like the french term for + + + align:start position:0% +we always like the french term for +summarization reason it's actually blue + + align:start position:0% +summarization reason it's actually blue + + + align:start position:0% +summarization reason it's actually blue +tones terminal + + align:start position:0% +tones terminal + + + align:start position:0% +tones terminal +okay the and this is the accent + + align:start position:0% +okay the and this is the accent + + + align:start position:0% +okay the and this is the accent +helodendria + + align:start position:0% +helodendria + + + align:start position:0% +helodendria +that means + + align:start position:0% +that means + + + align:start position:0% +that means +the end + + align:start position:0% +the end + + + align:start position:0% +the end +branches + + align:start position:0% +branches + + + align:start position:0% +branches +tilo means end + + align:start position:0% + + + + align:start position:0% + +teleology the study of purposes and ends + + align:start position:0% +teleology the study of purposes and ends + + + align:start position:0% +teleology the study of purposes and ends +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the end branches dendrites are the + + align:start position:0% +the end branches dendrites are the + + + align:start position:0% +the end branches dendrites are the +branches + + align:start position:0% + + + + align:start position:0% + +that's where you have synaptic + + align:start position:0% +that's where you have synaptic + + + align:start position:0% +that's where you have synaptic +potentials where we get + + align:start position:0% +potentials where we get + + + align:start position:0% +potentials where we get +neurotransmitters released and we'll be + + align:start position:0% +neurotransmitters released and we'll be + + + align:start position:0% +neurotransmitters released and we'll be +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +okay now let's just take a look at two + + align:start position:0% +okay now let's just take a look at two + + + align:start position:0% +okay now let's just take a look at two +neurons there's actually three neurons + + align:start position:0% +neurons there's actually three neurons + + + align:start position:0% +neurons there's actually three neurons +in the picture here i want to talk about + + align:start position:0% +in the picture here i want to talk about + + + align:start position:0% +in the picture here i want to talk about +the two with long axons + + align:start position:0% +the two with long axons + + + align:start position:0% +the two with long axons +one + + align:start position:0% +one + + + align:start position:0% +one +is an axon that comes in through the + + align:start position:0% +is an axon that comes in through the + + + align:start position:0% +is an axon that comes in through the +dorsal root of the spinal cord okay the + + align:start position:0% +dorsal root of the spinal cord okay the + + + align:start position:0% +dorsal root of the spinal cord okay the +ending + + align:start position:0% +ending + + + align:start position:0% +ending +is in these endings out in the near the + + align:start position:0% +is in these endings out in the near the + + + align:start position:0% +is in these endings out in the near the +body surface + + align:start position:0% +body surface + + + align:start position:0% +body surface +you have many axons that have endings + + align:start position:0% +you have many axons that have endings + + + align:start position:0% +you have many axons that have endings +like that on your skin + + align:start position:0% +like that on your skin + + + align:start position:0% +like that on your skin +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then + + align:start position:0% +and then + + + align:start position:0% +and then +the axon begins about right there + + align:start position:0% +the axon begins about right there + + + align:start position:0% +the axon begins about right there +okay and notice there's no cell body + + align:start position:0% +okay and notice there's no cell body + + + align:start position:0% +okay and notice there's no cell body +there + + align:start position:0% +there + + + align:start position:0% +there +but that's where the axon begins and + + align:start position:0% +but that's where the axon begins and + + + align:start position:0% +but that's where the axon begins and +the axon goes + + align:start position:0% +the axon goes + + + align:start position:0% +the axon goes +right by the cell body which is off to + + align:start position:0% +right by the cell body which is off to + + + align:start position:0% +right by the cell body which is off to +the side here + + align:start position:0% +the side here + + + align:start position:0% +the side here +and reaches + + align:start position:0% +and reaches + + + align:start position:0% +and reaches +terminals inside the central nervous + + align:start position:0% +terminals inside the central nervous + + + align:start position:0% +terminals inside the central nervous +system this is peripheral nervous system + + align:start position:0% +system this is peripheral nervous system + + + align:start position:0% +system this is peripheral nervous system +cns their main central nervous system + + align:start position:0% +cns their main central nervous system + + + align:start position:0% +cns their main central nervous system +okay + + align:start position:0% + + + + align:start position:0% + +drg + + align:start position:0% + + + + align:start position:0% + +dorsal + + align:start position:0% +dorsal + + + align:start position:0% +dorsal +root + + align:start position:0% + + + + align:start position:0% + +it's a dorsal root ganglion cell + + align:start position:0% +it's a dorsal root ganglion cell + + + align:start position:0% +it's a dorsal root ganglion cell +the ganglion is a collection of those + + align:start position:0% +the ganglion is a collection of those + + + align:start position:0% +the ganglion is a collection of those +cells + + align:start position:0% +cells + + + align:start position:0% +cells +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so one cell is in the dorsal root + + align:start position:0% +so one cell is in the dorsal root + + + align:start position:0% +so one cell is in the dorsal root +ganglion it's a dorsal root ganglion + + align:start position:0% +ganglion it's a dorsal root ganglion + + + align:start position:0% +ganglion it's a dorsal root ganglion +cell + + align:start position:0% +cell + + + align:start position:0% +cell +okay + + align:start position:0% +okay + + + align:start position:0% +okay +it's also + + align:start position:0% +it's also + + + align:start position:0% +it's also +referred to sometimes as a primary + + align:start position:0% +referred to sometimes as a primary + + + align:start position:0% +referred to sometimes as a primary +sensory neuron but i'll be defining that + + align:start position:0% +sensory neuron but i'll be defining that + + + align:start position:0% +sensory neuron but i'll be defining that +for you later + + align:start position:0% + + + + align:start position:0% + +okay now functionally we can look at the + + align:start position:0% +okay now functionally we can look at the + + + align:start position:0% +okay now functionally we can look at the +motor neuron in exactly the same we same + + align:start position:0% +motor neuron in exactly the same we same + + + align:start position:0% +motor neuron in exactly the same we same +way we'll put the receptive region + + align:start position:0% + + + + align:start position:0% + +clear over on the right and that's the + + align:start position:0% +clear over on the right and that's the + + + align:start position:0% +clear over on the right and that's the +cell body and dendrites inside the cns + + align:start position:0% +cell body and dendrites inside the cns + + + align:start position:0% +cell body and dendrites inside the cns +the central nervous system okay and the + + align:start position:0% +the central nervous system okay and the + + + align:start position:0% +the central nervous system okay and the +motor neuron + + align:start position:0% +motor neuron + + + align:start position:0% +motor neuron +then we have the axon + + align:start position:0% +then we have the axon + + + align:start position:0% +then we have the axon +and the axon + + align:start position:0% + + + + align:start position:0% + +just starting right there + + align:start position:0% +just starting right there + + + align:start position:0% +just starting right there +this one is starting right there + + align:start position:0% +this one is starting right there + + + align:start position:0% +this one is starting right there +that region is called + + align:start position:0% + + + + align:start position:0% + +the axon + + align:start position:0% + + + + align:start position:0% + +helic + + align:start position:0% + + + + align:start position:0% + +yep + + align:start position:0% +yep + + + align:start position:0% +yep +go back to my pen + + align:start position:0% + + + + align:start position:0% + +x and helic beginning point of the axon + + align:start position:0% +x and helic beginning point of the axon + + + align:start position:0% +x and helic beginning point of the axon +where the action potential detection + + align:start position:0% +where the action potential detection + + + align:start position:0% +where the action potential detection +exponential normally + + align:start position:0% +exponential normally + + + align:start position:0% +exponential normally +begins + + align:start position:0% +begins + + + align:start position:0% +begins +okay + + align:start position:0% + + + + align:start position:0% + +now in the case of the motor neuron + + align:start position:0% +now in the case of the motor neuron + + + align:start position:0% +now in the case of the motor neuron +again we can follow the axon to the ax + + align:start position:0% +again we can follow the axon to the ax + + + align:start position:0% +again we can follow the axon to the ax +antilodandria the endings + + align:start position:0% +antilodandria the endings + + + align:start position:0% +antilodandria the endings +which the case of motor neuron is on a + + align:start position:0% +which the case of motor neuron is on a + + + align:start position:0% +which the case of motor neuron is on a +muscle cell + + align:start position:0% + + + + align:start position:0% + +but functionally now we can look at + + align:start position:0% +but functionally now we can look at + + + align:start position:0% +but functionally now we can look at +those two neurons + + align:start position:0% +those two neurons + + + align:start position:0% +those two neurons +and describe the same kinds of processes + + align:start position:0% +and describe the same kinds of processes + + + align:start position:0% +and describe the same kinds of processes +happening in these three divisions + + align:start position:0% +happening in these three divisions + + + align:start position:0% +happening in these three divisions +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now + + align:start position:0% +so now + + + align:start position:0% +so now +let's + + align:start position:0% +let's + + + align:start position:0% +let's +take just a piece of e1 of those axons + + align:start position:0% +take just a piece of e1 of those axons + + + align:start position:0% +take just a piece of e1 of those axons +okay and look at it + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% +here + + + align:start position:0% +here +you see that we're dealing with a + + align:start position:0% + + + + align:start position:0% + +axis cylinder sometimes called a tube + + align:start position:0% +axis cylinder sometimes called a tube + + + align:start position:0% +axis cylinder sometimes called a tube +okay formed by the axonal membrane + + align:start position:0% + + + + align:start position:0% + +i just sliced out a piece of it there + + align:start position:0% +i just sliced out a piece of it there + + + align:start position:0% +i just sliced out a piece of it there +and i'm represent + + align:start position:0% +and i'm represent + + + align:start position:0% +and i'm represent +representing + + align:start position:0% +representing + + + align:start position:0% +representing +the distribution relative distribution + + align:start position:0% +the distribution relative distribution + + + align:start position:0% +the distribution relative distribution +of the positive and negative + + align:start position:0% +of the positive and negative + + + align:start position:0% +of the positive and negative +charges + + align:start position:0% +charges + + + align:start position:0% +charges +showing that it's normally positive on + + align:start position:0% +showing that it's normally positive on + + + align:start position:0% +showing that it's normally positive on +the outside unless an action potential + + align:start position:0% +the outside unless an action potential + + + align:start position:0% +the outside unless an action potential +is going by + + align:start position:0% +is going by + + + align:start position:0% +is going by +and i've taken a piece of the axon right + + align:start position:0% +and i've taken a piece of the axon right + + + align:start position:0% +and i've taken a piece of the axon right +when an action potential is there okay + + align:start position:0% + + + + align:start position:0% + +now first of all + + align:start position:0% +now first of all + + + align:start position:0% +now first of all +on the right there + + align:start position:0% +on the right there + + + align:start position:0% +on the right there +if we're recording from + + align:start position:0% + + + + align:start position:0% + +the x the axon when it's quiet there's + + align:start position:0% +the x the axon when it's quiet there's + + + align:start position:0% +the x the axon when it's quiet there's +no action potentials + + align:start position:0% +no action potentials + + + align:start position:0% +no action potentials +we put two electrodes on the outside of + + align:start position:0% +we put two electrodes on the outside of + + + align:start position:0% +we put two electrodes on the outside of +course we'll get no nothing in our + + align:start position:0% +course we'll get no nothing in our + + + align:start position:0% +course we'll get no nothing in our +recording we put two act + + align:start position:0% +recording we put two act + + + align:start position:0% +recording we put two act +two little probes in the inside we'll + + align:start position:0% +two little probes in the inside we'll + + + align:start position:0% +two little probes in the inside we'll +get nothing if we put one on the outside + + align:start position:0% +get nothing if we put one on the outside + + + align:start position:0% +get nothing if we put one on the outside +one the inside will find that the inside + + align:start position:0% +one the inside will find that the inside + + + align:start position:0% +one the inside will find that the inside +is negative about 70 millivolts + + align:start position:0% +is negative about 70 millivolts + + + align:start position:0% +is negative about 70 millivolts +a little more a little less + + align:start position:0% +a little more a little less + + + align:start position:0% +a little more a little less +depending on the cell + + align:start position:0% +depending on the cell + + + align:start position:0% +depending on the cell +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now if we trigger an action potential + + align:start position:0% +now if we trigger an action potential + + + align:start position:0% +now if we trigger an action potential +and we're recording from + + align:start position:0% +and we're recording from + + + align:start position:0% +and we're recording from +this type of + + align:start position:0% +this type of + + + align:start position:0% +this type of +arrangement + + align:start position:0% + + + + align:start position:0% + +okay we can construct the picture that + + align:start position:0% +okay we can construct the picture that + + + align:start position:0% +okay we can construct the picture that +i've shown + + align:start position:0% +i've shown + + + align:start position:0% +i've shown +on the left and i've graphed + + align:start position:0% +on the left and i've graphed + + + align:start position:0% +on the left and i've graphed +down below + + align:start position:0% +down below + + + align:start position:0% +down below +that graph would show + + align:start position:0% +that graph would show + + + align:start position:0% +that graph would show +the recording you would get if you were + + align:start position:0% +the recording you would get if you were + + + align:start position:0% +the recording you would get if you were +at one point + + align:start position:0% +at one point + + + align:start position:0% +at one point +looking at the on rush of + + align:start position:0% +looking at the on rush of + + + align:start position:0% +looking at the on rush of +the action potential as it passed by and + + align:start position:0% +the action potential as it passed by and + + + align:start position:0% +the action potential as it passed by and +you would be plotting + + align:start position:0% +you would be plotting + + + align:start position:0% +you would be plotting +potential against time + + align:start position:0% +potential against time + + + align:start position:0% +potential against time +but as i've shown it here we're actually + + align:start position:0% +but as i've shown it here we're actually + + + align:start position:0% +but as i've shown it here we're actually +looking at the spatial distribution of + + align:start position:0% +looking at the spatial distribution of + + + align:start position:0% +looking at the spatial distribution of +potentials across the membrane + + align:start position:0% +potentials across the membrane + + + align:start position:0% +potentials across the membrane +as the action potential goes from right + + align:start position:0% +as the action potential goes from right + + + align:start position:0% +as the action potential goes from right +to left there + + align:start position:0% +to left there + + + align:start position:0% +to left there +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we're in front here we're in front of + + align:start position:0% +so we're in front here we're in front of + + + align:start position:0% +so we're in front here we're in front of +the action potential + + align:start position:0% +the action potential + + + align:start position:0% +the action potential +and there we're at minus 70. + + align:start position:0% +and there we're at minus 70. + + + align:start position:0% +and there we're at minus 70. +okay + + align:start position:0% +okay + + + align:start position:0% +okay +then + + align:start position:0% +then + + + align:start position:0% +then +the action potential arrives + + align:start position:0% +the action potential arrives + + + align:start position:0% +the action potential arrives +and you get the implosion of sodium as i + + align:start position:0% +and you get the implosion of sodium as i + + + align:start position:0% +and you get the implosion of sodium as i +show there and you get the + + align:start position:0% +show there and you get the + + + align:start position:0% +show there and you get the +depolarization okay and it goes + + align:start position:0% + + + + align:start position:0% + +more than 70 millivolt + + align:start position:0% +more than 70 millivolt + + + align:start position:0% +more than 70 millivolt +okay + + align:start position:0% +okay + + + align:start position:0% +okay +usually goes up to about + + align:start position:0% +usually goes up to about + + + align:start position:0% +usually goes up to about +30 millivolts positive but then it + + align:start position:0% +30 millivolts positive but then it + + + align:start position:0% +30 millivolts positive but then it +quickly recovers as you see there + + align:start position:0% +quickly recovers as you see there + + + align:start position:0% +quickly recovers as you see there +and you get some after potentials until + + align:start position:0% +and you get some after potentials until + + + align:start position:0% +and you get some after potentials until +you get back to the resting potential + + align:start position:0% + + + + align:start position:0% + +now the main explanation for the + + align:start position:0% +now the main explanation for the + + + align:start position:0% +now the main explanation for the +rapid depolarization of the membrane as + + align:start position:0% +rapid depolarization of the membrane as + + + align:start position:0% +rapid depolarization of the membrane as +i said is the implosion of sodium ions + + align:start position:0% +i said is the implosion of sodium ions + + + align:start position:0% +i said is the implosion of sodium ions +and + + align:start position:0% +and + + + align:start position:0% +and +well it starts to recover you get an + + align:start position:0% +well it starts to recover you get an + + + align:start position:0% +well it starts to recover you get an +opening of the potassium channels + + align:start position:0% +opening of the potassium channels + + + align:start position:0% +opening of the potassium channels +further than they already are and the + + align:start position:0% +further than they already are and the + + + align:start position:0% +further than they already are and the +closing of the sodium channels okay + + align:start position:0% +closing of the sodium channels okay + + + align:start position:0% +closing of the sodium channels okay +and it's + + align:start position:0% +and it's + + + align:start position:0% +and it's +that + + align:start position:0% +that + + + align:start position:0% +that +extra opening of potassium channels that + + align:start position:0% +extra opening of potassium channels that + + + align:start position:0% +extra opening of potassium channels that +results in the + + align:start position:0% +results in the + + + align:start position:0% +results in the +after potential there so it becomes a + + align:start position:0% +after potential there so it becomes a + + + align:start position:0% +after potential there so it becomes a +little more than minus 70 initially + + align:start position:0% +little more than minus 70 initially + + + align:start position:0% +little more than minus 70 initially +until you get a recovery of the resting + + align:start position:0% +until you get a recovery of the resting + + + align:start position:0% +until you get a recovery of the resting +state + + align:start position:0% + + + + align:start position:0% + +okay and this just shows a picture of + + align:start position:0% +okay and this just shows a picture of + + + align:start position:0% +okay and this just shows a picture of +the another picture of the action + + align:start position:0% +the another picture of the action + + + align:start position:0% +the another picture of the action +potential + + align:start position:0% +potential + + + align:start position:0% +potential +at these different stages it's just + + align:start position:0% +at these different stages it's just + + + align:start position:0% +at these different stages it's just +showing you sodium and potassium + + align:start position:0% +showing you sodium and potassium + + + align:start position:0% +showing you sodium and potassium +channels + + align:start position:0% +channels + + + align:start position:0% +channels +and the distribution of + + align:start position:0% +and the distribution of + + + align:start position:0% +and the distribution of +these ions on either side of the + + align:start position:0% +these ions on either side of the + + + align:start position:0% +these ions on either side of the +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +so you see at the far left some + + align:start position:0% +so you see at the far left some + + + align:start position:0% +so you see at the far left some +potassium channels open some closed and + + align:start position:0% +potassium channels open some closed and + + + align:start position:0% +potassium channels open some closed and +you see the closed sodium channels and + + align:start position:0% +you see the closed sodium channels and + + + align:start position:0% +you see the closed sodium channels and +then + + align:start position:0% +then + + + align:start position:0% +then +the actual potential + + align:start position:0% +the actual potential + + + align:start position:0% +the actual potential +is getting close + + align:start position:0% +is getting close + + + align:start position:0% +is getting close +just before it's triggered use the + + align:start position:0% +just before it's triggered use the + + + align:start position:0% +just before it's triggered use the +sodium channels start to open + + align:start position:0% +sodium channels start to open + + + align:start position:0% +sodium channels start to open +and at the peak they're all open + + align:start position:0% +and at the peak they're all open + + + align:start position:0% +and at the peak they're all open +you still have some potassium channels + + align:start position:0% +you still have some potassium channels + + + align:start position:0% +you still have some potassium channels +open some closed and then + + align:start position:0% +open some closed and then + + + align:start position:0% +open some closed and then +in the fourth region there + + align:start position:0% + + + + align:start position:0% + +you see the + + align:start position:0% +you see the + + + align:start position:0% +you see the +more the potassium channels open and now + + align:start position:0% +more the potassium channels open and now + + + align:start position:0% +more the potassium channels open and now +the sodium channels are closed as the + + align:start position:0% +the sodium channels are closed as the + + + align:start position:0% +the sodium channels are closed as the +recovery + + align:start position:0% +recovery + + + align:start position:0% +recovery +occurs until you get back to the initial + + align:start position:0% +occurs until you get back to the initial + + + align:start position:0% +occurs until you get back to the initial +state + + align:start position:0% + + + + align:start position:0% + +now that was + + align:start position:0% +now that was + + + align:start position:0% +now that was +explanation of the action potential + + align:start position:0% +explanation of the action potential + + + align:start position:0% +explanation of the action potential +in terms of changing conductance sodium + + align:start position:0% +in terms of changing conductance sodium + + + align:start position:0% +in terms of changing conductance sodium +for sodium and potassium ions across + + align:start position:0% +for sodium and potassium ions across + + + align:start position:0% +for sodium and potassium ions across +this membrane was worked out by hodgkin + + align:start position:0% +this membrane was worked out by hodgkin + + + align:start position:0% +this membrane was worked out by hodgkin +and huxley + + align:start position:0% +and huxley + + + align:start position:0% +and huxley +and this is a picture from hodgkin in + + align:start position:0% +and this is a picture from hodgkin in + + + align:start position:0% +and this is a picture from hodgkin in +1964 in which he's depicting + + align:start position:0% +1964 in which he's depicting + + + align:start position:0% +1964 in which he's depicting +the voltage + + align:start position:0% +the voltage + + + align:start position:0% +the voltage +potential difference across the membrane + + align:start position:0% +potential difference across the membrane + + + align:start position:0% +potential difference across the membrane +with the dashed line and then he's + + align:start position:0% +with the dashed line and then he's + + + align:start position:0% +with the dashed line and then he's +showing + + align:start position:0% + + + + align:start position:0% + +sodium conductance and potassium + + align:start position:0% +sodium conductance and potassium + + + align:start position:0% +sodium conductance and potassium +conductance + + align:start position:0% +conductance + + + align:start position:0% +conductance +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and how they're changing + + align:start position:0% +and how they're changing + + + align:start position:0% +and how they're changing +it was a very simple model that could + + align:start position:0% +it was a very simple model that could + + + align:start position:0% +it was a very simple model that could +completely account for the shape of the + + align:start position:0% +completely account for the shape of the + + + align:start position:0% +completely account for the shape of the +action action potential + + align:start position:0% +action action potential + + + align:start position:0% +action action potential +and you see the whole thing is a crane + + align:start position:0% +and you see the whole thing is a crane + + + align:start position:0% +and you see the whole thing is a crane +in a few milliseconds + + align:start position:0% + + + + align:start position:0% + +now what i've said so far + + align:start position:0% +now what i've said so far + + + align:start position:0% +now what i've said so far +can explain + + align:start position:0% +can explain + + + align:start position:0% +can explain +conduction in an unmyelinated accent + + align:start position:0% +conduction in an unmyelinated accent + + + align:start position:0% +conduction in an unmyelinated accent +that's just a bare axon + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and here you're + + align:start position:0% +and here you're + + + align:start position:0% +and here you're +you have a picture of that + + align:start position:0% +you have a picture of that + + + align:start position:0% +you have a picture of that +wave of depolarization that's going down + + align:start position:0% +wave of depolarization that's going down + + + align:start position:0% +wave of depolarization that's going down +the membrane + + align:start position:0% +the membrane + + + align:start position:0% +the membrane +in this case from left to right and then + + align:start position:0% +in this case from left to right and then + + + align:start position:0% +in this case from left to right and then +showing a picture of the membrane + + align:start position:0% +showing a picture of the membrane + + + align:start position:0% +showing a picture of the membrane +at three different times + + align:start position:0% + + + + align:start position:0% + +but many axons this is a cartoon of an + + align:start position:0% +but many axons this is a cartoon of an + + + align:start position:0% +but many axons this is a cartoon of an +axon with a myelin sheath + + align:start position:0% +axon with a myelin sheath + + + align:start position:0% +axon with a myelin sheath +and + + align:start position:0% + + + + align:start position:0% + +they've enlarged the axon and made it + + align:start position:0% +they've enlarged the axon and made it + + + align:start position:0% +they've enlarged the axon and made it +very short + + align:start position:0% +very short + + + align:start position:0% +very short +okay but right here + + align:start position:0% +okay but right here + + + align:start position:0% +okay but right here +you see a + + align:start position:0% +you see a + + + align:start position:0% +you see a +a cell + + align:start position:0% +a cell + + + align:start position:0% +a cell +as seen in cross-section that's a cell + + align:start position:0% +as seen in cross-section that's a cell + + + align:start position:0% +as seen in cross-section that's a cell +that has wrapped its membrane around and + + align:start position:0% +that has wrapped its membrane around and + + + align:start position:0% +that has wrapped its membrane around and +around + + align:start position:0% +around + + + align:start position:0% +around +the axon + + align:start position:0% +the axon + + + align:start position:0% +the axon +the cell is called a glial cell + + align:start position:0% +the cell is called a glial cell + + + align:start position:0% +the cell is called a glial cell +a particular type of glial cell depends + + align:start position:0% +a particular type of glial cell depends + + + align:start position:0% +a particular type of glial cell depends +on whether you're in the central nervous + + align:start position:0% +on whether you're in the central nervous + + + align:start position:0% +on whether you're in the central nervous +system or the peripheral nervous system + + align:start position:0% +system or the peripheral nervous system + + + align:start position:0% +system or the peripheral nervous system +okay + + align:start position:0% + + + + align:start position:0% + +if we're dealing with a motor neuron so + + align:start position:0% +if we're dealing with a motor neuron so + + + align:start position:0% +if we're dealing with a motor neuron so +we're in the pms + + align:start position:0% +we're in the pms + + + align:start position:0% +we're in the pms +we're dealing with + + align:start position:0% + + + + align:start position:0% + +schwarm cells + + align:start position:0% +schwarm cells + + + align:start position:0% +schwarm cells +if we're dealing with the cns + + align:start position:0% + + + + align:start position:0% + +we're dealing with + + align:start position:0% +we're dealing with + + + align:start position:0% +we're dealing with +oops + + align:start position:0% + + + + align:start position:0% + +we're dealing with + + align:start position:0% +we're dealing with + + + align:start position:0% +we're dealing with +allego + + align:start position:0% + + + + align:start position:0% + +dendrocytes or oligodendroglia + + align:start position:0% +dendrocytes or oligodendroglia + + + align:start position:0% +dendrocytes or oligodendroglia +now these terms come from + + align:start position:0% +now these terms come from + + + align:start position:0% +now these terms come from +greek and latin in this case greek oligo + + align:start position:0% +greek and latin in this case greek oligo + + + align:start position:0% +greek and latin in this case greek oligo +means few + + align:start position:0% +means few + + + align:start position:0% +means few +dendro few branches + + align:start position:0% +dendro few branches + + + align:start position:0% +dendro few branches +site means cell okay + + align:start position:0% +site means cell okay + + + align:start position:0% +site means cell okay +the cell with few branches + + align:start position:0% +the cell with few branches + + + align:start position:0% +the cell with few branches +okay because there are other glial cells + + align:start position:0% +okay because there are other glial cells + + + align:start position:0% +okay because there are other glial cells +in the cns that have many more branches + + align:start position:0% +in the cns that have many more branches + + + align:start position:0% +in the cns that have many more branches +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the schwann cell is named after + + align:start position:0% +the schwann cell is named after + + + align:start position:0% +the schwann cell is named after +mr schwann + + align:start position:0% +mr schwann + + + align:start position:0% +mr schwann +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Applause] + + align:start position:0% + + + + align:start position:0% + +it's a wonderful cell it does a lot of + + align:start position:0% +it's a wonderful cell it does a lot of + + + align:start position:0% +it's a wonderful cell it does a lot of +interesting things and we'll be talking + + align:start position:0% +interesting things and we'll be talking + + + align:start position:0% +interesting things and we'll be talking +about it a number of times in the class + + align:start position:0% +about it a number of times in the class + + + align:start position:0% +about it a number of times in the class +now what does that do for us + + align:start position:0% +now what does that do for us + + + align:start position:0% +now what does that do for us +what + + align:start position:0% +what + + + align:start position:0% +what +do we need myelin for + + align:start position:0% +do we need myelin for + + + align:start position:0% +do we need myelin for +we think of as an insulator and it is in + + align:start position:0% +we think of as an insulator and it is in + + + align:start position:0% +we think of as an insulator and it is in +many ways because when you have that + + align:start position:0% +many ways because when you have that + + + align:start position:0% +many ways because when you have that +tight wrapping of the schwann cell + + align:start position:0% +tight wrapping of the schwann cell + + + align:start position:0% +tight wrapping of the schwann cell +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +you + + align:start position:0% +you + + + align:start position:0% +you +tremendously change the membrane + + align:start position:0% +tremendously change the membrane + + + align:start position:0% +tremendously change the membrane +capacitance and you cannot get + + align:start position:0% +capacitance and you cannot get + + + align:start position:0% +capacitance and you cannot get +it blocks these this ionic conduction + + align:start position:0% +it blocks these this ionic conduction + + + align:start position:0% +it blocks these this ionic conduction +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but it does another thing + + align:start position:0% +but it does another thing + + + align:start position:0% +but it does another thing +with the change in capacitance of the + + align:start position:0% +with the change in capacitance of the + + + align:start position:0% +with the change in capacitance of the +membrane you get much more rapid + + align:start position:0% +membrane you get much more rapid + + + align:start position:0% +membrane you get much more rapid +decremental conduction down the axon + + align:start position:0% +decremental conduction down the axon + + + align:start position:0% +decremental conduction down the axon +okay + + align:start position:0% + + + + align:start position:0% + +so what happens is that + + align:start position:0% +so what happens is that + + + align:start position:0% +so what happens is that +depolarization + + align:start position:0% +depolarization + + + align:start position:0% +depolarization +at the beginning there the axon helic + + align:start position:0% +at the beginning there the axon helic + + + align:start position:0% +at the beginning there the axon helic +triggers the action potential in the + + align:start position:0% +triggers the action potential in the + + + align:start position:0% +triggers the action potential in the +axon hilic region that spreads very + + align:start position:0% +axon hilic region that spreads very + + + align:start position:0% +axon hilic region that spreads very +rapidly down the axon of course it gets + + align:start position:0% +rapidly down the axon of course it gets + + + align:start position:0% +rapidly down the axon of course it gets +weaker because it's decremental but it + + align:start position:0% +weaker because it's decremental but it + + + align:start position:0% +weaker because it's decremental but it +reaches the next node which is close + + align:start position:0% +reaches the next node which is close + + + align:start position:0% +reaches the next node which is close +enough + + align:start position:0% +enough + + + align:start position:0% +enough +so it exceeds the threshold + + align:start position:0% +so it exceeds the threshold + + + align:start position:0% +so it exceeds the threshold +for firing an action bench so the little + + align:start position:0% +for firing an action bench so the little + + + align:start position:0% +for firing an action bench so the little +bare part of the membrane fires an + + align:start position:0% +bare part of the membrane fires an + + + align:start position:0% +bare part of the membrane fires an +action potential + + align:start position:0% +action potential + + + align:start position:0% +action potential +this only works if you have these little + + align:start position:0% +this only works if you have these little + + + align:start position:0% +this only works if you have these little +nodes where there's no myelin + + align:start position:0% +nodes where there's no myelin + + + align:start position:0% +nodes where there's no myelin +so there's myelin and then there's a + + align:start position:0% +so there's myelin and then there's a + + + align:start position:0% +so there's myelin and then there's a +little unmyelinated region and there's + + align:start position:0% +little unmyelinated region and there's + + + align:start position:0% +little unmyelinated region and there's +more myelin and another a myelinate + + align:start position:0% +more myelin and another a myelinate + + + align:start position:0% +more myelin and another a myelinate +region and so forth all the way down the + + align:start position:0% +region and so forth all the way down the + + + align:start position:0% +region and so forth all the way down the +accent + + align:start position:0% +accent + + + align:start position:0% +accent +and that's what they're showing here + + align:start position:0% +and that's what they're showing here + + + align:start position:0% +and that's what they're showing here +so basically the action potential is + + align:start position:0% +so basically the action potential is + + + align:start position:0% +so basically the action potential is +jumping from node to node and because + + align:start position:0% +jumping from node to node and because + + + align:start position:0% +jumping from node to node and because +the conduction is so rapid between nodes + + align:start position:0% +the conduction is so rapid between nodes + + + align:start position:0% +the conduction is so rapid between nodes +the detrimental conduction the speed of + + align:start position:0% +the detrimental conduction the speed of + + + align:start position:0% +the detrimental conduction the speed of +action potential conduction is much + + align:start position:0% +action potential conduction is much + + + align:start position:0% +action potential conduction is much +greater than in the unmyonated axon + + align:start position:0% +greater than in the unmyonated axon + + + align:start position:0% +greater than in the unmyonated axon +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that jumping from node to node is called + + align:start position:0% +that jumping from node to node is called + + + align:start position:0% +that jumping from node to node is called +saltatory + + align:start position:0% +saltatory + + + align:start position:0% +saltatory +conduction okay + + align:start position:0% + + + + align:start position:0% + +saltations are jumps + + align:start position:0% +saltations are jumps + + + align:start position:0% +saltations are jumps +saltatory conduction + + align:start position:0% + + + + align:start position:0% + +here's a picture of that + + align:start position:0% +here's a picture of that + + + align:start position:0% +here's a picture of that +well sorry we can first of all dealing + + align:start position:0% +well sorry we can first of all dealing + + + align:start position:0% +well sorry we can first of all dealing +with why it's faster + + align:start position:0% +with why it's faster + + + align:start position:0% +with why it's faster +you can draw an equivalent circuit for a + + align:start position:0% +you can draw an equivalent circuit for a + + + align:start position:0% +you can draw an equivalent circuit for a +patch of membrane in terms of resistance + + align:start position:0% +patch of membrane in terms of resistance + + + align:start position:0% +patch of membrane in terms of resistance +across the membrane capacitance across + + align:start position:0% +across the membrane capacitance across + + + align:start position:0% +across the membrane capacitance across +the membrane and along the membrane + + align:start position:0% +the membrane and along the membrane + + + align:start position:0% +the membrane and along the membrane +along the axial direction of the + + align:start position:0% +along the axial direction of the + + + align:start position:0% +along the axial direction of the +membrane that's our survey and that the + + align:start position:0% +membrane that's our survey and that the + + + align:start position:0% +membrane that's our survey and that the +two critical ones here are the + + align:start position:0% +two critical ones here are the + + + align:start position:0% +two critical ones here are the +capacitance and the + + align:start position:0% +capacitance and the + + + align:start position:0% +capacitance and the +axial resistance we just + + align:start position:0% +axial resistance we just + + + align:start position:0% +axial resistance we just +look at that in terms of these passive + + align:start position:0% +look at that in terms of these passive + + + align:start position:0% +look at that in terms of these passive +cable properties + + align:start position:0% +cable properties + + + align:start position:0% +cable properties +it's showing a piece of membrane here + + align:start position:0% +it's showing a piece of membrane here + + + align:start position:0% +it's showing a piece of membrane here +extracellular fluid at the top and the + + align:start position:0% +extracellular fluid at the top and the + + + align:start position:0% +extracellular fluid at the top and the +cytoplasm inside the cell on the bottom + + align:start position:0% +cytoplasm inside the cell on the bottom + + + align:start position:0% +cytoplasm inside the cell on the bottom +and the representing + + align:start position:0% +and the representing + + + align:start position:0% +and the representing +resistance for current flow along the + + align:start position:0% +resistance for current flow along the + + + align:start position:0% +resistance for current flow along the +direction of the axon + + align:start position:0% +direction of the axon + + + align:start position:0% +direction of the axon +is r sub a resistance is shown at the + + align:start position:0% +is r sub a resistance is shown at the + + + align:start position:0% +is r sub a resistance is shown at the +bottom and then at any point along the + + align:start position:0% +bottom and then at any point along the + + + align:start position:0% +bottom and then at any point along the +membrane the membrane has a certain + + align:start position:0% +membrane the membrane has a certain + + + align:start position:0% +membrane the membrane has a certain +resistance to current flow but it also + + align:start position:0% +resistance to current flow but it also + + + align:start position:0% +resistance to current flow but it also +has the capacitance + + align:start position:0% +has the capacitance + + + align:start position:0% +has the capacitance +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and when we add myelin we're + + align:start position:0% +and when we add myelin we're + + + align:start position:0% +and when we add myelin we're +decreasing the capacitance + + align:start position:0% +decreasing the capacitance + + + align:start position:0% +decreasing the capacitance +okay + + align:start position:0% + + + + align:start position:0% + +i won't go through the conduction of the + + align:start position:0% +i won't go through the conduction of the + + + align:start position:0% +i won't go through the conduction of the +potential here it's a little model + + align:start position:0% +potential here it's a little model + + + align:start position:0% +potential here it's a little model +but the rate of passive spread of the + + align:start position:0% +but the rate of passive spread of the + + + align:start position:0% +but the rate of passive spread of the +current down the axis cylinder is + + align:start position:0% +current down the axis cylinder is + + + align:start position:0% +current down the axis cylinder is +inversely proportional to the + + align:start position:0% +inversely proportional to the + + + align:start position:0% +inversely proportional to the +axial resistance and the + + align:start position:0% +axial resistance and the + + + align:start position:0% +axial resistance and the +membrane capacitance + + align:start position:0% +membrane capacitance + + + align:start position:0% +membrane capacitance +so + + align:start position:0% +so + + + align:start position:0% +so +if cm decreases by itself + + align:start position:0% +if cm decreases by itself + + + align:start position:0% +if cm decreases by itself +rate will increase + + align:start position:0% +rate will increase + + + align:start position:0% +rate will increase +okay and there's an additional effect + + align:start position:0% +okay and there's an additional effect + + + align:start position:0% +okay and there's an additional effect +because when the axon diameter increases + + align:start position:0% +because when the axon diameter increases + + + align:start position:0% +because when the axon diameter increases +the rate also increases now that's true + + align:start position:0% +the rate also increases now that's true + + + align:start position:0% +the rate also increases now that's true +for unmyelinated accidents too + + align:start position:0% +for unmyelinated accidents too + + + align:start position:0% +for unmyelinated accidents too +okay the reason is + + align:start position:0% +okay the reason is + + + align:start position:0% +okay the reason is +actual resistance decreases when we + + align:start position:0% +actual resistance decreases when we + + + align:start position:0% +actual resistance decreases when we +increase the diameter but increases in + + align:start position:0% +increase the diameter but increases in + + + align:start position:0% +increase the diameter but increases in +proportion to d squared + + align:start position:0% +proportion to d squared + + + align:start position:0% +proportion to d squared +and + + align:start position:0% +and + + + align:start position:0% +and +you have an opposite effect due to the + + align:start position:0% +you have an opposite effect due to the + + + align:start position:0% +you have an opposite effect due to the +change in + + align:start position:0% +change in + + + align:start position:0% +change in +membrane capacitance but it's only in + + align:start position:0% +membrane capacitance but it's only in + + + align:start position:0% +membrane capacitance but it's only in +proportion to d so we get + + align:start position:0% +proportion to d so we get + + + align:start position:0% +proportion to d so we get +there's two ways then to increase the + + align:start position:0% +there's two ways then to increase the + + + align:start position:0% +there's two ways then to increase the +rate + + align:start position:0% +rate + + + align:start position:0% +rate +of current flow down the axon + + align:start position:0% + + + + align:start position:0% + +one is to increase the diameter and the + + align:start position:0% +one is to increase the diameter and the + + + align:start position:0% +one is to increase the diameter and the +other is + + align:start position:0% +other is + + + align:start position:0% +other is +myelin + + align:start position:0% + + + + align:start position:0% + +and the myelin only works with the nodes + + align:start position:0% +and the myelin only works with the nodes + + + align:start position:0% +and the myelin only works with the nodes +okay this is a picture of current flow + + align:start position:0% +okay this is a picture of current flow + + + align:start position:0% +okay this is a picture of current flow +in a myelinated axon + + align:start position:0% +in a myelinated axon + + + align:start position:0% +in a myelinated axon +and it's showing + + align:start position:0% +and it's showing + + + align:start position:0% +and it's showing +in the graph here + + align:start position:0% +in the graph here + + + align:start position:0% +in the graph here +distance along the axon + + align:start position:0% +distance along the axon + + + align:start position:0% +distance along the axon +and + + align:start position:0% + + + + align:start position:0% + +so you see the rate of + + align:start position:0% + + + + align:start position:0% + +potential change there and you see the + + align:start position:0% +potential change there and you see the + + + align:start position:0% +potential change there and you see the +very rapid + + align:start position:0% +very rapid + + + align:start position:0% +very rapid +conduction and then the slower + + align:start position:0% +conduction and then the slower + + + align:start position:0% +conduction and then the slower +conduction at the node than very rapid + + align:start position:0% +conduction at the node than very rapid + + + align:start position:0% +conduction at the node than very rapid +reductionist or conduction of the node + + align:start position:0% +reductionist or conduction of the node + + + align:start position:0% +reductionist or conduction of the node +but remember + + align:start position:0% +but remember + + + align:start position:0% +but remember +it works only because the threshold is + + align:start position:0% +it works only because the threshold is + + + align:start position:0% +it works only because the threshold is +exceeded at the nodes and that's a large + + align:start position:0% +exceeded at the nodes and that's a large + + + align:start position:0% +exceeded at the nodes and that's a large +enough + + align:start position:0% +enough + + + align:start position:0% +enough +potential change to spread down to the + + align:start position:0% +potential change to spread down to the + + + align:start position:0% +potential change to spread down to the +next node and trigger the action + + align:start position:0% +next node and trigger the action + + + align:start position:0% +next node and trigger the action +potential so it's basically jumping + + align:start position:0% +potential so it's basically jumping + + + align:start position:0% +potential so it's basically jumping +producing saltations + + align:start position:0% +producing saltations + + + align:start position:0% +producing saltations +that's what saltatory conduction is + + align:start position:0% + + + + align:start position:0% + +okay now + + align:start position:0% +okay now + + + align:start position:0% +okay now +if we look at all these terms on the + + align:start position:0% +if we look at all these terms on the + + + align:start position:0% +if we look at all these terms on the +left we should know what they mean + + align:start position:0% +left we should know what they mean + + + align:start position:0% +left we should know what they mean +you know what membrane polarization is + + align:start position:0% +you know what membrane polarization is + + + align:start position:0% +you know what membrane polarization is +in terms of + + align:start position:0% +in terms of + + + align:start position:0% +in terms of +distribution of ions across the membrane + + align:start position:0% +distribution of ions across the membrane + + + align:start position:0% +distribution of ions across the membrane +we can record it with an electrode you + + align:start position:0% +we can record it with an electrode you + + + align:start position:0% +we can record it with an electrode you +know what a graded response is + + align:start position:0% + + + + align:start position:0% + +decremental conduction or + + align:start position:0% +decremental conduction or + + + align:start position:0% +decremental conduction or +non-decremental + + align:start position:0% + + + + align:start position:0% + +non-decremental and we get the all or + + align:start position:0% +non-decremental and we get the all or + + + align:start position:0% +non-decremental and we get the all or +none response the action potential + + align:start position:0% + + + + align:start position:0% + +and we've also looked at the after + + align:start position:0% +and we've also looked at the after + + + align:start position:0% +and we've also looked at the after +potentials + + align:start position:0% +potentials + + + align:start position:0% +potentials +okay so now we can go to these terms + + align:start position:0% +okay so now we can go to these terms + + + align:start position:0% +okay so now we can go to these terms +used to talk about synaptic action what + + align:start position:0% +used to talk about synaptic action what + + + align:start position:0% +used to talk about synaptic action what +happens when the potential reaches the + + align:start position:0% +happens when the potential reaches the + + + align:start position:0% +happens when the potential reaches the +axon endings + + align:start position:0% +axon endings + + + align:start position:0% +axon endings +okay + + align:start position:0% + + + + align:start position:0% + +where there are + + align:start position:0% +where there are + + + align:start position:0% +where there are +contacts with other cells the synapse + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and to introduce that we'll look at this + + align:start position:0% +and to introduce that we'll look at this + + + align:start position:0% +and to introduce that we'll look at this +cartoon + + align:start position:0% +cartoon + + + align:start position:0% +cartoon +showing recording + + align:start position:0% + + + + align:start position:0% + +from the big yellow cell there + + align:start position:0% +from the big yellow cell there + + + align:start position:0% +from the big yellow cell there +and from two cells that provide that are + + align:start position:0% +and from two cells that provide that are + + + align:start position:0% +and from two cells that provide that are +connected to it one cell the pink one + + align:start position:0% +connected to it one cell the pink one + + + align:start position:0% +connected to it one cell the pink one +there + + align:start position:0% +there + + + align:start position:0% +there +is connected with an excitatory synapse + + align:start position:0% +is connected with an excitatory synapse + + + align:start position:0% +is connected with an excitatory synapse +and the little blue one there they show + + align:start position:0% +and the little blue one there they show + + + align:start position:0% +and the little blue one there they show +connected with inhibitory snaps + + align:start position:0% +connected with inhibitory snaps + + + align:start position:0% +connected with inhibitory snaps +okay + + align:start position:0% + + + + align:start position:0% + +in each case we can + + align:start position:0% + + + + align:start position:0% + +stimulate + + align:start position:0% + + + + align:start position:0% + +the cell providing input and we can + + align:start position:0% +the cell providing input and we can + + + align:start position:0% +the cell providing input and we can +record what happens post-synaptically + + align:start position:0% +record what happens post-synaptically + + + align:start position:0% +record what happens post-synaptically +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so if we get an action potential + + align:start position:0% +so if we get an action potential + + + align:start position:0% +so if we get an action potential +it's not actually showing the stimulus + + align:start position:0% +it's not actually showing the stimulus + + + align:start position:0% +it's not actually showing the stimulus +it's just recording the action potential + + align:start position:0% +it's just recording the action potential + + + align:start position:0% +it's just recording the action potential +from the blue or the pink cell okay + + align:start position:0% +from the blue or the pink cell okay + + + align:start position:0% +from the blue or the pink cell okay +so showing of the recording of the + + align:start position:0% +so showing of the recording of the + + + align:start position:0% +so showing of the recording of the +action potential then it shows what + + align:start position:0% +action potential then it shows what + + + align:start position:0% +action potential then it shows what +happens in the cell on the other side of + + align:start position:0% +happens in the cell on the other side of + + + align:start position:0% +happens in the cell on the other side of +the synapse + + align:start position:0% +the synapse + + + align:start position:0% +the synapse +if it's a depolarization + + align:start position:0% +if it's a depolarization + + + align:start position:0% +if it's a depolarization +the top one we call it an excitatory + + align:start position:0% +the top one we call it an excitatory + + + align:start position:0% +the top one we call it an excitatory +post-synaptic potential in epsb + + align:start position:0% +post-synaptic potential in epsb + + + align:start position:0% +post-synaptic potential in epsb +excitatory because it's bringing the + + align:start position:0% +excitatory because it's bringing the + + + align:start position:0% +excitatory because it's bringing the +membrane closer + + align:start position:0% +membrane closer + + + align:start position:0% +membrane closer +to the threshold for triggering an + + align:start position:0% +to the threshold for triggering an + + + align:start position:0% +to the threshold for triggering an +action potential + + align:start position:0% +action potential + + + align:start position:0% +action potential +you say but you can't get an action + + align:start position:0% +you say but you can't get an action + + + align:start position:0% +you say but you can't get an action +potential in the cell you already said + + align:start position:0% +potential in the cell you already said + + + align:start position:0% +potential in the cell you already said +that they don't conduct action potential + + align:start position:0% +that they don't conduct action potential + + + align:start position:0% +that they don't conduct action potential +so that's true + + align:start position:0% +so that's true + + + align:start position:0% +so that's true +but remember + + align:start position:0% +but remember + + + align:start position:0% +but remember +that epsp will get conducted it will get + + align:start position:0% +that epsp will get conducted it will get + + + align:start position:0% +that epsp will get conducted it will get +conducted away from the point the + + align:start position:0% +conducted away from the point the + + + align:start position:0% +conducted away from the point the +synapse + + align:start position:0% + + + + align:start position:0% + +and what counts is how big the + + align:start position:0% +and what counts is how big the + + + align:start position:0% +and what counts is how big the +depolarization is at the axon hillock + + align:start position:0% +depolarization is at the axon hillock + + + align:start position:0% +depolarization is at the axon hillock +which is right near the cell body okay + + align:start position:0% + + + + align:start position:0% + +this would be the region of the all the + + align:start position:0% +this would be the region of the all the + + + align:start position:0% +this would be the region of the all the +way down the memory + + align:start position:0% +way down the memory + + + align:start position:0% +way down the memory +is about the same amplitude throughout + + align:start position:0% +is about the same amplitude throughout + + + align:start position:0% +is about the same amplitude throughout +thank you bob + + align:start position:0% +thank you bob + + + align:start position:0% +thank you bob +it's about the same amplitude throughout + + align:start position:0% +it's about the same amplitude throughout + + + align:start position:0% +it's about the same amplitude throughout +that's right the very important + + align:start position:0% + + + + align:start position:0% + +that's why i said it's like a row of + + align:start position:0% +that's why i said it's like a row of + + + align:start position:0% +that's why i said it's like a row of +dominoes once you start the first one + + align:start position:0% + + + + align:start position:0% + +it goes all the way down + + align:start position:0% +it goes all the way down + + + align:start position:0% +it goes all the way down +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so here we've got the same kind of + + align:start position:0% +okay so here we've got the same kind of + + + align:start position:0% +okay so here we've got the same kind of +action potential in the two input cells + + align:start position:0% +action potential in the two input cells + + + align:start position:0% +action potential in the two input cells +the blue and the red the shown in blue + + align:start position:0% +the blue and the red the shown in blue + + + align:start position:0% +the blue and the red the shown in blue +and the red there but the effect in the + + align:start position:0% +and the red there but the effect in the + + + align:start position:0% +and the red there but the effect in the +postsynaptic cell is very different + + align:start position:0% +postsynaptic cell is very different + + + align:start position:0% +postsynaptic cell is very different +why + + align:start position:0% +why + + + align:start position:0% +why +well there's something different + + align:start position:0% +well there's something different + + + align:start position:0% +well there's something different +happening at those xn terminals + + align:start position:0% +happening at those xn terminals + + + align:start position:0% +happening at those xn terminals +okay there's different molecules being + + align:start position:0% +okay there's different molecules being + + + align:start position:0% +okay there's different molecules being +released and different receptors in the + + align:start position:0% +released and different receptors in the + + + align:start position:0% +released and different receptors in the +postsynaptic membrane + + align:start position:0% +postsynaptic membrane + + + align:start position:0% +postsynaptic membrane +and that determines what's happening to + + align:start position:0% +and that determines what's happening to + + + align:start position:0% +and that determines what's happening to +the postsynaptic membrane okay that's + + align:start position:0% +the postsynaptic membrane okay that's + + + align:start position:0% +the postsynaptic membrane okay that's +why you get an excitatory postsynaptic + + align:start position:0% +why you get an excitatory postsynaptic + + + align:start position:0% +why you get an excitatory postsynaptic +potential moving the membrane + + align:start position:0% +potential moving the membrane + + + align:start position:0% +potential moving the membrane +the cell closer + + align:start position:0% +the cell closer + + + align:start position:0% +the cell closer +at its axon hillock they are closer to + + align:start position:0% +at its axon hillock they are closer to + + + align:start position:0% +at its axon hillock they are closer to +the point of triggering an action + + align:start position:0% +the point of triggering an action + + + align:start position:0% +the point of triggering an action +potential but in the case of an + + align:start position:0% +potential but in the case of an + + + align:start position:0% +potential but in the case of an +inhibitory postsynaptic potential the + + align:start position:0% +inhibitory postsynaptic potential the + + + align:start position:0% +inhibitory postsynaptic potential the +ipsp is moving the cell away from the + + align:start position:0% +ipsp is moving the cell away from the + + + align:start position:0% +ipsp is moving the cell away from the +threshold making it less likely to fire + + align:start position:0% +threshold making it less likely to fire + + + align:start position:0% +threshold making it less likely to fire +an action potential + + align:start position:0% +an action potential + + + align:start position:0% +an action potential +so that's why we call it inhibitory + + align:start position:0% +so that's why we call it inhibitory + + + align:start position:0% +so that's why we call it inhibitory +postsynaptic potential + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now think about putting this together + + align:start position:0% +now think about putting this together + + + align:start position:0% +now think about putting this together +with + + align:start position:0% +with + + + align:start position:0% +with +let's think about decremental conduction + + align:start position:0% +let's think about decremental conduction + + + align:start position:0% +let's think about decremental conduction +in the cell whoops + + align:start position:0% +in the cell whoops + + + align:start position:0% +in the cell whoops +okay + + align:start position:0% +okay + + + align:start position:0% +okay +let's draw a cell here + + align:start position:0% +let's draw a cell here + + + align:start position:0% +let's draw a cell here +and draw several inputs coming into it + + align:start position:0% +and draw several inputs coming into it + + + align:start position:0% +and draw several inputs coming into it +okay + + align:start position:0% + + + + align:start position:0% + +and here's its axon going up + + align:start position:0% +and here's its axon going up + + + align:start position:0% +and here's its axon going up +and let's say we have one action + + align:start position:0% +and let's say we have one action + + + align:start position:0% +and let's say we have one action +potential there one action potential + + align:start position:0% +potential there one action potential + + + align:start position:0% +potential there one action potential +here and one action potential here i've + + align:start position:0% +here and one action potential here i've + + + align:start position:0% +here and one action potential here i've +just shown it in a moment in time + + align:start position:0% +just shown it in a moment in time + + + align:start position:0% +just shown it in a moment in time +they're all rushing down to the accent + + align:start position:0% +they're all rushing down to the accent + + + align:start position:0% +they're all rushing down to the accent +terminals + + align:start position:0% +terminals + + + align:start position:0% +terminals +okay and they're all going to cause + + align:start position:0% +okay and they're all going to cause + + + align:start position:0% +okay and they're all going to cause +epsp's + + align:start position:0% + + + + align:start position:0% + +they're going to summate okay so if + + align:start position:0% +they're going to summate okay so if + + + align:start position:0% +they're going to summate okay so if +we're recording here + + align:start position:0% +we're recording here + + + align:start position:0% +we're recording here +at the axon hillig just one of them + + align:start position:0% +at the axon hillig just one of them + + + align:start position:0% +at the axon hillig just one of them +might be a little blip in the membrane + + align:start position:0% +might be a little blip in the membrane + + + align:start position:0% +might be a little blip in the membrane +potential like that if two of them + + align:start position:0% +potential like that if two of them + + + align:start position:0% +potential like that if two of them +arrive it'll be bigger if three of them + + align:start position:0% +arrive it'll be bigger if three of them + + + align:start position:0% +arrive it'll be bigger if three of them +arrive it'll be bigger still and if this + + align:start position:0% +arrive it'll be bigger still and if this + + + align:start position:0% +arrive it'll be bigger still and if this +is the threshold + + align:start position:0% +is the threshold + + + align:start position:0% +is the threshold +you see we might reach the threshold and + + align:start position:0% +you see we might reach the threshold and + + + align:start position:0% +you see we might reach the threshold and +trigger an action potential okay + + align:start position:0% + + + + align:start position:0% + +that effect is called spatial summation + + align:start position:0% +that effect is called spatial summation + + + align:start position:0% +that effect is called spatial summation +so multiple + + align:start position:0% +so multiple + + + align:start position:0% +so multiple +terminals contacting the cell + + align:start position:0% +terminals contacting the cell + + + align:start position:0% +terminals contacting the cell +if you have enough inputs + + align:start position:0% +if you have enough inputs + + + align:start position:0% +if you have enough inputs +through these different axons coming in + + align:start position:0% +through these different axons coming in + + + align:start position:0% +through these different axons coming in +they can summate + + align:start position:0% + + + + align:start position:0% + +at the axon hill it can result in the + + align:start position:0% +at the axon hill it can result in the + + + align:start position:0% +at the axon hill it can result in the +firing of an action potential when a + + align:start position:0% +firing of an action potential when a + + + align:start position:0% +firing of an action potential when a +single input would not have done that + + align:start position:0% +single input would not have done that + + + align:start position:0% +single input would not have done that +okay + + align:start position:0% + + + + align:start position:0% + +let's draw another cell here + + align:start position:0% + + + + align:start position:0% + +and show another kind of summation + + align:start position:0% +and show another kind of summation + + + align:start position:0% +and show another kind of summation +temporal summation here we have a series + + align:start position:0% +temporal summation here we have a series + + + align:start position:0% +temporal summation here we have a series +of action potentials in this axon + + align:start position:0% +of action potentials in this axon + + + align:start position:0% +of action potentials in this axon +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +i'll graph that here + + align:start position:0% + + + + align:start position:0% + +so here's the first one arrives little + + align:start position:0% +so here's the first one arrives little + + + align:start position:0% +so here's the first one arrives little +epsb + + align:start position:0% +epsb + + + align:start position:0% +epsb +the next one arrives a little bit later + + align:start position:0% +the next one arrives a little bit later + + + align:start position:0% +the next one arrives a little bit later +but the first one hasn't decayed all the + + align:start position:0% +but the first one hasn't decayed all the + + + align:start position:0% +but the first one hasn't decayed all the +way yet okay so it gets a little higher + + align:start position:0% +way yet okay so it gets a little higher + + + align:start position:0% +way yet okay so it gets a little higher +and a little higher a little higher and + + align:start position:0% +and a little higher a little higher and + + + align:start position:0% +and a little higher a little higher and +then + + align:start position:0% +then + + + align:start position:0% +then +with enough summation + + align:start position:0% +with enough summation + + + align:start position:0% +with enough summation +it might succeed the threshold and fire + + align:start position:0% +it might succeed the threshold and fire + + + align:start position:0% +it might succeed the threshold and fire +and action potential okay + + align:start position:0% +and action potential okay + + + align:start position:0% +and action potential okay +that would be temporal summation + + align:start position:0% +that would be temporal summation + + + align:start position:0% +that would be temporal summation +okay because + + align:start position:0% +okay because + + + align:start position:0% +okay because +each little postsynaptic potential takes + + align:start position:0% +each little postsynaptic potential takes + + + align:start position:0% +each little postsynaptic potential takes +a little time to decay + + align:start position:0% +a little time to decay + + + align:start position:0% +a little time to decay +so if another one arrives + + align:start position:0% +so if another one arrives + + + align:start position:0% +so if another one arrives +on top of the first one before the first + + align:start position:0% +on top of the first one before the first + + + align:start position:0% +on top of the first one before the first +one is decayed you'll get a summation + + align:start position:0% +one is decayed you'll get a summation + + + align:start position:0% +one is decayed you'll get a summation +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so spatial and temporal summation pretty + + align:start position:0% +so spatial and temporal summation pretty + + + align:start position:0% +so spatial and temporal summation pretty +critical events in the way the nervous + + align:start position:0% +critical events in the way the nervous + + + align:start position:0% +critical events in the way the nervous +system works + + align:start position:0% +system works + + + align:start position:0% +system works +because there's a tremendous amount of + + align:start position:0% +because there's a tremendous amount of + + + align:start position:0% +because there's a tremendous amount of +convergence + + align:start position:0% +convergence + + + align:start position:0% +convergence +of inputs on neurons + + align:start position:0% + + + + align:start position:0% + +remember i mentioned in the motor cortex + + align:start position:0% +remember i mentioned in the motor cortex + + + align:start position:0% +remember i mentioned in the motor cortex +remember how many synapses i said were + + align:start position:0% +remember how many synapses i said were + + + align:start position:0% +remember how many synapses i said were +found on one cell on the average in the + + align:start position:0% +found on one cell on the average in the + + + align:start position:0% +found on one cell on the average in the +monkey motor cortex + + align:start position:0% +monkey motor cortex + + + align:start position:0% +monkey motor cortex +60 000 + + align:start position:0% +60 000 + + + align:start position:0% +60 000 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +a spatial summation is + + align:start position:0% +a spatial summation is + + + align:start position:0% +a spatial summation is +a major + + align:start position:0% + + + + align:start position:0% + +process + + align:start position:0% +process + + + align:start position:0% +process +okay now + + align:start position:0% +okay now + + + align:start position:0% +okay now +why are some + + align:start position:0% +why are some + + + align:start position:0% +why are some +synapses excitatory others inhibitory + + align:start position:0% +synapses excitatory others inhibitory + + + align:start position:0% +synapses excitatory others inhibitory +wire synapse is different + + align:start position:0% + + + + align:start position:0% + +it was difficult to explain them + + align:start position:0% +it was difficult to explain them + + + align:start position:0% +it was difficult to explain them +when it was argued that synapses just + + align:start position:0% +when it was argued that synapses just + + + align:start position:0% +when it was argued that synapses just +acted by + + align:start position:0% +acted by + + + align:start position:0% +acted by +electrical effects only and that was + + align:start position:0% +electrical effects only and that was + + + align:start position:0% +electrical effects only and that was +believed for a long time + + align:start position:0% +believed for a long time + + + align:start position:0% +believed for a long time +in the early part of the + + align:start position:0% +in the early part of the + + + align:start position:0% +in the early part of the +20th century + + align:start position:0% +20th century + + + align:start position:0% +20th century +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but then + + align:start position:0% + + + + align:start position:0% + +otto lowey who was studying + + align:start position:0% +otto lowey who was studying + + + align:start position:0% +otto lowey who was studying +the audit the + + align:start position:0% +the audit the + + + align:start position:0% +the audit the +innovation of the viscera and + + align:start position:0% +innovation of the viscera and + + + align:start position:0% +innovation of the viscera and +other organs like the heart + + align:start position:0% +other organs like the heart + + + align:start position:0% +other organs like the heart +using frogs as his subjects + + align:start position:0% +using frogs as his subjects + + + align:start position:0% +using frogs as his subjects +had a dream + + align:start position:0% + + + + align:start position:0% + +in it + + align:start position:0% +in it + + + align:start position:0% +in it +he realized how he could demonstrate + + align:start position:0% +he realized how he could demonstrate + + + align:start position:0% +he realized how he could demonstrate +it was chemical transmission with the + + align:start position:0% +it was chemical transmission with the + + + align:start position:0% +it was chemical transmission with the +synapse + + align:start position:0% + + + + align:start position:0% + +the only trouble was he forgot the dream + + align:start position:0% +the only trouble was he forgot the dream + + + align:start position:0% +the only trouble was he forgot the dream +and he got up in the morning and he + + align:start position:0% +and he got up in the morning and he + + + align:start position:0% +and he got up in the morning and he +couldn't remember + + align:start position:0% +couldn't remember + + + align:start position:0% +couldn't remember +so what did he do + + align:start position:0% +so what did he do + + + align:start position:0% +so what did he do +fortunately he had the same dream the + + align:start position:0% +fortunately he had the same dream the + + + align:start position:0% +fortunately he had the same dream the +next night he left paper by his bed so + + align:start position:0% +next night he left paper by his bed so + + + align:start position:0% +next night he left paper by his bed so +he would write it down but he decided + + align:start position:0% +he would write it down but he decided + + + align:start position:0% +he would write it down but he decided +not to take the chance he got up and + + align:start position:0% +not to take the chance he got up and + + + align:start position:0% +not to take the chance he got up and +went to the lab + + align:start position:0% +went to the lab + + + align:start position:0% +went to the lab +that's the story + + align:start position:0% +that's the story + + + align:start position:0% +that's the story +he was studying the innovation of the + + align:start position:0% +he was studying the innovation of the + + + align:start position:0% +he was studying the innovation of the +frog heart and the frog heart is + + align:start position:0% +frog heart and the frog heart is + + + align:start position:0% +frog heart and the frog heart is +innovated by two major nerves + + align:start position:0% +innovated by two major nerves + + + align:start position:0% +innovated by two major nerves +okay + + align:start position:0% +okay + + + align:start position:0% +okay +of the peripheral nervous system one is + + align:start position:0% +of the peripheral nervous system one is + + + align:start position:0% +of the peripheral nervous system one is +called the accelerator nerve because if + + align:start position:0% +called the accelerator nerve because if + + + align:start position:0% +called the accelerator nerve because if +you stimulate it electrically it causes + + align:start position:0% +you stimulate it electrically it causes + + + align:start position:0% +you stimulate it electrically it causes +the heart to speed up the other + + align:start position:0% +the heart to speed up the other + + + align:start position:0% +the heart to speed up the other +decelerator nerve because you can slow + + align:start position:0% +decelerator nerve because you can slow + + + align:start position:0% +decelerator nerve because you can slow +the heart down we know that those we now + + align:start position:0% +the heart down we know that those we now + + + align:start position:0% +the heart down we know that those we now +know that those are the connections of + + align:start position:0% +know that those are the connections of + + + align:start position:0% +know that those are the connections of +sympathetic and parasympathetic + + align:start position:0% +sympathetic and parasympathetic + + + align:start position:0% +sympathetic and parasympathetic +divisions of the autonomic nervous + + align:start position:0% +divisions of the autonomic nervous + + + align:start position:0% +divisions of the autonomic nervous +system and we will + + align:start position:0% +system and we will + + + align:start position:0% +system and we will +describe those and you'll read about it + + align:start position:0% +describe those and you'll read about it + + + align:start position:0% +describe those and you'll read about it +in your book + + align:start position:0% + + + + align:start position:0% + +so here's what he did he put + + align:start position:0% +so here's what he did he put + + + align:start position:0% +so here's what he did he put +two frog hearts and separate petri + + align:start position:0% +two frog hearts and separate petri + + + align:start position:0% +two frog hearts and separate petri +dishes each attached to those two nerves + + align:start position:0% +dishes each attached to those two nerves + + + align:start position:0% +dishes each attached to those two nerves +which are now severed from the nervous + + align:start position:0% +which are now severed from the nervous + + + align:start position:0% +which are now severed from the nervous +system but they were still alive + + align:start position:0% +system but they were still alive + + + align:start position:0% +system but they were still alive +and the hearts were beating okay + + align:start position:0% +and the hearts were beating okay + + + align:start position:0% +and the hearts were beating okay +now if he caused one heart to speed up + + align:start position:0% +now if he caused one heart to speed up + + + align:start position:0% +now if he caused one heart to speed up +by stimulating the accelerator nerve and + + align:start position:0% +by stimulating the accelerator nerve and + + + align:start position:0% +by stimulating the accelerator nerve and +he did that for a while + + align:start position:0% +he did that for a while + + + align:start position:0% +he did that for a while +and then he took some of the fluid from + + align:start position:0% +and then he took some of the fluid from + + + align:start position:0% +and then he took some of the fluid from +around that heart and moved the fluid + + align:start position:0% +around that heart and moved the fluid + + + align:start position:0% +around that heart and moved the fluid +to the other petri dish + + align:start position:0% +to the other petri dish + + + align:start position:0% +to the other petri dish +the second heart would speed up + + align:start position:0% +the second heart would speed up + + + align:start position:0% +the second heart would speed up +without having its nerve stimulated + + align:start position:0% +without having its nerve stimulated + + + align:start position:0% +without having its nerve stimulated +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so it had to be a chemical effect he did + + align:start position:0% +so it had to be a chemical effect he did + + + align:start position:0% +so it had to be a chemical effect he did +the same thing for deceleration okay and + + align:start position:0% +the same thing for deceleration okay and + + + align:start position:0% +the same thing for deceleration okay and +showed a similar thing + + align:start position:0% +showed a similar thing + + + align:start position:0% +showed a similar thing +and he said that the + + align:start position:0% +and he said that the + + + align:start position:0% +and he said that the +material he named them just + + align:start position:0% +material he named them just + + + align:start position:0% +material he named them just +according to the function in the first + + align:start position:0% +according to the function in the first + + + align:start position:0% +according to the function in the first +one acceleron stuff in german + + align:start position:0% +one acceleron stuff in german + + + align:start position:0% +one acceleron stuff in german +okay accelerator stuff from the + + align:start position:0% +okay accelerator stuff from the + + + align:start position:0% +okay accelerator stuff from the +accelerator nerve + + align:start position:0% +accelerator nerve + + + align:start position:0% +accelerator nerve +uh or the + + align:start position:0% +uh or the + + + align:start position:0% +uh or the +why where did he get this + + align:start position:0% + + + + align:start position:0% + +the vague nerve + + align:start position:0% +the vague nerve + + + align:start position:0% +the vague nerve +okay is the nerve + + align:start position:0% +okay is the nerve + + + align:start position:0% +okay is the nerve +that when stimulated slows the heart + + align:start position:0% +that when stimulated slows the heart + + + align:start position:0% +that when stimulated slows the heart +down + + align:start position:0% +down + + + align:start position:0% +down +okay and later it was and it wasn't + + align:start position:0% +okay and later it was and it wasn't + + + align:start position:0% +okay and later it was and it wasn't +known at his time but + + align:start position:0% +known at his time but + + + align:start position:0% +known at his time but +not very long afterwards it was + + align:start position:0% +not very long afterwards it was + + + align:start position:0% +not very long afterwards it was +discovered that + + align:start position:0% +discovered that + + + align:start position:0% +discovered that +vegas stuff for vagustuff + + align:start position:0% +vegas stuff for vagustuff + + + align:start position:0% +vegas stuff for vagustuff +is + + align:start position:0% +is + + + align:start position:0% +is +what + + align:start position:0% + + + + align:start position:0% + +it slows the heart down acetylcholine + + align:start position:0% +it slows the heart down acetylcholine + + + align:start position:0% +it slows the heart down acetylcholine +the same neurotransmitter that exit the + + align:start position:0% +the same neurotransmitter that exit the + + + align:start position:0% +the same neurotransmitter that exit the +neuromuscular junction of striated + + align:start position:0% +neuromuscular junction of striated + + + align:start position:0% +neuromuscular junction of striated +muscles okay + + align:start position:0% +muscles okay + + + align:start position:0% +muscles okay +also acts + + align:start position:0% +also acts + + + align:start position:0% +also acts +in the autonomic nervous system + + align:start position:0% +in the autonomic nervous system + + + align:start position:0% +in the autonomic nervous system +okay acceleron stuff + + align:start position:0% +okay acceleron stuff + + + align:start position:0% +okay acceleron stuff +what causes the heart to speed up a + + align:start position:0% +what causes the heart to speed up a + + + align:start position:0% +what causes the heart to speed up a +different neurotransmitter okay + + align:start position:0% +different neurotransmitter okay + + + align:start position:0% +different neurotransmitter okay +norepinephrine or nor adrenaline + + align:start position:0% +norepinephrine or nor adrenaline + + + align:start position:0% +norepinephrine or nor adrenaline +okay + + align:start position:0% +okay + + + align:start position:0% +okay +similar to adrenaline really released by + + align:start position:0% +similar to adrenaline really released by + + + align:start position:0% +similar to adrenaline really released by +the adrenal medulla + + align:start position:0% +the adrenal medulla + + + align:start position:0% +the adrenal medulla +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay and that's where we'll start next + + align:start position:0% +okay and that's where we'll start next + + + align:start position:0% +okay and that's where we'll start next +time \ No newline at end of file diff --git a/Y8CXbAesjaU.txt b/Y8CXbAesjaU.txt new file mode 100644 index 0000000000000000000000000000000000000000..9321ea44e81fbedbfb4ace13641e5c3d392fbe9f --- /dev/null +++ b/Y8CXbAesjaU.txt @@ -0,0 +1,8539 @@ +align:start position:0% + +okay let's get + + align:start position:0% +okay let's get + + + align:start position:0% +okay let's get +started um they're filming today for the + + align:start position:0% +started um they're filming today for the + + + align:start position:0% +started um they're filming today for the +ocw uh materials for UniFi so we're all + + align:start position:0% +ocw uh materials for UniFi so we're all + + + align:start position:0% +ocw uh materials for UniFi so we're all +going to be in a + + align:start position:0% + + + + align:start position:0% + +movie we've got a challenging lecture + + align:start position:0% +movie we've got a challenging lecture + + + align:start position:0% +movie we've got a challenging lecture +today because probably the most + + align:start position:0% +today because probably the most + + + align:start position:0% +today because probably the most +complicated uh bit of work to do + + align:start position:0% +complicated uh bit of work to do + + + align:start position:0% +complicated uh bit of work to do +conceptually is our last lecture um in + + align:start position:0% +conceptually is our last lecture um in + + + align:start position:0% +conceptually is our last lecture um in +propulsion and the basic objective of + + align:start position:0% +propulsion and the basic objective of + + + align:start position:0% +propulsion and the basic objective of +that lecture is + + align:start position:0% +that lecture is + + + align:start position:0% +that lecture is +to again show how the moving blade rows + + align:start position:0% +to again show how the moving blade rows + + + align:start position:0% +to again show how the moving blade rows +in this + + align:start position:0% +in this + + + align:start position:0% +in this +engine can change the stagnation + + align:start position:0% +engine can change the stagnation + + + align:start position:0% +engine can change the stagnation +temperatures change the stagnation + + align:start position:0% +temperatures change the stagnation + + + align:start position:0% +temperatures change the stagnation +pressures and then connect that to cycle + + align:start position:0% +pressures and then connect that to cycle + + + align:start position:0% +pressures and then connect that to cycle +analysis and then connect that up to um + + align:start position:0% +analysis and then connect that up to um + + + align:start position:0% +analysis and then connect that up to um +Mission performance so this is the last + + align:start position:0% +Mission performance so this is the last + + + align:start position:0% +Mission performance so this is the last +bit I just want to point out in this + + align:start position:0% +bit I just want to point out in this + + + align:start position:0% +bit I just want to point out in this +picture up here and when you look at + + align:start position:0% +picture up here and when you look at + + + align:start position:0% +picture up here and when you look at +this engine the VAR things that you're + + align:start position:0% +this engine the VAR things that you're + + + align:start position:0% +this engine the VAR things that you're +looking at so this engine when it spins + + align:start position:0% +looking at so this engine when it spins + + + align:start position:0% +looking at so this engine when it spins +you see the rotating blades right these + + align:start position:0% +you see the rotating blades right these + + + align:start position:0% +you see the rotating blades right these +are called rotors so those are labeled + + align:start position:0% +are called rotors so those are labeled + + + align:start position:0% +are called rotors so those are labeled +with RS on that diagram now what you + + align:start position:0% +with RS on that diagram now what you + + + align:start position:0% +with RS on that diagram now what you +don't see because they've been cut away + + align:start position:0% +don't see because they've been cut away + + + align:start position:0% +don't see because they've been cut away +and pulled off of this are that between + + align:start position:0% +and pulled off of this are that between + + + align:start position:0% +and pulled off of this are that between +each one of those rotating blades and + + align:start position:0% +each one of those rotating blades and + + + align:start position:0% +each one of those rotating blades and +and if you you know look up in here if + + align:start position:0% +and if you you know look up in here if + + + align:start position:0% +and if you you know look up in here if +you've got The Right View you can see it + + align:start position:0% +you've got The Right View you can see it + + + align:start position:0% +you've got The Right View you can see it +or if you look over here you can see + + align:start position:0% +or if you look over here you can see + + + align:start position:0% +or if you look over here you can see +them in between each one of those + + align:start position:0% +them in between each one of those + + + align:start position:0% +them in between each one of those +rotating blades is a stationary set of + + align:start position:0% +rotating blades is a stationary set of + + + align:start position:0% +rotating blades is a stationary set of +blades called + + align:start position:0% +blades called + + + align:start position:0% +blades called +sters right so that the construction of + + align:start position:0% +sters right so that the construction of + + + align:start position:0% +sters right so that the construction of +these is a rotating blade row a + + align:start position:0% +these is a rotating blade row a + + + align:start position:0% +these is a rotating blade row a +stationary blade row rotating stationary + + align:start position:0% +stationary blade row rotating stationary + + + align:start position:0% +stationary blade row rotating stationary +rotating stationary back and forth and + + align:start position:0% +rotating stationary back and forth and + + + align:start position:0% +rotating stationary back and forth and +what we want to do is describe how that + + align:start position:0% +what we want to do is describe how that + + + align:start position:0% +what we want to do is describe how that +imparts power to the flow or how you use + + align:start position:0% +imparts power to the flow or how you use + + + align:start position:0% +imparts power to the flow or how you use +that to extract power from the flow as + + align:start position:0% +that to extract power from the flow as + + + align:start position:0% +that to extract power from the flow as +well how does it change if you change + + align:start position:0% +well how does it change if you change + + + align:start position:0% +well how does it change if you change +the shape of the blades or the speed + + align:start position:0% +the shape of the blades or the speed + + + align:start position:0% +the shape of the blades or the speed +that the blades go that's the last piece + + align:start position:0% +that the blades go that's the last piece + + + align:start position:0% +that the blades go that's the last piece +of the propulsion work so we + + align:start position:0% + + + + align:start position:0% + +finished the first part of that in the + + align:start position:0% +finished the first part of that in the + + + align:start position:0% +finished the first part of that in the +last lecture which was to talk about how + + align:start position:0% +last lecture which was to talk about how + + + align:start position:0% +last lecture which was to talk about how +you could have flow with one enthalpy + + align:start position:0% +you could have flow with one enthalpy + + + align:start position:0% +you could have flow with one enthalpy +coming in some unsteady process which is + + align:start position:0% +coming in some unsteady process which is + + + align:start position:0% +coming in some unsteady process which is +our um moving blade rows and then steady + + align:start position:0% +our um moving blade rows and then steady + + + align:start position:0% +our um moving blade rows and then steady +flow coming out with a different + + align:start position:0% +flow coming out with a different + + + align:start position:0% +flow coming out with a different +enthalpy and we want to again look at + + align:start position:0% +enthalpy and we want to again look at + + + align:start position:0% +enthalpy and we want to again look at +the details of what happens in that box + + align:start position:0% + + + + align:start position:0% + +that box here is drawn in a little bit + + align:start position:0% +that box here is drawn in a little bit + + + align:start position:0% +that box here is drawn in a little bit +more detail where we now have the moving + + align:start position:0% +more detail where we now have the moving + + + align:start position:0% +more detail where we now have the moving +blade row + + align:start position:0% +blade row + + + align:start position:0% +blade row +here and what we care + + align:start position:0% +here and what we care + + + align:start position:0% +here and what we care +about on + + align:start position:0% +about on + + + align:start position:0% +about on +this is the axial + + align:start position:0% +this is the axial + + + align:start position:0% +this is the axial +flux of angular + + align:start position:0% +flux of angular + + + align:start position:0% +flux of angular +momentum because that's what's going to + + align:start position:0% +momentum because that's what's going to + + + align:start position:0% +momentum because that's what's going to +put the torque on the shaft or that's + + align:start position:0% +put the torque on the shaft or that's + + + align:start position:0% +put the torque on the shaft or that's +what putting torque into the shaft with + + align:start position:0% +what putting torque into the shaft with + + + align:start position:0% +what putting torque into the shaft with +the turban which is the back part of + + align:start position:0% +the turban which is the back part of + + + align:start position:0% +the turban which is the back part of +this + + align:start position:0% +this + + + align:start position:0% +this +does it puts some torque on this and + + align:start position:0% +does it puts some torque on this and + + + align:start position:0% +does it puts some torque on this and +then your + + align:start position:0% +then your + + + align:start position:0% +then your +flux of angular momentum it's coming in + + align:start position:0% +flux of angular momentum it's coming in + + + align:start position:0% +flux of angular momentum it's coming in +you have zero angular momentum coming + + align:start position:0% +you have zero angular momentum coming + + + align:start position:0% +you have zero angular momentum coming +into the engine and these blades then + + align:start position:0% +into the engine and these blades then + + + align:start position:0% +into the engine and these blades then +cause it to have some angular + + align:start position:0% +cause it to have some angular + + + align:start position:0% +cause it to have some angular +momentum right so it's the axial flux of + + align:start position:0% +momentum right so it's the axial flux of + + + align:start position:0% +momentum right so it's the axial flux of +angular momentum that relates to that uh + + align:start position:0% +angular momentum that relates to that uh + + + align:start position:0% +angular momentum that relates to that uh +torque and then to connect that to the + + align:start position:0% +torque and then to connect that to the + + + align:start position:0% +torque and then to connect that to the +power you multiply it by the rate at + + align:start position:0% +power you multiply it by the rate at + + + align:start position:0% +power you multiply it by the rate at +which you're doing work so that's the + + align:start position:0% +which you're doing work so that's the + + + align:start position:0% +which you're doing work so that's the +rotational + + align:start position:0% +rotational + + + align:start position:0% +rotational +rate and remember that these are vectors + + align:start position:0% +rate and remember that these are vectors + + + align:start position:0% +rate and remember that these are vectors +so positive torque is a torque in the + + align:start position:0% +so positive torque is a torque in the + + + align:start position:0% +so positive torque is a torque in the +direction of rotation negative torque is + + align:start position:0% +direction of rotation negative torque is + + + align:start position:0% +direction of rotation negative torque is +a torque opposite to the direction of + + align:start position:0% +a torque opposite to the direction of + + + align:start position:0% +a torque opposite to the direction of +rotation you then use the steady flow + + align:start position:0% +rotation you then use the steady flow + + + align:start position:0% +rotation you then use the steady flow +energy + + align:start position:0% +energy + + + align:start position:0% +energy +equation to connect that power to the + + align:start position:0% +equation to connect that power to the + + + align:start position:0% +equation to connect that power to the +change in enthalpy total enthalpy so + + align:start position:0% +change in enthalpy total enthalpy so + + + align:start position:0% +change in enthalpy total enthalpy so +that's mass flow time Delta + + align:start position:0% +that's mass flow time Delta + + + align:start position:0% +that's mass flow time Delta +HT and this + + align:start position:0% +HT and this + + + align:start position:0% +HT and this +is the part of it which is torque equal + + align:start position:0% +is the part of it which is torque equal + + + align:start position:0% +is the part of it which is torque equal +to flux axial flux that's the mass flow + + align:start position:0% +to flux axial flux that's the mass flow + + + align:start position:0% +to flux axial flux that's the mass flow +part angular momentum is the + + align:start position:0% +part angular momentum is the + + + align:start position:0% +part angular momentum is the +RV C RvB where V here is the tangential + + align:start position:0% +RV C RvB where V here is the tangential + + + align:start position:0% +RV C RvB where V here is the tangential +or circumferential component you take + + align:start position:0% +or circumferential component you take + + + align:start position:0% +or circumferential component you take +change in + + align:start position:0% +change in + + + align:start position:0% +change in +enthalpy equate it to change in the flux + + align:start position:0% +enthalpy equate it to change in the flux + + + align:start position:0% +enthalpy equate it to change in the flux +of angular momentum and you're + + align:start position:0% +of angular momentum and you're + + + align:start position:0% +of angular momentum and you're +done if you change the Vel velocity + + align:start position:0% +done if you change the Vel velocity + + + align:start position:0% +done if you change the Vel velocity +tangentially with a ra with a blade + + align:start position:0% +tangentially with a ra with a blade + + + align:start position:0% +tangentially with a ra with a blade +row and you have that blade row moving + + align:start position:0% +row and you have that blade row moving + + + align:start position:0% +row and you have that blade row moving +you get a change in the stagnation + + align:start position:0% +you get a change in the stagnation + + + align:start position:0% +you get a change in the stagnation +temperature right that's the enthalpy CP + + align:start position:0% +temperature right that's the enthalpy CP + + + align:start position:0% +temperature right that's the enthalpy CP +Delta t + + align:start position:0% +Delta t + + + align:start position:0% +Delta t +total so that's what we got to last + + align:start position:0% +total so that's what we got to last + + + align:start position:0% +total so that's what we got to last +lecture are there questions about that + + align:start position:0% +lecture are there questions about that + + + align:start position:0% +lecture are there questions about that +before we go on to the blades + + align:start position:0% + + + + align:start position:0% + +themselves so key things to remember + + align:start position:0% +themselves so key things to remember + + + align:start position:0% +themselves so key things to remember +about this + + align:start position:0% +about this + + + align:start position:0% +about this +we're going to be trying to solve for + + align:start position:0% +we're going to be trying to solve for + + + align:start position:0% +we're going to be trying to solve for +the change in tangential + + align:start position:0% +the change in tangential + + + align:start position:0% +the change in tangential +velocity in the rotating blade + + align:start position:0% + + + + align:start position:0% + +rows because that'll give us the change + + align:start position:0% +rows because that'll give us the change + + + align:start position:0% +rows because that'll give us the change +in temperature across the blade row that + + align:start position:0% +in temperature across the blade row that + + + align:start position:0% +in temperature across the blade row that +would go into a cycle analysis so we're + + align:start position:0% +would go into a cycle analysis so we're + + + align:start position:0% +would go into a cycle analysis so we're +looking for change in tangential + + align:start position:0% +looking for change in tangential + + + align:start position:0% +looking for change in tangential +velocity in the rotating blade + + align:start position:0% +velocity in the rotating blade + + + align:start position:0% +velocity in the rotating blade +rows + + align:start position:0% +rows + + + align:start position:0% +rows +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +now first thing I have to do + + align:start position:0% + + + + align:start position:0% + +is show you the overall features of how + + align:start position:0% +is show you the overall features of how + + + align:start position:0% +is show you the overall features of how +how the various exchange works and I put + + align:start position:0% +how the various exchange works and I put + + + align:start position:0% +how the various exchange works and I put +this up last lecture as well which is + + align:start position:0% +this up last lecture as well which is + + + align:start position:0% +this up last lecture as well which is +just another picture of the same thing + + align:start position:0% +just another picture of the same thing + + + align:start position:0% +just another picture of the same thing +but it has the benefit of having the + + align:start position:0% +but it has the benefit of having the + + + align:start position:0% +but it has the benefit of having the +pressure and the velocity on + + align:start position:0% +pressure and the velocity on + + + align:start position:0% +pressure and the velocity on +it so + + align:start position:0% + + + + align:start position:0% + +conceptually what happens here is that + + align:start position:0% +conceptually what happens here is that + + + align:start position:0% +conceptually what happens here is that +the rotating blade row puts in some + + align:start position:0% +the rotating blade row puts in some + + + align:start position:0% +the rotating blade row puts in some +energy then the stationary one converts + + align:start position:0% +energy then the stationary one converts + + + align:start position:0% +energy then the stationary one converts +that from swirling kinetic energy back + + align:start position:0% +that from swirling kinetic energy back + + + align:start position:0% +that from swirling kinetic energy back +into internal energy and then I add some + + align:start position:0% +into internal energy and then I add some + + + align:start position:0% +into internal energy and then I add some +more with the next blade row and then + + align:start position:0% +more with the next blade row and then + + + align:start position:0% +more with the next blade row and then +the stationary one converts it to + + align:start position:0% +the stationary one converts it to + + + align:start position:0% +the stationary one converts it to +internal and then I add some more and + + align:start position:0% +internal and then I add some more and + + + align:start position:0% +internal and then I add some more and +then another one converts it Etc and you + + align:start position:0% +then another one converts it Etc and you + + + align:start position:0% +then another one converts it Etc and you +can see how many blade rows I might have + + align:start position:0% +can see how many blade rows I might have + + + align:start position:0% +can see how many blade rows I might have +I could have 18 or 20 in a machine like + + align:start position:0% +I could have 18 or 20 in a machine like + + + align:start position:0% +I could have 18 or 20 in a machine like +this and each time you're keeping the + + align:start position:0% +this and each time you're keeping the + + + align:start position:0% +this and each time you're keeping the +velocity pretty constant so that the ax + + align:start position:0% +velocity pretty constant so that the ax + + + align:start position:0% +velocity pretty constant so that the ax +component of kinetic energy through the + + align:start position:0% +component of kinetic energy through the + + + align:start position:0% +component of kinetic energy through the +machine is about the + + align:start position:0% +machine is about the + + + align:start position:0% +machine is about the +same but you keep adding swirling + + align:start position:0% +same but you keep adding swirling + + + align:start position:0% +same but you keep adding swirling +components convert that into internal + + align:start position:0% +components convert that into internal + + + align:start position:0% +components convert that into internal +add some more swirl convert it to + + align:start position:0% +add some more swirl convert it to + + + align:start position:0% +add some more swirl convert it to +internal right so let me put a few more + + align:start position:0% +internal right so let me put a few more + + + align:start position:0% +internal right so let me put a few more +words around + + align:start position:0% + + + + align:start position:0% + +that and these charts uh will be + + align:start position:0% +that and these charts uh will be + + + align:start position:0% +that and these charts uh will be +available I meant to have the handouts + + align:start position:0% +available I meant to have the handouts + + + align:start position:0% +available I meant to have the handouts +and we had a printer problem uh this + + align:start position:0% +and we had a printer problem uh this + + + align:start position:0% +and we had a printer problem uh this +morning so + + align:start position:0% +morning so + + + align:start position:0% +morning so +conceptually the rotating part adds or + + align:start position:0% +conceptually the rotating part adds or + + + align:start position:0% +conceptually the rotating part adds or +removes + + align:start position:0% +removes + + + align:start position:0% +removes +energy and it does this by changing the + + align:start position:0% +energy and it does this by changing the + + + align:start position:0% +energy and it does this by changing the +swirling component of kinetic energy and + + align:start position:0% +swirling component of kinetic energy and + + + align:start position:0% +swirling component of kinetic energy and +leaving the axial component about the + + align:start position:0% +leaving the axial component about the + + + align:start position:0% +leaving the axial component about the +same and what I put down here is + + align:start position:0% +same and what I put down here is + + + align:start position:0% +same and what I put down here is +something that you'll recognize what + + align:start position:0% +something that you'll recognize what + + + align:start position:0% +something that you'll recognize what +equation is + + align:start position:0% +equation is + + + align:start position:0% +equation is +that the beri equation right so this is + + align:start position:0% +that the beri equation right so this is + + + align:start position:0% +that the beri equation right so this is +one way you can think about the way this + + align:start position:0% +one way you can think about the way this + + + align:start position:0% +one way you can think about the way this +works you can write the bruli equation + + align:start position:0% +works you can write the bruli equation + + + align:start position:0% +works you can write the bruli equation +as having a component which is related + + align:start position:0% +as having a component which is related + + + align:start position:0% +as having a component which is related +to internal energy right that's pressure + + align:start position:0% +to internal energy right that's pressure + + + align:start position:0% +to internal energy right that's pressure +static pressure static + + align:start position:0% +static pressure static + + + align:start position:0% +static pressure static +temperature and then three components of + + align:start position:0% +temperature and then three components of + + + align:start position:0% +temperature and then three components of +velocity right I could break it up in in + + align:start position:0% +velocity right I could break it up in in + + + align:start position:0% +velocity right I could break it up in in +any uh three Vector components so + + align:start position:0% +any uh three Vector components so + + + align:start position:0% +any uh three Vector components so +there's a radial kinetic energy which + + align:start position:0% +there's a radial kinetic energy which + + + align:start position:0% +there's a radial kinetic energy which +doesn't change a lot as you go through + + align:start position:0% +doesn't change a lot as you go through + + + align:start position:0% +doesn't change a lot as you go through +this machine because it's in a pipe so + + align:start position:0% +this machine because it's in a pipe so + + + align:start position:0% +this machine because it's in a pipe so +there's not a lot of radial motion of + + align:start position:0% +there's not a lot of radial motion of + + + align:start position:0% +there's not a lot of radial motion of +the + + align:start position:0% +the + + + align:start position:0% +the +flow you've got the tangential component + + align:start position:0% +flow you've got the tangential component + + + align:start position:0% +flow you've got the tangential component +and the axial component which again + + align:start position:0% +and the axial component which again + + + align:start position:0% +and the axial component which again +doesn't change a lot through the device + + align:start position:0% +doesn't change a lot through the device + + + align:start position:0% +doesn't change a lot through the device +so what you do is the rotor puts in + + align:start position:0% +so what you do is the rotor puts in + + + align:start position:0% +so what you do is the rotor puts in +swirl and then the stator or the + + align:start position:0% +swirl and then the stator or the + + + align:start position:0% +swirl and then the stator or the +stationary part converts that swirl into + + align:start position:0% +stationary part converts that swirl into + + + align:start position:0% +stationary part converts that swirl into +internal + + align:start position:0% + + + + align:start position:0% + +energy and then the next rotor puts in + + align:start position:0% +energy and then the next rotor puts in + + + align:start position:0% +energy and then the next rotor puts in +more swirl then the Stater converts the + + align:start position:0% +more swirl then the Stater converts the + + + align:start position:0% +more swirl then the Stater converts the +swirl to internal energy so what happens + + align:start position:0% +swirl to internal energy so what happens + + + align:start position:0% +swirl to internal energy so what happens +as you go through a device like + + align:start position:0% +as you go through a device like + + + align:start position:0% +as you go through a device like +this is that the velocity sort of goes + + align:start position:0% +this is that the velocity sort of goes + + + align:start position:0% +this is that the velocity sort of goes +up and down but stays about constant and + + align:start position:0% +up and down but stays about constant and + + + align:start position:0% +up and down but stays about constant and +the pressure gradually gets higher and + + align:start position:0% +the pressure gradually gets higher and + + + align:start position:0% +the pressure gradually gets higher and +higher and higher until on the newest + + align:start position:0% +higher and higher until on the newest + + + align:start position:0% +higher and higher until on the newest +engines it may be 45 times the inlet + + align:start position:0% +engines it may be 45 times the inlet + + + align:start position:0% +engines it may be 45 times the inlet +pressure right so very significant + + align:start position:0% +pressure right so very significant + + + align:start position:0% +pressure right so very significant +pressure and temperature + + align:start position:0% + + + + align:start position:0% + +increases so + + align:start position:0% +increases so + + + align:start position:0% +increases so +again rotors add tangential swirl + + align:start position:0% +again rotors add tangential swirl + + + align:start position:0% +again rotors add tangential swirl +stators just convert + + align:start position:0% +stators just convert + + + align:start position:0% +stators just convert +it how does a stator convert the energy + + align:start position:0% + + + + align:start position:0% + +yep it redirects it redirects the + + align:start position:0% + + + + align:start position:0% + +flow remember this homework + + align:start position:0% +flow remember this homework + + + align:start position:0% +flow remember this homework +problem yeah this is a + + align:start position:0% + + + + align:start position:0% + +stater a set of Blade rows that take + + align:start position:0% +stater a set of Blade rows that take + + + align:start position:0% +stater a set of Blade rows that take +flow that's coming in if you think about + + align:start position:0% +flow that's coming in if you think about + + + align:start position:0% +flow that's coming in if you think about +this is the axial direction or is the + + align:start position:0% +this is the axial direction or is the + + + align:start position:0% +this is the axial direction or is the +tangential Direction vertically here an + + align:start position:0% +tangential Direction vertically here an + + + align:start position:0% +tangential Direction vertically here an +axial like + + align:start position:0% +axial like + + + align:start position:0% +axial like +this it takes flow in and it changes the + + align:start position:0% +this it takes flow in and it changes the + + + align:start position:0% +this it takes flow in and it changes the +direction of + + align:start position:0% +direction of + + + align:start position:0% +direction of +it now how many people there have + + align:start position:0% +it now how many people there have + + + align:start position:0% +it now how many people there have +trouble thinking about that as a + + align:start position:0% + + + + align:start position:0% + +stater does that make sense to you or + + align:start position:0% +stater does that make sense to you or + + + align:start position:0% +stater does that make sense to you or +does it just look like a set of veins + + align:start position:0% +does it just look like a set of veins + + + align:start position:0% +does it just look like a set of veins +set of air + + align:start position:0% + + + + align:start position:0% + +foils this is one of the difficulties + + align:start position:0% +foils this is one of the difficulties + + + align:start position:0% +foils this is one of the difficulties +that that people have with this which is + + align:start position:0% +that that people have with this which is + + + align:start position:0% +that that people have with this which is +why my daughter has been so kind as to + + align:start position:0% +why my daughter has been so kind as to + + + align:start position:0% +why my daughter has been so kind as to +make this for us as I + + align:start position:0% +make this for us as I + + + align:start position:0% +make this for us as I +said so I need to show you what it means + + align:start position:0% +said so I need to show you what it means + + + align:start position:0% +said so I need to show you what it means +to unwrap a + + align:start position:0% +to unwrap a + + + align:start position:0% +to unwrap a +compressor or unwrap a turbine so you + + align:start position:0% +compressor or unwrap a turbine so you + + + align:start position:0% +compressor or unwrap a turbine so you +have to you're going to have to be + + align:start position:0% +have to you're going to have to be + + + align:start position:0% +have to you're going to have to be +uh you + + align:start position:0% +uh you + + + align:start position:0% +uh you +know imaginative about + + align:start position:0% +know imaginative about + + + align:start position:0% +know imaginative about +this all right this is this + + align:start position:0% +this all right this is this + + + align:start position:0% +this all right this is this +compressor all + + align:start position:0% +compressor all + + + align:start position:0% +compressor all +right everyone + + align:start position:0% +right everyone + + + align:start position:0% +right everyone +see each one of these is a blade and + + align:start position:0% +see each one of these is a blade and + + + align:start position:0% +see each one of these is a blade and +we're going to say that this set of + + align:start position:0% +we're going to say that this set of + + + align:start position:0% +we're going to say that this set of +blades is stationary this set of blades + + align:start position:0% +blades is stationary this set of blades + + + align:start position:0% +blades is stationary this set of blades +is rotating in this one + + align:start position:0% +is rotating in this one + + + align:start position:0% +is rotating in this one +stationary right so it looks a little + + align:start position:0% +stationary right so it looks a little + + + align:start position:0% +stationary right so it looks a little +bit like this right these are all the + + align:start position:0% +bit like this right these are all the + + + align:start position:0% +bit like this right these are all the +angles the ones in between it turns out + + align:start position:0% +angles the ones in between it turns out + + + align:start position:0% +angles the ones in between it turns out +are at different angles and it goes from + + align:start position:0% +are at different angles and it goes from + + + align:start position:0% +are at different angles and it goes from +what 0 to 2 + + align:start position:0% +what 0 to 2 + + + align:start position:0% +what 0 to 2 +pi now I'm going to cut it and open it + + align:start position:0% +pi now I'm going to cut it and open it + + + align:start position:0% +pi now I'm going to cut it and open it +up and now what I have is a bunch of + + align:start position:0% +up and now what I have is a bunch of + + + align:start position:0% +up and now what I have is a bunch of +blades that go from 0 to 2 pi or an + + align:start position:0% +blades that go from 0 to 2 pi or an + + + align:start position:0% +blades that go from 0 to 2 pi or an +infinite row that's just stationary and + + align:start position:0% +infinite row that's just stationary and + + + align:start position:0% +infinite row that's just stationary and +then an infinite row that's moving down + + align:start position:0% +then an infinite row that's moving down + + + align:start position:0% +then an infinite row that's moving down +or up right this is the moving part + + align:start position:0% +or up right this is the moving part + + + align:start position:0% +or up right this is the moving part +right now look at that picture each one + + align:start position:0% +right now look at that picture each one + + + align:start position:0% +right now look at that picture each one +of those blades at an angle in an + + align:start position:0% +of those blades at an angle in an + + + align:start position:0% +of those blades at an angle in an +infinite row is just a blade + + align:start position:0% +infinite row is just a blade + + + align:start position:0% +infinite row is just a blade +row and that's what it means to unwrap a + + align:start position:0% +row and that's what it means to unwrap a + + + align:start position:0% +row and that's what it means to unwrap a +compressor and we'll solve the problem + + align:start position:0% +compressor and we'll solve the problem + + + align:start position:0% +compressor and we'll solve the problem +in this sort of + + align:start position:0% +in this sort of + + + align:start position:0% +in this sort of +frame are questions about + + align:start position:0% +frame are questions about + + + align:start position:0% +frame are questions about +that yes in that problem aren aren't we + + align:start position:0% +that yes in that problem aren aren't we + + + align:start position:0% +that yes in that problem aren aren't we +saying that the streamlines are coming + + align:start position:0% +saying that the streamlines are coming + + + align:start position:0% +saying that the streamlines are coming +in kind of well you have velocity the + + align:start position:0% +in kind of well you have velocity the + + + align:start position:0% +in kind of well you have velocity the +angle just com straight through it it it + + align:start position:0% +angle just com straight through it it it + + + align:start position:0% +angle just com straight through it it it +could be but it turns out that if you + + align:start position:0% +could be but it turns out that if you + + + align:start position:0% +could be but it turns out that if you +have a lot of veins the flow tends to + + align:start position:0% +have a lot of veins the flow tends to + + + align:start position:0% +have a lot of veins the flow tends to +follow the veins right so that problem + + align:start position:0% +follow the veins right so that problem + + + align:start position:0% +follow the veins right so that problem +is a stater so it's just a fixed set of + + align:start position:0% +is a stater so it's just a fixed set of + + + align:start position:0% +is a stater so it's just a fixed set of +veins so again think about it like this + + align:start position:0% +veins so again think about it like this + + + align:start position:0% +veins so again think about it like this +the flow is coming in straight now these + + align:start position:0% +the flow is coming in straight now these + + + align:start position:0% +the flow is coming in straight now these +veins cause it to swirl which is the + + align:start position:0% +veins cause it to swirl which is the + + + align:start position:0% +veins cause it to swirl which is the +same thing when you look at this of + + align:start position:0% +same thing when you look at this of + + + align:start position:0% +same thing when you look at this of +saying the flow comes in straight and + + align:start position:0% +saying the flow comes in straight and + + + align:start position:0% +saying the flow comes in straight and +then it goes in this direction but are + + align:start position:0% +then it goes in this direction but are + + + align:start position:0% +then it goes in this direction but are +we not saying it's coming in straight + + align:start position:0% +we not saying it's coming in straight + + + align:start position:0% +we not saying it's coming in straight +there oh yeah it's coming in an angle + + align:start position:0% +there oh yeah it's coming in an angle + + + align:start position:0% +there oh yeah it's coming in an angle +there so it would be like saying it + + align:start position:0% +there so it would be like saying it + + + align:start position:0% +there so it would be like saying it +comes in an angle and it changes its + + align:start position:0% +comes in an angle and it changes its + + + align:start position:0% +comes in an angle and it changes its +angle somewhat what causes it com in + + align:start position:0% +angle somewhat what causes it com in + + + align:start position:0% +angle somewhat what causes it com in +that initi oh maybe another set of Blade + + align:start position:0% +that initi oh maybe another set of Blade + + + align:start position:0% +that initi oh maybe another set of Blade +rows in front of + + align:start position:0% +rows in front of + + + align:start position:0% +rows in front of +it right so that's just a general + + align:start position:0% +it right so that's just a general + + + align:start position:0% +it right so that's just a general +problem but the way that this then + + align:start position:0% +problem but the way that this then + + + align:start position:0% +problem but the way that this then +converts kinetic energy into into + + align:start position:0% +converts kinetic energy into into + + + align:start position:0% +converts kinetic energy into into +internal energy if you remember this + + align:start position:0% +internal energy if you remember this + + + align:start position:0% +internal energy if you remember this +that the flow area coming into this + + align:start position:0% + + + + align:start position:0% + +was different right so you have a + + align:start position:0% +was different right so you have a + + + align:start position:0% +was different right so you have a +perpendicular distance across this pipe + + align:start position:0% +perpendicular distance across this pipe + + + align:start position:0% +perpendicular distance across this pipe +and a perpendicular distance across that + + align:start position:0% +and a perpendicular distance across that + + + align:start position:0% +and a perpendicular distance across that +pipe coming + + align:start position:0% +pipe coming + + + align:start position:0% +pipe coming +out and they're different thickness + + align:start position:0% +out and they're different thickness + + + align:start position:0% +out and they're different thickness +pipes so it's just like a nozzle right a + + align:start position:0% +pipes so it's just like a nozzle right a + + + align:start position:0% +pipes so it's just like a nozzle right a +nozzle takes internal energy and + + align:start position:0% +nozzle takes internal energy and + + + align:start position:0% +nozzle takes internal energy and +converts it to kinetic energy this does + + align:start position:0% +converts it to kinetic energy this does + + + align:start position:0% +converts it to kinetic energy this does +the same thing you've got a small pipe + + align:start position:0% +the same thing you've got a small pipe + + + align:start position:0% +the same thing you've got a small pipe +if you think about it that gets to be a + + align:start position:0% +if you think about it that gets to be a + + + align:start position:0% +if you think about it that gets to be a +big + + align:start position:0% +big + + + align:start position:0% +big +pipe converts kinetic + + align:start position:0% +pipe converts kinetic + + + align:start position:0% +pipe converts kinetic +energy lower speed flow higher internal + + align:start position:0% +energy lower speed flow higher internal + + + align:start position:0% +energy lower speed flow higher internal +energy at the + + align:start position:0% +energy at the + + + align:start position:0% +energy at the +exit so there are forces on these blades + + align:start position:0% +exit so there are forces on these blades + + + align:start position:0% +exit so there are forces on these blades +there are torqus but they're not moving + + align:start position:0% +there are torqus but they're not moving + + + align:start position:0% +there are torqus but they're not moving +so they don't do any work they just take + + align:start position:0% +so they don't do any work they just take + + + align:start position:0% +so they don't do any work they just take +one kind of energy and turn it into + + align:start position:0% +one kind of energy and turn it into + + + align:start position:0% +one kind of energy and turn it into +another is that + + align:start position:0% + + + + align:start position:0% + +okay conceptually you have to really be + + align:start position:0% +okay conceptually you have to really be + + + align:start position:0% +okay conceptually you have to really be +able to unwrap the the + + align:start position:0% +able to unwrap the the + + + align:start position:0% +able to unwrap the the +compressor so flow in this direction is + + align:start position:0% +compressor so flow in this direction is + + + align:start position:0% +compressor so flow in this direction is +tangential flow in this direction is + + align:start position:0% + + + + align:start position:0% + +axial + + align:start position:0% + + + + align:start position:0% + +questions yes that area looks like it's + + align:start position:0% +questions yes that area looks like it's + + + align:start position:0% +questions yes that area looks like it's +that's that area is bigger so you're + + align:start position:0% +that's that area is bigger so you're + + + align:start position:0% +that's that area is bigger so you're +comparing that to a nozzle so in ter so + + align:start position:0% +comparing that to a nozzle so in ter so + + + align:start position:0% +comparing that to a nozzle so in ter so +kinetic energy would be going up across + + align:start position:0% +kinetic energy would be going up across + + + align:start position:0% +kinetic energy would be going up across +that oh no since this is bigger kinetic + + align:start position:0% +that oh no since this is bigger kinetic + + + align:start position:0% +that oh no since this is bigger kinetic +energy go down you'd have a lower speed + + align:start position:0% +energy go down you'd have a lower speed + + + align:start position:0% +energy go down you'd have a lower speed +flow um at the exit of this than at the + + align:start position:0% +flow um at the exit of this than at the + + + align:start position:0% +flow um at the exit of this than at the +inlet so this would be something if you + + align:start position:0% +inlet so this would be something if you + + + align:start position:0% +inlet so this would be something if you +look at it that takes some of the swirl + + align:start position:0% +look at it that takes some of the swirl + + + align:start position:0% +look at it that takes some of the swirl +some of the tangential component of + + align:start position:0% +some of the tangential component of + + + align:start position:0% +some of the tangential component of +velocity and converts it into higher + + align:start position:0% +velocity and converts it into higher + + + align:start position:0% +velocity and converts it into higher +static + + align:start position:0% +static + + + align:start position:0% +static +pressure which is what Staters + + align:start position:0% + + + + align:start position:0% + +do there are also Staters in the turban + + align:start position:0% +do there are also Staters in the turban + + + align:start position:0% +do there are also Staters in the turban +that do the opposite as you'd expect + + align:start position:0% +that do the opposite as you'd expect + + + align:start position:0% +that do the opposite as you'd expect +compressors and Staters are sort of + + align:start position:0% +compressors and Staters are sort of + + + align:start position:0% +compressors and Staters are sort of +mirror images of each other one puts + + align:start position:0% +mirror images of each other one puts + + + align:start position:0% +mirror images of each other one puts +work in the other takes work out + + align:start position:0% + + + + align:start position:0% + +people all right with the setup for the + + align:start position:0% + + + + align:start position:0% + +problem because now we've + + align:start position:0% +problem because now we've + + + align:start position:0% +problem because now we've +got some + + align:start position:0% +got some + + + align:start position:0% +got some +rules and we're just at the stage where + + align:start position:0% +rules and we're just at the stage where + + + align:start position:0% +rules and we're just at the stage where +it's useful for you to have the handouts + + align:start position:0% +it's useful for you to have the handouts + + + align:start position:0% +it's useful for you to have the handouts +because I want you to draw on top of + + align:start position:0% +because I want you to draw on top of + + + align:start position:0% +because I want you to draw on top of +these handouts so these are the charts + + align:start position:0% +these handouts so these are the charts + + + align:start position:0% +these handouts so these are the charts +that we'll pass + + align:start position:0% +that we'll pass + + + align:start position:0% +that we'll pass +around so you'll have all these rules in + + align:start position:0% +around so you'll have all these rules in + + + align:start position:0% +around so you'll have all these rules in +front of you + + align:start position:0% + + + + align:start position:0% + +I'll let you get the charts + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that is an unwrapped set of Blade + + align:start position:0% + + + + align:start position:0% + +rows which is + + align:start position:0% +rows which is + + + align:start position:0% +rows which is +exactly what this green and pink and + + align:start position:0% +exactly what this green and pink and + + + align:start position:0% +exactly what this green and pink and +blue thing is I've taken a set of + + align:start position:0% +blue thing is I've taken a set of + + + align:start position:0% +blue thing is I've taken a set of +blades and I've unwrapped + + align:start position:0% +blades and I've unwrapped + + + align:start position:0% +blades and I've unwrapped +them and then what I did in that picture + + align:start position:0% +them and then what I did in that picture + + + align:start position:0% +them and then what I did in that picture +to make it complicated was I turned it + + align:start position:0% +to make it complicated was I turned it + + + align:start position:0% +to make it complicated was I turned it +like this + + align:start position:0% + + + + align:start position:0% + +so you've got axial flow coming in the + + align:start position:0% +so you've got axial flow coming in the + + + align:start position:0% +so you've got axial flow coming in the +top and then you've got that middle + + align:start position:0% +top and then you've got that middle + + + align:start position:0% +top and then you've got that middle +blade row moving in this + + align:start position:0% +blade row moving in this + + + align:start position:0% +blade row moving in this +Direction all right so you see how I got + + align:start position:0% +Direction all right so you see how I got + + + align:start position:0% +Direction all right so you see how I got +that I took a set of blades and I opened + + align:start position:0% +that I took a set of blades and I opened + + + align:start position:0% +that I took a set of blades and I opened +them up like + + align:start position:0% +them up like + + + align:start position:0% +them up like +this all right + + align:start position:0% + + + + align:start position:0% + +this stuff on the right hand side is + + align:start position:0% +this stuff on the right hand side is + + + align:start position:0% +this stuff on the right hand side is +what you have to learn how to + + align:start position:0% +what you have to learn how to + + + align:start position:0% +what you have to learn how to +do and the whole + + align:start position:0% +do and the whole + + + align:start position:0% +do and the whole +purpose of these + + align:start position:0% +purpose of these + + + align:start position:0% +purpose of these +drawings is for you to determine what + + align:start position:0% +drawings is for you to determine what + + + align:start position:0% +drawings is for you to determine what +the tangential velocity is coming into + + align:start position:0% +the tangential velocity is coming into + + + align:start position:0% +the tangential velocity is coming into +the rotor and what the tangential + + align:start position:0% +the rotor and what the tangential + + + align:start position:0% +the rotor and what the tangential +velocity is coming out of the + + align:start position:0% +velocity is coming out of the + + + align:start position:0% +velocity is coming out of the +rotor because that's what goes into the + + align:start position:0% +rotor because that's what goes into the + + + align:start position:0% +rotor because that's what goes into the +oiler turbine equation that's what tells + + align:start position:0% +oiler turbine equation that's what tells + + + align:start position:0% +oiler turbine equation that's what tells +you what the net flux of angular + + align:start position:0% +you what the net flux of angular + + + align:start position:0% +you what the net flux of angular +momentum is if you know the change in + + align:start position:0% +momentum is if you know the change in + + + align:start position:0% +momentum is if you know the change in +tangential velocity so again this + + align:start position:0% +tangential velocity so again this + + + align:start position:0% +tangential velocity so again this +is axial if I can write this better + + align:start position:0% +is axial if I can write this better + + + align:start position:0% +is axial if I can write this better +here + + align:start position:0% +here + + + align:start position:0% +here +axial and this is + + align:start position:0% + + + + align:start position:0% + +tangential so your purpose in this is to + + align:start position:0% +tangential so your purpose in this is to + + + align:start position:0% +tangential so your purpose in this is to +solve for VB and VC + + align:start position:0% +solve for VB and VC + + + align:start position:0% +solve for VB and VC +change in tangential velocity at the + + align:start position:0% +change in tangential velocity at the + + + align:start position:0% +change in tangential velocity at the +front of and the back of the moving + + align:start position:0% +front of and the back of the moving + + + align:start position:0% +front of and the back of the moving +blade + + align:start position:0% + + + + align:start position:0% + +row now what are all the other lines + + align:start position:0% + + + + align:start position:0% + +here these the dashed + + align:start position:0% +here these the dashed + + + align:start position:0% +here these the dashed +lines are what the flow velocities look + + align:start position:0% +lines are what the flow velocities look + + + align:start position:0% +lines are what the flow velocities look +like for someone who's sitting + + align:start position:0% + + + + align:start position:0% + +on the moving blades + + align:start position:0% +on the moving blades + + + align:start position:0% +on the moving blades +and I warned you about this the way you + + align:start position:0% +and I warned you about this the way you + + + align:start position:0% +and I warned you about this the way you +have to solve these problems is you go + + align:start position:0% +have to solve these problems is you go + + + align:start position:0% +have to solve these problems is you go +from stationary to rotating frame to + + align:start position:0% +from stationary to rotating frame to + + + align:start position:0% +from stationary to rotating frame to +stationary frame to rotating frame to + + align:start position:0% +stationary frame to rotating frame to + + + align:start position:0% +stationary frame to rotating frame to +stationary frame to rotating frame so + + align:start position:0% +stationary frame to rotating frame so + + + align:start position:0% +stationary frame to rotating frame so +you have to do a transformation between + + align:start position:0% +you have to do a transformation between + + + align:start position:0% +you have to do a transformation between +those frames between each and every + + align:start position:0% +those frames between each and every + + + align:start position:0% +those frames between each and every +blade + + align:start position:0% + + + + align:start position:0% + +row now luckily there's only one + + align:start position:0% +row now luckily there's only one + + + align:start position:0% +row now luckily there's only one +difference between the frames and that's + + align:start position:0% +difference between the frames and that's + + + align:start position:0% +difference between the frames and that's +that one has tangential velocity the + + align:start position:0% +that one has tangential velocity the + + + align:start position:0% +that one has tangential velocity the +other doesn't so you don't have to do + + align:start position:0% +other doesn't so you don't have to do + + + align:start position:0% +other doesn't so you don't have to do +fancy you know + + align:start position:0% +fancy you know + + + align:start position:0% +fancy you know +Vector um calculus to get between them + + align:start position:0% +Vector um calculus to get between them + + + align:start position:0% +Vector um calculus to get between them +you just have to add this tangential + + align:start position:0% +you just have to add this tangential + + + align:start position:0% +you just have to add this tangential +velocity on and then remove it every + + align:start position:0% +velocity on and then remove it every + + + align:start position:0% +velocity on and then remove it every +time you go back and + + align:start position:0% +time you go back and + + + align:start position:0% +time you go back and +forth + + align:start position:0% +forth + + + align:start position:0% +forth +okay now there's a set of rules that + + align:start position:0% +okay now there's a set of rules that + + + align:start position:0% +okay now there's a set of rules that +we're going to follow and I'm going to + + align:start position:0% +we're going to follow and I'm going to + + + align:start position:0% +we're going to follow and I'm going to +walk you through this and then I've got + + align:start position:0% +walk you through this and then I've got + + + align:start position:0% +walk you through this and then I've got +two problems for you to do there are two + + align:start position:0% +two problems for you to do there are two + + + align:start position:0% +two problems for you to do there are two +animated files on the web and there's + + align:start position:0% +animated files on the web and there's + + + align:start position:0% +animated files on the web and there's +also a Java Java applet on the web that + + align:start position:0% +also a Java Java applet on the web that + + + align:start position:0% +also a Java Java applet on the web that +you can use to draw these so there's a + + align:start position:0% +you can use to draw these so there's a + + + align:start position:0% +you can use to draw these so there's a +lot of things that you can use to drill + + align:start position:0% +lot of things that you can use to drill + + + align:start position:0% +lot of things that you can use to drill +yourself and practice on how to do it + + align:start position:0% +yourself and practice on how to do it + + + align:start position:0% +yourself and practice on how to do it +these are the + + align:start position:0% + + + + align:start position:0% + +rules and if you apply these you'll be + + align:start position:0% +rules and if you apply these you'll be + + + align:start position:0% +rules and if you apply these you'll be +in good + + align:start position:0% +in good + + + align:start position:0% +in good +shape and I'm going to work through and + + align:start position:0% +shape and I'm going to work through and + + + align:start position:0% +shape and I'm going to work through and +apply them once and then you guys will + + align:start position:0% +apply them once and then you guys will + + + align:start position:0% +apply them once and then you guys will +do it twice on your + + align:start position:0% +do it twice on your + + + align:start position:0% +do it twice on your +own always consider a blade in a + + align:start position:0% +own always consider a blade in a + + + align:start position:0% +own always consider a blade in a +reference frame attached to the blade so + + align:start position:0% +reference frame attached to the blade so + + + align:start position:0% +reference frame attached to the blade so +if you're in a stationary blade row make + + align:start position:0% +if you're in a stationary blade row make + + + align:start position:0% +if you're in a stationary blade row make +sure you're in the stationary reference + + align:start position:0% +sure you're in the stationary reference + + + align:start position:0% +sure you're in the stationary reference +frame + + align:start position:0% +frame + + + align:start position:0% +frame +if you're on a moving blade row + + align:start position:0% +if you're on a moving blade row + + + align:start position:0% +if you're on a moving blade row +transform yourself into the rotating + + align:start position:0% +transform yourself into the rotating + + + align:start position:0% +transform yourself into the rotating +reference + + align:start position:0% +reference + + + align:start position:0% +reference +frame that's why you have to change + + align:start position:0% +frame that's why you have to change + + + align:start position:0% +frame that's why you have to change +reference frames every blade row through + + align:start position:0% +reference frames every blade row through + + + align:start position:0% +reference frames every blade row through +the + + align:start position:0% +the + + + align:start position:0% +the +compressor for + + align:start position:0% +compressor for + + + align:start position:0% +compressor for +unified we're going to assume that axial + + align:start position:0% +unified we're going to assume that axial + + + align:start position:0% +unified we're going to assume that axial +velocity and radius are + + align:start position:0% +velocity and radius are + + + align:start position:0% +velocity and radius are +constant which means that when you go + + align:start position:0% +constant which means that when you go + + + align:start position:0% +constant which means that when you go +back to the oiler turban equation + + align:start position:0% + + + + align:start position:0% + +I'm going to assume that this R is + + align:start position:0% +I'm going to assume that this R is + + + align:start position:0% +I'm going to assume that this R is +constant RC is the same as + + align:start position:0% +constant RC is the same as + + + align:start position:0% +constant RC is the same as +RB there's no change in the axial + + align:start position:0% +RB there's no change in the axial + + + align:start position:0% +RB there's no change in the axial +component so just simplifies things if + + align:start position:0% +component so just simplifies things if + + + align:start position:0% +component so just simplifies things if +you're going to do it formally for a + + align:start position:0% +you're going to do it formally for a + + + align:start position:0% +you're going to do it formally for a +real device you wouldn't make that + + align:start position:0% +real device you wouldn't make that + + + align:start position:0% +real device you wouldn't make that +assumption so this is just advice always + + align:start position:0% +assumption so this is just advice always + + + align:start position:0% +assumption so this is just advice always +consider + + align:start position:0% +consider + + + align:start position:0% +consider +the blade and the reference frame + + align:start position:0% +the blade and the reference frame + + + align:start position:0% +the blade and the reference frame +attached to the + + align:start position:0% +attached to the + + + align:start position:0% +attached to the +blade this is an assumption that we're + + align:start position:0% +blade this is an assumption that we're + + + align:start position:0% +blade this is an assumption that we're +going to make and then the rest are some + + align:start position:0% +going to make and then the rest are some + + + align:start position:0% +going to make and then the rest are some +rules one rule is that the flow always + + align:start position:0% +rules one rule is that the flow always + + + align:start position:0% +rules one rule is that the flow always +leaves blades at the trailing edge + + align:start position:0% +leaves blades at the trailing edge + + + align:start position:0% +leaves blades at the trailing edge +angle you guys have had enough + + align:start position:0% +angle you guys have had enough + + + align:start position:0% +angle you guys have had enough +aerodynamics that you can tell me what's + + align:start position:0% +aerodynamics that you can tell me what's + + + align:start position:0% +aerodynamics that you can tell me what's +wrong with that statement when does that + + align:start position:0% +wrong with that statement when does that + + + align:start position:0% +wrong with that statement when does that +not + + align:start position:0% +not + + + align:start position:0% +not +happen so if this is + + align:start position:0% + + + + align:start position:0% + +my stall someone mentioned if this is my + + align:start position:0% +my stall someone mentioned if this is my + + + align:start position:0% +my stall someone mentioned if this is my +blade + + align:start position:0% +blade + + + align:start position:0% +blade +and the flow is coming in it will tend + + align:start position:0% +and the flow is coming in it will tend + + + align:start position:0% +and the flow is coming in it will tend +to stick to this blade and head off in + + align:start position:0% +to stick to this blade and head off in + + + align:start position:0% +to stick to this blade and head off in +that + + align:start position:0% +that + + + align:start position:0% +that +direction that's what produces the lift + + align:start position:0% +direction that's what produces the lift + + + align:start position:0% +direction that's what produces the lift +I've got momentum coming in like this I + + align:start position:0% +I've got momentum coming in like this I + + + align:start position:0% +I've got momentum coming in like this I +put the momentum down like that I must + + align:start position:0% +put the momentum down like that I must + + + align:start position:0% +put the momentum down like that I must +get a force opposite to it right so air + + align:start position:0% +get a force opposite to it right so air + + + align:start position:0% +get a force opposite to it right so air +foils and these are just spinning air + + align:start position:0% +foils and these are just spinning air + + + align:start position:0% +foils and these are just spinning air +foils you know change the direction of + + align:start position:0% +foils you know change the direction of + + + align:start position:0% +foils you know change the direction of +the flow that produces the + + align:start position:0% +the flow that produces the + + + align:start position:0% +the flow that produces the +forces the only time that this does not + + align:start position:0% +forces the only time that this does not + + + align:start position:0% +forces the only time that this does not +hold is if you have stall and the flow + + align:start position:0% +hold is if you have stall and the flow + + + align:start position:0% +hold is if you have stall and the flow +separ Ates from the + + align:start position:0% +separ Ates from the + + + align:start position:0% +separ Ates from the +blade we're going to assume that this is + + align:start position:0% +blade we're going to assume that this is + + + align:start position:0% +blade we're going to assume that this is +a well-designed + + align:start position:0% +a well-designed + + + align:start position:0% +a well-designed +machine you do get a lot of fancy kinds + + align:start position:0% +machine you do get a lot of fancy kinds + + + align:start position:0% +machine you do get a lot of fancy kinds +of stalls in these engines but it's not + + align:start position:0% +of stalls in these engines but it's not + + + align:start position:0% +of stalls in these engines but it's not +the first thing you're going to try and + + align:start position:0% +the first thing you're going to try and + + + align:start position:0% +the first thing you're going to try and +solve right so you're going to assume + + align:start position:0% +solve right so you're going to assume + + + align:start position:0% +solve right so you're going to assume +that the flow always leaves at the + + align:start position:0% +that the flow always leaves at the + + + align:start position:0% +that the flow always leaves at the +trailing edge + + align:start position:0% + + + + align:start position:0% + +angle one of the things that's useful + + align:start position:0% +angle one of the things that's useful + + + align:start position:0% +angle one of the things that's useful +and I'll show you in a minute is that + + align:start position:0% +and I'll show you in a minute is that + + + align:start position:0% +and I'll show you in a minute is that +you're going to check the inlet flow + + align:start position:0% +you're going to check the inlet flow + + + align:start position:0% +you're going to check the inlet flow +angle to make sure that the flow coming + + align:start position:0% +angle to make sure that the flow coming + + + align:start position:0% +angle to make sure that the flow coming +into the blade + + align:start position:0% +into the blade + + + align:start position:0% +into the blade +is roughly aligned with the blade + + align:start position:0% +is roughly aligned with the blade + + + align:start position:0% +is roughly aligned with the blade +Leading Edge you know if it's coming in + + align:start position:0% +Leading Edge you know if it's coming in + + + align:start position:0% +Leading Edge you know if it's coming in +like this it usually means you have + + align:start position:0% +like this it usually means you have + + + align:start position:0% +like this it usually means you have +something wrong in your velocity + + align:start position:0% +something wrong in your velocity + + + align:start position:0% +something wrong in your velocity +triangles already mentioned this you can + + align:start position:0% +triangles already mentioned this you can + + + align:start position:0% +triangles already mentioned this you can +only have work across the moving blade + + align:start position:0% +only have work across the moving blade + + + align:start position:0% +only have work across the moving blade +rows so your whole objective is to find + + align:start position:0% +rows so your whole objective is to find + + + align:start position:0% +rows so your whole objective is to find +out what's the tangential component of + + align:start position:0% + + + + align:start position:0% + +velocity + + align:start position:0% +velocity + + + align:start position:0% +velocity +across the moving blade + + align:start position:0% + + + + align:start position:0% + +row + + align:start position:0% +row + + + align:start position:0% +row +and that is in the stationary reference + + align:start position:0% +and that is in the stationary reference + + + align:start position:0% +and that is in the stationary reference +frame that + + align:start position:0% + + + + align:start position:0% + +velocity if you know the change in + + align:start position:0% +velocity if you know the change in + + + align:start position:0% +velocity if you know the change in +stationary reference frame tangential + + align:start position:0% +stationary reference frame tangential + + + align:start position:0% +stationary reference frame tangential +velocity and it increases in the + + align:start position:0% +velocity and it increases in the + + + align:start position:0% +velocity and it increases in the +direction of rotor motion that means + + align:start position:0% +direction of rotor motion that means + + + align:start position:0% +direction of rotor motion that means +you've done work on it you've added + + align:start position:0% +you've done work on it you've added + + + align:start position:0% +you've done work on it you've added +swirl if it decreases in the direction + + align:start position:0% +swirl if it decreases in the direction + + + align:start position:0% +swirl if it decreases in the direction +of rotor motion you've taken work out + + align:start position:0% +of rotor motion you've taken work out + + + align:start position:0% +of rotor motion you've taken work out +you've can swirl out so the purpose of + + align:start position:0% +you've can swirl out so the purpose of + + + align:start position:0% +you've can swirl out so the purpose of +these rotating blades is to put in + + align:start position:0% +these rotating blades is to put in + + + align:start position:0% +these rotating blades is to put in +swirling kinetic energy so the + + align:start position:0% +swirling kinetic energy so the + + + align:start position:0% +swirling kinetic energy so the +stationary ones can convert it into + + align:start position:0% +stationary ones can convert it into + + + align:start position:0% +stationary ones can convert it into +internal energy and you go on and on and + + align:start position:0% +internal energy and you go on and on and + + + align:start position:0% +internal energy and you go on and on and +on all right before I go ahead and do an + + align:start position:0% +on all right before I go ahead and do an + + + align:start position:0% +on all right before I go ahead and do an +example questions about that + + align:start position:0% +example questions about that + + + align:start position:0% +example questions about that +stuff + + align:start position:0% +stuff + + + align:start position:0% +stuff +Yes actually kind the same question from + + align:start position:0% +Yes actually kind the same question from + + + align:start position:0% +Yes actually kind the same question from +before with that diagram the tring + + align:start position:0% +before with that diagram the tring + + + align:start position:0% +before with that diagram the tring +Ed this diagram are are we going from + + align:start position:0% +Ed this diagram are are we going from + + + align:start position:0% +Ed this diagram are are we going from +top bottom yep you will go through from + + align:start position:0% +top bottom yep you will go through from + + + align:start position:0% +top bottom yep you will go through from +top to bottom this is the front of the + + align:start position:0% +top to bottom this is the front of the + + + align:start position:0% +top to bottom this is the front of the +engine this is the back of the engine + + align:start position:0% +engine this is the back of the engine + + + align:start position:0% +engine this is the back of the engine +when you come off the guide + + align:start position:0% +when you come off the guide + + + align:start position:0% +when you come off the guide +is down right yes it is + + align:start position:0% +is down right yes it is + + + align:start position:0% +is down right yes it is +then well you're going to see that it it + + align:start position:0% +then well you're going to see that it it + + + align:start position:0% +then well you're going to see that it it +happens to line up exactly with these + + align:start position:0% +happens to line up exactly with these + + + align:start position:0% +happens to line up exactly with these +blades when you're in the reference + + align:start position:0% +blades when you're in the reference + + + align:start position:0% +blades when you're in the reference +frame of those blades so for this little + + align:start position:0% +frame of those blades so for this little + + + align:start position:0% +frame of those blades so for this little +person sitting on the blades this looks + + align:start position:0% +person sitting on the blades this looks + + + align:start position:0% +person sitting on the blades this looks +just + + align:start position:0% +just + + + align:start position:0% +just +fine and that's what I've got to show + + align:start position:0% +fine and that's what I've got to show + + + align:start position:0% +fine and that's what I've got to show +you that's how you're going to follow + + align:start position:0% +you that's how you're going to follow + + + align:start position:0% +you that's how you're going to follow +these + + align:start position:0% +these + + + align:start position:0% +these +rules right and you end up with shocks + + align:start position:0% +rules right and you end up with shocks + + + align:start position:0% +rules right and you end up with shocks +those we're going to assume that this is + + align:start position:0% +those we're going to assume that this is + + + align:start position:0% +those we're going to assume that this is +um shock free largely incompressible + + align:start position:0% +um shock free largely incompressible + + + align:start position:0% +um shock free largely incompressible +flow um for the purposes of unified + + align:start position:0% +flow um for the purposes of unified + + + align:start position:0% +flow um for the purposes of unified +these things do spin with tip mock + + align:start position:0% +these things do spin with tip mock + + + align:start position:0% +these things do spin with tip mock +numbers of8 or one or 1.2 and you do get + + align:start position:0% +numbers of8 or one or 1.2 and you do get + + + align:start position:0% +numbers of8 or one or 1.2 and you do get +a lot of compressible flow effects but + + align:start position:0% +a lot of compressible flow effects but + + + align:start position:0% +a lot of compressible flow effects but +we're not going to address + + align:start position:0% + + + + align:start position:0% + +them okay now I want you to do the same + + align:start position:0% +them okay now I want you to do the same + + + align:start position:0% +them okay now I want you to do the same +things that I do on your handouts + + align:start position:0% + + + + align:start position:0% + +okay we're going to follow these + + align:start position:0% +okay we're going to follow these + + + align:start position:0% +okay we're going to follow these +rules the first thing that we said to do + + align:start position:0% +rules the first thing that we said to do + + + align:start position:0% +rules the first thing that we said to do +is check the incoming angle of attack of + + align:start position:0% +is check the incoming angle of attack of + + + align:start position:0% +is check the incoming angle of attack of +the + + align:start position:0% +the + + + align:start position:0% +the +flow so from the perspective of an air + + align:start position:0% +flow so from the perspective of an air + + + align:start position:0% +flow so from the perspective of an air +foil this would be the angle of attack + + align:start position:0% +foil this would be the angle of attack + + + align:start position:0% +foil this would be the angle of attack +on that air foil + + align:start position:0% + + + + align:start position:0% + +right you have to you know put yourself + + align:start position:0% +right you have to you know put yourself + + + align:start position:0% +right you have to you know put yourself +in the frame of reference of sitting on + + align:start position:0% +in the frame of reference of sitting on + + + align:start position:0% +in the frame of reference of sitting on +an airplane's Wing + + align:start position:0% +an airplane's Wing + + + align:start position:0% +an airplane's Wing +here so + + align:start position:0% +here so + + + align:start position:0% +here so +if the higher the alpha here the higher + + align:start position:0% +if the higher the alpha here the higher + + + align:start position:0% +if the higher the alpha here the higher +the angle of attack but that's + + align:start position:0% +the angle of attack but that's + + + align:start position:0% +the angle of attack but that's +reasonable you'd expect to have a + + align:start position:0% +reasonable you'd expect to have a + + + align:start position:0% +reasonable you'd expect to have a +positive angle of attack coming into + + align:start position:0% +positive angle of attack coming into + + + align:start position:0% +positive angle of attack coming into +these + + align:start position:0% +these + + + align:start position:0% +these +blades okay if it were negative you + + align:start position:0% +blades okay if it were negative you + + + align:start position:0% +blades okay if it were negative you +might worry a little bit but something + + align:start position:0% +might worry a little bit but something + + + align:start position:0% +might worry a little bit but something +was + + align:start position:0% +was + + + align:start position:0% +was +wrong the next rule is assume that the + + align:start position:0% +wrong the next rule is assume that the + + + align:start position:0% +wrong the next rule is assume that the +flow always + + align:start position:0% +flow always + + + align:start position:0% +flow always +leaves the blade at the trailing edge + + align:start position:0% + + + + align:start position:0% + +angle which is + + align:start position:0% +angle which is + + + align:start position:0% +angle which is +this that is this Vector right + + align:start position:0% + + + + align:start position:0% + +here VB that is + + align:start position:0% +here VB that is + + + align:start position:0% +here VB that is +VB or big VB which is the total velocity + + align:start position:0% +VB or big VB which is the total velocity + + + align:start position:0% +VB or big VB which is the total velocity +and Little V is the tangential component + + align:start position:0% +and Little V is the tangential component + + + align:start position:0% +and Little V is the tangential component +of + + align:start position:0% +of + + + align:start position:0% +of +that right so you just solved part of + + align:start position:0% +that right so you just solved part of + + + align:start position:0% +that right so you just solved part of +the problem you just found the + + align:start position:0% +the problem you just found the + + + align:start position:0% +the problem you just found the +tangential + + align:start position:0% +tangential + + + align:start position:0% +tangential +component of Tang of the + + align:start position:0% +component of Tang of the + + + align:start position:0% +component of Tang of the +Velocity in the stationary reference + + align:start position:0% +Velocity in the stationary reference + + + align:start position:0% +Velocity in the stationary reference +frame coming into the rotor it's this + + align:start position:0% +frame coming into the rotor it's this + + + align:start position:0% +frame coming into the rotor it's this +little green arrow right here can people + + align:start position:0% +little green arrow right here can people + + + align:start position:0% +little green arrow right here can people +see that + + align:start position:0% + + + + align:start position:0% + +okay that's sort of the easy part you + + align:start position:0% +okay that's sort of the easy part you + + + align:start position:0% +okay that's sort of the easy part you +haven't gotten into a moving blade row + + align:start position:0% + + + + align:start position:0% + +yet now this does not look good right to + + align:start position:0% +yet now this does not look good right to + + + align:start position:0% +yet now this does not look good right to +have flow coming into this blade and + + align:start position:0% +have flow coming into this blade and + + + align:start position:0% +have flow coming into this blade and +it's almost perpendicular to + + align:start position:0% +it's almost perpendicular to + + + align:start position:0% +it's almost perpendicular to +it when you transform to the reference + + align:start position:0% +it when you transform to the reference + + + align:start position:0% +it when you transform to the reference +frame of this rotor you'll see that it + + align:start position:0% +frame of this rotor you'll see that it + + + align:start position:0% +frame of this rotor you'll see that it +lines up with it + + align:start position:0% +lines up with it + + + align:start position:0% +lines up with it +beautifully and the way you transform to + + align:start position:0% +beautifully and the way you transform to + + + align:start position:0% +beautifully and the way you transform to +the reference frame of this rotor is you + + align:start position:0% +the reference frame of this rotor is you + + + align:start position:0% +the reference frame of this rotor is you +take this + + align:start position:0% +take this + + + align:start position:0% +take this +velocity and you now + + align:start position:0% +velocity and you now + + + align:start position:0% +velocity and you now +add depending on + + align:start position:0% + + + + align:start position:0% + +your uh sort frame of reference + + align:start position:0% +your uh sort frame of reference + + + align:start position:0% +your uh sort frame of reference +subtract the + + align:start position:0% + + + + align:start position:0% + +speed of the reference + + align:start position:0% + + + + align:start position:0% + +frame so yeah unclear my + + align:start position:0% +frame so yeah unclear my + + + align:start position:0% +frame so yeah unclear my +apologies if you are in this reference + + align:start position:0% +apologies if you are in this reference + + + align:start position:0% +apologies if you are in this reference +frame and you want to transform it to a + + align:start position:0% +frame and you want to transform it to a + + + align:start position:0% +frame and you want to transform it to a +reference frame of someone sitting on + + align:start position:0% +reference frame of someone sitting on + + + align:start position:0% +reference frame of someone sitting on +these + + align:start position:0% +these + + + align:start position:0% +these +blades you need to take account of the + + align:start position:0% +blades you need to take account of the + + + align:start position:0% +blades you need to take account of the +speed of this reference frame with + + align:start position:0% +speed of this reference frame with + + + align:start position:0% +speed of this reference frame with +respect to that one + + align:start position:0% + + + + align:start position:0% + +so this reference frame is moving past + + align:start position:0% +so this reference frame is moving past + + + align:start position:0% +so this reference frame is moving past +this one in this direction at Omega r or + + align:start position:0% +this one in this direction at Omega r or + + + align:start position:0% +this one in this direction at Omega r or +from this perspective this one's moving + + align:start position:0% +from this perspective this one's moving + + + align:start position:0% +from this perspective this one's moving +past this one in this direction that was + + align:start position:0% +past this one in this direction that was + + + align:start position:0% +past this one in this direction that was +a lot of uh thises in that + + align:start position:0% + + + + align:start position:0% + +statement let me finish the vector + + align:start position:0% +statement let me finish the vector + + + align:start position:0% +statement let me finish the vector +addition here and then we'll talk about + + align:start position:0% +addition here and then we'll talk about + + + align:start position:0% +addition here and then we'll talk about +it so if I add the stationary frame flow + + align:start position:0% +it so if I add the stationary frame flow + + + align:start position:0% +it so if I add the stationary frame flow +Vector to the + + align:start position:0% +Vector to the + + + align:start position:0% +Vector to the +Omega r that gets me to the rotating + + align:start position:0% +Omega r that gets me to the rotating + + + align:start position:0% +Omega r that gets me to the rotating +frame I then end up with I'll try and be + + align:start position:0% +frame I then end up with I'll try and be + + + align:start position:0% +frame I then end up with I'll try and be +assistant + + align:start position:0% +assistant + + + align:start position:0% +assistant +here the relative + + align:start position:0% +here the relative + + + align:start position:0% +here the relative +frame velocity which you can see lines + + align:start position:0% +frame velocity which you can see lines + + + align:start position:0% +frame velocity which you can see lines +up + + align:start position:0% +up + + + align:start position:0% +up +nicely with these + + align:start position:0% + + + + align:start position:0% + +blades so we've just done a frame change + + align:start position:0% + + + + align:start position:0% + +now it makes sense because it lines up + + align:start position:0% +now it makes sense because it lines up + + + align:start position:0% +now it makes sense because it lines up +with the blades and I told you it ought + + align:start position:0% +with the blades and I told you it ought + + + align:start position:0% +with the blades and I told you it ought +to roughly line up with the + + align:start position:0% +to roughly line up with the + + + align:start position:0% +to roughly line up with the +blades does it make sense to you + + align:start position:0% +blades does it make sense to you + + + align:start position:0% +blades does it make sense to you +conceptually + + align:start position:0% +conceptually + + + align:start position:0% +conceptually +no think about having the flow coming in + + align:start position:0% +no think about having the flow coming in + + + align:start position:0% +no think about having the flow coming in +straight to these + + align:start position:0% +straight to these + + + align:start position:0% +straight to these +blades into the rotor so look at the + + align:start position:0% +blades into the rotor so look at the + + + align:start position:0% +blades into the rotor so look at the +case where the flow comes into + + align:start position:0% +case where the flow comes into + + + align:start position:0% +case where the flow comes into +them + + align:start position:0% +them + + + align:start position:0% +them +straight and assume they're not moving + + align:start position:0% +straight and assume they're not moving + + + align:start position:0% +straight and assume they're not moving +then you just see the flow coming + + align:start position:0% +then you just see the flow coming + + + align:start position:0% +then you just see the flow coming +straight at you now assume you start to + + align:start position:0% +straight at you now assume you start to + + + align:start position:0% +straight at you now assume you start to +move in this + + align:start position:0% +move in this + + + align:start position:0% +move in this +direction which way do you feel the wind + + align:start position:0% +direction which way do you feel the wind + + + align:start position:0% +direction which way do you feel the wind +blowing on your face so you start to + + align:start position:0% +blowing on your face so you start to + + + align:start position:0% +blowing on your face so you start to +move in this direction + + align:start position:0% + + + + align:start position:0% + +then you start to feel the wind on this + + align:start position:0% +then you start to feel the wind on this + + + align:start position:0% +then you start to feel the wind on this +on your face in this direction right if + + align:start position:0% +on your face in this direction right if + + + align:start position:0% +on your face in this direction right if +you're sitting here on the blade you + + align:start position:0% +you're sitting here on the blade you + + + align:start position:0% +you're sitting here on the blade you +start moving this direction so just + + align:start position:0% +start moving this direction so just + + + align:start position:0% +start moving this direction so just +think about it I'm the rotating blade + + align:start position:0% +think about it I'm the rotating blade + + + align:start position:0% +think about it I'm the rotating blade +right I'm sitting here and the FL is + + align:start position:0% +right I'm sitting here and the FL is + + + align:start position:0% +right I'm sitting here and the FL is +coming straight at me and I start to + + align:start position:0% +coming straight at me and I start to + + + align:start position:0% +coming straight at me and I start to +move right so I'm going to start to feel + + align:start position:0% +move right so I'm going to start to feel + + + align:start position:0% +move right so I'm going to start to feel +flow coming at me this way opposite to + + align:start position:0% +flow coming at me this way opposite to + + + align:start position:0% +flow coming at me this way opposite to +my direction of + + align:start position:0% +my direction of + + + align:start position:0% +my direction of +motion right so that's exactly what you + + align:start position:0% +motion right so that's exactly what you + + + align:start position:0% +motion right so that's exactly what you +see up here as these blades start to + + align:start position:0% +see up here as these blades start to + + + align:start position:0% +see up here as these blades start to +move in this + + align:start position:0% +move in this + + + align:start position:0% +move in this +direction this flow Vector which was + + align:start position:0% +direction this flow Vector which was + + + align:start position:0% +direction this flow Vector which was +initially like this turns around and + + align:start position:0% +initially like this turns around and + + + align:start position:0% +initially like this turns around and +starts blowing for the person sitting on + + align:start position:0% +starts blowing for the person sitting on + + + align:start position:0% +starts blowing for the person sitting on +these blades opposite to the direction + + align:start position:0% +these blades opposite to the direction + + + align:start position:0% +these blades opposite to the direction +of motion + + align:start position:0% +of motion + + + align:start position:0% +of motion +so conceptually that ought to make sense + + align:start position:0% +so conceptually that ought to make sense + + + align:start position:0% +so conceptually that ought to make sense +to you if you think about yourself + + align:start position:0% +to you if you think about yourself + + + align:start position:0% +to you if you think about yourself +sitting on these + + align:start position:0% +sitting on these + + + align:start position:0% +sitting on these +blades does that + + align:start position:0% +blades does that + + + align:start position:0% +blades does that +help some yes some no + + align:start position:0% +help some yes some no + + + align:start position:0% +help some yes some no +some all + + align:start position:0% +some all + + + align:start position:0% +some all +right now you're almost done in the + + align:start position:0% +right now you're almost done in the + + + align:start position:0% +right now you're almost done in the +reference frame of this blade now you + + align:start position:0% +reference frame of this blade now you + + + align:start position:0% +reference frame of this blade now you +assume that it + + align:start position:0% +assume that it + + + align:start position:0% +assume that it +leaves at the flow angle or at the + + align:start position:0% +leaves at the flow angle or at the + + + align:start position:0% +leaves at the flow angle or at the +trailing edge angle that is this which I + + align:start position:0% +trailing edge angle that is this which I + + + align:start position:0% +trailing edge angle that is this which I +keep drawing in in red to stay + + align:start position:0% +keep drawing in in red to stay + + + align:start position:0% +keep drawing in in red to stay +consistent over + + align:start position:0% + + + + align:start position:0% + +here so that's the flow angle leaving + + align:start position:0% +here so that's the flow angle leaving + + + align:start position:0% +here so that's the flow angle leaving +these + + align:start position:0% +these + + + align:start position:0% +these +blades and + + align:start position:0% +blades and + + + align:start position:0% +blades and +now what I really care about + + align:start position:0% +now what I really care about + + + align:start position:0% +now what I really care about +again + + align:start position:0% +again + + + align:start position:0% +again +is this + + align:start position:0% +is this + + + align:start position:0% +is this +component in the stationary frame so how + + align:start position:0% +component in the stationary frame so how + + + align:start position:0% +component in the stationary frame so how +do I get back to the stationary + + align:start position:0% +do I get back to the stationary + + + align:start position:0% +do I get back to the stationary +frame I add Omega R which is + + align:start position:0% +frame I add Omega R which is + + + align:start position:0% +frame I add Omega R which is +if I've got pen here I add aega r i + + align:start position:0% +if I've got pen here I add aega r i + + + align:start position:0% +if I've got pen here I add aega r i +don't have the right color pen which is + + align:start position:0% +don't have the right color pen which is + + + align:start position:0% +don't have the right color pen which is +this black line on the bottom to this + + align:start position:0% +this black line on the bottom to this + + + align:start position:0% +this black line on the bottom to this +red vector and now + + align:start position:0% +red vector and now + + + align:start position:0% +red vector and now +I'm back to the stationary + + align:start position:0% + + + + align:start position:0% + +frame and the component of that I care + + align:start position:0% +frame and the component of that I care + + + align:start position:0% +frame and the component of that I care +about is the tangential component which + + align:start position:0% +about is the tangential component which + + + align:start position:0% +about is the tangential component which +is that little green Vector along the + + align:start position:0% +is that little green Vector along the + + + align:start position:0% +is that little green Vector along the +bottom + + align:start position:0% + + + + align:start position:0% + +yep look like before we had primes as + + align:start position:0% +yep look like before we had primes as + + + align:start position:0% +yep look like before we had primes as +our uh exit part + + align:start position:0% +our uh exit part + + + align:start position:0% +our uh exit part +and non Prime is our entry no let me now + + align:start position:0% +and non Prime is our entry no let me now + + + align:start position:0% +and non Prime is our entry no let me now +explain the nomenclature which I wanted + + align:start position:0% +explain the nomenclature which I wanted + + + align:start position:0% +explain the nomenclature which I wanted +to stay away from a little bit on this + + align:start position:0% +to stay away from a little bit on this + + + align:start position:0% +to stay away from a little bit on this +the the the a the B and the C are for + + align:start position:0% +the the the a the B and the C are for + + + align:start position:0% +the the the a the B and the C are for +whether you're Upstream of this blade + + align:start position:0% +whether you're Upstream of this blade + + + align:start position:0% +whether you're Upstream of this blade +row this one or this one so that's what + + align:start position:0% +row this one or this one so that's what + + + align:start position:0% +row this one or this one so that's what +the subscripts are the primes mean that + + align:start position:0% +the subscripts are the primes mean that + + + align:start position:0% +the subscripts are the primes mean that +you're in the relative + + align:start position:0% +you're in the relative + + + align:start position:0% +you're in the relative +frame so this is the relative frame + + align:start position:0% +frame so this is the relative frame + + + align:start position:0% +frame so this is the relative frame +velocity and the unprimed means you're + + align:start position:0% +velocity and the unprimed means you're + + + align:start position:0% +velocity and the unprimed means you're +in the stationary frame that's what the + + align:start position:0% +in the stationary frame that's what the + + + align:start position:0% +in the stationary frame that's what the +the symbols mean I want to sort of stay + + align:start position:0% +the symbols mean I want to sort of stay + + + align:start position:0% +the symbols mean I want to sort of stay +away from the symbols um for starters So + + align:start position:0% +away from the symbols um for starters So + + + align:start position:0% +away from the symbols um for starters So +This is complicated you're going to work + + align:start position:0% +This is complicated you're going to work + + + align:start position:0% +This is complicated you're going to work +a problem on this in a moment let me + + align:start position:0% +a problem on this in a moment let me + + + align:start position:0% +a problem on this in a moment let me +just go through the steps + + align:start position:0% +just go through the steps + + + align:start position:0% +just go through the steps +again you assume the flow leaves the + + align:start position:0% +again you assume the flow leaves the + + + align:start position:0% +again you assume the flow leaves the +trailing Edge at the trailing edge + + align:start position:0% +trailing Edge at the trailing edge + + + align:start position:0% +trailing Edge at the trailing edge +angle so that gives you this vector + + align:start position:0% +angle so that gives you this vector + + + align:start position:0% +angle so that gives you this vector +basically this flow has turned or added + + align:start position:0% +basically this flow has turned or added + + + align:start position:0% +basically this flow has turned or added +some swirl but since it's not moving + + align:start position:0% +some swirl but since it's not moving + + + align:start position:0% +some swirl but since it's not moving +it's not done any work it's just + + align:start position:0% +it's not done any work it's just + + + align:start position:0% +it's not done any work it's just +converted internal energy to kinetic + + align:start position:0% +converted internal energy to kinetic + + + align:start position:0% +converted internal energy to kinetic +energy I then put myself in the + + align:start position:0% +energy I then put myself in the + + + align:start position:0% +energy I then put myself in the +reference frame of the moving blade by + + align:start position:0% +reference frame of the moving blade by + + + align:start position:0% +reference frame of the moving blade by +subtracting its + + align:start position:0% + + + + align:start position:0% + +velocity and that gives me the red + + align:start position:0% +velocity and that gives me the red + + + align:start position:0% +velocity and that gives me the red +Vector which the person on the blade + + align:start position:0% +Vector which the person on the blade + + + align:start position:0% +Vector which the person on the blade +would + + align:start position:0% +would + + + align:start position:0% +would +see I then say well the blade the the + + align:start position:0% +see I then say well the blade the the + + + align:start position:0% +see I then say well the blade the the +flow will always leave this blade + + align:start position:0% +flow will always leave this blade + + + align:start position:0% +flow will always leave this blade +attached to the to the blade at the + + align:start position:0% +attached to the to the blade at the + + + align:start position:0% +attached to the to the blade at the +trailing edge + + align:start position:0% +trailing edge + + + align:start position:0% +trailing edge +angle so that blue Vector then which I + + align:start position:0% +angle so that blue Vector then which I + + + align:start position:0% +angle so that blue Vector then which I +should have drawn is red here in the + + align:start position:0% +should have drawn is red here in the + + + align:start position:0% +should have drawn is red here in the +relative + + align:start position:0% +relative + + + align:start position:0% +relative +frame I'll draw it on this + + align:start position:0% + + + + align:start position:0% + +one my pens + + align:start position:0% +one my pens + + + align:start position:0% +one my pens +work that Vector is this + + align:start position:0% + + + + align:start position:0% + +one then what I carry about is this + + align:start position:0% +one then what I carry about is this + + + align:start position:0% +one then what I carry about is this +tangential component of the stationary + + align:start position:0% +tangential component of the stationary + + + align:start position:0% +tangential component of the stationary +frame velocity so I add back on to get + + align:start position:0% +frame velocity so I add back on to get + + + align:start position:0% +frame velocity so I add back on to get +back to the stationary frame I add back + + align:start position:0% +back to the stationary frame I add back + + + align:start position:0% +back to the stationary frame I add back +on the rotating + + align:start position:0% +on the rotating + + + align:start position:0% +on the rotating +component I get the total flow Vector + + align:start position:0% +component I get the total flow Vector + + + align:start position:0% +component I get the total flow Vector +which you now see has more swirl so this + + align:start position:0% +which you now see has more swirl so this + + + align:start position:0% +which you now see has more swirl so this +is a compressor it's added swirling + + align:start position:0% +is a compressor it's added swirling + + + align:start position:0% +is a compressor it's added swirling +kinetic energy to the flow + + align:start position:0% +kinetic energy to the flow + + + align:start position:0% +kinetic energy to the flow +yeah uh bime and cime leave the same + + align:start position:0% +yeah uh bime and cime leave the same + + + align:start position:0% +yeah uh bime and cime leave the same +um B Prime and C prime those are + + align:start position:0% +um B Prime and C prime those are + + + align:start position:0% +um B Prime and C prime those are +different it comes in at this angle and + + align:start position:0% +different it comes in at this angle and + + + align:start position:0% +different it comes in at this angle and +leaves at a little bit different angle + + align:start position:0% +leaves at a little bit different angle + + + align:start position:0% +leaves at a little bit different angle +these blades don't have a lot of turning + + align:start position:0% +these blades don't have a lot of turning + + + align:start position:0% +these blades don't have a lot of turning +in them but you'll see there's a little + + align:start position:0% +in them but you'll see there's a little + + + align:start position:0% +in them but you'll see there's a little +right it goes from this to + + align:start position:0% + + + + align:start position:0% + +this over + + align:start position:0% +this over + + + align:start position:0% +this over +the um there is no work done over the + + align:start position:0% +the um there is no work done over the + + + align:start position:0% +the um there is no work done over the +stator there are forces + + align:start position:0% +stator there are forces + + + align:start position:0% +stator there are forces +but since it's not a moving blade row + + align:start position:0% +but since it's not a moving blade row + + + align:start position:0% +but since it's not a moving blade row +those torqus there's no rate of applying + + align:start position:0% +those torqus there's no rate of applying + + + align:start position:0% +those torqus there's no rate of applying +the torqu there's no power added to the + + align:start position:0% +the torqu there's no power added to the + + + align:start position:0% +the torqu there's no power added to the +flow they just change the direction so + + align:start position:0% +flow they just change the direction so + + + align:start position:0% +flow they just change the direction so +you get forces and you calculate those + + align:start position:0% +you get forces and you calculate those + + + align:start position:0% +you get forces and you calculate those +in homework but since it's not a moving + + align:start position:0% +in homework but since it's not a moving + + + align:start position:0% +in homework but since it's not a moving +blade row no power at it right the this + + align:start position:0% +blade row no power at it right the this + + + align:start position:0% +blade row no power at it right the this +is a lot of sort of complex ideas all at + + align:start position:0% +is a lot of sort of complex ideas all at + + + align:start position:0% +is a lot of sort of complex ideas all at +once and the only way to do it is to + + align:start position:0% +once and the only way to do it is to + + + align:start position:0% +once and the only way to do it is to +practice it Okay and the rules will be + + align:start position:0% +practice it Okay and the rules will be + + + align:start position:0% +practice it Okay and the rules will be +good to you if you follow the rules and + + align:start position:0% +good to you if you follow the rules and + + + align:start position:0% +good to you if you follow the rules and +you work your way through these um blade + + align:start position:0% +you work your way through these um blade + + + align:start position:0% +you work your way through these um blade +rows um you will end up with being able + + align:start position:0% +rows um you will end up with being able + + + align:start position:0% +rows um you will end up with being able +to to do this kind of analysis so what + + align:start position:0% +to to do this kind of analysis so what + + + align:start position:0% +to to do this kind of analysis so what +I've got here are two + + align:start position:0% +I've got here are two + + + align:start position:0% +I've got here are two +problems and the first one only has two + + align:start position:0% +problems and the first one only has two + + + align:start position:0% +problems and the first one only has two +blade rows on it I'll hand it out so you + + align:start position:0% +blade rows on it I'll hand it out so you + + + align:start position:0% +blade rows on it I'll hand it out so you +can draw on + + align:start position:0% +can draw on + + + align:start position:0% +can draw on +it um since that's sometimes helpful and + + align:start position:0% +it um since that's sometimes helpful and + + + align:start position:0% +it um since that's sometimes helpful and +I'll put it up here as well um let me + + align:start position:0% +I'll put it up here as well um let me + + + align:start position:0% +I'll put it up here as well um let me +first show you the problem + + align:start position:0% + + + + align:start position:0% + +these are two blade rows this one is + + align:start position:0% +these are two blade rows this one is + + + align:start position:0% +these are two blade rows this one is +stationary this one's + + align:start position:0% + + + + align:start position:0% + +moving and I want to know is it a + + align:start position:0% +moving and I want to know is it a + + + align:start position:0% +moving and I want to know is it a +compressor or a + + align:start position:0% +compressor or a + + + align:start position:0% +compressor or a +turban how do you know if it's a + + align:start position:0% +turban how do you know if it's a + + + align:start position:0% +turban how do you know if it's a +compressor or a + + align:start position:0% + + + + align:start position:0% + +turbine a compressor puts in swirl in + + align:start position:0% +turbine a compressor puts in swirl in + + + align:start position:0% +turbine a compressor puts in swirl in +the direction of rotor motion a turbine + + align:start position:0% +the direction of rotor motion a turbine + + + align:start position:0% +the direction of rotor motion a turbine +takes it out in the direction of rotor + + align:start position:0% +takes it out in the direction of rotor + + + align:start position:0% +takes it out in the direction of rotor +motion so you need to do the velocity + + align:start position:0% +motion so you need to do the velocity + + + align:start position:0% +motion so you need to do the velocity +triangles on this and just follow your + + align:start position:0% +triangles on this and just follow your + + + align:start position:0% +triangles on this and just follow your +way through the rules um so let me hand + + align:start position:0% +way through the rules um so let me hand + + + align:start position:0% +way through the rules um so let me hand +out these Carl do you want to help + + align:start position:0% +out these Carl do you want to help + + + align:start position:0% +out these Carl do you want to help +me and you can draw right on top of them + + align:start position:0% +me and you can draw right on top of them + + + align:start position:0% +me and you can draw right on top of them +as I said + + align:start position:0% + + + + align:start position:0% + +oh hang on pass + + align:start position:0% + + + + align:start position:0% + +one so so + + align:start position:0% + + + + align:start position:0% + +how you vales + + align:start position:0% +how you vales + + + align:start position:0% +how you vales +toega + + align:start position:0% + + + + align:start position:0% + +R oh yeah I will draw them here one of + + align:start position:0% +R oh yeah I will draw them here one of + + + align:start position:0% +R oh yeah I will draw them here one of +the important things about this is to + + align:start position:0% +the important things about this is to + + + align:start position:0% +the important things about this is to +actually draw it to scale or else you + + align:start position:0% +actually draw it to scale or else you + + + align:start position:0% +actually draw it to scale or else you +can get some funny + + align:start position:0% + + + + align:start position:0% + +answers right yeah there was just a good + + align:start position:0% +answers right yeah there was just a good + + + align:start position:0% +answers right yeah there was just a good +question + + align:start position:0% +question + + + align:start position:0% +question +here um when you draw draw these it's + + align:start position:0% +here um when you draw draw these it's + + + align:start position:0% +here um when you draw draw these it's +important when you draw the triangles + + align:start position:0% +important when you draw the triangles + + + align:start position:0% +important when you draw the triangles +that the length of the vectors be right + + align:start position:0% +that the length of the vectors be right + + + align:start position:0% +that the length of the vectors be right +so if I've here drawn a mega r as this + + align:start position:0% +so if I've here drawn a mega r as this + + + align:start position:0% +so if I've here drawn a mega r as this +long and W axial as this + + align:start position:0% +long and W axial as this + + + align:start position:0% +long and W axial as this +long it's important to draw them those + + align:start position:0% +long it's important to draw them those + + + align:start position:0% +long it's important to draw them those +lengths right or your triangles will + + align:start position:0% +lengths right or your triangles will + + + align:start position:0% +lengths right or your triangles will +come out misshapen and you can make the + + align:start position:0% +come out misshapen and you can make the + + + align:start position:0% +come out misshapen and you can make the +wrong + + align:start position:0% + + + + align:start position:0% + +conclusion so you need to be neat about + + align:start position:0% +conclusion so you need to be neat about + + + align:start position:0% +conclusion so you need to be neat about +it in other words you can draw it right + + align:start position:0% +it in other words you can draw it right + + + align:start position:0% +it in other words you can draw it right +on top of these three vectors you can + + align:start position:0% +on top of these three vectors you can + + + align:start position:0% +on top of these three vectors you can +start your triangles right on top of + + align:start position:0% + + + + align:start position:0% + +these oh I'd give them three or four + + align:start position:0% +these oh I'd give them three or four + + + align:start position:0% +these oh I'd give them three or four +minutes at least to go through this + + align:start position:0% + + + + align:start position:0% + +and draw it right on top of this so that + + align:start position:0% +and draw it right on top of this so that + + + align:start position:0% +and draw it right on top of this so that +it's to scale yeah the triangle so you + + align:start position:0% +it's to scale yeah the triangle so you + + + align:start position:0% +it's to scale yeah the triangle so you +know here for example you could say well + + align:start position:0% +know here for example you could say well + + + align:start position:0% +know here for example you could say well +the flow coming out of this stationary + + align:start position:0% +the flow coming out of this stationary + + + align:start position:0% +the flow coming out of this stationary +blade row looks like this right because + + align:start position:0% +blade row looks like this right because + + + align:start position:0% +blade row looks like this right because +it's got to have this length and it's + + align:start position:0% +it's got to have this length and it's + + + align:start position:0% +it's got to have this length and it's +got to have this + + align:start position:0% +got to have this + + + align:start position:0% +got to have this +angle okay and then subtract off + + align:start position:0% +angle okay and then subtract off + + + align:start position:0% +angle okay and then subtract off +this that same length Okay yeah and then + + align:start position:0% +this that same length Okay yeah and then + + + align:start position:0% +this that same length Okay yeah and then +this would be sort of the relative frame + + align:start position:0% +this would be sort of the relative frame + + + align:start position:0% +this would be sort of the relative frame +one okay so this what I mean by draw it + + align:start position:0% +one okay so this what I mean by draw it + + + align:start position:0% +one okay so this what I mean by draw it +right on top of it like that all right + + align:start position:0% + + + + align:start position:0% + +yed we at the + + align:start position:0% +yed we at the + + + align:start position:0% +yed we at the +end you need the change across this you + + align:start position:0% +end you need the change across this you + + + align:start position:0% +end you need the change across this you +need need the inlet and the outlet we're + + align:start position:0% +need need the inlet and the outlet we're + + + align:start position:0% +need need the inlet and the outlet we're +not looking at the total change from + + align:start position:0% +not looking at the total change from + + + align:start position:0% +not looking at the total change from +well yep but there is a um conversion um + + align:start position:0% +well yep but there is a um conversion um + + + align:start position:0% +well yep but there is a um conversion um +between these two so this converts + + align:start position:0% +between these two so this converts + + + align:start position:0% +between these two so this converts +energy and then this adds it so if you + + align:start position:0% +energy and then this adds it so if you + + + align:start position:0% +energy and then this adds it so if you +want to know the total amount added you + + align:start position:0% +want to know the total amount added you + + + align:start position:0% +want to know the total amount added you +have to know the inlet the outlet for + + align:start position:0% +have to know the inlet the outlet for + + + align:start position:0% +have to know the inlet the outlet for +this because this puts in some + + align:start position:0% +this because this puts in some + + + align:start position:0% +this because this puts in some +tangential velocity you can sort of see + + align:start position:0% +tangential velocity you can sort of see + + + align:start position:0% +tangential velocity you can sort of see +here but it doesn't add any energy and + + align:start position:0% +here but it doesn't add any energy and + + + align:start position:0% +here but it doesn't add any energy and +what you want to know is how much energy + + align:start position:0% +what you want to know is how much energy + + + align:start position:0% +what you want to know is how much energy +is added or taken + + align:start position:0% + + + + align:start position:0% + +away just a function + + align:start position:0% +away just a function + + + align:start position:0% +away just a function +of it's a function of the difference in + + align:start position:0% +of it's a function of the difference in + + + align:start position:0% +of it's a function of the difference in +tangential velocity here versus here in + + align:start position:0% +tangential velocity here versus here in + + + align:start position:0% +tangential velocity here versus here in +the stationary + + align:start position:0% + + + + align:start position:0% + +frame so go ahead and draw the triangles + + align:start position:0% +frame so go ahead and draw the triangles + + + align:start position:0% +frame so go ahead and draw the triangles +and then we'll have + + align:start position:0% +and then we'll have + + + align:start position:0% +and then we'll have +this is going like that that's going to + + align:start position:0% +this is going like that that's going to + + + align:start position:0% +this is going like that that's going to +have even more instance it's yeah it's + + align:start position:0% +have even more instance it's yeah it's + + + align:start position:0% +have even more instance it's yeah it's +going to give it more yeah yeah but you + + align:start position:0% +going to give it more yeah yeah but you + + + align:start position:0% +going to give it more yeah yeah but you +need to draw them + + align:start position:0% + + + + align:start position:0% + +out oh this is + + align:start position:0% + + + + align:start position:0% + +good draw it right on top of here oh + + align:start position:0% +good draw it right on top of here oh + + + align:start position:0% +good draw it right on top of here oh +okay just to get the well that you get + + align:start position:0% +okay just to get the well that you get + + + align:start position:0% +okay just to get the well that you get +you you can say hey this angle is + + align:start position:0% +you you can say hey this angle is + + + align:start position:0% +you you can say hey this angle is +exactly this angle okay you know and + + align:start position:0% +exactly this angle okay you know and + + + align:start position:0% +exactly this angle okay you know and +then you can say well I'm going to add + + align:start position:0% +then you can say well I'm going to add + + + align:start position:0% +then you can say well I'm going to add +this Vector on to here okay and that + + align:start position:0% +this Vector on to here okay and that + + + align:start position:0% +this Vector on to here okay and that +gives you this sort of one in the + + align:start position:0% +gives you this sort of one in the + + + align:start position:0% +gives you this sort of one in the +relative frame so so just keep these + + align:start position:0% +relative frame so so just keep these + + + align:start position:0% +relative frame so so just keep these +lengths all right it's easier to just + + align:start position:0% +lengths all right it's easier to just + + + align:start position:0% +lengths all right it's easier to just +draw them right on top of that this + + align:start position:0% +draw them right on top of that this + + + align:start position:0% +draw them right on top of that this +looks good really + + align:start position:0% + + + + align:start position:0% + +good yeah so this this one the flow + + align:start position:0% +good yeah so this this one the flow + + + align:start position:0% +good yeah so this this one the flow +coming in is just coming in straight so + + align:start position:0% +coming in is just coming in straight so + + + align:start position:0% +coming in is just coming in straight so +then what you want to do is say well the + + align:start position:0% +then what you want to do is say well the + + + align:start position:0% +then what you want to do is say well the +flow is leaving these blades at this + + align:start position:0% +flow is leaving these blades at this + + + align:start position:0% +flow is leaving these blades at this +angle and then you want to subtract this + + align:start position:0% +angle and then you want to subtract this + + + align:start position:0% +angle and then you want to subtract this +to get into this Blade's reference frame + + align:start position:0% +to get into this Blade's reference frame + + + align:start position:0% +to get into this Blade's reference frame +so go all the way out to here which is + + align:start position:0% +so go all the way out to here which is + + + align:start position:0% +so go all the way out to here which is +roughly what you + + align:start position:0% +roughly what you + + + align:start position:0% +roughly what you +did yeah give us another minute or two + + align:start position:0% +did yeah give us another minute or two + + + align:start position:0% +did yeah give us another minute or two +at least + + align:start position:0% +at least + + + align:start position:0% +at least +car and then this is the relative one + + align:start position:0% +car and then this is the relative one + + + align:start position:0% +car and then this is the relative one +and same thing this is the now the + + align:start position:0% +and same thing this is the now the + + + align:start position:0% +and same thing this is the now the +relative angle it's the angle that comes + + align:start position:0% +relative angle it's the angle that comes + + + align:start position:0% +relative angle it's the angle that comes +off the blade so you need to then get + + align:start position:0% +off the blade so you need to then get + + + align:start position:0% +off the blade so you need to then get +back to this and then you want to look + + align:start position:0% +back to this and then you want to look + + + align:start position:0% +back to this and then you want to look +in this for what's the tangential + + align:start position:0% +in this for what's the tangential + + + align:start position:0% +in this for what's the tangential +component + + align:start position:0% + + + + align:start position:0% + +how you + + align:start position:0% + + + + align:start position:0% + +doing you got the right thing here + + align:start position:0% + + + + align:start position:0% + +you draw right on top of the vectors + + align:start position:0% +you draw right on top of the vectors + + + align:start position:0% +you draw right on top of the vectors +then you don't get any messed + + align:start position:0% + + + + align:start position:0% + +up no this is good people are on top of + + align:start position:0% +up no this is good people are on top of + + + align:start position:0% +up no this is good people are on top of +this + + align:start position:0% + + + + align:start position:0% + +actually all right get your answers in I + + align:start position:0% +actually all right get your answers in I + + + align:start position:0% +actually all right get your answers in I +I've walked around and and more than + + align:start position:0% +I've walked around and and more than + + + align:start position:0% +I've walked around and and more than +half of you appear to have this uh well + + align:start position:0% +half of you appear to have this uh well + + + align:start position:0% +half of you appear to have this uh well +in hand which uh will mean that we may + + align:start position:0% +in hand which uh will mean that we may + + + align:start position:0% +in hand which uh will mean that we may +have just enough time to to do another + + align:start position:0% +have just enough time to to do another + + + align:start position:0% +have just enough time to to do another +one + + align:start position:0% +one + + + align:start position:0% +one +um and if and if not we'll have plenty + + align:start position:0% +um and if and if not we'll have plenty + + + align:start position:0% +um and if and if not we'll have plenty +of opportunity with with homeworks and + + align:start position:0% +of opportunity with with homeworks and + + + align:start position:0% +of opportunity with with homeworks and +recitations uh to go through more + + align:start position:0% +recitations uh to go through more + + + align:start position:0% +recitations uh to go through more +examples of + + align:start position:0% +examples of + + + align:start position:0% +examples of +this uh so get your answers in and then + + align:start position:0% +this uh so get your answers in and then + + + align:start position:0% +this uh so get your answers in and then +I'll work through + + align:start position:0% +I'll work through + + + align:start position:0% +I'll work through +it um up + + align:start position:0% + + + + align:start position:0% + +here okay so most people picked a + + align:start position:0% +here okay so most people picked a + + + align:start position:0% +here okay so most people picked a +compressor if you did that's the right + + align:start position:0% +compressor if you did that's the right + + + align:start position:0% +compressor if you did that's the right +answer I hope you got to it for the + + align:start position:0% +answer I hope you got to it for the + + + align:start position:0% +answer I hope you got to it for the +right reason I was actually have to say + + align:start position:0% +right reason I was actually have to say + + + align:start position:0% +right reason I was actually have to say +impressed walking around here that um + + align:start position:0% +impressed walking around here that um + + + align:start position:0% +impressed walking around here that um +most of you went ahead and did this + + align:start position:0% +most of you went ahead and did this + + + align:start position:0% +most of you went ahead and did this +quite well and it is challenging because + + align:start position:0% +quite well and it is challenging because + + + align:start position:0% +quite well and it is challenging because +you've got to think about unwrapping the + + align:start position:0% +you've got to think about unwrapping the + + + align:start position:0% +you've got to think about unwrapping the +compressor and thinking about things + + align:start position:0% +compressor and thinking about things + + + align:start position:0% +compressor and thinking about things +rotating and now instead they're going + + align:start position:0% +rotating and now instead they're going + + + align:start position:0% +rotating and now instead they're going +from left to right and you've got to + + align:start position:0% +from left to right and you've got to + + + align:start position:0% +from left to right and you've got to +work your way through all the frame + + align:start position:0% +work your way through all the frame + + + align:start position:0% +work your way through all the frame +changes but uh most of you were on top + + align:start position:0% +changes but uh most of you were on top + + + align:start position:0% +changes but uh most of you were on top +of it which is + + align:start position:0% +of it which is + + + align:start position:0% +of it which is +good right so just follow the rules so + + align:start position:0% +good right so just follow the rules so + + + align:start position:0% +good right so just follow the rules so +let me sort of show you uh how to do + + align:start position:0% +let me sort of show you uh how to do + + + align:start position:0% +let me sort of show you uh how to do +this I wish I had a little bit thicker + + align:start position:0% +this I wish I had a little bit thicker + + + align:start position:0% +this I wish I had a little bit thicker +pens + + align:start position:0% +pens + + + align:start position:0% +pens +but I think you'll be able to follow + + align:start position:0% +but I think you'll be able to follow + + + align:start position:0% +but I think you'll be able to follow +along so first this is the whole + + align:start position:0% +along so first this is the whole + + + align:start position:0% +along so first this is the whole +velocity Vector coming into this blade + + align:start position:0% +velocity Vector coming into this blade + + + align:start position:0% +velocity Vector coming into this blade +row there's nothing more it's pure axial + + align:start position:0% +row there's nothing more it's pure axial + + + align:start position:0% +row there's nothing more it's pure axial +flow coming in and then I say the flow + + align:start position:0% +flow coming in and then I say the flow + + + align:start position:0% +flow coming in and then I say the flow +leaves that not that stationary blade + + align:start position:0% +leaves that not that stationary blade + + + align:start position:0% +leaves that not that stationary blade +row at this angle beta + + align:start position:0% +row at this angle beta + + + align:start position:0% +row at this angle beta +B so + + align:start position:0% +B so + + + align:start position:0% +B so +that's beta + + align:start position:0% +that's beta + + + align:start position:0% +that's beta +B and then I need to put it in the + + align:start position:0% +B and then I need to put it in the + + + align:start position:0% +B and then I need to put it in the +reference frame of the rotor + + align:start position:0% +reference frame of the rotor + + + align:start position:0% +reference frame of the rotor +so + + align:start position:0% +so + + + align:start position:0% +so +I + + align:start position:0% + + + + align:start position:0% + +subtract the rotor + + align:start position:0% +subtract the rotor + + + align:start position:0% +subtract the rotor +velocity and that then gives me in the + + align:start position:0% +velocity and that then gives me in the + + + align:start position:0% +velocity and that then gives me in the +axial or in the rotating reference + + align:start position:0% + + + + align:start position:0% + +frame the + + align:start position:0% +frame the + + + align:start position:0% +frame the +velocity coming into this blade row and + + align:start position:0% +velocity coming into this blade row and + + + align:start position:0% +velocity coming into this blade row and +it looks about right it's it's roughly + + align:start position:0% +it looks about right it's it's roughly + + + align:start position:0% +it looks about right it's it's roughly +lined up with the Leading Edge on those + + align:start position:0% +lined up with the Leading Edge on those + + + align:start position:0% +lined up with the Leading Edge on those +air foils so that's + + align:start position:0% + + + + align:start position:0% + +good then and this gives me one very + + align:start position:0% +good then and this gives me one very + + + align:start position:0% +good then and this gives me one very +important thing I also have the + + align:start position:0% +important thing I also have the + + + align:start position:0% +important thing I also have the +tangential component here in + + align:start position:0% + + + + align:start position:0% + +green of velocity in the stationary + + align:start position:0% +green of velocity in the stationary + + + align:start position:0% +green of velocity in the stationary +reference frame coming into the + + align:start position:0% +reference frame coming into the + + + align:start position:0% +reference frame coming into the +rotor now I do the same thing at the + + align:start position:0% +rotor now I do the same thing at the + + + align:start position:0% +rotor now I do the same thing at the +back of this but now I'm in the + + align:start position:0% + + + + align:start position:0% + +in the uh rotating reference frame so + + align:start position:0% +in the uh rotating reference frame so + + + align:start position:0% +in the uh rotating reference frame so +I've got velocity leaving + + align:start position:0% +I've got velocity leaving + + + align:start position:0% +I've got velocity leaving +this following the blade + + align:start position:0% +this following the blade + + + align:start position:0% +this following the blade +angle I then add back in this velocity + + align:start position:0% +angle I then add back in this velocity + + + align:start position:0% +angle I then add back in this velocity +to get me back to the stationary + + align:start position:0% + + + + align:start position:0% + +frame that gives me my stationary frame + + align:start position:0% + + + + align:start position:0% + +Vector I look for the the tangential + + align:start position:0% +Vector I look for the the tangential + + + align:start position:0% +Vector I look for the the tangential +component of that which is this + + align:start position:0% +component of that which is this + + + align:start position:0% +component of that which is this +part and I say that the tangential + + align:start position:0% +part and I say that the tangential + + + align:start position:0% +part and I say that the tangential +component has increased across the blade + + align:start position:0% +component has increased across the blade + + + align:start position:0% +component has increased across the blade +row where increase is measured in the + + align:start position:0% +row where increase is measured in the + + + align:start position:0% +row where increase is measured in the +direction of rotation + + align:start position:0% +direction of rotation + + + align:start position:0% +direction of rotation +therefore it's a + + align:start position:0% + + + + align:start position:0% + +compressor questions about + + align:start position:0% +compressor questions about + + + align:start position:0% +compressor questions about +that yes can you also look at that as + + align:start position:0% +that yes can you also look at that as + + + align:start position:0% +that yes can you also look at that as +the tangential components going that way + + align:start position:0% +the tangential components going that way + + + align:start position:0% +the tangential components going that way +meaning the work is going + + align:start position:0% +meaning the work is going + + + align:start position:0% +meaning the work is going +Downstream well again the whole point + + align:start position:0% +Downstream well again the whole point + + + align:start position:0% +Downstream well again the whole point +the point of these is that they take a + + align:start position:0% +the point of these is that they take a + + + align:start position:0% +the point of these is that they take a +flux which is the axial component of the + + align:start position:0% +flux which is the axial component of the + + + align:start position:0% +flux which is the axial component of the +flow of angular momentum and change it + + align:start position:0% +flow of angular momentum and change it + + + align:start position:0% +flow of angular momentum and change it +and the angular momentum here is you + + align:start position:0% +and the angular momentum here is you + + + align:start position:0% +and the angular momentum here is you +know in the direction of rotor motion so + + align:start position:0% +know in the direction of rotor motion so + + + align:start position:0% +know in the direction of rotor motion so +again I would just think about yourself + + align:start position:0% +again I would just think about yourself + + + align:start position:0% +again I would just think about yourself +as a fluid particle and you're traveling + + align:start position:0% +as a fluid particle and you're traveling + + + align:start position:0% +as a fluid particle and you're traveling +through this engine right and you come + + align:start position:0% +through this engine right and you come + + + align:start position:0% +through this engine right and you come +in and you've got no angular momentum + + align:start position:0% +in and you've got no angular momentum + + + align:start position:0% +in and you've got no angular momentum +and then whammo you hit these blade + + align:start position:0% +and then whammo you hit these blade + + + align:start position:0% +and then whammo you hit these blade +rows right and now your flux of angular + + align:start position:0% +rows right and now your flux of angular + + + align:start position:0% +rows right and now your flux of angular +momentum is changed you have some + + align:start position:0% +momentum is changed you have some + + + align:start position:0% +momentum is changed you have some +positive flux of swirl going through the + + align:start position:0% +positive flux of swirl going through the + + + align:start position:0% +positive flux of swirl going through the +engine and each one of these blade rows + + align:start position:0% +engine and each one of these blade rows + + + align:start position:0% +engine and each one of these blade rows +keeps changing that as you go + + align:start position:0% +keeps changing that as you go + + + align:start position:0% +keeps changing that as you go +through right and it's only the moving + + align:start position:0% +through right and it's only the moving + + + align:start position:0% +through right and it's only the moving +ones that add the energy the stationary + + align:start position:0% +ones that add the energy the stationary + + + align:start position:0% +ones that add the energy the stationary +ones just convert it from swirl back + + align:start position:0% +ones just convert it from swirl back + + + align:start position:0% +ones just convert it from swirl back +into the axial Direction and in doing + + align:start position:0% +into the axial Direction and in doing + + + align:start position:0% +into the axial Direction and in doing +that convert it to internal + + align:start position:0% +that convert it to internal + + + align:start position:0% +that convert it to internal +energy okay how are we on time we are at + + align:start position:0% +energy okay how are we on time we are at + + + align:start position:0% +energy okay how are we on time we are at +the + + align:start position:0% +the + + + align:start position:0% +the +um about three minutes to go before the + + align:start position:0% +um about three minutes to go before the + + + align:start position:0% +um about three minutes to go before the +end here there's another problem that I + + align:start position:0% +end here there's another problem that I + + + align:start position:0% +end here there's another problem that I +had hoped to get to here and I want to + + align:start position:0% +had hoped to get to here and I want to + + + align:start position:0% +had hoped to get to here and I want to +show you um just the + + align:start position:0% +show you um just the + + + align:start position:0% +show you um just the +animated uh image for it can you run the + + align:start position:0% +animated uh image for it can you run the + + + align:start position:0% +animated uh image for it can you run the +q30 + + align:start position:0% +q30 + + + align:start position:0% +q30 +one no not not that one well first if + + align:start position:0% +one no not not that one well first if + + + align:start position:0% +one no not not that one well first if +you look on the web + + align:start position:0% +you look on the web + + + align:start position:0% +you look on the web +page there's an interactive program that + + align:start position:0% +page there's an interactive program that + + + align:start position:0% +page there's an interactive program that +you can use for drawing velocity + + align:start position:0% +you can use for drawing velocity + + + align:start position:0% +you can use for drawing velocity +triangles that a student from unified + + align:start position:0% +triangles that a student from unified + + + align:start position:0% +triangles that a student from unified +wrote it's a little uh Java + + align:start position:0% +wrote it's a little uh Java + + + align:start position:0% +wrote it's a little uh Java +applet and where's + + align:start position:0% +applet and where's + + + align:start position:0% +applet and where's +the the GIF on here I bet you I can find + + align:start position:0% +the the GIF on here I bet you I can find + + + align:start position:0% +the the GIF on here I bet you I can find +it yeah hang + + align:start position:0% + + + + align:start position:0% + +on + + align:start position:0% + + + + align:start position:0% + +and this is the second problem and you + + align:start position:0% +and this is the second problem and you + + + align:start position:0% +and this is the second problem and you +don't see the whole thing up here but + + align:start position:0% +don't see the whole thing up here but + + + align:start position:0% +don't see the whole thing up here but +this is a graphical image that you can + + align:start position:0% +this is a graphical image that you can + + + align:start position:0% +this is a graphical image that you can +click on it'll go through and it'll draw + + align:start position:0% +click on it'll go through and it'll draw + + + align:start position:0% +click on it'll go through and it'll draw +each of the vectors for + + align:start position:0% +each of the vectors for + + + align:start position:0% +each of the vectors for +you right so the answer for these as you + + align:start position:0% +you right so the answer for these as you + + + align:start position:0% +you right so the answer for these as you +can see here is animated so you can go + + align:start position:0% +can see here is animated so you can go + + + align:start position:0% +can see here is animated so you can go +ahead and try this the other one that we + + align:start position:0% +ahead and try this the other one that we + + + align:start position:0% +ahead and try this the other one that we +just did is also animated so if you have + + align:start position:0% +just did is also animated so if you have + + + align:start position:0% +just did is also animated so if you have +some questions about what I've done here + + align:start position:0% +some questions about what I've done here + + + align:start position:0% +some questions about what I've done here +you can go through and follow it and + + align:start position:0% +you can go through and follow it and + + + align:start position:0% +you can go through and follow it and +make sure you're following the + + align:start position:0% +make sure you're following the + + + align:start position:0% +make sure you're following the +rules right so there are a couple + + align:start position:0% +rules right so there are a couple + + + align:start position:0% +rules right so there are a couple +resources there to help you if you if + + align:start position:0% +resources there to help you if you if + + + align:start position:0% +resources there to help you if you if +you're you're confused and I can always + + align:start position:0% +you're you're confused and I can always + + + align:start position:0% +you're you're confused and I can always +help + + align:start position:0% +help + + + align:start position:0% +help +you all right + + align:start position:0% +you all right + + + align:start position:0% +you all right +so that's just to point you to the + + align:start position:0% +so that's just to point you to the + + + align:start position:0% +so that's just to point you to the +resources again about a week and a half + + align:start position:0% +resources again about a week and a half + + + align:start position:0% +resources again about a week and a half +from now we will have the propulsion + + align:start position:0% +from now we will have the propulsion + + + align:start position:0% +from now we will have the propulsion +quiz there will be a question much like + + align:start position:0% +quiz there will be a question much like + + + align:start position:0% +quiz there will be a question much like +this one that you just solved on the + + align:start position:0% +this one that you just solved on the + + + align:start position:0% +this one that you just solved on the +quiz where you have to draw you know two + + align:start position:0% +quiz where you have to draw you know two + + + align:start position:0% +quiz where you have to draw you know two +or three velocity triangles and identify + + align:start position:0% +or three velocity triangles and identify + + + align:start position:0% +or three velocity triangles and identify +you know is work being put in or taken + + align:start position:0% +you know is work being put in or taken + + + align:start position:0% +you know is work being put in or taken +out right so this is something I want + + align:start position:0% +out right so this is something I want + + + align:start position:0% +out right so this is something I want +you to practice and and it's nice + + align:start position:0% +you to practice and and it's nice + + + align:start position:0% +you to practice and and it's nice +because it achieves the objectives of + + align:start position:0% +because it achieves the objectives of + + + align:start position:0% +because it achieves the objectives of +getting you all the way from details of + + align:start position:0% +getting you all the way from details of + + + align:start position:0% +getting you all the way from details of +Blade shapes all the way up to Mission + + align:start position:0% +Blade shapes all the way up to Mission + + + align:start position:0% +Blade shapes all the way up to Mission +performance and you've got a homework + + align:start position:0% +performance and you've got a homework + + + align:start position:0% +performance and you've got a homework +problem on this engine too where I ask + + align:start position:0% +problem on this engine too where I ask + + + align:start position:0% +problem on this engine too where I ask +you to go and measure the angles on the + + align:start position:0% +you to go and measure the angles on the + + + align:start position:0% +you to go and measure the angles on the +engine and tell me how fast the blades + + align:start position:0% +engine and tell me how fast the blades + + + align:start position:0% +engine and tell me how fast the blades +spin so do it in reverse here I've told + + align:start position:0% +spin so do it in reverse here I've told + + + align:start position:0% +spin so do it in reverse here I've told +you how fast they spin and given you the + + align:start position:0% +you how fast they spin and given you the + + + align:start position:0% +you how fast they spin and given you the +Angles and ask for the work instead I'm + + align:start position:0% +Angles and ask for the work instead I'm + + + align:start position:0% +Angles and ask for the work instead I'm +going to have you measure the Angles and + + align:start position:0% +going to have you measure the Angles and + + + align:start position:0% +going to have you measure the Angles and +BAS Bas on this kind of analysis + + align:start position:0% +BAS Bas on this kind of analysis + + + align:start position:0% +BAS Bas on this kind of analysis +determine how fast they must be + + align:start position:0% +determine how fast they must be + + + align:start position:0% +determine how fast they must be +spinning okay questions before we wrap + + align:start position:0% +spinning okay questions before we wrap + + + align:start position:0% +spinning okay questions before we wrap +up yeah + + align:start position:0% +up yeah + + + align:start position:0% +up yeah +when which do they decide first speed or + + align:start position:0% +when which do they decide first speed or + + + align:start position:0% +when which do they decide first speed or +the shap BL the question was when + + align:start position:0% +the shap BL the question was when + + + align:start position:0% +the shap BL the question was when +they're actually designing these things + + align:start position:0% +they're actually designing these things + + + align:start position:0% +they're actually designing these things +what do they decide first the rotor + + align:start position:0% +what do they decide first the rotor + + + align:start position:0% +what do they decide first the rotor +speed or the shape of the blade um the + + align:start position:0% +speed or the shape of the blade um the + + + align:start position:0% +speed or the shape of the blade um the +answer is yes you start out with a cycle + + align:start position:0% +answer is yes you start out with a cycle + + + align:start position:0% +answer is yes you start out with a cycle +analysis for this so you determine how + + align:start position:0% +analysis for this so you determine how + + + align:start position:0% +analysis for this so you determine how +much pressure you need then you look + + align:start position:0% +much pressure you need then you look + + + align:start position:0% +much pressure you need then you look +back at your old engines and you say + + align:start position:0% +back at your old engines and you say + + + align:start position:0% +back at your old engines and you say +well for each one of these blade rows + + align:start position:0% +well for each one of these blade rows + + + align:start position:0% +well for each one of these blade rows +how much pressure rise was I able to + + align:start position:0% +how much pressure rise was I able to + + + align:start position:0% +how much pressure rise was I able to +produce and you know what those shapes + + align:start position:0% +produce and you know what those shapes + + + align:start position:0% +produce and you know what those shapes +used to be and you know how fast you + + align:start position:0% +used to be and you know how fast you + + + align:start position:0% +used to be and you know how fast you +spun those blades as well and how fast + + align:start position:0% +spun those blades as well and how fast + + + align:start position:0% +spun those blades as well and how fast +you spin them is tied to your structural + + align:start position:0% +you spin them is tied to your structural + + + align:start position:0% +you spin them is tied to your structural +capabilities of the materials and then + + align:start position:0% +capabilities of the materials and then + + + align:start position:0% +capabilities of the materials and then +what you typically do when you design + + align:start position:0% +what you typically do when you design + + + align:start position:0% +what you typically do when you design +you say well I'm going to try and spin + + align:start position:0% +you say well I'm going to try and spin + + + align:start position:0% +you say well I'm going to try and spin +it a little faster push that a little + + align:start position:0% +it a little faster push that a little + + + align:start position:0% +it a little faster push that a little +more maybe I'll turn the flow a little + + align:start position:0% +more maybe I'll turn the flow a little + + + align:start position:0% +more maybe I'll turn the flow a little +bit more than I did in the past so I + + align:start position:0% +bit more than I did in the past so I + + + align:start position:0% +bit more than I did in the past so I +could eek out a little bit more + + align:start position:0% +could eek out a little bit more + + + align:start position:0% +could eek out a little bit more +pressurized per blade row and if I'm + + align:start position:0% +pressurized per blade row and if I'm + + + align:start position:0% +pressurized per blade row and if I'm +really good and I do that for all my + + align:start position:0% +really good and I do that for all my + + + align:start position:0% +really good and I do that for all my +blade rows maybe I don't have to carry + + align:start position:0% +blade rows maybe I don't have to carry + + + align:start position:0% +blade rows maybe I don't have to carry +around one of these backstages anymore + + align:start position:0% +around one of these backstages anymore + + + align:start position:0% +around one of these backstages anymore +and now I shorten the whole engine it + + align:start position:0% +and now I shorten the whole engine it + + + align:start position:0% +and now I shorten the whole engine it +gets lighter improves my range um so you + + align:start position:0% +gets lighter improves my range um so you + + + align:start position:0% +gets lighter improves my range um so you +you do it all at once but with some + + align:start position:0% +you do it all at once but with some + + + align:start position:0% +you do it all at once but with some +knowledge of what you've done in the + + align:start position:0% +knowledge of what you've done in the + + + align:start position:0% +knowledge of what you've done in the +past + + align:start position:0% + + + + align:start position:0% + +yeah try and see if it works then it + + align:start position:0% +yeah try and see if it works then it + + + align:start position:0% +yeah try and see if it works then it +works improve it a little bit how much + + align:start position:0% +works improve it a little bit how much + + + align:start position:0% +works improve it a little bit how much +is try it and see if it works and then + + align:start position:0% +is try it and see if it works and then + + + align:start position:0% +is try it and see if it works and then +if it works improve it a little bit very + + align:start position:0% +if it works improve it a little bit very + + + align:start position:0% +if it works improve it a little bit very +little these days because you have a lot + + align:start position:0% +little these days because you have a lot + + + align:start position:0% +little these days because you have a lot +of advanced um computational tools to + + align:start position:0% +of advanced um computational tools to + + + align:start position:0% +of advanced um computational tools to +help you design each and every aspect of + + align:start position:0% +help you design each and every aspect of + + + align:start position:0% +help you design each and every aspect of +this uh and it cost you a million + + align:start position:0% +this uh and it cost you a million + + + align:start position:0% +this uh and it cost you a million +dollars a day to test one of these so + + align:start position:0% +dollars a day to test one of these so + + + align:start position:0% +dollars a day to test one of these so +you just don't have and to build it you + + align:start position:0% +you just don't have and to build it you + + + align:start position:0% +you just don't have and to build it you +know each one of these turbine blades + + align:start position:0% +know each one of these turbine blades + + + align:start position:0% +know each one of these turbine blades +maybe + + align:start position:0% +maybe + + + align:start position:0% +maybe +$5,000 you just don't have all the money + + align:start position:0% +$5,000 you just don't have all the money + + + align:start position:0% +$5,000 you just don't have all the money +to just test it and try it and see if it + + align:start position:0% +to just test it and try it and see if it + + + align:start position:0% +to just test it and try it and see if it +works you've sort of got to go from + + align:start position:0% +works you've sort of got to go from + + + align:start position:0% +works you've sort of got to go from +fundamentals and and uh design it what + + align:start position:0% +fundamentals and and uh design it what + + + align:start position:0% +fundamentals and and uh design it what +sort of tools is it software tools or + + align:start position:0% +sort of tools is it software tools or + + + align:start position:0% +sort of tools is it software tools or +yeah it's so software tools to take + + align:start position:0% +yeah it's so software tools to take + + + align:start position:0% +yeah it's so software tools to take +equations like these that we've worked + + align:start position:0% +equations like these that we've worked + + + align:start position:0% +equations like these that we've worked +with and solve them for each small + + align:start position:0% +with and solve them for each small + + + align:start position:0% +with and solve them for each small +particle of + + align:start position:0% +particle of + + + align:start position:0% +particle of +flow right and add them all up and + + align:start position:0% +flow right and add them all up and + + + align:start position:0% +flow right and add them all up and +integrate them + + align:start position:0% + + + + align:start position:0% + +all all right please fill out your + + align:start position:0% +all all right please fill out your + + + align:start position:0% +all all right please fill out your +muddiest part of the lecture cards I + + align:start position:0% +muddiest part of the lecture cards I + + + align:start position:0% +muddiest part of the lecture cards I +will respond to those I get on an + + align:start position:0% +will respond to those I get on an + + + align:start position:0% +will respond to those I get on an +airplane tonight so until I sort of land + + align:start position:0% +airplane tonight so until I sort of land + + + align:start position:0% +airplane tonight so until I sort of land +on the ground back there um I won't have + + align:start position:0% +on the ground back there um I won't have + + + align:start position:0% +on the ground back there um I won't have +them all posted up but I will endeavor + + align:start position:0% +them all posted up but I will endeavor + + + align:start position:0% +them all posted up but I will endeavor +to do that uh and I think we've got one + + align:start position:0% +to do that uh and I think we've got one + + + align:start position:0% +to do that uh and I think we've got one +more recitation before the quiz all + + align:start position:0% +more recitation before the quiz all + + + align:start position:0% +more recitation before the quiz all +right thanks \ No newline at end of file diff --git a/YnF1b_Kqf88.txt b/YnF1b_Kqf88.txt new file mode 100644 index 0000000000000000000000000000000000000000..93b5b2a890a4bd0977bffb0285badbddfa65a8a1 --- /dev/null +++ b/YnF1b_Kqf88.txt @@ -0,0 +1,768 @@ +So far, there are a lot of +ways to clone genes. + +I've given you two. + +Later in the course, I'll give +you a third, but we cloned it + +here by its function, +complementation. + +We cloned it here on +the basis of the + +protein it actually made. + +Now, how do we analyze +these genes? + +How do you know which gene +we're dealing with? + +How do we study it? + +Let's turn to that. + +Analyzing our gene. + +Well, let's suppose we +have our cell, maybe + +it's our yeast cell. + +It's Arg1 again. + +We'll go back to yeast. + +It's got its yeast DNA it's also +got this circle that has + +our plasmid here. + +Circle is plasmid. + +How are we going to +study that gene? + +We know that yeast is +able to now grow. + +We can grow up that yeast. + +We can purify DNA from it. + +But wait a second. + +How do we get our plasmids away +from the chromosomal DNA? + +Aren't we back in the same +boat of you can't + +purify DNA from DNA? + +Thankfully, this is easy. + +Little circles of DNA have +different biochemical + +properties than the long, linear +chromosomes or the big + +chunks of DNA. + +And you can use biochemistry to +separate little circles of + +DNA from big chunks of DNA. + +So no problem. + +You can purify the plasmids. + +Purify the plasmid, +and there it is. + +It's back again. + +And now, you've got +your Arg1 gene. + +How do I study it? + +Well, the first thing I might +want to find out about my Arg1 + +gene, is how big +is that insert. + +How can I find out how +big that insert is? + +AUDIENCE: Electrophoresis. + +ERIC LANDER: Electrophoresis. + +I first have to cut +out the insert. + +How do I do that? + +AUDIENCE: The restriction +enzyme. + +ERIC LANDER: My restriction +enzyme, EcoRI. + +I cut with EcoRI and it +liberates the insert. + +And then I take a gel, which can +be made out of different + +substances, and I put +my DNA there. + +Agarose is particularly nice +stuff, which is basically + +Jell-O. And I turn on +an electric field. + +DNA is what, positively charged +or negatively charged? + +AUDIENCE: Negative. + +ERIC LANDER: So what kind of +charge do I want to put here? + +AUDIENCE: Positive. + +ERIC LANDER: What charge +do I put here? + +AUDIENCE: Negative. + +ERIC LANDER: What happens +if I do it backwards? + +Bad. + +Everybody does it backwards +in the lab at some point. + +So then you do this. + +The DNA goes this way and it +turns out that agarose is this + +matrix of cross links +and all that. + +And DNA molecules wiggle through +like a snake, through + +this matrix, and little ones go +much faster than big ones. + +So what happens is, little DNA +molecules move faster than big + +DNA molecules. + +And if I stop at some point, and +I add a dye that sticks to + +DNA, and look at it with a +fluorescent light, I can + +actually see where the +DNA molecules are. + +So I've grown up a ton of this +plasmid, lots of it, couple of + +micrograms of it. + +I cut it, I add it to the top of +my well here, I turn on the + +electricity, and it wiggle, +wiggle, wiggles through. + +This is the vector, and +this is the insert. + +It might be actually, that I +found another plasmid that + +could do this too, that +rescued yeast. + +It had a vector and maybe +at a different insert. + +Maybe I had one, I don't know +why, that had the same insert + +right there. + +In any case, the first +characterization that I would + +do is look at the size +of my insert. + +How big is that insert? + +I might find out that the insert +is one kilobase, 1,000 + +bases, or one KB, or 2 KB +or something like that. + +That's a first order of +characterization. + +Now, of course, what I +really want to know + +about the insert, sequence. + +I want the DNA sequencing +insert, right? + +Let's not just mess around with, +it's got 1,000 bases, I + +want to know what are those +bases in what order. + +So that means I have to +invent DNA sequencing. + +All right. + +So how am I going to invent +DNA sequencing? + +This is a little tough. + +I have my piece of DNA. + +I cut it out. + +Here's my piece of DNA, +5 prime to 3 prime, + +5 prime to 3 prime. + +Let's give it a sequence +ATTAAGAATGCAT, et cetera. + +DNA sequencing is actually +remarkably cute. + +I take a primer just like +Kornberg did back when he was + +discovering polymerase. + +Here's my primer, let's say. + +Here's my primer. + +Here's the matching template. + +And what did Kornberg +teaches us? + +He taught us that if we add +polymerase, what will + +polymerase do? + +It'll add the right +bases, right? + +TACGTA onward. + +If we could look really fast, +maybe we could just + +see it going by. + +But we can't look really fast. + +If we just add polymerase, +it'll just zip up + +and add all the bases. + +But someone had a +clever trick. + +The clever trick is this. + +Suppose I threw in a smidgen +of defective Ts, Ts that + +couldn't be extended +for some reason? + +I'll call that T star. + +What happens if a defective +T goes in there? + +Can't be extended anymore. + +And what happens then +to my reaction? + +It comes to a halt. + +Ah, but what happened if +I put in a good T? + +Then instead, what would +the next base be? + +A. Then what would happen? + +C, G. Then what's next? + +T. And what would happen if +I put in a defective T? + +It would stop. + +Now, maybe instead the defective +T didn't go in. + +And it would go on, and the +next T that it encounters, + +maybe it would put a +defective T there. + +Or maybe it would put +a defective T there. + +Now, of course, I just have +a little smidgen of + +defective T, right? + +So which of these will happen? + +Will it sometimes stop +at the first T? + +Sometimes at the second? + +Sometimes at the third? + +I'll actually get a series +of molecules. + +What will the lengths of those +molecules tell me? + +Where the Ts are. + +Kind of cute. + +This is very cute. + +So if I do that reaction, I'll +call that the defective Ts, I + +could see that there is some +molecules, stop here at this + +very small size, some stop here, +some stop here, some + +stop there, some stop there. + +And what have I just learned? + +The sizes, the lengths of the +fragments that end in T. + +But that's not good. + +I also want to know the As. + +AUDIENCE: Do it with +defective As. + +ERIC LANDER: Do it will +defective As, right? + +I'll just use defective As. + +And then I'll see the +As stop there. + +And then I'll do it with +defective Cs, and I'll do it + +with defective Gs. + +And I'll see exactly where the +molecules are, the lengths of + +the molecules that end +in A, T, C, and G. + +And I've just read the +sequence, haven't I? + +Pretty cool. + +This actually is so cool, +it won a Nobel Prize. + +I mean cool usually means won +a Nobel Prize or something + +like that in this class. + +So actually, how do +I visualize the + +little letters there? + +So the little fragments +on the gel? + +I visualize the little +fragments back in + +ancient days, yes? + +AUDIENCE: How do you +know [INAUDIBLE] + +necessarily be inserted +in every place + +where there is a letter? + +ERIC LANDER: I'd make +the right ratio. + +I'd choose a ratio of defective +to good Ts. + +Like if I choose 1% defective +T's, then about 1% of the + +time, I put in the defective +T it turns out. + +It turns out to work OK. + +I just put in a smidgen of +defective Ts, like 1%, and 1% + +of the time it stops here, and +1% here, and 1% there. + +So and then, of course, to see +them in old days, what people + +did was they made these primers +radioactive, and these + +radioactive primers here within +the gel would be held + +up against a piece of x-ray +film, and you would see where + +little radioactive bands were. + +That's how you could visualize +the primers, because it turns + +out you have too little primer +to see it even with my + +fluorescent dye. + +But a little radioactivity, +you add radioactivity, you + +take the gel off, you put on a +piece of, I guess you've got + +to wrap it with Saran. + +You'd better be standing +behind a shield. + +So you're standing behind a +plastic shield, you reach + +around the shield, you wrap +it with Saran Wrap. + +You then put x-ray film on. + +You are you doing this +in a dark room. + +You then seal it up. + +You put it in the freezer +for two weeks. + +You take it out. + +You develop it. + +You get your magic marker, and +you follow where all the + +little bands are. + +And that's DNA sequencing. + +It's cool. + +It won a Nobel Prize. + +It's also like really tedious. + +So little tricks were done to +speed it up, some nice pieces + +of engineering. + +Instead of visualizing our DNA, +faster DNA sequencing, + +what happens instead? + +What people did, which was very +cool, was they simply + +took the As, Ts, Cs and Gs, +the defective ones, they + +attached a colored +dye to each one. + +The As were green, and the Ts +were blue and the Gs were red. + +Now, when I run it out, I can +do it with fluorescence. + +And I can see the Ts all glow +one color, and the As glow + +another color. + +Now, it turns out, of course, +if they're glowing four + +different colors, I don't +actually need to run them in + +separate lanes. + +I could run them in the +same lane, right? + +So I could run them all in a +single lane, and I'd see Ts + +and As, and Gs. + +And now, instead of putting this +up against the piece of + +x-ray film, I could do +this in a very thin + +tube called a capillary. + +And instead of holding it up to +an x-ray film, I could just + +put a laser detector. + +I can turn on the electricity +and watch the fragments go by + +and just look at it with +my laser detector. + +Shines a light. + +I say, oh yeah, green, +red, blue. + +That's the sequence. + +This made it a lot +easier than that. + +I actually got involved in +molecular biology when it was + +still that. + +That is a lot better. + +By the way, I didn't tell +you what the defective + +Ts were, did I? + +AUDIENCE: [INAUDIBLE]. + +ERIC LANDER: Sorry? + +AUDIENCE: [INAUDIBLE]. + +ERIC LANDER: Well, they gotta +have something that prevents + +them from being extended, +right? + +What prevents them from +being extended? + +Do we remember how +DNA is extended? + +We have a sugar phosphate +backbone, right? + +Phosphate, base, 5 prime. + +Where do we extend, what base? + +3 prime. + +And what do we use +to extend on? + +The 3 prime hydroxyl. + +Remember, DNA has no hydroxyl +at its 2 prime position. + +Its normal DNA is +2 prime deoxy. + +How do you think we prevent +it from being extended? + +AUDIENCE: 2 prime [INAUDIBLE]. + +ERIC LANDER: 2 prime, +3 prime dideoxy. + +Defective just means 2 prime, +3 prime dideoxy. + +See, we tell you about these +structure not just so you + +memorize structures, but because +those are the tricks + +we use in the trade. + +Now, you get yourself some 2 +prime, 3 prime dideoxies. + +You put in a smidgen, +maybe 1%. + +You run your reaction. + +Those dideoxies have dyes, +spelled differently, D-Y-E + +color dyes attached to them. + +And you sit there with +your laser detector. + +Turns out to be even better. + +If you have one capillary, +you could have two. + +If you have two, you could have +three, and the machines + +that were built around 1999 +had 96 capillaries. + +I'll call it 100. + +You could sit there and read +700 bases every hour. + +You can do this maybe +20 hours in the day + +because it's automated. + +You could do this +360 days a year. + +And at MIT, we had 100 machines +during the Human + +Genome Project. + +And if you do the arithmetic, we +could read about 60 billion + +bases a year, 60 billion bases +a year during the height of + +the Human Genome Project. + +Now, this is pretty cool, but +it ain't nothing compared to + +what we're doing +10 years later. + +Currently, we are doing +60 billion bases every + +10 minutes at MIT. + +There's a little trick that I'll +tell you about next time + +of how DNA sequencing went from +that, where you could do + +about 250 letters a day, when I +first got involved in this, + +to that, where at a large +facility like MIT, you could + +do 60 billion letters a day, to +today when you can do about + +60 billion letters +in 10 minutes. + +We'll touch on that next time. \ No newline at end of file diff --git a/Z9ppHdZXJxs.txt b/Z9ppHdZXJxs.txt new file mode 100644 index 0000000000000000000000000000000000000000..61d55d627069522d71a5d197a3bcce2ac8383230 --- /dev/null +++ b/Z9ppHdZXJxs.txt @@ -0,0 +1,1587 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +the capacitance attenuator demonstrates + + align:start position:0% +the capacitance attenuator demonstrates + + + align:start position:0% +the capacitance attenuator demonstrates +the nature of solutions to Lassa + + align:start position:0% + + + + align:start position:0% + +equation this is the two-dimensional + + align:start position:0% +equation this is the two-dimensional + + + align:start position:0% +equation this is the two-dimensional +form of L Plaza's equation in cartisian + + align:start position:0% +form of L Plaza's equation in cartisian + + + align:start position:0% +form of L Plaza's equation in cartisian +coordinates X and + + align:start position:0% + + + + align:start position:0% + +Y product solutions to this equation + + align:start position:0% +Y product solutions to this equation + + + align:start position:0% +Y product solutions to this equation +illustrate the nature of a potential + + align:start position:0% +illustrate the nature of a potential + + + align:start position:0% +illustrate the nature of a potential +that is periodic in One Direction the X + + align:start position:0% +that is periodic in One Direction the X + + + align:start position:0% +that is periodic in One Direction the X +Direction + + align:start position:0% + + + + align:start position:0% + +the hyperbolic sign function which is a + + align:start position:0% +the hyperbolic sign function which is a + + + align:start position:0% +the hyperbolic sign function which is a +combination of + + align:start position:0% +combination of + + + align:start position:0% +combination of +exponentials represents the essentially + + align:start position:0% +exponentials represents the essentially + + + align:start position:0% +exponentials represents the essentially +exponential decay in a direction + + align:start position:0% +exponential decay in a direction + + + align:start position:0% +exponential decay in a direction +perpendicular to the direction of + + align:start position:0% +perpendicular to the direction of + + + align:start position:0% +perpendicular to the direction of +periodicity + + align:start position:0% + + + + align:start position:0% + +why the potential can be viewed as the + + align:start position:0% +why the potential can be viewed as the + + + align:start position:0% +why the potential can be viewed as the +vertical dimension on this floor this is + + align:start position:0% +vertical dimension on this floor this is + + + align:start position:0% +vertical dimension on this floor this is +the + + align:start position:0% + + + + align:start position:0% + +potential the X Direction the direction + + align:start position:0% +potential the X Direction the direction + + + align:start position:0% +potential the X Direction the direction +of periodicity is that direction and + + align:start position:0% +of periodicity is that direction and + + + align:start position:0% +of periodicity is that direction and +here's our sign + + align:start position:0% + + + + align:start position:0% + +function this is the y + + align:start position:0% +function this is the y + + + align:start position:0% +function this is the y +direction and here's our hyperbolic sign + + align:start position:0% + + + + align:start position:0% + +function more of the X + + align:start position:0% +function more of the X + + + align:start position:0% +function more of the X +dependence and the Y + + align:start position:0% +dependence and the Y + + + align:start position:0% +dependence and the Y +dependence lines of equip potential on + + align:start position:0% +dependence lines of equip potential on + + + align:start position:0% +dependence lines of equip potential on +our model are represented by these wires + + align:start position:0% + + + + align:start position:0% + +lines of constant altitude are the lines + + align:start position:0% +lines of constant altitude are the lines + + + align:start position:0% +lines of constant altitude are the lines +of equip + + align:start position:0% + + + + align:start position:0% + +potential this particular one is + + align:start position:0% + + + + align:start position:0% + +rectangular here's another way to to + + align:start position:0% +rectangular here's another way to to + + + align:start position:0% +rectangular here's another way to to +represent our potential function this is + + align:start position:0% +represent our potential function this is + + + align:start position:0% +represent our potential function this is +the X Direction This is the Y + + align:start position:0% +the X Direction This is the Y + + + align:start position:0% +the X Direction This is the Y +Direction with these clamps we're + + align:start position:0% +Direction with these clamps we're + + + align:start position:0% +Direction with these clamps we're +holding the membrane down on these + + align:start position:0% +holding the membrane down on these + + + align:start position:0% +holding the membrane down on these +edges on this Edge we're going to raise + + align:start position:0% +edges on this Edge we're going to raise + + + align:start position:0% +edges on this Edge we're going to raise +the + + align:start position:0% + + + + align:start position:0% + +potential these boundaries are clamped + + align:start position:0% +potential these boundaries are clamped + + + align:start position:0% +potential these boundaries are clamped +to zero potential + + align:start position:0% +to zero potential + + + align:start position:0% +to zero potential +now we've raised this potential to a + + align:start position:0% +now we've raised this potential to a + + + align:start position:0% +now we've raised this potential to a +potential + + align:start position:0% + + + + align:start position:0% + +V under uniform tension the membrane + + align:start position:0% +V under uniform tension the membrane + + + align:start position:0% +V under uniform tension the membrane +altitude satisfies llosa's + + align:start position:0% + + + + align:start position:0% + +equation far from the elevated Edge the + + align:start position:0% +equation far from the elevated Edge the + + + align:start position:0% +equation far from the elevated Edge the +membrane then has the same shape as with + + align:start position:0% +membrane then has the same shape as with + + + align:start position:0% +membrane then has the same shape as with +the + + align:start position:0% +the + + + align:start position:0% +the +model rather than using wires to show + + align:start position:0% +model rather than using wires to show + + + align:start position:0% +model rather than using wires to show +the lines of equal altitude the equal + + align:start position:0% +the lines of equal altitude the equal + + + align:start position:0% +the lines of equal altitude the equal +potentials we now use back lighting + + align:start position:0% + + + + align:start position:0% + +here's what it looks like from the + + align:start position:0% + + + + align:start position:0% + +top the elevated potential is + + align:start position:0% + + + + align:start position:0% + +uniform not a sign function + + align:start position:0% + + + + align:start position:0% + +however the square distribution can be + + align:start position:0% +however the square distribution can be + + + align:start position:0% +however the square distribution can be +represented by a 4A + + align:start position:0% +represented by a 4A + + + align:start position:0% +represented by a 4A +Series this amounts to a superposition + + align:start position:0% +Series this amounts to a superposition + + + align:start position:0% +Series this amounts to a superposition +of solutions like the one we've + + align:start position:0% +of solutions like the one we've + + + align:start position:0% +of solutions like the one we've +seen except they have more Wiggles in + + align:start position:0% +seen except they have more Wiggles in + + + align:start position:0% +seen except they have more Wiggles in +the X + + align:start position:0% +the X + + + align:start position:0% +the X +Direction and therefore Decay more + + align:start position:0% +Direction and therefore Decay more + + + align:start position:0% +Direction and therefore Decay more +rapidly in the y + + align:start position:0% + + + + align:start position:0% + +direction what we see is the potential + + align:start position:0% +direction what we see is the potential + + + align:start position:0% +direction what we see is the potential +potential if three of the walls + + align:start position:0% +potential if three of the walls + + + align:start position:0% +potential if three of the walls +enclosing a rectangular region are + + align:start position:0% +enclosing a rectangular region are + + + align:start position:0% +enclosing a rectangular region are +grounded and the fourth has a uniform + + align:start position:0% +grounded and the fourth has a uniform + + + align:start position:0% +grounded and the fourth has a uniform +distribution in + + align:start position:0% + + + + align:start position:0% + +potential the electric field lines are + + align:start position:0% +potential the electric field lines are + + + align:start position:0% +potential the electric field lines are +perpendicular to the equip potentials + + align:start position:0% +perpendicular to the equip potentials + + + align:start position:0% +perpendicular to the equip potentials +and follow Paths of steepest + + align:start position:0% +and follow Paths of steepest + + + align:start position:0% +and follow Paths of steepest +descent if they begin on positive + + align:start position:0% +descent if they begin on positive + + + align:start position:0% +descent if they begin on positive +charges + + align:start position:0% +charges + + + align:start position:0% +charges +here they terminate on negative charges + + align:start position:0% +here they terminate on negative charges + + + align:start position:0% +here they terminate on negative charges +on the boundaries + + align:start position:0% + + + + align:start position:0% + +a boundary that has zero + + align:start position:0% +a boundary that has zero + + + align:start position:0% +a boundary that has zero +potential nevertheless supports surface + + align:start position:0% +potential nevertheless supports surface + + + align:start position:0% +potential nevertheless supports surface +charges the surface charge is + + align:start position:0% +charges the surface charge is + + + align:start position:0% +charges the surface charge is +proportional to the slope of the + + align:start position:0% +proportional to the slope of the + + + align:start position:0% +proportional to the slope of the +adjacent + + align:start position:0% + + + + align:start position:0% + +potential this is a cross-section of the + + align:start position:0% +potential this is a cross-section of the + + + align:start position:0% +potential this is a cross-section of the +electrical system that has been + + align:start position:0% +electrical system that has been + + + align:start position:0% +electrical system that has been +pictured these boundaries are + + align:start position:0% +pictured these boundaries are + + + align:start position:0% +pictured these boundaries are +grounded while this one is at the + + align:start position:0% +grounded while this one is at the + + + align:start position:0% +grounded while this one is at the +potential V + + align:start position:0% +potential V + + + align:start position:0% +potential V +if V were positive this charge on the + + align:start position:0% +if V were positive this charge on the + + + align:start position:0% +if V were positive this charge on the +lower surface would be + + align:start position:0% + + + + align:start position:0% + +negative in the actual experiment a + + align:start position:0% +negative in the actual experiment a + + + align:start position:0% +negative in the actual experiment a +conducting box is grounded on two side + + align:start position:0% +conducting box is grounded on two side + + + align:start position:0% +conducting box is grounded on two side +surfaces and virtually grounded on the + + align:start position:0% +surfaces and virtually grounded on the + + + align:start position:0% +surfaces and virtually grounded on the +bottom surface through a small resistor + + align:start position:0% + + + + align:start position:0% + +R in the experiment the resistance R is + + align:start position:0% +R in the experiment the resistance R is + + + align:start position:0% +R in the experiment the resistance R is +the 1 megga ohm resistance of this scope + + align:start position:0% +the 1 megga ohm resistance of this scope + + + align:start position:0% +the 1 megga ohm resistance of this scope +which is used to measure the voltage of + + align:start position:0% +which is used to measure the voltage of + + + align:start position:0% +which is used to measure the voltage of +the lower + + align:start position:0% +the lower + + + align:start position:0% +the lower +electrode here are the grounded side + + align:start position:0% +electrode here are the grounded side + + + align:start position:0% +electrode here are the grounded side +walls their spacing is + + align:start position:0% +walls their spacing is + + + align:start position:0% +walls their spacing is +a the top electrode here a distance B + + align:start position:0% +a the top electrode here a distance B + + + align:start position:0% +a the top electrode here a distance B +above is driven by this AC + + align:start position:0% + + + + align:start position:0% + +Source here's the top + + align:start position:0% +Source here's the top + + + align:start position:0% +Source here's the top +electrode its potential is determined by + + align:start position:0% +electrode its potential is determined by + + + align:start position:0% +electrode its potential is determined by +the oscillator + + align:start position:0% + + + + align:start position:0% + +that's the top trace of the scope + + align:start position:0% +that's the top trace of the scope + + + align:start position:0% +that's the top trace of the scope +pattern here's the bottom + + align:start position:0% +pattern here's the bottom + + + align:start position:0% +pattern here's the bottom +electrode its potential is measured by + + align:start position:0% +electrode its potential is measured by + + + align:start position:0% +electrode its potential is measured by +the bottom trace on the + + align:start position:0% +the bottom trace on the + + + align:start position:0% +the bottom trace on the +scope we'll use our solutions to llosa's + + align:start position:0% +scope we'll use our solutions to llosa's + + + align:start position:0% +scope we'll use our solutions to llosa's +equation to find the net charge on the + + align:start position:0% +equation to find the net charge on the + + + align:start position:0% +equation to find the net charge on the +lower + + align:start position:0% + + + + align:start position:0% + +electrode before we make any + + align:start position:0% +electrode before we make any + + + align:start position:0% +electrode before we make any +measurements we should put our second + + align:start position:0% +measurements we should put our second + + + align:start position:0% +measurements we should put our second +side wall on the apparatus + + align:start position:0% + + + + align:start position:0% + +conservation of charge requires that the + + align:start position:0% +conservation of charge requires that the + + + align:start position:0% +conservation of charge requires that the +current through the 1 megga ohm + + align:start position:0% +current through the 1 megga ohm + + + align:start position:0% +current through the 1 megga ohm +resistance of the scope be the rate of + + align:start position:0% +resistance of the scope be the rate of + + + align:start position:0% +resistance of the scope be the rate of +change of this charge with respect to + + align:start position:0% + + + + align:start position:0% + +time Q is proportional to the driving + + align:start position:0% + + + + align:start position:0% + +voltage our input voltage varies + + align:start position:0% +voltage our input voltage varies + + + align:start position:0% +voltage our input voltage varies +sinusoidally in time so the measured + + align:start position:0% +sinusoidally in time so the measured + + + align:start position:0% +sinusoidally in time so the measured +output voltage is 90° out of phase with + + align:start position:0% +output voltage is 90° out of phase with + + + align:start position:0% +output voltage is 90° out of phase with +the input voltage + + align:start position:0% + + + + align:start position:0% + +our modal solution predicts the + + align:start position:0% +our modal solution predicts the + + + align:start position:0% +our modal solution predicts the +normalized peak amplitude of this output + + align:start position:0% +normalized peak amplitude of this output + + + align:start position:0% +normalized peak amplitude of this output +voltage v + + align:start position:0% +voltage v + + + align:start position:0% +voltage v +subo u is proportional to the input + + align:start position:0% +subo u is proportional to the input + + + align:start position:0% +subo u is proportional to the input +voltage + + align:start position:0% +voltage + + + align:start position:0% +voltage +V the experiment is designed to + + align:start position:0% +V the experiment is designed to + + + align:start position:0% +V the experiment is designed to +demonstrate the dependence of the output + + align:start position:0% +demonstrate the dependence of the output + + + align:start position:0% +demonstrate the dependence of the output +voltage on the spacing b the spacing + + align:start position:0% +voltage on the spacing b the spacing + + + align:start position:0% +voltage on the spacing b the spacing +between the input and output electrodes + + align:start position:0% +between the input and output electrodes + + + align:start position:0% +between the input and output electrodes +the decay of the potential in the + + align:start position:0% +the decay of the potential in the + + + align:start position:0% +the decay of the potential in the +direction perpendicular to the electrode + + align:start position:0% +direction perpendicular to the electrode + + + align:start position:0% +direction perpendicular to the electrode +is the reason for the hyperbolic sign in + + align:start position:0% +is the reason for the hyperbolic sign in + + + align:start position:0% +is the reason for the hyperbolic sign in +the + + align:start position:0% + + + + align:start position:0% + +denominator according to our Theory the + + align:start position:0% +denominator according to our Theory the + + + align:start position:0% +denominator according to our Theory the +natural log of the normalized output + + align:start position:0% +natural log of the normalized output + + + align:start position:0% +natural log of the normalized output +voltage has this dependence on the + + align:start position:0% +voltage has this dependence on the + + + align:start position:0% +voltage has this dependence on the +distance between input and output + + align:start position:0% + + + + align:start position:0% + +electrodes on the log plot with + + align:start position:0% +electrodes on the log plot with + + + align:start position:0% +electrodes on the log plot with +increasing B over a the function quickly + + align:start position:0% +increasing B over a the function quickly + + + align:start position:0% +increasing B over a the function quickly +becomes a straight line + + align:start position:0% +becomes a straight line + + + align:start position:0% +becomes a straight line +with a slope minus + + align:start position:0% + + + + align:start position:0% + +pi as the lower electrode is + + align:start position:0% +pi as the lower electrode is + + + align:start position:0% +pi as the lower electrode is +withdrawn its potential decreases + + align:start position:0% + + + + align:start position:0% + +exponentially the output voltage decays + + align:start position:0% +exponentially the output voltage decays + + + align:start position:0% +exponentially the output voltage decays +with electrod + + align:start position:0% +with electrod + + + align:start position:0% +with electrod +spacing because charges induced on the + + align:start position:0% +spacing because charges induced on the + + + align:start position:0% +spacing because charges induced on the +input + + align:start position:0% +input + + + align:start position:0% +input +electrode have their images either on + + align:start position:0% +electrode have their images either on + + + align:start position:0% +electrode have their images either on +the side walls of the + + align:start position:0% +the side walls of the + + + align:start position:0% +the side walls of the +box or on the output + + align:start position:0% + + + + align:start position:0% + +electrode if B over a is small almost + + align:start position:0% +electrode if B over a is small almost + + + align:start position:0% +electrode if B over a is small almost +all of the images are on the output + + align:start position:0% +all of the images are on the output + + + align:start position:0% +all of the images are on the output +electrode but as we withdraw it more and + + align:start position:0% +electrode but as we withdraw it more and + + + align:start position:0% +electrode but as we withdraw it more and +more of the images are on the side walls + + align:start position:0% +more of the images are on the side walls + + + align:start position:0% +more of the images are on the side walls +and fewer on the output + + align:start position:0% + + + + align:start position:0% + +electrode how well does the theory + + align:start position:0% +electrode how well does the theory + + + align:start position:0% +electrode how well does the theory +predict this attenuation curve here are + + align:start position:0% +predict this attenuation curve here are + + + align:start position:0% +predict this attenuation curve here are +the + + align:start position:0% +the + + + align:start position:0% +the +numbers to put data on our normalized + + align:start position:0% +numbers to put data on our normalized + + + align:start position:0% +numbers to put data on our normalized +plot we first evaluate U + + align:start position:0% + + + + align:start position:0% + +we have a width W of 17 + + align:start position:0% +we have a width W of 17 + + + align:start position:0% +we have a width W of 17 +cm the frequency 100 + + align:start position:0% +cm the frequency 100 + + + align:start position:0% +cm the frequency 100 +Herz the scope resistance is 1 megga + + align:start position:0% +Herz the scope resistance is 1 megga + + + align:start position:0% +Herz the scope resistance is 1 megga +ohm with an input of 10 volts Peak U + + align:start position:0% +ohm with an input of 10 volts Peak U + + + align:start position:0% +ohm with an input of 10 volts Peak U +equal 48 molts + + align:start position:0% + + + + align:start position:0% + +Peak for a equal 4.4 + + align:start position:0% +Peak for a equal 4.4 + + + align:start position:0% +Peak for a equal 4.4 +cm and a spacing between input and + + align:start position:0% +cm and a spacing between input and + + + align:start position:0% +cm and a spacing between input and +output electrodes b equal 1 + + align:start position:0% +output electrodes b equal 1 + + + align:start position:0% +output electrodes b equal 1 +cm we may measure 28 molts + + align:start position:0% + + + + align:start position:0% + +Peak this data point falls about + + align:start position:0% + + + + align:start position:0% + +here here are some other data points + + align:start position:0% +here here are some other data points + + + align:start position:0% +here here are some other data points +that we've + + align:start position:0% + + + + align:start position:0% + +taken according to our model the output + + align:start position:0% +taken according to our model the output + + + align:start position:0% +taken according to our model the output +voltage should be proportional to the + + align:start position:0% +voltage should be proportional to the + + + align:start position:0% +voltage should be proportional to the +frequency + + align:start position:0% + + + + align:start position:0% + +this is true if the frequency is taken + + align:start position:0% +this is true if the frequency is taken + + + align:start position:0% +this is true if the frequency is taken +from 100 Hertz to 200 + + align:start position:0% + + + + align:start position:0% + +htz remember the upper Trace is the + + align:start position:0% +htz remember the upper Trace is the + + + align:start position:0% +htz remember the upper Trace is the +upper driving electrode and on a + + align:start position:0% +upper driving electrode and on a + + + align:start position:0% +upper driving electrode and on a +different scale the lower one is the + + align:start position:0% +different scale the lower one is the + + + align:start position:0% +different scale the lower one is the +lower electrode + + align:start position:0% + + + + align:start position:0% + +voltage however if the frequency is + + align:start position:0% +voltage however if the frequency is + + + align:start position:0% +voltage however if the frequency is +taken from 1,000 Herz to 2,000 + + align:start position:0% +taken from 1,000 Herz to 2,000 + + + align:start position:0% +taken from 1,000 Herz to 2,000 +Herz the output ceases to be linear in + + align:start position:0% +Herz the output ceases to be linear in + + + align:start position:0% +Herz the output ceases to be linear in +the + + align:start position:0% + + + + align:start position:0% + +frequency with the frequency this High + + align:start position:0% +frequency with the frequency this High + + + align:start position:0% +frequency with the frequency this High +the current through the output resistor + + align:start position:0% +the current through the output resistor + + + align:start position:0% +the current through the output resistor +is too large too large to make the + + align:start position:0% +is too large too large to make the + + + align:start position:0% +is too large too large to make the +potential of the output electrode + + align:start position:0% + + + + align:start position:0% + +negligible we have demonstrated how + + align:start position:0% +negligible we have demonstrated how + + + align:start position:0% +negligible we have demonstrated how +solutions to Lassa equation that that + + align:start position:0% +solutions to Lassa equation that that + + + align:start position:0% +solutions to Lassa equation that that +are periodic in One Direction decay in + + align:start position:0% +are periodic in One Direction decay in + + + align:start position:0% +are periodic in One Direction decay in +the perpendicular Direction \ No newline at end of file diff --git a/ZApVXJZF7pE.txt b/ZApVXJZF7pE.txt new file mode 100644 index 0000000000000000000000000000000000000000..598ce3e33b6ec3c4bf6dafff6fa60a7d8b84ef7b --- /dev/null +++ b/ZApVXJZF7pE.txt @@ -0,0 +1,443 @@ +align:start position:0% + +so we're now beginning to make our + + align:start position:0% +so we're now beginning to make our + + + align:start position:0% +so we're now beginning to make our +complete study of rigid body motions + + align:start position:0% +complete study of rigid body motions + + + align:start position:0% +complete study of rigid body motions +about fixed axis let's consider + + align:start position:0% +about fixed axis let's consider + + + align:start position:0% +about fixed axis let's consider +something like a bicycle wheel here's + + align:start position:0% +something like a bicycle wheel here's + + + align:start position:0% +something like a bicycle wheel here's +the center of mass of the wheel and our + + align:start position:0% +the center of mass of the wheel and our + + + align:start position:0% +the center of mass of the wheel and our +bicycle wheel is the center of mass has + + align:start position:0% +bicycle wheel is the center of mass has + + + align:start position:0% +bicycle wheel is the center of mass has +some velocity and here's ground and + + align:start position:0% +some velocity and here's ground and + + + align:start position:0% +some velocity and here's ground and +we're going to call this the reference + + align:start position:0% +we're going to call this the reference + + + align:start position:0% +we're going to call this the reference +frame is the + + align:start position:0% +frame is the + + + align:start position:0% +frame is the +ground + + align:start position:0% +ground + + + align:start position:0% +ground +frame now if the bicycle wheel is + + align:start position:0% +frame now if the bicycle wheel is + + + align:start position:0% +frame now if the bicycle wheel is +rolling then there'll be some type of + + align:start position:0% +rolling then there'll be some type of + + + align:start position:0% +rolling then there'll be some type of +rotational motion of the wheel so you + + align:start position:0% +rotational motion of the wheel so you + + + align:start position:0% +rotational motion of the wheel so you +can imagine point on the rim is rotating + + align:start position:0% +can imagine point on the rim is rotating + + + align:start position:0% +can imagine point on the rim is rotating +and so what we have here is a angular + + align:start position:0% +and so what we have here is a angular + + + align:start position:0% +and so what we have here is a angular +velocity of this bicycle which will + + align:start position:0% +velocity of this bicycle which will + + + align:start position:0% +velocity of this bicycle which will +write like this our Vector Omega and + + align:start position:0% +write like this our Vector Omega and + + + align:start position:0% +write like this our Vector Omega and +we'll use our right hand rule to + + align:start position:0% +we'll use our right hand rule to + + + align:start position:0% +we'll use our right hand rule to +establish that direction for Omega and + + align:start position:0% +establish that direction for Omega and + + + align:start position:0% +establish that direction for Omega and +now in this reference frame we have + + align:start position:0% +now in this reference frame we have + + + align:start position:0% +now in this reference frame we have +translational motion of the center of + + align:start position:0% +translational motion of the center of + + + align:start position:0% +translational motion of the center of +mass and we have rotational motion + + align:start position:0% +mass and we have rotational motion + + + align:start position:0% +mass and we have rotational motion +around the center of mass if we go to + + align:start position:0% +around the center of mass if we go to + + + align:start position:0% +around the center of mass if we go to +the + + align:start position:0% +the + + + align:start position:0% +the +center of + + align:start position:0% +center of + + + align:start position:0% +center of +mass reference + + align:start position:0% +mass reference + + + align:start position:0% +mass reference +frame so if you want to just a little + + align:start position:0% +frame so if you want to just a little + + + align:start position:0% +frame so if you want to just a little +cartoon to show that here's your + + align:start position:0% +cartoon to show that here's your + + + align:start position:0% +cartoon to show that here's your +Observer and your Observer is moving + + align:start position:0% +Observer and your Observer is moving + + + align:start position:0% +Observer and your Observer is moving +with v + + align:start position:0% +with v + + + align:start position:0% +with v +cm and so in that + + align:start position:0% +cm and so in that + + + align:start position:0% +cm and so in that +frame the center of Mass is at + + align:start position:0% +frame the center of Mass is at + + + align:start position:0% +frame the center of Mass is at +rest + + align:start position:0% +rest + + + align:start position:0% +rest +and the only thing we have is + + align:start position:0% +and the only thing we have is + + + align:start position:0% +and the only thing we have is +rotation + + align:start position:0% +rotation + + + align:start position:0% +rotation +about the + + align:start position:0% +about the + + + align:start position:0% +about the +center of + + align:start position:0% +center of + + + align:start position:0% +center of +mass and so in this picture we we our + + align:start position:0% +mass and so in this picture we we our + + + align:start position:0% +mass and so in this picture we we our +motivation will be that the total + + align:start position:0% +motivation will be that the total + + + align:start position:0% +motivation will be that the total +external + + align:start position:0% +external + + + align:start position:0% +external +force causes the center of Mass to + + align:start position:0% +force causes the center of Mass to + + + align:start position:0% +force causes the center of Mass to +accelerate and that's how we can figure + + align:start position:0% +accelerate and that's how we can figure + + + align:start position:0% +accelerate and that's how we can figure +out the center of mass motion and in + + align:start position:0% +out the center of mass motion and in + + + align:start position:0% +out the center of mass motion and in +this picture we we no longer have to + + align:start position:0% +this picture we we no longer have to + + + align:start position:0% +this picture we we no longer have to +consider translational motion and what + + align:start position:0% +consider translational motion and what + + + align:start position:0% +consider translational motion and what +we'll study and learn to analyze is just + + align:start position:0% +we'll study and learn to analyze is just + + + align:start position:0% +we'll study and learn to analyze is just +pure rotation about the center of mass + + align:start position:0% +pure rotation about the center of mass + + + align:start position:0% +pure rotation about the center of mass +so torque will produce angular + + align:start position:0% +so torque will produce angular + + + align:start position:0% +so torque will produce angular +acceleration we can talk about the + + align:start position:0% +acceleration we can talk about the + + + align:start position:0% +acceleration we can talk about the +rotational energy about the center of + + align:start position:0% +rotational energy about the center of + + + align:start position:0% +rotational energy about the center of +mass and so we'll begin our analysis of + + align:start position:0% +mass and so we'll begin our analysis of + + + align:start position:0% +mass and so we'll begin our analysis of +rotational motion of translation and + + align:start position:0% +rotational motion of translation and + + + align:start position:0% +rotational motion of translation and +rotation by focusing + + align:start position:0% +rotation by focusing + + + align:start position:0% +rotation by focusing +our interest in the center of mass frame + + align:start position:0% +our interest in the center of mass frame + + + align:start position:0% +our interest in the center of mass frame +so we've just isolated the rotational + + align:start position:0% + + + + align:start position:0% + +motion \ No newline at end of file diff --git a/ZPpuDMk9BOU.txt b/ZPpuDMk9BOU.txt new file mode 100644 index 0000000000000000000000000000000000000000..9309584283a240fdbac1ae82d4220793157f2da3 --- /dev/null +++ b/ZPpuDMk9BOU.txt @@ -0,0 +1,356 @@ +Okay, it's finally time to investigate issues +caused by asynchronous inputs to a sequential + +logic circuit. + +By "asynchronous" we mean that the timing +of transitions on the input is completely + +independent of the timing of the sequential +logic clock. + +This situation arises when the inputs arrive +from the outside world where the timing of + +events is not under our control. + +As we saw at the end of Chapter 5, to ensure +reliable operation of the state registers + +inputs to a sequential logic system have to +obey setup and hold time constraints relative + +to the rising edge of the system clock. + +Clearly if the input can change at anytime, +it can change at time that would violate the + +setup and hold times. + +Maybe we can come up with a synchronizer circuit +that takes an unsynchronized input signal + +and produces a synchronized signal that only +changes shortly after the rising edge of the + +clock. + +We'd use a synchronizer on each asynchronous +input and solve our timing problems that way. + +Here's a detailed specification for our synchronizer. + +The synchronizer has two inputs, IN and CLK, +which have transitions at time t_IN and t_C + +respectively. + +If IN's transition happens sufficiently before +C's transition, we want the synchronizer to + +output a 1 within some bounded time t_D after +CLK's transition. + +And if CLK's transition happens sufficient +before IN's transition, we want the synchronizer + +to output a 0 within time t_D after CLK's +transition. + +Finally, if the two transitions are closer +together than some specified interval t_E, + +the synchronizer can output either a 0 or +a 1 within time t_D of CLK's transition. + +Either answer is fine so long as it's a stable +digital 0 or digital 1 by the specified deadline. + +This turns out to be an unsolvable problem! + +For no finite values of t_E and t_D can we +build a synchronizer that's guaranteed to + +meet this specification even when using components +that are 100% reliable. + +But can't we just use a D register to solve +the problem? + +We'll connect IN to the register's data input +and connect CLK to the register's clock input. + +We'll set the decision time t_D to the propagation +delay of the register and the allowable error + +interval to the larger of the register's setup +and hold times. + +Our theory is that if the rising edge of IN +occurs at least t_SETUP before the rising + +edge of CLK, the register is guaranteed to +output a 1. + +And if IN transitions more than t_HOLD after +the rising edge of CLK, the register is guaranteed + +to output a 0. + +So far, so good. + +If IN transitions during the setup and hold +times with respect to the rising edge on CLK, + +we know we've violated the dynamic discipline +and we can't tell whether the register will + +store a 0 or a 1. + +But in this case, our specification lets us +produce either answer, so we're good to go, + +right? + +Sadly, we're not good to go. + +We're lured by the digital abstraction into +assuming that even if we violate the dynamic + +discipline that Q must be either 1 or 0 after +the propagation delay. + +But that isn't a valid assumption as we'll +see when we look more carefully at the operation + +of the register's master latch when B and +C change at about the same time. + +Recall that the master latch is really just +a lenient MUX that can be configured as a + +bi-stable storage element using a positive +feedback loop. + +When the latch is in memory mode, it's essentially +a two-gate cyclic circuit whose behavior has + +two constraints: +the voltage transfer characteristic of the + +two-gate circuit, shown in green on the graph, +and that V_IN = V_OUT, a constraint that's + +shown in red on the graph. + +These two curves intersect at three points. + +Our concern is the middle point of intersection. + +If IN and CLK change at the same time, the +voltage on Q may be in transition at the time + +the MUX closes and enables the positive feedback +loop. + +So the initial voltage in the feedback loop +may happen to be at or very near the voltage + +of the middle intersection point. + +When Q is at the metastable voltage, the storage +loop is in an unstable equilibrium called + +the metastable state. + +In theory the system could balance at this +point forever, but a small change in the voltages + +in the loop will move the system away from +the metastable equilibrium point and set it + +irrevocably in motion towards the stable equilibrium +points. + +Here's the issue we face: we can't bound the +amount of time the system will spend in the + +metastable state. + +Here's what we know about the metastable state. + +It's in the forbidden zone of the digital +signaling specifications and so corresponds + +to an invalid logic level. + +Violating the dynamic discipline means that +our register is no longer guaranteed to produce + +a digital output in bounded time. + +A persistent invalid logic level can wreak +both logical and electrical havoc in our sequential + +logic circuit. + +Since combinational logic gates with invalid +inputs have unpredictable outputs, an invalid + +signal may corrupt the state and output values +in our sequential system. + +At the electrical level, if an input to a +CMOS gate is at the metastable voltage, both + +PFET and NFET switches controlled by that +input would be conducting, so we'd have a + +path between V_DD and GROUND, causing a spike +in the system's power dissipation. + +It's an unstable equilibrium and will eventually +be resolved by a transition to one of the + +two stable equilibrium points. + +You can see from the graph that the metastable +voltage is in the high-gain region of the + +VTC, so a small change in V_IN results in +a large change in V_OUT, and once away from + +the metastable point the loop voltage will +move towards 0 or V_DD. + +The time it takes for the system to evolve +to a stable equilibrium is related to how + +close Q's voltage was to the metastable point +when the positive feedback loop was enabled. + +The closer Q's initial voltage is to the metastable +voltage, the longer it will take for the system + +to resolve the metastability. + +But since there's no lower bound on how close +Q is to the metastable voltage, there's no + +upper bound on the time it will take for resolution. + +In other words, if you specify a bound, e.g., +t_D, on the time available for resolution, + +there's a range of initial Q voltages that +won't be resolved within that time. + +If the system goes metastable at some point +in time, then there's a non-zero probability + +that the system will still be metastable after +some interval T, for any finite choice of + +T. +The good news is that the probability of being + +metastable at the end of the interval decreases +exponentially with increasing T. + +Note that every bistable system has at least +one metastable state. + +So metastability is the price we pay for building +storage elements from positive feedback loops. + +If you'd like to read a more thorough discussion +of synchronizers and related problems and + +learn about the mathematics behind the exponential +probabilities, please see Chapter 10 of the + +Course Notes. + +Our approach to dealing with asynchronous +inputs is to put the potentially metastable + +value coming out of our D-register synchronizer +into "quarantine" by adding a second register + +hooked to the output of the first register. + +If a transition on the input violates the +dynamic discipline and causes the first register + +to go metastable, it's not immediately an +issue since the metastable value is stopped + +from entering the system by the second register. + +In fact, during the first half of the clock +cycle, the master latch in the second register + +is closed, so the metastable value is being +completely ignored. + +It's only at the next clock edge, an entire +clock period later, that the second D register + +will need a valid and stable input. + +There's still some probability that the first +register will be metastable after an entire + +clock period, but we can make that probability +as low as we wish by choosing a sufficiently + +long clock period. + +In other words, the output of the second register, +which provides the signal used by the internal + +combinational logic, will be stable and valid +with a probability of our choosing. + +Validity is not 100% guaranteed, but the failure +times are measured in years or decades, so + +it's not an issue in practice. + +Without the second register, the system might +see a metastability failure every handful + +of hours - the exact failure rate depends +on the transition frequencies and gains in + +the circuit. + +What happens if our clock period is short +but we want a long quarantine time? + +We can use multiple quarantine registers in +series. + +It's the total delay between when the first +register goes metastable and when the synchronized + +input is used by the internal logic that determines +the failure probability. + +The bottom line? + +We can use synchronizing registers to quarantine +potentially metastable signals for some period + +of time. + +Since the probability of still being metastable +decreases exponentially with the quarantine + +time, we can reduce the failure probability +to any desired level. + +Not a 100% guaranteed, but close enough that +metastability is not a practical issue if + +we use our quarantine strategy. \ No newline at end of file diff --git a/Z_5uLqcwDgM.txt b/Z_5uLqcwDgM.txt new file mode 100644 index 0000000000000000000000000000000000000000..83563e63670db6fd3eaad2ec676994b83de5eb94 --- /dev/null +++ b/Z_5uLqcwDgM.txt @@ -0,0 +1,6323 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay let's go so if you want to know the + + align:start position:0% +okay let's go so if you want to know the + + + align:start position:0% +okay let's go so if you want to know the +subject of today's class its ax equal B + + align:start position:0% +subject of today's class its ax equal B + + + align:start position:0% +subject of today's class its ax equal B +I got started writing down different + + align:start position:0% +I got started writing down different + + + align:start position:0% +I got started writing down different +possibilities for ax equal B and I got + + align:start position:0% +possibilities for ax equal B and I got + + + align:start position:0% +possibilities for ax equal B and I got +carried away + + align:start position:0% +carried away + + + align:start position:0% +carried away +there's it just appears all over the + + align:start position:0% +there's it just appears all over the + + + align:start position:0% +there's it just appears all over the +place and the four different sizes + + align:start position:0% +place and the four different sizes + + + align:start position:0% +place and the four different sizes +different ranks different situations + + align:start position:0% +different ranks different situations + + + align:start position:0% +different ranks different situations +nearly singular not nearly singular and + + align:start position:0% +nearly singular not nearly singular and + + + align:start position:0% +nearly singular not nearly singular and +the question is what do you do in each + + align:start position:0% +the question is what do you do in each + + + align:start position:0% +the question is what do you do in each +case so can I outline my little two + + align:start position:0% +case so can I outline my little two + + + align:start position:0% +case so can I outline my little two +pages of notes here and then pick on one + + align:start position:0% +pages of notes here and then pick on one + + + align:start position:0% +pages of notes here and then pick on one +or two of these topics to develop today + + align:start position:0% +or two of these topics to develop today + + + align:start position:0% +or two of these topics to develop today +and a little more on Friday about + + align:start position:0% +and a little more on Friday about + + + align:start position:0% +and a little more on Friday about +gram-schmidt so I won't do much of much + + align:start position:0% +gram-schmidt so I won't do much of much + + + align:start position:0% +gram-schmidt so I won't do much of much +if any of gram-schmidt today but I will + + align:start position:0% +if any of gram-schmidt today but I will + + + align:start position:0% +if any of gram-schmidt today but I will +do the others okay + + align:start position:0% +do the others okay + + + align:start position:0% +do the others okay +so the problem is ax equal B that + + align:start position:0% +so the problem is ax equal B that + + + align:start position:0% +so the problem is ax equal B that +problem has come from somewhere we have + + align:start position:0% +problem has come from somewhere we have + + + align:start position:0% +problem has come from somewhere we have +to produce some kind of an answer X okay + + align:start position:0% +to produce some kind of an answer X okay + + + align:start position:0% +to produce some kind of an answer X okay +so I'm sort of going from good to bad or + + align:start position:0% +so I'm sort of going from good to bad or + + + align:start position:0% +so I'm sort of going from good to bad or +good or easy to difficult in this list + + align:start position:0% +good or easy to difficult in this list + + + align:start position:0% +good or easy to difficult in this list +so well except for number zero which is + + align:start position:0% +so well except for number zero which is + + + align:start position:0% +so well except for number zero which is +an answer in all cases the using the + + align:start position:0% +an answer in all cases the using the + + + align:start position:0% +an answer in all cases the using the +pseudo-inverse that I introduced last + + align:start position:0% +pseudo-inverse that I introduced last + + + align:start position:0% +pseudo-inverse that I introduced last +time so that deals with zero eigenvalues + + align:start position:0% +time so that deals with zero eigenvalues + + + align:start position:0% +time so that deals with zero eigenvalues +and zero singular values by saying + + align:start position:0% +and zero singular values by saying + + + align:start position:0% +and zero singular values by saying +they're inverse is also 0 which is kind + + align:start position:0% +they're inverse is also 0 which is kind + + + align:start position:0% +they're inverse is also 0 which is kind +of wild so we'll come back to the + + align:start position:0% +of wild so we'll come back to the + + + align:start position:0% +of wild so we'll come back to the +meaning of the pseudo inverse but now + + align:start position:0% +meaning of the pseudo inverse but now + + + align:start position:0% +meaning of the pseudo inverse but now +I'm I want to get real here about + + align:start position:0% +I'm I want to get real here about + + + align:start position:0% +I'm I want to get real here about +different situations so number one is + + align:start position:0% +different situations so number one is + + + align:start position:0% +different situations so number one is +the good normal case when a person has a + + align:start position:0% +the good normal case when a person has a + + + align:start position:0% +the good normal case when a person has a +square matrix of reasonable size + + align:start position:0% +square matrix of reasonable size + + + align:start position:0% +square matrix of reasonable size +reasonable condition the condition + + align:start position:0% +reasonable condition the condition + + + align:start position:0% +reasonable condition the condition +number o the condition number I should + + align:start position:0% +number o the condition number I should + + + align:start position:0% +number o the condition number I should +call it Sigma one + + align:start position:0% +call it Sigma one + + + align:start position:0% +call it Sigma one +over Sigma n it's a ratio of the largest + + align:start position:0% +over Sigma n it's a ratio of the largest + + + align:start position:0% +over Sigma n it's a ratio of the largest +to the smallest singular value and let's + + align:start position:0% +to the smallest singular value and let's + + + align:start position:0% +to the smallest singular value and let's +say that's within reason not more than a + + align:start position:0% +say that's within reason not more than a + + + align:start position:0% +say that's within reason not more than a +thousand or something then normal + + align:start position:0% +thousand or something then normal + + + align:start position:0% +thousand or something then normal +ordinary elimination is going to work + + align:start position:0% +ordinary elimination is going to work + + + align:start position:0% +ordinary elimination is going to work +and MATLAB the command that would + + align:start position:0% +and MATLAB the command that would + + + align:start position:0% +and MATLAB the command that would +produce the answer is just backslash but + + align:start position:0% +produce the answer is just backslash but + + + align:start position:0% +produce the answer is just backslash but +so this is the normal case now in cases + + align:start position:0% +so this is the normal case now in cases + + + align:start position:0% +so this is the normal case now in cases +that follow or have problems of some + + align:start position:0% +that follow or have problems of some + + + align:start position:0% +that follow or have problems of some +kind and I guess I'm hoping that this is + + align:start position:0% +kind and I guess I'm hoping that this is + + + align:start position:0% +kind and I guess I'm hoping that this is +a sort of useful dictionary of what to + + align:start position:0% +a sort of useful dictionary of what to + + + align:start position:0% +a sort of useful dictionary of what to +do for for you and me both okay so we + + align:start position:0% +do for for you and me both okay so we + + + align:start position:0% +do for for you and me both okay so we +have this case here where we have too + + align:start position:0% +have this case here where we have too + + + align:start position:0% +have this case here where we have too +many equations so it's a pretty normal + + align:start position:0% +many equations so it's a pretty normal + + + align:start position:0% +many equations so it's a pretty normal +case and it's the we'll think mostly of + + align:start position:0% +case and it's the we'll think mostly of + + + align:start position:0% +case and it's the we'll think mostly of +solving by least squares which leads us + + align:start position:0% +solving by least squares which leads us + + + align:start position:0% +solving by least squares which leads us +to the normal equation so this is + + align:start position:0% +to the normal equation so this is + + + align:start position:0% +to the normal equation so this is +standard happens all the time in + + align:start position:0% +standard happens all the time in + + + align:start position:0% +standard happens all the time in +statistics and I'm thinking in the + + align:start position:0% +statistics and I'm thinking in the + + + align:start position:0% +statistics and I'm thinking in the +reasonable case so that's that would be + + align:start position:0% +reasonable case so that's that would be + + + align:start position:0% +reasonable case so that's that would be +X hat the solution a transfer this this + + align:start position:0% +X hat the solution a transfer this this + + + align:start position:0% +X hat the solution a transfer this this +matrix would be invertible and + + align:start position:0% +matrix would be invertible and + + + align:start position:0% +matrix would be invertible and +reasonable size so we could actually + + align:start position:0% +reasonable size so we could actually + + + align:start position:0% +reasonable size so we could actually +backslash would still solve that problem + + align:start position:0% +backslash would still solve that problem + + + align:start position:0% +backslash would still solve that problem +backslash doesn't require a square + + align:start position:0% +backslash doesn't require a square + + + align:start position:0% +backslash doesn't require a square +matrix to give you an answer so that's + + align:start position:0% +matrix to give you an answer so that's + + + align:start position:0% +matrix to give you an answer so that's +that's the good case where you would + + align:start position:0% +that's the good case where you would + + + align:start position:0% +that's the good case where you would +just the matrix is not too big so it's + + align:start position:0% +just the matrix is not too big so it's + + + align:start position:0% +just the matrix is not too big so it's +not unreasonable to to form a transpose + + align:start position:0% +not unreasonable to to form a transpose + + + align:start position:0% +not unreasonable to to form a transpose +a okay now there is the other extreme + + align:start position:0% +a okay now there is the other extreme + + + align:start position:0% +a okay now there is the other extreme +and like what's exciting for us is so + + align:start position:0% +and like what's exciting for us is so + + + align:start position:0% +and like what's exciting for us is so +this is the underdetermined case I don't + + align:start position:0% +this is the underdetermined case I don't + + + align:start position:0% +this is the underdetermined case I don't +have enough equations so I have to put + + align:start position:0% +have enough equations so I have to put + + + align:start position:0% +have enough equations so I have to put +something more in to get a specific + + align:start position:0% +something more in to get a specific + + + align:start position:0% +something more in to get a specific +answer and what makes it exciting for us + + align:start position:0% +answer and what makes it exciting for us + + + align:start position:0% +answer and what makes it exciting for us +is that that's typical of deep learning + + align:start position:0% +is that that's typical of deep learning + + + align:start position:0% +is that that's typical of deep learning +there are so many weights in a deep + + align:start position:0% +there are so many weights in a deep + + + align:start position:0% +there are so many weights in a deep +neural network that the weights would be + + align:start position:0% +neural network that the weights would be + + + align:start position:0% +neural network that the weights would be +the unknowns + + align:start position:0% + + + + align:start position:0% + +it wouldn't be necessarily linear + + align:start position:0% +it wouldn't be necessarily linear + + + align:start position:0% +it wouldn't be necessarily linear +wouldn't be linear but still the idea is + + align:start position:0% +wouldn't be linear but still the idea is + + + align:start position:0% +wouldn't be linear but still the idea is +the same that we we have many solutions + + align:start position:0% +the same that we we have many solutions + + + align:start position:0% +the same that we we have many solutions +and we have to pick one or we have to + + align:start position:0% +and we have to pick one or we have to + + + align:start position:0% +and we have to pick one or we have to +pick an algorithm and then it will find + + align:start position:0% +pick an algorithm and then it will find + + + align:start position:0% +pick an algorithm and then it will find +one and so we could pick the minimum + + align:start position:0% +one and so we could pick the minimum + + + align:start position:0% +one and so we could pick the minimum +norm solution the shortest solution that + + align:start position:0% +norm solution the shortest solution that + + + align:start position:0% +norm solution the shortest solution that +would be an l2 answer or we could go to + + align:start position:0% +would be an l2 answer or we could go to + + + align:start position:0% +would be an l2 answer or we could go to +l1 and a big question that's I think + + align:start position:0% +l1 and a big question that's I think + + + align:start position:0% +l1 and a big question that's I think +might be settled in 2018 is does deep + + align:start position:0% +might be settled in 2018 is does deep + + + align:start position:0% +might be settled in 2018 is does deep +learning and the iteration from + + align:start position:0% +learning and the iteration from + + + align:start position:0% +learning and the iteration from +stochastic gradient descent that we'll + + align:start position:0% +stochastic gradient descent that we'll + + + align:start position:0% +stochastic gradient descent that we'll +see soon pretty soon does it go to the + + align:start position:0% +see soon pretty soon does it go to the + + + align:start position:0% +see soon pretty soon does it go to the +minimum L what does it pick out an l1 + + align:start position:0% +minimum L what does it pick out an l1 + + + align:start position:0% +minimum L what does it pick out an l1 +solution that that's really like an + + align:start position:0% +solution that that's really like an + + + align:start position:0% +solution that that's really like an +exciting math question you know for a + + align:start position:0% +exciting math question you know for a + + + align:start position:0% +exciting math question you know for a +long time it was sort of standard to say + + align:start position:0% +long time it was sort of standard to say + + + align:start position:0% +long time it was sort of standard to say +these deep learning AI codes are + + align:start position:0% +these deep learning AI codes are + + + align:start position:0% +these deep learning AI codes are +fantastic but what are they doing we + + align:start position:0% +fantastic but what are they doing we + + + align:start position:0% +fantastic but what are they doing we +don't know + + align:start position:0% +don't know + + + align:start position:0% +don't know +you know the interior but where we when + + align:start position:0% +you know the interior but where we when + + + align:start position:0% +you know the interior but where we when +I say we I don't mean I other people are + + align:start position:0% +I say we I don't mean I other people are + + + align:start position:0% +I say we I don't mean I other people are +getting there and I'm gonna tell you as + + align:start position:0% +getting there and I'm gonna tell you as + + + align:start position:0% +getting there and I'm gonna tell you as +much as I can about it when we get there + + align:start position:0% +much as I can about it when we get there + + + align:start position:0% +much as I can about it when we get there +okay so that's those are pretty standard + + align:start position:0% +okay so that's those are pretty standard + + + align:start position:0% +okay so that's those are pretty standard +cases M equals N and greater than them M + + align:start position:0% +cases M equals N and greater than them M + + + align:start position:0% +cases M equals N and greater than them M +less than n but not crazy okay now let + + align:start position:0% +less than n but not crazy okay now let + + + align:start position:0% +less than n but not crazy okay now let +me the second board will have like more + + align:start position:0% +me the second board will have like more + + + align:start position:0% +me the second board will have like more +difficult problems where usually because + + align:start position:0% +difficult problems where usually because + + + align:start position:0% +difficult problems where usually because +they're nearly singular in some way the + + align:start position:0% +they're nearly singular in some way the + + + align:start position:0% +they're nearly singular in some way the +columns are nearly dependent okay so + + align:start position:0% +columns are nearly dependent okay so + + + align:start position:0% +columns are nearly dependent okay so +look for that would be the columns in + + align:start position:0% +look for that would be the columns in + + + align:start position:0% +look for that would be the columns in +bad condition you just picked a terrible + + align:start position:0% +bad condition you just picked a terrible + + + align:start position:0% +bad condition you just picked a terrible +basis or nature did or somehow you've + + align:start position:0% +basis or nature did or somehow you've + + + align:start position:0% +basis or nature did or somehow you've +got a matrix a whose columns are + + align:start position:0% +got a matrix a whose columns are + + + align:start position:0% +got a matrix a whose columns are +virtually dependent almost linearly + + align:start position:0% +virtually dependent almost linearly + + + align:start position:0% +virtually dependent almost linearly +dependent the inverse matrix is really + + align:start position:0% +dependent the inverse matrix is really + + + align:start position:0% +dependent the inverse matrix is really +but it exists then that's when you you + + align:start position:0% +but it exists then that's when you you + + + align:start position:0% +but it exists then that's when you you +go in and you fix the columns you + + align:start position:0% +go in and you fix the columns you + + + align:start position:0% +go in and you fix the columns you +orthogonalize columns instead of + + align:start position:0% +orthogonalize columns instead of + + + align:start position:0% +orthogonalize columns instead of +accepting the columns a 1 a 2 up to a n + + align:start position:0% +accepting the columns a 1 a 2 up to a n + + + align:start position:0% +accepting the columns a 1 a 2 up to a n +of the given matrix you go in and you + + align:start position:0% +of the given matrix you go in and you + + + align:start position:0% +of the given matrix you go in and you +find orthonormal column vectors in that + + align:start position:0% +find orthonormal column vectors in that + + + align:start position:0% +find orthonormal column vectors in that +column space an orthonormal basis Q 1 to + + align:start position:0% +column space an orthonormal basis Q 1 to + + + align:start position:0% +column space an orthonormal basis Q 1 to +Q n and the two are connected by + + align:start position:0% +Q n and the two are connected by + + + align:start position:0% +Q n and the two are connected by +gram-schmidt and the famous matrix + + align:start position:0% +gram-schmidt and the famous matrix + + + align:start position:0% +gram-schmidt and the famous matrix +statement of gram-schmidt is here are + + align:start position:0% +statement of gram-schmidt is here are + + + align:start position:0% +statement of gram-schmidt is here are +the columns of a here are the columns of + + align:start position:0% +the columns of a here are the columns of + + + align:start position:0% +the columns of a here are the columns of +Q and there's a triangular matrix that + + align:start position:0% +Q and there's a triangular matrix that + + + align:start position:0% +Q and there's a triangular matrix that +connects the two so that is a central + + align:start position:0% +connects the two so that is a central + + + align:start position:0% +connects the two so that is a central +topic gram-schmidt in that idea of + + align:start position:0% +topic gram-schmidt in that idea of + + + align:start position:0% +topic gram-schmidt in that idea of +orthogonal Ising it just appears + + align:start position:0% +orthogonal Ising it just appears + + + align:start position:0% +orthogonal Ising it just appears +everywhere pairs all over course six in + + align:start position:0% +everywhere pairs all over course six in + + + align:start position:0% +everywhere pairs all over course six in +many many situations with different + + align:start position:0% +many many situations with different + + + align:start position:0% +many many situations with different +names so that I'm sort of saving a + + align:start position:0% +names so that I'm sort of saving a + + + align:start position:0% +names so that I'm sort of saving a +little bit till next time and let me + + align:start position:0% +little bit till next time and let me + + + align:start position:0% +little bit till next time and let me +tell you why because just the + + align:start position:0% +tell you why because just the + + + align:start position:0% +tell you why because just the +organization of gram-schmidt is + + align:start position:0% +organization of gram-schmidt is + + + align:start position:0% +organization of gram-schmidt is +interesting so gram-schmidt you could do + + align:start position:0% +interesting so gram-schmidt you could do + + + align:start position:0% +interesting so gram-schmidt you could do +the normal way so that's what I teach in + + align:start position:0% +the normal way so that's what I teach in + + + align:start position:0% +the normal way so that's what I teach in +1806 just just take every column as it + + align:start position:0% +1806 just just take every column as it + + + align:start position:0% +1806 just just take every column as it +comes subtract off projections onto + + align:start position:0% +comes subtract off projections onto + + + align:start position:0% +comes subtract off projections onto +their previous stuff get it orthogonal + + align:start position:0% +their previous stuff get it orthogonal + + + align:start position:0% +their previous stuff get it orthogonal +to the previous guys normalize it to be + + align:start position:0% +to the previous guys normalize it to be + + + align:start position:0% +to the previous guys normalize it to be +a unit vector then you've got that + + align:start position:0% +a unit vector then you've got that + + + align:start position:0% +a unit vector then you've got that +column go on sorry say that again and + + align:start position:0% +column go on sorry say that again and + + + align:start position:0% +column go on sorry say that again and +then I'll say it again two days from now + + align:start position:0% +then I'll say it again two days from now + + + align:start position:0% +then I'll say it again two days from now +so gram-schmidt the idea is you take the + + align:start position:0% +so gram-schmidt the idea is you take the + + + align:start position:0% +so gram-schmidt the idea is you take the +columns you you say the second column is + + align:start position:0% +columns you you say the second column is + + + align:start position:0% +columns you you say the second column is +some common second orthogonal vector Q 2 + + align:start position:0% +some common second orthogonal vector Q 2 + + + align:start position:0% +some common second orthogonal vector Q 2 +will be some combination of columns one + + align:start position:0% +will be some combination of columns one + + + align:start position:0% +will be some combination of columns one +and two orthogonal to the first ya + + align:start position:0% +and two orthogonal to the first ya + + + align:start position:0% +and two orthogonal to the first ya +what's lust to do and and there's + + align:start position:0% +what's lust to do and and there's + + + align:start position:0% +what's lust to do and and there's +another order which is really + + align:start position:0% +another order which is really + + + align:start position:0% +another order which is really +the better order to do gram-schmidt and + + align:start position:0% +the better order to do gram-schmidt and + + + align:start position:0% +the better order to do gram-schmidt and +it allows you to do column pivoting so + + align:start position:0% +it allows you to do column pivoting so + + + align:start position:0% +it allows you to do column pivoting so +this is my topic for next time to see + + align:start position:0% +this is my topic for next time to see + + + align:start position:0% +this is my topic for next time to see +gram-schmidt more carefully right + + align:start position:0% +gram-schmidt more carefully right + + + align:start position:0% +gram-schmidt more carefully right +okay yeah column pivoting means you + + align:start position:0% +okay yeah column pivoting means you + + + align:start position:0% +okay yeah column pivoting means you +allow yourself to take the you the + + align:start position:0% +allow yourself to take the you the + + + align:start position:0% +allow yourself to take the you the +columns might not come in a good order + + align:start position:0% +columns might not come in a good order + + + align:start position:0% +columns might not come in a good order +so you allow yourself to reorder them we + + align:start position:0% +so you allow yourself to reorder them we + + + align:start position:0% +so you allow yourself to reorder them we +know that you have to do that for + + align:start position:0% +know that you have to do that for + + + align:start position:0% +know that you have to do that for +elimination right and in the elimination + + align:start position:0% +elimination right and in the elimination + + + align:start position:0% +elimination right and in the elimination +it would be rows so elimination we would + + align:start position:0% +it would be rows so elimination we would + + + align:start position:0% +it would be rows so elimination we would +have a the matrix a and its we take the + + align:start position:0% +have a the matrix a and its we take the + + + align:start position:0% +have a the matrix a and its we take the +first row as the first pivot row and + + align:start position:0% +first row as the first pivot row and + + + align:start position:0% +first row as the first pivot row and +then the second row and then the third + + align:start position:0% +then the second row and then the third + + + align:start position:0% +then the second row and then the third +row but if the pivot is so that if the + + align:start position:0% +row but if the pivot is so that if the + + + align:start position:0% +row but if the pivot is so that if the +pivot is too small and reorder the rows + + align:start position:0% +pivot is too small and reorder the rows + + + align:start position:0% +pivot is too small and reorder the rows +so it's it's its row ordering that comes + + align:start position:0% +so it's it's its row ordering that comes + + + align:start position:0% +so it's it's its row ordering that comes +up in elimination and you well MATLAB + + align:start position:0% +up in elimination and you well MATLAB + + + align:start position:0% +up in elimination and you well MATLAB +just systematically says okay that's the + + align:start position:0% +just systematically says okay that's the + + + align:start position:0% +just systematically says okay that's the +pivot that's coming up the third pivot + + align:start position:0% +pivot that's coming up the third pivot + + + align:start position:0% +pivot that's coming up the third pivot +comes up out of the third row but MATLAB + + align:start position:0% +comes up out of the third row but MATLAB + + + align:start position:0% +comes up out of the third row but MATLAB +says look down that whole third column + + align:start position:0% +says look down that whole third column + + + align:start position:0% +says look down that whole third column +for a better pivot a bigger pivot switch + + align:start position:0% +for a better pivot a bigger pivot switch + + + align:start position:0% +for a better pivot a bigger pivot switch +do we do a row exchange so there are + + align:start position:0% +do we do a row exchange so there are + + + align:start position:0% +do we do a row exchange so there are +lots of permutations then you end up + + align:start position:0% +lots of permutations then you end up + + + align:start position:0% +lots of permutations then you end up +with a something there that permutes the + + align:start position:0% +with a something there that permutes the + + + align:start position:0% +with a something there that permutes the +rows and then that gets factored into + + align:start position:0% +rows and then that gets factored into + + + align:start position:0% +rows and then that gets factored into +Leu so I'm saying something that about + + align:start position:0% +Leu so I'm saying something that about + + + align:start position:0% +Leu so I'm saying something that about +elimination that that just sort of side + + align:start position:0% +elimination that that just sort of side + + + align:start position:0% +elimination that that just sort of side +comment that you you would never do + + align:start position:0% +comment that you you would never do + + + align:start position:0% +comment that you you would never do +elimination without considering the + + align:start position:0% +elimination without considering the + + + align:start position:0% +elimination without considering the +possibility of row exchanges and then + + align:start position:0% +possibility of row exchanges and then + + + align:start position:0% +possibility of row exchanges and then +this is + + align:start position:0% + + + + align:start position:0% + +gram-schmidt orthogonalization so this + + align:start position:0% +gram-schmidt orthogonalization so this + + + align:start position:0% +gram-schmidt orthogonalization so this +is the Lu world here's the QR world and + + align:start position:0% +is the Lu world here's the QR world and + + + align:start position:0% +is the Lu world here's the QR world and +here it happens to be columns that + + align:start position:0% +here it happens to be columns that + + + align:start position:0% +here it happens to be columns that +you're commuting so that's coming that + + align:start position:0% +you're commuting so that's coming that + + + align:start position:0% +you're commuting so that's coming that +this is section 2.2 but there's more a + + align:start position:0% +this is section 2.2 but there's more a + + + align:start position:0% +this is section 2.2 but there's more a +2.2 has quite a bit in it including + + align:start position:0% +2.2 has quite a bit in it including + + + align:start position:0% +2.2 has quite a bit in it including +number 0 the pseudo-inverse and + + align:start position:0% +number 0 the pseudo-inverse and + + + align:start position:0% +number 0 the pseudo-inverse and +including some of these things actually + + align:start position:0% +including some of these things actually + + + align:start position:0% +including some of these things actually +this will be also in 2.0 and maybe this + + align:start position:0% +this will be also in 2.0 and maybe this + + + align:start position:0% +this will be also in 2.0 and maybe this +is what I'm like saying more about today + + align:start position:0% +is what I'm like saying more about today + + + align:start position:0% +is what I'm like saying more about today +so this would be a put a little star for + + align:start position:0% +so this would be a put a little star for + + + align:start position:0% +so this would be a put a little star for +today here what do you do so this is a + + align:start position:0% +today here what do you do so this is a + + + align:start position:0% +today here what do you do so this is a +case where the matrix is nearly singular + + align:start position:0% +case where the matrix is nearly singular + + + align:start position:0% +case where the matrix is nearly singular +you're you're in danger its inverse is + + align:start position:0% +you're you're in danger its inverse is + + + align:start position:0% +you're you're in danger its inverse is +gonna be big unreasonably big and I + + align:start position:0% +gonna be big unreasonably big and I + + + align:start position:0% +gonna be big unreasonably big and I +wrote inverse problems there because + + align:start position:0% +wrote inverse problems there because + + + align:start position:0% +wrote inverse problems there because +inverse problem is that's a type of + + align:start position:0% + + + + align:start position:0% + +problem that you need application that + + align:start position:0% +problem that you need application that + + + align:start position:0% +problem that you need application that +you often need to solve or that you the + + align:start position:0% +you often need to solve or that you the + + + align:start position:0% +you often need to solve or that you the +engineering and and science have to + + align:start position:0% +engineering and and science have to + + + align:start position:0% +engineering and and science have to +solve + + align:start position:0% +solve + + + align:start position:0% +solve +so I'll just say a little more about + + align:start position:0% +so I'll just say a little more about + + + align:start position:0% +so I'll just say a little more about +that but that's a typical application in + + align:start position:0% +that but that's a typical application in + + + align:start position:0% +that but that's a typical application in +which you get your near singular your + + align:start position:0% +which you get your near singular your + + + align:start position:0% +which you get your near singular your +matrix isn't good enough to invert well + + align:start position:0% +matrix isn't good enough to invert well + + + align:start position:0% +matrix isn't good enough to invert well +of course you could over say well I'll + + align:start position:0% +of course you could over say well I'll + + + align:start position:0% +of course you could over say well I'll +just use the pseudo inverse but that's + + align:start position:0% +just use the pseudo inverse but that's + + + align:start position:0% +just use the pseudo inverse but that's +numerically that's like cheating you've + + align:start position:0% +numerically that's like cheating you've + + + align:start position:0% +numerically that's like cheating you've +got a you got to get in there and do + + align:start position:0% +got a you got to get in there and do + + + align:start position:0% +got a you got to get in there and do +something about it + + align:start position:0% +something about it + + + align:start position:0% +something about it +so inverse problems would be examples + + align:start position:0% + + + + align:start position:0% + +actually as I write that I think that + + align:start position:0% +actually as I write that I think that + + + align:start position:0% +actually as I write that I think that +would be a topic that I should add that + + align:start position:0% +would be a topic that I should add that + + + align:start position:0% +would be a topic that I should add that +to the list of potential topics for a + + align:start position:0% +to the list of potential topics for a + + + align:start position:0% +to the list of potential topics for a +for a three week project to look up a + + align:start position:0% +for a three week project to look up a + + + align:start position:0% +for a three week project to look up a +book on inverse problems so what do I + + align:start position:0% +book on inverse problems so what do I + + + align:start position:0% +book on inverse problems so what do I +mean by the inverse problem I'll just + + align:start position:0% +mean by the inverse problem I'll just + + + align:start position:0% +mean by the inverse problem I'll just +finish this thought where of what's an + + align:start position:0% +finish this thought where of what's an + + + align:start position:0% +finish this thought where of what's an +inverse problem typically you you you + + align:start position:0% +inverse problem typically you you you + + + align:start position:0% +inverse problem typically you you you +know about their system say a network + + align:start position:0% +know about their system say a network + + + align:start position:0% +know about their system say a network +like trying to + + align:start position:0% +like trying to + + + align:start position:0% +like trying to +RLC Network and you give it a voltage or + + align:start position:0% +RLC Network and you give it a voltage or + + + align:start position:0% +RLC Network and you give it a voltage or +a current you give it an input and you + + align:start position:0% +a current you give it an input and you + + + align:start position:0% +a current you give it an input and you +find the output you find out what + + align:start position:0% +find the output you find out what + + + align:start position:0% +find the output you find out what +current flows what the voltages are but + + align:start position:0% +current flows what the voltages are but + + + align:start position:0% +current flows what the voltages are but +inverse problems are suppose you know + + align:start position:0% +inverse problems are suppose you know + + + align:start position:0% +inverse problems are suppose you know +the response to different voltages what + + align:start position:0% +the response to different voltages what + + + align:start position:0% +the response to different voltages what +were the what was the network you see + + align:start position:0% +were the what was the network you see + + + align:start position:0% +were the what was the network you see +that the problem let me say it again + + align:start position:0% +that the problem let me say it again + + + align:start position:0% +that the problem let me say it again +discover what the network is from its + + align:start position:0% +discover what the network is from its + + + align:start position:0% +discover what the network is from its +outputs so that turns out to typically + + align:start position:0% +outputs so that turns out to typically + + + align:start position:0% +outputs so that turns out to typically +be a problem that gives nearly singular + + align:start position:0% +be a problem that gives nearly singular + + + align:start position:0% +be a problem that gives nearly singular +matrices that's that's a difficult + + align:start position:0% +matrices that's that's a difficult + + + align:start position:0% +matrices that's that's a difficult +problem you sort of near a lot of nearby + + align:start position:0% +problem you sort of near a lot of nearby + + + align:start position:0% +problem you sort of near a lot of nearby +networks would give virtually the same + + align:start position:0% +networks would give virtually the same + + + align:start position:0% +networks would give virtually the same +output so so you have a matrix that's + + align:start position:0% +output so so you have a matrix that's + + + align:start position:0% +output so so you have a matrix that's +nearly singular it's got singular values + + align:start position:0% +nearly singular it's got singular values + + + align:start position:0% +nearly singular it's got singular values +very close to zero what do you do then + + align:start position:0% +very close to zero what do you do then + + + align:start position:0% +very close to zero what do you do then +well the world of inverse problems + + align:start position:0% +well the world of inverse problems + + + align:start position:0% +well the world of inverse problems +thinks of adding a penalty term some + + align:start position:0% +thinks of adding a penalty term some + + + align:start position:0% +thinks of adding a penalty term some +kind of a penalty term when I minimize + + align:start position:0% +kind of a penalty term when I minimize + + + align:start position:0% +kind of a penalty term when I minimize +this thing just by itself in the usual + + align:start position:0% +this thing just by itself in the usual + + + align:start position:0% +this thing just by itself in the usual +way a transpose a has a giant inverse + + align:start position:0% +way a transpose a has a giant inverse + + + align:start position:0% +way a transpose a has a giant inverse +the matrix a is badly conditioned it + + align:start position:0% +the matrix a is badly conditioned it + + + align:start position:0% +the matrix a is badly conditioned it +takes vectors Verge almost to zero so + + align:start position:0% +takes vectors Verge almost to zero so + + + align:start position:0% +takes vectors Verge almost to zero so +that a transpose a is has got a giant + + align:start position:0% +that a transpose a is has got a giant + + + align:start position:0% +that a transpose a is has got a giant +inverse and you're you're at risk of + + align:start position:0% +inverse and you're you're at risk of + + + align:start position:0% +inverse and you're you're at risk of +losing everything to roundoff so you + + align:start position:0% +losing everything to roundoff so you + + + align:start position:0% +losing everything to roundoff so you +this is the solution you could call it a + + align:start position:0% +this is the solution you could call it a + + + align:start position:0% +this is the solution you could call it a +kind of cheap solution but it's + + align:start position:0% +kind of cheap solution but it's + + + align:start position:0% +kind of cheap solution but it's +everybody uses it so I won't put that + + align:start position:0% +everybody uses it so I won't put that + + + align:start position:0% +everybody uses it so I won't put that +word on videotape but that that sort of + + align:start position:0% +word on videotape but that that sort of + + + align:start position:0% +word on videotape but that that sort of +resolves a problem but then the question + + align:start position:0% +resolves a problem but then the question + + + align:start position:0% +resolves a problem but then the question +it it shifts a problem anyway - what + + align:start position:0% +it it shifts a problem anyway - what + + + align:start position:0% +it it shifts a problem anyway - what +number what should be the penalty how + + align:start position:0% +number what should be the penalty how + + + align:start position:0% +number what should be the penalty how +much should you penalize it you see as + + align:start position:0% +much should you penalize it you see as + + + align:start position:0% +much should you penalize it you see as +you as you buy adding that + + align:start position:0% +you as you buy adding that + + + align:start position:0% +you as you buy adding that +you're gonna make it invertible and if + + align:start position:0% +you're gonna make it invertible and if + + + align:start position:0% +you're gonna make it invertible and if +you make this bigger and bigger and + + align:start position:0% +you make this bigger and bigger and + + + align:start position:0% +you make this bigger and bigger and +bigger it's more and more well + + align:start position:0% +bigger it's more and more well + + + align:start position:0% +bigger it's more and more well +conditioned it resolves the trouble here + + align:start position:0% +conditioned it resolves the trouble here + + + align:start position:0% +conditioned it resolves the trouble here +and I'm so this is like today I'm gonna + + align:start position:0% +and I'm so this is like today I'm gonna + + + align:start position:0% +and I'm so this is like today I'm gonna +do more with that so that I'll stop + + align:start position:0% +do more with that so that I'll stop + + + align:start position:0% +do more with that so that I'll stop +there and pick it up after saying + + align:start position:0% +there and pick it up after saying + + + align:start position:0% +there and pick it up after saying +something about 6 & 7 + + align:start position:0% +something about 6 & 7 + + + align:start position:0% +something about 6 & 7 +I hope this is helpful it was helpful to + + align:start position:0% +I hope this is helpful it was helpful to + + + align:start position:0% +I hope this is helpful it was helpful to +me certainly to to see all these + + align:start position:0% +me certainly to to see all these + + + align:start position:0% +me certainly to to see all these +possibilities and to write down sort of + + align:start position:0% +possibilities and to write down sort of + + + align:start position:0% +possibilities and to write down sort of +what you what the symptom is it's like a + + align:start position:0% +what you what the symptom is it's like a + + + align:start position:0% +what you what the symptom is it's like a +doctor like a linear equation doctor + + align:start position:0% +doctor like a linear equation doctor + + + align:start position:0% +doctor like a linear equation doctor +like you look for the symptoms and then + + align:start position:0% +like you look for the symptoms and then + + + align:start position:0% +like you look for the symptoms and then +you propose some some something at CVS + + align:start position:0% +you propose some some something at CVS + + + align:start position:0% +you propose some some something at CVS +that works or it doesn't work but you do + + align:start position:0% +that works or it doesn't work but you do + + + align:start position:0% +that works or it doesn't work but you do +something about it okay so so when the + + align:start position:0% +something about it okay so so when the + + + align:start position:0% +something about it okay so so when the +problem is too big so up to now the + + align:start position:0% +problem is too big so up to now the + + + align:start position:0% +problem is too big so up to now the +problems have not been giant out of + + align:start position:0% +problems have not been giant out of + + + align:start position:0% +problems have not been giant out of +course it's so but now when it's too big + + align:start position:0% +course it's so but now when it's too big + + + align:start position:0% +course it's so but now when it's too big +well maybe it's still in Corbett really + + align:start position:0% +well maybe it's still in Corbett really + + + align:start position:0% +well maybe it's still in Corbett really +big then this is in 2.1 so that's to + + align:start position:0% +big then this is in 2.1 so that's to + + + align:start position:0% +big then this is in 2.1 so that's to +come back to the word I could have + + align:start position:0% +come back to the word I could have + + + align:start position:0% +come back to the word I could have +written in here if I was just gonna + + align:start position:0% +written in here if I was just gonna + + + align:start position:0% +written in here if I was just gonna +write one word would be interation + + align:start position:0% +write one word would be interation + + + align:start position:0% +write one word would be interation +iterative methods meaning you take a + + align:start position:0% +iterative methods meaning you take a + + + align:start position:0% +iterative methods meaning you take a +step like well conjugate gradient method + + align:start position:0% +step like well conjugate gradient method + + + align:start position:0% +step like well conjugate gradient method +is the is the hero of iterative methods + + align:start position:0% +is the is the hero of iterative methods + + + align:start position:0% +is the is the hero of iterative methods +and then there that name I raced is + + align:start position:0% +and then there that name I raced is + + + align:start position:0% +and then there that name I raced is +Krylov and there are other names + + align:start position:0% +Krylov and there are other names + + + align:start position:0% +Krylov and there are other names +associated with iterative methods so + + align:start position:0% +associated with iterative methods so + + + align:start position:0% +associated with iterative methods so +that's the section that we passed over + + align:start position:0% +that's the section that we passed over + + + align:start position:0% +that's the section that we passed over +just just to get rolling but we'll come + + align:start position:0% +just just to get rolling but we'll come + + + align:start position:0% +just just to get rolling but we'll come +back to so then that that one you never + + align:start position:0% +back to so then that that one you never + + + align:start position:0% +back to so then that that one you never +get the exact answer but you get closer + + align:start position:0% +get the exact answer but you get closer + + + align:start position:0% +get the exact answer but you get closer +and closer + + align:start position:0% +and closer + + + align:start position:0% +and closer +if the iterative method is successful + + align:start position:0% +if the iterative method is successful + + + align:start position:0% +if the iterative method is successful +like conjugate gradients you get + + align:start position:0% +like conjugate gradients you get + + + align:start position:0% +like conjugate gradients you get +pretty close pretty fast and then you + + align:start position:0% +pretty close pretty fast and then you + + + align:start position:0% +pretty close pretty fast and then you +say okay I'll take it + + align:start position:0% +say okay I'll take it + + + align:start position:0% +say okay I'll take it +and then finally way too big like no + + align:start position:0% +and then finally way too big like no + + + align:start position:0% +and then finally way too big like no +we're not in core just your matrix you + + align:start position:0% +we're not in core just your matrix you + + + align:start position:0% +we're not in core just your matrix you +just have a giant giant problem which of + + align:start position:0% +just have a giant giant problem which of + + + align:start position:0% +just have a giant giant problem which of +course is happening these days and then + + align:start position:0% +course is happening these days and then + + + align:start position:0% +course is happening these days and then +one way to do it is your matrix you I + + align:start position:0% +one way to do it is your matrix you I + + + align:start position:0% +one way to do it is your matrix you I +mean you you can't even look at the + + align:start position:0% +mean you you can't even look at the + + + align:start position:0% +mean you you can't even look at the +matrix a much less a transpose a + + align:start position:0% +matrix a much less a transpose a + + + align:start position:0% +matrix a much less a transpose a +transpose a would be like unthinkable + + align:start position:0% +transpose a would be like unthinkable + + + align:start position:0% +transpose a would be like unthinkable +you couldn't do it in in the in the in a + + align:start position:0% +you couldn't do it in in the in the in a + + + align:start position:0% +you couldn't do it in in the in the in a +year so randomized linear algebra has + + align:start position:0% +year so randomized linear algebra has + + + align:start position:0% +year so randomized linear algebra has +popped up and that the idea there which + + align:start position:0% +popped up and that the idea there which + + + align:start position:0% +popped up and that the idea there which +will see is to use probability to sample + + align:start position:0% +will see is to use probability to sample + + + align:start position:0% +will see is to use probability to sample +the matrix and work with your samples so + + align:start position:0% +the matrix and work with your samples so + + + align:start position:0% +the matrix and work with your samples so +if the matrix is reasonably it is not is + + align:start position:0% +if the matrix is reasonably it is not is + + + align:start position:0% +if the matrix is reasonably it is not is +too way too big but not too crazy so to + + align:start position:0% +too way too big but not too crazy so to + + + align:start position:0% +too way too big but not too crazy so to +speak then you could sample the columns + + align:start position:0% +speak then you could sample the columns + + + align:start position:0% +speak then you could sample the columns +and the rows and get a an answer from + + align:start position:0% +and the rows and get a an answer from + + + align:start position:0% +and the rows and get a an answer from +the sample see if I sample the columns + + align:start position:0% +the sample see if I sample the columns + + + align:start position:0% +the sample see if I sample the columns +of a matrix I'm getting something so + + align:start position:0% +of a matrix I'm getting something so + + + align:start position:0% +of a matrix I'm getting something so +said what is sampling mean let me just + + align:start position:0% +said what is sampling mean let me just + + + align:start position:0% +said what is sampling mean let me just +complete this say say add add a little + + align:start position:0% +complete this say say add add a little + + + align:start position:0% +complete this say say add add a little +to this sample of matrix so I have a + + align:start position:0% +to this sample of matrix so I have a + + + align:start position:0% +to this sample of matrix so I have a +giant matrix a might be sparse of course + + align:start position:0% +giant matrix a might be sparse of course + + + align:start position:0% +giant matrix a might be sparse of course +I didn't distinguish over there sparse + + align:start position:0% +I didn't distinguish over there sparse + + + align:start position:0% +I didn't distinguish over there sparse +things that would be another thing so if + + align:start position:0% +things that would be another thing so if + + + align:start position:0% +things that would be another thing so if +I just take a random X random X's more + + align:start position:0% +I just take a random X random X's more + + + align:start position:0% +I just take a random X random X's more +than one but not the full n dimensions + + align:start position:0% +than one but not the full n dimensions + + + align:start position:0% +than one but not the full n dimensions +those will give me random guys in the + + align:start position:0% +those will give me random guys in the + + + align:start position:0% +those will give me random guys in the +column space and if the matrix is kind + + align:start position:0% +column space and if the matrix is kind + + + align:start position:0% +column space and if the matrix is kind +of reasonable those will give me it + + align:start position:0% +of reasonable those will give me it + + + align:start position:0% +of reasonable those will give me it +won't take too many to have a pretty + + align:start position:0% +won't take too many to have a pretty + + + align:start position:0% +won't take too many to have a pretty +reasonable I + + align:start position:0% +reasonable I + + + align:start position:0% +reasonable I +of what that column space is like and + + align:start position:0% +of what that column space is like and + + + align:start position:0% +of what that column space is like and +and with its right-hand side so so this + + align:start position:0% +and with its right-hand side so so this + + + align:start position:0% +and with its right-hand side so so this +world of randomized linear algebra has + + align:start position:0% +world of randomized linear algebra has + + + align:start position:0% +world of randomized linear algebra has +grown because it had to and of course + + align:start position:0% +grown because it had to and of course + + + align:start position:0% +grown because it had to and of course +you any statement it can never say for + + align:start position:0% +you any statement it can never say for + + + align:start position:0% +you any statement it can never say for +sure you're gonna get the right answer + + align:start position:0% +sure you're gonna get the right answer + + + align:start position:0% +sure you're gonna get the right answer +but but but so using the inequalities of + + align:start position:0% +but but but so using the inequalities of + + + align:start position:0% +but but but so using the inequalities of +probability you can often say that + + align:start position:0% +probability you can often say that + + + align:start position:0% +probability you can often say that +you're the chance of being way off is + + align:start position:0% +you're the chance of being way off is + + + align:start position:0% +you're the chance of being way off is +you know less than one in two to the 20s + + align:start position:0% +you know less than one in two to the 20s + + + align:start position:0% +you know less than one in two to the 20s +or something so so the answer is in + + align:start position:0% +or something so so the answer is in + + + align:start position:0% +or something so so the answer is in +reality you you get that you get a good + + align:start position:0% +reality you you get that you get a good + + + align:start position:0% +reality you you get that you get a good +answer okay that is like the end of this + + align:start position:0% +answer okay that is like the end of this + + + align:start position:0% +answer okay that is like the end of this +chapter two point four so here this is + + align:start position:0% +chapter two point four so here this is + + + align:start position:0% +chapter two point four so here this is +all chapter two really the the iterative + + align:start position:0% +all chapter two really the the iterative + + + align:start position:0% +all chapter two really the the iterative +methods in to one all that most of this + + align:start position:0% +methods in to one all that most of this + + + align:start position:0% +methods in to one all that most of this +is in two point two big is two point + + align:start position:0% +is in two point two big is two point + + + align:start position:0% +is in two point two big is two point +three and then really big is randomized + + align:start position:0% +three and then really big is randomized + + + align:start position:0% +three and then really big is randomized +in two point four okay so now where are + + align:start position:0% +in two point four okay so now where are + + + align:start position:0% +in two point four okay so now where are +we + + align:start position:0% +we + + + align:start position:0% +we +you're going to let me know or not if + + align:start position:0% +you're going to let me know or not if + + + align:start position:0% +you're going to let me know or not if +this is useful the C but you're sort of + + align:start position:0% +this is useful the C but you're sort of + + + align:start position:0% +this is useful the C but you're sort of +you sort of see what what are real-life + + align:start position:0% +you sort of see what what are real-life + + + align:start position:0% +you sort of see what what are real-life +problems and of course we're highly + + align:start position:0% +problems and of course we're highly + + + align:start position:0% +problems and of course we're highly +especially interested in getting to the + + align:start position:0% +especially interested in getting to the + + + align:start position:0% +especially interested in getting to the +deep learning examples which are + + align:start position:0% +deep learning examples which are + + + align:start position:0% +deep learning examples which are +underdetermined yeah then when you're + + align:start position:0% +underdetermined yeah then when you're + + + align:start position:0% +underdetermined yeah then when you're +under determined you've got many + + align:start position:0% +under determined you've got many + + + align:start position:0% +under determined you've got many +solutions and the question is which one + + align:start position:0% +solutions and the question is which one + + + align:start position:0% +solutions and the question is which one +is a good one and in deep learning I + + align:start position:0% +is a good one and in deep learning I + + + align:start position:0% +is a good one and in deep learning I +just I can't resist saying another word + + align:start position:0% +just I can't resist saying another word + + + align:start position:0% +just I can't resist saying another word +you hope so there are many solutions + + align:start position:0% +you hope so there are many solutions + + + align:start position:0% +you hope so there are many solutions +what to do well your your pick some + + align:start position:0% +what to do well your your pick some + + + align:start position:0% +what to do well your your pick some +algorithm like steepest descent which is + + align:start position:0% +algorithm like steepest descent which is + + + align:start position:0% +algorithm like steepest descent which is +going to find a solution so you're like + + align:start position:0% +going to find a solution so you're like + + + align:start position:0% +going to find a solution so you're like +you hope it's a good one and what is a + + align:start position:0% +you hope it's a good one and what is a + + + align:start position:0% +you hope it's a good one and what is a +good one mean verses are not good one + + align:start position:0% +good one mean verses are not good one + + + align:start position:0% +good one mean verses are not good one +they're all solutions a good one means + + align:start position:0% +they're all solutions a good one means + + + align:start position:0% +they're all solutions a good one means +that when you apply it to the test + + align:start position:0% +that when you apply it to the test + + + align:start position:0% +that when you apply it to the test +data that you haven't yet seen it gives + + align:start position:0% +data that you haven't yet seen it gives + + + align:start position:0% +data that you haven't yet seen it gives +good results on the test data you've + + align:start position:0% +good results on the test data you've + + + align:start position:0% +good results on the test data you've +really the solution has learned + + align:start position:0% +really the solution has learned + + + align:start position:0% +really the solution has learned +something from the training data and it + + align:start position:0% +something from the training data and it + + + align:start position:0% +something from the training data and it +works on the test data so that's the the + + align:start position:0% +works on the test data so that's the the + + + align:start position:0% +works on the test data so that's the the +the big question in deep learning how + + align:start position:0% +the big question in deep learning how + + + align:start position:0% +the big question in deep learning how +does it happen that you by doing + + align:start position:0% +does it happen that you by doing + + + align:start position:0% +does it happen that you by doing +gradient descent or whatever algorithm + + align:start position:0% +gradient descent or whatever algorithm + + + align:start position:0% +gradient descent or whatever algorithm +how does that algorithm sort of bias the + + align:start position:0% +how does that algorithm sort of bias the + + + align:start position:0% +how does that algorithm sort of bias the +solution it's called implicit bias how + + align:start position:0% +solution it's called implicit bias how + + + align:start position:0% +solution it's called implicit bias how +does that algorithm bias a solution + + align:start position:0% +does that algorithm bias a solution + + + align:start position:0% +does that algorithm bias a solution +toward one toward a solution that's that + + align:start position:0% +toward one toward a solution that's that + + + align:start position:0% +toward one toward a solution that's that +generalizes that works on test data and + + align:start position:0% +generalizes that works on test data and + + + align:start position:0% +generalizes that works on test data and +you can think of algorithms which would + + align:start position:0% +you can think of algorithms which would + + + align:start position:0% +you can think of algorithms which would +give it approach a solution that did not + + align:start position:0% +give it approach a solution that did not + + + align:start position:0% +give it approach a solution that did not +work on test data so that's what you + + align:start position:0% +work on test data so that's what you + + + align:start position:0% +work on test data so that's what you +want to stay away from you want the ones + + align:start position:0% +want to stay away from you want the ones + + + align:start position:0% +want to stay away from you want the ones +that work so there's very deep math + + align:start position:0% +that work so there's very deep math + + + align:start position:0% +that work so there's very deep math +questions there which are kind of knew + + align:start position:0% +questions there which are kind of knew + + + align:start position:0% +questions there which are kind of knew +they didn't arise until they did and + + align:start position:0% +they didn't arise until they did and + + + align:start position:0% +they didn't arise until they did and +will try to save some of what's what's + + align:start position:0% +will try to save some of what's what's + + + align:start position:0% +will try to save some of what's what's +being understood okay can I focus now on + + align:start position:0% +being understood okay can I focus now on + + + align:start position:0% +being understood okay can I focus now on +for the rest the rest of today on this + + align:start position:0% +for the rest the rest of today on this + + + align:start position:0% +for the rest the rest of today on this +case when the matrix is nearly singular + + align:start position:0% +case when the matrix is nearly singular + + + align:start position:0% +case when the matrix is nearly singular +so you could apply elimination but it + + align:start position:0% +so you could apply elimination but it + + + align:start position:0% +so you could apply elimination but it +would give a poor result but so the then + + align:start position:0% +would give a poor result but so the then + + + align:start position:0% +would give a poor result but so the then +one solution is well yeah + + align:start position:0% +one solution is well yeah + + + align:start position:0% +one solution is well yeah +one solution is the SVD I only mentioned + + align:start position:0% +one solution is the SVD I only mentioned + + + align:start position:0% +one solution is the SVD I only mentioned +the SVD here as an algorithm but of + + align:start position:0% +the SVD here as an algorithm but of + + + align:start position:0% +the SVD here as an algorithm but of +course it is the SVD would give you + + align:start position:0% +course it is the SVD would give you + + + align:start position:0% +course it is the SVD would give you +gives you gives you an answer boy where + + align:start position:0% +gives you gives you an answer boy where + + + align:start position:0% +gives you gives you an answer boy where +should that have gone well space over + + align:start position:0% +should that have gone well space over + + + align:start position:0% +should that have gone well space over +here the SVD so that produces you you + + align:start position:0% +here the SVD so that produces you you + + + align:start position:0% +here the SVD so that produces you you +have a equal u Sigma V transpose and + + align:start position:0% +have a equal u Sigma V transpose and + + + align:start position:0% +have a equal u Sigma V transpose and +then a inverse is V Sigma inverse u + + align:start position:0% +then a inverse is V Sigma inverse u + + + align:start position:0% +then a inverse is V Sigma inverse u +transpose okay + + align:start position:0% + + + + align:start position:0% + +so we're in the case here we're talking + + align:start position:0% +so we're in the case here we're talking + + + align:start position:0% +so we're in the case here we're talking +about number five nearly singular where + + align:start position:0% +about number five nearly singular where + + + align:start position:0% +about number five nearly singular where +Sigma has some very small singular + + align:start position:0% +Sigma has some very small singular + + + align:start position:0% +Sigma has some very small singular +values then Sigma inverse has some very + + align:start position:0% +values then Sigma inverse has some very + + + align:start position:0% +values then Sigma inverse has some very +big singular values so this is you're + + align:start position:0% +big singular values so this is you're + + + align:start position:0% +big singular values so this is you're +really in kind of wild wild territory + + align:start position:0% +really in kind of wild wild territory + + + align:start position:0% +really in kind of wild wild territory +here with with very big inverses so that + + align:start position:0% +here with with very big inverses so that + + + align:start position:0% +here with with very big inverses so that +would that would be one way to do it but + + align:start position:0% +would that would be one way to do it but + + + align:start position:0% +would that would be one way to do it but +this is a this is a way to regularize + + align:start position:0% +this is a this is a way to regularize + + + align:start position:0% +this is a this is a way to regularize +the problem so let's just pay attention + + align:start position:0% +the problem so let's just pay attention + + + align:start position:0% +the problem so let's just pay attention +to that okay okay so suppose I minimize + + align:start position:0% +to that okay okay so suppose I minimize + + + align:start position:0% +to that okay okay so suppose I minimize +the sum of ax minus B squared and Delta + + align:start position:0% +the sum of ax minus B squared and Delta + + + align:start position:0% +the sum of ax minus B squared and Delta +squared times the size of x squared and + + align:start position:0% +squared times the size of x squared and + + + align:start position:0% +squared times the size of x squared and +I'm going to use the l2 norm it's gonna + + align:start position:0% +I'm going to use the l2 norm it's gonna + + + align:start position:0% +I'm going to use the l2 norm it's gonna +be at least squares a peanut least + + align:start position:0% +be at least squares a peanut least + + + align:start position:0% +be at least squares a peanut least +squares with penalty so of course it's + + align:start position:0% +squares with penalty so of course it's + + + align:start position:0% +squares with penalty so of course it's +the l2 norm here - yep okay suppose I + + align:start position:0% +the l2 norm here - yep okay suppose I + + + align:start position:0% +the l2 norm here - yep okay suppose I +solve that for a delta for some I choose + + align:start position:0% +solve that for a delta for some I choose + + + align:start position:0% +solve that for a delta for some I choose +I have to choose a delta a positive + + align:start position:0% +I have to choose a delta a positive + + + align:start position:0% +I have to choose a delta a positive +Delta and when I choose a positive Delta + + align:start position:0% +Delta and when I choose a positive Delta + + + align:start position:0% +Delta and when I choose a positive Delta +then I have a solvable problem + + align:start position:0% +then I have a solvable problem + + + align:start position:0% +then I have a solvable problem +even if this goes to zero or a does + + align:start position:0% +even if this goes to zero or a does + + + align:start position:0% +even if this goes to zero or a does +crazy things this is going to keep me + + align:start position:0% +crazy things this is going to keep me + + + align:start position:0% +crazy things this is going to keep me +away from singular in fact what equation + + align:start position:0% +away from singular in fact what equation + + + align:start position:0% +away from singular in fact what equation +does that lead to so that's a least + + align:start position:0% +does that lead to so that's a least + + + align:start position:0% +does that lead to so that's a least +squares problem with an extra penalty + + align:start position:0% +squares problem with an extra penalty + + + align:start position:0% +squares problem with an extra penalty +term so it would come I suppose let's + + align:start position:0% +term so it would come I suppose let's + + + align:start position:0% +term so it would come I suppose let's +see if I write the equations a delta I x + + align:start position:0% +see if I write the equations a delta I x + + + align:start position:0% +see if I write the equations a delta I x +equals B 0 maybe that is the least + + align:start position:0% +equals B 0 maybe that is the least + + + align:start position:0% +equals B 0 maybe that is the least +squares equation the usual normal + + align:start position:0% +squares equation the usual normal + + + align:start position:0% +squares equation the usual normal +equation for this + + align:start position:0% +equation for this + + + align:start position:0% +equation for this +augmented system because what's the + + align:start position:0% +augmented system because what's the + + + align:start position:0% +augmented system because what's the +error here this is the new big a a star + + align:start position:0% +error here this is the new big a a star + + + align:start position:0% +error here this is the new big a a star +let's say X equals this is the new B so + + align:start position:0% +let's say X equals this is the new B so + + + align:start position:0% +let's say X equals this is the new B so +if I apply least-squares to that what do + + align:start position:0% +if I apply least-squares to that what do + + + align:start position:0% +if I apply least-squares to that what do +I do I minimize the sum of squares and I + + align:start position:0% +I do I minimize the sum of squares and I + + + align:start position:0% +I do I minimize the sum of squares and I +so I'm in so least squares would + + align:start position:0% +so I'm in so least squares would + + + align:start position:0% +so I'm in so least squares would +minimize ax minus B squared that would + + align:start position:0% +minimize ax minus B squared that would + + + align:start position:0% +minimize ax minus B squared that would +be the from the first components and + + align:start position:0% +be the from the first components and + + + align:start position:0% +be the from the first components and +Delta squared x squared from the last + + align:start position:0% +Delta squared x squared from the last + + + align:start position:0% +Delta squared x squared from the last +component which is exactly what we said + + align:start position:0% +component which is exactly what we said + + + align:start position:0% +component which is exactly what we said +we were doing so in a way this is the + + align:start position:0% +we were doing so in a way this is the + + + align:start position:0% +we were doing so in a way this is the +equation that saw that the penalty + + align:start position:0% +equation that saw that the penalty + + + align:start position:0% +equation that saw that the penalty +method is solving and the question is so + + align:start position:0% +method is solving and the question is so + + + align:start position:0% +method is solving and the question is so +one question natural is watch what's + + align:start position:0% +one question natural is watch what's + + + align:start position:0% +one question natural is watch what's +your Delta B well that's that questions + + align:start position:0% +your Delta B well that's that questions + + + align:start position:0% +your Delta B well that's that questions +beyond us today that it's it's a balance + + align:start position:0% +beyond us today that it's it's a balance + + + align:start position:0% +beyond us today that it's it's a balance +of how what you can believe and how much + + align:start position:0% +of how what you can believe and how much + + + align:start position:0% +of how what you can believe and how much +noise is in the system and everything + + align:start position:0% +noise is in the system and everything + + + align:start position:0% +noise is in the system and everything +yeah choice of Delta what we could ask + + align:start position:0% +yeah choice of Delta what we could ask + + + align:start position:0% +yeah choice of Delta what we could ask +is the math question what happens as + + align:start position:0% +is the math question what happens as + + + align:start position:0% +is the math question what happens as +Delta goes to 0 so suppose I solve this + + align:start position:0% +Delta goes to 0 so suppose I solve this + + + align:start position:0% +Delta goes to 0 so suppose I solve this +problem let's see I could write it + + align:start position:0% +problem let's see I could write it + + + align:start position:0% +problem let's see I could write it +differently shall I write there what + + align:start position:0% +differently shall I write there what + + + align:start position:0% +differently shall I write there what +would be the equation here this part + + align:start position:0% +would be the equation here this part + + + align:start position:0% +would be the equation here this part +would give us the a transpose a and then + + align:start position:0% +would give us the a transpose a and then + + + align:start position:0% +would give us the a transpose a and then +this part would give us just the + + align:start position:0% +this part would give us just the + + + align:start position:0% +this part would give us just the +identity x equals a transpose B I think + + align:start position:0% +identity x equals a transpose B I think + + + align:start position:0% +identity x equals a transpose B I think +yeah wouldn't that be so really I've + + align:start position:0% +yeah wouldn't that be so really I've + + + align:start position:0% +yeah wouldn't that be so really I've +written here what that is is a star + + align:start position:0% +written here what that is is a star + + + align:start position:0% +written here what that is is a star +transpose a star that this is least + + align:start position:0% +transpose a star that this is least + + + align:start position:0% +transpose a star that this is least +squares on this gives it gives that + + align:start position:0% +squares on this gives it gives that + + + align:start position:0% +squares on this gives it gives that +equation so all of those are equivalent + + align:start position:0% +equation so all of those are equivalent + + + align:start position:0% +equation so all of those are equivalent +all of those would be equivalent + + align:start position:0% +all of those would be equivalent + + + align:start position:0% +all of those would be equivalent +statements of what the penalized problem + + align:start position:0% +statements of what the penalized problem + + + align:start position:0% +statements of what the penalized problem +is that you're solving and then the + + align:start position:0% +is that you're solving and then the + + + align:start position:0% +is that you're solving and then the +question is as Delta goes to 0 what + + align:start position:0% +question is as Delta goes to 0 what + + + align:start position:0% +question is as Delta goes to 0 what +happens of course something you're when + + align:start position:0% +happens of course something you're when + + + align:start position:0% +happens of course something you're when +Delta goes to 0 you're you're falling + + align:start position:0% +Delta goes to 0 you're you're falling + + + align:start position:0% +Delta goes to 0 you're you're falling +off the cliff something something quite + + align:start position:0% +off the cliff something something quite + + + align:start position:0% +off the cliff something something quite +different it's suddenly going to happen + + align:start position:0% +different it's suddenly going to happen + + + align:start position:0% +different it's suddenly going to happen +there maybe we could even understand + + align:start position:0% +there maybe we could even understand + + + align:start position:0% +there maybe we could even understand +this this question with a 1 by 1 matrix + + align:start position:0% +this this question with a 1 by 1 matrix + + + align:start position:0% +this this question with a 1 by 1 matrix +yeah I think this section starts with a + + align:start position:0% +yeah I think this section starts with a + + + align:start position:0% +yeah I think this section starts with a +1 by 1 suppose a is just a number okay + + align:start position:0% +1 by 1 suppose a is just a number okay + + + align:start position:0% +1 by 1 suppose a is just a number okay +maybe I'll just put that on this board + + align:start position:0% +maybe I'll just put that on this board + + + align:start position:0% +maybe I'll just put that on this board +here suppose a is just a number so what + + align:start position:0% +here suppose a is just a number so what + + + align:start position:0% +here suppose a is just a number so what +am I gonna call that number just one by + + align:start position:0% +am I gonna call that number just one by + + + align:start position:0% +am I gonna call that number just one by +one let me call it Sigma because it's + + align:start position:0% +one let me call it Sigma because it's + + + align:start position:0% +one let me call it Sigma because it's +certainly the leading singular value + + align:start position:0% +certainly the leading singular value + + + align:start position:0% +certainly the leading singular value +okay so so what's my equation that I'm + + align:start position:0% +okay so so what's my equation that I'm + + + align:start position:0% +okay so so what's my equation that I'm +solving a transpose a would be Sigma + + align:start position:0% +solving a transpose a would be Sigma + + + align:start position:0% +solving a transpose a would be Sigma +square plus Delta square one by one X + + align:start position:0% +square plus Delta square one by one X + + + align:start position:0% +square plus Delta square one by one X +should I give some subscript here I + + align:start position:0% +should I give some subscript here I + + + align:start position:0% +should I give some subscript here I +should really to do it right this is the + + align:start position:0% +should really to do it right this is the + + + align:start position:0% +should really to do it right this is the +solution for a given Delta and I'm + + align:start position:0% +solution for a given Delta and I'm + + + align:start position:0% +solution for a given Delta and I'm +asking what happened so that solution + + align:start position:0% +asking what happened so that solution + + + align:start position:0% +asking what happened so that solution +will exist fine this matrix is certainly + + align:start position:0% +will exist fine this matrix is certainly + + + align:start position:0% +will exist fine this matrix is certainly +invertible that's positive semi definite + + align:start position:0% +invertible that's positive semi definite + + + align:start position:0% +invertible that's positive semi definite +at least that's positive semi definite + + align:start position:0% +at least that's positive semi definite + + + align:start position:0% +at least that's positive semi definite +and what about delta squared i it is + + align:start position:0% +and what about delta squared i it is + + + align:start position:0% +and what about delta squared i it is +positive definite of course just the + + align:start position:0% +positive definite of course just the + + + align:start position:0% +positive definite of course just the +identity with a factor so this is a + + align:start position:0% +identity with a factor so this is a + + + align:start position:0% +identity with a factor so this is a +positive definite matrix it's there i + + align:start position:0% +positive definite matrix it's there i + + + align:start position:0% +positive definite matrix it's there i +certainly have a solution and let me + + align:start position:0% +certainly have a solution and let me + + + align:start position:0% +certainly have a solution and let me +keep going on this one by one case this + + align:start position:0% +keep going on this one by one case this + + + align:start position:0% +keep going on this one by one case this +would be a transfer a is just a sigma i + + align:start position:0% +would be a transfer a is just a sigma i + + + align:start position:0% +would be a transfer a is just a sigma i +think it's just sigma p okay so this is + + align:start position:0% +think it's just sigma p okay so this is + + + align:start position:0% +think it's just sigma p okay so this is +a is one by one and there are two cases + + align:start position:0% +a is one by one and there are two cases + + + align:start position:0% +a is one by one and there are two cases +here sigma bigger than zero or sigma + + align:start position:0% +here sigma bigger than zero or sigma + + + align:start position:0% +here sigma bigger than zero or sigma +equals zero + + align:start position:0% +equals zero + + + align:start position:0% +equals zero +and in either case we I just want to + + align:start position:0% +and in either case we I just want to + + + align:start position:0% +and in either case we I just want to +know what's the limit so so the answer X + + align:start position:0% +know what's the limit so so the answer X + + + align:start position:0% +know what's the limit so so the answer X +yeah let me just take the right hand + + align:start position:0% +yeah let me just take the right hand + + + align:start position:0% +yeah let me just take the right hand +side + + align:start position:0% +side + + + align:start position:0% +side +no that's fine yep okay so am i + + align:start position:0% +no that's fine yep okay so am i + + + align:start position:0% +no that's fine yep okay so am i +competing okay the using the penalized + + align:start position:0% +competing okay the using the penalized + + + align:start position:0% +competing okay the using the penalized +thing on a one by one problem which you + + align:start position:0% +thing on a one by one problem which you + + + align:start position:0% +thing on a one by one problem which you +could say is kind of a little bit small + + align:start position:0% +could say is kind of a little bit small + + + align:start position:0% +could say is kind of a little bit small +for so solving this equation or + + align:start position:0% +for so solving this equation or + + + align:start position:0% +for so solving this equation or +equivalently minimizing this so I'm I'm + + align:start position:0% +equivalently minimizing this so I'm I'm + + + align:start position:0% +equivalently minimizing this so I'm I'm +here I'm finding the minimum of a was + + align:start position:0% +here I'm finding the minimum of a was + + + align:start position:0% +here I'm finding the minimum of a was +Sigma X minus B squared plus Delta + + align:start position:0% +Sigma X minus B squared plus Delta + + + align:start position:0% +Sigma X minus B squared plus Delta +squared x squared I'm because I'm hoping + + align:start position:0% +squared x squared I'm because I'm hoping + + + align:start position:0% +squared x squared I'm because I'm hoping +that if I found that you see it's just + + align:start position:0% +that if I found that you see it's just + + + align:start position:0% +that if I found that you see it's just +one by one just a number and I'm hoping + + align:start position:0% +one by one just a number and I'm hoping + + + align:start position:0% +one by one just a number and I'm hoping +that if calculate calculus will agree + + align:start position:0% +that if calculate calculus will agree + + + align:start position:0% +that if calculate calculus will agree +with linear algebra here that if I find + + align:start position:0% +with linear algebra here that if I find + + + align:start position:0% +with linear algebra here that if I find +the minimum of this so let me write it + + align:start position:0% +the minimum of this so let me write it + + + align:start position:0% +the minimum of this so let me write it +out Sigma squared x squared and Delta + + align:start position:0% +out Sigma squared x squared and Delta + + + align:start position:0% +out Sigma squared x squared and Delta +squared x squared and then minus 2 Sigma + + align:start position:0% +squared x squared and then minus 2 Sigma + + + align:start position:0% +squared x squared and then minus 2 Sigma +X B and then plus B squared and now I'm + + align:start position:0% +X B and then plus B squared and now I'm + + + align:start position:0% +X B and then plus B squared and now I'm +going to find the minimum which means + + align:start position:0% +going to find the minimum which means + + + align:start position:0% +going to find the minimum which means +I'd set the derivative to 0 so I get 2 + + align:start position:0% +I'd set the derivative to 0 so I get 2 + + + align:start position:0% +I'd set the derivative to 0 so I get 2 +Sigma squared and 2 Delta squared I get + + align:start position:0% +Sigma squared and 2 Delta squared I get + + + align:start position:0% +Sigma squared and 2 Delta squared I get +a 2 here and this gives me the X + + align:start position:0% +a 2 here and this gives me the X + + + align:start position:0% +a 2 here and this gives me the X +derivative is 2 Sigma B so I get a 2 + + align:start position:0% +derivative is 2 Sigma B so I get a 2 + + + align:start position:0% +derivative is 2 Sigma B so I get a 2 +there and I'm ok I just cancelled both + + align:start position:0% +there and I'm ok I just cancelled both + + + align:start position:0% +there and I'm ok I just cancelled both +the twos and that's the equation so I + + align:start position:0% +the twos and that's the equation so I + + + align:start position:0% +the twos and that's the equation so I +can solve that equation X is Sigma B + + align:start position:0% +can solve that equation X is Sigma B + + + align:start position:0% +can solve that equation X is Sigma B +Sigma over Sigma squared plus Delta + + align:start position:0% +Sigma over Sigma squared plus Delta + + + align:start position:0% +Sigma over Sigma squared plus Delta +squared B so it's really that quantity I + + align:start position:0% +squared B so it's really that quantity I + + + align:start position:0% +squared B so it's really that quantity I +want to let Delta go to 0 so again what + + align:start position:0% +want to let Delta go to 0 so again what + + + align:start position:0% +want to let Delta go to 0 so again what +am I doing here I'm taking a 1 by 1 + + align:start position:0% +am I doing here I'm taking a 1 by 1 + + + align:start position:0% +am I doing here I'm taking a 1 by 1 +example just to see what happens in the + + align:start position:0% +example just to see what happens in the + + + align:start position:0% +example just to see what happens in the +limit + + align:start position:0% +limit + + + align:start position:0% +limit +as sigma-delta sorry Delta goes to 0 + + align:start position:0% +as sigma-delta sorry Delta goes to 0 + + + align:start position:0% +as sigma-delta sorry Delta goes to 0 +what happens so I just have to look at + + align:start position:0% +what happens so I just have to look at + + + align:start position:0% +what happens so I just have to look at +that what is the limit of that thing in + + align:start position:0% +that what is the limit of that thing in + + + align:start position:0% +that what is the limit of that thing in +a circle as Delta goes to 0 that's so + + align:start position:0% +a circle as Delta goes to 0 that's so + + + align:start position:0% +a circle as Delta goes to 0 that's so +I'm finding out for a one by one problem + + align:start position:0% +I'm finding out for a one by one problem + + + align:start position:0% +I'm finding out for a one by one problem +what a penalized least squares problem + + align:start position:0% +what a penalized least squares problem + + + align:start position:0% +what a penalized least squares problem +Ridge regression could all over the + + align:start position:0% +Ridge regression could all over the + + + align:start position:0% +Ridge regression could all over the +place what happens ok so what happens to + + align:start position:0% +place what happens ok so what happens to + + + align:start position:0% +place what happens ok so what happens to +that number as Delta goes to 0 1 over + + align:start position:0% +that number as Delta goes to 0 1 over + + + align:start position:0% +that number as Delta goes to 0 1 over +Sigma so now the Delta go to 0 so that + + align:start position:0% +Sigma so now the Delta go to 0 so that + + + align:start position:0% +Sigma so now the Delta go to 0 so that +approaches 1 over Sigma right because + + align:start position:0% +approaches 1 over Sigma right because + + + align:start position:0% +approaches 1 over Sigma right because +Delta disappears and Sigma over Sigma + + align:start position:0% +Delta disappears and Sigma over Sigma + + + align:start position:0% +Delta disappears and Sigma over Sigma +squared 1 over Sigma so it approaches + + align:start position:0% +squared 1 over Sigma so it approaches + + + align:start position:0% +squared 1 over Sigma so it approaches +the inverse but but what's the other + + align:start position:0% +the inverse but but what's the other + + + align:start position:0% +the inverse but but what's the other +possibility here the other possibility + + align:start position:0% +possibility here the other possibility + + + align:start position:0% +possibility here the other possibility +is that Sigma is 0 + + align:start position:0% +is that Sigma is 0 + + + align:start position:0% +is that Sigma is 0 +I didn't say whether this matrix is 1 by + + align:start position:0% +I didn't say whether this matrix is 1 by + + + align:start position:0% +I didn't say whether this matrix is 1 by +1 matrix was invertible or not if Sigma + + align:start position:0% +1 matrix was invertible or not if Sigma + + + align:start position:0% +1 matrix was invertible or not if Sigma +is not 0 then I go to 1 over Sigma if + + align:start position:0% +is not 0 then I go to 1 over Sigma if + + + align:start position:0% +is not 0 then I go to 1 over Sigma if +Sigma is really small it'll take a while + + align:start position:0% +Sigma is really small it'll take a while + + + align:start position:0% +Sigma is really small it'll take a while +Delta will have to get small small small + + align:start position:0% +Delta will have to get small small small + + + align:start position:0% +Delta will have to get small small small +even compared to Sigma until till + + align:start position:0% +even compared to Sigma until till + + + align:start position:0% +even compared to Sigma until till +finally that term goes away and I'm just + + align:start position:0% +finally that term goes away and I'm just + + + align:start position:0% +finally that term goes away and I'm just +have 1 over Sigma but what if Sigma is 0 + + align:start position:0% +have 1 over Sigma but what if Sigma is 0 + + + align:start position:0% +have 1 over Sigma but what if Sigma is 0 +sorry to get excited about 0 who would + + align:start position:0% +sorry to get excited about 0 who would + + + align:start position:0% +sorry to get excited about 0 who would +get excited about 0 ok so this is the + + align:start position:0% +get excited about 0 ok so this is the + + + align:start position:0% +get excited about 0 ok so this is the +case when this is 1 over Sigma if Sigma + + align:start position:0% +case when this is 1 over Sigma if Sigma + + + align:start position:0% +case when this is 1 over Sigma if Sigma +is positive and what does it approach if + + align:start position:0% +is positive and what does it approach if + + + align:start position:0% +is positive and what does it approach if +Sigma is 0 0 because this is 0 it will + + align:start position:0% +Sigma is 0 0 because this is 0 it will + + + align:start position:0% +Sigma is 0 0 because this is 0 it will +the whole problem was like disappeared + + align:start position:0% +the whole problem was like disappeared + + + align:start position:0% +the whole problem was like disappeared +here the Sigma was 0 here's a Sigma so + + align:start position:0% +here the Sigma was 0 here's a Sigma so + + + align:start position:0% +here the Sigma was 0 here's a Sigma so +anyway + + align:start position:0% + + + + align:start position:0% + +Sigma will be if Sigma is 0 and I'm + + align:start position:0% +Sigma will be if Sigma is 0 and I'm + + + align:start position:0% +Sigma will be if Sigma is 0 and I'm +getting 0 all the time but I have a + + align:start position:0% +getting 0 all the time but I have a + + + align:start position:0% +getting 0 all the time but I have a +decent problem because the del + + align:start position:0% +decent problem because the del + + + align:start position:0% +decent problem because the del +- squared is there I have a decent + + align:start position:0% +- squared is there I have a decent + + + align:start position:0% +- squared is there I have a decent +problem until the last minute my problem + + align:start position:0% +problem until the last minute my problem + + + align:start position:0% +problem until the last minute my problem +falls apart Delta goes to 0 and I have a + + align:start position:0% +falls apart Delta goes to 0 and I have a + + + align:start position:0% +falls apart Delta goes to 0 and I have a +zero equals zero problem I'm lost but + + align:start position:0% +zero equals zero problem I'm lost but + + + align:start position:0% +zero equals zero problem I'm lost but +the point is the penalty kept me + + align:start position:0% +the point is the penalty kept me + + + align:start position:0% +the point is the penalty kept me +positive kept me with this Delta squared + + align:start position:0% +positive kept me with this Delta squared + + + align:start position:0% +positive kept me with this Delta squared +term until the last critical moment even + + align:start position:0% +term until the last critical moment even + + + align:start position:0% +term until the last critical moment even +it kept me positive even if that was + + align:start position:0% +it kept me positive even if that was + + + align:start position:0% +it kept me positive even if that was +zero if that is zero and this is zero I + + align:start position:0% +zero if that is zero and this is zero I + + + align:start position:0% +zero if that is zero and this is zero I +still have something here so I still + + align:start position:0% +still have something here so I still + + + align:start position:0% +still have something here so I still +have a problem to solve and what's the + + align:start position:0% +have a problem to solve and what's the + + + align:start position:0% +have a problem to solve and what's the +limit then so a 1 over Sigma if Sigma is + + align:start position:0% +limit then so a 1 over Sigma if Sigma is + + + align:start position:0% +limit then so a 1 over Sigma if Sigma is +positive and what's the answer if Sigma + + align:start position:0% +positive and what's the answer if Sigma + + + align:start position:0% +positive and what's the answer if Sigma +is not positive it's 0 just tell me it's + + align:start position:0% +is not positive it's 0 just tell me it's + + + align:start position:0% +is not positive it's 0 just tell me it's +again I'm getting 0 well I get 0 all the + + align:start position:0% +again I'm getting 0 well I get 0 all the + + + align:start position:0% +again I'm getting 0 well I get 0 all the +way and I get 0 in the limit and now let + + align:start position:0% +way and I get 0 in the limit and now let + + + align:start position:0% +way and I get 0 in the limit and now let +me just ask what have I got here what + + align:start position:0% +me just ask what have I got here what + + + align:start position:0% +me just ask what have I got here what +what is this this sudden bifurcation + + align:start position:0% +what is this this sudden bifurcation + + + align:start position:0% +what is this this sudden bifurcation +that's what's the do I recognize this + + align:start position:0% +that's what's the do I recognize this + + + align:start position:0% +that's what's the do I recognize this +the the inverse in the limit as Delta + + align:start position:0% +the the inverse in the limit as Delta + + + align:start position:0% +the the inverse in the limit as Delta +goes to 0 is either 1 over Sigma if it's + + align:start position:0% +goes to 0 is either 1 over Sigma if it's + + + align:start position:0% +goes to 0 is either 1 over Sigma if it's +if that makes sense + + align:start position:0% +if that makes sense + + + align:start position:0% +if that makes sense +or at 0 which is not like 1 over segment + + align:start position:0% +or at 0 which is not like 1 over segment + + + align:start position:0% +or at 0 which is not like 1 over segment +1 over Sigma as Sigma goes to 0 the + + align:start position:0% +1 over Sigma as Sigma goes to 0 the + + + align:start position:0% +1 over Sigma as Sigma goes to 0 the +thing this thing is getting bigger and + + align:start position:0% +thing this thing is getting bigger and + + + align:start position:0% +thing this thing is getting bigger and +bigger + + align:start position:0% +bigger + + + align:start position:0% +bigger +but at Sigma equals 0 its 0 you see + + align:start position:0% +but at Sigma equals 0 its 0 you see + + + align:start position:0% +but at Sigma equals 0 its 0 you see +that's a really that's a strange kind of + + align:start position:0% +that's a really that's a strange kind of + + + align:start position:0% +that's a really that's a strange kind of +a limit and what word now it would be + + align:start position:0% +a limit and what word now it would be + + + align:start position:0% +a limit and what word now it would be +over there what have I found here in + + align:start position:0% +over there what have I found here in + + + align:start position:0% +over there what have I found here in +this limit you say say it again because + + align:start position:0% +this limit you say say it again because + + + align:start position:0% +this limit you say say it again because +it was exactly right there's + + align:start position:0% +it was exactly right there's + + + align:start position:0% +it was exactly right there's +pseudo-inverse so this this this system + + align:start position:0% +pseudo-inverse so this this this system + + + align:start position:0% +pseudo-inverse so this this this system +choose Delta greater than zero then + + align:start position:0% +choose Delta greater than zero then + + + align:start position:0% +choose Delta greater than zero then +Delta are going to 0 the solution goes + + align:start position:0% +Delta are going to 0 the solution goes + + + align:start position:0% +Delta are going to 0 the solution goes +to the pseudo-inverse + + align:start position:0% + + + + align:start position:0% + +that's the key fact that that is when + + align:start position:0% +that's the key fact that that is when + + + align:start position:0% +that's the key fact that that is when +Delta is really really small then this + + align:start position:0% +Delta is really really small then this + + + align:start position:0% +Delta is really really small then this +behaves in a pretty crazy way if Delta + + align:start position:0% +behaves in a pretty crazy way if Delta + + + align:start position:0% +behaves in a pretty crazy way if Delta +is really really small then and then + + align:start position:0% +is really really small then and then + + + align:start position:0% +is really really small then and then +Sigma is bigger or it's zero if it's + + align:start position:0% +Sigma is bigger or it's zero if it's + + + align:start position:0% +Sigma is bigger or it's zero if it's +bigger you go this way if it's zero you + + align:start position:0% +bigger you go this way if it's zero you + + + align:start position:0% +bigger you go this way if it's zero you +go that way so that's that's the message + + align:start position:0% +go that way so that's that's the message + + + align:start position:0% +go that way so that's that's the message +and that this there's penalized these + + align:start position:0% +and that this there's penalized these + + + align:start position:0% +and that this there's penalized these +squares approaches as the penalty gets + + align:start position:0% +squares approaches as the penalty gets + + + align:start position:0% +squares approaches as the penalty gets +smaller and smaller approaches the + + align:start position:0% +smaller and smaller approaches the + + + align:start position:0% +smaller and smaller approaches the +correct answer the always correct answer + + align:start position:0% +correct answer the always correct answer + + + align:start position:0% +correct answer the always correct answer +with that sudden split between zero and + + align:start position:0% +with that sudden split between zero and + + + align:start position:0% +with that sudden split between zero and +not zero that we associate with the + + align:start position:0% +not zero that we associate with the + + + align:start position:0% +not zero that we associate with the +pseudo-inverse yeah of course in a + + align:start position:0% +pseudo-inverse yeah of course in a + + + align:start position:0% +pseudo-inverse yeah of course in a +practical case you're trying to find the + + align:start position:0% +practical case you're trying to find the + + + align:start position:0% +practical case you're trying to find the +the resistances and inductances in a + + align:start position:0% +the resistances and inductances in a + + + align:start position:0% +the resistances and inductances in a +circuit by trying the circuit and + + align:start position:0% + + + + align:start position:0% + +looking at the output B and figuring out + + align:start position:0% +looking at the output B and figuring out + + + align:start position:0% +looking at the output B and figuring out +what input what what the so the unknown + + align:start position:0% +what input what what the so the unknown + + + align:start position:0% +what input what what the so the unknown +X is the is the unknown system + + align:start position:0% +X is the is the unknown system + + + align:start position:0% +X is the is the unknown system +parameters the voltage and not the + + align:start position:0% +parameters the voltage and not the + + + align:start position:0% +parameters the voltage and not the +voltage and current but the but the + + align:start position:0% +voltage and current but the but the + + + align:start position:0% +voltage and current but the but the +resistance and inductance and + + align:start position:0% +resistance and inductance and + + + align:start position:0% +resistance and inductance and +capacitance okay so that's now I've only + + align:start position:0% +capacitance okay so that's now I've only + + + align:start position:0% +capacitance okay so that's now I've only +proved that in the one by one case you + + align:start position:0% +proved that in the one by one case you + + + align:start position:0% +proved that in the one by one case you +may say that's not much of a proof in + + align:start position:0% +may say that's not much of a proof in + + + align:start position:0% +may say that's not much of a proof in +the one by one case we could see it + + align:start position:0% +the one by one case we could see it + + + align:start position:0% +the one by one case we could see it +happen in front of our eyes + + align:start position:0% +happen in front of our eyes + + + align:start position:0% +happen in front of our eyes +so really step I haven't taken here is + + align:start position:0% +so really step I haven't taken here is + + + align:start position:0% +so really step I haven't taken here is +to complete that to any matrix a so + + align:start position:0% +to complete that to any matrix a so + + + align:start position:0% +to complete that to any matrix a so +that's the statement then that's the + + align:start position:0% +that's the statement then that's the + + + align:start position:0% +that's the statement then that's the +statement + + align:start position:0% + + + + align:start position:0% + +so that's the statement for any or any + + align:start position:0% +so that's the statement for any or any + + + align:start position:0% +so that's the statement for any or any +matrix a this matrix a transpose A plus + + align:start position:0% +matrix a this matrix a transpose A plus + + + align:start position:0% +matrix a this matrix a transpose A plus +Delta squared inverse times a transpose + + align:start position:0% +Delta squared inverse times a transpose + + + align:start position:0% +Delta squared inverse times a transpose +that's the solution matrix to our + + align:start position:0% +that's the solution matrix to our + + + align:start position:0% +that's the solution matrix to our +problem right yep that's what I wrote + + align:start position:0% +problem right yep that's what I wrote + + + align:start position:0% +problem right yep that's what I wrote +down up there I take the inverse and pop + + align:start position:0% +down up there I take the inverse and pop + + + align:start position:0% +down up there I take the inverse and pop +it over there that approaches a plus the + + align:start position:0% +it over there that approaches a plus the + + + align:start position:0% +it over there that approaches a plus the +pseudo inverse and that's what we just + + align:start position:0% +pseudo inverse and that's what we just + + + align:start position:0% +pseudo inverse and that's what we just +checked for one by one one by one this + + align:start position:0% +checked for one by one one by one this + + + align:start position:0% +checked for one by one one by one this +was Sigma over Sigma squared plus Delta + + align:start position:0% +was Sigma over Sigma squared plus Delta + + + align:start position:0% +was Sigma over Sigma squared plus Delta +squared and it went to either to 1 over + + align:start position:0% +squared and it went to either to 1 over + + + align:start position:0% +squared and it went to either to 1 over +Sigma or to 0 it split in the limit it + + align:start position:0% +Sigma or to 0 it split in the limit it + + + align:start position:0% +Sigma or to 0 it split in the limit it +shows that limits are can be delicate + + align:start position:0% +shows that limits are can be delicate + + + align:start position:0% +shows that limits are can be delicate +you know the limit as Delta goes to 0 + + align:start position:0% +you know the limit as Delta goes to 0 + + + align:start position:0% +you know the limit as Delta goes to 0 +this thing it suddenly discontinuous + + align:start position:0% +this thing it suddenly discontinuous + + + align:start position:0% +this thing it suddenly discontinuous +it's it's it's this number that's + + align:start position:0% +it's it's it's this number that's + + + align:start position:0% +it's it's it's this number that's +growing and then suddenly at 0 it falls + + align:start position:0% +growing and then suddenly at 0 it falls + + + align:start position:0% +growing and then suddenly at 0 it falls +back to 0 anyway that would be the + + align:start position:0% +back to 0 anyway that would be the + + + align:start position:0% +back to 0 anyway that would be the +statement actually statisticians + + align:start position:0% +statement actually statisticians + + + align:start position:0% +statement actually statisticians +discovered the pseudo inverse like + + align:start position:0% +discovered the pseudo inverse like + + + align:start position:0% +discovered the pseudo inverse like +independently of linear algebra history + + align:start position:0% +independently of linear algebra history + + + align:start position:0% +independently of linear algebra history +of it because statisticians did exactly + + align:start position:0% +of it because statisticians did exactly + + + align:start position:0% +of it because statisticians did exactly +that to regularize the problem they + + align:start position:0% +that to regularize the problem they + + + align:start position:0% +that to regularize the problem they +introduced a penalty and worked with + + align:start position:0% +introduced a penalty and worked with + + + align:start position:0% +introduced a penalty and worked with +this matrix so so statisticians were the + + align:start position:0% +this matrix so so statisticians were the + + + align:start position:0% +this matrix so so statisticians were the +first to see that that yeah to think of + + align:start position:0% +first to see that that yeah to think of + + + align:start position:0% +first to see that that yeah to think of +that as a natural thing to do in in a + + align:start position:0% +that as a natural thing to do in in a + + + align:start position:0% +that as a natural thing to do in in a +practical case at a penalty okay so I + + align:start position:0% +practical case at a penalty okay so I + + + align:start position:0% +practical case at a penalty okay so I +guess so this is adding a penalty but + + align:start position:0% +guess so this is adding a penalty but + + + align:start position:0% +guess so this is adding a penalty but +remember that we stayed with L two norms + + align:start position:0% +remember that we stayed with L two norms + + + align:start position:0% +remember that we stayed with L two norms +staying with l2 least-squares we could + + align:start position:0% +staying with l2 least-squares we could + + + align:start position:0% +staying with l2 least-squares we could +ask what happens yeah + + align:start position:0% +ask what happens yeah + + + align:start position:0% +ask what happens yeah +suppose the penalty is the l1 norm + + align:start position:0% +suppose the penalty is the l1 norm + + + align:start position:0% +suppose the penalty is the l1 norm +suppose I minimize I'm not up to do this + + align:start position:0% +suppose I minimize I'm not up to do this + + + align:start position:0% +suppose I minimize I'm not up to do this +today + + align:start position:0% +today + + + align:start position:0% +today +suppose I minimize that maybe let's say + + align:start position:0% +suppose I minimize that maybe let's say + + + align:start position:0% +suppose I minimize that maybe let's say +I'll do l2 but I'll do the penalty guy + + align:start position:0% +I'll do l2 but I'll do the penalty guy + + + align:start position:0% +I'll do l2 but I'll do the penalty guy +in the l1 norm I guess I'm not yeah I'm + + align:start position:0% +in the l1 norm I guess I'm not yeah I'm + + + align:start position:0% +in the l1 norm I guess I'm not yeah I'm +certainly not an expert on that or you + + align:start position:0% +certainly not an expert on that or you + + + align:start position:0% +certainly not an expert on that or you +could even think just that power so that + + align:start position:0% +could even think just that power so that + + + align:start position:0% +could even think just that power so that +would have a name that statisticians a + + align:start position:0% +would have a name that statisticians a + + + align:start position:0% +would have a name that statisticians a +statistician invented this it's called + + align:start position:0% +statistician invented this it's called + + + align:start position:0% +statistician invented this it's called +the lasso in the l1 norm and it's a big + + align:start position:0% +the lasso in the l1 norm and it's a big + + + align:start position:0% +the lasso in the l1 norm and it's a big +deal snow decisions like the l1 norm + + align:start position:0% +deal snow decisions like the l1 norm + + + align:start position:0% +deal snow decisions like the l1 norm +because because it really because it + + align:start position:0% +because because it really because it + + + align:start position:0% +because because it really because it +gives sparse solutions it gives you give + + align:start position:0% +gives sparse solutions it gives you give + + + align:start position:0% +gives sparse solutions it gives you give +sort of more genuine solutions without a + + align:start position:0% +sort of more genuine solutions without a + + + align:start position:0% +sort of more genuine solutions without a +whole lot of little little components in + + align:start position:0% +whole lot of little little components in + + + align:start position:0% +whole lot of little little components in +the answer yep so that this was an + + align:start position:0% +the answer yep so that this was an + + + align:start position:0% +the answer yep so that this was an +important step and so maybe let me just + + align:start position:0% +important step and so maybe let me just + + + align:start position:0% +important step and so maybe let me just +say again we're where we are in that big + + align:start position:0% +say again we're where we are in that big + + + align:start position:0% +say again we're where we are in that big +list the the the the two important ones + + align:start position:0% +list the the the the two important ones + + + align:start position:0% +list the the the the two important ones +that I haven't done yet are these + + align:start position:0% +that I haven't done yet are these + + + align:start position:0% +that I haven't done yet are these +iterative methods in 2.1 so that's like + + align:start position:0% +iterative methods in 2.1 so that's like + + + align:start position:0% +iterative methods in 2.1 so that's like +conventional linear algebra just how to + + align:start position:0% +conventional linear algebra just how to + + + align:start position:0% +conventional linear algebra just how to +deal with a big matrix maybe with some + + align:start position:0% +deal with a big matrix maybe with some + + + align:start position:0% +deal with a big matrix maybe with some +special structure that's what linear + + align:start position:0% +special structure that's what linear + + + align:start position:0% +special structure that's what linear +algebra is numerical linear algebra is + + align:start position:0% +algebra is numerical linear algebra is + + + align:start position:0% +algebra is numerical linear algebra is +all about and then gram-schmidt with or + + align:start position:0% +all about and then gram-schmidt with or + + + align:start position:0% +all about and then gram-schmidt with or +without pivoting which is a workhorse of + + align:start position:0% +without pivoting which is a workhorse of + + + align:start position:0% +without pivoting which is a workhorse of +of numerical computing and I think I + + align:start position:0% +of numerical computing and I think I + + + align:start position:0% +of numerical computing and I think I +better save that for next time + + align:start position:0% +better save that for next time + + + align:start position:0% +better save that for next time +so so this is the one + + align:start position:0% +so so this is the one + + + align:start position:0% +so so this is the one +picked for this time and we saw what + + align:start position:0% +picked for this time and we saw what + + + align:start position:0% +picked for this time and we saw what +happened in l2 well we saw it for one by + + align:start position:0% +happened in l2 well we saw it for one by + + + align:start position:0% +happened in l2 well we saw it for one by +one would you want to extend to prove + + align:start position:0% +one would you want to extend to prove + + + align:start position:0% +one would you want to extend to prove +this for any a going beyond one by one + + align:start position:0% +this for any a going beyond one by one + + + align:start position:0% +this for any a going beyond one by one +how would you prove such a thing for any + + align:start position:0% +how would you prove such a thing for any + + + align:start position:0% +how would you prove such a thing for any +a I guess I'm I'm not going to do it it + + align:start position:0% +a I guess I'm I'm not going to do it it + + + align:start position:0% +a I guess I'm I'm not going to do it it +it's too painful but but how would you + + align:start position:0% +it's too painful but but how would you + + + align:start position:0% +it's too painful but but how would you +do it you would use the SVD if you want + + align:start position:0% +do it you would use the SVD if you want + + + align:start position:0% +do it you would use the SVD if you want +to prove something about matrices about + + align:start position:0% +to prove something about matrices about + + + align:start position:0% +to prove something about matrices about +any matrix the SVD is the best thing you + + align:start position:0% +any matrix the SVD is the best thing you + + + align:start position:0% +any matrix the SVD is the best thing you +could have the best tool you could have + + align:start position:0% +could have the best tool you could have + + + align:start position:0% +could have the best tool you could have +I can write this in terms of the SVD I + + align:start position:0% +I can write this in terms of the SVD I + + + align:start position:0% +I can write this in terms of the SVD I +just plug in I just plug in a equals + + align:start position:0% +just plug in I just plug in a equals + + + align:start position:0% +just plug in I just plug in a equals +whatever the SVD tells me to put in + + align:start position:0% +whatever the SVD tells me to put in + + + align:start position:0% +whatever the SVD tells me to put in +there you Sigma V transpose plug it in + + align:start position:0% +there you Sigma V transpose plug it in + + + align:start position:0% +there you Sigma V transpose plug it in +there simplify it using the fact that + + align:start position:0% +there simplify it using the fact that + + + align:start position:0% +there simplify it using the fact that +these are orthogonal you know I always + + align:start position:0% +these are orthogonal you know I always + + + align:start position:0% +these are orthogonal you know I always +if I have any good luck it'll I'll get + + align:start position:0% +if I have any good luck it'll I'll get + + + align:start position:0% +if I have any good luck it'll I'll get +an identity somewhere from there and an + + align:start position:0% +an identity somewhere from there and an + + + align:start position:0% +an identity somewhere from there and an +identity somewhere from there and it'll + + align:start position:0% +identity somewhere from there and it'll + + + align:start position:0% +identity somewhere from there and it'll +all simplify it'll all diagonalize + + align:start position:0% +all simplify it'll all diagonalize + + + align:start position:0% +all simplify it'll all diagonalize +that's what the SVD really does this + + align:start position:0% +that's what the SVD really does this + + + align:start position:0% +that's what the SVD really does this +turns my messy problem into a problem + + align:start position:0% +turns my messy problem into a problem + + + align:start position:0% +turns my messy problem into a problem +about their diagonal matrix Sigma in the + + align:start position:0% +about their diagonal matrix Sigma in the + + + align:start position:0% +about their diagonal matrix Sigma in the +middle so I might as well put Sigma in + + align:start position:0% +middle so I might as well put Sigma in + + + align:start position:0% +middle so I might as well put Sigma in +the middle yeah why not before we give + + align:start position:0% +the middle yeah why not before we give + + + align:start position:0% +the middle yeah why not before we give +up on it + + align:start position:0% + + + + align:start position:0% + +a special case of that but the really + + align:start position:0% +a special case of that but the really + + + align:start position:0% +a special case of that but the really +the genuine case would be when a is + + align:start position:0% +the genuine case would be when a is + + + align:start position:0% +the genuine case would be when a is +Sigma Sigma transpose Sigma plus Delta + + align:start position:0% +Sigma Sigma transpose Sigma plus Delta + + + align:start position:0% +Sigma Sigma transpose Sigma plus Delta +squared i inverse times Sigma transpose + + align:start position:0% +squared i inverse times Sigma transpose + + + align:start position:0% +squared i inverse times Sigma transpose +approaches the pseudo inverse Sigma plus + + align:start position:0% +approaches the pseudo inverse Sigma plus + + + align:start position:0% +approaches the pseudo inverse Sigma plus +and the point is the matrix Sigma here + + align:start position:0% +and the point is the matrix Sigma here + + + align:start position:0% +and the point is the matrix Sigma here +is diagonal and oh I'm practically there + + align:start position:0% +is diagonal and oh I'm practically there + + + align:start position:0% +is diagonal and oh I'm practically there +actually why am i close to being being + + align:start position:0% +actually why am i close to being being + + + align:start position:0% +actually why am i close to being being +able to read this off well everything is + + align:start position:0% +able to read this off well everything is + + + align:start position:0% +able to read this off well everything is +diagonal here diagonal diagonal diagonal + + align:start position:0% +diagonal here diagonal diagonal diagonal + + + align:start position:0% +diagonal here diagonal diagonal diagonal +and what's happening on those diagonal + + align:start position:0% +and what's happening on those diagonal + + + align:start position:0% +and what's happening on those diagonal +entries so you had to take my word that + + align:start position:0% +entries so you had to take my word that + + + align:start position:0% +entries so you had to take my word that +when I plugged in the SVD the U and the + + align:start position:0% +when I plugged in the SVD the U and the + + + align:start position:0% +when I plugged in the SVD the U and the +V kind of got got separated out to the + + align:start position:0% +V kind of got got separated out to the + + + align:start position:0% +V kind of got got separated out to the +far left and the far right and it was + + align:start position:0% +far left and the far right and it was + + + align:start position:0% +far left and the far right and it was +that that stayed in the middle so it's + + align:start position:0% +that that stayed in the middle so it's + + + align:start position:0% +that that stayed in the middle so it's +really this is the heart of it and how + + align:start position:0% +really this is the heart of it and how + + + align:start position:0% +really this is the heart of it and how +do you suppose so that's a diagonal + + align:start position:0% +do you suppose so that's a diagonal + + + align:start position:0% +do you suppose so that's a diagonal +matrix so I'm just looking what happens + + align:start position:0% +matrix so I'm just looking what happens + + + align:start position:0% +matrix so I'm just looking what happens +on each diagonal entry and which problem + + align:start position:0% +on each diagonal entry and which problem + + + align:start position:0% +on each diagonal entry and which problem +is that well the the question of what's + + align:start position:0% +is that well the the question of what's + + + align:start position:0% +is that well the the question of what's +happening on a typical diagonal entry of + + align:start position:0% +happening on a typical diagonal entry of + + + align:start position:0% +happening on a typical diagonal entry of +this thing is is what question the + + align:start position:0% +this thing is is what question the + + + align:start position:0% +this thing is is what question the +one-by-one case now one by one because + + align:start position:0% +one-by-one case now one by one because + + + align:start position:0% +one-by-one case now one by one because +each entry in the diagonal is not even + + align:start position:0% +each entry in the diagonal is not even + + + align:start position:0% +each entry in the diagonal is not even +noticing the others yeah so so that's + + align:start position:0% +noticing the others yeah so so that's + + + align:start position:0% +noticing the others yeah so so that's +the logic and it would be in the notes + + align:start position:0% +the logic and it would be in the notes + + + align:start position:0% +the logic and it would be in the notes +prove it first for one by one and + + align:start position:0% +prove it first for one by one and + + + align:start position:0% +prove it first for one by one and +secondly for diagonal this and finally + + align:start position:0% +secondly for diagonal this and finally + + + align:start position:0% +secondly for diagonal this and finally +for with A's and they're using the SVD + + align:start position:0% +for with A's and they're using the SVD + + + align:start position:0% +for with A's and they're using the SVD +with you and be transposed to two to get + + align:start position:0% +with you and be transposed to two to get + + + align:start position:0% +with you and be transposed to two to get +out of the way and bring us back to here + + align:start position:0% +out of the way and bring us back to here + + + align:start position:0% +out of the way and bring us back to here +okay so that's the theory but really I I + + align:start position:0% +okay so that's the theory but really I I + + + align:start position:0% +okay so that's the theory but really I I +guess I'm thinking that far the most + + align:start position:0% +guess I'm thinking that far the most + + + align:start position:0% +guess I'm thinking that far the most +important thing message in today's + + align:start position:0% +important thing message in today's + + + align:start position:0% +important thing message in today's +lecture is in this list of different + + align:start position:0% +lecture is in this list of different + + + align:start position:0% +lecture is in this list of different +types of problems that appear and + + align:start position:0% +types of problems that appear and + + + align:start position:0% +types of problems that appear and +different ways to work with them and we + + align:start position:0% +different ways to work with them and we + + + align:start position:0% +different ways to work with them and we +haven't done gram-schmidt and that will + + align:start position:0% +haven't done gram-schmidt and that will + + + align:start position:0% +haven't done gram-schmidt and that will +be and we haven't done it eration so + + align:start position:0% +be and we haven't done it eration so + + + align:start position:0% +be and we haven't done it eration so +this is I'm kind of this chapter as a + + align:start position:0% +this is I'm kind of this chapter as a + + + align:start position:0% +this is I'm kind of this chapter as a +survey of well more than a survey of + + align:start position:0% +survey of well more than a survey of + + + align:start position:0% +survey of well more than a survey of +what numerical linear algebra is about + + align:start position:0% +what numerical linear algebra is about + + + align:start position:0% +what numerical linear algebra is about +and I haven't done random yet I'm sorry + + align:start position:0% +and I haven't done random yet I'm sorry + + + align:start position:0% +and I haven't done random yet I'm sorry +that's coming - so three pieces are + + align:start position:0% +that's coming - so three pieces are + + + align:start position:0% +that's coming - so three pieces are +still to come but let's take the last + + align:start position:0% +still to come but let's take the last + + + align:start position:0% +still to come but let's take the last +two minutes off and call it a day \ No newline at end of file diff --git a/Zh4eqhcZjcg.txt b/Zh4eqhcZjcg.txt new file mode 100644 index 0000000000000000000000000000000000000000..6e006ec66dee4cbdc49ce760b16e842e12017b1b --- /dev/null +++ b/Zh4eqhcZjcg.txt @@ -0,0 +1,9098 @@ +align:start position:0% + +okay why don't we get + + align:start position:0% +okay why don't we get + + + align:start position:0% +okay why don't we get +started um the end of the term + + align:start position:0% +started um the end of the term + + + align:start position:0% +started um the end of the term +approaches so please do uh get to work + + align:start position:0% +approaches so please do uh get to work + + + align:start position:0% +approaches so please do uh get to work +on the design projects if you're not + + align:start position:0% +on the design projects if you're not + + + align:start position:0% +on the design projects if you're not +already doing that the homework lengths + + align:start position:0% +already doing that the homework lengths + + + align:start position:0% +already doing that the homework lengths +are being tapered down to open up room + + align:start position:0% +are being tapered down to open up room + + + align:start position:0% +are being tapered down to open up room +to do that so you know please don't + + align:start position:0% +to do that so you know please don't + + + align:start position:0% +to do that so you know please don't +leave it to the last moment + + align:start position:0% +leave it to the last moment + + + align:start position:0% +leave it to the last moment +um and I and I know this is Project + + align:start position:0% +um and I and I know this is Project + + + align:start position:0% +um and I and I know this is Project +season so I know many people have a lot + + align:start position:0% +season so I know many people have a lot + + + align:start position:0% +season so I know many people have a lot +of them going on so try to start early + + align:start position:0% +of them going on so try to start early + + + align:start position:0% +of them going on so try to start early +um everything I'm going to talk about + + align:start position:0% +um everything I'm going to talk about + + + align:start position:0% +um everything I'm going to talk about +today is in principles of Power + + align:start position:0% +today is in principles of Power + + + align:start position:0% +today is in principles of Power +Electronics chapter + + align:start position:0% +Electronics chapter + + + align:start position:0% +Electronics chapter + + align:start position:0% + + + + align:start position:0% + +um just as a review of what we talked + + align:start position:0% +um just as a review of what we talked + + + align:start position:0% +um just as a review of what we talked +about last time we said if I thought + + align:start position:0% +about last time we said if I thought + + + align:start position:0% +about last time we said if I thought +about a power + + align:start position:0% +about a power + + + align:start position:0% +about a power +converter and it's + + align:start position:0% +converter and it's + + + align:start position:0% +converter and it's +filter um if I have a filter like an LC + + align:start position:0% + + + + align:start position:0% + +filter + + align:start position:0% +filter + + + align:start position:0% +filter +um I have some CF and LF right which I'm + + align:start position:0% +um I have some CF and LF right which I'm + + + align:start position:0% +um I have some CF and LF right which I'm +looking back into from the power + + align:start position:0% +looking back into from the power + + + align:start position:0% +looking back into from the power +converter and the problem is if I'm + + align:start position:0% +converter and the problem is if I'm + + + align:start position:0% +converter and the problem is if I'm +driving current into this filter if I + + align:start position:0% +driving current into this filter if I + + + align:start position:0% +driving current into this filter if I +sort of don't worry about the voltage + + align:start position:0% +sort of don't worry about the voltage + + + align:start position:0% +sort of don't worry about the voltage +source but just think about you know + + align:start position:0% +source but just think about you know + + + align:start position:0% +source but just think about you know +maybe this Source impedance is a short + + align:start position:0% +maybe this Source impedance is a short + + + align:start position:0% +maybe this Source impedance is a short +circuit CF and LF are in parallel so + + align:start position:0% +circuit CF and LF are in parallel so + + + align:start position:0% +circuit CF and LF are in parallel so +I'll get a really Peak and impedance and + + align:start position:0% +I'll get a really Peak and impedance and + + + align:start position:0% +I'll get a really Peak and impedance and +a lot of circulating current if I sort + + align:start position:0% +a lot of circulating current if I sort + + + align:start position:0% +a lot of circulating current if I sort +of have have any drive at the cut off + + align:start position:0% +of have have any drive at the cut off + + + align:start position:0% +of have have any drive at the cut off +frequency of the filter and we said both + + align:start position:0% +frequency of the filter and we said both + + + align:start position:0% +frequency of the filter and we said both +this very lightly damped system and the + + align:start position:0% +this very lightly damped system and the + + + align:start position:0% +this very lightly damped system and the +output impedance can be modified by + + align:start position:0% +output impedance can be modified by + + + align:start position:0% +output impedance can be modified by +adding a damping leg of one kind or + + align:start position:0% +adding a damping leg of one kind or + + + align:start position:0% +adding a damping leg of one kind or +another so maybe what I do is I take uh + + align:start position:0% +another so maybe what I do is I take uh + + + align:start position:0% +another so maybe what I do is I take uh +an additional C damp and R damp so that + + align:start position:0% +an additional C damp and R damp so that + + + align:start position:0% +an additional C damp and R damp so that +at the cut off c damps a short circuit + + align:start position:0% +at the cut off c damps a short circuit + + + align:start position:0% +at the cut off c damps a short circuit +or close to it so R damp is in parallel + + align:start position:0% +or close to it so R damp is in parallel + + + align:start position:0% +or close to it so R damp is in parallel +with LF and CF and I reduce the output + + align:start position:0% +with LF and CF and I reduce the output + + + align:start position:0% +with LF and CF and I reduce the output +impedance of the filter so right so + + align:start position:0% +impedance of the filter so right so + + + align:start position:0% +impedance of the filter so right so +maybe um this Z + + align:start position:0% +maybe um this Z + + + align:start position:0% +maybe um this Z +out looks something like this versus + + align:start position:0% +out looks something like this versus + + + align:start position:0% +out looks something like this versus +Omega on a log + + align:start position:0% +Omega on a log + + + align:start position:0% +Omega on a log +scale maybe at low frequencies it rises + + align:start position:0% +scale maybe at low frequencies it rises + + + align:start position:0% +scale maybe at low frequencies it rises +as Omega L at high frequency it falls as + + align:start position:0% +as Omega L at high frequency it falls as + + + align:start position:0% +as Omega L at high frequency it falls as +one over Omega C and you know I'll get + + align:start position:0% +one over Omega C and you know I'll get + + + align:start position:0% +one over Omega C and you know I'll get +some peaking in here which is limited by + + align:start position:0% +some peaking in here which is limited by + + + align:start position:0% +some peaking in here which is limited by +you know the magnitude of Z out Max is + + align:start position:0% +you know the magnitude of Z out Max is + + + align:start position:0% +you know the magnitude of Z out Max is +related to the damping resistor here and + + align:start position:0% +related to the damping resistor here and + + + align:start position:0% +related to the damping resistor here and +if the damping resistor parallel would + + align:start position:0% +if the damping resistor parallel would + + + align:start position:0% +if the damping resistor parallel would +be exactly the damping + + align:start position:0% +be exactly the damping + + + align:start position:0% +be exactly the damping +resistance now the reason we care about + + align:start position:0% +resistance now the reason we care about + + + align:start position:0% +resistance now the reason we care about +that is both because we don't want a lot + + align:start position:0% +that is both because we don't want a lot + + + align:start position:0% +that is both because we don't want a lot +of peing and undamped behavior in this + + align:start position:0% +of peing and undamped behavior in this + + + align:start position:0% +of peing and undamped behavior in this +filter but it's also true that if I look + + align:start position:0% +filter but it's also true that if I look + + + align:start position:0% +filter but it's also true that if I look +in the other direction into the power + + align:start position:0% +in the other direction into the power + + + align:start position:0% +in the other direction into the power +converter and say what's the input + + align:start position:0% +converter and say what's the input + + + align:start position:0% +converter and say what's the input +impedance looking into the power + + align:start position:0% +impedance looking into the power + + + align:start position:0% +impedance looking into the power +converter incrementally if I have some + + align:start position:0% +converter incrementally if I have some + + + align:start position:0% +converter incrementally if I have some +VN and then + + align:start position:0% +VN and then + + + align:start position:0% +VN and then +some I + + align:start position:0% +some I + + + align:start position:0% +some I +in to the converter and and the + + align:start position:0% +in to the converter and and the + + + align:start position:0% +in to the converter and and the +converter is regulating it's going to + + align:start position:0% +converter is regulating it's going to + + + align:start position:0% +converter is regulating it's going to +maintain a constant voltage across its + + align:start position:0% +maintain a constant voltage across its + + + align:start position:0% +maintain a constant voltage across its +load or equivalently it's going to draw + + align:start position:0% +load or equivalently it's going to draw + + + align:start position:0% +load or equivalently it's going to draw +ideal constant power to maintain its + + align:start position:0% +ideal constant power to maintain its + + + align:start position:0% +ideal constant power to maintain its +load that means its IV + + align:start position:0% +load that means its IV + + + align:start position:0% +load that means its IV +characteristic + + align:start position:0% +characteristic + + + align:start position:0% +characteristic +VN I + + align:start position:0% +VN I + + + align:start position:0% +VN I +in looks like + + align:start position:0% +in looks like + + + align:start position:0% +in looks like +this right because VN is uh proportional + + align:start position:0% +this right because VN is uh proportional + + + align:start position:0% +this right because VN is uh proportional +to 1 over I in right and so if we're + + align:start position:0% +to 1 over I in right and so if we're + + + align:start position:0% +to 1 over I in right and so if we're +sitting at some operating Point say this + + align:start position:0% +sitting at some operating Point say this + + + align:start position:0% +sitting at some operating Point say this +is + + align:start position:0% +is + + + align:start position:0% +is +I + + align:start position:0% +I + + + align:start position:0% +I +in and this is + + align:start position:0% + + + + align:start position:0% + +VN + + align:start position:0% + + + + align:start position:0% + +incrementally this slope is DV and D + + align:start position:0% + + + + align:start position:0% + +in evaluated at VN I in is equal to a a + + align:start position:0% +in evaluated at VN I in is equal to a a + + + align:start position:0% +in evaluated at VN I in is equal to a a +negative resistor because this slope is + + align:start position:0% +negative resistor because this slope is + + + align:start position:0% +negative resistor because this slope is +negative right so it turns out to be + + align:start position:0% +negative right so it turns out to be + + + align:start position:0% +negative right so it turns out to be +minus uh P + + align:start position:0% +minus uh P + + + align:start position:0% +minus uh P +out over I in^ + + align:start position:0% +out over I in^ + + + align:start position:0% +out over I in^ +2 okay and so basically if I'm looking + + align:start position:0% +2 okay and so basically if I'm looking + + + align:start position:0% +2 okay and so basically if I'm looking +into the converter from the filter I'm + + align:start position:0% +into the converter from the filter I'm + + + align:start position:0% +into the converter from the filter I'm +effectively + + align:start position:0% +effectively + + + align:start position:0% +effectively +seeing a negative resistor here and that + + align:start position:0% +seeing a negative resistor here and that + + + align:start position:0% +seeing a negative resistor here and that +negative resistor can make this whole + + align:start position:0% +negative resistor can make this whole + + + align:start position:0% +negative resistor can make this whole +thing oscillate so we always want to + + align:start position:0% +thing oscillate so we always want to + + + align:start position:0% +thing oscillate so we always want to +make the output in P of my filter very + + align:start position:0% +make the output in P of my filter very + + + align:start position:0% +make the output in P of my filter very +small compared to the magnitude of my + + align:start position:0% +small compared to the magnitude of my + + + align:start position:0% +small compared to the magnitude of my +negative input resistance here here in + + align:start position:0% +negative input resistance here here in + + + align:start position:0% +negative input resistance here here in +order to make sure that this whole + + align:start position:0% +order to make sure that this whole + + + align:start position:0% +order to make sure that this whole +system won't + + align:start position:0% +system won't + + + align:start position:0% +system won't +oscillate okay so that was sort of the + + align:start position:0% +oscillate okay so that was sort of the + + + align:start position:0% +oscillate okay so that was sort of the +what I hoped you took away from last + + align:start position:0% +what I hoped you took away from last + + + align:start position:0% +what I hoped you took away from last +class are there any questions about + + align:start position:0% + + + + align:start position:0% + +that okay so today I want to talk about + + align:start position:0% +that okay so today I want to talk about + + + align:start position:0% +that okay so today I want to talk about +something a little bit different we've + + align:start position:0% +something a little bit different we've + + + align:start position:0% +something a little bit different we've +kind of uh brushed lightly over one + + align:start position:0% +kind of uh brushed lightly over one + + + align:start position:0% +kind of uh brushed lightly over one +topic or neglected one kind of effect + + align:start position:0% +topic or neglected one kind of effect + + + align:start position:0% +topic or neglected one kind of effect +that you often have to contend with an + + align:start position:0% +that you often have to contend with an + + + align:start position:0% +that you often have to contend with an +Emi filter designs and just to + + align:start position:0% +Emi filter designs and just to + + + align:start position:0% +Emi filter designs and just to +illustrate how important this General + + align:start position:0% +illustrate how important this General + + + align:start position:0% +illustrate how important this General +topic is what this is is this is a power + + align:start position:0% +topic is what this is is this is a power + + + align:start position:0% +topic is what this is is this is a power +factor corrected laptop power supply + + align:start position:0% +factor corrected laptop power supply + + + align:start position:0% +factor corrected laptop power supply +which somebody gave me and you know + + align:start position:0% +which somebody gave me and you know + + + align:start position:0% +which somebody gave me and you know +that's what happens the power supplies + + align:start position:0% +that's what happens the power supplies + + + align:start position:0% +that's what happens the power supplies +people give me um and if you look at + + align:start position:0% +people give me um and if you look at + + + align:start position:0% +people give me um and if you look at +this you know here is + + align:start position:0% +this you know here is + + + align:start position:0% +this you know here is +the twice line frequency energy buffer + + align:start position:0% +the twice line frequency energy buffer + + + align:start position:0% +the twice line frequency energy buffer +over here here's the power stage there's + + align:start position:0% +over here here's the power stage there's + + + align:start position:0% +over here here's the power stage there's +a rectifier up front but a whole good + + align:start position:0% +a rectifier up front but a whole good + + + align:start position:0% +a rectifier up front but a whole good +chunk of this converter right over here + + align:start position:0% +chunk of this converter right over here + + + align:start position:0% +chunk of this converter right over here +is the Emi filter for plugging into the + + align:start position:0% +is the Emi filter for plugging into the + + + align:start position:0% +is the Emi filter for plugging into the +wall + + align:start position:0% +wall + + + align:start position:0% +wall +okay and we're going to talk about how + + align:start position:0% +okay and we're going to talk about how + + + align:start position:0% +okay and we're going to talk about how +you would structure things in a line + + align:start position:0% +you would structure things in a line + + + align:start position:0% +you would structure things in a line +interfaced application but also in a + + align:start position:0% +interfaced application but also in a + + + align:start position:0% +interfaced application but also in a +bunch of other applications and there's + + align:start position:0% +bunch of other applications and there's + + + align:start position:0% +bunch of other applications and there's +one kind of aspect we haven't really uh + + align:start position:0% +one kind of aspect we haven't really uh + + + align:start position:0% +one kind of aspect we haven't really uh +focused on yet and to set that + + align:start position:0% +focused on yet and to set that + + + align:start position:0% +focused on yet and to set that +up let me just give you instead of an AC + + align:start position:0% +up let me just give you instead of an AC + + + align:start position:0% +up let me just give you instead of an AC +application let me talk about a DC + + align:start position:0% +application let me talk about a DC + + + align:start position:0% +application let me talk about a DC +application so suppose I wanted to + + align:start position:0% +application so suppose I wanted to + + + align:start position:0% +application so suppose I wanted to +connect a power converter in a vehicle + + align:start position:0% +connect a power converter in a vehicle + + + align:start position:0% +connect a power converter in a vehicle +and this could be a regular vehicle or + + align:start position:0% +and this could be a regular vehicle or + + + align:start position:0% +and this could be a regular vehicle or +an electrical vehicle + + align:start position:0% + + + + align:start position:0% + +um here's my + + align:start position:0% +um here's my + + + align:start position:0% +um here's my +battery okay and this is let me call + + align:start position:0% +battery okay and this is let me call + + + align:start position:0% +battery okay and this is let me call +this ground this is like the chassis of + + align:start position:0% +this ground this is like the chassis of + + + align:start position:0% +this ground this is like the chassis of +the vehicle okay that's where the + + align:start position:0% +the vehicle okay that's where the + + + align:start position:0% +the vehicle okay that's where the +battery might be + + align:start position:0% +battery might be + + + align:start position:0% +battery might be +tied um I'm going to plug a power + + align:start position:0% +tied um I'm going to plug a power + + + align:start position:0% +tied um I'm going to plug a power +converter into this I'm going to have + + align:start position:0% +converter into this I'm going to have + + + align:start position:0% +converter into this I'm going to have +some cabling right to carry the ground + + align:start position:0% +some cabling right to carry the ground + + + align:start position:0% +some cabling right to carry the ground +and the battery voltage over to whatever + + align:start position:0% +and the battery voltage over to whatever + + + align:start position:0% +and the battery voltage over to whatever +I'm + + align:start position:0% +I'm + + + align:start position:0% +I'm +powering okay all right so here's my + + align:start position:0% +powering okay all right so here's my + + + align:start position:0% +powering okay all right so here's my +cabling cabling in the real world + + align:start position:0% +cabling cabling in the real world + + + align:start position:0% +cabling cabling in the real world +doesn't have zero impedance but let's + + align:start position:0% +doesn't have zero impedance but let's + + + align:start position:0% +doesn't have zero impedance but let's +not worry about that too much now I'm + + align:start position:0% +not worry about that too much now I'm + + + align:start position:0% +not worry about that too much now I'm +going to go dutifully put in my Emi + + align:start position:0% +going to go dutifully put in my Emi + + + align:start position:0% +going to go dutifully put in my Emi +filter okay so maybe I have uh + + align:start position:0% +filter okay so maybe I have uh + + + align:start position:0% +filter okay so maybe I have uh +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +LF + + align:start position:0% +LF + + + align:start position:0% +LF +CF okay and I'll be really smart maybe + + align:start position:0% +CF okay and I'll be really smart maybe + + + align:start position:0% +CF okay and I'll be really smart maybe +I'll say okay let me put in a damping + + align:start position:0% +I'll say okay let me put in a damping + + + align:start position:0% +I'll say okay let me put in a damping +resistor so here I have Rd and + + align:start position:0% +resistor so here I have Rd and + + + align:start position:0% +resistor so here I have Rd and +CD okay so I've sort of done my damping + + align:start position:0% +CD okay so I've sort of done my damping + + + align:start position:0% +CD okay so I've sort of done my damping +job here that's my filter + + align:start position:0% +job here that's my filter + + + align:start position:0% +job here that's my filter +now I'll connect up my converter and + + align:start position:0% +now I'll connect up my converter and + + + align:start position:0% +now I'll connect up my converter and +maybe my converter is a boost converter + + align:start position:0% +maybe my converter is a boost converter + + + align:start position:0% +maybe my converter is a boost converter +right so you know here's my Boost + + align:start position:0% +right so you know here's my Boost + + + align:start position:0% +right so you know here's my Boost +converter it has an inductor has a + + align:start position:0% + + + + align:start position:0% + +transistor diode output cap okay and + + align:start position:0% +transistor diode output cap okay and + + + align:start position:0% +transistor diode output cap okay and +here's my load resistor and I won't + + align:start position:0% +here's my load resistor and I won't + + + align:start position:0% +here's my load resistor and I won't +worry about the details of load too much + + align:start position:0% +worry about the details of load too much + + + align:start position:0% +worry about the details of load too much +and keep in mind this whole thing is + + align:start position:0% +and keep in mind this whole thing is + + + align:start position:0% +and keep in mind this whole thing is +indeed reference to ground but there's + + align:start position:0% +indeed reference to ground but there's + + + align:start position:0% +indeed reference to ground but there's +some cabling so let me just worry about + + align:start position:0% +some cabling so let me just worry about + + + align:start position:0% +some cabling so let me just worry about +this I'll call this vs source + + align:start position:0% + + + + align:start position:0% + +because it's the source of my + + align:start position:0% +because it's the source of my + + + align:start position:0% +because it's the source of my +transistor okay with reference to + + align:start position:0% +transistor okay with reference to + + + align:start position:0% +transistor okay with reference to +ground okay so what do I intend to + + align:start position:0% +ground okay so what do I intend to + + + align:start position:0% +ground okay so what do I intend to +happen in this converter what I intend + + align:start position:0% +happen in this converter what I intend + + + align:start position:0% +happen in this converter what I intend +to happen is right I draw a current from + + align:start position:0% +to happen is right I draw a current from + + + align:start position:0% +to happen is right I draw a current from +my battery it goes through the cable + + align:start position:0% +my battery it goes through the cable + + + align:start position:0% +my battery it goes through the cable +goes through the filter enters the + + align:start position:0% +goes through the filter enters the + + + align:start position:0% +goes through the filter enters the +converter and you know it might go down + + align:start position:0% +converter and you know it might go down + + + align:start position:0% +converter and you know it might go down +through the switch at sometimes or it + + align:start position:0% +through the switch at sometimes or it + + + align:start position:0% +through the switch at sometimes or it +might go down through through the diode + + align:start position:0% +might go down through through the diode + + + align:start position:0% +might go down through through the diode +into the output sometimes but basically + + align:start position:0% +into the output sometimes but basically + + + align:start position:0% +into the output sometimes but basically +it goes through there then it returns in + + align:start position:0% +it goes through there then it returns in + + + align:start position:0% +it goes through there then it returns in +this Loop right so this is the current + + align:start position:0% +this Loop right so this is the current + + + align:start position:0% +this Loop right so this is the current +path I'm really using to power this + + align:start position:0% +path I'm really using to power this + + + align:start position:0% +path I'm really using to power this +converter right and I filtered that + + align:start position:0% +converter right and I filtered that + + + align:start position:0% +converter right and I filtered that +current path here's my + + align:start position:0% +current path here's my + + + align:start position:0% +current path here's my +filter okay that's good um + + align:start position:0% +filter okay that's good um + + + align:start position:0% +filter okay that's good um +but if I think about it I've got a heat + + align:start position:0% +but if I think about it I've got a heat + + + align:start position:0% +but if I think about it I've got a heat +snc the switch in the diode right so + + align:start position:0% +snc the switch in the diode right so + + + align:start position:0% +snc the switch in the diode right so +let's just think about the transistor + + align:start position:0% +let's just think about the transistor + + + align:start position:0% +let's just think about the transistor +and let's remember how we do that uh so + + align:start position:0% +and let's remember how we do that uh so + + + align:start position:0% +and let's remember how we do that uh so +maybe here I have my + + align:start position:0% +maybe here I have my + + + align:start position:0% +maybe here I have my +transistor here's my transistor and then + + align:start position:0% +transistor here's my transistor and then + + + align:start position:0% +transistor here's my transistor and then +I'm going to put down a thermal + + align:start position:0% +I'm going to put down a thermal + + + align:start position:0% +I'm going to put down a thermal +pad and then I'm going to connect that + + align:start position:0% +pad and then I'm going to connect that + + + align:start position:0% +pad and then I'm going to connect that +thermal pad on the other side of that + + align:start position:0% +thermal pad on the other side of that + + + align:start position:0% +thermal pad on the other side of that +thermal pad will be whatever I'm heat + + align:start position:0% +thermal pad will be whatever I'm heat + + + align:start position:0% +thermal pad will be whatever I'm heat +syncing the device + + align:start position:0% +syncing the device + + + align:start position:0% +syncing the device +to okay what I'm often heat syncing the + + align:start position:0% +to okay what I'm often heat syncing the + + + align:start position:0% +to okay what I'm often heat syncing the +device to is either the case of the + + align:start position:0% +device to is either the case of the + + + align:start position:0% +device to is either the case of the +power supply and that case of the power + + align:start position:0% +power supply and that case of the power + + + align:start position:0% +power supply and that case of the power +supply is basically often connected back + + align:start position:0% +supply is basically often connected back + + + align:start position:0% +supply is basically often connected back +to ground in fact sometimes you'll use + + align:start position:0% +to ground in fact sometimes you'll use + + + align:start position:0% +to ground in fact sometimes you'll use +the case of the whole thing to be ground + + align:start position:0% +the case of the whole thing to be ground + + + align:start position:0% +the case of the whole thing to be ground +okay and if I think about a transistor + + align:start position:0% +okay and if I think about a transistor + + + align:start position:0% +okay and if I think about a transistor +in fact what's the the package of the + + align:start position:0% +in fact what's the the package of the + + + align:start position:0% +in fact what's the the package of the +transistor if you have like a t247 or + + align:start position:0% +transistor if you have like a t247 or + + + align:start position:0% +transistor if you have like a t247 or +to220 or something that's actually the + + align:start position:0% +to220 or something that's actually the + + + align:start position:0% +to220 or something that's actually the +drain node of this thing so what I have + + align:start position:0% +drain node of this thing so what I have + + + align:start position:0% +drain node of this thing so what I have +is essentially a piece of metal here a + + align:start position:0% +is essentially a piece of metal here a + + + align:start position:0% +is essentially a piece of metal here a +thin insulator for electrical insulation + + align:start position:0% +thin insulator for electrical insulation + + + align:start position:0% +thin insulator for electrical insulation +and then a ground so what is that that's + + align:start position:0% +and then a ground so what is that that's + + + align:start position:0% +and then a ground so what is that that's +a capacitor right so it turns out that + + align:start position:0% +a capacitor right so it turns out that + + + align:start position:0% +a capacitor right so it turns out that +in most power supplies like + + align:start position:0% +in most power supplies like + + + align:start position:0% +in most power supplies like +this there's going to be a significant + + align:start position:0% +this there's going to be a significant + + + align:start position:0% +this there's going to be a significant +parasitic + + align:start position:0% +parasitic + + + align:start position:0% +parasitic +capacitance I'll just call it CP + + align:start position:0% +capacitance I'll just call it CP + + + align:start position:0% +capacitance I'll just call it CP +parasitic capacitance that gets back to + + align:start position:0% +parasitic capacitance that gets back to + + + align:start position:0% +parasitic capacitance that gets back to +ground because ground is the chassis of + + align:start position:0% +ground because ground is the chassis of + + + align:start position:0% +ground because ground is the chassis of +the vehicle even if you didn't have a + + align:start position:0% +the vehicle even if you didn't have a + + + align:start position:0% +the vehicle even if you didn't have a +heat sink you know you have a node + + align:start position:0% +heat sink you know you have a node + + + align:start position:0% +heat sink you know you have a node +flapping up and down there's stuff + + align:start position:0% +flapping up and down there's stuff + + + align:start position:0% +flapping up and down there's stuff +around it and so there is going to be + + align:start position:0% +around it and so there is going to be + + + align:start position:0% +around it and so there is going to be +some capacitance back to ground + + align:start position:0% +some capacitance back to ground + + + align:start position:0% +some capacitance back to ground +everybody buy + + align:start position:0% + + + + align:start position:0% + +that and so you kind of have this + + align:start position:0% +that and so you kind of have this + + + align:start position:0% +that and so you kind of have this +opportunity to have another uh current + + align:start position:0% +opportunity to have another uh current + + + align:start position:0% +opportunity to have another uh current +path that goes something like + + align:start position:0% +path that goes something like + + + align:start position:0% +path that goes something like +this uh current can flow through this + + align:start position:0% +this uh current can flow through this + + + align:start position:0% +this uh current can flow through this +lead right it could flow uh maybe even + + align:start position:0% +lead right it could flow uh maybe even + + + align:start position:0% +lead right it could flow uh maybe even +here up to here and back to ground or it + + align:start position:0% +here up to here and back to ground or it + + + align:start position:0% +here up to here and back to ground or it +could flow up through this capacitor and + + align:start position:0% +could flow up through this capacitor and + + + align:start position:0% +could flow up through this capacitor and +through this inductor back to ground but + + align:start position:0% +through this inductor back to ground but + + + align:start position:0% +through this inductor back to ground but +nonetheless there is a path at least one + + align:start position:0% +nonetheless there is a path at least one + + + align:start position:0% +nonetheless there is a path at least one +path that's not going through a filter + + align:start position:0% +path that's not going through a filter + + + align:start position:0% +path that's not going through a filter +inductor so I really to the extent that + + align:start position:0% +inductor so I really to the extent that + + + align:start position:0% +inductor so I really to the extent that +this node is slapping up and down with + + align:start position:0% +this node is slapping up and down with + + + align:start position:0% +this node is slapping up and down with +respect to something very close to the + + align:start position:0% +respect to something very close to the + + + align:start position:0% +respect to something very close to the +ground I'm going to get a bunch of + + align:start position:0% +ground I'm going to get a bunch of + + + align:start position:0% +ground I'm going to get a bunch of +current through this parasitic + + align:start position:0% +current through this parasitic + + + align:start position:0% +current through this parasitic +capacitance at high frequency not DC + + align:start position:0% +capacitance at high frequency not DC + + + align:start position:0% +capacitance at high frequency not DC +current just AC current okay and if this + + align:start position:0% +current just AC current okay and if this + + + align:start position:0% +current just AC current okay and if this +long if this lead is kind of long that + + align:start position:0% +long if this lead is kind of long that + + + align:start position:0% +long if this lead is kind of long that +looks just like an antenna right and I'm + + align:start position:0% +looks just like an antenna right and I'm + + + align:start position:0% +looks just like an antenna right and I'm +right next to my radio so I run + + align:start position:0% +right next to my radio so I run + + + align:start position:0% +right next to my radio so I run +into um electromagnetic interference + + align:start position:0% +into um electromagnetic interference + + + align:start position:0% +into um electromagnetic interference +that I'm causing not necessarily through + + align:start position:0% +that I'm causing not necessarily through + + + align:start position:0% +that I'm causing not necessarily through +this + + align:start position:0% +this + + + align:start position:0% +this +lead but current coming through the + + align:start position:0% +lead but current coming through the + + + align:start position:0% +lead but current coming through the +other power + + align:start position:0% +other power + + + align:start position:0% +other power +lead okay + + align:start position:0% +lead okay + + + align:start position:0% +lead okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and this is a problem and in fact I + + align:start position:0% +and this is a problem and in fact I + + + align:start position:0% +and this is a problem and in fact I +mentioned earlier in the class when we + + align:start position:0% +mentioned earlier in the class when we + + + align:start position:0% +mentioned earlier in the class when we +set up our line impedance stabilization + + align:start position:0% +set up our line impedance stabilization + + + align:start position:0% +set up our line impedance stabilization +Network to measure everything usually + + align:start position:0% +Network to measure everything usually + + + align:start position:0% +Network to measure everything usually +you actually have one Len for measuring + + align:start position:0% +you actually have one Len for measuring + + + align:start position:0% +you actually have one Len for measuring +the noise on the hot line and another + + align:start position:0% +the noise on the hot line and another + + + align:start position:0% +the noise on the hot line and another +listen for measuring the noise on the + + align:start position:0% +listen for measuring the noise on the + + + align:start position:0% +listen for measuring the noise on the +return line so you really have to keep + + align:start position:0% +return line so you really have to keep + + + align:start position:0% +return line so you really have to keep +the Emi in both of these leads small + + align:start position:0% +the Emi in both of these leads small + + + align:start position:0% +the Emi in both of these leads small +okay so what I want to do today is just + + align:start position:0% +okay so what I want to do today is just + + + align:start position:0% +okay so what I want to do today is just +talk about how we + + align:start position:0% +talk about how we + + + align:start position:0% +talk about how we +represent um noise in these situations + + align:start position:0% +represent um noise in these situations + + + align:start position:0% +represent um noise in these situations +and then how do we design filters that + + align:start position:0% +and then how do we design filters that + + + align:start position:0% +and then how do we design filters that +deal with those no that noise okay so + + align:start position:0% +deal with those no that noise okay so + + + align:start position:0% +deal with those no that noise okay so +before I go on um are there any + + align:start position:0% +before I go on um are there any + + + align:start position:0% +before I go on um are there any +questions about what the the issue + + align:start position:0% + + + + align:start position:0% + +is okay so let me think about maybe + + align:start position:0% +is okay so let me think about maybe + + + align:start position:0% +is okay so let me think about maybe +another example where this comes up + + align:start position:0% +another example where this comes up + + + align:start position:0% +another example where this comes up +okay um and this this would be something + + align:start position:0% +okay um and this this would be something + + + align:start position:0% +okay um and this this would be something +like that power supply that I'm passing + + align:start position:0% +like that power supply that I'm passing + + + align:start position:0% +like that power supply that I'm passing +around would be plugged into so maybe + + align:start position:0% +around would be plugged into so maybe + + + align:start position:0% +around would be plugged into so maybe +what I have is at home what do you have + + align:start position:0% +what I have is at home what do you have + + + align:start position:0% +what I have is at home what do you have +you have an AC Supply right so here's my + + align:start position:0% +you have an AC Supply right so here's my + + + align:start position:0% +you have an AC Supply right so here's my +AC Supply and I have the hot terminal + + align:start position:0% +AC Supply and I have the hot terminal + + + align:start position:0% +AC Supply and I have the hot terminal +that's the black wire right running + + align:start position:0% +that's the black wire right running + + + align:start position:0% +that's the black wire right running +around your house black is for death + + align:start position:0% +around your house black is for death + + + align:start position:0% +around your house black is for death +don't get near that you have the neutral + + align:start position:0% +don't get near that you have the neutral + + + align:start position:0% +don't get near that you have the neutral +wire which is usually white okay and + + align:start position:0% +wire which is usually white okay and + + + align:start position:0% +wire which is usually white okay and +you're going to carry some cabling + + align:start position:0% +you're going to carry some cabling + + + align:start position:0% +you're going to carry some cabling +inside your walls hot and neutral + + align:start position:0% +inside your walls hot and neutral + + + align:start position:0% +inside your walls hot and neutral +okay and I should say that neutral back + + align:start position:0% +okay and I should say that neutral back + + + align:start position:0% +okay and I should say that neutral back +at the service + + align:start position:0% +at the service + + + align:start position:0% +at the service +entrance somewhere is actually tends to + + align:start position:0% +entrance somewhere is actually tends to + + + align:start position:0% +entrance somewhere is actually tends to +be tied to ground right so the + + align:start position:0% +be tied to ground right so the + + + align:start position:0% +be tied to ground right so the +neutral is going to be um near + + align:start position:0% +neutral is going to be um near + + + align:start position:0% +neutral is going to be um near +ground but it doesn't actually have to + + align:start position:0% +ground but it doesn't actually have to + + + align:start position:0% +ground but it doesn't actually have to +be precisely at + + align:start position:0% +be precisely at + + + align:start position:0% +be precisely at +Ground okay um and you know it'll it'll + + align:start position:0% +Ground okay um and you know it'll it'll + + + align:start position:0% +Ground okay um and you know it'll it'll +be close somewhere right um and very + + align:start position:0% +be close somewhere right um and very + + + align:start position:0% +be close somewhere right um and very +often when if if I think about what + + align:start position:0% +often when if if I think about what + + + align:start position:0% +often when if if I think about what +wires are going out to the boxes usually + + align:start position:0% +wires are going out to the boxes usually + + + align:start position:0% +wires are going out to the boxes usually +there will also be a ground wire that's + + align:start position:0% +there will also be a ground wire that's + + + align:start position:0% +there will also be a ground wire that's +connected to ground right and that's + + align:start position:0% +connected to ground right and that's + + + align:start position:0% +connected to ground right and that's +usually the green or the or the + + align:start position:0% +usually the green or the or the + + + align:start position:0% +usually the green or the or the +uninsulated wire and if you have a three + + align:start position:0% +uninsulated wire and if you have a three + + + align:start position:0% +uninsulated wire and if you have a three +terminal plug one of those goes to the + + align:start position:0% +terminal plug one of those goes to the + + + align:start position:0% +terminal plug one of those goes to the +ground one goes to neutral one goes to + + align:start position:0% +ground one goes to neutral one goes to + + + align:start position:0% +ground one goes to neutral one goes to +hot okay if you have a two terminal plug + + align:start position:0% +hot okay if you have a two terminal plug + + + align:start position:0% +hot okay if you have a two terminal plug +they get rid of this and they just don't + + align:start position:0% +they get rid of this and they just don't + + + align:start position:0% +they get rid of this and they just don't +have an explicit ground going okay make + + align:start position:0% +have an explicit ground going okay make + + + align:start position:0% +have an explicit ground going okay make +sense + + align:start position:0% +sense + + + align:start position:0% +sense +everybody so what happens + + align:start position:0% +everybody so what happens + + + align:start position:0% +everybody so what happens +again okay this is going to plug into my + + align:start position:0% +again okay this is going to plug into my + + + align:start position:0% +again okay this is going to plug into my +whatever my device is and I'll have + + align:start position:0% +whatever my device is and I'll have + + + align:start position:0% +whatever my device is and I'll have +terminal one Terminal Two you know for + + align:start position:0% +terminal one Terminal Two you know for + + + align:start position:0% +terminal one Terminal Two you know for +hot and neutral and then um I may have + + align:start position:0% +hot and neutral and then um I may have + + + align:start position:0% +hot and neutral and then um I may have +some parasitic + + align:start position:0% +some parasitic + + + align:start position:0% +some parasitic +path why might I have a parasitic path + + align:start position:0% +path why might I have a parasitic path + + + align:start position:0% +path why might I have a parasitic path +one reason is in a lot of + + align:start position:0% +one reason is in a lot of + + + align:start position:0% +one reason is in a lot of +equipment we tend to ground the case of + + align:start position:0% +equipment we tend to ground the case of + + + align:start position:0% +equipment we tend to ground the case of +the equipment so if it has a three + + align:start position:0% +the equipment so if it has a three + + + align:start position:0% +the equipment so if it has a three +terminal plug you plug it into the wall + + align:start position:0% +terminal plug you plug it into the wall + + + align:start position:0% +terminal plug you plug it into the wall +that ground connection coming out of + + align:start position:0% +that ground connection coming out of + + + align:start position:0% +that ground connection coming out of +that third terminal is going to the case + + align:start position:0% +that third terminal is going to the case + + + align:start position:0% +that third terminal is going to the case +of the device why because suppose + + align:start position:0% +of the device why because suppose + + + align:start position:0% +of the device why because suppose +there's some fault inside the equipment + + align:start position:0% +there's some fault inside the equipment + + + align:start position:0% +there's some fault inside the equipment +and that fault shorts the hot terminal + + align:start position:0% +and that fault shorts the hot terminal + + + align:start position:0% +and that fault shorts the hot terminal +of the + + align:start position:0% +of the + + + align:start position:0% +of the +case you don't want somebody walking up + + align:start position:0% +case you don't want somebody walking up + + + align:start position:0% +case you don't want somebody walking up +and touching the surface of that thing + + align:start position:0% +and touching the surface of that thing + + + align:start position:0% +and touching the surface of that thing +getting electrocuted right so if they + + align:start position:0% +getting electrocuted right so if they + + + align:start position:0% +getting electrocuted right so if they +ground the case and some fault happens + + align:start position:0% +ground the case and some fault happens + + + align:start position:0% +ground the case and some fault happens +inside huge current will flow it'll blow + + align:start position:0% +inside huge current will flow it'll blow + + + align:start position:0% +inside huge current will flow it'll blow +the breaker and then things will be + + align:start position:0% +the breaker and then things will be + + + align:start position:0% +the breaker and then things will be +disconnected and you'll be safe okay so + + align:start position:0% +disconnected and you'll be safe okay so + + + align:start position:0% +disconnected and you'll be safe okay so +very often there's an explicit + + align:start position:0% +very often there's an explicit + + + align:start position:0% +very often there's an explicit +connection between the case the device + + align:start position:0% +connection between the case the device + + + align:start position:0% +connection between the case the device +and ground + + align:start position:0% +and ground + + + align:start position:0% +and ground +okay and since the case happens to + + align:start position:0% +okay and since the case happens to + + + align:start position:0% +okay and since the case happens to +surround whatever the device is like the + + align:start position:0% +surround whatever the device is like the + + + align:start position:0% +surround whatever the device is like the +power supply it could be in fact if I + + align:start position:0% +power supply it could be in fact if I + + + align:start position:0% +power supply it could be in fact if I +had a boost PFC circuit it looks exactly + + align:start position:0% +had a boost PFC circuit it looks exactly + + + align:start position:0% +had a boost PFC circuit it looks exactly +like the structure I just drew except + + align:start position:0% +like the structure I just drew except + + + align:start position:0% +like the structure I just drew except +that instead of being powered by DC it's + + align:start position:0% +that instead of being powered by DC it's + + + align:start position:0% +that instead of being powered by DC it's +powered by AC and I essentially insert a + + align:start position:0% +powered by AC and I essentially insert a + + + align:start position:0% +powered by AC and I essentially insert a +rectifier here right that's what a boost + + align:start position:0% +rectifier here right that's what a boost + + + align:start position:0% +rectifier here right that's what a boost +rectifier looks like right the front end + + align:start position:0% +rectifier looks like right the front end + + + align:start position:0% +rectifier looks like right the front end +of a lot of power supplies so you know + + align:start position:0% +of a lot of power supplies so you know + + + align:start position:0% +of a lot of power supplies so you know +this structure can kind of very much + + align:start position:0% +this structure can kind of very much + + + align:start position:0% +this structure can kind of very much +represent what would happen in the AC + + align:start position:0% +represent what would happen in the AC + + + align:start position:0% +represent what would happen in the AC +case too except that somewhere I put a + + align:start position:0% +case too except that somewhere I put a + + + align:start position:0% +case too except that somewhere I put a +usually a full bridge to rectify an ac + + align:start position:0% +usually a full bridge to rectify an ac + + + align:start position:0% +usually a full bridge to rectify an ac +voltage which I'd have over here to DC + + align:start position:0% +voltage which I'd have over here to DC + + + align:start position:0% +voltage which I'd have over here to DC +that my converter then processes okay so + + align:start position:0% +that my converter then processes okay so + + + align:start position:0% +that my converter then processes okay so +the consequence of that is is even + + align:start position:0% +the consequence of that is is even + + + align:start position:0% +the consequence of that is is even +though I don't intended to be + + align:start position:0% +though I don't intended to be + + + align:start position:0% +though I don't intended to be +there right there's going to be some + + align:start position:0% +there right there's going to be some + + + align:start position:0% +there right there's going to be some +virtual third terminal which is + + align:start position:0% +virtual third terminal which is + + + align:start position:0% +virtual third terminal which is +connected by some parasitic capacitance + + align:start position:0% +connected by some parasitic capacitance + + + align:start position:0% +connected by some parasitic capacitance +again back to ground + + align:start position:0% + + + + align:start position:0% + +okay even if the case isn't connected to + + align:start position:0% +okay even if the case isn't connected to + + + align:start position:0% +okay even if the case isn't connected to +ground ground is around you right + + align:start position:0% +ground ground is around you right + + + align:start position:0% +ground ground is around you right +there's going to be some flow possibly + + align:start position:0% +there's going to be some flow possibly + + + align:start position:0% +there's going to be some flow possibly +through that okay any questions about + + align:start position:0% + + + + align:start position:0% + +that I should I should have noted by the + + align:start position:0% +that I should I should have noted by the + + + align:start position:0% +that I should I should have noted by the +way and I'll come back to this it's a + + align:start position:0% +way and I'll come back to this it's a + + + align:start position:0% +way and I'll come back to this it's a +little bit easier to see in this case of + + align:start position:0% +little bit easier to see in this case of + + + align:start position:0% +little bit easier to see in this case of +the DC + + align:start position:0% +the DC + + + align:start position:0% +the DC +case if I've done this and now I have + + align:start position:0% +case if I've done this and now I have + + + align:start position:0% +case if I've done this and now I have +very peaky currents coming through this + + align:start position:0% +very peaky currents coming through this + + + align:start position:0% +very peaky currents coming through this +um parasitic + + align:start position:0% +um parasitic + + + align:start position:0% +um parasitic +capacitance I have high frequency + + align:start position:0% +capacitance I have high frequency + + + align:start position:0% +capacitance I have high frequency +currents flowing on this lead right if + + align:start position:0% +currents flowing on this lead right if + + + align:start position:0% +currents flowing on this lead right if +this if this uh pathway has some you + + align:start position:0% +this if this uh pathway has some you + + + align:start position:0% +this if this uh pathway has some you +know parasitic resistance and maybe a + + align:start position:0% +know parasitic resistance and maybe a + + + align:start position:0% +know parasitic resistance and maybe a +little parasitic inductance from all the + + align:start position:0% +little parasitic inductance from all the + + + align:start position:0% +little parasitic inductance from all the +wiring I can develop a voltage drop + + align:start position:0% +wiring I can develop a voltage drop + + + align:start position:0% +wiring I can develop a voltage drop +across here and so this voltage is + + align:start position:0% +across here and so this voltage is + + + align:start position:0% +across here and so this voltage is +nonzero I'll see what's called Ground + + align:start position:0% +nonzero I'll see what's called Ground + + + align:start position:0% +nonzero I'll see what's called Ground +bounce and maybe you've experienced this + + align:start position:0% +bounce and maybe you've experienced this + + + align:start position:0% +bounce and maybe you've experienced this +when you've tried to measure like just + + align:start position:0% +when you've tried to measure like just + + + align:start position:0% +when you've tried to measure like just +ground on your some circuit you're + + align:start position:0% +ground on your some circuit you're + + + align:start position:0% +ground on your some circuit you're +building and and it looks like it's got + + align:start position:0% +building and and it looks like it's got + + + align:start position:0% +building and and it looks like it's got +a bunch of high frequency junk on it + + align:start position:0% +a bunch of high frequency junk on it + + + align:start position:0% +a bunch of high frequency junk on it +that's exactly due to this kind of + + align:start position:0% +that's exactly due to this kind of + + + align:start position:0% +that's exactly due to this kind of +phenomena okay so we can + + align:start position:0% +phenomena okay so we can + + + align:start position:0% +phenomena okay so we can +see even though I intend this know to be + + align:start position:0% +see even though I intend this know to be + + + align:start position:0% +see even though I intend this know to be +in an Ideal World this is to be a zero + + align:start position:0% +in an Ideal World this is to be a zero + + + align:start position:0% +in an Ideal World this is to be a zero +resistance zero inductance wire and I + + align:start position:0% +resistance zero inductance wire and I + + + align:start position:0% +resistance zero inductance wire and I +intended there to be no voltage there + + align:start position:0% +intended there to be no voltage there + + + align:start position:0% +intended there to be no voltage there +because it's not an Ideal wire it's a + + align:start position:0% +because it's not an Ideal wire it's a + + + align:start position:0% +because it's not an Ideal wire it's a +real one there will be ground bounce + + align:start position:0% +real one there will be ground bounce + + + align:start position:0% +real one there will be ground bounce +here that I have to contain + + align:start position:0% +here that I have to contain + + + align:start position:0% +here that I have to contain +with okay so um when I go to think + + align:start position:0% +with okay so um when I go to think + + + align:start position:0% +with okay so um when I go to think +about um + + align:start position:0% +about um + + + align:start position:0% +about um +this + + align:start position:0% +this + + + align:start position:0% +this +network okay maybe I will think about a + + align:start position:0% +network okay maybe I will think about a + + + align:start position:0% +network okay maybe I will think about a +current into terminal one that I'm going + + align:start position:0% +current into terminal one that I'm going + + + align:start position:0% +current into terminal one that I'm going +to call + + align:start position:0% +to call + + + align:start position:0% +to call +i1 I'm going to think about a current + + align:start position:0% +i1 I'm going to think about a current + + + align:start position:0% +i1 I'm going to think about a current +into Terminal Two that I'm going to call + + align:start position:0% +into Terminal Two that I'm going to call + + + align:start position:0% +into Terminal Two that I'm going to call +I2 again I could talk about the voltage + + align:start position:0% +I2 again I could talk about the voltage + + + align:start position:0% +I2 again I could talk about the voltage +at terminal one with respect to ground + + align:start position:0% +at terminal one with respect to ground + + + align:start position:0% +at terminal one with respect to ground +I'm going to call that V1 and I can + + align:start position:0% +I'm going to call that V1 and I can + + + align:start position:0% +I'm going to call that V1 and I can +think about the voltage at Terminal 2 + + align:start position:0% +think about the voltage at Terminal 2 + + + align:start position:0% +think about the voltage at Terminal 2 +with respect to ground then I'm going to + + align:start position:0% +with respect to ground then I'm going to + + + align:start position:0% +with respect to ground then I'm going to +call that V2 right and I will recognize + + align:start position:0% +call that V2 right and I will recognize + + + align:start position:0% +call that V2 right and I will recognize +that yeah V2 should be close to ground + + align:start position:0% +that yeah V2 should be close to ground + + + align:start position:0% +that yeah V2 should be close to ground +because back through a bunch of wiring + + align:start position:0% +because back through a bunch of wiring + + + align:start position:0% +because back through a bunch of wiring +it is tied to ground but that's a DC not + + align:start position:0% +it is tied to ground but that's a DC not + + + align:start position:0% +it is tied to ground but that's a DC not +NE and even a DC there's some resistance + + align:start position:0% +NE and even a DC there's some resistance + + + align:start position:0% +NE and even a DC there's some resistance +there right so I can think about V1 V2 + + align:start position:0% +there right so I can think about V1 V2 + + + align:start position:0% +there right so I can think about V1 V2 +i1 and I2 as being sort of the net + + align:start position:0% +i1 and I2 as being sort of the net + + + align:start position:0% +i1 and I2 as being sort of the net +currents flowing into my + + align:start position:0% +currents flowing into my + + + align:start position:0% +currents flowing into my +device any questions about that + + align:start position:0% + + + + align:start position:0% + +so what do I intend to happen in this + + align:start position:0% +so what do I intend to happen in this + + + align:start position:0% +so what do I intend to happen in this +device I don't I didn't really want this + + align:start position:0% +device I don't I didn't really want this + + + align:start position:0% +device I don't I didn't really want this +parasitic capacitance I'm just getting + + align:start position:0% +parasitic capacitance I'm just getting + + + align:start position:0% +parasitic capacitance I'm just getting +it right so so the ideal path for that + + align:start position:0% +it right so so the ideal path for that + + + align:start position:0% +it right so so the ideal path for that +I'm thinking okay this is how my + + align:start position:0% +I'm thinking okay this is how my + + + align:start position:0% +I'm thinking okay this is how my +converter should work right is I should + + align:start position:0% +converter should work right is I should + + + align:start position:0% +converter should work right is I should +have current that's sort of coming from + + align:start position:0% +have current that's sort of coming from + + + align:start position:0% +have current that's sort of coming from +the power the the voltage source into + + align:start position:0% +the power the the voltage source into + + + align:start position:0% +the power the the voltage source into +terminal one coming back out Terminal 2 + + align:start position:0% +terminal one coming back out Terminal 2 + + + align:start position:0% +terminal one coming back out Terminal 2 +and doing this kind of loop right around + + align:start position:0% +and doing this kind of loop right around + + + align:start position:0% +and doing this kind of loop right around +like this + + align:start position:0% +like this + + + align:start position:0% +like this +okay and that's fine + + align:start position:0% +okay and that's fine + + + align:start position:0% +okay and that's fine +um but because of this parasitic there + + align:start position:0% +um but because of this parasitic there + + + align:start position:0% +um but because of this parasitic there +can be some other path that I might want + + align:start position:0% +can be some other path that I might want + + + align:start position:0% +can be some other path that I might want +to think about + + align:start position:0% +to think about + + + align:start position:0% +to think about +okay and if I didn't have this other + + align:start position:0% +okay and if I didn't have this other + + + align:start position:0% +okay and if I didn't have this other +path what would I have I'd have i1 is + + align:start position:0% +path what would I have I'd have i1 is + + + align:start position:0% +path what would I have I'd have i1 is +equal to minus I2 right that's the ideal + + align:start position:0% +equal to minus I2 right that's the ideal + + + align:start position:0% +equal to minus I2 right that's the ideal +case when this other path doesn't exist + + align:start position:0% +case when this other path doesn't exist + + + align:start position:0% +case when this other path doesn't exist +all right um if the other path does EX + + align:start position:0% +all right um if the other path does EX + + + align:start position:0% +all right um if the other path does EX +exist right we get what we would call a + + align:start position:0% +exist right we get what we would call a + + + align:start position:0% +exist right we get what we would call a +common mode signal that I'm going to + + align:start position:0% +common mode signal that I'm going to + + + align:start position:0% +common mode signal that I'm going to +call + + align:start position:0% + + + + align:start position:0% + +ICM common mode current common mode + + align:start position:0% +ICM common mode current common mode + + + align:start position:0% +ICM common mode current common mode +because I think of it as coming through + + align:start position:0% +because I think of it as coming through + + + align:start position:0% +because I think of it as coming through +somehow the two leads together into the + + align:start position:0% +somehow the two leads together into the + + + align:start position:0% +somehow the two leads together into the +device and then out through the device + + align:start position:0% +device and then out through the device + + + align:start position:0% +device and then out through the device +through some third path does that make + + align:start position:0% +through some third path does that make + + + align:start position:0% +through some third path does that make +sense + + align:start position:0% +sense + + + align:start position:0% +sense +everybody and this common mode current + + align:start position:0% +everybody and this common mode current + + + align:start position:0% +everybody and this common mode current +okay um maybe I would think of as + + align:start position:0% +okay um maybe I would think of as + + + align:start position:0% +okay um maybe I would think of as +flowing like + + align:start position:0% +flowing like + + + align:start position:0% +flowing like +this half of it coming in this terminal + + align:start position:0% +this half of it coming in this terminal + + + align:start position:0% +this half of it coming in this terminal +so I'm going to call this 1 12 + + align:start position:0% +so I'm going to call this 1 12 + + + align:start position:0% +so I'm going to call this 1 12 +ICM half of it coming through this + + align:start position:0% +ICM half of it coming through this + + + align:start position:0% +ICM half of it coming through this +terminal this is 1 12 + + align:start position:0% +terminal this is 1 12 + + + align:start position:0% +terminal this is 1 12 +ICM and then you know it comes out the + + align:start position:0% +ICM and then you know it comes out the + + + align:start position:0% +ICM and then you know it comes out the +other side of the device and returns to + + align:start position:0% +other side of the device and returns to + + + align:start position:0% +other side of the device and returns to +ground like + + align:start position:0% +ground like + + + align:start position:0% +ground like +this + + align:start position:0% +this + + + align:start position:0% +this +okay so that's this is what I'm thinking + + align:start position:0% +okay so that's this is what I'm thinking + + + align:start position:0% +okay so that's this is what I'm thinking +of as my common mode + + align:start position:0% +of as my common mode + + + align:start position:0% +of as my common mode +current the current that I was thinking + + align:start position:0% +current the current that I was thinking + + + align:start position:0% +current the current that I was thinking +of flowing around the loop which I have + + align:start position:0% +of flowing around the loop which I have + + + align:start position:0% +of flowing around the loop which I have +in the ideal case we would call this the + + align:start position:0% +in the ideal case we would call this the + + + align:start position:0% +in the ideal case we would call this the +differential mode + + align:start position:0% +differential mode + + + align:start position:0% +differential mode +current + + align:start position:0% +current + + + align:start position:0% +current +okay so how would I represent the common + + align:start position:0% +okay so how would I represent the common + + + align:start position:0% +okay so how would I represent the common +mode and differential mode current well + + align:start position:0% +mode and differential mode current well + + + align:start position:0% +mode and differential mode current well +by definition by what I've told you + + align:start position:0% +by definition by what I've told you + + + align:start position:0% +by definition by what I've told you +ICM is equal to i1 + I2 right by you + + align:start position:0% +ICM is equal to i1 + I2 right by you + + + align:start position:0% +ICM is equal to i1 + I2 right by you +know if I basically make this a super + + align:start position:0% +know if I basically make this a super + + + align:start position:0% +know if I basically make this a super +node icm's coming out but I'm calling + + align:start position:0% +node icm's coming out but I'm calling + + + align:start position:0% +node icm's coming out but I'm calling +that ICM so it must be equal to i1 plus + + align:start position:0% +that ICM so it must be equal to i1 plus + + + align:start position:0% +that ICM so it must be equal to i1 plus +I2 everybody buy + + align:start position:0% +I2 everybody buy + + + align:start position:0% +I2 everybody buy +that now I got to Define what I think + + align:start position:0% +that now I got to Define what I think + + + align:start position:0% +that now I got to Define what I think +about this differential mode current + + align:start position:0% +about this differential mode current + + + align:start position:0% +about this differential mode current +okay in the case when I didn't have ICM + + align:start position:0% +okay in the case when I didn't have ICM + + + align:start position:0% +okay in the case when I didn't have ICM +uh the differential mode current would + + align:start position:0% +uh the differential mode current would + + + align:start position:0% +uh the differential mode current would +be you know i1 would equal IDM and I2 + + align:start position:0% +be you know i1 would equal IDM and I2 + + + align:start position:0% +be you know i1 would equal IDM and I2 +would be equal to minus + + align:start position:0% +would be equal to minus + + + align:start position:0% +would be equal to minus +IDM right the way we tend to define the + + align:start position:0% +IDM right the way we tend to define the + + + align:start position:0% +IDM right the way we tend to define the +differential IAL mode current + + align:start position:0% +differential IAL mode current + + + align:start position:0% +differential IAL mode current +IDM is simply as being the average of + + align:start position:0% +IDM is simply as being the average of + + + align:start position:0% +IDM is simply as being the average of +the currents I thought I was going to + + align:start position:0% +the currents I thought I was going to + + + align:start position:0% +the currents I thought I was going to +get so I would call it i1 minus I2 over + + align:start position:0% +get so I would call it i1 minus I2 over + + + align:start position:0% +get so I would call it i1 minus I2 over +2 okay so this is sort of um and and the + + align:start position:0% +2 okay so this is sort of um and and the + + + align:start position:0% +2 okay so this is sort of um and and the +reason I'm emphasizing it this way is + + align:start position:0% +reason I'm emphasizing it this way is + + + align:start position:0% +reason I'm emphasizing it this way is +just because these are the definitions + + align:start position:0% +just because these are the definitions + + + align:start position:0% +just because these are the definitions +of the common mode and differential mode + + align:start position:0% +of the common mode and differential mode + + + align:start position:0% +of the common mode and differential mode +components okay if I went and said okay + + align:start position:0% +components okay if I went and said okay + + + align:start position:0% +components okay if I went and said okay +if I if I you if I apply those two + + align:start position:0% +if I if I you if I apply those two + + + align:start position:0% +if I if I you if I apply those two +definitions what I get for i1 and I2 if + + align:start position:0% +definitions what I get for i1 and I2 if + + + align:start position:0% +definitions what I get for i1 and I2 if +I recombine this is I get + + align:start position:0% +I recombine this is I get + + + align:start position:0% +I recombine this is I get +i1 is equal to uh I + + align:start position:0% +i1 is equal to uh I + + + align:start position:0% +i1 is equal to uh I +DM plus 12 + + align:start position:0% +DM plus 12 + + + align:start position:0% +DM plus 12 +ICM and I2 is equal to minus + + align:start position:0% +ICM and I2 is equal to minus + + + align:start position:0% +ICM and I2 is equal to minus +IDM plus 12 + + align:start position:0% +IDM plus 12 + + + align:start position:0% +IDM plus 12 +ICM okay so by using things this way + + align:start position:0% +ICM okay so by using things this way + + + align:start position:0% +ICM okay so by using things this way +what I'm really saying is okay uh if I + + align:start position:0% +what I'm really saying is okay uh if I + + + align:start position:0% +what I'm really saying is okay uh if I +had no common mode current I'd have IDM + + align:start position:0% +had no common mode current I'd have IDM + + + align:start position:0% +had no common mode current I'd have IDM +in terminal one and minus IDM and + + align:start position:0% +in terminal one and minus IDM and + + + align:start position:0% +in terminal one and minus IDM and +Terminal 2 that's what I going into + + align:start position:0% +Terminal 2 that's what I going into + + + align:start position:0% +Terminal 2 that's what I going into +Terminal Two that's what I expect and + + align:start position:0% +Terminal Two that's what I expect and + + + align:start position:0% +Terminal Two that's what I expect and +then I'm saying that each of these two + + align:start position:0% +then I'm saying that each of these two + + + align:start position:0% +then I'm saying that each of these two +terminals is carrying half the common + + align:start position:0% +terminals is carrying half the common + + + align:start position:0% +terminals is carrying half the common +mode current that's that's essentially + + align:start position:0% +mode current that's that's essentially + + + align:start position:0% +mode current that's that's essentially +what the different that's essentially + + align:start position:0% +what the different that's essentially + + + align:start position:0% +what the different that's essentially +what the definition + + align:start position:0% +what the definition + + + align:start position:0% +what the definition +says okay does that make sense to + + align:start position:0% + + + + align:start position:0% + +everybody um + + align:start position:0% + + + + align:start position:0% + +what about voltages right I've focused + + align:start position:0% +what about voltages right I've focused + + + align:start position:0% +what about voltages right I've focused +on the currents here but I've said I + + align:start position:0% +on the currents here but I've said I + + + align:start position:0% +on the currents here but I've said I +have a voltage at terminal one and a + + align:start position:0% +have a voltage at terminal one and a + + + align:start position:0% +have a voltage at terminal one and a +voltage at Terminal Two and I can't + + align:start position:0% +voltage at Terminal Two and I can't + + + align:start position:0% +voltage at Terminal Two and I can't +assume that the voltage of Terminal 2 is + + align:start position:0% +assume that the voltage of Terminal 2 is + + + align:start position:0% +assume that the voltage of Terminal 2 is +ground because of this ground balce kind + + align:start position:0% +ground because of this ground balce kind + + + align:start position:0% +ground because of this ground balce kind +of stuff going on and it's not and the + + align:start position:0% +of stuff going on and it's not and the + + + align:start position:0% +of stuff going on and it's not and the +fact there's a bunch of cabling here + + align:start position:0% +fact there's a bunch of cabling here + + + align:start position:0% +fact there's a bunch of cabling here +whether it's you know switching ground + + align:start position:0% +whether it's you know switching ground + + + align:start position:0% +whether it's you know switching ground +bounce or not there's some difference + + align:start position:0% +bounce or not there's some difference + + + align:start position:0% +bounce or not there's some difference +between that and + + align:start position:0% +between that and + + + align:start position:0% +between that and +ground so um we can also come up with + + align:start position:0% +ground so um we can also come up with + + + align:start position:0% +ground so um we can also come up with +definitions of voltage okay the common + + align:start position:0% +definitions of voltage okay the common + + + align:start position:0% +definitions of voltage okay the common +mode voltage + + align:start position:0% +mode voltage + + + align:start position:0% +mode voltage +if I'm going to look at the input point + + align:start position:0% +if I'm going to look at the input point + + + align:start position:0% +if I'm going to look at the input point +so I'm going to look at this point here + + align:start position:0% +so I'm going to look at this point here + + + align:start position:0% +so I'm going to look at this point here +okay I could Define the common mode + + align:start position:0% +okay I could Define the common mode + + + align:start position:0% +okay I could Define the common mode +voltage at the input of the device as + + align:start position:0% +voltage at the input of the device as + + + align:start position:0% +voltage at the input of the device as +being + + align:start position:0% +being + + + align:start position:0% +being +vcm is equal to V1 + V2 over two okay so + + align:start position:0% +vcm is equal to V1 + V2 over two okay so + + + align:start position:0% +vcm is equal to V1 + V2 over two okay so +basically the common mode voltage is the + + align:start position:0% +basically the common mode voltage is the + + + align:start position:0% +basically the common mode voltage is the +average of the two voltages + + align:start position:0% +average of the two voltages + + + align:start position:0% +average of the two voltages +driving node one and node + + align:start position:0% +driving node one and node + + + align:start position:0% +driving node one and node +two the differential mode voltage + + align:start position:0% +two the differential mode voltage + + + align:start position:0% +two the differential mode voltage +BDM is simply equal to V1 minus + + align:start position:0% +BDM is simply equal to V1 minus + + + align:start position:0% +BDM is simply equal to V1 minus +V2 okay if I thought about it you know + + align:start position:0% +V2 okay if I thought about it you know + + + align:start position:0% +V2 okay if I thought about it you know +V1 with respect to ground minus V2 with + + align:start position:0% +V1 with respect to ground minus V2 with + + + align:start position:0% +V1 with respect to ground minus V2 with +respect to ground is this voltage + + align:start position:0% +respect to ground is this voltage + + + align:start position:0% +respect to ground is this voltage +vdm right that's the voltage into which + + align:start position:0% +vdm right that's the voltage into which + + + align:start position:0% +vdm right that's the voltage into which +I was intending to sort of apply to my + + align:start position:0% +I was intending to sort of apply to my + + + align:start position:0% +I was intending to sort of apply to my +device right it's the the difference in + + align:start position:0% +device right it's the the difference in + + + align:start position:0% +device right it's the the difference in +the true terminals is sort of my input + + align:start position:0% +the true terminals is sort of my input + + + align:start position:0% +the true terminals is sort of my input +of my device so that is the differential + + align:start position:0% +of my device so that is the differential + + + align:start position:0% +of my device so that is the differential +mode voltage the common mode voltage I'm + + align:start position:0% +mode voltage the common mode voltage I'm + + + align:start position:0% +mode voltage the common mode voltage I'm +just defining is the average + + align:start position:0% +just defining is the average + + + align:start position:0% +just defining is the average +and if I put those two things together + + align:start position:0% +and if I put those two things together + + + align:start position:0% +and if I put those two things together +what I get is that V1 is equal to a + + align:start position:0% +what I get is that V1 is equal to a + + + align:start position:0% +what I get is that V1 is equal to a +vcm plus 12 + + align:start position:0% +vcm plus 12 + + + align:start position:0% +vcm plus 12 +vdm and V2 is equal to vcm minus 12 + + align:start position:0% +vdm and V2 is equal to vcm minus 12 + + + align:start position:0% +vdm and V2 is equal to vcm minus 12 +vdm okay so I'm issuing a + + align:start position:0% +vdm okay so I'm issuing a + + + align:start position:0% +vdm okay so I'm issuing a +decomposition of you know voltage one + + align:start position:0% +decomposition of you know voltage one + + + align:start position:0% +decomposition of you know voltage one +and voltage two with respect to ground + + align:start position:0% +and voltage two with respect to ground + + + align:start position:0% +and voltage two with respect to ground +and current one current to into common + + align:start position:0% +and current one current to into common + + + align:start position:0% +and current one current to into common +mode and differential mode + + align:start position:0% +mode and differential mode + + + align:start position:0% +mode and differential mode +components okay so this is just a + + align:start position:0% +components okay so this is just a + + + align:start position:0% +components okay so this is just a +decomposition by the way uh you know + + align:start position:0% +decomposition by the way uh you know + + + align:start position:0% +decomposition by the way uh you know +it's kind of funny because you notice + + align:start position:0% +it's kind of funny because you notice + + + align:start position:0% +it's kind of funny because you notice +that ICM is i1 plus I2 and then vcm is + + align:start position:0% +that ICM is i1 plus I2 and then vcm is + + + align:start position:0% +that ICM is i1 plus I2 and then vcm is +the average and the differential Mode's + + align:start position:0% +the average and the differential Mode's + + + align:start position:0% +the average and the differential Mode's +defined the other way around one of the + + align:start position:0% +defined the other way around one of the + + + align:start position:0% +defined the other way around one of the +reasons why you define it this way is + + align:start position:0% +reasons why you define it this way is + + + align:start position:0% +reasons why you define it this way is +because if I said What's the total + + align:start position:0% +because if I said What's the total + + + align:start position:0% +because if I said What's the total +power flowing here right I could say it + + align:start position:0% +power flowing here right I could say it + + + align:start position:0% +power flowing here right I could say it +was you know p i could write as being + + align:start position:0% +was you know p i could write as being + + + align:start position:0% +was you know p i could write as being +equal to V1 * i1 that's sort of the + + align:start position:0% +equal to V1 * i1 that's sort of the + + + align:start position:0% +equal to V1 * i1 that's sort of the +power into this + + align:start position:0% +power into this + + + align:start position:0% +power into this +port um with respect to ground plus V2 + + align:start position:0% +port um with respect to ground plus V2 + + + align:start position:0% +port um with respect to ground plus V2 +I2 and if I work that out that works out + + align:start position:0% +I2 and if I work that out that works out + + + align:start position:0% +I2 and if I work that out that works out +to be precisely equal to + + align:start position:0% +to be precisely equal to + + + align:start position:0% +to be precisely equal to +vcm ICM plus + + align:start position:0% +vcm ICM plus + + + align:start position:0% +vcm ICM plus +vdm IDM all right so whether I + + align:start position:0% +vdm IDM all right so whether I + + + align:start position:0% +vdm IDM all right so whether I +decompose if I take my voltage and + + align:start position:0% +decompose if I take my voltage and + + + align:start position:0% +decompose if I take my voltage and +currents and I decompose into a common + + align:start position:0% +currents and I decompose into a common + + + align:start position:0% +currents and I decompose into a common +differential mode it preserves the + + align:start position:0% +differential mode it preserves the + + + align:start position:0% +differential mode it preserves the +notion of power + + align:start position:0% +notion of power + + + align:start position:0% +notion of power +okay so that's just kind of a convenient + + align:start position:0% +okay so that's just kind of a convenient + + + align:start position:0% +okay so that's just kind of a convenient +handy fact it's not important from the + + align:start position:0% +handy fact it's not important from the + + + align:start position:0% +handy fact it's not important from the +perspective of we're trying to use + + align:start position:0% +perspective of we're trying to use + + + align:start position:0% +perspective of we're trying to use +common mode and differential mode to + + align:start position:0% +common mode and differential mode to + + + align:start position:0% +common mode and differential mode to +deliver power I'm really trying to + + align:start position:0% +deliver power I'm really trying to + + + align:start position:0% +deliver power I'm really trying to +deliver my power into this thing through + + align:start position:0% +deliver my power into this thing through + + + align:start position:0% +deliver my power into this thing through +differential mode that's the notion of + + align:start position:0% +differential mode that's the notion of + + + align:start position:0% +differential mode that's the notion of +how this thing's supposed to work I + + align:start position:0% +how this thing's supposed to work I + + + align:start position:0% +how this thing's supposed to work I +really don't want any current flowing in + + align:start position:0% +really don't want any current flowing in + + + align:start position:0% +really don't want any current flowing in +my ground + + align:start position:0% + + + + align:start position:0% + +path but the the the other reason why + + align:start position:0% +path but the the the other reason why + + + align:start position:0% +path but the the the other reason why +people think about + + align:start position:0% +people think about + + + align:start position:0% +people think about +this um Decon composition of voltages + + align:start position:0% +this um Decon composition of voltages + + + align:start position:0% +this um Decon composition of voltages +and currents is because I tend to use + + align:start position:0% +and currents is because I tend to use + + + align:start position:0% +and currents is because I tend to use +different techniques to fix common mode + + align:start position:0% +different techniques to fix common mode + + + align:start position:0% +different techniques to fix common mode +noise and differential mode + + align:start position:0% +noise and differential mode + + + align:start position:0% +noise and differential mode +noise okay and so knowing like + + align:start position:0% +noise okay and so knowing like + + + align:start position:0% +noise okay and so knowing like +decomposing it that way tells you what + + align:start position:0% +decomposing it that way tells you what + + + align:start position:0% +decomposing it that way tells you what +technique should I use to make a better + + align:start position:0% +technique should I use to make a better + + + align:start position:0% +technique should I use to make a better +filter okay so let's think about this + + align:start position:0% +filter okay so let's think about this + + + align:start position:0% +filter okay so let's think about this +for a + + align:start position:0% +for a + + + align:start position:0% +for a +second + + align:start position:0% +second + + + align:start position:0% +second +um what might I do in a filter + + align:start position:0% +um what might I do in a filter + + + align:start position:0% +um what might I do in a filter +design well let let's let's go design a + + align:start position:0% +design well let let's let's go design a + + + align:start position:0% +design well let let's let's go design a +filter for this thing now and keep in + + align:start position:0% +filter for this thing now and keep in + + + align:start position:0% +filter for this thing now and keep in +mind we're going to have to put some + + align:start position:0% +mind we're going to have to put some + + + align:start position:0% +mind we're going to have to put some +kind of filtering to deal with the fact + + align:start position:0% +kind of filtering to deal with the fact + + + align:start position:0% +kind of filtering to deal with the fact +that I can't allow lots of high + + align:start position:0% +that I can't allow lots of high + + + align:start position:0% +that I can't allow lots of high +frequency currents through you know this + + align:start position:0% +frequency currents through you know this + + + align:start position:0% +frequency currents through you know this +path right so I can't just say do what I + + align:start position:0% +path right so I can't just say do what I + + + align:start position:0% +path right so I can't just say do what I +I did before and just have sort of a + + align:start position:0% +I did before and just have sort of a + + + align:start position:0% +I did before and just have sort of a +single-ended kind of filter that filters + + align:start position:0% +single-ended kind of filter that filters + + + align:start position:0% +single-ended kind of filter that filters +One path I'm going to have to do + + align:start position:0% +One path I'm going to have to do + + + align:start position:0% +One path I'm going to have to do +something that filters kind of both + + align:start position:0% +something that filters kind of both + + + align:start position:0% +something that filters kind of both +leads going to my converter okay now in + + align:start position:0% +leads going to my converter okay now in + + + align:start position:0% +leads going to my converter okay now in +some cases you can get away + + align:start position:0% +some cases you can get away + + + align:start position:0% +some cases you can get away +with a single-ended filter right if this + + align:start position:0% +with a single-ended filter right if this + + + align:start position:0% +with a single-ended filter right if this +whole thing were built on top of a + + align:start position:0% +whole thing were built on top of a + + + align:start position:0% +whole thing were built on top of a +ground plane and there was no wires + + align:start position:0% +ground plane and there was no wires + + + align:start position:0% +ground plane and there was no wires +going anywhere right and there's just + + align:start position:0% +going anywhere right and there's just + + + align:start position:0% +going anywhere right and there's just +one big ground plane well then sure you + + align:start position:0% +one big ground plane well then sure you + + + align:start position:0% +one big ground plane well then sure you +only need to filter one lead because + + align:start position:0% +only need to filter one lead because + + + align:start position:0% +only need to filter one lead because +everything else is traveling in the big + + align:start position:0% +everything else is traveling in the big + + + align:start position:0% +everything else is traveling in the big +ground plane but if you have a device + + align:start position:0% +ground plane but if you have a device + + + align:start position:0% +ground plane but if you have a device +that's connected over some cabling you + + align:start position:0% +that's connected over some cabling you + + + align:start position:0% +that's connected over some cabling you +better think twice because there could + + align:start position:0% +better think twice because there could + + + align:start position:0% +better think twice because there could +be some unintended path back okay all + + align:start position:0% +be some unintended path back okay all + + + align:start position:0% +be some unintended path back okay all +right so let's go think about how I + + align:start position:0% +right so let's go think about how I + + + align:start position:0% +right so let's go think about how I +would design a filter to deal with this + + align:start position:0% +would design a filter to deal with this + + + align:start position:0% +would design a filter to deal with this +um so here I go here is my device + + align:start position:0% +um so here I go here is my device + + + align:start position:0% +um so here I go here is my device +again um and here's + + align:start position:0% +again um and here's + + + align:start position:0% +again um and here's +one two and ter my unintended terminal + + align:start position:0% +one two and ter my unintended terminal + + + align:start position:0% +one two and ter my unintended terminal +three right and if I thought about let + + align:start position:0% +three right and if I thought about let + + + align:start position:0% +three right and if I thought about let +me just think about and it's not quite + + align:start position:0% +me just think about and it's not quite + + + align:start position:0% +me just think about and it's not quite +true but let me just think about for + + align:start position:0% +true but let me just think about for + + + align:start position:0% +true but let me just think about for +Simplicity as my converter being a + + align:start position:0% +Simplicity as my converter being a + + + align:start position:0% +Simplicity as my converter being a +source of drawing common and + + align:start position:0% +source of drawing common and + + + align:start position:0% +source of drawing common and +differential mode + + align:start position:0% +differential mode + + + align:start position:0% +differential mode +currents okay so I might think of it + + align:start position:0% +currents okay so I might think of it + + + align:start position:0% +currents okay so I might think of it +this way I might think of this coming in + + align:start position:0% +this way I might think of this coming in + + + align:start position:0% +this way I might think of this coming in +here and + + align:start position:0% +here and + + + align:start position:0% +here and +drawing a differential mode current + + align:start position:0% +drawing a differential mode current + + + align:start position:0% +drawing a differential mode current +IDM right and that would include the + + align:start position:0% +IDM right and that would include the + + + align:start position:0% +IDM right and that would include the +power current plus any switching noise + + align:start position:0% +power current plus any switching noise + + + align:start position:0% +power current plus any switching noise +or something coming between these two + + align:start position:0% +or something coming between these two + + + align:start position:0% +or something coming between these two +terminals okay and then if I thought + + align:start position:0% +terminals okay and then if I thought + + + align:start position:0% +terminals okay and then if I thought +well I might be driving some common mode + + align:start position:0% +well I might be driving some common mode + + + align:start position:0% +well I might be driving some common mode +currents what would that be I'd + + align:start position:0% +currents what would that be I'd + + + align:start position:0% +currents what would that be I'd +have 1 + + align:start position:0% +have 1 + + + align:start position:0% +have 1 +12 ICM being drawn this way + + align:start position:0% +12 ICM being drawn this way + + + align:start position:0% +12 ICM being drawn this way +out here and + + align:start position:0% + + + + align:start position:0% + +12 ICM being drawn this way to the + + align:start position:0% +12 ICM being drawn this way to the + + + align:start position:0% +12 ICM being drawn this way to the +output and then this would be ICM to + + align:start position:0% +output and then this would be ICM to + + + align:start position:0% +output and then this would be ICM to +ground through through my parasitic + + align:start position:0% +ground through through my parasitic + + + align:start position:0% +ground through through my parasitic +capacitance back to + + align:start position:0% +capacitance back to + + + align:start position:0% +capacitance back to +ground does that make sense + + align:start position:0% + + + + align:start position:0% + +everybody so let's just let me pre + + align:start position:0% +everybody so let's just let me pre + + + align:start position:0% +everybody so let's just let me pre +pretend for a moment IDM is + + align:start position:0% +pretend for a moment IDM is + + + align:start position:0% +pretend for a moment IDM is +zero let's just think I have common mode + + align:start position:0% +zero let's just think I have common mode + + + align:start position:0% +zero let's just think I have common mode +currents that are being drawn together + + align:start position:0% +currents that are being drawn together + + + align:start position:0% +currents that are being drawn together +through pins and ones and twos and going + + align:start position:0% +through pins and ones and twos and going + + + align:start position:0% +through pins and ones and twos and going +back through + + align:start position:0% +back through + + + align:start position:0% +back through +ground all right what would I do to + + align:start position:0% +ground all right what would I do to + + + align:start position:0% +ground all right what would I do to +filter it well he said the first thing I + + align:start position:0% +filter it well he said the first thing I + + + align:start position:0% +filter it well he said the first thing I +usually put in my + + align:start position:0% +usually put in my + + + align:start position:0% +usually put in my +filter is a capacitor between the two + + align:start position:0% +filter is a capacitor between the two + + + align:start position:0% +filter is a capacitor between the two +leads right and I'm going to call this + + align:start position:0% +leads right and I'm going to call this + + + align:start position:0% +leads right and I'm going to call this +for reasons we'll discuss I'm going to + + align:start position:0% +for reasons we'll discuss I'm going to + + + align:start position:0% +for reasons we'll discuss I'm going to +call this C + + align:start position:0% +call this C + + + align:start position:0% +call this C +subx + + align:start position:0% +subx + + + align:start position:0% +subx +okay does this capacitor really do + + align:start position:0% +okay does this capacitor really do + + + align:start position:0% +okay does this capacitor really do +anything if I thought + + align:start position:0% +anything if I thought + + + align:start position:0% +anything if I thought +about um if the currents are kind of + + align:start position:0% +about um if the currents are kind of + + + align:start position:0% +about um if the currents are kind of +equally coming this + + align:start position:0% +equally coming this + + + align:start position:0% +equally coming this +way right this capacitor is sort of like + + align:start position:0% +way right this capacitor is sort of like + + + align:start position:0% +way right this capacitor is sort of like +an open circuit to those + + align:start position:0% + + + + align:start position:0% + +currents right or if V1 and V2 the + + align:start position:0% +currents right or if V1 and V2 the + + + align:start position:0% +currents right or if V1 and V2 the +voltages are going up and down together + + align:start position:0% +voltages are going up and down together + + + align:start position:0% +voltages are going up and down together +it has a common mode component to the + + align:start position:0% +it has a common mode component to the + + + align:start position:0% +it has a common mode component to the +voltages C subx is drawing no + + align:start position:0% +voltages C subx is drawing no + + + align:start position:0% +voltages C subx is drawing no +current so for the common mode case you + + align:start position:0% +current so for the common mode case you + + + align:start position:0% +current so for the common mode case you +know I mean c subx might as well not be + + align:start position:0% +know I mean c subx might as well not be + + + align:start position:0% +know I mean c subx might as well not be +there + + align:start position:0% +there + + + align:start position:0% +there +right so what could I do to deal with C + + align:start position:0% +right so what could I do to deal with C + + + align:start position:0% +right so what could I do to deal with C +subx well one thing I could do is put in + + align:start position:0% +subx well one thing I could do is put in + + + align:start position:0% +subx well one thing I could do is put in +what's known as a common mode + + align:start position:0% +what's known as a common mode + + + align:start position:0% +what's known as a common mode +choke okay what is a common mode choke a + + align:start position:0% +choke okay what is a common mode choke a + + + align:start position:0% +choke okay what is a common mode choke a +common mode choke is essentially a + + align:start position:0% + + + + align:start position:0% + +Transformer that's wound like this is + + align:start position:0% +Transformer that's wound like this is + + + align:start position:0% +Transformer that's wound like this is +has equal numbers of turns on each on + + align:start position:0% +has equal numbers of turns on each on + + + align:start position:0% +has equal numbers of turns on each on +each side and it's wound with its dots + + align:start position:0% +each side and it's wound with its dots + + + align:start position:0% +each side and it's wound with its dots +like + + align:start position:0% +like + + + align:start position:0% +like +this okay + + align:start position:0% +this okay + + + align:start position:0% +this okay +so if this were an ideal Transformer and + + align:start position:0% +so if this were an ideal Transformer and + + + align:start position:0% +so if this were an ideal Transformer and +I said okay let's pretend that CX is an + + align:start position:0% +I said okay let's pretend that CX is an + + + align:start position:0% +I said okay let's pretend that CX is an +open circuit here okay how much current + + align:start position:0% +open circuit here okay how much current + + + align:start position:0% +open circuit here okay how much current +can flow together through these + + align:start position:0% +can flow together through these + + + align:start position:0% +can flow together through these +two ideal Transformer + + align:start position:0% + + + + align:start position:0% + +windings can I get a common mode + + align:start position:0% +windings can I get a common mode + + + align:start position:0% +windings can I get a common mode +component through an ideal + + align:start position:0% + + + + align:start position:0% + +Transformer nobody's willing to bet on + + align:start position:0% +Transformer nobody's willing to bet on + + + align:start position:0% +Transformer nobody's willing to bet on +that it's got to be zero right because + + align:start position:0% +that it's got to be zero right because + + + align:start position:0% +that it's got to be zero right because +in an ideal Transformer whatever comes + + align:start position:0% +in an ideal Transformer whatever comes + + + align:start position:0% +in an ideal Transformer whatever comes +into this dot comes out of that dot + + align:start position:0% +into this dot comes out of that dot + + + align:start position:0% +into this dot comes out of that dot +right it's an end to end Transformer or + + align:start position:0% +right it's an end to end Transformer or + + + align:start position:0% +right it's an end to end Transformer or +one to one Transformer so you it an + + align:start position:0% +one to one Transformer so you it an + + + align:start position:0% +one to one Transformer so you it an +ideal Transformer only allows + + align:start position:0% +ideal Transformer only allows + + + align:start position:0% +ideal Transformer only allows +differential mode + + align:start position:0% +differential mode + + + align:start position:0% +differential mode +current so that's why it's called a + + align:start position:0% +current so that's why it's called a + + + align:start position:0% +current so that's why it's called a +common mode choke it chokes off the + + align:start position:0% +common mode choke it chokes off the + + + align:start position:0% +common mode choke it chokes off the +common mode + + align:start position:0% +common mode + + + align:start position:0% +common mode +current okay well what would I do in my + + align:start position:0% +current okay well what would I do in my + + + align:start position:0% +current okay well what would I do in my +filter design this thing makes like a + + align:start position:0% +filter design this thing makes like a + + + align:start position:0% +filter design this thing makes like a +perfect perfect inductor against common + + align:start position:0% +perfect perfect inductor against common + + + align:start position:0% +perfect perfect inductor against common +mode currents in some sense if I want to + + align:start position:0% +mode currents in some sense if I want to + + + align:start position:0% +mode currents in some sense if I want to +think about that if I could go out and + + align:start position:0% +think about that if I could go out and + + + align:start position:0% +think about that if I could go out and +buy myself an ideal + + align:start position:0% +buy myself an ideal + + + align:start position:0% +buy myself an ideal +Transformer now I can't go buy myself an + + align:start position:0% +Transformer now I can't go buy myself an + + + align:start position:0% +Transformer now I can't go buy myself an +ideal Transformer why because you know + + align:start position:0% +ideal Transformer why because you know + + + align:start position:0% +ideal Transformer why because you know +they don't sell them at Digi key um what + + align:start position:0% +they don't sell them at Digi key um what + + + align:start position:0% +they don't sell them at Digi key um what +what do I have to think of in terms of + + align:start position:0% +what do I have to think of in terms of + + + align:start position:0% +what do I have to think of in terms of +parasitics sem my Transformer well one + + align:start position:0% +parasitics sem my Transformer well one + + + align:start position:0% +parasitics sem my Transformer well one +thing as I I said I could put a + + align:start position:0% +thing as I I said I could put a + + + align:start position:0% +thing as I I said I could put a +magnetizing inductance L + + align:start position:0% +magnetizing inductance L + + + align:start position:0% +magnetizing inductance L +mu on one side of you know if this is + + align:start position:0% +mu on one side of you know if this is + + + align:start position:0% +mu on one side of you know if this is +the ideal Transformer + + align:start position:0% +the ideal Transformer + + + align:start position:0% +the ideal Transformer +part right I can put an magnetizing L mu + + align:start position:0% +part right I can put an magnetizing L mu + + + align:start position:0% +part right I can put an magnetizing L mu +across one of the terminals now they + + align:start position:0% +across one of the terminals now they + + + align:start position:0% +across one of the terminals now they +have the same winding so they'd have the + + align:start position:0% +have the same winding so they'd have the + + + align:start position:0% +have the same winding so they'd have the +same inductance whichever place I put it + + align:start position:0% +same inductance whichever place I put it + + + align:start position:0% +same inductance whichever place I put it +right but I could also represent L mu as + + align:start position:0% +right but I could also represent L mu as + + + align:start position:0% +right but I could also represent L mu as +2 L mu in parallel with 2 L mu right so + + align:start position:0% +2 L mu in parallel with 2 L mu right so + + + align:start position:0% +2 L mu in parallel with 2 L mu right so +another way I could write this is I + + align:start position:0% +another way I could write this is I + + + align:start position:0% +another way I could write this is I +could put 2 L mu on this side and to + + align:start position:0% +could put 2 L mu on this side and to + + + align:start position:0% +could put 2 L mu on this side and to +make it symmetric I could put 2 L + + align:start position:0% +make it symmetric I could put 2 L + + + align:start position:0% +make it symmetric I could put 2 L +mu on the other side of the + + align:start position:0% +mu on the other side of the + + + align:start position:0% +mu on the other side of the +Transformer okay so I have some + + align:start position:0% +Transformer okay so I have some + + + align:start position:0% +Transformer okay so I have some +magnetizing on on each side and maybe I + + align:start position:0% +magnetizing on on each side and maybe I + + + align:start position:0% +magnetizing on on each side and maybe I +should + + align:start position:0% +should + + + align:start position:0% +should +have intending it drw this in pink + + align:start position:0% +have intending it drw this in pink + + + align:start position:0% +have intending it drw this in pink +although I'm not sure you can see the + + align:start position:0% +although I'm not sure you can see the + + + align:start position:0% +although I'm not sure you can see the +difference just to illustrate that these + + align:start position:0% +difference just to illustrate that these + + + align:start position:0% +difference just to illustrate that these +are parasitic components okay what else + + align:start position:0% +are parasitic components okay what else + + + align:start position:0% +are parasitic components okay what else +do I have I also have leakage inductance + + align:start position:0% +do I have I also have leakage inductance + + + align:start position:0% +do I have I also have leakage inductance +and if this is symmetrically + + align:start position:0% +and if this is symmetrically + + + align:start position:0% +and if this is symmetrically +wound + + align:start position:0% +wound + + + align:start position:0% +wound +um I would have L leakage here and an + + align:start position:0% +um I would have L leakage here and an + + + align:start position:0% +um I would have L leakage here and an +equal L leakage + + align:start position:0% +equal L leakage + + + align:start position:0% +equal L leakage +here and that would represent sort of a + + align:start position:0% +here and that would represent sort of a + + + align:start position:0% +here and that would represent sort of a +model for real + + align:start position:0% +model for real + + + align:start position:0% +model for real +transformer okay so in principle if this + + align:start position:0% +transformer okay so in principle if this + + + align:start position:0% +transformer okay so in principle if this +is an ungapped Transformer + + align:start position:0% +is an ungapped Transformer + + + align:start position:0% +is an ungapped Transformer +common mode current could come go + + align:start position:0% +common mode current could come go + + + align:start position:0% +common mode current could come go +through the 2 L mu the magnetizing + + align:start position:0% +through the 2 L mu the magnetizing + + + align:start position:0% +through the 2 L mu the magnetizing +inductance on each side through the + + align:start position:0% +inductance on each side through the + + + align:start position:0% +inductance on each side through the +leakage and then in here right so it + + align:start position:0% +leakage and then in here right so it + + + align:start position:0% +leakage and then in here right so it +does pose a a path for common mode + + align:start position:0% +does pose a a path for common mode + + + align:start position:0% +does pose a a path for common mode +current in the real world but it's a + + align:start position:0% +current in the real world but it's a + + + align:start position:0% +current in the real world but it's a +very high impedance path because if it + + align:start position:0% +very high impedance path because if it + + + align:start position:0% +very high impedance path because if it +this Transformers ungapped L mu is a + + align:start position:0% +this Transformers ungapped L mu is a + + + align:start position:0% +this Transformers ungapped L mu is a +pretty big + + align:start position:0% +pretty big + + + align:start position:0% +pretty big +number + + align:start position:0% +number + + + align:start position:0% +number +okay that's inductive choking what would + + align:start position:0% +okay that's inductive choking what would + + + align:start position:0% +okay that's inductive choking what would +I do to get rid of of the um what would + + align:start position:0% +I do to get rid of of the um what would + + + align:start position:0% +I do to get rid of of the um what would +I do to get rid of of the + + align:start position:0% +I do to get rid of of the + + + align:start position:0% +I do to get rid of of the +um help filter these common mode + + align:start position:0% +um help filter these common mode + + + align:start position:0% +um help filter these common mode +currents maybe what I would do is I + + align:start position:0% +currents maybe what I would do is I + + + align:start position:0% +currents maybe what I would do is I +would go in and i' put in a capacitor + + align:start position:0% +would go in and i' put in a capacitor + + + align:start position:0% +would go in and i' put in a capacitor +and I'm going to call this Cy to ground + + align:start position:0% + + + + align:start position:0% + +here and another Cy to ground + + align:start position:0% +here and another Cy to ground + + + align:start position:0% +here and another Cy to ground +here right so I help what you'll see is + + align:start position:0% +here right so I help what you'll see is + + + align:start position:0% +here right so I help what you'll see is +you know half of half CM could come + + align:start position:0% +you know half of half CM could come + + + align:start position:0% +you know half of half CM could come +through here come up through this + + align:start position:0% +through here come up through this + + + align:start position:0% +through here come up through this +capacitor and happily circulate there + + align:start position:0% +capacitor and happily circulate there + + + align:start position:0% +capacitor and happily circulate there +that's a low impedance capacitive path + + align:start position:0% +that's a low impedance capacitive path + + + align:start position:0% +that's a low impedance capacitive path +at high frequency same thing here it can + + align:start position:0% +at high frequency same thing here it can + + + align:start position:0% +at high frequency same thing here it can +kind of circulate this way right because + + align:start position:0% +kind of circulate this way right because + + + align:start position:0% +kind of circulate this way right because +these these guys are + + align:start position:0% +these these guys are + + + align:start position:0% +these these guys are +connected + + align:start position:0% +connected + + + align:start position:0% +connected +okay and so the current at high + + align:start position:0% +okay and so the current at high + + + align:start position:0% +okay and so the current at high +frequency wants to go through the C + + align:start position:0% +frequency wants to go through the C + + + align:start position:0% +frequency wants to go through the C +wi but doesn't want to go this way + + align:start position:0% +wi but doesn't want to go this way + + + align:start position:0% +wi but doesn't want to go this way +because of the high magnetizing + + align:start position:0% +because of the high magnetizing + + + align:start position:0% +because of the high magnetizing +inductance does that make sense + + align:start position:0% + + + + align:start position:0% + +everybody the this is actually very + + align:start position:0% +everybody the this is actually very + + + align:start position:0% +everybody the this is actually very +convenient okay because if we think + + align:start position:0% +convenient okay because if we think + + + align:start position:0% +convenient okay because if we think +about it we have common mode currents + + align:start position:0% +about it we have common mode currents + + + align:start position:0% +about it we have common mode currents +but we also have differential mode + + align:start position:0% +but we also have differential mode + + + align:start position:0% +but we also have differential mode +currents right if this is my + + align:start position:0% +currents right if this is my + + + align:start position:0% +currents right if this is my +differential mode current here IDM IDM + + align:start position:0% +differential mode current here IDM IDM + + + align:start position:0% +differential mode current here IDM IDM +is coming this way where would the + + align:start position:0% +is coming this way where would the + + + align:start position:0% +is coming this way where would the +differential mode current flow um let me + + align:start position:0% +differential mode current flow um let me + + + align:start position:0% +differential mode current flow um let me +ignore CX and Cy let's pretend they're + + align:start position:0% +ignore CX and Cy let's pretend they're + + + align:start position:0% +ignore CX and Cy let's pretend they're +not there for the moment where would the + + align:start position:0% +not there for the moment where would the + + + align:start position:0% +not there for the moment where would the +differential mode current flow well it + + align:start position:0% +differential mode current flow well it + + + align:start position:0% +differential mode current flow well it +could go through LM but think about it + + align:start position:0% +could go through LM but think about it + + + align:start position:0% +could go through LM but think about it +this way differential mode current + + align:start position:0% +this way differential mode current + + + align:start position:0% +this way differential mode current +doesn't mind going in this + + align:start position:0% +doesn't mind going in this + + + align:start position:0% +doesn't mind going in this +and out of this dot right the this + + align:start position:0% +and out of this dot right the this + + + align:start position:0% +and out of this dot right the this +common mode choke the ideal one is a + + align:start position:0% +common mode choke the ideal one is a + + + align:start position:0% +common mode choke the ideal one is a +perfect short for differential mode + + align:start position:0% +perfect short for differential mode + + + align:start position:0% +perfect short for differential mode +currents so the differential mode + + align:start position:0% +currents so the differential mode + + + align:start position:0% +currents so the differential mode +currents don't go through the + + align:start position:0% +currents don't go through the + + + align:start position:0% +currents don't go through the +magnetizing inductance they just go + + align:start position:0% +magnetizing inductance they just go + + + align:start position:0% +magnetizing inductance they just go +through the ideal portion of the + + align:start position:0% +through the ideal portion of the + + + align:start position:0% +through the ideal portion of the +Transformer and so you don't magnetize + + align:start position:0% +Transformer and so you don't magnetize + + + align:start position:0% +Transformer and so you don't magnetize +the core and so even if you have high + + align:start position:0% +the core and so even if you have high + + + align:start position:0% +the core and so even if you have high +differential mode currents because this + + align:start position:0% +differential mode currents because this + + + align:start position:0% +differential mode currents because this +is what you're delivering power to the + + align:start position:0% +is what you're delivering power to the + + + align:start position:0% +is what you're delivering power to the +device through they don't magnetize the + + align:start position:0% +device through they don't magnetize the + + + align:start position:0% +device through they don't magnetize the +core and so you don't need a big common + + align:start position:0% +core and so you don't need a big common + + + align:start position:0% +core and so you don't need a big common +mode choke to get a high effective + + align:start position:0% +mode choke to get a high effective + + + align:start position:0% +mode choke to get a high effective +common mode + + align:start position:0% +common mode + + + align:start position:0% +common mode +inductance okay because it doesn't store + + align:start position:0% +inductance okay because it doesn't store + + + align:start position:0% +inductance okay because it doesn't store +any energy at least it doesn't store any + + align:start position:0% +any energy at least it doesn't store any + + + align:start position:0% +any energy at least it doesn't store any +differential mode + + align:start position:0% + + + + align:start position:0% + +energy any questions about + + align:start position:0% +energy any questions about + + + align:start position:0% +energy any questions about +that so to the extent that the + + align:start position:0% +that so to the extent that the + + + align:start position:0% +that so to the extent that the +differential mode currents don't go + + align:start position:0% +differential mode currents don't go + + + align:start position:0% +differential mode currents don't go +through the magnetizing inductance I can + + align:start position:0% +through the magnetizing inductance I can + + + align:start position:0% +through the magnetizing inductance I can +get very high magnetizing inductance + + align:start position:0% +get very high magnetizing inductance + + + align:start position:0% +get very high magnetizing inductance +with very few turns by using an ungapped + + align:start position:0% +with very few turns by using an ungapped + + + align:start position:0% +with very few turns by using an ungapped +core and it's not going to be very large + + align:start position:0% +core and it's not going to be very large + + + align:start position:0% +core and it's not going to be very large +and by the way in the one I'm passing + + align:start position:0% +and by the way in the one I'm passing + + + align:start position:0% +and by the way in the one I'm passing +around here may I steal this back I + + align:start position:0% +around here may I steal this back I + + + align:start position:0% +around here may I steal this back I +don't do this make it over to the right + + align:start position:0% +don't do this make it over to the right + + + align:start position:0% +don't do this make it over to the right +hand side of the class yeah so see these + + align:start position:0% +hand side of the class yeah so see these + + + align:start position:0% +hand side of the class yeah so see these +guys here these are com these are common + + align:start position:0% +guys here these are com these are common + + + align:start position:0% +guys here these are com these are common +mode chokes right here okay and actually + + align:start position:0% +mode chokes right here okay and actually + + + align:start position:0% +mode chokes right here okay and actually +what you'll see is the two sets of + + align:start position:0% +what you'll see is the two sets of + + + align:start position:0% +what you'll see is the two sets of +windings are identical and they're split + + align:start position:0% +windings are identical and they're split + + + align:start position:0% +windings are identical and they're split +up on the core they're split up on the + + align:start position:0% +up on the core they're split up on the + + + align:start position:0% +up on the core they're split up on the +core actually to help enhance the amount + + align:start position:0% +core actually to help enhance the amount + + + align:start position:0% +core actually to help enhance the amount +of leakage inductance that we have from + + align:start position:0% +of leakage inductance that we have from + + + align:start position:0% +of leakage inductance that we have from +those but it's + + align:start position:0% +those but it's + + + align:start position:0% +those but it's +symmetric and ungapped cores okay and + + align:start position:0% +symmetric and ungapped cores okay and + + + align:start position:0% +symmetric and ungapped cores okay and +that's very convenient + + align:start position:0% +that's very convenient + + + align:start position:0% +that's very convenient +why well I said if I wanted to kill the + + align:start position:0% +why well I said if I wanted to kill the + + + align:start position:0% +why well I said if I wanted to kill the +common mode component of + + align:start position:0% +common mode component of + + + align:start position:0% +common mode component of +current + + align:start position:0% +current + + + align:start position:0% +current +okay I want it to cycle through + + align:start position:0% +okay I want it to cycle through + + + align:start position:0% +okay I want it to cycle through +Cy and my filter then if I were to + + align:start position:0% +Cy and my filter then if I were to + + + align:start position:0% +Cy and my filter then if I were to +redraw this let me just consider the + + align:start position:0% +redraw this let me just consider the + + + align:start position:0% +redraw this let me just consider the +common mode components so if I just + + align:start position:0% +common mode components so if I just + + + align:start position:0% +common mode components so if I just +considered the common mode component so + + align:start position:0% +considered the common mode component so + + + align:start position:0% +considered the common mode component so +this is the CM only + + align:start position:0% +this is the CM only + + + align:start position:0% +this is the CM only +okay I have half + + align:start position:0% + + + + align:start position:0% + +CM half + + align:start position:0% +CM half + + + align:start position:0% +CM half +ICM 1 half + + align:start position:0% + + + + align:start position:0% + +ICM + + align:start position:0% +ICM + + + align:start position:0% +ICM +okay here I have Cy here I have + + align:start position:0% +okay here I have Cy here I have + + + align:start position:0% +okay here I have Cy here I have +Cy and then these are both going to + + align:start position:0% +Cy and then these are both going to + + + align:start position:0% +Cy and then these are both going to +ground which is connected back here okay + + align:start position:0% +ground which is connected back here okay + + + align:start position:0% +ground which is connected back here okay +then I'm going through L + + align:start position:0% +then I'm going through L + + + align:start position:0% +then I'm going through L +leakage on each side and 2 L mu on each + + align:start position:0% + + + + align:start position:0% + +side right because the ideal portion of + + align:start position:0% +side right because the ideal portion of + + + align:start position:0% +side right because the ideal portion of +the Transformer is now gone right and + + align:start position:0% +the Transformer is now gone right and + + + align:start position:0% +the Transformer is now gone right and +then this is connected back to my input + + align:start position:0% +then this is connected back to my input + + + align:start position:0% +then this is connected back to my input +which I'll just treat as a short circuit + + align:start position:0% +which I'll just treat as a short circuit + + + align:start position:0% +which I'll just treat as a short circuit +okay so the currents here basically + + align:start position:0% +okay so the currents here basically + + + align:start position:0% +okay so the currents here basically +form um and I'm acknowledging that I + + align:start position:0% +form um and I'm acknowledging that I + + + align:start position:0% +form um and I'm acknowledging that I +have ground connected back here too + + align:start position:0% +have ground connected back here too + + + align:start position:0% +have ground connected back here too +right so basically the currents form an + + align:start position:0% +right so basically the currents form an + + + align:start position:0% +right so basically the currents form an +LC + + align:start position:0% +LC + + + align:start position:0% +LC +filter that I could think of if I + + align:start position:0% +filter that I could think of if I + + + align:start position:0% +filter that I could think of if I +mirrored this I could redraw this as + + align:start position:0% +mirrored this I could redraw this as + + + align:start position:0% +mirrored this I could redraw this as +this um so let me just mirror everything + + align:start position:0% +this um so let me just mirror everything + + + align:start position:0% +this um so let me just mirror everything +that looks sort of like it's in parallel + + align:start position:0% +that looks sort of like it's in parallel + + + align:start position:0% +that looks sort of like it's in parallel +reflected across ground and what I would + + align:start position:0% +reflected across ground and what I would + + + align:start position:0% +reflected across ground and what I would +get is this L + + align:start position:0% +get is this L + + + align:start position:0% +get is this L +mu L leakage over + + align:start position:0% +mu L leakage over + + + align:start position:0% +mu L leakage over +two ICM + + align:start position:0% + + + + align:start position:0% + +2cy and then this is shorted this way + + align:start position:0% +2cy and then this is shorted this way + + + align:start position:0% +2cy and then this is shorted this way +okay so putting aside damping which I'm + + align:start position:0% +okay so putting aside damping which I'm + + + align:start position:0% +okay so putting aside damping which I'm +not talking about here right basically I + + align:start position:0% +not talking about here right basically I + + + align:start position:0% +not talking about here right basically I +have a filter comprising 2cy is my + + align:start position:0% +have a filter comprising 2cy is my + + + align:start position:0% +have a filter comprising 2cy is my +capacitor and L mu plus half the leakage + + align:start position:0% +capacitor and L mu plus half the leakage + + + align:start position:0% +capacitor and L mu plus half the leakage +as my + + align:start position:0% +as my + + + align:start position:0% +as my +inductor okay make sense + + align:start position:0% +inductor okay make sense + + + align:start position:0% +inductor okay make sense +everybody and that's + + align:start position:0% +everybody and that's + + + align:start position:0% +everybody and that's +handy because this C suby if I come back + + align:start position:0% +handy because this C suby if I come back + + + align:start position:0% +handy because this C suby if I come back +to my real system can be connected + + align:start position:0% +to my real system can be connected + + + align:start position:0% +to my real system can be connected +between the negative terminal and the + + align:start position:0% +between the negative terminal and the + + + align:start position:0% +between the negative terminal and the +positive terminal to ground it turns out + + align:start position:0% +positive terminal to ground it turns out + + + align:start position:0% +positive terminal to ground it turns out +I'm not allowed to use a very big y + + align:start position:0% +I'm not allowed to use a very big y + + + align:start position:0% +I'm not allowed to use a very big y +capacitor I'm not allowed to connect a + + align:start position:0% +capacitor I'm not allowed to connect a + + + align:start position:0% +capacitor I'm not allowed to connect a +big capacitor between say hot my my ac + + align:start position:0% +big capacitor between say hot my my ac + + + align:start position:0% +big capacitor between say hot my my ac +voltage coming in and ground + + align:start position:0% +voltage coming in and ground + + + align:start position:0% +voltage coming in and ground +why because first of all we're not + + align:start position:0% +why because first of all we're not + + + align:start position:0% +why because first of all we're not +supposed to carry currents in ground + + align:start position:0% +supposed to carry currents in ground + + + align:start position:0% +supposed to carry currents in ground +right this is actually allowing current + + align:start position:0% +right this is actually allowing current + + + align:start position:0% +right this is actually allowing current +to flow in the ground wire right devices + + align:start position:0% +to flow in the ground wire right devices + + + align:start position:0% +to flow in the ground wire right devices +like gfis you might have a GFI in your + + align:start position:0% +like gfis you might have a GFI in your + + + align:start position:0% +like gfis you might have a GFI in your +bathroom a ground fault interruptor what + + align:start position:0% +bathroom a ground fault interruptor what + + + align:start position:0% +bathroom a ground fault interruptor what +they're really doing is they're looking + + align:start position:0% +they're really doing is they're looking + + + align:start position:0% +they're really doing is they're looking +at the + + align:start position:0% +at the + + + align:start position:0% +at the +difference between these two currents or + + align:start position:0% +difference between these two currents or + + + align:start position:0% +difference between these two currents or +equivalently they're looking for current + + align:start position:0% +equivalently they're looking for current + + + align:start position:0% +equivalently they're looking for current +going into the ground if they see + + align:start position:0% +going into the ground if they see + + + align:start position:0% +going into the ground if they see +current going to the ground they think + + align:start position:0% +current going to the ground they think + + + align:start position:0% +current going to the ground they think +ah something's wrong somebody's being + + align:start position:0% +ah something's wrong somebody's being + + + align:start position:0% +ah something's wrong somebody's being +electrocuted and currents flowing + + align:start position:0% +electrocuted and currents flowing + + + align:start position:0% +electrocuted and currents flowing +through them shut everything + + align:start position:0% +through them shut everything + + + align:start position:0% +through them shut everything +off okay so if you allowed your device + + align:start position:0% +off okay so if you allowed your device + + + align:start position:0% +off okay so if you allowed your device +to put a bunch of current into the + + align:start position:0% +to put a bunch of current into the + + + align:start position:0% +to put a bunch of current into the +ground it's going to mess things like + + align:start position:0% +ground it's going to mess things like + + + align:start position:0% +ground it's going to mess things like +that up so they put very strict limits + + align:start position:0% +that up so they put very strict limits + + + align:start position:0% +that up so they put very strict limits +on how much current you're allowed to + + align:start position:0% +on how much current you're allowed to + + + align:start position:0% +on how much current you're allowed to +put into ground and for 60 htz currents + + align:start position:0% +put into ground and for 60 htz currents + + + align:start position:0% +put into ground and for 60 htz currents +which is what they're really looking at + + align:start position:0% +which is what they're really looking at + + + align:start position:0% +which is what they're really looking at +or 50 HZ in + + align:start position:0% +or 50 HZ in + + + align:start position:0% +or 50 HZ in +Europe + + align:start position:0% +Europe + + + align:start position:0% +Europe +um this y capacitor is very limited in + + align:start position:0% +um this y capacitor is very limited in + + + align:start position:0% +um this y capacitor is very limited in +value depending upon the application you + + align:start position:0% +value depending upon the application you + + + align:start position:0% +value depending upon the application you +know you might be talking like five + + align:start position:0% +know you might be talking like five + + + align:start position:0% +know you might be talking like five +nanofarads very very small + + align:start position:0% +nanofarads very very small + + + align:start position:0% +nanofarads very very small +capacitors so I don't get a very + + align:start position:0% +capacitors so I don't get a very + + + align:start position:0% +capacitors so I don't get a very +big capacitor value that I'm allowed to + + align:start position:0% +big capacitor value that I'm allowed to + + + align:start position:0% +big capacitor value that I'm allowed to +use how do I get all my filtering well I + + align:start position:0% +use how do I get all my filtering well I + + + align:start position:0% +use how do I get all my filtering well I +have the magnetizing inductance which + + align:start position:0% +have the magnetizing inductance which + + + align:start position:0% +have the magnetizing inductance which +can be huge so I have a tiny capacitor + + align:start position:0% +can be huge so I have a tiny capacitor + + + align:start position:0% +can be huge so I have a tiny capacitor +but a really big inductor and that gives + + align:start position:0% +but a really big inductor and that gives + + + align:start position:0% +but a really big inductor and that gives +me a I can still get a low cut off + + align:start position:0% +me a I can still get a low cut off + + + align:start position:0% +me a I can still get a low cut off +frequency and very good filtering for + + align:start position:0% +frequency and very good filtering for + + + align:start position:0% +frequency and very good filtering for +common mode + + align:start position:0% +common mode + + + align:start position:0% +common mode +signals does that make sense + + align:start position:0% + + + + align:start position:0% + +everybody and the reason I get away with + + align:start position:0% +everybody and the reason I get away with + + + align:start position:0% +everybody and the reason I get away with +that is because the high power currents + + align:start position:0% +that is because the high power currents + + + align:start position:0% +that is because the high power currents +the differential mode currents are not + + align:start position:0% +the differential mode currents are not + + + align:start position:0% +the differential mode currents are not +magnetizing the Transformer core + + align:start position:0% +magnetizing the Transformer core + + + align:start position:0% +magnetizing the Transformer core +so that's common mode only let's think + + align:start position:0% +so that's common mode only let's think + + + align:start position:0% +so that's common mode only let's think +about differential mode only for a + + align:start position:0% +about differential mode only for a + + + align:start position:0% +about differential mode only for a +moment and you notice when I drew the + + align:start position:0% +moment and you notice when I drew the + + + align:start position:0% +moment and you notice when I drew the +common mode filter I completely ignored + + align:start position:0% +common mode filter I completely ignored + + + align:start position:0% +common mode filter I completely ignored +this x capacitor because he's not doing + + align:start position:0% +this x capacitor because he's not doing + + + align:start position:0% +this x capacitor because he's not doing +anything for the common mode + + align:start position:0% +anything for the common mode + + + align:start position:0% +anything for the common mode +component let's think about the + + align:start position:0% +component let's think about the + + + align:start position:0% +component let's think about the +differential mode + + align:start position:0% + + + + align:start position:0% + +only so suppose here's my device + + align:start position:0% +only so suppose here's my device + + + align:start position:0% +only so suppose here's my device +right if I'm only thinking about the + + align:start position:0% +right if I'm only thinking about the + + + align:start position:0% +right if I'm only thinking about the +differential mode components I have IDM + + align:start position:0% + + + + align:start position:0% + +right I'm pretending common mode zero + + align:start position:0% +right I'm pretending common mode zero + + + align:start position:0% +right I'm pretending common mode zero +now I have an x capacitor C + + align:start position:0% + + + + align:start position:0% + +subx okay which is sitting between + + align:start position:0% +subx okay which is sitting between + + + align:start position:0% +subx okay which is sitting between +terminal one and two so this provides + + align:start position:0% +terminal one and two so this provides + + + align:start position:0% +terminal one and two so this provides +you know if I have a high frequency + + align:start position:0% +you know if I have a high frequency + + + align:start position:0% +you know if I have a high frequency +component to + + align:start position:0% +component to + + + align:start position:0% +component to +IDM it provides a low impedance path for + + align:start position:0% +IDM it provides a low impedance path for + + + align:start position:0% +IDM it provides a low impedance path for +it to flow through for at high + + align:start position:0% +it to flow through for at high + + + align:start position:0% +it to flow through for at high +frequencies + + align:start position:0% +frequencies + + + align:start position:0% +frequencies +um if I look back into this and I'm you + + align:start position:0% +um if I look back into this and I'm you + + + align:start position:0% +um if I look back into this and I'm you +know for filter purposes let me just + + align:start position:0% +know for filter purposes let me just + + + align:start position:0% +know for filter purposes let me just +ignore the source voltage right the + + align:start position:0% +ignore the source voltage right the + + + align:start position:0% +ignore the source voltage right the +ideal + + align:start position:0% +ideal + + + align:start position:0% +ideal +Transformer portion of my Transformer + + align:start position:0% +Transformer portion of my Transformer + + + align:start position:0% +Transformer portion of my Transformer +carries all the differential mode + + align:start position:0% +carries all the differential mode + + + align:start position:0% +carries all the differential mode +current so I don't magnetize the core so + + align:start position:0% +current so I don't magnetize the core so + + + align:start position:0% +current so I don't magnetize the core so +basically the differential mode the + + align:start position:0% +basically the differential mode the + + + align:start position:0% +basically the differential mode the +magnetizing inductance is essentially + + align:start position:0% +magnetizing inductance is essentially + + + align:start position:0% +magnetizing inductance is essentially +shorted out okay but the leakage + + align:start position:0% +shorted out okay but the leakage + + + align:start position:0% +shorted out okay but the leakage +inductance is not okay so what I'm + + align:start position:0% +inductance is not okay so what I'm + + + align:start position:0% +inductance is not okay so what I'm +really going to see at differential + + align:start position:0% +really going to see at differential + + + align:start position:0% +really going to see at differential +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +mode is the following I'm going to see + + align:start position:0% +mode is the following I'm going to see + + + align:start position:0% +mode is the following I'm going to see +how I'm going to see the leakage + + align:start position:0% +how I'm going to see the leakage + + + align:start position:0% +how I'm going to see the leakage +inductance here and the leakage + + align:start position:0% +inductance here and the leakage + + + align:start position:0% +inductance here and the leakage +inductance on this side because there's + + align:start position:0% +inductance on this side because there's + + + align:start position:0% +inductance on this side because there's +two leakage inductance the Transformer + + align:start position:0% +two leakage inductance the Transformer + + + align:start position:0% +two leakage inductance the Transformer +and then if I connect this at the bottom + + align:start position:0% +and then if I connect this at the bottom + + + align:start position:0% +and then if I connect this at the bottom +that's fine um I should say we also have + + align:start position:0% +that's fine um I should say we also have + + + align:start position:0% +that's fine um I should say we also have +the Y capacitors connected to ground + + align:start position:0% +the Y capacitors connected to ground + + + align:start position:0% +the Y capacitors connected to ground +from a differential mode perspective + + align:start position:0% +from a differential mode perspective + + + align:start position:0% +from a differential mode perspective +what that looks like is a y capacitor + + align:start position:0% +what that looks like is a y capacitor + + + align:start position:0% +what that looks like is a y capacitor +here + + align:start position:0% +here + + + align:start position:0% +here +and a y capacitor here and the ground is + + align:start position:0% +and a y capacitor here and the ground is + + + align:start position:0% +and a y capacitor here and the ground is +sort of like a virtual open nothing's + + align:start position:0% +sort of like a virtual open nothing's + + + align:start position:0% +sort of like a virtual open nothing's +flowing in ground so these guys just + + align:start position:0% +flowing in ground so these guys just + + + align:start position:0% +flowing in ground so these guys just +sort of look in + + align:start position:0% +sort of look in + + + align:start position:0% +sort of look in +series right so maybe what I could think + + align:start position:0% +series right so maybe what I could think + + + align:start position:0% +series right so maybe what I could think +of if I thought about this is net + + align:start position:0% +of if I thought about this is net + + + align:start position:0% +of if I thought about this is net +controlling the current flow around this + + align:start position:0% +controlling the current flow around this + + + align:start position:0% +controlling the current flow around this +Loop what I really have is + + align:start position:0% +Loop what I really have is + + + align:start position:0% +Loop what I really have is +IDM I + + align:start position:0% +IDM I + + + align:start position:0% +IDM I +have C + + align:start position:0% +have C + + + align:start position:0% +have C +subx plus 1 12 C + + align:start position:0% +subx plus 1 12 C + + + align:start position:0% +subx plus 1 12 C +suby and C subx by the way can be very + + align:start position:0% +suby and C subx by the way can be very + + + align:start position:0% +suby and C subx by the way can be very +big there's no actual limit on it I mean + + align:start position:0% +big there's no actual limit on it I mean + + + align:start position:0% +big there's no actual limit on it I mean +I don't want to carry too much 60 HZ + + align:start position:0% +I don't want to carry too much 60 HZ + + + align:start position:0% +I don't want to carry too much 60 HZ +current in it but it's not got to be + + align:start position:0% +current in it but it's not got to be + + + align:start position:0% +current in it but it's not got to be +tiny like the Y capacitor does because + + align:start position:0% +tiny like the Y capacitor does because + + + align:start position:0% +tiny like the Y capacitor does because +it's not connected to ground okay and + + align:start position:0% +it's not connected to ground okay and + + + align:start position:0% +it's not connected to ground okay and +then I effectively have if I consider + + align:start position:0% +then I effectively have if I consider + + + align:start position:0% +then I effectively have if I consider +these two paths together I have a net 2 + + align:start position:0% +these two paths together I have a net 2 + + + align:start position:0% +these two paths together I have a net 2 +L leakage here and this forms my LC + + align:start position:0% +L leakage here and this forms my LC + + + align:start position:0% +L leakage here and this forms my LC +filter now C subx can be pretty big so + + align:start position:0% +filter now C subx can be pretty big so + + + align:start position:0% +filter now C subx can be pretty big so +this cacure can be relatively big the + + align:start position:0% +this cacure can be relatively big the + + + align:start position:0% +this cacure can be relatively big the +leakage inductance is small it's just + + align:start position:0% +leakage inductance is small it's just + + + align:start position:0% +leakage inductance is small it's just +the leakage inductance my Transformer + + align:start position:0% +the leakage inductance my Transformer + + + align:start position:0% +the leakage inductance my Transformer +and that actually stores energy right if + + align:start position:0% +and that actually stores energy right if + + + align:start position:0% +and that actually stores energy right if +I'm if I'm passing differential mode + + align:start position:0% +I'm if I'm passing differential mode + + + align:start position:0% +I'm if I'm passing differential mode +currents to deliver power and those + + align:start position:0% +currents to deliver power and those + + + align:start position:0% +currents to deliver power and those +currents are you know amps or tens of + + align:start position:0% +currents are you know amps or tens of + + + align:start position:0% +currents are you know amps or tens of +amps that's storing energy in the in the + + align:start position:0% +amps that's storing energy in the in the + + + align:start position:0% +amps that's storing energy in the in the +net leakage right but still the leakage + + align:start position:0% +net leakage right but still the leakage + + + align:start position:0% +net leakage right but still the leakage +is relatively small compared to the + + align:start position:0% +is relatively small compared to the + + + align:start position:0% +is relatively small compared to the +magnetizing a few percent maybe right so + + align:start position:0% +magnetizing a few percent maybe right so + + + align:start position:0% +magnetizing a few percent maybe right so +I can still keep my Transformer pretty + + align:start position:0% +I can still keep my Transformer pretty + + + align:start position:0% +I can still keep my Transformer pretty +small and now I for differential mode I + + align:start position:0% +small and now I for differential mode I + + + align:start position:0% +small and now I for differential mode I +get a big capacitor dominated by the x + + align:start position:0% +get a big capacitor dominated by the x + + + align:start position:0% +get a big capacitor dominated by the x +capacitor and then the leakage of my + + align:start position:0% +capacitor and then the leakage of my + + + align:start position:0% +capacitor and then the leakage of my +common mode + + align:start position:0% + + + + align:start position:0% + +choke are there questions about + + align:start position:0% + + + + align:start position:0% + +that so what do I want to know when I'm + + align:start position:0% +that so what do I want to know when I'm + + + align:start position:0% +that so what do I want to know when I'm +designing a filter right if my problem + + align:start position:0% +designing a filter right if my problem + + + align:start position:0% +designing a filter right if my problem +is common mode + + align:start position:0% +is common mode + + + align:start position:0% +is common mode +noise beefing + + align:start position:0% +noise beefing + + + align:start position:0% +noise beefing +up the x capacitor + + align:start position:0% +up the x capacitor + + + align:start position:0% +up the x capacitor +here is going to do Zippo right because + + align:start position:0% +here is going to do Zippo right because + + + align:start position:0% +here is going to do Zippo right because +the common Moon current doesn't even + + align:start position:0% +the common Moon current doesn't even + + + align:start position:0% +the common Moon current doesn't even +flow through that it's a virtual + + align:start position:0% +flow through that it's a virtual + + + align:start position:0% +flow through that it's a virtual +open increasing my leakage inductance + + align:start position:0% +open increasing my leakage inductance + + + align:start position:0% +open increasing my leakage inductance +well I could but it's not going to help + + align:start position:0% +well I could but it's not going to help + + + align:start position:0% +well I could but it's not going to help +much because at common mode you know + + align:start position:0% +much because at common mode you know + + + align:start position:0% +much because at common mode you know +this guy is what's dominating the + + align:start position:0% +this guy is what's dominating the + + + align:start position:0% +this guy is what's dominating the +impedance right the the magneti is + + align:start position:0% +impedance right the the magneti is + + + align:start position:0% +impedance right the the magneti is +dominating the impedance so if I have + + align:start position:0% +dominating the impedance so if I have + + + align:start position:0% +dominating the impedance so if I have +common mode noise what I really need to + + align:start position:0% +common mode noise what I really need to + + + align:start position:0% +common mode noise what I really need to +do is um increase the magnetizing + + align:start position:0% +do is um increase the magnetizing + + + align:start position:0% +do is um increase the magnetizing +inductance component that's what would + + align:start position:0% +inductance component that's what would + + + align:start position:0% +inductance component that's what would +help me or maybe have another pair of Y + + align:start position:0% +help me or maybe have another pair of Y + + + align:start position:0% +help me or maybe have another pair of Y +capacitors over here and make a higher + + align:start position:0% +capacitors over here and make a higher + + + align:start position:0% +capacitors over here and make a higher +order filter okay but I want to focus on + + align:start position:0% +order filter okay but I want to focus on + + + align:start position:0% +order filter okay but I want to focus on +the elements the magnetizing inductance + + align:start position:0% +the elements the magnetizing inductance + + + align:start position:0% +the elements the magnetizing inductance +and the Y capacitors that dominate my + + align:start position:0% +and the Y capacitors that dominate my + + + align:start position:0% +and the Y capacitors that dominate my +common mode + + align:start position:0% +common mode + + + align:start position:0% +common mode +filtering if the thing that's killing me + + align:start position:0% +filtering if the thing that's killing me + + + align:start position:0% +filtering if the thing that's killing me +is differential mode + + align:start position:0% +is differential mode + + + align:start position:0% +is differential mode +noise then I might as well not worry + + align:start position:0% +noise then I might as well not worry + + + align:start position:0% +noise then I might as well not worry +about the magnetizing inductance because + + align:start position:0% +about the magnetizing inductance because + + + align:start position:0% +about the magnetizing inductance because +it's not helping + + align:start position:0% +it's not helping + + + align:start position:0% +it's not helping +me um and I ought to focus on on the x + + align:start position:0% +me um and I ought to focus on on the x + + + align:start position:0% +me um and I ought to focus on on the x +capacitor and the leakage components or + + align:start position:0% +capacitor and the leakage components or + + + align:start position:0% +capacitor and the leakage components or +adding in another filter stage and + + align:start position:0% +adding in another filter stage and + + + align:start position:0% +adding in another filter stage and +worrying about the leakage components + + align:start position:0% +worrying about the leakage components + + + align:start position:0% +worrying about the leakage components +okay so we can really think about the + + align:start position:0% +okay so we can really think about the + + + align:start position:0% +okay so we can really think about the +strategy used to design these filters in + + align:start position:0% +strategy used to design these filters in + + + align:start position:0% +strategy used to design these filters in +terms of the common mode and + + align:start position:0% +terms of the common mode and + + + align:start position:0% +terms of the common mode and +differential mode components and I'm + + align:start position:0% +differential mode components and I'm + + + align:start position:0% +differential mode components and I'm +using different elements to help me + + align:start position:0% +using different elements to help me + + + align:start position:0% +using different elements to help me +build the filter and pass the + + align:start position:0% +build the filter and pass the + + + align:start position:0% +build the filter and pass the +specifications now in the final analysis + + align:start position:0% +specifications now in the final analysis + + + align:start position:0% +specifications now in the final analysis +when I go to measure this stuff and I'm + + align:start position:0% +when I go to measure this stuff and I'm + + + align:start position:0% +when I go to measure this stuff and I'm +doing um you know I'm doing my Emi + + align:start position:0% +doing um you know I'm doing my Emi + + + align:start position:0% +doing um you know I'm doing my Emi +testing what I'm really coming back and + + align:start position:0% +testing what I'm really coming back and + + + align:start position:0% +testing what I'm really coming back and +doing is + + align:start position:0% +doing is + + + align:start position:0% +doing is +um setting up a lizen on this lead and + + align:start position:0% +um setting up a lizen on this lead and + + + align:start position:0% +um setting up a lizen on this lead and +looking you know from the sources + + align:start position:0% +looking you know from the sources + + + align:start position:0% +looking you know from the sources +perspective looking in the Ripple in I2 + + align:start position:0% +perspective looking in the Ripple in I2 + + + align:start position:0% +perspective looking in the Ripple in I2 +looking in the Ripple in i1 or + + align:start position:0% +looking in the Ripple in i1 or + + + align:start position:0% +looking in the Ripple in i1 or +equivalently the voltage on the lizen + + align:start position:0% +equivalently the voltage on the lizen + + + align:start position:0% +equivalently the voltage on the lizen +for this lead and the voltage on the + + align:start position:0% +for this lead and the voltage on the + + + align:start position:0% +for this lead and the voltage on the +lizen for this lead so my Emi + + align:start position:0% +lizen for this lead so my Emi + + + align:start position:0% +lizen for this lead so my Emi +measurements aren't done in terms of + + align:start position:0% +measurements aren't done in terms of + + + align:start position:0% +measurements aren't done in terms of +common mode and differential mode but + + align:start position:0% +common mode and differential mode but + + + align:start position:0% +common mode and differential mode but +there will be common mode and + + align:start position:0% +there will be common mode and + + + align:start position:0% +there will be common mode and +differential mod components to those + + align:start position:0% +differential mod components to those + + + align:start position:0% +differential mod components to those +that I can go think about and we often + + align:start position:0% +that I can go think about and we often + + + align:start position:0% +that I can go think about and we often +figure out ways to uh separate those + + align:start position:0% +figure out ways to uh separate those + + + align:start position:0% +figure out ways to uh separate those +because I'm going to do different things + + align:start position:0% +because I'm going to do different things + + + align:start position:0% +because I'm going to do different things +in my filter to fix them okay what might + + align:start position:0% +in my filter to fix them okay what might + + + align:start position:0% +in my filter to fix them okay what might +I do if I wanted like if I just had this + + align:start position:0% +I do if I wanted like if I just had this + + + align:start position:0% +I do if I wanted like if I just had this +device and I wanted to go figure out the + + align:start position:0% +device and I wanted to go figure out the + + + align:start position:0% +device and I wanted to go figure out the +common mode current going into it how + + align:start position:0% +common mode current going into it how + + + align:start position:0% +common mode current going into it how +how do you think I'd do + + align:start position:0% + + + + align:start position:0% + +that I could go get a current probe and + + align:start position:0% +that I could go get a current probe and + + + align:start position:0% +that I could go get a current probe and +grab both of the this lead and this lead + + align:start position:0% +grab both of the this lead and this lead + + + align:start position:0% +grab both of the this lead and this lead +together through the current probe right + + align:start position:0% +together through the current probe right + + + align:start position:0% +together through the current probe right +so only the sum of the currents is what + + align:start position:0% +so only the sum of the currents is what + + + align:start position:0% +so only the sum of the currents is what +I measured which is precisely the common + + align:start position:0% +I measured which is precisely the common + + + align:start position:0% +I measured which is precisely the common +mode + + align:start position:0% +mode + + + align:start position:0% +mode +current right so I could grab a current + + align:start position:0% +current right so I could grab a current + + + align:start position:0% +current right so I could grab a current +probe and say oh do I have common mode + + align:start position:0% +probe and say oh do I have common mode + + + align:start position:0% +probe and say oh do I have common mode +current oh I do I better think about + + align:start position:0% +current oh I do I better think about + + + align:start position:0% +current oh I do I better think about +fixing the common mode or if I grabed + + align:start position:0% +fixing the common mode or if I grabed + + + align:start position:0% +fixing the common mode or if I grabed +this lead through the probe in One + + align:start position:0% +this lead through the probe in One + + + align:start position:0% +this lead through the probe in One +Direction and I flipped I2 and I + + align:start position:0% +Direction and I flipped I2 and I + + + align:start position:0% +Direction and I flipped I2 and I +measured you know i1 +- I2 i1 +- I2 is + + align:start position:0% +measured you know i1 +- I2 i1 +- I2 is + + + align:start position:0% +measured you know i1 +- I2 i1 +- I2 is +precisely + + align:start position:0% +precisely + + + align:start position:0% +precisely +twice the differential mode + + align:start position:0% +twice the differential mode + + + align:start position:0% +twice the differential mode +current so I can kind of separate out + + align:start position:0% +current so I can kind of separate out + + + align:start position:0% +current so I can kind of separate out +common mode and differential mode + + align:start position:0% +common mode and differential mode + + + align:start position:0% +common mode and differential mode +currents I can do the same thing with + + align:start position:0% +currents I can do the same thing with + + + align:start position:0% +currents I can do the same thing with +voltages if I look at the average of the + + align:start position:0% +voltages if I look at the average of the + + + align:start position:0% +voltages if I look at the average of the +voltages at terminal one and two if + + align:start position:0% +voltages at terminal one and two if + + + align:start position:0% +voltages at terminal one and two if +they're bouncing up together and down + + align:start position:0% +they're bouncing up together and down + + + align:start position:0% +they're bouncing up together and down +together that's common mode if they're + + align:start position:0% +together that's common mode if they're + + + align:start position:0% +together that's common mode if they're +doing this that's differential mode + + align:start position:0% +doing this that's differential mode + + + align:start position:0% +doing this that's differential mode +right so I can use differential probes + + align:start position:0% +right so I can use differential probes + + + align:start position:0% +right so I can use differential probes +or sometimes some sometimes what you can + + align:start position:0% +or sometimes some sometimes what you can + + + align:start position:0% +or sometimes some sometimes what you can +do is you how much your ground's + + align:start position:0% +do is you how much your ground's + + + align:start position:0% +do is you how much your ground's +bouncing and say yeah that's related to + + align:start position:0% +bouncing and say yeah that's related to + + + align:start position:0% +bouncing and say yeah that's related to +my common mode but I'll think different + + align:start position:0% +my common mode but I'll think different + + + align:start position:0% +my common mode but I'll think different +about um how I will deal with those and + + align:start position:0% +about um how I will deal with those and + + + align:start position:0% +about um how I will deal with those and +even when you're making measurements you + + align:start position:0% +even when you're making measurements you + + + align:start position:0% +even when you're making measurements you +tend to do this actually if you look at + + align:start position:0% +tend to do this actually if you look at + + + align:start position:0% +tend to do this actually if you look at +this cord you see this kind of cylinder + + align:start position:0% +this cord you see this kind of cylinder + + + align:start position:0% +this cord you see this kind of cylinder +on this cord all that cylinder is is + + align:start position:0% +on this cord all that cylinder is is + + + align:start position:0% +on this cord all that cylinder is is +basically a ring a toal ring a ferite + + align:start position:0% +basically a ring a toal ring a ferite + + + align:start position:0% +basically a ring a toal ring a ferite +through which both leads are slipped so + + align:start position:0% +through which both leads are slipped so + + + align:start position:0% +through which both leads are slipped so +this is just a one- turn common mode + + align:start position:0% +this is just a one- turn common mode + + + align:start position:0% +this is just a one- turn common mode +choke right it's helping keep common + + align:start position:0% +choke right it's helping keep common + + + align:start position:0% +choke right it's helping keep common +mode noise out and it's very high + + align:start position:0% +mode noise out and it's very high + + + align:start position:0% +mode noise out and it's very high +impedance to common mode gives you + + align:start position:0% +impedance to common mode gives you + + + align:start position:0% +impedance to common mode gives you +almost no impedance to differential + + align:start position:0% +almost no impedance to differential + + + align:start position:0% +almost no impedance to differential +mode okay and that's why you can get a + + align:start position:0% +mode okay and that's why you can get a + + + align:start position:0% +mode okay and that's why you can get a +lot of filtering with a very small + + align:start position:0% +lot of filtering with a very small + + + align:start position:0% +lot of filtering with a very small +core so that's just a notion that + + align:start position:0% +core so that's just a notion that + + + align:start position:0% +core so that's just a notion that +everything I've said about filtering is + + align:start position:0% +everything I've said about filtering is + + + align:start position:0% +everything I've said about filtering is +true and sometimes you only need + + align:start position:0% +true and sometimes you only need + + + align:start position:0% +true and sometimes you only need +differential filtering if you're + + align:start position:0% +differential filtering if you're + + + align:start position:0% +differential filtering if you're +building something over a ground plane + + align:start position:0% +building something over a ground plane + + + align:start position:0% +building something over a ground plane +and currents can return wherever they + + align:start position:0% +and currents can return wherever they + + + align:start position:0% +and currents can return wherever they +may in the ground plane that's not a + + align:start position:0% +may in the ground plane that's not a + + + align:start position:0% +may in the ground plane that's not a +problem but if you're going to build + + align:start position:0% +problem but if you're going to build + + + align:start position:0% +problem but if you're going to build +something with you know some pair of + + align:start position:0% +something with you know some pair of + + + align:start position:0% +something with you know some pair of +wires going out to the wall or to your + + align:start position:0% +wires going out to the wall or to your + + + align:start position:0% +wires going out to the wall or to your +car battery or to your something else + + align:start position:0% +car battery or to your something else + + + align:start position:0% +car battery or to your something else +you better start thinking in terms of + + align:start position:0% +you better start thinking in terms of + + + align:start position:0% +you better start thinking in terms of +common mode and differential mode uh + + align:start position:0% +common mode and differential mode uh + + + align:start position:0% +common mode and differential mode uh +voltages and currents for + + align:start position:0% + + + + align:start position:0% + +noise any + + align:start position:0% +noise any + + + align:start position:0% +noise any +questions yeah so the common mode and + + align:start position:0% +questions yeah so the common mode and + + + align:start position:0% +questions yeah so the common mode and +the differential mode do they both uh + + align:start position:0% +the differential mode do they both uh + + + align:start position:0% +the differential mode do they both uh +occur s simultaneously or do they just + + align:start position:0% +occur s simultaneously or do they just + + + align:start position:0% +occur s simultaneously or do they just +um are they like situations that occur + + align:start position:0% +um are they like situations that occur + + + align:start position:0% +um are they like situations that occur +separately well different things might + + align:start position:0% +separately well different things might + + + align:start position:0% +separately well different things might +drive common mode and differential no + + align:start position:0% +drive common mode and differential no + + + align:start position:0% +drive common mode and differential no +mode noise but typically they're + + align:start position:0% +mode noise but typically they're + + + align:start position:0% +mode noise but typically they're +occurring together right and it's just a + + align:start position:0% +occurring together right and it's just a + + + align:start position:0% +occurring together right and it's just a +question of what you're seeing on pin + + align:start position:0% +question of what you're seeing on pin + + + align:start position:0% +question of what you're seeing on pin +one and what you're seeing on pin two in + + align:start position:0% +one and what you're seeing on pin two in + + + align:start position:0% +one and what you're seeing on pin two in +terms of voltage and current so they + + align:start position:0% +terms of voltage and current so they + + + align:start position:0% +terms of voltage and current so they +occur together but what's dominant may + + align:start position:0% +occur together but what's dominant may + + + align:start position:0% +occur together but what's dominant may +be um May depend upon the situation + + align:start position:0% +be um May depend upon the situation + + + align:start position:0% +be um May depend upon the situation +right so if I if I suddenly increase the + + align:start position:0% +right so if I if I suddenly increase the + + + align:start position:0% +right so if I if I suddenly increase the +parasitic + + align:start position:0% +parasitic + + + align:start position:0% +parasitic +capacitance of my transistor to ground + + align:start position:0% +capacitance of my transistor to ground + + + align:start position:0% +capacitance of my transistor to ground +suddenly I'd probably see a bunch of + + align:start position:0% +suddenly I'd probably see a bunch of + + + align:start position:0% +suddenly I'd probably see a bunch of +common mode noise there too even if I + + align:start position:0% +common mode noise there too even if I + + + align:start position:0% +common mode noise there too even if I +have a differential mode + + align:start position:0% +have a differential mode + + + align:start position:0% +have a differential mode +component okay so you know if I'm making + + align:start position:0% +component okay so you know if I'm making + + + align:start position:0% +component okay so you know if I'm making +this third terminal current path easier + + align:start position:0% +this third terminal current path easier + + + align:start position:0% +this third terminal current path easier +that's probably going to lead to + + align:start position:0% +that's probably going to lead to + + + align:start position:0% +that's probably going to lead to +different common mode noise for example + + align:start position:0% +different common mode noise for example + + + align:start position:0% +different common mode noise for example +but no they occur together you've got to + + align:start position:0% +but no they occur together you've got to + + + align:start position:0% +but no they occur together you've got to +filter both at the same + + align:start position:0% +filter both at the same + + + align:start position:0% +filter both at the same +time other + + align:start position:0% + + + + align:start position:0% + +questions okay next class we're going to + + align:start position:0% +questions okay next class we're going to + + + align:start position:0% +questions okay next class we're going to +take up an entirely new class of + + align:start position:0% +take up an entirely new class of + + + align:start position:0% +take up an entirely new class of +converter but uh I we will do that + + align:start position:0% +converter but uh I we will do that + + + align:start position:0% +converter but uh I we will do that +tomorrow have a great day \ No newline at end of file diff --git a/Zuc7ApKTiO0.txt b/Zuc7ApKTiO0.txt new file mode 100644 index 0000000000000000000000000000000000000000..fa5fd7fecebd063fa70c56278c1b47a80f59391d --- /dev/null +++ b/Zuc7ApKTiO0.txt @@ -0,0 +1,3891 @@ +align:start position:0% + +And our next speaker is Brock Yordi from + + align:start position:0% +And our next speaker is Brock Yordi from + + + align:start position:0% +And our next speaker is Brock Yordi from +the Geothermal Drilling Association. And + + align:start position:0% +the Geothermal Drilling Association. And + + + align:start position:0% +the Geothermal Drilling Association. And +he had the pleasure of collaborating + + align:start position:0% +he had the pleasure of collaborating + + + align:start position:0% +he had the pleasure of collaborating +with Brock this past summer to do um + + align:start position:0% +with Brock this past summer to do um + + + align:start position:0% +with Brock this past summer to do um +geothermal driller pre-apprentice uh + + align:start position:0% +geothermal driller pre-apprentice uh + + + align:start position:0% +geothermal driller pre-apprentice uh +program. + + align:start position:0% +program. + + + align:start position:0% +program. +>> Should not have taken that. + + align:start position:0% +>> Should not have taken that. + + + align:start position:0% +>> Should not have taken that. +>> So how does this work? Do I still have + + align:start position:0% +>> So how does this work? Do I still have + + + align:start position:0% +>> So how does this work? Do I still have +20 minutes or uh + + align:start position:0% +20 minutes or uh + + + align:start position:0% +20 minutes or uh +Sorry, Brock. + + align:start position:0% + + + + align:start position:0% + +>> They wanted you to put it on the next + + align:start position:0% +>> They wanted you to put it on the next + + + align:start position:0% +>> They wanted you to put it on the next +guy. + + align:start position:0% +guy. + + + align:start position:0% +guy. +>> Excellent. + + align:start position:0% +>> Excellent. + + + align:start position:0% +>> Excellent. +>> So, we're going to do introduction to + + align:start position:0% +>> So, we're going to do introduction to + + + align:start position:0% +>> So, we're going to do introduction to +geothermal drilling a bridged in 20 + + align:start position:0% +geothermal drilling a bridged in 20 + + + align:start position:0% +geothermal drilling a bridged in 20 +minutes. Um, there's plenty of things in + + align:start position:0% +minutes. Um, there's plenty of things in + + + align:start position:0% +minutes. Um, there's plenty of things in +here and we have heard about how + + align:start position:0% +here and we have heard about how + + + align:start position:0% +here and we have heard about how +drilling affects us. And I think any of + + align:start position:0% +drilling affects us. And I think any of + + + align:start position:0% +drilling affects us. And I think any of +you that are flipping the television and + + align:start position:0% +you that are flipping the television and + + + align:start position:0% +you that are flipping the television and +you come across FX and you see the movie + + align:start position:0% +you come across FX and you see the movie + + + align:start position:0% +you come across FX and you see the movie +Armageddon, you can see that the major + + align:start position:0% +Armageddon, you can see that the major + + + align:start position:0% +Armageddon, you can see that the major +premise is it's easier to teach drillers + + align:start position:0% +premise is it's easier to teach drillers + + + align:start position:0% +premise is it's easier to teach drillers +to be astronauts than it is to teach an + + align:start position:0% +to be astronauts than it is to teach an + + + align:start position:0% +to be astronauts than it is to teach an +astronaut to be a driller. When Ben + + align:start position:0% +astronaut to be a driller. When Ben + + + align:start position:0% +astronaut to be a driller. When Ben +Affleck asked that question, uh, some + + align:start position:0% +Affleck asked that question, uh, some + + + align:start position:0% +Affleck asked that question, uh, some +choice words were used by m Michael Bay, + + align:start position:0% +choice words were used by m Michael Bay, + + + align:start position:0% +choice words were used by m Michael Bay, +but in reality, suspension of disbelief + + align:start position:0% +but in reality, suspension of disbelief + + + align:start position:0% +but in reality, suspension of disbelief +is what we're looking at. + + align:start position:0% + + + + align:start position:0% + +jump past that. Okay, here's my warning. + + align:start position:0% +jump past that. Okay, here's my warning. + + + align:start position:0% +jump past that. Okay, here's my warning. +The following presentation features + + align:start position:0% +The following presentation features + + + align:start position:0% +The following presentation features +tribal drilling knowledge acquired by + + align:start position:0% +tribal drilling knowledge acquired by + + + align:start position:0% +tribal drilling knowledge acquired by +drilling professionals or under the + + align:start position:0% +drilling professionals or under the + + + align:start position:0% +drilling professionals or under the +supervision of geothermal professionals. + + align:start position:0% +supervision of geothermal professionals. + + + align:start position:0% +supervision of geothermal professionals. +Accordingly, me must insist that + + align:start position:0% +Accordingly, me must insist that + + + align:start position:0% +Accordingly, me must insist that +everyone who engages with drilling in + + align:start position:0% +everyone who engages with drilling in + + + align:start position:0% +everyone who engages with drilling in +this presentation consider this advice. + + align:start position:0% +this presentation consider this advice. + + + align:start position:0% +this presentation consider this advice. +Drilling is the imperfect combination of + + align:start position:0% +Drilling is the imperfect combination of + + + align:start position:0% +Drilling is the imperfect combination of +science, physics, and self-taught tribal + + align:start position:0% +science, physics, and self-taught tribal + + + align:start position:0% +science, physics, and self-taught tribal +knowledge compounded over years of + + align:start position:0% +knowledge compounded over years of + + + align:start position:0% +knowledge compounded over years of +success and failure. Drilling is a + + align:start position:0% +success and failure. Drilling is a + + + align:start position:0% +success and failure. Drilling is a +disruptive process. We know this. The + + align:start position:0% +disruptive process. We know this. The + + + align:start position:0% +disruptive process. We know this. The +key to the success lies in your + + align:start position:0% +key to the success lies in your + + + align:start position:0% +key to the success lies in your +conscious choice of the drilling program + + align:start position:0% +conscious choice of the drilling program + + + align:start position:0% +conscious choice of the drilling program +that minimizes the impact of the + + align:start position:0% +that minimizes the impact of the + + + align:start position:0% +that minimizes the impact of the +surrounding environment. That's the bore + + align:start position:0% +surrounding environment. That's the bore + + + align:start position:0% +surrounding environment. That's the bore +hole. That's the neighbors. That's the + + align:start position:0% +hole. That's the neighbors. That's the + + + align:start position:0% +hole. That's the neighbors. That's the +project staying on time. + + align:start position:0% +project staying on time. + + + align:start position:0% +project staying on time. +Drillers, contractors, engineers, + + align:start position:0% +Drillers, contractors, engineers, + + + align:start position:0% +Drillers, contractors, engineers, +scientists, and clients have entered in + + align:start position:0% +scientists, and clients have entered in + + + align:start position:0% +scientists, and clients have entered in +a powerful partnership to uncover the + + align:start position:0% +a powerful partnership to uncover the + + + align:start position:0% +a powerful partnership to uncover the +mysteries of the subsurface. We are + + align:start position:0% +mysteries of the subsurface. We are + + + align:start position:0% +mysteries of the subsurface. We are +discovering the unknown together. + + align:start position:0% +discovering the unknown together. + + + align:start position:0% +discovering the unknown together. +And how are we going to do that? A + + align:start position:0% +And how are we going to do that? A + + + align:start position:0% +And how are we going to do that? A +bridge version 20 minutes, right? + + align:start position:0% +bridge version 20 minutes, right? + + + align:start position:0% +bridge version 20 minutes, right? +It's simple. We have a drilling system. + + align:start position:0% +It's simple. We have a drilling system. + + + align:start position:0% +It's simple. We have a drilling system. +And we've seen this from uh the OG + + align:start position:0% +And we've seen this from uh the OG + + + align:start position:0% +And we've seen this from uh the OG +Garren Eubanks to as we've talked a lot + + align:start position:0% +Garren Eubanks to as we've talked a lot + + + align:start position:0% +Garren Eubanks to as we've talked a lot +geology + + align:start position:0% +geology + + + align:start position:0% +geology +formation hydraulics depth to water + + align:start position:0% +formation hydraulics depth to water + + + align:start position:0% +formation hydraulics depth to water +subsurface challenges. Those are the + + align:start position:0% +subsurface challenges. Those are the + + + align:start position:0% +subsurface challenges. Those are the +things that I'm thinking about when we + + align:start position:0% +things that I'm thinking about when we + + + align:start position:0% +things that I'm thinking about when we +say can we drill this next. That's going + + align:start position:0% +say can we drill this next. That's going + + + align:start position:0% +say can we drill this next. That's going +to align into my drilling capabilities. + + align:start position:0% +to align into my drilling capabilities. + + + align:start position:0% +to align into my drilling capabilities. +This is my drilling system. So, what can + + align:start position:0% +This is my drilling system. So, what can + + + align:start position:0% +This is my drilling system. So, what can +my rig capable of doing? From horsepower + + align:start position:0% +my rig capable of doing? From horsepower + + + align:start position:0% +my rig capable of doing? From horsepower +to rotation to pull down to pullback to + + align:start position:0% +to rotation to pull down to pullback to + + + align:start position:0% +to rotation to pull down to pullback to +diameter, depth, angle. This is all + + align:start position:0% +diameter, depth, angle. This is all + + + align:start position:0% +diameter, depth, angle. This is all +going to drive our cost. Next, choice of + + align:start position:0% +going to drive our cost. Next, choice of + + + align:start position:0% +going to drive our cost. Next, choice of +drilling method. Back to that drilling + + align:start position:0% +drilling method. Back to that drilling + + + align:start position:0% +drilling method. Back to that drilling +program. Is it going to be using mud + + align:start position:0% +program. Is it going to be using mud + + + align:start position:0% +program. Is it going to be using mud +pumps, air compressors, sonic, dual + + align:start position:0% +pumps, air compressors, sonic, dual + + + align:start position:0% +pumps, air compressors, sonic, dual +rotary, reverse circulation? There are + + align:start position:0% +rotary, reverse circulation? There are + + + align:start position:0% +rotary, reverse circulation? There are +plenty. Hopefully, one day we get a rock + + align:start position:0% +plenty. Hopefully, one day we get a rock + + + align:start position:0% +plenty. Hopefully, one day we get a rock +melter, right? Maybe a laser. We keep + + align:start position:0% +melter, right? Maybe a laser. We keep + + + align:start position:0% +melter, right? Maybe a laser. We keep +seeing things come out all the time. + + align:start position:0% +seeing things come out all the time. + + + align:start position:0% +seeing things come out all the time. +Finally, as much as we want to say + + align:start position:0% +Finally, as much as we want to say + + + align:start position:0% +Finally, as much as we want to say +autonomy is coming and it's really cool + + align:start position:0% +autonomy is coming and it's really cool + + + align:start position:0% +autonomy is coming and it's really cool +watching the Dragon Rocket go up and uh + + align:start position:0% +watching the Dragon Rocket go up and uh + + + align:start position:0% +watching the Dragon Rocket go up and uh +there's nobody really at the control, + + align:start position:0% +there's nobody really at the control, + + + align:start position:0% +there's nobody really at the control, +but they still uh individual can be at + + align:start position:0% +but they still uh individual can be at + + + align:start position:0% +but they still uh individual can be at +that stick at any moment. And this + + align:start position:0% +that stick at any moment. And this + + + align:start position:0% +that stick at any moment. And this +processing right here will always be + + align:start position:0% +processing right here will always be + + + align:start position:0% +processing right here will always be +very important to what we're doing. So + + align:start position:0% +very important to what we're doing. So + + + align:start position:0% +very important to what we're doing. So +our driller, our drilling company, our + + align:start position:0% +our driller, our drilling company, our + + + align:start position:0% +our driller, our drilling company, our +contractor's qualifications, what + + align:start position:0% +contractor's qualifications, what + + + align:start position:0% +contractor's qualifications, what +special tools do they bring, what + + align:start position:0% +special tools do they bring, what + + + align:start position:0% +special tools do they bring, what +methods, what applied science and + + align:start position:0% +methods, what applied science and + + + align:start position:0% +methods, what applied science and +fundamentals. + + align:start position:0% +fundamentals. + + + align:start position:0% +fundamentals. +So as I think of that, the driller and + + align:start position:0% +So as I think of that, the driller and + + + align:start position:0% +So as I think of that, the driller and +we talk about workforce development, we + + align:start position:0% +we talk about workforce development, we + + + align:start position:0% +we talk about workforce development, we +talk about developing this, the liftoff + + align:start position:0% +talk about developing this, the liftoff + + + align:start position:0% +talk about developing this, the liftoff +report talks about where we need to be, + + align:start position:0% +report talks about where we need to be, + + + align:start position:0% +report talks about where we need to be, +what we need for workforce. He and Ia + + align:start position:0% +what we need for workforce. He and Ia + + + align:start position:0% +what we need for workforce. He and Ia +and I with Stacy right here in the front + + align:start position:0% +and I with Stacy right here in the front + + + align:start position:0% +and I with Stacy right here in the front +row with the the time and uh we we have + + align:start position:0% +row with the the time and uh we we have + + + align:start position:0% +row with the the time and uh we we have +collaborated a ton on workforce + + align:start position:0% +collaborated a ton on workforce + + + align:start position:0% +collaborated a ton on workforce +development and developing these + + align:start position:0% +development and developing these + + + align:start position:0% +development and developing these +drillers. But the critical system that I + + align:start position:0% +drillers. But the critical system that I + + + align:start position:0% +drillers. But the critical system that I +just showed you doesn't work without a + + align:start position:0% +just showed you doesn't work without a + + + align:start position:0% +just showed you doesn't work without a +competent drill crew that's working in + + align:start position:0% +competent drill crew that's working in + + + align:start position:0% +competent drill crew that's working in +safety first because we're rotating, + + align:start position:0% +safety first because we're rotating, + + + align:start position:0% +safety first because we're rotating, +we're per cussing, we're lifting things + + align:start position:0% +we're per cussing, we're lifting things + + + align:start position:0% +we're per cussing, we're lifting things +over our heads. So, as that drill crew + + align:start position:0% +over our heads. So, as that drill crew + + + align:start position:0% +over our heads. So, as that drill crew +steps up into this critical system, + + align:start position:0% +steps up into this critical system, + + + align:start position:0% +steps up into this critical system, +what's their goal for the day, what is + + align:start position:0% +what's their goal for the day, what is + + + align:start position:0% +what's their goal for the day, what is +the quality of the installation, what is + + align:start position:0% +the quality of the installation, what is + + + align:start position:0% +the quality of the installation, what is +the site and environmental impacts and + + align:start position:0% +the site and environmental impacts and + + + align:start position:0% +the site and environmental impacts and +management, what is the goal for project + + align:start position:0% +management, what is the goal for project + + + align:start position:0% +management, what is the goal for project +completion, staying on time, staying + + align:start position:0% +completion, staying on time, staying + + + align:start position:0% +completion, staying on time, staying +under budget. Did I say under budget? + + align:start position:0% +under budget. Did I say under budget? + + + align:start position:0% +under budget. Did I say under budget? +And I'm a drill guy. Whoa. preparation + + align:start position:0% +And I'm a drill guy. Whoa. preparation + + + align:start position:0% +And I'm a drill guy. Whoa. preparation +and planning for unseen issues, + + align:start position:0% +and planning for unseen issues, + + + align:start position:0% +and planning for unseen issues, +for foreseen issues, weather, you know, + + align:start position:0% +for foreseen issues, weather, you know, + + + align:start position:0% +for foreseen issues, weather, you know, +those challenging geologies, + + align:start position:0% +those challenging geologies, + + + align:start position:0% +those challenging geologies, +roles and responsibilities of that crew, + + align:start position:0% +roles and responsibilities of that crew, + + + align:start position:0% +roles and responsibilities of that crew, +the driller, rig operation. This is a + + align:start position:0% +the driller, rig operation. This is a + + + align:start position:0% +the driller, rig operation. This is a +complex process that has microscond + + align:start position:0% +complex process that has microscond + + + align:start position:0% +complex process that has microscond +adjustments that need to be made at + + align:start position:0% +adjustments that need to be made at + + + align:start position:0% +adjustments that need to be made at +times. They need to understand this so + + align:start position:0% +times. They need to understand this so + + + align:start position:0% +times. They need to understand this so +they can have effective product + + align:start position:0% +they can have effective product + + + align:start position:0% +they can have effective product +installation and we get effective + + align:start position:0% +installation and we get effective + + + align:start position:0% +installation and we get effective +resource extraction so we have good + + align:start position:0% +resource extraction so we have good + + + align:start position:0% +resource extraction so we have good +project completion and good + + align:start position:0% +project completion and good + + + align:start position:0% +project completion and good +recordkeeping. We have an assistant + + align:start position:0% +recordkeeping. We have an assistant + + + align:start position:0% +recordkeeping. We have an assistant +driller there supporting that driller + + align:start position:0% +driller there supporting that driller + + + align:start position:0% +driller there supporting that driller +rig support tool handling product + + align:start position:0% +rig support tool handling product + + + align:start position:0% +rig support tool handling product +assembly getting into the standards that + + align:start position:0% +assembly getting into the standards that + + + align:start position:0% +assembly getting into the standards that +we just talked about from pressure + + align:start position:0% +we just talked about from pressure + + + align:start position:0% +we just talked about from pressure +testing to making sure our grout making + + align:start position:0% +testing to making sure our grout making + + + align:start position:0% +testing to making sure our grout making +sure we're making that right hole. And + + align:start position:0% +sure we're making that right hole. And + + + align:start position:0% +sure we're making that right hole. And +then finally, our field technician who + + align:start position:0% +then finally, our field technician who + + + align:start position:0% +then finally, our field technician who +is doing the solids control management + + align:start position:0% +is doing the solids control management + + + align:start position:0% +is doing the solids control management +because let's face it, we love this + + align:start position:0% +because let's face it, we love this + + + align:start position:0% +because let's face it, we love this +concept of drilling and putting bore + + align:start position:0% +concept of drilling and putting bore + + + align:start position:0% +concept of drilling and putting bore +holes in. We forget about the cubic + + align:start position:0% +holes in. We forget about the cubic + + + align:start position:0% +holes in. We forget about the cubic +yards of material we pull out of the + + align:start position:0% +yards of material we pull out of the + + + align:start position:0% +yards of material we pull out of the +ground and how we're going to do that + + align:start position:0% +ground and how we're going to do that + + + align:start position:0% +ground and how we're going to do that +five times to 90 times to 600 to a + + align:start position:0% +five times to 90 times to 600 to a + + + align:start position:0% +five times to 90 times to 600 to a +thousand times. + + align:start position:0% +thousand times. + + + align:start position:0% +thousand times. +And we have to be able to manage that. + + align:start position:0% +And we have to be able to manage that. + + + align:start position:0% +And we have to be able to manage that. +So three people we can get away with + + align:start position:0% +So three people we can get away with + + + align:start position:0% +So three people we can get away with +two. It depends on the project, the + + align:start position:0% +two. It depends on the project, the + + + align:start position:0% +two. It depends on the project, the +timeline and the expectations. + + align:start position:0% +timeline and the expectations. + + + align:start position:0% +timeline and the expectations. +Okay, we're all going to become drillers + + align:start position:0% +Okay, we're all going to become drillers + + + align:start position:0% +Okay, we're all going to become drillers +today. + + align:start position:0% +today. + + + align:start position:0% +today. +This is the basic fundamentals. I am + + align:start position:0% +This is the basic fundamentals. I am + + + align:start position:0% +This is the basic fundamentals. I am +exerting force against our geology. And + + align:start position:0% +exerting force against our geology. And + + + align:start position:0% +exerting force against our geology. And +then I have to cut it. So is that in + + align:start position:0% +then I have to cut it. So is that in + + + align:start position:0% +then I have to cut it. So is that in +rotation? Is that in percussion? Is that + + align:start position:0% +rotation? Is that in percussion? Is that + + + align:start position:0% +rotation? Is that in percussion? Is that +in velocity? Is that in frequency? As we + + align:start position:0% +in velocity? Is that in frequency? As we + + + align:start position:0% +in velocity? Is that in frequency? As we +see with sonic drilling. Next, I have to + + align:start position:0% +see with sonic drilling. Next, I have to + + + align:start position:0% +see with sonic drilling. Next, I have to +remove those solids or it's not a bore + + align:start position:0% +remove those solids or it's not a bore + + + align:start position:0% +remove those solids or it's not a bore +hole, right? It's just a uh thing that + + align:start position:0% +hole, right? It's just a uh thing that + + + align:start position:0% +hole, right? It's just a uh thing that +we got stuck in. And man, we don't drill + + align:start position:0% +we got stuck in. And man, we don't drill + + + align:start position:0% +we got stuck in. And man, we don't drill +more bore holes. So, I have to flush it. + + align:start position:0% +more bore holes. So, I have to flush it. + + + align:start position:0% +more bore holes. So, I have to flush it. +I can do this either mechanically, + + align:start position:0% +I can do this either mechanically, + + + align:start position:0% +I can do this either mechanically, +that's with augers, that's with uh + + align:start position:0% +that's with augers, that's with uh + + + align:start position:0% +that's with augers, that's with uh +frequency, or flushing with water, air, + + align:start position:0% +frequency, or flushing with water, air, + + + align:start position:0% +frequency, or flushing with water, air, +drilling fluids, engineered solutions. + + align:start position:0% +drilling fluids, engineered solutions. + + + align:start position:0% +drilling fluids, engineered solutions. +This is straight air rotary. We can see + + align:start position:0% +This is straight air rotary. We can see + + + align:start position:0% +This is straight air rotary. We can see +one's going into some rock here, and we + + align:start position:0% +one's going into some rock here, and we + + + align:start position:0% +one's going into some rock here, and we +have one going into a blue green shale. + + align:start position:0% +have one going into a blue green shale. + + + align:start position:0% +have one going into a blue green shale. +Nice, clean, out of the way. No water + + align:start position:0% +Nice, clean, out of the way. No water + + + align:start position:0% +Nice, clean, out of the way. No water +table here. How many times are we + + align:start position:0% +table here. How many times are we + + + align:start position:0% +table here. How many times are we +intersecting water tables and producing + + align:start position:0% +intersecting water tables and producing + + + align:start position:0% +intersecting water tables and producing +water? This is a big piece for us in our + + align:start position:0% +water? This is a big piece for us in our + + + align:start position:0% +water? This is a big piece for us in our +cost, in our responsibility as a + + align:start position:0% +cost, in our responsibility as a + + + align:start position:0% +cost, in our responsibility as a +driller. Here's mud rotary conventional. + + align:start position:0% +driller. Here's mud rotary conventional. + + + align:start position:0% +driller. Here's mud rotary conventional. +Man, it looks messy. So, we immediately + + align:start position:0% +Man, it looks messy. So, we immediately + + + align:start position:0% +Man, it looks messy. So, we immediately +go, we want to go back to that other + + align:start position:0% +go, we want to go back to that other + + + align:start position:0% +go, we want to go back to that other +slide, but we can't. We have to select + + align:start position:0% +slide, but we can't. We have to select + + + align:start position:0% +slide, but we can't. We have to select +the right method for the right geology. + + align:start position:0% +the right method for the right geology. + + + align:start position:0% +the right method for the right geology. +So, we get into engineered drilling + + align:start position:0% +So, we get into engineered drilling + + + align:start position:0% +So, we get into engineered drilling +solutions. Uh Jordan, I drilled with the + + align:start position:0% +solutions. Uh Jordan, I drilled with the + + + align:start position:0% +solutions. Uh Jordan, I drilled with the +US military to 2400 feet with bubbles. + + align:start position:0% +US military to 2400 feet with bubbles. + + + align:start position:0% +US military to 2400 feet with bubbles. +Got the nickname Captain Bubbles for + + align:start position:0% +Got the nickname Captain Bubbles for + + + align:start position:0% +Got the nickname Captain Bubbles for +that entire project. We can use foam + + align:start position:0% +that entire project. We can use foam + + + align:start position:0% +that entire project. We can use foam +with low hydraulic hydraulic + + align:start position:0% +with low hydraulic hydraulic + + + align:start position:0% +with low hydraulic hydraulic +conductivity and carry those cutings + + align:start position:0% +conductivity and carry those cutings + + + align:start position:0% +conductivity and carry those cutings +out. Mud, mud rotary, why it's been + + align:start position:0% +out. Mud, mud rotary, why it's been + + + align:start position:0% +out. Mud, mud rotary, why it's been +predominant throughout geothermal is + + align:start position:0% +predominant throughout geothermal is + + + align:start position:0% +predominant throughout geothermal is +because again it's low influence to our + + align:start position:0% +because again it's low influence to our + + + align:start position:0% +because again it's low influence to our +ground, but it creates two waist streams + + align:start position:0% +ground, but it creates two waist streams + + + align:start position:0% +ground, but it creates two waist streams +and we've decided those waist streams + + align:start position:0% +and we've decided those waist streams + + + align:start position:0% +and we've decided those waist streams +are much harder to get rid of. + + align:start position:0% +are much harder to get rid of. + + + align:start position:0% +are much harder to get rid of. +So, let's look at this. We're going to + + align:start position:0% +So, let's look at this. We're going to + + + align:start position:0% +So, let's look at this. We're going to +talk conventional rotary. We could get + + align:start position:0% +talk conventional rotary. We could get + + + align:start position:0% +talk conventional rotary. We could get +into dual rotary. And I'll say competent + + align:start position:0% +into dual rotary. And I'll say competent + + + align:start position:0% +into dual rotary. And I'll say competent +drilling companies, they're good. And + + align:start position:0% +drilling companies, they're good. And + + + align:start position:0% +drilling companies, they're good. And +they have invested in lots of different + + align:start position:0% +they have invested in lots of different + + + align:start position:0% +they have invested in lots of different +pieces of equipment. And here's the + + align:start position:0% +pieces of equipment. And here's the + + + align:start position:0% +pieces of equipment. And here's the +deal. They're going to sell you on their + + align:start position:0% +deal. They're going to sell you on their + + + align:start position:0% +deal. They're going to sell you on their +system. And sometimes those systems are + + align:start position:0% +system. And sometimes those systems are + + + align:start position:0% +system. And sometimes those systems are +bougie bore holes that go 850 ft at an + + align:start position:0% +bougie bore holes that go 850 ft at an + + + align:start position:0% +bougie bore holes that go 850 ft at an +angle. And we need that because of the + + align:start position:0% +angle. And we need that because of the + + + align:start position:0% +angle. And we need that because of the +footprint in the solution. And there's + + align:start position:0% +footprint in the solution. And there's + + + align:start position:0% +footprint in the solution. And there's +other times where we can simplify this. + + align:start position:0% +other times where we can simplify this. + + + align:start position:0% +other times where we can simplify this. +And if you look at the liftoff report + + align:start position:0% +And if you look at the liftoff report + + + align:start position:0% +And if you look at the liftoff report +with 80 million B buildings, we need + + align:start position:0% +with 80 million B buildings, we need + + + align:start position:0% +with 80 million B buildings, we need +that holistic approach of everybody + + align:start position:0% +that holistic approach of everybody + + + align:start position:0% +that holistic approach of everybody +drilling. This is Armageddon, right? We + + align:start position:0% +drilling. This is Armageddon, right? We + + + align:start position:0% +drilling. This is Armageddon, right? We +saw 3 degrees Celsius by 2100. That + + align:start position:0% +saw 3 degrees Celsius by 2100. That + + + align:start position:0% +saw 3 degrees Celsius by 2100. That +meteor is coming here. We all get to be + + align:start position:0% +meteor is coming here. We all get to be + + + align:start position:0% +meteor is coming here. We all get to be +Ben Affleck and Bruce Willis in this + + align:start position:0% +Ben Affleck and Bruce Willis in this + + + align:start position:0% +Ben Affleck and Bruce Willis in this +situation. So as we look at this, we + + align:start position:0% +situation. So as we look at this, we + + + align:start position:0% +situation. So as we look at this, we +have mud drilling. I need to be able to + + align:start position:0% +have mud drilling. I need to be able to + + + align:start position:0% +have mud drilling. I need to be able to +remove solids from the bottom of the + + align:start position:0% +remove solids from the bottom of the + + + align:start position:0% +remove solids from the bottom of the +bore hole at the bit face at somewhere + + align:start position:0% +bore hole at the bit face at somewhere + + + align:start position:0% +bore hole at the bit face at somewhere +between 60 and 150 feet per minute. Low + + align:start position:0% +between 60 and 150 feet per minute. Low + + + align:start position:0% +between 60 and 150 feet per minute. Low +conductivity. I'm not going to force on + + align:start position:0% +conductivity. I'm not going to force on + + + align:start position:0% +conductivity. I'm not going to force on +those fragile formations. I get into + + align:start position:0% +those fragile formations. I get into + + + align:start position:0% +those fragile formations. I get into +air. I think about Stan Lee and + + align:start position:0% +air. I think about Stan Lee and + + + align:start position:0% +air. I think about Stan Lee and +Spider-Man. With great power comes great + + align:start position:0% +Spider-Man. With great power comes great + + + align:start position:0% +Spider-Man. With great power comes great +responsibility. Holy cow, I can move + + align:start position:0% +responsibility. Holy cow, I can move + + + align:start position:0% +responsibility. Holy cow, I can move +cutings out of the hole at 7500 feet per + + align:start position:0% +cutings out of the hole at 7500 feet per + + + align:start position:0% +cutings out of the hole at 7500 feet per +minute. + + align:start position:0% +minute. + + + align:start position:0% +minute. +job should be done under budget, on + + align:start position:0% +job should be done under budget, on + + + align:start position:0% +job should be done under budget, on +time, like super fast. We'll have cars + + align:start position:0% +time, like super fast. We'll have cars + + + align:start position:0% +time, like super fast. We'll have cars +going back over that road, right? But + + align:start position:0% +going back over that road, right? But + + + align:start position:0% +going back over that road, right? But +that's competent rock formations. That's + + align:start position:0% +that's competent rock formations. That's + + + align:start position:0% +that's competent rock formations. That's +no water. What happens when we start + + align:start position:0% +no water. What happens when we start + + + align:start position:0% +no water. What happens when we start +those waist streams? So then we start + + align:start position:0% +those waist streams? So then we start + + + align:start position:0% +those waist streams? So then we start +engineering solutions either in mud or + + align:start position:0% +engineering solutions either in mud or + + + align:start position:0% +engineering solutions either in mud or +in foam and we can start changing what + + align:start position:0% +in foam and we can start changing what + + + align:start position:0% +in foam and we can start changing what +we need. the influence to that borehole + + align:start position:0% +we need. the influence to that borehole + + + align:start position:0% +we need. the influence to that borehole +wall. As we talk about that thermal + + align:start position:0% +wall. As we talk about that thermal + + + align:start position:0% +wall. As we talk about that thermal +conductivity test, as we talk about + + align:start position:0% +conductivity test, as we talk about + + + align:start position:0% +conductivity test, as we talk about +all of those pieces of influencing and + + align:start position:0% +all of those pieces of influencing and + + + align:start position:0% +all of those pieces of influencing and +minimizing that impact come from us + + align:start position:0% +minimizing that impact come from us + + + align:start position:0% +minimizing that impact come from us +matching the right drilling method to + + align:start position:0% +matching the right drilling method to + + + align:start position:0% +matching the right drilling method to +what we're going to be in. + + align:start position:0% +what we're going to be in. + + + align:start position:0% +what we're going to be in. +So what do I need out of that drilling + + align:start position:0% +So what do I need out of that drilling + + + align:start position:0% +So what do I need out of that drilling +program? I need an efficient rate of + + align:start position:0% +program? I need an efficient rate of + + + align:start position:0% +program? I need an efficient rate of +penetration because let's face it, uh, + + align:start position:0% +penetration because let's face it, uh, + + + align:start position:0% +penetration because let's face it, uh, +with the drilling companies that are in + + align:start position:0% +with the drilling companies that are in + + + align:start position:0% +with the drilling companies that are in +here, time and diesel fuel, regardless + + align:start position:0% +here, time and diesel fuel, regardless + + + align:start position:0% +here, time and diesel fuel, regardless +of our waist stream, because guess what + + align:start position:0% +of our waist stream, because guess what + + + align:start position:0% +of our waist stream, because guess what +clients, you're a co-generator, that's + + align:start position:0% +clients, you're a co-generator, that's + + + align:start position:0% +clients, you're a co-generator, that's +your waist stream. We're just managing + + align:start position:0% +your waist stream. We're just managing + + + align:start position:0% +your waist stream. We're just managing +it for us. Time and diesel fuel are the + + align:start position:0% +it for us. Time and diesel fuel are the + + + align:start position:0% +it for us. Time and diesel fuel are the +most expensive pieces for our projects. + + align:start position:0% +most expensive pieces for our projects. + + + align:start position:0% +most expensive pieces for our projects. +So, I need to be able to have good rate + + align:start position:0% +So, I need to be able to have good rate + + + align:start position:0% +So, I need to be able to have good rate +of penetration and good production. + + align:start position:0% +of penetration and good production. + + + align:start position:0% +of penetration and good production. +Next, while doing that, I have to + + align:start position:0% +Next, while doing that, I have to + + + align:start position:0% +Next, while doing that, I have to +minimize the impact to the bore hole and + + align:start position:0% +minimize the impact to the bore hole and + + + align:start position:0% +minimize the impact to the bore hole and +think about how I'm influencing that + + align:start position:0% +think about how I'm influencing that + + + align:start position:0% +think about how I'm influencing that +downhole geology. I talked about geology + + align:start position:0% +downhole geology. I talked about geology + + + align:start position:0% +downhole geology. I talked about geology +next to it. I said, "Formation + + align:start position:0% +next to it. I said, "Formation + + + align:start position:0% +next to it. I said, "Formation +hydraulics." I want you to think about + + align:start position:0% +hydraulics." I want you to think about + + + align:start position:0% +hydraulics." I want you to think about +um I was in wood shop. There's this + + align:start position:0% +um I was in wood shop. There's this + + + align:start position:0% +um I was in wood shop. There's this +really cute uh individual next to me. + + align:start position:0% +really cute uh individual next to me. + + + align:start position:0% +really cute uh individual next to me. +It's Mother's Day. We're building + + align:start position:0% +It's Mother's Day. We're building + + + align:start position:0% +It's Mother's Day. We're building +birdhouses. I want to ask her to prom. + + align:start position:0% +birdhouses. I want to ask her to prom. + + + align:start position:0% +birdhouses. I want to ask her to prom. +So, I grab my birdhouse with the pine + + align:start position:0% +So, I grab my birdhouse with the pine + + + align:start position:0% +So, I grab my birdhouse with the pine +and I drive all the screws in it and I + + align:start position:0% +and I drive all the screws in it and I + + + align:start position:0% +and I drive all the screws in it and I +get it done. It fell apart two months + + align:start position:0% +get it done. It fell apart two months + + + align:start position:0% +get it done. It fell apart two months +later in mom's yard. Amanda's birdhouse, + + align:start position:0% +later in mom's yard. Amanda's birdhouse, + + + align:start position:0% +later in mom's yard. Amanda's birdhouse, +I helped her pre-drill all the holes. We + + align:start position:0% +I helped her pre-drill all the holes. We + + + align:start position:0% +I helped her pre-drill all the holes. We +set it. We put the wood glue. Our + + align:start position:0% +set it. We put the wood glue. Our + + + align:start position:0% +set it. We put the wood glue. Our +geology is the same way. When we break + + align:start position:0% +geology is the same way. When we break + + + align:start position:0% +geology is the same way. When we break +that fracture gradient, just the same as + + align:start position:0% +that fracture gradient, just the same as + + + align:start position:0% +that fracture gradient, just the same as +if I drive a screw into this right now + + align:start position:0% +if I drive a screw into this right now + + + align:start position:0% +if I drive a screw into this right now +and split this table. I can putty that. + + align:start position:0% +and split this table. I can putty that. + + + align:start position:0% +and split this table. I can putty that. +I can do things to it, but I can't fix + + align:start position:0% +I can do things to it, but I can't fix + + + align:start position:0% +I can do things to it, but I can't fix +the damage I've done to mother nature. + + align:start position:0% +the damage I've done to mother nature. + + + align:start position:0% +the damage I've done to mother nature. +So beyond that, we get through those + + align:start position:0% +So beyond that, we get through those + + + align:start position:0% +So beyond that, we get through those +fragile subsurface formations, we get + + align:start position:0% +fragile subsurface formations, we get + + + align:start position:0% +fragile subsurface formations, we get +into water production. + + align:start position:0% +into water production. + + + align:start position:0% +into water production. +I want you to watch the news right now. + + align:start position:0% +I want you to watch the news right now. + + + align:start position:0% +I want you to watch the news right now. +Thank you. Um + + align:start position:0% +Thank you. Um + + + align:start position:0% +Thank you. Um +Princeton and Arizona came out with a + + align:start position:0% +Princeton and Arizona came out with a + + + align:start position:0% +Princeton and Arizona came out with a +connection between surface water and + + align:start position:0% +connection between surface water and + + + align:start position:0% +connection between surface water and +groundwater talking about fossilized + + align:start position:0% +groundwater talking about fossilized + + + align:start position:0% +groundwater talking about fossilized +water. Holy cow, it's the drill guy + + align:start position:0% +water. Holy cow, it's the drill guy + + + align:start position:0% +water. Holy cow, it's the drill guy +talking environmentalism now. It's weird + + align:start position:0% +talking environmentalism now. It's weird + + + align:start position:0% +talking environmentalism now. It's weird +time. Drill, baby, drill. No drill, + + align:start position:0% +time. Drill, baby, drill. No drill, + + + align:start position:0% +time. Drill, baby, drill. No drill, +better drill. We need better people + + align:start position:0% +better drill. We need better people + + + align:start position:0% +better drill. We need better people +drilling professionally. So we are + + align:start position:0% +drilling professionally. So we are + + + align:start position:0% +drilling professionally. So we are +pumping fossilized water out of + + align:start position:0% +pumping fossilized water out of + + + align:start position:0% +pumping fossilized water out of +aquifers. That's going to take 10 years + + align:start position:0% +aquifers. That's going to take 10 years + + + align:start position:0% +aquifers. That's going to take 10 years +to 10,000 to 100,000 years to replace. + + align:start position:0% +to 10,000 to 100,000 years to replace. + + + align:start position:0% +to 10,000 to 100,000 years to replace. +So we saved the planet by 2100, but we + + align:start position:0% +So we saved the planet by 2100, but we + + + align:start position:0% +So we saved the planet by 2100, but we +exploited all our groundwater and went + + align:start position:0% +exploited all our groundwater and went + + + align:start position:0% +exploited all our groundwater and went +into the Atlantic. Did we save + + align:start position:0% +into the Atlantic. Did we save + + + align:start position:0% +into the Atlantic. Did we save +ourselves? + + align:start position:0% +ourselves? + + + align:start position:0% +ourselves? +So we have to understand as we produce + + align:start position:0% +So we have to understand as we produce + + + align:start position:0% +So we have to understand as we produce +that water and how much and the + + align:start position:0% +that water and how much and the + + + align:start position:0% +that water and how much and the +influence. But beyond that, as we go + + align:start position:0% +influence. But beyond that, as we go + + + align:start position:0% +influence. But beyond that, as we go +deeper, we have to start thinking about + + align:start position:0% +deeper, we have to start thinking about + + + align:start position:0% +deeper, we have to start thinking about +volatile gases, CO2, hydrogen sulfide, + + align:start position:0% +volatile gases, CO2, hydrogen sulfide, + + + align:start position:0% +volatile gases, CO2, hydrogen sulfide, +methane. And on that minimal impact, as + + align:start position:0% +methane. And on that minimal impact, as + + + align:start position:0% +methane. And on that minimal impact, as +we step back, dust, noise, drill solids, + + align:start position:0% +we step back, dust, noise, drill solids, + + + align:start position:0% +we step back, dust, noise, drill solids, +as we look at more campuses being done, + + align:start position:0% +as we look at more campuses being done, + + + align:start position:0% +as we look at more campuses being done, +man, Ball State, they didn't care how + + align:start position:0% +man, Ball State, they didn't care how + + + align:start position:0% +man, Ball State, they didn't care how +many dump trucks came through. Those + + align:start position:0% +many dump trucks came through. Those + + + align:start position:0% +many dump trucks came through. Those +were all Indiana farm kids. + + align:start position:0% +were all Indiana farm kids. + + + align:start position:0% +were all Indiana farm kids. +You go to Yale, you go to um Forom and + + align:start position:0% +You go to Yale, you go to um Forom and + + + align:start position:0% +You go to Yale, you go to um Forom and +you start thinking about how we're + + align:start position:0% +you start thinking about how we're + + + align:start position:0% +you start thinking about how we're +removing cutings and people are like, + + align:start position:0% +removing cutings and people are like, + + + align:start position:0% +removing cutings and people are like, +"Why are there 10 dump trucks a day + + align:start position:0% +"Why are there 10 dump trucks a day + + + align:start position:0% +"Why are there 10 dump trucks a day +coming through here?" We we have to + + align:start position:0% +coming through here?" We we have to + + + align:start position:0% +coming through here?" We we have to +think about the impact to our neighbors. + + align:start position:0% +think about the impact to our neighbors. + + + align:start position:0% +think about the impact to our neighbors. +Finally, I need data gathering. I need + + align:start position:0% +Finally, I need data gathering. I need + + + align:start position:0% +Finally, I need data gathering. I need +real-time analysis of that subsurface as + + align:start position:0% +real-time analysis of that subsurface as + + + align:start position:0% +real-time analysis of that subsurface as +those formations change as uh we have + + align:start position:0% +those formations change as uh we have + + + align:start position:0% +those formations change as uh we have +challenges as we have loss zones because + + align:start position:0% +challenges as we have loss zones because + + + align:start position:0% +challenges as we have loss zones because +I have to effectively be able to grout + + align:start position:0% +I have to effectively be able to grout + + + align:start position:0% +I have to effectively be able to grout +that so that I have the right influence + + align:start position:0% +that so that I have the right influence + + + align:start position:0% +that so that I have the right influence +to the loops. + + align:start position:0% +to the loops. + + + align:start position:0% +to the loops. +So the results of me doing this right + + align:start position:0% +So the results of me doing this right + + + align:start position:0% +So the results of me doing this right +the hole is going to be open meaning I + + align:start position:0% +the hole is going to be open meaning I + + + align:start position:0% +the hole is going to be open meaning I +can get product into it. It's going to + + align:start position:0% +can get product into it. It's going to + + + align:start position:0% +can get product into it. It's going to +be gauge again my drilling influencing + + align:start position:0% +be gauge again my drilling influencing + + + align:start position:0% +be gauge again my drilling influencing +my geology. If we specify a six-inch + + align:start position:0% +my geology. If we specify a six-inch + + + align:start position:0% +my geology. If we specify a six-inch +bore hole and we look at the cubic feet + + align:start position:0% +bore hole and we look at the cubic feet + + + align:start position:0% +bore hole and we look at the cubic feet +or the cubic yards of grout we want to + + align:start position:0% +or the cubic yards of grout we want to + + + align:start position:0% +or the cubic yards of grout we want to +put in there and we end up with this + + align:start position:0% +put in there and we end up with this + + + align:start position:0% +put in there and we end up with this +oblong boiler hole, we just saw what + + align:start position:0% +oblong boiler hole, we just saw what + + + align:start position:0% +oblong boiler hole, we just saw what +Garren talked about. We heard what Mark + + align:start position:0% +Garren talked about. We heard what Mark + + + align:start position:0% +Garren talked about. We heard what Mark +was talking about. We've screwed up and + + align:start position:0% +was talking about. We've screwed up and + + + align:start position:0% +was talking about. We've screwed up and +now we have an ineffective system. So I + + align:start position:0% +now we have an ineffective system. So I + + + align:start position:0% +now we have an ineffective system. So I +need gauge. I need stable so that I can + + align:start position:0% +need gauge. I need stable so that I can + + + align:start position:0% +need gauge. I need stable so that I can +get in and out of it. It needs to be + + align:start position:0% +get in and out of it. It needs to be + + + align:start position:0% +get in and out of it. It needs to be +straight in the desired direction. + + align:start position:0% +straight in the desired direction. + + + align:start position:0% +straight in the desired direction. +And we need seamless product + + align:start position:0% +And we need seamless product + + + align:start position:0% +And we need seamless product +installation. Loop to bottom, drought to + + align:start position:0% +installation. Loop to bottom, drought to + + + align:start position:0% +installation. Loop to bottom, drought to +top. So I can have efficient resource + + align:start position:0% +top. So I can have efficient resource + + + align:start position:0% +top. So I can have efficient resource +extraction. + + align:start position:0% + + + + align:start position:0% + +Sounds easy. But then we get into this + + align:start position:0% +Sounds easy. But then we get into this + + + align:start position:0% +Sounds easy. But then we get into this +situation right here. All different + + align:start position:0% +situation right here. All different + + + align:start position:0% +situation right here. All different +types of drill solids. How mother nature + + align:start position:0% +types of drill solids. How mother nature + + + align:start position:0% +types of drill solids. How mother nature +reacts to us. How our subsurface works. + + align:start position:0% +reacts to us. How our subsurface works. + + + align:start position:0% +reacts to us. How our subsurface works. +These spoils as I get them out of the + + align:start position:0% +These spoils as I get them out of the + + + align:start position:0% +These spoils as I get them out of the +hole. How do I handle them? + + align:start position:0% +hole. How do I handle them? + + + align:start position:0% +hole. How do I handle them? +6inch bore hole to 400T. It's 2.9 cubic + + align:start position:0% +6inch bore hole to 400T. It's 2.9 cubic + + + align:start position:0% +6inch bore hole to 400T. It's 2.9 cubic +yards. Oh, by the way, that's why we + + align:start position:0% +yards. Oh, by the way, that's why we + + + align:start position:0% +yards. Oh, by the way, that's why we +have three people on a drill crew + + align:start position:0% +have three people on a drill crew + + + align:start position:0% +have three people on a drill crew +because there is a lot. If we're going + + align:start position:0% +because there is a lot. If we're going + + + align:start position:0% +because there is a lot. If we're going +to increase production, you need to be + + align:start position:0% +to increase production, you need to be + + + align:start position:0% +to increase production, you need to be +able to move this stuff away. 6 inch + + align:start position:0% +able to move this stuff away. 6 inch + + + align:start position:0% +able to move this stuff away. 6 inch +850T hole is 6.17 cubic yards. So, as we + + align:start position:0% +850T hole is 6.17 cubic yards. So, as we + + + align:start position:0% +850T hole is 6.17 cubic yards. So, as we +start thinking about this, how many dump + + align:start position:0% +start thinking about this, how many dump + + + align:start position:0% +start thinking about this, how many dump +trucks and back trucks am I bringing + + align:start position:0% +trucks and back trucks am I bringing + + + align:start position:0% +trucks and back trucks am I bringing +into this project? + + align:start position:0% +into this project? + + + align:start position:0% +into this project? +Loop installation. as we specify two + + align:start position:0% +Loop installation. as we specify two + + + align:start position:0% +Loop installation. as we specify two +loops, you know, um the BEu building + + align:start position:0% +loops, you know, um the BEu building + + + align:start position:0% +loops, you know, um the BEu building +with the Ryan 1500 ft. We think about + + align:start position:0% +with the Ryan 1500 ft. We think about + + + align:start position:0% +with the Ryan 1500 ft. We think about +all these different pieces. I need a + + align:start position:0% +all these different pieces. I need a + + + align:start position:0% +all these different pieces. I need a +good effective drilling program so I can + + align:start position:0% +good effective drilling program so I can + + + align:start position:0% +good effective drilling program so I can +have good grouting process. + + align:start position:0% +have good grouting process. + + + align:start position:0% +have good grouting process. +This loop should be in the center and + + align:start position:0% +This loop should be in the center and + + + align:start position:0% +This loop should be in the center and +that trim should be on top of it. But + + align:start position:0% +that trim should be on top of it. But + + + align:start position:0% +that trim should be on top of it. But +I'm really bad at paint. And uh this is + + align:start position:0% +I'm really bad at paint. And uh this is + + + align:start position:0% +I'm really bad at paint. And uh this is +what we get. So here's our trim to + + align:start position:0% +what we get. So here's our trim to + + + align:start position:0% +what we get. So here's our trim to +bottom, our loop to bottom. My + + align:start position:0% +bottom, our loop to bottom. My + + + align:start position:0% +bottom, our loop to bottom. My +individual starts mixing the grout to + + align:start position:0% +individual starts mixing the grout to + + + align:start position:0% +individual starts mixing the grout to +the specified specifications that we + + align:start position:0% +the specified specifications that we + + + align:start position:0% +the specified specifications that we +need. The right amount of water, the + + align:start position:0% +need. The right amount of water, the + + + align:start position:0% +need. The right amount of water, the +right amount of bentonite, the right + + align:start position:0% +right amount of bentonite, the right + + + align:start position:0% +right amount of bentonite, the right +amount of graphite or sand. + + align:start position:0% +amount of graphite or sand. + + + align:start position:0% +amount of graphite or sand. +I start filling that bore hole. As I + + align:start position:0% +I start filling that bore hole. As I + + + align:start position:0% +I start filling that bore hole. As I +fill that bore hole, that trim needs to + + align:start position:0% +fill that bore hole, that trim needs to + + + align:start position:0% +fill that bore hole, that trim needs to +stay 10 feet submerged in the grout. So, + + align:start position:0% +stay 10 feet submerged in the grout. So, + + + align:start position:0% +stay 10 feet submerged in the grout. So, +I have continuous grout column coming + + align:start position:0% +I have continuous grout column coming + + + align:start position:0% +I have continuous grout column coming +out. We talk about now we're going to + + align:start position:0% +out. We talk about now we're going to + + + align:start position:0% +out. We talk about now we're going to +leave the trim in at bottom. No, we're + + align:start position:0% +leave the trim in at bottom. No, we're + + + align:start position:0% +leave the trim in at bottom. No, we're +not going to do this. I started my + + align:start position:0% +not going to do this. I started my + + + align:start position:0% +not going to do this. I started my +career after Yordian Sons at + + align:start position:0% +career after Yordian Sons at + + + align:start position:0% +career after Yordian Sons at +Hallebertton. I studied grouts for 10 + + align:start position:0% +Hallebertton. I studied grouts for 10 + + + align:start position:0% +Hallebertton. I studied grouts for 10 +years. + + align:start position:0% +years. + + + align:start position:0% +years. +I'm bringing this grout column out of + + align:start position:0% +I'm bringing this grout column out of + + + align:start position:0% +I'm bringing this grout column out of +the hole with my Trimmy and that's what + + align:start position:0% +the hole with my Trimmy and that's what + + + align:start position:0% +the hole with my Trimmy and that's what +I want to see. I want to see grout to + + align:start position:0% +I want to see. I want to see grout to + + + align:start position:0% +I want to see. I want to see grout to +surface. I need to effectively be able + + align:start position:0% +surface. I need to effectively be able + + + align:start position:0% +surface. I need to effectively be able +to look at that grout and know that I + + align:start position:0% +to look at that grout and know that I + + + align:start position:0% +to look at that grout and know that I +had a good + + align:start position:0% +had a good + + + align:start position:0% +had a good +column come out that I didn't have + + align:start position:0% +column come out that I didn't have + + + align:start position:0% +column come out that I didn't have +channeling in that as we have these + + align:start position:0% +channeling in that as we have these + + + align:start position:0% +channeling in that as we have these +discussions about ah it just needs to be + + align:start position:0% +discussions about ah it just needs to be + + + align:start position:0% +discussions about ah it just needs to be +four feet in the ground. No, I need to + + align:start position:0% +four feet in the ground. No, I need to + + + align:start position:0% +four feet in the ground. No, I need to +see this because this is protecting us. + + align:start position:0% +see this because this is protecting us. + + + align:start position:0% +see this because this is protecting us. +I need to see it come to surface. + + align:start position:0% +I need to see it come to surface. + + + align:start position:0% +I need to see it come to surface. +Why? because I am replacing the native + + align:start position:0% +Why? because I am replacing the native + + + align:start position:0% +Why? because I am replacing the native +material that I just destroyed with + + align:start position:0% +material that I just destroyed with + + + align:start position:0% +material that I just destroyed with +something that meets or exceeds Thank + + align:start position:0% +something that meets or exceeds Thank + + + align:start position:0% +something that meets or exceeds Thank +you. our ceiling capability. It's got to + + align:start position:0% +you. our ceiling capability. It's got to + + + align:start position:0% +you. our ceiling capability. It's got to +have a better standard. I need to ensure + + align:start position:0% +have a better standard. I need to ensure + + + align:start position:0% +have a better standard. I need to ensure +continuous contact between the loops and + + align:start position:0% +continuous contact between the loops and + + + align:start position:0% +continuous contact between the loops and +bore holes. We got some brilliant + + align:start position:0% +bore holes. We got some brilliant + + + align:start position:0% +bore holes. We got some brilliant +individuals in here. You ask them what + + align:start position:0% +individuals in here. You ask them what + + + align:start position:0% +individuals in here. You ask them what +happens if we have a bad grout column in + + align:start position:0% +happens if we have a bad grout column in + + + align:start position:0% +happens if we have a bad grout column in +that air pocket. I need to completely + + align:start position:0% +that air pocket. I need to completely + + + align:start position:0% +that air pocket. I need to completely +seal the annular space to prevent + + align:start position:0% +seal the annular space to prevent + + + align:start position:0% +seal the annular space to prevent +co-mingling of aquifers and prevent + + align:start position:0% +co-mingling of aquifers and prevent + + + align:start position:0% +co-mingling of aquifers and prevent +surface contamination. As we look at + + align:start position:0% +surface contamination. As we look at + + + align:start position:0% +surface contamination. As we look at +these projects and we go, "Hey, there's + + align:start position:0% +these projects and we go, "Hey, there's + + + align:start position:0% +these projects and we go, "Hey, there's +this open area. Let's put a bore field + + align:start position:0% +this open area. Let's put a bore field + + + align:start position:0% +this open area. Let's put a bore field +here. Is it lowland? Is it does it + + align:start position:0% +here. Is it lowland? Is it does it + + + align:start position:0% +here. Is it lowland? Is it does it +flood?" My favorite question to ask when + + align:start position:0% +flood?" My favorite question to ask when + + + align:start position:0% +flood?" My favorite question to ask when +I show up on these projects is why isn't + + align:start position:0% +I show up on these projects is why isn't + + + align:start position:0% +I show up on these projects is why isn't +there a Starbucks here? + + align:start position:0% +there a Starbucks here? + + + align:start position:0% +there a Starbucks here? +If not, my greatest generation, my + + align:start position:0% +If not, my greatest generation, my + + + align:start position:0% +If not, my greatest generation, my +grandfather, they were really good at + + align:start position:0% +grandfather, they were really good at + + + align:start position:0% +grandfather, they were really good at +burying things. And we're gonna find it. + + align:start position:0% +burying things. And we're gonna find it. + + + align:start position:0% +burying things. And we're gonna find it. +So I need to prevent that surface + + align:start position:0% +So I need to prevent that surface + + + align:start position:0% +So I need to prevent that surface +contamination. I need to comply with + + align:start position:0% +contamination. I need to comply with + + + align:start position:0% +contamination. I need to comply with +federal state laws and I need that + + align:start position:0% +federal state laws and I need that + + + align:start position:0% +federal state laws and I need that +thermal conductivity and borehole + + align:start position:0% +thermal conductivity and borehole + + + align:start position:0% +thermal conductivity and borehole +integrity to stay. This is my method + + align:start position:0% +integrity to stay. This is my method + + + align:start position:0% +integrity to stay. This is my method +when we check out my hour presentation + + align:start position:0% +when we check out my hour presentation + + + align:start position:0% +when we check out my hour presentation +not abridged. So we can get into this. + + align:start position:0% +not abridged. So we can get into this. + + + align:start position:0% +not abridged. So we can get into this. +This is what I want to talk about. + + align:start position:0% +This is what I want to talk about. + + + align:start position:0% +This is what I want to talk about. +Success to a drilling project is managed + + align:start position:0% +Success to a drilling project is managed + + + align:start position:0% +Success to a drilling project is managed +through these points and whether we're + + align:start position:0% +through these points and whether we're + + + align:start position:0% +through these points and whether we're +doing this all because of the climate + + align:start position:0% +doing this all because of the climate + + + align:start position:0% +doing this all because of the climate +change. Right? We have to understand how + + align:start position:0% +change. Right? We have to understand how + + + align:start position:0% +change. Right? We have to understand how +this is changing our drill and build + + align:start position:0% +this is changing our drill and build + + + align:start position:0% +this is changing our drill and build +schedule. Next, other construction + + align:start position:0% +schedule. Next, other construction + + + align:start position:0% +schedule. Next, other construction +operations. What are our regulations? + + align:start position:0% +operations. What are our regulations? + + + align:start position:0% +operations. What are our regulations? +Location, location, location, project + + align:start position:0% +Location, location, location, project + + + align:start position:0% +Location, location, location, project +timeline, and then neighbors. How am I + + align:start position:0% +timeline, and then neighbors. How am I + + + align:start position:0% +timeline, and then neighbors. How am I +sharing that site? How am I protecting + + align:start position:0% +sharing that site? How am I protecting + + + align:start position:0% +sharing that site? How am I protecting +mother nature? This is the reality of + + align:start position:0% +mother nature? This is the reality of + + + align:start position:0% +mother nature? This is the reality of +projects from downtown Los Angeles for + + align:start position:0% +projects from downtown Los Angeles for + + + align:start position:0% +projects from downtown Los Angeles for +George Lucas to right here just outside + + align:start position:0% +George Lucas to right here just outside + + + align:start position:0% +George Lucas to right here just outside +of Boston to a very tight location, + + align:start position:0% +of Boston to a very tight location, + + + align:start position:0% +of Boston to a very tight location, +urban, a church. + + align:start position:0% +urban, a church. + + + align:start position:0% +urban, a church. +This is what kicks our butt, everybody. + + align:start position:0% +This is what kicks our butt, everybody. + + + align:start position:0% +This is what kicks our butt, everybody. +And this is if there was a slide to take + + align:start position:0% +And this is if there was a slide to take + + + align:start position:0% +And this is if there was a slide to take +a picture of, this is the one because + + align:start position:0% +a picture of, this is the one because + + + align:start position:0% +a picture of, this is the one because +every time I get on a new call to + + align:start position:0% +every time I get on a new call to + + + align:start position:0% +every time I get on a new call to +troubleshoot a problematic project, I + + align:start position:0% +troubleshoot a problematic project, I + + + align:start position:0% +troubleshoot a problematic project, I +add to this slide. So if green local + + align:start position:0% +add to this slide. So if green local + + + align:start position:0% +add to this slide. So if green local +geology should not be an issue, we + + align:start position:0% +geology should not be an issue, we + + + align:start position:0% +geology should not be an issue, we +should have an effective amount of test + + align:start position:0% +should have an effective amount of test + + + align:start position:0% +should have an effective amount of test +bore holes to know. So if I'm drilling a + + align:start position:0% +bore holes to know. So if I'm drilling a + + + align:start position:0% +bore holes to know. So if I'm drilling a +600 hole project and I do two bore + + align:start position:0% +600 hole project and I do two bore + + + align:start position:0% +600 hole project and I do two bore +holes, is that a rep representative + + align:start position:0% +holes, is that a rep representative + + + align:start position:0% +holes, is that a rep representative +sample? No. That doesn't get us what we + + align:start position:0% +sample? No. That doesn't get us what we + + + align:start position:0% +sample? No. That doesn't get us what we +need. We need that subsurface data. + + align:start position:0% +need. We need that subsurface data. + + + align:start position:0% +need. We need that subsurface data. +What's hard? Man-made subsurface + + align:start position:0% +What's hard? Man-made subsurface + + + align:start position:0% +What's hard? Man-made subsurface +obstructions and contaminants, + + align:start position:0% +obstructions and contaminants, + + + align:start position:0% +obstructions and contaminants, +problematic subsurfaces as we get into + + align:start position:0% +problematic subsurfaces as we get into + + + align:start position:0% +problematic subsurfaces as we get into +fragile formations or water or artisian + + align:start position:0% +fragile formations or water or artisian + + + align:start position:0% +fragile formations or water or artisian +flow and utilities. And those are the + + align:start position:0% +flow and utilities. And those are the + + + align:start position:0% +flow and utilities. And those are the +things that we have to be planning with + + align:start position:0% +things that we have to be planning with + + + align:start position:0% +things that we have to be planning with +the right qualified contractor. So if I + + align:start position:0% +the right qualified contractor. So if I + + + align:start position:0% +the right qualified contractor. So if I +have that right qualified contractor and + + align:start position:0% +have that right qualified contractor and + + + align:start position:0% +have that right qualified contractor and +we have our pilot team right there, the + + align:start position:0% +we have our pilot team right there, the + + + align:start position:0% +we have our pilot team right there, the +pilot tutorial, thank you. uh watching + + align:start position:0% +pilot tutorial, thank you. uh watching + + + align:start position:0% +pilot tutorial, thank you. uh watching +skillings drill and that was a wonderful + + align:start position:0% +skillings drill and that was a wonderful + + + align:start position:0% +skillings drill and that was a wonderful +experience with all of them. What am I + + align:start position:0% +experience with all of them. What am I + + + align:start position:0% +experience with all of them. What am I +doing to choose this project? If you + + align:start position:0% +doing to choose this project? If you + + + align:start position:0% +doing to choose this project? If you +call me as a contractor, equipment + + align:start position:0% +call me as a contractor, equipment + + + align:start position:0% +call me as a contractor, equipment +availability, tooling, drilling method, + + align:start position:0% +availability, tooling, drilling method, + + + align:start position:0% +availability, tooling, drilling method, +compatibility with the location, site + + align:start position:0% +compatibility with the location, site + + + align:start position:0% +compatibility with the location, site +footprint, environmental demand, what is + + align:start position:0% +footprint, environmental demand, what is + + + align:start position:0% +footprint, environmental demand, what is +my timeline, what is the borefield + + align:start position:0% +my timeline, what is the borefield + + + align:start position:0% +my timeline, what is the borefield +design and borehole design, project + + align:start position:0% +design and borehole design, project + + + align:start position:0% +design and borehole design, project +restoration and cleanup. That's a big + + align:start position:0% +restoration and cleanup. That's a big + + + align:start position:0% +restoration and cleanup. That's a big +piece is managing our projects so that + + align:start position:0% +piece is managing our projects so that + + + align:start position:0% +piece is managing our projects so that +CSM or Clark or whoever you're using for + + align:start position:0% +CSM or Clark or whoever you're using for + + + align:start position:0% +CSM or Clark or whoever you're using for +your GC isn't like you're going to drill + + align:start position:0% +your GC isn't like you're going to drill + + + align:start position:0% +your GC isn't like you're going to drill +another bore hole and we're going to + + align:start position:0% +another bore hole and we're going to + + + align:start position:0% +another bore hole and we're going to +walk around in 18 inches of slop. You + + align:start position:0% +walk around in 18 inches of slop. You + + + align:start position:0% +walk around in 18 inches of slop. You +know what are my licenses? Am I + + align:start position:0% +know what are my licenses? Am I + + + align:start position:0% +know what are my licenses? Am I +accredited? These are all pieces. + + align:start position:0% +accredited? These are all pieces. + + + align:start position:0% +accredited? These are all pieces. +This is what we can do at test bore + + align:start position:0% +This is what we can do at test bore + + + align:start position:0% +This is what we can do at test bore +holes when we're surgical. + + align:start position:0% +holes when we're surgical. + + + align:start position:0% +holes when we're surgical. +You can see this project. We had snow + + align:start position:0% +You can see this project. We had snow + + + align:start position:0% +You can see this project. We had snow +and rain. It was Chicago. It was the end + + align:start position:0% +and rain. It was Chicago. It was the end + + + align:start position:0% +and rain. It was Chicago. It was the end +of October. This is how we left the job + + align:start position:0% +of October. This is how we left the job + + + align:start position:0% +of October. This is how we left the job +site. So, lessons learned. + + align:start position:0% +site. So, lessons learned. + + + align:start position:0% +site. So, lessons learned. +Every contractor is going to have an + + align:start position:0% +Every contractor is going to have an + + + align:start position:0% +Every contractor is going to have an +argument on why their method's the best. + + align:start position:0% +argument on why their method's the best. + + + align:start position:0% +argument on why their method's the best. +It's your choice how you move along with + + align:start position:0% +It's your choice how you move along with + + + align:start position:0% +It's your choice how you move along with +that. You know, we need to optimize + + align:start position:0% +that. You know, we need to optimize + + + align:start position:0% +that. You know, we need to optimize +drilling every chance we can get. + + align:start position:0% +drilling every chance we can get. + + + align:start position:0% +drilling every chance we can get. +What do I want? I want qualified + + align:start position:0% +What do I want? I want qualified + + + align:start position:0% +What do I want? I want qualified +contractors. I want the right drilling + + align:start position:0% +contractors. I want the right drilling + + + align:start position:0% +contractors. I want the right drilling +method for the area. I want test bore + + align:start position:0% +method for the area. I want test bore + + + align:start position:0% +method for the area. I want test bore +holes. I want test wells that give us + + align:start position:0% +holes. I want test wells that give us + + + align:start position:0% +holes. I want test wells that give us +the right data. I want us to think about + + align:start position:0% +the right data. I want us to think about + + + align:start position:0% +the right data. I want us to think about +what we did successfully before and how + + align:start position:0% +what we did successfully before and how + + + align:start position:0% +what we did successfully before and how +we loop and grout that. That was 21ish + + align:start position:0% +we loop and grout that. That was 21ish + + + align:start position:0% +we loop and grout that. That was 21ish +minutes. Thank you, Stacy. Thank you, + + align:start position:0% +minutes. Thank you, Stacy. Thank you, + + + align:start position:0% +minutes. Thank you, Stacy. Thank you, +everybody. \ No newline at end of file diff --git a/_75zfIar62c.txt b/_75zfIar62c.txt new file mode 100644 index 0000000000000000000000000000000000000000..1d70e489e6a3cf1dccd8c3f326661e0e04ce5976 --- /dev/null +++ b/_75zfIar62c.txt @@ -0,0 +1,4945 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high-quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +HONG LIU: So first, do you +have any questions regarding + +this Hawking-Page transition +we talked about last time + +because we were running +out of time, so it + +was a little bit hurried. + +Do you have any +questions about that? + +AUDIENCE: So what's the +original thermal AdS stat? + +Did you put some random +[INAUDIBLE] onto that metric, + +and it will generate +some [INAUDIBLE]? + +HONG LIU: Sorry? + +Say it again? + +AUDIENCE: So what's the +original thermal AdS state? + +HONG LIU: The thermal +AdS state-- you couple + +AdS to a thermal bath. + +And then whatever +excitation will + +be generated by that thermal +bath will be generated. + +So mostly it's the graviton gas. + +It's the gas of the massless +particles inside AdS. + +So that essentially. + +The field theory procedure +to go to cleaning space + +and to make the +cleaning time periodic. + +And that physically should +be interpreted as you + +just a coupled decisions +to your thermal bath. + +AUDIENCE: I have a question +not really related to this. + +But I'm just wondering +why do we want + +to consider [INAUDIBLE] +on a sphere, + +because previously we +discussed about [INAUDIBLE] 4, + +which is reality. + +What is this? + +HONG LIU: So normally when +we look at the theory, + +you want to look at the +theory from as many angles as + +possible. + +So some of them may not be +able to directly realize it + +in the experiment. + +But still, it's useful from +a theoretical perspective + +because that gives you +additional insights. + +So we see that the +physics on the sphere + +is actually quite rich. + +So that actually gives you +some insight into the dynamics + +and also into the +duality itself. + +Yeah. + +AUDIENCE: So there's no +condensed matter system + +essentially like that. + +HONG LIU: Oh, if you're +talking about condensed matter + +applications, you may even +imagine in some systems, + +you may be able to +put it on a sphere. + +Certainly, you can put it +on a two-dimensional sphere. + +And I can imagine you can put +it-- you can manipulate say, + +and put some spins on the +two-dimensional sphere. + +Yeah, you might be +able to do that. + +Any other questions? + +Yes? + +AUDIENCE: [INAUDIBLE] +you said there + +are two kinds of +[INAUDIBLE] connected + +on the same [INAUDIBLE]. + +HONG LIU: Yes. + +AUDIENCE: So it's like two CFTs? + +HONG LIU: No, it's a single CFT. + +It's just a different sector +of the CFT contributes. + +AUDIENCE: So it's like 0 quantum +critical point [INAUDIBLE]? + +HONG LIU: No, this is a +first-order phase transition. + +So it's not the +quantum critical point. + +So the picture is that +you have a temperature. + +So it's some TC. + +So below TC, you +have a phase which + +we call the thermal AdS phase. + +And in this you have a +big black hole phase. + +So translated from the +field theory side-- so this + +goes running to the states which +energy scales into the power 0 + +contributes. + +And here, it's dominated by the +state of energy O (N square). + +Of course, in the +thermal ensemble, + +every state in +principle contributes. + +And in this phase, it's +dominated by the contribution + +of the no energy state. + +And here, it's dominated +by the high-energy state. + +And really the high-energy state +also has a much higher entropy. + +And then they dominate +your thermal ensemble. + +Does this answer your question? + +AUDIENCE: Yeah, this looks +like in any transition, + +you have [INAUDIBLE] carry +energy and also [INAUDIBLE]. + +HONG LIU: Yeah, it is a +little bit similar to that. + +There's also an +entropy thing there. + +Yeah, it's a balance +between two things. + +But the details +is very different. + +The details are different. + +There's some +qualitative similarity. + +AUDIENCE: So I read on +the paper [INAUDIBLE]. + +He said that the Hawking-Page +transition on the field theory + +side is due to some +kind of deconfinement + +and confinement of QCD. + +HONG LIU: Yeah, so that's a +heuristic way to say about it. + +So the key thing is that here, +it's not really a confinement + +or not confined because +in the [INAUDIBLE] series, + +there's no confinement. + +It's just scaled in +[? Warren's ?] theory. + +And so in the sense he says +this is confined-- so he + +called this a confined phase. + +And this is a deconfined phase-- +it's based on the following. + +It just refers to +these two behaviors. + +So in QCD, which will generating +confinement or deconfinement-- + +so in QCD, we have +[INAUDIBLE] 3. + +But if you scale +into infinity, then + +you will find in QCD +in the confined phase, + +the free energy will +scale as N with N power 0. + +But in the deconfined +phase, which + +is scale-- obviously +the N square. + +So that aspect of +scaling is the same + +as a serious risk confinement. + +So that aspect is similar. + +So he essentially +refers to this aspect. + +But on the sphere, every +state has to be a singlet. + +So in some sense, +this notion there + +is no genuinely +notion of confinement + +as we say in the QCD +in the flat space case. + +If you read his +paper, he actually + +described this very clearly. + +Yeah, he just called this +a deconfinement transition + +the heuristic way. + +Yes? + +AUDIENCE: I have a question +about the sum by which we + +calculate partition function. + +The previous class on +Monday, you wrote it as sum + +over energies. + +The degeneracy of that +[INAUDIBLE] factor. + +And you noticed +that both of these + +grew at exponential to +something times N squared. + +One was positive, +and one was negative. + +I was wondering if it's +possible that sum diverges? + +HONG LIU: No, that +sum does not diverge. + +That sum is always +proportional to n square. + +Yeah, depending on what +you mean the sum diverges. + +So that's just from the +definition of your partition + +function. + +So it's just the sum +of all possible states. + +And then you can just +reach this-- yeah, when + +you have a large +number of states, + +you can just roughly write it as +a continuous integral and then + +with the density of states. + +And so the key is +that what happens + +to the density of states-- +so you're asking maybe + +whether this +integral will diverge + +when it equals infinity. + +So when it equals +infinity, you will + +see that say supposing +E scale as N cubed. + +Then you will see that +the density of state + +actually does not +grow that fast. + +And actually, it's only +for the E of O(N squared), + +then they scale in the same way. + +They scale in the same way. + +So that's why you +have this balance. + +And if you are not in the +scaling with [INAUDIBLE]. + +If you have N cubed, and +then this will dominate. + +So that factor +will be suppressed. + +Any other questions? + +OK, very good. + +So now let's go to entanglement. + +So first, let me say a few +words about entanglement entropy + +itself. + +So this is very +elementary stuff, + +even though maybe +not everybody knows. + +So let's consider a quantum +system, just a general quantum + +system. + +So let's separate the +degrees of freedom + +into two parts, say A +plus B. So AB together + +is the whole system. + +We just separated the +degrees of freedom. + +So essentially by +definition, the Hilbert + +space of the system-- then +we'll have a tensor structure. + +So the full Hilbert space +will be a tensor product + +over the Hilbert +space for the A part + +and tensored with the +Hilbert space in the B part. + +OK? + +And consider, of +course, in general, we + +have an infinite +dimensional system. + +But in the case if you have +say a [INAUDIBLE] Hilbert + +space-- so i f this M +dimension, this is N dimension, + +then the total Hilbert space +will be M times N dimension. + +And the typical wave function +will have the form-- will be + +some sum-- say you can write +it in some basis in A and times + +some wave function +writing some bases in B. + +And this actually means that +the Hilbert space is a tensor + +product. + +It's just your wave form can +typically have this form. + +So we say that AB-- so we say +that in the states psi that AB + +are entangled if psi cannot be +written as a single product-- + +rather than the sum of product +and if you just have a single + +product. + +So for a simple state, +it might be easy to see. + +But if I write the very +complicated state which + +many-- in principle, +write the state + +in some bases which look +at the complicated sum. + +But they may be some other +bases and be a simple product. + +So in general, it's +actually hard to tell. + +In general, it's hard to tell, +even though it's easy to say. + +But in general, +it's hard to say. + +So the entangled +entropy-- so let me just + +call it EE just to save space. + +EE essentially +provides a measure + +to quantify the entanglement +between A and B-- + +because even in the case +which you know this state is + +in entangled state, +you may still + +want to ask how much +they are entangled. + +Entanglement entropy provides +the way to quantify it. + +So the definitions +are very simple. + +So first we look at +this the density matrix + +for the total system. + +So if the system is +in the state psi, + +then the density matrix +for the total system + +would be just on the psi +conjugate-- psi itself. + +So in this basic matrix, +we just trace out + +all the degrees of freedom in +B. So since the Hilbert space + +have a tensor product structure, +you can always do this. + +Then what you get is you +get this the density matrix. + +And then here, you +get a density matrix + +which only depends on the +degree of freedom in A. + +And then we just calculate +the Von Neumann entropy + +corresponding to this row +A. So entangled entropy + +is just defined to be +[INAUDIBLE] entropy associates + +resistance in the matrix +rho A. So this rho A + +is often called the +reduced density matrix. + +And the Von Neumann entropy +associated with the reduced + +density matrix is defined +as the entanglement entropy. + +OK? + +So this provides a +very good the measure + +because say if SA is equal to +0, from our knowledge of the Von + +Neumann entropy, +you can immediately + +deduce where the SA is equal +to 0 if only if the rhos A, + +this density matrix +is a pure state. + +It's a pure state. + +And then from here, you can also +deduce rho A is a pure state. + +This reduced density matrix +comes from this procedure + +as a pure state. + +Only if the psi can be +written as a simple product. + +So this tells you as +when SA is non-zero, + +then you can be sure this +state must be non-entangled. + +So whenever SA is +equal to 0, you + +can be sure this +is non-entangled. + +When SA is not +equal to 0, you know + +for sure A and B must be +entangled in this state. + +So that's why this +is a good measure. + +OK? + +And then the value of +SA then will tell you + +how entangled the system is. + +And also, you may +immediately ask + +the question what happens +instead of defining the rho A? + +Of course, you can +also do the same thing. + +You trace out A to define +out rho B and then the + +define the entropy +for the rho B. OK? + +Define entropy for the +rho B. But you can easily + +show for any pure state +psi SA always equals to SB. + +So it doesn't matter +which are symmetric. + +So it doesn't matter which +one you're looking at. + +So this is very easy +to prove, essentially + +just following from something +called a Schmidt decomposition. + +And essentially right to this +state in terms of Schmidt + +decomposition between the +degrees of freedom rho A and B. + +And then you can show that +rho A and rho B essentially + +have the same eigenvalues. + +And if rho A and rho B have the +same eigenvalues, of course, + +then the entropy will be the +same, because the entropy only + +depends on the eigenvalues. + +OK? + +Any questions about this? + +Good. + +So here is what a mixed +state-- about a pure state, + +let me just say a side remark. + +So if AB, the total system is +in a mixed state-- so far always + +is in the pure state. + +But suppose it's +in the mixed state. + +Suppose the system itself is +described by a density matrix. + +So the total system +itself is spread. + +In general, SA is +not equal to SB. + +OK? + +Not only in general, +it's not equal to-- SA + +is not equal to SB. + +And in such a case, the +entanglement entropy + +also contains classical +statistical correlations + +of the mixed state-- +of the mixed state-- + +so in addition to +quantum correlations. + +It's almost trivial to see +because the people suppose + +here is not a pure state. + +So here you replace it +by the density matrix. + +And when you trace all the B +in this density matrix, then, + +of course, there's still +some original uncertainty + +in the previous density +matrix remaining in A. + +And then they will come into +this entropy-- so as defined, + +will depend on the +classical uncertainties-- + +classical statistical +uncertainties + +of your original density matrix. + +So for a mixed state-- so +that's why for a mixed state, + +the internal entropy is not a +very good measure of quantum + +entanglements, because +it's contaminated + +by classical +statistical information. + +But for today, we +all need to talk + +about the pure-- mostly +talk about the pure. + +Yeah, we actually +talk about in general. + +But I want you to +keep this in mind. + +So any questions so far? + +So just to give you an a +little bit more intuition, + +let's look at this +very simple example + +to calculate entangled entropy. + +So let's consider +a two-spin system. + +So let's consider you +have two spins, OK? + +So this is my A and B. So this +has a two-dimensional Hilbert + +space. + +This has a two-dimensional +Hilbert space. + +Altogether, you have a +four-dimensional Hilbert space. + +So for example, so let +me consider such a state. + +So this looks like +a complicated state. + +But actually, this can be +written as a single product, + +because you it can +be written at OK, + +I hope this notation is for me. + +It's OK with you. + +You just A and B-- +A spin and B spin. + +So even though in this +space, this is written as + +say a sum of state. + +It looks the entangleds. + +But in fact, it's not +because you can write it + +in terms of a simple product. + +So this is another +entangled state. + +Of course, for the simple +system, it's very easy to tell. + +But to give you a +complicated system + +with many, many, +degrees of freedom, + +then it becomes very hard. + +And then entangled +entropy becomes useful. + +So now let me give you an +example to calculated entangled + +entropy. + +So let's consider +a state like this. + +So let's see some parameter. + +So clearly this state is +entangled because you cannot + +write it as a simple product. + +So now, let's check it. + +Now, let's check it. + +So you can look at the full +density matrix of the system. + +You just look at this-- +the bra and the ket itself. + +And then just do the product. + +And you get the quotient theta-- +under the [INAUDIBLE] terms. + +So you just take the +product with itself. + +And then let's try +to find what's rho A. + +So you trace out +degrees of freedom of B. + +So this is our B, +the second spin. + +And now let's trace out +degrees of freedom B-- + +trace out the second spin-- +so rho A. Goes one into we + +trace out the B in here. + +So when you trace +out the B, you just + +take the end product +between these two. + +So these are the same. + +So this will remain. + +And so you have this. + +And similarly, this +one you have that. + +These two are the same. + +So when you take the +trace, this is nonzero. + +But this too will give +you 0, because this one is + +orthogonal to this one. + +And this spin is +orthogonal to that spin. + +So that's what you get. + +And then now you can usually +just write down the entropy. + +So this is the entangled +entropy for these two states-- + +for this two spin system +as a general function + +of this parameter theta. + +So now let's plot these +as a function of S theta. + +So clearly, this is +a period function. + +We only need to go to pi over 2. + +And then you have +something like this. + +And you can easily +plot that function. + +You will see +something like this. + +So when theta is equal to 0. + +This is equal to 0 +because this term is 0. + +This term is also 0 because +of the quotient theta + +square is equal to 1. + +When theta equals to +pi over 2, this term + +becomes 0 and this +term also becomes, + +because it's [INAUDIBLE] 0. + +But this maximum in the +pi over 2 or pi over 4. + +So I had a pi over 4. + +Of course, you can also go +to the pi equals to minus 4. + +OK, you can go do plus minus 4. + +I didn't go to the [INAUDIBLE]. + +Yeah, anyway, so these are +called the maximum entangled + +states. + +This is a maximum entangled. + +So this is a state in which +you have the highest entropy. + +Any questions so far? + +AUDIENCE: You switched it. + +It should be up down. + +It's down. + +HONG LIU: Right, that's right. + +OK, good. + +So let me also say a few +things about the properties + +of the entanglement entropy. + +So there are many properties +you can derive from here. + +Let me only say a +few important ones. + +OK, so one property of +the entangled entropy + +is called subadditivity +condition. + +So if you can see that +the two systems A and B, + +then you can show that +S(AB), the entropy + +for the total system, +is smaller than the sum + +of the separate system. + +So when I write AB, I +mean the combined system. + +OK? + +And this is greater than +the difference between them. + +So this is so-called the +subadditive condition. + +And then intuitively, +you can understand. + +So if you have entropy +of A and entropy of B, + +you add them together, then it's +larger than the entropy of AB + +because there is +some redundancy. + +There might be some +redundancy here. + +Yeah, because when +you add AB together, + +there may be some common +correlation between them. + +And so this is +greater than that. + +OK, intuitively that's +what this inequality means. + +And also there are some property +for the strong subadditivity + +condition. + +AUDIENCE: I don't +quite understand-- + +HONG LIU: Yes? + +AUDIENCE: What S of +A and S of B means? + +HONG LIU: So this is +the entropy for the A. + +This is the entropy for the B. + +AUDIENCE: Don't we +need this to partition + +system A into two subsystems? + +HONG LIU: No, you don't-- +let me explain my notation. + +So S(A) means the +entropy equals 1 + +if you integrate out +everything else except A. + +And S(B) means you +integrate everything + +else except B. +And S(AB) be means + +to integrate everything +else except A and B. + +And this is S(AB). + +AUDIENCE: But in our case, A +and B is all that there is. + +HONG LIU: No, no, no. + +Now I'm just doing generally. + +Once I have this definition, +so this can be-- even + +AB is a total-- yeah, so this +can apply both to the case + +I said earlier-- say +if you divide-- here I + +just-- so this AB does not +have to be the same as that AB. + +Here I'm just talking +about only two subsystems. + +AUDIENCE: So it's +for example, S(A) + +is like-- A and the supplement +as two parts of the system. + +And they could have +some entanglement. + +S(A) is just an +entanglement field. + +HONG LIU: A, S(A) +is the entanglement + +of A with the rest. + +And S(B) is the entanglement +of B between B and the rest. + +And the S(AB) is +entangled between the AB + +together with the rest. + +Yes. + +AUDIENCE: So to clarify one +thing, when you say S of A, + +we have this whole system. + +It means that trace +everything which is not A? + +HONG LIU: Yeah, that's right. + +Any more questions about this? + +So here when I write +to those expressions, + +I assume A and B don't +have interceptions, OK? + +I assume A and B don't +have interceptions. + +You can also have the strong +subbadditivity condition. + +So this is pretty easy to prove. + +If we have time, it takes +five minutes to prove. + +But the strong subadditivity +which I'm going to write down. + +So strong additivity is +involving three systems. + +Now, you have to add +the three systems. + +And then greater than ABC-- OK? + +So, again, intuitively, the +meaning of that inequality + +is clear. + +So the first +inequality just says + +that I have two systems here. + +And the sum of +these two systems-- + +the entropy of +these two systems-- + +is greater than the sum +between the combined + +system and the intersection +between the two systems, + +OK, because C in the +section between the two. + +And ABC is the whole +thing combined. + +And similarly here, he said +they have S(A) and S(B). + +I have two A and B. So +I trace out the system. + +Outside A, I get entropy for A. +I trace the system outside B, + +anyway for B. This +inequality says if now you + +attach A C to A and C to B, a +common system to both A and B. + +And then the resulting system +will be larger than the B form. + +So if you add something, +we increase the entropy. + +That, of course, is +intuitively clear, + +because if you have entropy +essentially parameterized + +the unknown part of the system. + +And if you add the third +system, and then this + +just increase your unknown and +then increase your entropy. + +So this strong +subadditivity condition + +is actually very hard to prove. + +It's very hard to prove. + +It can get rather mathematical +and requires some effort + +to do it. + +But this one is +pretty easy to do. + +Yes? + +AUDIENCE: Can [INAUDIBLE] about +the first of the two equations? + +For strong subadditivity, +what's the first equation? + +HONG LIU: Yeah, +so this means-- so + +look at this as a single system. + +This is a single system. + +That means that the sum of these +two-- the entropy of this two + +system is greater than +the sum of the combined + +system under the intersection. + +Any questions about this? + +Good. + +So this concludes the +very simple introduction + +to the entangled entropy. + +AUDIENCE: Does +the first one have + +any implications of topology? + +HONG LIU: Sorry, what +do you mean by topology? + +AUDIENCE: Because it's like the +intersection of the combined + +thing. + +HONG LIU: Yeah, so +as classical entropy, + +this is a very simple thing. + +You can easily convince +yourself if ABC + +are classical systems, and +just classical distributions, + +describe classical +probabilities, + +statistical distributions. + +And then with those things, you +can understand this inequality + +just by drawing this kind of +standard diagram corresponding + +to the different sets. + +The quantum mechanics proving +those things are actually + +not trivial are not trivial. + +Quantum mechanically, +they no longer come in + +a very intuitive way. + +Yes? + +AUDIENCE: I was noticing +something curious + +about the last line classically. + +If A and B are the same, I think +the equation will still hold. + +But quantumly-- + +HONG LIU: It still holds. + +AUDIENCE: Doesn't it +not hold quantumly? + +HONG LIU: No, they are supposed +to hold quantum mechanically. + +AUDIENCE: But we are under the +assumption that A, B, and C-- + +they don't overlap, right? + +I'm saying if A and B +are totally overlapping. + +HONG LIU: No, but +this inequality + +I'm writing in a way which +they are not intersecting. + +You can write them in a +way which they intersect. + +And I'm just +writing in this way. + +So the condition for +this particular form ABC + +is not supposed to intersect. + +AUDIENCE: Right, I'm saying +if we set A equals to B. + +HONG LIU: No, no, then you +cannot use this equation. + +Then you have to +write the equation + +in somewhat different way, which +apply to the intersection case. + +You can do them just choosing +to write in the way which + +did only intersect. + +AUDIENCE: OK, but the +thing I want to say + +is that we can still keep the +bottom equation classically, + +even if we took-- + +HONG LIU: No, both are +applied classically. + +Both are trivial classically. + +You can understand very +easily classically. + +It's just quantum mechanically, +it's no longer trivial. + +Quantum mechanics is +no longer trivial. + +And there are various ways +you can write those equations. + +I'm just choosing to write the +way which ABC don't intersect. + +And you can also write +the way, just rename them + +so that they intersect. + +AUDIENCE: So [INAUDIBLE]. + +So this is true for any +entanglement state we choose? + +HONG LIU: Any state, +yeah, density matrix. + +Whether it's a pure +state or density matrix, + +it doesn't matter-- +a general statement. + +OK, good. + +So this concludes the +short introduction + +to the entangled entropy itself. + +And you may know that the +entanglement entropy actually + +plays a very important role. + +Entanglement and +entanglement entropy + +itself plays a very important +role in quantum information + +and quantum computing because +of quantum entanglement + +is the kind of +quantum correlations + +which you don't +have classically. + +So this EPR paradox and +the [INAUDIBLE] inequality, + +and the teleportation-- +all those things + +that take advantage of. + +But that's not our +main point here. + +So what I'm going +to talk about next + +is actually entangled +entropy is also + +starting playing a +very important role + +in our understanding of +many-body physics and the space + +time. + +So now, let's talk about +the entanglement entropy + +in many-body systems in +quantum many-body systems. + +So I hope you're familiar with +this word many-body systems. + +It's just a system of a +large number of particles + +or a large number +of constituents. + +So quantum field theory issue +is a many-bodied system. + +Any quantum field theory +is a many-body system. + +But this also includes +many other lattice systems, + +which condensed +matter people use, + +which are not necessary +quantum fields-- can be written + +as a quantum field theory. + +OK? + +So now let's again consider +just a simplified case. + +Let's consider a system which +is composed of A and B-- + +so A plus B. And then I will +say some trivial statements. + +So if H is HA plus HB. + +So now we talk +about Hamiltonian. + +So far, I'm not using +actually many-body systems. + +What I'm talking about are +pretty generic systems. + +So even the +Hamiltonian is actually + +just a direct sum +of the Hamiltonian + +for A and Hamiltonian for B. + +If they don't couple, then of +course, the [INAUDIBLE] state + +or, in particular, the +ground state is unentangled. + +So you just find the ground +state of each system. + +And then that's the ground +state of the total system. + +And also, in general, if you +start with the initial stage, + +which is unentangled, with +the initial state, which + +is unentangled, it will +remain unentangled. + +So if you started with +an unentangled state, + +you wove it using this +Hamiltonian, of course, + +it will just act on +the specific part. + +And then you will +remain unentangled. + +OK? + +And now let's consider we +have H equals to HA plus HB. + +But now they also +have interactions + +between the A and the B. +So A and B are coupled. + +Then in general, we can just +repeat what he said here. + +Then the ground state +is now entangled. + +OK, and now if you start +with the initial state, + +even if you start with the +initial unentangled state, + +it becomes entangled on +Hamiltonian evolution. + +So in general, we +will expect-- so just + +based on this +general expectation-- + +so you would expect +the ground state + +of a typical many-body +system will be actually + +rather entangled. + +It will be rather entangled +unless the Hamiltonian factor + +rides into all three particles. + +The factor rides into +the Hilbert space + +at each point-- for +each degree of freedom. + +But now let's talk about +the many-body systems + +we're interested in. + +So they're either typical +condensed matter systems + +or quantum field series. + +So in typical condensed matter +systems, we face this problem. + +So in typical generic condensed +matter systems of quantum field + +theory, in general, +no matter how + +you divide A and B-- so +generic H AB is non-zero. + +But not only is +H AB is non-zero, + +it's in general, H AB-- so the +whole Hamiltonian, including + +H AB is local. + +This is a very +important concept. + +It's local. + +But local will +mean the following. + +For example, let me +give you an example. + +For example, one of the very +important condensed matter + +systems is, of course, +the Heisenberg model. + +So essentially, you +have the Hamiltonian. + +So you can see the lattice +in whatever dimension + +you're interested in whatever +kind of lattice you are. + +At each lattice, +there is a spin. + +So consider you have +a lattice of spins. + +And then you'll have nearest +neighbor interactions + +between the +neighboring spins, so + +some of the nearest neighbors. + +So you can imagine you +have a lattice system. + +And each point on the +lattice, you have a spin. + +And each spin interacts +only with the spins nearby. + +So this is a local interaction. + +So by local interaction, means +that the only direct couple + +to the spin falls +distance away from it. + +So this is an example +of a local system. + +And all our QFTs +are local systems. + +All our QFTs are local systems. + +For example, let me just +write down the phi 4 + +theory, for example, +phi 4 theory. + +Then phi at each +point-- so now you + +have to go back to your first +day of your quantum field + +theory where you +emphasize locality. + +So the phi evaluated +at each point now + +is independent of +degrees of freedom. + +Under the quantum +field theory, it's + +a Hilbert space of +a tensor product + +of the degrees of freedom. + +OK? + +Under the form of the Lagrangian +say if you discretize it-- + +and this is only +involving coupling + +between the neighboring +point, because the derivative + +is only dependent on +the second derivative. + +And this only depends +on the value of phi + +at the single point. + +So the typical +quantum field theory + +as far as you have found +a number of derivatives, + +it's all local. + +It's all OK intact. + +It's all local. + +OK? + +So in other words, in +these kind of systems, + +let me go back here. + +So this is very important. + +In other words, in +these kind of systems, + +so let me just +imagine-- so let me just + +say this box is the whole thing. + +It's the whole whatever +space I live in. + +And I divide it into A B. + +So this tells you that for +typical condensed matter + +or quantum field series, +the H AB is only supported. + +So let me call this epsilon. + +So that tells that H +AB is only supported + +near the boundary +between A and B, + +because there is only +local interactions. + +So the part of the Hamiltonian +which directly covers A and B + +is only within this part. + +And this epsilon is added +on the lattice spacing + +is order of lattice spacing, +which in the case of a lattice + +system or in a +quantum field theory, + +it would be your +short distance cutoff. + +So if you try to discretize +your field theory, + +then this will be a +short distance cutoff. + +So similarly, I can +consider another shape of A. + +So suppose I can +see the circular A. + +And then, again, +the part of which + +H AB is only supported in +the region between these two + +dashed lines. + +And those dashed +would be considered + +to be very close to the +A. I'm just going to pick. + +But this should be the +short distance cutoff. + +OK? + +And again, the H AB is +only supported in here. + +So this is an important +feature of which + +you have a local Hamiltonian. + +Let me just write one more word. + +So H AB only involves +degrees of freedom + +here-- the boundary of A. So +this means the boundary of A. + +So this turns out to have very, +very important implications-- + +the fact that the +Hamiltonian is local. + +And that they only direct +and mediate coupling + +between the degrees of freedom +near the boundary of A. + +And they have very +important consequences. + +So now I'm just +telling you the result + +which is a result of +having accumulated + +for many, many years +since the early '90s. + +So then when I +find in the ground + +state of a local +Hamiltonian in general + +you may construct some kind +of evil counterexamples. + +But in general, in +the ground state + +of a local Hamiltonian-- +in the ground + +state of a local +Hamiltonian-- any + +just choose any region +A-- you integrate out + +the degrees of +freedom outside of it. + +So let me emphasize +an important point. + +Let me just pause to +emphasize an important, which + +is only increasing +what I'm saying here. + +In this definition of the +entangled matrix which I just + +erased, you just need +to have a partition + +of a degree of freedom +between A and B. + +The way you partition +it does not matter. + +How you partition +it does not matter. + +You can partition it in +whatever way you want. + +But for typical this +kind of lattice system + +or for quantum field theory, +there's a very large partition. + +And the partition is just +based on the locality. + +It's just based on the degrees +of freedom at each point. + +You just factorize +your Hilbert space + +in terms of degrees of +freedom at each point. + +So of course in the lattice +system, it's obvious. + +You have a spin at each lattice. + +And for the quantum +field theory, + +you just factorize your +degrees of freedom. + +At each point, you +factorize them. + +And so this locality +provides a natural partition + +of your degrees of freedom. + +And when we talk +about A and the B, + +we always talk about in +terms of the space location. + +And it's natural to talk +about the partition in terms + +of just your metric locations. + +So is this point clear? + +I just want to +emphasize this point. + +So then you find that in +general for the ground + +state of a local Hamiltonian +satisfy so-called area + +law is that the leading term +of the entanglement entropy + +is given by the area +of the boundary of A-- + +this applies no +matter which dimension + +you are in generic +dimensions-- and divide it + +by a short distance cutoff +of the lattice spacing. + +It's some number. + +So A is a dimensionless number. + +So area-- we can see the +d-dimensional theory-- + +so d-dimensional system. + +Then the spatial dimension +will be d minus 1. + +And then you go to the +boundary of some region. + +The boundary of region A. +Then that will be a d minus 2 + +dimensional surface. + +And then this would be +the area of that surface. + +So this may cover a +dimensionless number. + +And then you can have +some pre-factor here + +which depend on your systems. + +So this formula tells you +a very important physics. + +So this formula tells you +a very important physics. + +This tells you that +generically if you-- + +in such kind of systems, +AB are entangled. + +But the entanglement between +AB between A is complementary, + +which I just call A +and B, are dominated + +by short-range entanglements +near the boundary of A + +where this H AB is supported. + +OK? + +So this is also very intuitive +once you load the answer-- + +once you load the +answer, because we + +emphasized that H AB only +coupled to degrees of freedom + +nearby. + +And then we look +at the ground state + +you find most of the +degrees of freedom in here + +don't entangle with B. Only +the degrees of freedom them + +near the boundary of A are +entangled with B because + +of this interaction. + +This local interaction +directly leads + +to the entanglement between +the degrees of freedom nearby. + +And those degrees of freedom, +if they are far away, + +they might be entangled. + +But they are not dominant. + +OK? + +So I have put many dots here. + +So included in those dots +are possible long-range + +entanglements. + +Because when you find +the ground state, + +you really have to extremize +the energy of the total system. + +You don't only look +at the small part. + +So there's always some kind +of long-range entanglement + +beyond this H AB. + +But this formula tells you +that this short distance + +entanglement dominates. + +Yes? + +AUDIENCE: One question-- in QFT +in general, like [INAUDIBLE], + +there's really all +the interactions + +are perfectly local, I believe. + +But in string theory, are there +any non-local interactions + +that occur. + +Are there any interactions +with non-local? + +HONG LIU: Yeah, it will +depend on the scale. + +In string theory when +we say non-local, + +it's non-local at the +alpha prime scale. + +And that alpha prime can +perfectly be our short distance + +cutoff here. + +When I talk about +local and non-local, + +I'm talking about +infinite versus finite. + +For example, here, +when I talk about + +whether this is +a local system, I + +don't have to have +a nearest neighbor. + +As far as this matches +this point only directly + +coupled to the finite +distance neighbor. + +And this can see the +local Hamiltonian. + +But from the quantum field +theory point of view, + +this might be +considered non-local. + +You see what I mean? + +Depending on your scale. + +AUDIENCE: So is +there anything that + +appears in string theory which +is non-local at any scale? + +Or is the non-locality +just some-- + +HONG LIU: Yeah, so +the string theory + +itself does not give +you that non-locality, + +but the black hole may. + +AUDIENCE: Oh, interesting. + +HONG LIU: The black +hole seems to give you + +some kind of non-locality which +we don't fully understand. + +So that's why the black +hole is so puzzling. + +And the [INAUDIBLE] of +string theory, you're + +non-local in the +scale of alpha prime. + +Yeah, if it's alpha +prime sufficient small, + +it's like a local theory. + +And even if alpha prime is +big, if you look at very much, + +it is still like local. + +AUDIENCE: I see. + +HONG LIU: Yeah, but black +hole can make things + +very long distance. + +So that's the tricky +thing about black holes. + +OK, so this is +something which are + +is interesting and was first +discovered in the early '90s. + +But in hindsight, +it's very intuitive. + +In hindsight, it's +very intuitive. + +So even though this formula, +even though this term + +is universal, but this +coefficient is actually + +highly non-universal. + +Normally, by saying +universal, we + +mean something which is +common to different systems. + +So this coefficient actually +depends on the details + +of individual systems. + +Say if you calculate for +the Heisenberg model, + +or if you calculate for the +free scale of field theory, + +or free fermion theory, and +then this coefficient in general + +is different, are depending +on how you define your cutoff. + +So even though this +formula is universal, + +but those pre-factors actually +are highly non-universal. + +But the partial +excitement-- there + +are many things people +are excited about in terms + +of entropy. + +This is one thing, +this area law, + +because the area law is nice. + +Then this can be used as +a distinguishing property + +of a ground state. + +If you go to a +highly excited state, + +then you find the generic +distribution inside + +and A and B will be entangled. + +And [INAUDIBLE] highly excited. + +But only in the ground state, +somehow only near the boundary + +they are entangled. + +This is also makes sense, +because if it were high energy + +then you can excite it, +because from the very far away + +from H AB, then of course, +everything would be entangled. + +AUDIENCE: So just +one other question. + +So why are you +dividing by epsilon? + +HONG LIU: No, this +estimation is a number. + +Making the dimension +is numbered. + +This is only a short-distance +information here. + +So that is spatial +short-distance cut off. + +AUDIENCE: Right, +the only reason I + +ask is that intuitively it +seems that the entropy should + +be proportional to this thin +volume around the boundary. + +But that doesn't-- +OK, I don't know. + +HONG LIU: Yeah, you have to make +it into a dimensionless number. + +You have to be +proportional to the area. + +So there's a very simple way +to understand that thing. + +So the area divided by lattice +spacing-- so what is this guy? + +This is wonderfully +a lattice volume. + +That is the lattice +area on the surface. + +So essentially this tells you +how many degrees of freedom + +are lying on that boundary. + +AUDIENCE: OK, interesting. + +HONG LIU: Yeah, OK? + +So is this clear? + +OK, I think I'm spending +too much time on this. + +Anyway, so excited +in the last decade-- + +the main excitement +about entangled + +entropy in the last decade. + +The one thing is +about this behavior, + +then you can use it as a +characterization of the ground + +state. + +But a lot of the +excitement about this thing + +is on those dot, dot, dots. + +So people actually find +that the subleading term-- + +some excitement. + +Yeah, I'm just saying-- +from last decade people + +have discover that the +subleading terms in entangled + +entropy other than +this area term which + +come in from long-range +entanglements. + +So this captures the +short-range entanglement + +from the long-range +entanglement can actually + +provide important +characterizations of a system. + +So let me just +mention two examples. + +So it will be little +bit fast because we + +are a little bit-- do you +want a break for the last day? + +AUDIENCE: Well, when +you say it like that-- + +HONG LIU: OK, good. + +OK, thanks. + +So let me just quickly +talk about two examples + +because I want to talk +about the holographic case. + +So the first thing is something +called the topological can + +be used to characterize +so-called topological order + +in 2 plus 1 dimensions. + +So since the '90s, mid +'80s, and the '980s, + +people discovered +that if you look + +at the typical gapped +system-- so when + +we say a gapped system means +that system between the ground + +state and the first excited +state have a finite energy gap. + +So our general understanding +of a gap system is that + +in the ground state because +you have a finite gap, + +and there's sufficient +low energies, + +you simply cannot +excite anything. + +You have low energy because you +have a finite gap to the first + +excited state. + +You cannot excite anything. + +So essentially, when you look +at the correlation functions, + +we can look at +all the variables. + +They all only have +short-range correlations. + +The cannot have +long-range correlation, + +because there's nothing to +propagate you to long distance. + +And because long +distance requires + +massive degrees of freedom. + +And because you have a gap, you +don't have such massive degrees + +of freedom. + +So the typical conventional +idea about the gap system + +is that all correlations +should be short-ranged. + +And so this is a +condition that meets them. + +But in the late +'80s and early '90s, + +our colleague, Xiao-Gang +Wen, he introduced + +this notion of a +topological ordered system + +based on fractional +quantum Hall effect. + +So he actually reasoned that +there can be gap systems even + +though I have a finite gap, +but in the ground state + +actually contain +long-range correlations-- + +nontrivial, long-range +correlations. + +And those long-range +correlations cannot be seen + +using the standard observables. + +So if you are using the +standard observables-- say + +correlation functions of local +operators, you don't see them. + +You only see the +short-range correlations. + +And those long-range +correlations + +are topological in nature. + +You have to see it +in some subtle ways. + +And then in the '80s, except +in the late '80s, early '90s, + +he was trying to argue +in some [INAUDIBLE] way + +to argue there is such kind +of subtle correlations. + +But then around 2000, +maybe 2005, then + +he realized actually you can +see it very easily directly + +from the ground +state wave function. + +You just calculate +the entangled entropy. + +You just calculate +entangled entropy. + +So in entangled entropy, +you always have this-- + +so this is a 2 plus 1 +system, and then the boundary + +is just a line. + +So essentially, you +just have a boundary. + +It's a number-- the +length of the boundary + +divided by your +cutoff, but then it + +turns out for these kind of +topological ordered system, + +there is a finite constant +as a subleading term. + +And this finite constant is +independent of the shape of A + +and independent of length +of A and independent + +of whatever A is purely +topological in nature. + +And so if you have +achieved a gap system then + +this gamma will be 0. + +So you look at a free +massive scale of field-- + +then this gamma will be 0. + +But for those topological +ordered systems, + +this gamma would be non-zero. + +And it tells you actually there +is long-range correlations + +which are encoded in the +entanglement entropy, + +because this cannot come from +the local thing because this + +does not depend on the shape of +A, does not depend on N sub A, + +does not depend +on anything of A. + +So this is really +topological in nature. + +It tells you this can only +be some long-range, subtle + +correlation, which +is only capture + +by these entangled +entropy rather + +than by the standard +correlation functions. + +OK + +So this is one discovery which +is generated a lot of interest + +in the entangled entropy +because now this can + +be used to define the phases. + +OK, you can actually +define non-trivial phases + +using this number. + +And so this is the first thing. + +So this is about in +condensed matter systems. + +In quantum field theories , +this can be used to characterize + +the number of degrees +of freedom of a QFT. + +Again, this is a long story. + +But I don't have time. + +So let me just tell +you a short story. + +So first let me look at 1 +plus 1 dimensions, a CFT. + +So for 1 plus 1 dimension +of CFT or important + +the quantity is so-called +essential charge. + +So have you all heard of +essential charge or not really? + +It just says, imagine you have +a 1 plus 1 dimensional CFT. + +And for each CFT, you can +define a single number, which + +is called the center charge. + +And this center charge +is very important + +because it controls +the asymptotic density + +of state of the system. + +So if you look at the system +go to very high energies, + +and the density of +state essentially + +is controlled by this number C. + +So essentially C can +be used to characterize + +a number of degrees of freedom. + +And the C will appear +in many other places. + +But I don't have +time to explain. + +But anyway, there's something +called the central charge, + +which can be used to +characterize numbers of degrees + +of freedom of the system. + +And thus, if you look at the +entanglement entropy for 1 + +plus 1 dimensional system for +1 plus 1 dimension of CFT. + +So in 1 plus 1 +dimension, you only + +have a line in the +spatial direction. + +So then this takes A just to +be a sacrament of length l. + +Then you find when +you integrate out + +everything else, the +entangled entropy + +for the A given by C divided +by 3 log L divided by epsilon. + +Again, epsilon is a +short distance cutoff. + +And the C is your center charge. + +So you see that the +entanglement entropy-- first you + +notice that formula +becomes degenerate when + +you go to the two dimensions. + +It's equal to 1 +plus 1 dimensions. + +1 plus 1 dimension the were +played by something like this. + +You have log epsilon. + +So the key important +thing is not the prefactor + +because of the log. + +The prefactor is +actually reversal. + +And it's actually controlled +by the central charge. + +So that saves you from +entangled entropy. + +You can actually read +the central charge + +and actually read what +are the numbers of degrees + +of was freedom of the system. + +So the fact that the central +charge in the 1 plus 1 + +dimensional CFT captures the +number of degrees of freedom + +was known-- known +before people thought + +about entangled entropy. + +But it turned out-- and +people spent many years + +trying too hard to generalize +this concept to higher + +dimensional series. + +And it turned out they are +very hard to generalize. + +People didn't really +know how to do it. + +But now we know +because you can just + +generalize the entangled +entropy to higher dimensions. + +And then you find the same +kind of central charge + +which appeared. + +You find again +things can be defined + +as analog of the single +charge in 1 plus 1 dimension + +appears in the entangled entropy +in the higher dimensions. + +And then they can be +used to characterize + +the number degrees of freedom. + +And so in some sense, the +entangled entropy really + +provides a unified way to +think about this central charge + +and to characterize the +number of degrees of freedom + +across all dimensions-- +across all dimensions. + +And so this is a key formula. + +Actually, I first realized by +our old friend Frank Wilczek + +when they studied +free field theory. + +And people later generalized +to show this actually + +works for any CFT. + +Good. + +So now finally, we can talk +about holographic entangled + +entropy with lots +of preparations. + +So this just gives +you some taste + +of actually why we are actually +interested in entangled entropy + +and why this actually not only +people in quantum computing + +or quantum information +people are interested in it. + +People are doing +condensed matter-- people + +doing quantum field theory +are also interested in it. + +And now people who are +doing string theory + +are also interested +in it because + +of this holographic +entanglement entropy. + +So suppose we have our CFT. + +So a two-dimensional +CFT with a gravity + +dual-- so a dual to some +theory in d plus 1 dimensional + +[INAUDIBLE] space time. + +So let me give you origin A. How +do I find the entangled-- what + +is the counterpart +of this entangled + +entropy on the gravity side? + +So this is the question. + +So let me just draw this figure. + +Suppose this is +the box again that + +represents your total system. + +And then this carves +out of region A. + +Then the question what +does this translate into? + +And the graph decides. + +OK, so now in the +boundary, we have + +some region A is equal to 0. + +So for this question, in +some sense it's difficult + +because it's not +like other questions + +we've talked about before. + +So we also know +partition function. + +You can say the partition +function cannot be the same. + +Those things appear +to be natural. + +Here, there is no natural +thing you can think about, + +because you cannot +define entangled entropy + +as a partition function. + +Entangled entropy have to +involve in so-called trace + +out the degrees of freedom. + +Then take the logarithm. + +It's highly non-local and +a complicated procedure. + +And it's obvious how you would +define on the gravity side-- + +how you would guess +on the gravity side. + +So it's quite remarkable +and the Ryu-Takayanagi, + +they just made the guess. + +And then worked. + +So the proposal is just find +the minimal area surface, + +let me call gamma A, +which extends in the back + +and with the boundary +of A as the boundary. + +You first find the surface. + +And then you say the +entangled entropy for A + +is just the area of this +gamma A divided by 40 Newton. + +And this is the Ryu-Takayanagi. + +So the idea is that you find +a surface of a minimal area + +is going into the back, but +ending on the boundary of A. + +So this is your gamma A. And +you find such a minimal surface. + +Then you divide by 40 Newton. + +OK? + +So let me just +mention one thing. + +Let me just note a simple +scene, because again, + +the A of the boundary, this +is d minus 2 dimensional. + +And A and the gamma A are +all d minus 1 dimensional. + +So this is d minus +2 dimension is + +what we said before +because A is just + +a region in your +spatial section. + +So A is a d minus 1 dimensional. + +And the boundary A will +d minus 2 dimensional. + +And the gamma A +would be a surface + +which is ending on the boundary +of A. This ends on that thing. + +So this is also the d +minus 1 dimensional. + +And this is d minus +1 dimensional. + +So this area have +dimension d minus 1. + +And that's precisely +the dimension + +of G Newton in the d plus +1 dimensional [INAUDIBLE] + +of space time. + +And then this is a +dimensionless number. + +OK, because we did it +the SA with dimensions. + +So you can say this is +a very difficult guess. + +You can also say this is a very +simple guess, because clearly + +this formula is motivated by +the black hole entropy formula. + +You may say, ah, +black hole entropy + +is something divided 4GN. + +If it is entangled +entropy, it's also entropy. + +Maybe it's also +something divided by 4GN. + +And maybe it's some +surface divided by 4GN. + +And then the special surface +would be the minimal surface. + +So in some sense, it's +a very naive guess. + +And you could say it's +a very simple guess. + +But as I said, it's also +a very difficult guess, + +because essentially, +other than that, you don't + +have other starting points. + +Yes? + +AUDIENCE: So [INAUDIBLE]. + +So we have A in the CFT. + +Where do we know exactly +where to place A in the AdS? + +Because it's not-- + +HONG LIU: This is +a good question. + +This is what I'm +going to say next. + +Yeah, but let me +just emphasize that. + +So when we talk +about A, we're always + +talking about the +constant time slice, + +because you have to +specify some time. + +And actually, when we +consider the ground state + +or typical state does +not depend on time. + +And it actually does not +matter which slice we choose. + +You just choose a time slice. + +And then you specify +region A, because to talk + +about degrees of +freedom, you only + +talk about it in +the spatial section. + +So if you have a ground state +or have any state which does not + +depend on time, then +the gravity side + +also does not depend on time. + +It's a time-dependent geometry. + +So time slicing in the +field series naturally + +extends in the gravity side. + +So in the gravity +side, this surface + +would be in the constant +time slicing, which + +would go to the gravity side. + +AUDIENCE: Professor, +one more thing. + +With the CFT and +AdS-- I know we like + +to think one existing on +the boundary of the other. + +But how does-- that's sort +of an abstraction, right? + +HONG LIU: No, that you +should really consider + +as a real thing-- real stuff. + +Yeah, if you just think +of that as an abstraction, + +then you miss a +lot of intuition, + +because you use that +as a genuine boundary, + +will give you a +lot of intuition. + +And many things +become very natural. + +Many things become very natural. + +Yes? + +AUDIENCE: So comparing +to the other formula that + +also has an area +of the boundary, + +all this tells us +is just it helps + +us count the number of +degrees of freedom in the CFT. + +So it all it tells +us is basically + +the epsilon in the denominator? + +HONG LIU: No, no, they have a +complete different dimension. + +No, this one higher dimension. + +AUDIENCE: So that's +another strange-- + +HONG LIU: No, this is +not strange at all, + +because they're not +supposed to be the same. + +No, this is the +way it should be. + +So this is d minus +1 dimensional. + +And that is the d +minus 2 dimensional. + +It's just completely different. + +AUDIENCE: Well, right, +but they are not-- there + +is something the +same about them. + +HONG LIU: No, there is +something to same about them. + +But these two have +completely different physics. + +So this has a close analog +with black hole physics. + +Don't think they're +motivated by that formula. + +I think they're motivated +by the black hole formula. + +And people also try to connect +that formula to the black hole + +formula. + +That's another story. + +Anyway, it doesn't matter. + +OK, good. + +So this is a guess. + +Yes? + +AUDIENCE: So is this result for +the ground state on the CFT? + +HONG LIU: No, this is valid. + +Yeah, for the +time-independent state. + +The eigenstate is not +invoked with time. + +AUDIENCE: The thing +I don't understand + +is on the site of the +CFT, there is this state + +that you did as an +input to calculate + +the entanglement entropy. + +And what's the corresponding +thing on the AdS side? + +HONG LIU: The AdS side is +the corresponding geometry. + +So it's as said before, each +state on the field theory + +should correspond +to some geometry + +with normalizable modes. + +Yeah, so it's the +corresponding geometry. + +And the ground state, then +this will be just pure ideas. + +And if you look at the +final temperature state, + +then this will be +the black hole. + +And then if you are able to +construct some other geometry + +corresponding to some other +state, you can use that. + +AUDIENCE: How about this entropy +on independent on which state + +we choose for CFT? + +HONG LIU: No, of +course it depends. + +No this formula does not. + +But the geometry does. + +The geometry does. + +This is a minimal surface in +whatever [INAUDIBLE] geometry. + +AUDIENCE: Does the region-- +after we choose the region, + +we can choose any state-- + +HONG LIU: Yes, yes. + +AUDIENCE: And as +a minimal surface, + +is it independent on +which state we choose? + +HONG LIU: Of course, it +would depend on which state + +you choose, because +each state corresponds + +to a different geometry. + +And the minimal surface +depends on your geometry. + +So each state-- so +remember previously, + +the state on the +CFT side is mapped + +to the geometry with +normalizable boundary + +conditions with +normalizable modes. + +Yeah, anyway, just let +me say just geometry. + +So a state with the geometry. + +If you have a different state, +you have a different geometry. + +But by definition, +all this geometry + +would be asymptotic AdS. + +So in a boundary, they +should all be asymptotic AdS. + +And so that what means to +have [INAUDIBLE] mode excited. + +OK? + +Yes? + +AUDIENCE: So this +entropy formula + +takes into account the entropy +of gravitational excitations + +in AdS, if you can +put it that way. + +But black hole entropy-- + +HONG LIU: No, let's try +not to jump too fast. + +And I think you are trying +to extrapolate too fast. + +This formula is +supposed to calculate + +the entangled entropy +in the field series + +side in the [INAUDIBLE] +limit and the notch + +lambda toward coupling limit. + +And we can talk about the +gravitational interpretation + +later. + +But this formula is about +the field series entanglement + +entropy. + +OK? + +Good. + +Any other questions? + +OK, good. + +So there are many support of it. + +So this is a rule of the game. + +You make a guess. + +Then you do a check. + +If the check worked, then +that gives you confidence, + +and then you do another check. + +And here you find it will fail. + +And if you do a sufficient +number of checks, + +then people believed you. + +Then people will believe you. + +And everybody +started checking it. + +And then sooner or +later we will see + +whether this fails or works. + +Anyway, so this is nice because +this is simple to compute, + +because finding a minimal +surface on the gravity side + +is in some sense, it's a +straightforward a mathematical + +problem conceptually, +even though technically it + +may not be simple. + +But it's straightforward +conceptually. + +Anyway, so you can use these +to calculate many quantities. + +Let me just say in +support of this-- + +let me just say it in +words just to save time. + +So the first thing +you should check + +is that this satisfies the +subadditive condition which + +we wrote down earlier, +because that's + +a very non-trivial condition. + +It should be satisfied +by the entropy. + +So first, you should check that, +because if you violate that, + +than this proposal is gone. + +And then there are +other things that you + +can try to use to reproduce +all the known behavior we know + +about entangled +entropy, for example, + +this behavior and this +behavior-- this area along. + +And then we actually +build up confidence + +by checking all +those known results. + +And then you can try +to derive [INAUDIBLE] + +and to see whether [INAUDIBLE] +makes physical sense. + +So essentially, +that's how it works. + +And this is nice also +at the tactical level, + +because entangled entropy is +something very hard to compute. + +I don't know. + +You guys may not have experience +of calculating entangled + +entropy. + +But ask Frank Wilczek. + +He was one of the +first few people + +to do it in some +free field theory. + +Even for free field +theory, people could mostly + +do it in 1 plus 1 dimension. + +Going beyond 1 plus 1 dimension +free scalar field theory in 2 + +plus 1 dimension +3 plus 1 dimension + +for some simple region +like a circle or sphere + +you have to do a +numerical calculation. + +You have to discretize +the field theory + +to do very massive +numerical calculation. + +It's not easy to compute. + +But this guy is actually easy +to compute in comparison. + +So this guy at the +technical level + +provides a huge convenience +to calculate many things. + +Yeah, so this is a side remark. + +So now let's just do +some calculations. + +So first, let me show +that this actually + +satisfies strong subaddivity. + +So remember, the formula +we had before is S(AC), + +unfortunately I erased it. + +OK, so this is one +of the inequalities. + +So we are just drawing +it 1 plus 1 dimension + +because it's easy to draw. + +But a similar thing can +be easily generalized + +in a higher dimension. + +So let's look at just the +line in 1 plus 1 dimension. + +So this can call +this region A. This + +is region C. This is region B. + +You can also make them separate. + +It doesn't matter. + +You can also make them separate. + +It's easy to work out. + +So I'm just giving +you one cases. + +So suppose a minimal service +for the AC reading is like this. + +And the minimal +surface the BC reading + +would be like this-- so +minimal surface like that. + +So let me call this curve gamma +AC and this curve gamma BC. + +OK, I could not find +the colored chalk today. + +So I did not have +the colored chalk. + +Let me see whether +this chalk works. + +Is this the colored chalk? + +Yes. + +So now, let me define +two other surfaces. + +Let me call this one gamma +1 and this one gamma 2. + +In principle, I should use +two different chalks for that. + +You think it looks +like something? + +OK, anyway, so we have +gamma AC plus gamma + +BC equals to gamma +1 plus gamma 2 + +because-- gamma AC-- this +is length-- gamma BC is + +equal to gamma 1 plus gamma 2. + +And then just from +the definition + +of the minimal +surface, then the gamma + +1 must be greater than gamma +C in terms of the length + +because the minimal +surface associated with C + +must be the minimal area. + +It must be smaller than gamma 1. + +Under the area of gamma 2 must +be greater than gamma ABC, + +because the gamma 2 is +the boundary is the ABC. + +And the gamma 2 must be +greater than gamma BC + +because this is supposed +to be the minimal surface. + +So now we conclude that +gamma AC plus gamma + +BC is greater than +gamma ABC plus gamma C. + +And then this translates +into that formula. + +OK? + +Very simple, and elegant proof-- +very simple and elegant proof. + +And now you can prove +another inequality. + +You can prove +another inequality, + +which is S(AC) plus S(BC) +greater than S(A) and S(B). + +So now, I will define +another surface. + +OK? + +So now, let me just +redraw it-- A, C, B. + +So I have AC like this. + +I have BC like this. + +And now, let me call this one +gamma 1 tilde-- this one gamma + +2 tilde. + +This is annoying. + +OK. + +And again, gamma AB plus +gamma AC plus gamma BC + +equals to gamma 1 tilde +plus gamma 2 tilde. + +So the gamma 1 tilde +ends in A. Gamma + +2 tilde ends in B. +That means gamma + +1 tilde must be greater than +gamma A and gamma 2 tilde + +must be greater +than gamma B. OK? + +So now you show that +gamma AC plus gamma + +BC is greater than gamma A plus +gamma B. So this is very easy. + +So this is a very +simple and elegant. + +So if you want to really +to be impressed by this, + +I urge you to look at the +proof of the strong subaddivity + +itself in say in some textbook +or in the original papers. + +It's actually +highly non-trivial. + +You need some double, +double concave functions. + +It's quite a height involved. + +OK, so this is a +great confidence boost + +that satisfies the strong +subadditivity condition. + +So now, let's look +at the last one. + +Let's try to reproduce +this formula. + +Let's try to do a +simple calculation + +to reproduce this formula. + +So this formula is supposed +to be true for any CFT. + +This should be also applied +for the holographic CFT + +and to check whether +this formula works. + +The reason you would like to +choose an example which is new. + +But this example +is the simplest. + +So that's the reason +I choose this example, + +even though it's just +reproduced all the results. + +So let's now look at the +entangled entropy of 1 + +plus 1 dimensional CFT. + +So here, now you +have a CFT 1 plus 1 + +should be dual to the AdS3. + +You will do some theory in AdS3. + +So the S squared-- so let's +only look at the vacuum + +then we just work with AdS3. + +So let me write down +the AdS3 metric. + +So dx is the +boundary directions. + +So as I said, each +CFT is characterized + +by a central charge. + +And you can obtain +a central charge + +from various different ways. + +And again, from the +holographic, you + +can try to express +the single charge + +in terms of gravity quantities. + +And there is many ways to derive +it that we will not go through + +with that calculation. + +So let me just write +down the results. + +So far the holographic +CFTs, the single charge + +is related to the +gravity quantity + +by 3R divided by 2 G Newton. + +So this is a result +which I just caught. + +I will not derive it for you. + +But you can derive it +in many different ways. + +So for CFT, to do +a gravity idea 3, + +its central charge +is given by 3R, + +which is the AdS radius divided +by 2 times the Newton constant. + +And the Newton constant +in three dimensions + +has mass dimension 1. + +So this is a +dimensionless number-- + +a dimensionless number. + +So now let's calculate +the entanglement entropy + +using that formula. + +So this now reduced +your calculation + +very similar to our +Wilson loop calculation. + +So let's call this +L divided by 2. + +So lets call this X direction. + +So this is a V direction. + +So this is L divided by 2. + +This is minus L divided by 2. + +This region is A. +Then we need to find + +a curve, because this now 1 plus +1 dimensions-- one dimensions. + +So we need to find the curve +which end on this segment of A. + +OK? + +So is this clear? + +So this is the x direction. + +And so this is 0, x equals to 0. + +Yes? + +OK. + +So what we need to find is find +the minimal surface connecting + +these two points-- a minimal +curve-- a minimal length + +curve connecting +these two points. + +So it's as we said +before, we should + +look at the constant time slice +because this is a vacuum which + +is time independent. + +Let's look at the +constant time slice. + +The constant time +slice, the metric + +becomes-- so in this +space, the metric becomes r + +square divided by z square +because the time does not + +change. + +So now if I treat the x as a +function of z, and then these + +will become. + +So this curve lets +me parametrize + +x as a function of z. + +Then this just becomes r +square divided by z square 1 + +plus x prime square dz square. + +And so this is dl square. + +So the length of +the curve square + +would be just +parametrized by this guy. + +OK? + +And we have to satisfy +the boundary condition-- + +by symmetry, we only need to +consider the right stuff OK, + +because it's symmetric. + +So we impose the boundary +condition at the x + +z equal to 0. + +It's L divided by 2. + +We can see the right half. + +So now you can just write down +the entanglement entropy now. + +So S(A) will be 1 over 4GN. + +So I integrate +half of the curve. + +Let me just call +here z is equal to 0. + +Let me call this point z0. + +So I just integrate +from 0 to z0. + +Z0 we will find out when you +find out this minimal length + +curve. + +So this one will be r/z dz. + +Then just taking the +square root of this guy-- + +the square of 1 +over x prime square. + +So this is the length +and the times 2, + +because we only can see +that this is half of it. + +And now you extremize it. + +Then you find the +minimal length curve. + +And then you plug +the solution here. + +Then you find the action. + +Actually we don't +need to extremize it, + +because this is a +well-known problem. + +And this is called +the Poincare disk. + +So this is a prototype of a +two-dimensional hyperbolic + +space. + +And the minimal length curve +inside your hyperbolic space + +is maybe a 16th century problem. + +Yeah, I don't know. + +Actually, maybe 17th century. + +Anyway, so the answer +is actually very long. + +But you can also easily +work out yourself. + +So the result is actually +this is just exactly a circle. + +OK? + +Exactly a half circle. + +So that's actually +a half circle. + +That means that x equals 2. + +The half circle with a +radius L divided by 2. + +So this has just +become L squared + +divided by 4 minus d square. + +In particular, z0 corresponding +to the point which + +x equal to 0 just L divided 2. + +So now you just +plug this into here. + +You just plug this here. + +Let me just write it a +little bit fast, because we + +are a little bit out of time. + +So you plug this in. + +Then you can scale the z out. + +You can scale z to be scaled +L divided by 2 factors out. + +And let me just scale it. + +You can rewrite the +integral as follows. + +So after the scaling +it's say 2z scale + +with L divided by 2z +to do the scaling. + +Then you find this +expression becomes 2r/4GN. + +And the upper limit becomes 1. + +And the lower limit you see. + +When you plug this in, +actually the lower limit + +is divergent because +there's 1 over z here. + +As always, we need +to put the cutoff. + +And also, this divergence +is expected because of below + +that here it depends +on short distance + +cutoff it would be divergent. + +So we need to for the +short-distance cutoff here. + +So let me put it here epsilon. + +And this will be 2 +epsilon divided by L + +when I do this scaling. + +And then you have +dz/z 1 minus d square. + +So the integral reduces +to something like this. + +And now you can evaluate +this integral trivially. + +Then you find the epsilon +goes to the limit. + +Then you find the one term +survives 2r divided by 4GN log + +L divided by epsilon. + +So now let's try +to rewrite in terms + +of this C-- we +rewrite in terms of C. + +So this is 1/3 3r divided by +2GN log L divided by epsilon. + +And so this is precisely +that formula C divided by 3 + +log L of epsilon. + +And with that, you just count +from the minimal surface + +in the hyperbolic +space is a circle. + +And it takes a lot of effort +to calculate this thing, + +even to do a free field +series calculation. + +But in gravity you +can do it very easily. + +So now let me just +quickly mention + +what happens if you do +at a finite temperature. + +So you can also do this +at a finite temperature. + +So since we're out of time, +we'll be doing it a little bit + +fast. + +So first doing it at a +finite temperature is easier. + +Let me just say finite T. +And then I will connect + +to the black hole entropy. + +I will show that +this formula actually + +reduces to the black hole +entropy in some limits. + +So for these problems, +actually, it's + +easier to consider +CFT on the circle. + +OK. + +So when the CFT +is on the circle, + +the boundary will be +a circle because this + +is 1 plus 1 dimension. + +So remember, in +the global ideas, + +it's like sitting +there in the boundary. + +And in the 1 plus 1 dimensional +case and the boundary + +is just really a circle. + +And this is the bark + +And a finite temperature, +you put the black hole there. + +Let me just put the +black hole here. + +OK? + +Just put the black hole there. + +So now you can ask the +following question. + +So now let's consider +some reaching A. So + +let's consider A is very small. + +Yo can work out the +minimal surface. + +So it acts the same as +our Wilson loop story. + +So you find a minimal surface. + +But if A is sufficiently +small, then the geometry around + +here is still AdS. + +And then you just +get a minimal surface + +around here-- so a +small deformation + +from the vacuum behavior. + +So we'll make A +larger and larger. + +So this z0 depends on L. If +we make L larger and larger, + +this is z0 will be +deeper in the bark. + +So if you make A larger, so +this will go more to the bark + +and then will be +deformed, and then we'll + +see the black hole geometry. + +But now to answer +the question how + +about if I make A to be +larger-- this region to be + +A to be larger than the half +of the size of the circle. + +So the minimal surface +should be able to be + +to be smoothly +deformed back into A. + +So now you have to do +something like this. + +It turns out the minimal surface +want to go around the horizon + +and then doing +something like this. + +AUDIENCE: Why don't you do +it the other way around? + +HONG LIU: No, it's +because the other won't. + +It's because A is like this. + +And if you do +something like this, + +then it can be +deformed back into A. + +It's mostly without +crossing the black hole. + +AUDIENCE: Yes, or it could be +like a phase jump or something + +at some point when one +surface becomes longer than + +[INAUDIBLE]. + +HONG LIU: No, in this +situation, it's not that thing. + +It's something like this. + +Now, if you make A even +longer, eventually, + +let's take the A even longer. + +And that would be +something like this. + +Yeah, because you always +want to hug near the horizon. + +And eventually, we'll +make A to be tiny, + +then it will become +something like this. + +You have something +close on the horizon. + +Then you have +something like this. + +It's roughly +something like this. + +Yeah, is it clear to you? + +It doesn't matter. + +[LAUGHTER] + +So now let's consider-- +anyway, yeah, + +let me just draw this again. + +It actually does matter. + +Sorry. + +So let's take A +to be very small. + +Let's take A to be a very big. + +This part will be very small. + +So we are finally we +will go like this. + +Anyway, something like this +when you hug the black hole. + +And eventually, when +these two points shrink, + +so take A with the total region. + +Take A to be the total space. + +What do you get? + +Then what you see that the +minimal surface essentially + +is just essentially a surface +hugger on the horizon. + +And this is a precise +black hole formula, + +because then this is a +imprecise a black hole formula. + +And this is a situation you +expect it to be black hole + +formula, because if you take +the A to be the host space, + +then rho A is just equal to +the rho of the whole system. + +And the S(A) by definition +is just equal to the S + +of the whole system. + +And this is just a thermal +density, a thermal entropy. + +And this is given by +the black hole formula. + +It's given by the +black hole formula. + +And this is given +by [INAUDIBLE]. + +So you find in these +special cases, actually, + +you recover the +black hole formula. + +So I have some small things. + +We can talk a little bit more. + +But I think we'll skip it. + +You can also show that actually +for general dimensions, + +you always recover the area +more without the details + +of the geometry, because no +matter what kind of dimension + +you look at, the +typical state which will + +be normalizable to geometry. + +When you approach the AdS-- +when you approach the boundary, + +it's always like AdS. + +And then you find in +a higher dimension, + +it's always like this. + +It says, when this +minimal surface + +is close to the boundary, +it becomes perpendicular + +to the boundary. + +Here is a circle, +then of course, + +it's perpendicular +to the boundary. + +But you see this +feature is actually + +generalized to higher +dimensions-- to any dimensions. + +So what you see is that +in the general dimension, + +a minimal surface will be +just near the boundary will + +be just perpendicular to +going down from everywhere. + +And then from +there, you can show + +that you always have the +area law from this behavior. + +You always have the area law. + +So this can give you an +exercise for yourself. + +Yeah, so let me just +finish by saying + +a couple of philosophical +remarks, and then we'll finish. + +So this RT formula +is really remarkable, + +because it's actually, +as I said, technically + +provides a very simple way to +calculate entangled entropy. + +But actually, conceptually, +it's even more profound + +because it tells you that +the space time is related + +to the entanglement, because +it simulates something which + +is very subtle from the field +theory side, because this S(A), + +as we said, you have to do +some complicated procedure + +to trace out degrees of +freedom-- take the log. + +And that turns out to be +related to the geometry + +in a very simple way. + +So essentially, you see that +entanglement-- it's just + +captured by the space time. + +And in particular, +it's something + +you can say the +geometry is essentially + +equal to the +quantum information. + +So this is a very exciting +also from the gravity + +perspective, because if they +ask you if you really understand + +this duality, then you can +actually using the quantum + +information of the field theory +to understand the subtle things + +about the geometry. + +It just tells you the +geometry is actually + +equal to the +quantum information. + +So for many years, actually not +that many years, so previously, + +we have people doing +quantum information. + +And we have people doing +this matter, which is + +the quantum many-body system. + +And this matter, or QCD, so this +is kind of quantum many-body. + +And then we have people doing +black hole, string theory, + +and the gravity. + +So they are all very +different fields. + +But now, they're all connected +by this holographic duality. + +Somehow essentially, +they connect all of them. + +So now, we essentially +just see a unified picture, + +a unified paradigm, to +understand all quantum systems, + +including quantum systems +without gravity, with gravity. + +So I will stop here. + +[APPLAUSE] \ No newline at end of file diff --git a/_7JPHNCT1Qo.txt b/_7JPHNCT1Qo.txt new file mode 100644 index 0000000000000000000000000000000000000000..da5e5a358ebc8597997382f78a8156dd09a16a26 --- /dev/null +++ b/_7JPHNCT1Qo.txt @@ -0,0 +1,803 @@ +align:start position:0% + +I would now like to calculate the + + align:start position:0% +I would now like to calculate the + + + align:start position:0% +I would now like to calculate the +potential function for two other + + align:start position:0% +potential function for two other + + + align:start position:0% +potential function for two other +conservative forces that we encounter + + align:start position:0% +conservative forces that we encounter + + + align:start position:0% +conservative forces that we encounter +all the time spring forces and + + align:start position:0% +all the time spring forces and + + + align:start position:0% +all the time spring forces and +gravitational forces will begin with + + align:start position:0% +gravitational forces will begin with + + + align:start position:0% +gravitational forces will begin with +spring forces so first off let's begin + + align:start position:0% +spring forces so first off let's begin + + + align:start position:0% +spring forces so first off let's begin +with some type of coordinate system + + align:start position:0% +with some type of coordinate system + + + align:start position:0% +with some type of coordinate system +suppose we have a spring we have a block + + align:start position:0% +suppose we have a spring we have a block + + + align:start position:0% +suppose we have a spring we have a block +this is my point X equal equal Ibrahim + + align:start position:0% +this is my point X equal equal Ibrahim + + + align:start position:0% +this is my point X equal equal Ibrahim +unstretched length of the spring and now + + align:start position:0% +unstretched length of the spring and now + + + align:start position:0% +unstretched length of the spring and now +whether we stretch it or compress it + + align:start position:0% +whether we stretch it or compress it + + + align:start position:0% +whether we stretch it or compress it +here I'll stretch it I'll introduce a + + align:start position:0% +here I'll stretch it I'll introduce a + + + align:start position:0% +here I'll stretch it I'll introduce a +coordinate function X unit vector I and + + align:start position:0% +coordinate function X unit vector I and + + + align:start position:0% +coordinate function X unit vector I and +my spring force F is minus KX I where X + + align:start position:0% +my spring force F is minus KX I where X + + + align:start position:0% +my spring force F is minus KX I where X +can be positive for a stretched spring + + align:start position:0% +can be positive for a stretched spring + + + align:start position:0% +can be positive for a stretched spring +forces and then a negative I hat + + align:start position:0% +forces and then a negative I hat + + + align:start position:0% +forces and then a negative I hat +direction when X is negative negative + + align:start position:0% +direction when X is negative negative + + + align:start position:0% +direction when X is negative negative +times negative means the spring force is + + align:start position:0% +times negative means the spring force is + + + align:start position:0% +times negative means the spring force is +in the positive I hat direction when + + align:start position:0% +in the positive I hat direction when + + + align:start position:0% +in the positive I hat direction when +it's compressed so this is a force + + align:start position:0% +it's compressed so this is a force + + + align:start position:0% +it's compressed so this is a force +that's a restoring force always back to + + align:start position:0% +that's a restoring force always back to + + + align:start position:0% +that's a restoring force always back to +equilibrium this is a example of a + + align:start position:0% +equilibrium this is a example of a + + + align:start position:0% +equilibrium this is a example of a +conservative force and now let's + + align:start position:0% +conservative force and now let's + + + align:start position:0% +conservative force and now let's +calculate the change in potential energy + + align:start position:0% +calculate the change in potential energy + + + align:start position:0% +calculate the change in potential energy +and then introduce a zero reference + + align:start position:0% +and then introduce a zero reference + + + align:start position:0% +and then introduce a zero reference +point and get a potential function for + + align:start position:0% +point and get a potential function for + + + align:start position:0% +point and get a potential function for +this force so the first calculation is + + align:start position:0% +this force so the first calculation is + + + align:start position:0% +this force so the first calculation is +straightforward so if we took our + + align:start position:0% +straightforward so if we took our + + + align:start position:0% +straightforward so if we took our +displacement to be DX I had and we take + + align:start position:0% +displacement to be DX I had and we take + + + align:start position:0% +displacement to be DX I had and we take +the dot product of F n yes we get DX I + + align:start position:0% +the dot product of F n yes we get DX I + + + align:start position:0% +the dot product of F n yes we get DX I +had that I had as 1 times DX and that's + + align:start position:0% +had that I had as 1 times DX and that's + + + align:start position:0% +had that I had as 1 times DX and that's +just the X component of the force + + align:start position:0% +just the X component of the force + + + align:start position:0% +just the X component of the force +displacement my and minus sign because + + align:start position:0% +displacement my and minus sign because + + + align:start position:0% +displacement my and minus sign because +the X component of the force is negative + + align:start position:0% +the X component of the force is negative + + + align:start position:0% +the X component of the force is negative +K X and so now if we were to start our + + align:start position:0% +K X and so now if we were to start our + + + align:start position:0% +K X and so now if we were to start our +system so again for our initial state + + align:start position:0% +system so again for our initial state + + + align:start position:0% +system so again for our initial state +let's say that the block from the + + align:start position:0% +let's say that the block from the + + + align:start position:0% +let's say that the block from the +unstretched position as is stretched X I + + align:start position:0% +unstretched position as is stretched X I + + + align:start position:0% +unstretched position as is stretched X I +and our final state whether it's + + align:start position:0% +and our final state whether it's + + + align:start position:0% +and our final state whether it's +stretched or compressed it won't matter + + align:start position:0% +stretched or compressed it won't matter + + + align:start position:0% +stretched or compressed it won't matter +but we'll just stretch it out a little + + align:start position:0% +but we'll just stretch it out a little + + + align:start position:0% +but we'll just stretch it out a little +bit more 2x final so now let's calculate + + align:start position:0% +bit more 2x final so now let's calculate + + + align:start position:0% +bit more 2x final so now let's calculate +the change in potential energy between + + align:start position:0% +the change in potential energy between + + + align:start position:0% +the change in potential energy between +our initial and our final States + + align:start position:0% +our initial and our final States + + + align:start position:0% +our initial and our final States +now recall there's a minus sign because + + align:start position:0% +now recall there's a minus sign because + + + align:start position:0% +now recall there's a minus sign because +it's minus W conservative that's minus + + align:start position:0% +it's minus W conservative that's minus + + + align:start position:0% +it's minus W conservative that's minus +the integral X initial 2x final of minus + + align:start position:0% +the integral X initial 2x final of minus + + + align:start position:0% +the integral X initial 2x final of minus +K X DX we have two minus signs + + align:start position:0% +K X DX we have two minus signs + + + align:start position:0% +K X DX we have two minus signs +that's our integration variable if you + + align:start position:0% +that's our integration variable if you + + + align:start position:0% +that's our integration variable if you +want to see it in all the detail and + + align:start position:0% +want to see it in all the detail and + + + align:start position:0% +want to see it in all the detail and +when you simply integrate X prime DX + + align:start position:0% +when you simply integrate X prime DX + + + align:start position:0% +when you simply integrate X prime DX +Prime you get X prime squared over two + + align:start position:0% +Prime you get X prime squared over two + + + align:start position:0% +Prime you get X prime squared over two +and so the change in potential energy + + align:start position:0% +and so the change in potential energy + + + align:start position:0% +and so the change in potential energy +between these two states is one-half K X + + align:start position:0% +between these two states is one-half K X + + + align:start position:0% +between these two states is one-half K X +final squared minus one-half K X initial + + align:start position:0% +final squared minus one-half K X initial + + + align:start position:0% +final squared minus one-half K X initial +squared and that's physically meaningful + + align:start position:0% +squared and that's physically meaningful + + + align:start position:0% +squared and that's physically meaningful +if I take my system initially and I the + + align:start position:0% +if I take my system initially and I the + + + align:start position:0% +if I take my system initially and I the +system ends up in the final state then + + align:start position:0% +system ends up in the final state then + + + align:start position:0% +system ends up in the final state then +what I'm calculating is minus the work + + align:start position:0% +what I'm calculating is minus the work + + + align:start position:0% +what I'm calculating is minus the work +done by the spring force on the block as + + align:start position:0% +done by the spring force on the block as + + + align:start position:0% +done by the spring force on the block as +it goes from the initial state to the + + align:start position:0% +it goes from the initial state to the + + + align:start position:0% +it goes from the initial state to the +final state I'm not talking about the + + align:start position:0% +final state I'm not talking about the + + + align:start position:0% +final state I'm not talking about the +work that an external agent does and + + align:start position:0% +work that an external agent does and + + + align:start position:0% +work that an external agent does and +stretching and or compressing it this is + + align:start position:0% +stretching and or compressing it this is + + + align:start position:0% +stretching and or compressing it this is +explicitly the work done by the spring + + align:start position:0% +explicitly the work done by the spring + + + align:start position:0% +explicitly the work done by the spring +force on the block as it goes from the + + align:start position:0% +force on the block as it goes from the + + + align:start position:0% +force on the block as it goes from the +initial state to the final state I + + align:start position:0% +initial state to the final state I + + + align:start position:0% +initial state to the final state I +introduced the minus sign and our + + align:start position:0% +introduced the minus sign and our + + + align:start position:0% +introduced the minus sign and our +definition of potential energy and so + + align:start position:0% +definition of potential energy and so + + + align:start position:0% +definition of potential energy and so +this quantity represents the negative of + + align:start position:0% +this quantity represents the negative of + + + align:start position:0% +this quantity represents the negative of +the work done by the spring force as the + + align:start position:0% +the work done by the spring force as the + + + align:start position:0% +the work done by the spring force as the +system goes from the initial to the + + align:start position:0% +system goes from the initial to the + + + align:start position:0% +system goes from the initial to the +final states now you may have already + + align:start position:0% +final states now you may have already + + + align:start position:0% +final states now you may have already +thought about it but the reference point + + align:start position:0% +thought about it but the reference point + + + align:start position:0% +thought about it but the reference point +that we're going to use is x equals 0 + + align:start position:0% +that we're going to use is x equals 0 + + + align:start position:0% +that we're going to use is x equals 0 +the unstretched length of the spring and + + align:start position:0% +the unstretched length of the spring and + + + align:start position:0% +the unstretched length of the spring and +our reference potential at that point + + align:start position:0% +our reference potential at that point + + + align:start position:0% +our reference potential at that point +will be 0 so our reference point is + + align:start position:0% +will be 0 so our reference point is + + + align:start position:0% +will be 0 so our reference point is +actually the zero point for the + + align:start position:0% +actually the zero point for the + + + align:start position:0% +actually the zero point for the +potential and then our arbitrary state + + align:start position:0% + + + + align:start position:0% + +we can call this the reference state if + + align:start position:0% +we can call this the reference state if + + + align:start position:0% +we can call this the reference state if +you like that's probably better than the + + align:start position:0% +you like that's probably better than the + + + align:start position:0% +you like that's probably better than the +reference point our arbitrary state will + + align:start position:0% +reference point our arbitrary state will + + + align:start position:0% +reference point our arbitrary state will +be at some arbitrary stretch or compress + + align:start position:0% +be at some arbitrary stretch or compress + + + align:start position:0% +be at some arbitrary stretch or compress +and our potential energy function at + + align:start position:0% +and our potential energy function at + + + align:start position:0% +and our potential energy function at +that reference minus + + align:start position:0% +that reference minus + + + align:start position:0% +that reference minus +the potential energy at the arbitrary + + align:start position:0% +the potential energy at the arbitrary + + + align:start position:0% +the potential energy at the arbitrary +state - the reference state well if we + + align:start position:0% +state - the reference state well if we + + + align:start position:0% +state - the reference state well if we +set X I equal to 0 and X final equal to + + align:start position:0% +set X I equal to 0 and X final equal to + + + align:start position:0% +set X I equal to 0 and X final equal to +X as we have in this expression we + + align:start position:0% +X as we have in this expression we + + + align:start position:0% +X as we have in this expression we +simply get 1/2 K x squared so the + + align:start position:0% +simply get 1/2 K x squared so the + + + align:start position:0% +simply get 1/2 K x squared so the +potential energy function equals our + + align:start position:0% +potential energy function equals our + + + align:start position:0% +potential energy function equals our +reference potential plus 1/2 K x squared + + align:start position:0% +reference potential plus 1/2 K x squared + + + align:start position:0% +reference potential plus 1/2 K x squared +and we've defined that our reference + + align:start position:0% +and we've defined that our reference + + + align:start position:0% +and we've defined that our reference +potential to be 0 it could have been + + align:start position:0% +potential to be 0 it could have been + + + align:start position:0% +potential to be 0 it could have been +anything but we're making it 0 so that + + align:start position:0% +anything but we're making it 0 so that + + + align:start position:0% +anything but we're making it 0 so that +we get a nice function 1/2 K x squared + + align:start position:0% +we get a nice function 1/2 K x squared + + + align:start position:0% +we get a nice function 1/2 K x squared +and again it's always worthwhile to plot + + align:start position:0% +and again it's always worthwhile to plot + + + align:start position:0% +and again it's always worthwhile to plot +that function it's a nice parabola U of + + align:start position:0% +that function it's a nice parabola U of + + + align:start position:0% +that function it's a nice parabola U of +X X and you can see down here that's our + + align:start position:0% +X X and you can see down here that's our + + + align:start position:0% +X X and you can see down here that's our +reference point \ No newline at end of file diff --git a/_PwhiWxHK8o.txt b/_PwhiWxHK8o.txt new file mode 100644 index 0000000000000000000000000000000000000000..19e9e90c5aa3185ccbf8dbb779ec3ae92e3f5f28 --- /dev/null +++ b/_PwhiWxHK8o.txt @@ -0,0 +1,2292 @@ +PATRICK WINSTON: So +where are we? + +We started off with simple +methods for learning stuff. + +Then, we talked a little about +a purchase of learning that + +we're vaguely inspired by. + +The fact that our heads are +stuffed with neurons, and that + +we seemed to have evolved +from primates. + +Then, we talked about looking at +the problem and address the + +issue of [? phrenology ?] + +and how it's possible +to learn concepts. + +But now, we're coming full +circle back to the beginning + +and thinking about how to +divide up a space with + +decision boundaries. + +But whereas, you do it with +a neural net or a nearest + +neighbors or a ID tree. + +Those are very simple ideas +that work very often. + +Today, we're going to talk about +a very sophisticated + +idea that still has +a implementation. + +So this needs to be +in the tool bag of + +every civilized person. + +This is about support +vector machines, an + +idea that was developed. + +Well, I want to talk to +you today about how + +ideas develop, actually. + +Because you look at stuff like +this in a book, and you think, + +well, Vladimir Vapnik just +figured this out one Saturday + +afternoon when the weather was +too bad to go outside. + +That's not how it happens. + +It happens very differently. + +I want to talk to you +a little about that. + +The next thing about great +things that were done by + +people who are still alive +is you can ask them + +how they did it. + +You can't do that +with Fourier. + +You can't say to Fourier, +how did you do it? + +Did you dream it up on +a Saturday afternoon? + +But can call Vapnik on the phone +and ask him questions. + +That's the stuff I'm going +to talk about toward + +the end of the hour. + +Well, it's all about decision +boundaries. + +And now, we have several +techniques that we can use to + +draw some decision boundaries. + +And here's the same problem. + +And if we drew decision +boundaries in here, we might + +get something that would +look like maybe this. + +If we were doing a nearest +neighbor approach, and if + +we're doing ID trees, we'll just +draw in a line like that. + +And if we're doing neural nets, +well, you can put in a + +lot of straight lines wherever +you like with a neural net, + +depending on how it's +trained up. + +Or if you just simply go in +there and design it, so you + +could do that if you wanted. + +And you would think that after +people have been working on + +this sort of stuff for 50 or 75 +years that there wouldn't + +be any tricks in the bag left. + +And that's when everybody got +surprised, because around the + +early '90s Vladimir Vapnik +introduced the ideas I'm about + +to talk to you about. + +So what Vapnik says is +something like this. + +Here you have a space, and you +have some negative examples, + +and you have some positive +examples. + +How do you divide the positive +examples from + +the negative examples? + +And what he says that we want +to do is we want to draw a + +straight line. + +But which straight line +is the question. + +Well, we want to draw +a straight line. + +Well, would this be a +good straight line? + +One that went up like that? + +Probably not so hot. + +How about one that's +just right here? + +Well, that might separate them, +but it seems awfully + +close to the negative +examples. + +So maybe what we ought to do +is we ought to draw our + +straight line in here, +sort of like this. + +And that line is drawn with a +view toward putting in the + +widest street that separates the +positive samples from the + +negative samples. + +That's why I call it the +widest street approach. + +So that makes way of putting +in the decision boundary-- + +is to put in a straight line but +in contrast with the way + +ID tree puts in a +straight line. + +It tries to put the line in in +such a way as the separation + +between the positive and +negative examples. + +That street is as wide +as possible. + +All right. + +So you might think to do that in +the UROP project, and then, + +let it go with that. + +What's the big deal? + +So what we've got to do is we've +got to go through why + +it's a big deal. + +So first of all, we like to +think about how you would make + +a decision rule that would use +that decision boundary. + +So what I'm going to ask you to +imagine is that we've got a + +vector of any length that you +like, constrained to be + +perpendicular to the median, or +if you like, perpendicular + +to the gutters. + +It's perpendicular to the median +line of the street. + +All right, it's drawn in such +a way that that's true. + +We don't know anything about +it's length, yet. + +Then, we also have some unknown, +say, right here. + +And we have a vector that +points to it by excel. + +So now, what we're really +interested in is whether or + +not that unknown is on the right +side of the street or on + +the left side of the street. + +So what we'd what to do is want +to project that vector, + +u, down on to one that's +perpendicular to the street. + +Because then, we'll have the +distance in this direction or + +a number that's proportional +to this in this direction. + +And the further out we go, the +closer we'll get to being on + +the right side of the street, +where the right side of the + +street is not the correct side +but actually the right side of + +the street. + +So what we can do is we can say, +let's take w and dot it + +with u and measure whether or +not that number is equal to or + +greater than some constant, c. + +So remember that the dot +product has taken the + +projection onto w. + +And the bigger that projection +is, the further out along this + +line the projection will lie. + +And eventually it will be so +big that the projection + +crosses the median line of the +street, and we'll say it must + +be a positive sample. + +Or we could say, without loss +of generality that the dot + +product plus some constant, b, +is equal to or greater than 0. + +If that's true, then it's +a positive sample. + +So that's our decision rule. + +And this is the first in several +elements that we're + +going to have to line up to +understand this idea called + +support vector machines. + +So that's the decision rule. + +And the trouble is we don't know +what constant to use, and + +we don't know which +w to use either. + +We know that w has to be +perpendicular to the median + +line of the street. + +But there's lot of w's that +are perpendicular to the + +median line of the street, +because it + +could be of any length. + +So we don't have enough +constraint here to fix a + +particular b or a +particular w. + +Are you with me so far? + +All right. + +And this, by the way, we get +just by saying that c + +equals minus b. + +What we're going to do next is +we're going to lay on some + +additional constraints whether +you're toward putting enough + +constraint on the situation that +we can actually calculate + +a b and a w. + +So what we're going to say is +this, that if we look at this + +quantity that we're checking out +to be greater than or less + +than 0 to make our decision, +then, what we're going to do + +is we're going to say that if we +take that vector w, and we + +take the dot product of that +with some x plus, some + +positive sample, now. + +This is not an unknown. + +This is a positive sample. + +If we take the dot product of +those two vectors, and we had + +b just like in our decision +rule, we're going to want that + +to be equal to or +greater than 1. + +So in other words, you can be +an unknown anywhere in this + +street and be just a little bit +greater or just a little + +bit less than 0. + +But if you're a positive sample, +we're going to insist + +that this decision function +gives the + +value of one or greater. + +Likewise, if w thought it was +some negative sample is + +provided to us, then we're going +to say that has to be + +equal to or less than minus 1. + +All right. + +So if you're a minus sample, +like one of these two guys or + +any minus sample that may lie +down here, this function that + +gives us the decision rule must +return minus 1 or less. + +So there's a separation +of distance here. + +Minus 1 to plus 1 for +all of the samples. + +So that's cool. + +But we're not quite done, +because carrying around two + +equations like this, +it's a pain. + +So what we're going to do is +we're going to introduce + +another variable to make +like a little easier. + +Like many things that we do, and +when we develop this kind + +of stuff, introducing this +variable is not something that + +God says has to be done. + +What is it? + +We introduced this additional +stuff to do what? + +To make the mathematics more +convenient, so mathematical + +convenience. + +So what we're going to do is +we're going to introduce a + +variable, y sub i, such that y +sub i is equal to plus 1 for + +plus samples and minus 1 +for negative samples. + +All right. + +So for each sample, we're going +to have a value for this + +new quantity we've +introduced, y. + +And the value of y is going to +be determined by whether it's + +a positive sample or +negative sample. + +If it's a positive sample it's +got to be plus 1 for this + +situation up here, and it's +going to be minus 1 for this + +situation down here. + +So what we're going to do with +this first equation is we're + +going to multiply it by y sub +i, and that is now x of i, + +plus b is equal to or +greater than 1. + +And then, you know what +we're going to do? + +We're going to multiply the left +side of this equation by + +y sub i, as well. + +So the second equation becomes +y sub i times x sub i plus b. + +And now, what does that +do over here? + +We multiplied this guy +times minus 1. + +So it used to be the case that +that was less than minus 1. + +So if we multiply it by minus +1, then it has to be greater + +than plus 1. + +The two equations are the same, +because that introduces + +this little mathematical +convenience. + +So now, we can say that y sub +i times x sub i plus b. + +Well, what we're going to do-- + +Brett? + +STUDENT: What happened +to the w? + +PATRICK WINSTON: Oh, did +I leave out a w? + +I'm sorry. + +Thank you. + +Yeah, I wouldn't have gotten +very far with that. + +So that's dot it with +w, dot it with w. + +Thank you, Brett. + +Those are all vectors. + +I'll pretty soon forget to put +the little vector marks on + +there, but you know +what I mean. + +So that's w plus b. + +And now, let me bring that 1 +over to the left side, and + +that's equal to or +greater than 0. + +All right. + +With Brett's correction, I +think everything's OK. + +But we're going to take one more +step, and we're going to + +say that y sub i times x sub +i times w plus b minus 1. + +It's always got to be equal +to or greater than 0. + +But what I'm going to +say is if we're for + +x sub i in a gutter. + +So there's always going to be +greater than 0, but we're + +going to add the additional +constraint that it's going to + +be exactly 0 for all the samples +that end up in the + +gutters here of the street. + +So the value of that expression +is going to be + +exactly 0 for that sample, 0 +for this sample and this + +sample, not 0 for that sample. + +It's got to be greater than 1. + +All right? + +So that's step number two. + +And this is step number one. + +OK. + +So now, we've just got some +expressions to talk about, + +some constraints. + +Now, what are we trying +to do here? + +I forgot. + +Oh, I remember now. + +We're trying to figure out how +to arrange for the line to be + +such at the street separating +the pluses from the minuses as + +wide as possible. + +So maybe we better figure out +how we can express the + +distance between the +two gutters. + +Let's just repeat our drawing. + +We've got some minuses here, got +pluses out here, and we've + +got gutters that are +going down here. + +And now, we've got a vector here +to a minus, and we've got + +a vector here to a plus. + +So we'll call that x plus +and this x minus. + +So what's the width +of the street? + +I don't know, yet. + +But what we can do is we can +take the difference of those + +two vectors, and that will +be a vector that + +looks like this, right? + +So that's x plus +minus x minus. + +So now, if I only had a unit +normal that's normal to the + +median line of the street, if +it's a unit normal, then I + +could just take the dot product +or that unit normal + +and this difference vector, and +that would be the width of + +the street, right? + +So in other words, if I had a +unit vector in that direction, + +then I could just dot the two +together, and that would be + +the width of the street. + +So let me write that down +before I forget. + +So the width is equal to +x plus minus x minus. + +OK. + +That's the difference vector. + +And now, I've got to multiple +it by unit vector. + +But wait a minute. + +I said that that w is +a normal, right? + +The w is a normal. + +So what I can do is I can +multiply this times w, and + +then, we'll divide by the +magnitude of w, and that will + +make it a unit vector. + +So that dot product, not a +product, that dot product is, + +in fact, a scalar, and it's +the width of the street. + +It doesn't do as much good, +because it doesn't look like + +we get much out of it. + +Oh, but I don't know. + +Let's see, what can +we get out of it? + +Oh gee, we've got this equation +over here, this + +equation that constrains +the samples + +that lie in the gutter. + +So if we have a positive sample, +for example, then this + +is plus 1, and we have +this equation. + +So it says that x plus times w +is equal to, oh, 1 minus b. + +See, I'm just taking this part +here, this vector here, and + +I'm dotting it with x plus. + +So that's this piece +right here. + +y is 1 for this kind +of sample. + +So I'll just take the 1 and the +b back over to the other + +side, and I've got 1 minus b. + +OK? + +Well, we can do the same +trick with x minus. + +If we've got a negative sample, + +then y sub i is negative. + +That gives us our negative +w times dot over x sub i. + +But now, we take this stuff back +over to the right side, + +and we get 1 plus b. + +So that all licenses to rewrite +this thing as 2 over + +the magnitude of w. + +How did I get there? + +Well, I decided I was going to +enforce this constraint. + +I noted that the width of the +street has got to be this + +difference vector times +a unit vector. + +Then, I used the constraint to +plug back some values here. + +And I discovered to my delight +and amazement that the width + +of the street is 2 over +the magnitude of w. + +Yes, Brett? + +STUDENT: So your first x +plus is minus b, and x + +minus is 1 plus b. + +PATRICK WINSTON: Yeah. + +STUDENT: So you're +subtracting it? + +PATRICK WINSTON: Let's see. + +If I've got a minus here, then +that makes that minus, and + +then, the b is minus, and when I +take the b over to the other + +side it becomes plus. + +STUDENT: Yeah, so if you +subtract the left with the + +right [INAUDIBLE]. + +PATRICK WINSTON: No. + +No, sorry. + +This expression here +is 1 plus b. + +Trust me it works. + +I haven't got my legs all +tangled up like last Friday, + +well, not yet, anyway. + +It's possible. + +There's going to be a lot of +algebra here eventually. + +So this quantity here, this +is miracle number three. + +This quantity here is the +width of the street. + +And what we're trying to +do is we're trying to + +maximize that, right? + +So we want to maximize 2 over +the magnitude of w if we're to + +get the widest street under +the constraints that we've + +decided that we're going +to work with. + +All right. + +So that means that it's OK to +maximize 1 over w, instead. + +We just drop the constant. + +And that means that it's +OK to minimize the + +magnitude of w, right? + +And that means that it's OK +to minimize 1/2 times the + +magnitude of w squared. + +Right, Brett? + +Why did I do that? + +Why did I multiply by +1/2 and square it? + +STUDENT: Because it's +mathematically convenient. + +PATRICK WINSTON: It's +mathematically convenient. + +Thank you. + +So this is point number three +in the development. + +So where do we go? + +We decided that was going +to be our decision rule. + +We're going to see which side +of the line we're on. + +We decided to constrain the +situation, so the value of the + +decision rule is plus 1 in the +gutters for the positive + +samples and minus 1 +in the gutters for + +the negative samples. + +And then, we discovered that +maximizing the width of the + +street led us to an expression +like that, + +which we wish to maximize. + +Should we take a break? + +Should we get coffee? + +Too bad, we can't do that in +this kind of situation. + +But we would if we could. + +And I'm sure when Vapnik +got to this point, he + +went out for coffee. + +So now, we back up, and we say, +well, let's let these + +expressions start developing +into a song. + +Not like that, that's vapid, +speaking of Vapnik. + +What song is it going to sing? + +We've got an expression here +that we'd like to find the + +minimum of, the extremum of. + +And we've got some constraints +here that we + +would like to honor. + +What are we going to do? + +Let me put what we're going +to do to you in + +the form of a puzzle. + +Is it got something to +do with Legendre? + +Has it got something +to do with Laplace? + +Or does it have something +to do with Lagrange? + +She says Lagrange. + +Actually, all three were said +to be on Fourier's Doctoral + +Defense Committee-- must have +been quite an example. + +But we want to talk about +Lagrange, because we've got a + +situation here. + +Is this 1801? + +1802? + +1802. + +We learned in 1802 that if we +going to find the extremum of + +a function with constraints, +then we're going to have to + +use Lagrange multipliers. + +That would give us a new +expression, which we can + +maximize or minimize without +thinking about + +the constraints anymore. + +That's how Lagrange +multipliers work. + +So this brings us to miracle +number four, developmental + +piece number four. + +And it works like this. + +We're going to say that L-- + +the thing we're going to try +to maximize in order to + +maximize the width +of the street-- + +is equal to 1/2 times the +magnitude of that vector, w, + +squared minus. + +And now, we've got to have +a summation over all the + +constraints. + +And each or those constraints is +going to have a multiplier, + +alpha sub i. + +And then, we write down +the constraint. + +And when we write down +a constraint, + +there it is up there. + +And I've got to be hyper +careful here, because, + +otherwise, I'll get lost +in the algebra. + +So the constraint is y sub i +times vector, w, dotted with + +vector x sub i plus b, and +now, I've got a closing + +parenthesis, a minus 1. + +That's the end of my constraint, +like so. + +I sure hope I've got that right, +because I'll be in deep + +trouble if that's wrong. + +Anybody see any bugs in that? + +That looks right. doesn't it? + +We've got the original thing +we're trying to work with. + +Now, we've got Lagrange +multipliers all multiplied. + +It's back to that constraint +up there, where each + +constraint is constrained +to be 0. + +Well, there's a little bit of +mathematical slight of hand + +here, because in the end, the +ones that are going to be 0, + +the Lagrange multipliers here. + +The ones that are going to be +non 0 are going to be the ones + +connected with vectors that +lie in the gutter. + +The rest are going to be 0. + +But in any event, we can pretend +that this is what + +we're doing. + +I don't care whether it's +a maximum or minimum. + +I've lost track. + +But what we're going to do is +we're going to try to find an + +extremum of that. + +So what do we do? + +What does 1801 teach us about? + +Finding the maximum-- + +well, we've got to find the +derivatives and set them to 0. + +And then, after we've done that, +a little bit of that + +manipulation, we're going +to see a wonderful + +song start to emerge. + +So let's see if we can do it. + +Let's take the partial of L, the +Lagrangian, with respect + +to the vector, w. + +Oh my God, how do you +differentiate with + +respect to a vector? + +It turns out that it has a form +that looks exactly like + +differentiating with respect +to a scalar. + +And the way you prove that to +yourself is you just expand + +everything in terms of all of +the vector's components. + +You differentiate those with +respect to what you're + +differentiating with respect +to, and everything + +turns out the same. + +So what you get when you +differentiate this with + +respect to the vector, w, is 2 +comes down, and we have just + +magnitude of w. + +Was it the magnitude of w? + +Yeah, like so. + +Was it the magnitude of w? + +Oh, it's not the +magnitude of w. + +It's just w, like so, no +magnitude involved. + +Then, we've got a w over here, +so we've got to differentiate + +this part with respect +to w, as well. + +But that part's a lot easier, +because all we + +have there is a w. + +There's no magnitude. + +It's not raised to any power. + +So what's w multiplied by? + +Well, it's multiplied by x and +y sub i and alpha sub i. + +All right. + +So that means that this +expression, this derivative of + +the Lagrangian, with respect to +w is going to be equal to w + +minus the sum of alpha sub i, +y sub i, x sub i, and that's + +got to be set to 0. + +And that implies that w is equal +to the sum of some alpha + +i, some scalars, times this +minus 1 or plus 1 variable + +times x sub i over i. + +And now, the math is +beginning to sing. + +Because it tells us that the +vector w is a linear sum of + +the samples, all the samples +or some of the sample. + +It didn't have to be that way. + +It could have been raised +to a power. + +It could have been +a logarithm. + +All sorts of horrible +things could have + +happened when we did this. + +But when we did this, we +discovered that w is going to + +be equal to a linear some +of these vectors here. + +Some of the vectors in the +sample set, and I say some, + +because for some alpha +will be 0. + +All right. + +So this is something that we +want to take note of as + +something important. + +Now, of course, we've got to +differentiate L with respect + +to anything else it might +vary, so we've got to + +differentiate L with respect +to b, as well. + +So what's that going +to be equal to? + +Well, there's no b in here, so +that makes no contribution. + +This part here doesn't have a +b in it, so that makes no + +contribution. + +There's no b over here, so that +makes no contribution. + +So we've got alpha i times +y sub i times b. + +That has a contribution. + +So that's going to be the sum +of alpha i times y sub i. + +And then, we're differentiating +with respect + +to b, so that disappears. + +There's a minus sign here, and +that's equal to 0, or that + +implies that the sum of the +alpha i times y sub + +i is equal to 0. + +Hm, that looks like that might +be helpful somewhere. + +And now, it's time +for more coffee. + +By the way, these coffee +periods take months. + +You stare at it. + +You work on something else. + +You've got to worry +about your finals. + +And you think about +it some more. + +And eventually, you come +back from coffee + +and do the next thing. + +Oh, what is the next thing? + +Well, we've still got this +expression that we're trying + +to find the minimum for. + +And you say to yourself, this +is really a job for the + +numerical analysts. + +Those guys know about +this sort of stuff. + +Because of that little power +in there, that square. + +This is a so-called quadratic +optimization problem. + +So at this point, you would be +inclined to hand this problem + +over to a numerical analysts. + +They'll come back in a few +weeks with an algorithm. + +You implement the algorithm. + +And maybe things work. + +Maybe they don't converge. + +But any case, you don't +worry about it. + +But we're not going to do that, +because we want to do a + +little bit more math, because +we're interested + +in stuff like this. + +We're interested in the fact +that the decision vector is a + +linear sum of the samples. + +So we're going to work a little +harder on this stuff. + +And in particular, now that +we've got an expression for w, + +this one right here, we're +going to plug it back in + +there, and we're going to plug +it back in here and see what + +happens to that thing +we're trying to find + +the extremum of. + +Is everybody relaxed, +taking deep breath? + +Actually, this is the +easiest part. + +This is just doing a little +bit of the algebra. + +So the think we're trying +to maximize or + +minimize is equal to 1/2. + +And now, we've got to +have this vector + +here in there twice. + +Right? + +Because we're multiplying +the two together. + +So let's see. + +We've got from that expression +up there, one of those w's + +will just be the sum of the +alpha i times y sub i times + +the vector x sub i. + +And then, we've got the +other one, too. + +So that's just going to +be the sum of alpha. + +Now, I'm going to, actually, +eventually, squish those two + +sums together into a double +summation, so I have to keep + +the indexes straight. + +So I'm just going to write +that as alpha sub j, y + +sub j, x sub j. + +So those are my two vectors and +I'm going to take the dot + +product of those. + +That's the first piece, right? + +Boy, this is hard. + +So minus, and now, the next term +looks like alpha i, y sub + +i, x sub i times w. + +So you've got a whole +bunch of these. + +We've got a sum of alpha i times +y sub i times x sub i, + +and then, that gets multiplied +times w. + +So we'll put this like this, the +sum of alpha j, y sub j, x + +sub j in there like that. + +And then, that's the dot +product like that. + +That wasn't as bad +as I thought. + +Now, I've got to deal with the +next term, the alpha i times y + +sub i times b. + +So that's minus sub of alpha +i times y sub i times b. + +And then, to finish it off, we +have plus the sum of alpha sub + +i minus 1 up there, minus 1 in +front of the summation, such + +as the sum of the alphas. + +Are you with me so far? + +Just a little algebra. + +It looks good. + +I think I haven't +mucked it, yet. + +Let's see. + +alpha i times y sub i times +b. b is a constant. + +So pull that out there, and +then, I just got the sum of + +alpha sub i times y sub i. + +Oh, that's good. + +That's 0. + +Now, so for every one of these +terms, we dot it with this + +whole expression. + +So that's just like taking this +thing here and dotting + +those two things together, +right? + +Oh, but that's just the same +thing we've got here. + +So now, what we can do is we +can say that we can rewrite + +this Lagrangian as-- + +we've got that sum of alpha i. + +That's the positive element. + +And then, we've got one of +these and half of these. + +So that's minus 1/2. + +And now, I'll just convert that +whole works into a double + +sum over both i and j of alpha +i times alpha j times y sub i + +times y sub j times x sub +i dotted with x of j. + +We sure went through a lot of +trouble to get there, but now, + +we've got it. + +And we know that what we're +trying to do is we're trying + +to find a maximum of +that expression. + +And that's the one we're +going to had off to + +the numerical analysts. + +So if we're going to had this +off to the numerical analysts + +anyway, why did I go to +all this trouble? + +Good question. + +Do you have any idea why I +went to all this trouble? + +Because I wanted to find out +the dependence of this + +expression. + +Wanda is telling me. + +I'm translating as I go. + +She's telling me in Romanian. + +I want to find what this +maximization depends on with + +respect these vectors, the +x, the sample vectors. + +And what I've discovered is that +the optimization depends + +only on the dot product +of pairs of samples. + +And that's something we +want to keep in mind. + +That's why I put it +in royal purple. + +Now, up here, so let's see. + +What do we call that +one up there? + +That's two. + +I guess, we'll call this +piece here three. + +This piece here is four. + +And now, there's +one more piece. + +Because I want to take that w, +and not only stick it back + +into that Lagrangian, I want +to stick it back into the + +decision rule. + +So now, my decision rule with +this expression for w is going + +to be w plugged into +that thing. + +So the decision rule is going to +look like the sum of alpha + +i times y sub i times x sub +i dotted with the unknown + +vector, like so. + +And we're going to, +I guess, add b. + +And we're going to say, if +that's greater than or equal + +to 0, then plus. + +So you see why the math is +beginning to sing to us now. + +Because now, we discover that +the decision rule, also, + +depends only on the dot product +of those sample + +vectors and the unknown. + +So the total of dependence +of all of the + +math on the dot products. + +All right. + +And now, I hear a whisper. + +Someone is saying, I +don't believe that + +mathematicians can do it. + +I don't think those numerical +analysts can find the + +optimization. + +I want to be sure of it. + +Give me ocular proof. + +So I'd like to run a +demonstration of it. + +OK. + +There's our sample problem. + +The one I started the +hour out with. + +Now, if the optimization +algorithm doesn't get stuck in + +a local maximum or something, +it should find a nice, + +straight line separating those +two guys to finding the widest + +street between the minuses +and the pluses. + +So in just a couple of steps, +you can see down + +there in step 11. + +It's decided that it's done +as much as it can on the + +optimization. + +And it's got three alphas. + +And you can see that the two +negative samples both figure + +into the solution, the weights +on the Lagrangian multipliers + +are given by those little +yellow bars. + +So the two negatives participate +in the solution as + +one of the positives, but the +other positive doesn't. + +So it has a 0 weight. + +So everything worked out well. + +Now, I said, as long as it +doesn't get stuck on a local + +maximum, guess what, those +mathematical friends of ours + +can tell us and prove +to us that this + +thing is a convex space. + +That means it can never get +stuck in a local maximum. + +So in contrast with things like +neural nets, where you + +have a plague of local maxima, +this guy never gets stuck in a + +local maxima. + +Let's try some other examples. + +Here's two vertical points-- + +no surprises there, right? + +Well, you say, well, +maybe it can't deal + +with diagonal points. + +Sure it can. + +How about this thing here? + +Yeah, it only needed two of the +points since any two, a + +plus or minus, will +define the street. + +Let's try this guy. + +Oh. + +What do you think? + +What happened here? + +Well, we're screwed, right? + +Because it's linearly +inseparable-- + +bad news. + +So in situations where it's +linearly inseparable, the + +mechanism struggles, and +eventually, it will just slow + +down and you truncate +it, because it's + +not making any progress. + +And you see the red dots there +are ones that it got wrong. + +So you say, well, too bad for +our side-- doesn't look like + +it's all that good anyway. + +But then, a powerful idea comes +to the rescue, when + +stuck switch to another +perspective. + +So if we don't like the space +that we're in, because it + +gives examples that are not +linearly separable, then we + +can say, oh, shoot. + +Here's our space. + +Here are two points. + +Here are two other points. + +We can't separate them. + +But if we could somehow get them +into another space, maybe + +we can separate them, because +they look like this in the + +other space, and they're +easy to separate. + +So what we need, then, is a +transformation that will take + +us from the space we're in into +a space where things are + +more convenient, so we're +going to call that + +transformation phi +with a vector, x. + +That's the transformation. + +And now, here's the reason +for all the magic. + +I said, that the maximization +only depends on dot products. + +So all I need to do the +maximization is the + +transformation of one vector +dotted with the transformation + +of another vector, like so. + +That's what I need to maximize, +or to find the + +maximum on. + +Then, in order to recognize-- + +where did it go? + +Underneath the chalkboard. + +Oh, yes. + +Here it is. + +To recognize, all I need +is dot products, too. + +So for that one I need phi of +x dotted with phi of u. + +And just to make this a little +bit more consistent, the + +notation, I'll call that +x j and this x sub i. + +And that's x sub i. + +Those are the quantities I +need in order to do it. + +So that means that if I have a +function, let's call it k of x + +sub i and x sub j, that's equal +to phi of x sub i dotted + +with phi of x sub j. + +Then, I'm done. + +This is what I need. + +I don't actually need this. + +All I need is that function, k, +which happens to be called + +a kernel function, which +provides me with the dot + +product of those two vectors +in another space. + +I don't have to know +the transformation + +into the other space. + +And that's the reason that +this stuff is a miracle. + +So what are some of the kernels +that are popular? + +One is the linear kernel that +says that u dotted with v plus + +1 to the n-th is such a kernel, +because it's got u in + +it and v in it, the +two vectors. + +And this is what the dot product +is in the other space. + +So that's one choice. + +Another choice is a kernel +that looks like + +this, e to the minus. + +Let's take the dot product +of the difference + +of those two guys. + +Let's take the magnitude +of that and + +divide it by some sigma. + +That's a second kind of kernel +that we can use. + +So let's go back and see if we +can solve this problem by + +transforming it into another +space where we have another + +perspective. + +So that's it. + +That's another kernel. + +And so sure, we can. + +And that's the answer when +transformed back into the + +original space. + +We can also try doing that +with a so-called + +radial basis kernel. + +That's the one with the +exponential in it. + +We can learn on that one. + +Boom. + +No problem. + +So we've got a general method +that's convex and guaranteed + +to produce a global solution. + +We've got a mechanism that +easily allows us to transform + +this into another space. + +So it works like a charm. + +Of course, it doesn't remove +all possible problems. + +Look at that exponential +thing here. + +If we choose a sigma that is +small enough, then those + +sigmas are essentially shrunk +right around the sample + +points, and we could +get overfitting. + +So it doesn't immunize us +against overfitting, but it + +does immunize us against local +maxima and does provide us + +with a general mechanism for +doing a transformation into + +another space with a +better perspective. + +Now, the history lesson, all +this stuff feels fairly new. + +It feels like it's younger +than you are. + +Here's the history of it. + +Vapnik immigrated from the +Soviet Union to the United + +States in about 1991. + +Nobody ever heard of this stuff +before he immigrated. + +He actually had done this work +on the basic support vector + +idea in his Ph.D. thesis +at Moscow University + +in the early '60s. + +But it wasn't possible for him +to do anything with it, + +because they didn't have any +computers they could try + +anything out with. + +So he spent the next 25 years at +some oncology institute in + +the Soviet Union doing +applications. + +Somebody from Bell Labs +discovers him, invites him + +over to the United States +where, subsequently, he + +decides to immigrate. + +In 1992, or thereabouts, Vapnik +submits three papers to + +NIPS, the Neural Information +Processing Systems journal. + +All of them were rejected. + +He's still sore about it, +but it's motivating. + +So around 1992, 1993, Bell +Labs was interested in + +hand-written character +recognition + +and in neural nets. + +Vapnik thinks that +neural nets-- + +what would be a good +word to use? + +I can think of the vernacular, +but he thinks that + +they're not very good. + +So he bets a colleague a good +dinner that support vector + +machines will eventually do +better at handwriting + +recognition then neural nets. + +And it's a dinner bet, right? + +It's not that big of deal. + +But as Napoleon said, it's +amazing what a soldier will do + +for a bit of ribbon. + +So that makes colleague, who's +working on this problem with + +handwritten recognition, decides +to try a support + +vector machine with a kernel, +in which n equals 2, just + +slightly nonlinear, works +like a charm. + +Was this the first time anybody +tried a kernel? + +Vapnik actually had the idea in +his thesis but never though + +it was very important. + +As soon as it was shown to work +in the early '90s on the + +problem handwriting recognition, +Vapnik + +resuscitated the idea of the +kernel, began to develop it, + +and became an essential part of +the whole approach of using + +support vector machines. + +So the main point about this +is that it was 30 years in + +between the concept and anybody +ever hearing about it. + +It was 30 years between Vapnik's +understanding of + +kernels and his appreciation +of their importance. + +And that's the way things often +go, great ideas followed + +by long periods of nothing +happening, followed by an + +epiphanous moment when the +original idea seemed to have + +great power with just a +little bit of a twist. + +And then, the world +never looks back. + +And Vapnik, who nobody ever +heard of until the early '90s, + +becomes famous for something +that everybody knows about + +today who does machine +learning. \ No newline at end of file diff --git a/_TEMQhpsGFg.txt b/_TEMQhpsGFg.txt new file mode 100644 index 0000000000000000000000000000000000000000..718ed2ed90da9a6e69dd0581816faa160e561bb5 --- /dev/null +++ b/_TEMQhpsGFg.txt @@ -0,0 +1,5467 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +last time we talked about the + + align:start position:0% +last time we talked about the + + + align:start position:0% +last time we talked about the +photoelectric effect what was that what + + align:start position:0% +photoelectric effect what was that what + + + align:start position:0% +photoelectric effect what was that what +were the important points yes yes okay + + align:start position:0% +were the important points yes yes okay + + + align:start position:0% +were the important points yes yes okay +so the idea of quantization of + + align:start position:0% +so the idea of quantization of + + + align:start position:0% +so the idea of quantization of +electromagnetic radiation and photons + + align:start position:0% +electromagnetic radiation and photons + + + align:start position:0% +electromagnetic radiation and photons +and the photon has an energy H times nu + + align:start position:0% +and the photon has an energy H times nu + + + align:start position:0% +and the photon has an energy H times nu +nu is the frequency and the evidence was + + align:start position:0% +nu is the frequency and the evidence was + + + align:start position:0% +nu is the frequency and the evidence was +mostly from a plot of what versus what + + align:start position:0% +mostly from a plot of what versus what + + + align:start position:0% +mostly from a plot of what versus what +somebody else yes exactly + + align:start position:0% +somebody else yes exactly + + + align:start position:0% +somebody else yes exactly +and and the the slope of that plot which + + align:start position:0% +and and the the slope of that plot which + + + align:start position:0% +and and the the slope of that plot which +was H is universal it doesn't matter + + align:start position:0% +was H is universal it doesn't matter + + + align:start position:0% +was H is universal it doesn't matter +where the electron came from and this + + align:start position:0% +where the electron came from and this + + + align:start position:0% +where the electron came from and this +was really an amazing thing and then the + + align:start position:0% +was really an amazing thing and then the + + + align:start position:0% +was really an amazing thing and then the +other thing we talked about was compton + + align:start position:0% +other thing we talked about was compton + + + align:start position:0% +other thing we talked about was compton +scattering and what did compton + + align:start position:0% +scattering and what did compton + + + align:start position:0% +scattering and what did compton +scattering tell us yes yes and and so + + align:start position:0% +scattering tell us yes yes and and so + + + align:start position:0% +scattering tell us yes yes and and so +we're all we're we're interested in the + + align:start position:0% +we're all we're we're interested in the + + + align:start position:0% +we're all we're we're interested in the +particle like character of what we think + + align:start position:0% +particle like character of what we think + + + align:start position:0% +particle like character of what we think +of as waves and we we saw that the waves + + align:start position:0% +of as waves and we we saw that the waves + + + align:start position:0% +of as waves and we we saw that the waves +were particles and particles or at least + + align:start position:0% +were particles and particles or at least + + + align:start position:0% +were particles and particles or at least +packets and these packets had definite + + align:start position:0% +packets and these packets had definite + + + align:start position:0% +packets and these packets had definite +momentum and that was a wonderful + + align:start position:0% + + + + align:start position:0% + +observation so today this is the menu of + + align:start position:0% +observation so today this is the menu of + + + align:start position:0% +observation so today this is the menu of +what i'm going to talk about and at the + + align:start position:0% +what i'm going to talk about and at the + + + align:start position:0% +what i'm going to talk about and at the +end there's a magic word spectra and i + + align:start position:0% +end there's a magic word spectra and i + + + align:start position:0% +end there's a magic word spectra and i +like that + + align:start position:0% +like that + + + align:start position:0% +like that +because what we're going to be + + align:start position:0% +because what we're going to be + + + align:start position:0% +because what we're going to be +discovering today is that the internal + + align:start position:0% +discovering today is that the internal + + + align:start position:0% +discovering today is that the internal +structure of atoms and molecules we are + + align:start position:0% +structure of atoms and molecules we are + + + align:start position:0% +structure of atoms and molecules we are +not allowed to observe it directly but + + align:start position:0% +not allowed to observe it directly but + + + align:start position:0% +not allowed to observe it directly but +it's surprising and it's encoded in + + align:start position:0% +it's surprising and it's encoded in + + + align:start position:0% +it's surprising and it's encoded in +something which we can observe which is + + align:start position:0% +something which we can observe which is + + + align:start position:0% +something which we can observe which is +a spectrum and the spectrum that I will + + align:start position:0% +a spectrum and the spectrum that I will + + + align:start position:0% +a spectrum and the spectrum that I will +show you at the end is one that is + + align:start position:0% +show you at the end is one that is + + + align:start position:0% +show you at the end is one that is +contains essentially no information but + + align:start position:0% +contains essentially no information but + + + align:start position:0% +contains essentially no information but +acts attempt acts as a template for what + + align:start position:0% +acts attempt acts as a template for what + + + align:start position:0% +acts attempt acts as a template for what +we really want to know about how things + + align:start position:0% +we really want to know about how things + + + align:start position:0% +we really want to know about how things +are different from hydrogen atom and + + align:start position:0% +are different from hydrogen atom and + + + align:start position:0% +are different from hydrogen atom and +that's the beginning of our our + + align:start position:0% +that's the beginning of our our + + + align:start position:0% +that's the beginning of our our +exploration of the structure of atoms + + align:start position:0% +exploration of the structure of atoms + + + align:start position:0% +exploration of the structure of atoms +and molecules it's through the spectrum + + align:start position:0% +and molecules it's through the spectrum + + + align:start position:0% +and molecules it's through the spectrum +and it's how it's different from in + + align:start position:0% +and it's how it's different from in + + + align:start position:0% +and it's how it's different from in +subtle ways the spectrum of the hydrogen + + align:start position:0% +subtle ways the spectrum of the hydrogen + + + align:start position:0% +subtle ways the spectrum of the hydrogen +atom ok so we're going to turn our focus + + align:start position:0% +atom ok so we're going to turn our focus + + + align:start position:0% +atom ok so we're going to turn our focus +today to the electron as opposed to + + align:start position:0% +today to the electron as opposed to + + + align:start position:0% +today to the electron as opposed to +light and we're going to play the same + + align:start position:0% +light and we're going to play the same + + + align:start position:0% +light and we're going to play the same +game we know the electron is a particle + + align:start position:0% +game we know the electron is a particle + + + align:start position:0% +game we know the electron is a particle +does anyone tell me why we know that is + + align:start position:0% +does anyone tell me why we know that is + + + align:start position:0% +does anyone tell me why we know that is +there any anybody who's got a clue you + + align:start position:0% +there any anybody who's got a clue you + + + align:start position:0% +there any anybody who's got a clue you +could get oh good yes yes I love that + + align:start position:0% +could get oh good yes yes I love that + + + align:start position:0% +could get oh good yes yes I love that +experiment that's the Millican + + align:start position:0% +experiment that's the Millican + + + align:start position:0% +experiment that's the Millican +experiment and and one of the reasons I + + align:start position:0% +experiment and and one of the reasons I + + + align:start position:0% +experiment and and one of the reasons I +love it is because Milliken and Mulliken + + align:start position:0% +love it is because Milliken and Mulliken + + + align:start position:0% +love it is because Milliken and Mulliken +are two different people and it's so I + + align:start position:0% +are two different people and it's so I + + + align:start position:0% +are two different people and it's so I +find that it's really easy to come up + + align:start position:0% +find that it's really easy to come up + + + align:start position:0% +find that it's really easy to come up +with one of them and I remember Mulliken + + align:start position:0% +with one of them and I remember Mulliken + + + align:start position:0% +with one of them and I remember Mulliken +is a spectroscopy and Milliken was a + + align:start position:0% +is a spectroscopy and Milliken was a + + + align:start position:0% +is a spectroscopy and Milliken was a +different kind of physicist and but + + align:start position:0% +different kind of physicist and but + + + align:start position:0% +different kind of physicist and but +they're both famous and they both have + + align:start position:0% +they're both famous and they both have + + + align:start position:0% +they're both famous and they both have +connections to important universities + + align:start position:0% +connections to important universities + + + align:start position:0% +connections to important universities +University of Chicago for Milliken and + + align:start position:0% +University of Chicago for Milliken and + + + align:start position:0% +University of Chicago for Milliken and +Mulliken MIT and Caltech okay + + align:start position:0% + + + + align:start position:0% + +so we're we're going to be looking at + + align:start position:0% +so we're we're going to be looking at + + + align:start position:0% +so we're we're going to be looking at +something that we know as a particle and + + align:start position:0% +something that we know as a particle and + + + align:start position:0% +something that we know as a particle and +we're going to show that it has wave + + align:start position:0% +we're going to show that it has wave + + + align:start position:0% +we're going to show that it has wave +characteristics and and so we want to be + + align:start position:0% +characteristics and and so we want to be + + + align:start position:0% +characteristics and and so we want to be +able to show that the electron has a + + align:start position:0% +able to show that the electron has a + + + align:start position:0% +able to show that the electron has a +wavelength and it follows the same + + align:start position:0% +wavelength and it follows the same + + + align:start position:0% +wavelength and it follows the same +equation that we used to describe the + + align:start position:0% +equation that we used to describe the + + + align:start position:0% +equation that we used to describe the +behavior of electromagnetic radiation so + + align:start position:0% +behavior of electromagnetic radiation so + + + align:start position:0% +behavior of electromagnetic radiation so +how would we control the momentum of an + + align:start position:0% +how would we control the momentum of an + + + align:start position:0% +how would we control the momentum of an +electron yes okay so we know we know we + + align:start position:0% +electron yes okay so we know we know we + + + align:start position:0% +electron yes okay so we know we know we +can easily measure the momentum of a + + align:start position:0% +can easily measure the momentum of a + + + align:start position:0% +can easily measure the momentum of a +particle that's not a big challenge and + + align:start position:0% +particle that's not a big challenge and + + + align:start position:0% +particle that's not a big challenge and +but then how would we measure its + + align:start position:0% +but then how would we measure its + + + align:start position:0% +but then how would we measure its +wavelength yes yes we basically use some + + align:start position:0% +wavelength yes yes we basically use some + + + align:start position:0% +wavelength yes yes we basically use some +material which acts as a ruler we have a + + align:start position:0% +material which acts as a ruler we have a + + + align:start position:0% +material which acts as a ruler we have a +thin metal foil and the distances + + align:start position:0% +thin metal foil and the distances + + + align:start position:0% +thin metal foil and the distances +between atoms in the foil + + align:start position:0% +between atoms in the foil + + + align:start position:0% +between atoms in the foil +are constant and and so that's the ruler + + align:start position:0% +are constant and and so that's the ruler + + + align:start position:0% +are constant and and so that's the ruler +against which we measure the wavelength + + align:start position:0% +against which we measure the wavelength + + + align:start position:0% +against which we measure the wavelength +of light and so we'll talk about the + + align:start position:0% +of light and so we'll talk about the + + + align:start position:0% +of light and so we'll talk about the +Geiger Marsden the Davis and Germer + + align:start position:0% +Geiger Marsden the Davis and Germer + + + align:start position:0% +Geiger Marsden the Davis and Germer +experiment where we measure the + + align:start position:0% +experiment where we measure the + + + align:start position:0% +experiment where we measure the +wavelength and then we'll talk about the + + align:start position:0% +wavelength and then we'll talk about the + + + align:start position:0% +wavelength and then we'll talk about the +Geiger Marsden experiment where we say + + align:start position:0% +Geiger Marsden experiment where we say + + + align:start position:0% +Geiger Marsden experiment where we say +well my atoms have electrons in them and + + align:start position:0% +well my atoms have electrons in them and + + + align:start position:0% +well my atoms have electrons in them and +what is the structure of an atom + + align:start position:0% +what is the structure of an atom + + + align:start position:0% +what is the structure of an atom +remember we can't look inside so we have + + align:start position:0% +remember we can't look inside so we have + + + align:start position:0% +remember we can't look inside so we have +to use some kind of an experiment to be + + align:start position:0% +to use some kind of an experiment to be + + + align:start position:0% +to use some kind of an experiment to be +able to look inside the atom now + + align:start position:0% +able to look inside the atom now + + + align:start position:0% +able to look inside the atom now +physicists are very have one trick they + + align:start position:0% +physicists are very have one trick they + + + align:start position:0% +physicists are very have one trick they +often use and that to find out the + + align:start position:0% +often use and that to find out the + + + align:start position:0% +often use and that to find out the +internal structure of something they + + align:start position:0% +internal structure of something they + + + align:start position:0% +internal structure of something they +shoot a particle or a wave at it that + + align:start position:0% +shoot a particle or a wave at it that + + + align:start position:0% +shoot a particle or a wave at it that +has a wavelength comparable to the + + align:start position:0% +has a wavelength comparable to the + + + align:start position:0% +has a wavelength comparable to the +distances you're hoping to measure and + + align:start position:0% +distances you're hoping to measure and + + + align:start position:0% +distances you're hoping to measure and +so if you have a very high energy probe + + align:start position:0% +so if you have a very high energy probe + + + align:start position:0% +so if you have a very high energy probe +particle it will have a very short + + align:start position:0% +particle it will have a very short + + + align:start position:0% +particle it will have a very short +wavelength and it will look sort of like + + align:start position:0% +wavelength and it will look sort of like + + + align:start position:0% +wavelength and it will look sort of like +a bullet and we know how bullets scatter + + align:start position:0% +a bullet and we know how bullets scatter + + + align:start position:0% +a bullet and we know how bullets scatter +off of targets or hit targets and we + + align:start position:0% +off of targets or hit targets and we + + + align:start position:0% +off of targets or hit targets and we +also if we choose the wavelength to be + + align:start position:0% +also if we choose the wavelength to be + + + align:start position:0% +also if we choose the wavelength to be +comparable to the distances we're + + align:start position:0% +comparable to the distances we're + + + align:start position:0% +comparable to the distances we're +expecting to measure then we're going to + + align:start position:0% +expecting to measure then we're going to + + + align:start position:0% +expecting to measure then we're going to +see diffraction this is a kind of + + align:start position:0% +see diffraction this is a kind of + + + align:start position:0% +see diffraction this is a kind of +subject that lends itself to exam + + align:start position:0% +subject that lends itself to exam + + + align:start position:0% +subject that lends itself to exam +questions ok so let's start out by + + align:start position:0% +questions ok so let's start out by + + + align:start position:0% +questions ok so let's start out by +talking about the Geiger Marsden + + align:start position:0% +talking about the Geiger Marsden + + + align:start position:0% +talking about the Geiger Marsden +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +I think the Davidson Germer experiment + + align:start position:0% +I think the Davidson Germer experiment + + + align:start position:0% +I think the Davidson Germer experiment +so we have a beam of x-rays and or a + + align:start position:0% +so we have a beam of x-rays and or a + + + align:start position:0% +so we have a beam of x-rays and or a +beam of electrons either one and we have + + align:start position:0% +beam of electrons either one and we have + + + align:start position:0% +beam of electrons either one and we have +a aluminum foil and we have since it's + + align:start position:0% +a aluminum foil and we have since it's + + + align:start position:0% +a aluminum foil and we have since it's +an intense beam we wanted to stop most + + align:start position:0% +an intense beam we wanted to stop most + + + align:start position:0% +an intense beam we wanted to stop most +of it before it hits a detector and so + + align:start position:0% +of it before it hits a detector and so + + + align:start position:0% +of it before it hits a detector and so +this is some kind of a screen or and so + + align:start position:0% +this is some kind of a screen or and so + + + align:start position:0% +this is some kind of a screen or and so +what we're looking for is when the + + align:start position:0% +what we're looking for is when the + + + align:start position:0% +what we're looking for is when the +x-rays or the electrons scatter off of + + align:start position:0% +x-rays or the electrons scatter off of + + + align:start position:0% +x-rays or the electrons scatter off of +this ruler we get something that appears + + align:start position:0% +this ruler we get something that appears + + + align:start position:0% +this ruler we get something that appears +on the screen as + + align:start position:0% + + + + align:start position:0% + +pairs of circles these are this is the + + align:start position:0% +pairs of circles these are this is the + + + align:start position:0% +pairs of circles these are this is the +powder pattern because this is a multi + + align:start position:0% +powder pattern because this is a multi + + + align:start position:0% +powder pattern because this is a multi +crystalline subject object but in each + + align:start position:0% +crystalline subject object but in each + + + align:start position:0% +crystalline subject object but in each +object we have a bunch of equally spaced + + align:start position:0% +object we have a bunch of equally spaced + + + align:start position:0% +object we have a bunch of equally spaced +atoms where this is the lattice constant + + align:start position:0% +atoms where this is the lattice constant + + + align:start position:0% +atoms where this is the lattice constant +and this is the square root of 2 tangent + + align:start position:0% +and this is the square root of 2 tangent + + + align:start position:0% +and this is the square root of 2 tangent +lattice constant so each atom has + + align:start position:0% +lattice constant so each atom has + + + align:start position:0% +lattice constant so each atom has +nearest neighbors and second nearest + + align:start position:0% +nearest neighbors and second nearest + + + align:start position:0% +nearest neighbors and second nearest +neighbors and so we have two rulers + + align:start position:0% +neighbors and so we have two rulers + + + align:start position:0% +neighbors and so we have two rulers +going on and one ruler will give one set + + align:start position:0% +going on and one ruler will give one set + + + align:start position:0% +going on and one ruler will give one set +of rings and the other ruler will give a + + align:start position:0% +of rings and the other ruler will give a + + + align:start position:0% +of rings and the other ruler will give a +different set of rings and because these + + align:start position:0% +different set of rings and because these + + + align:start position:0% +different set of rings and because these +particles are randomly oriented instead + + align:start position:0% +particles are randomly oriented instead + + + align:start position:0% +particles are randomly oriented instead +of having spots you have circles and + + align:start position:0% +of having spots you have circles and + + + align:start position:0% +of having spots you have circles and +there's all sorts of information in + + align:start position:0% +there's all sorts of information in + + + align:start position:0% +there's all sorts of information in +these part of powder patterns but + + align:start position:0% +these part of powder patterns but + + + align:start position:0% +these part of powder patterns but +basically they're they're saying well + + align:start position:0% +basically they're they're saying well + + + align:start position:0% +basically they're they're saying well +we're seeing a structure which is + + align:start position:0% +we're seeing a structure which is + + + align:start position:0% +we're seeing a structure which is +related to something we know how would + + align:start position:0% +related to something we know how would + + + align:start position:0% +related to something we know how would +we know the distance between atoms in a + + align:start position:0% +we know the distance between atoms in a + + + align:start position:0% +we know the distance between atoms in a +in a foil using macroscopic measurements + + align:start position:0% +in a foil using macroscopic measurements + + + align:start position:0% +in a foil using macroscopic measurements +yes you're hot today that's it yes so + + align:start position:0% +yes you're hot today that's it yes so + + + align:start position:0% +yes you're hot today that's it yes so +it's a it's a simple matter to know at + + align:start position:0% +it's a it's a simple matter to know at + + + align:start position:0% +it's a it's a simple matter to know at +least what is the magnitude of the + + align:start position:0% +least what is the magnitude of the + + + align:start position:0% +least what is the magnitude of the +distance there's there's an issue of + + align:start position:0% +distance there's there's an issue of + + + align:start position:0% +distance there's there's an issue of +what is the crystal structure and there + + align:start position:0% +what is the crystal structure and there + + + align:start position:0% +what is the crystal structure and there +are different structures and that will + + align:start position:0% +are different structures and that will + + + align:start position:0% +are different structures and that will +give rise to different features in the + + align:start position:0% +give rise to different features in the + + + align:start position:0% +give rise to different features in the +powder pattern but the important thing + + align:start position:0% +powder pattern but the important thing + + + align:start position:0% +powder pattern but the important thing +is we do this we we look at the pattern + + align:start position:0% +is we do this we we look at the pattern + + + align:start position:0% +is we do this we we look at the pattern +that emerges when we shoot x-rays at + + align:start position:0% +that emerges when we shoot x-rays at + + + align:start position:0% +that emerges when we shoot x-rays at +this screen and we already know that + + align:start position:0% +this screen and we already know that + + + align:start position:0% +this screen and we already know that +x-rays have wavelengths and so and we + + align:start position:0% +x-rays have wavelengths and so and we + + + align:start position:0% +x-rays have wavelengths and so and we +can and we know that they have momentum + + align:start position:0% +can and we know that they have momentum + + + align:start position:0% +can and we know that they have momentum +and because we we we we know about the + + align:start position:0% +and because we we we we know about the + + + align:start position:0% +and because we we we we know about the +scattering of + + align:start position:0% + + + + align:start position:0% + +photons and as a result we we know that + + align:start position:0% +photons and as a result we we know that + + + align:start position:0% +photons and as a result we we know that +we can predict exactly what the the + + align:start position:0% +we can predict exactly what the the + + + align:start position:0% +we can predict exactly what the the +pattern associated with the x-ray + + align:start position:0% +pattern associated with the x-ray + + + align:start position:0% +pattern associated with the x-ray +scattering is going to be and then we do + + align:start position:0% +scattering is going to be and then we do + + + align:start position:0% +scattering is going to be and then we do +the same thing with electrons and now + + align:start position:0% +the same thing with electrons and now + + + align:start position:0% +the same thing with electrons and now +for the electrons we can true can + + align:start position:0% +for the electrons we can true can + + + align:start position:0% +for the electrons we can true can +control the momentum that's easy and + + align:start position:0% +control the momentum that's easy and + + + align:start position:0% +control the momentum that's easy and +what we want to know is what is the + + align:start position:0% +what we want to know is what is the + + + align:start position:0% +what we want to know is what is the +wavelength and we have the wavelength of + + align:start position:0% +wavelength and we have the wavelength of + + + align:start position:0% +wavelength and we have the wavelength of +the x-rays and so what we do is we vary + + align:start position:0% +the x-rays and so what we do is we vary + + + align:start position:0% +the x-rays and so what we do is we vary +the momentum of the electrons until the + + align:start position:0% +the momentum of the electrons until the + + + align:start position:0% +the momentum of the electrons until the +powder pattern for the electron of the + + align:start position:0% +powder pattern for the electron of the + + + align:start position:0% +powder pattern for the electron of the +diffraction pattern for the electron is + + align:start position:0% +diffraction pattern for the electron is + + + align:start position:0% +diffraction pattern for the electron is +exactly the same as the diffraction + + align:start position:0% +exactly the same as the diffraction + + + align:start position:0% +exactly the same as the diffraction +pattern for the x-ray and we discover + + align:start position:0% +pattern for the x-ray and we discover + + + align:start position:0% +pattern for the x-ray and we discover +that for the electron we have the same + + align:start position:0% +that for the electron we have the same + + + align:start position:0% +that for the electron we have the same +result okay so we have now photons they + + align:start position:0% +result okay so we have now photons they + + + align:start position:0% +result okay so we have now photons they +have wavelengths and momenta the + + align:start position:0% +have wavelengths and momenta the + + + align:start position:0% +have wavelengths and momenta the +momentum was the surprise for the + + align:start position:0% +momentum was the surprise for the + + + align:start position:0% +momentum was the surprise for the +photons and we have particles which have + + align:start position:0% +photons and we have particles which have + + + align:start position:0% +photons and we have particles which have +wavelengths in momentum and the + + align:start position:0% +wavelengths in momentum and the + + + align:start position:0% +wavelengths in momentum and the +wavelength was a surprise for the + + align:start position:0% +wavelength was a surprise for the + + + align:start position:0% +wavelength was a surprise for the +particle so it doesn't matter everything + + align:start position:0% +particle so it doesn't matter everything + + + align:start position:0% +particle so it doesn't matter everything +follows this equation and this equation + + align:start position:0% +follows this equation and this equation + + + align:start position:0% +follows this equation and this equation +was anticipated by + + align:start position:0% +was anticipated by + + + align:start position:0% +was anticipated by +Debray who in his PhD thesis you know + + align:start position:0% +Debray who in his PhD thesis you know + + + align:start position:0% +Debray who in his PhD thesis you know +he's a person about your age and he + + align:start position:0% +he's a person about your age and he + + + align:start position:0% +he's a person about your age and he +wrote his thesis in 1924 and among other + + align:start position:0% +wrote his thesis in 1924 and among other + + + align:start position:0% +wrote his thesis in 1924 and among other +brilliant things he said that everything + + align:start position:0% +brilliant things he said that everything + + + align:start position:0% +brilliant things he said that everything +should follow this simple equation and + + align:start position:0% + + + + align:start position:0% + +that was a brave statement and it it it + + align:start position:0% +that was a brave statement and it it it + + + align:start position:0% +that was a brave statement and it it it +predicted that the broy was going to + + align:start position:0% +predicted that the broy was going to + + + align:start position:0% +predicted that the broy was going to +make a lot of brilliant statements in + + align:start position:0% +make a lot of brilliant statements in + + + align:start position:0% +make a lot of brilliant statements in +his career and this was just the first + + align:start position:0% +his career and this was just the first + + + align:start position:0% +his career and this was just the first +of and one of the nicest but we'll hear + + align:start position:0% +of and one of the nicest but we'll hear + + + align:start position:0% +of and one of the nicest but we'll hear +a little bit more about the broy by the + + align:start position:0% +a little bit more about the broy by the + + + align:start position:0% +a little bit more about the broy by the +time i finished with this lecture okay + + align:start position:0% + + + + align:start position:0% + +so we're now worried about atoms and we + + align:start position:0% +so we're now worried about atoms and we + + + align:start position:0% +so we're now worried about atoms and we +already know that atoms have a diameter + + align:start position:0% +already know that atoms have a diameter + + + align:start position:0% +already know that atoms have a diameter +roughly we know that from the density + + align:start position:0% +roughly we know that from the density + + + align:start position:0% +roughly we know that from the density +the typical size we like to have + + align:start position:0% +the typical size we like to have + + + align:start position:0% +the typical size we like to have +quantities that describe microscopic + + align:start position:0% +quantities that describe microscopic + + + align:start position:0% +quantities that describe microscopic +objects which are not like ten to the + + align:start position:0% +objects which are not like ten to the + + + align:start position:0% +objects which are not like ten to the +minus twenty but like one to a hundred + + align:start position:0% +minus twenty but like one to a hundred + + + align:start position:0% +minus twenty but like one to a hundred +and and so the angstrom unit which is a + + align:start position:0% +and and so the angstrom unit which is a + + + align:start position:0% +and and so the angstrom unit which is a +ten to the minus ten meters is a very + + align:start position:0% +ten to the minus ten meters is a very + + + align:start position:0% +ten to the minus ten meters is a very +useful thing for talking about sizes of + + align:start position:0% +useful thing for talking about sizes of + + + align:start position:0% +useful thing for talking about sizes of +atoms and molecules okay so if we have + + align:start position:0% +atoms and molecules okay so if we have + + + align:start position:0% +atoms and molecules okay so if we have +an atom of a size about one angstrom we + + align:start position:0% +an atom of a size about one angstrom we + + + align:start position:0% +an atom of a size about one angstrom we +can use this equation to say well what + + align:start position:0% +can use this equation to say well what + + + align:start position:0% +can use this equation to say well what +would it take for an electron to fit + + align:start position:0% +would it take for an electron to fit + + + align:start position:0% +would it take for an electron to fit +inside an atom so we specify this we + + align:start position:0% +inside an atom so we specify this we + + + align:start position:0% +inside an atom so we specify this we +know this we know that and that + + align:start position:0% +know this we know that and that + + + align:start position:0% +know this we know that and that +determines what the momentum would have + + align:start position:0% +determines what the momentum would have + + + align:start position:0% +determines what the momentum would have +to be and these are all simple + + align:start position:0% +to be and these are all simple + + + align:start position:0% +to be and these are all simple +calculations and since I don't like + + align:start position:0% +calculations and since I don't like + + + align:start position:0% +calculations and since I don't like +doing calculations on the board and I + + align:start position:0% +doing calculations on the board and I + + + align:start position:0% +doing calculations on the board and I +don't really need to do this now + + align:start position:0% +don't really need to do this now + + + align:start position:0% +don't really need to do this now +you need to be able to do them quickly + + align:start position:0% +you need to be able to do them quickly + + + align:start position:0% +you need to be able to do them quickly +if I ask you on the exam but basically + + align:start position:0% +if I ask you on the exam but basically + + + align:start position:0% +if I ask you on the exam but basically +what we end up finding out is that the + + align:start position:0% +what we end up finding out is that the + + + align:start position:0% +what we end up finding out is that the +velocity of the electron + + align:start position:0% +velocity of the electron + + + align:start position:0% +velocity of the electron +but have to be 7.25 times ten to the six + + align:start position:0% +but have to be 7.25 times ten to the six + + + align:start position:0% +but have to be 7.25 times ten to the six +meters per second which is okay it's + + align:start position:0% +meters per second which is okay it's + + + align:start position:0% +meters per second which is okay it's +pretty fast it's a few percent of the + + align:start position:0% +pretty fast it's a few percent of the + + + align:start position:0% +pretty fast it's a few percent of the +speed of light but that would correspond + + align:start position:0% +speed of light but that would correspond + + + align:start position:0% +speed of light but that would correspond +to a kinetic energy which is two point + + align:start position:0% +to a kinetic energy which is two point + + + align:start position:0% +to a kinetic energy which is two point +four times ten to the minus seven joules + + align:start position:0% +four times ten to the minus seven joules + + + align:start position:0% +four times ten to the minus seven joules +remember I don't like these kinds of + + align:start position:0% +remember I don't like these kinds of + + + align:start position:0% +remember I don't like these kinds of +Units but it also corresponds to doing a + + align:start position:0% +Units but it also corresponds to doing a + + + align:start position:0% +Units but it also corresponds to doing a +unit conversion 149 electron volts + + align:start position:0% +unit conversion 149 electron volts + + + align:start position:0% +unit conversion 149 electron volts +electron volts are a good unit for + + align:start position:0% +electron volts are a good unit for + + + align:start position:0% +electron volts are a good unit for +energy for atoms because the ionization + + align:start position:0% +energy for atoms because the ionization + + + align:start position:0% +energy for atoms because the ionization +energy the energy it takes to pull an + + align:start position:0% +energy the energy it takes to pull an + + + align:start position:0% +energy the energy it takes to pull an +electron off of an atom is always + + align:start position:0% +electron off of an atom is always + + + align:start position:0% +electron off of an atom is always +somewhere between five and fifteen + + align:start position:0% +somewhere between five and fifteen + + + align:start position:0% +somewhere between five and fifteen +electron volts so you always want to + + align:start position:0% +electron volts so you always want to + + + align:start position:0% +electron volts so you always want to +calibrate yourself your insight in terms + + align:start position:0% +calibrate yourself your insight in terms + + + align:start position:0% +calibrate yourself your insight in terms +of numbers which are in the small scale + + align:start position:0% +of numbers which are in the small scale + + + align:start position:0% +of numbers which are in the small scale +rather than having to remember the + + align:start position:0% +rather than having to remember the + + + align:start position:0% +rather than having to remember the +exponent okay all right 149 electron + + align:start position:0% +exponent okay all right 149 electron + + + align:start position:0% +exponent okay all right 149 electron +volts should that bother you well it + + align:start position:0% +volts should that bother you well it + + + align:start position:0% +volts should that bother you well it +can't bother you yet because you don't + + align:start position:0% +can't bother you yet because you don't + + + align:start position:0% +can't bother you yet because you don't +know about how what the ionization + + align:start position:0% +know about how what the ionization + + + align:start position:0% +know about how what the ionization +energy is but I just told you it's + + align:start position:0% +energy is but I just told you it's + + + align:start position:0% +energy is but I just told you it's +between five and fifteen this is a + + align:start position:0% +between five and fifteen this is a + + + align:start position:0% +between five and fifteen this is a +factor of 10 too big so this is going to + + align:start position:0% +factor of 10 too big so this is going to + + + align:start position:0% +factor of 10 too big so this is going to +be a problem + + align:start position:0% +be a problem + + + align:start position:0% +be a problem +why how is it possible for things so + + align:start position:0% +why how is it possible for things so + + + align:start position:0% +why how is it possible for things so +small to have an electron fitting in + + align:start position:0% +small to have an electron fitting in + + + align:start position:0% +small to have an electron fitting in +that small size without it just leaving + + align:start position:0% +that small size without it just leaving + + + align:start position:0% +that small size without it just leaving +because it's just way too high energy + + align:start position:0% +because it's just way too high energy + + + align:start position:0% +because it's just way too high energy +and so that leads us to say to ask + + align:start position:0% +and so that leads us to say to ask + + + align:start position:0% +and so that leads us to say to ask +questions about well what is the + + align:start position:0% +questions about well what is the + + + align:start position:0% +questions about well what is the +internal structure of an atom how can an + + align:start position:0% +internal structure of an atom how can an + + + align:start position:0% +internal structure of an atom how can an +atom somehow accommodate this electron + + align:start position:0% +atom somehow accommodate this electron + + + align:start position:0% +atom somehow accommodate this electron +which needs to somehow fit inside + + align:start position:0% + + + + align:start position:0% + +and so that was the basis for the Geiger + + align:start position:0% +and so that was the basis for the Geiger + + + align:start position:0% +and so that was the basis for the Geiger +Marsden experiment now the Geiger + + align:start position:0% +Marsden experiment now the Geiger + + + align:start position:0% +Marsden experiment now the Geiger +Marsden experiment looked very similar + + align:start position:0% +Marsden experiment looked very similar + + + align:start position:0% +Marsden experiment looked very similar +to the the previous experiment and here + + align:start position:0% +to the the previous experiment and here + + + align:start position:0% +to the the previous experiment and here +we have whoops + + align:start position:0% +we have whoops + + + align:start position:0% +we have whoops +Melvin articles alpha particles our + + align:start position:0% +Melvin articles alpha particles our + + + align:start position:0% +Melvin articles alpha particles our +helium two plus ions and they're + + align:start position:0% +helium two plus ions and they're + + + align:start position:0% +helium two plus ions and they're +produced by radioactive decay and they + + align:start position:0% +produced by radioactive decay and they + + + align:start position:0% +produced by radioactive decay and they +have a tremendous amount of energy more + + align:start position:0% +have a tremendous amount of energy more + + + align:start position:0% +have a tremendous amount of energy more +energy than was possible in the days + + align:start position:0% +energy than was possible in the days + + + align:start position:0% +energy than was possible in the days +these experiments were doing to create + + align:start position:0% +these experiments were doing to create + + + align:start position:0% +these experiments were doing to create +for a particle in fact one of the + + align:start position:0% +for a particle in fact one of the + + + align:start position:0% +for a particle in fact one of the +earliest experiments or apparatuses + + align:start position:0% +earliest experiments or apparatuses + + + align:start position:0% +earliest experiments or apparatuses +capable of producing very high-energy + + align:start position:0% +capable of producing very high-energy + + + align:start position:0% +capable of producing very high-energy +electrons was built by Robert Van de + + align:start position:0% +electrons was built by Robert Van de + + + align:start position:0% +electrons was built by Robert Van de +Graaff here at MIT and this was the this + + align:start position:0% +Graaff here at MIT and this was the this + + + align:start position:0% +Graaff here at MIT and this was the this +was in the form of cylindrical towers + + align:start position:0% +was in the form of cylindrical towers + + + align:start position:0% +was in the form of cylindrical towers +right near the parking garage and it was + + align:start position:0% +right near the parking garage and it was + + + align:start position:0% +right near the parking garage and it was +there for the first ten years I was at + + align:start position:0% +there for the first ten years I was at + + + align:start position:0% +there for the first ten years I was at +MIT I'm very old but that's still fairly + + align:start position:0% +MIT I'm very old but that's still fairly + + + align:start position:0% +MIT I'm very old but that's still fairly +recent but anyway + + align:start position:0% +recent but anyway + + + align:start position:0% +recent but anyway +Van de Graaff could make high-energy + + align:start position:0% +Van de Graaff could make high-energy + + + align:start position:0% +Van de Graaff could make high-energy +particles and it was really neat and + + align:start position:0% +particles and it was really neat and + + + align:start position:0% +particles and it was really neat and +what he could do was dwarfed by boat + + align:start position:0% +what he could do was dwarfed by boat + + + align:start position:0% +what he could do was dwarfed by boat +what can be done in electron + + align:start position:0% +what can be done in electron + + + align:start position:0% +what can be done in electron +accelerators and now but in the days + + align:start position:0% +accelerators and now but in the days + + + align:start position:0% +accelerators and now but in the days +when the the Geiger Marsden experiment + + align:start position:0% +when the the Geiger Marsden experiment + + + align:start position:0% +when the the Geiger Marsden experiment +was done which was nineteen eleven there + + align:start position:0% +was done which was nineteen eleven there + + + align:start position:0% +was done which was nineteen eleven there +was no way of making and controlling the + + align:start position:0% +was no way of making and controlling the + + + align:start position:0% +was no way of making and controlling the +energy of an electron or of any particle + + align:start position:0% +energy of an electron or of any particle + + + align:start position:0% +energy of an electron or of any particle +and here we have some some particles + + align:start position:0% +and here we have some some particles + + + align:start position:0% +and here we have some some particles +which are produced by radioactive decay + + align:start position:0% +which are produced by radioactive decay + + + align:start position:0% +which are produced by radioactive decay +which have tremendous energy so they're + + align:start position:0% +which have tremendous energy so they're + + + align:start position:0% +which have tremendous energy so they're +heavy and they have high energy and so + + align:start position:0% +heavy and they have high energy and so + + + align:start position:0% +heavy and they have high energy and so +that means the wavelength is very small + + align:start position:0% + + + + align:start position:0% + +we + + align:start position:0% +we + + + align:start position:0% +we +want to use these helium ions yes yes + + align:start position:0% +want to use these helium ions yes yes + + + align:start position:0% +want to use these helium ions yes yes +but but you would need a very high + + align:start position:0% +but but you would need a very high + + + align:start position:0% +but but you would need a very high +voltage and though that that is + + align:start position:0% +voltage and though that that is + + + align:start position:0% +voltage and though that that is +something we could imagine doing now but + + align:start position:0% +something we could imagine doing now but + + + align:start position:0% +something we could imagine doing now but +in 1911 the ability to do that sort of + + align:start position:0% +in 1911 the ability to do that sort of + + + align:start position:0% +in 1911 the ability to do that sort of +thing with control was not not there + + align:start position:0% +thing with control was not not there + + + align:start position:0% +thing with control was not not there +there there needed to be vetted vance's + + align:start position:0% +there there needed to be vetted vance's + + + align:start position:0% +there there needed to be vetted vance's +in vacuum technology there needed to be + + align:start position:0% +in vacuum technology there needed to be + + + align:start position:0% +in vacuum technology there needed to be +advances in power supplies I mean we're + + align:start position:0% +advances in power supplies I mean we're + + + align:start position:0% +advances in power supplies I mean we're +talking about very high voltages and you + + align:start position:0% +talking about very high voltages and you + + + align:start position:0% +talking about very high voltages and you +wouldn't want to do that in your + + align:start position:0% +wouldn't want to do that in your + + + align:start position:0% +wouldn't want to do that in your +laboratory even now with the capability + + align:start position:0% +laboratory even now with the capability + + + align:start position:0% +laboratory even now with the capability +when I was a graduate student we had + + align:start position:0% +when I was a graduate student we had + + + align:start position:0% +when I was a graduate student we had +these things called Spellman power + + align:start position:0% +these things called Spellman power + + + align:start position:0% +these things called Spellman power +supplies and they could produce 40 + + align:start position:0% +supplies and they could produce 40 + + + align:start position:0% +supplies and they could produce 40 +kilovolts they were really scary but + + align:start position:0% +kilovolts they were really scary but + + + align:start position:0% +kilovolts they were really scary but +that's nothing compared to what you need + + align:start position:0% +that's nothing compared to what you need + + + align:start position:0% +that's nothing compared to what you need +okay so we want bullets we want to have + + align:start position:0% +okay so we want bullets we want to have + + + align:start position:0% +okay so we want bullets we want to have +these helium particles interacting with + + align:start position:0% +these helium particles interacting with + + + align:start position:0% +these helium particles interacting with +a in milla foil and so we have a whole + + align:start position:0% +a in milla foil and so we have a whole + + + align:start position:0% +a in milla foil and so we have a whole +array of atoms here and we have a little + + align:start position:0% +array of atoms here and we have a little + + + align:start position:0% +array of atoms here and we have a little +hole here and what's going to happen is + + align:start position:0% +hole here and what's going to happen is + + + align:start position:0% +hole here and what's going to happen is +this radiation is going to hit these + + align:start position:0% +this radiation is going to hit these + + + align:start position:0% +this radiation is going to hit these +atoms and there's going to be back + + align:start position:0% +atoms and there's going to be back + + + align:start position:0% +atoms and there's going to be back +scatter and forward scattering and the + + align:start position:0% +scatter and forward scattering and the + + + align:start position:0% +scatter and forward scattering and the +crucial experiment was to measure the + + align:start position:0% +crucial experiment was to measure the + + + align:start position:0% +crucial experiment was to measure the +ratio of back scattering to forward + + align:start position:0% +ratio of back scattering to forward + + + align:start position:0% +ratio of back scattering to forward +scattering now if we have a target that + + align:start position:0% +scattering now if we have a target that + + + align:start position:0% +scattering now if we have a target that +it looks sort of like a smear then the + + align:start position:0% +it looks sort of like a smear then the + + + align:start position:0% +it looks sort of like a smear then the +forward and backward scattering would be + + align:start position:0% +forward and backward scattering would be + + + align:start position:0% +forward and backward scattering would be +similar if we have a target it looked + + align:start position:0% +similar if we have a target it looked + + + align:start position:0% +similar if we have a target it looked +like a bunch of tiny + + align:start position:0% +like a bunch of tiny + + + align:start position:0% +like a bunch of tiny +points there would very rarely be + + align:start position:0% +points there would very rarely be + + + align:start position:0% +points there would very rarely be +backscattering all of the scattering + + align:start position:0% +backscattering all of the scattering + + + align:start position:0% +backscattering all of the scattering +would be forward because most of the + + align:start position:0% +would be forward because most of the + + + align:start position:0% +would be forward because most of the +particles don't hit anything and so what + + align:start position:0% +particles don't hit anything and so what + + + align:start position:0% +particles don't hit anything and so what +was found and what was a surprise is + + align:start position:0% +was found and what was a surprise is + + + align:start position:0% +was found and what was a surprise is +that there was very little back + + align:start position:0% +that there was very little back + + + align:start position:0% +that there was very little back +scattering and that implied that the + + align:start position:0% +scattering and that implied that the + + + align:start position:0% +scattering and that implied that the +ratio of the size of the target to the + + align:start position:0% +ratio of the size of the target to the + + + align:start position:0% +ratio of the size of the target to the +size of the particle was enormous the + + align:start position:0% +size of the particle was enormous the + + + align:start position:0% +size of the particle was enormous the +particles that scattered the the alpha + + align:start position:0% +particles that scattered the the alpha + + + align:start position:0% +particles that scattered the the alpha +particles were tiny they had a size + + align:start position:0% +particles were tiny they had a size + + + align:start position:0% +particles were tiny they had a size +something like 10 to the minus 4 times + + align:start position:0% +something like 10 to the minus 4 times + + + align:start position:0% +something like 10 to the minus 4 times +the typical dimension of an atom so this + + align:start position:0% +the typical dimension of an atom so this + + + align:start position:0% +the typical dimension of an atom so this +is jellien and this is a perfectly + + align:start position:0% +is jellien and this is a perfectly + + + align:start position:0% +is jellien and this is a perfectly +reasonable approach that + + align:start position:0% +reasonable approach that + + + align:start position:0% +reasonable approach that +that the char the positive and negative + + align:start position:0% +that the char the positive and negative + + + align:start position:0% +that the char the positive and negative +charges that make up an atom are + + align:start position:0% +charges that make up an atom are + + + align:start position:0% +charges that make up an atom are +distributed uniformly this was the + + align:start position:0% +distributed uniformly this was the + + + align:start position:0% +distributed uniformly this was the +surprise so how do we explain now if + + align:start position:0% +surprise so how do we explain now if + + + align:start position:0% +surprise so how do we explain now if +atoms that are scattering the alpha + + align:start position:0% +atoms that are scattering the alpha + + + align:start position:0% +atoms that are scattering the alpha +particles are really small even compared + + align:start position:0% +particles are really small even compared + + + align:start position:0% +particles are really small even compared +to the 1 angstrom well how do they stick + + align:start position:0% +to the 1 angstrom well how do they stick + + + align:start position:0% +to the 1 angstrom well how do they stick +together + + align:start position:0% +together + + + align:start position:0% +together +why is material matter not compressible + + align:start position:0% +why is material matter not compressible + + + align:start position:0% +why is material matter not compressible +so what is going on here and so + + align:start position:0% + + + + align:start position:0% + +I'm not exactly sure of the genealogy + + align:start position:0% +I'm not exactly sure of the genealogy + + + align:start position:0% +I'm not exactly sure of the genealogy +here but Geiger and Marsden were workers + + align:start position:0% +here but Geiger and Marsden were workers + + + align:start position:0% +here but Geiger and Marsden were workers +or students in the Rutherford lab and + + align:start position:0% +or students in the Rutherford lab and + + + align:start position:0% +or students in the Rutherford lab and +the old man wanted to save face or to + + align:start position:0% +the old man wanted to save face or to + + + align:start position:0% +the old man wanted to save face or to +say oh here's an experiment we learned + + align:start position:0% +say oh here's an experiment we learned + + + align:start position:0% +say oh here's an experiment we learned +something from this you know this is + + align:start position:0% +something from this you know this is + + + align:start position:0% +something from this you know this is +what we do this is my job + + align:start position:0% +what we do this is my job + + + align:start position:0% +what we do this is my job +but anyway so rather heard said well + + align:start position:0% +but anyway so rather heard said well + + + align:start position:0% +but anyway so rather heard said well +maybe it's like this we have a nucleus + + align:start position:0% +maybe it's like this we have a nucleus + + + align:start position:0% +maybe it's like this we have a nucleus +and we have the electrons okay so we + + align:start position:0% +and we have the electrons okay so we + + + align:start position:0% +and we have the electrons okay so we +have a nucleus where all the positive + + align:start position:0% +have a nucleus where all the positive + + + align:start position:0% +have a nucleus where all the positive +charge of the atom and most of the mass + + align:start position:0% +charge of the atom and most of the mass + + + align:start position:0% +charge of the atom and most of the mass +resides and we have electrons in + + align:start position:0% +resides and we have electrons in + + + align:start position:0% +resides and we have electrons in +circular orbits so maybe these circular + + align:start position:0% +circular orbits so maybe these circular + + + align:start position:0% +circular orbits so maybe these circular +orbits explain why you can't compress + + align:start position:0% +orbits explain why you can't compress + + + align:start position:0% +orbits explain why you can't compress +atoms to something that would be + + align:start position:0% +atoms to something that would be + + + align:start position:0% +atoms to something that would be +commensurate with the size of the nuclei + + align:start position:0% +commensurate with the size of the nuclei + + + align:start position:0% +commensurate with the size of the nuclei +that the electrons cause a repulsion and + + align:start position:0% +that the electrons cause a repulsion and + + + align:start position:0% +that the electrons cause a repulsion and +the structure is stable so this is a + + align:start position:0% +the structure is stable so this is a + + + align:start position:0% +the structure is stable so this is a +pretty reasonable hypothesis until one + + align:start position:0% +pretty reasonable hypothesis until one + + + align:start position:0% +pretty reasonable hypothesis until one +analyzes it so what we have is a + + align:start position:0% +analyzes it so what we have is a + + + align:start position:0% +analyzes it so what we have is a +positive charge here negative charge + + align:start position:0% +positive charge here negative charge + + + align:start position:0% +positive charge here negative charge +here and so there is Coulomb attraction + + align:start position:0% +here and so there is Coulomb attraction + + + align:start position:0% +here and so there is Coulomb attraction +and there's centrifugal force of + + align:start position:0% +and there's centrifugal force of + + + align:start position:0% +and there's centrifugal force of +centripetal acceleration and we have to + + align:start position:0% +centripetal acceleration and we have to + + + align:start position:0% +centripetal acceleration and we have to +have these two things match so the + + align:start position:0% +have these two things match so the + + + align:start position:0% +have these two things match so the +inward force is is the charge on the + + align:start position:0% +inward force is is the charge on the + + + align:start position:0% +inward force is is the charge on the +electron squared over 4pi epsilon 0 and + + align:start position:0% +electron squared over 4pi epsilon 0 and + + + align:start position:0% +electron squared over 4pi epsilon 0 and +r squared and the centrifugal is its + + align:start position:0% + + + + align:start position:0% + +okay this is you know you know all this + + align:start position:0% +okay this is you know you know all this + + + align:start position:0% +okay this is you know you know all this +you know how to do this have known it + + align:start position:0% +you know how to do this have known it + + + align:start position:0% +you know how to do this have known it +since high school probably and so you + + align:start position:0% +since high school probably and so you + + + align:start position:0% +since high school probably and so you +can combine all these things say they + + align:start position:0% +can combine all these things say they + + + align:start position:0% +can combine all these things say they +inward and outward the Internet force is + + align:start position:0% +inward and outward the Internet force is + + + align:start position:0% +inward and outward the Internet force is +exactly canceling the outward force and + + align:start position:0% +exactly canceling the outward force and + + + align:start position:0% +exactly canceling the outward force and +you can solve for the velocity and the + + align:start position:0% +you can solve for the velocity and the + + + align:start position:0% +you can solve for the velocity and the +velocity is Q the electrons squared over + + align:start position:0% +velocity is Q the electrons squared over + + + align:start position:0% +velocity is Q the electrons squared over +4 PI epsilon zero mass of the electron + + align:start position:0% +4 PI epsilon zero mass of the electron + + + align:start position:0% +4 PI epsilon zero mass of the electron +and the radius this is a trivial + + align:start position:0% +and the radius this is a trivial + + + align:start position:0% +and the radius this is a trivial +derivation I won't insult you by jumping + + align:start position:0% +derivation I won't insult you by jumping + + + align:start position:0% +derivation I won't insult you by jumping +to do it and try to increase your + + align:start position:0% +to do it and try to increase your + + + align:start position:0% +to do it and try to increase your +understanding of the equation because + + align:start position:0% +understanding of the equation because + + + align:start position:0% +understanding of the equation because +you already understand it so this is the + + align:start position:0% +you already understand it so this is the + + + align:start position:0% +you already understand it so this is the +requirement for the radius of a circular + + align:start position:0% +requirement for the radius of a circular + + + align:start position:0% +requirement for the radius of a circular +orbit and it has the mass IV this is the + + align:start position:0% +orbit and it has the mass IV this is the + + + align:start position:0% +orbit and it has the mass IV this is the +requirement for the velocity and this is + + align:start position:0% +requirement for the velocity and this is + + + align:start position:0% +requirement for the velocity and this is +the radius here okay so we know all that + + align:start position:0% +the radius here okay so we know all that + + + align:start position:0% +the radius here okay so we know all that +and so there's nothing about + + align:start position:0% +and so there's nothing about + + + align:start position:0% +and so there's nothing about +quantization yet we know that for any + + align:start position:0% +quantization yet we know that for any + + + align:start position:0% +quantization yet we know that for any +radius the electron will have a certain + + align:start position:0% +radius the electron will have a certain + + + align:start position:0% +radius the electron will have a certain +velocity and we can choose whatever + + align:start position:0% +velocity and we can choose whatever + + + align:start position:0% +velocity and we can choose whatever +radius we want whatever velocity we want + + align:start position:0% +radius we want whatever velocity we want + + + align:start position:0% +radius we want whatever velocity we want +and that corresponds to whatever energy + + align:start position:0% +and that corresponds to whatever energy + + + align:start position:0% +and that corresponds to whatever energy +we get okay + + align:start position:0% + + + + align:start position:0% + +so what we're interested in is the the + + align:start position:0% +so what we're interested in is the the + + + align:start position:0% +so what we're interested in is the the +frequency of the over the and so that + + align:start position:0% +frequency of the over the and so that + + + align:start position:0% +frequency of the over the and so that +will be one over the time it takes for + + align:start position:0% +will be one over the time it takes for + + + align:start position:0% +will be one over the time it takes for +the electron to go around and one over + + align:start position:0% +the electron to go around and one over + + + align:start position:0% +the electron to go around and one over +the time it takes for electrons to go + + align:start position:0% +the time it takes for electrons to go + + + align:start position:0% +the time it takes for electrons to go +around is two pi are the circumference + + align:start position:0% +around is two pi are the circumference + + + align:start position:0% +around is two pi are the circumference +divided by the velocity so we have the + + align:start position:0% +divided by the velocity so we have the + + + align:start position:0% +divided by the velocity so we have the +velocity is equal to I mean the + + align:start position:0% +velocity is equal to I mean the + + + align:start position:0% +velocity is equal to I mean the +frequency is equal to one or two PI R + + align:start position:0% +frequency is equal to one or two PI R + + + align:start position:0% +frequency is equal to one or two PI R +and we can we can write an equation for + + align:start position:0% +and we can we can write an equation for + + + align:start position:0% +and we can we can write an equation for +this and that's in the notes and there + + align:start position:0% +this and that's in the notes and there + + + align:start position:0% +this and that's in the notes and there +in fact there was a typo in the notes + + align:start position:0% +in fact there was a typo in the notes + + + align:start position:0% +in fact there was a typo in the notes +which has been corrected in red but I + + align:start position:0% +which has been corrected in red but I + + + align:start position:0% +which has been corrected in red but I +don't need to tell you what it is and + + align:start position:0% +don't need to tell you what it is and + + + align:start position:0% +don't need to tell you what it is and +and so we we can calculate this + + align:start position:0% +and so we we can calculate this + + + align:start position:0% +and so we we can calculate this +frequency and what well the reason we + + align:start position:0% +frequency and what well the reason we + + + align:start position:0% +frequency and what well the reason we +calculate the frequency is because we + + align:start position:0% +calculate the frequency is because we + + + align:start position:0% +calculate the frequency is because we +know if we have electrons moving back + + align:start position:0% +know if we have electrons moving back + + + align:start position:0% +know if we have electrons moving back +and forth at some frequency they're + + align:start position:0% +and forth at some frequency they're + + + align:start position:0% +and forth at some frequency they're +going to radiate electromagnetic + + align:start position:0% +going to radiate electromagnetic + + + align:start position:0% +going to radiate electromagnetic +radiation at that frequency well where + + align:start position:0% +radiation at that frequency well where + + + align:start position:0% +radiation at that frequency well where +did that energy come from it came from + + align:start position:0% +did that energy come from it came from + + + align:start position:0% +did that energy come from it came from +the motion of the electron so it has to + + align:start position:0% +the motion of the electron so it has to + + + align:start position:0% +the motion of the electron so it has to +give up kinetic energy now the energy is + + align:start position:0% +give up kinetic energy now the energy is + + + align:start position:0% +give up kinetic energy now the energy is +the kinetic energy plus the potential + + align:start position:0% +the kinetic energy plus the potential + + + align:start position:0% +the kinetic energy plus the potential +energy and so if it gives up energy + + align:start position:0% +energy and so if it gives up energy + + + align:start position:0% +energy and so if it gives up energy +there's some of these two things has to + + align:start position:0% +there's some of these two things has to + + + align:start position:0% +there's some of these two things has to +decrease and what happens is this + + align:start position:0% +decrease and what happens is this + + + align:start position:0% +decrease and what happens is this +decreases faster than this increases and + + align:start position:0% +decreases faster than this increases and + + + align:start position:0% +decreases faster than this increases and +what ends up happening is that the + + align:start position:0% +what ends up happening is that the + + + align:start position:0% +what ends up happening is that the +electron + + align:start position:0% + + + + align:start position:0% + +as a death spiral what happens will be + + align:start position:0% +as a death spiral what happens will be + + + align:start position:0% +as a death spiral what happens will be +that the electron will go in a spiral + + align:start position:0% +that the electron will go in a spiral + + + align:start position:0% +that the electron will go in a spiral +going faster and faster as it goes to + + align:start position:0% +going faster and faster as it goes to + + + align:start position:0% +going faster and faster as it goes to +smaller and smaller radius and + + align:start position:0% +smaller and smaller radius and + + + align:start position:0% +smaller and smaller radius and +annihilate itself so this is garbage + + align:start position:0% +annihilate itself so this is garbage + + + align:start position:0% +annihilate itself so this is garbage +this can't be true it violates laws that + + align:start position:0% +this can't be true it violates laws that + + + align:start position:0% +this can't be true it violates laws that +everybody knows are right and so one + + align:start position:0% +everybody knows are right and so one + + + align:start position:0% +everybody knows are right and so one +needs to find a way to live with this + + align:start position:0% + + + + align:start position:0% + +now what really doesn't need to find a + + align:start position:0% +now what really doesn't need to find a + + + align:start position:0% +now what really doesn't need to find a +way to live with it until you realize + + align:start position:0% +way to live with it until you realize + + + align:start position:0% +way to live with it until you realize +what happens because this picture + + align:start position:0% +what happens because this picture + + + align:start position:0% +what happens because this picture +subject to a couple of hypotheses + + align:start position:0% +subject to a couple of hypotheses + + + align:start position:0% +subject to a couple of hypotheses +predicts an infinite number of ten digit + + align:start position:0% +predicts an infinite number of ten digit + + + align:start position:0% +predicts an infinite number of ten digit +numbers you know it's not an accident + + align:start position:0% +numbers you know it's not an accident + + + align:start position:0% +numbers you know it's not an accident +maybe one prediction would be fine but + + align:start position:0% +maybe one prediction would be fine but + + + align:start position:0% +maybe one prediction would be fine but +that all of the lines in the spectra of + + align:start position:0% +that all of the lines in the spectra of + + + align:start position:0% +that all of the lines in the spectra of +hydrogen atom helium ion lithium doubly + + align:start position:0% +hydrogen atom helium ion lithium doubly + + + align:start position:0% +hydrogen atom helium ion lithium doubly +charged ion all of those are predicted + + align:start position:0% +charged ion all of those are predicted + + + align:start position:0% +charged ion all of those are predicted +with no adjustable parameters to + + align:start position:0% +with no adjustable parameters to + + + align:start position:0% +with no adjustable parameters to +measurement accuracy now at the time + + align:start position:0% +measurement accuracy now at the time + + + align:start position:0% +measurement accuracy now at the time +this was being done the measurement + + align:start position:0% +this was being done the measurement + + + align:start position:0% +this was being done the measurement +accuracy might have been only a part a + + align:start position:0% +accuracy might have been only a part a + + + align:start position:0% +accuracy might have been only a part a +thousand or maybe a part in a million + + align:start position:0% +thousand or maybe a part in a million + + + align:start position:0% +thousand or maybe a part in a million +but a part antenna tenth we're starting + + align:start position:0% +but a part antenna tenth we're starting + + + align:start position:0% +but a part antenna tenth we're starting +to beyond that we're starting to get + + align:start position:0% +to beyond that we're starting to get + + + align:start position:0% +to beyond that we're starting to get +into fundamental physics but this is an + + align:start position:0% +into fundamental physics but this is an + + + align:start position:0% +into fundamental physics but this is an +astonishing thing and so I have to + + align:start position:0% +astonishing thing and so I have to + + + align:start position:0% +astonishing thing and so I have to +explain what the additional assumptions + + align:start position:0% +explain what the additional assumptions + + + align:start position:0% +explain what the additional assumptions +were because we've got something that + + align:start position:0% +were because we've got something that + + + align:start position:0% +were because we've got something that +predicts things we have no business + + align:start position:0% +predicts things we have no business + + + align:start position:0% +predicts things we have no business +knowing and that there was no + + align:start position:0% +knowing and that there was no + + + align:start position:0% +knowing and that there was no +explanation for the spectrum before + + align:start position:0% +explanation for the spectrum before + + + align:start position:0% +explanation for the spectrum before +these experiments or this picture was + + align:start position:0% +these experiments or this picture was + + + align:start position:0% +these experiments or this picture was +developed so we have to first find a way + + align:start position:0% +developed so we have to first find a way + + + align:start position:0% +developed so we have to first find a way +whether it's believable or not of + + align:start position:0% +whether it's believable or not of + + + align:start position:0% +whether it's believable or not of +getting rid of the radiator + + align:start position:0% +getting rid of the radiator + + + align:start position:0% +getting rid of the radiator +collapse so poor proposed that angular + + align:start position:0% +collapse so poor proposed that angular + + + align:start position:0% +collapse so poor proposed that angular +momentum L vector R cross P is conserved + + align:start position:0% +momentum L vector R cross P is conserved + + + align:start position:0% +momentum L vector R cross P is conserved +well we know that angular momentum is + + align:start position:0% +well we know that angular momentum is + + + align:start position:0% +well we know that angular momentum is +conserved but for a microscopic system + + align:start position:0% +conserved but for a microscopic system + + + align:start position:0% +conserved but for a microscopic system +what it means to be conserved may be a + + align:start position:0% +what it means to be conserved may be a + + + align:start position:0% +what it means to be conserved may be a +little bit more subtle he proposed that + + align:start position:0% +little bit more subtle he proposed that + + + align:start position:0% +little bit more subtle he proposed that +angular momentum is conserved and that + + align:start position:0% +angular momentum is conserved and that + + + align:start position:0% +angular momentum is conserved and that +the angular momentum the magnitude of + + align:start position:0% +the angular momentum the magnitude of + + + align:start position:0% +the angular momentum the magnitude of +the angular momentum had to have a + + align:start position:0% +the angular momentum had to have a + + + align:start position:0% +the angular momentum had to have a +particular value and that value was + + align:start position:0% +particular value and that value was + + + align:start position:0% +particular value and that value was +integer times H bar H bar is the + + align:start position:0% +integer times H bar H bar is the + + + align:start position:0% +integer times H bar H bar is the +Planck's constant divided by 2 pi now + + align:start position:0% +Planck's constant divided by 2 pi now + + + align:start position:0% +Planck's constant divided by 2 pi now +this is complete nonsense + + align:start position:0% +this is complete nonsense + + + align:start position:0% +this is complete nonsense +why should it be conserved so or why + + align:start position:0% +why should it be conserved so or why + + + align:start position:0% +why should it be conserved so or why +should it be restricted to this set of + + align:start position:0% +should it be restricted to this set of + + + align:start position:0% +should it be restricted to this set of +values well the reason we accept that + + align:start position:0% +values well the reason we accept that + + + align:start position:0% +values well the reason we accept that +it's restricted is because it gives the + + align:start position:0% +it's restricted is because it gives the + + + align:start position:0% +it's restricted is because it gives the +energy levels that are observed now + + align:start position:0% +energy levels that are observed now + + + align:start position:0% +energy levels that are observed now +before I get to energy level I do ok we + + align:start position:0% +before I get to energy level I do ok we + + + align:start position:0% +before I get to energy level I do ok we +have energy levels we find that the + + align:start position:0% +have energy levels we find that the + + + align:start position:0% +have energy levels we find that the +energy is equal to minus some constant + + align:start position:0% +energy is equal to minus some constant + + + align:start position:0% +energy is equal to minus some constant +over N squared same n is in here this is + + align:start position:0% +over N squared same n is in here this is + + + align:start position:0% +over N squared same n is in here this is +the Redbird constant and it's something + + align:start position:0% +the Redbird constant and it's something + + + align:start position:0% +the Redbird constant and it's something +that you can measure it's basically a + + align:start position:0% +that you can measure it's basically a + + + align:start position:0% +that you can measure it's basically a +whole bunch of fundamental constants + + align:start position:0% +whole bunch of fundamental constants + + + align:start position:0% +whole bunch of fundamental constants +combined and so it has a value and + + align:start position:0% + + + + align:start position:0% + +this is one of the numbers in my + + align:start position:0% +this is one of the numbers in my + + + align:start position:0% +this is one of the numbers in my +permanent memory and that's the value of + + align:start position:0% +permanent memory and that's the value of + + + align:start position:0% +permanent memory and that's the value of +the Redbird consonant in reciprocal + + align:start position:0% +the Redbird consonant in reciprocal + + + align:start position:0% +the Redbird consonant in reciprocal +centimeter units and to get it into + + align:start position:0% +centimeter units and to get it into + + + align:start position:0% +centimeter units and to get it into +energy unit to multiply by H times C or + + align:start position:0% +energy unit to multiply by H times C or + + + align:start position:0% +energy unit to multiply by H times C or +to get into frequency you just + + align:start position:0% +to get into frequency you just + + + align:start position:0% +to get into frequency you just +multiplied by the speed of light so + + align:start position:0% +multiplied by the speed of light so + + + align:start position:0% +multiplied by the speed of light so +anyway this is a number that is known to + + align:start position:0% +anyway this is a number that is known to + + + align:start position:0% +anyway this is a number that is known to +many decimal places and it is generated + + align:start position:0% +many decimal places and it is generated + + + align:start position:0% +many decimal places and it is generated +by this this idea that the angular + + align:start position:0% +by this this idea that the angular + + + align:start position:0% +by this this idea that the angular +momentum has to be certain values + + align:start position:0% +momentum has to be certain values + + + align:start position:0% +momentum has to be certain values +conservation is good that's easy this is + + align:start position:0% +conservation is good that's easy this is + + + align:start position:0% +conservation is good that's easy this is +weird + + align:start position:0% +weird + + + align:start position:0% +weird +and it's also wrong because we find out + + align:start position:0% +and it's also wrong because we find out + + + align:start position:0% +and it's also wrong because we find out +later that the possible values of n + + align:start position:0% +later that the possible values of n + + + align:start position:0% +later that the possible values of n +include zero which would completely mess + + align:start position:0% +include zero which would completely mess + + + align:start position:0% +include zero which would completely mess +up the the Bohr model but anyway this + + align:start position:0% +up the the Bohr model but anyway this + + + align:start position:0% +up the the Bohr model but anyway this +then in combination with this amazing + + align:start position:0% + + + + align:start position:0% + +statement that okay we have the nth + + align:start position:0% +statement that okay we have the nth + + + align:start position:0% +statement that okay we have the nth +energy and the n prime energy and the + + align:start position:0% +energy and the n prime energy and the + + + align:start position:0% +energy and the n prime energy and the +spectrum corresponds to the frequency + + align:start position:0% + + + + align:start position:0% + +corresponds to H E and minus e n prime + + align:start position:0% +corresponds to H E and minus e n prime + + + align:start position:0% +corresponds to H E and minus e n prime +or H + + align:start position:0% + + + + align:start position:0% + +so everything we see in the emission + + align:start position:0% +so everything we see in the emission + + + align:start position:0% +so everything we see in the emission +spectrum of the hydrogen atom or in a + + align:start position:0% +spectrum of the hydrogen atom or in a + + + align:start position:0% +spectrum of the hydrogen atom or in a +gas which is mostly h2 there are our + + align:start position:0% +gas which is mostly h2 there are our + + + align:start position:0% +gas which is mostly h2 there are our +transitions associated with the free + + align:start position:0% +transitions associated with the free + + + align:start position:0% +transitions associated with the free +atoms and they're always around and this + + align:start position:0% +atoms and they're always around and this + + + align:start position:0% +atoms and they're always around and this +simple equation based on the River + + align:start position:0% +simple equation based on the River + + + align:start position:0% +simple equation based on the River +equation this says the spectra are + + align:start position:0% +equation this says the spectra are + + + align:start position:0% +equation this says the spectra are +telling us about the energy level + + align:start position:0% +telling us about the energy level + + + align:start position:0% +telling us about the energy level +differences and it's a simple equation + + align:start position:0% +differences and it's a simple equation + + + align:start position:0% +differences and it's a simple equation +and it's true it's true an incredibly + + align:start position:0% +and it's true it's true an incredibly + + + align:start position:0% +and it's true it's true an incredibly +high accuracy and it tells you nothing + + align:start position:0% +high accuracy and it tells you nothing + + + align:start position:0% +high accuracy and it tells you nothing +except the mass of the particles because + + align:start position:0% +except the mass of the particles because + + + align:start position:0% +except the mass of the particles because +the mass of the particle for this River + + align:start position:0% +the mass of the particle for this River + + + align:start position:0% +the mass of the particle for this River +equation we have it expressed in terms + + align:start position:0% +equation we have it expressed in terms + + + align:start position:0% +equation we have it expressed in terms +of the mass of the electron but it + + align:start position:0% +of the mass of the electron but it + + + align:start position:0% +of the mass of the electron but it +really should be the reduced mass of the + + align:start position:0% +really should be the reduced mass of the + + + align:start position:0% +really should be the reduced mass of the +mass of the nucleus times the mass of + + align:start position:0% +mass of the nucleus times the mass of + + + align:start position:0% +mass of the nucleus times the mass of +the electron or the mass of the nucleus + + align:start position:0% +the electron or the mass of the nucleus + + + align:start position:0% +the electron or the mass of the nucleus +plus the mass of the electron and this + + align:start position:0% +plus the mass of the electron and this + + + align:start position:0% +plus the mass of the electron and this +is something we know for all two body + + align:start position:0% +is something we know for all two body + + + align:start position:0% +is something we know for all two body +interactions that was known well before + + align:start position:0% +interactions that was known well before + + + align:start position:0% +interactions that was known well before +the time of these experiments if you + + align:start position:0% +the time of these experiments if you + + + align:start position:0% +the time of these experiments if you +have two things interacting the reduced + + align:start position:0% +have two things interacting the reduced + + + align:start position:0% +have two things interacting the reduced +mass is what you want rather than the + + align:start position:0% +mass is what you want rather than the + + + align:start position:0% +mass is what you want rather than the +individual masses and so the only + + align:start position:0% +individual masses and so the only + + + align:start position:0% +individual masses and so the only +information in these one electron + + align:start position:0% +information in these one electron + + + align:start position:0% +information in these one electron +spectra is the mass of the atom of the + + align:start position:0% +spectra is the mass of the atom of the + + + align:start position:0% +spectra is the mass of the atom of the +nucleus and there's not much difference + + align:start position:0% +nucleus and there's not much difference + + + align:start position:0% +nucleus and there's not much difference +in the mass in this reduced mass effect + + align:start position:0% +in the mass in this reduced mass effect + + + align:start position:0% +in the mass in this reduced mass effect +but it's enough to say this is a + + align:start position:0% +but it's enough to say this is a + + + align:start position:0% +but it's enough to say this is a +spectrum of hydrogen as opposed to + + align:start position:0% +spectrum of hydrogen as opposed to + + + align:start position:0% +spectrum of hydrogen as opposed to +lithium 2-plus okay but we still have a + + align:start position:0% +lithium 2-plus okay but we still have a + + + align:start position:0% +lithium 2-plus okay but we still have a +problem a very serious problem + + align:start position:0% + + + + align:start position:0% + +why is the angular momentum conserved + + align:start position:0% +why is the angular momentum conserved + + + align:start position:0% +why is the angular momentum conserved +why is the angular momentum forced to + + align:start position:0% +why is the angular momentum forced to + + + align:start position:0% +why is the angular momentum forced to +have a certain value well I've really + + align:start position:0% +have a certain value well I've really + + + align:start position:0% +have a certain value well I've really +finished this lecture pretty fast but + + align:start position:0% +finished this lecture pretty fast but + + + align:start position:0% +finished this lecture pretty fast but +yeah so let me just let's just get to + + align:start position:0% +yeah so let me just let's just get to + + + align:start position:0% +yeah so let me just let's just get to +the end and I will go back alright so + + align:start position:0% + + + + align:start position:0% + +the problem is this electron is assumed + + align:start position:0% +the problem is this electron is assumed + + + align:start position:0% +the problem is this electron is assumed +to be a particle and it's assumed to be + + align:start position:0% +to be a particle and it's assumed to be + + + align:start position:0% +to be a particle and it's assumed to be +moving so the equation of Maxwell's + + align:start position:0% +moving so the equation of Maxwell's + + + align:start position:0% +moving so the equation of Maxwell's +equations all of the equations about + + align:start position:0% +equations all of the equations about + + + align:start position:0% +equations all of the equations about +motion of charged particles say if it's + + align:start position:0% +motion of charged particles say if it's + + + align:start position:0% +motion of charged particles say if it's +moving its gonna Radian or if it's + + align:start position:0% +moving its gonna Radian or if it's + + + align:start position:0% +moving its gonna Radian or if it's +awesome it's gonna radiate so maybe the + + align:start position:0% +awesome it's gonna radiate so maybe the + + + align:start position:0% +awesome it's gonna radiate so maybe the +problem is it's not moving its remember + + align:start position:0% +problem is it's not moving its remember + + + align:start position:0% +problem is it's not moving its remember +the particles are both particles and + + align:start position:0% +the particles are both particles and + + + align:start position:0% +the particles are both particles and +waves and so we could imagine that + + align:start position:0% + + + + align:start position:0% + +around the circular orbit we have + + align:start position:0% +around the circular orbit we have + + + align:start position:0% +around the circular orbit we have +standing waves no motion and so and this + + align:start position:0% +standing waves no motion and so and this + + + align:start position:0% +standing waves no motion and so and this +led to the serene equation which talks + + align:start position:0% +led to the serene equation which talks + + + align:start position:0% +led to the serene equation which talks +about the states of the electron that + + align:start position:0% +about the states of the electron that + + + align:start position:0% +about the states of the electron that +are allowed and it's a wave it's + + align:start position:0% +are allowed and it's a wave it's + + + align:start position:0% +are allowed and it's a wave it's +basically the classical wave equation + + align:start position:0% +basically the classical wave equation + + + align:start position:0% +basically the classical wave equation +with a couple little twists and the + + align:start position:0% +with a couple little twists and the + + + align:start position:0% +with a couple little twists and the +thing about waves you remember we can + + align:start position:0% +thing about waves you remember we can + + + align:start position:0% +thing about waves you remember we can +have constructive and destructive + + align:start position:0% +have constructive and destructive + + + align:start position:0% +have constructive and destructive +interference we can have standing waves + + align:start position:0% + + + + align:start position:0% + +so there doesn't need to be a motion of + + align:start position:0% +so there doesn't need to be a motion of + + + align:start position:0% +so there doesn't need to be a motion of +a particle there could be some static + + align:start position:0% +a particle there could be some static + + + align:start position:0% +a particle there could be some static +description of the probability of + + align:start position:0% +description of the probability of + + + align:start position:0% +description of the probability of +finding the electron everywhere around + + align:start position:0% +finding the electron everywhere around + + + align:start position:0% +finding the electron everywhere around +this orbit and that's the Schrodinger + + align:start position:0% +this orbit and that's the Schrodinger + + + align:start position:0% +this orbit and that's the Schrodinger +equation and so in the next lecture I'm + + align:start position:0% +equation and so in the next lecture I'm + + + align:start position:0% +equation and so in the next lecture I'm +going to talk about the classical wave + + align:start position:0% +going to talk about the classical wave + + + align:start position:0% +going to talk about the classical wave +equation which will be the warm-up for + + align:start position:0% +equation which will be the warm-up for + + + align:start position:0% +equation which will be the warm-up for +the shorter equation and the shorter + + align:start position:0% +the shorter equation and the shorter + + + align:start position:0% +the shorter equation and the shorter +equation explains everything people have + + align:start position:0% +equation explains everything people have + + + align:start position:0% +equation explains everything people have +made some really fantastic philosophical + + align:start position:0% +made some really fantastic philosophical + + + align:start position:0% +made some really fantastic philosophical +statements about the sharee + + align:start position:0% +statements about the sharee + + + align:start position:0% +statements about the sharee +it contains everything that we need to + + align:start position:0% +it contains everything that we need to + + + align:start position:0% +it contains everything that we need to +know the problem is we can't solve the + + align:start position:0% +know the problem is we can't solve the + + + align:start position:0% +know the problem is we can't solve the +equation exactly but it's true + + align:start position:0% +equation exactly but it's true + + + align:start position:0% +equation exactly but it's true +and it's it it it contains everything + + align:start position:0% +and it's it it it contains everything + + + align:start position:0% +and it's it it it contains everything +that we'd ever want to know about the + + align:start position:0% +that we'd ever want to know about the + + + align:start position:0% +that we'd ever want to know about the +microscopic structure of atoms and + + align:start position:0% +microscopic structure of atoms and + + + align:start position:0% +microscopic structure of atoms and +molecules so we've been led by these + + align:start position:0% +molecules so we've been led by these + + + align:start position:0% +molecules so we've been led by these +very simple experiments which now you + + align:start position:0% +very simple experiments which now you + + + align:start position:0% +very simple experiments which now you +could do really trivially you wouldn't + + align:start position:0% +could do really trivially you wouldn't + + + align:start position:0% +could do really trivially you wouldn't +have to be a smart student of a smart + + align:start position:0% +have to be a smart student of a smart + + + align:start position:0% +have to be a smart student of a smart +advisor or a stupid adviser you would + + align:start position:0% +advisor or a stupid adviser you would + + + align:start position:0% +advisor or a stupid adviser you would +you would be able to do these + + align:start position:0% +you would be able to do these + + + align:start position:0% +you would be able to do these +experiments and you could say yeah this + + align:start position:0% +experiments and you could say yeah this + + + align:start position:0% +experiments and you could say yeah this +is all very weird but we already know + + align:start position:0% +is all very weird but we already know + + + align:start position:0% +is all very weird but we already know +now we know that spectra are everything + + align:start position:0% +now we know that spectra are everything + + + align:start position:0% +now we know that spectra are everything +and I'm a spectroscopy I'm very proud of + + align:start position:0% +and I'm a spectroscopy I'm very proud of + + + align:start position:0% +and I'm a spectroscopy I'm very proud of +this because the idea that you can make + + align:start position:0% +this because the idea that you can make + + + align:start position:0% +this because the idea that you can make +a few measurements and say something + + align:start position:0% +a few measurements and say something + + + align:start position:0% +a few measurements and say something +about the internal structure of an atom + + align:start position:0% +about the internal structure of an atom + + + align:start position:0% +about the internal structure of an atom +or molecule that's a fantastic thing and + + align:start position:0% +or molecule that's a fantastic thing and + + + align:start position:0% +or molecule that's a fantastic thing and +what we've seen the spectrum of one + + align:start position:0% +what we've seen the spectrum of one + + + align:start position:0% +what we've seen the spectrum of one +electron atoms is something which is + + align:start position:0% +electron atoms is something which is + + + align:start position:0% +electron atoms is something which is +really simple it's the temporary + + align:start position:0% +really simple it's the temporary + + + align:start position:0% +really simple it's the temporary +template for understanding all + + align:start position:0% +template for understanding all + + + align:start position:0% +template for understanding all +complexity because everything is + + align:start position:0% +complexity because everything is + + + align:start position:0% +complexity because everything is +different from hydrogen hydrogen has a + + align:start position:0% +different from hydrogen hydrogen has a + + + align:start position:0% +different from hydrogen hydrogen has a +point charge at the center it's not + + align:start position:0% +point charge at the center it's not + + + align:start position:0% +point charge at the center it's not +quite a point charge and that's actually + + align:start position:0% +quite a point charge and that's actually + + + align:start position:0% +quite a point charge and that's actually +a subject of even modern physics + + align:start position:0% +a subject of even modern physics + + + align:start position:0% +a subject of even modern physics +and other atoms are not a point charge + + align:start position:0% +and other atoms are not a point charge + + + align:start position:0% +and other atoms are not a point charge +because they have electrons and so + + align:start position:0% +because they have electrons and so + + + align:start position:0% +because they have electrons and so +there's a concentration of charge the + + align:start position:0% +there's a concentration of charge the + + + align:start position:0% +there's a concentration of charge the +the thing to which the electron is + + align:start position:0% +the thing to which the electron is + + + align:start position:0% +the thing to which the electron is +attached is space filling and so that + + align:start position:0% +attached is space filling and so that + + + align:start position:0% +attached is space filling and so that +really results in a shift of the energy + + align:start position:0% +really results in a shift of the energy + + + align:start position:0% +really results in a shift of the energy +levels and the shift of the energy + + align:start position:0% +levels and the shift of the energy + + + align:start position:0% +levels and the shift of the energy +levels and how that shift depends on the + + align:start position:0% +levels and how that shift depends on the + + + align:start position:0% +levels and how that shift depends on the +orbital angular momentum tells you + + align:start position:0% +orbital angular momentum tells you + + + align:start position:0% +orbital angular momentum tells you +something about the shape of this charge + + align:start position:0% +something about the shape of this charge + + + align:start position:0% +something about the shape of this charge +distribution the radial shape and and so + + align:start position:0% +distribution the radial shape and and so + + + align:start position:0% +distribution the radial shape and and so +everything we do in spectroscopy is + + align:start position:0% +everything we do in spectroscopy is + + + align:start position:0% +everything we do in spectroscopy is +somehow reference to something we + + align:start position:0% +somehow reference to something we + + + align:start position:0% +somehow reference to something we +understand perfectly but which is not a + + align:start position:0% +understand perfectly but which is not a + + + align:start position:0% +understand perfectly but which is not a +much interest but it's a template for + + align:start position:0% +much interest but it's a template for + + + align:start position:0% +much interest but it's a template for +building up our understanding of + + align:start position:0% +building up our understanding of + + + align:start position:0% +building up our understanding of +everything and this is a kind of a + + align:start position:0% +everything and this is a kind of a + + + align:start position:0% +everything and this is a kind of a +radical statement and I get to say this + + align:start position:0% +radical statement and I get to say this + + + align:start position:0% +radical statement and I get to say this +because I'm up here and and I do this + + align:start position:0% +because I'm up here and and I do this + + + align:start position:0% +because I'm up here and and I do this +for a living I mean not teaching but + + align:start position:0% +for a living I mean not teaching but + + + align:start position:0% +for a living I mean not teaching but +research and I really believe that the + + align:start position:0% +research and I really believe that the + + + align:start position:0% +research and I really believe that the +the things that we are enabled to + + align:start position:0% +the things that we are enabled to + + + align:start position:0% +the things that we are enabled to +observe about the microscopic structure + + align:start position:0% +observe about the microscopic structure + + + align:start position:0% +observe about the microscopic structure +of things are encoded in something + + align:start position:0% +of things are encoded in something + + + align:start position:0% +of things are encoded in something +completely unlike looking at it and our + + align:start position:0% +completely unlike looking at it and our + + + align:start position:0% +completely unlike looking at it and our +job is to figure out how to break that + + align:start position:0% +job is to figure out how to break that + + + align:start position:0% +job is to figure out how to break that +code and that's what I've done for the + + align:start position:0% +code and that's what I've done for the + + + align:start position:0% +code and that's what I've done for the +last 50 years and it's fun okay so what + + align:start position:0% +last 50 years and it's fun okay so what + + + align:start position:0% +last 50 years and it's fun okay so what +more can I say to amuse you for five or + + align:start position:0% +more can I say to amuse you for five or + + + align:start position:0% +more can I say to amuse you for five or +six minutes not much because I've + + align:start position:0% +six minutes not much because I've + + + align:start position:0% +six minutes not much because I've +skipped a lot of really great stuff but + + align:start position:0% +skipped a lot of really great stuff but + + + align:start position:0% +skipped a lot of really great stuff but +go back to boy the boy had the + + align:start position:0% +go back to boy the boy had the + + + align:start position:0% +go back to boy the boy had the +hypothesis that there is an integer + + align:start position:0% +hypothesis that there is an integer + + + align:start position:0% +hypothesis that there is an integer +number of wavelengths around the + + align:start position:0% +number of wavelengths around the + + + align:start position:0% +number of wavelengths around the +circular orbit and that was telling you + + align:start position:0% +circular orbit and that was telling you + + + align:start position:0% +circular orbit and that was telling you +that it's stable because if it weren't + + align:start position:0% +that it's stable because if it weren't + + + align:start position:0% +that it's stable because if it weren't +an integer number of wavelengths the + + align:start position:0% +an integer number of wavelengths the + + + align:start position:0% +an integer number of wavelengths the +electron would self annihilate but that + + align:start position:0% + + + + align:start position:0% + +that takes a valid point and moves it + + align:start position:0% +that takes a valid point and moves it + + + align:start position:0% +that takes a valid point and moves it +into something which is a little bit + + align:start position:0% +into something which is a little bit + + + align:start position:0% +into something which is a little bit +wrong because we're not trying to have a + + align:start position:0% +wrong because we're not trying to have a + + + align:start position:0% +wrong because we're not trying to have a +particle moving we're having a + + align:start position:0% +particle moving we're having a + + + align:start position:0% +particle moving we're having a +distribution of probabilities and there + + align:start position:0% +distribution of probabilities and there + + + align:start position:0% +distribution of probabilities and there +are still wavelengths and nodal + + align:start position:0% +are still wavelengths and nodal + + + align:start position:0% +are still wavelengths and nodal +structures and the stable solutions do + + align:start position:0% +structures and the stable solutions do + + + align:start position:0% +structures and the stable solutions do +involve the particle not self + + align:start position:0% +involve the particle not self + + + align:start position:0% +involve the particle not self +annihilating and so debris scores + + align:start position:0% +annihilating and so debris scores + + + align:start position:0% +annihilating and so debris scores +another triple I mean he didn't come up + + align:start position:0% +another triple I mean he didn't come up + + + align:start position:0% +another triple I mean he didn't come up +with the Schrodinger equation so that's + + align:start position:0% +with the Schrodinger equation so that's + + + align:start position:0% +with the Schrodinger equation so that's +the homerun that it says okay we have + + align:start position:0% +the homerun that it says okay we have + + + align:start position:0% +the homerun that it says okay we have +the material now to explain everything + + align:start position:0% +the material now to explain everything + + + align:start position:0% +the material now to explain everything +so I'm now going to the next lecture + + align:start position:0% +so I'm now going to the next lecture + + + align:start position:0% +so I'm now going to the next lecture +will be just introducing the mathematics + + align:start position:0% +will be just introducing the mathematics + + + align:start position:0% +will be just introducing the mathematics +of the wave equation and the crucial + + align:start position:0% +of the wave equation and the crucial + + + align:start position:0% +of the wave equation and the crucial +ideas and that will lead into the + + align:start position:0% +ideas and that will lead into the + + + align:start position:0% +ideas and that will lead into the +following lecture where we all talk + + align:start position:0% +following lecture where we all talk + + + align:start position:0% +following lecture where we all talk +about this writing equation so I can + + align:start position:0% +about this writing equation so I can + + + align:start position:0% +about this writing equation so I can +stop now + + align:start position:0% +stop now + + + align:start position:0% +stop now +Thanks \ No newline at end of file diff --git a/_qixt0NLc9I.txt b/_qixt0NLc9I.txt new file mode 100644 index 0000000000000000000000000000000000000000..42a3cb8e14135dc64c976abfc46791d43a7af251 --- /dev/null +++ b/_qixt0NLc9I.txt @@ -0,0 +1,9579 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu welcome back from this from + + align:start position:0% +ocw.mit.edu welcome back from this from + + + align:start position:0% +ocw.mit.edu welcome back from this from +this short + + align:start position:0% +this short + + + align:start position:0% +this short +break Remember by now we know a little + + align:start position:0% +break Remember by now we know a little + + + align:start position:0% +break Remember by now we know a little +bit about how lasers work we know how + + align:start position:0% +bit about how lasers work we know how + + + align:start position:0% +bit about how lasers work we know how +light amplification comes + + align:start position:0% +light amplification comes + + + align:start position:0% +light amplification comes +about excuse me we even know how a laser + + align:start position:0% +about excuse me we even know how a laser + + + align:start position:0% +about excuse me we even know how a laser +starts now let's look + + align:start position:0% +starts now let's look + + + align:start position:0% +starts now let's look +at what causes the bandwidth of the + + align:start position:0% +at what causes the bandwidth of the + + + align:start position:0% +at what causes the bandwidth of the +laser okay and what does that bring with + + align:start position:0% +laser okay and what does that bring with + + + align:start position:0% +laser okay and what does that bring with +it what sort of properties of lasers + + align:start position:0% +it what sort of properties of lasers + + + align:start position:0% +it what sort of properties of lasers +will come with it so here it is we have + + align:start position:0% +will come with it so here it is we have + + + align:start position:0% +will come with it so here it is we have +the bandwidth of the of the amplifier + + align:start position:0% +the bandwidth of the of the amplifier + + + align:start position:0% +the bandwidth of the of the amplifier +which is really the the tuning range of + + align:start position:0% +which is really the the tuning range of + + + align:start position:0% +which is really the the tuning range of +the laser so let me remind you that + + align:start position:0% +the laser so let me remind you that + + + align:start position:0% +the laser so let me remind you that +we're dealing now with a essentially a + + align:start position:0% +we're dealing now with a essentially a + + + align:start position:0% +we're dealing now with a essentially a +three-level system where there's a pump + + align:start position:0% +three-level system where there's a pump + + + align:start position:0% +three-level system where there's a pump +that's creating a population inversion + + align:start position:0% +that's creating a population inversion + + + align:start position:0% +that's creating a population inversion +between three and two levels and as + + align:start position:0% +between three and two levels and as + + + align:start position:0% +between three and two levels and as +we've shown before you know we get gain + + align:start position:0% +we've shown before you know we get gain + + + align:start position:0% +we've shown before you know we get gain +at this at this frequency at this 3 to2 + + align:start position:0% +at this at this frequency at this 3 to2 + + + align:start position:0% +at this at this frequency at this 3 to2 +frequency and uh the amount of gain + + align:start position:0% +frequency and uh the amount of gain + + + align:start position:0% +frequency and uh the amount of gain +depends again on some constants but the + + align:start position:0% +depends again on some constants but the + + + align:start position:0% +depends again on some constants but the +key thing is the population difference + + align:start position:0% +key thing is the population difference + + + align:start position:0% +key thing is the population difference +and the width then depends on what and + + align:start position:0% +and the width then depends on what and + + + align:start position:0% +and the width then depends on what and +that's what we want to find out in this + + align:start position:0% +that's what we want to find out in this + + + align:start position:0% +that's what we want to find out in this +in this + + align:start position:0% +in this + + + align:start position:0% +in this +section well the width here can depend + + align:start position:0% +section well the width here can depend + + + align:start position:0% +section well the width here can depend +is determined by all sorts of things one + + align:start position:0% +is determined by all sorts of things one + + + align:start position:0% +is determined by all sorts of things one +is the fact uh that there is spontaneous + + align:start position:0% +is the fact uh that there is spontaneous + + + align:start position:0% +is the fact uh that there is spontaneous +emission as you know when light Decay + + align:start position:0% +emission as you know when light Decay + + + align:start position:0% +emission as you know when light Decay +when atoms Decay they radiate uh an + + align:start position:0% +when atoms Decay they radiate uh an + + + align:start position:0% +when atoms Decay they radiate uh an +exponential uh uh waveform and that just + + align:start position:0% +exponential uh uh waveform and that just + + + align:start position:0% +exponential uh uh waveform and that just +like we showed before has a width so if + + align:start position:0% +like we showed before has a width so if + + + align:start position:0% +like we showed before has a width so if +that was the dominant effect then that + + align:start position:0% +that was the dominant effect then that + + + align:start position:0% +that was the dominant effect then that +the whole width would be essentially the + + align:start position:0% +the whole width would be essentially the + + + align:start position:0% +the whole width would be essentially the +effect of spontaneous emission but in + + align:start position:0% +effect of spontaneous emission but in + + + align:start position:0% +effect of spontaneous emission but in +say something like a gas M we have + + align:start position:0% +say something like a gas M we have + + + align:start position:0% +say something like a gas M we have +collisions and collisions can + + align:start position:0% +collisions and collisions can + + + align:start position:0% +collisions and collisions can +effectively shorten this uh this uh this + + align:start position:0% +effectively shorten this uh this uh this + + + align:start position:0% +effectively shorten this uh this uh this +uh transition time this Decay time and + + align:start position:0% +uh transition time this Decay time and + + + align:start position:0% +uh transition time this Decay time and +essentially will broaden the width and + + align:start position:0% +essentially will broaden the width and + + + align:start position:0% +essentially will broaden the width and +uh and also the dler effect because + + align:start position:0% +uh and also the dler effect because + + + align:start position:0% +uh and also the dler effect because +atoms are moving there is as we're all + + align:start position:0% +atoms are moving there is as we're all + + + align:start position:0% +atoms are moving there is as we're all +familiar with the with the dler shift in + + align:start position:0% +familiar with the with the dler shift in + + + align:start position:0% +familiar with the with the dler shift in +the frequencies again that can cause uh + + align:start position:0% +the frequencies again that can cause uh + + + align:start position:0% +the frequencies again that can cause uh +broadening so this width here can be + + align:start position:0% +broadening so this width here can be + + + align:start position:0% +broadening so this width here can be +quite complicated could be made up for + + align:start position:0% +quite complicated could be made up for + + + align:start position:0% +quite complicated could be made up for +gases it could be made up from + + align:start position:0% +gases it could be made up from + + + align:start position:0% +gases it could be made up from +spontaneous emission Collision dupler + + align:start position:0% +spontaneous emission Collision dupler + + + align:start position:0% +spontaneous emission Collision dupler +and what have you and for solids uh for + + align:start position:0% +and what have you and for solids uh for + + + align:start position:0% +and what have you and for solids uh for +solid amplifiers they have other + + align:start position:0% +solid amplifiers they have other + + + align:start position:0% +solid amplifiers they have other +broadening sources so basically this is + + align:start position:0% +broadening sources so basically this is + + + align:start position:0% +broadening sources so basically this is +not a trivial uh width here it it it uh + + align:start position:0% +not a trivial uh width here it it it uh + + + align:start position:0% +not a trivial uh width here it it it uh +but it can be measured and then can be + + align:start position:0% +but it can be measured and then can be + + + align:start position:0% +but it can be measured and then can be +attributed to uh all sorts of uh effects + + align:start position:0% +attributed to uh all sorts of uh effects + + + align:start position:0% +attributed to uh all sorts of uh effects +now I see that uh we have a phone call + + align:start position:0% +now I see that uh we have a phone call + + + align:start position:0% +now I see that uh we have a phone call +so let's take this phone call uh right + + align:start position:0% +so let's take this phone call uh right + + + align:start position:0% +so let's take this phone call uh right +now uh Dr Zio uh one quick question can + + align:start position:0% +now uh Dr Zio uh one quick question can + + + align:start position:0% +now uh Dr Zio uh one quick question can +you be a little louder please uh yes one + + align:start position:0% +you be a little louder please uh yes one + + + align:start position:0% +you be a little louder please uh yes one +quick question regarding the pump where + + align:start position:0% +quick question regarding the pump where + + + align:start position:0% +quick question regarding the pump where +are you calling from by the way Harford + + align:start position:0% +are you calling from by the way Harford + + + align:start position:0% +are you calling from by the way Harford +Graduate Center Harford yes + + align:start position:0% +Graduate Center Harford yes + + + align:start position:0% +Graduate Center Harford yes +uhhuh uh one quick question regarding + + align:start position:0% +uhhuh uh one quick question regarding + + + align:start position:0% +uhhuh uh one quick question regarding +the pump yes uh could you just explain + + align:start position:0% +the pump yes uh could you just explain + + + align:start position:0% +the pump yes uh could you just explain +how that starts if we were to look at + + align:start position:0% +how that starts if we were to look at + + + align:start position:0% +how that starts if we were to look at +the pump + + align:start position:0% +the pump + + + align:start position:0% +the pump +schematically uh is that some high + + align:start position:0% +schematically uh is that some high + + + align:start position:0% +schematically uh is that some high +voltage being applied exciting those + + align:start position:0% +voltage being applied exciting those + + + align:start position:0% +voltage being applied exciting those +electrons oh well I tell you what so far + + align:start position:0% +electrons oh well I tell you what so far + + + align:start position:0% +electrons oh well I tell you what so far +I just wanted to indicate that there is + + align:start position:0% +I just wanted to indicate that there is + + + align:start position:0% +I just wanted to indicate that there is +a pump uh if you can wait just a little + + align:start position:0% +a pump uh if you can wait just a little + + + align:start position:0% +a pump uh if you can wait just a little +bit I'm going to show you uh when I + + align:start position:0% +bit I'm going to show you uh when I + + + align:start position:0% +bit I'm going to show you uh when I +discuss the variety of lasers that they + + align:start position:0% +discuss the variety of lasers that they + + + align:start position:0% +discuss the variety of lasers that they +are and show you what the pump is in + + align:start position:0% +are and show you what the pump is in + + + align:start position:0% +are and show you what the pump is in +each in each case like in some cases + + align:start position:0% +each in each case like in some cases + + + align:start position:0% +each in each case like in some cases +it's going to be light beam in some + + align:start position:0% +it's going to be light beam in some + + + align:start position:0% +it's going to be light beam in some +cases will be uh collisions in some + + align:start position:0% +cases will be uh collisions in some + + + align:start position:0% +cases will be uh collisions in some +cases it'll be electrons colliding with + + align:start position:0% +cases it'll be electrons colliding with + + + align:start position:0% +cases it'll be electrons colliding with +something and in the case of the helium + + align:start position:0% +something and in the case of the helium + + + align:start position:0% +something and in the case of the helium +neon it'll be helium colliding with neon + + align:start position:0% +neon it'll be helium colliding with neon + + + align:start position:0% +neon it'll be helium colliding with neon +so if you just wait a little bit and and + + align:start position:0% +so if you just wait a little bit and and + + + align:start position:0% +so if you just wait a little bit and and +see how that goes then can uh get back + + align:start position:0% +see how that goes then can uh get back + + + align:start position:0% +see how that goes then can uh get back +to me if I'm not clear okay okay thank + + align:start position:0% +to me if I'm not clear okay okay thank + + + align:start position:0% +to me if I'm not clear okay okay thank +you very much + + align:start position:0% +you very much + + + align:start position:0% +you very much +good all right so uh and I encourage you + + align:start position:0% +good all right so uh and I encourage you + + + align:start position:0% +good all right so uh and I encourage you +to uh to ask questions uh + + align:start position:0% +to uh to ask questions uh + + + align:start position:0% +to uh to ask questions uh +anytime um so then then the width of the + + align:start position:0% +anytime um so then then the width of the + + + align:start position:0% +anytime um so then then the width of the +just to summarize then the width of the + + align:start position:0% +just to summarize then the width of the + + + align:start position:0% +just to summarize then the width of the +of the uh laser amplifier then is as I + + align:start position:0% +of the uh laser amplifier then is as I + + + align:start position:0% +of the uh laser amplifier then is as I +say is made up of all sorts of things + + align:start position:0% +say is made up of all sorts of things + + + align:start position:0% +say is made up of all sorts of things +and and of course it depends on which is + + align:start position:0% +and and of course it depends on which is + + + align:start position:0% +and and of course it depends on which is +the dominant one if there isn't a if the + + align:start position:0% +the dominant one if there isn't a if the + + + align:start position:0% +the dominant one if there isn't a if the +Collision is not the dominant one maybe + + align:start position:0% +Collision is not the dominant one maybe + + + align:start position:0% +Collision is not the dominant one maybe +the dler is or if the dler is not + + align:start position:0% +the dler is or if the dler is not + + + align:start position:0% +the dler is or if the dler is not +dominant maybe the the spontaneous + + align:start position:0% +dominant maybe the the spontaneous + + + align:start position:0% +dominant maybe the the spontaneous +emission lifetime is and + + align:start position:0% +emission lifetime is and + + + align:start position:0% +emission lifetime is and +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +but in any case uh we're going to have a + + align:start position:0% +but in any case uh we're going to have a + + + align:start position:0% +but in any case uh we're going to have a +certain width and and and now let's see + + align:start position:0% +certain width and and and now let's see + + + align:start position:0% +certain width and and and now let's see +what what can happen because we have + + align:start position:0% +what what can happen because we have + + + align:start position:0% +what what can happen because we have +this uh this width all right so so in + + align:start position:0% +this uh this width all right so so in + + + align:start position:0% +this uh this width all right so so in +fact this is the width that determines + + align:start position:0% +fact this is the width that determines + + + align:start position:0% +fact this is the width that determines +actually the spectrum of uh of laser + + align:start position:0% +actually the spectrum of uh of laser + + + align:start position:0% +actually the spectrum of uh of laser +life all right so let's uh then do a + + align:start position:0% +life all right so let's uh then do a + + + align:start position:0% +life all right so let's uh then do a +little review here uh we said before + + align:start position:0% +little review here uh we said before + + + align:start position:0% +little review here uh we said before +that uh what I've drawn here here's the + + align:start position:0% +that uh what I've drawn here here's the + + + align:start position:0% +that uh what I've drawn here here's the +amplifier here's the bandwidth of the + + align:start position:0% +amplifier here's the bandwidth of the + + + align:start position:0% +amplifier here's the bandwidth of the +amplifier here the modes of the of the + + align:start position:0% +amplifier here the modes of the of the + + + align:start position:0% +amplifier here the modes of the of the +resonator and here in dotted I've drawn + + align:start position:0% +resonator and here in dotted I've drawn + + + align:start position:0% +resonator and here in dotted I've drawn +what I call the loss line which is made + + align:start position:0% +what I call the loss line which is made + + + align:start position:0% +what I call the loss line which is made +up of one minus r 1 minus reflectivity + + align:start position:0% +up of one minus r 1 minus reflectivity + + + align:start position:0% +up of one minus r 1 minus reflectivity +uh which is then equal to the + + align:start position:0% +uh which is then equal to the + + + align:start position:0% +uh which is then equal to the +transmission of the the mirror plus the + + align:start position:0% +transmission of the the mirror plus the + + + align:start position:0% +transmission of the the mirror plus the +absorption in the mirror a but whatever + + align:start position:0% +absorption in the mirror a but whatever + + + align:start position:0% +absorption in the mirror a but whatever +it is that's the loss Line This is the + + align:start position:0% +it is that's the loss Line This is the + + + align:start position:0% +it is that's the loss Line This is the +loss that you have the gain has to + + align:start position:0% +loss that you have the gain has to + + + align:start position:0% +loss that you have the gain has to +overcome before you can you get + + align:start position:0% +overcome before you can you get + + + align:start position:0% +overcome before you can you get +oscillation over here so in in this in + + align:start position:0% +oscillation over here so in in this in + + + align:start position:0% +oscillation over here so in in this in +this uh situation the gain is below the + + align:start position:0% +this uh situation the gain is below the + + + align:start position:0% +this uh situation the gain is below the +loss line and no lazing no lazing occurs + + align:start position:0% +loss line and no lazing no lazing occurs + + + align:start position:0% +loss line and no lazing no lazing occurs +all right so so the first thing we have + + align:start position:0% +all right so so the first thing we have + + + align:start position:0% +all right so so the first thing we have +to do in order to to L then we have to + + align:start position:0% +to do in order to to L then we have to + + + align:start position:0% +to do in order to to L then we have to +increase the gain the amplify above the + + align:start position:0% +increase the gain the amplify above the + + + align:start position:0% +increase the gain the amplify above the +loss line in this particular case + + align:start position:0% +loss line in this particular case + + + align:start position:0% +loss line in this particular case +there's there's one cavity mode here and + + align:start position:0% +there's there's one cavity mode here and + + + align:start position:0% +there's there's one cavity mode here and +as we mentioned before then then the the + + align:start position:0% +as we mentioned before then then the the + + + align:start position:0% +as we mentioned before then then the the +gain here is bigger than the loss at + + align:start position:0% +gain here is bigger than the loss at + + + align:start position:0% +gain here is bigger than the loss at +this value so therefore the laser will + + align:start position:0% +this value so therefore the laser will + + + align:start position:0% +this value so therefore the laser will +oscillate spontaneous emission will + + align:start position:0% +oscillate spontaneous emission will + + + align:start position:0% +oscillate spontaneous emission will +start it off and the output you get this + + align:start position:0% +start it off and the output you get this + + + align:start position:0% +start it off and the output you get this +Delta function uh output all right + + align:start position:0% +Delta function uh output all right + + + align:start position:0% +Delta function uh output all right +that's what we call is a a single a + + align:start position:0% +that's what we call is a a single a + + + align:start position:0% +that's what we call is a a single a +single frequency laser all right now + + align:start position:0% +single frequency laser all right now + + + align:start position:0% +single frequency laser all right now +when we have more modes under the gain + + align:start position:0% +when we have more modes under the gain + + + align:start position:0% +when we have more modes under the gain +curve like like over here in in this + + align:start position:0% +curve like like over here in in this + + + align:start position:0% +curve like like over here in in this +particular case the cavity spacing + + align:start position:0% +particular case the cavity spacing + + + align:start position:0% +particular case the cavity spacing +remember it depends on the length of the + + align:start position:0% +remember it depends on the length of the + + + align:start position:0% +remember it depends on the length of the +cavity so the longer the cavity the + + align:start position:0% +cavity so the longer the cavity the + + + align:start position:0% +cavity so the longer the cavity the +closer the spacings are because C over + + align:start position:0% +closer the spacings are because C over + + + align:start position:0% +closer the spacings are because C over +2L is the separation so in this + + align:start position:0% +2L is the separation so in this + + + align:start position:0% +2L is the separation so in this +particular case I show three modes under + + align:start position:0% +particular case I show three modes under + + + align:start position:0% +particular case I show three modes under +the gang curve now even at this mode + + align:start position:0% +the gang curve now even at this mode + + + align:start position:0% +the gang curve now even at this mode +here there's enough gain to overcome the + + align:start position:0% +here there's enough gain to overcome the + + + align:start position:0% +here there's enough gain to overcome the +loss because this is the loss line so in + + align:start position:0% +loss because this is the loss line so in + + + align:start position:0% +loss because this is the loss line so in +a way I'll get three laser frequencies + + align:start position:0% +a way I'll get three laser frequencies + + + align:start position:0% +a way I'll get three laser frequencies +uh + + align:start position:0% +uh + + + align:start position:0% +uh +oscillated and and of course if the band + + align:start position:0% +oscillated and and of course if the band + + + align:start position:0% +oscillated and and of course if the band +with the amplifier were bigger then I + + align:start position:0% +with the amplifier were bigger then I + + + align:start position:0% +with the amplifier were bigger then I +would get even more frequencies + + align:start position:0% +would get even more frequencies + + + align:start position:0% +would get even more frequencies +oscillating now again if you don't + + align:start position:0% +oscillating now again if you don't + + + align:start position:0% +oscillating now again if you don't +believe me we have a nice little + + align:start position:0% +believe me we have a nice little + + + align:start position:0% +believe me we have a nice little +demonstration for you all right a + + align:start position:0% +demonstration for you all right a + + + align:start position:0% +demonstration for you all right a +demonstration that is based on on the + + align:start position:0% +demonstration that is based on on the + + + align:start position:0% +demonstration that is based on on the +spectrum of laser light you know so so + + align:start position:0% +spectrum of laser light you know so so + + + align:start position:0% +spectrum of laser light you know so so +the the the idea here is to have a way + + align:start position:0% +the the the idea here is to have a way + + + align:start position:0% +the the the idea here is to have a way +of examining this the Spectrum using a a + + align:start position:0% +of examining this the Spectrum using a a + + + align:start position:0% +of examining this the Spectrum using a a +what we call a scanning fabri proo + + align:start position:0% +what we call a scanning fabri proo + + + align:start position:0% +what we call a scanning fabri proo +cavity or a high resolution spectrometer + + align:start position:0% +cavity or a high resolution spectrometer + + + align:start position:0% +cavity or a high resolution spectrometer +that will tell you whether the laser is + + align:start position:0% +that will tell you whether the laser is + + + align:start position:0% +that will tell you whether the laser is +oscillating in in one or two or three or + + align:start position:0% +oscillating in in one or two or three or + + + align:start position:0% +oscillating in in one or two or three or +more modes and so on so now let's look + + align:start position:0% +more modes and so on so now let's look + + + align:start position:0% +more modes and so on so now let's look +at this demonstration on the spectrum of + + align:start position:0% +at this demonstration on the spectrum of + + + align:start position:0% +at this demonstration on the spectrum of +uh laser + + align:start position:0% + + + + align:start position:0% + +line the spectrum of laser light + + align:start position:0% +line the spectrum of laser light + + + align:start position:0% +line the spectrum of laser light +for + + align:start position:0% +for + + + align:start position:0% +for +example is the spectrum is it a single + + align:start position:0% +example is the spectrum is it a single + + + align:start position:0% +example is the spectrum is it a single +frequency or is it multiple frequency or + + align:start position:0% +frequency or is it multiple frequency or + + + align:start position:0% +frequency or is it multiple frequency or +what have in fact we're going to look at + + align:start position:0% +what have in fact we're going to look at + + + align:start position:0% +what have in fact we're going to look at +the spectrum of light from two lasers + + align:start position:0% +the spectrum of light from two lasers + + + align:start position:0% +the spectrum of light from two lasers +two helium neon lasers we have this + + align:start position:0% +two helium neon lasers we have this + + + align:start position:0% +two helium neon lasers we have this +laser here with external + + align:start position:0% +laser here with external + + + align:start position:0% +laser here with external +mirrors and the one over here with + + align:start position:0% +mirrors and the one over here with + + + align:start position:0% +mirrors and the one over here with +internal + + align:start position:0% +internal + + + align:start position:0% +internal +mirrors and the way we're going to look + + align:start position:0% +mirrors and the way we're going to look + + + align:start position:0% +mirrors and the way we're going to look +at the Spectrum is by using the optical + + align:start position:0% +at the Spectrum is by using the optical + + + align:start position:0% +at the Spectrum is by using the optical +Spectrum analyzer here + + align:start position:0% +Spectrum analyzer here + + + align:start position:0% +Spectrum analyzer here +so now let me turn on the this laser + + align:start position:0% +so now let me turn on the this laser + + + align:start position:0% +so now let me turn on the this laser +with external mirrors and the light from + + align:start position:0% +with external mirrors and the light from + + + align:start position:0% +with external mirrors and the light from +the laser then is reflected by this + + align:start position:0% +the laser then is reflected by this + + + align:start position:0% +the laser then is reflected by this +mirror and this mirror and here it is + + align:start position:0% +mirror and this mirror and here it is + + + align:start position:0% +mirror and this mirror and here it is +going right into this Optical Spectrum + + align:start position:0% +going right into this Optical Spectrum + + + align:start position:0% +going right into this Optical Spectrum +analyzer which is a scanning fabri Paro + + align:start position:0% +analyzer which is a scanning fabri Paro + + + align:start position:0% +analyzer which is a scanning fabri Paro +cavity the output + + align:start position:0% +cavity the output + + + align:start position:0% +cavity the output +of the spectrum analyzer then goes to an + + align:start position:0% +of the spectrum analyzer then goes to an + + + align:start position:0% +of the spectrum analyzer then goes to an +oscilloscope over there + + align:start position:0% + + + + align:start position:0% + +as we can see on the oscilloscope we + + align:start position:0% +as we can see on the oscilloscope we + + + align:start position:0% +as we can see on the oscilloscope we +have more than one + + align:start position:0% +have more than one + + + align:start position:0% +have more than one +frequency in fact we have several + + align:start position:0% +frequency in fact we have several + + + align:start position:0% +frequency in fact we have several +frequencies sometimes three and + + align:start position:0% +frequencies sometimes three and + + + align:start position:0% +frequencies sometimes three and +sometimes even + + align:start position:0% +sometimes even + + + align:start position:0% +sometimes even +four the + + align:start position:0% +four the + + + align:start position:0% +four the +spacing uh of the modes here is about + + align:start position:0% +spacing uh of the modes here is about + + + align:start position:0% +spacing uh of the modes here is about +270 MHz which is consistent with the + + align:start position:0% +270 MHz which is consistent with the + + + align:start position:0% +270 MHz which is consistent with the +length of the of the laser C cavity of + + align:start position:0% +length of the of the laser C cavity of + + + align:start position:0% +length of the of the laser C cavity of +56 uh + + align:start position:0% + + + + align:start position:0% + +CM now the first thing I'm going to do + + align:start position:0% +CM now the first thing I'm going to do + + + align:start position:0% +CM now the first thing I'm going to do +is see whether the polarization of all + + align:start position:0% +is see whether the polarization of all + + + align:start position:0% +is see whether the polarization of all +these laser frequencies is the same or + + align:start position:0% +these laser frequencies is the same or + + + align:start position:0% +these laser frequencies is the same or +not so what I'm going to do is + + align:start position:0% +not so what I'm going to do is + + + align:start position:0% +not so what I'm going to do is +insert a + + align:start position:0% +insert a + + + align:start position:0% +insert a +polarizer in the + + align:start position:0% + + + + align:start position:0% + +beam and then rotate the the polarizer + + align:start position:0% +beam and then rotate the the polarizer + + + align:start position:0% +beam and then rotate the the polarizer +in fact let me + + align:start position:0% +in fact let me + + + align:start position:0% +in fact let me +up the gain a little bit + + align:start position:0% + + + + align:start position:0% + +here and let me rotate the + + align:start position:0% +here and let me rotate the + + + align:start position:0% +here and let me rotate the +polarizer or the transmission axis of + + align:start position:0% +polarizer or the transmission axis of + + + align:start position:0% +polarizer or the transmission axis of +the polarizer to see whether the + + align:start position:0% +the polarizer to see whether the + + + align:start position:0% +the polarizer to see whether the +polarization is the same for all of them + + align:start position:0% +polarization is the same for all of them + + + align:start position:0% +polarization is the same for all of them +and as you can see I + + align:start position:0% +and as you can see I + + + align:start position:0% +and as you can see I +can extinguish all of them when the + + align:start position:0% +can extinguish all of them when the + + + align:start position:0% +can extinguish all of them when the +polarization is + + align:start position:0% +polarization is + + + align:start position:0% +polarization is +horizontal and bring them all + + align:start position:0% +horizontal and bring them all + + + align:start position:0% +horizontal and bring them all +up when the the + + align:start position:0% +up when the the + + + align:start position:0% +up when the the +polarization + + align:start position:0% +polarization + + + align:start position:0% +polarization +is is + + align:start position:0% +is is + + + align:start position:0% +is is +vertical and remember this is the this + + align:start position:0% +vertical and remember this is the this + + + align:start position:0% +vertical and remember this is the this +is the light that was plain polarized so + + align:start position:0% +is the light that was plain polarized so + + + align:start position:0% +is the light that was plain polarized so +now we've shown that indeed all the + + align:start position:0% +now we've shown that indeed all the + + + align:start position:0% +now we've shown that indeed all the +frequencies that come out from this + + align:start position:0% +frequencies that come out from this + + + align:start position:0% +frequencies that come out from this +laser all of them are are uh have the + + align:start position:0% +laser all of them are are uh have the + + + align:start position:0% +laser all of them are are uh have the +same polarization polarization in the in + + align:start position:0% +same polarization polarization in the in + + + align:start position:0% +same polarization polarization in the in +the vertical plane so now let me take + + align:start position:0% +the vertical plane so now let me take + + + align:start position:0% +the vertical plane so now let me take +the polarizer out and readjust the gain + + align:start position:0% +the polarizer out and readjust the gain + + + align:start position:0% +the polarizer out and readjust the gain +on the uh on the scope so back now to + + align:start position:0% +on the uh on the scope so back now to + + + align:start position:0% +on the uh on the scope so back now to +the to the three frequencies you can see + + align:start position:0% +the to the three frequencies you can see + + + align:start position:0% +the to the three frequencies you can see +that they move around + + align:start position:0% +that they move around + + + align:start position:0% +that they move around +because the the cavity is drifting in + + align:start position:0% +because the the cavity is drifting in + + + align:start position:0% +because the the cavity is drifting in +length due to the air currents or or + + align:start position:0% +length due to the air currents or or + + + align:start position:0% +length due to the air currents or or +temperature effects or what have you and + + align:start position:0% +temperature effects or what have you and + + + align:start position:0% +temperature effects or what have you and +even in fact as I speak or as I tap on + + align:start position:0% +even in fact as I speak or as I tap on + + + align:start position:0% +even in fact as I speak or as I tap on +the cavity you can see that I can + + align:start position:0% +the cavity you can see that I can + + + align:start position:0% +the cavity you can see that I can +create a mess of the uh of the of the + + align:start position:0% +create a mess of the uh of the of the + + + align:start position:0% +create a mess of the uh of the of the +spectrum just by simply + + align:start position:0% +spectrum just by simply + + + align:start position:0% +spectrum just by simply +uh + + align:start position:0% +uh + + + align:start position:0% +uh +tapping if I lean on the table you can + + align:start position:0% +tapping if I lean on the table you can + + + align:start position:0% +tapping if I lean on the table you can +see again that I can make the + + align:start position:0% +see again that I can make the + + + align:start position:0% +see again that I can make the +frequencies uh wander + + align:start position:0% + + + + align:start position:0% + +around now the fact that I have more + + align:start position:0% +around now the fact that I have more + + + align:start position:0% +around now the fact that I have more +than one frequency means there is enough + + align:start position:0% +than one frequency means there is enough + + + align:start position:0% +than one frequency means there is enough +gain for several frequencies to to + + align:start position:0% +gain for several frequencies to to + + + align:start position:0% +gain for several frequencies to to +oscillate due to the fact that the gain + + align:start position:0% +oscillate due to the fact that the gain + + + align:start position:0% +oscillate due to the fact that the gain +medium has has some uh bandwidth not + + align:start position:0% +medium has has some uh bandwidth not + + + align:start position:0% +medium has has some uh bandwidth not +very huge but some bandwidth now I can + + align:start position:0% +very huge but some bandwidth now I can + + + align:start position:0% +very huge but some bandwidth now I can +make the laser go at frequency by by + + align:start position:0% +make the laser go at frequency by by + + + align:start position:0% +make the laser go at frequency by by +introducing loss by simply misaligning + + align:start position:0% +introducing loss by simply misaligning + + + align:start position:0% +introducing loss by simply misaligning +the cavity to introduce loss so you can + + align:start position:0% +the cavity to introduce loss so you can + + + align:start position:0% +the cavity to introduce loss so you can +see here I've got only two frequencies + + align:start position:0% +see here I've got only two frequencies + + + align:start position:0% +see here I've got only two frequencies +and in fact I'm going to up + + align:start position:0% +and in fact I'm going to up + + + align:start position:0% +and in fact I'm going to up +the sensitivity of the of the scope + + align:start position:0% +the sensitivity of the of the scope + + + align:start position:0% +the sensitivity of the of the scope +because the power goes down when I'm + + align:start position:0% +because the power goes down when I'm + + + align:start position:0% +because the power goes down when I'm +miss a line you can see here I + + align:start position:0% +miss a line you can see here I + + + align:start position:0% +miss a line you can see here I +have essentially two two frequency and + + align:start position:0% +have essentially two two frequency and + + + align:start position:0% +have essentially two two frequency and +if I add more + + align:start position:0% +if I add more + + + align:start position:0% +if I add more +loss I + + align:start position:0% +loss I + + + align:start position:0% +loss I +can I can have only one one frequency so + + align:start position:0% +can I can have only one one frequency so + + + align:start position:0% +can I can have only one one frequency so +in a way I can run this laser at one + + align:start position:0% +in a way I can run this laser at one + + + align:start position:0% +in a way I can run this laser at one +frequency but it's it's difficult to + + align:start position:0% +frequency but it's it's difficult to + + + align:start position:0% +frequency but it's it's difficult to +keep the other one + + align:start position:0% +keep the other one + + + align:start position:0% +keep the other one +out and uh and then you can see that as + + align:start position:0% +out and uh and then you can see that as + + + align:start position:0% +out and uh and then you can see that as +I lean on the + + align:start position:0% +I lean on the + + + align:start position:0% +I lean on the +cavity I can make this frequency move + + align:start position:0% +cavity I can make this frequency move + + + align:start position:0% +cavity I can make this frequency move +around now generally that's not a good + + align:start position:0% +around now generally that's not a good + + + align:start position:0% +around now generally that's not a good +way of getting single frequency and we + + align:start position:0% +way of getting single frequency and we + + + align:start position:0% +way of getting single frequency and we +have other techniques for getting single + + align:start position:0% +have other techniques for getting single + + + align:start position:0% +have other techniques for getting single +frequency which we'll discuss later for + + align:start position:0% +frequency which we'll discuss later for + + + align:start position:0% +frequency which we'll discuss later for +this laser it's best to to align it for + + align:start position:0% +this laser it's best to to align it for + + + align:start position:0% +this laser it's best to to align it for +the highest power out and and this way + + align:start position:0% +the highest power out and and this way + + + align:start position:0% +the highest power out and and this way +we'll automatically get more than than + + align:start position:0% +we'll automatically get more than than + + + align:start position:0% +we'll automatically get more than than +one uh more than one frequency and for a + + align:start position:0% +one uh more than one frequency and for a + + + align:start position:0% +one uh more than one frequency and for a +lot of applications this is uh this is + + align:start position:0% +lot of applications this is uh this is + + + align:start position:0% +lot of applications this is uh this is +fine all right so to summarize then this + + align:start position:0% +fine all right so to summarize then this + + + align:start position:0% +fine all right so to summarize then this +laser that that is 56 cm long or the + + align:start position:0% +laser that that is 56 cm long or the + + + align:start position:0% +laser that that is 56 cm long or the +cavity is 56 cm long then gives us about + + align:start position:0% +cavity is 56 cm long then gives us about + + + align:start position:0% +cavity is 56 cm long then gives us about +three + + align:start position:0% +three + + + align:start position:0% +three +modes and the spacing between each mode + + align:start position:0% +modes and the spacing between each mode + + + align:start position:0% +modes and the spacing between each mode +is about 270 + + align:start position:0% +is about 270 + + + align:start position:0% +is about 270 +MHz and all the modes have the same + + align:start position:0% +MHz and all the modes have the same + + + align:start position:0% +MHz and all the modes have the same +polarization now we're ready to look at + + align:start position:0% +polarization now we're ready to look at + + + align:start position:0% +polarization now we're ready to look at +the the other laser the the laser that + + align:start position:0% +the the other laser the the laser that + + + align:start position:0% +the the other laser the the laser that +has internal mirrors and also shorter in + + align:start position:0% +has internal mirrors and also shorter in + + + align:start position:0% +has internal mirrors and also shorter in +length so when we come back then we look + + align:start position:0% +length so when we come back then we look + + + align:start position:0% +length so when we come back then we look +at uh that + + align:start position:0% +at uh that + + + align:start position:0% +at uh that +laser now we're ready to look at the + + align:start position:0% +laser now we're ready to look at the + + + align:start position:0% +laser now we're ready to look at the +Spectrum of this laser here with + + align:start position:0% +Spectrum of this laser here with + + + align:start position:0% +Spectrum of this laser here with +internal + + align:start position:0% +internal + + + align:start position:0% +internal +mirrors the setup for looking at the + + align:start position:0% +mirrors the setup for looking at the + + + align:start position:0% +mirrors the setup for looking at the +Spectrum is the same as before but let + + align:start position:0% +Spectrum is the same as before but let + + + align:start position:0% +Spectrum is the same as before but let +me just remind you of it here's the + + align:start position:0% +me just remind you of it here's the + + + align:start position:0% +me just remind you of it here's the +output of the laser we reflected by this + + align:start position:0% +output of the laser we reflected by this + + + align:start position:0% +output of the laser we reflected by this +mirror this mirror into the scanning + + align:start position:0% +mirror this mirror into the scanning + + + align:start position:0% +mirror this mirror into the scanning +fabric Paro + + align:start position:0% +fabric Paro + + + align:start position:0% +fabric Paro +cavity the output of the cavity then + + align:start position:0% +cavity the output of the cavity then + + + align:start position:0% +cavity the output of the cavity then +goes onto the oscilloscope over + + align:start position:0% +goes onto the oscilloscope over + + + align:start position:0% +goes onto the oscilloscope over +there now as you can see on the scope + + align:start position:0% +there now as you can see on the scope + + + align:start position:0% +there now as you can see on the scope +and let me adjust the the center of the + + align:start position:0% +and let me adjust the the center of the + + + align:start position:0% +and let me adjust the the center of the +scan as you can see we have two big + + align:start position:0% +scan as you can see we have two big + + + align:start position:0% +scan as you can see we have two big +modes and these are spaced by + + align:start position:0% +modes and these are spaced by + + + align:start position:0% +modes and these are spaced by +680 mahz which is consistent with the + + align:start position:0% +680 mahz which is consistent with the + + + align:start position:0% +680 mahz which is consistent with the +length of the cavity of the laser cavity + + align:start position:0% +length of the cavity of the laser cavity + + + align:start position:0% +length of the cavity of the laser cavity +of 22 + + align:start position:0% +of 22 + + + align:start position:0% +of 22 +cm uh given by the 5 680 MHz is given by + + align:start position:0% +cm uh given by the 5 680 MHz is given by + + + align:start position:0% +cm uh given by the 5 680 MHz is given by +c over2 l the spacing between + + align:start position:0% +c over2 l the spacing between + + + align:start position:0% +c over2 l the spacing between +longitudinal modes so these are two + + align:start position:0% +longitudinal modes so these are two + + + align:start position:0% +longitudinal modes so these are two +longitudinal modes uh of the laser this + + align:start position:0% +longitudinal modes uh of the laser this + + + align:start position:0% +longitudinal modes uh of the laser this +little fell here is a uh is a third mode + + align:start position:0% +little fell here is a uh is a third mode + + + align:start position:0% +little fell here is a uh is a third mode +that's coming in at an odd position + + align:start position:0% +that's coming in at an odd position + + + align:start position:0% +that's coming in at an odd position +because the free spectral range of the + + align:start position:0% +because the free spectral range of the + + + align:start position:0% +because the free spectral range of the +scanning fabri Pro cavity is uh not + + align:start position:0% +scanning fabri Pro cavity is uh not + + + align:start position:0% +scanning fabri Pro cavity is uh not +quite large enough so we're getting a + + align:start position:0% +quite large enough so we're getting a + + + align:start position:0% +quite large enough so we're getting a +wraparound from another another order so + + align:start position:0% +wraparound from another another order so + + + align:start position:0% +wraparound from another another order so +let's not worry about this one uh too + + align:start position:0% +let's not worry about this one uh too + + + align:start position:0% +let's not worry about this one uh too +much so let's look at essentially the + + align:start position:0% +much so let's look at essentially the + + + align:start position:0% +much so let's look at essentially the +the two main longitudinal modes uh of + + align:start position:0% +the two main longitudinal modes uh of + + + align:start position:0% +the two main longitudinal modes uh of +this + + align:start position:0% + + + + align:start position:0% + +laser now Let's uh uh let's look at now + + align:start position:0% +laser now Let's uh uh let's look at now + + + align:start position:0% +laser now Let's uh uh let's look at now +the uh the polarization of uh of these + + align:start position:0% +the uh the polarization of uh of these + + + align:start position:0% +the uh the polarization of uh of these +moldes so now what I'm going to do is + + align:start position:0% +moldes so now what I'm going to do is + + + align:start position:0% +moldes so now what I'm going to do is +take + + align:start position:0% +take + + + align:start position:0% +take +polarizer and as we did with the other + + align:start position:0% +polarizer and as we did with the other + + + align:start position:0% +polarizer and as we did with the other +laser let's take the polarizer and look + + align:start position:0% +laser let's take the polarizer and look + + + align:start position:0% +laser let's take the polarizer and look +at the uh the Spectrum now if we look at + + align:start position:0% +at the uh the Spectrum now if we look at + + + align:start position:0% +at the uh the Spectrum now if we look at +the scope after I make a slight + + align:start position:0% +the scope after I make a slight + + + align:start position:0% +the scope after I make a slight +adjustment of the gain because of the + + align:start position:0% +adjustment of the gain because of the + + + align:start position:0% +adjustment of the gain because of the +loss in the in the polarizer now what + + align:start position:0% +loss in the in the polarizer now what + + + align:start position:0% +loss in the in the polarizer now what +I'm going to do is look at the Spectrum + + align:start position:0% +I'm going to do is look at the Spectrum + + + align:start position:0% +I'm going to do is look at the Spectrum +of the laser + + align:start position:0% +of the laser + + + align:start position:0% +of the laser +light on the scope as a function of of + + align:start position:0% +light on the scope as a function of of + + + align:start position:0% +light on the scope as a function of of +polarization so first you can see with + + align:start position:0% +polarization so first you can see with + + + align:start position:0% +polarization so first you can see with +the polarization set at this angle you + + align:start position:0% +the polarization set at this angle you + + + align:start position:0% +the polarization set at this angle you +can see essentially we have + + align:start position:0% +can see essentially we have + + + align:start position:0% +can see essentially we have +predominantly one one + + align:start position:0% +predominantly one one + + + align:start position:0% +predominantly one one +mode and then if + + align:start position:0% +mode and then if + + + align:start position:0% +mode and then if +I rotate the transmission axis of the + + align:start position:0% +I rotate the transmission axis of the + + + align:start position:0% +I rotate the transmission axis of the +polarizer I can exting this + + align:start position:0% +polarizer I can exting this + + + align:start position:0% +polarizer I can exting this +mode + + align:start position:0% +mode + + + align:start position:0% +mode +and and bring up bring up the other one + + align:start position:0% +and and bring up bring up the other one + + + align:start position:0% +and and bring up bring up the other one +now let me just Center the mode on the + + align:start position:0% +now let me just Center the mode on the + + + align:start position:0% +now let me just Center the mode on the +scope so I can bring up the other one + + align:start position:0% +scope so I can bring up the other one + + + align:start position:0% +scope so I can bring up the other one +you can see indeed I have single + + align:start position:0% +you can see indeed I have single + + + align:start position:0% +you can see indeed I have single +frequency + + align:start position:0% +frequency + + + align:start position:0% +frequency +operation on just one mode so I either + + align:start position:0% +operation on just one mode so I either + + + align:start position:0% +operation on just one mode so I either +have this mode here or if I rotate the + + align:start position:0% +have this mode here or if I rotate the + + + align:start position:0% +have this mode here or if I rotate the +polarizer I can bring + + align:start position:0% +polarizer I can bring + + + align:start position:0% +polarizer I can bring +up can bring out the other one so again + + align:start position:0% +up can bring out the other one so again + + + align:start position:0% +up can bring out the other one so again +let me go + + align:start position:0% +let me go + + + align:start position:0% +let me go +back to the first one + + align:start position:0% +back to the first one + + + align:start position:0% +back to the first one +and then to the one over + + align:start position:0% +and then to the one over + + + align:start position:0% +and then to the one over +here now this is different from what we + + align:start position:0% +here now this is different from what we + + + align:start position:0% +here now this is different from what we +had with the laser with external mirrors + + align:start position:0% +had with the laser with external mirrors + + + align:start position:0% +had with the laser with external mirrors +and and and the Brewster Windows where + + align:start position:0% +and and and the Brewster Windows where + + + align:start position:0% +and and and the Brewster Windows where +we found that all the modes + + align:start position:0% +we found that all the modes + + + align:start position:0% +we found that all the modes +were the same of the same polarization + + align:start position:0% +were the same of the same polarization + + + align:start position:0% +were the same of the same polarization +now here we find that one mode is one + + align:start position:0% +now here we find that one mode is one + + + align:start position:0% +now here we find that one mode is one +polarization and and the other one is + + align:start position:0% +polarization and and the other one is + + + align:start position:0% +polarization and and the other one is +polarized orthogonal to the first one + + align:start position:0% +polarized orthogonal to the first one + + + align:start position:0% +polarized orthogonal to the first one +and in fact this this explains why the + + align:start position:0% +and in fact this this explains why the + + + align:start position:0% +and in fact this this explains why the +output of the laser wasn't uh uh wasn't + + align:start position:0% +output of the laser wasn't uh uh wasn't + + + align:start position:0% +output of the laser wasn't uh uh wasn't +plain + + align:start position:0% +plain + + + align:start position:0% +plain +polarized as as in the external mirror + + align:start position:0% +polarized as as in the external mirror + + + align:start position:0% +polarized as as in the external mirror +cavity now this is very interesting that + + align:start position:0% +cavity now this is very interesting that + + + align:start position:0% +cavity now this is very interesting that +because we have internal mirrors the uh + + align:start position:0% +because we have internal mirrors the uh + + + align:start position:0% +because we have internal mirrors the uh +the the the the modes are have + + align:start position:0% +the the the the modes are have + + + align:start position:0% +the the the the modes are have +orthogonal polarizations at least + + align:start position:0% +orthogonal polarizations at least + + + align:start position:0% +orthogonal polarizations at least +adjacent modes have orthogonal + + align:start position:0% +adjacent modes have orthogonal + + + align:start position:0% +adjacent modes have orthogonal +polarizations and in fact this is a + + align:start position:0% +polarizations and in fact this is a + + + align:start position:0% +polarizations and in fact this is a +very easy way of selecting single + + align:start position:0% +very easy way of selecting single + + + align:start position:0% +very easy way of selecting single +frequency operation by simply placing a + + align:start position:0% +frequency operation by simply placing a + + + align:start position:0% +frequency operation by simply placing a +polarizer uh in the beam and then + + align:start position:0% +polarizer uh in the beam and then + + + align:start position:0% +polarizer uh in the beam and then +selecting uh selecting one one frequency + + align:start position:0% +selecting uh selecting one one frequency + + + align:start position:0% +selecting uh selecting one one frequency +now let's let's look at the this single + + align:start position:0% +now let's let's look at the this single + + + align:start position:0% +now let's let's look at the this single +frequency uh + + align:start position:0% +frequency uh + + + align:start position:0% +frequency uh +Behavior if I want to tune the the laser + + align:start position:0% +Behavior if I want to tune the the laser + + + align:start position:0% +Behavior if I want to tune the the laser +frequency I + + align:start position:0% +frequency I + + + align:start position:0% +frequency I +simply blow some air onto onto the laser + + align:start position:0% +simply blow some air onto onto the laser + + + align:start position:0% +simply blow some air onto onto the laser +to yeah I blew too + + align:start position:0% +to yeah I blew too + + + align:start position:0% +to yeah I blew too +much do it + + align:start position:0% +much do it + + + align:start position:0% +much do it +again + + align:start position:0% +again + + + align:start position:0% +again +so you can see that I can + + align:start position:0% +so you can see that I can + + + align:start position:0% +so you can see that I can +scan the laser frequency by simply + + align:start position:0% +scan the laser frequency by simply + + + align:start position:0% +scan the laser frequency by simply +changing the length of the cavity in + + align:start position:0% +changing the length of the cavity in + + + align:start position:0% +changing the length of the cavity in +this case I'm cooling off the uh uh the + + align:start position:0% +this case I'm cooling off the uh uh the + + + align:start position:0% +this case I'm cooling off the uh uh the +cavity now let me also point out that + + align:start position:0% +cavity now let me also point out that + + + align:start position:0% +cavity now let me also point out that +the line width that you see the line + + align:start position:0% +the line width that you see the line + + + align:start position:0% +the line width that you see the line +width that you see here is not the laser + + align:start position:0% +width that you see here is not the laser + + + align:start position:0% +width that you see here is not the laser +line width at all uh the linewidth that + + align:start position:0% +line width at all uh the linewidth that + + + align:start position:0% +line width at all uh the linewidth that +you see here is determined by the + + align:start position:0% +you see here is determined by the + + + align:start position:0% +you see here is determined by the +scanning fabric Paro cavity + + align:start position:0% + + + + align:start position:0% + +the line with the true line with the + + align:start position:0% +the line with the true line with the + + + align:start position:0% +the line with the true line with the +laser is is very narrow in fact uh uh in + + align:start position:0% +laser is is very narrow in fact uh uh in + + + align:start position:0% +laser is is very narrow in fact uh uh in +principle it's a fraction of a + + align:start position:0% +principle it's a fraction of a + + + align:start position:0% +principle it's a fraction of a +millerz uh but because laser Jitters and + + align:start position:0% +millerz uh but because laser Jitters and + + + align:start position:0% +millerz uh but because laser Jitters and +what have you'll get a little broadening + + align:start position:0% +what have you'll get a little broadening + + + align:start position:0% +what have you'll get a little broadening +but certainly nowhere near as uh as wide + + align:start position:0% +but certainly nowhere near as uh as wide + + + align:start position:0% +but certainly nowhere near as uh as wide +as what you see uh what you see over + + align:start position:0% +as what you see uh what you see over + + + align:start position:0% +as what you see uh what you see over +here and again let + + align:start position:0% +here and again let + + + align:start position:0% +here and again let +me bring up the + + align:start position:0% +me bring up the + + + align:start position:0% +me bring up the +elot the other + + align:start position:0% +elot the other + + + align:start position:0% +elot the other +polarization and again this one will + + align:start position:0% +polarization and again this one will + + + align:start position:0% +polarization and again this one will +also + + align:start position:0% + + + + align:start position:0% + +tune across the gain + + align:start position:0% + + + + align:start position:0% + +curve of the + + align:start position:0% +curve of the + + + align:start position:0% +curve of the +cavity I mean a gain curve of the uh of + + align:start position:0% +cavity I mean a gain curve of the uh of + + + align:start position:0% +cavity I mean a gain curve of the uh of +the medium of the of the + + align:start position:0% + + + + align:start position:0% + +laser well I hope you've enjoyed this + + align:start position:0% +laser well I hope you've enjoyed this + + + align:start position:0% +laser well I hope you've enjoyed this +demonstration as + + align:start position:0% +demonstration as + + + align:start position:0% +demonstration as +well uh I think there's a lot to be + + align:start position:0% +well uh I think there's a lot to be + + + align:start position:0% +well uh I think there's a lot to be +learned and as you know this is a it's a + + align:start position:0% +learned and as you know this is a it's a + + + align:start position:0% +learned and as you know this is a it's a +brief course it's not too mathematical + + align:start position:0% +brief course it's not too mathematical + + + align:start position:0% +brief course it's not too mathematical +so don't expect that you'll be able to + + align:start position:0% +so don't expect that you'll be able to + + + align:start position:0% +so don't expect that you'll be able to +answer all the questions uh just based + + align:start position:0% +answer all the questions uh just based + + + align:start position:0% +answer all the questions uh just based +on on this course but I hope that this + + align:start position:0% +on on this course but I hope that this + + + align:start position:0% +on on this course but I hope that this +will will trigger your excitement and + + align:start position:0% +will will trigger your excitement and + + + align:start position:0% +will will trigger your excitement and +maybe you want to go take other courses + + align:start position:0% +maybe you want to go take other courses + + + align:start position:0% +maybe you want to go take other courses +or maybe start opening up books now + + align:start position:0% +or maybe start opening up books now + + + align:start position:0% +or maybe start opening up books now +there are still more to uh to lasers and + + align:start position:0% +there are still more to uh to lasers and + + + align:start position:0% +there are still more to uh to lasers and +uh now what I would like to uh to get to + + align:start position:0% +uh now what I would like to uh to get to + + + align:start position:0% +uh now what I would like to uh to get to +is the uh is the Optics of of the laser + + align:start position:0% +is the uh is the Optics of of the laser + + + align:start position:0% +is the uh is the Optics of of the laser +beam and that is you know the shape the + + align:start position:0% +beam and that is you know the shape the + + + align:start position:0% +beam and that is you know the shape the +shape of the laser beam that comes out + + align:start position:0% +shape of the laser beam that comes out + + + align:start position:0% +shape of the laser beam that comes out +from lasers I'm I'm talked a little bit + + align:start position:0% +from lasers I'm I'm talked a little bit + + + align:start position:0% +from lasers I'm I'm talked a little bit +about it before and uh and I'd like now + + align:start position:0% +about it before and uh and I'd like now + + + align:start position:0% +about it before and uh and I'd like now +to uh to start uh uh talking about it + + align:start position:0% +to uh to start uh uh talking about it + + + align:start position:0% +to uh to start uh uh talking about it +again I'm not going to get into the math + + align:start position:0% +again I'm not going to get into the math + + + align:start position:0% +again I'm not going to get into the math +because this is not uh this is not the + + align:start position:0% +because this is not uh this is not the + + + align:start position:0% +because this is not uh this is not the +uh the right course for it all right so + + align:start position:0% +uh the right course for it all right so + + + align:start position:0% +uh the right course for it all right so +so forgive me if if I uh if I don't + + align:start position:0% +so forgive me if if I uh if I don't + + + align:start position:0% +so forgive me if if I uh if I don't +convince you uh completely but if you + + align:start position:0% +convince you uh completely but if you + + + align:start position:0% +convince you uh completely but if you +have any questions please go ahead and + + align:start position:0% +have any questions please go ahead and + + + align:start position:0% +have any questions please go ahead and +and ask it and maybe this will give me + + align:start position:0% +and ask it and maybe this will give me + + + align:start position:0% +and ask it and maybe this will give me +an opportunity to uh explain a little + + align:start position:0% +an opportunity to uh explain a little + + + align:start position:0% +an opportunity to uh explain a little +bit better what I what I mean so now + + align:start position:0% +bit better what I what I mean so now + + + align:start position:0% +bit better what I what I mean so now +let's turn to the uh Optics of uh of + + align:start position:0% +let's turn to the uh Optics of uh of + + + align:start position:0% +let's turn to the uh Optics of uh of +laser beams and and as as I mentioned + + align:start position:0% +laser beams and and as as I mentioned + + + align:start position:0% +laser beams and and as as I mentioned +before the shape of of the of the laser + + align:start position:0% +before the shape of of the of the laser + + + align:start position:0% +before the shape of of the of the laser +be is determined by by the mirrors if + + align:start position:0% +be is determined by by the mirrors if + + + align:start position:0% +be is determined by by the mirrors if +you have two two plain mirrors then the + + align:start position:0% +you have two two plain mirrors then the + + + align:start position:0% +you have two two plain mirrors then the +the uh the beam bouncing backwards and + + align:start position:0% +the uh the beam bouncing backwards and + + + align:start position:0% +the uh the beam bouncing backwards and +forwards here will be will be columnated + + align:start position:0% +forwards here will be will be columnated + + + align:start position:0% +forwards here will be will be columnated +and if you leave leak it out here it'll + + align:start position:0% +and if you leave leak it out here it'll + + + align:start position:0% +and if you leave leak it out here it'll +be it'll be cated uh if I had let's say + + align:start position:0% +be it'll be cated uh if I had let's say + + + align:start position:0% +be it'll be cated uh if I had let's say +a curved mirror and a plain mirror then + + align:start position:0% +a curved mirror and a plain mirror then + + + align:start position:0% +a curved mirror and a plain mirror then +then I'll have the beam shape inside the + + align:start position:0% +then I'll have the beam shape inside the + + + align:start position:0% +then I'll have the beam shape inside the +cavity will be something like this will + + align:start position:0% +cavity will be something like this will + + + align:start position:0% +cavity will be something like this will +be big on one side small on the other + + align:start position:0% +be big on one side small on the other + + + align:start position:0% +be big on one side small on the other +and then and then the beam leaving this + + align:start position:0% +and then and then the beam leaving this + + + align:start position:0% +and then and then the beam leaving this +mirror will will also expand just like + + align:start position:0% +mirror will will also expand just like + + + align:start position:0% +mirror will will also expand just like +it expands into here will expand to the + + align:start position:0% +it expands into here will expand to the + + + align:start position:0% +it expands into here will expand to the +other side so the beam will will expand + + align:start position:0% +other side so the beam will will expand + + + align:start position:0% +other side so the beam will will expand +depending on what we call the waist of + + align:start position:0% +depending on what we call the waist of + + + align:start position:0% +depending on what we call the waist of +the + + align:start position:0% +the + + + align:start position:0% +the +beam all right now uh if you have two + + align:start position:0% +beam all right now uh if you have two + + + align:start position:0% +beam all right now uh if you have two +curved mirrors let's say two concave + + align:start position:0% +curved mirrors let's say two concave + + + align:start position:0% +curved mirrors let's say two concave +mirrors then then the beam shape will + + align:start position:0% +mirrors then then the beam shape will + + + align:start position:0% +mirrors then then the beam shape will +look something like this and again will + + align:start position:0% +look something like this and again will + + + align:start position:0% +look something like this and again will +expand coming out but uh one shouldn't + + align:start position:0% +expand coming out but uh one shouldn't + + + align:start position:0% +expand coming out but uh one shouldn't +worry because all you have to do just + + align:start position:0% +worry because all you have to do just + + + align:start position:0% +worry because all you have to do just +like I showed before with the lenses you + + align:start position:0% +like I showed before with the lenses you + + + align:start position:0% +like I showed before with the lenses you +can bring it back to any size to any + + align:start position:0% +can bring it back to any size to any + + + align:start position:0% +can bring it back to any size to any +size you want uh and uh and for example + + align:start position:0% +size you want uh and uh and for example + + + align:start position:0% +size you want uh and uh and for example +in this in this next demonstration that + + align:start position:0% +in this in this next demonstration that + + + align:start position:0% +in this in this next demonstration that +that we're going to have uh we're also + + align:start position:0% +that we're going to have uh we're also + + + align:start position:0% +that we're going to have uh we're also +going to do the the following we're + + align:start position:0% +going to do the the following we're + + + align:start position:0% +going to do the the following we're +going to put lenses at the outputs of + + align:start position:0% +going to put lenses at the outputs of + + + align:start position:0% +going to put lenses at the outputs of +beams and we're going to demonstrate uh + + align:start position:0% +beams and we're going to demonstrate uh + + + align:start position:0% +beams and we're going to demonstrate uh +this region here + + align:start position:0% +this region here + + + align:start position:0% +this region here +uh for you and in fact we're also going + + align:start position:0% +uh for you and in fact we're also going + + + align:start position:0% +uh for you and in fact we're also going +to put an aperture here and we're going + + align:start position:0% +to put an aperture here and we're going + + + align:start position:0% +to put an aperture here and we're going +to clean up the beam because sometimes + + align:start position:0% +to clean up the beam because sometimes + + + align:start position:0% +to clean up the beam because sometimes +the lenses are not perfect the uh + + align:start position:0% +the lenses are not perfect the uh + + + align:start position:0% +the lenses are not perfect the uh +mirrors of lasers are not perfect when + + align:start position:0% +mirrors of lasers are not perfect when + + + align:start position:0% +mirrors of lasers are not perfect when +the light goes through them and there + + align:start position:0% +the light goes through them and there + + + align:start position:0% +the light goes through them and there +was all sorts of distortion so by + + align:start position:0% +was all sorts of distortion so by + + + align:start position:0% +was all sorts of distortion so by +putting an apperture here what we call + + align:start position:0% +putting an apperture here what we call + + + align:start position:0% +putting an apperture here what we call +spatial filter will clean up the beam + + align:start position:0% +spatial filter will clean up the beam + + + align:start position:0% +spatial filter will clean up the beam +and we'll have a very clean looking uh + + align:start position:0% +and we'll have a very clean looking uh + + + align:start position:0% +and we'll have a very clean looking uh +looking spot so uh so I think now we're + + align:start position:0% +looking spot so uh so I think now we're + + + align:start position:0% +looking spot so uh so I think now we're +ready for for this uh next demonstration + + align:start position:0% +ready for for this uh next demonstration + + + align:start position:0% +ready for for this uh next demonstration +on on the Optics of laser beams and here + + align:start position:0% +on on the Optics of laser beams and here + + + align:start position:0% +on on the Optics of laser beams and here +all we're try to show you is is the the + + align:start position:0% +all we're try to show you is is the the + + + align:start position:0% +all we're try to show you is is the the +shape of of laser beam in uh in a tank + + align:start position:0% +shape of of laser beam in uh in a tank + + + align:start position:0% +shape of of laser beam in uh in a tank +of water because it's difficult to do + + align:start position:0% +of water because it's difficult to do + + + align:start position:0% +of water because it's difficult to do +that uh in air to visualize uh the laser + + align:start position:0% +that uh in air to visualize uh the laser + + + align:start position:0% +that uh in air to visualize uh the laser +beam now I want you to remember one + + align:start position:0% +beam now I want you to remember one + + + align:start position:0% +beam now I want you to remember one +thing you know I've been saying about + + align:start position:0% +thing you know I've been saying about + + + align:start position:0% +thing you know I've been saying about +how small the spot is and what have you + + align:start position:0% +how small the spot is and what have you + + + align:start position:0% +how small the spot is and what have you +the focus spot in in this case you're + + align:start position:0% +the focus spot in in this case you're + + + align:start position:0% +the focus spot in in this case you're +going to be limited not by uh the laser + + align:start position:0% +going to be limited not by uh the laser + + + align:start position:0% +going to be limited not by uh the laser +you're going to be limited by by + + align:start position:0% +you're going to be limited by by + + + align:start position:0% +you're going to be limited by by +recording resolution and especially TV + + align:start position:0% +recording resolution and especially TV + + + align:start position:0% +recording resolution and especially TV +resolution + + align:start position:0% +resolution + + + align:start position:0% +resolution +so so please don't think that the beam + + align:start position:0% +so so please don't think that the beam + + + align:start position:0% +so so please don't think that the beam +you're going to see the narrow spot of + + align:start position:0% +you're going to see the narrow spot of + + + align:start position:0% +you're going to see the narrow spot of +the beam you're going to see is really + + align:start position:0% +the beam you're going to see is really + + + align:start position:0% +the beam you're going to see is really +what is is is that big it's really much + + align:start position:0% +what is is is that big it's really much + + + align:start position:0% +what is is is that big it's really much +smaller than that and it's a limitation + + align:start position:0% +smaller than that and it's a limitation + + + align:start position:0% +smaller than that and it's a limitation +of of I say of this medium of Television + + align:start position:0% +of of I say of this medium of Television + + + align:start position:0% +of of I say of this medium of Television +right now that that it looks big but at + + align:start position:0% +right now that that it looks big but at + + + align:start position:0% +right now that that it looks big but at +least it will give you some idea of of + + align:start position:0% +least it will give you some idea of of + + + align:start position:0% +least it will give you some idea of of +what this beam looks like so I think now + + align:start position:0% +what this beam looks like so I think now + + + align:start position:0% +what this beam looks like so I think now +we're ready let's look at this this + + align:start position:0% +we're ready let's look at this this + + + align:start position:0% +we're ready let's look at this this +demonstration on various aspects of uh + + align:start position:0% +demonstration on various aspects of uh + + + align:start position:0% +demonstration on various aspects of uh +the Optics of laser + + align:start position:0% + + + + align:start position:0% + +beams + + align:start position:0% + + + + align:start position:0% + +the light beam from a + + align:start position:0% +the light beam from a + + + align:start position:0% +the light beam from a +laser is as close to an ideal beam as + + align:start position:0% +laser is as close to an ideal beam as + + + align:start position:0% +laser is as close to an ideal beam as +one can get what I mean by that that the + + align:start position:0% +one can get what I mean by that that the + + + align:start position:0% +one can get what I mean by that that the +properties of this beam the propagation + + align:start position:0% +properties of this beam the propagation + + + align:start position:0% +properties of this beam the propagation +properties are limited by fundamental + + align:start position:0% +properties are limited by fundamental + + + align:start position:0% +properties are limited by fundamental +laws of + + align:start position:0% +laws of + + + align:start position:0% +laws of +physics for example laws of + + align:start position:0% +physics for example laws of + + + align:start position:0% +physics for example laws of +defraction and not by the properties of + + align:start position:0% +defraction and not by the properties of + + + align:start position:0% +defraction and not by the properties of +the light + + align:start position:0% +the light + + + align:start position:0% +the light +source for example a laser beam from a + + align:start position:0% +source for example a laser beam from a + + + align:start position:0% +source for example a laser beam from a +well behaved laser can be + + align:start position:0% +well behaved laser can be + + + align:start position:0% +well behaved laser can be +cated + + align:start position:0% +cated + + + align:start position:0% +cated +to a very + + align:start position:0% +to a very + + + align:start position:0% +to a very +small + + align:start position:0% +small + + + align:start position:0% +small +angle this angle is determined by as I + + align:start position:0% +angle this angle is determined by as I + + + align:start position:0% +angle this angle is determined by as I +say the laws of defraction which is the + + align:start position:0% +say the laws of defraction which is the + + + align:start position:0% +say the laws of defraction which is the +wavelength of the light divided by the + + align:start position:0% +wavelength of the light divided by the + + + align:start position:0% +wavelength of the light divided by the +diameter of the + + align:start position:0% +diameter of the + + + align:start position:0% +diameter of the +beam and doesn't say anything about the + + align:start position:0% +beam and doesn't say anything about the + + + align:start position:0% +beam and doesn't say anything about the +size of the source of the properties of + + align:start position:0% +size of the source of the properties of + + + align:start position:0% +size of the source of the properties of +the source and that is the ideal + + align:start position:0% +the source and that is the ideal + + + align:start position:0% +the source and that is the ideal +colation limit on a on a + + align:start position:0% +colation limit on a on a + + + align:start position:0% +colation limit on a on a +beam the same time a laser beam can be + + align:start position:0% +beam the same time a laser beam can be + + + align:start position:0% +beam the same time a laser beam can be +focused to a very small spot the size of + + align:start position:0% +focused to a very small spot the size of + + + align:start position:0% +focused to a very small spot the size of +that spot is again determined by laws of + + align:start position:0% +that spot is again determined by laws of + + + align:start position:0% +that spot is again determined by laws of +defraction which is the wavelength of + + align:start position:0% +defraction which is the wavelength of + + + align:start position:0% +defraction which is the wavelength of +the light divided by the diameter of the + + align:start position:0% +the light divided by the diameter of the + + + align:start position:0% +the light divided by the diameter of the +of the beam multiplied by the focal + + align:start position:0% +of the beam multiplied by the focal + + + align:start position:0% +of the beam multiplied by the focal +length of the lens and if we choose the + + align:start position:0% +length of the lens and if we choose the + + + align:start position:0% +length of the lens and if we choose the +diameter of the beam and the focal + + align:start position:0% +diameter of the beam and the focal + + + align:start position:0% +diameter of the beam and the focal +length of the lens about equal then the + + align:start position:0% +length of the lens about equal then the + + + align:start position:0% +length of the lens about equal then the +spot size would be of the order of the + + align:start position:0% +spot size would be of the order of the + + + align:start position:0% +spot size would be of the order of the +wavelength of light and again doesn't + + align:start position:0% +wavelength of light and again doesn't + + + align:start position:0% +wavelength of light and again doesn't +say anything about the physical size of + + align:start position:0% +say anything about the physical size of + + + align:start position:0% +say anything about the physical size of +the light source or what have you as we + + align:start position:0% +the light source or what have you as we + + + align:start position:0% +the light source or what have you as we +would have uh in a case of a AR clamp or + + align:start position:0% +would have uh in a case of a AR clamp or + + + align:start position:0% +would have uh in a case of a AR clamp or +any other kind of uh light source now in + + align:start position:0% +any other kind of uh light source now in + + + align:start position:0% +any other kind of uh light source now in +these demonstrations that follow we're + + align:start position:0% +these demonstrations that follow we're + + + align:start position:0% +these demonstrations that follow we're +going to illustrate some of these basic + + align:start position:0% +going to illustrate some of these basic + + + align:start position:0% +going to illustrate some of these basic +properties of uh of laser + + align:start position:0% +properties of uh of laser + + + align:start position:0% +properties of uh of laser +beams what we going to start with is + + align:start position:0% +beams what we going to start with is + + + align:start position:0% +beams what we going to start with is +this laser here which is a helium neon + + align:start position:0% +this laser here which is a helium neon + + + align:start position:0% +this laser here which is a helium neon +laser and here is the beam from the + + align:start position:0% +laser and here is the beam from the + + + align:start position:0% +laser and here is the beam from the +laser we're going to reflect it by this + + align:start position:0% +laser we're going to reflect it by this + + + align:start position:0% +laser we're going to reflect it by this +mirror + + align:start position:0% +mirror + + + align:start position:0% +mirror +here and then reflect It Again by this + + align:start position:0% +here and then reflect It Again by this + + + align:start position:0% +here and then reflect It Again by this +mirror here and let the beam fall on the + + align:start position:0% +mirror here and let the beam fall on the + + + align:start position:0% +mirror here and let the beam fall on the +on the + + align:start position:0% +on the + + + align:start position:0% +on the +screen now you might be able to get a a + + align:start position:0% +screen now you might be able to get a a + + + align:start position:0% +screen now you might be able to get a a +better feeling for the beam if I use the + + align:start position:0% +better feeling for the beam if I use the + + + align:start position:0% +better feeling for the beam if I use the +black card maybe the colors will come + + align:start position:0% +black card maybe the colors will come + + + align:start position:0% +black card maybe the colors will come +out better so here is essentially the + + align:start position:0% +out better so here is essentially the + + + align:start position:0% +out better so here is essentially the +beam coming up from directly from uh + + align:start position:0% +beam coming up from directly from uh + + + align:start position:0% +beam coming up from directly from uh +from this uh laser and it's very + + align:start position:0% +from this uh laser and it's very + + + align:start position:0% +from this uh laser and it's very +difficult very difficult to to tell + + align:start position:0% +difficult very difficult to to tell + + + align:start position:0% +difficult very difficult to to tell +what's going on it looks pretty pretty + + align:start position:0% +what's going on it looks pretty pretty + + + align:start position:0% +what's going on it looks pretty pretty +uh pretty + + align:start position:0% +uh pretty + + + align:start position:0% +uh pretty +colate + + align:start position:0% +colate + + + align:start position:0% +colate +now what the first thing I'm going to do + + align:start position:0% +now what the first thing I'm going to do + + + align:start position:0% +now what the first thing I'm going to do +is is expand the beam and see and see + + align:start position:0% +is is expand the beam and see and see + + + align:start position:0% +is is expand the beam and see and see +what it looks like so I'm going to take + + align:start position:0% +what it looks like so I'm going to take + + + align:start position:0% +what it looks like so I'm going to take +a short focal length lens and I'm going + + align:start position:0% +a short focal length lens and I'm going + + + align:start position:0% +a short focal length lens and I'm going +to place it in the way of the + + align:start position:0% +to place it in the way of the + + + align:start position:0% +to place it in the way of the +beam and here on the screen now we + + align:start position:0% +beam and here on the screen now we + + + align:start position:0% +beam and here on the screen now we +see we see the uh we see the uh the + + align:start position:0% +see we see the uh we see the uh the + + + align:start position:0% +see we see the uh we see the uh the +expanded beam now if we go take a + + align:start position:0% +expanded beam now if we go take a + + + align:start position:0% +expanded beam now if we go take a +closeup we can see that uh it's got + + align:start position:0% +closeup we can see that uh it's got + + + align:start position:0% +closeup we can see that uh it's got +rings and what have you now these these + + align:start position:0% +rings and what have you now these these + + + align:start position:0% +rings and what have you now these these +rings that you see or these fringes are + + align:start position:0% +rings that you see or these fringes are + + + align:start position:0% +rings that you see or these fringes are +due to the fact that the laser beam has + + align:start position:0% +due to the fact that the laser beam has + + + align:start position:0% +due to the fact that the laser beam has +to go through Optical components like + + align:start position:0% +to go through Optical components like + + + align:start position:0% +to go through Optical components like +the output mirror of the laser has to be + + align:start position:0% +the output mirror of the laser has to be + + + align:start position:0% +the output mirror of the laser has to be +reflected by these mirrors and then has + + align:start position:0% +reflected by these mirrors and then has + + + align:start position:0% +reflected by these mirrors and then has +to pass through this lens over here and + + align:start position:0% +to pass through this lens over here and + + + align:start position:0% +to pass through this lens over here and +and they all corrupt the the laser beam + + align:start position:0% +and they all corrupt the the laser beam + + + align:start position:0% +and they all corrupt the the laser beam +but we can easily get rid of these + + align:start position:0% +but we can easily get rid of these + + + align:start position:0% +but we can easily get rid of these +Effects by placing a pinhole here is the + + align:start position:0% +Effects by placing a pinhole here is the + + + align:start position:0% +Effects by placing a pinhole here is the +uh here's the here's the + + align:start position:0% +uh here's the here's the + + + align:start position:0% +uh here's the here's the +pinhole and and what I can do I can just + + align:start position:0% +pinhole and and what I can do I can just + + + align:start position:0% +pinhole and and what I can do I can just +place the pin hole in front of this lens + + align:start position:0% +place the pin hole in front of this lens + + + align:start position:0% +place the pin hole in front of this lens +or at the focus of this lens here and uh + + align:start position:0% +or at the focus of this lens here and uh + + + align:start position:0% +or at the focus of this lens here and uh +if I have my adjustment + + align:start position:0% +if I have my adjustment + + + align:start position:0% +if I have my adjustment +right I have then socalled the space Al + + align:start position:0% +right I have then socalled the space Al + + + align:start position:0% +right I have then socalled the space Al +filtered uh laser beam as you can see on + + align:start position:0% +filtered uh laser beam as you can see on + + + align:start position:0% +filtered uh laser beam as you can see on +the screen now we got rid of the all + + align:start position:0% +the screen now we got rid of the all + + + align:start position:0% +the screen now we got rid of the all +these rings and this is as close to an + + align:start position:0% +these rings and this is as close to an + + + align:start position:0% +these rings and this is as close to an +ideal laser beam as one one can get now + + align:start position:0% +ideal laser beam as one one can get now + + + align:start position:0% +ideal laser beam as one one can get now +what we see here is is the the speckle + + align:start position:0% +what we see here is is the the speckle + + + align:start position:0% +what we see here is is the the speckle +so if I move the screen a little bit you + + align:start position:0% +so if I move the screen a little bit you + + + align:start position:0% +so if I move the screen a little bit you +can see I can wash out the speckle so + + align:start position:0% +can see I can wash out the speckle so + + + align:start position:0% +can see I can wash out the speckle so +when it's still you can see the the + + align:start position:0% +when it's still you can see the the + + + align:start position:0% +when it's still you can see the the +speckle pattern because the surface is + + align:start position:0% +speckle pattern because the surface is + + + align:start position:0% +speckle pattern because the surface is +not uh is not smooth but otherwise you + + align:start position:0% +not uh is not smooth but otherwise you + + + align:start position:0% +not uh is not smooth but otherwise you +don't see any any any fringes uh on the + + align:start position:0% +don't see any any any fringes uh on the + + + align:start position:0% +don't see any any any fringes uh on the +beam and + + align:start position:0% +beam and + + + align:start position:0% +beam and +also uh the there's an intensity + + align:start position:0% +also uh the there's an intensity + + + align:start position:0% +also uh the there's an intensity +distribution which is which is + + align:start position:0% +distribution which is which is + + + align:start position:0% +distribution which is which is +essentially Gan squar the field is Gan + + align:start position:0% +essentially Gan squar the field is Gan + + + align:start position:0% +essentially Gan squar the field is Gan +but the intens distribution is uh is Gan + + align:start position:0% +but the intens distribution is uh is Gan + + + align:start position:0% +but the intens distribution is uh is Gan +squared so that essentially drops off + + align:start position:0% +squared so that essentially drops off + + + align:start position:0% +squared so that essentially drops off +the zero in the in the wings all right + + align:start position:0% +the zero in the in the wings all right + + + align:start position:0% +the zero in the in the wings all right +so this is this is a so-called spatially + + align:start position:0% +so this is this is a so-called spatially + + + align:start position:0% +so this is this is a so-called spatially +filtered laser beam and for some + + align:start position:0% +filtered laser beam and for some + + + align:start position:0% +filtered laser beam and for some +experiments it's very important to to uh + + align:start position:0% +experiments it's very important to to uh + + + align:start position:0% +experiments it's very important to to uh +spatially filter the beam especially in + + align:start position:0% +spatially filter the beam especially in + + + align:start position:0% +spatially filter the beam especially in +interferometry and and what have you + + align:start position:0% + + + + align:start position:0% + +now I'm going to uh well no before I do + + align:start position:0% +now I'm going to uh well no before I do + + + align:start position:0% +now I'm going to uh well no before I do +anything else I'm going to show you that + + align:start position:0% +anything else I'm going to show you that + + + align:start position:0% +anything else I'm going to show you that +that the the placing of the pin hole is + + align:start position:0% +that the the placing of the pin hole is + + + align:start position:0% +that the the placing of the pin hole is +uh is very + + align:start position:0% +uh is very + + + align:start position:0% +uh is very +critical if I if we can now take a close + + align:start position:0% +critical if I if we can now take a close + + + align:start position:0% +critical if I if we can now take a close +up of the of the spot now if I move the + + align:start position:0% +up of the of the spot now if I move the + + + align:start position:0% +up of the of the spot now if I move the +pinhole slightly you can see that that + + align:start position:0% +pinhole slightly you can see that that + + + align:start position:0% +pinhole slightly you can see that that +the first of all the beam disappears + + align:start position:0% +the first of all the beam disappears + + + align:start position:0% +the first of all the beam disappears +because this pin hole is only of the + + align:start position:0% +because this pin hole is only of the + + + align:start position:0% +because this pin hole is only of the +order of about 12 microns or so and + + align:start position:0% +order of about 12 microns or so and + + + align:start position:0% +order of about 12 microns or so and +another point that one has to watch out + + align:start position:0% +another point that one has to watch out + + + align:start position:0% +another point that one has to watch out +for when using such a pinhole as a + + align:start position:0% +for when using such a pinhole as a + + + align:start position:0% +for when using such a pinhole as a +special filter is that if the pinhole + + align:start position:0% +special filter is that if the pinhole + + + align:start position:0% +special filter is that if the pinhole +interrupts any part of the laser + + align:start position:0% +interrupts any part of the laser + + + align:start position:0% +interrupts any part of the laser +beam the now let's look at the the the + + align:start position:0% +beam the now let's look at the the the + + + align:start position:0% +beam the now let's look at the the the +inset again that this this Gan + + align:start position:0% +inset again that this this Gan + + + align:start position:0% +inset again that this this Gan +distribution in the beam gets gets + + align:start position:0% +distribution in the beam gets gets + + + align:start position:0% +distribution in the beam gets gets +affected and you will start to see all + + align:start position:0% +affected and you will start to see all + + + align:start position:0% +affected and you will start to see all +kinds of uh defraction rings so again + + align:start position:0% +kinds of uh defraction rings so again + + + align:start position:0% +kinds of uh defraction rings so again +for the special filter to work the the + + align:start position:0% +for the special filter to work the the + + + align:start position:0% +for the special filter to work the the +uh the the pinhole must not cut any of + + align:start position:0% +uh the the pinhole must not cut any of + + + align:start position:0% +uh the the pinhole must not cut any of +the essential part of the of the laser + + align:start position:0% +the essential part of the of the laser + + + align:start position:0% +the essential part of the of the laser +beam now what I'm going to do is is + + align:start position:0% +beam now what I'm going to do is is + + + align:start position:0% +beam now what I'm going to do is is +cumate uh this this beam of light and + + align:start position:0% +cumate uh this this beam of light and + + + align:start position:0% +cumate uh this this beam of light and +here what I will use is a uh a simple + + align:start position:0% +here what I will use is a uh a simple + + + align:start position:0% +here what I will use is a uh a simple +two lens uh two lens + + align:start position:0% +two lens uh two lens + + + align:start position:0% +two lens uh two lens +cator and uh I'll place it over + + align:start position:0% +cator and uh I'll place it over + + + align:start position:0% +cator and uh I'll place it over +here and uh + + align:start position:0% + + + + align:start position:0% + +and here it + + align:start position:0% +and here it + + + align:start position:0% +and here it +is here's the here's the output from the + + align:start position:0% +is here's the here's the output from the + + + align:start position:0% +is here's the here's the output from the +from the cator on the black card and see + + align:start position:0% +from the cator on the black card and see + + + align:start position:0% +from the cator on the black card and see +that obviously you can't check on the + + align:start position:0% +that obviously you can't check on the + + + align:start position:0% +that obviously you can't check on the +exact colation but you can see that the + + align:start position:0% +exact colation but you can see that the + + + align:start position:0% +exact colation but you can see that the +beam can be can be uh simply uh + + align:start position:0% +beam can be can be uh simply uh + + + align:start position:0% +beam can be can be uh simply uh +columnated all right now the next thing + + align:start position:0% +columnated all right now the next thing + + + align:start position:0% +columnated all right now the next thing +that one sometime wants to do wants to + + align:start position:0% +that one sometime wants to do wants to + + + align:start position:0% +that one sometime wants to do wants to +focus the laser beams again if I take a + + align:start position:0% +focus the laser beams again if I take a + + + align:start position:0% +focus the laser beams again if I take a +simple + + align:start position:0% +simple + + + align:start position:0% +simple +lens and again place it in the + + align:start position:0% +lens and again place it in the + + + align:start position:0% +lens and again place it in the +beam now I + + align:start position:0% +beam now I + + + align:start position:0% +beam now I +can focus let's look at the beam again I + + align:start position:0% +can focus let's look at the beam again I + + + align:start position:0% +can focus let's look at the beam again I +can focus to a tiny spot and back out + + align:start position:0% +can focus to a tiny spot and back out + + + align:start position:0% +can focus to a tiny spot and back out +again here we are let me Focus the small + + align:start position:0% +again here we are let me Focus the small + + + align:start position:0% +again here we are let me Focus the small +spot now it's very + + align:start position:0% +spot now it's very + + + align:start position:0% +spot now it's very +difficult to see the size of the of the + + align:start position:0% +difficult to see the size of the of the + + + align:start position:0% +difficult to see the size of the of the +spot or even the shape of this focused + + align:start position:0% +spot or even the shape of this focused + + + align:start position:0% +spot or even the shape of this focused +gan + + align:start position:0% +gan + + + align:start position:0% +gan +gussan + + align:start position:0% +gussan + + + align:start position:0% +gussan +beam remember I said before they can be + + align:start position:0% +beam remember I said before they can be + + + align:start position:0% +beam remember I said before they can be +focused to to a spot size of the order + + align:start position:0% +focused to to a spot size of the order + + + align:start position:0% +focused to to a spot size of the order +of the wavelength uh of + + align:start position:0% +of the wavelength uh of + + + align:start position:0% +of the wavelength uh of +light and it's not so easy to see it on + + align:start position:0% +light and it's not so easy to see it on + + + align:start position:0% +light and it's not so easy to see it on +this card so what we're going to do when + + align:start position:0% +this card so what we're going to do when + + + align:start position:0% +this card so what we're going to do when +we come back we're going to uh get a + + align:start position:0% +we come back we're going to uh get a + + + align:start position:0% +we come back we're going to uh get a +water tank and pass the light beam the + + align:start position:0% +water tank and pass the light beam the + + + align:start position:0% +water tank and pass the light beam the +focus light beam laser beam into the + + align:start position:0% +focus light beam laser beam into the + + + align:start position:0% +focus light beam laser beam into the +water tank and we'll add some scatterers + + align:start position:0% +water tank and we'll add some scatterers + + + align:start position:0% +water tank and we'll add some scatterers +to enhance the uh the the this the + + align:start position:0% +to enhance the uh the the this the + + + align:start position:0% +to enhance the uh the the this the +scaning from the laser beam by the water + + align:start position:0% +scaning from the laser beam by the water + + + align:start position:0% +scaning from the laser beam by the water +and then you'll see you get a better + + align:start position:0% +and then you'll see you get a better + + + align:start position:0% +and then you'll see you get a better +picture for for the focusing of uh of + + align:start position:0% +picture for for the focusing of uh of + + + align:start position:0% +picture for for the focusing of uh of +this gaussian uh laser beam so when we + + align:start position:0% +this gaussian uh laser beam so when we + + + align:start position:0% +this gaussian uh laser beam so when we +come back we'll have that already for + + align:start position:0% +come back we'll have that already for + + + align:start position:0% +come back we'll have that already for +you we have now placed the water tank in + + align:start position:0% +you we have now placed the water tank in + + + align:start position:0% +you we have now placed the water tank in +place so that we can pass the laser beam + + align:start position:0% +place so that we can pass the laser beam + + + align:start position:0% +place so that we can pass the laser beam +through it and visualize the the laser + + align:start position:0% +through it and visualize the the laser + + + align:start position:0% +through it and visualize the the laser +beam as it passes through the through + + align:start position:0% +beam as it passes through the through + + + align:start position:0% +beam as it passes through the through +the through the water we've also here is + + align:start position:0% +the through the water we've also here is + + + align:start position:0% +the through the water we've also here is +the tank by the way and uh We've also + + align:start position:0% +the tank by the way and uh We've also + + + align:start position:0% +the tank by the way and uh We've also +added uh few drops of milk to enhance + + align:start position:0% +added uh few drops of milk to enhance + + + align:start position:0% +added uh few drops of milk to enhance +the scaning and that's why the water + + align:start position:0% +the scaning and that's why the water + + + align:start position:0% +the scaning and that's why the water +looks + + align:start position:0% +looks + + + align:start position:0% +looks +murky in addition we've tilted the tank + + align:start position:0% +murky in addition we've tilted the tank + + + align:start position:0% +murky in addition we've tilted the tank +a little bit so that we can get a better + + align:start position:0% +a little bit so that we can get a better + + + align:start position:0% +a little bit so that we can get a better +angle for the for the camera now the + + align:start position:0% +angle for the for the camera now the + + + align:start position:0% +angle for the for the camera now the +setup is just like we had it before but + + align:start position:0% +setup is just like we had it before but + + + align:start position:0% +setup is just like we had it before but +let me remind you of it here's the laser + + align:start position:0% +let me remind you of it here's the laser + + + align:start position:0% +let me remind you of it here's the laser +is's a beam from the laser reflected by + + align:start position:0% +is's a beam from the laser reflected by + + + align:start position:0% +is's a beam from the laser reflected by +this mirror here then we pass it through + + align:start position:0% +this mirror here then we pass it through + + + align:start position:0% +this mirror here then we pass it through +a polarization Rotator here so that we + + align:start position:0% +a polarization Rotator here so that we + + + align:start position:0% +a polarization Rotator here so that we +can adjust the polarization for uh + + align:start position:0% +can adjust the polarization for uh + + + align:start position:0% +can adjust the polarization for uh +maximum scattered light for the camera + + align:start position:0% +maximum scattered light for the camera + + + align:start position:0% +maximum scattered light for the camera +and then the output after the + + align:start position:0% +and then the output after the + + + align:start position:0% +and then the output after the +polarization Rotator gets reflected by + + align:start position:0% +polarization Rotator gets reflected by + + + align:start position:0% +polarization Rotator gets reflected by +this mirror here into this short focal + + align:start position:0% +this mirror here into this short focal + + + align:start position:0% +this mirror here into this short focal +length lens the spatial filter we had + + align:start position:0% +length lens the spatial filter we had + + + align:start position:0% +length lens the spatial filter we had +before and then the colat the output of + + align:start position:0% +before and then the colat the output of + + + align:start position:0% +before and then the colat the output of +the cator is here before it goes into + + align:start position:0% +the cator is here before it goes into + + + align:start position:0% +the cator is here before it goes into +the tank and then out here after it + + align:start position:0% +the tank and then out here after it + + + align:start position:0% +the tank and then out here after it +leaves leaves the tank + + align:start position:0% +leaves leaves the tank + + + align:start position:0% +leaves leaves the tank +now in order to visualize the beam as it + + align:start position:0% +now in order to visualize the beam as it + + + align:start position:0% +now in order to visualize the beam as it +propagates in the water we'll have to + + align:start position:0% +propagates in the water we'll have to + + + align:start position:0% +propagates in the water we'll have to +turn the room lights down but let me + + align:start position:0% +turn the room lights down but let me + + + align:start position:0% +turn the room lights down but let me +tell you what I'm going to do when the + + align:start position:0% +tell you what I'm going to do when the + + + align:start position:0% +tell you what I'm going to do when the +room lights are + + align:start position:0% +room lights are + + + align:start position:0% +room lights are +down I'm going to first look at the + + align:start position:0% +down I'm going to first look at the + + + align:start position:0% +down I'm going to first look at the +columnated beam in the water and then + + align:start position:0% +columnated beam in the water and then + + + align:start position:0% +columnated beam in the water and then +I'm going to take this lens and another + + align:start position:0% +I'm going to take this lens and another + + + align:start position:0% +I'm going to take this lens and another +lens like this and I'm going to place it + + align:start position:0% +lens like this and I'm going to place it + + + align:start position:0% +lens like this and I'm going to place it +over + + align:start position:0% + + + + align:start position:0% + +here so that we can focus the light into + + align:start position:0% +here so that we can focus the light into + + + align:start position:0% +here so that we can focus the light into +into the tank all right so and then we + + align:start position:0% +into the tank all right so and then we + + + align:start position:0% +into the tank all right so and then we +can explore the region around around the + + align:start position:0% +can explore the region around around the + + + align:start position:0% +can explore the region around around the +focus so now we're ready to turn the + + align:start position:0% +focus so now we're ready to turn the + + + align:start position:0% +focus so now we're ready to turn the +room lights down and look at the region + + align:start position:0% +room lights down and look at the region + + + align:start position:0% +room lights down and look at the region +around the focus uh by simply observing + + align:start position:0% +around the focus uh by simply observing + + + align:start position:0% +around the focus uh by simply observing +the scattered light uh in the + + align:start position:0% + + + + align:start position:0% + +water now that the room lights are + + align:start position:0% +water now that the room lights are + + + align:start position:0% +water now that the room lights are +dimmed and the camera focused into the + + align:start position:0% +dimmed and the camera focused into the + + + align:start position:0% +dimmed and the camera focused into the +tank first thing we see is is the + + align:start position:0% +tank first thing we see is is the + + + align:start position:0% +tank first thing we see is is the +columnated beam or the scattered light + + align:start position:0% +columnated beam or the scattered light + + + align:start position:0% +columnated beam or the scattered light +associated with the col cated beam + + align:start position:0% +associated with the col cated beam + + + align:start position:0% +associated with the col cated beam +there's not much I can really say about + + align:start position:0% +there's not much I can really say about + + + align:start position:0% +there's not much I can really say about +that more interesting is when I put a a + + align:start position:0% +that more interesting is when I put a a + + + align:start position:0% +that more interesting is when I put a a +lens before the before the + + align:start position:0% +lens before the before the + + + align:start position:0% +lens before the before the +tank and look at the focal + + align:start position:0% + + + + align:start position:0% + +region here we are I'm going to adjust + + align:start position:0% +region here we are I'm going to adjust + + + align:start position:0% +region here we are I'm going to adjust +the position of the lens so that the + + align:start position:0% +the position of the lens so that the + + + align:start position:0% +the position of the lens so that the +waist or the focused region focal region + + align:start position:0% +waist or the focused region focal region + + + align:start position:0% +waist or the focused region focal region +is in the center of your of your + + align:start position:0% +is in the center of your of your + + + align:start position:0% +is in the center of your of your +screen now the things that you can + + align:start position:0% +screen now the things that you can + + + align:start position:0% +screen now the things that you can +observe is that laser beam coming in + + align:start position:0% +observe is that laser beam coming in + + + align:start position:0% +observe is that laser beam coming in +from from the left then is then focused + + align:start position:0% +from from the left then is then focused + + + align:start position:0% +from from the left then is then focused +to a uh a region where the spot is small + + align:start position:0% +to a uh a region where the spot is small + + + align:start position:0% +to a uh a region where the spot is small +spot size is small then expands again on + + align:start position:0% +spot size is small then expands again on + + + align:start position:0% +spot size is small then expands again on +the other side now because of the + + align:start position:0% +the other side now because of the + + + align:start position:0% +the other side now because of the +limitation of Television + + align:start position:0% +limitation of Television + + + align:start position:0% +limitation of Television +recording and especially recording of + + align:start position:0% +recording and especially recording of + + + align:start position:0% +recording and especially recording of +color especially red you do better if + + align:start position:0% +color especially red you do better if + + + align:start position:0% +color especially red you do better if +you want to see how narrow that focal + + align:start position:0% +you want to see how narrow that focal + + + align:start position:0% +you want to see how narrow that focal +region is you do better if you turn down + + align:start position:0% +region is you do better if you turn down + + + align:start position:0% +region is you do better if you turn down +the color turn off the color and look at + + align:start position:0% +the color turn off the color and look at + + + align:start position:0% +the color turn off the color and look at +it in black and + + align:start position:0% +it in black and + + + align:start position:0% +it in black and +white if you do that you'll see that + + align:start position:0% +white if you do that you'll see that + + + align:start position:0% +white if you do that you'll see that +that the the focal region is now + + align:start position:0% +that the the focal region is now + + + align:start position:0% +that the the focal region is now +narrower than it is when when it's + + align:start position:0% + + + + align:start position:0% + +red but in fact the truth is that you + + align:start position:0% +red but in fact the truth is that you + + + align:start position:0% +red but in fact the truth is that you +cannot really observe in this way the + + align:start position:0% +cannot really observe in this way the + + + align:start position:0% +cannot really observe in this way the +the uh the true size of the of the + + align:start position:0% +the uh the true size of the of the + + + align:start position:0% +the uh the true size of the of the +focused spot because that's only uh few + + align:start position:0% +focused spot because that's only uh few + + + align:start position:0% +focused spot because that's only uh few +microns and it's going to be limited by + + align:start position:0% +microns and it's going to be limited by + + + align:start position:0% +microns and it's going to be limited by +television resolution uh in any case but + + align:start position:0% +television resolution uh in any case but + + + align:start position:0% +television resolution uh in any case but +at least you get a feel for the fact + + align:start position:0% +at least you get a feel for the fact + + + align:start position:0% +at least you get a feel for the fact +that the beam is pretty narrow at the at + + align:start position:0% +that the beam is pretty narrow at the at + + + align:start position:0% +that the beam is pretty narrow at the at +the focus another thing you want to + + align:start position:0% +the focus another thing you want to + + + align:start position:0% +the focus another thing you want to +observe is that the region around the + + align:start position:0% +observe is that the region around the + + + align:start position:0% +observe is that the region around the +the + + align:start position:0% +the + + + align:start position:0% +the +focus is is reasonably + + align:start position:0% +focus is is reasonably + + + align:start position:0% +focus is is reasonably +uh constant in in in diameter and that's + + align:start position:0% +uh constant in in in diameter and that's + + + align:start position:0% +uh constant in in in diameter and that's +called the ra region where the expansion + + align:start position:0% +called the ra region where the expansion + + + align:start position:0% +called the ra region where the expansion +of the beam is not so big but after that + + align:start position:0% +of the beam is not so big but after that + + + align:start position:0% +of the beam is not so big but after that +then the beam expands one side and then + + align:start position:0% +then the beam expands one side and then + + + align:start position:0% +then the beam expands one side and then +symmetrically symmetrically the the + + align:start position:0% +symmetrically symmetrically the the + + + align:start position:0% +symmetrically symmetrically the the +other side of the beam the intensity + + align:start position:0% +other side of the beam the intensity + + + align:start position:0% +other side of the beam the intensity +distribution if I take a slice anywhere + + align:start position:0% +distribution if I take a slice anywhere + + + align:start position:0% +distribution if I take a slice anywhere +along the beam the intensity + + align:start position:0% +along the beam the intensity + + + align:start position:0% +along the beam the intensity +distribution is still Galan or Gan squar + + align:start position:0% +distribution is still Galan or Gan squar + + + align:start position:0% +distribution is still Galan or Gan squar +the field distribution is Gan intensity + + align:start position:0% +the field distribution is Gan intensity + + + align:start position:0% +the field distribution is Gan intensity +is Galan + + align:start position:0% +is Galan + + + align:start position:0% +is Galan +squared + + align:start position:0% +squared + + + align:start position:0% +squared +the the other uh thing to observe is + + align:start position:0% +the the other uh thing to observe is + + + align:start position:0% +the the other uh thing to observe is +that the + + align:start position:0% +that the + + + align:start position:0% +that the +curvature now at the focal at the + + align:start position:0% +curvature now at the focal at the + + + align:start position:0% +curvature now at the focal at the +focus or at the the middle of that ra + + align:start position:0% +focus or at the the middle of that ra + + + align:start position:0% +focus or at the the middle of that ra +range what we call the focus or the + + align:start position:0% +range what we call the focus or the + + + align:start position:0% +range what we call the focus or the +waist of the beam the curvature is the + + align:start position:0% +waist of the beam the curvature is the + + + align:start position:0% +waist of the beam the curvature is the +radius of curvature is is infinite which + + align:start position:0% +radius of curvature is is infinite which + + + align:start position:0% +radius of curvature is is infinite which +means that we have a plain + + align:start position:0% +means that we have a plain + + + align:start position:0% +means that we have a plain +wave now the it stays plain within the + + align:start position:0% +wave now the it stays plain within the + + + align:start position:0% +wave now the it stays plain within the +ra region or close to Plaine and then + + align:start position:0% +ra region or close to Plaine and then + + + align:start position:0% +ra region or close to Plaine and then +then we develop the curvature so we have + + align:start position:0% +then we develop the curvature so we have + + + align:start position:0% +then we develop the curvature so we have +an expanding Beam on one side expanding + + align:start position:0% +an expanding Beam on one side expanding + + + align:start position:0% +an expanding Beam on one side expanding +Beam on the other side in fact if we go + + align:start position:0% +Beam on the other side in fact if we go + + + align:start position:0% +Beam on the other side in fact if we go +far away the curvature the radius of + + align:start position:0% +far away the curvature the radius of + + + align:start position:0% +far away the curvature the radius of +curvature is the same as if we had a + + align:start position:0% +curvature is the same as if we had a + + + align:start position:0% +curvature is the same as if we had a +spherical wave starting at the at the + + align:start position:0% +spherical wave starting at the at the + + + align:start position:0% +spherical wave starting at the at the +waist all right that's with this lens + + align:start position:0% +waist all right that's with this lens + + + align:start position:0% +waist all right that's with this lens +now I'm going to take this lens off and + + align:start position:0% +now I'm going to take this lens off and + + + align:start position:0% +now I'm going to take this lens off and +place another lens that is little + + align:start position:0% +place another lens that is little + + + align:start position:0% +place another lens that is little +shorter in in uh in focal + + align:start position:0% +shorter in in uh in focal + + + align:start position:0% +shorter in in uh in focal +length + + align:start position:0% +length + + + align:start position:0% +length +and here we + + align:start position:0% +and here we + + + align:start position:0% +and here we +are I let me turn it + + align:start position:0% +are I let me turn it + + + align:start position:0% +are I let me turn it +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +around and then let me again Center it + + align:start position:0% +around and then let me again Center it + + + align:start position:0% +around and then let me again Center it +so that you can the waist is the middle + + align:start position:0% +so that you can the waist is the middle + + + align:start position:0% +so that you can the waist is the middle +of your screen you can see now the + + align:start position:0% +of your screen you can see now the + + + align:start position:0% +of your screen you can see now the +Divergence is is different showing that + + align:start position:0% +Divergence is is different showing that + + + align:start position:0% +Divergence is is different showing that +it's a shorter focal length length now + + align:start position:0% +it's a shorter focal length length now + + + align:start position:0% +it's a shorter focal length length now +if I move it to one side you can see + + align:start position:0% +if I move it to one side you can see + + + align:start position:0% +if I move it to one side you can see +that the beam gets quite big very + + align:start position:0% +that the beam gets quite big very + + + align:start position:0% +that the beam gets quite big very +quickly and also the same to the other + + align:start position:0% +quickly and also the same to the other + + + align:start position:0% +quickly and also the same to the other +side and then + + align:start position:0% + + + + align:start position:0% + +the and then but the other thing you + + align:start position:0% +the and then but the other thing you + + + align:start position:0% +the and then but the other thing you +notice that the r range or the region + + align:start position:0% +notice that the r range or the region + + + align:start position:0% +notice that the r range or the region +around Focus now is smaller so it's a + + align:start position:0% +around Focus now is smaller so it's a + + + align:start position:0% +around Focus now is smaller so it's a +tighter uh Focus than in the previous + + align:start position:0% +tighter uh Focus than in the previous + + + align:start position:0% +tighter uh Focus than in the previous +case and as the as the uh focal length + + align:start position:0% +case and as the as the uh focal length + + + align:start position:0% +case and as the as the uh focal length +of the lens gets bigger and bigger then + + align:start position:0% +of the lens gets bigger and bigger then + + + align:start position:0% +of the lens gets bigger and bigger then +the r region gets bigger and bigger also + + align:start position:0% +the r region gets bigger and bigger also + + + align:start position:0% +the r region gets bigger and bigger also +so here we are the shorter focal L lens + + align:start position:0% +so here we are the shorter focal L lens + + + align:start position:0% +so here we are the shorter focal L lens +and again if you want to see a nice + + align:start position:0% +and again if you want to see a nice + + + align:start position:0% +and again if you want to see a nice +small focal region then you want to turn + + align:start position:0% +small focal region then you want to turn + + + align:start position:0% +small focal region then you want to turn +down your color and look at it in uh in + + align:start position:0% +down your color and look at it in uh in + + + align:start position:0% +down your color and look at it in uh in +black and + + align:start position:0% + + + + align:start position:0% + +white well now you can say that you know + + align:start position:0% +white well now you can say that you know + + + align:start position:0% +white well now you can say that you know +all about the nice things uh about a + + align:start position:0% +all about the nice things uh about a + + + align:start position:0% +all about the nice things uh about a +laser in this next part I'm going to + + align:start position:0% +laser in this next part I'm going to + + + align:start position:0% +laser in this next part I'm going to +start telling you about uh about sort of + + align:start position:0% +start telling you about uh about sort of + + + align:start position:0% +start telling you about uh about sort of +problems uh that uh and other issues + + align:start position:0% +problems uh that uh and other issues + + + align:start position:0% +problems uh that uh and other issues +about about laser in fact I call it uh + + align:start position:0% +about about laser in fact I call it uh + + + align:start position:0% +about about laser in fact I call it uh +other issues and problems relating to + + align:start position:0% +other issues and problems relating to + + + align:start position:0% +other issues and problems relating to +lasers the the first one is and again + + align:start position:0% +lasers the the first one is and again + + + align:start position:0% +lasers the the first one is and again +without doing any math uh I want to tell + + align:start position:0% +without doing any math uh I want to tell + + + align:start position:0% +without doing any math uh I want to tell +you about uh about amplifier + + align:start position:0% +you about uh about amplifier + + + align:start position:0% +you about uh about amplifier +limitations and uh and what can go wrong + + align:start position:0% +limitations and uh and what can go wrong + + + align:start position:0% +limitations and uh and what can go wrong +in uh in amplifiers all right so here we + + align:start position:0% +in uh in amplifiers all right so here we + + + align:start position:0% +in uh in amplifiers all right so here we +go again we have our three-level system + + align:start position:0% +go again we have our three-level system + + + align:start position:0% +go again we have our three-level system +which is the simplest of amplifiers we + + align:start position:0% +which is the simplest of amplifiers we + + + align:start position:0% +which is the simplest of amplifiers we +have we have the pump and uh and then we + + align:start position:0% +have we have the pump and uh and then we + + + align:start position:0% +have we have the pump and uh and then we +take some of these atoms from here put + + align:start position:0% +take some of these atoms from here put + + + align:start position:0% +take some of these atoms from here put +them up here and we have a population + + align:start position:0% +them up here and we have a population + + + align:start position:0% +them up here and we have a population +difference and and uh if there were no + + align:start position:0% +difference and and uh if there were no + + + align:start position:0% +difference and and uh if there were no +lazing as we mentioned before these + + align:start position:0% +lazing as we mentioned before these + + + align:start position:0% +lazing as we mentioned before these +atoms here would drop down to level two + + align:start position:0% +atoms here would drop down to level two + + + align:start position:0% +atoms here would drop down to level two +and through spontaneous emission just + + align:start position:0% +and through spontaneous emission just + + + align:start position:0% +and through spontaneous emission just +like uh it's like over here so if you + + align:start position:0% +like uh it's like over here so if you + + + align:start position:0% +like uh it's like over here so if you +just leave the the amplifier alone and + + align:start position:0% +just leave the the amplifier alone and + + + align:start position:0% +just leave the the amplifier alone and +there is no uh cavity let's say then + + align:start position:0% +there is no uh cavity let's say then + + + align:start position:0% +there is no uh cavity let's say then +what happens is that the uh the atoms + + align:start position:0% +what happens is that the uh the atoms + + + align:start position:0% +what happens is that the uh the atoms +will drop by spontaneous emission and uh + + align:start position:0% +will drop by spontaneous emission and uh + + + align:start position:0% +will drop by spontaneous emission and uh +and there will be no uh and there and + + align:start position:0% +and there will be no uh and there and + + + align:start position:0% +and there will be no uh and there and +then uh uh they all after a while will + + align:start position:0% +then uh uh they all after a while will + + + align:start position:0% +then uh uh they all after a while will +all drop will all drop down by emitting + + align:start position:0% +all drop will all drop down by emitting + + + align:start position:0% +all drop will all drop down by emitting +spontaneous emission if there is a + + align:start position:0% +spontaneous emission if there is a + + + align:start position:0% +spontaneous emission if there is a +cavity and spontaneous emission gets the + + align:start position:0% +cavity and spontaneous emission gets the + + + align:start position:0% +cavity and spontaneous emission gets the +laser going then what's going to happen + + align:start position:0% +laser going then what's going to happen + + + align:start position:0% +laser going then what's going to happen +is that these atoms will be driven down + + align:start position:0% +is that these atoms will be driven down + + + align:start position:0% +is that these atoms will be driven down +by stimulated + + align:start position:0% +by stimulated + + + align:start position:0% +by stimulated +emission now as you can see as you drive + + align:start position:0% +emission now as you can see as you drive + + + align:start position:0% +emission now as you can see as you drive +these atoms down they're going to go to + + align:start position:0% +these atoms down they're going to go to + + + align:start position:0% +these atoms down they're going to go to +this level two and we have to know what + + align:start position:0% +this level two and we have to know what + + + align:start position:0% +this level two and we have to know what +happens to them when they're in level + + align:start position:0% +happens to them when they're in level + + + align:start position:0% +happens to them when they're in level +two if level two if the atoms can't get + + align:start position:0% +two if level two if the atoms can't get + + + align:start position:0% +two if level two if the atoms can't get +out of level two + + align:start position:0% +out of level two + + + align:start position:0% +out of level two +then as you can guess sooner or later + + align:start position:0% +then as you can guess sooner or later + + + align:start position:0% +then as you can guess sooner or later +level two is going to have more atoms in + + align:start position:0% +level two is going to have more atoms in + + + align:start position:0% +level two is going to have more atoms in +it than level three and as we know + + align:start position:0% +it than level three and as we know + + + align:start position:0% +it than level three and as we know +that's a no no in lasers that means it + + align:start position:0% +that's a no no in lasers that means it + + + align:start position:0% +that's a no no in lasers that means it +becomes absorption here not gain because + + align:start position:0% +becomes absorption here not gain because + + + align:start position:0% +becomes absorption here not gain because +n lower now is bigger than n upper so we + + align:start position:0% +n lower now is bigger than n upper so we + + + align:start position:0% +n lower now is bigger than n upper so we +have a problem on our hands so this then + + align:start position:0% +have a problem on our hands so this then + + + align:start position:0% +have a problem on our hands so this then +this laser then if then will become like + + align:start position:0% +this laser then if then will become like + + + align:start position:0% +this laser then if then will become like +a pulse laser because you start with + + align:start position:0% +a pulse laser because you start with + + + align:start position:0% +a pulse laser because you start with +gain a lot of gain and if you lay it + + align:start position:0% +gain a lot of gain and if you lay it + + + align:start position:0% +gain a lot of gain and if you lay it +will lay for a short time until the + + align:start position:0% +will lay for a short time until the + + + align:start position:0% +will lay for a short time until the +populations are equalized and then boom + + align:start position:0% +populations are equalized and then boom + + + align:start position:0% +populations are equalized and then boom +the laser goes goes out so the the + + align:start position:0% +the laser goes goes out so the the + + + align:start position:0% +the laser goes goes out so the the +question now is well what do you do + + align:start position:0% +question now is well what do you do + + + align:start position:0% +question now is well what do you do +about it if if indeed level two starts + + align:start position:0% +about it if if indeed level two starts + + + align:start position:0% +about it if if indeed level two starts +to fill up and and won't go down again + + align:start position:0% +to fill up and and won't go down again + + + align:start position:0% +to fill up and and won't go down again +you have to you have to solve that + + align:start position:0% +you have to you have to solve that + + + align:start position:0% +you have to you have to solve that +problem so what what you do you have to + + align:start position:0% +problem so what what you do you have to + + + align:start position:0% +problem so what what you do you have to +come up with a way of making this level + + align:start position:0% +come up with a way of making this level + + + align:start position:0% +come up with a way of making this level +here uh Decay down either through + + align:start position:0% +here uh Decay down either through + + + align:start position:0% +here uh Decay down either through +spontaneous emission by choosing the + + align:start position:0% +spontaneous emission by choosing the + + + align:start position:0% +spontaneous emission by choosing the +right system or maybe by adding uh other + + align:start position:0% +right system or maybe by adding uh other + + + align:start position:0% +right system or maybe by adding uh other +gases or what have you to through + + align:start position:0% +gases or what have you to through + + + align:start position:0% +gases or what have you to through +collisions to bring this level down by + + align:start position:0% +collisions to bring this level down by + + + align:start position:0% +collisions to bring this level down by +by Collision there many tricks and so so + + align:start position:0% +by Collision there many tricks and so so + + + align:start position:0% +by Collision there many tricks and so so +a a continuous laser then has to have a + + align:start position:0% +a a continuous laser then has to have a + + + align:start position:0% +a a continuous laser then has to have a +mechanism for getting rid of this this + + align:start position:0% +mechanism for getting rid of this this + + + align:start position:0% +mechanism for getting rid of this this +bottleneck of this level two it has to + + align:start position:0% +bottleneck of this level two it has to + + + align:start position:0% +bottleneck of this level two it has to +bring it down so that and it's got to be + + align:start position:0% +bring it down so that and it's got to be + + + align:start position:0% +bring it down so that and it's got to be +fast much faster than these things + + align:start position:0% +fast much faster than these things + + + align:start position:0% +fast much faster than these things +coming in because otherwise then this is + + align:start position:0% +coming in because otherwise then this is + + + align:start position:0% +coming in because otherwise then this is +going to build up and you have just like + + align:start position:0% +going to build up and you have just like + + + align:start position:0% +going to build up and you have just like +backing of water tanks uh it'll just + + align:start position:0% +backing of water tanks uh it'll just + + + align:start position:0% +backing of water tanks uh it'll just +back up the water water will back up and + + align:start position:0% +back up the water water will back up and + + + align:start position:0% +back up the water water will back up and +will not will not go away so so the uh + + align:start position:0% +will not will not go away so so the uh + + + align:start position:0% +will not will not go away so so the uh +the key thing here is that to make the + + align:start position:0% +the key thing here is that to make the + + + align:start position:0% +the key thing here is that to make the +relaxation time here what we call gamma + + align:start position:0% +relaxation time here what we call gamma + + + align:start position:0% +relaxation time here what we call gamma +21 which is one over effective lifetime + + align:start position:0% +21 which is one over effective lifetime + + + align:start position:0% +21 which is one over effective lifetime +between level two and one to be bigger + + align:start position:0% +between level two and one to be bigger + + + align:start position:0% +between level two and one to be bigger +bigger gamma 21 has to be bigger than + + align:start position:0% +bigger gamma 21 has to be bigger than + + + align:start position:0% +bigger gamma 21 has to be bigger than +than uh gamma 32 which is 1 over T 32 so + + align:start position:0% +than uh gamma 32 which is 1 over T 32 so + + + align:start position:0% +than uh gamma 32 which is 1 over T 32 so +in order to maintain N3 minus N2 as + + align:start position:0% +in order to maintain N3 minus N2 as + + + align:start position:0% +in order to maintain N3 minus N2 as +something uh positive more than zero in + + align:start position:0% +something uh positive more than zero in + + + align:start position:0% +something uh positive more than zero in +the steady state then we need to uh have + + align:start position:0% +the steady state then we need to uh have + + + align:start position:0% +the steady state then we need to uh have +this gamma 21 this DC rate here has to + + align:start position:0% +this gamma 21 this DC rate here has to + + + align:start position:0% +this gamma 21 this DC rate here has to +be faster than than the DC rate into + + align:start position:0% +be faster than than the DC rate into + + + align:start position:0% +be faster than than the DC rate into +level two the rest is the constants is + + align:start position:0% +level two the rest is the constants is + + + align:start position:0% +level two the rest is the constants is +like N1 the number in the uh in the + + align:start position:0% +like N1 the number in the uh in the + + + align:start position:0% +like N1 the number in the uh in the +lower level plus the power in the pump + + align:start position:0% +lower level plus the power in the pump + + + align:start position:0% +lower level plus the power in the pump +and so on but basically the key things + + align:start position:0% +and so on but basically the key things + + + align:start position:0% +and so on but basically the key things +are that these uh relaxation rates at + + align:start position:0% +are that these uh relaxation rates at + + + align:start position:0% +are that these uh relaxation rates at +this one is bigger than this one if not + + align:start position:0% +this one is bigger than this one if not + + + align:start position:0% +this one is bigger than this one if not +then essentially you get a a pulse laser + + align:start position:0% +then essentially you get a a pulse laser + + + align:start position:0% +then essentially you get a a pulse laser +and as we'll see later in uh in uh + + align:start position:0% +and as we'll see later in uh in uh + + + align:start position:0% +and as we'll see later in uh in uh +different amplifiers this is taken care + + align:start position:0% +different amplifiers this is taken care + + + align:start position:0% +different amplifiers this is taken care +of uh uh differently all right so + + align:start position:0% +of uh uh differently all right so + + + align:start position:0% +of uh uh differently all right so +obviously this is a problem that you + + align:start position:0% +obviously this is a problem that you + + + align:start position:0% +obviously this is a problem that you +you've got toh worry about that's why + + align:start position:0% +you've got toh worry about that's why + + + align:start position:0% +you've got toh worry about that's why +you don't make anything lace some some + + align:start position:0% +you don't make anything lace some some + + + align:start position:0% +you don't make anything lace some some +materials make better lasers than others + + align:start position:0% +materials make better lasers than others + + + align:start position:0% +materials make better lasers than others +all right that's about one of the + + align:start position:0% +all right that's about one of the + + + align:start position:0% +all right that's about one of the +problems in amplifiers now let me talk + + align:start position:0% +problems in amplifiers now let me talk + + + align:start position:0% +problems in amplifiers now let me talk +now about something even more basic okay + + align:start position:0% +now about something even more basic okay + + + align:start position:0% +now about something even more basic okay +and that's about cavities where cavities + + align:start position:0% +and that's about cavities where cavities + + + align:start position:0% +and that's about cavities where cavities +can can go wrong so so my topic here is + + align:start position:0% +can can go wrong so so my topic here is + + + align:start position:0% +can can go wrong so so my topic here is +on on uh on cavities + + align:start position:0% +on on uh on cavities + + + align:start position:0% +on on uh on cavities +and so far we we've talked about the + + align:start position:0% +and so far we we've talked about the + + + align:start position:0% +and so far we we've talked about the +cavities with curved mirrors and but we + + align:start position:0% +cavities with curved mirrors and but we + + + align:start position:0% +cavities with curved mirrors and but we +haven't said anything about the spacing + + align:start position:0% +haven't said anything about the spacing + + + align:start position:0% +haven't said anything about the spacing +between between the two mirrors if the + + align:start position:0% +between between the two mirrors if the + + + align:start position:0% +between between the two mirrors if the +if let's say these are two concave + + align:start position:0% +if let's say these are two concave + + + align:start position:0% +if let's say these are two concave +mirrors and I bring them close then the + + align:start position:0% +mirrors and I bring them close then the + + + align:start position:0% +mirrors and I bring them close then the +mode inside will look something like + + align:start position:0% +mode inside will look something like + + + align:start position:0% +mode inside will look something like +this little fat waste here if I pull + + align:start position:0% +this little fat waste here if I pull + + + align:start position:0% +this little fat waste here if I pull +them apart a little bit then I I begin + + align:start position:0% +them apart a little bit then I I begin + + + align:start position:0% +them apart a little bit then I I begin +to get a mode that looks like this with + + align:start position:0% +to get a mode that looks like this with + + + align:start position:0% +to get a mode that looks like this with +a with a waist here that is smaller + + align:start position:0% +a with a waist here that is smaller + + + align:start position:0% +a with a waist here that is smaller +and also I I'm not really doing it here + + align:start position:0% +and also I I'm not really doing it here + + + align:start position:0% +and also I I'm not really doing it here +because I'm not going into the details + + align:start position:0% +because I'm not going into the details + + + align:start position:0% +because I'm not going into the details +but basically the curvature of the field + + align:start position:0% +but basically the curvature of the field + + + align:start position:0% +but basically the curvature of the field +inside the cavity at the mirror is the + + align:start position:0% +inside the cavity at the mirror is the + + + align:start position:0% +inside the cavity at the mirror is the +same as the curvature of the mirror so + + align:start position:0% +same as the curvature of the mirror so + + + align:start position:0% +same as the curvature of the mirror so +that you can get reflection back again + + align:start position:0% +that you can get reflection back again + + + align:start position:0% +that you can get reflection back again +all right so we're not really going into + + align:start position:0% +all right so we're not really going into + + + align:start position:0% +all right so we're not really going into +that uh in this in this course now if I + + align:start position:0% +that uh in this in this course now if I + + + align:start position:0% +that uh in this in this course now if I +pull the mirrors even further apart I + + align:start position:0% +pull the mirrors even further apart I + + + align:start position:0% +pull the mirrors even further apart I +see that I I create this waste here + + align:start position:0% +see that I I create this waste here + + + align:start position:0% +see that I I create this waste here +which is very small it's about the small + + align:start position:0% +which is very small it's about the small + + + align:start position:0% +which is very small it's about the small +uh it becomes very small much smaller + + align:start position:0% +uh it becomes very small much smaller + + + align:start position:0% +uh it becomes very small much smaller +than I've had it before + + align:start position:0% +than I've had it before + + + align:start position:0% +than I've had it before +then what happens when when I pull the + + align:start position:0% +then what happens when when I pull the + + + align:start position:0% +then what happens when when I pull the +mirrors even further apart from that + + align:start position:0% +mirrors even further apart from that + + + align:start position:0% +mirrors even further apart from that +from that condition all right so let's + + align:start position:0% +from that condition all right so let's + + + align:start position:0% +from that condition all right so let's +see let's see let's see what happens in + + align:start position:0% +see let's see let's see what happens in + + + align:start position:0% +see let's see let's see what happens in +this simplified version well this is + + align:start position:0% +this simplified version well this is + + + align:start position:0% +this simplified version well this is +what's going to happen if I pull it if I + + align:start position:0% +what's going to happen if I pull it if I + + + align:start position:0% +what's going to happen if I pull it if I +pull the two mirrors now further away + + align:start position:0% +pull the two mirrors now further away + + + align:start position:0% +pull the two mirrors now further away +than than in here then what what happens + + align:start position:0% +than than in here then what what happens + + + align:start position:0% +than than in here then what what happens +is the light starts to walk out will not + + align:start position:0% +is the light starts to walk out will not + + + align:start position:0% +is the light starts to walk out will not +be contained inside the cavity because + + align:start position:0% +be contained inside the cavity because + + + align:start position:0% +be contained inside the cavity because +what's nice here is the lights getting + + align:start position:0% +what's nice here is the lights getting + + + align:start position:0% +what's nice here is the lights getting +refocused back into the cavity and going + + align:start position:0% +refocused back into the cavity and going + + + align:start position:0% +refocused back into the cavity and going +backwards and forwards without leaving + + align:start position:0% +backwards and forwards without leaving + + + align:start position:0% +backwards and forwards without leaving +the cavity it's all in these in all + + align:start position:0% +the cavity it's all in these in all + + + align:start position:0% +the cavity it's all in these in all +these these in all these cavities but + + align:start position:0% +these these in all these cavities but + + + align:start position:0% +these these in all these cavities but +here uh-uh I exceeded some Rule and and + + align:start position:0% +here uh-uh I exceeded some Rule and and + + + align:start position:0% +here uh-uh I exceeded some Rule and and +the light will start walking out which + + align:start position:0% +the light will start walking out which + + + align:start position:0% +the light will start walking out which +means now in order to make this L I have + + align:start position:0% +means now in order to make this L I have + + + align:start position:0% +means now in order to make this L I have +to have much bigger amplifier to + + align:start position:0% +to have much bigger amplifier to + + + align:start position:0% +to have much bigger amplifier to +overcome the Sloss usually lasers will + + align:start position:0% +overcome the Sloss usually lasers will + + + align:start position:0% +overcome the Sloss usually lasers will +will quit lazing unless you have a very + + align:start position:0% +will quit lazing unless you have a very + + + align:start position:0% +will quit lazing unless you have a very +high uh gain uh medium here and this is + + align:start position:0% +high uh gain uh medium here and this is + + + align:start position:0% +high uh gain uh medium here and this is +called the unstable so-called unstable + + align:start position:0% +called the unstable so-called unstable + + + align:start position:0% +called the unstable so-called unstable +resonator all these others are stable + + align:start position:0% +resonator all these others are stable + + + align:start position:0% +resonator all these others are stable +called stable resat is unstable I know I + + align:start position:0% +called stable resat is unstable I know I + + + align:start position:0% +called stable resat is unstable I know I +haven't used many formulas in this in + + align:start position:0% +haven't used many formulas in this in + + + align:start position:0% +haven't used many formulas in this in +this course but here is one here's a + + align:start position:0% +this course but here is one here's a + + + align:start position:0% +this course but here is one here's a +simple one I'll give it to you so if you + + align:start position:0% +simple one I'll give it to you so if you + + + align:start position:0% +simple one I'll give it to you so if you +this is in terms of uh in terms of the + + align:start position:0% +this is in terms of uh in terms of the + + + align:start position:0% +this is in terms of uh in terms of the +radi of curvature of the mirrors is Row + + align:start position:0% +radi of curvature of the mirrors is Row + + + align:start position:0% +radi of curvature of the mirrors is Row +one and row two and they can be uh + + align:start position:0% +one and row two and they can be uh + + + align:start position:0% +one and row two and they can be uh +concave or convex they're written for + + align:start position:0% +concave or convex they're written for + + + align:start position:0% +concave or convex they're written for +concave but if any of the mirrors are + + align:start position:0% +concave but if any of the mirrors are + + + align:start position:0% +concave but if any of the mirrors are +convex and you have to change the sign L + + align:start position:0% +convex and you have to change the sign L + + + align:start position:0% +convex and you have to change the sign L +is the separation between the two + + align:start position:0% +is the separation between the two + + + align:start position:0% +is the separation between the two +mirrors and this little formula here + + align:start position:0% +mirrors and this little formula here + + + align:start position:0% +mirrors and this little formula here +tells you when the cavity is unstable it + + align:start position:0% +tells you when the cavity is unstable it + + + align:start position:0% +tells you when the cavity is unstable it +turns out the cavity is unstable when + + align:start position:0% +turns out the cavity is unstable when + + + align:start position:0% +turns out the cavity is unstable when +when uh 1 - L / Row 1 * 1 - L / row2 the + + align:start position:0% +when uh 1 - L / Row 1 * 1 - L / row2 the + + + align:start position:0% +when uh 1 - L / Row 1 * 1 - L / row2 the +product of these two quantities is uh is + + align:start position:0% +product of these two quantities is uh is + + + align:start position:0% +product of these two quantities is uh is +if it's between zero and one then the + + align:start position:0% +if it's between zero and one then the + + + align:start position:0% +if it's between zero and one then the +cavity is stable if it's outside that + + align:start position:0% +cavity is stable if it's outside that + + + align:start position:0% +cavity is stable if it's outside that +the cavity is unstable and this is one + + align:start position:0% +the cavity is unstable and this is one + + + align:start position:0% +the cavity is unstable and this is one +example where the cavity is unstable so + + align:start position:0% +example where the cavity is unstable so + + + align:start position:0% +example where the cavity is unstable so +you can have the best mirrors you can + + align:start position:0% +you can have the best mirrors you can + + + align:start position:0% +you can have the best mirrors you can +have the best amplifier but if you don't + + align:start position:0% +have the best amplifier but if you don't + + + align:start position:0% +have the best amplifier but if you don't +have the alignment right and the length + + align:start position:0% +have the alignment right and the length + + + align:start position:0% +have the alignment right and the length +separation right for given curvatures + + align:start position:0% +separation right for given curvatures + + + align:start position:0% +separation right for given curvatures +the laser will not oscillate and people + + align:start position:0% +the laser will not oscillate and people + + + align:start position:0% +the laser will not oscillate and people +think you don't know what doing but all + + align:start position:0% +think you don't know what doing but all + + + align:start position:0% +think you don't know what doing but all +you have to do is go back to this + + align:start position:0% +you have to do is go back to this + + + align:start position:0% +you have to do is go back to this +formula and make sure that you stay you + + align:start position:0% +formula and make sure that you stay you + + + align:start position:0% +formula and make sure that you stay you +stay inside it so that's that's a + + align:start position:0% +stay inside it so that's that's a + + + align:start position:0% +stay inside it so that's that's a +problem with with uh common problem with + + align:start position:0% +problem with with uh common problem with + + + align:start position:0% +problem with with uh common problem with +uh with resonators and this uh also + + align:start position:0% +uh with resonators and this uh also + + + align:start position:0% +uh with resonators and this uh also +tells you this formula also tells you + + align:start position:0% +tells you this formula also tells you + + + align:start position:0% +tells you this formula also tells you +whether you can use convex mirrors and + + align:start position:0% +whether you can use convex mirrors and + + + align:start position:0% +whether you can use convex mirrors and +turns that again on certain conditions + + align:start position:0% +turns that again on certain conditions + + + align:start position:0% +turns that again on certain conditions +you can use a concave mirror and a + + align:start position:0% +you can use a concave mirror and a + + + align:start position:0% +you can use a concave mirror and a +convex mirror but to use two convex + + align:start position:0% +convex mirror but to use two convex + + + align:start position:0% +convex mirror but to use two convex +mirrors that's a no no because that will + + align:start position:0% +mirrors that's a no no because that will + + + align:start position:0% +mirrors that's a no no because that will +not satisfy this condition as say if + + align:start position:0% +not satisfy this condition as say if + + + align:start position:0% +not satisfy this condition as say if +you're more interested interested then + + align:start position:0% +you're more interested interested then + + + align:start position:0% +you're more interested interested then +you have to consult uh uh the + + align:start position:0% +you have to consult uh uh the + + + align:start position:0% +you have to consult uh uh the +literature now uh I'd like to uh talk + + align:start position:0% +literature now uh I'd like to uh talk + + + align:start position:0% +literature now uh I'd like to uh talk +about the uh the the spectrum of a laser + + align:start position:0% +about the uh the the spectrum of a laser + + + align:start position:0% +about the uh the the spectrum of a laser +in more detail now before we we said + + align:start position:0% +in more detail now before we we said + + + align:start position:0% +in more detail now before we we said +that uh the laser will be single + + align:start position:0% +that uh the laser will be single + + + align:start position:0% +that uh the laser will be single +frequency if you have only one mode + + align:start position:0% +frequency if you have only one mode + + + align:start position:0% +frequency if you have only one mode +under the gain curve and if you have + + align:start position:0% +under the gain curve and if you have + + + align:start position:0% +under the gain curve and if you have +more than more more than one mode then + + align:start position:0% +more than more more than one mode then + + + align:start position:0% +more than more more than one mode then +you have more frequencies at least the + + align:start position:0% +you have more frequencies at least the + + + align:start position:0% +you have more frequencies at least the +possibilities of more frequencies is + + align:start position:0% +possibilities of more frequencies is + + + align:start position:0% +possibilities of more frequencies is +oscillating now a lot of + + align:start position:0% +oscillating now a lot of + + + align:start position:0% +oscillating now a lot of +applications are can't tolerate more + + align:start position:0% +applications are can't tolerate more + + + align:start position:0% +applications are can't tolerate more +than one frequency for example + + align:start position:0% +than one frequency for example + + + align:start position:0% +than one frequency for example +communication interferometry holography + + align:start position:0% +communication interferometry holography + + + align:start position:0% +communication interferometry holography +and all these a lot of sensors they + + align:start position:0% +and all these a lot of sensors they + + + align:start position:0% +and all these a lot of sensors they +cannot tolerate more than one uh + + align:start position:0% +cannot tolerate more than one uh + + + align:start position:0% +cannot tolerate more than one uh +frequency but so for some other + + align:start position:0% +frequency but so for some other + + + align:start position:0% +frequency but so for some other +applications you know it's fine like uh + + align:start position:0% +applications you know it's fine like uh + + + align:start position:0% +applications you know it's fine like uh +uh materials processing medical + + align:start position:0% +uh materials processing medical + + + align:start position:0% +uh materials processing medical +applications CDs and so on uh you know + + align:start position:0% +applications CDs and so on uh you know + + + align:start position:0% +applications CDs and so on uh you know +more than one frequency is is okay so + + align:start position:0% +more than one frequency is is okay so + + + align:start position:0% +more than one frequency is is okay so +now let's see how one can select a + + align:start position:0% +now let's see how one can select a + + + align:start position:0% +now let's see how one can select a +single frequency from a essentially a + + align:start position:0% +single frequency from a essentially a + + + align:start position:0% +single frequency from a essentially a +multi frequency laser now in the + + align:start position:0% +multi frequency laser now in the + + + align:start position:0% +multi frequency laser now in the +demonstration we showed you that uh we + + align:start position:0% +demonstration we showed you that uh we + + + align:start position:0% +demonstration we showed you that uh we +showed you that all these modes can can + + align:start position:0% +showed you that all these modes can can + + + align:start position:0% +showed you that all these modes can can +happen and we showed you that if we + + align:start position:0% +happen and we showed you that if we + + + align:start position:0% +happen and we showed you that if we +lower the gain or misalign a little bit + + align:start position:0% +lower the gain or misalign a little bit + + + align:start position:0% +lower the gain or misalign a little bit +we can bring the gain down so only one + + align:start position:0% +we can bring the gain down so only one + + + align:start position:0% +we can bring the gain down so only one +mode will oscillate but that's not a + + align:start position:0% +mode will oscillate but that's not a + + + align:start position:0% +mode will oscillate but that's not a +smart way of doing it because you lose a + + align:start position:0% +smart way of doing it because you lose a + + + align:start position:0% +smart way of doing it because you lose a +lot of power output so the idea here is + + align:start position:0% +lot of power output so the idea here is + + + align:start position:0% +lot of power output so the idea here is +to have how do you how do you have a + + align:start position:0% +to have how do you how do you have a + + + align:start position:0% +to have how do you how do you have a +long laser right with lots of + + align:start position:0% +long laser right with lots of + + + align:start position:0% +long laser right with lots of +possibility lots of modes a lot of gain + + align:start position:0% +possibility lots of modes a lot of gain + + + align:start position:0% +possibility lots of modes a lot of gain +in there and only select one one uh one + + align:start position:0% +in there and only select one one uh one + + + align:start position:0% +in there and only select one one uh one +frequency out of that + + align:start position:0% +frequency out of that + + + align:start position:0% +frequency out of that +uh that mess of frequencies okay so + + align:start position:0% +uh that mess of frequencies okay so + + + align:start position:0% +uh that mess of frequencies okay so +let's see now uh how we might uh do it + + align:start position:0% +let's see now uh how we might uh do it + + + align:start position:0% +let's see now uh how we might uh do it +so this section then is on the SE single + + align:start position:0% +so this section then is on the SE single + + + align:start position:0% +so this section then is on the SE single +frequency uh + + align:start position:0% +frequency uh + + + align:start position:0% +frequency uh +selection and and I remind you again of + + align:start position:0% +selection and and I remind you again of + + + align:start position:0% +selection and and I remind you again of +having let's say long cavity here with a + + align:start position:0% +having let's say long cavity here with a + + + align:start position:0% +having let's say long cavity here with a +long uh uh gain medium and and I have + + align:start position:0% +long uh uh gain medium and and I have + + + align:start position:0% +long uh uh gain medium and and I have +lots of modes under the uh bandwidth of + + align:start position:0% +lots of modes under the uh bandwidth of + + + align:start position:0% +lots of modes under the uh bandwidth of +the amplifier here's my loss line so all + + align:start position:0% +the amplifier here's my loss line so all + + + align:start position:0% +the amplifier here's my loss line so all +these modes here will oscillate and you + + align:start position:0% +these modes here will oscillate and you + + + align:start position:0% +these modes here will oscillate and you +can get all these all these frequencies + + align:start position:0% +can get all these all these frequencies + + + align:start position:0% +can get all these all these frequencies +so the question here is how do I select + + align:start position:0% +so the question here is how do I select + + + align:start position:0% +so the question here is how do I select +than uh one of these frequencies and not + + align:start position:0% +than uh one of these frequencies and not + + + align:start position:0% +than uh one of these frequencies and not +and not all of them well there are many + + align:start position:0% +and not all of them well there are many + + + align:start position:0% +and not all of them well there are many +ways the the most common way is what we + + align:start position:0% +ways the the most common way is what we + + + align:start position:0% +ways the the most common way is what we +call an ethyl we place this shorter + + align:start position:0% +call an ethyl we place this shorter + + + align:start position:0% +call an ethyl we place this shorter +cavity within the the long cavity again + + align:start position:0% +cavity within the the long cavity again + + + align:start position:0% +cavity within the the long cavity again +uh over here we have the modes of the of + + align:start position:0% +uh over here we have the modes of the of + + + align:start position:0% +uh over here we have the modes of the of +the long cavity where there's all space + + align:start position:0% +the long cavity where there's all space + + + align:start position:0% +the long cavity where there's all space +c over 2 L apart and for the short + + align:start position:0% +c over 2 L apart and for the short + + + align:start position:0% +c over 2 L apart and for the short +cavity the length is a so the modes are + + align:start position:0% +cavity the length is a so the modes are + + + align:start position:0% +cavity the length is a so the modes are +spaced for this C it's a piece of glass + + align:start position:0% +spaced for this C it's a piece of glass + + + align:start position:0% +spaced for this C it's a piece of glass +or two mirrors that are parallel and the + + align:start position:0% +or two mirrors that are parallel and the + + + align:start position:0% +or two mirrors that are parallel and the +space is a so the mode spacing is C over + + align:start position:0% +space is a so the mode spacing is C over + + + align:start position:0% +space is a so the mode spacing is C over +2 a for this short one so now the whole + + align:start position:0% +2 a for this short one so now the whole + + + align:start position:0% +2 a for this short one so now the whole +idea is to couple the mode from this + + align:start position:0% +idea is to couple the mode from this + + + align:start position:0% +idea is to couple the mode from this +cavity like this one here with one of + + align:start position:0% +cavity like this one here with one of + + + align:start position:0% +cavity like this one here with one of +the modes from the long cavity which is + + align:start position:0% +the modes from the long cavity which is + + + align:start position:0% +the modes from the long cavity which is +over here and and when they're coupled + + align:start position:0% +over here and and when they're coupled + + + align:start position:0% +over here and and when they're coupled +when they're perfectly coupled like this + + align:start position:0% +when they're perfectly coupled like this + + + align:start position:0% +when they're perfectly coupled like this +then only at this frequency will I get + + align:start position:0% +then only at this frequency will I get + + + align:start position:0% +then only at this frequency will I get +enough gain to overcome uh the loss in + + align:start position:0% +enough gain to overcome uh the loss in + + + align:start position:0% +enough gain to overcome uh the loss in +in in the cavity and the laser will + + align:start position:0% +in in the cavity and the laser will + + + align:start position:0% +in in the cavity and the laser will +oscillate over here at this frequency + + align:start position:0% +oscillate over here at this frequency + + + align:start position:0% +oscillate over here at this frequency +which is determined by the overlap of + + align:start position:0% +which is determined by the overlap of + + + align:start position:0% +which is determined by the overlap of +these two product of these two now at + + align:start position:0% +these two product of these two now at + + + align:start position:0% +these two product of these two now at +any other frequency while before they + + align:start position:0% +any other frequency while before they + + + align:start position:0% +any other frequency while before they +oscillated now they see this this uh uh + + align:start position:0% +oscillated now they see this this uh uh + + + align:start position:0% +oscillated now they see this this uh uh +uh loss because of this because the your + + align:start position:0% +uh loss because of this because the your + + + align:start position:0% +uh loss because of this because the your +off resonance with respect to that + + align:start position:0% +off resonance with respect to that + + + align:start position:0% +off resonance with respect to that +cavity so the transmission is is is low + + align:start position:0% +cavity so the transmission is is is low + + + align:start position:0% +cavity so the transmission is is is low +and then and then you they will not uh + + align:start position:0% +and then and then you they will not uh + + + align:start position:0% +and then and then you they will not uh +they will not oscillate so only only the + + align:start position:0% +they will not oscillate so only only the + + + align:start position:0% +they will not oscillate so only only the +overlap of between the short cavity and + + align:start position:0% +overlap of between the short cavity and + + + align:start position:0% +overlap of between the short cavity and +the and the long cavity uh they then + + align:start position:0% +the and the long cavity uh they then + + + align:start position:0% +the and the long cavity uh they then +they will get enough gain to overcome + + align:start position:0% +they will get enough gain to overcome + + + align:start position:0% +they will get enough gain to overcome +the loss and then you'll get you'll get + + align:start position:0% +the loss and then you'll get you'll get + + + align:start position:0% +the loss and then you'll get you'll get +lazing at any other value you don't so + + align:start position:0% +lazing at any other value you don't so + + + align:start position:0% +lazing at any other value you don't so +this is a way of selecting single single + + align:start position:0% +this is a way of selecting single single + + + align:start position:0% +this is a way of selecting single single +frequency now if you don't like this + + align:start position:0% +frequency now if you don't like this + + + align:start position:0% +frequency now if you don't like this +frequency you want some other frequency + + align:start position:0% +frequency you want some other frequency + + + align:start position:0% +frequency you want some other frequency +all you have to do is you tune you tune + + align:start position:0% +all you have to do is you tune you tune + + + align:start position:0% +all you have to do is you tune you tune +this this little cavity either by + + align:start position:0% +this this little cavity either by + + + align:start position:0% +this this little cavity either by +rotating this or by adjusting the + + align:start position:0% +rotating this or by adjusting the + + + align:start position:0% +rotating this or by adjusting the +distance so you can move this resonance + + align:start position:0% +distance so you can move this resonance + + + align:start position:0% +distance so you can move this resonance +around and you can select any of these + + align:start position:0% +around and you can select any of these + + + align:start position:0% +around and you can select any of these +modes you want if you want somewhere in + + align:start position:0% +modes you want if you want somewhere in + + + align:start position:0% +modes you want if you want somewhere in +between then not only you have to tune + + align:start position:0% +between then not only you have to tune + + + align:start position:0% +between then not only you have to tune +the short cavity but you also have to + + align:start position:0% +the short cavity but you also have to + + + align:start position:0% +the short cavity but you also have to +tune the uh the long cavity + + align:start position:0% +tune the uh the long cavity + + + align:start position:0% +tune the uh the long cavity +it and uh and then this this is a very + + align:start position:0% +it and uh and then this this is a very + + + align:start position:0% +it and uh and then this this is a very +as I say this is a very popular way of + + align:start position:0% +as I say this is a very popular way of + + + align:start position:0% +as I say this is a very popular way of +uh of getting uh single frequency uh and + + align:start position:0% +uh of getting uh single frequency uh and + + + align:start position:0% +uh of getting uh single frequency uh and +and it's used uh quite a bit it's a pain + + align:start position:0% +and it's used uh quite a bit it's a pain + + + align:start position:0% +and it's used uh quite a bit it's a pain +in the neck to put things inside the + + align:start position:0% +in the neck to put things inside the + + + align:start position:0% +in the neck to put things inside the +cavity because any loss then will will + + align:start position:0% +cavity because any loss then will will + + + align:start position:0% +cavity because any loss then will will +start cutting your your gain down uh + + align:start position:0% +start cutting your your gain down uh + + + align:start position:0% +start cutting your your gain down uh +effective gain and your laser output + + align:start position:0% +effective gain and your laser output + + + align:start position:0% +effective gain and your laser output +power will uh will drop but this is a a + + align:start position:0% +power will uh will drop but this is a a + + + align:start position:0% +power will uh will drop but this is a a +convenient way of getting single + + align:start position:0% +convenient way of getting single + + + align:start position:0% +convenient way of getting single +frequency so you don't have to worry + + align:start position:0% +frequency so you don't have to worry + + + align:start position:0% +frequency so you don't have to worry +about the fact that lasers can put out + + align:start position:0% +about the fact that lasers can put out + + + align:start position:0% +about the fact that lasers can put out +many many frequencies there are + + align:start position:0% +many many frequencies there are + + + align:start position:0% +many many frequencies there are +techniques to select only one and to be + + align:start position:0% +techniques to select only one and to be + + + align:start position:0% +techniques to select only one and to be +able to to tune + + align:start position:0% +able to to tune + + + align:start position:0% +able to to tune +that now let me uh talk about other + + align:start position:0% +that now let me uh talk about other + + + align:start position:0% +that now let me uh talk about other +problems with uh with lasers and that is + + align:start position:0% +problems with uh with lasers and that is + + + align:start position:0% +problems with uh with lasers and that is +the in frequency and intensity + + align:start position:0% +the in frequency and intensity + + + align:start position:0% +the in frequency and intensity +variations and then we'll do that very + + align:start position:0% +variations and then we'll do that very + + + align:start position:0% +variations and then we'll do that very +briefly because you know one thinks + + align:start position:0% +briefly because you know one thinks + + + align:start position:0% +briefly because you know one thinks +begins to think that lasers are always + + align:start position:0% +begins to think that lasers are always + + + align:start position:0% +begins to think that lasers are always +ideal they're not let's go back to our + + align:start position:0% +ideal they're not let's go back to our + + + align:start position:0% +ideal they're not let's go back to our +simple picture of of a laser and here's + + align:start position:0% +simple picture of of a laser and here's + + + align:start position:0% +simple picture of of a laser and here's +the gain here's the cavity mode and + + align:start position:0% +the gain here's the cavity mode and + + + align:start position:0% +the gain here's the cavity mode and +here's the here's the the oscillation of + + align:start position:0% +here's the here's the the oscillation of + + + align:start position:0% +here's the here's the the oscillation of +the laser now what determines this + + align:start position:0% +the laser now what determines this + + + align:start position:0% +the laser now what determines this +frequency well as we've seen from way + + align:start position:0% +frequency well as we've seen from way + + + align:start position:0% +frequency well as we've seen from way +before we we saw that it depends on this + + align:start position:0% +before we we saw that it depends on this + + + align:start position:0% +before we we saw that it depends on this +integer Q which is the number of half + + align:start position:0% +integer Q which is the number of half + + + align:start position:0% +integer Q which is the number of half +wavelengths between the two mirrors + + align:start position:0% +wavelengths between the two mirrors + + + align:start position:0% +wavelengths between the two mirrors +multiplied by c over2 l so it certainly + + align:start position:0% +multiplied by c over2 l so it certainly + + + align:start position:0% +multiplied by c over2 l so it certainly +depends on L so if L changes if L + + align:start position:0% +depends on L so if L changes if L + + + align:start position:0% +depends on L so if L changes if L +changes here then the cavity mode will + + align:start position:0% +changes here then the cavity mode will + + + align:start position:0% +changes here then the cavity mode will +change and of course we'll pull the + + align:start position:0% +change and of course we'll pull the + + + align:start position:0% +change and of course we'll pull the +laser frequency with it so so that the + + align:start position:0% +laser frequency with it so so that the + + + align:start position:0% +laser frequency with it so so that the +laser frequency can move around if the + + align:start position:0% +laser frequency can move around if the + + + align:start position:0% +laser frequency can move around if the +cavity uh moves around and and uh and + + align:start position:0% +cavity uh moves around and and uh and + + + align:start position:0% +cavity uh moves around and and uh and +and then a simple expression here for + + align:start position:0% +and then a simple expression here for + + + align:start position:0% +and then a simple expression here for +Delta F over F the change in the + + align:start position:0% +Delta F over F the change in the + + + align:start position:0% +Delta F over F the change in the +frequency over the frequency is simply + + align:start position:0% +frequency over the frequency is simply + + + align:start position:0% +frequency over the frequency is simply +the change of the length of the cavity + + align:start position:0% +the change of the length of the cavity + + + align:start position:0% +the change of the length of the cavity +or what we call the optical length + + align:start position:0% +or what we call the optical length + + + align:start position:0% +or what we call the optical length +because if there's a refractive index uh + + align:start position:0% +because if there's a refractive index uh + + + align:start position:0% +because if there's a refractive index uh +here that will change the physical + + align:start position:0% +here that will change the physical + + + align:start position:0% +here that will change the physical +length because you have to multiply by + + align:start position:0% +length because you have to multiply by + + + align:start position:0% +length because you have to multiply by +the refractive index divided by L so + + align:start position:0% +the refractive index divided by L so + + + align:start position:0% +the refractive index divided by L so +then the change in the frequency the + + align:start position:0% +then the change in the frequency the + + + align:start position:0% +then the change in the frequency the +fractional change in frequency Delta F + + align:start position:0% +fractional change in frequency Delta F + + + align:start position:0% +fractional change in frequency Delta F +over f is the same as Delta L over l so + + align:start position:0% +over f is the same as Delta L over l so + + + align:start position:0% +over f is the same as Delta L over l so +if you want good stability you have to + + align:start position:0% +if you want good stability you have to + + + align:start position:0% +if you want good stability you have to +keep Delta L over L small + + align:start position:0% +keep Delta L over L small + + + align:start position:0% +keep Delta L over L small +the uh the other thing is the uh is the + + align:start position:0% +the uh the other thing is the uh is the + + + align:start position:0% +the uh the other thing is the uh is the +intensity of the laser what determines + + align:start position:0% +intensity of the laser what determines + + + align:start position:0% +intensity of the laser what determines +the intensity of the laser and does it + + align:start position:0% +the intensity of the laser and does it + + + align:start position:0% +the intensity of the laser and does it +stay constant well we know that the + + align:start position:0% +stay constant well we know that the + + + align:start position:0% +stay constant well we know that the +amplifier of course determines the + + align:start position:0% +amplifier of course determines the + + + align:start position:0% +amplifier of course determines the +intensity and uh and the but the change + + align:start position:0% +intensity and uh and the but the change + + + align:start position:0% +intensity and uh and the but the change +in intensity will depend on uh the pump + + align:start position:0% +in intensity will depend on uh the pump + + + align:start position:0% +in intensity will depend on uh the pump +if the pump here changes uh whatever it + + align:start position:0% +if the pump here changes uh whatever it + + + align:start position:0% +if the pump here changes uh whatever it +does to the to the medium if it changes + + align:start position:0% +does to the to the medium if it changes + + + align:start position:0% +does to the to the medium if it changes +magnitude then it's going to uh change + + align:start position:0% +magnitude then it's going to uh change + + + align:start position:0% +magnitude then it's going to uh change +the intensity or if you misalign as we + + align:start position:0% +the intensity or if you misalign as we + + + align:start position:0% +the intensity or if you misalign as we +showed you in the demonstration if you + + align:start position:0% +showed you in the demonstration if you + + + align:start position:0% +showed you in the demonstration if you +misalign one of the mirrors here you + + align:start position:0% +misalign one of the mirrors here you + + + align:start position:0% +misalign one of the mirrors here you +will get more loss which means that you + + align:start position:0% +will get more loss which means that you + + + align:start position:0% +will get more loss which means that you +need more gain to overcome the loss + + align:start position:0% +need more gain to overcome the loss + + + align:start position:0% +need more gain to overcome the loss +which means the intensity will drop and + + align:start position:0% +which means the intensity will drop and + + + align:start position:0% +which means the intensity will drop and +so on so the many ways of reducing laser + + align:start position:0% +so on so the many ways of reducing laser + + + align:start position:0% +so on so the many ways of reducing laser +intensity so to keep it constant all + + align:start position:0% +intensity so to keep it constant all + + + align:start position:0% +intensity so to keep it constant all +right to keep Delta I over I small then + + align:start position:0% +right to keep Delta I over I small then + + + align:start position:0% +right to keep Delta I over I small then +you need to keep an eye on all these uh + + align:start position:0% +you need to keep an eye on all these uh + + + align:start position:0% +you need to keep an eye on all these uh +on all these effects okay and I think + + align:start position:0% +on all these effects okay and I think + + + align:start position:0% +on all these effects okay and I think +this is about brings me to to the end of + + align:start position:0% +this is about brings me to to the end of + + + align:start position:0% +this is about brings me to to the end of +this uh of this + + align:start position:0% +this uh of this + + + align:start position:0% +this uh of this +session uh in the next session we're + + align:start position:0% +session uh in the next session we're + + + align:start position:0% +session uh in the next session we're +going to talk about another property of + + align:start position:0% +going to talk about another property of + + + align:start position:0% +going to talk about another property of +lasers and that's + + align:start position:0% +lasers and that's + + + align:start position:0% +lasers and that's +associated with with transverse modes + + align:start position:0% +associated with with transverse modes + + + align:start position:0% +associated with with transverse modes +these are these are the the the when you + + align:start position:0% +these are these are the the the when you + + + align:start position:0% +these are these are the the the when you +look at a laser that's oscillating + + align:start position:0% +look at a laser that's oscillating + + + align:start position:0% +look at a laser that's oscillating +transverse modes instead of seeing the + + align:start position:0% +transverse modes instead of seeing the + + + align:start position:0% +transverse modes instead of seeing the +single spot you see uh many kinds of + + align:start position:0% +single spot you see uh many kinds of + + + align:start position:0% +single spot you see uh many kinds of +many spots and that for some + + align:start position:0% +many spots and that for some + + + align:start position:0% +many spots and that for some +applications is a is a no no and you've + + align:start position:0% +applications is a is a no no and you've + + + align:start position:0% +applications is a is a no no and you've +got to get rid of them \ No newline at end of file diff --git a/_uKBaTKZa6c.txt b/_uKBaTKZa6c.txt new file mode 100644 index 0000000000000000000000000000000000000000..ddc8a8797c50bdcd8d6f0e882eb20dfd3d67d9ce --- /dev/null +++ b/_uKBaTKZa6c.txt @@ -0,0 +1,987 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu now I'm going to show + + align:start position:0% +ocw.mit.edu now I'm going to show + + + align:start position:0% +ocw.mit.edu now I'm going to show +another way of reducing Fringe contrast + + align:start position:0% +another way of reducing Fringe contrast + + + align:start position:0% +another way of reducing Fringe contrast +this one has to do with the polarization + + align:start position:0% +this one has to do with the polarization + + + align:start position:0% +this one has to do with the polarization +of the light coming out out from each + + align:start position:0% +of the light coming out out from each + + + align:start position:0% +of the light coming out out from each +arm of the interferometer the setup is + + align:start position:0% +arm of the interferometer the setup is + + + align:start position:0% +arm of the interferometer the setup is +the same as we had before except that + + align:start position:0% +the same as we had before except that + + + align:start position:0% +the same as we had before except that +I've added a polarizer here to clean up + + align:start position:0% +I've added a polarizer here to clean up + + + align:start position:0% +I've added a polarizer here to clean up +the the polarization before we enter the + + align:start position:0% +the the polarization before we enter the + + + align:start position:0% +the the polarization before we enter the +the + + align:start position:0% +the + + + align:start position:0% +the +interferometer so first let's check on + + align:start position:0% +interferometer so first let's check on + + + align:start position:0% +interferometer so first let's check on +the + + align:start position:0% +the + + + align:start position:0% +the +polarization coming out of each arm of + + align:start position:0% +polarization coming out of each arm of + + + align:start position:0% +polarization coming out of each arm of +the inter fomer in the present setup and + + align:start position:0% +the inter fomer in the present setup and + + + align:start position:0% +the inter fomer in the present setup and +I'll do this by putting a + + align:start position:0% +I'll do this by putting a + + + align:start position:0% +I'll do this by putting a +polarizer out + + align:start position:0% +polarizer out + + + align:start position:0% +polarizer out +here + + align:start position:0% + + + + align:start position:0% + +and then I'm going to block each + + align:start position:0% + + + + align:start position:0% + +arm and check on the polarization now as + + align:start position:0% +arm and check on the polarization now as + + + align:start position:0% +arm and check on the polarization now as +we can + + align:start position:0% +we can + + + align:start position:0% +we can +see the on the + + align:start position:0% +see the on the + + + align:start position:0% +see the on the +screen that + + align:start position:0% +screen that + + + align:start position:0% +screen that +the that when when the arrow of the + + align:start position:0% +the that when when the arrow of the + + + align:start position:0% +the that when when the arrow of the +polarizer or the transmission axis of + + align:start position:0% +polarizer or the transmission axis of + + + align:start position:0% +polarizer or the transmission axis of +the polarizer is along the horizontal I + + align:start position:0% +the polarizer is along the horizontal I + + + align:start position:0% +the polarizer is along the horizontal I +have a lot of light and when the arrow + + align:start position:0% +have a lot of light and when the arrow + + + align:start position:0% +have a lot of light and when the arrow +is + + align:start position:0% +is + + + align:start position:0% +is +vertical I've extinguish the light which + + align:start position:0% +vertical I've extinguish the light which + + + align:start position:0% +vertical I've extinguish the light which +means that the light coming out from + + align:start position:0% +means that the light coming out from + + + align:start position:0% +means that the light coming out from +this arm of the interferometer is plain + + align:start position:0% +this arm of the interferometer is plain + + + align:start position:0% +this arm of the interferometer is plain +polarized in the in the horizontal + + align:start position:0% +polarized in the in the horizontal + + + align:start position:0% +polarized in the in the horizontal +Direction all right that's for this arm + + align:start position:0% +Direction all right that's for this arm + + + align:start position:0% +Direction all right that's for this arm +now I'll check on the beam coming out + + align:start position:0% +now I'll check on the beam coming out + + + align:start position:0% +now I'll check on the beam coming out +from the other arm from this arm here + + align:start position:0% +from the other arm from this arm here + + + align:start position:0% +from the other arm from this arm here +and again there's a lot of light when + + align:start position:0% +and again there's a lot of light when + + + align:start position:0% +and again there's a lot of light when +the arrow is + + align:start position:0% +the arrow is + + + align:start position:0% +the arrow is +horizontal and it's extinguished when + + align:start position:0% +horizontal and it's extinguished when + + + align:start position:0% +horizontal and it's extinguished when +the arrow is vertical which says that + + align:start position:0% +the arrow is vertical which says that + + + align:start position:0% +the arrow is vertical which says that +the + + align:start position:0% +the + + + align:start position:0% +the +polarization of the light coming out of + + align:start position:0% +polarization of the light coming out of + + + align:start position:0% +polarization of the light coming out of +the two arms + + align:start position:0% +the two arms + + + align:start position:0% +the two arms +is the + + align:start position:0% +is the + + + align:start position:0% +is the +same and in the horizontal Direction now + + align:start position:0% +same and in the horizontal Direction now + + + align:start position:0% +same and in the horizontal Direction now +I'm going to rotate the pl of + + align:start position:0% +I'm going to rotate the pl of + + + align:start position:0% +I'm going to rotate the pl of +polarization of the light coming out + + align:start position:0% +polarization of the light coming out + + + align:start position:0% +polarization of the light coming out +from this arm by using this quad wave + + align:start position:0% +from this arm by using this quad wave + + + align:start position:0% +from this arm by using this quad wave +plate which I will insert in this + + align:start position:0% + + + + align:start position:0% + +arm now as we know light going through a + + align:start position:0% +arm now as we know light going through a + + + align:start position:0% +arm now as we know light going through a +quarter wave plates twice uh the its + + align:start position:0% +quarter wave plates twice uh the its + + + align:start position:0% +quarter wave plates twice uh the its +polarization will be + + align:start position:0% +polarization will be + + + align:start position:0% +polarization will be +rotated as as we'll see so so now I want + + align:start position:0% +rotated as as we'll see so so now I want + + + align:start position:0% +rotated as as we'll see so so now I want +to show that the light from this arm + + align:start position:0% +to show that the light from this arm + + + align:start position:0% +to show that the light from this arm +going through this polarizer here onto + + align:start position:0% +going through this polarizer here onto + + + align:start position:0% +going through this polarizer here onto +the + + align:start position:0% +the + + + align:start position:0% +the +screen is is going to have its plan of + + align:start position:0% +screen is is going to have its plan of + + + align:start position:0% +screen is is going to have its plan of +polarization changed as I rotate the the + + align:start position:0% +polarization changed as I rotate the the + + + align:start position:0% +polarization changed as I rotate the the +uh alignment of this quad wave plate so + + align:start position:0% +uh alignment of this quad wave plate so + + + align:start position:0% +uh alignment of this quad wave plate so +with the arrow over here we can see we + + align:start position:0% +with the arrow over here we can see we + + + align:start position:0% +with the arrow over here we can see we +have a uh a lot of light and as + + align:start position:0% +have a uh a lot of light and as + + + align:start position:0% +have a uh a lot of light and as +I rotate the quarter wave + + align:start position:0% +I rotate the quarter wave + + + align:start position:0% +I rotate the quarter wave +plate I see that I can extinguish the + + align:start position:0% +plate I see that I can extinguish the + + + align:start position:0% +plate I see that I can extinguish the +light which means now the polarization + + align:start position:0% +light which means now the polarization + + + align:start position:0% +light which means now the polarization +of the light coming out from this arm is + + align:start position:0% +of the light coming out from this arm is + + + align:start position:0% +of the light coming out from this arm is +orthogonal to the transmission axis of + + align:start position:0% +orthogonal to the transmission axis of + + + align:start position:0% +orthogonal to the transmission axis of +the polarizer so good so in this way + + align:start position:0% +the polarizer so good so in this way + + + align:start position:0% +the polarizer so good so in this way +then I can rotate the plane of + + align:start position:0% +then I can rotate the plane of + + + align:start position:0% +then I can rotate the plane of +polarization from 0 to 90° by simply + + align:start position:0% +polarization from 0 to 90° by simply + + + align:start position:0% +polarization from 0 to 90° by simply +rotating the quarter wave + + align:start position:0% +rotating the quarter wave + + + align:start position:0% +rotating the quarter wave +plate all right now I'm ready to to look + + align:start position:0% +plate all right now I'm ready to to look + + + align:start position:0% +plate all right now I'm ready to to look +at the effect of polarization rotation + + align:start position:0% +at the effect of polarization rotation + + + align:start position:0% +at the effect of polarization rotation +on The Fringe contrast and what I'll do + + align:start position:0% +on The Fringe contrast and what I'll do + + + align:start position:0% +on The Fringe contrast and what I'll do +first I will take out the + + align:start position:0% +first I will take out the + + + align:start position:0% +first I will take out the +polarizer so now I have then two beams + + align:start position:0% +polarizer so now I have then two beams + + + align:start position:0% +polarizer so now I have then two beams +coming out from the + + align:start position:0% +coming out from the + + + align:start position:0% +coming out from the +interferometer one + + align:start position:0% +interferometer one + + + align:start position:0% +interferometer one +has polarization in the horizontal plane + + align:start position:0% +has polarization in the horizontal plane + + + align:start position:0% +has polarization in the horizontal plane +this one here I can change the state of + + align:start position:0% +this one here I can change the state of + + + align:start position:0% +this one here I can change the state of +polarization anywhere from horizontal to + + align:start position:0% +polarization anywhere from horizontal to + + + align:start position:0% +polarization anywhere from horizontal to +to Vertical so let's look at the + + align:start position:0% +to Vertical so let's look at the + + + align:start position:0% +to Vertical so let's look at the +screen and we see that we have good + + align:start position:0% +screen and we see that we have good + + + align:start position:0% +screen and we see that we have good +contrast in this + + align:start position:0% +contrast in this + + + align:start position:0% +contrast in this +position then as I rotate the plane of + + align:start position:0% +position then as I rotate the plane of + + + align:start position:0% +position then as I rotate the plane of +polarization of this + + align:start position:0% +polarization of this + + + align:start position:0% +polarization of this +arm by + + align:start position:0% +arm by + + + align:start position:0% +arm by +90° you can see that The Fringe + + align:start position:0% +90° you can see that The Fringe + + + align:start position:0% +90° you can see that The Fringe +contrast disappears and in fact in this + + align:start position:0% +contrast disappears and in fact in this + + + align:start position:0% +contrast disappears and in fact in this +position you don't even see any fringes + + align:start position:0% +position you don't even see any fringes + + + align:start position:0% +position you don't even see any fringes +at all if I go + + align:start position:0% + + + + align:start position:0% + +back to the original position you see + + align:start position:0% +back to the original position you see + + + align:start position:0% +back to the original position you see +that the + + align:start position:0% +that the + + + align:start position:0% +that the +contrast comes back let me go back + + align:start position:0% +contrast comes back let me go back + + + align:start position:0% +contrast comes back let me go back +again + + align:start position:0% +again + + + align:start position:0% +again +wash out the fringes because the + + align:start position:0% +wash out the fringes because the + + + align:start position:0% +wash out the fringes because the +polarizations are + + align:start position:0% +polarizations are + + + align:start position:0% +polarizations are +orthogonal and just to show you that + + align:start position:0% +orthogonal and just to show you that + + + align:start position:0% +orthogonal and just to show you that +indeed I'm not hiding + + align:start position:0% +indeed I'm not hiding + + + align:start position:0% +indeed I'm not hiding +anything I'm going to show that there's + + align:start position:0% +anything I'm going to show that there's + + + align:start position:0% +anything I'm going to show that there's +still light coming out from each arm + + align:start position:0% +still light coming out from each arm + + + align:start position:0% +still light coming out from each arm +light coming out from this arm and light + + align:start position:0% +light coming out from this arm and light + + + align:start position:0% +light coming out from this arm and light +coming out from this arm but when I + + align:start position:0% +coming out from this arm but when I + + + align:start position:0% +coming out from this arm but when I +superimpose them there's no there's no + + align:start position:0% +superimpose them there's no there's no + + + align:start position:0% +superimpose them there's no there's no +interference now let me put it + + align:start position:0% +interference now let me put it + + + align:start position:0% +interference now let me put it +back to the position position where the + + align:start position:0% +back to the position position where the + + + align:start position:0% +back to the position position where the +polarization are equal and indeed we get + + align:start position:0% +polarization are equal and indeed we get + + + align:start position:0% +polarization are equal and indeed we get +the good contrast back again so in + + align:start position:0% +the good contrast back again so in + + + align:start position:0% +the good contrast back again so in +conclusion we've shown that orthogonally + + align:start position:0% +conclusion we've shown that orthogonally + + + align:start position:0% +conclusion we've shown that orthogonally +polarized light does not interfere and + + align:start position:0% +polarized light does not interfere and + + + align:start position:0% +polarized light does not interfere and +that's why we get very low contrast + + align:start position:0% +that's why we get very low contrast + + + align:start position:0% +that's why we get very low contrast +fringes when we try to interfere + + align:start position:0% +fringes when we try to interfere + + + align:start position:0% +fringes when we try to interfere +orthogonally polarized light so then in + + align:start position:0% +orthogonally polarized light so then in + + + align:start position:0% +orthogonally polarized light so then in +a any interferometer experiment you have + + align:start position:0% +a any interferometer experiment you have + + + align:start position:0% +a any interferometer experiment you have +to make sure that the polarization is is + + align:start position:0% +to make sure that the polarization is is + + + align:start position:0% +to make sure that the polarization is is +the same coming out from each arm of the + + align:start position:0% +the same coming out from each arm of the + + + align:start position:0% +the same coming out from each arm of the +interferometer the question I want to + + align:start position:0% +interferometer the question I want to + + + align:start position:0% +interferometer the question I want to +leave with you is why orthony polarized + + align:start position:0% +leave with you is why orthony polarized + + + align:start position:0% +leave with you is why orthony polarized +light does not + + align:start position:0% + + + + align:start position:0% + +interfere \ No newline at end of file diff --git a/a1ZCeFpeW0o.txt b/a1ZCeFpeW0o.txt new file mode 100644 index 0000000000000000000000000000000000000000..c2164fa928648f3ab190e04bff3f767454c79c29 --- /dev/null +++ b/a1ZCeFpeW0o.txt @@ -0,0 +1,14352 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencare at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu keep on talking about uh + + align:start position:0% +ocw.mit.edu keep on talking about uh + + + align:start position:0% +ocw.mit.edu keep on talking about uh +principal component analysis which we + + align:start position:0% +principal component analysis which we + + + align:start position:0% +principal component analysis which we +essentially introduced as a way to work + + align:start position:0% +essentially introduced as a way to work + + + align:start position:0% +essentially introduced as a way to work +with a bunch of data so we have the the + + align:start position:0% +with a bunch of data so we have the the + + + align:start position:0% +with a bunch of data so we have the the +data that's given to us when we want to + + align:start position:0% +data that's given to us when we want to + + + align:start position:0% +data that's given to us when we want to +do PCA is a bunch of vectors X1 xn all + + align:start position:0% +do PCA is a bunch of vectors X1 xn all + + + align:start position:0% +do PCA is a bunch of vectors X1 xn all +right + + align:start position:0% + + + + align:start position:0% + +so so they're random + + align:start position:0% + + + + align:start position:0% + +vectors in r d okay and what we mention + + align:start position:0% +vectors in r d okay and what we mention + + + align:start position:0% +vectors in r d okay and what we mention +is that we're going to be using uh uh + + align:start position:0% +is that we're going to be using uh uh + + + align:start position:0% +is that we're going to be using uh uh +linear algebra in particular uh the + + align:start position:0% +linear algebra in particular uh the + + + align:start position:0% +linear algebra in particular uh the +spectral theorem that guarantees to us + + align:start position:0% +spectral theorem that guarantees to us + + + align:start position:0% +spectral theorem that guarantees to us +that if I look at the cence Matrix of + + align:start position:0% +that if I look at the cence Matrix of + + + align:start position:0% +that if I look at the cence Matrix of +this guys or its empirical cence Matrix + + align:start position:0% +this guys or its empirical cence Matrix + + + align:start position:0% +this guys or its empirical cence Matrix +since they're symmetric real matrices + + align:start position:0% +since they're symmetric real matrices + + + align:start position:0% +since they're symmetric real matrices +and they're positive semi-definite there + + align:start position:0% +and they're positive semi-definite there + + + align:start position:0% +and they're positive semi-definite there +exists a diagonalization into non- + + align:start position:0% +exists a diagonalization into non- + + + align:start position:0% +exists a diagonalization into non- +negative again values all right and so + + align:start position:0% +negative again values all right and so + + + align:start position:0% +negative again values all right and so +here those things live in Rd so it's a + + align:start position:0% +here those things live in Rd so it's a + + + align:start position:0% +here those things live in Rd so it's a +really large space and uh uh what we + + align:start position:0% +really large space and uh uh what we + + + align:start position:0% +really large space and uh uh what we +want to do is to map it down into a + + align:start position:0% +want to do is to map it down into a + + + align:start position:0% +want to do is to map it down into a +space that we can visualize hopefully a + + align:start position:0% +space that we can visualize hopefully a + + + align:start position:0% +space that we can visualize hopefully a +space of size two or three or if not + + align:start position:0% +space of size two or three or if not + + + align:start position:0% +space of size two or three or if not +then we're just going to take more and + + align:start position:0% +then we're just going to take more and + + + align:start position:0% +then we're just going to take more and +start looking at subspaces Al together + + align:start position:0% +start looking at subspaces Al together + + + align:start position:0% +start looking at subspaces Al together +all right so think of the case where D + + align:start position:0% +all right so think of the case where D + + + align:start position:0% +all right so think of the case where D +is + + align:start position:0% +is + + + align:start position:0% +is +large + + align:start position:0% +large + + + align:start position:0% +large +but not larger than n all right so let's + + align:start position:0% +but not larger than n all right so let's + + + align:start position:0% +but not larger than n all right so let's +say you have a large number of points so + + align:start position:0% +say you have a large number of points so + + + align:start position:0% +say you have a large number of points so +the question is is it possible to + + align:start position:0% +the question is is it possible to + + + align:start position:0% +the question is is it possible to +project those things onto a low + + align:start position:0% +project those things onto a low + + + align:start position:0% +project those things onto a low +dimensional space d + + align:start position:0% +dimensional space d + + + align:start position:0% +dimensional space d +Prime which is much less than D so think + + align:start position:0% +Prime which is much less than D so think + + + align:start position:0% +Prime which is much less than D so think +of D Prime of equals say two or or + + align:start position:0% +of D Prime of equals say two or or + + + align:start position:0% +of D Prime of equals say two or or +three and so that you keep as much + + align:start position:0% +three and so that you keep as much + + + align:start position:0% +three and so that you keep as much +information about the cloud point that + + align:start position:0% +information about the cloud point that + + + align:start position:0% +information about the cloud point that +you had originally all right so again + + align:start position:0% +you had originally all right so again + + + align:start position:0% +you had originally all right so again +the example that we could have is that + + align:start position:0% +the example that we could have is that + + + align:start position:0% +the example that we could have is that +X1 to xn for say XI for patient I is + + align:start position:0% +X1 to xn for say XI for patient I is + + + align:start position:0% +X1 to xn for say XI for patient I is +recording a bunch of uh body + + align:start position:0% +recording a bunch of uh body + + + align:start position:0% +recording a bunch of uh body +measurements and maybe blood pressure uh + + align:start position:0% +measurements and maybe blood pressure uh + + + align:start position:0% +measurements and maybe blood pressure uh +some symptoms Etc and then we have a + + align:start position:0% +some symptoms Etc and then we have a + + + align:start position:0% +some symptoms Etc and then we have a +cloud of nend patients and we're trying + + align:start position:0% +cloud of nend patients and we're trying + + + align:start position:0% +cloud of nend patients and we're trying +to visualize maybe to see if we if I + + align:start position:0% +to visualize maybe to see if we if I + + + align:start position:0% +to visualize maybe to see if we if I +could see for example that there's two + + align:start position:0% +could see for example that there's two + + + align:start position:0% +could see for example that there's two +groups of patients maybe I would know + + align:start position:0% +groups of patients maybe I would know + + + align:start position:0% +groups of patients maybe I would know +that I have two groups of different + + align:start position:0% +that I have two groups of different + + + align:start position:0% +that I have two groups of different +disease or maybe two groups of different + + align:start position:0% +disease or maybe two groups of different + + + align:start position:0% +disease or maybe two groups of different +patients that respond differently to + + align:start position:0% +patients that respond differently to + + + align:start position:0% +patients that respond differently to +particular disease or drug Etc all right + + align:start position:0% +particular disease or drug Etc all right + + + align:start position:0% +particular disease or drug Etc all right +so visualizing is going to give us quite + + align:start position:0% +so visualizing is going to give us quite + + + align:start position:0% +so visualizing is going to give us quite +bit of insight about what this uh the + + align:start position:0% +bit of insight about what this uh the + + + align:start position:0% +bit of insight about what this uh the +spatial uh uh arrangement of those uh + + align:start position:0% +spatial uh uh arrangement of those uh + + + align:start position:0% +spatial uh uh arrangement of those uh +vectors are and so PCA says well you + + align:start position:0% +vectors are and so PCA says well you + + + align:start position:0% +vectors are and so PCA says well you +know here of course in this question one + + align:start position:0% +know here of course in this question one + + + align:start position:0% +know here of course in this question one +thing is not defined is what is + + align:start position:0% +thing is not defined is what is + + + align:start position:0% +thing is not defined is what is +information and we said that one thing + + align:start position:0% +information and we said that one thing + + + align:start position:0% +information and we said that one thing +we might want to do when we project is + + align:start position:0% +we might want to do when we project is + + + align:start position:0% +we might want to do when we project is +that points start to not collide with + + align:start position:0% +that points start to not collide with + + + align:start position:0% +that points start to not collide with +each other and so that means we're + + align:start position:0% +each other and so that means we're + + + align:start position:0% +each other and so that means we're +trying to find directions where after I + + align:start position:0% +trying to find directions where after I + + + align:start position:0% +trying to find directions where after I +project the puns are still pretty spread + + align:start position:0% +project the puns are still pretty spread + + + align:start position:0% +project the puns are still pretty spread +out and so I can see what's going on and + + align:start position:0% +out and so I can see what's going on and + + + align:start position:0% +out and so I can see what's going on and +PCA says okay so there's many ways to + + align:start position:0% +PCA says okay so there's many ways to + + + align:start position:0% +PCA says okay so there's many ways to +answer this question and PC says let's + + align:start position:0% +answer this question and PC says let's + + + align:start position:0% +answer this question and PC says let's +just find a a Subspace of Dimension D + + align:start position:0% +just find a a Subspace of Dimension D + + + align:start position:0% +just find a a Subspace of Dimension D +Prime that keeps as much coant structure + + align:start position:0% +Prime that keeps as much coant structure + + + align:start position:0% +Prime that keeps as much coant structure +as possible and uh and uh uh the reason + + align:start position:0% +as possible and uh and uh uh the reason + + + align:start position:0% +as possible and uh and uh uh the reason +is that uh uh those directions are the + + align:start position:0% +is that uh uh those directions are the + + + align:start position:0% +is that uh uh those directions are the +ones that maximize the variance which is + + align:start position:0% +ones that maximize the variance which is + + + align:start position:0% +ones that maximize the variance which is +a proxy for the spread there's many many + + align:start position:0% +a proxy for the spread there's many many + + + align:start position:0% +a proxy for the spread there's many many +ways to do this there's actually a um + + align:start position:0% +ways to do this there's actually a um + + + align:start position:0% +ways to do this there's actually a um +Google video that was released maybe + + align:start position:0% +Google video that was released maybe + + + align:start position:0% +Google video that was released maybe +last week about the data visualization + + align:start position:0% +last week about the data visualization + + + align:start position:0% +last week about the data visualization +team of Google uh that shows you + + align:start position:0% +team of Google uh that shows you + + + align:start position:0% +team of Google uh that shows you +something called tisy + + align:start position:0% +something called tisy + + + align:start position:0% +something called tisy +uh which is essentially something that + + align:start position:0% +uh which is essentially something that + + + align:start position:0% +uh which is essentially something that +tries to do that it takes points in very + + align:start position:0% +tries to do that it takes points in very + + + align:start position:0% +tries to do that it takes points in very +high dimensions and tries to map them in + + align:start position:0% +high dimensions and tries to map them in + + + align:start position:0% +high dimensions and tries to map them in +lower Dimensions so that you can + + align:start position:0% +lower Dimensions so that you can + + + align:start position:0% +lower Dimensions so that you can +actually visualize them and TIY is some + + align:start position:0% +actually visualize them and TIY is some + + + align:start position:0% +actually visualize them and TIY is some +alternative to PCA that gives another + + align:start position:0% +alternative to PCA that gives another + + + align:start position:0% +alternative to PCA that gives another +definition for the word information all + + align:start position:0% +definition for the word information all + + + align:start position:0% +definition for the word information all +right I I'll talk about this towards the + + align:start position:0% +right I I'll talk about this towards the + + + align:start position:0% +right I I'll talk about this towards the +end how you can actually somewhat + + align:start position:0% +end how you can actually somewhat + + + align:start position:0% +end how you can actually somewhat +automatically extend everything we've + + align:start position:0% +automatically extend everything we've + + + align:start position:0% +automatically extend everything we've +said for PCA to an infinite family of of + + align:start position:0% +said for PCA to an infinite family of of + + + align:start position:0% +said for PCA to an infinite family of of +of + + align:start position:0% +of + + + align:start position:0% +of +procedures all right so how do we do + + align:start position:0% +procedures all right so how do we do + + + align:start position:0% +procedures all right so how do we do +this this well the way we do this is as + + align:start position:0% +this this well the way we do this is as + + + align:start position:0% +this this well the way we do this is as +follows right so remember given those + + align:start position:0% +follows right so remember given those + + + align:start position:0% +follows right so remember given those +guys we can form something which is + + align:start position:0% +guys we can form something which is + + + align:start position:0% +guys we can form something which is +called s which is the + + align:start position:0% +called s which is the + + + align:start position:0% +called s which is the +sample or the + + align:start position:0% + + + + align:start position:0% + +empirical covariance + + align:start position:0% + + + + align:start position:0% + +Matrix okay and since uh from couple + + align:start position:0% +Matrix okay and since uh from couple + + + align:start position:0% +Matrix okay and since uh from couple +slides ago we know that s has a a again + + align:start position:0% +slides ago we know that s has a a again + + + align:start position:0% +slides ago we know that s has a a again +value decomposition s is equal to p d p + + align:start position:0% +value decomposition s is equal to p d p + + + align:start position:0% +value decomposition s is equal to p d p +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +where p is + + align:start position:0% + + + + align:start position:0% + +orthogonal okay so that's where we use + + align:start position:0% +orthogonal okay so that's where we use + + + align:start position:0% +orthogonal okay so that's where we use +our linear algebra result so that means + + align:start position:0% +our linear algebra result so that means + + + align:start position:0% +our linear algebra result so that means +that ppose P is equal to P PP + + align:start position:0% +that ppose P is equal to P PP + + + align:start position:0% +that ppose P is equal to P PP +transpose which is the + + align:start position:0% +transpose which is the + + + align:start position:0% +transpose which is the +identity okay so remember s is a d byd + + align:start position:0% +identity okay so remember s is a d byd + + + align:start position:0% +identity okay so remember s is a d byd +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +right and so p is also d by D and + + align:start position:0% +right and so p is also d by D and + + + align:start position:0% +right and so p is also d by D and +D is + + align:start position:0% + + + + align:start position:0% + +diagonal and uh + + align:start position:0% +diagonal and uh + + + align:start position:0% +diagonal and uh +and I'm actually going to take without + + align:start position:0% +and I'm actually going to take without + + + align:start position:0% +and I'm actually going to take without +loss of generality I'm going to assume + + align:start position:0% +loss of generality I'm going to assume + + + align:start position:0% +loss of generality I'm going to assume +that D so it's going to be diagonal and + + align:start position:0% +that D so it's going to be diagonal and + + + align:start position:0% +that D so it's going to be diagonal and +I'm going to have something that looks + + align:start position:0% +I'm going to have something that looks + + + align:start position:0% +I'm going to have something that looks +like Lambda one uh yeah Lambda one to + + align:start position:0% +like Lambda one uh yeah Lambda one to + + + align:start position:0% +like Lambda one uh yeah Lambda one to +Lambda D those are called the agon + + align:start position:0% +Lambda D those are called the agon + + + align:start position:0% +Lambda D those are called the agon +values of + + align:start position:0% +values of + + + align:start position:0% +values of +s what we know is that the Lambda JS are + + align:start position:0% +s what we know is that the Lambda JS are + + + align:start position:0% +s what we know is that the Lambda JS are +non negative and actually what I'm going + + align:start position:0% +non negative and actually what I'm going + + + align:start position:0% +non negative and actually what I'm going +to assume without loss of generality is + + align:start position:0% +to assume without loss of generality is + + + align:start position:0% +to assume without loss of generality is +Lambda one is larger than Lambda 2 which + + align:start position:0% +Lambda one is larger than Lambda 2 which + + + align:start position:0% +Lambda one is larger than Lambda 2 which +is + + align:start position:0% +is + + + align:start position:0% +is +larger than Lambda d + + align:start position:0% +larger than Lambda d + + + align:start position:0% +larger than Lambda d +okay because in particular this + + align:start position:0% +okay because in particular this + + + align:start position:0% +okay because in particular this +decomposition the spectral decomposition + + align:start position:0% +decomposition the spectral decomposition + + + align:start position:0% +decomposition the spectral decomposition +is not entirely unique I could + + align:start position:0% +is not entirely unique I could + + + align:start position:0% +is not entirely unique I could +permute The Columns of p and I would + + align:start position:0% +permute The Columns of p and I would + + + align:start position:0% +permute The Columns of p and I would +still have an orthogonal Matrix and to + + align:start position:0% +still have an orthogonal Matrix and to + + + align:start position:0% +still have an orthogonal Matrix and to +balance that I would also have to + + align:start position:0% +balance that I would also have to + + + align:start position:0% +balance that I would also have to +permute the entries of D okay so there's + + align:start position:0% +permute the entries of D okay so there's + + + align:start position:0% +permute the entries of D okay so there's +as many decompositions as their + + align:start position:0% +as many decompositions as their + + + align:start position:0% +as many decompositions as their +permutations right so there's actually + + align:start position:0% +permutations right so there's actually + + + align:start position:0% +permutations right so there's actually +quite a bit but the bag of igen values + + align:start position:0% +quite a bit but the bag of igen values + + + align:start position:0% +quite a bit but the bag of igen values +is unique right if I give the set of + + align:start position:0% +is unique right if I give the set of + + + align:start position:0% +is unique right if I give the set of +igen values is unique the ordering is + + align:start position:0% +igen values is unique the ordering is + + + align:start position:0% +igen values is unique the ordering is +certainly not not unique okay so here + + align:start position:0% +certainly not not unique okay so here + + + align:start position:0% +certainly not not unique okay so here +I'm just going to pick I'm going to nail + + align:start position:0% +I'm just going to pick I'm going to nail + + + align:start position:0% +I'm just going to pick I'm going to nail +down one particular permutation actually + + align:start position:0% +down one particular permutation actually + + + align:start position:0% +down one particular permutation actually +maybe two in case in case I have equ + + align:start position:0% +maybe two in case in case I have equ + + + align:start position:0% +maybe two in case in case I have equ +qualities but let's say there's let's + + align:start position:0% +qualities but let's say there's let's + + + align:start position:0% +qualities but let's say there's let's +say I pick one that satisfies this and + + align:start position:0% +say I pick one that satisfies this and + + + align:start position:0% +say I pick one that satisfies this and +the reason why I do this is really not + + align:start position:0% +the reason why I do this is really not + + + align:start position:0% +the reason why I do this is really not +very important is just to say when I + + align:start position:0% +very important is just to say when I + + + align:start position:0% +very important is just to say when I +talk I'm going to want to talk about the + + align:start position:0% +talk I'm going to want to talk about the + + + align:start position:0% +talk I'm going to want to talk about the +largest of those ion values so it's just + + align:start position:0% +largest of those ion values so it's just + + + align:start position:0% +largest of those ion values so it's just +going to be easier for me to say that + + align:start position:0% +going to be easier for me to say that + + + align:start position:0% +going to be easier for me to say that +this one is limda one rather than say + + align:start position:0% +this one is limda one rather than say + + + align:start position:0% +this one is limda one rather than say +it's LDA 7even all right so this is just + + align:start position:0% +it's LDA 7even all right so this is just + + + align:start position:0% +it's LDA 7even all right so this is just +to say that the largest tag in value + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% +of + + + align:start position:0% +of +s is Lambda one okay if I didn't do that + + align:start position:0% +s is Lambda one okay if I didn't do that + + + align:start position:0% +s is Lambda one okay if I didn't do that +I would just call it maybe Lambda Max + + align:start position:0% +I would just call it maybe Lambda Max + + + align:start position:0% +I would just call it maybe Lambda Max +and you would just know which one I'm + + align:start position:0% +and you would just know which one I'm + + + align:start position:0% +and you would just know which one I'm +talking + + align:start position:0% +talking + + + align:start position:0% +talking +about all right so + + align:start position:0% +about all right so + + + align:start position:0% +about all right so +um + + align:start position:0% +um + + + align:start position:0% +um +so what's happening now is that uh + + align:start position:0% +so what's happening now is that uh + + + align:start position:0% +so what's happening now is that uh +um if I look at D then uh it turns out + + align:start position:0% +um if I look at D then uh it turns out + + + align:start position:0% +um if I look at D then uh it turns out +that if I start so if I do p transpose + + align:start position:0% +that if I start so if I do p transpose + + + align:start position:0% +that if I start so if I do p transpose +XI I am actually projecting my XI and + + align:start position:0% +XI I am actually projecting my XI and + + + align:start position:0% +XI I am actually projecting my XI and +basically changing the the bases for my + + align:start position:0% +basically changing the the bases for my + + + align:start position:0% +basically changing the the bases for my +XI and now D is the empirical cience + + align:start position:0% +XI and now D is the empirical cience + + + align:start position:0% +XI and now D is the empirical cience +Matrix of those guys all right so let's + + align:start position:0% +Matrix of those guys all right so let's + + + align:start position:0% +Matrix of those guys all right so let's +check that so what it means is that if I + + align:start position:0% +check that so what it means is that if I + + + align:start position:0% +check that so what it means is that if I +look + + align:start position:0% + + + + align:start position:0% + +at so what I claim is that P transpose + + align:start position:0% +at so what I claim is that P transpose + + + align:start position:0% +at so what I claim is that P transpose +XI that's a new Vector let's call it Yi + + align:start position:0% +XI that's a new Vector let's call it Yi + + + align:start position:0% +XI that's a new Vector let's call it Yi +it's equal it's also in + + align:start position:0% +it's equal it's also in + + + align:start position:0% +it's equal it's also in +Rd and what I claim is that the cence + + align:start position:0% +Rd and what I claim is that the cence + + + align:start position:0% +Rd and what I claim is that the cence +Matrix of this guy is actually now uh uh + + align:start position:0% +Matrix of this guy is actually now uh uh + + + align:start position:0% +Matrix of this guy is actually now uh uh +this diagonal matrix which means in + + align:start position:0% +this diagonal matrix which means in + + + align:start position:0% +this diagonal matrix which means in +particular that if they were gussan then + + align:start position:0% +particular that if they were gussan then + + + align:start position:0% +particular that if they were gussan then +they would be independent but I need + + align:start position:0% +they would be independent but I need + + + align:start position:0% +they would be independent but I need +also know now that there's no + + align:start position:0% +also know now that there's no + + + align:start position:0% +also know now that there's no +correlation across coordinates of Yi + + align:start position:0% +correlation across coordinates of Yi + + + align:start position:0% +correlation across coordinates of Yi +okay so to prove this uh let me + + align:start position:0% + + + + align:start position:0% + +assume that xar + + align:start position:0% +assume that xar + + + align:start position:0% +assume that xar +is equal to zero and the reason why I do + + align:start position:0% +is equal to zero and the reason why I do + + + align:start position:0% +is equal to zero and the reason why I do +this is because it's just annoying to + + align:start position:0% +this is because it's just annoying to + + + align:start position:0% +this is because it's just annoying to +carry out all this centering constantly + + align:start position:0% +carry out all this centering constantly + + + align:start position:0% +carry out all this centering constantly +when I talk about s all right so when + + align:start position:0% +when I talk about s all right so when + + + align:start position:0% +when I talk about s all right so when +xar is equal to zero that implies that s + + align:start position:0% +xar is equal to zero that implies that s + + + align:start position:0% +xar is equal to zero that implies that s +has this very simple form it's of the + + align:start position:0% +has this very simple form it's of the + + + align:start position:0% +has this very simple form it's of the +form sum from I = 1 to n of x i x i + + align:start position:0% +form sum from I = 1 to n of x i x i + + + align:start position:0% +form sum from I = 1 to n of x i x i +transpose right so that's my S but what + + align:start position:0% +transpose right so that's my S but what + + + align:start position:0% +transpose right so that's my S but what +I want is the S of Y so okay that + + align:start position:0% +I want is the S of Y so okay that + + + align:start position:0% +I want is the S of Y so okay that +implies also that P * xar + + align:start position:0% +implies also that P * xar + + + align:start position:0% +implies also that P * xar +which is equal to P * xar is also equal + + align:start position:0% +which is equal to P * xar is also equal + + + align:start position:0% +which is equal to P * xar is also equal +to zero right so that means that Y + + align:start position:0% +to zero right so that means that Y + + + align:start position:0% +to zero right so that means that Y +Bar y has me zero if this is zero so if + + align:start position:0% +Bar y has me zero if this is zero so if + + + align:start position:0% +Bar y has me zero if this is zero so if +I look at the sample cence Matrix of Y + + align:start position:0% +I look at the sample cence Matrix of Y + + + align:start position:0% +I look at the sample cence Matrix of Y +it's just going to be something that + + align:start position:0% +it's just going to be something that + + + align:start position:0% +it's just going to be something that +looks like the sum of the outer products + + align:start position:0% +looks like the sum of the outer products + + + align:start position:0% +looks like the sum of the outer products +or the yi yi + + align:start position:0% +or the yi yi + + + align:start position:0% +or the yi yi +transpose okay and again the reason why + + align:start position:0% +transpose okay and again the reason why + + + align:start position:0% +transpose okay and again the reason why +I make this + + align:start position:0% +I make this + + + align:start position:0% +I make this +assumption is so that I don't have to + + align:start position:0% +assumption is so that I don't have to + + + align:start position:0% +assumption is so that I don't have to +write minus X bar bar X bar + + align:start position:0% +write minus X bar bar X bar + + + align:start position:0% +write minus X bar bar X bar +transpose but you can do it and it's + + align:start position:0% +transpose but you can do it and it's + + + align:start position:0% +transpose but you can do it and it's +going to work exactly the + + align:start position:0% +going to work exactly the + + + align:start position:0% +going to work exactly the +same all right so now I look at this S + + align:start position:0% +same all right so now I look at this S + + + align:start position:0% +same all right so now I look at this S +Prime and so what is this S + + align:start position:0% +Prime and so what is this S + + + align:start position:0% +Prime and so what is this S +Prime well I'm just going to replace Yi + + align:start position:0% +Prime well I'm just going to replace Yi + + + align:start position:0% +Prime well I'm just going to replace Yi +with pxi right so it's the sum from I = + + align:start position:0% +with pxi right so it's the sum from I = + + + align:start position:0% +with pxi right so it's the sum from I = +1 to n of PX I pxi + + align:start position:0% +1 to n of PX I pxi + + + align:start position:0% +1 to n of PX I pxi +transpose which is equal + + align:start position:0% +transpose which is equal + + + align:start position:0% +transpose which is equal +to the sum from sorry there's a one over + + align:start position:0% +to the sum from sorry there's a one over + + + align:start position:0% +to the sum from sorry there's a one over +n + + align:start position:0% + + + + align:start position:0% + +so it's equal to 1/ n sum from I = 1 to + + align:start position:0% +so it's equal to 1/ n sum from I = 1 to + + + align:start position:0% +so it's equal to 1/ n sum from I = 1 to +n of PX + + align:start position:0% + + + + align:start position:0% + +i x i transpose P + + align:start position:0% +i x i transpose P + + + align:start position:0% +i x i transpose P +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +agreed I justed that the transpose of ab + + align:start position:0% +agreed I justed that the transpose of ab + + + align:start position:0% +agreed I justed that the transpose of ab +is transpose of B times the transpose of + + align:start position:0% + + + + align:start position:0% + +a and so now I can push the sum in right + + align:start position:0% +a and so now I can push the sum in right + + + align:start position:0% +a and so now I can push the sum in right +P does not depend on I so this thing + + align:start position:0% +P does not depend on I so this thing + + + align:start position:0% +P does not depend on I so this thing +here is equal to p s p + + align:start position:0% +here is equal to p s p + + + align:start position:0% +here is equal to p s p +transpose because the sum of the X IX I + + align:start position:0% +transpose because the sum of the X IX I + + + align:start position:0% +transpose because the sum of the X IX I +transpose divided by n is + + align:start position:0% +transpose divided by n is + + + align:start position:0% +transpose divided by n is +s but what is PSP transpose well we know + + align:start position:0% +s but what is PSP transpose well we know + + + align:start position:0% +s but what is PSP transpose well we know +that P that s sorry is equal to sorry + + align:start position:0% +that P that s sorry is equal to sorry + + + align:start position:0% +that P that s sorry is equal to sorry +that's P transpose right so this was + + align:start position:0% +that's P transpose right so this was + + + align:start position:0% +that's P transpose right so this was +with a ppose sorry I made a an important + + align:start position:0% +with a ppose sorry I made a an important + + + align:start position:0% +with a ppose sorry I made a an important +mistake here so Yi is ppose Xi so this + + align:start position:0% +mistake here so Yi is ppose Xi so this + + + align:start position:0% +mistake here so Yi is ppose Xi so this +is ppose and ppose here which means that + + align:start position:0% +is ppose and ppose here which means that + + + align:start position:0% +is ppose and ppose here which means that +this is p transpose and this is double + + align:start position:0% +this is p transpose and this is double + + + align:start position:0% +this is p transpose and this is double +transpose which is just nothing and that + + align:start position:0% +transpose which is just nothing and that + + + align:start position:0% +transpose which is just nothing and that +transpose and nothing + + align:start position:0% +transpose and nothing + + + align:start position:0% +transpose and nothing +okay so now I write S as p d p transpose + + align:start position:0% +okay so now I write S as p d p transpose + + + align:start position:0% +okay so now I write S as p d p transpose +that's the spectral uh decomposition + + align:start position:0% +that's the spectral uh decomposition + + + align:start position:0% +that's the spectral uh decomposition +that I had before that's my value comp + + align:start position:0% +that I had before that's my value comp + + + align:start position:0% +that I had before that's my value comp +position which means that now if I look + + align:start position:0% +position which means that now if I look + + + align:start position:0% +position which means that now if I look +at S Prime it's p transpose times p d + + align:start position:0% +at S Prime it's p transpose times p d + + + align:start position:0% +at S Prime it's p transpose times p d +ppose p but now ppose p is the identity + + align:start position:0% +ppose p but now ppose p is the identity + + + align:start position:0% +ppose p but now ppose p is the identity +ppose p is the identity so this is + + align:start position:0% +ppose p is the identity so this is + + + align:start position:0% +ppose p is the identity so this is +actually just equal to + + align:start position:0% +actually just equal to + + + align:start position:0% +actually just equal to +D + + align:start position:0% +D + + + align:start position:0% +D +okay and again you can check that this + + align:start position:0% +okay and again you can check that this + + + align:start position:0% +okay and again you can check that this +also works if you have to Center all + + align:start position:0% +also works if you have to Center all + + + align:start position:0% +also works if you have to Center all +those guys as you go right but if you + + align:start position:0% +those guys as you go right but if you + + + align:start position:0% +those guys as you go right but if you +think about it uh this is the same thing + + align:start position:0% +think about it uh this is the same thing + + + align:start position:0% +think about it uh this is the same thing +as saying that I just replace x i by x i + + align:start position:0% +as saying that I just replace x i by x i + + + align:start position:0% +as saying that I just replace x i by x i +minus xar and then it's true that Y Bar + + align:start position:0% +minus xar and then it's true that Y Bar + + + align:start position:0% +minus xar and then it's true that Y Bar +is also uh the P times x IUS X + + align:start position:0% +is also uh the P times x IUS X + + + align:start position:0% +is also uh the P times x IUS X +bar all right so now we have that D is + + align:start position:0% +bar all right so now we have that D is + + + align:start position:0% +bar all right so now we have that D is +the erical cience Matrix of those guys + + align:start position:0% +the erical cience Matrix of those guys + + + align:start position:0% +the erical cience Matrix of those guys +the Y eyes which are ppose X eyes and so + + align:start position:0% +the Y eyes which are ppose X eyes and so + + + align:start position:0% +the Y eyes which are ppose X eyes and so +in particular what it means is that if I + + align:start position:0% +in particular what it means is that if I + + + align:start position:0% +in particular what it means is that if I +look at the + + align:start position:0% +look at the + + + align:start position:0% +look at the +ciance of Y + + align:start position:0% +ciance of Y + + + align:start position:0% +ciance of Y +say + + align:start position:0% +say + + + align:start position:0% +say +j y + + align:start position:0% +j y + + + align:start position:0% +j y +k right so that's the ciance of the jth + + align:start position:0% +k right so that's the ciance of the jth + + + align:start position:0% +k right so that's the ciance of the jth +coordinate of Y and the K coordinate of + + align:start position:0% +coordinate of Y and the K coordinate of + + + align:start position:0% +coordinate of Y and the K coordinate of +Y I'm just not putting an index but + + align:start position:0% +Y I'm just not putting an index but + + + align:start position:0% +Y I'm just not putting an index but +maybe let's say the first one or + + align:start position:0% +maybe let's say the first one or + + + align:start position:0% +maybe let's say the first one or +something like this any of them they are + + align:start position:0% +something like this any of them they are + + + align:start position:0% +something like this any of them they are +IID then what is this coar it's actually + + align:start position:0% +IID then what is this coar it's actually + + + align:start position:0% +IID then what is this coar it's actually +zero if if J is different from K and the + + align:start position:0% +zero if if J is different from K and the + + + align:start position:0% +zero if if J is different from K and the +co variance between YJ and YJ which is + + align:start position:0% +co variance between YJ and YJ which is + + + align:start position:0% +co variance between YJ and YJ which is +just the variance of YJ is equal to + + align:start position:0% +just the variance of YJ is equal to + + + align:start position:0% +just the variance of YJ is equal to +Lambda J the J largest igen + + align:start position:0% +Lambda J the J largest igen + + + align:start position:0% +Lambda J the J largest igen +value okay so the igen values capture + + align:start position:0% +value okay so the igen values capture + + + align:start position:0% +value okay so the igen values capture +the + + align:start position:0% +the + + + align:start position:0% +the +variance of my uh observations in this + + align:start position:0% +variance of my uh observations in this + + + align:start position:0% +variance of my uh observations in this +new coordinate system and they're + + align:start position:0% +new coordinate system and they're + + + align:start position:0% +new coordinate system and they're +completely orthogonal so what does that + + align:start position:0% +completely orthogonal so what does that + + + align:start position:0% +completely orthogonal so what does that +mean well again remember if I chop off + + align:start position:0% +mean well again remember if I chop off + + + align:start position:0% +mean well again remember if I chop off +the head of my um of my gaussian in + + align:start position:0% +the head of my um of my gaussian in + + + align:start position:0% +the head of my um of my gaussian in +multi-dimensions we said that what we + + align:start position:0% +multi-dimensions we said that what we + + + align:start position:0% +multi-dimensions we said that what we +started from was something that looked + + align:start position:0% +started from was something that looked + + + align:start position:0% +started from was something that looked +like this + + align:start position:0% +like this + + + align:start position:0% +like this +right and we said well there's One + + align:start position:0% +right and we said well there's One + + + align:start position:0% +right and we said well there's One +Direction that's important that's this + + align:start position:0% +Direction that's important that's this + + + align:start position:0% +Direction that's important that's this +guy and one important that this this guy + + align:start position:0% +guy and one important that this this guy + + + align:start position:0% +guy and one important that this this guy +when I apply the transformation ppose + + align:start position:0% +when I apply the transformation ppose + + + align:start position:0% +when I apply the transformation ppose +what I'm doing is I'm realigning this + + align:start position:0% +what I'm doing is I'm realigning this + + + align:start position:0% +what I'm doing is I'm realigning this +thing with the new Axis or in a way + + align:start position:0% +thing with the new Axis or in a way + + + align:start position:0% +thing with the new Axis or in a way +rather to be fair I'm not actually + + align:start position:0% +rather to be fair I'm not actually + + + align:start position:0% +rather to be fair I'm not actually +realigning the I'm not really realigning + + align:start position:0% +realigning the I'm not really realigning + + + align:start position:0% +realigning the I'm not really realigning +the uh ellipses with with the axis I'm + + align:start position:0% +the uh ellipses with with the axis I'm + + + align:start position:0% +the uh ellipses with with the axis I'm +really realigning the axis with the + + align:start position:0% +really realigning the axis with the + + + align:start position:0% +really realigning the axis with the +ellipses right so really what I'm doing + + align:start position:0% +ellipses right so really what I'm doing + + + align:start position:0% +ellipses right so really what I'm doing +is I'm saying after I apply P I'm just + + align:start position:0% +is I'm saying after I apply P I'm just + + + align:start position:0% +is I'm saying after I apply P I'm just +rotating this coordinate system so now + + align:start position:0% +rotating this coordinate system so now + + + align:start position:0% +rotating this coordinate system so now +it + + align:start position:0% +it + + + align:start position:0% +it +becomes uh this + + align:start position:0% + + + + align:start position:0% + +guy okay and now my ellipse is actually + + align:start position:0% +guy okay and now my ellipse is actually + + + align:start position:0% +guy okay and now my ellipse is actually +completely aligned and and and what + + align:start position:0% +completely aligned and and and what + + + align:start position:0% +completely aligned and and and what +happens here is that this coordinate is + + align:start position:0% +happens here is that this coordinate is + + + align:start position:0% +happens here is that this coordinate is +independent of that coordinate and + + align:start position:0% +independent of that coordinate and + + + align:start position:0% +independent of that coordinate and +that's what we read here + + align:start position:0% +that's what we read here + + + align:start position:0% +that's what we read here +okay if they're gussan I didn't really + + align:start position:0% +okay if they're gussan I didn't really + + + align:start position:0% +okay if they're gussan I didn't really +tell you this I'm only making statements + + align:start position:0% +tell you this I'm only making statements + + + align:start position:0% +tell you this I'm only making statements +about Co variances if they're gussian + + align:start position:0% +about Co variances if they're gussian + + + align:start position:0% +about Co variances if they're gussian +those imply statements about + + align:start position:0% + + + + align:start position:0% + +independence okay so as I said the + + align:start position:0% +independence okay so as I said the + + + align:start position:0% +independence okay so as I said the +variance now Lambda one is actually the + + align:start position:0% +variance now Lambda one is actually the + + + align:start position:0% +variance now Lambda one is actually the +variance + + align:start position:0% + + + + align:start position:0% + +of P transpose x + + align:start position:0% +of P transpose x + + + align:start position:0% +of P transpose x +i but if I look now at at the so this is + + align:start position:0% +i but if I look now at at the so this is + + + align:start position:0% +i but if I look now at at the so this is +a vector so I need to look at + + align:start position:0% +a vector so I need to look at + + + align:start position:0% +a vector so I need to look at +the uh first coordinate of this guy + + align:start position:0% + + + + align:start position:0% + +right so it turns out that doing this is + + align:start position:0% +right so it turns out that doing this is + + + align:start position:0% +right so it turns out that doing this is +actually the same thing as looking at + + align:start position:0% +actually the same thing as looking at + + + align:start position:0% +actually the same thing as looking at +the + + align:start position:0% +the + + + align:start position:0% +the +variance or of what well the First + + align:start position:0% +variance or of what well the First + + + align:start position:0% +variance or of what well the First +Column of P times uh x i right so that's + + align:start position:0% +Column of P times uh x i right so that's + + + align:start position:0% +Column of P times uh x i right so that's +the variance of the I'm going to call it + + align:start position:0% +the variance of the I'm going to call it + + + align:start position:0% +the variance of the I'm going to call it +V1 transpose XI + + align:start position:0% +V1 transpose XI + + + align:start position:0% +V1 transpose XI +where + + align:start position:0% + + + + align:start position:0% + +P so the V1 VD in our D + + align:start position:0% +P so the V1 VD in our D + + + align:start position:0% +P so the V1 VD in our D +are igen + + align:start position:0% +are igen + + + align:start position:0% +are igen +vectors and each VI is associated to + + align:start position:0% +vectors and each VI is associated to + + + align:start position:0% +vectors and each VI is associated to +Lambda I okay so that's what we saw when + + align:start position:0% +Lambda I okay so that's what we saw when + + + align:start position:0% +Lambda I okay so that's what we saw when +we talked about this tic composition a + + align:start position:0% +we talked about this tic composition a + + + align:start position:0% +we talked about this tic composition a +couple slides back uh that's the one + + align:start position:0% +couple slides back uh that's the one + + + align:start position:0% +couple slides back uh that's the one +here + + align:start position:0% +here + + + align:start position:0% +here +okay uh so if I call The Columns of P V1 + + align:start position:0% +okay uh so if I call The Columns of P V1 + + + align:start position:0% +okay uh so if I call The Columns of P V1 +to VD this is what's happening okay so + + align:start position:0% +to VD this is what's happening okay so + + + align:start position:0% +to VD this is what's happening okay so +when I look at lambda1 it's just the + + align:start position:0% +when I look at lambda1 it's just the + + + align:start position:0% +when I look at lambda1 it's just the +variance of XI in the product with + + align:start position:0% +variance of XI in the product with + + + align:start position:0% +variance of XI in the product with +V1 and we made this picture right when + + align:start position:0% +V1 and we made this picture right when + + + align:start position:0% +V1 and we made this picture right when +we said well let's say V1 is here and + + align:start position:0% +we said well let's say V1 is here and + + + align:start position:0% +we said well let's say V1 is here and +then X1 is here and if V1 has the as a + + align:start position:0% +then X1 is here and if V1 has the as a + + + align:start position:0% +then X1 is here and if V1 has the as a +unit Norm + + align:start position:0% +unit Norm + + + align:start position:0% +unit Norm +then uh the inner product between x i + + align:start position:0% +then uh the inner product between x i + + + align:start position:0% +then uh the inner product between x i +and V1 is just the length of this guy + + align:start position:0% +and V1 is just the length of this guy + + + align:start position:0% +and V1 is just the length of this guy +here right so that's the variance of the + + align:start position:0% +here right so that's the variance of the + + + align:start position:0% +here right so that's the variance of the +XI that's the length of XI so this is + + align:start position:0% +XI that's the length of XI so this is + + + align:start position:0% +XI that's the length of XI so this is +zero that's the length of XI when I + + align:start position:0% +zero that's the length of XI when I + + + align:start position:0% +zero that's the length of XI when I +project it onto the direction that's + + align:start position:0% +project it onto the direction that's + + + align:start position:0% +project it onto the direction that's +Spann by V1 if V1 has lengths two this + + align:start position:0% +Spann by V1 if V1 has lengths two this + + + align:start position:0% +Spann by V1 if V1 has lengths two this +is really just twice this length if v v + + align:start position:0% +is really just twice this length if v v + + + align:start position:0% +is really just twice this length if v v +VI is length three it's three times this + + align:start position:0% +VI is length three it's three times this + + + align:start position:0% +VI is length three it's three times this +but it turns that that since p + + align:start position:0% +but it turns that that since p + + + align:start position:0% +but it turns that that since p +satisfies ppose p is equal to the + + align:start position:0% +satisfies ppose p is equal to the + + + align:start position:0% +satisfies ppose p is equal to the +identity that's an orthogonal Matrix + + align:start position:0% +identity that's an orthogonal Matrix + + + align:start position:0% +identity that's an orthogonal Matrix +that's right here then this actually + + align:start position:0% +that's right here then this actually + + + align:start position:0% +that's right here then this actually +implies this is actually saying the same + + align:start position:0% +implies this is actually saying the same + + + align:start position:0% +implies this is actually saying the same +thing as VI transpose or VJ transpose VJ + + align:start position:0% +thing as VI transpose or VJ transpose VJ + + + align:start position:0% +thing as VI transpose or VJ transpose VJ +which is really the norm square of + + align:start position:0% +which is really the norm square of + + + align:start position:0% +which is really the norm square of +VJ is equal to one and VJ transpose VK + + align:start position:0% +VJ is equal to one and VJ transpose VK + + + align:start position:0% +VJ is equal to one and VJ transpose VK +is equal to zero if J is different from + + align:start position:0% +is equal to zero if J is different from + + + align:start position:0% +is equal to zero if J is different from +K + + align:start position:0% +K + + + align:start position:0% +K +okay the igen vectors are orthogonal to + + align:start position:0% +okay the igen vectors are orthogonal to + + + align:start position:0% +okay the igen vectors are orthogonal to +each other and they're actually all of + + align:start position:0% +each other and they're actually all of + + + align:start position:0% +each other and they're actually all of +Norm + + align:start position:0% + + + + align:start position:0% + +one so now I know that this is in De + + align:start position:0% +one so now I know that this is in De + + + align:start position:0% +one so now I know that this is in De +Direction and so when I look about I + + align:start position:0% +Direction and so when I look about I + + + align:start position:0% +Direction and so when I look about I +look at + + align:start position:0% +look at + + + align:start position:0% +look at +V1 transpose XI I'm really measuring + + align:start position:0% +V1 transpose XI I'm really measuring + + + align:start position:0% +V1 transpose XI I'm really measuring +exactly this length and that's what is + + align:start position:0% +exactly this length and that's what is + + + align:start position:0% +exactly this length and that's what is +this length is the length of the + + align:start position:0% +this length is the length of the + + + align:start position:0% +this length is the length of the +projection of XI onto this line that's + + align:start position:0% +projection of XI onto this line that's + + + align:start position:0% +projection of XI onto this line that's +the line that's panned by V1 so if I had + + align:start position:0% +the line that's panned by V1 so if I had + + + align:start position:0% +the line that's panned by V1 so if I had +a very high dimensional + + align:start position:0% +a very high dimensional + + + align:start position:0% +a very high dimensional +problem and I started to to uh look at + + align:start position:0% +problem and I started to to uh look at + + + align:start position:0% +problem and I started to to uh look at +the direction V1 let's say V1 now is not + + align:start position:0% +the direction V1 let's say V1 now is not + + + align:start position:0% +the direction V1 let's say V1 now is not +a vector it's any direction then if I + + align:start position:0% +a vector it's any direction then if I + + + align:start position:0% +a vector it's any direction then if I +start if I want to do this uh lower + + align:start position:0% +start if I want to do this uh lower + + + align:start position:0% +start if I want to do this uh lower +dimensional projection then I have to + + align:start position:0% +dimensional projection then I have to + + + align:start position:0% +dimensional projection then I have to +understand how the XI project onto the + + align:start position:0% +understand how the XI project onto the + + + align:start position:0% +understand how the XI project onto the +line that span by V1 because this is all + + align:start position:0% +line that span by V1 because this is all + + + align:start position:0% +line that span by V1 because this is all +all that I'm going to be keeping at the + + align:start position:0% +all that I'm going to be keeping at the + + + align:start position:0% +all that I'm going to be keeping at the +end of the day about my + + align:start position:0% +end of the day about my + + + align:start position:0% +end of the day about my +XX so what we want is to find a + + align:start position:0% +XX so what we want is to find a + + + align:start position:0% +XX so what we want is to find a +direction where those XIs those + + align:start position:0% +direction where those XIs those + + + align:start position:0% +direction where those XIs those +projections have a lot of variance and + + align:start position:0% +projections have a lot of variance and + + + align:start position:0% +projections have a lot of variance and +we know that the variance of XI on this + + align:start position:0% +we know that the variance of XI on this + + + align:start position:0% +we know that the variance of XI on this +direction is actually exactly given by + + align:start position:0% +direction is actually exactly given by + + + align:start position:0% +direction is actually exactly given by +Lambda + + align:start position:0% + + + + align:start position:0% + +one okay + + align:start position:0% +one okay + + + align:start position:0% +one okay +so uh sorry that's the uh uh empirical + + align:start position:0% +so uh sorry that's the uh uh empirical + + + align:start position:0% +so uh sorry that's the uh uh empirical +VAR um yeah I should call it variance + + align:start position:0% +VAR um yeah I should call it variance + + + align:start position:0% +VAR um yeah I should call it variance +hat that's the empirical variance + + align:start position:0% +hat that's the empirical variance + + + align:start position:0% +hat that's the empirical variance +everything is empirical here we're + + align:start position:0% +everything is empirical here we're + + + align:start position:0% +everything is empirical here we're +talking about the empirical conance + + align:start position:0% +talking about the empirical conance + + + align:start position:0% +talking about the empirical conance +Matrix all right and so in I also have + + align:start position:0% +Matrix all right and so in I also have + + + align:start position:0% +Matrix all right and so in I also have +that Lambda + + align:start position:0% +that Lambda + + + align:start position:0% +that Lambda +2 is the empirical variance of when I + + align:start position:0% +2 is the empirical variance of when I + + + align:start position:0% +2 is the empirical variance of when I +project XI onto V2 which is the second + + align:start position:0% +project XI onto V2 which is the second + + + align:start position:0% +project XI onto V2 which is the second +one right just for exactly this + + align:start position:0% + + + + align:start position:0% + +reason okay any + + align:start position:0% + + + + align:start position:0% + +question all right so Lambda JS are + + align:start position:0% +question all right so Lambda JS are + + + align:start position:0% +question all right so Lambda JS are +going to be important for us right + + align:start position:0% +going to be important for us right + + + align:start position:0% +going to be important for us right +Lambda J measured the spread of the + + align:start position:0% +Lambda J measured the spread of the + + + align:start position:0% +Lambda J measured the spread of the +points when I project them onto a line + + align:start position:0% +points when I project them onto a line + + + align:start position:0% +points when I project them onto a line +which is a one-dimensional space right + + align:start position:0% +which is a one-dimensional space right + + + align:start position:0% +which is a one-dimensional space right +and so I'm going to have let's say I + + align:start position:0% +and so I'm going to have let's say I + + + align:start position:0% +and so I'm going to have let's say I +want to pick only one I'm going to have + + align:start position:0% +want to pick only one I'm going to have + + + align:start position:0% +want to pick only one I'm going to have +to find the onedimensional space that + + align:start position:0% +to find the onedimensional space that + + + align:start position:0% +to find the onedimensional space that +carries the most variant + + align:start position:0% +carries the most variant + + + align:start position:0% +carries the most variant +and uh and I claim that V1 is the one + + align:start position:0% +and uh and I claim that V1 is the one + + + align:start position:0% +and uh and I claim that V1 is the one +that actually does that maximizes the + + align:start position:0% +that actually does that maximizes the + + + align:start position:0% +that actually does that maximizes the +spread okay so the + + align:start position:0% + + + + align:start position:0% + +claim so for + + align:start position:0% + + + + align:start position:0% + +any + + align:start position:0% +any + + + align:start position:0% +any +direction u in our D and by Direction I + + align:start position:0% +direction u in our D and by Direction I + + + align:start position:0% +direction u in our D and by Direction I +really just mean that the norm + + align:start position:0% +really just mean that the norm + + + align:start position:0% +really just mean that the norm +of U is equal to one okay I need to play + + align:start position:0% +of U is equal to one okay I need to play + + + align:start position:0% +of U is equal to one okay I need to play +fair I'm going to compare myself to + + align:start position:0% +fair I'm going to compare myself to + + + align:start position:0% +fair I'm going to compare myself to +other things of length one so I need to + + align:start position:0% +other things of length one so I need to + + + align:start position:0% +other things of length one so I need to +play fair and look at directions of + + align:start position:0% +play fair and look at directions of + + + align:start position:0% +play fair and look at directions of +length one now if I'm interested in the + + align:start position:0% +length one now if I'm interested in the + + + align:start position:0% +length one now if I'm interested in the +empirical + + align:start position:0% + + + + align:start position:0% + +variance of + + align:start position:0% +variance of + + + align:start position:0% +variance of +X1 transpose uh sorry U transpose + + align:start position:0% +X1 transpose uh sorry U transpose + + + align:start position:0% +X1 transpose uh sorry U transpose +X1 U transpose + + align:start position:0% +X1 U transpose + + + align:start position:0% +X1 U transpose +xn then this thing + + align:start position:0% +xn then this thing + + + align:start position:0% +xn then this thing +is + + align:start position:0% + + + + align:start position:0% + +maximized for U equals V1 where V1 is + + align:start position:0% +maximized for U equals V1 where V1 is + + + align:start position:0% +maximized for U equals V1 where V1 is +the aen vector Associated to Lambda 1 + + align:start position:0% +the aen vector Associated to Lambda 1 + + + align:start position:0% +the aen vector Associated to Lambda 1 +and Lambda 1 is not any aen value it's + + align:start position:0% +and Lambda 1 is not any aen value it's + + + align:start position:0% +and Lambda 1 is not any aen value it's +the largest of all + + align:start position:0% +the largest of all + + + align:start position:0% +the largest of all +those right this is the largest Aon + + align:start position:0% + + + + align:start position:0% + +value so why is that + + align:start position:0% + + + + align:start position:0% + +true well there's also a claim is that + + align:start position:0% +true well there's also a claim is that + + + align:start position:0% +true well there's also a claim is that +for any direction + + align:start position:0% +for any direction + + + align:start position:0% +for any direction +U so that's one and two the + + align:start position:0% + + + + align:start position:0% + +variance of U transpose X now this is + + align:start position:0% +variance of U transpose X now this is + + + align:start position:0% +variance of U transpose X now this is +just a random variable and I'm looking + + align:start position:0% +just a random variable and I'm looking + + + align:start position:0% +just a random variable and I'm looking +about the true variance this is + + align:start position:0% + + + + align:start position:0% + +maximized + + align:start position:0% +maximized + + + align:start position:0% +maximized +maximized for you equals let's call it + + align:start position:0% + + + + align:start position:0% + +W1 where w + + align:start position:0% + + + + align:start position:0% + +one is the igen + + align:start position:0% + + + + align:start position:0% + +vector of Sigma now I'm talking about + + align:start position:0% +vector of Sigma now I'm talking about + + + align:start position:0% +vector of Sigma now I'm talking about +the true variance whereas here I was + + align:start position:0% +the true variance whereas here I was + + + align:start position:0% +the true variance whereas here I was +talking about the empirical variance so + + align:start position:0% +talking about the empirical variance so + + + align:start position:0% +talking about the empirical variance so +the true variance is the vectors of the + + align:start position:0% +the true variance is the vectors of the + + + align:start position:0% +the true variance is the vectors of the +true Sigma + + align:start position:0% + + + + align:start position:0% + +Associated to the + + align:start position:0% +Associated to the + + + align:start position:0% +Associated to the +largest igen + + align:start position:0% +largest igen + + + align:start position:0% +largest igen +value + + align:start position:0% +value + + + align:start position:0% +value +of + + align:start position:0% + + + + align:start position:0% + +Sigma so I did not give it a name here + + align:start position:0% +Sigma so I did not give it a name here + + + align:start position:0% +Sigma so I did not give it a name here +that was Lambda one for the empirical + + align:start position:0% +that was Lambda one for the empirical + + + align:start position:0% +that was Lambda one for the empirical +one for the true one you can give it + + align:start position:0% +one for the true one you can give it + + + align:start position:0% +one for the true one you can give it +another name mu1 if you + + align:start position:0% +another name mu1 if you + + + align:start position:0% +another name mu1 if you +want uh but uh that's just uh that's + + align:start position:0% +want uh but uh that's just uh that's + + + align:start position:0% +want uh but uh that's just uh that's +just the same thing all it's saying is + + align:start position:0% +just the same thing all it's saying is + + + align:start position:0% +just the same thing all it's saying is +like wherever I see empirical I can + + align:start position:0% +like wherever I see empirical I can + + + align:start position:0% +like wherever I see empirical I can +remove + + align:start position:0% + + + + align:start position:0% + +it okay so why is this claim true well + + align:start position:0% +it okay so why is this claim true well + + + align:start position:0% +it okay so why is this claim true well +let's look at the second one for + + align:start position:0% + + + + align:start position:0% + +example so what is the + + align:start position:0% +example so what is the + + + align:start position:0% +example so what is the +variance of U transpose X + + align:start position:0% +variance of U transpose X + + + align:start position:0% +variance of U transpose X +right so that's what I want to + + align:start position:0% +right so that's what I want to + + + align:start position:0% +right so that's what I want to +know so that's the expectation so let's + + align:start position:0% +know so that's the expectation so let's + + + align:start position:0% +know so that's the expectation so let's +assume that + + align:start position:0% + + + + align:start position:0% + +X is zero again for same reasons as + + align:start position:0% +X is zero again for same reasons as + + + align:start position:0% +X is zero again for same reasons as +before so what is the variance is just + + align:start position:0% +before so what is the variance is just + + + align:start position:0% +before so what is the variance is just +the expectation of the square + + align:start position:0% + + + + align:start position:0% + +right right I just need to I don't need + + align:start position:0% +right right I just need to I don't need + + + align:start position:0% +right right I just need to I don't need +to remove the expectation and the + + align:start position:0% +to remove the expectation and the + + + align:start position:0% +to remove the expectation and the +expectation of the square is just the + + align:start position:0% +expectation of the square is just the + + + align:start position:0% +expectation of the square is just the +expectation of U transpose X and then + + align:start position:0% +expectation of U transpose X and then + + + align:start position:0% +expectation of U transpose X and then +I'm going to write the other one X + + align:start position:0% +I'm going to write the other one X + + + align:start position:0% +I'm going to write the other one X +transpose + + align:start position:0% + + + + align:start position:0% + +U okay and we know that this is + + align:start position:0% +U okay and we know that this is + + + align:start position:0% +U okay and we know that this is +deterministic so I'm just going to take + + align:start position:0% +deterministic so I'm just going to take + + + align:start position:0% +deterministic so I'm just going to take +that this is just U transpose + + align:start position:0% +that this is just U transpose + + + align:start position:0% +that this is just U transpose +expectation of x X transpose + + align:start position:0% +expectation of x X transpose + + + align:start position:0% +expectation of x X transpose +U and what is this + + align:start position:0% + + + + align:start position:0% + +guy this coari Sigma right that's just + + align:start position:0% +guy this coari Sigma right that's just + + + align:start position:0% +guy this coari Sigma right that's just +what Sigma + + align:start position:0% +what Sigma + + + align:start position:0% +what Sigma +is so the variance I can write as U + + align:start position:0% +is so the variance I can write as U + + + align:start position:0% +is so the variance I can write as U +transpose Sigma U we've made this + + align:start position:0% +transpose Sigma U we've made this + + + align:start position:0% +transpose Sigma U we've made this +computation + + align:start position:0% +computation + + + align:start position:0% +computation +before and now what I want to claim is + + align:start position:0% +before and now what I want to claim is + + + align:start position:0% +before and now what I want to claim is +that this thing is actually less than + + align:start position:0% +that this thing is actually less than + + + align:start position:0% +that this thing is actually less than +the largest ton + + align:start position:0% +the largest ton + + + align:start position:0% +the largest ton +value which I actually called Lambda 1 + + align:start position:0% +value which I actually called Lambda 1 + + + align:start position:0% +value which I actually called Lambda 1 +here here I should probably not and the + + align:start position:0% +here here I should probably not and the + + + align:start position:0% +here here I should probably not and the +p is wow okay + + align:start position:0% +p is wow okay + + + align:start position:0% +p is wow okay +um okay so uh okay let's just pretend + + align:start position:0% +um okay so uh okay let's just pretend + + + align:start position:0% +um okay so uh okay let's just pretend +everything is uh is is not empirical all + + align:start position:0% +everything is uh is is not empirical all + + + align:start position:0% +everything is uh is is not empirical all +right so now I'm going to write Sigma as + + align:start position:0% +right so now I'm going to write Sigma as + + + align:start position:0% +right so now I'm going to write Sigma as +P Lambda 1 Lambda + + align:start position:0% +P Lambda 1 Lambda + + + align:start position:0% +P Lambda 1 Lambda +n ppose that's just the endic position + + align:start position:0% +n ppose that's just the endic position + + + align:start position:0% +n ppose that's just the endic position +where I admittedly uh uh uh reuse the + + align:start position:0% +where I admittedly uh uh uh reuse the + + + align:start position:0% +where I admittedly uh uh uh reuse the +same notation as I did for S so I should + + align:start position:0% +same notation as I did for S so I should + + + align:start position:0% +same notation as I did for S so I should +really put some primes everywhere so you + + align:start position:0% +really put some primes everywhere so you + + + align:start position:0% +really put some primes everywhere so you +know those are things are actually + + align:start position:0% +know those are things are actually + + + align:start position:0% +know those are things are actually +different in practice right so this is + + align:start position:0% +different in practice right so this is + + + align:start position:0% +different in practice right so this is +just the decomposition of + + align:start position:0% +just the decomposition of + + + align:start position:0% +just the decomposition of +Sigma we seem confuse H you have a + + align:start position:0% +Sigma we seem confuse H you have a + + + align:start position:0% +Sigma we seem confuse H you have a +question + + align:start position:0% + + + + align:start position:0% + +yeah so okay + + align:start position:0% + + + + align:start position:0% + +so I can make everything I'm saying I + + align:start position:0% +so I can make everything I'm saying I + + + align:start position:0% +so I can make everything I'm saying I +can talk about either the variance or + + align:start position:0% +can talk about either the variance or + + + align:start position:0% +can talk about either the variance or +the empirical variance and you can just + + align:start position:0% +the empirical variance and you can just + + + align:start position:0% +the empirical variance and you can just +add the word empirical in front of it + + align:start position:0% +add the word empirical in front of it + + + align:start position:0% +add the word empirical in front of it +whenever you want the same thing works + + align:start position:0% +whenever you want the same thing works + + + align:start position:0% +whenever you want the same thing works +but just for the sake of uh removing the + + align:start position:0% +but just for the sake of uh removing the + + + align:start position:0% +but just for the sake of uh removing the +confusion let's just do it again with + + align:start position:0% +confusion let's just do it again with + + + align:start position:0% +confusion let's just do it again with +h let's just do it again with h s all + + align:start position:0% +h let's just do it again with h s all + + + align:start position:0% +h let's just do it again with h s all +right so I'm just going to do everything + + align:start position:0% +right so I'm just going to do everything + + + align:start position:0% +right so I'm just going to do everything +with s so I'm going to assume that xar + + align:start position:0% +with s so I'm going to assume that xar + + + align:start position:0% +with s so I'm going to assume that xar +is equal to zero and here I'm going to + + align:start position:0% +is equal to zero and here I'm going to + + + align:start position:0% +is equal to zero and here I'm going to +talk about the empirical variance which + + align:start position:0% +talk about the empirical variance which + + + align:start position:0% +talk about the empirical variance which +is just 1 / n sum from I = 1 to n of U + + align:start position:0% +is just 1 / n sum from I = 1 to n of U + + + align:start position:0% +is just 1 / n sum from I = 1 to n of U +transpose x i^ 2 so it's the same thing + + align:start position:0% +transpose x i^ 2 so it's the same thing + + + align:start position:0% +transpose x i^ 2 so it's the same thing +everywhere you see an expectation you + + align:start position:0% +everywhere you see an expectation you + + + align:start position:0% +everywhere you see an expectation you +just put an average + + align:start position:0% + + + + align:start position:0% + +right okay and then I get one over n sum + + align:start position:0% +right okay and then I get one over n sum + + + align:start position:0% +right okay and then I get one over n sum +from I = 1 to n of x i x i transpose and + + align:start position:0% +from I = 1 to n of x i x i transpose and + + + align:start position:0% +from I = 1 to n of x i x i transpose and +now I'm going to call this guy s + + align:start position:0% +now I'm going to call this guy s + + + align:start position:0% +now I'm going to call this guy s +okay because that's what it it is so + + align:start position:0% +okay because that's what it it is so + + + align:start position:0% +okay because that's what it it is so +this is U transpose Su but just the fact + + align:start position:0% +this is U transpose Su but just the fact + + + align:start position:0% +this is U transpose Su but just the fact +that I could just replace the + + align:start position:0% +that I could just replace the + + + align:start position:0% +that I could just replace the +expectation by averages everywhere you + + align:start position:0% +expectation by averages everywhere you + + + align:start position:0% +expectation by averages everywhere you +can tell that the thing is going to work + + align:start position:0% +can tell that the thing is going to work + + + align:start position:0% +can tell that the thing is going to work +for either one or the other so now this + + align:start position:0% +for either one or the other so now this + + + align:start position:0% +for either one or the other so now this +thing was actually so now I don't have + + align:start position:0% +thing was actually so now I don't have + + + align:start position:0% +thing was actually so now I don't have +any problem with my notation this is + + align:start position:0% +any problem with my notation this is + + + align:start position:0% +any problem with my notation this is +actually the uh decomposition of s + + align:start position:0% +actually the uh decomposition of s + + + align:start position:0% +actually the uh decomposition of s +that's the spectral de composition in in + + align:start position:0% +that's the spectral de composition in in + + + align:start position:0% +that's the spectral de composition in in +its two inag values and so + + align:start position:0% +its two inag values and so + + + align:start position:0% +its two inag values and so +now what I have is that uh when I look + + align:start position:0% +now what I have is that uh when I look + + + align:start position:0% +now what I have is that uh when I look +at U transpose + + align:start position:0% +at U transpose + + + align:start position:0% +at U transpose +s this is actually equal to pu + + align:start position:0% +s this is actually equal to pu + + + align:start position:0% +s this is actually equal to pu +U + + align:start position:0% +U + + + align:start position:0% +U +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +s + + align:start position:0% + + + + align:start position:0% + +p + + align:start position:0% +p + + + align:start position:0% +p +okay uh there's a transpose somewhere + + align:start position:0% +okay uh there's a transpose somewhere + + + align:start position:0% +okay uh there's a transpose somewhere +that's this + + align:start position:0% +that's this + + + align:start position:0% +that's this +guy and that's this + + align:start position:0% +guy and that's this + + + align:start position:0% +guy and that's this +guy + + align:start position:0% + + + + align:start position:0% + +okay now + + align:start position:0% +okay now + + + align:start position:0% +okay now +sorry that's not P that's + + align:start position:0% +sorry that's not P that's + + + align:start position:0% +sorry that's not P that's +d That's that that's d right that's this + + align:start position:0% +d That's that that's d right that's this + + + align:start position:0% +d That's that that's d right that's this +diagonal + + align:start position:0% + + + + align:start position:0% + +matrix okay let's look at this thing and + + align:start position:0% +matrix okay let's look at this thing and + + + align:start position:0% +matrix okay let's look at this thing and +let's call P transpose U let's call it B + + align:start position:0% +let's call P transpose U let's call it B + + + align:start position:0% +let's call P transpose U let's call it B +okay so that's also a vector in + + align:start position:0% +okay so that's also a vector in + + + align:start position:0% +okay so that's also a vector in +Rd what is it it's just I take a unit + + align:start position:0% +Rd what is it it's just I take a unit + + + align:start position:0% +Rd what is it it's just I take a unit +vector and then I apply P transposed to + + align:start position:0% +vector and then I apply P transposed to + + + align:start position:0% +vector and then I apply P transposed to +it so that's basically what happens to a + + align:start position:0% +it so that's basically what happens to a + + + align:start position:0% +it so that's basically what happens to a +unit Vector when I apply the same change + + align:start position:0% +unit Vector when I apply the same change + + + align:start position:0% +unit Vector when I apply the same change +of basis that I did right so I'm just + + align:start position:0% +of basis that I did right so I'm just + + + align:start position:0% +of basis that I did right so I'm just +changing my my my Aral system and I just + + align:start position:0% +changing my my my Aral system and I just + + + align:start position:0% +changing my my my Aral system and I just +with the same way I did for the other + + align:start position:0% +with the same way I did for the other + + + align:start position:0% +with the same way I did for the other +ones so what's happening when I write + + align:start position:0% +ones so what's happening when I write + + + align:start position:0% +ones so what's happening when I write +this well now I have that U transpose Su + + align:start position:0% +this well now I have that U transpose Su + + + align:start position:0% +this well now I have that U transpose Su +is B transpose + + align:start position:0% +is B transpose + + + align:start position:0% +is B transpose +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +DB but now doing B transpose DB when D + + align:start position:0% +DB but now doing B transpose DB when D + + + align:start position:0% +DB but now doing B transpose DB when D +is diagonal and B is the vector is a + + align:start position:0% +is diagonal and B is the vector is a + + + align:start position:0% +is diagonal and B is the vector is a +very simple thing right they can expand + + align:start position:0% +very simple thing right they can expand + + + align:start position:0% +very simple thing right they can expand +it this is what this is just the sum + + align:start position:0% +it this is what this is just the sum + + + align:start position:0% +it this is what this is just the sum +from Jal one to + + align:start position:0% +from Jal one to + + + align:start position:0% +from Jal one to +D of Lambda J BJ s + + align:start position:0% + + + + align:start position:0% + +right so that's just like Matrix Vector + + align:start position:0% +right so that's just like Matrix Vector + + + align:start position:0% +right so that's just like Matrix Vector +multiplication and in particular I know + + align:start position:0% +multiplication and in particular I know + + + align:start position:0% +multiplication and in particular I know +that the largest of those guys is Lambda + + align:start position:0% +that the largest of those guys is Lambda + + + align:start position:0% +that the largest of those guys is Lambda +one and those guys are all non- negative + + align:start position:0% +one and those guys are all non- negative + + + align:start position:0% +one and those guys are all non- negative +so this thing is actually less than + + align:start position:0% +so this thing is actually less than + + + align:start position:0% +so this thing is actually less than +Lambda 1 times the sum from J = 1 to D + + align:start position:0% +Lambda 1 times the sum from J = 1 to D + + + align:start position:0% +Lambda 1 times the sum from J = 1 to D +of Lambda + + align:start position:0% + + + + align:start position:0% + +j^2 uh sorry BJ + + align:start position:0% + + + + align:start position:0% + +s and and this is just the norm of + + align:start position:0% + + + + align:start position:0% + +B + + align:start position:0% +B + + + align:start position:0% +B +squared so if I want to prove what's on + + align:start position:0% +squared so if I want to prove what's on + + + align:start position:0% +squared so if I want to prove what's on +the slide all I need to check is that B + + align:start position:0% +the slide all I need to check is that B + + + align:start position:0% +the slide all I need to check is that B +has a norm which + + align:start position:0% +has a norm which + + + align:start position:0% +has a norm which +is at most one it's going to be at most + + align:start position:0% +is at most one it's going to be at most + + + align:start position:0% +is at most one it's going to be at most +one why well because B is really just a + + align:start position:0% +one why well because B is really just a + + + align:start position:0% +one why well because B is really just a +change of basis for U right and so if I + + align:start position:0% +change of basis for U right and so if I + + + align:start position:0% +change of basis for U right and so if I +take a vector I'm just changing its + + align:start position:0% +take a vector I'm just changing its + + + align:start position:0% +take a vector I'm just changing its +basis I'm certainly not changing its + + align:start position:0% +basis I'm certainly not changing its + + + align:start position:0% +basis I'm certainly not changing its +length think of a rotation and I can + + align:start position:0% +length think of a rotation and I can + + + align:start position:0% +length think of a rotation and I can +also flip it but think of a rotation and + + align:start position:0% +also flip it but think of a rotation and + + + align:start position:0% +also flip it but think of a rotation and +so + + align:start position:0% +so + + + align:start position:0% +so +now uh well actually for Vector it's + + align:start position:0% +now uh well actually for Vector it's + + + align:start position:0% +now uh well actually for Vector it's +just going to be a rotation and so now + + align:start position:0% +just going to be a rotation and so now + + + align:start position:0% +just going to be a rotation and so now +what I have I just have to check that + + align:start position:0% +what I have I just have to check that + + + align:start position:0% +what I have I just have to check that +the norm of B squared is equal to what + + align:start position:0% +the norm of B squared is equal to what + + + align:start position:0% +the norm of B squared is equal to what +well it's equal to the norm of ppose u^ + + align:start position:0% +well it's equal to the norm of ppose u^ + + + align:start position:0% +well it's equal to the norm of ppose u^ +2 which is equal to U transpose p ppose + + align:start position:0% +2 which is equal to U transpose p ppose + + + align:start position:0% +2 which is equal to U transpose p ppose +u but p is orthogonal so this thing is + + align:start position:0% +u but p is orthogonal so this thing is + + + align:start position:0% +u but p is orthogonal so this thing is +actually just the identity so that's + + align:start position:0% +actually just the identity so that's + + + align:start position:0% +actually just the identity so that's +just U transpose U + + align:start position:0% +just U transpose U + + + align:start position:0% +just U transpose U +which is equal to the norm + + align:start position:0% +which is equal to the norm + + + align:start position:0% +which is equal to the norm +u^2 which is equal to + + align:start position:0% +u^2 which is equal to + + + align:start position:0% +u^2 which is equal to +one because I took you to have Norm one + + align:start position:0% +one because I took you to have Norm one + + + align:start position:0% +one because I took you to have Norm one +in the first + + align:start position:0% +in the first + + + align:start position:0% +in the first +place and so this your right was + + align:start position:0% +place and so this your right was + + + align:start position:0% +place and so this your right was +actually of Norm equal to one I just + + align:start position:0% +actually of Norm equal to one I just + + + align:start position:0% +actually of Norm equal to one I just +need to have it less but it's equal and + + align:start position:0% +need to have it less but it's equal and + + + align:start position:0% +need to have it less but it's equal and +so what I'm left with is that this thing + + align:start position:0% +so what I'm left with is that this thing + + + align:start position:0% +so what I'm left with is that this thing +is actually equal to Lambda one so I + + align:start position:0% +is actually equal to Lambda one so I + + + align:start position:0% +is actually equal to Lambda one so I +know that for every U that I pick so + + align:start position:0% +know that for every U that I pick so + + + align:start position:0% +know that for every U that I pick so +that has + + align:start position:0% +that has + + + align:start position:0% +that has +Norm right so I'm just reminding you + + align:start position:0% +Norm right so I'm just reminding you + + + align:start position:0% +Norm right so I'm just reminding you +that U here is Norm squared equal to one + + align:start position:0% +that U here is Norm squared equal to one + + + align:start position:0% +that U here is Norm squared equal to one +for every U that I pick this U transpose + + align:start position:0% +for every U that I pick this U transpose + + + align:start position:0% +for every U that I pick this U transpose +Su is at most Lambda + + align:start position:0% +Su is at most Lambda + + + align:start position:0% +Su is at most Lambda +one right so that's the U transpose Su + + align:start position:0% +one right so that's the U transpose Su + + + align:start position:0% +one right so that's the U transpose Su +is at most Lambda + + align:start position:0% +is at most Lambda + + + align:start position:0% +is at most Lambda +one and we know that that's the variance + + align:start position:0% +one and we know that that's the variance + + + align:start position:0% +one and we know that that's the variance +that's the empirical variance when I + + align:start position:0% +that's the empirical variance when I + + + align:start position:0% +that's the empirical variance when I +project my points onto Direction span by + + align:start position:0% +project my points onto Direction span by + + + align:start position:0% +project my points onto Direction span by +U so now I have an empirical variance + + align:start position:0% +U so now I have an empirical variance + + + align:start position:0% +U so now I have an empirical variance +which is at most Lambda one but I also + + align:start position:0% +which is at most Lambda one but I also + + + align:start position:0% +which is at most Lambda one but I also +know that if I take you to be anything + + align:start position:0% +know that if I take you to be anything + + + align:start position:0% +know that if I take you to be anything +something very specific I mean it was on + + align:start position:0% +something very specific I mean it was on + + + align:start position:0% +something very specific I mean it was on +the previous board if I take U to be + + align:start position:0% +the previous board if I take U to be + + + align:start position:0% +the previous board if I take U to be +equal to V1 then this thing is actually + + align:start position:0% +equal to V1 then this thing is actually + + + align:start position:0% +equal to V1 then this thing is actually +not an inequality this is + + align:start position:0% +not an inequality this is + + + align:start position:0% +not an inequality this is +inequality and the reason is when I + + align:start position:0% +inequality and the reason is when I + + + align:start position:0% +inequality and the reason is when I +actually take U to be V1 all of these + + align:start position:0% +actually take U to be V1 all of these + + + align:start position:0% +actually take U to be V1 all of these +BJs are going to be zero except for the + + align:start position:0% +BJs are going to be zero except for the + + + align:start position:0% +BJs are going to be zero except for the +one that's B1 which is itself equal to + + align:start position:0% +one that's B1 which is itself equal to + + + align:start position:0% +one that's B1 which is itself equal to +one okay so I mean we can briefly check + + align:start position:0% +one okay so I mean we can briefly check + + + align:start position:0% +one okay so I mean we can briefly check +this but if I take + + align:start position:0% + + + + align:start position:0% + +V + + align:start position:0% + + + + align:start position:0% + +If U is equal to + + align:start position:0% +If U is equal to + + + align:start position:0% +If U is equal to +V1 so what I have is that U transpose + + align:start position:0% +V1 so what I have is that U transpose + + + align:start position:0% +V1 so what I have is that U transpose +Su is equal to the sum sorry is equal to + + align:start position:0% +Su is equal to the sum sorry is equal to + + + align:start position:0% +Su is equal to the sum sorry is equal to +um P transpose + + align:start position:0% +um P transpose + + + align:start position:0% +um P transpose +V1 D ppose B1 uh V1 but what is ppose V1 + + align:start position:0% +V1 D ppose B1 uh V1 but what is ppose V1 + + + align:start position:0% +V1 D ppose B1 uh V1 but what is ppose V1 +well remember v p + + align:start position:0% +well remember v p + + + align:start position:0% +well remember v p +transpose is just the vector it's just + + align:start position:0% +transpose is just the vector it's just + + + align:start position:0% +transpose is just the vector it's just +the Matrix that has vectors V1 transpose + + align:start position:0% +the Matrix that has vectors V1 transpose + + + align:start position:0% +the Matrix that has vectors V1 transpose +here V2 transpose here all the way to VD + + align:start position:0% +here V2 transpose here all the way to VD + + + align:start position:0% +here V2 transpose here all the way to VD +transpose here and we know that when I + + align:start position:0% +transpose here and we know that when I + + + align:start position:0% +transpose here and we know that when I +take VJ transpose + + align:start position:0% +take VJ transpose + + + align:start position:0% +take VJ transpose +VK I get zero if J is different from K + + align:start position:0% +VK I get zero if J is different from K + + + align:start position:0% +VK I get zero if J is different from K +and if I if J is equal to k i get one + + align:start position:0% +and if I if J is equal to k i get one + + + align:start position:0% +and if I if J is equal to k i get one +okay so P + + align:start position:0% +okay so P + + + align:start position:0% +okay so P +transpose V1 is equal to + + align:start position:0% + + + + align:start position:0% + +what + + align:start position:0% + + + + align:start position:0% + +so take V1 here and multiply it so when + + align:start position:0% +so take V1 here and multiply it so when + + + align:start position:0% +so take V1 here and multiply it so when +I the first coordinate is going to be V1 + + align:start position:0% +I the first coordinate is going to be V1 + + + align:start position:0% +I the first coordinate is going to be V1 +transpose V1 which is + + align:start position:0% +transpose V1 which is + + + align:start position:0% +transpose V1 which is +one the second coordinate is going to be + + align:start position:0% +one the second coordinate is going to be + + + align:start position:0% +one the second coordinate is going to be +V2 transpose + + align:start position:0% +V2 transpose + + + align:start position:0% +V2 transpose +V1 which is zero and so I get zeros all + + align:start position:0% +V1 which is zero and so I get zeros all + + + align:start position:0% +V1 which is zero and so I get zeros all +the way + + align:start position:0% +the way + + + align:start position:0% +the way +right so that means that this thing here + + align:start position:0% +right so that means that this thing here + + + align:start position:0% +right so that means that this thing here +is really just the vector + + align:start position:0% +is really just the vector + + + align:start position:0% +is really just the vector +one z z 0 and here this is just the + + align:start position:0% +one z z 0 and here this is just the + + + align:start position:0% +one z z 0 and here this is just the +vector one0 Z 0 so when I multiply it + + align:start position:0% +vector one0 Z 0 so when I multiply it + + + align:start position:0% +vector one0 Z 0 so when I multiply it +with this guy I'm only picking up the + + align:start position:0% +with this guy I'm only picking up the + + + align:start position:0% +with this guy I'm only picking up the +the the top left element of D which is + + align:start position:0% +the the top left element of D which is + + + align:start position:0% +the the top left element of D which is +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +one so for everyone it's less than lamb + + align:start position:0% +one so for everyone it's less than lamb + + + align:start position:0% +one so for everyone it's less than lamb +Lambda 1 and for V1 it's equal to Lambda + + align:start position:0% +Lambda 1 and for V1 it's equal to Lambda + + + align:start position:0% +Lambda 1 and for V1 it's equal to Lambda +1 which means that it's maximized for uh + + align:start position:0% +1 which means that it's maximized for uh + + + align:start position:0% +1 which means that it's maximized for uh +a equals V1 and that's where I said that + + align:start position:0% +a equals V1 and that's where I said that + + + align:start position:0% +a equals V1 and that's where I said that +this is the fanciest non-convex problem + + align:start position:0% +this is the fanciest non-convex problem + + + align:start position:0% +this is the fanciest non-convex problem +we know how to solve + + align:start position:0% +we know how to solve + + + align:start position:0% +we know how to solve +this was a problem that was definitely + + align:start position:0% +this was a problem that was definitely + + + align:start position:0% +this was a problem that was definitely +non-convex we're maximizing a convex + + align:start position:0% +non-convex we're maximizing a convex + + + align:start position:0% +non-convex we're maximizing a convex +function of our sphere but we know that + + align:start position:0% +function of our sphere but we know that + + + align:start position:0% +function of our sphere but we know that +V1 which is something I mean of course + + align:start position:0% +V1 which is something I mean of course + + + align:start position:0% +V1 which is something I mean of course +you still have to believe me that you + + align:start position:0% +you still have to believe me that you + + + align:start position:0% +you still have to believe me that you +can compute the spectral decomposition + + align:start position:0% +can compute the spectral decomposition + + + align:start position:0% +can compute the spectral decomposition +efficiently uh but uh uh essentially if + + align:start position:0% +efficiently uh but uh uh essentially if + + + align:start position:0% +efficiently uh but uh uh essentially if +you've taken linear algebra you know + + align:start position:0% +you've taken linear algebra you know + + + align:start position:0% +you've taken linear algebra you know +that you can diagonalize a matrix and so + + align:start position:0% +that you can diagonalize a matrix and so + + + align:start position:0% +that you can diagonalize a matrix and so +you get that V1 is just the maximum so + + align:start position:0% +you get that V1 is just the maximum so + + + align:start position:0% +you get that V1 is just the maximum so +you can find your maximum just by + + align:start position:0% +you can find your maximum just by + + + align:start position:0% +you can find your maximum just by +looking at the spectral decomposition + + align:start position:0% +looking at the spectral decomposition + + + align:start position:0% +looking at the spectral decomposition +you don't have to do any optimization or + + align:start position:0% +you don't have to do any optimization or + + + align:start position:0% +you don't have to do any optimization or +anything like this + + align:start position:0% +anything like this + + + align:start position:0% +anything like this +all right so let's recap where are + + align:start position:0% +all right so let's recap where are + + + align:start position:0% +all right so let's recap where are +we we've established that if I start + + align:start position:0% +we we've established that if I start + + + align:start position:0% +we we've established that if I start +with my empirical cence Matrix I can + + align:start position:0% +with my empirical cence Matrix I can + + + align:start position:0% +with my empirical cence Matrix I can +diagonalize it in ppose sorry PDP + + align:start position:0% +diagonalize it in ppose sorry PDP + + + align:start position:0% +diagonalize it in ppose sorry PDP +transpose and then if I take Theon + + align:start position:0% +transpose and then if I take Theon + + + align:start position:0% +transpose and then if I take Theon +Vector Associated to the largest Dion + + align:start position:0% +Vector Associated to the largest Dion + + + align:start position:0% +Vector Associated to the largest Dion +value so if I permute The Columns of p + + align:start position:0% +value so if I permute The Columns of p + + + align:start position:0% +value so if I permute The Columns of p +in such a way and and and of D's in such + + align:start position:0% +in such a way and and and of D's in such + + + align:start position:0% +in such a way and and and of D's in such +a way that they're ordered from the + + align:start position:0% +a way that they're ordered from the + + + align:start position:0% +a way that they're ordered from the +largest to the smallest when I look at + + align:start position:0% +largest to the smallest when I look at + + + align:start position:0% +largest to the smallest when I look at +the diagonal elements of D then if I + + align:start position:0% +the diagonal elements of D then if I + + + align:start position:0% +the diagonal elements of D then if I +pick the First Column of P it's V1 and + + align:start position:0% +pick the First Column of P it's V1 and + + + align:start position:0% +pick the First Column of P it's V1 and +V1 is the distance is the is the + + align:start position:0% +V1 is the distance is the is the + + + align:start position:0% +V1 is the distance is the is the +direction on which if I project my + + align:start position:0% +direction on which if I project my + + + align:start position:0% +direction on which if I project my +points they're going to carry the most + + align:start position:0% +points they're going to carry the most + + + align:start position:0% +points they're going to carry the most +empirical + + align:start position:0% +empirical + + + align:start position:0% +empirical +variance well that's a good way if I + + align:start position:0% +variance well that's a good way if I + + + align:start position:0% +variance well that's a good way if I +told you pick One + + align:start position:0% +told you pick One + + + align:start position:0% +told you pick One +Direction on which along which if you + + align:start position:0% +Direction on which along which if you + + + align:start position:0% +Direction on which along which if you +were to project your points they would + + align:start position:0% +were to project your points they would + + + align:start position:0% +were to project your points they would +be as spread out as possible that's + + align:start position:0% +be as spread out as possible that's + + + align:start position:0% +be as spread out as possible that's +probably the one you would pick and so + + align:start position:0% +probably the one you would pick and so + + + align:start position:0% +probably the one you would pick and so +that's exactly what PCA is doing for us + + align:start position:0% +that's exactly what PCA is doing for us + + + align:start position:0% +that's exactly what PCA is doing for us +it says okay if you ask me to take D + + align:start position:0% +it says okay if you ask me to take D + + + align:start position:0% +it says okay if you ask me to take D +Prime equal to one I will take V1 just + + align:start position:0% +Prime equal to one I will take V1 just + + + align:start position:0% +Prime equal to one I will take V1 just +the direction I will just take the + + align:start position:0% +the direction I will just take the + + + align:start position:0% +the direction I will just take the +direction that Spann by V1 and that's + + align:start position:0% +direction that Spann by V1 and that's + + + align:start position:0% +direction that Spann by V1 and that's +just when I come back to this picture + + align:start position:0% +just when I come back to this picture + + + align:start position:0% +just when I come back to this picture +that was here + + align:start position:0% + + + + align:start position:0% + +before this is + + align:start position:0% +before this is + + + align:start position:0% +before this is +V1 now of course here I have only V I + + align:start position:0% +V1 now of course here I have only V I + + + align:start position:0% +V1 now of course here I have only V I +only have two of them so V2 has to be + + align:start position:0% +only have two of them so V2 has to be + + + align:start position:0% +only have two of them so V2 has to be +this guy or this guy or I mean or this + + align:start position:0% +this guy or this guy or I mean or this + + + align:start position:0% +this guy or this guy or I mean or this +thing right I mean I don't know them up + + align:start position:0% +thing right I mean I don't know them up + + + align:start position:0% +thing right I mean I don't know them up +to sign so but then if I have three you + + align:start position:0% +to sign so but then if I have three you + + + align:start position:0% +to sign so but then if I have three you +know think of like an olive in three + + align:start position:0% +know think of like an olive in three + + + align:start position:0% +know think of like an olive in three +dimensions then maybe I have One + + align:start position:0% +dimensions then maybe I have One + + + align:start position:0% +dimensions then maybe I have One +Direction that's slightly more elongated + + align:start position:0% +Direction that's slightly more elongated + + + align:start position:0% +Direction that's slightly more elongated +than the other one and so I'm going to + + align:start position:0% +than the other one and so I'm going to + + + align:start position:0% +than the other one and so I'm going to +pick the second one and so the procedure + + align:start position:0% +pick the second one and so the procedure + + + align:start position:0% +pick the second one and so the procedure +is to say well first I'm going to pick + + align:start position:0% +is to say well first I'm going to pick + + + align:start position:0% +is to say well first I'm going to pick +V1 the same way I picked V I picked V1 + + align:start position:0% +V1 the same way I picked V I picked V1 + + + align:start position:0% +V1 the same way I picked V I picked V1 +the first place so the first Direction + + align:start position:0% +the first place so the first Direction + + + align:start position:0% +the first place so the first Direction +I'm taking is the leading egant vector + + align:start position:0% +I'm taking is the leading egant vector + + + align:start position:0% +I'm taking is the leading egant vector +and then I'm looking for a + + align:start position:0% +and then I'm looking for a + + + align:start position:0% +and then I'm looking for a +direction well if I found one the one + + align:start position:0% +direction well if I found one the one + + + align:start position:0% +direction well if I found one the one +I'm going to want to find if you say you + + align:start position:0% +I'm going to want to find if you say you + + + align:start position:0% +I'm going to want to find if you say you +can take D equal 2 you're going to need + + align:start position:0% +can take D equal 2 you're going to need + + + align:start position:0% +can take D equal 2 you're going to need +a basis for this guy so the second one + + align:start position:0% +a basis for this guy so the second one + + + align:start position:0% +a basis for this guy so the second one +has to be orthogonal to the first one + + align:start position:0% +has to be orthogonal to the first one + + + align:start position:0% +has to be orthogonal to the first one +you've already picked and so the second + + align:start position:0% +you've already picked and so the second + + + align:start position:0% +you've already picked and so the second +one you pick is the one that's just + + align:start position:0% +one you pick is the one that's just + + + align:start position:0% +one you pick is the one that's just +among all those that are orthogonal to + + align:start position:0% +among all those that are orthogonal to + + + align:start position:0% +among all those that are orthogonal to +V1 maximize the empirical variance when + + align:start position:0% +V1 maximize the empirical variance when + + + align:start position:0% +V1 maximize the empirical variance when +you project onto + + align:start position:0% +you project onto + + + align:start position:0% +you project onto +it and it turns out that this is + + align:start position:0% +it and it turns out that this is + + + align:start position:0% +it and it turns out that this is +actually exactly V2 you don't have to + + align:start position:0% +actually exactly V2 you don't have to + + + align:start position:0% +actually exactly V2 you don't have to +redo anything again your comp position + + align:start position:0% +redo anything again your comp position + + + align:start position:0% +redo anything again your comp position +this is just the second column of + + align:start position:0% +this is just the second column of + + + align:start position:0% +this is just the second column of +P + + align:start position:0% + + + + align:start position:0% + +clearly V2 is orthogonal to V1 right we + + align:start position:0% +clearly V2 is orthogonal to V1 right we + + + align:start position:0% +clearly V2 is orthogonal to V1 right we +just used it here + + align:start position:0% +just used it here + + + align:start position:0% +just used it here +here this zero here just say this V2 is + + align:start position:0% +here this zero here just say this V2 is + + + align:start position:0% +here this zero here just say this V2 is +orthogonal to V1 right so they're like + + align:start position:0% +orthogonal to V1 right so they're like + + + align:start position:0% +orthogonal to V1 right so they're like +this and now what I said what this slide + + align:start position:0% +this and now what I said what this slide + + + align:start position:0% +this and now what I said what this slide +tells you extra is that V2 among all + + align:start position:0% +tells you extra is that V2 among all + + + align:start position:0% +tells you extra is that V2 among all +those directions that are orthogonal I + + align:start position:0% +those directions that are orthogonal I + + + align:start position:0% +those directions that are orthogonal I +mean there's still D minus one of them + + align:start position:0% +mean there's still D minus one of them + + + align:start position:0% +mean there's still D minus one of them +this is the one that maximizes the say + + align:start position:0% +this is the one that maximizes the say + + + align:start position:0% +this is the one that maximizes the say +residual empirical variance the one that + + align:start position:0% +residual empirical variance the one that + + + align:start position:0% +residual empirical variance the one that +was not explained by the first direction + + align:start position:0% +was not explained by the first direction + + + align:start position:0% +was not explained by the first direction +that you picked and you can check that I + + align:start position:0% +that you picked and you can check that I + + + align:start position:0% +that you picked and you can check that I +mean it's becoming a bit more cumbersome + + align:start position:0% +mean it's becoming a bit more cumbersome + + + align:start position:0% +mean it's becoming a bit more cumbersome +uh to write down but you can check that + + align:start position:0% +uh to write down but you can check that + + + align:start position:0% +uh to write down but you can check that +if you're not convinced please raise + + align:start position:0% +if you're not convinced please raise + + + align:start position:0% +if you're not convinced please raise +your concerned I mean basically one way + + align:start position:0% +your concerned I mean basically one way + + + align:start position:0% +your concerned I mean basically one way +to view this + + align:start position:0% + + + + align:start position:0% + +is to I mean you're not really dropping + + align:start position:0% +is to I mean you're not really dropping + + + align:start position:0% +is to I mean you're not really dropping +a coordinate because V1 is not a + + align:start position:0% +a coordinate because V1 is not a + + + align:start position:0% +a coordinate because V1 is not a +coordinate but let's assume actually for + + align:start position:0% +coordinate but let's assume actually for + + + align:start position:0% +coordinate but let's assume actually for +Simplicity that V1 was actually equal to + + align:start position:0% +Simplicity that V1 was actually equal to + + + align:start position:0% +Simplicity that V1 was actually equal to +E1 that the direction that carries the + + align:start position:0% +E1 that the direction that carries the + + + align:start position:0% +E1 that the direction that carries the +most variant is the one that just says + + align:start position:0% +most variant is the one that just says + + + align:start position:0% +most variant is the one that just says +just look at the first coordinate of X + + align:start position:0% +just look at the first coordinate of X + + + align:start position:0% +just look at the first coordinate of X +right so if that was the case then + + align:start position:0% +right so if that was the case then + + + align:start position:0% +right so if that was the case then +clearly the orthogonal directions are + + align:start position:0% +clearly the orthogonal directions are + + + align:start position:0% +clearly the orthogonal directions are +the one that comprise of only of the + + align:start position:0% +the one that comprise of only of the + + + align:start position:0% +the one that comprise of only of the +coordinates 2 to D so you could actually + + align:start position:0% +coordinates 2 to D so you could actually + + + align:start position:0% +coordinates 2 to D so you could actually +just drop the first coordinate and do + + align:start position:0% +just drop the first coordinate and do + + + align:start position:0% +just drop the first coordinate and do +the same thing on a slightly shorter + + align:start position:0% +the same thing on a slightly shorter + + + align:start position:0% +the same thing on a slightly shorter +Vector of length D minus one and then + + align:start position:0% +Vector of length D minus one and then + + + align:start position:0% +Vector of length D minus one and then +you would just look at the largest ion + + align:start position:0% +you would just look at the largest ion + + + align:start position:0% +you would just look at the largest ion +Vector of the guys etc etc so in a way + + align:start position:0% +Vector of the guys etc etc so in a way + + + align:start position:0% +Vector of the guys etc etc so in a way +that's what's happening except that you + + align:start position:0% +that's what's happening except that you + + + align:start position:0% +that's what's happening except that you +rotate it before you actually do this + + align:start position:0% +rotate it before you actually do this + + + align:start position:0% +rotate it before you actually do this +that's exactly what's + + align:start position:0% +that's exactly what's + + + align:start position:0% +that's exactly what's +happening okay + + align:start position:0% + + + + align:start position:0% + +so what we put together here is + + align:start position:0% +so what we put together here is + + + align:start position:0% +so what we put together here is +essentially three things one was + + align:start position:0% +essentially three things one was + + + align:start position:0% +essentially three things one was +statistics statistics says if you want + + align:start position:0% +statistics statistics says if you want + + + align:start position:0% +statistics statistics says if you want +spread if you want information you + + align:start position:0% +spread if you want information you + + + align:start position:0% +spread if you want information you +should be looking at + + align:start position:0% +should be looking at + + + align:start position:0% +should be looking at +variance the second one was optimization + + align:start position:0% +variance the second one was optimization + + + align:start position:0% +variance the second one was optimization +optimization said well if you want to + + align:start position:0% +optimization said well if you want to + + + align:start position:0% +optimization said well if you want to +maximize spread well you have to + + align:start position:0% +maximize spread well you have to + + + align:start position:0% +maximize spread well you have to +maximize variance in a certain direction + + align:start position:0% +maximize variance in a certain direction + + + align:start position:0% +maximize variance in a certain direction +and that means ma maximizing over the + + align:start position:0% +and that means ma maximizing over the + + + align:start position:0% +and that means ma maximizing over the +sphere of vectors that have unit + + align:start position:0% +sphere of vectors that have unit + + + align:start position:0% +sphere of vectors that have unit +norm and that's an optimization problem + + align:start position:0% +norm and that's an optimization problem + + + align:start position:0% +norm and that's an optimization problem +which actually turned out to be + + align:start position:0% +which actually turned out to be + + + align:start position:0% +which actually turned out to be +difficult but then the third thing that + + align:start position:0% +difficult but then the third thing that + + + align:start position:0% +difficult but then the third thing that +we used to solve this problem was linear + + align:start position:0% +we used to solve this problem was linear + + + align:start position:0% +we used to solve this problem was linear +algebra linear algebra said well it + + align:start position:0% +algebra linear algebra said well it + + + align:start position:0% +algebra linear algebra said well it +looks like it's a difficult optimization + + align:start position:0% +looks like it's a difficult optimization + + + align:start position:0% +looks like it's a difficult optimization +problem but it turns out that the answer + + align:start position:0% +problem but it turns out that the answer + + + align:start position:0% +problem but it turns out that the answer +comes in almost I mean it's not a closed + + align:start position:0% +comes in almost I mean it's not a closed + + + align:start position:0% +comes in almost I mean it's not a closed +form but those things are so used that + + align:start position:0% +form but those things are so used that + + + align:start position:0% +form but those things are so used that +it's almost a close form says just pick + + align:start position:0% +it's almost a close form says just pick + + + align:start position:0% +it's almost a close form says just pick +the igen vectors in order of their + + align:start position:0% +the igen vectors in order of their + + + align:start position:0% +the igen vectors in order of their +Associated igen values from largest to + + align:start position:0% +Associated igen values from largest to + + + align:start position:0% +Associated igen values from largest to +smallest okay and that's why principal + + align:start position:0% +smallest okay and that's why principal + + + align:start position:0% +smallest okay and that's why principal +component analysis has been so popular + + align:start position:0% +component analysis has been so popular + + + align:start position:0% +component analysis has been so popular +and has has gained huge amount of + + align:start position:0% +and has has gained huge amount of + + + align:start position:0% +and has has gained huge amount of +traction since we had computers that + + align:start position:0% +traction since we had computers that + + + align:start position:0% +traction since we had computers that +were allowed to compute uh uh igen + + align:start position:0% +were allowed to compute uh uh igen + + + align:start position:0% +were allowed to compute uh uh igen +values and igen vectors for matrices of + + align:start position:0% +values and igen vectors for matrices of + + + align:start position:0% +values and igen vectors for matrices of +gigantic sizes you can actually do that + + align:start position:0% +gigantic sizes you can actually do that + + + align:start position:0% +gigantic sizes you can actually do that +if I give you I don't know the this + + align:start position:0% +if I give you I don't know the this + + + align:start position:0% +if I give you I don't know the this +Google video for example is talking + + align:start position:0% +Google video for example is talking + + + align:start position:0% +Google video for example is talking +about words right they want to do just a + + align:start position:0% +about words right they want to do just a + + + align:start position:0% +about words right they want to do just a +say principal component analysis of + + align:start position:0% +say principal component analysis of + + + align:start position:0% +say principal component analysis of +words so I give you all the words in the + + align:start position:0% +words so I give you all the words in the + + + align:start position:0% +words so I give you all the words in the +dictionary and uh um sorry well you + + align:start position:0% +dictionary and uh um sorry well you + + + align:start position:0% +dictionary and uh um sorry well you +would have to have a representation for + + align:start position:0% +would have to have a representation for + + + align:start position:0% +would have to have a representation for +words so it's a little more difficult uh + + align:start position:0% +words so it's a little more difficult uh + + + align:start position:0% +words so it's a little more difficult uh +but um how do I do this + + align:start position:0% +but um how do I do this + + + align:start position:0% +but um how do I do this +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh let's say for example pages of a book + + align:start position:0% +uh let's say for example pages of a book + + + align:start position:0% +uh let's say for example pages of a book +okay I want to understand the pages of a + + align:start position:0% +okay I want to understand the pages of a + + + align:start position:0% +okay I want to understand the pages of a +book and all I I need to turn it into a + + align:start position:0% +book and all I I need to turn it into a + + + align:start position:0% +book and all I I need to turn it into a +number and a page of a book is basically + + align:start position:0% +number and a page of a book is basically + + + align:start position:0% +number and a page of a book is basically +the word count right so I just count the + + align:start position:0% +the word count right so I just count the + + + align:start position:0% +the word count right so I just count the +number of time the shows up number of + + align:start position:0% +number of time the shows up number of + + + align:start position:0% +number of time the shows up number of +times n shows up number of time dog + + align:start position:0% +times n shows up number of time dog + + + align:start position:0% +times n shows up number of time dog +shows up and so that gives me a a vector + + align:start position:0% +shows up and so that gives me a a vector + + + align:start position:0% +shows up and so that gives me a a vector +it's in pretty high Dimensions it's as + + align:start position:0% +it's in pretty high Dimensions it's as + + + align:start position:0% +it's in pretty high Dimensions it's as +many dimensions as their word in + + align:start position:0% +many dimensions as their word in + + + align:start position:0% +many dimensions as their word in +dictionary and now I want to visual ize + + align:start position:0% +dictionary and now I want to visual ize + + + align:start position:0% +dictionary and now I want to visual ize +how those pages get together are two + + align:start position:0% +how those pages get together are two + + + align:start position:0% +how those pages get together are two +pages very similar or not and so what + + align:start position:0% +pages very similar or not and so what + + + align:start position:0% +pages very similar or not and so what +you would do is essentially just compute + + align:start position:0% +you would do is essentially just compute + + + align:start position:0% +you would do is essentially just compute +the largest Aon Vector of this Matrix + + align:start position:0% +the largest Aon Vector of this Matrix + + + align:start position:0% +the largest Aon Vector of this Matrix +maybe the two largest and then project + + align:start position:0% +maybe the two largest and then project + + + align:start position:0% +maybe the two largest and then project +this into a plane okay yeah can we + + align:start position:0% +this into a plane okay yeah can we + + + align:start position:0% +this into a plane okay yeah can we +assume the number of + + align:start position:0% +assume the number of + + + align:start position:0% +assume the number of +points yeah but there's many pages in + + align:start position:0% +points yeah but there's many pages in + + + align:start position:0% +points yeah but there's many pages in +the world there probably there's + + align:start position:0% +the world there probably there's + + + align:start position:0% +the world there probably there's +probably more pages in the world than + + align:start position:0% +probably more pages in the world than + + + align:start position:0% +probably more pages in the world than +there's words in the + + align:start position:0% +there's words in the + + + align:start position:0% +there's words in the +dictionary + + align:start position:0% +dictionary + + + align:start position:0% +dictionary +um okay yeah so of course if you in high + + align:start position:0% +um okay yeah so of course if you in high + + + align:start position:0% +um okay yeah so of course if you in high +dimensions and you don't have enough + + align:start position:0% +dimensions and you don't have enough + + + align:start position:0% +dimensions and you don't have enough +points it's going to be clearly an issue + + align:start position:0% +points it's going to be clearly an issue + + + align:start position:0% +points it's going to be clearly an issue +if you have two points then the leading + + align:start position:0% +if you have two points then the leading + + + align:start position:0% +if you have two points then the leading +Egon Vector is going to be just the line + + align:start position:0% +Egon Vector is going to be just the line + + + align:start position:0% +Egon Vector is going to be just the line +that goes through those two points okay + + align:start position:0% +that goes through those two points okay + + + align:start position:0% +that goes through those two points okay +regardless of what the dimension is and + + align:start position:0% +regardless of what the dimension is and + + + align:start position:0% +regardless of what the dimension is and +clearly you're not learning + + align:start position:0% +clearly you're not learning + + + align:start position:0% +clearly you're not learning +anything okay so um so you have to pick + + align:start position:0% +anything okay so um so you have to pick + + + align:start position:0% +anything okay so um so you have to pick +say the K largest ones if you go all the + + align:start position:0% +say the K largest ones if you go all the + + + align:start position:0% +say the K largest ones if you go all the +way you're just reordering your thing + + align:start position:0% +way you're just reordering your thing + + + align:start position:0% +way you're just reordering your thing +and you're not actually gaining anything + + align:start position:0% +and you're not actually gaining anything + + + align:start position:0% +and you're not actually gaining anything +you start from d and you go to D so at + + align:start position:0% +you start from d and you go to D so at + + + align:start position:0% +you start from d and you go to D so at +some point this procedure has to stop + + align:start position:0% +some point this procedure has to stop + + + align:start position:0% +some point this procedure has to stop +and let's say it stops at K now of + + align:start position:0% +and let's say it stops at K now of + + + align:start position:0% +and let's say it stops at K now of +course you should ask me a question + + align:start position:0% +course you should ask me a question + + + align:start position:0% +course you should ask me a question +which is how do you choose K right so + + align:start position:0% +which is how do you choose K right so + + + align:start position:0% +which is how do you choose K right so +that's of course a natural question the + + align:start position:0% +that's of course a natural question the + + + align:start position:0% +that's of course a natural question the +probably the basic answer is just pick k + + align:start position:0% +probably the basic answer is just pick k + + + align:start position:0% +probably the basic answer is just pick k +equals 3 because you can actually + + align:start position:0% +equals 3 because you can actually + + + align:start position:0% +equals 3 because you can actually +visualize it but people what happens if + + align:start position:0% +visualize it but people what happens if + + + align:start position:0% +visualize it but people what happens if +I take K is equal to + + align:start position:0% +I take K is equal to + + + align:start position:0% +I take K is equal to +four if I take K is equal to + + align:start position:0% +four if I take K is equal to + + + align:start position:0% +four if I take K is equal to +four I'm not going to be able to plot + + align:start position:0% +four I'm not going to be able to plot + + + align:start position:0% +four I'm not going to be able to plot +points in four dimensions well I could I + + align:start position:0% +points in four dimensions well I could I + + + align:start position:0% +points in four dimensions well I could I +could add collar I could you know try to + + align:start position:0% +could add collar I could you know try to + + + align:start position:0% +could add collar I could you know try to +be a little smart about it but it's + + align:start position:0% +be a little smart about it but it's + + + align:start position:0% +be a little smart about it but it's +actually quite difficult and so what + + align:start position:0% +actually quite difficult and so what + + + align:start position:0% +actually quite difficult and so what +people T tend to do if you have four + + align:start position:0% +people T tend to do if you have four + + + align:start position:0% +people T tend to do if you have four +dimensions they actually do a bunch of + + align:start position:0% +dimensions they actually do a bunch of + + + align:start position:0% +dimensions they actually do a bunch of +two-dimensional plots right and that's + + align:start position:0% +two-dimensional plots right and that's + + + align:start position:0% +two-dimensional plots right and that's +what a computer a computer is not very + + align:start position:0% +what a computer a computer is not very + + + align:start position:0% +what a computer a computer is not very +good I mean by default they don't spit + + align:start position:0% +good I mean by default they don't spit + + + align:start position:0% +good I mean by default they don't spit +out threedimensional plots so let's say + + align:start position:0% +out threedimensional plots so let's say + + + align:start position:0% +out threedimensional plots so let's say +they want to plot only two dimensional + + align:start position:0% +they want to plot only two dimensional + + + align:start position:0% +they want to plot only two dimensional +things so they're going to take the + + align:start position:0% +things so they're going to take the + + + align:start position:0% +things so they're going to take the +first Direction so say V1 V2 let's say + + align:start position:0% +first Direction so say V1 V2 let's say + + + align:start position:0% +first Direction so say V1 V2 let's say +you have three but you want to have only + + align:start position:0% +you have three but you want to have only + + + align:start position:0% +you have three but you want to have only +two dimensional plots and then it's + + align:start position:0% +two dimensional plots and then it's + + + align:start position:0% +two dimensional plots and then it's +going to do V1 V3 and then V2 + + align:start position:0% + + + + align:start position:0% + +V3 so really you take all three of them + + align:start position:0% +V3 so really you take all three of them + + + align:start position:0% +V3 so really you take all three of them +but it's really just showing you all you + + align:start position:0% +but it's really just showing you all you + + + align:start position:0% +but it's really just showing you all you +know choices of pairs of those guys + + align:start position:0% +know choices of pairs of those guys + + + align:start position:0% +know choices of pairs of those guys +right so if you were to keep K's equal + + align:start position:0% +right so if you were to keep K's equal + + + align:start position:0% +right so if you were to keep K's equal +to uh uh five you would have five choose + + align:start position:0% +to uh uh five you would have five choose + + + align:start position:0% +to uh uh five you would have five choose +two different + + align:start position:0% +two different + + + align:start position:0% +two different +plots um okay so this is the actual + + align:start position:0% +plots um okay so this is the actual + + + align:start position:0% +plots um okay so this is the actual +principal component algorithm how it's + + align:start position:0% +principal component algorithm how it's + + + align:start position:0% +principal component algorithm how it's +implemented and it's actually fairly + + align:start position:0% +implemented and it's actually fairly + + + align:start position:0% +implemented and it's actually fairly +simple I mean it looks like there's lots + + align:start position:0% +simple I mean it looks like there's lots + + + align:start position:0% +simple I mean it looks like there's lots +of steps but really there's only one + + align:start position:0% +of steps but really there's only one + + + align:start position:0% +of steps but really there's only one +that's important so the first one is the + + align:start position:0% +that's important so the first one is the + + + align:start position:0% +that's important so the first one is the +input I give you a bunch of points X1 to + + align:start position:0% +input I give you a bunch of points X1 to + + + align:start position:0% +input I give you a bunch of points X1 to +xn in D Dimensions okay and the step two + + align:start position:0% +xn in D Dimensions okay and the step two + + + align:start position:0% +xn in D Dimensions okay and the step two +is we'll compute their empirical ciance + + align:start position:0% +is we'll compute their empirical ciance + + + align:start position:0% +is we'll compute their empirical ciance +Matrix S okay the points themselves we + + align:start position:0% +Matrix S okay the points themselves we + + + align:start position:0% +Matrix S okay the points themselves we +don't really care we care about their + + align:start position:0% +don't really care we care about their + + + align:start position:0% +don't really care we care about their +empirical ciance Matrix so it's a d byd + + align:start position:0% +empirical ciance Matrix so it's a d byd + + + align:start position:0% +empirical ciance Matrix so it's a d byd +Matrix now I'm going to feed that and + + align:start position:0% +Matrix now I'm going to feed that and + + + align:start position:0% +Matrix now I'm going to feed that and +that's where the actual computation + + align:start position:0% +that's where the actual computation + + + align:start position:0% +that's where the actual computation +starts happening I'm going to feed that + + align:start position:0% +starts happening I'm going to feed that + + + align:start position:0% +starts happening I'm going to feed that +to something that knows how to + + align:start position:0% +to something that knows how to + + + align:start position:0% +to something that knows how to +diagonalize this Matrix and you have to + + align:start position:0% +diagonalize this Matrix and you have to + + + align:start position:0% +diagonalize this Matrix and you have to +trust me if I want to compute the K + + align:start position:0% +trust me if I want to compute the K + + + align:start position:0% +trust me if I want to compute the K +largest agen values and my Matrix is d + + align:start position:0% +largest agen values and my Matrix is d + + + align:start position:0% +largest agen values and my Matrix is d +by D it's going to take me about K * d^ + + align:start position:0% +by D it's going to take me about K * d^ + + + align:start position:0% +by D it's going to take me about K * d^ + + align:start position:0% + + + align:start position:0% +operations okay so if I want only three + + align:start position:0% +operations okay so if I want only three + + + align:start position:0% +operations okay so if I want only three +it's three * d square which is about d + + align:start position:0% +it's three * d square which is about d + + + align:start position:0% +it's three * d square which is about d +square is the time for me it takes to + + align:start position:0% +square is the time for me it takes to + + + align:start position:0% +square is the time for me it takes to +just even read The Matrix Sigma so + + align:start position:0% +just even read The Matrix Sigma so + + + align:start position:0% +just even read The Matrix Sigma so +that's not too + + align:start position:0% +that's not too + + + align:start position:0% +that's not too +bad so what it's going to spit out of + + align:start position:0% +bad so what it's going to spit out of + + + align:start position:0% +bad so what it's going to spit out of +course is the diagonal matrix D and uh + + align:start position:0% +course is the diagonal matrix D and uh + + + align:start position:0% +course is the diagonal matrix D and uh +those are nice because they allow me to + + align:start position:0% +those are nice because they allow me to + + + align:start position:0% +those are nice because they allow me to +tell me which of the coordinates which + + align:start position:0% +tell me which of the coordinates which + + + align:start position:0% +tell me which of the coordinates which +of the columns of P what is the order in + + align:start position:0% +of the columns of P what is the order in + + + align:start position:0% +of the columns of P what is the order in +which I should be taking The Columns of + + align:start position:0% +which I should be taking The Columns of + + + align:start position:0% +which I should be taking The Columns of +P but but what's really important to me + + align:start position:0% +P but but what's really important to me + + + align:start position:0% +P but but what's really important to me +is V1 to VD because those are going to + + align:start position:0% +is V1 to VD because those are going to + + + align:start position:0% +is V1 to VD because those are going to +be the ones I'm going to be using to + + align:start position:0% +be the ones I'm going to be using to + + + align:start position:0% +be the ones I'm going to be using to +draw those + + align:start position:0% +draw those + + + align:start position:0% +draw those +plots and now I'm going to say okay I + + align:start position:0% +plots and now I'm going to say okay I + + + align:start position:0% +plots and now I'm going to say okay I +need to actually choose some uh set K + + align:start position:0% +need to actually choose some uh set K + + + align:start position:0% +need to actually choose some uh set K +and I'm going to basically truncate and + + align:start position:0% +and I'm going to basically truncate and + + + align:start position:0% +and I'm going to basically truncate and +look only at the first K Columns of + + align:start position:0% +look only at the first K Columns of + + + align:start position:0% +look only at the first K Columns of +P okay once I have those columns what I + + align:start position:0% +P okay once I have those columns what I + + + align:start position:0% +P okay once I have those columns what I +want to do is to project onto the linear + + align:start position:0% +want to do is to project onto the linear + + + align:start position:0% +want to do is to project onto the linear +span of those columns and there's + + align:start position:0% +span of those columns and there's + + + align:start position:0% +span of those columns and there's +actually a NE simple way to do this + + align:start position:0% +actually a NE simple way to do this + + + align:start position:0% +actually a NE simple way to do this +which is just take this Matrix p which + + align:start position:0% +which is just take this Matrix p which + + + align:start position:0% +which is just take this Matrix p which +is really the Matrix of projection onto + + align:start position:0% +is really the Matrix of projection onto + + + align:start position:0% +is really the Matrix of projection onto +the linear span of those K columns and + + align:start position:0% +the linear span of those K columns and + + + align:start position:0% +the linear span of those K columns and +you just take PK transpose and then you + + align:start position:0% +you just take PK transpose and then you + + + align:start position:0% +you just take PK transpose and then you +apply this to every single one of your + + align:start position:0% +apply this to every single one of your + + + align:start position:0% +apply this to every single one of your +points okay now PK transpose PK is a + + align:start position:0% +points okay now PK transpose PK is a + + + align:start position:0% +points okay now PK transpose PK is a +what what is the size of the Matrix + + align:start position:0% + + + + align:start position:0% + +PK yeah + + align:start position:0% +PK yeah + + + align:start position:0% +PK yeah +tally so PK is just this Matrix I take + + align:start position:0% +tally so PK is just this Matrix I take + + + align:start position:0% +tally so PK is just this Matrix I take +V1 and I stop at VK Vo + + align:start position:0% +V1 and I stop at VK Vo + + + align:start position:0% +V1 and I stop at VK Vo +d by K right each of the column is an + + align:start position:0% +d by K right each of the column is an + + + align:start position:0% +d by K right each of the column is an +igen Vector it's of Dimension d That's + + align:start position:0% +igen Vector it's of Dimension d That's + + + align:start position:0% +igen Vector it's of Dimension d That's +Just I mean that's a vector in the + + align:start position:0% +Just I mean that's a vector in the + + + align:start position:0% +Just I mean that's a vector in the +original space so I have this D byk + + align:start position:0% +original space so I have this D byk + + + align:start position:0% +original space so I have this D byk +Matrix right so all it is is if I had my + + align:start position:0% +Matrix right so all it is is if I had my + + + align:start position:0% +Matrix right so all it is is if I had my +uh well well I'm going to talk in a + + align:start position:0% +uh well well I'm going to talk in a + + + align:start position:0% +uh well well I'm going to talk in a +second about PK transpose PK transpose + + align:start position:0% +second about PK transpose PK transpose + + + align:start position:0% +second about PK transpose PK transpose +is just this guy where I stop at the K + + align:start position:0% +is just this guy where I stop at the K + + + align:start position:0% +is just this guy where I stop at the K +Vector okay so PK transpose is K by D so + + align:start position:0% +Vector okay so PK transpose is K by D so + + + align:start position:0% +Vector okay so PK transpose is K by D so +now when I take Yi which is PK transpose + + align:start position:0% +now when I take Yi which is PK transpose + + + align:start position:0% +now when I take Yi which is PK transpose +XI I end up with a point which is in K + + align:start position:0% +XI I end up with a point which is in K + + + align:start position:0% +XI I end up with a point which is in K +Dimensions I have only K coordinates so + + align:start position:0% +Dimensions I have only K coordinates so + + + align:start position:0% +Dimensions I have only K coordinates so +I took every single one of my original + + align:start position:0% +I took every single one of my original + + + align:start position:0% +I took every single one of my original +points XI which had D coordinates and I + + align:start position:0% +points XI which had D coordinates and I + + + align:start position:0% +points XI which had D coordinates and I +turned it into a point that has only K + + align:start position:0% +turned it into a point that has only K + + + align:start position:0% +turned it into a point that has only K +coordinates particular I could have K is + + align:start position:0% +coordinates particular I could have K is + + + align:start position:0% +coordinates particular I could have K is +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +two this Matrix is exactly the one that + + align:start position:0% +two this Matrix is exactly the one that + + + align:start position:0% +two this Matrix is exactly the one that +projects right if you think about it for + + align:start position:0% +projects right if you think about it for + + + align:start position:0% +projects right if you think about it for +one second this is just the Matrix that + + align:start position:0% +one second this is just the Matrix that + + + align:start position:0% +one second this is just the Matrix that +says well we actually did that several + + align:start position:0% +says well we actually did that several + + + align:start position:0% +says well we actually did that several +times it's the Matrix right that was + + align:start position:0% +times it's the Matrix right that was + + + align:start position:0% +times it's the Matrix right that was +this P transpose U that showed up + + align:start position:0% +this P transpose U that showed up + + + align:start position:0% +this P transpose U that showed up +somewhere right and so that's just the + + align:start position:0% +somewhere right and so that's just the + + + align:start position:0% +somewhere right and so that's just the +Matrix that take your point x in say + + align:start position:0% +Matrix that take your point x in say + + + align:start position:0% +Matrix that take your point x in say +three dimensions and then just you know + + align:start position:0% +three dimensions and then just you know + + + align:start position:0% +three dimensions and then just you know +project it down to two Dimensions okay + + align:start position:0% +project it down to two Dimensions okay + + + align:start position:0% +project it down to two Dimensions okay +and that's just you know goes to the + + align:start position:0% +and that's just you know goes to the + + + align:start position:0% +and that's just you know goes to the +closest point uh in this in this + + align:start position:0% +closest point uh in this in this + + + align:start position:0% +closest point uh in this in this +Subspace now here the the the floor is + + align:start position:0% +Subspace now here the the the floor is + + + align:start position:0% +Subspace now here the the the floor is +flat but we have you know we can pick + + align:start position:0% +flat but we have you know we can pick + + + align:start position:0% +flat but we have you know we can pick +any Subspace we want depending on what + + align:start position:0% +any Subspace we want depending on what + + + align:start position:0% +any Subspace we want depending on what +the lambdas are so the lambdas were + + align:start position:0% +the lambdas are so the lambdas were + + + align:start position:0% +the lambdas are so the lambdas were +important for us to be able to identify + + align:start position:0% +important for us to be able to identify + + + align:start position:0% +important for us to be able to identify +which columns to + + align:start position:0% +which columns to + + + align:start position:0% +which columns to +pick the fact that we assume that they + + align:start position:0% +pick the fact that we assume that they + + + align:start position:0% +pick the fact that we assume that they +were ordered tells us that we can pick + + align:start position:0% +were ordered tells us that we can pick + + + align:start position:0% +were ordered tells us that we can pick +the first ones if they were not ordered + + align:start position:0% +the first ones if they were not ordered + + + align:start position:0% +the first ones if they were not ordered +it would be just a subset of the columns + + align:start position:0% +it would be just a subset of the columns + + + align:start position:0% +it would be just a subset of the columns +depending on what the size of the I + + align:start position:0% +depending on what the size of the I + + + align:start position:0% +depending on what the size of the I +value is so each uh each column is + + align:start position:0% +value is so each uh each column is + + + align:start position:0% +value is so each uh each column is +labeled and so then of course we still + + align:start position:0% +labeled and so then of course we still + + + align:start position:0% +labeled and so then of course we still +have this question of how do I pick K + + align:start position:0% +have this question of how do I pick K + + + align:start position:0% +have this question of how do I pick K +right uh so there's definitely the + + align:start position:0% +right uh so there's definitely the + + + align:start position:0% +right uh so there's definitely the +matter of convenience maybe two is + + align:start position:0% +matter of convenience maybe two is + + + align:start position:0% +matter of convenience maybe two is +convenient if it works for two you don't + + align:start position:0% +convenient if it works for two you don't + + + align:start position:0% +convenient if it works for two you don't +have to go any further but uh uh you + + align:start position:0% +have to go any further but uh uh you + + + align:start position:0% +have to go any further but uh uh you +might want to say well originally I did + + align:start position:0% +might want to say well originally I did + + + align:start position:0% +might want to say well originally I did +that to actually keep as much + + align:start position:0% +that to actually keep as much + + + align:start position:0% +that to actually keep as much +information as possible I know that the + + align:start position:0% +information as possible I know that the + + + align:start position:0% +information as possible I know that the +ultimate thing is to keep as much + + align:start position:0% +ultimate thing is to keep as much + + + align:start position:0% +ultimate thing is to keep as much +information which would be K is equal to + + align:start position:0% +information which would be K is equal to + + + align:start position:0% +information which would be K is equal to +D that's as much information as you want + + align:start position:0% +D that's as much information as you want + + + align:start position:0% +D that's as much information as you want +but that's essentially the same question + + align:start position:0% +but that's essentially the same question + + + align:start position:0% +but that's essentially the same question +about well you know if I want to + + align:start position:0% +about well you know if I want to + + + align:start position:0% +about well you know if I want to +compress a JPEG image how much could you + + align:start position:0% +compress a JPEG image how much could you + + + align:start position:0% +compress a JPEG image how much could you +know how much information should I keep + + align:start position:0% +know how much information should I keep + + + align:start position:0% +know how much information should I keep +so it's like still visible and so + + align:start position:0% +so it's like still visible and so + + + align:start position:0% +so it's like still visible and so +there's some rules for that but none of + + align:start position:0% +there's some rules for that but none of + + + align:start position:0% +there's some rules for that but none of +them is actually really a science so + + align:start position:0% +them is actually really a science so + + + align:start position:0% +them is actually really a science so +it's really a matter of what you think + + align:start position:0% +it's really a matter of what you think + + + align:start position:0% +it's really a matter of what you think +is actually tolerable and we're just + + align:start position:0% +is actually tolerable and we're just + + + align:start position:0% +is actually tolerable and we're just +going to start replacing this Choice by + + align:start position:0% +going to start replacing this Choice by + + + align:start position:0% +going to start replacing this Choice by +maybe some another parameter so we're + + align:start position:0% +maybe some another parameter so we're + + + align:start position:0% +maybe some another parameter so we're +here we're going to basically replace K + + align:start position:0% +here we're going to basically replace K + + + align:start position:0% +here we're going to basically replace K +by Alpha and so we just do stuff so the + + align:start position:0% +by Alpha and so we just do stuff so the + + + align:start position:0% +by Alpha and so we just do stuff so the +first one that people do that is + + align:start position:0% +first one that people do that is + + + align:start position:0% +first one that people do that is +probably the most popular one no okay + + align:start position:0% +probably the most popular one no okay + + + align:start position:0% +probably the most popular one no okay +the most popular one is definitely take + + align:start position:0% +the most popular one is definitely take + + + align:start position:0% +the most popular one is definitely take +K is equal to two or three uh because + + align:start position:0% +K is equal to two or three uh because + + + align:start position:0% +K is equal to two or three uh because +it's just convenient to + + align:start position:0% +it's just convenient to + + + align:start position:0% +it's just convenient to +visualize the second most popular one is + + align:start position:0% +visualize the second most popular one is + + + align:start position:0% +visualize the second most popular one is +the scre + + align:start position:0% +the scre + + + align:start position:0% +the scre +plot so the scre plot remember I have my + + align:start position:0% +plot so the scre plot remember I have my + + + align:start position:0% +plot so the scre plot remember I have my +values Lambda + + align:start position:0% +values Lambda + + + align:start position:0% +values Lambda +JS and I've chosen the Lambda J is to + + align:start position:0% +JS and I've chosen the Lambda J is to + + + align:start position:0% +JS and I've chosen the Lambda J is to +decrease right so the indices are chosen + + align:start position:0% +decrease right so the indices are chosen + + + align:start position:0% +decrease right so the indices are chosen +in such a way that Lambda is a + + align:start position:0% +in such a way that Lambda is a + + + align:start position:0% +in such a way that Lambda is a +decreasing function so I have Lambda 1 + + align:start position:0% +decreasing function so I have Lambda 1 + + + align:start position:0% +decreasing function so I have Lambda 1 +and let's say it's this guy here and + + align:start position:0% +and let's say it's this guy here and + + + align:start position:0% +and let's say it's this guy here and +then I have Lambda two and it say it's + + align:start position:0% +then I have Lambda two and it say it's + + + align:start position:0% +then I have Lambda two and it say it's +this guy here and then I have Lambda + + align:start position:0% +this guy here and then I have Lambda + + + align:start position:0% +this guy here and then I have Lambda +three and let's say it's this guy here + + align:start position:0% +three and let's say it's this guy here + + + align:start position:0% +three and let's say it's this guy here +Lambda four Lambda five Lambda six and + + align:start position:0% +Lambda four Lambda five Lambda six and + + + align:start position:0% +Lambda four Lambda five Lambda six and +all I care about is that this thing + + align:start position:0% +all I care about is that this thing + + + align:start position:0% +all I care about is that this thing +decreases right the scre plot says + + align:start position:0% +decreases right the scre plot says + + + align:start position:0% +decreases right the scre plot says +something like this if there's an + + align:start position:0% +something like this if there's an + + + align:start position:0% +something like this if there's an +inflection point meaning that you can + + align:start position:0% +inflection point meaning that you can + + + align:start position:0% +inflection point meaning that you can +sort of do something like this and then + + align:start position:0% +sort of do something like this and then + + + align:start position:0% +sort of do something like this and then +something like this you should stop at + + align:start position:0% +something like this you should stop at + + + align:start position:0% +something like this you should stop at +three that's what the scre plot tells + + align:start position:0% +three that's what the scre plot tells + + + align:start position:0% +three that's what the scre plot tells +you what it's saying in a way + + align:start position:0% +you what it's saying in a way + + + align:start position:0% +you what it's saying in a way +is that the percentage + + align:start position:0% +is that the percentage + + + align:start position:0% +is that the percentage +of the marginal increment of explained + + align:start position:0% +of the marginal increment of explained + + + align:start position:0% +of the marginal increment of explained +variance that you get starts to decrease + + align:start position:0% +variance that you get starts to decrease + + + align:start position:0% +variance that you get starts to decrease +after you pass this inflection point so + + align:start position:0% +after you pass this inflection point so + + + align:start position:0% +after you pass this inflection point so +let's see why I say this + + align:start position:0% +let's see why I say this + + + align:start position:0% +let's see why I say this +well here what I have so this thing this + + align:start position:0% +well here what I have so this thing this + + + align:start position:0% +well here what I have so this thing this +ratio that you see there is actually the + + align:start position:0% +ratio that you see there is actually the + + + align:start position:0% +ratio that you see there is actually the +percentage of of explained variance okay + + align:start position:0% +percentage of of explained variance okay + + + align:start position:0% +percentage of of explained variance okay +okay so what it means is that if I look + + align:start position:0% +okay so what it means is that if I look + + + align:start position:0% +okay so what it means is that if I look +at Lambda 1 + Lambda + + align:start position:0% +at Lambda 1 + Lambda + + + align:start position:0% +at Lambda 1 + Lambda +K and then I divide by Lambda + + align:start position:0% +K and then I divide by Lambda + + + align:start position:0% +K and then I divide by Lambda +1 plus Lambda + + align:start position:0% +1 plus Lambda + + + align:start position:0% +1 plus Lambda +D well what is this well this Lambda 1 + + align:start position:0% +D well what is this well this Lambda 1 + + + align:start position:0% +D well what is this well this Lambda 1 +plus Lambda D is the total amount of + + align:start position:0% +plus Lambda D is the total amount of + + + align:start position:0% +plus Lambda D is the total amount of +variance that I get in my points right + + align:start position:0% +variance that I get in my points right + + + align:start position:0% +variance that I get in my points right +that's the trace of Sigma okay so that's + + align:start position:0% +that's the trace of Sigma okay so that's + + + align:start position:0% +that's the trace of Sigma okay so that's +the variance in the first Direction the + + align:start position:0% +the variance in the first Direction the + + + align:start position:0% +the variance in the first Direction the +first plus the variance in the second + + align:start position:0% +first plus the variance in the second + + + align:start position:0% +first plus the variance in the second +Direction plus the variance in the third + + align:start position:0% +Direction plus the variance in the third + + + align:start position:0% +Direction plus the variance in the third +Direction that's basically all the + + align:start position:0% +Direction that's basically all the + + + align:start position:0% +Direction that's basically all the +variance that I have + + align:start position:0% +variance that I have + + + align:start position:0% +variance that I have +possible + + align:start position:0% +possible + + + align:start position:0% +possible +okay now this is is the variance that I + + align:start position:0% +okay now this is is the variance that I + + + align:start position:0% +okay now this is is the variance that I +kept in the first Direction This is the + + align:start position:0% +kept in the first Direction This is the + + + align:start position:0% +kept in the first Direction This is the +variance that I kept in the second + + align:start position:0% +variance that I kept in the second + + + align:start position:0% +variance that I kept in the second +Direction all the way to the variance + + align:start position:0% +Direction all the way to the variance + + + align:start position:0% +Direction all the way to the variance +that I kept in the case Direction so I + + align:start position:0% +that I kept in the case Direction so I + + + align:start position:0% +that I kept in the case Direction so I +know that this number is always less + + align:start position:0% +know that this number is always less + + + align:start position:0% +know that this number is always less +than or equal to one and it's larger + + align:start position:0% +than or equal to one and it's larger + + + align:start position:0% +than or equal to one and it's larger +than one and this is just the proportion + + align:start position:0% +than one and this is just the proportion + + + align:start position:0% +than one and this is just the proportion +say of + + align:start position:0% +say of + + + align:start position:0% +say of +variance + + align:start position:0% + + + + align:start position:0% + +explained by + + align:start position:0% +explained by + + + align:start position:0% +explained by +V1 to VK or simply the proportion of + + align:start position:0% +V1 to VK or simply the proportion of + + + align:start position:0% +V1 to VK or simply the proportion of +explained variance by my PCA say okay so + + align:start position:0% +explained variance by my PCA say okay so + + + align:start position:0% +explained variance by my PCA say okay so +now what this thing is telling me says + + align:start position:0% +now what this thing is telling me says + + + align:start position:0% +now what this thing is telling me says +well if I look at this thing and I start + + align:start position:0% +well if I look at this thing and I start + + + align:start position:0% +well if I look at this thing and I start +seeing this inflection point it's saying + + align:start position:0% +seeing this inflection point it's saying + + + align:start position:0% +seeing this inflection point it's saying +oh here you're gaining a lot and lot of + + align:start position:0% +oh here you're gaining a lot and lot of + + + align:start position:0% +oh here you're gaining a lot and lot of +variance and then at some point you stop + + align:start position:0% +variance and then at some point you stop + + + align:start position:0% +variance and then at some point you stop +gaining a lot in your uh in your + + align:start position:0% +gaining a lot in your uh in your + + + align:start position:0% +gaining a lot in your uh in your +proportion of explained variance so this + + align:start position:0% +proportion of explained variance so this + + + align:start position:0% +proportion of explained variance so this +will translate in something where when I + + align:start position:0% +will translate in something where when I + + + align:start position:0% +will translate in something where when I +look at this ratio Lambda 1 plus Lambda + + align:start position:0% +look at this ratio Lambda 1 plus Lambda + + + align:start position:0% +look at this ratio Lambda 1 plus Lambda +k / Lambda 1 plus Lambda D this would + + align:start position:0% +k / Lambda 1 plus Lambda D this would + + + align:start position:0% +k / Lambda 1 plus Lambda D this would +translate into a function that would + + align:start position:0% +translate into a function that would + + + align:start position:0% +translate into a function that would +look like this and what it's telling you + + align:start position:0% +look like this and what it's telling you + + + align:start position:0% +look like this and what it's telling you +is says well maybe you should stop here + + align:start position:0% +is says well maybe you should stop here + + + align:start position:0% +is says well maybe you should stop here +because here every time you add one you + + align:start position:0% +because here every time you add one you + + + align:start position:0% +because here every time you add one you +don't get as much as you did before you + + align:start position:0% +don't get as much as you did before you + + + align:start position:0% +don't get as much as you did before you +actually get like smaller marginal + + align:start position:0% +actually get like smaller marginal + + + align:start position:0% +actually get like smaller marginal +returns + + align:start position:0% + + + + align:start position:0% + +okay so there's uh uh explained variance + + align:start position:0% +okay so there's uh uh explained variance + + + align:start position:0% +okay so there's uh uh explained variance +is the is the numeric Ator of this ratio + + align:start position:0% +is the is the numeric Ator of this ratio + + + align:start position:0% +is the is the numeric Ator of this ratio +and the tool Varian is the denominator + + align:start position:0% +and the tool Varian is the denominator + + + align:start position:0% +and the tool Varian is the denominator +those are pretty straightforward uh uh + + align:start position:0% +those are pretty straightforward uh uh + + + align:start position:0% +those are pretty straightforward uh uh +terms that you would want to use for + + align:start position:0% +terms that you would want to use for + + + align:start position:0% +terms that you would want to use for +this all right so if your goal is to do + + align:start position:0% +this all right so if your goal is to do + + + align:start position:0% +this all right so if your goal is to do +data visualization okay so why would you + + align:start position:0% +data visualization okay so why would you + + + align:start position:0% +data visualization okay so why would you +take K larger than two uh let's say if + + align:start position:0% +take K larger than two uh let's say if + + + align:start position:0% +take K larger than two uh let's say if +you take K larger than six you can start + + align:start position:0% +you take K larger than six you can start + + + align:start position:0% +you take K larger than six you can start +to imagine that you're going to have six + + align:start position:0% +to imagine that you're going to have six + + + align:start position:0% +to imagine that you're going to have six +choose two which starts to be annoying + + align:start position:0% +choose two which starts to be annoying + + + align:start position:0% +choose two which starts to be annoying +and if you have K is equal to 10 because + + align:start position:0% +and if you have K is equal to 10 because + + + align:start position:0% +and if you have K is equal to 10 because +you know you could start in dimension + + align:start position:0% +you know you could start in dimension + + + align:start position:0% +you know you could start in dimension +50,000 and then k equal to 10 would be + + align:start position:0% +50,000 and then k equal to 10 would be + + + align:start position:0% +50,000 and then k equal to 10 would be +the place where you have this thing + + align:start position:0% +the place where you have this thing + + + align:start position:0% +the place where you have this thing +that's a lot of plots that you would + + align:start position:0% +that's a lot of plots that you would + + + align:start position:0% +that's a lot of plots that you would +have to show so it's not always for data + + align:start position:0% +have to show so it's not always for data + + + align:start position:0% +have to show so it's not always for data +visualization + + align:start position:0% +visualization + + + align:start position:0% +visualization +once I've actually done this I've + + align:start position:0% +once I've actually done this I've + + + align:start position:0% +once I've actually done this I've +actually effectively reduced the + + align:start position:0% +actually effectively reduced the + + + align:start position:0% +actually effectively reduced the +dimension of my problem and what I could + + align:start position:0% +dimension of my problem and what I could + + + align:start position:0% +dimension of my problem and what I could +do with what I have is do a regression + + align:start position:0% +do with what I have is do a regression + + + align:start position:0% +do with what I have is do a regression +on those guys the the V1 so I forgot to + + align:start position:0% +on those guys the the V1 so I forgot to + + + align:start position:0% +on those guys the the V1 so I forgot to +tell you why is it called principal + + align:start position:0% +tell you why is it called principal + + + align:start position:0% +tell you why is it called principal +component analysis well the VJs that I + + align:start position:0% +component analysis well the VJs that I + + + align:start position:0% +component analysis well the VJs that I +keep V1 to VK are + + align:start position:0% + + + + align:start position:0% + +called principal + + align:start position:0% + + + + align:start position:0% + +components + + align:start position:0% + + + + align:start position:0% + +and they effectively act as a summary of + + align:start position:0% +and they effectively act as a summary of + + + align:start position:0% +and they effectively act as a summary of +my XI right when I mentioned image + + align:start position:0% +my XI right when I mentioned image + + + align:start position:0% +my XI right when I mentioned image +compression I started with a point XI + + align:start position:0% +compression I started with a point XI + + + align:start position:0% +compression I started with a point XI +that was D numbers let's say 50,000 + + align:start position:0% +that was D numbers let's say 50,000 + + + align:start position:0% +that was D numbers let's say 50,000 +numbers and now I'm saying actually you + + align:start position:0% +numbers and now I'm saying actually you + + + align:start position:0% +numbers and now I'm saying actually you +can throw out those 50,000 numbers if + + align:start position:0% +can throw out those 50,000 numbers if + + + align:start position:0% +can throw out those 50,000 numbers if +you actually know only the K numbers + + align:start position:0% +you actually know only the K numbers + + + align:start position:0% +you actually know only the K numbers +that you need the six numbers that you + + align:start position:0% +that you need the six numbers that you + + + align:start position:0% +that you need the six numbers that you +need you're going to have something that + + align:start position:0% +need you're going to have something that + + + align:start position:0% +need you're going to have something that +was pretty close to getting what the + + align:start position:0% +was pretty close to getting what the + + + align:start position:0% +was pretty close to getting what the +what information you had so in a way + + align:start position:0% +what information you had so in a way + + + align:start position:0% +what information you had so in a way +there's form of compression that's going + + align:start position:0% +there's form of compression that's going + + + align:start position:0% +there's form of compression that's going +on here and and what what you can do is + + align:start position:0% +on here and and what what you can do is + + + align:start position:0% +on here and and what what you can do is +that those principal components you can + + align:start position:0% +that those principal components you can + + + align:start position:0% +that those principal components you can +actually use now for regression right if + + align:start position:0% +actually use now for regression right if + + + align:start position:0% +actually use now for regression right if +I want to regress y onto X that's very + + align:start position:0% +I want to regress y onto X that's very + + + align:start position:0% +I want to regress y onto X that's very +high + + align:start position:0% +high + + + align:start position:0% +high +dimensional before I do this if I don't + + align:start position:0% +dimensional before I do this if I don't + + + align:start position:0% +dimensional before I do this if I don't +have enough points maybe what I can + + align:start position:0% +have enough points maybe what I can + + + align:start position:0% +have enough points maybe what I can +actually do is to do principal component + + align:start position:0% +actually do is to do principal component + + + align:start position:0% +actually do is to do principal component +reg uh uh analysis throughout my exis + + align:start position:0% +reg uh uh analysis throughout my exis + + + align:start position:0% +reg uh uh analysis throughout my exis +replace them by those compressed + + align:start position:0% +replace them by those compressed + + + align:start position:0% +replace them by those compressed +versions and do linear regression on + + align:start position:0% +versions and do linear regression on + + + align:start position:0% +versions and do linear regression on +those guys and that's called principal + + align:start position:0% +those guys and that's called principal + + + align:start position:0% +those guys and that's called principal +component regression not surprisingly + + align:start position:0% +component regression not surprisingly + + + align:start position:0% +component regression not surprisingly +and that's something that's pretty + + align:start position:0% +and that's something that's pretty + + + align:start position:0% +and that's something that's pretty +popular and you can do with K is equal + + align:start position:0% +popular and you can do with K is equal + + + align:start position:0% +popular and you can do with K is equal +to 10 for + + align:start position:0% + + + + align:start position:0% + +example all right so for data + + align:start position:0% +example all right so for data + + + align:start position:0% +example all right so for data +visualization uh I did not find a + + align:start position:0% +visualization uh I did not find a + + + align:start position:0% +visualization uh I did not find a +Thanksgiving themed uh picture but uh I + + align:start position:0% +Thanksgiving themed uh picture but uh I + + + align:start position:0% +Thanksgiving themed uh picture but uh I +found one that has turkey in + + align:start position:0% +found one that has turkey in + + + align:start position:0% +found one that has turkey in +it get it all right and uh all right so + + align:start position:0% +it get it all right and uh all right so + + + align:start position:0% +it get it all right and uh all right so +uh this is actually a gene data set uh + + align:start position:0% +uh this is actually a gene data set uh + + + align:start position:0% +uh this is actually a gene data set uh +that was uh so they just so when you see + + align:start position:0% +that was uh so they just so when you see + + + align:start position:0% +that was uh so they just so when you see +something like this you can imagine that + + align:start position:0% +something like this you can imagine that + + + align:start position:0% +something like this you can imagine that +someone has been pre pre-processing the + + align:start position:0% +someone has been pre pre-processing the + + + align:start position:0% +someone has been pre pre-processing the +hell out of this thing this is not like + + align:start position:0% +hell out of this thing this is not like + + + align:start position:0% +hell out of this thing this is not like +oh I collect data on 23 and me and I'm + + align:start position:0% +oh I collect data on 23 and me and I'm + + + align:start position:0% +oh I collect data on 23 and me and I'm +just going to run PCA on this just + + align:start position:0% +just going to run PCA on this just + + + align:start position:0% +just going to run PCA on this just +doesn't happen like that and um so what + + align:start position:0% +doesn't happen like that and um so what + + + align:start position:0% +doesn't happen like that and um so what +happened is that so let's assume that uh + + align:start position:0% +happened is that so let's assume that uh + + + align:start position:0% +happened is that so let's assume that uh +this was a bunch of pre-processed data + + align:start position:0% +this was a bunch of pre-processed data + + + align:start position:0% +this was a bunch of pre-processed data +which are uh gene expression levels uh + + align:start position:0% +which are uh gene expression levels uh + + + align:start position:0% +which are uh gene expression levels uh +so 500,000 genes among uh + + align:start position:0% +so 500,000 genes among uh + + + align:start position:0% +so 500,000 genes among uh +400400 Europeans so here I actually have + + align:start position:0% +400400 Europeans so here I actually have + + + align:start position:0% +400400 Europeans so here I actually have +less observations that I have + + align:start position:0% +less observations that I have + + + align:start position:0% +less observations that I have +samples and uh and that's when you use + + align:start position:0% +samples and uh and that's when you use + + + align:start position:0% +samples and uh and that's when you use +principal component regression most of + + align:start position:0% +principal component regression most of + + + align:start position:0% +principal component regression most of +the time so it doesn't stop you and uh + + align:start position:0% +the time so it doesn't stop you and uh + + + align:start position:0% +the time so it doesn't stop you and uh +and then what you do is you say okay I + + align:start position:0% +and then what you do is you say okay I + + + align:start position:0% +and then what you do is you say okay I +have those 50 500,000 genes among 40 uh + + align:start position:0% +have those 50 500,000 genes among 40 uh + + + align:start position:0% +have those 50 500,000 genes among 40 uh +400 so here that means that there's + + align:start position:0% +400 so here that means that there's + + + align:start position:0% +400 so here that means that there's +14400 points here and I actually take + + align:start position:0% +14400 points here and I actually take + + + align:start position:0% +14400 points here and I actually take +those 500,000 directions right so each + + align:start position:0% +those 500,000 directions right so each + + + align:start position:0% +those 500,000 directions right so each +person has a vector of five size 500,000 + + align:start position:0% +person has a vector of five size 500,000 + + + align:start position:0% +person has a vector of five size 500,000 +genes that attached to them and I + + align:start position:0% +genes that attached to them and I + + + align:start position:0% +genes that attached to them and I +project them onto two Dimensions which + + align:start position:0% +project them onto two Dimensions which + + + align:start position:0% +project them onto two Dimensions which +should be extremely lossy right I lose a + + align:start position:0% +should be extremely lossy right I lose a + + + align:start position:0% +should be extremely lossy right I lose a +lot of information and indeed I do + + align:start position:0% +lot of information and indeed I do + + + align:start position:0% +lot of information and indeed I do +because I'm one of these guys and I'm + + align:start position:0% +because I'm one of these guys and I'm + + + align:start position:0% +because I'm one of these guys and I'm +pretty sure I'm very different from this + + align:start position:0% +pretty sure I'm very different from this + + + align:start position:0% +pretty sure I'm very different from this +guy even though probably from an + + align:start position:0% +guy even though probably from an + + + align:start position:0% +guy even though probably from an +American perspective it's we're all the + + align:start position:0% +American perspective it's we're all the + + + align:start position:0% +American perspective it's we're all the +same uh but uh I think we have like + + align:start position:0% +same uh but uh I think we have like + + + align:start position:0% +same uh but uh I think we have like +slightly different uh genomes and uh and + + align:start position:0% +slightly different uh genomes and uh and + + + align:start position:0% +slightly different uh genomes and uh and +so the thing is now we have this uh so + + align:start position:0% +so the thing is now we have this uh so + + + align:start position:0% +so the thing is now we have this uh so +you see there's lots of Swiss that + + align:start position:0% +you see there's lots of Swiss that + + + align:start position:0% +you see there's lots of Swiss that +participate in this but actually those + + align:start position:0% +participate in this but actually those + + + align:start position:0% +participate in this but actually those +two principal components recover sort of + + align:start position:0% +two principal components recover sort of + + + align:start position:0% +two principal components recover sort of +the map of Europe I mean okay again uh + + align:start position:0% +the map of Europe I mean okay again uh + + + align:start position:0% +the map of Europe I mean okay again uh +this is actually maybe fine grain uh for + + align:start position:0% +this is actually maybe fine grain uh for + + + align:start position:0% +this is actually maybe fine grain uh for +you guys but you right here there's + + align:start position:0% +you guys but you right here there's + + + align:start position:0% +you guys but you right here there's +Portugal and Spain which are uh those + + align:start position:0% +Portugal and Spain which are uh those + + + align:start position:0% +Portugal and Spain which are uh those +colar so here is colar coded and here is + + align:start position:0% +colar so here is colar coded and here is + + + align:start position:0% +colar so here is colar coded and here is +turkey of course uh which we know has + + align:start position:0% +turkey of course uh which we know has + + + align:start position:0% +turkey of course uh which we know has +very different um uh uh genomes right so + + align:start position:0% +very different um uh uh genomes right so + + + align:start position:0% +very different um uh uh genomes right so +uh Turks are very at the boundary right + + align:start position:0% +uh Turks are very at the boundary right + + + align:start position:0% +uh Turks are very at the boundary right +so you can see all the greens they stay + + align:start position:0% +so you can see all the greens they stay + + + align:start position:0% +so you can see all the greens they stay +very far apart from everything else and + + align:start position:0% +very far apart from everything else and + + + align:start position:0% +very far apart from everything else and +then the rest here is pretty mixed uh + + align:start position:0% +then the rest here is pretty mixed uh + + + align:start position:0% +then the rest here is pretty mixed uh +but you know it sort of recovers if you + + align:start position:0% +but you know it sort of recovers if you + + + align:start position:0% +but you know it sort of recovers if you +look at the color it sort of recovers + + align:start position:0% +look at the color it sort of recovers + + + align:start position:0% +look at the color it sort of recovers +that so in a way those two principal + + align:start position:0% +that so in a way those two principal + + + align:start position:0% +that so in a way those two principal +components are just the geographic + + align:start position:0% +components are just the geographic + + + align:start position:0% +components are just the geographic +feature so if you insist on taking only + + align:start position:0% +feature so if you insist on taking only + + + align:start position:0% +feature so if you insist on taking only +two geograph two uh uh to to compress + + align:start position:0% +two geograph two uh uh to to compress + + + align:start position:0% +two geograph two uh uh to to compress +all the gomic information of these + + align:start position:0% +all the gomic information of these + + + align:start position:0% +all the gomic information of these +people into two numbers what you're + + align:start position:0% +people into two numbers what you're + + + align:start position:0% +people into two numbers what you're +actually going to get is longitude and + + align:start position:0% +actually going to get is longitude and + + + align:start position:0% +actually going to get is longitude and +latitude which you know is somewhat + + align:start position:0% +latitude which you know is somewhat + + + align:start position:0% +latitude which you know is somewhat +surprising but not so much if you think + + align:start position:0% +surprising but not so much if you think + + + align:start position:0% +surprising but not so much if you think +that it's been pre-processed all right + + align:start position:0% +that it's been pre-processed all right + + + align:start position:0% +that it's been pre-processed all right +um + + align:start position:0% +um + + + align:start position:0% +um +so okay so what do you do uh uh Beyond + + align:start position:0% +so okay so what do you do uh uh Beyond + + + align:start position:0% +so okay so what do you do uh uh Beyond +um practice well you know you could try + + align:start position:0% +um practice well you know you could try + + + align:start position:0% +um practice well you know you could try +to actually study those things if you + + align:start position:0% +to actually study those things if you + + + align:start position:0% +to actually study those things if you +think about it for a second we did not + + align:start position:0% +think about it for a second we did not + + + align:start position:0% +think about it for a second we did not +do any + + align:start position:0% +do any + + + align:start position:0% +do any +statistics I talked to to you about IID + + align:start position:0% +statistics I talked to to you about IID + + + align:start position:0% +statistics I talked to to you about IID +observations but we never used the fact + + align:start position:0% +observations but we never used the fact + + + align:start position:0% +observations but we never used the fact +that they were independent right the way + + align:start position:0% +that they were independent right the way + + + align:start position:0% +that they were independent right the way +we typically use independent to have + + align:start position:0% +we typically use independent to have + + + align:start position:0% +we typically use independent to have +Central limit the maybe uh I mentioned + + align:start position:0% +Central limit the maybe uh I mentioned + + + align:start position:0% +Central limit the maybe uh I mentioned +the fact that the co variances if they + + align:start position:0% +the fact that the co variances if they + + + align:start position:0% +the fact that the co variances if they +were Gan would actually give me + + align:start position:0% +were Gan would actually give me + + + align:start position:0% +were Gan would actually give me +something which is independent we didn't + + align:start position:0% +something which is independent we didn't + + + align:start position:0% +something which is independent we didn't +care this was a data analysis data + + align:start position:0% +care this was a data analysis data + + + align:start position:0% +care this was a data analysis data +mining process that we did I give you + + align:start position:0% +mining process that we did I give you + + + align:start position:0% +mining process that we did I give you +points and you just you know put them + + align:start position:0% +points and you just you know put them + + + align:start position:0% +points and you just you know put them +through the crank there was an algorithm + + align:start position:0% +through the crank there was an algorithm + + + align:start position:0% +through the crank there was an algorithm +in six steps and you just put it through + + align:start position:0% +in six steps and you just put it through + + + align:start position:0% +in six steps and you just put it through +and that's what you got now of course + + align:start position:0% +and that's what you got now of course + + + align:start position:0% +and that's what you got now of course +there's some work which studies says + + align:start position:0% +there's some work which studies says + + + align:start position:0% +there's some work which studies says +okay if my data is actually generated + + align:start position:0% +okay if my data is actually generated + + + align:start position:0% +okay if my data is actually generated +from some process maybe my points are + + align:start position:0% +from some process maybe my points are + + + align:start position:0% +from some process maybe my points are +multivariate gaussian with some + + align:start position:0% +multivariate gaussian with some + + + align:start position:0% +multivariate gaussian with some +structure on the ciance how well am I + + align:start position:0% +structure on the ciance how well am I + + + align:start position:0% +structure on the ciance how well am I +recovering the ciance structure and + + align:start position:0% +recovering the ciance structure and + + + align:start position:0% +recovering the ciance structure and +that's where statistics kicks in and + + align:start position:0% +that's where statistics kicks in and + + + align:start position:0% +that's where statistics kicks in and +that's where we stop all right so this + + align:start position:0% +that's where we stop all right so this + + + align:start position:0% +that's where we stop all right so this +is actually a bit more difficult to to + + align:start position:0% +is actually a bit more difficult to to + + + align:start position:0% +is actually a bit more difficult to to +study but in a way it's not entirely + + align:start position:0% +study but in a way it's not entirely + + + align:start position:0% +study but in a way it's not entirely +satisfactory because we could work for a + + align:start position:0% +satisfactory because we could work for a + + + align:start position:0% +satisfactory because we could work for a +couple boards and I would just basically + + align:start position:0% +couple boards and I would just basically + + + align:start position:0% +couple boards and I would just basically +sort of reverse engineer this and find + + align:start position:0% +sort of reverse engineer this and find + + + align:start position:0% +sort of reverse engineer this and find +some models under which it's a good idea + + align:start position:0% +some models under which it's a good idea + + + align:start position:0% +some models under which it's a good idea +to do that all right and what are those + + align:start position:0% +to do that all right and what are those + + + align:start position:0% +to do that all right and what are those +models well those are the models that + + align:start position:0% +models well those are the models that + + + align:start position:0% +models well those are the models that +sort of give you sort of prominent + + align:start position:0% +sort of give you sort of prominent + + + align:start position:0% +sort of give you sort of prominent +directions that you want to find and it + + align:start position:0% +directions that you want to find and it + + + align:start position:0% +directions that you want to find and it +will say yes if you have enough + + align:start position:0% +will say yes if you have enough + + + align:start position:0% +will say yes if you have enough +observations you will find those + + align:start position:0% +observations you will find those + + + align:start position:0% +observations you will find those +Direction along which your data is + + align:start position:0% +Direction along which your data is + + + align:start position:0% +Direction along which your data is +elongated okay so that's essentially uh + + align:start position:0% +elongated okay so that's essentially uh + + + align:start position:0% +elongated okay so that's essentially uh +uh uh what you want to do okay so um + + align:start position:0% +uh uh what you want to do okay so um + + + align:start position:0% +uh uh what you want to do okay so um +that's exactly uh what this thing is + + align:start position:0% +that's exactly uh what this thing is + + + align:start position:0% +that's exactly uh what this thing is +telling you so where does the statistics + + align:start position:0% +telling you so where does the statistics + + + align:start position:0% +telling you so where does the statistics +Lie from well everything remember so + + align:start position:0% +Lie from well everything remember so + + + align:start position:0% +Lie from well everything remember so +actually that's where Elena was confused + + align:start position:0% +actually that's where Elena was confused + + + align:start position:0% +actually that's where Elena was confused +the idea was to say well if I uh uh I + + align:start position:0% +the idea was to say well if I uh uh I + + + align:start position:0% +the idea was to say well if I uh uh I +have a true ciance Matrix Sigma and I'm + + align:start position:0% +have a true ciance Matrix Sigma and I'm + + + align:start position:0% +have a true ciance Matrix Sigma and I'm +never really have access to it I'm just + + align:start position:0% +never really have access to it I'm just + + + align:start position:0% +never really have access to it I'm just +running PCA on the empirical ciance + + align:start position:0% +running PCA on the empirical ciance + + + align:start position:0% +running PCA on the empirical ciance +Matrix how do those results relate right + + align:start position:0% +Matrix how do those results relate right + + + align:start position:0% +Matrix how do those results relate right +and this is something that you can study + + align:start position:0% +and this is something that you can study + + + align:start position:0% +and this is something that you can study +so for example if n goes to infinity and + + align:start position:0% +so for example if n goes to infinity and + + + align:start position:0% +so for example if n goes to infinity and +the and the size of your uh and the size + + align:start position:0% +the and the size of your uh and the size + + + align:start position:0% +the and the size of your uh and the size +of your um uh uh the the number of + + align:start position:0% +of your um uh uh the the number of + + + align:start position:0% +of your um uh uh the the number of +points your dimension is fixed then s + + align:start position:0% +points your dimension is fixed then s + + + align:start position:0% +points your dimension is fixed then s +goes to Sigma in any sense you want + + align:start position:0% +goes to Sigma in any sense you want + + + align:start position:0% +goes to Sigma in any sense you want +maybe each entry is going to each entry + + align:start position:0% +maybe each entry is going to each entry + + + align:start position:0% +maybe each entry is going to each entry +of Sigma for example so s is a good + + align:start position:0% +of Sigma for example so s is a good + + + align:start position:0% +of Sigma for example so s is a good +estimator we know that the empirical + + align:start position:0% +estimator we know that the empirical + + + align:start position:0% +estimator we know that the empirical +variance is a consistent estimator and + + align:start position:0% +variance is a consistent estimator and + + + align:start position:0% +variance is a consistent estimator and +if D is fixed this is actually not an + + align:start position:0% +if D is fixed this is actually not an + + + align:start position:0% +if D is fixed this is actually not an +issue so in particular if you run PCA on + + align:start position:0% +issue so in particular if you run PCA on + + + align:start position:0% +issue so in particular if you run PCA on +the sample cence Matrix you look at say + + align:start position:0% +the sample cence Matrix you look at say + + + align:start position:0% +the sample cence Matrix you look at say +V1 then V1 is going to converge to the + + align:start position:0% +V1 then V1 is going to converge to the + + + align:start position:0% +V1 then V1 is going to converge to the +largest agon Vector of Sigma as n goes + + align:start position:0% +largest agon Vector of Sigma as n goes + + + align:start position:0% +largest agon Vector of Sigma as n goes +to Infinity but for D + + align:start position:0% +to Infinity but for D + + + align:start position:0% +to Infinity but for D +fixed and that's you know that's a story + + align:start position:0% +fixed and that's you know that's a story + + + align:start position:0% +fixed and that's you know that's a story +that we know since you know the 60s more + + align:start position:0% +that we know since you know the 60s more + + + align:start position:0% +that we know since you know the 60s more +recently people have started challenging + + align:start position:0% +recently people have started challenging + + + align:start position:0% +recently people have started challenging +this because what's happening when you + + align:start position:0% +this because what's happening when you + + + align:start position:0% +this because what's happening when you +fix the dimension and let the sample + + align:start position:0% +fix the dimension and let the sample + + + align:start position:0% +fix the dimension and let the sample +size go to Infinity you're certainly not + + align:start position:0% +size go to Infinity you're certainly not + + + align:start position:0% +size go to Infinity you're certainly not +allowing for + + align:start position:0% +allowing for + + + align:start position:0% +allowing for +this right it's certainly not explaining + + align:start position:0% +this right it's certainly not explaining + + + align:start position:0% +this right it's certainly not explaining +to you anything about the fact when D is + + align:start position:0% +to you anything about the fact when D is + + + align:start position:0% +to you anything about the fact when D is +equal to 500,000 and N is equal to 14 + + align:start position:0% +equal to 500,000 and N is equal to 14 + + + align:start position:0% +equal to 500,000 and N is equal to 14 +because when D is fixed and N goes to + + align:start position:0% +because when D is fixed and N goes to + + + align:start position:0% +because when D is fixed and N goes to +Infinity in particular n is much larger + + align:start position:0% +Infinity in particular n is much larger + + + align:start position:0% +Infinity in particular n is much larger +than D which is not the case here and so + + align:start position:0% +than D which is not the case here and so + + + align:start position:0% +than D which is not the case here and so +when n is much larger than d uh things + + align:start position:0% +when n is much larger than d uh things + + + align:start position:0% +when n is much larger than d uh things +go well but if D is less than n it's not + + align:start position:0% +go well but if D is less than n it's not + + + align:start position:0% +go well but if D is less than n it's not +clear what happens in particular if D is + + align:start position:0% +clear what happens in particular if D is + + + align:start position:0% +clear what happens in particular if D is +of the order of + + align:start position:0% +of the order of + + + align:start position:0% +of the order of +n what's happening so there's an entire + + align:start position:0% +n what's happening so there's an entire + + + align:start position:0% +n what's happening so there's an entire +theory in mathematics that's called + + align:start position:0% +theory in mathematics that's called + + + align:start position:0% +theory in mathematics that's called +random Matrix theory that studies the + + align:start position:0% +random Matrix theory that studies the + + + align:start position:0% +random Matrix theory that studies the +behavior of exactly this questions what + + align:start position:0% +behavior of exactly this questions what + + + align:start position:0% +behavior of exactly this questions what +is the behavior of the spectrum the igen + + align:start position:0% +is the behavior of the spectrum the igen + + + align:start position:0% +is the behavior of the spectrum the igen +values and the igen vectors of a matrix + + align:start position:0% +values and the igen vectors of a matrix + + + align:start position:0% +values and the igen vectors of a matrix +in which I put random numbers and I let + + align:start position:0% +in which I put random numbers and I let + + + align:start position:0% +in which I put random numbers and I let +so think the Matrix I'm interested in + + align:start position:0% +so think the Matrix I'm interested in + + + align:start position:0% +so think the Matrix I'm interested in +here is the Matrix of x's when I stack + + align:start position:0% +here is the Matrix of x's when I stack + + + align:start position:0% +here is the Matrix of x's when I stack +all my x's next to each other so that's + + align:start position:0% +all my x's next to each other so that's + + + align:start position:0% +all my x's next to each other so that's +a matrix of size say uh d by n right so + + align:start position:0% +a matrix of size say uh d by n right so + + + align:start position:0% +a matrix of size say uh d by n right so +each column is of size d it's one person + + align:start position:0% +each column is of size d it's one person + + + align:start position:0% +each column is of size d it's one person +and so I put them and when I let the + + align:start position:0% +and so I put them and when I let the + + + align:start position:0% +and so I put them and when I let the +Matrix go to Infinity I let both both d + + align:start position:0% +Matrix go to Infinity I let both both d + + + align:start position:0% +Matrix go to Infinity I let both both d +and n Go to Infinity but I want the + + align:start position:0% +and n Go to Infinity but I want the + + + align:start position:0% +and n Go to Infinity but I want the +aspect ratio D Over N to go to some + + align:start position:0% +aspect ratio D Over N to go to some + + + align:start position:0% +aspect ratio D Over N to go to some +constant that's what they do all right + + align:start position:0% +constant that's what they do all right + + + align:start position:0% +constant that's what they do all right +and what's nice is that in the end you + + align:start position:0% +and what's nice is that in the end you + + + align:start position:0% +and what's nice is that in the end you +have this constant let's call it gamma + + align:start position:0% +have this constant let's call it gamma + + + align:start position:0% +have this constant let's call it gamma +that shows up in all the astics and then + + align:start position:0% +that shows up in all the astics and then + + + align:start position:0% +that shows up in all the astics and then +you can replace it by D over n and you + + align:start position:0% +you can replace it by D over n and you + + + align:start position:0% +you can replace it by D over n and you +know that you have you still have a + + align:start position:0% +know that you have you still have a + + + align:start position:0% +know that you have you still have a +handle of both the dimension and the + + align:start position:0% +handle of both the dimension and the + + + align:start position:0% +handle of both the dimension and the +sample size whereas usually the + + align:start position:0% +sample size whereas usually the + + + align:start position:0% +sample size whereas usually the +dimension goes away as you let N Go to + + align:start position:0% +dimension goes away as you let N Go to + + + align:start position:0% +dimension goes away as you let N Go to +Infinity with without having Dimension + + align:start position:0% +Infinity with without having Dimension + + + align:start position:0% +Infinity with without having Dimension +contr and so now when this happens as + + align:start position:0% +contr and so now when this happens as + + + align:start position:0% +contr and so now when this happens as +soon as D Over N goes to a constant you + + align:start position:0% +soon as D Over N goes to a constant you + + + align:start position:0% +soon as D Over N goes to a constant you +can show that essentially uh there's an + + align:start position:0% +can show that essentially uh there's an + + + align:start position:0% +can show that essentially uh there's an +angle between the largest Aon Vector of + + align:start position:0% +angle between the largest Aon Vector of + + + align:start position:0% +angle between the largest Aon Vector of +uh Sigma and the largest value of + + align:start position:0% +uh Sigma and the largest value of + + + align:start position:0% +uh Sigma and the largest value of +largest Aon Vector of s as n and D go to + + align:start position:0% +largest Aon Vector of s as n and D go to + + + align:start position:0% +largest Aon Vector of s as n and D go to +Infinity there's always an angle you can + + align:start position:0% +Infinity there's always an angle you can + + + align:start position:0% +Infinity there's always an angle you can +actually write it explicitly and it's an + + align:start position:0% +actually write it explicitly and it's an + + + align:start position:0% +actually write it explicitly and it's an +angle that depends on this ratio gamma + + align:start position:0% +angle that depends on this ratio gamma + + + align:start position:0% +angle that depends on this ratio gamma +this asmic ratio of the ovine and so + + align:start position:0% +this asmic ratio of the ovine and so + + + align:start position:0% +this asmic ratio of the ovine and so +there's been a lot + + align:start position:0% +there's been a lot + + + align:start position:0% +there's been a lot +of understanding how to correct how to + + align:start position:0% +of understanding how to correct how to + + + align:start position:0% +of understanding how to correct how to +pay attention to this this creates some + + align:start position:0% +pay attention to this this creates some + + + align:start position:0% +pay attention to this this creates some +biases that were sort of overlooked + + align:start position:0% +biases that were sort of overlooked + + + align:start position:0% +biases that were sort of overlooked +before in particular when I do + + align:start position:0% +before in particular when I do + + + align:start position:0% +before in particular when I do +this this is not the proportion of + + align:start position:0% +this this is not the proportion of + + + align:start position:0% +this this is not the proportion of +explained variance when n and D are + + align:start position:0% +explained variance when n and D are + + + align:start position:0% +explained variance when n and D are +similar this is an estimated number + + align:start position:0% +similar this is an estimated number + + + align:start position:0% +similar this is an estimated number +computed from s this is computed from s + + align:start position:0% +computed from s this is computed from s + + + align:start position:0% +computed from s this is computed from s +all these guys are computed from s so + + align:start position:0% +all these guys are computed from s so + + + align:start position:0% +all these guys are computed from s so +those are actually not exactly where you + + align:start position:0% +those are actually not exactly where you + + + align:start position:0% +those are actually not exactly where you +want them to be and there's some nice + + align:start position:0% +want them to be and there's some nice + + + align:start position:0% +want them to be and there's some nice +work that allows you to recalibrate what + + align:start position:0% +work that allows you to recalibrate what + + + align:start position:0% +work that allows you to recalibrate what +this ratio should be how this ratio + + align:start position:0% +this ratio should be how this ratio + + + align:start position:0% +this ratio should be how this ratio +should be computed so it's a better + + align:start position:0% +should be computed so it's a better + + + align:start position:0% +should be computed so it's a better +representative of what the percentage of + + align:start position:0% +representative of what the percentage of + + + align:start position:0% +representative of what the percentage of +or the proportion of explained variance + + align:start position:0% +or the proportion of explained variance + + + align:start position:0% +or the proportion of explained variance +actually + + align:start position:0% +actually + + + align:start position:0% +actually +is all right so then of course there's + + align:start position:0% +is all right so then of course there's + + + align:start position:0% +is all right so then of course there's +the question of so that's when D Over N + + align:start position:0% +the question of so that's when D Over N + + + align:start position:0% +the question of so that's when D Over N +goes to some constant so the best case + + align:start position:0% +goes to some constant so the best case + + + align:start position:0% +goes to some constant so the best case +that that was you know 60s D is fixed n + + align:start position:0% +that that was you know 60s D is fixed n + + + align:start position:0% +that that was you know 60s D is fixed n +is much larger than D and then renom + + align:start position:0% +is much larger than D and then renom + + + align:start position:0% +is much larger than D and then renom +Matrix Theory tells you well d and n are + + align:start position:0% +Matrix Theory tells you well d and n are + + + align:start position:0% +Matrix Theory tells you well d and n are +sort of the same order of magnitude when + + align:start position:0% +sort of the same order of magnitude when + + + align:start position:0% +sort of the same order of magnitude when +they go to Infinity the ratio goes to + + align:start position:0% +they go to Infinity the ratio goes to + + + align:start position:0% +they go to Infinity the ratio goes to +some constant think of it as being order + + align:start position:0% +some constant think of it as being order + + + align:start position:0% +some constant think of it as being order +one to be fair if D is 100 times larger + + align:start position:0% +one to be fair if D is 100 times larger + + + align:start position:0% +one to be fair if D is 100 times larger +than n it still works and uh it depends + + align:start position:0% +than n it still works and uh it depends + + + align:start position:0% +than n it still works and uh it depends +on what you think with the infinity is + + align:start position:0% +on what you think with the infinity is + + + align:start position:0% +on what you think with the infinity is +at this point but I think the random + + align:start position:0% +at this point but I think the random + + + align:start position:0% +at this point but I think the random +Matrix Theory results are very useful + + align:start position:0% +Matrix Theory results are very useful + + + align:start position:0% +Matrix Theory results are very useful +but then even in this case I told you + + align:start position:0% +but then even in this case I told you + + + align:start position:0% +but then even in this case I told you +that the leading aant Vector of s is + + align:start position:0% +that the leading aant Vector of s is + + + align:start position:0% +that the leading aant Vector of s is +actually an angle of the leading Aon + + align:start position:0% +actually an angle of the leading Aon + + + align:start position:0% +actually an angle of the leading Aon +Vector of uh right so what's happening + + align:start position:0% +Vector of uh right so what's happening + + + align:start position:0% +Vector of uh right so what's happening +is + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +so let's say that D Over N goes to some + + align:start position:0% +so let's say that D Over N goes to some + + + align:start position:0% +so let's say that D Over N goes to some +gamma okay and what I claim is that if + + align:start position:0% +gamma okay and what I claim is that if + + + align:start position:0% +gamma okay and what I claim is that if +you look at uh so that's V1 that's the + + align:start position:0% +you look at uh so that's V1 that's the + + + align:start position:0% +you look at uh so that's V1 that's the +V1 of s and then there's the V1 of uh so + + align:start position:0% +V1 of s and then there's the V1 of uh so + + + align:start position:0% +V1 of s and then there's the V1 of uh so +this should be of size + + align:start position:0% +this should be of size + + + align:start position:0% +this should be of size +one uh so that's the V1 of Sigma then + + align:start position:0% +one uh so that's the V1 of Sigma then + + + align:start position:0% +one uh so that's the V1 of Sigma then +those things are going to have an angle + + align:start position:0% +those things are going to have an angle + + + align:start position:0% +those things are going to have an angle +which is some function of gamma it's + + align:start position:0% +which is some function of gamma it's + + + align:start position:0% +which is some function of gamma it's +complicated but there's a function of + + align:start position:0% +complicated but there's a function of + + + align:start position:0% +complicated but there's a function of +gamma that you can see there under some + + align:start position:0% +gamma that you can see there under some + + + align:start position:0% +gamma that you can see there under some +model okay when gamma goes to Infinity + + align:start position:0% +model okay when gamma goes to Infinity + + + align:start position:0% +model okay when gamma goes to Infinity +which means that D is now much larer + + align:start position:0% +which means that D is now much larer + + + align:start position:0% +which means that D is now much larer +than n this angle is 90° which means + + align:start position:0% +than n this angle is 90° which means + + + align:start position:0% +than n this angle is 90° which means +that you're getting + + align:start position:0% +that you're getting + + + align:start position:0% +that you're getting +nothing + + align:start position:0% + + + + align:start position:0% + +yeah no right that's the consistent the + + align:start position:0% +yeah no right that's the consistent the + + + align:start position:0% +yeah no right that's the consistent the +fact that it's consistent when uh right + + align:start position:0% +fact that it's consistent when uh right + + + align:start position:0% +fact that it's consistent when uh right +so the angle is a + + align:start position:0% + + + + align:start position:0% + +function D is not a constant so if D is + + align:start position:0% +function D is not a constant so if D is + + + align:start position:0% +function D is not a constant so if D is +little o of n then gamma goes to zero + + align:start position:0% +little o of n then gamma goes to zero + + + align:start position:0% +little o of n then gamma goes to zero +and F of gamma goes to zero so F of + + align:start position:0% +and F of gamma goes to zero so F of + + + align:start position:0% +and F of gamma goes to zero so F of +gamma is a function that uh so for + + align:start position:0% +gamma is a function that uh so for + + + align:start position:0% +gamma is a function that uh so for +example if I look at so if F of gamma + + align:start position:0% +example if I look at so if F of gamma + + + align:start position:0% +example if I look at so if F of gamma +this is the sign of the angle for + + align:start position:0% +this is the sign of the angle for + + + align:start position:0% +this is the sign of the angle for +example then it's a function that starts + + align:start position:0% +example then it's a function that starts + + + align:start position:0% +example then it's a function that starts +at zero and that goes like + + align:start position:0% +at zero and that goes like + + + align:start position:0% +at zero and that goes like +this and um but as soon as gamma is + + align:start position:0% +this and um but as soon as gamma is + + + align:start position:0% +this and um but as soon as gamma is +positive it's it goes away from + + align:start position:0% +positive it's it goes away from + + + align:start position:0% +positive it's it goes away from +zero um all right so now what happens is + + align:start position:0% +zero um all right so now what happens is + + + align:start position:0% +zero um all right so now what happens is +that uh so when gamma goes to infin then + + align:start position:0% +that uh so when gamma goes to infin then + + + align:start position:0% +that uh so when gamma goes to infin then +this thing goes to a right angle which + + align:start position:0% +this thing goes to a right angle which + + + align:start position:0% +this thing goes to a right angle which +means I'm getting Just Junk right this + + align:start position:0% +means I'm getting Just Junk right this + + + align:start position:0% +means I'm getting Just Junk right this +is not my leing air Vector so how do you + + align:start position:0% +is not my leing air Vector so how do you + + + align:start position:0% +is not my leing air Vector so how do you +do this well just like everywhere in + + align:start position:0% +do this well just like everywhere in + + + align:start position:0% +do this well just like everywhere in +statistics you have to just make more + + align:start position:0% +statistics you have to just make more + + + align:start position:0% +statistics you have to just make more +assumptions you have to assume that + + align:start position:0% +assumptions you have to assume that + + + align:start position:0% +assumptions you have to assume that +you're not looking for the leading + + align:start position:0% +you're not looking for the leading + + + align:start position:0% +you're not looking for the leading +vector or the direction that carries the + + align:start position:0% +vector or the direction that carries the + + + align:start position:0% +vector or the direction that carries the +most variance but you're looking maybe + + align:start position:0% +most variance but you're looking maybe + + + align:start position:0% +most variance but you're looking maybe +for a special Direction and that's what + + align:start position:0% +for a special Direction and that's what + + + align:start position:0% +for a special Direction and that's what +sparse PCA is doing sparse PCA is saying + + align:start position:0% +sparse PCA is doing sparse PCA is saying + + + align:start position:0% +sparse PCA is doing sparse PCA is saying +I'm not looking for any Direction new + + align:start position:0% +I'm not looking for any Direction new + + + align:start position:0% +I'm not looking for any Direction new +that carries the most variance I'm only + + align:start position:0% +that carries the most variance I'm only + + + align:start position:0% +that carries the most variance I'm only +looking for a a direction U that is + + align:start position:0% +looking for a a direction U that is + + + align:start position:0% +looking for a a direction U that is +sparse think of it for example as having + + align:start position:0% +sparse think of it for example as having + + + align:start position:0% +sparse think of it for example as having +a 10 nonzero coordinates right so that's + + align:start position:0% +a 10 nonzero coordinates right so that's + + + align:start position:0% +a 10 nonzero coordinates right so that's +a lot of directions still to look from + + align:start position:0% +a lot of directions still to look from + + + align:start position:0% +a lot of directions still to look from +to look for but once you do this then + + align:start position:0% +to look for but once you do this then + + + align:start position:0% +to look for but once you do this then +you actually have not only there's a few + + align:start position:0% +you actually have not only there's a few + + + align:start position:0% +you actually have not only there's a few +things that actually you get from doing + + align:start position:0% +things that actually you get from doing + + + align:start position:0% +things that actually you get from doing +this the first one is you actually + + align:start position:0% +this the first one is you actually + + + align:start position:0% +this the first one is you actually +essentially replace d by + + align:start position:0% +essentially replace d by + + + align:start position:0% +essentially replace d by +K which means that n now just sorry not + + align:start position:0% +K which means that n now just sorry not + + + align:start position:0% +K which means that n now just sorry not +let's say s nonzero coefficients you + + align:start position:0% +let's say s nonzero coefficients you + + + align:start position:0% +let's say s nonzero coefficients you +replace d by S which means that n only + + align:start position:0% +replace d by S which means that n only + + + align:start position:0% +replace d by S which means that n only +has to be much lower than S for this + + align:start position:0% +has to be much lower than S for this + + + align:start position:0% +has to be much lower than S for this +thing to actually work now of course + + align:start position:0% +thing to actually work now of course + + + align:start position:0% +thing to actually work now of course +you've set your goal weaker your goal is + + align:start position:0% +you've set your goal weaker your goal is + + + align:start position:0% +you've set your goal weaker your goal is +not to find any Direction only a sparse + + align:start position:0% +not to find any Direction only a sparse + + + align:start position:0% +not to find any Direction only a sparse +Direction but there's something very + + align:start position:0% +Direction but there's something very + + + align:start position:0% +Direction but there's something very +valuable about sparse directions is that + + align:start position:0% +valuable about sparse directions is that + + + align:start position:0% +valuable about sparse directions is that +they actually are interpretable when I + + align:start position:0% +they actually are interpretable when I + + + align:start position:0% +they actually are interpretable when I +found the + + align:start position:0% +found the + + + align:start position:0% +found the +V let's say that the V that I found + + align:start position:0% +V let's say that the V that I found + + + align:start position:0% +V let's say that the V that I found +before was you know 0.2 and then 0.9 and + + align:start position:0% +before was you know 0.2 and then 0.9 and + + + align:start position:0% +before was you know 0.2 and then 0.9 and +then uh 1.1 minus minus three Etc so + + align:start position:0% +then uh 1.1 minus minus three Etc so + + + align:start position:0% +then uh 1.1 minus minus three Etc so +that was the coordinates of my leading + + align:start position:0% +that was the coordinates of my leading + + + align:start position:0% +that was the coordinates of my leading +aged Vector in the original coordinate + + align:start position:0% +aged Vector in the original coordinate + + + align:start position:0% +aged Vector in the original coordinate +system what does it mean well it means + + align:start position:0% +system what does it mean well it means + + + align:start position:0% +system what does it mean well it means +that if I see a large number that means + + align:start position:0% +that if I see a large number that means + + + align:start position:0% +that if I see a large number that means +that this V is very + + align:start position:0% +that this V is very + + + align:start position:0% +that this V is very +close right so that's my original uh + + align:start position:0% +close right so that's my original uh + + + align:start position:0% +close right so that's my original uh +coordinate system let's call it E1 and + + align:start position:0% +coordinate system let's call it E1 and + + + align:start position:0% +coordinate system let's call it E1 and +E2 so that's just you know one zero and + + align:start position:0% +E2 so that's just you know one zero and + + + align:start position:0% +E2 so that's just you know one zero and +then + + align:start position:0% +then + + + align:start position:0% +then +01 then clearly from the coordinates of + + align:start position:0% +01 then clearly from the coordinates of + + + align:start position:0% +01 then clearly from the coordinates of +v i can tell if my V is like this or + + align:start position:0% +v i can tell if my V is like this or + + + align:start position:0% +v i can tell if my V is like this or +it's like this or it's like this right + + align:start position:0% +it's like this or it's like this right + + + align:start position:0% +it's like this or it's like this right +well I mean it should they should all be + + align:start position:0% +well I mean it should they should all be + + + align:start position:0% +well I mean it should they should all be +of the same size right so so I can tell + + align:start position:0% +of the same size right so so I can tell + + + align:start position:0% +of the same size right so so I can tell +if it's here or here or + + align:start position:0% +if it's here or here or + + + align:start position:0% +if it's here or here or +here okay depending on like here that + + align:start position:0% +here okay depending on like here that + + + align:start position:0% +here okay depending on like here that +means I'm going to see something where + + align:start position:0% +means I'm going to see something where + + + align:start position:0% +means I'm going to see something where +the y-coordinate is much larer than the + + align:start position:0% +the y-coordinate is much larer than the + + + align:start position:0% +the y-coordinate is much larer than the +x coordinate here I'm going to see + + align:start position:0% +x coordinate here I'm going to see + + + align:start position:0% +x coordinate here I'm going to see +something where the x coordinate is much + + align:start position:0% +something where the x coordinate is much + + + align:start position:0% +something where the x coordinate is much +larer than the y-coordinate and here I'm + + align:start position:0% +larer than the y-coordinate and here I'm + + + align:start position:0% +larer than the y-coordinate and here I'm +going to see something where the x + + align:start position:0% +going to see something where the x + + + align:start position:0% +going to see something where the x +coordinate is about the same size of the + + align:start position:0% +coordinate is about the same size of the + + + align:start position:0% +coordinate is about the same size of the +y-coordinate so when things starts to be + + align:start position:0% +y-coordinate so when things starts to be + + + align:start position:0% +y-coordinate so when things starts to be +bigger you're going to have to make + + align:start position:0% +bigger you're going to have to make + + + align:start position:0% +bigger you're going to have to make +choices right what does it mean to be + + align:start position:0% +choices right what does it mean to be + + + align:start position:0% +choices right what does it mean to be +bigger when when D is 100,000 what do I + + align:start position:0% +bigger when when D is 100,000 what do I + + + align:start position:0% +bigger when when D is 100,000 what do I +mean those things have to some the sum + + align:start position:0% +mean those things have to some the sum + + + align:start position:0% +mean those things have to some the sum +of the squares of those guys have to be + + align:start position:0% +of the squares of those guys have to be + + + align:start position:0% +of the squares of those guys have to be +of equal to one so they're all very + + align:start position:0% +of equal to one so they're all very + + + align:start position:0% +of equal to one so they're all very +small numbers and so it's hard for you + + align:start position:0% +small numbers and so it's hard for you + + + align:start position:0% +small numbers and so it's hard for you +to tell which one is a big big number + + align:start position:0% +to tell which one is a big big number + + + align:start position:0% +to tell which one is a big big number +and which one's is a small number why + + align:start position:0% +and which one's is a small number why + + + align:start position:0% +and which one's is a small number why +would you want to know this because it's + + align:start position:0% +would you want to know this because it's + + + align:start position:0% +would you want to know this because it's +actually telling you that if V is very + + align:start position:0% +actually telling you that if V is very + + + align:start position:0% +actually telling you that if V is very +close to + + align:start position:0% +close to + + + align:start position:0% +close to +E1 then that means that E1 in the case + + align:start position:0% +E1 then that means that E1 in the case + + + align:start position:0% +E1 then that means that E1 in the case +of the gene example that would mean that + + align:start position:0% +of the gene example that would mean that + + + align:start position:0% +of the gene example that would mean that +E1 is the gene that's very important + + align:start position:0% +E1 is the gene that's very important + + + align:start position:0% +E1 is the gene that's very important +there's maybe there's actually just two + + align:start position:0% +there's maybe there's actually just two + + + align:start position:0% +there's maybe there's actually just two +genes that explain those two things and + + align:start position:0% +genes that explain those two things and + + + align:start position:0% +genes that explain those two things and +those are the genes that have been + + align:start position:0% +those are the genes that have been + + + align:start position:0% +those are the genes that have been +picked up there's two genes that encode + + align:start position:0% +picked up there's two genes that encode + + + align:start position:0% +picked up there's two genes that encode +you know geographic location and that's + + align:start position:0% +you know geographic location and that's + + + align:start position:0% +you know geographic location and that's +it and so it's very important for you to + + align:start position:0% +it and so it's very important for you to + + + align:start position:0% +it and so it's very important for you to +be able to interpret what V means where + + align:start position:0% +be able to interpret what V means where + + + align:start position:0% +be able to interpret what V means where +it has large values it means that maybe + + align:start position:0% +it has large values it means that maybe + + + align:start position:0% +it has large values it means that maybe +it's has large values for E1 E2 and E3 + + align:start position:0% +it's has large values for E1 E2 and E3 + + + align:start position:0% +it's has large values for E1 E2 and E3 +and it means that it's a combination of + + align:start position:0% +and it means that it's a combination of + + + align:start position:0% +and it means that it's a combination of +E1 E2 and E3 and now you can interpret + + align:start position:0% +E1 E2 and E3 and now you can interpret + + + align:start position:0% +E1 E2 and E3 and now you can interpret +because you have only three variables to + + align:start position:0% +because you have only three variables to + + + align:start position:0% +because you have only three variables to +to find and so sparse PCA builds that in + + align:start position:0% +to find and so sparse PCA builds that in + + + align:start position:0% +to find and so sparse PCA builds that in +sparse PCA says listen I'm gonna I'm + + align:start position:0% +sparse PCA says listen I'm gonna I'm + + + align:start position:0% +sparse PCA says listen I'm gonna I'm +going to want to have at most 10 nonzero + + align:start position:0% +going to want to have at most 10 nonzero + + + align:start position:0% +going to want to have at most 10 nonzero +coefficients and the rest I want to be + + align:start position:0% +coefficients and the rest I want to be + + + align:start position:0% +coefficients and the rest I want to be +zero I want to be able to be a + + align:start position:0% +zero I want to be able to be a + + + align:start position:0% +zero I want to be able to be a +combination of at most 10 of my original + + align:start position:0% +combination of at most 10 of my original + + + align:start position:0% +combination of at most 10 of my original +uh uh uh variables and now I can do + + align:start position:0% +uh uh uh variables and now I can do + + + align:start position:0% +uh uh uh variables and now I can do +interpretation so the problem with Spar + + align:start position:0% +interpretation so the problem with Spar + + + align:start position:0% +interpretation so the problem with Spar +B is that it becomes very difficult + + align:start position:0% +B is that it becomes very difficult + + + align:start position:0% +B is that it becomes very difficult +numerically to solve this problem I can + + align:start position:0% +numerically to solve this problem I can + + + align:start position:0% +numerically to solve this problem I can +write it right so the problem is simply + + align:start position:0% +write it right so the problem is simply + + + align:start position:0% +write it right so the problem is simply +you know + + align:start position:0% +you know + + + align:start position:0% +you know +maximize the variance U transpose say + + align:start position:0% +maximize the variance U transpose say + + + align:start position:0% +maximize the variance U transpose say +Su subject to well I want it to have u 2 + + align:start position:0% +Su subject to well I want it to have u 2 + + + align:start position:0% +Su subject to well I want it to have u 2 +equal to one so that's the that's the + + align:start position:0% +equal to one so that's the that's the + + + align:start position:0% +equal to one so that's the that's the +original PCA but now I also want that + + align:start position:0% +original PCA but now I also want that + + + align:start position:0% +original PCA but now I also want that +the sum of the indicators of the UJ that + + align:start position:0% +the sum of the indicators of the UJ that + + + align:start position:0% +the sum of the indicators of the UJ that +are not equal to zero is at most say + + align:start position:0% + + + + align:start position:0% + +10 this constraint is very non-convex so + + align:start position:0% +10 this constraint is very non-convex so + + + align:start position:0% +10 this constraint is very non-convex so +I can relax it to a convex one like we + + align:start position:0% +I can relax it to a convex one like we + + + align:start position:0% +I can relax it to a convex one like we +did for uh linear regression but now + + align:start position:0% +did for uh linear regression but now + + + align:start position:0% +did for uh linear regression but now +I've totally messed up with the fact + + align:start position:0% +I've totally messed up with the fact + + + align:start position:0% +I've totally messed up with the fact +that I could use linear algebra to solve + + align:start position:0% +that I could use linear algebra to solve + + + align:start position:0% +that I could use linear algebra to solve +this problem and so now you have to go + + align:start position:0% +this problem and so now you have to go + + + align:start position:0% +this problem and so now you have to go +to much more complicated optimization + + align:start position:0% +to much more complicated optimization + + + align:start position:0% +to much more complicated optimization +techniques which are called the + + align:start position:0% +techniques which are called the + + + align:start position:0% +techniques which are called the +semi-definite programs which do not + + align:start position:0% +semi-definite programs which do not + + + align:start position:0% +semi-definite programs which do not +scale well in high uh dimensions and so + + align:start position:0% +scale well in high uh dimensions and so + + + align:start position:0% +scale well in high uh dimensions and so +you have to do a bunch of Tricks uh + + align:start position:0% +you have to do a bunch of Tricks uh + + + align:start position:0% +you have to do a bunch of Tricks uh +numerical tricks but there are some + + align:start position:0% +numerical tricks but there are some + + + align:start position:0% +numerical tricks but there are some +packages that Implement some heuristics + + align:start position:0% +packages that Implement some heuristics + + + align:start position:0% +packages that Implement some heuristics +or some other things + + align:start position:0% +or some other things + + + align:start position:0% +or some other things +um iterative thresholding all sorts of + + align:start position:0% +um iterative thresholding all sorts of + + + align:start position:0% +um iterative thresholding all sorts of +various numerical tricks that you can do + + align:start position:0% +various numerical tricks that you can do + + + align:start position:0% +various numerical tricks that you can do +but the problem they're trying to solve + + align:start position:0% +but the problem they're trying to solve + + + align:start position:0% +but the problem they're trying to solve +is exactly this among all directions + + align:start position:0% +is exactly this among all directions + + + align:start position:0% +is exactly this among all directions +that I have Norm one of course because + + align:start position:0% +that I have Norm one of course because + + + align:start position:0% +that I have Norm one of course because +it's a direction that have at most say + + align:start position:0% +it's a direction that have at most say + + + align:start position:0% +it's a direction that have at most say +10 nonzero coordinates I want to find + + align:start position:0% +10 nonzero coordinates I want to find + + + align:start position:0% +10 nonzero coordinates I want to find +the one that maximizes the empirical + + align:start position:0% +the one that maximizes the empirical + + + align:start position:0% +the one that maximizes the empirical +variance + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% + + + + align:start position:0% + +um actually before let me let me just + + align:start position:0% +um actually before let me let me just + + + align:start position:0% +um actually before let me let me just +uh show you + + align:start position:0% + + + + align:start position:0% + +this I wanted to show you an output of + + align:start position:0% +this I wanted to show you an output of + + + align:start position:0% +this I wanted to show you an output of +um of + + align:start position:0% +um of + + + align:start position:0% +um of +uh PCA where people are actually trying + + align:start position:0% +uh PCA where people are actually trying + + + align:start position:0% +uh PCA where people are actually trying +to do + + align:start position:0% + + + + align:start position:0% + +directly + + align:start position:0% + + + + align:start position:0% + +there you + + align:start position:0% +there you + + + align:start position:0% +there you +go + + align:start position:0% + + + + align:start position:0% + +um so right + + align:start position:0% +um so right + + + align:start position:0% +um so right +here you see this is an what's this is + + align:start position:0% +here you see this is an what's this is + + + align:start position:0% +here you see this is an what's this is +SPSS that's a statistical software uh + + align:start position:0% +SPSS that's a statistical software uh + + + align:start position:0% +SPSS that's a statistical software uh +and uh this is an output that was uh + + align:start position:0% +and uh this is an output that was uh + + + align:start position:0% +and uh this is an output that was uh +pre-processed by a professional uh not + + align:start position:0% +pre-processed by a professional uh not + + + align:start position:0% +pre-processed by a professional uh not +pre-process postprocess right so that's + + align:start position:0% +pre-process postprocess right so that's + + + align:start position:0% +pre-process postprocess right so that's +something where they ran PCA so what is + + align:start position:0% +something where they ran PCA so what is + + + align:start position:0% +something where they ran PCA so what is +the data this is raw data about um you + + align:start position:0% +the data this is raw data about um you + + + align:start position:0% +the data this is raw data about um you +know you ask doctors what they think of + + align:start position:0% +know you ask doctors what they think of + + + align:start position:0% +know you ask doctors what they think of +a um the behavior of a particular sales + + align:start position:0% +a um the behavior of a particular sales + + + align:start position:0% +a um the behavior of a particular sales +representative for pharmaceutical + + align:start position:0% +representative for pharmaceutical + + + align:start position:0% +representative for pharmaceutical +companies pharmaceutical companies are + + align:start position:0% +companies pharmaceutical companies are + + + align:start position:0% +companies pharmaceutical companies are +trying to improve their Salesforce and + + align:start position:0% +trying to improve their Salesforce and + + + align:start position:0% +trying to improve their Salesforce and +they're asking doctors how they would + + align:start position:0% +they're asking doctors how they would + + + align:start position:0% +they're asking doctors how they would +they rate what do they value about their + + align:start position:0% +they rate what do they value about their + + + align:start position:0% +they rate what do they value about their +interaction with a sales representative + + align:start position:0% +interaction with a sales representative + + + align:start position:0% +interaction with a sales representative +right so basically there's a bunch of + + align:start position:0% +right so basically there's a bunch of + + + align:start position:0% +right so basically there's a bunch of +questions one is you know offers + + align:start position:0% +questions one is you know offers + + + align:start position:0% +questions one is you know offers +credible point of view + + align:start position:0% +credible point of view + + + align:start position:0% +credible point of view +on something Trends uh provides valuable + + align:start position:0% +on something Trends uh provides valuable + + + align:start position:0% +on something Trends uh provides valuable +networking opportunities right this is + + align:start position:0% +networking opportunities right this is + + + align:start position:0% +networking opportunities right this is +one question rate this on the scale from + + align:start position:0% +one question rate this on the scale from + + + align:start position:0% +one question rate this on the scale from +one to five that was the questions and + + align:start position:0% +one to five that was the questions and + + + align:start position:0% +one to five that was the questions and +they had a bunch of questions like this + + align:start position:0% +they had a bunch of questions like this + + + align:start position:0% +they had a bunch of questions like this +and then they asked you know a thousand + + align:start position:0% +and then they asked you know a thousand + + + align:start position:0% +and then they asked you know a thousand +doctors about to to make those ratings + + align:start position:0% +doctors about to to make those ratings + + + align:start position:0% +doctors about to to make those ratings +and what they want so each doctor now is + + align:start position:0% +and what they want so each doctor now is + + + align:start position:0% +and what they want so each doctor now is +a vector of ratings and they want to + + align:start position:0% +a vector of ratings and they want to + + + align:start position:0% +a vector of ratings and they want to +know if there's different groups of + + align:start position:0% +know if there's different groups of + + + align:start position:0% +know if there's different groups of +doctors what do doctors respond to if + + align:start position:0% +doctors what do doctors respond to if + + + align:start position:0% +doctors what do doctors respond to if +there's different groups then maybe they + + align:start position:0% +there's different groups then maybe they + + + align:start position:0% +there's different groups then maybe they +know that they can actually address them + + align:start position:0% +know that they can actually address them + + + align:start position:0% +know that they can actually address them +separately + + align:start position:0% +separately + + + align:start position:0% +separately +Etc and so to do that of course there's + + align:start position:0% +Etc and so to do that of course there's + + + align:start position:0% +Etc and so to do that of course there's +lots of questions and so what you want + + align:start position:0% +lots of questions and so what you want + + + align:start position:0% +lots of questions and so what you want +is to just first project into lower + + align:start position:0% +is to just first project into lower + + + align:start position:0% +is to just first project into lower +Dimensions so you can actually visualize + + align:start position:0% +Dimensions so you can actually visualize + + + align:start position:0% +Dimensions so you can actually visualize +what's going on and this is what was + + align:start position:0% +what's going on and this is what was + + + align:start position:0% +what's going on and this is what was +done for this right so these are the + + align:start position:0% +done for this right so these are the + + + align:start position:0% +done for this right so these are the +three first principal component that + + align:start position:0% +three first principal component that + + + align:start position:0% +three first principal component that +came out okay and there's no even though + + align:start position:0% +came out okay and there's no even though + + + align:start position:0% +came out okay and there's no even though +we ordered the values of the lambdas + + align:start position:0% +we ordered the values of the lambdas + + + align:start position:0% +we ordered the values of the lambdas +there's no reason why the entry + + align:start position:0% +there's no reason why the entry + + + align:start position:0% +there's no reason why the entry +of V should be ordered and if you look + + align:start position:0% +of V should be ordered and if you look + + + align:start position:0% +of V should be ordered and if you look +at the values of V here they look like + + align:start position:0% +at the values of V here they look like + + + align:start position:0% +at the values of V here they look like +they're pretty much ordered right starts + + align:start position:0% +they're pretty much ordered right starts + + + align:start position:0% +they're pretty much ordered right starts +at 7 point 784 then you're at point + + align:start position:0% +at 7 point 784 then you're at point + + + align:start position:0% +at 7 point 784 then you're at point +three around here there's something that + + align:start position:0% +three around here there's something that + + + align:start position:0% +three around here there's something that +goes up again and then you go down + + align:start position:0% +goes up again and then you go down + + + align:start position:0% +goes up again and then you go down +actually it's marked in red every time + + align:start position:0% +actually it's marked in red every time + + + align:start position:0% +actually it's marked in red every time +it goes up + + align:start position:0% +it goes up + + + align:start position:0% +it goes up +again okay and so now what they did is + + align:start position:0% +again okay and so now what they did is + + + align:start position:0% +again okay and so now what they did is +they said okay I need to interpret those + + align:start position:0% +they said okay I need to interpret those + + + align:start position:0% +they said okay I need to interpret those +guys I need to tell you what this is if + + align:start position:0% +guys I need to tell you what this is if + + + align:start position:0% +guys I need to tell you what this is if +you tell me there's a we found the + + align:start position:0% +you tell me there's a we found the + + + align:start position:0% +you tell me there's a we found the +principal component that really + + align:start position:0% +principal component that really + + + align:start position:0% +principal component that really +discriminates the doctors in two groups + + align:start position:0% +discriminates the doctors in two groups + + + align:start position:0% +discriminates the doctors in two groups +this the the drug company is going to + + align:start position:0% +this the the drug company is going to + + + align:start position:0% +this the the drug company is going to +come back to you and say okay what is + + align:start position:0% +come back to you and say okay what is + + + align:start position:0% +come back to you and say okay what is +this what is this characteristic and you + + align:start position:0% +this what is this characteristic and you + + + align:start position:0% +this what is this characteristic and you +say oh it's actually a linear + + align:start position:0% +say oh it's actually a linear + + + align:start position:0% +say oh it's actually a linear +combination of 40 characteristics and + + align:start position:0% +combination of 40 characteristics and + + + align:start position:0% +combination of 40 characteristics and +they said well you know we don't need + + align:start position:0% +they said well you know we don't need + + + align:start position:0% +they said well you know we don't need +you to do that right I mean it's cannot + + align:start position:0% +you to do that right I mean it's cannot + + + align:start position:0% +you to do that right I mean it's cannot +be a linear combination of anything you + + align:start position:0% +be a linear combination of anything you + + + align:start position:0% +be a linear combination of anything you +need to ask and so for that there's + + align:start position:0% +need to ask and so for that there's + + + align:start position:0% +need to ask and so for that there's +first of all there's a post-processing + + align:start position:0% +first of all there's a post-processing + + + align:start position:0% +first of all there's a post-processing +of of PCA which says okay once I + + align:start position:0% +of of PCA which says okay once I + + + align:start position:0% +of of PCA which says okay once I +actually say found three principal + + align:start position:0% +actually say found three principal + + + align:start position:0% +actually say found three principal +components that means that I found the + + align:start position:0% +components that means that I found the + + + align:start position:0% +components that means that I found the +this Dimension three space right on + + align:start position:0% +this Dimension three space right on + + + align:start position:0% +this Dimension three space right on +which I want to project my points in + + align:start position:0% +which I want to project my points in + + + align:start position:0% +which I want to project my points in +this space I can can pick any direction + + align:start position:0% +this space I can can pick any direction + + + align:start position:0% +this space I can can pick any direction +I want so the first thing is that you do + + align:start position:0% +I want so the first thing is that you do + + + align:start position:0% +I want so the first thing is that you do +some sort of local Arrangement so that + + align:start position:0% +some sort of local Arrangement so that + + + align:start position:0% +some sort of local Arrangement so that +those things look like they're + + align:start position:0% +those things look like they're + + + align:start position:0% +those things look like they're +increasing and then decreasing so you + + align:start position:0% +increasing and then decreasing so you + + + align:start position:0% +increasing and then decreasing so you +just like do you just change you rotate + + align:start position:0% +just like do you just change you rotate + + + align:start position:0% +just like do you just change you rotate +your uh coordinate system in this + + align:start position:0% +your uh coordinate system in this + + + align:start position:0% +your uh coordinate system in this +three-dimensional space that you've + + align:start position:0% +three-dimensional space that you've + + + align:start position:0% +three-dimensional space that you've +actually + + align:start position:0% +actually + + + align:start position:0% +actually +isolated and so once you do this the + + align:start position:0% +isolated and so once you do this the + + + align:start position:0% +isolated and so once you do this the +reason to do that is that it sort of + + align:start position:0% +reason to do that is that it sort of + + + align:start position:0% +reason to do that is that it sort of +makes some big sharp differences between + + align:start position:0% +makes some big sharp differences between + + + align:start position:0% +makes some big sharp differences between +large and small values of the + + align:start position:0% +large and small values of the + + + align:start position:0% +large and small values of the +coordinates of the thing you had and why + + align:start position:0% +coordinates of the thing you had and why + + + align:start position:0% +coordinates of the thing you had and why +do you want this because now you can say + + align:start position:0% +do you want this because now you can say + + + align:start position:0% +do you want this because now you can say +well I'm going to start looking at the + + align:start position:0% +well I'm going to start looking at the + + + align:start position:0% +well I'm going to start looking at the +ones that have large values and what do + + align:start position:0% +ones that have large values and what do + + + align:start position:0% +ones that have large values and what do +they say they say in-depth knowledge + + align:start position:0% +they say they say in-depth knowledge + + + align:start position:0% +they say they say in-depth knowledge +in-depth knowledge in-depth knowledge + + align:start position:0% +in-depth knowledge in-depth knowledge + + + align:start position:0% +in-depth knowledge in-depth knowledge +knowledge about this thing is clearly + + align:start position:0% +knowledge about this thing is clearly + + + align:start position:0% +knowledge about this thing is clearly +something that actually characterizes + + align:start position:0% +something that actually characterizes + + + align:start position:0% +something that actually characterizes +the knowledge of my uh uh sales + + align:start position:0% +the knowledge of my uh uh sales + + + align:start position:0% +the knowledge of my uh uh sales +representative and so that's something + + align:start position:0% +representative and so that's something + + + align:start position:0% +representative and so that's something +that doctors are sensitive to that's + + align:start position:0% +that doctors are sensitive to that's + + + align:start position:0% +that doctors are sensitive to that's +something that really discriminates the + + align:start position:0% +something that really discriminates the + + + align:start position:0% +something that really discriminates the +doctors in a way there's lots of + + align:start position:0% +doctors in a way there's lots of + + + align:start position:0% +doctors in a way there's lots of +variance along those things or at least + + align:start position:0% +variance along those things or at least + + + align:start position:0% +variance along those things or at least +a lot of variance uh uh I mean doctors + + align:start position:0% +a lot of variance uh uh I mean doctors + + + align:start position:0% +a lot of variance uh uh I mean doctors +are separated in terms of their + + align:start position:0% +are separated in terms of their + + + align:start position:0% +are separated in terms of their +experience with respect to this all + + align:start position:0% +experience with respect to this all + + + align:start position:0% +experience with respect to this all +right and so what they did is said okay + + align:start position:0% +right and so what they did is said okay + + + align:start position:0% +right and so what they did is said okay +all these guys some of those they have + + align:start position:0% +all these guys some of those they have + + + align:start position:0% +all these guys some of those they have +large values but I don't know how to + + align:start position:0% +large values but I don't know how to + + + align:start position:0% +large values but I don't know how to +interpret them and so I'm just going to + + align:start position:0% +interpret them and so I'm just going to + + + align:start position:0% +interpret them and so I'm just going to +put the first block and I'm going to + + align:start position:0% +put the first block and I'm going to + + + align:start position:0% +put the first block and I'm going to +call it medical knowledge because all + + align:start position:0% +call it medical knowledge because all + + + align:start position:0% +call it medical knowledge because all +those things are knowledge about Med + + align:start position:0% +those things are knowledge about Med + + + align:start position:0% +those things are knowledge about Med +medical stuff then here I didn't know + + align:start position:0% +medical stuff then here I didn't know + + + align:start position:0% +medical stuff then here I didn't know +how to interpret those guys but those + + align:start position:0% +how to interpret those guys but those + + + align:start position:0% +how to interpret those guys but those +guys there's a big clump of large + + align:start position:0% +guys there's a big clump of large + + + align:start position:0% +guys there's a big clump of large +coordinates and they're about you know + + align:start position:0% +coordinates and they're about you know + + + align:start position:0% +coordinates and they're about you know +respectful of my time listens friendly + + align:start position:0% +respectful of my time listens friendly + + + align:start position:0% +respectful of my time listens friendly +but courteous this is all about the + + align:start position:0% +but courteous this is all about the + + + align:start position:0% +but courteous this is all about the +quality of interaction so this block was + + align:start position:0% +quality of interaction so this block was + + + align:start position:0% +quality of interaction so this block was +actually called quality of + + align:start position:0% +actually called quality of + + + align:start position:0% +actually called quality of +interaction and then there was a third + + align:start position:0% +interaction and then there was a third + + + align:start position:0% +interaction and then there was a third +block which you can tell starts to be + + align:start position:0% +block which you can tell starts to be + + + align:start position:0% +block which you can tell starts to be +spreading a little thin there's just + + align:start position:0% +spreading a little thin there's just + + + align:start position:0% +spreading a little thin there's just +much less of them but this thing was + + align:start position:0% +much less of them but this thing was + + + align:start position:0% +much less of them but this thing was +actually called fair and critical + + align:start position:0% +actually called fair and critical + + + align:start position:0% +actually called fair and critical +opinion and so now you have three + + align:start position:0% +opinion and so now you have three + + + align:start position:0% +opinion and so now you have three +discriminating directions and you can + + align:start position:0% +discriminating directions and you can + + + align:start position:0% +discriminating directions and you can +actually give them a name wouldn't it be + + align:start position:0% +actually give them a name wouldn't it be + + + align:start position:0% +actually give them a name wouldn't it be +beautiful if all the numbers in the gray + + align:start position:0% +beautiful if all the numbers in the gray + + + align:start position:0% +beautiful if all the numbers in the gray +box came non zero and all the other + + align:start position:0% +box came non zero and all the other + + + align:start position:0% +box came non zero and all the other +numbers came zero there was no ad hoc + + align:start position:0% +numbers came zero there was no ad hoc + + + align:start position:0% +numbers came zero there was no ad hoc +choice I mean this is probably an + + align:start position:0% +choice I mean this is probably an + + + align:start position:0% +choice I mean this is probably an +afternoon of work to like scratch out + + align:start position:0% +afternoon of work to like scratch out + + + align:start position:0% +afternoon of work to like scratch out +all these numbers and put all these + + align:start position:0% +all these numbers and put all these + + + align:start position:0% +all these numbers and put all these +color codes Etc right whereas you could + + align:start position:0% +color codes Etc right whereas you could + + + align:start position:0% +color codes Etc right whereas you could +just have something that tells you okay + + align:start position:0% +just have something that tells you okay + + + align:start position:0% +just have something that tells you okay +here the nonzeros you know if you can + + align:start position:0% +here the nonzeros you know if you can + + + align:start position:0% +here the nonzeros you know if you can +actually make a story around why this + + align:start position:0% +actually make a story around why this + + + align:start position:0% +actually make a story around why this +group of thing actually makes sense such + + align:start position:0% +group of thing actually makes sense such + + + align:start position:0% +group of thing actually makes sense such +as it is medical knowledge then good for + + align:start position:0% +as it is medical knowledge then good for + + + align:start position:0% +as it is medical knowledge then good for +you otherwise you could just say I can't + + align:start position:0% +you otherwise you could just say I can't + + + align:start position:0% +you otherwise you could just say I can't +and that's what sparse PCA does for you + + align:start position:0% +and that's what sparse PCA does for you + + + align:start position:0% +and that's what sparse PCA does for you +sparse PCA outputs something where all + + align:start position:0% +sparse PCA outputs something where all + + + align:start position:0% +sparse PCA outputs something where all +these numbers would be zero and there + + align:start position:0% +these numbers would be zero and there + + + align:start position:0% +these numbers would be zero and there +would be exactly say 10 nonzero + + align:start position:0% +would be exactly say 10 nonzero + + + align:start position:0% +would be exactly say 10 nonzero +coordinates and you can turn this knob + + align:start position:0% +coordinates and you can turn this knob + + + align:start position:0% +coordinates and you can turn this knob +of 10 you could make it nine you know if + + align:start position:0% +of 10 you could make it nine you know if + + + align:start position:0% +of 10 you could make it nine you know if +you're depending on what your major is + + align:start position:0% +you're depending on what your major is + + + align:start position:0% +you're depending on what your major is +maybe you can actually go on with 20 of + + align:start position:0% +maybe you can actually go on with 20 of + + + align:start position:0% +maybe you can actually go on with 20 of +them and have the ability to tell the + + align:start position:0% +them and have the ability to tell the + + + align:start position:0% +them and have the ability to tell the +story about 20 different variables and + + align:start position:0% +story about 20 different variables and + + + align:start position:0% +story about 20 different variables and +how they fit in the same group and + + align:start position:0% +how they fit in the same group and + + + align:start position:0% +how they fit in the same group and +depending on how you f you could it's + + align:start position:0% +depending on how you f you could it's + + + align:start position:0% +depending on how you f you could it's +easy to re run the PCA depending on the + + align:start position:0% +easy to re run the PCA depending on the + + + align:start position:0% +easy to re run the PCA depending on the +value that you want here and so you + + align:start position:0% +value that you want here and so you + + + align:start position:0% +value that you want here and so you +could actually just come up with the one + + align:start position:0% +could actually just come up with the one + + + align:start position:0% +could actually just come up with the one +you prefer all right and so that's the + + align:start position:0% +you prefer all right and so that's the + + + align:start position:0% +you prefer all right and so that's the +sparse PCA thing which I'm trying to + + align:start position:0% +sparse PCA thing which I'm trying to + + + align:start position:0% +sparse PCA thing which I'm trying to +promote I mean I don't think this is not + + align:start position:0% +promote I mean I don't think this is not + + + align:start position:0% +promote I mean I don't think this is not +super well spread it's a fairly new idea + + align:start position:0% +super well spread it's a fairly new idea + + + align:start position:0% +super well spread it's a fairly new idea +maybe I don't know at most 10 years old + + align:start position:0% +maybe I don't know at most 10 years old + + + align:start position:0% +maybe I don't know at most 10 years old +and it's not completely well spread in + + align:start position:0% +and it's not completely well spread in + + + align:start position:0% +and it's not completely well spread in +in statistical packages but that's + + align:start position:0% +in statistical packages but that's + + + align:start position:0% +in statistical packages but that's +clearly what people are trying to + + align:start position:0% +clearly what people are trying to + + + align:start position:0% +clearly what people are trying to +emulate + + align:start position:0% +emulate + + + align:start position:0% +emulate +currently yes so what do that mean that + + align:start position:0% +currently yes so what do that mean that + + + align:start position:0% +currently yes so what do that mean that +the doctors have a lot of variance in + + align:start position:0% +the doctors have a lot of variance in + + + align:start position:0% +the doctors have a lot of variance in +medical knowledge quality of interaction + + align:start position:0% +medical knowledge quality of interaction + + + align:start position:0% +medical knowledge quality of interaction +Fair critical opinion saying these are + + align:start position:0% +Fair critical opinion saying these are + + + align:start position:0% +Fair critical opinion saying these are +like main things that doctors on some + + align:start position:0% +like main things that doctors on some + + + align:start position:0% +like main things that doctors on some +Doctors Care like we can sort of + + align:start position:0% +Doctors Care like we can sort of + + + align:start position:0% +Doctors Care like we can sort of +characterize a Doctor by oh he cares + + align:start position:0% +characterize a Doctor by oh he cares + + + align:start position:0% +characterize a Doctor by oh he cares +this much about medical knowledge this + + align:start position:0% +this much about medical knowledge this + + + align:start position:0% +this much about medical knowledge this +much about quality of interaction this + + align:start position:0% +much about quality of interaction this + + + align:start position:0% +much about quality of interaction this +opinion and thats most of story whats + + align:start position:0% +opinion and thats most of story whats + + + align:start position:0% +opinion and thats most of story whats +from drug + + align:start position:0% +from drug + + + align:start position:0% +from drug +represent not really um you see I mean + + align:start position:0% +represent not really um you see I mean + + + align:start position:0% +represent not really um you see I mean +okay let's say you pick only one so that + + align:start position:0% +okay let's say you pick only one so that + + + align:start position:0% +okay let's say you pick only one so that +means that you would take all your + + align:start position:0% + + + + align:start position:0% + +doctors and you would have One Direction + + align:start position:0% +doctors and you would have One Direction + + + align:start position:0% +doctors and you would have One Direction +which is quality of + + align:start position:0% +which is quality of + + + align:start position:0% +which is quality of +interaction and they would be just + + align:start position:0% +interaction and they would be just + + + align:start position:0% +interaction and they would be just +spread out points + + align:start position:0% + + + + align:start position:0% + +here okay so there's two things that can + + align:start position:0% +here okay so there's two things that can + + + align:start position:0% +here okay so there's two things that can +happen the first one is that there's a + + align:start position:0% +happen the first one is that there's a + + + align:start position:0% +happen the first one is that there's a +clump here and then there's a clump here + + align:start position:0% +clump here and then there's a clump here + + + align:start position:0% +clump here and then there's a clump here +right that still represents a lot of + + align:start position:0% +right that still represents a lot of + + + align:start position:0% +right that still represents a lot of +variance and if this happens probably + + align:start position:0% +variance and if this happens probably + + + align:start position:0% +variance and if this happens probably +want to go back in your data and see + + align:start position:0% +want to go back in your data and see + + + align:start position:0% +want to go back in your data and see +were these people you know visited by a + + align:start position:0% +were these people you know visited by a + + + align:start position:0% +were these people you know visited by a +different group than these people or + + align:start position:0% +different group than these people or + + + align:start position:0% +different group than these people or +maybe these people have a different you + + align:start position:0% +maybe these people have a different you + + + align:start position:0% +maybe these people have a different you +know specialty or I mean you have to + + align:start position:0% +know specialty or I mean you have to + + + align:start position:0% +know specialty or I mean you have to +look back at your data and try to + + align:start position:0% +look back at your data and try to + + + align:start position:0% +look back at your data and try to +understand what you would have different + + align:start position:0% +understand what you would have different + + + align:start position:0% +understand what you would have different +groups of people if it's like completely + + align:start position:0% +groups of people if it's like completely + + + align:start position:0% +groups of people if it's like completely +evenly spread out then all it's saying + + align:start position:0% +evenly spread out then all it's saying + + + align:start position:0% +evenly spread out then all it's saying +is that if you want to have a uniform + + align:start position:0% +is that if you want to have a uniform + + + align:start position:0% +is that if you want to have a uniform +qualitative interaction you need to take + + align:start position:0% +qualitative interaction you need to take + + + align:start position:0% +qualitative interaction you need to take +measures on this right you need to have + + align:start position:0% +measures on this right you need to have + + + align:start position:0% +measures on this right you need to have +this to not be a discrimination and so + + align:start position:0% +this to not be a discrimination and so + + + align:start position:0% +this to not be a discrimination and so +but I think really when it's becoming + + align:start position:0% +but I think really when it's becoming + + + align:start position:0% +but I think really when it's becoming +interesting it's not when it's + + align:start position:0% +interesting it's not when it's + + + align:start position:0% +interesting it's not when it's +completely sprad it's when there's a big + + align:start position:0% +completely sprad it's when there's a big + + + align:start position:0% +completely sprad it's when there's a big +group here and then there's almost no + + align:start position:0% +group here and then there's almost no + + + align:start position:0% +group here and then there's almost no +one here and then there's a big group + + align:start position:0% +one here and then there's a big group + + + align:start position:0% +one here and then there's a big group +here and then maybe there's something + + align:start position:0% +here and then maybe there's something + + + align:start position:0% +here and then maybe there's something +you can do and so so right those two + + align:start position:0% +you can do and so so right those two + + + align:start position:0% +you can do and so so right those two +things actually give you a lot of + + align:start position:0% +things actually give you a lot of + + + align:start position:0% +things actually give you a lot of +bearance okay so uh + + align:start position:0% +bearance okay so uh + + + align:start position:0% +bearance okay so uh +actually maybe I'll talk about this + + align:start position:0% +actually maybe I'll talk about this + + + align:start position:0% +actually maybe I'll talk about this +there's there's um here this is sort of + + align:start position:0% +there's there's um here this is sort of + + + align:start position:0% +there's there's um here this is sort of +a mixture right you have a mixture of + + align:start position:0% +a mixture right you have a mixture of + + + align:start position:0% +a mixture right you have a mixture of +two different populations of doctors + + align:start position:0% +two different populations of doctors + + + align:start position:0% +two different populations of doctors +right and uh it turns out that principal + + align:start position:0% +right and uh it turns out that principal + + + align:start position:0% +right and uh it turns out that principal +component analysis so what is a mixture + + align:start position:0% +component analysis so what is a mixture + + + align:start position:0% +component analysis so what is a mixture +is when you have different population + + align:start position:0% +is when you have different population + + + align:start position:0% +is when you have different population +think of like two Gans that are just + + align:start position:0% +think of like two Gans that are just + + + align:start position:0% +think of like two Gans that are just +centered at two different points and + + align:start position:0% +centered at two different points and + + + align:start position:0% +centered at two different points and +maybe they're in high dimensions and you + + align:start position:0% +maybe they're in high dimensions and you + + + align:start position:0% +maybe they're in high dimensions and you +want to those are clusters of people and + + align:start position:0% +want to those are clusters of people and + + + align:start position:0% +want to those are clusters of people and +you want to be able to differentiate + + align:start position:0% +you want to be able to differentiate + + + align:start position:0% +you want to be able to differentiate +those guys if you're in very high + + align:start position:0% +those guys if you're in very high + + + align:start position:0% +those guys if you're in very high +Dimensions it's going to be very + + align:start position:0% +Dimensions it's going to be very + + + align:start position:0% +Dimensions it's going to be very +difficult but one of the first + + align:start position:0% +difficult but one of the first + + + align:start position:0% +difficult but one of the first +processing tools that people do is to do + + align:start position:0% +processing tools that people do is to do + + + align:start position:0% +processing tools that people do is to do +PCA because if those things if you have + + align:start position:0% +PCA because if those things if you have + + + align:start position:0% +PCA because if those things if you have +one big group here and one big group + + align:start position:0% +one big group here and one big group + + + align:start position:0% +one big group here and one big group +here it means that there's a lot of + + align:start position:0% +here it means that there's a lot of + + + align:start position:0% +here it means that there's a lot of +variance along the direction that goes + + align:start position:0% +variance along the direction that goes + + + align:start position:0% +variance along the direction that goes +through the centers of those groups and + + align:start position:0% +through the centers of those groups and + + + align:start position:0% +through the centers of those groups and +that's essentially what happened here + + align:start position:0% +that's essentially what happened here + + + align:start position:0% +that's essentially what happened here +you could think of this as being two + + align:start position:0% +you could think of this as being two + + + align:start position:0% +you could think of this as being two +blur blobs in high Dimensions but you're + + align:start position:0% +blur blobs in high Dimensions but you're + + + align:start position:0% +blur blobs in high Dimensions but you're +really just projecting them into one + + align:start position:0% +really just projecting them into one + + + align:start position:0% +really just projecting them into one +dimension and this Dimension hopefully + + align:start position:0% +dimension and this Dimension hopefully + + + align:start position:0% +dimension and this Dimension hopefully +goes through the centers and so as a + + align:start position:0% +goes through the centers and so as a + + + align:start position:0% +goes through the centers and so as a +reprocessing so here I'm G to I'm going + + align:start position:0% +reprocessing so here I'm G to I'm going + + + align:start position:0% +reprocessing so here I'm G to I'm going +to stop here but PCA is not just made + + align:start position:0% +to stop here but PCA is not just made + + + align:start position:0% +to stop here but PCA is not just made +for you know Dimension reduction it's + + align:start position:0% +for you know Dimension reduction it's + + + align:start position:0% +for you know Dimension reduction it's +used for mixtures for example it's also + + align:start position:0% +used for mixtures for example it's also + + + align:start position:0% +used for mixtures for example it's also +used when you have graphical data what + + align:start position:0% +used when you have graphical data what + + + align:start position:0% +used when you have graphical data what +is the idea of PCA it just says if I + + align:start position:0% +is the idea of PCA it just says if I + + + align:start position:0% +is the idea of PCA it just says if I +have a matrix that seems to have low low + + align:start position:0% +have a matrix that seems to have low low + + + align:start position:0% +have a matrix that seems to have low low +rank meaning that there's a lot of those + + align:start position:0% +rank meaning that there's a lot of those + + + align:start position:0% +rank meaning that there's a lot of those +Lambda eyes that are very small and then + + align:start position:0% +Lambda eyes that are very small and then + + + align:start position:0% +Lambda eyes that are very small and then +I see that plus noise then it's a good + + align:start position:0% +I see that plus noise then it's a good + + + align:start position:0% +I see that plus noise then it's a good +idea to do PCA on this thing and in + + align:start position:0% +idea to do PCA on this thing and in + + + align:start position:0% +idea to do PCA on this thing and in +particular people use that in networks a + + align:start position:0% +particular people use that in networks a + + + align:start position:0% +particular people use that in networks a +lot so you take the adjacency Matrix of + + align:start position:0% +lot so you take the adjacency Matrix of + + + align:start position:0% +lot so you take the adjacency Matrix of +a graph well you sort of pre process it + + align:start position:0% +a graph well you sort of pre process it + + + align:start position:0% +a graph well you sort of pre process it +a little bit so it looks nice and then + + align:start position:0% +a little bit so it looks nice and then + + + align:start position:0% +a little bit so it looks nice and then +if you have for example two communities + + align:start position:0% +if you have for example two communities + + + align:start position:0% +if you have for example two communities +in there it should look like something + + align:start position:0% +in there it should look like something + + + align:start position:0% +in there it should look like something +that has that is uh low rank plus some + + align:start position:0% +that has that is uh low rank plus some + + + align:start position:0% +that has that is uh low rank plus some +noise and low rank means that there's + + align:start position:0% +noise and low rank means that there's + + + align:start position:0% +noise and low rank means that there's +just very few non-zero uh it means well + + align:start position:0% +just very few non-zero uh it means well + + + align:start position:0% +just very few non-zero uh it means well +low rank means this low rank means that + + align:start position:0% +low rank means this low rank means that + + + align:start position:0% +low rank means this low rank means that +if you do the screen plot you will see + + align:start position:0% +if you do the screen plot you will see + + + align:start position:0% +if you do the screen plot you will see +something like this which means that if + + align:start position:0% +something like this which means that if + + + align:start position:0% +something like this which means that if +you throw out all the smaller ones it + + align:start position:0% +you throw out all the smaller ones it + + + align:start position:0% +you throw out all the smaller ones it +should not really matter uh in the + + align:start position:0% +should not really matter uh in the + + + align:start position:0% +should not really matter uh in the +overall structure and uh and so you can + + align:start position:0% +overall structure and uh and so you can + + + align:start position:0% +overall structure and uh and so you can +use all this these techniques are used + + align:start position:0% +use all this these techniques are used + + + align:start position:0% +use all this these techniques are used +everywhere uh these days uh not just in + + align:start position:0% +everywhere uh these days uh not just in + + + align:start position:0% +everywhere uh these days uh not just in +PCA so we call it PCA statisticians but + + align:start position:0% +PCA so we call it PCA statisticians but + + + align:start position:0% +PCA so we call it PCA statisticians but +people call it spectral methods or + + align:start position:0% +people call it spectral methods or + + + align:start position:0% +people call it spectral methods or +SVD all right so + + align:start position:0% + + + + align:start position:0% + +everyone \ No newline at end of file diff --git a/a9FHHS6n-r4.txt b/a9FHHS6n-r4.txt new file mode 100644 index 0000000000000000000000000000000000000000..a58420f9d0043fbfa95f137bcffd6bec6e0017bd --- /dev/null +++ b/a9FHHS6n-r4.txt @@ -0,0 +1,2859 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation, or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: It's good to be back. + +I really want to thank +both Aaron and Will who + +took my teaching +duties over last week. + +You've been receiving +updates of the lecture notes, + +and, in particular, +as I don't want + +to go back over +some things, I would + +like you to read some of +the material you have there. + +In particular, the +part on projectors + +has been developed further. + +We will meet projectors +a lot in this space, + +because in quantum mechanics, +whenever you do a measurement, + +the effect of a +measurement is to act + +on a stage with a projector. + +So projectors are +absolutely important. + +And orthogonal +projectors are the ones + +that we're going to +use-- are the ones that + +are relevant in +quantum mechanics. + +There's a property, for +example, of projectors + +that is quite neat that is used +in maximization and fitting + +problems. + +And you will see +that in the PSET. + +In the PSET, the +last problem has + +to do with using a +projector to find + +best approximations to some +functions using polynomials. + +So there's lots of things +to say about projectors, + +and we'll find them along +when we go and do later stuff + +in the course. + +So please read that +part on projectors. + +The other thing is that much +of what we're going to do + +uses the notation that we have +for describing inner products-- + +for example, u, v. And +then, as we've mentioned, + +and this is in the notes-- +this, in the bracket notation, + +becomes something like this. + +And the bracket notation +of quantum mechanics + +is fairly nice for +many things, and it's + +used sometimes for +some applications. + +Everybody uses the bracket +notation for some applications. + +I hope to get to +one of those today. + +So much of the theory +we've developed + +is done with this as +the inner product. + +Nevertheless, the translation +to the language of bras and kets + +is very quick. + +So the way the notes are +going to be structured-- + +and we're still +working on the notes, + +and they're going +to chang a bit-- + +is that everything +regarding the math + +is being developed +more in this notation, + +but then we turn +into bras and kets + +and just go quickly +over all you've + +seen, just how it looks +with bras and kets + +so that you're familiar. + +Then, in the later +part of the course, + +we'll use sometimes bras and +kets, and sometimes this. + +And sometimes some +physicisists use + +this notation with parentheses. + +So for example, +Weinberg's recent book + +on quantum mechanics +uses this notation. + +It doesn't use bras and +kets I think at all. + +So you have to be ready +to work with any notation. + +The bra and ket notation +has some nice properties + +that make it very fast +to do things with it. + +It is very efficient. + +Nevertheless, in some ways this +notation is a little clearer. + +So many of the things we'll +develop is with this notation. + +So today I'm going +to develop the idea + +of the Hermitian +conjugator for an operator, + +or the adjoint of an operator. + +And this idea is generally a +little subtle, a little hard + +to understand. + +But we'll just go at it slowly +and try to make it very clear. + +So adjoints or Hermitian +operators, or Hermitian + +conjugates-- adjoints +or Hermitian conjugates. + +So the idea of Adjoints, +or Hermition conjugates, + +really begins with some +necessary background + +on what they're called-- +linear functionals. + +It sounds complicated, +but it's not. + +What is a linear functional? + +A linear functional +on V-- on a vector + +space V-- is a linear +map from V to the numbers + +F. We've always been +calling F the numbers. + +So it's just that, something +that, once you have a vector, + +you get a number +and it's linear. + +So a linear function of Phi, +if it's a linear functional, + +Phi on v belongs to F. +Phi acts on a vector, v, + +that belongs to the vector +space and gives you a number. + +So "linear" means Phi of v1 plus +v2 is Phi of v1 plus Phi of v2. + +And Phi of av, for a is +number, is a Phi of v. + +So seems simple, +and indeed it is. + +And we can construct examples +of linear functionals, + +some trivial ones, for example. + +Let Phi be a map that takes the +vector space, reals in three + +dimensions, to the real numbers. + +So how does it act? + +Phi acts on a vector, which +is x1, x2, and x3-- three + +components. + +And it must give +a numbers, so it + +could be 3x1 minus x2 plus +7x3, as simple as that. + +It's linear. + +x1, x2, and x3 are the +coordinates of a single vector. + +And whenever you have +this vector, that is, + +this triplet-- now, I +could have written it + +like this-- Phi of x1, +x2, and x3, as a vector. + +It looks like that. + +But it's easier to use +horizontal notation, + +so we'll write it like that. + +And, if you have +an inner product + +on this space-- on this three +dimensional vector space-- + +there's something you can say. + +Actually this Phi is +equal-- and this we + +call the vector V-- is +actually equal to u, + +inner product with v, where u is +the vector that has components + +3, minus 1, and +7, because if you + +take the inner product of +this vector with this vector, + +in three dimensions +real vector spaces-- + +inner product is a dot product. + +And then we make the dot +product of u with the vector V. + +Maybe I should have +called it v1, v2, v3. + +I'll change that-- +v1, v2, v3 here + +are components of the +vector-- v1, v2, and v3, + +not to be confused +with three vectors. + +This whole thing is a vector +V. So this linear functional, + +that, given a vector +gives me a number. + +The clever thing is +that the inner product + +is this thing that gives +you numbers out of vectors. + +So you've reconstructed +this linear functional + +as the inner product of some +vector with the vector you're + +acting on, so, where +u is given by that. + +The most important result +about linear functionals + +is that this is not an accident. + +This kind be that +very generally. + +So any time you give +me a linear functional, + +I can find a vector that, +using the inner product, + +acts on the vector you're +acting on the same way + +as the linear function of thus. + +The most general +linear functional + +is just some most general +vector acting this way. + +So let's state +that and prove it. + +So this is a theorem, it's +not a definition or anything + +like that. + +Let Phi be a linear +functional on v. Then + +there is a unique vector u +belonging to the vector space + +such that Phi acting +on v is equal to u, v. + +Since this is such +a canonical thing, + +you could even +invent a notation. + +Call this the linear +functional created by u, + +acting on v. Everybody +doesn't use this, + +but you could call it like that. + +This is a linear +functional acting on v, + +but it's labeled by u, which +is the vector that you've + +use there. + +This is important enough that we +better understand why it works. + +So I'll prove it. + +We're going to use +an orthonormal basis, + +say e1 up to en is an +orthonormal, O-N, basis. + +AUDIENCE: That +means we're assuming + +v is finite dimensional here? + +PROFESSOR: Sorry? + +AUDIENCE: We're assuming V is +finite dimensional, correct? + +PROFESSOR: Yeah, it's +finite dimensional + +I'm going to prove it using +a finite basis like that. + +Is true finite dimensional? + +I presume yes. + +AUDIENCE: If it's +not [INAUDIBLE]. + +PROFESSOR: What hypothesis? + +AUDIENCE: You say continuous +when you're talking + +[INAUDIBLE]. + +PROFESSOR: OK, I'll check. + +But let's just prove this one +finite dimensional like this. + +Let's take that. + +And now write the vector as a +superposition of these vectors. + +Now we know how to do that. + +We just have the components +of v along each basis vector. + +For example, the +component of v along e1 + +is precisely e1, v. +So then you go on + +like that until +you go en, v, en. + +I think you've derived this +a couple of times already, + +but this is a statement +you can review, + +and let's take it to be correct. + +Now let's consider what is +Phi acting on a v like that. + +Well, it's a linear map, so +it takes on a sum of vectors + +by acting on the +vectors, each one. + +So it should act on from +this plus that, plus that, + +plus that. + +Now, it acts on this vector. + +Well, this is a number. + +The number goes out. + +It's a linear function. + +So this is e1, v, Phi of e1, all +the way up to en, v Phi of en. + +Now this is a number, +so let's bring it + +into the inner product. + +Now, if you brought it in +on the side of V as a number + +it would go in just +like the number. + +If you bring it +into the left side, + +remember it's +conjugate homogeneous, + +so this enters as +a complex number. + +So this would be e1, Phi of +e1 star times V plus en, Phi + +of en star, v. And then we have +our result that this Phi of v + +has been written now. + +The left input is different +on each of these terms, + +but the right input is the same. + +So at this moment linearity +on the first input + +says that you can put here e1, +Phi of e1 star plus up to en, + +Phi of en star, v. And this +is the vector you were looking + +for, the vector U. Kind of +simple, at the end of the day + +you just used the basis +and made it clearer. + +It can always be constructed. + +Basically, the vector you want +is e1 times Phi of u1 star + +plus en up to Phi of en star. + +So if you know what the linear +map does to the basis vectors, + +you construct the +vector this way. + +Vector is done. + +The only thing to be +proven is that it's unique. + +Uniqueness is rather easy +to prove at this stage. + +Suppose you know that u +with v works and gives you + +the right answer. + +Well, you ask, is +there a u prime + +that also gives the +right answer for all v? + +Well, pass it to the +other side, and you + +would have u minus u prime, +would have zero inner product + +with v for all v. Pass +to the other side, + +take the difference, +and it's that. + +So u minus u prime +is a vector that + +has zero inner product +with any vector. + +And any such thing +as always zero. + +And perhaps the easiest way +to show that, in case you + +haven't seen that +before, if x with v + +equals 0 for all for all v. +What can you say about x? + +Well, take v is the value +for any v. So take v equal x. + +So you take x, x is equal to 0. + +And by the axioms of +the inner product, + +if a vector has 0 inner +product with itself, it's 0. + +So at this stage, you go +u minus u prime equals 0, + +and u is equal to u prime. + +So it's definitely +unique, you can't + +find another one that works. + +So we have this thing. + +This theorem is proven. + +And now let's use to +define this the adjoint, + +which is a very +interesting thing. + +So the adjoing, or +Hermitian conjugate, + +sometimes called +adjoint-- physicists + +use the name Hermitian +conjugate, which + +is more appropriate. + +Well, I don't know if +it's more appropriate. + +It's more pictorial if you +have a complex vector space. + +And if you're accustomed +with linear algebra + +about Hermition matrices, +and what they are, + +and that will show +up a little later, + +although with a +very curious twist. + +So given an operator T belonging +to the set of linear operators + +on a vector space, you +can define T dagger, + +also belonging to +l of v. So this + +is the aim-- constructing an +operator called the Hermitian + +conjugate. + +Now the way we're +going to do it is + +going to be defining +something that is a T star. + +Well, I said "T star" because +mathematicians in fact + +call it star. + +And most mathematicians, +they complex conjugate + +if a number is not +z star but z bar. + +So that's why we +call it T star and I + +may make this mistake +a few times today. + +We're going to use dagger. + +And so I will make +a definition that + +will tell you what T +dagger is supposed to be, + +acting on things. + +But it might not be obvious, +at least at first sight, + +that it's a linear operator. + +So let's see how does this go. + +Here is the claim. + +Consider the +following thing-- u, + +T, v-- this inner product of +u with T, v. And think of it + +as a linear functional. + +Well, it's certainly +a linear functional + +of v. It's a linear +functional because if you + +put a times v the a goes out. + +And if you put v1 plus +v2 you get it's linear. + +So it's linear, but +it's not the usual one's + +that we've been building, in +which the linear functional + +looks like u with v. I +just put an operator there. + +So by this theorem, +there must be some vector + +that this can be +represented as this acting + +with that vector inside here, +because any linear operator is + +some vector acting on the +vector-- on the vector + +v. Any linear functional, I'm +sorry-- not linear operator. + +Any linear functional-- +this is a linear functional. + +And every linear function can +be written as some vector acting + +on v. So there must +be a vector here. + +Now this vector surely +will depend on what u is. + +So we'll give it a name. + +It's a vector that depends on +U. I'll write it as T dagger u. + +At this moment, T dagger +is just a map from v + +to v. We said that this +thing that we must put here + +depends on u, and +it must be a vector. + +So it's some thing that +takes u and produces + +another vector +called T dagger on u. + +But we don't know +what T dagger is, + +and we don't even +know that it's linear. + +So at this moment it's just +a map, and it's a definition. + +This defines what T dagger +u is, because some vector-- + +it could be calculated exactly +the same way we calculated + +the other ones. + +So let's try to see +why it is linear. + +Claim T dagger belongs to +the linear operators in v. + +So how do we do that? + +Well, we can say the following. + +Consider u1 plus +u1 acting on Tv. + +Well, by definition, this would +be the T dagger of u1 plus u2, + +some function on u1 plus +u2, because whatever is here + +gets acted by T dagger +times v. On the other hand, + +this thing is equal +to u1, Tv plus u2, + +Tv, which is equal to T dagger +u1, v plus T dagger u2, v. + +And, by linearity, here you +get equal to T dagger u1 plus T + +dagger on u2. + +And then comparing this too-- +and this is true for arbitrary + +v-- you find that T dagger, +acting on this sum of vectors, + +is the same as this thing. + +And similarly, how about au, Tv? + +Well, this is equal to T dagger +on au, v. Now, T dagger on au, + +do you think the a goes +out as a or as a bar? + +Sorry? + +a or a-bar? + +What do you think T dagger +and au is supposed to be? + +a, because it's supposed to be +a linear operator, so no dagger + +here. + +You see-- well, I +didn't show it here. + +Any linear operator, T on av, +is supposed to be a T of v. + +And we're saying +T dagger is also + +a linear operator +in the vector space. + +So this should be with an a. + +We'll see what we get. + +Well, the a can go out here, +and it becomes a star u1, Tv, + +which is equal. + +I'm going through the left side. + +By definition, a +bar T dagger of u, + +v. And now the +constant can go in, + +and it goes back as +a, T dagger u, v. So + +this must be equal +to that, and you + +get what we're claiming here, +which is T dagger on au, + +is equal to a T dagger of u. + +So the operator is linear. + +So we've defined something +this way, and it's linear, + +and it's doing all +the right things. + +Now, you really feel +proud at this stage. + +This is still not +all that intuitive. + +What does this all do? + +So we're going to do +an example, and we're + +going to do one more property. + +Let me do one more property +and then stop for a second. + +So here is one property-- +ST dagger is supposed to be + +T dagger S dagger. + +So how do you get that? + +Not hard-- u, STv. + +Well, STv is really the +same as S acting on Tv. + +Now the first S can be +brought to the other side + +by the definition that +you can bring something + +to the other side. + +Put in a dagger. + +So the S is brought +there, and you + +get S dagger on u, T on v. And +then the T can be brought here + +and act on this one, and +you get T dagger S dagger u, + +v. So this thing is the +dagger of this thing, + +and that's the statement here. + +There's yet one more +simple property, + +that the dagger of S dagger +is S. You take dagger twice + +and you're back to +the same operator. + +Nothing has changed. + +So how do you do that? + +Take, for example, this-- take +u, put S dagger here, and put + +v. Now, by definition, +this is equal to-- you + +put the operator on the +other side, adding a dagger. + +So that's why we put +that one like this. + +The operator gets +daggers, so now you've + +got the double dagger. + +So at this moment, +however, you have + +to do something +to simplify this. + +The easiest thing to do is +probably the following-- + +to just flip these +two, which you + +can do the order +by putting a star. + +So this is equal. + +The left hand side +is equal to this. + +And now this S dagger can be +moved here and becomes an S. + +So this is u, Sv, and +you still have the star. + +And now reverse this by +eliminating the star, + +so you have S-- +I'm sorry, I have + +this notation completely wrong. + +Sv-- this is u. + +The u's v's are easily confused. + +So this is v, and this is u. + +I move the S, and then finally +I have Su, v without a star. + +I flipped it again. + +So then you compare these two, +and you get the desired result. + +OK, so we've gone +through this thing, which + +is the main result +of daggers, and I + +would like to see if +there are questions. + +Anything that has been unclear +as we've gone along here? + +And question? + +OK. + +No questions. + +So let's do a simple +example, and it's good + +because it's useful to +practice with explicit things. + +So here's an example. + +There's a vector space V, +which is three complex numbers, + +three component vectors-- +complex vectors. + +So a v is equal to v1, v2, v3-- +three numbers are all the vi. + +Each one belongs to +the complex number. + +So three complex numbers makes +a vector space like this. + +So somebody comes +along and gives you + +the following linear map-- +T on a vector, v1, v1, v3, + +gives you another vector. + +It's a linear map. + +So what is it? + +It's 0 times v1 plus 2v2 plus +iv3 for the first component. + +The first component +of the new vector-- I + +put the 0v1 just so you see that +it just depends on v2 and v3. + +The second component is +v1 minus iv2 plus 0v3. + +Those are not vectors. + +These are components. + +These are numbers. + +So this is just +a complex number. + +This is another complex +number, as it should be. + +Acting on three +complex numbers gives + +you, linearly, three other ones. + +And then the third component-- +they don't have space there, + +so I'll put it here-- +3iv1 plus v2 plus 7v3. + +And the question +is two questions. + +Find T dagger, and write +the matrix representations + +of T and T dagger. + +Write the matrices +T and T dagger + +using the standard basis +in which the three basis + +vectors are 1, 0, 0, 0, 1, +1, 0, 0, 1, 0, and 0, 0, 1. + +These are the three basis +vectors-- e1, e2, and e3. + +You know, to write the matrix +you need the basis vectors. + +So that's a problem. + +It's a good problem +in order to practice, + +to see that you +understand how to turn + +an operator into a matrix. + +And you don't get confused. + +Is it a row? + +Is it a column? + +How does it go? + +So let's do this. + +So first we're going to try to +find the rules for T dagger. + +So we have the following. + +You see, you use +the basic property. + +u on Tv is equal +to T dagger u on v. + +So let's try to compute the left +hand side, and then look at it + +and try to see if we could +derive the right hand side. + +So what is u supposed to be +a three component vector? + +So for that use, u +equals u1, u2, u3. + +OK, now implicit in all that is +that when somebody tells you-- + +OK, you've got a three +dimensional complex vector + +space what is the inner product? + +The inner product +is complex conjugate + +of the first component. + +That's first component of the +second, plus complex conjugate + +of the second times +star, times star. + +So it's just a generalization +of the dot product, + +but you complex conjugate +the first entries. + +So what is this? + +I should take the complex +conjugate of the first term + +here-- u1-- times the first one. + +So I have 2v2 plus iv3. + +This is the left hand side, +plus the complex conjugate + +of the second +component-- there's + +the second component-- +so u2 times v1 minus iv2 + +plus-- well, 0v3-- +his time I won't write + +it-- plus u3 bar +times the last vector, + +which is 3iv1 plus v2 plus 7v3. + +OK, that's the left hand side. + +I think I'm going to use +this blackboard here, + +because otherwise +the numbers are going + +to be hard to see from +one side to the other. + +So this information, +those two little proofs, + +are to be deleted. + +And now we have +this left hand side. + +Now, somehow when +you say, OK, now I'm + +going to try to figure out this +right hand side your head goes + +and looks in there +and says well, + +in the left hand side the +u's are sort of the ones that + +are alone, and the +v's are acted upon. + +Here the v's must be alone. + +So what I should do +is collect along v. + +So let's collect along v. So +let's put "something" times v1 + +plus "something" like v2 +plus "something" like v3. + +And then I will know what +is the vector T star this. + +So let's do that. + +So v1, let's collect. + +So you get u2 bar for +this v1, and 3iu3 bar. + +v2 will have 2u1 bar +minus iu2 bar plus u3 bar. + +I think I got them right. + +OK. + +And then v3, let's collect-- +iu1 bar, nothing here, + +and v3 7u3 bar. + +OK, and now I must say, OK, +this is the inner product + +of T dagger u times v3. + +So actually, T dagger on +u, which is u1, u2, u3, + +must be this vector with three +components for which this thing + +is the inner product of this +vector with the vector V. + +So I look at this +I say, well, what + +was the formula for +the inner product? + +Well, you complex conjugate +the first entry of this + +and multiply by the +first entry of that. + +Complex conjugate +the second entry. + +So here I should +put u2 minus 3iu3, + +because the complex +conjugate of that + +is that as multiplied by v1. + +So here I continue-- +2u1 plus iu2 plus u3. + +And, finally, +minus iu1 plus 7u3. + +And that's the answer +for this operator. + +So the operator +is there for you. + +The only thing we haven't +done is the matrices. + +Let me do a little +piece of one, and you + +try to compute the rest. + +Make sure you understand it. + +So suppose you get T +on the basis vector e1. + +It's easier than what it looks. + +I'm going to have to +write some things in order + +to give you a few +components, but then + +once you get a little practice, +or you look what it means, + +it will become clear. + +So what is T on e1? + +Well, it's T on +the vector 1, 0, 0. + +T on the vector 1, 0, 0-- look +at the top formula ther3-- + +is equal to 0, 1, and 3i. + +Top formula-- the v1 is +1, and all others are 0. + +And this is e2 plus 3ie3. + +So how do you read, +now, matrix elements? + +You remember the +formula that T on ei + +is supposed to be +Tkiek-- sum over k. + +So this thing is supposed +to be equal to T11e1 + +plus T21e2 plus T31e3. + +Your sum over the first index, +T of e1, is there for that. + +So then I read this, and I +see that T21 is equal to 1. + +This is equal to 3i. + +And this is equal to 0. + +So you've got a +piece of the matrix, + +and the rest I will just +tell you how you see it. + +But you should check it. + +You don't have to write +that much after you + +have a little +practice with this. + +But, the matrix T-- +what you've learned + +is that you have 0, 1, and 3i. + +So 0, 1, and 3i +are these numbers, + +in fact-- 0, 1, and 3i. + +And they go vertical. + +So 2, minus i, and 1 +is the next column. + +2, minus i, and 1 +is the next column, + +and the third one would be +i-- look at the v3 there. + +It has an i for the first entry, +a 0 for the second, and a 7. + +So this is the matrix. + +How about the matrix T dagger? + +Same thing-- once you've +done one, don't worry. + +Don't do the one. + +So this you look for +the first column. + +It's going to be a 0-- no u1 +here-- a 2, and a minus i. + +0, 2, and a minus i, then 1, +i, and 0, minus 3i, 1, and 7. + +And those are it. + +And look how nice. + +The second one is in fact +the Hermitian conjugate + +of the other. + +Transpose and complex +conjugate gives it to you. + +So that example suggests +that that, of course, + +is not an accident. + +So what do you need +for that to happen? + +Nobody said that what you're +supposed to do to find T dagger + +is transpose some +complex conjugate, + +but somehow that's what you +do once you have the matrix, + +or at least what +it seems that you + +do when you have the matrix. + +So let's see if we can +get that more generally. + +So end of example. + +Look at T dagger u, +v is equal to u, Tv. + +We know this is +the key equation. + +Everything comes from this. + +Now take u and v to be +orthonormal vectors, + +so u equal ei, and v equal ej. + +And these are orthonormal. + +The e's are going to be +orthonormal each time + +we say basis vectors-- +e, orthonormal. + +So put them here, so you +get T dagger on ei times ej + +is equal to ei, Tej. + +Now use the matrix action +on these operators. + +So T dagger on ei is +supposed to be T dagger kiek. + +The equation is something +worth knowing by heart. + +What is the matrix +representation? + +If the index of the +vector goes here, + +the sum index goes like that. + +So then you have ej here, +and here you have ei, + +and you have Tkjek. + +So now this basis orthonormal. + +This is a number, and +this is the basis. + +The number goes out. + +T dagger ki-- remember, +it's on the left side, + +so it should go out with a star. + +And then you have ekej. + +That's orthonormal, +so it's delta kej. + +The number here +goes out as well, + +and the inner product +gives delta ik. + +So what do we get? + +T dagger ji star +is equal to Tij. + +First, change i for j, so +it looks more familiar. + +So then you have T dagger +ij star is equal to Tji. + +And then take complex +conjugate, so that finally you + +have T dagger ij is +equal to Tji star. + +And that shows that, as long as +you have an orthonormal basis + +you can see the Hermitian +conjugate of the operator + +by taking the matrix, +and then what you usually + +call the Hermitian +conjugate of the matrix. + +But I want to +emphasize that, if you + +didn't have an +orthonormal basis-- if you + +have your operator, and you want +to calculate the dagger of it, + +and you find its +matrix representation. + +You take the Hermitian +conjugate of the matrix. + +It would be wrong if your basis +vectors are not orthonormal. + +It just fails. + +So what would happen if +the basis vectors are not + +orthonormal? + +Instead of having ei with +ej giving you delta iej, + +you have that ei with +ej is some number. + +And you can call it aij, or +alpha iej, or gij, I think, + +is maybe a better name. + +So if the basis is not +orthonormal, then ei with ej + +is some sort of gij. + +And then you go back here. + +And, instead of having deltas +here, you would have g's. + +So you would have the T +dagger star ki with gkj + +is equal to Tkj, gik. + +And there's no such +simple thing as saying, + +oh, well you just take +the matrix and complex + +conjugate and transpose. + +That's not the dagger. + +It's more complicated than that. + +If this matrix +should be invertible, + +you could pass this +to the other side + +using the inverse +of this matrix. + +And you can find a +formula for the dagger + +in terms of the g matrix, its +inverses and multiplications. + +So what do you learn from here? + +You learn a fundamental +fact, that the statement + +that an operator-- for +example, you have T. + +And you can find T +dagger as the adjoint. + +The adjoint operator, or the +Hermitian conjugate operator, + +has a basis +independent definition. + +It just needs that +statement that we've + +written many times +now, that T dagger u, + +v is defined via this relation. + +And it has nothing +to do with a basis. + +It's true for arbitrary vectors. + +Nevertheless, how you +construct T dagger, + +if you have a basis-- +well, sometimes + +it's a Hermitian +conjugate matrix, + +if your basis is orthonormal. + +But that statement, that +the dagger is the Hermitian + +conjugate basis, is a +little basis dependent, + +is not a universal +fact about the adjoint. + +It's not always +constructed that way. + +And there will be examples +where you will see that. + +Questions? + +No questions? + +Well, let's do brackets +for a few minutes + +so that you see a few +properties of them. + +With the same language, I'll +write formulas that we've-- OK, + +I wrote a formula here, in fact. + +So for example, +this formula-- if I + +want to write it with bras +and kets, I would write u Tv. + +And I could also +write it as u T v, + +because remember this +means-- the bra and the ket-- + +just says a way to make clear +that this object is a vector. + +But this vector is obtained +by acting T on the vector + +v. So it's T on the vector +v, because a vector v is just + +something, and when you put +it like that that's still + +the vector v. The kit +doesn't do much to it. + +It's almost like +putting an arrow, + +so that's why this thing is +really this thing as well. + +Now, on the other +hand, this thing-- + +let's say that this is +equal to v, T dagger u star. + +So then you would put here +that this is v T dagger u star. + +So this formula is something +that most people remember + +in physics, written perhaps +a little differently. + +Change v and u so that +this left hand side now + +reads u T dagger v. +And it has a star, + +and the right hand side +would become v T u. + +And just complex conjugated it. + +So u T dagger v is equal to v +T u star-- a nice formula that + +says how do you get to +understand what T dagger is. + +Well, if you know +T dagger's value + +in between any set +of states, then you + +know-- well, if you know T +between any set of states + +u and v, then you +can figure out what + +T dagger is between any same two +states by using this formula. + +What you have to do +is that this thing + +is equal to the reverse thing. + +So you go from right to +left and reverse it here. + +So you go v, then T, then +u, and you put a star, + +and that gives you that object. + +Another thing that we've +been doing all the time when + +we calculate, for +example, ei, T on ej. + +What is this? + +Well, you know what this is. + +Let's write it like that-- ei. + +Now T on ej is +the matrix T kjek. + +If this is an orthonormal +basis, here is a delta iek. + +So this is nothing else but Tij. + +So another way of writing that +matrix element, ij, of a matrix + +is to put an ei, an +ej here, and a T here. + +So people write it like +that-- Tij is ei comma Tej. + +Or, in bracket language, +they put ei T ej. + +So I need it to be +flexible and just + +be able to pass from one +notation to the other, + +because it helps you. + +One of the most helpful +things in this object + +is to understand, for example, +in bra and ket notation, what + +is the following object? + +What is ei ei? + +This seems like the +wrong kind of thing, + +because you were supposed to +have bras acting on vectors. + +So this would be on +the left of that, + +but otherwise it +would be too trivial. + +If it would be on the left of +it, it would give you a number. + +But think of this thing as +a object that stands there. + +And it's repeated +endlessly, so it's summed. + +So what is this object? + +Well, this object is a +sum of things like that, + +so this is really e1 e1 plus e2 +e2, and it goes on like that. + +Well, let it act on a vector. + +This kind of object +is an operator. + +Whenever you have +the bra and the ket + +sort of in this wrong +position-- the ket first, + +and the bra afterwards-- +this is, in Dirac's notation, + +an operator, a +particular operator. + +And you will see in general +how it is the general operator + +very soon. + +So look at this. + +You have something like +that, and why do we + +call it an operator? + +We call it an operator +business if it + +acts on a vector-- +you put a vector here, + +a bra-- this becomes a +number, and there's still + +a vector left. + +So this kind of structure, +acting on something like that, + +gives a vector, because +this thing goes in here, + +produces a number, and +the vector is left there. + +So for example, if you act with +this thing on the vector a-- + +an arbitrary vector +a-- what do you get? + +Whatever this operator +is is acted on a. + +Well, you remember that these +thing are the components of a, + +and these are the basis vectors. + +So this is nothing else +but the vector a again. + +You see, you can start with +a equals some alpha i's with + +ei's, and then you calculate +what are the alpha i's. + +You put an ej a, and this ej +on that gives you alpha j. + +So alpha j-- these +numbers are nothing else + +but these things, these numbers. + +So here you have the +number times the vector. + +The only difference is that +this is like ei alpha i. + +The number has +been to the right. + +So this thing acting on any +vector is the vector itself. + +So this is perhaps the +most fundamental relation + +in bracket notation, is that +the identity operator is this. + +Yes. + +AUDIENCE: Is that just 1 e +of i, or sum over all e of i? + +PROFESSOR: It's sum of over all. + +So here implicit sum is +the sum of all up to en en. + +You will see, if you +take just one of them, + +you will get what is an +orthogonal projector. + +Now this allows you +to do another piece + +of very nice Dirac notation. + +So let's do that. + +Suppose you have an +operator T. You put a 1 + +in front of it-- a T +and a 1 in front of it. + +And then you say, OK, +this 1, I'll put ei ei. + +Then comes the T, and then +comes the ej ej-- another 1. + +And then you look at +that and you suddenly + +see a number lying there. + +Why? + +Because this thing +is some number. + +So this is the magic +of the Dirac notation. + +You write all this +thing, and suddenly you + +see numbers have been +created in between. + +This number is nothing else +but this matrix representation + +of the operator. + +T, between this, is Tij. + +So this is ei Tij ej. + +So this formula is +very fundamental. + +It shows that the most general +operator that you can ever + +invent is some sort +of ket before a bra, + +and then you superimpose +them with these numbers which + +actually happen to be the matrix +representation of the operator. + +So the operator can +be written as a sum + +of, if this is an n by n matrix +n squared thinks of this form-- + +1 with 1, 1 with 2, 1 +with 3, and all of them. + +Bu then, you know this +formula is so important + +that people make +sure that you realize + +that you're summing +over i and j. + +So just put it there. + +Given an operator, these +are its matrix elements. + +And this is the operator written +back in abstract notation. + +The whole operator is +back there for you. + +I want to use the last +part of the lecture + +to discuss a theorem that +is pretty interesting, + +that allows you to +understand things + +about all these Hermitian +operators and unitary operators + +much more clearly. + +And it's a little +mysterious, this theorem, + +and let's see how it goes. + +So any questions about this +Dirac notation at this moment, + +anything that I wrote there? + +It takes a while +to get accustomed + +to the Dirac notation. + +But once you get +the hang of it, it's + +sort of fun and +easy to manipulate. + +No questions? + +Can't be. + +You can prove all +kinds of things + +with this matrix +representation of the identity. + +For example, you +can prove easily + +something you proved already, +that when you multiply + +two operators the +matrices multiply. + +You can prove all +kinds of things. + +Pretty much +everything we've done + +can also be proven this way. + +OK, so here comes the theorem +I want to ask you about. + +Suppose somebody comes +along, and they tell you, + +well, you know, +here's a vector v, + +and I'm going to have a linear +operator acting on this space. + +So the operator's +going to be T, and I'm + +going act with the vector v. + +And moreover, I +find that this is + +0 for all vectors v belonging +to the vector space. + +And the question is-- what can +we say about this operator? + +From all vectors it's just 0. + +So is this operator 0, maybe? + +Does it have to be 0? + +Can it be something else? + +OK, we've been talking about +real and complex vector spaces. + +And we've seen that +it's different. + +The inner product is +a little different. + +But let's think about this. + +Take two dimensions, +real vector space. + +The operator that +takes any vector + +and rotates it by 90 degrees, +that's a linear operator. + +And that is a non-trivial linear +operator, and it gives you 0. + +So case settled-- there's +no theorem here, nothing + +you can say about this operator. + +It may be non-zero. + +But here comes the catch. + +If you're talking complex +vector spaces, T is 0. + +It just is 0, can't +be anything else. + +Complex vector +spaces are different. + +You can't quite do that thing-- +rotate all vectors by something + +and do things. + +So that's a theorem +we want to understand. + +Theorem-- let v be a +complex inner product space. + +By that is a complex vector +space with an inner product. + +Then v, Tv equals +0 for all v implies + +that the operator is just 0. + +I traced a lot of my +confusions in quantum mechanics + +to not knowing +about this theorem, + +that somehow it must be true. + +I don't know why +it should be true, + +but somehow it's not, because +it really has exceptions. + +So here it is. + +We tried to prove that. + +It's so important, I think, +that it should be proven. + +And how could you prove that? + +And at first sight it seems +it's going to be difficult, + +because, if I do +just a formal proof, + +how is it going to +know that I'm not + +talking real or +complex vector spaces. + +So it must make a crucial +difference in the proof + +whether it's real or complex. + +So this property really sets +the complex vector spaces + +quite apart from the real ones. + +So let's see what +you would need to do. + +Well, here's a strategy-- +if I could prove that u, + +Tv is equal to 0 for all +u and all v. You see, + +the problem here is that +these two are the same vector. + +They're all vectors, but +they're the same vector. + +If I could prove that this +is 0 for all u and v, then + +what would I say? + +I would say, oh, if this +is 0 for all u and v, + +then pick u equal to Tv. + +And then you find +that Tv, Tv is 0, + +therefore Tv is the 0 vector. + +By the axiom of +the inner product, + +for all v is a 0 vector, +so T kills all vectors, + +therefore T is 0. + +So if I could prove this +is true, I would be done. + +Now, of course, +that's the difficulty. + +Well, I wouldn't say of course. + +This takes a leap +of faith to believe + +that this is the way +you're going to prove that. + +You could try to prove this, +and then it would follow. + +But maybe that's +difficult to prove. + +But actually that's +possible to prove. + +But how could you ever +prove that this is true? + +You could prove it +if you could somehow + +rewrite u and Tv as some +sort of something with a T + +and something plus some +other thing with a T, + +and that other thing plus some-- +all kinds of things like that. + +Because the things in which +this is the same as that are 0. + +So if you can do that-- if you +could re-express this left hand + +side as a sum of things of +that kind-- that would be 0. + +So let's try. + +So what can you try? + +You can put u plus v here, +and T of u plus v. That + +would be 0, because that's +a vector, same vector here. + +But that's not equal to this, +because it has the u, Tu, + +and it has the v Tv. + +And it has this in +a different order. + +So maybe we can subtract u +minus v, T of u minus v. Well, + +we're getting +there, but all this + +is question marks-- u, Tu, v, +Tv-- these cancel-- u, Tu, v, + +Tv. + +But, the cross-products, +what are they? + +Well here you have a u, Tv. + +And here you have a v, Tu. + +And do they cancel? + +No. + +Let's see. + +u, Tv, and up here +is u minus Tv about. + +But there's another minus, +so there's another one there. + +And v, Tu has a minus, +minus is a plus. + +So actually this gives me +two of this plus two of that. + +OK, it shouldn't have +been so easy anyway. + +So here is where you have to +have the small inspiration. + +Somehow it shouldn't +have worked, you know. + +If this had worked, the +theorem would read different. + +You could use a +real vector space. + +Nothing is imaginary there. + +So the fact that you have +a complex vector space + +might help. + +So somehow you have +to put i's there. + +So let's try i's here. + +So you put u plus iv +and T of u plus iv. + +Well, then you probably have +to subtract things as well, so + +u minus iv, T of u minus iv. + +These things will be 0 because +of the general structure-- + +the same operator here as here. + +And let's see what they are. + +Well, there's u, Tu, +and here's minus u, Tu, + +so the diagonal things go away-- +the minus iv, minus iv, iv, + +and a T. You have minus +iv, minus iv subtracted, + +so that also cancels. + +So there's the cross-products. + +Now you will say, well, +just like the minus signs, + +you're not going to get +anything because you're + +going to get 2 and 2. + +Let's see. + +Let's see what we +get with this one. + +You get u with Tiv, +so you get i u, Tv. + +But look, this i on the left, +however, when you take it out, + +becomes a minus i, so +you get minus i v, Tu. + +And the other +products [INAUDIBLE]. + +So let's look what you get +here-- a u with a minus iv + +and a minus here +gives you a 2 here. + +And the other +term, v, Tu-- well, + +this goes out as a plus i. + +But with a minus, it becomes +a minus i, so v, Tu is this. + +So there's a 2 here. + +So that's what these +terms give you. + +And now you've succeeded. + +Why? + +Because the relative +sign is negative. + +So who cares? + +You can divide by i, +and divide this by i. + +You are constructing something. + +So let me put here what you get. + +I can erase this blackboard. + +So what do we get? + +I claim that if you put +one quarter of u plus v, + +T u plus v minus u minus +v, T of u minus v, then, + +let's see, what do +we need to keep? + +We need to keep u and Tv. + +So divide this by +i plus 1 over i + +u plus iv, T of +u plus iv minus 1 + +over i, u minus iv, +T of u minus iv. + +And close it. + +You've divided by i. + +You get here four of these +ones, zero of these ones, + +and you got the +answer you wanted. + +So this whole thing +is written like that, + +and now, since this +is equal to u with Tv, + +by the conditions +of the theorem, + +any vector-- any vector +here-- these are all 0. + +You've shown that this is 0, +and therefore the operator is 0. + +And you should be +very satisfied, + +because the proof +made use of the fact + +that it was a +complex vector space. + +Otherwise you could +not add vectors + +with an imaginary number. + +And the imaginary +number made it all work. + +So the theorem is there. + +It's a pretty useful +theorem, so let's use it + +for the most +obvious application. + +People say that, +whenever you find that v, + +Tv is real for all +v, then this operator + +is Hermitian, or self-adjoint. + +That is, then, it implies +T dagger equals T. + +So let's show that. + +So let's take v, Tv. + +Proof. + +You take v, Tv, and +now this thing is real. + +So since this is real, you can +say it's equal to v, Tv star. + +Now, because it's real-- +that's the assumption. + +The number is real. + +Now, the star off an +inner product is Tv, v. + +But on the other +hand, this operator, + +by the definition of +adjoint, can be moved here. + +And this is equal +to T dagger v, v. So + +now you have done +this is equal to this. + +So if you put it +to one side, you + +get that T dagger minus T +on v times v is equal to 0. + +Or, since any inner +product that is 00-- + +it's complex conjugate is +0-- you can write it as v, + +T dagger minus v is 0 for all v. + +And so this is an actually +well known statement, + +that any operator that gives you +real things must be Hermitian. + +But it's not obvious, because +that theorem is not obvious. + +And now you can use a +theorem and say, well, + +since this is true for all +v, T dagger minus T is 0, + +and T dagger is equal to T. Then +you can also show, of course, + +if T dagger is equal to +T, this thing is real. + +So in fact, this +arrow is both ways. + +And this way is very easy, but +this way uses this theorem. + +There's another +kind of operators + +that are called +unitary operators. + +We'll talk a little more +about them next time. + +And they preserve +the norm of vectors. + +People define them +from you, and you + +see that they preserve +the norm of vectors. + +On the other hand, you +sometimes find an operator + +that preserves every norm. + +Is it unitary? + +You will say, yes, must be. + +How do you prove it? + +You need again that theorem. + +So this theorem is +really quite fundamental + +to understand the +properties of operators. + +And we'll continue +that next time. + +All right. \ No newline at end of file diff --git a/aHQxdnufLbg.txt b/aHQxdnufLbg.txt new file mode 100644 index 0000000000000000000000000000000000000000..6a23fd28c6efa85ec541937fd3eb1f8cbd6abcef --- /dev/null +++ b/aHQxdnufLbg.txt @@ -0,0 +1,10858 @@ +align:start position:0% + +we have seen I would say three sets of + + align:start position:0% +we have seen I would say three sets of + + + align:start position:0% +we have seen I would say three sets of +tools applied to the problem of + + align:start position:0% +tools applied to the problem of + + + align:start position:0% +tools applied to the problem of +projection theory. So at the beginning + + align:start position:0% +projection theory. So at the beginning + + + align:start position:0% +projection theory. So at the beginning +of the class first we talked about like + + align:start position:0% +of the class first we talked about like + + + align:start position:0% +of the class first we talked about like +double counting and then we talked about + + align:start position:0% +double counting and then we talked about + + + align:start position:0% +double counting and then we talked about +methods from 4A analysis and then in the + + align:start position:0% +methods from 4A analysis and then in the + + + align:start position:0% +methods from 4A analysis and then in the +last week we started our our third set + + align:start position:0% +last week we started our our third set + + + align:start position:0% +last week we started our our third set +of tools which are tools from + + align:start position:0% +of tools which are tools from + + + align:start position:0% +of tools which are tools from +combinatorial number theory. Um so um so + + align:start position:0% +combinatorial number theory. Um so um so + + + align:start position:0% +combinatorial number theory. Um so um so +this week we're going to finish our unit + + align:start position:0% +this week we're going to finish our unit + + + align:start position:0% +this week we're going to finish our unit +on tools from combinatorial number + + align:start position:0% +on tools from combinatorial number + + + align:start position:0% +on tools from combinatorial number +theory and projection theory. + + align:start position:0% +theory and projection theory. + + + align:start position:0% +theory and projection theory. +Okay. So uh the the goal for these two + + align:start position:0% +Okay. So uh the the goal for these two + + + align:start position:0% +Okay. So uh the the goal for these two +weeks + + align:start position:0% +weeks + + + align:start position:0% +weeks +is this projection theorem of banan cats + + align:start position:0% +is this projection theorem of banan cats + + + align:start position:0% +is this projection theorem of banan cats +and tao and it takes place over finite + + align:start position:0% +and tao and it takes place over finite + + + align:start position:0% +and tao and it takes place over finite +fields and the cool thing about it is + + align:start position:0% +fields and the cool thing about it is + + + align:start position:0% +fields and the cool thing about it is +that it distinguishes what's true over + + align:start position:0% +that it distinguishes what's true over + + + align:start position:0% +that it distinguishes what's true over +prime fields from what's true over other + + align:start position:0% +prime fields from what's true over other + + + align:start position:0% +prime fields from what's true over other +fields which none of our previous + + align:start position:0% +fields which none of our previous + + + align:start position:0% +fields which none of our previous +methods could could distinguish. + + align:start position:0% +methods could could distinguish. + + + align:start position:0% +methods could could distinguish. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +so this is our goal + + align:start position:0% + + + + align:start position:0% + +says that if x is a subset of fp^ 2 and + + align:start position:0% +says that if x is a subset of fp^ 2 and + + + align:start position:0% +says that if x is a subset of fp^ 2 and +it has size p to the sx, you can think + + align:start position:0% +it has size p to the sx, you can think + + + align:start position:0% +it has size p to the sx, you can think +of sx sort of like a dimension and sx is + + align:start position:0% +of sx sort of like a dimension and sx is + + + align:start position:0% +of sx sort of like a dimension and sx is +in between zero and two. So it's not too + + align:start position:0% +in between zero and two. So it's not too + + + align:start position:0% +in between zero and two. So it's not too +tiny and it's not everything. And we + + align:start position:0% +tiny and it's not everything. And we + + + align:start position:0% +tiny and it's not everything. And we +have a set of directions in FP. + + align:start position:0% +have a set of directions in FP. + + + align:start position:0% +have a set of directions in FP. +set of directions has size P to the SD + + align:start position:0% +set of directions has size P to the SD + + + align:start position:0% +set of directions has size P to the SD +and it's not too tiny. + + align:start position:0% + + + + align:start position:0% + +um then if I take the maximum over all + + align:start position:0% +um then if I take the maximum over all + + + align:start position:0% +um then if I take the maximum over all +of the directions of the size of the + + align:start position:0% +of the directions of the size of the + + + align:start position:0% +of the directions of the size of the +projection in that direction so at least + + align:start position:0% +projection in that direction so at least + + + align:start position:0% +projection in that direction so at least +um so the square root of x that so far + + align:start position:0% +um so the square root of x that so far + + + align:start position:0% +um so the square root of x that so far +that's not difficult to do um but then + + align:start position:0% +that's not difficult to do um but then + + + align:start position:0% +that's not difficult to do um but then +plus times a little bit more time p to + + align:start position:0% +plus times a little bit more time p to + + + align:start position:0% +plus times a little bit more time p to +the epsilon I'll call it epsilon p to + + align:start position:0% +the epsilon I'll call it epsilon p to + + + align:start position:0% +the epsilon I'll call it epsilon p to +the epsilon so this epsilon + + align:start position:0% +the epsilon so this epsilon + + + align:start position:0% +the epsilon so this epsilon +depends on these dimensions but it's + + align:start position:0% +depends on these dimensions but it's + + + align:start position:0% +depends on these dimensions but it's +positive + + align:start position:0% + + + + align:start position:0% + +Okay, so that's our goal and it's + + align:start position:0% +Okay, so that's our goal and it's + + + align:start position:0% +Okay, so that's our goal and it's +significant + + align:start position:0% +significant + + + align:start position:0% +significant +that this would not be true in other + + align:start position:0% +that this would not be true in other + + + align:start position:0% +that this would not be true in other +fields. So this is false + + align:start position:0% +fields. So this is false + + + align:start position:0% +fields. So this is false +in um f q^2 + + align:start position:0% +in um f q^2 + + + align:start position:0% +in um f q^2 +if q= p^2. + + align:start position:0% +if q= p^2. + + + align:start position:0% +if q= p^2. +Um and the example is + + align:start position:0% +Um and the example is + + + align:start position:0% +Um and the example is +that x is fp^2 and d is fp. + + align:start position:0% +that x is fp^2 and d is fp. + + + align:start position:0% +that x is fp^2 and d is fp. +And so then this thing is always fp. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +cool. So, even though this epsilon is a + + align:start position:0% +cool. So, even though this epsilon is a + + + align:start position:0% +cool. So, even though this epsilon is a +really tiny number, which we could make + + align:start position:0% +really tiny number, which we could make + + + align:start position:0% +really tiny number, which we could make +explicit if we worked hard, but we would + + align:start position:0% +explicit if we worked hard, but we would + + + align:start position:0% +explicit if we worked hard, but we would +then be disappointed. Uh, even though + + align:start position:0% +then be disappointed. Uh, even though + + + align:start position:0% +then be disappointed. Uh, even though +it's really tiny, um, this theorem is + + align:start position:0% +it's really tiny, um, this theorem is + + + align:start position:0% +it's really tiny, um, this theorem is +qualitatively an important improvement + + align:start position:0% +qualitatively an important improvement + + + align:start position:0% +qualitatively an important improvement +and it it has lots of applications. This + + align:start position:0% +and it it has lots of applications. This + + + align:start position:0% +and it it has lots of applications. This +and the version overr have lots of + + align:start position:0% +and the version overr have lots of + + + align:start position:0% +and the version overr have lots of +applications and almost everything in + + align:start position:0% +applications and almost everything in + + + align:start position:0% +applications and almost everything in +the rest of the course would will be + + align:start position:0% +the rest of the course would will be + + + align:start position:0% +the rest of the course would will be +based on that kind of whatever most of + + align:start position:0% +based on that kind of whatever most of + + + align:start position:0% +based on that kind of whatever most of +the directions we might go in. + + align:start position:0% +the directions we might go in. + + + align:start position:0% +the directions we might go in. +Okay. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +So last week we introduced combinatorial + + align:start position:0% +So last week we introduced combinatorial + + + align:start position:0% +So last week we introduced combinatorial +number theory and sum product theory and + + align:start position:0% +number theory and sum product theory and + + + align:start position:0% +number theory and sum product theory and +we proved a theorem which is in this + + align:start position:0% +we proved a theorem which is in this + + + align:start position:0% +we proved a theorem which is in this +direction. + + align:start position:0% +direction. + + + align:start position:0% +direction. +It's kind of the special case when x + + align:start position:0% +It's kind of the special case when x + + + align:start position:0% +It's kind of the special case when x +happens to be a product set a cross a. + + align:start position:0% +happens to be a product set a cross a. + + + align:start position:0% +happens to be a product set a cross a. +So our theorem one was last time if A is + + align:start position:0% +So our theorem one was last time if A is + + + align:start position:0% +So our theorem one was last time if A is +in FP + + align:start position:0% +in FP + + + align:start position:0% +in FP +and the size of A is P to the S A + + align:start position:0% +and the size of A is P to the S A + + + align:start position:0% +and the size of A is P to the S A +and D is a set of directions in FP. + + align:start position:0% +and D is a set of directions in FP. + + + align:start position:0% +and D is a set of directions in FP. +Uh and size of D is P to the SD. + + align:start position:0% + + + + align:start position:0% + +Um then if you take the maximum t + + align:start position:0% +Um then if you take the maximum t + + + align:start position:0% +Um then if you take the maximum t +of a + t * a which would be like pi subt + + align:start position:0% +of a + t * a which would be like pi subt + + + align:start position:0% +of a + t * a which would be like pi subt +of a cross a then that's at least um the + + align:start position:0% +of a cross a then that's at least um the + + + align:start position:0% +of a cross a then that's at least um the +size of a * p to the epsilon 1 + + align:start position:0% + + + + align:start position:0% + +that's a little bit bigger and this + + align:start position:0% +that's a little bit bigger and this + + + align:start position:0% +that's a little bit bigger and this +again would be false in other fields. So + + align:start position:0% +again would be false in other fields. So + + + align:start position:0% +again would be false in other fields. So +if if if our field had a sub field, you + + align:start position:0% +if if if our field had a sub field, you + + + align:start position:0% +if if if our field had a sub field, you +could choose these guys to both be the + + align:start position:0% +could choose these guys to both be the + + + align:start position:0% +could choose these guys to both be the +sub field and this would stay in the sub + + align:start position:0% +sub field and this would stay in the sub + + + align:start position:0% +sub field and this would stay in the sub +field. + + align:start position:0% +field. + + + align:start position:0% +field. +Okay, cool. + + align:start position:0% +Okay, cool. + + + align:start position:0% +Okay, cool. +All right, so uh our goal today is to + + align:start position:0% +All right, so uh our goal today is to + + + align:start position:0% +All right, so uh our goal today is to +get from here to there. + + align:start position:0% +get from here to there. + + + align:start position:0% +get from here to there. +And we were talking about it last time + + align:start position:0% +And we were talking about it last time + + + align:start position:0% +And we were talking about it last time +and I wanted to So at first this looks + + align:start position:0% +and I wanted to So at first this looks + + + align:start position:0% +and I wanted to So at first this looks +like a very special case. Um I'll try to + + align:start position:0% +like a very special case. Um I'll try to + + + align:start position:0% +like a very special case. Um I'll try to +argue that it's only a little bit + + align:start position:0% +argue that it's only a little bit + + + align:start position:0% +argue that it's only a little bit +special case and we'll see what what the + + align:start position:0% +special case and we'll see what what the + + + align:start position:0% +special case and we'll see what what the +issue is. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Um, so let me call this an attempt + + align:start position:0% + + + + align:start position:0% + +at BKT + + align:start position:0% +at BKT + + + align:start position:0% +at BKT +using uh theorem one. + + align:start position:0% + + + + align:start position:0% + +Okay. So we're going to do a proof by + + align:start position:0% +Okay. So we're going to do a proof by + + + align:start position:0% +Okay. So we're going to do a proof by +contradiction. + + align:start position:0% + + + + align:start position:0% + +We're going to say epsilon is very small + + align:start position:0% +We're going to say epsilon is very small + + + align:start position:0% +We're going to say epsilon is very small +and it's to be decided. + + align:start position:0% +and it's to be decided. + + + align:start position:0% +and it's to be decided. +And so then we'll assume + + align:start position:0% +And so then we'll assume + + + align:start position:0% +And so then we'll assume +that pi t of x is less than x * p to the + + align:start position:0% +that pi t of x is less than x * p to the + + + align:start position:0% +that pi t of x is less than x * p to the +epsilon for all the t's in d. So proof + + align:start position:0% +epsilon for all the t's in d. So proof + + + align:start position:0% +epsilon for all the t's in d. So proof +by contradiction. So we can assume that + + align:start position:0% +by contradiction. So we can assume that + + + align:start position:0% +by contradiction. So we can assume that +um and also without loss of generality + + align:start position:0% +um and also without loss of generality + + + align:start position:0% +um and also without loss of generality +we can suppose that zero and infinity + + align:start position:0% +we can suppose that zero and infinity + + + align:start position:0% +we can suppose that zero and infinity +are in our set of directions d. So in + + align:start position:0% +are in our set of directions d. So in + + + align:start position:0% +are in our set of directions d. So in +other words we include the horizontal + + align:start position:0% +other words we include the horizontal + + + align:start position:0% +other words we include the horizontal +projection and the vertical projection. + + align:start position:0% +projection and the vertical projection. + + + align:start position:0% +projection and the vertical projection. +So then we can make a set a so that a * + + align:start position:0% +So then we can make a set a so that a * + + + align:start position:0% +So then we can make a set a so that a * +a contains x and x is most of a * a. So + + align:start position:0% +a contains x and x is most of a * a. So + + + align:start position:0% +a contains x and x is most of a * a. So +the set A is pi 0 of X union pi infinity + + align:start position:0% +the set A is pi 0 of X union pi infinity + + + align:start position:0% +the set A is pi 0 of X union pi infinity +of X or the size of A bounded by size of + + align:start position:0% +of X or the size of A bounded by size of + + + align:start position:0% +of X or the size of A bounded by size of +X to the half * P to the epsilon + + align:start position:0% +X to the half * P to the epsilon + + + align:start position:0% +X to the half * P to the epsilon +and and X is contained in A * A. + + align:start position:0% +and and X is contained in A * A. + + + align:start position:0% +and and X is contained in A * A. +Okay. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +So x is a big subset of a product and we + + align:start position:0% +So x is a big subset of a product and we + + + align:start position:0% +So x is a big subset of a product and we +can apply theorem one to our product. + + align:start position:0% +can apply theorem one to our product. + + + align:start position:0% +can apply theorem one to our product. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +So theorem one tells us that the maximum + + align:start position:0% +So theorem one tells us that the maximum + + + align:start position:0% +So theorem one tells us that the maximum +t and d of pi t of a * a is big + + align:start position:0% +t and d of pi t of a * a is big + + + align:start position:0% +t and d of pi t of a * a is big +[Applause] + + align:start position:0% + + + + align:start position:0% + +and even bigger than that. So it's this + + align:start position:0% +and even bigger than that. So it's this + + + align:start position:0% +and even bigger than that. So it's this +is this could be epsilon 1. Um and + + align:start position:0% +is this could be epsilon 1. Um and + + + align:start position:0% +is this could be epsilon 1. Um and +epsilon 1 is much bigger than epsilon. + + align:start position:0% +epsilon 1 is much bigger than epsilon. + + + align:start position:0% +epsilon 1 is much bigger than epsilon. +So epsilon one came from a theorem + + align:start position:0% +So epsilon one came from a theorem + + + align:start position:0% +So epsilon one came from a theorem +that's already proven. It's some number + + align:start position:0% +that's already proven. It's some number + + + align:start position:0% +that's already proven. It's some number +and we get to choose epsilon as small as + + align:start position:0% +and we get to choose epsilon as small as + + + align:start position:0% +and we get to choose epsilon as small as +we like. So we choose it much smaller + + align:start position:0% +we like. So we choose it much smaller + + + align:start position:0% +we like. So we choose it much smaller +than epsilon. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +But this is not yet the + + align:start position:0% +But this is not yet the + + + align:start position:0% +But this is not yet the +projection theorem that we're aiming + + align:start position:0% +projection theorem that we're aiming + + + align:start position:0% +projection theorem that we're aiming +for. And the issue is + + align:start position:0% +for. And the issue is + + + align:start position:0% +for. And the issue is +we would like pi t of x to be big. + + align:start position:0% +we would like pi t of x to be big. + + + align:start position:0% +we would like pi t of x to be big. +So the issue is maybe pi t of x + + align:start position:0% +So the issue is maybe pi t of x + + + align:start position:0% +So the issue is maybe pi t of x +is much smaller than pi t of a cross a + + align:start position:0% + + + + align:start position:0% + +even though x is is a big chunk of a + + align:start position:0% +even though x is is a big chunk of a + + + align:start position:0% +even though x is is a big chunk of a +cross a. + + align:start position:0% +cross a. + + + align:start position:0% +cross a. +Let me make a picture of this enemy + + align:start position:0% +Let me make a picture of this enemy + + + align:start position:0% +Let me make a picture of this enemy +scenario. + + align:start position:0% + + + + align:start position:0% + +So here's the end of the scenario. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +So there's a set X + + align:start position:0% +So there's a set X + + + align:start position:0% +So there's a set X +which has a small projection. + + align:start position:0% +which has a small projection. + + + align:start position:0% +which has a small projection. +So we're going to be doing a projection + + align:start position:0% +So we're going to be doing a projection + + + align:start position:0% +So we're going to be doing a projection +say in this direction. + + align:start position:0% + + + + align:start position:0% + +projection at x is small. + + align:start position:0% +projection at x is small. + + + align:start position:0% +projection at x is small. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Okay. And x is a big portion of this + + align:start position:0% +Okay. And x is a big portion of this + + + align:start position:0% +Okay. And x is a big portion of this +larger set a cross a. + + align:start position:0% +larger set a cross a. + + + align:start position:0% +larger set a cross a. +So in blue we have a cross ax. + + align:start position:0% +So in blue we have a cross ax. + + + align:start position:0% +So in blue we have a cross ax. +And when we project that down, then we + + align:start position:0% +And when we project that down, then we + + + align:start position:0% +And when we project that down, then we +see + + align:start position:0% +see + + + align:start position:0% +see +a lot of stuff. + + align:start position:0% + + + + align:start position:0% + +Pi t a cross a without x. So we're + + align:start position:0% +Pi t a cross a without x. So we're + + + align:start position:0% +Pi t a cross a without x. So we're +worried that we may be so unlucky that + + align:start position:0% +worried that we may be so unlucky that + + + align:start position:0% +worried that we may be so unlucky that +even though pi t of a cross a is quite + + align:start position:0% +even though pi t of a cross a is quite + + + align:start position:0% +even though pi t of a cross a is quite +large and even though x is a big chunk + + align:start position:0% +large and even though x is a big chunk + + + align:start position:0% +large and even though x is a big chunk +of a cross a, nevertheless pi t of x is + + align:start position:0% +of a cross a, nevertheless pi t of x is + + + align:start position:0% +of a cross a, nevertheless pi t of x is +small. We're worried about that. + + align:start position:0% + + + + align:start position:0% + +Okay, so that's where we left off before + + align:start position:0% +Okay, so that's where we left off before + + + align:start position:0% +Okay, so that's where we left off before +vacation. + + align:start position:0% +vacation. + + + align:start position:0% +vacation. +And now what I'd like everyone to do is + + align:start position:0% +And now what I'd like everyone to do is + + + align:start position:0% +And now what I'd like everyone to do is +to try to think of an example where this + + align:start position:0% +to try to think of an example where this + + + align:start position:0% +to try to think of an example where this +happens. Does this ever actually happen + + align:start position:0% +happens. Does this ever actually happen + + + align:start position:0% +happens. Does this ever actually happen +that inside of a cross a you have a + + align:start position:0% +that inside of a cross a you have a + + + align:start position:0% +that inside of a cross a you have a +large subset x and the projection of x + + align:start position:0% +large subset x and the projection of x + + + align:start position:0% +large subset x and the projection of x +is small even though the projection of a + + align:start position:0% +is small even though the projection of a + + + align:start position:0% +is small even though the projection of a +cross a is big? + + align:start position:0% +cross a is big? + + + align:start position:0% +cross a is big? +Can you think of an example where that + + align:start position:0% +Can you think of an example where that + + + align:start position:0% +Can you think of an example where that +actually happens? + + align:start position:0% +actually happens? + + + align:start position:0% +actually happens? +>> Yeah, + + align:start position:0% +>> Yeah, + + + align:start position:0% +>> Yeah, +>> you could choose X to be like a + + align:start position:0% +>> you could choose X to be like a + + + align:start position:0% +>> you could choose X to be like a +diagonal. + + align:start position:0% +diagonal. + + + align:start position:0% +diagonal. +So like all the values like guess I I is + + align:start position:0% +So like all the values like guess I I is + + + align:start position:0% +So like all the values like guess I I is +in FP, + + align:start position:0% +in FP, + + + align:start position:0% +in FP, +>> right? Okay. So, + + align:start position:0% +>> right? Okay. So, + + + align:start position:0% +>> right? Okay. So, +so here's an example. So X, so X is + + align:start position:0% +so here's an example. So X, so X is + + + align:start position:0% +so here's an example. So X, so X is +going to be contained in A cross A. X is + + align:start position:0% +going to be contained in A cross A. X is + + + align:start position:0% +going to be contained in A cross A. X is +the set of all A comma A + + align:start position:0% +the set of all A comma A + + + align:start position:0% +the set of all A comma A +and A cross A. And so then if I take the + + align:start position:0% +and A cross A. And so then if I take the + + + align:start position:0% +and A cross A. And so then if I take the +projection + + align:start position:0% +projection + + + align:start position:0% +projection +um I guess in the direction minus one of + + align:start position:0% +um I guess in the direction minus one of + + + align:start position:0% +um I guess in the direction minus one of +X I just get zero. A minus A is always + + align:start position:0% +X I just get zero. A minus A is always + + + align:start position:0% +X I just get zero. A minus A is always +zero. So this is extremely small. Um + + align:start position:0% +zero. So this is extremely small. Um + + + align:start position:0% +zero. So this is extremely small. Um +okay but in this case this X is quite a + + align:start position:0% +okay but in this case this X is quite a + + + align:start position:0% +okay but in this case this X is quite a +bit smaller than the whole A cross A. + + align:start position:0% +bit smaller than the whole A cross A. + + + align:start position:0% +bit smaller than the whole A cross A. +So let me make a more pre uh precise + + align:start position:0% +So let me make a more pre uh precise + + + align:start position:0% +So let me make a more pre uh precise +question. Um + + align:start position:0% +question. Um + + + align:start position:0% +question. Um +so let's say a has size n + + align:start position:0% +so let's say a has size n + + + align:start position:0% +so let's say a has size n +and x is a subset of a cross a and it's + + align:start position:0% +and x is a subset of a cross a and it's + + + align:start position:0% +and x is a subset of a cross a and it's +really quite big. So I'm going to say x + + align:start position:0% +really quite big. So I'm going to say x + + + align:start position:0% +really quite big. So I'm going to say x +is bigger than well we're going to call + + align:start position:0% +is bigger than well we're going to call + + + align:start position:0% +is bigger than well we're going to call +it for now k inverse time n^2. Um but + + align:start position:0% +it for now k inverse time n^2. Um but + + + align:start position:0% +it for now k inverse time n^2. Um but +then maybe k is order of n to the 1 + + align:start position:0% +then maybe k is order of n to the 1 + + + align:start position:0% +then maybe k is order of n to the 1 +over,000. + + align:start position:0% + + + + align:start position:0% + +So it's really a big portion of a cross + + align:start position:0% +So it's really a big portion of a cross + + + align:start position:0% +So it's really a big portion of a cross +a + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +pi t of x is like way smaller + + align:start position:0% +pi t of x is like way smaller + + + align:start position:0% +pi t of x is like way smaller +than pi t. + + align:start position:0% + + + + align:start position:0% + +We could make that more precise too if + + align:start position:0% +We could make that more precise too if + + + align:start position:0% +We could make that more precise too if +we wanted to. + + align:start position:0% + + + + align:start position:0% + +And that that's the situation we have in + + align:start position:0% +And that that's the situation we have in + + + align:start position:0% +And that that's the situation we have in +our attempt, right? + + align:start position:0% + + + + align:start position:0% + +A is only a bit bigger than X. And so + + align:start position:0% +A is only a bit bigger than X. And so + + + align:start position:0% +A is only a bit bigger than X. And so +um let's say the size of A is N. It's + + align:start position:0% +um let's say the size of A is N. It's + + + align:start position:0% +um let's say the size of A is N. It's +just the definition of N. And then X + + align:start position:0% +just the definition of N. And then X + + + align:start position:0% +just the definition of N. And then X +would be bigger than like P to the minus + + align:start position:0% +would be bigger than like P to the minus + + + align:start position:0% +would be bigger than like P to the minus +a few epsilon + + align:start position:0% +a few epsilon + + + align:start position:0% +a few epsilon +size of A plus. So it's really a a good + + align:start position:0% +size of A plus. So it's really a a good + + + align:start position:0% +size of A plus. So it's really a a good +portion of that. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Right. So, could it still happen that + + align:start position:0% +Right. So, could it still happen that + + + align:start position:0% +Right. So, could it still happen that +the size of the projection of X is way + + align:start position:0% +the size of the projection of X is way + + + align:start position:0% +the size of the projection of X is way +smaller than the size of the projection + + align:start position:0% +smaller than the size of the projection + + + align:start position:0% +smaller than the size of the projection +of the whole thing? + + align:start position:0% + + + + align:start position:0% + +>> Like can you like pigeon hole principles + + align:start position:0% +>> Like can you like pigeon hole principles + + + align:start position:0% +>> Like can you like pigeon hole principles +like the fibers of the projection cross? + + align:start position:0% +like the fibers of the projection cross? + + + align:start position:0% +like the fibers of the projection cross? +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +And that like if X is big enough, you + + align:start position:0% +And that like if X is big enough, you + + + align:start position:0% +And that like if X is big enough, you +know, it has to be at least + + align:start position:0% +know, it has to be at least + + + align:start position:0% +know, it has to be at least +some nice number of those, + + align:start position:0% +some nice number of those, + + + align:start position:0% +some nice number of those, +>> right? So the suggestion is we can look + + align:start position:0% +>> right? So the suggestion is we can look + + + align:start position:0% +>> right? So the suggestion is we can look +at all of the fibers of the projection + + align:start position:0% +at all of the fibers of the projection + + + align:start position:0% +at all of the fibers of the projection +of A cross A and then we should pick X + + align:start position:0% +of A cross A and then we should pick X + + + align:start position:0% +of A cross A and then we should pick X +to be the union of of the big fibers. + + align:start position:0% + + + + align:start position:0% + +Yeah. Yeah, that's right. That's right. + + align:start position:0% +Yeah. Yeah, that's right. That's right. + + + align:start position:0% +Yeah. Yeah, that's right. That's right. +So in this enemy scenario, there have to + + align:start position:0% +So in this enemy scenario, there have to + + + align:start position:0% +So in this enemy scenario, there have to +be some very big fibers and some much + + align:start position:0% +be some very big fibers and some much + + + align:start position:0% +be some very big fibers and some much +smaller fibers. They have to be kind of + + align:start position:0% +smaller fibers. They have to be kind of + + + align:start position:0% +smaller fibers. They have to be kind of +different from each other. + + align:start position:0% +different from each other. + + + align:start position:0% +different from each other. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +Um Okay. But let's see if we can think + + align:start position:0% +Um Okay. But let's see if we can think + + + align:start position:0% +Um Okay. But let's see if we can think +of an example where this happens. + + align:start position:0% +of an example where this happens. + + + align:start position:0% +of an example where this happens. +That should erase + + align:start position:0% + + + + align:start position:0% + +some space. + + align:start position:0% +some space. + + + align:start position:0% +some space. +Okay. So, um I just going to continue + + align:start position:0% +Okay. So, um I just going to continue + + + align:start position:0% +Okay. So, um I just going to continue +below the line here. + + align:start position:0% + + + + align:start position:0% + +Okay. So first of all, can we even think + + align:start position:0% +Okay. So first of all, can we even think + + + align:start position:0% +Okay. So first of all, can we even think +of an example where the projection of of + + align:start position:0% +of an example where the projection of of + + + align:start position:0% +of an example where the projection of of +X or something would be small at all? Um + + align:start position:0% +X or something would be small at all? Um + + + align:start position:0% +X or something would be small at all? Um +so so an example um maybe X could be the + + align:start position:0% +so so an example um maybe X could be the + + + align:start position:0% +so so an example um maybe X could be the +numbers from one up to N cross the + + align:start position:0% +numbers from one up to N cross the + + + align:start position:0% +numbers from one up to N cross the +numbers from one up to N + + align:start position:0% +numbers from one up to N + + + align:start position:0% +numbers from one up to N +and then pi 1 of X is pretty small + + align:start position:0% +and then pi 1 of X is pretty small + + + align:start position:0% +and then pi 1 of X is pretty small +would be basically introduced from one + + align:start position:0% +would be basically introduced from one + + + align:start position:0% +would be basically introduced from one +up to 2N. + + align:start position:0% +up to 2N. + + + align:start position:0% +up to 2N. +So this would be quite small. + + align:start position:0% +So this would be quite small. + + + align:start position:0% +So this would be quite small. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um, + + align:start position:0% + + + + align:start position:0% + +so you could make you could make this a + + align:start position:0% +so you could make you could make this a + + + align:start position:0% +so you could make you could make this a +so x would be all of a cross a. Then the + + align:start position:0% +so x would be all of a cross a. Then the + + + align:start position:0% +so x would be all of a cross a. Then the +projection of a cross a would be small. + + align:start position:0% +projection of a cross a would be small. + + + align:start position:0% +projection of a cross a would be small. +But you could also inflate a to make it + + align:start position:0% +But you could also inflate a to make it + + + align:start position:0% +But you could also inflate a to make it +bigger than that. + + align:start position:0% +bigger than that. + + + align:start position:0% +bigger than that. +So we could take a to be the integers + + align:start position:0% +So we could take a to be the integers + + + align:start position:0% +So we could take a to be the integers +from one up to n union a tilda. + + align:start position:0% +from one up to n union a tilda. + + + align:start position:0% +from one up to n union a tilda. +Maybe the size of a tilda is also n but + + align:start position:0% +Maybe the size of a tilda is also n but + + + align:start position:0% +Maybe the size of a tilda is also n but +a tilda is unstructured or random. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Okay. So now if I take + + align:start position:0% +Okay. So now if I take + + + align:start position:0% +Okay. So now if I take +pi 1 of a cross a, + + align:start position:0% +pi 1 of a cross a, + + + align:start position:0% +pi 1 of a cross a, +it's at least as big as pi 1 of a tilda + + align:start position:0% +it's at least as big as pi 1 of a tilda + + + align:start position:0% +it's at least as big as pi 1 of a tilda +cross a tilda. + + align:start position:0% +cross a tilda. + + + align:start position:0% +cross a tilda. +and a tilda has nothing to do with + + align:start position:0% +and a tilda has nothing to do with + + + align:start position:0% +and a tilda has nothing to do with +numbers from one up to n. I could build + + align:start position:0% +numbers from one up to n. I could build + + + align:start position:0% +numbers from one up to n. I could build +some set where that's big. + + align:start position:0% + + + + align:start position:0% + +Okay, but pi 1 of x + + align:start position:0% +Okay, but pi 1 of x + + + align:start position:0% +Okay, but pi 1 of x +is only around n. + + align:start position:0% +is only around n. + + + align:start position:0% +is only around n. +So there could be a big gap between + + align:start position:0% +So there could be a big gap between + + + align:start position:0% +So there could be a big gap between +these guys. + + align:start position:0% + + + + align:start position:0% + +Um + + align:start position:0% +Um + + + align:start position:0% +Um +but this example is not so not such a + + align:start position:0% +but this example is not so not such a + + + align:start position:0% +but this example is not so not such a +problem for our strategy because in this + + align:start position:0% +problem for our strategy because in this + + + align:start position:0% +problem for our strategy because in this +example we just should have chosen the + + align:start position:0% +example we just should have chosen the + + + align:start position:0% +example we just should have chosen the +set A smaller. We'd like a to be we + + align:start position:0% +set A smaller. We'd like a to be we + + + align:start position:0% +set A smaller. We'd like a to be we +could we could choose a as we like. We + + align:start position:0% +could we could choose a as we like. We + + + align:start position:0% +could we could choose a as we like. We +could choose a smaller set a so that a + + align:start position:0% +could choose a smaller set a so that a + + + align:start position:0% +could choose a smaller set a so that a +actually with the smaller choice of a + + align:start position:0% +actually with the smaller choice of a + + + align:start position:0% +actually with the smaller choice of a +just these guys x would be a cross a and + + align:start position:0% +just these guys x would be a cross a and + + + align:start position:0% +just these guys x would be a cross a and +then we would be happy. + + align:start position:0% + + + + align:start position:0% + +Okay. So the key to the proof of uh of + + align:start position:0% +Okay. So the key to the proof of uh of + + + align:start position:0% +Okay. So the key to the proof of uh of +banan cat's tao is a theorem from + + align:start position:0% +banan cat's tao is a theorem from + + + align:start position:0% +banan cat's tao is a theorem from +cominator. It's called the balog sum + + align:start position:0% +cominator. It's called the balog sum + + + align:start position:0% +cominator. It's called the balog sum +gowowers theorem and it says that this + + align:start position:0% +gowowers theorem and it says that this + + + align:start position:0% +gowowers theorem and it says that this +example is pretty much the only way that + + align:start position:0% +example is pretty much the only way that + + + align:start position:0% +example is pretty much the only way that +pi 1 of x could be much smaller than pi + + align:start position:0% +pi 1 of x could be much smaller than pi + + + align:start position:0% +pi 1 of x could be much smaller than pi +1 of a cross a. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +This is called the balag seme gow + + align:start position:0% +This is called the balag seme gow + + + align:start position:0% +This is called the balag seme gow +theorem and it's uh another of the kind + + align:start position:0% +theorem and it's uh another of the kind + + + align:start position:0% +theorem and it's uh another of the kind +of uh central tools in the toolbox of + + align:start position:0% +of uh central tools in the toolbox of + + + align:start position:0% +of uh central tools in the toolbox of +additive combinatorics along with the + + align:start position:0% +additive combinatorics along with the + + + align:start position:0% +additive combinatorics along with the +plunicarusa inequalities that we talked + + align:start position:0% +plunicarusa inequalities that we talked + + + align:start position:0% +plunicarusa inequalities that we talked +about last time. All right. So it says + + align:start position:0% +about last time. All right. So it says + + + align:start position:0% +about last time. All right. So it says +if a and b are contained in an aelion + + align:start position:0% +if a and b are contained in an aelion + + + align:start position:0% +if a and b are contained in an aelion +group and they have size at most n + + align:start position:0% + + + + align:start position:0% + +uh and I have a subset of a cross b + + align:start position:0% +uh and I have a subset of a cross b + + + align:start position:0% +uh and I have a subset of a cross b +which is significant. + + align:start position:0% + + + + align:start position:0% + +It's a significant fraction + + align:start position:0% +It's a significant fraction + + + align:start position:0% +It's a significant fraction +and the projection of this subset in + + align:start position:0% +and the projection of this subset in + + + align:start position:0% +and the projection of this subset in +some direction is small. + + align:start position:0% + + + + align:start position:0% + +So, so here I want you to imagine that K + + align:start position:0% +So, so here I want you to imagine that K + + + align:start position:0% +So, so here I want you to imagine that K +is a lot smaller than N. So this is a + + align:start position:0% +is a lot smaller than N. So this is a + + + align:start position:0% +is a lot smaller than N. So this is a +big chunk of all the pairs A and B. And + + align:start position:0% +big chunk of all the pairs A and B. And + + + align:start position:0% +big chunk of all the pairs A and B. And +the smallest this could possibly be is + + align:start position:0% +the smallest this could possibly be is + + + align:start position:0% +the smallest this could possibly be is +around N because if you just fix one + + align:start position:0% +around N because if you just fix one + + + align:start position:0% +around N because if you just fix one +element of B, you'd have around N + + align:start position:0% +element of B, you'd have around N + + + align:start position:0% +element of B, you'd have around N +choices for this element of A. So that + + align:start position:0% +choices for this element of A. So that + + + align:start position:0% +choices for this element of A. So that +would already give you a round N here. + + align:start position:0% +would already give you a round N here. + + + align:start position:0% +would already give you a round N here. +So this is almost as small as possible. + + align:start position:0% +So this is almost as small as possible. + + + align:start position:0% +So this is almost as small as possible. +And then the conclusion is + + align:start position:0% +And then the conclusion is + + + align:start position:0% +And then the conclusion is +it's not necessarily the case that pi t + + align:start position:0% +it's not necessarily the case that pi t + + + align:start position:0% +it's not necessarily the case that pi t +of all of a cross b is small. We just + + align:start position:0% +of all of a cross b is small. We just + + + align:start position:0% +of all of a cross b is small. We just +saw a counter example to that. But we + + align:start position:0% +saw a counter example to that. But we + + + align:start position:0% +saw a counter example to that. But we +could find big pieces of a and b so that + + align:start position:0% +could find big pieces of a and b so that + + + align:start position:0% +could find big pieces of a and b so that +the projection of the big pieces is + + align:start position:0% +the projection of the big pieces is + + + align:start position:0% +the projection of the big pieces is +small. So then there exists a prime and + + align:start position:0% +small. So then there exists a prime and + + + align:start position:0% +small. So then there exists a prime and +b prime which are subsets of a and b. A + + align:start position:0% +b prime which are subsets of a and b. A + + + align:start position:0% +b prime which are subsets of a and b. A +prime and a b prime and b. So that um + + align:start position:0% +prime and a b prime and b. So that um + + + align:start position:0% +prime and a b prime and b. So that um +I'll say x prime is defined to be a + + align:start position:0% +I'll say x prime is defined to be a + + + align:start position:0% +I'll say x prime is defined to be a +prime cross b prime intersect x + + align:start position:0% +prime cross b prime intersect x + + + align:start position:0% +prime cross b prime intersect x +and x prime is still a big fraction of + + align:start position:0% +and x prime is still a big fraction of + + + align:start position:0% +and x prime is still a big fraction of +n^2. + + align:start position:0% +n^2. + + + align:start position:0% +n^2. +So k to the minus some constant power + + align:start position:0% +So k to the minus some constant power + + + align:start position:0% +So k to the minus some constant power +time n^2 + + align:start position:0% +time n^2 + + + align:start position:0% +time n^2 +and if I take pi t of a a prime a prime + + align:start position:0% +and if I take pi t of a a prime a prime + + + align:start position:0% +and if I take pi t of a a prime a prime +cross b prime that is less than k to + + align:start position:0% +cross b prime that is less than k to + + + align:start position:0% +cross b prime that is less than k to +some power* l. + + align:start position:0% +some power* l. + + + align:start position:0% +some power* l. +So this is small. + + align:start position:0% + + + + align:start position:0% + +So in this example here + + align:start position:0% +So in this example here + + + align:start position:0% +So in this example here +where a was like this, this part here + + align:start position:0% +where a was like this, this part here + + + align:start position:0% +where a was like this, this part here +would be the a prime and it would be + + align:start position:0% +would be the a prime and it would be + + + align:start position:0% +would be the a prime and it would be +symmetric in the a b prime and a prime + + align:start position:0% +symmetric in the a b prime and a prime + + + align:start position:0% +symmetric in the a b prime and a prime +would both be this. + + align:start position:0% + + + + align:start position:0% + +Okay, take a moment to digest that + + align:start position:0% +Okay, take a moment to digest that + + + align:start position:0% +Okay, take a moment to digest that +statement and see if you have questions + + align:start position:0% +statement and see if you have questions + + + align:start position:0% +statement and see if you have questions +or comments. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um so we will prove this probably + + align:start position:0% +Um so we will prove this probably + + + align:start position:0% +Um so we will prove this probably +starting later today but but most of it + + align:start position:0% +starting later today but but most of it + + + align:start position:0% +starting later today but but most of it +next class. Um but for the rest of this + + align:start position:0% +next class. Um but for the rest of this + + + align:start position:0% +next class. Um but for the rest of this +class we'll explore uh explore why this + + align:start position:0% +class we'll explore uh explore why this + + + align:start position:0% +class we'll explore uh explore why this +is useful and in particular we'll use it + + align:start position:0% +is useful and in particular we'll use it + + + align:start position:0% +is useful and in particular we'll use it +to prove the projection theorem. Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. Um, + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +all right. So let's do the proof + + align:start position:0% +all right. So let's do the proof + + + align:start position:0% +all right. So let's do the proof +of the Borgan textile projection + + align:start position:0% +of the Borgan textile projection + + + align:start position:0% +of the Borgan textile projection +theorem. + + align:start position:0% + + + + align:start position:0% + +Okay. So let's say epsilon is small to + + align:start position:0% +Okay. So let's say epsilon is small to + + + align:start position:0% +Okay. So let's say epsilon is small to +be decided. We're going to prove there's + + align:start position:0% +be decided. We're going to prove there's + + + align:start position:0% +be decided. We're going to prove there's +some small epsilon where this is true. + + align:start position:0% +some small epsilon where this is true. + + + align:start position:0% +some small epsilon where this is true. +And I'm going to write I write C less + + align:start position:0% +And I'm going to write I write C less + + + align:start position:0% +And I'm going to write I write C less +than tilda tilda D. It means that C is + + align:start position:0% +than tilda tilda D. It means that C is + + + align:start position:0% +than tilda tilda D. It means that C is +less than P to the big O of epsilon * D. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And now we're going to do a proof by + + align:start position:0% +And now we're going to do a proof by + + + align:start position:0% +And now we're going to do a proof by +contradiction. So we can suppose + + align:start position:0% +contradiction. So we can suppose + + + align:start position:0% +contradiction. So we can suppose +pi t of x + + align:start position:0% +pi t of x + + + align:start position:0% +pi t of x +is less sim less than or equal to p to + + align:start position:0% +is less sim less than or equal to p to + + + align:start position:0% +is less sim less than or equal to p to +the epsilon * x to the half for all the + + align:start position:0% +the epsilon * x to the half for all the + + + align:start position:0% +the epsilon * x to the half for all the +t and d. + + align:start position:0% + + + + align:start position:0% + +Okay. Um without loss of generality I + + align:start position:0% +Okay. Um without loss of generality I + + + align:start position:0% +Okay. Um without loss of generality I +can suppose that zero or infinity are in + + align:start position:0% +can suppose that zero or infinity are in + + + align:start position:0% +can suppose that zero or infinity are in +my directions and I'll take a to be pi 0 + + align:start position:0% +my directions and I'll take a to be pi 0 + + + align:start position:0% +my directions and I'll take a to be pi 0 +of x union pi infinity of x. + + align:start position:0% +of x union pi infinity of x. + + + align:start position:0% +of x union pi infinity of x. +And so now I know that x is a subset of + + align:start position:0% +And so now I know that x is a subset of + + + align:start position:0% +And so now I know that x is a subset of +a cross a. + + align:start position:0% +a cross a. + + + align:start position:0% +a cross a. +Um I'll say a size of a could be n and + + align:start position:0% +Um I'll say a size of a could be n and + + + align:start position:0% +Um I'll say a size of a could be n and +that is tilda tilda the square root of x + + align:start position:0% +that is tilda tilda the square root of x + + + align:start position:0% +that is tilda tilda the square root of x +up to some powers of p to the epsilon. + + align:start position:0% + + + + align:start position:0% + +Okay. And uh therefore x is greater + + align:start position:0% +Okay. And uh therefore x is greater + + + align:start position:0% +Okay. And uh therefore x is greater +tilda tilda n^ 2. So x is a big fraction + + align:start position:0% +tilda tilda n^ 2. So x is a big fraction + + + align:start position:0% +tilda tilda n^ 2. So x is a big fraction +of all of a cross a. + + align:start position:0% +of all of a cross a. + + + align:start position:0% +of all of a cross a. +Oh, + + align:start position:0% +Oh, + + + align:start position:0% +Oh, +next um I choose some other t1 + + align:start position:0% +next um I choose some other t1 + + + align:start position:0% +next um I choose some other t1 +in D and I know that pi t1 of x is less + + align:start position:0% +in D and I know that pi t1 of x is less + + + align:start position:0% +in D and I know that pi t1 of x is less +than tilda tilda n. + + align:start position:0% +than tilda tilda n. + + + align:start position:0% +than tilda tilda n. +Okay. + + align:start position:0% + + + + align:start position:0% + +And so when I once I know this the + + align:start position:0% +And so when I once I know this the + + + align:start position:0% +And so when I once I know this the +bality gowowers theorem tells me that it + + align:start position:0% +bality gowowers theorem tells me that it + + + align:start position:0% +bality gowowers theorem tells me that it +this comes from a product a prime a + + align:start position:0% +this comes from a product a prime a + + + align:start position:0% +this comes from a product a prime a +prime cross b prime. So sarity gow + + align:start position:0% +prime cross b prime. So sarity gow + + + align:start position:0% +prime cross b prime. So sarity gow +theorem says + + align:start position:0% +theorem says + + + align:start position:0% +theorem says +this a prime and a b prime and b and x + + align:start position:0% +this a prime and a b prime and b and x + + + align:start position:0% +this a prime and a b prime and b and x +prime is the part of x in this product a + + align:start position:0% +prime is the part of x in this product a + + + align:start position:0% +prime is the part of x in this product a +prime cross b prime. So first of all, x + + align:start position:0% +prime cross b prime. So first of all, x + + + align:start position:0% +prime cross b prime. So first of all, x +prime is still quite substantial and pi + + align:start position:0% +prime is still quite substantial and pi + + + align:start position:0% +prime is still quite substantial and pi +t1 of a prime cross b prime is small. + + align:start position:0% + + + + align:start position:0% + +And this means in other words that a + + align:start position:0% +And this means in other words that a + + + align:start position:0% +And this means in other words that a +prime plus t1 b prime is small. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And this here is + + align:start position:0% +And this here is + + + align:start position:0% +And this here is +um + + align:start position:0% +um + + + align:start position:0% +um +this information here we c uh is is is + + align:start position:0% +this information here we c uh is is is + + + align:start position:0% +this information here we c uh is is is +is strong in a helpful way that's + + align:start position:0% +is strong in a helpful way that's + + + align:start position:0% +is strong in a helpful way that's +stronger than this because here we can + + align:start position:0% +stronger than this because here we can + + + align:start position:0% +stronger than this because here we can +use the pluna rou inequalities. + + align:start position:0% + + + + align:start position:0% + +So once we know that a prime plus t1 b + + align:start position:0% +So once we know that a prime plus t1 b + + + align:start position:0% +So once we know that a prime plus t1 b +prime is small then plunicar rouia + + align:start position:0% +prime is small then plunicar rouia + + + align:start position:0% +prime is small then plunicar rouia +inequalities tell us that lots of other + + align:start position:0% +inequalities tell us that lots of other + + + align:start position:0% +inequalities tell us that lots of other +things are small. So for example a prime + + align:start position:0% +things are small. So for example a prime + + + align:start position:0% +things are small. So for example a prime +plus or minus a prime is also small. Um + + align:start position:0% +plus or minus a prime is also small. Um + + + align:start position:0% +plus or minus a prime is also small. Um +if I wanted to + + align:start position:0% +if I wanted to + + + align:start position:0% +if I wanted to +uh I could do a triple sum a prime plus + + align:start position:0% +uh I could do a triple sum a prime plus + + + align:start position:0% +uh I could do a triple sum a prime plus +a prime plus a prime is also small dot + + align:start position:0% +a prime plus a prime is also small dot + + + align:start position:0% +a prime plus a prime is also small dot +dot dot. You could do the same with B + + align:start position:0% +dot dot. You could do the same with B + + + align:start position:0% +dot dot. You could do the same with B +prime. + + align:start position:0% +prime. + + + align:start position:0% +prime. +Okay. So, + + align:start position:0% +Okay. So, + + + align:start position:0% +Okay. So, +so now we have see that A prime and B + + align:start position:0% +so now we have see that A prime and B + + + align:start position:0% +so now we have see that A prime and B +prime have a lot of structure. + + align:start position:0% +prime have a lot of structure. + + + align:start position:0% +prime have a lot of structure. +Have a lot of structure. And actually, + + align:start position:0% +Have a lot of structure. And actually, + + + align:start position:0% +Have a lot of structure. And actually, +I'll use the word symmetry. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +Right. Okay. + + align:start position:0% +Right. Okay. + + + align:start position:0% +Right. Okay. +Okay. So I actually I'll draw you a + + align:start position:0% +Okay. So I actually I'll draw you a + + + align:start position:0% +Okay. So I actually I'll draw you a +picture in a minute of how I visualize + + align:start position:0% +picture in a minute of how I visualize + + + align:start position:0% +picture in a minute of how I visualize +this and why why I use the word + + align:start position:0% +this and why why I use the word + + + align:start position:0% +this and why why I use the word +symmetry. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So next + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +so I have to make space I'm going to + + align:start position:0% +so I have to make space I'm going to + + + align:start position:0% +so I have to make space I'm going to +erase the statement of the theorem. + + align:start position:0% +erase the statement of the theorem. + + + align:start position:0% +erase the statement of the theorem. +We're going to try to prove that one of + + align:start position:0% +We're going to try to prove that one of + + + align:start position:0% +We're going to try to prove that one of +the projections of x is big. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% + + + + align:start position:0% + +All right. So now have a lema. It says + + align:start position:0% +All right. So now have a lema. It says + + + align:start position:0% +All right. So now have a lema. It says +if I have a subset y and a prime cross b + + align:start position:0% +if I have a subset y and a prime cross b + + + align:start position:0% +if I have a subset y and a prime cross b +prime, the subset we're going to care + + align:start position:0% +prime, the subset we're going to care + + + align:start position:0% +prime, the subset we're going to care +about is just x prime, but the lema is + + align:start position:0% +about is just x prime, but the lema is + + + align:start position:0% +about is just x prime, but the lema is +more general. Um, okay. And um a prime + + align:start position:0% +more general. Um, okay. And um a prime + + + align:start position:0% +more general. Um, okay. And um a prime +and b prime have these nice properties. + + align:start position:0% +and b prime have these nice properties. + + + align:start position:0% +and b prime have these nice properties. +So I'll just copy these two. + + align:start position:0% + + + + align:start position:0% + +So a prime + t1 b prime + + align:start position:0% +So a prime + t1 b prime + + + align:start position:0% +So a prime + t1 b prime +is small. + + align:start position:0% + + + + align:start position:0% + +A prime minus A prime is small and and Y + + align:start position:0% +A prime minus A prime is small and and Y + + + align:start position:0% +A prime minus A prime is small and and Y +itself is is is fairly large + + align:start position:0% +itself is is is fairly large + + + align:start position:0% +itself is is is fairly large +although I don't need to write it in the + + align:start position:0% +although I don't need to write it in the + + + align:start position:0% +although I don't need to write it in the +statement. + + align:start position:0% +statement. + + + align:start position:0% +statement. +Um then + + align:start position:0% +Um then + + + align:start position:0% +Um then +pi t of y so this is for any t so t is + + align:start position:0% +pi t of y so this is for any t so t is + + + align:start position:0% +pi t of y so this is for any t so t is +just anybody in fp different from t1. + + align:start position:0% + + + + align:start position:0% + +This guy is bigger than tilda tilda + + align:start position:0% +This guy is bigger than tilda tilda + + + align:start position:0% +This guy is bigger than tilda tilda +y / n^2 + + align:start position:0% +y / n^2 + + + align:start position:0% +y / n^2 +times pi in a different direction + + align:start position:0% +times pi in a different direction + + + align:start position:0% +times pi in a different direction +t over t1 + + align:start position:0% +t over t1 + + + align:start position:0% +t over t1 +of a prime cross a prime. + + align:start position:0% + + + + align:start position:0% + +Right? So we have a + + align:start position:0% +Right? So we have a + + + align:start position:0% +Right? So we have a +the biggest y could be is it could be + + align:start position:0% +the biggest y could be is it could be + + + align:start position:0% +the biggest y could be is it could be +have size around n squ in which case + + align:start position:0% +have size around n squ in which case + + + align:start position:0% +have size around n squ in which case +this would disappear. + + align:start position:0% +this would disappear. + + + align:start position:0% +this would disappear. +And so I say if we have a large subset + + align:start position:0% +And so I say if we have a large subset + + + align:start position:0% +And so I say if we have a large subset +of a prime cross b prime then the + + align:start position:0% +of a prime cross b prime then the + + + align:start position:0% +of a prime cross b prime then the +projection of that large subset y is + + align:start position:0% +projection of that large subset y is + + + align:start position:0% +projection of that large subset y is +bigger than the projection in a related + + align:start position:0% +bigger than the projection in a related + + + align:start position:0% +bigger than the projection in a related +angle of a whole product a prime cross a + + align:start position:0% +angle of a whole product a prime cross a + + + align:start position:0% +angle of a whole product a prime cross a +prime. This is good for us because we + + align:start position:0% +prime. This is good for us because we + + + align:start position:0% +prime. This is good for us because we +can apply theorem one to this. + + align:start position:0% +can apply theorem one to this. + + + align:start position:0% +can apply theorem one to this. +Um and um this is + + align:start position:0% +Um and um this is + + + align:start position:0% +Um and um this is +uh this inequality kind kind of ruling + + align:start position:0% +uh this inequality kind kind of ruling + + + align:start position:0% +uh this inequality kind kind of ruling +out the enemy scenario. We're ruling out + + align:start position:0% +out the enemy scenario. We're ruling out + + + align:start position:0% +out the enemy scenario. We're ruling out +the possibility that there's a big chunk + + align:start position:0% +the possibility that there's a big chunk + + + align:start position:0% +the possibility that there's a big chunk +of a prime cross b prime that got + + align:start position:0% +of a prime cross b prime that got + + + align:start position:0% +of a prime cross b prime that got +compressed even though the whole thing + + align:start position:0% +compressed even though the whole thing + + + align:start position:0% +compressed even though the whole thing +didn't. + + align:start position:0% + + + + align:start position:0% + +Okay, let me put over here some uh + + align:start position:0% +Okay, let me put over here some uh + + + align:start position:0% +Okay, let me put over here some uh +intuition. + + align:start position:0% + + + + align:start position:0% + +So my intuition is + + align:start position:0% +So my intuition is + + + align:start position:0% +So my intuition is +that a prime cross b prime is very + + align:start position:0% +that a prime cross b prime is very + + + align:start position:0% +that a prime cross b prime is very +symmetric. + + align:start position:0% +symmetric. + + + align:start position:0% +symmetric. +And so let me draw an exaggerated + + align:start position:0% +And so let me draw an exaggerated + + + align:start position:0% +And so let me draw an exaggerated +version. Suppose that a prime cross b + + align:start position:0% +version. Suppose that a prime cross b + + + align:start position:0% +version. Suppose that a prime cross b +prime just looked like a lattice. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And inside of there we have some + + align:start position:0% +And inside of there we have some + + + align:start position:0% +And inside of there we have some +substantial but kind of unstructured set + + align:start position:0% +substantial but kind of unstructured set + + + align:start position:0% +substantial but kind of unstructured set +Y. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +So if there were some angle where the + + align:start position:0% +So if there were some angle where the + + + align:start position:0% +So if there were some angle where the +projection of Y got compressed a lot. I + + align:start position:0% +projection of Y got compressed a lot. I + + + align:start position:0% +projection of Y got compressed a lot. I +claim that compression of the the whole + + align:start position:0% +claim that compression of the the whole + + + align:start position:0% +claim that compression of the the whole +lattice should get compressed a lot. + + align:start position:0% +lattice should get compressed a lot. + + + align:start position:0% +lattice should get compressed a lot. +Why? Because the lattice is symmetric. + + align:start position:0% +Why? Because the lattice is symmetric. + + + align:start position:0% +Why? Because the lattice is symmetric. +So I can cover the lattice by some + + align:start position:0% +So I can cover the lattice by some + + + align:start position:0% +So I can cover the lattice by some +translates of y and if each of those + + align:start position:0% +translates of y and if each of those + + + align:start position:0% +translates of y and if each of those +gets compressed a lot then the whole + + align:start position:0% +gets compressed a lot then the whole + + + align:start position:0% +gets compressed a lot then the whole +lattice should be compressed a lot. + + align:start position:0% +lattice should be compressed a lot. + + + align:start position:0% +lattice should be compressed a lot. +So + + align:start position:0% +So + + + align:start position:0% +So +recover + + align:start position:0% +recover + + + align:start position:0% +recover +a prime cross b prime by a few + + align:start position:0% +a prime cross b prime by a few + + + align:start position:0% +a prime cross b prime by a few +translates of y. + + align:start position:0% + + + + align:start position:0% + +And then we would get that the + + align:start position:0% +And then we would get that the + + + align:start position:0% +And then we would get that the +projection of the whole thing + + align:start position:0% +projection of the whole thing + + + align:start position:0% +projection of the whole thing +should be bounded by a few times the + + align:start position:0% +should be bounded by a few times the + + + align:start position:0% +should be bounded by a few times the +projection of y. + + align:start position:0% + + + + align:start position:0% + +Okay. So now let's carry out this + + align:start position:0% +Okay. So now let's carry out this + + + align:start position:0% +Okay. So now let's carry out this +intuition. We are going to cover y uh + + align:start position:0% +intuition. We are going to cover y uh + + + align:start position:0% +intuition. We are going to cover y uh +cover a prime cover something uh by + + align:start position:0% +cover a prime cover something uh by + + + align:start position:0% +cover a prime cover something uh by +translates of y. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +so let's consider + + align:start position:0% +so let's consider + + + align:start position:0% +so let's consider +y + t1 t2. These are some translates of + + align:start position:0% +y + t1 t2. These are some translates of + + + align:start position:0% +y + t1 t2. These are some translates of +y set of these guys + + align:start position:0% + + + + align:start position:0% + +where t1 is an a prime cross a prime + + align:start position:0% +where t1 is an a prime cross a prime + + + align:start position:0% +where t1 is an a prime cross a prime +minus a prime and t2 is in um this + + align:start position:0% +minus a prime and t2 is in um this + + + align:start position:0% +minus a prime and t2 is in um this +slightly weird looking thing + + align:start position:0% +slightly weird looking thing + + + align:start position:0% +slightly weird looking thing +there. + + align:start position:0% + + + + align:start position:0% + +Okay. And so these are a bunch of + + align:start position:0% +Okay. And so these are a bunch of + + + align:start position:0% +Okay. And so these are a bunch of +translates of y. And these translates of + + align:start position:0% +translates of y. And these translates of + + + align:start position:0% +translates of y. And these translates of +y + + align:start position:0% +y + + + align:start position:0% +y +cover uh + + align:start position:0% +cover uh + + + align:start position:0% +cover uh +cover somebody a lot of times. So for + + align:start position:0% +cover somebody a lot of times. So for + + + align:start position:0% +cover somebody a lot of times. So for +every um + + align:start position:0% +every um + + + align:start position:0% +every um +every y1 y2 + + align:start position:0% +every y1 y2 + + + align:start position:0% +every y1 y2 +let me do it this way. So for every a1 + + align:start position:0% +let me do it this way. So for every a1 + + + align:start position:0% +let me do it this way. So for every a1 +a2 in a prime cross a prime and for + + align:start position:0% +a2 in a prime cross a prime and for + + + align:start position:0% +a2 in a prime cross a prime and for +every y1 y2 + + align:start position:0% +every y1 y2 + + + align:start position:0% +every y1 y2 +in y there is a unique t1 t2 which is in + + align:start position:0% +in y there is a unique t1 t2 which is in + + + align:start position:0% +in y there is a unique t1 t2 which is in +this list. + + align:start position:0% +this list. + + + align:start position:0% +this list. +Um so that uh a1 so that y1 y2 + + align:start position:0% +Um so that uh a1 so that y1 y2 + + + align:start position:0% +Um so that uh a1 so that y1 y2 +plus t1 t2 is a1h. + + align:start position:0% + + + + align:start position:0% + +So this is easier to prove than it is to + + align:start position:0% +So this is easier to prove than it is to + + + align:start position:0% +So this is easier to prove than it is to +write down. + + align:start position:0% +write down. + + + align:start position:0% +write down. +Just solve for t1. t1 must be y1 a1 + + align:start position:0% +Just solve for t1. t1 must be y1 a1 + + + align:start position:0% +Just solve for t1. t1 must be y1 a1 +minus y1. And uh and these these guys + + align:start position:0% +minus y1. And uh and these these guys + + + align:start position:0% +minus y1. And uh and these these guys +both live in a prime. So t1 is in there. + + align:start position:0% +both live in a prime. So t1 is in there. + + + align:start position:0% +both live in a prime. So t1 is in there. +Um and uh + + align:start position:0% +Um and uh + + + align:start position:0% +Um and uh +um ah + + align:start position:0% +um ah + + + align:start position:0% +um ah +wait + + align:start position:0% +wait + + + align:start position:0% +wait +yeah sorry. So this is going to have to + + align:start position:0% +yeah sorry. So this is going to have to + + + align:start position:0% +yeah sorry. So this is going to have to +be -1 over t1 a prime. + + align:start position:0% +be -1 over t1 a prime. + + + align:start position:0% +be -1 over t1 a prime. +Okay. Now how does y2 work? um for every + + align:start position:0% +Okay. Now how does y2 work? um for every + + + align:start position:0% +Okay. Now how does y2 work? um for every +uh so t2 is going to be a2 minus y2 + + align:start position:0% +uh so t2 is going to be a2 minus y2 + + + align:start position:0% +uh so t2 is going to be a2 minus y2 +and the uh + + align:start position:0% +and the uh + + + align:start position:0% +and the uh +the a2 + + align:start position:0% +the a2 + + + align:start position:0% +the a2 +lives in b prime and the uh + + align:start position:0% + + + + align:start position:0% + +Um + + align:start position:0% + + + + align:start position:0% + +yeah. + + align:start position:0% + + + + align:start position:0% + +So the a2 lives here and the um y2 lives + + align:start position:0% +So the a2 lives here and the um y2 lives + + + align:start position:0% +So the a2 lives here and the um y2 lives +here. So the difference lives here where + + align:start position:0% +here. So the difference lives here where + + + align:start position:0% +here. So the difference lives here where +it's supposed to. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So So these translates + + align:start position:0% + + + + align:start position:0% + +of y + + align:start position:0% +of y + + + align:start position:0% +of y +cover a prime cross -1 over t1 a prime. + + align:start position:0% +cover a prime cross -1 over t1 a prime. + + + align:start position:0% +cover a prime cross -1 over t1 a prime. +They cover it + + align:start position:0% +They cover it + + + align:start position:0% +They cover it +y times. + + align:start position:0% +y times. + + + align:start position:0% +y times. +I cover each point in here y times + + align:start position:0% +I cover each point in here y times + + + align:start position:0% +I cover each point in here y times +because for each point in here I have y + + align:start position:0% +because for each point in here I have y + + + align:start position:0% +because for each point in here I have y +norm of y cardality of y choices for + + align:start position:0% +norm of y cardality of y choices for + + + align:start position:0% +norm of y cardality of y choices for +this guy and then uh there's one one in + + align:start position:0% +this guy and then uh there's one one in + + + align:start position:0% +this guy and then uh there's one one in +translation a set of translations that + + align:start position:0% +translation a set of translations that + + + align:start position:0% +translation a set of translations that +that lands here. + + align:start position:0% + + + + align:start position:0% + +Okay, does this sentence make sense? + + align:start position:0% + + + + align:start position:0% + +So we have rigged it that we've taken a + + align:start position:0% +So we have rigged it that we've taken a + + + align:start position:0% +So we have rigged it that we've taken a +bunch of translations of this set y and + + align:start position:0% +bunch of translations of this set y and + + + align:start position:0% +bunch of translations of this set y and +we have covered a nice uh product many + + align:start position:0% +we have covered a nice uh product many + + + align:start position:0% +we have covered a nice uh product many +times and the product we actually could + + align:start position:0% +times and the product we actually could + + + align:start position:0% +times and the product we actually could +have arranged the product to be a prime + + align:start position:0% +have arranged the product to be a prime + + + align:start position:0% +have arranged the product to be a prime +cross b prime that would have been a + + align:start position:0% +cross b prime that would have been a + + + align:start position:0% +cross b prime that would have been a +little easier than what we did but we + + align:start position:0% +little easier than what we did but we + + + align:start position:0% +little easier than what we did but we +have arranged that the product that + + align:start position:0% +have arranged that the product that + + + align:start position:0% +have arranged that the product that +we've covered is a prime cross a um + + align:start position:0% +we've covered is a prime cross a um + + + align:start position:0% +we've covered is a prime cross a um +dilation of a prime and that's a little + + align:start position:0% +dilation of a prime and that's a little + + + align:start position:0% +dilation of a prime and that's a little +bit better technically because it's + + align:start position:0% +bit better technically because it's + + + align:start position:0% +bit better technically because it's +going to be closer to theorem one. + + align:start position:0% + + + + align:start position:0% + +Okay. Now notice that this guy is small + + align:start position:0% +Okay. Now notice that this guy is small + + + align:start position:0% +Okay. Now notice that this guy is small +by hypothesis and this set here is also + + align:start position:0% +by hypothesis and this set here is also + + + align:start position:0% +by hypothesis and this set here is also +small. This is uh just a dilate of this. + + align:start position:0% +small. This is uh just a dilate of this. + + + align:start position:0% +small. This is uh just a dilate of this. +So these sets are small. So we took a + + align:start position:0% +So these sets are small. So we took a + + + align:start position:0% +So these sets are small. So we took a +few translations of Y and we covered + + align:start position:0% +few translations of Y and we covered + + + align:start position:0% +few translations of Y and we covered +this um product many times. And that + + align:start position:0% +this um product many times. And that + + + align:start position:0% +this um product many times. And that +means that at least typically each of + + align:start position:0% +means that at least typically each of + + + align:start position:0% +means that at least typically each of +the translations was covering a lot of + + align:start position:0% +the translations was covering a lot of + + + align:start position:0% +the translations was covering a lot of +the product. + + align:start position:0% + + + + align:start position:0% + +Okay. So that matches this intuition. + + align:start position:0% +Okay. So that matches this intuition. + + + align:start position:0% +Okay. So that matches this intuition. +So then we can say + + align:start position:0% +So then we can say + + + align:start position:0% +So then we can say +that pi t of a prime + + align:start position:0% +that pi t of a prime + + + align:start position:0% +that pi t of a prime +cross -1 / t t1 a prime + + align:start position:0% +cross -1 / t t1 a prime + + + align:start position:0% +cross -1 / t t1 a prime +that guy is bounded by um + + align:start position:0% +that guy is bounded by um + + + align:start position:0% +that guy is bounded by um +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um so we're going to take + + align:start position:0% +um so we're going to take + + + align:start position:0% +um so we're going to take +a prime minus a prime times um + + align:start position:0% +a prime minus a prime times um + + + align:start position:0% +a prime minus a prime times um +a prime plus t1 b prime. This is how + + align:start position:0% +a prime plus t1 b prime. This is how + + + align:start position:0% +a prime plus t1 b prime. This is how +many copies of y we took. For each one + + align:start position:0% +many copies of y we took. For each one + + + align:start position:0% +many copies of y we took. For each one +of them we have a projection. So that + + align:start position:0% +of them we have a projection. So that + + + align:start position:0% +of them we have a projection. So that +has the size pi t of y. + + align:start position:0% +has the size pi t of y. + + + align:start position:0% +has the size pi t of y. +And after doing that we've covered every + + align:start position:0% +And after doing that we've covered every + + + align:start position:0% +And after doing that we've covered every +point here y times. So we have this guy. + + align:start position:0% + + + + align:start position:0% + +Okay. These are hypothesis bounded by n. + + align:start position:0% +Okay. These are hypothesis bounded by n. + + + align:start position:0% +Okay. These are hypothesis bounded by n. +So this is n^2 over y + + align:start position:0% +So this is n^2 over y + + + align:start position:0% +So this is n^2 over y +pi t of y. + + align:start position:0% + + + + align:start position:0% + +And that's basically our final + + align:start position:0% +And that's basically our final + + + align:start position:0% +And that's basically our final +inequality. Put the pi t of y by itself. + + align:start position:0% +inequality. Put the pi t of y by itself. + + + align:start position:0% +inequality. Put the pi t of y by itself. +Pi t of y is greater tilda tilda y / n^2 + + align:start position:0% +Pi t of y is greater tilda tilda y / n^2 + + + align:start position:0% +Pi t of y is greater tilda tilda y / n^2 +times the size of this thingy which is + + align:start position:0% +times the size of this thingy which is + + + align:start position:0% +times the size of this thingy which is +equivalent to + + align:start position:0% +equivalent to + + + align:start position:0% +equivalent to +pi t / t1 a prime cross + + align:start position:0% + + + + align:start position:0% + +Okay, take a moment with that. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Um, so now let's finish the proof of the + + align:start position:0% +Um, so now let's finish the proof of the + + + align:start position:0% +Um, so now let's finish the proof of the +DK theorem. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +[Applause] + + align:start position:0% + + + + align:start position:0% + +So, we would like to estimate the + + align:start position:0% +So, we would like to estimate the + + + align:start position:0% +So, we would like to estimate the +maximum t in our direction set of pi t + + align:start position:0% +maximum t in our direction set of pi t + + + align:start position:0% +maximum t in our direction set of pi t +of x. + + align:start position:0% +of x. + + + align:start position:0% +of x. +That's at least + + align:start position:0% +That's at least + + + align:start position:0% +That's at least +the maximum t in our direction set of pi + + align:start position:0% +the maximum t in our direction set of pi + + + align:start position:0% +the maximum t in our direction set of pi +t of x prime. + + align:start position:0% +t of x prime. + + + align:start position:0% +t of x prime. +We're following up from over here. And + + align:start position:0% +We're following up from over here. And + + + align:start position:0% +We're following up from over here. And +here's x prime, which is a big chunk of + + align:start position:0% +here's x prime, which is a big chunk of + + + align:start position:0% +here's x prime, which is a big chunk of +a prime cross cross b prime. + + align:start position:0% +a prime cross cross b prime. + + + align:start position:0% +a prime cross cross b prime. +Okay. And now we can apply our lema. + + align:start position:0% +Okay. And now we can apply our lema. + + + align:start position:0% +Okay. And now we can apply our lema. +So the lema says + + align:start position:0% +So the lema says + + + align:start position:0% +So the lema says +that is at least as big as the maximum t + + align:start position:0% +that is at least as big as the maximum t + + + align:start position:0% +that is at least as big as the maximum t +in our direction set x prime / n^2. And + + align:start position:0% +in our direction set x prime / n^2. And + + + align:start position:0% +in our direction set x prime / n^2. And +then we have pi - t / t1 a prime cross a + + align:start position:0% +then we have pi - t / t1 a prime cross a + + + align:start position:0% +then we have pi - t / t1 a prime cross a +prime. + + align:start position:0% + + + + align:start position:0% + +Okay. Now x prime we already determined + + align:start position:0% +Okay. Now x prime we already determined + + + align:start position:0% +Okay. Now x prime we already determined +has size about n^2. So this factor + + align:start position:0% +has size about n^2. So this factor + + + align:start position:0% +has size about n^2. So this factor +disappears. + + align:start position:0% +disappears. + + + align:start position:0% +disappears. +And now we are looking at projections in + + align:start position:0% +And now we are looking at projections in + + + align:start position:0% +And now we are looking at projections in +many different directions of a prime + + align:start position:0% +many different directions of a prime + + + align:start position:0% +many different directions of a prime +cross a prime. That's exactly the thing + + align:start position:0% +cross a prime. That's exactly the thing + + + align:start position:0% +cross a prime. That's exactly the thing +that theorem one told us about. + + align:start position:0% +that theorem one told us about. + + + align:start position:0% +that theorem one told us about. +So by theorem one + + align:start position:0% +So by theorem one + + + align:start position:0% +So by theorem one +this is now greater sim sim n times um p + + align:start position:0% +this is now greater sim sim n times um p + + + align:start position:0% +this is now greater sim sim n times um p +to the epsilon one + + align:start position:0% +to the epsilon one + + + align:start position:0% +to the epsilon one +and that's the proof. + + align:start position:0% +and that's the proof. + + + align:start position:0% +and that's the proof. +So one of these is significantly bigger + + align:start position:0% +So one of these is significantly bigger + + + align:start position:0% +So one of these is significantly bigger +than + + align:start position:0% + + + + align:start position:0% + +the square<unk> of x * p to the epsilon + + align:start position:0% +the square<unk> of x * p to the epsilon + + + align:start position:0% +the square<unk> of x * p to the epsilon + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% + + + + align:start position:0% + +let me put up on here a little summary + + align:start position:0% +let me put up on here a little summary + + + align:start position:0% +let me put up on here a little summary +of what we did and then uh and then I'll + + align:start position:0% +of what we did and then uh and then I'll + + + align:start position:0% +of what we did and then uh and then I'll +let you look at the + + align:start position:0% +let you look at the + + + align:start position:0% +let you look at the +look down from above at the whole thing. + + align:start position:0% +look down from above at the whole thing. + + + align:start position:0% +look down from above at the whole thing. +So we're trying to get from theorem one + + align:start position:0% +So we're trying to get from theorem one + + + align:start position:0% +So we're trying to get from theorem one +to theorem bkt. + + align:start position:0% +to theorem bkt. + + + align:start position:0% +to theorem bkt. +And the enemy + + align:start position:0% +And the enemy + + + align:start position:0% +And the enemy +was that we have a set x in a cross a + + align:start position:0% +was that we have a set x in a cross a + + + align:start position:0% +was that we have a set x in a cross a +where x is around the same size as a + + align:start position:0% +where x is around the same size as a + + + align:start position:0% +where x is around the same size as a +cross a but + + align:start position:0% +cross a but + + + align:start position:0% +cross a but +the size of a projection of x is uh much + + align:start position:0% +the size of a projection of x is uh much + + + align:start position:0% +the size of a projection of x is uh much +smaller than the size of the projection + + align:start position:0% +smaller than the size of the projection + + + align:start position:0% +smaller than the size of the projection +of a cross a. That's our enemy. + + align:start position:0% +of a cross a. That's our enemy. + + + align:start position:0% +of a cross a. That's our enemy. +And we learned two pieces of wisdom + + align:start position:0% +And we learned two pieces of wisdom + + + align:start position:0% +And we learned two pieces of wisdom +about this enemy. One in the BSG theorem + + align:start position:0% +about this enemy. One in the BSG theorem + + + align:start position:0% +about this enemy. One in the BSG theorem +and one in the lema. + + align:start position:0% +and one in the lema. + + + align:start position:0% +and one in the lema. +So wisdom one in the enemy situation + + align:start position:0% +So wisdom one in the enemy situation + + + align:start position:0% +So wisdom one in the enemy situation +um X lives in a smaller product + + align:start position:0% +um X lives in a smaller product + + + align:start position:0% +um X lives in a smaller product +and the projection of the smaller + + align:start position:0% +and the projection of the smaller + + + align:start position:0% +and the projection of the smaller +product. + + align:start position:0% +product. + + + align:start position:0% +product. +So this the projection of the smaller + + align:start position:0% +So this the projection of the smaller + + + align:start position:0% +So this the projection of the smaller +product + + align:start position:0% +product + + + align:start position:0% +product +well it doesn't live in that but it has + + align:start position:0% +well it doesn't live in that but it has + + + align:start position:0% +well it doesn't live in that but it has +a so the enemy situation implies that X + + align:start position:0% +a so the enemy situation implies that X + + + align:start position:0% +a so the enemy situation implies that X +intersected with the smaller product is + + align:start position:0% +intersected with the smaller product is + + + align:start position:0% +intersected with the smaller product is +about the same as X. So a good chunk of + + align:start position:0% +about the same as X. So a good chunk of + + + align:start position:0% +about the same as X. So a good chunk of +X lives in a smaller product and the + + align:start position:0% +X lives in a smaller product and the + + + align:start position:0% +X lives in a smaller product and the +projection of the smaller product is + + align:start position:0% +projection of the smaller product is + + + align:start position:0% +projection of the smaller product is +about the same as the projection of X. + + align:start position:0% + + + + align:start position:0% + +Okay. So then we look at that situation + + align:start position:0% +Okay. So then we look at that situation + + + align:start position:0% +Okay. So then we look at that situation +and the second piece of wisdom was that + + align:start position:0% +and the second piece of wisdom was that + + + align:start position:0% +and the second piece of wisdom was that +if uh the projection of a smaller + + align:start position:0% +if uh the projection of a smaller + + + align:start position:0% +if uh the projection of a smaller +product of a product + + align:start position:0% +product of a product + + + align:start position:0% +product of a product +um + + align:start position:0% +um + + + align:start position:0% +um +if this is small + + align:start position:0% +if this is small + + + align:start position:0% +if this is small +um so if this is around + + align:start position:0% +um so if this is around + + + align:start position:0% +um so if this is around +the smallest it could be would be one of + + align:start position:0% +the smallest it could be would be one of + + + align:start position:0% +the smallest it could be would be one of +the factors for one t1 then this product + + align:start position:0% +the factors for one t1 then this product + + + align:start position:0% +the factors for one t1 then this product +becomes very symmetrical + + align:start position:0% +becomes very symmetrical + + + align:start position:0% +becomes very symmetrical +and Then the conclusion is for any + + align:start position:0% +and Then the conclusion is for any + + + align:start position:0% +and Then the conclusion is for any +subset X prime in the in this thing + + align:start position:0% +subset X prime in the in this thing + + + align:start position:0% +subset X prime in the in this thing +which is substantial + + align:start position:0% +which is substantial + + + align:start position:0% +which is substantial +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +then + + align:start position:0% +then + + + align:start position:0% +then +the projection of the subset actually is + + align:start position:0% +the projection of the subset actually is + + + align:start position:0% +the projection of the subset actually is +around the same as their direction the + + align:start position:0% +around the same as their direction the + + + align:start position:0% +around the same as their direction the +projection of the whole product. + + align:start position:0% + + + + align:start position:0% + +So the enemy situation can only really + + align:start position:0% +So the enemy situation can only really + + + align:start position:0% +So the enemy situation can only really +happen because X was mostly in a a + + align:start position:0% +happen because X was mostly in a a + + + align:start position:0% +happen because X was mostly in a a +smaller product that had a small + + align:start position:0% +smaller product that had a small + + + align:start position:0% +smaller product that had a small +projection + + align:start position:0% +projection + + + align:start position:0% +projection +and this situation is very symmetrical. + + align:start position:0% +and this situation is very symmetrical. + + + align:start position:0% +and this situation is very symmetrical. +So if a smaller product has one small + + align:start position:0% +So if a smaller product has one small + + + align:start position:0% +So if a smaller product has one small +projection then when you project it in + + align:start position:0% +projection then when you project it in + + + align:start position:0% +projection then when you project it in +other angles then um the projection of a + + align:start position:0% +other angles then um the projection of a + + + align:start position:0% +other angles then um the projection of a +big piece of it can't be way smaller + + align:start position:0% +big piece of it can't be way smaller + + + align:start position:0% +big piece of it can't be way smaller +than the projection of the whole thing. + + align:start position:0% + + + + align:start position:0% + +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +So, the whole story is on these boards. + + align:start position:0% +So, the whole story is on these boards. + + + align:start position:0% +So, the whole story is on these boards. +Uh, take a take a couple moments to look + + align:start position:0% +Uh, take a take a couple moments to look + + + align:start position:0% +Uh, take a take a couple moments to look +it over. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Have a question. So, should it be the + + align:start position:0% +>> Have a question. So, should it be the + + + align:start position:0% +>> Have a question. So, should it be the +case that the a prime there depends on + + align:start position:0% +case that the a prime there depends on + + + align:start position:0% +case that the a prime there depends on +t? + + align:start position:0% + + + + align:start position:0% + +>> Okay. So, the question is whether a + + align:start position:0% +>> Okay. So, the question is whether a + + + align:start position:0% +>> Okay. So, the question is whether a +prime depends on t. + + align:start position:0% +prime depends on t. + + + align:start position:0% +prime depends on t. +Um, so let's see where a prime appeared. + + align:start position:0% +Um, so let's see where a prime appeared. + + + align:start position:0% +Um, so let's see where a prime appeared. +So we have uh our set with many small + + align:start position:0% +So we have uh our set with many small + + + align:start position:0% +So we have uh our set with many small +projections + + align:start position:0% +projections + + + align:start position:0% +projections +and um okay and then in particular the + + align:start position:0% +and um okay and then in particular the + + + align:start position:0% +and um okay and then in particular the +t1 projection is small and so the balag + + align:start position:0% +t1 projection is small and so the balag + + + align:start position:0% +t1 projection is small and so the balag +summarity gow theorem says there's a + + align:start position:0% +summarity gow theorem says there's a + + + align:start position:0% +summarity gow theorem says there's a +prime and a and b prime and b so that + + align:start position:0% +prime and a and b prime and b so that + + + align:start position:0% +prime and a and b prime and b so that +the t1 projection of a prime cross b + + align:start position:0% +the t1 projection of a prime cross b + + + align:start position:0% +the t1 projection of a prime cross b +prime is small and this a prime depends + + align:start position:0% +prime is small and this a prime depends + + + align:start position:0% +prime is small and this a prime depends +on t1 + + align:start position:0% +on t1 + + + align:start position:0% +on t1 +>> right + + align:start position:0% +>> right + + + align:start position:0% +>> right +>> now later we're going to look at pi P of + + align:start position:0% +>> now later we're going to look at pi P of + + + align:start position:0% +>> now later we're going to look at pi P of +X for other T's. Um, + + align:start position:0% +X for other T's. Um, + + + align:start position:0% +X for other T's. Um, +one could, I guess, apply Boxed Gowers + + align:start position:0% +one could, I guess, apply Boxed Gowers + + + align:start position:0% +one could, I guess, apply Boxed Gowers +again to those other T's, but that's not + + align:start position:0% +again to those other T's, but that's not + + + align:start position:0% +again to those other T's, but that's not +what we're going to do. We we use T1 to + + align:start position:0% +what we're going to do. We we use T1 to + + + align:start position:0% +what we're going to do. We we use T1 to +find A prime and B prime. And then we're + + align:start position:0% +find A prime and B prime. And then we're + + + align:start position:0% +find A prime and B prime. And then we're +going to run with these same A prime and + + align:start position:0% +going to run with these same A prime and + + + align:start position:0% +going to run with these same A prime and +B prime even when we look at other T's. + + align:start position:0% +B prime even when we look at other T's. + + + align:start position:0% +B prime even when we look at other T's. +What did we learn? Once we have this one + + align:start position:0% +What did we learn? Once we have this one + + + align:start position:0% +What did we learn? Once we have this one +small projection, we learned uh Alex Gar + + align:start position:0% +small projection, we learned uh Alex Gar + + + align:start position:0% +small projection, we learned uh Alex Gar +told us this and then we learned from it + + align:start position:0% +told us this and then we learned from it + + + align:start position:0% +told us this and then we learned from it +some other stuff. So that what we + + align:start position:0% +some other stuff. So that what we + + + align:start position:0% +some other stuff. So that what we +actually used is this. + + align:start position:0% + + + + align:start position:0% + +So we so we then we use this stuff. So + + align:start position:0% +So we so we then we use this stuff. So + + + align:start position:0% +So we so we then we use this stuff. So +this is telling us that a prime cross b + + align:start position:0% +this is telling us that a prime cross b + + + align:start position:0% +this is telling us that a prime cross b +prime is quite symmetrical and that's + + align:start position:0% +prime is quite symmetrical and that's + + + align:start position:0% +prime is quite symmetrical and that's +what's helpful in the second part. + + align:start position:0% + + + + align:start position:0% + +>> Good. Other questions or comments + + align:start position:0% + + + + align:start position:0% + +don't we know that it's also kind of + + align:start position:0% + + + + align:start position:0% + +Yeah, the question is why don't we know + + align:start position:0% +Yeah, the question is why don't we know + + + align:start position:0% +Yeah, the question is why don't we know +that a itself is also kind of + + align:start position:0% +that a itself is also kind of + + + align:start position:0% +that a itself is also kind of +symmetrical? That might depend on + + align:start position:0% +symmetrical? That might depend on + + + align:start position:0% +symmetrical? That might depend on +exactly what we mean by symmetrical. + + align:start position:0% +exactly what we mean by symmetrical. + + + align:start position:0% +exactly what we mean by symmetrical. +But um an important thing an important + + align:start position:0% +But um an important thing an important + + + align:start position:0% +But um an important thing an important +way that a prime is better than a is + + align:start position:0% +way that a prime is better than a is + + + align:start position:0% +way that a prime is better than a is +that at this moment um + + align:start position:0% +that at this moment um + + + align:start position:0% +that at this moment um +a prime minus a prime is small. And we + + align:start position:0% +a prime minus a prime is small. And we + + + align:start position:0% +a prime minus a prime is small. And we +didn't know that about a. A could be, + + align:start position:0% +didn't know that about a. A could be, + + + align:start position:0% +didn't know that about a. A could be, +you know, you can think of A prime as A + + align:start position:0% +you know, you can think of A prime as A + + + align:start position:0% +you know, you can think of A prime as A +as being A prime plus some garbage and + + align:start position:0% +as being A prime plus some garbage and + + + align:start position:0% +as being A prime plus some garbage and +the garbage minus garbage is is not + + align:start position:0% +the garbage minus garbage is is not + + + align:start position:0% +the garbage minus garbage is is not +small. + + align:start position:0% + + + + align:start position:0% + +Why the the epsilon + + align:start position:0% +Why the the epsilon + + + align:start position:0% +Why the the epsilon +>> like the epsilon is different between + + align:start position:0% +>> like the epsilon is different between + + + align:start position:0% +>> like the epsilon is different between +the two because + + align:start position:0% +the two because + + + align:start position:0% +the two because +>> of the a prime plus minus a prime has + + align:start position:0% +>> of the a prime plus minus a prime has + + + align:start position:0% +>> of the a prime plus minus a prime has +like + + align:start position:0% +like + + + align:start position:0% +like +there's like a hidden factor there + + align:start position:0% +there's like a hidden factor there + + + align:start position:0% +there's like a hidden factor there +right? + + align:start position:0% +right? + + + align:start position:0% +right? +>> Yes. + + align:start position:0% +>> Yes. + + + align:start position:0% +>> Yes. +A prime plus minus a prime here there's + + align:start position:0% +A prime plus minus a prime here there's + + + align:start position:0% +A prime plus minus a prime here there's +a hidden factor which is p to the order + + align:start position:0% +a hidden factor which is p to the order + + + align:start position:0% +a hidden factor which is p to the order +of epsilon + + align:start position:0% +of epsilon + + + align:start position:0% +of epsilon +>> and you're right it's very important + + align:start position:0% +>> and you're right it's very important + + + align:start position:0% +>> and you're right it's very important +that the epsilon is different between + + align:start position:0% +that the epsilon is different between + + + align:start position:0% +that the epsilon is different between +the two theorems. Um + + align:start position:0% +the two theorems. Um + + + align:start position:0% +the two theorems. Um +so epsilon one is the epsilon in theorem + + align:start position:0% +so epsilon one is the epsilon in theorem + + + align:start position:0% +so epsilon one is the epsilon in theorem +one which was already kind of small if + + align:start position:0% +one which was already kind of small if + + + align:start position:0% +one which was already kind of small if +we had unwind the proof of theorem one + + align:start position:0% +we had unwind the proof of theorem one + + + align:start position:0% +we had unwind the proof of theorem one +and then in theorem bkt there's an + + align:start position:0% +and then in theorem bkt there's an + + + align:start position:0% +and then in theorem bkt there's an +epsilon and the epsilon and bkt is way + + align:start position:0% +epsilon and the epsilon and bkt is way + + + align:start position:0% +epsilon and the epsilon and bkt is way +smaller than the epsilon one and the + + align:start position:0% +smaller than the epsilon one and the + + + align:start position:0% +smaller than the epsilon one and the +reason we need that is um okay we + + align:start position:0% +reason we need that is um okay we + + + align:start position:0% +reason we need that is um okay we +started with this where we have a factor + + align:start position:0% +started with this where we have a factor + + + align:start position:0% +started with this where we have a factor +of p to the epsilon then um we did some + + align:start position:0% +of p to the epsilon then um we did some + + + align:start position:0% +of p to the epsilon then um we did some +stuff most important stuff is bsg so bs + + align:start position:0% +stuff most important stuff is bsg so bs + + + align:start position:0% +stuff most important stuff is bsg so bs +SG will lose like there'll be like a + + align:start position:0% +SG will lose like there'll be like a + + + align:start position:0% +SG will lose like there'll be like a +factor of 10 epsilon here uh that comes + + align:start position:0% +factor of 10 epsilon here uh that comes + + + align:start position:0% +factor of 10 epsilon here uh that comes +out of the proof of balm gowers. So here + + align:start position:0% +out of the proof of balm gowers. So here + + + align:start position:0% +out of the proof of balm gowers. So here +the these these things will be something + + align:start position:0% +the these these things will be something + + + align:start position:0% +the these these things will be something +like p to the 10 epsilon if you did them + + align:start position:0% +like p to the 10 epsilon if you did them + + + align:start position:0% +like p to the 10 epsilon if you did them +carefully and then you go along and + + align:start position:0% +carefully and then you go along and + + + align:start position:0% +carefully and then you go along and +we're following our proof. So here + + align:start position:0% +we're following our proof. So here + + + align:start position:0% +we're following our proof. So here +there's um we did a little bit more work + + align:start position:0% +there's um we did a little bit more work + + + align:start position:0% +there's um we did a little bit more work +in the proof of the lema. So there's p + + align:start position:0% +in the proof of the lema. So there's p + + + align:start position:0% +in the proof of the lema. So there's p +of this is hiding a p of 10 or 20 + + align:start position:0% +of this is hiding a p of 10 or 20 + + + align:start position:0% +of this is hiding a p of 10 or 20 +epsilon + + align:start position:0% +epsilon + + + align:start position:0% +epsilon +and then but here we have a gain of p to + + align:start position:0% +and then but here we have a gain of p to + + + align:start position:0% +and then but here we have a gain of p to +the epsilon 1. So the p to the epsilon + + align:start position:0% +the epsilon 1. So the p to the epsilon + + + align:start position:0% +the epsilon 1. So the p to the epsilon +one needs to dominate the p to the 20 + + align:start position:0% +one needs to dominate the p to the 20 + + + align:start position:0% +one needs to dominate the p to the 20 +epsilon that we lost at various steps in + + align:start position:0% +epsilon that we lost at various steps in + + + align:start position:0% +epsilon that we lost at various steps in +this process. So epsilon should be like + + align:start position:0% +this process. So epsilon should be like + + + align:start position:0% +this process. So epsilon should be like +120th of the size of epsilon one. + + align:start position:0% +120th of the size of epsilon one. + + + align:start position:0% +120th of the size of epsilon one. +Yeah. So we have to do a whole sequence + + align:start position:0% +Yeah. So we have to do a whole sequence + + + align:start position:0% +Yeah. So we have to do a whole sequence +of clever things to prove briang cat's + + align:start position:0% +of clever things to prove briang cat's + + + align:start position:0% +of clever things to prove briang cat's +ta theorem and each time we do something + + align:start position:0% +ta theorem and each time we do something + + + align:start position:0% +ta theorem and each time we do something +clever our epsilon gets smaller by a + + align:start position:0% +clever our epsilon gets smaller by a + + + align:start position:0% +clever our epsilon gets smaller by a +factor of 10 until you know we're so + + align:start position:0% +factor of 10 until you know we're so + + + align:start position:0% +factor of 10 until you know we're so +clever that we really can't see the + + align:start position:0% +clever that we really can't see the + + + align:start position:0% +clever that we really can't see the +epsilon. + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +>> Is there a conjecture bound for what + + align:start position:0% +>> Is there a conjecture bound for what + + + align:start position:0% +>> Is there a conjecture bound for what +possible epsilon could be? + + align:start position:0% +possible epsilon could be? + + + align:start position:0% +possible epsilon could be? +>> Ah, that's a great question. Yeah. So, + + align:start position:0% +>> Ah, that's a great question. Yeah. So, + + + align:start position:0% +>> Ah, that's a great question. Yeah. So, +the question is, is there a conjectured + + align:start position:0% +the question is, is there a conjectured + + + align:start position:0% +the question is, is there a conjectured +bound about the right epsilon? Um + + align:start position:0% +bound about the right epsilon? Um + + + align:start position:0% +bound about the right epsilon? Um +um yes. So, yes. So the conjecture so + + align:start position:0% +um yes. So, yes. So the conjecture so + + + align:start position:0% +um yes. So, yes. So the conjecture so +we're working right now over finite + + align:start position:0% +we're working right now over finite + + + align:start position:0% +we're working right now over finite +fields and the conjecture is that the + + align:start position:0% +fields and the conjecture is that the + + + align:start position:0% +fields and the conjecture is that the +worst case is a lattice + + align:start position:0% +worst case is a lattice + + + align:start position:0% +worst case is a lattice +and we wrote it down let's write it down + + align:start position:0% +and we wrote it down let's write it down + + + align:start position:0% +and we wrote it down let's write it down +again but we we wrote it down at the + + align:start position:0% +again but we we wrote it down at the + + + align:start position:0% +again but we we wrote it down at the +beginning of the course um + + align:start position:0% +beginning of the course um + + + align:start position:0% +beginning of the course um +okay so I think we're moving on I'll put + + align:start position:0% +okay so I think we're moving on I'll put + + + align:start position:0% +okay so I think we're moving on I'll put +it here + + align:start position:0% +it here + + + align:start position:0% +it here +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +okay so suppose we have x + + align:start position:0% +okay so suppose we have x + + + align:start position:0% +okay so suppose we have x +which is a subset of ft^2 squ and then + + align:start position:0% +which is a subset of ft^2 squ and then + + + align:start position:0% +which is a subset of ft^2 squ and then +we're going to take the maximum t and d + + align:start position:0% +we're going to take the maximum t and d + + + align:start position:0% +we're going to take the maximum t and d +pi t of x. Um, and this is bigger than I + + align:start position:0% +pi t of x. Um, and this is bigger than I + + + align:start position:0% +pi t of x. Um, and this is bigger than I +think it was d to the half x to the + + align:start position:0% +think it was d to the half x to the + + + align:start position:0% +think it was d to the half x to the +half. + + align:start position:0% + + + + align:start position:0% + +Um, + + align:start position:0% + + + + align:start position:0% + +maybe you should check it. I don't + + align:start position:0% +maybe you should check it. I don't + + + align:start position:0% +maybe you should check it. I don't +remember these. I don't quite remember + + align:start position:0% +remember these. I don't quite remember + + + align:start position:0% +remember these. I don't quite remember +these off the top of my head. So, I + + align:start position:0% +these off the top of my head. So, I + + + align:start position:0% +these off the top of my head. So, I +think + + align:start position:0% +think + + + align:start position:0% +think +And the way to remember it is that the + + align:start position:0% +And the way to remember it is that the + + + align:start position:0% +And the way to remember it is that the +example is that X is a lattice + + align:start position:0% + + + + align:start position:0% + +and then D is the set of rational + + align:start position:0% +and then D is the set of rational + + + align:start position:0% +and then D is the set of rational +numbers of small slope. + + align:start position:0% +numbers of small slope. + + + align:start position:0% +numbers of small slope. +Right? That was the case where the pro + + align:start position:0% +Right? That was the case where the pro + + + align:start position:0% +Right? That was the case where the pro +the case that we've seen so far where + + align:start position:0% +the case that we've seen so far where + + + align:start position:0% +the case that we've seen so far where +the projections are small. So if you + + align:start position:0% +the projections are small. So if you + + + align:start position:0% +the projections are small. So if you +compute with this you can check whether + + align:start position:0% +compute with this you can check whether + + + align:start position:0% +compute with this you can check whether +this is true or whether it needs to be + + align:start position:0% +this is true or whether it needs to be + + + align:start position:0% +this is true or whether it needs to be +modified a little bit. And then if you + + align:start position:0% +modified a little bit. And then if you + + + align:start position:0% +modified a little bit. And then if you +rewrite it in the language of BKT it + + align:start position:0% +rewrite it in the language of BKT it + + + align:start position:0% +rewrite it in the language of BKT it +gives you an exact formula for epsilon + + align:start position:0% +gives you an exact formula for epsilon + + + align:start position:0% +gives you an exact formula for epsilon +right and that is a wide openen problem + + align:start position:0% +right and that is a wide openen problem + + + align:start position:0% +right and that is a wide openen problem +um over FP but the version over R has + + align:start position:0% +um over FP but the version over R has + + + align:start position:0% +um over FP but the version over R has +been proven and and uh um I'll try at + + align:start position:0% +been proven and and uh um I'll try at + + + align:start position:0% +been proven and and uh um I'll try at +least to say to say at least some of the + + align:start position:0% +least to say to say at least some of the + + + align:start position:0% +least to say to say at least some of the +main ideas of the proof in the in the + + align:start position:0% +main ideas of the proof in the in the + + + align:start position:0% +main ideas of the proof in the in the +class. + + align:start position:0% +class. + + + align:start position:0% +class. +Yeah. + + align:start position:0% + + + + align:start position:0% + +Okay. Um + + align:start position:0% + + + + align:start position:0% + +so the the ideas that we've just been + + align:start position:0% +so the the ideas that we've just been + + + align:start position:0% +so the the ideas that we've just been +talking about when um going back and + + align:start position:0% +talking about when um going back and + + + align:start position:0% +talking about when um going back and +forth between whether a projection of + + align:start position:0% +forth between whether a projection of + + + align:start position:0% +forth between whether a projection of +the whole product is small whether a + + align:start position:0% +the whole product is small whether a + + + align:start position:0% +the whole product is small whether a +projection of a big chunk of the product + + align:start position:0% +projection of a big chunk of the product + + + align:start position:0% +projection of a big chunk of the product +is small um that is a theme in additive + + align:start position:0% +is small um that is a theme in additive + + + align:start position:0% +is small um that is a theme in additive +combinotaurics and I want to describe to + + align:start position:0% +combinotaurics and I want to describe to + + + align:start position:0% +combinotaurics and I want to describe to +you some of the other key words and + + align:start position:0% +you some of the other key words and + + + align:start position:0% +you some of the other key words and +ideas behind that theme to to flesh out + + align:start position:0% +ideas behind that theme to to flesh out + + + align:start position:0% +ideas behind that theme to to flesh out +the lecture and see how it I don't know + + align:start position:0% +the lecture and see how it I don't know + + + align:start position:0% +the lecture and see how it I don't know +how it fits in in general. + + align:start position:0% +how it fits in in general. + + + align:start position:0% +how it fits in in general. +Um, + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +all right. + + align:start position:0% +all right. + + + align:start position:0% +all right. +So section is called additive energy + + align:start position:0% +So section is called additive energy + + + align:start position:0% +So section is called additive energy +versus the size of a plus b. + + align:start position:0% + + + + align:start position:0% + +So these are two points of view about + + align:start position:0% +So these are two points of view about + + + align:start position:0% +So these are two points of view about +measuring the additive structure + + align:start position:0% +measuring the additive structure + + + align:start position:0% +measuring the additive structure +involved when you add um numbers in a to + + align:start position:0% +involved when you add um numbers in a to + + + align:start position:0% +involved when you add um numbers in a to +numbers in b. This one we've already + + align:start position:0% +numbers in b. This one we've already + + + align:start position:0% +numbers in b. This one we've already +met. Let me tell you what additive + + align:start position:0% +met. Let me tell you what additive + + + align:start position:0% +met. Let me tell you what additive +energy is. + + align:start position:0% +energy is. + + + align:start position:0% +energy is. +So definition + + align:start position:0% +So definition + + + align:start position:0% +So definition +if A and B are contained in an Aelian + + align:start position:0% +if A and B are contained in an Aelian + + + align:start position:0% +if A and B are contained in an Aelian +group + + align:start position:0% +group + + + align:start position:0% +group +the energy of AB + + align:start position:0% +the energy of AB + + + align:start position:0% +the energy of AB +is the number of quadruples + + align:start position:0% +is the number of quadruples + + + align:start position:0% +is the number of quadruples +A1 and A2 are in A. B1 and B2 + + align:start position:0% +A1 and A2 are in A. B1 and B2 + + + align:start position:0% +A1 and A2 are in A. B1 and B2 +are in B. So that a1 + b1 is equal to a2 + + align:start position:0% +are in B. So that a1 + b1 is equal to a2 + + + align:start position:0% +are in B. So that a1 + b1 is equal to a2 ++ b2. + + align:start position:0% + + + + align:start position:0% + +So if you add numbers from a and b, how + + align:start position:0% +So if you add numbers from a and b, how + + + align:start position:0% +So if you add numbers from a and b, how +many coincidences are there? Does it + + align:start position:0% +many coincidences are there? Does it + + + align:start position:0% +many coincidences are there? Does it +frequently happen that you get the same + + align:start position:0% +frequently happen that you get the same + + + align:start position:0% +frequently happen that you get the same +number? + + align:start position:0% +number? + + + align:start position:0% +number? +So another way of thinking about it is + + align:start position:0% +So another way of thinking about it is + + + align:start position:0% +So another way of thinking about it is +we could say r a b of z. the number of + + align:start position:0% +we could say r a b of z. the number of + + + align:start position:0% +we could say r a b of z. the number of +representations of Z as a sum somebody + + align:start position:0% +representations of Z as a sum somebody + + + align:start position:0% +representations of Z as a sum somebody +in A and somebody in B. So this is the + + align:start position:0% +in A and somebody in B. So this is the + + + align:start position:0% +in A and somebody in B. So this is the +number of ab + + align:start position:0% + + + + align:start position:0% + ++ b is z. + + align:start position:0% ++ b is z. + + + align:start position:0% ++ b is z. +And the additive energy ab is also equal + + align:start position:0% +And the additive energy ab is also equal + + + align:start position:0% +And the additive energy ab is also equal +to the sum over z r a b of z squ. + + align:start position:0% + + + + align:start position:0% + +So if this is large it means there are a + + align:start position:0% +So if this is large it means there are a + + + align:start position:0% +So if this is large it means there are a +lot of numbers that can be written as a + + align:start position:0% +lot of numbers that can be written as a + + + align:start position:0% +lot of numbers that can be written as a +plus b in many different ways. There are + + align:start position:0% +plus b in many different ways. There are + + + align:start position:0% +plus b in many different ways. There are +many additive coincidences. + + align:start position:0% + + + + align:start position:0% + +Okay. So um + + align:start position:0% +Okay. So um + + + align:start position:0% +Okay. So um +so for reference if a and b both have + + align:start position:0% +so for reference if a and b both have + + + align:start position:0% +so for reference if a and b both have +size n + + align:start position:0% +size n + + + align:start position:0% +size n +then think about how big or how small + + align:start position:0% +then think about how big or how small + + + align:start position:0% +then think about how big or how small +the additive energy could be. it's at + + align:start position:0% +the additive energy could be. it's at + + + align:start position:0% +the additive energy could be. it's at +least n squared. Um that happens if so + + align:start position:0% +least n squared. Um that happens if so + + + align:start position:0% +least n squared. Um that happens if so +there are n^2 obvious solutions to this + + align:start position:0% +there are n^2 obvious solutions to this + + + align:start position:0% +there are n^2 obvious solutions to this +which are a1 equals a2 and b1 equals b2 + + align:start position:0% + + + + align:start position:0% + +and um if if you have kind of a random + + align:start position:0% +and um if if you have kind of a random + + + align:start position:0% +and um if if you have kind of a random +set of integers or random subset of a + + align:start position:0% +set of integers or random subset of a + + + align:start position:0% +set of integers or random subset of a +big group those might be only the the + + align:start position:0% +big group those might be only the the + + + align:start position:0% +big group those might be only the the +only solutions. So here we have only + + align:start position:0% +only solutions. So here we have only + + + align:start position:0% +only solutions. So here we have only +trivial + + align:start position:0% +trivial + + + align:start position:0% +trivial +quadruples. + + align:start position:0% + + + + align:start position:0% + +Okay. And energy is at most n cubed + + align:start position:0% +Okay. And energy is at most n cubed + + + align:start position:0% +Okay. And energy is at most n cubed +because once you've picked three of + + align:start position:0% +because once you've picked three of + + + align:start position:0% +because once you've picked three of +these, the fourth one is determined by + + align:start position:0% +these, the fourth one is determined by + + + align:start position:0% +these, the fourth one is determined by +this equation. So there's at most n + + align:start position:0% +this equation. So there's at most n + + + align:start position:0% +this equation. So there's at most n +cubed of these additive quadruples. And + + align:start position:0% +cubed of these additive quadruples. And + + + align:start position:0% +cubed of these additive quadruples. And +um + + align:start position:0% + + + + align:start position:0% + +and this happens if a= b equals a + + align:start position:0% +and this happens if a= b equals a + + + align:start position:0% +and this happens if a= b equals a +subgroup of z. + + align:start position:0% +subgroup of z. + + + align:start position:0% +subgroup of z. +A and b are a subgroup of z. Then + + align:start position:0% +A and b are a subgroup of z. Then + + + align:start position:0% +A and b are a subgroup of z. Then +there's always a choice of b2 you can + + align:start position:0% +there's always a choice of b2 you can + + + align:start position:0% +there's always a choice of b2 you can +pick to solve this equation. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +cool. So having large energy is sort of + + align:start position:0% +cool. So having large energy is sort of + + + align:start position:0% +cool. So having large energy is sort of +having a lot of additive structure. And + + align:start position:0% +having a lot of additive structure. And + + + align:start position:0% +having a lot of additive structure. And +before we were sort of thinking that if + + align:start position:0% +before we were sort of thinking that if + + + align:start position:0% +before we were sort of thinking that if +a plus b is small then that would mean + + align:start position:0% +a plus b is small then that would mean + + + align:start position:0% +a plus b is small then that would mean +there's a lot of additive structure. Um + + align:start position:0% +there's a lot of additive structure. Um + + + align:start position:0% +there's a lot of additive structure. Um +how are those related to each other? + + align:start position:0% + + + + align:start position:0% + +Okay. Um, so there's a lema + + align:start position:0% +Okay. Um, so there's a lema + + + align:start position:0% +Okay. Um, so there's a lema +that says a * b a ^2 * b ^2 is at most + + align:start position:0% +that says a * b a ^2 * b ^2 is at most + + + align:start position:0% +that says a * b a ^2 * b ^2 is at most +the size of a + b times the energy + + align:start position:0% +the size of a + b times the energy + + + align:start position:0% +the size of a + b times the energy +between a and b. + + align:start position:0% +between a and b. + + + align:start position:0% +between a and b. +And this is uh the proof of this is just + + align:start position:0% +And this is uh the proof of this is just + + + align:start position:0% +And this is uh the proof of this is just +Koshy Schwarz. + + align:start position:0% +Koshy Schwarz. + + + align:start position:0% +Koshy Schwarz. +So if I add up on Z R A B of Z + + align:start position:0% +So if I add up on Z R A B of Z + + + align:start position:0% +So if I add up on Z R A B of Z +I get the size of A times the size of B. + + align:start position:0% +I get the size of A times the size of B. + + + align:start position:0% +I get the size of A times the size of B. +This is by double counting. So every + + align:start position:0% +This is by double counting. So every + + + align:start position:0% +This is by double counting. So every +time I add somebody in A and somebody in + + align:start position:0% +time I add somebody in A and somebody in + + + align:start position:0% +time I add somebody in A and somebody in +B I get some Z. I add this up I get all + + align:start position:0% +B I get some Z. I add this up I get all + + + align:start position:0% +B I get some Z. I add this up I get all +the pairs. + + align:start position:0% +the pairs. + + + align:start position:0% +the pairs. +So now + + align:start position:0% +So now + + + align:start position:0% +So now +uh a * b is the sum z of r a b of z and + + align:start position:0% +uh a * b is the sum z of r a b of z and + + + align:start position:0% +uh a * b is the sum z of r a b of z and +in this sum I only need to count the + + align:start position:0% +in this sum I only need to count the + + + align:start position:0% +in this sum I only need to count the +guys in a plus b because if z is not + + align:start position:0% +guys in a plus b because if z is not + + + align:start position:0% +guys in a plus b because if z is not +cannot be written as an a plus b at all + + align:start position:0% +cannot be written as an a plus b at all + + + align:start position:0% +cannot be written as an a plus b at all +it means that this was zero. + + align:start position:0% +it means that this was zero. + + + align:start position:0% +it means that this was zero. +Okay, now I koshi Schwarz. + + align:start position:0% +Okay, now I koshi Schwarz. + + + align:start position:0% +Okay, now I koshi Schwarz. +So I'm going to write it as the sum or a + + align:start position:0% +So I'm going to write it as the sum or a + + + align:start position:0% +So I'm going to write it as the sum or a ++ b of one to the 12 and the sum r a b + + align:start position:0% ++ b of one to the 12 and the sum r a b + + + align:start position:0% ++ b of one to the 12 and the sum r a b +of z squared to the 12. + + align:start position:0% + + + + align:start position:0% + +Okay, so that's the size of a + b to the + + align:start position:0% +Okay, so that's the size of a + b to the + + + align:start position:0% +Okay, so that's the size of a + b to the +12 times the energy to the 12. + + align:start position:0% +12 times the energy to the 12. + + + align:start position:0% +12 times the energy to the 12. +That's the per. + + align:start position:0% + + + + align:start position:0% + +All right. So we see from this that if + + align:start position:0% +All right. So we see from this that if + + + align:start position:0% +All right. So we see from this that if +the if a plus b is small then the energy + + align:start position:0% +the if a plus b is small then the energy + + + align:start position:0% +the if a plus b is small then the energy +must be large. You know we could bring + + align:start position:0% +must be large. You know we could bring + + + align:start position:0% +must be large. You know we could bring +the a plus b over to the other side. So + + align:start position:0% +the a plus b over to the other side. So + + + align:start position:0% +the a plus b over to the other side. So +people usually write this the energy is + + align:start position:0% +people usually write this the energy is + + + align:start position:0% +people usually write this the energy is +at least a 2 * b ^ 2 over a plus b. + + align:start position:0% + + + + align:start position:0% + +So for instance, if a and b have size n + + align:start position:0% +So for instance, if a and b have size n + + + align:start position:0% +So for instance, if a and b have size n +and a plus b is almost n, then the + + align:start position:0% +and a plus b is almost n, then the + + + align:start position:0% +and a plus b is almost n, then the +energy would be at least around n cubed, + + align:start position:0% +energy would be at least around n cubed, + + + align:start position:0% +energy would be at least around n cubed, +which is as big as it could be. + + align:start position:0% + + + + align:start position:0% + +All right? So a + b small + + align:start position:0% +All right? So a + b small + + + align:start position:0% +All right? So a + b small +implies + + align:start position:0% +implies + + + align:start position:0% +implies +that the energy is large. + + align:start position:0% + + + + align:start position:0% + +Now, do people think you can go the + + align:start position:0% +Now, do people think you can go the + + + align:start position:0% +Now, do people think you can go the +other way? If the energy is large, does + + align:start position:0% +other way? If the energy is large, does + + + align:start position:0% +other way? If the energy is large, does +that imply that a plus b is small? + + align:start position:0% + + + + align:start position:0% + +>> Good. No, because you could have some + + align:start position:0% +>> Good. No, because you could have some + + + align:start position:0% +>> Good. No, because you could have some +garbage. + + align:start position:0% +garbage. + + + align:start position:0% +garbage. +Okay. So energy + + align:start position:0% +Okay. So energy + + + align:start position:0% +Okay. So energy +of a large + + align:start position:0% +of a large + + + align:start position:0% +of a large +does not imply that a + b + + align:start position:0% +does not imply that a + b + + + align:start position:0% +does not imply that a + b +is small. + + align:start position:0% +is small. + + + align:start position:0% +is small. +Uh the example + + align:start position:0% +Uh the example + + + align:start position:0% +Uh the example +is that a = b equals numbers up to n. + + align:start position:0% +is that a = b equals numbers up to n. + + + align:start position:0% +is that a = b equals numbers up to n. +Somebody with a lot of additive + + align:start position:0% +Somebody with a lot of additive + + + align:start position:0% +Somebody with a lot of additive +structure union some garbage. + + align:start position:0% + + + + align:start position:0% + +Good. Now if you look at the definition + + align:start position:0% +Good. Now if you look at the definition + + + align:start position:0% +Good. Now if you look at the definition +of the energy, if I add some extra + + align:start position:0% +of the energy, if I add some extra + + + align:start position:0% +of the energy, if I add some extra +elements to A or to B, it can only + + align:start position:0% +elements to A or to B, it can only + + + align:start position:0% +elements to A or to B, it can only +increase the energy perhaps not very + + align:start position:0% +increase the energy perhaps not very + + + align:start position:0% +increase the energy perhaps not very +much. So the energy of this example is + + align:start position:0% +much. So the energy of this example is + + + align:start position:0% +much. So the energy of this example is +at least the energy of this example + + align:start position:0% +at least the energy of this example + + + align:start position:0% +at least the energy of this example +which is large. + + align:start position:0% +which is large. + + + align:start position:0% +which is large. +On the other hand, the garbage can make + + align:start position:0% +On the other hand, the garbage can make + + + align:start position:0% +On the other hand, the garbage can make +this a lot bigger. And this is basically + + align:start position:0% +this a lot bigger. And this is basically + + + align:start position:0% +this a lot bigger. And this is basically +the same example that we've been + + align:start position:0% +the same example that we've been + + + align:start position:0% +the same example that we've been +grappling with all class. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% + + + + align:start position:0% + +cool. + + align:start position:0% +cool. + + + align:start position:0% +cool. +So now + + align:start position:0% +So now + + + align:start position:0% +So now +we'll leave that up. + + align:start position:0% + + + + align:start position:0% + +Right. + + align:start position:0% +Right. + + + align:start position:0% +Right. +Okay. + + align:start position:0% + + + + align:start position:0% + +Now if the energy of A and B is is small + + align:start position:0% +Now if the energy of A and B is is small + + + align:start position:0% +Now if the energy of A and B is is small +that implies that the size of A plus B + + align:start position:0% +that implies that the size of A plus B + + + align:start position:0% +that implies that the size of A plus B +is large. That's just the contraositive + + align:start position:0% +is large. That's just the contraositive + + + align:start position:0% +is large. That's just the contraositive +of what we wrote before or you can see + + align:start position:0% +of what we wrote before or you can see + + + align:start position:0% +of what we wrote before or you can see +it from this formula. If this is small + + align:start position:0% +it from this formula. If this is small + + + align:start position:0% +it from this formula. If this is small +then this one must be large. + + align:start position:0% + + + + align:start position:0% + +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now + + align:start position:0% +Now + + + align:start position:0% +Now +um + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +now suppose I have a set x in a cross b + + align:start position:0% +now suppose I have a set x in a cross b + + + align:start position:0% +now suppose I have a set x in a cross b +and I look at pi 1 of x right. So + + align:start position:0% +and I look at pi 1 of x right. So + + + align:start position:0% +and I look at pi 1 of x right. So +remember that pi 1 of a cross b is just + + align:start position:0% +remember that pi 1 of a cross b is just + + + align:start position:0% +remember that pi 1 of a cross b is just +a + b. + + align:start position:0% +a + b. + + + align:start position:0% +a + b. +So when I take pi 1 of x it's sort of + + align:start position:0% +So when I take pi 1 of x it's sort of + + + align:start position:0% +So when I take pi 1 of x it's sort of +like a plus b. But I don't take all the + + align:start position:0% +like a plus b. But I don't take all the + + + align:start position:0% +like a plus b. But I don't take all the +pairs. I just take the pairs in x. + + align:start position:0% + + + + align:start position:0% + +Um + + align:start position:0% +Um + + + align:start position:0% +Um +and um + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +so if even if pi one of x were small, + + align:start position:0% +so if even if pi one of x were small, + + + align:start position:0% +so if even if pi one of x were small, +if x was a large set and pi1 of x were + + align:start position:0% +if x was a large set and pi1 of x were + + + align:start position:0% +if x was a large set and pi1 of x were +small, that would still produce a lot of + + align:start position:0% +small, that would still produce a lot of + + + align:start position:0% +small, that would still produce a lot of +energy. + + align:start position:0% +energy. + + + align:start position:0% +energy. +um because that would still be um a lot + + align:start position:0% +um because that would still be um a lot + + + align:start position:0% +um because that would still be um a lot +of numbers a bunch of numbers Z that + + align:start position:0% +of numbers a bunch of numbers Z that + + + align:start position:0% +of numbers a bunch of numbers Z that +have many representations of A plus B. + + align:start position:0% +have many representations of A plus B. + + + align:start position:0% +have many representations of A plus B. +Let me just write it down. U okay so + + align:start position:0% +Let me just write it down. U okay so + + + align:start position:0% +Let me just write it down. U okay so +yeah. So, so actually so let me recall + + align:start position:0% +yeah. So, so actually so let me recall + + + align:start position:0% +yeah. So, so actually so let me recall +that + + align:start position:0% +that + + + align:start position:0% +that +a + b large + + align:start position:0% +a + b large + + + align:start position:0% +a + b large +and x being a big fraction of of a * b + + align:start position:0% +and x being a big fraction of of a * b + + + align:start position:0% +and x being a big fraction of of a * b +that does not imply that pi 1 of x is + + align:start position:0% +that does not imply that pi 1 of x is + + + align:start position:0% +that does not imply that pi 1 of x is +large and this is again the main thing + + align:start position:0% +large and this is again the main thing + + + align:start position:0% +large and this is again the main thing +that we were struggling with but with + + align:start position:0% +that we were struggling with but with + + + align:start position:0% +that we were struggling with but with +energy this is true. So, lama um + + align:start position:0% +energy this is true. So, lama um + + + align:start position:0% +energy this is true. So, lama um +check exactly what it says. + + align:start position:0% + + + + align:start position:0% + +So lema um x² is less than or equal to + + align:start position:0% +So lema um x² is less than or equal to + + + align:start position:0% +So lema um x² is less than or equal to +p1 of x times the energy of ab. + + align:start position:0% + + + + align:start position:0% + +So if the energy is small + + align:start position:0% +So if the energy is small + + + align:start position:0% +So if the energy is small +um then pi1 of x is pretty big for every + + align:start position:0% +um then pi1 of x is pretty big for every + + + align:start position:0% +um then pi1 of x is pretty big for every +subset x or every large subset x. + + align:start position:0% + + + + align:start position:0% + +The proof is the almost the same as the + + align:start position:0% +The proof is the almost the same as the + + + align:start position:0% +The proof is the almost the same as the +previous proof. + + align:start position:0% +previous proof. + + + align:start position:0% +previous proof. +So proof rx of z is the number of ways + + align:start position:0% +So proof rx of z is the number of ways + + + align:start position:0% +So proof rx of z is the number of ways +of writing um a + b equal to z where the + + align:start position:0% +of writing um a + b equal to z where the + + + align:start position:0% +of writing um a + b equal to z where the +pair ab is an x and that's smaller than + + align:start position:0% +pair ab is an x and that's smaller than + + + align:start position:0% +pair ab is an x and that's smaller than +representations of z is a general sum of + + align:start position:0% +representations of z is a general sum of + + + align:start position:0% +representations of z is a general sum of +somebody a and b because we're only + + align:start position:0% +somebody a and b because we're only + + + align:start position:0% +somebody a and b because we're only +taking a a portion of the of the sums. + + align:start position:0% +taking a a portion of the of the sums. + + + align:start position:0% +taking a a portion of the of the sums. +Okay. So now x is the sum um on z of rx + + align:start position:0% +Okay. So now x is the sum um on z of rx + + + align:start position:0% +Okay. So now x is the sum um on z of rx +of z. + + align:start position:0% + + + + align:start position:0% + +And here in this sum we only have to + + align:start position:0% +And here in this sum we only have to + + + align:start position:0% +And here in this sum we only have to +take z's in pi 1 of x only have to + + align:start position:0% +take z's in pi 1 of x only have to + + + align:start position:0% +take z's in pi 1 of x only have to +consider those z's that can be written + + align:start position:0% +consider those z's that can be written + + + align:start position:0% +consider those z's that can be written +as the form a plus b where a and b are + + align:start position:0% +as the form a plus b where a and b are + + + align:start position:0% +as the form a plus b where a and b are +in x. + + align:start position:0% +in x. + + + align:start position:0% +in x. +So now we can koshy schwarz this and we + + align:start position:0% +So now we can koshy schwarz this and we + + + align:start position:0% +So now we can koshy schwarz this and we +get the size of pi 1 of x^ the 12 + + align:start position:0% +get the size of pi 1 of x^ the 12 + + + align:start position:0% +get the size of pi 1 of x^ the 12 +times uh a kind of energy thing which is + + align:start position:0% +times uh a kind of energy thing which is + + + align:start position:0% +times uh a kind of energy thing which is +smaller than the standard energy. So we + + align:start position:0% +smaller than the standard energy. So we + + + align:start position:0% +smaller than the standard energy. So we +have the sum rx of z ^ 2 to the 12 + + align:start position:0% +have the sum rx of z ^ 2 to the 12 + + + align:start position:0% +have the sum rx of z ^ 2 to the 12 +that's smaller than the sum ra of z ^ 2 + + align:start position:0% +that's smaller than the sum ra of z ^ 2 + + + align:start position:0% +that's smaller than the sum ra of z ^ 2 +to the 12 which gives us the energy. + + align:start position:0% + + + + align:start position:0% + +Okay, cool. So to summarize, + + align:start position:0% +Okay, cool. So to summarize, + + + align:start position:0% +Okay, cool. So to summarize, +having small energy implies that the + + align:start position:0% +having small energy implies that the + + + align:start position:0% +having small energy implies that the +subset is large, but it's stronger than + + align:start position:0% +subset is large, but it's stronger than + + + align:start position:0% +subset is large, but it's stronger than +that and it also implies that um that pi + + align:start position:0% +that and it also implies that um that pi + + + align:start position:0% +that and it also implies that um that pi +1 of x is large for all substantial + + align:start position:0% +1 of x is large for all substantial + + + align:start position:0% +1 of x is large for all substantial +subsets of a cross b. + + align:start position:0% +subsets of a cross b. + + + align:start position:0% +subsets of a cross b. +So it's stronger in a way which is + + align:start position:0% +So it's stronger in a way which is + + + align:start position:0% +So it's stronger in a way which is +exactly what we need in our discussion. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +so that suggests + + align:start position:0% +so that suggests + + + align:start position:0% +so that suggests +a better version of theorem one that we + + align:start position:0% +a better version of theorem one that we + + + align:start position:0% +a better version of theorem one that we +could have tried to prove. + + align:start position:0% + + + + align:start position:0% + +Um, let's erase this lema. + + align:start position:0% + + + + align:start position:0% + +So remember theorem one said that if we + + align:start position:0% +So remember theorem one said that if we + + + align:start position:0% +So remember theorem one said that if we +take the projection of a cross a in many + + align:start position:0% +take the projection of a cross a in many + + + align:start position:0% +take the projection of a cross a in many +directions, one of them has a large + + align:start position:0% +directions, one of them has a large + + + align:start position:0% +directions, one of them has a large +cardality. + + align:start position:0% +cardality. + + + align:start position:0% +cardality. +But we could have proved could have + + align:start position:0% +But we could have proved could have + + + align:start position:0% +But we could have proved could have +tried to prove something stronger that + + align:start position:0% +tried to prove something stronger that + + + align:start position:0% +tried to prove something stronger that +one of them has a small energy. Let me + + align:start position:0% +one of them has a small energy. Let me + + + align:start position:0% +one of them has a small energy. Let me +write it down. It's true and it's a + + align:start position:0% +write it down. It's true and it's a + + + align:start position:0% +write it down. It's true and it's a +theorem. + + align:start position:0% +theorem. + + + align:start position:0% +theorem. +Theorem two + + align:start position:0% +Theorem two + + + align:start position:0% +Theorem two +says + + align:start position:0% +says + + + align:start position:0% +says +um + + align:start position:0% + + + + align:start position:0% + +right so if a is a subset of fp size of + + align:start position:0% +right so if a is a subset of fp size of + + + align:start position:0% +right so if a is a subset of fp size of +a is p to the s a z less than s a less + + align:start position:0% +a is p to the s a z less than s a less + + + align:start position:0% +a is p to the s a z less than s a less +than one + + align:start position:0% +than one + + + align:start position:0% +than one +d is in fp size of d is p to the s d 0 z + + align:start position:0% +d is in fp size of d is p to the s d 0 z + + + align:start position:0% +d is in fp size of d is p to the s d 0 z +is less than sd + + align:start position:0% +is less than sd + + + align:start position:0% +is less than sd +then + + align:start position:0% +then + + + align:start position:0% +then +um I'm going to consider all the + + align:start position:0% +um I'm going to consider all the + + + align:start position:0% +um I'm going to consider all the +directions and pick the best one. And + + align:start position:0% +directions and pick the best one. And + + + align:start position:0% +directions and pick the best one. And +instead of looking at at the size of a + + align:start position:0% +instead of looking at at the size of a + + + align:start position:0% +instead of looking at at the size of a +plus ta, I'm going to look at the energy + + align:start position:0% +plus ta, I'm going to look at the energy + + + align:start position:0% +plus ta, I'm going to look at the energy +of a comma ta. + + align:start position:0% +of a comma ta. + + + align:start position:0% +of a comma ta. +And I'll take the minimum over all the + + align:start position:0% +And I'll take the minimum over all the + + + align:start position:0% +And I'll take the minimum over all the +t. + + align:start position:0% +t. + + + align:start position:0% +t. +Okay. So the biggest this energy could + + align:start position:0% +Okay. So the biggest this energy could + + + align:start position:0% +Okay. So the biggest this energy could +be is p to the 3 sa. It's the maximum + + align:start position:0% +be is p to the 3 sa. It's the maximum + + + align:start position:0% +be is p to the 3 sa. It's the maximum +possible energy. + + align:start position:0% +possible energy. + + + align:start position:0% +possible energy. +And we're going to say it's a little bit + + align:start position:0% +And we're going to say it's a little bit + + + align:start position:0% +And we're going to say it's a little bit +better than this. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Now because of this lema we + + align:start position:0% +Now because of this lema we + + + align:start position:0% +Now because of this lema we +automatically get not only a lower bound + + align:start position:0% +automatically get not only a lower bound + + + align:start position:0% +automatically get not only a lower bound +on pi t of a cross a but we get a lower + + align:start position:0% +on pi t of a cross a but we get a lower + + + align:start position:0% +on pi t of a cross a but we get a lower +bound on pi t of any big subset of a + + align:start position:0% +bound on pi t of any big subset of a + + + align:start position:0% +bound on pi t of any big subset of a +cross a. So this would automatically + + align:start position:0% +cross a. So this would automatically + + + align:start position:0% +cross a. So this would automatically +gives the BKT theorem. + + align:start position:0% + + + + align:start position:0% + +So in fact this easily implies a strong + + align:start position:0% +So in fact this easily implies a strong + + + align:start position:0% +So in fact this easily implies a strong +version of the BKT theorem which I think + + align:start position:0% +version of the BKT theorem which I think + + + align:start position:0% +version of the BKT theorem which I think +was also proven by BKT. + + align:start position:0% +was also proven by BKT. + + + align:start position:0% +was also proven by BKT. +And it says + + align:start position:0% +And it says + + + align:start position:0% +And it says +that um + + align:start position:0% +that um + + + align:start position:0% +that um +uh so + + align:start position:0% + + + + align:start position:0% + +x is p to the sx and d is as above. + + align:start position:0% +x is p to the sx and d is as above. + + + align:start position:0% +x is p to the sx and d is as above. +So not only you can say + + align:start position:0% +So not only you can say + + + align:start position:0% +So not only you can say +the maximum t and d pi t of x is large. + + align:start position:0% + + + + align:start position:0% + +So this so that that's the regular + + align:start position:0% +So this so that that's the regular + + + align:start position:0% +So this so that that's the regular +theorem + + align:start position:0% +theorem + + + align:start position:0% +theorem +and this follows from theorem two and + + align:start position:0% +and this follows from theorem two and + + + align:start position:0% +and this follows from theorem two and +using our lama + + align:start position:0% +using our lama + + + align:start position:0% +using our lama +but we could say that um uh + + align:start position:0% +but we could say that um uh + + + align:start position:0% +but we could say that um uh +that there so this is true but even + + align:start position:0% +that there so this is true but even + + + align:start position:0% +that there so this is true but even +better + + align:start position:0% + + + + align:start position:0% + +there is some t and d so that + + align:start position:0% +there is some t and d so that + + + align:start position:0% +there is some t and d so that +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +if y so if y is a subset of x and it's a + + align:start position:0% +if y so if y is a subset of x and it's a + + + align:start position:0% +if y so if y is a subset of x and it's a +substantial subset of x. + + align:start position:0% +substantial subset of x. + + + align:start position:0% +substantial subset of x. +Um then + + align:start position:0% +Um then + + + align:start position:0% +Um then +uh pi t of y is big. + + align:start position:0% + + + + align:start position:0% + +Okay. So the proof from here to here is + + align:start position:0% +Okay. So the proof from here to here is + + + align:start position:0% +Okay. So the proof from here to here is +you know we observed earlier that uh we + + align:start position:0% +you know we observed earlier that uh we + + + align:start position:0% +you know we observed earlier that uh we +can reduce to the case + + align:start position:0% +can reduce to the case + + + align:start position:0% +can reduce to the case +wow. Okay. + + align:start position:0% +wow. Okay. + + + align:start position:0% +wow. Okay. +Yeah, I guess I should say using ball + + align:start position:0% +Yeah, I guess I should say using ball + + + align:start position:0% +Yeah, I guess I should say using ball +ready gowers, we could reduce to the + + align:start position:0% +ready gowers, we could reduce to the + + + align:start position:0% +ready gowers, we could reduce to the +case where x is a big subset of a cross + + align:start position:0% +case where x is a big subset of a cross + + + align:start position:0% +case where x is a big subset of a cross +a and then y is a big subset of x. So y + + align:start position:0% +a and then y is a big subset of x. So y + + + align:start position:0% +a and then y is a big subset of x. So y +is a big subset of a cross a and then + + align:start position:0% +is a big subset of a cross a and then + + + align:start position:0% +is a big subset of a cross a and then +you use the energy bound to get this. + + align:start position:0% +you use the energy bound to get this. + + + align:start position:0% +you use the energy bound to get this. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um so let me say + + align:start position:0% +Um so let me say + + + align:start position:0% +Um so let me say +proof of theorem 2 plus bkt2 + + align:start position:0% +proof of theorem 2 plus bkt2 + + + align:start position:0% +proof of theorem 2 plus bkt2 +are similar to what we did in class + + align:start position:0% + + + + align:start position:0% + +and so they could be they're good + + align:start position:0% +and so they could be they're good + + + align:start position:0% +and so they could be they're good +optional exercises uh or they could be + + align:start position:0% +optional exercises uh or they could be + + + align:start position:0% +optional exercises uh or they could be +some some pieces of it might be required + + align:start position:0% +some some pieces of it might be required + + + align:start position:0% +some some pieces of it might be required +exercises. + + align:start position:0% + + + + align:start position:0% + +Okay. Um, + + align:start position:0% + + + + align:start position:0% + +cool. And I thought I should mention + + align:start position:0% +cool. And I thought I should mention + + + align:start position:0% +cool. And I thought I should mention +this. One of the things that Pablo + + align:start position:0% +this. One of the things that Pablo + + + align:start position:0% +this. One of the things that Pablo +impressed on me when we were talking + + align:start position:0% +impressed on me when we were talking + + + align:start position:0% +impressed on me when we were talking +over the vacation week was that + + align:start position:0% +over the vacation week was that + + + align:start position:0% +over the vacation week was that +this slightly stronger version is is is + + align:start position:0% +this slightly stronger version is is is + + + align:start position:0% +this slightly stronger version is is is +very is important in applications. Most + + align:start position:0% +very is important in applications. Most + + + align:start position:0% +very is important in applications. Most +of the applications actually depend on + + align:start position:0% +of the applications actually depend on + + + align:start position:0% +of the applications actually depend on +being able to say this slightly stronger + + align:start position:0% +being able to say this slightly stronger + + + align:start position:0% +being able to say this slightly stronger +thing. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. So now you might think you might + + align:start position:0% +Okay. So now you might think you might + + + align:start position:0% +Okay. So now you might think you might +ask yourself um + + align:start position:0% +ask yourself um + + + align:start position:0% +ask yourself um +maybe energy is actually a better thing + + align:start position:0% +maybe energy is actually a better thing + + + align:start position:0% +maybe energy is actually a better thing +to be talking about because a bound for + + align:start position:0% +to be talking about because a bound for + + + align:start position:0% +to be talking about because a bound for +the energy is is kind of stable under + + align:start position:0% +the energy is is kind of stable under + + + align:start position:0% +the energy is is kind of stable under +taking large subsets. + + align:start position:0% + + + + align:start position:0% + +And so maybe we should have been talking + + align:start position:0% +And so maybe we should have been talking + + + align:start position:0% +And so maybe we should have been talking +about energy all along. + + align:start position:0% +about energy all along. + + + align:start position:0% +about energy all along. +And it's reasonable to ask if you take + + align:start position:0% +And it's reasonable to ask if you take + + + align:start position:0% +And it's reasonable to ask if you take +our proof of theorem one and you just + + align:start position:0% +our proof of theorem one and you just + + + align:start position:0% +our proof of theorem one and you just +try to change all the cardalities to + + align:start position:0% +try to change all the cardalities to + + + align:start position:0% +try to change all the cardalities to +energies, could you adapt it and prove + + align:start position:0% +energies, could you adapt it and prove + + + align:start position:0% +energies, could you adapt it and prove +theorem two instead? + + align:start position:0% + + + + align:start position:0% + +Okay. And you you can't do that. Um and + + align:start position:0% +Okay. And you you can't do that. Um and + + + align:start position:0% +Okay. And you you can't do that. Um and +it's a good moment to recap the main + + align:start position:0% +it's a good moment to recap the main + + + align:start position:0% +it's a good moment to recap the main +idea in theorem one and also sort of uh + + align:start position:0% +idea in theorem one and also sort of uh + + + align:start position:0% +idea in theorem one and also sort of uh +a way of reflecting on the different big + + align:start position:0% +a way of reflecting on the different big + + + align:start position:0% +a way of reflecting on the different big +tools and how they're related to each + + align:start position:0% +tools and how they're related to each + + + align:start position:0% +tools and how they're related to each +other. + + align:start position:0% + + + + align:start position:0% + +All right. What should I erase? + + align:start position:0% +All right. What should I erase? + + + align:start position:0% +All right. What should I erase? +Maybe now I can erase the BSG theorem. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +okay. Actually, before I erase the BSG + + align:start position:0% +okay. Actually, before I erase the BSG + + + align:start position:0% +okay. Actually, before I erase the BSG +theorem, let me make a little comment + + align:start position:0% +theorem, let me make a little comment + + + align:start position:0% +theorem, let me make a little comment +about it. So, it's of it's there are a + + align:start position:0% +about it. So, it's of it's there are a + + + align:start position:0% +about it. So, it's of it's there are a +couple of closely related forms of the + + align:start position:0% +couple of closely related forms of the + + + align:start position:0% +couple of closely related forms of the +theorem. And another way I often say it + + align:start position:0% +theorem. And another way I often say it + + + align:start position:0% +theorem. And another way I often say it +is that if the energy of AB is large + + align:start position:0% +is that if the energy of AB is large + + + align:start position:0% +is that if the energy of AB is large +then there must be A prime and B prime + + align:start position:0% +then there must be A prime and B prime + + + align:start position:0% +then there must be A prime and B prime +so that the cardality of A prime plus B + + align:start position:0% +so that the cardality of A prime plus B + + + align:start position:0% +so that the cardality of A prime plus B +prime is small + + align:start position:0% + + + + align:start position:0% + +maybe I should yeah + + align:start position:0% +maybe I should yeah + + + align:start position:0% +maybe I should yeah +maybe I should me put it here. + + align:start position:0% + + + + align:start position:0% + +So theorem the SG variant + + align:start position:0% +So theorem the SG variant + + + align:start position:0% +So theorem the SG variant +this is the the way it's most commonly + + align:start position:0% +this is the the way it's most commonly + + + align:start position:0% +this is the the way it's most commonly +said so I would be a bit remiss not to + + align:start position:0% +said so I would be a bit remiss not to + + + align:start position:0% +said so I would be a bit remiss not to +show it to you. So if A and B are in the + + align:start position:0% +show it to you. So if A and B are in the + + + align:start position:0% +show it to you. So if A and B are in the +group + + align:start position:0% +group + + + align:start position:0% +group +and let's say A and B have size at most + + align:start position:0% +and let's say A and B have size at most + + + align:start position:0% +and let's say A and B have size at most +N + + align:start position:0% +N + + + align:start position:0% +N +and the energy of AB is large + + align:start position:0% +and the energy of AB is large + + + align:start position:0% +and the energy of AB is large +um energy of AB is greater than K + + align:start position:0% +um energy of AB is greater than K + + + align:start position:0% +um energy of AB is greater than K +inverse N cubed + + align:start position:0% +inverse N cubed + + + align:start position:0% +inverse N cubed +then it may not be the case that a plus + + align:start position:0% +then it may not be the case that a plus + + + align:start position:0% +then it may not be the case that a plus +b is small because of the example with + + align:start position:0% +b is small because of the example with + + + align:start position:0% +b is small because of the example with +garbage but we can get rid of the + + align:start position:0% +garbage but we can get rid of the + + + align:start position:0% +garbage but we can get rid of the +garbage. So there exists a prime in a + + align:start position:0% +garbage. So there exists a prime in a + + + align:start position:0% +garbage. So there exists a prime in a +and b prime in b so that um + + align:start position:0% +and b prime in b so that um + + + align:start position:0% +and b prime in b so that um +uh a prime + + align:start position:0% +uh a prime + + + align:start position:0% +uh a prime +a yeah so that they are substantial. Um + + align:start position:0% +a yeah so that they are substantial. Um + + + align:start position:0% +a yeah so that they are substantial. Um +so a prime and b prime are greater than + + align:start position:0% +so a prime and b prime are greater than + + + align:start position:0% +so a prime and b prime are greater than +or equal to k to the minus order of 1 n + + align:start position:0% +or equal to k to the minus order of 1 n + + + align:start position:0% +or equal to k to the minus order of 1 n +and + + align:start position:0% +and + + + align:start position:0% +and +a prime + b prime is less than or equal + + align:start position:0% +a prime + b prime is less than or equal + + + align:start position:0% +a prime + b prime is less than or equal +to k to the order of 1. + + align:start position:0% +to k to the order of 1. + + + align:start position:0% +to k to the order of 1. +So if we there's we can locate the + + align:start position:0% +So if we there's we can locate the + + + align:start position:0% +So if we there's we can locate the +correct structured parts then their + + align:start position:0% +correct structured parts then their + + + align:start position:0% +correct structured parts then their +subset is small after we remove some + + align:start position:0% +subset is small after we remove some + + + align:start position:0% +subset is small after we remove some +garbage. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +All right. So now let me remind you of + + align:start position:0% +All right. So now let me remind you of + + + align:start position:0% +All right. So now let me remind you of +one of the key ideas in the proof of + + align:start position:0% +one of the key ideas in the proof of + + + align:start position:0% +one of the key ideas in the proof of +theorem one. + + align:start position:0% + + + + align:start position:0% + +key idea + + align:start position:0% +key idea + + + align:start position:0% +key idea +in the proof of theorem one. + + align:start position:0% +in the proof of theorem one. + + + align:start position:0% +in the proof of theorem one. +So the key idea was based on the plume + + align:start position:0% +So the key idea was based on the plume + + + align:start position:0% +So the key idea was based on the plume +corusia inequality and it was an idea + + align:start position:0% +corusia inequality and it was an idea + + + align:start position:0% +corusia inequality and it was an idea +that I called contagious structure. + + align:start position:0% + + + + align:start position:0% + +So it said if a + t1 a is small + + align:start position:0% +So it said if a + t1 a is small + + + align:start position:0% +So it said if a + t1 a is small +and + + align:start position:0% +and + + + align:start position:0% +and +a + t2 a is small + + align:start position:0% +a + t2 a is small + + + align:start position:0% +a + t2 a is small +then + + align:start position:0% +then + + + align:start position:0% +then +a + t1 + t2 a is also small. + + align:start position:0% +a + t1 + t2 a is also small. + + + align:start position:0% +a + t1 + t2 a is also small. +Not quite as small but still pretty + + align:start position:0% +Not quite as small but still pretty + + + align:start position:0% +Not quite as small but still pretty +small. + + align:start position:0% + + + + align:start position:0% + +So this was the key thing. + + align:start position:0% +So this was the key thing. + + + align:start position:0% +So this was the key thing. +If um a plus a if a plus ta is small for + + align:start position:0% +If um a plus a if a plus ta is small for + + + align:start position:0% +If um a plus a if a plus ta is small for +a bunch of t and d then it would have to + + align:start position:0% +a bunch of t and d then it would have to + + + align:start position:0% +a bunch of t and d then it would have to +be small for an even bigger set of d by + + align:start position:0% +be small for an even bigger set of d by + + + align:start position:0% +be small for an even bigger set of d by +adding d or by multiplying d or by + + align:start position:0% +adding d or by multiplying d or by + + + align:start position:0% +adding d or by multiplying d or by +taking negatives and then there would be + + align:start position:0% +taking negatives and then there would be + + + align:start position:0% +taking negatives and then there would be +a huge set of t's where a plus ta was + + align:start position:0% +a huge set of t's where a plus ta was + + + align:start position:0% +a huge set of t's where a plus ta was +small and then that contradicts basic + + align:start position:0% +small and then that contradicts basic + + + align:start position:0% +small and then that contradicts basic +double counting. + + align:start position:0% +double counting. + + + align:start position:0% +double counting. +That's the proof. Okay. So what if we + + align:start position:0% +That's the proof. Okay. So what if we + + + align:start position:0% +That's the proof. Okay. So what if we +tried to work with energy throughout? So + + align:start position:0% +tried to work with energy throughout? So + + + align:start position:0% +tried to work with energy throughout? So +instead of trying to prove that a plus + + align:start position:0% +instead of trying to prove that a plus + + + align:start position:0% +instead of trying to prove that a plus +ta is big, we're going to try to prove + + align:start position:0% +ta is big, we're going to try to prove + + + align:start position:0% +ta is big, we're going to try to prove +that the energy is small. + + align:start position:0% +that the energy is small. + + + align:start position:0% +that the energy is small. +So we're doing a proof by contradiction. + + align:start position:0% +So we're doing a proof by contradiction. + + + align:start position:0% +So we're doing a proof by contradiction. +So the the analogous question would be + + align:start position:0% +So the the analogous question would be + + + align:start position:0% +So the the analogous question would be +if the energy between a and t1 of a is + + align:start position:0% +if the energy between a and t1 of a is + + + align:start position:0% +if the energy between a and t1 of a is +large + + align:start position:0% +large + + + align:start position:0% +large +and the energy between a and t2 of a is + + align:start position:0% +and the energy between a and t2 of a is + + + align:start position:0% +and the energy between a and t2 of a is +large. + + align:start position:0% +large. + + + align:start position:0% +large. +Then does that imply that the energy + + align:start position:0% +Then does that imply that the energy + + + align:start position:0% +Then does that imply that the energy +between A and T1 + T2 A is large. + + align:start position:0% + + + + align:start position:0% + +Okay, the answer is no. uh and it is the + + align:start position:0% +Okay, the answer is no. uh and it is the + + + align:start position:0% +Okay, the answer is no. uh and it is the +same issue that we saw before that when + + align:start position:0% +same issue that we saw before that when + + + align:start position:0% +same issue that we saw before that when +the we say the energy is large it means + + align:start position:0% +the we say the energy is large it means + + + align:start position:0% +the we say the energy is large it means +there's at least a piece of A and a + + align:start position:0% +there's at least a piece of A and a + + + align:start position:0% +there's at least a piece of A and a +piece of T1A that are very friendly with + + align:start position:0% +piece of T1A that are very friendly with + + + align:start position:0% +piece of T1A that are very friendly with +each other but it doesn't have to be all + + align:start position:0% +each other but it doesn't have to be all + + + align:start position:0% +each other but it doesn't have to be all +of them. So one piece of A must be very + + align:start position:0% +of them. So one piece of A must be very + + + align:start position:0% +of them. So one piece of A must be very +friendly with T1 A and one piece of A + + align:start position:0% +friendly with T1 A and one piece of A + + + align:start position:0% +friendly with T1 A and one piece of A +must be very friendly with T2A. + + align:start position:0% +must be very friendly with T2A. + + + align:start position:0% +must be very friendly with T2A. +But those could be two different pieces + + align:start position:0% +But those could be two different pieces + + + align:start position:0% +But those could be two different pieces +of A. And in that case we can't really + + align:start position:0% +of A. And in that case we can't really + + + align:start position:0% +of A. And in that case we can't really +learn anything more. Doesn't mean + + align:start position:0% +learn anything more. Doesn't mean + + + align:start position:0% +learn anything more. Doesn't mean +there's any piece of A that's friendly + + align:start position:0% +there's any piece of A that's friendly + + + align:start position:0% +there's any piece of A that's friendly +with both of them. + + align:start position:0% +with both of them. + + + align:start position:0% +with both of them. +So here's the example. Answer is no. + + align:start position:0% +So here's the example. Answer is no. + + + align:start position:0% +So here's the example. Answer is no. +Here's the example. So a might be the + + align:start position:0% +Here's the example. So a might be the + + + align:start position:0% +Here's the example. So a might be the +numbers up to n union t1 times the + + align:start position:0% +numbers up to n union t1 times the + + + align:start position:0% +numbers up to n union t1 times the +numbers up to n union t2 * the numbers + + align:start position:0% +numbers up to n union t2 * the numbers + + + align:start position:0% +numbers up to n union t2 * the numbers +up to + + align:start position:0% +up to + + + align:start position:0% +up to +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so then uh t1 a be t1 numbers up to n + + align:start position:0% +so then uh t1 a be t1 numbers up to n + + + align:start position:0% +so then uh t1 a be t1 numbers up to n +union dot dot dot t2 a this t2 numbers + + align:start position:0% +union dot dot dot t2 a this t2 numbers + + + align:start position:0% +union dot dot dot t2 a this t2 numbers +up to n union dot dot dot. + + align:start position:0% +up to n union dot dot dot. + + + align:start position:0% +up to n union dot dot dot. +So these two guys are very friendly. Not + + align:start position:0% +So these two guys are very friendly. Not + + + align:start position:0% +So these two guys are very friendly. Not +just because they're the same as each + + align:start position:0% +just because they're the same as each + + + align:start position:0% +just because they're the same as each +other. Not everybody who's the same as + + align:start position:0% +other. Not everybody who's the same as + + + align:start position:0% +other. Not everybody who's the same as +each other is friends, but because they + + align:start position:0% +each other is friends, but because they + + + align:start position:0% +each other is friends, but because they +have uh they're have a lot of additive + + align:start position:0% +have uh they're have a lot of additive + + + align:start position:0% +have uh they're have a lot of additive +structure. + + align:start position:0% +structure. + + + align:start position:0% +structure. +And therefore + + align:start position:0% +And therefore + + + align:start position:0% +And therefore +this guy is large. + + align:start position:0% +this guy is large. + + + align:start position:0% +this guy is large. +And + + align:start position:0% +And + + + align:start position:0% +And +uh these two guys are very friendly + + align:start position:0% +uh these two guys are very friendly + + + align:start position:0% +uh these two guys are very friendly +and therefore this guy is large. + + align:start position:0% +and therefore this guy is large. + + + align:start position:0% +and therefore this guy is large. +But there's nothing going on with T1 + + align:start position:0% +But there's nothing going on with T1 + + + align:start position:0% +But there's nothing going on with T1 +plus T1 and T2 are totally arbitrary and + + align:start position:0% +plus T1 and T2 are totally arbitrary and + + + align:start position:0% +plus T1 and T2 are totally arbitrary and +T1 plus T2 we would not typically have + + align:start position:0% +T1 plus T2 we would not typically have + + + align:start position:0% +T1 plus T2 we would not typically have +this large. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +all right + + align:start position:0% +all right + + + align:start position:0% +all right +if a T1 + T2 a is typically small. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +cool. So, it was actually kind of + + align:start position:0% +cool. So, it was actually kind of + + + align:start position:0% +cool. So, it was actually kind of +crucial in our proof of theorem one to + + align:start position:0% +crucial in our proof of theorem one to + + + align:start position:0% +crucial in our proof of theorem one to +talk about the cardality of the subset + + align:start position:0% +talk about the cardality of the subset + + + align:start position:0% +talk about the cardality of the subset +instead of the energy because in that + + align:start position:0% +instead of the energy because in that + + + align:start position:0% +instead of the energy because in that +setting we have the Pluna Roua + + align:start position:0% +setting we have the Pluna Roua + + + align:start position:0% +setting we have the Pluna Roua +inequalities and we get a great deal of + + align:start position:0% +inequalities and we get a great deal of + + + align:start position:0% +inequalities and we get a great deal of +structure from a single subset being + + align:start position:0% +structure from a single subset being + + + align:start position:0% +structure from a single subset being +small. We get lots of other things. + + align:start position:0% +small. We get lots of other things. + + + align:start position:0% +small. We get lots of other things. +On the other hand, it is nice eventually + + align:start position:0% +On the other hand, it is nice eventually + + + align:start position:0% +On the other hand, it is nice eventually +to get to theorem two because theorem + + align:start position:0% +to get to theorem two because theorem + + + align:start position:0% +to get to theorem two because theorem +two is stable if you replace the actual + + align:start position:0% +two is stable if you replace the actual + + + align:start position:0% +two is stable if you replace the actual +product a cross a by a subset which is + + align:start position:0% +product a cross a by a subset which is + + + align:start position:0% +product a cross a by a subset which is +almost all of it. + + align:start position:0% +almost all of it. + + + align:start position:0% +almost all of it. +So energy so so both so both looking at + + align:start position:0% +So energy so so both so both looking at + + + align:start position:0% +So energy so so both so both looking at +cardality and looking at energy has it + + align:start position:0% +cardality and looking at energy has it + + + align:start position:0% +cardality and looking at energy has it +have have good features. Energy + + align:start position:0% +have have good features. Energy + + + align:start position:0% +have have good features. Energy +estimates are stable undertaking subsets + + align:start position:0% +estimates are stable undertaking subsets + + + align:start position:0% +estimates are stable undertaking subsets +and the cardality estimates have this + + align:start position:0% +and the cardality estimates have this + + + align:start position:0% +and the cardality estimates have this +contagious structure thing. Those are + + align:start position:0% +contagious structure thing. Those are + + + align:start position:0% +contagious structure thing. Those are +both very helpful. + + align:start position:0% +both very helpful. + + + align:start position:0% +both very helpful. +And so um + + align:start position:0% +And so um + + + align:start position:0% +And so um +uh okay and um and bal + + align:start position:0% +uh okay and um and bal + + + align:start position:0% +uh okay and um and bal +this is important + + align:start position:0% +this is important + + + align:start position:0% +this is important +because + + align:start position:0% +because + + + align:start position:0% +because +uh okay even though having a big energy + + align:start position:0% +uh okay even though having a big energy + + + align:start position:0% +uh okay even though having a big energy +is not synonymous with having a small + + align:start position:0% +is not synonymous with having a small + + + align:start position:0% +is not synonymous with having a small +subset balm gar says they're very + + align:start position:0% +subset balm gar says they're very + + + align:start position:0% +subset balm gar says they're very +closely related and so by using balag + + align:start position:0% +closely related and so by using balag + + + align:start position:0% +closely related and so by using balag +samuris you can often get the best of + + align:start position:0% +samuris you can often get the best of + + + align:start position:0% +samuris you can often get the best of +both world worlds so if you were to + + align:start position:0% +both world worlds so if you were to + + + align:start position:0% +both world worlds so if you were to +pretend that you could have all the good + + align:start position:0% +pretend that you could have all the good + + + align:start position:0% +pretend that you could have all the good +features of of an energy bound and all + + align:start position:0% +features of of an energy bound and all + + + align:start position:0% +features of of an energy bound and all +the good features of a cardality bound. + + align:start position:0% +the good features of a cardality bound. + + + align:start position:0% +the good features of a cardality bound. +See what you could prove. Very often you + + align:start position:0% +See what you could prove. Very often you + + + align:start position:0% +See what you could prove. Very often you +can prove those things by using + + align:start position:0% +can prove those things by using + + + align:start position:0% +can prove those things by using +balacrated gowers to move back and + + align:start position:0% +balacrated gowers to move back and + + + align:start position:0% +balacrated gowers to move back and +forth. + + align:start position:0% + + + + align:start position:0% + +And Pablo gave the analysis seminar a + + align:start position:0% +And Pablo gave the analysis seminar a + + + align:start position:0% +And Pablo gave the analysis seminar a +few weeks ago and he gave an overview of + + align:start position:0% +few weeks ago and he gave an overview of + + + align:start position:0% +few weeks ago and he gave an overview of +recent developments in projection theory + + align:start position:0% +recent developments in projection theory + + + align:start position:0% +recent developments in projection theory +and he made the claim or suggestion that + + align:start position:0% +and he made the claim or suggestion that + + + align:start position:0% +and he made the claim or suggestion that +this theorem might be one of the most + + align:start position:0% +this theorem might be one of the most + + + align:start position:0% +this theorem might be one of the most +important or most used theorems in math + + align:start position:0% +important or most used theorems in math + + + align:start position:0% +important or most used theorems in math +in the last several decades. + + align:start position:0% +in the last several decades. + + + align:start position:0% +in the last several decades. +It was a It was a little provocative. + + align:start position:0% +It was a It was a little provocative. + + + align:start position:0% +It was a It was a little provocative. +I thought it was interesting. Uh and I + + align:start position:0% +I thought it was interesting. Uh and I + + + align:start position:0% +I thought it was interesting. Uh and I +have gradually been appreciating it uh + + align:start position:0% +have gradually been appreciating it uh + + + align:start position:0% +have gradually been appreciating it uh +more and more. I'm learning about it. Uh + + align:start position:0% +more and more. I'm learning about it. Uh + + + align:start position:0% +more and more. I'm learning about it. Uh +anyway, I would gradually appreciating + + align:start position:0% +anyway, I would gradually appreciating + + + align:start position:0% +anyway, I would gradually appreciating +it more and more. Um and um yeah, + + align:start position:0% +it more and more. Um and um yeah, + + + align:start position:0% +it more and more. Um and um yeah, +probably as we keep going, we'll see how + + align:start position:0% +probably as we keep going, we'll see how + + + align:start position:0% +probably as we keep going, we'll see how +this keeps being important. \ No newline at end of file diff --git a/c45ieqaUU4k.txt b/c45ieqaUU4k.txt new file mode 100644 index 0000000000000000000000000000000000000000..c7425a8b7cd0045d5882096120d250127e1ca756 --- /dev/null +++ b/c45ieqaUU4k.txt @@ -0,0 +1,1146 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: All right. + +We're going to get +started now. + +For those of you who don't know +me, I'm Josh Slocum, one + +of your TAs. + +And today's lecture is going to +be a primer on ray tracing + +to help you get started +on the final project. + +So first, we're going to start +with a little background. + +Tell you about ray tracing. + +Ray tracing is essentially +a physics simulation. + +You simulate the way photons +bounce around and interact + +with materials. + +And from that, you generate +an image of a scene. + +It's extremely parallel because +you can trace a whole + +bunch of photons bouncing +around at the same time. + +And it has a huge capacity +for photorealism. + +So like this sample seen here, +you have all sorts of + +reflections and light working in +ways that you don't see in + +a normal rendering program. + +The final project, as you know +if you've read the handout, is + +going to be groups of two +or three people each. + +And you'll be given a working +ray tracer program. + +A very slow one, but +one that works. + +And your objective is to make +it run as fast as possible. + +You can do pretty much anything +you want with a few + +restrictions we'll +talk about later. + +You can make algorithmic +improvements, parallelize it, + +change the way the rendering +works slightly. + +All sorts of things. + +Pretty much anything +you can think of. + +The only deliverables for the +final project are the + +preliminary report due next +week, in which you'll have to + +show us that you've profiled the +project, tell us what hot + +spots you've identified, and +ideas you have for speeding up + +the ray tracer, as well +as any actual work + +you've already done. + +The final project comes with two +built-in scenes that can + +be ray traced. + +Scene one, this one here, +is rendered much + +faster than scene two. + +And you're going to want to +work on that one first. + +And then, there's scene two, +which is slightly different. + +It has water and one +less sphere. + +These are the restrictions +on what you can do + +for the final project. + +The purpose of these +restrictions is basically just + +to make sure that everyone's +ray tracer is + +doing the same thing. + +So you're all working on the +same problem, and you're not + +achieving speed ups by +simplifying out some + +functionality of the program. + +Does anyone have any questions +about the final project + +before I move on? + +All right. + +Go ahead. + +AUDIENCE: [INAUDIBLE] + +we're going to do a third scene +similar to the first + +two, right? + +PROFESSOR: Oh. + +Yeah. + +In order to make sure that +you're following these rules, + +we're going to test your ray +tracer on one or more other + +scenes and make sure that +they render properly. + +But these are the two scenes +that you will be benchmarked + +on for your performance grade. + +All right. + +Next, we're going to go over how +ray tracing works and the + +big concepts used in the ray +tracer you'll be working on. + +So the basic idea behind the +rendering is you're going to + +construct a geometric model of +the scene you want to render, + +and so it will be made +of polygons, + +or spheres, or planes. + +And then within that model, you +insert a grid of pixels. + +They'll form the image you're +going to render. + +And then, you just project the +scene onto the grid of pixels, + +and you have some image. + +The way you do this with ray +tracing is you use a method + +called ray casting where you +take some camera and cast rays + +through each pixel +onto the scene. + +And then, whatever color object +the ray hits is the + +color that that pixel gets +shaded in the scene. + +This method of tracing rays is +called backwards ray tracing, + +because you're going in opposite +direction that + +photons go in when you're +actually observing something. + +So if this was an actual +scene, you'd have light + +bouncing here and +into you're eye. + +Whereas what you're doing is +you're tracing backwards from + +the eye to the object. + +Ray casting-- + +this image here is +a ray image-- + +is very primitive. + +It doesn't really +get you much. + +So what you can do is you +can improve your physics + +simulation by adding a whole +bunch more things on top of + +it, like shadows, and +reflections, and global + +illumination. + +All sorts of fun stuff. + +So if you want to start +simulating shadows, and + +reflections, and defraction, you +need to start recursively + +casting rays, which is +called ray tracing. + +So when your ray bounces off of +an object, you can cast a + +reflection ray at the same +angle mirrored from the + +perpendicular of the object and +see what color object that + +ray hits, and then, shade this +object with that color. + +You can also cast a refracted +ray, and use Snell's a lot to + +tell which direction it goes +in and do the same thing. + +And then, you can cast a shadow +ray at all the light + +sources in the scene. + +And if the shadow ray hits an +object before hitting the + +light source, then you know +that this object is in the + +shade and make it darker. + +And obviously, you have to limit +the recursion depth for + +your recursive tracing, because +otherwise, you'll + +never finish rendering. + +So, first way of improving +lighting is to start using + +direct illumination, which is +you have a light source at the + +top of the scene. + +And when you hit something like +a wall here, you then + +bounce a ray at the +light source. + +And depending on how far this +intersection A is from the + +light source, you shade either +brighter or darker. + +So it might be hard to see in +this light, but the wall gets + +darker the further away +it is from the light. + +And then, you do shadows the +same way, except at point B + +here, the rate it bounces from +the ground hits this ball. + +And so, point B is +in the shade. + +Now, you can improve on shadows +by making what's + +called soft shadows. + +Soft shadows are shadows +that form a gradient + +from darker to lighter. + +They happen when you have a +light source that's not a + +point light. + +So if you look at the shadows +around you in the room, you'll + +see there are gradients, +not just a + +solid block of darkness. + +And the way you achieve that +is when you get an + +intersection, when your ray +intersects a point, you cast + +multiple shadow rays at +different points along the + +light source. + +And depending on how many of +these rays hit something + +before hitting the light +source, you shade some + +proportion of the light being +casted, or the light coming + +from this light source. + +So you can see point D here, +none of the rays hit the light + +source, and so, it's in +a very dark area. + +Whereas point C, one of the rays +hits the light source, + +and so it's in a slightly +brighter area. + +And then reflection and +refraction work very similarly + +to shadows, except instead of +bouncing from here to the + +light source, you bounce off +this metal ball at the angle + +of reflection. + +And you bounce through this +glass ball using the angle of + +refraction. + +You can calculate using +Snell's law. + +Any questions before +we move on? + +All right. + +So as you can see pretty clearly +in this image, there's + +still some problems. + +The ceiling is completely +black. + +Shadows are mostly black. + +And there's no light being +transmitted through this glass + +ball either into the +shadow here. + +So there's definitely some +improvements we can make on + +our physics simulation. + +The first thing we're going to +look at is called global + +illumination, which is pretty +much any sort of illumination + +that doesn't come directly +from light sources. + +Now the reason this sort of +illumination is important is + +that there's actually a lot of +light that gets bounced around + +the room that doesn't +come directly + +from the light source. + +Like that white wall, if I shine +this laser pointer at + +it, as you can see, there's +still a lot of light + +bouncing off of it. + +It's not all being absorbed. + +So what you can do is you can +take your ray intersection, + +and you can use what's called +the Monte Carlo method, which + +is you take a whole bunch of +random samples and interpolate + +those samples to get some value +that approximates what + +the illuminant should be here. + +The problem with that, though, +is that when you trace + +backwards, you get this +exponential explosion of + +recursively cast rays. + +And you have no guarantee that +any of these paths will ever + +get to this light source. + +So what you have to do is trace +forwards, so you start + +at the light source, and you +cast photons in random + +directions and let them bounce +all around the scene until + +they get absorbed. + +Now, when a photon bounces, a +bunch of light gets absorbed. + +But not all the light. + +And so, the rest of the light +keeps reflecting. + +And depending on the kind of +material, different amounts + +and colors of light +will be reflected. + +So as you can see, this +ray here bounces + +off the orange wall. + +And so, orange light +gets reflected. + +This ray bounces off +the blue wall. + +And so, blue light +gets reflected. + +And this ray bounces off this +metal ball, and so it gets + +completely reflected up +towards the ceiling. + +So if you remember each bounce +in something called a photon + +map, then later, you can come +back and say, oh, there's so + +many photons in this area. + +And that's what these +yellow circles are. + +So the illuminance is going +to be approximately this. + +The problem with that is unless +you're simulating an + +extremely large number of +photons, you'll have an uneven + +distribution. + +So what you can do is you can +hybridize forwards ray tracing + +and the Monte Carlo method. + +So you construct your photon +map, which is represented in + +this image by all the red dots +scattered everywhere. + +And then you do backwards +ray tracing. + +Then when you reach a point, you +randomly sample different + +reflection rays and average +their illuminance to get the + +illuminance at this point. + +So you have blue illuminance +from the wall here. + +And then light gray from here +and darker gray from here. + +And the result is this sort of +pale blue, which you can't + +really see in the image because +the light's bad. + +Yeah, so backwards trace, +randomly sample, illumination. + +And any questions +before we go on? + +So it turns out even with +building a photon map and then + +randomly sampling the photon +map, calculating the + +irradiance can still +be very expensive. + +So what we've implemented to +speed that up is what's called + +an irradiance cache. + +And the way the irradiance +cache works is there are + +certain areas on objects that +will have pretty much the same + +irradiance. + +It's pretty much the same +irradiance levels. + +So you can interpolate +from nearby points. + +So what we do with the +irradiance cache is as the + +scene is rendering, if there +is a cache miss, then we + +calculate the irradiance for +some pixel which corresponds + +to a point in the scene. + +And then, if we then trace a +ray very near to that same + +pixel, you can then interpolate +from nearby cached + +irradiances and get something +that looks right. + +So if you take a look at this +image, where the green dots + +represent cache misses on these +big planer objects here. + +There's very few cache misses. + +And it's almost entirely +cache hits. + +Whereas at the interface between +different objects, the + +cache misses become +much more common. + +But overall, the number of +irradiance calculations is + +greatly reduced. + +And then, the third kind of +illumination that we implement + +is called caustics. + +Caustics are just light being +lensed into patterns of + +brighter and darker spaces, such +as you get from a light + +pointing towards a glass ball. + +Or if you ever see the sort of +wavy pattern on the bottom of + +a pool, that's also +from caustics. + +Caustics are also implemented +with the photon map, except + +it's created slightly +differently. + +Instead of bouncing photons +everywhere, photons are + +absorbed as soon as they +hit a diffuse object. + +So a photon might bounce off of +this metal sphere and then + +hit the wall, and it will +be immediately absorbed. + +Whereas if it hits this sphere, +it'll bounce, and + +bounce, and then be absorbed. + +So the objective of caustics +is to trace how photons are + +grouped based on the optical +properties of + +materials in the scene. + +And then, caustics are rendered +pretty simply. + +Because there's much fewer +photons than in the photon map + +for global illumination, you +don't need to use an + +irradiance cache. + +So you simply trace a ray to +a point and then sample the + +number of photons nearby. + +And you end up with something +like this if you just do + +caustics shading. + +So then at the end, you take +your direct illumination, and + +then add it to caustics, and +then add it to global + +illumination. + +And you get something that +looks like this. + +Any questions before we go +to the code overview? + +Go ahead. + +AUDIENCE: Do we weight +them equally? + +PROFESSOR: So the +question was, do + +we weight them equally? + +And the answer is yes. + +And you just sum +them together. + +Ideally, you were clever and +constructed your ray tracer so + +that they should be weighted +equally, because there's + +weighting done internally, +basically. + +So next, we're going to do a +quick overview of the code + +that will be in your +repositories just get you + +started and help you understand +how it works. + +First, we're going to start by +explaining some of the classes + +you'll find. + +First is SceneObject, which is +the parent class for all of + +the objects that will be used to +construct the scenes you'll + +be rendering. + +Every scene object has a ray +intersection method that's + +called whenever you +trace a ray. + +And it'll return where the ray + +intersection is and the object. + +And SceneObject is inherited by +these objects here, which + +all of the objects will +inherit from. + +Then we've got the Raytracer +class, which + +contains the main method. + +So it starts the program. + +And it also contains methods for +constructing the scene and + +then rendering the +scene once you've + +constructed the scene first. + +We have the LightSource class, +which is a base class for any + +light sources. + +In our ray tracer, the only +subclass is square photon + +light, which is this light at +the top of the scene here. + +And what that does, or what the +light class does, is it + +contains methods for +constructing the photon maps + +and getting illumination from +either global, or caustic, or + +direct sources. + +And then there's also the +iCache class, which + +essentially just implements +the iCache for you. + +Any questions? + +So basic execution overview. + +You have the main method +for Raytracer. + +Parses the command line. + +Constructs the scene. + +And the scene is just a +command line switch. + +So if you say S1, it'll +construct scene one. + +If you say S2, it'll construct +scene two. + +Then for each light source, it +tells the light source to make + +photon maps for the global +and caustic illumination. + +GUEST SPEAKER: I should mention +that we actually moved + +the main functionality +into [INAUDIBLE] + +so you can replace the data. + +You don't have to touch that. + +It just constructs the scene, +so that we can then add a + +scene [INAUDIBLE] from that. + +So you shouldn't need +to do that. + +PROFESSOR: OK. + +So that's changed then. + +Then, main calls the render +function of Raytracer. + +What the render function +does-- + +excuse me, method does-- + +is it casts a ray for each +pixel in the scene you're + +going to render, finds the +nearest intersection, and then + +computes the shading at that +intersection by recursively + +bouncing rays and [? painting ?] +the illuminance + +cache for illumination. + +And that's basically what +the Raytracer does. + +It's pretty simple. + +So we're also going to quickly +go over how the light source + +traces photons for direct +and global illumination. + +The difference is kind of +settled, but pretty important. + +With global illumination, you +want some total number of + +photons to be put in the map. + +And you put a photon in the +map whenever it hits some + +diffuse surface. + +And then, that photon then +continues bouncing around + +until it's absorbed. + +For caustic illumination, +it's pretty similar. + +You have some set number +of photons you want to + +get into the map. + +You cast a ray in some +random direction. + +And then, the ray intersects +with a diffuse material. + +You store the intersection +in the photon map. + +And then you break. + +You don't keep bouncing +the photons around. + +So that's basically it for +the code overview. + +This slide has some resources +that you can use if you want + +to learn more about +ray tracing. + +Some of these will explain +concepts that we haven't + +implemented. + +They're an interesting read, +but not needed if you don't + +want to read them. + +And also, there's no standard +way of doing global + +illumination or direct +illumination. + +So you may come across resources +that do things + +slightly different than our +reference implementation. + +That doesn't mean either +one is wrong. + +But you should be aware that +there will almost certainly be + +differences. + +Does anyone have +any questions? + +Go ahead. + +AUDIENCE: So we can use one +of those alternatives? + +PROFESSOR: Can you say +that louder please? + +AUDIENCE: So we can use one +of those alternatives? + +PROFESSOR: These aren't +implementations. + +They're descriptions of +how ray tracing works. + +You should not change your +code to work in this way. + +These are just to help with +clarification if you want to + +learn more about what's being +done in the code. + +Go ahead. + +AUDIENCE: [INAUDIBLE PHRASE] + +what specifically are we allowed +to change for the + +[INAUDIBLE]? + +PROFESSOR: So what +specifically are + +you allowed to change? + +AUDIENCE: Yeah. + +Which ever one's smaller +[INAUDIBLE PHRASE]. + +PROFESSOR: Anything not +prohibited by these rules, + +which are paraphrased from the +project handout, you can do. + +So basically, as long as you're +still performing the + +same essential calculations, +you're fine. + +Hmm? + +GUEST SPEAKER: I would say the +criteria for correctness is to + +look at the images, and +say that they look + +more or less the same. + +They don't give you a pixel +by pixel accurate. + +This isn't a graphics class +that actually does that. + +This should be almost +like a [INAUDIBLE]. + +PROFESSOR: They should visually +look the same. + +If you find some approximation +that looks almost the same and + +runs 100 times faster, +go for it. + +You can't say, for example, +simplify your ray tracer + +though by saying, OK, we're +only going to be able to + +render these two scenes, +but we'll be able to + +do it really fast. \ No newline at end of file diff --git a/cMaryERGZmY.txt b/cMaryERGZmY.txt new file mode 100644 index 0000000000000000000000000000000000000000..db814b1e5dcec7e6491ef9304f958bbe991d5314 --- /dev/null +++ b/cMaryERGZmY.txt @@ -0,0 +1,1079 @@ +The following content is +provided under a Creative + +Commons License. + +Your support will help MIT Open +Courseware continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT Open Courseware at + +ocw.mit.edu. + +OK we're going to do problem 3 +now on exam 2 from the fall + +2009 class. + +Let's talk a little bit about +what the problem concept is. + +This is doping. + +We're going to talk all about +doping semiconductors. + +As we say chemistry, where +doping is legal. + +So we're going to look at the +things we should probably know + +before attempting the problem. + +You want to review your +doping principles. + +How does doping works. + +What are the mechanisms, your +conduction mechanisms? + +So why does the material +conduct? + +What's actually happening? + +Your donor and acceptor levels, + +understanding which is which. + +And your p versus your +n type doping. + +What those mean. + +So look at those real quick +and do the problem. + +Let's go on. + +I wrote down the information +that we're + +given in the problem. + +The problem part a asks us to +find specifically how much + +gallium is needed to reach a +certain carrier concentration + +in our germanium. + +So we're doping gallium +into germanium. + +We're given the fact that the +germanium band gap is 0.7 + +electron volts. + +We know that we want to +achieve a carrier + +concentration of 3.091 times +10 to the 17 carriers per + +centimeter cubed. + +And we're working with 1 +kilogram of germanium. + +So we need to achieve this +density or this carrier + +concentration in one kilogram +of germanium. + +I've drawn schematically-- now +remember the germanium + +crystals are in 3-D so the bonds +don't actually look 90 + +degrees like this-- but I've +drawn just for visual a + +germanium crystal. + +So this is what a +pure germanium + +crystal would look like. + +I'm going to draw the band +structure for the pure + +germanium crystal now as well. + +When you see a problem that +gives you your band gap and it + +tells you this is about doping, +the first thing you + +want to do is just +get some points. + +Put some stuff on the paper +that you know to be true. + +So let's draw the +band structure. + +I'm going to abbreviate +conduction band with cb and + +valence band with vb. + +So here's my conduction band, +here's my valence band. + +We're told that this is here. + +We know our band gap +energy is 0.7. + +OK and I'm going to use +this blue to show + +where electrons are. + +This just shows that there's +electrons in the valence band + +going all the way up to the +top of the valence band. + +That's how the valence band +level is defined. + +So this easy points. + +You've got this on the paper, +we're good to go. + +Now what we're talking +about is putting + +gallium into germanium. + +So let's do that. + +Let's take out this germanium. + +And let's put a gallium +in its place. + +We'll put it in red. + +OK so this isn't exactly +correct yet. + +Germanium makes 4 bonds. + +If you look at the periodic +table you'll see that it has 4 + +valence electrons +to make bonds. + +But gallium does not. + +Gallium only has 3. + +So what that means is that one +of these bonds can't exist + +like this anymore. + +So the way I like to draw it, +is we still have an electron + +from this germanium but we're +missing one for this gallium. + +And this is what a hole +basically is, + +schematically, in doping. + +So we're going to write +this as hole plus. + +And the reason it has a positive +charge associated + +with it is because in our +neutral crystal with no + +charges you having an +electron there. + +And you've just removed an +electron and now it's + +positively charged. + +You have a positive charge in +this region of the crystal, + +which corresponds to +a missing electron. + +So we just created a hole. + +We have a hole here and +then it's going to + +result in what we call-- + +I'll use red again-- + +an acceptor level. + +And remember this band diagram +is an analogy for, these are + +the energy levels where your +electrons can exist. So we + +have these energy levels and the +valence band and we've got + +energy levels up in the +conduction band. + +What's just happened is that +this dopant has created an + +energy level slightly above +the valence band. + +If you have a donor level from +a different type of doping-- + +which we'll talk about +in a second-- + +you'll create a level right +below the conduction bands. + +So we've got some points. + +We understand the system now. + +It's just going well. + +So let's try to do a. + +So a, as I said before is asking +us to figure out the + +actual amount. + +We're looking for grams. This +is what we're looking for. + +Grams of gallium. + +That we need to put into a +kilogram of germanium to + +create a carrier concentration +of 3.091 times 10 to the 17 + +carriers per centimeter cubed. + +Not too bad of a problem. + +This is basically just +stoichiometry. + +Dimensional analysis. + +Here's how I did it and many +people did it this way. + +I start off. + +times 10 to the 17. + +And I always keep my units. + +That's really important. + +So we're going to write +this as carriers + +per centimeter cubed. + +Now we're also told in the +problem, we have the + +additional information that the +temperature is high enough + +that all of the sites +are ionized. + +What that means is that-- +let's take a look + +at this band diagram-- + +we have electrons existing +in the valence + +bands up to that level. + +We've doped and now the +temperature's high enough that + +these electrons can be excited, +one of them in this + +case can be excited to this +level here, the acceptor + +level, creating, of course, a +hole in the valence band. + +That's what it means that +it can be fully ionized. + +So basically every gallium +atom that we put into our + +material creates a carrier. + +And why do I say that? + +Because conduction is either, +the movement of electrons in + +the conduction bands, which +we don't have. Or it's the + +movement of holes in the valence +band, which we now + +have. So we're talking +about conduction. + +And so for every gallium atom +we put in, we're creating an + +acceptor level, which takes an +electron up, which creates + +some conduction in +the valence band. + +Now if we add lots and lots +of gallium atoms-- + +there's a lot more gallium +atoms in here-- + +we're going to actually see +many more of these levels + +showing up. + +And you're going to get what +almost looks like very thin + +bands, an acceptor band or +acceptor level there. + +So we start off like this. + +And I went into that's +digression because now I'm + +just going to say that +for every atom we + +put in we get 1 carrier. + +And then we're going to say-- + +I want to be sure I +get this right-- + +we have 6.02 times 10 to +the 23 atoms per mole. + +That's right. + +And then we have 1 mole. + +And notice how I'm being very +careful about the dimensional + +analysis here. + +Because if you put something +in the wrong top or bottom + +you're off by 46 powers. + +So don't make that mistake. + +We saw that a lot on the exam. + +So we're good here. + +Let's do our dimensional +analysis. + +We start off, we're looking +for this particular + +concentration carriers +per centimeter cubed. + +We have 1 atom creates +1 carrier. + +1 mole has this many atoms. +And one mole of-- we're + +talking about in this case-- + +gallium. + +I'll put Gallium here +to be clear. + +1 mole of gallium has +this much mass. + +And you're left with something +like this. + +You're left with 3.58 times 10 +to the negative 5 grams per + +centimeter. + +Grams gallium per centimeter +cubed. + +So we're looking good. + +We're pretty close to the answer +but we don't actually + +have the answer yet. + +Remember we're looking for +total grams of gallium. + +Not how many grams per +centimeter cubed. + +That's pretty easy because +we're told the we have 1 + +kilogram of germanium and we +know the density of germanium + +from our periodic table. + +So looking at our periodic +table we can look up + +germanium's density and we can +then back out how many + +centimeters cubed of germanium +we have. We'll + +do that right here. + +So 1 kilogram of germanium +is 1,000 grams, times-- + +we have the density, which is +going to be times 1 over the + +density, rather-- + +grams per centimeter cubed. + +And that's going to give us +187 centimeters cubed. + +And now we're good. + +Because we know here we have +3.58 times 10 to the negative + +5 grams of gallium per +centimeter cubed of germanium. + +We have this many centimeters +cubed of germanium. + +Multiply them together and you +get the answer, which is 6.69 + +times 10 to the negative +3 grams of gallium. + +So that's part a. + +Just dimensional analysis +and stoichiometry. + +But I stress, be careful about +the way these things are. + +Even I pause to make sure +they're correct because if you + +get this wrong, the whole +problem's wrong. + +You're off orders of 46. + +You're off by orders of 1,000 +here, so just be careful. + +Part b. + +We've actually already answered +when we drew it up, + +we threw down the +things we knew. + +We knew that we were +creating a hole. + +And a hole corresponds +to p type doping. + +How do I remember p and n? + +It's easy. p means positive. + +We've created a hole, which +has a positive charge. + +n, I think of as negative. + +So if you had put something else +in there like arsenic, + +arsenic would've had an extra +electron compared to + +germanium, which means you +have a negative charge. + +So n negative. + +So we have p type doping. + +We're done with part b. + +Easy. + +Part c. + +I'm just going to erase some of +this stuff here and we're + +going to draw a couple more +of these band diagrams. So + +basically what we're asked to do +now is to think about, what + +does this band diagram look +like at different + +temperatures? + +Because it actually looks +slightly different. + +I've drawn it here +schematically. + +But let's actually think +about what it looks + +like in real life. + +So let's do 2 more of these. + +And we'll use that one +as well for part c. + +OK so I'm drawing my +conduction bands. + +These are my conduction bands. + +These are my valence bands. + +I have the same band gap +for all of them. + +So you know band gap here, +here's the band gap. + +It's always worth +putting down. + +If you know it's true, +put it down. + +And we know that +in both cases-- + +let me just get rid of this +thing here; we're going to + +start from the beginning; +put our electron back-- + +we've created all these +acceptor levels. + +Because we've doped with more +than one gallium atom. + +We have many, many, 10 to the 17 +gallium atoms. Which sounds + +like a lot, but in a mole we +have 10 to the 23 spots in a + +mole of material. + +So it's 6 orders of +magnitude less. + +So we have these systems and +we're asked to do them at-- + +I'm going to keep going +back and forth-- + +300 k, 4.2 k and 1200 k. + +That's Kelvin. + +Let's go with the extremes +first. And we'll do the middle + +one, 300 k, once we have an +idea of what's happening. + +So basically, in the very +beginning when we to dope in a + +material, time t equals 0 and no +electrons have had a chance + +to move around. + +You have all your electrons in +the valence band, you have + +these open holes in your +acceptor levels. + +And the reason that electrons +would move between levels is + +if they have some energy +associated with them. + +Now why would something have +energy in a crystal? + +Well that's because of +thermal vibrations. + +It's a thermal energy they have. +So it's completely based + +on the temperature at which +the crystal exists. + +So at a very low temperature-- + +let me write that up +there for you, this + +is our basic equation-- + +at a very low temperature we +have a very low thermal + +energy. kBT: this is the +Boltzman's Constant. + +At a very high temperature, we +have a very high thermal + +energy, which means that these +electrons have the ability to + +move between levels +more easily. + +So here's our very +low temperature. + +At a very low temperature +we can actually + +calculate the energy. + +We'll find that the energy +here is about-- + +just so you have a scale-- + +it's about 0.00036 +electron volts. + +Now you say to yourself, wow +that is a lot less than 0.7 + +electron volts, which is +the energy of this gap. + +So there's no way these +electrons here can even make + +it up to this acceptor level. + +That's not exactly true. + +This is best thought of as an +average thermal energy that an + +electron will have. It's +based off of a + +distribution, if you will. + +So most electrons will have +around this energy. + +But some will have a little bit +more and some will have a + +little bit less. + +And very, very, very few at the +tail of that distribution + +will have enough energy to +actually make it up to one of + +these levels. + +So the way to do this problem, +to be actually fully correct, + +is to say that and explain it. + +I actually, when I did this +problem on the answer key, I + +have an electron, one electron +going up into one of these + +spots and the rest +are all empty. + +I denote that with a little +bit of blue here. + +But everything else is empty. + +We've got a hole here. + +So there is a finite, very +small, amount of conduction. + +But it's extremely small. + +And it's extremely unlikely to +have electrons moving around + +but probabilistically +it will happen. + +That's 4.2 Kelvin. + +Very, very low. + +Let's go to very, very high. + +Starting at the beginning again, +we know all of our + +electrons are in the +valence bands. + +At 1,200 we have an energy +of about 0.1 eV. + +Still less than 0.7. + +We have a significantly larger +proportion electrons in that + +distribution, which +are at 0.7. + +So we actually do have electrons +that will move up + +into the spots. + +And even many that'll move +up here as well. + +Because they can overcome +this 0.7 eV. + +So we've got some electrons, +they're going to move here, + +they're going to fill +up most of these. + +Because this delta here, the +difference between our + +acceptor level and our valence +band, is actually quite small. + +It's extremely small. + +That's another reason why +we have an electron + +moving up at 4.2. + +I should have mentioned that. + +This is very small. + +This gets pretty much +completely filled. + +And I'll denote that with +a blue line here. + +And we have some electrons, +even going up into here. + +What that means, that that has +to correspond to electrons + +being depleted out of +the valence band. + +This is the way you would +draw this picture. + +So we lose these electrons +from the valence band. + +Some jump up to the acceptor +levels and the rest will go up + +to the conduction band. + +So this is 1,200. + +We have more than enough energy +to reach this acceptor + +level and we have +probabilistically some + +electrons will make it up +to the conduction bands. + +That's the best way +to think about it. + +Now let's go back to our +middle temperature. + +I think the best way to do +this one is to just go + +somewhere in the middle. + +That's the safest play, right? + +So we're at a temperature +which corresponds + +to about 0.025 eV. + +Now that is obviously smaller +than the gap. + +Probabilistically we'll still +get some electrons in the gap. + +Diminishingly small. + +But we'll put one up there. + +OK maybe one goes up there. + +And it's still much bigger than +the delta here between + +the acceptor level and +the valence band top. + +So these electrons will still +pretty easily make their way + +into the acceptor level. + +Now I'll put a little +bit here. + +We're going to lose electrons +very slightly. + +That's how I would have +done that problem. + +It sort of looks like that +on the answer key. + +Now I want to emphasize that, +what is what's the + +importance of this? + +Well when you dope, you're +creating conduction. + +Why is that? + +Because the more we dope, the +more holes we have that can be + +played around with. + +So we have more and more +of these acceptor + +level energy levels. + +And what happens is these +electrons at finite + +temperatures-- + +temperatures above 0 Kelvin-- +will move into those levels. + +And they will cause conduction +in the valence band. + +And you know at high +temperatures, back over here, + +we have electrons moving to the +conduction band, which is + +traditionally what we think of +when we think of conduction, + +electrons moving around. + +So we have in this case +conduction in the conductor + +band as well as in +the valence band. + +So that's this problem. + +This problem was generally +pretty easy; many + +students got it right. + +The learning goals and +objectives we had from this + +problem were, number 1, to +understand doping principles. + +What it means to n +and p type dope. + +Holes versus electrons +and how you get them. + +So if you have germanium or +silicon, those are very common + +examples and you dope +things into them. + +So gallium or arsenic or +aluminum, for example. + +We talked about conduction +mechanisms-- + +just like here-- + +and we also talked about the +donor and acceptor levels. + +So the donor levels are just +slightly below the conduction + +band and are full +of electrons. + +And the acceptor levels are +just slightly above the + +valence band and initially +holes. + +So that's probablem 3 and I hope +you had good luck at It. \ No newline at end of file diff --git a/cU8uBaOfIuc.txt b/cU8uBaOfIuc.txt new file mode 100644 index 0000000000000000000000000000000000000000..283f005e4a34aff2a8aa817ea00d3edac14c2646 --- /dev/null +++ b/cU8uBaOfIuc.txt @@ -0,0 +1,1171 @@ +align:start position:0% + +hi today we're going to do a problem + + align:start position:0% +hi today we're going to do a problem + + + align:start position:0% +hi today we're going to do a problem +about similar matrices the problem is + + align:start position:0% +about similar matrices the problem is + + + align:start position:0% +about similar matrices the problem is +right here so the question asks which of + + align:start position:0% +right here so the question asks which of + + + align:start position:0% +right here so the question asks which of +the following statements are true and it + + align:start position:0% +the following statements are true and it + + + align:start position:0% +the following statements are true and it +asks you to explain why the first + + align:start position:0% +asks you to explain why the first + + + align:start position:0% +asks you to explain why the first +statement is if a and b are similar + + align:start position:0% +statement is if a and b are similar + + + align:start position:0% +statement is if a and b are similar +matrices then 2 a cub + a - 3 * the + + align:start position:0% +matrices then 2 a cub + a - 3 * the + + + align:start position:0% +matrices then 2 a cub + a - 3 * the +identity is similar to 2 * B Cubed + b - + + align:start position:0% +identity is similar to 2 * B Cubed + b - + + + align:start position:0% +identity is similar to 2 * B Cubed + b - +3 * the identity the second question + + align:start position:0% +3 * the identity the second question + + + align:start position:0% +3 * the identity the second question +asks if a and b are 3x3 matrices with + + align:start position:0% +asks if a and b are 3x3 matrices with + + + align:start position:0% +asks if a and b are 3x3 matrices with +igen values 1 0 and negative 1 then + + align:start position:0% +igen values 1 0 and negative 1 then + + + align:start position:0% +igen values 1 0 and negative 1 then +they're + + align:start position:0% +they're + + + align:start position:0% +they're +similar and the third part asks you + + align:start position:0% +similar and the third part asks you + + + align:start position:0% +similar and the third part asks you +whether these two J matrices are similar + + align:start position:0% +whether these two J matrices are similar + + + align:start position:0% +whether these two J matrices are similar +okay I'll give you a moment to hit pause + + align:start position:0% +okay I'll give you a moment to hit pause + + + align:start position:0% +okay I'll give you a moment to hit pause +and try it on your own I'll be back in + + align:start position:0% +and try it on your own I'll be back in + + + align:start position:0% +and try it on your own I'll be back in +just a moment and we can do it + + align:start position:0% +just a moment and we can do it + + + align:start position:0% +just a moment and we can do it +together + + align:start position:0% + + + + align:start position:0% + +okay and we're + + align:start position:0% + + + + align:start position:0% + +back let's start with part + + align:start position:0% +back let's start with part + + + align:start position:0% +back let's start with part +A Part + + align:start position:0% +A Part + + + align:start position:0% +A Part +A is + + align:start position:0% + + + + align:start position:0% + +true why well what does it mean for a + + align:start position:0% +true why well what does it mean for a + + + align:start position:0% +true why well what does it mean for a +and b to be similar + + align:start position:0% +and b to be similar + + + align:start position:0% +and b to be similar +right we + + align:start position:0% +right we + + + align:start position:0% +right we +know there's some Matrix + + align:start position:0% +know there's some Matrix + + + align:start position:0% +know there's some Matrix +M such that that's what ST + + align:start position:0% +M such that that's what ST + + + align:start position:0% +M such that that's what ST +means when I multiply M on the left or a + + align:start position:0% +means when I multiply M on the left or a + + + align:start position:0% +means when I multiply M on the left or a +on the left by m and the right by m + + align:start position:0% +on the left by m and the right by m + + + align:start position:0% +on the left by m and the right by m +inverse I get + + align:start position:0% +inverse I get + + + align:start position:0% +inverse I get +B okay so let's take that same Matrix + + align:start position:0% +B okay so let's take that same Matrix + + + align:start position:0% +B okay so let's take that same Matrix +M and multiply it and multiply it on the + + align:start position:0% +M and multiply it and multiply it on the + + + align:start position:0% +M and multiply it and multiply it on the +left and the right of 2 a Cub + a - 3 * + + align:start position:0% +left and the right of 2 a Cub + a - 3 * + + + align:start position:0% +left and the right of 2 a Cub + a - 3 * +the + + align:start position:0% + + + + align:start position:0% + +identity okay what do we get here well + + align:start position:0% +identity okay what do we get here well + + + align:start position:0% +identity okay what do we get here well +the point is what M * a cub * m inverse + + align:start position:0% +the point is what M * a cub * m inverse + + + align:start position:0% +the point is what M * a cub * m inverse +we can just write that as three M + + align:start position:0% + + + + align:start position:0% + +inverses uh similarly we have an m a m + + align:start position:0% +inverses uh similarly we have an m a m + + + align:start position:0% +inverses uh similarly we have an m a m +inverse + + align:start position:0% +inverse + + + align:start position:0% +inverse +and and M time the identity time M + + align:start position:0% +and and M time the identity time M + + + align:start position:0% +and and M time the identity time M +inverse good and so remember that M * a + + align:start position:0% +inverse good and so remember that M * a + + + align:start position:0% +inverse good and so remember that M * a +* m inverse is B so we just get 2 B + + align:start position:0% +* m inverse is B so we just get 2 B + + + align:start position:0% +* m inverse is B so we just get 2 B +Cubed right 3 + + align:start position:0% +Cubed right 3 + + + align:start position:0% +Cubed right 3 +B's plus B minus well M * the identity + + align:start position:0% +B's plus B minus well M * the identity + + + align:start position:0% +B's plus B minus well M * the identity +is just m so we just get the identity + + align:start position:0% +is just m so we just get the identity + + + align:start position:0% +is just m so we just get the identity +back and we have three times the + + align:start position:0% +back and we have three times the + + + align:start position:0% +back and we have three times the +identity good and this is sort of a + + align:start position:0% +identity good and this is sort of a + + + align:start position:0% +identity good and this is sort of a +General remark that if you have matrices + + align:start position:0% +General remark that if you have matrices + + + align:start position:0% +General remark that if you have matrices +A and B that are similar then any pols + + align:start position:0% +A and B that are similar then any pols + + + align:start position:0% +A and B that are similar then any pols +in these matrices A and B will be + + align:start position:0% +in these matrices A and B will be + + + align:start position:0% +in these matrices A and B will be +similar it's uh the exact same + + align:start position:0% +similar it's uh the exact same + + + align:start position:0% +similar it's uh the exact same +justification + + align:start position:0% +justification + + + align:start position:0% +justification +okay now let's go on to Part + + align:start position:0% +okay now let's go on to Part + + + align:start position:0% +okay now let's go on to Part +B okay so now A and B are 3x3 similar + + align:start position:0% +B okay so now A and B are 3x3 similar + + + align:start position:0% +B okay so now A and B are 3x3 similar +matrices with the same igen + + align:start position:0% +matrices with the same igen + + + align:start position:0% +matrices with the same igen +values and their igen values are + + align:start position:0% +values and their igen values are + + + align:start position:0% +values and their igen values are +distinct so it turns out that B is true + + align:start position:0% +distinct so it turns out that B is true + + + align:start position:0% +distinct so it turns out that B is true +as + + align:start position:0% + + + + align:start position:0% + +well okay and well why is that well a + + align:start position:0% +well okay and well why is that well a + + + align:start position:0% +well okay and well why is that well a +matrix with distinct igen values is + + align:start position:0% +matrix with distinct igen values is + + + align:start position:0% +matrix with distinct igen values is +diagonalizable so we can + + align:start position:0% +diagonalizable so we can + + + align:start position:0% +diagonalizable so we can +write + + align:start position:0% +write + + + align:start position:0% +write +a as s Lambda s + + align:start position:0% +a as s Lambda s + + + align:start position:0% +a as s Lambda s +inverse where um Lambda is just this + + align:start position:0% +inverse where um Lambda is just this + + + align:start position:0% +inverse where um Lambda is just this +igen value + + align:start position:0% +igen value + + + align:start position:0% +igen value +Matrix okay we can also write + + align:start position:0% +Matrix okay we can also write + + + align:start position:0% +Matrix okay we can also write +b as T Lambda T + + align:start position:0% +b as T Lambda T + + + align:start position:0% +b as T Lambda T +inverse where Lambda is the same in both + + align:start position:0% +inverse where Lambda is the same in both + + + align:start position:0% +inverse where Lambda is the same in both +cases because they have the same igen + + align:start position:0% +cases because they have the same igen + + + align:start position:0% +cases because they have the same igen +values good now I'll let you you uh so + + align:start position:0% +values good now I'll let you you uh so + + + align:start position:0% +values good now I'll let you you uh so +before we check it let's just say the + + align:start position:0% +before we check it let's just say the + + + align:start position:0% +before we check it let's just say the +point the point is if two matrices are + + align:start position:0% +point the point is if two matrices are + + + align:start position:0% +point the point is if two matrices are +similar to the same Matrix then they're + + align:start position:0% +similar to the same Matrix then they're + + + align:start position:0% +similar to the same Matrix then they're +similar to each other uh similarity is a + + align:start position:0% +similar to each other uh similarity is a + + + align:start position:0% +similar to each other uh similarity is a +transitive relation and I'll just let + + align:start position:0% +transitive relation and I'll just let + + + align:start position:0% +transitive relation and I'll just let +you you a check that you can + + align:start position:0% +you you a check that you can + + + align:start position:0% +you you a check that you can +um take TS + + align:start position:0% +um take TS + + + align:start position:0% +um take TS +inverse a Time TS inverse inverse and + + align:start position:0% +inverse a Time TS inverse inverse and + + + align:start position:0% +inverse a Time TS inverse inverse and +you'll get + + align:start position:0% +you'll get + + + align:start position:0% +you'll get +B + + align:start position:0% +B + + + align:start position:0% +B +good this this follows directly from + + align:start position:0% +good this this follows directly from + + + align:start position:0% +good this this follows directly from +just these two + + align:start position:0% +just these two + + + align:start position:0% +just these two +relations good now let's take on part + + align:start position:0% +relations good now let's take on part + + + align:start position:0% +relations good now let's take on part +C so part C is + + align:start position:0% +C so part C is + + + align:start position:0% +C so part C is +false + + align:start position:0% +false + + + align:start position:0% +false +let's come back over here and look at + + align:start position:0% +let's come back over here and look at + + + align:start position:0% +let's come back over here and look at +these two matrices J1 and J2 well the + + align:start position:0% +these two matrices J1 and J2 well the + + + align:start position:0% +these two matrices J1 and J2 well the +first thing you should see is that these + + align:start position:0% +first thing you should see is that these + + + align:start position:0% +first thing you should see is that these +two are Jordan blocks and they're + + align:start position:0% +two are Jordan blocks and they're + + + align:start position:0% +two are Jordan blocks and they're +different or they're sorry not Jordan + + align:start position:0% +different or they're sorry not Jordan + + + align:start position:0% +different or they're sorry not Jordan +blocks they're uh matricies in Jordan + + align:start position:0% +blocks they're uh matricies in Jordan + + + align:start position:0% +blocks they're uh matricies in Jordan +normal form and they're different + + align:start position:0% +normal form and they're different + + + align:start position:0% +normal form and they're different +matrices in Jordan normal form so they + + align:start position:0% +matrices in Jordan normal form so they + + + align:start position:0% +matrices in Jordan normal form so they +will not be similar but but let's + + align:start position:0% +will not be similar but but let's + + + align:start position:0% +will not be similar but but let's +actually see why okay so let's look + + align:start position:0% +actually see why okay so let's look + + + align:start position:0% +actually see why okay so let's look +at remember one of the things that + + align:start position:0% +at remember one of the things that + + + align:start position:0% +at remember one of the things that +similarity preserves are igen vectors + + align:start position:0% +similarity preserves are igen vectors + + + align:start position:0% +similarity preserves are igen vectors +and igen values so let's look at um the + + align:start position:0% +and igen values so let's look at um the + + + align:start position:0% +and igen values so let's look at um the +IG space with IG value minus one with + + align:start position:0% +IG space with IG value minus one with + + + align:start position:0% +IG space with IG value minus one with +these two + + align:start position:0% +these two + + + align:start position:0% +these two +matrices so um + + align:start position:0% +matrices so um + + + align:start position:0% +matrices so um +J1 plus the + + align:start position:0% +J1 plus the + + + align:start position:0% +J1 plus the +identity let's let's look at the null + + align:start position:0% +identity let's let's look at the null + + + align:start position:0% +identity let's let's look at the null +space of this Matrix so this is um + + align:start position:0% +space of this Matrix so this is um + + + align:start position:0% +space of this Matrix so this is um +just + + align:start position:0% +just + + + align:start position:0% +just +zero it's just Zero's on the diagonal + + align:start position:0% +zero it's just Zero's on the diagonal + + + align:start position:0% +zero it's just Zero's on the diagonal +and ones right above above the diagonal + + align:start position:0% +and ones right above above the diagonal + + + align:start position:0% +and ones right above above the diagonal +and + + align:start position:0% +and + + + align:start position:0% +and +J2 plus the + + align:start position:0% +J2 plus the + + + align:start position:0% +J2 plus the +identity well this is just 0 1 0 + + align:start position:0% +identity well this is just 0 1 0 + + + align:start position:0% +identity well this is just 0 1 0 +0 good so the point is that the null + + align:start position:0% +0 good so the point is that the null + + + align:start position:0% +0 good so the point is that the null +space of this um of this Matrix is just + + align:start position:0% +space of this um of this Matrix is just + + + align:start position:0% +space of this um of this Matrix is just +onedimensional so there's only one + + align:start position:0% +onedimensional so there's only one + + + align:start position:0% +onedimensional so there's only one +independent igen Vector of J1 with igen + + align:start position:0% +independent igen Vector of J1 with igen + + + align:start position:0% +independent igen Vector of J1 with igen +value minus one whereas the null space + + align:start position:0% +value minus one whereas the null space + + + align:start position:0% +value minus one whereas the null space +of this Matrix is + + align:start position:0% +of this Matrix is + + + align:start position:0% +of this Matrix is +two-dimensional um + + align:start position:0% +two-dimensional um + + + align:start position:0% +two-dimensional um +the um there are two independent igen + + align:start position:0% +the um there are two independent igen + + + align:start position:0% +the um there are two independent igen +vectors with igen value minus one so the + + align:start position:0% +vectors with igen value minus one so the + + + align:start position:0% +vectors with igen value minus one so the +dimension of the null space of J1 plus + + align:start position:0% +dimension of the null space of J1 plus + + + align:start position:0% +dimension of the null space of J1 plus +the identity this is uh one and this is + + align:start position:0% +the identity this is uh one and this is + + + align:start position:0% +the identity this is uh one and this is +two so they cannot possibly be similar + + align:start position:0% + + + + align:start position:0% + +good good so that completes the problem + + align:start position:0% +good good so that completes the problem + + + align:start position:0% +good good so that completes the problem +it's a nice exercise to do this more + + align:start position:0% +it's a nice exercise to do this more + + + align:start position:0% +it's a nice exercise to do this more +generally and you can use these + + align:start position:0% +generally and you can use these + + + align:start position:0% +generally and you can use these +techniques not just looking at the um + + align:start position:0% +techniques not just looking at the um + + + align:start position:0% +techniques not just looking at the um +the number of independent igen vectors + + align:start position:0% +the number of independent igen vectors + + + align:start position:0% +the number of independent igen vectors +and the null space of your J Matrix uh + + align:start position:0% +and the null space of your J Matrix uh + + + align:start position:0% +and the null space of your J Matrix uh +your J minus Lambda I Matrix but also + + align:start position:0% +your J minus Lambda I Matrix but also + + + align:start position:0% +your J minus Lambda I Matrix but also +powers of J minus Lambda I and their + + align:start position:0% +powers of J minus Lambda I and their + + + align:start position:0% +powers of J minus Lambda I and their +null spaces you can use this to show + + align:start position:0% +null spaces you can use this to show + + + align:start position:0% +null spaces you can use this to show +that any two uh matrices in Jordan + + align:start position:0% +that any two uh matrices in Jordan + + + align:start position:0% +that any two uh matrices in Jordan +normal form that are different are not + + align:start position:0% +normal form that are different are not + + + align:start position:0% +normal form that are different are not +sim similar the same method works and + + align:start position:0% +sim similar the same method works and + + + align:start position:0% +sim similar the same method works and +that's a nice exercise if you want to go + + align:start position:0% +that's a nice exercise if you want to go + + + align:start position:0% +that's a nice exercise if you want to go +a little further with similar matrices + + align:start position:0% +a little further with similar matrices + + + align:start position:0% +a little further with similar matrices +anyway let's let's just recap the + + align:start position:0% +anyway let's let's just recap the + + + align:start position:0% +anyway let's let's just recap the +properties we we saw here we saw that if + + align:start position:0% +properties we we saw here we saw that if + + + align:start position:0% +properties we we saw here we saw that if +we had two similar matrices then any + + align:start position:0% +we had two similar matrices then any + + + align:start position:0% +we had two similar matrices then any +pols in those matrices were similar and + + align:start position:0% +pols in those matrices were similar and + + + align:start position:0% +pols in those matrices were similar and +uh we saw that if we have two matrices + + align:start position:0% +uh we saw that if we have two matrices + + + align:start position:0% +uh we saw that if we have two matrices +that have the same distinct igen values + + align:start position:0% +that have the same distinct igen values + + + align:start position:0% +that have the same distinct igen values +then they're Sim then they're similar + + align:start position:0% +then they're Sim then they're similar + + + align:start position:0% +then they're Sim then they're similar +and we saw that um in a special case we + + align:start position:0% +and we saw that um in a special case we + + + align:start position:0% +and we saw that um in a special case we +saw that two matrices in Jordan normal + + align:start position:0% +saw that two matrices in Jordan normal + + + align:start position:0% +saw that two matrices in Jordan normal +form that are different are not similar + + align:start position:0% +form that are different are not similar + + + align:start position:0% +form that are different are not similar +thanks \ No newline at end of file diff --git a/dXtEEME3ue8.txt b/dXtEEME3ue8.txt new file mode 100644 index 0000000000000000000000000000000000000000..022fb18fd8964f4ce848d673ec8530487f3a77cf --- /dev/null +++ b/dXtEEME3ue8.txt @@ -0,0 +1,9347 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu the weekend is over time to + + align:start position:0% +ocw.mit.edu the weekend is over time to + + + align:start position:0% +ocw.mit.edu the weekend is over time to +get back to business so couple of + + align:start position:0% +get back to business so couple of + + + align:start position:0% +get back to business so couple of +announcements uh tomorrow we'll have + + align:start position:0% +announcements uh tomorrow we'll have + + + align:start position:0% +announcements uh tomorrow we'll have +quiz four based on homework for um I'll + + align:start position:0% +quiz four based on homework for um I'll + + + align:start position:0% +quiz four based on homework for um I'll +be available from 2:15 to 3:15 under + + align:start position:0% +be available from 2:15 to 3:15 under + + + align:start position:0% +be available from 2:15 to 3:15 under +normal office hours if you can't get + + align:start position:0% +normal office hours if you can't get + + + align:start position:0% +normal office hours if you can't get +into to see me at that time then just + + align:start position:0% +into to see me at that time then just + + + align:start position:0% +into to see me at that time then just +send a note and we'll arrange to meet at + + align:start position:0% +send a note and we'll arrange to meet at + + + align:start position:0% +send a note and we'll arrange to meet at +some other time and uh there's this + + align:start position:0% +some other time and uh there's this + + + align:start position:0% +some other time and uh there's this +actually uh Lori has made a signup sheet + + align:start position:0% +actually uh Lori has made a signup sheet + + + align:start position:0% +actually uh Lori has made a signup sheet +sort of five minute block so that if you + + align:start position:0% +sort of five minute block so that if you + + + align:start position:0% +sort of five minute block so that if you +do want to come by to look at regrades + + align:start position:0% +do want to come by to look at regrades + + + align:start position:0% +do want to come by to look at regrades +you don't have to be hanging around + + align:start position:0% +you don't have to be hanging around + + + align:start position:0% +you don't have to be hanging around +waiting for a long period of time and if + + align:start position:0% +waiting for a long period of time and if + + + align:start position:0% +waiting for a long period of time and if +you can't get in during that time + + align:start position:0% +you can't get in during that time + + + align:start position:0% +you can't get in during that time +there's no expiry you can get the uh + + align:start position:0% +there's no expiry you can get the uh + + + align:start position:0% +there's no expiry you can get the uh +grade change at some later date + + align:start position:0% +grade change at some later date + + + align:start position:0% +grade change at some later date +and uh we'll make sure we fix things up + + align:start position:0% +and uh we'll make sure we fix things up + + + align:start position:0% +and uh we'll make sure we fix things up +so uh last day we were talking about + + align:start position:0% +so uh last day we were talking about + + + align:start position:0% +so uh last day we were talking about +Cove valent bonding looking at linear + + align:start position:0% +Cove valent bonding looking at linear + + + align:start position:0% +Cove valent bonding looking at linear +combination of atomic orbitals into + + align:start position:0% +combination of atomic orbitals into + + + align:start position:0% +combination of atomic orbitals into +molecular orbitals and um we saw that + + align:start position:0% +molecular orbitals and um we saw that + + + align:start position:0% +molecular orbitals and um we saw that +there's a two types of molecular + + align:start position:0% +there's a two types of molecular + + + align:start position:0% +there's a two types of molecular +orbitals in uh involving S and P block + + align:start position:0% +orbitals in uh involving S and P block + + + align:start position:0% +orbitals in uh involving S and P block +elements that uh are germine to us we're + + align:start position:0% +elements that uh are germine to us we're + + + align:start position:0% +elements that uh are germine to us we're +not going to go into DB Block in any uh + + align:start position:0% +not going to go into DB Block in any uh + + + align:start position:0% +not going to go into DB Block in any uh +detail here at the level of 3091 I think + + align:start position:0% +detail here at the level of 3091 I think + + + align:start position:0% +detail here at the level of 3091 I think +that SNP block teaches you the rudiments + + align:start position:0% +that SNP block teaches you the rudiments + + + align:start position:0% +that SNP block teaches you the rudiments +and to go beyond that really requires + + align:start position:0% +and to go beyond that really requires + + + align:start position:0% +and to go beyond that really requires +some intensive uh quantum mechanics so + + align:start position:0% +some intensive uh quantum mechanics so + + + align:start position:0% +some intensive uh quantum mechanics so +we're going to stay with S&P block we + + align:start position:0% +we're going to stay with S&P block we + + + align:start position:0% +we're going to stay with S&P block we +saw that if we had two Atomic s orbitals + + align:start position:0% +saw that if we had two Atomic s orbitals + + + align:start position:0% +saw that if we had two Atomic s orbitals +when they Blended to form the molecular + + align:start position:0% +when they Blended to form the molecular + + + align:start position:0% +when they Blended to form the molecular +orbital it took on this sort of + + align:start position:0% +orbital it took on this sort of + + + align:start position:0% +orbital it took on this sort of +ellipsoidal shape we called that a sigma + + align:start position:0% +ellipsoidal shape we called that a sigma + + + align:start position:0% +ellipsoidal shape we called that a sigma +orbital and the characteristic of a + + align:start position:0% +orbital and the characteristic of a + + + align:start position:0% +orbital and the characteristic of a +sigma orbital is that you have + + align:start position:0% +sigma orbital is that you have + + + align:start position:0% +sigma orbital is that you have +continuous electron density from one + + align:start position:0% +continuous electron density from one + + + align:start position:0% +continuous electron density from one +nucleus to the other we said no holidays + + align:start position:0% +nucleus to the other we said no holidays + + + align:start position:0% +nucleus to the other we said no holidays +constant nuclear excuse me constant + + align:start position:0% +constant nuclear excuse me constant + + + align:start position:0% +constant nuclear excuse me constant +electronic dens + + align:start position:0% +electronic dens + + + align:start position:0% +electronic dens +we could then uh combine um an S orbital + + align:start position:0% +we could then uh combine um an S orbital + + + align:start position:0% +we could then uh combine um an S orbital +and a p orbital as for example in the + + align:start position:0% +and a p orbital as for example in the + + + align:start position:0% +and a p orbital as for example in the +case of hydrogen fluoride in the case of + + align:start position:0% +case of hydrogen fluoride in the case of + + + align:start position:0% +case of hydrogen fluoride in the case of +S Plus P we'll end up with an orbital + + align:start position:0% +S Plus P we'll end up with an orbital + + + align:start position:0% +S Plus P we'll end up with an orbital +that looks uh something like this and it + + align:start position:0% +that looks uh something like this and it + + + align:start position:0% +that looks uh something like this and it +is also termed an S excuse me a sigma + + align:start position:0% +is also termed an S excuse me a sigma + + + align:start position:0% +is also termed an S excuse me a sigma +orbital because again if you look from + + align:start position:0% +orbital because again if you look from + + + align:start position:0% +orbital because again if you look from +one nucleus to the other there is + + align:start position:0% +one nucleus to the other there is + + + align:start position:0% +one nucleus to the other there is +continuous electron density no holidays + + align:start position:0% +continuous electron density no holidays + + + align:start position:0% +continuous electron density no holidays +this Sigma orbitals are a little bit + + align:start position:0% +this Sigma orbitals are a little bit + + + align:start position:0% +this Sigma orbitals are a little bit +different in shape from that Sigma + + align:start position:0% +different in shape from that Sigma + + + align:start position:0% +different in shape from that Sigma +orbital but they're both sigmas and then + + align:start position:0% +orbital but they're both sigmas and then + + + align:start position:0% +orbital but they're both sigmas and then +we saw what could happen with P orbitals + + align:start position:0% +we saw what could happen with P orbitals + + + align:start position:0% +we saw what could happen with P orbitals +and there's two options here the first + + align:start position:0% +and there's two options here the first + + + align:start position:0% +and there's two options here the first +is shown uh when the two P orbitals meet + + align:start position:0% +is shown uh when the two P orbitals meet + + + align:start position:0% +is shown uh when the two P orbitals meet +axially on end when they meet ax on end + + align:start position:0% +axially on end when they meet ax on end + + + align:start position:0% +axially on end when they meet ax on end +these two lobes smear to give us the + + align:start position:0% +these two lobes smear to give us the + + + align:start position:0% +these two lobes smear to give us the +lobe shown in this cartoon again + + align:start position:0% +lobe shown in this cartoon again + + + align:start position:0% +lobe shown in this cartoon again +continuous electron density from one + + align:start position:0% +continuous electron density from one + + + align:start position:0% +continuous electron density from one +nucleus to the other that fits the + + align:start position:0% +nucleus to the other that fits the + + + align:start position:0% +nucleus to the other that fits the +definition of a sigma orbital and then + + align:start position:0% +definition of a sigma orbital and then + + + align:start position:0% +definition of a sigma orbital and then +something that only the PS can do when + + align:start position:0% +something that only the PS can do when + + + align:start position:0% +something that only the PS can do when +they smear laterally these lobes smear + + align:start position:0% +they smear laterally these lobes smear + + + align:start position:0% +they smear laterally these lobes smear +to give a a mole moleular lobe these + + align:start position:0% +to give a a mole moleular lobe these + + + align:start position:0% +to give a a mole moleular lobe these +lobes smear to give a molecular lobe + + align:start position:0% +lobes smear to give a molecular lobe + + + align:start position:0% +lobes smear to give a molecular lobe +these two loes collectively consist + + align:start position:0% +these two loes collectively consist + + + align:start position:0% +these two loes collectively consist +comprise one molecular orbital and the + + align:start position:0% +comprise one molecular orbital and the + + + align:start position:0% +comprise one molecular orbital and the +characteristic here is in contrast to + + align:start position:0% +characteristic here is in contrast to + + + align:start position:0% +characteristic here is in contrast to +zero uh holidays here you have zero + + align:start position:0% +zero uh holidays here you have zero + + + align:start position:0% +zero uh holidays here you have zero +density we have a noal plane normal to + + align:start position:0% +density we have a noal plane normal to + + + align:start position:0% +density we have a noal plane normal to +the board there is no electron density + + align:start position:0% +the board there is no electron density + + + align:start position:0% +the board there is no electron density +you can go clear line of sight from one + + align:start position:0% +you can go clear line of sight from one + + + align:start position:0% +you can go clear line of sight from one +nucleus to the other with zero electron + + align:start position:0% +nucleus to the other with zero electron + + + align:start position:0% +nucleus to the other with zero electron +density and this called a pi orbital Pi + + align:start position:0% +density and this called a pi orbital Pi + + + align:start position:0% +density and this called a pi orbital Pi +orbital and then we went on we looked at + + align:start position:0% +orbital and then we went on we looked at + + + align:start position:0% +orbital and then we went on we looked at +a couple of uh things like a nitrogen + + align:start position:0% +a couple of uh things like a nitrogen + + + align:start position:0% +a couple of uh things like a nitrogen +oxygen and Florine um but in case of + + align:start position:0% +oxygen and Florine um but in case of + + + align:start position:0% +oxygen and Florine um but in case of +nitrogen and oxygen we saw that in order + + align:start position:0% +nitrogen and oxygen we saw that in order + + + align:start position:0% +nitrogen and oxygen we saw that in order +to get the triple and double bond we + + align:start position:0% +to get the triple and double bond we + + + align:start position:0% +to get the triple and double bond we +needed a mix we need a mix of Sigma + + align:start position:0% +needed a mix we need a mix of Sigma + + + align:start position:0% +needed a mix we need a mix of Sigma +orbital and Pi orbital and that's the + + align:start position:0% +orbital and Pi orbital and that's the + + + align:start position:0% +orbital and Pi orbital and that's the +template if you're going to make a + + align:start position:0% +template if you're going to make a + + + align:start position:0% +template if you're going to make a +single Bond you may be able to get away + + align:start position:0% +single Bond you may be able to get away + + + align:start position:0% +single Bond you may be able to get away +with a a sigma but if you're going to + + align:start position:0% +with a a sigma but if you're going to + + + align:start position:0% +with a a sigma but if you're going to +make a multiple Bond a double bond or a + + align:start position:0% +make a multiple Bond a double bond or a + + + align:start position:0% +make a multiple Bond a double bond or a +triple bond you're going to have to have + + align:start position:0% +triple bond you're going to have to have + + + align:start position:0% +triple bond you're going to have to have +a mix of Sigma and pi and I think that's + + align:start position:0% +a mix of Sigma and pi and I think that's + + + align:start position:0% +a mix of Sigma and pi and I think that's +the way we ended the the lecture last + + align:start position:0% +the way we ended the the lecture last + + + align:start position:0% +the way we ended the the lecture last +day looking at energy level diagram + + align:start position:0% +day looking at energy level diagram + + + align:start position:0% +day looking at energy level diagram +and uh let's see what else do we have + + align:start position:0% +and uh let's see what else do we have + + + align:start position:0% +and uh let's see what else do we have +yeah so we saw this here's the end on + + align:start position:0% +yeah so we saw this here's the end on + + + align:start position:0% +yeah so we saw this here's the end on +end this is a sigma orbital coming from + + align:start position:0% +end this is a sigma orbital coming from + + + align:start position:0% +end this is a sigma orbital coming from +2p uh Atomic orbitals and remember the + + align:start position:0% +2p uh Atomic orbitals and remember the + + + align:start position:0% +2p uh Atomic orbitals and remember the +convention the Z axis is conventionally + + align:start position:0% +convention the Z axis is conventionally + + + align:start position:0% +convention the Z axis is conventionally +the axis along which the the two uh + + align:start position:0% +the axis along which the the two uh + + + align:start position:0% +the axis along which the the two uh +atoms bond and then this is the lateral + + align:start position:0% +atoms bond and then this is the lateral + + + align:start position:0% +atoms bond and then this is the lateral +uh smearing um to give us the pi orbital + + align:start position:0% +uh smearing um to give us the pi orbital + + + align:start position:0% +uh smearing um to give us the pi orbital +and I think I showed you that if you cut + + align:start position:0% +and I think I showed you that if you cut + + + align:start position:0% +and I think I showed you that if you cut +this it it looks this way we went into + + align:start position:0% +this it it looks this way we went into + + + align:start position:0% +this it it looks this way we went into +this and this and oh we just had a great + + align:start position:0% +this and this and oh we just had a great + + + align:start position:0% +this and this and oh we just had a great +time so now what I want to do is is I + + align:start position:0% +time so now what I want to do is is I + + + align:start position:0% +time so now what I want to do is is I +want to show that you can extend this + + align:start position:0% +want to show that you can extend this + + + align:start position:0% +want to show that you can extend this +business of multiple bonds to hybridized + + align:start position:0% +business of multiple bonds to hybridized + + + align:start position:0% +business of multiple bonds to hybridized +systems now I know Professor Binger uh + + align:start position:0% +systems now I know Professor Binger uh + + + align:start position:0% +systems now I know Professor Binger uh +last week talked about um methane and + + align:start position:0% +last week talked about um methane and + + + align:start position:0% +last week talked about um methane and +the way to rationalize methane was to + + align:start position:0% +the way to rationalize methane was to + + + align:start position:0% +the way to rationalize methane was to +mix S and P Atomic orbitals to make a + + align:start position:0% +mix S and P Atomic orbitals to make a + + + align:start position:0% +mix S and P Atomic orbitals to make a +hybridized orbital and the hybridized + + align:start position:0% +hybridized orbital and the hybridized + + + align:start position:0% +hybridized orbital and the hybridized +orbital that uh was constructed was the + + align:start position:0% +orbital that uh was constructed was the + + + align:start position:0% +orbital that uh was constructed was the +sp3 hybrid so in order to get the + + align:start position:0% +sp3 hybrid so in order to get the + + + align:start position:0% +sp3 hybrid so in order to get the +CH4 CH4 was explained + + align:start position:0% + + + + align:start position:0% + +explained in terms of the + + align:start position:0% +explained in terms of the + + + align:start position:0% +explained in terms of the +sp3 hybrid orbital hybrid + + align:start position:0% +sp3 hybrid orbital hybrid + + + align:start position:0% +sp3 hybrid orbital hybrid +orbit as you recall carbon in its + + align:start position:0% +orbit as you recall carbon in its + + + align:start position:0% +orbit as you recall carbon in its +veilance shell is + + align:start position:0% +veilance shell is + + + align:start position:0% +veilance shell is +uh has six six electrons in total but + + align:start position:0% +uh has six six electrons in total but + + + align:start position:0% +uh has six six electrons in total but +four veence electrons and the four + + align:start position:0% +four veence electrons and the four + + + align:start position:0% +four veence electrons and the four +veence electrons are depicted two in the + + align:start position:0% +veence electrons are depicted two in the + + + align:start position:0% +veence electrons are depicted two in the +S orbital and two in the P orbitals and + + align:start position:0% +S orbital and two in the P orbitals and + + + align:start position:0% +S orbital and two in the P orbitals and +clearly that configuration doesn't have + + align:start position:0% +clearly that configuration doesn't have + + + align:start position:0% +clearly that configuration doesn't have +the Capac to form four bonds somehow + + align:start position:0% +the Capac to form four bonds somehow + + + align:start position:0% +the Capac to form four bonds somehow +we've got to um generate four unpaired + + align:start position:0% +we've got to um generate four unpaired + + + align:start position:0% +we've got to um generate four unpaired +electrons and the sp3 was uh shown to + + align:start position:0% +electrons and the sp3 was uh shown to + + + align:start position:0% +electrons and the sp3 was uh shown to +take one of the S orbitals this is not a + + align:start position:0% +take one of the S orbitals this is not a + + + align:start position:0% +take one of the S orbitals this is not a +1 s it's let's say it's One S orbital + + align:start position:0% +1 s it's let's say it's One S orbital + + + align:start position:0% +1 s it's let's say it's One S orbital +and + + align:start position:0% +and + + + align:start position:0% +and +three p orbitals hence we get the term + + align:start position:0% +three p orbitals hence we get the term + + + align:start position:0% +three p orbitals hence we get the term +sp3 and these are equivalent and so now + + align:start position:0% +sp3 and these are equivalent and so now + + + align:start position:0% +sp3 and these are equivalent and so now +by the hund rule I've got four unpaired + + align:start position:0% +by the hund rule I've got four unpaired + + + align:start position:0% +by the hund rule I've got four unpaired +electrons ready to bond and since + + align:start position:0% +electrons ready to bond and since + + + align:start position:0% +electrons ready to bond and since +there's four four of them and they're + + align:start position:0% +there's four four of them and they're + + + align:start position:0% +there's four four of them and they're +equivalent in energy we dispose them + + align:start position:0% +equivalent in energy we dispose them + + + align:start position:0% +equivalent in energy we dispose them +equivalently in space so if I want to + + align:start position:0% +equivalently in space so if I want to + + + align:start position:0% +equivalently in space so if I want to +take a central point and put four struts + + align:start position:0% +take a central point and put four struts + + + align:start position:0% +take a central point and put four struts +off that Central Point symmetrically + + align:start position:0% +off that Central Point symmetrically + + + align:start position:0% +off that Central Point symmetrically +disposed in space this will form the + + align:start position:0% +disposed in space this will form the + + + align:start position:0% +disposed in space this will form the +struts that go from the center to the + + align:start position:0% +struts that go from the center to the + + + align:start position:0% +struts that go from the center to the +vertices of a tetrahedron and this gives + + align:start position:0% +vertices of a tetrahedron and this gives + + + align:start position:0% +vertices of a tetrahedron and this gives +us the 109 degree Bond angle and there's + + align:start position:0% +us the 109 degree Bond angle and there's + + + align:start position:0% +us the 109 degree Bond angle and there's +a whole host of compounds that are + + align:start position:0% +a whole host of compounds that are + + + align:start position:0% +a whole host of compounds that are +explained by this uh bonding + + align:start position:0% +explained by this uh bonding + + + align:start position:0% +explained by this uh bonding +configuration but now let's look at + + align:start position:0% +configuration but now let's look at + + + align:start position:0% +configuration but now let's look at +another one how about this molecule C2 + + align:start position:0% +another one how about this molecule C2 + + + align:start position:0% +another one how about this molecule C2 +H4 it's known as + + align:start position:0% +H4 it's known as + + + align:start position:0% +H4 it's known as +ethylene ethylene precursor to + + align:start position:0% +ethylene ethylene precursor to + + + align:start position:0% +ethylene ethylene precursor to +polyethylene and uh let's first of all + + align:start position:0% +polyethylene and uh let's first of all + + + align:start position:0% +polyethylene and uh let's first of all +start with the Lewis structure Lewis + + align:start position:0% +start with the Lewis structure Lewis + + + align:start position:0% +start with the Lewis structure Lewis +structure two carbons here and I've got + + align:start position:0% + + + + align:start position:0% + +hydrogens so remember I'm looking for + + align:start position:0% +hydrogens so remember I'm looking for + + + align:start position:0% +hydrogens so remember I'm looking for +octet around the carbon so one two three + + align:start position:0% +octet around the carbon so one two three + + + align:start position:0% +octet around the carbon so one two three +four four electrons around the left + + align:start position:0% +four four electrons around the left + + + align:start position:0% +four four electrons around the left +carbon let's bring in an electron from + + align:start position:0% +carbon let's bring in an electron from + + + align:start position:0% +carbon let's bring in an electron from +the hydrogen that way the hydrogen is + + align:start position:0% +the hydrogen that way the hydrogen is + + + align:start position:0% +the hydrogen that way the hydrogen is +ISO electronic with helium we'll bring + + align:start position:0% +ISO electronic with helium we'll bring + + + align:start position:0% +ISO electronic with helium we'll bring +an electron from the other hydrogen so + + align:start position:0% +an electron from the other hydrogen so + + + align:start position:0% +an electron from the other hydrogen so +this is ISO electronic with the helium + + align:start position:0% +this is ISO electronic with the helium + + + align:start position:0% +this is ISO electronic with the helium +and Al Carbon has 2 four six and if it + + align:start position:0% +and Al Carbon has 2 four six and if it + + + align:start position:0% +and Al Carbon has 2 four six and if it +could pick up two electrons from the + + align:start position:0% +could pick up two electrons from the + + + align:start position:0% +could pick up two electrons from the +right carbon it's in business and the + + align:start position:0% +right carbon it's in business and the + + + align:start position:0% +right carbon it's in business and the +right-handed carbon mimics the + + align:start position:0% +right-handed carbon mimics the + + + align:start position:0% +right-handed carbon mimics the +left-handed carbon and so hydrogen each + + align:start position:0% +left-handed carbon and so hydrogen each + + + align:start position:0% +left-handed carbon and so hydrogen each +donates an electron and now let's check + + align:start position:0% +donates an electron and now let's check + + + align:start position:0% +donates an electron and now let's check +the left carbon has two four 68 so it's + + align:start position:0% +the left carbon has two four 68 so it's + + + align:start position:0% +the left carbon has two four 68 so it's +octet stable the right Carbon 2 468 it's + + align:start position:0% +octet stable the right Carbon 2 468 it's + + + align:start position:0% +octet stable the right Carbon 2 468 it's +octet stable and the way to explain this + + align:start position:0% +octet stable and the way to explain this + + + align:start position:0% +octet stable and the way to explain this +is there's some kind of a double bond + + align:start position:0% +is there's some kind of a double bond + + + align:start position:0% +is there's some kind of a double bond +here so let's draw + + align:start position:0% +here so let's draw + + + align:start position:0% +here so let's draw +the double + + align:start position:0% +the double + + + align:start position:0% +the double +bond and for now we'll put the + + align:start position:0% +bond and for now we'll put the + + + align:start position:0% +bond and for now we'll put the +hydrogen's later on we'll get to the + + align:start position:0% +hydrogen's later on we'll get to the + + + align:start position:0% +hydrogen's later on we'll get to the +point where we see carbon and a strut + + align:start position:0% +point where we see carbon and a strut + + + align:start position:0% +point where we see carbon and a strut +we'll we'll assume that the default + + align:start position:0% +we'll we'll assume that the default + + + align:start position:0% +we'll we'll assume that the default +setting is if I don't write anything at + + align:start position:0% +setting is if I don't write anything at + + + align:start position:0% +setting is if I don't write anything at +the end of the strut assume that it + + align:start position:0% +the end of the strut assume that it + + + align:start position:0% +the end of the strut assume that it +means that there's hydrogen and here's + + align:start position:0% +means that there's hydrogen and here's + + + align:start position:0% +means that there's hydrogen and here's +something to always look for when you + + align:start position:0% +something to always look for when you + + + align:start position:0% +something to always look for when you +see a carbon check to see there's four + + align:start position:0% +see a carbon check to see there's four + + + align:start position:0% +see a carbon check to see there's four +struts off the carbon if there if you + + align:start position:0% +struts off the carbon if there if you + + + align:start position:0% +struts off the carbon if there if you +don't have four struts off the carbon + + align:start position:0% +don't have four struts off the carbon + + + align:start position:0% +don't have four struts off the carbon +start looking there's probably something + + align:start position:0% +start looking there's probably something + + + align:start position:0% +start looking there's probably something +missing + + align:start position:0% +missing + + + align:start position:0% +missing +okay so now how we going to explain this + + align:start position:0% +okay so now how we going to explain this + + + align:start position:0% +okay so now how we going to explain this +we've got a double bond we already know + + align:start position:0% +we've got a double bond we already know + + + align:start position:0% +we've got a double bond we already know +a double bond there's a tip off there + + align:start position:0% +a double bond there's a tip off there + + + align:start position:0% +a double bond there's a tip off there +that means we need a sigma and a pi but + + align:start position:0% +that means we need a sigma and a pi but + + + align:start position:0% +that means we need a sigma and a pi but +with + + align:start position:0% +with + + + align:start position:0% +with +four struts 109 degrees apart there's no + + align:start position:0% +four struts 109 degrees apart there's no + + + align:start position:0% +four struts 109 degrees apart there's no +way you can form a double bond so this + + align:start position:0% +way you can form a double bond so this + + + align:start position:0% +way you can form a double bond so this +isn't going to work the sp3 + + align:start position:0% +isn't going to work the sp3 + + + align:start position:0% +isn't going to work the sp3 +hybridization will not work but maybe + + align:start position:0% +hybridization will not work but maybe + + + align:start position:0% +hybridization will not work but maybe +there's something else we can do if we + + align:start position:0% +there's something else we can do if we + + + align:start position:0% +there's something else we can do if we +want to make a double bond if we want to + + align:start position:0% +want to make a double bond if we want to + + + align:start position:0% +want to make a double bond if we want to +make a double bond what we could do + + align:start position:0% +make a double bond what we could do + + + align:start position:0% +make a double bond what we could do +perhaps is to start with that same box + + align:start position:0% +perhaps is to start with that same box + + + align:start position:0% +perhaps is to start with that same box +structure and what's the Gambit here + + align:start position:0% +structure and what's the Gambit here + + + align:start position:0% +structure and what's the Gambit here +what I want to do is I want to save an + + align:start position:0% +what I want to do is I want to save an + + + align:start position:0% +what I want to do is I want to save an +unhybridized p orbital because the p + + align:start position:0% +unhybridized p orbital because the p + + + align:start position:0% +unhybridized p orbital because the p +orbital is your friend because only with + + align:start position:0% +orbital is your friend because only with + + + align:start position:0% +orbital is your friend because only with +a p orbital do you have the capacity to + + align:start position:0% +a p orbital do you have the capacity to + + + align:start position:0% +a p orbital do you have the capacity to +smear laterally and if you don't have + + align:start position:0% +smear laterally and if you don't have + + + align:start position:0% +smear laterally and if you don't have +the capacity to smear laterally you + + align:start position:0% +the capacity to smear laterally you + + + align:start position:0% +the capacity to smear laterally you +can't make a pi Bond so let's do + + align:start position:0% +can't make a pi Bond so let's do + + + align:start position:0% +can't make a pi Bond so let's do +something here but not burn all the P + + align:start position:0% +something here but not burn all the P + + + align:start position:0% +something here but not burn all the P +orbitals so how about doing this instead + + align:start position:0% +orbitals so how about doing this instead + + + align:start position:0% +orbitals so how about doing this instead +of making four what if I make three and + + align:start position:0% +of making four what if I make three and + + + align:start position:0% +of making four what if I make three and +save one of the P's so this is p it's + + align:start position:0% +save one of the P's so this is p it's + + + align:start position:0% +save one of the P's so this is p it's +unhybridized and these are hybridized so + + align:start position:0% +unhybridized and these are hybridized so + + + align:start position:0% +unhybridized and these are hybridized so +I'm going to take one of an S the only s + + align:start position:0% +I'm going to take one of an S the only s + + + align:start position:0% +I'm going to take one of an S the only s +I've got and I'm only going to take two + + align:start position:0% +I've got and I'm only going to take two + + + align:start position:0% +I've got and I'm only going to take two +of the PS so I'll call this SP2 + + align:start position:0% +of the PS so I'll call this SP2 + + + align:start position:0% +of the PS so I'll call this SP2 +hybridized so I got SP2 and P now let's + + align:start position:0% +hybridized so I got SP2 and P now let's + + + align:start position:0% +hybridized so I got SP2 and P now let's +go through the geometric rules if I have + + align:start position:0% +go through the geometric rules if I have + + + align:start position:0% +go through the geometric rules if I have +three struts symmetrically disposed + + align:start position:0% +three struts symmetrically disposed + + + align:start position:0% +three struts symmetrically disposed +because these are equivalent energies if + + align:start position:0% +because these are equivalent energies if + + + align:start position:0% +because these are equivalent energies if +they're symmetrically disposed in space + + align:start position:0% +they're symmetrically disposed in space + + + align:start position:0% +they're symmetrically disposed in space +they're going to describe first they're + + align:start position:0% +they're going to describe first they're + + + align:start position:0% +they're going to describe first they're +going to lie in a plane and they're + + align:start position:0% +going to lie in a plane and they're + + + align:start position:0% +going to lie in a plane and they're +going to be 120° apart lying in a plane + + align:start position:0% +going to be 120° apart lying in a plane + + + align:start position:0% +going to be 120° apart lying in a plane +that's what this tells + + align:start position:0% +that's what this tells + + + align:start position:0% +that's what this tells +me now I got the fourth one out here and + + align:start position:0% +me now I got the fourth one out here and + + + align:start position:0% +me now I got the fourth one out here and +where's the fourth one going to be it + + align:start position:0% +where's the fourth one going to be it + + + align:start position:0% +where's the fourth one going to be it +can be normal to the plane so I've got + + align:start position:0% +can be normal to the plane so I've got + + + align:start position:0% +can be normal to the plane so I've got +three sp2s lying at a plane and I've got + + align:start position:0% +three sp2s lying at a plane and I've got + + + align:start position:0% +three sp2s lying at a plane and I've got +an unhybridized + + align:start position:0% + + + + align:start position:0% + +P out of the plane hey this is starting + + align:start position:0% +P out of the plane hey this is starting + + + align:start position:0% +P out of the plane hey this is starting +to look good because what I could do is + + align:start position:0% +to look good because what I could do is + + + align:start position:0% +to look good because what I could do is +start bringing these together and maybe + + align:start position:0% +start bringing these together and maybe + + + align:start position:0% +start bringing these together and maybe +make something work so here's here's + + align:start position:0% +make something work so here's here's + + + align:start position:0% +make something work so here's here's +another sketch of what this looks like + + align:start position:0% +another sketch of what this looks like + + + align:start position:0% +another sketch of what this looks like +you can see the three um uh SP2 orbitals + + align:start position:0% +you can see the three um uh SP2 orbitals + + + align:start position:0% +you can see the three um uh SP2 orbitals +lying in a plane and then above and + + align:start position:0% +lying in a plane and then above and + + + align:start position:0% +lying in a plane and then above and +below this rather bloated dumbbell shape + + align:start position:0% +below this rather bloated dumbbell shape + + + align:start position:0% +below this rather bloated dumbbell shape +p orbital and there's the the top view + + align:start position:0% +p orbital and there's the the top view + + + align:start position:0% +p orbital and there's the the top view +all right now here's two of them + + align:start position:0% +all right now here's two of them + + + align:start position:0% +all right now here's two of them +opposing one another right they're + + align:start position:0% +opposing one another right they're + + + align:start position:0% +opposing one another right they're +opposing one another so if these are the + + align:start position:0% +opposing one another so if these are the + + + align:start position:0% +opposing one another so if these are the +carbons I could take these two SP2 + + align:start position:0% +carbons I could take these two SP2 + + + align:start position:0% +carbons I could take these two SP2 +orbitals blend them and I could make a + + align:start position:0% +orbitals blend them and I could make a + + + align:start position:0% +orbitals blend them and I could make a +sigma orbital + + align:start position:0% +sigma orbital + + + align:start position:0% +sigma orbital +and now what I've still got these + + align:start position:0% +and now what I've still got these + + + align:start position:0% +and now what I've still got these +unhybridized P orbitals I can bring + + align:start position:0% +unhybridized P orbitals I can bring + + + align:start position:0% +unhybridized P orbitals I can bring +those in and they'll smear top and + + align:start position:0% +those in and they'll smear top and + + + align:start position:0% +those in and they'll smear top and +bottom and now I've got a pi orbital a + + align:start position:0% +bottom and now I've got a pi orbital a + + + align:start position:0% +bottom and now I've got a pi orbital a +sigma and a pi gives me my double bond + + align:start position:0% +sigma and a pi gives me my double bond + + + align:start position:0% +sigma and a pi gives me my double bond +so by hybridizing SP2 I can give rise to + + align:start position:0% +so by hybridizing SP2 I can give rise to + + + align:start position:0% +so by hybridizing SP2 I can give rise to +the setting that will allow the + + align:start position:0% +the setting that will allow the + + + align:start position:0% +the setting that will allow the +formation of the double + + align:start position:0% +formation of the double + + + align:start position:0% +formation of the double +bond so there it is there's the sigma is + + align:start position:0% +bond so there it is there's the sigma is + + + align:start position:0% +bond so there it is there's the sigma is +in the center here SP2 plus SP2 and then + + align:start position:0% +in the center here SP2 plus SP2 and then + + + align:start position:0% +in the center here SP2 plus SP2 and then +the pies give me the double bond and + + align:start position:0% +the pies give me the double bond and + + + align:start position:0% +the pies give me the double bond and +remember the two lobes together + + align:start position:0% +remember the two lobes together + + + align:start position:0% +remember the two lobes together +constitute a single a single Pi Bond so + + align:start position:0% +constitute a single a single Pi Bond so + + + align:start position:0% +constitute a single a single Pi Bond so +that's great so we're just going to + + align:start position:0% +that's great so we're just going to + + + align:start position:0% +that's great so we're just going to +bring these two in so we'll take SP2 + + align:start position:0% +bring these two in so we'll take SP2 + + + align:start position:0% +bring these two in so we'll take SP2 +plus SP2 + + align:start position:0% +plus SP2 + + + align:start position:0% +plus SP2 +axially axially will give a sigma Bond + + align:start position:0% +axially axially will give a sigma Bond + + + align:start position:0% +axially axially will give a sigma Bond +and then P plus P + + align:start position:0% +and then P plus P + + + align:start position:0% +and then P plus P +laterally laterally will give the pi + + align:start position:0% +laterally laterally will give the pi + + + align:start position:0% +laterally laterally will give the pi +Bond and together this is the double + + align:start position:0% +Bond and together this is the double + + + align:start position:0% +Bond and together this is the double +bond and then the other sp2s are hanging + + align:start position:0% +bond and then the other sp2s are hanging + + + align:start position:0% +bond and then the other sp2s are hanging +off the edge and they each pick up a + + align:start position:0% +off the edge and they each pick up a + + + align:start position:0% +off the edge and they each pick up a +hydrogen so I can draw this molecule + + align:start position:0% +hydrogen so I can draw this molecule + + + align:start position:0% +hydrogen so I can draw this molecule +instead of this format that I've drawn + + align:start position:0% +instead of this format that I've drawn + + + align:start position:0% +instead of this format that I've drawn +here I could really draw it in the + + align:start position:0% +here I could really draw it in the + + + align:start position:0% +here I could really draw it in the +following manner here's carbon carbon + + align:start position:0% +following manner here's carbon carbon + + + align:start position:0% +following manner here's carbon carbon +and then show these as sort of I'm + + align:start position:0% +and then show these as sort of I'm + + + align:start position:0% +and then show these as sort of I'm +trying to give the idea that this is 120 + + align:start position:0% +trying to give the idea that this is 120 + + + align:start position:0% +trying to give the idea that this is 120 +degree angle and I'm going to leave the + + align:start position:0% +degree angle and I'm going to leave the + + + align:start position:0% +degree angle and I'm going to leave the +hydrogens off because you're a + + align:start position:0% +hydrogens off because you're a + + + align:start position:0% +hydrogens off because you're a +sophisticated audience I told you once I + + align:start position:0% +sophisticated audience I told you once I + + + align:start position:0% +sophisticated audience I told you once I +don't have to tell you again so there it + + align:start position:0% +don't have to tell you again so there it + + + align:start position:0% +don't have to tell you again so there it +is there's + + align:start position:0% +is there's + + + align:start position:0% +is there's +ethylene and just for grins and Chuckles + + align:start position:0% +ethylene and just for grins and Chuckles + + + align:start position:0% +ethylene and just for grins and Chuckles +you might want to see how to do one more + + align:start position:0% +you might want to see how to do one more + + + align:start position:0% +you might want to see how to do one more +form of hybridization if you want to do + + align:start position:0% +form of hybridization if you want to do + + + align:start position:0% +form of hybridization if you want to do +a really good job of welding you need a + + align:start position:0% +a really good job of welding you need a + + + align:start position:0% +a really good job of welding you need a +very very energy intensive fuel use + + align:start position:0% +very very energy intensive fuel use + + + align:start position:0% +very very energy intensive fuel use +ethylene excuse me acetylene acetylene + + align:start position:0% +ethylene excuse me acetylene acetylene + + + align:start position:0% +ethylene excuse me acetylene acetylene +acetylene is C2 + + align:start position:0% +acetylene is C2 + + + align:start position:0% +acetylene is C2 +H2 it's known as + + align:start position:0% +H2 it's known as + + + align:start position:0% +H2 it's known as +acetylene and if you go through the + + align:start position:0% +acetylene and if you go through the + + + align:start position:0% +acetylene and if you go through the +Lewis structure you'll conclude that + + align:start position:0% +Lewis structure you'll conclude that + + + align:start position:0% +Lewis structure you'll conclude that +you've got a triple bond there and we + + align:start position:0% +you've got a triple bond there and we + + + align:start position:0% +you've got a triple bond there and we +already saw last day the triple bond in + + align:start position:0% +already saw last day the triple bond in + + + align:start position:0% +already saw last day the triple bond in +nitrogen was almost one megga per mole + + align:start position:0% +nitrogen was almost one megga per mole + + + align:start position:0% +nitrogen was almost one megga per mole +so there a lot of energy in here so you + + align:start position:0% +so there a lot of energy in here so you + + + align:start position:0% +so there a lot of energy in here so you +get got your acetylene torch and your + + align:start position:0% +get got your acetylene torch and your + + + align:start position:0% +get got your acetylene torch and your +oxygen uh oxygen feed you're going to do + + align:start position:0% +oxygen uh oxygen feed you're going to do + + + align:start position:0% +oxygen uh oxygen feed you're going to do +a lot of you I said you need four struts + + align:start position:0% +a lot of you I said you need four struts + + + align:start position:0% +a lot of you I said you need four struts +so what's that there's a hydrogen + + align:start position:0% +so what's that there's a hydrogen + + + align:start position:0% +so what's that there's a hydrogen +hydrogen and triple bond in the center + + align:start position:0% +hydrogen and triple bond in the center + + + align:start position:0% +hydrogen and triple bond in the center +how you going to make a triple bond well + + align:start position:0% +how you going to make a triple bond well + + + align:start position:0% +how you going to make a triple bond well +instead of let's leave two unmixed P + + align:start position:0% +instead of let's leave two unmixed P + + + align:start position:0% +instead of let's leave two unmixed P +orbitals so then just instead of having + + align:start position:0% +orbitals so then just instead of having + + + align:start position:0% +orbitals so then just instead of having +one just up and down I could have one up + + align:start position:0% +one just up and down I could have one up + + + align:start position:0% +one just up and down I could have one up +and down and one in and out of the board + + align:start position:0% +and down and one in and out of the board + + + align:start position:0% +and down and one in and out of the board +I can form a double bond and what's left + + align:start position:0% +I can form a double bond and what's left + + + align:start position:0% +I can form a double bond and what's left +over and you can go through and + + align:start position:0% +over and you can go through and + + + align:start position:0% +over and you can go through and +rationalize that this would require SP + + align:start position:0% +rationalize that this would require SP + + + align:start position:0% +rationalize that this would require SP +hybridization SP plus + + align:start position:0% +hybridization SP plus + + + align:start position:0% +hybridization SP plus +unmixed P orbitals this pce smears with + + align:start position:0% +unmixed P orbitals this pce smears with + + + align:start position:0% +unmixed P orbitals this pce smears with +its neighbor to give a pi this P smears + + align:start position:0% +its neighbor to give a pi this P smears + + + align:start position:0% +its neighbor to give a pi this P smears +with its neighbor to give a pi and this + + align:start position:0% +with its neighbor to give a pi and this + + + align:start position:0% +with its neighbor to give a pi and this +smears actually to give a sigma so one + + align:start position:0% +smears actually to give a sigma so one + + + align:start position:0% +smears actually to give a sigma so one +Sigma plus 2 pi is triple bond that's + + align:start position:0% +Sigma plus 2 pi is triple bond that's + + + align:start position:0% +Sigma plus 2 pi is triple bond that's +the whole story + + align:start position:0% +the whole story + + + align:start position:0% +the whole story +cool so what are we learning here + + align:start position:0% +cool so what are we learning here + + + align:start position:0% +cool so what are we learning here +there's a there's a paradigm here and + + align:start position:0% +there's a there's a paradigm here and + + + align:start position:0% +there's a there's a paradigm here and +that is that coent Bond + + align:start position:0% +that is that coent Bond + + + align:start position:0% +that is that coent Bond +bonds Cove valent bonds a couple of + + align:start position:0% +bonds Cove valent bonds a couple of + + + align:start position:0% +bonds Cove valent bonds a couple of +couple of characteristics that I want + + align:start position:0% +couple of characteristics that I want + + + align:start position:0% +couple of characteristics that I want +you to know first of all they're + + align:start position:0% +you to know first of all they're + + + align:start position:0% +you to know first of all they're +saturated remember I said that ionic + + align:start position:0% +saturated remember I said that ionic + + + align:start position:0% +saturated remember I said that ionic +bonds are unsaturated and you said well + + align:start position:0% +bonds are unsaturated and you said well + + + align:start position:0% +bonds are unsaturated and you said well +okay don't tell me what they aren't tell + + align:start position:0% +okay don't tell me what they aren't tell + + + align:start position:0% +okay don't tell me what they aren't tell +me what they are well they what they + + align:start position:0% +me what they are well they what they + + + align:start position:0% +me what they are well they what they +aren't is in contrast to what these are + + align:start position:0% +aren't is in contrast to what these are + + + align:start position:0% +aren't is in contrast to what these are +so now I can finish the story what does + + align:start position:0% +so now I can finish the story what does + + + align:start position:0% +so now I can finish the story what does +it mean they're saturated once you put + + align:start position:0% +it mean they're saturated once you put + + + align:start position:0% +it mean they're saturated once you put +an electron from the hydrogen and an + + align:start position:0% +an electron from the hydrogen and an + + + align:start position:0% +an electron from the hydrogen and an +electron from the carbon into the + + align:start position:0% +electron from the carbon into the + + + align:start position:0% +electron from the carbon into the +orbital that's the end of the story + + align:start position:0% +orbital that's the end of the story + + + align:start position:0% +orbital that's the end of the story +we've taken care of business here + + align:start position:0% +we've taken care of business here + + + align:start position:0% +we've taken care of business here +there's no revisiting the situation + + align:start position:0% +there's no revisiting the situation + + + align:start position:0% +there's no revisiting the situation +unlike in the case of the ionic + + align:start position:0% +unlike in the case of the ionic + + + align:start position:0% +unlike in the case of the ionic +compounds where the positive attracts a + + align:start position:0% +compounds where the positive attracts a + + + align:start position:0% +compounds where the positive attracts a +negative but it has the capacity to + + align:start position:0% +negative but it has the capacity to + + + align:start position:0% +negative but it has the capacity to +track yet another negative yet another + + align:start position:0% +track yet another negative yet another + + + align:start position:0% +track yet another negative yet another +negative and the field is felt + + align:start position:0% +negative and the field is felt + + + align:start position:0% +negative and the field is felt +attenuating of course but it is palpable + + align:start position:0% +attenuating of course but it is palpable + + + align:start position:0% +attenuating of course but it is palpable +out to Infinity so we say that the ionic + + align:start position:0% +out to Infinity so we say that the ionic + + + align:start position:0% +out to Infinity so we say that the ionic +bonds are unsaturated The Cove valent + + align:start position:0% +bonds are unsaturated The Cove valent + + + align:start position:0% +bonds are unsaturated The Cove valent +bonds are saturated once you got two + + align:start position:0% +bonds are saturated once you got two + + + align:start position:0% +bonds are saturated once you got two +electrons in the orbital move on the + + align:start position:0% +electrons in the orbital move on the + + + align:start position:0% +electrons in the orbital move on the +second thing is what you're seeing here + + align:start position:0% +second thing is what you're seeing here + + + align:start position:0% +second thing is what you're seeing here +is that they are + + align:start position:0% +is that they are + + + align:start position:0% +is that they are +directional they're directional that is + + align:start position:0% +directional they're directional that is + + + align:start position:0% +directional they're directional that is +to say in the case of sp3 they're 109° + + align:start position:0% +to say in the case of sp3 they're 109° + + + align:start position:0% +to say in the case of sp3 they're 109° +apart off the central carbon that's the + + align:start position:0% +apart off the central carbon that's the + + + align:start position:0% +apart off the central carbon that's the +only hook on which you can hang another + + align:start position:0% +only hook on which you can hang another + + + align:start position:0% +only hook on which you can hang another +atom so if you make methane if you make + + align:start position:0% +atom so if you make methane if you make + + + align:start position:0% +atom so if you make methane if you make +carbon tetrachloride if you make Freon + + align:start position:0% +carbon tetrachloride if you make Freon + + + align:start position:0% +carbon tetrachloride if you make Freon +they're all going to + + align:start position:0% +they're all going to + + + align:start position:0% +they're all going to +be the same shaped molecule tetrahedral + + align:start position:0% +be the same shaped molecule tetrahedral + + + align:start position:0% +be the same shaped molecule tetrahedral +because the struts come off the central + + align:start position:0% +because the struts come off the central + + + align:start position:0% +because the struts come off the central +carbon look at this anything that gives + + align:start position:0% +carbon look at this anything that gives + + + align:start position:0% +carbon look at this anything that gives +me SP2 hybridization is going to be what + + align:start position:0% +me SP2 hybridization is going to be what + + + align:start position:0% +me SP2 hybridization is going to be what +what's the shape of that molecule it + + align:start position:0% +what's the shape of that molecule it + + + align:start position:0% +what's the shape of that molecule it +lies in a plane it's + + align:start position:0% +lies in a plane it's + + + align:start position:0% +lies in a plane it's +planer that's what it means to lie in a + + align:start position:0% +planer that's what it means to lie in a + + + align:start position:0% +planer that's what it means to lie in a +plane doesn't it and look at the shape + + align:start position:0% +plane doesn't it and look at the shape + + + align:start position:0% +plane doesn't it and look at the shape +they're always 120 degrees + + align:start position:0% +they're always 120 degrees + + + align:start position:0% +they're always 120 degrees +apart so this means that there's there's + + align:start position:0% +apart so this means that there's there's + + + align:start position:0% +apart so this means that there's there's +a relationship between the + + align:start position:0% +a relationship between the + + + align:start position:0% +a relationship between the +directionality of the bond and the shape + + align:start position:0% +directionality of the bond and the shape + + + align:start position:0% +directionality of the bond and the shape +of the molecule why are the bonds + + align:start position:0% +of the molecule why are the bonds + + + align:start position:0% +of the molecule why are the bonds +directional in first place because of + + align:start position:0% +directional in first place because of + + + align:start position:0% +directional in first place because of +electronic structure this is the theme + + align:start position:0% +electronic structure this is the theme + + + align:start position:0% +electronic structure this is the theme +of 3091 it's going to be echoed over and + + align:start position:0% +of 3091 it's going to be echoed over and + + + align:start position:0% +of 3091 it's going to be echoed over and +over again the electronic structure + + align:start position:0% +over again the electronic structure + + + align:start position:0% +over again the electronic structure +dictates everything it's just dominoes + + align:start position:0% +dictates everything it's just dominoes + + + align:start position:0% +dictates everything it's just dominoes +after is once you understand electronic + + align:start position:0% +after is once you understand electronic + + + align:start position:0% +after is once you understand electronic +structure we did all of this for one + + align:start position:0% +structure we did all of this for one + + + align:start position:0% +structure we did all of this for one +reason to achieve octet stability that's + + align:start position:0% +reason to achieve octet stability that's + + + align:start position:0% +reason to achieve octet stability that's +that's the you know if I peel away the + + align:start position:0% +that's the you know if I peel away the + + + align:start position:0% +that's the you know if I peel away the +board and I look in behind here there's + + align:start position:0% +board and I look in behind here there's + + + align:start position:0% +board and I look in behind here there's +two words octet stability that's the + + align:start position:0% +two words octet stability that's the + + + align:start position:0% +two words octet stability that's the +only thing that's going on here this + + align:start position:0% +only thing that's going on here this + + + align:start position:0% +only thing that's going on here this +system will do anything to achieve octet + + align:start position:0% +system will do anything to achieve octet + + + align:start position:0% +system will do anything to achieve octet +stability it's Savage it just does + + align:start position:0% +stability it's Savage it just does + + + align:start position:0% +stability it's Savage it just does +anything okay all right all right so now + + align:start position:0% +anything okay all right all right so now + + + align:start position:0% +anything okay all right all right so now +what I want to do is I want to make this + + align:start position:0% +what I want to do is I want to make this + + + align:start position:0% +what I want to do is I want to make this +a The Proposal that the electronic + + align:start position:0% +a The Proposal that the electronic + + + align:start position:0% +a The Proposal that the electronic +structure will dictate the shape of all + + align:start position:0% +structure will dictate the shape of all + + + align:start position:0% +structure will dictate the shape of all +molecules so let's put up a grand system + + align:start position:0% +molecules so let's put up a grand system + + + align:start position:0% +molecules so let's put up a grand system +and that's what I want to do I'll put + + align:start position:0% +and that's what I want to do I'll put + + + align:start position:0% +and that's what I want to do I'll put +that up and and work through it oh + + align:start position:0% +that up and and work through it oh + + + align:start position:0% +that up and and work through it oh +here's here's some more cartoons here's + + align:start position:0% +here's here's some more cartoons here's + + + align:start position:0% +here's here's some more cartoons here's +this is taken from another book so you + + align:start position:0% +this is taken from another book so you + + + align:start position:0% +this is taken from another book so you +see the pi Bond here and here's the + + align:start position:0% +see the pi Bond here and here's the + + + align:start position:0% +see the pi Bond here and here's the +sigma bond from the two sp2s and then + + align:start position:0% +sigma bond from the two sp2s and then + + + align:start position:0% +sigma bond from the two sp2s and then +the remaining sp2s this is supposed to + + align:start position:0% +the remaining sp2s this is supposed to + + + align:start position:0% +the remaining sp2s this is supposed to +indicate that this is coming out at you + + align:start position:0% +indicate that this is coming out at you + + + align:start position:0% +indicate that this is coming out at you +but I this does not give me the sense of + + align:start position:0% +but I this does not give me the sense of + + + align:start position:0% +but I this does not give me the sense of +120 degrees this is crummy art but + + align:start position:0% +120 degrees this is crummy art but + + + align:start position:0% +120 degrees this is crummy art but +really this is really crummy I'm taking + + align:start position:0% +really this is really crummy I'm taking + + + align:start position:0% +really this is really crummy I'm taking +that down it's horrible all right so now + + align:start position:0% +that down it's horrible all right so now + + + align:start position:0% +that down it's horrible all right so now +this is what I I put up this is the + + align:start position:0% +this is what I I put up this is the + + + align:start position:0% +this is what I I put up this is the +rules for determining molecular shape + + align:start position:0% +rules for determining molecular shape + + + align:start position:0% +rules for determining molecular shape +and and in our text it's known as + + align:start position:0% +and and in our text it's known as + + + align:start position:0% +and and in our text it's known as +electron domain Theory um if your your + + align:start position:0% +electron domain Theory um if your your + + + align:start position:0% +electron domain Theory um if your your +classmates down the hall in 5111 5112 + + align:start position:0% +classmates down the hall in 5111 5112 + + + align:start position:0% +classmates down the hall in 5111 5112 +instead of electron + + align:start position:0% +instead of electron + + + align:start position:0% +instead of electron +domain it's the same idea but they use a + + align:start position:0% +domain it's the same idea but they use a + + + align:start position:0% +domain it's the same idea but they use a +different term elect instead of electron + + align:start position:0% +different term elect instead of electron + + + align:start position:0% +different term elect instead of electron +domain Theory they call it uh v p which + + align:start position:0% +domain Theory they call it uh v p which + + + align:start position:0% +domain Theory they call it uh v p which +uh is called vasper so that they can + + align:start position:0% +uh is called vasper so that they can + + + align:start position:0% +uh is called vasper so that they can +pronounce it Vesper which I stands for + + align:start position:0% +pronounce it Vesper which I stands for + + + align:start position:0% +pronounce it Vesper which I stands for +veence uh excuse me veence sh + + align:start position:0% +veence uh excuse me veence sh + + + align:start position:0% +veence uh excuse me veence sh +electron pair + + align:start position:0% +electron pair + + + align:start position:0% +electron pair +repulsion electron pair repulsion and + + align:start position:0% +repulsion electron pair repulsion and + + + align:start position:0% +repulsion electron pair repulsion and +all of this will come clear in in about + + align:start position:0% +all of this will come clear in in about + + + align:start position:0% +all of this will come clear in in about +the next 15 minutes it'll start all + + align:start position:0% +the next 15 minutes it'll start all + + + align:start position:0% +the next 15 minutes it'll start all +making sense so here's a set of rules I + + align:start position:0% +making sense so here's a set of rules I + + + align:start position:0% +making sense so here's a set of rules I +generated these this isn't in the book + + align:start position:0% +generated these this isn't in the book + + + align:start position:0% +generated these this isn't in the book +and and all of this will be posted by by + + align:start position:0% +and and all of this will be posted by by + + + align:start position:0% +and and all of this will be posted by by +midafternoon so you can take it down if + + align:start position:0% +midafternoon so you can take it down if + + + align:start position:0% +midafternoon so you can take it down if +you want or you can just take it off the + + align:start position:0% +you want or you can just take it off the + + + align:start position:0% +you want or you can just take it off the +web in a little bit all right so I want + + align:start position:0% +web in a little bit all right so I want + + + align:start position:0% +web in a little bit all right so I want +to go through and and illustrate how + + align:start position:0% +to go through and and illustrate how + + + align:start position:0% +to go through and and illustrate how +this uh is used and so what I want to do + + align:start position:0% +this uh is used and so what I want to do + + + align:start position:0% +this uh is used and so what I want to do +is I want to use this in order to to + + align:start position:0% +is I want to use this in order to to + + + align:start position:0% +is I want to use this in order to to +deduce to infer the uh the molecular + + align:start position:0% +deduce to infer the uh the molecular + + + align:start position:0% +deduce to infer the uh the molecular +architecture of three molecules so let's + + align:start position:0% +architecture of three molecules so let's + + + align:start position:0% +architecture of three molecules so let's +start with this series uh + + align:start position:0% +start with this series uh + + + align:start position:0% +start with this series uh +sf6 + + align:start position:0% +sf6 + + + align:start position:0% +sf6 +brf5 and I F4 minus so these are three + + align:start position:0% +brf5 and I F4 minus so these are three + + + align:start position:0% +brf5 and I F4 minus so these are three +molecules and I would say okay tell me + + align:start position:0% +molecules and I would say okay tell me + + + align:start position:0% +molecules and I would say okay tell me +what's what the shapes of of these + + align:start position:0% +what's what the shapes of of these + + + align:start position:0% +what's what the shapes of of these +molecules + + align:start position:0% + + + + align:start position:0% + +uh What will what will it be + + align:start position:0% +uh What will what will it be + + + align:start position:0% +uh What will what will it be +so let's start with sf6 sf6 is + + align:start position:0% +so let's start with sf6 sf6 is + + + align:start position:0% +so let's start with sf6 sf6 is +interesting uh we're going to have some + + align:start position:0% +interesting uh we're going to have some + + + align:start position:0% +interesting uh we're going to have some +of that in a class later on when I teach + + align:start position:0% +of that in a class later on when I teach + + + align:start position:0% +of that in a class later on when I teach +uh diffusion sf6 is a very large + + align:start position:0% +uh diffusion sf6 is a very large + + + align:start position:0% +uh diffusion sf6 is a very large +molecule and very heavy it's about + + align:start position:0% +molecule and very heavy it's about + + + align:start position:0% +molecule and very heavy it's about +molecular weight is about 150 grams per + + align:start position:0% +molecular weight is about 150 grams per + + + align:start position:0% +molecular weight is about 150 grams per +mole its density is five times that of + + align:start position:0% +mole its density is five times that of + + + align:start position:0% +mole its density is five times that of +air uh but it's main claim to fame is + + align:start position:0% +air uh but it's main claim to fame is + + + align:start position:0% +air uh but it's main claim to fame is +that it's chemically rather inert and so + + align:start position:0% +that it's chemically rather inert and so + + + align:start position:0% +that it's chemically rather inert and so +it's used extensively in the metal + + align:start position:0% +it's used extensively in the metal + + + align:start position:0% +it's used extensively in the metal +casting industry uh if you look under + + align:start position:0% +casting industry uh if you look under + + + align:start position:0% +casting industry uh if you look under +the hood of the car you see aluminum + + align:start position:0% +the hood of the car you see aluminum + + + align:start position:0% +the hood of the car you see aluminum +castings magnesium casting for things + + align:start position:0% +castings magnesium casting for things + + + align:start position:0% +castings magnesium casting for things +like water pump housing and so on those + + align:start position:0% +like water pump housing and so on those + + + align:start position:0% +like water pump housing and so on those +castings were made under the protection + + align:start position:0% +castings were made under the protection + + + align:start position:0% +castings were made under the protection +of a blanket of sulfur hexafluoride + + align:start position:0% +of a blanket of sulfur hexafluoride + + + align:start position:0% +of a blanket of sulfur hexafluoride +because as as we already know aluminum + + align:start position:0% +because as as we already know aluminum + + + align:start position:0% +because as as we already know aluminum +and magnesium are really good metals and + + align:start position:0% +and magnesium are really good metals and + + + align:start position:0% +and magnesium are really good metals and +they will react violently with oxygen in + + align:start position:0% +they will react violently with oxygen in + + + align:start position:0% +they will react violently with oxygen in +the air so you have to when you when + + align:start position:0% +the air so you have to when you when + + + align:start position:0% +the air so you have to when you when +you're pouring mol in aluminum you've + + align:start position:0% +you're pouring mol in aluminum you've + + + align:start position:0% +you're pouring mol in aluminum you've +got to keep the oxygen in the air away + + align:start position:0% +got to keep the oxygen in the air away + + + align:start position:0% +got to keep the oxygen in the air away +from it and they use sf6 you could say + + align:start position:0% +from it and they use sf6 you could say + + + align:start position:0% +from it and they use sf6 you could say +well we could use a liquid flux but what + + align:start position:0% +well we could use a liquid flux but what + + + align:start position:0% +well we could use a liquid flux but what +if some of the liquid flux gets + + align:start position:0% +if some of the liquid flux gets + + + align:start position:0% +if some of the liquid flux gets +entrained in the casting and the casting + + align:start position:0% +entrained in the casting and the casting + + + align:start position:0% +entrained in the casting and the casting +becomes weak the wheel cracks there's a + + align:start position:0% +becomes weak the wheel cracks there's a + + + align:start position:0% +becomes weak the wheel cracks there's a +collision + + align:start position:0% +collision + + + align:start position:0% +collision +maybe people lose their lives people are + + align:start position:0% +maybe people lose their lives people are + + + align:start position:0% +maybe people lose their lives people are +sued so it's better to use a gasphase + + align:start position:0% +sued so it's better to use a gasphase + + + align:start position:0% +sued so it's better to use a gasphase +shield okay but the bad news is the SF + + align:start position:0% +shield okay but the bad news is the SF + + + align:start position:0% +shield okay but the bad news is the SF +bond which you can calculate the energy + + align:start position:0% +bond which you can calculate the energy + + + align:start position:0% +bond which you can calculate the energy +for right now using the polling formula + + align:start position:0% +for right now using the polling formula + + + align:start position:0% +for right now using the polling formula +it sits smack dab in the middle of the + + align:start position:0% +it sits smack dab in the middle of the + + + align:start position:0% +it sits smack dab in the middle of the +just off visible and so it this is a + + align:start position:0% +just off visible and so it this is a + + + align:start position:0% +just off visible and so it this is a +fantastic infrared absorber and this + + align:start position:0% +fantastic infrared absorber and this + + + align:start position:0% +fantastic infrared absorber and this +stuff goes up into the upper atmosphere + + align:start position:0% +stuff goes up into the upper atmosphere + + + align:start position:0% +stuff goes up into the upper atmosphere +and has greenhouse gas coefficient that + + align:start position:0% +and has greenhouse gas coefficient that + + + align:start position:0% +and has greenhouse gas coefficient that +is phenomenal and so the industry is + + align:start position:0% +is phenomenal and so the industry is + + + align:start position:0% +is phenomenal and so the industry is +under pressure get rid of this so if + + align:start position:0% +under pressure get rid of this so if + + + align:start position:0% +under pressure get rid of this so if +somebody in here wants to do something + + align:start position:0% +somebody in here wants to do something + + + align:start position:0% +somebody in here wants to do something +good for the environment and allow us to + + align:start position:0% +good for the environment and allow us to + + + align:start position:0% +good for the environment and allow us to +continue to make castings of aluminum + + align:start position:0% +continue to make castings of aluminum + + + align:start position:0% +continue to make castings of aluminum +magnesium and reduce the mass of the + + align:start position:0% +magnesium and reduce the mass of the + + + align:start position:0% +magnesium and reduce the mass of the +vehicles but do so in a way that doesn't + + align:start position:0% +vehicles but do so in a way that doesn't + + + align:start position:0% +vehicles but do so in a way that doesn't +damage the upper atmosphere you know + + align:start position:0% +damage the upper atmosphere you know + + + align:start position:0% +damage the upper atmosphere you know +this is the tradeoff you know somebody + + align:start position:0% +this is the tradeoff you know somebody + + + align:start position:0% +this is the tradeoff you know somebody +in this room's SL will be sitting in + + align:start position:0% +in this room's SL will be sitting in + + + align:start position:0% +in this room's SL will be sitting in +policy someday and what's The Simple + + align:start position:0% +policy someday and what's The Simple + + + align:start position:0% +policy someday and what's The Simple +Solution if I come and tell you that the + + align:start position:0% +Solution if I come and tell you that the + + + align:start position:0% +Solution if I come and tell you that the +greenhouse gas coefficient of sf6 is + + align:start position:0% +greenhouse gas coefficient of sf6 is + + + align:start position:0% +greenhouse gas coefficient of sf6 is +12,000 times that of CO2 what would you + + align:start position:0% +12,000 times that of CO2 what would you + + + align:start position:0% +12,000 times that of CO2 what would you +do say well let's just ban it + + align:start position:0% +do say well let's just ban it + + + align:start position:0% +do say well let's just ban it +all right well that's dumb okay that's + + align:start position:0% +all right well that's dumb okay that's + + + align:start position:0% +all right well that's dumb okay that's +really dumb because now we don't have + + align:start position:0% +really dumb because now we don't have + + + align:start position:0% +really dumb because now we don't have +aluminum and magnesium castings so now + + align:start position:0% +aluminum and magnesium castings so now + + + align:start position:0% +aluminum and magnesium castings so now +the mass of the automobiles go up so + + align:start position:0% +the mass of the automobiles go up so + + + align:start position:0% +the mass of the automobiles go up so +what was an MIT person do an MIT person + + align:start position:0% +what was an MIT person do an MIT person + + + align:start position:0% +what was an MIT person do an MIT person +would say well let's figure out what's + + align:start position:0% +would say well let's figure out what's + + + align:start position:0% +would say well let's figure out what's +the tailpipe emission tradeoff to + + align:start position:0% +the tailpipe emission tradeoff to + + + align:start position:0% +the tailpipe emission tradeoff to +cleaning the Atmosphere by not allowing + + align:start position:0% +cleaning the Atmosphere by not allowing + + + align:start position:0% +cleaning the Atmosphere by not allowing +sf6 to go into the atmosphere see you + + align:start position:0% +sf6 to go into the atmosphere see you + + + align:start position:0% +sf6 to go into the atmosphere see you +got to know some chemistry otherwise you + + align:start position:0% +got to know some chemistry otherwise you + + + align:start position:0% +got to know some chemistry otherwise you +just make dumb decisions all right that + + align:start position:0% +just make dumb decisions all right that + + + align:start position:0% +just make dumb decisions all right that +having been said I wonder what the + + align:start position:0% +having been said I wonder what the + + + align:start position:0% +having been said I wonder what the +structure of this molecule is okay so + + align:start position:0% +structure of this molecule is okay so + + + align:start position:0% +structure of this molecule is okay so +first thing we do + + align:start position:0% +first thing we do + + + align:start position:0% +first thing we do +is Lewis structure let's write the Lewis + + align:start position:0% +is Lewis structure let's write the Lewis + + + align:start position:0% +is Lewis structure let's write the Lewis +structure so I'm going to put sulfur in + + align:start position:0% +structure so I'm going to put sulfur in + + + align:start position:0% +structure so I'm going to put sulfur in +here and sulfur's got six veence + + align:start position:0% +here and sulfur's got six veence + + + align:start position:0% +here and sulfur's got six veence +electrons it's got six veence electrons + + align:start position:0% +electrons it's got six veence electrons + + + align:start position:0% +electrons it's got six veence electrons +right sulfur is 2 S2 2 + + align:start position:0% +right sulfur is 2 S2 2 + + + align:start position:0% +right sulfur is 2 S2 2 +P4 and so let's bring up a Florine + + align:start position:0% +P4 and so let's bring up a Florine + + + align:start position:0% +P4 and so let's bring up a Florine +florine's got seven veence electrons so + + align:start position:0% +florine's got seven veence electrons so + + + align:start position:0% +florine's got seven veence electrons so +there's 1 2 3 4 five 6 7 so now Florine + + align:start position:0% +there's 1 2 3 4 five 6 7 so now Florine + + + align:start position:0% +there's 1 2 3 4 five 6 7 so now Florine +by sharing one electron with sulfur + + align:start position:0% +by sharing one electron with sulfur + + + align:start position:0% +by sharing one electron with sulfur +becomes octet stable and and we can keep + + align:start position:0% +becomes octet stable and and we can keep + + + align:start position:0% +becomes octet stable and and we can keep +doing this I don't I'm not going to put + + align:start position:0% +doing this I don't I'm not going to put + + + align:start position:0% +doing this I don't I'm not going to put +all of these down I'm just going to put + + align:start position:0% +all of these down I'm just going to put + + + align:start position:0% +all of these down I'm just going to put +a single electron from each Florine + + align:start position:0% +a single electron from each Florine + + + align:start position:0% +a single electron from each Florine +you'll know that there's more like this + + align:start position:0% +you'll know that there's more like this + + + align:start position:0% +you'll know that there's more like this +and here's another + + align:start position:0% +and here's another + + + align:start position:0% +and here's another +Florine here's another + + align:start position:0% +Florine here's another + + + align:start position:0% +Florine here's another +Florine here's another + + align:start position:0% +Florine here's another + + + align:start position:0% +Florine here's another +Florine and here's another + + align:start position:0% + + + + align:start position:0% + +Florine so this is great all the flines + + align:start position:0% +Florine so this is great all the flines + + + align:start position:0% +Florine so this is great all the flines +are octat stable now let's see what's + + align:start position:0% +are octat stable now let's see what's + + + align:start position:0% +are octat stable now let's see what's +going on with sulfur it's got 2 4 6 8 10 + + align:start position:0% +going on with sulfur it's got 2 4 6 8 10 + + + align:start position:0% +going on with sulfur it's got 2 4 6 8 10 +12 12 it's got 12 electron that's that's + + align:start position:0% +12 12 it's got 12 electron that's that's + + + align:start position:0% +12 12 it's got 12 electron that's that's +some octet with 12 isn't + + align:start position:0% +some octet with 12 isn't + + + align:start position:0% +some octet with 12 isn't +it okay well let me tell you something + + align:start position:0% +it okay well let me tell you something + + + align:start position:0% +it okay well let me tell you something +with some of the very electronegative + + align:start position:0% +with some of the very electronegative + + + align:start position:0% +with some of the very electronegative +elements that have a very very high uh + + align:start position:0% +elements that have a very very high uh + + + align:start position:0% +elements that have a very very high uh +um average veence electron energies they + + align:start position:0% +um average veence electron energies they + + + align:start position:0% +um average veence electron energies they +can form and the ones that are in the + + align:start position:0% +can form and the ones that are in the + + + align:start position:0% +can form and the ones that are in the +dark blue are elements that on occasion + + align:start position:0% +dark blue are elements that on occasion + + + align:start position:0% +dark blue are elements that on occasion +can form expanded octets these are + + align:start position:0% +can form expanded octets these are + + + align:start position:0% +can form expanded octets these are +called expanded + + align:start position:0% + + + + align:start position:0% + +octets and the expanded octet is an at + + align:start position:0% +octets and the expanded octet is an at + + + align:start position:0% +octets and the expanded octet is an at +you + + align:start position:0% +you + + + align:start position:0% +you +if eight if octet stability is good and + + align:start position:0% +if eight if octet stability is good and + + + align:start position:0% +if eight if octet stability is good and +I have a huge appetite for for electrons + + align:start position:0% +I have a huge appetite for for electrons + + + align:start position:0% +I have a huge appetite for for electrons +I just might try to pull in a few more + + align:start position:0% +I just might try to pull in a few more + + + align:start position:0% +I just might try to pull in a few more +so it happens and let's look at the + + align:start position:0% +so it happens and let's look at the + + + align:start position:0% +so it happens and let's look at the +energy level diagram of that um now if + + align:start position:0% +energy level diagram of that um now if + + + align:start position:0% +energy level diagram of that um now if +I've got if I've got uh I've got here's + + align:start position:0% +I've got if I've got uh I've got here's + + + align:start position:0% +I've got if I've got uh I've got here's +my + + align:start position:0% +my + + + align:start position:0% +my +2s and here's my 2 + + align:start position:0% +2s and here's my 2 + + + align:start position:0% +2s and here's my 2 +p so this is one 2 3 4 five six there's + + align:start position:0% +p so this is one 2 3 4 five six there's + + + align:start position:0% +p so this is one 2 3 4 five six there's +my six veence electrons right but here + + align:start position:0% +my six veence electrons right but here + + + align:start position:0% +my six veence electrons right but here +what do I have I need to be able to form + + align:start position:0% +what do I have I need to be able to form + + + align:start position:0% +what do I have I need to be able to form +six pairs of bonds so I need to + + align:start position:0% +six pairs of bonds so I need to + + + align:start position:0% +six pairs of bonds so I need to +hybridize the best I can do is hybridize + + align:start position:0% +hybridize the best I can do is hybridize + + + align:start position:0% +hybridize the best I can do is hybridize +sp3 that'll give me four I need to get + + align:start position:0% +sp3 that'll give me four I need to get + + + align:start position:0% +sp3 that'll give me four I need to get +more you know where I'm going to go I'm + + align:start position:0% +more you know where I'm going to go I'm + + + align:start position:0% +more you know where I'm going to go I'm +going to go to the orbital store and + + align:start position:0% +going to go to the orbital store and + + + align:start position:0% +going to go to the orbital store and +where's the orbital store it's over here + + align:start position:0% +where's the orbital store it's over here + + + align:start position:0% +where's the orbital store it's over here +d d you know you say well wait a minute + + align:start position:0% +d d you know you say well wait a minute + + + align:start position:0% +d d you know you say well wait a minute +what talking about we're going to bring + + align:start position:0% +what talking about we're going to bring + + + align:start position:0% +what talking about we're going to bring +down the D's okay we'll bring down the + + align:start position:0% +down the D's okay we'll bring down the + + + align:start position:0% +down the D's okay we'll bring down the +D's and here's how we do it there's one + + align:start position:0% +D's and here's how we do it there's one + + + align:start position:0% +D's and here's how we do it there's one +two three I if I grab two of these D's + + align:start position:0% +two three I if I grab two of these D's + + + align:start position:0% +two three I if I grab two of these D's +and I mix s's PS and these two D's that + + align:start position:0% +and I mix s's PS and these two D's that + + + align:start position:0% +and I mix s's PS and these two D's that +can give me this + + align:start position:0% +can give me this + + + align:start position:0% +can give me this +configuration s P3 and I'm taking two of + + align:start position:0% +configuration s P3 and I'm taking two of + + + align:start position:0% +configuration s P3 and I'm taking two of +the D's sp3 2D and then I've got three + + align:start position:0% +the D's sp3 2D and then I've got three + + + align:start position:0% +the D's sp3 2D and then I've got three +d's left here unmixed so now hund rule + + align:start position:0% +d's left here unmixed so now hund rule + + + align:start position:0% +d's left here unmixed so now hund rule +six electrons 1 2 3 4 five six so this + + align:start position:0% +six electrons 1 2 3 4 five six so this + + + align:start position:0% +six electrons 1 2 3 4 five six so this +is how one can hybridize in order to + + align:start position:0% +is how one can hybridize in order to + + + align:start position:0% +is how one can hybridize in order to +allow for expanded octad right + + align:start position:0% +allow for expanded octad right + + + align:start position:0% +allow for expanded octad right +and also account for the the bonds that + + align:start position:0% +and also account for the the bonds that + + + align:start position:0% +and also account for the the bonds that +we're forming here all right so the what + + align:start position:0% +we're forming here all right so the what + + + align:start position:0% +we're forming here all right so the what +is called electron domain Theory each + + align:start position:0% +is called electron domain Theory each + + + align:start position:0% +is called electron domain Theory each +one of these orbitals here each one of + + align:start position:0% +one of these orbitals here each one of + + + align:start position:0% +one of these orbitals here each one of +these + + align:start position:0% +these + + + align:start position:0% +these +orbitals that has electron occupancy + + align:start position:0% +orbitals that has electron occupancy + + + align:start position:0% +orbitals that has electron occupancy +around the center atom each one of these + + align:start position:0% +around the center atom each one of these + + + align:start position:0% +around the center atom each one of these +is termed each one of these is termed an + + align:start position:0% +is termed each one of these is termed an + + + align:start position:0% +is termed each one of these is termed an +electron + + align:start position:0% +electron + + + align:start position:0% +electron +domain an electron domain and there's + + align:start position:0% +domain an electron domain and there's + + + align:start position:0% +domain an electron domain and there's +two types of electron domains those con + + align:start position:0% +two types of electron domains those con + + + align:start position:0% +two types of electron domains those con +those that involve bonds and and those + + align:start position:0% +those that involve bonds and and those + + + align:start position:0% +those that involve bonds and and those +that do not involve bonds so the the six + + align:start position:0% +that do not involve bonds so the the six + + + align:start position:0% +that do not involve bonds so the the six +that I've circled are bonding domains so + + align:start position:0% +that I've circled are bonding domains so + + + align:start position:0% +that I've circled are bonding domains so +these are all bonding domains and for + + align:start position:0% +these are all bonding domains and for + + + align:start position:0% +these are all bonding domains and for +example this one here which I'll put a + + align:start position:0% +example this one here which I'll put a + + + align:start position:0% +example this one here which I'll put a +square around it's off to the side it's + + align:start position:0% +square around it's off to the side it's + + + align:start position:0% +square around it's off to the side it's +a non-bonding domain it doesn't get + + align:start position:0% +a non-bonding domain it doesn't get + + + align:start position:0% +a non-bonding domain it doesn't get +involved in bonding but it's not even + + align:start position:0% +involved in bonding but it's not even + + + align:start position:0% +involved in bonding but it's not even +part of the central atom but okay so + + align:start position:0% +part of the central atom but okay so + + + align:start position:0% +part of the central atom but okay so +we'll we'll we'll see that in a second + + align:start position:0% +we'll we'll we'll see that in a second + + + align:start position:0% +we'll we'll we'll see that in a second +all right so I've got six electron + + align:start position:0% +all right so I've got six electron + + + align:start position:0% +all right so I've got six electron +domains and now I want to put up the + + align:start position:0% +domains and now I want to put up the + + + align:start position:0% +domains and now I want to put up the +skeletal structure so if I have my + + align:start position:0% +skeletal structure so if I have my + + + align:start position:0% +skeletal structure so if I have my +central sulfur here how can I put six + + align:start position:0% +central sulfur here how can I put six + + + align:start position:0% +central sulfur here how can I put six +domains symmetrically in Space the way I + + align:start position:0% +domains symmetrically in Space the way I + + + align:start position:0% +domains symmetrically in Space the way I +do that is I make essentially this this + + align:start position:0% +do that is I make essentially this this + + + align:start position:0% +do that is I make essentially this this +triple cross that con constitutes the + + align:start position:0% +triple cross that con constitutes the + + + align:start position:0% +triple cross that con constitutes the +coordinate system right X Y and Z this + + align:start position:0% +coordinate system right X Y and Z this + + + align:start position:0% +coordinate system right X Y and Z this +gives me six domains in uh symmetric + + align:start position:0% +gives me six domains in uh symmetric + + + align:start position:0% +gives me six domains in uh symmetric +disposition around a central atom and in + + align:start position:0% +disposition around a central atom and in + + + align:start position:0% +disposition around a central atom and in +this case so six electron domains + + align:start position:0% +this case so six electron domains + + + align:start position:0% +this case so six electron domains +implies octahedral + + align:start position:0% +implies octahedral + + + align:start position:0% +implies octahedral +skeleton octahedral skeleton skeleton of + + align:start position:0% +skeleton octahedral skeleton skeleton of + + + align:start position:0% +skeleton octahedral skeleton skeleton of +what it's the skeleton of the molecule + + align:start position:0% +what it's the skeleton of the molecule + + + align:start position:0% +what it's the skeleton of the molecule +it's where the electrons can reside and + + align:start position:0% +it's where the electrons can reside and + + + align:start position:0% +it's where the electrons can reside and +why is this called octahedral this is + + align:start position:0% +why is this called octahedral this is + + + align:start position:0% +why is this called octahedral this is +you look at this if you were to link + + align:start position:0% +you look at this if you were to link + + + align:start position:0% +you look at this if you were to link +these up in the plane so you link up + + align:start position:0% +these up in the plane so you link up + + + align:start position:0% +these up in the plane so you link up +four in the plane and then build a a + + align:start position:0% +four in the plane and then build a a + + + align:start position:0% +four in the plane and then build a a +pyramid to the top can you see that the + + align:start position:0% +pyramid to the top can you see that the + + + align:start position:0% +pyramid to the top can you see that the +pyramid to the top has four faces to it + + align:start position:0% +pyramid to the top has four faces to it + + + align:start position:0% +pyramid to the top has four faces to it +so four faces on the up four faces on + + align:start position:0% +so four faces on the up four faces on + + + align:start position:0% +so four faces on the up four faces on +the down four plus 4 is eight so + + align:start position:0% +the down four plus 4 is eight so + + + align:start position:0% +the down four plus 4 is eight so +octahedral eight-faced but I I look at + + align:start position:0% +octahedral eight-faced but I I look at + + + align:start position:0% +octahedral eight-faced but I I look at +that and I see the six struts and I do + + align:start position:0% +that and I see the six struts and I do + + + align:start position:0% +that and I see the six struts and I do +this cognitive discordance when I'm + + align:start position:0% +this cognitive discordance when I'm + + + align:start position:0% +this cognitive discordance when I'm +saying it's octahedral but I'm seeing + + align:start position:0% +saying it's octahedral but I'm seeing + + + align:start position:0% +saying it's octahedral but I'm seeing +six but just you just get used to it so + + align:start position:0% +six but just you just get used to it so + + + align:start position:0% +six but just you just get used to it so +this is octahedral and clearly we can + + align:start position:0% +this is octahedral and clearly we can + + + align:start position:0% +this is octahedral and clearly we can +put the flines at the ends of the + + align:start position:0% +put the flines at the ends of the + + + align:start position:0% +put the flines at the ends of the +struts so there's sf6 that's the shape + + align:start position:0% +struts so there's sf6 that's the shape + + + align:start position:0% +struts so there's sf6 that's the shape +of the molecule that's the shape of the + + align:start position:0% +of the molecule that's the shape of the + + + align:start position:0% +of the molecule that's the shape of the +molecule because we have six bonding + + align:start position:0% +molecule because we have six bonding + + + align:start position:0% +molecule because we have six bonding +domains all the bond all the domains + + align:start position:0% +domains all the bond all the domains + + + align:start position:0% +domains all the bond all the domains +are uh engaged in bonding so they're all + + align:start position:0% +are uh engaged in bonding so they're all + + + align:start position:0% +are uh engaged in bonding so they're all +the same there's no diff distinction + + align:start position:0% +the same there's no diff distinction + + + align:start position:0% +the same there's no diff distinction +between them so we have octahedral + + align:start position:0% +between them so we have octahedral + + + align:start position:0% +between them so we have octahedral +skeleton and in this this case we have + + align:start position:0% +skeleton and in this this case we have + + + align:start position:0% +skeleton and in this this case we have +an octahedral + + align:start position:0% +an octahedral + + + align:start position:0% +an octahedral +molecule octahedral + + align:start position:0% +molecule octahedral + + + align:start position:0% +molecule octahedral +molecule uh let's see what else can we + + align:start position:0% +molecule uh let's see what else can we + + + align:start position:0% +molecule uh let's see what else can we +say about it oh polar non-polar what do + + align:start position:0% +say about it oh polar non-polar what do + + + align:start position:0% +say about it oh polar non-polar what do +you think as soon as you see Florine you + + align:start position:0% +you think as soon as you see Florine you + + + align:start position:0% +you think as soon as you see Florine you +know it's just like in the mansurian + + align:start position:0% +know it's just like in the mansurian + + + align:start position:0% +know it's just like in the mansurian +canidate when someone says Florine you + + align:start position:0% +canidate when someone says Florine you + + + align:start position:0% +canidate when someone says Florine you +go ah Electro negative most Electro + + align:start position:0% +go ah Electro negative most Electro + + + align:start position:0% +go ah Electro negative most Electro +negative right so Bingo this is really + + align:start position:0% +negative right so Bingo this is really + + + align:start position:0% +negative right so Bingo this is really +super electronegative so we know this is + + align:start position:0% +super electronegative so we know this is + + + align:start position:0% +super electronegative so we know this is +a very polar bond but as I showed you + + align:start position:0% +a very polar bond but as I showed you + + + align:start position:0% +a very polar bond but as I showed you +last day there's six symmetrically + + align:start position:0% +last day there's six symmetrically + + + align:start position:0% +last day there's six symmetrically +disposed polar bond so it's a non-polar + + align:start position:0% + + + + align:start position:0% + +molecule terrific all right let's go on + + align:start position:0% +molecule terrific all right let's go on + + + align:start position:0% +molecule terrific all right let's go on +this is fun let's do the next one uh + + align:start position:0% +this is fun let's do the next one uh + + + align:start position:0% +this is fun let's do the next one uh +let's do bromine pentafluoride bromine + + align:start position:0% +let's do bromine pentafluoride bromine + + + align:start position:0% +let's do bromine pentafluoride bromine +pent + + align:start position:0% +pent + + + align:start position:0% +pent +fluide okay look at + + align:start position:0% +fluide okay look at + + + align:start position:0% +fluide okay look at +brf5 so according to this whoops let's + + align:start position:0% +brf5 so according to this whoops let's + + + align:start position:0% +brf5 so according to this whoops let's +go back to our our rules here write the + + align:start position:0% +go back to our our rules here write the + + + align:start position:0% +go back to our our rules here write the +Lew structure that'll give us electron + + align:start position:0% +Lew structure that'll give us electron + + + align:start position:0% +Lew structure that'll give us electron +distribution so here's bromine and it's + + align:start position:0% +distribution so here's bromine and it's + + + align:start position:0% +distribution so here's bromine and it's +got uh 1 2 3 four five 6 seven and each + + align:start position:0% +got uh 1 2 3 four five 6 seven and each + + + align:start position:0% +got uh 1 2 3 four five 6 seven and each +Florine is going to come up same as last + + align:start position:0% +Florine is going to come up same as last + + + align:start position:0% +Florine is going to come up same as last +time each Florine will + + align:start position:0% +time each Florine will + + + align:start position:0% +time each Florine will +share uh one electron with bromine so + + align:start position:0% +share uh one electron with bromine so + + + align:start position:0% +share uh one electron with bromine so +that'll give Florine its octet it's 2 4 + + align:start position:0% +that'll give Florine its octet it's 2 4 + + + align:start position:0% +that'll give Florine its octet it's 2 4 +68 and then I'm going to do the same + + align:start position:0% +68 and then I'm going to do the same + + + align:start position:0% +68 and then I'm going to do the same +there's the Florine 1 two3 another + + align:start position:0% +there's the Florine 1 two3 another + + + align:start position:0% +there's the Florine 1 two3 another +Florine another Florine + + align:start position:0% +Florine another Florine + + + align:start position:0% +Florine another Florine +uh another + + align:start position:0% +uh another + + + align:start position:0% +uh another +Florine so I got one two 3 four five and + + align:start position:0% +Florine so I got one two 3 four five and + + + align:start position:0% +Florine so I got one two 3 four five and +then I got a pair of electrons that are + + align:start position:0% +then I got a pair of electrons that are + + + align:start position:0% +then I got a pair of electrons that are +hanging around so FL so bromine has + + align:start position:0% +hanging around so FL so bromine has + + + align:start position:0% +hanging around so FL so bromine has +shared + + align:start position:0% +shared + + + align:start position:0% +shared +one of five of its one each of five of + + align:start position:0% +one of five of its one each of five of + + + align:start position:0% +one of five of its one each of five of +its electrons with the Florine and then + + align:start position:0% +its electrons with the Florine and then + + + align:start position:0% +its electrons with the Florine and then +there's a pair here that is unshared + + align:start position:0% +there's a pair here that is unshared + + + align:start position:0% +there's a pair here that is unshared +okay so first of all let's count the + + align:start position:0% +okay so first of all let's count the + + + align:start position:0% +okay so first of all let's count the +number of electron domains around the + + align:start position:0% +number of electron domains around the + + + align:start position:0% +number of electron domains around the +central bromine so I got 1 2 3 4 5 + + align:start position:0% +central bromine so I got 1 2 3 4 5 + + + align:start position:0% +central bromine so I got 1 2 3 4 5 +six six electron domains all right so + + align:start position:0% +six six electron domains all right so + + + align:start position:0% +six six electron domains all right so +but we're not panicking now because we + + align:start position:0% +but we're not panicking now because we + + + align:start position:0% +but we're not panicking now because we +know that expanded octets exist and it's + + align:start position:0% +know that expanded octets exist and it's + + + align:start position:0% +know that expanded octets exist and it's +okay all right but there's a difference + + align:start position:0% +okay all right but there's a difference + + + align:start position:0% +okay all right but there's a difference +here there's a difference so first of + + align:start position:0% +here there's a difference so first of + + + align:start position:0% +here there's a difference so first of +all six electron domains so that means + + align:start position:0% +all six electron domains so that means + + + align:start position:0% +all six electron domains so that means +again octahedral + + align:start position:0% +again octahedral + + + align:start position:0% +again octahedral +skeleton octahedral + + align:start position:0% +skeleton octahedral + + + align:start position:0% +skeleton octahedral +skeleton so the electrons and the bonds + + align:start position:0% +skeleton so the electrons and the bonds + + + align:start position:0% +skeleton so the electrons and the bonds +are going to be in this kind of a + + align:start position:0% +are going to be in this kind of a + + + align:start position:0% +are going to be in this kind of a +formation again with the bromine in the + + align:start position:0% +formation again with the bromine in the + + + align:start position:0% +formation again with the bromine in the +center but there's one little + + align:start position:0% +center but there's one little + + + align:start position:0% +center but there's one little +distinction here and that is that um + + align:start position:0% +distinction here and that is that um + + + align:start position:0% +distinction here and that is that um +there + + align:start position:0% +there + + + align:start position:0% +there +they're not all bonding domains you see + + align:start position:0% +they're not all bonding domains you see + + + align:start position:0% +they're not all bonding domains you see +this this pair over here is not involved + + align:start position:0% +this this pair over here is not involved + + + align:start position:0% +this this pair over here is not involved +in any bonding so I've got + + align:start position:0% +in any bonding so I've got + + + align:start position:0% +in any bonding so I've got +five five bonding + + align:start position:0% +five five bonding + + + align:start position:0% +five five bonding +domains five bonding domains and one + + align:start position:0% +domains five bonding domains and one + + + align:start position:0% +domains five bonding domains and one +nonbonding one non-bonding + + align:start position:0% +nonbonding one non-bonding + + + align:start position:0% +nonbonding one non-bonding +domain okay so the the five are in an + + align:start position:0% +domain okay so the the five are in an + + + align:start position:0% +domain okay so the the five are in an +oval and the one is in the is in the uh + + align:start position:0% +oval and the one is in the is in the uh + + + align:start position:0% +oval and the one is in the is in the uh +rectangle here all right and uh + + align:start position:0% +rectangle here all right and uh + + + align:start position:0% +rectangle here all right and uh +sometimes if you look at some old + + align:start position:0% +sometimes if you look at some old + + + align:start position:0% +sometimes if you look at some old +chemistry books they non-bonding is is + + align:start position:0% +chemistry books they non-bonding is is + + + align:start position:0% +chemistry books they non-bonding is is +one of these strange it's clear it's a + + align:start position:0% +one of these strange it's clear it's a + + + align:start position:0% +one of these strange it's clear it's a +late late Comer to the language + + align:start position:0% +late late Comer to the language + + + align:start position:0% +late late Comer to the language +sometimes people call these lone pairs + + align:start position:0% +sometimes people call these lone pairs + + + align:start position:0% +sometimes people call these lone pairs +they're lone pairs they're both both + + align:start position:0% +they're lone pairs they're both both + + + align:start position:0% +they're lone pairs they're both both +electrons come from the central atom and + + align:start position:0% +electrons come from the central atom and + + + align:start position:0% +electrons come from the central atom and +they haven't gotten picked up for any + + align:start position:0% +they haven't gotten picked up for any + + + align:start position:0% +they haven't gotten picked up for any +kind of uh Duty so they're just they're + + align:start position:0% +kind of uh Duty so they're just they're + + + align:start position:0% +kind of uh Duty so they're just they're +alone they're lone pairs all right so + + align:start position:0% +alone they're lone pairs all right so + + + align:start position:0% +alone they're lone pairs all right so +now let's take a look at the shape of + + align:start position:0% +now let's take a look at the shape of + + + align:start position:0% +now let's take a look at the shape of +the molecule the shape of the molecule + + align:start position:0% +the molecule the shape of the molecule + + + align:start position:0% +the molecule the shape of the molecule +it turns out that it doesn't really + + align:start position:0% +it turns out that it doesn't really + + + align:start position:0% +it turns out that it doesn't really +matter there's a symmetry here right it + + align:start position:0% +matter there's a symmetry here right it + + + align:start position:0% +matter there's a symmetry here right it +doesn't matter if I have the five flines + + align:start position:0% +doesn't matter if I have the five flines + + + align:start position:0% +doesn't matter if I have the five flines +in the plane and above or the five + + align:start position:0% +in the plane and above or the five + + + align:start position:0% +in the plane and above or the five +flines uh underneath and the lone pair + + align:start position:0% +flines uh underneath and the lone pair + + + align:start position:0% +flines uh underneath and the lone pair +up here those are symmetric one's just + + align:start position:0% +up here those are symmetric one's just + + + align:start position:0% +up here those are symmetric one's just +upside down from the other there there's + + align:start position:0% +upside down from the other there there's + + + align:start position:0% +upside down from the other there there's +nothing distinguishable so just to get + + align:start position:0% +nothing distinguishable so just to get + + + align:start position:0% +nothing distinguishable so just to get +this thing over with I'm going to put + + align:start position:0% +this thing over with I'm going to put + + + align:start position:0% +this thing over with I'm going to put +the flines in the + + align:start position:0% +the flines in the + + + align:start position:0% +the flines in the +plane okay so this is the um this is the + + align:start position:0% +plane okay so this is the um this is the + + + align:start position:0% +plane okay so this is the um this is the +XY plane and then the Z the Z direction + + align:start position:0% +XY plane and then the Z the Z direction + + + align:start position:0% +XY plane and then the Z the Z direction +is up here and then this is the the + + align:start position:0% +is up here and then this is the the + + + align:start position:0% +is up here and then this is the the +non-bonding pair is off to one side here + + align:start position:0% +non-bonding pair is off to one side here + + + align:start position:0% +non-bonding pair is off to one side here +so you don't don't see the electrons if + + align:start position:0% +so you don't don't see the electrons if + + + align:start position:0% +so you don't don't see the electrons if +you try to detect the shape of this + + align:start position:0% +you try to detect the shape of this + + + align:start position:0% +you try to detect the shape of this +molecule you simply see the atoms so + + align:start position:0% +molecule you simply see the atoms so + + + align:start position:0% +molecule you simply see the atoms so +you'll see bromine in the center and you + + align:start position:0% +you'll see bromine in the center and you + + + align:start position:0% +you'll see bromine in the center and you +see five flines about it and what's + + align:start position:0% +see five flines about it and what's + + + align:start position:0% +see five flines about it and what's +going to be the shape of this thing well + + align:start position:0% +going to be the shape of this thing well + + + align:start position:0% +going to be the shape of this thing well +four of the flines lie in a plane and + + align:start position:0% +four of the flines lie in a plane and + + + align:start position:0% +four of the flines lie in a plane and +then the fifth Florine lies above the + + align:start position:0% +then the fifth Florine lies above the + + + align:start position:0% +then the fifth Florine lies above the +plane dead center over the bromine so I + + align:start position:0% +plane dead center over the bromine so I + + + align:start position:0% +plane dead center over the bromine so I +can pitch a tent here and what am I + + align:start position:0% +can pitch a tent here and what am I + + + align:start position:0% +can pitch a tent here and what am I +going to have I'm going to have + + align:start position:0% +going to have I'm going to have + + + align:start position:0% +going to have I'm going to have +something that's square based and a + + align:start position:0% +something that's square based and a + + + align:start position:0% +something that's square based and a +pyramid so the molecule is square + + align:start position:0% +pyramid so the molecule is square + + + align:start position:0% +pyramid so the molecule is square +parameter Square parameter + + align:start position:0% +parameter Square parameter + + + align:start position:0% +parameter Square parameter +molecule the structure is still + + align:start position:0% +molecule the structure is still + + + align:start position:0% +molecule the structure is still +octahedral for the electrons but the + + align:start position:0% +octahedral for the electrons but the + + + align:start position:0% +octahedral for the electrons but the +molecule Square parameter + + align:start position:0% +molecule Square parameter + + + align:start position:0% +molecule Square parameter +molecule uh what else can we say about + + align:start position:0% +molecule uh what else can we say about + + + align:start position:0% +molecule uh what else can we say about +this oh how about uh is this polar or + + align:start position:0% +this oh how about uh is this polar or + + + align:start position:0% +this oh how about uh is this polar or +non-polar it's polar you can see there's + + align:start position:0% +non-polar it's polar you can see there's + + + align:start position:0% +non-polar it's polar you can see there's +asymmetry here there's extra electrons + + align:start position:0% +asymmetry here there's extra electrons + + + align:start position:0% +asymmetry here there's extra electrons +down on the bottom the way I've drawn it + + align:start position:0% +down on the bottom the way I've drawn it + + + align:start position:0% +down on the bottom the way I've drawn it +so that means that I could model this as + + align:start position:0% +so that means that I could model this as + + + align:start position:0% +so that means that I could model this as +a dipole with the the bottom part of it + + align:start position:0% +a dipole with the the bottom part of it + + + align:start position:0% +a dipole with the the bottom part of it +negative and the top part of it positive + + align:start position:0% +negative and the top part of it positive + + + align:start position:0% +negative and the top part of it positive +net neutral or we could draw it this way + + align:start position:0% +net neutral or we could draw it this way + + + align:start position:0% +net neutral or we could draw it this way +uh I think we were going to put an arrow + + align:start position:0% +uh I think we were going to put an arrow + + + align:start position:0% +uh I think we were going to put an arrow +pointing in the direction of the + + align:start position:0% +pointing in the direction of the + + + align:start position:0% +pointing in the direction of the +negative end of the dipole so that's + + align:start position:0% +negative end of the dipole so that's + + + align:start position:0% +negative end of the dipole so that's +good wow we're clicking now there's a + + align:start position:0% +good wow we're clicking now there's a + + + align:start position:0% +good wow we're clicking now there's a +piece of paper down here it's got more + + align:start position:0% +piece of paper down here it's got more + + + align:start position:0% +piece of paper down here it's got more +information on it let's get this one so + + align:start position:0% +information on it let's get this one so + + + align:start position:0% +information on it let's get this one so +I'm going to do let's do one more is so + + align:start position:0% +I'm going to do let's do one more is so + + + align:start position:0% +I'm going to do let's do one more is so +much fun let's do if4 if4 Tetra floro + + align:start position:0% + + + + align:start position:0% + +iodate if4 it's a it's a complex ion all + + align:start position:0% +iodate if4 it's a it's a complex ion all + + + align:start position:0% +iodate if4 it's a it's a complex ion all +right so we're g to we going do the same + + align:start position:0% +right so we're g to we going do the same + + + align:start position:0% +right so we're g to we going do the same +thing we write the Lewis structure and + + align:start position:0% +thing we write the Lewis structure and + + + align:start position:0% +thing we write the Lewis structure and +uh iodine one uh two three four five six + + align:start position:0% +uh iodine one uh two three four five six + + + align:start position:0% +uh iodine one uh two three four five six +7 okay so here's Florine 1 2 3 4 five + + align:start position:0% +7 okay so here's Florine 1 2 3 4 five + + + align:start position:0% +7 okay so here's Florine 1 2 3 4 five +six 7 so by sharing one electron with + + align:start position:0% +six 7 so by sharing one electron with + + + align:start position:0% +six 7 so by sharing one electron with +iodine Florine becomes octet stable so + + align:start position:0% +iodine Florine becomes octet stable so + + + align:start position:0% +iodine Florine becomes octet stable so +this one will do it as well you know + + align:start position:0% +this one will do it as well you know + + + align:start position:0% +this one will do it as well you know +I've got enough room here I think I'm + + align:start position:0% +I've got enough room here I think I'm + + + align:start position:0% +I've got enough room here I think I'm +going to go for the gold I'm going to + + align:start position:0% +going to go for the gold I'm going to + + + align:start position:0% +going to go for the gold I'm going to +put all the electrons here so there's + + align:start position:0% +put all the electrons here so there's + + + align:start position:0% +put all the electrons here so there's +Florine over here here's Florine + + align:start position:0% + + + + align:start position:0% + +so there's eight there and let's put + + align:start position:0% +so there's eight there and let's put + + + align:start position:0% +so there's eight there and let's put +another Florine up + + align:start position:0% + + + + align:start position:0% + +here going move that move this just a + + align:start position:0% +here going move that move this just a + + + align:start position:0% +here going move that move this just a +little bit going raise this put this off + + align:start position:0% +little bit going raise this put this off + + + align:start position:0% +little bit going raise this put this off +to the side I have four minus I put a + + align:start position:0% +to the side I have four minus I put a + + + align:start position:0% +to the side I have four minus I put a +Florine here 1 2 3 four five six 7even + + align:start position:0% +Florine here 1 2 3 four five six 7even + + + align:start position:0% +Florine here 1 2 3 four five six 7even +so there's the four + + align:start position:0% +so there's the four + + + align:start position:0% +so there's the four +flines and now let's look at the let's + + align:start position:0% +flines and now let's look at the let's + + + align:start position:0% +flines and now let's look at the let's +look at the electrons around iodine I + + align:start position:0% +look at the electrons around iodine I + + + align:start position:0% +look at the electrons around iodine I +gave 1 2 3 4 4 5 six 7 but you see this + + align:start position:0% +gave 1 2 3 4 4 5 six 7 but you see this + + + align:start position:0% +gave 1 2 3 4 4 5 six 7 but you see this +thing's net negative where did the net + + align:start position:0% +thing's net negative where did the net + + + align:start position:0% +thing's net negative where did the net +negative come from how does something + + align:start position:0% +negative come from how does something + + + align:start position:0% +negative come from how does something +become net negative it acquires an + + align:start position:0% +become net negative it acquires an + + + align:start position:0% +become net negative it acquires an +electron through electron transfer this + + align:start position:0% +electron through electron transfer this + + + align:start position:0% +electron through electron transfer this +is really cool because this is Cove + + align:start position:0% +is really cool because this is Cove + + + align:start position:0% +is really cool because this is Cove +valent bonding within something that is + + align:start position:0% +valent bonding within something that is + + + align:start position:0% +valent bonding within something that is +engaged in electron transfer so to make + + align:start position:0% +engaged in electron transfer so to make + + + align:start position:0% +engaged in electron transfer so to make +this thing this this complex ion net + + align:start position:0% +this thing this this complex ion net + + + align:start position:0% +this thing this this complex ion net +negative means that I had to throw one + + align:start position:0% +negative means that I had to throw one + + + align:start position:0% +negative means that I had to throw one +more electron in here into the mix and + + align:start position:0% +more electron in here into the mix and + + + align:start position:0% +more electron in here into the mix and +where is it going to go where do + + align:start position:0% +where is it going to go where do + + + align:start position:0% +where is it going to go where do +electrons live they live in orbitals and + + align:start position:0% +electrons live they live in orbitals and + + + align:start position:0% +electrons live they live in orbitals and +there is one orbital that's just waiting + + align:start position:0% +there is one orbital that's just waiting + + + align:start position:0% +there is one orbital that's just waiting +for it right here so I'm going to put + + align:start position:0% +for it right here so I'm going to put + + + align:start position:0% +for it right here so I'm going to put +this electron in here so now what do I + + align:start position:0% +this electron in here so now what do I + + + align:start position:0% +this electron in here so now what do I +have I've got one two three four bonding + + align:start position:0% +have I've got one two three four bonding + + + align:start position:0% +have I've got one two three four bonding +orbitals four orbitals where I have one + + align:start position:0% +orbitals four orbitals where I have one + + + align:start position:0% +orbitals four orbitals where I have one +electron from the iodine and one + + align:start position:0% +electron from the iodine and one + + + align:start position:0% +electron from the iodine and one +electron from the Florine so let's write + + align:start position:0% +electron from the Florine so let's write + + + align:start position:0% +electron from the Florine so let's write +that down four bonding + + align:start position:0% +that down four bonding + + + align:start position:0% +that down four bonding +domains and I'm still talking about the + + align:start position:0% +domains and I'm still talking about the + + + align:start position:0% +domains and I'm still talking about the +central iodine here's two of its + + align:start position:0% +central iodine here's two of its + + + align:start position:0% +central iodine here's two of its +electrons that had no place to go so + + align:start position:0% +electrons that had no place to go so + + + align:start position:0% +electrons that had no place to go so +that's one lone pair here's the seventh + + align:start position:0% +that's one lone pair here's the seventh + + + align:start position:0% +that's one lone pair here's the seventh +electron no place to go and then the net + + align:start position:0% +electron no place to go and then the net + + + align:start position:0% +electron no place to go and then the net +negative charge is an electron and it's + + align:start position:0% +negative charge is an electron and it's + + + align:start position:0% +negative charge is an electron and it's +sitting in this so there's + + align:start position:0% +sitting in this so there's + + + align:start position:0% +sitting in this so there's +two non-bonding domains two non-bonding + + align:start position:0% +two non-bonding domains two non-bonding + + + align:start position:0% +two non-bonding domains two non-bonding +domains for a total of six so this means + + align:start position:0% +domains for a total of six so this means + + + align:start position:0% +domains for a total of six so this means +six electron domains so that means + + align:start position:0% +six electron domains so that means + + + align:start position:0% +six electron domains so that means +octahedral skeleton again now question + + align:start position:0% +octahedral skeleton again now question + + + align:start position:0% +octahedral skeleton again now question +where do I put the + + align:start position:0% +where do I put the + + + align:start position:0% +where do I put the +flines well you say yeah put them at the + + align:start position:0% +flines well you say yeah put them at the + + + align:start position:0% +flines well you say yeah put them at the +end somewhere so there's two + + align:start position:0% +end somewhere so there's two + + + align:start position:0% +end somewhere so there's two +possibilities now unlike the other case + + align:start position:0% +possibilities now unlike the other case + + + align:start position:0% +possibilities now unlike the other case +see I've got this possibility this is + + align:start position:0% +see I've got this possibility this is + + + align:start position:0% +see I've got this possibility this is +door number one this is door number one + + align:start position:0% +door number one this is door number one + + + align:start position:0% +door number one this is door number one +I put the flines in the + + align:start position:0% +I put the flines in the + + + align:start position:0% +I put the flines in the +plane okay and door number two it's the + + align:start position:0% +plane okay and door number two it's the + + + align:start position:0% +plane okay and door number two it's the +same electron structure I'll put the + + align:start position:0% +same electron structure I'll put the + + + align:start position:0% +same electron structure I'll put the +flines above and + + align:start position:0% +flines above and + + + align:start position:0% +flines above and +below and then I'll put + + align:start position:0% +below and then I'll put + + + align:start position:0% +below and then I'll put +the electron pairs next to one another + + align:start position:0% +the electron pairs next to one another + + + align:start position:0% +the electron pairs next to one another +these are distinguishable + + align:start position:0% +these are distinguishable + + + align:start position:0% +these are distinguishable +agreed so what's it tell you is it says + + align:start position:0% +agreed so what's it tell you is it says + + + align:start position:0% +agreed so what's it tell you is it says +number three is maximize separation + + align:start position:0% +number three is maximize separation + + + align:start position:0% +number three is maximize separation +between domains number four give more + + align:start position:0% +between domains number four give more + + + align:start position:0% +between domains number four give more +space to non-bonding + + align:start position:0% +space to non-bonding + + + align:start position:0% +space to non-bonding +domains non-bonding domains let's think + + align:start position:0% +domains non-bonding domains let's think + + + align:start position:0% +domains non-bonding domains let's think +about the physics behind that why + + align:start position:0% +about the physics behind that why + + + align:start position:0% +about the physics behind that why +electrons that are in non-bonding + + align:start position:0% +electrons that are in non-bonding + + + align:start position:0% +electrons that are in non-bonding +domains are sitting there with no + + align:start position:0% +domains are sitting there with no + + + align:start position:0% +domains are sitting there with no +interaction with a nucleus whereas the + + align:start position:0% +interaction with a nucleus whereas the + + + align:start position:0% +interaction with a nucleus whereas the +ones that are in bonding domains they're + + align:start position:0% +ones that are in bonding domains they're + + + align:start position:0% +ones that are in bonding domains they're +on this axis see I've got two electrons + + align:start position:0% +on this axis see I've got two electrons + + + align:start position:0% +on this axis see I've got two electrons +sitting in here but they're they're + + align:start position:0% +sitting in here but they're they're + + + align:start position:0% +sitting in here but they're they're +scrunched in in between nuclei whereas + + align:start position:0% +scrunched in in between nuclei whereas + + + align:start position:0% +scrunched in in between nuclei whereas +these are just hanging out there + + align:start position:0% +these are just hanging out there + + + align:start position:0% +these are just hanging out there +negative just brandishing this negative + + align:start position:0% +negative just brandishing this negative + + + align:start position:0% +negative just brandishing this negative +charge you see and here's another + + align:start position:0% +charge you see and here's another + + + align:start position:0% +charge you see and here's another +negative charge so what is it going to + + align:start position:0% +negative charge so what is it going to + + + align:start position:0% +negative charge so what is it going to +try to do it's going to try to get as + + align:start position:0% +try to do it's going to try to get as + + + align:start position:0% +try to do it's going to try to get as +far apart as possible so that's why that + + align:start position:0% +far apart as possible so that's why that + + + align:start position:0% +far apart as possible so that's why that +rule is there number four so which of + + align:start position:0% +rule is there number four so which of + + + align:start position:0% +rule is there number four so which of +these two configurations keeps these + + align:start position:0% +these two configurations keeps these + + + align:start position:0% +these two configurations keeps these +farther apart from one another door + + align:start position:0% +farther apart from one another door + + + align:start position:0% +farther apart from one another door +number one or door number + + align:start position:0% +number one or door number + + + align:start position:0% +number one or door number +two number one one's up here one's up + + align:start position:0% +two number one one's up here one's up + + + align:start position:0% +two number one one's up here one's up +here these two are too close together so + + align:start position:0% +here these two are too close together so + + + align:start position:0% +here these two are too close together so +this is not what happens and in fact + + align:start position:0% +this is not what happens and in fact + + + align:start position:0% +this is not what happens and in fact +this is the structure of tetrao iodate + + align:start position:0% +this is the structure of tetrao iodate + + + align:start position:0% +this is the structure of tetrao iodate +so what do we see all we see is the + + align:start position:0% +so what do we see all we see is the + + + align:start position:0% +so what do we see all we see is the +atoms the iodine the four flines they + + align:start position:0% +atoms the iodine the four flines they + + + align:start position:0% +atoms the iodine the four flines they +lie in a plane and what's the top view + + align:start position:0% +lie in a plane and what's the top view + + + align:start position:0% +lie in a plane and what's the top view +of this thing it's a it's just a simple + + align:start position:0% +of this thing it's a it's just a simple + + + align:start position:0% +of this thing it's a it's just a simple +regular cross so you have flines at four + + align:start position:0% +regular cross so you have flines at four + + + align:start position:0% +regular cross so you have flines at four +corners of a square iodine in the center + + align:start position:0% +corners of a square iodine in the center + + + align:start position:0% +corners of a square iodine in the center +this is called Square um planer this is + + align:start position:0% +this is called Square um planer this is + + + align:start position:0% +this is called Square um planer this is +a square planer + + align:start position:0% +a square planer + + + align:start position:0% +a square planer +molecule Square planer + + align:start position:0% + + + + align:start position:0% + +molecule polar or + + align:start position:0% + + + + align:start position:0% + +non-polar it's it's non-polar this is + + align:start position:0% +non-polar it's it's non-polar this is + + + align:start position:0% +non-polar it's it's non-polar this is +cool look it's net negative but it's + + align:start position:0% +cool look it's net negative but it's + + + align:start position:0% +cool look it's net negative but it's +non-polar so that means that even though + + align:start position:0% +non-polar so that means that even though + + + align:start position:0% +non-polar so that means that even though +it has a net negative charge if I get + + align:start position:0% +it has a net negative charge if I get + + + align:start position:0% +it has a net negative charge if I get +really far away how do I model that + + align:start position:0% +really far away how do I model that + + + align:start position:0% +really far away how do I model that +thing how do I model it when I get + + align:start position:0% +thing how do I model it when I get + + + align:start position:0% +thing how do I model it when I get +really far away this is what it looks + + align:start position:0% +really far away this is what it looks + + + align:start position:0% +really far away this is what it looks +like Point charge negative see way out + + align:start position:0% +like Point charge negative see way out + + + align:start position:0% +like Point charge negative see way out +here I don't I don't know I don't care + + align:start position:0% +here I don't I don't know I don't care + + + align:start position:0% +here I don't I don't know I don't care +what the internal structure looks like I + + align:start position:0% +what the internal structure looks like I + + + align:start position:0% +what the internal structure looks like I +don't care about the electron this all + + align:start position:0% +don't care about the electron this all + + + align:start position:0% +don't care about the electron this all +symmetric + + align:start position:0% +symmetric + + + align:start position:0% +symmetric +anyways very very good all right so + + align:start position:0% +anyways very very good all right so + + + align:start position:0% +anyways very very good all right so +let's look at one more + + align:start position:0% +let's look at one more + + + align:start position:0% +let's look at one more +this is too much fun this is too much + + align:start position:0% +this is too much fun this is too much + + + align:start position:0% +this is too much fun this is too much +fun all right so um these all had but so + + align:start position:0% +fun all right so um these all had but so + + + align:start position:0% +fun all right so um these all had but so +what's the punchline of this one here + + align:start position:0% +what's the punchline of this one here + + + align:start position:0% +what's the punchline of this one here +you see we had three sf6 brf5 if4 minus + + align:start position:0% +you see we had three sf6 brf5 if4 minus + + + align:start position:0% +you see we had three sf6 brf5 if4 minus +they all had octahedral skeletons but + + align:start position:0% +they all had octahedral skeletons but + + + align:start position:0% +they all had octahedral skeletons but +the molecular architecture was different + + align:start position:0% +the molecular architecture was different + + + align:start position:0% +the molecular architecture was different +because of the relative number of + + align:start position:0% +because of the relative number of + + + align:start position:0% +because of the relative number of +bonding and + + align:start position:0% +bonding and + + + align:start position:0% +bonding and +non-bonding domains but they all started + + align:start position:0% +non-bonding domains but they all started + + + align:start position:0% +non-bonding domains but they all started +with octahedral skeleton now I'm going + + align:start position:0% +with octahedral skeleton now I'm going + + + align:start position:0% +with octahedral skeleton now I'm going +to do something else now I'm going to + + align:start position:0% +to do something else now I'm going to + + + align:start position:0% +to do something else now I'm going to +compare this series that have the same + + align:start position:0% +compare this series that have the same + + + align:start position:0% +compare this series that have the same +um formula the same formula so let's do + + align:start position:0% +um formula the same formula so let's do + + + align:start position:0% +um formula the same formula so let's do +three tetrafluorides + + align:start position:0% +three tetrafluorides + + + align:start position:0% +three tetrafluorides +cf4 + + align:start position:0% +cf4 + + + align:start position:0% +cf4 +sf4 and tetrao + + align:start position:0% +sf4 and tetrao + + + align:start position:0% +sf4 and tetrao +iodate see they all have Tetra it's F + + align:start position:0% +iodate see they all have Tetra it's F + + + align:start position:0% +iodate see they all have Tetra it's F +it's + + align:start position:0% +it's + + + align:start position:0% +it's +F4 and you're I'm going to show you + + align:start position:0% +F4 and you're I'm going to show you + + + align:start position:0% +F4 and you're I'm going to show you +three different things well what's this + + align:start position:0% +three different things well what's this + + + align:start position:0% +three different things well what's this +one you know this one in your head this + + align:start position:0% +one you know this one in your head this + + + align:start position:0% +one you know this one in your head this +is tetrahedral right this one here I + + align:start position:0% +is tetrahedral right this one here I + + + align:start position:0% +is tetrahedral right this one here I +just write it by inspection boom boom + + align:start position:0% +just write it by inspection boom boom + + + align:start position:0% +just write it by inspection boom boom +boom boom that's done + + align:start position:0% +boom boom that's done + + + align:start position:0% +boom boom that's done +finished polar non-polar FL + + align:start position:0% +finished polar non-polar FL + + + align:start position:0% +finished polar non-polar FL +green strongly Electro negative but + + align:start position:0% +green strongly Electro negative but + + + align:start position:0% +green strongly Electro negative but +symmetric bonds non-polar and this one + + align:start position:0% +symmetric bonds non-polar and this one + + + align:start position:0% +symmetric bonds non-polar and this one +we just did so if your memory is good + + align:start position:0% +we just did so if your memory is good + + + align:start position:0% +we just did so if your memory is good +you know that this one's Square + + align:start position:0% + + + + align:start position:0% + +planer okay now so let's do sf4 what's + + align:start position:0% +planer okay now so let's do sf4 what's + + + align:start position:0% +planer okay now so let's do sf4 what's +sf4 looks like what does it look like it + + align:start position:0% +sf4 looks like what does it look like it + + + align:start position:0% +sf4 looks like what does it look like it +looks something like this uh we start + + align:start position:0% +looks something like this uh we start + + + align:start position:0% +looks something like this uh we start +with the Le structure that's what it + + align:start position:0% +with the Le structure that's what it + + + align:start position:0% +with the Le structure that's what it +says up there so sulfur one two 3 four + + align:start position:0% +says up there so sulfur one two 3 four + + + align:start position:0% +says up there so sulfur one two 3 four +five six and Florin I'm going to put f f + + align:start position:0% +five six and Florin I'm going to put f f + + + align:start position:0% +five six and Florin I'm going to put f f +f and + + align:start position:0% +f and + + + align:start position:0% +f and +f uh actually I know what's coming I'm + + align:start position:0% +f uh actually I know what's coming I'm + + + align:start position:0% +f uh actually I know what's coming I'm +going to put the F over here + + align:start position:0% + + + + align:start position:0% + +so so there's seven Florine electrons + + align:start position:0% +so so there's seven Florine electrons + + + align:start position:0% +so so there's seven Florine electrons +from Florine and then the uh one from + + align:start position:0% +from Florine and then the uh one from + + + align:start position:0% +from Florine and then the uh one from +the sulfur makes eight so we have a + + align:start position:0% +the sulfur makes eight so we have a + + + align:start position:0% +the sulfur makes eight so we have a +bonding domain here octet stability and + + align:start position:0% +bonding domain here octet stability and + + + align:start position:0% +bonding domain here octet stability and +likewise the same will happen here + + align:start position:0% +likewise the same will happen here + + + align:start position:0% +likewise the same will happen here +here and + + align:start position:0% +here and + + + align:start position:0% +here and +here so what do we have 2 4 6 8 and two + + align:start position:0% +here so what do we have 2 4 6 8 and two + + + align:start position:0% +here so what do we have 2 4 6 8 and two +of the electrons from The sulfur are not + + align:start position:0% +of the electrons from The sulfur are not + + + align:start position:0% +of the electrons from The sulfur are not +involved in bonding so they constitute a + + align:start position:0% +involved in bonding so they constitute a + + + align:start position:0% +involved in bonding so they constitute a +non-bonding pair so I've got 2 4 6 8 10 + + align:start position:0% +non-bonding pair so I've got 2 4 6 8 10 + + + align:start position:0% +non-bonding pair so I've got 2 4 6 8 10 +I've got 10 uh bonding 10 electrons or + + align:start position:0% +I've got 10 uh bonding 10 electrons or + + + align:start position:0% +I've got 10 uh bonding 10 electrons or +let's say five electron domains there's + + align:start position:0% +let's say five electron domains there's + + + align:start position:0% +let's say five electron domains there's +five electron domains here that's + + align:start position:0% +five electron domains here that's + + + align:start position:0% +five electron domains here that's +different see here there's four electron + + align:start position:0% +different see here there's four electron + + + align:start position:0% +different see here there's four electron +domains here there's six electron + + align:start position:0% +domains here there's six electron + + + align:start position:0% +domains here there's six electron +domains + + align:start position:0% +domains + + + align:start position:0% +domains +4 Ed and they're all bonding and four + + align:start position:0% +4 Ed and they're all bonding and four + + + align:start position:0% +4 Ed and they're all bonding and four +bonding here is 6 Ed and for bonding and + + align:start position:0% +bonding here is 6 Ed and for bonding and + + + align:start position:0% +bonding here is 6 Ed and for bonding and +this is five Ed five electron domains + + align:start position:0% +this is five Ed five electron domains + + + align:start position:0% +this is five Ed five electron domains +for bonding gee they're all + + align:start position:0% +for bonding gee they're all + + + align:start position:0% +for bonding gee they're all +tetrafluoride and I've just proved that + + align:start position:0% +tetrafluoride and I've just proved that + + + align:start position:0% +tetrafluoride and I've just proved that +if you have four flines you got four + + align:start position:0% +if you have four flines you got four + + + align:start position:0% +if you have four flines you got four +bonds this is really consistent it's not + + align:start position:0% +bonds this is really consistent it's not + + + align:start position:0% +bonds this is really consistent it's not +terribly deep but anyways okay so here + + align:start position:0% +terribly deep but anyways okay so here + + + align:start position:0% +terribly deep but anyways okay so here +we are here we are no it's important at + + align:start position:0% +we are here we are no it's important at + + + align:start position:0% +we are here we are no it's important at +the end of the day you know at these + + align:start position:0% +the end of the day you know at these + + + align:start position:0% +the end of the day you know at these +things rationalized Okay so we've got + + align:start position:0% +things rationalized Okay so we've got + + + align:start position:0% +things rationalized Okay so we've got +four bonding and one + + align:start position:0% +four bonding and one + + + align:start position:0% +four bonding and one +nonbonding one non-bonding so how do I + + align:start position:0% +nonbonding one non-bonding so how do I + + + align:start position:0% +nonbonding one non-bonding so how do I +take if I have a central atom here how + + align:start position:0% +take if I have a central atom here how + + + align:start position:0% +take if I have a central atom here how +do I put five struts off it equally uh + + align:start position:0% +do I put five struts off it equally uh + + + align:start position:0% +do I put five struts off it equally uh +spaced so that's going to mean one two + + align:start position:0% +spaced so that's going to mean one two + + + align:start position:0% +spaced so that's going to mean one two +three in the plane one above and one + + align:start position:0% +three in the plane one above and one + + + align:start position:0% +three in the plane one above and one +below that's five okay so this is called + + align:start position:0% +below that's five okay so this is called + + + align:start position:0% +below that's five okay so this is called +uh you know the F the five struts this + + align:start position:0% +uh you know the F the five struts this + + + align:start position:0% +uh you know the F the five struts this +is called uh trigonal by pyramid and how + + align:start position:0% +is called uh trigonal by pyramid and how + + + align:start position:0% +is called uh trigonal by pyramid and how +do they get that if you look at the + + align:start position:0% +do they get that if you look at the + + + align:start position:0% +do they get that if you look at the +plane you can join the three in the + + align:start position:0% +plane you can join the three in the + + + align:start position:0% +plane you can join the three in the +plane this is 120° agreed if I'm looking + + align:start position:0% +plane this is 120° agreed if I'm looking + + + align:start position:0% +plane this is 120° agreed if I'm looking +down on this plane and now what I can do + + align:start position:0% +down on this plane and now what I can do + + + align:start position:0% +down on this plane and now what I can do +is I can make a pyramid here but this is + + align:start position:0% +is I can make a pyramid here but this is + + + align:start position:0% +is I can make a pyramid here but this is +a pyramid that has three faces so I've + + align:start position:0% +a pyramid that has three faces so I've + + + align:start position:0% +a pyramid that has three faces so I've +got this is called a trigonal pyramid + + align:start position:0% +got this is called a trigonal pyramid + + + align:start position:0% +got this is called a trigonal pyramid +this is a trigonal pyramid but this this + + align:start position:0% +this is a trigonal pyramid but this this + + + align:start position:0% +this is a trigonal pyramid but this this +would have above and below so it's a + + align:start position:0% +would have above and below so it's a + + + align:start position:0% +would have above and below so it's a +trigonal by pyramid trigonal B pyramid + + align:start position:0% +trigonal by pyramid trigonal B pyramid + + + align:start position:0% +trigonal by pyramid trigonal B pyramid +that's a fancy name for something that's + + align:start position:0% +that's a fancy name for something that's + + + align:start position:0% +that's a fancy name for something that's +got five struts sticking out of a simple + + align:start position:0% +got five struts sticking out of a simple + + + align:start position:0% +got five struts sticking out of a simple +atom okay trigonal by pyramid so now + + align:start position:0% +atom okay trigonal by pyramid so now + + + align:start position:0% +atom okay trigonal by pyramid so now +what are we going to do we're going to + + align:start position:0% +what are we going to do we're going to + + + align:start position:0% +what are we going to do we're going to +now put uh we're going to put the + + align:start position:0% +now put uh we're going to put the + + + align:start position:0% +now put uh we're going to put the +um got to put the + + align:start position:0% + + + + align:start position:0% + +flines so we've got two choices again + + align:start position:0% +flines so we've got two choices again + + + align:start position:0% +flines so we've got two choices again +we've got sulfur in the + + align:start position:0% +we've got sulfur in the + + + align:start position:0% +we've got sulfur in the +center 1 2 3 4 5 so here's one + + align:start position:0% +center 1 2 3 4 5 so here's one + + + align:start position:0% +center 1 2 3 4 5 so here's one +possibility is to put the the um + + align:start position:0% +possibility is to put the the um + + + align:start position:0% +possibility is to put the the um +non-bonding electrons in the in the the + + align:start position:0% +non-bonding electrons in the in the the + + + align:start position:0% +non-bonding electrons in the in the the +plane with the other + + align:start position:0% +plane with the other + + + align:start position:0% +plane with the other +flines this is called the equatorial + + align:start position:0% +flines this is called the equatorial + + + align:start position:0% +flines this is called the equatorial +position if you think of this as the + + align:start position:0% +position if you think of this as the + + + align:start position:0% +position if you think of this as the +globe okay there's North Pole South Pole + + align:start position:0% +globe okay there's North Pole South Pole + + + align:start position:0% +globe okay there's North Pole South Pole +and these three lie at the Equator so + + align:start position:0% +and these three lie at the Equator so + + + align:start position:0% +and these three lie at the Equator so +this is called the equatorial + + align:start position:0% +this is called the equatorial + + + align:start position:0% +this is called the equatorial +position this is equatorial so that's + + align:start position:0% +position this is equatorial so that's + + + align:start position:0% +position this is equatorial so that's +one possibility the other possibility is + + align:start position:0% +one possibility the other possibility is + + + align:start position:0% +one possibility the other possibility is +to put the lone pair either at the North + + align:start position:0% +to put the lone pair either at the North + + + align:start position:0% +to put the lone pair either at the North +Pole or the South + + align:start position:0% +Pole or the South + + + align:start position:0% +Pole or the South +Pole and if we use the same idea as + + align:start position:0% +Pole and if we use the same idea as + + + align:start position:0% +Pole and if we use the same idea as +before in other words we try to minimize + + align:start position:0% +before in other words we try to minimize + + + align:start position:0% +before in other words we try to minimize +the interaction between the uh unpaired + + align:start position:0% +the interaction between the uh unpaired + + + align:start position:0% +the interaction between the uh unpaired +electrons excuse me the the the + + align:start position:0% +electrons excuse me the the the + + + align:start position:0% +electrons excuse me the the the +non-bonding electrons and other atoms + + align:start position:0% +non-bonding electrons and other atoms + + + align:start position:0% +non-bonding electrons and other atoms +which one is going to give this less + + align:start position:0% +which one is going to give this less + + + align:start position:0% +which one is going to give this less +contact with its neighbors door number + + align:start position:0% +contact with its neighbors door number + + + align:start position:0% +contact with its neighbors door number +one or door number + + align:start position:0% +one or door number + + + align:start position:0% +one or door number +two see this one has actually your book + + align:start position:0% +two see this one has actually your book + + + align:start position:0% +two see this one has actually your book +even shows a little cartoon for this see + + align:start position:0% +even shows a little cartoon for this see + + + align:start position:0% +even shows a little cartoon for this see +if you put if you put it at equatorial + + align:start position:0% +if you put if you put it at equatorial + + + align:start position:0% +if you put if you put it at equatorial +position it's it's got two if you like + + align:start position:0% +position it's it's got two if you like + + + align:start position:0% +position it's it's got two if you like +two nearest flines okay whereas if if + + align:start position:0% +two nearest flines okay whereas if if + + + align:start position:0% +two nearest flines okay whereas if if +you put it at a polar location it's got + + align:start position:0% +you put it at a polar location it's got + + + align:start position:0% +you put it at a polar location it's got +three nearest fluin so if we use that + + align:start position:0% +three nearest fluin so if we use that + + + align:start position:0% +three nearest fluin so if we use that +this is called polar by that by that + + align:start position:0% +this is called polar by that by that + + + align:start position:0% +this is called polar by that by that +analysis door number one should be a + + align:start position:0% +analysis door number one should be a + + + align:start position:0% +analysis door number one should be a +minimal interaction and in fact that was + + align:start position:0% +minimal interaction and in fact that was + + + align:start position:0% +minimal interaction and in fact that was +one of the that was one of the things + + align:start position:0% +one of the that was one of the things + + + align:start position:0% +one of the that was one of the things +that we were told to do you see Place + + align:start position:0% +that we were told to do you see Place + + + align:start position:0% +that we were told to do you see Place +non-bonding domains this is rule number + + align:start position:0% +non-bonding domains this is rule number + + + align:start position:0% +non-bonding domains this is rule number +five non-bonding domains at equatorial + + align:start position:0% +five non-bonding domains at equatorial + + + align:start position:0% +five non-bonding domains at equatorial +positions in a trigonal B + + align:start position:0% +positions in a trigonal B + + + align:start position:0% +positions in a trigonal B +pyramid that's what you say if someone + + align:start position:0% +pyramid that's what you say if someone + + + align:start position:0% +pyramid that's what you say if someone +asks you to say something you know into + + align:start position:0% +asks you to say something you know into + + + align:start position:0% +asks you to say something you know into +a microphone just say that and + + align:start position:0% +a microphone just say that and + + + align:start position:0% +a microphone just say that and +okay and uh so so that means that means + + align:start position:0% +okay and uh so so that means that means + + + align:start position:0% +okay and uh so so that means that means +the molecule is going to look like + + align:start position:0% + + + + align:start position:0% + +this and this molecule is called seesaw + + align:start position:0% +this and this molecule is called seesaw + + + align:start position:0% +this and this molecule is called seesaw +seesaw or teeter totter because you + + align:start position:0% +seesaw or teeter totter because you + + + align:start position:0% +seesaw or teeter totter because you +don't see the non-bonding pair here your + + align:start position:0% +don't see the non-bonding pair here your + + + align:start position:0% +don't see the non-bonding pair here your +characterization apparatus would would + + align:start position:0% +characterization apparatus would would + + + align:start position:0% +characterization apparatus would would +find Florine sulfur Florine and then + + align:start position:0% +find Florine sulfur Florine and then + + + align:start position:0% +find Florine sulfur Florine and then +these two are underneath like a saw hor + + align:start position:0% +these two are underneath like a saw hor + + + align:start position:0% +these two are underneath like a saw hor +at + + align:start position:0% +at + + + align:start position:0% +at +120° and how about is this is this pole + + align:start position:0% +120° and how about is this is this pole + + + align:start position:0% +120° and how about is this is this pole +or + + align:start position:0% +or + + + align:start position:0% +or +nonpolar this is polar because I've got + + align:start position:0% +nonpolar this is polar because I've got + + + align:start position:0% +nonpolar this is polar because I've got +electrons over here so I could model + + align:start position:0% +electrons over here so I could model + + + align:start position:0% +electrons over here so I could model +this as a dipole or in this + + align:start position:0% +this as a dipole or in this + + + align:start position:0% +this as a dipole or in this +fashion + + align:start position:0% +fashion + + + align:start position:0% +fashion +okay so this has been really good see + + align:start position:0% +okay so this has been really good see + + + align:start position:0% +okay so this has been really good see +what else do we + + align:start position:0% +what else do we + + + align:start position:0% +what else do we +have so so far I've been doing this with + + align:start position:0% +have so so far I've been doing this with + + + align:start position:0% +have so so far I've been doing this with +um uh + + align:start position:0% +um uh + + + align:start position:0% +um uh +heteronuclear molecules but we can do + + align:start position:0% +heteronuclear molecules but we can do + + + align:start position:0% +heteronuclear molecules but we can do +this with homonuclear molecules so I + + align:start position:0% +this with homonuclear molecules so I + + + align:start position:0% +this with homonuclear molecules so I +want to show you um the two two + + align:start position:0% +want to show you um the two two + + + align:start position:0% +want to show you um the two two +conditions look at + + align:start position:0% +conditions look at + + + align:start position:0% +conditions look at +sp3 and I will look at + + align:start position:0% +sp3 and I will look at + + + align:start position:0% +sp3 and I will look at +SP2 all right I'm going to work with + + align:start position:0% +SP2 all right I'm going to work with + + + align:start position:0% +SP2 all right I'm going to work with +carbon alone no hydrogen so sp3 I start + + align:start position:0% +carbon alone no hydrogen so sp3 I start + + + align:start position:0% +carbon alone no hydrogen so sp3 I start +with the central carbon sp3 hybridized + + align:start position:0% +with the central carbon sp3 hybridized + + + align:start position:0% +with the central carbon sp3 hybridized +and carbon goes + + align:start position:0% +and carbon goes + + + align:start position:0% +and carbon goes +everywhere so each carbon has four + + align:start position:0% +everywhere so each carbon has four + + + align:start position:0% +everywhere so each carbon has four +nearest neighbors and they're all at 109 + + align:start position:0% +nearest neighbors and they're all at 109 + + + align:start position:0% +nearest neighbors and they're all at 109 +degrees and they all have the same strut + + align:start position:0% +degrees and they all have the same strut + + + align:start position:0% +degrees and they all have the same strut +length the same Bond length 1 2 3 4 and + + align:start position:0% +length the same Bond length 1 2 3 4 and + + + align:start position:0% +length the same Bond length 1 2 3 4 and +so on carbon here carbon up here and + + align:start position:0% +so on carbon here carbon up here and + + + align:start position:0% +so on carbon here carbon up here and +these are going in and out of the board + + align:start position:0% +these are going in and out of the board + + + align:start position:0% +these are going in and out of the board +but I think you can see that one thing + + align:start position:0% +but I think you can see that one thing + + + align:start position:0% +but I think you can see that one thing +is certain there will be regular arrays + + align:start position:0% +is certain there will be regular arrays + + + align:start position:0% +is certain there will be regular arrays +in three dimensions regular + + align:start position:0% +in three dimensions regular + + + align:start position:0% +in three dimensions regular +arrays regular 3D + + align:start position:0% +arrays regular 3D + + + align:start position:0% +arrays regular 3D +array and if you look at this from a + + align:start position:0% +array and if you look at this from a + + + align:start position:0% +array and if you look at this from a +distance what you'll find is this is + + align:start position:0% +distance what you'll find is this is + + + align:start position:0% +distance what you'll find is this is +forming the diamond cubic crystal + + align:start position:0% +forming the diamond cubic crystal + + + align:start position:0% +forming the diamond cubic crystal +structure Diamond cubic crystal + + align:start position:0% +structure Diamond cubic crystal + + + align:start position:0% +structure Diamond cubic crystal +structure + + align:start position:0% + + + + align:start position:0% + +in this instance carbon is hybridized + + align:start position:0% +in this instance carbon is hybridized + + + align:start position:0% +in this instance carbon is hybridized +sp3 and the consequence of that is um + + align:start position:0% +sp3 and the consequence of that is um + + + align:start position:0% +sp3 and the consequence of that is um +Diamond cubic now if carbon instead + + align:start position:0% +Diamond cubic now if carbon instead + + + align:start position:0% +Diamond cubic now if carbon instead +hybridizes SP2 we know that we have + + align:start position:0% +hybridizes SP2 we know that we have + + + align:start position:0% +hybridizes SP2 we know that we have +three bonds identical lying in the plane + + align:start position:0% +three bonds identical lying in the plane + + + align:start position:0% +three bonds identical lying in the plane +so this let's do that one so here's + + align:start position:0% + + + + align:start position:0% + +carbon carbon carbon carbon and then + + align:start position:0% +carbon carbon carbon carbon and then + + + align:start position:0% +carbon carbon carbon carbon and then +this one has one two and three over to + + align:start position:0% +this one has one two and three over to + + + align:start position:0% +this one has one two and three over to +here + + align:start position:0% + + + + align:start position:0% + +okay and what are we seeing here we're + + align:start position:0% +okay and what are we seeing here we're + + + align:start position:0% +okay and what are we seeing here we're +seeing a hexagonal pattern aren't we + + align:start position:0% +seeing a hexagonal pattern aren't we + + + align:start position:0% +seeing a hexagonal pattern aren't we +this is now this is just three of the + + align:start position:0% +this is now this is just three of the + + + align:start position:0% +this is now this is just three of the +bonds but I said look remember you got + + align:start position:0% +bonds but I said look remember you got + + + align:start position:0% +bonds but I said look remember you got +to keep me honest here look at this + + align:start position:0% +to keep me honest here look at this + + + align:start position:0% +to keep me honest here look at this +carbon how many sticks off of the carbon + + align:start position:0% +carbon how many sticks off of the carbon + + + align:start position:0% +carbon how many sticks off of the carbon +one two three I told you we better have + + align:start position:0% +one two three I told you we better have + + + align:start position:0% +one two three I told you we better have +four we better have four I only got + + align:start position:0% +four we better have four I only got + + + align:start position:0% +four we better have four I only got +three so what what happened where what + + align:start position:0% +three so what what happened where what + + + align:start position:0% +three so what what happened where what +where's the where's the last stick well + + align:start position:0% +where's the where's the last stick well + + + align:start position:0% +where's the where's the last stick well +I've taken I've taken this configuration + + align:start position:0% +I've taken I've taken this configuration + + + align:start position:0% +I've taken I've taken this configuration +over here all right S and P and I've + + align:start position:0% +over here all right S and P and I've + + + align:start position:0% +over here all right S and P and I've +mixed them to get SP2 that means there + + align:start position:0% +mixed them to get SP2 that means there + + + align:start position:0% +mixed them to get SP2 that means there +must be some p orbital here somewhere + + align:start position:0% +must be some p orbital here somewhere + + + align:start position:0% +must be some p orbital here somewhere +and where is it well it's sitting right + + align:start position:0% +and where is it well it's sitting right + + + align:start position:0% +and where is it well it's sitting right +here there's a p orbital here and + + align:start position:0% +here there's a p orbital here and + + + align:start position:0% +here there's a p orbital here and +there's a p orbital here and there's a p + + align:start position:0% +there's a p orbital here and there's a p + + + align:start position:0% +there's a p orbital here and there's a p +orbital here and there's a p orbital + + align:start position:0% +orbital here and there's a p orbital + + + align:start position:0% +orbital here and there's a p orbital +here and a p orbital here and a p + + align:start position:0% +here and a p orbital here and a p + + + align:start position:0% +here and a p orbital here and a p +orbital here and so on and so on and so + + align:start position:0% +orbital here and so on and so on and so + + + align:start position:0% +orbital here and so on and so on and so +on and it turns out that the bond length + + align:start position:0% +on and it turns out that the bond length + + + align:start position:0% +on and it turns out that the bond length +is such that these P orbitals are able + + align:start position:0% +is such that these P orbitals are able + + + align:start position:0% +is such that these P orbitals are able +are able to + + align:start position:0% +are able to + + + align:start position:0% +are able to +bond cooperatively okay and so they form + + align:start position:0% +bond cooperatively okay and so they form + + + align:start position:0% +bond cooperatively okay and so they form +p + + align:start position:0% +p + + + align:start position:0% +p +P bonds are are + + align:start position:0% + + + + align:start position:0% + +cooperative and they're so Cooperative + + align:start position:0% +cooperative and they're so Cooperative + + + align:start position:0% +cooperative and they're so Cooperative +that the electrons are not associated + + align:start position:0% +that the electrons are not associated + + + align:start position:0% +that the electrons are not associated +with any particular Bond we say that the + + align:start position:0% +with any particular Bond we say that the + + + align:start position:0% +with any particular Bond we say that the +electrons are + + align:start position:0% +electrons are + + + align:start position:0% +electrons are +delocalized and we'll see a little bit + + align:start position:0% +delocalized and we'll see a little bit + + + align:start position:0% +delocalized and we'll see a little bit +more of that later but you might as well + + align:start position:0% +more of that later but you might as well + + + align:start position:0% +more of that later but you might as well +learn it now they're + + align:start position:0% +learn it now they're + + + align:start position:0% +learn it now they're +delocalized this is the structure of + + align:start position:0% +delocalized this is the structure of + + + align:start position:0% +delocalized this is the structure of +graphite this is the structure of + + align:start position:0% +graphite this is the structure of + + + align:start position:0% +graphite this is the structure of +graphite and what do we have here we + + align:start position:0% +graphite and what do we have here we + + + align:start position:0% +graphite and what do we have here we +have strong Cove valent Bonds in the + + align:start position:0% +have strong Cove valent Bonds in the + + + align:start position:0% +have strong Cove valent Bonds in the +plane and then we have these weak de + + align:start position:0% +plane and then we have these weak de + + + align:start position:0% +plane and then we have these weak de +localized bonds normal to the plane so + + align:start position:0% +localized bonds normal to the plane so + + + align:start position:0% +localized bonds normal to the plane so +the planes can slide over one another + + align:start position:0% +the planes can slide over one another + + + align:start position:0% +the planes can slide over one another +which is what gives graphite its + + align:start position:0% +which is what gives graphite its + + + align:start position:0% +which is what gives graphite its +lubricity that's why you you squirt + + align:start position:0% +lubricity that's why you you squirt + + + align:start position:0% +lubricity that's why you you squirt +graphite powder into a lock in the + + align:start position:0% +graphite powder into a lock in the + + + align:start position:0% +graphite powder into a lock in the +winter time to give it some uh + + align:start position:0% +winter time to give it some uh + + + align:start position:0% +winter time to give it some uh +lubrication so these Glide over one + + align:start position:0% +lubrication so these Glide over one + + + align:start position:0% +lubrication so these Glide over one +another and furthermore it's not only + + align:start position:0% +another and furthermore it's not only + + + align:start position:0% +another and furthermore it's not only +lubricity you get electronic conduction + + align:start position:0% +lubricity you get electronic conduction + + + align:start position:0% +lubricity you get electronic conduction +and graphite has a mildly decent + + align:start position:0% +and graphite has a mildly decent + + + align:start position:0% +and graphite has a mildly decent +electronic conductivity unlike diamond + + align:start position:0% +electronic conductivity unlike diamond + + + align:start position:0% +electronic conductivity unlike diamond +where all of the electrons are tightly + + align:start position:0% +where all of the electrons are tightly + + + align:start position:0% +where all of the electrons are tightly +bound very tightly bound and by the way + + align:start position:0% +bound very tightly bound and by the way + + + align:start position:0% +bound very tightly bound and by the way +these bonds are very very strong the + + align:start position:0% +these bonds are very very strong the + + + align:start position:0% +these bonds are very very strong the +planes the bonds in the plane of + + align:start position:0% +planes the bonds in the plane of + + + align:start position:0% +planes the bonds in the plane of +graphite are extremely strong but plane + + align:start position:0% +graphite are extremely strong but plane + + + align:start position:0% +graphite are extremely strong but plane +to plane they Glide okay so you can + + align:start position:0% +to plane they Glide okay so you can + + + align:start position:0% +to plane they Glide okay so you can +think of these almost diamondlike + + align:start position:0% +think of these almost diamondlike + + + align:start position:0% +think of these almost diamondlike +rafts terms of the bond strength but + + align:start position:0% +rafts terms of the bond strength but + + + align:start position:0% +rafts terms of the bond strength but +these are flat and these are + + align:start position:0% +these are flat and these are + + + align:start position:0% +these are flat and these are +three-dimensional the other thing that + + align:start position:0% +three-dimensional the other thing that + + + align:start position:0% +three-dimensional the other thing that +happens is you have really really tight + + align:start position:0% +happens is you have really really tight + + + align:start position:0% +happens is you have really really tight +bonds what's this Optical properties + + align:start position:0% +bonds what's this Optical properties + + + align:start position:0% +bonds what's this Optical properties +here this one is transparent to visible + + align:start position:0% +here this one is transparent to visible + + + align:start position:0% +here this one is transparent to visible +light why electrons are tightly bound so + + align:start position:0% +light why electrons are tightly bound so + + + align:start position:0% +light why electrons are tightly bound so +you got + + align:start position:0% +you got + + + align:start position:0% +you got +this this uh really weak Photon visible + + align:start position:0% +this this uh really weak Photon visible + + + align:start position:0% +this this uh really weak Photon visible +light two electron V two electron volt + + align:start position:0% +light two electron V two electron volt + + + align:start position:0% +light two electron V two electron volt +Photon comes in and it can't excite + + align:start position:0% +Photon comes in and it can't excite + + + align:start position:0% +Photon comes in and it can't excite +anything but the bonds are so strong + + align:start position:0% +anything but the bonds are so strong + + + align:start position:0% +anything but the bonds are so strong +that it it it's refracted so one of the + + align:start position:0% +that it it it's refracted so one of the + + + align:start position:0% +that it it it's refracted so one of the +properties this is a very high + + align:start position:0% +properties this is a very high + + + align:start position:0% +properties this is a very high +refractive index very high refractive + + align:start position:0% +refractive index very high refractive + + + align:start position:0% +refractive index very high refractive +index whereas here electronic conduction + + align:start position:0% +index whereas here electronic conduction + + + align:start position:0% +index whereas here electronic conduction +means it's got very very + + align:start position:0% +means it's got very very + + + align:start position:0% +means it's got very very +low excitation and hence graphite is an + + align:start position:0% +low excitation and hence graphite is an + + + align:start position:0% +low excitation and hence graphite is an +absorber it appears black because any + + align:start position:0% +absorber it appears black because any + + + align:start position:0% +absorber it appears black because any +light that shines on it is + + align:start position:0% +light that shines on it is + + + align:start position:0% +light that shines on it is +absorbed see everything comes from the + + align:start position:0% +absorbed see everything comes from the + + + align:start position:0% +absorbed see everything comes from the +elect the electronic properties you can + + align:start position:0% +elect the electronic properties you can + + + align:start position:0% +elect the electronic properties you can +explain that it's lubricity and you can + + align:start position:0% +explain that it's lubricity and you can + + + align:start position:0% +explain that it's lubricity and you can +explain its electronic conduction and + + align:start position:0% +explain its electronic conduction and + + + align:start position:0% +explain its electronic conduction and +you can explain its absorption + + align:start position:0% +you can explain its absorption + + + align:start position:0% +you can explain its absorption +absorption of + + align:start position:0% + + + + align:start position:0% + +photons now elect I mentioned + + align:start position:0% +photons now elect I mentioned + + + align:start position:0% +photons now elect I mentioned +Electronics here and the the impact on + + align:start position:0% +Electronics here and the the impact on + + + align:start position:0% +Electronics here and the the impact on +photonics you see high index of fraction + + align:start position:0% +photonics you see high index of fraction + + + align:start position:0% +photonics you see high index of fraction +this is socially a very dangerous + + align:start position:0% +this is socially a very dangerous + + + align:start position:0% +this is socially a very dangerous +quantity because what happens is this is + + align:start position:0% +quantity because what happens is this is + + + align:start position:0% +quantity because what happens is this is +what makes Diamond so precious it's not + + align:start position:0% +what makes Diamond so precious it's not + + + align:start position:0% +what makes Diamond so precious it's not +just that it's rare it's how it + + align:start position:0% +just that it's rare it's how it + + + align:start position:0% +just that it's rare it's how it +functions in society it takes a small + + align:start position:0% +functions in society it takes a small + + + align:start position:0% +functions in society it takes a small +amount of diamond you know you're + + align:start position:0% +amount of diamond you know you're + + + align:start position:0% +amount of diamond you know you're +sitting you're just minding your own + + align:start position:0% +sitting you're just minding your own + + + align:start position:0% +sitting you're just minding your own +business you just went out just want to + + align:start position:0% +business you just went out just want to + + + align:start position:0% +business you just went out just want to +have a drink you're sitting there + + align:start position:0% +have a drink you're sitting there + + + align:start position:0% +have a drink you're sitting there +there's some gal sitting over in the + + align:start position:0% +there's some gal sitting over in the + + + align:start position:0% +there's some gal sitting over in the +corner this dimly lit Cafe she's got a + + align:start position:0% +corner this dimly lit Cafe she's got a + + + align:start position:0% +corner this dimly lit Cafe she's got a +diamond stud on that diamond stud takes + + align:start position:0% +diamond stud on that diamond stud takes + + + align:start position:0% +diamond stud on that diamond stud takes +a tiny tiny amount of lumens and thanks + + align:start position:0% +a tiny tiny amount of lumens and thanks + + + align:start position:0% +a tiny tiny amount of lumens and thanks +to this in CID property concentrates + + align:start position:0% +to this in CID property concentrates + + + align:start position:0% +to this in CID property concentrates +them and then shoots them across catches + + align:start position:0% +them and then shoots them across catches + + + align:start position:0% +them and then shoots them across catches +your eye and then the trouble starts + + align:start position:0% +your eye and then the trouble starts + + + align:start position:0% +your eye and then the trouble starts +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +this this sp3 hybridized carbon is very + + align:start position:0% +this this sp3 hybridized carbon is very + + + align:start position:0% +this this sp3 hybridized carbon is very +dangerous owing to this property now I + + align:start position:0% +dangerous owing to this property now I + + + align:start position:0% +dangerous owing to this property now I +draw your attention to the periodic + + align:start position:0% +draw your attention to the periodic + + + align:start position:0% +draw your attention to the periodic +table you know it may happen that some + + align:start position:0% +table you know it may happen that some + + + align:start position:0% +table you know it may happen that some +of you uh are going to feel compelled to + + align:start position:0% +of you uh are going to feel compelled to + + + align:start position:0% +of you uh are going to feel compelled to +uh make a long-term commitment to + + align:start position:0% +uh make a long-term commitment to + + + align:start position:0% +uh make a long-term commitment to +another person and and initiate that + + align:start position:0% +another person and and initiate that + + + align:start position:0% +another person and and initiate that +commitment with the presentation of a + + align:start position:0% +commitment with the presentation of a + + + align:start position:0% +commitment with the presentation of a +stone a stone typically made of diamond + + align:start position:0% +stone a stone typically made of diamond + + + align:start position:0% +stone a stone typically made of diamond +well I draw your attention to the fact + + align:start position:0% +well I draw your attention to the fact + + + align:start position:0% +well I draw your attention to the fact +that at room temperature the stable form + + align:start position:0% +that at room temperature the stable form + + + align:start position:0% +that at room temperature the stable form +of carbon is graphite now I want you to + + align:start position:0% +of carbon is graphite now I want you to + + + align:start position:0% +of carbon is graphite now I want you to +think about this if you want to present + + align:start position:0% +think about this if you want to present + + + align:start position:0% +think about this if you want to present +a ring that contains the stone that's + + align:start position:0% +a ring that contains the stone that's + + + align:start position:0% +a ring that contains the stone that's +symbolic of eternal love doesn't it make + + align:start position:0% +symbolic of eternal love doesn't it make + + + align:start position:0% +symbolic of eternal love doesn't it make +sense to present the stable form not the + + align:start position:0% +sense to present the stable form not the + + + align:start position:0% +sense to present the stable form not the +metastable + + align:start position:0% +metastable + + + align:start position:0% +metastable +form I mean I just I was just thinking + + align:start position:0% +form I mean I just I was just thinking + + + align:start position:0% +form I mean I just I was just thinking +about this but I mean know so my point + + align:start position:0% +about this but I mean know so my point + + + align:start position:0% +about this but I mean know so my point +is that this is the stable form I've + + align:start position:0% +is that this is the stable form I've + + + align:start position:0% +is that this is the stable form I've +done my part to explain it in terms of + + align:start position:0% +done my part to explain it in terms of + + + align:start position:0% +done my part to explain it in terms of +SP2 hybridization I leave it up to you + + align:start position:0% +SP2 hybridization I leave it up to you + + + align:start position:0% +SP2 hybridization I leave it up to you +to explain it to your sweetheart okay + + align:start position:0% +to explain it to your sweetheart okay + + + align:start position:0% +to explain it to your sweetheart okay +you have a nice day \ No newline at end of file diff --git a/eKlM1XRS3mg.txt b/eKlM1XRS3mg.txt new file mode 100644 index 0000000000000000000000000000000000000000..9db5a855cc05cf94875b0f22b8062b545c64b820 --- /dev/null +++ b/eKlM1XRS3mg.txt @@ -0,0 +1,1163 @@ +align:start position:0% + +hi everyone um in this video we're going + + align:start position:0% +hi everyone um in this video we're going + + + align:start position:0% +hi everyone um in this video we're going +to explore briefly the concept of a + + align:start position:0% +to explore briefly the concept of a + + + align:start position:0% +to explore briefly the concept of a +vector Subspace this is the problem that + + align:start position:0% +vector Subspace this is the problem that + + + align:start position:0% +vector Subspace this is the problem that +we're going to do we're given these four + + align:start position:0% +we're going to do we're given these four + + + align:start position:0% +we're going to do we're given these four +um different subsets of of + + align:start position:0% +um different subsets of of + + + align:start position:0% +um different subsets of of +R3 and we are asked to um figure out + + align:start position:0% +R3 and we are asked to um figure out + + + align:start position:0% +R3 and we are asked to um figure out +which of these is in fact um a sub space + + align:start position:0% +which of these is in fact um a sub space + + + align:start position:0% +which of these is in fact um a sub space +so I'll give you a few moments to uh try + + align:start position:0% +so I'll give you a few moments to uh try + + + align:start position:0% +so I'll give you a few moments to uh try +to do this on your own and then please + + align:start position:0% +to do this on your own and then please + + + align:start position:0% +to do this on your own and then please +come back to see whether you are + + align:start position:0% + + + + align:start position:0% + +right so hi again okay so before we + + align:start position:0% +right so hi again okay so before we + + + align:start position:0% +right so hi again okay so before we +start let's briefly recall what a vector + + align:start position:0% +start let's briefly recall what a vector + + + align:start position:0% +start let's briefly recall what a vector +Subspace is well Vector Subspace of + + align:start position:0% +Subspace is well Vector Subspace of + + + align:start position:0% +Subspace is well Vector Subspace of +course it's a subset um in this case a + + align:start position:0% +course it's a subset um in this case a + + + align:start position:0% +course it's a subset um in this case a +subset of R3 + + align:start position:0% +subset of R3 + + + align:start position:0% +subset of R3 +but it behaves like a vector space + + align:start position:0% +but it behaves like a vector space + + + align:start position:0% +but it behaves like a vector space +itself meaning that uh if we take um + + align:start position:0% +itself meaning that uh if we take um + + + align:start position:0% +itself meaning that uh if we take um +linear combination of elements in this + + align:start position:0% +linear combination of elements in this + + + align:start position:0% +linear combination of elements in this +subset uh what we get is still something + + align:start position:0% +subset uh what we get is still something + + + align:start position:0% +subset uh what we get is still something +in that subset + + align:start position:0% +in that subset + + + align:start position:0% +in that subset +subset okay and in class Professor + + align:start position:0% +subset okay and in class Professor + + + align:start position:0% +subset okay and in class Professor +Strang um showed you a few specific + + align:start position:0% +Strang um showed you a few specific + + + align:start position:0% +Strang um showed you a few specific +examples of subspaces which are related + + align:start position:0% +examples of subspaces which are related + + + align:start position:0% +examples of subspaces which are related +to matrices one of them was uh the null + + align:start position:0% +to matrices one of them was uh the null + + + align:start position:0% +to matrices one of them was uh the null +space of a matrix all the vectors that + + align:start position:0% +space of a matrix all the vectors that + + + align:start position:0% +space of a matrix all the vectors that +The Matrix sends to zero and the column + + align:start position:0% +The Matrix sends to zero and the column + + + align:start position:0% +The Matrix sends to zero and the column +space of a matrix which is the span of + + align:start position:0% +space of a matrix which is the span of + + + align:start position:0% +space of a matrix which is the span of +um the colum Matrix okay so let's see if + + align:start position:0% +um the colum Matrix okay so let's see if + + + align:start position:0% +um the colum Matrix okay so let's see if +we can apply what we've learned in + + align:start position:0% +we can apply what we've learned in + + + align:start position:0% +we can apply what we've learned in +lecture to um to our problem number one + + align:start position:0% +lecture to um to our problem number one + + + align:start position:0% +lecture to um to our problem number one +we are + + align:start position:0% +we are + + + align:start position:0% +we are +given a linear equation um um relation + + align:start position:0% +given a linear equation um um relation + + + align:start position:0% +given a linear equation um um relation +between uh B1 B2 and + + align:start position:0% +between uh B1 B2 and + + + align:start position:0% +between uh B1 B2 and +B3 um once it we have something linear + + align:start position:0% +B3 um once it we have something linear + + + align:start position:0% +B3 um once it we have something linear +we you know this is a philosophy that + + align:start position:0% +we you know this is a philosophy that + + + align:start position:0% +we you know this is a philosophy that +you'll learn in this class we can always + + align:start position:0% +you'll learn in this class we can always + + + align:start position:0% +you'll learn in this class we can always +write this as a matrix equation so in + + align:start position:0% +write this as a matrix equation so in + + + align:start position:0% +write this as a matrix equation so in +particular B1 + B2 minus B3 equal 0 we + + align:start position:0% +particular B1 + B2 minus B3 equal 0 we + + + align:start position:0% +particular B1 + B2 minus B3 equal 0 we +can just write it as the Matrix 1 1 -1 * + + align:start position:0% +can just write it as the Matrix 1 1 -1 * + + + align:start position:0% +can just write it as the Matrix 1 1 -1 * +B1 B2 + + align:start position:0% +B1 B2 + + + align:start position:0% +B1 B2 +B3 to + + align:start position:0% +B3 to + + + align:start position:0% +B3 to +zero so therefore B1 B2 and B3 precisely + + align:start position:0% +zero so therefore B1 B2 and B3 precisely + + + align:start position:0% +zero so therefore B1 B2 and B3 precisely +describe the m space + + align:start position:0% +describe the m space + + + align:start position:0% +describe the m space +of one one negative one and + + align:start position:0% +of one one negative one and + + + align:start position:0% +of one one negative one and +thus what we are given in the first + + align:start position:0% +thus what we are given in the first + + + align:start position:0% +thus what we are given in the first +question is a + + align:start position:0% +question is a + + + align:start position:0% +question is a +Subspace what about the second + + align:start position:0% +Subspace what about the second + + + align:start position:0% +Subspace what about the second +one again we given a relation between B1 + + align:start position:0% +one again we given a relation between B1 + + + align:start position:0% +one again we given a relation between B1 +and B2 B3 but it's not linear B3 is the + + align:start position:0% +and B2 B3 but it's not linear B3 is the + + + align:start position:0% +and B2 B3 but it's not linear B3 is the +product of B1 and B2 + + align:start position:0% +product of B1 and B2 + + + align:start position:0% +product of B1 and B2 +so right the your your guts tell you + + align:start position:0% +so right the your your guts tell you + + + align:start position:0% +so right the your your guts tell you +that this shouldn't be a vector space um + + align:start position:0% +that this shouldn't be a vector space um + + + align:start position:0% +that this shouldn't be a vector space um +and we need to but we need to prove why + + align:start position:0% +and we need to but we need to prove why + + + align:start position:0% +and we need to but we need to prove why +um okay + + align:start position:0% +um okay + + + align:start position:0% +um okay +well see that um the vector 1 1 + + align:start position:0% +well see that um the vector 1 1 + + + align:start position:0% +well see that um the vector 1 1 +1 is inside this subset because the + + align:start position:0% +1 is inside this subset because the + + + align:start position:0% +1 is inside this subset because the +third entry is the product one is the + + align:start position:0% +third entry is the product one is the + + + align:start position:0% +third entry is the product one is the +product of one and + + align:start position:0% +product of one and + + + align:start position:0% +product of one and +one if the subset were a Subspace itself + + align:start position:0% +one if the subset were a Subspace itself + + + align:start position:0% +one if the subset were a Subspace itself +then we would have two two and two in it + + align:start position:0% +then we would have two two and two in it + + + align:start position:0% +then we would have two two and two in it +as as well right because any multiple of + + align:start position:0% +as as well right because any multiple of + + + align:start position:0% +as as well right because any multiple of +a vector in the Subspace is inside the + + align:start position:0% +a vector in the Subspace is inside the + + + align:start position:0% +a vector in the Subspace is inside the +Subspace but is 222 described by this + + align:start position:0% +Subspace but is 222 described by this + + + align:start position:0% +Subspace but is 222 described by this +equation well no because the third entry + + align:start position:0% +equation well no because the third entry + + + align:start position:0% +equation well no because the third entry +two is not equal to 2 * 2 + + align:start position:0% +two is not equal to 2 * 2 + + + align:start position:0% +two is not equal to 2 * 2 +right + + align:start position:0% +right + + + align:start position:0% +right +so the example yeah in in number in + + align:start position:0% +so the example yeah in in number in + + + align:start position:0% +so the example yeah in in number in +number two is not uh + + align:start position:0% +number two is not uh + + + align:start position:0% +number two is not uh +Subspace + + align:start position:0% +Subspace + + + align:start position:0% +Subspace +okay let's try three + + align:start position:0% + + + + align:start position:0% + +and first so we are given so the subset + + align:start position:0% +and first so we are given so the subset + + + align:start position:0% +and first so we are given so the subset +in in question three is given as the + + align:start position:0% +in in question three is given as the + + + align:start position:0% +in in question three is given as the +linear span of these two vectors one 0 + + align:start position:0% +linear span of these two vectors one 0 + + + align:start position:0% +linear span of these two vectors one 0 +negative 1 and 1 Z + + align:start position:0% +negative 1 and 1 Z + + + align:start position:0% +negative 1 and 1 Z +1 plus the vector one0 0 okay so let's + + align:start position:0% +1 plus the vector one0 0 okay so let's + + + align:start position:0% +1 plus the vector one0 0 okay so let's +think about this geometrically we know + + align:start position:0% +think about this geometrically we know + + + align:start position:0% +think about this geometrically we know +that um the linear span of two linearly + + align:start position:0% +that um the linear span of two linearly + + + align:start position:0% +that um the linear span of two linearly +independent um vectors and these are + + align:start position:0% +independent um vectors and these are + + + align:start position:0% +independent um vectors and these are +obviously linearly independent is a + + align:start position:0% +obviously linearly independent is a + + + align:start position:0% +obviously linearly independent is a +plane in R3 so we have the plane and we + + align:start position:0% +plane in R3 so we have the plane and we + + + align:start position:0% +plane in R3 so we have the plane and we +add a vector to the point of this on + + align:start position:0% +add a vector to the point of this on + + + align:start position:0% +add a vector to the point of this on +this plane so what if the vector were + + align:start position:0% +this plane so what if the vector were + + + align:start position:0% +this plane so what if the vector were +lying on the plane well we're not going + + align:start position:0% +lying on the plane well we're not going + + + align:start position:0% +lying on the plane well we're not going +to change the plane right we're still + + align:start position:0% +to change the plane right we're still + + + align:start position:0% +to change the plane right we're still +going to remain in the plane uh what I'm + + align:start position:0% +going to remain in the plane uh what I'm + + + align:start position:0% +going to remain in the plane uh what I'm +hinting at is the f is the following + + align:start position:0% +hinting at is the f is the following + + + align:start position:0% +hinting at is the f is the following +thing that in fact one 0 is a linear + + align:start position:0% +thing that in fact one 0 is a linear + + + align:start position:0% +thing that in fact one 0 is a linear +combination of one Z negative 1 and one + + align:start position:0% +combination of one Z negative 1 and one + + + align:start position:0% +combination of one Z negative 1 and one +Z 1 and it's it's fairly obvious to see + + align:start position:0% +Z 1 and it's it's fairly obvious to see + + + align:start position:0% +Z 1 and it's it's fairly obvious to see +which linear + + align:start position:0% +which linear + + + align:start position:0% +which linear +combination of these two vectors it it + + align:start position:0% +combination of these two vectors it it + + + align:start position:0% +combination of these two vectors it it +is it's 12 1 Z negative + + align:start position:0% +is it's 12 1 Z negative + + + align:start position:0% +is it's 12 1 Z negative +1 12 1 Z + + align:start position:0% +1 12 1 Z + + + align:start position:0% +1 12 1 Z +1 so we can write the whole relation + + align:start position:0% +1 so we can write the whole relation + + + align:start position:0% +1 so we can write the whole relation +here in the following way B1 B2 2 + + align:start position:0% + + + + align:start position:0% + +B3 + + align:start position:0% +B3 + + + align:start position:0% +B3 +is one0 0 which we can write is this + + align:start position:0% +is one0 0 which we can write is this + + + align:start position:0% +is one0 0 which we can write is this +plus C1 1 0 1 1 and C2 1 0 + + align:start position:0% +plus C1 1 0 1 1 and C2 1 0 + + + align:start position:0% +plus C1 1 0 1 1 and C2 1 0 +1 and let me continue this here so B1 B2 + + align:start position:0% +1 and let me continue this here so B1 B2 + + + align:start position:0% +1 and let me continue this here so B1 B2 +and + + align:start position:0% +and + + + align:start position:0% +and +B3 is precisely C1 plus a + + align:start position:0% +B3 is precisely C1 plus a + + + align:start position:0% +B3 is precisely C1 plus a +half 1 1 -1 + C2 + a + + align:start position:0% +half 1 1 -1 + C2 + a + + + align:start position:0% +half 1 1 -1 + C2 + a +half of 1 0 + + align:start position:0% +half of 1 0 + + + align:start position:0% +half of 1 0 +1 so + + align:start position:0% +1 so + + + align:start position:0% +1 so +indeed the the points B1 B2 and B3 are + + align:start position:0% +indeed the the points B1 B2 and B3 are + + + align:start position:0% +indeed the the points B1 B2 and B3 are +um yeah described by the linear span one + + align:start position:0% +um yeah described by the linear span one + + + align:start position:0% +um yeah described by the linear span one +Z negative 1 and one Z one so + + align:start position:0% +Z negative 1 and one Z one so + + + align:start position:0% +Z negative 1 and one Z one so +it is a vector sub space + + align:start position:0% +it is a vector sub space + + + align:start position:0% +it is a vector sub space +itself and finally in order yeah let's + + align:start position:0% +itself and finally in order yeah let's + + + align:start position:0% +itself and finally in order yeah let's +let's look at number + + align:start position:0% + + + + align:start position:0% + +four so we have a similar situation I + + align:start position:0% +four so we have a similar situation I + + + align:start position:0% +four so we have a similar situation I +mean it's almost the same situation we + + align:start position:0% +mean it's almost the same situation we + + + align:start position:0% +mean it's almost the same situation we +again have the linear span of precisely + + align:start position:0% +again have the linear span of precisely + + + align:start position:0% +again have the linear span of precisely +um same vectors as in question three but + + align:start position:0% +um same vectors as in question three but + + + align:start position:0% +um same vectors as in question three but +this time we add the vector 0 1 0 to + + align:start position:0% +this time we add the vector 0 1 0 to + + + align:start position:0% +this time we add the vector 0 1 0 to +them now 0 one 0 is not in the span of + + align:start position:0% +them now 0 one 0 is not in the span of + + + align:start position:0% +them now 0 one 0 is not in the span of +these two vectors so the argument that + + align:start position:0% +these two vectors so the argument that + + + align:start position:0% +these two vectors so the argument that +we just showed for three doesn't + + align:start position:0% +we just showed for three doesn't + + + align:start position:0% +we just showed for three doesn't +work + + align:start position:0% +work + + + align:start position:0% +work +um but what we can what what we know + + align:start position:0% +um but what we can what what we know + + + align:start position:0% +um but what we can what what we know +about Vector sub space is the following + + align:start position:0% +about Vector sub space is the following + + + align:start position:0% +about Vector sub space is the following +thing it's follows almost triv from the + + align:start position:0% +thing it's follows almost triv from the + + + align:start position:0% +thing it's follows almost triv from the +aximum that zero needs to be inside the + + align:start position:0% +aximum that zero needs to be inside the + + + align:start position:0% +aximum that zero needs to be inside the +subset in order for it to be a Subspace + + align:start position:0% +subset in order for it to be a Subspace + + + align:start position:0% +subset in order for it to be a Subspace +it's a necessary condition okay well + + align:start position:0% +it's a necessary condition okay well + + + align:start position:0% +it's a necessary condition okay well +thises + + align:start position:0% +thises + + + align:start position:0% +thises +zero um is zero inside this subset + + align:start position:0% +zero um is zero inside this subset + + + align:start position:0% +zero um is zero inside this subset +meaning um can we + + align:start position:0% +meaning um can we + + + align:start position:0% +meaning um can we +find coefficients + + align:start position:0% + + + + align:start position:0% + +C1 and + + align:start position:0% + + + + align:start position:0% + +C2 plus 0 one Z to equal the zero + + align:start position:0% +C2 plus 0 one Z to equal the zero + + + align:start position:0% +C2 plus 0 one Z to equal the zero +vector and the answer is no + + align:start position:0% +vector and the answer is no + + + align:start position:0% +vector and the answer is no +and why is this we can um there's a very + + align:start position:0% +and why is this we can um there's a very + + + align:start position:0% +and why is this we can um there's a very +easy way to see it + + align:start position:0% +easy way to see it + + + align:start position:0% +easy way to see it +well any um we just look at yeah we just + + align:start position:0% +well any um we just look at yeah we just + + + align:start position:0% +well any um we just look at yeah we just +look at the second entry uh of of the + + align:start position:0% +look at the second entry uh of of the + + + align:start position:0% +look at the second entry uh of of the +vectors and we see that any multiple um + + align:start position:0% +vectors and we see that any multiple um + + + align:start position:0% +vectors and we see that any multiple um +so the the linear span of these two + + align:start position:0% +so the the linear span of these two + + + align:start position:0% +so the the linear span of these two +vectors will have as its second entry + + align:start position:0% +vectors will have as its second entry + + + align:start position:0% +vectors will have as its second entry +zero and when we add it to one we can + + align:start position:0% +zero and when we add it to one we can + + + align:start position:0% +zero and when we add it to one we can +never get a Zero Entry here so + + align:start position:0% +never get a Zero Entry here so + + + align:start position:0% +never get a Zero Entry here so +the subset in four is not the + + align:start position:0% +the subset in four is not the + + + align:start position:0% +the subset in four is not the +Subspace so yeah I hope this was useful + + align:start position:0% +Subspace so yeah I hope this was useful + + + align:start position:0% +Subspace so yeah I hope this was useful +and and just getting an intuition which + + align:start position:0% +and and just getting an intuition which + + + align:start position:0% +and and just getting an intuition which +subsets of our three are subspaces um I + + align:start position:0% +subsets of our three are subspaces um I + + + align:start position:0% +subsets of our three are subspaces um I +see you guys later \ No newline at end of file diff --git a/eNf8nH1yEYc.txt b/eNf8nH1yEYc.txt new file mode 100644 index 0000000000000000000000000000000000000000..d7489288da5ce84dea8db1cda92619a17d92c072 --- /dev/null +++ b/eNf8nH1yEYc.txt @@ -0,0 +1,1347 @@ +align:start position:0% + +now what should happen somehow this + + align:start position:0% +now what should happen somehow this + + + align:start position:0% +now what should happen somehow this +equation probably has solutions for all + + align:start position:0% +equation probably has solutions for all + + + align:start position:0% +equation probably has solutions for all +values of the energy but those solutions + + align:start position:0% +values of the energy but those solutions + + + align:start position:0% +values of the energy but those solutions +diverge and are not normalizable it's + + align:start position:0% +diverge and are not normalizable it's + + + align:start position:0% +diverge and are not normalizable it's +the kind of thing you will find with the + + align:start position:0% +the kind of thing you will find with the + + + align:start position:0% +the kind of thing you will find with the +shooting method what you're doing with + + align:start position:0% +shooting method what you're doing with + + + align:start position:0% +shooting method what you're doing with +your computer from the solution suddenly + + align:start position:0% +your computer from the solution suddenly + + + align:start position:0% +your computer from the solution suddenly +diverges up or diverges down it cannot + + align:start position:0% +diverges up or diverges down it cannot + + + align:start position:0% +diverges up or diverges down it cannot +be normalized but for some specific + + align:start position:0% +be normalized but for some specific + + + align:start position:0% +be normalized but for some specific +values it can be normalized so what we + + align:start position:0% +values it can be normalized so what we + + + align:start position:0% +values it can be normalized so what we +need is an intuition why this + + align:start position:0% +need is an intuition why this + + + align:start position:0% +need is an intuition why this +differential equation has normalizable + + align:start position:0% +differential equation has normalizable + + + align:start position:0% +differential equation has normalizable +solutions only if the energies curly e + + align:start position:0% +solutions only if the energies curly e + + + align:start position:0% +solutions only if the energies curly e +take specific values that's the + + align:start position:0% +take specific values that's the + + + align:start position:0% +take specific values that's the +intuition that we need for that we'll + + align:start position:0% +intuition that we need for that we'll + + + align:start position:0% +intuition that we need for that we'll +look at the equation a little closer and + + align:start position:0% +look at the equation a little closer and + + + align:start position:0% +look at the equation a little closer and +try to understand what happens at the + + align:start position:0% +try to understand what happens at the + + + align:start position:0% +try to understand what happens at the +place where it can get in trouble which + + align:start position:0% +place where it can get in trouble which + + + align:start position:0% +place where it can get in trouble which +is large X that's where you expect it to + + align:start position:0% +is large X that's where you expect it to + + + align:start position:0% +is large X that's where you expect it to +get in trouble so what does this + + align:start position:0% +get in trouble so what does this + + + align:start position:0% +get in trouble so what does this +equation become as u goes to plus minus + + align:start position:0% +equation become as u goes to plus minus + + + align:start position:0% +equation become as u goes to plus minus +infinity well this equation at that + + align:start position:0% +infinity well this equation at that + + + align:start position:0% +infinity well this equation at that +stage becomes like this the second Phi + + align:start position:0% +stage becomes like this the second Phi + + + align:start position:0% +stage becomes like this the second Phi +the u squared is roughly equal to u + + align:start position:0% +the u squared is roughly equal to u + + + align:start position:0% +the u squared is roughly equal to u +squared Phi because E is a constant it + + align:start position:0% +squared Phi because E is a constant it + + + align:start position:0% +squared Phi because E is a constant it +doesn't blow up so the differential + + align:start position:0% +doesn't blow up so the differential + + + align:start position:0% +doesn't blow up so the differential +equation the terms that are supposed to + + align:start position:0% +equation the terms that are supposed to + + + align:start position:0% +equation the terms that are supposed to +be largest in this right hand side is + + align:start position:0% +be largest in this right hand side is + + + align:start position:0% +be largest in this right hand side is +the you squirt so how the serve this + + align:start position:0% +the you squirt so how the serve this + + + align:start position:0% +the you squirt so how the serve this +look as a solution and you can see that + + align:start position:0% +look as a solution and you can see that + + + align:start position:0% +look as a solution and you can see that +that's definitely not like a power + + align:start position:0% +that's definitely not like a power + + + align:start position:0% +that's definitely not like a power +solution if you have a power of you say + + align:start position:0% +solution if you have a power of you say + + + align:start position:0% +solution if you have a power of you say +Phi equal u to the n after you + + align:start position:0% +Phi equal u to the n after you + + + align:start position:0% +Phi equal u to the n after you +differentiate the power goes down but + + align:start position:0% +differentiate the power goes down but + + + align:start position:0% +differentiate the power goes down but +here it goes up + + align:start position:0% +here it goes up + + + align:start position:0% +here it goes up +have a you you to the errand that the + + align:start position:0% +have a you you to the errand that the + + + align:start position:0% +have a you you to the errand that the +remedy is supposed to giving you to the + + align:start position:0% +remedy is supposed to giving you to the + + + align:start position:0% +remedy is supposed to giving you to the +n plus two but that doesn't work so + + align:start position:0% +n plus two but that doesn't work so + + + align:start position:0% +n plus two but that doesn't work so +that's not a power solution so it has to + + align:start position:0% +that's not a power solution so it has to + + + align:start position:0% +that's not a power solution so it has to +be different for what it is you can try + + align:start position:0% +be different for what it is you can try + + + align:start position:0% +be different for what it is you can try +a fie and what it should be is of the + + align:start position:0% +a fie and what it should be is of the + + + align:start position:0% +a fie and what it should be is of the +form e to the U squared it's kind of + + align:start position:0% +form e to the U squared it's kind of + + + align:start position:0% +form e to the U squared it's kind of +like that because this is the function + + align:start position:0% +like that because this is the function + + + align:start position:0% +like that because this is the function +that when you differentiate you bring + + align:start position:0% +that when you differentiate you bring + + + align:start position:0% +that when you differentiate you bring +down the derivative of this quantity + + align:start position:0% +down the derivative of this quantity + + + align:start position:0% +down the derivative of this quantity +could you say you when you differentiate + + align:start position:0% +could you say you when you differentiate + + + align:start position:0% +could you say you when you differentiate +again you can bring another you to get + + align:start position:0% +again you can bring another you to get + + + align:start position:0% +again you can bring another you to get +au squared or you can differentiate this + + align:start position:0% +au squared or you can differentiate this + + + align:start position:0% +au squared or you can differentiate this +one but if you differentiate the thing + + align:start position:0% +one but if you differentiate the thing + + + align:start position:0% +one but if you differentiate the thing +that is in the bottom you get something + + align:start position:0% +that is in the bottom you get something + + + align:start position:0% +that is in the bottom you get something +that diverges less so morally speaking + + align:start position:0% +that diverges less so morally speaking + + + align:start position:0% +that diverges less so morally speaking +this function is about right so output + + align:start position:0% +this function is about right so output + + + align:start position:0% +this function is about right so output +here for example into the alpha over two + + align:start position:0% +here for example into the alpha over two + + + align:start position:0% +here for example into the alpha over two +and I'll even put here are you okay can + + align:start position:0% +and I'll even put here are you okay can + + + align:start position:0% +and I'll even put here are you okay can +this work are you to the K times alpha U + + align:start position:0% +this work are you to the K times alpha U + + + align:start position:0% +this work are you to the K times alpha U +squared well if we take two derivatives + + align:start position:0% +squared well if we take two derivatives + + + align:start position:0% +squared well if we take two derivatives +if we take one derivative if I + + align:start position:0% +if we take one derivative if I + + + align:start position:0% +if we take one derivative if I +differentiate the U to the K I get U to + + align:start position:0% +differentiate the U to the K I get U to + + + align:start position:0% +differentiate the U to the K I get U to +the K minus one I lose powers of U if I + + align:start position:0% +the K minus one I lose powers of U if I + + + align:start position:0% +the K minus one I lose powers of U if I +differentiate exponential I get alpha + + align:start position:0% +differentiate exponential I get alpha + + + align:start position:0% +differentiate exponential I get alpha +times u times the same function see + + align:start position:0% +times u times the same function see + + + align:start position:0% +times u times the same function see +that's roughly speaking what's happening + + align:start position:0% +that's roughly speaking what's happening + + + align:start position:0% +that's roughly speaking what's happening +you differentiate the thing that + + align:start position:0% +you differentiate the thing that + + + align:start position:0% +you differentiate the thing that +diverges the most so if you + + align:start position:0% +diverges the most so if you + + + align:start position:0% +diverges the most so if you +differentiate twice each time in the + + align:start position:0% +differentiate twice each time in the + + + align:start position:0% +differentiate twice each time in the +first you get a factor of alpha + + align:start position:0% +first you get a factor of alpha + + + align:start position:0% +first you get a factor of alpha +times u squared Phi roughly this is plus + + align:start position:0% +times u squared Phi roughly this is plus + + + align:start position:0% +times u squared Phi roughly this is plus +sub leading + + align:start position:0% + + + + align:start position:0% + +when you differentiate a function and + + align:start position:0% +when you differentiate a function and + + + align:start position:0% +when you differentiate a function and +you're wanting to show the most + + align:start position:0% +you're wanting to show the most + + + align:start position:0% +you're wanting to show the most +divergent thing then you because we're + + align:start position:0% +divergent thing then you because we're + + + align:start position:0% +divergent thing then you because we're +looking at the most divergent part you + + align:start position:0% +looking at the most divergent part you + + + align:start position:0% +looking at the most divergent part you +will always differentiate this and this + + align:start position:0% +will always differentiate this and this + + + align:start position:0% +will always differentiate this and this +you to the case really spectator it + + align:start position:0% +you to the case really spectator it + + + align:start position:0% +you to the case really spectator it +doesn't do anything because when you + + align:start position:0% +doesn't do anything because when you + + + align:start position:0% +doesn't do anything because when you +differentiate that you get something + + align:start position:0% +differentiate that you get something + + + align:start position:0% +differentiate that you get something +much smaller that doesn't matter so yes + + align:start position:0% +much smaller that doesn't matter so yes + + + align:start position:0% +much smaller that doesn't matter so yes +with this Exponential's we get something + + align:start position:0% +with this Exponential's we get something + + + align:start position:0% +with this Exponential's we get something +like this side double prime should have + + align:start position:0% +like this side double prime should have + + + align:start position:0% +like this side double prime should have +been here + + align:start position:0% +been here + + + align:start position:0% +been here +and therefore you see that alpha is plus + + align:start position:0% +and therefore you see that alpha is plus + + + align:start position:0% +and therefore you see that alpha is plus +minus 1 alpha is plus minus 1 and those + + align:start position:0% +minus 1 alpha is plus minus 1 and those + + + align:start position:0% +minus 1 alpha is plus minus 1 and those +are likely to be approximate solutions + + align:start position:0% +are likely to be approximate solutions + + + align:start position:0% +are likely to be approximate solutions +at as X goes to infinity so we could + + align:start position:0% +at as X goes to infinity so we could + + + align:start position:0% +at as X goes to infinity so we could +expect solutions for alpha equal 1 and I + + align:start position:0% +expect solutions for alpha equal 1 and I + + + align:start position:0% +expect solutions for alpha equal 1 and I +will write it and all this I should say + + align:start position:0% +will write it and all this I should say + + + align:start position:0% +will write it and all this I should say +it's always as nu goes to infinity so + + align:start position:0% +it's always as nu goes to infinity so + + + align:start position:0% +it's always as nu goes to infinity so +always as u goes to infinity all what is + + align:start position:0% +always as u goes to infinity all what is + + + align:start position:0% +always as u goes to infinity all what is +in this blackboard so also as u goes to + + align:start position:0% +in this blackboard so also as u goes to + + + align:start position:0% +in this blackboard so also as u goes to +infinity we would expect maybe solutions + + align:start position:0% +infinity we would expect maybe solutions + + + align:start position:0% +infinity we would expect maybe solutions +of the form a U to the K e to the minus + + align:start position:0% +of the form a U to the K e to the minus + + + align:start position:0% +of the form a U to the K e to the minus +u squared over 2 plus B U to the K e to + + align:start position:0% +u squared over 2 plus B U to the K e to + + + align:start position:0% +u squared over 2 plus B U to the K e to +the U squared over to the two values of + + align:start position:0% +the U squared over to the two values of + + + align:start position:0% +the U squared over to the two values of +alpha alpha equal plus minus 1 are the + + align:start position:0% +alpha alpha equal plus minus 1 are the + + + align:start position:0% +alpha alpha equal plus minus 1 are the +possibilities for these two equations to + + align:start position:0% +possibilities for these two equations to + + + align:start position:0% +possibilities for these two equations to +match so you would expect things like + + align:start position:0% +match so you would expect things like + + + align:start position:0% +match so you would expect things like +this to be solutions and here you see + + align:start position:0% +this to be solutions and here you see + + + align:start position:0% +this to be solutions and here you see +the beginning of the danger well a minus + + align:start position:0% +the beginning of the danger well a minus + + + align:start position:0% +the beginning of the danger well a minus +u squared over two times a power sounds + + align:start position:0% +u squared over two times a power sounds + + + align:start position:0% +u squared over two times a power sounds +pretty good and but a u squared over two + + align:start position:0% +pretty good and but a u squared over two + + + align:start position:0% +pretty good and but a u squared over two +times the power sounds pretty bad so + + align:start position:0% +times the power sounds pretty bad so + + + align:start position:0% +times the power sounds pretty bad so +maybe this is what we want to happen + + align:start position:0% +maybe this is what we want to happen + + + align:start position:0% +maybe this is what we want to happen +this is not an exact solution of + + align:start position:0% +this is not an exact solution of + + + align:start position:0% +this is not an exact solution of +anything yet we're just looking at you + + align:start position:0% +anything yet we're just looking at you + + + align:start position:0% +anything yet we're just looking at you +going to plus minus infinity and maybe + + align:start position:0% +going to plus minus infinity and maybe + + + align:start position:0% +going to plus minus infinity and maybe +we'll have such a behavior or such a + + align:start position:0% +we'll have such a behavior or such a + + + align:start position:0% +we'll have such a behavior or such a +behavior but we want this one otherwise + + align:start position:0% +behavior but we want this one otherwise + + + align:start position:0% +behavior but we want this one otherwise +we will never be able to normalize it so + + align:start position:0% +we will never be able to normalize it so + + + align:start position:0% +we will never be able to normalize it so +here it is without any loss of + + align:start position:0% +here it is without any loss of + + + align:start position:0% +here it is without any loss of +generality and inspired by this this + + align:start position:0% +generality and inspired by this this + + + align:start position:0% +generality and inspired by this this +analysis is absolutely crucial you see + + align:start position:0% +analysis is absolutely crucial you see + + + align:start position:0% +analysis is absolutely crucial you see +we're following a very logical procedure + + align:start position:0% +we're following a very logical procedure + + + align:start position:0% +we're following a very logical procedure +cleaning the equation then looking where + + align:start position:0% +cleaning the equation then looking where + + + align:start position:0% +cleaning the equation then looking where +the divergence would happen and learning + + align:start position:0% +the divergence would happen and learning + + + align:start position:0% +the divergence would happen and learning +something about the form of the solution + + align:start position:0% +something about the form of the solution + + + align:start position:0% +something about the form of the solution +now without any loss of generality I can + + align:start position:0% +now without any loss of generality I can + + + align:start position:0% +now without any loss of generality I can +write I want to look I will write 5x + + align:start position:0% + + + + align:start position:0% + +it's gonna be not effects anymore u H of + + align:start position:0% +it's gonna be not effects anymore u H of + + + align:start position:0% +it's gonna be not effects anymore u H of +U times e to the minus u squared over 2 + + align:start position:0% +U times e to the minus u squared over 2 + + + align:start position:0% +U times e to the minus u squared over 2 +so it's an answered but this without any + + align:start position:0% +so it's an answered but this without any + + + align:start position:0% +so it's an answered but this without any +loss of generality because you can + + align:start position:0% +loss of generality because you can + + + align:start position:0% +loss of generality because you can +always write any function as another + + align:start position:0% +always write any function as another + + + align:start position:0% +always write any function as another +function times e to the minus u over 2 + + align:start position:0% +function times e to the minus u over 2 + + + align:start position:0% +function times e to the minus u over 2 +because you take the function u + + align:start position:0% +because you take the function u + + + align:start position:0% +because you take the function u +multiplied by e to the plus u over 2 and + + align:start position:0% +multiplied by e to the plus u over 2 and + + + align:start position:0% +multiplied by e to the plus u over 2 and +e to the minus u over 2 and it's written + + align:start position:0% +e to the minus u over 2 and it's written + + + align:start position:0% +e to the minus u over 2 and it's written +like that but this should be nice + + align:start position:0% +like that but this should be nice + + + align:start position:0% +like that but this should be nice +because it has sort of the right + + align:start position:0% +because it has sort of the right + + + align:start position:0% +because it has sort of the right +behavior already and here is the hope + + align:start position:0% +behavior already and here is the hope + + + align:start position:0% +behavior already and here is the hope +the hope is that this function now is + + align:start position:0% +the hope is that this function now is + + + align:start position:0% +the hope is that this function now is +the proxy for Phi if you know H you know + + align:start position:0% +the proxy for Phi if you know H you know + + + align:start position:0% +the proxy for Phi if you know H you know +Phi which is what you want and this + + align:start position:0% +Phi which is what you want and this + + + align:start position:0% +Phi which is what you want and this +function hopefully won't diverge this + + align:start position:0% +function hopefully won't diverge this + + + align:start position:0% +function hopefully won't diverge this +will be integrable so if this function + + align:start position:0% +will be integrable so if this function + + + align:start position:0% +will be integrable so if this function +doesn't diverge it will be a great thing + + align:start position:0% +doesn't diverge it will be a great thing + + + align:start position:0% +doesn't diverge it will be a great thing +in particular we could hope that each of + + align:start position:0% +in particular we could hope that each of + + + align:start position:0% +in particular we could hope that each of +you is a polynomial + + align:start position:0% +you is a polynomial + + + align:start position:0% +you is a polynomial +Gnomeo you see if somebody would have + + align:start position:0% +Gnomeo you see if somebody would have + + + align:start position:0% +Gnomeo you see if somebody would have +come and said look at that equation + + align:start position:0% +come and said look at that equation + + + align:start position:0% +come and said look at that equation +could that be a polynomial a polynomial + + align:start position:0% +could that be a polynomial a polynomial + + + align:start position:0% +could that be a polynomial a polynomial +something that ends up to some power X + + align:start position:0% +something that ends up to some power X + + + align:start position:0% +something that ends up to some power X +to the 20 or X to + + align:start position:0% +to the 20 or X to + + + align:start position:0% +to the 20 or X to +30 but it doesn't go up forever an + + align:start position:0% +30 but it doesn't go up forever an + + + align:start position:0% +30 but it doesn't go up forever an +exponential has all powers this solution + + align:start position:0% +exponential has all powers this solution + + + align:start position:0% +exponential has all powers this solution +this equation doesn't have a polynomial + + align:start position:0% +this equation doesn't have a polynomial + + + align:start position:0% +this equation doesn't have a polynomial +solution no polynomial will ever solve + + align:start position:0% +solution no polynomial will ever solve + + + align:start position:0% +solution no polynomial will ever solve +this but now that you've isolated the + + align:start position:0% +this but now that you've isolated the + + + align:start position:0% +this but now that you've isolated the +divergence there is a hope that a + + align:start position:0% +divergence there is a hope that a + + + align:start position:0% +divergence there is a hope that a +polynomial will work so for doing that + + align:start position:0% +polynomial will work so for doing that + + + align:start position:0% +polynomial will work so for doing that +exploring that hope I now have to + + align:start position:0% +exploring that hope I now have to + + + align:start position:0% +exploring that hope I now have to +substitute this is no assumption the + + align:start position:0% +substitute this is no assumption the + + + align:start position:0% +substitute this is no assumption the +differential equation for Phi implies a + + align:start position:0% +differential equation for Phi implies a + + + align:start position:0% +differential equation for Phi implies a +differential equation for age you just + + align:start position:0% +differential equation for age you just + + + align:start position:0% +differential equation for age you just +substitute this and look at it + + align:start position:0% +substitute this and look at it + + + align:start position:0% +substitute this and look at it +that's a one-line computation or two + + align:start position:0% +that's a one-line computation or two + + + align:start position:0% +that's a one-line computation or two +line computation I'll give the answer so + + align:start position:0% +line computation I'll give the answer so + + + align:start position:0% +line computation I'll give the answer so +what is the differential equation for H + + align:start position:0% +what is the differential equation for H + + + align:start position:0% +what is the differential equation for H +so back in star you get this second age + + align:start position:0% +so back in star you get this second age + + + align:start position:0% +so back in star you get this second age +the U squared minus 2 u th the u+ e + + align:start position:0% +the U squared minus 2 u th the u+ e + + + align:start position:0% +the U squared minus 2 u th the u+ e +minus 1 H equals 0 so you substitute + + align:start position:0% +minus 1 H equals 0 so you substitute + + + align:start position:0% +minus 1 H equals 0 so you substitute +that into this equation and you get this + + align:start position:0% +that into this equation and you get this + + + align:start position:0% +that into this equation and you get this +differential equation and now this is a + + align:start position:0% +differential equation and now this is a + + + align:start position:0% +differential equation and now this is a +differential equation for age we hope it + + align:start position:0% +differential equation for age we hope it + + + align:start position:0% +differential equation for age we hope it +has a polynomial solution you will see + + align:start position:0% +has a polynomial solution you will see + + + align:start position:0% +has a polynomial solution you will see +that it wants to have a polynomial + + align:start position:0% +that it wants to have a polynomial + + + align:start position:0% +that it wants to have a polynomial +solution but doesn't quite make it and + + align:start position:0% +solution but doesn't quite make it and + + + align:start position:0% +solution but doesn't quite make it and +then you will discover that quantization + + align:start position:0% +then you will discover that quantization + + + align:start position:0% +then you will discover that quantization +helps and suddenly you get a polynomial + + align:start position:0% +helps and suddenly you get a polynomial + + + align:start position:0% +helps and suddenly you get a polynomial +solution and everything works out \ No newline at end of file diff --git a/fdJ7hBBivQc.txt b/fdJ7hBBivQc.txt new file mode 100644 index 0000000000000000000000000000000000000000..c1f1455e4fdbdbe66bd0a36fc16d6a0f07816138 --- /dev/null +++ b/fdJ7hBBivQc.txt @@ -0,0 +1,1595 @@ +align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +this week we'll be talking about + + align:start position:0% +this week we'll be talking about + + + align:start position:0% +this week we'll be talking about +probably one of the most important + + align:start position:0% +probably one of the most important + + + align:start position:0% +probably one of the most important +aspects of Photography which is light as + + align:start position:0% +aspects of Photography which is light as + + + align:start position:0% +aspects of Photography which is light as +in + + align:start position:0% +in + + + align:start position:0% +in +photography writing or drawing with + + align:start position:0% +photography writing or drawing with + + + align:start position:0% +photography writing or drawing with +light it's a very content-rich + + align:start position:0% +light it's a very content-rich + + + align:start position:0% +light it's a very content-rich +conversation we're going to have and + + align:start position:0% +conversation we're going to have and + + + align:start position:0% +conversation we're going to have and +could really easily take up a full + + align:start position:0% +could really easily take up a full + + + align:start position:0% +could really easily take up a full +six-week course but for our purposes + + align:start position:0% +six-week course but for our purposes + + + align:start position:0% +six-week course but for our purposes +here we're going to give you something + + align:start position:0% +here we're going to give you something + + + align:start position:0% +here we're going to give you something +of an overview showing you various forms + + align:start position:0% +of an overview showing you various forms + + + align:start position:0% +of an overview showing you various forms +and characteristics + + align:start position:0% +and characteristics + + + align:start position:0% +and characteristics +of some light sources we can't address + + align:start position:0% +of some light sources we can't address + + + align:start position:0% +of some light sources we can't address +every conceivable possibility but what + + align:start position:0% +every conceivable possibility but what + + + align:start position:0% +every conceivable possibility but what +we can do is tweak your curiosity I hope + + align:start position:0% +we can do is tweak your curiosity I hope + + + align:start position:0% +we can do is tweak your curiosity I hope +so that you pay attention very close + + align:start position:0% +so that you pay attention very close + + + align:start position:0% +so that you pay attention very close +attention to what you're seeing as you + + align:start position:0% +attention to what you're seeing as you + + + align:start position:0% +attention to what you're seeing as you +change your own light sources looking at + + align:start position:0% +change your own light sources looking at + + + align:start position:0% +change your own light sources looking at +the shadows for + + align:start position:0% +the shadows for + + + align:start position:0% +the shadows for +example how do they and the highlights + + align:start position:0% +example how do they and the highlights + + + align:start position:0% +example how do they and the highlights +change as you move your light source and + + align:start position:0% +change as you move your light source and + + + align:start position:0% +change as you move your light source and +observe exactly what's going on when you + + align:start position:0% +observe exactly what's going on when you + + + align:start position:0% +observe exactly what's going on when you +make even some very minimal changes + + align:start position:0% +make even some very minimal changes + + + align:start position:0% +make even some very minimal changes +let's start with a simple piece of + + align:start position:0% +let's start with a simple piece of + + + align:start position:0% +let's start with a simple piece of +equipment a light box it's really easy + + align:start position:0% +equipment a light box it's really easy + + + align:start position:0% +equipment a light box it's really easy +to use when you're working with + + align:start position:0% +to use when you're working with + + + align:start position:0% +to use when you're working with +transparent material just by placing + + align:start position:0% +transparent material just by placing + + + align:start position:0% +transparent material just by placing +your work directly on top of the light + + align:start position:0% +your work directly on top of the light + + + align:start position:0% +your work directly on top of the light +box but you'll see later it can be also + + align:start position:0% +box but you'll see later it can be also + + + align:start position:0% +box but you'll see later it can be also +another General source of lighting so + + align:start position:0% +another General source of lighting so + + + align:start position:0% +another General source of lighting so +let's start with a picture of these two + + align:start position:0% +let's start with a picture of these two + + + align:start position:0% +let's start with a picture of these two +Petri dishes growing e Cola so that + + align:start position:0% +Petri dishes growing e Cola so that + + + align:start position:0% +Petri dishes growing e Cola so that +works in this image we're seeing small + + align:start position:0% +works in this image we're seeing small + + + align:start position:0% +works in this image we're seeing small +pieces of color plastic shapes about 3 + + align:start position:0% +pieces of color plastic shapes about 3 + + + align:start position:0% +pieces of color plastic shapes about 3 +mm across that are organizing or self + + align:start position:0% +mm across that are organizing or self + + + align:start position:0% +mm across that are organizing or self +assembling at the interface between two + + align:start position:0% +assembling at the interface between two + + + align:start position:0% +assembling at the interface between two +solutions they're becoming a flat + + align:start position:0% +solutions they're becoming a flat + + + align:start position:0% +solutions they're becoming a flat +assemblage at that interface and all I + + align:start position:0% +assemblage at that interface and all I + + + align:start position:0% +assemblage at that interface and all I +did was put the glass container holding + + align:start position:0% +did was put the glass container holding + + + align:start position:0% +did was put the glass container holding +all the material on the light box and + + align:start position:0% +all the material on the light box and + + + align:start position:0% +all the material on the light box and +here I'm making images of sugar crystals + + align:start position:0% +here I'm making images of sugar crystals + + + align:start position:0% +here I'm making images of sugar crystals +growing on sticks you know they serve + + align:start position:0% +growing on sticks you know they serve + + + align:start position:0% +growing on sticks you know they serve +you that sometimes when you order a cup + + align:start position:0% +you that sometimes when you order a cup + + + align:start position:0% +you that sometimes when you order a cup +of coffee so here is one rendition on a + + align:start position:0% +of coffee so here is one rendition on a + + + align:start position:0% +of coffee so here is one rendition on a +light box of the sugar and what I + + align:start position:0% +light box of the sugar and what I + + + align:start position:0% +light box of the sugar and what I +decided to do for the next one to Simply + + align:start position:0% +decided to do for the next one to Simply + + + align:start position:0% +decided to do for the next one to Simply +invert the image here's a picture that I + + align:start position:0% +invert the image here's a picture that I + + + align:start position:0% +invert the image here's a picture that I +made a number of years ago which I still + + align:start position:0% +made a number of years ago which I still + + + align:start position:0% +made a number of years ago which I still +like it's a picture about light a + + align:start position:0% +like it's a picture about light a + + + align:start position:0% +like it's a picture about light a +metaphor about light it was one of those + + align:start position:0% +metaphor about light it was one of those + + + align:start position:0% +metaphor about light it was one of those +lucky efforts when I just set up a + + align:start position:0% +lucky efforts when I just set up a + + + align:start position:0% +lucky efforts when I just set up a +magnifier and the paper and in 30 + + align:start position:0% +magnifier and the paper and in 30 + + + align:start position:0% +magnifier and the paper and in 30 +seconds I got the picture very unusual + + align:start position:0% +seconds I got the picture very unusual + + + align:start position:0% +seconds I got the picture very unusual +by the way so the image is intended to + + align:start position:0% +by the way so the image is intended to + + + align:start position:0% +by the way so the image is intended to +suggest a process of etching with light + + align:start position:0% +suggest a process of etching with light + + + align:start position:0% +suggest a process of etching with light +when we talked about it in our book no + + align:start position:0% +when we talked about it in our book no + + + align:start position:0% +when we talked about it in our book no +small matter about + + align:start position:0% +small matter about + + + align:start position:0% +small matter about +nanoscience in this image of something I + + align:start position:0% +nanoscience in this image of something I + + + align:start position:0% +nanoscience in this image of something I +assume you recognize by now we see a + + align:start position:0% +assume you recognize by now we see a + + + align:start position:0% +assume you recognize by now we see a +different kind of lighting that you've + + align:start position:0% +different kind of lighting that you've + + + align:start position:0% +different kind of lighting that you've +seen from previous images of the music + + align:start position:0% +seen from previous images of the music + + + align:start position:0% +seen from previous images of the music +box I shot from above with mostly + + align:start position:0% +box I shot from above with mostly + + + align:start position:0% +box I shot from above with mostly +daylight and then I turned on a little + + align:start position:0% +daylight and then I turned on a little + + + align:start position:0% +daylight and then I turned on a little +bit more light from a Tungsten lamp + + align:start position:0% +bit more light from a Tungsten lamp + + + align:start position:0% +bit more light from a Tungsten lamp +Above This is specific to this situation + + align:start position:0% +Above This is specific to this situation + + + align:start position:0% +Above This is specific to this situation +but you might find it helpful in yours + + align:start position:0% +but you might find it helpful in yours + + + align:start position:0% +but you might find it helpful in yours +look what happens when you just simply + + align:start position:0% +look what happens when you just simply + + + align:start position:0% +look what happens when you just simply +click and turn a light on from the light + + align:start position:0% +click and turn a light on from the light + + + align:start position:0% +click and turn a light on from the light +being off to the light being on you'll + + align:start position:0% +being off to the light being on you'll + + + align:start position:0% +being off to the light being on you'll +see how the image drastically changes by + + align:start position:0% +see how the image drastically changes by + + + align:start position:0% +see how the image drastically changes by +just adding an additional lamp from + + align:start position:0% +just adding an additional lamp from + + + align:start position:0% +just adding an additional lamp from +Above This fishing reel yep that's what + + align:start position:0% +Above This fishing reel yep that's what + + + align:start position:0% +Above This fishing reel yep that's what +it is by the way it is a fishing reel + + align:start position:0% +it is by the way it is a fishing reel + + + align:start position:0% +it is by the way it is a fishing reel +placed in a translucent green garbage + + align:start position:0% +placed in a translucent green garbage + + + align:start position:0% +placed in a translucent green garbage +can I thought it was fun to see what + + align:start position:0% +can I thought it was fun to see what + + + align:start position:0% +can I thought it was fun to see what +kind of quality I could get by shooting + + align:start position:0% +kind of quality I could get by shooting + + + align:start position:0% +kind of quality I could get by shooting +into a plastic translucent garbage can + + align:start position:0% +into a plastic translucent garbage can + + + align:start position:0% +into a plastic translucent garbage can +very specific to say the least again + + align:start position:0% +very specific to say the least again + + + align:start position:0% +very specific to say the least again +just by adding one additional light this + + align:start position:0% +just by adding one additional light this + + + align:start position:0% +just by adding one additional light this +time inside the vacuum chamber I'm + + align:start position:0% +time inside the vacuum chamber I'm + + + align:start position:0% +time inside the vacuum chamber I'm +Imaging we see what starts as this kind + + align:start position:0% +Imaging we see what starts as this kind + + + align:start position:0% +Imaging we see what starts as this kind +of image and becomes this image you'll + + align:start position:0% +of image and becomes this image you'll + + + align:start position:0% +of image and becomes this image you'll +see how it really changes with a simple + + align:start position:0% +see how it really changes with a simple + + + align:start position:0% +see how it really changes with a simple +addition of just one + + align:start position:0% +addition of just one + + + align:start position:0% +addition of just one +light in this image of a + + align:start position:0% +light in this image of a + + + align:start position:0% +light in this image of a +triangular-shaped water drop It's + + align:start position:0% +triangular-shaped water drop It's + + + align:start position:0% +triangular-shaped water drop It's +actually an etched area on a surface + + align:start position:0% +actually an etched area on a surface + + + align:start position:0% +actually an etched area on a surface +onto which we placed water you could see + + align:start position:0% +onto which we placed water you could see + + + align:start position:0% +onto which we placed water you could see +the reflection of the lamp on the water + + align:start position:0% +the reflection of the lamp on the water + + + align:start position:0% +the reflection of the lamp on the water +drop we just directed a lamp onto the + + align:start position:0% +drop we just directed a lamp onto the + + + align:start position:0% +drop we just directed a lamp onto the +water that's considered direct lighting + + align:start position:0% +water that's considered direct lighting + + + align:start position:0% +water that's considered direct lighting +when I shine the lamp onto a card in + + align:start position:0% +when I shine the lamp onto a card in + + + align:start position:0% +when I shine the lamp onto a card in +this case a gold card the light then + + align:start position:0% +this case a gold card the light then + + + align:start position:0% +this case a gold card the light then +bounced back onto the water drop and + + align:start position:0% +bounced back onto the water drop and + + + align:start position:0% +bounced back onto the water drop and +you'll see a completely different + + align:start position:0% +you'll see a completely different + + + align:start position:0% +you'll see a completely different +quality of lighting this is called + + align:start position:0% +quality of lighting this is called + + + align:start position:0% +quality of lighting this is called +Bounce lighting the bounce gives us + + align:start position:0% +Bounce lighting the bounce gives us + + + align:start position:0% +Bounce lighting the bounce gives us +diffuse lighting let's compare the + + align:start position:0% +diffuse lighting let's compare the + + + align:start position:0% +diffuse lighting let's compare the +two let's look at a quick test that I + + align:start position:0% +two let's look at a quick test that I + + + align:start position:0% +two let's look at a quick test that I +made for us to see the difference + + align:start position:0% +made for us to see the difference + + + align:start position:0% +made for us to see the difference +between two kinds of bounces in this + + align:start position:0% +between two kinds of bounces in this + + + align:start position:0% +between two kinds of bounces in this +case the bounce lighting will be used as + + align:start position:0% +case the bounce lighting will be used as + + + align:start position:0% +case the bounce lighting will be used as +fill lighting we'll use a white card and + + align:start position:0% +fill lighting we'll use a white card and + + + align:start position:0% +fill lighting we'll use a white card and +then we'll fill with a mirror the main + + align:start position:0% +then we'll fill with a mirror the main + + + align:start position:0% +then we'll fill with a mirror the main +source of light is daylight from a + + align:start position:0% +source of light is daylight from a + + + align:start position:0% +source of light is daylight from a +window so here's an image of the inside + + align:start position:0% +window so here's an image of the inside + + + align:start position:0% +window so here's an image of the inside +of the watch that we've seen before just + + align:start position:0% +of the watch that we've seen before just + + + align:start position:0% +of the watch that we've seen before just +with daylight on an overcast day here I + + align:start position:0% +with daylight on an overcast day here I + + + align:start position:0% +with daylight on an overcast day here I +added a white card on the side of the + + align:start position:0% +added a white card on the side of the + + + align:start position:0% +added a white card on the side of the +watch for a fill here is a mirror + + align:start position:0% +watch for a fill here is a mirror + + + align:start position:0% +watch for a fill here is a mirror +reflecting the daylight again as a fill + + align:start position:0% +reflecting the daylight again as a fill + + + align:start position:0% +reflecting the daylight again as a fill +onto the + + align:start position:0% +onto the + + + align:start position:0% +onto the +watch let's go back to the original just + + align:start position:0% +watch let's go back to the original just + + + align:start position:0% +watch let's go back to the original just +daylight then the + + align:start position:0% +daylight then the + + + align:start position:0% +daylight then the +card then the + + align:start position:0% +card then the + + + align:start position:0% +card then the +mirror back to the watch + + align:start position:0% +mirror back to the watch + + + align:start position:0% +mirror back to the watch +alone then adding the card then adding + + align:start position:0% +alone then adding the card then adding + + + align:start position:0% +alone then adding the card then adding +just the + + align:start position:0% +just the + + + align:start position:0% +just the +mirror let's zoom in to see the subtle + + align:start position:0% +mirror let's zoom in to see the subtle + + + align:start position:0% +mirror let's zoom in to see the subtle +differences in each of these cases now + + align:start position:0% +differences in each of these cases now + + + align:start position:0% +differences in each of these cases now +depending upon what your material is you + + align:start position:0% +depending upon what your material is you + + + align:start position:0% +depending upon what your material is you +might see much more dramatic changes but + + align:start position:0% +might see much more dramatic changes but + + + align:start position:0% +might see much more dramatic changes but +I encourage you to experiment with these + + align:start position:0% +I encourage you to experiment with these + + + align:start position:0% +I encourage you to experiment with these +ideas by the way here's another image I + + align:start position:0% +ideas by the way here's another image I + + + align:start position:0% +ideas by the way here's another image I +made this time using both the card and + + align:start position:0% +made this time using both the card and + + + align:start position:0% +made this time using both the card and +the mirror as a fill let's see them all + + align:start position:0% + + + + align:start position:0% + +together light is all about shadows as + + align:start position:0% +together light is all about shadows as + + + align:start position:0% +together light is all about shadows as +well and it is quite remarkable how + + align:start position:0% +well and it is quite remarkable how + + + align:start position:0% +well and it is quite remarkable how +small changes can change the shadow in + + align:start position:0% +small changes can change the shadow in + + + align:start position:0% +small changes can change the shadow in +images how a powerful direct light + + align:start position:0% +images how a powerful direct light + + + align:start position:0% +images how a powerful direct light +source can produce a significant Shadow + + align:start position:0% +source can produce a significant Shadow + + + align:start position:0% +source can produce a significant Shadow +and that shadow does in this image + + align:start position:0% +and that shadow does in this image + + + align:start position:0% +and that shadow does in this image +become a very strong compositional + + align:start position:0% +become a very strong compositional + + + align:start position:0% +become a very strong compositional +element here's where I'm using the light + + align:start position:0% +element here's where I'm using the light + + + align:start position:0% +element here's where I'm using the light +on this wafer showing the chip that sits + + align:start position:0% +on this wafer showing the chip that sits + + + align:start position:0% +on this wafer showing the chip that sits +next to it in this particular image I + + align:start position:0% +next to it in this particular image I + + + align:start position:0% +next to it in this particular image I +was playing around I decided to just use + + align:start position:0% +was playing around I decided to just use + + + align:start position:0% +was playing around I decided to just use +a slant of + + align:start position:0% +a slant of + + + align:start position:0% +a slant of +light uh maybe Emily Dickinson would be + + align:start position:0% +light uh maybe Emily Dickinson would be + + + align:start position:0% +light uh maybe Emily Dickinson would be +happy with that on this image I decided + + align:start position:0% +happy with that on this image I decided + + + align:start position:0% +happy with that on this image I decided +just to make sure that light was + + align:start position:0% +just to make sure that light was + + + align:start position:0% +just to make sure that light was +covering the entire wafer I actually + + align:start position:0% +covering the entire wafer I actually + + + align:start position:0% +covering the entire wafer I actually +like the first one better but it's + + align:start position:0% +like the first one better but it's + + + align:start position:0% +like the first one better but it's +something to think about about using + + align:start position:0% +something to think about about using + + + align:start position:0% +something to think about about using +light in terms of making + + align:start position:0% +light in terms of making + + + align:start position:0% +light in terms of making +compositions in this image I'm using a + + align:start position:0% +compositions in this image I'm using a + + + align:start position:0% +compositions in this image I'm using a +shadow to better communicate what the + + align:start position:0% +shadow to better communicate what the + + + align:start position:0% +shadow to better communicate what the +grading on the surface of this plastic + + align:start position:0% +grading on the surface of this plastic + + + align:start position:0% +grading on the surface of this plastic +is doing it's diffracting the light into + + align:start position:0% +is doing it's diffracting the light into + + + align:start position:0% +is doing it's diffracting the light into +various wavelengths I produced The + + align:start position:0% +various wavelengths I produced The + + + align:start position:0% +various wavelengths I produced The +Shadow by placing a card in front of the + + align:start position:0% +Shadow by placing a card in front of the + + + align:start position:0% +Shadow by placing a card in front of the +light source see how the image looks + + align:start position:0% +light source see how the image looks + + + align:start position:0% +light source see how the image looks +without the card + + align:start position:0% +without the card + + + align:start position:0% +without the card +Shadows alone can tell a story here + + align:start position:0% +Shadows alone can tell a story here + + + align:start position:0% +Shadows alone can tell a story here +we're trying to show something called + + align:start position:0% +we're trying to show something called + + + align:start position:0% +we're trying to show something called +the marangoni effect you know when you + + align:start position:0% +the marangoni effect you know when you + + + align:start position:0% +the marangoni effect you know when you +twirl a glass of wine we see some what + + align:start position:0% +twirl a glass of wine we see some what + + + align:start position:0% +twirl a glass of wine we see some what +what some people call tears of wine it's + + align:start position:0% +what some people call tears of wine it's + + + align:start position:0% +what some people call tears of wine it's +a complex phenomenon in this image I + + align:start position:0% +a complex phenomenon in this image I + + + align:start position:0% +a complex phenomenon in this image I +tried for quite a while to make an image + + align:start position:0% +tried for quite a while to make an image + + + align:start position:0% +tried for quite a while to make an image +depicting the maragoni effect not at all + + align:start position:0% +depicting the maragoni effect not at all + + + align:start position:0% +depicting the maragoni effect not at all +successful finally thinking that I + + align:start position:0% +successful finally thinking that I + + + align:start position:0% +successful finally thinking that I +should concentrate on the glass and the + + align:start position:0% +should concentrate on the glass and the + + + align:start position:0% +should concentrate on the glass and the +shadow that is being being produced then + + align:start position:0% +shadow that is being being produced then + + + align:start position:0% +shadow that is being being produced then +I finally focused in on what is the + + align:start position:0% +I finally focused in on what is the + + + align:start position:0% +I finally focused in on what is the +Maring GOI effect on its own as a + + align:start position:0% +Maring GOI effect on its own as a + + + align:start position:0% +Maring GOI effect on its own as a +shadow now for example looking at this + + align:start position:0% +shadow now for example looking at this + + + align:start position:0% +shadow now for example looking at this +small assemblage which is about 2 cm + + align:start position:0% +small assemblage which is about 2 cm + + + align:start position:0% +small assemblage which is about 2 cm +across I lit this with one light it's a + + align:start position:0% +across I lit this with one light it's a + + + align:start position:0% +across I lit this with one light it's a +monop point somewhat of a fiber optic + + align:start position:0% +monop point somewhat of a fiber optic + + + align:start position:0% +monop point somewhat of a fiber optic +source and you could see carefully if + + align:start position:0% +source and you could see carefully if + + + align:start position:0% +source and you could see carefully if +you look at this image where does the + + align:start position:0% +you look at this image where does the + + + align:start position:0% +you look at this image where does the +light source come from and hopefully you + + align:start position:0% +light source come from and hopefully you + + + align:start position:0% +light source come from and hopefully you +will figure out that if the shadow is + + align:start position:0% +will figure out that if the shadow is + + + align:start position:0% +will figure out that if the shadow is +here then the light source has to be + + align:start position:0% +here then the light source has to be + + + align:start position:0% +here then the light source has to be +around here in this next one I added a + + align:start position:0% +around here in this next one I added a + + + align:start position:0% +around here in this next one I added a +second light source that not only lights + + align:start position:0% +second light source that not only lights + + + align:start position:0% +second light source that not only lights +the device adds light to it but it also + + align:start position:0% +the device adds light to it but it also + + + align:start position:0% +the device adds light to it but it also +adds another + + align:start position:0% +adds another + + + align:start position:0% +adds another +Shadow and in this next one the second + + align:start position:0% +Shadow and in this next one the second + + + align:start position:0% +Shadow and in this next one the second +light source has been altered in terms + + align:start position:0% +light source has been altered in terms + + + align:start position:0% +light source has been altered in terms +of its direction + + align:start position:0% +of its direction + + + align:start position:0% +of its direction +and the height because the shadow that + + align:start position:0% +and the height because the shadow that + + + align:start position:0% +and the height because the shadow that +it casts is slightly longer and even + + align:start position:0% +it casts is slightly longer and even + + + align:start position:0% +it casts is slightly longer and even +more so in this final image where the + + align:start position:0% +more so in this final image where the + + + align:start position:0% +more so in this final image where the +light the second light source is very + + align:start position:0% +light the second light source is very + + + align:start position:0% +light the second light source is very +low compared to where it was and you + + align:start position:0% +low compared to where it was and you + + + align:start position:0% +low compared to where it was and you +know that again because the shadow is + + align:start position:0% +know that again because the shadow is + + + align:start position:0% +know that again because the shadow is +considerably longer now why bother + + align:start position:0% +considerably longer now why bother + + + align:start position:0% +considerably longer now why bother +looking at all this it really is once + + align:start position:0% +looking at all this it really is once + + + align:start position:0% +looking at all this it really is once +again learning to see so that when you + + align:start position:0% +again learning to see so that when you + + + align:start position:0% +again learning to see so that when you +play with your your own light sources + + align:start position:0% +play with your your own light sources + + + align:start position:0% +play with your your own light sources +with your own devices you're going to + + align:start position:0% +with your own devices you're going to + + + align:start position:0% +with your own devices you're going to +pay not only great attention to lighting + + align:start position:0% +pay not only great attention to lighting + + + align:start position:0% +pay not only great attention to lighting +of your device but the Shadows that the + + align:start position:0% +of your device but the Shadows that the + + + align:start position:0% +of your device but the Shadows that the +lighting will be producing it's + + align:start position:0% +lighting will be producing it's + + + align:start position:0% +lighting will be producing it's +important it might not seem that way at + + align:start position:0% +important it might not seem that way at + + + align:start position:0% +important it might not seem that way at +this point but I promise you it really + + align:start position:0% +this point but I promise you it really + + + align:start position:0% +this point but I promise you it really +is important \ No newline at end of file diff --git a/g0bXSXuLVb0.txt b/g0bXSXuLVb0.txt new file mode 100644 index 0000000000000000000000000000000000000000..2e97eaf9c05fe5b72b22dfddec849bf87adf33cf --- /dev/null +++ b/g0bXSXuLVb0.txt @@ -0,0 +1,16931 @@ +align:start position:0% + +all right welcome to + + align:start position:0% +all right welcome to + + + align:start position:0% +all right welcome to +practice problem session three double o + + align:start position:0% +practice problem session three double o + + + align:start position:0% +practice problem session three double o +six um + + align:start position:0% +six um + + + align:start position:0% +six um +today we are going to go through a bunch + + align:start position:0% +today we are going to go through a bunch + + + align:start position:0% +today we are going to go through a bunch +of problems which + + align:start position:0% +of problems which + + + align:start position:0% +of problems which +you should have already um i was + + align:start position:0% +you should have already um i was + + + align:start position:0% +you should have already um i was +thinking of skipping the very first + + align:start position:0% +thinking of skipping the very first + + + align:start position:0% +thinking of skipping the very first +problem because it's just a mechanical + + align:start position:0% +problem because it's just a mechanical + + + align:start position:0% +problem because it's just a mechanical +thing if we have time at the end we can + + align:start position:0% +thing if we have time at the end we can + + + align:start position:0% +thing if we have time at the end we can +come back to it but there's not really + + align:start position:0% +come back to it but there's not really + + + align:start position:0% +come back to it but there's not really +any + + align:start position:0% +any + + + align:start position:0% +any +insight i can give you in how to + + align:start position:0% +insight i can give you in how to + + + align:start position:0% +insight i can give you in how to +approach this problem it's just do you + + align:start position:0% +approach this problem it's just do you + + + align:start position:0% +approach this problem it's just do you +understand hashing + + align:start position:0% +understand hashing + + + align:start position:0% +understand hashing +so i want to go into the more creative + + align:start position:0% +so i want to go into the more creative + + + align:start position:0% +so i want to go into the more creative +problems first i'll start with + + align:start position:0% +problems first i'll start with + + + align:start position:0% +problems first i'll start with +problem three two hash sequence uh + + align:start position:0% +problem three two hash sequence uh + + + align:start position:0% +problem three two hash sequence uh +so i'll just read it and then our first + + align:start position:0% +so i'll just read it and then our first + + + align:start position:0% +so i'll just read it and then our first +task is to convert the la + + align:start position:0% +task is to convert the la + + + align:start position:0% +task is to convert the la +the word problem into a concise formal + + align:start position:0% +the word problem into a concise formal + + + align:start position:0% +the word problem into a concise formal +algorithms thing we need to achieve then + + align:start position:0% +algorithms thing we need to achieve then + + + align:start position:0% +algorithms thing we need to achieve then +we need to come up with ideas for how to + + align:start position:0% +we need to come up with ideas for how to + + + align:start position:0% +we need to come up with ideas for how to +achieve it and we need to check the + + align:start position:0% +achieve it and we need to check the + + + align:start position:0% +achieve it and we need to check the +details + + align:start position:0% +details + + + align:start position:0% +details +that'll be our general pattern so this + + align:start position:0% +that'll be our general pattern so this + + + align:start position:0% +that'll be our general pattern so this +problem says hash tables are not only + + align:start position:0% +problem says hash tables are not only + + + align:start position:0% +problem says hash tables are not only +useful for implementing set operations + + align:start position:0% +useful for implementing set operations + + + align:start position:0% +useful for implementing set operations +they can also be used to implement + + align:start position:0% +they can also be used to implement + + + align:start position:0% +they can also be used to implement +sequences + + align:start position:0% +sequences + + + align:start position:0% +sequences +remember from lecture two we have a set + + align:start position:0% +remember from lecture two we have a set + + + align:start position:0% +remember from lecture two we have a set +uh + + align:start position:0% +uh + + + align:start position:0% +uh +interface which is about querying items + + align:start position:0% +interface which is about querying items + + + align:start position:0% +interface which is about querying items +by either key and sort of intrinsic + + align:start position:0% +by either key and sort of intrinsic + + + align:start position:0% +by either key and sort of intrinsic +order + + align:start position:0% +order + + + align:start position:0% +order +that's about the items themselves versus + + align:start position:0% +that's about the items themselves versus + + + align:start position:0% +that's about the items themselves versus +a sequence interface that we started out + + align:start position:0% +a sequence interface that we started out + + + align:start position:0% +a sequence interface that we started out +with of linked lists and so on + + align:start position:0% +with of linked lists and so on + + + align:start position:0% +with of linked lists and so on +and arrays for uh where we're given an + + align:start position:0% +and arrays for uh where we're given an + + + align:start position:0% +and arrays for uh where we're given an +order we want to maintain that order and + + align:start position:0% +order we want to maintain that order and + + + align:start position:0% +order we want to maintain that order and +that order may not have anything to do + + align:start position:0% +that order may not have anything to do + + + align:start position:0% +that order may not have anything to do +with the + + align:start position:0% +with the + + + align:start position:0% +with the +items themselves that's what we call an + + align:start position:0% +items themselves that's what we call an + + + align:start position:0% +items themselves that's what we call an +extrinsic order we're told what the + + align:start position:0% +extrinsic order we're told what the + + + align:start position:0% +extrinsic order we're told what the +order is by saying insert this item + + align:start position:0% +order is by saying insert this item + + + align:start position:0% +order is by saying insert this item +after this one or append this one to the + + align:start position:0% +after this one or append this one to the + + + align:start position:0% +after this one or append this one to the +end or prepend it to the beginning + + align:start position:0% +end or prepend it to the beginning + + + align:start position:0% +end or prepend it to the beginning +so in lecture last week we saw hash + + align:start position:0% +so in lecture last week we saw hash + + + align:start position:0% +so in lecture last week we saw hash +tables implement + + align:start position:0% +tables implement + + + align:start position:0% +tables implement +sets and let me just remind you + + align:start position:0% +sets and let me just remind you + + + align:start position:0% +sets and let me just remind you +some things that they can do + + align:start position:0% +some things that they can do + + + align:start position:0% +some things that they can do +so we have on the one hand set + + align:start position:0% +so we have on the one hand set + + + align:start position:0% +so we have on the one hand set +hashing + + align:start position:0% + + + + align:start position:0% + +so this we're going to need this in a + + align:start position:0% +so this we're going to need this in a + + + align:start position:0% +so this we're going to need this in a +moment + + align:start position:0% +moment + + + align:start position:0% +moment +this is just a reminder from lecture we + + align:start position:0% +this is just a reminder from lecture we + + + align:start position:0% +this is just a reminder from lecture we +can build one in linear time + + align:start position:0% +can build one in linear time + + + align:start position:0% +can build one in linear time +expect it we can find an item in + + align:start position:0% +expect it we can find an item in + + + align:start position:0% +expect it we can find an item in +constant time + + align:start position:0% +constant time + + + align:start position:0% +constant time +expected by key and we can insert or + + align:start position:0% +expected by key and we can insert or + + + align:start position:0% +expected by key and we can insert or +delete an item + + align:start position:0% + + + + align:start position:0% + +in constant expected + + align:start position:0% +in constant expected + + + align:start position:0% +in constant expected +amortized + + align:start position:0% + + + + align:start position:0% + +okay uh so this is a black box that + + align:start position:0% +okay uh so this is a black box that + + + align:start position:0% +okay uh so this is a black box that +we're given + + align:start position:0% +we're given + + + align:start position:0% +we're given +and the problem + + align:start position:0% + + + + align:start position:0% + +statement says that imagine you're given + + align:start position:0% +statement says that imagine you're given + + + align:start position:0% +statement says that imagine you're given +a hash table as a black box which means + + align:start position:0% +a hash table as a black box which means + + + align:start position:0% +a hash table as a black box which means +we're given a thing that behave + + align:start position:0% +we're given a thing that behave + + + align:start position:0% +we're given a thing that behave +behaves just like a thank you to + + align:start position:0% +behaves just like a thank you to + + + align:start position:0% +behaves just like a thank you to +uh we're given something that is a hash + + align:start position:0% +uh we're given something that is a hash + + + align:start position:0% +uh we're given something that is a hash +table but + + align:start position:0% +table but + + + align:start position:0% +table but +it's black box in the sense that we're + + align:start position:0% +it's black box in the sense that we're + + + align:start position:0% +it's black box in the sense that we're +not allowed to reach in and change the + + align:start position:0% +not allowed to reach in and change the + + + align:start position:0% +not allowed to reach in and change the +implementation details we're supposed to + + align:start position:0% +implementation details we're supposed to + + + align:start position:0% +implementation details we're supposed to +use it as + + align:start position:0% +use it as + + + align:start position:0% +use it as +is just by calling its interface so in + + align:start position:0% +is just by calling its interface so in + + + align:start position:0% +is just by calling its interface so in +particular we're given these three + + align:start position:0% +particular we're given these three + + + align:start position:0% +particular we're given these three +operations i'll maybe also use + + align:start position:0% +operations i'll maybe also use + + + align:start position:0% +operations i'll maybe also use +it to iterate through the items so we're + + align:start position:0% +it to iterate through the items so we're + + + align:start position:0% +it to iterate through the items so we're +allowed to build something in linear + + align:start position:0% +allowed to build something in linear + + + align:start position:0% +allowed to build something in linear +time + + align:start position:0% +time + + + align:start position:0% +time +find and insert and delete and + + align:start position:0% +find and insert and delete and + + + align:start position:0% +find and insert and delete and +constantly expect it amortized + + align:start position:0% +constantly expect it amortized + + + align:start position:0% +constantly expect it amortized +and what the problem is asking is to + + align:start position:0% +and what the problem is asking is to + + + align:start position:0% +and what the problem is asking is to +build out of this data structure + + align:start position:0% +build out of this data structure + + + align:start position:0% +build out of this data structure +a sequence with particular time balance + + align:start position:0% +a sequence with particular time balance + + + align:start position:0% +a sequence with particular time balance +uh so this is what we call a reduction + + align:start position:0% + + + + align:start position:0% + +in that we're going to convert uh + + align:start position:0% +in that we're going to convert uh + + + align:start position:0% +in that we're going to convert uh +i guess technically we're reducing the + + align:start position:0% +i guess technically we're reducing the + + + align:start position:0% +i guess technically we're reducing the +sequence problem + + align:start position:0% +sequence problem + + + align:start position:0% +sequence problem +to the set problem um because we're + + align:start position:0% +to the set problem um because we're + + + align:start position:0% +to the set problem um because we're +showing how to solve the sequence + + align:start position:0% +showing how to solve the sequence + + + align:start position:0% +showing how to solve the sequence +problem using the set problem + + align:start position:0% +problem using the set problem + + + align:start position:0% +problem using the set problem +but the way we'll think about it is in + + align:start position:0% +but the way we'll think about it is in + + + align:start position:0% +but the way we'll think about it is in +the other direction we're given a data + + align:start position:0% +the other direction we're given a data + + + align:start position:0% +the other direction we're given a data +structure to solve set and we're going + + align:start position:0% +structure to solve set and we're going + + + align:start position:0% +structure to solve set and we're going +to convert it into a data structure that + + align:start position:0% +to convert it into a data structure that + + + align:start position:0% +to convert it into a data structure that +solves sequence + + align:start position:0% +solves sequence + + + align:start position:0% +solves sequence +so given that we already know how to do + + align:start position:0% +so given that we already know how to do + + + align:start position:0% +so given that we already know how to do +this from lecture we're going to learn + + align:start position:0% +this from lecture we're going to learn + + + align:start position:0% +this from lecture we're going to learn +how to do this + + align:start position:0% +how to do this + + + align:start position:0% +how to do this +this is teaching you new stuff in a + + align:start position:0% +this is teaching you new stuff in a + + + align:start position:0% +this is teaching you new stuff in a +problem set + + align:start position:0% +problem set + + + align:start position:0% +problem set +so the specific bounds that we're told + + align:start position:0% +so the specific bounds that we're told + + + align:start position:0% +so the specific bounds that we're told +to achieve are build + + align:start position:0% +to achieve are build + + + align:start position:0% +to achieve are build +and constant expected time + + align:start position:0% + + + + align:start position:0% + +get and set at + + align:start position:0% + + + + align:start position:0% + +inconstant expected time + + align:start position:0% +inconstant expected time + + + align:start position:0% +inconstant expected time +insert and delete app + + align:start position:0% + + + + align:start position:0% + +and linear expected time + + align:start position:0% + + + + align:start position:0% + +and insert and delete + + align:start position:0% +and insert and delete + + + align:start position:0% +and insert and delete +uh first and last + + align:start position:0% + + + + align:start position:0% + +and running out of room here + + align:start position:0% +and running out of room here + + + align:start position:0% +and running out of room here +constant expected amortized + + align:start position:0% + + + + align:start position:0% + +okay um so this is just what we're told + + align:start position:0% +okay um so this is just what we're told + + + align:start position:0% +okay um so this is just what we're told +to do + + align:start position:0% +to do + + + align:start position:0% +to do +and now we start thinking so we're given + + align:start position:0% +and now we start thinking so we're given + + + align:start position:0% +and now we start thinking so we're given +this + + align:start position:0% +this + + + align:start position:0% +this +we want to build this um and so + + align:start position:0% +we want to build this um and so + + + align:start position:0% +we want to build this um and so +i'm going to tell you a little bit about + + align:start position:0% +i'm going to tell you a little bit about + + + align:start position:0% +i'm going to tell you a little bit about +my thought process about when i'm + + align:start position:0% +my thought process about when i'm + + + align:start position:0% +my thought process about when i'm +presenting with a problem like this + + align:start position:0% +presenting with a problem like this + + + align:start position:0% +presenting with a problem like this +first thing is to read the problem + + align:start position:0% +first thing is to read the problem + + + align:start position:0% +first thing is to read the problem +and see okay what what's what's the hard + + align:start position:0% +and see okay what what's what's the hard + + + align:start position:0% +and see okay what what's what's the hard +part here + + align:start position:0% +part here + + + align:start position:0% +part here +what are the challenges so clearly we + + align:start position:0% +what are the challenges so clearly we + + + align:start position:0% +what are the challenges so clearly we +have to do all for all four of these + + align:start position:0% +have to do all for all four of these + + + align:start position:0% +have to do all for all four of these +types of operations + + align:start position:0% +types of operations + + + align:start position:0% +types of operations +building linear expected time that's + + align:start position:0% +building linear expected time that's + + + align:start position:0% +building linear expected time that's +basically everything we've seen + + align:start position:0% +basically everything we've seen + + + align:start position:0% +basically everything we've seen +uh get or set at in constant expected + + align:start position:0% +uh get or set at in constant expected + + + align:start position:0% +uh get or set at in constant expected +time that's fast + + align:start position:0% +time that's fast + + + align:start position:0% +time that's fast +and that feels kind of like this find + + align:start position:0% +and that feels kind of like this find + + + align:start position:0% +and that feels kind of like this find +operation + + align:start position:0% +operation + + + align:start position:0% +operation +so both of these seem pretty + + align:start position:0% +so both of these seem pretty + + + align:start position:0% +so both of these seem pretty +matchy-matchy so that + + align:start position:0% +matchy-matchy so that + + + align:start position:0% +matchy-matchy so that +looks like a good mapping i'm gonna try + + align:start position:0% +looks like a good mapping i'm gonna try + + + align:start position:0% +looks like a good mapping i'm gonna try +to build these operations using those + + align:start position:0% +to build these operations using those + + + align:start position:0% +to build these operations using those +operations + + align:start position:0% +operations + + + align:start position:0% +operations +insert and delete uh at a specific + + align:start position:0% +insert and delete uh at a specific + + + align:start position:0% +insert and delete uh at a specific +location + + align:start position:0% +location + + + align:start position:0% +location +in constant expected time sorry linear + + align:start position:0% +in constant expected time sorry linear + + + align:start position:0% +in constant expected time sorry linear +expected time + + align:start position:0% +expected time + + + align:start position:0% +expected time +that's big linear expected time means i + + align:start position:0% +that's big linear expected time means i + + + align:start position:0% +that's big linear expected time means i +can + + align:start position:0% +can + + + align:start position:0% +can +rebuild the entire data structure every + + align:start position:0% +rebuild the entire data structure every + + + align:start position:0% +rebuild the entire data structure every +time i do an operation + + align:start position:0% +time i do an operation + + + align:start position:0% +time i do an operation +so this is easy okay that's first thing + + align:start position:0% +so this is easy okay that's first thing + + + align:start position:0% +so this is easy okay that's first thing +you realize this + + align:start position:0% +you realize this + + + align:start position:0% +you realize this +is big great so i don't really have to + + align:start position:0% +is big great so i don't really have to + + + align:start position:0% +is big great so i don't really have to +worry + + align:start position:0% +worry + + + align:start position:0% +worry +about these operations i mean i do have + + align:start position:0% +about these operations i mean i do have + + + align:start position:0% +about these operations i mean i do have +to implement them but + + align:start position:0% +to implement them but + + + align:start position:0% +to implement them but +it's not hard to do it that fast because + + align:start position:0% +it's not hard to do it that fast because + + + align:start position:0% +it's not hard to do it that fast because +i can rebuild + + align:start position:0% +i can rebuild + + + align:start position:0% +i can rebuild +uh and then here insert and delete at + + align:start position:0% +uh and then here insert and delete at + + + align:start position:0% +uh and then here insert and delete at +the beginning and the end of the array + + align:start position:0% +the beginning and the end of the array + + + align:start position:0% +the beginning and the end of the array +these are the deck + + align:start position:0% +these are the deck + + + align:start position:0% +these are the deck +double ended queue operations can + + align:start position:0% +double ended queue operations can + + + align:start position:0% +double ended queue operations can +certainly leave at either end + + align:start position:0% +certainly leave at either end + + + align:start position:0% +certainly leave at either end +and constant expected amortized time + + align:start position:0% +and constant expected amortized time + + + align:start position:0% +and constant expected amortized time +this i feel like is + + align:start position:0% +this i feel like is + + + align:start position:0% +this i feel like is +a tricky one uh you've seen one way to + + align:start position:0% +a tricky one uh you've seen one way to + + + align:start position:0% +a tricky one uh you've seen one way to +do this in problem set + + align:start position:0% +do this in problem set + + + align:start position:0% +do this in problem set +but now we're gonna see another way with + + align:start position:0% +but now we're gonna see another way with + + + align:start position:0% +but now we're gonna see another way with +okay the other thing to notice is these + + align:start position:0% +okay the other thing to notice is these + + + align:start position:0% +okay the other thing to notice is these +expected words + + align:start position:0% +expected words + + + align:start position:0% +expected words +uh in this case we're told to use + + align:start position:0% +uh in this case we're told to use + + + align:start position:0% +uh in this case we're told to use +hashing but a lot of the problems + + align:start position:0% +hashing but a lot of the problems + + + align:start position:0% +hashing but a lot of the problems +you're not told how to solve it or what + + align:start position:0% +you're not told how to solve it or what + + + align:start position:0% +you're not told how to solve it or what +you should be basing your thing on + + align:start position:0% +you should be basing your thing on + + + align:start position:0% +you should be basing your thing on +and so expected is always a good keyword + + align:start position:0% +and so expected is always a good keyword + + + align:start position:0% +and so expected is always a good keyword +because it means randomization is + + align:start position:0% +because it means randomization is + + + align:start position:0% +because it means randomization is +involved somehow if you're told the + + align:start position:0% +involved somehow if you're told the + + + align:start position:0% +involved somehow if you're told the +bound is going to be expected + + align:start position:0% +bound is going to be expected + + + align:start position:0% +bound is going to be expected +you should you probably need to use + + align:start position:0% +you should you probably need to use + + + align:start position:0% +you should you probably need to use +randomization + + align:start position:0% +randomization + + + align:start position:0% +randomization +and in this class the only form of + + align:start position:0% +and in this class the only form of + + + align:start position:0% +and in this class the only form of +randomization you will use is + + align:start position:0% +randomization you will use is + + + align:start position:0% +randomization you will use is +essentially hashing + + align:start position:0% +essentially hashing + + + align:start position:0% +essentially hashing +so uh that's a good hint + + align:start position:0% +so uh that's a good hint + + + align:start position:0% +so uh that's a good hint +in this case we know that we're supposed + + align:start position:0% +in this case we know that we're supposed + + + align:start position:0% +in this case we know that we're supposed +to use hashing all right so + + align:start position:0% +to use hashing all right so + + + align:start position:0% +to use hashing all right so +this is going to be the challenge + + align:start position:0% + + + + align:start position:0% + +but any ideas on how we might tackle + + align:start position:0% +but any ideas on how we might tackle + + + align:start position:0% +but any ideas on how we might tackle +this problem how can we + + align:start position:0% +this problem how can we + + + align:start position:0% +this problem how can we +so set remember every item has a key + + align:start position:0% +so set remember every item has a key + + + align:start position:0% +so set remember every item has a key +in a sequence items are just items and + + align:start position:0% +in a sequence items are just items and + + + align:start position:0% +in a sequence items are just items and +we're told to insert and delete them at + + align:start position:0% +we're told to insert and delete them at + + + align:start position:0% +we're told to insert and delete them at +particular locations + + align:start position:0% +particular locations + + + align:start position:0% +particular locations +but they don't have keys so one of the + + align:start position:0% +but they don't have keys so one of the + + + align:start position:0% +but they don't have keys so one of the +challenges is going to be + + align:start position:0% +challenges is going to be + + + align:start position:0% +challenges is going to be +to take our items here give them keys so + + align:start position:0% +to take our items here give them keys so + + + align:start position:0% +to take our items here give them keys so +that we can store them in a set + + align:start position:0% +that we can store them in a set + + + align:start position:0% +that we can store them in a set +otherwise we can't use find + + align:start position:0% +otherwise we can't use find + + + align:start position:0% +otherwise we can't use find +there's no keys there there's no way to + + align:start position:0% +there's no keys there there's no way to + + + align:start position:0% +there's no keys there there's no way to +search by key + + align:start position:0% + + + + align:start position:0% + +ideas + + align:start position:0% + + + + align:start position:0% + +so let's think about what we want to do + + align:start position:0% +so let's think about what we want to do + + + align:start position:0% +so let's think about what we want to do +let's start with so build i think is + + align:start position:0% +let's start with so build i think is + + + align:start position:0% +let's start with so build i think is +fine if you + + align:start position:0% +fine if you + + + align:start position:0% +fine if you +just want to build a data structure you + + align:start position:0% +just want to build a data structure you + + + align:start position:0% +just want to build a data structure you +don't need to do anything + + align:start position:0% +don't need to do anything + + + align:start position:0% +don't need to do anything +the hard part are the queries or updates + + align:start position:0% +the hard part are the queries or updates + + + align:start position:0% +the hard part are the queries or updates +you want to be able to do on your data + + align:start position:0% +you want to be able to do on your data + + + align:start position:0% +you want to be able to do on your data +structure + + align:start position:0% +structure + + + align:start position:0% +structure +let's start with this operation get and + + align:start position:0% +let's start with this operation get and + + + align:start position:0% +let's start with this operation get and +set at so + + align:start position:0% +set at so + + + align:start position:0% +set at so +remember get at your given and index i + + align:start position:0% +remember get at your given and index i + + + align:start position:0% +remember get at your given and index i +and you want to + + align:start position:0% + + + + align:start position:0% + +find the item at position i + + align:start position:0% +find the item at position i + + + align:start position:0% +find the item at position i +and set at we're given + + align:start position:0% +and set at we're given + + + align:start position:0% +and set at we're given +a position and we want to change the + + align:start position:0% +a position and we want to change the + + + align:start position:0% +a position and we want to change the +item stored + + align:start position:0% +item stored + + + align:start position:0% +item stored +at that position at that index i now + + align:start position:0% +at that position at that index i now + + + align:start position:0% +at that position at that index i now +over here + + align:start position:0% +over here + + + align:start position:0% +over here +what we're given we can insert and + + align:start position:0% +what we're given we can insert and + + + align:start position:0% +what we're given we can insert and +delete + + align:start position:0% +delete + + + align:start position:0% +delete +but the main sort of lookup let's think + + align:start position:0% +but the main sort of lookup let's think + + + align:start position:0% +but the main sort of lookup let's think +about get at first + + align:start position:0% +about get at first + + + align:start position:0% +about get at first +the natural mapping given this arrow + + align:start position:0% +the natural mapping given this arrow + + + align:start position:0% +the natural mapping given this arrow +is find find will search for an item by + + align:start position:0% +is find find will search for an item by + + + align:start position:0% +is find find will search for an item by +key + + align:start position:0% +key + + + align:start position:0% +key +so here's just staring at that once you + + align:start position:0% +so here's just staring at that once you + + + align:start position:0% +so here's just staring at that once you +look at all the possible pairings you + + align:start position:0% +look at all the possible pairings you + + + align:start position:0% +look at all the possible pairings you +could do + + align:start position:0% +could do + + + align:start position:0% +could do +we have find by key over here and we + + align:start position:0% +we have find by key over here and we + + + align:start position:0% +we have find by key over here and we +need to implement get at by index + + align:start position:0% +need to implement get at by index + + + align:start position:0% +need to implement get at by index +so let's make the indices keys okay so + + align:start position:0% +so let's make the indices keys okay so + + + align:start position:0% +so let's make the indices keys okay so +this is idea number one + + align:start position:0% +this is idea number one + + + align:start position:0% +this is idea number one +uh index + + align:start position:0% + + + + align:start position:0% + +assign a key + + align:start position:0% +assign a key + + + align:start position:0% +assign a key +to each item + + align:start position:0% + + + + align:start position:0% + +equal to the index + + align:start position:0% +equal to the index + + + align:start position:0% +equal to the index +in the sequence + + align:start position:0% +in the sequence + + + align:start position:0% +in the sequence +okay so then when i do to implement get + + align:start position:0% +okay so then when i do to implement get + + + align:start position:0% +okay so then when i do to implement get +ad i can just call + + align:start position:0% +ad i can just call + + + align:start position:0% +ad i can just call +find of i + + align:start position:0% +find of i + + + align:start position:0% +find of i +if i is also a key and that should give + + align:start position:0% +if i is also a key and that should give + + + align:start position:0% +if i is also a key and that should give +me + + align:start position:0% +me + + + align:start position:0% +me +the thing that i want maybe for this to + + align:start position:0% +the thing that i want maybe for this to + + + align:start position:0% +the thing that i want maybe for this to +make sense let me tell you how i'm + + align:start position:0% +make sense let me tell you how i'm + + + align:start position:0% +make sense let me tell you how i'm +building + + align:start position:0% +building + + + align:start position:0% +building +so if i'm given say an array of items + + align:start position:0% +so if i'm given say an array of items + + + align:start position:0% +so if i'm given say an array of items +uh and they're both the only name + + align:start position:0% +uh and they're both the only name + + + align:start position:0% +uh and they're both the only name +conflict here is built so let me call + + align:start position:0% +conflict here is built so let me call + + + align:start position:0% +conflict here is built so let me call +this one + + align:start position:0% +this one + + + align:start position:0% +this one +sequence build + + align:start position:0% + + + + align:start position:0% + +and i'm going to implement it using set + + align:start position:0% +and i'm going to implement it using set + + + align:start position:0% +and i'm going to implement it using set +build + + align:start position:0% + + + + align:start position:0% + +and i'll use some short shorthand + + align:start position:0% +and i'll use some short shorthand + + + align:start position:0% +and i'll use some short shorthand +notation here let's say + + align:start position:0% +notation here let's say + + + align:start position:0% +notation here let's say +i want to make an object that has a key + + align:start position:0% +i want to make an object that has a key + + + align:start position:0% +i want to make an object that has a key +equal to i and a value + + align:start position:0% +equal to i and a value + + + align:start position:0% +equal to i and a value +equal to a of i + + align:start position:0% + + + + align:start position:0% + +that's my object notation for i + + align:start position:0% +that's my object notation for i + + + align:start position:0% +that's my object notation for i +equals 0 1 to + + align:start position:0% +equals 0 1 to + + + align:start position:0% +equals 0 1 to +size of a minus 1. + + align:start position:0% +size of a minus 1. + + + align:start position:0% +size of a minus 1. +that's a little bit code-like but not + + align:start position:0% +that's a little bit code-like but not + + + align:start position:0% +that's a little bit code-like but not +quite literal code + + align:start position:0% +quite literal code + + + align:start position:0% +quite literal code +so i'm just going to use this to say + + align:start position:0% +so i'm just going to use this to say + + + align:start position:0% +so i'm just going to use this to say +let's make an object that has two + + align:start position:0% +let's make an object that has two + + + align:start position:0% +let's make an object that has two +parts one is called the key so we can + + align:start position:0% +parts one is called the key so we can + + + align:start position:0% +parts one is called the key so we can +talk about the object.key + + align:start position:0% +talk about the object.key + + + align:start position:0% +talk about the object.key +so we can see which sets want to do and + + align:start position:0% +so we can see which sets want to do and + + + align:start position:0% +so we can see which sets want to do and +we're also going to store a value which + + align:start position:0% +we're also going to store a value which + + + align:start position:0% +we're also going to store a value which +is the actual item that we're given + + align:start position:0% +is the actual item that we're given + + + align:start position:0% +is the actual item that we're given +so i'm just because these are given in + + align:start position:0% +so i'm just because these are given in + + + align:start position:0% +so i'm just because these are given in +the sequence i'm just representing that + + align:start position:0% +the sequence i'm just representing that + + + align:start position:0% +the sequence i'm just representing that +sequence order by assigning i to be the + + align:start position:0% +sequence order by assigning i to be the + + + align:start position:0% +sequence order by assigning i to be the +key + + align:start position:0% +key + + + align:start position:0% +key +and so now if i want to find the item at + + align:start position:0% +and so now if i want to find the item at + + + align:start position:0% +and so now if i want to find the item at +index i + + align:start position:0% +index i + + + align:start position:0% +index i +i can do find of i and technically i + + align:start position:0% +i can do find of i and technically i + + + align:start position:0% +i can do find of i and technically i +should probably do dot + + align:start position:0% +should probably do dot + + + align:start position:0% +should probably do dot +value that will give me the actual item + + align:start position:0% +value that will give me the actual item + + + align:start position:0% +value that will give me the actual item +that's stored + + align:start position:0% +that's stored + + + align:start position:0% +that's stored +at that position when i do find of i i'm + + align:start position:0% +at that position when i do find of i i'm + + + align:start position:0% +at that position when i do find of i i'm +going to get this whole object + + align:start position:0% +going to get this whole object + + + align:start position:0% +going to get this whole object +with the key of i and then i want to get + + align:start position:0% +with the key of i and then i want to get + + + align:start position:0% +with the key of i and then i want to get +the value part of it + + align:start position:0% +the value part of it + + + align:start position:0% +the value part of it +so then set at i can just + + align:start position:0% +so then set at i can just + + + align:start position:0% +so then set at i can just +use this find operation to get + + align:start position:0% +use this find operation to get + + + align:start position:0% +use this find operation to get +the object and set its value to x + + align:start position:0% +the object and set its value to x + + + align:start position:0% +the object and set its value to x +boom we've implemented array like + + align:start position:0% +boom we've implemented array like + + + align:start position:0% +boom we've implemented array like +semantics get at + + align:start position:0% +semantics get at + + + align:start position:0% +semantics get at +i and set at i using + + align:start position:0% +i and set at i using + + + align:start position:0% +i and set at i using +a set if you've ever programmed in + + align:start position:0% +a set if you've ever programmed in + + + align:start position:0% +a set if you've ever programmed in +javascript this should feel very + + align:start position:0% +javascript this should feel very + + + align:start position:0% +javascript this should feel very +familiar because javascript + + align:start position:0% +familiar because javascript + + + align:start position:0% +familiar because javascript +actually implements arrays it's at least + + align:start position:0% +actually implements arrays it's at least + + + align:start position:0% +actually implements arrays it's at least +at the conceptual level + + align:start position:0% +at the conceptual level + + + align:start position:0% +at the conceptual level +as just general mapping types which are + + align:start position:0% +as just general mapping types which are + + + align:start position:0% +as just general mapping types which are +they call them objects but they are + + align:start position:0% +they call them objects but they are + + + align:start position:0% +they call them objects but they are +basically sets + + align:start position:0% +basically sets + + + align:start position:0% +basically sets +and if it's even grosser they convert + + align:start position:0% +and if it's even grosser they convert + + + align:start position:0% +and if it's even grosser they convert +the integers into strings and then index + + align:start position:0% +the integers into strings and then index + + + align:start position:0% +the integers into strings and then index +everything by the strings + + align:start position:0% +everything by the strings + + + align:start position:0% +everything by the strings +semantically anyway implementation + + align:start position:0% +semantically anyway implementation + + + align:start position:0% +semantically anyway implementation +details can be more efficient but + + align:start position:0% +details can be more efficient but + + + align:start position:0% +details can be more efficient but +conceptually that's what's going on and + + align:start position:0% +conceptually that's what's going on and + + + align:start position:0% +conceptually that's what's going on and +so that's the the idea we're doing here + + align:start position:0% +so that's the the idea we're doing here + + + align:start position:0% +so that's the the idea we're doing here +which seems great um any + + align:start position:0% +which seems great um any + + + align:start position:0% +which seems great um any +any problem so i have let's see there's + + align:start position:0% +any problem so i have let's see there's + + + align:start position:0% +any problem so i have let's see there's +insert and delete app + + align:start position:0% +insert and delete app + + + align:start position:0% +insert and delete app +as i mentioned what i'm going to do for + + align:start position:0% +as i mentioned what i'm going to do for + + + align:start position:0% +as i mentioned what i'm going to do for +those operations just rebuild the entire + + align:start position:0% +those operations just rebuild the entire + + + align:start position:0% +those operations just rebuild the entire +structure + + align:start position:0% +structure + + + align:start position:0% +structure +and just write that briefly + + align:start position:0% + + + + align:start position:0% + +basically uh let's just iterate all the + + align:start position:0% +basically uh let's just iterate all the + + + align:start position:0% +basically uh let's just iterate all the +items + + align:start position:0% +items + + + align:start position:0% +items +iterate all items + + align:start position:0% +iterate all items + + + align:start position:0% +iterate all items +um let's say into an array + + align:start position:0% +um let's say into an array + + + align:start position:0% +um let's say into an array +insert delete one of them + + align:start position:0% +insert delete one of them + + + align:start position:0% +insert delete one of them +and then rebuild okay + + align:start position:0% +and then rebuild okay + + + align:start position:0% +and then rebuild okay +if i was writing a pset answer i would + + align:start position:0% +if i was writing a pset answer i would + + + align:start position:0% +if i was writing a pset answer i would +say a little bit more detail what i + + align:start position:0% +say a little bit more detail what i + + + align:start position:0% +say a little bit more detail what i +mean in this step um i've done it in the + + align:start position:0% +mean in this step um i've done it in the + + + align:start position:0% +mean in this step um i've done it in the +notes not that hard + + align:start position:0% +notes not that hard + + + align:start position:0% +notes not that hard +but we can afford linear expected time i + + align:start position:0% +but we can afford linear expected time i + + + align:start position:0% +but we can afford linear expected time i +can afford to call build again + + align:start position:0% +can afford to call build again + + + align:start position:0% +can afford to call build again +i guess technically i'm calling this + + align:start position:0% +i guess technically i'm calling this + + + align:start position:0% +i guess technically i'm calling this +build sequence build + + align:start position:0% + + + + align:start position:0% + +uh so i can afford to just extract + + align:start position:0% +uh so i can afford to just extract + + + align:start position:0% +uh so i can afford to just extract +things into an array do the linear time + + align:start position:0% +things into an array do the linear time + + + align:start position:0% +things into an array do the linear time +operation on the array of + + align:start position:0% +operation on the array of + + + align:start position:0% +operation on the array of +with the shifting and everything and + + align:start position:0% +with the shifting and everything and + + + align:start position:0% +with the shifting and everything and +then just call build again yeah + + align:start position:0% +then just call build again yeah + + + align:start position:0% +then just call build again yeah +questions + + align:start position:0% + + + + align:start position:0% + +no these are separate definitions yeah + + align:start position:0% +no these are separate definitions yeah + + + align:start position:0% +no these are separate definitions yeah +sorry they got + + align:start position:0% +sorry they got + + + align:start position:0% +sorry they got +a little close so this is the definition + + align:start position:0% +a little close so this is the definition + + + align:start position:0% +a little close so this is the definition +of get at this is a definition of + + align:start position:0% +of get at this is a definition of + + + align:start position:0% +of get at this is a definition of +sequence build + + align:start position:0% +sequence build + + + align:start position:0% +sequence build +yeah thanks for asking + + align:start position:0% + + + + align:start position:0% + +okay all good yeah can you + + align:start position:0% +okay all good yeah can you + + + align:start position:0% +okay all good yeah can you +explain the answer explain insert and + + align:start position:0% +explain the answer explain insert and + + + align:start position:0% +explain the answer explain insert and +delete okay so + + align:start position:0% +delete okay so + + + align:start position:0% +delete okay so +maybe i should actually write one of + + align:start position:0% +maybe i should actually write one of + + + align:start position:0% +maybe i should actually write one of +them down + + align:start position:0% +them down + + + align:start position:0% +them down +or i'll just draw a picture maybe so we + + align:start position:0% +or i'll just draw a picture maybe so we + + + align:start position:0% +or i'll just draw a picture maybe so we +have this data structure + + align:start position:0% +have this data structure + + + align:start position:0% +have this data structure +which is now a sequence data structure + + align:start position:0% +which is now a sequence data structure + + + align:start position:0% +which is now a sequence data structure +represents some sequence of items and my + + align:start position:0% +represents some sequence of items and my + + + align:start position:0% +represents some sequence of items and my +goal is to say delete + + align:start position:0% +goal is to say delete + + + align:start position:0% +goal is to say delete +the i item so there's some items in here + + align:start position:0% +the i item so there's some items in here + + + align:start position:0% +the i item so there's some items in here +x0 + + align:start position:0% +x0 + + + align:start position:0% +x0 +up to xn minus 1. i want to remove x i + + align:start position:0% +up to xn minus 1. i want to remove x i + + + align:start position:0% +up to xn minus 1. i want to remove x i +from the sequence + + align:start position:0% +from the sequence + + + align:start position:0% +from the sequence +or i guess i should drop it this way + + align:start position:0% +or i guess i should drop it this way + + + align:start position:0% +or i guess i should drop it this way +it's coming out + + align:start position:0% +it's coming out + + + align:start position:0% +it's coming out +so uh what i'm going to do is first + + align:start position:0% +so uh what i'm going to do is first + + + align:start position:0% +so uh what i'm going to do is first +extract all the items from the sequence + + align:start position:0% +extract all the items from the sequence + + + align:start position:0% +extract all the items from the sequence +and i didn't write it but there's a + + align:start position:0% +and i didn't write it but there's a + + + align:start position:0% +and i didn't write it but there's a +an interface over here called itter + + align:start position:0% +an interface over here called itter + + + align:start position:0% +an interface over here called itter +which + + align:start position:0% +which + + + align:start position:0% +which +just gives me all the items in order so + + align:start position:0% +just gives me all the items in order so + + + align:start position:0% +just gives me all the items in order so +i'm going to extract + + align:start position:0% +i'm going to extract + + + align:start position:0% +i'm going to extract +this into an array sequence + + align:start position:0% + + + + align:start position:0% + +let's say i'll just build a static array + + align:start position:0% +let's say i'll just build a static array + + + align:start position:0% +let's say i'll just build a static array +of size + + align:start position:0% +of size + + + align:start position:0% +of size +n i also have a length operation that + + align:start position:0% +n i also have a length operation that + + + align:start position:0% +n i also have a length operation that +tells me how many + + align:start position:0% +tells me how many + + + align:start position:0% +tells me how many +items are in here and the the iter + + align:start position:0% +items are in here and the the iter + + + align:start position:0% +items are in here and the the iter +operation will give me all the items in + + align:start position:0% +operation will give me all the items in + + + align:start position:0% +operation will give me all the items in +order and so i'll put into my + + align:start position:0% +order and so i'll put into my + + + align:start position:0% +order and so i'll put into my +array x0 and then x1 and so on as they + + align:start position:0% +array x0 and then x1 and so on as they + + + align:start position:0% +array x0 and then x1 and so on as they +come out + + align:start position:0% +come out + + + align:start position:0% +come out +then i go to position i + + align:start position:0% +then i go to position i + + + align:start position:0% +then i go to position i +and i want to delete that item and shift + + align:start position:0% +and i want to delete that item and shift + + + align:start position:0% +and i want to delete that item and shift +all the others over this is the + + align:start position:0% +all the others over this is the + + + align:start position:0% +all the others over this is the +boring this is i think we even said how + + align:start position:0% +boring this is i think we even said how + + + align:start position:0% +boring this is i think we even said how +to do delete + + align:start position:0% +to do delete + + + align:start position:0% +to do delete +at in dynamic arrays + + align:start position:0% +at in dynamic arrays + + + align:start position:0% +at in dynamic arrays +in recitation 2 pretty sure so i'm just + + align:start position:0% +in recitation 2 pretty sure so i'm just + + + align:start position:0% +in recitation 2 pretty sure so i'm just +mimicking that i'm building + + align:start position:0% +mimicking that i'm building + + + align:start position:0% +mimicking that i'm building +this just to get the new order of things + + align:start position:0% +this just to get the new order of things + + + align:start position:0% +this just to get the new order of things +and then i'm applying + + align:start position:0% +and then i'm applying + + + align:start position:0% +and then i'm applying +via the build operation i'm building a + + align:start position:0% +via the build operation i'm building a + + + align:start position:0% +via the build operation i'm building a +totally new sequence + + align:start position:0% + + + + align:start position:0% + +and that's how i would implement delete + + align:start position:0% +and that's how i would implement delete + + + align:start position:0% +and that's how i would implement delete +app one way + + align:start position:0% +app one way + + + align:start position:0% +app one way +there are other ways yeah um + + align:start position:0% + + + + align:start position:0% + +how much space is this using uh oh it + + align:start position:0% +how much space is this using uh oh it + + + align:start position:0% +how much space is this using uh oh it +problem with space if you're inserting + + align:start position:0% +problem with space if you're inserting + + + align:start position:0% +problem with space if you're inserting +if you're inserting you probably want to + + align:start position:0% +if you're inserting you probably want to + + + align:start position:0% +if you're inserting you probably want to +allocate a static array of size n plus + + align:start position:0% +allocate a static array of size n plus + + + align:start position:0% +allocate a static array of size n plus +one you know exactly what's going to + + align:start position:0% +one you know exactly what's going to + + + align:start position:0% +one you know exactly what's going to +happen + + align:start position:0% +happen + + + align:start position:0% +happen +so just allocate a little bit bigger + + align:start position:0% +so just allocate a little bit bigger + + + align:start position:0% +so just allocate a little bit bigger +then you can do the shift + + align:start position:0% +then you can do the shift + + + align:start position:0% +then you can do the shift +you could also use dynamic arrays but + + align:start position:0% +you could also use dynamic arrays but + + + align:start position:0% +you could also use dynamic arrays but +then you would get maybe an + + align:start position:0% +then you would get maybe an + + + align:start position:0% +then you would get maybe an +it's not an amortized bound because + + align:start position:0% +it's not an amortized bound because + + + align:start position:0% +it's not an amortized bound because +you're only doing one insertion + + align:start position:0% +you're only doing one insertion + + + align:start position:0% +you're only doing one insertion +the point is this is really easy we can + + align:start position:0% +the point is this is really easy we can + + + align:start position:0% +the point is this is really easy we can +spend linear time + + align:start position:0% +spend linear time + + + align:start position:0% +spend linear time +so we can rebuild the we can rebuild + + align:start position:0% +so we can rebuild the we can rebuild + + + align:start position:0% +so we can rebuild the we can rebuild +this array + + align:start position:0% +this array + + + align:start position:0% +this array +three times if we want it question uh + + align:start position:0% +three times if we want it question uh + + + align:start position:0% +three times if we want it question uh +what if you weren't allowed + + align:start position:0% +what if you weren't allowed + + + align:start position:0% +what if you weren't allowed +externally uh non-constant space + + align:start position:0% +externally uh non-constant space + + + align:start position:0% +externally uh non-constant space +ah you gotta throw me open problems uh + + align:start position:0% +ah you gotta throw me open problems uh + + + align:start position:0% +ah you gotta throw me open problems uh +what if you only + + align:start position:0% +what if you only + + + align:start position:0% +what if you only +have constant extra space uh + + align:start position:0% + + + + align:start position:0% + +right then i think we need to use insert + + align:start position:0% +right then i think we need to use insert + + + align:start position:0% +right then i think we need to use insert +and delete + + align:start position:0% +and delete + + + align:start position:0% +and delete +so we could good question um + + align:start position:0% +so we could good question um + + + align:start position:0% +so we could good question um +we could conceptually do this shifting + + align:start position:0% +we could conceptually do this shifting + + + align:start position:0% +we could conceptually do this shifting +but do it using insert and delete + + align:start position:0% +but do it using insert and delete + + + align:start position:0% +but do it using insert and delete +so we can so let's do the + + align:start position:0% +so we can so let's do the + + + align:start position:0% +so we can so let's do the +delete case again so we want to + + align:start position:0% +delete case again so we want to + + + align:start position:0% +delete case again so we want to +here's x i we want to replace it with x + + align:start position:0% +here's x i we want to replace it with x + + + align:start position:0% +here's x i we want to replace it with x +i plus 1 + + align:start position:0% +i plus 1 + + + align:start position:0% +i plus 1 +and so on + + align:start position:0% + + + + align:start position:0% + +and so we can start out by deleting + + align:start position:0% +and so we can start out by deleting + + + align:start position:0% +and so we can start out by deleting +the item with key i that will get rid of + + align:start position:0% +the item with key i that will get rid of + + + align:start position:0% +the item with key i that will get rid of +this guy + + align:start position:0% +this guy + + + align:start position:0% +this guy +then we can delete the item with key i + + align:start position:0% +then we can delete the item with key i + + + align:start position:0% +then we can delete the item with key i +plus one + + align:start position:0% +plus one + + + align:start position:0% +plus one +give it and that gives us the item and + + align:start position:0% +give it and that gives us the item and + + + align:start position:0% +give it and that gives us the item and +then we can reassign its key to be + + align:start position:0% +then we can reassign its key to be + + + align:start position:0% +then we can reassign its key to be +i i instead of i plus 1 and then + + align:start position:0% +i i instead of i plus 1 and then + + + align:start position:0% +i i instead of i plus 1 and then +reinsert it + + align:start position:0% +reinsert it + + + align:start position:0% +reinsert it +so we can take this item out it has a + + align:start position:0% +so we can take this item out it has a + + + align:start position:0% +so we can take this item out it has a +key + + align:start position:0% +key + + + align:start position:0% +key +which is draw this properly + + align:start position:0% +which is draw this properly + + + align:start position:0% +which is draw this properly +so we have key i plus 1 + + align:start position:0% +so we have key i plus 1 + + + align:start position:0% +so we have key i plus 1 +and value x i plus 1 + + align:start position:0% +and value x i plus 1 + + + align:start position:0% +and value x i plus 1 +stored in this data structure then we + + align:start position:0% +stored in this data structure then we + + + align:start position:0% +stored in this data structure then we +update the key to i and then we reinsert + + align:start position:0% +update the key to i and then we reinsert + + + align:start position:0% +update the key to i and then we reinsert +it + + align:start position:0% +it + + + align:start position:0% +it +and it takes the place of this guy so + + align:start position:0% +and it takes the place of this guy so + + + align:start position:0% +and it takes the place of this guy so +you could do that you could go down this + + align:start position:0% +you could do that you could go down this + + + align:start position:0% +you could do that you could go down this +list + + align:start position:0% +list + + + align:start position:0% +list +and or not the list but you could + + align:start position:0% +and or not the list but you could + + + align:start position:0% +and or not the list but you could +iterate for i equals + + align:start position:0% +iterate for i equals + + + align:start position:0% +iterate for i equals +sorry for j equals i to n minus one and + + align:start position:0% +sorry for j equals i to n minus one and + + + align:start position:0% +sorry for j equals i to n minus one and +for each of those items + + align:start position:0% +for each of those items + + + align:start position:0% +for each of those items +delete it change its key reinsert it + + align:start position:0% +delete it change its key reinsert it + + + align:start position:0% +delete it change its key reinsert it +with a new key + + align:start position:0% +with a new key + + + align:start position:0% +with a new key +and then you don't have to build this + + align:start position:0% +and then you don't have to build this + + + align:start position:0% +and then you don't have to build this +intermediate data structure + + align:start position:0% +intermediate data structure + + + align:start position:0% +intermediate data structure +so if you're told to have been in + + align:start position:0% +so if you're told to have been in + + + align:start position:0% +so if you're told to have been in +myspace great and maybe you think of + + align:start position:0% +myspace great and maybe you think of + + + align:start position:0% +myspace great and maybe you think of +that as simpler i like to think of this + + align:start position:0% +that as simpler i like to think of this + + + align:start position:0% +that as simpler i like to think of this +as simpler because like + + align:start position:0% +as simpler because like + + + align:start position:0% +as simpler because like +the point is i have linear time i can do + + align:start position:0% +the point is i have linear time i can do + + + align:start position:0% +the point is i have linear time i can do +crazy + + align:start position:0% +crazy + + + align:start position:0% +crazy +silly very non-data structuresy things + + align:start position:0% +silly very non-data structuresy things + + + align:start position:0% +silly very non-data structuresy things +where i just start from scratch + + align:start position:0% +where i just start from scratch + + + align:start position:0% +where i just start from scratch +okay great but there's one more set of + + align:start position:0% +okay great but there's one more set of + + + align:start position:0% +okay great but there's one more set of +operations insert delete first and last + + align:start position:0% +operations insert delete first and last + + + align:start position:0% +operations insert delete first and last +are these easy good + + align:start position:0% +are these easy good + + + align:start position:0% +are these easy good +shall we try uh we can + + align:start position:0% +shall we try uh we can + + + align:start position:0% +shall we try uh we can +insert last + + align:start position:0% + + + + align:start position:0% + +so this is given an item x we want to + + align:start position:0% +so this is given an item x we want to + + + align:start position:0% +so this is given an item x we want to +add it to the end of the structure so + + align:start position:0% +add it to the end of the structure so + + + align:start position:0% +add it to the end of the structure so +that means its index is going to be + + align:start position:0% +that means its index is going to be + + + align:start position:0% +that means its index is going to be +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +because we start at 0 it's going to be + + align:start position:0% +because we start at 0 it's going to be + + + align:start position:0% +because we start at 0 it's going to be +equal to the length current length of + + align:start position:0% +equal to the length current length of + + + align:start position:0% +equal to the length current length of +the structure + + align:start position:0% +the structure + + + align:start position:0% +the structure +so let's just insert a new object + + align:start position:0% +so let's just insert a new object + + + align:start position:0% +so let's just insert a new object +which has key equal to the length + + align:start position:0% +which has key equal to the length + + + align:start position:0% +which has key equal to the length +and it has value equal to x + + align:start position:0% +and it has value equal to x + + + align:start position:0% +and it has value equal to x +we're done delete last similar just + + align:start position:0% +we're done delete last similar just + + + align:start position:0% +we're done delete last similar just +delete the item with key + + align:start position:0% +delete the item with key + + + align:start position:0% +delete the item with key +length minus one okay what about first + + align:start position:0% + + + + align:start position:0% + +this is supposed to add x to the + + align:start position:0% +this is supposed to add x to the + + + align:start position:0% +this is supposed to add x to the +beginning of my sequence + + align:start position:0% + + + + align:start position:0% + +well now i realize i have a problem + + align:start position:0% +well now i realize i have a problem + + + align:start position:0% +well now i realize i have a problem +because + + align:start position:0% +because + + + align:start position:0% +because +i want this new item to have key 0 + + align:start position:0% +i want this new item to have key 0 + + + align:start position:0% +i want this new item to have key 0 +because after i do an insert first get + + align:start position:0% +because after i do an insert first get + + + align:start position:0% +because after i do an insert first get +out of 0 should return this item + + align:start position:0% +out of 0 should return this item + + + align:start position:0% +out of 0 should return this item +but i already have an item with key 0 + + align:start position:0% +but i already have an item with key 0 + + + align:start position:0% +but i already have an item with key 0 +and an item with key 1 and an item with + + align:start position:0% +and an item with key 1 and an item with + + + align:start position:0% +and an item with key 1 and an item with +key + + align:start position:0% +key + + + align:start position:0% +key +2 and so on down the way and so if i + + align:start position:0% +2 and so on down the way and so if i + + + align:start position:0% +2 and so on down the way and so if i +wanted to give x a key of 0 i have to + + align:start position:0% +wanted to give x a key of 0 i have to + + + align:start position:0% +wanted to give x a key of 0 i have to +shift the keys of + + align:start position:0% +shift the keys of + + + align:start position:0% +shift the keys of +all of those items just like we were + + align:start position:0% +all of those items just like we were + + + align:start position:0% +all of those items just like we were +doing here and that's going to take + + align:start position:0% +doing here and that's going to take + + + align:start position:0% +doing here and that's going to take +linear time + + align:start position:0% +linear time + + + align:start position:0% +linear time +but we're supposed to do this in + + align:start position:0% +but we're supposed to do this in + + + align:start position:0% +but we're supposed to do this in +constant expected amortized time + + align:start position:0% +constant expected amortized time + + + align:start position:0% +constant expected amortized time +so that's no good so this idea + + align:start position:0% +so that's no good so this idea + + + align:start position:0% +so that's no good so this idea +is not enough it's not a bad idea it's + + align:start position:0% +is not enough it's not a bad idea it's + + + align:start position:0% +is not enough it's not a bad idea it's +still a good idea + + align:start position:0% +still a good idea + + + align:start position:0% +still a good idea +but it's no longer what we actually want + + align:start position:0% +but it's no longer what we actually want + + + align:start position:0% +but it's no longer what we actually want +to do it's only + + align:start position:0% +to do it's only + + + align:start position:0% +to do it's only +morally what we want to do so + + align:start position:0% +morally what we want to do so + + + align:start position:0% +morally what we want to do so +what do you have any thoughts on how we + + align:start position:0% +what do you have any thoughts on how we + + + align:start position:0% +what do you have any thoughts on how we +might get around this problem + + align:start position:0% +might get around this problem + + + align:start position:0% +might get around this problem +seems like inserting at position zero i + + align:start position:0% +seems like inserting at position zero i + + + align:start position:0% +seems like inserting at position zero i +need to shift everything down + + align:start position:0% +need to shift everything down + + + align:start position:0% +need to shift everything down +linear time that really sucks + + align:start position:0% + + + + align:start position:0% + +yep um you could + + align:start position:0% +yep um you could + + + align:start position:0% +yep um you could +create some sort of link to something + + align:start position:0% +create some sort of link to something + + + align:start position:0% +create some sort of link to something +else + + align:start position:0% +else + + + align:start position:0% +else +link this data structure with another + + align:start position:0% +link this data structure with another + + + align:start position:0% +link this data structure with another +one so we could build more than one set + + align:start position:0% +one so we could build more than one set + + + align:start position:0% +one so we could build more than one set +that's certainly allowed + + align:start position:0% +that's certainly allowed + + + align:start position:0% +that's certainly allowed +uh i don't know how to + + align:start position:0% +uh i don't know how to + + + align:start position:0% +uh i don't know how to +do oh i see you're saying maybe build a + + align:start position:0% +do oh i see you're saying maybe build a + + + align:start position:0% +do oh i see you're saying maybe build a +whole another structure for the + + align:start position:0% +whole another structure for the + + + align:start position:0% +whole another structure for the +items that come before xero yeah yeah + + align:start position:0% +items that come before xero yeah yeah + + + align:start position:0% +items that come before xero yeah yeah +actually that would work i think + + align:start position:0% + + + + align:start position:0% + +maybe uh it's like in the pset then you + + align:start position:0% +maybe uh it's like in the pset then you + + + align:start position:0% +maybe uh it's like in the pset then you +have to deal with when + + align:start position:0% +have to deal with when + + + align:start position:0% +have to deal with when +if you delete one of them it becomes + + align:start position:0% +if you delete one of them it becomes + + + align:start position:0% +if you delete one of them it becomes +empty then things get messy + + align:start position:0% +empty then things get messy + + + align:start position:0% +empty then things get messy +delete first is also going to be a + + align:start position:0% +delete first is also going to be a + + + align:start position:0% +delete first is also going to be a +problem because i delete the beginning + + align:start position:0% +problem because i delete the beginning + + + align:start position:0% +problem because i delete the beginning +of this data structure + + align:start position:0% + + + + align:start position:0% + +then i lose my zero item and i want the + + align:start position:0% +then i lose my zero item and i want the + + + align:start position:0% +then i lose my zero item and i want the +new zero item to be the + + align:start position:0% +new zero item to be the + + + align:start position:0% +new zero item to be the +one item that's again all the indices + + align:start position:0% +one item that's again all the indices + + + align:start position:0% +one item that's again all the indices +shift so delete and + + align:start position:0% +shift so delete and + + + align:start position:0% +shift so delete and +inserting at the first is heart so we + + align:start position:0% +inserting at the first is heart so we + + + align:start position:0% +inserting at the first is heart so we +could do that trick like in the pset but + + align:start position:0% +could do that trick like in the pset but + + + align:start position:0% +could do that trick like in the pset but +or in like in less problem session and + + align:start position:0% +or in like in less problem session and + + + align:start position:0% +or in like in less problem session and +so on um + + align:start position:0% +so on um + + + align:start position:0% +so on um +but there's a much simpler idea + + align:start position:0% + + + + align:start position:0% + +can you have an extra very to keep track + + align:start position:0% +can you have an extra very to keep track + + + align:start position:0% +can you have an extra very to keep track +where + + align:start position:0% +where + + + align:start position:0% +where +is that nice i have an extra variable + + align:start position:0% +is that nice i have an extra variable + + + align:start position:0% +is that nice i have an extra variable +to keep track of where the beginning is + + align:start position:0% + + + + align:start position:0% + +call this first this is going to be + + align:start position:0% +call this first this is going to be + + + align:start position:0% +call this first this is going to be +the key + + align:start position:0% + + + + align:start position:0% + +of the uh first + + align:start position:0% +of the uh first + + + align:start position:0% +of the uh first +item index zero + + align:start position:0% +item index zero + + + align:start position:0% +item index zero +another way to say this is let's just + + align:start position:0% +another way to say this is let's just + + + align:start position:0% +another way to say this is let's just +use negative integers + + align:start position:0% +use negative integers + + + align:start position:0% +use negative integers +right set sets work for any keys any + + align:start position:0% +right set sets work for any keys any + + + align:start position:0% +right set sets work for any keys any +integer keys okay actually we + + align:start position:0% +integer keys okay actually we + + + align:start position:0% +integer keys okay actually we +technically said they should use keys + + align:start position:0% +technically said they should use keys + + + align:start position:0% +technically said they should use keys +zero to u minus one + + align:start position:0% +zero to u minus one + + + align:start position:0% +zero to u minus one +but then uh if you have negative numbers + + align:start position:0% +but then uh if you have negative numbers + + + align:start position:0% +but then uh if you have negative numbers +you can + + align:start position:0% +you can + + + align:start position:0% +you can +easily fold do you know the string + + align:start position:0% +easily fold do you know the string + + + align:start position:0% +easily fold do you know the string +ah python negative numbers means + + align:start position:0% +ah python negative numbers means + + + align:start position:0% +ah python negative numbers means +something else but we're not using the + + align:start position:0% +something else but we're not using the + + + align:start position:0% +something else but we're not using the +python interface we're using our custom + + align:start position:0% +python interface we're using our custom + + + align:start position:0% +python interface we're using our custom +magical + + align:start position:0% +magical + + + align:start position:0% +magical +set interface which we show how to + + align:start position:0% +set interface which we show how to + + + align:start position:0% +set interface which we show how to +implement in recitation nuts + + align:start position:0% +implement in recitation nuts + + + align:start position:0% +implement in recitation nuts +which can take an arbitrary key it + + align:start position:0% +which can take an arbitrary key it + + + align:start position:0% +which can take an arbitrary key it +hashes that key + + align:start position:0% +hashes that key + + + align:start position:0% +hashes that key +and you know finds a place to put + + align:start position:0% +and you know finds a place to put + + + align:start position:0% +and you know finds a place to put +that item so we're not actually storing + + align:start position:0% +that item so we're not actually storing + + + align:start position:0% +that item so we're not actually storing +things in order here we're storing + + align:start position:0% +things in order here we're storing + + + align:start position:0% +things in order here we're storing +things in a hash table + + align:start position:0% +things in a hash table + + + align:start position:0% +things in a hash table +but we're not supposed to get into the + + align:start position:0% +but we're not supposed to get into the + + + align:start position:0% +but we're not supposed to get into the +implementation details + + align:start position:0% +implementation details + + + align:start position:0% +implementation details +i think the way we presented hashing + + align:start position:0% +i think the way we presented hashing + + + align:start position:0% +i think the way we presented hashing +with our + + align:start position:0% +with our + + + align:start position:0% +with our +universal hash functions we only allowed + + align:start position:0% +universal hash functions we only allowed + + + align:start position:0% +universal hash functions we only allowed +positive numbers + + align:start position:0% +positive numbers + + + align:start position:0% +positive numbers +so maybe technically i should point out + + align:start position:0% +so maybe technically i should point out + + + align:start position:0% +so maybe technically i should point out +if you have + + align:start position:0% + + + + align:start position:0% + +positive and negative numbers you can + + align:start position:0% +positive and negative numbers you can + + + align:start position:0% +positive and negative numbers you can +fold this in half + + align:start position:0% +fold this in half + + + align:start position:0% +fold this in half +by mapping zero to zero one to + + align:start position:0% +by mapping zero to zero one to + + + align:start position:0% +by mapping zero to zero one to +two two to four spreading it out + + align:start position:0% +two two to four spreading it out + + + align:start position:0% +two two to four spreading it out +and then you can take minus one and map + + align:start position:0% +and then you can take minus one and map + + + align:start position:0% +and then you can take minus one and map +it to plus one + + align:start position:0% +it to plus one + + + align:start position:0% +it to plus one +and minus two and map it to plus three + + align:start position:0% +and minus two and map it to plus three + + + align:start position:0% +and minus two and map it to plus three +so this is like + + align:start position:0% +so this is like + + + align:start position:0% +so this is like +uh multiplying each of these guys by 2 + + align:start position:0% +uh multiplying each of these guys by 2 + + + align:start position:0% +uh multiplying each of these guys by 2 +and multiplying each of these guys by + + align:start position:0% +and multiplying each of these guys by + + + align:start position:0% +and multiplying each of these guys by +minus 2 and adding 1. + + align:start position:0% +minus 2 and adding 1. + + + align:start position:0% +minus 2 and adding 1. +and then you get non-negative + + align:start position:0% +and then you get non-negative + + + align:start position:0% +and then you get non-negative +integers out of all integers this is a + + align:start position:0% +integers out of all integers this is a + + + align:start position:0% +integers out of all integers this is a +typical math trick for showing that the + + align:start position:0% +typical math trick for showing that the + + + align:start position:0% +typical math trick for showing that the +number of integers is equal to the + + align:start position:0% +number of integers is equal to the + + + align:start position:0% +number of integers is equal to the +number of + + align:start position:0% +number of + + + align:start position:0% +number of +non-negative integers which may seem + + align:start position:0% +non-negative integers which may seem + + + align:start position:0% +non-negative integers which may seem +weird to you but they're both + + align:start position:0% +weird to you but they're both + + + align:start position:0% +weird to you but they're both +countably infinite so you could + + align:start position:0% +countably infinite so you could + + + align:start position:0% +countably infinite so you could +if your structure only supports negative + + align:start position:0% +if your structure only supports negative + + + align:start position:0% +if your structure only supports negative +keys you could map negative keys in this + + align:start position:0% +keys you could map negative keys in this + + + align:start position:0% +keys you could map negative keys in this +way and + + align:start position:0% +way and + + + align:start position:0% +way and +throw them into the hash table okay so + + align:start position:0% +throw them into the hash table okay so + + + align:start position:0% +throw them into the hash table okay so +now + + align:start position:0% +now + + + align:start position:0% +now +i allow negative things for + + align:start position:0% +i allow negative things for + + + align:start position:0% +i allow negative things for +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +like that and so great if i want to + + align:start position:0% +like that and so great if i want to + + + align:start position:0% +like that and so great if i want to +insert at the beginning + + align:start position:0% +insert at the beginning + + + align:start position:0% +insert at the beginning +what i can do is just decrement my + + align:start position:0% + + + + align:start position:0% + +first variable which is keeping track of + + align:start position:0% +first variable which is keeping track of + + + align:start position:0% +first variable which is keeping track of +the index so initially first is going to + + align:start position:0% +the index so initially first is going to + + + align:start position:0% +the index so initially first is going to +be 0 + + align:start position:0% +be 0 + + + align:start position:0% +be 0 +so i'm going to add into my build first + + align:start position:0% +so i'm going to add into my build first + + + align:start position:0% +so i'm going to add into my build first +i'm going to say + + align:start position:0% +i'm going to say + + + align:start position:0% +i'm going to say +first equals zero + + align:start position:0% +first equals zero + + + align:start position:0% +first equals zero +because i start with key zero and when i + + align:start position:0% +because i start with key zero and when i + + + align:start position:0% +because i start with key zero and when i +initially build a structure + + align:start position:0% +initially build a structure + + + align:start position:0% +initially build a structure +and if i wanna if i need more room + + align:start position:0% +and if i wanna if i need more room + + + align:start position:0% +and if i wanna if i need more room +before zero i just set first to minus + + align:start position:0% +before zero i just set first to minus + + + align:start position:0% +before zero i just set first to minus +one + + align:start position:0% +one + + + align:start position:0% +one +and if i already have minus one element + + align:start position:0% +and if i already have minus one element + + + align:start position:0% +and if i already have minus one element +i'll decrement it to minus two decrement + + align:start position:0% +i'll decrement it to minus two decrement + + + align:start position:0% +i'll decrement it to minus two decrement +means decrease by one + + align:start position:0% +means decrease by one + + + align:start position:0% +means decrease by one +it shows my assembly language + + align:start position:0% +it shows my assembly language + + + align:start position:0% +it shows my assembly language +programming this is usually a built-in + + align:start position:0% +programming this is usually a built-in + + + align:start position:0% +programming this is usually a built-in +operation on + + align:start position:0% +operation on + + + align:start position:0% +operation on +most computers and then i can insert + + align:start position:0% +most computers and then i can insert + + + align:start position:0% +most computers and then i can insert +an item with key first + + align:start position:0% + + + + align:start position:0% + +and value x + + align:start position:0% + + + + align:start position:0% + +right now if i want to delete the first + + align:start position:0% +right now if i want to delete the first + + + align:start position:0% +right now if i want to delete the first +item i would delete + + align:start position:0% +item i would delete + + + align:start position:0% +item i would delete +the item with key first and then + + align:start position:0% +the item with key first and then + + + align:start position:0% +the item with key first and then +increment first + + align:start position:0% +increment first + + + align:start position:0% +increment first +and now all of my operations have to + + align:start position:0% +and now all of my operations have to + + + align:start position:0% +and now all of my operations have to +change a little bit let me use another + + align:start position:0% +change a little bit let me use another + + + align:start position:0% +change a little bit let me use another +color + + align:start position:0% +color + + + align:start position:0% +color +um because i was implicitly assuming + + align:start position:0% +um because i was implicitly assuming + + + align:start position:0% +um because i was implicitly assuming +here that all my indices started at i + + align:start position:0% +here that all my indices started at i + + + align:start position:0% +here that all my indices started at i +but now they start at first they + + align:start position:0% +but now they start at first they + + + align:start position:0% +but now they start at first they +index zero maps to key + + align:start position:0% +index zero maps to key + + + align:start position:0% +index zero maps to key +first and so the right thing to do here + + align:start position:0% +first and so the right thing to do here + + + align:start position:0% +first and so the right thing to do here +is + + align:start position:0% +is + + + align:start position:0% +is +plus first + + align:start position:0% + + + + align:start position:0% + +and plus first basically add a whole + + align:start position:0% +and plus first basically add a whole + + + align:start position:0% +and plus first basically add a whole +bunch of plus first + + align:start position:0% +bunch of plus first + + + align:start position:0% +bunch of plus first +throughout this one's probably fine if + + align:start position:0% +throughout this one's probably fine if + + + align:start position:0% +throughout this one's probably fine if +i'm globally rebuilding i can reassign + + align:start position:0% +i'm globally rebuilding i can reassign + + + align:start position:0% +i'm globally rebuilding i can reassign +all my labels + + align:start position:0% +all my labels + + + align:start position:0% +all my labels +but this one should be first plus + + align:start position:0% +but this one should be first plus + + + align:start position:0% +but this one should be first plus +plus length + + align:start position:0% +plus length + + + align:start position:0% +plus length +okay so just by keeping track of where + + align:start position:0% +okay so just by keeping track of where + + + align:start position:0% +okay so just by keeping track of where +my + + align:start position:0% +my + + + align:start position:0% +my +keys are starting i can do this shifting + + align:start position:0% +keys are starting i can do this shifting + + + align:start position:0% +keys are starting i can do this shifting +and not have to worry about stuff + + align:start position:0% +and not have to worry about stuff + + + align:start position:0% +and not have to worry about stuff +and this is a lot easier than having to + + align:start position:0% +and this is a lot easier than having to + + + align:start position:0% +and this is a lot easier than having to +worry about + + align:start position:0% +worry about + + + align:start position:0% +worry about +maintaining two structures and keeping + + align:start position:0% +maintaining two structures and keeping + + + align:start position:0% +maintaining two structures and keeping +them both non-empty and stuff like that + + align:start position:0% +them both non-empty and stuff like that + + + align:start position:0% +them both non-empty and stuff like that +because of if i assume my set has this + + align:start position:0% +because of if i assume my set has this + + + align:start position:0% +because of if i assume my set has this +power + + align:start position:0% +power + + + align:start position:0% +power +of dealing with negative integers and + + align:start position:0% +of dealing with negative integers and + + + align:start position:0% +of dealing with negative integers and +strings and whatever else + + align:start position:0% + + + + align:start position:0% + +oh why didn't i use a linked list + + align:start position:0% +oh why didn't i use a linked list + + + align:start position:0% +oh why didn't i use a linked list +because + + align:start position:0% +because + + + align:start position:0% +because +this linked lists are very bad at get + + align:start position:0% +this linked lists are very bad at get + + + align:start position:0% +this linked lists are very bad at get +and set at a given index + + align:start position:0% + + + + align:start position:0% + +this is not a linked list this is just + + align:start position:0% +this is not a linked list this is just + + + align:start position:0% +this is not a linked list this is just +storing a single number as + + align:start position:0% +storing a single number as + + + align:start position:0% +storing a single number as +integer in your data structure that says + + align:start position:0% +integer in your data structure that says + + + align:start position:0% +integer in your data structure that says +what is the smallest key in my data + + align:start position:0% +what is the smallest key in my data + + + align:start position:0% +what is the smallest key in my data +structure + + align:start position:0% +structure + + + align:start position:0% +structure +that's all it does it's a it's a counter + + align:start position:0% +that's all it does it's a it's a counter + + + align:start position:0% +that's all it does it's a it's a counter +okay so data structure keeps track of + + align:start position:0% +okay so data structure keeps track of + + + align:start position:0% +okay so data structure keeps track of +its length and it keeps track of the + + align:start position:0% +its length and it keeps track of the + + + align:start position:0% +its length and it keeps track of the +minimum key + + align:start position:0% +minimum key + + + align:start position:0% +minimum key +and so it will always consist the + + align:start position:0% +and so it will always consist the + + + align:start position:0% +and so it will always consist the +invariant is you'll always have keys + + align:start position:0% +invariant is you'll always have keys + + + align:start position:0% +invariant is you'll always have keys +from first up to first plus length minus + + align:start position:0% +from first up to first plus length minus + + + align:start position:0% +from first up to first plus length minus +one + + align:start position:0% +one + + + align:start position:0% +one +and that's what we're exploiting here + + align:start position:0% + + + + align:start position:0% + +we have no idea where first will be it + + align:start position:0% +we have no idea where first will be it + + + align:start position:0% +we have no idea where first will be it +depends how many operations you've done + + align:start position:0% +depends how many operations you've done + + + align:start position:0% +depends how many operations you've done +how many inserts at the beginning and so + + align:start position:0% +how many inserts at the beginning and so + + + align:start position:0% +how many inserts at the beginning and so +on but the keys + + align:start position:0% + + + + align:start position:0% + +keys will always be first + + align:start position:0% + + + + align:start position:0% + +to first plus length + + align:start position:0% +to first plus length + + + align:start position:0% +to first plus length +minus one this is what we call an + + align:start position:0% +minus one this is what we call an + + + align:start position:0% +minus one this is what we call an +invariant useful to write these things + + align:start position:0% +invariant useful to write these things + + + align:start position:0% +invariant useful to write these things +down + + align:start position:0% +down + + + align:start position:0% +down +so you can understand what the heck why + + align:start position:0% +so you can understand what the heck why + + + align:start position:0% +so you can understand what the heck why +is your data structure correct + + align:start position:0% +is your data structure correct + + + align:start position:0% +is your data structure correct +because of invariance like this which + + align:start position:0% +because of invariance like this which + + + align:start position:0% +because of invariance like this which +you can prove by induction + + align:start position:0% +you can prove by induction + + + align:start position:0% +you can prove by induction +by showing each time you do an operation + + align:start position:0% +by showing each time you do an operation + + + align:start position:0% +by showing each time you do an operation +this is maintained + + align:start position:0% +this is maintained + + + align:start position:0% +this is maintained +even when i'm changing first in order to + + align:start position:0% +even when i'm changing first in order to + + + align:start position:0% +even when i'm changing first in order to +maintain this invariant + + align:start position:0% + + + + align:start position:0% + +cool sometimes you come up with the + + align:start position:0% +cool sometimes you come up with the + + + align:start position:0% +cool sometimes you come up with the +invariant first in this case i came up + + align:start position:0% +invariant first in this case i came up + + + align:start position:0% +invariant first in this case i came up +with it + + align:start position:0% +with it + + + align:start position:0% +with it +episode uh post facto after the fact + + align:start position:0% +episode uh post facto after the fact + + + align:start position:0% +episode uh post facto after the fact +uh cool let's move on + + align:start position:0% +uh cool let's move on + + + align:start position:0% +uh cool let's move on +to problem three + + align:start position:0% + + + + align:start position:0% + +which is called critter sort and the + + align:start position:0% +which is called critter sort and the + + + align:start position:0% +which is called critter sort and the +other key thing i want you to learn + + align:start position:0% +other key thing i want you to learn + + + align:start position:0% +other key thing i want you to learn +about + + align:start position:0% +about + + + align:start position:0% +about +a question sorry um so when you do first + + align:start position:0% +a question sorry um so when you do first + + + align:start position:0% +a question sorry um so when you do first +first plus one is that a rebuilding of + + align:start position:0% +first plus one is that a rebuilding of + + + align:start position:0% +first plus one is that a rebuilding of +use this is just a sentence + + align:start position:0% +use this is just a sentence + + + align:start position:0% +use this is just a sentence +is not an algorithm or data structure + + align:start position:0% +is not an algorithm or data structure + + + align:start position:0% +is not an algorithm or data structure +this is a mathematical property + + align:start position:0% +this is a mathematical property + + + align:start position:0% +this is a mathematical property +this is not an assignment this is a + + align:start position:0% +this is not an assignment this is a + + + align:start position:0% +this is not an assignment this is a +mathematically is equal to but you are + + align:start position:0% +mathematically is equal to but you are + + + align:start position:0% +mathematically is equal to but you are +reinvesting it though + + align:start position:0% +reinvesting it though + + + align:start position:0% +reinvesting it though +because you're doing first plus one so + + align:start position:0% +because you're doing first plus one so + + + align:start position:0% +because you're doing first plus one so +are you asking about one of these + + align:start position:0% +are you asking about one of these + + + align:start position:0% +are you asking about one of these +operations + + align:start position:0% +operations + + + align:start position:0% +operations +like this one wait oh okay never mind i + + align:start position:0% +like this one wait oh okay never mind i + + + align:start position:0% +like this one wait oh okay never mind i +get it + + align:start position:0% +get it + + + align:start position:0% +get it +yeah okay so the other important + + align:start position:0% +yeah okay so the other important + + + align:start position:0% +yeah okay so the other important +takeaway i want you to get about reading + + align:start position:0% +takeaway i want you to get about reading + + + align:start position:0% +takeaway i want you to get about reading +our problem sets is that they have + + align:start position:0% +our problem sets is that they have + + + align:start position:0% +our problem sets is that they have +hidden humor inside + + align:start position:0% +hidden humor inside + + + align:start position:0% +hidden humor inside +i don't know if you've noticed but + + align:start position:0% +i don't know if you've noticed but + + + align:start position:0% +i don't know if you've noticed but +here's an example of a problem called + + align:start position:0% +here's an example of a problem called + + + align:start position:0% +here's an example of a problem called +critter sort + + align:start position:0% +critter sort + + + align:start position:0% +critter sort +ashley getum collects and trains pocket + + align:start position:0% +ashley getum collects and trains pocket + + + align:start position:0% +ashley getum collects and trains pocket +critters to fight other pocket critters + + align:start position:0% +critters to fight other pocket critters + + + align:start position:0% +critters to fight other pocket critters +in battle + + align:start position:0% +in battle + + + align:start position:0% +in battle +what is this a reference to digimon + + align:start position:0% +what is this a reference to digimon + + + align:start position:0% +what is this a reference to digimon +digimon + + align:start position:0% +digimon + + + align:start position:0% +digimon +wow you guys are so young pokemon + + align:start position:0% +wow you guys are so young pokemon + + + align:start position:0% +wow you guys are so young pokemon +the the old the ancient form pokemon is + + align:start position:0% +the the old the ancient form pokemon is + + + align:start position:0% +the the old the ancient form pokemon is +short for pocket monsters + + align:start position:0% +short for pocket monsters + + + align:start position:0% +short for pocket monsters +and in fact in the original anime okay + + align:start position:0% +and in fact in the original anime okay + + + align:start position:0% +and in fact in the original anime okay +actually + + align:start position:0% +actually + + + align:start position:0% +actually +i i don't know it was all after my time + + align:start position:0% +i i don't know it was all after my time + + + align:start position:0% +i i don't know it was all after my time +we can debate after so pocket critters + + align:start position:0% +we can debate after so pocket critters + + + align:start position:0% +we can debate after so pocket critters +is a reference to pokemons pocket + + align:start position:0% +is a reference to pokemons pocket + + + align:start position:0% +is a reference to pokemons pocket +monsters which is pokemon + + align:start position:0% +monsters which is pokemon + + + align:start position:0% +monsters which is pokemon +who's ashley getum + + align:start position:0% + + + + align:start position:0% + +ash ketchum is his full name in the + + align:start position:0% +ash ketchum is his full name in the + + + align:start position:0% +ash ketchum is his full name in the +english version + + align:start position:0% +english version + + + align:start position:0% +english version +um totally different name in the + + align:start position:0% +um totally different name in the + + + align:start position:0% +um totally different name in the +japanese version but + + align:start position:0% +japanese version but + + + align:start position:0% +japanese version but +they're both puns on collect them all + + align:start position:0% +they're both puns on collect them all + + + align:start position:0% +they're both puns on collect them all +right all right so that's the important + + align:start position:0% +right all right so that's the important + + + align:start position:0% +right all right so that's the important +stuff we'll see more jokes later + + align:start position:0% +stuff we'll see more jokes later + + + align:start position:0% +stuff we'll see more jokes later +so there's this setup but basically we + + align:start position:0% +so there's this setup but basically we + + + align:start position:0% +so there's this setup but basically we +have n + + align:start position:0% +have n + + + align:start position:0% +have n +critters and we want to sort them by + + align:start position:0% +critters and we want to sort them by + + + align:start position:0% +critters and we want to sort them by +four different things + + align:start position:0% +four different things + + + align:start position:0% +four different things +and so i'm just going to abstract this + + align:start position:0% +and so i'm just going to abstract this + + + align:start position:0% +and so i'm just going to abstract this +problem into sort + + align:start position:0% +problem into sort + + + align:start position:0% +problem into sort +m objects by the following types of keys + + align:start position:0% +m objects by the following types of keys + + + align:start position:0% +m objects by the following types of keys +and for each one we want to know what + + align:start position:0% +and for each one we want to know what + + + align:start position:0% +and for each one we want to know what +the best sorting algorithm is + + align:start position:0% +the best sorting algorithm is + + + align:start position:0% +the best sorting algorithm is +and there's this footnote that's very + + align:start position:0% +and there's this footnote that's very + + + align:start position:0% +and there's this footnote that's very +important it says faster correct + + align:start position:0% +important it says faster correct + + + align:start position:0% +important it says faster correct +algorithms will receive more points than + + align:start position:0% +algorithms will receive more points than + + + align:start position:0% +algorithms will receive more points than +slower + + align:start position:0% +slower + + + align:start position:0% +slower +correct algorithms also correct + + align:start position:0% +correct algorithms also correct + + + align:start position:0% +correct algorithms also correct +algorithms will receive more points than + + align:start position:0% +algorithms will receive more points than + + + align:start position:0% +algorithms will receive more points than +incorrect algorithms but that's implicit + + align:start position:0% +incorrect algorithms but that's implicit + + + align:start position:0% +incorrect algorithms but that's implicit +incorrect generally gets zero + + align:start position:0% +incorrect generally gets zero + + + align:start position:0% +incorrect generally gets zero +okay so uh part a + + align:start position:0% +okay so uh part a + + + align:start position:0% +okay so uh part a +uh it says species id but basically we + + align:start position:0% +uh it says species id but basically we + + + align:start position:0% +uh it says species id but basically we +have integers + + align:start position:0% +have integers + + + align:start position:0% +have integers +and the range minus and n + + align:start position:0% + + + + align:start position:0% + +so if i want to sort and integers in the + + align:start position:0% +so if i want to sort and integers in the + + + align:start position:0% +so if i want to sort and integers in the +range + + align:start position:0% +range + + + align:start position:0% +range +minus end to end what should i do + + align:start position:0% +minus end to end what should i do + + + align:start position:0% +minus end to end what should i do +reference to + + align:start position:0% +reference to + + + align:start position:0% +reference to +yesterday's lecture + + align:start position:0% + + + + align:start position:0% + +yeah radix sort yeah always a good + + align:start position:0% +yeah radix sort yeah always a good + + + align:start position:0% +yeah radix sort yeah always a good +answer for almost always a good answer + + align:start position:0% +answer for almost always a good answer + + + align:start position:0% +answer for almost always a good answer +when you + + align:start position:0% +when you + + + align:start position:0% +when you +have integers it's a good answer + + align:start position:0% +have integers it's a good answer + + + align:start position:0% +have integers it's a good answer +whenever you have small integers now + + align:start position:0% +whenever you have small integers now + + + align:start position:0% +whenever you have small integers now +radix sort the way we phrased it + + align:start position:0% +radix sort the way we phrased it + + + align:start position:0% +radix sort the way we phrased it +let me maybe put it down here uh radix + + align:start position:0% +let me maybe put it down here uh radix + + + align:start position:0% +let me maybe put it down here uh radix +sort + + align:start position:0% + + + + align:start position:0% + +sorts + + align:start position:0% +sorts + + + align:start position:0% +sorts +n integers in the range + + align:start position:0% +n integers in the range + + + align:start position:0% +n integers in the range +0 to u minus 1 + + align:start position:0% + + + + align:start position:0% + +in m plus + + align:start position:0% +in m plus + + + align:start position:0% +in m plus +m log base n of u + + align:start position:0% +m log base n of u + + + align:start position:0% +m log base n of u +time and in particular this is + + align:start position:0% +time and in particular this is + + + align:start position:0% +time and in particular this is +linear time if u + + align:start position:0% +linear time if u + + + align:start position:0% +linear time if u +is n to some constant power + + align:start position:0% + + + + align:start position:0% + +okay so can i just apply this as is to + + align:start position:0% +okay so can i just apply this as is to + + + align:start position:0% +okay so can i just apply this as is to +these integers + + align:start position:0% +these integers + + + align:start position:0% +these integers +no because they're negative so what + + align:start position:0% +no because they're negative so what + + + align:start position:0% +no because they're negative so what +should i do maybe i should do my folding + + align:start position:0% +should i do maybe i should do my folding + + + align:start position:0% +should i do maybe i should do my folding +trick we just saw how to take + + align:start position:0% +trick we just saw how to take + + + align:start position:0% +trick we just saw how to take +negative numbers and fold them in + + align:start position:0% +negative numbers and fold them in + + + align:start position:0% +negative numbers and fold them in +interspersed with positive numbers if i + + align:start position:0% +interspersed with positive numbers if i + + + align:start position:0% +interspersed with positive numbers if i +sort that + + align:start position:0% +sort that + + + align:start position:0% +sort that +will that work no + + align:start position:0% +will that work no + + + align:start position:0% +will that work no +because that does not preserve order it + + align:start position:0% +because that does not preserve order it + + + align:start position:0% +because that does not preserve order it +would + + align:start position:0% +would + + + align:start position:0% +would +intersperse it's just we want all the + + align:start position:0% +intersperse it's just we want all the + + + align:start position:0% +intersperse it's just we want all the +negative numbers to come before all the + + align:start position:0% +negative numbers to come before all the + + + align:start position:0% +negative numbers to come before all the +positive numbers yeah + + align:start position:0% +positive numbers yeah + + + align:start position:0% +positive numbers yeah +just add n yup boom plus n + + align:start position:0% +just add n yup boom plus n + + + align:start position:0% +just add n yup boom plus n +now we have integers in the range + + align:start position:0% +now we have integers in the range + + + align:start position:0% +now we have integers in the range +let's be careful 0 to 2n + + align:start position:0% + + + + align:start position:0% + +cool now we can apply this now u equals + + align:start position:0% +cool now we can apply this now u equals + + + align:start position:0% +cool now we can apply this now u equals +technically 2n plus 1 because we're only + + align:start position:0% +technically 2n plus 1 because we're only + + + align:start position:0% +technically 2n plus 1 because we're only +supposed to go to u minus 1. + + align:start position:0% +supposed to go to u minus 1. + + + align:start position:0% +supposed to go to u minus 1. +but that's fine that's linear and so we + + align:start position:0% +but that's fine that's linear and so we + + + align:start position:0% +but that's fine that's linear and so we +can sort in linear time + + align:start position:0% +can sort in linear time + + + align:start position:0% +can sort in linear time +easy this is a super easy problem okay + + align:start position:0% +easy this is a super easy problem okay + + + align:start position:0% +easy this is a super easy problem okay +but in each one we might need to do some + + align:start position:0% +but in each one we might need to do some + + + align:start position:0% +but in each one we might need to do some +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +all right part b is a little more + + align:start position:0% +all right part b is a little more + + + align:start position:0% +all right part b is a little more +interesting so we have strings + + align:start position:0% +interesting so we have strings + + + align:start position:0% +interesting so we have strings +over 26 letters + + align:start position:0% + + + + align:start position:0% + +of length + + align:start position:0% + + + + align:start position:0% + +at most 10 ceiling log + + align:start position:0% +at most 10 ceiling log + + + align:start position:0% +at most 10 ceiling log +n okay this is a little trickier + + align:start position:0% +n okay this is a little trickier + + + align:start position:0% +n okay this is a little trickier +what could i do again i'd like to see + + align:start position:0% +what could i do again i'd like to see + + + align:start position:0% +what could i do again i'd like to see +whether radix sort applies + + align:start position:0% +whether radix sort applies + + + align:start position:0% +whether radix sort applies +um i should say radix sort sorts + + align:start position:0% +um i should say radix sort sorts + + + align:start position:0% +um i should say radix sort sorts +i'd like to see if radix sort applies to + + align:start position:0% +i'd like to see if radix sort applies to + + + align:start position:0% +i'd like to see if radix sort applies to +do that i have to map these strings into + + align:start position:0% +do that i have to map these strings into + + + align:start position:0% +do that i have to map these strings into +integers somehow + + align:start position:0% +integers somehow + + + align:start position:0% +integers somehow +any way to do that + + align:start position:0% + + + + align:start position:0% + +this is easy if you understand radix + + align:start position:0% +this is easy if you understand radix + + + align:start position:0% +this is easy if you understand radix +sort yeah + + align:start position:0% +sort yeah + + + align:start position:0% +sort yeah +index the letters yeah + + align:start position:0% + + + + align:start position:0% + +yep we can we can map right so we can + + align:start position:0% +yep we can we can map right so we can + + + align:start position:0% +yep we can we can map right so we can +map a to zero + + align:start position:0% +map a to zero + + + align:start position:0% +map a to zero +b to one then one + + align:start position:0% + + + + align:start position:0% + +but we have a lot of letters + + align:start position:0% + + + + align:start position:0% + +there are only 26 letters but then we + + align:start position:0% +there are only 26 letters but then we + + + align:start position:0% +there are only 26 letters but then we +have uh 10 login + + align:start position:0% +have uh 10 login + + + align:start position:0% +have uh 10 login +letters in a string that is together a + + align:start position:0% +letters in a string that is together a + + + align:start position:0% +letters in a string that is together a +single key that we need to sort + + align:start position:0% + + + + align:start position:0% + +yeah i'm going to sort by the first + + align:start position:0% +yeah i'm going to sort by the first + + + align:start position:0% +yeah i'm going to sort by the first +first letter first start by the first + + align:start position:0% +first letter first start by the first + + + align:start position:0% +first letter first start by the first +letter then the second letter that is + + align:start position:0% +letter then the second letter that is + + + align:start position:0% +letter then the second letter that is +exactly the opposite of radix sort + + align:start position:0% +exactly the opposite of radix sort + + + align:start position:0% +exactly the opposite of radix sort +remember radix or we want to sort by the + + align:start position:0% +remember radix or we want to sort by the + + + align:start position:0% +remember radix or we want to sort by the +last letter + + align:start position:0% +last letter + + + align:start position:0% +last letter +and then the next the last letter and + + align:start position:0% +and then the next the last letter and + + + align:start position:0% +and then the next the last letter and +finally the first letter by the first + + align:start position:0% +finally the first letter by the first + + + align:start position:0% +finally the first letter by the first +one here it's alphabetized + + align:start position:0% +one here it's alphabetized + + + align:start position:0% +one here it's alphabetized +no to alphabetize we do want to in the + + align:start position:0% +no to alphabetize we do want to in the + + + align:start position:0% +no to alphabetize we do want to in the +end + + align:start position:0% +end + + + align:start position:0% +end +sort by the first letter but that's at + + align:start position:0% +sort by the first letter but that's at + + + align:start position:0% +sort by the first letter but that's at +the end oh wait so that at the end + + align:start position:0% +the end oh wait so that at the end + + + align:start position:0% +the end oh wait so that at the end +remember radix sorry always goes + + align:start position:0% +remember radix sorry always goes + + + align:start position:0% +remember radix sorry always goes +backwards from the least significant to + + align:start position:0% +backwards from the least significant to + + + align:start position:0% +backwards from the least significant to +the first to the most significant + + align:start position:0% +the first to the most significant + + + align:start position:0% +the first to the most significant +so indeed that is what we want to do + + align:start position:0% +so indeed that is what we want to do + + + align:start position:0% +so indeed that is what we want to do +you're just saying use radix work but + + align:start position:0% +you're just saying use radix work but + + + align:start position:0% +you're just saying use radix work but +what am i radix sort on + + align:start position:0% +what am i radix sort on + + + align:start position:0% +what am i radix sort on +what am i radix sorting on yeah on the + + align:start position:0% +what am i radix sorting on yeah on the + + + align:start position:0% +what am i radix sorting on yeah on the +on the last letters not the first + + align:start position:0% +on the last letters not the first + + + align:start position:0% +on the last letters not the first +letters so technically that would be + + align:start position:0% +letters so technically that would be + + + align:start position:0% +letters so technically that would be +using counting sort + + align:start position:0% +using counting sort + + + align:start position:0% +using counting sort +on the last letter counting start on the + + align:start position:0% +on the last letter counting start on the + + + align:start position:0% +on the last letter counting start on the +next last letter dot dot counting sort + + align:start position:0% +next last letter dot dot counting sort + + + align:start position:0% +next last letter dot dot counting sort +on the first letter + + align:start position:0% +on the first letter + + + align:start position:0% +on the first letter +but that is together radix sort on + + align:start position:0% +but that is together radix sort on + + + align:start position:0% +but that is together radix sort on +something or + + align:start position:0% +something or + + + align:start position:0% +something or +jason likes to call this tuple sorting + + align:start position:0% + + + + align:start position:0% + +tuple sort is the thing is the algorithm + + align:start position:0% +tuple sort is the thing is the algorithm + + + align:start position:0% +tuple sort is the thing is the algorithm +that says + + align:start position:0% +that says + + + align:start position:0% +that says +sort by the last thing then sort by the + + align:start position:0% +sort by the last thing then sort by the + + + align:start position:0% +sort by the last thing then sort by the +previous thing and so on + + align:start position:0% +previous thing and so on + + + align:start position:0% +previous thing and so on +you can also think of this as radix + + align:start position:0% +you can also think of this as radix + + + align:start position:0% +you can also think of this as radix +sorting on a number written in base 26. + + align:start position:0% + + + + align:start position:0% + +they're the same thing + + align:start position:0% + + + + align:start position:0% + +okay but in the end we can sort in + + align:start position:0% +okay but in the end we can sort in + + + align:start position:0% +okay but in the end we can sort in +linear time + + align:start position:0% +linear time + + + align:start position:0% +linear time +how do you tell the algorithm that you + + align:start position:0% +how do you tell the algorithm that you + + + align:start position:0% +how do you tell the algorithm that you +want a to come like + + align:start position:0% +want a to come like + + + align:start position:0% +want a to come like +just like not zero is less than one a is + + align:start position:0% +just like not zero is less than one a is + + + align:start position:0% +just like not zero is less than one a is +less than b + + align:start position:0% +less than b + + + align:start position:0% +less than b +right so i mean technically when you + + align:start position:0% +right so i mean technically when you + + + align:start position:0% +right so i mean technically when you +call something like tuple sort + + align:start position:0% +call something like tuple sort + + + align:start position:0% +call something like tuple sort +or maybe it's even clearer when you call + + align:start position:0% +or maybe it's even clearer when you call + + + align:start position:0% +or maybe it's even clearer when you call +it radix sort rakes are giving it a + + align:start position:0% +it radix sort rakes are giving it a + + + align:start position:0% +it radix sort rakes are giving it a +bunch of numbers + + align:start position:0% +bunch of numbers + + + align:start position:0% +bunch of numbers +so you're taking these strings and + + align:start position:0% +so you're taking these strings and + + + align:start position:0% +so you're taking these strings and +mapping them to numbers + + align:start position:0% +mapping them to numbers + + + align:start position:0% +mapping them to numbers +and when you do that you get to decide + + align:start position:0% +and when you do that you get to decide + + + align:start position:0% +and when you do that you get to decide +which letter is the most significant + + align:start position:0% +which letter is the most significant + + + align:start position:0% +which letter is the most significant +which is the least significant + + align:start position:0% +which is the least significant + + + align:start position:0% +which is the least significant +all right so you you will choose to + + align:start position:0% +all right so you you will choose to + + + align:start position:0% +all right so you you will choose to +always map the first letter in your + + align:start position:0% +always map the first letter in your + + + align:start position:0% +always map the first letter in your +string + + align:start position:0% +string + + + align:start position:0% +string +to position a two + + align:start position:0% +to position a two + + + align:start position:0% +to position a two +uh um value + + align:start position:0% +uh um value + + + align:start position:0% +uh um value +or the the position and positional + + align:start position:0% +or the the position and positional + + + align:start position:0% +or the the position and positional +notation + + align:start position:0% +notation + + + align:start position:0% +notation +position uh 26 to the power 10 log n + + align:start position:0% +position uh 26 to the power 10 log n + + + align:start position:0% +position uh 26 to the power 10 log n +right as the most significant so it's + + align:start position:0% +right as the most significant so it's + + + align:start position:0% +right as the most significant so it's +always most significant even if your + + align:start position:0% +always most significant even if your + + + align:start position:0% +always most significant even if your +string is of length one + + align:start position:0% +string is of length one + + + align:start position:0% +string is of length one +you want to put that in the most + + align:start position:0% +you want to put that in the most + + + align:start position:0% +you want to put that in the most +significant digit and you'll pad with + + align:start position:0% +significant digit and you'll pad with + + + align:start position:0% +significant digit and you'll pad with +zeros at the end if you + + align:start position:0% +zeros at the end if you + + + align:start position:0% +zeros at the end if you +run out of letters in your strings + + align:start position:0% +run out of letters in your strings + + + align:start position:0% +run out of letters in your strings +here how many times am i running + + align:start position:0% +here how many times am i running + + + align:start position:0% +here how many times am i running +counting sort oh + + align:start position:0% +counting sort oh + + + align:start position:0% +counting sort oh +10 log n times whoops yeah good question + + align:start position:0% +10 log n times whoops yeah good question + + + align:start position:0% +10 log n times whoops yeah good question +good point uh computed this wrong so + + align:start position:0% +good point uh computed this wrong so + + + align:start position:0% +good point uh computed this wrong so +uh right there are log n digits + + align:start position:0% +uh right there are log n digits + + + align:start position:0% +uh right there are log n digits +in the string uh so that + + align:start position:0% +in the string uh so that + + + align:start position:0% +in the string uh so that +is bad i mean it's okay + + align:start position:0% +is bad i mean it's okay + + + align:start position:0% +is bad i mean it's okay +we'll end up with a n log n running time + + align:start position:0% + + + + align:start position:0% + +however so that's the tuple sort so i + + align:start position:0% +however so that's the tuple sort so i + + + align:start position:0% +however so that's the tuple sort so i +should really + + align:start position:0% +should really + + + align:start position:0% +should really +if it's not equivalent if i run tuple + + align:start position:0% +if it's not equivalent if i run tuple + + + align:start position:0% +if it's not equivalent if i run tuple +sort letter by letter + + align:start position:0% +sort letter by letter + + + align:start position:0% +sort letter by letter +i'm going to do i'm running counting + + align:start position:0% +i'm going to do i'm running counting + + + align:start position:0% +i'm going to do i'm running counting +sort log n times and so i get n log n + + align:start position:0% +sort log n times and so i get n log n + + + align:start position:0% +sort log n times and so i get n log n +because each one takes linear time + + align:start position:0% +because each one takes linear time + + + align:start position:0% +because each one takes linear time +if i map my strings into numbers + + align:start position:0% +if i map my strings into numbers + + + align:start position:0% +if i map my strings into numbers +first radixor doesn't use base 26 it + + align:start position:0% +first radixor doesn't use base 26 it + + + align:start position:0% +first radixor doesn't use base 26 it +uses base n + + align:start position:0% +uses base n + + + align:start position:0% +uses base n +and then it will only run 10 times + + align:start position:0% +and then it will only run 10 times + + + align:start position:0% +and then it will only run 10 times +because uh you know 2 to the + + align:start position:0% +because uh you know 2 to the + + + align:start position:0% +because uh you know 2 to the +10 log n + + align:start position:0% +10 log n + + + align:start position:0% +10 log n +is n to the 10. + + align:start position:0% +is n to the 10. + + + align:start position:0% +is n to the 10. +and so uh the numbers that we're sorting + + align:start position:0% +and so uh the numbers that we're sorting + + + align:start position:0% +and so uh the numbers that we're sorting +are between 0 and n to the 10 + + align:start position:0% +are between 0 and n to the 10 + + + align:start position:0% +are between 0 and n to the 10 +and so u is n to the 10 and so that's + + align:start position:0% +and so u is n to the 10 and so that's + + + align:start position:0% +and so u is n to the 10 and so that's +the case when radix sort runs a linear + + align:start position:0% +the case when radix sort runs a linear + + + align:start position:0% +the case when radix sort runs a linear +time + + align:start position:0% +time + + + align:start position:0% +time +so if you run tuple sort letter by + + align:start position:0% +so if you run tuple sort letter by + + + align:start position:0% +so if you run tuple sort letter by +letter it's slow + + align:start position:0% +letter it's slow + + + align:start position:0% +letter it's slow +if you run radix sort it's doing a whole + + align:start position:0% +if you run radix sort it's doing a whole + + + align:start position:0% +if you run radix sort it's doing a whole +bunch of letters at once + + align:start position:0% +bunch of letters at once + + + align:start position:0% +bunch of letters at once +effectively it's doing log n letters at + + align:start position:0% +effectively it's doing log n letters at + + + align:start position:0% +effectively it's doing log n letters at +a time in a single + + align:start position:0% +a time in a single + + + align:start position:0% +a time in a single +call to counting sort and so the radix + + align:start position:0% +call to counting sort and so the radix + + + align:start position:0% +call to counting sort and so the radix +sort will actually + + align:start position:0% +sort will actually + + + align:start position:0% +sort will actually +win and get linear + + align:start position:0% +win and get linear + + + align:start position:0% +win and get linear +there's a subtlety here which is i'm + + align:start position:0% +there's a subtlety here which is i'm + + + align:start position:0% +there's a subtlety here which is i'm +assuming that we can actually + + align:start position:0% +assuming that we can actually + + + align:start position:0% +assuming that we can actually +take these strings and convert them into + + align:start position:0% +take these strings and convert them into + + + align:start position:0% +take these strings and convert them into +integers in + + align:start position:0% +integers in + + + align:start position:0% +integers in +constant time each and this problem set + + align:start position:0% +constant time each and this problem set + + + align:start position:0% +constant time each and this problem set +was ambiguous + + align:start position:0% +was ambiguous + + + align:start position:0% +was ambiguous +and both answers were accepted if you + + align:start position:0% +and both answers were accepted if you + + + align:start position:0% +and both answers were accepted if you +assume these letters are nice and + + align:start position:0% +assume these letters are nice and + + + align:start position:0% +assume these letters are nice and +compactly stored then + + align:start position:0% +compactly stored then + + + align:start position:0% +compactly stored then +and they fit in 10 words because a word + + align:start position:0% +and they fit in 10 words because a word + + + align:start position:0% +and they fit in 10 words because a word +is at least log n + + align:start position:0% +is at least log n + + + align:start position:0% +is at least log n +if it's long then you can actually do + + align:start position:0% +if it's long then you can actually do + + + align:start position:0% +if it's long then you can actually do +this + + align:start position:0% +this + + + align:start position:0% +this +if you store each letter in a separate + + align:start position:0% +if you store each letter in a separate + + + align:start position:0% +if you store each letter in a separate +word then just reading the entire input + + align:start position:0% +word then just reading the entire input + + + align:start position:0% +word then just reading the entire input +will take + + align:start position:0% +will take + + + align:start position:0% +will take +and log in time + + align:start position:0% + + + + align:start position:0% + +that's a subtlety which we don't need to + + align:start position:0% +that's a subtlety which we don't need to + + + align:start position:0% +that's a subtlety which we don't need to +worry too much about in this class yeah + + align:start position:0% + + + + align:start position:0% + +yeah there are 26 possible letters + + align:start position:0% +yeah there are 26 possible letters + + + align:start position:0% +yeah there are 26 possible letters +numbering them 0 to 25. um and then + + align:start position:0% +numbering them 0 to 25. um and then + + + align:start position:0% +numbering them 0 to 25. um and then +when we take a string like a + + align:start position:0% +when we take a string like a + + + align:start position:0% +when we take a string like a +a map this into 0 0 + + align:start position:0% +a map this into 0 0 + + + align:start position:0% +a map this into 0 0 +in base 26 + + align:start position:0% + + + + align:start position:0% + +that's a number if we do bb for example + + align:start position:0% +that's a number if we do bb for example + + + align:start position:0% +that's a number if we do bb for example +this is + + align:start position:0% +this is + + + align:start position:0% +this is +maps to 1 1 in base 26 which means + + align:start position:0% +maps to 1 1 in base 26 which means + + + align:start position:0% +maps to 1 1 in base 26 which means +uh 1 times 26 plus 1 + + align:start position:0% +uh 1 times 26 plus 1 + + + align:start position:0% +uh 1 times 26 plus 1 +which is 27. okay so that's that's the + + align:start position:0% +which is 27. okay so that's that's the + + + align:start position:0% +which is 27. okay so that's that's the +mapping that i mean + + align:start position:0% +mapping that i mean + + + align:start position:0% +mapping that i mean +you're mapping the whole string the + + align:start position:0% +you're mapping the whole string the + + + align:start position:0% +you're mapping the whole string the +whole string to a single number yeah + + align:start position:0% +whole string to a single number yeah + + + align:start position:0% +whole string to a single number yeah +and there's a subtlety because i want + + align:start position:0% +and there's a subtlety because i want + + + align:start position:0% +and there's a subtlety because i want +lexicographic i need to pad things with + + align:start position:0% +lexicographic i need to pad things with + + + align:start position:0% +lexicographic i need to pad things with +spaces at the end or pad them with a's + + align:start position:0% +spaces at the end or pad them with a's + + + align:start position:0% +spaces at the end or pad them with a's +at the end + + align:start position:0% +at the end + + + align:start position:0% +at the end +in case they're shorter than 10 log n + + align:start position:0% +in case they're shorter than 10 log n + + + align:start position:0% +in case they're shorter than 10 log n +okay uh cool that was b + + align:start position:0% + + + + align:start position:0% + +c is not very interesting it's integers + + align:start position:0% + + + + align:start position:0% + +in the range 0 to n squared + + align:start position:0% +in the range 0 to n squared + + + align:start position:0% +in the range 0 to n squared +this i can just solve with radix sort + + align:start position:0% +this i can just solve with radix sort + + + align:start position:0% +this i can just solve with radix sort +because my radix sort at this point + + align:start position:0% +because my radix sort at this point + + + align:start position:0% +because my radix sort at this point +we've done it + + align:start position:0% +we've done it + + + align:start position:0% +we've done it +it's our third time rate of sort we can + + align:start position:0% +it's our third time rate of sort we can + + + align:start position:0% +it's our third time rate of sort we can +sort as long as + + align:start position:0% +sort as long as + + + align:start position:0% +sort as long as +uh the integers are bounded by a + + align:start position:0% +uh the integers are bounded by a + + + align:start position:0% +uh the integers are bounded by a +polynomial here it's a + + align:start position:0% +polynomial here it's a + + + align:start position:0% +polynomial here it's a +fixed polynomial with constant exponent + + align:start position:0% +fixed polynomial with constant exponent + + + align:start position:0% +fixed polynomial with constant exponent +so this will + + align:start position:0% +so this will + + + align:start position:0% +so this will +and this is radix sort i like to saw + + align:start position:0% +and this is radix sort i like to saw + + + align:start position:0% +and this is radix sort i like to saw +that just calls counting sword twice + + align:start position:0% +that just calls counting sword twice + + + align:start position:0% +that just calls counting sword twice +uh linear time d is where things get + + align:start position:0% +uh linear time d is where things get + + + align:start position:0% +uh linear time d is where things get +more interesting + + align:start position:0% +more interesting + + + align:start position:0% +more interesting +let me get this phrasing same + + align:start position:0% +let me get this phrasing same + + + align:start position:0% +let me get this phrasing same +so + + align:start position:0% + + + + align:start position:0% + +v we have rational numbers of the form w + + align:start position:0% +v we have rational numbers of the form w + + + align:start position:0% +v we have rational numbers of the form w +over f this is + + align:start position:0% +over f this is + + + align:start position:0% +over f this is +win some win ratio + + align:start position:0% +win some win ratio + + + align:start position:0% +win some win ratio +always in the range zero to one as you + + align:start position:0% +always in the range zero to one as you + + + align:start position:0% +always in the range zero to one as you +say w is at most f + + align:start position:0% +say w is at most f + + + align:start position:0% +say w is at most f +and zero is less than w is + + align:start position:0% +and zero is less than w is + + + align:start position:0% +and zero is less than w is +some f is less than n squared because + + align:start position:0% +some f is less than n squared because + + + align:start position:0% +some f is less than n squared because +the + + align:start position:0% +the + + + align:start position:0% +the +that is really confusing it's less than + + align:start position:0% +that is really confusing it's less than + + + align:start position:0% +that is really confusing it's less than +n squared those are separate statements + + align:start position:0% +n squared those are separate statements + + + align:start position:0% +n squared those are separate statements +uh because the f actually comes from + + align:start position:0% +uh because the f actually comes from + + + align:start position:0% +uh because the f actually comes from +part c c is really a set up for this one + + align:start position:0% +part c c is really a set up for this one + + + align:start position:0% +part c c is really a set up for this one +um doesn't really matter what this means + + align:start position:0% +um doesn't really matter what this means + + + align:start position:0% +um doesn't really matter what this means +it's just that we have + + align:start position:0% +it's just that we have + + + align:start position:0% +it's just that we have +numbers w and f where w is always less + + align:start position:0% +numbers w and f where w is always less + + + align:start position:0% +numbers w and f where w is always less +than f and they're between 0 and n + + align:start position:0% +than f and they're between 0 and n + + + align:start position:0% +than f and they're between 0 and n +squared + + align:start position:0% +squared + + + align:start position:0% +squared +so you should think this is a good range + + align:start position:0% +so you should think this is a good range + + + align:start position:0% +so you should think this is a good range +for me right + + align:start position:0% +for me right + + + align:start position:0% +for me right +that i'm representing this rational in + + align:start position:0% +that i'm representing this rational in + + + align:start position:0% +that i'm representing this rational in +terms of two numbers between zero and n + + align:start position:0% +terms of two numbers between zero and n + + + align:start position:0% +terms of two numbers between zero and n +squared so + + align:start position:0% +squared so + + + align:start position:0% +squared so +there's like n to the fourth possible + + align:start position:0% +there's like n to the fourth possible + + + align:start position:0% +there's like n to the fourth possible +choices for what w + + align:start position:0% +choices for what w + + + align:start position:0% +choices for what w +and f are so the range of my values is n + + align:start position:0% +and f are so the range of my values is n + + + align:start position:0% +and f are so the range of my values is n +to the fourth that's the setting + + align:start position:0% +to the fourth that's the setting + + + align:start position:0% +to the fourth that's the setting +where rate of sort should run fast + + align:start position:0% +where rate of sort should run fast + + + align:start position:0% +where rate of sort should run fast +unfortunately these numbers + + align:start position:0% +unfortunately these numbers + + + align:start position:0% +unfortunately these numbers +what i want to sort by is not an integer + + align:start position:0% +what i want to sort by is not an integer + + + align:start position:0% +what i want to sort by is not an integer +it's a rational + + align:start position:0% +it's a rational + + + align:start position:0% +it's a rational +and that's annoying so there are + + align:start position:0% +and that's annoying so there are + + + align:start position:0% +and that's annoying so there are +a couple of ways to solve this problem + + align:start position:0% +a couple of ways to solve this problem + + + align:start position:0% +a couple of ways to solve this problem +uh + + align:start position:0% +uh + + + align:start position:0% +uh +in general a good way to solve sorting + + align:start position:0% +in general a good way to solve sorting + + + align:start position:0% +in general a good way to solve sorting +is to use merge sort workshop is always + + align:start position:0% +is to use merge sort workshop is always + + + align:start position:0% +is to use merge sort workshop is always +a good answer it's not the best answer + + align:start position:0% +a good answer it's not the best answer + + + align:start position:0% +a good answer it's not the best answer +in these cases we've we shaved off a log + + align:start position:0% +in these cases we've we shaved off a log + + + align:start position:0% +in these cases we've we shaved off a log +we got to linear time + + align:start position:0% +we got to linear time + + + align:start position:0% +we got to linear time +but n log n is pretty good it's pretty + + align:start position:0% +but n log n is pretty good it's pretty + + + align:start position:0% +but n log n is pretty good it's pretty +close to n so + + align:start position:0% +close to n so + + + align:start position:0% +close to n so +first goal might be can we even achieve + + align:start position:0% +first goal might be can we even achieve + + + align:start position:0% +first goal might be can we even achieve +n log n via merge sort + + align:start position:0% +n log n via merge sort + + + align:start position:0% +n log n via merge sort +what would i need to do in order to + + align:start position:0% +what would i need to do in order to + + + align:start position:0% +what would i need to do in order to +actually apply merge sort to this + + align:start position:0% +actually apply merge sort to this + + + align:start position:0% +actually apply merge sort to this +instance + + align:start position:0% + + + + align:start position:0% + +what does merge sword do to its keys + + align:start position:0% + + + + align:start position:0% + +sorry it isolates and compares them yeah + + align:start position:0% +sorry it isolates and compares them yeah + + + align:start position:0% +sorry it isolates and compares them yeah +right so there's an array data structure + + align:start position:0% +right so there's an array data structure + + + align:start position:0% +right so there's an array data structure +and it indexes into the array that's the + + align:start position:0% +and it indexes into the array that's the + + + align:start position:0% +and it indexes into the array that's the +isolation + + align:start position:0% +isolation + + + align:start position:0% +isolation +but then it the thing it actually does + + align:start position:0% +but then it the thing it actually does + + + align:start position:0% +but then it the thing it actually does +with the items themselves is always a + + align:start position:0% +with the items themselves is always a + + + align:start position:0% +with the items themselves is always a +comparison + + align:start position:0% +comparison + + + align:start position:0% +comparison +this is why we introduced the comparison + + align:start position:0% +this is why we introduced the comparison + + + align:start position:0% +this is why we introduced the comparison +model and proved an ad log and lower + + align:start position:0% +model and proved an ad log and lower + + + align:start position:0% +model and proved an ad log and lower +bound + + align:start position:0% +bound + + + align:start position:0% +bound +in the comparison model because merge + + align:start position:0% +in the comparison model because merge + + + align:start position:0% +in the comparison model because merge +sort and insertion sort and selection + + align:start position:0% +sort and insertion sort and selection + + + align:start position:0% +sort and insertion sort and selection +sort are all comparison algorithms + + align:start position:0% +sort are all comparison algorithms + + + align:start position:0% +sort are all comparison algorithms +rated sort is not but this one is but to + + align:start position:0% +rated sort is not but this one is but to + + + align:start position:0% +rated sort is not but this one is but to +run to apply merge sort i need to say + + align:start position:0% +run to apply merge sort i need to say + + + align:start position:0% +run to apply merge sort i need to say +how do i compare w i over + + align:start position:0% +how do i compare w i over + + + align:start position:0% +how do i compare w i over +f i versus + + align:start position:0% +f i versus + + + align:start position:0% +f i versus +w j over f j + + align:start position:0% + + + + align:start position:0% + +my computer only deals with integers we + + align:start position:0% +my computer only deals with integers we + + + align:start position:0% +my computer only deals with integers we +can't + + align:start position:0% +can't + + + align:start position:0% +can't +actually represent w i over f i + + align:start position:0% +actually represent w i over f i + + + align:start position:0% +actually represent w i over f i +explicitly in + + align:start position:0% +explicitly in + + + align:start position:0% +explicitly in +in binary because it has infinitely many + + align:start position:0% +in binary because it has infinitely many + + + align:start position:0% +in binary because it has infinitely many +bits + + align:start position:0% +bits + + + align:start position:0% +bits +but i can represent it implicitly by + + align:start position:0% +but i can represent it implicitly by + + + align:start position:0% +but i can represent it implicitly by +storing wi and fi + + align:start position:0% +storing wi and fi + + + align:start position:0% +storing wi and fi +yeah multiply by f i and fj yeah as + + align:start position:0% +yeah multiply by f i and fj yeah as + + + align:start position:0% +yeah multiply by f i and fj yeah as +when i went i didn't go to school but + + align:start position:0% +when i went i didn't go to school but + + + align:start position:0% +when i went i didn't go to school but +then we learned + + align:start position:0% +then we learned + + + align:start position:0% +then we learned +cross multiplication uh so it's which is + + align:start position:0% +cross multiplication uh so it's which is + + + align:start position:0% +cross multiplication uh so it's which is +the same as multiplying both sides by fi + + align:start position:0% +the same as multiplying both sides by fi + + + align:start position:0% +the same as multiplying both sides by fi +and multiplying both sides by f j as you + + align:start position:0% +and multiplying both sides by f j as you + + + align:start position:0% +and multiplying both sides by f j as you +said + + align:start position:0% +said + + + align:start position:0% +said +so then we get f i f j less than + + align:start position:0% +so then we get f i f j less than + + + align:start position:0% +so then we get f i f j less than +question mark uh f + + align:start position:0% +question mark uh f + + + align:start position:0% +question mark uh f +whatever f i w j + + align:start position:0% +whatever f i w j + + + align:start position:0% +whatever f i w j +uh when we do that we better make sure + + align:start position:0% +uh when we do that we better make sure + + + align:start position:0% +uh when we do that we better make sure +that the things are multiplying by our + + align:start position:0% +that the things are multiplying by our + + + align:start position:0% +that the things are multiplying by our +non-negative otherwise the sign flips + + align:start position:0% +non-negative otherwise the sign flips + + + align:start position:0% +non-negative otherwise the sign flips +but here we assume they're all + + align:start position:0% +but here we assume they're all + + + align:start position:0% +but here we assume they're all +non-negative + + align:start position:0% +non-negative + + + align:start position:0% +non-negative +so this is good and now we're just + + align:start position:0% +so this is good and now we're just + + + align:start position:0% +so this is good and now we're just +multiplying two integers here + + align:start position:0% +multiplying two integers here + + + align:start position:0% +multiplying two integers here +multiplying two integers here and + + align:start position:0% +multiplying two integers here and + + + align:start position:0% +multiplying two integers here and +comparing + + align:start position:0% +comparing + + + align:start position:0% +comparing +those are all things i can do in a word + + align:start position:0% +those are all things i can do in a word + + + align:start position:0% +those are all things i can do in a word +round okay + + align:start position:0% +round okay + + + align:start position:0% +round okay +so this was actually the intended + + align:start position:0% +so this was actually the intended + + + align:start position:0% +so this was actually the intended +solution when this problem was posed + + align:start position:0% +solution when this problem was posed + + + align:start position:0% +solution when this problem was posed +here's a way to do comparison sort we + + align:start position:0% +here's a way to do comparison sort we + + + align:start position:0% +here's a way to do comparison sort we +get n log n but in fact + + align:start position:0% +get n log n but in fact + + + align:start position:0% +get n log n but in fact +you can achieve linear time yeah + + align:start position:0% + + + + align:start position:0% + +uh i feel like there's a joke here like + + align:start position:0% +uh i feel like there's a joke here like + + + align:start position:0% +uh i feel like there's a joke here like +pikachu is superior that's always the + + align:start position:0% +pikachu is superior that's always the + + + align:start position:0% +pikachu is superior that's always the +answer + + align:start position:0% +answer + + + align:start position:0% +answer +so how do i tell whether one pokemon is + + align:start position:0% +so how do i tell whether one pokemon is + + + align:start position:0% +so how do i tell whether one pokemon is +superior to the other + + align:start position:0% +superior to the other + + + align:start position:0% +superior to the other +if i i multiply + + align:start position:0% +if i i multiply + + + align:start position:0% +if i i multiply +uh my i multiply i's + + align:start position:0% +uh my i multiply i's + + + align:start position:0% +uh my i multiply i's +f value with j's w value and i see + + align:start position:0% +f value with j's w value and i see + + + align:start position:0% +f value with j's w value and i see +whether that's greater than + + align:start position:0% +whether that's greater than + + + align:start position:0% +whether that's greater than +i's w value times j's f value + + align:start position:0% +i's w value times j's f value + + + align:start position:0% +i's w value times j's f value +and if it is so these are + + align:start position:0% +and if it is so these are + + + align:start position:0% +and if it is so these are +equivalent if this one is greater than + + align:start position:0% +equivalent if this one is greater than + + + align:start position:0% +equivalent if this one is greater than +this one i know that this is greater + + align:start position:0% +this one i know that this is greater + + + align:start position:0% +this one i know that this is greater +than this + + align:start position:0% +than this + + + align:start position:0% +than this +these are equivalent sentences by + + align:start position:0% +these are equivalent sentences by + + + align:start position:0% +these are equivalent sentences by +mathematics by algebra + + align:start position:0% +mathematics by algebra + + + align:start position:0% +mathematics by algebra +and so uh this is what i want to know + + align:start position:0% +and so uh this is what i want to know + + + align:start position:0% +and so uh this is what i want to know +this would say j is superior to i + + align:start position:0% +this would say j is superior to i + + + align:start position:0% +this would say j is superior to i +and so i determine that by actually + + align:start position:0% +and so i determine that by actually + + + align:start position:0% +and so i determine that by actually +doing this + + align:start position:0% +doing this + + + align:start position:0% +doing this +so then i don't have to divide and deal + + align:start position:0% +so then i don't have to divide and deal + + + align:start position:0% +so then i don't have to divide and deal +with real numbers + + align:start position:0% +with real numbers + + + align:start position:0% +with real numbers +because i don't know how cause i'm a + + align:start position:0% +because i don't know how cause i'm a + + + align:start position:0% +because i don't know how cause i'm a +computer + + align:start position:0% +computer + + + align:start position:0% +computer +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +we're all computers + + align:start position:0% + + + + align:start position:0% + +okay uh + + align:start position:0% + + + + align:start position:0% + +so it would be great if my numbers all + + align:start position:0% +so it would be great if my numbers all + + + align:start position:0% +so it would be great if my numbers all +had the same denominator + + align:start position:0% +had the same denominator + + + align:start position:0% +had the same denominator +if they all had the same f then i could + + align:start position:0% +if they all had the same f then i could + + + align:start position:0% +if they all had the same f then i could +just compare the w's + + align:start position:0% +just compare the w's + + + align:start position:0% +just compare the w's +so that's one intuition for why + + align:start position:0% +so that's one intuition for why + + + align:start position:0% +so that's one intuition for why +we can actually do this in linear time + + align:start position:0% +we can actually do this in linear time + + + align:start position:0% +we can actually do this in linear time +um + + align:start position:0% +um + + + align:start position:0% +um +but the the way i like to think about it + + align:start position:0% +but the the way i like to think about it + + + align:start position:0% +but the the way i like to think about it +so let's just draw + + align:start position:0% +so let's just draw + + + align:start position:0% +so let's just draw +the real interval from zero to one + + align:start position:0% +the real interval from zero to one + + + align:start position:0% +the real interval from zero to one +and there are various spots all over + + align:start position:0% +and there are various spots all over + + + align:start position:0% +and there are various spots all over +here + + align:start position:0% + + + + align:start position:0% + +um that represent i can't actually + + align:start position:0% +um that represent i can't actually + + + align:start position:0% +um that represent i can't actually +compute this but conceptually each of + + align:start position:0% +compute this but conceptually each of + + + align:start position:0% +compute this but conceptually each of +these wi over + + align:start position:0% +these wi over + + + align:start position:0% +these wi over +fi's falls somewhere in that interval + + align:start position:0% +fi's falls somewhere in that interval + + + align:start position:0% +fi's falls somewhere in that interval +from 0 to 1. + + align:start position:0% +from 0 to 1. + + + align:start position:0% +from 0 to 1. +and i want to sort them somehow + + align:start position:0% +and i want to sort them somehow + + + align:start position:0% +and i want to sort them somehow +so one thing that would be great is if i + + align:start position:0% +so one thing that would be great is if i + + + align:start position:0% +so one thing that would be great is if i +could take these real numbers and + + align:start position:0% +could take these real numbers and + + + align:start position:0% +could take these real numbers and +somehow + + align:start position:0% +somehow + + + align:start position:0% +somehow +map them to integers + + align:start position:0% + + + + align:start position:0% + +which are uniformly spaced maybe a + + align:start position:0% +which are uniformly spaced maybe a + + + align:start position:0% +which are uniformly spaced maybe a +little a few more of them + + align:start position:0% +little a few more of them + + + align:start position:0% +little a few more of them +but these go from zero to u minus one + + align:start position:0% +but these go from zero to u minus one + + + align:start position:0% +but these go from zero to u minus one +if i could get u relatively small and i + + align:start position:0% +if i could get u relatively small and i + + + align:start position:0% +if i could get u relatively small and i +could map + + align:start position:0% +could map + + + align:start position:0% +could map +each of these so i want the mapping to + + align:start position:0% +each of these so i want the mapping to + + + align:start position:0% +each of these so i want the mapping to +be order preserving + + align:start position:0% +be order preserving + + + align:start position:0% +be order preserving +and i want two very close but distinct + + align:start position:0% +and i want two very close but distinct + + + align:start position:0% +and i want two very close but distinct +items + + align:start position:0% +items + + + align:start position:0% +items +to map to distinct keys here i want them + + align:start position:0% +to map to distinct keys here i want them + + + align:start position:0% +to map to distinct keys here i want them +to map to distinct integers down here if + + align:start position:0% +to map to distinct integers down here if + + + align:start position:0% +to map to distinct integers down here if +i could do that then i just sort by the + + align:start position:0% +i could do that then i just sort by the + + + align:start position:0% +i could do that then i just sort by the +integers and that's the same as sorting + + align:start position:0% +integers and that's the same as sorting + + + align:start position:0% +integers and that's the same as sorting +by + + align:start position:0% +by + + + align:start position:0% +by +the real numbers and so at this point i + + align:start position:0% +the real numbers and so at this point i + + + align:start position:0% +the real numbers and so at this point i +wonder + + align:start position:0% +wonder + + + align:start position:0% +wonder +how close can two of these numbers be + + align:start position:0% +how close can two of these numbers be + + + align:start position:0% +how close can two of these numbers be +so how close + + align:start position:0% + + + + align:start position:0% + +can two keys e + + align:start position:0% +can two keys e + + + align:start position:0% +can two keys e +so i want to consider w i over f i + + align:start position:0% +so i want to consider w i over f i + + + align:start position:0% +so i want to consider w i over f i +minus w j over f j + + align:start position:0% +minus w j over f j + + + align:start position:0% +minus w j over f j +an absolute value okay + + align:start position:0% +an absolute value okay + + + align:start position:0% +an absolute value okay +now i do algebra um so this is + + align:start position:0% +now i do algebra um so this is + + + align:start position:0% +now i do algebra um so this is +i'd like to bring this into one ratio so + + align:start position:0% +i'd like to bring this into one ratio so + + + align:start position:0% +i'd like to bring this into one ratio so +this is + + align:start position:0% +this is + + + align:start position:0% +this is +i can do that by multiplying one by five + + align:start position:0% +i can do that by multiplying one by five + + + align:start position:0% +i can do that by multiplying one by five +one by f j + + align:start position:0% +one by f j + + + align:start position:0% +one by f j +and it's w i f j minus w + + align:start position:0% +and it's w i f j minus w + + + align:start position:0% +and it's w i f j minus w +j f i which should look a lot like + + align:start position:0% +j f i which should look a lot like + + + align:start position:0% +j f i which should look a lot like +something here + + align:start position:0% +something here + + + align:start position:0% +something here +uh but never mind so i'm sure there's a + + align:start position:0% +uh but never mind so i'm sure there's a + + + align:start position:0% +uh but never mind so i'm sure there's a +deep connection here i could probably + + align:start position:0% +deep connection here i could probably + + + align:start position:0% +deep connection here i could probably +use this to prove that + + align:start position:0% +use this to prove that + + + align:start position:0% +use this to prove that +or vice versa cool so + + align:start position:0% +or vice versa cool so + + + align:start position:0% +or vice versa cool so +with some absolute values same thing uh + + align:start position:0% +with some absolute values same thing uh + + + align:start position:0% +with some absolute values same thing uh +maybe + + align:start position:0% +maybe + + + align:start position:0% +maybe +these are non-negative so i can actually + + align:start position:0% +these are non-negative so i can actually + + + align:start position:0% +these are non-negative so i can actually +just put absolute values on the top part + + align:start position:0% +just put absolute values on the top part + + + align:start position:0% +just put absolute values on the top part +and okay wi is an integer fj is an + + align:start position:0% +and okay wi is an integer fj is an + + + align:start position:0% +and okay wi is an integer fj is an +integer w j is an integer + + align:start position:0% +integer w j is an integer + + + align:start position:0% +integer w j is an integer +f is an integer all greater than equal + + align:start position:0% +f is an integer all greater than equal + + + align:start position:0% +f is an integer all greater than equal +to zero + + align:start position:0% +to zero + + + align:start position:0% +to zero +so this thing is an integer + + align:start position:0% +so this thing is an integer + + + align:start position:0% +so this thing is an integer +so uh it could be equal to zero it's a + + align:start position:0% +so uh it could be equal to zero it's a + + + align:start position:0% +so uh it could be equal to zero it's a +non-negative integer because all the + + align:start position:0% +non-negative integer because all the + + + align:start position:0% +non-negative integer because all the +things are non-negative + + align:start position:0% +things are non-negative + + + align:start position:0% +things are non-negative +it could be equal to zero but if they're + + align:start position:0% +it could be equal to zero but if they're + + + align:start position:0% +it could be equal to zero but if they're +equal to zero that's actually identical + + align:start position:0% +equal to zero that's actually identical + + + align:start position:0% +equal to zero that's actually identical +ratios right if this is zero the whole + + align:start position:0% +ratios right if this is zero the whole + + + align:start position:0% +ratios right if this is zero the whole +thing is zero and so + + align:start position:0% +thing is zero and so + + + align:start position:0% +thing is zero and so +these two values were the same okay but + + align:start position:0% +these two values were the same okay but + + + align:start position:0% +these two values were the same okay but +let's suppose it's not zero if it's not + + align:start position:0% +let's suppose it's not zero if it's not + + + align:start position:0% +let's suppose it's not zero if it's not +zero it's actually at least + + align:start position:0% +zero it's actually at least + + + align:start position:0% +zero it's actually at least +one an absolute value because it's an + + align:start position:0% +one an absolute value because it's an + + + align:start position:0% +one an absolute value because it's an +integer + + align:start position:0% +integer + + + align:start position:0% +integer +what about the bottom f i so now we want + + align:start position:0% +what about the bottom f i so now we want + + + align:start position:0% +what about the bottom f i so now we want +this + + align:start position:0% +this + + + align:start position:0% +this +i want to know how small this ratio can + + align:start position:0% +i want to know how small this ratio can + + + align:start position:0% +i want to know how small this ratio can +be it's going to be small when this is + + align:start position:0% +be it's going to be small when this is + + + align:start position:0% +be it's going to be small when this is +small + + align:start position:0% +small + + + align:start position:0% +small +and this is big how big could fifj be + + align:start position:0% +and this is big how big could fifj be + + + align:start position:0% +and this is big how big could fifj be +well we're told that all the f's are + + align:start position:0% +well we're told that all the f's are + + + align:start position:0% +well we're told that all the f's are +less than n squared so this thing + + align:start position:0% +less than n squared so this thing + + + align:start position:0% +less than n squared so this thing +is at most n squared n to the fourth + + align:start position:0% +is at most n squared n to the fourth + + + align:start position:0% +is at most n squared n to the fourth +less than n to the fourth n squared + + align:start position:0% +less than n to the fourth n squared + + + align:start position:0% +less than n to the fourth n squared +minus one + + align:start position:0% +minus one + + + align:start position:0% +minus one +squared but less than n to the fourth + + align:start position:0% +squared but less than n to the fourth + + + align:start position:0% +squared but less than n to the fourth +uh f i is at most n squared f j is the + + align:start position:0% +uh f i is at most n squared f j is the + + + align:start position:0% +uh f i is at most n squared f j is the +most n squared + + align:start position:0% +most n squared + + + align:start position:0% +most n squared +so it's n squared squared so this is at + + align:start position:0% +so it's n squared squared so this is at + + + align:start position:0% +so it's n squared squared so this is at +least + + align:start position:0% +least + + + align:start position:0% +least +one over n to the fourth so the the + + align:start position:0% +one over n to the fourth so the the + + + align:start position:0% +one over n to the fourth so the the +closest the two points can get here + + align:start position:0% +closest the two points can get here + + + align:start position:0% +closest the two points can get here +is one over n to the fourth so what + + align:start position:0% +is one over n to the fourth so what + + + align:start position:0% +is one over n to the fourth so what +could i do + + align:start position:0% +could i do + + + align:start position:0% +could i do +to scale that up to make them + + align:start position:0% +to scale that up to make them + + + align:start position:0% +to scale that up to make them +kind of like integers multiply by n to + + align:start position:0% +kind of like integers multiply by n to + + + align:start position:0% +kind of like integers multiply by n to +the fourth + + align:start position:0% +the fourth + + + align:start position:0% +the fourth +so just multiply + + align:start position:0% +so just multiply + + + align:start position:0% +so just multiply +by n to the fourth and then + + align:start position:0% +by n to the fourth and then + + + align:start position:0% +by n to the fourth and then +floor so we're going to take + + align:start position:0% +floor so we're going to take + + + align:start position:0% +floor so we're going to take +each fi over + + align:start position:0% +each fi over + + + align:start position:0% +each fi over +i like to compute this ratio but i don't + + align:start position:0% +i like to compute this ratio but i don't + + + align:start position:0% +i like to compute this ratio but i don't +know how so + + align:start position:0% +know how so + + + align:start position:0% +know how so +instead i'm going to take f i multi okay + + align:start position:0% +instead i'm going to take f i multi okay + + + align:start position:0% +instead i'm going to take f i multi okay +conceptually what i want to do is + + align:start position:0% +conceptually what i want to do is + + + align:start position:0% +conceptually what i want to do is +multiply by n to the fourth and take the + + align:start position:0% +multiply by n to the fourth and take the + + + align:start position:0% +multiply by n to the fourth and take the +floor + + align:start position:0% +floor + + + align:start position:0% +floor +how do i actually do this + + align:start position:0% +how do i actually do this + + + align:start position:0% +how do i actually do this +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +in a machine that doesn't have real + + align:start position:0% +in a machine that doesn't have real + + + align:start position:0% +in a machine that doesn't have real +numbers like this + + align:start position:0% + + + + align:start position:0% + +and so i don't have a floor operation + + align:start position:0% +and so i don't have a floor operation + + + align:start position:0% +and so i don't have a floor operation +just have integer operations then i can + + align:start position:0% +just have integer operations then i can + + + align:start position:0% +just have integer operations then i can +uh take f i + + align:start position:0% +uh take f i + + + align:start position:0% +uh take f i +multiply it by n to the fourth + + align:start position:0% +multiply it by n to the fourth + + + align:start position:0% +multiply it by n to the fourth +and integer divide by w j + + align:start position:0% + + + + align:start position:0% + +that is the same that computes exactly + + align:start position:0% +that is the same that computes exactly + + + align:start position:0% +that is the same that computes exactly +this + + align:start position:0% +this + + + align:start position:0% +this +because i can do the multiplication of + + align:start position:0% +because i can do the multiplication of + + + align:start position:0% +because i can do the multiplication of +the division in either order + + align:start position:0% +the division in either order + + + align:start position:0% +the division in either order +uh in real space and then this does the + + align:start position:0% +uh in real space and then this does the + + + align:start position:0% +uh in real space and then this does the +floor at the appropriate time but this + + align:start position:0% +floor at the appropriate time but this + + + align:start position:0% +floor at the appropriate time but this +is just operations on integers + + align:start position:0% +is just operations on integers + + + align:start position:0% +is just operations on integers +and now these are integers representing + + align:start position:0% +and now these are integers representing + + + align:start position:0% +and now these are integers representing +how good my pokemon + + align:start position:0% +how good my pokemon + + + align:start position:0% +how good my pokemon +are that have the property that any two + + align:start position:0% +are that have the property that any two + + + align:start position:0% +are that have the property that any two +distinct ones + + align:start position:0% +distinct ones + + + align:start position:0% +distinct ones +before i take the floor any two distinct + + align:start position:0% +before i take the floor any two distinct + + + align:start position:0% +before i take the floor any two distinct +ones are at least one apart + + align:start position:0% +ones are at least one apart + + + align:start position:0% +ones are at least one apart +so after i take the floor they will + + align:start position:0% +so after i take the floor they will + + + align:start position:0% +so after i take the floor they will +remain one apart they will remain + + align:start position:0% +remain one apart they will remain + + + align:start position:0% +remain one apart they will remain +distinct integers + + align:start position:0% +distinct integers + + + align:start position:0% +distinct integers +and so i have successfully mapped my + + align:start position:0% +and so i have successfully mapped my + + + align:start position:0% +and so i have successfully mapped my +real numbers to integers where distinct + + align:start position:0% +real numbers to integers where distinct + + + align:start position:0% +real numbers to integers where distinct +real numbers map to distinct + + align:start position:0% +real numbers map to distinct + + + align:start position:0% +real numbers map to distinct +integers yeah wait so why is fi now in + + align:start position:0% +integers yeah wait so why is fi now in + + + align:start position:0% +integers yeah wait so why is fi now in +the numerator + + align:start position:0% + + + + align:start position:0% + +did i flip them yeah sorry please invert + + align:start position:0% +did i flip them yeah sorry please invert + + + align:start position:0% +did i flip them yeah sorry please invert +everything just here + + align:start position:0% +everything just here + + + align:start position:0% +everything just here +this is w and f5 that was just a typo + + align:start position:0% + + + + align:start position:0% + +that's all that okay + + align:start position:0% +that's all that okay + + + align:start position:0% +that's all that okay +are they both i's or js + + align:start position:0% +are they both i's or js + + + align:start position:0% +are they both i's or js +uh these should are supposed to both be + + align:start position:0% +uh these should are supposed to both be + + + align:start position:0% +uh these should are supposed to both be +eyes yeah + + align:start position:0% +eyes yeah + + + align:start position:0% +eyes yeah +thank you this was for each for each + + align:start position:0% +thank you this was for each for each + + + align:start position:0% +thank you this was for each for each +pokemon i + + align:start position:0% +pokemon i + + + align:start position:0% +pokemon i +we're going to compute this as our key + + align:start position:0% +we're going to compute this as our key + + + align:start position:0% +we're going to compute this as our key +then we're going to sort by those + + align:start position:0% +then we're going to sort by those + + + align:start position:0% +then we're going to sort by those +integer keys and that will sort the + + align:start position:0% +integer keys and that will sort the + + + align:start position:0% +integer keys and that will sort the +pokemon by the ratios + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +that's right for monster + + align:start position:0% + + + + align:start position:0% + +uh so my u was just a sorry this is + + align:start position:0% +uh so my u was just a sorry this is + + + align:start position:0% +uh so my u was just a sorry this is +uh a label on this thing can i help you + + align:start position:0% +uh a label on this thing can i help you + + + align:start position:0% +uh a label on this thing can i help you +yeah + + align:start position:0% + + + + align:start position:0% + +so uh now my u all right what is my u + + align:start position:0% +so uh now my u all right what is my u + + + align:start position:0% +so uh now my u all right what is my u +how what is my largest key + + align:start position:0% + + + + align:start position:0% + +occurs to me i really would like fi to + + align:start position:0% +occurs to me i really would like fi to + + + align:start position:0% +occurs to me i really would like fi to +be bigger than zero + + align:start position:0% +be bigger than zero + + + align:start position:0% +be bigger than zero +but yeah let's not worry about it + + align:start position:0% +but yeah let's not worry about it + + + align:start position:0% +but yeah let's not worry about it +uh how big could you be well the biggest + + align:start position:0% +uh how big could you be well the biggest + + + align:start position:0% +uh how big could you be well the biggest +this could be is if f + + align:start position:0% +this could be is if f + + + align:start position:0% +this could be is if f +i is small and this is big let's say f i + + align:start position:0% +i is small and this is big let's say f i + + + align:start position:0% +i is small and this is big let's say f i +can only go down to one otherwise i get + + align:start position:0% +can only go down to one otherwise i get + + + align:start position:0% +can only go down to one otherwise i get +a division by zero + + align:start position:0% +a division by zero + + + align:start position:0% +a division by zero +i have to deal with infinity especially + + align:start position:0% +i have to deal with infinity especially + + + align:start position:0% +i have to deal with infinity especially +probably the problem isn't even well + + align:start position:0% +probably the problem isn't even well + + + align:start position:0% +probably the problem isn't even well +defined then + + align:start position:0% +defined then + + + align:start position:0% +defined then +uh how big could this be well i know the + + align:start position:0% +uh how big could this be well i know the + + + align:start position:0% +uh how big could this be well i know the +w i's + + align:start position:0% +w i's + + + align:start position:0% +w i's +i'm sorry defined as positive oh good + + align:start position:0% +i'm sorry defined as positive oh good + + + align:start position:0% +i'm sorry defined as positive oh good +here's also a positive constraint here + + align:start position:0% +here's also a positive constraint here + + + align:start position:0% +here's also a positive constraint here +just i failed to + + align:start position:0% +just i failed to + + + align:start position:0% +just i failed to +preserve that constraint in my mapping + + align:start position:0% +preserve that constraint in my mapping + + + align:start position:0% +preserve that constraint in my mapping +from the word problem into the formal + + align:start position:0% +from the word problem into the formal + + + align:start position:0% +from the word problem into the formal +problem + + align:start position:0% + + + + align:start position:0% + +so f is at least one good but let's + + align:start position:0% +so f is at least one good but let's + + + align:start position:0% +so f is at least one good but let's +minim + + align:start position:0% +minim + + + align:start position:0% +minim +worst cases when it's one and when wi + + align:start position:0% +worst cases when it's one and when wi + + + align:start position:0% +worst cases when it's one and when wi +how big could it be well n squared minus + + align:start position:0% +how big could it be well n squared minus + + + align:start position:0% +how big could it be well n squared minus +one + + align:start position:0% +one + + + align:start position:0% +one +so this could be basically n squared + + align:start position:0% +so this could be basically n squared + + + align:start position:0% +so this could be basically n squared +times n to the fourth divided by one + + align:start position:0% +times n to the fourth divided by one + + + align:start position:0% +times n to the fourth divided by one +which is n to the sixth + + align:start position:0% +which is n to the sixth + + + align:start position:0% +which is n to the sixth +so w is sorry u the largest key i can + + align:start position:0% +so w is sorry u the largest key i can + + + align:start position:0% +so w is sorry u the largest key i can +have plus one + + align:start position:0% +have plus one + + + align:start position:0% +have plus one +is n to the sixth but that's okay + + align:start position:0% +is n to the sixth but that's okay + + + align:start position:0% +is n to the sixth but that's okay +because radix sort can handle any fixed + + align:start position:0% +because radix sort can handle any fixed + + + align:start position:0% +because radix sort can handle any fixed +polynomial in n + + align:start position:0% +polynomial in n + + + align:start position:0% +polynomial in n +so it's going to end up doing six + + align:start position:0% +so it's going to end up doing six + + + align:start position:0% +so it's going to end up doing six +counting sort passes + + align:start position:0% +counting sort passes + + + align:start position:0% +counting sort passes +yay that's problem three + + align:start position:0% +yay that's problem three + + + align:start position:0% +yay that's problem three +let's move on + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +so problem four mit has employed gank + + align:start position:0% +so problem four mit has employed gank + + + align:start position:0% +so problem four mit has employed gank +freri + + align:start position:0% +freri + + + align:start position:0% +freri +who's that + + align:start position:0% + + + + align:start position:0% + +frank gehry yep this is a common uh + + align:start position:0% +frank gehry yep this is a common uh + + + align:start position:0% +frank gehry yep this is a common uh +encoding that jason really likes + + align:start position:0% +encoding that jason really likes + + + align:start position:0% +encoding that jason really likes +i've grown to like it + + align:start position:0% +i've grown to like it + + + align:start position:0% +i've grown to like it +uh is this called spoonerism where you + + align:start position:0% +uh is this called spoonerism where you + + + align:start position:0% +uh is this called spoonerism where you +replace some + + align:start position:0% +replace some + + + align:start position:0% +replace some +some part of the beginning of your uh + + align:start position:0% +some part of the beginning of your uh + + + align:start position:0% +some part of the beginning of your uh +thing okay that's one joke there's + + align:start position:0% +thing okay that's one joke there's + + + align:start position:0% +thing okay that's one joke there's +another joke in this problem + + align:start position:0% +another joke in this problem + + + align:start position:0% +another joke in this problem +uh anyway they're building a new wing of + + align:start position:0% +uh anyway they're building a new wing of + + + align:start position:0% +uh anyway they're building a new wing of +this data center as one does + + align:start position:0% +this data center as one does + + + align:start position:0% +this data center as one does +uh we have a bunch of cubes if you read + + align:start position:0% +uh we have a bunch of cubes if you read + + + align:start position:0% +uh we have a bunch of cubes if you read +long enough you realize that's a red + + align:start position:0% +long enough you realize that's a red + + + align:start position:0% +long enough you realize that's a red +herring that's + + align:start position:0% +herring that's + + + align:start position:0% +herring that's +cubes do not play a role in this problem + + align:start position:0% +cubes do not play a role in this problem + + + align:start position:0% +cubes do not play a role in this problem +in the end + + align:start position:0% +in the end + + + align:start position:0% +in the end +what we have is a bunch of + + align:start position:0% +what we have is a bunch of + + + align:start position:0% +what we have is a bunch of +integers which happen to be the side + + align:start position:0% +integers which happen to be the side + + + align:start position:0% +integers which happen to be the side +length of the cube cubes but we just + + align:start position:0% +length of the cube cubes but we just + + + align:start position:0% +length of the cube cubes but we just +care about the side lengths not their + + align:start position:0% +care about the side lengths not their + + + align:start position:0% +care about the side lengths not their +volume or anything + + align:start position:0% +volume or anything + + + align:start position:0% +volume or anything +s + + align:start position:0% + + + + align:start position:0% + +n minus one + + align:start position:0% + + + + align:start position:0% + +and we want two + + align:start position:0% +and we want two + + + align:start position:0% +and we want two +numbers in s + + align:start position:0% + + + + align:start position:0% + +summing to h + + align:start position:0% + + + + align:start position:0% + +this is the side length not the number + + align:start position:0% +this is the side length not the number + + + align:start position:0% +this is the side length not the number +of sides so you got a cube + + align:start position:0% + + + + align:start position:0% + +cool i didn't know we'd be doing 3d + + align:start position:0% +cool i didn't know we'd be doing 3d + + + align:start position:0% +cool i didn't know we'd be doing 3d +geometry today ssi + + align:start position:0% +geometry today ssi + + + align:start position:0% +geometry today ssi +okay so you've got little cubes you've + + align:start position:0% +okay so you've got little cubes you've + + + align:start position:0% +okay so you've got little cubes you've +got big cubes + + align:start position:0% +got big cubes + + + align:start position:0% +got big cubes +okay this is the smaller side it's the + + align:start position:0% +okay this is the smaller side it's the + + + align:start position:0% +okay this is the smaller side it's the +biggest eye doesn't matter though + + align:start position:0% +biggest eye doesn't matter though + + + align:start position:0% +biggest eye doesn't matter though +they're just numbers + + align:start position:0% +they're just numbers + + + align:start position:0% +they're just numbers +okay we're not using them at all in the + + align:start position:0% +okay we're not using them at all in the + + + align:start position:0% +okay we're not using them at all in the +problem you're trying to like stack one + + align:start position:0% +problem you're trying to like stack one + + + align:start position:0% +problem you're trying to like stack one +cube on the other but + + align:start position:0% +cube on the other but + + + align:start position:0% +cube on the other but +all we really care about is two numbers + + align:start position:0% +all we really care about is two numbers + + + align:start position:0% +all we really care about is two numbers +who's whose sum + + align:start position:0% +who's whose sum + + + align:start position:0% +who's whose sum +regular old sum is exactly h ideally + + align:start position:0% +regular old sum is exactly h ideally + + + align:start position:0% +regular old sum is exactly h ideally +there's going to be two versions of this + + align:start position:0% +there's going to be two versions of this + + + align:start position:0% +there's going to be two versions of this +problem + + align:start position:0% +problem + + + align:start position:0% +problem +and so first goal is to solve this + + align:start position:0% +and so first goal is to solve this + + + align:start position:0% +and so first goal is to solve this +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +in linear expected time + + align:start position:0% + + + + align:start position:0% + +that's what the problem says so + + align:start position:0% +that's what the problem says so + + + align:start position:0% +that's what the problem says so +what do we know well linear time that's + + align:start position:0% +what do we know well linear time that's + + + align:start position:0% +what do we know well linear time that's +can't get much faster than that because + + align:start position:0% +can't get much faster than that because + + + align:start position:0% +can't get much faster than that because +we need that just to read the input + + align:start position:0% +we need that just to read the input + + + align:start position:0% +we need that just to read the input +expected time hashing + + align:start position:0% +expected time hashing + + + align:start position:0% +expected time hashing +right we're told basically we should use + + align:start position:0% +right we're told basically we should use + + + align:start position:0% +right we're told basically we should use +hashing now if we're really annoying + + align:start position:0% +hashing now if we're really annoying + + + align:start position:0% +hashing now if we're really annoying +maybe we throw that in even when you + + align:start position:0% +maybe we throw that in even when you + + + align:start position:0% +maybe we throw that in even when you +don't need it but + + align:start position:0% +don't need it but + + + align:start position:0% +don't need it but +that's pretty rare uh so when we see + + align:start position:0% +that's pretty rare uh so when we see + + + align:start position:0% +that's pretty rare uh so when we see +expected we should in a problem set + + align:start position:0% +expected we should in a problem set + + + align:start position:0% +expected we should in a problem set +setting like this in real life you never + + align:start position:0% +setting like this in real life you never + + + align:start position:0% +setting like this in real life you never +know what you should use but in + + align:start position:0% +know what you should use but in + + + align:start position:0% +know what you should use but in +our and was your learning in this class + + align:start position:0% +our and was your learning in this class + + + align:start position:0% +our and was your learning in this class +we're going to tell you basically + + align:start position:0% +we're going to tell you basically + + + align:start position:0% +we're going to tell you basically +what tricks you're allowed to use here + + align:start position:0% +what tricks you're allowed to use here + + + align:start position:0% +what tricks you're allowed to use here +you're allowed to use randomization so + + align:start position:0% +you're allowed to use randomization so + + + align:start position:0% +you're allowed to use randomization so +probably we need it + + align:start position:0% +probably we need it + + + align:start position:0% +probably we need it +indeed you need it to achieve this bound + + align:start position:0% +indeed you need it to achieve this bound + + + align:start position:0% +indeed you need it to achieve this bound +ah + + align:start position:0% + + + + align:start position:0% + +cool + + align:start position:0% +cool + + + align:start position:0% +cool +not obvious how to approach this problem + + align:start position:0% +not obvious how to approach this problem + + + align:start position:0% +not obvious how to approach this problem +with hashing so i'm going to give you + + align:start position:0% +with hashing so i'm going to give you + + + align:start position:0% +with hashing so i'm going to give you +uh the way i it's it's hard for me to + + align:start position:0% +uh the way i it's it's hard for me to + + + align:start position:0% +uh the way i it's it's hard for me to +not know this algorithm + + align:start position:0% +not know this algorithm + + + align:start position:0% +not know this algorithm +but um to me the first thing you should + + align:start position:0% +but um to me the first thing you should + + + align:start position:0% +but um to me the first thing you should +think about is if if i have linear time + + align:start position:0% +think about is if if i have linear time + + + align:start position:0% +think about is if if i have linear time +and n things and i'm going to use + + align:start position:0% +and n things and i'm going to use + + + align:start position:0% +and n things and i'm going to use +hashing + + align:start position:0% + + + + align:start position:0% + +the obvious thing to do is to take those + + align:start position:0% +the obvious thing to do is to take those + + + align:start position:0% +the obvious thing to do is to take those +n things and put them in a hash table + + align:start position:0% +n things and put them in a hash table + + + align:start position:0% +n things and put them in a hash table +build why not uh so let's just + + align:start position:0% +build why not uh so let's just + + + align:start position:0% +build why not uh so let's just +build a hash table + + align:start position:0% + + + + align:start position:0% + +on all the keys in s + + align:start position:0% +on all the keys in s + + + align:start position:0% +on all the keys in s +that's idea one + + align:start position:0% +that's idea one + + + align:start position:0% +that's idea one +seems like the first thing to try so + + align:start position:0% +seems like the first thing to try so + + + align:start position:0% +seems like the first thing to try so +what does that let me do + + align:start position:0% +what does that let me do + + + align:start position:0% +what does that let me do +it lets me i just erased the interface + + align:start position:0% +it lets me i just erased the interface + + + align:start position:0% +it lets me i just erased the interface +for hash tables but + + align:start position:0% +for hash tables but + + + align:start position:0% +for hash tables but +i can build a sequence out of it but + + align:start position:0% +i can build a sequence out of it but + + + align:start position:0% +i can build a sequence out of it but +normally it gives me a set interface + + align:start position:0% +normally it gives me a set interface + + + align:start position:0% +normally it gives me a set interface +so i can call find now in constant time + + align:start position:0% +so i can call find now in constant time + + + align:start position:0% +so i can call find now in constant time +it lets me given a number + + align:start position:0% +it lets me given a number + + + align:start position:0% +it lets me given a number +determine immediately whether that + + align:start position:0% +determine immediately whether that + + + align:start position:0% +determine immediately whether that +number is in s + + align:start position:0% +number is in s + + + align:start position:0% +number is in s +well that sounds interesting because i'm + + align:start position:0% +well that sounds interesting because i'm + + + align:start position:0% +well that sounds interesting because i'm +looking for two numbers in s + + align:start position:0% +looking for two numbers in s + + + align:start position:0% +looking for two numbers in s +so it lets me find one of them so i call + + align:start position:0% +so it lets me find one of them so i call + + + align:start position:0% +so it lets me find one of them so i call +it twice + + align:start position:0% +it twice + + + align:start position:0% +it twice +no uh calling it twice and only spending + + align:start position:0% +no uh calling it twice and only spending + + + align:start position:0% +no uh calling it twice and only spending +constant time on this beautiful data + + align:start position:0% +constant time on this beautiful data + + + align:start position:0% +constant time on this beautiful data +structure will not give you anything + + align:start position:0% +structure will not give you anything + + + align:start position:0% +structure will not give you anything +useful + + align:start position:0% + + + + align:start position:0% + +but we have linear time right so in + + align:start position:0% +but we have linear time right so in + + + align:start position:0% +but we have linear time right so in +addition to building a table + + align:start position:0% +addition to building a table + + + align:start position:0% +addition to building a table +we could call find on that table a + + align:start position:0% +we could call find on that table a + + + align:start position:0% +we could call find on that table a +linear number of times because each find + + align:start position:0% +linear number of times because each find + + + align:start position:0% +linear number of times because each find +only takes constant expected + + align:start position:0% +only takes constant expected + + + align:start position:0% +only takes constant expected +amortized time so if i do n of them that + + align:start position:0% +amortized time so if i do n of them that + + + align:start position:0% +amortized time so if i do n of them that +will take + + align:start position:0% +will take + + + align:start position:0% +will take +linear expected time the amortization + + align:start position:0% +linear expected time the amortization + + + align:start position:0% +linear expected time the amortization +disappears because + + align:start position:0% +disappears because + + + align:start position:0% +disappears because +i'm using it 10 times all right find + + align:start position:0% +i'm using it 10 times all right find + + + align:start position:0% +i'm using it 10 times all right find +never has amortization so + + align:start position:0% +never has amortization so + + + align:start position:0% +never has amortization so +it doesn't disappear because it was + + align:start position:0% +it doesn't disappear because it was + + + align:start position:0% +it doesn't disappear because it was +never there never mind + + align:start position:0% +never there never mind + + + align:start position:0% +never there never mind +i can afford n calls or five n calls + + align:start position:0% +i can afford n calls or five n calls + + + align:start position:0% +i can afford n calls or five n calls +to find because each one costs constant + + align:start position:0% +to find because each one costs constant + + + align:start position:0% +to find because each one costs constant +constant expected + + align:start position:0% +constant expected + + + align:start position:0% +constant expected +and the total for that will be linear + + align:start position:0% +and the total for that will be linear + + + align:start position:0% +and the total for that will be linear +time so next idea + + align:start position:0% +time so next idea + + + align:start position:0% +time so next idea +is let's just somehow call + + align:start position:0% +is let's just somehow call + + + align:start position:0% +is let's just somehow call +find + + align:start position:0% + + + + align:start position:0% + +a linear number of times + + align:start position:0% + + + + align:start position:0% + +okay okay uh so i want to find two + + align:start position:0% +okay okay uh so i want to find two + + + align:start position:0% +okay okay uh so i want to find two +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +summing to a given value h that wasn't + + align:start position:0% +summing to a given value h that wasn't + + + align:start position:0% +summing to a given value h that wasn't +maybe clear but h is given + + align:start position:0% +maybe clear but h is given + + + align:start position:0% +maybe clear but h is given +sorry um how long does it take to build + + align:start position:0% +sorry um how long does it take to build + + + align:start position:0% +sorry um how long does it take to build +the hash table + + align:start position:0% +the hash table + + + align:start position:0% +the hash table +how long does it take to build a hash + + align:start position:0% +how long does it take to build a hash + + + align:start position:0% +how long does it take to build a hash +table it was previously on this board + + align:start position:0% +table it was previously on this board + + + align:start position:0% +table it was previously on this board +linear expected time + + align:start position:0% + + + + align:start position:0% + +see previous lecture + + align:start position:0% +see previous lecture + + + align:start position:0% +see previous lecture +no two lectures ago ah okay + + align:start position:0% +no two lectures ago ah okay + + + align:start position:0% +no two lectures ago ah okay +well if we're gonna do this linear + + align:start position:0% +well if we're gonna do this linear + + + align:start position:0% +well if we're gonna do this linear +number of times i guess we should have a + + align:start position:0% +number of times i guess we should have a + + + align:start position:0% +number of times i guess we should have a +for loop + + align:start position:0% +for loop + + + align:start position:0% +for loop +let's do a for loop over the numbers + + align:start position:0% +let's do a for loop over the numbers + + + align:start position:0% +let's do a for loop over the numbers +this next idea + + align:start position:0% + + + + align:start position:0% + +loop over s + + align:start position:0% +loop over s + + + align:start position:0% +loop over s +and at this point we're done almost um + + align:start position:0% +and at this point we're done almost um + + + align:start position:0% +and at this point we're done almost um +space so i want to + + align:start position:0% +space so i want to + + + align:start position:0% +space so i want to +loop over the numbers and each one i + + align:start position:0% +loop over the numbers and each one i + + + align:start position:0% +loop over the numbers and each one i +want to do a find that's + + align:start position:0% +want to do a find that's + + + align:start position:0% +want to do a find that's +kind of all i have time to do so + + align:start position:0% +kind of all i have time to do so + + + align:start position:0% +kind of all i have time to do so +seems like a natural thing to try this + + align:start position:0% +seems like a natural thing to try this + + + align:start position:0% +seems like a natural thing to try this +this is by no means easy + + align:start position:0% +this is by no means easy + + + align:start position:0% +this is by no means easy +don't don't get me wrong having these + + align:start position:0% +don't don't get me wrong having these + + + align:start position:0% +don't don't get me wrong having these +ideas is well + + align:start position:0% +ideas is well + + + align:start position:0% +ideas is well +i'm explaining them as the obvious ideas + + align:start position:0% +i'm explaining them as the obvious ideas + + + align:start position:0% +i'm explaining them as the obvious ideas +they're not obvious + + align:start position:0% +they're not obvious + + + align:start position:0% +they're not obvious +but uh they are easy at least + + align:start position:0% +but uh they are easy at least + + + align:start position:0% +but uh they are easy at least +just not obvious to come up with the + + align:start position:0% +just not obvious to come up with the + + + align:start position:0% +just not obvious to come up with the +easy ideas so let's loop over s + + align:start position:0% +easy ideas so let's loop over s + + + align:start position:0% +easy ideas so let's loop over s +somehow called find using our hash table + + align:start position:0% +somehow called find using our hash table + + + align:start position:0% +somehow called find using our hash table +so the order is actually we're going to + + align:start position:0% +so the order is actually we're going to + + + align:start position:0% +so the order is actually we're going to +build the hash table + + align:start position:0% +build the hash table + + + align:start position:0% +build the hash table +then loop and inside the loop we're + + align:start position:0% +then loop and inside the loop we're + + + align:start position:0% +then loop and inside the loop we're +going to call find once per loop + + align:start position:0% +going to call find once per loop + + + align:start position:0% +going to call find once per loop +iteration so let's do it let's say + + align:start position:0% +iteration so let's do it let's say + + + align:start position:0% +iteration so let's do it let's say +for uh s-i-m-s + + align:start position:0% + + + + align:start position:0% + +so i want to find two numbers here i've + + align:start position:0% +so i want to find two numbers here i've + + + align:start position:0% +so i want to find two numbers here i've +exhaustively + + align:start position:0% +exhaustively + + + align:start position:0% +exhaustively +looped over one number i just need to + + align:start position:0% +looped over one number i just need to + + + align:start position:0% +looped over one number i just need to +find the second number that could + + align:start position:0% +find the second number that could + + + align:start position:0% +find the second number that could +possibly + + align:start position:0% +possibly + + + align:start position:0% +possibly +add up right i want to find + + align:start position:0% + + + + align:start position:0% + +whether there's an sj in s + + align:start position:0% +whether there's an sj in s + + + align:start position:0% +whether there's an sj in s +such that + + align:start position:0% +such that + + + align:start position:0% +such that +s i plus s j + + align:start position:0% +s i plus s j + + + align:start position:0% +s i plus s j +equals h + + align:start position:0% + + + + align:start position:0% + +can i do that query with find + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% + + + + align:start position:0% + +so what what does find do find says if i + + align:start position:0% +so what what does find do find says if i + + + align:start position:0% +so what what does find do find says if i +give you a key + + align:start position:0% +give you a key + + + align:start position:0% +give you a key +it will tell me whether like if i knew + + align:start position:0% +it will tell me whether like if i knew + + + align:start position:0% +it will tell me whether like if i knew +what sj was + + align:start position:0% +what sj was + + + align:start position:0% +what sj was +i it would tell me whether it's in s + + align:start position:0% + + + + align:start position:0% + +subtract h from s i and see whether that + + align:start position:0% +subtract h from s i and see whether that + + + align:start position:0% +subtract h from s i and see whether that +exists + + align:start position:0% +exists + + + align:start position:0% +exists +okay get it right h minus s-i let's + + align:start position:0% +okay get it right h minus s-i let's + + + align:start position:0% +okay get it right h minus s-i let's +get wrong + + align:start position:0% + + + + align:start position:0% + +i don't feel bad that you also got it + + align:start position:0% +i don't feel bad that you also got it + + + align:start position:0% +i don't feel bad that you also got it +wrong makes you feel better because i + + align:start position:0% +wrong makes you feel better because i + + + align:start position:0% +wrong makes you feel better because i +always get it wrong + + align:start position:0% +always get it wrong + + + align:start position:0% +always get it wrong +so a claim is this why because what we + + align:start position:0% +so a claim is this why because what we + + + align:start position:0% +so a claim is this why because what we +want to do + + align:start position:0% +want to do + + + align:start position:0% +want to do +is find well + + align:start position:0% +is find well + + + align:start position:0% +is find well +okay let's write see what it says over + + align:start position:0% +okay let's write see what it says over + + + align:start position:0% +okay let's write see what it says over +here so if we do h + + align:start position:0% +here so if we do h + + + align:start position:0% +here so if we do h +minus s i equals sj + + align:start position:0% +minus s i equals sj + + + align:start position:0% +minus s i equals sj +right so these are equivalent statements + + align:start position:0% +right so these are equivalent statements + + + align:start position:0% +right so these are equivalent statements +just by + + align:start position:0% +just by + + + align:start position:0% +just by +moving the si over and this is a query + + align:start position:0% +moving the si over and this is a query + + + align:start position:0% +moving the si over and this is a query +we can do + + align:start position:0% +we can do + + + align:start position:0% +we can do +we don't so let's remember these are + + align:start position:0% +we don't so let's remember these are + + + align:start position:0% +we don't so let's remember these are +things we know + + align:start position:0% + + + + align:start position:0% + +and sj is something we don't know + + align:start position:0% +and sj is something we don't know + + + align:start position:0% +and sj is something we don't know +although we know is that it's an s + + align:start position:0% +although we know is that it's an s + + + align:start position:0% +although we know is that it's an s +okay so we know these two things so if + + align:start position:0% +okay so we know these two things so if + + + align:start position:0% +okay so we know these two things so if +we bring them over to the same side + + align:start position:0% +we bring them over to the same side + + + align:start position:0% +we bring them over to the same side +we're searching for an unknown thing + + align:start position:0% +we're searching for an unknown thing + + + align:start position:0% +we're searching for an unknown thing +which is equal to exactly this thing + + align:start position:0% +which is equal to exactly this thing + + + align:start position:0% +which is equal to exactly this thing +that we can compute + + align:start position:0% +that we can compute + + + align:start position:0% +that we can compute +so we just compute h minus s i we call + + align:start position:0% +so we just compute h minus s i we call + + + align:start position:0% +so we just compute h minus s i we call +find that will tell us whether there is + + align:start position:0% +find that will tell us whether there is + + + align:start position:0% +find that will tell us whether there is +an sj + + align:start position:0% +an sj + + + align:start position:0% +an sj +equal to this okay so this is + + align:start position:0% +equal to this okay so this is + + + align:start position:0% +equal to this okay so this is +this is like a comment all right and + + align:start position:0% +this is like a comment all right and + + + align:start position:0% +this is like a comment all right and +then this is what we actually do + + align:start position:0% +then this is what we actually do + + + align:start position:0% +then this is what we actually do +and if there is a pair of numbers + + align:start position:0% +and if there is a pair of numbers + + + align:start position:0% +and if there is a pair of numbers +summing the h this will find it + + align:start position:0% +summing the h this will find it + + + align:start position:0% +summing the h this will find it +how much time did it take well we're + + align:start position:0% +how much time did it take well we're + + + align:start position:0% +how much time did it take well we're +doing n iterations of this loop + + align:start position:0% +doing n iterations of this loop + + + align:start position:0% +doing n iterations of this loop +each one we're calling a single find + + align:start position:0% +each one we're calling a single find + + + align:start position:0% +each one we're calling a single find +operation and + + align:start position:0% +operation and + + + align:start position:0% +operation and +find cos constant expected time + + align:start position:0% +find cos constant expected time + + + align:start position:0% +find cos constant expected time +and so the total is linear with respect + + align:start position:0% +and so the total is linear with respect + + + align:start position:0% +and so the total is linear with respect +to time + + align:start position:0% +to time + + + align:start position:0% +to time +great part a done + + align:start position:0% + + + + align:start position:0% + +then they throw part b at us to make it + + align:start position:0% +then they throw part b at us to make it + + + align:start position:0% +then they throw part b at us to make it +harder + + align:start position:0% + + + + align:start position:0% + +those pesky instructors + + align:start position:0% + + + + align:start position:0% + +so we read part b and part b + + align:start position:0% +so we read part b and part b + + + align:start position:0% +so we read part b and part b +says two things to make it harder + + align:start position:0% +says two things to make it harder + + + align:start position:0% +says two things to make it harder +so first of all we want linear worst + + align:start position:0% +so first of all we want linear worst + + + align:start position:0% +so first of all we want linear worst +case time + + align:start position:0% + + + + align:start position:0% + +and furthermore so we can't use hashing + + align:start position:0% +and furthermore so we can't use hashing + + + align:start position:0% +and furthermore so we can't use hashing +anymore + + align:start position:0% +anymore + + + align:start position:0% +anymore +furthermore uh so here we just needed to + + align:start position:0% +furthermore uh so here we just needed to + + + align:start position:0% +furthermore uh so here we just needed to +solve the exact problem to find whether + + align:start position:0% +solve the exact problem to find whether + + + align:start position:0% +solve the exact problem to find whether +the two numbers summing exactly to h + + align:start position:0% +the two numbers summing exactly to h + + + align:start position:0% +the two numbers summing exactly to h +now we would like to find the best + + align:start position:0% +now we would like to find the best + + + align:start position:0% +now we would like to find the best +solution smaller than or equal to h + + align:start position:0% +solution smaller than or equal to h + + + align:start position:0% +solution smaller than or equal to h +so find biggest + + align:start position:0% + + + + align:start position:0% + +pairwise sum + + align:start position:0% +pairwise sum + + + align:start position:0% +pairwise sum +that's less than or equal to h if no + + align:start position:0% +that's less than or equal to h if no + + + align:start position:0% +that's less than or equal to h if no +if there's no perfect pair but we're + + align:start position:0% +if there's no perfect pair but we're + + + align:start position:0% +if there's no perfect pair but we're +given + + align:start position:0% +given + + + align:start position:0% +given +a little bit of extra information + + align:start position:0% + + + + align:start position:0% + +which is we can assume h + + align:start position:0% + + + + align:start position:0% + +equals 600 n to the sixth + + align:start position:0% + + + + align:start position:0% + +it's a weird polynomial it took me a + + align:start position:0% +it's a weird polynomial it took me a + + + align:start position:0% +it's a weird polynomial it took me a +while to even notice that that was jerk + + align:start position:0% +while to even notice that that was jerk + + + align:start position:0% +while to even notice that that was jerk +in here + + align:start position:0% +in here + + + align:start position:0% +in here +6006 hiding in a polynomial + + align:start position:0% +6006 hiding in a polynomial + + + align:start position:0% +6006 hiding in a polynomial +all right so polynomial + + align:start position:0% +all right so polynomial + + + align:start position:0% +all right so polynomial +that should make you think radix sort it + + align:start position:0% +that should make you think radix sort it + + + align:start position:0% +that should make you think radix sort it +is radix or weak + + align:start position:0% +is radix or weak + + + align:start position:0% +is radix or weak +so that is a natural thing to try but in + + align:start position:0% +so that is a natural thing to try but in + + + align:start position:0% +so that is a natural thing to try but in +general even later in the semester when + + align:start position:0% +general even later in the semester when + + + align:start position:0% +general even later in the semester when +you see + + align:start position:0% +you see + + + align:start position:0% +you see +uh a nice polynomial with a fixed + + align:start position:0% +uh a nice polynomial with a fixed + + + align:start position:0% +uh a nice polynomial with a fixed +constant like this + + align:start position:0% +constant like this + + + align:start position:0% +constant like this +and it's somehow related to the integers + + align:start position:0% +and it's somehow related to the integers + + + align:start position:0% +and it's somehow related to the integers +we're dealing with you should think + + align:start position:0% +we're dealing with you should think + + + align:start position:0% +we're dealing with you should think +radix sort especially because now we + + align:start position:0% +radix sort especially because now we + + + align:start position:0% +radix sort especially because now we +want constant worst case time + + align:start position:0% +want constant worst case time + + + align:start position:0% +want constant worst case time +rate of source seems like a good thing + + align:start position:0% +rate of source seems like a good thing + + + align:start position:0% +rate of source seems like a good thing +to do don't know what to do with it yet + + align:start position:0% +to do don't know what to do with it yet + + + align:start position:0% +to do don't know what to do with it yet +in fact + + align:start position:0% +in fact + + + align:start position:0% +in fact +i can't even apply radix sort but idea + + align:start position:0% +i can't even apply radix sort but idea + + + align:start position:0% +i can't even apply radix sort but idea +one + + align:start position:0% +one + + + align:start position:0% +one +is radical just because i see that + + align:start position:0% +is radical just because i see that + + + align:start position:0% +is radical just because i see that +polynomial + + align:start position:0% +polynomial + + + align:start position:0% +polynomial +i think maybe i should try it + + align:start position:0% +i think maybe i should try it + + + align:start position:0% +i think maybe i should try it +now there's a problem here because we're + + align:start position:0% +now there's a problem here because we're + + + align:start position:0% +now there's a problem here because we're +given some numbers + + align:start position:0% +given some numbers + + + align:start position:0% +given some numbers +we're all some integers s i's we're also + + align:start position:0% +we're all some integers s i's we're also + + + align:start position:0% +we're all some integers s i's we're also +given h we're told now that h is a nice + + align:start position:0% +given h we're told now that h is a nice + + + align:start position:0% +given h we're told now that h is a nice +small polynomial + + align:start position:0% +small polynomial + + + align:start position:0% +small polynomial +we have no idea how big these numbers + + align:start position:0% +we have no idea how big these numbers + + + align:start position:0% +we have no idea how big these numbers +are + + align:start position:0% +are + + + align:start position:0% +are +so problem with this idea is that um + + align:start position:0% + + + + align:start position:0% + +when s i could be bigger than h we we + + align:start position:0% +when s i could be bigger than h we we + + + align:start position:0% +when s i could be bigger than h we we +have no idea how big + + align:start position:0% +have no idea how big + + + align:start position:0% +have no idea how big +the s i's are can i + + align:start position:0% +the s i's are can i + + + align:start position:0% +the s i's are can i +what can i say about s i's that are + + align:start position:0% +what can i say about s i's that are + + + align:start position:0% +what can i say about s i's that are +bigger than h + + align:start position:0% + + + + align:start position:0% + +for this problem + + align:start position:0% + + + + align:start position:0% + +summing to h oh i didn't say but all + + align:start position:0% +summing to h oh i didn't say but all + + + align:start position:0% +summing to h oh i didn't say but all +these numbers are non-negative that's + + align:start position:0% +these numbers are non-negative that's + + + align:start position:0% +these numbers are non-negative that's +important + + align:start position:0% +important + + + align:start position:0% +important +that looks like korean + + align:start position:0% +that looks like korean + + + align:start position:0% +that looks like korean +greater than or equal to zero + + align:start position:0% + + + + align:start position:0% + +yeah well they can't be a solution right + + align:start position:0% +yeah well they can't be a solution right + + + align:start position:0% +yeah well they can't be a solution right +if i'm finding a sum that's less than + + align:start position:0% +if i'm finding a sum that's less than + + + align:start position:0% +if i'm finding a sum that's less than +equal to h they're non-negative + + align:start position:0% +equal to h they're non-negative + + + align:start position:0% +equal to h they're non-negative +uh and any number any number that's + + align:start position:0% +uh and any number any number that's + + + align:start position:0% +uh and any number any number that's +greater than h + + align:start position:0% +greater than h + + + align:start position:0% +greater than h +i can just throw away they'll never be + + align:start position:0% +i can just throw away they'll never be + + + align:start position:0% +i can just throw away they'll never be +in a solution + + align:start position:0% +in a solution + + + align:start position:0% +in a solution +it's like already a single sum of one + + align:start position:0% +it's like already a single sum of one + + + align:start position:0% +it's like already a single sum of one +numbers here than h so two is only going + + align:start position:0% +numbers here than h so two is only going + + + align:start position:0% +numbers here than h so two is only going +to get bigger if they're non-negative + + align:start position:0% + + + + align:start position:0% + +so let's idea number two is let's just + + align:start position:0% +so let's idea number two is let's just + + + align:start position:0% +so let's idea number two is let's just +throw out all the big sis + + align:start position:0% +throw out all the big sis + + + align:start position:0% +throw out all the big sis +anything bigger than h now that won't + + align:start position:0% +anything bigger than h now that won't + + + align:start position:0% +anything bigger than h now that won't +change the answer because those can + + align:start position:0% +change the answer because those can + + + align:start position:0% +change the answer because those can +never be in a solution + + align:start position:0% +never be in a solution + + + align:start position:0% +never be in a solution +and now i have all the sis having the + + align:start position:0% +and now i have all the sis having the + + + align:start position:0% +and now i have all the sis having the +property that they're less than or equal + + align:start position:0% +property that they're less than or equal + + + align:start position:0% +property that they're less than or equal +to h + + align:start position:0% +to h + + + align:start position:0% +to h +and so they are small + + align:start position:0% +and so they are small + + + align:start position:0% +and so they are small +bounded by a fixed polynomial and now i + + align:start position:0% +bounded by a fixed polynomial and now i + + + align:start position:0% +bounded by a fixed polynomial and now i +can apply radix sort so after this idea + + align:start position:0% +can apply radix sort so after this idea + + + align:start position:0% +can apply radix sort so after this idea +i can apply this idea + + align:start position:0% +i can apply this idea + + + align:start position:0% +i can apply this idea +okay this gives you a flavor of how i + + align:start position:0% +okay this gives you a flavor of how i + + + align:start position:0% +okay this gives you a flavor of how i +like to think about problems + + align:start position:0% +like to think about problems + + + align:start position:0% +like to think about problems +i see clues like polynomial i think + + align:start position:0% +i see clues like polynomial i think + + + align:start position:0% +i see clues like polynomial i think +radix sort + + align:start position:0% +radix sort + + + align:start position:0% +radix sort +doesn't work but with some more ideas i + + align:start position:0% +doesn't work but with some more ideas i + + + align:start position:0% +doesn't work but with some more ideas i +can get it to work + + align:start position:0% +can get it to work + + + align:start position:0% +can get it to work +okay uh what good is it + + align:start position:0% +okay uh what good is it + + + align:start position:0% +okay uh what good is it +so now i've sorted si okay great s + + align:start position:0% +so now i've sorted si okay great s + + + align:start position:0% +so now i've sorted si okay great s +is sorted + + align:start position:0% + + + + align:start position:0% + +i guess we can try to do the same + + align:start position:0% +i guess we can try to do the same + + + align:start position:0% +i guess we can try to do the same +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +except i don't have a hash table anymore + + align:start position:0% +except i don't have a hash table anymore + + + align:start position:0% +except i don't have a hash table anymore +so let's just + + align:start position:0% +so let's just + + + align:start position:0% +so let's just +try doing a for loop over the s + + align:start position:0% +try doing a for loop over the s + + + align:start position:0% +try doing a for loop over the s +why not so let's do 4 + + align:start position:0% + + + + align:start position:0% + +s i and s but now it's sorted so + + align:start position:0% +s i and s but now it's sorted so + + + align:start position:0% +s i and s but now it's sorted so +presumably i should exploit the + + align:start position:0% +presumably i should exploit the + + + align:start position:0% +presumably i should exploit the +sorted order so let's do do them in + + align:start position:0% +sorted order so let's do do them in + + + align:start position:0% +sorted order so let's do do them in +order so i + + align:start position:0% +order so i + + + align:start position:0% +order so i +equals 0 1 up to n minus 1. + + align:start position:0% +equals 0 1 up to n minus 1. + + + align:start position:0% +equals 0 1 up to n minus 1. +let's say that s 0 is the smallest s 1 + + align:start position:0% +let's say that s 0 is the smallest s 1 + + + align:start position:0% +let's say that s 0 is the smallest s 1 +is the + + align:start position:0% +is the + + + align:start position:0% +is the +next smallest s n minus 1 is the biggest + + align:start position:0% +next smallest s n minus 1 is the biggest + + + align:start position:0% +next smallest s n minus 1 is the biggest +so i want to do something with this so i + + align:start position:0% +so i want to do something with this so i + + + align:start position:0% +so i want to do something with this so i +have s i and i want to figure out + + align:start position:0% +have s i and i want to figure out + + + align:start position:0% +have s i and i want to figure out +whether h minus s i is in there + + align:start position:0% + + + + align:start position:0% + +hard to do that better than ah + + align:start position:0% +hard to do that better than ah + + + align:start position:0% +hard to do that better than ah +actually i could do this with binary + + align:start position:0% +actually i could do this with binary + + + align:start position:0% +actually i could do this with binary +search right + + align:start position:0% +search right + + + align:start position:0% +search right +i know i'm looking for this value so i + + align:start position:0% +i know i'm looking for this value so i + + + align:start position:0% +i know i'm looking for this value so i +could + + align:start position:0% +could + + + align:start position:0% +could +and i have a sorted array now so i could + + align:start position:0% +and i have a sorted array now so i could + + + align:start position:0% +and i have a sorted array now so i could +binary search for h minus si + + align:start position:0% +binary search for h minus si + + + align:start position:0% +binary search for h minus si +and in login time i will find whether + + align:start position:0% +and in login time i will find whether + + + align:start position:0% +and in login time i will find whether +that guy is in there + + align:start position:0% +that guy is in there + + + align:start position:0% +that guy is in there +and if not keep looping i can keep track + + align:start position:0% +and if not keep looping i can keep track + + + align:start position:0% +and if not keep looping i can keep track +of the best thing that i've found + + align:start position:0% +of the best thing that i've found + + + align:start position:0% +of the best thing that i've found +and so in n log n time i can definitely + + align:start position:0% +and so in n log n time i can definitely + + + align:start position:0% +and so in n log n time i can definitely +solve this but i'd like to get + + align:start position:0% +solve this but i'd like to get + + + align:start position:0% +solve this but i'd like to get +linear time okay good question + + align:start position:0% + + + + align:start position:0% + +i'm not looking for s i i'm going to + + align:start position:0% +i'm not looking for s i i'm going to + + + align:start position:0% +i'm not looking for s i i'm going to +compute h minus s i + + align:start position:0% +compute h minus s i + + + align:start position:0% +compute h minus s i +so so this is maybe i shouldn't even + + align:start position:0% +so so this is maybe i shouldn't even + + + align:start position:0% +so so this is maybe i shouldn't even +write this down + + align:start position:0% + + + + align:start position:0% + +right so in particular if um + + align:start position:0% +right so in particular if um + + + align:start position:0% +right so in particular if um +if there are two items that sum to h i + + align:start position:0% +if there are two items that sum to h i + + + align:start position:0% +if there are two items that sum to h i +want to find it + + align:start position:0% +want to find it + + + align:start position:0% +want to find it +so uh so let's start with that so i'm + + align:start position:0% +so uh so let's start with that so i'm + + + align:start position:0% +so uh so let's start with that so i'm +binary searching for + + align:start position:0% +binary searching for + + + align:start position:0% +binary searching for +h minus s i in s so i could certainly do + + align:start position:0% +h minus s i in s so i could certainly do + + + align:start position:0% +h minus s i in s so i could certainly do +that + + align:start position:0% +that + + + align:start position:0% +that +and um if i if i find it great i found a + + align:start position:0% +and um if i if i find it great i found a + + + align:start position:0% +and um if i if i find it great i found a +pair that sums to exactly h if i don't + + align:start position:0% +pair that sums to exactly h if i don't + + + align:start position:0% +pair that sums to exactly h if i don't +find it + + align:start position:0% +find it + + + align:start position:0% +find it +binary search tells me not only that + + align:start position:0% +binary search tells me not only that + + + align:start position:0% +binary search tells me not only that +it's not there but it tells me what the + + align:start position:0% +it's not there but it tells me what the + + + align:start position:0% +it's not there but it tells me what the +previous + + align:start position:0% +previous + + + align:start position:0% +previous +and next value are so even though h + + align:start position:0% +and next value are so even though h + + + align:start position:0% +and next value are so even though h +minus s i isn't there i can get what the + + align:start position:0% +minus s i isn't there i can get what the + + + align:start position:0% +minus s i isn't there i can get what the +large + + align:start position:0% +large + + + align:start position:0% +large +the next largest thing and the next + + align:start position:0% +the next largest thing and the next + + + align:start position:0% +the next largest thing and the next +smallest thing what i want is the next + + align:start position:0% +smallest thing what i want is the next + + + align:start position:0% +smallest thing what i want is the next +smallest thing + + align:start position:0% +smallest thing + + + align:start position:0% +smallest thing +and that will be the largest sum i can + + align:start position:0% +and that will be the largest sum i can + + + align:start position:0% +and that will be the largest sum i can +get using s + + align:start position:0% +get using s + + + align:start position:0% +get using s +i and so then that's one candidate + + align:start position:0% +i and so then that's one candidate + + + align:start position:0% +i and so then that's one candidate +for a sum let's equal to h i want to + + align:start position:0% +for a sum let's equal to h i want to + + + align:start position:0% +for a sum let's equal to h i want to +find the largest one so i do a for loop + + align:start position:0% +find the largest one so i do a for loop + + + align:start position:0% +find the largest one so i do a for loop +i always keep track i take a list of all + + align:start position:0% +i always keep track i take a list of all + + + align:start position:0% +i always keep track i take a list of all +the candidates i got each time i do a + + align:start position:0% +the candidates i got each time i do a + + + align:start position:0% +the candidates i got each time i do a +four + + align:start position:0% +four + + + align:start position:0% +four +iteration of this loop i get one + + align:start position:0% +iteration of this loop i get one + + + align:start position:0% +iteration of this loop i get one +candidate then i take the largest one + + align:start position:0% +candidate then i take the largest one + + + align:start position:0% +candidate then i take the largest one +okay so return largest candidate + + align:start position:0% +okay so return largest candidate + + + align:start position:0% +okay so return largest candidate +so this gives me a candidate + + align:start position:0% +so this gives me a candidate + + + align:start position:0% +so this gives me a candidate +which is uh the previous item this is + + align:start position:0% +which is uh the previous item this is + + + align:start position:0% +which is uh the previous item this is +what we called + + align:start position:0% +what we called + + + align:start position:0% +what we called +find previous or find prev probably in + + align:start position:0% +find previous or find prev probably in + + + align:start position:0% +find previous or find prev probably in +our set interface + + align:start position:0% +our set interface + + + align:start position:0% +our set interface +and if you have a sorted set you can do + + align:start position:0% +and if you have a sorted set you can do + + + align:start position:0% +and if you have a sorted set you can do +that in log n time so this is an n log n + + align:start position:0% +that in log n time so this is an n log n + + + align:start position:0% +that in log n time so this is an n log n +solution + + align:start position:0% + + + + align:start position:0% + +i want because we do n iterations for + + align:start position:0% +i want because we do n iterations for + + + align:start position:0% +i want because we do n iterations for +the loop each binary search takes log n + + align:start position:0% +the loop each binary search takes log n + + + align:start position:0% +the loop each binary search takes log n +i want to get linear this + + align:start position:0% +i want to get linear this + + + align:start position:0% +i want to get linear this +is not obvious + + align:start position:0% + + + + align:start position:0% + +the best intuition i can think of for + + align:start position:0% +the best intuition i can think of for + + + align:start position:0% +the best intuition i can think of for +this next idea is + + align:start position:0% +this next idea is + + + align:start position:0% +this next idea is +well i start with a very small + + align:start position:0% +well i start with a very small + + + align:start position:0% +well i start with a very small +smallest item in s and i want to sum up + + align:start position:0% +smallest item in s and i want to sum up + + + align:start position:0% +smallest item in s and i want to sum up +to something that's kind of + + align:start position:0% +to something that's kind of + + + align:start position:0% +to something that's kind of +big i threw away all the items bigger + + align:start position:0% +big i threw away all the items bigger + + + align:start position:0% +big i threw away all the items bigger +than h + + align:start position:0% +than h + + + align:start position:0% +than h +if i start if s zero is like tiny like + + align:start position:0% +if i start if s zero is like tiny like + + + align:start position:0% +if i start if s zero is like tiny like +close to zero + + align:start position:0% +close to zero + + + align:start position:0% +close to zero +because it's the smallest one then maybe + + align:start position:0% +because it's the smallest one then maybe + + + align:start position:0% +because it's the smallest one then maybe +i should look at the + + align:start position:0% +i should look at the + + + align:start position:0% +i should look at the +end of the array because i want to + + align:start position:0% +end of the array because i want to + + + align:start position:0% +end of the array because i want to +compare or i want to add the smallest + + align:start position:0% +compare or i want to add the smallest + + + align:start position:0% +compare or i want to add the smallest +thing probably with the biggest thing + + align:start position:0% +thing probably with the biggest thing + + + align:start position:0% +thing probably with the biggest thing +that's as close as i can imagine uh + + align:start position:0% +that's as close as i can imagine uh + + + align:start position:0% +that's as close as i can imagine uh +so then + + align:start position:0% +so then + + + align:start position:0% +so then +so here's my sorted s this is the + + align:start position:0% +so here's my sorted s this is the + + + align:start position:0% +so here's my sorted s this is the +smallest item biggest item + + align:start position:0% +smallest item biggest item + + + align:start position:0% +smallest item biggest item +so i'm going to loop over these items + + align:start position:0% +so i'm going to loop over these items + + + align:start position:0% +so i'm going to loop over these items +one by one + + align:start position:0% +one by one + + + align:start position:0% +one by one +so let's start by comparing the first + + align:start position:0% +so let's start by comparing the first + + + align:start position:0% +so let's start by comparing the first +one with the last one + + align:start position:0% +one with the last one + + + align:start position:0% +one with the last one +the two-finger algorithm okay + + align:start position:0% + + + + align:start position:0% + +this is the big idea you're doing it all + + align:start position:0% +this is the big idea you're doing it all + + + align:start position:0% +this is the big idea you're doing it all +the time in this class it's super useful + + align:start position:0% +the time in this class it's super useful + + + align:start position:0% +the time in this class it's super useful +we saw it in merge sort for example and + + align:start position:0% +we saw it in merge sort for example and + + + align:start position:0% +we saw it in merge sort for example and +merging two lists + + align:start position:0% +merging two lists + + + align:start position:0% +merging two lists +we have fingers and two lists that + + align:start position:0% +we have fingers and two lists that + + + align:start position:0% +we have fingers and two lists that +advance and because they only advance + + align:start position:0% +advance and because they only advance + + + align:start position:0% +advance and because they only advance +it takes linear total time so we're + + align:start position:0% +it takes linear total time so we're + + + align:start position:0% +it takes linear total time so we're +going to do this kind of folded and + + align:start position:0% +going to do this kind of folded and + + + align:start position:0% +going to do this kind of folded and +backwards here we're going to start here + + align:start position:0% +backwards here we're going to start here + + + align:start position:0% +backwards here we're going to start here +this seems like a good candidate to + + align:start position:0% +this seems like a good candidate to + + + align:start position:0% +this seems like a good candidate to +start with now what else could this add + + align:start position:0% +start with now what else could this add + + + align:start position:0% +start with now what else could this add +with well maybe smaller items and + + align:start position:0% +with well maybe smaller items and + + + align:start position:0% +with well maybe smaller items and +maybe i have to go all the way through + + align:start position:0% +maybe i have to go all the way through + + + align:start position:0% +maybe i have to go all the way through +here and then i've got to advance my + + align:start position:0% +here and then i've got to advance my + + + align:start position:0% +here and then i've got to advance my +left finger + + align:start position:0% +left finger + + + align:start position:0% +left finger +yeah okay so uh here's the idea + + align:start position:0% +yeah okay so uh here's the idea + + + align:start position:0% +yeah okay so uh here's the idea +so um let's look at + + align:start position:0% +so um let's look at + + + align:start position:0% +so um let's look at +so i'm going to call this finger i this + + align:start position:0% +so i'm going to call this finger i this + + + align:start position:0% +so i'm going to call this finger i this +finger j + + align:start position:0% +finger j + + + align:start position:0% +finger j +so we want to sum two things so i guess + + align:start position:0% +so we want to sum two things so i guess + + + align:start position:0% +so we want to sum two things so i guess +another inspiration here is + + align:start position:0% +another inspiration here is + + + align:start position:0% +another inspiration here is +we want to add two things up and we have + + align:start position:0% +we want to add two things up and we have + + + align:start position:0% +we want to add two things up and we have +one algorithm that has the word two in + + align:start position:0% +one algorithm that has the word two in + + + align:start position:0% +one algorithm that has the word two in +it and it's the two finger algorithm + + align:start position:0% +it and it's the two finger algorithm + + + align:start position:0% +it and it's the two finger algorithm +so let's try that um so we're gonna + + align:start position:0% +so let's try that um so we're gonna + + + align:start position:0% +so let's try that um so we're gonna +start with i equals zero and j equals n + + align:start position:0% +start with i equals zero and j equals n + + + align:start position:0% +start with i equals zero and j equals n +minus one + + align:start position:0% +minus one + + + align:start position:0% +minus one +we're gonna look at s i plus s j + + align:start position:0% +we're gonna look at s i plus s j + + + align:start position:0% +we're gonna look at s i plus s j +and see how good it is it how close to + + align:start position:0% +and see how good it is it how close to + + + align:start position:0% +and see how good it is it how close to +summing to h is it + + align:start position:0% +summing to h is it + + + align:start position:0% +summing to h is it +well in particular it's either less than + + align:start position:0% +well in particular it's either less than + + + align:start position:0% +well in particular it's either less than +or equal to h + + align:start position:0% +or equal to h + + + align:start position:0% +or equal to h +or bigger than h + + align:start position:0% + + + + align:start position:0% + +if it's bigger than h so this sum is too + + align:start position:0% +if it's bigger than h so this sum is too + + + align:start position:0% +if it's bigger than h so this sum is too +big + + align:start position:0% +big + + + align:start position:0% +big +i can't even use it as a candidate well + + align:start position:0% +i can't even use it as a candidate well + + + align:start position:0% +i can't even use it as a candidate well +that means + + align:start position:0% +that means + + + align:start position:0% +that means +i really don't need this guy right it's + + align:start position:0% +i really don't need this guy right it's + + + align:start position:0% +i really don't need this guy right it's +too big overall this is i'm adding the + + align:start position:0% +too big overall this is i'm adding the + + + align:start position:0% +too big overall this is i'm adding the +smallest item + + align:start position:0% +smallest item + + + align:start position:0% +smallest item +to this item and it's too big well then + + align:start position:0% +to this item and it's too big well then + + + align:start position:0% +to this item and it's too big well then +i should go to the left i should move my + + align:start position:0% +i should go to the left i should move my + + + align:start position:0% +i should go to the left i should move my +right finger to the left + + align:start position:0% +right finger to the left + + + align:start position:0% +right finger to the left +so in this case uh we decrement j + + align:start position:0% +so in this case uh we decrement j + + + align:start position:0% +so in this case uh we decrement j +move the right finger to the left so i'm + + align:start position:0% +move the right finger to the left so i'm + + + align:start position:0% +move the right finger to the left so i'm +guessing in this case i'm going to + + align:start position:0% +guessing in this case i'm going to + + + align:start position:0% +guessing in this case i'm going to +increment i + + align:start position:0% + + + + align:start position:0% + +why if i add these two items up + + align:start position:0% +why if i add these two items up + + + align:start position:0% +why if i add these two items up +and this is too small smaller than h + + align:start position:0% +and this is too small smaller than h + + + align:start position:0% +and this is too small smaller than h +then this item was + + align:start position:0% +then this item was + + + align:start position:0% +then this item was +probably too small it might actually + + align:start position:0% +probably too small it might actually + + + align:start position:0% +probably too small it might actually +it's an okay solution it's less or equal + + align:start position:0% +it's an okay solution it's less or equal + + + align:start position:0% +it's an okay solution it's less or equal +to h so i should keep it as a candidate + + align:start position:0% +to h so i should keep it as a candidate + + + align:start position:0% +to h so i should keep it as a candidate +um let's say add + + align:start position:0% +um let's say add + + + align:start position:0% +um let's say add +candidate so i'm just going to keep a + + align:start position:0% +candidate so i'm just going to keep a + + + align:start position:0% +candidate so i'm just going to keep a +list of candidates + + align:start position:0% +list of candidates + + + align:start position:0% +list of candidates +that i see so this is a possible + + align:start position:0% +that i see so this is a possible + + + align:start position:0% +that i see so this is a possible +solution it might not be the best one + + align:start position:0% +solution it might not be the best one + + + align:start position:0% +solution it might not be the best one +but it's one to add to my list + + align:start position:0% +but it's one to add to my list + + + align:start position:0% +but it's one to add to my list +and then i'm going to increase i and now + + align:start position:0% +and then i'm going to increase i and now + + + align:start position:0% +and then i'm going to increase i and now +work with on this sub array + + align:start position:0% +work with on this sub array + + + align:start position:0% +work with on this sub array +because that will be a little bit bigger + + align:start position:0% +because that will be a little bit bigger + + + align:start position:0% +because that will be a little bit bigger +i can't go this way to make it bigger + + align:start position:0% +i can't go this way to make it bigger + + + align:start position:0% +i can't go this way to make it bigger +because i'm at the last item + + align:start position:0% +because i'm at the last item + + + align:start position:0% +because i'm at the last item +and it's not obvious that this works i + + align:start position:0% +and it's not obvious that this works i + + + align:start position:0% +and it's not obvious that this works i +think there's a nice invariant + + align:start position:0% +think there's a nice invariant + + + align:start position:0% +think there's a nice invariant +that will help + + align:start position:0% + + + + align:start position:0% + +somewhere wherever i put my piece of + + align:start position:0% +somewhere wherever i put my piece of + + + align:start position:0% +somewhere wherever i put my piece of +paper + + align:start position:0% + + + + align:start position:0% + +here's an invariant + + align:start position:0% + + + + align:start position:0% + +oh yes + + align:start position:0% + + + + align:start position:0% + +it's really clear this is the right + + align:start position:0% +it's really clear this is the right + + + align:start position:0% +it's really clear this is the right +thing to do in the first step and the + + align:start position:0% +thing to do in the first step and the + + + align:start position:0% +thing to do in the first step and the +tricky part is to argue that it works in + + align:start position:0% +tricky part is to argue that it works in + + + align:start position:0% +tricky part is to argue that it works in +all steps + + align:start position:0% +all steps + + + align:start position:0% +all steps +because when i really have the smallest + + align:start position:0% +because when i really have the smallest + + + align:start position:0% +because when i really have the smallest +item and the smaller and the largest + + align:start position:0% +item and the smaller and the largest + + + align:start position:0% +item and the smaller and the largest +item it's clear that i should advance + + align:start position:0% +item it's clear that i should advance + + + align:start position:0% +item it's clear that i should advance +one or the other + + align:start position:0% +one or the other + + + align:start position:0% +one or the other +i'm too small or too big but the way to + + align:start position:0% +i'm too small or too big but the way to + + + align:start position:0% +i'm too small or too big but the way to +prove it in general by induction + + align:start position:0% +prove it in general by induction + + + align:start position:0% +prove it in general by induction +is to show this invariant that so it in + + align:start position:0% +is to show this invariant that so it in + + + align:start position:0% +is to show this invariant that so it in +at some point through this execution i + + align:start position:0% +at some point through this execution i + + + align:start position:0% +at some point through this execution i +and j + + align:start position:0% +and j + + + align:start position:0% +and j +are somewhere and i want to say that if + + align:start position:0% +are somewhere and i want to say that if + + + align:start position:0% +are somewhere and i want to say that if +i take any j from the right + + align:start position:0% +i take any j from the right + + + align:start position:0% +i take any j from the right +any j prime to the right of j and any i + + align:start position:0% +any j prime to the right of j and any i + + + align:start position:0% +any j prime to the right of j and any i +prime to the left of i + + align:start position:0% +prime to the left of i + + + align:start position:0% +prime to the left of i +unstrictly then all of those pairs all + + align:start position:0% +unstrictly then all of those pairs all + + + align:start position:0% +unstrictly then all of those pairs all +those pairwise sums + + align:start position:0% +those pairwise sums + + + align:start position:0% +those pairwise sums +are either too big and that's when we + + align:start position:0% +are either too big and that's when we + + + align:start position:0% +are either too big and that's when we +decrease j + + align:start position:0% +decrease j + + + align:start position:0% +decrease j +or they're less than or equal to the + + align:start position:0% +or they're less than or equal to the + + + align:start position:0% +or they're less than or equal to the +largest candidate that we've seen so far + + align:start position:0% +largest candidate that we've seen so far + + + align:start position:0% +largest candidate that we've seen so far +that's because we add these candidates + + align:start position:0% +that's because we add these candidates + + + align:start position:0% +that's because we add these candidates +in there so + + align:start position:0% +in there so + + + align:start position:0% +in there so +this that invariant will hold by + + align:start position:0% +this that invariant will hold by + + + align:start position:0% +this that invariant will hold by +induction because whenever there's a + + align:start position:0% +induction because whenever there's a + + + align:start position:0% +induction because whenever there's a +possible thing that's + + align:start position:0% +possible thing that's + + + align:start position:0% +possible thing that's +good i add it to my candidate list and + + align:start position:0% +good i add it to my candidate list and + + + align:start position:0% +good i add it to my candidate list and +then at the end of the algorithm i just + + align:start position:0% +then at the end of the algorithm i just + + + align:start position:0% +then at the end of the algorithm i just +loop through my candidate list compute + + align:start position:0% +loop through my candidate list compute + + + align:start position:0% +loop through my candidate list compute +the max return that pair + + align:start position:0% + + + + align:start position:0% + +okay so that is two-finger algorithm + + align:start position:0% +okay so that is two-finger algorithm + + + align:start position:0% +okay so that is two-finger algorithm +which solves the non-exact + + align:start position:0% +which solves the non-exact + + + align:start position:0% +which solves the non-exact +problem in linear worst case time yeah + + align:start position:0% +problem in linear worst case time yeah + + + align:start position:0% +problem in linear worst case time yeah +oh i cannot right so what are the + + align:start position:0% +oh i cannot right so what are the + + + align:start position:0% +oh i cannot right so what are the +termination conditions when i + + align:start position:0% +termination conditions when i + + + align:start position:0% +termination conditions when i +equals j that's probably when you want + + align:start position:0% +equals j that's probably when you want + + + align:start position:0% +equals j that's probably when you want +to stop it depends you could say + + align:start position:0% +to stop it depends you could say + + + align:start position:0% +to stop it depends you could say +if i is greater than j stop + + align:start position:0% +if i is greater than j stop + + + align:start position:0% +if i is greater than j stop +uh return max candidate uh it's + + align:start position:0% +uh return max candidate uh it's + + + align:start position:0% +uh return max candidate uh it's +there are two ways to interpret this + + align:start position:0% +there are two ways to interpret this + + + align:start position:0% +there are two ways to interpret this +problem one is that the two values you + + align:start position:0% +problem one is that the two values you + + + align:start position:0% +problem one is that the two values you +choose in + + align:start position:0% +choose in + + + align:start position:0% +choose in +s need to be different values or you + + align:start position:0% +s need to be different values or you + + + align:start position:0% +s need to be different values or you +allow them to be the same value like + + align:start position:0% +allow them to be the same value like + + + align:start position:0% +allow them to be the same value like +they can both be h over two + + align:start position:0% +they can both be h over two + + + align:start position:0% +they can both be h over two +and either way is easy to solve if you + + align:start position:0% +and either way is easy to solve if you + + + align:start position:0% +and either way is easy to solve if you +if you want to allow + + align:start position:0% +if you want to allow + + + align:start position:0% +if you want to allow +s over 2 then i would put greater than + + align:start position:0% +s over 2 then i would put greater than + + + align:start position:0% +s over 2 then i would put greater than +here if you don't want to allow + + align:start position:0% +here if you don't want to allow + + + align:start position:0% +here if you don't want to allow +h over 2 then i have a greater than or + + align:start position:0% +h over 2 then i have a greater than or + + + align:start position:0% +h over 2 then i have a greater than or +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +either way both both of these problems + + align:start position:0% +either way both both of these problems + + + align:start position:0% +either way both both of these problems +you can solve both ways or both + + align:start position:0% +you can solve both ways or both + + + align:start position:0% +you can solve both ways or both +algorithms can handle both situations + + align:start position:0% +algorithms can handle both situations + + + align:start position:0% +algorithms can handle both situations +okay one more problem + + align:start position:0% + + + + align:start position:0% + +all right yeah a lot of time + + align:start position:0% +all right yeah a lot of time + + + align:start position:0% +all right yeah a lot of time +but i'm getting faster and faster so of + + align:start position:0% +but i'm getting faster and faster so of + + + align:start position:0% +but i'm getting faster and faster so of +course on the hardest problem i can do + + align:start position:0% +course on the hardest problem i can do + + + align:start position:0% +course on the hardest problem i can do +it the fastest + + align:start position:0% +it the fastest + + + align:start position:0% +it the fastest +all right so jet so meh + + align:start position:0% +all right so jet so meh + + + align:start position:0% +all right so jet so meh +jah this is a reference to jeff ma + + align:start position:0% +jah this is a reference to jeff ma + + + align:start position:0% +jah this is a reference to jeff ma +of the mit blackjack team who i got to + + align:start position:0% +of the mit blackjack team who i got to + + + align:start position:0% +of the mit blackjack team who i got to +see speak here at lsc + + align:start position:0% +see speak here at lsc + + + align:start position:0% +see speak here at lsc +a bunch of years ago but he's featured + + align:start position:0% +a bunch of years ago but he's featured + + + align:start position:0% +a bunch of years ago but he's featured +in the movie 21 and so on + + align:start position:0% +in the movie 21 and so on + + + align:start position:0% +in the movie 21 and so on +fictionalized um + + align:start position:0% +fictionalized um + + + align:start position:0% +fictionalized um +so as playing this game it's great great + + align:start position:0% +so as playing this game it's great great + + + align:start position:0% +so as playing this game it's great great +great setup you should definitely read + + align:start position:0% +great setup you should definitely read + + + align:start position:0% +great setup you should definitely read +this problem + + align:start position:0% +this problem + + + align:start position:0% +this problem +uh po k er + + align:start position:0% +uh po k er + + + align:start position:0% +uh po k er +and he has a deck of cards where each + + align:start position:0% +and he has a deck of cards where each + + + align:start position:0% +and he has a deck of cards where each +card has a letter of the alphabet on i + + align:start position:0% +card has a letter of the alphabet on i + + + align:start position:0% +card has a letter of the alphabet on i +get this + + align:start position:0% +get this + + + align:start position:0% +get this +the right way up so i of course have + + align:start position:0% +the right way up so i of course have + + + align:start position:0% +the right way up so i of course have +such a deck + + align:start position:0% +such a deck + + + align:start position:0% +such a deck +doesn't everyone you can buy these i + + align:start position:0% +doesn't everyone you can buy these i + + + align:start position:0% +doesn't everyone you can buy these i +have several actually + + align:start position:0% +have several actually + + + align:start position:0% +have several actually +um and so we can do a quick magic trick + + align:start position:0% +um and so we can do a quick magic trick + + + align:start position:0% +um and so we can do a quick magic trick +like uh pick a card any card here pick a + + align:start position:0% +like uh pick a card any card here pick a + + + align:start position:0% +like uh pick a card any card here pick a +card + + align:start position:0% + + + + align:start position:0% + +okay oh good choice i can't force so it + + align:start position:0% +okay oh good choice i can't force so it + + + align:start position:0% +okay oh good choice i can't force so it +doesn't really matter + + align:start position:0% +doesn't really matter + + + align:start position:0% +doesn't really matter +okay and uh so this is your card + + align:start position:0% +okay and uh so this is your card + + + align:start position:0% +okay and uh so this is your card +right and your card is an s right + + align:start position:0% +right and your card is an s right + + + align:start position:0% +right and your card is an s right +okay good okay no not all the cards are + + align:start position:0% +okay good okay no not all the cards are + + + align:start position:0% +okay good okay no not all the cards are +s's + + align:start position:0% + + + + align:start position:0% + +but he has mirrors in his glasses no i + + align:start position:0% +but he has mirrors in his glasses no i + + + align:start position:0% +but he has mirrors in his glasses no i +can reveal later how that's done + + align:start position:0% +can reveal later how that's done + + + align:start position:0% +can reveal later how that's done +um okay so a deck of cards each card has + + align:start position:0% +um okay so a deck of cards each card has + + + align:start position:0% +um okay so a deck of cards each card has +26 possible letters on it and + + align:start position:0% +26 possible letters on it and + + + align:start position:0% +26 possible letters on it and +uh there's this weird dealing process + + align:start position:0% +uh there's this weird dealing process + + + align:start position:0% +uh there's this weird dealing process +even just defining this problem it's + + align:start position:0% +even just defining this problem it's + + + align:start position:0% +even just defining this problem it's +going to take a little while oh here's + + align:start position:0% +going to take a little while oh here's + + + align:start position:0% +going to take a little while oh here's +my piece of paper + + align:start position:0% + + + + align:start position:0% + +so we have this dealing process here's + + align:start position:0% +so we have this dealing process here's + + + align:start position:0% +so we have this dealing process here's +an example + + align:start position:0% +an example + + + align:start position:0% +an example +it's in the problem a b c sorry + + align:start position:0% +it's in the problem a b c sorry + + + align:start position:0% +it's in the problem a b c sorry +d b c so that you know the order of the + + align:start position:0% +d b c so that you know the order of the + + + align:start position:0% +d b c so that you know the order of the +cards this is the top card this is the + + align:start position:0% +cards this is the top card this is the + + + align:start position:0% +cards this is the top card this is the +bottom card + + align:start position:0% +bottom card + + + align:start position:0% +bottom card +and now randomly you do a cut + + align:start position:0% +and now randomly you do a cut + + + align:start position:0% +and now randomly you do a cut +cut is this right so i take some chunk + + align:start position:0% +cut is this right so i take some chunk + + + align:start position:0% +cut is this right so i take some chunk +off the top + + align:start position:0% +off the top + + + align:start position:0% +off the top +move it to the bottom once randomly + + align:start position:0% +move it to the bottom once randomly + + + align:start position:0% +move it to the bottom once randomly +so for example i could take this cut + + align:start position:0% +so for example i could take this cut + + + align:start position:0% +so for example i could take this cut +and then what i would get is cdbc + + align:start position:0% +and then what i would get is cdbc + + + align:start position:0% +and then what i would get is cdbc +for for this part + + align:start position:0% +for for this part + + + align:start position:0% +for for this part +that's copied here and a b + + align:start position:0% +that's copied here and a b + + + align:start position:0% +that's copied here and a b +that's the so this is so the first thing + + align:start position:0% +that's the so this is so the first thing + + + align:start position:0% +that's the so this is so the first thing +we do is cut + + align:start position:0% +we do is cut + + + align:start position:0% +we do is cut +at i this is position i + + align:start position:0% +at i this is position i + + + align:start position:0% +at i this is position i +this example i equals two + + align:start position:0% +this example i equals two + + + align:start position:0% +this example i equals two +okay then we deal the top + + align:start position:0% +okay then we deal the top + + + align:start position:0% +okay then we deal the top +k cards so uh let's say we deal + + align:start position:0% +k cards so uh let's say we deal + + + align:start position:0% +k cards so uh let's say we deal +the top four cards k equals four so this + + align:start position:0% +the top four cards k equals four so this + + + align:start position:0% +the top four cards k equals four so this +is uh + + align:start position:0% +is uh + + + align:start position:0% +is uh +dl k so we get cdbc + + align:start position:0% +dl k so we get cdbc + + + align:start position:0% +dl k so we get cdbc +in that order but the order doesn't + + align:start position:0% +in that order but the order doesn't + + + align:start position:0% +in that order but the order doesn't +matter because the last operation we do + + align:start position:0% +matter because the last operation we do + + + align:start position:0% +matter because the last operation we do +in the problem is sort them + + align:start position:0% +in the problem is sort them + + + align:start position:0% +in the problem is sort them +which is b c c d + + align:start position:0% +which is b c c d + + + align:start position:0% +which is b c c d +okay like you do when you get a hand of + + align:start position:0% +okay like you do when you get a hand of + + + align:start position:0% +okay like you do when you get a hand of +cards you tend to sort them + + align:start position:0% +cards you tend to sort them + + + align:start position:0% +cards you tend to sort them +okay so this is a process given a deck + + align:start position:0% +okay so this is a process given a deck + + + align:start position:0% +okay so this is a process given a deck +so the deck here is + + align:start position:0% +so the deck here is + + + align:start position:0% +so the deck here is +fixed uh we call this + + align:start position:0% +fixed uh we call this + + + align:start position:0% +fixed uh we call this +process i think p of d comma i + + align:start position:0% +process i think p of d comma i + + + align:start position:0% +process i think p of d comma i +comma k we're told what d is we're told + + align:start position:0% +comma k we're told what d is we're told + + + align:start position:0% +comma k we're told what d is we're told +what k + + align:start position:0% +what k + + + align:start position:0% +what k +is i is chosen randomly + + align:start position:0% +is i is chosen randomly + + + align:start position:0% +is i is chosen randomly +and we'd like to know what happens with + + align:start position:0% +and we'd like to know what happens with + + + align:start position:0% +and we'd like to know what happens with +different eyes + + align:start position:0% + + + + align:start position:0% + +so so if you start this problem enough + + align:start position:0% +so so if you start this problem enough + + + align:start position:0% +so so if you start this problem enough +it begins to simplify this is a + + align:start position:0% +it begins to simplify this is a + + + align:start position:0% +it begins to simplify this is a +complicated setup + + align:start position:0% +complicated setup + + + align:start position:0% +complicated setup +but what's really going on is we're + + align:start position:0% +but what's really going on is we're + + + align:start position:0% +but what's really going on is we're +starting at position i and we're taking + + align:start position:0% +starting at position i and we're taking + + + align:start position:0% +starting at position i and we're taking +the next k cards from there + + align:start position:0% +the next k cards from there + + + align:start position:0% +the next k cards from there +cyclically so here we just took those + + align:start position:0% +cyclically so here we just took those + + + align:start position:0% +cyclically so here we just took those +four if i equaled three would deal d + + align:start position:0% +four if i equaled three would deal d + + + align:start position:0% +four if i equaled three would deal d +then b + + align:start position:0% +then b + + + align:start position:0% +then b +then c then a but then we sort them + + align:start position:0% +then c then a but then we sort them + + + align:start position:0% +then c then a but then we sort them +okay so we're getting different + + align:start position:0% +okay so we're getting different + + + align:start position:0% +okay so we're getting different +substrings of length k cyclically + + align:start position:0% +substrings of length k cyclically + + + align:start position:0% +substrings of length k cyclically +but uh then we're sorting those letters + + align:start position:0% +but uh then we're sorting those letters + + + align:start position:0% +but uh then we're sorting those letters +sorting is really crucial for this + + align:start position:0% +sorting is really crucial for this + + + align:start position:0% +sorting is really crucial for this +problem to at all be feasible + + align:start position:0% +problem to at all be feasible + + + align:start position:0% +problem to at all be feasible +it took me a while even to see how to + + align:start position:0% +it took me a while even to see how to + + + align:start position:0% +it took me a while even to see how to +solve this problem but the key is + + align:start position:0% +solve this problem but the key is + + + align:start position:0% +solve this problem but the key is +sorting + + align:start position:0% +sorting + + + align:start position:0% +sorting +that they get sorted because + + align:start position:0% +that they get sorted because + + + align:start position:0% +that they get sorted because +that means because we sort it doesn't + + align:start position:0% +that means because we sort it doesn't + + + align:start position:0% +that means because we sort it doesn't +matter whether you have a + + align:start position:0% +matter whether you have a + + + align:start position:0% +matter whether you have a +a b a + + align:start position:0% + + + + align:start position:0% + +these are all the same if you take these + + align:start position:0% +these are all the same if you take these + + + align:start position:0% +these are all the same if you take these +cards dealt + + align:start position:0% +cards dealt + + + align:start position:0% +cards dealt +you sort them to the same thing which is + + align:start position:0% +you sort them to the same thing which is + + + align:start position:0% +you sort them to the same thing which is +the one i didn't write + + align:start position:0% +the one i didn't write + + + align:start position:0% +the one i didn't write +a a b all these get sorted to the same + + align:start position:0% +a a b all these get sorted to the same + + + align:start position:0% +a a b all these get sorted to the same +thing + + align:start position:0% +thing + + + align:start position:0% +thing +so we lost some information when we sort + + align:start position:0% +so we lost some information when we sort + + + align:start position:0% +so we lost some information when we sort +lost the order + + align:start position:0% +lost the order + + + align:start position:0% +lost the order +the first question to get you thinking + + align:start position:0% +the first question to get you thinking + + + align:start position:0% +the first question to get you thinking +in this direction + + align:start position:0% +in this direction + + + align:start position:0% +in this direction +part a says build a data structure given + + align:start position:0% +part a says build a data structure given + + + align:start position:0% +part a says build a data structure given +d + + align:start position:0% +d + + + align:start position:0% +d +and k that lets you lets me know + + align:start position:0% +and k that lets you lets me know + + + align:start position:0% +and k that lets you lets me know +given two indices i and j do i + + align:start position:0% +given two indices i and j do i + + + align:start position:0% +given two indices i and j do i +end up with the exact same hand this + + align:start position:0% +end up with the exact same hand this + + + align:start position:0% +end up with the exact same hand this +thing is called a hand + + align:start position:0% + + + + align:start position:0% + +and it's exactly this pdik + + align:start position:0% +and it's exactly this pdik + + + align:start position:0% +and it's exactly this pdik +so i want to do p d i k and p d j + + align:start position:0% +so i want to do p d i k and p d j + + + align:start position:0% +so i want to do p d i k and p d j +k and i want to know j k and i want to + + align:start position:0% +k and i want to know j k and i want to + + + align:start position:0% +k and i want to know j k and i want to +know + + align:start position:0% +know + + + align:start position:0% +know +whether those two things are equal in + + align:start position:0% +whether those two things are equal in + + + align:start position:0% +whether those two things are equal in +constant time that's what this says + + align:start position:0% +constant time that's what this says + + + align:start position:0% +constant time that's what this says +constant time doesn't say worst case but + + align:start position:0% +constant time doesn't say worst case but + + + align:start position:0% +constant time doesn't say worst case but +worst case is possible + + align:start position:0% + + + + align:start position:0% + +uh and that sounds hard because i mean + + align:start position:0% +uh and that sounds hard because i mean + + + align:start position:0% +uh and that sounds hard because i mean +there's k symbols for one of them + + align:start position:0% +there's k symbols for one of them + + + align:start position:0% +there's k symbols for one of them +another k symbols for the other guy + + align:start position:0% +another k symbols for the other guy + + + align:start position:0% +another k symbols for the other guy +but we don't have to compare the symbols + + align:start position:0% +but we don't have to compare the symbols + + + align:start position:0% +but we don't have to compare the symbols +we just need to compare + + align:start position:0% +we just need to compare + + + align:start position:0% +we just need to compare +the sorting of those strings and this we + + align:start position:0% +the sorting of those strings and this we + + + align:start position:0% +the sorting of those strings and this we +can compress + + align:start position:0% +can compress + + + align:start position:0% +can compress +so this is a subtlety but what i really + + align:start position:0% +so this is a subtlety but what i really + + + align:start position:0% +so this is a subtlety but what i really +need to know is that there are three a's + + align:start position:0% +need to know is that there are three a's + + + align:start position:0% +need to know is that there are three a's +here + + align:start position:0% +here + + + align:start position:0% +here +and one b and zero c's + + align:start position:0% +and one b and zero c's + + + align:start position:0% +and one b and zero c's +and zero d's and zero e's and so on + + align:start position:0% +and zero d's and zero e's and so on + + + align:start position:0% +and zero d's and zero e's and so on +but uh because there's only 26 letters + + align:start position:0% +but uh because there's only 26 letters + + + align:start position:0% +but uh because there's only 26 letters +in this deck and indeed in this deck + + align:start position:0% +in this deck and indeed in this deck + + + align:start position:0% +in this deck and indeed in this deck +happens to have upper and lower case a + + align:start position:0% +happens to have upper and lower case a + + + align:start position:0% +happens to have upper and lower case a +through z but + + align:start position:0% +through z but + + + align:start position:0% +through z but +we might have n cards but they're only + + align:start position:0% +we might have n cards but they're only + + + align:start position:0% +we might have n cards but they're only +26 possible labels so in fact a lot of + + align:start position:0% +26 possible labels so in fact a lot of + + + align:start position:0% +26 possible labels so in fact a lot of +them are going to be equal if n is large + + align:start position:0% +them are going to be equal if n is large + + + align:start position:0% +them are going to be equal if n is large +so this is a good compression scheme + + align:start position:0% +so this is a good compression scheme + + + align:start position:0% +so this is a good compression scheme +because i to represent + + align:start position:0% +because i to represent + + + align:start position:0% +because i to represent +the things i get after sorting i just + + align:start position:0% +the things i get after sorting i just + + + align:start position:0% +the things i get after sorting i just +need to give you 26 numbers + + align:start position:0% +need to give you 26 numbers + + + align:start position:0% +need to give you 26 numbers +and for us 26 is small because 26 is a + + align:start position:0% +and for us 26 is small because 26 is a + + + align:start position:0% +and for us 26 is small because 26 is a +constant + + align:start position:0% +constant + + + align:start position:0% +constant +independent of the number of cards i + + align:start position:0% +independent of the number of cards i + + + align:start position:0% +independent of the number of cards i +just need to say how many a's are there + + align:start position:0% +just need to say how many a's are there + + + align:start position:0% +just need to say how many a's are there +could be anywhere between 0 and + + align:start position:0% +could be anywhere between 0 and + + + align:start position:0% +could be anywhere between 0 and +n how many b's are there between 0 and n + + align:start position:0% +n how many b's are there between 0 and n + + + align:start position:0% +n how many b's are there between 0 and n +how many c's are there between 0 and n + + align:start position:0% +how many c's are there between 0 and n + + + align:start position:0% +how many c's are there between 0 and n +so 26 numbers + + align:start position:0% +so 26 numbers + + + align:start position:0% +so 26 numbers +in the range 0 to n + + align:start position:0% + + + + align:start position:0% + +i like to think of this as a 26 digit + + align:start position:0% +i like to think of this as a 26 digit + + + align:start position:0% +i like to think of this as a 26 digit +number base n plus 1. + + align:start position:0% +number base n plus 1. + + + align:start position:0% +number base n plus 1. +we can map this into base n plus 1 + + align:start position:0% + + + + align:start position:0% + +and we get 26 digits + + align:start position:0% + + + + align:start position:0% + +in that base another way to say it is + + align:start position:0% +in that base another way to say it is + + + align:start position:0% +in that base another way to say it is +that the number of + + align:start position:0% +that the number of + + + align:start position:0% +that the number of +possible uh combinations here how many + + align:start position:0% +possible uh combinations here how many + + + align:start position:0% +possible uh combinations here how many +a's how many b's how many c's + + align:start position:0% +a's how many b's how many c's + + + align:start position:0% +a's how many b's how many c's +is um not even theta it is + + align:start position:0% +is um not even theta it is + + + align:start position:0% +is um not even theta it is +n plus one anything between zero and n + + align:start position:0% +n plus one anything between zero and n + + + align:start position:0% +n plus one anything between zero and n +uh to the power 26. + + align:start position:0% +uh to the power 26. + + + align:start position:0% +uh to the power 26. +this is a good polynomial + + align:start position:0% +this is a good polynomial + + + align:start position:0% +this is a good polynomial +so i can do stuff + + align:start position:0% +so i can do stuff + + + align:start position:0% +so i can do stuff +like radix sort + + align:start position:0% + + + + align:start position:0% + +cool so let me summarize a little bit + + align:start position:0% +cool so let me summarize a little bit + + + align:start position:0% +cool so let me summarize a little bit +how we solve part a + + align:start position:0% +how we solve part a + + + align:start position:0% +how we solve part a +so i want to build a data structure + + align:start position:0% +so i want to build a data structure + + + align:start position:0% +so i want to build a data structure +which is + + align:start position:0% +which is + + + align:start position:0% +which is +for each value i i know i'm going to end + + align:start position:0% +for each value i i know i'm going to end + + + align:start position:0% +for each value i i know i'm going to end +up serving these four + + align:start position:0% +up serving these four + + + align:start position:0% +up serving these four +cards or in general k cards so for those + + align:start position:0% +cards or in general k cards so for those + + + align:start position:0% +cards or in general k cards so for those +cards i would like to compute + + align:start position:0% +cards i would like to compute + + + align:start position:0% +cards i would like to compute +um how many a's how many b's how many + + align:start position:0% +um how many a's how many b's how many + + + align:start position:0% +um how many a's how many b's how many +c's are there and then just write down + + align:start position:0% +c's are there and then just write down + + + align:start position:0% +c's are there and then just write down +this number this is a number which i can + + align:start position:0% +this number this is a number which i can + + + align:start position:0% +this number this is a number which i can +write down in at most 26 words + + align:start position:0% +write down in at most 26 words + + + align:start position:0% +write down in at most 26 words +because we can represent numbers between + + align:start position:0% +because we can represent numbers between + + + align:start position:0% +because we can represent numbers between +0 and n in a single word + + align:start position:0% +0 and n in a single word + + + align:start position:0% +0 and n in a single word +that's the wb's at least login + + align:start position:0% +that's the wb's at least login + + + align:start position:0% +that's the wb's at least login +assumption uh + + align:start position:0% +assumption uh + + + align:start position:0% +assumption uh +so it's constant size in a constant + + align:start position:0% +so it's constant size in a constant + + + align:start position:0% +so it's constant size in a constant +number of numbers + + align:start position:0% +number of numbers + + + align:start position:0% +number of numbers +i can represent all i need to know about + + align:start position:0% +i can represent all i need to know about + + + align:start position:0% +i can represent all i need to know about +a thing of size + + align:start position:0% +a thing of size + + + align:start position:0% +a thing of size +of length k here because i don't need to + + align:start position:0% +of length k here because i don't need to + + + align:start position:0% +of length k here because i don't need to +know the individual which + + align:start position:0% +know the individual which + + + align:start position:0% +know the individual which +letter is where just need to know the + + align:start position:0% +letter is where just need to know the + + + align:start position:0% +letter is where just need to know the +sorted order so i just need to know this + + align:start position:0% +sorted order so i just need to know this + + + align:start position:0% +sorted order so i just need to know this +is called a frequency table + + align:start position:0% +is called a frequency table + + + align:start position:0% +is called a frequency table +how many a's how many b's and so if i + + align:start position:0% +how many a's how many b's and so if i + + + align:start position:0% +how many a's how many b's and so if i +can compute those + + align:start position:0% +can compute those + + + align:start position:0% +can compute those +then given that representation for + + align:start position:0% +then given that representation for + + + align:start position:0% +then given that representation for +starting at i + + align:start position:0% +starting at i + + + align:start position:0% +starting at i +and given that representation for + + align:start position:0% +and given that representation for + + + align:start position:0% +and given that representation for +starting it j say which would be these + + align:start position:0% +starting it j say which would be these + + + align:start position:0% +starting it j say which would be these +two and these two + + align:start position:0% +two and these two + + + align:start position:0% +two and these two +i can compare them by just comparing + + align:start position:0% +i can compare them by just comparing + + + align:start position:0% +i can compare them by just comparing +those 26 numbers + + align:start position:0% +those 26 numbers + + + align:start position:0% +those 26 numbers +they're all equal then they're the same + + align:start position:0% +they're all equal then they're the same + + + align:start position:0% +they're all equal then they're the same +string after sorting + + align:start position:0% +string after sorting + + + align:start position:0% +string after sorting +and if there's any difference then + + align:start position:0% +and if there's any difference then + + + align:start position:0% +and if there's any difference then +they're different so that's how i could + + align:start position:0% +they're different so that's how i could + + + align:start position:0% +they're different so that's how i could +do it in constant time + + align:start position:0% +do it in constant time + + + align:start position:0% +do it in constant time +if i can compute these representations + + align:start position:0% +if i can compute these representations + + + align:start position:0% +if i can compute these representations +and it's not hard to do that you + + align:start position:0% +and it's not hard to do that you + + + align:start position:0% +and it's not hard to do that you +it's called a sliding window technique + + align:start position:0% +it's called a sliding window technique + + + align:start position:0% +it's called a sliding window technique +where you compute it for the first + + align:start position:0% +where you compute it for the first + + + align:start position:0% +where you compute it for the first +k guys and then you remove this item and + + align:start position:0% +k guys and then you remove this item and + + + align:start position:0% +k guys and then you remove this item and +add this item + + align:start position:0% +add this item + + + align:start position:0% +add this item +into just by incrementing the counter + + align:start position:0% +into just by incrementing the counter + + + align:start position:0% +into just by incrementing the counter +for b decrementing the counter for a + + align:start position:0% +for b decrementing the counter for a + + + align:start position:0% +for b decrementing the counter for a +now i know this the representation for + + align:start position:0% +now i know this the representation for + + + align:start position:0% +now i know this the representation for +these guys + + align:start position:0% +these guys + + + align:start position:0% +these guys +make a copy of that which is a copy of + + align:start position:0% +make a copy of that which is a copy of + + + align:start position:0% +make a copy of that which is a copy of +those 26 numbers constant + + align:start position:0% +those 26 numbers constant + + + align:start position:0% +those 26 numbers constant +then i add on c remove b then i add on + + align:start position:0% +then i add on c remove b then i add on + + + align:start position:0% +then i add on c remove b then i add on +a remove c add on b + + align:start position:0% +a remove c add on b + + + align:start position:0% +a remove c add on b +remove d add on c remove b + + align:start position:0% +remove d add on c remove b + + + align:start position:0% +remove d add on c remove b +and add on d and remove c + + align:start position:0% +and add on d and remove c + + + align:start position:0% +and add on d and remove c +i got back to the beginning so now i + + align:start position:0% +i got back to the beginning so now i + + + align:start position:0% +i got back to the beginning so now i +have representation of those + + align:start position:0% +have representation of those + + + align:start position:0% +have representation of those +okay so i by sliding this window i'm + + align:start position:0% +okay so i by sliding this window i'm + + + align:start position:0% +okay so i by sliding this window i'm +only changing + + align:start position:0% +only changing + + + align:start position:0% +only changing +at the two ends i add one guy on i + + align:start position:0% +at the two ends i add one guy on i + + + align:start position:0% +at the two ends i add one guy on i +increment one of these counters + + align:start position:0% +increment one of these counters + + + align:start position:0% +increment one of these counters +i decrement one of these counters so in + + align:start position:0% +i decrement one of these counters so in + + + align:start position:0% +i decrement one of these counters so in +constant time + + align:start position:0% +constant time + + + align:start position:0% +constant time +given the representation of one of these + + align:start position:0% +given the representation of one of these + + + align:start position:0% +given the representation of one of these +substrings i can compute the + + align:start position:0% +substrings i can compute the + + + align:start position:0% +substrings i can compute the +representation + + align:start position:0% +representation + + + align:start position:0% +representation +of the next one that's how in linear + + align:start position:0% +of the next one that's how in linear + + + align:start position:0% +of the next one that's how in linear +time can build such a data structure + + align:start position:0% +time can build such a data structure + + + align:start position:0% +time can build such a data structure +that + + align:start position:0% +that + + + align:start position:0% +that +lets me tell whether any two hands are + + align:start position:0% +lets me tell whether any two hands are + + + align:start position:0% +lets me tell whether any two hands are +equal + + align:start position:0% +equal + + + align:start position:0% +equal +the next problem part b is given all + + align:start position:0% +the next problem part b is given all + + + align:start position:0% +the next problem part b is given all +these representations + + align:start position:0% +these representations + + + align:start position:0% +these representations +can you find which one is the most + + align:start position:0% +can you find which one is the most + + + align:start position:0% +can you find which one is the most +common because we're choosing i + + align:start position:0% +common because we're choosing i + + + align:start position:0% +common because we're choosing i +uniformly at random i want to know what + + align:start position:0% +uniformly at random i want to know what + + + align:start position:0% +uniformly at random i want to know what +the most likely + + align:start position:0% +the most likely + + + align:start position:0% +the most likely +hand that you get is and i think the + + align:start position:0% +hand that you get is and i think the + + + align:start position:0% +hand that you get is and i think the +easiest way to say this is you can do + + align:start position:0% +easiest way to say this is you can do + + + align:start position:0% +easiest way to say this is you can do +that by radix sorting + + align:start position:0% +that by radix sorting + + + align:start position:0% +that by radix sorting +you take all these representations they + + align:start position:0% +you take all these representations they + + + align:start position:0% +you take all these representations they +are nice numbers in the + + align:start position:0% +are nice numbers in the + + + align:start position:0% +are nice numbers in the +range 0 to n plus 1 to the 26th power + + align:start position:0% +range 0 to n plus 1 to the 26th power + + + align:start position:0% +range 0 to n plus 1 to the 26th power +so i can just run radix sort and sort + + align:start position:0% +so i can just run radix sort and sort + + + align:start position:0% +so i can just run radix sort and sort +them all and then do + + align:start position:0% +them all and then do + + + align:start position:0% +them all and then do +with a single scan through the array i + + align:start position:0% +with a single scan through the array i + + + align:start position:0% +with a single scan through the array i +can see which one is the most + + align:start position:0% +can see which one is the most + + + align:start position:0% +can see which one is the most +common or rather i can in single scan i + + align:start position:0% +common or rather i can in single scan i + + + align:start position:0% +common or rather i can in single scan i +can compute + + align:start position:0% +can compute + + + align:start position:0% +can compute +okay how many of the same things are at + + align:start position:0% +okay how many of the same things are at + + + align:start position:0% +okay how many of the same things are at +the front they're sorted then + + align:start position:0% +the front they're sorted then + + + align:start position:0% +the front they're sorted then +all the equal ones will be together so + + align:start position:0% +all the equal ones will be together so + + + align:start position:0% +all the equal ones will be together so +how many are there then how many + + align:start position:0% +how many are there then how many + + + align:start position:0% +how many are there then how many +equal ones next and how many forms + + align:start position:0% +equal ones next and how many forms + + + align:start position:0% +equal ones next and how many forms +before this next each time comparing + + align:start position:0% +before this next each time comparing + + + align:start position:0% +before this next each time comparing +each item to the previous one then i get + + align:start position:0% +each item to the previous one then i get + + + align:start position:0% +each item to the previous one then i get +frequency counts for all of these + + align:start position:0% +frequency counts for all of these + + + align:start position:0% +frequency counts for all of these +uh hands and then i do another scan to + + align:start position:0% +uh hands and then i do another scan to + + + align:start position:0% +uh hands and then i do another scan to +find the most common one + + align:start position:0% +find the most common one + + + align:start position:0% +find the most common one +and i can do another scan to find the + + align:start position:0% +and i can do another scan to find the + + + align:start position:0% +and i can do another scan to find the +lexically best one because that's + + align:start position:0% +lexically best one because that's + + + align:start position:0% +lexically best one because that's +lexically + + align:start position:0% +lexically + + + align:start position:0% +lexically +last one and that's how you solve + + align:start position:0% +last one and that's how you solve + + + align:start position:0% +last one and that's how you solve +problem five \ No newline at end of file diff --git a/g4lxRZ7T5_o.txt b/g4lxRZ7T5_o.txt new file mode 100644 index 0000000000000000000000000000000000000000..164596f7215668e49e126fff7110c5ddc09f42e3 --- /dev/null +++ b/g4lxRZ7T5_o.txt @@ -0,0 +1,8920 @@ +align:start position:0% + +but i want to pick up + + align:start position:0% +but i want to pick up + + + align:start position:0% +but i want to pick up +where we left off on monday and we were + + align:start position:0% +where we left off on monday and we were + + + align:start position:0% +where we left off on monday and we were +talking about the three + + align:start position:0% +talking about the three + + + align:start position:0% +talking about the three +brave lattices there are a couple more + + align:start position:0% +brave lattices there are a couple more + + + align:start position:0% +brave lattices there are a couple more +things that i want to say about them + + align:start position:0% +things that i want to say about them + + + align:start position:0% +things that i want to say about them +what we what we captured the key essence + + align:start position:0% +what we what we captured the key essence + + + align:start position:0% +what we what we captured the key essence +apart from there being these cubic + + align:start position:0% +apart from there being these cubic + + + align:start position:0% +apart from there being these cubic +crystals and and the different elements + + align:start position:0% +crystals and and the different elements + + + align:start position:0% +crystals and and the different elements +that + + align:start position:0% +that + + + align:start position:0% +that +that form them is this idea that you can + + align:start position:0% +that form them is this idea that you can + + + align:start position:0% +that form them is this idea that you can +go + + align:start position:0% +go + + + align:start position:0% +go +from the unit cell right + + align:start position:0% +from the unit cell right + + + align:start position:0% +from the unit cell right +you once you know the unit cell you + + align:start position:0% +you once you know the unit cell you + + + align:start position:0% +you once you know the unit cell you +could get the atom + + align:start position:0% +could get the atom + + + align:start position:0% +could get the atom +the atomic radius atomic radius right so + + align:start position:0% +the atomic radius atomic radius right so + + + align:start position:0% +the atomic radius atomic radius right so +that's kind of cool + + align:start position:0% +that's kind of cool + + + align:start position:0% +that's kind of cool +because you know information about + + align:start position:0% +because you know information about + + + align:start position:0% +because you know information about +things like for example + + align:start position:0% +things like for example + + + align:start position:0% +things like for example +uh packing right so then we had the + + align:start position:0% +uh packing right so then we had the + + + align:start position:0% +uh packing right so then we had the +packing fraction the atomic packing + + align:start position:0% +packing fraction the atomic packing + + + align:start position:0% +packing fraction the atomic packing +fraction + + align:start position:0% +fraction + + + align:start position:0% +fraction +calculated that right the maximum + + align:start position:0% +calculated that right the maximum + + + align:start position:0% +calculated that right the maximum +the max packing fraction right + + align:start position:0% +the max packing fraction right + + + align:start position:0% +the max packing fraction right +packing fraction + + align:start position:0% + + + + align:start position:0% + +uh we calculated things like the close + + align:start position:0% +uh we calculated things like the close + + + align:start position:0% +uh we calculated things like the close +pack direction + + align:start position:0% +pack direction + + + align:start position:0% +pack direction +okay but you can also go to things like + + align:start position:0% +okay but you can also go to things like + + + align:start position:0% +okay but you can also go to things like +the density once you know how to go back + + align:start position:0% +the density once you know how to go back + + + align:start position:0% +the density once you know how to go back +and forth + + align:start position:0% +and forth + + + align:start position:0% +and forth +right and and so for example if i had + + align:start position:0% +right and and so for example if i had + + + align:start position:0% +right and and so for example if i had +if i want the density of a material + + align:start position:0% +if i want the density of a material + + + align:start position:0% +if i want the density of a material +that's grams + + align:start position:0% +that's grams + + + align:start position:0% +that's grams +per centimeter cubed right that's the + + align:start position:0% +per centimeter cubed right that's the + + + align:start position:0% +per centimeter cubed right that's the +density + + align:start position:0% +density + + + align:start position:0% +density +right but you you could write the + + align:start position:0% +right but you you could write the + + + align:start position:0% +right but you you could write the +density in terms of the things we talked + + align:start position:0% +density in terms of the things we talked + + + align:start position:0% +density in terms of the things we talked +about on monday so again + + align:start position:0% +about on monday so again + + + align:start position:0% +about on monday so again +you know i want you to be able to go + + align:start position:0% +you know i want you to be able to go + + + align:start position:0% +you know i want you to be able to go +back and forth once you know that + + align:start position:0% +back and forth once you know that + + + align:start position:0% +back and forth once you know that +the unit cell and and you you know + + align:start position:0% +the unit cell and and you you know + + + align:start position:0% +the unit cell and and you you know +you can know something about the the + + align:start position:0% +you can know something about the the + + + align:start position:0% +you can know something about the the +radius of the atom maybe then you can + + align:start position:0% +radius of the atom maybe then you can + + + align:start position:0% +radius of the atom maybe then you can +get the density for example here + + align:start position:0% +get the density for example here + + + align:start position:0% +get the density for example here +um the density could be defined as + + align:start position:0% +um the density could be defined as + + + align:start position:0% +um the density could be defined as +the number of atoms + + align:start position:0% +the number of atoms + + + align:start position:0% +the number of atoms +in the cell right times + + align:start position:0% +in the cell right times + + + align:start position:0% +in the cell right times +the grams per mole of that element + + align:start position:0% +the grams per mole of that element + + + align:start position:0% +the grams per mole of that element +divided by the volume + + align:start position:0% +divided by the volume + + + align:start position:0% +divided by the volume +of the cell of the unit cell right + + align:start position:0% +of the cell of the unit cell right + + + align:start position:0% +of the cell of the unit cell right +times avogadro avogadro + + align:start position:0% +times avogadro avogadro + + + align:start position:0% +times avogadro avogadro +avogadro now you can go through the + + align:start position:0% +avogadro now you can go through the + + + align:start position:0% +avogadro now you can go through the +units and you can work out that this is + + align:start position:0% +units and you can work out that this is + + + align:start position:0% +units and you can work out that this is +grams per centimeter cubed + + align:start position:0% +grams per centimeter cubed + + + align:start position:0% +grams per centimeter cubed +right but and so so just as an example + + align:start position:0% +right but and so so just as an example + + + align:start position:0% +right but and so so just as an example +right if i had uh let's see the example + + align:start position:0% +right if i had uh let's see the example + + + align:start position:0% +right if i had uh let's see the example +i have is copper + + align:start position:0% +i have is copper + + + align:start position:0% +i have is copper +so example copper right + + align:start position:0% +so example copper right + + + align:start position:0% +so example copper right +so you know everything comes from the + + align:start position:0% +so you know everything comes from the + + + align:start position:0% +so you know everything comes from the +periodic table + + align:start position:0% +periodic table + + + align:start position:0% +periodic table +everything life class everything comes + + align:start position:0% +everything life class everything comes + + + align:start position:0% +everything life class everything comes +from the periodic table + + align:start position:0% +from the periodic table + + + align:start position:0% +from the periodic table +so i go to the i say i want to know + + align:start position:0% +so i go to the i say i want to know + + + align:start position:0% +so i go to the i say i want to know +stuff i go to the periodic table + + align:start position:0% +stuff i go to the periodic table + + + align:start position:0% +stuff i go to the periodic table +and instead of looking up the density i + + align:start position:0% +and instead of looking up the density i + + + align:start position:0% +and instead of looking up the density i +look up other things + + align:start position:0% +look up other things + + + align:start position:0% +look up other things +so i look up for example that it's fcc + + align:start position:0% +so i look up for example that it's fcc + + + align:start position:0% +so i look up for example that it's fcc +right and then i look up that it's + + align:start position:0% +right and then i look up that it's + + + align:start position:0% +right and then i look up that it's +63.55 grams per mole + + align:start position:0% +63.55 grams per mole + + + align:start position:0% +63.55 grams per mole +okay and i also look up the atomic + + align:start position:0% +okay and i also look up the atomic + + + align:start position:0% +okay and i also look up the atomic +radius so i look up these + + align:start position:0% +radius so i look up these + + + align:start position:0% +radius so i look up these +things right the atomic radius + + align:start position:0% + + + + align:start position:0% + +and that's equal to 1.3 angstroms + + align:start position:0% +and that's equal to 1.3 angstroms + + + align:start position:0% +and that's equal to 1.3 angstroms +so i look all this stuff up and the + + align:start position:0% +so i look all this stuff up and the + + + align:start position:0% +so i look all this stuff up and the +point is i can now + + align:start position:0% +point is i can now + + + align:start position:0% +point is i can now +go back and forth i can use the + + align:start position:0% +go back and forth i can use the + + + align:start position:0% +go back and forth i can use the +information because i know if it's a + + align:start position:0% +information because i know if it's a + + + align:start position:0% +information because i know if it's a +crystal + + align:start position:0% +crystal + + + align:start position:0% +crystal +and i know the crystal type fcc + + align:start position:0% +and i know the crystal type fcc + + + align:start position:0% +and i know the crystal type fcc +then i can use this information to get + + align:start position:0% +then i can use this information to get + + + align:start position:0% +then i can use this information to get +other other aspects right so other + + align:start position:0% +other other aspects right so other + + + align:start position:0% +other other aspects right so other +properties so for example + + align:start position:0% +properties so for example + + + align:start position:0% +properties so for example +i know that the radius of the atom + + align:start position:0% +i know that the radius of the atom + + + align:start position:0% +i know that the radius of the atom +for an fcc if it's close packed is for + + align:start position:0% +for an fcc if it's close packed is for + + + align:start position:0% +for an fcc if it's close packed is for +if it's + + align:start position:0% +if it's + + + align:start position:0% +if it's +if it's you know fcc one element + + align:start position:0% +if it's you know fcc one element + + + align:start position:0% +if it's you know fcc one element +remember it grows out until they touch + + align:start position:0% +remember it grows out until they touch + + + align:start position:0% +remember it grows out until they touch +right and and that got us how we get the + + align:start position:0% +right and and that got us how we get the + + + align:start position:0% +right and and that got us how we get the +radius of the atom + + align:start position:0% +radius of the atom + + + align:start position:0% +radius of the atom +and it's a root two over four + + align:start position:0% + + + + align:start position:0% + +well i also know that there's four atoms + + align:start position:0% +well i also know that there's four atoms + + + align:start position:0% +well i also know that there's four atoms +per unit cell + + align:start position:0% + + + + align:start position:0% + +because it's fcc i also know that the + + align:start position:0% +because it's fcc i also know that the + + + align:start position:0% +because it's fcc i also know that the +volume + + align:start position:0% +volume + + + align:start position:0% +volume +of the cell is simply the lattice + + align:start position:0% +of the cell is simply the lattice + + + align:start position:0% +of the cell is simply the lattice +constant cube because it's a cubic cell + + align:start position:0% +constant cube because it's a cubic cell + + + align:start position:0% +constant cube because it's a cubic cell +all the ones + + align:start position:0% +all the ones + + + align:start position:0% +all the ones +here are cubic so the volume of these + + align:start position:0% +here are cubic so the volume of these + + + align:start position:0% +here are cubic so the volume of these +cells are given from this information + + align:start position:0% +cells are given from this information + + + align:start position:0% +cells are given from this information +i can compute the density right so again + + align:start position:0% +i can compute the density right so again + + + align:start position:0% +i can compute the density right so again +it's it's it's going back and forth + + align:start position:0% +it's it's it's going back and forth + + + align:start position:0% +it's it's it's going back and forth +right the radius + + align:start position:0% +right the radius + + + align:start position:0% +right the radius +of the atoms packed in the lattice + + align:start position:0% +of the atoms packed in the lattice + + + align:start position:0% +of the atoms packed in the lattice +constants the number of atoms in the + + align:start position:0% +constants the number of atoms in the + + + align:start position:0% +constants the number of atoms in the +cell these are the things we talked + + align:start position:0% +cell these are the things we talked + + + align:start position:0% +cell these are the things we talked +about on monday + + align:start position:0% +about on monday + + + align:start position:0% +about on monday +and you can as you go back and forth you + + align:start position:0% +and you can as you go back and forth you + + + align:start position:0% +and you can as you go back and forth you +can do things like this + + align:start position:0% +can do things like this + + + align:start position:0% +can do things like this +okay all right good okay + + align:start position:0% +okay all right good okay + + + align:start position:0% +okay all right good okay +now we talked about the + + align:start position:0% +now we talked about the + + + align:start position:0% +now we talked about the +we talked about the uh the brave lattice + + align:start position:0% +we talked about the uh the brave lattice + + + align:start position:0% +we talked about the uh the brave lattice +there + + align:start position:0% +there + + + align:start position:0% +there +right and those are three bravais + + align:start position:0% +right and those are three bravais + + + align:start position:0% +right and those are three bravais +lattices that i want you to know + + align:start position:0% +lattices that i want you to know + + + align:start position:0% +lattices that i want you to know +brave + + align:start position:0% + + + + align:start position:0% + +lattice but the thing is that + + align:start position:0% +lattice but the thing is that + + + align:start position:0% +lattice but the thing is that +there's one there's something else you + + align:start position:0% +there's one there's something else you + + + align:start position:0% +there's one there's something else you +need to know + + align:start position:0% +need to know + + + align:start position:0% +need to know +in order to know what crystal you have + + align:start position:0% +in order to know what crystal you have + + + align:start position:0% +in order to know what crystal you have +right + + align:start position:0% +right + + + align:start position:0% +right +and so this is the fcc bravais lattice + + align:start position:0% +and so this is the fcc bravais lattice + + + align:start position:0% +and so this is the fcc bravais lattice +and there it is it's over there on the + + align:start position:0% +and there it is it's over there on the + + + align:start position:0% +and there it is it's over there on the +right it's the face centered cubic + + align:start position:0% +right it's the face centered cubic + + + align:start position:0% +right it's the face centered cubic +okay because then tight um and i'm gonna + + align:start position:0% +okay because then tight um and i'm gonna + + + align:start position:0% +okay because then tight um and i'm gonna +i'm gonna pass this around + + align:start position:0% +i'm gonna pass this around + + + align:start position:0% +i'm gonna pass this around +all right oh yeah i'm starting over here + + align:start position:0% +all right oh yeah i'm starting over here + + + align:start position:0% +all right oh yeah i'm starting over here +because i keep on starting over there + + align:start position:0% +because i keep on starting over there + + + align:start position:0% +because i keep on starting over there +and it's not fair it's not right yeah + + align:start position:0% +and it's not fair it's not right yeah + + + align:start position:0% +and it's not fair it's not right yeah +all right cut a couple of okay + + align:start position:0% +all right cut a couple of okay + + + align:start position:0% +all right cut a couple of okay +now um okay so that's fcc right so we're + + align:start position:0% +now um okay so that's fcc right so we're + + + align:start position:0% +now um okay so that's fcc right so we're +going to write down fcc but the thing is + + align:start position:0% +going to write down fcc but the thing is + + + align:start position:0% +going to write down fcc but the thing is +that see + + align:start position:0% +that see + + + align:start position:0% +that see +this is a stamp remember we emphasize so + + align:start position:0% +this is a stamp remember we emphasize so + + + align:start position:0% +this is a stamp remember we emphasize so +many + + align:start position:0% +many + + + align:start position:0% +many +it's a stamp of points + + align:start position:0% +it's a stamp of points + + + align:start position:0% +it's a stamp of points +that are equivalent that's what the + + align:start position:0% +that are equivalent that's what the + + + align:start position:0% +that are equivalent that's what the +lattice + + align:start position:0% +lattice + + + align:start position:0% +lattice +vectors are they are not the things that + + align:start position:0% +vectors are they are not the things that + + + align:start position:0% +vectors are they are not the things that +you put at that point + + align:start position:0% +you put at that point + + + align:start position:0% +you put at that point +that is something else now on monday we + + align:start position:0% +that is something else now on monday we + + + align:start position:0% +that is something else now on monday we +put the things there + + align:start position:0% +put the things there + + + align:start position:0% +put the things there +were atoms spherical particles and + + align:start position:0% +were atoms spherical particles and + + + align:start position:0% +were atoms spherical particles and +they're all the same + + align:start position:0% +they're all the same + + + align:start position:0% +they're all the same +that was our introduction to + + align:start position:0% +that was our introduction to + + + align:start position:0% +that was our introduction to +crystallography but + + align:start position:0% + + + + align:start position:0% + +the basis + + align:start position:0% + + + + align:start position:0% + +the basis can be more than just a single + + align:start position:0% +the basis can be more than just a single + + + align:start position:0% +the basis can be more than just a single +atom + + align:start position:0% +atom + + + align:start position:0% +atom +it can be more so how do we think about + + align:start position:0% +it can be more so how do we think about + + + align:start position:0% +it can be more so how do we think about +the basis + + align:start position:0% +the basis + + + align:start position:0% +the basis +right so here's a lattice this is a + + align:start position:0% +right so here's a lattice this is a + + + align:start position:0% +right so here's a lattice this is a +lattice of points i haven't + + align:start position:0% +lattice of points i haven't + + + align:start position:0% +lattice of points i haven't +the way you want to think about a + + align:start position:0% +the way you want to think about a + + + align:start position:0% +the way you want to think about a +lattice is a stamp without putting + + align:start position:0% +lattice is a stamp without putting + + + align:start position:0% +lattice is a stamp without putting +things there yet + + align:start position:0% +things there yet + + + align:start position:0% +things there yet +the basis is what you put there let's + + align:start position:0% +the basis is what you put there let's + + + align:start position:0% +the basis is what you put there let's +write that down because it's so + + align:start position:0% +write that down because it's so + + + align:start position:0% +write that down because it's so +important okay so the the lattice + + align:start position:0% +important okay so the the lattice + + + align:start position:0% +important okay so the the lattice +the lattice is oh we're going + + align:start position:0% +the lattice is oh we're going + + + align:start position:0% +the lattice is oh we're going +oh i'm going all caps how + + align:start position:0% +oh i'm going all caps how + + + align:start position:0% +oh i'm going all caps how +to repeat okay and + + align:start position:0% +to repeat okay and + + + align:start position:0% +to repeat okay and +the basis is + + align:start position:0% +the basis is + + + align:start position:0% +the basis is +what + + align:start position:0% + + + + align:start position:0% + +to repeat okay + + align:start position:0% +to repeat okay + + + align:start position:0% +to repeat okay +so if this is my lattice and i decide + + align:start position:0% +so if this is my lattice and i decide + + + align:start position:0% +so if this is my lattice and i decide +that i want to get a million downloads + + align:start position:0% +that i want to get a million downloads + + + align:start position:0% +that i want to get a million downloads +on youtube i'm going to put a cat there + + align:start position:0% +on youtube i'm going to put a cat there + + + align:start position:0% +on youtube i'm going to put a cat there +and this is my crystal it's a crystal of + + align:start position:0% +and this is my crystal it's a crystal of + + + align:start position:0% +and this is my crystal it's a crystal of +cats + + align:start position:0% +cats + + + align:start position:0% +cats +that's okay i have done nothing wrong + + align:start position:0% + + + + align:start position:0% + +because i have simply you know according + + align:start position:0% +because i have simply you know according + + + align:start position:0% +because i have simply you know according +to the rules of crystallography i've had + + align:start position:0% +to the rules of crystallography i've had + + + align:start position:0% +to the rules of crystallography i've had +a lattice and a basis and i've just + + align:start position:0% +a lattice and a basis and i've just + + + align:start position:0% +a lattice and a basis and i've just +defined my basis as a cat + + align:start position:0% +defined my basis as a cat + + + align:start position:0% +defined my basis as a cat +and that's that's the crystal you get + + align:start position:0% +and that's that's the crystal you get + + + align:start position:0% +and that's that's the crystal you get +but see the bases could also have been + + align:start position:0% +but see the bases could also have been + + + align:start position:0% +but see the bases could also have been +for example + + align:start position:0% +for example + + + align:start position:0% +for example +two atoms colored you know differently + + align:start position:0% +two atoms colored you know differently + + + align:start position:0% +two atoms colored you know differently +to show that they're different atoms + + align:start position:0% +to show that they're different atoms + + + align:start position:0% +to show that they're different atoms +and then this would be my crystal so the + + align:start position:0% +and then this would be my crystal so the + + + align:start position:0% +and then this would be my crystal so the +actual crystal + + align:start position:0% +actual crystal + + + align:start position:0% +actual crystal +that you get may be different + + align:start position:0% +that you get may be different + + + align:start position:0% +that you get may be different +than the lattice structure right so + + align:start position:0% +than the lattice structure right so + + + align:start position:0% +than the lattice structure right so +let's take a look so for example + + align:start position:0% +let's take a look so for example + + + align:start position:0% +let's take a look so for example +over here you know if my basis + + align:start position:0% +over here you know if my basis + + + align:start position:0% +over here you know if my basis +is a single atom nickel + + align:start position:0% +is a single atom nickel + + + align:start position:0% +is a single atom nickel +copper gold platinum + + align:start position:0% + + + + align:start position:0% + +well i showed you these from the + + align:start position:0% +well i showed you these from the + + + align:start position:0% +well i showed you these from the +periodic table on monday right we + + align:start position:0% +periodic table on monday right we + + + align:start position:0% +periodic table on monday right we +highlighted them when we talked about + + align:start position:0% +highlighted them when we talked about + + + align:start position:0% +highlighted them when we talked about +fcc + + align:start position:0% +fcc + + + align:start position:0% +fcc +then the crystal the crystal that you + + align:start position:0% +then the crystal the crystal that you + + + align:start position:0% +then the crystal the crystal that you +get + + align:start position:0% +get + + + align:start position:0% +get +is fcc these are the ones we did on + + align:start position:0% +is fcc these are the ones we did on + + + align:start position:0% +is fcc these are the ones we did on +monday + + align:start position:0% +monday + + + align:start position:0% +monday +right those are fcc crystals but but at + + align:start position:0% +right those are fcc crystals but but at + + + align:start position:0% +right those are fcc crystals but but at +the same time if my base is + + align:start position:0% +the same time if my base is + + + align:start position:0% +the same time if my base is +check this out oh + + align:start position:0% +check this out oh + + + align:start position:0% +check this out oh +the this is salt + + align:start position:0% +the this is salt + + + align:start position:0% +the this is salt +when you guys pour salt on your food do + + align:start position:0% +when you guys pour salt on your food do + + + align:start position:0% +when you guys pour salt on your food do +not see it + + align:start position:0% +not see it + + + align:start position:0% +not see it +anymore except as this this is salt + + align:start position:0% +anymore except as this this is salt + + + align:start position:0% +anymore except as this this is salt +this is salt it is uh + + align:start position:0% +this is salt it is uh + + + align:start position:0% +this is salt it is uh +let's see simple cubic + + align:start position:0% + + + + align:start position:0% + +is it though because a lattice + + align:start position:0% +is it though because a lattice + + + align:start position:0% +is it though because a lattice +a simple cubic remember the definition a + + align:start position:0% +a simple cubic remember the definition a + + + align:start position:0% +a simple cubic remember the definition a +simple cubic lattice would mean a stamp + + align:start position:0% +simple cubic lattice would mean a stamp + + + align:start position:0% +simple cubic lattice would mean a stamp +right of a simple cube where every + + align:start position:0% +right of a simple cube where every + + + align:start position:0% +right of a simple cube where every +corner is exactly + + align:start position:0% +corner is exactly + + + align:start position:0% +corner is exactly +the same exactly the same that's what a + + align:start position:0% +the same exactly the same that's what a + + + align:start position:0% +the same exactly the same that's what a +lattice is so this cannot be a simple + + align:start position:0% +lattice is so this cannot be a simple + + + align:start position:0% +lattice is so this cannot be a simple +cube + + align:start position:0% +cube + + + align:start position:0% +cube +this is not simple cubic because they're + + align:start position:0% +this is not simple cubic because they're + + + align:start position:0% +this is not simple cubic because they're +different + + align:start position:0% +different + + + align:start position:0% +different +they're different right at the corners + + align:start position:0% +they're different right at the corners + + + align:start position:0% +they're different right at the corners +i've got two blues and then two reds and + + align:start position:0% +i've got two blues and then two reds and + + + align:start position:0% +i've got two blues and then two reds and +then two other blues + + align:start position:0% +then two other blues + + + align:start position:0% +then two other blues +so they're not the same it cannot be a + + align:start position:0% +so they're not the same it cannot be a + + + align:start position:0% +so they're not the same it cannot be a +simple cubic structure + + align:start position:0% +simple cubic structure + + + align:start position:0% +simple cubic structure +this is an fcc lattice this is an fcc + + align:start position:0% +this is an fcc lattice this is an fcc + + + align:start position:0% +this is an fcc lattice this is an fcc +yeah i'm starting over here again i'm + + align:start position:0% +yeah i'm starting over here again i'm + + + align:start position:0% +yeah i'm starting over here again i'm +trying to even it out + + align:start position:0% +trying to even it out + + + align:start position:0% +trying to even it out +that's an fcc lattice but with a basis + + align:start position:0% +that's an fcc lattice but with a basis + + + align:start position:0% +that's an fcc lattice but with a basis +with the basis of sodium and chlorine + + align:start position:0% +with the basis of sodium and chlorine + + + align:start position:0% +with the basis of sodium and chlorine +so it's an fcc you can call it an fcc + + align:start position:0% +so it's an fcc you can call it an fcc + + + align:start position:0% +so it's an fcc you can call it an fcc +lattice + + align:start position:0% +lattice + + + align:start position:0% +lattice +but the basis is a sodium chloride pear + + align:start position:0% +but the basis is a sodium chloride pear + + + align:start position:0% +but the basis is a sodium chloride pear +and this has a name it's called the rock + + align:start position:0% +and this has a name it's called the rock + + + align:start position:0% +and this has a name it's called the rock +salt structure + + align:start position:0% + + + + align:start position:0% + +it's called the rock salt structure it's + + align:start position:0% +it's called the rock salt structure it's + + + align:start position:0% +it's called the rock salt structure it's +an fcc lattice with this two atom basis + + align:start position:0% +an fcc lattice with this two atom basis + + + align:start position:0% +an fcc lattice with this two atom basis +where + + align:start position:0% +where + + + align:start position:0% +where +look you can see the fcc lattice here + + align:start position:0% +look you can see the fcc lattice here + + + align:start position:0% +look you can see the fcc lattice here +look at those blue + + align:start position:0% +look at those blue + + + align:start position:0% +look at those blue +points right blue outlines in fcc + + align:start position:0% +points right blue outlines in fcc + + + align:start position:0% +points right blue outlines in fcc +lattice but now the basis + + align:start position:0% +lattice but now the basis + + + align:start position:0% +lattice but now the basis +is one atom here and one there so now i + + align:start position:0% +is one atom here and one there so now i + + + align:start position:0% +is one atom here and one there so now i +take that + + align:start position:0% +take that + + + align:start position:0% +take that +this pair and i put that at all the + + align:start position:0% +this pair and i put that at all the + + + align:start position:0% +this pair and i put that at all the +lattice points + + align:start position:0% +lattice points + + + align:start position:0% +lattice points +you see that you put that at all the + + align:start position:0% +you see that you put that at all the + + + align:start position:0% +you see that you put that at all the +lattice points of fcc + + align:start position:0% +lattice points of fcc + + + align:start position:0% +lattice points of fcc +and you've got salt and that is how you + + align:start position:0% +and you've got salt and that is how you + + + align:start position:0% +and you've got salt and that is how you +must see table salt from now on + + align:start position:0% +must see table salt from now on + + + align:start position:0% +must see table salt from now on +well we talked about diamond + + align:start position:0% + + + + align:start position:0% + +this is diamond what diamond is the same + + align:start position:0% +this is diamond what diamond is the same + + + align:start position:0% +this is diamond what diamond is the same +bravais lattice it doesn't look like it + + align:start position:0% +bravais lattice it doesn't look like it + + + align:start position:0% +bravais lattice it doesn't look like it +at first + + align:start position:0% +at first + + + align:start position:0% +at first +it doesn't look like it at first but see + + align:start position:0% +it doesn't look like it at first but see + + + align:start position:0% +it doesn't look like it at first but see +here + + align:start position:0% + + + + align:start position:0% + +here i have a different pair + + align:start position:0% +here i have a different pair + + + align:start position:0% +here i have a different pair +here i have a carbon-carbon pair or it + + align:start position:0% +here i have a carbon-carbon pair or it + + + align:start position:0% +here i have a carbon-carbon pair or it +could be + + align:start position:0% +could be + + + align:start position:0% +could be +or silicon silicon there are actually + + align:start position:0% +or silicon silicon there are actually + + + align:start position:0% +or silicon silicon there are actually +a number of pairs of atoms + + align:start position:0% +a number of pairs of atoms + + + align:start position:0% +a number of pairs of atoms +that would form this diamond + + align:start position:0% +that would form this diamond + + + align:start position:0% +that would form this diamond +in fact we specify because there are + + align:start position:0% +in fact we specify because there are + + + align:start position:0% +in fact we specify because there are +different types this is called cubic + + align:start position:0% +different types this is called cubic + + + align:start position:0% +different types this is called cubic +diamond + + align:start position:0% +diamond + + + align:start position:0% +diamond +crystal + + align:start position:0% + + + + align:start position:0% + +this is the cubic diamond crystal what + + align:start position:0% +this is the cubic diamond crystal what + + + align:start position:0% +this is the cubic diamond crystal what +is the lattice + + align:start position:0% +is the lattice + + + align:start position:0% +is the lattice +it's fcc it's fcc now let's take a look + + align:start position:0% +it's fcc it's fcc now let's take a look + + + align:start position:0% +it's fcc it's fcc now let's take a look +at that + + align:start position:0% +at that + + + align:start position:0% +at that +look there's my fcc here + + align:start position:0% +look there's my fcc here + + + align:start position:0% +look there's my fcc here +here here here right but inside of the + + align:start position:0% +here here here right but inside of the + + + align:start position:0% +here here here right but inside of the +scc i've got this pair of carbon atoms + + align:start position:0% +scc i've got this pair of carbon atoms + + + align:start position:0% +scc i've got this pair of carbon atoms +so + + align:start position:0% +so + + + align:start position:0% +so +now they're the same type of atom and + + align:start position:0% +now they're the same type of atom and + + + align:start position:0% +now they're the same type of atom and +instead of one being kind of in the + + align:start position:0% +instead of one being kind of in the + + + align:start position:0% +instead of one being kind of in the +middle of this edge + + align:start position:0% +middle of this edge + + + align:start position:0% +middle of this edge +as it was with sodium and chlorine now + + align:start position:0% +as it was with sodium and chlorine now + + + align:start position:0% +as it was with sodium and chlorine now +the other atom is kind of + + align:start position:0% +the other atom is kind of + + + align:start position:0% +the other atom is kind of +often a diagonal but it's still just a + + align:start position:0% +often a diagonal but it's still just a + + + align:start position:0% +often a diagonal but it's still just a +pair + + align:start position:0% +pair + + + align:start position:0% +pair +of atoms it's a pair of carbon atoms but + + align:start position:0% +of atoms it's a pair of carbon atoms but + + + align:start position:0% +of atoms it's a pair of carbon atoms but +if you look carefully at diamond and + + align:start position:0% +if you look carefully at diamond and + + + align:start position:0% +if you look carefully at diamond and +this + + align:start position:0% +this + + + align:start position:0% +this +doesn't go on in this picture but it + + align:start position:0% +doesn't go on in this picture but it + + + align:start position:0% +doesn't go on in this picture but it +does in in real life + + align:start position:0% +does in in real life + + + align:start position:0% +does in in real life +this is an fcc lattice of these pairs + + align:start position:0% +this is an fcc lattice of these pairs + + + align:start position:0% +this is an fcc lattice of these pairs +repeating everywhere that's what diamond + + align:start position:0% +repeating everywhere that's what diamond + + + align:start position:0% +repeating everywhere that's what diamond +is + + align:start position:0% +is + + + align:start position:0% +is +it's an fcc lattice so the symmetry + + align:start position:0% +it's an fcc lattice so the symmetry + + + align:start position:0% +it's an fcc lattice so the symmetry +is fcc but the basis + + align:start position:0% +is fcc but the basis + + + align:start position:0% +is fcc but the basis +is a carbon-carbon dimer right + + align:start position:0% +is a carbon-carbon dimer right + + + align:start position:0% +is a carbon-carbon dimer right +and that gives you cubic diamond + + align:start position:0% +and that gives you cubic diamond + + + align:start position:0% +and that gives you cubic diamond +okay so there's there's the brave + + align:start position:0% +okay so there's there's the brave + + + align:start position:0% +okay so there's there's the brave +lattice + + align:start position:0% +lattice + + + align:start position:0% +lattice +and there's the resulting crystal + + align:start position:0% +and there's the resulting crystal + + + align:start position:0% +and there's the resulting crystal +structure now + + align:start position:0% +structure now + + + align:start position:0% +structure now +speaking of diamond and this is a graph + + align:start position:0% +speaking of diamond and this is a graph + + + align:start position:0% +speaking of diamond and this is a graph +that i showed you + + align:start position:0% +that i showed you + + + align:start position:0% +that i showed you +a while ago when we were talking about + + align:start position:0% +a while ago when we were talking about + + + align:start position:0% +a while ago when we were talking about +the differences between + + align:start position:0% +the differences between + + + align:start position:0% +the differences between +diamond and graphite one of the things + + align:start position:0% +diamond and graphite one of the things + + + align:start position:0% +diamond and graphite one of the things +that you can see that's so important + + align:start position:0% +that you can see that's so important + + + align:start position:0% +that you can see that's so important +this is the same element two different + + align:start position:0% +this is the same element two different + + + align:start position:0% +this is the same element two different +crystal structures one of the things + + align:start position:0% +crystal structures one of the things + + + align:start position:0% +crystal structures one of the things +that you can see that's so important is + + align:start position:0% +that you can see that's so important is + + + align:start position:0% +that you can see that's so important is +how direction is going to be + + align:start position:0% +how direction is going to be + + + align:start position:0% +how direction is going to be +an important property you need to know + + align:start position:0% +an important property you need to know + + + align:start position:0% +an important property you need to know +how to identify + + align:start position:0% +how to identify + + + align:start position:0% +how to identify +direction because in you know in this + + align:start position:0% +direction because in you know in this + + + align:start position:0% +direction because in you know in this +case it looks like maybe if i point in + + align:start position:0% +case it looks like maybe if i point in + + + align:start position:0% +case it looks like maybe if i point in +different directions + + align:start position:0% +different directions + + + align:start position:0% +different directions +the thing would look kind of the same + + align:start position:0% +the thing would look kind of the same + + + align:start position:0% +the thing would look kind of the same +right and maybe have + + align:start position:0% +right and maybe have + + + align:start position:0% +right and maybe have +similar properties along but look at + + align:start position:0% +similar properties along but look at + + + align:start position:0% +similar properties along but look at +this this looks seriously directionally + + align:start position:0% +this this looks seriously directionally + + + align:start position:0% +this this looks seriously directionally +dependent + + align:start position:0% +dependent + + + align:start position:0% +dependent +it looks like if i if i did something + + align:start position:0% +it looks like if i if i did something + + + align:start position:0% +it looks like if i if i did something +like tried to carry charge or + + align:start position:0% +like tried to carry charge or + + + align:start position:0% +like tried to carry charge or +or thermal energy this way then it would + + align:start position:0% +or thermal energy this way then it would + + + align:start position:0% +or thermal energy this way then it would +be very very different than if i carry + + align:start position:0% +be very very different than if i carry + + + align:start position:0% +be very very different than if i carry +it this way + + align:start position:0% +it this way + + + align:start position:0% +it this way +well we have a word for that right + + align:start position:0% +well we have a word for that right + + + align:start position:0% +well we have a word for that right +that's called anisotropy + + align:start position:0% +that's called anisotropy + + + align:start position:0% +that's called anisotropy +and so this is + + align:start position:0% +and so this is + + + align:start position:0% +and so this is +another important word anisotropy + + align:start position:0% + + + + align:start position:0% + +the property if it's anisotropic then + + align:start position:0% +the property if it's anisotropic then + + + align:start position:0% +the property if it's anisotropic then +the property + + align:start position:0% +the property + + + align:start position:0% +the property +well it could be like electrical + + align:start position:0% +well it could be like electrical + + + align:start position:0% +well it could be like electrical +or thermal conductivity for example + + align:start position:0% +or thermal conductivity for example + + + align:start position:0% +or thermal conductivity for example +thermal conductivity could be like where + + align:start position:0% +thermal conductivity could be like where + + + align:start position:0% +thermal conductivity could be like where +it how it breaks + + align:start position:0% +it how it breaks + + + align:start position:0% +it how it breaks +the fracture right and so on + + align:start position:0% +the fracture right and so on + + + align:start position:0% +the fracture right and so on +but whatever the but that the property + + align:start position:0% +but whatever the but that the property + + + align:start position:0% +but whatever the but that the property +is uh + + align:start position:0% +is uh + + + align:start position:0% +is uh +um depends it's i'll just say it's + + align:start position:0% +um depends it's i'll just say it's + + + align:start position:0% +um depends it's i'll just say it's +directionally dependent + + align:start position:0% +directionally dependent + + + align:start position:0% +directionally dependent +directionally + + align:start position:0% +directionally + + + align:start position:0% +directionally +dependent so the reason i'm telling you + + align:start position:0% +dependent so the reason i'm telling you + + + align:start position:0% +dependent so the reason i'm telling you +this is that + + align:start position:0% +this is that + + + align:start position:0% +this is that +i now need a way i've we've come up with + + align:start position:0% +i now need a way i've we've come up with + + + align:start position:0% +i now need a way i've we've come up with +sort of ways to talk about + + align:start position:0% +sort of ways to talk about + + + align:start position:0% +sort of ways to talk about +crystals right but i i now need a way to + + align:start position:0% +crystals right but i i now need a way to + + + align:start position:0% +crystals right but i i now need a way to +specify + + align:start position:0% +specify + + + align:start position:0% +specify +where i am in a crystal and and maybe + + align:start position:0% +where i am in a crystal and and maybe + + + align:start position:0% +where i am in a crystal and and maybe +how the crystal cuts + + align:start position:0% +how the crystal cuts + + + align:start position:0% +how the crystal cuts +right i need a way to talk about + + align:start position:0% +right i need a way to talk about + + + align:start position:0% +right i need a way to talk about +directionality + + align:start position:0% +directionality + + + align:start position:0% +directionality +in these crystals and that's what i want + + align:start position:0% +in these crystals and that's what i want + + + align:start position:0% +in these crystals and that's what i want +you to + + align:start position:0% +you to + + + align:start position:0% +you to +that's that's the topic for today all + + align:start position:0% +that's that's the topic for today all + + + align:start position:0% +that's that's the topic for today all +right so the first question + + align:start position:0% +right so the first question + + + align:start position:0% +right so the first question +so so well so to jump to the the the + + align:start position:0% +so so well so to jump to the the the + + + align:start position:0% +so so well so to jump to the the the +punch line is there's these things + + align:start position:0% +punch line is there's these things + + + align:start position:0% +punch line is there's these things +called miller indices that's what we're + + align:start position:0% +called miller indices that's what we're + + + align:start position:0% +called miller indices that's what we're +going to learn today + + align:start position:0% +going to learn today + + + align:start position:0% +going to learn today +miller indices and they describe + + align:start position:0% +miller indices and they describe + + + align:start position:0% +miller indices and they describe +direction and cuts + + align:start position:0% +direction and cuts + + + align:start position:0% +direction and cuts +planes okay and the first question you + + align:start position:0% +planes okay and the first question you + + + align:start position:0% +planes okay and the first question you +can ask is where are you + + align:start position:0% +can ask is where are you + + + align:start position:0% +can ask is where are you +now where are you now it turns out that + + align:start position:0% +now where are you now it turns out that + + + align:start position:0% +now where are you now it turns out that +there + + align:start position:0% +there + + + align:start position:0% +there +are um there are these people called + + align:start position:0% +are um there are these people called + + + align:start position:0% +are um there are these people called +crystallographers + + align:start position:0% +crystallographers + + + align:start position:0% +crystallographers +and they came up with crystallography + + align:start position:0% +and they came up with crystallography + + + align:start position:0% +and they came up with crystallography +over the years + + align:start position:0% +over the years + + + align:start position:0% +over the years +and they have very strong ideas + + align:start position:0% +and they have very strong ideas + + + align:start position:0% +and they have very strong ideas +about notation so we'll be talking about + + align:start position:0% +about notation so we'll be talking about + + + align:start position:0% +about notation so we'll be talking about +crystallographer notation + + align:start position:0% +crystallographer notation + + + align:start position:0% +crystallographer notation +and we'll be very careful not to do + + align:start position:0% +and we'll be very careful not to do + + + align:start position:0% +and we'll be very careful not to do +anything that would upset + + align:start position:0% +anything that would upset + + + align:start position:0% +anything that would upset +a crystallographer because that is not + + align:start position:0% +a crystallographer because that is not + + + align:start position:0% +a crystallographer because that is not +something you want to see + + align:start position:0% +something you want to see + + + align:start position:0% +something you want to see +but but the the first question that you + + align:start position:0% +but but the the first question that you + + + align:start position:0% +but but the the first question that you +could ask + + align:start position:0% +could ask + + + align:start position:0% +could ask +is where are you so i'm going to draw + + align:start position:0% +is where are you so i'm going to draw + + + align:start position:0% +is where are you so i'm going to draw +the planes and we're going to the + + align:start position:0% +the planes and we're going to the + + + align:start position:0% +the planes and we're going to the +the axes we're always going to use the + + align:start position:0% +the axes we're always going to use the + + + align:start position:0% +the axes we're always going to use the +same notate + + align:start position:0% +same notate + + + align:start position:0% +same notate +the same axis directions just for + + align:start position:0% +the same axis directions just for + + + align:start position:0% +the same axis directions just for +simplicity in this class we're going to + + align:start position:0% +simplicity in this class we're going to + + + align:start position:0% +simplicity in this class we're going to +say that + + align:start position:0% +say that + + + align:start position:0% +say that +you know as we're talking about crystal + + align:start position:0% +you know as we're talking about crystal + + + align:start position:0% +you know as we're talking about crystal +structures that's y that's z + + align:start position:0% +structures that's y that's z + + + align:start position:0% +structures that's y that's z +and that's x x is coming out of the + + align:start position:0% +and that's x x is coming out of the + + + align:start position:0% +and that's x x is coming out of the +board y is going that way and z is going + + align:start position:0% +board y is going that way and z is going + + + align:start position:0% +board y is going that way and z is going +that way + + align:start position:0% +that way + + + align:start position:0% +that way +okay now if i if i want to know where i + + align:start position:0% +okay now if i if i want to know where i + + + align:start position:0% +okay now if i if i want to know where i +am then what i can do is draw the cube + + align:start position:0% +am then what i can do is draw the cube + + + align:start position:0% +am then what i can do is draw the cube +oh boy here we go okay there it is + + align:start position:0% +oh boy here we go okay there it is + + + align:start position:0% +oh boy here we go okay there it is +all right and i can just start looking + + align:start position:0% +all right and i can just start looking + + + align:start position:0% +all right and i can just start looking +at points but instead of having + + align:start position:0% +at points but instead of having + + + align:start position:0% +at points but instead of having +all sorts of different numbers + + align:start position:0% +all sorts of different numbers + + + align:start position:0% +all sorts of different numbers +crystallographers like to work + + align:start position:0% +crystallographers like to work + + + align:start position:0% +crystallographers like to work +with simple numbers so what we do is we + + align:start position:0% +with simple numbers so what we do is we + + + align:start position:0% +with simple numbers so what we do is we +define the position + + align:start position:0% +define the position + + + align:start position:0% +define the position +as the fraction + + align:start position:0% + + + + align:start position:0% + +of the cell edge + + align:start position:0% + + + + align:start position:0% + +okay so what that means is if i you know + + align:start position:0% +okay so what that means is if i you know + + + align:start position:0% +okay so what that means is if i you know +so okay first of all the origin is 0 + + align:start position:0% +so okay first of all the origin is 0 + + + align:start position:0% +so okay first of all the origin is 0 +0 0 right so that's 0 0 + + align:start position:0% +0 0 right so that's 0 0 + + + align:start position:0% +0 0 right so that's 0 0 +0 but it also means that you know if i + + align:start position:0% +0 but it also means that you know if i + + + align:start position:0% +0 but it also means that you know if i +had this point here + + align:start position:0% +had this point here + + + align:start position:0% +had this point here +that's going to be 1 0 0. + + align:start position:0% +that's going to be 1 0 0. + + + align:start position:0% +that's going to be 1 0 0. +it doesn't matter what a is remember a + + align:start position:0% +it doesn't matter what a is remember a + + + align:start position:0% +it doesn't matter what a is remember a +is the lattice constant it's the it's + + align:start position:0% +is the lattice constant it's the it's + + + align:start position:0% +is the lattice constant it's the it's +the size the edge of the cube + + align:start position:0% +the size the edge of the cube + + + align:start position:0% +the size the edge of the cube +which has a real value in different + + align:start position:0% +which has a real value in different + + + align:start position:0% +which has a real value in different +crystals right there's copper + + align:start position:0% +crystals right there's copper + + + align:start position:0% +crystals right there's copper +there's a and copper which we could + + align:start position:0% +there's a and copper which we could + + + align:start position:0% +there's a and copper which we could +compute + + align:start position:0% +compute + + + align:start position:0% +compute +but no when we specify positions in + + align:start position:0% +but no when we specify positions in + + + align:start position:0% +but no when we specify positions in +crystal we + + align:start position:0% +crystal we + + + align:start position:0% +crystal we +we do it as a fraction of that of that + + align:start position:0% +we do it as a fraction of that of that + + + align:start position:0% +we do it as a fraction of that of that +length okay so that + + align:start position:0% +length okay so that + + + align:start position:0% +length okay so that +that's for so this point for example + + align:start position:0% +that's for so this point for example + + + align:start position:0% +that's for so this point for example +would be one + + align:start position:0% +would be one + + + align:start position:0% +would be one +one one out there all right + + align:start position:0% +one one out there all right + + + align:start position:0% +one one out there all right +and and let's do one more at this point + + align:start position:0% +and and let's do one more at this point + + + align:start position:0% +and and let's do one more at this point +here right well that's going gonna be + + align:start position:0% +here right well that's going gonna be + + + align:start position:0% +here right well that's going gonna be +good and tight that's gonna be + + align:start position:0% +good and tight that's gonna be + + + align:start position:0% +good and tight that's gonna be +you know okay over a half now + + align:start position:0% +you know okay over a half now + + + align:start position:0% +you know okay over a half now +so it's a half and then + + align:start position:0% +so it's a half and then + + + align:start position:0% +so it's a half and then +one zero it went over a half + + align:start position:0% +one zero it went over a half + + + align:start position:0% +one zero it went over a half +over one up zero so it's a half okay + + align:start position:0% +over one up zero so it's a half okay + + + align:start position:0% +over one up zero so it's a half okay +good + + align:start position:0% +good + + + align:start position:0% +good +this is just where we are we're just + + align:start position:0% +this is just where we are we're just + + + align:start position:0% +this is just where we are we're just +getting warmed up but really what we + + align:start position:0% +getting warmed up but really what we + + + align:start position:0% +getting warmed up but really what we +need to know + + align:start position:0% +need to know + + + align:start position:0% +need to know +is where we're going and that goes from + + align:start position:0% +is where we're going and that goes from + + + align:start position:0% +is where we're going and that goes from +a point to a vector + + align:start position:0% +a point to a vector + + + align:start position:0% +a point to a vector +okay now again there are some fairly + + align:start position:0% +okay now again there are some fairly + + + align:start position:0% +okay now again there are some fairly +straightforward + + align:start position:0% +straightforward + + + align:start position:0% +straightforward +rules that we follow not that we don't + + align:start position:0% +rules that we follow not that we don't + + + align:start position:0% +rules that we follow not that we don't +know what vectors are + + align:start position:0% +know what vectors are + + + align:start position:0% +know what vectors are +we know what vectors are the point is do + + align:start position:0% +we know what vectors are the point is do + + + align:start position:0% +we know what vectors are the point is do +we know how to specify a vector + + align:start position:0% +we know how to specify a vector + + + align:start position:0% +we know how to specify a vector +in a way that a crystallographer would + + align:start position:0% +in a way that a crystallographer would + + + align:start position:0% +in a way that a crystallographer would +be happy with + + align:start position:0% +be happy with + + + align:start position:0% +be happy with +that's what we have to learn because + + align:start position:0% +that's what we have to learn because + + + align:start position:0% +that's what we have to learn because +again we don't want to make them + + align:start position:0% +again we don't want to make them + + + align:start position:0% +again we don't want to make them +upset so there's a set of very simple + + align:start position:0% +upset so there's a set of very simple + + + align:start position:0% +upset so there's a set of very simple +rules + + align:start position:0% +rules + + + align:start position:0% +rules +that you can follow and i've got this + + align:start position:0% +that you can follow and i've got this + + + align:start position:0% +that you can follow and i've got this +for the direction and i've got this for + + align:start position:0% +for the direction and i've got this for + + + align:start position:0% +for the direction and i've got this for +the planes + + align:start position:0% +the planes + + + align:start position:0% +the planes +so here are the rules for the direction + + align:start position:0% +so here are the rules for the direction + + + align:start position:0% +so here are the rules for the direction +here's a vector in a crystal + + align:start position:0% +here's a vector in a crystal + + + align:start position:0% +here's a vector in a crystal +origin o and here are different vectors + + align:start position:0% +origin o and here are different vectors + + + align:start position:0% +origin o and here are different vectors +and what we do + + align:start position:0% +and what we do + + + align:start position:0% +and what we do +is we okay we position it to start at + + align:start position:0% +is we okay we position it to start at + + + align:start position:0% +is we okay we position it to start at +the origin and then we read off + + align:start position:0% +the origin and then we read off + + + align:start position:0% +the origin and then we read off +the projections in terms of the unit + + align:start position:0% +the projections in terms of the unit + + + align:start position:0% +the projections in terms of the unit +cell dimensions + + align:start position:0% +cell dimensions + + + align:start position:0% +cell dimensions +a a is x right + + align:start position:0% +a a is x right + + + align:start position:0% +a a is x right +b is y and c is z now we know that those + + align:start position:0% +b is y and c is z now we know that those + + + align:start position:0% +b is y and c is z now we know that those +have the same length in a cubic crystal + + align:start position:0% +have the same length in a cubic crystal + + + align:start position:0% +have the same length in a cubic crystal +okay adjust to the smallest integer + + align:start position:0% +okay adjust to the smallest integer + + + align:start position:0% +okay adjust to the smallest integer +values that's really important + + align:start position:0% +values that's really important + + + align:start position:0% +values that's really important +and in close and square brackets no + + align:start position:0% +and in close and square brackets no + + + align:start position:0% +and in close and square brackets no +commas + + align:start position:0% +commas + + + align:start position:0% +commas +so let's do a few right so o + + align:start position:0% +so let's do a few right so o + + + align:start position:0% +so let's do a few right so o +a uh + + align:start position:0% +a uh + + + align:start position:0% +a uh +here are the x y z + + align:start position:0% +here are the x y z + + + align:start position:0% +here are the x y z +the x y z readout well you know this is + + align:start position:0% +the x y z readout well you know this is + + + align:start position:0% +the x y z readout well you know this is +one this is zero + + align:start position:0% +one this is zero + + + align:start position:0% +one this is zero +this is zero so this would give us this + + align:start position:0% +this is zero so this would give us this + + + align:start position:0% +this is zero so this would give us this +as the notation for the oa vector you + + align:start position:0% +as the notation for the oa vector you + + + align:start position:0% +as the notation for the oa vector you +see that there right + + align:start position:0% +see that there right + + + align:start position:0% +see that there right +notice i've already done step two so the + + align:start position:0% +notice i've already done step two so the + + + align:start position:0% +notice i've already done step two so the +second bullet there read off projections + + align:start position:0% +second bullet there read off projections + + + align:start position:0% +second bullet there read off projections +in terms of unit cell dimensions a b and + + align:start position:0% +in terms of unit cell dimensions a b and + + + align:start position:0% +in terms of unit cell dimensions a b and +c + + align:start position:0% +c + + + align:start position:0% +c +because it went all the way to the edge + + align:start position:0% +because it went all the way to the edge + + + align:start position:0% +because it went all the way to the edge +so it's a one + + align:start position:0% +so it's a one + + + align:start position:0% +so it's a one +it didn't go halfway it's not a half + + align:start position:0% +it didn't go halfway it's not a half + + + align:start position:0% +it didn't go halfway it's not a half +right okay good + + align:start position:0% +right okay good + + + align:start position:0% +right okay good +so ob okay well that's going to be + + align:start position:0% +so ob okay well that's going to be + + + align:start position:0% +so ob okay well that's going to be +1 along x 1 along y and 0. + + align:start position:0% +1 along x 1 along y and 0. + + + align:start position:0% +1 along x 1 along y and 0. +so that direction would be written as + + align:start position:0% +so that direction would be written as + + + align:start position:0% +so that direction would be written as +the 1 1 0 + + align:start position:0% +the 1 1 0 + + + align:start position:0% +the 1 1 0 +and oc would be one + + align:start position:0% +and oc would be one + + + align:start position:0% +and oc would be one +one one this is feeling kind of + + align:start position:0% +one one this is feeling kind of + + + align:start position:0% +one one this is feeling kind of +boring oh gesundheit but it gets + + align:start position:0% +boring oh gesundheit but it gets + + + align:start position:0% +boring oh gesundheit but it gets +exciting + + align:start position:0% +exciting + + + align:start position:0% +exciting +in just a sec because all we're doing + + align:start position:0% +in just a sec because all we're doing + + + align:start position:0% +in just a sec because all we're doing +here is we're going okay one + + align:start position:0% +here is we're going okay one + + + align:start position:0% +here is we're going okay one +zero zero right one one + + align:start position:0% +zero zero right one one + + + align:start position:0% +zero zero right one one +zero one one one okay + + align:start position:0% +zero one one one okay + + + align:start position:0% +zero one one one okay +good oh but now we go to od + + align:start position:0% +good oh but now we go to od + + + align:start position:0% +good oh but now we go to od +now od is one of these cases where we + + align:start position:0% +now od is one of these cases where we + + + align:start position:0% +now od is one of these cases where we +have to be careful + + align:start position:0% +have to be careful + + + align:start position:0% +have to be careful +right so od you see that it's going from + + align:start position:0% +right so od you see that it's going from + + + align:start position:0% +right so od you see that it's going from +here + + align:start position:0% +here + + + align:start position:0% +here +to there so along the x direction + + align:start position:0% +to there so along the x direction + + + align:start position:0% +to there so along the x direction +it's still going a full one of the edge + + align:start position:0% +it's still going a full one of the edge + + + align:start position:0% +it's still going a full one of the edge +along the y direction it's zero + + align:start position:0% +along the y direction it's zero + + + align:start position:0% +along the y direction it's zero +oh but along the z direction it's a half + + align:start position:0% +oh but along the z direction it's a half + + + align:start position:0% +oh but along the z direction it's a half +and so because crystallographers don't + + align:start position:0% +and so because crystallographers don't + + + align:start position:0% +and so because crystallographers don't +like fractions + + align:start position:0% +like fractions + + + align:start position:0% +like fractions +when they talk about directions we have + + align:start position:0% +when they talk about directions we have + + + align:start position:0% +when they talk about directions we have +to scale that up + + align:start position:0% +to scale that up + + + align:start position:0% +to scale that up +and so we just get rid of it we multiply + + align:start position:0% +and so we just get rid of it we multiply + + + align:start position:0% +and so we just get rid of it we multiply +everything by two + + align:start position:0% +everything by two + + + align:start position:0% +everything by two +we put it in brackets and everyone is + + align:start position:0% +we put it in brackets and everyone is + + + align:start position:0% +we put it in brackets and everyone is +happy + + align:start position:0% +happy + + + align:start position:0% +happy +two zero one that is the two zero one + + align:start position:0% +two zero one that is the two zero one + + + align:start position:0% +two zero one that is the two zero one +direction + + align:start position:0% +direction + + + align:start position:0% +direction +in this crystal that is the two zero one + + align:start position:0% +in this crystal that is the two zero one + + + align:start position:0% +in this crystal that is the two zero one +direction + + align:start position:0% + + + + align:start position:0% + +they don't like fractions no they don't + + align:start position:0% +they don't like fractions no they don't + + + align:start position:0% +they don't like fractions no they don't +like negative signs either + + align:start position:0% +like negative signs either + + + align:start position:0% +like negative signs either +they don't like negative signs but so so + + align:start position:0% +they don't like negative signs but so so + + + align:start position:0% +they don't like negative signs but so so +if i were doing oh + + align:start position:0% +if i were doing oh + + + align:start position:0% +if i were doing oh +d if i were doing o e okay that's just + + align:start position:0% +d if i were doing o e okay that's just + + + align:start position:0% +d if i were doing o e okay that's just +going in the other direction + + align:start position:0% +going in the other direction + + + align:start position:0% +going in the other direction +but so o e you know o e + + align:start position:0% +but so o e you know o e + + + align:start position:0% +but so o e you know o e +would be uh let's see minus + + align:start position:0% +would be uh let's see minus + + + align:start position:0% +would be uh let's see minus +okay well if i just jump to the to what + + align:start position:0% +okay well if i just jump to the to what + + + align:start position:0% +okay well if i just jump to the to what +we think it might be + + align:start position:0% +we think it might be + + + align:start position:0% +we think it might be +given what we just saw it would look + + align:start position:0% +given what we just saw it would look + + + align:start position:0% +given what we just saw it would look +like that but crystallographers don't + + align:start position:0% +like that but crystallographers don't + + + align:start position:0% +like that but crystallographers don't +like having negative + + align:start position:0% +like having negative + + + align:start position:0% +like having negative +you know these minuses inside of their + + align:start position:0% +you know these minuses inside of their + + + align:start position:0% +you know these minuses inside of their +brackets so we we write a bar + + align:start position:0% +brackets so we we write a bar + + + align:start position:0% +brackets so we we write a bar +so we write it like this 0 1 bar + + align:start position:0% +so we write it like this 0 1 bar + + + align:start position:0% +so we write it like this 0 1 bar +0. and that is the notation for going in + + align:start position:0% +0. and that is the notation for going in + + + align:start position:0% +0. and that is the notation for going in +the negative direction + + align:start position:0% +the negative direction + + + align:start position:0% +the negative direction +okay 0 1 bar 0. + + align:start position:0% +okay 0 1 bar 0. + + + align:start position:0% +okay 0 1 bar 0. +that would be o e did i get that right o + + align:start position:0% +that would be o e did i get that right o + + + align:start position:0% +that would be o e did i get that right o +e yeah + + align:start position:0% +e yeah + + + align:start position:0% +e yeah +and you can see that o f if you if you + + align:start position:0% +and you can see that o f if you if you + + + align:start position:0% +and you can see that o f if you if you +have the same kind of fund + + align:start position:0% +have the same kind of fund + + + align:start position:0% +have the same kind of fund +you would see that o f is + + align:start position:0% +you would see that o f is + + + align:start position:0% +you would see that o f is +the 1 1 2 direction that that's how you + + align:start position:0% +the 1 1 2 direction that that's how you + + + align:start position:0% +the 1 1 2 direction that that's how you +would write the o + + align:start position:0% +would write the o + + + align:start position:0% +would write the o +f vector right because you go a half a + + align:start position:0% +f vector right because you go a half a + + + align:start position:0% +f vector right because you go a half a +half + + align:start position:0% +half + + + align:start position:0% +half +a half a half and then and and one but + + align:start position:0% +a half a half and then and and one but + + + align:start position:0% +a half a half and then and and one but +they don't like the half so you multiply + + align:start position:0% +they don't like the half so you multiply + + + align:start position:0% +they don't like the half so you multiply +through by two you get the one one two + + align:start position:0% +through by two you get the one one two + + + align:start position:0% +through by two you get the one one two +right these are vectors and crystals now + + align:start position:0% +right these are vectors and crystals now + + + align:start position:0% +right these are vectors and crystals now +there are uh equivalences here because + + align:start position:0% +there are uh equivalences here because + + + align:start position:0% +there are uh equivalences here because +this is a cubic lattice + + align:start position:0% +this is a cubic lattice + + + align:start position:0% +this is a cubic lattice +right so you know if i look at this and + + align:start position:0% +right so you know if i look at this and + + + align:start position:0% +right so you know if i look at this and +say well + + align:start position:0% +say well + + + align:start position:0% +say well +okay if i went this way and i went that + + align:start position:0% +okay if i went this way and i went that + + + align:start position:0% +okay if i went this way and i went that +way where i wind up are equivalent + + align:start position:0% +way where i wind up are equivalent + + + align:start position:0% +way where i wind up are equivalent +points + + align:start position:0% +points + + + align:start position:0% +points +right where i wind up is is is + + align:start position:0% +right where i wind up is is is + + + align:start position:0% +right where i wind up is is is +you know you're winding up at the same + + align:start position:0% +you know you're winding up at the same + + + align:start position:0% +you know you're winding up at the same +place in a way in the crystal because + + align:start position:0% +place in a way in the crystal because + + + align:start position:0% +place in a way in the crystal because +the definition of that stamp in a cubic + + align:start position:0% +the definition of that stamp in a cubic + + + align:start position:0% +the definition of that stamp in a cubic +lattice is that those are all equivalent + + align:start position:0% +lattice is that those are all equivalent + + + align:start position:0% +lattice is that those are all equivalent +it doesn't matter what's on your basis + + align:start position:0% +it doesn't matter what's on your basis + + + align:start position:0% +it doesn't matter what's on your basis +right + + align:start position:0% +right + + + align:start position:0% +right +because it's defined by the bravais + + align:start position:0% +because it's defined by the bravais + + + align:start position:0% +because it's defined by the bravais +lattice + + align:start position:0% +lattice + + + align:start position:0% +lattice +that's the stamp okay so so we have a + + align:start position:0% +that's the stamp okay so so we have a + + + align:start position:0% +that's the stamp okay so so we have a +way of writing that too right so if i + + align:start position:0% +way of writing that too right so if i + + + align:start position:0% +way of writing that too right so if i +were to take so so the 101 that's the + + align:start position:0% +were to take so so the 101 that's the + + + align:start position:0% +were to take so so the 101 that's the +101 direction in the 110 direction + + align:start position:0% +101 direction in the 110 direction + + + align:start position:0% +101 direction in the 110 direction +cool um if i make it a little simpler + + align:start position:0% +cool um if i make it a little simpler + + + align:start position:0% +cool um if i make it a little simpler +you know i can say that the 100 + + align:start position:0% +you know i can say that the 100 + + + align:start position:0% +you know i can say that the 100 +and the 0.10 + + align:start position:0% +and the 0.10 + + + align:start position:0% +and the 0.10 +and the 001 oh let's do them all + + align:start position:0% +and the 001 oh let's do them all + + + align:start position:0% +and the 001 oh let's do them all +and the one bar ooh + + align:start position:0% +and the one bar ooh + + + align:start position:0% +and the one bar ooh +and the o1 bar o + + align:start position:0% +and the o1 bar o + + + align:start position:0% +and the o1 bar o +and the 001 bar all get me to equivalent + + align:start position:0% +and the 001 bar all get me to equivalent + + + align:start position:0% +and the 001 bar all get me to equivalent +places + + align:start position:0% +places + + + align:start position:0% +places +and we can call this a family just + + align:start position:0% +and we can call this a family just + + + align:start position:0% +and we can call this a family just +because we don't want to keep + + align:start position:0% +because we don't want to keep + + + align:start position:0% +because we don't want to keep +writing them if they're all equivalent + + align:start position:0% +writing them if they're all equivalent + + + align:start position:0% +writing them if they're all equivalent +we can we can say this is a family + + align:start position:0% +we can we can say this is a family + + + align:start position:0% +we can we can say this is a family +of directions and you got to be careful + + align:start position:0% +of directions and you got to be careful + + + align:start position:0% +of directions and you got to be careful +here + + align:start position:0% +here + + + align:start position:0% +here +because you can't use a bracket anymore + + align:start position:0% +because you can't use a bracket anymore + + + align:start position:0% +because you can't use a bracket anymore +because it would just be one of the + + align:start position:0% +because it would just be one of the + + + align:start position:0% +because it would just be one of the +directions instead + + align:start position:0% +directions instead + + + align:start position:0% +directions instead +we use uh sorry you can't yeah you can't + + align:start position:0% +we use uh sorry you can't yeah you can't + + + align:start position:0% +we use uh sorry you can't yeah you can't +use a square bracket instead we use this + + align:start position:0% +use a square bracket instead we use this + + + align:start position:0% +use a square bracket instead we use this +kind of bracket + + align:start position:0% +kind of bracket + + + align:start position:0% +kind of bracket +and we say it's the 100 family + + align:start position:0% +and we say it's the 100 family + + + align:start position:0% +and we say it's the 100 family +so if you see a direction written with + + align:start position:0% +so if you see a direction written with + + + align:start position:0% +so if you see a direction written with +brackets like that + + align:start position:0% +brackets like that + + + align:start position:0% +brackets like that +but then it means all of these + + align:start position:0% +but then it means all of these + + + align:start position:0% +but then it means all of these +directions + + align:start position:0% +directions + + + align:start position:0% +directions +this family of directions right but if + + align:start position:0% +this family of directions right but if + + + align:start position:0% +this family of directions right but if +you see it written with a bracket like + + align:start position:0% +you see it written with a bracket like + + + align:start position:0% +you see it written with a bracket like +this + + align:start position:0% +this + + + align:start position:0% +this +it means that one vector okay + + align:start position:0% +it means that one vector okay + + + align:start position:0% +it means that one vector okay +crystallographers you got to keep them + + align:start position:0% +crystallographers you got to keep them + + + align:start position:0% +crystallographers you got to keep them +happy you got to keep them happy + + align:start position:0% +happy you got to keep them happy + + + align:start position:0% +happy you got to keep them happy +all right now that is + + align:start position:0% +all right now that is + + + align:start position:0% +all right now that is +directions that is direction + + align:start position:0% +directions that is direction + + + align:start position:0% +directions that is direction +but what about cuts what about planes + + align:start position:0% +but what about cuts what about planes + + + align:start position:0% +but what about cuts what about planes +so we've got our vectors now we need our + + align:start position:0% +so we've got our vectors now we need our + + + align:start position:0% +so we've got our vectors now we need our +cuts we got to be able to specify these + + align:start position:0% +cuts we got to be able to specify these + + + align:start position:0% +cuts we got to be able to specify these +things + + align:start position:0% +things + + + align:start position:0% +things +and you know as we'll see + + align:start position:0% +and you know as we'll see + + + align:start position:0% +and you know as we'll see +as we'll see the the properties + + align:start position:0% +as we'll see the the properties + + + align:start position:0% +as we'll see the the properties +of of of materials of crystals + + align:start position:0% +of of of materials of crystals + + + align:start position:0% +of of of materials of crystals +especially the more anisotropic they are + + align:start position:0% +especially the more anisotropic they are + + + align:start position:0% +especially the more anisotropic they are +depend very heavily + + align:start position:0% +depend very heavily + + + align:start position:0% +depend very heavily +on what's in what direction right + + align:start position:0% +on what's in what direction right + + + align:start position:0% +on what's in what direction right +so for example if i have a plane in a + + align:start position:0% +so for example if i have a plane in a + + + align:start position:0% +so for example if i have a plane in a +crystal + + align:start position:0% +crystal + + + align:start position:0% +crystal +that doesn't have a high density of + + align:start position:0% +that doesn't have a high density of + + + align:start position:0% +that doesn't have a high density of +atoms and then i got another plane + + align:start position:0% +atoms and then i got another plane + + + align:start position:0% +atoms and then i got another plane +that's got a lot of density of atoms in + + align:start position:0% +that's got a lot of density of atoms in + + + align:start position:0% +that's got a lot of density of atoms in +that plane + + align:start position:0% +that plane + + + align:start position:0% +that plane +well you might expect those to have + + align:start position:0% +well you might expect those to have + + + align:start position:0% +well you might expect those to have +different responses + + align:start position:0% +different responses + + + align:start position:0% +different responses +to for example mechanical stress strain + + align:start position:0% +to for example mechanical stress strain + + + align:start position:0% +to for example mechanical stress strain +right let's say you push it you pull it + + align:start position:0% +right let's say you push it you pull it + + + align:start position:0% +right let's say you push it you pull it +you break it you hammer it + + align:start position:0% +you break it you hammer it + + + align:start position:0% +you break it you hammer it +maybe one of those planes if it doesn't + + align:start position:0% +maybe one of those planes if it doesn't + + + align:start position:0% +maybe one of those planes if it doesn't +have as many bonds in it + + align:start position:0% +have as many bonds in it + + + align:start position:0% +have as many bonds in it +right mike might break first this is one + + align:start position:0% +right mike might break first this is one + + + align:start position:0% +right mike might break first this is one +example so + + align:start position:0% +example so + + + align:start position:0% +example so +we got to know how to talk about these + + align:start position:0% +we got to know how to talk about these + + + align:start position:0% +we got to know how to talk about these +things we got to know how to talk about + + align:start position:0% +things we got to know how to talk about + + + align:start position:0% +things we got to know how to talk about +these things + + align:start position:0% +these things + + + align:start position:0% +these things +okay so now with planes i have another + + align:start position:0% +okay so now with planes i have another + + + align:start position:0% +okay so now with planes i have another +recipe + + align:start position:0% +recipe + + + align:start position:0% +recipe +to make crystallographers happy + + align:start position:0% +to make crystallographers happy + + + align:start position:0% +to make crystallographers happy +okay now first read off intersect oh + + align:start position:0% +okay now first read off intersect oh + + + align:start position:0% +okay now first read off intersect oh +well let's put an example up + + align:start position:0% +well let's put an example up + + + align:start position:0% +well let's put an example up +so i've got an example i'll do a few and + + align:start position:0% +so i've got an example i'll do a few and + + + align:start position:0% +so i've got an example i'll do a few and +then as always + + align:start position:0% +then as always + + + align:start position:0% +then as always +you guys need to do more to practice + + align:start position:0% +you guys need to do more to practice + + + align:start position:0% +you guys need to do more to practice +right so i'll do a few + + align:start position:0% +right so i'll do a few + + + align:start position:0% +right so i'll do a few +so i'm going to draw a plane and i'm + + align:start position:0% +so i'm going to draw a plane and i'm + + + align:start position:0% +so i'm going to draw a plane and i'm +going to make it a nice + + align:start position:0% +going to make it a nice + + + align:start position:0% +going to make it a nice +simple one here's my these are my axes x + + align:start position:0% +simple one here's my these are my axes x + + + align:start position:0% +simple one here's my these are my axes x +y z and i'm going to draw my + + align:start position:0% +y z and i'm going to draw my + + + align:start position:0% +y z and i'm going to draw my +cubic crystal my cubic unit cell sorry + + align:start position:0% +cubic crystal my cubic unit cell sorry + + + align:start position:0% +cubic crystal my cubic unit cell sorry +okay here we go and almost + + align:start position:0% +okay here we go and almost + + + align:start position:0% +okay here we go and almost +a cube okay now + + align:start position:0% +a cube okay now + + + align:start position:0% +a cube okay now +i want to take a plane here i'm going to + + align:start position:0% +i want to take a plane here i'm going to + + + align:start position:0% +i want to take a plane here i'm going to +take this top one so i'm going to take + + align:start position:0% +take this top one so i'm going to take + + + align:start position:0% +take this top one so i'm going to take +this + + align:start position:0% +this + + + align:start position:0% +this +and i'm going to go through those i want + + align:start position:0% +and i'm going to go through those i want + + + align:start position:0% +and i'm going to go through those i want +to know how do i describe that plane + + align:start position:0% +to know how do i describe that plane + + + align:start position:0% +to know how do i describe that plane +that cuts that way + + align:start position:0% +that cuts that way + + + align:start position:0% +that cuts that way +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +one these correspond to those crystal + + align:start position:0% +one these correspond to those crystal + + + align:start position:0% +one these correspond to those crystal +plane algorithm + + align:start position:0% +plane algorithm + + + align:start position:0% +plane algorithm +algorithm i hear a few of you + + align:start position:0% +algorithm i hear a few of you + + + align:start position:0% +algorithm i hear a few of you +like algorithms and computing of course + + align:start position:0% +like algorithms and computing of course + + + align:start position:0% +like algorithms and computing of course +six + + align:start position:0% +six + + + align:start position:0% +six +and so we got one whistle + + align:start position:0% +and so we got one whistle + + + align:start position:0% +and so we got one whistle +so here's the thing if i have a plane + + align:start position:0% +so here's the thing if i have a plane + + + align:start position:0% +so here's the thing if i have a plane +like this + + align:start position:0% +like this + + + align:start position:0% +like this +and i ask you where does it intercept + + align:start position:0% +and i ask you where does it intercept + + + align:start position:0% +and i ask you where does it intercept +where does it intercept the axis right + + align:start position:0% +where does it intercept the axis right + + + align:start position:0% +where does it intercept the axis right +well it's never going to intercept the x + + align:start position:0% +well it's never going to intercept the x + + + align:start position:0% +well it's never going to intercept the x +and y + + align:start position:0% +and y + + + align:start position:0% +and y +axes never + + align:start position:0% + + + + align:start position:0% + +it's never going to intercept them no + + align:start position:0% +it's never going to intercept them no + + + align:start position:0% +it's never going to intercept them no +matter what i do + + align:start position:0% +matter what i do + + + align:start position:0% +matter what i do +you say but what if i put it in the x y + + align:start position:0% +you say but what if i put it in the x y + + + align:start position:0% +you say but what if i put it in the x y +plane then it's it's always intercept no + + align:start position:0% +plane then it's it's always intercept no + + + align:start position:0% +plane then it's it's always intercept no +that's not what we mean by + + align:start position:0% +that's not what we mean by + + + align:start position:0% +that's not what we mean by +intercept right what i mean by intercept + + align:start position:0% +intercept right what i mean by intercept + + + align:start position:0% +intercept right what i mean by intercept +is + + align:start position:0% +is + + + align:start position:0% +is +it has to reach them eventually no + + align:start position:0% +it has to reach them eventually no + + + align:start position:0% +it has to reach them eventually no +matter where it is + + align:start position:0% +matter where it is + + + align:start position:0% +matter where it is +no matter where i position it it's got + + align:start position:0% +no matter where i position it it's got + + + align:start position:0% +no matter where i position it it's got +it but this never does + + align:start position:0% +it but this never does + + + align:start position:0% +it but this never does +this never does right and so the the + + align:start position:0% +this never does right and so the the + + + align:start position:0% +this never does right and so the the +intercepts + + align:start position:0% +intercepts + + + align:start position:0% +intercepts +you know for for the the the abc + + align:start position:0% +you know for for the the the abc + + + align:start position:0% +you know for for the the the abc +intercepts so we can write those here a + + align:start position:0% +intercepts so we can write those here a + + + align:start position:0% +intercepts so we can write those here a +okay i'll write the same way x y z + + align:start position:0% +okay i'll write the same way x y z + + + align:start position:0% +okay i'll write the same way x y z +intercepts + + align:start position:0% +intercepts + + + align:start position:0% +intercepts +it's infinite and it's infinite + + align:start position:0% +it's infinite and it's infinite + + + align:start position:0% +it's infinite and it's infinite +all right and then for the for the z + + align:start position:0% +all right and then for the for the z + + + align:start position:0% +all right and then for the for the z +okay here + + align:start position:0% +okay here + + + align:start position:0% +okay here +i'm intercepting at this at this part of + + align:start position:0% +i'm intercepting at this at this part of + + + align:start position:0% +i'm intercepting at this at this part of +z + + align:start position:0% +z + + + align:start position:0% +z +so i'm intercepting at one but the thing + + align:start position:0% +so i'm intercepting at one but the thing + + + align:start position:0% +so i'm intercepting at one but the thing +is oh + + align:start position:0% +is oh + + + align:start position:0% +is oh +man crystallographers don't like + + align:start position:0% +man crystallographers don't like + + + align:start position:0% +man crystallographers don't like +infinity either + + align:start position:0% +infinity either + + + align:start position:0% +infinity either +they don't and so what they do is they + + align:start position:0% +they don't and so what they do is they + + + align:start position:0% +they don't and so what they do is they +just take one over + + align:start position:0% +just take one over + + + align:start position:0% +just take one over +that's a nice way to fix infinity and so + + align:start position:0% +that's a nice way to fix infinity and so + + + align:start position:0% +that's a nice way to fix infinity and so +step two this would become zero zero + + align:start position:0% +step two this would become zero zero + + + align:start position:0% +step two this would become zero zero +and one over one is one right + + align:start position:0% +and one over one is one right + + + align:start position:0% +and one over one is one right +one over infinity is zero + + align:start position:0% +one over infinity is zero + + + align:start position:0% +one over infinity is zero +now we reduce to integer values and that + + align:start position:0% +now we reduce to integer values and that + + + align:start position:0% +now we reduce to integer values and that +there's no work to do there and then + + align:start position:0% +there's no work to do there and then + + + align:start position:0% +there's no work to do there and then +we are very careful about this + + align:start position:0% +we are very careful about this + + + align:start position:0% +we are very careful about this +we use parentheses no more brackets + + align:start position:0% +we use parentheses no more brackets + + + align:start position:0% +we use parentheses no more brackets +parentheses do not get this + + align:start position:0% +parentheses do not get this + + + align:start position:0% +parentheses do not get this +wrong because you you might be talking + + align:start position:0% +wrong because you you might be talking + + + align:start position:0% +wrong because you you might be talking +about a vector + + align:start position:0% +about a vector + + + align:start position:0% +about a vector +by accident you don't want to talk about + + align:start position:0% +by accident you don't want to talk about + + + align:start position:0% +by accident you don't want to talk about +a vector by accident so this is the zero + + align:start position:0% +a vector by accident so this is the zero + + + align:start position:0% +a vector by accident so this is the zero +zero one plane no commas + + align:start position:0% +zero one plane no commas + + + align:start position:0% +zero one plane no commas +remember the dislike of commas + + align:start position:0% + + + + align:start position:0% + +it's the zero zero one plane in this + + align:start position:0% +it's the zero zero one plane in this + + + align:start position:0% +it's the zero zero one plane in this +crystal + + align:start position:0% +crystal + + + align:start position:0% +crystal +that is a cut okay good and that's + + align:start position:0% +that is a cut okay good and that's + + + align:start position:0% +that is a cut okay good and that's +called a miller plane + + align:start position:0% +called a miller plane + + + align:start position:0% +called a miller plane +well if i if i do another example do one + + align:start position:0% +well if i if i do another example do one + + + align:start position:0% +well if i if i do another example do one +more + + align:start position:0% +more + + + align:start position:0% +more +and so that is + + align:start position:0% +and so that is + + + align:start position:0% +and so that is +that is this one i have it i've got a + + align:start position:0% +that is this one i have it i've got a + + + align:start position:0% +that is this one i have it i've got a +bunch of examples here + + align:start position:0% +bunch of examples here + + + align:start position:0% +bunch of examples here +and they can draw it you know better + + align:start position:0% +and they can draw it you know better + + + align:start position:0% +and they can draw it you know better +with the shading and stuff there but you + + align:start position:0% +with the shading and stuff there but you + + + align:start position:0% +with the shading and stuff there but you +see that's what we just did we did the + + align:start position:0% +see that's what we just did we did the + + + align:start position:0% +see that's what we just did we did the +001 plane that one there right + + align:start position:0% +001 plane that one there right + + + align:start position:0% +001 plane that one there right +there it is nice and big the 001 plane + + align:start position:0% +there it is nice and big the 001 plane + + + align:start position:0% +there it is nice and big the 001 plane +uh what what about that one that's the + + align:start position:0% +uh what what about that one that's the + + + align:start position:0% +uh what what about that one that's the +1-1-0 + + align:start position:0% + + + + align:start position:0% + +the 1-1-0 if you if you do the 1-1-0 + + align:start position:0% +the 1-1-0 if you if you do the 1-1-0 + + + align:start position:0% +the 1-1-0 if you if you do the 1-1-0 +1-1-0 i'm not going to try to draw it + + align:start position:0% +1-1-0 i'm not going to try to draw it + + + align:start position:0% +1-1-0 i'm not going to try to draw it +again what you get is + + align:start position:0% +again what you get is + + + align:start position:0% +again what you get is +step one you get one + + align:start position:0% +step one you get one + + + align:start position:0% +step one you get one +one infinity step two you get one + + align:start position:0% +one infinity step two you get one + + + align:start position:0% +one infinity step two you get one +one zero step three you get one one + + align:start position:0% +one zero step three you get one one + + + align:start position:0% +one zero step three you get one one +zero and step four you get one one zero + + align:start position:0% +zero and step four you get one one zero + + + align:start position:0% +zero and step four you get one one zero +those are the steps to identifying and + + align:start position:0% +those are the steps to identifying and + + + align:start position:0% +those are the steps to identifying and +labeling a crystal plane + + align:start position:0% +labeling a crystal plane + + + align:start position:0% +labeling a crystal plane +let's make it a little more complicated + + align:start position:0% +let's make it a little more complicated + + + align:start position:0% +let's make it a little more complicated +see you know we still haven't really + + align:start position:0% +see you know we still haven't really + + + align:start position:0% +see you know we still haven't really +done + + align:start position:0% +done + + + align:start position:0% +done +something where we take advantage of the + + align:start position:0% +something where we take advantage of the + + + align:start position:0% +something where we take advantage of the +rule + + align:start position:0% +rule + + + align:start position:0% +rule +of step three so let's make it harder + + align:start position:0% +of step three so let's make it harder + + + align:start position:0% +of step three so let's make it harder +let's bump it up + + align:start position:0% +let's bump it up + + + align:start position:0% +let's bump it up +so there's a slice remember i can slice + + align:start position:0% +so there's a slice remember i can slice + + + align:start position:0% +so there's a slice remember i can slice +the crystal + + align:start position:0% +the crystal + + + align:start position:0% +the crystal +in any way i want and i got to be able + + align:start position:0% +in any way i want and i got to be able + + + align:start position:0% +in any way i want and i got to be able +to write it down i got to be able to + + align:start position:0% +to write it down i got to be able to + + + align:start position:0% +to write it down i got to be able to +represent it + + align:start position:0% +represent it + + + align:start position:0% +represent it +on paper that's what this is about + + align:start position:0% +on paper that's what this is about + + + align:start position:0% +on paper that's what this is about +that's what the miller indices and the + + align:start position:0% +that's what the miller indices and the + + + align:start position:0% +that's what the miller indices and the +miller planes + + align:start position:0% +miller planes + + + align:start position:0% +miller planes +let us do okay well so this one i'm + + align:start position:0% +let us do okay well so this one i'm + + + align:start position:0% +let us do okay well so this one i'm +going to try to draw so + + align:start position:0% +going to try to draw so + + + align:start position:0% +going to try to draw so +so here i've got my axes and that's y + + align:start position:0% +so here i've got my axes and that's y + + + align:start position:0% +so here i've got my axes and that's y +and that's x and that's z here we go + + align:start position:0% +and that's x and that's z here we go + + + align:start position:0% +and that's x and that's z here we go +okay + + align:start position:0% + + + + align:start position:0% + +oh it's almost a cube now i've gone up + + align:start position:0% +oh it's almost a cube now i've gone up + + + align:start position:0% +oh it's almost a cube now i've gone up +here to three quarters high so i've gone + + align:start position:0% +here to three quarters high so i've gone + + + align:start position:0% +here to three quarters high so i've gone +up about three quarters there + + align:start position:0% +up about three quarters there + + + align:start position:0% +up about three quarters there +i've gone here to a half that's a half + + align:start position:0% +i've gone here to a half that's a half + + + align:start position:0% +i've gone here to a half that's a half +right of of the cell length this is + + align:start position:0% +right of of the cell length this is + + + align:start position:0% +right of of the cell length this is +three quarters + + align:start position:0% +three quarters + + + align:start position:0% +three quarters +of the cell length and then over i've + + align:start position:0% +of the cell length and then over i've + + + align:start position:0% +of the cell length and then over i've +gone all the way to one + + align:start position:0% +gone all the way to one + + + align:start position:0% +gone all the way to one +so now if i go through my steps on this + + align:start position:0% +so now if i go through my steps on this + + + align:start position:0% +so now if i go through my steps on this +one i've got + + align:start position:0% +one i've got + + + align:start position:0% +one i've got +a half and i've got one + + align:start position:0% +a half and i've got one + + + align:start position:0% +a half and i've got one +and i've got three quarters okay i'm + + align:start position:0% +and i've got three quarters okay i'm + + + align:start position:0% +and i've got three quarters okay i'm +gonna take the reciprocals + + align:start position:0% +gonna take the reciprocals + + + align:start position:0% +gonna take the reciprocals +okay that becomes two one four-thirds + + align:start position:0% +okay that becomes two one four-thirds + + + align:start position:0% +okay that becomes two one four-thirds +oh not happy yet + + align:start position:0% +oh not happy yet + + + align:start position:0% +oh not happy yet +not happy yet we don't like fractions we + + align:start position:0% +not happy yet we don't like fractions we + + + align:start position:0% +not happy yet we don't like fractions we +got to get rid of fractions so in step + + align:start position:0% +got to get rid of fractions so in step + + + align:start position:0% +got to get rid of fractions so in step +three + + align:start position:0% +three + + + align:start position:0% +three +we simply multiply through by three and + + align:start position:0% +we simply multiply through by three and + + + align:start position:0% +we simply multiply through by three and +we get + + align:start position:0% +we get + + + align:start position:0% +we get +six three uh four + + align:start position:0% +six three uh four + + + align:start position:0% +six three uh four +and then we can write down that plane + + align:start position:0% +and then we can write down that plane + + + align:start position:0% +and then we can write down that plane +that is this six + + align:start position:0% +that is this six + + + align:start position:0% +that is this six +three four plane okay + + align:start position:0% +three four plane okay + + + align:start position:0% +three four plane okay +and so on and so on now + + align:start position:0% +and so on and so on now + + + align:start position:0% +and so on and so on now +let's go back to let me erase this + + align:start position:0% +let's go back to let me erase this + + + align:start position:0% +let's go back to let me erase this +there's a couple things about + + align:start position:0% +there's a couple things about + + + align:start position:0% +there's a couple things about +the planes that once we know what the + + align:start position:0% +the planes that once we know what the + + + align:start position:0% +the planes that once we know what the +plane is + + align:start position:0% +plane is + + + align:start position:0% +plane is +we know some other things about it okay + + align:start position:0% +we know some other things about it okay + + + align:start position:0% +we know some other things about it okay +so let's talk about that now + + align:start position:0% + + + + align:start position:0% + +all right if i + + align:start position:0% + + + + align:start position:0% + +first of all + + align:start position:0% + + + + align:start position:0% + +a miller plane is not just one plane a + + align:start position:0% +a miller plane is not just one plane a + + + align:start position:0% +a miller plane is not just one plane a +miller plane is not just one plane + + align:start position:0% +miller plane is not just one plane + + + align:start position:0% +miller plane is not just one plane +a miller plane is an infinite set of + + align:start position:0% +a miller plane is an infinite set of + + + align:start position:0% +a miller plane is an infinite set of +planes + + align:start position:0% +planes + + + align:start position:0% +planes +okay so when i say a miller plane + + align:start position:0% + + + + align:start position:0% + +well very often + + align:start position:0% +well very often + + + align:start position:0% +well very often +what you do is what we've been doing + + align:start position:0% +what you do is what we've been doing + + + align:start position:0% +what you do is what we've been doing +right you know + + align:start position:0% +right you know + + + align:start position:0% +right you know +which is you define the plane that's + + align:start position:0% +which is you define the plane that's + + + align:start position:0% +which is you define the plane that's +kind of closest somehow to the origin + + align:start position:0% +kind of closest somehow to the origin + + + align:start position:0% +kind of closest somehow to the origin +right in the unit cell the one that cuts + + align:start position:0% +right in the unit cell the one that cuts + + + align:start position:0% +right in the unit cell the one that cuts +it you define it that way + + align:start position:0% +it you define it that way + + + align:start position:0% +it you define it that way +but actually what miller planes are + + align:start position:0% +but actually what miller planes are + + + align:start position:0% +but actually what miller planes are +infinite sets of planes + + align:start position:0% +infinite sets of planes + + + align:start position:0% +infinite sets of planes +and so i'm gonna put now i'm not a + + align:start position:0% +and so i'm gonna put now i'm not a + + + align:start position:0% +and so i'm gonna put now i'm not a +crystallographer + + align:start position:0% +crystallographer + + + align:start position:0% +crystallographer +so i can write infinity i'm okay with + + align:start position:0% +so i can write infinity i'm okay with + + + align:start position:0% +so i can write infinity i'm okay with +that + + align:start position:0% +that + + + align:start position:0% +that +it's an infinite set of planes + + align:start position:0% +it's an infinite set of planes + + + align:start position:0% +it's an infinite set of planes +okay they are equally spaced + + align:start position:0% +okay they are equally spaced + + + align:start position:0% +okay they are equally spaced +equally spaced + + align:start position:0% +equally spaced + + + align:start position:0% +equally spaced +and here's the key one should always be + + align:start position:0% +and here's the key one should always be + + + align:start position:0% +and here's the key one should always be +going through the origin if you want to + + align:start position:0% +going through the origin if you want to + + + align:start position:0% +going through the origin if you want to +look at it as a set of planes + + align:start position:0% +look at it as a set of planes + + + align:start position:0% +look at it as a set of planes +you got to put one at the origin that + + align:start position:0% +you got to put one at the origin that + + + align:start position:0% +you got to put one at the origin that +will help you think through + + align:start position:0% +will help you think through + + + align:start position:0% +will help you think through +what i mean okay so + + align:start position:0% +what i mean okay so + + + align:start position:0% +what i mean okay so +so if if one + + align:start position:0% +so if if one + + + align:start position:0% +so if if one +goes through the origin + + align:start position:0% + + + + align:start position:0% + +then what you see right away + + align:start position:0% + + + + align:start position:0% + +is how they repeat and because you know + + align:start position:0% +is how they repeat and because you know + + + align:start position:0% +is how they repeat and because you know +it's not just that i go in in that case + + align:start position:0% +it's not just that i go in in that case + + + align:start position:0% +it's not just that i go in in that case +you know let's take that one okay the + + align:start position:0% +you know let's take that one okay the + + + align:start position:0% +you know let's take that one okay the +001. + + align:start position:0% +001. + + + align:start position:0% +001. +now you say where's the next one in this + + align:start position:0% +now you say where's the next one in this + + + align:start position:0% +now you say where's the next one in this +infinite set of planes + + align:start position:0% +infinite set of planes + + + align:start position:0% +infinite set of planes +okay we'll put that one at the origin + + align:start position:0% +okay we'll put that one at the origin + + + align:start position:0% +okay we'll put that one at the origin +and make another one + + align:start position:0% +and make another one + + + align:start position:0% +and make another one +then put that one at the origin again + + align:start position:0% +then put that one at the origin again + + + align:start position:0% +then put that one at the origin again +and make another one that's how to think + + align:start position:0% +and make another one that's how to think + + + align:start position:0% +and make another one that's how to think +about this infinite set + + align:start position:0% +about this infinite set + + + align:start position:0% +about this infinite set +of planes okay but so if i if i had one + + align:start position:0% +of planes okay but so if i if i had one + + + align:start position:0% +of planes okay but so if i if i had one +that went halfway + + align:start position:0% +that went halfway + + + align:start position:0% +that went halfway +a 200 plane or an 02 plane + + align:start position:0% +a 200 plane or an 02 plane + + + align:start position:0% +a 200 plane or an 02 plane +as it would be if it's properly noted + + align:start position:0% +as it would be if it's properly noted + + + align:start position:0% +as it would be if it's properly noted +with miller indices + + align:start position:0% +with miller indices + + + align:start position:0% +with miller indices +well then you say well okay i've got one + + align:start position:0% +well then you say well okay i've got one + + + align:start position:0% +well then you say well okay i've got one +halfway + + align:start position:0% +halfway + + + align:start position:0% +halfway +you know isn't that it no the set of + + align:start position:0% +you know isn't that it no the set of + + + align:start position:0% +you know isn't that it no the set of +infinite planes + + align:start position:0% +infinite planes + + + align:start position:0% +infinite planes +also would have one at the origin one + + align:start position:0% +also would have one at the origin one + + + align:start position:0% +also would have one at the origin one +halfway one at the top + + align:start position:0% +halfway one at the top + + + align:start position:0% +halfway one at the top +because each time you put it back and + + align:start position:0% +because each time you put it back and + + + align:start position:0% +because each time you put it back and +you do your next one that's how to think + + align:start position:0% +you do your next one that's how to think + + + align:start position:0% +you do your next one that's how to think +about this + + align:start position:0% +about this + + + align:start position:0% +about this +infinite set of miller planes + + align:start position:0% +infinite set of miller planes + + + align:start position:0% +infinite set of miller planes +so you get you get this infinite set of + + align:start position:0% +so you get you get this infinite set of + + + align:start position:0% +so you get you get this infinite set of +planes + + align:start position:0% +planes + + + align:start position:0% +planes +that have i'm going to go to this + + align:start position:0% +that have i'm going to go to this + + + align:start position:0% +that have i'm going to go to this +picture okay + + align:start position:0% +picture okay + + + align:start position:0% +picture okay +there it is a 100 that just go on + + align:start position:0% +there it is a 100 that just go on + + + align:start position:0% +there it is a 100 that just go on +forever + + align:start position:0% +forever + + + align:start position:0% +forever +those are the miller planes and and what + + align:start position:0% +those are the miller planes and and what + + + align:start position:0% +those are the miller planes and and what +they have is a spacing between them and + + align:start position:0% +they have is a spacing between them and + + + align:start position:0% +they have is a spacing between them and +this + + align:start position:0% +this + + + align:start position:0% +this +is really important so this is the next + + align:start position:0% +is really important so this is the next + + + align:start position:0% +is really important so this is the next +thing i want to tell you + + align:start position:0% +thing i want to tell you + + + align:start position:0% +thing i want to tell you +right so i've got so a miller plane + + align:start position:0% +right so i've got so a miller plane + + + align:start position:0% +right so i've got so a miller plane +isn't just one it's infinite + + align:start position:0% +isn't just one it's infinite + + + align:start position:0% +isn't just one it's infinite +it's an infinite number of them and + + align:start position:0% +it's an infinite number of them and + + + align:start position:0% +it's an infinite number of them and +what that means is that when i give you + + align:start position:0% +what that means is that when i give you + + + align:start position:0% +what that means is that when i give you +when i give you this + + align:start position:0% +when i give you this + + + align:start position:0% +when i give you this +right or that or any + + align:start position:0% +right or that or any + + + align:start position:0% +right or that or any +miller plane i know what the spacing is + + align:start position:0% +miller plane i know what the spacing is + + + align:start position:0% +miller plane i know what the spacing is +between them + + align:start position:0% +between them + + + align:start position:0% +between them +that is enough information because + + align:start position:0% + + + + align:start position:0% + +the distance between planes + + align:start position:0% + + + + align:start position:0% + +right is + + align:start position:0% + + + + align:start position:0% + +actually here it's very easy to see the + + align:start position:0% +actually here it's very easy to see the + + + align:start position:0% +actually here it's very easy to see the +distance between these planes + + align:start position:0% +distance between these planes + + + align:start position:0% +distance between these planes +is a but the distance between the two oo + + align:start position:0% +is a but the distance between the two oo + + + align:start position:0% +is a but the distance between the two oo +planes + + align:start position:0% +planes + + + align:start position:0% +planes +is a over two + + align:start position:0% + + + + align:start position:0% + +and in fact for a cubic cell there's a + + align:start position:0% +and in fact for a cubic cell there's a + + + align:start position:0% +and in fact for a cubic cell there's a +formula that you can use for + + align:start position:0% +formula that you can use for + + + align:start position:0% +formula that you can use for +any two planes the distance between + + align:start position:0% +any two planes the distance between + + + align:start position:0% +any two planes the distance between +well let's say i'll i'll write the + + align:start position:0% +well let's say i'll i'll write the + + + align:start position:0% +well let's say i'll i'll write the +notation first but the distance + + align:start position:0% +notation first but the distance + + + align:start position:0% +notation first but the distance +and the plane there is + + align:start position:0% +and the plane there is + + + align:start position:0% +and the plane there is +equal to a and the distance of a 200 + + align:start position:0% +equal to a and the distance of a 200 + + + align:start position:0% +equal to a and the distance of a 200 +plane between planes is equal to a over + + align:start position:0% +plane between planes is equal to a over + + + align:start position:0% +plane between planes is equal to a over + + align:start position:0% + + + align:start position:0% +but there's a general formula of any + + align:start position:0% +but there's a general formula of any + + + align:start position:0% +but there's a general formula of any +h k l h k l the miller indices + + align:start position:0% +h k l h k l the miller indices + + + align:start position:0% +h k l h k l the miller indices +those are just variables but if those + + align:start position:0% +those are just variables but if those + + + align:start position:0% +those are just variables but if those +are the variables of the miller plane + + align:start position:0% +are the variables of the miller plane + + + align:start position:0% +are the variables of the miller plane +then the distance between two of them is + + align:start position:0% +then the distance between two of them is + + + align:start position:0% +then the distance between two of them is +this the length of the edge of the unit + + align:start position:0% +this the length of the edge of the unit + + + align:start position:0% +this the length of the edge of the unit +cell a + + align:start position:0% +cell a + + + align:start position:0% +cell a +divided by the square root of the + + align:start position:0% +divided by the square root of the + + + align:start position:0% +divided by the square root of the +squares + + align:start position:0% +squares + + + align:start position:0% +squares +added together h squared plus k squared + + align:start position:0% + + + + align:start position:0% + +plus l squared okay h squared plus k + + align:start position:0% +plus l squared okay h squared plus k + + + align:start position:0% +plus l squared okay h squared plus k +here so you see + + align:start position:0% +here so you see + + + align:start position:0% +here so you see +okay if it's 1 0 0 that's a that works + + align:start position:0% +okay if it's 1 0 0 that's a that works + + + align:start position:0% +okay if it's 1 0 0 that's a that works +if it's 2 0 0 a over 2 that works and + + align:start position:0% +if it's 2 0 0 a over 2 that works and + + + align:start position:0% +if it's 2 0 0 a over 2 that works and +it's general + + align:start position:0% +it's general + + + align:start position:0% +it's general +so now just by knowing but because i + + align:start position:0% +so now just by knowing but because i + + + align:start position:0% +so now just by knowing but because i +figured out how to write + + align:start position:0% +figured out how to write + + + align:start position:0% +figured out how to write +a plane in hkl notation i also know + + align:start position:0% +a plane in hkl notation i also know + + + align:start position:0% +a plane in hkl notation i also know +the distance between these infinite + + align:start position:0% +the distance between these infinite + + + align:start position:0% +the distance between these infinite +planes that becomes very very important + + align:start position:0% +planes that becomes very very important + + + align:start position:0% +planes that becomes very very important +once we shine x-rays on crystals next + + align:start position:0% +once we shine x-rays on crystals next + + + align:start position:0% +once we shine x-rays on crystals next +week that becomes very important + + align:start position:0% +week that becomes very important + + + align:start position:0% +week that becomes very important +okay okay so what else can we know + + align:start position:0% +okay okay so what else can we know + + + align:start position:0% +okay okay so what else can we know +from the miller planes okay + + align:start position:0% +from the miller planes okay + + + align:start position:0% +from the miller planes okay +so that's the distance between them and + + align:start position:0% +so that's the distance between them and + + + align:start position:0% +so that's the distance between them and +the other thing + + align:start position:0% +the other thing + + + align:start position:0% +the other thing +that actually becomes fairly + + align:start position:0% +that actually becomes fairly + + + align:start position:0% +that actually becomes fairly +self-evident when you play around with + + align:start position:0% +self-evident when you play around with + + + align:start position:0% +self-evident when you play around with +this a little bit that was on the slide + + align:start position:0% +this a little bit that was on the slide + + + align:start position:0% +this a little bit that was on the slide +before + + align:start position:0% +before + + + align:start position:0% +before +is that the + + align:start position:0% +is that the + + + align:start position:0% +is that the +let's see the uh or thought the plane + + align:start position:0% +let's see the uh or thought the plane + + + align:start position:0% +let's see the uh or thought the plane +and the plane and the direction + + align:start position:0% + + + + align:start position:0% + +with the same + + align:start position:0% + + + + align:start position:0% + +miller indices + + align:start position:0% + + + + align:start position:0% + +our orthogonal + + align:start position:0% + + + + align:start position:0% + +orthogonal orthogonal + + align:start position:0% +orthogonal orthogonal + + + align:start position:0% +orthogonal orthogonal +and you can see this from this very + + align:start position:0% +and you can see this from this very + + + align:start position:0% +and you can see this from this very +simple picture there's the 001 plane + + align:start position:0% +simple picture there's the 001 plane + + + align:start position:0% +simple picture there's the 001 plane +right but that's also the 001 vector + + align:start position:0% +right but that's also the 001 vector + + + align:start position:0% +right but that's also the 001 vector +just as we defined it today so the oo1 + + align:start position:0% +just as we defined it today so the oo1 + + + align:start position:0% +just as we defined it today so the oo1 +plane + + align:start position:0% +plane + + + align:start position:0% +plane +and the 001 vector are orthogonal right + + align:start position:0% +and the 001 vector are orthogonal right + + + align:start position:0% +and the 001 vector are orthogonal right +so this is an example the 001 plane + + align:start position:0% +so this is an example the 001 plane + + + align:start position:0% +so this is an example the 001 plane +is orthogonal to oh and i got to get + + align:start position:0% +is orthogonal to oh and i got to get + + + align:start position:0% +is orthogonal to oh and i got to get +this right + + align:start position:0% +this right + + + align:start position:0% +this right +the 001 vector oh + + align:start position:0% +the 001 vector oh + + + align:start position:0% +the 001 vector oh +no commas brackets parentheses + + align:start position:0% +no commas brackets parentheses + + + align:start position:0% +no commas brackets parentheses +no negatives no fractions + + align:start position:0% +no negatives no fractions + + + align:start position:0% +no negatives no fractions +no infinities i followed the rules + + align:start position:0% +no infinities i followed the rules + + + align:start position:0% +no infinities i followed the rules +and because of that these indices have + + align:start position:0% +and because of that these indices have + + + align:start position:0% +and because of that these indices have +meaning + + align:start position:0% +meaning + + + align:start position:0% +meaning +as i'm showing you right because of that + + align:start position:0% + + + + align:start position:0% + +now you can play around with this but + + align:start position:0% +now you can play around with this but + + + align:start position:0% +now you can play around with this but +this can also be fairly + + align:start position:0% +this can also be fairly + + + align:start position:0% +this can also be fairly +straightforwardly derived things like + + align:start position:0% +straightforwardly derived things like + + + align:start position:0% +straightforwardly derived things like +this + + align:start position:0% +this + + + align:start position:0% +this +but you don't need to know that + + align:start position:0% +but you don't need to know that + + + align:start position:0% +but you don't need to know that +derivation so i'm just telling it to you + + align:start position:0% +derivation so i'm just telling it to you + + + align:start position:0% +derivation so i'm just telling it to you +okay all right so so these are the kinds + + align:start position:0% +okay all right so so these are the kinds + + + align:start position:0% +okay all right so so these are the kinds +of things that you can do + + align:start position:0% +of things that you can do + + + align:start position:0% +of things that you can do +with miller indices but as i said in the + + align:start position:0% +with miller indices but as i said in the + + + align:start position:0% +with miller indices but as i said in the +beginning one of the things that you + + align:start position:0% +beginning one of the things that you + + + align:start position:0% +beginning one of the things that you +that you would want to know what planes + + align:start position:0% +that you would want to know what planes + + + align:start position:0% +that you would want to know what planes +you're talking about + + align:start position:0% +you're talking about + + + align:start position:0% +you're talking about +is because you want to know what the + + align:start position:0% +is because you want to know what the + + + align:start position:0% +is because you want to know what the +packing in that plane is + + align:start position:0% +packing in that plane is + + + align:start position:0% +packing in that plane is +just like we talked about packing right + + align:start position:0% +just like we talked about packing right + + + align:start position:0% +just like we talked about packing right +for uh well we talked about it before on + + align:start position:0% +for uh well we talked about it before on + + + align:start position:0% +for uh well we talked about it before on +monday the atomic packing fraction + + align:start position:0% +monday the atomic packing fraction + + + align:start position:0% +monday the atomic packing fraction +there it is the max packing fraction in + + align:start position:0% +there it is the max packing fraction in + + + align:start position:0% +there it is the max packing fraction in +a volume + + align:start position:0% +a volume + + + align:start position:0% +a volume +we also want to know especially if a + + align:start position:0% +we also want to know especially if a + + + align:start position:0% +we also want to know especially if a +crystal is anisotropic + + align:start position:0% +crystal is anisotropic + + + align:start position:0% +crystal is anisotropic +we want to know about packings in planes + + align:start position:0% +we want to know about packings in planes + + + align:start position:0% +we want to know about packings in planes +right + + align:start position:0% +right + + + align:start position:0% +right +and and so you know if you take a simple + + align:start position:0% +and and so you know if you take a simple + + + align:start position:0% +and and so you know if you take a simple +a very simple example like a simple + + align:start position:0% +a very simple example like a simple + + + align:start position:0% +a very simple example like a simple +cubic + + align:start position:0% +cubic + + + align:start position:0% +cubic +there's a simple cubic lattice and now + + align:start position:0% +there's a simple cubic lattice and now + + + align:start position:0% +there's a simple cubic lattice and now +we're all good with our notation right + + align:start position:0% +we're all good with our notation right + + + align:start position:0% +we're all good with our notation right +there's a simple cubic crystal + + align:start position:0% +there's a simple cubic crystal + + + align:start position:0% +there's a simple cubic crystal +okay the basis is one atom i i don't + + align:start position:0% +okay the basis is one atom i i don't + + + align:start position:0% +okay the basis is one atom i i don't +have anything else in here those are the + + align:start position:0% +have anything else in here those are the + + + align:start position:0% +have anything else in here those are the +atoms simple + + align:start position:0% +atoms simple + + + align:start position:0% +atoms simple +it must be polonium right and there's + + align:start position:0% +it must be polonium right and there's + + + align:start position:0% +it must be polonium right and there's +uh the 100 plane the one one o plane and + + align:start position:0% +uh the 100 plane the one one o plane and + + + align:start position:0% +uh the 100 plane the one one o plane and +the one one one plane + + align:start position:0% +the one one one plane + + + align:start position:0% +the one one one plane +one one one plane one one o plane + + align:start position:0% +one one one plane one one o plane + + + align:start position:0% +one one one plane one one o plane +right one oval plane now but as you can + + align:start position:0% +right one oval plane now but as you can + + + align:start position:0% +right one oval plane now but as you can +see + + align:start position:0% +see + + + align:start position:0% +see +the the density of atoms in these planes + + align:start position:0% +the the density of atoms in these planes + + + align:start position:0% +the the density of atoms in these planes +is different + + align:start position:0% +is different + + + align:start position:0% +is different +the density of atoms in these planes is + + align:start position:0% +the density of atoms in these planes is + + + align:start position:0% +the density of atoms in these planes is +different and that has a real + + align:start position:0% +different and that has a real + + + align:start position:0% +different and that has a real +serious uh impact on the properties + + align:start position:0% +serious uh impact on the properties + + + align:start position:0% +serious uh impact on the properties +right um so if we if we look at this + + align:start position:0% +right um so if we if we look at this + + + align:start position:0% +right um so if we if we look at this +so i'll do a couple quick examples if we + + align:start position:0% +so i'll do a couple quick examples if we + + + align:start position:0% +so i'll do a couple quick examples if we +look at this + + align:start position:0% +look at this + + + align:start position:0% +look at this +example of simple cubic that's a very + + align:start position:0% +example of simple cubic that's a very + + + align:start position:0% +example of simple cubic that's a very +easy case + + align:start position:0% +easy case + + + align:start position:0% +easy case +right and so for simple cubic + + align:start position:0% +right and so for simple cubic + + + align:start position:0% +right and so for simple cubic +for a simple cubic uh with uh + + align:start position:0% +for a simple cubic uh with uh + + + align:start position:0% +for a simple cubic uh with uh +lattice this a is called the lattice + + align:start position:0% +lattice this a is called the lattice + + + align:start position:0% +lattice this a is called the lattice +constant + + align:start position:0% +constant + + + align:start position:0% +constant +i've mentioned it a few times lattice + + align:start position:0% +i've mentioned it a few times lattice + + + align:start position:0% +i've mentioned it a few times lattice +constant a + + align:start position:0% +constant a + + + align:start position:0% +constant a +then you know if we look at the 1o0 + + align:start position:0% +then you know if we look at the 1o0 + + + align:start position:0% +then you know if we look at the 1o0 +plane + + align:start position:0% +plane + + + align:start position:0% +plane +then the area + + align:start position:0% + + + + align:start position:0% + +is a squared the area of that plane is a + + align:start position:0% +is a squared the area of that plane is a + + + align:start position:0% +is a squared the area of that plane is a +squared + + align:start position:0% +squared + + + align:start position:0% +squared +oh but the question is how many atoms + + align:start position:0% +oh but the question is how many atoms + + + align:start position:0% +oh but the question is how many atoms +are in that a squared + + align:start position:0% +are in that a squared + + + align:start position:0% +are in that a squared +well you do the same thing that we did + + align:start position:0% +well you do the same thing that we did + + + align:start position:0% +well you do the same thing that we did +before you but now so i'm looking at a + + align:start position:0% +before you but now so i'm looking at a + + + align:start position:0% +before you but now so i'm looking at a +plane + + align:start position:0% +plane + + + align:start position:0% +plane +here and i'm trying to figure out you + + align:start position:0% +here and i'm trying to figure out you + + + align:start position:0% +here and i'm trying to figure out you +know how many atoms are in this up well + + align:start position:0% +know how many atoms are in this up well + + + align:start position:0% +know how many atoms are in this up well +you know + + align:start position:0% +you know + + + align:start position:0% +you know +this is being shared in this whole big + + align:start position:0% +this is being shared in this whole big + + + align:start position:0% +this is being shared in this whole big +plane that goes on and on + + align:start position:0% +plane that goes on and on + + + align:start position:0% +plane that goes on and on +it's being shared by four other squares + + align:start position:0% +it's being shared by four other squares + + + align:start position:0% +it's being shared by four other squares +right and so there's a fourth of each + + align:start position:0% +right and so there's a fourth of each + + + align:start position:0% +right and so there's a fourth of each +atom in there so there's one atom + + align:start position:0% +atom in there so there's one atom + + + align:start position:0% +atom in there so there's one atom +effectively in that plane + + align:start position:0% +effectively in that plane + + + align:start position:0% +effectively in that plane +again this is in one of the simplest + + align:start position:0% +again this is in one of the simplest + + + align:start position:0% +again this is in one of the simplest +cases right + + align:start position:0% +cases right + + + align:start position:0% +cases right +but the number of atoms number of atoms + + align:start position:0% + + + + align:start position:0% + +is equal to one + + align:start position:0% +is equal to one + + + align:start position:0% +is equal to one +right and so the density + + align:start position:0% + + + + align:start position:0% + +of atoms per area is equal to one + + align:start position:0% +of atoms per area is equal to one + + + align:start position:0% +of atoms per area is equal to one +over a squared now that's a pretty easy + + align:start position:0% +over a squared now that's a pretty easy + + + align:start position:0% +over a squared now that's a pretty easy +case + + align:start position:0% +case + + + align:start position:0% +case +right if i did the one one one one o + + align:start position:0% +right if i did the one one one one o + + + align:start position:0% +right if i did the one one one one o +direction it's a little bit different + + align:start position:0% +direction it's a little bit different + + + align:start position:0% +direction it's a little bit different +because the area is now different right + + align:start position:0% +because the area is now different right + + + align:start position:0% +because the area is now different right +so the area + + align:start position:0% +so the area + + + align:start position:0% +so the area +in this case is + + align:start position:0% +in this case is + + + align:start position:0% +in this case is +root 2 a squared + + align:start position:0% +root 2 a squared + + + align:start position:0% +root 2 a squared +you see that the area in in that plane + + align:start position:0% +you see that the area in in that plane + + + align:start position:0% +you see that the area in in that plane +is different so the density of atoms + + align:start position:0% +is different so the density of atoms + + + align:start position:0% +is different so the density of atoms +in the plane is different okay + + align:start position:0% + + + + align:start position:0% + +so the density in the plane affects + + align:start position:0% +so the density in the plane affects + + + align:start position:0% +so the density in the plane affects +properties and i want to give you just a + + align:start position:0% +properties and i want to give you just a + + + align:start position:0% +properties and i want to give you just a +quick + + align:start position:0% +quick + + + align:start position:0% +quick +uh example of that in the why this + + align:start position:0% +uh example of that in the why this + + + align:start position:0% +uh example of that in the why this +matters because + + align:start position:0% +matters because + + + align:start position:0% +matters because +in fact this is one of the things all + + align:start position:0% +in fact this is one of the things all + + + align:start position:0% +in fact this is one of the things all +the way back to hook + + align:start position:0% +the way back to hook + + + align:start position:0% +the way back to hook +and the can his cannonballs and even way + + align:start position:0% +and the can his cannonballs and even way + + + align:start position:0% +and the can his cannonballs and even way +before that + + align:start position:0% +before that + + + align:start position:0% +before that +people notice this stuff does it i broke + + align:start position:0% +people notice this stuff does it i broke + + + align:start position:0% +people notice this stuff does it i broke +something + + align:start position:0% +something + + + align:start position:0% +something +but it always seems to slice in a + + align:start position:0% +but it always seems to slice in a + + + align:start position:0% +but it always seems to slice in a +certain way + + align:start position:0% +certain way + + + align:start position:0% +certain way +why is that why would something always + + align:start position:0% +why is that why would something always + + + align:start position:0% +why is that why would something always +break in the same way every time + + align:start position:0% +break in the same way every time + + + align:start position:0% +break in the same way every time +with the same kind of you know how does + + align:start position:0% +with the same kind of you know how does + + + align:start position:0% +with the same kind of you know how does +it what does whey mean here + + align:start position:0% +it what does whey mean here + + + align:start position:0% +it what does whey mean here +it means like the angles that form right + + align:start position:0% +it means like the angles that form right + + + align:start position:0% +it means like the angles that form right +so why are those angles always kind of + + align:start position:0% +so why are those angles always kind of + + + align:start position:0% +so why are those angles always kind of +the same + + align:start position:0% +the same + + + align:start position:0% +the same +right well it has to do with the + + align:start position:0% +right well it has to do with the + + + align:start position:0% +right well it has to do with the +strength the relative strength + + align:start position:0% +strength the relative strength + + + align:start position:0% +strength the relative strength +of the planes inside of these crystals + + align:start position:0% +of the planes inside of these crystals + + + align:start position:0% +of the planes inside of these crystals +right + + align:start position:0% +right + + + align:start position:0% +right +and in fact here's a beautiful uh piece + + align:start position:0% +and in fact here's a beautiful uh piece + + + align:start position:0% +and in fact here's a beautiful uh piece +of work on stretching a wire + + align:start position:0% +of work on stretching a wire + + + align:start position:0% +of work on stretching a wire +right so here you're taking a wire that + + align:start position:0% +right so here you're taking a wire that + + + align:start position:0% +right so here you're taking a wire that +is crystalline + + align:start position:0% +is crystalline + + + align:start position:0% +is crystalline +and you're pulling it and you can see + + align:start position:0% +and you're pulling it and you can see + + + align:start position:0% +and you're pulling it and you can see +how it breaks + + align:start position:0% +how it breaks + + + align:start position:0% +how it breaks +you can actually see how it breaks it's + + align:start position:0% +you can actually see how it breaks it's + + + align:start position:0% +you can actually see how it breaks it's +breaking along the weakest plane + + align:start position:0% +breaking along the weakest plane + + + align:start position:0% +breaking along the weakest plane +it's breaking along the weakest plane so + + align:start position:0% +it's breaking along the weakest plane so + + + align:start position:0% +it's breaking along the weakest plane so +if you want to think then about well + + align:start position:0% +if you want to think then about well + + + align:start position:0% +if you want to think then about well +okay how do i know how to make this + + align:start position:0% +okay how do i know how to make this + + + align:start position:0% +okay how do i know how to make this +stronger + + align:start position:0% +stronger + + + align:start position:0% +stronger +for example so it stops breaking you + + align:start position:0% +for example so it stops breaking you + + + align:start position:0% +for example so it stops breaking you +know the weakest link is + + align:start position:0% +know the weakest link is + + + align:start position:0% +know the weakest link is +is the weakest link right that was deep + + align:start position:0% +is the weakest link right that was deep + + + align:start position:0% +is the weakest link right that was deep +and and so yeah so you but so then + + align:start position:0% +and and so yeah so you but so then + + + align:start position:0% +and and so yeah so you but so then +that's the plane of the crystal that i + + align:start position:0% +that's the plane of the crystal that i + + + align:start position:0% +that's the plane of the crystal that i +need to think about + + align:start position:0% +need to think about + + + align:start position:0% +need to think about +how are atoms bonding together or + + align:start position:0% +how are atoms bonding together or + + + align:start position:0% +how are atoms bonding together or +packing in in that plane + + align:start position:0% +packing in in that plane + + + align:start position:0% +packing in in that plane +right this is real stuff this is this + + align:start position:0% +right this is real stuff this is this + + + align:start position:0% +right this is real stuff this is this +comes about + + align:start position:0% +comes about + + + align:start position:0% +comes about +in many of the properties not just the + + align:start position:0% +in many of the properties not just the + + + align:start position:0% +in many of the properties not just the +fracture but in many of the properties + + align:start position:0% +fracture but in many of the properties + + + align:start position:0% +fracture but in many of the properties +of these + + align:start position:0% +of these + + + align:start position:0% +of these +of these materials the the property as i + + align:start position:0% +of these materials the the property as i + + + align:start position:0% +of these materials the the property as i +said before + + align:start position:0% +said before + + + align:start position:0% +said before +depends heavily on which plane you're in + + align:start position:0% +depends heavily on which plane you're in + + + align:start position:0% +depends heavily on which plane you're in +and we'll see that more and more as one + + align:start position:0% +and we'll see that more and more as one + + + align:start position:0% +and we'll see that more and more as one +last example + + align:start position:0% +last example + + + align:start position:0% +last example +as one last example right of this you + + align:start position:0% +as one last example right of this you + + + align:start position:0% +as one last example right of this you +could go a little + + align:start position:0% +could go a little + + + align:start position:0% +could go a little +right so if i if i say again you go back + + align:start position:0% +right so if i if i say again you go back + + + align:start position:0% +right so if i if i say again you go back +to your periodic table + + align:start position:0% +to your periodic table + + + align:start position:0% +to your periodic table +and you take there was copper let's do + + align:start position:0% +and you take there was copper let's do + + + align:start position:0% +and you take there was copper let's do +nickel + + align:start position:0% +nickel + + + align:start position:0% +nickel +all right you take nickel + + align:start position:0% +all right you take nickel + + + align:start position:0% +all right you take nickel +and let's see i know that the atomic + + align:start position:0% +and let's see i know that the atomic + + + align:start position:0% +and let's see i know that the atomic +radius + + align:start position:0% +radius + + + align:start position:0% +radius +of nickel is 1.52 angstroms + + align:start position:0% +of nickel is 1.52 angstroms + + + align:start position:0% +of nickel is 1.52 angstroms +i've looked that up but i also know that + + align:start position:0% +i've looked that up but i also know that + + + align:start position:0% +i've looked that up but i also know that +it's bcc and this gives it away + + align:start position:0% +it's bcc and this gives it away + + + align:start position:0% +it's bcc and this gives it away +this gives me what i need the crystal + + align:start position:0% +this gives me what i need the crystal + + + align:start position:0% +this gives me what i need the crystal +symmetry + + align:start position:0% +symmetry + + + align:start position:0% +symmetry +the lattice gives me what i need because + + align:start position:0% +the lattice gives me what i need because + + + align:start position:0% +the lattice gives me what i need because +once i know that it's bcc then i also + + align:start position:0% +once i know that it's bcc then i also + + + align:start position:0% +once i know that it's bcc then i also +know + + align:start position:0% +know + + + align:start position:0% +know +that the the lattice edge goes as 4r + + align:start position:0% +that the the lattice edge goes as 4r + + + align:start position:0% +that the the lattice edge goes as 4r +over root 3. remember for an element + + align:start position:0% +over root 3. remember for an element + + + align:start position:0% +over root 3. remember for an element +like nickel + + align:start position:0% +like nickel + + + align:start position:0% +like nickel +the the packing direction is along the + + align:start position:0% +the the packing direction is along the + + + align:start position:0% +the the packing direction is along the +body diagonal + + align:start position:0% +body diagonal + + + align:start position:0% +body diagonal +that's what gave me this relationship + + align:start position:0% +that's what gave me this relationship + + + align:start position:0% +that's what gave me this relationship +back and forth + + align:start position:0% +back and forth + + + align:start position:0% +back and forth +unit cell edge radius of the atom right + + align:start position:0% +unit cell edge radius of the atom right + + + align:start position:0% +unit cell edge radius of the atom right +what's it so that means that in in + + align:start position:0% +what's it so that means that in in + + + align:start position:0% +what's it so that means that in in +nickel it's 3.5 + + align:start position:0% +nickel it's 3.5 + + + align:start position:0% +nickel it's 3.5 +angstroms and once i know what a is + + align:start position:0% +angstroms and once i know what a is + + + align:start position:0% +angstroms and once i know what a is +well then i can know what like the the + + align:start position:0% +well then i can know what like the the + + + align:start position:0% +well then i can know what like the the +you know in in one of the planes i say + + align:start position:0% +you know in in one of the planes i say + + + align:start position:0% +you know in in one of the planes i say +which plane is that i don't know let's + + align:start position:0% +which plane is that i don't know let's + + + align:start position:0% +which plane is that i don't know let's +look at the densities in the plane so + + align:start position:0% +look at the densities in the plane so + + + align:start position:0% +look at the densities in the plane so +for the 100 plane + + align:start position:0% +for the 100 plane + + + align:start position:0% +for the 100 plane +it's i'm just gonna give you the answer + + align:start position:0% +it's i'm just gonna give you the answer + + + align:start position:0% +it's i'm just gonna give you the answer +point + + align:start position:0% +point + + + align:start position:0% +point +five nine is the packing fraction + + align:start position:0% +five nine is the packing fraction + + + align:start position:0% +five nine is the packing fraction +packing density right this is the + + align:start position:0% +packing density right this is the + + + align:start position:0% +packing density right this is the +um sorry that's the fraction + + align:start position:0% + + + + align:start position:0% + +all i did is i used the periodic table + + align:start position:0% +all i did is i used the periodic table + + + align:start position:0% +all i did is i used the periodic table +to do what i just did for the simple + + align:start position:0% +to do what i just did for the simple + + + align:start position:0% +to do what i just did for the simple +cubic case but now for bcc + + align:start position:0% +cubic case but now for bcc + + + align:start position:0% +cubic case but now for bcc +and it's because of all the things that + + align:start position:0% +and it's because of all the things that + + + align:start position:0% +and it's because of all the things that +we've learned in the last two days that + + align:start position:0% +we've learned in the last two days that + + + align:start position:0% +we've learned in the last two days that +in those two lectures that we're able to + + align:start position:0% +in those two lectures that we're able to + + + align:start position:0% +in those two lectures that we're able to +do this kind of calculation and i can + + align:start position:0% +do this kind of calculation and i can + + + align:start position:0% +do this kind of calculation and i can +compare this plane + + align:start position:0% +compare this plane + + + align:start position:0% +compare this plane +with another plane with another plane + + align:start position:0% +with another plane with another plane + + + align:start position:0% +with another plane with another plane +right + + align:start position:0% +right + + + align:start position:0% +right +and think about how the atoms are packed + + align:start position:0% +and think about how the atoms are packed + + + align:start position:0% +and think about how the atoms are packed +differently within the anisotropy of the + + align:start position:0% +differently within the anisotropy of the + + + align:start position:0% +differently within the anisotropy of the +crystal + + align:start position:0% +crystal + + + align:start position:0% +crystal +okay friday bring parents + + align:start position:0% +okay friday bring parents + + + align:start position:0% +okay friday bring parents +bring parents + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/ghjOS7Q82s0.txt b/ghjOS7Q82s0.txt new file mode 100644 index 0000000000000000000000000000000000000000..d293a7202ab20dfe83e4907296bcdd18e1625a19 --- /dev/null +++ b/ghjOS7Q82s0.txt @@ -0,0 +1,1763 @@ +align:start position:0% + +okay well the idea of this first video + + align:start position:0% +okay well the idea of this first video + + + align:start position:0% +okay well the idea of this first video +is to tell you what's coming to give a + + align:start position:0% +is to tell you what's coming to give a + + + align:start position:0% +is to tell you what's coming to give a +kind of outline of what is reasonable + + align:start position:0% +kind of outline of what is reasonable + + + align:start position:0% +kind of outline of what is reasonable +will learn about ordinary differential + + align:start position:0% +will learn about ordinary differential + + + align:start position:0% +will learn about ordinary differential +equations and a big part of the series + + align:start position:0% +equations and a big part of the series + + + align:start position:0% +equations and a big part of the series +will be videos on first-order equations + + align:start position:0% +will be videos on first-order equations + + + align:start position:0% +will be videos on first-order equations +and videos on second-order equations + + align:start position:0% +and videos on second-order equations + + + align:start position:0% +and videos on second-order equations +those are the ones you see most in + + align:start position:0% +those are the ones you see most in + + + align:start position:0% +those are the ones you see most in +applications and those are the ones you + + align:start position:0% +applications and those are the ones you + + + align:start position:0% +applications and those are the ones you +can understand and solve when you're + + align:start position:0% +can understand and solve when you're + + + align:start position:0% +can understand and solve when you're +fortunate so first order equations means + + align:start position:0% +fortunate so first order equations means + + + align:start position:0% +fortunate so first order equations means +first derivatives come into the equation + + align:start position:0% +first derivatives come into the equation + + + align:start position:0% +first derivatives come into the equation +so we here's a that's a nice equation + + align:start position:0% +so we here's a that's a nice equation + + + align:start position:0% +so we here's a that's a nice equation +that we will solve we'll spend a lot of + + align:start position:0% +that we will solve we'll spend a lot of + + + align:start position:0% +that we will solve we'll spend a lot of +time on the derivative is that's the + + align:start position:0% +time on the derivative is that's the + + + align:start position:0% +time on the derivative is that's the +rate of change of Y the changes in the + + align:start position:0% +rate of change of Y the changes in the + + + align:start position:0% +rate of change of Y the changes in the +unknown Y as time goes forward are + + align:start position:0% +unknown Y as time goes forward are + + + align:start position:0% +unknown Y as time goes forward are +partly from depending on the solution + + align:start position:0% +partly from depending on the solution + + + align:start position:0% +partly from depending on the solution +itself that's the idea of a differential + + align:start position:0% +itself that's the idea of a differential + + + align:start position:0% +itself that's the idea of a differential +equation that it connects the changes + + align:start position:0% +equation that it connects the changes + + + align:start position:0% +equation that it connects the changes +with the function y as it is and then + + align:start position:0% +with the function y as it is and then + + + align:start position:0% +with the function y as it is and then +you have inputs called Q of T which + + align:start position:0% +you have inputs called Q of T which + + + align:start position:0% +you have inputs called Q of T which +continue to which produce their own + + align:start position:0% +continue to which produce their own + + + align:start position:0% +continue to which produce their own +change they go into the system they + + align:start position:0% +change they go into the system they + + + align:start position:0% +change they go into the system they +become part of Y and they grow decay + + align:start position:0% +become part of Y and they grow decay + + + align:start position:0% +become part of Y and they grow decay +oscillate whatever Y of T does so that + + align:start position:0% +oscillate whatever Y of T does so that + + + align:start position:0% +oscillate whatever Y of T does so that +that is a linear equation with the + + align:start position:0% +that is a linear equation with the + + + align:start position:0% +that is a linear equation with the +right-hand side with an input a forcing + + align:start position:0% +right-hand side with an input a forcing + + + align:start position:0% +right-hand side with an input a forcing +term and here is a nonlinear equation + + align:start position:0% +term and here is a nonlinear equation + + + align:start position:0% +term and here is a nonlinear equation +the derivative of Y the slope depends on + + align:start position:0% +the derivative of Y the slope depends on + + + align:start position:0% +the derivative of Y the slope depends on +Y so it's a differential equation but F + + align:start position:0% +Y so it's a differential equation but F + + + align:start position:0% +Y so it's a differential equation but F +of Y could be Y squared or Y cubed or + + align:start position:0% +of Y could be Y squared or Y cubed or + + + align:start position:0% +of Y could be Y squared or Y cubed or +the sine of Y or the exponential of Y so + + align:start position:0% +the sine of Y or the exponential of Y so + + + align:start position:0% +the sine of Y or the exponential of Y so +it could be not linear linear means that + + align:start position:0% +it could be not linear linear means that + + + align:start position:0% +it could be not linear linear means that +we see Y by itself + + align:start position:0% +we see Y by itself + + + align:start position:0% +we see Y by itself +here we won't well we'll come pretty + + align:start position:0% +here we won't well we'll come pretty + + + align:start position:0% +here we won't well we'll come pretty +close to getting a solution because it's + + align:start position:0% +close to getting a solution because it's + + + align:start position:0% +close to getting a solution because it's +a first-order equation and the the most + + align:start position:0% +a first-order equation and the the most + + + align:start position:0% +a first-order equation and the the most +general first-order equation the + + align:start position:0% +general first-order equation the + + + align:start position:0% +general first-order equation the +function would depend on T and Y the + + align:start position:0% +function would depend on T and Y the + + + align:start position:0% +function would depend on T and Y the +input would change with time + + align:start position:0% +input would change with time + + + align:start position:0% +input would change with time +here the input depends only on the + + align:start position:0% +here the input depends only on the + + + align:start position:0% +here the input depends only on the +current value of y I might think of Y as + + align:start position:0% +current value of y I might think of Y as + + + align:start position:0% +current value of y I might think of Y as +the money in a bank growing decaying + + align:start position:0% +the money in a bank growing decaying + + + align:start position:0% +the money in a bank growing decaying +oscillating or I might think of Y as the + + align:start position:0% +oscillating or I might think of Y as the + + + align:start position:0% +oscillating or I might think of Y as the +as a distance on a spring lots of + + align:start position:0% +as a distance on a spring lots of + + + align:start position:0% +as a distance on a spring lots of +applications coming okay so those are + + align:start position:0% +applications coming okay so those are + + + align:start position:0% +applications coming okay so those are +first-order equations and second-order + + align:start position:0% +first-order equations and second-order + + + align:start position:0% +first-order equations and second-order +have second derivatives the second + + align:start position:0% +have second derivatives the second + + + align:start position:0% +have second derivatives the second +derivative is the acceleration it it + + align:start position:0% +derivative is the acceleration it it + + + align:start position:0% +derivative is the acceleration it it +tells you about the bending of the curve + + align:start position:0% +tells you about the bending of the curve + + + align:start position:0% +tells you about the bending of the curve +if I have a graph the first derivative + + align:start position:0% +if I have a graph the first derivative + + + align:start position:0% +if I have a graph the first derivative +we know gives the slope of the graph is + + align:start position:0% +we know gives the slope of the graph is + + + align:start position:0% +we know gives the slope of the graph is +it going up is it going down is it a + + align:start position:0% +it going up is it going down is it a + + + align:start position:0% +it going up is it going down is it a +maximum the second derivative tells you + + align:start position:0% +maximum the second derivative tells you + + + align:start position:0% +maximum the second derivative tells you +the bending of the graph how it goes + + align:start position:0% +the bending of the graph how it goes + + + align:start position:0% +the bending of the graph how it goes +away from a straight line so and that's + + align:start position:0% +away from a straight line so and that's + + + align:start position:0% +away from a straight line so and that's +acceleration so Newton's law the physics + + align:start position:0% +acceleration so Newton's law the physics + + + align:start position:0% +acceleration so Newton's law the physics +we all live with would be acceleration + + align:start position:0% +we all live with would be acceleration + + + align:start position:0% +we all live with would be acceleration +is some force and there is a force that + + align:start position:0% +is some force and there is a force that + + + align:start position:0% +is some force and there is a force that +depends again linearly that's a key word + + align:start position:0% +depends again linearly that's a key word + + + align:start position:0% +depends again linearly that's a key word +on why does Y to the first power and + + align:start position:0% +on why does Y to the first power and + + + align:start position:0% +on why does Y to the first power and +here is a little bit more general + + align:start position:0% +here is a little bit more general + + + align:start position:0% +here is a little bit more general +equation in Newton's law the + + align:start position:0% +equation in Newton's law the + + + align:start position:0% +equation in Newton's law the +acceleration is multiplied by the mass + + align:start position:0% +acceleration is multiplied by the mass + + + align:start position:0% +acceleration is multiplied by the mass +so this includes a physical constant + + align:start position:0% +so this includes a physical constant + + + align:start position:0% +so this includes a physical constant +here the mass then there could be some + + align:start position:0% +here the mass then there could be some + + + align:start position:0% +here the mass then there could be some +damping if I have motion it may there + + align:start position:0% +damping if I have motion it may there + + + align:start position:0% +damping if I have motion it may there +may be friction slowing it down that + + align:start position:0% +may be friction slowing it down that + + + align:start position:0% +may be friction slowing it down that +depends on the first derivative the + + align:start position:0% +depends on the first derivative the + + + align:start position:0% +depends on the first derivative the +velocity and then there could be the + + align:start position:0% +velocity and then there could be the + + + align:start position:0% +velocity and then there could be the +same kind of force term that depends on + + align:start position:0% +same kind of force term that depends on + + + align:start position:0% +same kind of force term that depends on +Y itself and there could be some outside + + align:start position:0% +Y itself and there could be some outside + + + align:start position:0% +Y itself and there could be some outside +force some some other some person or + + align:start position:0% +force some some other some person or + + + align:start position:0% +force some some other some person or +machine that make creating movement an + + align:start position:0% +machine that make creating movement an + + + align:start position:0% +machine that make creating movement an +external forcing term so that's a big + + align:start position:0% +external forcing term so that's a big + + + align:start position:0% +external forcing term so that's a big +equation and let me just say at this + + align:start position:0% +equation and let me just say at this + + + align:start position:0% +equation and let me just say at this +point we let things be nonlinear and we + + align:start position:0% +point we let things be nonlinear and we + + + align:start position:0% +point we let things be nonlinear and we +had a pretty good chance if we get these + + align:start position:0% +had a pretty good chance if we get these + + + align:start position:0% +had a pretty good chance if we get these +to be nonlinear the chance at + + align:start position:0% +to be nonlinear the chance at + + + align:start position:0% +to be nonlinear the chance at +second-order has dropped and the further + + align:start position:0% +second-order has dropped and the further + + + align:start position:0% +second-order has dropped and the further +we go the more we need linearity and + + align:start position:0% +we go the more we need linearity and + + + align:start position:0% +we go the more we need linearity and +maybe even constant coefficients MB and + + align:start position:0% +maybe even constant coefficients MB and + + + align:start position:0% +maybe even constant coefficients MB and +K so that that's really the problem that + + align:start position:0% +K so that that's really the problem that + + + align:start position:0% +K so that that's really the problem that +we can solve as we get good at it is a + + align:start position:0% +we can solve as we get good at it is a + + + align:start position:0% +we can solve as we get good at it is a +linear equation second order let's say + + align:start position:0% +linear equation second order let's say + + + align:start position:0% +linear equation second order let's say +with constant coefficients that that's + + align:start position:0% +with constant coefficients that that's + + + align:start position:0% +with constant coefficients that that's +pretty much pushing what we can hope to + + align:start position:0% +pretty much pushing what we can hope to + + + align:start position:0% +pretty much pushing what we can hope to +do explicitly and really understand the + + align:start position:0% +do explicitly and really understand the + + + align:start position:0% +do explicitly and really understand the +solution because so linear with constant + + align:start position:0% +solution because so linear with constant + + + align:start position:0% +solution because so linear with constant +coefficients that that's say it again + + align:start position:0% +coefficients that that's say it again + + + align:start position:0% +coefficients that that's say it again +that's the good that's the good good + + align:start position:0% +that's the good that's the good good + + + align:start position:0% +that's the good that's the good good +equations and I think of solutions in + + align:start position:0% +equations and I think of solutions in + + + align:start position:0% +equations and I think of solutions in +two ways if I have a really nice + + align:start position:0% +two ways if I have a really nice + + + align:start position:0% +two ways if I have a really nice +function like a exponential + + align:start position:0% +function like a exponential + + + align:start position:0% +function like a exponential +Exponential's are the great functions of + + align:start position:0% +Exponential's are the great functions of + + + align:start position:0% +Exponential's are the great functions of +differential equations the great + + align:start position:0% +differential equations the great + + + align:start position:0% +differential equations the great +functions in this series you'll see them + + align:start position:0% +functions in this series you'll see them + + + align:start position:0% +functions in this series you'll see them +over and over Exponential's say f of T + + align:start position:0% +over and over Exponential's say f of T + + + align:start position:0% +over and over Exponential's say f of T +equal e to the T or e to the Omega T or + + align:start position:0% +equal e to the T or e to the Omega T or + + + align:start position:0% +equal e to the T or e to the Omega T or +e to the I Omega T that I is the square + + align:start position:0% +e to the I Omega T that I is the square + + + align:start position:0% +e to the I Omega T that I is the square +root of -1 in that in those cases we + + align:start position:0% +root of -1 in that in those cases we + + + align:start position:0% +root of -1 in that in those cases we +will get a similarly nice function for + + align:start position:0% +will get a similarly nice function for + + + align:start position:0% +will get a similarly nice function for +the solution those are the best we get + + align:start position:0% +the solution those are the best we get + + + align:start position:0% +the solution those are the best we get +we get a function that we know like + + align:start position:0% +we get a function that we know like + + + align:start position:0% +we get a function that we know like +Exponential's + + align:start position:0% +Exponential's + + + align:start position:0% +Exponential's +and we get solutions that we know second + + align:start position:0% +and we get solutions that we know second + + + align:start position:0% +and we get solutions that we know second +best R we get some more some function + + align:start position:0% +best R we get some more some function + + + align:start position:0% +best R we get some more some function +who we don't specially know in that case + + align:start position:0% +who we don't specially know in that case + + + align:start position:0% +who we don't specially know in that case +the solution probably involves an + + align:start position:0% +the solution probably involves an + + + align:start position:0% +the solution probably involves an +integral + + align:start position:0% +integral + + + align:start position:0% +integral +of F or two integrals of f we have a + + align:start position:0% +of F or two integrals of f we have a + + + align:start position:0% +of F or two integrals of f we have a +formula for it that formula includes an + + align:start position:0% +formula for it that formula includes an + + + align:start position:0% +formula for it that formula includes an +integration that we would have to do + + align:start position:0% +integration that we would have to do + + + align:start position:0% +integration that we would have to do +either look it up or do it numerically + + align:start position:0% +either look it up or do it numerically + + + align:start position:0% +either look it up or do it numerically +and then when we get to completely + + align:start position:0% +and then when we get to completely + + + align:start position:0% +and then when we get to completely +nonlinear functions or we or we have + + align:start position:0% +nonlinear functions or we or we have + + + align:start position:0% +nonlinear functions or we or we have +varying coefficients then we're going to + + align:start position:0% +varying coefficients then we're going to + + + align:start position:0% +varying coefficients then we're going to +go numerically so really the wide wide + + align:start position:0% +go numerically so really the wide wide + + + align:start position:0% +go numerically so really the wide wide +part of the subject ends up as numerical + + align:start position:0% +part of the subject ends up as numerical + + + align:start position:0% +part of the subject ends up as numerical +solutions but you've got a whole you've + + align:start position:0% +solutions but you've got a whole you've + + + align:start position:0% +solutions but you've got a whole you've +got a whole bunch of videos coming that + + align:start position:0% +got a whole bunch of videos coming that + + + align:start position:0% +got a whole bunch of videos coming that +give that have nice functions and nice + + align:start position:0% +give that have nice functions and nice + + + align:start position:0% +give that have nice functions and nice +solutions okay so that's first-order and + + align:start position:0% +solutions okay so that's first-order and + + + align:start position:0% +solutions okay so that's first-order and +second-order now there's more because a + + align:start position:0% +second-order now there's more because a + + + align:start position:0% +second-order now there's more because a +system doesn't usually consist of just a + + align:start position:0% +system doesn't usually consist of just a + + + align:start position:0% +system doesn't usually consist of just a +single resistor or a single spring in a + + align:start position:0% +single resistor or a single spring in a + + + align:start position:0% +single resistor or a single spring in a +in in reality we we have many equations + + align:start position:0% +in in reality we we have many equations + + + align:start position:0% +in in reality we we have many equations +and we need to how we need to deal with + + align:start position:0% +and we need to how we need to deal with + + + align:start position:0% +and we need to how we need to deal with +those so why is now a vector y 1 y 2 2 y + + align:start position:0% +those so why is now a vector y 1 y 2 2 y + + + align:start position:0% +those so why is now a vector y 1 y 2 2 y +n n different unknowns in different + + align:start position:0% +n n different unknowns in different + + + align:start position:0% +n n different unknowns in different +equations that's an equation so here + + align:start position:0% +equations that's an equation so here + + + align:start position:0% +equations that's an equation so here +this is an that is an N by n matrix so + + align:start position:0% + + + + align:start position:0% + +it's first-order constant coefficient so + + align:start position:0% +it's first-order constant coefficient so + + + align:start position:0% +it's first-order constant coefficient so +we'll be able to get somewhere but it's + + align:start position:0% +we'll be able to get somewhere but it's + + + align:start position:0% +we'll be able to get somewhere but it's +a system of n coupled equations and so + + align:start position:0% +a system of n coupled equations and so + + + align:start position:0% +a system of n coupled equations and so +is this one with the second derivative + + align:start position:0% +is this one with the second derivative + + + align:start position:0% +is this one with the second derivative +second derivative of the solution but + + align:start position:0% +second derivative of the solution but + + + align:start position:0% +second derivative of the solution but +again y1 to yn and we have a matrix + + align:start position:0% +again y1 to yn and we have a matrix + + + align:start position:0% +again y1 to yn and we have a matrix +usually a symmetric matrix there we hope + + align:start position:0% +usually a symmetric matrix there we hope + + + align:start position:0% +usually a symmetric matrix there we hope +multiplying Y so again linear constant + + align:start position:0% +multiplying Y so again linear constant + + + align:start position:0% +multiplying Y so again linear constant +coefficients but several equations at + + align:start position:0% +coefficients but several equations at + + + align:start position:0% +coefficients but several equations at +once and that will bring in the idea of + + align:start position:0% +once and that will bring in the idea of + + + align:start position:0% +once and that will bring in the idea of +eigenvalues and eigenvectors eigenvalues + + align:start position:0% +eigenvalues and eigenvectors eigenvalues + + + align:start position:0% +eigenvalues and eigenvectors eigenvalues +and eigenvectors is a key bit of linear + + align:start position:0% +and eigenvectors is a key bit of linear + + + align:start position:0% +and eigenvectors is a key bit of linear +algebra + + align:start position:0% +algebra + + + align:start position:0% +algebra +that makes these problems simple because + + align:start position:0% +that makes these problems simple because + + + align:start position:0% +that makes these problems simple because +it turns this coupled problem into n + + align:start position:0% +it turns this coupled problem into n + + + align:start position:0% +it turns this coupled problem into n +uncoupled problems and first-order + + align:start position:0% +uncoupled problems and first-order + + + align:start position:0% +uncoupled problems and first-order +equations that we can solve separately + + align:start position:0% +equations that we can solve separately + + + align:start position:0% +equations that we can solve separately +or n second-order equations that we can + + align:start position:0% +or n second-order equations that we can + + + align:start position:0% +or n second-order equations that we can +solve separately that's the goal with + + align:start position:0% +solve separately that's the goal with + + + align:start position:0% +solve separately that's the goal with +matrices is to uncouple them ok and then + + align:start position:0% +matrices is to uncouple them ok and then + + + align:start position:0% +matrices is to uncouple them ok and then +really the big reality of this subject + + align:start position:0% +really the big reality of this subject + + + align:start position:0% +really the big reality of this subject +is that solutions are found numerically + + align:start position:0% +is that solutions are found numerically + + + align:start position:0% +is that solutions are found numerically +and very efficiently and there's a lot + + align:start position:0% +and very efficiently and there's a lot + + + align:start position:0% +and very efficiently and there's a lot +to learn about that a lot to learn and + + align:start position:0% +to learn about that a lot to learn and + + + align:start position:0% +to learn about that a lot to learn and +MATLAB is a first-class package that + + align:start position:0% +MATLAB is a first-class package that + + + align:start position:0% +MATLAB is a first-class package that +solve that gives you numerical solutions + + align:start position:0% +solve that gives you numerical solutions + + + align:start position:0% +solve that gives you numerical solutions +with many options one of the options may + + align:start position:0% +with many options one of the options may + + + align:start position:0% +with many options one of the options may +be the favorite Oh de for ordinary + + align:start position:0% +be the favorite Oh de for ordinary + + + align:start position:0% +be the favorite Oh de for ordinary +differential equations 4 5 and that is + + align:start position:0% +differential equations 4 5 and that is + + + align:start position:0% +differential equations 4 5 and that is +numbers 4 5 + + align:start position:0% +numbers 4 5 + + + align:start position:0% +numbers 4 5 +well Cleve Moler who first wrote the + + align:start position:0% +well Cleve Moler who first wrote the + + + align:start position:0% +well Cleve Moler who first wrote the +package MATLAB is going to create a + + align:start position:0% +package MATLAB is going to create a + + + align:start position:0% +package MATLAB is going to create a +system of a series of parallel videos + + align:start position:0% +system of a series of parallel videos + + + align:start position:0% +system of a series of parallel videos +explaining the steps toward numerical + + align:start position:0% +explaining the steps toward numerical + + + align:start position:0% +explaining the steps toward numerical +solution those steps begin with a very + + align:start position:0% +solution those steps begin with a very + + + align:start position:0% +solution those steps begin with a very +simple method maybe I'll put the + + align:start position:0% +simple method maybe I'll put the + + + align:start position:0% +simple method maybe I'll put the +creator's name down boiler so you can + + align:start position:0% +creator's name down boiler so you can + + + align:start position:0% +creator's name down boiler so you can +know that because Euler was centuries + + align:start position:0% +know that because Euler was centuries + + + align:start position:0% +know that because Euler was centuries +ago he didn't have a computer but he had + + align:start position:0% +ago he didn't have a computer but he had + + + align:start position:0% +ago he didn't have a computer but he had +a simple way of approximating so Euler + + align:start position:0% +a simple way of approximating so Euler + + + align:start position:0% +a simple way of approximating so Euler +might be OD e1 and now we've left Euler + + align:start position:0% +might be OD e1 and now we've left Euler + + + align:start position:0% +might be OD e1 and now we've left Euler +behind Euler is fine but not at not + + align:start position:0% +behind Euler is fine but not at not + + + align:start position:0% +behind Euler is fine but not at not +sufficiently accurate OD 4 5 that 4 and + + align:start position:0% +sufficiently accurate OD 4 5 that 4 and + + + align:start position:0% +sufficiently accurate OD 4 5 that 4 and +5 indicate a much higher accuracy much + + align:start position:0% +5 indicate a much higher accuracy much + + + align:start position:0% +5 indicate a much higher accuracy much +more + + align:start position:0% +more + + + align:start position:0% +more +flexibility in that in that package so + + align:start position:0% +flexibility in that in that package so + + + align:start position:0% +flexibility in that in that package so +starting with Euler Cleve Moler will + + align:start position:0% +starting with Euler Cleve Moler will + + + align:start position:0% +starting with Euler Cleve Moler will +explain several steps that reach a + + align:start position:0% +explain several steps that reach a + + + align:start position:0% +explain several steps that reach a +really workhorse package so that's a + + align:start position:0% +really workhorse package so that's a + + + align:start position:0% +really workhorse package so that's a +parallel series that where you'll see + + align:start position:0% +parallel series that where you'll see + + + align:start position:0% +parallel series that where you'll see +the codes this will be a chalk and + + align:start position:0% +the codes this will be a chalk and + + + align:start position:0% +the codes this will be a chalk and +blackboard series where I'll find + + align:start position:0% +blackboard series where I'll find + + + align:start position:0% +blackboard series where I'll find +solutions of in exponential form and if + + align:start position:0% +solutions of in exponential form and if + + + align:start position:0% +solutions of in exponential form and if +I can I would like to conclude this + + align:start position:0% +I can I would like to conclude this + + + align:start position:0% +I can I would like to conclude this +series by reaching partial differential + + align:start position:0% +series by reaching partial differential + + + align:start position:0% +series by reaching partial differential +equations so I'll just write some + + align:start position:0% +equations so I'll just write some + + + align:start position:0% +equations so I'll just write some +partial differential equations here so + + align:start position:0% +partial differential equations here so + + + align:start position:0% +partial differential equations here so +you know what they mean and that's a + + align:start position:0% +you know what they mean and that's a + + + align:start position:0% +you know what they mean and that's a +goal which we I hope to reach so one + + align:start position:0% +goal which we I hope to reach so one + + + align:start position:0% +goal which we I hope to reach so one +partial equate differential equation + + align:start position:0% +partial equate differential equation + + + align:start position:0% +partial equate differential equation +would be d UD t you see partial + + align:start position:0% +would be d UD t you see partial + + + align:start position:0% +would be d UD t you see partial +derivatives is do you the second + + align:start position:0% +derivatives is do you the second + + + align:start position:0% +derivatives is do you the second +derivative so I have two variables now + + align:start position:0% +derivative so I have two variables now + + + align:start position:0% +derivative so I have two variables now +time which I always have and here is X + + align:start position:0% +time which I always have and here is X + + + align:start position:0% +time which I always have and here is X +in the space direction that's called the + + align:start position:0% +in the space direction that's called the + + + align:start position:0% +in the space direction that's called the +heat equation that's that that's a very + + align:start position:0% +heat equation that's that that's a very + + + align:start position:0% +heat equation that's that that's a very +important constant coefficient partial + + align:start position:0% +important constant coefficient partial + + + align:start position:0% +important constant coefficient partial +differential equation so P D e as + + align:start position:0% +differential equation so P D e as + + + align:start position:0% +differential equation so P D e as +distinct from OD e and so I write down + + align:start position:0% +distinct from OD e and so I write down + + + align:start position:0% +distinct from OD e and so I write down +one more the second derivative of U is + + align:start position:0% +one more the second derivative of U is + + + align:start position:0% +one more the second derivative of U is +the same right hand side second + + align:start position:0% +the same right hand side second + + + align:start position:0% +the same right hand side second +derivative in the x-direction that would + + align:start position:0% +derivative in the x-direction that would + + + align:start position:0% +derivative in the x-direction that would +be called the wave equation so this is + + align:start position:0% +be called the wave equation so this is + + + align:start position:0% +be called the wave equation so this is +this is like the first order equation in + + align:start position:0% +this is like the first order equation in + + + align:start position:0% +this is like the first order equation in +time it's like a big system in fact it's + + align:start position:0% +time it's like a big system in fact it's + + + align:start position:0% +time it's like a big system in fact it's +like a infinite size system of equations + + align:start position:0% +like a infinite size system of equations + + + align:start position:0% +like a infinite size system of equations +but first order in time or second order + + align:start position:0% +but first order in time or second order + + + align:start position:0% +but first order in time or second order +in time heat equation wave equation and + + align:start position:0% +in time heat equation wave equation and + + + align:start position:0% +in time heat equation wave equation and +I would like to also include a + + align:start position:0% + + + + align:start position:0% + +a Laplace equation + + align:start position:0% +a Laplace equation + + + align:start position:0% +a Laplace equation +well if we get there so those are goals + + align:start position:0% +well if we get there so those are goals + + + align:start position:0% +well if we get there so those are goals +for the end of the series that go beyond + + align:start position:0% +for the end of the series that go beyond + + + align:start position:0% +for the end of the series that go beyond +some courses in Odie's but the main goal + + align:start position:0% +some courses in Odie's but the main goal + + + align:start position:0% +some courses in Odie's but the main goal +here is to give you the standard a clear + + align:start position:0% +here is to give you the standard a clear + + + align:start position:0% +here is to give you the standard a clear +picture of the basic differential + + align:start position:0% +picture of the basic differential + + + align:start position:0% +picture of the basic differential +equations that we can solve and + + align:start position:0% +equations that we can solve and + + + align:start position:0% +equations that we can solve and +understand well I hope it goes well + + align:start position:0% +understand well I hope it goes well + + + align:start position:0% +understand well I hope it goes well +thanks \ No newline at end of file diff --git a/hRhGRuLLB1I.txt b/hRhGRuLLB1I.txt new file mode 100644 index 0000000000000000000000000000000000000000..26e74faf615a0e3e12e2de665c1aa76deaf8f867 --- /dev/null +++ b/hRhGRuLLB1I.txt @@ -0,0 +1,9171 @@ +align:start position:0% + +okay what were we talking about last + + align:start position:0% +okay what were we talking about last + + + align:start position:0% +okay what were we talking about last +time + + align:start position:0% +time + + + align:start position:0% +time +neuronal migration + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +we talked about the shepherd's crook + + align:start position:0% +we talked about the shepherd's crook + + + align:start position:0% +we talked about the shepherd's crook +cell right + + align:start position:0% +cell right + + + align:start position:0% +cell right +let's just + + align:start position:0% + + + + align:start position:0% + +i won't load that slide + + align:start position:0% +i won't load that slide + + + align:start position:0% +i won't load that slide +why + + align:start position:0% +why + + + align:start position:0% +why +was it so important + + align:start position:0% +was it so important + + + align:start position:0% +was it so important +to find that very that cell that could + + align:start position:0% +to find that very that cell that could + + + align:start position:0% +to find that very that cell that could +be identified + + align:start position:0% +be identified + + + align:start position:0% +be identified +be identified at such early stages + + align:start position:0% +be identified at such early stages + + + align:start position:0% +be identified at such early stages +you see some people didn't believe that + + align:start position:0% +you see some people didn't believe that + + + align:start position:0% +you see some people didn't believe that +you could get nuclear translocation + + align:start position:0% +you could get nuclear translocation + + + align:start position:0% +you could get nuclear translocation +in the midbrain + + align:start position:0% +in the midbrain + + + align:start position:0% +in the midbrain +where + + align:start position:0% +where + + + align:start position:0% +where +the thickness of the neural when the + + align:start position:0% +the thickness of the neural when the + + + align:start position:0% +the thickness of the neural when the +thickness of the neural tube was fairly + + align:start position:0% +thickness of the neural tube was fairly + + + align:start position:0% +thickness of the neural tube was fairly +grayed + + align:start position:0% +grayed + + + align:start position:0% +grayed +they thought you would need radial glial + + align:start position:0% +they thought you would need radial glial + + + align:start position:0% +they thought you would need radial glial +guidance + + align:start position:0% +guidance + + + align:start position:0% +guidance +so what other explanation could there be + + align:start position:0% +so what other explanation could there be + + + align:start position:0% +so what other explanation could there be +for those pictures well + + align:start position:0% +for those pictures well + + + align:start position:0% +for those pictures well +with the golgi + + align:start position:0% +with the golgi + + + align:start position:0% +with the golgi +method it's possible that they could be + + align:start position:0% +method it's possible that they could be + + + align:start position:0% +method it's possible that they could be +staining glia + + align:start position:0% + + + + align:start position:0% + +and then seeing bombs on the glia + + align:start position:0% +and then seeing bombs on the glia + + + align:start position:0% +and then seeing bombs on the glia +misinterpreting the pictures + + align:start position:0% +misinterpreting the pictures + + + align:start position:0% +misinterpreting the pictures +they had to be able to reconstruct the + + align:start position:0% +they had to be able to reconstruct the + + + align:start position:0% +they had to be able to reconstruct the +entire sequence and remember what they + + align:start position:0% +entire sequence and remember what they + + + align:start position:0% +entire sequence and remember what they +did they took if this was the surface of + + align:start position:0% +did they took if this was the surface of + + + align:start position:0% +did they took if this was the surface of +the tectum this is the ventricular layer + + align:start position:0% +the tectum this is the ventricular layer + + + align:start position:0% +the tectum this is the ventricular layer +and here's + + align:start position:0% +and here's + + + align:start position:0% +and here's +one of these elongated cells + + align:start position:0% +one of these elongated cells + + + align:start position:0% +one of these elongated cells +here's a cell body + + align:start position:0% +here's a cell body + + + align:start position:0% +here's a cell body +okay + + align:start position:0% +okay + + + align:start position:0% +okay +then + + align:start position:0% +then + + + align:start position:0% +then +very early on they saw that + + align:start position:0% + + + + align:start position:0% + +sorry i'm glad i should start here and + + align:start position:0% +sorry i'm glad i should start here and + + + align:start position:0% +sorry i'm glad i should start here and +they where they started + + align:start position:0% + + + + align:start position:0% + +let's do that + + align:start position:0% + + + + align:start position:0% + +the adult shepherd's crook cell is a + + align:start position:0% +the adult shepherd's crook cell is a + + + align:start position:0% +the adult shepherd's crook cell is a +neuron here with an axon that goes out + + align:start position:0% +neuron here with an axon that goes out + + + align:start position:0% +neuron here with an axon that goes out +like that + + align:start position:0% +like that + + + align:start position:0% +like that +it always has that characteristic + + align:start position:0% +it always has that characteristic + + + align:start position:0% +it always has that characteristic +it's not clear why it goes up a little + + align:start position:0% +it's not clear why it goes up a little + + + align:start position:0% +it's not clear why it goes up a little +bit before it goes out but it always has + + align:start position:0% +bit before it goes out but it always has + + + align:start position:0% +bit before it goes out but it always has +the shepherd's crook + + align:start position:0% +the shepherd's crook + + + align:start position:0% +the shepherd's crook +okay + + align:start position:0% +okay + + + align:start position:0% +okay +i'm not drawing the dendrites and + + align:start position:0% +i'm not drawing the dendrites and + + + align:start position:0% +i'm not drawing the dendrites and +everything because what's critical about + + align:start position:0% +everything because what's critical about + + + align:start position:0% +everything because what's critical about +identifying that cell was the + + align:start position:0% +identifying that cell was the + + + align:start position:0% +identifying that cell was the +way that the shape of the accent + + align:start position:0% +way that the shape of the accent + + + align:start position:0% +way that the shape of the accent +so that was the adult + + align:start position:0% +so that was the adult + + + align:start position:0% +so that was the adult +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then they went back successively to + + align:start position:0% +and then they went back successively to + + + align:start position:0% +and then they went back successively to +earlier stages + + align:start position:0% +earlier stages + + + align:start position:0% +earlier stages +withdrawal beat + + align:start position:0% +withdrawal beat + + + align:start position:0% +withdrawal beat +and they saw that + + align:start position:0% +and they saw that + + + align:start position:0% +and they saw that +a cell with the shepherd's crook but + + align:start position:0% +a cell with the shepherd's crook but + + + align:start position:0% +a cell with the shepherd's crook but +then they saw the connection there + + align:start position:0% +then they saw the connection there + + + align:start position:0% +then they saw the connection there +it might have disconnected from the + + align:start position:0% +it might have disconnected from the + + + align:start position:0% +it might have disconnected from the +ventricle already at that stage + + align:start position:0% +ventricle already at that stage + + + align:start position:0% +ventricle already at that stage +and then they went back a little bit + + align:start position:0% +and then they went back a little bit + + + align:start position:0% +and then they went back a little bit +earlier + + align:start position:0% +earlier + + + align:start position:0% +earlier +and they saw they still saw the + + align:start position:0% +and they saw they still saw the + + + align:start position:0% +and they saw they still saw the +shepherds crook + + align:start position:0% +shepherds crook + + + align:start position:0% +shepherds crook +and then + + align:start position:0% +and then + + + align:start position:0% +and then +the cell body was down here and it was + + align:start position:0% +the cell body was down here and it was + + + align:start position:0% +the cell body was down here and it was +connected here + + align:start position:0% +connected here + + + align:start position:0% +connected here +and then even earlier + + align:start position:0% +and then even earlier + + + align:start position:0% +and then even earlier +it looks like the first one i drew there + + align:start position:0% +it looks like the first one i drew there + + + align:start position:0% +it looks like the first one i drew there +so they went backwards in time + + align:start position:0% +so they went backwards in time + + + align:start position:0% +so they went backwards in time +they couldn't have been always mistaken + + align:start position:0% +they couldn't have been always mistaken + + + align:start position:0% +they couldn't have been always mistaken +the + + align:start position:0% +the + + + align:start position:0% +the +mistakingness for allele cell + + align:start position:0% +mistakingness for allele cell + + + align:start position:0% +mistakingness for allele cell +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that was the idea + + align:start position:0% +so that was the idea + + + align:start position:0% +so that was the idea +in other words the mechanism of + + align:start position:0% +in other words the mechanism of + + + align:start position:0% +in other words the mechanism of +migration + + align:start position:0% +migration + + + align:start position:0% +migration +in the czech midbrain for that + + align:start position:0% +in the czech midbrain for that + + + align:start position:0% +in the czech midbrain for that +particular cell was nuclear + + align:start position:0% +particular cell was nuclear + + + align:start position:0% +particular cell was nuclear +translocation + + align:start position:0% +translocation + + + align:start position:0% +translocation +okay + + align:start position:0% + + + + align:start position:0% + +okay so that's where we left off + + align:start position:0% +okay so that's where we left off + + + align:start position:0% +okay so that's where we left off +now let's talk about cell migration in + + align:start position:0% +now let's talk about cell migration in + + + align:start position:0% +now let's talk about cell migration in +the neocortex in the cerebellum + + align:start position:0% +the neocortex in the cerebellum + + + align:start position:0% +the neocortex in the cerebellum +where nuclear translocation is not the + + align:start position:0% +where nuclear translocation is not the + + + align:start position:0% +where nuclear translocation is not the +mechanism + + align:start position:0% +mechanism + + + align:start position:0% +mechanism +there are many similarities though in + + align:start position:0% +there are many similarities though in + + + align:start position:0% +there are many similarities though in +what the cells are doing + + align:start position:0% + + + + align:start position:0% + +but it's pretty clear now that in the + + align:start position:0% +but it's pretty clear now that in the + + + align:start position:0% +but it's pretty clear now that in the +neocortex + + align:start position:0% +neocortex + + + align:start position:0% +neocortex +when cells migrate they move along + + align:start position:0% +when cells migrate they move along + + + align:start position:0% +when cells migrate they move along +radioglial cells + + align:start position:0% +radioglial cells + + + align:start position:0% +radioglial cells +okay and many of them move along the + + align:start position:0% +okay and many of them move along the + + + align:start position:0% +okay and many of them move along the +same radioglia they go up to a structure + + align:start position:0% +same radioglia they go up to a structure + + + align:start position:0% +same radioglia they go up to a structure +called the cortical plate we'll look at + + align:start position:0% +called the cortical plate we'll look at + + + align:start position:0% +called the cortical plate we'll look at +pictures of that and finally you get the + + align:start position:0% +pictures of that and finally you get the + + + align:start position:0% +pictures of that and finally you get the +six layers + + align:start position:0% +six layers + + + align:start position:0% +six layers +of the neocortex + + align:start position:0% + + + + align:start position:0% + +and they show an inside out pattern of + + align:start position:0% +and they show an inside out pattern of + + + align:start position:0% +and they show an inside out pattern of +my + + align:start position:0% +my + + + align:start position:0% +my +movement uh + + align:start position:0% +movement uh + + + align:start position:0% +movement uh +as seen with these labeling methods + + align:start position:0% + + + + align:start position:0% + +they were actually known before it was + + align:start position:0% +they were actually known before it was + + + align:start position:0% +they were actually known before it was +really verified + + align:start position:0% +really verified + + + align:start position:0% +really verified +i put verified + + align:start position:0% +i put verified + + + align:start position:0% +i put verified +rather than demonstrated initially + + align:start position:0% +rather than demonstrated initially + + + align:start position:0% +rather than demonstrated initially +because these patterns were known before + + align:start position:0% +because these patterns were known before + + + align:start position:0% +because these patterns were known before +the autoradiography methods + + align:start position:0% + + + + align:start position:0% + +but they were more tedious methods they + + align:start position:0% +but they were more tedious methods they + + + align:start position:0% +but they were more tedious methods they +use for example vitamin a poisoning at + + align:start position:0% +use for example vitamin a poisoning at + + + align:start position:0% +use for example vitamin a poisoning at +different stages and vitamin a and high + + align:start position:0% +different stages and vitamin a and high + + + align:start position:0% +different stages and vitamin a and high +doses will kill + + align:start position:0% +doses will kill + + + align:start position:0% +doses will kill +the the immature cells + + align:start position:0% +the the immature cells + + + align:start position:0% +the the immature cells +okay so they could wipe out whole layers + + align:start position:0% +okay so they could wipe out whole layers + + + align:start position:0% +okay so they could wipe out whole layers +of neocortex when they were developing + + align:start position:0% +of neocortex when they were developing + + + align:start position:0% +of neocortex when they were developing +you can do the same thing with + + align:start position:0% +you can do the same thing with + + + align:start position:0% +you can do the same thing with +heat application + + align:start position:0% +heat application + + + align:start position:0% +heat application +it's not intense enough to kill every + + align:start position:0% +it's not intense enough to kill every + + + align:start position:0% +it's not intense enough to kill every +cell but it'll kill the + + align:start position:0% +cell but it'll kill the + + + align:start position:0% +cell but it'll kill the +the developing ones but it was these + + align:start position:0% +the developing ones but it was these + + + align:start position:0% +the developing ones but it was these +labeling methods that were the clearest + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +this is a picture from the sigmund + + align:start position:0% +this is a picture from the sigmund + + + align:start position:0% +this is a picture from the sigmund +graduate textbook + + align:start position:0% + + + + align:start position:0% + +it's just depicting + + align:start position:0% +it's just depicting + + + align:start position:0% +it's just depicting +an early stage + + align:start position:0% +an early stage + + + align:start position:0% +an early stage +of cortical development + + align:start position:0% + + + + align:start position:0% + +sort of in the middle of the cell + + align:start position:0% +sort of in the middle of the cell + + + align:start position:0% +sort of in the middle of the cell +migration period the hamster is born + + align:start position:0% +migration period the hamster is born + + + align:start position:0% +migration period the hamster is born +when this is still happening + + align:start position:0% +when this is still happening + + + align:start position:0% +when this is still happening +in fact this is about the stage they're + + align:start position:0% +in fact this is about the stage they're + + + align:start position:0% +in fact this is about the stage they're +born at okay then they're showing a + + align:start position:0% +born at okay then they're showing a + + + align:start position:0% +born at okay then they're showing a +column there through the neural tube in + + align:start position:0% +column there through the neural tube in + + + align:start position:0% +column there through the neural tube in +the left hemisphere of the brain + + align:start position:0% + + + + align:start position:0% + +they're showing that + + align:start position:0% +they're showing that + + + align:start position:0% +they're showing that +neurons can be seen moving along + + align:start position:0% +neurons can be seen moving along + + + align:start position:0% +neurons can be seen moving along +those blue cells which are the glia + + align:start position:0% +those blue cells which are the glia + + + align:start position:0% +those blue cells which are the glia +cells okay + + align:start position:0% + + + + align:start position:0% + +so here + + align:start position:0% +so here + + + align:start position:0% +so here +you see this cell and here you see the + + align:start position:0% +you see this cell and here you see the + + + align:start position:0% +you see this cell and here you see the +blow up and then you see the blue cell + + align:start position:0% +blow up and then you see the blue cell + + + align:start position:0% +blow up and then you see the blue cell +there + + align:start position:0% +there + + + align:start position:0% +there +which is attached here at the pita + + align:start position:0% +which is attached here at the pita + + + align:start position:0% +which is attached here at the pita +and it's i'm sorry here at the ventricle + + align:start position:0% +and it's i'm sorry here at the ventricle + + + align:start position:0% +and it's i'm sorry here at the ventricle +and here at the p the cell body for that + + align:start position:0% +and here at the p the cell body for that + + + align:start position:0% +and here at the p the cell body for that +radial glial cell is down here okay in + + align:start position:0% +radial glial cell is down here okay in + + + align:start position:0% +radial glial cell is down here okay in +the ventricular layer + + align:start position:0% + + + + align:start position:0% + +okay now the mitosis are happening + + align:start position:0% +okay now the mitosis are happening + + + align:start position:0% +okay now the mitosis are happening +here at the ventricle + + align:start position:0% +here at the ventricle + + + align:start position:0% +here at the ventricle +but not only right in the ventricle but + + align:start position:0% +but not only right in the ventricle but + + + align:start position:0% +but not only right in the ventricle but +also in a layer just deep to the + + align:start position:0% +also in a layer just deep to the + + + align:start position:0% +also in a layer just deep to the +ventricle where cells have + + align:start position:0% +ventricle where cells have + + + align:start position:0% +ventricle where cells have +even when they've detached from the + + align:start position:0% +even when they've detached from the + + + align:start position:0% +even when they've detached from the +ventricle you get another layer of + + align:start position:0% +ventricle you get another layer of + + + align:start position:0% +ventricle you get another layer of +mitotic cells there that's called the + + align:start position:0% +mitotic cells there that's called the + + + align:start position:0% +mitotic cells there that's called the +subventricular layer + + align:start position:0% +subventricular layer + + + align:start position:0% +subventricular layer +the artist just couldn't he he just + + align:start position:0% +the artist just couldn't he he just + + + align:start position:0% +the artist just couldn't he he just +assumed well this is above this this + + align:start position:0% +assumed well this is above this this + + + align:start position:0% +assumed well this is above this this +must be the sub ventricular layer he + + align:start position:0% +must be the sub ventricular layer he + + + align:start position:0% +must be the sub ventricular layer he +wasn't because he didn't know + + align:start position:0% +wasn't because he didn't know + + + align:start position:0% +wasn't because he didn't know +and somebody didn't check it + + align:start position:0% +and somebody didn't check it + + + align:start position:0% +and somebody didn't check it +so i'm pointing out a lot of textbooks + + align:start position:0% +so i'm pointing out a lot of textbooks + + + align:start position:0% +so i'm pointing out a lot of textbooks +make mistakes in anatomy + + align:start position:0% +make mistakes in anatomy + + + align:start position:0% +make mistakes in anatomy +okay + + align:start position:0% +okay + + + align:start position:0% +okay +this is + + align:start position:0% +this is + + + align:start position:0% +this is +up from a study at columbia university + + align:start position:0% +up from a study at columbia university + + + align:start position:0% +up from a study at columbia university +where they were first able to see + + align:start position:0% +where they were first able to see + + + align:start position:0% +where they were first able to see +migration + + align:start position:0% +migration + + + align:start position:0% +migration +in tissue culture with movement of the + + align:start position:0% +in tissue culture with movement of the + + + align:start position:0% +in tissue culture with movement of the +cell along the glial cell and here you + + align:start position:0% +cell along the glial cell and here you + + + align:start position:0% +cell along the glial cell and here you +have + + align:start position:0% +have + + + align:start position:0% +have +you can see that it's moving along in + + align:start position:0% +you can see that it's moving along in + + + align:start position:0% +you can see that it's moving along in +the 31 minutes they were looking at it + + align:start position:0% +the 31 minutes they were looking at it + + + align:start position:0% +the 31 minutes they were looking at it +here it moved that far + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +this now is showing + + align:start position:0% +this now is showing + + + align:start position:0% +this now is showing +different + + align:start position:0% +different + + + align:start position:0% +different +stages + + align:start position:0% +stages + + + align:start position:0% +stages +of development in the mouse or rat i + + align:start position:0% +of development in the mouse or rat i + + + align:start position:0% +of development in the mouse or rat i +think this is probably rat + + align:start position:0% +think this is probably rat + + + align:start position:0% +think this is probably rat +okay + + align:start position:0% +okay + + + align:start position:0% +okay +although they're very similar + + align:start position:0% +although they're very similar + + + align:start position:0% +although they're very similar +okay so vz here means a ventricular zone + + align:start position:0% +okay so vz here means a ventricular zone + + + align:start position:0% +okay so vz here means a ventricular zone +okay so the neural tube is very thin + + align:start position:0% +okay so the neural tube is very thin + + + align:start position:0% +okay so the neural tube is very thin +here it's basically a ventricular zone + + align:start position:0% +here it's basically a ventricular zone + + + align:start position:0% +here it's basically a ventricular zone +in a + + align:start position:0% +in a + + + align:start position:0% +in a +little bit of marginal zone there + + align:start position:0% +little bit of marginal zone there + + + align:start position:0% +little bit of marginal zone there +and you see + + align:start position:0% +and you see + + + align:start position:0% +and you see +they're depicting mitosis happening + + align:start position:0% +they're depicting mitosis happening + + + align:start position:0% +they're depicting mitosis happening +there at the ventricle + + align:start position:0% + + + + align:start position:0% + +then a little later + + align:start position:0% +then a little later + + + align:start position:0% +then a little later +you see some fibers appearing here and + + align:start position:0% +you see some fibers appearing here and + + + align:start position:0% +you see some fibers appearing here and +an intermediate zone and some cells + + align:start position:0% +an intermediate zone and some cells + + + align:start position:0% +an intermediate zone and some cells +appearing up here there's just a few + + align:start position:0% +appearing up here there's just a few + + + align:start position:0% +appearing up here there's just a few +they call that the pre-plate + + align:start position:0% +they call that the pre-plate + + + align:start position:0% +they call that the pre-plate +period + + align:start position:0% +period + + + align:start position:0% +period +there's a few cells right at the top but + + align:start position:0% +there's a few cells right at the top but + + + align:start position:0% +there's a few cells right at the top but +still the main thing going on is a lot + + align:start position:0% +still the main thing going on is a lot + + + align:start position:0% +still the main thing going on is a lot +of mitosis here + + align:start position:0% +of mitosis here + + + align:start position:0% +of mitosis here +the cell division is symmetrical + + align:start position:0% +the cell division is symmetrical + + + align:start position:0% +the cell division is symmetrical +so one cell's one one stem cells + + align:start position:0% +so one cell's one one stem cells + + + align:start position:0% +so one cell's one one stem cells +becoming two stem cells becoming four + + align:start position:0% +becoming two stem cells becoming four + + + align:start position:0% +becoming two stem cells becoming four +stem cells and so forth and the longer + + align:start position:0% +stem cells and so forth and the longer + + + align:start position:0% +stem cells and so forth and the longer +that happens + + align:start position:0% +that happens + + + align:start position:0% +that happens +the bigger the area of cortex + + align:start position:0% +the bigger the area of cortex + + + align:start position:0% +the bigger the area of cortex +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so in species like us + + align:start position:0% +so in species like us + + + align:start position:0% +so in species like us +we have such a large neocortex that + + align:start position:0% +we have such a large neocortex that + + + align:start position:0% +we have such a large neocortex that +stage is gonna go a lot longer + + align:start position:0% + + + + align:start position:0% + +and the cortex will become + + align:start position:0% +and the cortex will become + + + align:start position:0% +and the cortex will become +increasing area + + align:start position:0% +increasing area + + + align:start position:0% +increasing area +okay + + align:start position:0% + + + + align:start position:0% + +okay now when these a cell when you get + + align:start position:0% +okay now when these a cell when you get + + + align:start position:0% +okay now when these a cell when you get +asymmetric division and one cell becomes + + align:start position:0% +asymmetric division and one cell becomes + + + align:start position:0% +asymmetric division and one cell becomes +post-mitotic + + align:start position:0% +post-mitotic + + + align:start position:0% +post-mitotic +it + + align:start position:0% +it + + + align:start position:0% +it +attaches to + + align:start position:0% +attaches to + + + align:start position:0% +attaches to +an elongated cell that has now been it's + + align:start position:0% +an elongated cell that has now been it's + + + align:start position:0% +an elongated cell that has now been it's +been + + align:start position:0% +been + + + align:start position:0% +been +shown pretty convincingly it's not a + + align:start position:0% +shown pretty convincingly it's not a + + + align:start position:0% +shown pretty convincingly it's not a +neuron but a glial cell + + align:start position:0% +neuron but a glial cell + + + align:start position:0% +neuron but a glial cell +just like they showed in the previous + + align:start position:0% +just like they showed in the previous + + + align:start position:0% +just like they showed in the previous +picture + + align:start position:0% +picture + + + align:start position:0% +picture +here you see a + + align:start position:0% +here you see a + + + align:start position:0% +here you see a +they're depicting a glial cell with + + align:start position:0% +they're depicting a glial cell with + + + align:start position:0% +they're depicting a glial cell with +a cell migrating along it here another + + align:start position:0% +a cell migrating along it here another + + + align:start position:0% +a cell migrating along it here another +one up here + + align:start position:0% +one up here + + + align:start position:0% +one up here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +there's not one radial glial cell for + + align:start position:0% +there's not one radial glial cell for + + + align:start position:0% +there's not one radial glial cell for +every neuron there's a lot of neurons + + align:start position:0% +every neuron there's a lot of neurons + + + align:start position:0% +every neuron there's a lot of neurons +are using the same cells okay + + align:start position:0% +are using the same cells okay + + + align:start position:0% +are using the same cells okay +but basically all the cells that will + + align:start position:0% +but basically all the cells that will + + + align:start position:0% +but basically all the cells that will +end up in one column + + align:start position:0% +end up in one column + + + align:start position:0% +end up in one column +through the cortex + + align:start position:0% +through the cortex + + + align:start position:0% +through the cortex +are moving along one of the radial glial + + align:start position:0% +are moving along one of the radial glial + + + align:start position:0% +are moving along one of the radial glial +cells + + align:start position:0% +cells + + + align:start position:0% +cells +the intermediate zone is acquiring more + + align:start position:0% +the intermediate zone is acquiring more + + + align:start position:0% +the intermediate zone is acquiring more +axons here + + align:start position:0% +axons here + + + align:start position:0% +axons here +and that will become the white matter of + + align:start position:0% +and that will become the white matter of + + + align:start position:0% +and that will become the white matter of +the cortex above the ventricular layer + + align:start position:0% + + + + align:start position:0% + +these the cells migrate up to this bunch + + align:start position:0% +these the cells migrate up to this bunch + + + align:start position:0% +these the cells migrate up to this bunch +of cells here and that's called the + + align:start position:0% +of cells here and that's called the + + + align:start position:0% +of cells here and that's called the +cortical plate that's + + align:start position:0% +cortical plate that's + + + align:start position:0% +cortical plate that's +the developing layers of the neocortex + + align:start position:0% +the developing layers of the neocortex + + + align:start position:0% +the developing layers of the neocortex +okay that's a little later going to end + + align:start position:0% +okay that's a little later going to end + + + align:start position:0% +okay that's a little later going to end +up like this + + align:start position:0% +up like this + + + align:start position:0% +up like this +where you just have a thin ventricular + + align:start position:0% +where you just have a thin ventricular + + + align:start position:0% +where you just have a thin ventricular +layer they're not even showing the cells + + align:start position:0% +layer they're not even showing the cells + + + align:start position:0% +layer they're not even showing the cells +here then the white matter + + align:start position:0% +here then the white matter + + + align:start position:0% +here then the white matter +then the layers of cells in the cortex + + align:start position:0% + + + + align:start position:0% + +they're showing largest pyramidal cell + + align:start position:0% +they're showing largest pyramidal cell + + + align:start position:0% +they're showing largest pyramidal cell +in layer six it would actually be in + + align:start position:0% +in layer six it would actually be in + + + align:start position:0% +in layer six it would actually be in +layer five + + align:start position:0% +layer five + + + align:start position:0% +layer five +okay + + align:start position:0% +okay + + + align:start position:0% +okay +smaller cells here in layer four more + + align:start position:0% +smaller cells here in layer four more + + + align:start position:0% +smaller cells here in layer four more +primal cells and granule cells in layers + + align:start position:0% +primal cells and granule cells in layers + + + align:start position:0% +primal cells and granule cells in layers +two and three and very few cells up in + + align:start position:0% +two and three and very few cells up in + + + align:start position:0% +two and three and very few cells up in +layer one but lots of dendrites and + + align:start position:0% +layer one but lots of dendrites and + + + align:start position:0% +layer one but lots of dendrites and +axonal connections + + align:start position:0% +axonal connections + + + align:start position:0% +axonal connections +but they occur throughout all the layers + + align:start position:0% + + + + align:start position:0% + +okay now the other interesting thing + + align:start position:0% +okay now the other interesting thing + + + align:start position:0% +okay now the other interesting thing +about this is that when these cells move + + align:start position:0% +about this is that when these cells move + + + align:start position:0% +about this is that when these cells move +up + + align:start position:0% +up + + + align:start position:0% +up +they don't end up they're not dropped + + align:start position:0% +they don't end up they're not dropped + + + align:start position:0% +they don't end up they're not dropped +off down here they move past all the + + align:start position:0% +off down here they move past all the + + + align:start position:0% +off down here they move past all the +other cells in the cortical plate and + + align:start position:0% +other cells in the cortical plate and + + + align:start position:0% +other cells in the cortical plate and +they end up at the top + + align:start position:0% +they end up at the top + + + align:start position:0% +they end up at the top +okay so the latest born cells + + align:start position:0% +okay so the latest born cells + + + align:start position:0% +okay so the latest born cells +are more superficial + + align:start position:0% +are more superficial + + + align:start position:0% +are more superficial +and that's why we call it an inside out + + align:start position:0% +and that's why we call it an inside out + + + align:start position:0% +and that's why we call it an inside out +pattern of migration the cells on the + + align:start position:0% +pattern of migration the cells on the + + + align:start position:0% +pattern of migration the cells on the +inside here of the cortical plate were + + align:start position:0% +inside here of the cortical plate were + + + align:start position:0% +inside here of the cortical plate were +the first ones born the first ones to + + align:start position:0% +the first ones born the first ones to + + + align:start position:0% +the first ones born the first ones to +reach the cortical plate + + align:start position:0% +reach the cortical plate + + + align:start position:0% +reach the cortical plate +and the later ones pile up on top + + align:start position:0% +and the later ones pile up on top + + + align:start position:0% +and the later ones pile up on top +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that's what we mean by the inside out + + align:start position:0% +that's what we mean by the inside out + + + align:start position:0% +that's what we mean by the inside out +pattern + + align:start position:0% + + + + align:start position:0% + +so that means in the cortex here + + align:start position:0% +so that means in the cortex here + + + align:start position:0% +so that means in the cortex here +layer 6 + + align:start position:0% +layer 6 + + + align:start position:0% +layer 6 +cells were the first born now we could + + align:start position:0% +cells were the first born now we could + + + align:start position:0% +cells were the first born now we could +see that in autoradiographic pictures by + + align:start position:0% +see that in autoradiographic pictures by + + + align:start position:0% +see that in autoradiographic pictures by +labeling injecting tritiated thymidine + + align:start position:0% +labeling injecting tritiated thymidine + + + align:start position:0% +labeling injecting tritiated thymidine +to label mitotic cells + + align:start position:0% +to label mitotic cells + + + align:start position:0% +to label mitotic cells +in the + + align:start position:0% +in the + + + align:start position:0% +in the +inject the pregnant female or injector + + align:start position:0% +inject the pregnant female or injector + + + align:start position:0% +inject the pregnant female or injector +fetus would attribute the timodine at + + align:start position:0% +fetus would attribute the timodine at + + + align:start position:0% +fetus would attribute the timodine at +different stages and if you do it very + + align:start position:0% +different stages and if you do it very + + + align:start position:0% +different stages and if you do it very +very early and then just wait until the + + align:start position:0% +very early and then just wait until the + + + align:start position:0% +very early and then just wait until the +pups are born and they grow up + + align:start position:0% +pups are born and they grow up + + + align:start position:0% +pups are born and they grow up +you will see + + align:start position:0% +you will see + + + align:start position:0% +you will see +the radioactive cells here in layer six + + align:start position:0% +the radioactive cells here in layer six + + + align:start position:0% +the radioactive cells here in layer six +and if you do it very late + + align:start position:0% +and if you do it very late + + + align:start position:0% +and if you do it very late +in the hamster would have to be post + + align:start position:0% +in the hamster would have to be post + + + align:start position:0% +in the hamster would have to be post +natal + + align:start position:0% +natal + + + align:start position:0% +natal +you would see them up here in layers two + + align:start position:0% +you would see them up here in layers two + + + align:start position:0% +you would see them up here in layers two +and three + + align:start position:0% + + + + align:start position:0% + +excuse + + align:start position:0% +excuse + + + align:start position:0% +excuse +me + + align:start position:0% +me + + + align:start position:0% +me +m z means marginal zone okay + + align:start position:0% + + + + align:start position:0% + +the most superficial layer + + align:start position:0% +the most superficial layer + + + align:start position:0% +the most superficial layer +of the neural tube + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now let's look at + + align:start position:0% +so now let's look at + + + align:start position:0% +so now let's look at +a slightly different thing that happens + + align:start position:0% +a slightly different thing that happens + + + align:start position:0% +a slightly different thing that happens +in the cerebellar cortex + + align:start position:0% +in the cerebellar cortex + + + align:start position:0% +in the cerebellar cortex +we'll look at the + + align:start position:0% +we'll look at the + + + align:start position:0% +we'll look at the +proliferative cells and the post-mitotic + + align:start position:0% +proliferative cells and the post-mitotic + + + align:start position:0% +proliferative cells and the post-mitotic +granule cells okay + + align:start position:0% + + + + align:start position:0% + +now this is + + align:start position:0% + + + + align:start position:0% + +i may have taken these we mentioned this + + align:start position:0% +i may have taken these we mentioned this + + + align:start position:0% +i may have taken these we mentioned this +briefly from + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +this is the new slide then i'll repeat + + align:start position:0% +this is the new slide then i'll repeat + + + align:start position:0% +this is the new slide then i'll repeat +pictures from an earlier lecture + + align:start position:0% +pictures from an earlier lecture + + + align:start position:0% +pictures from an earlier lecture +the cells move from + + align:start position:0% +the cells move from + + + align:start position:0% +the cells move from +this specialized region of the inner + + align:start position:0% +this specialized region of the inner + + + align:start position:0% +this specialized region of the inner +plate we call it the rhombic lip it's a + + align:start position:0% +plate we call it the rhombic lip it's a + + + align:start position:0% +plate we call it the rhombic lip it's a +thick area looks like a lip when you + + align:start position:0% +thick area looks like a lip when you + + + align:start position:0% +thick area looks like a lip when you +look at it in + + align:start position:0% +look at it in + + + align:start position:0% +look at it in +dissection + + align:start position:0% +dissection + + + align:start position:0% +dissection +and they migrate into the roof plate + + align:start position:0% +and they migrate into the roof plate + + + align:start position:0% +and they migrate into the roof plate +and they form + + align:start position:0% +and they form + + + align:start position:0% +and they form +a proliferative layer there so that's + + align:start position:0% +a proliferative layer there so that's + + + align:start position:0% +a proliferative layer there so that's +different from the neocore it's a little + + align:start position:0% +different from the neocore it's a little + + + align:start position:0% +different from the neocore it's a little +bit like the subventricular there where + + align:start position:0% +bit like the subventricular there where + + + align:start position:0% +bit like the subventricular there where +cells move away from the ventricle but + + align:start position:0% +cells move away from the ventricle but + + + align:start position:0% +cells move away from the ventricle but +they remain proliferative + + align:start position:0% +they remain proliferative + + + align:start position:0% +they remain proliferative +but there they're right next to the + + align:start position:0% +but there they're right next to the + + + align:start position:0% +but there they're right next to the +ventricular layer here they're moving + + align:start position:0% +ventricular layer here they're moving + + + align:start position:0% +ventricular layer here they're moving +further away but they stay they keep + + align:start position:0% +further away but they stay they keep + + + align:start position:0% +further away but they stay they keep +undergoing mitosis okay + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +they really proliferate i mean this + + align:start position:0% +they really proliferate i mean this + + + align:start position:0% +they really proliferate i mean this +those granule cells end up + + align:start position:0% +those granule cells end up + + + align:start position:0% +those granule cells end up +you know + + align:start position:0% + + + + align:start position:0% + +enormous numbers of them they're + + align:start position:0% +enormous numbers of them they're + + + align:start position:0% +enormous numbers of them they're +probably as many granule cells in the + + align:start position:0% +probably as many granule cells in the + + + align:start position:0% +probably as many granule cells in the +cerebellum this there are there is to + + align:start position:0% +cerebellum this there are there is to + + + align:start position:0% +cerebellum this there are there is to +the brain + + align:start position:0% + + + + align:start position:0% + +okay so this is the earlier picture if + + align:start position:0% +okay so this is the earlier picture if + + + align:start position:0% +okay so this is the earlier picture if +you look here + + align:start position:0% +you look here + + + align:start position:0% +you look here +this is the earlier picture of the + + align:start position:0% +this is the earlier picture of the + + + align:start position:0% +this is the earlier picture of the +neural tube that developed early in + + align:start position:0% +neural tube that developed early in + + + align:start position:0% +neural tube that developed early in +development where you see the ailer + + align:start position:0% +development where you see the ailer + + + align:start position:0% +development where you see the ailer +plate and basal plate here and the + + align:start position:0% +plate and basal plate here and the + + + align:start position:0% +plate and basal plate here and the +stretched out roof plate of the typical + + align:start position:0% +stretched out roof plate of the typical + + + align:start position:0% +stretched out roof plate of the typical +of hindbrain + + align:start position:0% +of hindbrain + + + align:start position:0% +of hindbrain +the + + align:start position:0% +the + + + align:start position:0% +the +layer of proliferative cells that we + + align:start position:0% +layer of proliferative cells that we + + + align:start position:0% +layer of proliferative cells that we +call around the clip is there and cells + + align:start position:0% +call around the clip is there and cells + + + align:start position:0% +call around the clip is there and cells +are migrating into the roof plate and + + align:start position:0% +are migrating into the roof plate and + + + align:start position:0% +are migrating into the roof plate and +other cells are migrating down the ones + + align:start position:0% +other cells are migrating down the ones + + + align:start position:0% +other cells are migrating down the ones +that migrate down remember become + + align:start position:0% +that migrate down remember become + + + align:start position:0% +that migrate down remember become +cells of the pons they also become + + align:start position:0% +cells of the pons they also become + + + align:start position:0% +cells of the pons they also become +the inferior olive structure + + align:start position:0% +the inferior olive structure + + + align:start position:0% +the inferior olive structure +there's several structures that they + + align:start position:0% +there's several structures that they + + + align:start position:0% +there's several structures that they +become we're concerned right now with + + align:start position:0% +become we're concerned right now with + + + align:start position:0% +become we're concerned right now with +these that move into the roof plate okay + + align:start position:0% + + + + align:start position:0% + +this is the location that we're talking + + align:start position:0% +this is the location that we're talking + + + align:start position:0% +this is the location that we're talking +about the rostral end of the hindbrain + + align:start position:0% +about the rostral end of the hindbrain + + + align:start position:0% +about the rostral end of the hindbrain +and when animals + + align:start position:0% + + + + align:start position:0% + +like hamsters are born the whole + + align:start position:0% +like hamsters are born the whole + + + align:start position:0% +like hamsters are born the whole +cerebellum is very small i should show + + align:start position:0% +cerebellum is very small i should show + + + align:start position:0% +cerebellum is very small i should show +you some more pictures of that + + align:start position:0% +you some more pictures of that + + + align:start position:0% +you some more pictures of that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +because most of the development is + + align:start position:0% +because most of the development is + + + align:start position:0% +because most of the development is +postnatal okay now this is a picture + + align:start position:0% +postnatal okay now this is a picture + + + align:start position:0% +postnatal okay now this is a picture +from kahal + + align:start position:0% +from kahal + + + align:start position:0% +from kahal +and here's one of the things he saw if + + align:start position:0% +and here's one of the things he saw if + + + align:start position:0% +and here's one of the things he saw if +he looked at the cerebellar cortex real + + align:start position:0% +he looked at the cerebellar cortex real + + + align:start position:0% +he looked at the cerebellar cortex real +early on it was not only much + + align:start position:0% +early on it was not only much + + + align:start position:0% +early on it was not only much +thinner + + align:start position:0% +thinner + + + align:start position:0% +thinner +okay but he saw + + align:start position:0% +okay but he saw + + + align:start position:0% +okay but he saw +a dense layer of cells at the surface + + align:start position:0% +a dense layer of cells at the surface + + + align:start position:0% +a dense layer of cells at the surface +and he knew from studies of the + + align:start position:0% +and he knew from studies of the + + + align:start position:0% +and he knew from studies of the +cerebellum that those weren't there in + + align:start position:0% +cerebellum that those weren't there in + + + align:start position:0% +cerebellum that those weren't there in +the adult + + align:start position:0% +the adult + + + align:start position:0% +the adult +this was something + + align:start position:0% +this was something + + + align:start position:0% +this was something +peculiar to the developing animal right + + align:start position:0% +peculiar to the developing animal right + + + align:start position:0% +peculiar to the developing animal right +around birth and after birth in the + + align:start position:0% +around birth and after birth in the + + + align:start position:0% +around birth and after birth in the +mouth + + align:start position:0% + + + + align:start position:0% + +and he saw + + align:start position:0% +and he saw + + + align:start position:0% +and he saw +in using + + align:start position:0% +in using + + + align:start position:0% +in using +golgi methods and other methods what + + align:start position:0% +golgi methods and other methods what + + + align:start position:0% +golgi methods and other methods what +happened here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +he saw these cells with various shapes + + align:start position:0% +he saw these cells with various shapes + + + align:start position:0% +he saw these cells with various shapes +some of them were just little round + + align:start position:0% +some of them were just little round + + + align:start position:0% +some of them were just little round +cells some of them had processes + + align:start position:0% +cells some of them had processes + + + align:start position:0% +cells some of them had processes +okay + + align:start position:0% + + + + align:start position:0% + +the deeper ones tended to have two + + align:start position:0% +the deeper ones tended to have two + + + align:start position:0% +the deeper ones tended to have two +processes like that and then he also saw + + align:start position:0% +processes like that and then he also saw + + + align:start position:0% +processes like that and then he also saw +some + + align:start position:0% +some + + + align:start position:0% +some +of the third process going down + + align:start position:0% +of the third process going down + + + align:start position:0% +of the third process going down +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then especially later in development + + align:start position:0% +and then especially later in development + + + align:start position:0% +and then especially later in development +he would notice that + + align:start position:0% + + + + align:start position:0% + +the cell body appeared to be moving down + + align:start position:0% +the cell body appeared to be moving down + + + align:start position:0% +the cell body appeared to be moving down +the process that + + align:start position:0% +the process that + + + align:start position:0% +the process that +that was going ventrally okay + + align:start position:0% +that was going ventrally okay + + + align:start position:0% +that was going ventrally okay +so the p is up here + + align:start position:0% +so the p is up here + + + align:start position:0% +so the p is up here +this is the layer of proliferative cells + + align:start position:0% +this is the layer of proliferative cells + + + align:start position:0% +this is the layer of proliferative cells +he's just showing you a few of them it's + + align:start position:0% +he's just showing you a few of them it's + + + align:start position:0% +he's just showing you a few of them it's +very it packed very very densely with + + align:start position:0% +very it packed very very densely with + + + align:start position:0% +very it packed very very densely with +cells + + align:start position:0% + + + + align:start position:0% + +these big cells down here are very large + + align:start position:0% +these big cells down here are very large + + + align:start position:0% +these big cells down here are very large +cells of the proliferative layer of the + + align:start position:0% +cells of the proliferative layer of the + + + align:start position:0% +cells of the proliferative layer of the +cerebellum the purkinje cells + + align:start position:0% +cerebellum the purkinje cells + + + align:start position:0% +cerebellum the purkinje cells +those did not develop that way + + align:start position:0% +those did not develop that way + + + align:start position:0% +those did not develop that way +those came from the ventricular layer + + align:start position:0% +those came from the ventricular layer + + + align:start position:0% +those came from the ventricular layer +down here and they moved up + + align:start position:0% +down here and they moved up + + + align:start position:0% +down here and they moved up +much like we + + align:start position:0% +much like we + + + align:start position:0% +much like we +saw in the spinal cord and neocortex + + align:start position:0% +saw in the spinal cord and neocortex + + + align:start position:0% +saw in the spinal cord and neocortex +okay + + align:start position:0% + + + + align:start position:0% + +they're large cells so those cells are + + align:start position:0% +they're large cells so those cells are + + + align:start position:0% +they're large cells so those cells are +all there already they developed early + + align:start position:0% +all there already they developed early + + + align:start position:0% +all there already they developed early +just typical of larger cells + + align:start position:0% +just typical of larger cells + + + align:start position:0% +just typical of larger cells +many small cells develop late and that's + + align:start position:0% +many small cells develop late and that's + + + align:start position:0% +many small cells develop late and that's +what's happening here so here's the + + align:start position:0% +what's happening here so here's the + + + align:start position:0% +what's happening here so here's the +picture he put together + + align:start position:0% +picture he put together + + + align:start position:0% +picture he put together +these are the cells that move from the + + align:start position:0% +these are the cells that move from the + + + align:start position:0% +these are the cells that move from the +rhombic lip + + align:start position:0% +rhombic lip + + + align:start position:0% +rhombic lip +they grew processes + + align:start position:0% + + + + align:start position:0% + +when they became post-mitotic and many + + align:start position:0% +when they became post-mitotic and many + + + align:start position:0% +when they became post-mitotic and many +of the cells are undergoing mitosis they + + align:start position:0% +of the cells are undergoing mitosis they + + + align:start position:0% +of the cells are undergoing mitosis they +remember but when they became + + align:start position:0% +remember but when they became + + + align:start position:0% +remember but when they became +post-mitotic and began to differentiate + + align:start position:0% +post-mitotic and began to differentiate + + + align:start position:0% +post-mitotic and began to differentiate +they grew lateral processes + + align:start position:0% +they grew lateral processes + + + align:start position:0% +they grew lateral processes +now this would be the way they would + + align:start position:0% +now this would be the way they would + + + align:start position:0% +now this would be the way they would +look in a frontal section + + align:start position:0% +look in a frontal section + + + align:start position:0% +look in a frontal section +because these cells look different + + align:start position:0% +because these cells look different + + + align:start position:0% +because these cells look different +depending on the plane you look at them + + align:start position:0% +depending on the plane you look at them + + + align:start position:0% +depending on the plane you look at them +in + + align:start position:0% +in + + + align:start position:0% +in +okay + + align:start position:0% + + + + align:start position:0% + +the lateral processes here + + align:start position:0% +the lateral processes here + + + align:start position:0% +the lateral processes here +become + + align:start position:0% +become + + + align:start position:0% +become +both of them are accents + + align:start position:0% +both of them are accents + + + align:start position:0% +both of them are accents +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the cell has accents going in two + + align:start position:0% +the cell has accents going in two + + + align:start position:0% +the cell has accents going in two +directions + + align:start position:0% +directions + + + align:start position:0% +directions +okay we call them parallel fibers + + align:start position:0% +okay we call them parallel fibers + + + align:start position:0% +okay we call them parallel fibers +because there's enormous numbers of + + align:start position:0% +because there's enormous numbers of + + + align:start position:0% +because there's enormous numbers of +fibers all parallel with each other all + + align:start position:0% +fibers all parallel with each other all + + + align:start position:0% +fibers all parallel with each other all +doing the same thing okay + + align:start position:0% + + + + align:start position:0% + +now what about this this process going + + align:start position:0% +now what about this this process going + + + align:start position:0% +now what about this this process going +down well that's an axon too + + align:start position:0% +down well that's an axon too + + + align:start position:0% +down well that's an axon too +but the cell doesn't stay there it + + align:start position:0% +but the cell doesn't stay there it + + + align:start position:0% +but the cell doesn't stay there it +doesn't stay there with three axons + + align:start position:0% +doesn't stay there with three axons + + + align:start position:0% +doesn't stay there with three axons +coming out of it instead the cell body + + align:start position:0% +coming out of it instead the cell body + + + align:start position:0% +coming out of it instead the cell body +moves down the axon + + align:start position:0% +moves down the axon + + + align:start position:0% +moves down the axon +okay + + align:start position:0% +okay + + + align:start position:0% +okay +this process is always a little further + + align:start position:0% +this process is always a little further + + + align:start position:0% +this process is always a little further +down + + align:start position:0% +down + + + align:start position:0% +down +so here you see a cell let's move down + + align:start position:0% +so here you see a cell let's move down + + + align:start position:0% +so here you see a cell let's move down +further here let's move clear down to + + align:start position:0% +further here let's move clear down to + + + align:start position:0% +further here let's move clear down to +the level of the purkinje cell + + align:start position:0% +the level of the purkinje cell + + + align:start position:0% +the level of the purkinje cell +and then as it moves past the purkinje + + align:start position:0% +and then as it moves past the purkinje + + + align:start position:0% +and then as it moves past the purkinje +cells + + align:start position:0% +cells + + + align:start position:0% +cells +here it begins to differentiate + + align:start position:0% +here it begins to differentiate + + + align:start position:0% +here it begins to differentiate +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and finally + + align:start position:0% +and finally + + + align:start position:0% +and finally +you end up with cells like these + + align:start position:0% +you end up with cells like these + + + align:start position:0% +you end up with cells like these +the one furthest to the left would be + + align:start position:0% +the one furthest to the left would be + + + align:start position:0% +the one furthest to the left would be +the more mature + + align:start position:0% +the more mature + + + align:start position:0% +the more mature +granule cell of a cerebellum always + + align:start position:0% +granule cell of a cerebellum always + + + align:start position:0% +granule cell of a cerebellum always +located below + + align:start position:0% +located below + + + align:start position:0% +located below +the purkinje cell layer + + align:start position:0% +the purkinje cell layer + + + align:start position:0% +the purkinje cell layer +and it's now growing + + align:start position:0% +and it's now growing + + + align:start position:0% +and it's now growing +these specialized little dendrites that + + align:start position:0% +these specialized little dendrites that + + + align:start position:0% +these specialized little dendrites that +will receive input fibers + + align:start position:0% + + + + align:start position:0% + +just like the spinal cerebellar tracts + + align:start position:0% +just like the spinal cerebellar tracts + + + align:start position:0% +just like the spinal cerebellar tracts +or + + align:start position:0% +or + + + align:start position:0% +or +cell or the uh + + align:start position:0% +cell or the uh + + + align:start position:0% +cell or the uh +accents from coming from the pons okay + + align:start position:0% + + + + align:start position:0% + +so they're they're the major input layer + + align:start position:0% +so they're they're the major input layer + + + align:start position:0% +so they're they're the major input layer +of the cerebellum + + align:start position:0% +of the cerebellum + + + align:start position:0% +of the cerebellum +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the + + align:start position:0% +the + + + align:start position:0% +the +the axon then + + align:start position:0% +the axon then + + + align:start position:0% +the axon then +of the mature cell + + align:start position:0% +of the mature cell + + + align:start position:0% +of the mature cell +goes up to the superficial layer above + + align:start position:0% +goes up to the superficial layer above + + + align:start position:0% +goes up to the superficial layer above +the purkinje cell + + align:start position:0% +the purkinje cell + + + align:start position:0% +the purkinje cell +and forms parallel fibers + + align:start position:0% +and forms parallel fibers + + + align:start position:0% +and forms parallel fibers +each cell forming one parallel fiber + + align:start position:0% +each cell forming one parallel fiber + + + align:start position:0% +each cell forming one parallel fiber +okay + + align:start position:0% + + + + align:start position:0% + +so this just summarizes what we we're + + align:start position:0% +so this just summarizes what we we're + + + align:start position:0% +so this just summarizes what we we're +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +the cells migrate away from the peel + + align:start position:0% +the cells migrate away from the peel + + + align:start position:0% +the cells migrate away from the peel +surface they leave their axons behind + + align:start position:0% +surface they leave their axons behind + + + align:start position:0% +surface they leave their axons behind +sort of like a spider moving down its + + align:start position:0% +sort of like a spider moving down its + + + align:start position:0% +sort of like a spider moving down its +web + + align:start position:0% +web + + + align:start position:0% +web +they move past the big purkinje cells to + + align:start position:0% +they move past the big purkinje cells to + + + align:start position:0% +they move past the big purkinje cells to +the adult location that's where they + + align:start position:0% +the adult location that's where they + + + align:start position:0% +the adult location that's where they +grow their dendrites + + align:start position:0% +grow their dendrites + + + align:start position:0% +grow their dendrites +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and the cerebellum is an amazing + + align:start position:0% +and the cerebellum is an amazing + + + align:start position:0% +and the cerebellum is an amazing +structure because it's a very large + + align:start position:0% +structure because it's a very large + + + align:start position:0% +structure because it's a very large +cortical + + align:start position:0% +cortical + + + align:start position:0% +cortical +sheath + + align:start position:0% +sheath + + + align:start position:0% +sheath +and yet no matter where you look at it + + align:start position:0% +and yet no matter where you look at it + + + align:start position:0% +and yet no matter where you look at it +you see the same structures + + align:start position:0% +you see the same structures + + + align:start position:0% +you see the same structures +no matter where you look in the + + align:start position:0% +no matter where you look in the + + + align:start position:0% +no matter where you look in the +cerebellum the same kind of thing what's + + align:start position:0% +cerebellum the same kind of thing what's + + + align:start position:0% +cerebellum the same kind of thing what's +going on + + align:start position:0% + + + + align:start position:0% + +it's more uniform in structure than the + + align:start position:0% +it's more uniform in structure than the + + + align:start position:0% +it's more uniform in structure than the +neo than the neocortex + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so there at the end we were starting not + + align:start position:0% +so there at the end we were starting not + + + align:start position:0% +so there at the end we were starting not +to talk about migration we saw the + + align:start position:0% +to talk about migration we saw the + + + align:start position:0% +to talk about migration we saw the +migration how that happens + + align:start position:0% +migration how that happens + + + align:start position:0% +migration how that happens +then we talk about differentiation when + + align:start position:0% +then we talk about differentiation when + + + align:start position:0% +then we talk about differentiation when +the cells are growing their dendrites + + align:start position:0% +the cells are growing their dendrites + + + align:start position:0% +the cells are growing their dendrites +and accents + + align:start position:0% +and accents + + + align:start position:0% +and accents +okay + + align:start position:0% +okay + + + align:start position:0% +okay +we know that the accent often develops + + align:start position:0% +we know that the accent often develops + + + align:start position:0% +we know that the accent often develops +first + + align:start position:0% +first + + + align:start position:0% +first +we saw that for the shippers crook cell + + align:start position:0% +we saw that for the shippers crook cell + + + align:start position:0% +we saw that for the shippers crook cell +on the tectum the axon grew out even + + align:start position:0% +on the tectum the axon grew out even + + + align:start position:0% +on the tectum the axon grew out even +before the cell body reached + + align:start position:0% +before the cell body reached + + + align:start position:0% +before the cell body reached +its final position we saw the same thing + + align:start position:0% +its final position we saw the same thing + + + align:start position:0% +its final position we saw the same thing +for the granule cells even though the + + align:start position:0% +for the granule cells even though the + + + align:start position:0% +for the granule cells even though the +whole the movement was very different + + align:start position:0% +whole the movement was very different + + + align:start position:0% +whole the movement was very different +the axons grew + + align:start position:0% +the axons grew + + + align:start position:0% +the axons grew +earlier long before the cell was in its + + align:start position:0% +earlier long before the cell was in its + + + align:start position:0% +earlier long before the cell was in its +final position + + align:start position:0% +final position + + + align:start position:0% +final position +now when these processors are growing + + align:start position:0% +now when these processors are growing + + + align:start position:0% +now when these processors are growing +they have an active tip that's broader + + align:start position:0% +they have an active tip that's broader + + + align:start position:0% +they have an active tip that's broader +than the trunk of the axon we call it + + align:start position:0% +than the trunk of the axon we call it + + + align:start position:0% +than the trunk of the axon we call it +the growth column i'm going to show you + + align:start position:0% +the growth column i'm going to show you + + + align:start position:0% +the growth column i'm going to show you +some pictures of those + + align:start position:0% +some pictures of those + + + align:start position:0% +some pictures of those +including video clips + + align:start position:0% +including video clips + + + align:start position:0% +including video clips +and + + align:start position:0% +and + + + align:start position:0% +and +where they go depends on a number of + + align:start position:0% +where they go depends on a number of + + + align:start position:0% +where they go depends on a number of +factors one of them is + + align:start position:0% +factors one of them is + + + align:start position:0% +factors one of them is +we call selective adhesion + + align:start position:0% +we call selective adhesion + + + align:start position:0% +we call selective adhesion +the + + align:start position:0% +the + + + align:start position:0% +the +the active growth cone which you can + + align:start position:0% +the active growth cone which you can + + + align:start position:0% +the active growth cone which you can +imagine like my hand here these little + + align:start position:0% +imagine like my hand here these little + + + align:start position:0% +imagine like my hand here these little +processes extend out if you imagine now + + align:start position:0% +processes extend out if you imagine now + + + align:start position:0% +processes extend out if you imagine now +that the tips the tips of the fingers + + align:start position:0% +that the tips the tips of the fingers + + + align:start position:0% +that the tips the tips of the fingers +here are more adhesive to something on + + align:start position:0% +here are more adhesive to something on + + + align:start position:0% +here are more adhesive to something on +the surfaces they're growing on and they + + align:start position:0% +the surfaces they're growing on and they + + + align:start position:0% +the surfaces they're growing on and they +can't grow except on surfaces they don't + + align:start position:0% +can't grow except on surfaces they don't + + + align:start position:0% +can't grow except on surfaces they don't +grow through fluid space + + align:start position:0% +grow through fluid space + + + align:start position:0% +grow through fluid space +okay + + align:start position:0% +okay + + + align:start position:0% +okay +these grab on to the more adhesive + + align:start position:0% +these grab on to the more adhesive + + + align:start position:0% +these grab on to the more adhesive +substrates and then they get pulled + + align:start position:0% +substrates and then they get pulled + + + align:start position:0% +substrates and then they get pulled +along that's how the axon + + align:start position:0% +along that's how the axon + + + align:start position:0% +along that's how the axon +grows + + align:start position:0% + + + + align:start position:0% + +so this is one of calhoun's pictures of + + align:start position:0% +so this is one of calhoun's pictures of + + + align:start position:0% +so this is one of calhoun's pictures of +stages of nerve fiber development + + align:start position:0% + + + + align:start position:0% + +so you see the cell there + + align:start position:0% + + + + align:start position:0% + +beginning to grow it's axon + + align:start position:0% + + + + align:start position:0% + +first + + align:start position:0% +first + + + align:start position:0% +first +so in c it only has an axon there you + + align:start position:0% +so in c it only has an axon there you + + + align:start position:0% +so in c it only has an axon there you +see his picture of the growth cone and + + align:start position:0% +see his picture of the growth cone and + + + align:start position:0% +see his picture of the growth cone and +described this just from golgi methods + + align:start position:0% +described this just from golgi methods + + + align:start position:0% +described this just from golgi methods +without seeing them in tissue culture + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% +and then + + + align:start position:0% +and then +when it reaches its adult location it + + align:start position:0% +when it reaches its adult location it + + + align:start position:0% +when it reaches its adult location it +begins to mature forms its + + align:start position:0% +begins to mature forms its + + + align:start position:0% +begins to mature forms its +terminal arborization can also grow + + align:start position:0% +terminal arborization can also grow + + + align:start position:0% +terminal arborization can also grow +collaterals those can happen at various + + align:start position:0% +collaterals those can happen at various + + + align:start position:0% +collaterals those can happen at various +stages and then the cell body will be + + align:start position:0% +stages and then the cell body will be + + + align:start position:0% +stages and then the cell body will be +changing too growing its dendrites they + + align:start position:0% +changing too growing its dendrites they + + + align:start position:0% +changing too growing its dendrites they +usually grow somewhat later than the + + align:start position:0% +usually grow somewhat later than the + + + align:start position:0% +usually grow somewhat later than the +accent + + align:start position:0% + + + + align:start position:0% + +so that's kahal's picture + + align:start position:0% +so that's kahal's picture + + + align:start position:0% +so that's kahal's picture +and here's a + + align:start position:0% +and here's a + + + align:start position:0% +and here's a +particular kind of it's a freeze + + align:start position:0% +particular kind of it's a freeze + + + align:start position:0% +particular kind of it's a freeze +fracture picture of a growth cone + + align:start position:0% +fracture picture of a growth cone + + + align:start position:0% +fracture picture of a growth cone +showing you + + align:start position:0% +showing you + + + align:start position:0% +showing you +that there's a lot of things going on + + align:start position:0% +that there's a lot of things going on + + + align:start position:0% +that there's a lot of things going on +inside in fact there's many actin + + align:start position:0% +inside in fact there's many actin + + + align:start position:0% +inside in fact there's many actin +filaments there which are contractual + + align:start position:0% +filaments there which are contractual + + + align:start position:0% +filaments there which are contractual +proteins + + align:start position:0% +proteins + + + align:start position:0% +proteins +there's many organelles + + align:start position:0% +there's many organelles + + + align:start position:0% +there's many organelles +including mitochondria and vesicles + + align:start position:0% +including mitochondria and vesicles + + + align:start position:0% +including mitochondria and vesicles +and these little extensions are what we + + align:start position:0% +and these little extensions are what we + + + align:start position:0% +and these little extensions are what we +call + + align:start position:0% +call + + + align:start position:0% +call +philopodia okay + + align:start position:0% + + + + align:start position:0% + +filler podium would be the singular + + align:start position:0% + + + + align:start position:0% + +i haven't finished all the + + align:start position:0% +i haven't finished all the + + + align:start position:0% +i haven't finished all the +flash cube terms for the development + + align:start position:0% +flash cube terms for the development + + + align:start position:0% +flash cube terms for the development +lectures but i'm working on them so i + + align:start position:0% +lectures but i'm working on them so i + + + align:start position:0% +lectures but i'm working on them so i +will post that + + align:start position:0% +will post that + + + align:start position:0% +will post that +okay + + align:start position:0% + + + + align:start position:0% + +but the thing to remember about these is + + align:start position:0% +but the thing to remember about these is + + + align:start position:0% +but the thing to remember about these is +that they're transient structures okay + + align:start position:0% + + + + align:start position:0% + +these little structures extend and then + + align:start position:0% +these little structures extend and then + + + align:start position:0% +these little structures extend and then +they pull back and they extend and pull + + align:start position:0% +they pull back and they extend and pull + + + align:start position:0% +they pull back and they extend and pull +back + + align:start position:0% +back + + + align:start position:0% +back +so it's a very active structure and + + align:start position:0% +so it's a very active structure and + + + align:start position:0% +so it's a very active structure and +you'll see that in the pictures + + align:start position:0% + + + + align:start position:0% + +their motile structures + + align:start position:0% + + + + align:start position:0% + +and remember that at their tips they're + + align:start position:0% +and remember that at their tips they're + + + align:start position:0% +and remember that at their tips they're +more adhesive + + align:start position:0% +more adhesive + + + align:start position:0% +more adhesive +and when they contract then if the tip + + align:start position:0% +and when they contract then if the tip + + + align:start position:0% +and when they contract then if the tip +is + + align:start position:0% +is + + + align:start position:0% +is +adhering to a substrate the growth corn + + align:start position:0% +adhering to a substrate the growth corn + + + align:start position:0% +adhering to a substrate the growth corn +will tend to be pulled in that direction + + align:start position:0% +will tend to be pulled in that direction + + + align:start position:0% +will tend to be pulled in that direction +you see but if there's a lot of them + + align:start position:0% +you see but if there's a lot of them + + + align:start position:0% +you see but if there's a lot of them +pulling in every direction how can the + + align:start position:0% +pulling in every direction how can the + + + align:start position:0% +pulling in every direction how can the +thing move at all + + align:start position:0% +thing move at all + + + align:start position:0% +thing move at all +well it seems to we think it moves sort + + align:start position:0% +well it seems to we think it moves sort + + + align:start position:0% +well it seems to we think it moves sort +of as the result the vector sum of all + + align:start position:0% +of as the result the vector sum of all + + + align:start position:0% +of as the result the vector sum of all +the tensions on it + + align:start position:0% +the tensions on it + + + align:start position:0% +the tensions on it +okay + + align:start position:0% + + + + align:start position:0% + +and we know some of the molecules + + align:start position:0% +and we know some of the molecules + + + align:start position:0% +and we know some of the molecules +involve cell adhesion molecules + + align:start position:0% +involve cell adhesion molecules + + + align:start position:0% +involve cell adhesion molecules +one of them we call enchem neuronal + + align:start position:0% +one of them we call enchem neuronal + + + align:start position:0% +one of them we call enchem neuronal +salivation molecule but there's a number + + align:start position:0% +salivation molecule but there's a number + + + align:start position:0% +salivation molecule but there's a number +of adhesive molecules like that + + align:start position:0% + + + + align:start position:0% + +okay now one way that this is studied + + align:start position:0% +okay now one way that this is studied + + + align:start position:0% +okay now one way that this is studied +it's very difficult to see these things + + align:start position:0% +it's very difficult to see these things + + + align:start position:0% +it's very difficult to see these things +if we want to look at them in live + + align:start position:0% +if we want to look at them in live + + + align:start position:0% +if we want to look at them in live +action in the real brain + + align:start position:0% +action in the real brain + + + align:start position:0% +action in the real brain +that has been done but with great + + align:start position:0% +that has been done but with great + + + align:start position:0% +that has been done but with great +difficulty only recently if we have + + align:start position:0% +difficulty only recently if we have + + + align:start position:0% +difficulty only recently if we have +methods we can do that a lot of the work + + align:start position:0% +methods we can do that a lot of the work + + + align:start position:0% +methods we can do that a lot of the work +has been in tissue culture + + align:start position:0% +has been in tissue culture + + + align:start position:0% +has been in tissue culture +and this is just a picture of + + align:start position:0% + + + + align:start position:0% + +cultures from this could be either a + + align:start position:0% +cultures from this could be either a + + + align:start position:0% +cultures from this could be either a +dorsal root ganglion or a synthetic + + align:start position:0% +dorsal root ganglion or a synthetic + + + align:start position:0% +dorsal root ganglion or a synthetic +ganglion it's probably a dorsal root + + align:start position:0% +ganglion it's probably a dorsal root + + + align:start position:0% +ganglion it's probably a dorsal root +ganglion placed in culture + + align:start position:0% +ganglion placed in culture + + + align:start position:0% +ganglion placed in culture +and in this particular picture they're + + align:start position:0% +and in this particular picture they're + + + align:start position:0% +and in this particular picture they're +contrasting a culture + + align:start position:0% +contrasting a culture + + + align:start position:0% +contrasting a culture +where there was no particular growth + + align:start position:0% +where there was no particular growth + + + align:start position:0% +where there was no particular growth +factor + + align:start position:0% +factor + + + align:start position:0% +factor +and another one where they added this + + align:start position:0% +and another one where they added this + + + align:start position:0% +and another one where they added this +growth factor neuronal growth factor the + + align:start position:0% +growth factor neuronal growth factor the + + + align:start position:0% +growth factor neuronal growth factor the +first growth factor to be discovered ntf + + align:start position:0% +first growth factor to be discovered ntf + + + align:start position:0% +first growth factor to be discovered ntf +we call it + + align:start position:0% +we call it + + + align:start position:0% +we call it +the first member of the a family of + + align:start position:0% +the first member of the a family of + + + align:start position:0% +the first member of the a family of +growth factors we call the neurotrophins + + align:start position:0% +growth factors we call the neurotrophins + + + align:start position:0% +growth factors we call the neurotrophins +okay and so here with + + align:start position:0% +okay and so here with + + + align:start position:0% +okay and so here with +the right medium and with growth factor + + align:start position:0% +the right medium and with growth factor + + + align:start position:0% +the right medium and with growth factor +you can see + + align:start position:0% +you can see + + + align:start position:0% +you can see +the proliferation of axons coming out of + + align:start position:0% +the proliferation of axons coming out of + + + align:start position:0% +the proliferation of axons coming out of +that + + align:start position:0% +that + + + align:start position:0% +that +clump of cells + + align:start position:0% +clump of cells + + + align:start position:0% +clump of cells +and we can study the + + align:start position:0% +and we can study the + + + align:start position:0% +and we can study the +the growth columns and other properties + + align:start position:0% +the growth columns and other properties + + + align:start position:0% +the growth columns and other properties +of growth in tissue culture in a flat + + align:start position:0% +of growth in tissue culture in a flat + + + align:start position:0% +of growth in tissue culture in a flat +plate okay + + align:start position:0% +plate okay + + + align:start position:0% +plate okay +and there have been many studies like + + align:start position:0% +and there have been many studies like + + + align:start position:0% +and there have been many studies like +that and i'll show you now some video + + align:start position:0% +that and i'll show you now some video + + + align:start position:0% +that and i'll show you now some video +clips + + align:start position:0% + + + + align:start position:0% + +okay this just the first one just shows + + align:start position:0% +okay this just the first one just shows + + + align:start position:0% +okay this just the first one just shows +a large growth curve we might even have + + align:start position:0% +a large growth curve we might even have + + + align:start position:0% +a large growth curve we might even have +to turn out all the lights here because + + align:start position:0% +to turn out all the lights here because + + + align:start position:0% +to turn out all the lights here because +it's a little dim there + + align:start position:0% +it's a little dim there + + + align:start position:0% +it's a little dim there +it's that + + align:start position:0% +it's that + + + align:start position:0% +it's that +shadowy thing in the back there here's + + align:start position:0% +shadowy thing in the back there here's + + + align:start position:0% +shadowy thing in the back there here's +the trunk of the axon it's got some + + align:start position:0% +the trunk of the axon it's got some + + + align:start position:0% +the trunk of the axon it's got some +little processes coming up + + align:start position:0% +little processes coming up + + + align:start position:0% +little processes coming up +it's moving across the screen can you + + align:start position:0% +it's moving across the screen can you + + + align:start position:0% +it's moving across the screen can you +see it there + + align:start position:0% +see it there + + + align:start position:0% +see it there +and this is the end of it and you see + + align:start position:0% +and this is the end of it and you see + + + align:start position:0% +and this is the end of it and you see +there's a filler podium there's a whole + + align:start position:0% +there's a filler podium there's a whole + + + align:start position:0% +there's a filler podium there's a whole +bunch of pillow podium so let's watch it + + align:start position:0% +bunch of pillow podium so let's watch it + + + align:start position:0% +bunch of pillow podium so let's watch it +again it starts here and just look at + + align:start position:0% +again it starts here and just look at + + + align:start position:0% +again it starts here and just look at +what's happening there + + align:start position:0% + + + + align:start position:0% + +you'll see them extend and then they + + align:start position:0% +you'll see them extend and then they + + + align:start position:0% +you'll see them extend and then they +disappear and they extend again okay + + align:start position:0% +disappear and they extend again okay + + + align:start position:0% +disappear and they extend again okay +and the axon is gradually elongated so + + align:start position:0% +and the axon is gradually elongated so + + + align:start position:0% +and the axon is gradually elongated so +it's what's happening there is it's + + align:start position:0% +it's what's happening there is it's + + + align:start position:0% +it's what's happening there is it's +we're seeing the action at the growth + + align:start position:0% +we're seeing the action at the growth + + + align:start position:0% +we're seeing the action at the growth +cone but there's a lot of things going + + align:start position:0% +cone but there's a lot of things going + + + align:start position:0% +cone but there's a lot of things going +on in the cell too of course and one + + align:start position:0% +on in the cell too of course and one + + + align:start position:0% +on in the cell too of course and one +thing is it's adding membrane where's + + align:start position:0% +thing is it's adding membrane where's + + + align:start position:0% +thing is it's adding membrane where's +the membrane come from + + align:start position:0% +the membrane come from + + + align:start position:0% +the membrane come from +well it comes from the cell body + + align:start position:0% +well it comes from the cell body + + + align:start position:0% +well it comes from the cell body +and it's being transported down this + + align:start position:0% +and it's being transported down this + + + align:start position:0% +and it's being transported down this +axon in little vesicles + + align:start position:0% +axon in little vesicles + + + align:start position:0% +axon in little vesicles +okay the vesicles contain + + align:start position:0% +okay the vesicles contain + + + align:start position:0% +okay the vesicles contain +things too + + align:start position:0% +things too + + + align:start position:0% +things too +but the membrane of the vesicle becomes + + align:start position:0% +but the membrane of the vesicle becomes + + + align:start position:0% +but the membrane of the vesicle becomes +the membrane + + align:start position:0% +the membrane + + + align:start position:0% +the membrane +of the accent all right + + align:start position:0% + + + + align:start position:0% + +okay let's just look at the next one i + + align:start position:0% +okay let's just look at the next one i + + + align:start position:0% +okay let's just look at the next one i +guess i don't have to go back through + + align:start position:0% +guess i don't have to go back through + + + align:start position:0% +guess i don't have to go back through +all this + + align:start position:0% +all this + + + align:start position:0% +all this +okay this time you're gonna see + + align:start position:0% +okay this time you're gonna see + + + align:start position:0% +okay this time you're gonna see +two axons that don't belong together + + align:start position:0% +two axons that don't belong together + + + align:start position:0% +two axons that don't belong together +because they don't occur together in the + + align:start position:0% +because they don't occur together in the + + + align:start position:0% +because they don't occur together in the +real brain + + align:start position:0% +real brain + + + align:start position:0% +real brain +once from the retina once from a dorsal + + align:start position:0% +once from the retina once from a dorsal + + + align:start position:0% +once from the retina once from a dorsal +root ganglion + + align:start position:0% +root ganglion + + + align:start position:0% +root ganglion +you're + + align:start position:0% +you're + + + align:start position:0% +you're +see we're magnifying in 2400 + + align:start position:0% +see we're magnifying in 2400 + + + align:start position:0% +see we're magnifying in 2400 +but that of course is probably much more + + align:start position:0% +but that of course is probably much more + + + align:start position:0% +but that of course is probably much more +than that because of the size of this + + align:start position:0% +than that because of the size of this + + + align:start position:0% +than that because of the size of this +screen + + align:start position:0% +screen + + + align:start position:0% +screen +then the 60x acceleration okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +one here one here now watch what happens + + align:start position:0% +one here one here now watch what happens + + + align:start position:0% +one here one here now watch what happens +this one is retracting you see it's + + align:start position:0% +this one is retracting you see it's + + + align:start position:0% +this one is retracting you see it's +still hanging on there a little bit but + + align:start position:0% +still hanging on there a little bit but + + + align:start position:0% +still hanging on there a little bit but +it's going to withdraw those in the cell + + align:start position:0% +it's going to withdraw those in the cell + + + align:start position:0% +it's going to withdraw those in the cell +this is called growth cone collapse + + align:start position:0% + + + + align:start position:0% + +perhaps calling it retraction of the + + align:start position:0% +perhaps calling it retraction of the + + + align:start position:0% +perhaps calling it retraction of the +growth cone is a little more descriptive + + align:start position:0% +growth cone is a little more descriptive + + + align:start position:0% +growth cone is a little more descriptive +they're both both nice descriptive terms + + align:start position:0% +they're both both nice descriptive terms + + + align:start position:0% +they're both both nice descriptive terms +but that's very common when growth two + + align:start position:0% +but that's very common when growth two + + + align:start position:0% +but that's very common when growth two +pros two axons are growing in culture + + align:start position:0% +pros two axons are growing in culture + + + align:start position:0% +pros two axons are growing in culture +and they meet each other + + align:start position:0% +and they meet each other + + + align:start position:0% +and they meet each other +the growth cone of one touches the + + align:start position:0% +the growth cone of one touches the + + + align:start position:0% +the growth cone of one touches the +growth cone or the axon of another + + align:start position:0% +growth cone or the axon of another + + + align:start position:0% +growth cone or the axon of another +they either can cross over + + align:start position:0% +they either can cross over + + + align:start position:0% +they either can cross over +or one of them will retract + + align:start position:0% +or one of them will retract + + + align:start position:0% +or one of them will retract +one the growth cone can retract that's + + align:start position:0% +one the growth cone can retract that's + + + align:start position:0% +one the growth cone can retract that's +when it's filopodia touch the other and + + align:start position:0% +when it's filopodia touch the other and + + + align:start position:0% +when it's filopodia touch the other and +we find that that depends on which cells + + align:start position:0% +we find that that depends on which cells + + + align:start position:0% +we find that that depends on which cells +they are now if you have retinal axons + + align:start position:0% +they are now if you have retinal axons + + + align:start position:0% +they are now if you have retinal axons +meeting a dorsal root axon + + align:start position:0% +meeting a dorsal root axon + + + align:start position:0% +meeting a dorsal root axon +you usually get retraction when they + + align:start position:0% +you usually get retraction when they + + + align:start position:0% +you usually get retraction when they +touch each other + + align:start position:0% +touch each other + + + align:start position:0% +touch each other +if it's two dorsal root axons that touch + + align:start position:0% +if it's two dorsal root axons that touch + + + align:start position:0% +if it's two dorsal root axons that touch +each other + + align:start position:0% +each other + + + align:start position:0% +each other +they still often retract + + align:start position:0% +they still often retract + + + align:start position:0% +they still often retract +but they'll cross they they retract more + + align:start position:0% +but they'll cross they they retract more + + + align:start position:0% +but they'll cross they they retract more +than fifty percent of the time but they + + align:start position:0% +than fifty percent of the time but they + + + align:start position:0% +than fifty percent of the time but they +often also cross over each other + + align:start position:0% +often also cross over each other + + + align:start position:0% +often also cross over each other +okay + + align:start position:0% + + + + align:start position:0% + +now when they retract what happens they + + align:start position:0% +now when they retract what happens they + + + align:start position:0% +now when they retract what happens they +pull back + + align:start position:0% +pull back + + + align:start position:0% +pull back +and then after a very brief pause + + align:start position:0% +and then after a very brief pause + + + align:start position:0% +and then after a very brief pause +they'll start going again and usually + + align:start position:0% +they'll start going again and usually + + + align:start position:0% +they'll start going again and usually +when they start growing again they + + align:start position:0% +when they start growing again they + + + align:start position:0% +when they start growing again they +change direction slightly + + align:start position:0% +change direction slightly + + + align:start position:0% +change direction slightly +okay + + align:start position:0% + + + + align:start position:0% + +that's the most common thing to happen + + align:start position:0% + + + + align:start position:0% + +so now we'll look at three of them + + align:start position:0% +so now we'll look at three of them + + + align:start position:0% +so now we'll look at three of them +drawing + + align:start position:0% + + + + align:start position:0% + +this one here there's one there and + + align:start position:0% +this one here there's one there and + + + align:start position:0% +this one here there's one there and +there's one there + + align:start position:0% +there's one there + + + align:start position:0% +there's one there +you see them + + align:start position:0% +you see them + + + align:start position:0% +you see them +this one is going to branch + + align:start position:0% +this one is going to branch + + + align:start position:0% +this one is going to branch +it's seeing a lot of adhesion here and + + align:start position:0% +it's seeing a lot of adhesion here and + + + align:start position:0% +it's seeing a lot of adhesion here and +here + + align:start position:0% +here + + + align:start position:0% +here +less here and it ends up branching + + align:start position:0% +less here and it ends up branching + + + align:start position:0% +less here and it ends up branching +okay + + align:start position:0% +okay + + + align:start position:0% +okay +these two are touching each other + + align:start position:0% +these two are touching each other + + + align:start position:0% +these two are touching each other +and one of them + + align:start position:0% +and one of them + + + align:start position:0% +and one of them +is with is retracting this one's just + + align:start position:0% +is with is retracting this one's just + + + align:start position:0% +is with is retracting this one's just +pausing + + align:start position:0% + + + + align:start position:0% + +and then it keeps going + + align:start position:0% +and then it keeps going + + + align:start position:0% +and then it keeps going +and this one is continuing to retract + + align:start position:0% +and this one is continuing to retract + + + align:start position:0% +and this one is continuing to retract +you see the body the thickest part of + + align:start position:0% +you see the body the thickest part of + + + align:start position:0% +you see the body the thickest part of +the growth cones pulling way back + + align:start position:0% +the growth cones pulling way back + + + align:start position:0% +the growth cones pulling way back +it's lost all its processes here and + + align:start position:0% +it's lost all its processes here and + + + align:start position:0% +it's lost all its processes here and +this + + align:start position:0% +this + + + align:start position:0% +this +the distance of retraction + + align:start position:0% +the distance of retraction + + + align:start position:0% +the distance of retraction +can vary quite a bit + + align:start position:0% + + + + align:start position:0% + +we it's + + align:start position:0% +we it's + + + align:start position:0% +we it's +properties of the membrane + + align:start position:0% +properties of the membrane + + + align:start position:0% +properties of the membrane +but we also now know that there are + + align:start position:0% +but we also now know that there are + + + align:start position:0% +but we also now know that there are +secreted substances around that these + + align:start position:0% +secreted substances around that these + + + align:start position:0% +secreted substances around that these +things can be secreting molecules + + align:start position:0% +things can be secreting molecules + + + align:start position:0% +things can be secreting molecules +uh one of the molecules that causes that + + align:start position:0% +uh one of the molecules that causes that + + + align:start position:0% +uh one of the molecules that causes that +they call collapse and because + + align:start position:0% +they call collapse and because + + + align:start position:0% +they call collapse and because +it literally affects the membrane of the + + align:start position:0% +it literally affects the membrane of the + + + align:start position:0% +it literally affects the membrane of the +other cell and can induce the retraction + + align:start position:0% +other cell and can induce the retraction + + + align:start position:0% +other cell and can induce the retraction +now + + align:start position:0% +now + + + align:start position:0% +now +in the literature it's commonly believed + + align:start position:0% +in the literature it's commonly believed + + + align:start position:0% +in the literature it's commonly believed +that + + align:start position:0% +that + + + align:start position:0% +that +there's + + align:start position:0% +there's + + + align:start position:0% +there's +there's no way to predict you know how + + align:start position:0% +there's no way to predict you know how + + + align:start position:0% +there's no way to predict you know how +far they're going to go but in fact i've + + align:start position:0% +far they're going to go but in fact i've + + + align:start position:0% +far they're going to go but in fact i've +studied that literature and i found out + + align:start position:0% +studied that literature and i found out + + + align:start position:0% +studied that literature and i found out +that it's actually somewhat systematic + + align:start position:0% +that it's actually somewhat systematic + + + align:start position:0% +that it's actually somewhat systematic +that depending on the axon + + align:start position:0% +that depending on the axon + + + align:start position:0% +that depending on the axon +properties you'll get various not only + + align:start position:0% +properties you'll get various not only + + + align:start position:0% +properties you'll get various not only +different frequencies of retraction that + + align:start position:0% +different frequencies of retraction that + + + align:start position:0% +different frequencies of retraction that +is the probability it'll retract varies + + align:start position:0% +is the probability it'll retract varies + + + align:start position:0% +is the probability it'll retract varies +but also the distance it'll retract + + align:start position:0% +but also the distance it'll retract + + + align:start position:0% +but also the distance it'll retract +varies + + align:start position:0% +varies + + + align:start position:0% +varies +and i found out that that and i did this + + align:start position:0% +and i found out that that and i did this + + + align:start position:0% +and i found out that that and i did this +by computer simulation i didn't bring + + align:start position:0% +by computer simulation i didn't bring + + + align:start position:0% +by computer simulation i didn't bring +any of my simulation pictures but i + + align:start position:0% +any of my simulation pictures but i + + + align:start position:0% +any of my simulation pictures but i +showed that + + align:start position:0% +showed that + + + align:start position:0% +showed that +the distance it retracts makes an + + align:start position:0% +the distance it retracts makes an + + + align:start position:0% +the distance it retracts makes an +enormous difference in the pattern of + + align:start position:0% +enormous difference in the pattern of + + + align:start position:0% +enormous difference in the pattern of +axons you get in the culture + + align:start position:0% +axons you get in the culture + + + align:start position:0% +axons you get in the culture +the short distances will give you axons + + align:start position:0% +the short distances will give you axons + + + align:start position:0% +the short distances will give you axons +that are growing + + align:start position:0% +that are growing + + + align:start position:0% +that are growing +like they're glued to each other + + align:start position:0% +like they're glued to each other + + + align:start position:0% +like they're glued to each other +fasciculated + + align:start position:0% +fasciculated + + + align:start position:0% +fasciculated +and the large distances you get + + align:start position:0% +and the large distances you get + + + align:start position:0% +and the large distances you get +non-fasciculation and we're going to + + align:start position:0% +non-fasciculation and we're going to + + + align:start position:0% +non-fasciculation and we're going to +i'll show you pictures of what those + + align:start position:0% +i'll show you pictures of what those + + + align:start position:0% +i'll show you pictures of what those +things look like just + + align:start position:0% + + + + align:start position:0% + +this is just artifact debris + + align:start position:0% + + + + align:start position:0% + +that they're moving on a substrate okay + + align:start position:0% +that they're moving on a substrate okay + + + align:start position:0% +that they're moving on a substrate okay +they're moving on a plate that's coated + + align:start position:0% +they're moving on a plate that's coated + + + align:start position:0% +they're moving on a plate that's coated +with like poly lysine or something okay + + align:start position:0% + + + + align:start position:0% + +they and the substrate you grow them on + + align:start position:0% +they and the substrate you grow them on + + + align:start position:0% +they and the substrate you grow them on +will affect how they grow + + align:start position:0% +will affect how they grow + + + align:start position:0% +will affect how they grow +okay that's important + + align:start position:0% + + + + align:start position:0% + +okay this is i think this is the last + + align:start position:0% +okay this is i think this is the last + + + align:start position:0% +okay this is i think this is the last +one it shows a growth cone coming from + + align:start position:0% +one it shows a growth cone coming from + + + align:start position:0% +one it shows a growth cone coming from +the left and it's contacting a + + align:start position:0% +the left and it's contacting a + + + align:start position:0% +the left and it's contacting a +fibroblast + + align:start position:0% +fibroblast + + + align:start position:0% +fibroblast +that's a peripheral cell + + align:start position:0% +that's a peripheral cell + + + align:start position:0% +that's a peripheral cell +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now it's a sympathetic neuron + + align:start position:0% +now it's a sympathetic neuron + + + align:start position:0% +now it's a sympathetic neuron +a synthetic ganglion neuron and it could + + align:start position:0% +a synthetic ganglion neuron and it could + + + align:start position:0% +a synthetic ganglion neuron and it could +be this could be happening in + + align:start position:0% +be this could be happening in + + + align:start position:0% +be this could be happening in +the natural situation these these are + + align:start position:0% +the natural situation these these are + + + align:start position:0% +the natural situation these these are +peripheral cells + + align:start position:0% +peripheral cells + + + align:start position:0% +peripheral cells +contacting each other + + align:start position:0% + + + + align:start position:0% + +so here's the axon there's the growth + + align:start position:0% +so here's the axon there's the growth + + + align:start position:0% +so here's the axon there's the growth +column here's the fibroblast + + align:start position:0% +column here's the fibroblast + + + align:start position:0% +column here's the fibroblast +and it's met a barrier + + align:start position:0% +and it's met a barrier + + + align:start position:0% +and it's met a barrier +okay and what it does is it sort of it + + align:start position:0% +okay and what it does is it sort of it + + + align:start position:0% +okay and what it does is it sort of it +keeps stays very active and it sort of + + align:start position:0% +keeps stays very active and it sort of + + + align:start position:0% +keeps stays very active and it sort of +see it's moving along the surface sort + + align:start position:0% +see it's moving along the surface sort + + + align:start position:0% +see it's moving along the surface sort +of feels itself along the surface and in + + align:start position:0% +of feels itself along the surface and in + + + align:start position:0% +of feels itself along the surface and in +fact it's turned here now and it's + + align:start position:0% +fact it's turned here now and it's + + + align:start position:0% +fact it's turned here now and it's +growing along the surface this way + + align:start position:0% +growing along the surface this way + + + align:start position:0% +growing along the surface this way +yes + + align:start position:0% + + + + align:start position:0% + +from the cell body + + align:start position:0% +from the cell body + + + align:start position:0% +from the cell body +the that's a very important question + + align:start position:0% +the that's a very important question + + + align:start position:0% +the that's a very important question +these + + align:start position:0% +these + + + align:start position:0% +these +growing cells are metabolically very + + align:start position:0% +growing cells are metabolically very + + + align:start position:0% +growing cells are metabolically very +active + + align:start position:0% +active + + + align:start position:0% +active +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and it is + + align:start position:0% +and it is + + + align:start position:0% +and it is +shipping by + + align:start position:0% +shipping by + + + align:start position:0% +shipping by +anterograde transport mechanisms the + + align:start position:0% +anterograde transport mechanisms the + + + align:start position:0% +anterograde transport mechanisms the +vesicles down the axon okay + + align:start position:0% + + + + align:start position:0% + +does it happen in injury is the question + + align:start position:0% +does it happen in injury is the question + + + align:start position:0% +does it happen in injury is the question +and the answer is yes + + align:start position:0% +and the answer is yes + + + align:start position:0% +and the answer is yes +we will talk a little bit about + + align:start position:0% +we will talk a little bit about + + + align:start position:0% +we will talk a little bit about +regeneration soon + + align:start position:0% +regeneration soon + + + align:start position:0% +regeneration soon +in the peripheral nervous system + + align:start position:0% +in the peripheral nervous system + + + align:start position:0% +in the peripheral nervous system +especially when you have an injury you + + align:start position:0% +especially when you have an injury you + + + align:start position:0% +especially when you have an injury you +will get a lot of growth like this okay + + align:start position:0% +will get a lot of growth like this okay + + + align:start position:0% +will get a lot of growth like this okay +axons will attempt to regrow in many + + align:start position:0% +axons will attempt to regrow in many + + + align:start position:0% +axons will attempt to regrow in many +cases they will reform something + + align:start position:0% +cases they will reform something + + + align:start position:0% +cases they will reform something +approximating their original connections + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +see how we're doing on time here okay + + align:start position:0% +see how we're doing on time here okay + + + align:start position:0% +see how we're doing on time here okay +so now i'm going to describe two + + align:start position:0% +so now i'm going to describe two + + + align:start position:0% +so now i'm going to describe two +different + + align:start position:0% +different + + + align:start position:0% +different +kinds of growth in the that was + + align:start position:0% +kinds of growth in the that was + + + align:start position:0% +kinds of growth in the that was +discovered in the optic tract but now we + + align:start position:0% +discovered in the optic tract but now we + + + align:start position:0% +discovered in the optic tract but now we +know it happens also in the fibers + + align:start position:0% +know it happens also in the fibers + + + align:start position:0% +know it happens also in the fibers +growing into neocortex + + align:start position:0% +growing into neocortex + + + align:start position:0% +growing into neocortex +a number of other systems where you get + + align:start position:0% +a number of other systems where you get + + + align:start position:0% +a number of other systems where you get +some more things + + align:start position:0% +some more things + + + align:start position:0% +some more things +growth that looks different grows at a + + align:start position:0% +growth that looks different grows at a + + + align:start position:0% +growth that looks different grows at a +different rate has different properties + + align:start position:0% +different rate has different properties + + + align:start position:0% +different rate has different properties +okay so the properties of these growth + + align:start position:0% +okay so the properties of these growth + + + align:start position:0% +okay so the properties of these growth +cones must be different + + align:start position:0% +cones must be different + + + align:start position:0% +cones must be different +in two different stages of the same + + align:start position:0% +in two different stages of the same + + + align:start position:0% +in two different stages of the same +cell + + align:start position:0% +cell + + + align:start position:0% +cell +growing its accent okay + + align:start position:0% + + + + align:start position:0% + +and then we know a little bit about what + + align:start position:0% +and then we know a little bit about what + + + align:start position:0% +and then we know a little bit about what +they're doing they compete + + align:start position:0% +they're doing they compete + + + align:start position:0% +they're doing they compete +for space to terminate we know they're + + align:start position:0% +for space to terminate we know they're + + + align:start position:0% +for space to terminate we know they're +influenced by growth factors and these + + align:start position:0% +influenced by growth factors and these + + + align:start position:0% +influenced by growth factors and these +growth factors can play more than one + + align:start position:0% +growth factors can play more than one + + + align:start position:0% +growth factors can play more than one +role + + align:start position:0% +role + + + align:start position:0% +role +i'll describe a little bit of that in + + align:start position:0% +i'll describe a little bit of that in + + + align:start position:0% +i'll describe a little bit of that in +this class and we talk about it we spend + + align:start position:0% +this class and we talk about it we spend + + + align:start position:0% +this class and we talk about it we spend +sessions on that in the second term + + align:start position:0% +sessions on that in the second term + + + align:start position:0% +sessions on that in the second term +and of course if they're coming from the + + align:start position:0% +and of course if they're coming from the + + + align:start position:0% +and of course if they're coming from the +retina they have other problems to solve + + align:start position:0% +retina they have other problems to solve + + + align:start position:0% +retina they have other problems to solve +they + + align:start position:0% +they + + + align:start position:0% +they +they need to terminate in a very + + align:start position:0% +they need to terminate in a very + + + align:start position:0% +they need to terminate in a very +specific way in fact they're coming from + + align:start position:0% +specific way in fact they're coming from + + + align:start position:0% +specific way in fact they're coming from +the retina they terminate in the + + align:start position:0% +the retina they terminate in the + + + align:start position:0% +the retina they terminate in the +topographic way the same is true for + + align:start position:0% +topographic way the same is true for + + + align:start position:0% +topographic way the same is true for +those axons say the spinothalamic or the + + align:start position:0% +those axons say the spinothalamic or the + + + align:start position:0% +those axons say the spinothalamic or the +medial spinophilemic tractor medial in + + align:start position:0% +medial spinophilemic tractor medial in + + + align:start position:0% +medial spinophilemic tractor medial in +this case they have to terminate in the + + align:start position:0% +this case they have to terminate in the + + + align:start position:0% +this case they have to terminate in the +right place + + align:start position:0% +right place + + + align:start position:0% +right place +okay + + align:start position:0% +okay + + + align:start position:0% +okay +because there's a topographic map a map + + align:start position:0% +because there's a topographic map a map + + + align:start position:0% +because there's a topographic map a map +of the body surface or the retina okay + + align:start position:0% + + + + align:start position:0% + +and when they're elongating we know + + align:start position:0% +and when they're elongating we know + + + align:start position:0% +and when they're elongating we know +they're very specific and now we know + + align:start position:0% +they're very specific and now we know + + + align:start position:0% +they're very specific and now we know +there's different kinds of guidance + + align:start position:0% + + + + align:start position:0% + +there's chemical guidance of more than + + align:start position:0% +there's chemical guidance of more than + + + align:start position:0% +there's chemical guidance of more than +one kind there can be diffusing + + align:start position:0% +one kind there can be diffusing + + + align:start position:0% +one kind there can be diffusing +chemicals that can attract them or repel + + align:start position:0% +chemicals that can attract them or repel + + + align:start position:0% +chemicals that can attract them or repel +them you know you'd have to write this + + align:start position:0% +them you know you'd have to write this + + + align:start position:0% +them you know you'd have to write this +down we'll go over it later + + align:start position:0% +down we'll go over it later + + + align:start position:0% +down we'll go over it later +they can be attracted or repelled by a + + align:start position:0% +they can be attracted or repelled by a + + + align:start position:0% +they can be attracted or repelled by a +diffusing molecule or + + align:start position:0% +diffusing molecule or + + + align:start position:0% +diffusing molecule or +they can also they're act just by this + + align:start position:0% +they can also they're act just by this + + + align:start position:0% +they can also they're act just by this +there can be molecules on the surfaces + + align:start position:0% +there can be molecules on the surfaces + + + align:start position:0% +there can be molecules on the surfaces +they're contacting and those molecules + + align:start position:0% +they're contacting and those molecules + + + align:start position:0% +they're contacting and those molecules +can attract them or repel them also + + align:start position:0% +can attract them or repel them also + + + align:start position:0% +can attract them or repel them also +we know that glial cells play specific + + align:start position:0% +we know that glial cells play specific + + + align:start position:0% +we know that glial cells play specific +roles in axon growth we saw the + + align:start position:0% +roles in axon growth we saw the + + + align:start position:0% +roles in axon growth we saw the +importance of the glial cell in neuronal + + align:start position:0% +importance of the glial cell in neuronal + + + align:start position:0% +importance of the glial cell in neuronal +migration well they also play very + + align:start position:0% +migration well they also play very + + + align:start position:0% +migration well they also play very +important roles in the growth of accents + + align:start position:0% +important roles in the growth of accents + + + align:start position:0% +important roles in the growth of accents +the main environment + + align:start position:0% +the main environment + + + align:start position:0% +the main environment +that the axons are growing through is a + + align:start position:0% +that the axons are growing through is a + + + align:start position:0% +that the axons are growing through is a +forest of glial cells + + align:start position:0% +forest of glial cells + + + align:start position:0% +forest of glial cells +so when the axons grow into the optic + + align:start position:0% +so when the axons grow into the optic + + + align:start position:0% +so when the axons grow into the optic +tectum coming from the eye for example + + align:start position:0% +tectum coming from the eye for example + + + align:start position:0% +tectum coming from the eye for example +what do they mean + + align:start position:0% + + + + align:start position:0% + +they meet processes of neurons too but a + + align:start position:0% +they meet processes of neurons too but a + + + align:start position:0% +they meet processes of neurons too but a +lot of those processes are going through + + align:start position:0% +lot of those processes are going through + + + align:start position:0% +lot of those processes are going through +it's a forest of radial cells some of + + align:start position:0% +it's a forest of radial cells some of + + + align:start position:0% +it's a forest of radial cells some of +which will become glia others will + + align:start position:0% +which will become glia others will + + + align:start position:0% +which will become glia others will +become + + align:start position:0% +become + + + align:start position:0% +become +neurons + + align:start position:0% +neurons + + + align:start position:0% +neurons +okay + + align:start position:0% +okay + + + align:start position:0% +okay +then i'll say a little bit more about + + align:start position:0% +then i'll say a little bit more about + + + align:start position:0% +then i'll say a little bit more about +competitive interactions among axons and + + align:start position:0% +competitive interactions among axons and + + + align:start position:0% +competitive interactions among axons and +the various factors + + align:start position:0% +the various factors + + + align:start position:0% +the various factors +i've mentioned a few of them already + + align:start position:0% +i've mentioned a few of them already + + + align:start position:0% +i've mentioned a few of them already +influencing growing or regenerating + + align:start position:0% +influencing growing or regenerating + + + align:start position:0% +influencing growing or regenerating +or just axons going + + align:start position:0% +or just axons going + + + align:start position:0% +or just axons going +through collateral sprouting okay + + align:start position:0% + + + + align:start position:0% + +okay so here's a picture from our + + align:start position:0% +okay so here's a picture from our + + + align:start position:0% +okay so here's a picture from our +research + + align:start position:0% +research + + + align:start position:0% +research +about two modes of growth in the optic + + align:start position:0% +about two modes of growth in the optic + + + align:start position:0% +about two modes of growth in the optic +tract + + align:start position:0% +tract + + + align:start position:0% +tract +first we talk about the period of + + align:start position:0% +first we talk about the period of + + + align:start position:0% +first we talk about the period of +elongation + + align:start position:0% +elongation + + + align:start position:0% +elongation +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and the cells have this kind of + + align:start position:0% +and the cells have this kind of + + + align:start position:0% +and the cells have this kind of +appearance then + + align:start position:0% +appearance then + + + align:start position:0% +appearance then +they have + + align:start position:0% +they have + + + align:start position:0% +they have +little enlargements along their way + + align:start position:0% +little enlargements along their way + + + align:start position:0% +little enlargements along their way +little tiny processes and then an active + + align:start position:0% +little tiny processes and then an active + + + align:start position:0% +little tiny processes and then an active +growth cone + + align:start position:0% +growth cone + + + align:start position:0% +growth cone +they don't branch they + + align:start position:0% +they don't branch they + + + align:start position:0% +they don't branch they +very much they might fork but yet + + align:start position:0% +very much they might fork but yet + + + align:start position:0% +very much they might fork but yet +generally they won't form much branch + + align:start position:0% +generally they won't form much branch + + + align:start position:0% +generally they won't form much branch +branching at all + + align:start position:0% +branching at all + + + align:start position:0% +branching at all +and then the hamster they're born at + + align:start position:0% +and then the hamster they're born at + + + align:start position:0% +and then the hamster they're born at +this stage in the optic track and then + + align:start position:0% +this stage in the optic track and then + + + align:start position:0% +this stage in the optic track and then +the axons start sprouting collaterals + + align:start position:0% +the axons start sprouting collaterals + + + align:start position:0% +the axons start sprouting collaterals +and they don't just sprout collaterals + + align:start position:0% +and they don't just sprout collaterals + + + align:start position:0% +and they don't just sprout collaterals +in there where they're going to + + align:start position:0% +in there where they're going to + + + align:start position:0% +in there where they're going to +end up with + + align:start position:0% +end up with + + + align:start position:0% +end up with +an arbor they sprout them all over the + + align:start position:0% +an arbor they sprout them all over the + + + align:start position:0% +an arbor they sprout them all over the +place + + align:start position:0% +place + + + align:start position:0% +place +if an axon is growing through half the + + align:start position:0% +if an axon is growing through half the + + + align:start position:0% +if an axon is growing through half the +tectum it'll sprout little collaterals + + align:start position:0% +tectum it'll sprout little collaterals + + + align:start position:0% +tectum it'll sprout little collaterals +all along okay as you see there + + align:start position:0% +all along okay as you see there + + + align:start position:0% +all along okay as you see there +but then the accent will start to + + align:start position:0% +but then the accent will start to + + + align:start position:0% +but then the accent will start to +vocalize + + align:start position:0% +vocalize + + + align:start position:0% +vocalize +it'll pull in a lot of those collaterals + + align:start position:0% +it'll pull in a lot of those collaterals + + + align:start position:0% +it'll pull in a lot of those collaterals +and + + align:start position:0% +and + + + align:start position:0% +and +one of them will grow it might not be + + align:start position:0% +one of them will grow it might not be + + + align:start position:0% +one of them will grow it might not be +the one at the end + + align:start position:0% +the one at the end + + + align:start position:0% +the one at the end +like this one i'm showing growing along + + align:start position:0% +like this one i'm showing growing along + + + align:start position:0% +like this one i'm showing growing along +the way + + align:start position:0% +the way + + + align:start position:0% +the way +it's + + align:start position:0% + + + + align:start position:0% + +and then finally it will withdraw the + + align:start position:0% +and then finally it will withdraw the + + + align:start position:0% +and then finally it will withdraw the +other collaterals it might form more + + align:start position:0% +other collaterals it might form more + + + align:start position:0% +other collaterals it might form more +than one as i show here it's forming + + align:start position:0% +than one as i show here it's forming + + + align:start position:0% +than one as i show here it's forming +collaterals in another place also + + align:start position:0% +collaterals in another place also + + + align:start position:0% +collaterals in another place also +because many accents have more than one + + align:start position:0% +because many accents have more than one + + + align:start position:0% +because many accents have more than one +place where they terminate + + align:start position:0% +place where they terminate + + + align:start position:0% +place where they terminate +and then + + align:start position:0% +and then + + + align:start position:0% +and then +the differentiation continues and + + align:start position:0% +the differentiation continues and + + + align:start position:0% +the differentiation continues and +accents might end up for example + + align:start position:0% +accents might end up for example + + + align:start position:0% +accents might end up for example +terminating in one layer and not other + + align:start position:0% +terminating in one layer and not other + + + align:start position:0% +terminating in one layer and not other +so it simply withdraws + + align:start position:0% +so it simply withdraws + + + align:start position:0% +so it simply withdraws +its branches in some places and + + align:start position:0% +its branches in some places and + + + align:start position:0% +its branches in some places and +continues growing them in others + + align:start position:0% +continues growing them in others + + + align:start position:0% +continues growing them in others +okay + + align:start position:0% + + + + align:start position:0% + +when it withdraws sometimes we call it a + + align:start position:0% +when it withdraws sometimes we call it a + + + align:start position:0% +when it withdraws sometimes we call it a +a kind of pruning a self-pruning it's + + align:start position:0% +a kind of pruning a self-pruning it's + + + align:start position:0% +a kind of pruning a self-pruning it's +going + + align:start position:0% +going + + + align:start position:0% +going +through okay we can also prune them by + + align:start position:0% +through okay we can also prune them by + + + align:start position:0% +through okay we can also prune them by +making lesions damaging them + + align:start position:0% + + + + align:start position:0% + +and in the hamster this is all happening + + align:start position:0% +and in the hamster this is all happening + + + align:start position:0% +and in the hamster this is all happening +when the eyes are still closed after the + + align:start position:0% +when the eyes are still closed after the + + + align:start position:0% +when the eyes are still closed after the +eyes open there's a maturation of arbors + + align:start position:0% +eyes open there's a maturation of arbors + + + align:start position:0% +eyes open there's a maturation of arbors +that continues and we know from various + + align:start position:0% +that continues and we know from various + + + align:start position:0% +that continues and we know from various +studies that that maturation can be + + align:start position:0% +studies that that maturation can be + + + align:start position:0% +studies that that maturation can be +affected by visual input we don't know + + align:start position:0% +affected by visual input we don't know + + + align:start position:0% +affected by visual input we don't know +much about it in the tectum but it's + + align:start position:0% +much about it in the tectum but it's + + + align:start position:0% +much about it in the tectum but it's +well known in other parts the visual + + align:start position:0% +well known in other parts the visual + + + align:start position:0% +well known in other parts the visual +system + + align:start position:0% +system + + + align:start position:0% +system +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so finally end up with the mature arbors + + align:start position:0% +so finally end up with the mature arbors + + + align:start position:0% +so finally end up with the mature arbors +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so these are the two modes elongation + + align:start position:0% +so these are the two modes elongation + + + align:start position:0% +so these are the two modes elongation +and arborization we know that there are + + align:start position:0% +and arborization we know that there are + + + align:start position:0% +and arborization we know that there are +different proteins found in the cells + + align:start position:0% +different proteins found in the cells + + + align:start position:0% +different proteins found in the cells +during these two modes of growth i did + + align:start position:0% +during these two modes of growth i did + + + align:start position:0% +during these two modes of growth i did +some initial studies of this with ken + + align:start position:0% +some initial studies of this with ken + + + align:start position:0% +some initial studies of this with ken +moya who's been working in france since + + align:start position:0% +moya who's been working in france since + + + align:start position:0% +moya who's been working in france since +then + + align:start position:0% +then + + + align:start position:0% +then +but he's an american citizen he came to + + align:start position:0% +but he's an american citizen he came to + + + align:start position:0% +but he's an american citizen he came to +the to mit to do his graduate work he + + align:start position:0% +the to mit to do his graduate work he + + + align:start position:0% +the to mit to do his graduate work he +worked with me and bennowitz at harvard + + align:start position:0% +worked with me and bennowitz at harvard + + + align:start position:0% +worked with me and bennowitz at harvard +medical school + + align:start position:0% +medical school + + + align:start position:0% +medical school +and he + + align:start position:0% +and he + + + align:start position:0% +and he +looked at different stages of the + + align:start position:0% +looked at different stages of the + + + align:start position:0% +looked at different stages of the +development of these exons + + align:start position:0% +development of these exons + + + align:start position:0% +development of these exons +and found out that the cells were making + + align:start position:0% +and found out that the cells were making + + + align:start position:0% +and found out that the cells were making +protein and transporting different + + align:start position:0% +protein and transporting different + + + align:start position:0% +protein and transporting different +proteins at different stages so an + + align:start position:0% +proteins at different stages so an + + + align:start position:0% +proteins at different stages so an +elongation for example was transporting + + align:start position:0% +elongation for example was transporting + + + align:start position:0% +elongation for example was transporting +a lot of + + align:start position:0% +a lot of + + + align:start position:0% +a lot of +neuronal salivation molecule + + align:start position:0% +neuronal salivation molecule + + + align:start position:0% +neuronal salivation molecule +there are other proteins related to + + align:start position:0% +there are other proteins related to + + + align:start position:0% +there are other proteins related to +synapse formation that begin to appear + + align:start position:0% +synapse formation that begin to appear + + + align:start position:0% +synapse formation that begin to appear +during arborization + + align:start position:0% +during arborization + + + align:start position:0% +during arborization +we know also + + align:start position:0% +we know also + + + align:start position:0% +we know also +receptors can change they respond to + + align:start position:0% +receptors can change they respond to + + + align:start position:0% +receptors can change they respond to +various growth factors + + align:start position:0% +various growth factors + + + align:start position:0% +various growth factors +we weren't able to specify that but more + + align:start position:0% +we weren't able to specify that but more + + + align:start position:0% +we weren't able to specify that but more +of that has been found since that time + + align:start position:0% +of that has been found since that time + + + align:start position:0% +of that has been found since that time +we know that a particular molecule bcl2 + + align:start position:0% +we know that a particular molecule bcl2 + + + align:start position:0% +we know that a particular molecule bcl2 +is very important early on prevents the + + align:start position:0% +is very important early on prevents the + + + align:start position:0% +is very important early on prevents the +cell from dying + + align:start position:0% +cell from dying + + + align:start position:0% +cell from dying +okay it's an + + align:start position:0% +okay it's an + + + align:start position:0% +okay it's an +anti-apoptotic factor and now we also + + align:start position:0% +anti-apoptotic factor and now we also + + + align:start position:0% +anti-apoptotic factor and now we also +know it plays a role in axon outgrowth + + align:start position:0% +know it plays a role in axon outgrowth + + + align:start position:0% +know it plays a role in axon outgrowth +and there's many other proteins too + + align:start position:0% +and there's many other proteins too + + + align:start position:0% +and there's many other proteins too +so in elongation what we studied was the + + align:start position:0% +so in elongation what we studied was the + + + align:start position:0% +so in elongation what we studied was the +anatomy + + align:start position:0% +anatomy + + + align:start position:0% +anatomy +we saw that they grew rapidly + + align:start position:0% +we saw that they grew rapidly + + + align:start position:0% +we saw that they grew rapidly +80 to 100 microns an hour that might not + + align:start position:0% +80 to 100 microns an hour that might not + + + align:start position:0% +80 to 100 microns an hour that might not +seem so rapid to you it's about two + + align:start position:0% +seem so rapid to you it's about two + + + align:start position:0% +seem so rapid to you it's about two +millimeters a day but for a little cell + + align:start position:0% +millimeters a day but for a little cell + + + align:start position:0% +millimeters a day but for a little cell +that's pretty rapid + + align:start position:0% +that's pretty rapid + + + align:start position:0% +that's pretty rapid +okay + + align:start position:0% +okay + + + align:start position:0% +okay +in case you + + align:start position:0% + + + + align:start position:0% + +i + + align:start position:0% + + + + align:start position:0% + +that's a micron + + align:start position:0% +that's a micron + + + align:start position:0% +that's a micron +it's a greek letter mu + + align:start position:0% +it's a greek letter mu + + + align:start position:0% +it's a greek letter mu +but because i didn't bother to put the + + align:start position:0% +but because i didn't bother to put the + + + align:start position:0% +but because i didn't bother to put the +greek letter i'm not + + align:start position:0% + + + + align:start position:0% + +so i just use the u + + align:start position:0% +so i just use the u + + + align:start position:0% +so i just use the u +so 80 to 100 microns an hour about two + + align:start position:0% +so 80 to 100 microns an hour about two + + + align:start position:0% +so 80 to 100 microns an hour about two +millimeters a day + + align:start position:0% +millimeters a day + + + align:start position:0% +millimeters a day +and at that stage of growth when more + + align:start position:0% +and at that stage of growth when more + + + align:start position:0% +and at that stage of growth when more +and more axons appear in the track they + + align:start position:0% +and more axons appear in the track they + + + align:start position:0% +and more axons appear in the track they +grow up against each other they form a + + align:start position:0% +grow up against each other they form a + + + align:start position:0% +grow up against each other they form a +bundle or ribbon okay + + align:start position:0% +bundle or ribbon okay + + + align:start position:0% +bundle or ribbon okay +we call that fasciculation if they're + + align:start position:0% +we call that fasciculation if they're + + + align:start position:0% +we call that fasciculation if they're +fasciculated they form fascicles + + align:start position:0% +fasciculated they form fascicles + + + align:start position:0% +fasciculated they form fascicles +group they group together + + align:start position:0% +group they group together + + + align:start position:0% +group they group together +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and they're largely unbranched and they + + align:start position:0% +and they're largely unbranched and they + + + align:start position:0% +and they're largely unbranched and they +have this + + align:start position:0% +have this + + + align:start position:0% +have this +during elongation they have these + + align:start position:0% +during elongation they have these + + + align:start position:0% +during elongation they have these +swellings and fill a podia that occur + + align:start position:0% +swellings and fill a podia that occur + + + align:start position:0% +swellings and fill a podia that occur +it's almost like the whole axon is a + + align:start position:0% +it's almost like the whole axon is a + + + align:start position:0% +it's almost like the whole axon is a +growth cone okay because they have + + align:start position:0% +growth cone okay because they have + + + align:start position:0% +growth cone okay because they have +although there's the more active growth + + align:start position:0% +although there's the more active growth + + + align:start position:0% +although there's the more active growth +cone at the end they have many little + + align:start position:0% +cone at the end they have many little + + + align:start position:0% +cone at the end they have many little +filler podial on the way + + align:start position:0% + + + + align:start position:0% + +okay so now so that we're talking only + + align:start position:0% +okay so now so that we're talking only + + + align:start position:0% +okay so now so that we're talking only +about that top + + align:start position:0% + + + + align:start position:0% + +this area + + align:start position:0% +this area + + + align:start position:0% +this area +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that's the elongation + + align:start position:0% +that's the elongation + + + align:start position:0% +that's the elongation +and then when they arborize they slow + + align:start position:0% +and then when they arborize they slow + + + align:start position:0% +and then when they arborize they slow +down + + align:start position:0% +down + + + align:start position:0% +down +okay and my calculations for the hamster + + align:start position:0% +okay and my calculations for the hamster + + + align:start position:0% +okay and my calculations for the hamster +optic tract and the geniculate body when + + align:start position:0% +optic tract and the geniculate body when + + + align:start position:0% +optic tract and the geniculate body when +they arborize were that they grow at + + align:start position:0% +they arborize were that they grow at + + + align:start position:0% +they arborize were that they grow at +about a tenth the rate + + align:start position:0% +about a tenth the rate + + + align:start position:0% +about a tenth the rate +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now that's + + align:start position:0% +now that's + + + align:start position:0% +now that's +that's the + + align:start position:0% +that's the + + + align:start position:0% +that's the +average rate for a group of axons okay + + align:start position:0% +average rate for a group of axons okay + + + align:start position:0% +average rate for a group of axons okay +so i haven't + + align:start position:0% +so i haven't + + + align:start position:0% +so i haven't +the actual rate of an individual axon is + + align:start position:0% +the actual rate of an individual axon is + + + align:start position:0% +the actual rate of an individual axon is +not what i was able to measure + + align:start position:0% +not what i was able to measure + + + align:start position:0% +not what i was able to measure +okay we also know that when they grow + + align:start position:0% +okay we also know that when they grow + + + align:start position:0% +okay we also know that when they grow +like that they don't bundle + + align:start position:0% +like that they don't bundle + + + align:start position:0% +like that they don't bundle +they grow separate they stay away from + + align:start position:0% +they grow separate they stay away from + + + align:start position:0% +they grow separate they stay away from +each other they space themselves out so + + align:start position:0% +each other they space themselves out so + + + align:start position:0% +each other they space themselves out so +they're non-fasciculated + + align:start position:0% +they're non-fasciculated + + + align:start position:0% +they're non-fasciculated +with their branching they're undergoing + + align:start position:0% +with their branching they're undergoing + + + align:start position:0% +with their branching they're undergoing +a lot of branches so whereas one + + align:start position:0% +a lot of branches so whereas one + + + align:start position:0% +a lot of branches so whereas one +in elongation they're supporting one + + align:start position:0% +in elongation they're supporting one + + + align:start position:0% +in elongation they're supporting one +growth column when they're arborizing + + align:start position:0% +growth column when they're arborizing + + + align:start position:0% +growth column when they're arborizing +the same accent can be supporting many + + align:start position:0% +the same accent can be supporting many + + + align:start position:0% +the same accent can be supporting many +growth columns + + align:start position:0% +growth columns + + + align:start position:0% +growth columns +okay + + align:start position:0% +okay + + + align:start position:0% +okay +maybe that's why they slowed down + + align:start position:0% +maybe that's why they slowed down + + + align:start position:0% +maybe that's why they slowed down +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then we know that it's widespread a + + align:start position:0% +and then we know that it's widespread a + + + align:start position:0% +and then we know that it's widespread a +lot of branching but the branches are + + align:start position:0% +lot of branching but the branches are + + + align:start position:0% +lot of branching but the branches are +rather rudimentary and then later + + align:start position:0% +rather rudimentary and then later + + + align:start position:0% +rather rudimentary and then later +they vocalize they grow mainly in one + + align:start position:0% +they vocalize they grow mainly in one + + + align:start position:0% +they vocalize they grow mainly in one +place and they lose the others okay + + align:start position:0% + + + + align:start position:0% + +and in that period of early + + align:start position:0% +and in that period of early + + + align:start position:0% +and in that period of early +branch formation you can get branches + + align:start position:0% +branch formation you can get branches + + + align:start position:0% +branch formation you can get branches +appearing in places where the accent + + align:start position:0% +appearing in places where the accent + + + align:start position:0% +appearing in places where the accent +will not terminate later + + align:start position:0% +will not terminate later + + + align:start position:0% +will not terminate later +and sometimes they even seem to be + + align:start position:0% +and sometimes they even seem to be + + + align:start position:0% +and sometimes they even seem to be +growing arbors there but then they're + + align:start position:0% +growing arbors there but then they're + + + align:start position:0% +growing arbors there but then they're +withdrawn for example the optic tract + + align:start position:0% +withdrawn for example the optic tract + + + align:start position:0% +withdrawn for example the optic tract +will grow into the ventral posterior + + align:start position:0% +will grow into the ventral posterior + + + align:start position:0% +will grow into the ventral posterior +nucleus that's a symmetric sensory + + align:start position:0% +nucleus that's a symmetric sensory + + + align:start position:0% +nucleus that's a symmetric sensory +structure where they don't terminate + + align:start position:0% +structure where they don't terminate + + + align:start position:0% +structure where they don't terminate +there normally they grow in and then + + align:start position:0% +there normally they grow in and then + + + align:start position:0% +there normally they grow in and then +they pull out + + align:start position:0% +they pull out + + + align:start position:0% +they pull out +okay + + align:start position:0% +okay + + + align:start position:0% +okay +lateral posterior nucleus gets a lot of + + align:start position:0% +lateral posterior nucleus gets a lot of + + + align:start position:0% +lateral posterior nucleus gets a lot of +accidents in development many fewer in + + align:start position:0% +accidents in development many fewer in + + + align:start position:0% +accidents in development many fewer in +the adult it does get a few we used to + + align:start position:0% +the adult it does get a few we used to + + + align:start position:0% +the adult it does get a few we used to +think they didn't get any but with the + + align:start position:0% +think they didn't get any but with the + + + align:start position:0% +think they didn't get any but with the +sensitive methods we do see a few there + + align:start position:0% +sensitive methods we do see a few there + + + align:start position:0% +sensitive methods we do see a few there +but many more in development and then it + + align:start position:0% +but many more in development and then it + + + align:start position:0% +but many more in development and then it +was discovered by + + align:start position:0% +was discovered by + + + align:start position:0% +was discovered by +um + + align:start position:0% +um + + + align:start position:0% +um +you know + + align:start position:0% +you know + + + align:start position:0% +you know +italian neuroscientists working in + + align:start position:0% +italian neuroscientists working in + + + align:start position:0% +italian neuroscientists working in +switzerland that this happens in + + align:start position:0% +switzerland that this happens in + + + align:start position:0% +switzerland that this happens in +transcortical connections in the cat and + + align:start position:0% +transcortical connections in the cat and + + + align:start position:0% +transcortical connections in the cat and +probably all mammals + + align:start position:0% +probably all mammals + + + align:start position:0% +probably all mammals +you have whole transient connections + + align:start position:0% +you have whole transient connections + + + align:start position:0% +you have whole transient connections +forming and then they disappear + + align:start position:0% +forming and then they disappear + + + align:start position:0% +forming and then they disappear +sometimes they actually form synaptic + + align:start position:0% +sometimes they actually form synaptic + + + align:start position:0% +sometimes they actually form synaptic +connections and structures that they + + align:start position:0% +connections and structures that they + + + align:start position:0% +connections and structures that they +then withdraw from okay and other times + + align:start position:0% +then withdraw from okay and other times + + + align:start position:0% +then withdraw from okay and other times +just these little transient collaterals + + align:start position:0% +just these little transient collaterals + + + align:start position:0% +just these little transient collaterals +as i showed you for the optic tract + + align:start position:0% +as i showed you for the optic tract + + + align:start position:0% +as i showed you for the optic tract +okay + + align:start position:0% + + + + align:start position:0% + +and when that focalization is occurring + + align:start position:0% +and when that focalization is occurring + + + align:start position:0% +and when that focalization is occurring +that's when + + align:start position:0% +that's when + + + align:start position:0% +that's when +the topographic map + + align:start position:0% +the topographic map + + + align:start position:0% +the topographic map +becomes more precise + + align:start position:0% +becomes more precise + + + align:start position:0% +becomes more precise +okay there is a crude topography even at + + align:start position:0% +okay there is a crude topography even at + + + align:start position:0% +okay there is a crude topography even at +the beginning when they first start to + + align:start position:0% +the beginning when they first start to + + + align:start position:0% +the beginning when they first start to +arborize + + align:start position:0% +arborize + + + align:start position:0% +arborize +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but then it becomes more precise as they + + align:start position:0% +but then it becomes more precise as they + + + align:start position:0% +but then it becomes more precise as they +vocalize okay + + align:start position:0% +vocalize okay + + + align:start position:0% +vocalize okay +so that's + + align:start position:0% +so that's + + + align:start position:0% +so that's +we'll start there next time \ No newline at end of file diff --git a/hpM-siY2Bl0.txt b/hpM-siY2Bl0.txt new file mode 100644 index 0000000000000000000000000000000000000000..f2ec9eea3c196bbc9dcd939396f8677c74fc80bc --- /dev/null +++ b/hpM-siY2Bl0.txt @@ -0,0 +1,1875 @@ +align:start position:0% + +a common Active Learning technique that + + align:start position:0% +a common Active Learning technique that + + + align:start position:0% +a common Active Learning technique that +people often use or often maybe the + + align:start position:0% +people often use or often maybe the + + + align:start position:0% +people often use or often maybe the +first technique that they use is + + align:start position:0% +first technique that they use is + + + align:start position:0% +first technique that they use is +personal response system so that's an + + align:start position:0% +personal response system so that's an + + + align:start position:0% +personal response system so that's an +opportunity for students to to respond + + align:start position:0% +opportunity for students to to respond + + + align:start position:0% +opportunity for students to to respond +to a question and that can be anything + + align:start position:0% +to a question and that can be anything + + + align:start position:0% +to a question and that can be anything +that it's usually a multiple choice + + align:start position:0% +that it's usually a multiple choice + + + align:start position:0% +that it's usually a multiple choice +question but it doesn't have to be um + + align:start position:0% +question but it doesn't have to be um + + + align:start position:0% +question but it doesn't have to be um +and it can be anything from a show of + + align:start position:0% +and it can be anything from a show of + + + align:start position:0% +and it can be anything from a show of +hands who thinks the answer's a who + + align:start position:0% +hands who thinks the answer's a who + + + align:start position:0% +hands who thinks the answer's a who +thinks the answer is B who thinks the + + align:start position:0% +thinks the answer is B who thinks the + + + align:start position:0% +thinks the answer is B who thinks the +answer is C to Dedicated devices and + + align:start position:0% +answer is C to Dedicated devices and + + + align:start position:0% +answer is C to Dedicated devices and +applications that allow students to + + align:start position:0% +applications that allow students to + + + align:start position:0% +applications that allow students to +respond to questions so there's pros and + + align:start position:0% +respond to questions so there's pros and + + + align:start position:0% +respond to questions so there's pros and +cons for each of the different + + align:start position:0% +cons for each of the different + + + align:start position:0% +cons for each of the different +techniques but the essence of all the + + align:start position:0% +techniques but the essence of all the + + + align:start position:0% +techniques but the essence of all the +techniques is that students are given an + + align:start position:0% +techniques is that students are given an + + + align:start position:0% +techniques is that students are given an +opportunity to think about the answer + + align:start position:0% +opportunity to think about the answer + + + align:start position:0% +opportunity to think about the answer +that they would the answer they think is + + align:start position:0% +that they would the answer they think is + + + align:start position:0% +that they would the answer they think is +correct and and then respond to that and + + align:start position:0% +correct and and then respond to that and + + + align:start position:0% +correct and and then respond to that and +there is evidence to show research that + + align:start position:0% +there is evidence to show research that + + + align:start position:0% +there is evidence to show research that +shows that when students make a claim + + align:start position:0% +shows that when students make a claim + + + align:start position:0% +shows that when students make a claim +that are when they're asked to make a + + align:start position:0% +that are when they're asked to make a + + + align:start position:0% +that are when they're asked to make a +public response a public claim as to + + align:start position:0% +public response a public claim as to + + + align:start position:0% +public response a public claim as to +what they think the correct answer is + + align:start position:0% +what they think the correct answer is + + + align:start position:0% +what they think the correct answer is +that makes them more committed to the + + align:start position:0% +that makes them more committed to the + + + align:start position:0% +that makes them more committed to the +answer and then they're more likely to + + align:start position:0% +answer and then they're more likely to + + + align:start position:0% +answer and then they're more likely to +remember or to even notice if their + + align:start position:0% +remember or to even notice if their + + + align:start position:0% +remember or to even notice if their +answer is incorrect it primes the + + align:start position:0% +answer is incorrect it primes the + + + align:start position:0% +answer is incorrect it primes the +student for Learning and that's the + + align:start position:0% +student for Learning and that's the + + + align:start position:0% +student for Learning and that's the +biggest Advantage for any of the per + + align:start position:0% +biggest Advantage for any of the per + + + align:start position:0% +biggest Advantage for any of the per +these personal response systems the + + align:start position:0% +these personal response systems the + + + align:start position:0% +these personal response systems the +disadvantage with having students raise + + align:start position:0% +disadvantage with having students raise + + + align:start position:0% +disadvantage with having students raise +their hands is that in a big lecture + + align:start position:0% +their hands is that in a big lecture + + + align:start position:0% +their hands is that in a big lecture +hall it can be hard to to count right it + + align:start position:0% +hall it can be hard to to count right it + + + align:start position:0% +hall it can be hard to to count right it +can be hard to say okay how many people + + align:start position:0% +can be hard to say okay how many people + + + align:start position:0% +can be hard to say okay how many people +raised their hand when I said a how many + + align:start position:0% +raised their hand when I said a how many + + + align:start position:0% +raised their hand when I said a how many +when I said B Etc so that that can take + + align:start position:0% +when I said B Etc so that that can take + + + align:start position:0% +when I said B Etc so that that can take +up time and it can be pretty inaccurate + + align:start position:0% +up time and it can be pretty inaccurate + + + align:start position:0% +up time and it can be pretty inaccurate +um the other thing that people do + + align:start position:0% +um the other thing that people do + + + align:start position:0% +um the other thing that people do +sometimes is they'll use a like just a + + align:start position:0% +sometimes is they'll use a like just a + + + align:start position:0% +sometimes is they'll use a like just a +sheet of paper they'll put on letters + + align:start position:0% +sheet of paper they'll put on letters + + + align:start position:0% +sheet of paper they'll put on letters +and then the students can fold the paper + + align:start position:0% +and then the students can fold the paper + + + align:start position:0% +and then the students can fold the paper +up and depending on how they want to + + align:start position:0% +up and depending on how they want to + + + align:start position:0% +up and depending on how they want to +vote they just hold it up so that so + + align:start position:0% +vote they just hold it up so that so + + + align:start position:0% +vote they just hold it up so that so +that you know only really only you can + + align:start position:0% +that you know only really only you can + + + align:start position:0% +that you know only really only you can +see it point of fact is uh other + + align:start position:0% +see it point of fact is uh other + + + align:start position:0% +see it point of fact is uh other +students can kind of tell what the other + + align:start position:0% +students can kind of tell what the other + + + align:start position:0% +students can kind of tell what the other +students answered and and if I know that + + align:start position:0% +students answered and and if I know that + + + align:start position:0% +students answered and and if I know that +a friend of mine always gets the answer + + align:start position:0% +a friend of mine always gets the answer + + + align:start position:0% +a friend of mine always gets the answer +right then I might just look and see + + align:start position:0% +right then I might just look and see + + + align:start position:0% +right then I might just look and see +what he or she said and then and then + + align:start position:0% +what he or she said and then and then + + + align:start position:0% +what he or she said and then and then +answer the same so it might not give us + + align:start position:0% +answer the same so it might not give us + + + align:start position:0% +answer the same so it might not give us +a real accurate accurate uh measurement + + align:start position:0% +a real accurate accurate uh measurement + + + align:start position:0% +a real accurate accurate uh measurement +of what every student + + align:start position:0% +of what every student + + + align:start position:0% +of what every student +thinks um the other problem with that is + + align:start position:0% +thinks um the other problem with that is + + + align:start position:0% +thinks um the other problem with that is +that this can be hard to read in a big + + align:start position:0% +that this can be hard to read in a big + + + align:start position:0% +that this can be hard to read in a big +lecture hall sort of the first kind of + + align:start position:0% +lecture hall sort of the first kind of + + + align:start position:0% +lecture hall sort of the first kind of +uh digital or electronic personal + + align:start position:0% +uh digital or electronic personal + + + align:start position:0% +uh digital or electronic personal +response systems were these dedicated + + align:start position:0% +response systems were these dedicated + + + align:start position:0% +response systems were these dedicated +clickers is what they're called and + + align:start position:0% +clickers is what they're called and + + + align:start position:0% +clickers is what they're called and +students literally they they log in to + + align:start position:0% +students literally they they log in to + + + align:start position:0% +students literally they they log in to +the system they turn their devices on + + align:start position:0% +the system they turn their devices on + + + align:start position:0% +the system they turn their devices on +and you ask a question and then you just + + align:start position:0% +and you ask a question and then you just + + + align:start position:0% +and you ask a question and then you just +the students respond ABCD using the + + align:start position:0% +the students respond ABCD using the + + + align:start position:0% +the students respond ABCD using the +touchpad some some clickers let students + + align:start position:0% +touchpad some some clickers let students + + + align:start position:0% +touchpad some some clickers let students +actually type answers so open response + + align:start position:0% +actually type answers so open response + + + align:start position:0% +actually type answers so open response +they can actually type a word or a + + align:start position:0% +they can actually type a word or a + + + align:start position:0% +they can actually type a word or a +number a set of numbers so that can give + + align:start position:0% +number a set of numbers so that can give + + + align:start position:0% +number a set of numbers so that can give +you a little bit more flexibility and + + align:start position:0% +you a little bit more flexibility and + + + align:start position:0% +you a little bit more flexibility and +then the software on the instructor's + + align:start position:0% +then the software on the instructor's + + + align:start position:0% +then the software on the instructor's +computer will create a histogram of + + align:start position:0% +computer will create a histogram of + + + align:start position:0% +computer will create a histogram of +responses so you know right away the the + + align:start position:0% +responses so you know right away the the + + + align:start position:0% +responses so you know right away the the +distribution of responses if you have + + align:start position:0% +distribution of responses if you have + + + align:start position:0% +distribution of responses if you have +more than 70% of the students get the + + align:start position:0% +more than 70% of the students get the + + + align:start position:0% +more than 70% of the students get the +question right you probably just want to + + align:start position:0% +question right you probably just want to + + + align:start position:0% +question right you probably just want to +State the correct answer and move on uh + + align:start position:0% +State the correct answer and move on uh + + + align:start position:0% +State the correct answer and move on uh +you can also say if you didn't get it + + align:start position:0% +you can also say if you didn't get it + + + align:start position:0% +you can also say if you didn't get it +right uh here's some extra resources or + + align:start position:0% +right uh here's some extra resources or + + + align:start position:0% +right uh here's some extra resources or +go to the TA office hours or whatever + + align:start position:0% +go to the TA office hours or whatever + + + align:start position:0% +go to the TA office hours or whatever +but in but in general if more than 70% + + align:start position:0% +but in but in general if more than 70% + + + align:start position:0% +but in but in general if more than 70% +of the students get it right you can you + + align:start position:0% +of the students get it right you can you + + + align:start position:0% +of the students get it right you can you +can move on one thing I like to do is if + + align:start position:0% +can move on one thing I like to do is if + + + align:start position:0% +can move on one thing I like to do is if +I really have a resounding say 75% get + + align:start position:0% +I really have a resounding say 75% get + + + align:start position:0% +I really have a resounding say 75% get +get it right I like to ask a follow-up + + align:start position:0% +get it right I like to ask a follow-up + + + align:start position:0% +get it right I like to ask a follow-up +clicker question that says how confident + + align:start position:0% +clicker question that says how confident + + + align:start position:0% +clicker question that says how confident +were you in your answer because + + align:start position:0% +were you in your answer because + + + align:start position:0% +were you in your answer because +sometimes students will just guess + + align:start position:0% +sometimes students will just guess + + + align:start position:0% +sometimes students will just guess +and if you give them the opportunity to + + align:start position:0% +and if you give them the opportunity to + + + align:start position:0% +and if you give them the opportunity to +say yeah I got it right but I don't + + align:start position:0% +say yeah I got it right but I don't + + + align:start position:0% +say yeah I got it right but I don't +really know why that that might be the + + align:start position:0% +really know why that that might be the + + + align:start position:0% +really know why that that might be the +situation sometimes that a lot of people + + align:start position:0% +situation sometimes that a lot of people + + + align:start position:0% +situation sometimes that a lot of people +get it right but not that many people + + align:start position:0% +get it right but not that many people + + + align:start position:0% +get it right but not that many people +know what's going on so you want to know + + align:start position:0% +know what's going on so you want to know + + + align:start position:0% +know what's going on so you want to know +that too um if between 30 and 70 get it + + align:start position:0% +that too um if between 30 and 70 get it + + + align:start position:0% +that too um if between 30 and 70 get it +correct then I like to move into the + + align:start position:0% +correct then I like to move into the + + + align:start position:0% +correct then I like to move into the +pair share so I like to say okay let's + + align:start position:0% +pair share so I like to say okay let's + + + align:start position:0% +pair share so I like to say okay let's +divide up looks like we have a pretty + + align:start position:0% +divide up looks like we have a pretty + + + align:start position:0% +divide up looks like we have a pretty +good split of of answers so let's talk + + align:start position:0% +good split of of answers so let's talk + + + align:start position:0% +good split of of answers so let's talk +talk to each other and peer we can do + + align:start position:0% +talk to each other and peer we can do + + + align:start position:0% +talk to each other and peer we can do +some peer peer learning where peers can + + align:start position:0% +some peer peer learning where peers can + + + align:start position:0% +some peer peer learning where peers can +try to argue their point to their their + + align:start position:0% +try to argue their point to their their + + + align:start position:0% +try to argue their point to their their +whoever's sitting next to them and then + + align:start position:0% +whoever's sitting next to them and then + + + align:start position:0% +whoever's sitting next to them and then +I asked them to vote again now when + + align:start position:0% +I asked them to vote again now when + + + align:start position:0% +I asked them to vote again now when +things are working well uh people + + align:start position:0% +things are working well uh people + + + align:start position:0% +things are working well uh people +actually converge to the correct answer + + align:start position:0% +actually converge to the correct answer + + + align:start position:0% +actually converge to the correct answer +and and generally speaking I think it + + align:start position:0% +and and generally speaking I think it + + + align:start position:0% +and and generally speaking I think it +was Eric Missour has a has a preliminary + + align:start position:0% +was Eric Missour has a has a preliminary + + + align:start position:0% +was Eric Missour has a has a preliminary +research study that shows that when you + + align:start position:0% +research study that shows that when you + + + align:start position:0% +research study that shows that when you +put two students with the incorrect + + align:start position:0% +put two students with the incorrect + + + align:start position:0% +put two students with the incorrect +answer together they actually tend to + + align:start position:0% +answer together they actually tend to + + + align:start position:0% +answer together they actually tend to +converge to the correct answer because + + align:start position:0% +converge to the correct answer because + + + align:start position:0% +converge to the correct answer because +they argue each other out of their + + align:start position:0% +they argue each other out of their + + + align:start position:0% +they argue each other out of their +respective wrong + + align:start position:0% +respective wrong + + + align:start position:0% +respective wrong +answers so that can be pretty effective + + align:start position:0% +answers so that can be pretty effective + + + align:start position:0% +answers so that can be pretty effective +um you do have to have a pretty good + + align:start position:0% +um you do have to have a pretty good + + + align:start position:0% +um you do have to have a pretty good +distribution of incorrect answers for + + align:start position:0% +distribution of incorrect answers for + + + align:start position:0% +distribution of incorrect answers for +that to work if two students have the + + align:start position:0% +that to work if two students have the + + + align:start position:0% +that to work if two students have the +same incorrect answer generally speaking + + align:start position:0% +same incorrect answer generally speaking + + + align:start position:0% +same incorrect answer generally speaking +they stay embedded with the incorrect + + align:start position:0% +they stay embedded with the incorrect + + + align:start position:0% +they stay embedded with the incorrect +answer um if less than 30% of students + + align:start position:0% +answer um if less than 30% of students + + + align:start position:0% +answer um if less than 30% of students +get the correct answer you probably just + + align:start position:0% +get the correct answer you probably just + + + align:start position:0% +get the correct answer you probably just +want to stop and reformulate your + + align:start position:0% +want to stop and reformulate your + + + align:start position:0% +want to stop and reformulate your +explanation and really go over + + align:start position:0% +explanation and really go over + + + align:start position:0% +explanation and really go over +everything again because that's really + + align:start position:0% +everything again because that's really + + + align:start position:0% +everything again because that's really +not a lot of people that know what's + + align:start position:0% +not a lot of people that know what's + + + align:start position:0% +not a lot of people that know what's +going on so that's the en ballpark for + + align:start position:0% +going on so that's the en ballpark for + + + align:start position:0% +going on so that's the en ballpark for +how to proceed with the clicker + + align:start position:0% +how to proceed with the clicker + + + align:start position:0% +how to proceed with the clicker +questions um in between the pieces of + + align:start position:0% +questions um in between the pieces of + + + align:start position:0% +questions um in between the pieces of +paper and the clickers are some newer + + align:start position:0% +paper and the clickers are some newer + + + align:start position:0% +paper and the clickers are some newer +Technologies uh newer applications one + + align:start position:0% +Technologies uh newer applications one + + + align:start position:0% +Technologies uh newer applications one +is there's um a few applications for uh + + align:start position:0% +is there's um a few applications for uh + + + align:start position:0% +is there's um a few applications for uh +web enabled devices like crative uh + + align:start position:0% +web enabled devices like crative uh + + + align:start position:0% +web enabled devices like crative uh +which is a software that you can + + align:start position:0% +which is a software that you can + + + align:start position:0% +which is a software that you can +download um the in the instructor + + align:start position:0% +download um the in the instructor + + + align:start position:0% +download um the in the instructor +downloads it and then students log into + + align:start position:0% +downloads it and then students log into + + + align:start position:0% +downloads it and then students log into +a room using their web enabled device so + + align:start position:0% +a room using their web enabled device so + + + align:start position:0% +a room using their web enabled device so +they log in and then no one has to buy + + align:start position:0% +they log in and then no one has to buy + + + align:start position:0% +they log in and then no one has to buy +anything extra but you are assuming that + + align:start position:0% +anything extra but you are assuming that + + + align:start position:0% +anything extra but you are assuming that +every student has a web enable device + + align:start position:0% +every student has a web enable device + + + align:start position:0% +every student has a web enable device +and you are saying you're happy if they + + align:start position:0% +and you are saying you're happy if they + + + align:start position:0% +and you are saying you're happy if they +take them out in your class which may + + align:start position:0% +take them out in your class which may + + + align:start position:0% +take them out in your class which may +not be true for everyone so that's the + + align:start position:0% +not be true for everyone so that's the + + + align:start position:0% +not be true for everyone so that's the +issue with that um access and also + + align:start position:0% +issue with that um access and also + + + align:start position:0% +issue with that um access and also +whether you want the smartphones out an + + align:start position:0% +whether you want the smartphones out an + + + align:start position:0% +whether you want the smartphones out an +application that I think is a really + + align:start position:0% +application that I think is a really + + + align:start position:0% +application that I think is a really +great compromise is something called + + align:start position:0% +great compromise is something called + + + align:start position:0% +great compromise is something called +plickers with a p p l i c k RS and with + + align:start position:0% +plickers with a p p l i c k RS and with + + + align:start position:0% +plickers with a p p l i c k RS and with +that the instru instructor downloads an + + align:start position:0% +that the instru instructor downloads an + + + align:start position:0% +that the instru instructor downloads an +application on his or her smartphone or + + align:start position:0% +application on his or her smartphone or + + + align:start position:0% +application on his or her smartphone or +web enabled device uh well it has to be + + align:start position:0% +web enabled device uh well it has to be + + + align:start position:0% +web enabled device uh well it has to be +a device with a camera and the students + + align:start position:0% +a device with a camera and the students + + + align:start position:0% +a device with a camera and the students +and then you down and then the + + align:start position:0% +and then you down and then the + + + align:start position:0% +and then you down and then the +instructor downloads um these PDFs which + + align:start position:0% +instructor downloads um these PDFs which + + + align:start position:0% +instructor downloads um these PDFs which +are just pieces of paper with with um + + align:start position:0% +are just pieces of paper with with um + + + align:start position:0% +are just pieces of paper with with um +with these patterns on them they're all + + align:start position:0% +with these patterns on them they're all + + + align:start position:0% +with these patterns on them they're all +different and I believe you get 40 + + align:start position:0% +different and I believe you get 40 + + + align:start position:0% +different and I believe you get 40 +patterns for for free and they're + + align:start position:0% +patterns for for free and they're + + + align:start position:0% +patterns for for free and they're +reusable and so each one is unique and + + align:start position:0% +reusable and so each one is unique and + + + align:start position:0% +reusable and so each one is unique and +you give them to the students and + + align:start position:0% +you give them to the students and + + + align:start position:0% +you give them to the students and +students then vote ABC or D + + align:start position:0% +students then vote ABC or D + + + align:start position:0% +students then vote ABC or D +there's four sides to the shape and four + + align:start position:0% +there's four sides to the shape and four + + + align:start position:0% +there's four sides to the shape and four +letters a b c d and if they think the + + align:start position:0% +letters a b c d and if they think the + + + align:start position:0% +letters a b c d and if they think the +answer is a they hold it with the a at + + align:start position:0% +answer is a they hold it with the a at + + + align:start position:0% +answer is a they hold it with the a at +the top they think it's B they hold it + + align:start position:0% +the top they think it's B they hold it + + + align:start position:0% +the top they think it's B they hold it +with the B at the top Etc and you can + + align:start position:0% +with the B at the top Etc and you can + + + align:start position:0% +with the B at the top Etc and you can +use your web enabled device and you scan + + align:start position:0% +use your web enabled device and you scan + + + align:start position:0% +use your web enabled device and you scan +the crowd and that with the software and + + align:start position:0% +the crowd and that with the software and + + + align:start position:0% +the crowd and that with the software and +that actually picks up the responses and + + align:start position:0% +that actually picks up the responses and + + + align:start position:0% +that actually picks up the responses and +creates a histogram so I think that's a + + align:start position:0% +creates a histogram so I think that's a + + + align:start position:0% +creates a histogram so I think that's a +really nice compromise because it gives + + align:start position:0% +really nice compromise because it gives + + + align:start position:0% +really nice compromise because it gives +you the histogram it has student Anon + + align:start position:0% +you the histogram it has student Anon + + + align:start position:0% +you the histogram it has student Anon +anonymity and + + align:start position:0% +anonymity and + + + align:start position:0% +anonymity and +um students don't need anything but the + + align:start position:0% +um students don't need anything but the + + + align:start position:0% +um students don't need anything but the +piece of paper that you gave them and + + align:start position:0% +piece of paper that you gave them and + + + align:start position:0% +piece of paper that you gave them and +you can actually reuse the piece of + + align:start position:0% +you can actually reuse the piece of + + + align:start position:0% +you can actually reuse the piece of +paper we printed um sets on card stock + + align:start position:0% +paper we printed um sets on card stock + + + align:start position:0% +paper we printed um sets on card stock +which are pretty durable and we can use + + align:start position:0% +which are pretty durable and we can use + + + align:start position:0% +which are pretty durable and we can use +them over and over again so there's no + + align:start position:0% +them over and over again so there's no + + + align:start position:0% +them over and over again so there's no +there's the students don't need any + + align:start position:0% +there's the students don't need any + + + align:start position:0% +there's the students don't need any +extra technology for educators that are + + align:start position:0% +extra technology for educators that are + + + align:start position:0% +extra technology for educators that are +thinking about using some kind of + + align:start position:0% +thinking about using some kind of + + + align:start position:0% +thinking about using some kind of +personal response system uh for their + + align:start position:0% +personal response system uh for their + + + align:start position:0% +personal response system uh for their +for their students um there's a couple + + align:start position:0% +for their students um there's a couple + + + align:start position:0% +for their students um there's a couple +different levels of how far in to get + + align:start position:0% +different levels of how far in to get + + + align:start position:0% +different levels of how far in to get +and how fast the first step would be to + + align:start position:0% +and how fast the first step would be to + + + align:start position:0% +and how fast the first step would be to +construct some really good thoughtful + + align:start position:0% +construct some really good thoughtful + + + align:start position:0% +construct some really good thoughtful +questions that students can answer in a + + align:start position:0% +questions that students can answer in a + + + align:start position:0% +questions that students can answer in a +multiple choice way um that would let + + align:start position:0% +multiple choice way um that would let + + + align:start position:0% +multiple choice way um that would let +you use the clickers or show of hands or + + align:start position:0% +you use the clickers or show of hands or + + + align:start position:0% +you use the clickers or show of hands or +any of the other + + align:start position:0% +any of the other + + + align:start position:0% +any of the other +methods um it is important to construct + + align:start position:0% +methods um it is important to construct + + + align:start position:0% +methods um it is important to construct +the clicker questions in a way that are + + align:start position:0% +the clicker questions in a way that are + + + align:start position:0% +the clicker questions in a way that are +that students know they're really + + align:start position:0% +that students know they're really + + + align:start position:0% +that students know they're really +meaningful that you're not just asking + + align:start position:0% +meaningful that you're not just asking + + + align:start position:0% +meaningful that you're not just asking +kind of silly questions you want to ask + + align:start position:0% +kind of silly questions you want to ask + + + align:start position:0% +kind of silly questions you want to ask +some questions that that are are a bit + + align:start position:0% +some questions that that are are a bit + + + align:start position:0% +some questions that that are are a bit +rich and that also lend themselves as I + + align:start position:0% +rich and that also lend themselves as I + + + align:start position:0% +rich and that also lend themselves as I +said to if + + align:start position:0% +said to if + + + align:start position:0% +said to if +you know if a decent number don't get + + align:start position:0% +you know if a decent number don't get + + + align:start position:0% +you know if a decent number don't get +them right that lend themselves to that + + align:start position:0% +them right that lend themselves to that + + + align:start position:0% +them right that lend themselves to that +peer peer peer interaction the sort of + + align:start position:0% +peer peer peer interaction the sort of + + + align:start position:0% +peer peer peer interaction the sort of +debate with each other so you don't you + + align:start position:0% +debate with each other so you don't you + + + align:start position:0% +debate with each other so you don't you +want to think carefully about your + + align:start position:0% +want to think carefully about your + + + align:start position:0% +want to think carefully about your +learning outcomes what you want students + + align:start position:0% +learning outcomes what you want students + + + align:start position:0% +learning outcomes what you want students +to know or be able to do by the end of + + align:start position:0% +to know or be able to do by the end of + + + align:start position:0% +to know or be able to do by the end of +the class and you want to construct + + align:start position:0% +the class and you want to construct + + + align:start position:0% +the class and you want to construct +questions that help them get there and + + align:start position:0% +questions that help them get there and + + + align:start position:0% +questions that help them get there and +test whether they're there or not so you + + align:start position:0% +test whether they're there or not so you + + + align:start position:0% +test whether they're there or not so you +might use one or two or three questions + + align:start position:0% +might use one or two or three questions + + + align:start position:0% +might use one or two or three questions +in a class and and that might be it that + + align:start position:0% +in a class and and that might be it that + + + align:start position:0% +in a class and and that might be it that +might be all you do but you do want to + + align:start position:0% +might be all you do but you do want to + + + align:start position:0% +might be all you do but you do want to +make sure you construct the questions + + align:start position:0% +make sure you construct the questions + + + align:start position:0% +make sure you construct the questions +thoughtfully um + + align:start position:0% +thoughtfully um + + + align:start position:0% +thoughtfully um +the next sort of the if you want to go + + align:start position:0% +the next sort of the if you want to go + + + align:start position:0% +the next sort of the if you want to go +further in is uh to to think about what + + align:start position:0% +further in is uh to to think about what + + + align:start position:0% +further in is uh to to think about what +it is really think critically about your + + align:start position:0% +it is really think critically about your + + + align:start position:0% +it is really think critically about your +learning outcome what do I want students + + align:start position:0% +learning outcome what do I want students + + + align:start position:0% +learning outcome what do I want students +to get out of this class this particular + + align:start position:0% +to get out of this class this particular + + + align:start position:0% +to get out of this class this particular +class and then construct a series of + + align:start position:0% +class and then construct a series of + + + align:start position:0% +class and then construct a series of +clicker questions that really uh help + + align:start position:0% +clicker questions that really uh help + + + align:start position:0% +clicker questions that really uh help +students understand whether they get it + + align:start position:0% +students understand whether they get it + + + align:start position:0% +students understand whether they get it +or not help them argue their point with + + align:start position:0% +or not help them argue their point with + + + align:start position:0% +or not help them argue their point with +others or or encourage them to argue + + align:start position:0% +others or or encourage them to argue + + + align:start position:0% +others or or encourage them to argue +their their opinion or point with others + + align:start position:0% +their their opinion or point with others + + + align:start position:0% +their their opinion or point with others +and then ultimately come to to a + + align:start position:0% +and then ultimately come to to a + + + align:start position:0% +and then ultimately come to to a +realization or come to uh or come to + + align:start position:0% +realization or come to uh or come to + + + align:start position:0% +realization or come to uh or come to +attain the learning outcomes really by + + align:start position:0% +attain the learning outcomes really by + + + align:start position:0% +attain the learning outcomes really by +engagement with the clicker questions + + align:start position:0% +engagement with the clicker questions + + + align:start position:0% +engagement with the clicker questions +and by engagement in a subsequent + + align:start position:0% +and by engagement in a subsequent + + + align:start position:0% +and by engagement in a subsequent +discussion so where the clicker + + align:start position:0% +discussion so where the clicker + + + align:start position:0% +discussion so where the clicker +questions are really the core of your of + + align:start position:0% +questions are really the core of your of + + + align:start position:0% +questions are really the core of your of +your of your class and and the Learning + + align:start position:0% +your of your class and and the Learning + + + align:start position:0% +your of your class and and the Learning +Happens sort of uh threaded among those + + align:start position:0% +Happens sort of uh threaded among those + + + align:start position:0% +Happens sort of uh threaded among those +questions \ No newline at end of file diff --git a/ighcncy6qQ8.txt b/ighcncy6qQ8.txt new file mode 100644 index 0000000000000000000000000000000000000000..147bed634181cd3cc89eed65325b1a19c4c4f46f --- /dev/null +++ b/ighcncy6qQ8.txt @@ -0,0 +1,1221 @@ +align:start position:0% + +hi guys um today we are going to play + + align:start position:0% +hi guys um today we are going to play + + + align:start position:0% +hi guys um today we are going to play +around with the basics of igen values + + align:start position:0% +around with the basics of igen values + + + align:start position:0% +around with the basics of igen values +and igen vectors we're going to do the + + align:start position:0% +and igen vectors we're going to do the + + + align:start position:0% +and igen vectors we're going to do the +following problem um we're given this + + align:start position:0% +following problem um we're given this + + + align:start position:0% +following problem um we're given this +invertible Matrix + + align:start position:0% +invertible Matrix + + + align:start position:0% +invertible Matrix +a and we'll find the igen values and + + align:start position:0% +a and we'll find the igen values and + + + align:start position:0% +a and we'll find the igen values and +igen vectors not of a but of a + + align:start position:0% +igen vectors not of a but of a + + + align:start position:0% +igen vectors not of a but of a +squ and a inverse minus the + + align:start position:0% +squ and a inverse minus the + + + align:start position:0% +squ and a inverse minus the +identity um so this problem might seem + + align:start position:0% +identity um so this problem might seem + + + align:start position:0% +identity um so this problem might seem +daunting at + + align:start position:0% +daunting at + + + align:start position:0% +daunting at +first squaring a 3X3 Matrix or taking an + + align:start position:0% +first squaring a 3X3 Matrix or taking an + + + align:start position:0% +first squaring a 3X3 Matrix or taking an +inverse of a 3X3 Matrix is a fairly um + + align:start position:0% +inverse of a 3X3 Matrix is a fairly um + + + align:start position:0% +inverse of a 3X3 Matrix is a fairly um +compettition + + align:start position:0% +compettition + + + align:start position:0% +compettition +task but if you've seen Professor + + align:start position:0% +task but if you've seen Professor + + + align:start position:0% +task but if you've seen Professor +strang's lecture on igen Val and vectors + + align:start position:0% +strang's lecture on igen Val and vectors + + + align:start position:0% +strang's lecture on igen Val and vectors +you shouldn't be all too worried so I'll + + align:start position:0% +you shouldn't be all too worried so I'll + + + align:start position:0% +you shouldn't be all too worried so I'll +I'll give you a few few moments to um + + align:start position:0% +I'll give you a few few moments to um + + + align:start position:0% +I'll give you a few few moments to um +think of your own line of attack and + + align:start position:0% +think of your own line of attack and + + + align:start position:0% +think of your own line of attack and +then you'll see + + align:start position:0% + + + + align:start position:0% + +mine hi again okay so the observation + + align:start position:0% +mine hi again okay so the observation + + + align:start position:0% +mine hi again okay so the observation +that makes our life really easy is the + + align:start position:0% +that makes our life really easy is the + + + align:start position:0% +that makes our life really easy is the +following one so say uh V is an IG + + align:start position:0% +following one so say uh V is an IG + + + align:start position:0% +following one so say uh V is an IG +Vector with Associated I value Lambda to + + align:start position:0% +Vector with Associated I value Lambda to + + + align:start position:0% +Vector with Associated I value Lambda to +a The Matrix a okay um then if we hit V + + align:start position:0% +a The Matrix a okay um then if we hit V + + + align:start position:0% +a The Matrix a okay um then if we hit V +with a + + align:start position:0% +with a + + + align:start position:0% +with a +s well this we can write it as a * a + + align:start position:0% +s well this we can write it as a * a + + + align:start position:0% +s well this we can write it as a * a +v but AV is Lambda V right + + align:start position:0% +v but AV is Lambda V right + + + align:start position:0% +v but AV is Lambda V right +so have a Lambda V uh Lambda is a scalar + + align:start position:0% +so have a Lambda V uh Lambda is a scalar + + + align:start position:0% +so have a Lambda V uh Lambda is a scalar +so we can uh move it in front and get + + align:start position:0% +so we can uh move it in front and get + + + align:start position:0% +so we can uh move it in front and get +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +a and Lambda a v is when we plug in AV + + align:start position:0% +a and Lambda a v is when we plug in AV + + + align:start position:0% +a and Lambda a v is when we plug in AV +Lambda V is just Lambda squ V so what + + align:start position:0% +Lambda V is just Lambda squ V so what + + + align:start position:0% +Lambda V is just Lambda squ V so what +we've found out is that um if V is an + + align:start position:0% +we've found out is that um if V is an + + + align:start position:0% +we've found out is that um if V is an +igen Vector for a then it's also an igen + + align:start position:0% +igen Vector for a then it's also an igen + + + align:start position:0% +igen Vector for a then it's also an igen +Vector for a squ just that the igen + + align:start position:0% +Vector for a squ just that the igen + + + align:start position:0% +Vector for a squ just that the igen +value is the igen value squared + + align:start position:0% +value is the igen value squared + + + align:start position:0% +value is the igen value squared +similarly uh if we hit a + + align:start position:0% +similarly uh if we hit a + + + align:start position:0% +similarly uh if we hit a +inverse if you hit V V with a inverse so + + align:start position:0% +inverse if you hit V V with a inverse so + + + align:start position:0% +inverse if you hit V V with a inverse so +in this case we can write v + + align:start position:0% +in this case we can write v + + + align:start position:0% +in this case we can write v +as AV over + + align:start position:0% +as AV over + + + align:start position:0% +as AV over +Lambda given that of course Lambda is + + align:start position:0% +Lambda given that of course Lambda is + + + align:start position:0% +Lambda given that of course Lambda is +non zero but um the igen values of an + + align:start position:0% +non zero but um the igen values of an + + + align:start position:0% +non zero but um the igen values of an +invertible Matrix are always non zero + + align:start position:0% +invertible Matrix are always non zero + + + align:start position:0% +invertible Matrix are always non zero +which is an exercise you should uh you + + align:start position:0% +which is an exercise you should uh you + + + align:start position:0% +which is an exercise you should uh you +should do yourselves um + + align:start position:0% +should do yourselves um + + + align:start position:0% +should do yourselves um +so if we just then take out the a + + align:start position:0% +so if we just then take out the a + + + align:start position:0% +so if we just then take out the a +and combin it with a + + align:start position:0% + + + + align:start position:0% + +inverse this is the identity and so we + + align:start position:0% +inverse this is the identity and so we + + + align:start position:0% +inverse this is the identity and so we +get 1 over Lambda V so V is also an igen + + align:start position:0% +get 1 over Lambda V so V is also an igen + + + align:start position:0% +get 1 over Lambda V so V is also an igen +Vector for a inverse with IG value the + + align:start position:0% +Vector for a inverse with IG value the + + + align:start position:0% +Vector for a inverse with IG value the +is + + align:start position:0% +is + + + align:start position:0% +is +reciprocal of Lambda okay and from here + + align:start position:0% +reciprocal of Lambda okay and from here + + + align:start position:0% +reciprocal of Lambda okay and from here +of course a inverse minus the identity + + align:start position:0% +of course a inverse minus the identity + + + align:start position:0% +of course a inverse minus the identity +is Lambda inverse minus1 + + align:start position:0% + + + + align:start position:0% + +V so the I value ass yeah associated + + align:start position:0% +V so the I value ass yeah associated + + + align:start position:0% +V so the I value ass yeah associated +with so the value of a inverse minus D + + align:start position:0% +with so the value of a inverse minus D + + + align:start position:0% +with so the value of a inverse minus D +identity is 1/ Lambda minus minus + + align:start position:0% +identity is 1/ Lambda minus minus + + + align:start position:0% +identity is 1/ Lambda minus minus +one okay so what we've figured out is we + + align:start position:0% +one okay so what we've figured out is we + + + align:start position:0% +one okay so what we've figured out is we +just need to find the igen values and + + align:start position:0% +just need to find the igen values and + + + align:start position:0% +just need to find the igen values and +igen vectors of a and then um we have a + + align:start position:0% +igen vectors of a and then um we have a + + + align:start position:0% +igen vectors of a and then um we have a +way of finding what the I values and I + + align:start position:0% +way of finding what the I values and I + + + align:start position:0% +way of finding what the I values and I +vectors of um um those combination well + + align:start position:0% +vectors of um um those combination well + + + align:start position:0% +vectors of um um those combination well +a a squ and a inverse minus the identity + + align:start position:0% +a a squ and a inverse minus the identity + + + align:start position:0% +a a squ and a inverse minus the identity +will be okay um so how do we find the + + align:start position:0% +will be okay um so how do we find the + + + align:start position:0% +will be okay um so how do we find the +igen values + + align:start position:0% +igen values + + + align:start position:0% +igen values +well what does it mean + + align:start position:0% +well what does it mean + + + align:start position:0% +well what does it mean +for Lambda to be an nigen value of a it + + align:start position:0% +for Lambda to be an nigen value of a it + + + align:start position:0% +for Lambda to be an nigen value of a it +means that the Matrix a minus Lambda the + + align:start position:0% +means that the Matrix a minus Lambda the + + + align:start position:0% +means that the Matrix a minus Lambda the +identity is + + align:start position:0% +identity is + + + align:start position:0% +identity is +singular which is precisely the case + + align:start position:0% +singular which is precisely the case + + + align:start position:0% +singular which is precisely the case +when its determinant is + + align:start position:0% +when its determinant is + + + align:start position:0% +when its determinant is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we + + align:start position:0% +so we + + + align:start position:0% +so we +have we need to solve the following + + align:start position:0% +have we need to solve the following + + + align:start position:0% +have we need to solve the following +equation um L minus one + + align:start position:0% +equation um L minus one + + + align:start position:0% +equation um L minus one +two oh sorry 1 minus + + align:start position:0% +two oh sorry 1 minus + + + align:start position:0% +two oh sorry 1 minus +Lambda 2 + + align:start position:0% +Lambda 2 + + + align:start position:0% +Lambda 2 +3 0 1 - Lambda + + align:start position:0% +3 0 1 - Lambda + + + align:start position:0% +3 0 1 - Lambda +2 -2 and 0 1 for minus + + align:start position:0% +2 -2 and 0 1 for minus + + + align:start position:0% +2 -2 and 0 1 for minus +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +so U it's fairly obvious which column we + + align:start position:0% +so U it's fairly obvious which column we + + + align:start position:0% +so U it's fairly obvious which column we +should use to expand this this um + + align:start position:0% +should use to expand this this um + + + align:start position:0% +should use to expand this this um +determinant we should use the the First + + align:start position:0% +determinant we should use the the First + + + align:start position:0% +determinant we should use the the First +Column because we have only one non Zero + + align:start position:0% +Column because we have only one non Zero + + + align:start position:0% +Column because we have only one non Zero +Entry and so this is equal to + + align:start position:0% +Entry and so this is equal to + + + align:start position:0% +Entry and so this is equal to +1us + + align:start position:0% +1us + + + align:start position:0% +1us +Lambda times the + + align:start position:0% +Lambda times the + + + align:start position:0% +Lambda times the +determinant of the 2x2 + + align:start position:0% + + + + align:start position:0% + +matrix 1 - + + align:start position:0% +matrix 1 - + + + align:start position:0% +matrix 1 - +Lambda -2 1 4 - + + align:start position:0% +Lambda -2 1 4 - + + + align:start position:0% +Lambda -2 1 4 - +Lambda which + + align:start position:0% +Lambda which + + + align:start position:0% +Lambda which +is I'm going to take the computation up + + align:start position:0% + + + + align:start position:0% + +here minus Lambda + + align:start position:0% + + + + align:start position:0% + +um Lambda + + align:start position:0% +um Lambda + + + align:start position:0% +um Lambda +2- 5 Lambda + + + align:start position:0% +2- 5 Lambda + + + + align:start position:0% +2- 5 Lambda + +6 which is a fairly familiar quadratic + + align:start position:0% +6 which is a fairly familiar quadratic + + + align:start position:0% +6 which is a fairly familiar quadratic +and we + + align:start position:0% +and we + + + align:start position:0% +and we +can write it as a product of linear + + align:start position:0% +can write it as a product of linear + + + align:start position:0% +can write it as a product of linear +factors Lambda minus 2 Lambda minus + + align:start position:0% +factors Lambda minus 2 Lambda minus + + + align:start position:0% +factors Lambda minus 2 Lambda minus + + align:start position:0% + + + align:start position:0% +so the three igen values of a are one + + align:start position:0% +so the three igen values of a are one + + + align:start position:0% +so the three igen values of a are one +two and + + align:start position:0% +two and + + + align:start position:0% +two and +three okay so first half of our problem + + align:start position:0% +three okay so first half of our problem + + + align:start position:0% +three okay so first half of our problem +is done now we just need to find what + + align:start position:0% +is done now we just need to find what + + + align:start position:0% +is done now we just need to find what +the igen vectors associated with each of + + align:start position:0% +the igen vectors associated with each of + + + align:start position:0% +the igen vectors associated with each of +these igen values + + align:start position:0% +these igen values + + + align:start position:0% +these igen values +are uh how we do + + align:start position:0% +are uh how we do + + + align:start position:0% +are uh how we do +that + + align:start position:0% +that + + + align:start position:0% +that +well um + + align:start position:0% +well um + + + align:start position:0% +well um +say let's figure out what the I Vector + + align:start position:0% +say let's figure out what the I Vector + + + align:start position:0% +say let's figure out what the I Vector +associated with Lambda equals 1 is + + align:start position:0% +associated with Lambda equals 1 is + + + align:start position:0% +associated with Lambda equals 1 is +um so we know that the igen vector needs + + align:start position:0% +um so we know that the igen vector needs + + + align:start position:0% +um so we know that the igen vector needs +to be in the null space of a minus + + align:start position:0% +to be in the null space of a minus + + + align:start position:0% +to be in the null space of a minus +Lambda the identity so a minus the + + align:start position:0% +Lambda the identity so a minus the + + + align:start position:0% +Lambda the identity so a minus the +identity + + align:start position:0% +identity + + + align:start position:0% +identity +um B so let me write this + + align:start position:0% +um B so let me write this + + + align:start position:0% +um B so let me write this +out + + align:start position:0% + + + + align:start position:0% + +it's + + align:start position:0% +it's + + + align:start position:0% +it's + + align:start position:0% + + + align:start position:0% +z um + + align:start position:0% +z um + + + align:start position:0% +z um +three 2 + + align:start position:0% +three 2 + + + align:start position:0% +three 2 +three Z + + align:start position:0% + + + + align:start position:0% + +-20 uh + + align:start position:0% +-20 uh + + + align:start position:0% +-20 uh +1 and we see that the First Column is + + align:start position:0% +1 and we see that the First Column is + + + align:start position:0% +1 and we see that the First Column is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +so um well the first + + align:start position:0% +so um well the first + + + align:start position:0% +so um well the first +um therefore yeah the the first variable + + align:start position:0% +um therefore yeah the the first variable + + + align:start position:0% +um therefore yeah the the first variable +is will be our free variable if we want + + align:start position:0% +is will be our free variable if we want + + + align:start position:0% +is will be our free variable if we want +to solve this linear system of + + align:start position:0% +to solve this linear system of + + + align:start position:0% +to solve this linear system of +equations and we can just set it to one + + align:start position:0% +equations and we can just set it to one + + + align:start position:0% +equations and we can just set it to one +and it's not hard to see that the other + + align:start position:0% +and it's not hard to see that the other + + + align:start position:0% +and it's not hard to see that the other +two um entry should be + + align:start position:0% +two um entry should be + + + align:start position:0% +two um entry should be +zero so we can do yeah the same + + align:start position:0% +zero so we can do yeah the same + + + align:start position:0% +zero so we can do yeah the same +procedure with the other two igen values + + align:start position:0% +procedure with the other two igen values + + + align:start position:0% +procedure with the other two igen values +and yeah we'll we'll get yeah an igen + + align:start position:0% +and yeah we'll we'll get yeah an igen + + + align:start position:0% +and yeah we'll we'll get yeah an igen +value each for um oh sorry an igen + + align:start position:0% +value each for um oh sorry an igen + + + align:start position:0% +value each for um oh sorry an igen +Vector for each I value and in the end + + align:start position:0% +Vector for each I value and in the end + + + align:start position:0% +Vector for each I value and in the end +let me go back here + + align:start position:0% + + + + align:start position:0% + +so I'm going to um put our results in a + + align:start position:0% +so I'm going to um put our results in a + + + align:start position:0% +so I'm going to um put our results in a +little table so + + align:start position:0% +little table so + + + align:start position:0% +little table so +a + + align:start position:0% +a + + + align:start position:0% +a +squar inverse is the identity + + align:start position:0% +squar inverse is the identity + + + align:start position:0% +squar inverse is the identity +so the first row will be I + + align:start position:0% + + + + align:start position:0% + +values + + align:start position:0% +values + + + align:start position:0% +values +so it's going to be if Lambda is a NE + + align:start position:0% +so it's going to be if Lambda is a NE + + + align:start position:0% +so it's going to be if Lambda is a NE +value for then we saw that Lambda Square + + align:start position:0% +value for then we saw that Lambda Square + + + align:start position:0% +value for then we saw that Lambda Square +will be the value for a squ and Lambda + + align:start position:0% +will be the value for a squ and Lambda + + + align:start position:0% +will be the value for a squ and Lambda +in inverse minus one will be the I value + + align:start position:0% +in inverse minus one will be the I value + + + align:start position:0% +in inverse minus one will be the I value +for a inverse minus the identity and the + + align:start position:0% +for a inverse minus the identity and the + + + align:start position:0% +for a inverse minus the identity and the +I + + align:start position:0% + + + + align:start position:0% + +vectors will be the + + align:start position:0% +vectors will be the + + + align:start position:0% +vectors will be the +same okay we're done \ No newline at end of file diff --git a/jXf5Sz7V87I.txt b/jXf5Sz7V87I.txt new file mode 100644 index 0000000000000000000000000000000000000000..73ada932bac2749b2f1c0220ff12877a3c87a428 --- /dev/null +++ b/jXf5Sz7V87I.txt @@ -0,0 +1,483 @@ +align:start position:0% + +let us now take stock and summarize what + + align:start position:0% +let us now take stock and summarize what + + + align:start position:0% +let us now take stock and summarize what +we have done for these two processes the + + align:start position:0% +we have done for these two processes the + + + align:start position:0% +we have done for these two processes the +Bernoulli and the Poisson process and + + align:start position:0% +Bernoulli and the Poisson process and + + + align:start position:0% +Bernoulli and the Poisson process and +their relation the Poisson process runs + + align:start position:0% +their relation the Poisson process runs + + + align:start position:0% +their relation the Poisson process runs +in continuous time who are as for the + + align:start position:0% +in continuous time who are as for the + + + align:start position:0% +in continuous time who are as for the +Bernoulli process time is discrete and + + align:start position:0% +Bernoulli process time is discrete and + + + align:start position:0% +Bernoulli process time is discrete and +is divided into slots the Poisson + + align:start position:0% +is divided into slots the Poisson + + + align:start position:0% +is divided into slots the Poisson +process is defined by a single parameter + + align:start position:0% +process is defined by a single parameter + + + align:start position:0% +process is defined by a single parameter +lambda which is the intensity or arrival + + align:start position:0% +lambda which is the intensity or arrival + + + align:start position:0% +lambda which is the intensity or arrival +rate and tells us the expected number of + + align:start position:0% +rate and tells us the expected number of + + + align:start position:0% +rate and tells us the expected number of +arrivals per unit time for the Bernoulli + + align:start position:0% +arrivals per unit time for the Bernoulli + + + align:start position:0% +arrivals per unit time for the Bernoulli +process we have again one basic + + align:start position:0% +process we have again one basic + + + align:start position:0% +process we have again one basic +parameter which is the probability of + + align:start position:0% +parameter which is the probability of + + + align:start position:0% +parameter which is the probability of +success at any given trial or the + + align:start position:0% +success at any given trial or the + + + align:start position:0% +success at any given trial or the +probability of an arrival during each + + align:start position:0% +probability of an arrival during each + + + align:start position:0% +probability of an arrival during each +one of the slots based on our model we + + align:start position:0% +one of the slots based on our model we + + + align:start position:0% +one of the slots based on our model we +were interested in three kinds of + + align:start position:0% +were interested in three kinds of + + + align:start position:0% +were interested in three kinds of +quantities and we found the + + align:start position:0% +quantities and we found the + + + align:start position:0% +quantities and we found the +distributions of them the first quantity + + align:start position:0% +distributions of them the first quantity + + + align:start position:0% +distributions of them the first quantity +is the number of arrivals during a + + align:start position:0% +is the number of arrivals during a + + + align:start position:0% +is the number of arrivals during a +certain time interval for the discrete + + align:start position:0% +certain time interval for the discrete + + + align:start position:0% +certain time interval for the discrete +case the number of arrivals has a + + align:start position:0% +case the number of arrivals has a + + + align:start position:0% +case the number of arrivals has a +binomial distribution whereas for the + + align:start position:0% +binomial distribution whereas for the + + + align:start position:0% +binomial distribution whereas for the +Poisson case the distribution is that of + + align:start position:0% +Poisson case the distribution is that of + + + align:start position:0% +Poisson case the distribution is that of +a Poisson random variable then we looked + + align:start position:0% +a Poisson random variable then we looked + + + align:start position:0% +a Poisson random variable then we looked +at the time until the first arrival or + + align:start position:0% +at the time until the first arrival or + + + align:start position:0% +at the time until the first arrival or +the time between consecutive arrivals + + align:start position:0% +the time between consecutive arrivals + + + align:start position:0% +the time between consecutive arrivals +for the Bernoulli process that + + align:start position:0% +for the Bernoulli process that + + + align:start position:0% +for the Bernoulli process that +distribution is geometric for the + + align:start position:0% +distribution is geometric for the + + + align:start position:0% +distribution is geometric for the +Poisson process that distribution is + + align:start position:0% +Poisson process that distribution is + + + align:start position:0% +Poisson process that distribution is +exponential note that in this instance + + align:start position:0% +exponential note that in this instance + + + align:start position:0% +exponential note that in this instance +were dealing with a discrete random + + align:start position:0% +were dealing with a discrete random + + + align:start position:0% +were dealing with a discrete random +variable but here with a continuous + + align:start position:0% +variable but here with a continuous + + + align:start position:0% +variable but here with a continuous +random variable and then as a + + align:start position:0% +random variable and then as a + + + align:start position:0% +random variable and then as a +generalization we could find the time + + align:start position:0% +generalization we could find the time + + + align:start position:0% +generalization we could find the time +until the case arrival which in the + + align:start position:0% +until the case arrival which in the + + + align:start position:0% +until the case arrival which in the +present case is given by an Erlang + + align:start position:0% +present case is given by an Erlang + + + align:start position:0% +present case is given by an Erlang +distribution and for the Bernoulli case + + align:start position:0% +distribution and for the Bernoulli case + + + align:start position:0% +distribution and for the Bernoulli case +we developed one particular formula and + + align:start position:0% +we developed one particular formula and + + + align:start position:0% +we developed one particular formula and +that formula is actually known under the + + align:start position:0% +that formula is actually known under the + + + align:start position:0% +that formula is actually known under the +name of a Pascal distribution all of + + align:start position:0% +name of a Pascal distribution all of + + + align:start position:0% +name of a Pascal distribution all of +these results for the Poisson case were + + align:start position:0% +these results for the Poisson case were + + + align:start position:0% +these results for the Poisson case were +obtained because we used an + + align:start position:0% +obtained because we used an + + + align:start position:0% +obtained because we used an +approximation argument that is we had + + align:start position:0% +approximation argument that is we had + + + align:start position:0% +approximation argument that is we had +the results for the Bernoulli case but + + align:start position:0% +the results for the Bernoulli case but + + + align:start position:0% +the results for the Bernoulli case but +then we argued that the Poisson process + + align:start position:0% +then we argued that the Poisson process + + + align:start position:0% +then we argued that the Poisson process +is a limiting case of the Bernoulli + + align:start position:0% +is a limiting case of the Bernoulli + + + align:start position:0% +is a limiting case of the Bernoulli +process in which we take time divided + + align:start position:0% +process in which we take time divided + + + align:start position:0% +process in which we take time divided +into a large number of slots during each + + align:start position:0% +into a large number of slots during each + + + align:start position:0% +into a large number of slots during each +one of the slots however we have a small + + align:start position:0% +one of the slots however we have a small + + + align:start position:0% +one of the slots however we have a small +probability of an arrival and this is + + align:start position:0% +probability of an arrival and this is + + + align:start position:0% +probability of an arrival and this is +done in a way so that the product of + + align:start position:0% +done in a way so that the product of + + + align:start position:0% +done in a way so that the product of +these two numbers + + align:start position:0% +these two numbers + + + align:start position:0% +these two numbers +stays a constant by using a finer and + + align:start position:0% +stays a constant by using a finer and + + + align:start position:0% +stays a constant by using a finer and +finer discretization + + align:start position:0% +finer discretization + + + align:start position:0% +finer discretization +we could approach the Poisson process + + align:start position:0% +we could approach the Poisson process + + + align:start position:0% +we could approach the Poisson process +arbitrarily close by a Bernoulli process + + align:start position:0% +arbitrarily close by a Bernoulli process + + + align:start position:0% +arbitrarily close by a Bernoulli process +and then we used the Bernoulli formulas + + align:start position:0% +and then we used the Bernoulli formulas + + + align:start position:0% +and then we used the Bernoulli formulas +in which we took the limit as Delta was + + align:start position:0% +in which we took the limit as Delta was + + + align:start position:0% +in which we took the limit as Delta was +going to zero and this gave us the + + align:start position:0% +going to zero and this gave us the + + + align:start position:0% +going to zero and this gave us the +result for the Poisson case \ No newline at end of file diff --git a/jmsPn679o5k.txt b/jmsPn679o5k.txt new file mode 100644 index 0000000000000000000000000000000000000000..19df167b032bf41fa1d81bcad7cd66cc65933545 --- /dev/null +++ b/jmsPn679o5k.txt @@ -0,0 +1,3357 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at ocw. + +mit. edu. + +PROFESSOR: Once again +to put this in the + +context of where we are. + +We're talking about +producer theory. + +And we're talking +about how firms + +decide how much to produce. + +We started with a perfect +competition, and that nailed + +down the fact that with under +perfect competition we got the + +zero profit long run perfectly +elastic supply curve. + +We then, last time, talked +about monopoly as another + +extreme and talked about how +monopolists choose both their + +price and their quantity. + +They set margin around or equal +to marginal cost. That + +gives them a quantity. + +And then they choose the price +off the demand curve and how + +that leads to profits and how +that leads to monopolists + +producing less than the +competitive level. + +And we also ended by talking +about a perfectly price + +discriminating monopolist, one +that can actually charge each + +consumer their willingness to +pay and therefore, absorb all + +the social surplus. + +Now, I want to come back and +start, this morning, by + +talking again about price +discrimination and realizing + +that, in some sense, we know +that there's no such thing as + +perfect price discrimination. + +There's no monopolist out there +charging us literally + +exactly what we're +willing to pay. + +But there are lots of examples +of price discrimination in the + +real world. + +And sometimes they're +kind of obvious. + +Sometimes they're not. + +But what they all have in common +is the notion of trying + +to find some signal of our +willingness to pay and using + +that to set the price. + +So instead of being like our +original monopolist, just + +setting one price. + +Monopolists are forever trying +to find some signal, some + +underlying signal of our +willingness to pay and using + +that to set the price. + +OK. + +So for example, a classic +example we know is airlines. + +OK. + +What airlines do-- + +Airlines charge you more, for +example, if you book your + +ticket the last minute. + +And the notion of course-- or +towards the last minute. + +At the very last minute they may +end up charging you less. + +But as you get close to the date +when you want to leave, + +the price goes up. + +The notion, of course, is that +who is going to buy tickets + +close to the date they want to +leave. It's largely going to + +be business people, not +the vacation traveler. + +The vacation traveler is +going to plan ahead + +and buy far in advance. + +The one that's going to buy a +week before is the business + +person who just got a +meeting scheduled. + +Business people are going to +be less price sensitive. + +They're going to have a higher +willingness to pay. + +They've got to get +to the meeting. + +They're not paying anyway. + +The company's paying. + +And they're just to +do what they need + +to get to the meeting. + +So that's a less price +sensitive population. + +So that's the population +you want to hit + +with a higher price. + +So you want to price up tickets +that you buy towards + +the end because those are more +likely to be the people who + +are least price sensitive. + +So let's ask another question. + +Somebody tell me why do movie +theaters charge less for + +matinees than for +movies at night? + +Why do movie theaters +charge less? + +If you go see the first movie +of the day-- and you guys + +probably don't anymore. + +But when you were +kids you did. + +And when I take my take +my kids, I do. + +And that afternoon matinee +movie costs less. + +Why is that? + +Yeah. + +Anyone want to take +a chance at that? + +And related to it, you can +also ask the question. + +Why do restaurants have +early bird specials? + +Why, when you go to restaurant, +often will they + +charge you less if you go there +in the early hours as + +opposed to later? + +So what's going on with that? + +Someone tell me. + +Yeah. + +AUDIENCE: They're not +using up all their + +seats in the afternoon. + +So they might as well +lower the price. + +PROFESSOR: In the afternoon +they're not. + +Although the truth is, a lot +of the time they're-- + +If you look at a movie theater +today, it's almost never full, + +except for like the opening +night of a very popular movie. + +So that's part of it. + +But let's talk about +the demand side. + +What else is special about +the type of people? + +Why don't you go on what's +special about the type of + +people who want to see movies or +go to restaurants at those + +different times? + +They're not willing +to pay as much. + +PROFESSOR: Yeah, they're +basically people with a lot of + +free time on their hands. + +Right? + +The people who are going out +to dinner early, the people + +who see movies in the afternoon, +these are people + +who are unemployed or +have little kids. + +And they're just looking +to kill time. + +And so basically, these +are people who + +are willing to shop. + +These are people who are going +to say look, I've got to fill + +in some time. + +I don't have to go right now. + +I can go any time. + +So I'm going to be more +price sensitive. + +The people who are going to +dinner later, who are going + +out to the movie at night, +they're working all day. + +They have no choice. + +They have to see the +movie at night. + +Or they're in school all day. + +They have to see the +movie at night. + +They're less price elastic. + +So that's why you want +to set the movie + +price higher at night. + +Alternatively, another +reason could be-- + +One signal of willingness to +pay is price sensitivity. + +What's another signal? + +It's going to be income. + +Who's going to be seeing the +movies during the day and + +going to the dinner early? + +It's elderly individuals and +families with small kids who + +are the most resource +strapped. + +People who have plenty +of disposable income + +are going at night. + +They're working. + +They're young. + +They're singles and +young couples. + +They work all day or are +in school all day. + +They go at night. + +They have more disposable +income. + +The people going during the +day are the elders and the + +people with young kids who have +less disposable income. + +And as a result they're going +to be more price sensitive. + +So you want to charge +them a lower price. + +So that's another example +of price discrimination. + +OK, why does Disney World charge +you less if you live in + +the area than if you do not. + +This is true fact. + +Disney World charges you less if +you're from Orlando than if + +you're not from Orlando. + +Why is that? + +Someone tell me. + +Yeah. + +AUDIENCE: I think the Disney +can go any time. + +So you might as well you +might as well take + +them to other places. + +PROFESSOR: I mean, basically +the idea is look, if I just + +spent a grand on a plane ticket +to take my kids to + +Orlando to Disney World, I'm not +going to kvetch over $10 + +either way, getting in +or not getting in. + +But if I live in the area, +I may or may not go. + +I can go to a park, instead. + +I can go do something +else, instead. + +It's just one of many +choices for me. + +The point is, having paid the +fixed cost of getting to + +Orlando, I'm going to be much +less price sensitive about + +getting into the park than other +people who live there, + +who have lots of +other choices. + +Likewise, having paid the money +to get there, I have + +shown I have more disposable +income because I paid the + +money to get there. + +I've shown I have enough +disposable income that I'm + +willing to drop money on a plane +ticket to take my kids + +to Disney World. + +So I'm going to have +more income that we + +are willing to pay. + +OK, so basically the point +is companies are + +forever doing this. + +The ultimate example was, +briefly, Amazon.com started + +pricing by IP address. + +For a while, it was a +controversy over Amazon + +started literally charging, +getting people's IP addresses + +and literally adjusting prices +based on saying, oh, this + +person is from a university +library. + +University libraries aren't +price sensitive. + +We'll charge them +more, et cetera. + +That got shut down. + +But that was the ultimate form +of trying to be price + +discriminatory. + +That was as close as we'll +come to perfect price + +discrimination. + +The point is, in general, people +with market power, + +people that set the price above +marginal cost will in + +general be looking for parties +which are high income and low + +elasticity to which they can +charge a higher price. + +Yeah. + +AUDIENCE: Another example, like +MIT, they actually ask + +for your income statement. + +And then, based on that, they +give you their price. + +PROFESSOR: Well, see that's +very interesting. + +That's very interesting. + +MIT-- + +What's tricky about that is-- + +Is that about exploiting +price sensitivity? + +Or is that about equity? + +That's a bit harder because +MIT could claim-- + +And probably, actually, +it's true. + +They're not doing it. + +Because the truth is, +MIT could charge + +whatever they want. + +They'd still fill the class. + +Right? + +So it's not really about-- + +I think in MIT's case, it's +not really about price + +sensitivity. + +It's about income redistribution +and some notion + +of making sure low income +people can come and + +afford to be here. + +But that is a good point. + +The difficulty with empirical +economics is often, + +correlation versus causation. + +The same fact can have many +different descriptions, many + +different explanations. + +OK? + +So just wanted to give you some +brief examples to think + +about the fact that we see +price discrimination in + +reality all the time. + +Nonetheless, we do our classic +monopoly model. + +We assume there's one price. + +And the truth is the one price +monopolist is probably closer + +to the truth than the perfectly +price discriminating + +monopolist. But the truth, as +often in this course, is going + +to be somewhere in between. + +OK, questions about that. + +What I want to focus on +primarily, for this lecture, + +is where do monopolies +come from. + +How do monopolies arrive? + +How do we end up in this +situation, where instead of + +many firms competing to sell +a good, we only have one? + +And there's basically two +sources of monopolies, two + +sources that give birth to + +monopolies in modern societies. + +The first source is +cost advantages. + +The first source is +cost advantages. + +Some markets come with natural +cost advantages, natural + +reasons why there's a +benefit to being one + +player in the market. + +So for example, it could be +that there's, essentially, + +only one usable input. + +So let's say there's a +rock quarry in town. + +You've got to get rocks from. + +And there's just one +rock quarry. + +And rocks are really expensive +to transport. + +So basically, if you live in +that town, the person who owns + +that rock quarry is going to be +the monopolist. No one else + +is really going to compete +because it would cost them so + +much to transport rocks +from another + +quarry in another town. + +OK? + +Basically, the point is. + +Sometimes, there are +these fixed costs. + +And whoever has paid the fixed +cost has an enormous natural + +advantage over other +players, over other + +entrants to the markets. + +And we call those natural +monopolies. + +Natural monopolies-- + +Natural monopoly is a firm where +for all the relevant + +quantities over any relevant +range, the average cost for + +one firm is always below the +average cost of a new entrant. + +The average cost for the one +firm that's in the market is + +already always going to be below +the average cost for any + +new entrant. + +And that is going to be true +in markets with very large + +fixed costs and very small +marginal costs. + +A natural monopoly will occur +when there's very large fixed + +cost and very small marginal +cost. In that case, what we'll + +see is average cost is +always declining. + +Natural monopolies arise +when average + +cost is always declining. + +If average cost is always +declining, it's never going to + +make sense for another entrant +to come in the market. + +And an example we +could think of-- + +The best example I could think +is like a water utility, the + +folks who deliver water +to our houses. + +The fixed costs of delivering +water are enormous. + +You've got to lay the pipe +to deliver the water + +all through the town. + +Those are enormous +fixed costs. + +The marginal costs +are trivial. + +I mean, water is cheap. + +You get the water. + +You send it through the pipes. + +OK? + +It would never make sense to +have two companies deliver + +water throughout the town. + +It wouldn't make sense to have +another company come in, rip + +up the roads, lay a competing +set of pipes all through the + +town to compete. + +It just wouldn't make sense +because those fixed costs are + +so huge relative to the +marginal costs. + +They could never make money. + +That first company-- + +If a second company came in and +threatened to do that, the + +first company could always keep +the price low enough that + +that second company could never + +recover their fixed costs. + +Because the first company has +already paid the fixed cost, + +they're already in. + +A second company could +never come in and + +cover those fixed costs. + +So if we see figure 15-1. + +Here's an example of a firm, +of a water utility, low + +marginal cost. There was a +high fixed cost. So the + +initial average costs +are very high. + +But the average costs are +declining constantly because + +the marginal costs are low, +relative to fixed costs. + +OK? + +So if demand for the good goes +up, over some relevant range-- + +If demand gets to be infinite, +it may make sense to lay + +another set of pipes. + +You know, the first set of pipes +may get overwhelmed. + +But as long as demand can be met +by the set of pipes that's + +been laid, there's absolutely no +reason for another firm to + +enter this market. + +If another firm ever threatened +to do so, the first + +firm would just lower price and +say, look, you're going to + +have to spend so much money +putting that set of pipes in + +through town you'll never +be able to make it up. + +Because having laid those +set of pipes-- + +Remember what the shut +down condition is. + +As long as that first firm can +charge price greater than + +marginal, can charge price above +average variable cost, + +which is marginal cost +in this case. + +As long as that firm can charge +price above marginal + +cost, it will always +stay in business. + +And that second firm can't make +any money at a price near + +the marginal cost because they +can't cover their fixed cost. + +So they'll essentially +chase them out. + +So essentially, the fact that +they've had that set of pipes + +already laid down gives them a +threat, a credible threat, + +that that second firm +cannot enter. + +Thus, we call natural monopolies +are places where + +other firms face barriers +to entry. + +Natural monopolies are where +there are barriers to entry, + +where other firms cannot enter +because they'd have to pay + +those enormous fixed costs. + +And it would never make economic +sense to do so. + +OK. + +And in that case, you're going +to get a monopoly. + +And we call it a natural +monopoly because, in some + +sense, the monopoly is the +right thing to do. + +It is actually economically +efficient for there to be only + +one provider of water +in the town. + +That's the economically +efficient outcome. + +It is economically inefficient +to pay a second set of those + +enormous fixed costs. + +Now, then you say, well what +about the fact that monopolist + +will under produce water, +charge too much. + +We'll get to that in a minute. + +But when there's natural +monopolies, the goods should + +be delivered by a monopoly. + +That's the right thing to do. + +But there's a second reason why +monopolies arise, which is + +a little more pernicious, which +is government actions. + +Sometimes monopolies are +unnatural and created by the + +government. + +So a classic example is when +governments actually decide + +that they're going to deliver +a good and only they'll + +deliver the good, like +the postal service. + +When a government decides look, +we are just going to + +deliver this good. + +We're just going to have +the postal service. + +And for many, many years, if you +wanted to send a package + +from one place to another, you +had to do it through the + +postal service. + +Well, it turned out +of course, that + +wasn't a natural monopoly. + +As we know through the growth of +FedEx and others, there was + +actually quite a good distance +to compete in that market. + +And eventually, those other +folks delivering packages came + +in and competed in +that market. + +And in fact, in the US, it's +very rare to have a government + +provided good, a purely +government provided good. + +It's very rare. + +Historically, it wasn't. + +And in many other parts of +the world, it's not. + +In many other parts of the +world, governments run the + +banks, the airlines, +all utilities. + +So in many other parts of the +world, governments will + +actually set up these +monopolies + +through government action. + +And basically, that is something +which is not done + +much in the US but +done elsewhere. + +Now however, one place we do set +up monopolies in the US, + +which is pretty important, +is through + +the issuing of patents. + +If you invent, say a new drug, +and you patent it. + +You then have the exclusive +right to sell that chemical + +compound for 17 years. + +So if you come up with some new +chemical compound to treat + +whatever, you have the exclusive +right to market that + +chemical compound +for 17 years. + +That is a government sanctioned +monopoly. + +Now, is that a good thing +or a bad thing? + +Are patents-- + +The government has just +created a monopoly. + +Could someone tell me why that +might be actually a good thing + +for the government to do? + +Yeah. + +AUDIENCE: Schumpeter talks about +how it's a way to cause + +innovation. + +Because no one would put that +many dollars into drug + +research, if they weren't +going to be + +able to make money. + +Because the marginal cost was +so low that other people-- + +The cost of establishing a +pharmaceutical company + +[UNINTELLIGIBLE] +is really low. + +So other people would come +and cut out all their + +profits that they had. + +PROFESSOR: Exactly, if you put +all these resources into + +inventing a drug, it's not +like laying pipes. + +Once you invented it, someone +could just copy it the next + +day and produce it at the +same cost you can. + +So why would you ever do that? + +Why would you, as someone who, +even if you cared about the + +benefits to the world, still +want to make some money. + +Why would you spend billions +and millions of dollars + +inventing these new drugs? + +If the next day, someone +else can just say, + +that's a great idea. + +I'll produce that for $0.47 a +pill, just like you will. + +And you won't make +any money off it. + +And you'll have lost all this +money you invested. + +So the argument for patents is +you want an incentive for + +innovation, which suggests +there's a trade-off here. + +On the one hand, you want an +incentive for innovation. + +On the other hand, once you +create this monopoly, they can + +charge outrageous prices. + +There is a drug. + +There are drugs. + +Genzyme is very big company +started here in Massachusetts. + +And the whole reason they exist +is to create drugs for + +very, very rare diseases. + +Diseases that strike like +100,000 people a + +year but are deadly. + +Like Gaucher's disease is a +famous example of this one. + +So they create these drugs. + +They put billions of dollars +into research, + +create these drugs. + +And then, having created them +and gotten a patent, charge + +like $100,000 a year +to use the drugs. + +Drugs that cost, you know, +$500 a year to produce. + +Now on the one hand, if these +drugs didn't exist, + +people would die. + +These are literally +lifesaving drugs. + +These are people who used to +die, who now live because of + +these drugs. + +And these drugs never would have +been invented if Genzyme + +couldn't have made some +money off them. + +On the other hand, you've got +a product which costs $500 a + +year to make, and they're +charging $100,000 a year to + +people to use. + +And in particular, when it +comes to drugs like for + +treating AIDS in the developed +world where people cannot-- + +There's no way they can afford +that kind of money. + +That's a problem. + +Yeah. + +AUDIENCE: But aren't you not +only paying for them to + +produce the drug but +paying for all the + +research that went into-- + +PROFESSOR: Exactly, +that's right. + +You're paying for all +the research. + +That's why they never +would have + +invented it if they couldn't. + +So you're paying for +the research. + +They also take home a nice, +hefty profit at + +the end of the day. + +But that is true. + +You are also paying for the +research that goes into that. + +And people wouldn't put +that money up front. + +That research is funded +by investors. + +And investors would not invest +in Genzyme and give them money + +to do research if they weren't +going to get a return. + +So if Genzyme-- + +Of that $99,500 Genzyme makes +on that Gaucher's disease + +drug, most of it is going back +to pay the people who funded + +the research. + +But a healthy chunk is not. + +A healthy chunk is market +power monopoly profit. + +Yeah. + +AUDIENCE: Could the government +then have subsidies for some + +types of licensing to ensure +that the consumers are not + +affected because everyone +cannot afford the + +drug without it. + +PROFESSOR: I'm going to come +to that in a second. + +Now actually, let me just hold +that thought for a second + +because I want to actually show +you how we think about + +whether patent is a +good idea or not. + +So let's go to figure 15-2. + +I just want to, sort of, show +you how what you guys seem to + +understand intuitively, we can +illustrate in the kind of + +graphs we've been using. + +Once again, we want to think +about going back and forth + +between the intuition and the +graphical and mathematical + +aspects of this stuff. + +So here we have a monopolist. +Imagine that you have a good + +where the original demand +curve is D1. + +A good where the original demand +curve is D1 and the + +original consumer surplus is +that dotted area C plus 1 plus + +that slashed triangle. + +So it's based on the area above +the competitive price PC + +under the demand curve D1. + +So you have a good. + +It's some drug, which +people like. + +And there's some +demand for it. + +And it's produced competitively +at a price PC + +with the consumer surplus +of that triangle. + +Now, let's say a monopolist +comes along and says, we can + +make this drug way better. + +We could make a much better +drug, but we're going to need + +a patent for it. + +Well, two things happen. + +On the one hand, the demand +curve shifts way out. + +Now you've got something which +people value a lot more. + +They're much more willing to +pay for this better drug. + +OK? + +And that's the benefit. + +That's the innovation +effect on demand. + +On the other hand, the +price goes up to the + +monopolist's price. + +Where marginal revenue equals +marginal cost, they're going + +to produce at Q sub m and charge +a higher price P sub m. + +Whereas, if this is a perfectly +competitive firm, + +they produce much more, where D2 +hits the marginal cost and + +consumer surplus would +be much larger. + +So the trade off is, on the +one hand, you end up here. + +In this case I've drawn, you end +up with a larger consumer + +surplus, even with monopoly. + +But you could imagine drawing +the same graph, in the case + +where consumer surplus falls. + +You can imagine demand doesn't +go up that much. + +But the monopolist gets +the monopoly price. + +And you could imagine drawing +this triangle such that the + +new consumer surplus triangle +is smaller than the old + +consumer surplus triangle. + +OK? + +So it's not obvious which +way this goes. + +You have two effects. + +On the one hand, you have the +effect that demand shifts out. + +That creates a potential for +more social surplus. + +On the other hand, you have the +case that the monopolist + +artificially prices too high. + +That causes a reduction +in social surplus. + +In this case, the former +dominated the latter. + +But I hope you can see you can +draw this in cases where that + +wouldn't be true. + +And that's the tricky +thing with patents. + +It's going to depend. + +If you're patenting something +which is really demand + +increasing, that's great. + +But if you're patenting +something which is just a + +copycat of something that exists +and all you're doing is + +turning a competitive market-- + +In the limit, imagine I +somehow snookered the + +government into giving me a +patent for something which + +literally does no more +than what's existed. + +But somehow I could fool-- + +In that case, have to do a +little more or people wouldn't + +buy it, just a little more +than what existed. + +It wouldn't increase +demand much. + +But I would then have these +monopoly rents. + +OK? + +So that's basically the trade +off with patents. + +All right, question +about that. + +Now, let me move on then +and talk about-- + +The question was +raised about-- + +Well, couldn't the government +do something about this, in + +terms of trying to address +this problem. + +And we just talked about the +government as bad guy in + +creating this problem. + +Although, it's not necessarily +a problem + +in the case of patents. + +But there's also the role of +government as potential good + +guy, which is can the government +help in this case + +of natural monopoly? + +So natural monopoly, we've got +this awkward situation where + +clearly a monopoly +makes sense. + +It doesn't make sense to have +competitive people delivering + +water in town. + +But once you've got one person +delivering water, they'll + +charge you a fortune for it, +well above marginal cost. And + +that's inefficient. + +That lowers social surplus +relative to the optimal level + +of provision. + +So can the government +solve this problem? + +Could the government, for +example, come in and say look, + +we recognize there's +a natural monopoly. + +We recognize that you, Rubrico, +are the only company + +that makes sense to +deliver water. + +But we are going to regulate you +in a way to maximize the + +social surplus, given that +natural monopoly. + +So to see that, let's +go to the highly + +complicated figure 15-3. + +OK, we'll have to walk +through this slowly. + +It's a lot of stuff going +on here at once. + +OK? + +15-3. + +We're back to the usual curves +we were using last time. + +The demand curve is P +equals 24 minus Q. + +The cost curve is 12 +plus Q squared. + +So the marginal cost +is just 2Q. + +The competitive outcome was +to produce eight units + +at a price of 16. + +The monopoly outcome was +to produce six units + +at a price of 18. + +OK? + +And you ended up with the +monopolist causing a + +deadweight loss of C plus E. +That was where we were last + +time in this example. + +And let's say this was +a natural monopoly. + +So that's why there's +a monopolist there. + +Now, what if the government came +in and mandated that the + +monopolist can charge no more +than the competitive price? + +Let's say the government +knew what the + +competitive price was. + +The government says, +look, I took 14.01. + +I see this graph. + +I know the competitive +price is 16. + +So I'm going to say, +monopolist-- + +You're the monopolist. +You go ahead. + +And no one else can +deliver water. + +It makes sense for +you to do it. + +But I'm going to regulate that +you cannot charge consumers a + +price above 16. + +What you can see in that case, +is the government will turn + +the monopolist from a price +maker to a price taker. + +And in doing so, the government +will undo the + +poisoning effect we talked about +last time and cause the + +monopolist to behave as if it +was a competitive firm. + +So to see that, we have to ask, +well what's the marginal + +revenue curve now for the +monopolist, given this + +government mandate that it can +charge no more than 16? + +Well, the marginal revenue +curve, up to the point it + +sells six, is the old marginal +revenue curve. + +So we're working down this +marginal revenue curve. + +And up to that point, where +marginal revenue intersects + +marginal cost, that's the +marginal revenue curve. + +And that's where the monopolist +would stop. + +But the problem is the +monopolist isn't actually able + +to charge more than 16. + +So now, if it's charging 16, +now it asks itself well, + +should I produce that +seventh unit. + +Remember last time +we did the math. + +The monopolist should not +produce the seventh unit. + +Because last time we showed +that, because of that + +poisoning effect, profits would +fall if it produced that + +seventh unit. + +But now it's not true because +now it's only charging 16. + +So if it's charging 16, and if +it produces that seventh unit, + +it's still going to charge 16. + +The poisoning effect +has gone away. + +There's no more poisoning +effect. + +There's no loss to producing the +seventh unit because the + +most it can get is 16. + +It would like to price +it much higher. + +It can't. + +Since the most it can price at +is 16 he says, well gee, then + +there's no poisoning effect. + +I might as well produce at +the competitive level. + +And basically, what you can +see is if you tell the + +monopolist they can't charge +more than the competitive + +price, then they will produce +at the competitive level. + +And you'll end up at that +competitive outcome, even with + +a monopolist, because that will +be the profit maximizing + +thing for the monopolist +to do. + +So sounds like we've got a +pretty good solution here. + +Right? + +If there's a natural monopoly, +we just come in and say you + +can't charge more than the +competitive price. + +So in theory, government +can fix this. + +We've been talking about +government as a bad guy. + +Here's government +as a good guy. + +Government can come +in and fix this. + +What's the problem with that? + +What's the problem, in practice, +with carrying out + +what I just laid out +here in theory? + +Yeah. + +AUDIENCE: How does the +government know what the + +competitive price is? + +PROFESSOR: How does the +government know what the + +competitive price is? + +How does the government know +what these curves look like? + +Now, let's think about +both curves. + +OK, first the government +needs to know-- + +If it wants to know the +competitive price, it's got to + +know the demand curve and +the supply curve. + +Well the demand curve, in +principle, the government + +could learn. + +The government could go out and +survey people and get a + +sense of kind of, could collect +some data, could run + +some experiments and try to +find out from people. + +Gee, how much are you willing +to pay for another unit, + +another unit, another unit? + +So in principle, the government +could actually + +measure demand curve by +doing market research. + +Although in practice, +this is quite hard. + +It turns out in practice-- + +The first rule of economics is +believe what people do, not + +what they say. + +Turns out, if you ask people +what they're willing to pay, + +you get very silly answers, +relative to actually do it. + +So for example, this comes up +a lot in when the government + +needs to value environmental +damage. + +So if we need to ask how much +should we charge BP for the + +damage they did to the Gulf, we +need to value how sad are + +people that the wetlands +are ruined. + +Well, the only thing to +do is to ask people. + +And it turns out when +you do that, you get + +incredibly silly answers. + +Things like, for example, if you +ask people how sorry are + +you if 10 ducks died, they'll +say I'm this sad. + +Say how sad are you if +a million ducks died? + +They'll say, I'm the +same amount sad. + +OK, that doesn't make sense. + +You ask people what's it +worth to save a duck + +versus saving a whale. + +And you ask in that order, +they'll say saving a duck is + +worth $100, saving a whale +is worth $100. + +Or it's worth $150. + +You ask the other order. + +You say, how much is +it worth to save a + +whale and then a duck. + +Well then, saving a whale +is worth $300. + +And a duck's only worth +$50, same question + +just a different order. + +People do not give sensible +answers when you ask them what + +things are worth. + +The best way to know is to +actually vary the price, is to + +actually run experiments where +you actually say, OK, we have + +to actually give people +different prices and see how + +they behave, actually trace +out the demand curve. + +That turns out to be very hard +to do, especially for things + +like valuing damage +to wetlands. + +But even for things like valuing +prescription drugs, + +you've got to literally-- + +It's hard to run the experiment +where, literally, I + +give you a different price +than you for a + +prescription drug. + +That's a little bit tricky. + +So it's hard to get +the demand curve. + +So that's the first problem +the government faces. + +But in some sense, that's the +less difficult problem. + +It is tracing out the +demand curve. + +In principle, there +are ways to do it. + +In principle, you could run +experiments where you vary the + +price and you get that +demand curve. + +In practice, the difficulty +is firm supply + +curves are much harder. + +And why is that? + +Because let's say the government +comes to you and + +says, look I'm doing great. + +I've nailed down the +demand curve. + +I just need to know your supply +curve, so I can set + +your price. + +What's your supply +curve again? + +OK, what are you going to say? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Aw, this stuff +costs a fortune to make. + +You would not believe what it +costs this stuff to make. + +My supply curve-- + +12 plus Q squared? + +Ha! + +That's a joke. + +It's 30 plus 18Q squared. + +Are you kidding? + +My supply curve is crazy high. + +And the problem is, the +government doesn't know. + +Because with consumers, at least +I can run experiments to + +get the demand. + +With the firm, I can't get +inside their books. + +I can't really know. + +And if I get inside the books, +they can cook their books and + +make it look like stuff +costs more. + +How can I really know? + +Just like it's difficult for +the board of directors to + +figure out whether the CEO of a +company needs his own plane, + +it's very difficult for +government regulators to + +figure out what it actually +costs to produce these drugs. + +And as a result, it's very +hard to get this right. + +And the problem is if the +government gets it wrong, it + +can make it worse than not +regulating at all. + +So for example, if the +government came in, and let's + +say, the government said look, +I can't believe this firm. + +12 plus Q squared sounds way +too high for cost. I think + +marginal costs are much +lower than that. + +And I think the competitive +price should be 10 because I + +know the firm is going +to lie to me. + +I know they're going to tell +me numbers too big. + +So I'm going to say that +equilibrium should be + +competitive, should +be a price of 10. + +And at a price of 10, the firm +is now operating off the + +marginal revenue curve +at that low price + +because it's below 16. + +So at a price of 10, the firm +is going to set marginal + +revenue equal to marginal cost. +Well, marginal revenue + +at a price of 10 is the price. + +That's all they can +charge is 10. + +So they're going to set price +equal to marginal cost. The + +marginal cost with a +production of 10-- + +The marginal cost is 2Q. + +So set price equal to 2Q. + +Or 10 equals 2Q. + +Or Q equals five. + +They'll produce five units. + +They'll say look, if you're only +going to let me charge + +10, I'm only going to +produce five units. + +That's what I'll produce. + +That's what's optimal for +me at a price of 10. + +What you see is-- + +Now if you look at this graph +and you look at the firm + +producing five units. + +What you see is the firm +produces five units. + +Now, the total surplus +has fallen. + +It's just A plus B plus D. The +consumer surplus is very high. + +We don't have the horizontal +line of 10 here. + +But draw yourself that +horizontal line of 10, which + +is where the dashed line of five +intersects the marginal + +cost curve. + +You could see there's a +big consumer surplus. + +It's A plus B plus half of D and +a little producer surplus, + +which is that triangle that's +the lower half of D. But look + +what's happened to +social surplus. + +Before the government got +involved, the deadweight loss + +was just C plus E. Now the +government, by misregulating + +the price, has created +deadweight losses of C plus E + +plus F plus G plus H. The +government has just increased + +the deadweight loss a lot, +by getting involved and + +misregulating. + +And in particular, that area +that increases it-- + +Here's the interesting thing. + +Falling from eight to six caused +that little triangle. + +Falling from six to five, just +one more unit, causes a + +trapezoid, which is probably +bigger than that triangle. + +Why? + +Because we're moving +farther and farther + +away from the optimum. + +We're losing more and more +trades that were socially + +beneficial. + +Remember at the optimum, +deadweight loss is very small. + +But as you move farther and +farther away, that deadweight + +loss gets bigger and bigger. + +So this government +misregulation, instead of + +moving us to what's optimal, +by just moving us one below + +where we were as a monopolist +has caused all this huge extra + +deadweight loss and +made things worse. + +Indeed, it could be worse. + +Imagine the government chose a +price so low the firm just + +said, forget it. + +I'm going to shut down. + +You could lose all surplus +in this market. + +If the government came +in and said, no, we + +don't believe you. + +The price should be whatever. + +It wouldn't be, in this case, +because in this case, price is + +always greater than +marginal cost. + +But let's say the government +came in another case and set a + +price that was too low. + +It could just cause the +firm to shut down. + +Then all social surplus in the +market would disappear. + +OK? + +So basically, there's these +difficulties with the + +regulation, which is it's hard +to know how to set the price. + +Now in practice, of course, what +happens is governments + +set the price too high. + +In practice, the government +would much rather err on the + +side of letting monopolists make +a little money than err + +on the side of there being +too little of the good. + +So government, facing +uncertainty about what the + +right level to set is, will +typically end up erring on the + +side of monopolists, partly +because of the way of the + +nature of regulation. + +So let's say you are +president whatever. + +And you want to regulate +this new good. + +OK, somebody made the new good +and you want to regulate it. + +Well who are you going to hire +to be the regulator? + +Well clearly, someone who knows + +something about the market. + +So there's a new good. + +My favorite example +of an outdated + +technology is the umbrella. + +I really think we've +got to figure out a + +better way to do umbrellas. + +They suck. + +In the wind, they blow up. + +They're useless, right. + +There's got to be a better +umbrella out there. + +Let's say somebody finally +figures out a better umbrella. + +But they've got a +patent on it. + +And so you want to +regulate it. + +It's got some natural monopoly +producing it. + +It uses unobtanium. + +And the only can find it +in one place, Pandora. + +So they've got to-- + +They're the only guys-- + +Isn't that the stupidest name +ever for a material? + +How could they have not come +up with a better name than + +unobtanium? + +Anyway, so it uses unobtanium. + +And basically they have +this natural monopoly. + +So you want to regulate it + +Well, who are you going to +find to regulate it? + +Well you know, once there was an +expert in making umbrellas + +with unobtanium. + +That person who you're +going to hire. + +That's the right +person to hire. + +Unfortunately, that probably +means they're probably + +friendly with all the guys +that make umbrellas with + +unobtanium. + +And they're not going +to want to be too + +tough on their buddies. + +So the natural person who's +going to regulate, by their + +nature, is going to tend to be +someone who's going to think + +sort of on the industry's +side. + +Moreover, what are they going to +do after they're done being + +the regulator? + +They're going to go back into +the business of making + +umbrellas with unobtanium. + +So they're not going to want to +be too mean to the business + +because they're going to +be making money off + +it five years hence. + +So you've got this problem that +regulators are going to + +have a natural tendency to be +sort of friendly towards + +industry they're regulating. + +And that's going to lead +to an upward bias. + +The question is, how much is +that upward bias in the price + +relative to what the monopolist +would actually do. + +And much like a patent, +it depends. + +You can draw examples where +the government regulation + +would improve things and +examples where the government + +regulation would make +things worse. + +You can do examples +either way. + +And what, at least, is +interesting here is this is + +the first example we've seen +or one of the few examples + +we've seen where the government, +at least, could + +possibly make things better. + +Even though it's not +clear they will. + +At least, they could possibly +make things better. + +And that's because-- + +Why is that? + +This is a very important +insight. + +Why is that? + +That's because everything we've +dealt with so far, the + +market does everything well. + +We haven't needed +a government. + +What natural monopolies do is +they say, wow, here's a case + +of what we call a +market failure. + +The market has failed to +maximize social surplus. + +And that opens the door for +potential gains for government + +intervention. + +Basically, as long as markets +are functioning well in a + +competitive manner, there's no +door open for the government + +to make things better. + +The government can just +make things worse. + +It's only when there's market +failures, of which natural + +monopoly is one example, can +the government come in and + +potentially make +things better. + +It won't necessarily do so. + +But at least there's a door +open to doing so. + +Questions about that-- + +OK, the last thing I want to +talk about, today, is an + +example that's in between a +natural monopoly and no + +natural monopoly, which +is what we call + +a contestable market. + +A contestable market-- + +A contestable market is one +which says that there is a + +natural monopoly, but it's not +so big that someone couldn't + +come in and compete if the +profits got too large. + +Or another way of saying this +is, just because there's a + +monopoly doesn't mean there's +a whole lot of market power. + +Just because there's a monopoly +doesn't mean there's + +a whole lot of market power. + +So imagine a natural monopoly +market with a very modest + +fixed cost, a fixed cost +that's, you know, + +real but not enormous. + +As long that monopolist who +gets in first keeps their + +price near marginal cost, +no will ever enter. + +As long as they get their price +near marginal cost, no + +one will enter, even if they're +making a small profit. + +No one will enter because no one +could ever make money then + +and pay the fixed. + +No one could ever come in, +pay the fixed cost, + +and still make money. + +So no one's ever +going to enter. + +But if that price ever got too +far above marginal cost, then + +someone would say, ah, there's +so much profit to be made. + +That'll cover my fixed costs. + +I'm coming in. + +That's what we mean by +contestable market, a market + +which can exist with a monopoly +and can exist with + +someone making money. + +And yet ultimately, there's +sufficiently easy entry that, + +basically, the monopolist is +forced to behave almost like a + +competitive firm. + +So it's sort of like market +pressure on monopolists. + +It's a weird outcome where you +get a monopoly market but + +pricing close to competitive +levels because of + +this threat of entry. + +Now the most famous example +of this is in airlines and + +airline deregulation. + +Until the 1970s, the way +airlines worked in the US is + +there were private airline +companies. + +Many of them don't exist +anymore, Eastern, Pan Am. + +Ones you don't know about, +don't exist anymore. + +And they were regulated. + +It was a regulated oligopoly. + +We haven't really talked +about oligopolies yet. + +It was a few firms competing. + +But think of it as a monopoly. + +It's basically regulated +monopoly. + +In particular, they +had monopolies + +on different routes. + +So what happened is the +government would + +say New York to Boston. + +That is the route that Eastern +Airlines owns. + +And they fly that without +competition. + +But in order to make sure they +don't rip off the consumer, + +we're going to regulate +their prices. + +So Eastern Airlines, you fly +this without competition. + +But we're going to +regulate what you + +can charge the consumer. + +And this was because the +government viewed airlines as + +a natural monopoly. + +It said, look, airplanes are +really big and expensive. + +There's huge fixed cost to +becoming an airline. + +So we think this is a +natural monopoly. + +And we're going to +regulate it. + +However, economists started +pointing out, and experts + +started pointing out that no, +in fact, this was actually a + +very contestable market. + +That it turned out +it wasn't that + +expensive to produce airplanes. + +There were a lot of older +airplanes you could + +refurbish, et cetera. + +And that basically this is +a market where, if the + +government opened it up to +competition, you could + +actually get some-- + +That threat of entry +eventually could + +drive prices down. + +And so basically, after a lot of +debate, the government, in + +the late 1970s, did deregulate +airlines. + +One of the most important +changes in government policy + +in the 1970s was they +deregulated airlines. + +And what happened? + +Well, three things happened. + +First of all, prices +fell enormously. + +Prices fell by about a third. + +Flying from point A to point B +fell by a third, other places + +more extreme. + +When I was an undergraduate at +MIT, I could fly from Boston + +to Newark for $19 each way. + +There was this airline called +People's Express that was + +introduced in the wave of +deregulation in the 1980s. + +People's Express-- + +It was fascinating. + +I don't know what their planes +were held together by. + +And the thing was, you didn't +even buy a ticket. + +You just went and +waited on line. + +They let you on the plane. + +And when the plane was +full, they took off. + +And they made you pay +on the plane. + +I still, to this day, don't +know what happened if you + +didn't have the money, if they +like threw you off, get + +parachutes or something. + +I don't know what they did. + +But literally, they'd come down +the middle of the aisle + +with a little credit +card thing. + +And they'd make you +pay on the plane. + +I mean literally, it was cheaper +than taking a bus. + +It was incredible, +$19 each way. + +So prices came way, way down. + +The second effect was +many more routes + +were offered to consumers. + +Suddenly, routes which the +government had said, no that's + +not profitable. + +You shouldn't fly that. + +New entrants said, no, in +fact, it is profitable, + +government. + +You just had the cost +structure wrong. + +And it is profitable to fly from +Pittsburgh to Akron, or + +whatever, wherever +they now fly. + +There are hundreds more places +you can fly now than you could + +in the 1970s. + +Hundreds and hundreds of routes +that just didn't exist + +because the government +regulators assumed they + +weren't profitable. + +But in fact, they were. + +Once there was competition in +these contestable markets, + +they did turn out to +be profitable. + +And the final thing that +happened was that quality of + +airline travel deteriorated +massively. + +When I was a kid, and +you flew on planes. + +It was really nice. + +I mean there was tons +of leg room. + +You got tons of free food, +free movies, free drinks. + +And I didn't do that +when I was a kid. + +My parents did. + +Basically, it was an +unbelievably nice experience. + +It's not so nice now. + +I think as any of you who have +flown will attest to. + +Now they're charging +you for everything. + +And you can barely fit your legs +in if you're over 5'2". + +Now, why did this happen? + +Somebody tell me. + +Why did this happen? + +Why did deregulation lead from +a world where flights were + +unbelievably comfy to a world +where flights are uncomfy? + +Yeah. + +AUDIENCE: It's more profitable +to have more people taking it. + +And-- + +PROFESSOR: Sure, but that +was always true. + +It was always more profitable +to have + +more people on a plane. + +It was always more profitable +to not give them nice stuff. + +That hasn't changed. + +What has changed? + +Yeah. + +AUDIENCE: You have-- there's +competition. + +So they need to reduce +their cost more. + +PROFESSOR: What's that? + +AUDIENCE: There's more +competition. + +So they need to reduce +their cost. + +PROFESSOR: There is +more competition. + +But there was some competition +before. + +But you're right. + +Your about halfway there. + +What else? + +AUDIENCE: Consumers aren't +willing to pay for leg room + +and all that stuff. + +PROFESSOR: Basically before, if +there was a route with two + +airlines on it-- + +A lot of them, I said there's +two airlines. + +And you wanted to compete. + +How did you compete? + +You couldn't compete on price. + +Right? + +If Eastern and Pan Am were +flying New York to Boston, + +they couldn't compete +on price. + +The price was regulated. + +So how did they compete, by +being as nice as possible on + +everything else, even though +consumers didn't + +really value it. + +Well, once they competed on +price, they said, look, + +consumers don't really care +so much about this + +crappy airline food. + +We're going to get rid of +it and charge 20% less. + +And lo and behold, they did. + +What's ironic, of course, is +everyone bitches about how bad + +airlines are. + +But they don't bitch about +how cheap they are. + +It is so cheap to fly now, +compared to when I was a kid. + +Based on what happened is they +went from competing on + +non-price factors to +competing on price. + +There's always competitive +pressure. + +There's always competitive +pressure. + +It's just before, the +competition had to be on + +things which consumers +didn't like. + +But they liked it enough +that you might as + +well compete on it. + +Because it was not that +consumers didn't like it all. + +Obviously they liked +it some, or they + +wouldn't have bothered. + +Now they've moved to a more +efficient form of competition, + +which is to compete on price +rather than on quantity. + +Yeah. + +AUDIENCE: When you said the +government regulated the + +price, only wasn't that just +on the upper level + +that you got that? + +PROFESSOR: No. + +The government just regulated +the price. + +Now, so this is a big victory +for economists. + +Yay for economists-- + +We did a great job. + +But we whiffed on one thing. + +We whiffed on one thing, which +we did not foresee, which has + +led deregulation to be much +less beneficial than we + +thought it was going to be. + +What we whiffed on was the +hub and spoke system. + +We whiffed on the fact that, +while building airplanes is + +contestable, building slots +at airports is not. + +That there's a limited number +of slots at airports. + +And it's incredibly hard to +build a new airport because of + +environmental regulations +and other things. + +What that meant was there is +still a natural monopoly in + +airport slots, even if +there's not much of a + +natural monopoly in planes. + +The result is that now what +airlines do is funnel everyone + +through their hub and then +out to the spokes. + +And as a result, because of that +they have developed new + +quasi monopolies. + +So to fly from point A to point +B, for many A's and B's, + +only one airline flies it. + +Because it's economical +for them because + +point A is their hub. + +But airline B can't +get into that hub. + +They can't get a gate +at that hub. + +So as a result, they can't +effectively fly from A to B. + +So my wife is from +Minneapolis. + +We had to go to Minneapolis. + +Northwest had a monopoly on +going to Minneapolis. + +So I could fly from Boston to +LA for half the price of + +Boston to Minneapolis. + +Why, because Northwest +controlled all the gate slots + +in Minneapolis. + +They had a natural monopoly +on that resource. + +And that's what economists +missed. + +So deregulation worked in some +markets with a lot of + +competition. + +Like the New York to LA market +is very competitive. + +It did not work in other +markets, where there was this + +natural hub. + +And so one airline +could dominate. + +Or a few airlines +could dominate. + +And that's why you could +see some crazy pricing + +differentials. + +That's why, for example, +I could fly to + +Baltimore for $127. + +But to DC, it cost me $500, even +though they're less than + +an hour apart by car. + +This is because the constraint +on slots has limited the + +amount of competition +that can go on. + +And so that's sort of an example +of where competition + +can work and where it can't to +try to deal with these natural + +monopoly problems. + +All right, let me stop there. + +And we'll come back +on Wednesday + +and talk about oligopoly. + +Good luck tomorrow night +on the exam. + +It's tomorrow night? + +Yeah, tomorrow night. + +Good luck. + +Everyone looked confused +for a second. + +Next week-- + +Oh-- + +OK, just joking, April fools, +Halloween fools. + +Good luck next week +on the exam. \ No newline at end of file diff --git a/k0UZNZwPO8Q.txt b/k0UZNZwPO8Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..235dae81555ee6eb62aa1c043ad9f3c7b709654d --- /dev/null +++ b/k0UZNZwPO8Q.txt @@ -0,0 +1,3700 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK, let's +get started. + +We'll start a minute early and +then maybe we can finish a + +minute early if we're lucky. + +Today we want to talk about +the laws of large numbers. + +We want to talk about +convergence a little bit. + +We will not really get into +the strong law of large + +numbers, which we're going to +do later, because that's a + +kind of a mysterious, +difficult topic. + +And I wanted to put off really +talking about that until we + +got to the point where we could +make some use of it, + +which is not quite yet. + +So first, I want to review +what we've done + +just a little bit. + +We've said that probability +models are very natural things + +for real-world situations, +particularly those that are + +repeatable. + +And by repeatable, I mean they +use trials, which have + +essentially the same +initial conditions. + +They're essentially isolated +from each other. + +When I say they're isolated from +each other, I mean there + +isn't any apparent +contact that they + +have with each other. + +So for example, when you're +flipping coins, there's not + +one very unusual coin, +and that's the coin + +you use all the time. + +And then you try to use +those results to be + +typical of all coins. + +Have a fixed set of possible +outcomes for + +these multiple trials. + +And they have an essentially +random individual outcomes. + +Now, you'll see there's a real +problem here when I use the + +word "random" there and +"probability models" there + +because there is something +inherently + +circular in this argument. + +It's something that always +happens when you get into + +modeling where you're trying to +take the messy real-world + +and turn it into a nice, clean, +mathematical model. + +So that really, what we +all do, and we do this + +instinctively, is after we +start getting used to a + +particular model, we assume that +the real-world is like + +that model. + +If you don't think you +do that, think again. + +Because I think everyone does. + +So you really have that problem +of trying to figure + +out what's wrong with models, +how to go to better models, + +and we do this all the time. + +OK, for any model, an extended +model-- in other words, an + +extended mathematical model, for +a sequence or an n-tuple + +of independent identically +distributed repetitions is + +always well-defined +mathematically. + +We haven't proven that, +it's not trivial. + +But in fact, it's true. + +Relative frequencies and +sample averages. + +Relative frequencies apply to +events, and you can represent + +events in terms of indicator +functions and then use + +everything you know about +random variables + +to deal with them. + +Therefore, you can use +sample averages. + +In this extended model, +essentially become + +deterministic. + +And that's what the laws of +large numbers say in various + +different ways. + +And beyond knowing that they +become deterministic, our + +problem today is to decide +exactly what that means. + +The laws of large numbers +specify what "become + +deterministic" means. + +They only operates within +the extended model. + +In other words, laws of large +numbers don't apply to the + +real world. + +Well, we hope they apply to the +real world, but they only + +apply to the real world when the +model is good because you + +can only prove the laws of +large numbers within this + +model domain. + +Probability theory provides an +awful lot of consistency + +checks and ways to avoid +experimentation. + +In other words, I'm not claiming +here that you have to + +do experimentation with a large +number of so-called + +independent trials very often +because you have so many ways + +of checking on things. + +But every once in a while, you +have to do experimentation. + +And when you do, somehow or +other the idea of this large + +number of trials, and either IID +trials or trials which are + +somehow isolated from +each other. + +And we will soon get to talk +about Markov models. + +We will see that with Markov +models, you don't have the IID + +property, but you have enough +independence over time that + +you can still get these +sorts of results. + +So anyway, the determinism in +this large number of trials + +really underlies much of the +value of probability. + +OK, in other words, you +don't need to use this + +experimentation very often. + +But when you do, you really need +it because that's what + +you use to resolve conflicts, +and to settle on things, and + +to have different people who are +all trying to understand + +what's going on have some +idea of something + +they can agree on. + +OK, so that's enough for +probability models. + +That's enough for philosophy. + +We will come back to this +with little bits and + +pieces now and then. + +But at this point, we're really +going into talking + +about the mathematical +models themselves. + +OK, so let's talk about the +Markov bound, the Chebyshev + +bound, and the Chernoff bound. + +You should be reading the notes, +so I hope you know what + +all these things are +so I can go through + +them relatively quickly. + +If you think that using these +lectures slides that I'm + +passing out plus doing the +problems is sufficient for + +understanding this +course, you're + +really kidding yourself. + +I mean, the course is based on +this text, which explains + +things much more fully. + +It still has errors in it. + +It still has typos in It. + +But a whole lot fewer than these +lecture slides, so you + +should be reading them and then +using them try to get a + +better idea of what these +lectures mean, and using that + +to get the better idea +of what the exercises + +you're doing mean. + +Doing the exercises does not +do you any good whatsoever. + +The only thing that does you +some good is to do an exercise + +and then think about what it +has to do with anything. + +And if you don't do that second +part, then all you're + +doing is you're building +a very, + +very second rate computer. + +Your abilities as a computer +are about the same for the + +most part as the computer +in a coffee maker. + +You are really not up to what +a TV set does anymore. + +I mean, TV sets can do so much +computation that they're way + +beyond your abilities +at this point. + +So the only edge you have, the +only thing you can do to try + +to make yourself worthwhile is +to understand these things + +because computers cannot +do any of that + +understanding at all. + +So you're way ahead +of them there. + +OK, so what is the +Markov model? + +What it says is, if y is a +non-negative random variable-- + +in other words, it's a random +variable, which only takes one + +non-negative sample values. + +If it has an expectation, +expectation of y. + +And for any real y greater than +0, the probability that Y + +is greater than or equal to +little y is the expected value + +of Y divided by little y. + +The proof of it is by picture. + +If you don't like proofs by +pictures, you should get used + +to it because we will prove a +great number of things by + +pictures here. + +And I claim that a proof by +picture is better than a proof + +by algebra because if there's +anything wrong with it, you + +can see from looking +at it what it is. + +So we know that the expected +value of Y is the integral + +under the complimentary +distribution function. + +This square in here, this area +of Y times probability of Y + +greater or equal to Y. The +probability of Y greater than + +or equal, capital Y, the random +variable y greater than + +or equal to the number, +little y, is just that + +point right up there. + +This is the point y. + +This is the point probability +of capital Y + +greater than little y. + +It doesn't make any difference +when you're integrating + +whether you use a greater than +or equal to sign or a + +greater than sign. + +If you have a discontinuity, +the integral is the same no + +matter which way +you look at it. + +So this area here is y times +the probability that random + +variable y is greater than +or equal to number y. + +And all that the Markov bound +says is that this little + +rectangle here is less than or +equal to the integral under + +that curve. + +That's a perfectly +rigorous proof. + +We don't really care about +rigorous proofs here, anyway + +since we're trying to get at +the issue of how you use + +probability, but we don't want +to have proofs which mislead + +you about things. + +In other words, proofs +which aren't right. + +So we try to be right, and I +want you to learn to be right. + +But I don't want you to start +to worry too much about + +looking like a mathematician +when you prove things. + +OK, the Chebyshev inequality. + +If Z has a mean-- + +and when you say Z has a mean, +what you really mean is the + +expected value of the absolute +value of Z is finite. + +And it has a variance sigma +squared of Z. That's saying a + +little more than just +having a mean. + +Then, for any epsilon +greater than 0. + +In other words, this bound +works for any epsilon. + +The probability that the +absolute value of Z + +less than the mean. + +In other words, that it's +further away from the mean by + +more than epsilon, is less than +or equal to the variance + +of Z divided by epsilon +squared. + +Again, this is a very weak +bound, but it's very general. + +And therefore, it's +very useful. + +And the proof is simplicity +itself. + +You define a new random variable +y, which is Z minus + +the expected value of +Z quantity squared. + +The expected value of Y then is +the expected value of this, + +which is just the +variance of Z. + +So for any y greater than 0, +we'll use the Markov bound, + +which says the probability +that random variable Y is + +greater than or equal to number +little y is less than + +or equal to sigma +of Z squared. + +Namely, the expected value of +random variable Y divided by + +number Y. That's just +the Markov bound. + +And then, random variable Y is +greater than or equal to + +number y if and only if the +positive square root of + +capital Y-- we're dealing only +with positive non-negative + +things here-- + +is greater than or equal to the +square root of number y. + +And that's less than or equal +to sigma Z squared over y. + +And square root of Y is +just the magnitude + +of Z minus Z bar. + +We're setting epsilon equal to +square root of y yields the + +Chebyshev bound. + +Now, that's something which +I don't believe + +in memorizing proofs. + +I think that's a +terrible idea. + +But that's something so simple +and so often used that you + +just ought to think +in those terms. + +You ought to be able to see +that diagram of the Markov + +inequality. + +You ought to be able to +see why it is true. + +And you ought to understand +it well enough + +that you can use it. + +In other words, there's a big +difference in mathematics + +between knowing what a theorem +says and knowing that the + +theorem is true, and +really having a gut + +feeling for that theorem. + +I mean, you know this when +you deal with numbers. + +You know it when you deal +with integration or + +differentiation, or any of +those things you've known + +about for a long time. + +There's a big difference between +the things that you + +can really work with because +you understand them and you + +see them and those things that +you just know as something you + +don't really understand. + +This is something that you +really ought to understand and + +be able to see it. + +OK, the Chernoff bound +is the last of these. + +We will use this a great deal. + +It's a generating +function bound. + +And it says, for any number, +positive number z, and any + +positive number r greater than +0, such that the moment + +generating function-- the moment +generating function of + +a random variable z is a +function given the random + +variable z. + +It's a function of +a real number r. + +And that function is the +expected value of e to the rZ. + +It's called the generating +function because if you start + +taking derivatives of this and +evaluate them, that r equals + +0, what you get is the +various moments of z. + +You've probably seen +that at some point. + +If you haven't seen it, it's not +important here because we + +don't use that at all. + +What we really use is the fact +that this is a function. + +It's a function, which is +increasing as r increases + +because you put-- + +well, it just does. + +And what it says is the +probability that this random + +variable is greater than or +equal to the number z-- + +I should really use different +letters for these things. + +It's hard to talk about them-- + +is less than or equal to the +moment generating function + +times e to the minus rZ. + +And the proof is exactly the +same as the proof before. + +You might get the picture that +you can prove many, many + +different things from the +Markov inequality. + +And in fact, you can. + +You just put in whatever you +want to and you get a new + +inequality. + +And you can call it after +yourself if you want. + +I mean, Chernoff. + +Chernoff is still alive. + +Chernoff is a faculty +member at Harvard. + +And this is kind of curious +because he sort of slipped + +this in in a paper that he wrote +where he was trying to + +prove something difficult. + +And this is a relationship that +many mathematicians have + +used over many, many years. + +And it's so simple that they +didn't make any fuss about it. + +And he didn't make any +fuss about it. + +And he was sort of embarrassed +that many engineers, starting + +with Claude Shannon, found this +to be extraordinarily + +useful, and started calling +it the Chernoff bound. + +He was slightly embarrassed of +having this totally trivial + +thing suddenly be +named after him. + +But anyway, that's the +way it happened. + +And now it's a widely used tool +that we use all the time. + +So it's the same proof that we +had before for any y greater + +0, Markov says this. + +And therefore, you get that. + +This decreases exponentially +with Z, and + +that's why it's useful. + +I mean, the Markov inequality +only decays as + +1 over little y. + +The Chebyshev inequality decays +as 1 over y squared. + +This decays exponentially +with y. + +And therefore, when you start +dealing with large deviations, + +trying to talk about things that +are very, very unlikely + +when you get very, very far from +the mean, this is a very + +useful way to do it. + +And it's sort of the standard +way of doing it at this point. + +We won't use it right now, but +this is the right time to talk + +about it a little bit. + +OK, next topic we want to take +up is really these laws of + +large numbers, and something +about convergence. + +We want to understand a +little bit about that. + +And this picture that we've seen +before, we take X1, up to + +Xn as n independent identically + +distributed random variables. + +They each have mean expected +value of X. They each have + +variance sigma squared. + +You let Sn be the sum +of all of them. + +What we want to understand is, +how does S sub n behave? + +And more particularly, +how does Sn over n-- + +namely, the relative-- + +not the relative frequency, but +the sample average of x + +behave when you take +n samples? + +So this curve shows the +distribution function of S4, + +of S20, and of S50 when you have +a binary random variable + +with probability of 1 equal to +a quarter, probability of 0 + +equal to 3/4. + +And what you see graphically +is what you can see + +mathematically very +easily, too. + +The mean value of S sub +n is n times X bar. + +So the center point in these +curves is moving out within. + +You see the center point here. + +Center point somewhere +around there. + +Actually, the center point is +at-- yeah, just about what it + +looks like. + +And the center point here is +out somewhere around there. + +And you see the variance, you +see the variance going up + +linearly with n. + +Not with n squared, but with +n, which means the standard + +deviation is going up with +the square root of n. + +That's sort of why the law +of large numbers works. + +It's because the standard +deviation of these random-- + +of these sums only goes up with +the square root of n. + +So these curves, along with +moving out, become relatively + +more compressed relative to +how far out they are. + +This curve here is relatively +more compressed for its mean + +than this one is here. + +And that's more compressed +relative to this one. + +We get this a lot more +easily if we look + +at the sample average. + +Namely, S sub n over n. + +This is a random variable +of mean X bar. + +That's a random variable of +variance sigma squared over n. + +That's something that you ought +to just recognize and + +have very close to the top of +your consciousness because + +that again, is sort +of why the sample + +average starts to converge. + +So what happens then is for n +equals 4, you get this very + +"blech" curve. + +For n equals 20, it starts +looking a little more + +reasonable. + +For n equals 50, it's starting +to scrunch in and start to + +look like a unit step. + +And what we'll find is that the +intuitive way of looking + +at the law of large numbers, or +one of the more intuitive + +ways of looking at it, +is that the sample + +average starts to look-- + +starts to have a distribution +function, which + +looks like a unit step. + +And that step occurs +at the mean. + +So this curve here keeps +scrunching in. + +This part down here is +moving over that way. + +This part over here is +moving over that way. + +And it all gets close +to a unit step. + +OK, the variance of Sn over n, +as we've said, is equal to + +sigma squared over n. + +The limit of the variance as n +goes to infinity takes the + +limit of that. + +Don't even have to know the +definition of a limit, can see + +that when n gets large, +this get small. + +And this goes to 0. + +So the limit of this +goes to 0. + +Now, here's the important +thing. + +This equation says a whole lot +more than this equation says. + +Because this equation says how +quickly that approaches 0. + +All this says is it +approaches 0. + +So we've thrown away a lot that +we know, and now all we + +know is this. + +This 3 says that the convergence +is as 1/n. + +This doesn't say that. + +This just says that +it converges. + +Why would anyone in their right +mind want to replace an + +informative statement like this +with a not informative + +statement like this? + +Any ideas of why you might +want to do that? + +Any suggestions? + +AUDIENCE: Convenience. + +PROFESSOR: What? + +AUDIENCE: Convenience. + +Convenience. + +Sometimes you don't need to-- + +PROFESSOR: Well, yes, +convenience. + +But there's a much +stronger reason. + +This is a statement for +IID random variables. + +This law of large numbers, we +want it to apply to as many + +different situations +as possible. + +To things that aren't +quite IID. + +To things that don't +have a variance. + +And this statement here +is going to apply more + +generally than this. + +You can have situations where +the variance goes to 0 more + +slowly than 1/n if these random +variables are not + +independent. + +But you still have +this statement. + +And this statement is what we +really need, so this really + +says something, which is called + +convergence and mean square. + +Why mean square? + +Because this is the +mean squared. + +So obvious terminology. + +Mathematicians aren't always +very good at choosing + +terminology that makes sense +when you look at it, + +but this one does. + +Definition is a sequence of +random variables Y1, Y2, Y3, + +and so forth. + +Converges in mean square to a +random variable Y if this + +limit here is equal to 0. + +So in this case, Y, this random +variable Y, is really a + +deterministic random variable, +which is just the + +deterministic value, expected +value of X. This random + +variable here is this relative +frequency here. + +And this is saying that the +expected value of the relative + +frequency relative to the +expected value of X-- + +this is going to 0. + +This isn't saying +anything extra. + +This is just saying, if you're +not interested in the law of + +large numbers, you might be +interested in how a bunch of + +random variables approach some +other random variable. + +Now, if you look at a set of +real numbers and you say, does + +that set of real numbers +approach something? + +I mean, you have sort of a +complicated looking definition + +for that, which really +says that the numbers + +approach this constant. + +But a set of numbers is so much +more simple-minded than a + +set of random variables. + +I mean, a set of random +variables is-- + +I mean, not even their +distribution functions really + +explain what they are. + +There's also the relationship +between the + +distribution functions. + +So you're not going to find +anything very easy that says + +random variables converge. + +And you can expect to find the +number of different kinds of + +statements about convergence. + +And this is just going +to be one of them. + +This is something called +convergence and mean square-- + +yes? + +AUDIENCE: Going from 3 to 4, +we don't need IID anymore? + +So they can be just-- + +PROFESSOR: You can certainly +find examples where it's not + +IID, and this doesn't hold +and this does hold. + +The most interesting case where +this doesn't hold and + +this does hold is where you-- + +no, you still need a variance +for this to hold. + +Yeah, so I guess I can't really +construct any nice + +examples of n where this holds +and this doesn't hold. + +But there are some if you talk +about random variables that + +are not IID. + +I ought to have a problem +that does that. + +But so far, I don't. + +Now, the fact that this sample +average converges in mean + +square doesn't tell us directly +what might be more + +interesting. + +I mean, you look at that +statement and it doesn't + +really tell you what this +complementary distribution + +function looks like. + +I mean, to me the thing that +is closest to what I would + +think of as convergence is that +this sequence of random + +variables minus the random +variable, the convergence of + +that difference, approaches a +distribution function, which + +is the unit step. + +Which means that the probability +that you're + +anywhere off of that center +point is going to 0. + +I mean, that's a very easy +to interpret statement. + +The fact that the variance is +going to 0, I don't quite know + +how do interpret it, except +through Chebyshev's law, which + +gets me to the other +statement. + +So what I'm saying here is if +we apply Chebyshev to that + +statement before number 3-- + +this one-- + +which says what the +variance is. + +If we apply Chebyshev, then what +we get is the probability + +that the relative frequency +minus the mean, the absolute + +value of that is greater than +or equal to epsilon. + +That probability is less than or +equal to sigma squared over + +n times epsilon squared. + +You'll notice this is +a very peculiar + +statement in terms of epsilon. + +Because if you want to make +epsilon very small, so you get + +something strong here, +this term blows up. + +So the way you have to look at +this is pick some epsilon + +you're happy with. + +I mean, you might want these two +things to be within 1% of + +each other. + +Then, epsilon squared +here is 10,000. + +But by making n big enough, +that gets submerged. + +So excuse me. + +Epsilon squared is 1/10,000 +so 1 over + +epsilon squared is 10,000. + +So you need to make +n very large. + +Yes? + +AUDIENCE: So that's why at times +when n is too small and + +epsilon is too small as well, +you can get obvious things, + +like it's less than or equal +to a number greater than 1? + +PROFESSOR: Yes. + +And this inequality is not much +good because there's a + +very obvious inequality +that works. + +Yes. + +But the other thing is this +is a very weak inequality. + +So all this is doing is +giving you a bound. + +All it's doing is saying that +when n gets big enough, this + +number gets as small as +you want it to be. + +So you can get an arbitrary +accuracy of epsilon between + +sample average and mean. + +You can get that with +a probability + +1 minus this quantity. + +You can make that as close +to 1 as you wish if + +you increase n. + +So that gives us the law of +large numbers, and I haven't + +stated it formally, all the +formal jazz as in the notes. + +But it says, if you have IID +random variables with a finite + +variance, the limit of the +probability that Sn over n + +minus x bar, the absolute value +of that is greater than + +or equal to epsilon is equal to +0 in the limit, no matter + +how you choose epsilon. + +Namely, this is one of those +peculiar things in + +mathematics. + +It depends on who gets +the first choice. + +If I get to choose epsilon +and you get to + +choose n, then you win. + +You can make this go to 0. + +If you choose n and then I +choose epsilon, you lose. + +So it's only when you choose +first that you win. + +But still, this statement +works. + +For every epsilon greater +than 0, this limit + +here is equal to 0. + +Now, let's go immediately a +couple of pages beyond and + +look at this figure a little +bit because I think this + +figure tells what's going +on, I think better + +than anything else. + +You have the mean of x, which is +right in the center of this + +distribution function. + +As n gets larger and larger, +this distribution function + +here is going to be scrunching +in, which we sort of know + +because the variance +is going to 0. + +And we also sort of know it +because of what this weak law + +of large numbers tells us. + +And we have these. + +If we pick some given epsilon, +then we have-- + +if we look at a range of two +epsilon, epsilon on one side + +of the mean, epsilon on the +other side of the mean, then + +we can ask the question, how +well does this distribution + +function conform +to a unit step? + +Well, one easy way of looking at +that is saying, if we draw + +a rectangle here of width 2 +epsilon around X bar, when + +does this distribution function +get inside that + +rectangle and when does it +leave the rectangle? + +And what the weak law of large +numbers says is that if you + +pick epsilon and hold it fixed, +then delta 1 is going + +to 0 and delta 2 +is going to 0. + +And eventually-- + +I think this is dying out. + +Well, no problem. + +What this says is that as n gets +larger and larger, this + +quantity shrinks down to 0. + +That quantity up there +shrinks down to 0. + +And suddenly, you have something +which is, for all + +practical purposes, +a unit step. + +Namely, if you think about it a +little bit, how can you take + +an increasing curve, which +increases from 0 to 1, and say + +that's close to a unit step? + +Isn't this a nice +way of doing it? + +I mean, the function is +increasing so it can't do + +anything after it crosses +this point here. + +All it can do is increase, and +eventually it leaves again. + +Now, another thing. + +When you think about the weak +law of large numbers and you + +don't state it formally, one of +the important things is you + +can't make epsilon 0 here and +you can't make delta 0. + +You need both an epsilon and +a delta in this argument. + +And you can see that just by +looking at a reasonable + +distribution function. + +If you make epsilon equal to 0, +then you're asking, what's + +the probability that this sample +average is exactly + +equal to the mean? + +And in most cases, that's +equal to 0. + +Namely, you can't win +on that argument. + +And if you try to make +delta equal to 0. + +In other words, you ask-- + +then suddenly you're stuck over +here, and you're stuck + +way over there, and you can't +make epsilon small. + +So trying to say that a curve +looks like a step function, + +you really need two fudge +factors to do that. + +So the weak law of +large numbers. + +In terms of dealing with how +close you are to a step + +function, the weak law of large +numbers says about the + +only thing you can +reasonably say. + +OK, now let's go back +to the slide before. + +The weak law of large numbers +says that the limit as n goes + +to infinity of the probability +that the sample average is + +greater than or equal +to epsilon equals 0. + +And it says that for every +epsilon greater than 0. + +An equivalent statement is +this statement here. + +The probability that Sn over n +minus x bar is greater than or + +equal to epsilon is a +complicated looking animal, + +but it's just a number. + +It's just a number +between 0 and 1. + +It's a probability. + +So for every n, you get +a number up there. + +And what this is saying is that +that sequence of numbers + +is approaching 0. + +Another way to say that a +sequence of numbers approaches + +0 is this way down here. + +It says that for every epsilon +greater than 0 and every delta + +greater than 0, the probability +that this quantity + +is less than or equal +to delta is-- + +this probability is less than +or equal to delta for all + +large enough n. + +In other words, these funny +little things on the edge here + +for this next slide, the delta +1 and delta 2 are going to 0. + +So it's important to understand +this both ways. + +And now again, this quantity +here looks very much like-- + +these two equations look +very much alike. + +Except this one tells you +something more about + +convergence than +this one does. + +This says how this goes to 0. + +This only says that +it goes to 0. + +So again, we have +the same thing. + +The weak law of large numbers +says this weaker thing, and it + +says this weaker thing +because sometimes you + +need the weaker thing. + +And in this case, there +is a good example. + +The weak law of large numbers +is true, even if you don't + +have a variance. + +It's true under the +single condition + +that you have a mean. + +There's a nice proof in +the text about that. + +It's a proof that does +something, which we're going + +to do many, many times. + +You look at a random variable. + +You can't say what you want +to say about it, so + +you truncate it. + +You say, let me-- + +I mean, if you think a problem +is too hard, you look at a + +simpler problem. + +If you're drunk and you drop +a coin, you look for it + +underneath a light. + +You don't look for it where +it's dark, even though you + +dropped it where it's dark. + +So all of us do that. + +If we can't solve a problem, +we try to pose a simpler, + +similar problem that +we can solve. + +So you truncate this +random variable. + +When you truncate a random +variable, I mean you just take + +its distribution function +and you chop it off + +to a certain point. + +And what happens then? + +Well. at that point you +have a variance. + +You have a moment generating +function. + +You have all the things +you want. + +Nothing peculiar can happen +because the thing is bounded. + +So then the trick in proving the +weak law of large numbers + +under these more general +circumstances is to first + +truncate the random variable. + +You then have the weak +law of large numbers. + +And then the thing that you do +is in a very ticklish way, you + +start increasing n, +and you increase + +the truncation parameter. + +And if you do this in just the +right way, you wind up proving + +the theorem you want to prove. + +Now, I'm not saying you ought +to read that proof now. + +If you're sailing along with no +problems at all, you ought + +to read that proof now. + +If you don't quite have the +kind of mathematical + +background that I seem to be +often assuming in this course, + +you ought to skip that. + +You will have many opportunities +to understand + +the technique later. + +It's the technique which is +important, it's not the-- + +I mean, it's not so much +the actual proof. + +Now, the thing we didn't talk +about, about this picture + +here, is we say that a sequence +of random variables-- + +Y1, Y2, et cetera-- + +converges in probability to a +random variable y if for every + +epsilon greater than 0 and every +delta greater than 0, + +the probability that the n-th +random variable minus this + +funny random variable is greater +than or equal to + +epsilon, is less than +or equal to delta. + +That's saying the same thing +as this picture says. + +In this picture here, you can +draw each one of the Y sub n's + +minus Y. You think of +Y sub n minus Y as a + +single random variable. + +And then you get this kind of +curve here and the same + +interpretation works. + +So again, what you're saying +with convergence and + +probability is that the +distribution function of Yn + +minus Y is approaching a unit +step as n gets big. + +So that's really the meaning +of convergence and + +probability. + +I mean, you get this unit step +as n gets bigger and bigger. + +OK, so let's review all +of what we've done in + +the last half hour. + +If a random variable, generic +random variable x, has a + +standard deviation-- + +in other words, if it has +a finite variance. + +And if X1, X2 are IID with that +standard deviation, then + +the standard deviation of the +relative frequency is equal to + +the standard deviation +of x divided by the + +square root of n. + +So the standard deviation +is the relative + +of the sample average. + +Excuse me, sample average, +not relative frequency. + +Of the sample average is going +to 0 as n gets big. + +In the same way, if you have a +sequence of arbitrary random + +variables, which are converging +to Y in mean + +square, then Chebyshev shows +that it converges in + +probability. + +OK so mean square convergence +implies convergence in + +probability. + +Mean square convergence is a +funny statement which says + +that this sequence of random +variables has a standard + +deviation, which +is going to 0. + +And it's hard to see exactly +what that means because that + +standard deviation is a +complicated integral. + +And I don't know +what it means. + +But if you use the Chebyshev +inequality, then it means this + +very simple statement, which +says that this sequence has to + +converge in probability to Y. + +Mean square convergence then +implies convergence in + +probability. + +Reverse isn't true because-- + +and I can't give you an example +of it now, but I've + +already told you something +about it. + +Because I've said that's the +weak law of large numbers + +continues to hold if the generic +random variable has a + +mean, but doesn't have a +variance because of this + +truncation argument. + +Well, I mean, what it says +then is a variance is not + +required for the weak law of +large numbers to hold. + +And if the variance doesn't +hold, then you certainly don't + +have convergence +in mean square. + +So we have an example even +though you haven't proven that + +that example works. + +You have an example where the +weak law of large numbers + +holds, but convergence in mean +square does not hold. + +OK, and the final thing is +convergence in probability + +really means that the +distribution of Yn minus Y + +approaches the unit step. + +Yes? + +AUDIENCE: So in general, +convergence in probability + +doesn't imply convergence +in distribution. + +But it holds in this special +case because-- + +PROFESSOR: It does imply +convergence in distribution. + +We haven't talked about +convergence in + +distribution yet. + +Except it does not imply +convergence in mean square, + +which is a thing that +requires a variance. + +So you can have convergence +in probability without + +convergence in mean square, +but not the other way. + +I mean, convergence in mean +square, you just apply + +Chebyshev to it, +and suddenly-- + +presto, you have convergence +in probability. + +And incidentally, I +wish all of you + +would ask more questions. + +Because we're taking this video, +which is going to be + +shown to many people in many +different countries. + +And they ask themselves, would +it be better if I came to MIT + +and then I could sit-in class +and ask questions? + +And then they see these videos +and they say, ah, it doesn't + +make any difference, nobody +ask questions anyway. + +And because of that, MIT +will simply wither + +away at some point. + +So it's very important for you +to ask questions now and then. + +Now, let's go on to the +central limit theorem. + +This sum of n IID +random variables + +minus n times the mean-- + +in other words, we just +normalized it to 0 mean. + +S sub n minus n x bar is a +0 mean random variable. + +And it has variance n +times sigma squared. + +It also has second moment +n times sigma squared. + +And what that means is that you +take Sn minus n times the + +mean of x and divide it by the +square root of n times sigma. + +What you get is something +which is 0 + +mean and unit variance. + +So as you keep increasing n, +this random variable here, Sn + +minus n x bar over the square +root of n sigma, just sits + +there rock solid with the same +mean and the same variance, + +nothing ever happens to it. + +Except it has a distribution +function, and the distribution + +function changes. + +I mean, you see the distribution +function changing + +here as you let n get +larger and larger. + +In some sense, these steps are +getting smaller and smaller. + +So it looks like you're +approaching some particular + +curve and when we looked +at the Bernoulli case-- + +I guess it was just last time. + +When we looked at the Bernoulli +case, what we saw is + +that these steps here were +going as e to the minus + +difference from the mean squared +divided by 2 times + +sigma squared. + +Bunch of stuff, but what we saw +was that these steps were + +proportional to the density +of a Gaussian. + +In other words, this curve that +we're converging to is + +proportional to the distribution +function of the + +Gaussian random variable. + +We didn't completely prove that +because all we did was to + +show what happened to the PMF. + +We didn't really integrate +these things. + +We didn't really deal with all +of the small quantities. + +We said they weren't +important. + +But you sort of got the picture +of exactly why this + +convergence to a normal +distribution + +function takes place. + +And the theorem says this more +general thing that this + +convergence does, in +fact, take place. + +And that is what the central +limit theorem says. + +It says that that happens not +only for the Bernoulli case, + +but it happens for all +random variables, + +which have a variance. + +And the convergence is +relatively good if the random + +variables have a certain +moment that + +can be awful otherwise. + +So this expression on top then +is really the expression of + +the central limit theorem. + +It says not only does the +normalized sample average-- + +I'll call this whole thing the +normalized sample average + +because Sn minus n X bar has +variance square root of n + +times sigma sub x. + +So this normalized sample +average has mean 0 and + +standard deviation 1. + +Not only does it have mean 0 +and variance 1, but it also + +becomes closer and closer to +this Gaussian distribution. + +Why is that important? + +Well, if you start studying +noise and things like that, + +it's very important. + +Because it says that if you have +the sum of lots and lots + +of very, very small, unimportant +things, then what + +those things add up to if +they're relatively independent + +is something which is +almost Gaussian. + +You pick up a book on noise +theory or you pick up a book + +which is on communication, or +which is on control, or + +something like that, and after +you read a few chapters, you + +get the idea that all random +variables are Gaussian. + +This is particularly true +if you look at books on + +statistics. + +Many, many books on statistics, +particularly for + +undergraduates, the only random +variable they ever talk + +about is the normal +random variable. + +For some reason or other, you're +led to believe that all + +random variables are Gaussian. + +Well, of course, they aren't. + +But this says that a lot of +random variables, which are + +sums of large numbers of little +things, in fact are + +close to Gaussian. + +But we're interested in it +here for another reason. + +And we'll come to that +in a little bit. + +But let me make the comment that +the proofs that I gave + +you about the central +limit theorem for + +the Bernoulli case-- + +and if you fill-in those +epsilons and deltas there, + +that really was a valid proof. + +That technique does not work +at all when you have a + +non-Bernoulli situation. + +Because the situation is +very, very complicated. + +You wind up-- + +I mean, if you have a Bernoulli +case, you wind up + +with this nice, nice +distribution, which says that + +every step in the Bernoulli +distribution, you have terms + +that are increasing and then +terms that are decreasing. + +If you look at what happens +for a discrete random + +variable, which is not binary, +you have the most god awful + +distribution if you +try to look at the + +probability mass function. + +It is just awful. + +And the only thing which +looks nice is the + +distribution function. + +The distribution function +looks relatively nice. + +And why is hard to tell. + +And if you look at proofs of +it, it goes through Fourier + +transforms. + +In probability theory, Fourier +transforms are called + +characteristics functions, but +it's really the same thing. + +And you go through this very +complicated argument. + +I've been through it +a number of times. + +And to me, it's all algebra. + +And I'm not a person that just +accepts the fact that + +something is all +algebra easily. + +I keep trying to find ways of +making sense out of it. + +And I've never been able to make +sense out of it, but I'm + +convinced that it's true. + +So you just have to sort +of live with that. + +So anyway, the central limit +theorem does apply to the + +distribution function. + +Namely, exactly what +that says. + +The distribution function of +this normalized sample average + +does go into the distribution +function of the Gaussian. + +The PMFs do not converge +at all. + +And nothing else converges, +but just that one thing. + +OK, a sequence of random +variables converges in + +distribution-- + +this is what someone was asking +about just a second + +ago, but I don't think you were +really asking about that. + +But this is what convergence +in distribution means. + +It means it's the limit of the +distribution functions of a + +sequence of random variables. + +Turns into the distribution +function of some + +other random variable. + +Then you say that these random +variables converge in + +distribution to Z. And that's +a nice, useful thing. + +And the CLT, the Central Limit +Theorem, then says that this + +normalized sample average +converges in distribution to + +the distribution of a normal +random variable. + +Many people call that density +city phi and call the normal + +distribution phi. + +I don't know why. + +I mean, you've got to call it +something, so many people call + +it the same thing. + +This convergence and +distribution is really almost + +a misnomer. + +Because when random variables +converge in distribution to + +another random variable, I mean, +if you say something + +converges, usually you have the +idea that the thing which + +is converging to something else +is getting close to it in + +some sense. + +And the random variables aren't +getting close at all, + +it's only the distribution +functions + +that are getting close. + +If I take a sequence of IID +random variables, all of them + +have the same distribution +function. + +And therefore, a +sequence of IID + +random variables converges. + +And in fact, it's converged +right from the beginning to + +the same random variable, +to the same + +generic random variable. + +But they're not at all +close to each other. + +But you still call this +convergence in distribution. + +Why do we make such a big fuss +about convergence in + +distribution? + +Well, primarily because of the +central limit theorem because + +you would like to see that a +sequence of random variables, + +in fact, starts to look like +something that is interesting, + +which is the Gaussian random +variable after a while. + +It says we can do these +crazy things that + +statisticians do, and that-- + +well, fortunately, most +communication theorists are a + +little more careful than +statisticians. + +Somebody's going to hit me +for saying that, but + +I think it's true. + +But the central limit theorem, +in fact, does say that many of + +these sums of random variables +you look at can be reasonably + +approximated as being +Gaussian. + +So what we have now is +convergence in probability + +implies convergence +in distribution. + +And the proof, I will-- + +on the slides, I always +abbreviate proof by Pf. + +And sometimes Pf is just what +it sounds like it, it's + +"poof." It is not quite a proof, +and you have to look at + +those to get the actual proof. + +But this says the convergence +is a sequence of Yn's in + +probability means that it +converges to a unit step. + +That's exactly what convergence + +in probability mean. + +It converges to a unit step, +and ti converges everywhere + +but at the step itself. + +If you look at the definition +of convergence in + +distribution, and I might not +have said it carefully enough + +when I defined it back here. + +Oh, yes, I did. + +Remarkable. + +Often I make up these slides +when I'm half asleep, and they + +don't always say what I +intended them to say. + +And my evil twin brother comes +in and changes them later. + +But here I said it right. + +A sequence of random variables +converges in distribution to + +another random variable Z if the +limit of the distribution + +function is equal +to the limit-- + +if the limit of the distribution +function of the Z + +sub n is equal to the +distribution function of Z. + +But it only says for all Z +where this distribution + +function is continuous. + +You can't really expect much +more than that because if + +you're looking at +a distribution-- + +if you're looking at a +limiting distribution + +function, which looks like this, +especially for the law + +of large numbers, all we've +been able to show is that + +these distributions come in down +here very close, go up + +and get out very +close up there. + +We haven't said anything +about where they + +cross this actual line. + +And there's nothing in the +argument about the weak law of + +large numbers, which says +anything about what happens + +right exactly at the mean. + +But that's something +that's the central + +limit theorem says-- + +Yes? + +AUDIENCE: What's the Zn? + +That's not the sample mean? + +PROFESSOR: When we use the Zn's +for the central limit + +theorem, then what I mean by +the Z sub n's here is those + +normalized random variables Sn +minus n x bar over square root + +of n times sigma. + +And in all of these definitions +of convergence, + +the random variables, which are +converging to something, + +are always rather peculiar. + +Sometimes they're the +sample averages. + +Sometimes they're the normalized +sample averages. + +God knows what they are. + +But what mathematicians +like to do-- + +and there's a good reason for +what they like to do-- + +is they like to define different +kinds of convergence + +in general terms, and then apply +them to the specific + +thing that you're +interested in. + +OK, so the central limit +theorem says that this + +normalized sum converges in +distribution to phi, but it + +only has to converge where the +distribution function is + +continuous. + +Yes? + +AUDIENCE: So the theorem applies +to the distribution. + +Why doesn't it apply to PMF? + +PROFESSOR: Well, if you look at +the example we have here, + +if you look at the PDF for +this normalized random + +variable, you find something +which is + +jumping up, jumping up. + +If we look at it for n equals +50, it's still jumping up. + +The jumps are smaller. + +But if you look at the +PDF for this-- + +well, if you look at the +distribution function for the + +normal, it has a density. + +This PDF function for the +things which you want to + +approach a limit never +have a density. + +All the time they have a PDF. + +The steps are getting +smaller and smaller. + +And you can see that here as +you're up to n equals 50. + +You can see these little +tiny steps here. + +But you still have a PMF. + +You'll want to look at it +in terms of density. + +You have to look at in +terms of impulses. + +And there's no way you can say +an impulse is starting to + +approach a smooth curve. + +OK, so we have this proof that +converges in probability, + +implies convergence +in distribution. + +And since convergence in mean +square implies convergence in + +probability, and convergence +in probability implies + +convergence in distribution, +we suddenly have the + +convergence in mean square +implies convergence in + +distribution also. + +And you have this nice picture +in the book of all the things + +that converge in distribution. + +Inside of that-- + +this is distribution. + +Inside of that is all the +things that converge in + +probability. + +And inside of that is +all the things that + +converge in mean square. + +Now, there's a paradox here. + +And what the paradox is, is that +the central limit theorem + +says something very, very strong +about how Sn over n-- + +namely, the sample average-- + +converges to the mean. + +The convergence in distribution +is a very weak + +form of convergence. + +So how is this weak form of +convergence telling you + +something that says specific +about how a sample average + +converges to the mean? + +It tells you much more +than the weak law of + +large numbers does. + +Because it tells you if you at +this thing, it's starting to + +approach a normal distribution +function. + +And the resolution +of that paradox-- + +and this is important +I think-- + +is that the random variables +converge in distribution to + +the central limit theorem +are these + +normalized random variables. + +The ones that converge in +probability are the things + +which are normalizing in terms +of the mean, but you're not + +normalizing them in +terms of variance. + +So when you look at one curve +relative to the other curve, + +one curve is a squashed down +version of the other curve. + +I mean, look at those pictures +we have for that example. + +If you look at a sequence of +distribution functions for S + +sub n over n, what you find is +things which are squashing + +down into a unit step. + +If you look at what you have +for the normalized random + +variables, normalized to unit +variance, what you have is + +something which is not squashing +down at all. + +It gives the whole shape +of the thing. + +You can get from one curve to +the other just by squashing or + +expanding on the x-axis. + +That's the only difference +between them. + +So the central limit theorem +says when you don't squash, + +you get this nice Gaussian +distribution function. + +The weak law of large numbers +says when you do squash, you + +get a unit step. + +Now, which tells you more? + +Well, if you have the central +limit theorem, it tells you a + +lot more because it says, if +you look at this unit step + +here, and you expand it out by +a factor of square root of n, + +what you're going to get is +something that goes like this. + +The central limit theorem tells +you exactly what the + +distribution function +is at x bar. + +It tells you that that's +converging to what? + +What's the probability that the +sum of a large number of + +random variables is greater +than n times the mean? + +What is it approximately? + +AUDIENCE: 1/2. + +PROFESSOR: 1/2. + +That's what this says. + +This is a distribution +function. + +It's converging to +the distribution + +function of the normal. + +It hits that point, the +normal is centered + +on this x bar here. + +And it hits that point +exactly at 1/2. + +This says the probability of +being on that side is 1/2. + +The probability of being +on this side is 1/2. + +So you see, the central limit +theorem is telling you a whole + +lot more about how this is +converging than the weak law + +of large numbers is. + +Now, I come back to the +question I asked + +you a long time ago. + +Why is the weak law +of large numbers-- + +why do you see it used more +often than the central limit + +theorem since it's so +much less powerful? + +Well, it's the same +answer as before. + +It's less powerful, but it +applies to a much larger + +number of cases. + +And in many situations, all +you want is that weaker + +statement that tells you +everything you want to know, + +but it tells you that weaker +statement for this enormous + +variety of different +situations. + +Mean square convergence applies +to fewer things. + +Well, of course, convergence +in distribution applies for + +even more things. + +But we saw that when you're +dealing with the central limit + +theorem, all bets are off on +that because it's talking + +about a different sequence of +random variables, which might + +or might not converge. + +OK, so finally, convergence +with probability 1. + +Many people call convergence +with probability 1 convergence + +almost surely, or convergence +almost everywhere. + +You will see this almost +everywhere. + +Now, why do I want to use +convergence with probability, + +and why is that a dangerous +thing to do? + +When you say things are +converging with probability 1, + +it sounds very much like you're +saying they converge in + +probability because you're +using the word + +"probability" in each. + +The two are very, very +different concepts. + +And therefore, it would seem +like you should avoid the word + +"probability" in this second one +and say convergence almost + +surely or convergence +almost everywhere. + +And the reason I don't like +those is they don't make any + +sense, unless you understand +measure theory. + +And we're not assuming +that you understand + +measure theory here. + +If you wanted to do that first +problem in the last problem + +set, you had to understand +measure theory. + +And I apologize for that, I +didn't mean to do that to you. + +But this notion of convergence +with probability 1, I think + +you can understand that. + +I think you can get a good sense +of what it means without + +knowing any measure theory. + +And at least that's what +we're trying to do. + +OK, so let's go on. + +We've already said that a random +variable is a lot more + +complicated thing than +a number is. + +I think those of you who +thought you understood + +probability theory pretty well, +I probably managed to + +confuse you enough to get you +to the point where you think + +you're not on totally +safe ground talking + +about random variables. + +And you're certainly not on very +safe ground talking about + +how random variables converge +to each other. + +And that's good because to reach +a greater understanding + +of something, you have to get +to the point where you're a + +little bit confused first. + +So I've intentionally +tried to-- + +well, I haven't tried +to make this more + +confusing than necessary. + +But in fact, it's not as simple +as what elementary + +courses would make +you believe. + +OK, this notion of convergence +with probability 1, which we + +abbreviate WP1, is something +that we're not going to talk + +about a great deal until we +come to renewal processes. + +And the reason is we won't need +it a great deal until we + +come to renewal processes. + +But you ought to know that +there's something like that + +hanging out there. + +And you ought to have some +idea of what it is. + +So here's the definition +of it. + +A sequence of random variables +convergence with probability 1 + +to some other random +variable Z all in + +the same sample space. + +If the probability of sample +points in omega-- + +now remember, that a sample +point implies a value for each + +one of these random variables. + +So in a sense, you can think of +a sample point as, more or + +less, equivalent to a sample +path of this sequence of + +random variables here. + +OK, so for omega and capital +Omega, it says the limit as n + +goes to infinity of these random +variables at the point + +omega is equal to what this +extra random variable is at + +the point-- + +and it says that the probability +of that whole + +thing is equal to 1. + +Now, how many of you can +look at that statement + +and see what it means? + +Well, I'm sure some of you can +because you've seen it before. + +But understanding what that +statement means, even though + +it's a very simple statement, +is not very easy. + +So there's the statement +up there. + +Let's try to parse it. + +In other words, break it down +into what it's talking about. + +For each sample point omega, +that sample point is going to + +map into a sequence of-- + +so each sample point maps into +this sample path of values for + +this sequence of random +variables. + +Some of those sequences-- + +OK, this now is a sequence +of numbers. + +So each omega goes into some +sequence of numbers. + +And that also is unquestionably +close to this + +final generic random variable, +capital Z evaluated at omega. + +Now, some of these sequences +here, sequences of real + +numbers, we all know what a +limit of real numbers is. + +I hope you do. + +I know that many of you don't. + +And we'll talk about it later +when we start talking about + +the strong law of +large numbers. + +But this does, perhaps, +have a limit. + +It perhaps doesn't +have a limit. + +If you look at a sequence 1, 2, +1, 2, 1, 2, 1, 2, forever, + +that doesn't have a limit +because it doesn't start to + +get close to anything. + +It keeps wandering +around forever. + +If you look at a sequence which +is 1 for 10 terms, then + +it's 2 the 11th term, and then +it's 1 for 100 terms, 2 for 1 + +more term, 1 for 1,000 terms, +then 2 for the next term, and + +so forth, that's a much +more tricky case. + +Because in that sequence, +pretty soon + +all you see is 1's. + +You look for an awful long way +and you don't see any 2's. + +That does not converge just +because the definition of + +convergence. + +And when you work with +convergence for a long time, + +after a while you're very +happy that that doesn't + +converge because it would +play all sorts of + +havoc with all of analysis. + +So anyway, there is this idea +that these numbers either + +converge or they +don't converge. + +When these numbers converge, +they might or might not + +converge to this. + +So for every omega in this +sample space, you have this + +sequence here. + +That sequence might converge. + +If it does converge, it might +converge to this or it might + +converge to something else. + +And what this is saying here is +you take this entire set of + +sequences here. + +Namely, you take the entire +set of omega. + +And for each one of those +omegas, this might or might + +not converge. + +You look at the set of +omega for which this + +sequence does converge. + +And for which it does converge +to Z of omega. + +And now you look at that set +and what convergence with + +probability 1 means is that that +set turns out to be an + +event, and that event turns +out to have probability 1. + +Which says that for almost +everything that happens, you + +look at this sample sequence +and it has a + +limit, which is this. + +And that's true in +probability. + +It's not true for +most sequences. + +Let me give you a very quick +and simple example. + +Look at this Bernoulli case, and +suppose the probability of + +a 1 is one quarter and the +probability of a 0 is 3/4. + +Look at what happens when you +take an extraordinarily large + +number of trials and you ask +for those sample sequences + +that you take. + +What's going to happen +to them? + +Well, this says that if you +look at the relative + +frequency of 1's-- + +well, if they converge in this +sense, if the set of relative + +frequencies-- + +excuse me. + +If the set of sample averages +converges in this sense, then + +it says with probability 1, that +sample average is going + +to converge to one quarter. + +Now, that doesn't mean that most +sequences are going to + +converge that way. + +Because most sequences are +going to converge to 1/2. + +There are many more sequences +with half 1's and half 0's + +than there are with +three quarter 1's + +and one quarter 0's-- + +with three quarter 0's +and one quarter 1's. + +So there are many more of +one than the other. + +But those particular sequences, +which have + +probability-- + +those particular sequences which +have relative frequency + +one quarter are much more likely +than those which have + +relative frequency one half. + +Because the ones with +relative frequency + +one half are so unlikely. + +That's a complicated +set of ideas. + +You sort of know that it has +to be true because of these + +other laws of large numbers. + +And this is simply extending +those laws of large numbers + +one more step to say not only +does the distribution function + +of that sample average converge +to what it should + +converge to, but also for +these sequences with + +probability 1, they converge. + +If you look at the sequence for +long enough, the sample + +average is going to converge to +what it should for that one + +particular sample sequence. + +OK, the strong law of large +numbers then says that if X1, + +X2, and so forth are IID random +variables, and they + +have an expected value, which +is less than infinity, then + +the sample average converges +to the actual average with + +probability 1. + +In other words, it says with +probability 1, you look at + +this sequence forever. + +I don't know how you look +at a sequence forever. + +I've never figured that out. + +But if you could look at it +forever, then with probability + +1, it would come out with the +right relative frequency. + +It'll take a lot of investment +of time when we get to chapter + +4 to try to sort that out. + +Wanted to tell you a little bit +about it, read about in + +notes a little bit in chapter +1, and we will + +come back to it. + +And I think you will +then understand it. + +OK, with that, we are +done with chapter 1. + +Next time we will go into +Poisson processes. + +If you're upset by all of the +abstraction in chapter 1, you + +will be very happy when we get +into Poisson processes because + +there's nothing abstract +there at all. + +Everything you could reasonably +say about Poisson + +processes is either obviously +true or obviously false. + +I mean, there's nothing that's +strange there at all. + +After you understand it, +everything works. + +So we'll do that next time. \ No newline at end of file diff --git a/kAX_PRnliMo.txt b/kAX_PRnliMo.txt new file mode 100644 index 0000000000000000000000000000000000000000..9191f89b0ac425ec350da64eb9b5a17037c55130 --- /dev/null +++ b/kAX_PRnliMo.txt @@ -0,0 +1,19059 @@ +align:start position:0% + +uh so let's start with one of the + + align:start position:0% +uh so let's start with one of the + + + align:start position:0% +uh so let's start with one of the +deepest questions humans have ever asked + + align:start position:0% +deepest questions humans have ever asked + + + align:start position:0% +deepest questions humans have ever asked +themselves + + align:start position:0% +themselves + + + align:start position:0% +themselves +we're not messing around in this class + + align:start position:0% +we're not messing around in this class + + + align:start position:0% +we're not messing around in this class +we're going for it and one of the + + align:start position:0% +we're going for it and one of the + + + align:start position:0% +we're going for it and one of the +deepest questions is where does + + align:start position:0% +deepest questions is where does + + + align:start position:0% +deepest questions is where does +knowledge come from + + align:start position:0% +knowledge come from + + + align:start position:0% +knowledge come from +and as you'll know if you've taken even + + align:start position:0% +and as you'll know if you've taken even + + + align:start position:0% +and as you'll know if you've taken even +a teeny bit of philosophy or read even a + + align:start position:0% +a teeny bit of philosophy or read even a + + + align:start position:0% +a teeny bit of philosophy or read even a +teeny bit you know that some of the kind + + align:start position:0% +teeny bit you know that some of the kind + + + align:start position:0% +teeny bit you know that some of the kind +of classic views in western philosophy + + align:start position:0% +of classic views in western philosophy + + + align:start position:0% +of classic views in western philosophy +especially the empiricist lock and hume + + align:start position:0% +especially the empiricist lock and hume + + + align:start position:0% +especially the empiricist lock and hume +argue that all knowledge comes from + + align:start position:0% +argue that all knowledge comes from + + + align:start position:0% +argue that all knowledge comes from +experience + + align:start position:0% +experience + + + align:start position:0% +experience +right + + align:start position:0% +right + + + align:start position:0% +right +on the other hand there are all a number + + align:start position:0% +on the other hand there are all a number + + + align:start position:0% +on the other hand there are all a number +of other schools of thought on western + + align:start position:0% +of other schools of thought on western + + + align:start position:0% +of other schools of thought on western +philosophy of which a dominant figure is + + align:start position:0% +philosophy of which a dominant figure is + + + align:start position:0% +philosophy of which a dominant figure is +emanuel kant who argued that experience + + align:start position:0% +emanuel kant who argued that experience + + + align:start position:0% +emanuel kant who argued that experience +alone is not enough + + align:start position:0% +alone is not enough + + + align:start position:0% +alone is not enough +you can't just have experience and + + align:start position:0% +you can't just have experience and + + + align:start position:0% +you can't just have experience and +figure out all the stuff we have figured + + align:start position:0% +figure out all the stuff we have figured + + + align:start position:0% +figure out all the stuff we have figured +out + + align:start position:0% +out + + + align:start position:0% +out +and so he argued that there has to be + + align:start position:0% +and so he argued that there has to be + + + align:start position:0% +and so he argued that there has to be +what he called a priori + + align:start position:0% +what he called a priori + + + align:start position:0% +what he called a priori +conditions of cognition which can't be + + align:start position:0% +conditions of cognition which can't be + + + align:start position:0% +conditions of cognition which can't be +derived from experience themselves but + + align:start position:0% +derived from experience themselves but + + + align:start position:0% +derived from experience themselves but +have to be given prior to it + + align:start position:0% +have to be given prior to it + + + align:start position:0% +have to be given prior to it +okay so you have to you have to have to + + align:start position:0% +okay so you have to you have to have to + + + align:start position:0% +okay so you have to you have to have to +build some structure into a mind or + + align:start position:0% +build some structure into a mind or + + + align:start position:0% +build some structure into a mind or +brain to get it off the ground it can't + + align:start position:0% +brain to get it off the ground it can't + + + align:start position:0% +brain to get it off the ground it can't +just start with absolutely nothing and + + align:start position:0% +just start with absolutely nothing and + + + align:start position:0% +just start with absolutely nothing and +get anywhere + + align:start position:0% +get anywhere + + + align:start position:0% +get anywhere +okay and he also argued that one of the + + align:start position:0% +okay and he also argued that one of the + + + align:start position:0% +okay and he also argued that one of the +key elements of this a priori structure + + align:start position:0% +key elements of this a priori structure + + + align:start position:0% +key elements of this a priori structure +that you have to build in + + align:start position:0% +that you have to build in + + + align:start position:0% +that you have to build in +was space and time + + align:start position:0% +was space and time + + + align:start position:0% +was space and time +okay + + align:start position:0% +okay + + + align:start position:0% +okay +organizing principles of + + align:start position:0% +organizing principles of + + + align:start position:0% +organizing principles of +cognition and thinking + + align:start position:0% +cognition and thinking + + + align:start position:0% +cognition and thinking +and so in his version of it space is + + align:start position:0% +and so in his version of it space is + + + align:start position:0% +and so in his version of it space is +nothing but the form of all appearances + + align:start position:0% +nothing but the form of all appearances + + + align:start position:0% +nothing but the form of all appearances +of outer sense and it can be given prior + + align:start position:0% +of outer sense and it can be given prior + + + align:start position:0% +of outer sense and it can be given prior +to all actual perceptions and so exist + + align:start position:0% +to all actual perceptions and so exist + + + align:start position:0% +to all actual perceptions and so exist +in the mind a priori + + align:start position:0% +in the mind a priori + + + align:start position:0% +in the mind a priori +and can contain prior to all experience + + align:start position:0% +and can contain prior to all experience + + + align:start position:0% +and can contain prior to all experience +principles which determine the relations + + align:start position:0% +principles which determine the relations + + + align:start position:0% +principles which determine the relations +of these objects + + align:start position:0% +of these objects + + + align:start position:0% +of these objects +okay + + align:start position:0% +okay + + + align:start position:0% +okay +well + + align:start position:0% +well + + + align:start position:0% +well +is that just empty philosophical hot air + + align:start position:0% +is that just empty philosophical hot air + + + align:start position:0% +is that just empty philosophical hot air +um it's kind of hard to understand + + align:start position:0% +um it's kind of hard to understand + + + align:start position:0% +um it's kind of hard to understand +exactly what he means you actually have + + align:start position:0% +exactly what he means you actually have + + + align:start position:0% +exactly what he means you actually have +to go spend + + align:start position:0% +to go spend + + + align:start position:0% +to go spend +a good deal of time with kant reading + + align:start position:0% +a good deal of time with kant reading + + + align:start position:0% +a good deal of time with kant reading +him to make any sense of it + + align:start position:0% +him to make any sense of it + + + align:start position:0% +him to make any sense of it +or cheat and get your friends to tell + + align:start position:0% +or cheat and get your friends to tell + + + align:start position:0% +or cheat and get your friends to tell +you as i do + + align:start position:0% +you as i do + + + align:start position:0% +you as i do +but no i'll argue it's not just empty + + align:start position:0% +but no i'll argue it's not just empty + + + align:start position:0% +but no i'll argue it's not just empty +philosophical hot air + + align:start position:0% +philosophical hot air + + + align:start position:0% +philosophical hot air +that these are in some important sense + + align:start position:0% +that these are in some important sense + + + align:start position:0% +that these are in some important sense +empirical questions and there are + + align:start position:0% +empirical questions and there are + + + align:start position:0% +empirical questions and there are +empirical questions that our field + + align:start position:0% +empirical questions that our field + + + align:start position:0% +empirical questions that our field +addresses very directly + + align:start position:0% +addresses very directly + + + align:start position:0% +addresses very directly +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so on wednesday we'll talk about + + align:start position:0% +and so on wednesday we'll talk about + + + align:start position:0% +and so on wednesday we'll talk about +whether + + align:start position:0% +whether + + + align:start position:0% +whether +your representations of space in your + + align:start position:0% +your representations of space in your + + + align:start position:0% +your representations of space in your +head are innate or not it's pretty much + + align:start position:0% +head are innate or not it's pretty much + + + align:start position:0% +head are innate or not it's pretty much +directly what kant + + align:start position:0% +directly what kant + + + align:start position:0% +directly what kant +is talking about or the modern version + + align:start position:0% +is talking about or the modern version + + + align:start position:0% +is talking about or the modern version +of what he was talking about + + align:start position:0% +of what he was talking about + + + align:start position:0% +of what he was talking about +and today we'll talk about which aspects + + align:start position:0% +and today we'll talk about which aspects + + + align:start position:0% +and today we'll talk about which aspects +of the brain are renate and which are + + align:start position:0% +of the brain are renate and which are + + + align:start position:0% +of the brain are renate and which are +learned okay that's the agenda + + align:start position:0% +learned okay that's the agenda + + + align:start position:0% +learned okay that's the agenda +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this little kind of easter egg brain + + align:start position:0% +so this little kind of easter egg brain + + + align:start position:0% +so this little kind of easter egg brain +here + + align:start position:0% +here + + + align:start position:0% +here +very schematically shows you some of the + + align:start position:0% +very schematically shows you some of the + + + align:start position:0% +very schematically shows you some of the +regions that we've been talking about in + + align:start position:0% +regions that we've been talking about in + + + align:start position:0% +regions that we've been talking about in +this class so far with regions that are + + align:start position:0% +this class so far with regions that are + + + align:start position:0% +this class so far with regions that are +to varying degrees specialized for + + align:start position:0% +to varying degrees specialized for + + + align:start position:0% +to varying degrees specialized for +processing things like shape and color + + align:start position:0% +processing things like shape and color + + + align:start position:0% +processing things like shape and color +and motion and faces and places and + + align:start position:0% +and motion and faces and places and + + + align:start position:0% +and motion and faces and places and +bodies right visually processing all of + + align:start position:0% +bodies right visually processing all of + + + align:start position:0% +bodies right visually processing all of +these things in approximately those + + align:start position:0% +these things in approximately those + + + align:start position:0% +these things in approximately those +locations + + align:start position:0% +locations + + + align:start position:0% +locations +and as i've mentioned these regions uh + + align:start position:0% +and as i've mentioned these regions uh + + + align:start position:0% +and as i've mentioned these regions uh +are present in approximately the same + + align:start position:0% +are present in approximately the same + + + align:start position:0% +are present in approximately the same +location with some individual + + align:start position:0% +location with some individual + + + align:start position:0% +location with some individual +variability in pretty much every normal + + align:start position:0% +variability in pretty much every normal + + + align:start position:0% +variability in pretty much every normal +person + + align:start position:0% +person + + + align:start position:0% +person +one of my lab members says you keep + + align:start position:0% +one of my lab members says you keep + + + align:start position:0% +one of my lab members says you keep +saying that it's just not true there's + + align:start position:0% +saying that it's just not true there's + + + align:start position:0% +saying that it's just not true there's +like some percent of subjects who just + + align:start position:0% +like some percent of subjects who just + + + align:start position:0% +like some percent of subjects who just +don't show these things he's kind of + + align:start position:0% +don't show these things he's kind of + + + align:start position:0% +don't show these things he's kind of +right okay so maybe like i don't know + + align:start position:0% +right okay so maybe like i don't know + + + align:start position:0% +right okay so maybe like i don't know +five ten percent of subjects you + + align:start position:0% +five ten percent of subjects you + + + align:start position:0% +five ten percent of subjects you +wouldn't see some of these things and + + align:start position:0% +wouldn't see some of these things and + + + align:start position:0% +wouldn't see some of these things and +we've never actually done the serious + + align:start position:0% +we've never actually done the serious + + + align:start position:0% +we've never actually done the serious +work of bringing those subjects back + + align:start position:0% +work of bringing those subjects back + + + align:start position:0% +work of bringing those subjects back +scanning the hell out of them and + + align:start position:0% +scanning the hell out of them and + + + align:start position:0% +scanning the hell out of them and +finding out whether they were just + + align:start position:0% +finding out whether they were just + + + align:start position:0% +finding out whether they were just +asleep in the scanner it was a bad + + align:start position:0% +asleep in the scanner it was a bad + + + align:start position:0% +asleep in the scanner it was a bad +scanner day or whatever it was + + align:start position:0% +scanner day or whatever it was + + + align:start position:0% +scanner day or whatever it was +i bet they all have them and it's just + + align:start position:0% +i bet they all have them and it's just + + + align:start position:0% +i bet they all have them and it's just +sometimes you don't see it but i'm + + align:start position:0% +sometimes you don't see it but i'm + + + align:start position:0% +sometimes you don't see it but i'm +trying to be a little more honest okay + + align:start position:0% +trying to be a little more honest okay + + + align:start position:0% +trying to be a little more honest okay +but you just look at this even this very + + align:start position:0% +but you just look at this even this very + + + align:start position:0% +but you just look at this even this very +schematic version of it you say like how + + align:start position:0% +schematic version of it you say like how + + + align:start position:0% +schematic version of it you say like how +would you build this system how would + + align:start position:0% +would you build this system how would + + + align:start position:0% +would you build this system how would +you start with an embryo and build into + + align:start position:0% +you start with an embryo and build into + + + align:start position:0% +you start with an embryo and build into +a genome or build into whatever + + align:start position:0% +a genome or build into whatever + + + align:start position:0% +a genome or build into whatever +experience is going to happen + + align:start position:0% +experience is going to happen + + + align:start position:0% +experience is going to happen +to this developing organism how would it + + align:start position:0% +to this developing organism how would it + + + align:start position:0% +to this developing organism how would it +end up with this very particular + + align:start position:0% +end up with this very particular + + + align:start position:0% +end up with this very particular +structure with those things in + + align:start position:0% +structure with those things in + + + align:start position:0% +structure with those things in +approximately the same place or at least + + align:start position:0% +approximately the same place or at least + + + align:start position:0% +approximately the same place or at least +the same relative positions in all + + align:start position:0% +the same relative positions in all + + + align:start position:0% +the same relative positions in all +subjects like the face bits are always + + align:start position:0% +subjects like the face bits are always + + + align:start position:0% +subjects like the face bits are always +lateral to the color bits the place bits + + align:start position:0% +lateral to the color bits the place bits + + + align:start position:0% +lateral to the color bits the place bits +are medial to the color bits + + align:start position:0% +are medial to the color bits + + + align:start position:0% +are medial to the color bits +the kind of shape bits are out on the + + align:start position:0% +the kind of shape bits are out on the + + + align:start position:0% +the kind of shape bits are out on the +lateral surface it's like always like + + align:start position:0% +lateral surface it's like always like + + + align:start position:0% +lateral surface it's like always like +that how do you build a system like that + + align:start position:0% +that how do you build a system like that + + + align:start position:0% +that how do you build a system like that +i find it hard not to immediately think + + align:start position:0% +i find it hard not to immediately think + + + align:start position:0% +i find it hard not to immediately think +well some aspect of this must be innate + + align:start position:0% +well some aspect of this must be innate + + + align:start position:0% +well some aspect of this must be innate +or how would it be so damn similar in + + align:start position:0% +or how would it be so damn similar in + + + align:start position:0% +or how would it be so damn similar in +each individual + + align:start position:0% +each individual + + + align:start position:0% +each individual +right + + align:start position:0% +right + + + align:start position:0% +right +um + + align:start position:0% +um + + + align:start position:0% +um +but it's not the only hypothesis + + align:start position:0% +but it's not the only hypothesis + + + align:start position:0% +but it's not the only hypothesis +um + + align:start position:0% +um + + + align:start position:0% +um +some big part of it even if some aspect + + align:start position:0% +some big part of it even if some aspect + + + align:start position:0% +some big part of it even if some aspect +of this is innate + + align:start position:0% +of this is innate + + + align:start position:0% +of this is innate +some big part of it may also be learned + + align:start position:0% +some big part of it may also be learned + + + align:start position:0% +some big part of it may also be learned +or derived from experience + + align:start position:0% +or derived from experience + + + align:start position:0% +or derived from experience +okay so what do you guys think + + align:start position:0% +okay so what do you guys think + + + align:start position:0% +okay so what do you guys think +do you think the fact that these + + align:start position:0% +do you think the fact that these + + + align:start position:0% +do you think the fact that these +structures are in systematically the + + align:start position:0% +structures are in systematically the + + + align:start position:0% +structures are in systematically the +same place across subjects mean you have + + align:start position:0% +same place across subjects mean you have + + + align:start position:0% +same place across subjects mean you have +to + + align:start position:0% +to + + + align:start position:0% +to +build in all that stuff somehow figure + + align:start position:0% +build in all that stuff somehow figure + + + align:start position:0% +build in all that stuff somehow figure +out how to get a a bunch of a's and t's + + align:start position:0% +out how to get a a bunch of a's and t's + + + align:start position:0% +out how to get a a bunch of a's and t's +and g's and c's in your dna to give you + + align:start position:0% +and g's and c's in your dna to give you + + + align:start position:0% +and g's and c's in your dna to give you +a blueprint for how to build that + + align:start position:0% +a blueprint for how to build that + + + align:start position:0% +a blueprint for how to build that +structure + + align:start position:0% + + + + align:start position:0% + +what do you think + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +it's i mean it's a combination but it's + + align:start position:0% +it's i mean it's a combination but it's + + + align:start position:0% +it's i mean it's a combination but it's +hard to then think about + + align:start position:0% +hard to then think about + + + align:start position:0% +hard to then think about +how that system evolves over time + + align:start position:0% +how that system evolves over time + + + align:start position:0% +how that system evolves over time +generations + + align:start position:0% + + + + align:start position:0% + +yeah so to some extent + + align:start position:0% +yeah so to some extent + + + align:start position:0% +yeah so to some extent +experience what i mean here is learn + + align:start position:0% +experience what i mean here is learn + + + align:start position:0% +experience what i mean here is learn +from experience within each individual + + align:start position:0% +from experience within each individual + + + align:start position:0% +from experience within each individual +like you could argue that innate really + + align:start position:0% +like you could argue that innate really + + + align:start position:0% +like you could argue that innate really +means + + align:start position:0% +means + + + align:start position:0% +means +learn through the experience of our + + align:start position:0% +learn through the experience of our + + + align:start position:0% +learn through the experience of our +ancestors and hence wired into the dna + + align:start position:0% +ancestors and hence wired into the dna + + + align:start position:0% +ancestors and hence wired into the dna +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +anyway i find this not an obvious + + align:start position:0% +anyway i find this not an obvious + + + align:start position:0% +anyway i find this not an obvious +question and so we'll talk about what + + align:start position:0% +question and so we'll talk about what + + + align:start position:0% +question and so we'll talk about what +what the data say here + + align:start position:0% +what the data say here + + + align:start position:0% +what the data say here +so first of all we're going to do some + + align:start position:0% +so first of all we're going to do some + + + align:start position:0% +so first of all we're going to do some +very basic facts about brain development + + align:start position:0% +very basic facts about brain development + + + align:start position:0% +very basic facts about brain development +just to get the picture of what we're + + align:start position:0% +just to get the picture of what we're + + + align:start position:0% +just to get the picture of what we're +talking about physically with the + + align:start position:0% +talking about physically with the + + + align:start position:0% +talking about physically with the +development of brains + + align:start position:0% +development of brains + + + align:start position:0% +development of brains +so we can ask what is present at birth + + align:start position:0% +so we can ask what is present at birth + + + align:start position:0% +so we can ask what is present at birth +and so turns out that most of the + + align:start position:0% +and so turns out that most of the + + + align:start position:0% +and so turns out that most of the +neurons in the adult brain + + align:start position:0% +neurons in the adult brain + + + align:start position:0% +neurons in the adult brain +uh are generated before birth okay so + + align:start position:0% +uh are generated before birth okay so + + + align:start position:0% +uh are generated before birth okay so +most of the actual neurons are generated + + align:start position:0% +most of the actual neurons are generated + + + align:start position:0% +most of the actual neurons are generated +early you're not making whole a whole + + align:start position:0% +early you're not making whole a whole + + + align:start position:0% +early you're not making whole a whole +lot more after birth a few but not a lot + + align:start position:0% +lot more after birth a few but not a lot + + + align:start position:0% +lot more after birth a few but not a lot +further the current view is that most of + + align:start position:0% +further the current view is that most of + + + align:start position:0% +further the current view is that most of +the long-range connections that means + + align:start position:0% +the long-range connections that means + + + align:start position:0% +the long-range connections that means +like a connection between this part and + + align:start position:0% +like a connection between this part and + + + align:start position:0% +like a connection between this part and +that part of the brain are also present + + align:start position:0% +that part of the brain are also present + + + align:start position:0% +that part of the brain are also present +at birth + + align:start position:0% +at birth + + + align:start position:0% +at birth +okay + + align:start position:0% + + + + align:start position:0% + +nonetheless even though a lot of stuff + + align:start position:0% +nonetheless even though a lot of stuff + + + align:start position:0% +nonetheless even though a lot of stuff +is present at birth a lot of stuff + + align:start position:0% +is present at birth a lot of stuff + + + align:start position:0% +is present at birth a lot of stuff +changes in the first couple years of + + align:start position:0% +changes in the first couple years of + + + align:start position:0% +changes in the first couple years of +life + + align:start position:0% +life + + + align:start position:0% +life +most obviously the brain doubles in + + align:start position:0% +most obviously the brain doubles in + + + align:start position:0% +most obviously the brain doubles in +volume in the first year + + align:start position:0% +volume in the first year + + + align:start position:0% +volume in the first year +from a two-week-old to a one-year-old to + + align:start position:0% +from a two-week-old to a one-year-old to + + + align:start position:0% +from a two-week-old to a one-year-old to +a two-year-old + + align:start position:0% +a two-year-old + + + align:start position:0% +a two-year-old +right + + align:start position:0% +right + + + align:start position:0% +right +um + + align:start position:0% +um + + + align:start position:0% +um +the cortical thickness + + align:start position:0% +the cortical thickness + + + align:start position:0% +the cortical thickness +you can see here the dark stuff which is + + align:start position:0% +you can see here the dark stuff which is + + + align:start position:0% +you can see here the dark stuff which is +the gray matter out there + + align:start position:0% +the gray matter out there + + + align:start position:0% +the gray matter out there +increases + + align:start position:0% +increases + + + align:start position:0% +increases +sharply between years + + align:start position:0% +sharply between years + + + align:start position:0% +sharply between years +one and two + + align:start position:0% + + + + align:start position:0% + +but also the complexity of each + + align:start position:0% +but also the complexity of each + + + align:start position:0% +but also the complexity of each +individual neuron increases dramatically + + align:start position:0% +individual neuron increases dramatically + + + align:start position:0% +individual neuron increases dramatically +in the first few years of life so here's + + align:start position:0% +in the first few years of life so here's + + + align:start position:0% +in the first few years of life so here's +a schematic picture of a piece of gray + + align:start position:0% +a schematic picture of a piece of gray + + + align:start position:0% +a schematic picture of a piece of gray +matter here where you have some number + + align:start position:0% +matter here where you have some number + + + align:start position:0% +matter here where you have some number +of neurons here with a few little + + align:start position:0% +of neurons here with a few little + + + align:start position:0% +of neurons here with a few little +you know processes and a few connections + + align:start position:0% +you know processes and a few connections + + + align:start position:0% +you know processes and a few connections +and over + + align:start position:0% +and over + + + align:start position:0% +and over +the first couple years of life those + + align:start position:0% +the first couple years of life those + + + align:start position:0% +the first couple years of life those +connections get much more dense + + align:start position:0% +connections get much more dense + + + align:start position:0% +connections get much more dense +and the neurons get much more complex + + align:start position:0% +and the neurons get much more complex + + + align:start position:0% +and the neurons get much more complex +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay and the final thing that really + + align:start position:0% +okay and the final thing that really + + + align:start position:0% +okay and the final thing that really +matters early on in development is that + + align:start position:0% +matters early on in development is that + + + align:start position:0% +matters early on in development is that +myelination + + align:start position:0% +myelination + + + align:start position:0% +myelination +happens rapidly in the first few years + + align:start position:0% +happens rapidly in the first few years + + + align:start position:0% +happens rapidly in the first few years +and remember + + align:start position:0% +and remember + + + align:start position:0% +and remember +myelin this is a little reminder neuron + + align:start position:0% +myelin this is a little reminder neuron + + + align:start position:0% +myelin this is a little reminder neuron +with that yellow stuff which is a bunch + + align:start position:0% +with that yellow stuff which is a bunch + + + align:start position:0% +with that yellow stuff which is a bunch +of cells that wrap around the axons the + + align:start position:0% +of cells that wrap around the axons the + + + align:start position:0% +of cells that wrap around the axons the +long processes of a neuron and that + + align:start position:0% +long processes of a neuron and that + + + align:start position:0% +long processes of a neuron and that +myelin sheath builds up a lot over the + + align:start position:0% +myelin sheath builds up a lot over the + + + align:start position:0% +myelin sheath builds up a lot over the +first couple of years and that's + + align:start position:0% +first couple of years and that's + + + align:start position:0% +first couple of years and that's +important because the myelin sheath + + align:start position:0% +important because the myelin sheath + + + align:start position:0% +important because the myelin sheath +enables those neurons to send their + + align:start position:0% +enables those neurons to send their + + + align:start position:0% +enables those neurons to send their +signals faster down their axons okay + + align:start position:0% +signals faster down their axons okay + + + align:start position:0% +signals faster down their axons okay +okay and this is just a picture of + + align:start position:0% +okay and this is just a picture of + + + align:start position:0% +okay and this is just a picture of +different of a vertical slice like this + + align:start position:0% +different of a vertical slice like this + + + align:start position:0% +different of a vertical slice like this +through the anatomy of + + align:start position:0% +through the anatomy of + + + align:start position:0% +through the anatomy of +infants of different ages from 107 days + + align:start position:0% +infants of different ages from 107 days + + + align:start position:0% +infants of different ages from 107 days +up to about a year and the colored stuff + + align:start position:0% +up to about a year and the colored stuff + + + align:start position:0% +up to about a year and the colored stuff +in the middle is degree of myelination + + align:start position:0% +in the middle is degree of myelination + + + align:start position:0% +in the middle is degree of myelination +which you can see with various kinds of + + align:start position:0% +which you can see with various kinds of + + + align:start position:0% +which you can see with various kinds of +anatomical scans you can see it starts + + align:start position:0% +anatomical scans you can see it starts + + + align:start position:0% +anatomical scans you can see it starts +at 107 days with a tiny little bit in + + align:start position:0% +at 107 days with a tiny little bit in + + + align:start position:0% +at 107 days with a tiny little bit in +the middle and it gets more and more + + align:start position:0% +the middle and it gets more and more + + + align:start position:0% +the middle and it gets more and more +myelinated and moves from center to + + align:start position:0% +myelinated and moves from center to + + + align:start position:0% +myelinated and moves from center to +periphery + + align:start position:0% +periphery + + + align:start position:0% +periphery +over the first year of life + + align:start position:0% +over the first year of life + + + align:start position:0% +over the first year of life +okay so all those + + align:start position:0% +okay so all those + + + align:start position:0% +okay so all those +uh fiber pathways are getting kind of + + align:start position:0% +uh fiber pathways are getting kind of + + + align:start position:0% +uh fiber pathways are getting kind of +accelerated as they get wrapped with + + align:start position:0% +accelerated as they get wrapped with + + + align:start position:0% +accelerated as they get wrapped with +myelin and head and head sped up + + align:start position:0% +myelin and head and head sped up + + + align:start position:0% +myelin and head and head sped up +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +all right so bottom line + + align:start position:0% +all right so bottom line + + + align:start position:0% +all right so bottom line +is most neurons and long long-range + + align:start position:0% +is most neurons and long long-range + + + align:start position:0% +is most neurons and long long-range +connections are in place at birth but + + align:start position:0% +connections are in place at birth but + + + align:start position:0% +connections are in place at birth but +development continues rapidly in the + + align:start position:0% +development continues rapidly in the + + + align:start position:0% +development continues rapidly in the +first two years + + align:start position:0% +first two years + + + align:start position:0% +first two years +especially increasing complexity of + + align:start position:0% +especially increasing complexity of + + + align:start position:0% +especially increasing complexity of +neurons and synapses and myelination of + + align:start position:0% +neurons and synapses and myelination of + + + align:start position:0% +neurons and synapses and myelination of +long-range connections and white matter + + align:start position:0% +long-range connections and white matter + + + align:start position:0% +long-range connections and white matter +okay so it's just basic anatomy nothing + + align:start position:0% +okay so it's just basic anatomy nothing + + + align:start position:0% +okay so it's just basic anatomy nothing +functional yet + + align:start position:0% +functional yet + + + align:start position:0% +functional yet +okay now we're going to consider in some + + align:start position:0% +okay now we're going to consider in some + + + align:start position:0% +okay now we're going to consider in some +detail the case of face perception + + align:start position:0% +detail the case of face perception + + + align:start position:0% +detail the case of face perception +not really because that's what i work on + + align:start position:0% +not really because that's what i work on + + + align:start position:0% +not really because that's what i work on +or used to work on mostly + + align:start position:0% +or used to work on mostly + + + align:start position:0% +or used to work on mostly +but just because there's a very rich set + + align:start position:0% +but just because there's a very rich set + + + align:start position:0% +but just because there's a very rich set +of data where people have grappled with + + align:start position:0% +of data where people have grappled with + + + align:start position:0% +of data where people have grappled with +this question in the case of face + + align:start position:0% +this question in the case of face + + + align:start position:0% +this question in the case of face +perception next time we'll talk about + + align:start position:0% +perception next time we'll talk about + + + align:start position:0% +perception next time we'll talk about +the navigation network and reorientation + + align:start position:0% +the navigation network and reorientation + + + align:start position:0% +the navigation network and reorientation +what parts of that system might be + + align:start position:0% +what parts of that system might be + + + align:start position:0% +what parts of that system might be +and ate and learned so + + align:start position:0% +and ate and learned so + + + align:start position:0% +and ate and learned so +so i'll just say right out at the + + align:start position:0% +so i'll just say right out at the + + + align:start position:0% +so i'll just say right out at the +beginning that this is an extremely + + align:start position:0% +beginning that this is an extremely + + + align:start position:0% +beginning that this is an extremely +active area where every time i turn + + align:start position:0% +active area where every time i turn + + + align:start position:0% +active area where every time i turn +around another paper comes out that + + align:start position:0% +around another paper comes out that + + + align:start position:0% +around another paper comes out that +contradicts a previously published + + align:start position:0% +contradicts a previously published + + + align:start position:0% +contradicts a previously published +finding and so + + align:start position:0% +finding and so + + + align:start position:0% +finding and so +that makes it fun but it means there + + align:start position:0% +that makes it fun but it means there + + + align:start position:0% +that makes it fun but it means there +isn't going to be some really tight + + align:start position:0% +isn't going to be some really tight + + + align:start position:0% +isn't going to be some really tight +perfect story here and i'd rather take + + align:start position:0% +perfect story here and i'd rather take + + + align:start position:0% +perfect story here and i'd rather take +you guys straight to the cutting edge + + align:start position:0% +you guys straight to the cutting edge + + + align:start position:0% +you guys straight to the cutting edge +even though it's kind of a mess + + align:start position:0% +even though it's kind of a mess + + + align:start position:0% +even though it's kind of a mess +then give you a nicely packaged but + + align:start position:0% +then give you a nicely packaged but + + + align:start position:0% +then give you a nicely packaged but +surely wrong picture okay because again + + align:start position:0% +surely wrong picture okay because again + + + align:start position:0% +surely wrong picture okay because again +i think what matters most in this area + + align:start position:0% +i think what matters most in this area + + + align:start position:0% +i think what matters most in this area +is how do you go about answering these + + align:start position:0% +is how do you go about answering these + + + align:start position:0% +is how do you go about answering these +questions rather than what is the + + align:start position:0% +questions rather than what is the + + + align:start position:0% +questions rather than what is the +current state of the thoughts about the + + align:start position:0% +current state of the thoughts about the + + + align:start position:0% +current state of the thoughts about the +answers okay so how are we going to + + align:start position:0% +answers okay so how are we going to + + + align:start position:0% +answers okay so how are we going to +think about how does face perception + + align:start position:0% +think about how does face perception + + + align:start position:0% +think about how does face perception +develop + + align:start position:0% +develop + + + align:start position:0% +develop +well just to get started i'm going to + + align:start position:0% +well just to get started i'm going to + + + align:start position:0% +well just to get started i'm going to +show you a very brief movie + + align:start position:0% +show you a very brief movie + + + align:start position:0% +show you a very brief movie +of a 72 hour old monkey + + align:start position:0% + + + + align:start position:0% + +see what you think + + align:start position:0% + + + + align:start position:0% + +he's sleepy + + align:start position:0% + + + + align:start position:0% + +he's pretty interested in that face + + align:start position:0% +he's pretty interested in that face + + + align:start position:0% +he's pretty interested in that face +and watch now + + align:start position:0% + + + + align:start position:0% + +pretty cute huh + + align:start position:0% +pretty cute huh + + + align:start position:0% +pretty cute huh +so what do you think + + align:start position:0% +so what do you think + + + align:start position:0% +so what do you think +um + + align:start position:0% +um + + + align:start position:0% +um +what does this tell us about face + + align:start position:0% +what does this tell us about face + + + align:start position:0% +what does this tell us about face +perception + + align:start position:0% +perception + + + align:start position:0% +perception +yeah the charge is moving + + align:start position:0% +yeah the charge is moving + + + align:start position:0% +yeah the charge is moving +good question good for you + + align:start position:0% +good question good for you + + + align:start position:0% +good question good for you +clearly is that right quiet quietly all + + align:start position:0% +clearly is that right quiet quietly all + + + align:start position:0% +clearly is that right quiet quietly all +right + + align:start position:0% +right + + + align:start position:0% +right +um + + align:start position:0% +um + + + align:start position:0% +um +uh yes so clearly asked did they try + + align:start position:0% +uh yes so clearly asked did they try + + + align:start position:0% +uh yes so clearly asked did they try +moving just anything in front of him + + align:start position:0% +moving just anything in front of him + + + align:start position:0% +moving just anything in front of him +absolutely the right question so that + + align:start position:0% +absolutely the right question so that + + + align:start position:0% +absolutely the right question so that +monkey seems pretty interested in that + + align:start position:0% +monkey seems pretty interested in that + + + align:start position:0% +monkey seems pretty interested in that +face but a face is a moving thing motion + + align:start position:0% +face but a face is a moving thing motion + + + align:start position:0% +face but a face is a moving thing motion +is very salient to young primates humans + + align:start position:0% +is very salient to young primates humans + + + align:start position:0% +is very salient to young primates humans +and monkeys and many others absolutely + + align:start position:0% +and monkeys and many others absolutely + + + align:start position:0% +and monkeys and many others absolutely +um what else did you see in here + + align:start position:0% + + + + align:start position:0% + +yeah it started + + align:start position:0% + + + + align:start position:0% + +yeah kind of i mean the the person + + align:start position:0% +yeah kind of i mean the the person + + + align:start position:0% +yeah kind of i mean the the person +the adult human there was moving their + + align:start position:0% +the adult human there was moving their + + + align:start position:0% +the adult human there was moving their +mouth open like this + + align:start position:0% +mouth open like this + + + align:start position:0% +mouth open like this +and then he was doing something with + + align:start position:0% +and then he was doing something with + + + align:start position:0% +and then he was doing something with +their mouth so + + align:start position:0% +their mouth so + + + align:start position:0% +their mouth so +what would that require + + align:start position:0% + + + + align:start position:0% + +yeah good question good question 72 + + align:start position:0% +yeah good question good question 72 + + + align:start position:0% +yeah good question good question 72 +hours is damned early but it's not zero + + align:start position:0% +hours is damned early but it's not zero + + + align:start position:0% +hours is damned early but it's not zero +experience right so who knows what + + align:start position:0% +experience right so who knows what + + + align:start position:0% +experience right so who knows what +they've managed to pick up that early + + align:start position:0% +they've managed to pick up that early + + + align:start position:0% +they've managed to pick up that early +they're actually studies in humans which + + align:start position:0% +they're actually studies in humans which + + + align:start position:0% +they're actually studies in humans which +i'm hoping heather knows better than me + + align:start position:0% +i'm hoping heather knows better than me + + + align:start position:0% +i'm hoping heather knows better than me +those andy meltzoff things how young are + + align:start position:0% +those andy meltzoff things how young are + + + align:start position:0% +those andy meltzoff things how young are +those humans those are like first hour + + align:start position:0% + + + + align:start position:0% + +yeah so there's studies in humans where + + align:start position:0% +yeah so there's studies in humans where + + + align:start position:0% +yeah so there's studies in humans where +you can show versions of that with um + + align:start position:0% +you can show versions of that with um + + + align:start position:0% +you can show versions of that with um +newborn infants copying you know the + + align:start position:0% +newborn infants copying you know the + + + align:start position:0% +newborn infants copying you know the +experimenter comes up and sticks their + + align:start position:0% +experimenter comes up and sticks their + + + align:start position:0% +experimenter comes up and sticks their +tongue out at the infant and the infant + + align:start position:0% +tongue out at the infant and the infant + + + align:start position:0% +tongue out at the infant and the infant +does that back kinda sorta certainly + + align:start position:0% +does that back kinda sorta certainly + + + align:start position:0% +does that back kinda sorta certainly +within the first two days maybe even + + align:start position:0% +within the first two days maybe even + + + align:start position:0% +within the first two days maybe even +earlier + + align:start position:0% +earlier + + + align:start position:0% +earlier +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so it's very suggestive it's + + align:start position:0% +okay so it's very suggestive it's + + + align:start position:0% +okay so it's very suggestive it's +tantalizing but we need control + + align:start position:0% +tantalizing but we need control + + + align:start position:0% +tantalizing but we need control +conditions it doesn't tell us right + + align:start position:0% +conditions it doesn't tell us right + + + align:start position:0% +conditions it doesn't tell us right +everything we need to know + + align:start position:0% +everything we need to know + + + align:start position:0% +everything we need to know +okay so if we think about it + + align:start position:0% +okay so if we think about it + + + align:start position:0% +okay so if we think about it +there's sort of ends of the kind of + + align:start position:0% +there's sort of ends of the kind of + + + align:start position:0% +there's sort of ends of the kind of +hypothesis space about how all of this + + align:start position:0% +hypothesis space about how all of this + + + align:start position:0% +hypothesis space about how all of this +could go + + align:start position:0% +could go + + + align:start position:0% +could go +as alana mentioned everything is both + + align:start position:0% +as alana mentioned everything is both + + + align:start position:0% +as alana mentioned everything is both +kind of genes and experience that's true + + align:start position:0% +kind of genes and experience that's true + + + align:start position:0% +kind of genes and experience that's true +but they're very very importantly + + align:start position:0% +but they're very very importantly + + + align:start position:0% +but they're very very importantly +different ways in which genes and + + align:start position:0% +different ways in which genes and + + + align:start position:0% +different ways in which genes and +experience can act together some in + + align:start position:0% +experience can act together some in + + + align:start position:0% +experience can act together some in +which a big part of the you know heft of + + align:start position:0% +which a big part of the you know heft of + + + align:start position:0% +which a big part of the you know heft of +the uh of what um what the adult form + + align:start position:0% +the uh of what um what the adult form + + + align:start position:0% +the uh of what um what the adult form +has might be built in and other stories + + align:start position:0% +has might be built in and other stories + + + align:start position:0% +has might be built in and other stories +where most of the structure comes from + + align:start position:0% +where most of the structure comes from + + + align:start position:0% +where most of the structure comes from +experience so just because everything is + + align:start position:0% +experience so just because everything is + + + align:start position:0% +experience so just because everything is +both doesn't mean we shouldn't flesh out + + align:start position:0% +both doesn't mean we shouldn't flesh out + + + align:start position:0% +both doesn't mean we shouldn't flesh out +exactly what comes from what + + align:start position:0% +exactly what comes from what + + + align:start position:0% +exactly what comes from what +so on the kind of one end of the + + align:start position:0% +so on the kind of one end of the + + + align:start position:0% +so on the kind of one end of the +spectrum + + align:start position:0% +spectrum + + + align:start position:0% +spectrum +you might imagine that there's some very + + align:start position:0% +you might imagine that there's some very + + + align:start position:0% +you might imagine that there's some very +very rudimentary precursor + + align:start position:0% +very rudimentary precursor + + + align:start position:0% +very rudimentary precursor +that has to be built in + + align:start position:0% +that has to be built in + + + align:start position:0% +that has to be built in +plus a learning mechanism + + align:start position:0% +plus a learning mechanism + + + align:start position:0% +plus a learning mechanism +okay or a bunch of rudimentary + + align:start position:0% +okay or a bunch of rudimentary + + + align:start position:0% +okay or a bunch of rudimentary +precursors which are just there to get + + align:start position:0% +precursors which are just there to get + + + align:start position:0% +precursors which are just there to get +the system to learn in the right way + + align:start position:0% +the system to learn in the right way + + + align:start position:0% +the system to learn in the right way +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so we'll talk um shortly about the + + align:start position:0% +and so we'll talk um shortly about the + + + align:start position:0% +and so we'll talk um shortly about the +idea that there might be some kind of + + align:start position:0% +idea that there might be some kind of + + + align:start position:0% +idea that there might be some kind of +innate template for faces that gets + + align:start position:0% +innate template for faces that gets + + + align:start position:0% +innate template for faces that gets +monkeys and humans to look at faces and + + align:start position:0% +monkeys and humans to look at faces and + + + align:start position:0% +monkeys and humans to look at faces and +then the idea is once you get them to + + align:start position:0% +then the idea is once you get them to + + + align:start position:0% +then the idea is once you get them to +look at a face then experience can take + + align:start position:0% +look at a face then experience can take + + + align:start position:0% +look at a face then experience can take +over from there and do the rest okay so + + align:start position:0% +over from there and do the rest okay so + + + align:start position:0% +over from there and do the rest okay so +you got to get them to collect the right + + align:start position:0% +you got to get them to collect the right + + + align:start position:0% +you got to get them to collect the right +input + + align:start position:0% +input + + + align:start position:0% +input +uh and there's lots of interesting + + align:start position:0% +uh and there's lots of interesting + + + align:start position:0% +uh and there's lots of interesting +computational work going on now where + + align:start position:0% +computational work going on now where + + + align:start position:0% +computational work going on now where +people are using various computational + + align:start position:0% +people are using various computational + + + align:start position:0% +people are using various computational +models to say + + align:start position:0% +models to say + + + align:start position:0% +models to say +what can develop what do we have to + + align:start position:0% +what can develop what do we have to + + + align:start position:0% +what can develop what do we have to +build into say a convolutional neural + + align:start position:0% +build into say a convolutional neural + + + align:start position:0% +build into say a convolutional neural +network or some other kind of + + align:start position:0% +network or some other kind of + + + align:start position:0% +network or some other kind of +computational model + + align:start position:0% +computational model + + + align:start position:0% +computational model +to get it to do some complicated thing i + + align:start position:0% +to get it to do some complicated thing i + + + align:start position:0% +to get it to do some complicated thing i +just came from a job talk the last hour + + align:start position:0% +just came from a job talk the last hour + + + align:start position:0% +just came from a job talk the last hour +really amazing talk where guys showing + + align:start position:0% +really amazing talk where guys showing + + + align:start position:0% +really amazing talk where guys showing +that if you build in basically + + align:start position:0% +that if you build in basically + + + align:start position:0% +that if you build in basically +curiosity early on in a network you get + + align:start position:0% +curiosity early on in a network you get + + + align:start position:0% +curiosity early on in a network you get +much more general learners than if you + + align:start position:0% +much more general learners than if you + + + align:start position:0% +much more general learners than if you +build in um a + + align:start position:0% +build in um a + + + align:start position:0% +build in um a +a bunch of goals for a developing + + align:start position:0% +a bunch of goals for a developing + + + align:start position:0% +a bunch of goals for a developing +network to to seek anyways very active + + align:start position:0% +network to to seek anyways very active + + + align:start position:0% +network to to seek anyways very active +area + + align:start position:0% +area + + + align:start position:0% +area +and the paper that i just decided to + + align:start position:0% +and the paper that i just decided to + + + align:start position:0% +and the paper that i just decided to +assign to you guys just kind of skim it + + align:start position:0% +assign to you guys just kind of skim it + + + align:start position:0% +assign to you guys just kind of skim it +and get the gist right the basic idea + + align:start position:0% +and get the gist right the basic idea + + + align:start position:0% +and get the gist right the basic idea +this is from shimon almond is a very + + align:start position:0% +this is from shimon almond is a very + + + align:start position:0% +this is from shimon almond is a very +deep thinker in this field and he argues + + align:start position:0% +deep thinker in this field and he argues + + + align:start position:0% +deep thinker in this field and he argues +that + + align:start position:0% +that + + + align:start position:0% +that +hands are very important and infants + + align:start position:0% +hands are very important and infants + + + align:start position:0% +hands are very important and infants +faces are important but so are hands + + align:start position:0% +faces are important but so are hands + + + align:start position:0% +faces are important but so are hands +because hands do stuff and we're social + + align:start position:0% +because hands do stuff and we're social + + + align:start position:0% +because hands do stuff and we're social +primates and we want to learn from other + + align:start position:0% +primates and we want to learn from other + + + align:start position:0% +primates and we want to learn from other +social primates like our parents and + + align:start position:0% +social primates like our parents and + + + align:start position:0% +social primates like our parents and +watching their hands is extremely + + align:start position:0% +watching their hands is extremely + + + align:start position:0% +watching their hands is extremely +informative whatever they're doing with + + align:start position:0% +informative whatever they're doing with + + + align:start position:0% +informative whatever they're doing with +their hands is probably stuff we need to + + align:start position:0% +their hands is probably stuff we need to + + + align:start position:0% +their hands is probably stuff we need to +learn about + + align:start position:0% +learn about + + + align:start position:0% +learn about +and further we need to know where + + align:start position:0% +and further we need to know where + + + align:start position:0% +and further we need to know where +they're looking right so gay's + + align:start position:0% +they're looking right so gay's + + + align:start position:0% +they're looking right so gay's +perception like i think i did this demo + + align:start position:0% +perception like i think i did this demo + + + align:start position:0% +perception like i think i did this demo +before if i'm talking to you guys when i + + align:start position:0% +before if i'm talking to you guys when i + + + align:start position:0% +before if i'm talking to you guys when i +start doing that it's really hard even + + align:start position:0% +start doing that it's really hard even + + + align:start position:0% +start doing that it's really hard even +though you know i'm just faking you out + + align:start position:0% +though you know i'm just faking you out + + + align:start position:0% +though you know i'm just faking you out +not to like have your attention pulled + + align:start position:0% +not to like have your attention pulled + + + align:start position:0% +not to like have your attention pulled +over there right + + align:start position:0% +over there right + + + align:start position:0% +over there right +and infants need to learn that as well + + align:start position:0% +and infants need to learn that as well + + + align:start position:0% +and infants need to learn that as well +so shimon olmen's basic idea is you can + + align:start position:0% +so shimon olmen's basic idea is you can + + + align:start position:0% +so shimon olmen's basic idea is you can +start with an extremely rudimentary + + align:start position:0% +start with an extremely rudimentary + + + align:start position:0% +start with an extremely rudimentary +system + + align:start position:0% +system + + + align:start position:0% +system +and all you have to build in is this + + align:start position:0% +and all you have to build in is this + + + align:start position:0% +and all you have to build in is this +idea that he calls mover right so the + + align:start position:0% +idea that he calls mover right so the + + + align:start position:0% +idea that he calls mover right so the +idea is that if you look in a whole set + + align:start position:0% +idea is that if you look in a whole set + + + align:start position:0% +idea is that if you look in a whole set +of say youtube videos and you just look + + align:start position:0% +of say youtube videos and you just look + + + align:start position:0% +of say youtube videos and you just look +for patches of the image that are moving + + align:start position:0% +for patches of the image that are moving + + + align:start position:0% +for patches of the image that are moving +that's no good it won't be a hand it + + align:start position:0% +that's no good it won't be a hand it + + + align:start position:0% +that's no good it won't be a hand it +might be a you know a whole animal or a + + align:start position:0% +might be a you know a whole animal or a + + + align:start position:0% +might be a you know a whole animal or a +face or something else but if you look + + align:start position:0% +face or something else but if you look + + + align:start position:0% +face or something else but if you look +in youtube videos or proxy for natural + + align:start position:0% +in youtube videos or proxy for natural + + + align:start position:0% +in youtube videos or proxy for natural +experience it's okay it's not perfect + + align:start position:0% +experience it's okay it's not perfect + + + align:start position:0% +experience it's okay it's not perfect +but it's something you look for a patch + + align:start position:0% +but it's something you look for a patch + + + align:start position:0% +but it's something you look for a patch +of the image that moves over + + align:start position:0% +of the image that moves over + + + align:start position:0% +of the image that moves over +and then causes another previously + + align:start position:0% +and then causes another previously + + + align:start position:0% +and then causes another previously +stationary image patch to move + + align:start position:0% +stationary image patch to move + + + align:start position:0% +stationary image patch to move +that's what happens when we pick stuff + + align:start position:0% +that's what happens when we pick stuff + + + align:start position:0% +that's what happens when we pick stuff +up okay and so his idea is you can build + + align:start position:0% +up okay and so his idea is you can build + + + align:start position:0% +up okay and so his idea is you can build +in this extremely simple thing mover + + align:start position:0% +in this extremely simple thing mover + + + align:start position:0% +in this extremely simple thing mover +right which is a very simple visual + + align:start position:0% +right which is a very simple visual + + + align:start position:0% +right which is a very simple visual +algorithm can find image patches that + + align:start position:0% +algorithm can find image patches that + + + align:start position:0% +algorithm can find image patches that +move over and cause another image or + + align:start position:0% +move over and cause another image or + + + align:start position:0% +move over and cause another image or +then then the two image patches move + + align:start position:0% +then then the two image patches move + + + align:start position:0% +then then the two image patches move +together and mover will enable you to + + align:start position:0% +together and mover will enable you to + + + align:start position:0% +together and mover will enable you to +identify hands in images pretty well he + + align:start position:0% +identify hands in images pretty well he + + + align:start position:0% +identify hands in images pretty well he +looks in youtube videos and shows that + + align:start position:0% +looks in youtube videos and shows that + + + align:start position:0% +looks in youtube videos and shows that +it's really good at picking out hands + + align:start position:0% +it's really good at picking out hands + + + align:start position:0% +it's really good at picking out hands +and then further once you've picked out + + align:start position:0% +and then further once you've picked out + + + align:start position:0% +and then further once you've picked out +hands that's a really important teaching + + align:start position:0% +hands that's a really important teaching + + + align:start position:0% +hands that's a really important teaching +signal and teaching you to read gays + + align:start position:0% +signal and teaching you to read gays + + + align:start position:0% +signal and teaching you to read gays +because often people look at their hands + + align:start position:0% +because often people look at their hands + + + align:start position:0% +because often people look at their hands +before they do things with them + + align:start position:0% +before they do things with them + + + align:start position:0% +before they do things with them +yeah so the idea is there's a very + + align:start position:0% +yeah so the idea is there's a very + + + align:start position:0% +yeah so the idea is there's a very +active ferment now in computational + + align:start position:0% +active ferment now in computational + + + align:start position:0% +active ferment now in computational +modeling saying how can we start with + + align:start position:0% +modeling saying how can we start with + + + align:start position:0% +modeling saying how can we start with +just the most rudimentary minimalist + + align:start position:0% +just the most rudimentary minimalist + + + align:start position:0% +just the most rudimentary minimalist +stuff that has to be built in + + align:start position:0% +stuff that has to be built in + + + align:start position:0% +stuff that has to be built in +and then build on experience to get the + + align:start position:0% +and then build on experience to get the + + + align:start position:0% +and then build on experience to get the +rest from there is that idea sort of + + align:start position:0% +rest from there is that idea sort of + + + align:start position:0% +rest from there is that idea sort of +clear it's worth reading that paper + + align:start position:0% +clear it's worth reading that paper + + + align:start position:0% +clear it's worth reading that paper +though it's beautifully written he's + + align:start position:0% +though it's beautifully written he's + + + align:start position:0% +though it's beautifully written he's +brilliant okay so that's the kind of one + + align:start position:0% +brilliant okay so that's the kind of one + + + align:start position:0% +brilliant okay so that's the kind of one +end of the spectrum nobody thinks that + + align:start position:0% +end of the spectrum nobody thinks that + + + align:start position:0% +end of the spectrum nobody thinks that +you um that you learn absolutely + + align:start position:0% +you um that you learn absolutely + + + align:start position:0% +you um that you learn absolutely +everything from experience you got to + + align:start position:0% +everything from experience you got to + + + align:start position:0% +everything from experience you got to +build in something plus we know all + + align:start position:0% +build in something plus we know all + + + align:start position:0% +build in something plus we know all +those neurons are there at birth and so + + align:start position:0% +those neurons are there at birth and so + + + align:start position:0% +those neurons are there at birth and so +the idea is like some version + + align:start position:0% +the idea is like some version + + + align:start position:0% +the idea is like some version +the minimalist + + align:start position:0% +the minimalist + + + align:start position:0% +the minimalist +minimalist nativist view says you build + + align:start position:0% +minimalist nativist view says you build + + + align:start position:0% +minimalist nativist view says you build +in a few very rudimentary things and + + align:start position:0% +in a few very rudimentary things and + + + align:start position:0% +in a few very rudimentary things and +they're enough to bootstrap learning + + align:start position:0% +they're enough to bootstrap learning + + + align:start position:0% +they're enough to bootstrap learning +okay + + align:start position:0% +okay + + + align:start position:0% +okay +on the other end of the spectrum + + align:start position:0% +on the other end of the spectrum + + + align:start position:0% +on the other end of the spectrum +uh you might think and many have + + align:start position:0% +uh you might think and many have + + + align:start position:0% +uh you might think and many have +proposed that we're born with a you know + + align:start position:0% +proposed that we're born with a you know + + + align:start position:0% +proposed that we're born with a you know +nearly adult-like system that only needs + + align:start position:0% +nearly adult-like system that only needs + + + align:start position:0% +nearly adult-like system that only needs +kind of fine-tuning from experience + + align:start position:0% +kind of fine-tuning from experience + + + align:start position:0% +kind of fine-tuning from experience +right nobody nobody thinks that + + align:start position:0% +right nobody nobody thinks that + + + align:start position:0% +right nobody nobody thinks that +zero experience is necessary that would + + align:start position:0% +zero experience is necessary that would + + + align:start position:0% +zero experience is necessary that would +be kind of crazy + + align:start position:0% +be kind of crazy + + + align:start position:0% +be kind of crazy +um or implausible + + align:start position:0% +um or implausible + + + align:start position:0% +um or implausible +um but on the other extreme uh this view + + align:start position:0% +um but on the other extreme uh this view + + + align:start position:0% +um but on the other extreme uh this view +is that most of the stuff is built in + + align:start position:0% +is that most of the stuff is built in + + + align:start position:0% +is that most of the stuff is built in +okay everybody get the theoretical space + + align:start position:0% +okay everybody get the theoretical space + + + align:start position:0% +okay everybody get the theoretical space +here that we're considering + + align:start position:0% +here that we're considering + + + align:start position:0% +here that we're considering +okay so what kind of data can constrain + + align:start position:0% +okay so what kind of data can constrain + + + align:start position:0% +okay so what kind of data can constrain +these questions + + align:start position:0% +these questions + + + align:start position:0% +these questions +uh well one obvious question is what is + + align:start position:0% +uh well one obvious question is what is + + + align:start position:0% +uh well one obvious question is what is +present at birth right what is the + + align:start position:0% +present at birth right what is the + + + align:start position:0% +present at birth right what is the +initial state or as close as we can get + + align:start position:0% +initial state or as close as we can get + + + align:start position:0% +initial state or as close as we can get +to it okay + + align:start position:0% +to it okay + + + align:start position:0% +to it okay +then we can ask how does the system + + align:start position:0% +then we can ask how does the system + + + align:start position:0% +then we can ask how does the system +change over time from birth onward + + align:start position:0% +change over time from birth onward + + + align:start position:0% +change over time from birth onward +and then we can ask what are the causal + + align:start position:0% +and then we can ask what are the causal + + + align:start position:0% +and then we can ask what are the causal +roles of experience and biological + + align:start position:0% +roles of experience and biological + + + align:start position:0% +roles of experience and biological +maturation in that change after birth + + align:start position:0% +maturation in that change after birth + + + align:start position:0% +maturation in that change after birth +okay so that's kind of the whole set of + + align:start position:0% +okay so that's kind of the whole set of + + + align:start position:0% +okay so that's kind of the whole set of +questions we need to answer to + + align:start position:0% +questions we need to answer to + + + align:start position:0% +questions we need to answer to +understand how development works + + align:start position:0% +understand how development works + + + align:start position:0% +understand how development works +and a very central if not the central + + align:start position:0% +and a very central if not the central + + + align:start position:0% +and a very central if not the central +challenge of development + + align:start position:0% +challenge of development + + + align:start position:0% +challenge of development +is that um experience and maturation are + + align:start position:0% +is that um experience and maturation are + + + align:start position:0% +is that um experience and maturation are +deeply confounded as you look from birth + + align:start position:0% +deeply confounded as you look from birth + + + align:start position:0% +deeply confounded as you look from birth +onward + + align:start position:0% +onward + + + align:start position:0% +onward +right so five-year-olds are both more + + align:start position:0% +right so five-year-olds are both more + + + align:start position:0% +right so five-year-olds are both more +mature they've had more time for their + + align:start position:0% +mature they've had more time for their + + + align:start position:0% +mature they've had more time for their +biological systems to wire themselves up + + align:start position:0% +biological systems to wire themselves up + + + align:start position:0% +biological systems to wire themselves up +including their bodies and their brains + + align:start position:0% +including their bodies and their brains + + + align:start position:0% +including their bodies and their brains +and the whole bit and maybe some of that + + align:start position:0% +and the whole bit and maybe some of that + + + align:start position:0% +and the whole bit and maybe some of that +is just kind of a on a maturational kind + + align:start position:0% +is just kind of a on a maturational kind + + + align:start position:0% +is just kind of a on a maturational kind +of autopilot but they've also had a lot + + align:start position:0% +of autopilot but they've also had a lot + + + align:start position:0% +of autopilot but they've also had a lot +more experience so one of the central + + align:start position:0% +more experience so one of the central + + + align:start position:0% +more experience so one of the central +challenges of development is try to + + align:start position:0% +challenges of development is try to + + + align:start position:0% +challenges of development is try to +figure out how those later stages like + + align:start position:0% +figure out how those later stages like + + + align:start position:0% +figure out how those later stages like +two months old one year old 10 years old + + align:start position:0% +two months old one year old 10 years old + + + align:start position:0% +two months old one year old 10 years old +how that how how those changes that + + align:start position:0% +how that how how those changes that + + + align:start position:0% +how that how how those changes that +happen between birth and those stages + + align:start position:0% +happen between birth and those stages + + + align:start position:0% +happen between birth and those stages +can how can we tease apart which of that + + align:start position:0% +can how can we tease apart which of that + + + align:start position:0% +can how can we tease apart which of that +came from just you know maturation and + + align:start position:0% +came from just you know maturation and + + + align:start position:0% +came from just you know maturation and +which came from experience all right + + align:start position:0% +which came from experience all right + + + align:start position:0% +which came from experience all right +okay + + align:start position:0% +okay + + + align:start position:0% +okay +importantly things that happen well + + align:start position:0% +importantly things that happen well + + + align:start position:0% +importantly things that happen well +after birth + + align:start position:0% +after birth + + + align:start position:0% +after birth +um need not be learned + + align:start position:0% +um need not be learned + + + align:start position:0% +um need not be learned +right + + align:start position:0% + + + + align:start position:0% + +right so think about puberty puberty is + + align:start position:0% +right so think about puberty puberty is + + + align:start position:0% +right so think about puberty puberty is +going to happen around 10 11 12 right + + align:start position:0% +going to happen around 10 11 12 right + + + align:start position:0% +going to happen around 10 11 12 right +and okay you gotta eat and have some + + align:start position:0% +and okay you gotta eat and have some + + + align:start position:0% +and okay you gotta eat and have some +basic inputs to your system but it's + + align:start position:0% +basic inputs to your system but it's + + + align:start position:0% +basic inputs to your system but it's +pretty much going to happen right it's + + align:start position:0% +pretty much going to happen right it's + + + align:start position:0% +pretty much going to happen right it's +not a product of what you were taught + + align:start position:0% +not a product of what you were taught + + + align:start position:0% +not a product of what you were taught +right or the particular information that + + align:start position:0% +right or the particular information that + + + align:start position:0% +right or the particular information that +landed on your sensory + + align:start position:0% +landed on your sensory + + + align:start position:0% +landed on your sensory +receptors i'm sure there's some obscure + + align:start position:0% +receptors i'm sure there's some obscure + + + align:start position:0% +receptors i'm sure there's some obscure +influences that i don't know about but + + align:start position:0% +influences that i don't know about but + + + align:start position:0% +influences that i don't know about but +mostly it's on a developmental autopilot + + align:start position:0% +mostly it's on a developmental autopilot + + + align:start position:0% +mostly it's on a developmental autopilot +it's just going to happen okay so keep + + align:start position:0% +it's just going to happen okay so keep + + + align:start position:0% +it's just going to happen okay so keep +in mind this is really important the + + align:start position:0% +in mind this is really important the + + + align:start position:0% +in mind this is really important the +things that happen well after birth + + align:start position:0% +things that happen well after birth + + + align:start position:0% +things that happen well after birth +aren't necessarily learned it might be + + align:start position:0% +aren't necessarily learned it might be + + + align:start position:0% +aren't necessarily learned it might be +just maturation that's continuing right + + align:start position:0% +just maturation that's continuing right + + + align:start position:0% +just maturation that's continuing right +okay just as like being five feet tall + + align:start position:0% +okay just as like being five feet tall + + + align:start position:0% +okay just as like being five feet tall +versus a foot and a half tall isn't + + align:start position:0% +versus a foot and a half tall isn't + + + align:start position:0% +versus a foot and a half tall isn't +really learned it's just a maturational + + align:start position:0% +really learned it's just a maturational + + + align:start position:0% +really learned it's just a maturational +you know + + align:start position:0% +you know + + + align:start position:0% +you know +program that unfolds + + align:start position:0% +program that unfolds + + + align:start position:0% +program that unfolds +okay so we can ask these three questions + + align:start position:0% +okay so we can ask these three questions + + + align:start position:0% +okay so we can ask these three questions +um both behaviorally and neurally and + + align:start position:0% +um both behaviorally and neurally and + + + align:start position:0% +um both behaviorally and neurally and +ultimately we want them to tell the same + + align:start position:0% +ultimately we want them to tell the same + + + align:start position:0% +ultimately we want them to tell the same +story when i said there's some chaos in + + align:start position:0% +story when i said there's some chaos in + + + align:start position:0% +story when i said there's some chaos in +this field right now i mean that + + align:start position:0% +this field right now i mean that + + + align:start position:0% +this field right now i mean that +basically they're not converging very + + align:start position:0% +basically they're not converging very + + + align:start position:0% +basically they're not converging very +well yet but that's fun + + align:start position:0% +well yet but that's fun + + + align:start position:0% +well yet but that's fun +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +sometimes it's aggravating but mostly + + align:start position:0% +sometimes it's aggravating but mostly + + + align:start position:0% +sometimes it's aggravating but mostly +it's fun okay so let's start with some + + align:start position:0% +it's fun okay so let's start with some + + + align:start position:0% +it's fun okay so let's start with some +behavioral data so let's consider the + + align:start position:0% +behavioral data so let's consider the + + + align:start position:0% +behavioral data so let's consider the +initial state of face perception in + + align:start position:0% +initial state of face perception in + + + align:start position:0% +initial state of face perception in +newborns okay + + align:start position:0% +newborns okay + + + align:start position:0% +newborns okay +so we can ask what kind of perceptual + + align:start position:0% +so we can ask what kind of perceptual + + + align:start position:0% +so we can ask what kind of perceptual +phase perceptual abilities are present + + align:start position:0% +phase perceptual abilities are present + + + align:start position:0% +phase perceptual abilities are present +in newborns and we can ask whether they + + align:start position:0% +in newborns and we can ask whether they + + + align:start position:0% +in newborns and we can ask whether they +can detect a face that is destr + + align:start position:0% +can detect a face that is destr + + + align:start position:0% +can detect a face that is destr +discriminate a face from a non-face + + align:start position:0% +discriminate a face from a non-face + + + align:start position:0% +discriminate a face from a non-face +whether it's a body or an + + align:start position:0% +whether it's a body or an + + + align:start position:0% +whether it's a body or an +object or something else + + align:start position:0% +object or something else + + + align:start position:0% +object or something else +we can ask about preferred attention to + + align:start position:0% +we can ask about preferred attention to + + + align:start position:0% +we can ask about preferred attention to +faces do they to newborns want to look + + align:start position:0% +faces do they to newborns want to look + + + align:start position:0% +faces do they to newborns want to look +at faces more than non-faces + + align:start position:0% +at faces more than non-faces + + + align:start position:0% +at faces more than non-faces +we can ask about the ability to + + align:start position:0% +we can ask about the ability to + + + align:start position:0% +we can ask about the ability to +recognize faces to discriminate one face + + align:start position:0% +recognize faces to discriminate one face + + + align:start position:0% +recognize faces to discriminate one face +from another + + align:start position:0% +from another + + + align:start position:0% +from another +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um and we can ask about the ability to + + align:start position:0% +um and we can ask about the ability to + + + align:start position:0% +um and we can ask about the ability to +recognize faces across image changes + + align:start position:0% +recognize faces across image changes + + + align:start position:0% +recognize faces across image changes +right so we spent a lot of time in the + + align:start position:0% +right so we spent a lot of time in the + + + align:start position:0% +right so we spent a lot of time in the +first few lectures talking about the + + align:start position:0% +first few lectures talking about the + + + align:start position:0% +first few lectures talking about the +central problem of invariance in + + align:start position:0% +central problem of invariance in + + + align:start position:0% +central problem of invariance in +envision about how do you know that this + + align:start position:0% +envision about how do you know that this + + + align:start position:0% +envision about how do you know that this +image that you're looking at here is the + + align:start position:0% +image that you're looking at here is the + + + align:start position:0% +image that you're looking at here is the +same person as that image even those are + + align:start position:0% +same person as that image even those are + + + align:start position:0% +same person as that image even those are +those are very different images + + align:start position:0% +those are very different images + + + align:start position:0% +those are very different images +and actually this image on your retina + + align:start position:0% +and actually this image on your retina + + + align:start position:0% +and actually this image on your retina +right now + + align:start position:0% +right now + + + align:start position:0% +right now +uh is more different than this image on + + align:start position:0% +uh is more different than this image on + + + align:start position:0% +uh is more different than this image on +your retina than if we got one of you + + align:start position:0% +your retina than if we got one of you + + + align:start position:0% +your retina than if we got one of you +and came up had you come up here and + + align:start position:0% +and came up had you come up here and + + + align:start position:0% +and came up had you come up here and +had you look forward so the image + + align:start position:0% +had you look forward so the image + + + align:start position:0% +had you look forward so the image +changes that result from a change in + + align:start position:0% +changes that result from a change in + + + align:start position:0% +changes that result from a change in +orientation are greater than the image + + align:start position:0% +orientation are greater than the image + + + align:start position:0% +orientation are greater than the image +changes that result from a change in + + align:start position:0% +changes that result from a change in + + + align:start position:0% +changes that result from a change in +identity so it's a big computational + + align:start position:0% +identity so it's a big computational + + + align:start position:0% +identity so it's a big computational +challenge when is that solved + + align:start position:0% +challenge when is that solved + + + align:start position:0% +challenge when is that solved +and then there are these kind of + + align:start position:0% +and then there are these kind of + + + align:start position:0% +and then there are these kind of +so-called signatures of face perception + + align:start position:0% +so-called signatures of face perception + + + align:start position:0% +so-called signatures of face perception +uh that we've talked about a little bit + + align:start position:0% +uh that we've talked about a little bit + + + align:start position:0% +uh that we've talked about a little bit +for example the inversion effect recall + + align:start position:0% +for example the inversion effect recall + + + align:start position:0% +for example the inversion effect recall +the inversion effect is larger in + + align:start position:0% +the inversion effect is larger in + + + align:start position:0% +the inversion effect is larger in +magnitude for faces than non-faces so we + + align:start position:0% +magnitude for faces than non-faces so we + + + align:start position:0% +magnitude for faces than non-faces so we +can ask when + + align:start position:0% +can ask when + + + align:start position:0% +can ask when +uh those things develop okay so let's + + align:start position:0% +uh those things develop okay so let's + + + align:start position:0% +uh those things develop okay so let's +start with face detection and face + + align:start position:0% +start with face detection and face + + + align:start position:0% +start with face detection and face +preferred attention to faces + + align:start position:0% +preferred attention to faces + + + align:start position:0% +preferred attention to faces +well so classic studies from the early + + align:start position:0% +well so classic studies from the early + + + align:start position:0% +well so classic studies from the early +90s and actually some of them going back + + align:start position:0% +90s and actually some of them going back + + + align:start position:0% +90s and actually some of them going back +to the 70s uh did the following very + + align:start position:0% +to the 70s uh did the following very + + + align:start position:0% +to the 70s uh did the following very +low-tech thing a low-tech drawing of a + + align:start position:0% +low-tech thing a low-tech drawing of a + + + align:start position:0% +low-tech thing a low-tech drawing of a +low-tech experiment you take a newborn + + align:start position:0% +low-tech experiment you take a newborn + + + align:start position:0% +low-tech experiment you take a newborn +infant in this case they're you know + + align:start position:0% +infant in this case they're you know + + + align:start position:0% +infant in this case they're you know +less than an hour old right you've got + + align:start position:0% +less than an hour old right you've got + + + align:start position:0% +less than an hour old right you've got +to set up in maternity wards + + align:start position:0% +to set up in maternity wards + + + align:start position:0% +to set up in maternity wards +you want the data that's what you do + + align:start position:0% +you want the data that's what you do + + + align:start position:0% +you want the data that's what you do +um of course you have to ask the parents + + align:start position:0% +um of course you have to ask the parents + + + align:start position:0% +um of course you have to ask the parents +and all of that + + align:start position:0% +and all of that + + + align:start position:0% +and all of that +but then you take this infant and you + + align:start position:0% +but then you take this infant and you + + + align:start position:0% +but then you take this infant and you +sit them on a person's lap with video + + align:start position:0% +sit them on a person's lap with video + + + align:start position:0% +sit them on a person's lap with video +camera overhead + + align:start position:0% +camera overhead + + + align:start position:0% +camera overhead +and you move different objects over the + + align:start position:0% +and you move different objects over the + + + align:start position:0% +and you move different objects over the +infant's head + + align:start position:0% +infant's head + + + align:start position:0% +infant's head +okay and the different objects that were + + align:start position:0% +okay and the different objects that were + + + align:start position:0% +okay and the different objects that were +moved in this case were + + align:start position:0% +moved in this case were + + + align:start position:0% +moved in this case were +were patterns that were drawn on this + + align:start position:0% +were patterns that were drawn on this + + + align:start position:0% +were patterns that were drawn on this +paddle that's moved over the infant's + + align:start position:0% +paddle that's moved over the infant's + + + align:start position:0% +paddle that's moved over the infant's +head + + align:start position:0% +head + + + align:start position:0% +head +and the pattern could be a schematic + + align:start position:0% +and the pattern could be a schematic + + + align:start position:0% +and the pattern could be a schematic +face like that + + align:start position:0% +face like that + + + align:start position:0% +face like that +a scrambled schematic face like that and + + align:start position:0% +a scrambled schematic face like that and + + + align:start position:0% +a scrambled schematic face like that and +a blank with nothing in it okay + + align:start position:0% +a blank with nothing in it okay + + + align:start position:0% +a blank with nothing in it okay +and what you measure is how far does the + + align:start position:0% +and what you measure is how far does the + + + align:start position:0% +and what you measure is how far does the +infant turn their head or their eyes + + align:start position:0% +infant turn their head or their eyes + + + align:start position:0% +infant turn their head or their eyes +following that paddle as you move it + + align:start position:0% +following that paddle as you move it + + + align:start position:0% +following that paddle as you move it +over them + + align:start position:0% +over them + + + align:start position:0% +over them +okay nice low-tech measure + + align:start position:0% +okay nice low-tech measure + + + align:start position:0% +okay nice low-tech measure +and what you find is they turn their + + align:start position:0% +and what you find is they turn their + + + align:start position:0% +and what you find is they turn their +heads and their eyes farther when it's + + align:start position:0% +heads and their eyes farther when it's + + + align:start position:0% +heads and their eyes farther when it's +an actual schematic face than when it's + + align:start position:0% +an actual schematic face than when it's + + + align:start position:0% +an actual schematic face than when it's +a scrambled schematic face or a blank + + align:start position:0% +a scrambled schematic face or a blank + + + align:start position:0% +a scrambled schematic face or a blank +okay within an hour of birth + + align:start position:0% +okay within an hour of birth + + + align:start position:0% +okay within an hour of birth +now you can still say well their their + + align:start position:0% +now you can still say well their their + + + align:start position:0% +now you can still say well their their +parents probably smiled at them quickly + + align:start position:0% +parents probably smiled at them quickly + + + align:start position:0% +parents probably smiled at them quickly +before they were snatched away to do the + + align:start position:0% +before they were snatched away to do the + + + align:start position:0% +before they were snatched away to do the +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +so they had some face experience but boy + + align:start position:0% +so they had some face experience but boy + + + align:start position:0% +so they had some face experience but boy +not a whole lot and this is a very + + align:start position:0% +not a whole lot and this is a very + + + align:start position:0% +not a whole lot and this is a very +abstract face here so this has long been + + align:start position:0% +abstract face here so this has long been + + + align:start position:0% +abstract face here so this has long been +taken as one of the key bits of evidence + + align:start position:0% +taken as one of the key bits of evidence + + + align:start position:0% +taken as one of the key bits of evidence +that + + align:start position:0% +that + + + align:start position:0% +that +something + + align:start position:0% +something + + + align:start position:0% +something +seems likely to be innate about faces + + align:start position:0% +seems likely to be innate about faces + + + align:start position:0% +seems likely to be innate about faces +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but now what needs to be innate for that + + align:start position:0% +but now what needs to be innate for that + + + align:start position:0% +but now what needs to be innate for that +right + + align:start position:0% +right + + + align:start position:0% +right +um + + align:start position:0% +um + + + align:start position:0% +um +and it's a kind of bizarre thing where + + align:start position:0% +and it's a kind of bizarre thing where + + + align:start position:0% +and it's a kind of bizarre thing where +this happens in the first two months of + + align:start position:0% +this happens in the first two months of + + + align:start position:0% +this happens in the first two months of +life and goes away and there's a lot of + + align:start position:0% +life and goes away and there's a lot of + + + align:start position:0% +life and goes away and there's a lot of +consideration of what that means maybe + + align:start position:0% +consideration of what that means maybe + + + align:start position:0% +consideration of what that means maybe +the first two months is enough to + + align:start position:0% +the first two months is enough to + + + align:start position:0% +the first two months is enough to +bootstrap learning in the way i was just + + align:start position:0% +bootstrap learning in the way i was just + + + align:start position:0% +bootstrap learning in the way i was just +talking about bootstrapping getting + + align:start position:0% +talking about bootstrapping getting + + + align:start position:0% +talking about bootstrapping getting +attention to the right places + + align:start position:0% +attention to the right places + + + align:start position:0% +attention to the right places +um + + align:start position:0% +um + + + align:start position:0% +um +but there's also a huge literature of + + align:start position:0% +but there's also a huge literature of + + + align:start position:0% +but there's also a huge literature of +this phenomenon where there's a big + + align:start position:0% +this phenomenon where there's a big + + + align:start position:0% +this phenomenon where there's a big +debate about exactly how simple those + + align:start position:0% +debate about exactly how simple those + + + align:start position:0% +debate about exactly how simple those +cues need to be so people have done many + + align:start position:0% +cues need to be so people have done many + + + align:start position:0% +cues need to be so people have done many +variations of this + + align:start position:0% +variations of this + + + align:start position:0% +variations of this +and one + + align:start position:0% +and one + + + align:start position:0% +and one +dominant story + + align:start position:0% +dominant story + + + align:start position:0% +dominant story +is that all you need is a pattern that + + align:start position:0% +is that all you need is a pattern that + + + align:start position:0% +is that all you need is a pattern that +has more stuff on the top than on the + + align:start position:0% +has more stuff on the top than on the + + + align:start position:0% +has more stuff on the top than on the +bottom + + align:start position:0% +bottom + + + align:start position:0% +bottom +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and that's enough that infants will + + align:start position:0% +and that's enough that infants will + + + align:start position:0% +and that's enough that infants will +follow this more than that + + align:start position:0% +follow this more than that + + + align:start position:0% +follow this more than that +uh and the idea is that in the visual + + align:start position:0% +uh and the idea is that in the visual + + + align:start position:0% +uh and the idea is that in the visual +environment of an infant that's + + align:start position:0% +environment of an infant that's + + + align:start position:0% +environment of an infant that's +sufficient to pick out faces + + align:start position:0% +sufficient to pick out faces + + + align:start position:0% +sufficient to pick out faces +okay so there's been pushback against + + align:start position:0% +okay so there's been pushback against + + + align:start position:0% +okay so there's been pushback against +this view as well it's probably a little + + align:start position:0% +this view as well it's probably a little + + + align:start position:0% +this view as well it's probably a little +more complicated than that we won't go + + align:start position:0% +more complicated than that we won't go + + + align:start position:0% +more complicated than that we won't go +down the rabbit hole of all those + + align:start position:0% +down the rabbit hole of all those + + + align:start position:0% +down the rabbit hole of all those +details but whatever it is it's pretty + + align:start position:0% +details but whatever it is it's pretty + + + align:start position:0% +details but whatever it is it's pretty +simple + + align:start position:0% +simple + + + align:start position:0% +simple +okay so this is another example of what + + align:start position:0% +okay so this is another example of what + + + align:start position:0% +okay so this is another example of what +i was mentioning before with the omen + + align:start position:0% +i was mentioning before with the omen + + + align:start position:0% +i was mentioning before with the omen +case this is a this is a case where it + + align:start position:0% +case this is a this is a case where it + + + align:start position:0% +case this is a this is a case where it +may be possible to build in something + + align:start position:0% +may be possible to build in something + + + align:start position:0% +may be possible to build in something +pretty basic + + align:start position:0% +pretty basic + + + align:start position:0% +pretty basic +a pretty basic template and then let + + align:start position:0% +a pretty basic template and then let + + + align:start position:0% +a pretty basic template and then let +learning take it from there + + align:start position:0% +learning take it from there + + + align:start position:0% +learning take it from there +make sense if the infants are looking at + + align:start position:0% +make sense if the infants are looking at + + + align:start position:0% +make sense if the infants are looking at +faces then they can use some kind of + + align:start position:0% +faces then they can use some kind of + + + align:start position:0% +faces then they can use some kind of +synaptic plasticity whatever and learn + + align:start position:0% +synaptic plasticity whatever and learn + + + align:start position:0% +synaptic plasticity whatever and learn +from their experience to discriminate + + align:start position:0% +from their experience to discriminate + + + align:start position:0% +from their experience to discriminate +one face from another okay + + align:start position:0% +one face from another okay + + + align:start position:0% +one face from another okay +so these things are present uh within a + + align:start position:0% +so these things are present uh within a + + + align:start position:0% +so these things are present uh within a +day or two + + align:start position:0% +day or two + + + align:start position:0% +day or two +what about discrimination of individual + + align:start position:0% +what about discrimination of individual + + + align:start position:0% +what about discrimination of individual +identity + + align:start position:0% +identity + + + align:start position:0% +identity +first problem how are we going to be + + align:start position:0% +first problem how are we going to be + + + align:start position:0% +first problem how are we going to be +able to tell what a newborn can see + + align:start position:0% +able to tell what a newborn can see + + + align:start position:0% +able to tell what a newborn can see +all right + + align:start position:0% +all right + + + align:start position:0% +all right +and so i didn't want you guys to be too + + align:start position:0% +and so i didn't want you guys to be too + + + align:start position:0% +and so i didn't want you guys to be too +thrown by this method in the last + + align:start position:0% +thrown by this method in the last + + + align:start position:0% +thrown by this method in the last +assignment so i told you where there's a + + align:start position:0% +assignment so i told you where there's a + + + align:start position:0% +assignment so i told you where there's a +version of the + + align:start position:0% +version of the + + + align:start position:0% +version of the +explanation i'm just going to give so if + + align:start position:0% +explanation i'm just going to give so if + + + align:start position:0% +explanation i'm just going to give so if +you already watched that my apologies + + align:start position:0% +you already watched that my apologies + + + align:start position:0% +you already watched that my apologies +you can read your email for a minute um + + align:start position:0% +you can read your email for a minute um + + + align:start position:0% +you can read your email for a minute um +so + + align:start position:0% +so + + + align:start position:0% +so +the classic experiment + + align:start position:0% +the classic experiment + + + align:start position:0% +the classic experiment +a classic experiment + + align:start position:0% +a classic experiment + + + align:start position:0% +a classic experiment +that enabled us to really kind of ask + + align:start position:0% +that enabled us to really kind of ask + + + align:start position:0% +that enabled us to really kind of ask +how a newborn nonverbal infant and what + + align:start position:0% +how a newborn nonverbal infant and what + + + align:start position:0% +how a newborn nonverbal infant and what +they see in the world uh was done by + + align:start position:0% +they see in the world uh was done by + + + align:start position:0% +they see in the world uh was done by +kelman and spelke liz spelhy up at + + align:start position:0% +kelman and spelke liz spelhy up at + + + align:start position:0% +kelman and spelke liz spelhy up at +harvard was at the forefront of getting + + align:start position:0% +harvard was at the forefront of getting + + + align:start position:0% +harvard was at the forefront of getting +this method to really tell us a huge + + align:start position:0% +this method to really tell us a huge + + + align:start position:0% +this method to really tell us a huge +great deal about what infants see and + + align:start position:0% +great deal about what infants see and + + + align:start position:0% +great deal about what infants see and +understand about the world and this + + align:start position:0% +understand about the world and this + + + align:start position:0% +understand about the world and this +method that i'm about to show to you has + + align:start position:0% +method that i'm about to show to you has + + + align:start position:0% +method that i'm about to show to you has +been the basis of what's sometimes + + align:start position:0% +been the basis of what's sometimes + + + align:start position:0% +been the basis of what's sometimes +called the infancy revolution which is + + align:start position:0% +called the infancy revolution which is + + + align:start position:0% +called the infancy revolution which is +basically the insight that actually + + align:start position:0% +basically the insight that actually + + + align:start position:0% +basically the insight that actually +infants know a lot their perceptual + + align:start position:0% +infants know a lot their perceptual + + + align:start position:0% +infants know a lot their perceptual +systems are really sophisticated they + + align:start position:0% +systems are really sophisticated they + + + align:start position:0% +systems are really sophisticated they +know about physics they know all kinds + + align:start position:0% +know about physics they know all kinds + + + align:start position:0% +know about physics they know all kinds +of social stuff within a few months of + + align:start position:0% +of social stuff within a few months of + + + align:start position:0% +of social stuff within a few months of +life they know a lot and that's been a + + align:start position:0% +life they know a lot and that's been a + + + align:start position:0% +life they know a lot and that's been a +radical change in our understanding of + + align:start position:0% +radical change in our understanding of + + + align:start position:0% +radical change in our understanding of +development based on just behavioral + + align:start position:0% +development based on just behavioral + + + align:start position:0% +development based on just behavioral +work so here's the method + + align:start position:0% +work so here's the method + + + align:start position:0% +work so here's the method +okay so what spelkey did i always forget + + align:start position:0% +okay so what spelkey did i always forget + + + align:start position:0% +okay so what spelkey did i always forget +to bring the demo hang on one moment + + align:start position:0% + + + + align:start position:0% + +we don't need much okay + + align:start position:0% +we don't need much okay + + + align:start position:0% +we don't need much okay +okay so she showed infants + + align:start position:0% +okay so she showed infants + + + align:start position:0% +okay so she showed infants +stuff like this okay my hand the two + + align:start position:0% +stuff like this okay my hand the two + + + align:start position:0% +stuff like this okay my hand the two +hands are not there you just arrange to + + align:start position:0% +hands are not there you just arrange to + + + align:start position:0% +hands are not there you just arrange to +see this okay + + align:start position:0% +see this okay + + + align:start position:0% +see this okay +so even if you hadn't seen me imagine if + + align:start position:0% +so even if you hadn't seen me imagine if + + + align:start position:0% +so even if you hadn't seen me imagine if +you hadn't seen me pick up the phone in + + align:start position:0% +you hadn't seen me pick up the phone in + + + align:start position:0% +you hadn't seen me pick up the phone in +the pen and you didn't already know what + + align:start position:0% +the pen and you didn't already know what + + + align:start position:0% +the pen and you didn't already know what +they were + + align:start position:0% +they were + + + align:start position:0% +they were +and you're seeing this okay that's what + + align:start position:0% +and you're seeing this okay that's what + + + align:start position:0% +and you're seeing this okay that's what +they see + + align:start position:0% +they see + + + align:start position:0% +they see +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so now the question is when infants + + align:start position:0% +and so now the question is when infants + + + align:start position:0% +and so now the question is when infants +see that do they think that that's this + + align:start position:0% +see that do they think that that's this + + + align:start position:0% +see that do they think that that's this +this thing + + align:start position:0% +this thing + + + align:start position:0% +this thing +behind a rectangle or do they think it's + + align:start position:0% +behind a rectangle or do they think it's + + + align:start position:0% +behind a rectangle or do they think it's +two separate bits moving behind the + + align:start position:0% +two separate bits moving behind the + + + align:start position:0% +two separate bits moving behind the +rectangle it could be two separate bits + + align:start position:0% +rectangle it could be two separate bits + + + align:start position:0% +rectangle it could be two separate bits +moving together right everybody get the + + align:start position:0% +moving together right everybody get the + + + align:start position:0% +moving together right everybody get the +question + + align:start position:0% +question + + + align:start position:0% +question +okay so how would we know what the + + align:start position:0% +okay so how would we know what the + + + align:start position:0% +okay so how would we know what the +infants thought was back there + + align:start position:0% +infants thought was back there + + + align:start position:0% +infants thought was back there +okay + + align:start position:0% +okay + + + align:start position:0% +okay +well we use what's known as habituation + + align:start position:0% +well we use what's known as habituation + + + align:start position:0% +well we use what's known as habituation +of looking time again you sit the infant + + align:start position:0% +of looking time again you sit the infant + + + align:start position:0% +of looking time again you sit the infant +on a parent's lap and you show them + + align:start position:0% +on a parent's lap and you show them + + + align:start position:0% +on a parent's lap and you show them +stuff and you just measure how long they + + align:start position:0% +stuff and you just measure how long they + + + align:start position:0% +stuff and you just measure how long they +look it's magnificently low-tech + + align:start position:0% +look it's magnificently low-tech + + + align:start position:0% +look it's magnificently low-tech +but really profound okay + + align:start position:0% +but really profound okay + + + align:start position:0% +but really profound okay +so what we're going to show here is how + + align:start position:0% +so what we're going to show here is how + + + align:start position:0% +so what we're going to show here is how +long the infant looks on each trial + + align:start position:0% +long the infant looks on each trial + + + align:start position:0% +long the infant looks on each trial +as a function of + + align:start position:0% +as a function of + + + align:start position:0% +as a function of +how many times you do it + + align:start position:0% +how many times you do it + + + align:start position:0% +how many times you do it +so you show the infant this the first + + align:start position:0% +so you show the infant this the first + + + align:start position:0% +so you show the infant this the first +time and they look for 40 seconds that's + + align:start position:0% +time and they look for 40 seconds that's + + + align:start position:0% +time and they look for 40 seconds that's +a long time you show them again they + + align:start position:0% +a long time you show them again they + + + align:start position:0% +a long time you show them again they +look for 35 seconds and so forth and by + + align:start position:0% +look for 35 seconds and so forth and by + + + align:start position:0% +look for 35 seconds and so forth and by +the fifth or sixth time the infant is + + align:start position:0% +the fifth or sixth time the infant is + + + align:start position:0% +the fifth or sixth time the infant is +bored + + align:start position:0% +bored + + + align:start position:0% +bored +like been there done that bored + + align:start position:0% +like been there done that bored + + + align:start position:0% +like been there done that bored +right + + align:start position:0% +right + + + align:start position:0% +right +okay now they're bored now we have a + + align:start position:0% +okay now they're bored now we have a + + + align:start position:0% +okay now they're bored now we have a +moment to say okay what did you think it + + align:start position:0% +moment to say okay what did you think it + + + align:start position:0% +moment to say okay what did you think it +was + + align:start position:0% +was + + + align:start position:0% +was +and so now what you can ask is + + align:start position:0% +and so now what you can ask is + + + align:start position:0% +and so now what you can ask is +what are they um what do they think + + align:start position:0% +what are they um what do they think + + + align:start position:0% +what are they um what do they think +you then show them either this or this + + align:start position:0% +you then show them either this or this + + + align:start position:0% +you then show them either this or this +and you ask them which of those they're + + align:start position:0% +and you ask them which of those they're + + + align:start position:0% +and you ask them which of those they're +bored to + + align:start position:0% +bored to + + + align:start position:0% +bored to +right so the idea is + + align:start position:0% +right so the idea is + + + align:start position:0% +right so the idea is +if when looking at this they thought + + align:start position:0% +if when looking at this they thought + + + align:start position:0% +if when looking at this they thought +there was a continuous line behind the + + align:start position:0% +there was a continuous line behind the + + + align:start position:0% +there was a continuous line behind the +occluder + + align:start position:0% +occluder + + + align:start position:0% +occluder +then they should be more bored by this + + align:start position:0% +then they should be more bored by this + + + align:start position:0% +then they should be more bored by this +but if they thought that was two + + align:start position:0% +but if they thought that was two + + + align:start position:0% +but if they thought that was two +separate pieces then they should be more + + align:start position:0% +separate pieces then they should be more + + + align:start position:0% +separate pieces then they should be more +bored by that does that make sense + + align:start position:0% +bored by that does that make sense + + + align:start position:0% +bored by that does that make sense +because it's the same thing they're + + align:start position:0% +because it's the same thing they're + + + align:start position:0% +because it's the same thing they're +already bored with it's not exactly the + + align:start position:0% +already bored with it's not exactly the + + + align:start position:0% +already bored with it's not exactly the +same the occluder isn't there but + + align:start position:0% +same the occluder isn't there but + + + align:start position:0% +same the occluder isn't there but +right but it's more similar + + align:start position:0% +right but it's more similar + + + align:start position:0% +right but it's more similar +okay so here's the data here's what they + + align:start position:0% +okay so here's the data here's what they + + + align:start position:0% +okay so here's the data here's what they +find so what does that mean what do the + + align:start position:0% +find so what does that mean what do the + + + align:start position:0% +find so what does that mean what do the +infants see when you show them this + + align:start position:0% +infants see when you show them this + + + align:start position:0% +infants see when you show them this +it's right there in the data look at the + + align:start position:0% +it's right there in the data look at the + + + align:start position:0% +it's right there in the data look at the +the first test trial here this is the + + align:start position:0% +the first test trial here this is the + + + align:start position:0% +the first test trial here this is the +first test trial when you show the + + align:start position:0% +first test trial when you show the + + + align:start position:0% +first test trial when you show the +the complete line or the broken line + + align:start position:0% +the complete line or the broken line + + + align:start position:0% +the complete line or the broken line +what do they see here + + align:start position:0% +what do they see here + + + align:start position:0% +what do they see here +yeah they saw the complete one that's + + align:start position:0% +yeah they saw the complete one that's + + + align:start position:0% +yeah they saw the complete one that's +why when you present the complete one + + align:start position:0% +why when you present the complete one + + + align:start position:0% +why when you present the complete one +again they're still bored + + align:start position:0% +again they're still bored + + + align:start position:0% +again they're still bored +already saw that make sense + + align:start position:0% +already saw that make sense + + + align:start position:0% +already saw that make sense +so isn't that awesome it's so low-tech + + align:start position:0% +so isn't that awesome it's so low-tech + + + align:start position:0% +so isn't that awesome it's so low-tech +and so simple but this is how you can + + align:start position:0% +and so simple but this is how you can + + + align:start position:0% +and so simple but this is how you can +ask an infant what do you see + + align:start position:0% +ask an infant what do you see + + + align:start position:0% +ask an infant what do you see +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +why does it switch positions + + align:start position:0% +why does it switch positions + + + align:start position:0% +why does it switch positions +you know frankly i never understand why + + align:start position:0% +you know frankly i never understand why + + + align:start position:0% +you know frankly i never understand why +infant development people do a second + + align:start position:0% +infant development people do a second + + + align:start position:0% +infant development people do a second +and third trial seems to me by this + + align:start position:0% +and third trial seems to me by this + + + align:start position:0% +and third trial seems to me by this +point the jig is up i think it's just + + align:start position:0% +point the jig is up i think it's just + + + align:start position:0% +point the jig is up i think it's just +because it's hard to get enough infants + + align:start position:0% +because it's hard to get enough infants + + + align:start position:0% +because it's hard to get enough infants +and you need more data and so they do a + + align:start position:0% +and you need more data and so they do a + + + align:start position:0% +and you need more data and so they do a +second third trial but to me that's a + + align:start position:0% +second third trial but to me that's a + + + align:start position:0% +second third trial but to me that's a +diagnostic one and that's probably not a + + align:start position:0% +diagnostic one and that's probably not a + + + align:start position:0% +diagnostic one and that's probably not a +significant switch but whatever's going + + align:start position:0% +significant switch but whatever's going + + + align:start position:0% +significant switch but whatever's going +on out there is obviously much less + + align:start position:0% +on out there is obviously much less + + + align:start position:0% +on out there is obviously much less +important than this heather do you have + + align:start position:0% +important than this heather do you have + + + align:start position:0% +important than this heather do you have +a better answer than that why do they do + + align:start position:0% +a better answer than that why do they do + + + align:start position:0% +a better answer than that why do they do +those other trials they always do and it + + align:start position:0% +those other trials they always do and it + + + align:start position:0% +those other trials they always do and it +just seems like what + + align:start position:0% + + + + align:start position:0% + +yeah i don't either + + align:start position:0% + + + + align:start position:0% + +oh you do it every which way but you do + + align:start position:0% +oh you do it every which way but you do + + + align:start position:0% +oh you do it every which way but you do +it pretty fast you know they get bored + + align:start position:0% +it pretty fast you know they get bored + + + align:start position:0% +it pretty fast you know they get bored +and you don't want to wait half an hour + + align:start position:0% +and you don't want to wait half an hour + + + align:start position:0% +and you don't want to wait half an hour +and come back right and you can do that + + align:start position:0% +and come back right and you can do that + + + align:start position:0% +and come back right and you can do that +then that would be a memory question + + align:start position:0% +then that would be a memory question + + + align:start position:0% +then that would be a memory question +right + + align:start position:0% +right + + + align:start position:0% +right +um + + align:start position:0% +um + + + align:start position:0% +um +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +jimmy i'm just curious uh is this + + align:start position:0% +jimmy i'm just curious uh is this + + + align:start position:0% +jimmy i'm just curious uh is this +conserved between inputs do they all see + + align:start position:0% +conserved between inputs do they all see + + + align:start position:0% +conserved between inputs do they all see +complete lines or + + align:start position:0% +complete lines or + + + align:start position:0% +complete lines or +it's pretty robust well okay so first of + + align:start position:0% +it's pretty robust well okay so first of + + + align:start position:0% +it's pretty robust well okay so first of +all these methods are awesome that you + + align:start position:0% +all these methods are awesome that you + + + align:start position:0% +all these methods are awesome that you +can learn these kind of deep things + + align:start position:0% +can learn these kind of deep things + + + align:start position:0% +can learn these kind of deep things +about perception in infants um but these + + align:start position:0% +about perception in infants um but these + + + align:start position:0% +about perception in infants um but these +data are noisy as hell there's no error + + align:start position:0% +data are noisy as hell there's no error + + + align:start position:0% +data are noisy as hell there's no error +bars on this plot but i bet if there + + align:start position:0% +bars on this plot but i bet if there + + + align:start position:0% +bars on this plot but i bet if there +were you'd have to run a lot of infants + + align:start position:0% +were you'd have to run a lot of infants + + + align:start position:0% +were you'd have to run a lot of infants +to + + align:start position:0% +to + + + align:start position:0% +to +get to the point where you reach + + align:start position:0% +get to the point where you reach + + + align:start position:0% +get to the point where you reach +significance because a lot of times the + + align:start position:0% +significance because a lot of times the + + + align:start position:0% +significance because a lot of times the +infants will just you know throw up or + + align:start position:0% +infants will just you know throw up or + + + align:start position:0% +infants will just you know throw up or +you know they'll just do what they do + + align:start position:0% +you know they'll just do what they do + + + align:start position:0% +you know they'll just do what they do +all kinds of random things so the data + + align:start position:0% +all kinds of random things so the data + + + align:start position:0% +all kinds of random things so the data +extremely noisy and it's very hard to + + align:start position:0% +extremely noisy and it's very hard to + + + align:start position:0% +extremely noisy and it's very hard to +get enough data within an infant to say + + align:start position:0% +get enough data within an infant to say + + + align:start position:0% +get enough data within an infant to say +anything about the difference between + + align:start position:0% +anything about the difference between + + + align:start position:0% +anything about the difference between +one infant and another by the way + + align:start position:0% +one infant and another by the way + + + align:start position:0% +one infant and another by the way +there's an there's a very exciting + + align:start position:0% +there's an there's a very exciting + + + align:start position:0% +there's an there's a very exciting +development going on in this department + + align:start position:0% +development going on in this department + + + align:start position:0% +development going on in this department +right now where kim scott who's a former + + align:start position:0% +right now where kim scott who's a former + + + align:start position:0% +right now where kim scott who's a former +grad student of this department has + + align:start position:0% +grad student of this department has + + + align:start position:0% +grad student of this department has +figured out how to do looking time + + align:start position:0% +figured out how to do looking time + + + align:start position:0% +figured out how to do looking time +experiments like this online + + align:start position:0% +experiments like this online + + + align:start position:0% +experiments like this online +okay and that's hugely important because + + align:start position:0% +okay and that's hugely important because + + + align:start position:0% +okay and that's hugely important because +the number one bottleneck in this kind + + align:start position:0% +the number one bottleneck in this kind + + + align:start position:0% +the number one bottleneck in this kind +of developmental research has been + + align:start position:0% +of developmental research has been + + + align:start position:0% +of developmental research has been +finding enough infants + + align:start position:0% +finding enough infants + + + align:start position:0% +finding enough infants +or getting enough data per infant and so + + align:start position:0% +or getting enough data per infant and so + + + align:start position:0% +or getting enough data per infant and so +i think that's she's going to just crack + + align:start position:0% +i think that's she's going to just crack + + + align:start position:0% +i think that's she's going to just crack +it wide open talia + + align:start position:0% +it wide open talia + + + align:start position:0% +it wide open talia +i guess i'm a little bit confused how we + + align:start position:0% +i guess i'm a little bit confused how we + + + align:start position:0% +i guess i'm a little bit confused how we +know like what the infant like really + + align:start position:0% +know like what the infant like really + + + align:start position:0% +know like what the infant like really +saw based on how long they've looked at + + align:start position:0% +saw based on how long they've looked at + + + align:start position:0% +saw based on how long they've looked at +something + + align:start position:0% +something + + + align:start position:0% +something +like + + align:start position:0% +like + + + align:start position:0% +like +could it be that maybe they look at like + + align:start position:0% +could it be that maybe they look at like + + + align:start position:0% +could it be that maybe they look at like +the + + align:start position:0% +the + + + align:start position:0% +the +like maybe they look at the broken + + align:start position:0% +like maybe they look at the broken + + + align:start position:0% +like maybe they look at the broken +sticks longer because it's like what + + align:start position:0% +sticks longer because it's like what + + + align:start position:0% +sticks longer because it's like what +they thought was behind it so they're + + align:start position:0% +they thought was behind it so they're + + + align:start position:0% +they thought was behind it so they're +like now excited that they get to see it + + align:start position:0% +like now excited that they get to see it + + + align:start position:0% +like now excited that they get to see it +maybe but then why would you get this + + align:start position:0% +maybe but then why would you get this + + + align:start position:0% +maybe but then why would you get this +so we know from this that the more + + align:start position:0% +so we know from this that the more + + + align:start position:0% +so we know from this that the more +familiar it looks the less time they + + align:start position:0% +familiar it looks the less time they + + + align:start position:0% +familiar it looks the less time they +look + + align:start position:0% +look + + + align:start position:0% +look +so you would have to come up with yeah + + align:start position:0% +so you would have to come up with yeah + + + align:start position:0% +so you would have to come up with yeah +there's there's wiggle room in these + + align:start position:0% +there's there's wiggle room in these + + + align:start position:0% +there's there's wiggle room in these +data but you'd have to come your account + + align:start position:0% +data but you'd have to come your account + + + align:start position:0% +data but you'd have to come your account +would have to say why would they look + + align:start position:0% +would have to say why would they look + + + align:start position:0% +would have to say why would they look +less and less and less long when we + + align:start position:0% +less and less and less long when we + + + align:start position:0% +less and less and less long when we +repeat the exact same thing + + align:start position:0% +repeat the exact same thing + + + align:start position:0% +repeat the exact same thing +right and you could you could tell a + + align:start position:0% +right and you could you could tell a + + + align:start position:0% +right and you could you could tell a +story like okay + + align:start position:0% +story like okay + + + align:start position:0% +story like okay +you know it's it's a little bit + + align:start position:0% +you know it's it's a little bit + + + align:start position:0% +you know it's it's a little bit +different because the occluder isn't + + align:start position:0% +different because the occluder isn't + + + align:start position:0% +different because the occluder isn't +there but it's a little bit the same and + + align:start position:0% +there but it's a little bit the same and + + + align:start position:0% +there but it's a little bit the same and +that's kind of edgy and fun or you know + + align:start position:0% +that's kind of edgy and fun or you know + + + align:start position:0% +that's kind of edgy and fun or you know +you could tell another story but i think + + align:start position:0% +you could tell another story but i think + + + align:start position:0% +you could tell another story but i think +the bulk of the developmental literature + + align:start position:0% +the bulk of the developmental literature + + + align:start position:0% +the bulk of the developmental literature +shows that when you do this kind of + + align:start position:0% +shows that when you do this kind of + + + align:start position:0% +shows that when you do this kind of +stuff it's a change that makes infants + + align:start position:0% +stuff it's a change that makes infants + + + align:start position:0% +stuff it's a change that makes infants +look more + + align:start position:0% +look more + + + align:start position:0% +look more +i'm going to go on unless they're + + align:start position:0% +i'm going to go on unless they're + + + align:start position:0% +i'm going to go on unless they're +questions of clarification just because + + align:start position:0% +questions of clarification just because + + + align:start position:0% +questions of clarification just because +there's so much other cool stuff okay + + align:start position:0% +there's so much other cool stuff okay + + + align:start position:0% +there's so much other cool stuff okay +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +uh okay so how can we use this to study + + align:start position:0% +uh okay so how can we use this to study + + + align:start position:0% +uh okay so how can we use this to study +face recognition that was just a sidebar + + align:start position:0% +face recognition that was just a sidebar + + + align:start position:0% +face recognition that was just a sidebar +on the method + + align:start position:0% +on the method + + + align:start position:0% +on the method +okay so there's a lab in italy where + + align:start position:0% +okay so there's a lab in italy where + + + align:start position:0% +okay so there's a lab in italy where +they have a infant psychology lab next + + align:start position:0% +they have a infant psychology lab next + + + align:start position:0% +they have a infant psychology lab next +to a maternity ward and they've been + + align:start position:0% +to a maternity ward and they've been + + + align:start position:0% +to a maternity ward and they've been +doing all these awesome studies + + align:start position:0% +doing all these awesome studies + + + align:start position:0% +doing all these awesome studies +um okay and they test one to three day + + align:start position:0% +um okay and they test one to three day + + + align:start position:0% +um okay and they test one to three day +old infants + + align:start position:0% +old infants + + + align:start position:0% +old infants +and so one of the things they did is + + align:start position:0% +and so one of the things they did is + + + align:start position:0% +and so one of the things they did is +show infants just like the paradigm i + + align:start position:0% +show infants just like the paradigm i + + + align:start position:0% +show infants just like the paradigm i +just showed you they show you they show + + align:start position:0% +just showed you they show you they show + + + align:start position:0% +just showed you they show you they show +the infant the same face again and again + + align:start position:0% +the infant the same face again and again + + + align:start position:0% +the infant the same face again and again +and again that's the habituation phase + + align:start position:0% +and again that's the habituation phase + + + align:start position:0% +and again that's the habituation phase +and then you sh um this is a slightly + + align:start position:0% +and then you sh um this is a slightly + + + align:start position:0% +and then you sh um this is a slightly +different one you give them a choice of + + align:start position:0% +different one you give them a choice of + + + align:start position:0% +different one you give them a choice of +whether they + + align:start position:0% +whether they + + + align:start position:0% +whether they +uh actually you don't give them a choice + + align:start position:0% +uh actually you don't give them a choice + + + align:start position:0% +uh actually you don't give them a choice +i take it back yeah you showed this + + align:start position:0% +i take it back yeah you showed this + + + align:start position:0% +i take it back yeah you showed this +condition or that condition + + align:start position:0% +condition or that condition + + + align:start position:0% +condition or that condition +and you see how long they look at each + + align:start position:0% +and you see how long they look at each + + + align:start position:0% +and you see how long they look at each +uh across different infants and so this + + align:start position:0% +uh across different infants and so this + + + align:start position:0% +uh across different infants and so this +is the same person from a different + + align:start position:0% +is the same person from a different + + + align:start position:0% +is the same person from a different +viewpoint actually pretty subtle as we + + align:start position:0% +viewpoint actually pretty subtle as we + + + align:start position:0% +viewpoint actually pretty subtle as we +discussed with the jenkins study way + + align:start position:0% +discussed with the jenkins study way + + + align:start position:0% +discussed with the jenkins study way +back + + align:start position:0% +back + + + align:start position:0% +back +and that's a different person that + + align:start position:0% +and that's a different person that + + + align:start position:0% +and that's a different person that +viewpoint and what they found + + align:start position:0% +viewpoint and what they found + + + align:start position:0% +viewpoint and what they found +is that there's a it's hard to see but a + + align:start position:0% +is that there's a it's hard to see but a + + + align:start position:0% +is that there's a it's hard to see but a +very low p level means that there's a + + align:start position:0% +very low p level means that there's a + + + align:start position:0% +very low p level means that there's a +significant difference in how much the + + align:start position:0% +significant difference in how much the + + + align:start position:0% +significant difference in how much the +infants looked at those two + + align:start position:0% +infants looked at those two + + + align:start position:0% +infants looked at those two +so that's pretty amazing one to three + + align:start position:0% +so that's pretty amazing one to three + + + align:start position:0% +so that's pretty amazing one to three +day old infants can apparently + + align:start position:0% +day old infants can apparently + + + align:start position:0% +day old infants can apparently +recognize the identity of a face + + align:start position:0% +recognize the identity of a face + + + align:start position:0% +recognize the identity of a face +a novel individual they don't already + + align:start position:0% +a novel individual they don't already + + + align:start position:0% +a novel individual they don't already +know + + align:start position:0% +know + + + align:start position:0% +know +with similar looking faces without hair + + align:start position:0% +with similar looking faces without hair + + + align:start position:0% +with similar looking faces without hair +and a cross view changes wow + + align:start position:0% +and a cross view changes wow + + + align:start position:0% +and a cross view changes wow +right so that's pretty impressive + + align:start position:0% +right so that's pretty impressive + + + align:start position:0% +right so that's pretty impressive +um okay and so then they've done all + + align:start position:0% +um okay and so then they've done all + + + align:start position:0% +um okay and so then they've done all +kinds of other variants if you have them + + align:start position:0% +kinds of other variants if you have them + + + align:start position:0% +kinds of other variants if you have them +rotate all the way from front profile + + align:start position:0% +rotate all the way from front profile + + + align:start position:0% +rotate all the way from front profile +there's no longer a significant + + align:start position:0% +there's no longer a significant + + + align:start position:0% +there's no longer a significant +difference infants can't do that + + align:start position:0% +difference infants can't do that + + + align:start position:0% +difference infants can't do that +and then they do all kinds of other + + align:start position:0% +and then they do all kinds of other + + + align:start position:0% +and then they do all kinds of other +variants if you show them the same + + align:start position:0% +variants if you show them the same + + + align:start position:0% +variants if you show them the same +individual and then habituate to that + + align:start position:0% +individual and then habituate to that + + + align:start position:0% +individual and then habituate to that +they can tell the difference between + + align:start position:0% +they can tell the difference between + + + align:start position:0% +they can tell the difference between +viewpoint that's the same and that's + + align:start position:0% +viewpoint that's the same and that's + + + align:start position:0% +viewpoint that's the same and that's +different + + align:start position:0% +different + + + align:start position:0% +different +right even though it's the same identity + + align:start position:0% +right even though it's the same identity + + + align:start position:0% +right even though it's the same identity +so you can use this to test what they + + align:start position:0% +so you can use this to test what they + + + align:start position:0% +so you can use this to test what they +think is same or different which is a + + align:start position:0% +think is same or different which is a + + + align:start position:0% +think is same or different which is a +deep question to ask if you're + + align:start position:0% +deep question to ask if you're + + + align:start position:0% +deep question to ask if you're +interested in representations and + + align:start position:0% +interested in representations and + + + align:start position:0% +interested in representations and +cognition the question of + + align:start position:0% +cognition the question of + + + align:start position:0% +cognition the question of +what an infant or an animal or a bunch + + align:start position:0% +what an infant or an animal or a bunch + + + align:start position:0% +what an infant or an animal or a bunch +of neurons thinks is the same or + + align:start position:0% +of neurons thinks is the same or + + + align:start position:0% +of neurons thinks is the same or +different is the essence of + + align:start position:0% +different is the essence of + + + align:start position:0% +different is the essence of +characterizing what it represents yeah + + align:start position:0% +characterizing what it represents yeah + + + align:start position:0% +characterizing what it represents yeah +quite quietly + + align:start position:0% + + + + align:start position:0% + +uh down here + + align:start position:0% +uh down here + + + align:start position:0% +uh down here +yeah yeah they do so here basically it's + + align:start position:0% +yeah yeah they do so here basically it's + + + align:start position:0% +yeah yeah they do so here basically it's +either identical or it's different in + + align:start position:0% +either identical or it's different in + + + align:start position:0% +either identical or it's different in +some respect + + align:start position:0% +some respect + + + align:start position:0% +some respect +so + + align:start position:0% +so + + + align:start position:0% +so +like given a choice + + align:start position:0% +like given a choice + + + align:start position:0% +like given a choice +when it's rotated anyway + + align:start position:0% +when it's rotated anyway + + + align:start position:0% +when it's rotated anyway +the familiar one is more similar but + + align:start position:0% +the familiar one is more similar but + + + align:start position:0% +the familiar one is more similar but +down here this one is more similar in + + align:start position:0% +down here this one is more similar in + + + align:start position:0% +down here this one is more similar in +viewpoint yeah + + align:start position:0% +viewpoint yeah + + + align:start position:0% +viewpoint yeah +and + + align:start position:0% +and + + + align:start position:0% +and +these are not like those in + + align:start position:0% + + + + align:start position:0% + +um well as little as possible as i say i + + align:start position:0% +um well as little as possible as i say i + + + align:start position:0% +um well as little as possible as i say i +mean they've seen some but not very many + + align:start position:0% +mean they've seen some but not very many + + + align:start position:0% +mean they've seen some but not very many +and they haven't seen these faces right + + align:start position:0% +and they haven't seen these faces right + + + align:start position:0% +and they haven't seen these faces right +so you know when you when you're trying + + align:start position:0% +so you know when you when you're trying + + + align:start position:0% +so you know when you when you're trying +to get those in innateness questions you + + align:start position:0% +to get those in innateness questions you + + + align:start position:0% +to get those in innateness questions you +go as close to birth as you can but you + + align:start position:0% +go as close to birth as you can but you + + + align:start position:0% +go as close to birth as you can but you +can't you know usually go into the very + + align:start position:0% +can't you know usually go into the very + + + align:start position:0% +can't you know usually go into the very +moment of birth itself right and so + + align:start position:0% +moment of birth itself right and so + + + align:start position:0% +moment of birth itself right and so +there's usually some experience and it's + + align:start position:0% +there's usually some experience and it's + + + align:start position:0% +there's usually some experience and it's +a challenge but this is pretty early + + align:start position:0% +a challenge but this is pretty early + + + align:start position:0% +a challenge but this is pretty early +yeah so couldn't that just mean that + + align:start position:0% +yeah so couldn't that just mean that + + + align:start position:0% +yeah so couldn't that just mean that +like + + align:start position:0% +like + + + align:start position:0% +like +the base perception network is just like + + align:start position:0% +the base perception network is just like + + + align:start position:0% +the base perception network is just like +developed really quickly like right + + align:start position:0% +developed really quickly like right + + + align:start position:0% +developed really quickly like right +after like it could it could based on + + align:start position:0% +after like it could it could based on + + + align:start position:0% +after like it could it could based on +these data alone it could + + align:start position:0% +these data alone it could + + + align:start position:0% +these data alone it could +um that's considered kind of unlikely + + align:start position:0% +um that's considered kind of unlikely + + + align:start position:0% +um that's considered kind of unlikely +but i agree that that's consistent with + + align:start position:0% +but i agree that that's consistent with + + + align:start position:0% +but i agree that that's consistent with +these data like you know in the first + + align:start position:0% +these data like you know in the first + + + align:start position:0% +these data like you know in the first +two days of life the whole thing wires + + align:start position:0% +two days of life the whole thing wires + + + align:start position:0% +two days of life the whole thing wires +itself up but that's be pretty unusual + + align:start position:0% +itself up but that's be pretty unusual + + + align:start position:0% +itself up but that's be pretty unusual +it's not what you it's not really + + align:start position:0% +it's not what you it's not really + + + align:start position:0% +it's not what you it's not really +consistent with those you know + + align:start position:0% +consistent with those you know + + + align:start position:0% +consistent with those you know +samples of neurons that people have + + align:start position:0% +samples of neurons that people have + + + align:start position:0% +samples of neurons that people have +looked at elsewhere in the brain but you + + align:start position:0% +looked at elsewhere in the brain but you + + + align:start position:0% +looked at elsewhere in the brain but you +know maybe there's like a special little + + align:start position:0% +know maybe there's like a special little + + + align:start position:0% +know maybe there's like a special little +circuit that just wires itself up really + + align:start position:0% +circuit that just wires itself up really + + + align:start position:0% +circuit that just wires itself up really +fast so not likely but possible + + align:start position:0% +fast so not likely but possible + + + align:start position:0% +fast so not likely but possible +okay all right + + align:start position:0% +okay all right + + + align:start position:0% +okay all right +now you might say well + + align:start position:0% +now you might say well + + + align:start position:0% +now you might say well +maybe there's some kind of simple visual + + align:start position:0% +maybe there's some kind of simple visual + + + align:start position:0% +maybe there's some kind of simple visual +features that are short of you know an + + align:start position:0% +features that are short of you know an + + + align:start position:0% +features that are short of you know an +actual face representation here this + + align:start position:0% +actual face representation here this + + + align:start position:0% +actual face representation here this +doesn't show us that this is something + + align:start position:0% +doesn't show us that this is something + + + align:start position:0% +doesn't show us that this is something +about faces per se even though it can + + align:start position:0% +about faces per se even though it can + + + align:start position:0% +about faces per se even though it can +generalize across viewpoints so it's + + align:start position:0% +generalize across viewpoints so it's + + + align:start position:0% +generalize across viewpoints so it's +it's not just like pixel intensity right + + align:start position:0% +it's not just like pixel intensity right + + + align:start position:0% +it's not just like pixel intensity right +um so what is the classic way we ask + + align:start position:0% +um so what is the classic way we ask + + + align:start position:0% +um so what is the classic way we ask +this question in face perception where + + align:start position:0% +this question in face perception where + + + align:start position:0% +this question in face perception where +we ask where is this really something + + align:start position:0% +we ask where is this really something + + + align:start position:0% +we ask where is this really something +about faces or is it something about the + + align:start position:0% +about faces or is it something about the + + + align:start position:0% +about faces or is it something about the +low-level perceptual properties of the + + align:start position:0% +low-level perceptual properties of the + + + align:start position:0% +low-level perceptual properties of the +face + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +turn it upside down god's gift to the + + align:start position:0% +turn it upside down god's gift to the + + + align:start position:0% +turn it upside down god's gift to the +face researcher right + + align:start position:0% +face researcher right + + + align:start position:0% +face researcher right +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +oh i guess that was not on this slide + + align:start position:0% +oh i guess that was not on this slide + + + align:start position:0% +oh i guess that was not on this slide +okay right okay so now in the next + + align:start position:0% +okay right okay so now in the next + + + align:start position:0% +okay right okay so now in the next +experiment they present whole faces + + align:start position:0% +experiment they present whole faces + + + align:start position:0% +experiment they present whole faces +or just the internal features without + + align:start position:0% +or just the internal features without + + + align:start position:0% +or just the internal features without +hair or just the external features + + align:start position:0% +hair or just the external features + + + align:start position:0% +hair or just the external features +without hair + + align:start position:0% +without hair + + + align:start position:0% +without hair +so + + align:start position:0% +so + + + align:start position:0% +so +the infants can do that at the top they + + align:start position:0% +the infants can do that at the top they + + + align:start position:0% +the infants can do that at the top they +know those two are different they can do + + align:start position:0% +know those two are different they can do + + + align:start position:0% +know those two are different they can do +this here and they can do that there + + align:start position:0% +this here and they can do that there + + + align:start position:0% +this here and they can do that there +okay not too shocking yet just tells you + + align:start position:0% +okay not too shocking yet just tells you + + + align:start position:0% +okay not too shocking yet just tells you +any of those cues can support + + align:start position:0% +any of those cues can support + + + align:start position:0% +any of those cues can support +performance + + align:start position:0% +performance + + + align:start position:0% +performance +but + + align:start position:0% +but + + + align:start position:0% +but +now we can ask is that just pattern + + align:start position:0% +now we can ask is that just pattern + + + align:start position:0% +now we can ask is that just pattern +matching + + align:start position:0% +matching + + + align:start position:0% +matching +no it's not because when you turn them + + align:start position:0% +no it's not because when you turn them + + + align:start position:0% +no it's not because when you turn them +upside down you find that + + align:start position:0% +upside down you find that + + + align:start position:0% +upside down you find that +only + + align:start position:0% +only + + + align:start position:0% +only +let's see it's only performance in this + + align:start position:0% +let's see it's only performance in this + + + align:start position:0% +let's see it's only performance in this +case + + align:start position:0% +case + + + align:start position:0% +case +that suffers when you turn them upside + + align:start position:0% +that suffers when you turn them upside + + + align:start position:0% +that suffers when you turn them upside +down not this case or that case + + align:start position:0% +down not this case or that case + + + align:start position:0% +down not this case or that case +okay so that shows that there are a + + align:start position:0% +okay so that shows that there are a + + + align:start position:0% +okay so that shows that there are a +variety of cues here the infants can be + + align:start position:0% +variety of cues here the infants can be + + + align:start position:0% +variety of cues here the infants can be +using but when you show them just the + + align:start position:0% +using but when you show them just the + + + align:start position:0% +using but when you show them just the +internal features the actual + + align:start position:0% +internal features the actual + + + align:start position:0% +internal features the actual +face proper + + align:start position:0% +face proper + + + align:start position:0% +face proper +that part the ability to do this + + align:start position:0% +that part the ability to do this + + + align:start position:0% +that part the ability to do this +discrimination goes away when you turn + + align:start position:0% +discrimination goes away when you turn + + + align:start position:0% +discrimination goes away when you turn +it upside down + + align:start position:0% +it upside down + + + align:start position:0% +it upside down +so that part at least seems to be at + + align:start position:0% +so that part at least seems to be at + + + align:start position:0% +so that part at least seems to be at +least somewhat phase specific or has a + + align:start position:0% +least somewhat phase specific or has a + + + align:start position:0% +least somewhat phase specific or has a +signature of face-specific processing + + align:start position:0% +signature of face-specific processing + + + align:start position:0% +signature of face-specific processing +make sense + + align:start position:0% +make sense + + + align:start position:0% +make sense +okay i mean as a pattern + + align:start position:0% +okay i mean as a pattern + + + align:start position:0% +okay i mean as a pattern +it'd be just as easy to recognize this + + align:start position:0% +it'd be just as easy to recognize this + + + align:start position:0% +it'd be just as easy to recognize this +upside down and distinguish it from that + + align:start position:0% +upside down and distinguish it from that + + + align:start position:0% +upside down and distinguish it from that +upside down if it was just the pixels + + align:start position:0% +upside down if it was just the pixels + + + align:start position:0% +upside down if it was just the pixels +you were registering but if you were + + align:start position:0% +you were registering but if you were + + + align:start position:0% +you were registering but if you were +doing face processing that's something + + align:start position:0% +doing face processing that's something + + + align:start position:0% +doing face processing that's something +like adult face processing you'd expect + + align:start position:0% +like adult face processing you'd expect + + + align:start position:0% +like adult face processing you'd expect +that inversion effect + + align:start position:0% +that inversion effect + + + align:start position:0% +that inversion effect +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so um + + align:start position:0% +all right so um + + + align:start position:0% +all right so um +so where are we oh and i should just say + + align:start position:0% +so where are we oh and i should just say + + + align:start position:0% +so where are we oh and i should just say +like + + align:start position:0% +like + + + align:start position:0% +like +even this is actively debated in fact + + align:start position:0% +even this is actively debated in fact + + + align:start position:0% +even this is actively debated in fact +the author of this study + + align:start position:0% +the author of this study + + + align:start position:0% +the author of this study +um + + align:start position:0% +um + + + align:start position:0% +um +considers this not to be evidence that + + align:start position:0% +considers this not to be evidence that + + + align:start position:0% +considers this not to be evidence that +that uh that that processing is face + + align:start position:0% +that uh that that processing is face + + + align:start position:0% +that uh that that processing is face +specific i think she's got some of the + + align:start position:0% +specific i think she's got some of the + + + align:start position:0% +specific i think she's got some of the +strongest evidence ever but she's got + + align:start position:0% +strongest evidence ever but she's got + + + align:start position:0% +strongest evidence ever but she's got +some counter-argument about how in the + + align:start position:0% +some counter-argument about how in the + + + align:start position:0% +some counter-argument about how in the +inverted phases they don't look as long + + align:start position:0% +inverted phases they don't look as long + + + align:start position:0% +inverted phases they don't look as long +in the habituation phase and so it's + + align:start position:0% +in the habituation phase and so it's + + + align:start position:0% +in the habituation phase and so it's +like i'm telling you these cool methods + + align:start position:0% +like i'm telling you these cool methods + + + align:start position:0% +like i'm telling you these cool methods +but boy every one of them can be fought + + align:start position:0% +but boy every one of them can be fought + + + align:start position:0% +but boy every one of them can be fought +over + + align:start position:0% +over + + + align:start position:0% +over +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so where are we um we've just shown the + + align:start position:0% +so where are we um we've just shown the + + + align:start position:0% +so where are we um we've just shown the +discrimination of individual identity is + + align:start position:0% +discrimination of individual identity is + + + align:start position:0% +discrimination of individual identity is +present very in very young newborns + + align:start position:0% +present very in very young newborns + + + align:start position:0% +present very in very young newborns +recognition across viewpoints + + align:start position:0% +recognition across viewpoints + + + align:start position:0% +recognition across viewpoints +and inversion effects are all present + + align:start position:0% +and inversion effects are all present + + + align:start position:0% +and inversion effects are all present +within the first few days of life + + align:start position:0% +within the first few days of life + + + align:start position:0% +within the first few days of life +okay so newborns have very impressive + + align:start position:0% +okay so newborns have very impressive + + + align:start position:0% +okay so newborns have very impressive +face perception abilities + + align:start position:0% +face perception abilities + + + align:start position:0% +face perception abilities +um and that's particularly surprising + + align:start position:0% +um and that's particularly surprising + + + align:start position:0% +um and that's particularly surprising +given that their acuity is terrible + + align:start position:0% +given that their acuity is terrible + + + align:start position:0% +given that their acuity is terrible +right their their vision is really + + align:start position:0% +right their their vision is really + + + align:start position:0% +right their their vision is really +blurry uh for for young infants so it's + + align:start position:0% +blurry uh for for young infants so it's + + + align:start position:0% +blurry uh for for young infants so it's +amazing that they can do these things + + align:start position:0% +amazing that they can do these things + + + align:start position:0% +amazing that they can do these things +but now there's room for quibbling about + + align:start position:0% +but now there's room for quibbling about + + + align:start position:0% +but now there's room for quibbling about +whether this is really a face-specific + + align:start position:0% +whether this is really a face-specific + + + align:start position:0% +whether this is really a face-specific +system right so the inversion effect is + + align:start position:0% +system right so the inversion effect is + + + align:start position:0% +system right so the inversion effect is +suggestive but they haven't totally + + align:start position:0% +suggestive but they haven't totally + + + align:start position:0% +suggestive but they haven't totally +nailed the case about what's being + + align:start position:0% +nailed the case about what's being + + + align:start position:0% +nailed the case about what's being +tapped into here is it really face + + align:start position:0% +tapped into here is it really face + + + align:start position:0% +tapped into here is it really face +perception per se something specific to + + align:start position:0% +perception per se something specific to + + + align:start position:0% +perception per se something specific to +face perception or is it some more + + align:start position:0% +face perception or is it some more + + + align:start position:0% +face perception or is it some more +generic kind of + + align:start position:0% +generic kind of + + + align:start position:0% +generic kind of +object perception okay and further we + + align:start position:0% +object perception okay and further we + + + align:start position:0% +object perception okay and further we +want to know what happens after that + + align:start position:0% +want to know what happens after that + + + align:start position:0% +want to know what happens after that +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so um you don't need to memorize this + + align:start position:0% +so um you don't need to memorize this + + + align:start position:0% +so um you don't need to memorize this +table i'm just gonna make a few simple + + align:start position:0% +table i'm just gonna make a few simple + + + align:start position:0% +table i'm just gonna make a few simple +points with it there are lots and lots + + align:start position:0% +points with it there are lots and lots + + + align:start position:0% +points with it there are lots and lots +of studies where people have tested + + align:start position:0% +of studies where people have tested + + + align:start position:0% +of studies where people have tested +behaviorally all kinds of different + + align:start position:0% +behaviorally all kinds of different + + + align:start position:0% +behaviorally all kinds of different +aspects of face perception and the basic + + align:start position:0% +aspects of face perception and the basic + + + align:start position:0% +aspects of face perception and the basic +story is that by age four + + align:start position:0% +story is that by age four + + + align:start position:0% +story is that by age four +you see the little smiley face means + + align:start position:0% +you see the little smiley face means + + + align:start position:0% +you see the little smiley face means +that you know this you know adult-like + + align:start position:0% +that you know this you know adult-like + + + align:start position:0% +that you know this you know adult-like +property of the face perception system + + align:start position:0% +property of the face perception system + + + align:start position:0% +property of the face perception system +is present by age four so all of those + + align:start position:0% +is present by age four so all of those + + + align:start position:0% +is present by age four so all of those +signatures of face perception that are + + align:start position:0% +signatures of face perception that are + + + align:start position:0% +signatures of face perception that are +present in adults are present by age + + align:start position:0% +present in adults are present by age + + + align:start position:0% +present in adults are present by age +four + + align:start position:0% +four + + + align:start position:0% +four +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and in fact much of the action is much + + align:start position:0% +and in fact much of the action is much + + + align:start position:0% +and in fact much of the action is much +before that + + align:start position:0% +before that + + + align:start position:0% +before that +um you can see that all of these things + + align:start position:0% +um you can see that all of these things + + + align:start position:0% +um you can see that all of these things +are present at the earliest age they've + + align:start position:0% +are present at the earliest age they've + + + align:start position:0% +are present at the earliest age they've +ever been tested the little square means + + align:start position:0% +ever been tested the little square means + + + align:start position:0% +ever been tested the little square means +nobody's tested it at that age right so + + align:start position:0% +nobody's tested it at that age right so + + + align:start position:0% +nobody's tested it at that age right so +um you know all this stuff is developing + + align:start position:0% +um you know all this stuff is developing + + + align:start position:0% +um you know all this stuff is developing +very fast + + align:start position:0% +very fast + + + align:start position:0% +very fast +right + + align:start position:0% +right + + + align:start position:0% +right +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +one particularly important thing here + + align:start position:0% +one particularly important thing here + + + align:start position:0% +one particularly important thing here +that you read about a little bit but + + align:start position:0% +that you read about a little bit but + + + align:start position:0% +that you read about a little bit but +that i want to take a moment to make + + align:start position:0% +that i want to take a moment to make + + + align:start position:0% +that i want to take a moment to make +sure you understand because it's so + + align:start position:0% +sure you understand because it's so + + + align:start position:0% +sure you understand because it's so +interesting and cool + + align:start position:0% +interesting and cool + + + align:start position:0% +interesting and cool +is the phenomenon of perceptual + + align:start position:0% +is the phenomenon of perceptual + + + align:start position:0% +is the phenomenon of perceptual +narrowing okay and this happens in face + + align:start position:0% +narrowing okay and this happens in face + + + align:start position:0% +narrowing okay and this happens in face +perception and it happens in + + align:start position:0% +perception and it happens in + + + align:start position:0% +perception and it happens in +phoneme perception in speech + + align:start position:0% +phoneme perception in speech + + + align:start position:0% +phoneme perception in speech +and i'm going to do a demo here so i'm + + align:start position:0% +and i'm going to do a demo here so i'm + + + align:start position:0% +and i'm going to do a demo here so i'm +going to show you a monkey face briefly + + align:start position:0% +going to show you a monkey face briefly + + + align:start position:0% +going to show you a monkey face briefly +okay it's going to come on in a second + + align:start position:0% +okay it's going to come on in a second + + + align:start position:0% +okay it's going to come on in a second +and you just look at it here we go boom + + align:start position:0% +and you just look at it here we go boom + + + align:start position:0% +and you just look at it here we go boom +there it is okay + + align:start position:0% +there it is okay + + + align:start position:0% +there it is okay +okay in a moment i'm going to show you + + align:start position:0% +okay in a moment i'm going to show you + + + align:start position:0% +okay in a moment i'm going to show you +another monkey face + + align:start position:0% +another monkey face + + + align:start position:0% +another monkey face +and you're gonna say shout out same if + + align:start position:0% +and you're gonna say shout out same if + + + align:start position:0% +and you're gonna say shout out same if +you think it's the same and different if + + align:start position:0% +you think it's the same and different if + + + align:start position:0% +you think it's the same and different if +you think it's different + + align:start position:0% +you think it's different + + + align:start position:0% +you think it's different +and huh if you don't know + + align:start position:0% +and huh if you don't know + + + align:start position:0% +and huh if you don't know +how many people don't know + + align:start position:0% +how many people don't know + + + align:start position:0% +how many people don't know +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +it's different right + + align:start position:0% +it's different right + + + align:start position:0% +it's different right +okay well okay maybe that was too hard + + align:start position:0% +okay well okay maybe that was too hard + + + align:start position:0% +okay well okay maybe that was too hard +let's try it with a human okay remember + + align:start position:0% +let's try it with a human okay remember + + + align:start position:0% +let's try it with a human okay remember +how hard that was now let's try it with + + align:start position:0% +how hard that was now let's try it with + + + align:start position:0% +how hard that was now let's try it with +a human face i'm going to show you a + + align:start position:0% +a human face i'm going to show you a + + + align:start position:0% +a human face i'm going to show you a +human face everybody ready here we go + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay and i'm going to show you another + + align:start position:0% +okay and i'm going to show you another + + + align:start position:0% +okay and i'm going to show you another +human and you're going to say is it same + + align:start position:0% +human and you're going to say is it same + + + align:start position:0% +human and you're going to say is it same +or different + + align:start position:0% +or different + + + align:start position:0% +or different +here we go + + align:start position:0% +here we go + + + align:start position:0% +here we go +duh + + align:start position:0% +duh + + + align:start position:0% +duh +easy right + + align:start position:0% +easy right + + + align:start position:0% +easy right +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so here's the amazing thing + + align:start position:0% +so here's the amazing thing + + + align:start position:0% +so here's the amazing thing +you were better at that monkey face task + + align:start position:0% +you were better at that monkey face task + + + align:start position:0% +you were better at that monkey face task +when you were six months old + + align:start position:0% +when you were six months old + + + align:start position:0% +when you were six months old +you could do that monkey face task when + + align:start position:0% +you could do that monkey face task when + + + align:start position:0% +you could do that monkey face task when +you were six months old + + align:start position:0% +you were six months old + + + align:start position:0% +you were six months old +one of the things that you have learned + + align:start position:0% +one of the things that you have learned + + + align:start position:0% +one of the things that you have learned +from experience is that you don't need + + align:start position:0% +from experience is that you don't need + + + align:start position:0% +from experience is that you don't need +that information and you threw away your + + align:start position:0% +that information and you threw away your + + + align:start position:0% +that information and you threw away your +ability to do that but you had it when + + align:start position:0% +ability to do that but you had it when + + + align:start position:0% +ability to do that but you had it when +you were six months old + + align:start position:0% +you were six months old + + + align:start position:0% +you were six months old +isn't that awesome and interesting + + align:start position:0% +isn't that awesome and interesting + + + align:start position:0% +isn't that awesome and interesting +okay that's called perceptual narrowing + + align:start position:0% +okay that's called perceptual narrowing + + + align:start position:0% +okay that's called perceptual narrowing +okay so the experiments in particular do + + align:start position:0% +okay so the experiments in particular do + + + align:start position:0% +okay so the experiments in particular do +the following you use that preferential + + align:start position:0% +the following you use that preferential + + + align:start position:0% +the following you use that preferential +looking paradigm + + align:start position:0% +looking paradigm + + + align:start position:0% +looking paradigm +the preferential looking to the novel + + align:start position:0% +the preferential looking to the novel + + + align:start position:0% +the preferential looking to the novel +face in infants as your measure of + + align:start position:0% +face in infants as your measure of + + + align:start position:0% +face in infants as your measure of +discrimination ability what can they + + align:start position:0% +discrimination ability what can they + + + align:start position:0% +discrimination ability what can they +discriminate okay and so you show two + + align:start position:0% +discriminate okay and so you show two + + + align:start position:0% +discriminate okay and so you show two +human faces two different individuals + + align:start position:0% +human faces two different individuals + + + align:start position:0% +human faces two different individuals +like this + + align:start position:0% +like this + + + align:start position:0% +like this +and so now uh what you see is that at + + align:start position:0% +and so now uh what you see is that at + + + align:start position:0% +and so now uh what you see is that at +six months nine months in adulthood uh + + align:start position:0% +six months nine months in adulthood uh + + + align:start position:0% +six months nine months in adulthood uh +people preferentially look to the + + align:start position:0% +people preferentially look to the + + + align:start position:0% +people preferentially look to the +um novel face more than the familiar + + align:start position:0% +um novel face more than the familiar + + + align:start position:0% +um novel face more than the familiar +face okay that's just what we've just + + align:start position:0% +face okay that's just what we've just + + + align:start position:0% +face okay that's just what we've just +done people like to look at the new + + align:start position:0% +done people like to look at the new + + + align:start position:0% +done people like to look at the new +thing not the old thing okay + + align:start position:0% +thing not the old thing okay + + + align:start position:0% +thing not the old thing okay +um + + align:start position:0% +um + + + align:start position:0% +um +however + + align:start position:0% +however + + + align:start position:0% +however +if we do six months nine months oh yeah + + align:start position:0% +if we do six months nine months oh yeah + + + align:start position:0% +if we do six months nine months oh yeah +that's what we just said okay they can + + align:start position:0% +that's what we just said okay they can + + + align:start position:0% +that's what we just said okay they can +do that so now if you try this on monkey + + align:start position:0% +do that so now if you try this on monkey + + + align:start position:0% +do that so now if you try this on monkey +faces + + align:start position:0% +faces + + + align:start position:0% +faces +you find that adults + + align:start position:0% +you find that adults + + + align:start position:0% +you find that adults +are like you know us we're barely able + + align:start position:0% +are like you know us we're barely able + + + align:start position:0% +are like you know us we're barely able +to tell the familiar from the novel + + align:start position:0% +to tell the familiar from the novel + + + align:start position:0% +to tell the familiar from the novel +we're not so good at monkey-faced + + align:start position:0% +we're not so good at monkey-faced + + + align:start position:0% +we're not so good at monkey-faced +discrimination + + align:start position:0% +discrimination + + + align:start position:0% +discrimination +nine-month-olds are the same + + align:start position:0% +nine-month-olds are the same + + + align:start position:0% +nine-month-olds are the same +but + + align:start position:0% +but + + + align:start position:0% +but +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +at six months + + align:start position:0% +at six months + + + align:start position:0% +at six months +infants can discriminate the monkey + + align:start position:0% +infants can discriminate the monkey + + + align:start position:0% +infants can discriminate the monkey +faces + + align:start position:0% +faces + + + align:start position:0% +faces +and you could too if somebody had asked + + align:start position:0% +and you could too if somebody had asked + + + align:start position:0% +and you could too if somebody had asked +you + + align:start position:0% +you + + + align:start position:0% +you +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +there's very similar phenomena with + + align:start position:0% +there's very similar phenomena with + + + align:start position:0% +there's very similar phenomena with +phonemes like those of you who are not + + align:start position:0% +phonemes like those of you who are not + + + align:start position:0% +phonemes like those of you who are not +native speakers of english may be aware + + align:start position:0% +native speakers of english may be aware + + + align:start position:0% +native speakers of english may be aware +of some phonemes in english if you + + align:start position:0% +of some phonemes in english if you + + + align:start position:0% +of some phonemes in english if you +learned it relatively late that are hard + + align:start position:0% +learned it relatively late that are hard + + + align:start position:0% +learned it relatively late that are hard +for you to discriminate + + align:start position:0% +for you to discriminate + + + align:start position:0% +for you to discriminate +um there are sounds in uh hindi i forget + + align:start position:0% +um there are sounds in uh hindi i forget + + + align:start position:0% +um there are sounds in uh hindi i forget +it's like a da and a ta that sound + + align:start position:0% +it's like a da and a ta that sound + + + align:start position:0% +it's like a da and a ta that sound +identical to me but that are just like + + align:start position:0% +identical to me but that are just like + + + align:start position:0% +identical to me but that are just like +completely obviously different to native + + align:start position:0% +completely obviously different to native + + + align:start position:0% +completely obviously different to native +hindi speakers + + align:start position:0% +hindi speakers + + + align:start position:0% +hindi speakers +and all languages have this so of the + + align:start position:0% +and all languages have this so of the + + + align:start position:0% +and all languages have this so of the +kinds of phonemes that are discriminated + + align:start position:0% +kinds of phonemes that are discriminated + + + align:start position:0% +kinds of phonemes that are discriminated +in any language in the world you could + + align:start position:0% +in any language in the world you could + + + align:start position:0% +in any language in the world you could +discriminate all of those when you were + + align:start position:0% +discriminate all of those when you were + + + align:start position:0% +discriminate all of those when you were +six months old + + align:start position:0% +six months old + + + align:start position:0% +six months old +and one of the things you do when you + + align:start position:0% +and one of the things you do when you + + + align:start position:0% +and one of the things you do when you +learn a language is just throw together + + align:start position:0% +learn a language is just throw together + + + align:start position:0% +learn a language is just throw together +in the same bag things that are actually + + align:start position:0% +in the same bag things that are actually + + + align:start position:0% +in the same bag things that are actually +different that other people can + + align:start position:0% +different that other people can + + + align:start position:0% +different that other people can +discriminate if your language doesn't + + align:start position:0% +discriminate if your language doesn't + + + align:start position:0% +discriminate if your language doesn't +discriminate + + align:start position:0% +discriminate + + + align:start position:0% +discriminate +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so you get that with phonemes and + + align:start position:0% +and so you get that with phonemes and + + + align:start position:0% +and so you get that with phonemes and +you get it with faces + + align:start position:0% +you get it with faces + + + align:start position:0% +you get it with faces +okay everybody get what perceptual + + align:start position:0% +okay everybody get what perceptual + + + align:start position:0% +okay everybody get what perceptual +narrowing is okay + + align:start position:0% +narrowing is okay + + + align:start position:0% +narrowing is okay +okay you also get this i mentioned this + + align:start position:0% +okay you also get this i mentioned this + + + align:start position:0% +okay you also get this i mentioned this +way back uh with perceiving faces of + + align:start position:0% +way back uh with perceiving faces of + + + align:start position:0% +way back uh with perceiving faces of +other races right not just faces of + + align:start position:0% +other races right not just faces of + + + align:start position:0% +other races right not just faces of +other species but if you grow up in an + + align:start position:0% +other species but if you grow up in an + + + align:start position:0% +other species but if you grow up in an +environment where you're + + align:start position:0% +environment where you're + + + align:start position:0% +environment where you're +uh only + + align:start position:0% +uh only + + + align:start position:0% +uh only +exposed to + + align:start position:0% +exposed to + + + align:start position:0% +exposed to +races a b and c and you later have to + + align:start position:0% +races a b and c and you later have to + + + align:start position:0% +races a b and c and you later have to +discriminate faces of races d e and f + + align:start position:0% +discriminate faces of races d e and f + + + align:start position:0% +discriminate faces of races d e and f +you're not so good at it + + align:start position:0% +you're not so good at it + + + align:start position:0% +you're not so good at it +right all the same deal okay + + align:start position:0% +right all the same deal okay + + + align:start position:0% +right all the same deal okay +um + + align:start position:0% +um + + + align:start position:0% +um +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so + + align:start position:0% +so + + + align:start position:0% +so +how would we know + + align:start position:0% +how would we know + + + align:start position:0% +how would we know +whether this change + + align:start position:0% +whether this change + + + align:start position:0% +whether this change +between six months and older + + align:start position:0% +between six months and older + + + align:start position:0% +between six months and older +is just maturation it's just some kind + + align:start position:0% +is just maturation it's just some kind + + + align:start position:0% +is just maturation it's just some kind +of developmental program that's going on + + align:start position:0% +of developmental program that's going on + + + align:start position:0% +of developmental program that's going on +on autopilot independent of what you see + + align:start position:0% +on autopilot independent of what you see + + + align:start position:0% +on autopilot independent of what you see +or whether it's learned from experience + + align:start position:0% + + + + align:start position:0% + +josh + + align:start position:0% +josh + + + align:start position:0% +josh +you control for experience absolutely + + align:start position:0% +you control for experience absolutely + + + align:start position:0% +you control for experience absolutely +like the sugita paper + + align:start position:0% +like the sugita paper + + + align:start position:0% +like the sugita paper +okay so we'll get to that in a second so + + align:start position:0% +okay so we'll get to that in a second so + + + align:start position:0% +okay so we'll get to that in a second so +we started with these key questions what + + align:start position:0% +we started with these key questions what + + + align:start position:0% +we started with these key questions what +is the initial state at birth and we + + align:start position:0% +is the initial state at birth and we + + + align:start position:0% +is the initial state at birth and we +showed impressive perceptual abilities + + align:start position:0% +showed impressive perceptual abilities + + + align:start position:0% +showed impressive perceptual abilities +within a few days + + align:start position:0% +within a few days + + + align:start position:0% +within a few days +although people dispute whether those + + align:start position:0% +although people dispute whether those + + + align:start position:0% +although people dispute whether those +abilities are a face-specific system + + align:start position:0% +abilities are a face-specific system + + + align:start position:0% +abilities are a face-specific system +and we don't know much about what that + + align:start position:0% +and we don't know much about what that + + + align:start position:0% +and we don't know much about what that +system is other than it works + + align:start position:0% +system is other than it works + + + align:start position:0% +system is other than it works +surprisingly well given the low acuity + + align:start position:0% +surprisingly well given the low acuity + + + align:start position:0% +surprisingly well given the low acuity +and we showed that how it changes after + + align:start position:0% +and we showed that how it changes after + + + align:start position:0% +and we showed that how it changes after +that there's perceptual narrowing + + align:start position:0% +that there's perceptual narrowing + + + align:start position:0% +that there's perceptual narrowing +between 6 and 12 months + + align:start position:0% +between 6 and 12 months + + + align:start position:0% +between 6 and 12 months +but a great deal is not known about what + + align:start position:0% +but a great deal is not known about what + + + align:start position:0% +but a great deal is not known about what +happens then and so now we're on to this + + align:start position:0% +happens then and so now we're on to this + + + align:start position:0% +happens then and so now we're on to this +question of how are we going to + + align:start position:0% +question of how are we going to + + + align:start position:0% +question of how are we going to +unconfound + + align:start position:0% +unconfound + + + align:start position:0% +unconfound +the what changes after birth whether + + align:start position:0% +the what changes after birth whether + + + align:start position:0% +the what changes after birth whether +it's maturation or experience + + align:start position:0% +it's maturation or experience + + + align:start position:0% +it's maturation or experience +and i'm not going to have time to get to + + align:start position:0% +and i'm not going to have time to get to + + + align:start position:0% +and i'm not going to have time to get to +these other awesome methods we're going + + align:start position:0% +these other awesome methods we're going + + + align:start position:0% +these other awesome methods we're going +to focus on controlled rearing of which + + align:start position:0% +to focus on controlled rearing of which + + + align:start position:0% +to focus on controlled rearing of which +you read the sugita paper okay + + align:start position:0% +you read the sugita paper okay + + + align:start position:0% +you read the sugita paper okay +so just to remind you of the basics most + + align:start position:0% +so just to remind you of the basics most + + + align:start position:0% +so just to remind you of the basics most +of you seem to get the paper just fine + + align:start position:0% +of you seem to get the paper just fine + + + align:start position:0% +of you seem to get the paper just fine +the big idea was again using this + + align:start position:0% +the big idea was again using this + + + align:start position:0% +the big idea was again using this +preferential looking method what sugita + + align:start position:0% +preferential looking method what sugita + + + align:start position:0% +preferential looking method what sugita +at all showed + + align:start position:0% +at all showed + + + align:start position:0% +at all showed +is that when they reared monkeys for six + + align:start position:0% +is that when they reared monkeys for six + + + align:start position:0% +is that when they reared monkeys for six +12 or 24 months without ever letting + + align:start position:0% +12 or 24 months without ever letting + + + align:start position:0% +12 or 24 months without ever letting +them see a face and then tested them on + + align:start position:0% +them see a face and then tested them on + + + align:start position:0% +them see a face and then tested them on +the very first session that they ever + + align:start position:0% +the very first session that they ever + + + align:start position:0% +the very first session that they ever +saw faces + + align:start position:0% +saw faces + + + align:start position:0% +saw faces +they found with prep preferential + + align:start position:0% +they found with prep preferential + + + align:start position:0% +they found with prep preferential +looking + + align:start position:0% +looking + + + align:start position:0% +looking +they found that on the very first + + align:start position:0% +they found that on the very first + + + align:start position:0% +they found that on the very first +exposure to faces the monkeys looked + + align:start position:0% +exposure to faces the monkeys looked + + + align:start position:0% +exposure to faces the monkeys looked +more at faces compared to novel objects + + align:start position:0% +more at faces compared to novel objects + + + align:start position:0% +more at faces compared to novel objects +right they showed that face preference + + align:start position:0% +right they showed that face preference + + + align:start position:0% +right they showed that face preference +sort of akin to the + + align:start position:0% +sort of akin to the + + + align:start position:0% +sort of akin to the +infants looking at the paddle + + align:start position:0% +infants looking at the paddle + + + align:start position:0% +infants looking at the paddle +and they discriminated between faces + + align:start position:0% +and they discriminated between faces + + + align:start position:0% +and they discriminated between faces +very similar faces with adult-like + + align:start position:0% +very similar faces with adult-like + + + align:start position:0% +very similar faces with adult-like +accuracy + + align:start position:0% +accuracy + + + align:start position:0% +accuracy +in this part i don't know if you found + + align:start position:0% +in this part i don't know if you found + + + align:start position:0% +in this part i don't know if you found +it surprising but when this paper came + + align:start position:0% +it surprising but when this paper came + + + align:start position:0% +it surprising but when this paper came +out i was like whoa + + align:start position:0% +out i was like whoa + + + align:start position:0% +out i was like whoa +that is crazy right because as i said + + align:start position:0% +that is crazy right because as i said + + + align:start position:0% +that is crazy right because as i said +the whole space of sensible hypotheses + + align:start position:0% +the whole space of sensible hypotheses + + + align:start position:0% +the whole space of sensible hypotheses +is okay maybe a lot of stuff is innate + + align:start position:0% +is okay maybe a lot of stuff is innate + + + align:start position:0% +is okay maybe a lot of stuff is innate +but you're still going to need + + align:start position:0% +but you're still going to need + + + align:start position:0% +but you're still going to need +experience to tone it up for god's sake + + align:start position:0% +experience to tone it up for god's sake + + + align:start position:0% +experience to tone it up for god's sake +right who would think the entire adult + + align:start position:0% +right who would think the entire adult + + + align:start position:0% +right who would think the entire adult +ability + + align:start position:0% +ability + + + align:start position:0% +ability +could exist without any experience at + + align:start position:0% +could exist without any experience at + + + align:start position:0% +could exist without any experience at +all so i don't know if you had that + + align:start position:0% +all so i don't know if you had that + + + align:start position:0% +all so i don't know if you had that +reaction but i think that's a sensible + + align:start position:0% +reaction but i think that's a sensible + + + align:start position:0% +reaction but i think that's a sensible +reaction it's a pretty astonishing + + align:start position:0% +reaction it's a pretty astonishing + + + align:start position:0% +reaction it's a pretty astonishing +finding in that paper + + align:start position:0% +finding in that paper + + + align:start position:0% +finding in that paper +unfortunately there's one author on that + + align:start position:0% +unfortunately there's one author on that + + + align:start position:0% +unfortunately there's one author on that +paper it was done once and it's such a + + align:start position:0% +paper it was done once and it's such a + + + align:start position:0% +paper it was done once and it's such a +labor-intensive study that probably + + align:start position:0% +labor-intensive study that probably + + + align:start position:0% +labor-intensive study that probably +nobody will ever try to replicate it so + + align:start position:0% +nobody will ever try to replicate it so + + + align:start position:0% +nobody will ever try to replicate it so +in the back of many people's minds is + + align:start position:0% +in the back of many people's minds is + + + align:start position:0% +in the back of many people's minds is +like really can that really be true or + + align:start position:0% +like really can that really be true or + + + align:start position:0% +like really can that really be true or +it's like is there something funny here + + align:start position:0% +it's like is there something funny here + + + align:start position:0% +it's like is there something funny here +so i hope somebody replicates it someday + + align:start position:0% +so i hope somebody replicates it someday + + + align:start position:0% +so i hope somebody replicates it someday +but + + align:start position:0% +but + + + align:start position:0% +but +um + + align:start position:0% +um + + + align:start position:0% +um +but it hasn't been done yet + + align:start position:0% +but it hasn't been done yet + + + align:start position:0% +but it hasn't been done yet +okay the other thing that you guys + + align:start position:0% +okay the other thing that you guys + + + align:start position:0% +okay the other thing that you guys +presumably noticed is there was + + align:start position:0% +presumably noticed is there was + + + align:start position:0% +presumably noticed is there was +perceptual narrowing in that study there + + align:start position:0% +perceptual narrowing in that study there + + + align:start position:0% +perceptual narrowing in that study there +were many interesting things in there + + align:start position:0% +were many interesting things in there + + + align:start position:0% +were many interesting things in there +it's actually quite a rich paper + + align:start position:0% +it's actually quite a rich paper + + + align:start position:0% +it's actually quite a rich paper +but after the initial testing session no + + align:start position:0% +but after the initial testing session no + + + align:start position:0% +but after the initial testing session no +matter how long the deprivation the + + align:start position:0% +matter how long the deprivation the + + + align:start position:0% +matter how long the deprivation the +monkeys were then housed in either an + + align:start position:0% +monkeys were then housed in either an + + + align:start position:0% +monkeys were then housed in either an +environment with just humans or just + + align:start position:0% +environment with just humans or just + + + align:start position:0% +environment with just humans or just +monkeys + + align:start position:0% +monkeys + + + align:start position:0% +monkeys +and so whether that was 6 12 or 24 + + align:start position:0% +and so whether that was 6 12 or 24 + + + align:start position:0% +and so whether that was 6 12 or 24 +months after birth alder all of face + + align:start position:0% +months after birth alder all of face + + + align:start position:0% +months after birth alder all of face +deprivation they then + + align:start position:0% +deprivation they then + + + align:start position:0% +deprivation they then +lost their ability at that point to + + align:start position:0% +lost their ability at that point to + + + align:start position:0% +lost their ability at that point to +discriminate the unexperienced faces + + align:start position:0% +discriminate the unexperienced faces + + + align:start position:0% +discriminate the unexperienced faces +okay so they went through perceptual + + align:start position:0% +okay so they went through perceptual + + + align:start position:0% +okay so they went through perceptual +narrowing did that all make sense to you + + align:start position:0% +narrowing did that all make sense to you + + + align:start position:0% +narrowing did that all make sense to you +guys you got that good + + align:start position:0% +guys you got that good + + + align:start position:0% +guys you got that good +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so anyway that suggests that + + align:start position:0% +all right so anyway that suggests that + + + align:start position:0% +all right so anyway that suggests that +an awful lot of the face perception + + align:start position:0% +an awful lot of the face perception + + + align:start position:0% +an awful lot of the face perception +system uh is present without any + + align:start position:0% +system uh is present without any + + + align:start position:0% +system uh is present without any +exposure to faces and that's pretty + + align:start position:0% +exposure to faces and that's pretty + + + align:start position:0% +exposure to faces and that's pretty +astonishing + + align:start position:0% +astonishing + + + align:start position:0% +astonishing +okay what experience seems to do there + + align:start position:0% +okay what experience seems to do there + + + align:start position:0% +okay what experience seems to do there +is not create abilities but eliminate + + align:start position:0% +is not create abilities but eliminate + + + align:start position:0% +is not create abilities but eliminate +them right for the + + align:start position:0% +them right for the + + + align:start position:0% +them right for the +species that you don't see + + align:start position:0% +species that you don't see + + + align:start position:0% +species that you don't see +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so first reaction really + + align:start position:0% +so first reaction really + + + align:start position:0% +so first reaction really +uh second reaction is there any way to + + align:start position:0% +uh second reaction is there any way to + + + align:start position:0% +uh second reaction is there any way to +account for this in terms of some + + align:start position:0% +account for this in terms of some + + + align:start position:0% +account for this in terms of some +non-phase specific system i think you + + align:start position:0% +non-phase specific system i think you + + + align:start position:0% +non-phase specific system i think you +can but it takes some work and the uh + + align:start position:0% +can but it takes some work and the uh + + + align:start position:0% +can but it takes some work and the uh +counter explanations are really + + align:start position:0% +counter explanations are really + + + align:start position:0% +counter explanations are really +difficult you could say well maybe this + + align:start position:0% +difficult you could say well maybe this + + + align:start position:0% +difficult you could say well maybe this +was all being carried by some more + + align:start position:0% +was all being carried by some more + + + align:start position:0% +was all being carried by some more +generic object system um they didn't + + align:start position:0% +generic object system um they didn't + + + align:start position:0% +generic object system um they didn't +test inverted faces unfortunately + + align:start position:0% +test inverted faces unfortunately + + + align:start position:0% +test inverted faces unfortunately +if but it was carried by a generic + + align:start position:0% +if but it was carried by a generic + + + align:start position:0% +if but it was carried by a generic +object system why would you find the + + align:start position:0% +object system why would you find the + + + align:start position:0% +object system why would you find the +perceptual narrowing why would they have + + align:start position:0% +perceptual narrowing why would they have + + + align:start position:0% +perceptual narrowing why would they have +lost their ability for the unexperienced + + align:start position:0% +lost their ability for the unexperienced + + + align:start position:0% +lost their ability for the unexperienced +species so i think that story is hard to + + align:start position:0% +species so i think that story is hard to + + + align:start position:0% +species so i think that story is hard to +tell + + align:start position:0% +tell + + + align:start position:0% +tell +and of course other question i'm sure + + align:start position:0% +and of course other question i'm sure + + + align:start position:0% +and of course other question i'm sure +you guys are wondering is what is going + + align:start position:0% +you guys are wondering is what is going + + + align:start position:0% +you guys are wondering is what is going +on in those monkeys brains yeah + + align:start position:0% +on in those monkeys brains yeah + + + align:start position:0% +on in those monkeys brains yeah +okay so let's get to that let's talk + + align:start position:0% +okay so let's get to that let's talk + + + align:start position:0% +okay so let's get to that let's talk +about what we know about development of + + align:start position:0% +about what we know about development of + + + align:start position:0% +about what we know about development of +this system by looking at brains um and + + align:start position:0% +this system by looking at brains um and + + + align:start position:0% +this system by looking at brains um and +first of all there's been lots of work + + align:start position:0% +first of all there's been lots of work + + + align:start position:0% +first of all there's been lots of work +on this in older kids age five and up + + align:start position:0% +on this in older kids age five and up + + + align:start position:0% +on this in older kids age five and up +going back uh over a decade + + align:start position:0% +going back uh over a decade + + + align:start position:0% +going back uh over a decade +it's now clear that all of that basic + + align:start position:0% +it's now clear that all of that basic + + + align:start position:0% +it's now clear that all of that basic +machinery i showed you is present by age + + align:start position:0% +machinery i showed you is present by age + + + align:start position:0% +machinery i showed you is present by age +five in most kids age five it's + + align:start position:0% +five in most kids age five it's + + + align:start position:0% +five in most kids age five it's +continuing to change after that but you + + align:start position:0% +continuing to change after that but you + + + align:start position:0% +continuing to change after that but you +can detect most of that stuff by age + + align:start position:0% +can detect most of that stuff by age + + + align:start position:0% +can detect most of that stuff by age +five or six or seven something like that + + align:start position:0% +five or six or seven something like that + + + align:start position:0% +five or six or seven something like that +okay + + align:start position:0% +okay + + + align:start position:0% +okay +trouble is that's cool but age five is + + align:start position:0% +trouble is that's cool but age five is + + + align:start position:0% +trouble is that's cool but age five is +late right with respect to experience + + align:start position:0% +late right with respect to experience + + + align:start position:0% +late right with respect to experience +and with respect to all those behavioral + + align:start position:0% +and with respect to all those behavioral + + + align:start position:0% +and with respect to all those behavioral +abilities that i showed you + + align:start position:0% +abilities that i showed you + + + align:start position:0% +abilities that i showed you +so uh we need to go earlier + + align:start position:0% +so uh we need to go earlier + + + align:start position:0% +so uh we need to go earlier +and so a couple years ago rebecca sacks + + align:start position:0% +and so a couple years ago rebecca sacks + + + align:start position:0% +and so a couple years ago rebecca sacks +who's + + align:start position:0% +who's + + + align:start position:0% +who's +straight up there two floors up + + align:start position:0% +straight up there two floors up + + + align:start position:0% +straight up there two floors up +um + + align:start position:0% +um + + + align:start position:0% +um +started scanning infants okay and this + + align:start position:0% +started scanning infants okay and this + + + align:start position:0% +started scanning infants okay and this +is as heather can tell you almost + + align:start position:0% +is as heather can tell you almost + + + align:start position:0% +is as heather can tell you almost +impossible + + align:start position:0% +impossible + + + align:start position:0% +impossible +it is right on the edge okay + + align:start position:0% +it is right on the edge okay + + + align:start position:0% +it is right on the edge okay +it took rebecca and her lab many many + + align:start position:0% +it took rebecca and her lab many many + + + align:start position:0% +it took rebecca and her lab many many +years of work over five years just to + + align:start position:0% +years of work over five years just to + + + align:start position:0% +years of work over five years just to +get the system going + + align:start position:0% +get the system going + + + align:start position:0% +get the system going +there were all kinds of technical + + align:start position:0% +there were all kinds of technical + + + align:start position:0% +there were all kinds of technical +advances like making scanning coils that + + align:start position:0% +advances like making scanning coils that + + + align:start position:0% +advances like making scanning coils that +were optimized for infants and + + align:start position:0% +were optimized for infants and + + + align:start position:0% +were optimized for infants and +comfortable for infants + + align:start position:0% +comfortable for infants + + + align:start position:0% +comfortable for infants +rebecca herself went to great lengths + + align:start position:0% +rebecca herself went to great lengths + + + align:start position:0% +rebecca herself went to great lengths +including + + align:start position:0% +including + + + align:start position:0% +including +producing some of her own subjects + + align:start position:0% +producing some of her own subjects + + + align:start position:0% +producing some of her own subjects +that's her son arthur there and her two + + align:start position:0% +that's her son arthur there and her two + + + align:start position:0% +that's her son arthur there and her two +um grad that her grad student in postdoc + + align:start position:0% +um grad that her grad student in postdoc + + + align:start position:0% +um grad that her grad student in postdoc +who were working with her + + align:start position:0% +who were working with her + + + align:start position:0% +who were working with her +um but all of this massive effort was + + align:start position:0% +um but all of this massive effort was + + + align:start position:0% +um but all of this massive effort was +worth it because what they found was + + align:start position:0% +worth it because what they found was + + + align:start position:0% +worth it because what they found was +first for comparison this is adults with + + align:start position:0% +first for comparison this is adults with + + + align:start position:0% +first for comparison this is adults with +a contrast of faces versus scenes okay + + align:start position:0% +a contrast of faces versus scenes okay + + + align:start position:0% +a contrast of faces versus scenes okay +so this is basically the ppa in blue + + align:start position:0% +so this is basically the ppa in blue + + + align:start position:0% +so this is basically the ppa in blue +responding more to scenes + + align:start position:0% +responding more to scenes + + + align:start position:0% +responding more to scenes +and the ffa in here and some other face + + align:start position:0% +and the ffa in here and some other face + + + align:start position:0% +and the ffa in here and some other face +selective bits responding more to faces + + align:start position:0% +selective bits responding more to faces + + + align:start position:0% +selective bits responding more to faces +and adults + + align:start position:0% +and adults + + + align:start position:0% +and adults +what do you see in six month old infants + + align:start position:0% +what do you see in six month old infants + + + align:start position:0% +what do you see in six month old infants +it's astonishingly similar + + align:start position:0% +it's astonishingly similar + + + align:start position:0% +it's astonishingly similar +right you can really see a very similar + + align:start position:0% +right you can really see a very similar + + + align:start position:0% +right you can really see a very similar +layout + + align:start position:0% +layout + + + align:start position:0% +layout +of the functional organization of the + + align:start position:0% +of the functional organization of the + + + align:start position:0% +of the functional organization of the +brain already by six months + + align:start position:0% +brain already by six months + + + align:start position:0% +brain already by six months +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's a huge advance that pushes way + + align:start position:0% +so that's a huge advance that pushes way + + + align:start position:0% +so that's a huge advance that pushes way +back the timeline + + align:start position:0% +back the timeline + + + align:start position:0% +back the timeline +by which these things had developed + + align:start position:0% +by which these things had developed + + + align:start position:0% +by which these things had developed +previously everybody's talking about oh + + align:start position:0% +previously everybody's talking about oh + + + align:start position:0% +previously everybody's talking about oh +what changes after age five age five + + align:start position:0% +what changes after age five age five + + + align:start position:0% +what changes after age five age five +come on okay it's mostly there by age + + align:start position:0% +come on okay it's mostly there by age + + + align:start position:0% +come on okay it's mostly there by age +six okay + + align:start position:0% +six okay + + + align:start position:0% +six okay +now importantly + + align:start position:0% +now importantly + + + align:start position:0% +now importantly +um though it's these systems are not + + align:start position:0% +um though it's these systems are not + + + align:start position:0% +um though it's these systems are not +adult-like their selectivities are very + + align:start position:0% +adult-like their selectivities are very + + + align:start position:0% +adult-like their selectivities are very +different those regions are less + + align:start position:0% +different those regions are less + + + align:start position:0% +different those regions are less +selective in infants than they are in + + align:start position:0% +selective in infants than they are in + + + align:start position:0% +selective in infants than they are in +adults but the spatial layout + + align:start position:0% +adults but the spatial layout + + + align:start position:0% +adults but the spatial layout +is there already by six months + + align:start position:0% +is there already by six months + + + align:start position:0% +is there already by six months +um + + align:start position:0% +um + + + align:start position:0% +um +and that importantly constrains whatever + + align:start position:0% +and that importantly constrains whatever + + + align:start position:0% +and that importantly constrains whatever +our model is of development that pushes + + align:start position:0% +our model is of development that pushes + + + align:start position:0% +our model is of development that pushes +it way back + + align:start position:0% +it way back + + + align:start position:0% +it way back +okay so now the next questions are + + align:start position:0% +okay so now the next questions are + + + align:start position:0% +okay so now the next questions are +what is it about that region or those + + align:start position:0% +what is it about that region or those + + + align:start position:0% +what is it about that region or those +particular regions that makes them + + align:start position:0% +particular regions that makes them + + + align:start position:0% +particular regions that makes them +become face specific right + + align:start position:0% +become face specific right + + + align:start position:0% +become face specific right +uh already by six months how do how does + + align:start position:0% +uh already by six months how do how does + + + align:start position:0% +uh already by six months how do how does +it how does the face system know to take + + align:start position:0% +it how does the face system know to take + + + align:start position:0% +it how does the face system know to take +up residence in that systematic location + + align:start position:0% +up residence in that systematic location + + + align:start position:0% +up residence in that systematic location +in the brain + + align:start position:0% +in the brain + + + align:start position:0% +in the brain +and what is the role of experience in + + align:start position:0% +and what is the role of experience in + + + align:start position:0% +and what is the role of experience in +their construction + + align:start position:0% +their construction + + + align:start position:0% +their construction +and how could we ever answer this + + align:start position:0% +and how could we ever answer this + + + align:start position:0% +and how could we ever answer this +and one way to answer that is to use an + + align:start position:0% +and one way to answer that is to use an + + + align:start position:0% +and one way to answer that is to use an +animal model okay + + align:start position:0% +animal model okay + + + align:start position:0% +animal model okay +so there's been yes + + align:start position:0% +so there's been yes + + + align:start position:0% +so there's been yes +can you ask a similar question about + + align:start position:0% +can you ask a similar question about + + + align:start position:0% +can you ask a similar question about +i sorry i didn't hear about what um + + align:start position:0% +i sorry i didn't hear about what um + + + align:start position:0% +i sorry i didn't hear about what um +general physical layout like why why + + align:start position:0% +general physical layout like why why + + + align:start position:0% +general physical layout like why why +does your stomach always come in the + + align:start position:0% +does your stomach always come in the + + + align:start position:0% +does your stomach always come in the +same place um and would it + + align:start position:0% +same place um and would it + + + align:start position:0% +same place um and would it +maybe be the same mechanism that uh + + align:start position:0% +maybe be the same mechanism that uh + + + align:start position:0% +maybe be the same mechanism that uh +guides like + + align:start position:0% +guides like + + + align:start position:0% +guides like +development of any organs and the layout + + align:start position:0% +development of any organs and the layout + + + align:start position:0% +development of any organs and the layout +of the body + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +now i don't know much about how hearts + + align:start position:0% +now i don't know much about how hearts + + + align:start position:0% +now i don't know much about how hearts +and kidneys and livers develop but my + + align:start position:0% +and kidneys and livers develop but my + + + align:start position:0% +and kidneys and livers develop but my +understanding is that's pretty much kind + + align:start position:0% +understanding is that's pretty much kind + + + align:start position:0% +understanding is that's pretty much kind +of wired in like there's some + + align:start position:0% +of wired in like there's some + + + align:start position:0% +of wired in like there's some +there's some + + align:start position:0% +there's some + + + align:start position:0% +there's some +chunks of dna that tell you how to build + + align:start position:0% +chunks of dna that tell you how to build + + + align:start position:0% +chunks of dna that tell you how to build +a kidney and where to put in your body + + align:start position:0% +a kidney and where to put in your body + + + align:start position:0% +a kidney and where to put in your body +right + + align:start position:0% +right + + + align:start position:0% +right +and so that is one of the hypotheses + + align:start position:0% +and so that is one of the hypotheses + + + align:start position:0% +and so that is one of the hypotheses +here it's a tempting hypothesis right + + align:start position:0% +here it's a tempting hypothesis right + + + align:start position:0% +here it's a tempting hypothesis right +there's all that structure it's a very + + align:start position:0% +there's all that structure it's a very + + + align:start position:0% +there's all that structure it's a very +tempting hypothesis + + align:start position:0% +tempting hypothesis + + + align:start position:0% +tempting hypothesis +but that doesn't mean it's necessarily + + align:start position:0% +but that doesn't mean it's necessarily + + + align:start position:0% +but that doesn't mean it's necessarily +right + + align:start position:0% +right + + + align:start position:0% +right +yeah it's absolutely it's it's a + + align:start position:0% +yeah it's absolutely it's it's a + + + align:start position:0% +yeah it's absolutely it's it's a +hypothesis we should consider and take + + align:start position:0% +hypothesis we should consider and take + + + align:start position:0% +hypothesis we should consider and take +seriously + + align:start position:0% +seriously + + + align:start position:0% +seriously +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so but we want data we want to find out + + align:start position:0% +so but we want data we want to find out + + + align:start position:0% +so but we want data we want to find out +okay so animal models + + align:start position:0% +okay so animal models + + + align:start position:0% +okay so animal models +so starting a few years ago marge + + align:start position:0% +so starting a few years ago marge + + + align:start position:0% +so starting a few years ago marge +livingstone over at harvard med school + + align:start position:0% +livingstone over at harvard med school + + + align:start position:0% +livingstone over at harvard med school +over there a couple miles over there + + align:start position:0% +over there a couple miles over there + + + align:start position:0% +over there a couple miles over there +started doing these also really + + align:start position:0% +started doing these also really + + + align:start position:0% +started doing these also really +amazingly heroic studies where she was + + align:start position:0% +amazingly heroic studies where she was + + + align:start position:0% +amazingly heroic studies where she was +scanning infant monkeys okay now this is + + align:start position:0% +scanning infant monkeys okay now this is + + + align:start position:0% +scanning infant monkeys okay now this is +really hard to read so let me tell you + + align:start position:0% +really hard to read so let me tell you + + + align:start position:0% +really hard to read so let me tell you +what we got here + + align:start position:0% +what we got here + + + align:start position:0% +what we got here +we have the cortex this is all the same + + align:start position:0% +we have the cortex this is all the same + + + align:start position:0% +we have the cortex this is all the same +animal at different time points in each + + align:start position:0% +animal at different time points in each + + + align:start position:0% +animal at different time points in each +of these things is the cortex unfolded + + align:start position:0% +of these things is the cortex unfolded + + + align:start position:0% +of these things is the cortex unfolded +mathematically and flattened so you can + + align:start position:0% +mathematically and flattened so you can + + + align:start position:0% +mathematically and flattened so you can +see the whole thing i don't expect you + + align:start position:0% +see the whole thing i don't expect you + + + align:start position:0% +see the whole thing i don't expect you +to know what's where i can barely tell + + align:start position:0% +to know what's where i can barely tell + + + align:start position:0% +to know what's where i can barely tell +myself + + align:start position:0% +myself + + + align:start position:0% +myself +uh but if you look at it what you see is + + align:start position:0% +uh but if you look at it what you see is + + + align:start position:0% +uh but if you look at it what you see is +at 81 days of age there's just blue + + align:start position:0% +at 81 days of age there's just blue + + + align:start position:0% +at 81 days of age there's just blue +stuff there's no orange stuff the orange + + align:start position:0% +stuff there's no orange stuff the orange + + + align:start position:0% +stuff there's no orange stuff the orange +stuff is the face selective response in + + align:start position:0% +stuff is the face selective response in + + + align:start position:0% +stuff is the face selective response in +fact if you look down you start to see + + align:start position:0% +fact if you look down you start to see + + + align:start position:0% +fact if you look down you start to see +oh that looks yeah yeah okay that looks + + align:start position:0% +oh that looks yeah yeah okay that looks + + + align:start position:0% +oh that looks yeah yeah okay that looks +pretty systematic starts replicating + + align:start position:0% +pretty systematic starts replicating + + + align:start position:0% +pretty systematic starts replicating +after that + + align:start position:0% +after that + + + align:start position:0% +after that +okay and so the claim is you don't see + + align:start position:0% +okay and so the claim is you don't see + + + align:start position:0% +okay and so the claim is you don't see +face selectivity until about 170 days + + align:start position:0% +face selectivity until about 170 days + + + align:start position:0% +face selectivity until about 170 days +after birth in monkeys okay that's about + + align:start position:0% +after birth in monkeys okay that's about + + + align:start position:0% +after birth in monkeys okay that's about +here here's another monkey for + + align:start position:0% +here here's another monkey for + + + align:start position:0% +here here's another monkey for +comparison if you stare at it you'll see + + align:start position:0% +comparison if you stare at it you'll see + + + align:start position:0% +comparison if you stare at it you'll see +okay there's these systematic bits boom + + align:start position:0% +okay there's these systematic bits boom + + + align:start position:0% +okay there's these systematic bits boom +boom boom boom + + align:start position:0% +boom boom boom + + + align:start position:0% +boom boom boom +and maybe a little hint at 170 but you + + align:start position:0% +and maybe a little hint at 170 but you + + + align:start position:0% +and maybe a little hint at 170 but you +know there's some garbage up there but + + align:start position:0% +know there's some garbage up there but + + + align:start position:0% +know there's some garbage up there but +nothing systematic before that + + align:start position:0% +nothing systematic before that + + + align:start position:0% +nothing systematic before that +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so there's no control over here of the + + align:start position:0% +so there's no control over here of the + + + align:start position:0% +so there's no control over here of the +environment this is like monkeys normal + + align:start position:0% +environment this is like monkeys normal + + + align:start position:0% +environment this is like monkeys normal +monkeys who have exposure to human faces + + align:start position:0% +monkeys who have exposure to human faces + + + align:start position:0% +monkeys who have exposure to human faces +and monkey faces hanging out in the lab + + align:start position:0% +and monkey faces hanging out in the lab + + + align:start position:0% +and monkey faces hanging out in the lab +yeah we haven't gone to controlled + + align:start position:0% +yeah we haven't gone to controlled + + + align:start position:0% +yeah we haven't gone to controlled +hearing yet it's coming okay first thing + + align:start position:0% +hearing yet it's coming okay first thing + + + align:start position:0% +hearing yet it's coming okay first thing +is just when does it develop in monkeys + + align:start position:0% +is just when does it develop in monkeys + + + align:start position:0% +is just when does it develop in monkeys +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so + + align:start position:0% +all right so + + + align:start position:0% +all right so +are you surprised by this + + align:start position:0% +are you surprised by this + + + align:start position:0% +are you surprised by this +it's not there here it is there there + + align:start position:0% +it's not there here it is there there + + + align:start position:0% +it's not there here it is there there +you should be surprised why are you + + align:start position:0% +you should be surprised why are you + + + align:start position:0% +you should be surprised why are you +surprised + + align:start position:0% + + + + align:start position:0% + +is this what you guys predicted quietly + + align:start position:0% +is this what you guys predicted quietly + + + align:start position:0% +is this what you guys predicted quietly +i guess you surprised me uh + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +what is up with that + + align:start position:0% +what is up with that + + + align:start position:0% +what is up with that +absolutely + + align:start position:0% +absolutely + + + align:start position:0% +absolutely +the sugita paper really made it look + + align:start position:0% +the sugita paper really made it look + + + align:start position:0% +the sugita paper really made it look +like that system was innate right no + + align:start position:0% +like that system was innate right no + + + align:start position:0% +like that system was innate right no +experience boom they're fine it was just + + align:start position:0% +experience boom they're fine it was just + + + align:start position:0% +experience boom they're fine it was just +behavior but it was a good behavioral + + align:start position:0% +behavior but it was a good behavioral + + + align:start position:0% +behavior but it was a good behavioral +study so why the hell isn't it here + + align:start position:0% + + + + align:start position:0% + +everybody with the program how + + align:start position:0% +everybody with the program how + + + align:start position:0% +everybody with the program how +surprising that is + + align:start position:0% +surprising that is + + + align:start position:0% +surprising that is +um okay so a bunch of things + + align:start position:0% +um okay so a bunch of things + + + align:start position:0% +um okay so a bunch of things +first of all and it gets stable after + + align:start position:0% +first of all and it gets stable after + + + align:start position:0% +first of all and it gets stable after +that right and and replicable well the + + align:start position:0% +that right and and replicable well the + + + align:start position:0% +that right and and replicable well the +first thing is one's a behavioral + + align:start position:0% +first thing is one's a behavioral + + + align:start position:0% +first thing is one's a behavioral +measure and one's a neural measure + + align:start position:0% +measure and one's a neural measure + + + align:start position:0% +measure and one's a neural measure +maybe those fabulous behavioral measures + + align:start position:0% +maybe those fabulous behavioral measures + + + align:start position:0% +maybe those fabulous behavioral measures +weren't actually being driven by some + + align:start position:0% +weren't actually being driven by some + + + align:start position:0% +weren't actually being driven by some +phase specific system wouldn't that be + + align:start position:0% +phase specific system wouldn't that be + + + align:start position:0% +phase specific system wouldn't that be +sad right i mean they did lots of + + align:start position:0% +sad right i mean they did lots of + + + align:start position:0% +sad right i mean they did lots of +controls it was a nice idea i thought + + align:start position:0% +controls it was a nice idea i thought + + + align:start position:0% +controls it was a nice idea i thought +they did as well as they could but who + + align:start position:0% +they did as well as they could but who + + + align:start position:0% +they did as well as they could but who +knows maybe + + align:start position:0% +knows maybe + + + align:start position:0% +knows maybe +those monkeys could do that task with + + align:start position:0% +those monkeys could do that task with + + + align:start position:0% +those monkeys could do that task with +some other system and they didn't need + + align:start position:0% +some other system and they didn't need + + + align:start position:0% +some other system and they didn't need +their face system for it that's one + + align:start position:0% +their face system for it that's one + + + align:start position:0% +their face system for it that's one +possibility right then you could have + + align:start position:0% +possibility right then you could have + + + align:start position:0% +possibility right then you could have +the face system not develop till later + + align:start position:0% +the face system not develop till later + + + align:start position:0% +the face system not develop till later +but the monkeys could do it before + + align:start position:0% +but the monkeys could do it before + + + align:start position:0% +but the monkeys could do it before +but the other thing is + + align:start position:0% +but the other thing is + + + align:start position:0% +but the other thing is +noticed that sugita didn't test their + + align:start position:0% +noticed that sugita didn't test their + + + align:start position:0% +noticed that sugita didn't test their +monkeys until + + align:start position:0% +monkeys until + + + align:start position:0% +monkeys until +that the youngest ones six months of age + + align:start position:0% +that the youngest ones six months of age + + + align:start position:0% +that the youngest ones six months of age +so maybe + + align:start position:0% +so maybe + + + align:start position:0% +so maybe +um it just got wired up just before + + align:start position:0% +um it just got wired up just before + + + align:start position:0% +um it just got wired up just before +right there right they were tested okay + + align:start position:0% +right there right they were tested okay + + + align:start position:0% +right there right they were tested okay +so it seemed contradictory at first but + + align:start position:0% +so it seemed contradictory at first but + + + align:start position:0% +so it seemed contradictory at first but +it's not completely literally + + align:start position:0% +it's not completely literally + + + align:start position:0% +it's not completely literally +contradictory + + align:start position:0% +contradictory + + + align:start position:0% +contradictory +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +all right so now + + align:start position:0% +all right so now + + + align:start position:0% +all right so now +the fact that this stuff doesn't show up + + align:start position:0% +the fact that this stuff doesn't show up + + + align:start position:0% +the fact that this stuff doesn't show up +until here + + align:start position:0% +until here + + + align:start position:0% +until here +does that mean that this face system + + align:start position:0% +does that mean that this face system + + + align:start position:0% +does that mean that this face system +requires experience to develop + + align:start position:0% + + + + align:start position:0% + +you know the answer because whenever i + + align:start position:0% +you know the answer because whenever i + + + align:start position:0% +you know the answer because whenever i +ask that question the answer is always + + align:start position:0% +ask that question the answer is always + + + align:start position:0% +ask that question the answer is always +no why does it why does that not imply + + align:start position:0% +no why does it why does that not imply + + + align:start position:0% +no why does it why does that not imply +that you need experience with faces to + + align:start position:0% +that you need experience with faces to + + + align:start position:0% +that you need experience with faces to +wire up it's tempting you look at it's + + align:start position:0% +wire up it's tempting you look at it's + + + align:start position:0% +wire up it's tempting you look at it's +like okay you had to look at faces all + + align:start position:0% +like okay you had to look at faces all + + + align:start position:0% +like okay you had to look at faces all +this time before you wired it up but + + align:start position:0% +this time before you wired it up but + + + align:start position:0% +this time before you wired it up but +there it is very tempting + + align:start position:0% +there it is very tempting + + + align:start position:0% +there it is very tempting +but is it jessica no + + align:start position:0% +but is it jessica no + + + align:start position:0% +but is it jessica no +so what's your name + + align:start position:0% + + + + align:start position:0% + +bailey oh sorry you told me that like + + align:start position:0% +bailey oh sorry you told me that like + + + align:start position:0% +bailey oh sorry you told me that like +six times + + align:start position:0% +six times + + + align:start position:0% +six times +merely + + align:start position:0% +merely + + + align:start position:0% +merely +due to + + align:start position:0% +due to + + + align:start position:0% +due to +i'm sure physical yeah could be just + + align:start position:0% +i'm sure physical yeah could be just + + + align:start position:0% +i'm sure physical yeah could be just +maturation i keep making the same point + + align:start position:0% +maturation i keep making the same point + + + align:start position:0% +maturation i keep making the same point +because it's important + + align:start position:0% +because it's important + + + align:start position:0% +because it's important +right just because it shows up later + + align:start position:0% +right just because it shows up later + + + align:start position:0% +right just because it shows up later +doesn't mean it's learned + + align:start position:0% +doesn't mean it's learned + + + align:start position:0% +doesn't mean it's learned +right maybe it's like puberty or height + + align:start position:0% +right maybe it's like puberty or height + + + align:start position:0% +right maybe it's like puberty or height +or something like that it's on some + + align:start position:0% +or something like that it's on some + + + align:start position:0% +or something like that it's on some +developmental program that's just going + + align:start position:0% +developmental program that's just going + + + align:start position:0% +developmental program that's just going +to unfold independent of what you see + + align:start position:0% +to unfold independent of what you see + + + align:start position:0% +to unfold independent of what you see +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +how would we find out + + align:start position:0% +how would we find out + + + align:start position:0% +how would we find out +we would do controlled rearing and + + align:start position:0% +we would do controlled rearing and + + + align:start position:0% +we would do controlled rearing and +that's exactly what these guys did + + align:start position:0% +that's exactly what these guys did + + + align:start position:0% +that's exactly what these guys did +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so in another paper that just came out a + + align:start position:0% +so in another paper that just came out a + + + align:start position:0% +so in another paper that just came out a +couple years ago + + align:start position:0% +couple years ago + + + align:start position:0% +couple years ago +they raised baby monkeys without ever + + align:start position:0% +they raised baby monkeys without ever + + + align:start position:0% +they raised baby monkeys without ever +letting them see a face much like sugita + + align:start position:0% +letting them see a face much like sugita + + + align:start position:0% +letting them see a face much like sugita +did they use welder's masks every time + + align:start position:0% +did they use welder's masks every time + + + align:start position:0% +did they use welder's masks every time +they were in the lab so the monkeys + + align:start position:0% +they were in the lab so the monkeys + + + align:start position:0% +they were in the lab so the monkeys +never got to see faces + + align:start position:0% +never got to see faces + + + align:start position:0% +never got to see faces +and like sugita they went to lengths to + + align:start position:0% +and like sugita they went to lengths to + + + align:start position:0% +and like sugita they went to lengths to +treat the monkeys nicely they heard the + + align:start position:0% +treat the monkeys nicely they heard the + + + align:start position:0% +treat the monkeys nicely they heard the +calls of their con specifics they got + + align:start position:0% +calls of their con specifics they got + + + align:start position:0% +calls of their con specifics they got +lots of attention they had rich visual + + align:start position:0% +lots of attention they had rich visual + + + align:start position:0% +lots of attention they had rich visual +experience they just didn't see faces so + + align:start position:0% +experience they just didn't see faces so + + + align:start position:0% +experience they just didn't see faces so +it sounds kind of tragic and horrible at + + align:start position:0% +it sounds kind of tragic and horrible at + + + align:start position:0% +it sounds kind of tragic and horrible at +first but it's actually not that bad + + align:start position:0% +first but it's actually not that bad + + + align:start position:0% +first but it's actually not that bad +they had social contact and visual + + align:start position:0% +they had social contact and visual + + + align:start position:0% +they had social contact and visual +experience they just never saw faces + + align:start position:0% +experience they just never saw faces + + + align:start position:0% +experience they just never saw faces +okay + + align:start position:0% +okay + + + align:start position:0% +okay +both this study and the sugita study all + + align:start position:0% +both this study and the sugita study all + + + align:start position:0% +both this study and the sugita study all +right + + align:start position:0% +right + + + align:start position:0% +right +okay so they can hear and smell other + + align:start position:0% +okay so they can hear and smell other + + + align:start position:0% +okay so they can hear and smell other +monkeys + + align:start position:0% +monkeys + + + align:start position:0% +monkeys +um + + align:start position:0% +um + + + align:start position:0% +um +so the face deprived monkeys saw no + + align:start position:0% +so the face deprived monkeys saw no + + + align:start position:0% +so the face deprived monkeys saw no +faces at all until 90 days old and at + + align:start position:0% +faces at all until 90 days old and at + + + align:start position:0% +faces at all until 90 days old and at +that point they went straight into the + + align:start position:0% +that point they went straight into the + + + align:start position:0% +that point they went straight into the +scanner okay and the first time they saw + + align:start position:0% +scanner okay and the first time they saw + + + align:start position:0% +scanner okay and the first time they saw +faces was inside an mri machine getting + + align:start position:0% +faces was inside an mri machine getting + + + align:start position:0% +faces was inside an mri machine getting +scanned okay + + align:start position:0% +scanned okay + + + align:start position:0% +scanned okay +so what do you think are the face + + align:start position:0% +so what do you think are the face + + + align:start position:0% +so what do you think are the face +deprived monkeys gonna show face patches + + align:start position:0% + + + + align:start position:0% + +so there's no way to tell because we + + align:start position:0% +so there's no way to tell because we + + + align:start position:0% +so there's no way to tell because we +have all these contradictory bits of + + align:start position:0% +have all these contradictory bits of + + + align:start position:0% +have all these contradictory bits of +evidence here + + align:start position:0% +evidence here + + + align:start position:0% +evidence here +right + + align:start position:0% +right + + + align:start position:0% +right +from sugita you might think yes + + align:start position:0% + + + + align:start position:0% + +hard to tell so let's just look at the + + align:start position:0% +hard to tell so let's just look at the + + + align:start position:0% +hard to tell so let's just look at the +data okay so here first is a normally + + align:start position:0% +data okay so here first is a normally + + + align:start position:0% +data okay so here first is a normally +um normally reared monkey 260 days old + + align:start position:0% +um normally reared monkey 260 days old + + + align:start position:0% +um normally reared monkey 260 days old +just for comparison and those are those + + align:start position:0% +just for comparison and those are those + + + align:start position:0% +just for comparison and those are those +face patches in yellow + + align:start position:0% +face patches in yellow + + + align:start position:0% +face patches in yellow +in + + align:start position:0% +in + + + align:start position:0% +in +two different monkeys here b4 and b5 + + align:start position:0% +two different monkeys here b4 and b5 + + + align:start position:0% +two different monkeys here b4 and b5 +left and right hemisphere okay so those + + align:start position:0% +left and right hemisphere okay so those + + + align:start position:0% +left and right hemisphere okay so those +yellow bits are the face patches okay + + align:start position:0% +yellow bits are the face patches okay + + + align:start position:0% +yellow bits are the face patches okay +normal 260 day old monkey now we're + + align:start position:0% +normal 260 day old monkey now we're + + + align:start position:0% +normal 260 day old monkey now we're +going to see a face deprived monkey 260 + + align:start position:0% +going to see a face deprived monkey 260 + + + align:start position:0% +going to see a face deprived monkey 260 +days old this monkey was face deprived + + align:start position:0% +days old this monkey was face deprived + + + align:start position:0% +days old this monkey was face deprived +that entire time + + align:start position:0% +that entire time + + + align:start position:0% +that entire time +up until scanning + + align:start position:0% +up until scanning + + + align:start position:0% +up until scanning +no face patches + + align:start position:0% +no face patches + + + align:start position:0% +no face patches +the plot thickens + + align:start position:0% + + + + align:start position:0% + +no face patches at all + + align:start position:0% +no face patches at all + + + align:start position:0% +no face patches at all +so these guys published this paper in a + + align:start position:0% +so these guys published this paper in a + + + align:start position:0% +so these guys published this paper in a +very high profile journal and said that + + align:start position:0% +very high profile journal and said that + + + align:start position:0% +very high profile journal and said that +this is the title of the paper seeing + + align:start position:0% +this is the title of the paper seeing + + + align:start position:0% +this is the title of the paper seeing +faces is necessary for face domain + + align:start position:0% +faces is necessary for face domain + + + align:start position:0% +faces is necessary for face domain +formation + + align:start position:0% +formation + + + align:start position:0% +formation +okay face domain just means face + + align:start position:0% +okay face domain just means face + + + align:start position:0% +okay face domain just means face +selective patch + + align:start position:0% +selective patch + + + align:start position:0% +selective patch +okay + + align:start position:0% +okay + + + align:start position:0% +okay +everybody see + + align:start position:0% +everybody see + + + align:start position:0% +everybody see +you deprive them of face experience you + + align:start position:0% +you deprive them of face experience you + + + align:start position:0% +you deprive them of face experience you +don't see it + + align:start position:0% +don't see it + + + align:start position:0% +don't see it +okay that's pretty interesting + + align:start position:0% +okay that's pretty interesting + + + align:start position:0% +okay that's pretty interesting +um and it strongly suggests that the + + align:start position:0% +um and it strongly suggests that the + + + align:start position:0% +um and it strongly suggests that the +face system is not an a but depends on + + align:start position:0% +face system is not an a but depends on + + + align:start position:0% +face system is not an a but depends on +face experience + + align:start position:0% +face experience + + + align:start position:0% +face experience +doesn't it + + align:start position:0% + + + + align:start position:0% + +rare casework the answer is yes it does + + align:start position:0% +rare casework the answer is yes it does + + + align:start position:0% +rare casework the answer is yes it does +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh and it feels like it contradicts the + + align:start position:0% +uh and it feels like it contradicts the + + + align:start position:0% +uh and it feels like it contradicts the +sugita finding right + + align:start position:0% +sugita finding right + + + align:start position:0% +sugita finding right +but not exactly you could still wiggle + + align:start position:0% +but not exactly you could still wiggle + + + align:start position:0% +but not exactly you could still wiggle +out of it right you could say okay + + align:start position:0% +out of it right you could say okay + + + align:start position:0% +out of it right you could say okay +the thing that sugita was studying + + align:start position:0% +the thing that sugita was studying + + + align:start position:0% +the thing that sugita was studying +doesn't use those patches so it's not + + align:start position:0% +doesn't use those patches so it's not + + + align:start position:0% +doesn't use those patches so it's not +flat out contradictory sugita was + + align:start position:0% +flat out contradictory sugita was + + + align:start position:0% +flat out contradictory sugita was +measuring behavior these guys are + + align:start position:0% +measuring behavior these guys are + + + align:start position:0% +measuring behavior these guys are +looking at brains it's kind of + + align:start position:0% +looking at brains it's kind of + + + align:start position:0% +looking at brains it's kind of +unsatisfying but it's in principle + + align:start position:0% +unsatisfying but it's in principle + + + align:start position:0% +unsatisfying but it's in principle +possible + + align:start position:0% +possible + + + align:start position:0% +possible +me and everyone else has been nudging + + align:start position:0% +me and everyone else has been nudging + + + align:start position:0% +me and everyone else has been nudging +these guys to run the sugita behavioral + + align:start position:0% +these guys to run the sugita behavioral + + + align:start position:0% +these guys to run the sugita behavioral +experiment on your monkeys please + + align:start position:0% +experiment on your monkeys please + + + align:start position:0% +experiment on your monkeys please +and i gather that's getting going but i + + align:start position:0% +and i gather that's getting going but i + + + align:start position:0% +and i gather that's getting going but i +haven't seen any of the data yet + + align:start position:0% +haven't seen any of the data yet + + + align:start position:0% +haven't seen any of the data yet +yeah so we don't know how that's going + + align:start position:0% +yeah so we don't know how that's going + + + align:start position:0% +yeah so we don't know how that's going +to result okay so let's take stock what + + align:start position:0% +to result okay so let's take stock what + + + align:start position:0% +to result okay so let's take stock what +is what is the initial state we show + + align:start position:0% +is what is the initial state we show + + + align:start position:0% +is what is the initial state we show +with behavior that there is both + + align:start position:0% +with behavior that there is both + + + align:start position:0% +with behavior that there is both +attention to faces and um + + align:start position:0% +attention to faces and um + + + align:start position:0% +attention to faces and um +in present in newborn humans and face + + align:start position:0% +in present in newborn humans and face + + + align:start position:0% +in present in newborn humans and face +specificity seems like it but it's not + + align:start position:0% +specificity seems like it but it's not + + + align:start position:0% +specificity seems like it but it's not +totally nailed + + align:start position:0% +totally nailed + + + align:start position:0% +totally nailed +uh whereas functional mri says there's + + align:start position:0% +uh whereas functional mri says there's + + + align:start position:0% +uh whereas functional mri says there's +no evidence for face specificity at + + align:start position:0% +no evidence for face specificity at + + + align:start position:0% +no evidence for face specificity at +birth at least in monkeys right that's + + align:start position:0% +birth at least in monkeys right that's + + + align:start position:0% +birth at least in monkeys right that's +other + + align:start position:0% +other + + + align:start position:0% +other +yeah okay so how are we going to + + align:start position:0% +yeah okay so how are we going to + + + align:start position:0% +yeah okay so how are we going to +reconcile this with all the behavioral + + align:start position:0% +reconcile this with all the behavioral + + + align:start position:0% +reconcile this with all the behavioral +results i showed you that there seems to + + align:start position:0% +results i showed you that there seems to + + + align:start position:0% +results i showed you that there seems to +be a lot of face abilities present in + + align:start position:0% +be a lot of face abilities present in + + + align:start position:0% +be a lot of face abilities present in +newborns + + align:start position:0% +newborns + + + align:start position:0% +newborns +well one possibility is that face + + align:start position:0% +well one possibility is that face + + + align:start position:0% +well one possibility is that face +specificity exists that behaviorally + + align:start position:0% +specificity exists that behaviorally + + + align:start position:0% +specificity exists that behaviorally +but mri feels oh sorry phase specificity + + align:start position:0% +but mri feels oh sorry phase specificity + + + align:start position:0% +but mri feels oh sorry phase specificity +exists in the brain but mri fails to + + align:start position:0% +exists in the brain but mri fails to + + + align:start position:0% +exists in the brain but mri fails to +detect it + + align:start position:0% +detect it + + + align:start position:0% +detect it +right there's a whole rhythm rule about + + align:start position:0% +right there's a whole rhythm rule about + + + align:start position:0% +right there's a whole rhythm rule about +whether functional mri works well in + + align:start position:0% +whether functional mri works well in + + + align:start position:0% +whether functional mri works well in +infants it's barely possible as i + + align:start position:0% +infants it's barely possible as i + + + align:start position:0% +infants it's barely possible as i +mentioned it's also hard with infant + + align:start position:0% +mentioned it's also hard with infant + + + align:start position:0% +mentioned it's also hard with infant +monkeys their blood flow regulation is + + align:start position:0% +monkeys their blood flow regulation is + + + align:start position:0% +monkeys their blood flow regulation is +different they're squirming and wiggling + + align:start position:0% +different they're squirming and wiggling + + + align:start position:0% +different they're squirming and wiggling +there are a million issues with scanning + + align:start position:0% +there are a million issues with scanning + + + align:start position:0% +there are a million issues with scanning +babies whether human or monkey and so + + align:start position:0% +babies whether human or monkey and so + + + align:start position:0% +babies whether human or monkey and so +you could always say well it was there + + align:start position:0% +you could always say well it was there + + + align:start position:0% +you could always say well it was there +and just the mri data are just kind of + + align:start position:0% +and just the mri data are just kind of + + + align:start position:0% +and just the mri data are just kind of +crappy or blood flow regulation to the + + align:start position:0% +crappy or blood flow regulation to the + + + align:start position:0% +crappy or blood flow regulation to the +brain develops later an argument many + + align:start position:0% +brain develops later an argument many + + + align:start position:0% +brain develops later an argument many +people have made + + align:start position:0% +people have made + + + align:start position:0% +people have made +however a paper was published last week + + align:start position:0% +however a paper was published last week + + + align:start position:0% +however a paper was published last week +that argues against that hypothesis + + align:start position:0% +that argues against that hypothesis + + + align:start position:0% +that argues against that hypothesis +the same group just showed that the + + align:start position:0% +the same group just showed that the + + + align:start position:0% +the same group just showed that the +sonata sensory touch system + + align:start position:0% +sonata sensory touch system + + + align:start position:0% +sonata sensory touch system +is totally in place by 11 days in baby + + align:start position:0% +is totally in place by 11 days in baby + + + align:start position:0% +is totally in place by 11 days in baby +monkeys + + align:start position:0% +monkeys + + + align:start position:0% +monkeys +so that suggests that you can get really + + align:start position:0% +so that suggests that you can get really + + + align:start position:0% +so that suggests that you can get really +nice functional mri data at 11 days of + + align:start position:0% +nice functional mri data at 11 days of + + + align:start position:0% +nice functional mri data at 11 days of +age in baby monkeys and it makes it less + + align:start position:0% +age in baby monkeys and it makes it less + + + align:start position:0% +age in baby monkeys and it makes it less +likely that this is some kind of + + align:start position:0% +likely that this is some kind of + + + align:start position:0% +likely that this is some kind of +spurious failure to detect something + + align:start position:0% +spurious failure to detect something + + + align:start position:0% +spurious failure to detect something +that was actually there + + align:start position:0% +that was actually there + + + align:start position:0% +that was actually there +okay + + align:start position:0% +okay + + + align:start position:0% +okay +i'm not going to test you on every + + align:start position:0% +i'm not going to test you on every + + + align:start position:0% +i'm not going to test you on every +little detail here i want you to think + + align:start position:0% +little detail here i want you to think + + + align:start position:0% +little detail here i want you to think +about the logic of how you can ask these + + align:start position:0% +about the logic of how you can ask these + + + align:start position:0% +about the logic of how you can ask these +questions okay + + align:start position:0% +questions okay + + + align:start position:0% +questions okay +um okay the other possibility is that + + align:start position:0% +um okay the other possibility is that + + + align:start position:0% +um okay the other possibility is that +the face abilities that we showed + + align:start position:0% +the face abilities that we showed + + + align:start position:0% +the face abilities that we showed +behaviorally are using some more generic + + align:start position:0% +behaviorally are using some more generic + + + align:start position:0% +behaviorally are using some more generic +object recognition system not using this + + align:start position:0% +object recognition system not using this + + + align:start position:0% +object recognition system not using this +face selective system in the brain + + align:start position:0% +face selective system in the brain + + + align:start position:0% +face selective system in the brain +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so how does it change over time well we + + align:start position:0% +so how does it change over time well we + + + align:start position:0% +so how does it change over time well we +showed that behaviorally in humans at + + align:start position:0% +showed that behaviorally in humans at + + + align:start position:0% +showed that behaviorally in humans at +least all the hallmarks of + + align:start position:0% +least all the hallmarks of + + + align:start position:0% +least all the hallmarks of +phase-specific processing are present by + + align:start position:0% +phase-specific processing are present by + + + align:start position:0% +phase-specific processing are present by +h4 and we get this perceptual narrowing + + align:start position:0% +h4 and we get this perceptual narrowing + + + align:start position:0% +h4 and we get this perceptual narrowing +between 6 and 12 months + + align:start position:0% +between 6 and 12 months + + + align:start position:0% +between 6 and 12 months +but then we show that with functional + + align:start position:0% +but then we show that with functional + + + align:start position:0% +but then we show that with functional +mri at least in monkeys there's no + + align:start position:0% +mri at least in monkeys there's no + + + align:start position:0% +mri at least in monkeys there's no +evidence for face specificity before 200 + + align:start position:0% +evidence for face specificity before 200 + + + align:start position:0% +evidence for face specificity before 200 +days + + align:start position:0% + + + + align:start position:0% + +i gather they're working on it + + align:start position:0% +i gather they're working on it + + + align:start position:0% +i gather they're working on it +but i haven't seen any of the data yet + + align:start position:0% +but i haven't seen any of the data yet + + + align:start position:0% +but i haven't seen any of the data yet +yeah um + + align:start position:0% +yeah um + + + align:start position:0% +yeah um +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +though that lack of face specificity is + + align:start position:0% +though that lack of face specificity is + + + align:start position:0% +though that lack of face specificity is +consistent with the idea that all that + + align:start position:0% +consistent with the idea that all that + + + align:start position:0% +consistent with the idea that all that +human early face recognition behavior is + + align:start position:0% +human early face recognition behavior is + + + align:start position:0% +human early face recognition behavior is +driven by a different system because + + align:start position:0% +driven by a different system because + + + align:start position:0% +driven by a different system because +they don't have their face system yet + + align:start position:0% +they don't have their face system yet + + + align:start position:0% +they don't have their face system yet +presumably + + align:start position:0% +presumably + + + align:start position:0% +presumably +but it's also consistent with this idea + + align:start position:0% +but it's also consistent with this idea + + + align:start position:0% +but it's also consistent with this idea +that you know it's just failing to be + + align:start position:0% +that you know it's just failing to be + + + align:start position:0% +that you know it's just failing to be +detected + + align:start position:0% +detected + + + align:start position:0% +detected +even though i said that's probably not + + align:start position:0% +even though i said that's probably not + + + align:start position:0% +even though i said that's probably not +true given you can detect other stuff it + + align:start position:0% +true given you can detect other stuff it + + + align:start position:0% +true given you can detect other stuff it +might be true here + + align:start position:0% +might be true here + + + align:start position:0% +might be true here +the ability to see things with mri + + align:start position:0% +the ability to see things with mri + + + align:start position:0% +the ability to see things with mri +depend depends where you're looking at + + align:start position:0% +depend depends where you're looking at + + + align:start position:0% +depend depends where you're looking at +the brain + + align:start position:0% +the brain + + + align:start position:0% +the brain +so + + align:start position:0% +so + + + align:start position:0% +so +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so what about + + align:start position:0% +so what about + + + align:start position:0% +so what about +these causal roles of structured + + align:start position:0% +these causal roles of structured + + + align:start position:0% +these causal roles of structured +experience + + align:start position:0% +experience + + + align:start position:0% +experience +um + + align:start position:0% +um + + + align:start position:0% +um +and uh biological maturation okay so we + + align:start position:0% +and uh biological maturation okay so we + + + align:start position:0% +and uh biological maturation okay so we +argued that early face experience isn't + + align:start position:0% +argued that early face experience isn't + + + align:start position:0% +argued that early face experience isn't +crucial for the face recognition system + + align:start position:0% +crucial for the face recognition system + + + align:start position:0% +crucial for the face recognition system +that was the sugita paper you read + + align:start position:0% +that was the sugita paper you read + + + align:start position:0% +that was the sugita paper you read +but now functional mri is showing that + + align:start position:0% +but now functional mri is showing that + + + align:start position:0% +but now functional mri is showing that +face experience + + align:start position:0% +face experience + + + align:start position:0% +face experience +is necessary for the development of face + + align:start position:0% +is necessary for the development of face + + + align:start position:0% +is necessary for the development of face +patches + + align:start position:0% +patches + + + align:start position:0% +patches +at least in monkeys + + align:start position:0% +at least in monkeys + + + align:start position:0% +at least in monkeys +and so a very sensible reaction is what + + align:start position:0% +and so a very sensible reaction is what + + + align:start position:0% +and so a very sensible reaction is what +what what how are we going to make sense + + align:start position:0% +what what how are we going to make sense + + + align:start position:0% +what what how are we going to make sense +of this this is a big conundrum + + align:start position:0% +of this this is a big conundrum + + + align:start position:0% +of this this is a big conundrum +it's going to get worse on monday where + + align:start position:0% +it's going to get worse on monday where + + + align:start position:0% +it's going to get worse on monday where +there's yet more contradictory data + + align:start position:0% +there's yet more contradictory data + + + align:start position:0% +there's yet more contradictory data +and further if that face system + + align:start position:0% +and further if that face system + + + align:start position:0% +and further if that face system +isn't innate + + align:start position:0% +isn't innate + + + align:start position:0% +isn't innate +then what if anything is innate about + + align:start position:0% +then what if anything is innate about + + + align:start position:0% +then what if anything is innate about +face perception + + align:start position:0% +face perception + + + align:start position:0% +face perception +right so + + align:start position:0% +right so + + + align:start position:0% +right so +maybe what all these data are telling us + + align:start position:0% +maybe what all these data are telling us + + + align:start position:0% +maybe what all these data are telling us +is not that much + + align:start position:0% +is not that much + + + align:start position:0% +is not that much +maybe just a bias to look at faces + + align:start position:0% +maybe just a bias to look at faces + + + align:start position:0% +maybe just a bias to look at faces +or some very simple image template + + align:start position:0% +or some very simple image template + + + align:start position:0% +or some very simple image template +that's sufficient in the environment of + + align:start position:0% +that's sufficient in the environment of + + + align:start position:0% +that's sufficient in the environment of +infants to get them to look at faces + + align:start position:0% +infants to get them to look at faces + + + align:start position:0% +infants to get them to look at faces +right so there's a lot of studies i + + align:start position:0% +right so there's a lot of studies i + + + align:start position:0% +right so there's a lot of studies i +didn't have time to work into this + + align:start position:0% +didn't have time to work into this + + + align:start position:0% +didn't have time to work into this +lecture where people stick cameras on + + align:start position:0% +lecture where people stick cameras on + + + align:start position:0% +lecture where people stick cameras on +the foreheads of + + align:start position:0% +the foreheads of + + + align:start position:0% +the foreheads of +newborns and they collect what is the + + align:start position:0% +newborns and they collect what is the + + + align:start position:0% +newborns and they collect what is the +typical visual experience of a newborn + + align:start position:0% +typical visual experience of a newborn + + + align:start position:0% +typical visual experience of a newborn +and then you can take that you can take + + align:start position:0% +and then you can take that you can take + + + align:start position:0% +and then you can take that you can take +that experience and ask what kind of + + align:start position:0% +that experience and ask what kind of + + + align:start position:0% +that experience and ask what kind of +you know you can write + + align:start position:0% +you know you can write + + + align:start position:0% +you know you can write +machine learning code to say what would + + align:start position:0% +machine learning code to say what would + + + align:start position:0% +machine learning code to say what would +you have to build in to reliably pick + + align:start position:0% +you have to build in to reliably pick + + + align:start position:0% +you have to build in to reliably pick +out the faces in typical infant input + + align:start position:0% +out the faces in typical infant input + + + align:start position:0% +out the faces in typical infant input +it's probably not that complicated + + align:start position:0% +it's probably not that complicated + + + align:start position:0% +it's probably not that complicated +because infants don't see that many + + align:start position:0% +because infants don't see that many + + + align:start position:0% +because infants don't see that many +different kinds of things right + + align:start position:0% +different kinds of things right + + + align:start position:0% +different kinds of things right +okay + + align:start position:0% +okay + + + align:start position:0% +okay +we showed early visual discrimination + + align:start position:0% +we showed early visual discrimination + + + align:start position:0% +we showed early visual discrimination +abilities + + align:start position:0% +abilities + + + align:start position:0% +abilities +faces in newborn infants but again it's + + align:start position:0% +faces in newborn infants but again it's + + + align:start position:0% +faces in newborn infants but again it's +not clear that's part of the specific + + align:start position:0% +not clear that's part of the specific + + + align:start position:0% +not clear that's part of the specific +system + + align:start position:0% +system + + + align:start position:0% +system +and we showed that the face patches at + + align:start position:0% +and we showed that the face patches at + + + align:start position:0% +and we showed that the face patches at +least in monkeys seem to require + + align:start position:0% +least in monkeys seem to require + + + align:start position:0% +least in monkeys seem to require +experience okay i'm just recapping here + + align:start position:0% +experience okay i'm just recapping here + + + align:start position:0% +experience okay i'm just recapping here +but now there's this big question of + + align:start position:0% +but now there's this big question of + + + align:start position:0% +but now there's this big question of +how do those face patches know where to + + align:start position:0% +how do those face patches know where to + + + align:start position:0% +how do those face patches know where to +develop in the brain right like here + + align:start position:0% +develop in the brain right like here + + + align:start position:0% +develop in the brain right like here +they are in humans these little purple + + align:start position:0% +they are in humans these little purple + + + align:start position:0% +they are in humans these little purple +blobs the occipital face area i've got + + align:start position:0% +blobs the occipital face area i've got + + + align:start position:0% +blobs the occipital face area i've got +two different fusiform face areas + + align:start position:0% +two different fusiform face areas + + + align:start position:0% +two different fusiform face areas +because + + align:start position:0% +because + + + align:start position:0% +because +various people think there's two i'm not + + align:start position:0% +various people think there's two i'm not + + + align:start position:0% +various people think there's two i'm not +sure i don't really care doesn't matter + + align:start position:0% +sure i don't really care doesn't matter + + + align:start position:0% +sure i don't really care doesn't matter +anyway how do they know to land right + + align:start position:0% +anyway how do they know to land right + + + align:start position:0% +anyway how do they know to land right +there + + align:start position:0% +there + + + align:start position:0% +there +okay we keep bringing up this question + + align:start position:0% +okay we keep bringing up this question + + + align:start position:0% +okay we keep bringing up this question +and dancing around it but so far i've + + align:start position:0% +and dancing around it but so far i've + + + align:start position:0% +and dancing around it but so far i've +given you no + + align:start position:0% +given you no + + + align:start position:0% +given you no +no + + align:start position:0% +no + + + align:start position:0% +no +basis for thinking about this + + align:start position:0% +basis for thinking about this + + + align:start position:0% +basis for thinking about this +one possibility + + align:start position:0% +one possibility + + + align:start position:0% +one possibility +is that + + align:start position:0% +is that + + + align:start position:0% +is that +infants monkey and humans + + align:start position:0% +infants monkey and humans + + + align:start position:0% +infants monkey and humans +are born with some earlier kind of + + align:start position:0% +are born with some earlier kind of + + + align:start position:0% +are born with some earlier kind of +selectivity of that patch of brain + + align:start position:0% +selectivity of that patch of brain + + + align:start position:0% +selectivity of that patch of brain +it's not a whole like face template it's + + align:start position:0% +it's not a whole like face template it's + + + align:start position:0% +it's not a whole like face template it's +not a whole face system maybe it's a + + align:start position:0% +not a whole face system maybe it's a + + + align:start position:0% +not a whole face system maybe it's a +bias for curvy things + + align:start position:0% +bias for curvy things + + + align:start position:0% +bias for curvy things +right and then somehow that makes the + + align:start position:0% +right and then somehow that makes the + + + align:start position:0% +right and then somehow that makes the +faces land there and the system wires + + align:start position:0% +faces land there and the system wires + + + align:start position:0% +faces land there and the system wires +itself up it's not exactly clear how + + align:start position:0% +itself up it's not exactly clear how + + + align:start position:0% +itself up it's not exactly clear how +that would go + + align:start position:0% +that would go + + + align:start position:0% +that would go +but that's one kind of story + + align:start position:0% +but that's one kind of story + + + align:start position:0% +but that's one kind of story +story is based on this fact i told you + + align:start position:0% +story is based on this fact i told you + + + align:start position:0% +story is based on this fact i told you +at the beginning of the lecture which is + + align:start position:0% +at the beginning of the lecture which is + + + align:start position:0% +at the beginning of the lecture which is +most of the long-range connectivity of + + align:start position:0% +most of the long-range connectivity of + + + align:start position:0% +most of the long-range connectivity of +the brain is present at birth + + align:start position:0% +the brain is present at birth + + + align:start position:0% +the brain is present at birth +and so maybe the particular connections + + align:start position:0% +and so maybe the particular connections + + + align:start position:0% +and so maybe the particular connections +of that patch of brain + + align:start position:0% +of that patch of brain + + + align:start position:0% +of that patch of brain +are already there at birth and maybe + + align:start position:0% +are already there at birth and maybe + + + align:start position:0% +are already there at birth and maybe +that patch of connections are sufficient + + align:start position:0% +that patch of connections are sufficient + + + align:start position:0% +that patch of connections are sufficient +to somehow gate the input to that system + + align:start position:0% +to somehow gate the input to that system + + + align:start position:0% +to somehow gate the input to that system +and arrange for it to end up being phase + + align:start position:0% +and arrange for it to end up being phase + + + align:start position:0% +and arrange for it to end up being phase +specific + + align:start position:0% +specific + + + align:start position:0% +specific +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this is a very active area of + + align:start position:0% +so this is a very active area of + + + align:start position:0% +so this is a very active area of +investigation + + align:start position:0% +investigation + + + align:start position:0% +investigation +and there's other very active ongoing + + align:start position:0% +and there's other very active ongoing + + + align:start position:0% +and there's other very active ongoing +kinds of investigation where people are + + align:start position:0% +kinds of investigation where people are + + + align:start position:0% +kinds of investigation where people are +trying to understand how this + + align:start position:0% +trying to understand how this + + + align:start position:0% +trying to understand how this +development might work + + align:start position:0% +development might work + + + align:start position:0% +development might work +one way people are looking at this i + + align:start position:0% +one way people are looking at this i + + + align:start position:0% +one way people are looking at this i +mentioned this briefly but i think it's + + align:start position:0% +mentioned this briefly but i think it's + + + align:start position:0% +mentioned this briefly but i think it's +super exciting as people are asking with + + align:start position:0% +super exciting as people are asking with + + + align:start position:0% +super exciting as people are asking with +deep nets and other kinds of modeling + + align:start position:0% +deep nets and other kinds of modeling + + + align:start position:0% +deep nets and other kinds of modeling +what do you have to build into a system + + align:start position:0% +what do you have to build into a system + + + align:start position:0% +what do you have to build into a system +to get it to produce face recognition + + align:start position:0% +to get it to produce face recognition + + + align:start position:0% +to get it to produce face recognition +abilities + + align:start position:0% +abilities + + + align:start position:0% +abilities +if you're if you're trying to make a + + align:start position:0% +if you're if you're trying to make a + + + align:start position:0% +if you're if you're trying to make a +deep net you're trying to make it really + + align:start position:0% +deep net you're trying to make it really + + + align:start position:0% +deep net you're trying to make it really +good at face recognition + + align:start position:0% +good at face recognition + + + align:start position:0% +good at face recognition +do you need to give it a template of + + align:start position:0% +do you need to give it a template of + + + align:start position:0% +do you need to give it a template of +faces do you need to give it only + + align:start position:0% +faces do you need to give it only + + + align:start position:0% +faces do you need to give it only +experience with faces what do you need + + align:start position:0% +experience with faces what do you need + + + align:start position:0% +experience with faces what do you need +to build into it to get it to be really + + align:start position:0% +to build into it to get it to be really + + + align:start position:0% +to build into it to get it to be really +good right and so that's a very active + + align:start position:0% +good right and so that's a very active + + + align:start position:0% +good right and so that's a very active +area of investigation + + align:start position:0% +area of investigation + + + align:start position:0% +area of investigation +and you can actually some ongoing work + + align:start position:0% +and you can actually some ongoing work + + + align:start position:0% +and you can actually some ongoing work +with + + align:start position:0% +with + + + align:start position:0% +with +jim de carlo's lab we're asking okay + + align:start position:0% +jim de carlo's lab we're asking okay + + + align:start position:0% +jim de carlo's lab we're asking okay +deep nets don't have topography next + + align:start position:0% +deep nets don't have topography next + + + align:start position:0% +deep nets don't have topography next +door units in a deep net doesn't mean + + align:start position:0% +door units in a deep net doesn't mean + + + align:start position:0% +door units in a deep net doesn't mean +anything what's next door versus far + + align:start position:0% +anything what's next door versus far + + + align:start position:0% +anything what's next door versus far +apart location doesn't need anything in + + align:start position:0% +apart location doesn't need anything in + + + align:start position:0% +apart location doesn't need anything in +a deep net but you can make it mean + + align:start position:0% +a deep net but you can make it mean + + + align:start position:0% +a deep net but you can make it mean +something and then you can ask + + align:start position:0% +something and then you can ask + + + align:start position:0% +something and then you can ask +when and whether and how and why you get + + align:start position:0% +when and whether and how and why you get + + + align:start position:0% +when and whether and how and why you get +face patches + + align:start position:0% +face patches + + + align:start position:0% +face patches +in a deep net + + align:start position:0% +in a deep net + + + align:start position:0% +in a deep net +okay and what computational role they + + align:start position:0% +okay and what computational role they + + + align:start position:0% +okay and what computational role they +serve well totally weirdly i'm i'm + + align:start position:0% +serve well totally weirdly i'm i'm + + + align:start position:0% +serve well totally weirdly i'm i'm +finishing early but i'm not going to + + align:start position:0% +finishing early but i'm not going to + + + align:start position:0% +finishing early but i'm not going to +finish i'll take questions and then i'll + + align:start position:0% +finish i'll take questions and then i'll + + + align:start position:0% +finish i'll take questions and then i'll +maybe add a little bit more + + align:start position:0% +maybe add a little bit more + + + align:start position:0% +maybe add a little bit more +um i think that was all i had here right + + align:start position:0% +um i think that was all i had here right + + + align:start position:0% +um i think that was all i had here right +um any questions about all this + + align:start position:0% +um any questions about all this + + + align:start position:0% +um any questions about all this +if it feels a little bit chaotic so i've + + align:start position:0% +if it feels a little bit chaotic so i've + + + align:start position:0% +if it feels a little bit chaotic so i've +sort of said x and not x and x but + + align:start position:0% +sort of said x and not x and x but + + + align:start position:0% +sort of said x and not x and x but +they're not exactly x and not x they're + + align:start position:0% +they're not exactly x and not x they're + + + align:start position:0% +they're not exactly x and not x they're +just yeah sure do um so fmri can detect + + align:start position:0% +just yeah sure do um so fmri can detect + + + align:start position:0% +just yeah sure do um so fmri can detect +activity and like fossils right and with + + align:start position:0% +activity and like fossils right and with + + + align:start position:0% +activity and like fossils right and with +fossils you said we can contain millions + + align:start position:0% +fossils you said we can contain millions + + + align:start position:0% +fossils you said we can contain millions +of neurons + + align:start position:0% +of neurons + + + align:start position:0% +of neurons +so um is it possible that + + align:start position:0% +so um is it possible that + + + align:start position:0% +so um is it possible that +the neurons that are specific to places + + align:start position:0% +the neurons that are specific to places + + + align:start position:0% +the neurons that are specific to places +are distributed at an ova throughout the + + align:start position:0% +are distributed at an ova throughout the + + + align:start position:0% +are distributed at an ova throughout the +brain and somehow the function kind of + + align:start position:0% +brain and somehow the function kind of + + + align:start position:0% +brain and somehow the function kind of +think it's spatially clustered yeah but + + align:start position:0% +think it's spatially clustered yeah but + + + align:start position:0% +think it's spatially clustered yeah but +the neurons themselves already exist + + align:start position:0% +the neurons themselves already exist + + + align:start position:0% +the neurons themselves already exist +absolutely that's a great hypothesis + + align:start position:0% +absolutely that's a great hypothesis + + + align:start position:0% +absolutely that's a great hypothesis +it's absolutely possible everybody get + + align:start position:0% +it's absolutely possible everybody get + + + align:start position:0% +it's absolutely possible everybody get +the idea you have all those face neurons + + align:start position:0% +the idea you have all those face neurons + + + align:start position:0% +the idea you have all those face neurons +at birth and maybe they're face specific + + align:start position:0% +at birth and maybe they're face specific + + + align:start position:0% +at birth and maybe they're face specific +at birth but they're spatially spread + + align:start position:0% +at birth but they're spatially spread + + + align:start position:0% +at birth but they're spatially spread +out and then they have to find each + + align:start position:0% +out and then they have to find each + + + align:start position:0% +out and then they have to find each +other + + align:start position:0% +other + + + align:start position:0% +other +and hang out together next to each other + + align:start position:0% +and hang out together next to each other + + + align:start position:0% +and hang out together next to each other +before you ever get an mri signal it's + + align:start position:0% +before you ever get an mri signal it's + + + align:start position:0% +before you ever get an mri signal it's +totally possible logically it seems to + + align:start position:0% +totally possible logically it seems to + + + align:start position:0% +totally possible logically it seems to +me quite unlikely actually because it + + align:start position:0% +me quite unlikely actually because it + + + align:start position:0% +me quite unlikely actually because it +can be very hard for all those neurons + + align:start position:0% +can be very hard for all those neurons + + + align:start position:0% +can be very hard for all those neurons +with their necessary connections which + + align:start position:0% +with their necessary connections which + + + align:start position:0% +with their necessary connections which +is after all how they become face + + align:start position:0% +is after all how they become face + + + align:start position:0% +is after all how they become face +specific is what their inputs are and + + align:start position:0% +specific is what their inputs are and + + + align:start position:0% +specific is what their inputs are and +what they're connected to it'd be very + + align:start position:0% +what they're connected to it'd be very + + + align:start position:0% +what they're connected to it'd be very +hard for them to migrate spatially + + align:start position:0% +hard for them to migrate spatially + + + align:start position:0% +hard for them to migrate spatially +across the brain + + align:start position:0% +across the brain + + + align:start position:0% +across the brain +maintaining their connections yes you're + + align:start position:0% +maintaining their connections yes you're + + + align:start position:0% +maintaining their connections yes you're +going to push back go forward like mine + + align:start position:0% +going to push back go forward like mine + + + align:start position:0% +going to push back go forward like mine +grades they should be liquid functional + + align:start position:0% +grades they should be liquid functional + + + align:start position:0% +grades they should be liquid functional +but since you said like + + align:start position:0% +but since you said like + + + align:start position:0% +but since you said like +review they care about what their papers + + align:start position:0% +review they care about what their papers + + + align:start position:0% +review they care about what their papers +are doing so maybe it's just like on + + align:start position:0% +are doing so maybe it's just like on + + + align:start position:0% +are doing so maybe it's just like on +every mirror on hobbies but the you know + + align:start position:0% +every mirror on hobbies but the you know + + + align:start position:0% +every mirror on hobbies but the you know +next week that's and this chain moves it + + align:start position:0% +next week that's and this chain moves it + + + align:start position:0% +next week that's and this chain moves it +back until like that orientation but + + align:start position:0% +back until like that orientation but + + + align:start position:0% +back until like that orientation but +that deprivation is the most efficient + + align:start position:0% +that deprivation is the most efficient + + + align:start position:0% +that deprivation is the most efficient +way to have all that it's totally + + align:start position:0% +way to have all that it's totally + + + align:start position:0% +way to have all that it's totally +possible totally possible + + align:start position:0% +possible totally possible + + + align:start position:0% +possible totally possible +absolutely + + align:start position:0% +absolutely + + + align:start position:0% +absolutely +yep + + align:start position:0% +yep + + + align:start position:0% +yep +other questions this is kind of wide + + align:start position:0% +other questions this is kind of wide + + + align:start position:0% +other questions this is kind of wide +open nobody knows + + align:start position:0% +open nobody knows + + + align:start position:0% +open nobody knows +right + + align:start position:0% + + + + align:start position:0% + +let me just see what else i have time + + align:start position:0% +let me just see what else i have time + + + align:start position:0% +let me just see what else i have time +for briefly + + align:start position:0% +for briefly + + + align:start position:0% +for briefly +um + + align:start position:0% + + + + align:start position:0% + +so funny i took out all these slides + + align:start position:0% +so funny i took out all these slides + + + align:start position:0% +so funny i took out all these slides +because i just thought i'm going to + + align:start position:0% +because i just thought i'm going to + + + align:start position:0% +because i just thought i'm going to +run out of time and go over and drive + + align:start position:0% +run out of time and go over and drive + + + align:start position:0% +run out of time and go over and drive +everyone crazy + + align:start position:0% + + + + align:start position:0% + +and i moved all this stuff to the other + + align:start position:0% +and i moved all this stuff to the other + + + align:start position:0% +and i moved all this stuff to the other +lecture + + align:start position:0% +lecture + + + align:start position:0% +lecture +maybe i will just + + align:start position:0% + + + + align:start position:0% + +hmm + + align:start position:0% +hmm + + + align:start position:0% +hmm +all right hang on let me just glance at + + align:start position:0% +all right hang on let me just glance at + + + align:start position:0% +all right hang on let me just glance at +the lineup for + + align:start position:0% +the lineup for + + + align:start position:0% +the lineup for +wednesday + + align:start position:0% + + + + align:start position:0% + +yeah is there + + align:start position:0% +yeah is there + + + align:start position:0% +yeah is there +the perceptual narrowing + + align:start position:0% +the perceptual narrowing + + + align:start position:0% +the perceptual narrowing +is really + + align:start position:0% +is really + + + align:start position:0% +is really +surprising fascinating + + align:start position:0% +surprising fascinating + + + align:start position:0% +surprising fascinating +does anybody have a + + align:start position:0% +does anybody have a + + + align:start position:0% +does anybody have a +model for + + align:start position:0% + + + + align:start position:0% + +how that processing might work or what + + align:start position:0% +how that processing might work or what + + + align:start position:0% +how that processing might work or what +it might be for i mean it feels like a + + align:start position:0% +it might be for i mean it feels like a + + + align:start position:0% +it might be for i mean it feels like a +lot of the um assumptions or like the + + align:start position:0% +lot of the um assumptions or like the + + + align:start position:0% +lot of the um assumptions or like the +sort of the common sense assumptions + + align:start position:0% +sort of the common sense assumptions + + + align:start position:0% +sort of the common sense assumptions +um when we look at fmri and + + align:start position:0% +um when we look at fmri and + + + align:start position:0% +um when we look at fmri and +you know when we look at + + align:start position:0% +you know when we look at + + + align:start position:0% +you know when we look at +neural signals is that they all mean + + align:start position:0% +neural signals is that they all mean + + + align:start position:0% +neural signals is that they all mean +positive things + + align:start position:0% +positive things + + + align:start position:0% +positive things +um but maybe a lot of the signals a lot + + align:start position:0% +um but maybe a lot of the signals a lot + + + align:start position:0% +um but maybe a lot of the signals a lot +of activity might be inhibitory + + align:start position:0% +of activity might be inhibitory + + + align:start position:0% +of activity might be inhibitory +you know might be the opposite + + align:start position:0% +you know might be the opposite + + + align:start position:0% +you know might be the opposite +totally yeah but how would that explain + + align:start position:0% +totally yeah but how would that explain + + + align:start position:0% +totally yeah but how would that explain +perceptual narrowing + + align:start position:0% +perceptual narrowing + + + align:start position:0% +perceptual narrowing +well if if what you're learning is what + + align:start position:0% +well if if what you're learning is what + + + align:start position:0% +well if if what you're learning is what +to ignore then maybe it takes a lot of + + align:start position:0% +to ignore then maybe it takes a lot of + + + align:start position:0% +to ignore then maybe it takes a lot of +effort to ignore things and um + + align:start position:0% +effort to ignore things and um + + + align:start position:0% +effort to ignore things and um +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +you know i'm not really i'm not you + + align:start position:0% +you know i'm not really i'm not you + + + align:start position:0% +you know i'm not really i'm not you +exactly yeah no it's a good point that + + align:start position:0% +exactly yeah no it's a good point that + + + align:start position:0% +exactly yeah no it's a good point that +like you know i mentioned at the + + align:start position:0% +like you know i mentioned at the + + + align:start position:0% +like you know i mentioned at the +beginning one of the + + align:start position:0% +beginning one of the + + + align:start position:0% +beginning one of the +limitations of functional mri is we + + align:start position:0% +limitations of functional mri is we + + + align:start position:0% +limitations of functional mri is we +don't know what the actual + + align:start position:0% +don't know what the actual + + + align:start position:0% +don't know what the actual +neurophysiological basis of the bold + + align:start position:0% +neurophysiological basis of the bold + + + align:start position:0% +neurophysiological basis of the bold +signal is it could be anything that that + + align:start position:0% +signal is it could be anything that that + + + align:start position:0% +signal is it could be anything that that +increases your metabolic costs and hence + + align:start position:0% +increases your metabolic costs and hence + + + align:start position:0% +increases your metabolic costs and hence +changes blood flow but one of the things + + align:start position:0% +changes blood flow but one of the things + + + align:start position:0% +changes blood flow but one of the things +that increases metabolic costs is + + align:start position:0% +that increases metabolic costs is + + + align:start position:0% +that increases metabolic costs is +inhibiting other neurons right and so + + align:start position:0% +inhibiting other neurons right and so + + + align:start position:0% +inhibiting other neurons right and so +way back in the early days of actually + + align:start position:0% +way back in the early days of actually + + + align:start position:0% +way back in the early days of actually +pet imaging before functional mri came + + align:start position:0% +pet imaging before functional mri came + + + align:start position:0% +pet imaging before functional mri came +along there was kind of an early proto + + align:start position:0% +along there was kind of an early proto + + + align:start position:0% +along there was kind of an early proto +version of a face specific paper it + + align:start position:0% +version of a face specific paper it + + + align:start position:0% +version of a face specific paper it +wasn't didn't nail everything but it was + + align:start position:0% +wasn't didn't nail everything but it was + + + align:start position:0% +wasn't didn't nail everything but it was +it was not bad for 1981 when i think it + + align:start position:0% +it was not bad for 1981 when i think it + + + align:start position:0% +it was not bad for 1981 when i think it +was published + + align:start position:0% +was published + + + align:start position:0% +was published +and the person who did that paper + + align:start position:0% +and the person who did that paper + + + align:start position:0% +and the person who did that paper +justine sergio + + align:start position:0% +justine sergio + + + align:start position:0% +justine sergio +argued that it's very very ambiguous + + align:start position:0% +argued that it's very very ambiguous + + + align:start position:0% +argued that it's very very ambiguous +what it means to find a hot spot in the + + align:start position:0% +what it means to find a hot spot in the + + + align:start position:0% +what it means to find a hot spot in the +brain where the activity the metabolic + + align:start position:0% +brain where the activity the metabolic + + + align:start position:0% +brain where the activity the metabolic +activity is higher say when you look at + + align:start position:0% +activity is higher say when you look at + + + align:start position:0% +activity is higher say when you look at +faces that are than objects their point + + align:start position:0% +faces that are than objects their point + + + align:start position:0% +faces that are than objects their point +was that could be the part of the brain + + align:start position:0% +was that could be the part of the brain + + + align:start position:0% +was that could be the part of the brain +that really sucks at face recognition + + align:start position:0% +that really sucks at face recognition + + + align:start position:0% +that really sucks at face recognition +that's the part that's going ah i can't + + align:start position:0% +that's the part that's going ah i can't + + + align:start position:0% +that's the part that's going ah i can't +deal with this thing what is this thing + + align:start position:0% +deal with this thing what is this thing + + + align:start position:0% +deal with this thing what is this thing +right that's really bad at it and the + + align:start position:0% +right that's really bad at it and the + + + align:start position:0% +right that's really bad at it and the +neurons are firing a lot it's sort of + + align:start position:0% +neurons are firing a lot it's sort of + + + align:start position:0% +neurons are firing a lot it's sort of +facetious but sort of not right and + + align:start position:0% +facetious but sort of not right and + + + align:start position:0% +facetious but sort of not right and +that's probably not the right account + + align:start position:0% +that's probably not the right account + + + align:start position:0% +that's probably not the right account +but it is an important reminder that we + + align:start position:0% +but it is an important reminder that we + + + align:start position:0% +but it is an important reminder that we +actually don't know + + align:start position:0% +actually don't know + + + align:start position:0% +actually don't know +um what actual kind of neural activity + + align:start position:0% +um what actual kind of neural activity + + + align:start position:0% +um what actual kind of neural activity +is driving those things and whether it's + + align:start position:0% +is driving those things and whether it's + + + align:start position:0% +is driving those things and whether it's +um + + align:start position:0% +um + + + align:start position:0% +um +whether it's excitatory or inhibitory + + align:start position:0% +whether it's excitatory or inhibitory + + + align:start position:0% +whether it's excitatory or inhibitory +absolutely uh hang on one second i feel + + align:start position:0% +absolutely uh hang on one second i feel + + + align:start position:0% +absolutely uh hang on one second i feel +like there was another part of what you + + align:start position:0% +like there was another part of what you + + + align:start position:0% +like there was another part of what you +said that i was going to engage on no it + + align:start position:0% +said that i was going to engage on no it + + + align:start position:0% +said that i was going to engage on no it +would feel it feels like somehow + + align:start position:0% +would feel it feels like somehow + + + align:start position:0% +would feel it feels like somehow +possibly connected to the the potential + + align:start position:0% +possibly connected to the the potential + + + align:start position:0% +possibly connected to the the potential +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah possibly we'd have to work it out + + align:start position:0% +yeah possibly we'd have to work it out + + + align:start position:0% +yeah possibly we'd have to work it out +um in one of the lectures + + align:start position:0% +um in one of the lectures + + + align:start position:0% +um in one of the lectures +i mentioned about other racing factors + + align:start position:0% +i mentioned about other racing factors + + + align:start position:0% +i mentioned about other racing factors +yeah and then probably + + align:start position:0% +yeah and then probably + + + align:start position:0% +yeah and then probably +based on the experiment + + align:start position:0% +based on the experiment + + + align:start position:0% +based on the experiment +or the child for some adult kid + + align:start position:0% +or the child for some adult kid + + + align:start position:0% +or the child for some adult kid +yes + + align:start position:0% + + + + align:start position:0% + +okay long range wiring + + align:start position:0% +okay long range wiring + + + align:start position:0% +okay long range wiring +okay which is very different than all + + align:start position:0% +okay which is very different than all + + + align:start position:0% +okay which is very different than all +the circuits that live in each little + + align:start position:0% +the circuits that live in each little + + + align:start position:0% +the circuits that live in each little +patch of cortex remember i showed you + + align:start position:0% +patch of cortex remember i showed you + + + align:start position:0% +patch of cortex remember i showed you +this big change in the complexity of + + align:start position:0% +this big change in the complexity of + + + align:start position:0% +this big change in the complexity of +neurons and their + + align:start position:0% +neurons and their + + + align:start position:0% +neurons and their +uh the number of connections + + align:start position:0% +uh the number of connections + + + align:start position:0% +uh the number of connections +oops except we've lost it + + align:start position:0% + + + + align:start position:0% + +now um + + align:start position:0% +now um + + + align:start position:0% +now um +right so they're changing a lot within + + align:start position:0% +right so they're changing a lot within + + + align:start position:0% +right so they're changing a lot within +each patch of cortex right so those + + align:start position:0% +each patch of cortex right so those + + + align:start position:0% +each patch of cortex right so those +local circuits that are doing + + align:start position:0% +local circuits that are doing + + + align:start position:0% +local circuits that are doing +computations are surely changing a lot + + align:start position:0% +computations are surely changing a lot + + + align:start position:0% +computations are surely changing a lot +over the first couple years it's just a + + align:start position:0% +over the first couple years it's just a + + + align:start position:0% +over the first couple years it's just a +long range connections between that + + align:start position:0% +long range connections between that + + + align:start position:0% +long range connections between that +patch and some remote region like where + + align:start position:0% +patch and some remote region like where + + + align:start position:0% +patch and some remote region like where +it gets its inputs and where it sends + + align:start position:0% +it gets its inputs and where it sends + + + align:start position:0% +it gets its inputs and where it sends +its outputs to + + align:start position:0% +its outputs to + + + align:start position:0% +its outputs to +um but hang on a second you asked + + align:start position:0% +um but hang on a second you asked + + + align:start position:0% +um but hang on a second you asked +something um + + align:start position:0% +something um + + + align:start position:0% +something um +there's also very interesting stuff + + align:start position:0% +there's also very interesting stuff + + + align:start position:0% +there's also very interesting stuff +about the other race effect i did + + align:start position:0% +about the other race effect i did + + + align:start position:0% +about the other race effect i did +mention that a a month ago or so didn't + + align:start position:0% +mention that a a month ago or so didn't + + + align:start position:0% +mention that a a month ago or so didn't +i which is another version of this + + align:start position:0% +i which is another version of this + + + align:start position:0% +i which is another version of this +uh perceptual narrowing + + align:start position:0% +uh perceptual narrowing + + + align:start position:0% +uh perceptual narrowing +and in fact a friend of mine who's a + + align:start position:0% +and in fact a friend of mine who's a + + + align:start position:0% +and in fact a friend of mine who's a +great face researcher has not yet + + align:start position:0% +great face researcher has not yet + + + align:start position:0% +great face researcher has not yet +published this paper but she found the + + align:start position:0% +published this paper but she found the + + + align:start position:0% +published this paper but she found the +following totally that's right you + + align:start position:0% +following totally that's right you + + + align:start position:0% +following totally that's right you +mentioned the adoption studies right so + + align:start position:0% +mentioned the adoption studies right so + + + align:start position:0% +mentioned the adoption studies right so +what she has done is ask + + align:start position:0% +what she has done is ask + + + align:start position:0% +what she has done is ask +did i tell you guys about this already i + + align:start position:0% +did i tell you guys about this already i + + + align:start position:0% +did i tell you guys about this already i +feel like i did but maybe not anyway so + + align:start position:0% +feel like i did but maybe not anyway so + + + align:start position:0% +feel like i did but maybe not anyway so +if you what you find is that people are + + align:start position:0% +if you what you find is that people are + + + align:start position:0% +if you what you find is that people are +you know you know they all look alike + + align:start position:0% +you know you know they all look alike + + + align:start position:0% +you know you know they all look alike +whoever they are if you've seen fewer of + + align:start position:0% +whoever they are if you've seen fewer of + + + align:start position:0% +whoever they are if you've seen fewer of +them than whoever we are + + align:start position:0% +them than whoever we are + + + align:start position:0% +them than whoever we are +you are less good at discriminating them + + align:start position:0% +you are less good at discriminating them + + + align:start position:0% +you are less good at discriminating them +that's just what it is + + align:start position:0% +that's just what it is + + + align:start position:0% +that's just what it is +but so eleanor mccone asked if there's a + + align:start position:0% +but so eleanor mccone asked if there's a + + + align:start position:0% +but so eleanor mccone asked if there's a +um + + align:start position:0% +um + + + align:start position:0% +um +if there's a developmental timeline for + + align:start position:0% +if there's a developmental timeline for + + + align:start position:0% +if there's a developmental timeline for +getting your way out of the other race + + align:start position:0% +getting your way out of the other race + + + align:start position:0% +getting your way out of the other race +effect + + align:start position:0% +effect + + + align:start position:0% +effect +and so what she did was she's in + + align:start position:0% +and so what she did was she's in + + + align:start position:0% +and so what she did was she's in +australia and she got various + + align:start position:0% +australia and she got various + + + align:start position:0% +australia and she got various +communities of people who moved from you + + align:start position:0% +communities of people who moved from you + + + align:start position:0% +communities of people who moved from you +know dominant racial composition x to + + align:start position:0% +know dominant racial composition x to + + + align:start position:0% +know dominant racial composition x to +dominant racial composition y + + align:start position:0% +dominant racial composition y + + + align:start position:0% +dominant racial composition y +and who made that move at different ages + + align:start position:0% +and who made that move at different ages + + + align:start position:0% +and who made that move at different ages +and so what she finds is that actually + + align:start position:0% +and so what she finds is that actually + + + align:start position:0% +and so what she finds is that actually +much like learning the phonemes of a + + align:start position:0% +much like learning the phonemes of a + + + align:start position:0% +much like learning the phonemes of a +language which you know even if you use + + align:start position:0% +language which you know even if you use + + + align:start position:0% +language which you know even if you use +okay let me back up a second i said that + + align:start position:0% +okay let me back up a second i said that + + + align:start position:0% +okay let me back up a second i said that +with phonemes you can discriminate all + + align:start position:0% +with phonemes you can discriminate all + + + align:start position:0% +with phonemes you can discriminate all +those phonemes of all the world's + + align:start position:0% +those phonemes of all the world's + + + align:start position:0% +those phonemes of all the world's +languages at birth and by six months + + align:start position:0% +languages at birth and by six months + + + align:start position:0% +languages at birth and by six months +you've thrown away the abilities for all + + align:start position:0% +you've thrown away the abilities for all + + + align:start position:0% +you've thrown away the abilities for all +the phonemes you can't discriminate + + align:start position:0% +the phonemes you can't discriminate + + + align:start position:0% +the phonemes you can't discriminate +however + + align:start position:0% +however + + + align:start position:0% +however +if you then go learn a foreign language + + align:start position:0% +if you then go learn a foreign language + + + align:start position:0% +if you then go learn a foreign language +sometime between six months and say 12 + + align:start position:0% +sometime between six months and say 12 + + + align:start position:0% +sometime between six months and say 12 +you can become a native speaker so you + + align:start position:0% +you can become a native speaker so you + + + align:start position:0% +you can become a native speaker so you +can learn them back right so there's + + align:start position:0% +can learn them back right so there's + + + align:start position:0% +can learn them back right so there's +another window gets narrowed but you + + align:start position:0% +another window gets narrowed but you + + + align:start position:0% +another window gets narrowed but you +still have a window to learn the back + + align:start position:0% +still have a window to learn the back + + + align:start position:0% +still have a window to learn the back +okay + + align:start position:0% +okay + + + align:start position:0% +okay +after you're like 12 15 whatever forget + + align:start position:0% +after you're like 12 15 whatever forget + + + align:start position:0% +after you're like 12 15 whatever forget +it you won't be a native speaker right + + align:start position:0% +it you won't be a native speaker right + + + align:start position:0% +it you won't be a native speaker right +same deal with the other race effect + + align:start position:0% +same deal with the other race effect + + + align:start position:0% +same deal with the other race effect +this is exactly what mccoy found with + + align:start position:0% +this is exactly what mccoy found with + + + align:start position:0% +this is exactly what mccoy found with +the other race effect + + align:start position:0% +the other race effect + + + align:start position:0% +the other race effect +people who moved to a different dominant + + align:start position:0% +people who moved to a different dominant + + + align:start position:0% +people who moved to a different dominant +racial + + align:start position:0% +racial + + + align:start position:0% +racial +community + + align:start position:0% +community + + + align:start position:0% +community +um learned the ability to kind of + + align:start position:0% +um learned the ability to kind of + + + align:start position:0% +um learned the ability to kind of +natively discriminate people in that + + align:start position:0% +natively discriminate people in that + + + align:start position:0% +natively discriminate people in that +other race if they moved before age 12. + + align:start position:0% +other race if they moved before age 12. + + + align:start position:0% +other race if they moved before age 12. +so it really seems like there's some + + align:start position:0% +so it really seems like there's some + + + align:start position:0% +so it really seems like there's some +general ability oh i remember david's + + align:start position:0% +general ability oh i remember david's + + + align:start position:0% +general ability oh i remember david's +other question why does this make sense + + align:start position:0% +other question why does this make sense + + + align:start position:0% +other question why does this make sense +i don't know exactly why it makes sense + + align:start position:0% +i don't know exactly why it makes sense + + + align:start position:0% +i don't know exactly why it makes sense +but certainly + + align:start position:0% +but certainly + + + align:start position:0% +but certainly +neural activity is expensive + + align:start position:0% +neural activity is expensive + + + align:start position:0% +neural activity is expensive +metabolically + + align:start position:0% +metabolically + + + align:start position:0% +metabolically +and we don't want to make discrimination + + align:start position:0% +and we don't want to make discrimination + + + align:start position:0% +and we don't want to make discrimination +we don't have to + + align:start position:0% +we don't have to + + + align:start position:0% +we don't have to +and so it can it can be just that the + + align:start position:0% +and so it can it can be just that the + + + align:start position:0% +and so it can it can be just that the +nervous system is learning what kinds of + + align:start position:0% +nervous system is learning what kinds of + + + align:start position:0% +nervous system is learning what kinds of +discriminations it needs to make in its + + align:start position:0% +discriminations it needs to make in its + + + align:start position:0% +discriminations it needs to make in its +environment and what kind it doesn't + + align:start position:0% +environment and what kind it doesn't + + + align:start position:0% +environment and what kind it doesn't +right and with the case of phonemes it's + + align:start position:0% +right and with the case of phonemes it's + + + align:start position:0% +right and with the case of phonemes it's +actually part of what you're doing in + + align:start position:0% +actually part of what you're doing in + + + align:start position:0% +actually part of what you're doing in +speech perception is you want to know + + align:start position:0% +speech perception is you want to know + + + align:start position:0% +speech perception is you want to know +like every time + + align:start position:0% +like every time + + + align:start position:0% +like every time +you know i say ba it sounds different in + + align:start position:0% +you know i say ba it sounds different in + + + align:start position:0% +you know i say ba it sounds different in +all different contexts and so part of + + align:start position:0% +all different contexts and so part of + + + align:start position:0% +all different contexts and so part of +the + + align:start position:0% +the + + + align:start position:0% +the +essence of the difficulty in speech + + align:start position:0% +essence of the difficulty in speech + + + align:start position:0% +essence of the difficulty in speech +recognition is understanding that all + + align:start position:0% +recognition is understanding that all + + + align:start position:0% +recognition is understanding that all +those different bars are the same sound + + align:start position:0% +those different bars are the same sound + + + align:start position:0% +those different bars are the same sound +right + + align:start position:0% +right + + + align:start position:0% +right +and so part of what perceptual narrowing + + align:start position:0% +and so part of what perceptual narrowing + + + align:start position:0% +and so part of what perceptual narrowing +might be doing is kind of saying all + + align:start position:0% +might be doing is kind of saying all + + + align:start position:0% +might be doing is kind of saying all +those things you know da ta whatever it + + align:start position:0% +those things you know da ta whatever it + + + align:start position:0% +those things you know da ta whatever it +is in hindi um those are all going to + + align:start position:0% +is in hindi um those are all going to + + + align:start position:0% +is in hindi um those are all going to +count as the same thing + + align:start position:0% +count as the same thing + + + align:start position:0% +count as the same thing +and that's going to help you process + + align:start position:0% +and that's going to help you process + + + align:start position:0% +and that's going to help you process +speech in your native language but + + align:start position:0% +speech in your native language but + + + align:start position:0% +speech in your native language but +hinder you when you try to learn a + + align:start position:0% +hinder you when you try to learn a + + + align:start position:0% +hinder you when you try to learn a +foreign language + + align:start position:0% + + + + align:start position:0% + +yeah so something i'm wondering with um + + align:start position:0% +yeah so something i'm wondering with um + + + align:start position:0% +yeah so something i'm wondering with um +perceptual narration is like how + + align:start position:0% +perceptual narration is like how + + + align:start position:0% +perceptual narration is like how +general like the starting point is so + + align:start position:0% +general like the starting point is so + + + align:start position:0% +general like the starting point is so +i'm basically wanted because in the + + align:start position:0% +i'm basically wanted because in the + + + align:start position:0% +i'm basically wanted because in the +studies they've like compared human and + + align:start position:0% +studies they've like compared human and + + + align:start position:0% +studies they've like compared human and +monkey faces yeah and i'm wondering if + + align:start position:0% +monkey faces yeah and i'm wondering if + + + align:start position:0% +monkey faces yeah and i'm wondering if +there's any correlation with how similar + + align:start position:0% +there's any correlation with how similar + + + align:start position:0% +there's any correlation with how similar +the dna is if the thought like how + + align:start position:0% +the dna is if the thought like how + + + align:start position:0% +the dna is if the thought like how +they're able to discriminate between the + + align:start position:0% +they're able to discriminate between the + + + align:start position:0% +they're able to discriminate between the +faces so whether that's like different + + align:start position:0% +faces so whether that's like different + + + align:start position:0% +faces so whether that's like different +types of monkeys or like different + + align:start position:0% +types of monkeys or like different + + + align:start position:0% +types of monkeys or like different +animals i'm not getting it right early + + align:start position:0% +animals i'm not getting it right early + + + align:start position:0% +animals i'm not getting it right early +on they can discriminate you can + + align:start position:0% +on they can discriminate you can + + + align:start position:0% +on they can discriminate you can +discriminate both right + + align:start position:0% +discriminate both right + + + align:start position:0% +discriminate both right +so what's the question so i'm wondering + + align:start position:0% +so what's the question so i'm wondering + + + align:start position:0% +so what's the question so i'm wondering +like what other animals can they + + align:start position:0% +like what other animals can they + + + align:start position:0% +like what other animals can they +discriminate and what i see i see how + + align:start position:0% +discriminate and what i see i see how + + + align:start position:0% +discriminate and what i see i see how +far does it go yeah good question + + align:start position:0% +far does it go yeah good question + + + align:start position:0% +far does it go yeah good question +i don't know that anybody has asked + + align:start position:0% +i don't know that anybody has asked + + + align:start position:0% +i don't know that anybody has asked +little kids if they can discriminate + + align:start position:0% +little kids if they can discriminate + + + align:start position:0% +little kids if they can discriminate +other kinds of + + align:start position:0% +other kinds of + + + align:start position:0% +other kinds of +faces other than monkey faces + + align:start position:0% +faces other than monkey faces + + + align:start position:0% +faces other than monkey faces +um i'm sure there's some limit to it + + align:start position:0% +um i'm sure there's some limit to it + + + align:start position:0% +um i'm sure there's some limit to it +like fish faces + + align:start position:0% +like fish faces + + + align:start position:0% +like fish faces +probably i don't know + + align:start position:0% +probably i don't know + + + align:start position:0% +probably i don't know +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um + + align:start position:0% +um + + + align:start position:0% +um +but there's also actually in terms of + + align:start position:0% +but there's also actually in terms of + + + align:start position:0% +but there's also actually in terms of +that extended i don't know the answer to + + align:start position:0% +that extended i don't know the answer to + + + align:start position:0% +that extended i don't know the answer to +that yeah there's going to be some limit + + align:start position:0% +that yeah there's going to be some limit + + + align:start position:0% +that yeah there's going to be some limit +but in terms of the question of um how + + align:start position:0% +but in terms of the question of um how + + + align:start position:0% +but in terms of the question of um how +far you can accept you know + + align:start position:0% +far you can accept you know + + + align:start position:0% +far you can accept you know +how long can you relearn those abilities + + align:start position:0% +how long can you relearn those abilities + + + align:start position:0% +how long can you relearn those abilities +or maintain them it's not like + + align:start position:0% +or maintain them it's not like + + + align:start position:0% +or maintain them it's not like +perceptual narrowing um is going to + + align:start position:0% +perceptual narrowing um is going to + + + align:start position:0% +perceptual narrowing um is going to +happen at six months automatically so if + + align:start position:0% +happen at six months automatically so if + + + align:start position:0% +happen at six months automatically so if +you manipulate it so the the studies on + + align:start position:0% +you manipulate it so the the studies on + + + align:start position:0% +you manipulate it so the the studies on +humans + + align:start position:0% +humans + + + align:start position:0% +humans +if you send i feel like i said this in + + align:start position:0% +if you send i feel like i said this in + + + align:start position:0% +if you send i feel like i said this in +here before but it must have been + + align:start position:0% +here before but it must have been + + + align:start position:0% +here before but it must have been +somewhere else + + align:start position:0% +somewhere else + + + align:start position:0% +somewhere else +if you send parents home + + align:start position:0% +if you send parents home + + + align:start position:0% +if you send parents home +with books with monkey pictures in them + + align:start position:0% +with books with monkey pictures in them + + + align:start position:0% +with books with monkey pictures in them +parents of six month olds + + align:start position:0% +parents of six month olds + + + align:start position:0% +parents of six month olds +and you say look every night go through + + align:start position:0% +and you say look every night go through + + + align:start position:0% +and you say look every night go through +the book with your kids and say there's + + align:start position:0% +the book with your kids and say there's + + + align:start position:0% +the book with your kids and say there's +monkey joe and there's monkey bob and + + align:start position:0% +monkey joe and there's monkey bob and + + + align:start position:0% +monkey joe and there's monkey bob and +there's monkey whoever with your kids + + align:start position:0% +there's monkey whoever with your kids + + + align:start position:0% +there's monkey whoever with your kids +and you have them do that from age six + + align:start position:0% +and you have them do that from age six + + + align:start position:0% +and you have them do that from age six +months to 12 months they don't + + align:start position:0% +months to 12 months they don't + + + align:start position:0% +months to 12 months they don't +perceptually narrow because they + + align:start position:0% +perceptually narrow because they + + + align:start position:0% +perceptually narrow because they +continue to get that experience + + align:start position:0% +continue to get that experience + + + align:start position:0% +continue to get that experience +right + + align:start position:0% +right + + + align:start position:0% +right +interestingly + + align:start position:0% +interestingly + + + align:start position:0% +interestingly +if the parents go home and just say look + + align:start position:0% +if the parents go home and just say look + + + align:start position:0% +if the parents go home and just say look +look + + align:start position:0% +look + + + align:start position:0% +look +that doesn't do it + + align:start position:0% +that doesn't do it + + + align:start position:0% +that doesn't do it +you have to give them some social cue + + align:start position:0% +you have to give them some social cue + + + align:start position:0% +you have to give them some social cue +that is essentially saying this thing is + + align:start position:0% +that is essentially saying this thing is + + + align:start position:0% +that is essentially saying this thing is +different from that thing + + align:start position:0% +different from that thing + + + align:start position:0% +different from that thing +if you do that with an infant even they + + align:start position:0% +if you do that with an infant even they + + + align:start position:0% +if you do that with an infant even they +don't really understand language much + + align:start position:0% +don't really understand language much + + + align:start position:0% +don't really understand language much +they get that cue and they learn to + + align:start position:0% +they get that cue and they learn to + + + align:start position:0% +they get that cue and they learn to +discriminate or they maintain their + + align:start position:0% +discriminate or they maintain their + + + align:start position:0% +discriminate or they maintain their +ability to discriminate monkey faces + + align:start position:0% + + + + align:start position:0% + +yeah does that hold up even when they're + + align:start position:0% +yeah does that hold up even when they're + + + align:start position:0% +yeah does that hold up even when they're +like past 12 months old + + align:start position:0% +like past 12 months old + + + align:start position:0% +like past 12 months old +uh well i'm guessing it will be just + + align:start position:0% +uh well i'm guessing it will be just + + + align:start position:0% +uh well i'm guessing it will be just +like the case that uh mccone showed with + + align:start position:0% +like the case that uh mccone showed with + + + align:start position:0% +like the case that uh mccone showed with +other race effects right i'm guessing + + align:start position:0% +other race effects right i'm guessing + + + align:start position:0% +other race effects right i'm guessing +the other species effect would be + + align:start position:0% +the other species effect would be + + + align:start position:0% +the other species effect would be +like the other race effect in that if + + align:start position:0% +like the other race effect in that if + + + align:start position:0% +like the other race effect in that if +you say start working in a monkey lab + + align:start position:0% +you say start working in a monkey lab + + + align:start position:0% +you say start working in a monkey lab +when you're eight years old + + align:start position:0% +when you're eight years old + + + align:start position:0% +when you're eight years old +that would be weird but you could + + align:start position:0% +that would be weird but you could + + + align:start position:0% +that would be weird but you could +or you + + align:start position:0% +or you + + + align:start position:0% +or you +i don't know whatever anyway that you + + align:start position:0% +i don't know whatever anyway that you + + + align:start position:0% +i don't know whatever anyway that you +would be able to relearn it + + align:start position:0% +would be able to relearn it + + + align:start position:0% +would be able to relearn it +on the same time scale that you would + + align:start position:0% +on the same time scale that you would + + + align:start position:0% +on the same time scale that you would +relearn + + align:start position:0% +relearn + + + align:start position:0% +relearn +um you know relearn or learn for the + + align:start position:0% +um you know relearn or learn for the + + + align:start position:0% +um you know relearn or learn for the +first time uh previously unfamiliar + + align:start position:0% +first time uh previously unfamiliar + + + align:start position:0% +first time uh previously unfamiliar +races of faces but maybe those are + + align:start position:0% +races of faces but maybe those are + + + align:start position:0% +races of faces but maybe those are +slightly different timelines + + align:start position:0% +slightly different timelines + + + align:start position:0% +slightly different timelines +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +could you do something similar um with + + align:start position:0% +could you do something similar um with + + + align:start position:0% +could you do something similar um with +like the monkey faces but would like + + align:start position:0% +like the monkey faces but would like + + + align:start position:0% +like the monkey faces but would like +phonemes of different languages + + align:start position:0% +phonemes of different languages + + + align:start position:0% +phonemes of different languages +i'm sure you can and i'm sure that has + + align:start position:0% +i'm sure you can and i'm sure that has + + + align:start position:0% +i'm sure you can and i'm sure that has +been done but i don't know that + + align:start position:0% +been done but i don't know that + + + align:start position:0% +been done but i don't know that +literature yeah yeah you mean like keep + + align:start position:0% +literature yeah yeah you mean like keep + + + align:start position:0% +literature yeah yeah you mean like keep +well okay i mean it essentially does get + + align:start position:0% +well okay i mean it essentially does get + + + align:start position:0% +well okay i mean it essentially does get +done right so kids who stay in + + align:start position:0% +done right so kids who stay in + + + align:start position:0% +done right so kids who stay in +environments + + align:start position:0% +environments + + + align:start position:0% +environments +let me think about this well certainly a + + align:start position:0% +let me think about this well certainly a + + + align:start position:0% +let me think about this well certainly a +a an infant who's being raised in a + + align:start position:0% +a an infant who's being raised in a + + + align:start position:0% +a an infant who's being raised in a +bilingual environment will maintain + + align:start position:0% +bilingual environment will maintain + + + align:start position:0% +bilingual environment will maintain +their ability to discriminate those + + align:start position:0% +their ability to discriminate those + + + align:start position:0% +their ability to discriminate those +phonemes from any of the languages they + + align:start position:0% +phonemes from any of the languages they + + + align:start position:0% +phonemes from any of the languages they +hear right + + align:start position:0% +hear right + + + align:start position:0% +hear right +it's you're saying that like with the + + align:start position:0% +it's you're saying that like with the + + + align:start position:0% +it's you're saying that like with the +monkeys i need like some kind of social + + align:start position:0% +monkeys i need like some kind of social + + + align:start position:0% +monkeys i need like some kind of social +cue + + align:start position:0% +cue + + + align:start position:0% +cue +to like know that i suspect that's true + + align:start position:0% +to like know that i suspect that's true + + + align:start position:0% +to like know that i suspect that's true +i don't know this literature well enough + + align:start position:0% +i don't know this literature well enough + + + align:start position:0% +i don't know this literature well enough +i do know yeah actually it's coming back + + align:start position:0% +i do know yeah actually it's coming back + + + align:start position:0% +i do know yeah actually it's coming back +dimly heather do you know this janet + + align:start position:0% +dimly heather do you know this janet + + + align:start position:0% +dimly heather do you know this janet +werker + + align:start position:0% +werker + + + align:start position:0% +werker +i okay so janet werker is this amazing + + align:start position:0% +i okay so janet werker is this amazing + + + align:start position:0% +i okay so janet werker is this amazing +infant phoneme perception researcher and + + align:start position:0% +infant phoneme perception researcher and + + + align:start position:0% +infant phoneme perception researcher and +i'm pretty sure + + align:start position:0% +i'm pretty sure + + + align:start position:0% +i'm pretty sure +that if you present infants with just + + align:start position:0% +that if you present infants with just + + + align:start position:0% +that if you present infants with just +like a tv in the background with a + + align:start position:0% +like a tv in the background with a + + + align:start position:0% +like a tv in the background with a +foreign language + + align:start position:0% +foreign language + + + align:start position:0% +foreign language +um even if the infant doesn't have much + + align:start position:0% +um even if the infant doesn't have much + + + align:start position:0% +um even if the infant doesn't have much +else to do that's not enough and you + + align:start position:0% +else to do that's not enough and you + + + align:start position:0% +else to do that's not enough and you +need to like look at them and engage + + align:start position:0% +need to like look at them and engage + + + align:start position:0% +need to like look at them and engage +with them and speak mother ease like hey + + align:start position:0% +with them and speak mother ease like hey + + + align:start position:0% +with them and speak mother ease like hey +infant blah blah right + + align:start position:0% +infant blah blah right + + + align:start position:0% +infant blah blah right +i think you need to do all of that for + + align:start position:0% +i think you need to do all of that for + + + align:start position:0% +i think you need to do all of that for +them to maintain it but i'm yeah that's + + align:start position:0% +them to maintain it but i'm yeah that's + + + align:start position:0% +them to maintain it but i'm yeah that's +correct i think it also has to be + + align:start position:0% +correct i think it also has to be + + + align:start position:0% +correct i think it also has to be +interaction they can't also + + align:start position:0% +interaction they can't also + + + align:start position:0% +interaction they can't also +be watching there's been confidence + + align:start position:0% + + + + align:start position:0% + +it has to be what it has to be like a + + align:start position:0% +it has to be what it has to be like a + + + align:start position:0% +it has to be what it has to be like a +lot it can't be yeah like skype + + align:start position:0% +lot it can't be yeah like skype + + + align:start position:0% +lot it can't be yeah like skype +personally yeah which might somebody was + + align:start position:0% +personally yeah which might somebody was + + + align:start position:0% +personally yeah which might somebody was +like joint and gen or something like you + + align:start position:0% +like joint and gen or something like you + + + align:start position:0% +like joint and gen or something like you +can interact in different ways in person + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% +oh + + + align:start position:0% +oh +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +question about like how long that can + + align:start position:0% +question about like how long that can + + + align:start position:0% +question about like how long that can +last like if someone's + + align:start position:0% +last like if someone's + + + align:start position:0% +last like if someone's +someone spoke for a language when they + + align:start position:0% +someone spoke for a language when they + + + align:start position:0% +someone spoke for a language when they +were younger and moved somewhere else if + + align:start position:0% +were younger and moved somewhere else if + + + align:start position:0% +were younger and moved somewhere else if +we're adopted then they stop speaking + + align:start position:0% +we're adopted then they stop speaking + + + align:start position:0% +we're adopted then they stop speaking +behind us + + align:start position:0% + + + + align:start position:0% + +would they + + align:start position:0% +would they + + + align:start position:0% +would they +um sort of contain that ability + + align:start position:0% + + + + align:start position:0% + +i don't know i'm sure there's a + + align:start position:0% +i don't know i'm sure there's a + + + align:start position:0% +i don't know i'm sure there's a +literature on that you don't know that + + align:start position:0% +literature on that you don't know that + + + align:start position:0% +literature on that you don't know that +dana do you sorry like so you're you're + + align:start position:0% +dana do you sorry like so you're you're + + + align:start position:0% +dana do you sorry like so you're you're +raised bilingual and then you stop + + align:start position:0% +raised bilingual and then you stop + + + align:start position:0% +raised bilingual and then you stop +having the experience early on from your + + align:start position:0% +having the experience early on from your + + + align:start position:0% +having the experience early on from your +second language and then you're + + align:start position:0% +second language and then you're + + + align:start position:0% +second language and then you're +re-exposed later + + align:start position:0% +re-exposed later + + + align:start position:0% +re-exposed later +at age eight + + align:start position:0% +at age eight + + + align:start position:0% +at age eight +yeah you still have the + + align:start position:0% + + + + align:start position:0% + +but then that's not consistent with + + align:start position:0% +but then that's not consistent with + + + align:start position:0% +but then that's not consistent with +perceptual narrowing + + align:start position:0% +perceptual narrowing + + + align:start position:0% +perceptual narrowing +if you're exposed before two years yeah + + align:start position:0% +if you're exposed before two years yeah + + + align:start position:0% +if you're exposed before two years yeah +yeah and then you move away + + align:start position:0% +yeah and then you move away + + + align:start position:0% +yeah and then you move away +if it goes beyond that six month thing + + align:start position:0% +if it goes beyond that six month thing + + + align:start position:0% +if it goes beyond that six month thing +yeah okay + + align:start position:0% +yeah okay + + + align:start position:0% +yeah okay +i think that's the case yeah you might + + align:start position:0% +i think that's the case yeah you might + + + align:start position:0% +i think that's the case yeah you might +not have the higher structure but if you + + align:start position:0% +not have the higher structure but if you + + + align:start position:0% +not have the higher structure but if you +like you learn + + align:start position:0% +like you learn + + + align:start position:0% +like you learn +the syntax and some vocabulary like + + align:start position:0% +the syntax and some vocabulary like + + + align:start position:0% +the syntax and some vocabulary like +you'll have a better accent than someone + + align:start position:0% +you'll have a better accent than someone + + + align:start position:0% +you'll have a better accent than someone +who did not have that early experience + + align:start position:0% +who did not have that early experience + + + align:start position:0% +who did not have that early experience +might not be able to differentiate + + align:start position:0% +might not be able to differentiate + + + align:start position:0% +might not be able to differentiate +emotions + + align:start position:0% +emotions + + + align:start position:0% +emotions +but we just talked about this + + align:start position:0% + + + + align:start position:0% + +okay good one more question josh so do + + align:start position:0% +okay good one more question josh so do + + + align:start position:0% +okay good one more question josh so do +we know cases where there's like + + align:start position:0% +we know cases where there's like + + + align:start position:0% +we know cases where there's like +an inclusive sort of mismatch between + + align:start position:0% +an inclusive sort of mismatch between + + + align:start position:0% +an inclusive sort of mismatch between +fmri and bayern munich sort of + + align:start position:0% +fmri and bayern munich sort of + + + align:start position:0% +fmri and bayern munich sort of +information + + align:start position:0% +information + + + align:start position:0% +information +like like this yeah like but this + + align:start position:0% +like like this yeah like but this + + + align:start position:0% +like like this yeah like but this +probably in some other domain of some of + + align:start position:0% +probably in some other domain of some of + + + align:start position:0% +probably in some other domain of some of +those + + align:start position:0% +those + + + align:start position:0% +those +you know basically images + + align:start position:0% +you know basically images + + + align:start position:0% +you know basically images +oh god i don't have my you know + + align:start position:0% +oh god i don't have my you know + + + align:start position:0% +oh god i don't have my you know +dictionary of knowledge filed that way + + align:start position:0% +dictionary of knowledge filed that way + + + align:start position:0% +dictionary of knowledge filed that way +so i can pull up an instance of that but + + align:start position:0% +so i can pull up an instance of that but + + + align:start position:0% +so i can pull up an instance of that but +i'm sure there are loads of those + + align:start position:0% +i'm sure there are loads of those + + + align:start position:0% +i'm sure there are loads of those +yeah well because when we because we're + + align:start position:0% +yeah well because when we because we're + + + align:start position:0% +yeah well because when we because we're +making all these assumptions about which + + align:start position:0% +making all these assumptions about which + + + align:start position:0% +making all these assumptions about which +behavioral ability is subserved by some + + align:start position:0% +behavioral ability is subserved by some + + + align:start position:0% +behavioral ability is subserved by some +particular activation in the brain and + + align:start position:0% +particular activation in the brain and + + + align:start position:0% +particular activation in the brain and +mostly we don't know + + align:start position:0% +mostly we don't know + + + align:start position:0% +mostly we don't know +right we know we know when we have the + + align:start position:0% +right we know we know when we have the + + + align:start position:0% +right we know we know when we have the +rare opportunities to do causal tests we + + align:start position:0% +rare opportunities to do causal tests we + + + align:start position:0% +rare opportunities to do causal tests we +have a better idea that that system is + + align:start position:0% +have a better idea that that system is + + + align:start position:0% +have a better idea that that system is +at least causally involved in that + + align:start position:0% +at least causally involved in that + + + align:start position:0% +at least causally involved in that +behavioral ability + + align:start position:0% +behavioral ability + + + align:start position:0% +behavioral ability +um but yeah often those links are much + + align:start position:0% +um but yeah often those links are much + + + align:start position:0% +um but yeah often those links are much +looser than we'd like + + align:start position:0% +looser than we'd like + + + align:start position:0% +looser than we'd like +all right see you guys wednesday + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/l88D4r74gtM.txt b/l88D4r74gtM.txt new file mode 100644 index 0000000000000000000000000000000000000000..5bb57640c48dd04847ca31b8f852e3e20622619c --- /dev/null +++ b/l88D4r74gtM.txt @@ -0,0 +1,7028 @@ +align:start position:0% + +okay the this is the review uh lecture + + align:start position:0% +okay the this is the review uh lecture + + + align:start position:0% +okay the this is the review uh lecture +for the first part of the course uh the + + align:start position:0% +for the first part of the course uh the + + + align:start position:0% +for the first part of the course uh the +axal B part of the course uh and + + align:start position:0% +axal B part of the course uh and + + + align:start position:0% +axal B part of the course uh and +um the exam will emphasize chapter 3 + + align:start position:0% +um the exam will emphasize chapter 3 + + + align:start position:0% +um the exam will emphasize chapter 3 +cuz those are the chapter 3 was about + + align:start position:0% +cuz those are the chapter 3 was about + + + align:start position:0% +cuz those are the chapter 3 was about +the rectangular matrices where we had + + align:start position:0% +the rectangular matrices where we had + + + align:start position:0% +the rectangular matrices where we had +null spaces and no spaces of a transpose + + align:start position:0% +null spaces and no spaces of a transpose + + + align:start position:0% +null spaces and no spaces of a transpose +and ranks and all the things that are so + + align:start position:0% +and ranks and all the things that are so + + + align:start position:0% +and ranks and all the things that are so +clear when the Matrix is square and + + align:start position:0% +clear when the Matrix is square and + + + align:start position:0% +clear when the Matrix is square and +invertible they + + align:start position:0% +invertible they + + + align:start position:0% +invertible they +became things to think about for uh + + align:start position:0% +became things to think about for uh + + + align:start position:0% +became things to think about for uh +rectangular + + align:start position:0% +rectangular + + + align:start position:0% +rectangular +matrices so uh and Vector spaces and sub + + align:start position:0% +matrices so uh and Vector spaces and sub + + + align:start position:0% +matrices so uh and Vector spaces and sub +spaces and above all those four + + align:start position:0% +spaces and above all those four + + + align:start position:0% +spaces and above all those four +subspaces okay I'm thinking to start at + + align:start position:0% +subspaces okay I'm thinking to start at + + + align:start position:0% +subspaces okay I'm thinking to start at +least I'll just look at old exams read + + align:start position:0% +least I'll just look at old exams read + + + align:start position:0% +least I'll just look at old exams read +out questions write on the board what I + + align:start position:0% +out questions write on the board what I + + + align:start position:0% +out questions write on the board what I +need to and we can see what the answers + + align:start position:0% +need to and we can see what the answers + + + align:start position:0% +need to and we can see what the answers +are uh the first one I see is one I can + + align:start position:0% +are uh the first one I see is one I can + + + align:start position:0% +are uh the first one I see is one I can +just read out well I'll write a little + + align:start position:0% +just read out well I'll write a little + + + align:start position:0% +just read out well I'll write a little +suppose U V and W are non non zero + + align:start position:0% +suppose U V and W are non non zero + + + align:start position:0% +suppose U V and W are non non zero +vectors in r + + align:start position:0% + + + + align:start position:0% + +s what are the possible they span a a + + align:start position:0% +s what are the possible they span a a + + + align:start position:0% +s what are the possible they span a a +vector space they span a Subspace of our + + align:start position:0% +vector space they span a Subspace of our + + + align:start position:0% +vector space they span a Subspace of our +s and what are the possible + + align:start position:0% +s and what are the possible + + + align:start position:0% +s and what are the possible +Dimensions so it's a straightforward + + align:start position:0% +Dimensions so it's a straightforward + + + align:start position:0% +Dimensions so it's a straightforward +question what are the possible + + align:start position:0% +question what are the possible + + + align:start position:0% +question what are the possible +dimensions of the Subspace spaned by UV + + align:start position:0% +dimensions of the Subspace spaned by UV + + + align:start position:0% +dimensions of the Subspace spaned by UV +and + + align:start position:0% +and + + + align:start position:0% +and +W okay I + + align:start position:0% +W okay I + + + align:start position:0% +W okay I +one two or three right one two or three + + align:start position:0% +one two or three right one two or three + + + align:start position:0% +one two or three right one two or three +couldn't be more because we've only got + + align:start position:0% +couldn't be more because we've only got + + + align:start position:0% +couldn't be more because we've only got +three + + align:start position:0% +three + + + align:start position:0% +three +vectors and couldn't be zero + + align:start position:0% +vectors and couldn't be zero + + + align:start position:0% +vectors and couldn't be zero +because + + align:start position:0% +because + + + align:start position:0% +because +uh cuz I told you the vectors were + + align:start position:0% +uh cuz I told you the vectors were + + + align:start position:0% +uh cuz I told you the vectors were +nonzero otherwise if if if I allowed the + + align:start position:0% +nonzero otherwise if if if I allowed the + + + align:start position:0% +nonzero otherwise if if if I allowed the +possibility that those were all the zero + + align:start position:0% +possibility that those were all the zero + + + align:start position:0% +possibility that those were all the zero +Vector then the Zero Dimensional + + align:start position:0% +Vector then the Zero Dimensional + + + align:start position:0% +Vector then the Zero Dimensional +Subspace would have been in there okay + + align:start position:0% +Subspace would have been in there okay + + + align:start position:0% +Subspace would have been in there okay +now can I jump to uh a more serious + + align:start position:0% +now can I jump to uh a more serious + + + align:start position:0% +now can I jump to uh a more serious +question okay we have a 5x3 + + align:start position:0% +question okay we have a 5x3 + + + align:start position:0% +question okay we have a 5x3 +matrix and I'm calling it + + align:start position:0% +matrix and I'm calling it + + + align:start position:0% +matrix and I'm calling it +U I'm saying it's in ealon form and it + + align:start position:0% +U I'm saying it's in ealon form and it + + + align:start position:0% +U I'm saying it's in ealon form and it +has three pivots r equal three three + + align:start position:0% + + + + align:start position:0% + +pivots okay first question what's the + + align:start position:0% +pivots okay first question what's the + + + align:start position:0% +pivots okay first question what's the +null space + + align:start position:0% +null space + + + align:start position:0% +null space +what's the null space of this Matrix U + + align:start position:0% +what's the null space of this Matrix U + + + align:start position:0% +what's the null space of this Matrix U +so this Matrix is 5 by3 and I I find it + + align:start position:0% +so this Matrix is 5 by3 and I I find it + + + align:start position:0% +so this Matrix is 5 by3 and I I find it +helpful + + align:start position:0% +helpful + + + align:start position:0% +helpful +to just see visually what 5x3 means what + + align:start position:0% +to just see visually what 5x3 means what + + + align:start position:0% +to just see visually what 5x3 means what +that shape is three columns three + + align:start position:0% +that shape is three columns three + + + align:start position:0% +that shape is three columns three +columns in U then five rows three pivots + + align:start position:0% +columns in U then five rows three pivots + + + align:start position:0% +columns in U then five rows three pivots +and what's the null space the null space + + align:start position:0% +and what's the null space the null space + + + align:start position:0% +and what's the null space the null space +of U is + + align:start position:0% +of U is + + + align:start position:0% +of U is +and it asks for a spe of course I'm + + align:start position:0% +and it asks for a spe of course I'm + + + align:start position:0% +and it asks for a spe of course I'm +looking for an answer that isn't just + + align:start position:0% +looking for an answer that isn't just + + + align:start position:0% +looking for an answer that isn't just +the definition of the null space but is + + align:start position:0% +the definition of the null space but is + + + align:start position:0% +the definition of the null space but is +the null space of this Matrix with this + + align:start position:0% +the null space of this Matrix with this + + + align:start position:0% +the null space of this Matrix with this +information and what is it it's only the + + align:start position:0% +information and what is it it's only the + + + align:start position:0% +information and what is it it's only the +zero Vector because we're told that the + + align:start position:0% +zero Vector because we're told that the + + + align:start position:0% +zero Vector because we're told that the +rank is three so those three columns + + align:start position:0% +rank is three so those three columns + + + align:start position:0% +rank is three so those three columns +must be + + align:start position:0% +must be + + + align:start position:0% +must be +independent no combination of those Comm + + align:start position:0% +independent no combination of those Comm + + + align:start position:0% +independent no combination of those Comm +of those columns is the zero Vector + + align:start position:0% +of those columns is the zero Vector + + + align:start position:0% +of those columns is the zero Vector +except so the only thing in this null + + align:start position:0% +except so the only thing in this null + + + align:start position:0% +except so the only thing in this null +space is the zero vector and I could + + align:start position:0% +space is the zero vector and I could + + + align:start position:0% +space is the zero vector and I could +even say what that Vector is 0 0 0 + + align:start position:0% +even say what that Vector is 0 0 0 + + + align:start position:0% +even say what that Vector is 0 0 0 +that's okay so that's what's in the null + + align:start position:0% +that's okay so that's what's in the null + + + align:start position:0% +that's okay so that's what's in the null +space all right let me + + align:start position:0% +space all right let me + + + align:start position:0% +space all right let me +go on with this question has multiple + + align:start position:0% +go on with this question has multiple + + + align:start position:0% +go on with this question has multiple +Parts + + align:start position:0% +Parts + + + align:start position:0% +Parts +um what's + + align:start position:0% +um what's + + + align:start position:0% +um what's +the oh now it asks you about a 10x3 + + align:start position:0% +the oh now it asks you about a 10x3 + + + align:start position:0% +the oh now it asks you about a 10x3 +matrix B which is the Matrix U and 2 U + + align:start position:0% + + + + align:start position:0% + +it actually I would probably be writing + + align:start position:0% +it actually I would probably be writing + + + align:start position:0% +it actually I would probably be writing +R if uh if and maybe I should be writing + + align:start position:0% +R if uh if and maybe I should be writing + + + align:start position:0% +R if uh if and maybe I should be writing +R here now the the this this exam goes + + align:start position:0% +R here now the the this this exam goes + + + align:start position:0% +R here now the the this this exam goes +back a few years when I emphasized youu + + align:start position:0% +back a few years when I emphasized youu + + + align:start position:0% +back a few years when I emphasized youu +more than + + align:start position:0% +more than + + + align:start position:0% +more than +R uh now what's the echelon form for + + align:start position:0% +R uh now what's the echelon form for + + + align:start position:0% +R uh now what's the echelon form for +that + + align:start position:0% +that + + + align:start position:0% +that +Matrix so the echelon form what's the + + align:start position:0% +Matrix so the echelon form what's the + + + align:start position:0% +Matrix so the echelon form what's the +rank and what's the echelon form + + align:start position:0% + + + + align:start position:0% + +let's suppose this is in reduced Echelon + + align:start position:0% +let's suppose this is in reduced Echelon + + + align:start position:0% +let's suppose this is in reduced Echelon +form so that I could be using the letter + + align:start position:0% +form so that I could be using the letter + + + align:start position:0% +form so that I could be using the letter +R so I'll I'll ask for the reduced row + + align:start position:0% +R so I'll I'll ask for the reduced row + + + align:start position:0% +R so I'll I'll ask for the reduced row +Echelon form so imagine that these are U + + align:start position:0% +Echelon form so imagine that these are U + + + align:start position:0% +Echelon form so imagine that these are U +is + + align:start position:0% +is + + + align:start position:0% +is +in reduced row Echelon form but now I've + + align:start position:0% +in reduced row Echelon form but now I've + + + align:start position:0% +in reduced row Echelon form but now I've +got I've doubled the height of the + + align:start position:0% +got I've doubled the height of the + + + align:start position:0% +got I've doubled the height of the +Matrix what will happen when we do row + + align:start position:0% +Matrix what will happen when we do row + + + align:start position:0% +Matrix what will happen when we do row +reduction what row reduction will take + + align:start position:0% +reduction what row reduction will take + + + align:start position:0% +reduction what row reduction will take +us to what Matrix + + align:start position:0% + + + + align:start position:0% + +here so you start doing + + align:start position:0% +here so you start doing + + + align:start position:0% +here so you start doing +elimination you're doing elimination on + + align:start position:0% +elimination you're doing elimination on + + + align:start position:0% +elimination you're doing elimination on +single rows but of course we're allowed + + align:start position:0% +single rows but of course we're allowed + + + align:start position:0% +single rows but of course we're allowed +to think of blocks so what well what's + + align:start position:0% +to think of blocks so what well what's + + + align:start position:0% +to think of blocks so what well what's +the answer look like U and z or r i + + align:start position:0% +the answer look like U and z or r i + + + align:start position:0% +the answer look like U and z or r i +let's I'll stay with this letter U but + + align:start position:0% +let's I'll stay with this letter U but + + + align:start position:0% +let's I'll stay with this letter U but +I'm really thinking it's in reduced form + + align:start position:0% +I'm really thinking it's in reduced form + + + align:start position:0% +I'm really thinking it's in reduced form +and zero + + align:start position:0% +and zero + + + align:start position:0% +and zero +okay fine then uh it asks oh further it + + align:start position:0% +okay fine then uh it asks oh further it + + + align:start position:0% +okay fine then uh it asks oh further it +asks about this + + align:start position:0% +asks about this + + + align:start position:0% +asks about this +Matrix u u u and + + align:start position:0% +Matrix u u u and + + + align:start position:0% +Matrix u u u and +zero okay what's the echelon form of + + align:start position:0% +zero okay what's the echelon form of + + + align:start position:0% +zero okay what's the echelon form of +this so it's just like practice and + + align:start position:0% +this so it's just like practice and + + + align:start position:0% +this so it's just like practice and +thinking through what would row + + align:start position:0% +thinking through what would row + + + align:start position:0% +thinking through what would row +elimination what would row reduction + + align:start position:0% +elimination what would row reduction + + + align:start position:0% +elimination what would row reduction +do have I thought this through so what + + align:start position:0% +do have I thought this through so what + + + align:start position:0% +do have I thought this through so what +what are we if we start doing + + align:start position:0% +what are we if we start doing + + + align:start position:0% +what are we if we start doing +elimination basically we're going to + + align:start position:0% +elimination basically we're going to + + + align:start position:0% +elimination basically we're going to +subtract these rows from these so it's + + align:start position:0% +subtract these rows from these so it's + + + align:start position:0% +subtract these rows from these so it's +going to take us + + align:start position:0% +going to take us + + + align:start position:0% +going to take us +to U + + align:start position:0% +to U + + + align:start position:0% +to U +u0 and minus U I guess + + align:start position:0% + + + + align:start position:0% + +right take the thing all the way to uh R + + align:start position:0% +right take the thing all the way to uh R + + + align:start position:0% +right take the thing all the way to uh R +let's let's suppose U is really R + + align:start position:0% +let's let's suppose U is really R + + + align:start position:0% +let's let's suppose U is really R +suppose that we're really going for the + + align:start position:0% +suppose that we're really going for the + + + align:start position:0% +suppose that we're really going for the +reduced row Echelon form then would we + + align:start position:0% +reduced row Echelon form then would we + + + align:start position:0% +reduced row Echelon form then would we +stop there + + align:start position:0% + + + + align:start position:0% + +no uh we would clean out we would we + + align:start position:0% +no uh we would clean out we would we + + + align:start position:0% +no uh we would clean out we would we +could use this to is that right can I so + + align:start position:0% +could use this to is that right can I so + + + align:start position:0% +could use this to is that right can I so +I took this row these rows away from + + align:start position:0% +I took this row these rows away from + + + align:start position:0% +I took this row these rows away from +these to get there now I take these rows + + align:start position:0% +these to get there now I take these rows + + + align:start position:0% +these to get there now I take these rows +away from these so that gives me + + align:start position:0% + + + + align:start position:0% + +zero there and now what uh what more + + align:start position:0% +zero there and now what uh what more + + + align:start position:0% +zero there and now what uh what more +would I do if I'm really shooting for R + + align:start position:0% +would I do if I'm really shooting for R + + + align:start position:0% +would I do if I'm really shooting for R +the reduced row Echelon + + align:start position:0% +the reduced row Echelon + + + align:start position:0% +the reduced row Echelon +form I I would then I want plus ones in + + align:start position:0% +form I I would then I want plus ones in + + + align:start position:0% +form I I would then I want plus ones in +the pivot so I would multiply through by + + align:start position:0% +the pivot so I would multiply through by + + + align:start position:0% +the pivot so I would multiply through by +minus one to get plus there so + + align:start position:0% +minus one to get plus there so + + + align:start position:0% +minus one to get plus there so +essentially I'm + + align:start position:0% +essentially I'm + + + align:start position:0% +essentially I'm +seeing uh reduced row Echelon form there + + align:start position:0% +seeing uh reduced row Echelon form there + + + align:start position:0% +seeing uh reduced row Echelon form there +and there and and there's just one + + align:start position:0% +and there and and there's just one + + + align:start position:0% +and there and and there's just one +little twist still to go do you see what + + align:start position:0% +little twist still to go do you see what + + + align:start position:0% +little twist still to go do you see what +that final twist might + + align:start position:0% +that final twist might + + + align:start position:0% +that final twist might +be uh to to + + align:start position:0% +be uh to to + + + align:start position:0% +be uh to to +have if if U is in reduced row Echelon + + align:start position:0% +have if if U is in reduced row Echelon + + + align:start position:0% +have if if U is in reduced row Echelon +form and now I'm looking at u u + + align:start position:0% +form and now I'm looking at u u + + + align:start position:0% +form and now I'm looking at u u +there's one little step to take this + + align:start position:0% +there's one little step to take this + + + align:start position:0% +there's one little step to take this +isn't like a big deal at all but but if + + align:start position:0% +isn't like a big deal at all but but if + + + align:start position:0% +isn't like a big deal at all but but if +I really want this to be in reduced + + align:start position:0% +I really want this to be in reduced + + + align:start position:0% +I really want this to be in reduced +form what would I still might might I + + align:start position:0% +form what would I still might might I + + + align:start position:0% +form what would I still might might I +still have to + + align:start position:0% +still have to + + + align:start position:0% +still have to +do I I might have some zero rows here I + + align:start position:0% +do I I might have some zero rows here I + + + align:start position:0% +do I I might have some zero rows here I +might have some zero rows here that + + align:start position:0% +might have some zero rows here that + + + align:start position:0% +might have some zero rows here that +strictly should move to the bottom well + + align:start position:0% +strictly should move to the bottom well + + + align:start position:0% +strictly should move to the bottom well +I'm not going to make a project out of + + align:start position:0% +I'm not going to make a project out of + + + align:start position:0% +I'm not going to make a project out of +that okay what's the rank of that Matrix + + align:start position:0% + + + + align:start position:0% + +what's the rank of this Matrix + + align:start position:0% +what's the rank of this Matrix + + + align:start position:0% +what's the rank of this Matrix +C given that I know that the original U + + align:start position:0% +C given that I know that the original U + + + align:start position:0% +C given that I know that the original U +has rank + + align:start position:0% +has rank + + + align:start position:0% +has rank +three what's the rank of this + + align:start position:0% +three what's the rank of this + + + align:start position:0% +three what's the rank of this +guy six right that has rank six I can + + align:start position:0% +guy six right that has rank six I can + + + align:start position:0% +guy six right that has rank six I can +tell what was what's the rank of this B + + align:start position:0% +tell what was what's the rank of this B + + + align:start position:0% +tell what was what's the rank of this B +while while we're at + + align:start position:0% +while while we're at + + + align:start position:0% +while while we're at +it the rank of B is that six or three + + align:start position:0% +it the rank of B is that six or three + + + align:start position:0% +it the rank of B is that six or three +three is right three is Right CU we + + align:start position:0% +three is right three is Right CU we + + + align:start position:0% +three is right three is Right CU we +actually got it to where we could just + + align:start position:0% +actually got it to where we could just + + + align:start position:0% +actually got it to where we could just +see three pivots okay U and oh now + + align:start position:0% +see three pivots okay U and oh now + + + align:start position:0% +see three pivots okay U and oh now +finally just easy one what's the + + align:start position:0% +finally just easy one what's the + + + align:start position:0% +finally just easy one what's the +dimension of the null + + align:start position:0% + + + + align:start position:0% + +space of the null space of C + + align:start position:0% + + + + align:start position:0% + +transpose oh boy okay so what do I if I + + align:start position:0% +transpose oh boy okay so what do I if I + + + align:start position:0% +transpose oh boy okay so what do I if I +want the dimension of a null space I + + align:start position:0% +want the dimension of a null space I + + + align:start position:0% +want the dimension of a null space I +want to know the size of the Matrix so + + align:start position:0% +want to know the size of the Matrix so + + + align:start position:0% +want to know the size of the Matrix so +what's the size of the Matrix + + align:start position:0% +what's the size of the Matrix + + + align:start position:0% +what's the size of the Matrix +C it looks like + + align:start position:0% +C it looks like + + + align:start position:0% +C it looks like +it's 10x 6 is it 10 by 6 so C is 10 by + + align:start position:0% +it's 10x 6 is it 10 by 6 so C is 10 by + + + align:start position:0% +it's 10x 6 is it 10 by 6 so C is 10 by +6 so m is + + align:start position:0% +6 so m is + + + align:start position:0% +6 so m is +10 so C has 10 row 10 rows C transpose + + align:start position:0% +10 so C has 10 row 10 rows C transpose + + + align:start position:0% +10 so C has 10 row 10 rows C transpose +has 10 columns so there are 10 columns + + align:start position:0% +has 10 columns so there are 10 columns + + + align:start position:0% +has 10 columns so there are 10 columns +there so how many free variables have I + + align:start position:0% +there so how many free variables have I + + + align:start position:0% +there so how many free variables have I +got once I I start with the 10 columns + + align:start position:0% +got once I I start with the 10 columns + + + align:start position:0% +got once I I start with the 10 columns +in C transpose that's the M for the + + align:start position:0% +in C transpose that's the M for the + + + align:start position:0% +in C transpose that's the M for the +original + + align:start position:0% +original + + + align:start position:0% +original +C and what do I subtract + + align:start position:0% +C and what do I subtract + + + align:start position:0% +C and what do I subtract +off six because we said that was the + + align:start position:0% +off six because we said that was the + + + align:start position:0% +off six because we said that was the +rank so I'm left with four thanks okay + + align:start position:0% +rank so I'm left with four thanks okay + + + align:start position:0% +rank so I'm left with four thanks okay +so I think that's the right answer the + + align:start position:0% +so I think that's the right answer the + + + align:start position:0% +so I think that's the right answer the +dimension of the null space of C + + align:start position:0% +dimension of the null space of C + + + align:start position:0% +dimension of the null space of C +transpose would be four right okay yeah + + align:start position:0% +transpose would be four right okay yeah + + + align:start position:0% +transpose would be four right okay yeah +okay let me so that that's one question + + align:start position:0% +okay let me so that that's one question + + + align:start position:0% +okay let me so that that's one question +at least it um brought in um some some + + align:start position:0% +at least it um brought in um some some + + + align:start position:0% +at least it um brought in um some some +of the uh Dimension counts okay here's + + align:start position:0% +of the uh Dimension counts okay here's + + + align:start position:0% +of the uh Dimension counts okay here's +another type of + + align:start position:0% + + + + align:start position:0% + +question I give you an + + align:start position:0% +question I give you an + + + align:start position:0% +question I give you an +equation ax = + + align:start position:0% + + + + align:start position:0% + +242 and I give you the complete + + align:start position:0% + + + + align:start position:0% + +solution but I don't give you the Matrix + + align:start position:0% + + + + align:start position:0% + +and another there + + align:start position:0% +and another there + + + align:start position:0% +and another there +another Vector + + align:start position:0% +another Vector + + + align:start position:0% +another Vector + + align:start position:0% + + + + align:start position:0% + +okay all right my first question is + + align:start position:0% +okay all right my first question is + + + align:start position:0% +okay all right my first question is +what's the dimension of the row + + align:start position:0% +what's the dimension of the row + + + align:start position:0% +what's the dimension of the row +space of the Matrix a + + align:start position:0% +space of the Matrix a + + + align:start position:0% +space of the Matrix a +so the main thing that you want to get + + align:start position:0% +so the main thing that you want to get + + + align:start position:0% +so the main thing that you want to get +from this question is that a question + + align:start position:0% +from this question is that a question + + + align:start position:0% +from this question is that a question +could start this + + align:start position:0% +could start this + + + align:start position:0% +could start this +way sort of backward Way by by giving + + align:start position:0% +way sort of backward Way by by giving + + + align:start position:0% +way sort of backward Way by by giving +you the answer and not telling you what + + align:start position:0% +you the answer and not telling you what + + + align:start position:0% +you the answer and not telling you what +the problem is but we can get a lot of + + align:start position:0% +the problem is but we can get a lot of + + + align:start position:0% +the problem is but we can get a lot of +information and sometimes we can get + + align:start position:0% +information and sometimes we can get + + + align:start position:0% +information and sometimes we can get +complete information about that Matrix a + + align:start position:0% +complete information about that Matrix a + + + align:start position:0% +complete information about that Matrix a +okay so what's the dimension of the row + + align:start position:0% +okay so what's the dimension of the row + + + align:start position:0% +okay so what's the dimension of the row +space of a what's the rank tell tell me + + align:start position:0% +space of a what's the rank tell tell me + + + align:start position:0% +space of a what's the rank tell tell me +about what's the size of the Matrix yeah + + align:start position:0% +about what's the size of the Matrix yeah + + + align:start position:0% +about what's the size of the Matrix yeah +just this is these are the things we + + align:start position:0% +just this is these are the things we + + + align:start position:0% +just this is these are the things we +want to think about what's the what's + + align:start position:0% +want to think about what's the what's + + + align:start position:0% +want to think about what's the what's +the uh what what's the shape of the + + align:start position:0% +the uh what what's the shape of the + + + align:start position:0% +the uh what what's the shape of the +Matrix first of + + align:start position:0% + + + + align:start position:0% + +all it certainly has three + + align:start position:0% + + + + align:start position:0% + +rows but is it all is it + + align:start position:0% +rows but is it all is it + + + align:start position:0% +rows but is it all is it +3x3 the the X's that it multiplies have + + align:start position:0% +3x3 the the X's that it multiplies have + + + align:start position:0% +3x3 the the X's that it multiplies have +three components so that just does the + + align:start position:0% +three components so that just does the + + + align:start position:0% +three components so that just does the +Matrix have three columns also yes so + + align:start position:0% +Matrix have three columns also yes so + + + align:start position:0% +Matrix have three columns also yes so +I'm seeing the same length in in B three + + align:start position:0% +I'm seeing the same length in in B three + + + align:start position:0% +I'm seeing the same length in in B three +and also in a so a is a 3X3 + + align:start position:0% + + + + align:start position:0% + +Matrix and + + align:start position:0% +Matrix and + + + align:start position:0% +Matrix and +uh what's the what's its + + align:start position:0% +uh what's the what's its + + + align:start position:0% +uh what's the what's its +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +rank it's + + align:start position:0% +rank it's + + + align:start position:0% +rank it's +rank tell me something about it n space + + align:start position:0% +rank tell me something about it n space + + + align:start position:0% +rank tell me something about it n space +I heard the right answer for the rank + + align:start position:0% +I heard the right answer for the rank + + + align:start position:0% +I heard the right answer for the rank +the rank is one in this + + align:start position:0% +the rank is one in this + + + align:start position:0% +the rank is one in this +case + + align:start position:0% + + + + align:start position:0% + +why because was the dimension of the + + align:start position:0% +why because was the dimension of the + + + align:start position:0% +why because was the dimension of the +null space so the + + align:start position:0% +null space so the + + + align:start position:0% +null space so the +dimension of the null space of + + align:start position:0% +dimension of the null space of + + + align:start position:0% +dimension of the null space of +a + + align:start position:0% +a + + + align:start position:0% +a +is from knowing that that's the complete + + align:start position:0% +is from knowing that that's the complete + + + align:start position:0% +is from knowing that that's the complete +solution it's two I'm seeing two vectors + + align:start position:0% +solution it's two I'm seeing two vectors + + + align:start position:0% +solution it's two I'm seeing two vectors +here and they're independent in + + align:start position:0% +here and they're independent in + + + align:start position:0% +here and they're independent in +the n space of a because they have to be + + align:start position:0% +the n space of a because they have to be + + + align:start position:0% +the n space of a because they have to be +in the no space of a if I'm allowed to + + align:start position:0% +in the no space of a if I'm allowed to + + + align:start position:0% +in the no space of a if I'm allowed to +throw in to the solution any amount of + + align:start position:0% +throw in to the solution any amount of + + + align:start position:0% +throw in to the solution any amount of +those + + align:start position:0% +those + + + align:start position:0% +those +vectors that tells me that's the no + + align:start position:0% +vectors that tells me that's the no + + + align:start position:0% +vectors that tells me that's the no +space part then so the dimension of the + + align:start position:0% +space part then so the dimension of the + + + align:start position:0% +space part then so the dimension of the +no space is two and then I of course I + + align:start position:0% +no space is two and then I of course I + + + align:start position:0% +no space is two and then I of course I +know the dimensions of all the all all + + align:start position:0% +know the dimensions of all the all all + + + align:start position:0% +know the dimensions of all the all all +four such + + align:start position:0% +four such + + + align:start position:0% +four such +faces now actually it asks what's the + + align:start position:0% + + + + align:start position:0% + +Matrix what's what's the Matrix in this + + align:start position:0% +Matrix what's what's the Matrix in this + + + align:start position:0% +Matrix what's what's the Matrix in this +case + + align:start position:0% + + + + align:start position:0% + +um do we want to shall I try to figure + + align:start position:0% +um do we want to shall I try to figure + + + align:start position:0% +um do we want to shall I try to figure +that out + + align:start position:0% + + + + align:start position:0% + +sure let's you'd like me to do it okay + + align:start position:0% +sure let's you'd like me to do it okay + + + align:start position:0% +sure let's you'd like me to do it okay +uh so what about the Matrix or I'll let + + align:start position:0% +uh so what about the Matrix or I'll let + + + align:start position:0% +uh so what about the Matrix or I'll let +me at least start it okay if a * this x + + align:start position:0% +me at least start it okay if a * this x + + + align:start position:0% +me at least start it okay if a * this x +gives 242 what does that tell me about + + align:start position:0% +gives 242 what does that tell me about + + + align:start position:0% +gives 242 what does that tell me about +the Matrix + + align:start position:0% +the Matrix + + + align:start position:0% +the Matrix +a if a * that + + align:start position:0% +a if a * that + + + align:start position:0% +a if a * that +X solves that equation then that tells + + align:start position:0% +X solves that equation then that tells + + + align:start position:0% +X solves that equation then that tells +me that the First Column is + + align:start position:0% +me that the First Column is + + + align:start position:0% +me that the First Column is +the First Column of a + + align:start position:0% +the First Column of a + + + align:start position:0% +the First Column of a +is one 2 1 right the First Column of a + + align:start position:0% +is one 2 1 right the First Column of a + + + align:start position:0% +is one 2 1 right the First Column of a +has to be 1 2 1 because if I multiply by + + align:start position:0% +has to be 1 2 1 because if I multiply by + + + align:start position:0% +has to be 1 2 1 because if I multiply by +X that's going to multiply just the + + align:start position:0% +X that's going to multiply just the + + + align:start position:0% +X that's going to multiply just the +First Column and give me 2 42 and then + + align:start position:0% +First Column and give me 2 42 and then + + + align:start position:0% +First Column and give me 2 42 and then +I've got two more columns to + + align:start position:0% +I've got two more columns to + + + align:start position:0% +I've got two more columns to +find and what information have I got to + + align:start position:0% +find and what information have I got to + + + align:start position:0% +find and what information have I got to +find them + + align:start position:0% +find them + + + align:start position:0% +find them +with I've got the null + + align:start position:0% +with I've got the null + + + align:start position:0% +with I've got the null +space so the fact that this is in the + + align:start position:0% +space so the fact that this is in the + + + align:start position:0% +space so the fact that this is in the +null space what does does that tell me + + align:start position:0% +null space what does does that tell me + + + align:start position:0% +null space what does does that tell me +about the Matrix a matrix that has 0 01 + + align:start position:0% +about the Matrix a matrix that has 0 01 + + + align:start position:0% +about the Matrix a matrix that has 0 01 +in its null + + align:start position:0% +in its null + + + align:start position:0% +in its null +space that tells me that the last column + + align:start position:0% +space that tells me that the last column + + + align:start position:0% +space that tells me that the last column +of the Matrix is zero because this is in + + align:start position:0% +of the Matrix is zero because this is in + + + align:start position:0% +of the Matrix is zero because this is in +the null space the last column has to be + + align:start position:0% +the null space the last column has to be + + + align:start position:0% +the null space the last column has to be +zero and because this is in the null + + align:start position:0% +zero and because this is in the null + + + align:start position:0% +zero and because this is in the null +space what's the second + + align:start position:0% +space what's the second + + + align:start position:0% +space what's the second +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +column well this in the n space means + + align:start position:0% +column well this in the n space means + + + align:start position:0% +column well this in the n space means +that if I multiply a by that Vector I + + align:start position:0% +that if I multiply a by that Vector I + + + align:start position:0% +that if I multiply a by that Vector I +must be getting zero so I think that + + align:start position:0% +must be getting zero so I think that + + + align:start position:0% +must be getting zero so I think that +better be -1 -2 and + + align:start position:0% +better be -1 -2 and + + + align:start position:0% +better be -1 -2 and +-1 okay that's a type of question that + + align:start position:0% +-1 okay that's a type of question that + + + align:start position:0% +-1 okay that's a type of question that +just brings out the the information + + align:start position:0% +just brings out the the information + + + align:start position:0% +just brings out the the information +that's in that complete + + align:start position:0% +that's in that complete + + + align:start position:0% +that's in that complete +solution + + align:start position:0% +solution + + + align:start position:0% +solution +okay and then actually I go on to ask + + align:start position:0% +okay and then actually I go on to ask + + + align:start position:0% +okay and then actually I go on to ask +what vectors for what vectors B can axal + + align:start position:0% +what vectors for what vectors B can axal + + + align:start position:0% +what vectors for what vectors B can axal +B be solved a x = b can be solved + + align:start position:0% + + + + align:start position:0% + +if what so I'm looking for a condition + + align:start position:0% +if what so I'm looking for a condition + + + align:start position:0% +if what so I'm looking for a condition +on B if any can it be solved for every + + align:start position:0% +on B if any can it be solved for every + + + align:start position:0% +on B if any can it be solved for every +for every right hand side + + align:start position:0% +for every right hand side + + + align:start position:0% +for every right hand side +B no definitely + + align:start position:0% +B no definitely + + + align:start position:0% +B no definitely +not when could it be solved well what's + + align:start position:0% +not when could it be solved well what's + + + align:start position:0% +not when could it be solved well what's +the I actually say in this in the in the + + align:start position:0% +the I actually say in this in the in the + + + align:start position:0% +the I actually say in this in the in the +exam don't just tell me + + align:start position:0% +exam don't just tell me + + + align:start position:0% +exam don't just tell me +if B is in the and what would what does + + align:start position:0% +if B is in the and what would what does + + + align:start position:0% +if B is in the and what would what does +the exam say there in the column space + + align:start position:0% +the exam say there in the column space + + + align:start position:0% +the exam say there in the column space +because I do know that uh that that it + + align:start position:0% +because I do know that uh that that it + + + align:start position:0% +because I do know that uh that that it +can be solved exactly when B is in the + + align:start position:0% +can be solved exactly when B is in the + + + align:start position:0% +can be solved exactly when B is in the +column space so I guess I'm asking you + + align:start position:0% +column space so I guess I'm asking you + + + align:start position:0% +column space so I guess I'm asking you +what is the column space for this Matrix + + align:start position:0% +what is the column space for this Matrix + + + align:start position:0% +what is the column space for this Matrix +so so what is if B has the + + align:start position:0% +so so what is if B has the + + + align:start position:0% +so so what is if B has the +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +form so I guess I'm asking you what's + + align:start position:0% +form so I guess I'm asking you what's + + + align:start position:0% +form so I guess I'm asking you what's +the column space of this Matrix + + align:start position:0% +the column space of this Matrix + + + align:start position:0% +the column space of this Matrix +and what is + + align:start position:0% +and what is + + + align:start position:0% +and what is +it + + align:start position:0% +it + + + align:start position:0% +it +it's uh so the column space of that + + align:start position:0% +it's uh so the column space of that + + + align:start position:0% +it's uh so the column space of that +Matrix is all + + align:start position:0% +Matrix is all + + + align:start position:0% +Matrix is all +multiples b b is a multiple of one 12 + + align:start position:0% +multiples b b is a multiple of one 12 + + + align:start position:0% +multiples b b is a multiple of one 12 +one + + align:start position:0% +one + + + align:start position:0% +one +right I can solve the thing if it's a + + align:start position:0% +right I can solve the thing if it's a + + + align:start position:0% +right I can solve the thing if it's a +multiple of one two one and of course + + align:start position:0% +multiple of one two one and of course + + + align:start position:0% +multiple of one two one and of course +sure + + align:start position:0% +sure + + + align:start position:0% +sure +enough uh this oh yeah that was a + + align:start position:0% +enough uh this oh yeah that was a + + + align:start position:0% +enough uh this oh yeah that was a +multiple of one two one and so I had a + + align:start position:0% +multiple of one two one and so I had a + + + align:start position:0% +multiple of one two one and so I had a +solution so this is a case where we've + + align:start position:0% +solution so this is a case where we've + + + align:start position:0% +solution so this is a case where we've +got lots of null + + align:start position:0% +got lots of null + + + align:start position:0% +got lots of null +space let me just + + align:start position:0% +space let me just + + + align:start position:0% +space let me just +recall that the The Other Extreme when + + align:start position:0% +recall that the The Other Extreme when + + + align:start position:0% +recall that the The Other Extreme when +the no when when the rank is Big don't + + align:start position:0% +the no when when the rank is Big don't + + + align:start position:0% +the no when when the rank is Big don't +forget those those cases don't + + align:start position:0% +forget those those cases don't + + + align:start position:0% +forget those those cases don't +forget don't forget the + + align:start position:0% +forget don't forget the + + + align:start position:0% +forget don't forget the +other the + + align:start position:0% +other the + + + align:start position:0% +other the +other + + align:start position:0% +other + + + align:start position:0% +other +cases when R is as big as it can be Ral + + align:start position:0% +cases when R is as big as it can be Ral + + + align:start position:0% +cases when R is as big as it can be Ral +M or Ral n those are those we had a full + + align:start position:0% +M or Ral n those are those we had a full + + + align:start position:0% +M or Ral n those are those we had a full +lecture on that full rank full lecture + + align:start position:0% +lecture on that full rank full lecture + + + align:start position:0% +lecture on that full rank full lecture +and uh important important case + + align:start position:0% + + + + align:start position:0% + +okay I'll just move on I think this is + + align:start position:0% +okay I'll just move on I think this is + + + align:start position:0% +okay I'll just move on I think this is +the best type of review it just brings + + align:start position:0% +the best type of review it just brings + + + align:start position:0% +the best type of review it just brings +these ideas out uh apologies for the + + align:start position:0% +these ideas out uh apologies for the + + + align:start position:0% +these ideas out uh apologies for the +camera while I recover glasses and and + + align:start position:0% +camera while I recover glasses and and + + + align:start position:0% +camera while I recover glasses and and +uh exam okay + + align:start position:0% + + + + align:start position:0% + +how about a few true false ones actually + + align:start position:0% +how about a few true false ones actually + + + align:start position:0% +how about a few true false ones actually +there won't be a true false on the quiz + + align:start position:0% +there won't be a true false on the quiz + + + align:start position:0% +there won't be a true false on the quiz +but it's it gives us a moment of quick + + align:start position:0% +but it's it gives us a moment of quick + + + align:start position:0% +but it's it gives us a moment of quick +review + + align:start position:0% +review + + + align:start position:0% +review +uh here's one if the null space I have a + + align:start position:0% +uh here's one if the null space I have a + + + align:start position:0% +uh here's one if the null space I have a +square + + align:start position:0% +square + + + align:start position:0% +square +Matrix if its null space is just the + + align:start position:0% +Matrix if its null space is just the + + + align:start position:0% +Matrix if its null space is just the +zero + + align:start position:0% +zero + + + align:start position:0% +zero +Vector what about the null space of a + + align:start position:0% +Vector what about the null space of a + + + align:start position:0% +Vector what about the null space of a +transpose if the null space of a a is + + align:start position:0% +transpose if the null space of a a is + + + align:start position:0% +transpose if the null space of a a is +just a zero vector and the Matrix is + + align:start position:0% +just a zero vector and the Matrix is + + + align:start position:0% +just a zero vector and the Matrix is +square what do I know about the null + + align:start position:0% +square what do I know about the null + + + align:start position:0% +square what do I know about the null +space of a + + align:start position:0% +space of a + + + align:start position:0% +space of a +transpose also the Zer Vector good and + + align:start position:0% +transpose also the Zer Vector good and + + + align:start position:0% +transpose also the Zer Vector good and +that's a very very important fact + + align:start position:0% +that's a very very important fact + + + align:start position:0% +that's a very very important fact +okay uh how about + + align:start position:0% +okay uh how about + + + align:start position:0% +okay uh how about +this the look at the space of 5x five + + align:start position:0% +this the look at the space of 5x five + + + align:start position:0% +this the look at the space of 5x five +matrices as a vector + + align:start position:0% +matrices as a vector + + + align:start position:0% +matrices as a vector +space so it's actually a 25 dimensional + + align:start position:0% +space so it's actually a 25 dimensional + + + align:start position:0% +space so it's actually a 25 dimensional +Vector space all 5x5 matrices look at + + align:start position:0% +Vector space all 5x5 matrices look at + + + align:start position:0% +Vector space all 5x5 matrices look at +the invertible + + align:start position:0% +the invertible + + + align:start position:0% +the invertible +matrices do they form a + + align:start position:0% +matrices do they form a + + + align:start position:0% +matrices do they form a +Subspace so I have this 5 by this this + + align:start position:0% +Subspace so I have this 5 by this this + + + align:start position:0% +Subspace so I have this 5 by this this +space of all 5x five matrices I can add + + align:start position:0% +space of all 5x five matrices I can add + + + align:start position:0% +space of all 5x five matrices I can add +them I can multiply by numbers but now I + + align:start position:0% +them I can multiply by numbers but now I + + + align:start position:0% +them I can multiply by numbers but now I +narrow down to the invertible ones and I + + align:start position:0% +narrow down to the invertible ones and I + + + align:start position:0% +narrow down to the invertible ones and I +ask are they a Subspace and you your + + align:start position:0% +ask are they a Subspace and you your + + + align:start position:0% +ask are they a Subspace and you your +answer + + align:start position:0% +answer + + + align:start position:0% +answer +is quiet but nevertheless + + align:start position:0% +is quiet but nevertheless + + + align:start position:0% +is quiet but nevertheless +definite no + + align:start position:0% +definite no + + + align:start position:0% +definite no +right no cuz if I add two invertible + + align:start position:0% +right no cuz if I add two invertible + + + align:start position:0% +right no cuz if I add two invertible +matrices I have no idea if the answer is + + align:start position:0% +matrices I have no idea if the answer is + + + align:start position:0% +matrices I have no idea if the answer is +invertible If I multiply that invertible + + align:start position:0% +invertible If I multiply that invertible + + + align:start position:0% +invertible If I multiply that invertible +well it doesn't even have the zero + + align:start position:0% +well it doesn't even have the zero + + + align:start position:0% +well it doesn't even have the zero +Matrix in it it couldn't be a + + align:start position:0% +Matrix in it it couldn't be a + + + align:start position:0% +Matrix in it it couldn't be a +subst I have to be able to multiply by + + align:start position:0% +subst I have to be able to multiply by + + + align:start position:0% +subst I have to be able to multiply by +zero and stay in my Subspace and the + + align:start position:0% +zero and stay in my Subspace and the + + + align:start position:0% +zero and stay in my Subspace and the +invertible ones wouldn't work well the + + align:start position:0% +invertible ones wouldn't work well the + + + align:start position:0% +invertible ones wouldn't work well the +the singular ones wouldn't work either + + align:start position:0% +the singular ones wouldn't work either + + + align:start position:0% +the singular ones wouldn't work either +they have zero the zero Matrix is in the + + align:start position:0% +they have zero the zero Matrix is in the + + + align:start position:0% +they have zero the zero Matrix is in the +singular matrices but + + align:start position:0% +singular matrices but + + + align:start position:0% +singular matrices but +if I add two singular matrices I don't + + align:start position:0% +if I add two singular matrices I don't + + + align:start position:0% +if I add two singular matrices I don't +know if the answer is singular or not + + align:start position:0% +know if the answer is singular or not + + + align:start position:0% +know if the answer is singular or not +okay so uh another true + + align:start position:0% +okay so uh another true + + + align:start position:0% +okay so uh another true +false if B here we go here's it if b^2 + + align:start position:0% +false if B here we go here's it if b^2 + + + align:start position:0% +false if B here we go here's it if b^2 +equals 0 then b equals Z true or false + + align:start position:0% +equals 0 then b equals Z true or false + + + align:start position:0% +equals 0 then b equals Z true or false +if b^2 = 0 true + + align:start position:0% +if b^2 = 0 true + + + align:start position:0% +if b^2 = 0 true +false b^2 = 0 B has to be a square + + align:start position:0% +false b^2 = 0 B has to be a square + + + align:start position:0% +false b^2 = 0 B has to be a square +square Matrix so that I can multiply by + + align:start position:0% +square Matrix so that I can multiply by + + + align:start position:0% +square Matrix so that I can multiply by +itself does that + + align:start position:0% +itself does that + + + align:start position:0% +itself does that +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +that b is + + align:start position:0% + + + + align:start position:0% + +zero are there matrices whose square + + align:start position:0% +zero are there matrices whose square + + + align:start position:0% +zero are there matrices whose square +could be the zero + + align:start position:0% + + + + align:start position:0% + +Matrix yes or no yes there + + align:start position:0% +Matrix yes or no yes there + + + align:start position:0% +Matrix yes or no yes there +are there are matrices whose square is + + align:start position:0% +are there are matrices whose square is + + + align:start position:0% +are there are matrices whose square is +the zero Matrix so this statement is + + align:start position:0% +the zero Matrix so this statement is + + + align:start position:0% +the zero Matrix so this statement is +false if b^2 is z we don't know that b + + align:start position:0% +false if b^2 is z we don't know that b + + + align:start position:0% +false if b^2 is z we don't know that b +is z for example the best thing example + + align:start position:0% +is z for example the best thing example + + + align:start position:0% +is z for example the best thing example +is that Matrix that Matrix is a is a + + align:start position:0% +is that Matrix that Matrix is a is a + + + align:start position:0% +is that Matrix that Matrix is a is a +dangerous Matrix it uh it will come up + + align:start position:0% +dangerous Matrix it uh it will come up + + + align:start position:0% +dangerous Matrix it uh it will come up +in later parts of this course as an + + align:start position:0% +in later parts of this course as an + + + align:start position:0% +in later parts of this course as an +example of what can go wrong and here is + + align:start position:0% +example of what can go wrong and here is + + + align:start position:0% +example of what can go wrong and here is +a real simple so this so if I square + + align:start position:0% +a real simple so this so if I square + + + align:start position:0% +a real simple so this so if I square +that Matrix I do get the zero + + align:start position:0% +that Matrix I do get the zero + + + align:start position:0% +that Matrix I do get the zero +Matrix uh and it shows of + + align:start position:0% +Matrix uh and it shows of + + + align:start position:0% +Matrix uh and it shows of +course uh yeah yeah okay + + align:start position:0% +course uh yeah yeah okay + + + align:start position:0% +course uh yeah yeah okay +all right + + align:start position:0% +all right + + + align:start position:0% +all right +um here here a system + + align:start position:0% +um here here a system + + + align:start position:0% +um here here a system +of okay a system of n equations in N + + align:start position:0% +of okay a system of n equations in N + + + align:start position:0% +of okay a system of n equations in N +unknowns is + + align:start position:0% +unknowns is + + + align:start position:0% +unknowns is +solvable for every right hand side if + + align:start position:0% +solvable for every right hand side if + + + align:start position:0% +solvable for every right hand side if +the columns are + + align:start position:0% +the columns are + + + align:start position:0% +the columns are +independent okay can I say that again + + align:start position:0% +independent okay can I say that again + + + align:start position:0% +independent okay can I say that again +it's I'll write it down then for short n + + align:start position:0% +it's I'll write it down then for short n + + + align:start position:0% +it's I'll write it down then for short n +by + + align:start position:0% +by + + + align:start position:0% +by +n Matrix independent + + align:start position:0% + + + + align:start position:0% + +columns then the question is does axal B + + align:start position:0% +columns then the question is does axal B + + + align:start position:0% +columns then the question is does axal B +is it always + + align:start position:0% + + + + align:start position:0% + +Sol and the answer is yes yes or no + + align:start position:0% +Sol and the answer is yes yes or no + + + align:start position:0% +Sol and the answer is yes yes or no +right okay um which let's see let's + + align:start position:0% +right okay um which let's see let's + + + align:start position:0% +right okay um which let's see let's +have did you watch that quiz there was a + + align:start position:0% +have did you watch that quiz there was a + + + align:start position:0% +have did you watch that quiz there was a +quiz uh program on TV for a few weeks + + align:start position:0% +quiz uh program on TV for a few weeks + + + align:start position:0% +quiz uh program on TV for a few weeks +did you see that what was the name of + + align:start position:0% +did you see that what was the name of + + + align:start position:0% +did you see that what was the name of +that winning a million dollars or + + align:start position:0% +that winning a million dollars or + + + align:start position:0% +that winning a million dollars or +something how to be a millionaire with + + align:start position:0% +something how to be a millionaire with + + + align:start position:0% +something how to be a millionaire with +some crazy guy what was his name as the + + align:start position:0% +some crazy guy what was his name as the + + + align:start position:0% +some crazy guy what was his name as the +MC reges right reges okay if you saw + + align:start position:0% +MC reges right reges okay if you saw + + + align:start position:0% +MC reges right reges okay if you saw +this like when you should have been + + align:start position:0% +this like when you should have been + + + align:start position:0% +this like when you should have been +doing Vine alra of course um uh but I + + align:start position:0% +doing Vine alra of course um uh but I + + + align:start position:0% +doing Vine alra of course um uh but I +didn't have to do the homework so I was + + align:start position:0% +didn't have to do the homework so I was + + + align:start position:0% +didn't have to do the homework so I was +watching it uh + + align:start position:0% +watching it uh + + + align:start position:0% +watching it uh +so there were three the the interesting + + align:start position:0% +so there were three the the interesting + + + align:start position:0% +so there were three the the interesting +the novel point was there were three + + align:start position:0% +the novel point was there were three + + + align:start position:0% +the novel point was there were three +ways that you could get help right uh + + align:start position:0% +ways that you could get help right uh + + + align:start position:0% +ways that you could get help right uh +but you could only use each way once so + + align:start position:0% +but you could only use each way once so + + + align:start position:0% +but you could only use each way once so +you couldn't like use them all the time + + align:start position:0% +you couldn't like use them all the time + + + align:start position:0% +you couldn't like use them all the time +so you remember that you could so you + + align:start position:0% +so you remember that you could so you + + + align:start position:0% +so you remember that you could so you +could pull the audience and that was a + + align:start position:0% +could pull the audience and that was a + + + align:start position:0% +could pull the audience and that was a +very that was 100% successful way so + + align:start position:0% +very that was 100% successful way so + + + align:start position:0% +very that was 100% successful way so +I'll pull the audience on this uh if if + + align:start position:0% +I'll pull the audience on this uh if if + + + align:start position:0% +I'll pull the audience on this uh if if +uh the other possibility another + + align:start position:0% +uh the other possibility another + + + align:start position:0% +uh the other possibility another +possibility you could call your friend + + align:start position:0% +possibility you could call your friend + + + align:start position:0% +possibility you could call your friend +right or he's your friend until he gives + + align:start position:0% +right or he's your friend until he gives + + + align:start position:0% +right or he's your friend until he gives +you the wrong + + align:start position:0% +you the wrong + + + align:start position:0% +you the wrong +answer that that turned out to be very + + align:start position:0% +answer that that turned out to be very + + + align:start position:0% +answer that that turned out to be very +unreliable you know you call up your + + align:start position:0% +unreliable you know you call up your + + + align:start position:0% +unreliable you know you call up your +brother or something and ask him for the + + align:start position:0% +brother or something and ask him for the + + + align:start position:0% +brother or something and ask him for the +capital of whatever Bosnia what does he + + align:start position:0% +capital of whatever Bosnia what does he + + + align:start position:0% +capital of whatever Bosnia what does he +know he makes some guest and it cost you + + align:start position:0% +know he makes some guest and it cost you + + + align:start position:0% +know he makes some guest and it cost you +half a million so uh but let's but + + align:start position:0% +half a million so uh but let's but + + + align:start position:0% +half a million so uh but let's but +calling the audience always works uh so + + align:start position:0% +calling the audience always works uh so + + + align:start position:0% +calling the audience always works uh so +what's let me let me say yes if I yes or + + align:start position:0% +what's let me let me say yes if I yes or + + + align:start position:0% +what's let me let me say yes if I yes or +no if I have Square Matrix independent + + align:start position:0% +no if I have Square Matrix independent + + + align:start position:0% +no if I have Square Matrix independent +columns is ax B always solvable maybe + + align:start position:0% +columns is ax B always solvable maybe + + + align:start position:0% +columns is ax B always solvable maybe +just hands up for + + align:start position:0% + + + + align:start position:0% + +that few and who says + + align:start position:0% +that few and who says + + + align:start position:0% +that few and who says +no oh gosh this audience is not + + align:start position:0% +no oh gosh this audience is not + + + align:start position:0% +no oh gosh this audience is not +reliable 50 + + align:start position:0% +reliable 50 + + + align:start position:0% +reliable 50 +50 um I guess I'd say I'd vote Yes + + align:start position:0% +50 um I guess I'd say I'd vote Yes + + + align:start position:0% +50 um I guess I'd say I'd vote Yes +because uh independent columns that + + align:start position:0% +because uh independent columns that + + + align:start position:0% +because uh independent columns that +means that the rank is the full size N I + + align:start position:0% +means that the rank is the full size N I + + + align:start position:0% +means that the rank is the full size N I +have a matrix of rank n uh that means + + align:start position:0% +have a matrix of rank n uh that means + + + align:start position:0% +have a matrix of rank n uh that means +it's I mean it's Square so it's an + + align:start position:0% +it's I mean it's Square so it's an + + + align:start position:0% +it's I mean it's Square so it's an +invertible Matrix and nothing nothing + + align:start position:0% +invertible Matrix and nothing nothing + + + align:start position:0% +invertible Matrix and nothing nothing +could go wrong yeah so that's that's the + + align:start position:0% +could go wrong yeah so that's that's the + + + align:start position:0% +could go wrong yeah so that's that's the +good case that we always expected in + + align:start position:0% +good case that we always expected in + + + align:start position:0% +good case that we always expected in +Chapter 2 but of course chapter 3 is + + align:start position:0% +Chapter 2 but of course chapter 3 is + + + align:start position:0% +Chapter 2 but of course chapter 3 is +that's uh uh only one of the + + align:start position:0% +that's uh uh only one of the + + + align:start position:0% +that's uh uh only one of the +possibilities okay let me let me move on + + align:start position:0% +possibilities okay let me let me move on + + + align:start position:0% +possibilities okay let me let me move on +to uh another + + align:start position:0% +to uh another + + + align:start position:0% +to uh another +um uh + + align:start position:0% +um uh + + + align:start position:0% +um uh +another uh question from an old quiz + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay um let's + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +see um okay I'm going to give you a + + align:start position:0% + + + + align:start position:0% + +matrix but I'm going to give it to you + + align:start position:0% +matrix but I'm going to give it to you + + + align:start position:0% +matrix but I'm going to give it to you +as a product of a couple of matrices 1 1 + + align:start position:0% +as a product of a couple of matrices 1 1 + + + align:start position:0% +as a product of a couple of matrices 1 1 +Z 0 1 + + align:start position:0% +Z 0 1 + + + align:start position:0% +Z 0 1 +0 1 0 + + align:start position:0% +0 1 0 + + + align:start position:0% +0 1 0 + + align:start position:0% + + + align:start position:0% +times another Matrix 1 0 -1 + + align:start position:0% +times another Matrix 1 0 -1 + + + align:start position:0% +times another Matrix 1 0 -1 +2 0 1 1 + + align:start position:0% +2 0 1 1 + + + align:start position:0% +2 0 1 1 +-1 and all + + align:start position:0% +-1 and all + + + align:start position:0% +-1 and all +zeros + + align:start position:0% +zeros + + + align:start position:0% +zeros +okay I would like to ask you questions + + align:start position:0% +okay I would like to ask you questions + + + align:start position:0% +okay I would like to ask you questions +about that + + align:start position:0% +about that + + + align:start position:0% +about that +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +without doing the + + align:start position:0% +without doing the + + + align:start position:0% +without doing the +multiplication and finding the Matrix B + + align:start position:0% + + + + align:start position:0% + +can you can you tell me something can we + + align:start position:0% +can you can you tell me something can we + + + align:start position:0% +can you can you tell me something can we +can I so I'll ask questions about this + + align:start position:0% +can I so I'll ask questions about this + + + align:start position:0% +can I so I'll ask questions about this +Matrix B and I'll answer them without + + align:start position:0% +Matrix B and I'll answer them without + + + align:start position:0% +Matrix B and I'll answer them without +multiplying it out for example I'm going + + align:start position:0% +multiplying it out for example I'm going + + + align:start position:0% +multiplying it out for example I'm going +to ask you for a basis for the null + + align:start position:0% + + + + align:start position:0% + +space a basis for the null + + align:start position:0% +space a basis for the null + + + align:start position:0% +space a basis for the null +space so I'm going to solve BX = Z so so + + align:start position:0% +space so I'm going to solve BX = Z so so + + + align:start position:0% +space so I'm going to solve BX = Z so so +give me a basis + + align:start position:0% + + + + align:start position:0% + +for for the null space of + + align:start position:0% + + + + align:start position:0% + +B let's see what dimension am I in what + + align:start position:0% +B let's see what dimension am I in what + + + align:start position:0% +B let's see what dimension am I in what +what this the null space of B is the + + align:start position:0% +what this the null space of B is the + + + align:start position:0% +what this the null space of B is the +Subspace of + + align:start position:0% +Subspace of + + + align:start position:0% +Subspace of +R what size vectors am I looking for + + align:start position:0% + + + + align:start position:0% + +here cuz if we don't know the size we + + align:start position:0% +here cuz if we don't know the size we + + + align:start position:0% +here cuz if we don't know the size we +aren't going to find it right + + align:start position:0% +aren't going to find it right + + + align:start position:0% +aren't going to find it right +the N this Matrix is 3x4 + + align:start position:0% + + + + align:start position:0% + +obviously so if we're looking for the + + align:start position:0% +obviously so if we're looking for the + + + align:start position:0% +obviously so if we're looking for the +null space we're looking for those + + align:start position:0% +null space we're looking for those + + + align:start position:0% +null space we're looking for those +vectors X in R4 okay so the null space + + align:start position:0% +vectors X in R4 okay so the null space + + + align:start position:0% +vectors X in R4 okay so the null space +of B is certainly a Subspace of + + align:start position:0% + + + + align:start position:0% + +R4 what do you think its Dimension is of + + align:start position:0% +R4 what do you think its Dimension is of + + + align:start position:0% +R4 what do you think its Dimension is of +course once we find the basis we would + + align:start position:0% +course once we find the basis we would + + + align:start position:0% +course once we find the basis we would +know the dimension immediately but let + + align:start position:0% +know the dimension immediately but let + + + align:start position:0% +know the dimension immediately but let +stop first what's the rank of this + + align:start position:0% +stop first what's the rank of this + + + align:start position:0% +stop first what's the rank of this +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +B uh let's see what that Matrix is that + + align:start position:0% +B uh let's see what that Matrix is that + + + align:start position:0% +B uh let's see what that Matrix is that +Matrix invertible that square one + + align:start position:0% + + + + align:start position:0% + +there let's say sure I think it is yeah + + align:start position:0% +there let's say sure I think it is yeah + + + align:start position:0% +there let's say sure I think it is yeah +yeah yes that Matrix B looks in + + align:start position:0% +yeah yes that Matrix B looks in + + + align:start position:0% +yeah yes that Matrix B looks in +verbal is that is that pretty clear + + align:start position:0% +verbal is that is that pretty clear + + + align:start position:0% +verbal is that is that pretty clear +yeah yeah Al so I've gone wrong in this + + align:start position:0% +yeah yeah Al so I've gone wrong in this + + + align:start position:0% +yeah yeah Al so I've gone wrong in this +uh course already + + align:start position:0% +uh course already + + + align:start position:0% +uh course already +but I'll I'll still hope that that + + align:start position:0% +but I'll I'll still hope that that + + + align:start position:0% +but I'll I'll still hope that that +Matrix is Inver yeah yeah because if I + + align:start position:0% +Matrix is Inver yeah yeah because if I + + + align:start position:0% +Matrix is Inver yeah yeah because if I +look for a combination of those three + + align:start position:0% +look for a combination of those three + + + align:start position:0% +look for a combination of those three +columns well I couldn't use uh this + + align:start position:0% +columns well I couldn't use uh this + + + align:start position:0% +columns well I couldn't use uh this +middle column because it would have a + + align:start position:0% +middle column because it would have a + + + align:start position:0% +middle column because it would have a +one in in a in in a position that I that + + align:start position:0% +one in in a in in a position that I that + + + align:start position:0% +one in in a in in a position that I that +that only is otherwise all zero so a + + align:start position:0% +that only is otherwise all zero so a + + + align:start position:0% +that only is otherwise all zero so a +combination that gives zero can't use + + align:start position:0% +combination that gives zero can't use + + + align:start position:0% +combination that gives zero can't use +that column and then the other two are + + align:start position:0% +that column and then the other two are + + + align:start position:0% +that column and then the other two are +clearly independent except so that + + align:start position:0% +clearly independent except so that + + + align:start position:0% +clearly independent except so that +Matrix is + + align:start position:0% +Matrix is + + + align:start position:0% +Matrix is +invertible later we could take it + + align:start position:0% +invertible later we could take it + + + align:start position:0% +invertible later we could take it +determinant or other things okay + + align:start position:0% +determinant or other things okay + + + align:start position:0% +determinant or other things okay +uh what's the setup if I have an + + align:start position:0% +uh what's the setup if I have an + + + align:start position:0% +uh what's the setup if I have an +invertible Matrix a nice invertible + + align:start position:0% +invertible Matrix a nice invertible + + + align:start position:0% +invertible Matrix a nice invertible +Square Matrix times this + + align:start position:0% +Square Matrix times this + + + align:start position:0% +Square Matrix times this +guy that's a second factor and I'm + + align:start position:0% +guy that's a second factor and I'm + + + align:start position:0% +guy that's a second factor and I'm +looking for the null space does this + + align:start position:0% +looking for the null space does this + + + align:start position:0% +looking for the null space does this +have any + + align:start position:0% + + + + align:start position:0% + +effect is the n so what I'm asking is is + + align:start position:0% +effect is the n so what I'm asking is is + + + align:start position:0% +effect is the n so what I'm asking is is +the null space of B the same as the + + align:start position:0% +the null space of B the same as the + + + align:start position:0% +the null space of B the same as the +space of just this + + align:start position:0% + + + + align:start position:0% + +part I think + + align:start position:0% +part I think + + + align:start position:0% +part I think +so I think + + align:start position:0% +so I think + + + align:start position:0% +so I think +so if if BX is zero then multiplying by + + align:start position:0% +so if if BX is zero then multiplying by + + + align:start position:0% +so if if BX is zero then multiplying by +that guy I'll still have zero but also + + align:start position:0% +that guy I'll still have zero but also + + + align:start position:0% +that guy I'll still have zero but also +if if this time some X gives zero I + + align:start position:0% +if if this time some X gives zero I + + + align:start position:0% +if if this time some X gives zero I +could always multiply on the left by the + + align:start position:0% +could always multiply on the left by the + + + align:start position:0% +could always multiply on the left by the +inverse of that because it is invertible + + align:start position:0% +inverse of that because it is invertible + + + align:start position:0% +inverse of that because it is invertible +and I would discover that this time + + align:start position:0% +and I would discover that this time + + + align:start position:0% +and I would discover that this time +times the x is Z + + align:start position:0% +times the x is Z + + + align:start position:0% +times the x is Z +just you want me to write some of that + + align:start position:0% +just you want me to write some of that + + + align:start position:0% +just you want me to write some of that +down if I have a product here C + + align:start position:0% +down if I have a product here C + + + align:start position:0% +down if I have a product here C +* times uh D + + align:start position:0% +* times uh D + + + align:start position:0% +* times uh D +say and if C is + + align:start position:0% +say and if C is + + + align:start position:0% +say and if C is +invertible the null + + align:start position:0% +invertible the null + + + align:start position:0% +invertible the null +space of CD will will be the same as the + + align:start position:0% +space of CD will will be the same as the + + + align:start position:0% +space of CD will will be the same as the +null space of D if C is + + align:start position:0% + + + + align:start position:0% + +inverted multiplying by an invert Matrix + + align:start position:0% +inverted multiplying by an invert Matrix + + + align:start position:0% +inverted multiplying by an invert Matrix +on the left can't change the null + + align:start position:0% +on the left can't change the null + + + align:start position:0% +on the left can't change the null +space okay so basically I'm asking you + + align:start position:0% +space okay so basically I'm asking you + + + align:start position:0% +space okay so basically I'm asking you +for the null space of this + + align:start position:0% +for the null space of this + + + align:start position:0% +for the null space of this +one I don't have to do the + + align:start position:0% +one I don't have to do the + + + align:start position:0% +one I don't have to do the +multiplication because I'm CU I see is + + align:start position:0% +multiplication because I'm CU I see is + + + align:start position:0% +multiplication because I'm CU I see is +in that first factor C is + + align:start position:0% +in that first factor C is + + + align:start position:0% +in that first factor C is +invertible it's not going to change the + + align:start position:0% +invertible it's not going to change the + + + align:start position:0% +invertible it's not going to change the +nement okay so can we just write down a + + align:start position:0% +nement okay so can we just write down a + + + align:start position:0% +nement okay so can we just write down a +basis now for the no space so what's the + + align:start position:0% +basis now for the no space so what's the + + + align:start position:0% +basis now for the no space so what's the +basis for the no space of that so so + + align:start position:0% +basis for the no space of that so so + + + align:start position:0% +basis for the no space of that so so +basis + + align:start position:0% +basis + + + align:start position:0% +basis +for the null + + align:start position:0% +for the null + + + align:start position:0% +for the null +space I'm looking for the + + align:start position:0% +space I'm looking for the + + + align:start position:0% +space I'm looking for the +two there are two pivot columns + + align:start position:0% +two there are two pivot columns + + + align:start position:0% +two there are two pivot columns +obviously it clearly has rank two I'm + + align:start position:0% +obviously it clearly has rank two I'm + + + align:start position:0% +obviously it clearly has rank two I'm +looking for the two special Solutions + + align:start position:0% +looking for the two special Solutions + + + align:start position:0% +looking for the two special Solutions +they'll come from the third and the + + align:start position:0% + + + + align:start position:0% + +fourth the free variables okay so if the + + align:start position:0% +fourth the free variables okay so if the + + + align:start position:0% +fourth the free variables okay so if the +third free variable is a one then I + + align:start position:0% +third free variable is a one then I + + + align:start position:0% +third free variable is a one then I +think probably I need a minus one there + + align:start position:0% +think probably I need a minus one there + + + align:start position:0% +think probably I need a minus one there +and a one there looks like you agree + + align:start position:0% +and a one there looks like you agree + + + align:start position:0% +and a one there looks like you agree +that if I then do that multiplication + + align:start position:0% +that if I then do that multiplication + + + align:start position:0% +that if I then do that multiplication +I'll get zero and if I have one in the + + align:start position:0% +I'll get zero and if I have one in the + + + align:start position:0% +I'll get zero and if I have one in the +fourth variable then maybe I need a one + + align:start position:0% +fourth variable then maybe I need a one + + + align:start position:0% +fourth variable then maybe I need a one +in the second variable and maybe a minus + + align:start position:0% +in the second variable and maybe a minus + + + align:start position:0% +in the second variable and maybe a minus +2 in the 3 so I just reason that through + + align:start position:0% +2 in the 3 so I just reason that through + + + align:start position:0% +2 in the 3 so I just reason that through +and then if I look back I see sure + + align:start position:0% +and then if I look back I see sure + + + align:start position:0% +and then if I look back I see sure +enough that the free variable part that + + align:start position:0% +enough that the free variable part that + + + align:start position:0% +enough that the free variable part that +I sometimes call F that up that two by + + align:start position:0% +I sometimes call F that up that two by + + + align:start position:0% +I sometimes call F that up that two by +two corner is sitting here with all its + + align:start position:0% +two corner is sitting here with all its + + + align:start position:0% +two corner is sitting here with all its +signs + + align:start position:0% + + + + align:start position:0% + +reversed so that's here I'm seeing minus + + align:start position:0% +reversed so that's here I'm seeing minus + + + align:start position:0% +reversed so that's here I'm seeing minus +F and here I'm seeing the identity in + + align:start position:0% +F and here I'm seeing the identity in + + + align:start position:0% +F and here I'm seeing the identity in +the null space Matrix okay so that's the + + align:start position:0% +the null space Matrix okay so that's the + + + align:start position:0% +the null space Matrix okay so that's the +null space uh another question is solve + + align:start position:0% +null space uh another question is solve + + + align:start position:0% +null space uh another question is solve +BX = + + align:start position:0% +BX = + + + align:start position:0% +BX = +101 okay so that was that's one question + + align:start position:0% +101 okay so that was that's one question + + + align:start position:0% +101 okay so that was that's one question +now solve complete solution + + align:start position:0% + + + + align:start position:0% + +to BX + + align:start position:0% +to BX + + + align:start position:0% +to BX +equals + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +okay yeah so I guess I'm seeing if I + + align:start position:0% +okay yeah so I guess I'm seeing if I + + + align:start position:0% +okay yeah so I guess I'm seeing if I +wanted to get + + align:start position:0% +wanted to get + + + align:start position:0% +wanted to get +one1 what's what's a particular solution + + align:start position:0% +one1 what's what's a particular solution + + + align:start position:0% +one1 what's what's a particular solution +so I'm looking for a particular solution + + align:start position:0% +so I'm looking for a particular solution + + + align:start position:0% +so I'm looking for a particular solution +and then the null space part + + align:start position:0% + + + + align:start position:0% + +okay actually the first column of + + align:start position:0% +okay actually the first column of + + + align:start position:0% +okay actually the first column of +B what's the First Column of our Matrix + + align:start position:0% +B what's the First Column of our Matrix + + + align:start position:0% +B what's the First Column of our Matrix +B it's the vector + + align:start position:0% +B it's the vector + + + align:start position:0% +B it's the vector +101 the First Column of our Matrix + + align:start position:0% +101 the First Column of our Matrix + + + align:start position:0% +101 the First Column of our Matrix +agrees with the right hand side so I I + + align:start position:0% +agrees with the right hand side so I I + + + align:start position:0% +agrees with the right hand side so I I +guess I'm thinking X particular plus x n + + align:start position:0% +guess I'm thinking X particular plus x n + + + align:start position:0% +guess I'm thinking X particular plus x n +space will be the particular solution + + align:start position:0% +space will be the particular solution + + + align:start position:0% +space will be the particular solution +since the first column of B is exactly + + align:start position:0% +since the first column of B is exactly + + + align:start position:0% +since the first column of B is exactly +right that's great and then I have c + + align:start position:0% +right that's great and then I have c + + + align:start position:0% +right that's great and then I have c +times that first null space vector and B + + align:start position:0% +times that first null space vector and B + + + align:start position:0% +times that first null space vector and B +times the other no space + + align:start position:0% +times the other no space + + + align:start position:0% +times the other no space +Vector right the two the the the no + + align:start position:0% +Vector right the two the the the no + + + align:start position:0% +Vector right the two the the the no +space part of the solution as always is + + align:start position:0% +space part of the solution as always is + + + align:start position:0% +space part of the solution as always is +as the has the uh arbitrary constants + + align:start position:0% +as the has the uh arbitrary constants + + + align:start position:0% +as the has the uh arbitrary constants +the particular solution doesn't have any + + align:start position:0% +the particular solution doesn't have any + + + align:start position:0% +the particular solution doesn't have any +arbitrary constants it's one particular + + align:start position:0% +arbitrary constants it's one particular + + + align:start position:0% +arbitrary constants it's one particular +solution and in this case it that one + + align:start position:0% +solution and in this case it that one + + + align:start position:0% +solution and in this case it that one +would do it okay fine + + align:start position:0% +would do it okay fine + + + align:start position:0% +would do it okay fine +uh so that those are questions taken + + align:start position:0% +uh so that those are questions taken + + + align:start position:0% +uh so that those are questions taken +from old quizzes any questions coming to + + align:start position:0% +from old quizzes any questions coming to + + + align:start position:0% +from old quizzes any questions coming to +mind yeah I don't understand how you got + + align:start position:0% +mind yeah I don't understand how you got + + + align:start position:0% +mind yeah I don't understand how you got +particular this x particular guy okay + + align:start position:0% +particular this x particular guy okay + + + align:start position:0% +particular this x particular guy okay +well so that particular X particular + + align:start position:0% +well so that particular X particular + + + align:start position:0% +well so that particular X particular +uh says + + align:start position:0% +uh says + + + align:start position:0% +uh says +that see when I multiply by this guy I'm + + align:start position:0% +that see when I multiply by this guy I'm + + + align:start position:0% +that see when I multiply by this guy I'm +going to get the First Column of + + align:start position:0% +going to get the First Column of + + + align:start position:0% +going to get the First Column of +B that if that's a solution when I when + + align:start position:0% +B that if that's a solution when I when + + + align:start position:0% +B that if that's a solution when I when +I multiply b b * this x will be the + + align:start position:0% +I multiply b b * this x will be the + + + align:start position:0% +I multiply b b * this x will be the +first column of B and so I'm saying that + + align:start position:0% +first column of B and so I'm saying that + + + align:start position:0% +first column of B and so I'm saying that +the First Column of this + + align:start position:0% +the First Column of this + + + align:start position:0% +the First Column of this +B agrees with the right hand side so I'm + + align:start position:0% +B agrees with the right hand side so I'm + + + align:start position:0% +B agrees with the right hand side so I'm +saying that look at the look at the + + align:start position:0% +saying that look at the look at the + + + align:start position:0% +saying that look at the look at the +First Column of that Matrix B if you do + + align:start position:0% +First Column of that Matrix B if you do + + + align:start position:0% +First Column of that Matrix B if you do +the + + align:start position:0% +the + + + align:start position:0% +the +multiplication it's so what's the first + + align:start position:0% +multiplication it's so what's the first + + + align:start position:0% +multiplication it's so what's the first +column of that Matrix is that how do you + + align:start position:0% +column of that Matrix is that how do you + + + align:start position:0% +column of that Matrix is that how do you +do that multiplication I multiply that + + align:start position:0% +do that multiplication I multiply that + + + align:start position:0% +do that multiplication I multiply that +matrix by that First Column and it picks + + align:start position:0% +matrix by that First Column and it picks + + + align:start position:0% +matrix by that First Column and it picks +one1 so the first problem of B is + + align:start position:0% +one1 so the first problem of B is + + + align:start position:0% +one1 so the first problem of B is +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +that and therefore a particular solution + + align:start position:0% +that and therefore a particular solution + + + align:start position:0% +that and therefore a particular solution +will be this + + align:start position:0% +will be this + + + align:start position:0% +will be this +guy + + align:start position:0% +guy + + + align:start position:0% +guy +yeah okay yes is particular solution is + + align:start position:0% +yeah okay yes is particular solution is + + + align:start position:0% +yeah okay yes is particular solution is +there only one particular solution no + + align:start position:0% +there only one particular solution no + + + align:start position:0% +there only one particular solution no +not at all no I could uh I mean this is + + align:start position:0% +not at all no I could uh I mean this is + + + align:start position:0% +not at all no I could uh I mean this is +a nice one but any solution could be the + + align:start position:0% +a nice one but any solution could be the + + + align:start position:0% +a nice one but any solution could be the +particular solution + + align:start position:0% +particular solution + + + align:start position:0% +particular solution +any any of the solutions can be the + + align:start position:0% +any any of the solutions can be the + + + align:start position:0% +any any of the solutions can be the +particular one that we pick + + align:start position:0% +particular one that we pick + + + align:start position:0% +particular one that we pick +out um so so uh like this + + align:start position:0% +out um so so uh like this + + + align:start position:0% +out um so so uh like this +plus plus this would be another + + align:start position:0% +plus plus this would be another + + + align:start position:0% +plus plus this would be another +particular solution it would be in other + + align:start position:0% +particular solution it would be in other + + + align:start position:0% +particular solution it would be in other +words it be another + + align:start position:0% +words it be another + + + align:start position:0% +words it be another +solution particular is just telling us + + align:start position:0% +solution particular is just telling us + + + align:start position:0% +solution particular is just telling us +only take one but it's not telling us + + align:start position:0% +only take one but it's not telling us + + + align:start position:0% +only take one but it's not telling us +which one we have to take we take the + + align:start position:0% +which one we have to take we take the + + + align:start position:0% +which one we have to take we take the +most convenient one I guess in this in + + align:start position:0% +most convenient one I guess in this in + + + align:start position:0% +most convenient one I guess in this in +this problem that that one good other + + align:start position:0% +this problem that that one good other + + + align:start position:0% +this problem that that one good other +questions yeah and and this pattern of + + align:start position:0% +questions yeah and and this pattern of + + + align:start position:0% +questions yeah and and this pattern of +particular plus null space of course + + align:start position:0% +particular plus null space of course + + + align:start position:0% +particular plus null space of course +that's going + + align:start position:0% +that's going + + + align:start position:0% +that's going +throughout mathematics of linear + + align:start position:0% +throughout mathematics of linear + + + align:start position:0% +throughout mathematics of linear +systems we're really doing mathematics + + align:start position:0% +systems we're really doing mathematics + + + align:start position:0% +systems we're really doing mathematics +of linear systems here our systems are + + align:start position:0% +of linear systems here our systems are + + + align:start position:0% +of linear systems here our systems are +discreet and they're finite dimensional + + align:start position:0% +discreet and they're finite dimensional + + + align:start position:0% +discreet and they're finite dimensional +and so it's linear algebra + + align:start position:0% +and so it's linear algebra + + + align:start position:0% +and so it's linear algebra +but this particular plus null space goes + + align:start position:0% +but this particular plus null space goes + + + align:start position:0% +but this particular plus null space goes +that doesn't depend on having finite + + align:start position:0% +that doesn't depend on having finite + + + align:start position:0% +that doesn't depend on having finite +matrices that that go that spreads much + + align:start position:0% +matrices that that go that spreads much + + + align:start position:0% +matrices that that go that spreads much +spreads + + align:start position:0% +spreads + + + align:start position:0% +spreads +everywhere okay I'm going to just like + + align:start position:0% +everywhere okay I'm going to just like + + + align:start position:0% +everywhere okay I'm going to just like +to encourage you to take problems out of + + align:start position:0% +to encourage you to take problems out of + + + align:start position:0% +to encourage you to take problems out of +the book let me do the same + + align:start position:0% +the book let me do the same + + + align:start position:0% +the book let me do the same +myself + + align:start position:0% +myself + + + align:start position:0% +myself +um okay well here's some easy true or + + align:start position:0% +um okay well here's some easy true or + + + align:start position:0% +um okay well here's some easy true or +falses + + align:start position:0% +falses + + + align:start position:0% +falses +I don't know why the author put these in + + align:start position:0% +I don't know why the author put these in + + + align:start position:0% +I don't know why the author put these in +here + + align:start position:0% +here + + + align:start position:0% +here +okay ifal n then the row space equals + + align:start position:0% +okay ifal n then the row space equals + + + align:start position:0% +okay ifal n then the row space equals +the column space so these are true + + align:start position:0% +the column space so these are true + + + align:start position:0% +the column space so these are true +falses if m equal n so that means the + + align:start position:0% +falses if m equal n so that means the + + + align:start position:0% +falses if m equal n so that means the +Matrix is square then the row space + + align:start position:0% +Matrix is square then the row space + + + align:start position:0% +Matrix is square then the row space +equals the column + + align:start position:0% +equals the column + + + align:start position:0% +equals the column +space false good good what is equal + + align:start position:0% +space false good good what is equal + + + align:start position:0% +space false good good what is equal +there what can I say is equal if well + + align:start position:0% +there what can I say is equal if well + + + align:start position:0% +there what can I say is equal if well +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah it so that's definitely false the + + align:start position:0% +yeah it so that's definitely false the + + + align:start position:0% +yeah it so that's definitely false the +row space and the column space and and + + align:start position:0% +row space and the column space and and + + + align:start position:0% +row space and the column space and and +this Matrix is like always a good + + align:start position:0% +this Matrix is like always a good + + + align:start position:0% +this Matrix is like always a good +example to consider so there's a square + + align:start position:0% +example to consider so there's a square + + + align:start position:0% +example to consider so there's a square +Matrix but its row + + align:start position:0% +Matrix but its row + + + align:start position:0% +Matrix but its row +space is the multiples of 01 and its + + align:start position:0% +space is the multiples of 01 and its + + + align:start position:0% +space is the multiples of 01 and its +column space is the multiples of one + + align:start position:0% +column space is the multiples of one + + + align:start position:0% +column space is the multiples of one +zero very different the row space and + + align:start position:0% +zero very different the row space and + + + align:start position:0% +zero very different the row space and +column space are totally different for + + align:start position:0% +column space are totally different for + + + align:start position:0% +column space are totally different for +that Matrix now of course if the Matrix + + align:start position:0% +that Matrix now of course if the Matrix + + + align:start position:0% +that Matrix now of course if the Matrix +was symmetric + + align:start position:0% +was symmetric + + + align:start position:0% +was symmetric +well then clearly the row space equals + + align:start position:0% +well then clearly the row space equals + + + align:start position:0% +well then clearly the row space equals +the column okay um how about this + + align:start position:0% +the column okay um how about this + + + align:start position:0% +the column okay um how about this +question the matrices a and minus a + + align:start position:0% +question the matrices a and minus a + + + align:start position:0% +question the matrices a and minus a +share the same four + + align:start position:0% + + + + align:start position:0% + +subspaces do the matrices a and minus a + + align:start position:0% +subspaces do the matrices a and minus a + + + align:start position:0% +subspaces do the matrices a and minus a +have the same column space do they have + + align:start position:0% +have the same column space do they have + + + align:start position:0% +have the same column space do they have +the same null space do they have same + + align:start position:0% +the same null space do they have same + + + align:start position:0% +the same null space do they have same +row space what's the answer on that yes + + align:start position:0% +row space what's the answer on that yes + + + align:start position:0% +row space what's the answer on that yes +or no yes good + + align:start position:0% +or no yes good + + + align:start position:0% +or no yes good +okay uh how about this if a and b have + + align:start position:0% +okay uh how about this if a and b have + + + align:start position:0% +okay uh how about this if a and b have +the same four subspaces then a is a + + align:start position:0% +the same four subspaces then a is a + + + align:start position:0% +the same four subspaces then a is a +multiple of + + align:start position:0% +multiple of + + + align:start position:0% +multiple of +B if suppose suppose those subspaces are + + align:start position:0% +B if suppose suppose those subspaces are + + + align:start position:0% +B if suppose suppose those subspaces are +the + + align:start position:0% +the + + + align:start position:0% +the +same then is a a multiple of + + align:start position:0% + + + + align:start position:0% + +B okay just I don't how do you answer a + + align:start position:0% +B okay just I don't how do you answer a + + + align:start position:0% +B okay just I don't how do you answer a +question like + + align:start position:0% +question like + + + align:start position:0% +question like +that of course if you want to answer it + + align:start position:0% +that of course if you want to answer it + + + align:start position:0% +that of course if you want to answer it +yes then I would then you'd have to + + align:start position:0% +yes then I would then you'd have to + + + align:start position:0% +yes then I would then you'd have to +think think of a reason why if you want + + align:start position:0% +think think of a reason why if you want + + + align:start position:0% +think think of a reason why if you want +to answer no way then you would and and + + align:start position:0% +to answer no way then you would and and + + + align:start position:0% +to answer no way then you would and and +and I would sort of like first I would + + align:start position:0% +and I would sort of like first I would + + + align:start position:0% +and I would sort of like first I would +try to think + + align:start position:0% +try to think + + + align:start position:0% +try to think +no I would say can I come up with an + + align:start position:0% +no I would say can I come up with an + + + align:start position:0% +no I would say can I come up with an +example where it isn't + + align:start position:0% +example where it isn't + + + align:start position:0% +example where it isn't +true let me repeat the question and then + + align:start position:0% +true let me repeat the question and then + + + align:start position:0% +true let me repeat the question and then +write the answer okay so I'll repeat + + align:start position:0% +write the answer okay so I'll repeat + + + align:start position:0% +write the answer okay so I'll repeat +that question if so true or false if a + + align:start position:0% +that question if so true or false if a + + + align:start position:0% +that question if so true or false if a +and b have the same + + align:start position:0% + + + + align:start position:0% + +four + + align:start position:0% + + + + align:start position:0% + +subspaces + + align:start position:0% +subspaces + + + align:start position:0% +subspaces +then a is some multiple of + + align:start position:0% +then a is some multiple of + + + align:start position:0% +then a is some multiple of +B true or false how do you how do you + + align:start position:0% +B true or false how do you how do you + + + align:start position:0% +B true or false how do you how do you +feel about at this + + align:start position:0% +feel about at this + + + align:start position:0% +feel about at this +inst got quite a few true so I take a + + align:start position:0% +inst got quite a few true so I take a + + + align:start position:0% +inst got quite a few true so I take a +pole so how many think + + align:start position:0% +pole so how many think + + + align:start position:0% +pole so how many think +true + + align:start position:0% +true + + + align:start position:0% +true +okay gave you every chance to think + + align:start position:0% +okay gave you every chance to think + + + align:start position:0% +okay gave you every chance to think +about that + + align:start position:0% + + + + align:start position:0% + +uh let's see so what I would just take + + align:start position:0% +uh let's see so what I would just take + + + align:start position:0% +uh let's see so what I would just take +extreme cases if it was me + + align:start position:0% +extreme cases if it was me + + + align:start position:0% +extreme cases if it was me +uh so when do I + + align:start position:0% +uh so when do I + + + align:start position:0% +uh so when do I +know well I would suppose a matrix is + + align:start position:0% +know well I would suppose a matrix is + + + align:start position:0% +know well I would suppose a matrix is +invertible suppose a is an invertible + + align:start position:0% +invertible suppose a is an invertible + + + align:start position:0% +invertible suppose a is an invertible +Matrix then what suppose it's 6x6 + + align:start position:0% +Matrix then what suppose it's 6x6 + + + align:start position:0% +Matrix then what suppose it's 6x6 +invertible Matrix then what's its row + + align:start position:0% +invertible Matrix then what's its row + + + align:start position:0% +invertible Matrix then what's its row +space + + align:start position:0% +space + + + align:start position:0% +space +and it column space is all + + align:start position:0% +and it column space is all + + + align:start position:0% +and it column space is all +of R + + align:start position:0% +of R + + + align:start position:0% +of R +six and the null space and the n space + + align:start position:0% +six and the null space and the n space + + + align:start position:0% +six and the null space and the n space +of a transposed would + + align:start position:0% +of a transposed would + + + align:start position:0% +of a transposed would +be the zero Vector so every invertible + + align:start position:0% +be the zero Vector so every invertible + + + align:start position:0% +be the zero Vector so every invertible +Matrix is going to give that + + align:start position:0% +Matrix is going to give that + + + align:start position:0% +Matrix is going to give that +answer if I have a 6x6 invertible Matrix + + align:start position:0% +answer if I have a 6x6 invertible Matrix + + + align:start position:0% +answer if I have a 6x6 invertible Matrix +I know what those subspaces are heck + + align:start position:0% +I know what those subspaces are heck + + + align:start position:0% +I know what those subspaces are heck +that was back in Chapter 2 when I didn't + + align:start position:0% +that was back in Chapter 2 when I didn't + + + align:start position:0% +that was back in Chapter 2 when I didn't +even know what sub spaces + + align:start position:0% +even know what sub spaces + + + align:start position:0% +even know what sub spaces +were the row space and column space are + + align:start position:0% +were the row space and column space are + + + align:start position:0% +were the row space and column space are +both all six dimensional space the whole + + align:start position:0% +both all six dimensional space the whole + + + align:start position:0% +both all six dimensional space the whole +space and the rank is six in other words + + align:start position:0% +space and the rank is six in other words + + + align:start position:0% +space and the rank is six in other words +and the null spaces have zero Dimension + + align:start position:0% +and the null spaces have zero Dimension + + + align:start position:0% +and the null spaces have zero Dimension +so do you see now the + + align:start position:0% +so do you see now the + + + align:start position:0% +so do you see now the +answer so A and B could be for example + + align:start position:0% +answer so A and B could be for example + + + align:start position:0% +answer so A and B could be for example +any so I'm going to say + + align:start position:0% +any so I'm going to say + + + align:start position:0% +any so I'm going to say +false because A and B for example so an + + align:start position:0% + + + + align:start position:0% + +example A and B + + align:start position:0% +example A and B + + + align:start position:0% +example A and B +any + + align:start position:0% +any + + + align:start position:0% +any +invertible + + align:start position:0% + + + + align:start position:0% + +6x6 + + align:start position:0% +6x6 + + + align:start position:0% +6x6 +6x6 so those would have the same four + + align:start position:0% +6x6 so those would have the same four + + + align:start position:0% +6x6 so those would have the same four +subspaces but they wouldn't be the same + + align:start position:0% +subspaces but they wouldn't be the same + + + align:start position:0% +subspaces but they wouldn't be the same +of course there should be something + + align:start position:0% +of course there should be something + + + align:start position:0% +of course there should be something +about those matrices that would be the + + align:start position:0% +about those matrices that would be the + + + align:start position:0% +about those matrices that would be the +same so it's sort of a natural problem + + align:start position:0% +same so it's sort of a natural problem + + + align:start position:0% +same so it's sort of a natural problem +so now actually we're getting to a math + + align:start position:0% +so now actually we're getting to a math + + + align:start position:0% +so now actually we're getting to a math +question the answer + + align:start position:0% +question the answer + + + align:start position:0% +question the answer +is this is not true + + align:start position:0% +is this is not true + + + align:start position:0% +is this is not true +one Matrix doesn't have to be a multiple + + align:start position:0% +one Matrix doesn't have to be a multiple + + + align:start position:0% +one Matrix doesn't have to be a multiple +of the other but some there must be + + align:start position:0% +of the other but some there must be + + + align:start position:0% +of the other but some there must be +something that's + + align:start position:0% +something that's + + + align:start position:0% +something that's +true and that would be sort of like a + + align:start position:0% +true and that would be sort of like a + + + align:start position:0% +true and that would be sort of like a +natural question to ask if they have the + + align:start position:0% +natural question to ask if they have the + + + align:start position:0% +natural question to ask if they have the +same subspaces same four subspaces then + + align:start position:0% +same subspaces same four subspaces then + + + align:start position:0% +same subspaces same four subspaces then +what what uh could you uh you know what + + align:start position:0% +what what uh could you uh you know what + + + align:start position:0% +what what uh could you uh you know what +could you then say about those + + align:start position:0% +could you then say about those + + + align:start position:0% +could you then say about those +matrices yeah maybe I I'll let me leave + + align:start position:0% +matrices yeah maybe I I'll let me leave + + + align:start position:0% +matrices yeah maybe I I'll let me leave +that as a as an open question just sort + + align:start position:0% +that as a as an open question just sort + + + align:start position:0% +that as a as an open question just sort +of the for for uh uh uh cuz the Instinct + + align:start position:0% +of the for for uh uh uh cuz the Instinct + + + align:start position:0% +of the for for uh uh uh cuz the Instinct +wasn't necessarily + + align:start position:0% +wasn't necessarily + + + align:start position:0% +wasn't necessarily +right but I hope you now see that the + + align:start position:0% +right but I hope you now see that the + + + align:start position:0% +right but I hope you now see that the +the correct answer is false and then you + + align:start position:0% +the correct answer is false and then you + + + align:start position:0% +the correct answer is false and then you +might think okay well they certainly do + + align:start position:0% +might think okay well they certainly do + + + align:start position:0% +might think okay well they certainly do +have the same + + align:start position:0% +have the same + + + align:start position:0% +have the same +rank but + + align:start position:0% +rank but + + + align:start position:0% +rank but +do + + align:start position:0% +do + + + align:start position:0% +do +um obviously if they have the same four + + align:start position:0% +um obviously if they have the same four + + + align:start position:0% +um obviously if they have the same four +sub spaces they have the same + + align:start position:0% +sub spaces they have the same + + + align:start position:0% +sub spaces they have the same +rank uh I might say if they have this 12 + + align:start position:0% +rank uh I might say if they have this 12 + + + align:start position:0% +rank uh I might say if they have this 12 +yeah yeah I could extend that question + + align:start position:0% +yeah yeah I could extend that question + + + align:start position:0% +yeah yeah I could extend that question +and think about other possibilities and + + align:start position:0% +and think about other possibilities and + + + align:start position:0% +and think about other possibilities and +finally come up with something that was + + align:start position:0% +finally come up with something that was + + + align:start position:0% +finally come up with something that was +true uh but I won't uh um press that one + + align:start position:0% +true uh but I won't uh um press that one + + + align:start position:0% +true uh but I won't uh um press that one +let me let me keep going with practice + + align:start position:0% +let me let me keep going with practice + + + align:start position:0% +let me let me keep going with practice +question and these practice questions + + align:start position:0% +question and these practice questions + + + align:start position:0% +question and these practice questions +are quite uh appropriate I think for the + + align:start position:0% +are quite uh appropriate I think for the + + + align:start position:0% +are quite uh appropriate I think for the +exam okay + + align:start position:0% +exam okay + + + align:start position:0% +exam okay +uh let's + + align:start position:0% +uh let's + + + align:start position:0% +uh let's +see if if I exchange two rows of a which + + align:start position:0% +see if if I exchange two rows of a which + + + align:start position:0% +see if if I exchange two rows of a which +subspaces stay the + + align:start position:0% +subspaces stay the + + + align:start position:0% +subspaces stay the +same so I'm trying to take out questions + + align:start position:0% +same so I'm trying to take out questions + + + align:start position:0% +same so I'm trying to take out questions +that we can answer without you know we + + align:start position:0% +that we can answer without you know we + + + align:start position:0% +that we can answer without you know we +can answer quickly if I if I have a + + align:start position:0% +can answer quickly if I if I have a + + + align:start position:0% +can answer quickly if I if I have a +matrix a and I exchange two of its rows + + align:start position:0% +matrix a and I exchange two of its rows + + + align:start position:0% +matrix a and I exchange two of its rows +which subspaces stay the + + align:start position:0% +which subspaces stay the + + + align:start position:0% +which subspaces stay the +same the row space does stay the + + align:start position:0% +same the row space does stay the + + + align:start position:0% +same the row space does stay the +same and the no space good good correct + + align:start position:0% +same and the no space good good correct + + + align:start position:0% +same and the no space good good correct +column place would be a wrong answer + + align:start position:0% +column place would be a wrong answer + + + align:start position:0% +column place would be a wrong answer +okay uh oh here's a question oh this + + align:start position:0% +okay uh oh here's a question oh this + + + align:start position:0% +okay uh oh here's a question oh this +leads into a next chapter why can the + + align:start position:0% +leads into a next chapter why can the + + + align:start position:0% +leads into a next chapter why can the +vector 1 2 3 not be a row and also in + + align:start position:0% +vector 1 2 3 not be a row and also in + + + align:start position:0% +vector 1 2 3 not be a row and also in +the n space let me let me close with + + align:start position:0% +the n space let me let me close with + + + align:start position:0% +the n space let me let me close with +this question closes so V this this 1 2 + + align:start position:0% +this question closes so V this this 1 2 + + + align:start position:0% +this question closes so V this this 1 2 +3 can't + + align:start position:0% + + + + align:start position:0% + +be in the null space of a matrix + + align:start position:0% +be in the null space of a matrix + + + align:start position:0% +be in the null space of a matrix +and the row + + align:start position:0% + + + + align:start position:0% + +space and my question is why not why + + align:start position:0% + + + + align:start position:0% + +not so this is a question that we can + + align:start position:0% +not so this is a question that we can + + + align:start position:0% +not so this is a question that we can +cuz it's sort of asked in a + + align:start position:0% +cuz it's sort of asked in a + + + align:start position:0% +cuz it's sort of asked in a +straightforward way we can figure out an + + align:start position:0% +straightforward way we can figure out an + + + align:start position:0% +straightforward way we can figure out an +answer well actually yeah + + align:start position:0% +answer well actually yeah + + + align:start position:0% +answer well actually yeah +I'll even pin it down it can't be in the + + align:start position:0% +I'll even pin it down it can't be in the + + + align:start position:0% +I'll even pin it down it can't be in the +no space and and be a + + align:start position:0% +no space and and be a + + + align:start position:0% +no space and and be a +row I'll even pin it down further ask + + align:start position:0% +row I'll even pin it down further ask + + + align:start position:0% +row I'll even pin it down further ask +you ask it to be a row of + + align:start position:0% +you ask it to be a row of + + + align:start position:0% +you ask it to be a row of +a why + + align:start position:0% +a why + + + align:start position:0% +a why +not so I'm this is now I'm we know the + + align:start position:0% +not so I'm this is now I'm we know the + + + align:start position:0% +not so I'm this is now I'm we know the +dimensions of these + + align:start position:0% +dimensions of these + + + align:start position:0% +dimensions of these +spaces but now I'm asking you sort of + + align:start position:0% +spaces but now I'm asking you sort of + + + align:start position:0% +spaces but now I'm asking you sort of +like the overlap between so the null + + align:start position:0% +like the overlap between so the null + + + align:start position:0% +like the overlap between so the null +space and the row space those are in the + + align:start position:0% +space and the row space those are in the + + + align:start position:0% +space and the row space those are in the +same nend dimensional + + align:start position:0% + + + + align:start position:0% + +space those are those are both subspaces + + align:start position:0% +space those are those are both subspaces + + + align:start position:0% +space those are those are both subspaces +of nend dimensional space and I'm + + align:start position:0% +of nend dimensional space and I'm + + + align:start position:0% +of nend dimensional space and I'm +basically saying they can't + + align:start position:0% +basically saying they can't + + + align:start position:0% +basically saying they can't +overlap I can't have a vector like this + + align:start position:0% +overlap I can't have a vector like this + + + align:start position:0% +overlap I can't have a vector like this +typical Vector that's in the null space + + align:start position:0% +typical Vector that's in the null space + + + align:start position:0% +typical Vector that's in the null space +and it's also a row of the Matrix why is + + align:start position:0% +and it's also a row of the Matrix why is + + + align:start position:0% +and it's also a row of the Matrix why is +that so that's a new sort of idea let's + + align:start position:0% +that so that's a new sort of idea let's + + + align:start position:0% +that so that's a new sort of idea let's +just see what it would mean I mean that + + align:start position:0% +just see what it would mean I mean that + + + align:start position:0% +just see what it would mean I mean that +a * this + + align:start position:0% +a * this + + + align:start position:0% +a * this +V why can this a * this V it can't be + + align:start position:0% +V why can this a * this V it can't be + + + align:start position:0% +V why can this a * this V it can't be +zero oh well if if it's + + align:start position:0% +zero oh well if if it's + + + align:start position:0% +zero oh well if if it's +zero so this is I'm getting it into the + + align:start position:0% +zero so this is I'm getting it into the + + + align:start position:0% +zero so this is I'm getting it into the +null space + + align:start position:0% +null space + + + align:start position:0% +null space +here so this is now let's put that ve + + align:start position:0% +here so this is now let's put that ve + + + align:start position:0% +here so this is now let's put that ve +now that Vector is in the null space why + + align:start position:0% +now that Vector is in the null space why + + + align:start position:0% +now that Vector is in the null space why +can't one why can't the first row of the + + align:start position:0% +can't one why can't the first row of the + + + align:start position:0% +can't one why can't the first row of the +Matrix be 1 2 3 + + align:start position:0% +Matrix be 1 2 3 + + + align:start position:0% +Matrix be 1 2 3 +I can fill out the Matrix as I like why + + align:start position:0% +I can fill out the Matrix as I like why + + + align:start position:0% +I can fill out the Matrix as I like why +is that + + align:start position:0% + + + + align:start position:0% + +impossible now you're seeing it's + + align:start position:0% +impossible now you're seeing it's + + + align:start position:0% +impossible now you're seeing it's +impossible + + align:start position:0% +impossible + + + align:start position:0% +impossible +right and that if that was a row of the + + align:start position:0% +right and that if that was a row of the + + + align:start position:0% +right and that if that was a row of the +Matrix and in the null space that number + + align:start position:0% +Matrix and in the null space that number + + + align:start position:0% +Matrix and in the null space that number +would not be zero it would be + + align:start position:0% +would not be zero it would be + + + align:start position:0% +would not be zero it would be +14 right so now we actually are + + align:start position:0% +14 right so now we actually are + + + align:start position:0% +14 right so now we actually are +beginning to get a more complete picture + + align:start position:0% +beginning to get a more complete picture + + + align:start position:0% +beginning to get a more complete picture +of these four + + align:start position:0% +of these four + + + align:start position:0% +of these four +subspaces the two that are over in in in + + align:start position:0% +subspaces the two that are over in in in + + + align:start position:0% +subspaces the two that are over in in in +nend dimensional + + align:start position:0% +nend dimensional + + + align:start position:0% +nend dimensional +space they actually only share the zero + + align:start position:0% +space they actually only share the zero + + + align:start position:0% +space they actually only share the zero +VOR the intersection of the null space + + align:start position:0% +VOR the intersection of the null space + + + align:start position:0% +VOR the intersection of the null space +and the row space is only the + + align:start position:0% +and the row space is only the + + + align:start position:0% +and the row space is only the +zero and in fact the null space is + + align:start position:0% +zero and in fact the null space is + + + align:start position:0% +zero and in fact the null space is +perpendicular to the Rose space that'll + + align:start position:0% +perpendicular to the Rose space that'll + + + align:start position:0% +perpendicular to the Rose space that'll +be the first topic on let's see we have + + align:start position:0% +be the first topic on let's see we have + + + align:start position:0% +be the first topic on let's see we have +a holiday Monday and I'll see you + + align:start position:0% +a holiday Monday and I'll see you + + + align:start position:0% +a holiday Monday and I'll see you +Wednesday with + + align:start position:0% +Wednesday with + + + align:start position:0% +Wednesday with +perpendiculars and I'll see a price so + + align:start position:0% +perpendiculars and I'll see a price so + + + align:start position:0% +perpendiculars and I'll see a price so +good luck on the + + align:start position:0% +good luck on the + + + align:start position:0% +good luck on the +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +way \ No newline at end of file diff --git a/lFngfmE9RCc.txt b/lFngfmE9RCc.txt new file mode 100644 index 0000000000000000000000000000000000000000..168023e24ab23f1875ffa3367464e6f1997ad055 --- /dev/null +++ b/lFngfmE9RCc.txt @@ -0,0 +1,2119 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality, educational + +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: We ended up the last +lecture talking about + +dynamic programming. + +And we'll spend all of +today on that topic. + +We showed how it could be used +to provide a practical + +solution to the shortest path +problem, a solution that would + +allow us to solve what +was, in principle, a + +complex problem quickly. + +And we talked about the +properties that make it + +possible to solve that problem +and, in general, the + +properties we need to make +dynamic programming + +applicable. + +So let's return to that +topic right now. + +What we looked at is we looked +at two properties. + +The first was optimal +substructure. + +And you recall what this meant +is that we can construct a + +globally optimal solution by +combining solutions to local + +subproblems. + +So we've looked at a lot of +problems already this term + +that have optimal +substructure-- + +merge sort, for example, which +exploits the fact that a list + +can be sorted by first sorting +components of it and then + +combining those. + +So merge sort exhibited +optimal substructure. + +The second property we looked +at was overlapping + +subproblems. + +And what this meant was that in +the course of running our + +algorithm, we would end +up solving the same + +problem more than once. + +And that is what gave us the +power of using memoization, to + +use table lookup instead of +re-computing the solution. + +Notice that merge_sort does +not have overlapping + +subproblems. + +There's no reason that we would +expect, if we're sorting + +a list, that we would +ever encounter the + +same sublist twice. + +And so in fact, we cannot +use dynamic + +programming to solve sorting. + +Because it has one of these +properties, but not both. + +So how about shortest path? + +Does it have these properties? + +Well, let's first think about +optimal substructure. + +You might begin by asking the +question if I knew the + +shortest path from A to B, and +I knew the shortest path from + +B to C, can I necessarily +combine those to get the + +shortest path from A to C? + +No, exactly right. + +Because for example, maybe +there's a direct link from A + +to C. So we can't combine +them that way. + +So that gives us +the question-- + +Oh, pardon? + +[INAUDIBLE] + +PROFESSOR: --Almost +got it there. + +So that gives us the question, +what is the optimal + +substructure here? + +Well, there is something we do +know about shortest path, that + +if I have the shortest path +from one node to another. + +And I take any sub path +of that, I will have-- + +so let's say I have a path +that goes from-- + +let's say I know that the +shortest path from A to C is A + +to B to D to E to C. If this is +the shortest path from A to + +C, I know that this is +the shortest path + +from B to E. Right? + +Because otherwise, I wouldn't +have bothered going through D. + +If there were, for example, a +link directly from B to E, + +then the shortest path +from A to C would not + +have included this. + +So that's the optimal +substructure I have, and + +that's the substructure that I +exploited last time in showing + +you the dynamic programming +solution to the + +shortest path problem. + +You also recall that we looked +at the shortest path. + +We'd found overlapping +subproblems. + +Because I would end up solving +the same intermediate problem + +multiple times, figuring +out how to get + +from one node to another. + +So indeed, we saw that the +shortest path problem + +exhibited both of these +properties and therefore, was + +amenable to solution by the +dynamic programming. + +And in fact, we ran it and we +saw that it ran quite quickly. + +It's not immediately obvious, +but the 0-1 knapsack problem + +also exhibits both of +these properties. + +You'll recall a few lectures +ago, and also in a problem set + +not so long ago, we looked at +a recursive solution to the + +0-1 knapsack problem. + +It's called "solve" +in this code. + +It uses backtracking to +implement the decision tree. + +if we look at the decision +tree we had there-- + +I gave you a small example +here of the + +0-1 knapsack problem. + +I've got A, B, C and D. I've got +some values, and I've got + +some weights. + +We started by saying at the +beginning, we looked at this + +node here, where we had decided +not to take anything . + +We still had the list A, B, +C, and D to consider. + +The total value of our items was +0, and for our example, I + +think we had 5 pounds +of material left, + +or 5 units of weight. + +We then considered a decision. + +What happens if we take A? + +Well, if we take A, we have B, +C, and D left to consider. + +We now look at this node +and say, all right, + +our value is 6 -- + +the value of A. But we only +have 2 pounds left. + +We then considered going +depth first, left + +first in this case. + +This is the depth- +first search. + +We've looked at that before. + +All right, let's consider +the next branch. + +Well the next branch we'll +consider C. Well we discover-- + +no we'd consider B rather. + +We can't take B, because +B weighs 3. + +So this is a branch that +we can't get to. + +We can elect the other decision +not to take B, in + +which case we still have C +and D left to consider. + +And still 6 and 2. + +We then proceed and said right, +well can we take C? + +Yes we can. + +And that leaves us with +a value of 14 + +and no weight left. + +So since we have no available +weights, we might as well stop + +considering things. + +So this is a terminal node. + +We then back up, and said all +right, let's consider the + +decision where we don't +take C. Can we take D? + +And the answer is no because +it weighs too much. + +And then we're done. + +And so we see on this side of +the tree, we've explored + +various possibilities. + +And this is our best +option so far. + +And we can walk through and now +we consider well, what if + +we don't take A? + +Well then we have these +decisions to make. + +And eventually, we can +look at the whole + +thing and make a decision. + +By the way, I noticed this +morning that there was an + +error on your handout. + +I chose not to correct it in +the slide so that you would + +notice it was in your +handout as well. + +What should node 18 be? + +What's the error here? + +Pardon? + +[INAUDIBLE] + +PROFESSOR: Right. + +That should be the empty one. + +Right? + +Because we considered +everything. + +And in fact, typically all of +your bottom nodes should + +either have 0 weights or no +items left to consider. + +Not very deep, just a typo but +has the advantage that by + +looking for it, you can see +whether you understand how + +we're constructing these +decision trees. + +So this is a very common +way to deal with an + +optimization problem. + +You consider all combinations +of decisions in + +a systematic way. + +And when you're done, you +choose the best one. + +So this is using depth-first +search and backtracking. + +And this is essentially what you +did in your problem set. + +Now what you saw in your problem +set is that if the set + +of items is even moderately +large, this algorithm can take + +a very long time to run. + +How long? + +Well, at each level of the tree +we're deciding whether to + +keep or not keep one item. + +So what's the maximum +depth of the tree? + +How many levels can +this tree go? + +If we have n items-- + +Pardon? + +[INAUDIBLE] + +PROFESSOR: n levels-- + +exactly. + +So if we have n items, +it can go n levels-- + +Good grab. + +All right, how many nodes do +we have at each level? + +Well, at level 0 we +have only 1 node. + +But what's the down +at the bottom? + +Let's say we have an enormous +amount of weight so that in + +fact we never run out of +weight in our knapsack. + +We'll have quite a broad +tree, right? + +How many nodes at level 2? + +At each level, right? + +Down here we have up +to 4 nodes, up to 8 + +nodes, up to 16 nodes. + +So if we had say, 39, 40 items, +at level 39 we'd have 2 + +to the 39th nodes-- + +pretty darn big tree. + +All right? + +Not very deep, but very bushy. + +So we know that for any +reasonable number of items and + +a reasonable amount of +weight, this is just + +not going to work. + +And that's why when you wrote +your problem set, and you were + +trying to solve the optimal set +of courses to take, you + +could only run it on a small +subset of the courses at MIT. + +Because if we gave you +everything-- and we gave you a + +lot for a test-- + +you noticed it effectively +just wouldn't finish. + +So now we have to ask the +question well, can we use + +dynamic programming to +solve this problem? + +And in particular, that boils +down to the question of does + +this solution exhibit optimal +substructure and overlapping + +subproblems? + +Well, optimal substructure is +easily visible in both the + +decision tree and the code. + +Right? + +Each parent node combines +the solution-- + +We can look at the code +since you have the + +subtree in your handout-- + +or the decision tree +in your handout. + +And the key place in the code is +where we combine decisions + +from lower down in the +tree as we go up. + +So at each parent node, +we select the + +better of the two children. + +Right? + +If the left child is better +than the right child, we + +select the left. + +Otherwise, we select +the right. + +And we just percolate +up the tree. + +So there's clearly optimal +substructure here, that we can + +solve the higher nodes with +solutions to the lower nodes. + +And we see that again in the +code where it says choose + +better branch. + +It's less obvious to answer the +question whether or not + +there are overlapping +subproblems. + +If we go back and look +at the tree-- + +At first glance, it may appear +that there are no overlapping + +subproblems. + +You'll notice that at +each node we're + +solving a different problem. + +Right? + +The problem is described in some +sense by this fortuple. + +But if I've already taken A and +C, and I have D left to + +consider, what should I do? + +Where up here I've taken A, and +I have B, C, and D left to + +consider, what should I do? + +And by design of the decision +tree, each node is different. + +Right? + +We're not considering the same +thing over and over again. + +So you might look at it and say, +well, we're out of luck. + +There are no overlapping +subproblems. + +Not true. + +So let's think hard for a second +and ask in what sense + +are there overlapping +subproblems? + +When are we potentially, +at least, + +solving the same problem? + +Well what is the problem +we're actually solving? + +We're solving the problem that +can in some sense be stated as + +follows- at each node, we're +saying what should we do about + +the nodes left to consider? + +So we're solving a problem +given a set of items-- + +what items we have at a node. + +Given an available weight, which +items should we take? + +What's missing from this? + +It says nothing about the items +you've already taken. + +In order to decide what to take +next, we need to know how + +much weight we have available. + +But we don't need to know why +we have that much weight + +available, which items we have +previously decided to take. + +That part of the for tuple turns +out not to be relevant + +to the problem I still +have to solve. + +Why is that important? + +Because there may be many +different sets of items I + +could take. + +It would add up to the +same total weight. + +Therefore, leaving me the +same problem to solve. + +And that's the key observation +that tells us we can use + +dynamic programming to solve +the 0-1 knapsack problem. + +Does that-- + +I should ask the positive +question-- does that make + +sense to anybody? + +Raise your hand if +it makes sense-- + +a small number of hands. + +Raise your hands if it +doesn't make sense. + +OK. + +Can any of you to whom +it doesn't make + +sense formulate a question? + +No, it's hard. + +AUDIENCE: Total weight, or +the same total value? + +PROFESSOR: The same +total weight. + +Because-- + +the question is are there many +sets of items with the same + +total value or the same +total weight? + +There might be many with the +same total value, but that + +doesn't really matter. + +Because in choosing what to do +next, as I go down the tree, I + +don't care what the value +is above the tree. + +Because I'll still try and find +the best solution I can + +to the remaining subproblem. + +If a value above is a million, +or the value above is 3, it + +doesn't matter what +I should do next. + +AUDIENCE: Which makes sense. + +But if you use different things +to get that weight, + +wouldn't you have a different +set of items to choose from? + +PROFESSOR: Right. + +So the question is it makes +sense if there are many + +different sets of items that +would have the same total + +weight, but what +I'm going to-- + +but, wouldn't I have different +items to choose from? + +Well you'll notice that I +do have to look at what + +items I have left. + +But as I go through-- + +let's assume here that I have +a list of items to take. + +As I go through from the front, +say, I'll label each + +node of the tree. + +Each item will have either a 0 +or a 1, depending upon whether + +I decided to take it or not. + +And then what I have +to consider is + +the remaining items. + +And let's say the values of +the first two items-- + +the first four items-- + +were, well, let's say they were +all one, just to make + +life simple. + +Well that'll be confusing, since +I'm using that for taken + +or not taken. + +Let's say their values +were all 2. + +When I get here, and I'm +deciding what to do with these + +items, I might-- + +so this tells me that +I've used up 4 + +pounds of my allotment. + +Right? + +But if I had done this one, I +would also use up 4 pounds of + +my allotment. + +And so, which of these I take +or don't take is independent + +of how I got here. + +I do have to keep track of +which items are still + +available to me. + +But I don't care how I've +used up those 4 pounds. + +And obviously, there are a lot +of ways to choose two that + +will use up 4 pounds +here, right? + +But the solution to this part +of the problem will be + +independent of which +two I took. + +That make sense now? + +Therefore, as long as there is +a prefix of my list of items, + +such that multiple things add up +to the same weight, I will + +have overlapping subproblems. + +Now you could imagine a +situation in which no + +combination added to the same +weight, in which case dynamic + +programming wouldn't +buy me anything. + +It would still find the right +answer, but it wouldn't speed + +anything up. + +But in practice, for most 0-1 +knapsack problems-- they may + +not be this simple-- + +but you could expect-- + +and we'll see this complexity +later-- + +that as long as your possible +weights are being chosen from + +a relatively small set, you'll +have many things add up to the + +same thing-- + +particularly as you get further +down this list and + +have a lot longer prefix +to consider. + +So indeed I do have overlapping +subproblems. + +That answer the question? + +All right, now. + +People feel better about +what's going on? + +OK. + +Maybe looking at some code +will make it even + +clearer, and maybe not. + +Anyway, I do appreciate +the questions. + +Since it's sometimes hard for me +to appreciate what's coming + +across and what's not +coming across. + +You should get rewarded for +good questions, as well as + +good answers. + +All right, so now +let's look at a + +dynamic programming solution. + +I've just taken the +previously-- + +the example we looked at +before was solve-- + +made it fast solve. + +And I've added a parameter +of memo. + +This is the same kind of trick +we used last time for our + +shortest path problem. + +I should point out +that I'm using-- + +this calls to mind a dirty, +little secret of Python, one I + +have previously been hiding +because it's so ugly I just + +hate to talk about it. + +But I figured at some point, +honesty is the right policy. + +What I'd like is the first +time I call fast solve, I + +shouldn't have to know that +there's even a memo. + +Fast solve should have the +same interface as solve. + +The items to consider and the +available weight, and that's + +all you should need to know. + +Because the memo is part of the +implementation, not part + +of the specification +of solving the + +0-1 knapsack problem. + +We've made that argument +several times, + +earlier in the semester. + +And so you might think that what +I should therefore do is + +to initialize the memo to, +say the empty dictionary. + +I'm going to use dictionaries +for memos, as before. + +And then just check and if it's +the empty one, that means + +it's the first-- + +I can know whether it's +the-- it'll work fine + +for the first call. + +Well it doesn't work fine. + +And here's the dirty, +little secret. + +In Python, when you have a +parameter with a default + +value, that default value +is evaluated once. + +So the way the Python system +works is it will process all + +of the def statements +and evaluate the + +right-hand side here once. + +And then every time the function +is called, without + +this optional argument, it will +use the value it found + +when it evaluated the +def statement. + +Now if this value is immutable, +it doesn't matter. + +None will be none forever. + +28 will be 28 forever. + +3.7 will be 3.7 forever. + +But if this is a mutable value, +for example a dict, + +then what will happen is it will +create an object which + +will be initially an +empty dictionary. + +But then every time fast solve +is called without this + +argument, it will access +the same object. + +So if I call fast solve to solve +one problem, and in the + +course of that, it builds +up a big dictionary. + +And then I call it again to +solve another problem, instead + +of starting with the empty +dictionary, it will start with + +the same object it started with +the first time, which is + +by now a dictionary filled +with values. + +And so I will get the +wrong answer. + +This is a subtlety, and it's a +common kind of bug in Python. + +And I confess to having been +bitten by it very recently, as + +in yesterday, myself. + +So it's worth remembering. + +And there's a simple workaround, +which is the + +default value is the +immutable value. + +I chose none. + +And what I say when I enter it +is if the memo is none, it + +means it's been invoked. + +And now I'll initialize it +to the empty dictionary. + +And now every time it will get +a new one, because we know + +what this statement says is +allocate a new object of type + +dict, and initialize +it to empty. + +This will happen dynamically +when the thing is invoked, + +rather than statically +at the time Python + +processes the diffs. + +It's a silly little problem. + +I hate to bring it up. + +I don't think it should +work that way, but it + +does work that way. + +So we're stuck. + +Yeah. + +[INAUDIBLE] + +PROFESSOR: I'm sorry. + +You've have to speak +more loudly. + +[INAUDIBLE] + +PROFESSOR: Well, why doesn't +my first call-- + +So the question is when I go to +test it, say, why don't I + +start by calling it with fast +solve in an empty dictionary? + +And it's because, as we'll see +when I get there, I want solve + +and fast solve, in this case, +to have the same interface. + +And in fact, you can say I want +them to have the same + +specification. + +Because in fact, imagine that +you wrote a program that + +called solve many times. + +And it was slow, and then +you took 6.00-- + +So, I know why it's +slow, because I've + +used a stupid solve. + +Let me use dynamic +programming. + +I want to then be able to not +name the new one fast solve, + +but replace the old solve +by the new solve. + +And have all the programs that +you solve still work. + +That will not happen if I insist +that the new solve has + +an extra argument. + +Now I could put what's called +a wrapper in and call solve, + +and then have it call fast solve +with the extra argument. + +And that would work too. + +That would be an equally +good solution to + +address this problem. + +But does that make sense? + +So either one would work. + +I chose this one but what +wouldn't work in a practical + +engineering sense is to change +the specification of solve. + +All right? + +So it's a silly little thing, +but since people do get bitten + +by it, I figure I should +tell you about it. + +And I guess while I'm on the +subject of silly little + +things, I'll tell you one more +thing before we go back to + +this algorithm. + +Down here in the place where +I'm testing it, you'll note + +that I've imported something +called sys, and then said + +sys.setrecursionlimit to 2000. + +In Python, there's a maximum +depth of recursion. + +When this is exceeded, it +raises an exception-- + +depth exceeded. + +As it happens, the default +value for that + +is some tiny number-- + +I forget what it is-- + +such that when I run this on an +interesting size example, + +it crashes that exception. + +So all I'm doing here +is saying no, I + +know what I'm doing. + +It's OK to recurse to +a greater depth. + +And I've set it to 2000 +here, which is + +plenty for what I need. + +I could set it to 20,000. + +I could set it to 50,000. + +Again, if you're writing a +serious program, you'll + +probably find that the default +value for the depth of + +recursion is not enough, and +you might want to reset it. + +I don't expect you to remember +how to do this. + +I expect you to remember +that it's possible. + +And if you need to do it, you +can Google "recursion limit + +Python" and it will tell +you how to change it. + +But again, I've found +in testing this, the + +default was too small. + +Ok. + +Let's go look at the code +now for fast solve. + +It's got the items to consider, +what's available, + +the available weight, +and a memo. + +And I'm going to keep track +of the number of calls. + +Just for pedagogical +reasons, we'll want + +to review that later. + +OK, so I'll initialize +the memo if it's + +the first time through. + +And then the first thing I'll do +is I'm going to code what I + +have available essentially the +way I've coded it here-- so + +what items are remaining +by using an index. + +So my items are going to +be a set of lists. + +And I'm going to just sort +of keep track of + +where I am in the list-- + +just march through exactly the +way I'd marched through here. + +And so if the list of +things to consider, + +the length of it-- + +because every time the length +is the same, it + +will be the same list. + +Since I'm systematically +examining a prefix. + +I'm not shuffling the +list each time. + +So the length can be used +to tell me what I've + +already looked at. + +So if I've looked at that +sublist before, with this + +available weight, it will +be in the memo. + +And I'll just look +up the solution-- + +result equals memo of +[UNINTELLIGIBLE] + +to consider avail. + +So those will be my keys +for my dictionary. + +The key will be a pair of +essentially which items I have + +left to consider, which is coded +by a number, and the + +amount of weight, +another number. + +Or if there's nothing left to +consider, or there's no weight + +available, then I'll return +0 and the empty tuple-- + +no value, didn't +take anything. + +Otherwise, I'm now in the +interesting case. + +If to consider subzero, the +first one here, if the weight + +of that is greater than what I +have available, then I know I + +can't take it. + +Right? + +So I'll just lop it off and call +fast solve recursively + +with the remaining list-- + +same old value of avail +and the same old memo. + +Otherwise, well now I have an +option of taking the first + +element in the list. + +I'll set the item to that +element, and I'll + +consider taking it. + +So I'll call fast solve +with to consider + +without the first item. + +But the amount of weight will +be available now is what was + +available before minus the +weight of that item. + +This is my left branch, +if you will, where I + +decide to take the item. + +And so now I'm solving +a smaller problem. + +The list is smaller, and +I have less weight. + +The next thing I'll do is +consider not taking the item. + +So I'll call fast solve +again with the + +remainder of the list. + +But avail and memo +are not changed. + +That's the right branch. + +And you'll remember our decision +tree the right branch + +avail and weight were +never changed. + +Because I elected not +to take that item. + +Then I'll just choose the +better of the two + +alternatives, as before. + +And when I'm done, I'll update +the memo with the solution to + +the problem I just solved. + +All right? + +So it's exactly the same as +the recursive solution you + +looked at a few weeks ago. + +Except I've added this notion +of a memo to keep track of + +what we've already done. + +Well let's see how +well it works. + +So I've got this test program. + +Just so things are repeatable, +I'd set the C to 0 -- + +doesn't matter what I set it to, +this just says instead of + +getting a random value each +time, I'll get the same C so + +I'll get the same sequence of +pseudo-random numbers-- + +makes it easier to debug. + +I'll have this global +variable num calls. + +I'm arbitrarily setting the +capacity to eight times the + +maximum weight. + +So I'm saying the maximum +value of an item is 10. + +The maximum weight is 10. + +This just says runs slowly is +false, as in don't run the + +slow version. + +Run only the fast version. + +We'll come back to that. + +I set the capacity of +the Knapsack to 8 + +times the max weight. + +And then for the number of +items-- and I'm just going to + +go through a different +number of items, + +4, 8 16, up to 1024-- + +I'm going to call build +many items. + +Again, we've seen this +program before. + +That just takes a number of +items, a maximum value, and a + +maximum weight, and builds some +set of items, choosing + +the values and weights at random +from the ones we've + +offered it. + +This saves me. + +I wasn't going to type a +set of 1024 items, I + +guarantee you that. + +If it runs slowly, then I'm +going to test it on both fast + +solve and solve. + +Notice that these are the names +of the functions, not + +invocations of the functions. + +Because remember functions, +like everything else in + +Python, are just objects. + +Otherwise, my tests will be +only the tuple fast solve. + +And then for each function in +tests, I'm going to set the + +number of calls to 0. + +I'm going to load up a timer, +just because I'm curious how + +long it takes. + +And then I'll call the func. + +Notice again, getting back to +what we talked about before, + +both fast solve and +solve get called + +with the same arguments. + +I could not have done this +trick if fast solve had + +required an extra parameter. + +And then I'll just see +how well it did. + +So let's start with this +equal to true. + +So in that case we'll +test both of them. + +And let's see how we do. + +So it's chugging along. + +And we see that if I have 4 +items, fast solve made 29 + +calls, took this much time. + +The good news, by the way, +you'll notice that fast solve + +and solve gave me the same +value each time. + +We would hope so, right? + +Because they're both supposed +to find an optimal solution. + +They could find different +sets of items. + +That would be OK. + +But they better add up +to the same value. + +But we seem to be stuck here. + +So you'll notice at 16, +Solve made 131,000 + +calls, fast solve 3,500-- + +only took a third of a second. + +But we seem to be kind +of stuck at-- + +actually, fast solve +only made 1,200. + +At 32, fast solve made +3,500 calls. + +But solve seems to be stuck. + +Should this be a shocker that +going from 16 to 32 made a big + +difference? + +Well remember here we're talking +about 2 to the 16 + +possibilities to investigate, +which is not a huge number. + +But now we're at 2 to the 32, +which is quite a large number. + +And so we could wait quite +a long time for solve to + +actually finish. + +And in fact, we're not going +to wait that long. + +We'll interrupt it. + +So let's see how well +fast solve works. + +We just call that. + +So we'll set this to false. + +It says don't run slowly, i.e. + +Don't call solve. + +So not only did we not get stuck +at 32 items way up here, + +we didn't get stuck +at 1024 items. + +Huge difference, right? + +Instead of only being able to +process a set of 16, we can + +process a set of over 1,000. + +And in fact, I don't know how +much higher we can go. + +I didn't try anything bigger. + +But even this-- + +big difference between getting +stuck here and not getting + +stuck here. + +And in fact, not only did +not get stuck, it + +was only two seconds. + +So let's ask ourselves +the question-- how + +fast is this growing? + +Not very fast-- + +more or less, what we see +here-- and this is not + +something we can guarantee. + +But in this case, what we see is +as we double the number of + +items, the number of calls +kind of doubles as well. + +So we're actually growing +pretty slowly. + +Well, OK that's good. + +But suppose we want to look at +it a little bit more carefully + +and consider the question of +what does govern the running + +time of fast solve. + +Well we know that looking +things up in the dict is + +constant time. + +So that's OK. + +So what's going to govern it is +every time we have to add + +an element to the memo, it's +going to slow us down. + +Because you're gonna have +to solve a problem. + +Every time we can just look +something up in the memo, + +we'll get our answer back +instantaneously. + +So if we think about the running +time, it's going to be + +related to how many different +key value pairs might we have + +to compute for the memo. + +Well what governs that? + +So we know that the keys in +the memo are pairs of to + +consider and avail. + +And so we know that the number +of possible different keys + +will be the number of possible +values in to consider, + +multiplied by the number of +possible values of avail. + +Right? + +How many possible values of +to consider are there? + +What governs that? + +That's the easy question. + +Number of items, right? + +Because I'm just marching across +this list, chopping off + +one item at a time. + +At most I can chop off +n items, if the list + +is of length n. + +Avail is more complicated. + +What does avail depend upon? + +It depends upon, well, the +initial available weight. + +If the initial available weight +is 0, well then it's + +gonna end really quickly. + +If it's really big, I might +have to churn longer. + +But it also depends-- + +and this is the key thing-- + +on the number of different +weights, that sets of items + +can add up to. + +Because you'll recall the whole +secret here was that we + +said that different sets of +items could actually have the + +same total weight. + +And that's why we had this +business of overlapping + +subproblems. + +Now here, since I only had 10 +possible weights, that tells + +me that I can't have very many +different combinations. + +Right? + +That any set of say, one item +has to be 0 through 10, or 0 + +through 9, I forget +which it was. + +But either way, that means +that alI only have 10 + +different possible sums +for sets of length 1. + +Whereas if my weights ranged +over 100, I would have 100 + +different possibilities +for sets of length 1. + +So that's an important factor +in governing it. + +So it's a complicated situation, +but just to see + +what happens, try and remember +how long this took for 1024. + +It took 2.2 seconds. + +I'm going to allow 20 +different weights. + +And let's see what happens. + +It took roughly twice as long. + +So that's sort of what we +would have expected. + +So again, we're going to +see the running time + +is related to that. + +So we can see that +it's actually a + +fairly complicated thing. + +Suppose I did something really +nasty and went up here where I + +built my items-- + +so here you'll see, when I built +my items I chose the + +weight between 1 +and max weight. + +And these were all integers-- + +ints. + +Suppose instead of +that, I do this. + +So here after I choose my value +between 1 and 10, I'm + +going to multiply it by some +random number between 0 and 1. + +We've all seen random.random. + +So now how many possible +different weights + +am I going to have? + +A huge number, right? + +The number of random numbers, +real floats between 0 and 1 is + +close to infinite, right? + +And so in fact, now I'm going +to see that with reasonable + +probability, every single item +will have a different weight. + +And so, things adding up to the +same could still happen, + +even if they're all different. + +But it's not very probable. + +So let's see what happens +when I run it now. + +It's slowing down +pretty quickly. + +Pretty much where the other +one stopped right? + +Remember we got through +16 with Slowsolve + +but not through 32? + +Because effectively, I've now +reduced the fast solve to the + +same as solve. + +It will never find anything +in the memo, so it's doing + +exactly the same amount of +work that solve did. + +And it will run very slowly. + +OK, life is hard. + +But this is what you'd expect, +because deep down we know the + +0-1 knapsack problem is +exponential, inherently + +exponential. + +And while I think dynamic +programming is kind of + +miraculous how well it usually +works, it's not miraculous in + +the liturgical sense, right? + +It's not actually performing +a miracle in solving an + +exponential problem +in linear time. + +It can in all things go bad. + +The exponential, and that's +what it is here. + +This kind of algorithm is called +pseudo-polynomial. + +It kind of runs in polynomial +time, but not when things are + +really bad. + +And I won't go into the details +of pseudo-polynomial, + +but if any of you are in Course +6, you'll hear about it + +in 6.006 and 6.046. + +OK, we can adjourn. + +I'll see you all on Thursday. + +And we're not going to +wait for this to + +finish, because it won't. \ No newline at end of file diff --git a/lGaMKrtiTc8.txt b/lGaMKrtiTc8.txt new file mode 100644 index 0000000000000000000000000000000000000000..e1faa1455af58958e642135711cc86ad0326ffc0 --- /dev/null +++ b/lGaMKrtiTc8.txt @@ -0,0 +1,2587 @@ +align:start position:0% + +here's a well thrown disc but have you + + align:start position:0% +here's a well thrown disc but have you + + + align:start position:0% +here's a well thrown disc but have you +ever thrown one badly so that as it + + align:start position:0% +ever thrown one badly so that as it + + + align:start position:0% +ever thrown one badly so that as it +spins there's a wobble this wobble + + align:start position:0% +spins there's a wobble this wobble + + + align:start position:0% +spins there's a wobble this wobble +rotates with a different frequency than + + align:start position:0% +rotates with a different frequency than + + + align:start position:0% +rotates with a different frequency than +the dis itself spins in this video we're + + align:start position:0% +the dis itself spins in this video we're + + + align:start position:0% +the dis itself spins in this video we're +going to describe mathematically the + + align:start position:0% +going to describe mathematically the + + + align:start position:0% +going to describe mathematically the +motion of all the points on this badly + + align:start position:0% +motion of all the points on this badly + + + align:start position:0% +motion of all the points on this badly +thrown disc this video is part of the + + align:start position:0% +thrown disc this video is part of the + + + align:start position:0% +thrown disc this video is part of the +linearity video series many complex + + align:start position:0% +linearity video series many complex + + + align:start position:0% +linearity video series many complex +systems are modeled or approximated + + align:start position:0% +systems are modeled or approximated + + + align:start position:0% +systems are modeled or approximated +linearly because of the mathematical + + align:start position:0% +linearly because of the mathematical + + + align:start position:0% +linearly because of the mathematical +advantages hi my name is Dan Fry and I'm + + align:start position:0% +advantages hi my name is Dan Fry and I'm + + + align:start position:0% +advantages hi my name is Dan Fry and I'm +a professor of Engineering Systems and + + align:start position:0% +a professor of Engineering Systems and + + + align:start position:0% +a professor of Engineering Systems and +mechanical engineering at MIT and I use + + align:start position:0% +mechanical engineering at MIT and I use + + + align:start position:0% +mechanical engineering at MIT and I use +rigid body kinematics myself when + + align:start position:0% +rigid body kinematics myself when + + + align:start position:0% +rigid body kinematics myself when +designing radio controlled + + align:start position:0% +designing radio controlled + + + align:start position:0% +designing radio controlled +aircraft before watching this video you + + align:start position:0% +aircraft before watching this video you + + + align:start position:0% +aircraft before watching this video you +should be familiar with igen values and + + align:start position:0% +should be familiar with igen values and + + + align:start position:0% +should be familiar with igen values and +igen vectors the standard basis E1 E2 E3 + + align:start position:0% +igen vectors the standard basis E1 E2 E3 + + + align:start position:0% +igen vectors the standard basis E1 E2 E3 +R3 and orthogonal + + align:start position:0% +R3 and orthogonal + + + align:start position:0% +R3 and orthogonal +matrices after watching this video + + align:start position:0% +matrices after watching this video + + + align:start position:0% +matrices after watching this video +you'll be able to identify rotation + + align:start position:0% +you'll be able to identify rotation + + + align:start position:0% +you'll be able to identify rotation +matrices decompose the motion of the + + align:start position:0% +matrices decompose the motion of the + + + align:start position:0% +matrices decompose the motion of the +badly thrown disc into translational and + + align:start position:0% +badly thrown disc into translational and + + + align:start position:0% +badly thrown disc into translational and +rotational components and write the + + align:start position:0% +rotational components and write the + + + align:start position:0% +rotational components and write the +rotational motion of the disk as a + + align:start position:0% +rotational motion of the disk as a + + + align:start position:0% +rotational motion of the disk as a +product of rotation + + align:start position:0% + + + + align:start position:0% + +matrices our goal is to describe the + + align:start position:0% +matrices our goal is to describe the + + + align:start position:0% +matrices our goal is to describe the +motion of the dis + + align:start position:0% +motion of the dis + + + align:start position:0% +motion of the dis +the disc is a rigid body it doesn't + + align:start position:0% +the disc is a rigid body it doesn't + + + align:start position:0% +the disc is a rigid body it doesn't +stretch Bend or deform in any way when + + align:start position:0% +stretch Bend or deform in any way when + + + align:start position:0% +stretch Bend or deform in any way when +it is + + align:start position:0% +it is + + + align:start position:0% +it is +thrown in this video we're not + + align:start position:0% +thrown in this video we're not + + + align:start position:0% +thrown in this video we're not +interested in why the dis moves the way + + align:start position:0% +interested in why the dis moves the way + + + align:start position:0% +interested in why the dis moves the way +it does that is we're not trying to + + align:start position:0% +it does that is we're not trying to + + + align:start position:0% +it does that is we're not trying to +describe the torqus and forces that + + align:start position:0% +describe the torqus and forces that + + + align:start position:0% +describe the torqus and forces that +govern the motion we simply want to + + align:start position:0% +govern the motion we simply want to + + + align:start position:0% +govern the motion we simply want to +describe the motion + + align:start position:0% +describe the motion + + + align:start position:0% +describe the motion +mathematically this is a job for rigid + + align:start position:0% +mathematically this is a job for rigid + + + align:start position:0% +mathematically this is a job for rigid +body + + align:start position:0% +body + + + align:start position:0% +body +kinematics we're going to describe the + + align:start position:0% +kinematics we're going to describe the + + + align:start position:0% +kinematics we're going to describe the +motion by decomposing it into + + align:start position:0% +motion by decomposing it into + + + align:start position:0% +motion by decomposing it into +translation + + align:start position:0% +translation + + + align:start position:0% +translation +and rotational + + align:start position:0% +and rotational + + + align:start position:0% +and rotational +components we'll start with the + + align:start position:0% +components we'll start with the + + + align:start position:0% +components we'll start with the +mathematics of rotation + + align:start position:0% +mathematics of rotation + + + align:start position:0% +mathematics of rotation +matrices this will allow us to build up + + align:start position:0% +matrices this will allow us to build up + + + align:start position:0% +matrices this will allow us to build up +to a description of the wobbly + + align:start position:0% + + + + align:start position:0% + +Dis Let's Start with some linear algebra + + align:start position:0% +Dis Let's Start with some linear algebra + + + align:start position:0% +Dis Let's Start with some linear algebra +a rotation is a mapping that takes any + + align:start position:0% +a rotation is a mapping that takes any + + + align:start position:0% +a rotation is a mapping that takes any +Vector in R3 to some other Vector in R3 + + align:start position:0% +Vector in R3 to some other Vector in R3 + + + align:start position:0% +Vector in R3 to some other Vector in R3 +via rotation about some axis by some + + align:start position:0% +via rotation about some axis by some + + + align:start position:0% +via rotation about some axis by some +angle rotations don't change the length + + align:start position:0% +angle rotations don't change the length + + + align:start position:0% +angle rotations don't change the length +of a vector so if you scale a vector and + + align:start position:0% +of a vector so if you scale a vector and + + + align:start position:0% +of a vector so if you scale a vector and +then rotate it you get the same thing as + + align:start position:0% +then rotate it you get the same thing as + + + align:start position:0% +then rotate it you get the same thing as +if you first rotate it and then scale + + align:start position:0% +if you first rotate it and then scale + + + align:start position:0% +if you first rotate it and then scale +the + + align:start position:0% +the + + + align:start position:0% +the +vector also if you take two + + align:start position:0% +vector also if you take two + + + align:start position:0% +vector also if you take two +vectors sum them and then rotate the sum + + align:start position:0% +vectors sum them and then rotate the sum + + + align:start position:0% +vectors sum them and then rotate the sum +this is equal to the vector you would + + align:start position:0% +this is equal to the vector you would + + + align:start position:0% +this is equal to the vector you would +get if you first rotate both vectors and + + align:start position:0% +get if you first rotate both vectors and + + + align:start position:0% +get if you first rotate both vectors and +then add them + + align:start position:0% +then add them + + + align:start position:0% +then add them +these two properties together mean that + + align:start position:0% +these two properties together mean that + + + align:start position:0% +these two properties together mean that +rotations act linearly on vectors and by + + align:start position:0% +rotations act linearly on vectors and by + + + align:start position:0% +rotations act linearly on vectors and by +definition linear operations can be + + align:start position:0% +definition linear operations can be + + + align:start position:0% +definition linear operations can be +represented by + + align:start position:0% +represented by + + + align:start position:0% +represented by +matrices but what does a rotation Matrix + + align:start position:0% +matrices but what does a rotation Matrix + + + align:start position:0% +matrices but what does a rotation Matrix +look + + align:start position:0% +look + + + align:start position:0% +look +like we can learn a lot about a matrix + + align:start position:0% +like we can learn a lot about a matrix + + + align:start position:0% +like we can learn a lot about a matrix +by examining its igen values and igen + + align:start position:0% +by examining its igen values and igen + + + align:start position:0% +by examining its igen values and igen +vectors recall that a vector v is an + + align:start position:0% +vectors recall that a vector v is an + + + align:start position:0% +vectors recall that a vector v is an +igen Vector of a matrix if it is sent to + + align:start position:0% +igen Vector of a matrix if it is sent to + + + align:start position:0% +igen Vector of a matrix if it is sent to +a scalar multiple of itself when acted + + align:start position:0% +a scalar multiple of itself when acted + + + align:start position:0% +a scalar multiple of itself when acted +upon by The Matrix that scalar is the + + align:start position:0% +upon by The Matrix that scalar is the + + + align:start position:0% +upon by The Matrix that scalar is the +igen + + align:start position:0% +igen + + + align:start position:0% +igen +value consider a rotation of 60° about + + align:start position:0% +value consider a rotation of 60° about + + + align:start position:0% +value consider a rotation of 60° about +the axis defined by the vector E1 + E2 + + align:start position:0% +the axis defined by the vector E1 + E2 + + + align:start position:0% +the axis defined by the vector E1 + E2 +pause the video here and determine one + + align:start position:0% +pause the video here and determine one + + + align:start position:0% +pause the video here and determine one +igen value and igen + + align:start position:0% + + + + align:start position:0% + +vector by the definition of an igen + + align:start position:0% +vector by the definition of an igen + + + align:start position:0% +vector by the definition of an igen +Vector the vector E1 + E2 which points + + align:start position:0% +Vector the vector E1 + E2 which points + + + align:start position:0% +Vector the vector E1 + E2 which points +along the axis of rotation is an igen + + align:start position:0% +along the axis of rotation is an igen + + + align:start position:0% +along the axis of rotation is an igen +Vector with igen value one this is + + align:start position:0% +Vector with igen value one this is + + + align:start position:0% +Vector with igen value one this is +because the vector is unchanged by the + + align:start position:0% +because the vector is unchanged by the + + + align:start position:0% +because the vector is unchanged by the +rotation + + align:start position:0% +rotation + + + align:start position:0% +rotation +Matrix suppose you have a rotation + + align:start position:0% +Matrix suppose you have a rotation + + + align:start position:0% +Matrix suppose you have a rotation +Matrix such that E1 and E2 are both igen + + align:start position:0% +Matrix such that E1 and E2 are both igen + + + align:start position:0% +Matrix such that E1 and E2 are both igen +vectors with igen value + + align:start position:0% +vectors with igen value + + + align:start position:0% +vectors with igen value +one what would this mean about the + + align:start position:0% +one what would this mean about the + + + align:start position:0% +one what would this mean about the +rotation pause the video and think about + + align:start position:0% +rotation pause the video and think about + + + align:start position:0% +rotation pause the video and think about +this + + align:start position:0% + + + + align:start position:0% + +the entire XY plane will be unchanged by + + align:start position:0% +the entire XY plane will be unchanged by + + + align:start position:0% +the entire XY plane will be unchanged by +this rotation this is only possible if + + align:start position:0% +this rotation this is only possible if + + + align:start position:0% +this rotation this is only possible if +the Matrix is the identity Matrix this + + align:start position:0% +the Matrix is the identity Matrix this + + + align:start position:0% +the Matrix is the identity Matrix this +is the null rotation nothing + + align:start position:0% + + + + align:start position:0% + +happens what are the igen values and + + align:start position:0% +happens what are the igen values and + + + align:start position:0% +happens what are the igen values and +igen vectors of a + + align:start position:0% +igen vectors of a + + + align:start position:0% +igen vectors of a +180° rotation about the z-axis pause the + + align:start position:0% +180° rotation about the z-axis pause the + + + align:start position:0% +180° rotation about the z-axis pause the +video + + align:start position:0% + + + + align:start position:0% + +this rotation Matrix has one IG value of + + align:start position:0% +this rotation Matrix has one IG value of + + + align:start position:0% +this rotation Matrix has one IG value of +one corresponding to the vector E3 which + + align:start position:0% +one corresponding to the vector E3 which + + + align:start position:0% +one corresponding to the vector E3 which +points along the axis of + + align:start position:0% +points along the axis of + + + align:start position:0% +points along the axis of +rotation but it has more en vectors any + + align:start position:0% +rotation but it has more en vectors any + + + align:start position:0% +rotation but it has more en vectors any +Vector in the XY plane is sent to its + + align:start position:0% +Vector in the XY plane is sent to its + + + align:start position:0% +Vector in the XY plane is sent to its +negative by the rotation so any Vector + + align:start position:0% +negative by the rotation so any Vector + + + align:start position:0% +negative by the rotation so any Vector +in the XY plane is an IG Vector with + + align:start position:0% +in the XY plane is an IG Vector with + + + align:start position:0% +in the XY plane is an IG Vector with +igen value minus + + align:start position:0% +igen value minus + + + align:start position:0% +igen value minus +one now let's consider a rotation by + + align:start position:0% +one now let's consider a rotation by + + + align:start position:0% +one now let's consider a rotation by +some angle Theta that is not an integer + + align:start position:0% +some angle Theta that is not an integer + + + align:start position:0% +some angle Theta that is not an integer +multiple of Pi clockwise about the + + align:start position:0% +multiple of Pi clockwise about the + + + align:start position:0% +multiple of Pi clockwise about the +z-axis write a matrix that represents + + align:start position:0% +z-axis write a matrix that represents + + + align:start position:0% +z-axis write a matrix that represents +such a + + align:start position:0% + + + + align:start position:0% + +rotation compute the igen values of this + + align:start position:0% +rotation compute the igen values of this + + + align:start position:0% +rotation compute the igen values of this +Matrix and use the definition of an igen + + align:start position:0% +Matrix and use the definition of an igen + + + align:start position:0% +Matrix and use the definition of an igen +Vector to explain why this makes sense + + align:start position:0% +Vector to explain why this makes sense + + + align:start position:0% +Vector to explain why this makes sense +pause the video + + align:start position:0% + + + + align:start position:0% + +you should have found one real igen + + align:start position:0% +you should have found one real igen + + + align:start position:0% +you should have found one real igen +value equal to one and two complex + + align:start position:0% +value equal to one and two complex + + + align:start position:0% +value equal to one and two complex +conjugate igen values the real IG value + + align:start position:0% +conjugate igen values the real IG value + + + align:start position:0% +conjugate igen values the real IG value +corresponds to the IG Vector E3 which is + + align:start position:0% +corresponds to the IG Vector E3 which is + + + align:start position:0% +corresponds to the IG Vector E3 which is +sent to Itself by the rotation hence the + + align:start position:0% +sent to Itself by the rotation hence the + + + align:start position:0% +sent to Itself by the rotation hence the +igen value of one the fact that the + + align:start position:0% +igen value of one the fact that the + + + align:start position:0% +igen value of one the fact that the +other two igen values are complex means + + align:start position:0% +other two igen values are complex means + + + align:start position:0% +other two igen values are complex means +that no other Vector is sent to a real + + align:start position:0% +that no other Vector is sent to a real + + + align:start position:0% +that no other Vector is sent to a real +scalar multiple of + + align:start position:0% +scalar multiple of + + + align:start position:0% +scalar multiple of +itself this makes sense geometrically + + align:start position:0% +itself this makes sense geometrically + + + align:start position:0% +itself this makes sense geometrically +because no other Vector points in the + + align:start position:0% +because no other Vector points in the + + + align:start position:0% +because no other Vector points in the +same direction it started in after being + + align:start position:0% + + + + align:start position:0% + +rotated now how do we describe any + + align:start position:0% +rotated now how do we describe any + + + align:start position:0% +rotated now how do we describe any +general rotation about an arbitrary + + align:start position:0% +general rotation about an arbitrary + + + align:start position:0% +general rotation about an arbitrary +axis well a matrix is completely defined + + align:start position:0% +axis well a matrix is completely defined + + + align:start position:0% +axis well a matrix is completely defined +by how it acts on basis vectors since a + + align:start position:0% +by how it acts on basis vectors since a + + + align:start position:0% +by how it acts on basis vectors since a +rotation doesn't change the lengths of + + align:start position:0% +rotation doesn't change the lengths of + + + align:start position:0% +rotation doesn't change the lengths of +vectors or the angles between two + + align:start position:0% +vectors or the angles between two + + + align:start position:0% +vectors or the angles between two +vectors A rotated basis will also be a + + align:start position:0% +vectors A rotated basis will also be a + + + align:start position:0% +vectors A rotated basis will also be a +basis for + + align:start position:0% +basis for + + + align:start position:0% +basis for +R3 this tells us that any rotation + + align:start position:0% +R3 this tells us that any rotation + + + align:start position:0% +R3 this tells us that any rotation +Matrix can be described as an orthogonal + + align:start position:0% +Matrix can be described as an orthogonal + + + align:start position:0% +Matrix can be described as an orthogonal +Matrix The Columns are the vectors each + + align:start position:0% +Matrix The Columns are the vectors each + + + align:start position:0% +Matrix The Columns are the vectors each +standard basis Vector is sent to is it + + align:start position:0% +standard basis Vector is sent to is it + + + align:start position:0% +standard basis Vector is sent to is it +true that all orthogonal matrices rotate + + align:start position:0% +true that all orthogonal matrices rotate + + + align:start position:0% +true that all orthogonal matrices rotate +vectors pause the video + + align:start position:0% + + + + align:start position:0% + +nope here's an orthogonal Matrix that is + + align:start position:0% +nope here's an orthogonal Matrix that is + + + align:start position:0% +nope here's an orthogonal Matrix that is +not a rotation it's a reflection the + + align:start position:0% +not a rotation it's a reflection the + + + align:start position:0% +not a rotation it's a reflection the +rule is that only an orthogonal Matrix + + align:start position:0% +rule is that only an orthogonal Matrix + + + align:start position:0% +rule is that only an orthogonal Matrix +whose determinant is positive one is a + + align:start position:0% + + + + align:start position:0% + +rotation but let's get back to thinking + + align:start position:0% +rotation but let's get back to thinking + + + align:start position:0% +rotation but let's get back to thinking +about rigid body k itics remember we + + align:start position:0% +about rigid body k itics remember we + + + align:start position:0% +about rigid body k itics remember we +want to describe the motion of the dis + + align:start position:0% +want to describe the motion of the dis + + + align:start position:0% +want to describe the motion of the dis +we've talked about rotation matrices but + + align:start position:0% +we've talked about rotation matrices but + + + align:start position:0% +we've talked about rotation matrices but +we've left out a very important + + align:start position:0% +we've left out a very important + + + align:start position:0% +we've left out a very important +component + + align:start position:0% +component + + + align:start position:0% +component +time how will we describe time dependent + + align:start position:0% +time how will we describe time dependent + + + align:start position:0% +time how will we describe time dependent +rotation that's right time dependent + + align:start position:0% +rotation that's right time dependent + + + align:start position:0% +rotation that's right time dependent +matrices let's start by modeling a + + align:start position:0% +matrices let's start by modeling a + + + align:start position:0% +matrices let's start by modeling a +simple motion the rotation of a disc as + + align:start position:0% +simple motion the rotation of a disc as + + + align:start position:0% +simple motion the rotation of a disc as +it spins clockwise about the positive Z + + align:start position:0% +it spins clockwise about the positive Z + + + align:start position:0% +it spins clockwise about the positive Z +axis we know how to write a matrix that + + align:start position:0% +axis we know how to write a matrix that + + + align:start position:0% +axis we know how to write a matrix that +describes Rotation by an angle Theta + + align:start position:0% +describes Rotation by an angle Theta + + + align:start position:0% +describes Rotation by an angle Theta +about the + + align:start position:0% +about the + + + align:start position:0% +about the +z-axis how would you make this rotation + + align:start position:0% +z-axis how would you make this rotation + + + align:start position:0% +z-axis how would you make this rotation +time dependent pause the video and + + align:start position:0% + + + + align:start position:0% + +discuss the obvious choice here is to + + align:start position:0% +discuss the obvious choice here is to + + + align:start position:0% +discuss the obvious choice here is to +Simply make Theta a function of time but + + align:start position:0% +Simply make Theta a function of time but + + + align:start position:0% +Simply make Theta a function of time but +how does it depend on time + + align:start position:0% +how does it depend on time + + + align:start position:0% +how does it depend on time +to write an explicit function we need to + + align:start position:0% +to write an explicit function we need to + + + align:start position:0% +to write an explicit function we need to +know the rate Omega at which the dis is + + align:start position:0% +know the rate Omega at which the dis is + + + align:start position:0% +know the rate Omega at which the dis is +rotating assume the disc spins with + + align:start position:0% +rotating assume the disc spins with + + + align:start position:0% +rotating assume the disc spins with +constant angular + + align:start position:0% +constant angular + + + align:start position:0% +constant angular +velocity we can easily calculate Omega + + align:start position:0% +velocity we can easily calculate Omega + + + align:start position:0% +velocity we can easily calculate Omega +by counting the revolutions per second + + align:start position:0% +by counting the revolutions per second + + + align:start position:0% +by counting the revolutions per second +and there's our Matrix for a spinning + + align:start position:0% +and there's our Matrix for a spinning + + + align:start position:0% +and there's our Matrix for a spinning +but not wobbling + + align:start position:0% + + + + align:start position:0% + +disc now let's try a slightly more + + align:start position:0% +disc now let's try a slightly more + + + align:start position:0% +disc now let's try a slightly more +difficult example let's describe the + + align:start position:0% +difficult example let's describe the + + + align:start position:0% +difficult example let's describe the +motion of this wobbly spinning disc as + + align:start position:0% +motion of this wobbly spinning disc as + + + align:start position:0% +motion of this wobbly spinning disc as +it rotates on this + + align:start position:0% +it rotates on this + + + align:start position:0% +it rotates on this +stick the disc is itself rotating + + align:start position:0% +stick the disc is itself rotating + + + align:start position:0% +stick the disc is itself rotating +clockwise about its Center of mass when + + align:start position:0% +clockwise about its Center of mass when + + + align:start position:0% +clockwise about its Center of mass when +viewed from the positive Z + + align:start position:0% +viewed from the positive Z + + + align:start position:0% +viewed from the positive Z +axis as before we can find the rotation + + align:start position:0% +axis as before we can find the rotation + + + align:start position:0% +axis as before we can find the rotation +rate Omega D of a marked Point by + + align:start position:0% +rate Omega D of a marked Point by + + + align:start position:0% +rate Omega D of a marked Point by +counting the revolutions per second + + align:start position:0% +counting the revolutions per second + + + align:start position:0% +counting the revolutions per second +assume Omega D is constant + + align:start position:0% +assume Omega D is constant + + + align:start position:0% +assume Omega D is constant +now observe the slight tilt of the dis + + align:start position:0% +now observe the slight tilt of the dis + + + align:start position:0% +now observe the slight tilt of the dis +off of + + align:start position:0% +off of + + + align:start position:0% +off of +horizontal this tilt is created by a + + align:start position:0% +horizontal this tilt is created by a + + + align:start position:0% +horizontal this tilt is created by a +rotation about a tilt axis the Tilt axis + + align:start position:0% +rotation about a tilt axis the Tilt axis + + + align:start position:0% +rotation about a tilt axis the Tilt axis +is the vector in the XY plane about + + align:start position:0% +is the vector in the XY plane about + + + align:start position:0% +is the vector in the XY plane about +which the disc is rotated by some small + + align:start position:0% +which the disc is rotated by some small + + + align:start position:0% +which the disc is rotated by some small +angle Theta creating the + + align:start position:0% +angle Theta creating the + + + align:start position:0% +angle Theta creating the +Tilt The Wobble is created because the + + align:start position:0% +Tilt The Wobble is created because the + + + align:start position:0% +Tilt The Wobble is created because the +Tilt axis is rotating clockwise about + + align:start position:0% +Tilt axis is rotating clockwise about + + + align:start position:0% +Tilt axis is rotating clockwise about +the posi positive + + align:start position:0% +the posi positive + + + align:start position:0% +the posi positive +z-axis we can visualize this by + + align:start position:0% +z-axis we can visualize this by + + + align:start position:0% +z-axis we can visualize this by +observing that the normal Vector to the + + align:start position:0% +observing that the normal Vector to the + + + align:start position:0% +observing that the normal Vector to the +dis rotates in a cone shape about the + + align:start position:0% +dis rotates in a cone shape about the + + + align:start position:0% +dis rotates in a cone shape about the +z-axis by tracking the normal vector's + + align:start position:0% +z-axis by tracking the normal vector's + + + align:start position:0% +z-axis by tracking the normal vector's +revolutions per second we can find the + + align:start position:0% +revolutions per second we can find the + + + align:start position:0% +revolutions per second we can find the +rotation rate of the wobble Omega W of + + align:start position:0% +rotation rate of the wobble Omega W of + + + align:start position:0% +rotation rate of the wobble Omega W of +the normal Vector this is also the + + align:start position:0% +the normal Vector this is also the + + + align:start position:0% +the normal Vector this is also the +rotation rate for the Tilt axis we + + align:start position:0% +rotation rate for the Tilt axis we + + + align:start position:0% +rotation rate for the Tilt axis we +assume Omega W is constant notice that + + align:start position:0% +assume Omega W is constant notice that + + + align:start position:0% +assume Omega W is constant notice that +Omega D and Omega W are different + + align:start position:0% +Omega D and Omega W are different + + + align:start position:0% +Omega D and Omega W are different +rotation + + align:start position:0% +rotation + + + align:start position:0% +rotation +rates for Simplicity we assume that the + + align:start position:0% +rates for Simplicity we assume that the + + + align:start position:0% +rates for Simplicity we assume that the +marked Point begins along the + + align:start position:0% +marked Point begins along the + + + align:start position:0% +marked Point begins along the +xaxis and the initial tilt axis aligns + + align:start position:0% +xaxis and the initial tilt axis aligns + + + align:start position:0% +xaxis and the initial tilt axis aligns +with the x-axis with the Tilt angle + + align:start position:0% +with the x-axis with the Tilt angle + + + align:start position:0% +with the x-axis with the Tilt angle +Theta let's start by creating a sequence + + align:start position:0% +Theta let's start by creating a sequence + + + align:start position:0% +Theta let's start by creating a sequence +of rotations that rotates The Marked + + align:start position:0% +of rotations that rotates The Marked + + + align:start position:0% +of rotations that rotates The Marked +point to the angle Omega D * + + align:start position:0% +point to the angle Omega D * + + + align:start position:0% +point to the angle Omega D * +T and the tilt AIS to the angle Omega W + + align:start position:0% +T and the tilt AIS to the angle Omega W + + + align:start position:0% +T and the tilt AIS to the angle Omega W +* t for any time + + align:start position:0% +* t for any time + + + align:start position:0% +* t for any time +T to describe this motion we are going + + align:start position:0% +T to describe this motion we are going + + + align:start position:0% +T to describe this motion we are going +to decompose the behavior into a + + align:start position:0% +to decompose the behavior into a + + + align:start position:0% +to decompose the behavior into a +sequence of rotations about E1 E2 and E3 + + align:start position:0% +sequence of rotations about E1 E2 and E3 + + + align:start position:0% +sequence of rotations about E1 E2 and E3 +which have the benefit of being easy to + + align:start position:0% +which have the benefit of being easy to + + + align:start position:0% +which have the benefit of being easy to +describe + + align:start position:0% +describe + + + align:start position:0% +describe +mathematically I want to start by + + align:start position:0% +mathematically I want to start by + + + align:start position:0% +mathematically I want to start by +eliminating the tilt of the dis so we + + align:start position:0% +eliminating the tilt of the dis so we + + + align:start position:0% +eliminating the tilt of the dis so we +can imagine it spinning parallel to the + + align:start position:0% +can imagine it spinning parallel to the + + + align:start position:0% +can imagine it spinning parallel to the +ground what is the Matrix that undoes + + align:start position:0% +ground what is the Matrix that undoes + + + align:start position:0% +ground what is the Matrix that undoes +the tilt of theta degrees about the + + align:start position:0% +the tilt of theta degrees about the + + + align:start position:0% +the tilt of theta degrees about the +xais pause and write down a + + align:start position:0% + + + + align:start position:0% + +matrix we rotate by an angle Nega Theta + + align:start position:0% +matrix we rotate by an angle Nega Theta + + + align:start position:0% +matrix we rotate by an angle Nega Theta +about the positive X AIS which is + + align:start position:0% +about the positive X AIS which is + + + align:start position:0% +about the positive X AIS which is +represented by this + + align:start position:0% +represented by this + + + align:start position:0% +represented by this +Matrix now I rotate the marked Point + + align:start position:0% +Matrix now I rotate the marked Point + + + align:start position:0% +Matrix now I rotate the marked Point +clockwise about the + + align:start position:0% +clockwise about the + + + align:start position:0% +clockwise about the +z-axis by the angle Omega D minus Omega + + align:start position:0% +z-axis by the angle Omega D minus Omega + + + align:start position:0% +z-axis by the angle Omega D minus Omega +W the quantity time + + align:start position:0% +W the quantity time + + + align:start position:0% +W the quantity time +T this Matrix describes the angle + + align:start position:0% +T this Matrix describes the angle + + + align:start position:0% +T this Matrix describes the angle +difference traveled by The Marked Point + + align:start position:0% +difference traveled by The Marked Point + + + align:start position:0% +difference traveled by The Marked Point +relative to the position of the Tilt + + align:start position:0% +relative to the position of the Tilt + + + align:start position:0% +relative to the position of the Tilt +axis now we need to make sure that we + + align:start position:0% +axis now we need to make sure that we + + + align:start position:0% +axis now we need to make sure that we +tilt the disc again so that we can + + align:start position:0% +tilt the disc again so that we can + + + align:start position:0% +tilt the disc again so that we can +describe the + + align:start position:0% +describe the + + + align:start position:0% +describe the +wobble since we assume the Tilt axis + + align:start position:0% +wobble since we assume the Tilt axis + + + align:start position:0% +wobble since we assume the Tilt axis +begins along the + + align:start position:0% +begins along the + + + align:start position:0% +begins along the +xais we rotate the disc back to the + + align:start position:0% +xais we rotate the disc back to the + + + align:start position:0% +xais we rotate the disc back to the +initial tilted position by Theta deg + + align:start position:0% +initial tilted position by Theta deg + + + align:start position:0% +initial tilted position by Theta deg +this + + align:start position:0% +this + + + align:start position:0% +this +counterclockwise time independent + + align:start position:0% +counterclockwise time independent + + + align:start position:0% +counterclockwise time independent +rotation about the xais is represented + + align:start position:0% +rotation about the xais is represented + + + align:start position:0% +rotation about the xais is represented +by this + + align:start position:0% + + + + align:start position:0% + +Matrix finally we must describe the + + align:start position:0% +Matrix finally we must describe the + + + align:start position:0% +Matrix finally we must describe the +wobble created by the rotation of the + + align:start position:0% +wobble created by the rotation of the + + + align:start position:0% +wobble created by the rotation of the +Tilt axis the Tilt axis is rotating + + align:start position:0% +Tilt axis the Tilt axis is rotating + + + align:start position:0% +Tilt axis the Tilt axis is rotating +clockwise about the positive z-axis with + + align:start position:0% +clockwise about the positive z-axis with + + + align:start position:0% +clockwise about the positive z-axis with +rotation rate Omega + + align:start position:0% +rotation rate Omega + + + align:start position:0% +rotation rate Omega +W so at time T is it has rotated by + + align:start position:0% +W so at time T is it has rotated by + + + align:start position:0% +W so at time T is it has rotated by +Omega WT de which is what this Matrix + + align:start position:0% +Omega WT de which is what this Matrix + + + align:start position:0% +Omega WT de which is what this Matrix +does how will we combine these matrices + + align:start position:0% +does how will we combine these matrices + + + align:start position:0% +does how will we combine these matrices +to describe the motion of the mark point + + align:start position:0% +to describe the motion of the mark point + + + align:start position:0% +to describe the motion of the mark point +pause and + + align:start position:0% + + + + align:start position:0% + +discuss we multiply the matrices + + align:start position:0% +discuss we multiply the matrices + + + align:start position:0% +discuss we multiply the matrices +together the order we apply each Matrix + + align:start position:0% +together the order we apply each Matrix + + + align:start position:0% +together the order we apply each Matrix +matters we must perform the rotations in + + align:start position:0% +matters we must perform the rotations in + + + align:start position:0% +matters we must perform the rotations in +the same order we decompose the motion + + align:start position:0% +the same order we decompose the motion + + + align:start position:0% +the same order we decompose the motion +because matrices do not multiply + + align:start position:0% + + + + align:start position:0% + +commutatively let's understand + + align:start position:0% +commutatively let's understand + + + align:start position:0% +commutatively let's understand +geometrically why this worked the angle + + align:start position:0% +geometrically why this worked the angle + + + align:start position:0% +geometrically why this worked the angle +of the marker is changed in two steps of + + align:start position:0% +of the marker is changed in two steps of + + + align:start position:0% +of the marker is changed in two steps of +this process first a rotation by angle + + align:start position:0% +this process first a rotation by angle + + + align:start position:0% +this process first a rotation by angle +Omega D minus Omega W * T then by an + + align:start position:0% +Omega D minus Omega W * T then by an + + + align:start position:0% +Omega D minus Omega W * T then by an +angle Omega W * T in the end it ends up + + align:start position:0% +angle Omega W * T in the end it ends up + + + align:start position:0% +angle Omega W * T in the end it ends up +exactly where it should at Omega D * + + align:start position:0% +exactly where it should at Omega D * + + + align:start position:0% +exactly where it should at Omega D * +T only the final Matrix affects the Tilt + + align:start position:0% +T only the final Matrix affects the Tilt + + + align:start position:0% +T only the final Matrix affects the Tilt +axis rotating it by the angle Omega W * + + align:start position:0% +axis rotating it by the angle Omega W * + + + align:start position:0% +axis rotating it by the angle Omega W * +T because the dis is a rigid object by + + align:start position:0% +T because the dis is a rigid object by + + + align:start position:0% +T because the dis is a rigid object by +describing the position of the mark + + align:start position:0% +describing the position of the mark + + + align:start position:0% +describing the position of the mark +point and the Tilt axis for all times + + align:start position:0% +point and the Tilt axis for all times + + + align:start position:0% +point and the Tilt axis for all times +with + + align:start position:0% +with + + + align:start position:0% +with +matrices we've actually described the + + align:start position:0% +matrices we've actually described the + + + align:start position:0% +matrices we've actually described the +the position of every point on the + + align:start position:0% +the position of every point on the + + + align:start position:0% +the position of every point on the +disk we can find the location of any + + align:start position:0% +disk we can find the location of any + + + align:start position:0% +disk we can find the location of any +point at time T by applying this Matrix + + align:start position:0% +point at time T by applying this Matrix + + + align:start position:0% +point at time T by applying this Matrix +operation to any Vector on the initial + + align:start position:0% +operation to any Vector on the initial + + + align:start position:0% +operation to any Vector on the initial +dis now let's go back to the badly + + align:start position:0% +dis now let's go back to the badly + + + align:start position:0% +dis now let's go back to the badly +thrown dis we can apply the rotational + + align:start position:0% +thrown dis we can apply the rotational + + + align:start position:0% +thrown dis we can apply the rotational +transformation directly to our thrown + + align:start position:0% +transformation directly to our thrown + + + align:start position:0% +transformation directly to our thrown +dis all that is left to consider is the + + align:start position:0% +dis all that is left to consider is the + + + align:start position:0% +dis all that is left to consider is the +translation + + align:start position:0% + + + + align:start position:0% + +if you throw a disc and watch it from + + align:start position:0% +if you throw a disc and watch it from + + + align:start position:0% +if you throw a disc and watch it from +the side we can ignore the rotations and + + align:start position:0% +the side we can ignore the rotations and + + + align:start position:0% +the side we can ignore the rotations and +focus on the translation of the center + + align:start position:0% +focus on the translation of the center + + + align:start position:0% +focus on the translation of the center +point of the + + align:start position:0% +point of the + + + align:start position:0% +point of the +disc for the small time interval that + + align:start position:0% +disc for the small time interval that + + + align:start position:0% +disc for the small time interval that +we're interested in describing the dis + + align:start position:0% +we're interested in describing the dis + + + align:start position:0% +we're interested in describing the dis +moves in a straight horizontal path so + + align:start position:0% +moves in a straight horizontal path so + + + align:start position:0% +moves in a straight horizontal path so +this vector equation approximates the + + align:start position:0% +this vector equation approximates the + + + align:start position:0% +this vector equation approximates the +translation because the dis is a rigid + + align:start position:0% +translation because the dis is a rigid + + + align:start position:0% +translation because the dis is a rigid +object we get the full description of + + align:start position:0% +object we get the full description of + + + align:start position:0% +object we get the full description of +the motion by simply adding in the + + align:start position:0% +the motion by simply adding in the + + + align:start position:0% +the motion by simply adding in the +translation to the rotation of the + + align:start position:0% +translation to the rotation of the + + + align:start position:0% +translation to the rotation of the +wobbly disc to obtain the following + + align:start position:0% +wobbly disc to obtain the following + + + align:start position:0% +wobbly disc to obtain the following +equation of motion for any point on the + + align:start position:0% +equation of motion for any point on the + + + align:start position:0% +equation of motion for any point on the +disc if you thought this problem was + + align:start position:0% +disc if you thought this problem was + + + align:start position:0% +disc if you thought this problem was +cool you're not the only one Richard + + align:start position:0% +cool you're not the only one Richard + + + align:start position:0% +cool you're not the only one Richard +Fineman studied the kinematics and the + + align:start position:0% +Fineman studied the kinematics and the + + + align:start position:0% +Fineman studied the kinematics and the +Dynamics of the wobbly disc he was able + + align:start position:0% +Dynamics of the wobbly disc he was able + + + align:start position:0% +Dynamics of the wobbly disc he was able +to show that the rotation rate of the + + align:start position:0% +to show that the rotation rate of the + + + align:start position:0% +to show that the rotation rate of the +special marked Point Omega D was exactly + + align:start position:0% +special marked Point Omega D was exactly + + + align:start position:0% +special marked Point Omega D was exactly +twice the rotation rate Omega W of the + + align:start position:0% +twice the rotation rate Omega W of the + + + align:start position:0% +twice the rotation rate Omega W of the +Tilt axis this realization ultimately + + align:start position:0% +Tilt axis this realization ultimately + + + align:start position:0% +Tilt axis this realization ultimately +led to insights into the behavior of + + align:start position:0% +led to insights into the behavior of + + + align:start position:0% +led to insights into the behavior of +electrons + + align:start position:0% + + + + align:start position:0% + +in this video we saw that rotation + + align:start position:0% +in this video we saw that rotation + + + align:start position:0% +in this video we saw that rotation +matrices are orthogonal matrices with + + align:start position:0% +matrices are orthogonal matrices with + + + align:start position:0% +matrices are orthogonal matrices with +determinant equal to POS one the + + align:start position:0% +determinant equal to POS one the + + + align:start position:0% +determinant equal to POS one the +kinematics of rigid bodies involves + + align:start position:0% +kinematics of rigid bodies involves + + + align:start position:0% +kinematics of rigid bodies involves +breaking a problem into translation and + + align:start position:0% +breaking a problem into translation and + + + align:start position:0% +breaking a problem into translation and +rotation the rotations may be decomposed + + align:start position:0% +rotation the rotations may be decomposed + + + align:start position:0% +rotation the rotations may be decomposed +into several time dependent rotation + + align:start position:0% +into several time dependent rotation + + + align:start position:0% +into several time dependent rotation +matrices that are multiplied + + align:start position:0% +matrices that are multiplied + + + align:start position:0% +matrices that are multiplied +together the matrix product + + align:start position:0% +together the matrix product + + + align:start position:0% +together the matrix product +added to the translation describes the + + align:start position:0% +added to the translation describes the + + + align:start position:0% +added to the translation describes the +location at any time of all points on + + align:start position:0% +location at any time of all points on + + + align:start position:0% +location at any time of all points on +the rigid body I hope you'll try to + + align:start position:0% +the rigid body I hope you'll try to + + + align:start position:0% +the rigid body I hope you'll try to +describe the Motions of various rotating + + align:start position:0% +describe the Motions of various rotating + + + align:start position:0% +describe the Motions of various rotating +objects that you encounter have fun and + + align:start position:0% +objects that you encounter have fun and + + + align:start position:0% +objects that you encounter have fun and +good luck + + align:start position:0% + + + + align:start position:0% + +[Music] \ No newline at end of file diff --git a/mJziV7sAZm4.txt b/mJziV7sAZm4.txt new file mode 100644 index 0000000000000000000000000000000000000000..b856cf2a0b77da2bbdffade9c249b3b0ed5cf970 --- /dev/null +++ b/mJziV7sAZm4.txt @@ -0,0 +1,9299 @@ +align:start position:0% + +we spend the last few lectures + + align:start position:0% +we spend the last few lectures + + + align:start position:0% +we spend the last few lectures +developing the theory of graph limits + + align:start position:0% +developing the theory of graph limits + + + align:start position:0% +developing the theory of graph limits +and one of the motivations I gave at the + + align:start position:0% +and one of the motivations I gave at the + + + align:start position:0% +and one of the motivations I gave at the +beginning of the lecture on graph lines + + align:start position:0% +beginning of the lecture on graph lines + + + align:start position:0% +beginning of the lecture on graph lines +was that there were certain graph + + align:start position:0% +was that there were certain graph + + + align:start position:0% +was that there were certain graph +inequalities specifically if I tell you + + align:start position:0% +inequalities specifically if I tell you + + + align:start position:0% +inequalities specifically if I tell you +that your graph has edge density 1/2 + + align:start position:0% +that your graph has edge density 1/2 + + + align:start position:0% +that your graph has edge density 1/2 +what's the minimum possible c4 density + + align:start position:0% +what's the minimum possible c4 density + + + align:start position:0% +what's the minimum possible c4 density +okay so for those kinds of problems + + align:start position:0% +okay so for those kinds of problems + + + align:start position:0% +okay so for those kinds of problems +graph limits gives us a very nice + + align:start position:0% +graph limits gives us a very nice + + + align:start position:0% +graph limits gives us a very nice +language for describing what the answer + + align:start position:0% +language for describing what the answer + + + align:start position:0% +language for describing what the answer +is I also sometimes for solving these + + align:start position:0% +is I also sometimes for solving these + + + align:start position:0% +is I also sometimes for solving these +problems so today I want to dive more + + align:start position:0% +problems so today I want to dive more + + + align:start position:0% +problems so today I want to dive more +into these types of problems + + align:start position:0% +into these types of problems + + + align:start position:0% +into these types of problems +specifically we're going to be talking + + align:start position:0% +specifically we're going to be talking + + + align:start position:0% +specifically we're going to be talking +about homomorphism density inequalities + + align:start position:0% + + + + align:start position:0% + +so trying to understand what is the + + align:start position:0% +so trying to understand what is the + + + align:start position:0% +so trying to understand what is the +relationship between possible sub graph + + align:start position:0% +relationship between possible sub graph + + + align:start position:0% +relationship between possible sub graph +densities or homomorphism densities + + align:start position:0% +densities or homomorphism densities + + + align:start position:0% +densities or homomorphism densities +within a large graph we've seen this + + align:start position:0% +within a large graph we've seen this + + + align:start position:0% +within a large graph we've seen this +kind of problems in the past so one of + + align:start position:0% +kind of problems in the past so one of + + + align:start position:0% +kind of problems in the past so one of +the very first theorems that we did in + + align:start position:0% +the very first theorems that we did in + + + align:start position:0% +the very first theorems that we did in +this course was Terron Sturm and + + align:start position:0% +this course was Terron Sturm and + + + align:start position:0% +this course was Terron Sturm and +men-tel's theorem so specifically for + + align:start position:0% +men-tel's theorem so specifically for + + + align:start position:0% +men-tel's theorem so specifically for +mental serum it tells us something about + + align:start position:0% +mental serum it tells us something about + + + align:start position:0% +mental serum it tells us something about +possible edge versus triangle densities + + align:start position:0% +possible edge versus triangle densities + + + align:start position:0% +possible edge versus triangle densities +in the graph which is something that I + + align:start position:0% +in the graph which is something that I + + + align:start position:0% +in the graph which is something that I +want to spend the first part of today's + + align:start position:0% +want to spend the first part of today's + + + align:start position:0% +want to spend the first part of today's +lecture focusing on so what is the + + align:start position:0% +lecture focusing on so what is the + + + align:start position:0% +lecture focusing on so what is the +possible relationship what are all the + + align:start position:0% +possible relationship what are all the + + + align:start position:0% +possible relationship what are all the +possible edge versus ten edge versus + + align:start position:0% +possible edge versus ten edge versus + + + align:start position:0% +possible edge versus ten edge versus +triangle densities in a graph main house + + align:start position:0% +triangle densities in a graph main house + + + align:start position:0% +triangle densities in a graph main house +theorem tells us something namely that + + align:start position:0% +theorem tells us something namely that + + + align:start position:0% +theorem tells us something namely that +if your edge density exceeds one half + + align:start position:0% +if your edge density exceeds one half + + + align:start position:0% +if your edge density exceeds one half +then your triangle density cannot be 0 + + align:start position:0% +then your triangle density cannot be 0 + + + align:start position:0% +then your triangle density cannot be 0 +so that's what men-tel's theorem tells + + align:start position:0% +so that's what men-tel's theorem tells + + + align:start position:0% +so that's what men-tel's theorem tells +us and let me write it down like this so + + align:start position:0% +us and let me write it down like this so + + + align:start position:0% +us and let me write it down like this so +the statement I just said the one that + + align:start position:0% +the statement I just said the one that + + + align:start position:0% +the statement I just said the one that +bought me Intel stay + + align:start position:0% +bought me Intel stay + + + align:start position:0% +bought me Intel stay +and more generally for Terron student + + align:start position:0% +and more generally for Terron student + + + align:start position:0% +and more generally for Terron student +tells us that if the K R + 1 density W + + align:start position:0% +tells us that if the K R + 1 density W + + + align:start position:0% +tells us that if the K R + 1 density W +is 1 0 then necessarily the edge density + + align:start position:0% +is 1 0 then necessarily the edge density + + + align:start position:0% +is 1 0 then necessarily the edge density +is at most 1 minus 1 over R so this is + + align:start position:0% +is at most 1 minus 1 over R so this is + + + align:start position:0% +is at most 1 minus 1 over R so this is +what it tells us it gives us some + + align:start position:0% +what it tells us it gives us some + + + align:start position:0% +what it tells us it gives us some +information about what are the possible + + align:start position:0% +information about what are the possible + + + align:start position:0% +information about what are the possible +densities but I would like to know you + + align:start position:0% +densities but I would like to know you + + + align:start position:0% +densities but I would like to know you +know more generally or a complete + + align:start position:0% +know more generally or a complete + + + align:start position:0% +know more generally or a complete +picture of what is a set of H verses + + align:start position:0% +picture of what is a set of H verses + + + align:start position:0% +picture of what is a set of H verses +triangle density inequalities so let me + + align:start position:0% +triangle density inequalities so let me + + + align:start position:0% +triangle density inequalities so let me +draw a picture that is captures what + + align:start position:0% +draw a picture that is captures what + + + align:start position:0% +draw a picture that is captures what +we're looking for so here is on the + + align:start position:0% +we're looking for so here is on the + + + align:start position:0% +we're looking for so here is on the +x-axis I have all the possible edge + + align:start position:0% +x-axis I have all the possible edge + + + align:start position:0% +x-axis I have all the possible edge +densities and on the vertical axis I + + align:start position:0% +densities and on the vertical axis I + + + align:start position:0% +densities and on the vertical axis I +have the triangle density and I would + + align:start position:0% +have the triangle density and I would + + + align:start position:0% +have the triangle density and I would +like to know what is the set of feasible + + align:start position:0% +like to know what is the set of feasible + + + align:start position:0% +like to know what is the set of feasible +points in this box then tells theorem + + align:start position:0% +points in this box then tells theorem + + + align:start position:0% +points in this box then tells theorem +tells us already something namely when + + align:start position:0% +tells us already something namely when + + + align:start position:0% +tells us already something namely when +can you so this this region 0 the + + align:start position:0% +can you so this this region 0 the + + + align:start position:0% +can you so this this region 0 the +horizontal lying at 0 extends and most + + align:start position:0% +horizontal lying at 0 extends and most + + + align:start position:0% +horizontal lying at 0 extends and most +until the halfway point beyond this + + align:start position:0% +until the halfway point beyond this + + + align:start position:0% +until the halfway point beyond this +point it's not a part of the feasible + + align:start position:0% +point it's not a part of the feasible + + + align:start position:0% +point it's not a part of the feasible +region so so far that's the information + + align:start position:0% +region so so far that's the information + + + align:start position:0% +region so so far that's the information +that we know our discussion about graph + + align:start position:0% +that we know our discussion about graph + + + align:start position:0% +that we know our discussion about graph +limits and in particular ok so let me + + align:start position:0% +limits and in particular ok so let me + + + align:start position:0% +limits and in particular ok so let me +first write down what is the question so + + align:start position:0% +first write down what is the question so + + + align:start position:0% +first write down what is the question so +if you look at the set of possible edge + + align:start position:0% +if you look at the set of possible edge + + + align:start position:0% +if you look at the set of possible edge +vs. triangle densities okay so there's + + align:start position:0% +vs. triangle densities okay so there's + + + align:start position:0% +vs. triangle densities okay so there's +this region here what is this region so + + align:start position:0% +this region here what is this region so + + + align:start position:0% +this region here what is this region so +it's a subset of this unit square + + align:start position:0% +it's a subset of this unit square + + + align:start position:0% +it's a subset of this unit square +we would like to understand what is the + + align:start position:0% +we would like to understand what is the + + + align:start position:0% +we would like to understand what is the +set of all possibilities become practice + + align:start position:0% +set of all possibilities become practice + + + align:start position:0% +set of all possibilities become practice +of the space of griffons tells us that + + align:start position:0% +of the space of griffons tells us that + + + align:start position:0% +of the space of griffons tells us that +this region is compact so let me call + + align:start position:0% +this region is compact so let me call + + + align:start position:0% +this region is compact so let me call +this region d23 for triangle versus edge + + align:start position:0% +this region d23 for triangle versus edge + + + align:start position:0% +this region d23 for triangle versus edge +versus triangle so dq3 is compact + + align:start position:0% +versus triangle so dq3 is compact + + + align:start position:0% +versus triangle so dq3 is compact +because the space of graph founders + + align:start position:0% +because the space of graph founders + + + align:start position:0% +because the space of graph founders +compact under the cut metric and + + align:start position:0% +compact under the cut metric and + + + align:start position:0% +compact under the cut metric and +densities are continuous under cut + + align:start position:0% +densities are continuous under cut + + + align:start position:0% +densities are continuous under cut +distance so in particular you if you + + align:start position:0% +distance so in particular you if you + + + align:start position:0% +distance so in particular you if you +have some limit point of some sequence + + align:start position:0% +have some limit point of some sequence + + + align:start position:0% +have some limit point of some sequence +of graphs that limit points achieved by + + align:start position:0% +of graphs that limit points achieved by + + + align:start position:0% +of graphs that limit points achieved by +a corresponding limit graph all okay so + + align:start position:0% +a corresponding limit graph all okay so + + + align:start position:0% +a corresponding limit graph all okay so +you really have a nice closed region + + align:start position:0% +you really have a nice closed region + + + align:start position:0% +you really have a nice closed region +over here all right so we don't have to + + align:start position:0% +over here all right so we don't have to + + + align:start position:0% +over here all right so we don't have to +you know should be able to tell with the + + align:start position:0% +you know should be able to tell with the + + + align:start position:0% +you know should be able to tell with the +answer's no this is a region there + + align:start position:0% +answer's no this is a region there + + + align:start position:0% +answer's no this is a region there +should not be any additional quantifiers + + align:start position:0% +should not be any additional quantifiers + + + align:start position:0% +should not be any additional quantifiers +no optimizer zero missing this point + + align:start position:0% +no optimizer zero missing this point + + + align:start position:0% +no optimizer zero missing this point +missing that pole is a closed region + + align:start position:0% +missing that pole is a closed region + + + align:start position:0% +missing that pole is a closed region +okay so what is this closed region + + align:start position:0% +okay so what is this closed region + + + align:start position:0% +okay so what is this closed region +equivalent me we can ask the following + + align:start position:0% +equivalent me we can ask the following + + + align:start position:0% +equivalent me we can ask the following +question + + align:start position:0% +question + + + align:start position:0% +question +suppose I give you the edge density in + + align:start position:0% +suppose I give you the edge density in + + + align:start position:0% +suppose I give you the edge density in +other words look at a particular + + align:start position:0% +other words look at a particular + + + align:start position:0% +other words look at a particular +horizontal place in this picture what is + + align:start position:0% +horizontal place in this picture what is + + + align:start position:0% +horizontal place in this picture what is +the maximum and minimum possible + + align:start position:0% + + + + align:start position:0% + +triangle densities + + align:start position:0% + + + + align:start position:0% + +okay so I tell you that the edge density + + align:start position:0% +okay so I tell you that the edge density + + + align:start position:0% +okay so I tell you that the edge density +is 0.75 what is the upper and lower + + align:start position:0% +is 0.75 what is the upper and lower + + + align:start position:0% +is 0.75 what is the upper and lower +boundaries of this region I want you to + + align:start position:0% +boundaries of this region I want you to + + + align:start position:0% +boundaries of this region I want you to +think about why this region is the + + align:start position:0% +think about why this region is the + + + align:start position:0% +think about why this region is the +vertical cross section is a line segment + + align:start position:0% +vertical cross section is a line segment + + + align:start position:0% +vertical cross section is a line segment +you cannot have any holes it's a bet + + align:start position:0% +you cannot have any holes it's a bet + + + align:start position:0% +you cannot have any holes it's a bet +that requires an argument and then I'll + + align:start position:0% +that requires an argument and then I'll + + + align:start position:0% +that requires an argument and then I'll +let you think about that okay so I want + + align:start position:0% +let you think about that okay so I want + + + align:start position:0% +let you think about that okay so I want +to complete this picture and I'll show + + align:start position:0% +to complete this picture and I'll show + + + align:start position:0% +to complete this picture and I'll show +you some proofs and at the end of what + + align:start position:0% +you some proofs and at the end of what + + + align:start position:0% +you some proofs and at the end of what +by the middle of today's lecture we'll + + align:start position:0% +by the middle of today's lecture we'll + + + align:start position:0% +by the middle of today's lecture we'll +see a picture of what this region looks + + align:start position:0% +see a picture of what this region looks + + + align:start position:0% +see a picture of what this region looks +like alright first let me do the easier + + align:start position:0% +like alright first let me do the easier + + + align:start position:0% +like alright first let me do the easier +direction which is to find the upper + + align:start position:0% +direction which is to find the upper + + + align:start position:0% +direction which is to find the upper +boundary of this region so what is the + + align:start position:0% +boundary of this region so what is the + + + align:start position:0% +boundary of this region so what is the +maximum possible triangle density for a + + align:start position:0% +maximum possible triangle density for a + + + align:start position:0% +maximum possible triangle density for a +given edge density and the the answer + + align:start position:0% +given edge density and the the answer + + + align:start position:0% +given edge density and the the answer +okay so it turns out to be what hour the + + align:start position:0% +okay so it turns out to be what hour the + + + align:start position:0% +okay so it turns out to be what hour the +result I'll tell you it's a special case + + align:start position:0% +result I'll tell you it's a special case + + + align:start position:0% +result I'll tell you it's a special case +of what's called cruise car cattle now + + align:start position:0% + + + + align:start position:0% + +think about it this way suppose I give + + align:start position:0% +think about it this way suppose I give + + + align:start position:0% +think about it this way suppose I give +you a very large number of vertices and + + align:start position:0% +you a very large number of vertices and + + + align:start position:0% +you a very large number of vertices and +I give you some large number of edges + + align:start position:0% +I give you some large number of edges + + + align:start position:0% +I give you some large number of edges +and I want you to put the edges into the + + align:start position:0% +and I want you to put the edges into the + + + align:start position:0% +and I want you to put the edges into the +graph in a way that generates as many + + align:start position:0% +graph in a way that generates as many + + + align:start position:0% +graph in a way that generates as many +triangles as possible intuitively how + + align:start position:0% +triangles as possible intuitively how + + + align:start position:0% +triangles as possible intuitively how +should you put the edges in to try to + + align:start position:0% +should you put the edges in to try to + + + align:start position:0% +should you put the edges in to try to +make as many triangles as you can in a + + align:start position:0% +make as many triangles as you can in a + + + align:start position:0% +make as many triangles as you can in a +click so you put all the edges as + + align:start position:0% +click so you put all the edges as + + + align:start position:0% +click so you put all the edges as +closely together as possible try to form + + align:start position:0% +closely together as possible try to form + + + align:start position:0% +closely together as possible try to form +a clique so maximize number of triangles + + align:start position:0% +a clique so maximize number of triangles + + + align:start position:0% +a clique so maximize number of triangles +by forming a creek + + align:start position:0% + + + + align:start position:0% + +and now this indeed the answer and this + + align:start position:0% +and now this indeed the answer and this + + + align:start position:0% +and now this indeed the answer and this +is what we'll proof at least in the + + align:start position:0% +is what we'll proof at least in the + + + align:start position:0% +is what we'll proof at least in the +graph densities version so we will show + + align:start position:0% +graph densities version so we will show + + + align:start position:0% +graph densities version so we will show +that the upper boundary is given by the + + align:start position:0% +that the upper boundary is given by the + + + align:start position:0% +that the upper boundary is given by the +curve y equals to X to the three half + + align:start position:0% +curve y equals to X to the three half + + + align:start position:0% +curve y equals to X to the three half +which okay so don't worry about the + + align:start position:0% +which okay so don't worry about the + + + align:start position:0% +which okay so don't worry about the +specific function but what's important + + align:start position:0% +specific function but what's important + + + align:start position:0% +specific function but what's important +is that the upper bound is achieved by + + align:start position:0% +is that the upper bound is achieved by + + + align:start position:0% +is that the upper bound is achieved by +the following graph Oh namely there's + + align:start position:0% +the following graph Oh namely there's + + + align:start position:0% +the following graph Oh namely there's +the graph on corresponding to a clique + + align:start position:0% + + + + align:start position:0% + +for this graph on here the edge density + + align:start position:0% +for this graph on here the edge density + + + align:start position:0% +for this graph on here the edge density +is a squared and the triangle density is + + align:start position:0% +is a squared and the triangle density is + + + align:start position:0% +is a squared and the triangle density is +a cube and it turns out this graph on is + + align:start position:0% +a cube and it turns out this graph on is + + + align:start position:0% +a cube and it turns out this graph on is +the best that you can do with a given + + align:start position:0% +the best that you can do with a given + + + align:start position:0% +the best that you can do with a given +edge density in order to generate as + + align:start position:0% +edge density in order to generate as + + + align:start position:0% +edge density in order to generate as +many triangles or the most triangle + + align:start position:0% +many triangles or the most triangle + + + align:start position:0% +many triangles or the most triangle +density possible or in other words we'll + + align:start position:0% +density possible or in other words we'll + + + align:start position:0% +density possible or in other words we'll +proof is that the triangle density so + + align:start position:0% +proof is that the triangle density so + + + align:start position:0% +proof is that the triangle density so +throughout W will be a graph oh sorry W + + align:start position:0% +throughout W will be a graph oh sorry W + + + align:start position:0% +throughout W will be a graph oh sorry W +is always a graph on so values between 0 + + align:start position:0% +is always a graph on so values between 0 + + + align:start position:0% +is always a graph on so values between 0 +& 1 then you have the following + + align:start position:0% +& 1 then you have the following + + + align:start position:0% +& 1 then you have the following +inequality okay so let's prove it + + align:start position:0% +inequality okay so let's prove it + + + align:start position:0% +inequality okay so let's prove it +but first let me draw you what this + + align:start position:0% +but first let me draw you what this + + + align:start position:0% +but first let me draw you what this +shape looks like + + align:start position:0% + + + + align:start position:0% + +because of the relationship between + + align:start position:0% +because of the relationship between + + + align:start position:0% +because of the relationship between +graphs and graph limits any of these + + align:start position:0% +graphs and graph limits any of these + + + align:start position:0% +graphs and graph limits any of these +inequalities about graph limits about + + align:start position:0% +inequalities about graph limits about + + + align:start position:0% +inequalities about graph limits about +griffons it's sufficient to prove the + + align:start position:0% +griffons it's sufficient to prove the + + + align:start position:0% +griffons it's sufficient to prove the +corresponding inequality for graphs + + align:start position:0% +corresponding inequality for graphs + + + align:start position:0% +corresponding inequality for graphs +right because the set of graphs is dense + + align:start position:0% +right because the set of graphs is dense + + + align:start position:0% +right because the set of graphs is dense +within the space of griffons according + + align:start position:0% +within the space of griffons according + + + align:start position:0% +within the space of griffons according +to the topology maybe the cut metric + + align:start position:0% +to the topology maybe the cut metric + + + align:start position:0% +to the topology maybe the cut metric +that we discussed so it suffices to show + + align:start position:0% + + + + align:start position:0% + +corresponding inequality about graphs + + align:start position:0% +corresponding inequality about graphs + + + align:start position:0% +corresponding inequality about graphs +namely that the k3 density in the graph + + align:start position:0% +namely that the k3 density in the graph + + + align:start position:0% +namely that the k3 density in the graph +is at most K 2 pencil T in the graph + + align:start position:0% +is at most K 2 pencil T in the graph + + + align:start position:0% +is at most K 2 pencil T in the graph +raised to the power 3 half okay so let + + align:start position:0% +raised to the power 3 half okay so let + + + align:start position:0% +raised to the power 3 half okay so let +me pull label this point out just a + + align:start position:0% +me pull label this point out just a + + + align:start position:0% +me pull label this point out just a +little bit more this inequality is a + + align:start position:0% +little bit more this inequality is a + + + align:start position:0% +little bit more this inequality is a +subset of those inequalities up there + + align:start position:0% +subset of those inequalities up there + + + align:start position:0% +subset of those inequalities up there +because graphs sit inside a space of + + align:start position:0% +because graphs sit inside a space of + + + align:start position:0% +because graphs sit inside a space of +griffons but because they sit inside in + + align:start position:0% +griffons but because they sit inside in + + + align:start position:0% +griffons but because they sit inside in +a dense dense subset if you know this + + align:start position:0% +a dense dense subset if you know this + + + align:start position:0% +a dense dense subset if you know this +inequality and everything is continuous + + align:start position:0% +inequality and everything is continuous + + + align:start position:0% +inequality and everything is continuous +then you know that inequality so these + + align:start position:0% +then you know that inequality so these + + + align:start position:0% +then you know that inequality so these +two are equivalent to each other now + + align:start position:0% +two are equivalent to each other now + + + align:start position:0% +two are equivalent to each other now +with graphs and specifically these + + align:start position:0% +with graphs and specifically these + + + align:start position:0% +with graphs and specifically these +counts here okay so triangle densities + + align:start position:0% +counts here okay so triangle densities + + + align:start position:0% +counts here okay so triangle densities +and edge densities they correspond to + + align:start position:0% +and edge densities they correspond to + + + align:start position:0% +and edge densities they correspond to +counting closed walks in the graph so in + + align:start position:0% +counting closed walks in the graph so in + + + align:start position:0% +counting closed walks in the graph so in +particular if we're interested in the + + align:start position:0% +particular if we're interested in the + + + align:start position:0% +particular if we're interested in the +cave number of k3 homomorphisms in the + + align:start position:0% +cave number of k3 homomorphisms in the + + + align:start position:0% +cave number of k3 homomorphisms in the +graph this is the same as counting + + align:start position:0% +graph this is the same as counting + + + align:start position:0% +graph this is the same as counting +closed walks of length 3 and there was + + align:start position:0% +closed walks of length 3 and there was + + + align:start position:0% +closed walks of length 3 and there was +an important identity we used earlier + + align:start position:0% +an important identity we used earlier + + + align:start position:0% +an important identity we used earlier +when we were discussing the proof of + + align:start position:0% +when we were discussing the proof of + + + align:start position:0% +when we were discussing the proof of +quasi random graphs that for counting + + align:start position:0% +quasi random graphs that for counting + + + align:start position:0% +quasi random graphs that for counting +closed walks you should look at the + + align:start position:0% +closed walks you should look at the + + + align:start position:0% +closed walks you should look at the +spectral moment so that's a very + + align:start position:0% +spectral moment so that's a very + + + align:start position:0% +spectral moment so that's a very +important tool to look at the spectral + + align:start position:0% +important tool to look at the spectral + + + align:start position:0% +important tool to look at the spectral +moment maybe here the third power of the + + align:start position:0% +moment maybe here the third power of the + + + align:start position:0% +moment maybe here the third power of the +eigenvalues of the adjacency matrix + + align:start position:0% +eigenvalues of the adjacency matrix + + + align:start position:0% +eigenvalues of the adjacency matrix +office + + align:start position:0% + + + + align:start position:0% + +this is TV I can values of the adjacency + + align:start position:0% +this is TV I can values of the adjacency + + + align:start position:0% +this is TV I can values of the adjacency +matrix I claim that this sum here is + + align:start position:0% +matrix I claim that this sum here is + + + align:start position:0% +matrix I claim that this sum here is +upper bounded by a corresponding sum of + + align:start position:0% +upper bounded by a corresponding sum of + + + align:start position:0% +upper bounded by a corresponding sum of +squares raised to the power that + + align:start position:0% +squares raised to the power that + + + align:start position:0% +squares raised to the power that +normalizes the first time I saw this I + + align:start position:0% +normalizes the first time I saw this I + + + align:start position:0% +normalizes the first time I saw this I +was a bit confused because I remember + + align:start position:0% +was a bit confused because I remember + + + align:start position:0% +was a bit confused because I remember +how our maintaining quality shouldn't go + + align:start position:0% +how our maintaining quality shouldn't go + + + align:start position:0% +how our maintaining quality shouldn't go +the other way but actually not this is + + align:start position:0% +the other way but actually not this is + + + align:start position:0% +the other way but actually not this is +the correct direction so let me let me + + align:start position:0% +the correct direction so let me let me + + + align:start position:0% +the correct direction so let me let me +remind you why so if you have positive T + + align:start position:0% +remind you why so if you have positive T + + + align:start position:0% +remind you why so if you have positive T +then playing that and you have a bunch + + align:start position:0% +then playing that and you have a bunch + + + align:start position:0% +then playing that and you have a bunch +of no negative Rios then the claim is + + align:start position:0% +of no negative Rios then the claim is + + + align:start position:0% +of no negative Rios then the claim is +that this teeth power sum is less than + + align:start position:0% +that this teeth power sum is less than + + + align:start position:0% +that this teeth power sum is less than +or equal to the teeth power saw now + + align:start position:0% +or equal to the teeth power saw now + + + align:start position:0% +or equal to the teeth power saw now +there are several ways to to see why + + align:start position:0% +there are several ways to to see why + + + align:start position:0% +there are several ways to to see why +this is true you can do induction but + + align:start position:0% +this is true you can do induction but + + + align:start position:0% +this is true you can do induction but +let me show you one way which is quite + + align:start position:0% +let me show you one way which is quite + + + align:start position:0% +let me show you one way which is quite +neat because it's homogeneous in the + + align:start position:0% +neat because it's homogeneous in the + + + align:start position:0% +neat because it's homogeneous in the +variables I can assume that the sum is + + align:start position:0% +variables I can assume that the sum is + + + align:start position:0% +variables I can assume that the sum is +one in which case the left hand side is + + align:start position:0% +one in which case the left hand side is + + + align:start position:0% +one in which case the left hand side is +equal to this sum of teeth powers and so + + align:start position:0% +equal to this sum of teeth powers and so + + + align:start position:0% +equal to this sum of teeth powers and so +because I assumed that everything is + + align:start position:0% +because I assumed that everything is + + + align:start position:0% +because I assumed that everything is +non-negative + + align:start position:0% +non-negative + + + align:start position:0% +non-negative +everything is all these aids are between + + align:start position:0% +everything is all these aids are between + + + align:start position:0% +everything is all these aids are between +0 and 1 so now the sum is less than or + + align:start position:0% +0 and 1 so now the sum is less than or + + + align:start position:0% +0 and 1 so now the sum is less than or +equal to same sum without the T's which + + align:start position:0% +equal to same sum without the T's which + + + align:start position:0% +equal to same sum without the T's which +is the right + + align:start position:0% + + + + align:start position:0% + +okay so so this is true and now we have + + align:start position:0% +okay so so this is true and now we have + + + align:start position:0% +okay so so this is true and now we have +this sum of square surf eigenvalues + + align:start position:0% +this sum of square surf eigenvalues + + + align:start position:0% +this sum of square surf eigenvalues +which is also a moment of the moment of + + align:start position:0% +which is also a moment of the moment of + + + align:start position:0% +which is also a moment of the moment of +the eigenvalues namely corresponding to + + align:start position:0% +the eigenvalues namely corresponding to + + + align:start position:0% +the eigenvalues namely corresponding to +K 2 so the same inequality is true for + + align:start position:0% +K 2 so the same inequality is true for + + + align:start position:0% +K 2 so the same inequality is true for +graph homomorphisms and to get to the + + align:start position:0% +graph homomorphisms and to get to the + + + align:start position:0% +graph homomorphisms and to get to the +inequality for densities we just divide + + align:start position:0% +inequality for densities we just divide + + + align:start position:0% +inequality for densities we just divide +by the number of vertices raised to the + + align:start position:0% +by the number of vertices raised to the + + + align:start position:0% +by the number of vertices raised to the +third power on both sides and and we get + + align:start position:0% +third power on both sides and and we get + + + align:start position:0% +third power on both sides and and we get +inequality that we're looking for okay + + align:start position:0% +inequality that we're looking for okay + + + align:start position:0% +inequality that we're looking for okay +so that's the proof of the upper dog any + + align:start position:0% +so that's the proof of the upper dog any + + + align:start position:0% +so that's the proof of the upper dog any +questions there is something that + + align:start position:0% +questions there is something that + + + align:start position:0% +questions there is something that +bothers me slightly about this look it's + + align:start position:0% +bothers me slightly about this look it's + + + align:start position:0% +bothers me slightly about this look it's +a correct proof so there's nothing + + align:start position:0% +a correct proof so there's nothing + + + align:start position:0% +a correct proof so there's nothing +nothing wrong with this proof everything + + align:start position:0% +nothing wrong with this proof everything + + + align:start position:0% +nothing wrong with this proof everything +is kosher everything is correct you + + align:start position:0% +is kosher everything is correct you + + + align:start position:0% +is kosher everything is correct you +might ask is there a way to do this + + align:start position:0% +might ask is there a way to do this + + + align:start position:0% +might ask is there a way to do this +spectral argument in graph phones you + + align:start position:0% +spectral argument in graph phones you + + + align:start position:0% +spectral argument in graph phones you +know without passing two graphs and yes + + align:start position:0% +know without passing two graphs and yes + + + align:start position:0% +know without passing two graphs and yes +you can because for graph phones you can + + align:start position:0% +you can because for graph phones you can + + + align:start position:0% +you can because for graph phones you can +also talk about a spectrum it turns out + + align:start position:0% +also talk about a spectrum it turns out + + + align:start position:0% +also talk about a spectrum it turns out +to be a compact operator so its spectrum + + align:start position:0% +to be a compact operator so its spectrum + + + align:start position:0% +to be a compact operator so its spectrum +makes sense you have to develop a little + + align:start position:0% +makes sense you have to develop a little + + + align:start position:0% +makes sense you have to develop a little +bit more theory about the spectrum of + + align:start position:0% +bit more theory about the spectrum of + + + align:start position:0% +bit more theory about the spectrum of +compact operators but everything more or + + align:start position:0% +compact operators but everything more or + + + align:start position:0% +compact operators but everything more or +less works exactly the same way it's + + align:start position:0% +less works exactly the same way it's + + + align:start position:0% +less works exactly the same way it's +just easier to talk about graphs but + + align:start position:0% +just easier to talk about graphs but + + + align:start position:0% +just easier to talk about graphs but +what bothers me about this proof is that + + align:start position:0% +what bothers me about this proof is that + + + align:start position:0% +what bothers me about this proof is that +we started with what I would call a + + align:start position:0% +we started with what I would call a + + + align:start position:0% +we started with what I would call a +physical inequality meaning that it only + + align:start position:0% +physical inequality meaning that it only + + + align:start position:0% +physical inequality meaning that it only +has to do with the actual edges and sub + + align:start position:0% +has to do with the actual edges and sub + + + align:start position:0% +has to do with the actual edges and sub +graph densities but the proof involved + + align:start position:0% +graph densities but the proof involved + + + align:start position:0% +graph densities but the proof involved +going to the spectrum and that bothers + + align:start position:0% +going to the spectrum and that bothers + + + align:start position:0% +going to the spectrum and that bothers +me a little bit then there's nothing + + align:start position:0% +me a little bit then there's nothing + + + align:start position:0% +me a little bit then there's nothing +incorrect about it but somehow in my + + align:start position:0% +incorrect about it but somehow in my + + + align:start position:0% +incorrect about it but somehow in my +mind a physical inequality deserves a + + align:start position:0% +mind a physical inequality deserves a + + + align:start position:0% +mind a physical inequality deserves a +physical proof so physical I use the + + align:start position:0% +physical proof so physical I use the + + + align:start position:0% +physical proof so physical I use the +word + + align:start position:0% +word + + + align:start position:0% +word +physical in contrast to frequency which + + align:start position:0% +physical in contrast to frequency which + + + align:start position:0% +physical in contrast to frequency which +is coming from Fourier analysis and + + align:start position:0% +is coming from Fourier analysis and + + + align:start position:0% +is coming from Fourier analysis and +that's the next thing we'll do in this + + align:start position:0% +that's the next thing we'll do in this + + + align:start position:0% +that's the next thing we'll do in this +course but this proof goes to the + + align:start position:0% +course but this proof goes to the + + + align:start position:0% +course but this proof goes to the +spectrum it goes to something beyond the + + align:start position:0% +spectrum it goes to something beyond the + + + align:start position:0% +spectrum it goes to something beyond the +physical domain okay that's it's neat + + align:start position:0% +physical domain okay that's it's neat + + + align:start position:0% +physical domain okay that's it's neat +but I want to show you a different proof + + align:start position:0% +but I want to show you a different proof + + + align:start position:0% +but I want to show you a different proof +that stays within the physical domain + + align:start position:0% +that stays within the physical domain + + + align:start position:0% +that stays within the physical domain +and this other proof I mean it's always + + align:start position:0% +and this other proof I mean it's always + + + align:start position:0% +and this other proof I mean it's always +nice to see some different proofs + + align:start position:0% +nice to see some different proofs + + + align:start position:0% +nice to see some different proofs +because you can use it to apply to + + align:start position:0% +because you can use it to apply to + + + align:start position:0% +because you can use it to apply to +different situations and there are some + + align:start position:0% +different situations and there are some + + + align:start position:0% +different situations and there are some +situations where you might not be able + + align:start position:0% +situations where you might not be able + + + align:start position:0% +situations where you might not be able +to use this spectral spectral + + align:start position:0% +to use this spectral spectral + + + align:start position:0% +to use this spectral spectral +characterization for example what if + + align:start position:0% +characterization for example what if + + + align:start position:0% +characterization for example what if +your K 3 is now OK for similar + + align:start position:0% +your K 3 is now OK for similar + + + align:start position:0% +your K 3 is now OK for similar +inequality is true but this proof + + align:start position:0% +inequality is true but this proof + + + align:start position:0% +inequality is true but this proof +doesn't show it at least not directly + + align:start position:0% +doesn't show it at least not directly + + + align:start position:0% +doesn't show it at least not directly +you have to do a little bit of extra + + align:start position:0% +you have to do a little bit of extra + + + align:start position:0% +you have to do a little bit of extra +work so let me show you a different + + align:start position:0% +work so let me show you a different + + + align:start position:0% +work so let me show you a different +proof of the upper bound and we'll prove + + align:start position:0% +proof of the upper bound and we'll prove + + + align:start position:0% +proof of the upper bound and we'll prove +a slightly stronger statement namely + + align:start position:0% +a slightly stronger statement namely + + + align:start position:0% +a slightly stronger statement namely +that for all not just square phones but + + align:start position:0% +that for all not just square phones but + + + align:start position:0% +that for all not just square phones but +it's not so important but for all + + align:start position:0% +it's not so important but for all + + + align:start position:0% +it's not so important but for all +symmetric measurable functions from the + + align:start position:0% +symmetric measurable functions from the + + + align:start position:0% +symmetric measurable functions from the +Union Square to R 1 has the following + + align:start position:0% +Union Square to R 1 has the following + + + align:start position:0% +Union Square to R 1 has the following +inequality namely that the K 3 density + + align:start position:0% +inequality namely that the K 3 density + + + align:start position:0% +inequality namely that the K 3 density +in W is upper bounded by the K 2 density + + align:start position:0% +in W is upper bounded by the K 2 density + + + align:start position:0% +in W is upper bounded by the K 2 density +of W squared raised to power + + align:start position:0% +of W squared raised to power + + + align:start position:0% +of W squared raised to power +three-halves here the square is meant to + + align:start position:0% +three-halves here the square is meant to + + + align:start position:0% +three-halves here the square is meant to +be a point wise square + + align:start position:0% + + + + align:start position:0% + +so a couple of things if you were graph + + align:start position:0% +so a couple of things if you were graph + + + align:start position:0% +so a couple of things if you were graph +is a graph on a graph then or if it's a + + align:start position:0% +is a graph on a graph then or if it's a + + + align:start position:0% +is a graph on a graph then or if it's a +graph then 0 comma 1 value so taking + + align:start position:0% +graph then 0 comma 1 value so taking + + + align:start position:0% +graph then 0 comma 1 value so taking +this point my square doesn't do anything + + align:start position:0% +this point my square doesn't do anything + + + align:start position:0% +this point my square doesn't do anything +if you're graphing you can always put + + align:start position:0% +if you're graphing you can always put + + + align:start position:0% +if you're graphing you can always put +one more inequality that replaces it by + + align:start position:0% +one more inequality that replaces it by + + + align:start position:0% +one more inequality that replaces it by +the thing that we're looking for because + + align:start position:0% +the thing that we're looking for because + + + align:start position:0% +the thing that we're looking for because +W is always bounded between 0 and 1 so + + align:start position:0% +W is always bounded between 0 and 1 so + + + align:start position:0% +W is always bounded between 0 and 1 so +it's a slightly stronger inequality okay + + align:start position:0% +it's a slightly stronger inequality okay + + + align:start position:0% +it's a slightly stronger inequality okay +and let me show it to you by writing + + align:start position:0% +and let me show it to you by writing + + + align:start position:0% +and let me show it to you by writing +down a series of inequalities and + + align:start position:0% +down a series of inequalities and + + + align:start position:0% +down a series of inequalities and +applying the Cauchy Schwarz inequality + + align:start position:0% +applying the Cauchy Schwarz inequality + + + align:start position:0% +applying the Cauchy Schwarz inequality +repeatedly so it's again in exercise in + + align:start position:0% +repeatedly so it's again in exercise in + + + align:start position:0% +repeatedly so it's again in exercise in +using Cauchy Schwarz and we will apply + + align:start position:0% +using Cauchy Schwarz and we will apply + + + align:start position:0% +using Cauchy Schwarz and we will apply +three applications of Cauchy Schwarz + + align:start position:0% + + + + align:start position:0% + +essentially three applications one + + align:start position:0% +essentially three applications one + + + align:start position:0% +essentially three applications one +corresponding to every edge of this + + align:start position:0% +corresponding to every edge of this + + + align:start position:0% +corresponding to every edge of this +triangle so let me begin by writing down + + align:start position:0% +triangle so let me begin by writing down + + + align:start position:0% +triangle so let me begin by writing down +the expression in griffons corresponding + + align:start position:0% +the expression in griffons corresponding + + + align:start position:0% +the expression in griffons corresponding +to the k3 density okay I'm going to + + align:start position:0% +to the k3 density okay I'm going to + + + align:start position:0% +to the k3 density okay I'm going to +apply Cauchy Schwarz by so I'm going to + + align:start position:0% +apply Cauchy Schwarz by so I'm going to + + + align:start position:0% +apply Cauchy Schwarz by so I'm going to +apply Cauchy Schwarz to the variable X + + align:start position:0% +apply Cauchy Schwarz to the variable X + + + align:start position:0% +apply Cauchy Schwarz to the variable X +holding all the other variables constant + + align:start position:0% +holding all the other variables constant + + + align:start position:0% +holding all the other variables constant +so hold dy and DZ constant going to + + align:start position:0% +so hold dy and DZ constant going to + + + align:start position:0% +so hold dy and DZ constant going to +apply to DX you see there are two + + align:start position:0% +apply to DX you see there are two + + + align:start position:0% +apply to DX you see there are two +factors that involve the variable X so + + align:start position:0% +factors that involve the variable X so + + + align:start position:0% +factors that involve the variable X so +apply Cauchy Schwarz to them you split + + align:start position:0% +apply Cauchy Schwarz to them you split + + + align:start position:0% +apply Cauchy Schwarz to them you split +each of them into an l2 + + align:start position:0% + + + + align:start position:0% + +so one of these factors become that by + + align:start position:0% +so one of these factors become that by + + + align:start position:0% +so one of these factors become that by +the way all of these are definite + + align:start position:0% +the way all of these are definite + + + align:start position:0% +the way all of these are definite +integral's I'm just omitting the domain + + align:start position:0% +integral's I'm just omitting the domain + + + align:start position:0% +integral's I'm just omitting the domain +of integration so all the integrals are + + align:start position:0% +of integration so all the integrals are + + + align:start position:0% +of integration so all the integrals are +integrated over from zero to one so the + + align:start position:0% +integrated over from zero to one so the + + + align:start position:0% +integrated over from zero to one so the +second application or so the second + + align:start position:0% +second application or so the second + + + align:start position:0% +second application or so the second +factor becomes that and the third factor + + align:start position:0% +factor becomes that and the third factor + + + align:start position:0% +factor becomes that and the third factor +is left intact + + align:start position:0% + + + + align:start position:0% + +okay so that's the first application of + + align:start position:0% +okay so that's the first application of + + + align:start position:0% +okay so that's the first application of +cauchy-schwarz you apply with respect to + + align:start position:0% +cauchy-schwarz you apply with respect to + + + align:start position:0% +cauchy-schwarz you apply with respect to +DX to these two factors split them like + + align:start position:0% +DX to these two factors split them like + + + align:start position:0% +DX to these two factors split them like +that thank you there is a normalization + + align:start position:0% +that thank you there is a normalization + + + align:start position:0% +that thank you there is a normalization +missing yeah okay guess what the second + + align:start position:0% +missing yeah okay guess what the second + + + align:start position:0% +missing yeah okay guess what the second +step is we're gonna apply Cauchy Schwarz + + align:start position:0% +step is we're gonna apply Cauchy Schwarz + + + align:start position:0% +step is we're gonna apply Cauchy Schwarz +again but now to dy one more variable + + align:start position:0% + + + + align:start position:0% + +Toshi shorts with respect to dy there + + align:start position:0% +Toshi shorts with respect to dy there + + + align:start position:0% +Toshi shorts with respect to dy there +are two factors now that involved the + + align:start position:0% +are two factors now that involved the + + + align:start position:0% +are two factors now that involved the +letter Y so I apply Cauchy Schwarz and I + + align:start position:0% +letter Y so I apply Cauchy Schwarz and I + + + align:start position:0% +letter Y so I apply Cauchy Schwarz and I +get the following the first factor now + + align:start position:0% +get the following the first factor now + + + align:start position:0% +get the following the first factor now +just becomes the l2 norm of W the second + + align:start position:0% +just becomes the l2 norm of W the second + + + align:start position:0% +just becomes the l2 norm of W the second +factor does not involve Y so it is left + + align:start position:0% +factor does not involve Y so it is left + + + align:start position:0% +factor does not involve Y so it is left +intact and the third factor is can't + + align:start position:0% +intact and the third factor is can't + + + align:start position:0% +intact and the third factor is can't +integrate it with respect to Y after + + align:start position:0% +integrate it with respect to Y after + + + align:start position:0% +integrate it with respect to Y after +taking squid + + align:start position:0% + + + + align:start position:0% + +and there's now DZ that remains last + + align:start position:0% +and there's now DZ that remains last + + + align:start position:0% +and there's now DZ that remains last +step now you can guess you integrate + + align:start position:0% +step now you can guess you integrate + + + align:start position:0% +step now you can guess you integrate +with respect to DZ and apply coffee + + align:start position:0% +with respect to DZ and apply coffee + + + align:start position:0% +with respect to DZ and apply coffee +shorts black coffee shorts to the last + + align:start position:0% +shorts black coffee shorts to the last + + + align:start position:0% +shorts black coffee shorts to the last +two factors and they'll actually do + + align:start position:0% +two factors and they'll actually do + + + align:start position:0% +two factors and they'll actually do +outside integral goes away so you get + + align:start position:0% +outside integral goes away so you get + + + align:start position:0% +outside integral goes away so you get +this product and you see every single + + align:start position:0% +this product and you see every single + + + align:start position:0% +this product and you see every single +term is just the l2 norm of W so that + + align:start position:0% +term is just the l2 norm of W so that + + + align:start position:0% +term is just the l2 norm of W so that +which is the same as what I wrote over + + align:start position:0% +which is the same as what I wrote over + + + align:start position:0% +which is the same as what I wrote over +here okay + + align:start position:0% +here okay + + + align:start position:0% +here okay +any questions yeah okay great question + + align:start position:0% +any questions yeah okay great question + + + align:start position:0% +any questions yeah okay great question +so where do I use the fact that W is + + align:start position:0% +so where do I use the fact that W is + + + align:start position:0% +so where do I use the fact that W is +symmetric well so let's see in some + + align:start position:0% +symmetric well so let's see in some + + + align:start position:0% +symmetric well so let's see in some +sense we're not using the fact that W is + + align:start position:0% +sense we're not using the fact that W is + + + align:start position:0% +sense we're not using the fact that W is +symmetric because there's a slightly + + align:start position:0% +symmetric because there's a slightly + + + align:start position:0% +symmetric because there's a slightly +more general inequality you can write + + align:start position:0% +more general inequality you can write + + + align:start position:0% +more general inequality you can write +down and actually the question gives me + + align:start position:0% +down and actually the question gives me + + + align:start position:0% +down and actually the question gives me +a good chance to do a slight diversion + + align:start position:0% +a good chance to do a slight diversion + + + align:start position:0% +a good chance to do a slight diversion +into how this inequality is related to + + align:start position:0% +into how this inequality is related to + + + align:start position:0% +into how this inequality is related to +holders inequality okay so this is + + align:start position:0% +holders inequality okay so this is + + + align:start position:0% +holders inequality okay so this is +actually one of my favorite inequalities + + align:start position:0% +actually one of my favorite inequalities + + + align:start position:0% +actually one of my favorite inequalities +for this kind of combinatorial + + align:start position:0% +for this kind of combinatorial + + + align:start position:0% +for this kind of combinatorial +inequalities on graphics + + align:start position:0% +inequalities on graphics + + + align:start position:0% +inequalities on graphics +so many of you may be familiar with + + align:start position:0% +so many of you may be familiar with + + + align:start position:0% +so many of you may be familiar with +holders inequality in the following form + + align:start position:0% +holders inequality in the following form + + + align:start position:0% +holders inequality in the following form +if I have three functions if I integrate + + align:start position:0% +if I have three functions if I integrate + + + align:start position:0% +if I have three functions if I integrate +them then you can upper bound this + + align:start position:0% +them then you can upper bound this + + + align:start position:0% +them then you can upper bound this +integral by the product of the l-3 norms + + align:start position:0% +integral by the product of the l-3 norms + + + align:start position:0% +integral by the product of the l-3 norms +and likewise if you have more functions + + align:start position:0% +and likewise if you have more functions + + + align:start position:0% +and likewise if you have more functions +so if you apply just this inequality + + align:start position:0% +so if you apply just this inequality + + + align:start position:0% +so if you apply just this inequality +directly you get a weaker estimate okay + + align:start position:0% +directly you get a weaker estimate okay + + + align:start position:0% +directly you get a weaker estimate okay +so you don't get anything that's quite + + align:start position:0% +so you don't get anything that's quite + + + align:start position:0% +so you don't get anything that's quite +as strong as what you're looking for + + align:start position:0% +as strong as what you're looking for + + + align:start position:0% +as strong as what you're looking for +over there so what happens is that if + + align:start position:0% +over there so what happens is that if + + + align:start position:0% +over there so what happens is that if +you know so if F G and H each depends + + align:start position:0% +you know so if F G and H each depends + + + align:start position:0% +you know so if F G and H each depends +only on a subset of the coordinates + + align:start position:0% + + + + align:start position:0% + +in the following way that after pens are + + align:start position:0% +in the following way that after pens are + + + align:start position:0% +in the following way that after pens are +only X&Y G depends only on X and Z and H + + align:start position:0% +only X&Y G depends only on X and Z and H + + + align:start position:0% +only X&Y G depends only on X and Z and H +depends only on y and z then if you + + align:start position:0% +depends only on y and z then if you + + + align:start position:0% +depends only on y and z then if you +repeat that proof verbatim with three + + align:start position:0% +repeat that proof verbatim with three + + + align:start position:0% +repeat that proof verbatim with three +different functions you'll find that you + + align:start position:0% +different functions you'll find that you + + + align:start position:0% +different functions you'll find that you +can upper bound this product this + + align:start position:0% +can upper bound this product this + + + align:start position:0% +can upper bound this product this +integral by the product of the l2 norms + + align:start position:0% + + + + align:start position:0% + +are two norms are in general less than + + align:start position:0% +are two norms are in general less than + + + align:start position:0% +are two norms are in general less than +or equal to the l3 norm so here were + + align:start position:0% +or equal to the l3 norm so here were + + + align:start position:0% +or equal to the l3 norm so here were +inside the probability measure space so + + align:start position:0% +inside the probability measure space so + + + align:start position:0% +inside the probability measure space so +the entire spaces volume one so this is + + align:start position:0% +the entire spaces volume one so this is + + + align:start position:0% +the entire spaces volume one so this is +a stronger inequality and this is the + + align:start position:0% +a stronger inequality and this is the + + + align:start position:0% +a stronger inequality and this is the +inequality that comes up over them + + align:start position:0% + + + + align:start position:0% + +great so question is you're entirely + + align:start position:0% +great so question is you're entirely + + + align:start position:0% +great so question is you're entirely +crafty whether proof of this so the + + align:start position:0% +crafty whether proof of this so the + + + align:start position:0% +crafty whether proof of this so the +reason why I mentioned that this result + + align:start position:0% +reason why I mentioned that this result + + + align:start position:0% +reason why I mentioned that this result +is a special case of Crisco Kitana so + + align:start position:0% +is a special case of Crisco Kitana so + + + align:start position:0% +is a special case of Crisco Kitana so +Crisco katana actually is a stronger + + align:start position:0% +Crisco katana actually is a stronger + + + align:start position:0% +Crisco katana actually is a stronger +result which tells you precisely how + + align:start position:0% +result which tells you precisely how + + + align:start position:0% +result which tells you precisely how +many how you should construct a graph so + + align:start position:0% +many how you should construct a graph so + + + align:start position:0% +many how you should construct a graph so +Givens exactly M edges what's the + + align:start position:0% +Givens exactly M edges what's the + + + align:start position:0% +Givens exactly M edges what's the +maximum number of triangles and the + + align:start position:0% +maximum number of triangles and the + + + align:start position:0% +maximum number of triangles and the +statement of theorem is actually I mean + + align:start position:0% +statement of theorem is actually I mean + + + align:start position:0% +statement of theorem is actually I mean +it's a very precise result it tells you + + align:start position:0% +it's a very precise result it tells you + + + align:start position:0% +it's a very precise result it tells you +for example if you have K choose two + + align:start position:0% +for example if you have K choose two + + + align:start position:0% +for example if you have K choose two +edges you have at most K choose three + + align:start position:0% +edges you have at most K choose three + + + align:start position:0% +edges you have at most K choose three +triangles it's not just at a density + + align:start position:0% +triangles it's not just at a density + + + align:start position:0% +triangles it's not just at a density +level but exactly and even if the number + + align:start position:0% +level but exactly and even if the number + + + align:start position:0% +level but exactly and even if the number +of edges is not in the form of K choose + + align:start position:0% +of edges is not in the form of K choose + + + align:start position:0% +of edges is not in the form of K choose +two it tells you what to do and actually + + align:start position:0% +two it tells you what to do and actually + + + align:start position:0% +two it tells you what to do and actually +the answer is pretty easy to describe + + align:start position:0% +the answer is pretty easy to describe + + + align:start position:0% +the answer is pretty easy to describe +it's almost intuitive so if you know I + + align:start position:0% +it's almost intuitive so if you know I + + + align:start position:0% +it's almost intuitive so if you know I +give you a bunch of matchsticks and ask + + align:start position:0% +give you a bunch of matchsticks and ask + + + align:start position:0% +give you a bunch of matchsticks and ask +you to construct a graph with as many + + align:start position:0% +you to construct a graph with as many + + + align:start position:0% +you to construct a graph with as many +triangles as you can you know what + + align:start position:0% +triangles as you can you know what + + + align:start position:0% +triangles as you can you know what +should you do you start with one two and + + align:start position:0% +should you do you start with one two and + + + align:start position:0% +should you do you start with one two and +you're filling a triangle you know start + + align:start position:0% +you're filling a triangle you know start + + + align:start position:0% +you're filling a triangle you know start +filling a triangle another vertex one + + align:start position:0% +filling a triangle another vertex one + + + align:start position:0% +filling a triangle another vertex one +two three four you keep going and that's + + align:start position:0% +two three four you keep going and that's + + + align:start position:0% +two three four you keep going and that's +the best way to do it and that's what + + align:start position:0% +the best way to do it and that's what + + + align:start position:0% +the best way to do it and that's what +Crisco katana tells you okay so that's a + + align:start position:0% +Crisco katana tells you okay so that's a + + + align:start position:0% +Crisco katana tells you okay so that's a +more precise version of this inequality + + align:start position:0% +more precise version of this inequality + + + align:start position:0% +more precise version of this inequality +and the Crisco katana the combinatorial + + align:start position:0% +and the Crisco katana the combinatorial + + + align:start position:0% +and the Crisco katana the combinatorial +version is proofed via a combinatorial + + align:start position:0% +version is proofed via a combinatorial + + + align:start position:0% +version is proofed via a combinatorial +shifting argument also known as a + + align:start position:0% +shifting argument also known as a + + + align:start position:0% +shifting argument also known as a +compression argument namely if you start + + align:start position:0% +compression argument namely if you start + + + align:start position:0% +compression argument namely if you start +with a given graph there are some + + align:start position:0% +with a given graph there are some + + + align:start position:0% +with a given graph there are some +transformations you do to that graph to + + align:start position:0% +transformations you do to that graph to + + + align:start position:0% +transformations you do to that graph to +push your edges in one direction that + + align:start position:0% +push your edges in one direction that + + + align:start position:0% +push your edges in one direction that +saves the number of edges exactly the + + align:start position:0% +saves the number of edges exactly the + + + align:start position:0% +saves the number of edges exactly the +same but increases the number of + + align:start position:0% +same but increases the number of + + + align:start position:0% +same but increases the number of +triangles at each step and eventually + + align:start position:0% +triangles at each step and eventually + + + align:start position:0% +triangles at each step and eventually +you push everything into a creek that's + + align:start position:0% +you push everything into a creek that's + + + align:start position:0% +you push everything into a creek that's +something you can read about it's a very + + align:start position:0% +something you can read about it's a very + + + align:start position:0% +something you can read about it's a very +nice result other questions + + align:start position:0% + + + + align:start position:0% + +all right so we solved the upper bound + + align:start position:0% +all right so we solved the upper bound + + + align:start position:0% +all right so we solved the upper bound +and that is in the from an example isn't + + align:start position:0% +and that is in the from an example isn't + + + align:start position:0% +and that is in the from an example isn't +from this upper bound proof we see that + + align:start position:0% +from this upper bound proof we see that + + + align:start position:0% +from this upper bound proof we see that +it's the upper bound now let me tell you + + align:start position:0% +it's the upper bound now let me tell you + + + align:start position:0% +it's the upper bound now let me tell you +a fairly general result that says + + align:start position:0% +a fairly general result that says + + + align:start position:0% +a fairly general result that says +something about graph theoretic + + align:start position:0% +something about graph theoretic + + + align:start position:0% +something about graph theoretic +inequalities in a button for specific + + align:start position:0% +inequalities in a button for specific + + + align:start position:0% +inequalities in a button for specific +kind of linear inequalities so here's a + + align:start position:0% +kind of linear inequalities so here's a + + + align:start position:0% +kind of linear inequalities so here's a +theorem due to Bala Bosch I'm interested + + align:start position:0% +theorem due to Bala Bosch I'm interested + + + align:start position:0% +theorem due to Bala Bosch I'm interested +in an inequality of the form like so I'm + + align:start position:0% +in an inequality of the form like so I'm + + + align:start position:0% +in an inequality of the form like so I'm +interested in inequality of this form + + align:start position:0% + + + + align:start position:0% + +where I have a bunch of real + + align:start position:0% +where I have a bunch of real + + + align:start position:0% +where I have a bunch of real +coefficients and I'm looking at a linear + + align:start position:0% +coefficients and I'm looking at a linear + + + align:start position:0% +coefficients and I'm looking at a linear +combination of the clique densities I + + align:start position:0% +combination of the clique densities I + + + align:start position:0% +combination of the clique densities I +would like to know if this inequality is + + align:start position:0% +would like to know if this inequality is + + + align:start position:0% +would like to know if this inequality is +true so somebody gives you this + + align:start position:0% +true so somebody gives you this + + + align:start position:0% +true so somebody gives you this +inequality whatever the numbers may be + + align:start position:0% +inequality whatever the numbers may be + + + align:start position:0% +inequality whatever the numbers may be +you can also have a constant term right + + align:start position:0% +you can also have a constant term right + + + align:start position:0% +you can also have a constant term right +the constant term corresponds to R + + align:start position:0% +the constant term corresponds to R + + + align:start position:0% +the constant term corresponds to R +equals to 1 right so the point density + + align:start position:0% +equals to 1 right so the point density + + + align:start position:0% +equals to 1 right so the point density +that's the constant term and asks you to + + align:start position:0% +that's the constant term and asks you to + + + align:start position:0% +that's the constant term and asks you to +decide it's this inequality true if so + + align:start position:0% +decide it's this inequality true if so + + + align:start position:0% +decide it's this inequality true if so +prove it if not find a counterexample + + align:start position:0% + + + + align:start position:0% + +okay so the theorem tells you that this + + align:start position:0% +okay so the theorem tells you that this + + + align:start position:0% +okay so the theorem tells you that this +is actually not hard to do so this + + align:start position:0% +is actually not hard to do so this + + + align:start position:0% +is actually not hard to do so this +inequality holds for all G if and only + + align:start position:0% +inequality holds for all G if and only + + + align:start position:0% +inequality holds for all G if and only +if it holds + + align:start position:0% +if it holds + + + align:start position:0% +if it holds +whenever G is a clique + + align:start position:0% + + + + align:start position:0% + +maybe somebody gives you this inequality + + align:start position:0% +maybe somebody gives you this inequality + + + align:start position:0% +maybe somebody gives you this inequality +about linear inequality about Creek + + align:start position:0% +about linear inequality about Creek + + + align:start position:0% +about linear inequality about Creek +densities than to check this inequality + + align:start position:0% +densities than to check this inequality + + + align:start position:0% +densities than to check this inequality +you only have to check over all cliques + + align:start position:0% +you only have to check over all cliques + + + align:start position:0% +you only have to check over all cliques +G which is much easier than checking for + + align:start position:0% +G which is much easier than checking for + + + align:start position:0% +G which is much easier than checking for +all graphs right for each click G this + + align:start position:0% +all graphs right for each click G this + + + align:start position:0% +all graphs right for each click G this +is just some specific expression you can + + align:start position:0% +is just some specific expression you can + + + align:start position:0% +is just some specific expression you can +buy down and you can you can check so I + + align:start position:0% +buy down and you can you can check so I + + + align:start position:0% +buy down and you can you can check so I +want to show you the proof of Bolla + + align:start position:0% +want to show you the proof of Bolla + + + align:start position:0% +want to show you the proof of Bolla +bashas theorem it's it's a quite nice + + align:start position:0% +bashas theorem it's it's a quite nice + + + align:start position:0% +bashas theorem it's it's a quite nice +result but before that any questions + + align:start position:0% +result but before that any questions + + + align:start position:0% +result but before that any questions +about the statement all right so the + + align:start position:0% +about the statement all right so the + + + align:start position:0% +about the statement all right so the +reason I say that this is very easy to + + align:start position:0% +reason I say that this is very easy to + + + align:start position:0% +reason I say that this is very easy to +check if I actually give you what the + + align:start position:0% +check if I actually give you what the + + + align:start position:0% +check if I actually give you what the +numbers are it's because this inequality + + align:start position:0% +numbers are it's because this inequality + + + align:start position:0% +numbers are it's because this inequality +four clicks so inequality is equivalent + + align:start position:0% +four clicks so inequality is equivalent + + + align:start position:0% +four clicks so inequality is equivalent +to just a statement but the inequality + + align:start position:0% +to just a statement but the inequality + + + align:start position:0% +to just a statement but the inequality +that I'm writing down now where I tell + + align:start position:0% +that I'm writing down now where I tell + + + align:start position:0% +that I'm writing down now where I tell +you precisely what the our clique + + align:start position:0% +you precisely what the our clique + + + align:start position:0% +you precisely what the our clique +density is in n click that's just some + + align:start position:0% +density is in n click that's just some + + + align:start position:0% +density is in n click that's just some +combinatorial expression so to check + + align:start position:0% +combinatorial expression so to check + + + align:start position:0% +combinatorial expression so to check +whether this inequality is true for all + + align:start position:0% +whether this inequality is true for all + + + align:start position:0% +whether this inequality is true for all +graphs I just have to check the specific + + align:start position:0% +graphs I just have to check the specific + + + align:start position:0% +graphs I just have to check the specific +inequality for all integers and which is + + align:start position:0% +inequality for all integers and which is + + + align:start position:0% +inequality for all integers and which is +straightforward + + align:start position:0% + + + + align:start position:0% + +all right so let's see how to prove that + + align:start position:0% +all right so let's see how to prove that + + + align:start position:0% +all right so let's see how to prove that +inequality up there and here we're I + + align:start position:0% +inequality up there and here we're I + + + align:start position:0% +inequality up there and here we're I +mean we're not going to exactly use the + + align:start position:0% +mean we're not going to exactly use the + + + align:start position:0% +mean we're not going to exactly use the +theorems about griffons but it's useful + + align:start position:0% +theorems about griffons but it's useful + + + align:start position:0% +theorems about griffons but it's useful +to think about graphics so first okay so + + align:start position:0% +to think about graphics so first okay so + + + align:start position:0% +to think about graphics so first okay so +in the if and only if one of the + + align:start position:0% +in the if and only if one of the + + + align:start position:0% +in the if and only if one of the +directions is trivial okay so let's get + + align:start position:0% +directions is trivial okay so let's get + + + align:start position:0% +directions is trivial okay so let's get +that out of the way first + + align:start position:0% +that out of the way first + + + align:start position:0% +that out of the way first +but also so for the if direction first + + align:start position:0% +but also so for the if direction first + + + align:start position:0% +but also so for the if direction first +note that this is true for all graphs if + + align:start position:0% +note that this is true for all graphs if + + + align:start position:0% +note that this is true for all graphs if +and only if it is true for all graph + + align:start position:0% +and only if it is true for all graph + + + align:start position:0% +and only if it is true for all graph +phones and where I replace G by W by the + + align:start position:0% +phones and where I replace G by W by the + + + align:start position:0% +phones and where I replace G by W by the +general theory of graph limits and + + align:start position:0% +general theory of graph limits and + + + align:start position:0% +general theory of graph limits and +whatnot this is this is true so in + + align:start position:0% +whatnot this is this is true so in + + + align:start position:0% +whatnot this is this is true so in +particular there's one class of graphs + + align:start position:0% +particular there's one class of graphs + + + align:start position:0% +particular there's one class of graphs +that I would like to look at namely I + + align:start position:0% +that I would like to look at namely I + + + align:start position:0% +that I would like to look at namely I +want to consider the set of note + + align:start position:0% +want to consider the set of note + + + align:start position:0% +want to consider the set of note +weighted so yeah so I want to consider + + align:start position:0% +weighted so yeah so I want to consider + + + align:start position:0% +weighted so yeah so I want to consider +the set of note weighted simple graphs + + align:start position:0% + + + + align:start position:0% + +so note weighted simple graphs by this I + + align:start position:0% +so note weighted simple graphs by this I + + + align:start position:0% +so note weighted simple graphs by this I +mean a graph where some of the edges are + + align:start position:0% +mean a graph where some of the edges are + + + align:start position:0% +mean a graph where some of the edges are +present and I have a node wait wait for + + align:start position:0% +present and I have a node wait wait for + + + align:start position:0% +present and I have a node wait wait for +each node and to normalize things + + align:start position:0% +each node and to normalize things + + + align:start position:0% +each node and to normalize things +properly I'm going to assume that the + + align:start position:0% +properly I'm going to assume that the + + + align:start position:0% +properly I'm going to assume that the +nodes weights add up to 1 now you see + + align:start position:0% +nodes weights add up to 1 now you see + + + align:start position:0% +nodes weights add up to 1 now you see +that each graph like that you can + + align:start position:0% +that each graph like that you can + + + align:start position:0% +that each graph like that you can +represent it by a graph on + + align:start position:0% + + + + align:start position:0% + +where so you can have a graph own + + align:start position:0% +where so you can have a graph own + + + align:start position:0% +where so you can have a graph own +they're not meant to be the same picture + + align:start position:0% +they're not meant to be the same picture + + + align:start position:0% +they're not meant to be the same picture +but you know you have some platform like + + align:start position:0% +but you know you have some platform like + + + align:start position:0% +but you know you have some platform like +this which corresponds to a node + + align:start position:0% +this which corresponds to a node + + + align:start position:0% +this which corresponds to a node +weighted graph and the set of such node + + align:start position:0% +weighted graph and the set of such node + + + align:start position:0% +weighted graph and the set of such node +weighted graphs is dense in the space of + + align:start position:0% +weighted graphs is dense in the space of + + + align:start position:0% +weighted graphs is dense in the space of +griffons in particular as far as graph + + align:start position:0% +griffons in particular as far as graph + + + align:start position:0% +griffons in particular as far as graph +densities are concerned they include all + + align:start position:0% +densities are concerned they include all + + + align:start position:0% +densities are concerned they include all +the simple graphs so it's the physis i + + align:start position:0% +the simple graphs so it's the physis i + + + align:start position:0% +the simple graphs so it's the physis i +mean it's in its equivalent to this okay + + align:start position:0% +mean it's in its equivalent to this okay + + + align:start position:0% +mean it's in its equivalent to this okay +the inequality is equivalent to it being + + align:start position:0% +the inequality is equivalent to it being + + + align:start position:0% +the inequality is equivalent to it being +true for all known weighted simple + + align:start position:0% +true for all known weighted simple + + + align:start position:0% +true for all known weighted simple +graphs but for this space of graphs + + align:start position:0% +graphs but for this space of graphs + + + align:start position:0% +graphs but for this space of graphs +suppose that the inequality fails it's + + align:start position:0% +suppose that the inequality fails it's + + + align:start position:0% +suppose that the inequality fails it's +post inequality is false then there + + align:start position:0% +post inequality is false then there + + + align:start position:0% +post inequality is false then there +exists a node weighted simple graph + + align:start position:0% + + + + align:start position:0% + +going to actually drop the word simple + + align:start position:0% +going to actually drop the word simple + + + align:start position:0% +going to actually drop the word simple +from now on so no weighted graph H such + + align:start position:0% +from now on so no weighted graph H such + + + align:start position:0% +from now on so no weighted graph H such +that half of H being the above sum is + + align:start position:0% +that half of H being the above sum is + + + align:start position:0% +that half of H being the above sum is +less than zero and there could be as + + align:start position:0% +less than zero and there could be as + + + align:start position:0% +less than zero and there could be as +many possibilities for such an H but let + + align:start position:0% +many possibilities for such an H but let + + + align:start position:0% +many possibilities for such an H but let +me choose one among all the possible HS + + align:start position:0% +me choose one among all the possible HS + + + align:start position:0% +me choose one among all the possible HS +let's choose one that is minimal in the + + align:start position:0% +let's choose one that is minimal in the + + + align:start position:0% +let's choose one that is minimal in the +sense that it has the smallest possible + + align:start position:0% +sense that it has the smallest possible + + + align:start position:0% +sense that it has the smallest possible +number of nodes so it is minimum + + align:start position:0% + + + + align:start position:0% + +right as a minimum number of notes and + + align:start position:0% +right as a minimum number of notes and + + + align:start position:0% +right as a minimum number of notes and +furthermore among all H with this number + + align:start position:0% +furthermore among all H with this number + + + align:start position:0% +furthermore among all H with this number +of notes choose the note weights which + + align:start position:0% +of notes choose the note weights which + + + align:start position:0% +of notes choose the note weights which +were to note by a1 through am summing to + + align:start position:0% +were to note by a1 through am summing to + + + align:start position:0% +were to note by a1 through am summing to +1 chooses note weights so that this + + align:start position:0% +1 chooses note weights so that this + + + align:start position:0% +1 chooses note weights so that this +expression this sum is minimized and by + + align:start position:0% +expression this sum is minimized and by + + + align:start position:0% +expression this sum is minimized and by +compactness and now we're not even + + align:start position:0% +compactness and now we're not even + + + align:start position:0% +compactness and now we're not even +talking about compactness space of graph + + align:start position:0% +talking about compactness space of graph + + + align:start position:0% +talking about compactness space of graph +once you have a finite number of + + align:start position:0% +once you have a finite number of + + + align:start position:0% +once you have a finite number of +parameters it's continuous function so + + align:start position:0% +parameters it's continuous function so + + + align:start position:0% +parameters it's continuous function so +just by compactness there exists such an + + align:start position:0% +just by compactness there exists such an + + + align:start position:0% +just by compactness there exists such an +H for which the minimum is achieved this + + align:start position:0% +H for which the minimum is achieved this + + + align:start position:0% +H for which the minimum is achieved this +is minimizing over integers and here + + align:start position:0% +is minimizing over integers and here + + + align:start position:0% +is minimizing over integers and here +minimizing over finite set of bounded + + align:start position:0% +minimizing over finite set of bounded + + + align:start position:0% +minimizing over finite set of bounded +real numbers so the name of the game now + + align:start position:0% +real numbers so the name of the game now + + + align:start position:0% +real numbers so the name of the game now +is we have this H which is minimizing + + align:start position:0% +is we have this H which is minimizing + + + align:start position:0% +is we have this H which is minimizing +and I want to show that H has certain + + align:start position:0% +and I want to show that H has certain + + + align:start position:0% +and I want to show that H has certain +properties if it doesn't have these + + align:start position:0% +properties if it doesn't have these + + + align:start position:0% +properties if it doesn't have these +properties I can decrease those values + + align:start position:0% + + + + align:start position:0% + +okay so let's see what properties this H + + align:start position:0% +okay so let's see what properties this H + + + align:start position:0% +okay so let's see what properties this H +must have if it has the minimum number + + align:start position:0% +must have if it has the minimum number + + + align:start position:0% +must have if it has the minimum number +of nodes and f of H is minimum possible + + align:start position:0% + + + + align:start position:0% + +the first I claim that all the node + + align:start position:0% +the first I claim that all the node + + + align:start position:0% +the first I claim that all the node +weights are positive if not I can delete + + align:start position:0% +weights are positive if not I can delete + + + align:start position:0% +weights are positive if not I can delete +that node and decrease the number of + + align:start position:0% +that node and decrease the number of + + + align:start position:0% +that node and decrease the number of +nodes I would like to claim that H must + + align:start position:0% +nodes I would like to claim that H must + + + align:start position:0% +nodes I would like to claim that H must +be a complete graph because if some IJ + + align:start position:0% +be a complete graph because if some IJ + + + align:start position:0% +be a complete graph because if some IJ +is not an edge of H so here is different + + align:start position:0% +is not an edge of H so here is different + + + align:start position:0% +is not an edge of H so here is different +from J I don't allow loops H is simple + + align:start position:0% +from J I don't allow loops H is simple + + + align:start position:0% +from J I don't allow loops H is simple +then let's think about what this + + align:start position:0% +then let's think about what this + + + align:start position:0% +then let's think about what this +expression F F H should be so I don't + + align:start position:0% +expression F F H should be so I don't + + + align:start position:0% +expression F F H should be so I don't +want write this down but I won't imagine + + align:start position:0% +want write this down but I won't imagine + + + align:start position:0% +want write this down but I won't imagine +in your head right so you mean you have + + align:start position:0% +in your head right so you mean you have + + + align:start position:0% +in your head right so you mean you have +this this graph on H I'm looking at the + + align:start position:0% +this this graph on H I'm looking at the + + + align:start position:0% +this this graph on H I'm looking at the +creek density it's some polynomial in + + align:start position:0% +creek density it's some polynomial in + + + align:start position:0% +creek density it's some polynomial in +fact it's some multi linear poly it's um + + align:start position:0% +fact it's some multi linear poly it's um + + + align:start position:0% +fact it's some multi linear poly it's um +it's some polynomial in in these node + + align:start position:0% +it's some polynomial in in these node + + + align:start position:0% +it's some polynomial in in these node +weights okay so I want to understand + + align:start position:0% +weights okay so I want to understand + + + align:start position:0% +weights okay so I want to understand +like what is the shape of this + + align:start position:0% +like what is the shape of this + + + align:start position:0% +like what is the shape of this +polynomial as a function of the node + + align:start position:0% +polynomial as a function of the node + + + align:start position:0% +polynomial as a function of the node +weights an observed that has to be + + align:start position:0% +weights an observed that has to be + + + align:start position:0% +weights an observed that has to be +multilinear + + align:start position:0% + + + + align:start position:0% + +in has to be multilinear in particular + + align:start position:0% +in has to be multilinear in particular + + + align:start position:0% +in has to be multilinear in particular +in alpha I and alpha J okay it's a + + align:start position:0% +in alpha I and alpha J okay it's a + + + align:start position:0% +in alpha I and alpha J okay it's a +polynomial that should be clear it is + + align:start position:0% +polynomial that should be clear it is + + + align:start position:0% +polynomial that should be clear it is +multi linear because well you know you + + align:start position:0% +multi linear because well you know you + + + align:start position:0% +multi linear because well you know you +have okay why is it multi learning why + + align:start position:0% +have okay why is it multi learning why + + + align:start position:0% +have okay why is it multi learning why +do I not have alpha I squared that's a + + align:start position:0% +do I not have alpha I squared that's a + + + align:start position:0% +do I not have alpha I squared that's a +term either view okay so we're + + align:start position:0% +term either view okay so we're + + + align:start position:0% +term either view okay so we're +forbidding so here's of a 1 over 2 of 3 + + align:start position:0% +forbidding so here's of a 1 over 2 of 3 + + + align:start position:0% +forbidding so here's of a 1 over 2 of 3 +or 4 so this understand you know what + + align:start position:0% +or 4 so this understand you know what + + + align:start position:0% +or 4 so this understand you know what +the triangle density you know if you + + align:start position:0% +the triangle density you know if you + + + align:start position:0% +the triangle density you know if you +write down the triangle density that's + + align:start position:0% +write down the triangle density that's + + + align:start position:0% +write down the triangle density that's +an expression in in terms of the + + align:start position:0% +an expression in in terms of the + + + align:start position:0% +an expression in in terms of the +parameters think about what comes out + + align:start position:0% +parameters think about what comes out + + + align:start position:0% +parameters think about what comes out +what it looks like and they essentially + + align:start position:0% +what it looks like and they essentially + + + align:start position:0% +what it looks like and they essentially +consist of you choosing a sub graph you + + align:start position:0% +consist of you choosing a sub graph you + + + align:start position:0% +consist of you choosing a sub graph you +cannot have read please okay so it's + + align:start position:0% +cannot have read please okay so it's + + + align:start position:0% +cannot have read please okay so it's +it's multi linear so it's multi linear + + align:start position:0% +it's multi linear so it's multi linear + + + align:start position:0% +it's multi linear so it's multi linear +in particular in alpha I and alpha J so + + align:start position:0% + + + + align:start position:0% + +so no term has the product of I alpha J + + align:start position:0% +so no term has the product of I alpha J + + + align:start position:0% +so no term has the product of I alpha J +in it because I J is not an edge so so + + align:start position:0% +in it because I J is not an edge so so + + + align:start position:0% +in it because I J is not an edge so so +here's what we're really using that + + align:start position:0% +here's what we're really using that + + + align:start position:0% +here's what we're really using that +we're only considering click densities + + align:start position:0% + + + + align:start position:0% + +I said turn up there is completely false + + align:start position:0% +I said turn up there is completely false + + + align:start position:0% +I said turn up there is completely false +without the assumption of Creek + + align:start position:0% +without the assumption of Creek + + + align:start position:0% +without the assumption of Creek +densities if we have a general + + align:start position:0% +densities if we have a general + + + align:start position:0% +densities if we have a general +inequality general linear inequality + + align:start position:0% +inequality general linear inequality + + + align:start position:0% +inequality general linear inequality +than the statement is completely false + + align:start position:0% + + + + align:start position:0% + +so it's multi linear so if we now fix + + align:start position:0% +so it's multi linear so if we now fix + + + align:start position:0% +so it's multi linear so if we now fix +all the other variables and just think + + align:start position:0% +all the other variables and just think + + + align:start position:0% +all the other variables and just think +about how to optimize how to minimize + + align:start position:0% +about how to optimize how to minimize + + + align:start position:0% +about how to optimize how to minimize +half a page by tweaking alpha I and + + align:start position:0% +half a page by tweaking alpha I and + + + align:start position:0% +half a page by tweaking alpha I and +alpha J well it's linear so you should + + align:start position:0% +alpha J well it's linear so you should + + + align:start position:0% +alpha J well it's linear so you should +minimize it by setting one of them to be + + align:start position:0% +minimize it by setting one of them to be + + + align:start position:0% +minimize it by setting one of them to be +zero and that would then decrease the + + align:start position:0% +zero and that would then decrease the + + + align:start position:0% +zero and that would then decrease the +number of nodes so can shift alpha I and + + align:start position:0% +number of nodes so can shift alpha I and + + + align:start position:0% +number of nodes so can shift alpha I and +alpha J while preserving Phi plus alpha + + align:start position:0% +alpha J while preserving Phi plus alpha + + + align:start position:0% +alpha J while preserving Phi plus alpha +J and not changing so not increasing f + + align:start position:0% +J and not changing so not increasing f + + + align:start position:0% +J and not changing so not increasing f +of H and then we get either alpha is + + align:start position:0% +of H and then we get either alpha is + + + align:start position:0% +of H and then we get either alpha is +equal to 0 or alpha J to go to zero in + + align:start position:0% +equal to 0 or alpha J to go to zero in + + + align:start position:0% +equal to 0 or alpha J to go to zero in +which case we decrease the number of + + align:start position:0% +which case we decrease the number of + + + align:start position:0% +which case we decrease the number of +nodes thereby contradicting the + + align:start position:0% +nodes thereby contradicting the + + + align:start position:0% +nodes thereby contradicting the +minimality assumption ok + + align:start position:0% + + + + align:start position:0% + +so this argument here then tells you + + align:start position:0% +so this argument here then tells you + + + align:start position:0% +so this argument here then tells you +that H must be a cook so hence H is + + align:start position:0% +that H must be a cook so hence H is + + + align:start position:0% +that H must be a cook so hence H is +complete and if H is complete then as a + + align:start position:0% +complete and if H is complete then as a + + + align:start position:0% +complete and if H is complete then as a +polynomial in these alphas what should + + align:start position:0% +polynomial in these alphas what should + + + align:start position:0% +polynomial in these alphas what should +it look like + + align:start position:0% +it look like + + + align:start position:0% +it look like +well has to be symmetric with respect to + + align:start position:0% +well has to be symmetric with respect to + + + align:start position:0% +well has to be symmetric with respect to +all these alphas so in particular it has + + align:start position:0% +all these alphas so in particular it has + + + align:start position:0% +all these alphas so in particular it has +to be so since H is complete we see that + + align:start position:0% +to be so since H is complete we see that + + + align:start position:0% +to be so since H is complete we see that +in fact now you can write down exactly + + align:start position:0% +in fact now you can write down exactly + + + align:start position:0% +in fact now you can write down exactly +what f of H is in terms of the + + align:start position:0% +what f of H is in terms of the + + + align:start position:0% +what f of H is in terms of the +parameters described in the problem + + align:start position:0% +parameters described in the problem + + + align:start position:0% +parameters described in the problem +namely it's C R times R factorial times + + align:start position:0% +namely it's C R times R factorial times + + + align:start position:0% +namely it's C R times R factorial times +SR where s r is a symmetric polynomial + + align:start position:0% +SR where s r is a symmetric polynomial + + + align:start position:0% +SR where s r is a symmetric polynomial +where you look at you choose R of the + + align:start position:0% +where you look at you choose R of the + + + align:start position:0% +where you look at you choose R of the +terms R of these alphas for each term in + + align:start position:0% +terms R of these alphas for each term in + + + align:start position:0% +terms R of these alphas for each term in +this sum + + align:start position:0% +this sum + + + align:start position:0% +this sum +it's just elementary symmetric + + align:start position:0% +it's just elementary symmetric + + + align:start position:0% +it's just elementary symmetric +polynomial and I would like to know + + align:start position:0% +polynomial and I would like to know + + + align:start position:0% +polynomial and I would like to know +given such a polynomial how to minimize + + align:start position:0% +given such a polynomial how to minimize + + + align:start position:0% +given such a polynomial how to minimize +this number by choosing the alphas but + + align:start position:0% +this number by choosing the alphas but + + + align:start position:0% +this number by choosing the alphas but +if you think about what happens if you + + align:start position:0% +if you think about what happens if you + + + align:start position:0% +if you think about what happens if you +fix again everything but two of the + + align:start position:0% +fix again everything but two of the + + + align:start position:0% +fix again everything but two of the +alphas so by fixing all I say alpha 3 to + + align:start position:0% +alphas so by fixing all I say alpha 3 to + + + align:start position:0% +alphas so by fixing all I say alpha 3 to +offer n we find that so as a function in + + align:start position:0% +offer n we find that so as a function in + + + align:start position:0% +offer n we find that so as a function in +just alpha 1 and alpha 2 f of H has the + + align:start position:0% +just alpha 1 and alpha 2 f of H has the + + + align:start position:0% +just alpha 1 and alpha 2 f of H has the +following form + + align:start position:0% + + + + align:start position:0% + +and because it's symmetric these two + + align:start position:0% +and because it's symmetric these two + + + align:start position:0% +and because it's symmetric these two +bees actually the same so if we now very + + align:start position:0% +bees actually the same so if we now very + + + align:start position:0% +bees actually the same so if we now very +alpha-1 and alpha-2 but fixing + + align:start position:0% +alpha-1 and alpha-2 but fixing + + + align:start position:0% +alpha-1 and alpha-2 but fixing +everything else because alpha-1 plus + + align:start position:0% +everything else because alpha-1 plus + + + align:start position:0% +everything else because alpha-1 plus +alpha-2 it's constant i can even get rid + + align:start position:0% +alpha-2 it's constant i can even get rid + + + align:start position:0% +alpha-2 it's constant i can even get rid +of this linear part so that linear part + + align:start position:0% +of this linear part so that linear part + + + align:start position:0% +of this linear part so that linear part +is as fixed as a constant I want to + + align:start position:0% +is as fixed as a constant I want to + + + align:start position:0% +is as fixed as a constant I want to +minimize this expression with alpha 1 + + align:start position:0% +minimize this expression with alpha 1 + + + align:start position:0% +minimize this expression with alpha 1 +and alpha 2 plus alpha 2 how fixed so + + align:start position:0% +and alpha 2 plus alpha 2 how fixed so + + + align:start position:0% +and alpha 2 plus alpha 2 how fixed so +there are two possibilities depending on + + align:start position:0% +there are two possibilities depending on + + + align:start position:0% +there are two possibilities depending on +whether C is positive or negative or I + + align:start position:0% +whether C is positive or negative or I + + + align:start position:0% +whether C is positive or negative or I +guess zero so if you're here so + + align:start position:0% +guess zero so if you're here so + + + align:start position:0% +guess zero so if you're here so +depending if C is positive or negative + + align:start position:0% + + + + align:start position:0% + +half it's minimized by either alpha the + + align:start position:0% +half it's minimized by either alpha the + + + align:start position:0% +half it's minimized by either alpha the +two alphas equal to each other or one of + + align:start position:0% +two alphas equal to each other or one of + + + align:start position:0% +two alphas equal to each other or one of +two alphas should be zero + + align:start position:0% +two alphas should be zero + + + align:start position:0% +two alphas should be zero +the latter cannot occur because we + + align:start position:0% +the latter cannot occur because we + + + align:start position:0% +the latter cannot occur because we +assume minimality so the first must + + align:start position:0% +assume minimality so the first must + + + align:start position:0% +assume minimality so the first must +occur and hence by symmetry if you apply + + align:start position:0% +occur and hence by symmetry if you apply + + + align:start position:0% +occur and hence by symmetry if you apply +the same argument to all the other + + align:start position:0% +the same argument to all the other + + + align:start position:0% +the same argument to all the other +alphas all the alphas are equal to each + + align:start position:0% +alphas all the alphas are equal to each + + + align:start position:0% +alphas all the alphas are equal to each +other which means that H is a simple + + align:start position:0% +other which means that H is a simple + + + align:start position:0% +other which means that H is a simple +trick it's basically an unweighted + + align:start position:0% +trick it's basically an unweighted + + + align:start position:0% +trick it's basically an unweighted +clique all right so in other words if + + align:start position:0% +clique all right so in other words if + + + align:start position:0% +clique all right so in other words if +this inequality fails for some H some + + align:start position:0% +this inequality fails for some H some + + + align:start position:0% +this inequality fails for some H some +node weighted H that it must fail for a + + align:start position:0% +node weighted H that it must fail for a + + + align:start position:0% +node weighted H that it must fail for a +simple click H and that's the claim + + align:start position:0% +simple click H and that's the claim + + + align:start position:0% +simple click H and that's the claim +above + + align:start position:0% + + + + align:start position:0% + +okay question if there are two ends yeah + + align:start position:0% +okay question if there are two ends yeah + + + align:start position:0% +okay question if there are two ends yeah +that's thank you so these are two yeah + + align:start position:0% +that's thank you so these are two yeah + + + align:start position:0% +that's thank you so these are two yeah +so these are two different + + align:start position:0% + + + + align:start position:0% + +I'll get questions why can we assume + + align:start position:0% +I'll get questions why can we assume + + + align:start position:0% +I'll get questions why can we assume +that you can choose H so that F of HS + + align:start position:0% +that you can choose H so that F of HS + + + align:start position:0% +that you can choose H so that F of HS +minimized + + align:start position:0% +minimized + + + align:start position:0% +minimized +it's because once okay so you agreed the + + align:start position:0% +it's because once okay so you agreed the + + + align:start position:0% +it's because once okay so you agreed the +first thing you can minimize because the + + align:start position:0% +first thing you can minimize because the + + + align:start position:0% +first thing you can minimize because the +number of notes is a positive integer so + + align:start position:0% +number of notes is a positive integer so + + + align:start position:0% +number of notes is a positive integer so +if there's a counter example we'll + + align:start position:0% +if there's a counter example we'll + + + align:start position:0% +if there's a counter example we'll +choose the minimum counter example now + + align:start position:0% +choose the minimum counter example now + + + align:start position:0% +choose the minimum counter example now +you fix that number of vertices and the + + align:start position:0% +you fix that number of vertices and the + + + align:start position:0% +you fix that number of vertices and the +number of then this is an optimization + + align:start position:0% +number of then this is an optimization + + + align:start position:0% +number of then this is an optimization +problem it's a minimizing continuous + + align:start position:0% +problem it's a minimizing continuous + + + align:start position:0% +problem it's a minimizing continuous +function with a finite number of + + align:start position:0% +function with a finite number of + + + align:start position:0% +function with a finite number of +variables so it has a minimum just by + + align:start position:0% +variables so it has a minimum just by + + + align:start position:0% +variables so it has a minimum just by +compactness of a continuous function so + + align:start position:0% +compactness of a continuous function so + + + align:start position:0% +compactness of a continuous function so +I choose that minimizer any more + + align:start position:0% +I choose that minimizer any more + + + align:start position:0% +I choose that minimizer any more +questions okay so we have this rather + + align:start position:0% +questions okay so we have this rather + + + align:start position:0% +questions okay so we have this rather +general looking theorem so in the second + + align:start position:0% +general looking theorem so in the second + + + align:start position:0% +general looking theorem so in the second +part of today's lecture + + align:start position:0% +part of today's lecture + + + align:start position:0% +part of today's lecture +after taking a short break I want to + + align:start position:0% +after taking a short break I want to + + + align:start position:0% +after taking a short break I want to +discuss what are some of the + + align:start position:0% +discuss what are some of the + + + align:start position:0% +discuss what are some of the +consequences and also variations of that + + align:start position:0% +consequences and also variations of that + + + align:start position:0% +consequences and also variations of that +statement up there and I want to also + + align:start position:0% +statement up there and I want to also + + + align:start position:0% +statement up there and I want to also +show you what the rest of this picture + + align:start position:0% +show you what the rest of this picture + + + align:start position:0% +show you what the rest of this picture +looks like so let's continue to deduce + + align:start position:0% +looks like so let's continue to deduce + + + align:start position:0% +looks like so let's continue to deduce +some consequences of this theorem up + + align:start position:0% +some consequences of this theorem up + + + align:start position:0% +some consequences of this theorem up +there that tells us that it is pretty + + align:start position:0% +there that tells us that it is pretty + + + align:start position:0% +there that tells us that it is pretty +easy to decide linear inequalities + + align:start position:0% +easy to decide linear inequalities + + + align:start position:0% +easy to decide linear inequalities +between clique densities namely to + + align:start position:0% +between clique densities namely to + + + align:start position:0% +between clique densities namely to +decided just check the inequalities on + + align:start position:0% +decided just check the inequalities on + + + align:start position:0% +decided just check the inequalities on +cliques so as a corollary for each for + + align:start position:0% +cliques so as a corollary for each for + + + align:start position:0% +cliques so as a corollary for each for +each n for each and the extremal points + + align:start position:0% + + + + align:start position:0% + +so the extremal points + + align:start position:0% +so the extremal points + + + align:start position:0% +so the extremal points +of the convex hull this set where I + + align:start position:0% +of the convex hull this set where I + + + align:start position:0% +of the convex hull this set where I +record the Creek densities overall graph + + align:start position:0% +record the Creek densities overall graph + + + align:start position:0% +record the Creek densities overall graph +phones W so so think about this set as + + align:start position:0% +phones W so so think about this set as + + + align:start position:0% +phones W so so think about this set as +the higher dimensional generalization of + + align:start position:0% +the higher dimensional generalization of + + + align:start position:0% +the higher dimensional generalization of +that picture I drew up there but no nope + + align:start position:0% +that picture I drew up there but no nope + + + align:start position:0% +that picture I drew up there but no nope +previously we had N equals to 3 we were + + align:start position:0% +previously we had N equals to 3 we were + + + align:start position:0% +previously we had N equals to 3 we were +still interested in N equals to 3 but in + + align:start position:0% +still interested in N equals to 3 but in + + + align:start position:0% +still interested in N equals to 3 but in +general you have this set sitting in + + align:start position:0% +general you have this set sitting in + + + align:start position:0% +general you have this set sitting in +this box and okay so it's it's some set + + align:start position:0% +this box and okay so it's it's some set + + + align:start position:0% +this box and okay so it's it's some set +and if I take the convex hull of this + + align:start position:0% +and if I take the convex hull of this + + + align:start position:0% +and if I take the convex hull of this +set what that theorem tells us and of + + align:start position:0% +set what that theorem tells us and of + + + align:start position:0% +set what that theorem tells us and of +course maybe one bit of extra + + align:start position:0% +course maybe one bit of extra + + + align:start position:0% +course maybe one bit of extra +computation but what it tells us is that + + align:start position:0% +computation but what it tells us is that + + + align:start position:0% +computation but what it tells us is that +the extremal points are precisely the + + align:start position:0% +the extremal points are precisely the + + + align:start position:0% +the extremal points are precisely the +points given by W equals to K M evaluate + + align:start position:0% +points given by W equals to K M evaluate + + + align:start position:0% +points given by W equals to K M evaluate +find what this point is for each M you + + align:start position:0% +find what this point is for each M you + + + align:start position:0% +find what this point is for each M you +have a bunch of points and those are the + + align:start position:0% +have a bunch of points and those are the + + + align:start position:0% +have a bunch of points and those are the +convex hull so LLL astray by drawing + + align:start position:0% +convex hull so LLL astray by drawing + + + align:start position:0% +convex hull so LLL astray by drawing +what the points are for the picture over + + align:start position:0% +what the points are for the picture over + + + align:start position:0% +what the points are for the picture over +there but it essentially follows from + + align:start position:0% +there but it essentially follows from + + + align:start position:0% +there but it essentially follows from +polar botches theorem with one expert of + + align:start position:0% +polar botches theorem with one expert of + + + align:start position:0% +polar botches theorem with one expert of +computation to make sure that all of + + align:start position:0% +computation to make sure that all of + + + align:start position:0% +computation to make sure that all of +these are actually their extremal points + + align:start position:0% +these are actually their extremal points + + + align:start position:0% +these are actually their extremal points +of the convex hull none of them is + + align:start position:0% +of the convex hull none of them is + + + align:start position:0% +of the convex hull none of them is +contained in the convex hull of the + + align:start position:0% +contained in the convex hull of the + + + align:start position:0% +contained in the convex hull of the +other points so for example we can also + + align:start position:0% +other points so for example we can also + + + align:start position:0% +other points so for example we can also +produce very easily + + align:start position:0% +produce very easily + + + align:start position:0% +produce very easily +pterence theorem + + align:start position:0% + + + + align:start position:0% + +so what is Tehran's theorem tell us it + + align:start position:0% +so what is Tehran's theorem tell us it + + + align:start position:0% +so what is Tehran's theorem tell us it +tells us that if the R plus 1 density R + + align:start position:0% +tells us that if the R plus 1 density R + + + align:start position:0% +tells us that if the R plus 1 density R +plus 1 click density is 0 then the K 2 + + align:start position:0% +plus 1 click density is 0 then the K 2 + + + align:start position:0% +plus 1 click density is 0 then the K 2 +density is at most 1 minus R so why does + + align:start position:0% +density is at most 1 minus R so why does + + + align:start position:0% +density is at most 1 minus R so why does +Tehran's term follow from the above + + align:start position:0% +Tehran's term follow from the above + + + align:start position:0% +Tehran's term follow from the above +claims it should follow because all the + + align:start position:0% +claims it should follow because all the + + + align:start position:0% +claims it should follow because all the +data here has to do with qlik densities + + align:start position:0% +data here has to do with qlik densities + + + align:start position:0% +data here has to do with qlik densities +and everything which so far says that if + + align:start position:0% +and everything which so far says that if + + + align:start position:0% +and everything which so far says that if +you just want to understand linear + + align:start position:0% +you just want to understand linear + + + align:start position:0% +you just want to understand linear +inequalities between Creek densities + + align:start position:0% +inequalities between Creek densities + + + align:start position:0% +inequalities between Creek densities +it's super easy + + align:start position:0% + + + + align:start position:0% + +maybe I draw the picture for triangles + + align:start position:0% +maybe I draw the picture for triangles + + + align:start position:0% +maybe I draw the picture for triangles +and then you'll see what it's like so + + align:start position:0% +and then you'll see what it's like so + + + align:start position:0% +and then you'll see what it's like so +the corollary tells us for this picture + + align:start position:0% +the corollary tells us for this picture + + + align:start position:0% +the corollary tells us for this picture +corresponding to N equals to 3 what the + + align:start position:0% +corresponding to N equals to 3 what the + + + align:start position:0% +corresponding to N equals to 3 what the +points the extreme points of the convex + + align:start position:0% +points the extreme points of the convex + + + align:start position:0% +points the extreme points of the convex +hull are so maybe let me draw these + + align:start position:0% +hull are so maybe let me draw these + + + align:start position:0% +hull are so maybe let me draw these +points for you so one of these points is + + align:start position:0% +points for you so one of these points is + + + align:start position:0% +points for you so one of these points is +it's 1/2 comma 0 so that corresponds to + + align:start position:0% +it's 1/2 comma 0 so that corresponds to + + + align:start position:0% +it's 1/2 comma 0 so that corresponds to +men-tel's theorem now if you go to the + + align:start position:0% +men-tel's theorem now if you go to the + + + align:start position:0% +men-tel's theorem now if you go to the +other values of M you find that those + + align:start position:0% +other values of M you find that those + + + align:start position:0% +other values of M you find that those +points so the extreme points they are of + + align:start position:0% +points so the extreme points they are of + + + align:start position:0% +points so the extreme points they are of +the form n minus 1 divided by m m minus + + align:start position:0% +the form n minus 1 divided by m m minus + + + align:start position:0% +the form n minus 1 divided by m m minus +1 and minus 2 divided by M Squared for + + align:start position:0% +1 and minus 2 divided by M Squared for + + + align:start position:0% +1 and minus 2 divided by M Squared for +positive integers + + align:start position:0% +positive integers + + + align:start position:0% +positive integers +M okay so for m equal stitute that's the + + align:start position:0% +M okay so for m equal stitute that's the + + + align:start position:0% +M okay so for m equal stitute that's the +point that we just drew and the next + + align:start position:0% +point that we just drew and the next + + + align:start position:0% +point that we just drew and the next +point okay so next two points one-third + + align:start position:0% +point okay so next two points one-third + + + align:start position:0% +point okay so next two points one-third +and 1/4 + + align:start position:0% +and 1/4 + + + align:start position:0% +and 1/4 +they are at if you plug it in + + align:start position:0% +they are at if you plug it in + + + align:start position:0% + +so - thank you 2/3 and 3/4 they + + align:start position:0% +so - thank you 2/3 and 3/4 they + + + align:start position:0% +so - thank you 2/3 and 3/4 they +correspond to two nines and in 3/8 so + + align:start position:0% +correspond to two nines and in 3/8 so + + + align:start position:0% +correspond to two nines and in 3/8 so +let me show you where these points are + + align:start position:0% +let me show you where these points are + + + align:start position:0% +let me show you where these points are +so they are at here and over there and + + align:start position:0% +so they are at here and over there and + + + align:start position:0% +so they are at here and over there and +you have this sequence of points going + + align:start position:0% +you have this sequence of points going + + + align:start position:0% +you have this sequence of points going +up so this is the convex hull and from + + align:start position:0% +up so this is the convex hull and from + + + align:start position:0% +up so this is the convex hull and from +that information you should already be + + align:start position:0% +that information you should already be + + + align:start position:0% +that information you should already be +able to deduce men-tel's theorem right + + align:start position:0% +able to deduce men-tel's theorem right + + + align:start position:0% +able to deduce men-tel's theorem right +because this right half is not part of + + align:start position:0% +because this right half is not part of + + + align:start position:0% +because this right half is not part of +this convex hull so that's one man tells + + align:start position:0% +this convex hull so that's one man tells + + + align:start position:0% +this convex hull so that's one man tells +theorem is and similarly the deduction + + align:start position:0% +theorem is and similarly the deduction + + + align:start position:0% +theorem is and similarly the deduction +the tehran's theorem also follows by a + + align:start position:0% +the tehran's theorem also follows by a + + + align:start position:0% +the tehran's theorem also follows by a +similar logic so okay so you have this + + align:start position:0% +similar logic so okay so you have this + + + align:start position:0% +similar logic so okay so you have this +sequence of points now it happens that + + align:start position:0% +sequence of points now it happens that + + + align:start position:0% +sequence of points now it happens that +all of these points lie on a curve so + + align:start position:0% +all of these points lie on a curve so + + + align:start position:0% +all of these points lie on a curve so +let me try to draw what this this extra + + align:start position:0% +let me try to draw what this this extra + + + align:start position:0% +let me try to draw what this this extra +curve is ok so there's some curve + + align:start position:0% + + + + align:start position:0% + +there's some curve like that the + + align:start position:0% +there's some curve like that the + + + align:start position:0% +there's some curve like that the +equation of this curve happens to be X + + align:start position:0% +equation of this curve happens to be X + + + align:start position:0% +equation of this curve happens to be X +2x minus 1 + + align:start position:0% +2x minus 1 + + + align:start position:0% +2x minus 1 +and because the regions is contained in + + align:start position:0% +and because the regions is contained in + + + align:start position:0% +and because the regions is contained in +the convex all the yellow points it has + + align:start position:0% +the convex all the yellow points it has + + + align:start position:0% +the convex all the yellow points it has +certainly lies above this convex red + + align:start position:0% +certainly lies above this convex red + + + align:start position:0% +certainly lies above this convex red +curve you've seen this red curve before + + align:start position:0% + + + + align:start position:0% + +from where + + align:start position:0% + + + + align:start position:0% + +so what is the same saying that if your + + align:start position:0% +so what is the same saying that if your + + + align:start position:0% +so what is the same saying that if your +edge density is beyond above 1/2 then + + align:start position:0% +edge density is beyond above 1/2 then + + + align:start position:0% +edge density is beyond above 1/2 then +you have some lower bound on the + + align:start position:0% +you have some lower bound on the + + + align:start position:0% +you have some lower bound on the +triangle density where have we seen this + + align:start position:0% +triangle density where have we seen this + + + align:start position:0% +triangle density where have we seen this +before problem set 1 there's a problem + + align:start position:0% +before problem set 1 there's a problem + + + align:start position:0% +before problem set 1 there's a problem +problem set 1 that says exactly this + + align:start position:0% +problem set 1 that says exactly this + + + align:start position:0% +problem set 1 that says exactly this +inequality so go back and compare what I + + align:start position:0% +inequality so go back and compare what I + + + align:start position:0% +inequality so go back and compare what I +did ok but of course the the convex hull + + align:start position:0% +did ok but of course the the convex hull + + + align:start position:0% +did ok but of course the the convex hull +result helps you even a little bit more + + align:start position:0% +result helps you even a little bit more + + + align:start position:0% +result helps you even a little bit more +right namely that you can draw line + + align:start position:0% +right namely that you can draw line + + + align:start position:0% +right namely that you can draw line +segments between these convex hull + + align:start position:0% +segments between these convex hull + + + align:start position:0% +segments between these convex hull +points so you have some polygonal region + + align:start position:0% +points so you have some polygonal region + + + align:start position:0% +points so you have some polygonal region +there lower bounds the actual region ok + + align:start position:0% +there lower bounds the actual region ok + + + align:start position:0% +there lower bounds the actual region ok +so what is the actual region so leaving + + align:start position:0% +so what is the actual region so leaving + + + align:start position:0% +so what is the actual region so leaving +you in suspense but so let me tell you + + align:start position:0% +you in suspense but so let me tell you + + + align:start position:0% +you in suspense but so let me tell you +what the actual region is now so it + + align:start position:0% +what the actual region is now so it + + + align:start position:0% +what the actual region is now so it +turns out to be actually it's beautiful + + align:start position:0% +turns out to be actually it's beautiful + + + align:start position:0% +turns out to be actually it's beautiful +and it's quite deep that the region is + + align:start position:0% +and it's quite deep that the region is + + + align:start position:0% +and it's quite deep that the region is +now completely understood and it's a + + align:start position:0% +now completely understood and it's a + + + align:start position:0% +now completely understood and it's a +fairly recent results only about 10 + + align:start position:0% +fairly recent results only about 10 + + + align:start position:0% +fairly recent results only about 10 +years ago roughly that there are some + + align:start position:0% +years ago roughly that there are some + + + align:start position:0% +years ago roughly that there are some +concave curves the sequence of scallops + + align:start position:0% +concave curves the sequence of scallops + + + align:start position:0% +concave curves the sequence of scallops +going up to the top right corner and + + align:start position:0% +going up to the top right corner and + + + align:start position:0% +going up to the top right corner and +this is understood to be the complete + + align:start position:0% +this is understood to be the complete + + + align:start position:0% +this is understood to be the complete +region between these lower and upper + + align:start position:0% +region between these lower and upper + + + align:start position:0% +region between these lower and upper +curves so this is the complete set of + + align:start position:0% +curves so this is the complete set of + + + align:start position:0% +curves so this is the complete set of +feasible regions for edge versus + + align:start position:0% +feasible regions for edge versus + + + align:start position:0% +feasible regions for edge versus +triangle densities ok so this lower + + align:start position:0% +triangle densities ok so this lower + + + align:start position:0% +triangle densities ok so this lower +curve is a difficult result due to rasp + + align:start position:0% +curve is a difficult result due to rasp + + + align:start position:0% +curve is a difficult result due to rasp +or off and I want to just give you a + + align:start position:0% +or off and I want to just give you a + + + align:start position:0% +or off and I want to just give you a +statement what what this curve is and + + align:start position:0% +statement what what this curve is and + + + align:start position:0% +statement what what this curve is and +grasp or off came up with this machinery + + align:start position:0% +grasp or off came up with this machinery + + + align:start position:0% +grasp or off came up with this machinery +this technique now by the name of flag + + align:start position:0% +this technique now by the name of flag + + + align:start position:0% +this technique now by the name of flag +algebra so he came up with his name + + align:start position:0% + + + + align:start position:0% + +so I won't really tell you what flag + + align:start position:0% +so I won't really tell you what flag + + + align:start position:0% +so I won't really tell you what flag +algebra is but it's kind of a + + align:start position:0% +algebra is but it's kind of a + + + align:start position:0% +algebra is but it's kind of a +computerized way of doing cauchy-schwarz + + align:start position:0% +computerized way of doing cauchy-schwarz + + + align:start position:0% +computerized way of doing cauchy-schwarz +inequality so many of our proofs for + + align:start position:0% +inequality so many of our proofs for + + + align:start position:0% +inequality so many of our proofs for +these craft weather inequalities they go + + align:start position:0% +these craft weather inequalities they go + + + align:start position:0% +these craft weather inequalities they go +through some kind of cauchy-schwarz or + + align:start position:0% +through some kind of cauchy-schwarz or + + + align:start position:0% +through some kind of cauchy-schwarz or +sum of squares equivalently but there + + align:start position:0% +sum of squares equivalently but there + + + align:start position:0% +sum of squares equivalently but there +are some you know very large or + + align:start position:0% +are some you know very large or + + + align:start position:0% +are some you know very large or +difficult inequalities you can also + + align:start position:0% +difficult inequalities you can also + + + align:start position:0% +difficult inequalities you can also +prove this way but it may be difficult + + align:start position:0% +prove this way but it may be difficult + + + align:start position:0% +prove this way but it may be difficult +to find exactly what is the actual + + align:start position:0% +to find exactly what is the actual + + + align:start position:0% +to find exactly what is the actual +inequality the chain of Cauchy Schwarz + + align:start position:0% +inequality the chain of Cauchy Schwarz + + + align:start position:0% +inequality the chain of Cauchy Schwarz +or the sum of squares that you you + + align:start position:0% +or the sum of squares that you you + + + align:start position:0% +or the sum of squares that you you +should write down so this machinery flag + + align:start position:0% +should write down so this machinery flag + + + align:start position:0% +should write down so this machinery flag +algebra is a language is a framework for + + align:start position:0% +algebra is a language is a framework for + + + align:start position:0% +algebra is a language is a framework for +setting up those sum of squares + + align:start position:0% +setting up those sum of squares + + + align:start position:0% +setting up those sum of squares +inequalities in the context of proving + + align:start position:0% +inequalities in the context of proving + + + align:start position:0% +inequalities in the context of proving +graph theoretic inequalities so it can + + align:start position:0% +graph theoretic inequalities so it can + + + align:start position:0% +graph theoretic inequalities so it can +be used in many different ways and + + align:start position:0% +be used in many different ways and + + + align:start position:0% +be used in many different ways and +notably a lot of people have used + + align:start position:0% +notably a lot of people have used + + + align:start position:0% +notably a lot of people have used +serious computer computations if I want + + align:start position:0% +serious computer computations if I want + + + align:start position:0% +serious computer computations if I want +to prove something is true I plug it + + align:start position:0% +to prove something is true I plug it + + + align:start position:0% +to prove something is true I plug it +into what's called a semi definite + + align:start position:0% +into what's called a semi definite + + + align:start position:0% +into what's called a semi definite +program that allows me to decide what + + align:start position:0% +program that allows me to decide what + + + align:start position:0% +program that allows me to decide what +kinds of cauchy-schwarz inequality I + + align:start position:0% +kinds of cauchy-schwarz inequality I + + + align:start position:0% +kinds of cauchy-schwarz inequality I +should be applying to derive the result + + align:start position:0% +should be applying to derive the result + + + align:start position:0% +should be applying to derive the result +I want to prove so that's what flag + + align:start position:0% +I want to prove so that's what flag + + + align:start position:0% +I want to prove so that's what flag +algebra roughly is so what Ross Perot + + align:start position:0% +algebra roughly is so what Ross Perot + + + align:start position:0% +algebra roughly is so what Ross Perot +proved is the following ross perot's + + align:start position:0% +proved is the following ross perot's + + + align:start position:0% +proved is the following ross perot's +theorem which is strong up there that's + + align:start position:0% +theorem which is strong up there that's + + + align:start position:0% +theorem which is strong up there that's +the lower curve is that for fixed okay + + align:start position:0% +the lower curve is that for fixed okay + + + align:start position:0% +the lower curve is that for fixed okay +so for a fixed value of edge densities + + align:start position:0% + + + + align:start position:0% + +if it lies between two specific points + + align:start position:0% +if it lies between two specific points + + + align:start position:0% +if it lies between two specific points +drawn the ball + + align:start position:0% + + + + align:start position:0% + +the minimum value of triangle density + + align:start position:0% +the minimum value of triangle density + + + align:start position:0% +the minimum value of triangle density +with that fixed value of edge density is + + align:start position:0% +with that fixed value of edge density is + + + align:start position:0% +with that fixed value of edge density is +obtained via the following construction + + align:start position:0% + + + + align:start position:0% + +it's attained by the step function graph + + align:start position:0% +it's attained by the step function graph + + + align:start position:0% +it's attained by the step function graph +on corresponding to to a K clique so a + + align:start position:0% +on corresponding to to a K clique so a + + + align:start position:0% +on corresponding to to a K clique so a +complete graph on K vertices with node + + align:start position:0% +complete graph on K vertices with node + + + align:start position:0% +complete graph on K vertices with node +weights now 4 1 3 over K sum into 1 and + + align:start position:0% +weights now 4 1 3 over K sum into 1 and + + + align:start position:0% +weights now 4 1 3 over K sum into 1 and +such that the first K minus 1 of the + + align:start position:0% +such that the first K minus 1 of the + + + align:start position:0% +such that the first K minus 1 of the +node weights are equal and the last one + + align:start position:0% +node weights are equal and the last one + + + align:start position:0% +node weights are equal and the last one +is smaller all right and the point here + + align:start position:0% +is smaller all right and the point here + + + align:start position:0% +is smaller all right and the point here +is that if you are given a specific edge + + align:start position:0% +is that if you are given a specific edge + + + align:start position:0% +is that if you are given a specific edge +weight edge density then there's a + + align:start position:0% +weight edge density then there's a + + + align:start position:0% +weight edge density then there's a +unique choice of these alphas that + + align:start position:0% +unique choice of these alphas that + + + align:start position:0% +unique choice of these alphas that +achieved that edge density and that is + + align:start position:0% +achieved that edge density and that is + + + align:start position:0% +achieved that edge density and that is +the graph on you should use that + + align:start position:0% +the graph on you should use that + + + align:start position:0% +the graph on you should use that +minimizes the triangle density describes + + align:start position:0% +minimizes the triangle density describes + + + align:start position:0% +minimizes the triangle density describes +the lower curve you can write down + + align:start position:0% +the lower curve you can write down + + + align:start position:0% +the lower curve you can write down +specific equations for the lower curve + + align:start position:0% +specific equations for the lower curve + + + align:start position:0% +specific equations for the lower curve +but it's not so important this is a more + + align:start position:0% +but it's not so important this is a more + + + align:start position:0% +but it's not so important this is a more +important description these are the + + align:start position:0% +important description these are the + + + align:start position:0% +important description these are the +graphs that come out and what is + + align:start position:0% +graphs that come out and what is + + + align:start position:0% +graphs that come out and what is +something that is actually quite I mean + + align:start position:0% +something that is actually quite I mean + + + align:start position:0% +something that is actually quite I mean +part why you should suspect this theorem + + align:start position:0% +part why you should suspect this theorem + + + align:start position:0% +part why you should suspect this theorem +is difficult is that unlike Tehran's + + align:start position:0% +is difficult is that unlike Tehran's + + + align:start position:0% +is difficult is that unlike Tehran's +theorem right appearance term which + + align:start position:0% +theorem right appearance term which + + + align:start position:0% +theorem right appearance term which +corresponds to all those discrete points + + align:start position:0% +corresponds to all those discrete points + + + align:start position:0% +corresponds to all those discrete points +interest or the minimizer is unique I + + align:start position:0% +interest or the minimizer is unique I + + + align:start position:0% +interest or the minimizer is unique I +tell you at the number I tell you that + + align:start position:0% +tell you at the number I tell you that + + + align:start position:0% +tell you at the number I tell you that +the edge density is 2/3 + + align:start position:0% +the edge density is 2/3 + + + align:start position:0% +the edge density is 2/3 +I want me to minimize the number of + + align:start position:0% +I want me to minimize the number of + + + align:start position:0% +I want me to minimize the number of +triangles nothing turns there but it + + align:start position:0% +triangles nothing turns there but it + + + align:start position:0% +triangles nothing turns there but it +turns out that this extremal point is is + + align:start position:0% +turns out that this extremal point is is + + + align:start position:0% +turns out that this extremal point is is +unique essentially corresponds to a + + align:start position:0% +unique essentially corresponds to a + + + align:start position:0% +unique essentially corresponds to a +complete three-part a graph + + align:start position:0% +complete three-part a graph + + + align:start position:0% +complete three-part a graph +before the intermediate values the + + align:start position:0% +before the intermediate values the + + + align:start position:0% +before the intermediate values the +constructions are not unique so unless + + align:start position:0% + + + + align:start position:0% + +the k2 density is exactly of this form + + align:start position:0% +the k2 density is exactly of this form + + + align:start position:0% +the k2 density is exactly of this form +the minimizer is not unique and the + + align:start position:0% +the minimizer is not unique and the + + + align:start position:0% +the minimizer is not unique and the +reason why it is not unique is that you + + align:start position:0% +reason why it is not unique is that you + + + align:start position:0% +reason why it is not unique is that you +can replace okay so so what's going on + + align:start position:0% +can replace okay so so what's going on + + + align:start position:0% +can replace okay so so what's going on +here so you have this graph on for 1 + + align:start position:0% +here so you have this graph on for 1 + + + align:start position:0% +here so you have this graph on for 1 +alpha 2 alpha 3 I can replace this graph + + align:start position:0% +alpha 2 alpha 3 I can replace this graph + + + align:start position:0% +alpha 2 alpha 3 I can replace this graph +on here by any triangle free graph all + + align:start position:0% +on here by any triangle free graph all + + + align:start position:0% +on here by any triangle free graph all +of the same edge density and there are + + align:start position:0% +of the same edge density and there are + + + align:start position:0% +of the same edge density and there are +lots and lots of them and the non + + align:start position:0% +lots and lots of them and the non + + + align:start position:0% +lots and lots of them and the non +uniqueness of the minimizer makes this + + align:start position:0% +uniqueness of the minimizer makes this + + + align:start position:0% +uniqueness of the minimizer makes this +minimization problem much more difficult + + align:start position:0% + + + + align:start position:0% + +so ross perot proved this result for x + + align:start position:0% +so ross perot proved this result for x + + + align:start position:0% +so ross perot proved this result for x +verses triangle densities and this + + align:start position:0% +verses triangle densities and this + + + align:start position:0% +verses triangle densities and this +program was later completed to k4 and + + align:start position:0% +program was later completed to k4 and + + + align:start position:0% +program was later completed to k4 and +more generally to kr so k4 is due to a + + align:start position:0% +more generally to kr so k4 is due to a + + + align:start position:0% +more generally to kr so k4 is due to a +result of Nikki for off and the kr + + align:start position:0% +result of Nikki for off and the kr + + + align:start position:0% +result of Nikki for off and the kr +result of right so a similar picture + + align:start position:0% +result of right so a similar picture + + + align:start position:0% +result of right so a similar picture +it's more or less that picture up there + + align:start position:0% +it's more or less that picture up there + + + align:start position:0% +it's more or less that picture up there +but with the actual numbers shifted if + + align:start position:0% +but with the actual numbers shifted if + + + align:start position:0% +but with the actual numbers shifted if +instead of H versus triangle it is now H + + align:start position:0% +instead of H versus triangle it is now H + + + align:start position:0% +instead of H versus triangle it is now H +versus kr I should say that it's worth + + align:start position:0% +versus kr I should say that it's worth + + + align:start position:0% +versus kr I should say that it's worth +this is a picture that I drew up there + + align:start position:0% +this is a picture that I drew up there + + + align:start position:0% +this is a picture that I drew up there +and this is roughly the picture you see + + align:start position:0% +and this is roughly the picture you see + + + align:start position:0% +and this is roughly the picture you see +in textbooks + + align:start position:0% +in textbooks + + + align:start position:0% +in textbooks +you know how they draw this these + + align:start position:0% +you know how they draw this these + + + align:start position:0% +you know how they draw this these +scallops I once plot + + align:start position:0% +scallops I once plot + + + align:start position:0% +scallops I once plot +what this picture looks like in + + align:start position:0% +what this picture looks like in + + + align:start position:0% +what this picture looks like in +mathematica just to see for myself what + + align:start position:0% +mathematica just to see for myself what + + + align:start position:0% +mathematica just to see for myself what +the actual graph is and it doesn't + + align:start position:0% +the actual graph is and it doesn't + + + align:start position:0% +the actual graph is and it doesn't +actually look like that the the concave + + align:start position:0% +actually look like that the the concave + + + align:start position:0% +actually look like that the the concave +nurse it's very subtle if you draw on a + + align:start position:0% +nurse it's very subtle if you draw on a + + + align:start position:0% +nurse it's very subtle if you draw on a +computer they look like straight lines + + align:start position:0% +computer they look like straight lines + + + align:start position:0% +computer they look like straight lines +so in some sense that's a cartoon right + + align:start position:0% +so in some sense that's a cartoon right + + + align:start position:0% +so in some sense that's a cartoon right +so the the concave nurse is charactered + + align:start position:0% +so the the concave nurse is charactered + + + align:start position:0% +so the the concave nurse is charactered +so it's not actually as concave I said + + align:start position:0% +so it's not actually as concave I said + + + align:start position:0% +so it's not actually as concave I said +they're strong but I think it's a good + + align:start position:0% +they're strong but I think it's a good + + + align:start position:0% +they're strong but I think it's a good +illustration of what's happening in + + align:start position:0% +illustration of what's happening in + + + align:start position:0% +illustration of what's happening in +reality okay questions so on one hand + + align:start position:0% +reality okay questions so on one hand + + + align:start position:0% +reality okay questions so on one hand +every polynomial graph inequality well I + + align:start position:0% +every polynomial graph inequality well I + + + align:start position:0% +every polynomial graph inequality well I +mean by polynomial graph inequality so + + align:start position:0% +mean by polynomial graph inequality so + + + align:start position:0% +mean by polynomial graph inequality so +something like suppose I have some + + align:start position:0% +something like suppose I have some + + + align:start position:0% +something like suppose I have some +inequality of this form so and I want to + + align:start position:0% +inequality of this form so and I want to + + + align:start position:0% +inequality of this form so and I want to +know is this true + + align:start position:0% +know is this true + + + align:start position:0% +know is this true +it turns out that I don't actually need + + align:start position:0% +it turns out that I don't actually need + + + align:start position:0% +it turns out that I don't actually need +these squares in some sense because I + + align:start position:0% +these squares in some sense because I + + + align:start position:0% +these squares in some sense because I +can always replace them by what happens + + align:start position:0% +can always replace them by what happens + + + align:start position:0% +can always replace them by what happens +if you take disjoint unions so all I'm + + align:start position:0% +if you take disjoint unions so all I'm + + + align:start position:0% +if you take disjoint unions so all I'm +trying to say is that every polynomial + + align:start position:0% +trying to say is that every polynomial + + + align:start position:0% +trying to say is that every polynomial +graph inequality can be written as a + + align:start position:0% +graph inequality can be written as a + + + align:start position:0% +graph inequality can be written as a +linear graph in equality of densities + + align:start position:0% + + + + align:start position:0% + +but nevertheless this still captures a + + align:start position:0% +but nevertheless this still captures a + + + align:start position:0% +but nevertheless this still captures a +very large class of graph inequalities + + align:start position:0% +very large class of graph inequalities + + + align:start position:0% +very large class of graph inequalities +and if I just give you some arbitrary + + align:start position:0% +and if I just give you some arbitrary + + + align:start position:0% +and if I just give you some arbitrary +one that is not of that form it can be + + align:start position:0% +one that is not of that form it can be + + + align:start position:0% +one that is not of that form it can be +often very difficult to decide whether + + align:start position:0% +often very difficult to decide whether + + + align:start position:0% +often very difficult to decide whether +it is true or not right so over here + + align:start position:0% +it is true or not right so over here + + + align:start position:0% +it is true or not right so over here +it's not so hard you just plug it in and + + align:start position:0% +it's not so hard you just plug it in and + + + align:start position:0% +it's not so hard you just plug it in and +you can decide whether it is true I mean + + align:start position:0% +you can decide whether it is true I mean + + + align:start position:0% +you can decide whether it is true I mean +it's turns out to decide whether this + + align:start position:0% +it's turns out to decide whether this + + + align:start position:0% +it's turns out to decide whether this +inequality is true is it's really a + + align:start position:0% +inequality is true is it's really a + + + align:start position:0% +inequality is true is it's really a +polynomial then you just you just check + + align:start position:0% +polynomial then you just you just check + + + align:start position:0% +polynomial then you just you just check +it's not too hard to do but in general + + align:start position:0% +it's not too hard to do but in general + + + align:start position:0% +it's not too hard to do but in general +suppose I give you an inequality of this + + align:start position:0% +suppose I give you an inequality of this + + + align:start position:0% +suppose I give you an inequality of this +form so some generalized version of a + + align:start position:0% +form so some generalized version of a + + + align:start position:0% +form so some generalized version of a +linear inequality like that it's an even + + align:start position:0% +linear inequality like that it's an even + + + align:start position:0% +linear inequality like that it's an even +decidable if the inequality holds + + align:start position:0% +decidable if the inequality holds + + + align:start position:0% +decidable if the inequality holds +decidable in the sense of like touring + + align:start position:0% +decidable in the sense of like touring + + + align:start position:0% +decidable in the sense of like touring +halting problem so is there some + + align:start position:0% +halting problem so is there some + + + align:start position:0% +halting problem so is there some +computer program just give you this + + align:start position:0% +computer program just give you this + + + align:start position:0% +computer program just give you this +inequality is is it true can you write a + + align:start position:0% +inequality is is it true can you write a + + + align:start position:0% +inequality is is it true can you write a +computer program that decides the + + align:start position:0% +computer program that decides the + + + align:start position:0% +computer program that decides the +truthful is it turns out okay so before + + align:start position:0% +truthful is it turns out okay so before + + + align:start position:0% +truthful is it turns out okay so before +telling you what the answer is let me + + align:start position:0% +telling you what the answer is let me + + + align:start position:0% +telling you what the answer is let me +just put it in some context what about + + align:start position:0% +just put it in some context what about + + + align:start position:0% +just put it in some context what about +more classical questions that before we + + align:start position:0% +more classical questions that before we + + + align:start position:0% +more classical questions that before we +jump in to graph theory if I give you + + align:start position:0% +jump in to graph theory if I give you + + + align:start position:0% +jump in to graph theory if I give you +some polynomial P over the real numbers + + align:start position:0% +some polynomial P over the real numbers + + + align:start position:0% +some polynomial P over the real numbers +okay so yes and I want to check + + align:start position:0% + + + + align:start position:0% + +is that true okay so this is this is not + + align:start position:0% +is that true okay so this is this is not + + + align:start position:0% +is that true okay so this is this is not +you hard this is not too hard but you + + align:start position:0% +you hard this is not too hard but you + + + align:start position:0% +you hard this is not too hard but you +know when if you have multivariate for + + align:start position:0% +know when if you have multivariate for + + + align:start position:0% +know when if you have multivariate for +all real does anyone know the answer is + + align:start position:0% +all real does anyone know the answer is + + + align:start position:0% +all real does anyone know the answer is +this decidable okay so yes you can + + align:start position:0% +this decidable okay so yes you can + + + align:start position:0% +this decidable okay so yes you can +imagine these things were study pretty + + align:start position:0% +imagine these things were study pretty + + + align:start position:0% +imagine these things were study pretty +classically and so it turns out that + + align:start position:0% +classically and so it turns out that + + + align:start position:0% +classically and so it turns out that +every first warder theory over the real + + align:start position:0% +every first warder theory over the real + + + align:start position:0% +every first warder theory over the real +numbers is decidable so this is a result + + align:start position:0% +numbers is decidable so this is a result + + + align:start position:0% +numbers is decidable so this is a result +of tarski + + align:start position:0% +of tarski + + + align:start position:0% +of tarski +and particular such questions are + + align:start position:0% +and particular such questions are + + + align:start position:0% +and particular such questions are +decidable and in fact there's a very + + align:start position:0% +decidable and in fact there's a very + + + align:start position:0% +decidable and in fact there's a very +nice characterization of so there's a + + align:start position:0% +nice characterization of so there's a + + + align:start position:0% +nice characterization of so there's a +result called Alton's theorem that tells + + align:start position:0% +result called Alton's theorem that tells + + + align:start position:0% +result called Alton's theorem that tells +you that every such polynomial if it is + + align:start position:0% +you that every such polynomial if it is + + + align:start position:0% +you that every such polynomial if it is +non-negative then if and only if it can + + align:start position:0% +non-negative then if and only if it can + + + align:start position:0% +non-negative then if and only if it can +be written as a sum of squares of + + align:start position:0% +be written as a sum of squares of + + + align:start position:0% +be written as a sum of squares of +rational functions so there's a very + + align:start position:0% +rational functions so there's a very + + + align:start position:0% +rational functions so there's a very +nice characterization of positiveness of + + align:start position:0% +nice characterization of positiveness of + + + align:start position:0% +nice characterization of positiveness of +polynomials over the reals but now I + + align:start position:0% +polynomials over the reals but now I + + + align:start position:0% +polynomials over the reals but now I +change the question and I ask what about + + align:start position:0% +change the question and I ask what about + + + align:start position:0% +change the question and I ask what about +over the integers right so if I give + + align:start position:0% +over the integers right so if I give + + + align:start position:0% +over the integers right so if I give +your polynomial is it always + + align:start position:0% +your polynomial is it always + + + align:start position:0% +your polynomial is it always +non-negative if I have integer entries + + align:start position:0% +non-negative if I have integer entries + + + align:start position:0% +non-negative if I have integer entries +what is this decidable okay so it turns + + align:start position:0% +what is this decidable okay so it turns + + + align:start position:0% +what is this decidable okay so it turns +out this is not decidable and this is + + align:start position:0% +out this is not decidable and this is + + + align:start position:0% +out this is not decidable and this is +related so it's more or less the same as + + align:start position:0% +related so it's more or less the same as + + + align:start position:0% +related so it's more or less the same as +the undecidability of Diophantine + + align:start position:0% +the undecidability of Diophantine + + + align:start position:0% +the undecidability of Diophantine +equations + + align:start position:0% + + + + align:start position:0% + +and which is also known as Hubbard's + + align:start position:0% +and which is also known as Hubbard's + + + align:start position:0% +and which is also known as Hubbard's +tenth problem so there's no computer + + align:start position:0% +tenth problem so there's no computer + + + align:start position:0% +tenth problem so there's no computer +program where we give you a dire + + align:start position:0% +program where we give you a dire + + + align:start position:0% +program where we give you a dire +fainting equation and solves the + + align:start position:0% +fainting equation and solves the + + + align:start position:0% +fainting equation and solves the +equation or even tells you whether the + + align:start position:0% +equation or even tells you whether the + + + align:start position:0% +equation or even tells you whether the +solutes whether the equation has a + + align:start position:0% +solutes whether the equation has a + + + align:start position:0% +solutes whether the equation has a +solution no this is part of what makes + + align:start position:0% +solution no this is part of what makes + + + align:start position:0% +solution no this is part of what makes +number theory mixed our finding + + align:start position:0% +number theory mixed our finding + + + align:start position:0% +number theory mixed our finding +equations interesting so it's it's + + align:start position:0% +equations interesting so it's it's + + + align:start position:0% +equations interesting so it's it's +undecidable value no we we can talk + + align:start position:0% +undecidable value no we we can talk + + + align:start position:0% +undecidable value no we we can talk +about it okay so the undecidability is a + + align:start position:0% +about it okay so the undecidability is a + + + align:start position:0% +about it okay so the undecidability is a +famous result due to Mathias image so + + align:start position:0% +famous result due to Mathias image so + + + align:start position:0% +famous result due to Mathias image so +what about graph theoretic inequalities + + align:start position:0% +what about graph theoretic inequalities + + + align:start position:0% +what about graph theoretic inequalities +so yes a graph homomorphism inequality + + align:start position:0% + + + + align:start position:0% + +decidable + + align:start position:0% + + + + align:start position:0% + +I mean the question should ask yourself + + align:start position:0% +I mean the question should ask yourself + + + align:start position:0% +I mean the question should ask yourself +is which one is a closer to there's a + + align:start position:0% +is which one is a closer to there's a + + + align:start position:0% +is which one is a closer to there's a +closer to deciding the positiveness of + + align:start position:0% +closer to deciding the positiveness of + + + align:start position:0% +closer to deciding the positiveness of +polynomials over reals or over integers + + align:start position:0% +polynomials over reals or over integers + + + align:start position:0% +polynomials over reals or over integers +on one hand you might think that it is + + align:start position:0% +on one hand you might think that it is + + + align:start position:0% +on one hand you might think that it is +more similar to the question of + + align:start position:0% +more similar to the question of + + + align:start position:0% +more similar to the question of +polynomials over real so first of all + + align:start position:0% +polynomials over real so first of all + + + align:start position:0% +polynomials over real so first of all +why it's similar to polynomials I hope + + align:start position:0% +why it's similar to polynomials I hope + + + align:start position:0% +why it's similar to polynomials I hope +that's at least intuitively it's I mean + + align:start position:0% +that's at least intuitively it's I mean + + + align:start position:0% +that's at least intuitively it's I mean +nothing is a proof but intuitively it + + align:start position:0% +nothing is a proof but intuitively it + + + align:start position:0% +nothing is a proof but intuitively it +feels somewhat similar to polynomials + + align:start position:0% +feels somewhat similar to polynomials + + + align:start position:0% +feels somewhat similar to polynomials +and all of these guys you can write down + + align:start position:0% +and all of these guys you can write down + + + align:start position:0% +and all of these guys you can write down +as polynomial like quantities we saw + + align:start position:0% +as polynomial like quantities we saw + + + align:start position:0% +as polynomial like quantities we saw +this earlier in the proof of polar + + align:start position:0% +this earlier in the proof of polar + + + align:start position:0% +this earlier in the proof of polar +Bosh's theorem so you might think it's + + align:start position:0% +Bosh's theorem so you might think it's + + + align:start position:0% +Bosh's theorem so you might think it's +similar to ríos because well for + + align:start position:0% +similar to ríos because well for + + + align:start position:0% +similar to ríos because well for +griffons you can take arbitrary real + + align:start position:0% +griffons you can take arbitrary real + + + align:start position:0% +griffons you can take arbitrary real +weights so it feels like the reals so it + + align:start position:0% +weights so it feels like the reals so it + + + align:start position:0% +weights so it feels like the reals so it +turns out due to a theorem of Hitomi and + + align:start position:0% +turns out due to a theorem of Hitomi and + + + align:start position:0% +turns out due to a theorem of Hitomi and +noren that the answer is not it is not + + align:start position:0% +noren that the answer is not it is not + + + align:start position:0% +noren that the answer is not it is not +decidable and roughly the reason has to + + align:start position:0% +decidable and roughly the reason has to + + + align:start position:0% +decidable and roughly the reason has to +deal with this picture even though the + + align:start position:0% +deal with this picture even though the + + + align:start position:0% +deal with this picture even though the +space of graphics is not discrete it's a + + align:start position:0% +space of graphics is not discrete it's a + + + align:start position:0% +space of graphics is not discrete it's a +very continuous object even if you just + + align:start position:0% +very continuous object even if you just + + + align:start position:0% +very continuous object even if you just +look at this picture here you have a + + align:start position:0% +look at this picture here you have a + + + align:start position:0% +look at this picture here you have a +bunch of discrete points along this + + align:start position:0% +bunch of discrete points along this + + + align:start position:0% +bunch of discrete points along this +scallop so here's a potential strategy + + align:start position:0% +scallop so here's a potential strategy + + + align:start position:0% +scallop so here's a potential strategy +for proving the undecidability of graph + + align:start position:0% +for proving the undecidability of graph + + + align:start position:0% +for proving the undecidability of graph +homomorphism inequalities i start by + + align:start position:0% +homomorphism inequalities i start by + + + align:start position:0% +homomorphism inequalities i start by +just restricting myself to this curve I + + align:start position:0% +just restricting myself to this curve I + + + align:start position:0% +just restricting myself to this curve I +restrict myself to the red curve if you + + align:start position:0% +restrict myself to the red curve if you + + + align:start position:0% +restrict myself to the red curve if you +restrict yourself to the red curve then + + align:start position:0% +restrict yourself to the red curve then + + + align:start position:0% +restrict yourself to the red curve then +the set of possibilities is now discrete + + align:start position:0% +the set of possibilities is now discrete + + + align:start position:0% +the set of possibilities is now discrete +set which is like the positive integers + + align:start position:0% + + + + align:start position:0% + +and now I start with I can reduce the + + align:start position:0% +and now I start with I can reduce the + + + align:start position:0% +and now I start with I can reduce the +problem to the problem of decidability + + align:start position:0% +problem to the problem of decidability + + + align:start position:0% +problem to the problem of decidability +of integer inequalities I start with an + + align:start position:0% +of integer inequalities I start with an + + + align:start position:0% +of integer inequalities I start with an +integer inequality I convert it to an + + align:start position:0% +integer inequality I convert it to an + + + align:start position:0% +integer inequality I convert it to an +inequality about points on this red + + align:start position:0% +inequality about points on this red + + + align:start position:0% +inequality about points on this red +curve and that turns into a + + align:start position:0% +curve and that turns into a + + + align:start position:0% +curve and that turns into a +corresponding graph inequality which + + align:start position:0% +corresponding graph inequality which + + + align:start position:0% +corresponding graph inequality which +must then be undecidable so so this + + align:start position:0% +must then be undecidable so so this + + + align:start position:0% +must then be undecidable so so this +undecidability result is related to the + + align:start position:0% +undecidability result is related to the + + + align:start position:0% +undecidability result is related to the +discreteness of points on this on this + + align:start position:0% +discreteness of points on this on this + + + align:start position:0% +discreteness of points on this on this +red curve but you know so general + + align:start position:0% +red curve but you know so general + + + align:start position:0% +red curve but you know so general +undecidability results are interesting + + align:start position:0% +undecidability results are interesting + + + align:start position:0% +undecidability results are interesting +but often we're interested in specific + + align:start position:0% +but often we're interested in specific + + + align:start position:0% +but often we're interested in specific +problems so I'll give you some specific + + align:start position:0% +problems so I'll give you some specific + + + align:start position:0% +problems so I'll give you some specific +inequality and asks is it true and there + + align:start position:0% +inequality and asks is it true and there + + + align:start position:0% +inequality and asks is it true and there +are lots of interesting open problems of + + align:start position:0% +are lots of interesting open problems of + + + align:start position:0% +are lots of interesting open problems of +that type my favorite one and also a + + align:start position:0% +that type my favorite one and also a + + + align:start position:0% +that type my favorite one and also a +very important problem in extrema graph + + align:start position:0% +very important problem in extrema graph + + + align:start position:0% +very important problem in extrema graph +theory is known as sidorenko's + + align:start position:0% +theory is known as sidorenko's + + + align:start position:0% +theory is known as sidorenko's +conjecture okay so still rankles + + align:start position:0% +conjecture okay so still rankles + + + align:start position:0% +conjecture okay so still rankles +conjecture it's a conjecture says that + + align:start position:0% +conjecture it's a conjecture says that + + + align:start position:0% +conjecture it's a conjecture says that +if H is bipartite then the H density in + + align:start position:0% +if H is bipartite then the H density in + + + align:start position:0% +if H is bipartite then the H density in +G or W is at least the edge density + + align:start position:0% +G or W is at least the edge density + + + align:start position:0% +G or W is at least the edge density +raised to the power of the number of + + align:start position:0% +raised to the power of the number of + + + align:start position:0% +raised to the power of the number of +edges of H so we saw one example of this + + align:start position:0% +edges of H so we saw one example of this + + + align:start position:0% +edges of H so we saw one example of this +inequality when H is the for cycle just + + align:start position:0% +inequality when H is the for cycle just + + + align:start position:0% +inequality when H is the for cycle just +when we discussed quasi randomness so we + + align:start position:0% +when we discussed quasi randomness so we + + + align:start position:0% +when we discussed quasi randomness so we +saw that this is true in the homework + + align:start position:0% +saw that this is true in the homework + + + align:start position:0% +saw that this is true in the homework +you'll have a few more so in the next + + align:start position:0% +you'll have a few more so in the next + + + align:start position:0% +you'll have a few more so in the next +problem homework you have a few more + + align:start position:0% +problem homework you have a few more + + + align:start position:0% +problem homework you have a few more +examples where you're asked to show this + + align:start position:0% +examples where you're asked to show this + + + align:start position:0% +examples where you're asked to show this +inequality it has open we do know any + + align:start position:0% +inequality it has open we do know any + + + align:start position:0% +inequality it has open we do know any +counter examples and the first open + + align:start position:0% +counter examples and the first open + + + align:start position:0% +counter examples and the first open +example it's known as something called a + + align:start position:0% +example it's known as something called a + + + align:start position:0% +example it's known as something called a +mobius strip + + align:start position:0% + + + + align:start position:0% + +so the Mobius strip graph which is a + + align:start position:0% +so the Mobius strip graph which is a + + + align:start position:0% +so the Mobius strip graph which is a +fancy name for the graph consisting of + + align:start position:0% +fancy name for the graph consisting of + + + align:start position:0% +fancy name for the graph consisting of +taking a k55 and removing a 10 cycle so + + align:start position:0% +taking a k55 and removing a 10 cycle so + + + align:start position:0% +taking a k55 and removing a 10 cycle so +that's the graph it is open whether this + + align:start position:0% +that's the graph it is open whether this + + + align:start position:0% +that's the graph it is open whether this +inequality holds for that graph there + + align:start position:0% +inequality holds for that graph there + + + align:start position:0% +inequality holds for that graph there +and this is something of great interest + + align:start position:0% +and this is something of great interest + + + align:start position:0% +and this is something of great interest +so if you can make progress on this + + align:start position:0% +so if you can make progress on this + + + align:start position:0% +so if you can make progress on this +problem people will be very excited now + + align:start position:0% +problem people will be very excited now + + + align:start position:0% +problem people will be very excited now +okay why this is called a mobius strip + + align:start position:0% +okay why this is called a mobius strip + + + align:start position:0% +okay why this is called a mobius strip +let's took me awhile to figure out so + + align:start position:0% +let's took me awhile to figure out so + + + align:start position:0% +let's took me awhile to figure out so +there are many different interpretations + + align:start position:0% +there are many different interpretations + + + align:start position:0% +there are many different interpretations +I think the reason why it's called a + + align:start position:0% +I think the reason why it's called a + + + align:start position:0% +I think the reason why it's called a +mobius strip is that if you think about + + align:start position:0% +mobius strip is that if you think about + + + align:start position:0% +mobius strip is that if you think about +the usual simplicial complex for a + + align:start position:0% +the usual simplicial complex for a + + + align:start position:0% +the usual simplicial complex for a +mobius strip and then this is the face + + align:start position:0% +mobius strip and then this is the face + + + align:start position:0% +mobius strip and then this is the face +vertex incidence bipartite graph so five + + align:start position:0% +vertex incidence bipartite graph so five + + + align:start position:0% +vertex incidence bipartite graph so five +vertices one for each face five where + + align:start position:0% +vertices one for each face five where + + + align:start position:0% +vertices one for each face five where +does this one for each vertex and if you + + align:start position:0% +does this one for each vertex and if you + + + align:start position:0% +does this one for each vertex and if you +draw the incidence structure that's the + + align:start position:0% +draw the incidence structure that's the + + + align:start position:0% +draw the incidence structure that's the +graph I'm not sure if there's + + align:start position:0% +graph I'm not sure if there's + + + align:start position:0% +graph I'm not sure if there's +topological formulation will help you + + align:start position:0% +topological formulation will help you + + + align:start position:0% +topological formulation will help you +improving sidorenko's conjecture or to + + align:start position:0% +improving sidorenko's conjecture or to + + + align:start position:0% +improving sidorenko's conjecture or to +disprove it but certainly that that's + + align:start position:0% +disprove it but certainly that that's + + + align:start position:0% +disprove it but certainly that that's +why it's called a mobius strip and there + + align:start position:0% +why it's called a mobius strip and there + + + align:start position:0% +why it's called a mobius strip and there +are some people believe who believe that + + align:start position:0% +are some people believe who believe that + + + align:start position:0% +are some people believe who believe that +it may be false it's still open + + align:start position:0% +it may be false it's still open + + + align:start position:0% +it may be false it's still open +I still + + align:start position:0% + + + + align:start position:0% + +the one last thing I want to mention is + + align:start position:0% +the one last thing I want to mention is + + + align:start position:0% +the one last thing I want to mention is +that even though the inequality written + + align:start position:0% +that even though the inequality written + + + align:start position:0% +that even though the inequality written +up there in general is undecidable if + + align:start position:0% +up there in general is undecidable if + + + align:start position:0% +up there in general is undecidable if +you only want to know whether this + + align:start position:0% +you only want to know whether this + + + align:start position:0% +you only want to know whether this +inequality is true up to an epsilon + + align:start position:0% +inequality is true up to an epsilon + + + align:start position:0% +inequality is true up to an epsilon +error then it is decidable in fact + + align:start position:0% +error then it is decidable in fact + + + align:start position:0% +error then it is decidable in fact +there's an algorithm that week I can + + align:start position:0% +there's an algorithm that week I can + + + align:start position:0% +there's an algorithm that week I can +tell you so so there exist algorithm + + align:start position:0% +tell you so so there exist algorithm + + + align:start position:0% +tell you so so there exist algorithm +that decides for every epsilon that + + align:start position:0% + + + + align:start position:0% + +besides so I just want to know whether + + align:start position:0% +besides so I just want to know whether + + + align:start position:0% +besides so I just want to know whether +that inequality is true pitaya loan + + align:start position:0% +that inequality is true pitaya loan + + + align:start position:0% +that inequality is true pitaya loan +epsilon error meaning it decides + + align:start position:0% +epsilon error meaning it decides + + + align:start position:0% +epsilon error meaning it decides +correctly that this inequality is true + + align:start position:0% +correctly that this inequality is true + + + align:start position:0% +correctly that this inequality is true +up to an epsilon error for Oh G or + + align:start position:0% +up to an epsilon error for Oh G or + + + align:start position:0% +up to an epsilon error for Oh G or +outputs G such that the sum here is + + align:start position:0% +outputs G such that the sum here is + + + align:start position:0% +outputs G such that the sum here is +negative okay so up to an epsilon live + + align:start position:0% +negative okay so up to an epsilon live + + + align:start position:0% +negative okay so up to an epsilon live +error I can give you an algorithm and + + align:start position:0% +error I can give you an algorithm and + + + align:start position:0% +error I can give you an algorithm and +the algorithm follows I mean it's it's + + align:start position:0% +the algorithm follows I mean it's it's + + + align:start position:0% +the algorithm follows I mean it's it's +not too hard to describe basically the + + align:start position:0% +not too hard to describe basically the + + + align:start position:0% +not too hard to describe basically the +idea is that if I take an epsilon + + align:start position:0% +idea is that if I take an epsilon + + + align:start position:0% +idea is that if I take an epsilon +regular partition then all the data + + align:start position:0% +regular partition then all the data + + + align:start position:0% +regular partition then all the data +about H densities can be encoded in the + + align:start position:0% +about H densities can be encoded in the + + + align:start position:0% +about H densities can be encoded in the +epsilon regular partition so apply even + + align:start position:0% +epsilon regular partition so apply even + + + align:start position:0% +epsilon regular partition so apply even +a weak regularity lemma is no and then + + align:start position:0% +a weak regularity lemma is no and then + + + align:start position:0% +a weak regularity lemma is no and then +we can test the bounded number of + + align:start position:0% +we can test the bounded number of + + + align:start position:0% +we can test the bounded number of +possibilities + + align:start position:0% + + + + align:start position:0% + +with some fixed number of hearts and by + + align:start position:0% +with some fixed number of hearts and by + + + align:start position:0% +with some fixed number of hearts and by +the counting lemma you lose some epsilon + + align:start position:0% +the counting lemma you lose some epsilon + + + align:start position:0% +the counting lemma you lose some epsilon +error if I check overall weighted graphs + + align:start position:0% +error if I check overall weighted graphs + + + align:start position:0% +error if I check overall weighted graphs +on some boundary parts whose edge + + align:start position:0% +on some boundary parts whose edge + + + align:start position:0% +on some boundary parts whose edge +weights are multiples of Epsilon let's + + align:start position:0% +weights are multiples of Epsilon let's + + + align:start position:0% +weights are multiples of Epsilon let's +say whether this is true if it's true + + align:start position:0% +say whether this is true if it's true + + + align:start position:0% +say whether this is true if it's true +then it is true with this epsilon if it + + align:start position:0% +then it is true with this epsilon if it + + + align:start position:0% +then it is true with this epsilon if it +is false then I can already output a + + align:start position:0% +is false then I can already output a + + + align:start position:0% +is false then I can already output a +counterexample + + align:start position:0% +counterexample + + + align:start position:0% +counterexample +so there's only finitely many + + align:start position:0% +so there's only finitely many + + + align:start position:0% +so there's only finitely many +possibilities as a result of weak + + align:start position:0% +possibilities as a result of weak + + + align:start position:0% +possibilities as a result of weak +regularity lemma and therefore this + + align:start position:0% +regularity lemma and therefore this + + + align:start position:0% +regularity lemma and therefore this +version here is decidable so today we + + align:start position:0% +version here is decidable so today we + + + align:start position:0% +version here is decidable so today we +saw many different graph theoretic + + align:start position:0% +saw many different graph theoretic + + + align:start position:0% +saw many different graph theoretic +inequalities and some general results + + align:start position:0% +inequalities and some general results + + + align:start position:0% +inequalities and some general results +and there are lots of open problems + + align:start position:0% +and there are lots of open problems + + + align:start position:0% +and there are lots of open problems +about graph homomorphism inequalities ok + + align:start position:0% +about graph homomorphism inequalities ok + + + align:start position:0% +about graph homomorphism inequalities ok +so this concludes roughly the extreme of + + align:start position:0% +so this concludes roughly the extreme of + + + align:start position:0% +so this concludes roughly the extreme of +graph theory section of this course so + + align:start position:0% +graph theory section of this course so + + + align:start position:0% +graph theory section of this course so +starting from next lecture we will be + + align:start position:0% +starting from next lecture we will be + + + align:start position:0% +starting from next lecture we will be +looking at Roth's theorem so looking at + + align:start position:0% +looking at Roth's theorem so looking at + + + align:start position:0% +looking at Roth's theorem so looking at +the 4-year analytic proof of Roth's + + align:start position:0% +the 4-year analytic proof of Roth's + + + align:start position:0% +the 4-year analytic proof of Roth's +theorem \ No newline at end of file diff --git a/o9nW0uBqvEo.txt b/o9nW0uBqvEo.txt new file mode 100644 index 0000000000000000000000000000000000000000..ba27d4931dde47f3a7c2caa89205f3587409d7b4 --- /dev/null +++ b/o9nW0uBqvEo.txt @@ -0,0 +1,10883 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mmit.edu. Okay, + + align:start position:0% +ocw.mmit.edu. Okay, + + + align:start position:0% +ocw.mmit.edu. Okay, +folks. Welcome back. Hope you had a nice + + align:start position:0% +folks. Welcome back. Hope you had a nice + + + align:start position:0% +folks. Welcome back. Hope you had a nice +long weekend with no classes. You got + + align:start position:0% +long weekend with no classes. You got + + + align:start position:0% +long weekend with no classes. You got +caught up on all those problem sets that + + align:start position:0% +caught up on all those problem sets that + + + align:start position:0% +caught up on all those problem sets that +have been sneaking up on you. You + + align:start position:0% +have been sneaking up on you. You + + + align:start position:0% +have been sneaking up on you. You +enjoyed watching the Patriots and Tom + + align:start position:0% +enjoyed watching the Patriots and Tom + + + align:start position:0% +enjoyed watching the Patriots and Tom +Brady come back. Oops. Sorry, I'm + + align:start position:0% +Brady come back. Oops. Sorry, I'm + + + align:start position:0% +Brady come back. Oops. Sorry, I'm +showing my local + + align:start position:0% +showing my local + + + align:start position:0% +showing my local +bias. Before we talk about today's + + align:start position:0% +bias. Before we talk about today's + + + align:start position:0% +bias. Before we talk about today's +topic, I want to take a second to set + + align:start position:0% +topic, I want to take a second to set + + + align:start position:0% +topic, I want to take a second to set +the stage and I want you to stop and + + align:start position:0% +the stage and I want you to stop and + + + align:start position:0% +the stage and I want you to stop and +think about what you've seen so far in + + align:start position:0% +think about what you've seen so far in + + + align:start position:0% +think about what you've seen so far in +this course. We're coming up on the end + + align:start position:0% +this course. We're coming up on the end + + + align:start position:0% +this course. We're coming up on the end +of the first section of the course and + + align:start position:0% +of the first section of the course and + + + align:start position:0% +of the first section of the course and +you've already seen a lot. Certainly + + align:start position:0% +you've already seen a lot. Certainly + + + align:start position:0% +you've already seen a lot. Certainly +learned about fundamentals of + + align:start position:0% +learned about fundamentals of + + + align:start position:0% +learned about fundamentals of +computation. You've uh seen different + + align:start position:0% +computation. You've uh seen different + + + align:start position:0% +computation. You've uh seen different +kinds of data structures both mutable + + align:start position:0% +kinds of data structures both mutable + + + align:start position:0% +kinds of data structures both mutable +and immutable. So tupils and lists, + + align:start position:0% +and immutable. So tupils and lists, + + + align:start position:0% +and immutable. So tupils and lists, +dictionaries, different ways of pulling + + align:start position:0% +dictionaries, different ways of pulling + + + align:start position:0% +dictionaries, different ways of pulling +things together. You've seen a range of + + align:start position:0% +things together. You've seen a range of + + + align:start position:0% +things together. You've seen a range of +algorithms from simple linear code to + + align:start position:0% +algorithms from simple linear code to + + + align:start position:0% +algorithms from simple linear code to +loops, fors and whiles. You've seen + + align:start position:0% +loops, fors and whiles. You've seen + + + align:start position:0% +loops, fors and whiles. You've seen +iterative algorithms. You've seen + + align:start position:0% +iterative algorithms. You've seen + + + align:start position:0% +iterative algorithms. You've seen +recursive algorithms. Uh you've seen + + align:start position:0% +recursive algorithms. Uh you've seen + + + align:start position:0% +recursive algorithms. Uh you've seen +classes of + + align:start position:0% +classes of + + + align:start position:0% +classes of +algorithms, divide and conquer, greedy + + align:start position:0% +algorithms, divide and conquer, greedy + + + align:start position:0% +algorithms, divide and conquer, greedy +algorithms, bisection search, a range of + + align:start position:0% +algorithms, bisection search, a range of + + + align:start position:0% +algorithms, bisection search, a range of +things. And then most recently you saw + + align:start position:0% +things. And then most recently you saw + + + align:start position:0% +things. And then most recently you saw +pulling things together with classes, a + + align:start position:0% +pulling things together with classes, a + + + align:start position:0% +pulling things together with classes, a +way to group together data that belongs + + align:start position:0% +way to group together data that belongs + + + align:start position:0% +way to group together data that belongs +together along with methods or + + align:start position:0% +together along with methods or + + + align:start position:0% +together along with methods or +procedures that are designed to + + align:start position:0% +procedures that are designed to + + + align:start position:0% +procedures that are designed to +manipulate that data. So you've had + + align:start position:0% +manipulate that data. So you've had + + + align:start position:0% +manipulate that data. So you've had +actually a fairly good coverage already + + align:start position:0% +actually a fairly good coverage already + + + align:start position:0% +actually a fairly good coverage already +of a lot of the fundamentals of + + align:start position:0% +of a lot of the fundamentals of + + + align:start position:0% +of a lot of the fundamentals of +computation and you're starting to get + + align:start position:0% +computation and you're starting to get + + + align:start position:0% +computation and you're starting to get +geared up to be able to tackle a pretty + + align:start position:0% +geared up to be able to tackle a pretty + + + align:start position:0% +geared up to be able to tackle a pretty +interesting range of problems. + + align:start position:0% +interesting range of problems. + + + align:start position:0% +interesting range of problems. +Today and Monday, we're going to take a + + align:start position:0% +Today and Monday, we're going to take a + + + align:start position:0% +Today and Monday, we're going to take a +little bit of a different look at + + align:start position:0% +little bit of a different look at + + + align:start position:0% +little bit of a different look at +computation because now that you've got + + align:start position:0% +computation because now that you've got + + + align:start position:0% +computation because now that you've got +the tools to start building up your own + + align:start position:0% +the tools to start building up your own + + + align:start position:0% +the tools to start building up your own +personal armamentum of of tools, we'd + + align:start position:0% +personal armamentum of of tools, we'd + + + align:start position:0% +personal armamentum of of tools, we'd +like to ask a couple of important + + align:start position:0% +like to ask a couple of important + + + align:start position:0% +like to ask a couple of important +questions. The primary one of which is + + align:start position:0% +questions. The primary one of which is + + + align:start position:0% +questions. The primary one of which is +how efficient are my algorithms? And by + + align:start position:0% +how efficient are my algorithms? And by + + + align:start position:0% +how efficient are my algorithms? And by +efficiency, we'll see it refers both to + + align:start position:0% +efficiency, we'll see it refers both to + + + align:start position:0% +efficiency, we'll see it refers both to +space and time, but primarily to time. + + align:start position:0% +space and time, but primarily to time. + + + align:start position:0% +space and time, but primarily to time. +And we'd like to know both how fast are + + align:start position:0% +And we'd like to know both how fast are + + + align:start position:0% +And we'd like to know both how fast are +my algorithms going to run and how could + + align:start position:0% +my algorithms going to run and how could + + + align:start position:0% +my algorithms going to run and how could +I reason about that performance. And + + align:start position:0% +I reason about that performance. And + + + align:start position:0% +I reason about that performance. And +that's what we're going to do with + + align:start position:0% +that's what we're going to do with + + + align:start position:0% +that's what we're going to do with +today's topics. We're going to talk + + align:start position:0% +today's topics. We're going to talk + + + align:start position:0% +today's topics. We're going to talk +about orders of growth. We'll define + + align:start position:0% +about orders of growth. We'll define + + + align:start position:0% +about orders of growth. We'll define +what that means in a few minutes. We're + + align:start position:0% +what that means in a few minutes. We're + + + align:start position:0% +what that means in a few minutes. We're +going to talk about what's called the + + align:start position:0% +going to talk about what's called the + + + align:start position:0% +going to talk about what's called the +big O notation. And we're going to begin + + align:start position:0% +big O notation. And we're going to begin + + + align:start position:0% +big O notation. And we're going to begin +to explore different classes of + + align:start position:0% +to explore different classes of + + + align:start position:0% +to explore different classes of +algorithms. Before we do that though, + + align:start position:0% +algorithms. Before we do that though, + + + align:start position:0% +algorithms. Before we do that though, +let's talk about + + align:start position:0% +let's talk about + + + align:start position:0% +let's talk about +why. And I want to suggest to you there + + align:start position:0% +why. And I want to suggest to you there + + + align:start position:0% +why. And I want to suggest to you there +are two reasons this is important to be + + align:start position:0% +are two reasons this is important to be + + + align:start position:0% +are two reasons this is important to be +considering. The first question is how + + align:start position:0% +considering. The first question is how + + + align:start position:0% +considering. The first question is how +could we reason about an algorithm + + align:start position:0% +could we reason about an algorithm + + + align:start position:0% +could we reason about an algorithm +something you write in order to predict + + align:start position:0% +something you write in order to predict + + + align:start position:0% +something you write in order to predict +how much time is it going to need to + + align:start position:0% +how much time is it going to need to + + + align:start position:0% +how much time is it going to need to +solve a problem of a particular size. I + + align:start position:0% +solve a problem of a particular size. I + + + align:start position:0% +solve a problem of a particular size. I +might be testing my code on smallcale + + align:start position:0% +might be testing my code on smallcale + + + align:start position:0% +might be testing my code on smallcale +examples and I want to know if I run it + + align:start position:0% +examples and I want to know if I run it + + + align:start position:0% +examples and I want to know if I run it +on a really big one how long is it going + + align:start position:0% +on a really big one how long is it going + + + align:start position:0% +on a really big one how long is it going +to take? Can I predict that? Can I make + + align:start position:0% +to take? Can I predict that? Can I make + + + align:start position:0% +to take? Can I predict that? Can I make +guess about how much um time I'm going + + align:start position:0% +guess about how much um time I'm going + + + align:start position:0% +guess about how much um time I'm going +to need to to solve this problem? + + align:start position:0% +to need to to solve this problem? + + + align:start position:0% +to need to to solve this problem? +Especially if it's in a real world + + align:start position:0% +Especially if it's in a real world + + + align:start position:0% +Especially if it's in a real world +circumstance where time is going to be + + align:start position:0% +circumstance where time is going to be + + + align:start position:0% +circumstance where time is going to be +crucial. Equally important is going the + + align:start position:0% +crucial. Equally important is going the + + + align:start position:0% +crucial. Equally important is going the +other direction. We want you to begin to + + align:start position:0% +other direction. We want you to begin to + + + align:start position:0% +other direction. We want you to begin to +reason about the algorithms you write to + + align:start position:0% +reason about the algorithms you write to + + + align:start position:0% +reason about the algorithms you write to +be able to say how do certain choices in + + align:start position:0% +be able to say how do certain choices in + + + align:start position:0% +be able to say how do certain choices in +a design of an algorithm influence how + + align:start position:0% +a design of an algorithm influence how + + + align:start position:0% +a design of an algorithm influence how +much time it's going to take. If I + + align:start position:0% +much time it's going to take. If I + + + align:start position:0% +much time it's going to take. If I +choose to do this recursively, is that + + align:start position:0% +choose to do this recursively, is that + + + align:start position:0% +choose to do this recursively, is that +going to be different than iteratively? + + align:start position:0% +going to be different than iteratively? + + + align:start position:0% +going to be different than iteratively? +If I choose to do this with a particular + + align:start position:0% +If I choose to do this with a particular + + + align:start position:0% +If I choose to do this with a particular +kind of structure in my algorithm, what + + align:start position:0% +kind of structure in my algorithm, what + + + align:start position:0% +kind of structure in my algorithm, what +does that say about the amount of time + + align:start position:0% +does that say about the amount of time + + + align:start position:0% +does that say about the amount of time +I'm going to need? And you're going to + + align:start position:0% +I'm going to need? And you're going to + + + align:start position:0% +I'm going to need? And you're going to +see there's a nice association between + + align:start position:0% +see there's a nice association between + + + align:start position:0% +see there's a nice association between +classes of algorithms and the interior + + align:start position:0% +classes of algorithms and the interior + + + align:start position:0% +classes of algorithms and the interior +structure of them. And in particular, we + + align:start position:0% +structure of them. And in particular, we + + + align:start position:0% +structure of them. And in particular, we +want to ask some fundamental questions. + + align:start position:0% +want to ask some fundamental questions. + + + align:start position:0% +want to ask some fundamental questions. +Are there fundamental limits to how much + + align:start position:0% +Are there fundamental limits to how much + + + align:start position:0% +Are there fundamental limits to how much +time it's going to take to solve a + + align:start position:0% +time it's going to take to solve a + + + align:start position:0% +time it's going to take to solve a +particular problem? no matter what kind + + align:start position:0% +particular problem? no matter what kind + + + align:start position:0% +particular problem? no matter what kind +of algorithm I design around this and + + align:start position:0% +of algorithm I design around this and + + + align:start position:0% +of algorithm I design around this and +we'll see that there's some nice + + align:start position:0% +we'll see that there's some nice + + + align:start position:0% +we'll see that there's some nice +challenges about that. So that's what + + align:start position:0% +challenges about that. So that's what + + + align:start position:0% +challenges about that. So that's what +we're going to do over the next two + + align:start position:0% +we're going to do over the next two + + + align:start position:0% +we're going to do over the next two +days. Before we do though, let's maybe + + align:start position:0% +days. Before we do though, let's maybe + + + align:start position:0% +days. Before we do though, let's maybe +ask the obvious question, why should we + + align:start position:0% +ask the obvious question, why should we + + + align:start position:0% +ask the obvious question, why should we +care? Could be on a quiz might matter to + + align:start position:0% +care? Could be on a quiz might matter to + + + align:start position:0% +care? Could be on a quiz might matter to +you. Better choice is because it + + align:start position:0% +you. Better choice is because it + + + align:start position:0% +you. Better choice is because it +actually makes a difference. And I say + + align:start position:0% +actually makes a difference. And I say + + + align:start position:0% +actually makes a difference. And I say +that because it may not be as obvious to + + align:start position:0% +that because it may not be as obvious to + + + align:start position:0% +that because it may not be as obvious to +you as it was in an earlier generation. + + align:start position:0% +you as it was in an earlier generation. + + + align:start position:0% +you as it was in an earlier generation. +So, people with my gray hair or what's + + align:start position:0% +So, people with my gray hair or what's + + + align:start position:0% +So, people with my gray hair or what's +left of my gray hair like to tell + + align:start position:0% +left of my gray hair like to tell + + + align:start position:0% +left of my gray hair like to tell +stories. I'll make it short, but I + + align:start position:0% +stories. I'll make it short, but I + + + align:start position:0% +stories. I'll make it short, but I +started + + align:start position:0% +started + + + align:start position:0% +started +programming 41 years ago. No, sorry, 45 + + align:start position:0% +programming 41 years ago. No, sorry, 45 + + + align:start position:0% +programming 41 years ago. No, sorry, 45 +years ago on punch cards. You don't know + + align:start position:0% +years ago on punch cards. You don't know + + + align:start position:0% +years ago on punch cards. You don't know +what those are unless you've been to a + + align:start position:0% +what those are unless you've been to a + + + align:start position:0% +what those are unless you've been to a +museum on a machine that filled a half a + + align:start position:0% +museum on a machine that filled a half a + + + align:start position:0% +museum on a machine that filled a half a +room and that took about five minutes to + + align:start position:0% +room and that took about five minutes to + + + align:start position:0% +room and that took about five minutes to +execute what you can do in a fraction of + + align:start position:0% +execute what you can do in a fraction of + + + align:start position:0% +execute what you can do in a fraction of +a second on your phone. Right? This is + + align:start position:0% +a second on your phone. Right? This is + + + align:start position:0% +a second on your phone. Right? This is +to tell you you're living in a great + + align:start position:0% +to tell you you're living in a great + + + align:start position:0% +to tell you you're living in a great +time, not independent of what's going to + + align:start position:0% +time, not independent of what's going to + + + align:start position:0% +time, not independent of what's going to +happen on November 8th. + + align:start position:0% +happen on November 8th. + + + align:start position:0% +happen on November 8th. +All right, we'll stay away from those + + align:start position:0% +All right, we'll stay away from those + + + align:start position:0% +All right, we'll stay away from those +topics as well, won't we? My point is, + + align:start position:0% +topics as well, won't we? My point is, + + + align:start position:0% +topics as well, won't we? My point is, +yeah, I tell old stories. I'm an old + + align:start position:0% +yeah, I tell old stories. I'm an old + + + align:start position:0% +yeah, I tell old stories. I'm an old +guy. But you might argue, look, + + align:start position:0% +guy. But you might argue, look, + + + align:start position:0% +guy. But you might argue, look, +computers are getting so much faster. + + align:start position:0% +computers are getting so much faster. + + + align:start position:0% +computers are getting so much faster. +Does it really matter? And I want to say + + align:start position:0% +Does it really matter? And I want to say + + + align:start position:0% +Does it really matter? And I want to say +to you, maybe it's obvious to you, yes, + + align:start position:0% +to you, maybe it's obvious to you, yes, + + + align:start position:0% +to you, maybe it's obvious to you, yes, +absolutely it does. Because in + + align:start position:0% +absolutely it does. Because in + + + align:start position:0% +absolutely it does. Because in +conjunction with us getting faster + + align:start position:0% +conjunction with us getting faster + + + align:start position:0% +conjunction with us getting faster +computers, we're increasing the sizes of + + align:start position:0% +computers, we're increasing the sizes of + + + align:start position:0% +computers, we're increasing the sizes of +the problems. The data sets we want to + + align:start position:0% +the problems. The data sets we want to + + + align:start position:0% +the problems. The data sets we want to +analyze are getting massive. And I'll + + align:start position:0% +analyze are getting massive. And I'll + + + align:start position:0% +analyze are getting massive. And I'll +give you an example. I just pulled this + + align:start position:0% +give you an example. I just pulled this + + + align:start position:0% +give you an example. I just pulled this +off of Google, of course. In 2014, I + + align:start position:0% +off of Google, of course. In 2014, I + + + align:start position:0% +off of Google, of course. In 2014, I +don't have more recent numbers, Google + + align:start position:0% +don't have more recent numbers, Google + + + align:start position:0% +don't have more recent numbers, Google +served, I think I have that number + + align:start position:0% +served, I think I have that number + + + align:start position:0% +served, I think I have that number +right, 30 trillion pages on the + + align:start position:0% +right, 30 trillion pages on the + + + align:start position:0% +right, 30 trillion pages on the +web. It's either 30 trillion or 30 + + align:start position:0% +web. It's either 30 trillion or 30 + + + align:start position:0% +web. It's either 30 trillion or 30 +quadrillion. I can't count that many + + align:start position:0% +quadrillion. I can't count that many + + + align:start position:0% +quadrillion. I can't count that many +zeros there. It covered a 100 million + + align:start position:0% +zeros there. It covered a 100 million + + + align:start position:0% +zeros there. It covered a 100 million +gigabytes of data. And I suggest to you, + + align:start position:0% +gigabytes of data. And I suggest to you, + + + align:start position:0% +gigabytes of data. And I suggest to you, +if you want to find a piece of + + align:start position:0% +if you want to find a piece of + + + align:start position:0% +if you want to find a piece of +information on the web, can you write a + + align:start position:0% +information on the web, can you write a + + + align:start position:0% +information on the web, can you write a +simple little search algorithm that's + + align:start position:0% +simple little search algorithm that's + + + align:start position:0% +simple little search algorithm that's +going to sequentially go through all the + + align:start position:0% +going to sequentially go through all the + + + align:start position:0% +going to sequentially go through all the +pages and find anything in any + + align:start position:0% +pages and find anything in any + + + align:start position:0% +pages and find anything in any +reasonable amount of time? Probably not, + + align:start position:0% +reasonable amount of time? Probably not, + + + align:start position:0% +reasonable amount of time? Probably not, +right? It's just growing a way too fast. + + align:start position:0% +right? It's just growing a way too fast. + + + align:start position:0% +right? It's just growing a way too fast. +This, by the way, is of course why + + align:start position:0% +This, by the way, is of course why + + + align:start position:0% +This, by the way, is of course why +Google makes a lot of money off of their + + align:start position:0% +Google makes a lot of money off of their + + + align:start position:0% +Google makes a lot of money off of their +um their map reduce algorithm for + + align:start position:0% +um their map reduce algorithm for + + + align:start position:0% +um their map reduce algorithm for +searching the web. Written, by the way, + + align:start position:0% +searching the web. Written, by the way, + + + align:start position:0% +searching the web. Written, by the way, +or co-written by an MIT grad and the + + align:start position:0% +or co-written by an MIT grad and the + + + align:start position:0% +or co-written by an MIT grad and the +parent of a current MIT student. So, + + align:start position:0% +parent of a current MIT student. So, + + + align:start position:0% +parent of a current MIT student. So, +there's a nice hook in there. Not that + + align:start position:0% +there's a nice hook in there. Not that + + + align:start position:0% +there's a nice hook in there. Not that +Google pays MIT royalties for that + + align:start position:0% +Google pays MIT royalties for that + + + align:start position:0% +Google pays MIT royalties for that +wonderful thing, by the way. All right, + + align:start position:0% +wonderful thing, by the way. All right, + + + align:start position:0% +wonderful thing, by the way. All right, +bad jokes aside, searching Google, ton + + align:start position:0% +bad jokes aside, searching Google, ton + + + align:start position:0% +bad jokes aside, searching Google, ton +of time. Searching a genomics data set, + + align:start position:0% +of time. Searching a genomics data set, + + + align:start position:0% +of time. Searching a genomics data set, +ton of time. The the data sets are + + align:start position:0% +ton of time. The the data sets are + + + align:start position:0% +ton of time. The the data sets are +growing so fast. You're working for the + + align:start position:0% +growing so fast. You're working for the + + + align:start position:0% +growing so fast. You're working for the +US government, you want to track + + align:start position:0% +US government, you want to track + + + align:start position:0% +US government, you want to track +terrorists using image surveillance from + + align:start position:0% +terrorists using image surveillance from + + + align:start position:0% +terrorists using image surveillance from +around the world, growing incredibly + + align:start position:0% +around the world, growing incredibly + + + align:start position:0% +around the world, growing incredibly +rapidly. Pick a problem. the data sets + + align:start position:0% +rapidly. Pick a problem. the data sets + + + align:start position:0% +rapidly. Pick a problem. the data sets +grow so quickly that even if the + + align:start position:0% +grow so quickly that even if the + + + align:start position:0% +grow so quickly that even if the +computers speed up, you still need to + + align:start position:0% +computers speed up, you still need to + + + align:start position:0% +computers speed up, you still need to +think about how do I come up with + + align:start position:0% +think about how do I come up with + + + align:start position:0% +think about how do I come up with +efficient ways to solve those problems. + + align:start position:0% +efficient ways to solve those problems. + + + align:start position:0% +efficient ways to solve those problems. +So I want to suggest to you while + + align:start position:0% +So I want to suggest to you while + + + align:start position:0% +So I want to suggest to you while +sometimes simple solutions are great, + + align:start position:0% +sometimes simple solutions are great, + + + align:start position:0% +sometimes simple solutions are great, +they're the easy ones to rate to write, + + align:start position:0% +they're the easy ones to rate to write, + + + align:start position:0% +they're the easy ones to rate to write, +sorry, at times you need to be more + + align:start position:0% +sorry, at times you need to be more + + + align:start position:0% +sorry, at times you need to be more +sophisticated. Therefore, we want to + + align:start position:0% +sophisticated. Therefore, we want to + + + align:start position:0% +sophisticated. Therefore, we want to +reason about how do we measure + + align:start position:0% +reason about how do we measure + + + align:start position:0% +reason about how do we measure +efficiency and how do we relate + + align:start position:0% +efficiency and how do we relate + + + align:start position:0% +efficiency and how do we relate +algorithm design choices to the cost + + align:start position:0% +algorithm design choices to the cost + + + align:start position:0% +algorithm design choices to the cost +that's going to be associated with it. + + align:start position:0% +that's going to be associated with it. + + + align:start position:0% +that's going to be associated with it. +Okay, even when we do that, we've got a + + align:start position:0% +Okay, even when we do that, we've got a + + + align:start position:0% +Okay, even when we do that, we've got a +choice to make because we could talk + + align:start position:0% +choice to make because we could talk + + + align:start position:0% +choice to make because we could talk +about both efficiency in terms of time + + align:start position:0% +about both efficiency in terms of time + + + align:start position:0% +about both efficiency in terms of time +or in terms of space, meaning how much + + align:start position:0% +or in terms of space, meaning how much + + + align:start position:0% +or in terms of space, meaning how much +storage do I have inside the computer? + + align:start position:0% +storage do I have inside the computer? + + + align:start position:0% +storage do I have inside the computer? +And the reason that's relevant is + + align:start position:0% +And the reason that's relevant is + + + align:start position:0% +And the reason that's relevant is +there's actually in many cases a + + align:start position:0% +there's actually in many cases a + + + align:start position:0% +there's actually in many cases a +trade-off between those two. And you've + + align:start position:0% +trade-off between those two. And you've + + + align:start position:0% +trade-off between those two. And you've +actually seen an example which you may + + align:start position:0% +actually seen an example which you may + + + align:start position:0% +actually seen an example which you may +or may not remember. You may recall when + + align:start position:0% +or may not remember. You may recall when + + + align:start position:0% +or may not remember. You may recall when +we introduced dictionaries, I showed you + + align:start position:0% +we introduced dictionaries, I showed you + + + align:start position:0% +we introduced dictionaries, I showed you +a variation where you could compute + + align:start position:0% +a variation where you could compute + + + align:start position:0% +a variation where you could compute +Fibonacci using the dictionary to keep + + align:start position:0% +Fibonacci using the dictionary to keep + + + align:start position:0% +Fibonacci using the dictionary to keep +track of intermediate values. And we'll + + align:start position:0% +track of intermediate values. And we'll + + + align:start position:0% +track of intermediate values. And we'll +see in next week that it actually + + align:start position:0% +see in next week that it actually + + + align:start position:0% +see in next week that it actually +tremendously reduces the time + + align:start position:0% +tremendously reduces the time + + + align:start position:0% +tremendously reduces the time +complexity. That's called a trade-off in + + align:start position:0% +complexity. That's called a trade-off in + + + align:start position:0% +complexity. That's called a trade-off in +the sense that sometimes I can premputee + + align:start position:0% +the sense that sometimes I can premputee + + + align:start position:0% +the sense that sometimes I can premputee +portions of the answer, store them away + + align:start position:0% +portions of the answer, store them away + + + align:start position:0% +portions of the answer, store them away +so that when I try and do a bigger + + align:start position:0% +so that when I try and do a bigger + + + align:start position:0% +so that when I try and do a bigger +version of the answer, I can just look + + align:start position:0% +version of the answer, I can just look + + + align:start position:0% +version of the answer, I can just look +up those portions. So there's going to + + align:start position:0% +up those portions. So there's going to + + + align:start position:0% +up those portions. So there's going to +be a trade-off here. We're going to + + align:start position:0% +be a trade-off here. We're going to + + + align:start position:0% +be a trade-off here. We're going to +focus for purposes of this lecture and + + align:start position:0% +focus for purposes of this lecture and + + + align:start position:0% +focus for purposes of this lecture and +the next one on time efficiency. How + + align:start position:0% +the next one on time efficiency. How + + + align:start position:0% +the next one on time efficiency. How +much time is it going to take our + + align:start position:0% +much time is it going to take our + + + align:start position:0% +much time is it going to take our +algorithms to solve a + + align:start position:0% +algorithms to solve a + + + align:start position:0% +algorithms to solve a +problem? + + align:start position:0% +problem? + + + align:start position:0% +problem? +Okay. What are the challenges in doing + + align:start position:0% +Okay. What are the challenges in doing + + + align:start position:0% +Okay. What are the challenges in doing +that before we look at the actual tools? + + align:start position:0% +that before we look at the actual tools? + + + align:start position:0% +that before we look at the actual tools? +And in fact, this is going to lead into + + align:start position:0% +And in fact, this is going to lead into + + + align:start position:0% +And in fact, this is going to lead into +the + + align:start position:0% +the + + + align:start position:0% +the +tools. The first one is even if I've + + align:start position:0% +tools. The first one is even if I've + + + align:start position:0% +tools. The first one is even if I've +decided on an algorithm, there are lots + + align:start position:0% +decided on an algorithm, there are lots + + + align:start position:0% +decided on an algorithm, there are lots +of ways to implement them. A while loop + + align:start position:0% +of ways to implement them. A while loop + + + align:start position:0% +of ways to implement them. A while loop +and a for loop might have slightly + + align:start position:0% +and a for loop might have slightly + + + align:start position:0% +and a for loop might have slightly +different behavior. I could choose to do + + align:start position:0% +different behavior. I could choose to do + + + align:start position:0% +different behavior. I could choose to do +it with temporary variables or using + + align:start position:0% +it with temporary variables or using + + + align:start position:0% +it with temporary variables or using +direct substitution. Lots of little + + align:start position:0% +direct substitution. Lots of little + + + align:start position:0% +direct substitution. Lots of little +choices. So an algorithm could be + + align:start position:0% +choices. So an algorithm could be + + + align:start position:0% +choices. So an algorithm could be +implemented many different ways. How do + + align:start position:0% +implemented many different ways. How do + + + align:start position:0% +implemented many different ways. How do +I measure the actual efficiency of the + + align:start position:0% +I measure the actual efficiency of the + + + align:start position:0% +I measure the actual efficiency of the +algorithm? Second one is I might for a + + align:start position:0% +algorithm? Second one is I might for a + + + align:start position:0% +algorithm? Second one is I might for a +given problem have different choices of + + align:start position:0% +given problem have different choices of + + + align:start position:0% +given problem have different choices of +algorithm. A recursive solution versus + + align:start position:0% +algorithm. A recursive solution versus + + + align:start position:0% +algorithm. A recursive solution versus +an iterative one using divide and + + align:start position:0% +an iterative one using divide and + + + align:start position:0% +an iterative one using divide and +conquered versus straightforward search. + + align:start position:0% +conquered versus straightforward search. + + + align:start position:0% +conquered versus straightforward search. +We're going to see some examples of + + align:start position:0% +We're going to see some examples of + + + align:start position:0% +We're going to see some examples of +that. So I've got to somehow separate + + align:start position:0% +that. So I've got to somehow separate + + + align:start position:0% +that. So I've got to somehow separate +those pieces out. And in particular, I'd + + align:start position:0% +those pieces out. And in particular, I'd + + + align:start position:0% +those pieces out. And in particular, I'd +like to separate out the choice of + + align:start position:0% +like to separate out the choice of + + + align:start position:0% +like to separate out the choice of +implementation from the choice of + + align:start position:0% +implementation from the choice of + + + align:start position:0% +implementation from the choice of +algorithm. I want to measure how hard is + + align:start position:0% +algorithm. I want to measure how hard is + + + align:start position:0% +algorithm. I want to measure how hard is +the algorithm. Not can I come up with a + + align:start position:0% +the algorithm. Not can I come up with a + + + align:start position:0% +the algorithm. Not can I come up with a +slightly more efficient way of coming up + + align:start position:0% +slightly more efficient way of coming up + + + align:start position:0% +slightly more efficient way of coming up +with an + + align:start position:0% +with an + + + align:start position:0% +with an +implementation. So here are three ways I + + align:start position:0% +implementation. So here are three ways I + + + align:start position:0% +implementation. So here are three ways I +might do it. And we're going to look at + + align:start position:0% +might do it. And we're going to look at + + + align:start position:0% +might do it. And we're going to look at +each one of them very briefly. The + + align:start position:0% +each one of them very briefly. The + + + align:start position:0% +each one of them very briefly. The +obvious one is we could be scientists. + + align:start position:0% +obvious one is we could be scientists. + + + align:start position:0% +obvious one is we could be scientists. +time it, write the code, run a bunch of + + align:start position:0% +time it, write the code, run a bunch of + + + align:start position:0% +time it, write the code, run a bunch of +test case, run a timer, use that to try + + align:start position:0% +test case, run a timer, use that to try + + + align:start position:0% +test case, run a timer, use that to try +and come up with a way of estimating + + align:start position:0% +and come up with a way of estimating + + + align:start position:0% +and come up with a way of estimating +efficiency. We'll see some challenges + + align:start position:0% +efficiency. We'll see some challenges + + + align:start position:0% +efficiency. We'll see some challenges +with that. Slightly more abstractly, we + + align:start position:0% +with that. Slightly more abstractly, we + + + align:start position:0% +with that. Slightly more abstractly, we +could count operations. + + align:start position:0% +could count operations. + + + align:start position:0% +could count operations. +We could say here are the set of + + align:start position:0% +We could say here are the set of + + + align:start position:0% +We could say here are the set of +fundamental operations, mathematical + + align:start position:0% +fundamental operations, mathematical + + + align:start position:0% +fundamental operations, mathematical +operations, comparisons, setting values, + + align:start position:0% +operations, comparisons, setting values, + + + align:start position:0% +operations, comparisons, setting values, +retrieving values and simply say how + + align:start position:0% +retrieving values and simply say how + + + align:start position:0% +retrieving values and simply say how +many of those operations do I use in my + + align:start position:0% +many of those operations do I use in my + + + align:start position:0% +many of those operations do I use in my +algorithm as a function of the size of + + align:start position:0% +algorithm as a function of the size of + + + align:start position:0% +algorithm as a function of the size of +the input and that could be used to give + + align:start position:0% +the input and that could be used to give + + + align:start position:0% +the input and that could be used to give +us a sense of + + align:start position:0% +us a sense of + + + align:start position:0% +us a sense of +efficiency. We're going to see both of + + align:start position:0% +efficiency. We're going to see both of + + + align:start position:0% +efficiency. We're going to see both of +those are flawed somewhat more in the + + align:start position:0% +those are flawed somewhat more in the + + + align:start position:0% +those are flawed somewhat more in the +first case than the second one. And so + + align:start position:0% +first case than the second one. And so + + + align:start position:0% +first case than the second one. And so +we're going to abstract that second one + + align:start position:0% +we're going to abstract that second one + + + align:start position:0% +we're going to abstract that second one +to a more abstract notion of something + + align:start position:0% +to a more abstract notion of something + + + align:start position:0% +to a more abstract notion of something +we call an order of growth. And I'll + + align:start position:0% +we call an order of growth. And I'll + + + align:start position:0% +we call an order of growth. And I'll +come back to that in a couple of + + align:start position:0% +come back to that in a couple of + + + align:start position:0% +come back to that in a couple of +minutes. This is the one we're going to + + align:start position:0% +minutes. This is the one we're going to + + + align:start position:0% +minutes. This is the one we're going to +focus on. It's one that computer + + align:start position:0% +focus on. It's one that computer + + + align:start position:0% +focus on. It's one that computer +scientists use. It leads to what we call + + align:start position:0% +scientists use. It leads to what we call + + + align:start position:0% +scientists use. It leads to what we call +complexity classes. So order of growth + + align:start position:0% +complexity classes. So order of growth + + + align:start position:0% +complexity classes. So order of growth +or bigo notation is a way of abstractly + + align:start position:0% +or bigo notation is a way of abstractly + + + align:start position:0% +or bigo notation is a way of abstractly +describing the behavior of an algorithm + + align:start position:0% +describing the behavior of an algorithm + + + align:start position:0% +describing the behavior of an algorithm +and especially the equivalences of + + align:start position:0% +and especially the equivalences of + + + align:start position:0% +and especially the equivalences of +different + + align:start position:0% +different + + + align:start position:0% +different +algorithms. But let's look at those + + align:start position:0% +algorithms. But let's look at those + + + align:start position:0% +algorithms. But let's look at those +timing. Python provides a timer for you. + + align:start position:0% +timing. Python provides a timer for you. + + + align:start position:0% +timing. Python provides a timer for you. +You could import the time module and + + align:start position:0% +You could import the time module and + + + align:start position:0% +You could import the time module and +then you can call as you can see right + + align:start position:0% +then you can call as you can see right + + + align:start position:0% +then you can call as you can see right +down here. I might have defined a really + + align:start position:0% +down here. I might have defined a really + + + align:start position:0% +down here. I might have defined a really +simple little function convert Celsius + + align:start position:0% +simple little function convert Celsius + + + align:start position:0% +simple little function convert Celsius +to Fahrenheit. And in particular, I + + align:start position:0% +to Fahrenheit. And in particular, I + + + align:start position:0% +to Fahrenheit. And in particular, I +could invoke the clock method from the + + align:start position:0% +could invoke the clock method from the + + + align:start position:0% +could invoke the clock method from the +time module. And what that does is it + + align:start position:0% +time module. And what that does is it + + + align:start position:0% +time module. And what that does is it +gives me a number as the the number of + + align:start position:0% +gives me a number as the the number of + + + align:start position:0% +gives me a number as the the number of +some fractions of a second currently + + align:start position:0% +some fractions of a second currently + + + align:start position:0% +some fractions of a second currently +there. Having done that, I could call + + align:start position:0% +there. Having done that, I could call + + + align:start position:0% +there. Having done that, I could call +the function and then I could call the + + align:start position:0% +the function and then I could call the + + + align:start position:0% +the function and then I could call the +clock again and take the difference to + + align:start position:0% +clock again and take the difference to + + + align:start position:0% +clock again and take the difference to +tell me how much time it took to execute + + align:start position:0% +tell me how much time it took to execute + + + align:start position:0% +tell me how much time it took to execute +this. It's going to be a tiny amount of + + align:start position:0% +this. It's going to be a tiny amount of + + + align:start position:0% +this. It's going to be a tiny amount of +time. And then I could certainly print + + align:start position:0% +time. And then I could certainly print + + + align:start position:0% +time. And then I could certainly print +out some statistics. + + align:start position:0% +out some statistics. + + + align:start position:0% +out some statistics. +I could do that over a large number of + + align:start position:0% +I could do that over a large number of + + + align:start position:0% +I could do that over a large number of +runs, different sizes of the input, and + + align:start position:0% +runs, different sizes of the input, and + + + align:start position:0% +runs, different sizes of the input, and +come up with a sense of how much time + + align:start position:0% +come up with a sense of how much time + + + align:start position:0% +come up with a sense of how much time +does it + + align:start position:0% +does it + + + align:start position:0% +does it +take. Here's the problem with that. Not + + align:start position:0% +take. Here's the problem with that. Not + + + align:start position:0% +take. Here's the problem with that. Not +a bad + + align:start position:0% +a bad + + + align:start position:0% +a bad +idea. Again, my goal is to evaluate + + align:start position:0% +idea. Again, my goal is to evaluate + + + align:start position:0% +idea. Again, my goal is to evaluate +algorithms. Do different algorithms have + + align:start position:0% +algorithms. Do different algorithms have + + + align:start position:0% +algorithms. Do different algorithms have +different amounts of time associated + + align:start position:0% +different amounts of time associated + + + align:start position:0% +different amounts of time associated +with them? The good news is that if I + + align:start position:0% +with them? The good news is that if I + + + align:start position:0% +with them? The good news is that if I +measure running time, it will certainly + + align:start position:0% +measure running time, it will certainly + + + align:start position:0% +measure running time, it will certainly +vary as the algorithm changes, which is + + align:start position:0% +vary as the algorithm changes, which is + + + align:start position:0% +vary as the algorithm changes, which is +what I want to measure measure. Sorry. + + align:start position:0% +what I want to measure measure. Sorry. + + + align:start position:0% +what I want to measure measure. Sorry. +But one of the problems is that it will + + align:start position:0% +But one of the problems is that it will + + + align:start position:0% +But one of the problems is that it will +also vary as a function of the + + align:start position:0% +also vary as a function of the + + + align:start position:0% +also vary as a function of the +implementation. Right? If I use a loop + + align:start position:0% +implementation. Right? If I use a loop + + + align:start position:0% +implementation. Right? If I use a loop +that's got a couple of more steps inside + + align:start position:0% +that's got a couple of more steps inside + + + align:start position:0% +that's got a couple of more steps inside +of it in one algorithm than another, + + align:start position:0% +of it in one algorithm than another, + + + align:start position:0% +of it in one algorithm than another, +it's going to change the time. And I + + align:start position:0% +it's going to change the time. And I + + + align:start position:0% +it's going to change the time. And I +don't really care about that difference. + + align:start position:0% +don't really care about that difference. + + + align:start position:0% +don't really care about that difference. +So I'm confounding or conflating + + align:start position:0% +So I'm confounding or conflating + + + align:start position:0% +So I'm confounding or conflating +implementation influence on time with + + align:start position:0% +implementation influence on time with + + + align:start position:0% +implementation influence on time with +algorithm influence on time. Not so + + align:start position:0% +algorithm influence on time. Not so + + + align:start position:0% +algorithm influence on time. Not so +good. Worse timing will depend on the + + align:start position:0% +good. Worse timing will depend on the + + + align:start position:0% +good. Worse timing will depend on the +computer. My Mac here is pretty old. + + align:start position:0% +computer. My Mac here is pretty old. + + + align:start position:0% +computer. My Mac here is pretty old. +Well, at least for computer versions is + + align:start position:0% +Well, at least for computer versions is + + + align:start position:0% +Well, at least for computer versions is +about 5 years old. I'm sure some of you + + align:start position:0% +about 5 years old. I'm sure some of you + + + align:start position:0% +about 5 years old. I'm sure some of you +have much more recent Macs or uh other + + align:start position:0% +have much more recent Macs or uh other + + + align:start position:0% +have much more recent Macs or uh other +kinds of machines. Your speeds may + + align:start position:0% +kinds of machines. Your speeds may + + + align:start position:0% +kinds of machines. Your speeds may +different from mine. That's not going to + + align:start position:0% +different from mine. That's not going to + + + align:start position:0% +different from mine. That's not going to +help me in trying to measure this. And + + align:start position:0% +help me in trying to measure this. And + + + align:start position:0% +help me in trying to measure this. And +even if I could measure it on smalls + + align:start position:0% +even if I could measure it on smalls + + + align:start position:0% +even if I could measure it on smalls +size problems, it doesn't necessarily + + align:start position:0% +size problems, it doesn't necessarily + + + align:start position:0% +size problems, it doesn't necessarily +predict what happens when I go to really + + align:start position:0% +predict what happens when I go to really + + + align:start position:0% +predict what happens when I go to really +large size problems because of issues + + align:start position:0% +large size problems because of issues + + + align:start position:0% +large size problems because of issues +like the time it takes to get things out + + align:start position:0% +like the time it takes to get things out + + + align:start position:0% +like the time it takes to get things out +of memory and bring them back into the + + align:start position:0% +of memory and bring them back into the + + + align:start position:0% +of memory and bring them back into the +computer. So what it says is that timing + + align:start position:0% +computer. So what it says is that timing + + + align:start position:0% +computer. So what it says is that timing +does vary based on what I'd like to + + align:start position:0% +does vary based on what I'd like to + + + align:start position:0% +does vary based on what I'd like to +measure, but it varies on a lot of other + + align:start position:0% +measure, but it varies on a lot of other + + + align:start position:0% +measure, but it varies on a lot of other +factors and it's really not all that + + align:start position:0% +factors and it's really not all that + + + align:start position:0% +factors and it's really not all that +valuable. Okay, got rid of the first + + align:start position:0% +valuable. Okay, got rid of the first + + + align:start position:0% +valuable. Okay, got rid of the first +one. Let's abstract + + align:start position:0% +one. Let's abstract + + + align:start position:0% +one. Let's abstract +that. By abstract, I'm going to make the + + align:start position:0% +that. By abstract, I'm going to make the + + + align:start position:0% +that. By abstract, I'm going to make the +following assumption. I'm going to + + align:start position:0% +following assumption. I'm going to + + + align:start position:0% +following assumption. I'm going to +identify a set of primitive + + align:start position:0% +identify a set of primitive + + + align:start position:0% +identify a set of primitive +operations. We kind of get to say what + + align:start position:0% +operations. We kind of get to say what + + + align:start position:0% +operations. We kind of get to say what +they are, but the obvious one is to say, + + align:start position:0% +they are, but the obvious one is to say, + + + align:start position:0% +they are, but the obvious one is to say, +what does the machine do for me + + align:start position:0% +what does the machine do for me + + + align:start position:0% +what does the machine do for me +automatically? That would be things like + + align:start position:0% +automatically? That would be things like + + + align:start position:0% +automatically? That would be things like +arithmetic or mathematical operations, + + align:start position:0% +arithmetic or mathematical operations, + + + align:start position:0% +arithmetic or mathematical operations, +multiplication, division, + + align:start position:0% +multiplication, division, + + + align:start position:0% +multiplication, division, +subtraction, + + align:start position:0% +subtraction, + + + align:start position:0% +subtraction, +comparisons, something equal to another + + align:start position:0% +comparisons, something equal to another + + + align:start position:0% +comparisons, something equal to another +thing, something greater than, something + + align:start position:0% +thing, something greater than, something + + + align:start position:0% +thing, something greater than, something +less than, assignments, set a name to a + + align:start position:0% +less than, assignments, set a name to a + + + align:start position:0% +less than, assignments, set a name to a +value, and retrieval from memory. I'm + + align:start position:0% +value, and retrieval from memory. I'm + + + align:start position:0% +value, and retrieval from memory. I'm +going to assume that all of these + + align:start position:0% +going to assume that all of these + + + align:start position:0% +going to assume that all of these +operations take about the same amount of + + align:start position:0% +operations take about the same amount of + + + align:start position:0% +operations take about the same amount of +time inside my + + align:start position:0% +time inside my + + + align:start position:0% +time inside my +machine. Nice thing here is then it + + align:start position:0% +machine. Nice thing here is then it + + + align:start position:0% +machine. Nice thing here is then it +doesn't matter which machine I'm using. + + align:start position:0% +doesn't matter which machine I'm using. + + + align:start position:0% +doesn't matter which machine I'm using. +And I'm measuring how long does the + + align:start position:0% +And I'm measuring how long does the + + + align:start position:0% +And I'm measuring how long does the +algorithm take by counting how many + + align:start position:0% +algorithm take by counting how many + + + align:start position:0% +algorithm take by counting how many +operations of this type are done inside + + align:start position:0% +operations of this type are done inside + + + align:start position:0% +operations of this type are done inside +of the algorithm. And I'm going to use + + align:start position:0% +of the algorithm. And I'm going to use + + + align:start position:0% +of the algorithm. And I'm going to use +that count to come up with a number of + + align:start position:0% +that count to come up with a number of + + + align:start position:0% +that count to come up with a number of +operations executed as a function of the + + align:start position:0% +operations executed as a function of the + + + align:start position:0% +operations executed as a function of the +size of the input. And if I'm lucky, + + align:start position:0% +size of the input. And if I'm lucky, + + + align:start position:0% +size of the input. And if I'm lucky, +that'll give me a sense of what's the + + align:start position:0% +that'll give me a sense of what's the + + + align:start position:0% +that'll give me a sense of what's the +efficiency of the + + align:start position:0% +efficiency of the + + + align:start position:0% +efficiency of the +algorithm. So this one's pretty boring. + + align:start position:0% +algorithm. So this one's pretty boring. + + + align:start position:0% +algorithm. So this one's pretty boring. +It's got three steps, right? A + + align:start position:0% +It's got three steps, right? A + + + align:start position:0% +It's got three steps, right? A +multiplication, a division, and an + + align:start position:0% +multiplication, a division, and an + + + align:start position:0% +multiplication, a division, and an +addition. Four if you count the return. + + align:start position:0% +addition. Four if you count the return. + + + align:start position:0% +addition. Four if you count the return. +But if I had a little thing here that + + align:start position:0% +But if I had a little thing here that + + + align:start position:0% +But if I had a little thing here that +added up the integers from zero up to x, + + align:start position:0% +added up the integers from zero up to x, + + + align:start position:0% +added up the integers from zero up to x, +I've got a little loop inside here and I + + align:start position:0% +I've got a little loop inside here and I + + + align:start position:0% +I've got a little loop inside here and I +could count operations. So in this case, + + align:start position:0% +could count operations. So in this case, + + + align:start position:0% +could count operations. So in this case, +it's just as I said three operations + + align:start position:0% +it's just as I said three operations + + + align:start position:0% +it's just as I said three operations +here. I've got one operation. I'm doing + + align:start position:0% +here. I've got one operation. I'm doing + + + align:start position:0% +here. I've got one operation. I'm doing +an assignment and then inside here in + + align:start position:0% +an assignment and then inside here in + + + align:start position:0% +an assignment and then inside here in +essence there's one operation to set I + + align:start position:0% +essence there's one operation to set I + + + align:start position:0% +essence there's one operation to set I +to a value from that iterator. Initially + + align:start position:0% +to a value from that iterator. Initially + + + align:start position:0% +to a value from that iterator. Initially +it's going to be zero and then it's + + align:start position:0% +it's going to be zero and then it's + + + align:start position:0% +it's going to be zero and then it's +going to be one and you get the idea. + + align:start position:0% +going to be one and you get the idea. + + + align:start position:0% +going to be one and you get the idea. +And + + align:start position:0% +And + + + align:start position:0% +And +here that's actually two operations. + + align:start position:0% +here that's actually two operations. + + + align:start position:0% +here that's actually two operations. +It's nice Python shorthand. But what is + + align:start position:0% +It's nice Python shorthand. But what is + + + align:start position:0% +It's nice Python shorthand. But what is +that operation? It says take the value + + align:start position:0% +that operation? It says take the value + + + align:start position:0% +that operation? It says take the value +of total and the value of I add them + + align:start position:0% +of total and the value of I add them + + + align:start position:0% +of total and the value of I add them +together. It's one operation. And then + + align:start position:0% +together. It's one operation. And then + + + align:start position:0% +together. It's one operation. And then +set that value or rather set the name + + align:start position:0% +set that value or rather set the name + + + align:start position:0% +set that value or rather set the name +total to that new value. So second + + align:start position:0% +total to that new value. So second + + + align:start position:0% +total to that new value. So second +operation. So you can see in here I've + + align:start position:0% +operation. So you can see in here I've + + + align:start position:0% +operation. So you can see in here I've +got three operations. And what else do I + + align:start position:0% +got three operations. And what else do I + + + align:start position:0% +got three operations. And what else do I +have? Well, I'm going to go through this + + align:start position:0% +have? Well, I'm going to go through this + + + align:start position:0% +have? Well, I'm going to go through this +loop x times, right? I do it for i + + align:start position:0% +loop x times, right? I do it for i + + + align:start position:0% +loop x times, right? I do it for i +equals z then for i equal 1 and so on. + + align:start position:0% +equals z then for i equal 1 and so on. + + + align:start position:0% +equals z then for i equal 1 and so on. +So I'm going to run through that loop x + + align:start position:0% +So I'm going to run through that loop x + + + align:start position:0% +So I'm going to run through that loop x +times. And if I put that together, I get + + align:start position:0% +times. And if I put that together, I get + + + align:start position:0% +times. And if I put that together, I get +a nice little + + align:start position:0% +a nice little + + + align:start position:0% +a nice little +expression 1 + + + align:start position:0% +expression 1 + + + + align:start position:0% +expression 1 + +3x. Actually, I probably cheated here. I + + align:start position:0% +3x. Actually, I probably cheated here. I + + + align:start position:0% +3x. Actually, I probably cheated here. I +shouldn't say cheated. I probably should + + align:start position:0% +shouldn't say cheated. I probably should + + + align:start position:0% +shouldn't say cheated. I probably should +have counted the return as one more + + align:start position:0% +have counted the return as one more + + + align:start position:0% +have counted the return as one more +operation. So that would be 1 plus 3x + + + align:start position:0% +operation. So that would be 1 plus 3x + + + + align:start position:0% +operation. So that would be 1 plus 3x + +1 or 3x + 2 + + align:start position:0% +1 or 3x + 2 + + + align:start position:0% +1 or 3x + 2 +operations. Why should you care? + + align:start position:0% +operations. Why should you care? + + + align:start position:0% +operations. Why should you care? +It's a little closer to what I'd like + + align:start position:0% +It's a little closer to what I'd like + + + align:start position:0% +It's a little closer to what I'd like +because now I've got an expression that + + align:start position:0% +because now I've got an expression that + + + align:start position:0% +because now I've got an expression that +tells me something about how much time + + align:start position:0% +tells me something about how much time + + + align:start position:0% +tells me something about how much time +is this going to take as I change the + + align:start position:0% +is this going to take as I change the + + + align:start position:0% +is this going to take as I change the +size of the problem. If x is equal to + + align:start position:0% +size of the problem. If x is equal to + + + align:start position:0% +size of the problem. If x is equal to +10, it's going to take me 32 operations. + + align:start position:0% +10, it's going to take me 32 operations. + + + align:start position:0% +10, it's going to take me 32 operations. +If x is equal to 100, 302 operations. If + + align:start position:0% +If x is equal to 100, 302 operations. If + + + align:start position:0% +If x is equal to 100, 302 operations. If +x is equal to a,000, 30,2 operations. + + align:start position:0% +x is equal to a,000, 30,2 operations. + + + align:start position:0% +x is equal to a,000, 30,2 operations. +And if I wanted the actual time, I just + + align:start position:0% +And if I wanted the actual time, I just + + + align:start position:0% +And if I wanted the actual time, I just +multiply that by whatever that constant + + align:start position:0% +multiply that by whatever that constant + + + align:start position:0% +multiply that by whatever that constant +amount of time is for each operation. + + align:start position:0% +amount of time is for each operation. + + + align:start position:0% +amount of time is for each operation. +I've got a good estimate of + + align:start position:0% +I've got a good estimate of + + + align:start position:0% +I've got a good estimate of +that. Sounds pretty good. + + align:start position:0% +that. Sounds pretty good. + + + align:start position:0% +that. Sounds pretty good. +Not quite what we want, but it's + + align:start position:0% +Not quite what we want, but it's + + + align:start position:0% +Not quite what we want, but it's +close. So if I was counting operations, + + align:start position:0% +close. So if I was counting operations, + + + align:start position:0% +close. So if I was counting operations, +what could I say about it? First of all, + + align:start position:0% +what could I say about it? First of all, + + + align:start position:0% +what could I say about it? First of all, +it certainly depends on the algorithm. + + align:start position:0% +it certainly depends on the algorithm. + + + align:start position:0% +it certainly depends on the algorithm. +That's great. Number of operations is + + align:start position:0% +That's great. Number of operations is + + + align:start position:0% +That's great. Number of operations is +going to directly relate to the + + align:start position:0% +going to directly relate to the + + + align:start position:0% +going to directly relate to the +algorithm I'm trying to measure, which + + align:start position:0% +algorithm I'm trying to measure, which + + + align:start position:0% +algorithm I'm trying to measure, which +is what I'm + + align:start position:0% +is what I'm + + + align:start position:0% +is what I'm +after. Unfortunately, it still depends a + + align:start position:0% +after. Unfortunately, it still depends a + + + align:start position:0% +after. Unfortunately, it still depends a +little bit on the implementation. Let me + + align:start position:0% +little bit on the implementation. Let me + + + align:start position:0% +little bit on the implementation. Let me +show you what I mean by that by backing + + align:start position:0% +show you what I mean by that by backing + + + align:start position:0% +show you what I mean by that by backing +up for a second. + + align:start position:0% +up for a second. + + + align:start position:0% +up for a second. +Suppose I were to change this for loop + + align:start position:0% +Suppose I were to change this for loop + + + align:start position:0% +Suppose I were to change this for loop +to a while loop. I'll set I equal to + + align:start position:0% +to a while loop. I'll set I equal to + + + align:start position:0% +to a while loop. I'll set I equal to +zero outside of the loop and then while + + align:start position:0% +zero outside of the loop and then while + + + align:start position:0% +zero outside of the loop and then while +I is less than x + one, I'll do the + + align:start position:0% +I is less than x + one, I'll do the + + + align:start position:0% +I is less than x + one, I'll do the +things inside of that. That would + + align:start position:0% +things inside of that. That would + + + align:start position:0% +things inside of that. That would +actually add one more operation inside + + align:start position:0% +actually add one more operation inside + + + align:start position:0% +actually add one more operation inside +the loop because I both have to set the + + align:start position:0% +the loop because I both have to set the + + + align:start position:0% +the loop because I both have to set the +value of i and I have to test the value + + align:start position:0% +value of i and I have to test the value + + + align:start position:0% +value of i and I have to test the value +of i as well as doing the other + + align:start position:0% +of i as well as doing the other + + + align:start position:0% +of i as well as doing the other +operations down here. And so rather than + + align:start position:0% +operations down here. And so rather than + + + align:start position:0% +operations down here. And so rather than +getting 3x + 1, I would get 4x + 1. Eh, + + align:start position:0% +getting 3x + 1, I would get 4x + 1. Eh, + + + align:start position:0% +getting 3x + 1, I would get 4x + 1. Eh, +as the government says, what's the + + align:start position:0% +as the government says, what's the + + + align:start position:0% +as the government says, what's the +difference between three and four? You + + align:start position:0% +difference between three and four? You + + + align:start position:0% +difference between three and four? You +know, when you're talking about really + + align:start position:0% +know, when you're talking about really + + + align:start position:0% +know, when you're talking about really +big + + align:start position:0% +big + + + align:start position:0% +big +numbers, problem is in terms of + + align:start position:0% +numbers, problem is in terms of + + + align:start position:0% +numbers, problem is in terms of +counting, it does depend. And I'm going + + align:start position:0% +counting, it does depend. And I'm going + + + align:start position:0% +counting, it does depend. And I'm going +to get rid of that in a second. So it + + align:start position:0% +to get rid of that in a second. So it + + + align:start position:0% +to get rid of that in a second. So it +still depends a little bit on the + + align:start position:0% +still depends a little bit on the + + + align:start position:0% +still depends a little bit on the +implementation. I remind you, I wanted + + align:start position:0% +implementation. I remind you, I wanted + + + align:start position:0% +implementation. I remind you, I wanted +to measure impact of the + + align:start position:0% +to measure impact of the + + + align:start position:0% +to measure impact of the +algorithm. The other good news is the + + align:start position:0% +algorithm. The other good news is the + + + align:start position:0% +algorithm. The other good news is the +count is independent of which computer I + + align:start position:0% +count is independent of which computer I + + + align:start position:0% +count is independent of which computer I +run on. As long as those all my + + align:start position:0% +run on. As long as those all my + + + align:start position:0% +run on. As long as those all my +computers come with the same set of + + align:start position:0% +computers come with the same set of + + + align:start position:0% +computers come with the same set of +basic operations, I don't care what the + + align:start position:0% +basic operations, I don't care what the + + + align:start position:0% +basic operations, I don't care what the +time of my computer is versus yours to + + align:start position:0% +time of my computer is versus yours to + + + align:start position:0% +time of my computer is versus yours to +do those operations. I'm measuring how + + align:start position:0% +do those operations. I'm measuring how + + + align:start position:0% +do those operations. I'm measuring how +much time it would take. And I should + + align:start position:0% +much time it would take. And I should + + + align:start position:0% +much time it would take. And I should +say by the way, one of the reasons I + + align:start position:0% +say by the way, one of the reasons I + + + align:start position:0% +say by the way, one of the reasons I +want to do it is less to know is it + + align:start position:0% +want to do it is less to know is it + + + align:start position:0% +want to do it is less to know is it +going to take 37.42 ftocs or not, but + + align:start position:0% +going to take 37.42 ftocs or not, but + + + align:start position:0% +going to take 37.42 ftocs or not, but +rather to say if this algorithm has a + + align:start position:0% +rather to say if this algorithm has a + + + align:start position:0% +rather to say if this algorithm has a +particular behavior, if I double the + + align:start position:0% +particular behavior, if I double the + + + align:start position:0% +particular behavior, if I double the +size of the input, does that double the + + align:start position:0% +size of the input, does that double the + + + align:start position:0% +size of the input, does that double the +amount of time I need? Does that + + align:start position:0% +amount of time I need? Does that + + + align:start position:0% +amount of time I need? Does that +quadruple the amount of time I need? + + align:start position:0% +quadruple the amount of time I need? + + + align:start position:0% +quadruple the amount of time I need? +Does it increase it by a factor of 10? + + align:start position:0% +Does it increase it by a factor of 10? + + + align:start position:0% +Does it increase it by a factor of 10? +And here what matters isn't the speed of + + align:start position:0% +And here what matters isn't the speed of + + + align:start position:0% +And here what matters isn't the speed of +the computer, it's the number of + + align:start position:0% +the computer, it's the number of + + + align:start position:0% +the computer, it's the number of +operations. The last one I'm not going + + align:start position:0% +operations. The last one I'm not going + + + align:start position:0% +operations. The last one I'm not going +to really worry about, but we'd have to + + align:start position:0% +to really worry about, but we'd have to + + + align:start position:0% +to really worry about, but we'd have to +really think about what are the + + align:start position:0% +really think about what are the + + + align:start position:0% +really think about what are the +operations we want to count. I made an + + align:start position:0% +operations we want to count. I made an + + + align:start position:0% +operations we want to count. I made an +assumption that the amount of time it + + align:start position:0% +assumption that the amount of time it + + + align:start position:0% +assumption that the amount of time it +takes to retrieve something from memory + + align:start position:0% +takes to retrieve something from memory + + + align:start position:0% +takes to retrieve something from memory +is the same as the amount of time it + + align:start position:0% +is the same as the amount of time it + + + align:start position:0% +is the same as the amount of time it +takes to do a numerical computation. + + align:start position:0% +takes to do a numerical computation. + + + align:start position:0% +takes to do a numerical computation. +that may not be accurate but this one + + align:start position:0% +that may not be accurate but this one + + + align:start position:0% +that may not be accurate but this one +can probably be dealt with by just + + align:start position:0% +can probably be dealt with by just + + + align:start position:0% +can probably be dealt with by just +agreeing on what are the common + + align:start position:0% +agreeing on what are the common + + + align:start position:0% +agreeing on what are the common +operations and then doing the + + align:start position:0% +operations and then doing the + + + align:start position:0% +operations and then doing the +measurement. So this is + + align:start position:0% +measurement. So this is + + + align:start position:0% +measurement. So this is +closer. Excuse me. It certainly that + + align:start position:0% +closer. Excuse me. It certainly that + + + align:start position:0% +closer. Excuse me. It certainly that +count varies for different inputs and we + + align:start position:0% +count varies for different inputs and we + + + align:start position:0% +count varies for different inputs and we +can use it to come up with a + + align:start position:0% +can use it to come up with a + + + align:start position:0% +can use it to come up with a +relationship between the inputs and the + + align:start position:0% +relationship between the inputs and the + + + align:start position:0% +relationship between the inputs and the +count. And for the most part it reflects + + align:start position:0% +count. And for the most part it reflects + + + align:start position:0% +count. And for the most part it reflects +the algorithm, not the + + align:start position:0% +the algorithm, not the + + + align:start position:0% +the algorithm, not the +implementation. But it's still got that + + align:start position:0% +implementation. But it's still got that + + + align:start position:0% +implementation. But it's still got that +last piece left there. So I need to get + + align:start position:0% +last piece left there. So I need to get + + + align:start position:0% +last piece left there. So I need to get +rid of the last + + align:start position:0% +rid of the last + + + align:start position:0% +rid of the last +piece. So what can we say here? Timing + + align:start position:0% +piece. So what can we say here? Timing + + + align:start position:0% +piece. So what can we say here? Timing +and counting do evaluate or reflect + + align:start position:0% +and counting do evaluate or reflect + + + align:start position:0% +and counting do evaluate or reflect +implementations. I don't want that. + + align:start position:0% +implementations. I don't want that. + + + align:start position:0% +implementations. I don't want that. +Timing also evaluates the machines. What + + align:start position:0% +Timing also evaluates the machines. What + + + align:start position:0% +Timing also evaluates the machines. What +I want to do is just evaluate the + + align:start position:0% +I want to do is just evaluate the + + + align:start position:0% +I want to do is just evaluate the +algorithm and especially I want to + + align:start position:0% +algorithm and especially I want to + + + align:start position:0% +algorithm and especially I want to +understand how does it scale. I'm going + + align:start position:0% +understand how does it scale. I'm going + + + align:start position:0% +understand how does it scale. I'm going +to say what I said a few minutes ago + + align:start position:0% +to say what I said a few minutes ago + + + align:start position:0% +to say what I said a few minutes ago +again. If I were to take an algorithm + + align:start position:0% +again. If I were to take an algorithm + + + align:start position:0% +again. If I were to take an algorithm +and I say I know what its complexity is. + + align:start position:0% +and I say I know what its complexity is. + + + align:start position:0% +and I say I know what its complexity is. +My question is if I double the size of + + align:start position:0% +My question is if I double the size of + + + align:start position:0% +My question is if I double the size of +the input, what does it say to the + + align:start position:0% +the input, what does it say to the + + + align:start position:0% +the input, what does it say to the +speed? Because that's going to tell me + + align:start position:0% +speed? Because that's going to tell me + + + align:start position:0% +speed? Because that's going to tell me +something about the algorithm. I want to + + align:start position:0% +something about the algorithm. I want to + + + align:start position:0% +something about the algorithm. I want to +say what happens when I scale it. And in + + align:start position:0% +say what happens when I scale it. And in + + + align:start position:0% +say what happens when I scale it. And in +particular, I want to relate that to the + + align:start position:0% +particular, I want to relate that to the + + + align:start position:0% +particular, I want to relate that to the +size of the + + align:start position:0% +size of the + + + align:start position:0% +size of the +input. So here's what we're going to do. + + align:start position:0% +input. So here's what we're going to do. + + + align:start position:0% +input. So here's what we're going to do. +We're going to introduce orders of + + align:start position:0% +We're going to introduce orders of + + + align:start position:0% +We're going to introduce orders of +growth. It's a wonderful tool in + + align:start position:0% +growth. It's a wonderful tool in + + + align:start position:0% +growth. It's a wonderful tool in +computer science. And what we're going + + align:start position:0% +computer science. And what we're going + + + align:start position:0% +computer science. And what we're going +to focus on is that idea of counting + + align:start position:0% +to focus on is that idea of counting + + + align:start position:0% +to focus on is that idea of counting +operations, but we're not going to worry + + align:start position:0% +operations, but we're not going to worry + + + align:start position:0% +operations, but we're not going to worry +about small variations, whether it's + + align:start position:0% +about small variations, whether it's + + + align:start position:0% +about small variations, whether it's +three or four steps inside of the loop. + + align:start position:0% +three or four steps inside of the loop. + + + align:start position:0% +three or four steps inside of the loop. +We're going to show that that doesn't + + align:start position:0% +We're going to show that that doesn't + + + align:start position:0% +We're going to show that that doesn't +matter. And if you think about my + + align:start position:0% +matter. And if you think about my + + + align:start position:0% +matter. And if you think about my +statement of does it double in terms of + + align:start position:0% +statement of does it double in terms of + + + align:start position:0% +statement of does it double in terms of +size or speed or not, or sorry, time or + + align:start position:0% +size or speed or not, or sorry, time or + + + align:start position:0% +size or speed or not, or sorry, time or +not, whether it goes from 3 to six or + + align:start position:0% +not, whether it goes from 3 to six or + + + align:start position:0% +not, whether it goes from 3 to six or +four to eight, it's still a doubling. So + + align:start position:0% +four to eight, it's still a doubling. So + + + align:start position:0% +four to eight, it's still a doubling. So +I don't care about those pieces inside. + + align:start position:0% +I don't care about those pieces inside. + + + align:start position:0% +I don't care about those pieces inside. +I'm going to focus on what happens when + + align:start position:0% +I'm going to focus on what happens when + + + align:start position:0% +I'm going to focus on what happens when +the size of the problem gets arbitrarily + + align:start position:0% +the size of the problem gets arbitrarily + + + align:start position:0% +the size of the problem gets arbitrarily +large. I don't care about counting + + align:start position:0% +large. I don't care about counting + + + align:start position:0% +large. I don't care about counting +things from zero up to x when x is 10 or + + align:start position:0% +things from zero up to x when x is 10 or + + + align:start position:0% +things from zero up to x when x is 10 or +20. What happens when it's a million, + + align:start position:0% +20. What happens when it's a million, + + + align:start position:0% +20. What happens when it's a million, +100 million? What's the asmtoic behavior + + align:start position:0% +100 million? What's the asmtoic behavior + + + align:start position:0% +100 million? What's the asmtoic behavior +of this? And I want to relate that time + + align:start position:0% +of this? And I want to relate that time + + + align:start position:0% +of this? And I want to relate that time +needed against the size of the input so + + align:start position:0% +needed against the size of the input so + + + align:start position:0% +needed against the size of the input so +I can make that comparison I + + align:start position:0% +I can make that comparison I + + + align:start position:0% +I can make that comparison I +suggested. Okay. So to do that we have + + align:start position:0% +suggested. Okay. So to do that we have + + + align:start position:0% +suggested. Okay. So to do that we have +to do a couple of things. We have to + + align:start position:0% +to do a couple of things. We have to + + + align:start position:0% +to do a couple of things. We have to +decide what are we going to measure and + + align:start position:0% +decide what are we going to measure and + + + align:start position:0% +decide what are we going to measure and +then we have to think about how do we + + align:start position:0% +then we have to think about how do we + + + align:start position:0% +then we have to think about how do we +count without worrying about + + align:start position:0% +count without worrying about + + + align:start position:0% +count without worrying about +implementation + + align:start position:0% +implementation + + + align:start position:0% +implementation +details. So we're going to express + + align:start position:0% +details. So we're going to express + + + align:start position:0% +details. So we're going to express +efficiency in terms of size of input. + + align:start position:0% +efficiency in terms of size of input. + + + align:start position:0% +efficiency in terms of size of input. +And usually this is going to be obvious. + + align:start position:0% +And usually this is going to be obvious. + + + align:start position:0% +And usually this is going to be obvious. +If I've got a procedure that takes one + + align:start position:0% +If I've got a procedure that takes one + + + align:start position:0% +If I've got a procedure that takes one +argument that's an integer, the size of + + align:start position:0% +argument that's an integer, the size of + + + align:start position:0% +argument that's an integer, the size of +the integer is the thing I'm going to + + align:start position:0% +the integer is the thing I'm going to + + + align:start position:0% +the integer is the thing I'm going to +measure things in. If I double the size + + align:start position:0% +measure things in. If I double the size + + + align:start position:0% +measure things in. If I double the size +of that integer, what happens to the + + align:start position:0% +of that integer, what happens to the + + + align:start position:0% +of that integer, what happens to the +computation? If I'm computing something + + align:start position:0% +computation? If I'm computing something + + + align:start position:0% +computation? If I'm computing something +over a list, typically the length of the + + align:start position:0% +over a list, typically the length of the + + + align:start position:0% +over a list, typically the length of the +list is going to be the thing I'm going + + align:start position:0% +list is going to be the thing I'm going + + + align:start position:0% +list is going to be the thing I'm going +to use to characterize the size of the + + align:start position:0% +to use to characterize the size of the + + + align:start position:0% +to use to characterize the size of the +problem. If I've got, and we'll see this + + align:start position:0% +problem. If I've got, and we'll see this + + + align:start position:0% +problem. If I've got, and we'll see this +in a second, a function that takes more + + align:start position:0% +in a second, a function that takes more + + + align:start position:0% +in a second, a function that takes more +than one argument, I get to decide + + align:start position:0% +than one argument, I get to decide + + + align:start position:0% +than one argument, I get to decide +what's the parameter I want to use. If + + align:start position:0% +what's the parameter I want to use. If + + + align:start position:0% +what's the parameter I want to use. If +I'm searching to see is this element in + + align:start position:0% +I'm searching to see is this element in + + + align:start position:0% +I'm searching to see is this element in +that list, typically I want to worry + + align:start position:0% +that list, typically I want to worry + + + align:start position:0% +that list, typically I want to worry +about what's the size of the list, not + + align:start position:0% +about what's the size of the list, not + + + align:start position:0% +about what's the size of the list, not +what's the size of the element. But we + + align:start position:0% +what's the size of the element. But we + + + align:start position:0% +what's the size of the element. But we +have to specify what is it we're + + align:start position:0% +have to specify what is it we're + + + align:start position:0% +have to specify what is it we're +measuring. And we're going to see + + align:start position:0% +measuring. And we're going to see + + + align:start position:0% +measuring. And we're going to see +examples of that in just a second. + + align:start position:0% + + + + align:start position:0% + +Okay, so now we start thinking about + + align:start position:0% +Okay, so now we start thinking about + + + align:start position:0% +Okay, so now we start thinking about +that sounds great. Certainly, if I'm + + align:start position:0% +that sounds great. Certainly, if I'm + + + align:start position:0% +that sounds great. Certainly, if I'm +computing something numeric, sum of + + align:start position:0% +computing something numeric, sum of + + + align:start position:0% +computing something numeric, sum of +integers from zero up to x, it's kind of + + align:start position:0% +integers from zero up to x, it's kind of + + + align:start position:0% +integers from zero up to x, it's kind of +obvious. X is the size of my problem. + + align:start position:0% +obvious. X is the size of my problem. + + + align:start position:0% +obvious. X is the size of my problem. +How many steps does it take? I can count + + align:start position:0% +How many steps does it take? I can count + + + align:start position:0% +How many steps does it take? I can count +that. But in some cases, the amount of + + align:start position:0% +that. But in some cases, the amount of + + + align:start position:0% +that. But in some cases, the amount of +time the code takes is going to depend + + align:start position:0% +time the code takes is going to depend + + + align:start position:0% +time the code takes is going to depend +on the input. So let's take this little + + align:start position:0% +on the input. So let's take this little + + + align:start position:0% +on the input. So let's take this little +piece of code here. And I do hope by + + align:start position:0% +piece of code here. And I do hope by + + + align:start position:0% +piece of code here. And I do hope by +now, even though we flash up code, + + align:start position:0% +now, even though we flash up code, + + + align:start position:0% +now, even though we flash up code, +you're already beginning to recognize + + align:start position:0% +you're already beginning to recognize + + + align:start position:0% +you're already beginning to recognize +what does it do? Not the least of which + + align:start position:0% +what does it do? Not the least of which + + + align:start position:0% +what does it do? Not the least of which +by the clever name that we chose. But + + align:start position:0% +by the clever name that we chose. But + + + align:start position:0% +by the clever name that we chose. But +this is obviously just a little + + align:start position:0% +this is obviously just a little + + + align:start position:0% +this is obviously just a little +function. It runs through a loop running + + align:start position:0% +function. It runs through a loop running + + + align:start position:0% +function. It runs through a loop running +let I sorry a for loop that takes I for + + align:start position:0% +let I sorry a for loop that takes I for + + + align:start position:0% +let I sorry a for loop that takes I for +each element in a list L. And it's + + align:start position:0% +each element in a list L. And it's + + + align:start position:0% +each element in a list L. And it's +checking to see is I equal to the + + align:start position:0% +checking to see is I equal to the + + + align:start position:0% +checking to see is I equal to the +element I've provided. And when it is, + + align:start position:0% +element I've provided. And when it is, + + + align:start position:0% +element I've provided. And when it is, +I'm going to return true. If I get all + + align:start position:0% +I'm going to return true. If I get all + + + align:start position:0% +I'm going to return true. If I get all +the way through the loop and I didn't + + align:start position:0% +the way through the loop and I didn't + + + align:start position:0% +the way through the loop and I didn't +find it, I'm going to return false. This + + align:start position:0% +find it, I'm going to return false. This + + + align:start position:0% +find it, I'm going to return false. This +is just saying is E in my input list + + align:start position:0% +is just saying is E in my input list + + + align:start position:0% +is just saying is E in my input list +L. How many steps is this going to + + align:start position:0% +L. How many steps is this going to + + + align:start position:0% +L. How many steps is this going to +take? Well, we can certainly count the + + align:start position:0% +take? Well, we can certainly count the + + + align:start position:0% +take? Well, we can certainly count the +number of steps in the loop, right? + + align:start position:0% +number of steps in the loop, right? + + + align:start position:0% +number of steps in the loop, right? +We've got a set I, we got to compare I, + + align:start position:0% +We've got a set I, we got to compare I, + + + align:start position:0% +We've got a set I, we got to compare I, +and potentially we got a return. So, + + align:start position:0% +and potentially we got a return. So, + + + align:start position:0% +and potentially we got a return. So, +there's at most three steps inside the + + align:start position:0% +there's at most three steps inside the + + + align:start position:0% +there's at most three steps inside the +loop, + + align:start position:0% +loop, + + + align:start position:0% +loop, +but depends on how lucky I'm feeling, + + align:start position:0% +but depends on how lucky I'm feeling, + + + align:start position:0% +but depends on how lucky I'm feeling, +right? If E happens to be the first + + align:start position:0% +right? If E happens to be the first + + + align:start position:0% +right? If E happens to be the first +element in the list, it goes through the + + align:start position:0% +element in the list, it goes through the + + + align:start position:0% +element in the list, it goes through the +loop once, I'm done. Great. + + align:start position:0% +loop once, I'm done. Great. + + + align:start position:0% +loop once, I'm done. Great. +I'm not always that lucky. If E is not + + align:start position:0% +I'm not always that lucky. If E is not + + + align:start position:0% +I'm not always that lucky. If E is not +in the list, then it will go through + + align:start position:0% +in the list, then it will go through + + + align:start position:0% +in the list, then it will go through +this entire loop until it gets all the + + align:start position:0% +this entire loop until it gets all the + + + align:start position:0% +this entire loop until it gets all the +way through the elements of L before + + align:start position:0% +way through the elements of L before + + + align:start position:0% +way through the elements of L before +saying + + align:start position:0% +saying + + + align:start position:0% +saying +false. So this sort of a best case + + align:start position:0% +false. So this sort of a best case + + + align:start position:0% +false. So this sort of a best case +scenario. This is the worst case + + align:start position:0% +scenario. This is the worst case + + + align:start position:0% +scenario. This is the worst case +scenario. Again, if I'm assigned to say, + + align:start position:0% +scenario. Again, if I'm assigned to say, + + + align:start position:0% +scenario. Again, if I'm assigned to say, +well, let's run some trials. Let's do a + + align:start position:0% +well, let's run some trials. Let's do a + + + align:start position:0% +well, let's run some trials. Let's do a +bunch of examples and see how many steps + + align:start position:0% +bunch of examples and see how many steps + + + align:start position:0% +bunch of examples and see how many steps +does it go through. And that would be + + align:start position:0% +does it go through. And that would be + + + align:start position:0% +does it go through. And that would be +the average case. On average, I'm likely + + align:start position:0% +the average case. On average, I'm likely + + + align:start position:0% +the average case. On average, I'm likely +to look at half the elements in the list + + align:start position:0% +to look at half the elements in the list + + + align:start position:0% +to look at half the elements in the list +before I find it. Right? I'm lucky, it's + + align:start position:0% +before I find it. Right? I'm lucky, it's + + + align:start position:0% +before I find it. Right? I'm lucky, it's +early on. If I'm not so lucky, it's + + align:start position:0% +early on. If I'm not so lucky, it's + + + align:start position:0% +early on. If I'm not so lucky, it's +later on. Which one do I use? Well, + + align:start position:0% +later on. Which one do I use? Well, + + + align:start position:0% +later on. Which one do I use? Well, +we're going to focus on this + + align:start position:0% +we're going to focus on this + + + align:start position:0% +we're going to focus on this +one because that gives you an upper + + align:start position:0% +one because that gives you an upper + + + align:start position:0% +one because that gives you an upper +bound on the amount of time it's going + + align:start position:0% +bound on the amount of time it's going + + + align:start position:0% +bound on the amount of time it's going +to take. What happens in the worstc case + + align:start position:0% +to take. What happens in the worstc case + + + align:start position:0% +to take. What happens in the worstc case +scenario? We will find at times it's + + align:start position:0% +scenario? We will find at times it's + + + align:start position:0% +scenario? We will find at times it's +valuable to look at the average case to + + align:start position:0% +valuable to look at the average case to + + + align:start position:0% +valuable to look at the average case to +give us a rough sense of what's going to + + align:start position:0% +give us a rough sense of what's going to + + + align:start position:0% +give us a rough sense of what's going to +happen on average. But usually when we + + align:start position:0% +happen on average. But usually when we + + + align:start position:0% +happen on average. But usually when we +talk about complexity, we're going to + + align:start position:0% +talk about complexity, we're going to + + + align:start position:0% +talk about complexity, we're going to +focus on the worst case + + align:start position:0% +focus on the worst case + + + align:start position:0% +focus on the worst case +behavior. So to say it a little bit + + align:start position:0% +behavior. So to say it a little bit + + + align:start position:0% +behavior. So to say it a little bit +different way, let's go back to my + + align:start position:0% +different way, let's go back to my + + + align:start position:0% +different way, let's go back to my +example. Suppose you given a list L of + + align:start position:0% +example. Suppose you given a list L of + + + align:start position:0% +example. Suppose you given a list L of +some length, length of L. We call that N + + align:start position:0% +some length, length of L. We call that N + + + align:start position:0% +some length, length of L. We call that N +if you like. Then my best case would be + + align:start position:0% +if you like. Then my best case would be + + + align:start position:0% +if you like. Then my best case would be +the minimum running time. And in this + + align:start position:0% +the minimum running time. And in this + + + align:start position:0% +the minimum running time. And in this +case it would be for the first element + + align:start position:0% +case it would be for the first element + + + align:start position:0% +case it would be for the first element +in the list. Notice in that case the + + align:start position:0% +in the list. Notice in that case the + + + align:start position:0% +in the list. Notice in that case the +number of steps I take would be + + align:start position:0% +number of steps I take would be + + + align:start position:0% +number of steps I take would be +independent of the length of L. That's + + align:start position:0% +independent of the length of L. That's + + + align:start position:0% +independent of the length of L. That's +great. Doesn't matter how long the list + + align:start position:0% +great. Doesn't matter how long the list + + + align:start position:0% +great. Doesn't matter how long the list +is. If I'm always going to find that the + + align:start position:0% +is. If I'm always going to find that the + + + align:start position:0% +is. If I'm always going to find that the +first element, I'm done. The average + + align:start position:0% +first element, I'm done. The average + + + align:start position:0% +first element, I'm done. The average +case would be the average over the + + align:start position:0% +case would be the average over the + + + align:start position:0% +case would be the average over the +number of steps I take depending on the + + align:start position:0% +number of steps I take depending on the + + + align:start position:0% +number of steps I take depending on the +length of the list. It's going to grow + + align:start position:0% +length of the list. It's going to grow + + + align:start position:0% +length of the list. It's going to grow +linearly with the length of the list. + + align:start position:0% +linearly with the length of the list. + + + align:start position:0% +linearly with the length of the list. +It's a good practical measure. But the + + align:start position:0% +It's a good practical measure. But the + + + align:start position:0% +It's a good practical measure. But the +one I want to focus on will be the worst + + align:start position:0% +one I want to focus on will be the worst + + + align:start position:0% +one I want to focus on will be the worst +case. And here the amount of time as + + align:start position:0% +case. And here the amount of time as + + + align:start position:0% +case. And here the amount of time as +we're going to see in a couple of slides + + align:start position:0% +we're going to see in a couple of slides + + + align:start position:0% +we're going to see in a couple of slides +is linear in the size of the problem. + + align:start position:0% +is linear in the size of the problem. + + + align:start position:0% +is linear in the size of the problem. +Meaning if I double the length of the + + align:start position:0% +Meaning if I double the length of the + + + align:start position:0% +Meaning if I double the length of the +list in the worst case it's going to + + align:start position:0% +list in the worst case it's going to + + + align:start position:0% +list in the worst case it's going to +take me twice as much time to find that + + align:start position:0% +take me twice as much time to find that + + + align:start position:0% +take me twice as much time to find that +it's not there. If I increase the length + + align:start position:0% +it's not there. If I increase the length + + + align:start position:0% +it's not there. If I increase the length +of the list by a factor of 10 in the + + align:start position:0% +of the list by a factor of 10 in the + + + align:start position:0% +of the list by a factor of 10 in the +worst case it's going to take me 10 + + align:start position:0% +worst case it's going to take me 10 + + + align:start position:0% +worst case it's going to take me 10 +times as much time as it did in the + + align:start position:0% +times as much time as it did in the + + + align:start position:0% +times as much time as it did in the +earlier case to find out that the + + align:start position:0% +earlier case to find out that the + + + align:start position:0% +earlier case to find out that the +problem's not there. And that linear + + align:start position:0% +problem's not there. And that linear + + + align:start position:0% +problem's not there. And that linear +relationship is what I want to capture. + + align:start position:0% +relationship is what I want to capture. + + + align:start position:0% +relationship is what I want to capture. +So, we're going to focus on that. What's + + align:start position:0% +So, we're going to focus on that. What's + + + align:start position:0% +So, we're going to focus on that. What's +the worst case + + align:start position:0% +the worst case + + + align:start position:0% +the worst case +behavior? And we're about ready to start + + align:start position:0% +behavior? And we're about ready to start + + + align:start position:0% +behavior? And we're about ready to start +talking about orders of growth. But here + + align:start position:0% +talking about orders of growth. But here + + + align:start position:0% +talking about orders of growth. But here +then is what orders of growth are going + + align:start position:0% +then is what orders of growth are going + + + align:start position:0% +then is what orders of growth are going +to provide for me. I want to evaluate + + align:start position:0% +to provide for me. I want to evaluate + + + align:start position:0% +to provide for me. I want to evaluate +efficiency, particularly when the input + + align:start position:0% +efficiency, particularly when the input + + + align:start position:0% +efficiency, particularly when the input +is very large. What happens when I + + align:start position:0% +is very large. What happens when I + + + align:start position:0% +is very large. What happens when I +really scale this up? I want to express + + align:start position:0% +really scale this up? I want to express + + + align:start position:0% +really scale this up? I want to express +the growth of the program's runtime as + + align:start position:0% +the growth of the program's runtime as + + + align:start position:0% +the growth of the program's runtime as +that input grows. Not the exact runtime, + + align:start position:0% +that input grows. Not the exact runtime, + + + align:start position:0% +that input grows. Not the exact runtime, +but that notion of if I double it, how + + align:start position:0% +but that notion of if I double it, how + + + align:start position:0% +but that notion of if I double it, how +much longer does it take? What's the + + align:start position:0% +much longer does it take? What's the + + + align:start position:0% +much longer does it take? What's the +relationship between increasing the size + + align:start position:0% +relationship between increasing the size + + + align:start position:0% +relationship between increasing the size +of the input and the increase in the + + align:start position:0% +of the input and the increase in the + + + align:start position:0% +of the input and the increase in the +amount of time it takes to solve it? + + align:start position:0% +amount of time it takes to solve it? + + + align:start position:0% +amount of time it takes to solve it? +We're going to put an upper bound on + + align:start position:0% +We're going to put an upper bound on + + + align:start position:0% +We're going to put an upper bound on +that growth. And if you haven't seen + + align:start position:0% +that growth. And if you haven't seen + + + align:start position:0% +that growth. And if you haven't seen +this in math, it basically says, I want + + align:start position:0% +this in math, it basically says, I want + + + align:start position:0% +this in math, it basically says, I want +to come up with a description that is at + + align:start position:0% +to come up with a description that is at + + + align:start position:0% +to come up with a description that is at +least as big as sorry, as big as or + + align:start position:0% +least as big as sorry, as big as or + + + align:start position:0% +least as big as sorry, as big as or +bigger than the actual amount of time it + + align:start position:0% +bigger than the actual amount of time it + + + align:start position:0% +bigger than the actual amount of time it +goes it's going to take. And I'm going + + align:start position:0% +goes it's going to take. And I'm going + + + align:start position:0% +goes it's going to take. And I'm going +to not worry about being precise. We're + + align:start position:0% +to not worry about being precise. We're + + + align:start position:0% +to not worry about being precise. We're +going to talk about being order of + + align:start position:0% +going to talk about being order of + + + align:start position:0% +going to talk about being order of +rather than exite exact. I don't need to + + align:start position:0% +rather than exite exact. I don't need to + + + align:start position:0% +rather than exite exact. I don't need to +know to the phentoc how long this is + + align:start position:0% +know to the phentoc how long this is + + + align:start position:0% +know to the phentoc how long this is +going to take or to exactly one + + align:start position:0% +going to take or to exactly one + + + align:start position:0% +going to take or to exactly one +operation how long it's going to take. + + align:start position:0% +operation how long it's going to take. + + + align:start position:0% +operation how long it's going to take. +But I want to say things like this is + + align:start position:0% +But I want to say things like this is + + + align:start position:0% +But I want to say things like this is +going to grow linearly. I double the + + align:start position:0% +going to grow linearly. I double the + + + align:start position:0% +going to grow linearly. I double the +size of the input. It doubles the amount + + align:start position:0% +size of the input. It doubles the amount + + + align:start position:0% +size of the input. It doubles the amount +of time. Or this is going to grow + + align:start position:0% +of time. Or this is going to grow + + + align:start position:0% +of time. Or this is going to grow +quadratically. I double the size of the + + align:start position:0% +quadratically. I double the size of the + + + align:start position:0% +quadratically. I double the size of the +input. It's going to take four times as + + align:start position:0% +input. It's going to take four times as + + + align:start position:0% +input. It's going to take four times as +much time to solve it. Or if I'm really + + align:start position:0% +much time to solve it. Or if I'm really + + + align:start position:0% +much time to solve it. Or if I'm really +lucky, this is going to have constant + + align:start position:0% +lucky, this is going to have constant + + + align:start position:0% +lucky, this is going to have constant +growth. No matter how I change the + + align:start position:0% +growth. No matter how I change the + + + align:start position:0% +growth. No matter how I change the +input, it's not going to take any more + + align:start position:0% +input, it's not going to take any more + + + align:start position:0% +input, it's not going to take any more +time. To do that, we're going to look at + + align:start position:0% +time. To do that, we're going to look at + + + align:start position:0% +time. To do that, we're going to look at +the largest factors in the runtime. + + align:start position:0% +the largest factors in the runtime. + + + align:start position:0% +the largest factors in the runtime. +Which piece of the program takes the + + align:start position:0% +Which piece of the program takes the + + + align:start position:0% +Which piece of the program takes the +most time? And so in orders of growth, + + align:start position:0% +most time? And so in orders of growth, + + + align:start position:0% +most time? And so in orders of growth, +we are going to look for a as tight as + + align:start position:0% +we are going to look for a as tight as + + + align:start position:0% +we are going to look for a as tight as +possible an upper bound on the growth as + + align:start position:0% +possible an upper bound on the growth as + + + align:start position:0% +possible an upper bound on the growth as +a function of the size of the input in + + align:start position:0% +a function of the size of the input in + + + align:start position:0% +a function of the size of the input in +the worst case. Nice long + + align:start position:0% + + + + align:start position:0% + +definition. Almost ready to look at some + + align:start position:0% +definition. Almost ready to look at some + + + align:start position:0% +definition. Almost ready to look at some +examples. So here's the notation we're + + align:start position:0% +examples. So here's the notation we're + + + align:start position:0% +examples. So here's the notation we're +going to use. It's called bigo notation, + + align:start position:0% +going to use. It's called bigo notation, + + + align:start position:0% +going to use. It's called bigo notation, +I have to admit. And John's not here + + align:start position:0% +I have to admit. And John's not here + + + align:start position:0% +I have to admit. And John's not here +today to remind me the history. I think + + align:start position:0% +today to remind me the history. I think + + + align:start position:0% +today to remind me the history. I think +it comes because we used omocrron. God + + align:start position:0% +it comes because we used omocrron. God + + + align:start position:0% +it comes because we used omocrron. God +knows why. Sounds like something from uh + + align:start position:0% +knows why. Sounds like something from uh + + + align:start position:0% +knows why. Sounds like something from uh +Futurramama, but we used omocron as our + + align:start position:0% +Futurramama, but we used omocron as our + + + align:start position:0% +Futurramama, but we used omocron as our +our symbol to define this. I'm having + + align:start position:0% +our symbol to define this. I'm having + + + align:start position:0% +our symbol to define this. I'm having +such good luck with bad jokes today. + + align:start position:0% +such good luck with bad jokes today. + + + align:start position:0% +such good luck with bad jokes today. +You're not even wincing when I throw + + align:start position:0% +You're not even wincing when I throw + + + align:start position:0% +You're not even wincing when I throw +those things out. But that's okay. It's + + align:start position:0% +those things out. But that's okay. It's + + + align:start position:0% +those things out. But that's okay. It's +called bigo notation. Well, you're going + + align:start position:0% +called bigo notation. Well, you're going + + + align:start position:0% +called bigo notation. Well, you're going +to use it. We're going to describe the + + align:start position:0% +to use it. We're going to describe the + + + align:start position:0% +to use it. We're going to describe the +rules of it. It's just the tradition of + + align:start position:0% +rules of it. It's just the tradition of + + + align:start position:0% +rules of it. It's just the tradition of +it. It describes the worst case because + + align:start position:0% +it. It describes the worst case because + + + align:start position:0% +it. It describes the worst case because +it's often the bottleneck we're after. + + align:start position:0% +it's often the bottleneck we're after. + + + align:start position:0% +it's often the bottleneck we're after. +And as we said, it's going to express + + align:start position:0% +And as we said, it's going to express + + + align:start position:0% +And as we said, it's going to express +the growth of the program relative to + + align:start position:0% +the growth of the program relative to + + + align:start position:0% +the growth of the program relative to +the input + + align:start position:0% +the input + + + align:start position:0% +the input +size. Okay, let's see how we go from + + align:start position:0% +size. Okay, let's see how we go from + + + align:start position:0% +size. Okay, let's see how we go from +counting operations to getting to orders + + align:start position:0% +counting operations to getting to orders + + + align:start position:0% +counting operations to getting to orders +of growth. Then we're going to define + + align:start position:0% +of growth. Then we're going to define + + + align:start position:0% +of growth. Then we're going to define +some examples of order growth and we're + + align:start position:0% +some examples of order growth and we're + + + align:start position:0% +some examples of order growth and we're +going to start looking at + + align:start position:0% +going to start looking at + + + align:start position:0% +going to start looking at +algorithms. Here's a piece of code + + align:start position:0% +algorithms. Here's a piece of code + + + align:start position:0% +algorithms. Here's a piece of code +you've seen before. Again, hopefully you + + align:start position:0% +you've seen before. Again, hopefully you + + + align:start position:0% +you've seen before. Again, hopefully you +recognize or can see fairly quickly what + + align:start position:0% +recognize or can see fairly quickly what + + + align:start position:0% +recognize or can see fairly quickly what +it's doing. Computing factorial the + + align:start position:0% +it's doing. Computing factorial the + + + align:start position:0% +it's doing. Computing factorial the +iterative way. Basically, remember n + + align:start position:0% +iterative way. Basically, remember n + + + align:start position:0% +iterative way. Basically, remember n +factorial is n * n -1 * n minus2 all the + + align:start position:0% +factorial is n * n -1 * n minus2 all the + + + align:start position:0% +factorial is n * n -1 * n minus2 all the +way down to one. Hopefully assuming n is + + align:start position:0% +way down to one. Hopefully assuming n is + + + align:start position:0% +way down to one. Hopefully assuming n is +a a non- negative integer here. We're + + align:start position:0% +a a non- negative integer here. We're + + + align:start position:0% +a a non- negative integer here. We're +going to set up an internal variable + + align:start position:0% +going to set up an internal variable + + + align:start position:0% +going to set up an internal variable +called answer. And then we're just going + + align:start position:0% +called answer. And then we're just going + + + align:start position:0% +called answer. And then we're just going +to run over a loop. As long as n is + + align:start position:0% +to run over a loop. As long as n is + + + align:start position:0% +to run over a loop. As long as n is +bigger than one, we're going to multiply + + align:start position:0% +bigger than one, we're going to multiply + + + align:start position:0% +bigger than one, we're going to multiply +answer by n, store it back into answer, + + align:start position:0% +answer by n, store it back into answer, + + + align:start position:0% +answer by n, store it back into answer, +decrease m by one. We'll keep doing that + + align:start position:0% +decrease m by one. We'll keep doing that + + + align:start position:0% +decrease m by one. We'll keep doing that +until we get out of the loop. And we're + + align:start position:0% +until we get out of the loop. And we're + + + align:start position:0% +until we get out of the loop. And we're +going to return + + align:start position:0% +going to return + + + align:start position:0% +going to return +answer. Going to start by counting + + align:start position:0% + + + + align:start position:0% + +steps. And that's by the way just to + + align:start position:0% +steps. And that's by the way just to + + + align:start position:0% +steps. And that's by the way just to +remind you that in fact there are two + + align:start position:0% +remind you that in fact there are two + + + align:start position:0% +remind you that in fact there are two +steps here. So what do I have? I've got + + align:start position:0% +steps here. So what do I have? I've got + + + align:start position:0% +steps here. So what do I have? I've got +one step up there to set answer to one. + + align:start position:0% +one step up there to set answer to one. + + + align:start position:0% +one step up there to set answer to one. +I'm setting up + + align:start position:0% +I'm setting up + + + align:start position:0% +I'm setting up +n. Sorry, I'm not setting up n. I'm + + align:start position:0% +n. Sorry, I'm not setting up n. I'm + + + align:start position:0% +n. Sorry, I'm not setting up n. I'm +going to test n and then I'm going to do + + align:start position:0% +going to test n and then I'm going to do + + + align:start position:0% +going to test n and then I'm going to do +two steps here because I got to multiply + + align:start position:0% +two steps here because I got to multiply + + + align:start position:0% +two steps here because I got to multiply +answer by n and then set it to answer. + + align:start position:0% +answer by n and then set it to answer. + + + align:start position:0% +answer by n and then set it to answer. +And I've similarly got two steps there + + align:start position:0% +And I've similarly got two steps there + + + align:start position:0% +And I've similarly got two steps there +because I'm subtracting one from n and + + align:start position:0% +because I'm subtracting one from n and + + + align:start position:0% +because I'm subtracting one from n and +then setting it to n. So I've got two + + + align:start position:0% +then setting it to n. So I've got two + + + + align:start position:0% +then setting it to n. So I've got two + +4 plus the test which is + + align:start position:0% +4 plus the test which is + + + align:start position:0% +4 plus the test which is +five. I got one outside here. I got one + + align:start position:0% +five. I got one outside here. I got one + + + align:start position:0% +five. I got one outside here. I got one +outside there. And I'm going to go + + align:start position:0% +outside there. And I'm going to go + + + align:start position:0% +outside there. And I'm going to go +through this loop n times. So I would + + align:start position:0% +through this loop n times. So I would + + + align:start position:0% +through this loop n times. So I would +suggest that if I count number of steps, + + align:start position:0% +suggest that if I count number of steps, + + + align:start position:0% +suggest that if I count number of steps, +it's 1 + 5 n + + + align:start position:0% +it's 1 + 5 n + + + + align:start position:0% +it's 1 + 5 n + +1. + + align:start position:0% +1. + + + align:start position:0% +1. +Okay, sort of what we did before. 5 n + + + align:start position:0% +Okay, sort of what we did before. 5 n + + + + align:start position:0% +Okay, sort of what we did before. 5 n + +2 is the total number of steps that I + + align:start position:0% +2 is the total number of steps that I + + + align:start position:0% +2 is the total number of steps that I +use here. But now I'm interested in + + align:start position:0% +use here. But now I'm interested in + + + align:start position:0% +use here. But now I'm interested in +what's the worst case behavior. Well, in + + align:start position:0% +what's the worst case behavior. Well, in + + + align:start position:0% +what's the worst case behavior. Well, in +this case, it is the worst case behavior + + align:start position:0% +this case, it is the worst case behavior + + + align:start position:0% +this case, it is the worst case behavior +because it doesn't have decisions + + align:start position:0% +because it doesn't have decisions + + + align:start position:0% +because it doesn't have decisions +anywhere in here. But I just want to + + align:start position:0% +anywhere in here. But I just want to + + + align:start position:0% +anywhere in here. But I just want to +know what's the asimtoic complexity. And + + align:start position:0% +know what's the asimtoic complexity. And + + + align:start position:0% +know what's the asimtoic complexity. And +I'm going to say oh sorry that is to say + + align:start position:0% +I'm going to say oh sorry that is to say + + + align:start position:0% +I'm going to say oh sorry that is to say +I could do this different ways. I could + + align:start position:0% +I could do this different ways. I could + + + align:start position:0% +I could do this different ways. I could +have done this with two steps like that. + + align:start position:0% +have done this with two steps like that. + + + align:start position:0% +have done this with two steps like that. +That would have made it not just 1 plus + + align:start position:0% +That would have made it not just 1 plus + + + align:start position:0% +That would have made it not just 1 plus +5 n plus1 would have made it 1 plus 6 n + + align:start position:0% +5 n plus1 would have made it 1 plus 6 n + + + align:start position:0% +5 n plus1 would have made it 1 plus 6 n +plus1 because I've got an extra + + align:start position:0% +plus1 because I've got an extra + + + align:start position:0% +plus1 because I've got an extra +step. I put that up because I want to + + align:start position:0% +step. I put that up because I want to + + + align:start position:0% +step. I put that up because I want to +remind you I don't care about + + align:start position:0% +remind you I don't care about + + + align:start position:0% +remind you I don't care about +implementation differences. And so I + + align:start position:0% +implementation differences. And so I + + + align:start position:0% +implementation differences. And so I +want to know what captures both of those + + align:start position:0% +want to know what captures both of those + + + align:start position:0% +want to know what captures both of those +behaviors. In in ambigo notation, I say + + align:start position:0% +behaviors. In in ambigo notation, I say + + + align:start position:0% +behaviors. In in ambigo notation, I say +that's order + + align:start position:0% +that's order + + + align:start position:0% +that's order +n grows + + align:start position:0% +n grows + + + align:start position:0% +n grows +linearly. I'm going to keep doing this + + align:start position:0% +linearly. I'm going to keep doing this + + + align:start position:0% +linearly. I'm going to keep doing this +to you until you really do wse at me. If + + align:start position:0% +to you until you really do wse at me. If + + + align:start position:0% +to you until you really do wse at me. If +I were to double the size of n, whether + + align:start position:0% +I were to double the size of n, whether + + + align:start position:0% +I were to double the size of n, whether +I use this version or that version, the + + align:start position:0% +I use this version or that version, the + + + align:start position:0% +I use this version or that version, the +amount of time, the number of steps, + + align:start position:0% +amount of time, the number of steps, + + + align:start position:0% +amount of time, the number of steps, +it's basically going to double. Now, you + + align:start position:0% +it's basically going to double. Now, you + + + align:start position:0% +it's basically going to double. Now, you +say, wait a minute, you know, 5 n plus + + align:start position:0% +say, wait a minute, you know, 5 n plus + + + align:start position:0% +say, wait a minute, you know, 5 n plus +two, you know, if n is is uh 10, that's + + align:start position:0% +two, you know, if n is is uh 10, that's + + + align:start position:0% +two, you know, if n is is uh 10, that's +52. Is if n is 20, that's 102. That's + + align:start position:0% +52. Is if n is 20, that's 102. That's + + + align:start position:0% +52. Is if n is 20, that's 102. That's +not quite doubling. And you're right. + + align:start position:0% +not quite doubling. And you're right. + + + align:start position:0% +not quite doubling. And you're right. +But remember, we really care about this + + align:start position:0% +But remember, we really care about this + + + align:start position:0% +But remember, we really care about this +in the asmtotic case. When n gets really + + align:start position:0% +in the asmtotic case. When n gets really + + + align:start position:0% +in the asmtotic case. When n gets really +big, those extra little pieces don't + + align:start position:0% +big, those extra little pieces don't + + + align:start position:0% +big, those extra little pieces don't +matter. And so what we're going to do is + + align:start position:0% +matter. And so what we're going to do is + + + align:start position:0% +matter. And so what we're going to do is +we're going to ignore the additive + + align:start position:0% +we're going to ignore the additive + + + align:start position:0% +we're going to ignore the additive +constants and we're going to ignore the + + align:start position:0% +constants and we're going to ignore the + + + align:start position:0% +constants and we're going to ignore the +multiplicative constants when we talk + + align:start position:0% +multiplicative constants when we talk + + + align:start position:0% +multiplicative constants when we talk +about orders of + + align:start position:0% +about orders of + + + align:start position:0% +about orders of +growth. So what does O of N + + align:start position:0% +growth. So what does O of N + + + align:start position:0% +growth. So what does O of N +measure? Well, I'm just summarizing + + align:start position:0% +measure? Well, I'm just summarizing + + + align:start position:0% +measure? Well, I'm just summarizing +here. We want to describe how much time + + align:start position:0% +here. We want to describe how much time + + + align:start position:0% +here. We want to describe how much time +is needed to compute or how does the + + align:start position:0% +is needed to compute or how does the + + + align:start position:0% +is needed to compute or how does the +amount of time rather needed to compute + + align:start position:0% +amount of time rather needed to compute + + + align:start position:0% +amount of time rather needed to compute +a problem grow as the size of the + + align:start position:0% +a problem grow as the size of the + + + align:start position:0% +a problem grow as the size of the +problem itself grows. So we want an + + align:start position:0% +problem itself grows. So we want an + + + align:start position:0% +problem itself grows. So we want an +expression that counts that asmtoic + + align:start position:0% +expression that counts that asmtoic + + + align:start position:0% +expression that counts that asmtoic +behavior and we're going to focus as a + + align:start position:0% +behavior and we're going to focus as a + + + align:start position:0% +behavior and we're going to focus as a +consequence on the term that grows most + + align:start position:0% +consequence on the term that grows most + + + align:start position:0% +consequence on the term that grows most +rapidly. + + align:start position:0% +rapidly. + + + align:start position:0% +rapidly. +So, here are some + + align:start position:0% +So, here are some + + + align:start position:0% +So, here are some +examples. And I know if you're following + + align:start position:0% +examples. And I know if you're following + + + align:start position:0% +examples. And I know if you're following +along, you can already see the answers + + align:start position:0% +along, you can already see the answers + + + align:start position:0% +along, you can already see the answers +here. But we're going to do this to + + align:start position:0% +here. But we're going to do this to + + + align:start position:0% +here. But we're going to do this to +simply give you a sense of that. If I'm + + align:start position:0% +simply give you a sense of that. If I'm + + + align:start position:0% +simply give you a sense of that. If I'm +counting operations and I come up with + + align:start position:0% +counting operations and I come up with + + + align:start position:0% +counting operations and I come up with +an expression that has n^2 + 2 n + 2 + + align:start position:0% +an expression that has n^2 + 2 n + 2 + + + align:start position:0% +an expression that has n^2 + 2 n + 2 +operations, that expression I say is + + align:start position:0% +operations, that expression I say is + + + align:start position:0% +operations, that expression I say is +order n + + align:start position:0% +order n + + + align:start position:0% +order n +squ. The two and the 2n don't matter. + + align:start position:0% +squ. The two and the 2n don't matter. + + + align:start position:0% +squ. The two and the 2n don't matter. +And think about what happens if you make + + align:start position:0% +And think about what happens if you make + + + align:start position:0% +And think about what happens if you make +n really big, right? N^ squ is much more + + align:start position:0% +n really big, right? N^ squ is much more + + + align:start position:0% +n really big, right? N^ squ is much more +dominant than the other terms. we say + + align:start position:0% +dominant than the other terms. we say + + + align:start position:0% +dominant than the other terms. we say +that's order n^ + + align:start position:0% +that's order n^ + + + align:start position:0% +that's order n^ +squ even this expression we say is order + + align:start position:0% +squ even this expression we say is order + + + align:start position:0% +squ even this expression we say is order +n^ squ now in this case for lower values + + align:start position:0% +n^ squ now in this case for lower values + + + align:start position:0% +n^ squ now in this case for lower values +of n this term is going to be the big + + align:start position:0% +of n this term is going to be the big + + + align:start position:0% +of n this term is going to be the big +one in terms of number of steps I have + + align:start position:0% +one in terms of number of steps I have + + + align:start position:0% +one in terms of number of steps I have +no idea how I wrote such an inefficient + + align:start position:0% +no idea how I wrote such an inefficient + + + align:start position:0% +no idea how I wrote such an inefficient +inefficient algorithm that it took 100 + + align:start position:0% +inefficient algorithm that it took 100 + + + align:start position:0% +inefficient algorithm that it took 100 +thousand steps to do something but if I + + align:start position:0% +thousand steps to do something but if I + + + align:start position:0% +thousand steps to do something but if I +had that expression for smaller values + + align:start position:0% +had that expression for smaller values + + + align:start position:0% +had that expression for smaller values +of n this matters a lot this is a really + + align:start position:0% +of n this matters a lot this is a really + + + align:start position:0% +of n this matters a lot this is a really +big number but I'm interested in the + + align:start position:0% +big number but I'm interested in the + + + align:start position:0% +big number but I'm interested in the +growth and that's the term that + + align:start position:0% +growth and that's the term that + + + align:start position:0% +growth and that's the term that +dominates + + align:start position:0% +dominates + + + align:start position:0% +dominates +And you see the idea or begin to see the + + align:start position:0% +And you see the idea or begin to see the + + + align:start position:0% +And you see the idea or begin to see the +idea here. When I have oop sorry before + + align:start position:0% +idea here. When I have oop sorry before + + + align:start position:0% +idea here. When I have oop sorry before +I go back there when I have + + align:start position:0% +I go back there when I have + + + align:start position:0% +I go back there when I have +expressions if it's a polomial + + align:start position:0% +expressions if it's a polomial + + + align:start position:0% +expressions if it's a polomial +expression it's the highest order term + + align:start position:0% +expression it's the highest order term + + + align:start position:0% +expression it's the highest order term +that's the term that captures the + + align:start position:0% +that's the term that captures the + + + align:start position:0% +that's the term that captures the +complexity. Both of these are + + align:start position:0% +complexity. Both of these are + + + align:start position:0% +complexity. Both of these are +quadratic. This + + align:start position:0% +quadratic. This + + + align:start position:0% +quadratic. This +term is order n because n grows faster + + align:start position:0% +term is order n because n grows faster + + + align:start position:0% +term is order n because n grows faster +than log of n. + + align:start position:0% +than log of n. + + + align:start position:0% +than log of n. +This funky looking term even though that + + align:start position:0% +This funky looking term even though that + + + align:start position:0% +This funky looking term even though that +looks like the big number there and it + + align:start position:0% +looks like the big number there and it + + + align:start position:0% +looks like the big number there and it +is a big number that expression we say + + align:start position:0% +is a big number that expression we say + + + align:start position:0% +is a big number that expression we say +is order n login because again if I plot + + align:start position:0% +is order n login because again if I plot + + + align:start position:0% +is order n login because again if I plot +out as how this changes as I make n + + align:start position:0% +out as how this changes as I make n + + + align:start position:0% +out as how this changes as I make n +really large this term eventually takes + + align:start position:0% +really large this term eventually takes + + + align:start position:0% +really large this term eventually takes +over as the dominant + + align:start position:0% +over as the dominant + + + align:start position:0% +over as the dominant +term. What about that + + align:start position:0% +term. What about that + + + align:start position:0% +term. What about that +one? What's the big term there? How many + + align:start position:0% +one? What's the big term there? How many + + + align:start position:0% +one? What's the big term there? How many +people think it's n to the 30th? Show of + + align:start position:0% +people think it's n to the 30th? Show of + + + align:start position:0% +people think it's n to the 30th? Show of +hands. How many people think it's 3 to + + align:start position:0% +hands. How many people think it's 3 to + + + align:start position:0% +hands. How many people think it's 3 to +the n? Show of hands. Thank you. You're + + align:start position:0% +the n? Show of hands. Thank you. You're + + + align:start position:0% +the n? Show of hands. Thank you. You're +following along. You're also paying + + align:start position:0% +following along. You're also paying + + + align:start position:0% +following along. You're also paying +attention. How many people think I + + align:start position:0% +attention. How many people think I + + + align:start position:0% +attention. How many people think I +should stop asking questions? No show of + + align:start position:0% +should stop asking questions? No show of + + + align:start position:0% +should stop asking questions? No show of +hands. All right. But you're right. + + align:start position:0% +hands. All right. But you're right. + + + align:start position:0% +hands. All right. But you're right. +Exponentials are much worse than powers. + + align:start position:0% +Exponentials are much worse than powers. + + + align:start position:0% +Exponentials are much worse than powers. +Even something like this. Again, it's + + align:start position:0% +Even something like this. Again, it's + + + align:start position:0% +Even something like this. Again, it's +going to take a big value of n before it + + align:start position:0% +going to take a big value of n before it + + + align:start position:0% +going to take a big value of n before it +gets there. But it does get there. And + + align:start position:0% +gets there. But it does get there. And + + + align:start position:0% +gets there. But it does get there. And +that, by the way, is important because + + align:start position:0% +that, by the way, is important because + + + align:start position:0% +that, by the way, is important because +we're going to see later on in the term + + align:start position:0% +we're going to see later on in the term + + + align:start position:0% +we're going to see later on in the term +that there are some problems where it's + + align:start position:0% +that there are some problems where it's + + + align:start position:0% +that there are some problems where it's +believed that all of the solutions are + + align:start position:0% +believed that all of the solutions are + + + align:start position:0% +believed that all of the solutions are +exponential. And that's a pain because + + align:start position:0% +exponential. And that's a pain because + + + align:start position:0% +exponential. And that's a pain because +it says it's always going to be + + align:start position:0% +it says it's always going to be + + + align:start position:0% +it says it's always going to be +expensive to compute. So that's how + + align:start position:0% +expensive to compute. So that's how + + + align:start position:0% +expensive to compute. So that's how +we're going to reason about these + + align:start position:0% +we're going to reason about these + + + align:start position:0% +we're going to reason about these +things. And to see it visually, here are + + align:start position:0% +things. And to see it visually, here are + + + align:start position:0% +things. And to see it visually, here are +the difference between differences + + align:start position:0% +the difference between differences + + + align:start position:0% +the difference between differences +between those different classes. + + align:start position:0% +between those different classes. + + + align:start position:0% +between those different classes. +Something that's constant, the amount of + + align:start position:0% +Something that's constant, the amount of + + + align:start position:0% +Something that's constant, the amount of +time doesn't change as I change the size + + align:start position:0% +time doesn't change as I change the size + + + align:start position:0% +time doesn't change as I change the size +of the input. Something that linear + + align:start position:0% +of the input. Something that linear + + + align:start position:0% +of the input. Something that linear +grows as a straight line, as you would + + align:start position:0% +grows as a straight line, as you would + + + align:start position:0% +grows as a straight line, as you would +expect. Nice behavior. Quadratic starts + + align:start position:0% +expect. Nice behavior. Quadratic starts + + + align:start position:0% +expect. Nice behavior. Quadratic starts +to grow more quickly. log is always + + align:start position:0% +to grow more quickly. log is always + + + align:start position:0% +to grow more quickly. log is always +better than linear because it slows down + + align:start position:0% +better than linear because it slows down + + + align:start position:0% +better than linear because it slows down +as we increase the size. N log n log n + + align:start position:0% +as we increase the size. N log n log n + + + align:start position:0% +as we increase the size. N log n log n +or log linear is a funky term, but we're + + align:start position:0% +or log linear is a funky term, but we're + + + align:start position:0% +or log linear is a funky term, but we're +going to see it's a very common + + align:start position:0% +going to see it's a very common + + + align:start position:0% +going to see it's a very common +complexity for really valuable + + align:start position:0% +complexity for really valuable + + + align:start position:0% +complexity for really valuable +algorithms in computer science and it + + align:start position:0% +algorithms in computer science and it + + + align:start position:0% +algorithms in computer science and it +has a nice behavior sort of between the + + align:start position:0% +has a nice behavior sort of between the + + + align:start position:0% +has a nice behavior sort of between the +linear and the quadratic an exponential + + align:start position:0% +linear and the quadratic an exponential + + + align:start position:0% +linear and the quadratic an exponential +blows up. Just to remind you of that, oh + + align:start position:0% +blows up. Just to remind you of that, oh + + + align:start position:0% +blows up. Just to remind you of that, oh +sorry, let me show you how we're going + + align:start position:0% +sorry, let me show you how we're going + + + align:start position:0% +sorry, let me show you how we're going +to do the reasoning about + + align:start position:0% +to do the reasoning about + + + align:start position:0% +to do the reasoning about +this. So here's how we're going to + + align:start position:0% +this. So here's how we're going to + + + align:start position:0% +this. So here's how we're going to +reason about it. + + align:start position:0% +reason about it. + + + align:start position:0% +reason about it. +We've already seen some code where I + + align:start position:0% +We've already seen some code where I + + + align:start position:0% +We've already seen some code where I +started working through this process of + + align:start position:0% +started working through this process of + + + align:start position:0% +started working through this process of +counting operations. Here are the tools + + align:start position:0% +counting operations. Here are the tools + + + align:start position:0% +counting operations. Here are the tools +I want you to use. Given a piece of + + align:start position:0% +I want you to use. Given a piece of + + + align:start position:0% +I want you to use. Given a piece of +code, you're going to reason about each + + align:start position:0% +code, you're going to reason about each + + + align:start position:0% +code, you're going to reason about each +chunk of code + + align:start position:0% +chunk of code + + + align:start position:0% +chunk of code +separately. If you've got + + align:start position:0% +separately. If you've got + + + align:start position:0% +separately. If you've got +sequential pieces of code, then the + + align:start position:0% +sequential pieces of code, then the + + + align:start position:0% +sequential pieces of code, then the +rules are called the law of addition for + + align:start position:0% +rules are called the law of addition for + + + align:start position:0% +rules are called the law of addition for +for order of growth is that the order of + + align:start position:0% +for order of growth is that the order of + + + align:start position:0% +for order of growth is that the order of +growth of the combination is the + + align:start position:0% +growth of the combination is the + + + align:start position:0% +growth of the combination is the +combination of the order of the + + align:start position:0% +combination of the order of the + + + align:start position:0% +combination of the order of the +growth. Say that quickly 10 times. But + + align:start position:0% +growth. Say that quickly 10 times. But + + + align:start position:0% +growth. Say that quickly 10 times. But +let's look at an example of that. Here + + align:start position:0% +let's look at an example of that. Here + + + align:start position:0% +let's look at an example of that. Here +are two loops. You've already seen + + align:start position:0% +are two loops. You've already seen + + + align:start position:0% +are two loops. You've already seen +examples of how to reason about those + + align:start position:0% +examples of how to reason about those + + + align:start position:0% +examples of how to reason about those +loops. For this one, it's linear in the + + align:start position:0% +loops. For this one, it's linear in the + + + align:start position:0% +loops. For this one, it's linear in the +size of n. I'm going to go through the + + align:start position:0% +size of n. I'm going to go through the + + + align:start position:0% +size of n. I'm going to go through the +loop end times doing a constant amount + + align:start position:0% +loop end times doing a constant amount + + + align:start position:0% +loop end times doing a constant amount +of things each time around. By what I + + align:start position:0% +of things each time around. By what I + + + align:start position:0% +of things each time around. By what I +just showed, that's order n. This one + + align:start position:0% +just showed, that's order n. This one + + + align:start position:0% +just showed, that's order n. This one +again, I'm doing just a constant number + + align:start position:0% +again, I'm doing just a constant number + + + align:start position:0% +again, I'm doing just a constant number +of things inside the loop. But + + align:start position:0% +of things inside the loop. But + + + align:start position:0% +of things inside the loop. But +notice that it's n squared. So that's + + align:start position:0% +notice that it's n squared. So that's + + + align:start position:0% +notice that it's n squared. So that's +order + + align:start position:0% +order + + + align:start position:0% +order +n^2 n * n. The combination is I have to + + align:start position:0% +n^2 n * n. The combination is I have to + + + align:start position:0% +n^2 n * n. The combination is I have to +do this work and then that work. So I + + align:start position:0% +do this work and then that work. So I + + + align:start position:0% +do this work and then that work. So I +write that as saying that is order of n + + align:start position:0% +write that as saying that is order of n + + + align:start position:0% +write that as saying that is order of n +plus order of + + align:start position:0% +plus order of + + + align:start position:0% +plus order of +n^2. But by this up here that is the + + align:start position:0% +n^2. But by this up here that is the + + + align:start position:0% +n^2. But by this up here that is the +same as saying what's the order of + + align:start position:0% +same as saying what's the order of + + + align:start position:0% +same as saying what's the order of +growth of n + n^2. Oh yeah we just saw + + align:start position:0% +growth of n + n^2. Oh yeah we just saw + + + align:start position:0% +growth of n + n^2. Oh yeah we just saw +that says it's + + align:start position:0% +that says it's + + + align:start position:0% +that says it's +n^2. So addition or the law of addition + + align:start position:0% +n^2. So addition or the law of addition + + + align:start position:0% +n^2. So addition or the law of addition +lets me reason about the fact that this + + align:start position:0% +lets me reason about the fact that this + + + align:start position:0% +lets me reason about the fact that this +will be an order n squ algorithm. + + align:start position:0% +will be an order n squ algorithm. + + + align:start position:0% +will be an order n squ algorithm. +Second one I'm going to use is called + + align:start position:0% +Second one I'm going to use is called + + + align:start position:0% +Second one I'm going to use is called +the law of + + align:start position:0% +the law of + + + align:start position:0% +the law of +multiplication and this says when I have + + align:start position:0% +multiplication and this says when I have + + + align:start position:0% +multiplication and this says when I have +nested statements or nested loops I need + + align:start position:0% +nested statements or nested loops I need + + + align:start position:0% +nested statements or nested loops I need +to reason about those and in that case + + align:start position:0% +to reason about those and in that case + + + align:start position:0% +to reason about those and in that case +what I'm going to argue or not argue + + align:start position:0% +what I'm going to argue or not argue + + + align:start position:0% +what I'm going to argue or not argue +state is that the order of growth here + + align:start position:0% +state is that the order of growth here + + + align:start position:0% +state is that the order of growth here +is a multiplication that is when I have + + align:start position:0% +is a multiplication that is when I have + + + align:start position:0% +is a multiplication that is when I have +nested things I figure out what's the + + align:start position:0% +nested things I figure out what's the + + + align:start position:0% +nested things I figure out what's the +order of growth of the inner part what's + + align:start position:0% +order of growth of the inner part what's + + + align:start position:0% +order of growth of the inner part what's +the order of growth of the outer part + + align:start position:0% +the order of growth of the outer part + + + align:start position:0% +the order of growth of the outer part +and I'm going to multiply try again I'm + + align:start position:0% +and I'm going to multiply try again I'm + + + align:start position:0% +and I'm going to multiply try again I'm +going to multiply together those orders + + align:start position:0% +going to multiply together those orders + + + align:start position:0% +going to multiply together those orders +of growth to get the overall order of + + align:start position:0% +of growth to get the overall order of + + + align:start position:0% +of growth to get the overall order of +growth. If you think about it, it makes + + align:start position:0% +growth. If you think about it, it makes + + + align:start position:0% +growth. If you think about it, it makes +sense. Look at my little example here. + + align:start position:0% +sense. Look at my little example here. + + + align:start position:0% +sense. Look at my little example here. +It's a trivial little example, but I'm + + align:start position:0% +It's a trivial little example, but I'm + + + align:start position:0% +It's a trivial little example, but I'm +looping for I from zero up to + + align:start position:0% +looping for I from zero up to + + + align:start position:0% +looping for I from zero up to +N. For every value of I, I'm looping for + + align:start position:0% +N. For every value of I, I'm looping for + + + align:start position:0% +N. For every value of I, I'm looping for +J from zero up to N, and I'm printing + + align:start position:0% +J from zero up to N, and I'm printing + + + align:start position:0% +J from zero up to N, and I'm printing +out A. I'm the fs. I'm saying A lot. Oh, + + align:start position:0% +out A. I'm the fs. I'm saying A lot. Oh, + + + align:start position:0% +out A. I'm the fs. I'm saying A lot. Oh, +come on. At least throw something at me + + align:start position:0% +come on. At least throw something at me + + + align:start position:0% +come on. At least throw something at me +when it's that bad, right? Want to make + + align:start position:0% +when it's that bad, right? Want to make + + + align:start position:0% +when it's that bad, right? Want to make +sure you're still awake. Okay, you get + + align:start position:0% +sure you're still awake. Okay, you get + + + align:start position:0% +sure you're still awake. Okay, you get +the idea. But what I want to show you + + align:start position:0% +the idea. But what I want to show you + + + align:start position:0% +the idea. But what I want to show you +here is notice the order of growth. + + align:start position:0% +here is notice the order of growth. + + + align:start position:0% +here is notice the order of growth. +That's order n, right? I'm doing that n + + align:start position:0% +That's order n, right? I'm doing that n + + + align:start position:0% +That's order n, right? I'm doing that n +times. But I'm doing that for each value + + align:start position:0% +times. But I'm doing that for each value + + + align:start position:0% +times. But I'm doing that for each value +of i. The outer piece here loops also n + + align:start position:0% +of i. The outer piece here loops also n + + + align:start position:0% +of i. The outer piece here loops also n +times. For each value of i, I'm doing + + align:start position:0% +times. For each value of i, I'm doing + + + align:start position:0% +times. For each value of i, I'm doing +order n things. So I'm doing order of n + + align:start position:0% +order n things. So I'm doing order of n + + + align:start position:0% +order n things. So I'm doing order of n +times order of n steps. And by that law, + + align:start position:0% +times order of n steps. And by that law, + + + align:start position:0% +times order of n steps. And by that law, +that is the same of order of n * n or n + + align:start position:0% +that is the same of order of n * n or n + + + align:start position:0% +that is the same of order of n * n or n +squ. So this is a quadratic + + align:start position:0% +squ. So this is a quadratic + + + align:start position:0% +squ. So this is a quadratic +expression. You're going to see that a + + align:start position:0% +expression. You're going to see that a + + + align:start position:0% +expression. You're going to see that a +lot. Nested loops typically typically + + align:start position:0% +lot. Nested loops typically typically + + + align:start position:0% +lot. Nested loops typically typically +have that kind of behavior. Not always, + + align:start position:0% +have that kind of behavior. Not always, + + + align:start position:0% +have that kind of behavior. Not always, +but typically have that kind of + + align:start position:0% +but typically have that kind of + + + align:start position:0% +but typically have that kind of +behavior. So what you're going to see is + + align:start position:0% +behavior. So what you're going to see is + + + align:start position:0% +behavior. So what you're going to see is +there's a set of complexity classes and + + align:start position:0% +there's a set of complexity classes and + + + align:start position:0% +there's a set of complexity classes and +we're about to start filling these + + align:start position:0% +we're about to start filling these + + + align:start position:0% +we're about to start filling these +in. Order one is constant says amount of + + align:start position:0% +in. Order one is constant says amount of + + + align:start position:0% +in. Order one is constant says amount of +time it takes doesn't depend on the size + + align:start position:0% +time it takes doesn't depend on the size + + + align:start position:0% +time it takes doesn't depend on the size +of the problem. These are really rare + + align:start position:0% +of the problem. These are really rare + + + align:start position:0% +of the problem. These are really rare +that you get. They tend to be trivial + + align:start position:0% +that you get. They tend to be trivial + + + align:start position:0% +that you get. They tend to be trivial +pieces of code, but they're valuable. + + align:start position:0% +pieces of code, but they're valuable. + + + align:start position:0% +pieces of code, but they're valuable. +Log in reflects logarithmic runtime. You + + align:start position:0% +Log in reflects logarithmic runtime. You + + + align:start position:0% +Log in reflects logarithmic runtime. You +can sort of read the rest of them. These + + align:start position:0% +can sort of read the rest of them. These + + + align:start position:0% +can sort of read the rest of them. These +are the kinds of things we're going to + + align:start position:0% +are the kinds of things we're going to + + + align:start position:0% +are the kinds of things we're going to +deal with. We are going to see examples + + align:start position:0% +deal with. We are going to see examples + + + align:start position:0% +deal with. We are going to see examples +here, here, and here. And later on, + + align:start position:0% +here, here, and here. And later on, + + + align:start position:0% +here, here, and here. And later on, +we're come back and see these which are + + align:start position:0% +we're come back and see these which are + + + align:start position:0% +we're come back and see these which are +really nice examples to have. Just to + + align:start position:0% +really nice examples to have. Just to + + + align:start position:0% +really nice examples to have. Just to +remind you why these orders of growth + + align:start position:0% +remind you why these orders of growth + + + align:start position:0% +remind you why these orders of growth +matter. Sorry, that's just reminding you + + align:start position:0% +matter. Sorry, that's just reminding you + + + align:start position:0% +matter. Sorry, that's just reminding you +what they look like. We've already done + + align:start position:0% +what they look like. We've already done + + + align:start position:0% +what they look like. We've already done +that. + + align:start position:0% +that. + + + align:start position:0% +that. +Here's the difference between constant + + align:start position:0% +Here's the difference between constant + + + align:start position:0% +Here's the difference between constant +log linear log linear squared and + + align:start position:0% +log linear log linear squared and + + + align:start position:0% +log linear log linear squared and +exponential. When n is equal to 10, 100, + + align:start position:0% +exponential. When n is equal to 10, 100, + + + align:start position:0% +exponential. When n is equal to 10, 100, +a thousand, or a + + align:start position:0% +a thousand, or a + + + align:start position:0% +a thousand, or a +million. I know you know this, but I + + align:start position:0% +million. I know you know this, but I + + + align:start position:0% +million. I know you know this, but I +want to drive home the difference. + + align:start position:0% +want to drive home the difference. + + + align:start position:0% +want to drive home the difference. +Something that's constant is wonderful. + + align:start position:0% +Something that's constant is wonderful. + + + align:start position:0% +Something that's constant is wonderful. +No matter how big the problem is, takes + + align:start position:0% +No matter how big the problem is, takes + + + align:start position:0% +No matter how big the problem is, takes +the same amount of time. Something that + + align:start position:0% +the same amount of time. Something that + + + align:start position:0% +the same amount of time. Something that +lo that is log is pretty nice. Increases + + align:start position:0% +lo that is log is pretty nice. Increases + + + align:start position:0% +lo that is log is pretty nice. Increases +the size of the problem by 10. It + + align:start position:0% +the size of the problem by 10. It + + + align:start position:0% +the size of the problem by 10. It +increases by a factor of two. from + + align:start position:0% +increases by a factor of two. from + + + align:start position:0% +increases by a factor of two. from +another 10, it only increases by a + + align:start position:0% +another 10, it only increases by a + + + align:start position:0% +another 10, it only increases by a +factor of of another 50%. It only + + align:start position:0% +factor of of another 50%. It only + + + align:start position:0% +factor of of another 50%. It only +increases a little bit. That's a + + align:start position:0% +increases a little bit. That's a + + + align:start position:0% +increases a little bit. That's a +gorgeous kind of problem to have. + + align:start position:0% +gorgeous kind of problem to have. + + + align:start position:0% +gorgeous kind of problem to have. +Linear, not so bad. I go from 10 to 100 + + align:start position:0% +Linear, not so bad. I go from 10 to 100 + + + align:start position:0% +Linear, not so bad. I go from 10 to 100 +to a,000 to a million. You can see log + + align:start position:0% +to a,000 to a million. You can see log + + + align:start position:0% +to a,000 to a million. You can see log +linear is not bad either, right? A + + align:start position:0% +linear is not bad either, right? A + + + align:start position:0% +linear is not bad either, right? A +factor of 10 increase here is only a + + align:start position:0% +factor of 10 increase here is only a + + + align:start position:0% +factor of 10 increase here is only a +factor of 20 increase there. A factor of + + align:start position:0% +factor of 20 increase there. A factor of + + + align:start position:0% +factor of 20 increase there. A factor of +10 increase there is only a factor of of + + align:start position:0% +10 increase there is only a factor of of + + + align:start position:0% +10 increase there is only a factor of of +30 increase there. So log linear doesn't + + align:start position:0% +30 increase there. So log linear doesn't + + + align:start position:0% +30 increase there. So log linear doesn't +grow that badly. + + align:start position:0% +grow that badly. + + + align:start position:0% +grow that badly. +But look at the difference between n^2 + + align:start position:0% +But look at the difference between n^2 + + + align:start position:0% +But look at the difference between n^2 +and 2 to the + + align:start position:0% +and 2 to the + + + align:start position:0% +and 2 to the +n. I actually did think of printing this + + align:start position:0% +n. I actually did think of printing this + + + align:start position:0% +n. I actually did think of printing this +out. By the way, Python will compute + + align:start position:0% +out. By the way, Python will compute + + + align:start position:0% +out. By the way, Python will compute +this, but it was taking pages and pages + + align:start position:0% +this, but it was taking pages and pages + + + align:start position:0% +this, but it was taking pages and pages +and pages. I didn't want to do it. You + + align:start position:0% +and pages. I didn't want to do it. You + + + align:start position:0% +and pages. I didn't want to do it. You +get the point. Exponential always much + + align:start position:0% +get the point. Exponential always much + + + align:start position:0% +get the point. Exponential always much +worse always much worse than than than a + + align:start position:0% +worse always much worse than than than a + + + align:start position:0% +worse always much worse than than than a +quadratic or or a power expression. And + + align:start position:0% +quadratic or or a power expression. And + + + align:start position:0% +quadratic or or a power expression. And +you really see the difference here. + + align:start position:0% +you really see the difference here. + + + align:start position:0% +you really see the difference here. +Okay. All right. The reason I put this + + align:start position:0% +Okay. All right. The reason I put this + + + align:start position:0% +Okay. All right. The reason I put this +up is as you design algorithms, your + + align:start position:0% +up is as you design algorithms, your + + + align:start position:0% +up is as you design algorithms, your +goal is to be as high up in this listing + + align:start position:0% +goal is to be as high up in this listing + + + align:start position:0% +goal is to be as high up in this listing +as you can. The closer you are to the + + align:start position:0% +as you can. The closer you are to the + + + align:start position:0% +as you can. The closer you are to the +top of this list, the better off you + + align:start position:0% +top of this list, the better off you + + + align:start position:0% +top of this list, the better off you +are. If you have a solution that's down + + align:start position:0% +are. If you have a solution that's down + + + align:start position:0% +are. If you have a solution that's down +here, bring a sleeping bag and some + + align:start position:0% +here, bring a sleeping bag and some + + + align:start position:0% +here, bring a sleeping bag and some +coffee. You're going to be there for a + + align:start position:0% +coffee. You're going to be there for a + + + align:start position:0% +coffee. You're going to be there for a +while, right? You really want to try and + + align:start position:0% +while, right? You really want to try and + + + align:start position:0% +while, right? You really want to try and +avoid that if you can. So now what we + + align:start position:0% +avoid that if you can. So now what we + + + align:start position:0% +avoid that if you can. So now what we +want to do both for the rest of today, + + align:start position:0% +want to do both for the rest of today, + + + align:start position:0% +want to do both for the rest of today, +the last 15 minutes and then next week + + align:start position:0% +the last 15 minutes and then next week + + + align:start position:0% +the last 15 minutes and then next week +is start identifying common algorithms + + align:start position:0% +is start identifying common algorithms + + + align:start position:0% +is start identifying common algorithms +and what is their complexity. And as I + + align:start position:0% +and what is their complexity. And as I + + + align:start position:0% +and what is their complexity. And as I +said to you way back at the beginning of + + align:start position:0% +said to you way back at the beginning of + + + align:start position:0% +said to you way back at the beginning of +this lecture, which I'm sure you + + align:start position:0% +this lecture, which I'm sure you + + + align:start position:0% +this lecture, which I'm sure you +remember, it's not just to be able to + + align:start position:0% +remember, it's not just to be able to + + + align:start position:0% +remember, it's not just to be able to +identify the complexity. I want you to + + align:start position:0% +identify the complexity. I want you to + + + align:start position:0% +identify the complexity. I want you to +see how choices in algorithm design are + + align:start position:0% +see how choices in algorithm design are + + + align:start position:0% +see how choices in algorithm design are +going to lead to particular kinds of + + align:start position:0% +going to lead to particular kinds of + + + align:start position:0% +going to lead to particular kinds of +consequences in terms of what this is + + align:start position:0% +consequences in terms of what this is + + + align:start position:0% +consequences in terms of what this is +going to cost you. That's your goal + + align:start position:0% +going to cost you. That's your goal + + + align:start position:0% +going to cost you. That's your goal +here. All right, we've already seen some + + align:start position:0% +here. All right, we've already seen some + + + align:start position:0% +here. All right, we've already seen some +examples. I'm going to do one more here, + + align:start position:0% +examples. I'm going to do one more here, + + + align:start position:0% +examples. I'm going to do one more here, +but simple iterative loop algorithms are + + align:start position:0% +but simple iterative loop algorithms are + + + align:start position:0% +but simple iterative loop algorithms are +typically + + align:start position:0% +typically + + + align:start position:0% +typically +linear. Here's another version of + + align:start position:0% +linear. Here's another version of + + + align:start position:0% +linear. Here's another version of +searching. Imagine I have an unsorted + + align:start position:0% +searching. Imagine I have an unsorted + + + align:start position:0% +searching. Imagine I have an unsorted +list, arbitrary order. Here's another + + align:start position:0% +list, arbitrary order. Here's another + + + align:start position:0% +list, arbitrary order. Here's another +way of doing the linear search. Looks a + + align:start position:0% +way of doing the linear search. Looks a + + + align:start position:0% +way of doing the linear search. Looks a +little bit faster. I'm going to set a + + align:start position:0% +little bit faster. I'm going to set a + + + align:start position:0% +little bit faster. I'm going to set a +flag initially to false. And then I'm + + align:start position:0% +flag initially to false. And then I'm + + + align:start position:0% +flag initially to false. And then I'm +going to loop for I from zero up to the + + align:start position:0% +going to loop for I from zero up to the + + + align:start position:0% +going to loop for I from zero up to the +length of L. I'm going to use that to + + align:start position:0% +length of L. I'm going to use that to + + + align:start position:0% +length of L. I'm going to use that to +index into the list, pull out each + + align:start position:0% +index into the list, pull out each + + + align:start position:0% +index into the list, pull out each +element of the list list in turn and + + align:start position:0% +element of the list list in turn and + + + align:start position:0% +element of the list list in turn and +check to see is it the thing I'm looking + + align:start position:0% +check to see is it the thing I'm looking + + + align:start position:0% +check to see is it the thing I'm looking +for. As soon as I find it, I'm going to + + align:start position:0% +for. As soon as I find it, I'm going to + + + align:start position:0% +for. As soon as I find it, I'm going to +send sorry set the flag to true. Okay? + + align:start position:0% +send sorry set the flag to true. Okay? + + + align:start position:0% +send sorry set the flag to true. Okay? +So that when I return out of the loop, I + + align:start position:0% +So that when I return out of the loop, I + + + align:start position:0% +So that when I return out of the loop, I +can just return found. And if I found + + align:start position:0% +can just return found. And if I found + + + align:start position:0% +can just return found. And if I found +it, it'll be true. If I never found it, + + align:start position:0% +it, it'll be true. If I never found it, + + + align:start position:0% +it, it'll be true. If I never found it, +found will still be false and I'll + + align:start position:0% +found will still be false and I'll + + + align:start position:0% +found will still be false and I'll +return + + align:start position:0% +return + + + align:start position:0% +return +it. We could count the operations here, + + align:start position:0% +it. We could count the operations here, + + + align:start position:0% +it. We could count the operations here, +but you've already seen examples of + + align:start position:0% +but you've already seen examples of + + + align:start position:0% +but you've already seen examples of +doing that. This is linear because I'm + + align:start position:0% +doing that. This is linear because I'm + + + align:start position:0% +doing that. This is linear because I'm +looping n times if n is the length of + + align:start position:0% +looping n times if n is the length of + + + align:start position:0% +looping n times if n is the length of +the list over there. And the number of + + align:start position:0% +the list over there. And the number of + + + align:start position:0% +the list over there. And the number of +things I do inside the loop is + + align:start position:0% +things I do inside the loop is + + + align:start position:0% +things I do inside the loop is +constant. Now you might say, wait a + + align:start position:0% +constant. Now you might say, wait a + + + align:start position:0% +constant. Now you might say, wait a +minute, this is really brain damaged or + + align:start position:0% +minute, this is really brain damaged or + + + align:start position:0% +minute, this is really brain damaged or +if you're being more politically + + align:start position:0% +if you're being more politically + + + align:start position:0% +if you're being more politically +correct, computationally challenged. + + align:start position:0% +correct, computationally challenged. + + + align:start position:0% +correct, computationally challenged. +Okay, in the sense of once I found it, + + align:start position:0% +Okay, in the sense of once I found it, + + + align:start position:0% +Okay, in the sense of once I found it, +why bother looking at the rest of the + + align:start position:0% +why bother looking at the rest of the + + + align:start position:0% +why bother looking at the rest of the +list? So in fact, I could just return + + align:start position:0% +list? So in fact, I could just return + + + align:start position:0% +list? So in fact, I could just return +true right here. + + align:start position:0% +true right here. + + + align:start position:0% +true right here. +Does that change the order of growth of + + align:start position:0% +Does that change the order of growth of + + + align:start position:0% +Does that change the order of growth of +this + + align:start position:0% +this + + + align:start position:0% +this +algorithm? + + align:start position:0% +algorithm? + + + align:start position:0% +algorithm? +No. Changes the average time. I'm going + + align:start position:0% +No. Changes the average time. I'm going + + + align:start position:0% +No. Changes the average time. I'm going +to stop faster. But remember, the order + + align:start position:0% +to stop faster. But remember, the order + + + align:start position:0% +to stop faster. But remember, the order +of growth captures what's the worst case + + align:start position:0% +of growth captures what's the worst case + + + align:start position:0% +of growth captures what's the worst case +behavior. And the worst case behavior is + + align:start position:0% +behavior. And the worst case behavior is + + + align:start position:0% +behavior. And the worst case behavior is +the elements not in the list. I got to + + align:start position:0% +the elements not in the list. I got to + + + align:start position:0% +the elements not in the list. I got to +look at everything. So this will be an + + align:start position:0% +look at everything. So this will be an + + + align:start position:0% +look at everything. So this will be an +example of a linear algorithm. And you + + align:start position:0% +example of a linear algorithm. And you + + + align:start position:0% +example of a linear algorithm. And you +can see I'm looping length of L times + + align:start position:0% +can see I'm looping length of L times + + + align:start position:0% +can see I'm looping length of L times +over the loop inside of there. It's + + align:start position:0% +over the loop inside of there. It's + + + align:start position:0% +over the loop inside of there. It's +taking me order one to test it. So, it's + + align:start position:0% +taking me order one to test it. So, it's + + + align:start position:0% +taking me order one to test it. So, it's +order n. And if I were to actually count + + align:start position:0% +order n. And if I were to actually count + + + align:start position:0% +order n. And if I were to actually count +it, there's the expression. It's 1 plus + + align:start position:0% +it, there's the expression. It's 1 plus + + + align:start position:0% +it, there's the expression. It's 1 plus +4 n + 1, which is 4 n plus2, which by my + + align:start position:0% +4 n + 1, which is 4 n plus2, which by my + + + align:start position:0% +4 n + 1, which is 4 n plus2, which by my +rule says I don't care about the + + align:start position:0% +rule says I don't care about the + + + align:start position:0% +rule says I don't care about the +additive constant. I only care about the + + align:start position:0% +additive constant. I only care about the + + + align:start position:0% +additive constant. I only care about the +dominant term. And I don't care about + + align:start position:0% +dominant term. And I don't care about + + + align:start position:0% +dominant term. And I don't care about +that multip multiplicative constant. + + align:start position:0% +that multip multiplicative constant. + + + align:start position:0% +that multip multiplicative constant. +It's order + + align:start position:0% +It's order + + + align:start position:0% +It's order +n example of a template. You're going to + + align:start position:0% +n example of a template. You're going to + + + align:start position:0% +n example of a template. You're going to +see a + + align:start position:0% +see a + + + align:start position:0% +see a +lot. + + align:start position:0% +lot. + + + align:start position:0% +lot. +Now, okay, order n where n is the length + + align:start position:0% +Now, okay, order n where n is the length + + + align:start position:0% +Now, okay, order n where n is the length +of the list. And I need to specify that. + + align:start position:0% +of the list. And I need to specify that. + + + align:start position:0% +of the list. And I need to specify that. +That's the thing I'm after. + + align:start position:0% +That's the thing I'm after. + + + align:start position:0% +That's the thing I'm after. +If you think about it, I cheated. Sorry, + + align:start position:0% +If you think about it, I cheated. Sorry, + + + align:start position:0% +If you think about it, I cheated. Sorry, +I never cheat. I'm tenured. I never + + align:start position:0% +I never cheat. I'm tenured. I never + + + align:start position:0% +I never cheat. I'm tenured. I never +cheat. I just mislead you + + align:start position:0% +cheat. I just mislead you + + + align:start position:0% +cheat. I just mislead you +badly. Not a + + align:start position:0% +badly. Not a + + + align:start position:0% +badly. Not a +chance. How do I know that accessing an + + align:start position:0% +chance. How do I know that accessing an + + + align:start position:0% +chance. How do I know that accessing an +element of the list takes constant time? + + align:start position:0% +element of the list takes constant time? + + + align:start position:0% +element of the list takes constant time? +I made an assumption about that. And + + align:start position:0% +I made an assumption about that. And + + + align:start position:0% +I made an assumption about that. And +this is a reasonable thing to ask about + + align:start position:0% +this is a reasonable thing to ask about + + + align:start position:0% +this is a reasonable thing to ask about +both. What am I assuming about the + + align:start position:0% +both. What am I assuming about the + + + align:start position:0% +both. What am I assuming about the +constant operations? And how do I know + + align:start position:0% +constant operations? And how do I know + + + align:start position:0% +constant operations? And how do I know +that's actually true? + + align:start position:0% +that's actually true? + + + align:start position:0% +that's actually true? +Well, it gives me a chance to point out + + align:start position:0% +Well, it gives me a chance to point out + + + align:start position:0% +Well, it gives me a chance to point out +something that Python does very + + align:start position:0% +something that Python does very + + + align:start position:0% +something that Python does very +effectively. Not all languages do. But + + align:start position:0% +effectively. Not all languages do. But + + + align:start position:0% +effectively. Not all languages do. But +think about a list. Suppose I've got a + + align:start position:0% +think about a list. Suppose I've got a + + + align:start position:0% +think about a list. Suppose I've got a +list that's all integers. I'm going to + + align:start position:0% +list that's all integers. I'm going to + + + align:start position:0% +list that's all integers. I'm going to +need some amount of memory to represent + + align:start position:0% +need some amount of memory to represent + + + align:start position:0% +need some amount of memory to represent +each integer. So if a bite is eight + + align:start position:0% +each integer. So if a bite is eight + + + align:start position:0% +each integer. So if a bite is eight +bits, I might reserve four bytes or 32 + + align:start position:0% +bits, I might reserve four bytes or 32 + + + align:start position:0% +bits, I might reserve four bytes or 32 +bits to cover any reasonable sized + + align:start position:0% +bits to cover any reasonable sized + + + align:start position:0% +bits to cover any reasonable sized +integer. When I represent a list, I + + align:start position:0% +integer. When I represent a list, I + + + align:start position:0% +integer. When I represent a list, I +could simply have each of them in turn. + + align:start position:0% +could simply have each of them in turn. + + + align:start position:0% +could simply have each of them in turn. +So what do I need to know? I'm going to + + align:start position:0% +So what do I need to know? I'm going to + + + align:start position:0% +So what do I need to know? I'm going to +allocate out a particular length, say + + align:start position:0% +allocate out a particular length, say + + + align:start position:0% +allocate out a particular length, say +four bytes, 32 bits, 32 sequential + + align:start position:0% +four bytes, 32 bits, 32 sequential + + + align:start position:0% +four bytes, 32 bits, 32 sequential +elements of of memory to represent each + + align:start position:0% +elements of of memory to represent each + + + align:start position:0% +elements of of memory to represent each +integer. And then I just need to know + + align:start position:0% +integer. And then I just need to know + + + align:start position:0% +integer. And then I just need to know +where's the first part of the list. + + align:start position:0% +where's the first part of the list. + + + align:start position:0% +where's the first part of the list. +What's the address in memory of the + + align:start position:0% +What's the address in memory of the + + + align:start position:0% +What's the address in memory of the +first part of the list? And to get to + + align:start position:0% +first part of the list? And to get to + + + align:start position:0% +first part of the list? And to get to +the E element, I take that base plus + + align:start position:0% +the E element, I take that base plus + + + align:start position:0% +the E element, I take that base plus +four bytes times I and I can go straight + + align:start position:0% +four bytes times I and I can go straight + + + align:start position:0% +four bytes times I and I can go straight +to this point without having to walk + + align:start position:0% +to this point without having to walk + + + align:start position:0% +to this point without having to walk +down the list. That's nice. Okay, it + + align:start position:0% +down the list. That's nice. Okay, it + + + align:start position:0% +down the list. That's nice. Okay, it +says in fact I can get to any element of + + align:start position:0% +says in fact I can get to any element of + + + align:start position:0% +says in fact I can get to any element of +memory. Sorry, any element of the list + + align:start position:0% +memory. Sorry, any element of the list + + + align:start position:0% +memory. Sorry, any element of the list +in constant + + align:start position:0% +in constant + + + align:start position:0% +in constant +time. Okay, now what if the things I'm + + align:start position:0% +time. Okay, now what if the things I'm + + + align:start position:0% +time. Okay, now what if the things I'm +representing aren't integers? They're + + align:start position:0% +representing aren't integers? They're + + + align:start position:0% +representing aren't integers? They're +arbitrary things and they take up a big + + align:start position:0% +arbitrary things and they take up a big + + + align:start position:0% +arbitrary things and they take up a big +chunk of space. Well, if the list is + + align:start position:0% +chunk of space. Well, if the list is + + + align:start position:0% +chunk of space. Well, if the list is +heterogeneous, we use a nice technique + + align:start position:0% +heterogeneous, we use a nice technique + + + align:start position:0% +heterogeneous, we use a nice technique +called indirection. And that simply says + + align:start position:0% +called indirection. And that simply says + + + align:start position:0% +called indirection. And that simply says +we again have a list. We know the + + align:start position:0% +we again have a list. We know the + + + align:start position:0% +we again have a list. We know the +address of this point. We know the + + align:start position:0% +address of this point. We know the + + + align:start position:0% +address of this point. We know the +address therefore of the e element of + + align:start position:0% +address therefore of the e element of + + + align:start position:0% +address therefore of the e element of +this list. But inside of here, we don't + + align:start position:0% +this list. But inside of here, we don't + + + align:start position:0% +this list. But inside of here, we don't +store the actual value. We store a + + align:start position:0% +store the actual value. We store a + + + align:start position:0% +store the actual value. We store a +pointer to where it is in memory, which + + align:start position:0% +pointer to where it is in memory, which + + + align:start position:0% +pointer to where it is in memory, which +is what these things are indicating. So + + align:start position:0% +is what these things are indicating. So + + + align:start position:0% +is what these things are indicating. So +they can be arbitrary size, but again, I + + align:start position:0% +they can be arbitrary size, but again, I + + + align:start position:0% +they can be arbitrary size, but again, I +can get to any element in constant time, + + align:start position:0% +can get to any element in constant time, + + + align:start position:0% +can get to any element in constant time, +which is exactly what I want. So that's + + align:start position:0% +which is exactly what I want. So that's + + + align:start position:0% +which is exactly what I want. So that's +great. Okay. Now, suppose I tell you + + align:start position:0% +great. Okay. Now, suppose I tell you + + + align:start position:0% +great. Okay. Now, suppose I tell you +that the list is sorted. It's in + + align:start position:0% +that the list is sorted. It's in + + + align:start position:0% +that the list is sorted. It's in +increasing order. I can be more clever + + align:start position:0% +increasing order. I can be more clever + + + align:start position:0% +increasing order. I can be more clever +about my algorithm because now as I loop + + align:start position:0% +about my algorithm because now as I loop + + + align:start position:0% +about my algorithm because now as I loop +through it, I can say if it's the thing + + align:start position:0% +through it, I can say if it's the thing + + + align:start position:0% +through it, I can say if it's the thing +I'm looking for, just return true. If + + align:start position:0% +I'm looking for, just return true. If + + + align:start position:0% +I'm looking for, just return true. If +the element of the list is bigger than + + align:start position:0% +the element of the list is bigger than + + + align:start position:0% +the element of the list is bigger than +the thing I'm looking for, I'm done. I + + align:start position:0% +the thing I'm looking for, I'm done. I + + + align:start position:0% +the thing I'm looking for, I'm done. I +don't need to look at the rest of the + + align:start position:0% +don't need to look at the rest of the + + + align:start position:0% +don't need to look at the rest of the +list because I know it can't be there + + align:start position:0% +list because I know it can't be there + + + align:start position:0% +list because I know it can't be there +because it's ordered or sorted, I can + + align:start position:0% +because it's ordered or sorted, I can + + + align:start position:0% +because it's ordered or sorted, I can +just return false. If I get all the way + + align:start position:0% +just return false. If I get all the way + + + align:start position:0% +just return false. If I get all the way +through the loop, I can return false. + + align:start position:0% +through the loop, I can return false. + + + align:start position:0% +through the loop, I can return false. +So, I only have to look until I get to a + + align:start position:0% +So, I only have to look until I get to a + + + align:start position:0% +So, I only have to look until I get to a +point where the thing in the list is + + align:start position:0% +point where the thing in the list is + + + align:start position:0% +point where the thing in the list is +bigger than what I'm looking for. It's + + align:start position:0% +bigger than what I'm looking for. It's + + + align:start position:0% +bigger than what I'm looking for. It's +the order of growth here. + + align:start position:0% +the order of growth here. + + + align:start position:0% +the order of growth here. +Again the average time behavior will be + + align:start position:0% +Again the average time behavior will be + + + align:start position:0% +Again the average time behavior will be +faster but the order of growth is I've + + align:start position:0% +faster but the order of growth is I've + + + align:start position:0% +faster but the order of growth is I've +got to do order of length of the list to + + align:start position:0% +got to do order of length of the list to + + + align:start position:0% +got to do order of length of the list to +go through the loop order of one to do + + align:start position:0% +go through the loop order of one to do + + + align:start position:0% +go through the loop order of one to do +the test and in the worst case again I + + align:start position:0% +the test and in the worst case again I + + + align:start position:0% +the test and in the worst case again I +still have to go through the entire + + align:start position:0% +still have to go through the entire + + + align:start position:0% +still have to go through the entire +list. So the order of growth here is the + + align:start position:0% +list. So the order of growth here is the + + + align:start position:0% +list. So the order of growth here is the +same. It is again linear in the length + + align:start position:0% +same. It is again linear in the length + + + align:start position:0% +same. It is again linear in the length +of the list even though the runtime will + + align:start position:0% +of the list even though the runtime will + + + align:start position:0% +of the list even though the runtime will +be different depending on whether it's + + align:start position:0% +be different depending on whether it's + + + align:start position:0% +be different depending on whether it's +sorted or + + align:start position:0% +sorted or + + + align:start position:0% +sorted or +not. I want you to hold on to that idea + + align:start position:0% +not. I want you to hold on to that idea + + + align:start position:0% +not. I want you to hold on to that idea +because we're going to come back to the + + align:start position:0% +because we're going to come back to the + + + align:start position:0% +because we're going to come back to the +sorted list next week to see that there + + align:start position:0% +sorted list next week to see that there + + + align:start position:0% +sorted list next week to see that there +actually are much more efficient ways to + + align:start position:0% +actually are much more efficient ways to + + + align:start position:0% +actually are much more efficient ways to +use the fact that a list is sorted to do + + align:start position:0% +use the fact that a list is sorted to do + + + align:start position:0% +use the fact that a list is sorted to do +the search. But both of these versions + + align:start position:0% +the search. But both of these versions + + + align:start position:0% +the search. But both of these versions +same order of growth order + + align:start position:0% +same order of growth order + + + align:start position:0% +same order of growth order +n. Okay. So lurching there lurching + + align:start position:0% +n. Okay. So lurching there lurching + + + align:start position:0% +n. Okay. So lurching there lurching +through a list right sorry searching + + align:start position:0% +through a list right sorry searching + + + align:start position:0% +through a list right sorry searching +through a list in sequence is linear + + align:start position:0% +through a list in sequence is linear + + + align:start position:0% +through a list in sequence is linear +because of that loop. There are other + + align:start position:0% +because of that loop. There are other + + + align:start position:0% +because of that loop. There are other +things that have a similar flavor and + + align:start position:0% +things that have a similar flavor and + + + align:start position:0% +things that have a similar flavor and +I'm going to do these quickly to get to + + align:start position:0% +I'm going to do these quickly to get to + + + align:start position:0% +I'm going to do these quickly to get to +the last example. Imagine I give you a + + align:start position:0% +the last example. Imagine I give you a + + + align:start position:0% +the last example. Imagine I give you a +string of of um characters that are all + + align:start position:0% +string of of um characters that are all + + + align:start position:0% +string of of um characters that are all +assumed to be composed of decimal + + align:start position:0% +assumed to be composed of decimal + + + align:start position:0% +assumed to be composed of decimal +digits. I just want to add them all up. + + align:start position:0% +digits. I just want to add them all up. + + + align:start position:0% +digits. I just want to add them all up. +This is also linear because there's the + + align:start position:0% +This is also linear because there's the + + + align:start position:0% +This is also linear because there's the +loop. I'm going to loop over the + + align:start position:0% +loop. I'm going to loop over the + + + align:start position:0% +loop. I'm going to loop over the +characters in the string. I'm going to + + align:start position:0% +characters in the string. I'm going to + + + align:start position:0% +characters in the string. I'm going to +uh cast them into integers, add them in, + + align:start position:0% +uh cast them into integers, add them in, + + + align:start position:0% +uh cast them into integers, add them in, +and return the value. This is linear in + + align:start position:0% +and return the value. This is linear in + + + align:start position:0% +and return the value. This is linear in +the length of the input + + align:start position:0% +the length of the input + + + align:start position:0% +the length of the input +s. Notice the pattern that loop that an + + align:start position:0% +s. Notice the pattern that loop that an + + + align:start position:0% +s. Notice the pattern that loop that an +iterative loop. It's got that linear + + align:start position:0% +iterative loop. It's got that linear + + + align:start position:0% +iterative loop. It's got that linear +behavior because inside of the loop, + + align:start position:0% +behavior because inside of the loop, + + + align:start position:0% +behavior because inside of the loop, +constant number of things that I'm + + align:start position:0% +constant number of things that I'm + + + align:start position:0% +constant number of things that I'm +executing. We already looked at fact + + align:start position:0% +executing. We already looked at fact + + + align:start position:0% +executing. We already looked at fact +iter. Same idea. There's the loop. I'm + + align:start position:0% +iter. Same idea. There's the loop. I'm + + + align:start position:0% +iter. Same idea. There's the loop. I'm +going to do that n times. Inside the + + align:start position:0% +going to do that n times. Inside the + + + align:start position:0% +going to do that n times. Inside the +loop, a constant amount of things. So + + align:start position:0% +loop, a constant amount of things. So + + + align:start position:0% +loop, a constant amount of things. So +we're looping around it is order n. + + align:start position:0% +we're looping around it is order n. + + + align:start position:0% +we're looping around it is order n. +There's the actual expression. But + + align:start position:0% +There's the actual expression. But + + + align:start position:0% +There's the actual expression. But +again, the pattern I want you to see + + align:start position:0% +again, the pattern I want you to see + + + align:start position:0% +again, the pattern I want you to see +here is that this is order + + align:start position:0% +here is that this is order + + + align:start position:0% +here is that this is order +n. + + align:start position:0% +n. + + + align:start position:0% +n. +Okay, last example for today. I know + + align:start position:0% +Okay, last example for today. I know + + + align:start position:0% +Okay, last example for today. I know +you're all secretly looking at your + + align:start position:0% +you're all secretly looking at your + + + align:start position:0% +you're all secretly looking at your +watches. Standard loops typically + + align:start position:0% +watches. Standard loops typically + + + align:start position:0% +watches. Standard loops typically +linear. What about nested loops? What + + align:start position:0% +linear. What about nested loops? What + + + align:start position:0% +linear. What about nested loops? What +about loops that have loops inside of + + align:start position:0% +about loops that have loops inside of + + + align:start position:0% +about loops that have loops inside of +them? How long do they take? And I want + + align:start position:0% +them? How long do they take? And I want + + + align:start position:0% +them? How long do they take? And I want +to show you a couple of examples. + + align:start position:0% +to show you a couple of examples. + + + align:start position:0% +to show you a couple of examples. +And mostly I want to show you how to + + align:start position:0% +And mostly I want to show you how to + + + align:start position:0% +And mostly I want to show you how to +reason about + + align:start position:0% +reason about + + + align:start position:0% +reason about +them. Suppose I gave you two lists + + align:start position:0% +them. Suppose I gave you two lists + + + align:start position:0% +them. Suppose I gave you two lists +composed of of integers and I want to + + align:start position:0% +composed of of integers and I want to + + + align:start position:0% +composed of of integers and I want to +know is the first list a subset of the + + align:start position:0% +know is the first list a subset of the + + + align:start position:0% +know is the first list a subset of the +second + + align:start position:0% +second + + + align:start position:0% +second +list. Code's in the handout by the way + + align:start position:0% +list. Code's in the handout by the way + + + align:start position:0% +list. Code's in the handout by the way +if you want to go run it. But basically + + align:start position:0% +if you want to go run it. But basically + + + align:start position:0% +if you want to go run it. But basically +the simple idea would be I'm going to + + align:start position:0% +the simple idea would be I'm going to + + + align:start position:0% +the simple idea would be I'm going to +loop over every element in the first + + align:start position:0% +loop over every element in the first + + + align:start position:0% +loop over every element in the first +list. And for each one of those I want + + align:start position:0% +list. And for each one of those I want + + + align:start position:0% +list. And for each one of those I want +to say is it in the second list? So I'll + + align:start position:0% +to say is it in the second list? So I'll + + + align:start position:0% +to say is it in the second list? So I'll +use the same kind of trick. I'll set up + + align:start position:0% +use the same kind of trick. I'll set up + + + align:start position:0% +use the same kind of trick. I'll set up +a flag that's initially false. And then + + align:start position:0% +a flag that's initially false. And then + + + align:start position:0% +a flag that's initially false. And then +I'm going to loop over everything in the + + align:start position:0% +I'm going to loop over everything in the + + + align:start position:0% +I'm going to loop over everything in the +second list. And if that thing is equal + + align:start position:0% +second list. And if that thing is equal + + + align:start position:0% +second list. And if that thing is equal +to the thing I'm looking for, I'll set + + align:start position:0% +to the thing I'm looking for, I'll set + + + align:start position:0% +to the thing I'm looking for, I'll set +match to true and break out of the loop. + + align:start position:0% +match to true and break out of the loop. + + + align:start position:0% +match to true and break out of the loop. +The inner loop. If I get all the way + + align:start position:0% +The inner loop. If I get all the way + + + align:start position:0% +The inner loop. If I get all the way +through the second list and I haven't + + align:start position:0% +through the second list and I haven't + + + align:start position:0% +through the second list and I haven't +found the thing I'm looking for, when I + + align:start position:0% +found the thing I'm looking for, when I + + + align:start position:0% +found the thing I'm looking for, when I +break out or come out of this loop, + + align:start position:0% +break out or come out of this loop, + + + align:start position:0% +break out or come out of this loop, +matched in that case will still be false + + align:start position:0% +matched in that case will still be false + + + align:start position:0% +matched in that case will still be false +and I'll return false. But if up here I + + align:start position:0% +and I'll return false. But if up here I + + + align:start position:0% +and I'll return false. But if up here I +found something that matched, match will + + align:start position:0% +found something that matched, match will + + + align:start position:0% +found something that matched, match will +be true. I break out of it. It's not + + align:start position:0% +be true. I break out of it. It's not + + + align:start position:0% +be true. I break out of it. It's not +false. Therefore, I return true. + + align:start position:0% +false. Therefore, I return true. + + + align:start position:0% +false. Therefore, I return true. +I want you to look at the code. You + + align:start position:0% +I want you to look at the code. You + + + align:start position:0% +I want you to look at the code. You +should be able to look at this and + + align:start position:0% +should be able to look at this and + + + align:start position:0% +should be able to look at this and +realize what it's doing. For each + + align:start position:0% +realize what it's doing. For each + + + align:start position:0% +realize what it's doing. For each +element in the first list, I walk + + align:start position:0% +element in the first list, I walk + + + align:start position:0% +element in the first list, I walk +through the second list to say, is that + + align:start position:0% +through the second list to say, is that + + + align:start position:0% +through the second list to say, is that +element there? If it is, I return true. + + align:start position:0% +element there? If it is, I return true. + + + align:start position:0% +element there? If it is, I return true. +If that's true for all of the elements + + align:start position:0% +If that's true for all of the elements + + + align:start position:0% +If that's true for all of the elements +in the first list, I return true + + align:start position:0% +in the first list, I return true + + + align:start position:0% +in the first list, I return true +overall. Okay. Order of + + align:start position:0% + + + + align:start position:0% + +growth. Outer loop. This loop, I'm going + + align:start position:0% +growth. Outer loop. This loop, I'm going + + + align:start position:0% +growth. Outer loop. This loop, I'm going +to execute the length of L1 times. + + align:start position:0% +to execute the length of L1 times. + + + align:start position:0% +to execute the length of L1 times. +Right? I've got to walk down that first + + align:start position:0% +Right? I've got to walk down that first + + + align:start position:0% +Right? I've got to walk down that first +list. If I call that n, it's going to + + align:start position:0% +list. If I call that n, it's going to + + + align:start position:0% +list. If I call that n, it's going to +take that n times over the over loop, + + align:start position:0% +take that n times over the over loop, + + + align:start position:0% +take that n times over the over loop, +outer loop. But what about in + + align:start position:0% +outer loop. But what about in + + + align:start position:0% +outer loop. But what about in +here? All of the earlier examples, we + + align:start position:0% +here? All of the earlier examples, we + + + align:start position:0% +here? All of the earlier examples, we +had a constant number of operations + + align:start position:0% +had a constant number of operations + + + align:start position:0% +had a constant number of operations +inside of the loop. Here, we don't. + + align:start position:0% +inside of the loop. Here, we don't. + + + align:start position:0% +inside of the loop. Here, we don't. +We've got another loop that's looping + + align:start position:0% +We've got another loop that's looping + + + align:start position:0% +We've got another loop that's looping +over in part in in principle all the + + align:start position:0% +over in part in in principle all the + + + align:start position:0% +over in part in in principle all the +elements of the second list. So it each + + align:start position:0% +elements of the second list. So it each + + + align:start position:0% +elements of the second list. So it each +iteration is going to execute the inner + + align:start position:0% +iteration is going to execute the inner + + + align:start position:0% +iteration is going to execute the inner +loop up to length of L2 times where + + align:start position:0% +loop up to length of L2 times where + + + align:start position:0% +loop up to length of L2 times where +inside of this inner loop there is a + + align:start position:0% +inside of this inner loop there is a + + + align:start position:0% +inside of this inner loop there is a +constant number of + + align:start position:0% +constant number of + + + align:start position:0% +constant number of +operations. Ah + + align:start position:0% +operations. Ah + + + align:start position:0% +operations. Ah +nice. That's the multiplicative law of + + align:start position:0% +nice. That's the multiplicative law of + + + align:start position:0% +nice. That's the multiplicative law of +orders of growth. It says if this is + + align:start position:0% +orders of growth. It says if this is + + + align:start position:0% +orders of growth. It says if this is +order length L1 and we're going to do + + align:start position:0% +order length L1 and we're going to do + + + align:start position:0% +order length L1 and we're going to do +that then order length of L2 times the + + align:start position:0% +that then order length of L2 times the + + + align:start position:0% +that then order length of L2 times the +order growth is a product. + + align:start position:0% +order growth is a product. + + + align:start position:0% +order growth is a product. +And the most common or the worst case + + align:start position:0% +And the most common or the worst case + + + align:start position:0% +And the most common or the worst case +behavior is going to be when the lists + + align:start position:0% +behavior is going to be when the lists + + + align:start position:0% +behavior is going to be when the lists +are of the same length and none of the + + align:start position:0% +are of the same length and none of the + + + align:start position:0% +are of the same length and none of the +elements of L1 are in L2. And in that + + align:start position:0% +elements of L1 are in L2. And in that + + + align:start position:0% +elements of L1 are in L2. And in that +case, we're going to get something + + align:start position:0% +case, we're going to get something + + + align:start position:0% +case, we're going to get something +that's order n + + align:start position:0% +that's order n + + + align:start position:0% +that's order n +squad where n is the length of the list + + align:start position:0% +squad where n is the length of the list + + + align:start position:0% +squad where n is the length of the list +in terms of number of + + align:start position:0% +in terms of number of + + + align:start position:0% +in terms of number of +operations. I don't really care about + + align:start position:0% +operations. I don't really care about + + + align:start position:0% +operations. I don't really care about +subsets. I got one more example. We + + align:start position:0% +subsets. I got one more example. We + + + align:start position:0% +subsets. I got one more example. We +could similarly do intersection. I + + align:start position:0% +could similarly do intersection. I + + + align:start position:0% +could similarly do intersection. I +wanted to say uh what is the + + align:start position:0% +wanted to say uh what is the + + + align:start position:0% +wanted to say uh what is the +intersection of two lists? what elements + + align:start position:0% +intersection of two lists? what elements + + + align:start position:0% +intersection of two lists? what elements +are in both list one and list two. Same + + align:start position:0% +are in both list one and list two. Same + + + align:start position:0% +are in both list one and list two. Same +basic idea here. I've got a pair of + + align:start position:0% +basic idea here. I've got a pair of + + + align:start position:0% +basic idea here. I've got a pair of +nested loops. I'm looping over + + align:start position:0% +nested loops. I'm looping over + + + align:start position:0% +nested loops. I'm looping over +everything in L1. For that, I'm looping + + align:start position:0% +everything in L1. For that, I'm looping + + + align:start position:0% +everything in L1. For that, I'm looping +over everything in in L2. And if they + + align:start position:0% +over everything in in L2. And if they + + + align:start position:0% +over everything in in L2. And if they +are the same, I'm going to put that into + + align:start position:0% +are the same, I'm going to put that into + + + align:start position:0% +are the same, I'm going to put that into +my temporary variable. Once I've done + + align:start position:0% +my temporary variable. Once I've done + + + align:start position:0% +my temporary variable. Once I've done +that, I need to clean things up. So, I'm + + align:start position:0% +that, I need to clean things up. So, I'm + + + align:start position:0% +that, I need to clean things up. So, I'm +going to write another loop that sets up + + align:start position:0% +going to write another loop that sets up + + + align:start position:0% +going to write another loop that sets up +an internal variable and then run + + align:start position:0% +an internal variable and then run + + + align:start position:0% +an internal variable and then run +through everything in the list I + + align:start position:0% +through everything in the list I + + + align:start position:0% +through everything in the list I +accumulated, making sure that it's not + + align:start position:0% +accumulated, making sure that it's not + + + align:start position:0% +accumulated, making sure that it's not +already there. And as long as it isn't, + + align:start position:0% +already there. And as long as it isn't, + + + align:start position:0% +already there. And as long as it isn't, +I'm going to put it into the result and + + align:start position:0% +I'm going to put it into the result and + + + align:start position:0% +I'm going to put it into the result and +return + + align:start position:0% +return + + + align:start position:0% +return +it. I did it quickly. You can look + + align:start position:0% +it. I did it quickly. You can look + + + align:start position:0% +it. I did it quickly. You can look +through it. You'll see it does the right + + align:start position:0% +through it. You'll see it does the right + + + align:start position:0% +through it. You'll see it does the right +thing. What I want you to see is what's + + align:start position:0% +thing. What I want you to see is what's + + + align:start position:0% +thing. What I want you to see is what's +the order of growth. I need to look at + + align:start position:0% +the order of growth. I need to look at + + + align:start position:0% +the order of growth. I need to look at +this piece. Then I need to look at that + + align:start position:0% +this piece. Then I need to look at that + + + align:start position:0% +this piece. Then I need to look at that +piece. This + + align:start position:0% +piece. This + + + align:start position:0% +piece. This +piece. Well, it's order length L1 to do + + align:start position:0% +piece. Well, it's order length L1 to do + + + align:start position:0% +piece. Well, it's order length L1 to do +the o outer loop. For each version of + + align:start position:0% +the o outer loop. For each version of + + + align:start position:0% +the o outer loop. For each version of +E1, I've got to do order of length L2 + + align:start position:0% +E1, I've got to do order of length L2 + + + align:start position:0% +E1, I've got to do order of length L2 +things inside to accumulate them. So + + align:start position:0% +things inside to accumulate them. So + + + align:start position:0% +things inside to accumulate them. So +that's quadratic. + + align:start position:0% +that's quadratic. + + + align:start position:0% +that's quadratic. +What about the second loop? Well, this + + align:start position:0% +What about the second loop? Well, this + + + align:start position:0% +What about the second loop? Well, this +one is a little more subtle. I'm only + + align:start position:0% +one is a little more subtle. I'm only + + + align:start position:0% +one is a little more subtle. I'm only +looping over temp, which is at most + + align:start position:0% +looping over temp, which is at most + + + align:start position:0% +looping over temp, which is at most +going to be length L1 long, + + align:start position:0% +going to be length L1 long, + + + align:start position:0% +going to be length L1 long, +but I'm checking to see is that element + + align:start position:0% +but I'm checking to see is that element + + + align:start position:0% +but I'm checking to see is that element +in a + + align:start position:0% +in a + + + align:start position:0% +in a +list? And it depends on the + + align:start position:0% +list? And it depends on the + + + align:start position:0% +list? And it depends on the +implementation, but typically that's + + align:start position:0% +implementation, but typically that's + + + align:start position:0% +implementation, but typically that's +going to take up to the length of the + + align:start position:0% +going to take up to the length of the + + + align:start position:0% +going to take up to the length of the +list to do it. I got to look to see is + + align:start position:0% +list to do it. I got to look to see is + + + align:start position:0% +list to do it. I got to look to see is +it there or not. And so that inner loop, + + align:start position:0% +it there or not. And so that inner loop, + + + align:start position:0% +it there or not. And so that inner loop, +if we assume the lists are the same + + align:start position:0% +if we assume the lists are the same + + + align:start position:0% +if we assume the lists are the same +size, is also going to take potentially + + align:start position:0% +size, is also going to take potentially + + + align:start position:0% +size, is also going to take potentially +up to length L1 steps. And so this is + + align:start position:0% +up to length L1 steps. And so this is + + + align:start position:0% +up to length L1 steps. And so this is +again quadratic. It's actually two + + align:start position:0% +again quadratic. It's actually two + + + align:start position:0% +again quadratic. It's actually two +quadratics, one for the first nested + + align:start position:0% +quadratics, one for the first nested + + + align:start position:0% +quadratics, one for the first nested +loop, one for the second one because + + align:start position:0% +loop, one for the second one because + + + align:start position:0% +loop, one for the second one because +there's an implicit second loop right + + align:start position:0% +there's an implicit second loop right + + + align:start position:0% +there's an implicit second loop right +there. But overall, it's + + align:start position:0% +there. But overall, it's + + + align:start position:0% +there. But overall, it's +quadratic. So what you see in general, + + align:start position:0% +quadratic. So what you see in general, + + + align:start position:0% +quadratic. So what you see in general, +this is a really dumb way to compute n^ + + align:start position:0% +this is a really dumb way to compute n^ + + + align:start position:0% +this is a really dumb way to compute n^ +squ. When you have nested loops, + + align:start position:0% +squ. When you have nested loops, + + + align:start position:0% +squ. When you have nested loops, +typically it's going to be quadratic + + align:start position:0% +typically it's going to be quadratic + + + align:start position:0% +typically it's going to be quadratic +behavior. And so what we've done then is + + align:start position:0% +behavior. And so what we've done then is + + + align:start position:0% +behavior. And so what we've done then is +we've started to build up examples. + + align:start position:0% +we've started to build up examples. + + + align:start position:0% +we've started to build up examples. +You've now seen simple looping + + align:start position:0% +You've now seen simple looping + + + align:start position:0% +You've now seen simple looping +mechanisms, simple iterative mechanisms, + + align:start position:0% +mechanisms, simple iterative mechanisms, + + + align:start position:0% +mechanisms, simple iterative mechanisms, +nested loops. They tend to naturally + + align:start position:0% +nested loops. They tend to naturally + + + align:start position:0% +nested loops. They tend to naturally +give rise to linear and quadratic + + align:start position:0% +give rise to linear and quadratic + + + align:start position:0% +give rise to linear and quadratic +complexity. And next time we're going to + + align:start position:0% +complexity. And next time we're going to + + + align:start position:0% +complexity. And next time we're going to +start looking at more interesting + + align:start position:0% +start looking at more interesting + + + align:start position:0% +start looking at more interesting +classes. And we'll see you next time. \ No newline at end of file diff --git a/oi1Jb-dGsWU.txt b/oi1Jb-dGsWU.txt new file mode 100644 index 0000000000000000000000000000000000000000..96d813c3561d14ff8e3d15ce22637b875ead9a55 --- /dev/null +++ b/oi1Jb-dGsWU.txt @@ -0,0 +1,203 @@ +Welcome to Part 2 of 6.004x! + +In this part of the course, we turn our attention +to the design and implementation of digital + +systems that can perform useful computations +on different types of binary data. + +We'll come up with a general-purpose design +for these systems, we which we call "computers", + +so that they can serve as useful tools in +many diverse application areas. + +Computers were first used to perform numeric +calculations in science and engineering, but + +today they are used as the central control +element in any system where complex behavior + +is required. + +We have a lot to do in this chapter, so let's +get started! + +Suppose we want to design a system to compute +the factorial function on some numeric argument + +N. +N! is defined as the product of N times N-1 + +times N-2, and so on down to 1. + +We can use a programming language like C to +describe the sequence of operations necessary + +to perform the factorial computation. + +In this program there are two variables, "a" +and "b". + +"a" is used to accumulate the answer as we +compute it step-by-step. + +"b" is used to hold the next value we need +to multiply. + +"b" starts with the value of the numeric argument +N. + +The DO loop is where the work gets done: on +each loop iteration we perform one of the + +multiplies from the factorial formula, updating +the value of the accumulator "a" with the + +result, then decrementing "b" in preparation +for the next loop iteration. + +If we want to implement a digital system that +performs this sequence of operations, it makes + +sense to use sequential logic! + +Here's the state transition diagram for a +high-level finite-state machine designed to + +perform the necessary computations in the +desired order. + +We call this a high-level FSM since the "outputs" +of each state are more than simple logic levels. + +They are formulas indicating operations to +be performed on source variables, storing + +the result in a destination variable. + +The sequence of states visited while the FSM +is running mirrors the steps performed by + +the execution of the C program. + +The FSM repeats the LOOP state until the new +value to be stored in "b" is equal to 0, at + +which point the FSM transitions into the final +DONE state. + +The high-level FSM is useful when designing +the circuitry necessary to implement the desired + +computation using our digital logic building +blocks. + +We'll use 32-bit D-registers to hold the "a" +and "b" values. + +And we'll need a 2-bit D-register to hold +the 2-bit encoding of the current state, i.e., + +the encoding for either START, LOOP or DONE. + +We'll include logic to compute the inputs +required to implement the correct state transitions. + +In this case, we need to know if the new value +for "b" is zero or not. + +And, finally, we'll need logic to perform +multiply and decrement, and to select which + +value should be loaded into the "a" and "b" +registers at the end of each FSM cycle. + +Let's start by designing the logic that implements +the desired computations - we call this part + +of the logic the "datapath". + +First we'll need two 32-bit D-registers to +hold the "a" and "b" values. + +Then we'll draw the combinational logic blocks +needed to compute the values to be stored + +in those registers. + +In the START state , we need the constant +1 to load into the "a" register and the constant + +N to load into the "b" register. + +In the LOOP state, we need to compute a*b +for the "a" register and b-1 for the "b" register. + +Finally, in the DONE state , we need to be +able to reload each register with its current + +value. + +We'll use multiplexers to select the appropriate +value to load into each of the data registers. + +These multiplexers are controlled by 2-bit +select signals that choose which of the three + +32-bit input values will be the 32-bit value +to be loaded into the register. + +So by choosing the appropriate values for +WASEL and WBSEL, we can make the datapath + +compute the desired values at each step in +the FSM's operation. + +Next we'll add the combinational logic needed +to control the FSM's state transitions. + +In this case, we need to test if the new value +to be loaded into the "b" register is zero. + +The Z signal from the datapath will be 1 if +that's the case and 0 otherwise. + +Now we're all set to add the hardware for +the control FSM, which has one input (Z) from + +the datapath and generates two 2-bit outputs +(WASEL and WBSEL) to control the datapath. + +Here's the truth table for the FSM's combinational +logic. + +S is the current state, encoded as a 2-bit +value, and S' is the next state. + +Using our skills from Part 1 of the course, +we're ready to draw a schematic for the system! + +We know how to design the appropriate multiplier +and decrement circuitry. + +And we can use our standard register-and-ROM +implementation for the control FSM. + +The Z signal from the datapath is combined +with the 2 bits of current state to form the + +3 inputs to the combinational logic, in this +case realized by a read-only memory with 2^3=8 + +locations. + +Each ROM location has the appropriate values +for the 6 output bits: 2 bits each for WASEL, + +WBSEL, and next state. + +The table on the right shows the ROM contents, +which are easily determined from the table + +on the previous slide. \ No newline at end of file diff --git a/pW6tqp1zRrg.txt b/pW6tqp1zRrg.txt new file mode 100644 index 0000000000000000000000000000000000000000..005ee6d3d9508dcb8014b4a2b0e8a72dd588bb5a --- /dev/null +++ b/pW6tqp1zRrg.txt @@ -0,0 +1,91 @@ +align:start position:0% + +we now look at representing vectors by + + align:start position:0% +we now look at representing vectors by + + + align:start position:0% +we now look at representing vectors by +their magnitude and direction + + align:start position:0% + + + + align:start position:0% + +in this example we have a force here we + + align:start position:0% +in this example we have a force here we + + + align:start position:0% +in this example we have a force here we +can represent this force by its + + align:start position:0% +can represent this force by its + + + align:start position:0% +can represent this force by its +magnitude which is the length of the + + align:start position:0% +magnitude which is the length of the + + + align:start position:0% +magnitude which is the length of the +vector and the angle from the x-axis + + align:start position:0% +vector and the angle from the x-axis + + + align:start position:0% +vector and the angle from the x-axis +going towards the y-axis we can also + + align:start position:0% +going towards the y-axis we can also + + + align:start position:0% +going towards the y-axis we can also +separately represent the velocity as a + + align:start position:0% +separately represent the velocity as a + + + align:start position:0% +separately represent the velocity as a +vector with its own magnitude and + + align:start position:0% +vector with its own magnitude and + + + align:start position:0% +vector with its own magnitude and +direction notice that in this example + + align:start position:0% +direction notice that in this example + + + align:start position:0% +direction notice that in this example +the velocity is in a different direction + + align:start position:0% +the velocity is in a different direction + + + align:start position:0% +the velocity is in a different direction +than the force \ No newline at end of file diff --git a/qIJx2PRGKqw.txt b/qIJx2PRGKqw.txt new file mode 100644 index 0000000000000000000000000000000000000000..c2916de903be674167e7b50edf91f25a503de657 --- /dev/null +++ b/qIJx2PRGKqw.txt @@ -0,0 +1,352 @@ +[MUSIC PLAYING] + +PROFESSOR: Hello +everyone, today we're + +going to learn how a Solar +Cell is able to turn light + +generated mobile charges +into electricity. + +Today's lesson +will use everything + +we've learned in the past videos +to understand this effect. + +So, make sure you +understand the material + +from the previous +videos before watching. + +First, let's go over the +structure of a Solar Cell. + +Here's a cell that I made. + +And we can see that a +metal ribbon is connected + +to the top metal contacts, +which form a grid. + +The spaces between +the grid lines + +allow light to enter the cell. + +If we flip over the cell we +see the entire back surface + +is coated with +metal, which allows + +easy extraction of charge +from the back surface. + +Additionally, we have +another metal ribbon + +that's connected +to the backside. + +Now, let's hook +up our Solar Cell + +to an ammeter to +measure the current. + +So, here we have an ammeter +connected to our Solar Cell + +and our light source which +will simulate the sun. + +And we can see that if we +turn on our light source + +we start to read a current +flowing out of our Solar Cell. + +In this case about 0.12 +amps or 120 milliamps. + +Now, if we turn off the +light the output of the cell + +drops to zero and we no +longer read any current. + +We know from our +last demo the light + +generates mobile +charges and silicon. + +But how do these mobile charges +become a electric current + +coming out of our Solar Cell? + +The secret has to +do with doping. + +The top layer is doped with +phosphorus, shown in blue. + +Well the bottom layer is +doped in boron, shown in red. + +The different dopants +interact in a way, + +which we'll describe shortly, +to create an electric field + +in our device where +the Boron-doped and + +Phosphorous-doped regions meet. + +It is this electric field +that acts as a one way valve + +in our Solar Cell for +electrons and holes. + +An electric field +is created when + +positive and negative +charges are separated. + +As you know, opposite charges +attract and like charges repel. + +We'll exploit this +property by creating + +a sheet of positive charges on +the left and negative charges + +on the right, thus producing +an electric field, which + +we denote with the +Greek letter z. + +If you were to insert a +negatively charged particle, + +such as an electron, +into this field + +it would move toward +the positive charges. + +Alternatively, if you put a +positively charged particle + +it would move toward +the negative charges. + +We're able to create an electric +field inside our Solar Cell + +by using different dopants +on either side of the device. + +Here we have our silicon +lattice, which is un-doped. + +We'll start by replacing +some of the silicon atoms + +with phosphorus +atoms on one side. + +On the opposite side +we'll put in boron atoms. + +To focus on our dopant +atoms and the mobile + +charges they introduce we'll +fade out the silicon lattice. + +Recall that phosphorus +atoms introduce + +static positive charges in +mobile negative charges. + +While boron atoms introduce +static negative charges + +in mobile positive charges. + +All the mobile charges are +free to move around at random. + +A process known as diffusion. + +Here we see a single +electron moving around + +on its random walk. + +During this random motion if +an electron and hole encounter + +each other they neutralize +and effectively vanish. + +As this process of +holes and electrons + +randomly defusing +and neutralizing + +as the interface +continues, the total number + +of mobile charges in +the device decreases. + +This leaves a region +at the interface + +of immobile static charges +where the net charge + +is negative on one side +and positive on the other. + +These opposing sheets of +charge create an electric field + +of the interface, which at +this point is very weak. + +As charges continue +to diffuse, they're + +still able to move across +this weak electric field + +and neutralize. + +As this happens, the +sheets of net positive + +and net negative +static charges widen + +and the electric field +grows in strength. + +Now that the electric +field is stronger, + +as other mobile charges +continue to move and diffuse + +around the lattice, +they're now repelled + +by the field and electrons +to the left and holes stay + +to the right. + +It is this electric +field that separates + +light generated mobile +charges and pushes them + +to the extreme +ends of the device. + +The image we see now is +our Solar Cell in the dark. + +However, recall that our +silicon atoms are still present. + +And if light strikes +our silicon atom, + +a mobile hole and +electron is generated. + +As these mobile charges +move around randomly + +there's a chance that +they will randomly + +encounter the electric field. + +The mobile electron will get +repelled by the electric field. + +However, the mobile hole will +get swept to the other side + +by the electric field. + +Now, let's zoom out. + +We can see that after the +electric field has pushed + +our light excited electron +and hole to the left + +and right respectively, we now +have an extra negative charge + +on the left and extra +positive charge on the right. + +If we connect a wire to +short the two opposite sides + +together the excess +electrons are + +attracted to the excess +holes on the opposite side. + +This attraction is what drives +electricity through our wire. + +As light continually +shines on the Solar Cell + +charges are constantly being +pushed out of the device + +and driving the +electric current. + +Now hopefully you +understand the basics + +of how these amazing, but +rather simple, devices work. + +We hope that this knowledge will +provide the basic foundation + +while tackling more difficult +and abstract concepts while you + +learn the material +in this course. + +I'm Joe Sullivan, +thanks for watching. \ No newline at end of file diff --git a/qfimubh_67Q.txt b/qfimubh_67Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..72877b5990b6ad1cdfa8892b356fb72b9ebd7678 --- /dev/null +++ b/qfimubh_67Q.txt @@ -0,0 +1,1043 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +the global Health crises that began in + + align:start position:0% +the global Health crises that began in + + + align:start position:0% +the global Health crises that began in +2019 brought new uses for existing + + align:start position:0% +2019 brought new uses for existing + + + align:start position:0% +2019 brought new uses for existing +technology for example some smartphones + + align:start position:0% +technology for example some smartphones + + + align:start position:0% +technology for example some smartphones +have a find my phone feature that uses + + align:start position:0% +have a find my phone feature that uses + + + align:start position:0% +have a find my phone feature that uses +phone to phone Bluetooth signals to + + align:start position:0% +phone to phone Bluetooth signals to + + + align:start position:0% +phone to phone Bluetooth signals to +locate the missing phone + + align:start position:0% +locate the missing phone + + + align:start position:0% +locate the missing phone +scientists and Engineers realized that + + align:start position:0% +scientists and Engineers realized that + + + align:start position:0% +scientists and Engineers realized that +this feature could be used to let phones + + align:start position:0% +this feature could be used to let phones + + + align:start position:0% +this feature could be used to let phones +estimate whether they were too close for + + align:start position:0% +estimate whether they were too close for + + + align:start position:0% +estimate whether they were too close for +too long to someone who later tested + + align:start position:0% +too long to someone who later tested + + + align:start position:0% +too long to someone who later tested +positive for covet + + align:start position:0% +positive for covet + + + align:start position:0% +positive for covet +this would help extend the ability of + + align:start position:0% +this would help extend the ability of + + + align:start position:0% +this would help extend the ability of +Public Health teams to conduct contact + + align:start position:0% +Public Health teams to conduct contact + + + align:start position:0% +Public Health teams to conduct contact +tracing efforts at a time when they were + + align:start position:0% +tracing efforts at a time when they were + + + align:start position:0% +tracing efforts at a time when they were +overwhelmed with the number of new cases + + align:start position:0% +overwhelmed with the number of new cases + + + align:start position:0% +overwhelmed with the number of new cases +that they needed to trace + + align:start position:0% +that they needed to trace + + + align:start position:0% +that they needed to trace +in March of 2020 Lincoln laboratory + + align:start position:0% +in March of 2020 Lincoln laboratory + + + align:start position:0% +in March of 2020 Lincoln laboratory +established the private automated + + align:start position:0% +established the private automated + + + align:start position:0% +established the private automated +contact tracing or pact program to + + align:start position:0% +contact tracing or pact program to + + + align:start position:0% +contact tracing or pact program to +develop a bluetooth-based contact + + align:start position:0% +develop a bluetooth-based contact + + + align:start position:0% +develop a bluetooth-based contact +tracing and exposure notification system + + align:start position:0% +tracing and exposure notification system + + + align:start position:0% +tracing and exposure notification system +for covid + + align:start position:0% +for covid + + + align:start position:0% +for covid +the packed team was a partnership among + + align:start position:0% +the packed team was a partnership among + + + align:start position:0% +the packed team was a partnership among +cryptographers Physicians privacy + + align:start position:0% +cryptographers Physicians privacy + + + align:start position:0% +cryptographers Physicians privacy +experts scientists and engineers + + align:start position:0% +experts scientists and engineers + + + align:start position:0% +experts scientists and engineers +efforts like pact which touched + + align:start position:0% +efforts like pact which touched + + + align:start position:0% +efforts like pact which touched +thousands of lives work because of + + align:start position:0% +thousands of lives work because of + + + align:start position:0% +thousands of lives work because of +collaboration between many organizations + + align:start position:0% +collaboration between many organizations + + + align:start position:0% +collaboration between many organizations +and between teams within each of these + + align:start position:0% +and between teams within each of these + + + align:start position:0% +and between teams within each of these +organizations + + align:start position:0% +organizations + + + align:start position:0% +organizations +the packed design provided a secure and + + align:start position:0% +the packed design provided a secure and + + + align:start position:0% +the packed design provided a secure and +Anonymous way of determining whether you + + align:start position:0% +Anonymous way of determining whether you + + + align:start position:0% +Anonymous way of determining whether you +well + + align:start position:0% +well + + + align:start position:0% +well +your phone was recently in contact with + + align:start position:0% +your phone was recently in contact with + + + align:start position:0% +your phone was recently in contact with +someone who later reported having covet + + align:start position:0% +someone who later reported having covet + + + align:start position:0% +someone who later reported having covet +Apple and Google decided to adopt the + + align:start position:0% +Apple and Google decided to adopt the + + + align:start position:0% +Apple and Google decided to adopt the +packed protocol and both support for + + align:start position:0% +packed protocol and both support for + + + align:start position:0% +packed protocol and both support for +this functionality into the IOS and + + align:start position:0% +this functionality into the IOS and + + + align:start position:0% +this functionality into the IOS and +Android phone operating systems + + align:start position:0% +Android phone operating systems + + + align:start position:0% +Android phone operating systems +the service they deployed is called + + align:start position:0% +the service they deployed is called + + + align:start position:0% +the service they deployed is called +exposure notifications and it is in use + + align:start position:0% +exposure notifications and it is in use + + + align:start position:0% +exposure notifications and it is in use +in many regions around the world + + align:start position:0% + + + + align:start position:0% + +one of the major challenges The Pact + + align:start position:0% +one of the major challenges The Pact + + + align:start position:0% +one of the major challenges The Pact +team faced was to quantify how well + + align:start position:0% +team faced was to quantify how well + + + align:start position:0% +team faced was to quantify how well +Bluetooth and cell phones works for + + align:start position:0% +Bluetooth and cell phones works for + + + align:start position:0% +Bluetooth and cell phones works for +exposure notification + + align:start position:0% +exposure notification + + + align:start position:0% +exposure notification +Lincoln laboratory developed test + + align:start position:0% +Lincoln laboratory developed test + + + align:start position:0% +Lincoln laboratory developed test +strategies that modeled real-life + + align:start position:0% +strategies that modeled real-life + + + align:start position:0% +strategies that modeled real-life +situations to evaluate the success and + + align:start position:0% +situations to evaluate the success and + + + align:start position:0% +situations to evaluate the success and +limits of contact tracing + + align:start position:0% +limits of contact tracing + + + align:start position:0% +limits of contact tracing +for example they considered where + + align:start position:0% +for example they considered where + + + align:start position:0% +for example they considered where +participants were located how the + + align:start position:0% +participants were located how the + + + align:start position:0% +participants were located how the +phone's microenvironment might affect + + align:start position:0% +phone's microenvironment might affect + + + align:start position:0% +phone's microenvironment might affect +its signal strength and how the + + align:start position:0% +its signal strength and how the + + + align:start position:0% +its signal strength and how the +notification system worked + + align:start position:0% +notification system worked + + + align:start position:0% +notification system worked +the question we run into is what is the + + align:start position:0% +the question we run into is what is the + + + align:start position:0% +the question we run into is what is the +science behind being able to tell how + + align:start position:0% +science behind being able to tell how + + + align:start position:0% +science behind being able to tell how +close people are based on Bluetooth + + align:start position:0% +close people are based on Bluetooth + + + align:start position:0% +close people are based on Bluetooth +signals let's talk about the science of + + align:start position:0% +signals let's talk about the science of + + + align:start position:0% +signals let's talk about the science of +radio signals + + align:start position:0% +radio signals + + + align:start position:0% +radio signals +you know how cell phones get five bars + + align:start position:0% +you know how cell phones get five bars + + + align:start position:0% +you know how cell phones get five bars +sometimes and other times only one or if + + align:start position:0% +sometimes and other times only one or if + + + align:start position:0% +sometimes and other times only one or if +you go to a place where cell service is + + align:start position:0% +you go to a place where cell service is + + + align:start position:0% +you go to a place where cell service is +weak you might not get any bars and your + + align:start position:0% +weak you might not get any bars and your + + + align:start position:0% +weak you might not get any bars and your +phone may even tell you it can't connect + + align:start position:0% +phone may even tell you it can't connect + + + align:start position:0% +phone may even tell you it can't connect +at all this happens because radio + + align:start position:0% +at all this happens because radio + + + align:start position:0% +at all this happens because radio +frequency energy gets weaker the further + + align:start position:0% +frequency energy gets weaker the further + + + align:start position:0% +frequency energy gets weaker the further +away you are from a tower + + align:start position:0% +away you are from a tower + + + align:start position:0% +away you are from a tower +in urban areas there are many Towers + + align:start position:0% +in urban areas there are many Towers + + + align:start position:0% +in urban areas there are many Towers +available to your phone so even when you + + align:start position:0% +available to your phone so even when you + + + align:start position:0% +available to your phone so even when you +move around you're always pretty close + + align:start position:0% +move around you're always pretty close + + + align:start position:0% +move around you're always pretty close +to a tower in some remote areas the + + align:start position:0% +to a tower in some remote areas the + + + align:start position:0% +to a tower in some remote areas the +coverage is spotty because you might be + + align:start position:0% +coverage is spotty because you might be + + + align:start position:0% +coverage is spotty because you might be +too far away from the nearest Tower this + + align:start position:0% +too far away from the nearest Tower this + + + align:start position:0% +too far away from the nearest Tower this +phenomenon is called propagation loss + + align:start position:0% +phenomenon is called propagation loss + + + align:start position:0% +phenomenon is called propagation loss +the longer the distance between radios + + align:start position:0% +the longer the distance between radios + + + align:start position:0% +the longer the distance between radios +or cell phone and Tower in our example + + align:start position:0% +or cell phone and Tower in our example + + + align:start position:0% +or cell phone and Tower in our example +the weaker the energy + + align:start position:0% +the weaker the energy + + + align:start position:0% +the weaker the energy +if the RF energy is too low the receiver + + align:start position:0% +if the RF energy is too low the receiver + + + align:start position:0% +if the RF energy is too low the receiver +can't detect the specific pattern of + + align:start position:0% +can't detect the specific pattern of + + + align:start position:0% +can't detect the specific pattern of +energy the signal from the energy in the + + align:start position:0% +energy the signal from the energy in the + + + align:start position:0% +energy the signal from the energy in the +background the noise or the static + + align:start position:0% +background the noise or the static + + + align:start position:0% +background the noise or the static +we can take this observation and turn it + + align:start position:0% +we can take this observation and turn it + + + align:start position:0% +we can take this observation and turn it +into a game + + align:start position:0% +into a game + + + align:start position:0% +into a game +by looking for signals from radios we + + align:start position:0% +by looking for signals from radios we + + + align:start position:0% +by looking for signals from radios we +can tell whether they are nearby or Far + + align:start position:0% +can tell whether they are nearby or Far + + + align:start position:0% +can tell whether they are nearby or Far +Away by looking at how much RF energy + + align:start position:0% +Away by looking at how much RF energy + + + align:start position:0% +Away by looking at how much RF energy +we're receiving from a specific radio or + + align:start position:0% +we're receiving from a specific radio or + + + align:start position:0% +we're receiving from a specific radio or +its signal strength + + align:start position:0% +its signal strength + + + align:start position:0% +its signal strength +with this we can play hide and seek + + align:start position:0% +with this we can play hide and seek + + + align:start position:0% +with this we can play hide and seek +trying to find people hiding by looking + + align:start position:0% +trying to find people hiding by looking + + + align:start position:0% +trying to find people hiding by looking +at the amount of RF energy that their + + align:start position:0% +at the amount of RF energy that their + + + align:start position:0% +at the amount of RF energy that their +Bluetooth Beacon is transmitting to our + + align:start position:0% +Bluetooth Beacon is transmitting to our + + + align:start position:0% +Bluetooth Beacon is transmitting to our +device + + align:start position:0% + + + + align:start position:0% + +Engineers call the signal strength + + align:start position:0% +Engineers call the signal strength + + + align:start position:0% +Engineers call the signal strength +measurement a receive signal strength + + align:start position:0% +measurement a receive signal strength + + + align:start position:0% +measurement a receive signal strength +indicator or RSSI for short + + align:start position:0% +indicator or RSSI for short + + + align:start position:0% +indicator or RSSI for short +the RSSI number tells us how strong or + + align:start position:0% +the RSSI number tells us how strong or + + + align:start position:0% +the RSSI number tells us how strong or +weak a signal is compared to background + + align:start position:0% +weak a signal is compared to background + + + align:start position:0% +weak a signal is compared to background +energy + + align:start position:0% +energy + + + align:start position:0% +energy +signal strength is proportional to + + align:start position:0% +signal strength is proportional to + + + align:start position:0% +signal strength is proportional to +distance so we can tell how close or far + + align:start position:0% +distance so we can tell how close or far + + + align:start position:0% +distance so we can tell how close or far +away someone is by looking at the RSSI + + align:start position:0% +away someone is by looking at the RSSI + + + align:start position:0% +away someone is by looking at the RSSI +value + + align:start position:0% +value + + + align:start position:0% +value +however RSSI isn't foolproof RF signals + + align:start position:0% +however RSSI isn't foolproof RF signals + + + align:start position:0% +however RSSI isn't foolproof RF signals +can actually be blocked by buildings or + + align:start position:0% +can actually be blocked by buildings or + + + align:start position:0% +can actually be blocked by buildings or +terrain making things appear further + + align:start position:0% +terrain making things appear further + + + align:start position:0% +terrain making things appear further +away than they actually are + + align:start position:0% +away than they actually are + + + align:start position:0% +away than they actually are +for our experiments rather than using a + + align:start position:0% +for our experiments rather than using a + + + align:start position:0% +for our experiments rather than using a +cell phone + + align:start position:0% +cell phone + + + align:start position:0% +cell phone +we will be duplicating a Bluetooth hide + + align:start position:0% +we will be duplicating a Bluetooth hide + + + align:start position:0% +we will be duplicating a Bluetooth hide +and seek game using Adafruit circuit + + align:start position:0% +and seek game using Adafruit circuit + + + align:start position:0% +and seek game using Adafruit circuit +boards we'll walk you through how to set + + align:start position:0% +boards we'll walk you through how to set + + + align:start position:0% +boards we'll walk you through how to set +up and program your boards so that you + + align:start position:0% +up and program your boards so that you + + + align:start position:0% +up and program your boards so that you +can try out a modern version of hide and + + align:start position:0% +can try out a modern version of hide and + + + align:start position:0% +can try out a modern version of hide and +seek with your friends + + align:start position:0% +seek with your friends + + + align:start position:0% +seek with your friends +the goals for this experiment are two + + align:start position:0% +the goals for this experiment are two + + + align:start position:0% +the goals for this experiment are two +work Hands-On with a small development + + align:start position:0% +work Hands-On with a small development + + + align:start position:0% +work Hands-On with a small development +board + + align:start position:0% +board + + + align:start position:0% +board +become familiar with and even write code + + align:start position:0% +become familiar with and even write code + + + align:start position:0% +become familiar with and even write code +for a development board + + align:start position:0% +for a development board + + + align:start position:0% +for a development board +start to understand the physics of radio + + align:start position:0% +start to understand the physics of radio + + + align:start position:0% +start to understand the physics of radio +frequency or RF propagation + + align:start position:0% +frequency or RF propagation + + + align:start position:0% +frequency or RF propagation +collaborate with the team to enact an + + align:start position:0% +collaborate with the team to enact an + + + align:start position:0% +collaborate with the team to enact an +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +learn about game development + + align:start position:0% +learn about game development + + + align:start position:0% +learn about game development +what else can you do with these supplies + + align:start position:0% +what else can you do with these supplies + + + align:start position:0% +what else can you do with these supplies +and have fun + + align:start position:0% +and have fun + + + align:start position:0% +and have fun +best of luck + + align:start position:0% +best of luck + + + align:start position:0% +best of luck +and happy Hunting \ No newline at end of file diff --git a/qypsPGqNF6Q.txt b/qypsPGqNF6Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..874f69ed32b094b6ff051996f5f37494c6458084 --- /dev/null +++ b/qypsPGqNF6Q.txt @@ -0,0 +1,6787 @@ +align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +There are several things I want to do + + align:start position:0% +There are several things I want to do + + + align:start position:0% +There are several things I want to do +today. First, I want to know what you + + align:start position:0% +today. First, I want to know what you + + + align:start position:0% +today. First, I want to know what you +got out of the + + align:start position:0% +got out of the + + + align:start position:0% +got out of the +commentary of last week of the Lady Eve. + + align:start position:0% +commentary of last week of the Lady Eve. + + + align:start position:0% +commentary of last week of the Lady Eve. +Second, I want to know what you got out + + align:start position:0% +Second, I want to know what you got out + + + align:start position:0% +Second, I want to know what you got out +of the reading for today. The chapter of + + align:start position:0% +of the reading for today. The chapter of + + + align:start position:0% +of the reading for today. The chapter of +mine on imagination and the chapter on + + align:start position:0% +mine on imagination and the chapter on + + + align:start position:0% +mine on imagination and the chapter on +idealization. + + align:start position:0% +idealization. + + + align:start position:0% +idealization. +Third, I want to give you a little + + align:start position:0% +Third, I want to give you a little + + + align:start position:0% +Third, I want to give you a little +preparation about + + align:start position:0% +preparation about + + + align:start position:0% +preparation about +um today's movie which is + + align:start position:0% +um today's movie which is + + + align:start position:0% +um today's movie which is +Ami and fourth there are some + + align:start position:0% +Ami and fourth there are some + + + align:start position:0% +Ami and fourth there are some +supplementary material that I can give + + align:start position:0% +supplementary material that I can give + + + align:start position:0% +supplementary material that I can give +you particularly in relation to the + + align:start position:0% +you particularly in relation to the + + + align:start position:0% +you particularly in relation to the +aesthetics that you were reading for the + + align:start position:0% +aesthetics that you were reading for the + + + align:start position:0% +aesthetics that you were reading for the +first the second week uh out of of + + align:start position:0% +first the second week uh out of of + + + align:start position:0% +first the second week uh out of of +reality transformed which I asked you to + + align:start position:0% +reality transformed which I asked you to + + + align:start position:0% +reality transformed which I asked you to +read for last + + align:start position:0% +read for last + + + align:start position:0% +read for last +week. Isn't that right? Yeah. All right. + + align:start position:0% +week. Isn't that right? Yeah. All right. + + + align:start position:0% +week. Isn't that right? Yeah. All right. +The result is that I'm going to try to + + align:start position:0% +The result is that I'm going to try to + + + align:start position:0% +The result is that I'm going to try to +talk as little as pos possible and this + + align:start position:0% +talk as little as pos possible and this + + + align:start position:0% +talk as little as pos possible and this +will get us started with the part of a + + align:start position:0% +will get us started with the part of a + + + align:start position:0% +will get us started with the part of a +course in which your discussion is very + + align:start position:0% +course in which your discussion is very + + + align:start position:0% +course in which your discussion is very +important. I want to know how any of + + align:start position:0% +important. I want to know how any of + + + align:start position:0% +important. I want to know how any of +this material is affecting you. + + align:start position:0% +this material is affecting you. + + + align:start position:0% +this material is affecting you. +What I'm going to do is go around the + + align:start position:0% +What I'm going to do is go around the + + + align:start position:0% +What I'm going to do is go around the +class the way I do every time in order + + align:start position:0% +class the way I do every time in order + + + align:start position:0% +class the way I do every time in order +to get to know you better and remember + + align:start position:0% +to get to know you better and remember + + + align:start position:0% +to get to know you better and remember +your names. But when I get to your name, + + align:start position:0% +your names. But when I get to your name, + + + align:start position:0% +your names. But when I get to your name, +you can, and I hope you will stop me to + + align:start position:0% +you can, and I hope you will stop me to + + + align:start position:0% +you can, and I hope you will stop me to +make any comments you want on any of + + align:start position:0% +make any comments you want on any of + + + align:start position:0% +make any comments you want on any of +those things that I mentioned. Uh, + + align:start position:0% +those things that I mentioned. Uh, + + + align:start position:0% +those things that I mentioned. Uh, +reality + + align:start position:0% +reality + + + align:start position:0% +reality +transformed, imagination, + + align:start position:0% + + + + align:start position:0% + +idealization, the Lady Eve, and the + + align:start position:0% +idealization, the Lady Eve, and the + + + align:start position:0% +idealization, the Lady Eve, and the +commentary on Lady Eve. Um and if any of + + align:start position:0% +commentary on Lady Eve. Um and if any of + + + align:start position:0% +commentary on Lady Eve. Um and if any of +you uh for instance carry here um know + + align:start position:0% +you uh for instance carry here um know + + + align:start position:0% +you uh for instance carry here um know +Ami you can say something about + + align:start position:0% +Ami you can say something about + + + align:start position:0% +Ami you can say something about +that. So this is the time for the class + + align:start position:0% +that. So this is the time for the class + + + align:start position:0% +that. So this is the time for the class +to become fully involved as I hope you + + align:start position:0% +to become fully involved as I hope you + + + align:start position:0% +to become fully involved as I hope you +will be throughout the + + align:start position:0% +will be throughout the + + + align:start position:0% +will be throughout the +term. First let me start on my list. Um + + align:start position:0% +term. First let me start on my list. Um + + + align:start position:0% +term. First let me start on my list. Um +and forgive me if I am still learning + + align:start position:0% +and forgive me if I am still learning + + + align:start position:0% +and forgive me if I am still learning +your names because I haven't seen you + + align:start position:0% +your names because I haven't seen you + + + align:start position:0% +your names because I haven't seen you +for a week. Uh Edward Song. + + align:start position:0% +for a week. Uh Edward Song. + + + align:start position:0% +for a week. Uh Edward Song. +anything you want to say in your + + align:start position:0% +anything you want to say in your + + + align:start position:0% +anything you want to say in your +defense? + + align:start position:0% +defense? + + + align:start position:0% +defense? +Um, I don't know. Just in the reading, I + + align:start position:0% +Um, I don't know. Just in the reading, I + + + align:start position:0% +Um, I don't know. Just in the reading, I +don't really have a very strong like + + align:start position:0% +don't really have a very strong like + + + align:start position:0% +don't really have a very strong like +background in philosophy. So, I find it + + align:start position:0% +background in philosophy. So, I find it + + + align:start position:0% +background in philosophy. So, I find it +kind of interesting to just learn about + + align:start position:0% +kind of interesting to just learn about + + + align:start position:0% +kind of interesting to just learn about +the different theories that you + + align:start position:0% +the different theories that you + + + align:start position:0% +the different theories that you +mentioned as you're like uh resolving + + align:start position:0% +mentioned as you're like uh resolving + + + align:start position:0% +mentioned as you're like uh resolving +the differences a lot of times between + + align:start position:0% +the differences a lot of times between + + + align:start position:0% +the differences a lot of times between +two conflicting theories. And I find + + align:start position:0% +two conflicting theories. And I find + + + align:start position:0% +two conflicting theories. And I find +that uh pretty interesting just to like + + align:start position:0% +that uh pretty interesting just to like + + + align:start position:0% +that uh pretty interesting just to like +get more background. + + align:start position:0% +get more background. + + + align:start position:0% +get more background. +Um, what was what did you get out of the + + align:start position:0% +Um, what was what did you get out of the + + + align:start position:0% +Um, what was what did you get out of the +chapter on imagination? + + align:start position:0% + + + + align:start position:0% + +I guess like when I was you've done that + + align:start position:0% +I guess like when I was you've done that + + + align:start position:0% +I guess like when I was you've done that +for this week, right? So I I just I + + align:start position:0% +for this week, right? So I I just I + + + align:start position:0% +for this week, right? So I I just I +guess I realized that uh imagination + + align:start position:0% +guess I realized that uh imagination + + + align:start position:0% +guess I realized that uh imagination +actually takes part in a lot of + + align:start position:0% +actually takes part in a lot of + + + align:start position:0% +actually takes part in a lot of +different things that you don't really + + align:start position:0% +different things that you don't really + + + align:start position:0% +different things that you don't really +attribute to it and like once you uh sit + + align:start position:0% +attribute to it and like once you uh sit + + + align:start position:0% +attribute to it and like once you uh sit +there and think + + align:start position:0% +there and think + + + align:start position:0% +there and think +about just what kind of things go into + + align:start position:0% +about just what kind of things go into + + + align:start position:0% +about just what kind of things go into +uh making decisions and even coming up + + align:start position:0% +uh making decisions and even coming up + + + align:start position:0% +uh making decisions and even coming up +with new ideas and imagination does play + + align:start position:0% +with new ideas and imagination does play + + + align:start position:0% +with new ideas and imagination does play +a large part in that. Okay. Um, remember + + align:start position:0% +a large part in that. Okay. Um, remember + + + align:start position:0% +a large part in that. Okay. Um, remember +your back is to the camera and I don't + + align:start position:0% +your back is to the camera and I don't + + + align:start position:0% +your back is to the camera and I don't +know how much of what you're + + align:start position:0% +know how much of what you're + + + align:start position:0% +know how much of what you're +saying is adequate, but in general, + + align:start position:0% +saying is adequate, but in general, + + + align:start position:0% +saying is adequate, but in general, +project as much as you can as if you + + align:start position:0% +project as much as you can as if you + + + align:start position:0% +project as much as you can as if you +were on a stage. Don't sit back and uh + + align:start position:0% +were on a stage. Don't sit back and uh + + + align:start position:0% +were on a stage. Don't sit back and uh +mumble the way MIT students like to do. + + align:start position:0% +mumble the way MIT students like to do. + + + align:start position:0% +mumble the way MIT students like to do. +Um, not and not you in particular, but + + align:start position:0% +Um, not and not you in particular, but + + + align:start position:0% +Um, not and not you in particular, but +all of you. All right, any question + + align:start position:0% +all of you. All right, any question + + + align:start position:0% +all of you. All right, any question +about that? + + align:start position:0% +about that? + + + align:start position:0% +about that? +Um, David Levenson, + + align:start position:0% +Um, David Levenson, + + + align:start position:0% +Um, David Levenson, +I was thinking on the, uh, comment on + + align:start position:0% +I was thinking on the, uh, comment on + + + align:start position:0% +I was thinking on the, uh, comment on +the Lady Eve, uh, like how you were + + align:start position:0% +the Lady Eve, uh, like how you were + + + align:start position:0% +the Lady Eve, uh, like how you were +saying, it's really interesting that the + + align:start position:0% +saying, it's really interesting that the + + + align:start position:0% +saying, it's really interesting that the +woman's perspective on how I never + + align:start position:0% +woman's perspective on how I never + + + align:start position:0% +woman's perspective on how I never +noticed how Eve's clothing and like + + align:start position:0% +noticed how Eve's clothing and like + + + align:start position:0% +noticed how Eve's clothing and like +general appearance changed when, uh, + + align:start position:0% +general appearance changed when, uh, + + + align:start position:0% +general appearance changed when, uh, +after Hopsy found out that she was a + + align:start position:0% +after Hopsy found out that she was a + + + align:start position:0% +after Hopsy found out that she was a +card shark, how like she started + + align:start position:0% +card shark, how like she started + + + align:start position:0% +card shark, how like she started +dressing more formally almost as opposed + + align:start position:0% +dressing more formally almost as opposed + + + align:start position:0% +dressing more formally almost as opposed +to informally. More elegant. More + + align:start position:0% +to informally. More elegant. More + + + align:start position:0% +to informally. More elegant. More +elegant. Yeah. less approachable and + + align:start position:0% +elegant. Yeah. less approachable and + + + align:start position:0% +elegant. Yeah. less approachable and +more more uh yeah just more elegant and + + align:start position:0% +more more uh yeah just more elegant and + + + align:start position:0% +more more uh yeah just more elegant and +more like unapproachable and more like + + align:start position:0% +more like unapproachable and more like + + + align:start position:0% +more like unapproachable and more like +lady like all those interesting + + align:start position:0% +lady like all those interesting + + + align:start position:0% +lady like all those interesting +con right all people have their warm + + align:start position:0% +con right all people have their warm + + + align:start position:0% +con right all people have their warm +side and their cold + + align:start position:0% +side and their cold + + + align:start position:0% +side and their cold +side and given the way in which women + + align:start position:0% +side and given the way in which women + + + align:start position:0% +side and given the way in which women +have been treated by men it's not + + align:start position:0% +have been treated by men it's not + + + align:start position:0% +have been treated by men it's not +surprising that the cold side often + + align:start position:0% +surprising that the cold side often + + + align:start position:0% +surprising that the cold side often +turns out to be a defended icy the + + align:start position:0% +turns out to be a defended icy the + + + align:start position:0% +turns out to be a defended icy the +self-p protection that uh different kind + + align:start position:0% +self-p protection that uh different kind + + + align:start position:0% +self-p protection that uh different kind +of women can turn into an art form. And + + align:start position:0% +of women can turn into an art form. And + + + align:start position:0% +of women can turn into an art form. And +what's interesting along those lines is + + align:start position:0% +what's interesting along those lines is + + + align:start position:0% +what's interesting along those lines is +that once Gene becomes Eve or be just + + align:start position:0% +that once Gene becomes Eve or be just + + + align:start position:0% +that once Gene becomes Eve or be just +before she becomes Eve, after she's been + + align:start position:0% +before she becomes Eve, after she's been + + + align:start position:0% +before she becomes Eve, after she's been +hurt, after she's been rejected as the + + align:start position:0% +hurt, after she's been rejected as the + + + align:start position:0% +hurt, after she's been rejected as the +as Jean, let's say, uh we see how + + align:start position:0% +as Jean, let's say, uh we see how + + + align:start position:0% +as Jean, let's say, uh we see how +sophisticated she can be, uh in her cold + + align:start position:0% +sophisticated she can be, uh in her cold + + + align:start position:0% +sophisticated she can be, uh in her cold +manner with the fur hat and the fur coat + + align:start position:0% +manner with the fur hat and the fur coat + + + align:start position:0% +manner with the fur hat and the fur coat +and the withdrawn + + align:start position:0% +and the withdrawn + + + align:start position:0% +and the withdrawn +um manner that she has. Notice + + align:start position:0% +um manner that she has. Notice + + + align:start position:0% +um manner that she has. Notice +incidentally that um Charles who is also + + align:start position:0% +incidentally that um Charles who is also + + + align:start position:0% +incidentally that um Charles who is also +hurt but in a different + + align:start position:0% +hurt but in a different + + + align:start position:0% +hurt but in a different +way. He is sort of blank. He looks over + + align:start position:0% +way. He is sort of blank. He looks over + + + align:start position:0% +way. He is sort of blank. He looks over +the railing. U he doesn't look elegant. + + align:start position:0% +the railing. U he doesn't look elegant. + + + align:start position:0% +the railing. U he doesn't look elegant. +He just looks depressed and miserable. + + align:start position:0% +He just looks depressed and miserable. + + + align:start position:0% +He just looks depressed and miserable. +Whereas she is making her miserable into + + align:start position:0% +Whereas she is making her miserable into + + + align:start position:0% +Whereas she is making her miserable into +a work of art. Misery into a work of + + align:start position:0% +a work of art. Misery into a work of + + + align:start position:0% +a work of art. Misery into a work of +art. So there the two sides of women. uh + + align:start position:0% +art. So there the two sides of women. uh + + + align:start position:0% +art. So there the two sides of women. uh +and in general I think as I mentioned in + + align:start position:0% +and in general I think as I mentioned in + + + align:start position:0% +and in general I think as I mentioned in +the first class there's there is the + + align:start position:0% +the first class there's there is the + + + align:start position:0% +the first class there's there is the +tradition in the myth of + + align:start position:0% +tradition in the myth of + + + align:start position:0% +tradition in the myth of +creation of Eve who is the mother of + + align:start position:0% +creation of Eve who is the mother of + + + align:start position:0% +creation of Eve who is the mother of +humanity and therefore a motherly + + align:start position:0% +humanity and therefore a motherly + + + align:start position:0% +humanity and therefore a motherly +uh + + align:start position:0% +uh + + + align:start position:0% +uh +image but one who also has somehow + + align:start position:0% +image but one who also has somehow + + + align:start position:0% +image but one who also has somehow +fallen from grace + + align:start position:0% +fallen from grace + + + align:start position:0% +fallen from grace +uh indicating maybe there's another side + + align:start position:0% +uh indicating maybe there's another side + + + align:start position:0% +uh indicating maybe there's another side +to her and that other side in uh a good + + align:start position:0% +to her and that other side in uh a good + + + align:start position:0% +to her and that other side in uh a good +of Talmudic mythology for instance + + align:start position:0% +of Talmudic mythology for instance + + + align:start position:0% +of Talmudic mythology for instance +appears in a being called Lilith who is + + align:start position:0% +appears in a being called Lilith who is + + + align:start position:0% +appears in a being called Lilith who is +really the first woman and she is the + + align:start position:0% +really the first woman and she is the + + + align:start position:0% +really the first woman and she is the +earth spirit and generally thought to be + + align:start position:0% +earth spirit and generally thought to be + + + align:start position:0% +earth spirit and generally thought to be +evil. Now there's a good deal of + + align:start position:0% +evil. Now there's a good deal of + + + align:start position:0% +evil. Now there's a good deal of +male sexology involved in this attitudes + + align:start position:0% +male sexology involved in this attitudes + + + align:start position:0% +male sexology involved in this attitudes +of males towards women that there's + + align:start position:0% +of males towards women that there's + + + align:start position:0% +of males towards women that there's +women can be motherly but they can also + + align:start position:0% +women can be motherly but they can also + + + align:start position:0% +women can be motherly but they can also +be somehow destructive or vile or evil. + + align:start position:0% +be somehow destructive or vile or evil. + + + align:start position:0% +be somehow destructive or vile or evil. +Um without analyzing how it is they that + + align:start position:0% +Um without analyzing how it is they that + + + align:start position:0% +Um without analyzing how it is they that +men put them into that condition. So in + + align:start position:0% +men put them into that condition. So in + + + align:start position:0% +men put them into that condition. So in +a sense the movie is reopening all of + + align:start position:0% +a sense the movie is reopening all of + + + align:start position:0% +a sense the movie is reopening all of +that. uh there are these two sides of + + align:start position:0% +that. uh there are these two sides of + + + align:start position:0% +that. uh there are these two sides of +Eve and it results from the inability on + + align:start position:0% +Eve and it results from the inability on + + + align:start position:0% +Eve and it results from the inability on +the part of the male to accept her as + + align:start position:0% +the part of the male to accept her as + + + align:start position:0% +the part of the male to accept her as +she is or to have learned the lesson + + align:start position:0% +she is or to have learned the lesson + + + align:start position:0% +she is or to have learned the lesson +that she was trying to teach when um he + + align:start position:0% +that she was trying to teach when um he + + + align:start position:0% +that she was trying to teach when um he +confronts her with a photograph or just + + align:start position:0% +confronts her with a photograph or just + + + align:start position:0% +confronts her with a photograph or just +actually before he confronts her with a + + align:start position:0% +actually before he confronts her with a + + + align:start position:0% +actually before he confronts her with a +photograph. Uh that the good girls + + align:start position:0% +photograph. Uh that the good girls + + + align:start position:0% +photograph. Uh that the good girls +aren't as good as men think and the + + align:start position:0% +aren't as good as men think and the + + + align:start position:0% +aren't as good as men think and the +girls aren't anywhere as bad as men + + align:start position:0% +girls aren't anywhere as bad as men + + + align:start position:0% +girls aren't anywhere as bad as men +think they can be. So that there people + + align:start position:0% +think they can be. So that there people + + + align:start position:0% +think they can be. So that there people +women in particular have a mixture of + + align:start position:0% +women in particular have a mixture of + + + align:start position:0% +women in particular have a mixture of +the two and what isn't spelled out but + + align:start position:0% +the two and what isn't spelled out but + + + align:start position:0% +the two and what isn't spelled out but +it's obvious given their social order + + align:start position:0% +it's obvious given their social order + + + align:start position:0% +it's obvious given their social order +he's very wealthy he's member of the a + + align:start position:0% +he's very wealthy he's member of the a + + + align:start position:0% +he's very wealthy he's member of the a +lady went to Yale and she's just a girl + + align:start position:0% +lady went to Yale and she's just a girl + + + align:start position:0% +lady went to Yale and she's just a girl +on the ship um it's because the ruling + + align:start position:0% +on the ship um it's because the ruling + + + align:start position:0% +on the ship um it's because the ruling +class the males have have arranged it + + align:start position:0% +class the males have have arranged it + + + align:start position:0% +class the males have have arranged it +that way that he is responsible for the + + align:start position:0% +that way that he is responsible for the + + + align:start position:0% +that way that he is responsible for the +separation between these two aspects of + + align:start position:0% +separation between these two aspects of + + + align:start position:0% +separation between these two aspects of +female + + align:start position:0% +female + + + align:start position:0% +female +character. And so what she's doing is + + align:start position:0% +character. And so what she's doing is + + + align:start position:0% +character. And so what she's doing is +teaching him a lesson. All right? You + + align:start position:0% +teaching him a lesson. All right? You + + + align:start position:0% +teaching him a lesson. All right? You +think I'm no good. I'll show you how no + + align:start position:0% +think I'm no good. I'll show you how no + + + align:start position:0% +think I'm no good. I'll show you how no +good I can be. uh and therefore the + + align:start position:0% +good I can be. uh and therefore the + + + align:start position:0% +good I can be. uh and therefore the +separation is is accentuated and and + + align:start position:0% +separation is is accentuated and and + + + align:start position:0% +separation is is accentuated and and +dramatized making us wonder about the + + align:start position:0% +dramatized making us wonder about the + + + align:start position:0% +dramatized making us wonder about the +nature of the myth to begin with and + + align:start position:0% +nature of the myth to begin with and + + + align:start position:0% +nature of the myth to begin with and +then at the end it's + + align:start position:0% +then at the end it's + + + align:start position:0% +then at the end it's +overcome because for reasons uh of her + + align:start position:0% +overcome because for reasons uh of her + + + align:start position:0% +overcome because for reasons uh of her +her good nature and his good nature uh + + align:start position:0% +her good nature and his good nature uh + + + align:start position:0% +her good nature and his good nature uh +they harmonize the different aspects and + + align:start position:0% +they harmonize the different aspects and + + + align:start position:0% +they harmonize the different aspects and +live happily ever after. Right? So that + + align:start position:0% +live happily ever after. Right? So that + + + align:start position:0% +live happily ever after. Right? So that +that's the resolution of the problem + + align:start position:0% +that's the resolution of the problem + + + align:start position:0% +that's the resolution of the problem +built into the mythic separation between + + align:start position:0% +built into the mythic separation between + + + align:start position:0% +built into the mythic separation between +the different parts of + + align:start position:0% +the different parts of + + + align:start position:0% +the different parts of +women. Anything else? + + align:start position:0% +women. Anything else? + + + align:start position:0% +women. Anything else? +Um just part did anybody else want to + + align:start position:0% +Um just part did anybody else want to + + + align:start position:0% +Um just part did anybody else want to +say anything about the myth of male and + + align:start position:0% +say anything about the myth of male and + + + align:start position:0% +say anything about the myth of male and +female and of creativity + + align:start position:0% +female and of creativity + + + align:start position:0% +female and of creativity +in the late Eve? + + align:start position:0% +in the late Eve? + + + align:start position:0% +in the late Eve? +I want to make a couple of comments + + align:start position:0% +I want to make a couple of comments + + + align:start position:0% +I want to make a couple of comments +about the + + align:start position:0% +about the + + + align:start position:0% +about the +commentary. Unfortunately, we couldn't + + align:start position:0% +commentary. Unfortunately, we couldn't + + + align:start position:0% +commentary. Unfortunately, we couldn't +watch it all last time and I don't want + + align:start position:0% +watch it all last time and I don't want + + + align:start position:0% +watch it all last time and I don't want +to go back to it now because we have + + align:start position:0% +to go back to it now because we have + + + align:start position:0% +to go back to it now because we have +other things and if anything we're the + + align:start position:0% +other things and if anything we're the + + + align:start position:0% +other things and if anything we're the +term is so crowded. Um, we'll not I + + align:start position:0% +term is so crowded. Um, we'll not I + + + align:start position:0% +term is so crowded. Um, we'll not I +think have enough time for your + + align:start position:0% +think have enough time for your + + + align:start position:0% +think have enough time for your +discussions which I really care about. + + align:start position:0% +discussions which I really care about. + + + align:start position:0% +discussions which I really care about. +So, I'll rely on what you learned from + + align:start position:0% +So, I'll rely on what you learned from + + + align:start position:0% +So, I'll rely on what you learned from +the commentary itself. But would anybody + + align:start position:0% +the commentary itself. But would anybody + + + align:start position:0% +the commentary itself. But would anybody +like to say something about what you + + align:start position:0% +like to say something about what you + + + align:start position:0% +like to say something about what you +learned from that commentary? Remember + + align:start position:0% +learned from that commentary? Remember + + + align:start position:0% +learned from that commentary? Remember +my idea was first week you would sit + + align:start position:0% +my idea was first week you would sit + + + align:start position:0% +my idea was first week you would sit +back and enjoy this screw ball + + align:start position:0% +back and enjoy this screw ball + + + align:start position:0% +back and enjoy this screw ball +comedy and the masterpiece of its within + + align:start position:0% +comedy and the masterpiece of its within + + + align:start position:0% +comedy and the masterpiece of its within +its genre and the second week you would + + align:start position:0% +its genre and the second week you would + + + align:start position:0% +its genre and the second week you would +begin to acquire if you haven't already + + align:start position:0% +begin to acquire if you haven't already + + + align:start position:0% +begin to acquire if you haven't already +what is what it is to watch a movie by + + align:start position:0% +what is what it is to watch a movie by + + + align:start position:0% +what is what it is to watch a movie by +seeing what a highly trained uh expert + + align:start position:0% +seeing what a highly trained uh expert + + + align:start position:0% +seeing what a highly trained uh expert +scholar in the field presents to you as + + align:start position:0% +scholar in the field presents to you as + + + align:start position:0% +scholar in the field presents to you as +her reading of the + + align:start position:0% +her reading of the + + + align:start position:0% +her reading of the +movie and therefore or your experiencing + + align:start position:0% +movie and therefore or your experiencing + + + align:start position:0% +movie and therefore or your experiencing +of it through + + align:start position:0% +of it through + + + align:start position:0% +of it through +her. So, what did you get out of um + + align:start position:0% +her. So, what did you get out of um + + + align:start position:0% +her. So, what did you get out of um +Marian Keane's + + align:start position:0% +Marian Keane's + + + align:start position:0% +Marian Keane's +commentary? Um + + align:start position:0% +commentary? Um + + + align:start position:0% +commentary? Um +what remind me of your name + + align:start position:0% + + + + align:start position:0% + +L? Yeah, L. Right. + + align:start position:0% +L? Yeah, L. Right. + + + align:start position:0% +L? Yeah, L. Right. +So in your book that's repelling. Um so + + align:start position:0% +So in your book that's repelling. Um so + + + align:start position:0% +So in your book that's repelling. Um so +in your book uh the reality horn uh you + + align:start position:0% +in your book uh the reality horn uh you + + + align:start position:0% +in your book uh the reality horn uh you +talk about um how one of the advantages + + align:start position:0% +talk about um how one of the advantages + + + align:start position:0% +talk about um how one of the advantages +that uh a filmmaker has is that he can + + align:start position:0% +that uh a filmmaker has is that he can + + + align:start position:0% +that uh a filmmaker has is that he can +focus the audience's attention on um + + align:start position:0% +focus the audience's attention on um + + + align:start position:0% +focus the audience's attention on um +some particular very specific portion of + + align:start position:0% +some particular very specific portion of + + + align:start position:0% +some particular very specific portion of +the stage or like a particular person + + align:start position:0% +the stage or like a particular person + + + align:start position:0% +the stage or like a particular person +talking. And that's something that um a + + align:start position:0% +talking. And that's something that um a + + + align:start position:0% +talking. And that's something that um a +person who's uh doing a ballet or maybe + + align:start position:0% +person who's uh doing a ballet or maybe + + + align:start position:0% +person who's uh doing a ballet or maybe +a person who's just performing on stage + + align:start position:0% +a person who's just performing on stage + + + align:start position:0% +a person who's just performing on stage +doesn't have because you can't uh be + + align:start position:0% +doesn't have because you can't uh be + + + align:start position:0% +doesn't have because you can't uh be +sure that the audience's attention is + + align:start position:0% +sure that the audience's attention is + + + align:start position:0% +sure that the audience's attention is +focused on exactly what is important. + + align:start position:0% +focused on exactly what is important. + + + align:start position:0% +focused on exactly what is important. +And in terms of the commentary, what + + align:start position:0% +And in terms of the commentary, what + + + align:start position:0% +And in terms of the commentary, what +particular remarks of her illustrate + + align:start position:0% +particular remarks of her illustrate + + + align:start position:0% +particular remarks of her illustrate +that? So, I think one scene was when uh + + align:start position:0% +that? So, I think one scene was when uh + + + align:start position:0% +that? So, I think one scene was when uh +both were in um + + align:start position:0% +both were in um + + + align:start position:0% +both were in um +uh Lady Eve's room on the uh the boat + + align:start position:0% +uh Lady Eve's room on the uh the boat + + + align:start position:0% +uh Lady Eve's room on the uh the boat +and she was she had her arm around um + + align:start position:0% +and she was she had her arm around um + + + align:start position:0% +and she was she had her arm around um +him and it just really focused on just + + align:start position:0% +him and it just really focused on just + + + align:start position:0% +him and it just really focused on just +her and him and you realized there's a + + align:start position:0% +her and him and you realized there's a + + + align:start position:0% +her and him and you realized there's a +lot of tension in the air and I think um + + align:start position:0% +lot of tension in the air and I think um + + + align:start position:0% +lot of tension in the air and I think um +the commentary helped to uh highlight + + align:start position:0% +the commentary helped to uh highlight + + + align:start position:0% +the commentary helped to uh highlight +scenes like that and maybe you realize + + align:start position:0% +scenes like that and maybe you realize + + + align:start position:0% +scenes like that and maybe you realize +that in fact that technique was very + + align:start position:0% +that in fact that technique was very + + + align:start position:0% +that in fact that technique was very +very effective and very important. As + + align:start position:0% +very effective and very important. As + + + align:start position:0% +very effective and very important. As +you're watching a movie, as I'm watching + + align:start position:0% +you're watching a movie, as I'm watching + + + align:start position:0% +you're watching a movie, as I'm watching +a movie, I don't think of the fact that + + align:start position:0% +a movie, I don't think of the fact that + + + align:start position:0% +a movie, I don't think of the fact that +this shot is a long shot. This shot is a + + align:start position:0% +this shot is a long shot. This shot is a + + + align:start position:0% +this shot is a long shot. This shot is a +middle shot, this shot is a closeup, + + align:start position:0% +middle shot, this shot is a closeup, + + + align:start position:0% +middle shot, this shot is a closeup, +right? Uh the commentator here kept + + align:start position:0% +right? Uh the commentator here kept + + + align:start position:0% +right? Uh the commentator here kept +emphasizing that and in relation to + + align:start position:0% +emphasizing that and in relation to + + + align:start position:0% +emphasizing that and in relation to +what's really going on. So that uh her + + align:start position:0% +what's really going on. So that uh her + + + align:start position:0% +what's really going on. So that uh her +the vulnerability of Jean uh appears in + + align:start position:0% +the vulnerability of Jean uh appears in + + + align:start position:0% +the vulnerability of Jean uh appears in +the midshot when she's talking to her + + align:start position:0% +the midshot when she's talking to her + + + align:start position:0% +the midshot when she's talking to her +father and uh + + align:start position:0% +father and uh + + + align:start position:0% +father and uh +Gerald and we then see her face + + align:start position:0% +Gerald and we then see her face + + + align:start position:0% +Gerald and we then see her face +differently because somehow the midshot + + align:start position:0% +differently because somehow the midshot + + + align:start position:0% +differently because somehow the midshot +has its own special aesthetic character + + align:start position:0% +has its own special aesthetic character + + + align:start position:0% +has its own special aesthetic character +or the close-ups. Um uh for instance + + align:start position:0% +or the close-ups. Um uh for instance + + + align:start position:0% +or the close-ups. Um uh for instance +when she starts uh crying because she + + align:start position:0% +when she starts uh crying because she + + + align:start position:0% +when she starts uh crying because she +feels that he has misused her after the + + align:start position:0% +feels that he has misused her after the + + + align:start position:0% +feels that he has misused her after the +uh photograph has been he he shows + + align:start position:0% +uh photograph has been he he shows + + + align:start position:0% +uh photograph has been he he shows +reminds her of the photograph and she + + align:start position:0% +reminds her of the photograph and she + + + align:start position:0% +reminds her of the photograph and she +and says that he knew all along. Uh so + + align:start position:0% +and says that he knew all along. Uh so + + + align:start position:0% +and says that he knew all along. Uh so +he was toying with her and that's what + + align:start position:0% +he was toying with her and that's what + + + align:start position:0% +he was toying with her and that's what +hurts her most of all. you know that was + + align:start position:0% +hurts her most of all. you know that was + + + align:start position:0% +hurts her most of all. you know that was +cheap + + align:start position:0% +cheap + + + align:start position:0% +cheap +and vulgar if you if you really knew and + + align:start position:0% +and vulgar if you if you really knew and + + + align:start position:0% +and vulgar if you if you really knew and +were doing it just to humiliate me and + + align:start position:0% +were doing it just to humiliate me and + + + align:start position:0% +were doing it just to humiliate me and +we feel that uh particularly in the + + align:start position:0% +we feel that uh particularly in the + + + align:start position:0% +we feel that uh particularly in the +great presentation of Barbara Standard + + align:start position:0% +great presentation of Barbara Standard + + + align:start position:0% +great presentation of Barbara Standard +because it's a closeup and we're our + + align:start position:0% +because it's a closeup and we're our + + + align:start position:0% +because it's a closeup and we're our +attention is called to the fact that is + + align:start position:0% +attention is called to the fact that is + + + align:start position:0% +attention is called to the fact that is +closeup. Now that is that's the kind of + + align:start position:0% +closeup. Now that is that's the kind of + + + align:start position:0% +closeup. Now that is that's the kind of +thing I was hoping you would get from + + align:start position:0% +thing I was hoping you would get from + + + align:start position:0% +thing I was hoping you would get from +the commentary. There are other other + + align:start position:0% +the commentary. There are other other + + + align:start position:0% +the commentary. There are other other +things as well. Does anybody else want + + align:start position:0% +things as well. Does anybody else want + + + align:start position:0% +things as well. Does anybody else want +to say something about that? About the + + align:start position:0% +to say something about that? About the + + + align:start position:0% +to say something about that? About the +utility of the of the commentary as a + + align:start position:0% +utility of the of the commentary as a + + + align:start position:0% +utility of the of the commentary as a +way of helping you to get the technical + + align:start position:0% +way of helping you to get the technical + + + align:start position:0% +way of helping you to get the technical +devices and find points that enable the + + align:start position:0% +devices and find points that enable the + + + align:start position:0% +devices and find points that enable the +movie to convey the feelings and the + + align:start position:0% +movie to convey the feelings and the + + + align:start position:0% +movie to convey the feelings and the +reality that it does. + + align:start position:0% + + + + align:start position:0% + +Um, no, don't tell me + + align:start position:0% + + + + align:start position:0% + +Peter. Yeah, I guess the whole was based + + align:start position:0% +Peter. Yeah, I guess the whole was based + + + align:start position:0% +Peter. Yeah, I guess the whole was based +on the cinematography of the movie, + + align:start position:0% +on the cinematography of the movie, + + + align:start position:0% +on the cinematography of the movie, +right? It wasn't anything to do with the + + align:start position:0% +right? It wasn't anything to do with the + + + align:start position:0% +right? It wasn't anything to do with the +story line or any why + + align:start position:0% +story line or any why + + + align:start position:0% +story line or any why +how um + + align:start position:0% +how um + + + align:start position:0% +how um +so I've only seen half the movie, + + align:start position:0% +so I've only seen half the movie, + + + align:start position:0% +so I've only seen half the movie, +but given how the male main male + + align:start position:0% +but given how the male main male + + + align:start position:0% +but given how the male main male +character is able to is convinced that + + align:start position:0% +character is able to is convinced that + + + align:start position:0% +character is able to is convinced that +when he sees uh Eve for the second time + + align:start position:0% +when he sees uh Eve for the second time + + + align:start position:0% +when he sees uh Eve for the second time +as the duchess, how he's convinced that + + align:start position:0% +as the duchess, how he's convinced that + + + align:start position:0% +as the duchess, how he's convinced that +it's not, you know, the lady the woman + + align:start position:0% +it's not, you know, the lady the woman + + + align:start position:0% +it's not, you know, the lady the woman +he met at at the boat. I wish there was + + align:start position:0% +he met at at the boat. I wish there was + + + align:start position:0% +he met at at the boat. I wish there was +more explanation of how things the + + align:start position:0% +more explanation of how things the + + + align:start position:0% +more explanation of how things the +storyline works out in the movie instead + + align:start position:0% +storyline works out in the movie instead + + + align:start position:0% +storyline works out in the movie instead +of just depicting this is, you know, + + align:start position:0% +of just depicting this is, you know, + + + align:start position:0% +of just depicting this is, you know, +this is a close-up shot and this is what + + align:start position:0% +this is a close-up shot and this is what + + + align:start position:0% +this is a close-up shot and this is what +it means. No, but u it's more than just + + align:start position:0% +it means. No, but u it's more than just + + + align:start position:0% +it means. No, but u it's more than just +the technique. It's also the story. Uh, + + align:start position:0% +the technique. It's also the story. Uh, + + + align:start position:0% +the technique. It's also the story. Uh, +for instance, when um the commentary + + align:start position:0% +for instance, when um the commentary + + + align:start position:0% +for instance, when um the commentary +calls attention to + + align:start position:0% +calls attention to + + + align:start position:0% +calls attention to +the fuzziness in the image when Charles + + align:start position:0% +the fuzziness in the image when Charles + + + align:start position:0% +the fuzziness in the image when Charles +is on his knees putting on the new shoes + + align:start position:0% +is on his knees putting on the new shoes + + + align:start position:0% +is on his knees putting on the new shoes +to uh Barbara Stanwick, though he's + + align:start position:0% +to uh Barbara Stanwick, though he's + + + align:start position:0% +to uh Barbara Stanwick, though he's +close to her sexual region, and so he + + align:start position:0% +close to her sexual region, and so he + + + align:start position:0% +close to her sexual region, and so he +his mind goes fuzzy and swimming around + + align:start position:0% +his mind goes fuzzy and swimming around + + + align:start position:0% +his mind goes fuzzy and swimming around +and then and we see it in the image. + + align:start position:0% +and then and we see it in the image. + + + align:start position:0% +and then and we see it in the image. +Well, the calling our attention to the + + align:start position:0% +Well, the calling our attention to the + + + align:start position:0% +Well, the calling our attention to the +nature of that fuzzy image is a way of + + align:start position:0% +nature of that fuzzy image is a way of + + + align:start position:0% +nature of that fuzzy image is a way of +indicating the state of his mind. And + + align:start position:0% +indicating the state of his mind. And + + + align:start position:0% +indicating the state of his mind. And +you might have missed that if uh you + + align:start position:0% +you might have missed that if uh you + + + align:start position:0% +you might have missed that if uh you +hadn't been had that pointed out to you. + + align:start position:0% +hadn't been had that pointed out to you. + + + align:start position:0% +hadn't been had that pointed out to you. +What's important is the two go together. + + align:start position:0% +What's important is the two go together. + + + align:start position:0% +What's important is the two go together. +I mean, this is an effective way of + + align:start position:0% +I mean, this is an effective way of + + + align:start position:0% +I mean, this is an effective way of +doing that. Uh so I think you you may + + align:start position:0% +doing that. Uh so I think you you may + + + align:start position:0% +doing that. Uh so I think you you may +not be doing her justice that she tells + + align:start position:0% +not be doing her justice that she tells + + + align:start position:0% +not be doing her justice that she tells +it's more than just telling you the + + align:start position:0% +it's more than just telling you the + + + align:start position:0% +it's more than just telling you the +angles. I mean the uh close-ups and not + + align:start position:0% +angles. I mean the uh close-ups and not + + + align:start position:0% +angles. I mean the uh close-ups and not +non close-ups at the same time. Anybody + + align:start position:0% +non close-ups at the same time. Anybody + + + align:start position:0% +non close-ups at the same time. Anybody +wants anything more about this? + + align:start position:0% +wants anything more about this? + + + align:start position:0% +wants anything more about this? +Well, the scene we've been talking + + align:start position:0% +Well, the scene we've been talking + + + align:start position:0% +Well, the scene we've been talking +about, well, no, actually the scene he + + align:start position:0% +about, well, no, actually the scene he + + + align:start position:0% +about, well, no, actually the scene he +mentioned, not the not the one putting + + align:start position:0% +mentioned, not the not the one putting + + + align:start position:0% +mentioned, not the not the one putting +on the shoe, + + align:start position:0% +on the shoe, + + + align:start position:0% +on the shoe, +um I didn't really understand uh why it + + align:start position:0% +um I didn't really understand uh why it + + + align:start position:0% +um I didn't really understand uh why it +was so watchable at first because I was + + align:start position:0% +was so watchable at first because I was + + + align:start position:0% +was so watchable at first because I was +I I mean I did realize afterwards like + + align:start position:0% +I I mean I did realize afterwards like + + + align:start position:0% +I I mean I did realize afterwards like +that the camera was just in one position + + align:start position:0% +that the camera was just in one position + + + align:start position:0% +that the camera was just in one position +for the whole time and very little + + align:start position:0% +for the whole time and very little + + + align:start position:0% +for the whole time and very little +happened. + + align:start position:0% +happened. + + + align:start position:0% +happened. +But like I was I mean I was entertained + + align:start position:0% +But like I was I mean I was entertained + + + align:start position:0% +But like I was I mean I was entertained +the whole time but then I realized like + + align:start position:0% +the whole time but then I realized like + + + align:start position:0% +the whole time but then I realized like +sort of as she was talking about it and + + align:start position:0% +sort of as she was talking about it and + + + align:start position:0% +sort of as she was talking about it and +just just that that works like and then + + align:start position:0% +just just that that works like and then + + + align:start position:0% +just just that that works like and then +it's like a it's very stylistic um and + + align:start position:0% +it's like a it's very stylistic um and + + + align:start position:0% +it's like a it's very stylistic um and +you I mean I don't think you see it + + align:start position:0% +you I mean I don't think you see it + + + align:start position:0% +you I mean I don't think you see it +nearly as much in cinema today. It's + + align:start position:0% +nearly as much in cinema today. It's + + + align:start position:0% +nearly as much in cinema today. It's +just that long shot where the camera's + + align:start position:0% +just that long shot where the camera's + + + align:start position:0% +just that long shot where the camera's +not moving at all. Well, um, possibly + + align:start position:0% +not moving at all. Well, um, possibly + + + align:start position:0% +not moving at all. Well, um, possibly +some of you will want to read my new + + align:start position:0% +some of you will want to read my new + + + align:start position:0% +some of you will want to read my new +book that I've + + align:start position:0% +book that I've + + + align:start position:0% +book that I've +mentioned, three philosophical + + align:start position:0% +mentioned, three philosophical + + + align:start position:0% +mentioned, three philosophical +filmmakers, Hitchcock, Wells, and + + align:start position:0% +filmmakers, Hitchcock, Wells, and + + + align:start position:0% +filmmakers, Hitchcock, Wells, and +because in the chapter on I discussed + + align:start position:0% +because in the chapter on I discussed + + + align:start position:0% +because in the chapter on I discussed +his intention for a long stretch of his + + align:start position:0% +his intention for a long stretch of his + + + align:start position:0% +his intention for a long stretch of his +career not to move the camera. When he + + align:start position:0% +career not to move the camera. When he + + + align:start position:0% +career not to move the camera. When he +was younger, he used to move it with a + + align:start position:0% +was younger, he used to move it with a + + + align:start position:0% +was younger, he used to move it with a +great a great deal. And then later um he + + align:start position:0% +great a great deal. And then later um he + + + align:start position:0% +great a great deal. And then later um he +developed his ideas about the actors + + align:start position:0% +developed his ideas about the actors + + + align:start position:0% +developed his ideas about the actors +being the real directors and the + + align:start position:0% +being the real directors and the + + + align:start position:0% +being the real directors and the +function of the so-called director is to + + align:start position:0% +function of the so-called director is to + + + align:start position:0% +function of the so-called director is to +give them an opportunity to show forth + + align:start position:0% +give them an opportunity to show forth + + + align:start position:0% +give them an opportunity to show forth +what there is in the movie and that if + + align:start position:0% +what there is in the movie and that if + + + align:start position:0% +what there is in the movie and that if +the camera is too active then your + + align:start position:0% +the camera is too active then your + + + align:start position:0% +the camera is too active then your +attention gets deflected away from the + + align:start position:0% +attention gets deflected away from the + + + align:start position:0% +attention gets deflected away from the +actors to the cinematography. And so in + + align:start position:0% +actors to the cinematography. And so in + + + align:start position:0% +actors to the cinematography. And so in +his later period he let the camera + + align:start position:0% +his later period he let the camera + + + align:start position:0% +his later period he let the camera +remain stationary as much as possible. + + align:start position:0% +remain stationary as much as possible. + + + align:start position:0% +remain stationary as much as possible. +But the point is that he would also at + + align:start position:0% +But the point is that he would also at + + + align:start position:0% +But the point is that he would also at +crucial + + align:start position:0% +crucial + + + align:start position:0% +crucial +moments make certain effects by moving + + align:start position:0% +moments make certain effects by moving + + + align:start position:0% +moments make certain effects by moving +the camera the way he does. So that that + + align:start position:0% +the camera the way he does. So that that + + + align:start position:0% +the camera the way he does. So that that +I think is part of what was going on. Uh + + align:start position:0% +I think is part of what was going on. Uh + + + align:start position:0% +I think is part of what was going on. Uh +Sergis does both move and the camera and + + align:start position:0% +Sergis does both move and the camera and + + + align:start position:0% +Sergis does both move and the camera and +leave it stationary. And there's a + + align:start position:0% +leave it stationary. And there's a + + + align:start position:0% +leave it stationary. And there's a +meaning for the different uses + + align:start position:0% +meaning for the different uses + + + align:start position:0% +meaning for the different uses +particularly in his case because I think + + align:start position:0% +particularly in his case because I think + + + align:start position:0% +particularly in his case because I think +the movie is a masterpiece and that when + + align:start position:0% +the movie is a masterpiece and that when + + + align:start position:0% +the movie is a masterpiece and that when +he does one or the other it's with um + + align:start position:0% +he does one or the other it's with um + + + align:start position:0% +he does one or the other it's with um +the reason of conveying ideas and doing + + align:start position:0% +the reason of conveying ideas and doing + + + align:start position:0% +the reason of conveying ideas and doing +it very effectively. At this point, I do + + align:start position:0% +it very effectively. At this point, I do + + + align:start position:0% +it very effectively. At this point, I do +want to say something about the + + align:start position:0% +want to say something about the + + + align:start position:0% +want to say something about the +commentary that + + align:start position:0% +commentary that + + + align:start position:0% +commentary that +uh belongs to the part you didn't see, + + align:start position:0% +uh belongs to the part you didn't see, + + + align:start position:0% +uh belongs to the part you didn't see, +but I'm sure you all remember the scene + + align:start position:0% +but I'm sure you all remember the scene + + + align:start position:0% +but I'm sure you all remember the scene +when Charles proposes to + + align:start position:0% +when Charles proposes to + + + align:start position:0% +when Charles proposes to +Eve, right? the second half + + align:start position:0% +Eve, right? the second half + + + align:start position:0% +Eve, right? the second half +um in a way that she had predicted + + align:start position:0% +um in a way that she had predicted + + + align:start position:0% +um in a way that she had predicted +saying one day we'll be out on a riding + + align:start position:0% +saying one day we'll be out on a riding + + + align:start position:0% +saying one day we'll be out on a riding +horses and going through a glade and + + align:start position:0% +horses and going through a glade and + + + align:start position:0% +horses and going through a glade and +then we'll come upon this incredible + + align:start position:0% +then we'll come upon this incredible + + + align:start position:0% +then we'll come upon this incredible +sunset and we'll have to stop and watch + + align:start position:0% +sunset and we'll have to stop and watch + + + align:start position:0% +sunset and we'll have to stop and watch +it and you know the sunset is a kind of + + align:start position:0% +it and you know the sunset is a kind of + + + align:start position:0% +it and you know the sunset is a kind of +cliche of some romantic place in which + + align:start position:0% +cliche of some romantic place in which + + + align:start position:0% +cliche of some romantic place in which +people fall in love with each other in a + + align:start position:0% +people fall in love with each other in a + + + align:start position:0% +people fall in love with each other in a +very idealistic way right and of course + + align:start position:0% +very idealistic way right and of course + + + align:start position:0% +very idealistic way right and of course +this is being satarized it's saterized + + align:start position:0% +this is being satarized it's saterized + + + align:start position:0% +this is being satarized it's saterized +by Eve + + align:start position:0% +by Eve + + + align:start position:0% +by Eve +and also uh satarites for with evil + + align:start position:0% +and also uh satarites for with evil + + + align:start position:0% +and also uh satarites for with evil +intent because she's chosen that as a + + align:start position:0% +intent because she's chosen that as a + + + align:start position:0% +intent because she's chosen that as a +trick to catch him to make sure he + + align:start position:0% +trick to catch him to make sure he + + + align:start position:0% +trick to catch him to make sure he +proposes put him in the right mood but + + align:start position:0% +proposes put him in the right mood but + + + align:start position:0% +proposes put him in the right mood but +it's also sat satarized by the filmmaker + + align:start position:0% +it's also sat satarized by the filmmaker + + + align:start position:0% +it's also sat satarized by the filmmaker +and so we have to keep both of these in + + align:start position:0% +and so we have to keep both of these in + + + align:start position:0% +and so we have to keep both of these in +mind the reason I'm bringing this up + + align:start position:0% +mind the reason I'm bringing this up + + + align:start position:0% +mind the reason I'm bringing this up +right now is that incredible and + + align:start position:0% +right now is that incredible and + + + align:start position:0% +right now is that incredible and +wonderful funny scene in which the horse + + align:start position:0% +wonderful funny scene in which the horse + + + align:start position:0% +wonderful funny scene in which the horse +keeps nuzzling + + align:start position:0% +keeps nuzzling + + + align:start position:0% +keeps nuzzling +ing the the back of Charles's head while + + align:start position:0% +ing the the back of Charles's head while + + + align:start position:0% +ing the the back of Charles's head while +he's trying to propose to Eve. Right. + + align:start position:0% +he's trying to propose to Eve. Right. + + + align:start position:0% +he's trying to propose to Eve. Right. +And what + + align:start position:0% +And what + + + align:start position:0% +And what +um um I can't now remember what the + + align:start position:0% +um um I can't now remember what the + + + align:start position:0% +um um I can't now remember what the +commentator says, but I have a feeling + + align:start position:0% +commentator says, but I have a feeling + + + align:start position:0% +commentator says, but I have a feeling +at the time uh that she sort of misses + + align:start position:0% +at the time uh that she sort of misses + + + align:start position:0% +at the time uh that she sort of misses +the point. The point is not that um this + + align:start position:0% +the point. The point is not that um this + + + align:start position:0% +the point. The point is not that um this +is the film making filmmaker talking + + align:start position:0% +is the film making filmmaker talking + + + align:start position:0% +is the film making filmmaker talking +about the making of films which is a + + align:start position:0% +about the making of films which is a + + + align:start position:0% +about the making of films which is a +recurrent theme in her analysis. it. The + + align:start position:0% +recurrent theme in her analysis. it. The + + + align:start position:0% +recurrent theme in her analysis. it. The +theme itself goes back to ideas of um + + align:start position:0% +theme itself goes back to ideas of um + + + align:start position:0% +theme itself goes back to ideas of um +Stanley Cavll the professor at Harvard I + + align:start position:0% +Stanley Cavll the professor at Harvard I + + + align:start position:0% +Stanley Cavll the professor at Harvard I +told you who wrote that book called the + + align:start position:0% +told you who wrote that book called the + + + align:start position:0% +told you who wrote that book called the +world viewed and had many students at + + align:start position:0% +world viewed and had many students at + + + align:start position:0% +world viewed and had many students at +Harvard and I think Marian Kee may may + + align:start position:0% +Harvard and I think Marian Kee may may + + + align:start position:0% +Harvard and I think Marian Kee may may +have been a student of his and she + + align:start position:0% +have been a student of his and she + + + align:start position:0% +have been a student of his and she +refers to his book uh pursuits of + + align:start position:0% +refers to his book uh pursuits of + + + align:start position:0% +refers to his book uh pursuits of +happiness uh in relation to the idea of + + align:start position:0% +happiness uh in relation to the idea of + + + align:start position:0% +happiness uh in relation to the idea of +movies being + + align:start position:0% +movies being + + + align:start position:0% +movies being +self-reflective. Let me get into a + + align:start position:0% +self-reflective. Let me get into a + + + align:start position:0% +self-reflective. Let me get into a +little degression here. You remember the + + align:start position:0% +little degression here. You remember the + + + align:start position:0% +little degression here. You remember the +when the scenes when Charles is standing + + align:start position:0% +when the scenes when Charles is standing + + + align:start position:0% +when the scenes when Charles is standing +on the deck of the ship and these + + align:start position:0% +on the deck of the ship and these + + + align:start position:0% +on the deck of the ship and these +strange men go back and forth and she + + align:start position:0% +strange men go back and forth and she + + + align:start position:0% +strange men go back and forth and she +interprets them as being uh comments by + + align:start position:0% +interprets them as being uh comments by + + + align:start position:0% +interprets them as being uh comments by +the the film director to the fact that + + align:start position:0% +the the film director to the fact that + + + align:start position:0% +the the film director to the fact that +it's really a Halloween scene. It's not + + align:start position:0% +it's really a Halloween scene. It's not + + + align:start position:0% +it's really a Halloween scene. It's not +the real it's not really on a ship. And + + align:start position:0% +the real it's not really on a ship. And + + + align:start position:0% +the real it's not really on a ship. And +so it raises all kinds of aesthetic + + align:start position:0% +so it raises all kinds of aesthetic + + + align:start position:0% +so it raises all kinds of aesthetic +questions about what is the reality of + + align:start position:0% +questions about what is the reality of + + + align:start position:0% +questions about what is the reality of +films because it's all being done under + + align:start position:0% +films because it's all being done under + + + align:start position:0% +films because it's all being done under +artificial conditions but it's supposed + + align:start position:0% +artificial conditions but it's supposed + + + align:start position:0% +artificial conditions but it's supposed +to look like the real thing, right? Uh + + align:start position:0% +to look like the real thing, right? Uh + + + align:start position:0% +to look like the real thing, right? Uh +and then that comes back when there are + + align:start position:0% +and then that comes back when there are + + + align:start position:0% +and then that comes back when there are +these strange men who walk past um the + + align:start position:0% +these strange men who walk past um the + + + align:start position:0% +these strange men who walk past um the +father when he's trying to get his + + align:start position:0% +father when he's trying to get his + + + align:start position:0% +father when he's trying to get his +breakfast and has his infantile fit. + + align:start position:0% +breakfast and has his infantile fit. + + + align:start position:0% +breakfast and has his infantile fit. +remember again she interpreted that way + + align:start position:0% +remember again she interpreted that way + + + align:start position:0% +remember again she interpreted that way +that these are walk-ons and one says I + + align:start position:0% +that these are walk-ons and one says I + + + align:start position:0% +that these are walk-ons and one says I +can't speak and she said well maybe + + align:start position:0% +can't speak and she said well maybe + + + align:start position:0% +can't speak and she said well maybe +that's because uh you get if you're an + + align:start position:0% +that's because uh you get if you're an + + + align:start position:0% +that's because uh you get if you're an +extra and you get less money than people + + align:start position:0% +extra and you get less money than people + + + align:start position:0% +extra and you get less money than people +who speak and he was just an extra so he + + align:start position:0% +who speak and he was just an extra so he + + + align:start position:0% +who speak and he was just an extra so he +couldn't speak and all of this seemed to + + align:start position:0% +couldn't speak and all of this seemed to + + + align:start position:0% +couldn't speak and all of this seemed to +be very far-fetched uh and I'm I'm a + + align:start position:0% +be very far-fetched uh and I'm I'm a + + + align:start position:0% +be very far-fetched uh and I'm I'm a +critic of the Cavell view about the + + align:start position:0% +critic of the Cavell view about the + + + align:start position:0% +critic of the Cavell view about the +reflexivity of films but I think the + + align:start position:0% +reflexivity of films but I think the + + + align:start position:0% +reflexivity of films but I think the +great opportunity for seeing the hand of + + align:start position:0% +great opportunity for seeing the hand of + + + align:start position:0% +great opportunity for seeing the hand of +the + + align:start position:0% +the + + + align:start position:0% +the +cinematographer occurs in the scene with + + align:start position:0% +cinematographer occurs in the scene with + + + align:start position:0% +cinematographer occurs in the scene with +the + + align:start position:0% +the + + + align:start position:0% +the +horse because here's + + align:start position:0% +horse because here's + + + align:start position:0% +horse because here's +Charles trying to propose and being + + align:start position:0% +Charles trying to propose and being + + + align:start position:0% +Charles trying to propose and being +maneuvered and sort of following the + + align:start position:0% +maneuvered and sort of following the + + + align:start position:0% +maneuvered and sort of following the +script that she has written because she + + align:start position:0% +script that she has written because she + + + align:start position:0% +script that she has written because she +you mean earlier she said one day we'll + + align:start position:0% +you mean earlier she said one day we'll + + + align:start position:0% +you mean earlier she said one day we'll +be out and so on and and the horse will + + align:start position:0% +be out and so on and and the horse will + + + align:start position:0% +be out and so on and and the horse will +nuzzle my neck. As a matter of fact, did + + align:start position:0% +nuzzle my neck. As a matter of fact, did + + + align:start position:0% +nuzzle my neck. As a matter of fact, did +you notice the horse doesn't nuzzle her + + align:start position:0% +you notice the horse doesn't nuzzle her + + + align:start position:0% +you notice the horse doesn't nuzzle her +neck? Uh, it's Charles. And she turns + + align:start position:0% +neck? Uh, it's Charles. And she turns + + + align:start position:0% +neck? Uh, it's Charles. And she turns +and angrily and to say to the horse, + + align:start position:0% +and angrily and to say to the horse, + + + align:start position:0% +and angrily and to say to the horse, +"Stop that. She was wrong." Her + + align:start position:0% +"Stop that. She was wrong." Her + + + align:start position:0% +"Stop that. She was wrong." Her +prediction didn't come true at that + + align:start position:0% +prediction didn't come true at that + + + align:start position:0% +prediction didn't come true at that +moment. But the rest of it is the way + + align:start position:0% +moment. But the rest of it is the way + + + align:start position:0% +moment. But the rest of it is the way +she predicted it because the horse is + + align:start position:0% +she predicted it because the horse is + + + align:start position:0% +she predicted it because the horse is +nuzzling, but it's nuzzling Charles's. + + align:start position:0% +nuzzling, but it's nuzzling Charles's. + + + align:start position:0% +nuzzling, but it's nuzzling Charles's. +Now this delicate shift you know is + + align:start position:0% +Now this delicate shift you know is + + + align:start position:0% +Now this delicate shift you know is +obviously a con contrived + + align:start position:0% +obviously a con contrived + + + align:start position:0% +obviously a con contrived +uh remark a kind of commentary by the + + align:start position:0% +uh remark a kind of commentary by the + + + align:start position:0% +uh remark a kind of commentary by the +filmmaker and it's very funny when you + + align:start position:0% +filmmaker and it's very funny when you + + + align:start position:0% +filmmaker and it's very funny when you +realize the details but it's even + + align:start position:0% +realize the details but it's even + + + align:start position:0% +realize the details but it's even +funnier when you think of what Charles + + align:start position:0% +funnier when you think of what Charles + + + align:start position:0% +funnier when you think of what Charles +is saying he's saying these platitudes + + align:start position:0% +is saying he's saying these platitudes + + + align:start position:0% +is saying he's saying these platitudes +about there having come out of the glade + + align:start position:0% +about there having come out of the glade + + + align:start position:0% +about there having come out of the glade +and having known each other all you know + + align:start position:0% +and having known each other all you know + + + align:start position:0% +and having known each other all you know +all the way back + + align:start position:0% +all the way back + + + align:start position:0% +all the way back +Um, and the horse is sort of saying, + + align:start position:0% +Um, and the horse is sort of saying, + + + align:start position:0% +Um, and the horse is sort of saying, +"Oh, cut it out." You know, it's as if + + align:start position:0% +"Oh, cut it out." You know, it's as if + + + align:start position:0% +"Oh, cut it out." You know, it's as if +the horse was trying to knock some horse + + align:start position:0% +the horse was trying to knock some horse + + + align:start position:0% +the horse was trying to knock some horse +sense into Charles. He's saying, "No, + + align:start position:0% +sense into Charles. He's saying, "No, + + + align:start position:0% +sense into Charles. He's saying, "No, +cut. You know, you're what you're saying + + align:start position:0% +cut. You know, you're what you're saying + + + align:start position:0% +cut. You know, you're what you're saying +is absurd or and Charles keeps pushing + + align:start position:0% +is absurd or and Charles keeps pushing + + + align:start position:0% +is absurd or and Charles keeps pushing +him off and fighting against this + + align:start position:0% +him off and fighting against this + + + align:start position:0% +him off and fighting against this +interference in order to keep on talking + + align:start position:0% +interference in order to keep on talking + + + align:start position:0% +interference in order to keep on talking +coherently." + + align:start position:0% +coherently." + + + align:start position:0% +coherently." +Um also it makes one wonder where is + + align:start position:0% +Um also it makes one wonder where is + + + align:start position:0% +Um also it makes one wonder where is +Charles likely to find love. People + + align:start position:0% +Charles likely to find love. People + + + align:start position:0% +Charles likely to find love. People +assume that you find love from a + + align:start position:0% +assume that you find love from a + + + align:start position:0% +assume that you find love from a +person who is also a human being. And of + + align:start position:0% +person who is also a human being. And of + + + align:start position:0% +person who is also a human being. And of +course in this this uh period of + + align:start position:0% +course in this this uh period of + + + align:start position:0% +course in this this uh period of +history, a human being of the opposite + + align:start position:0% +history, a human being of the opposite + + + align:start position:0% +history, a human being of the opposite +sex. So Charles is looking for love out + + align:start position:0% +sex. So Charles is looking for love out + + + align:start position:0% +sex. So Charles is looking for love out +of the woman he wants to marry. + + align:start position:0% +of the woman he wants to marry. + + + align:start position:0% +of the woman he wants to marry. +But it's possible, as any uh lover of + + align:start position:0% +But it's possible, as any uh lover of + + + align:start position:0% +But it's possible, as any uh lover of +pets will tell you, that you can get + + align:start position:0% +pets will tell you, that you can get + + + align:start position:0% +pets will tell you, that you can get +more love or a different kind of love, + + align:start position:0% +more love or a different kind of love, + + + align:start position:0% +more love or a different kind of love, +but maybe a better trueer love from + + align:start position:0% +but maybe a better trueer love from + + + align:start position:0% +but maybe a better trueer love from +certain animals, dogs for instance, who + + align:start position:0% +certain animals, dogs for instance, who + + + align:start position:0% +certain animals, dogs for instance, who +are wonderfully faithful and loyal. Uh + + align:start position:0% +are wonderfully faithful and loyal. Uh + + + align:start position:0% +are wonderfully faithful and loyal. Uh +horses that can uh obey you and show a + + align:start position:0% +horses that can uh obey you and show a + + + align:start position:0% +horses that can uh obey you and show a +kind of love. And it's as if the horse + + align:start position:0% +kind of love. And it's as if the horse + + + align:start position:0% +kind of love. And it's as if the horse +is saying, "Forget about her. What about + + align:start position:0% +is saying, "Forget about her. What about + + + align:start position:0% +is saying, "Forget about her. What about +me?" + + align:start position:0% +me?" + + + align:start position:0% +me?" +And and you know whatever your view + + align:start position:0% +And and you know whatever your view + + + align:start position:0% +And and you know whatever your view +about the nature of love is between + + align:start position:0% +about the nature of love is between + + + align:start position:0% +about the nature of love is between +animals or human beings, it's very + + align:start position:0% +animals or human beings, it's very + + + align:start position:0% +animals or human beings, it's very +funny. And it's funny because one has to + + align:start position:0% +funny. And it's funny because one has to + + + align:start position:0% +funny. And it's funny because one has to +sort of hear the joking manner. One has + + align:start position:0% +sort of hear the joking manner. One has + + + align:start position:0% +sort of hear the joking manner. One has +to hear the cinematic voice of the + + align:start position:0% +to hear the cinematic voice of the + + + align:start position:0% +to hear the cinematic voice of the +filmmaker. And if you don't hear that, + + align:start position:0% +filmmaker. And if you don't hear that, + + + align:start position:0% +filmmaker. And if you don't hear that, +then you're missing something. If you + + align:start position:0% +then you're missing something. If you + + + align:start position:0% +then you're missing something. If you +just because it'll say, "No, what why + + align:start position:0% +just because it'll say, "No, what why + + + align:start position:0% +just because it'll say, "No, what why +why is the horse doing that? No. Why + + align:start position:0% +why is the horse doing that? No. Why + + + align:start position:0% +why is the horse doing that? No. Why +didn't uh uh the the filmmaker stop it + + align:start position:0% +didn't uh uh the the filmmaker stop it + + + align:start position:0% +didn't uh uh the the filmmaker stop it +and say do it again and hold on to the + + align:start position:0% +and say do it again and hold on to the + + + align:start position:0% +and say do it again and hold on to the +horse a little differently or you know + + align:start position:0% +horse a little differently or you know + + + align:start position:0% +horse a little differently or you know +train the let's have a take him out + + align:start position:0% +train the let's have a take him out + + + align:start position:0% +train the let's have a take him out +let's get a horse that's better trained + + align:start position:0% +let's get a horse that's better trained + + + align:start position:0% +let's get a horse that's better trained +on the contrary obviously that's what + + align:start position:0% +on the contrary obviously that's what + + + align:start position:0% +on the contrary obviously that's what +Sturgis wanted because it is so funny + + align:start position:0% +Sturgis wanted because it is so funny + + + align:start position:0% +Sturgis wanted because it is so funny +and because it has all of these + + align:start position:0% +and because it has all of these + + + align:start position:0% +and because it has all of these +ramifications now that I think is + + align:start position:0% +ramifications now that I think is + + + align:start position:0% +ramifications now that I think is +something you you would learn to look + + align:start position:0% +something you you would learn to look + + + align:start position:0% +something you you would learn to look +for and the commentary you see has + + align:start position:0% +for and the commentary you see has + + + align:start position:0% +for and the commentary you see has +elicited + + align:start position:0% +elicited + + + align:start position:0% +elicited +this from me because it was only after I + + align:start position:0% +this from me because it was only after I + + + align:start position:0% +this from me because it was only after I +saw that commentary that I got these + + align:start position:0% +saw that commentary that I got these + + + align:start position:0% +saw that commentary that I got these +ideas. Um, and that I think is a very + + align:start position:0% +ideas. Um, and that I think is a very + + + align:start position:0% +ideas. Um, and that I think is a very +useful uh phenomenon in the case of what + + align:start position:0% +useful uh phenomenon in the case of what + + + align:start position:0% +useful uh phenomenon in the case of what +you were watching last + + align:start position:0% +you were watching last + + + align:start position:0% +you were watching last +week. So, it's not merely a question of + + align:start position:0% +week. So, it's not merely a question of + + + align:start position:0% +week. So, it's not merely a question of +technique. It's not merely a question of + + align:start position:0% +technique. It's not merely a question of + + + align:start position:0% +technique. It's not merely a question of +close shots and long shots. It's also + + align:start position:0% +close shots and long shots. It's also + + + align:start position:0% +close shots and long shots. It's also +with these philosophical + + align:start position:0% +with these philosophical + + + align:start position:0% +with these philosophical +overtones in the context of the greatest + + align:start position:0% +overtones in the context of the greatest + + + align:start position:0% +overtones in the context of the greatest +myth in the in the world, the myth of + + align:start position:0% +myth in the in the world, the myth of + + + align:start position:0% +myth in the in the world, the myth of +creation. Some some experts say that all + + align:start position:0% +creation. Some some experts say that all + + + align:start position:0% +creation. Some some experts say that all +myths are myths of creation. That's not + + align:start position:0% +myths are myths of creation. That's not + + + align:start position:0% +myths are myths of creation. That's not +true. But the myth of creation for + + align:start position:0% +true. But the myth of creation for + + + align:start position:0% +true. But the myth of creation for +instance in the Bible is a very fertile + + align:start position:0% +instance in the Bible is a very fertile + + + align:start position:0% +instance in the Bible is a very fertile +and exciting myth. Whether or not do you + + align:start position:0% +and exciting myth. Whether or not do you + + + align:start position:0% +and exciting myth. Whether or not do you +believe the Bible is the word of God as + + align:start position:0% +believe the Bible is the word of God as + + + align:start position:0% +believe the Bible is the word of God as +mythology uh it has things that + + align:start position:0% +mythology uh it has things that + + + align:start position:0% +mythology uh it has things that +everybody has to learn. + + align:start position:0% +everybody has to learn. + + + align:start position:0% +everybody has to learn. +It's okay. + + align:start position:0% +It's okay. + + + align:start position:0% +It's okay. +Um since um I didn't call your name + + align:start position:0% +Um since um I didn't call your name + + + align:start position:0% +Um since um I didn't call your name +Carrie, why don't you continue in any + + align:start position:0% +Carrie, why don't you continue in any + + + align:start position:0% +Carrie, why don't you continue in any +way you want? Um well, I want to talk + + align:start position:0% +way you want? Um well, I want to talk + + + align:start position:0% +way you want? Um well, I want to talk +about um imagination as you talked about + + align:start position:0% +about um imagination as you talked about + + + align:start position:0% +about um imagination as you talked about +it. Okay, let's get into imagination and + + align:start position:0% +it. Okay, let's get into imagination and + + + align:start position:0% +it. Okay, let's get into imagination and +idealization. those two chapters not + + align:start position:0% +idealization. those two chapters not + + + align:start position:0% +idealization. those two chapters not +very long that I asked you to read today + + align:start position:0% +very long that I asked you to read today + + + align:start position:0% +very long that I asked you to read today +and that I hope you'll go back to and + + align:start position:0% +and that I hope you'll go back to and + + + align:start position:0% +and that I hope you'll go back to and +reread. I think it was actually in the + + align:start position:0% +reread. I think it was actually in the + + + align:start position:0% +reread. I think it was actually in the +idealization chapter that you about + + align:start position:0% +idealization chapter that you about + + + align:start position:0% +idealization chapter that you about +Czechov's story the kiss. Yeah. And how + + align:start position:0% +Czechov's story the kiss. Yeah. And how + + + align:start position:0% +Czechov's story the kiss. Yeah. And how +there's multiple epiphanies happening + + align:start position:0% +there's multiple epiphanies happening + + + align:start position:0% +there's multiple epiphanies happening +that like sort of connections between an + + align:start position:0% +that like sort of connections between an + + + align:start position:0% +that like sort of connections between an +imaginary world and an actual world and + + align:start position:0% +imaginary world and an actual world and + + + align:start position:0% +imaginary world and an actual world and +thinking about that in relation to how + + align:start position:0% +thinking about that in relation to how + + + align:start position:0% +thinking about that in relation to how +imagination operates an homaly. It's + + align:start position:0% +imagination operates an homaly. It's + + + align:start position:0% +imagination operates an homaly. It's +very contrasting because here you have + + align:start position:0% +very contrasting because here you have + + + align:start position:0% +very contrasting because here you have +this person who has their imagination + + align:start position:0% +this person who has their imagination + + + align:start position:0% +this person who has their imagination +working in the kiss and + + align:start position:0% +working in the kiss and + + + align:start position:0% +working in the kiss and +then turns out that it just turns up + + align:start position:0% +then turns out that it just turns up + + + align:start position:0% +then turns out that it just turns up +very badly for him and that's actually + + align:start position:0% +very badly for him and that's actually + + + align:start position:0% +very badly for him and that's actually +like how he becomes affected is through + + align:start position:0% +like how he becomes affected is through + + + align:start position:0% +like how he becomes affected is through +these moments where his imagination is + + align:start position:0% +these moments where his imagination is + + + align:start position:0% +these moments where his imagination is +either inspired or decayed and with + + align:start position:0% +either inspired or decayed and with + + + align:start position:0% +either inspired or decayed and with +Amaly it ends very good and she has a + + align:start position:0% +Amaly it ends very good and she has a + + + align:start position:0% +Amaly it ends very good and she has a +very fertile imagination throughout and + + align:start position:0% +very fertile imagination throughout and + + + align:start position:0% +very fertile imagination throughout and +it seems as if their their fertile + + align:start position:0% +it seems as if their their fertile + + + align:start position:0% +it seems as if their their fertile +imaginations are coming together and + + align:start position:0% +imaginations are coming together and + + + align:start position:0% +imaginations are coming together and +it's very much a success of the + + align:start position:0% +it's very much a success of the + + + align:start position:0% +it's very much a success of the +imagination. Would you say that her + + align:start position:0% +imagination. Would you say that her + + + align:start position:0% +imagination. Would you say that her +imagination is good in every respect? + + align:start position:0% +imagination is good in every respect? + + + align:start position:0% +imagination is good in every respect? +Um, I mean, I think it's a person's + + align:start position:0% +Um, I mean, I think it's a person's + + + align:start position:0% +Um, I mean, I think it's a person's +interior world and their confidence in + + align:start position:0% +interior world and their confidence in + + + align:start position:0% +interior world and their confidence in +their interior world relates to their + + align:start position:0% +their interior world relates to their + + + align:start position:0% +their interior world relates to their +imagination. Um, but she does these + + align:start position:0% +imagination. Um, but she does these + + + align:start position:0% +imagination. Um, but she does these +nasty things. I don't Well, I think I I + + align:start position:0% +nasty things. I don't Well, I think I I + + + align:start position:0% +nasty things. I don't Well, I think I I +think I don't think anything she does is + + align:start position:0% +think I don't think anything she does is + + + align:start position:0% +think I don't think anything she does is +I mean, everything she does is uh Oh, + + align:start position:0% +I mean, everything she does is uh Oh, + + + align:start position:0% +I mean, everything she does is uh Oh, +no. the productive the poor fruit seller + + align:start position:0% +no. the productive the poor fruit seller + + + align:start position:0% +no. the productive the poor fruit seller +who goes out of his mind and ends up in + + align:start position:0% +who goes out of his mind and ends up in + + + align:start position:0% +who goes out of his mind and ends up in +I won't I won't anticipate but you know + + align:start position:0% +I won't I won't anticipate but you know + + + align:start position:0% +I won't I won't anticipate but you know +who is it who is in consternation + + align:start position:0% +who is it who is in consternation + + + align:start position:0% +who is it who is in consternation +because of her it it is true her + + align:start position:0% +because of her it it is true her + + + align:start position:0% +because of her it it is true her +imagination it's definitely an + + align:start position:0% +imagination it's definitely an + + + align:start position:0% +imagination it's definitely an +idealization of the imagination or of + + align:start position:0% +idealization of the imagination or of + + + align:start position:0% +idealization of the imagination or of +people who have fertile imaginations + + align:start position:0% +people who have fertile imaginations + + + align:start position:0% +people who have fertile imaginations +elevating them above the everyday we + + align:start position:0% +elevating them above the everyday we + + + align:start position:0% +elevating them above the everyday we +don't feel about we don't feel it the + + align:start position:0% +don't feel about we don't feel it the + + + align:start position:0% +don't feel about we don't feel it the +way we do do with somebody who willfully + + align:start position:0% +way we do do with somebody who willfully + + + align:start position:0% +way we do do with somebody who willfully +murders another person to get his money. + + align:start position:0% +murders another person to get his money. + + + align:start position:0% +murders another person to get his money. +Uh we think of it perhaps as poetic + + align:start position:0% +Uh we think of it perhaps as poetic + + + align:start position:0% +Uh we think of it perhaps as poetic +justice because he's a man without + + align:start position:0% +justice because he's a man without + + + align:start position:0% +justice because he's a man without +imagination. So it's only poetically + + align:start position:0% +imagination. So it's only poetically + + + align:start position:0% +imagination. So it's only poetically +right that a person with it should sort + + align:start position:0% +right that a person with it should sort + + + align:start position:0% +right that a person with it should sort +of put him in his place and punish him + + align:start position:0% +of put him in his place and punish him + + + align:start position:0% +of put him in his place and punish him +and show us what what comes of not + + align:start position:0% +and show us what what comes of not + + + align:start position:0% +and show us what what comes of not +having imagination. Not only that, but + + align:start position:0% +having imagination. Not only that, but + + + align:start position:0% +having imagination. Not only that, but +by what she does, he it keeps to having + + align:start position:0% +by what she does, he it keeps to having + + + align:start position:0% +by what she does, he it keeps to having +to use his imagination to understand + + align:start position:0% +to use his imagination to understand + + + align:start position:0% +to use his imagination to understand +what's happening to him. This is totally + + align:start position:0% +what's happening to him. This is totally + + + align:start position:0% +what's happening to him. This is totally +irrational things. And so you can sort + + align:start position:0% +irrational things. And so you can sort + + + align:start position:0% +irrational things. And so you can sort +of see him whenever any of these things + + align:start position:0% +of see him whenever any of these things + + + align:start position:0% +of see him whenever any of these things +happen like how how did that happen? And + + align:start position:0% +happen like how how did that happen? And + + + align:start position:0% +happen like how how did that happen? And +he immediately just says well I must + + align:start position:0% +he immediately just says well I must + + + align:start position:0% +he immediately just says well I must +have I must have done that. He doesn't + + align:start position:0% +have I must have done that. He doesn't + + + align:start position:0% +have I must have done that. He doesn't +like imagine her coming into her which + + align:start position:0% +like imagine her coming into her which + + + align:start position:0% +like imagine her coming into her which +could happen eventually with him. So and + + align:start position:0% +could happen eventually with him. So and + + + align:start position:0% +could happen eventually with him. So and +also she does it in a good cause because + + align:start position:0% +also she does it in a good cause because + + + align:start position:0% +also she does it in a good cause because +the reason she feels she has to punish + + align:start position:0% +the reason she feels she has to punish + + + align:start position:0% +the reason she feels she has to punish +him is because of his bad behavior. But + + align:start position:0% +him is because of his bad behavior. But + + + align:start position:0% +him is because of his bad behavior. But +you all will experience this. Now in + + align:start position:0% +you all will experience this. Now in + + + align:start position:0% +you all will experience this. Now in +relation to Amale Lee, the reason I + + align:start position:0% +relation to Amale Lee, the reason I + + + align:start position:0% +relation to Amale Lee, the reason I +wanted to show you the movie is not only + + align:start position:0% +wanted to show you the movie is not only + + + align:start position:0% +wanted to show you the movie is not only +because it is all predicated upon the + + align:start position:0% +because it is all predicated upon the + + + align:start position:0% +because it is all predicated upon the +very nature of imagination as you will + + align:start position:0% +very nature of imagination as you will + + + align:start position:0% +very nature of imagination as you will +see + + align:start position:0% +see + + + align:start position:0% +see +instantly but and in her in Ammy Lee but + + align:start position:0% +instantly but and in her in Ammy Lee but + + + align:start position:0% +instantly but and in her in Ammy Lee but +it's also a very imaginative movie and + + align:start position:0% +it's also a very imaginative movie and + + + align:start position:0% +it's also a very imaginative movie and +that I think is the re one of the + + align:start position:0% +that I think is the re one of the + + + align:start position:0% +that I think is the re one of the +reasons why it became a worldwide + + align:start position:0% +reasons why it became a worldwide + + + align:start position:0% +reasons why it became a worldwide +triumph success beyond any expectation, + + align:start position:0% +triumph success beyond any expectation, + + + align:start position:0% +triumph success beyond any expectation, +commercial expectation on the part of + + align:start position:0% +commercial expectation on the part of + + + align:start position:0% +commercial expectation on the part of +the French filmmakers and and it's a + + align:start position:0% +the French filmmakers and and it's a + + + align:start position:0% +the French filmmakers and and it's a +wonderful movie. + + align:start position:0% +wonderful movie. + + + align:start position:0% +wonderful movie. +Um, she's there. What is this? Five + + align:start position:0% +Um, she's there. What is this? Five + + + align:start position:0% +Um, she's there. What is this? Five +Academy Award + + align:start position:0% +Academy Award + + + align:start position:0% +Academy Award +nominations. Uh, the feel-good movie of + + align:start position:0% +nominations. Uh, the feel-good movie of + + + align:start position:0% +nominations. Uh, the feel-good movie of +the year, She'll Change Your Life, so + + align:start position:0% +the year, She'll Change Your Life, so + + + align:start position:0% +the year, She'll Change Your Life, so +on. Uh, but + + align:start position:0% +on. Uh, but + + + align:start position:0% +on. Uh, but +also what I noticed first of all, I may + + align:start position:0% +also what I noticed first of all, I may + + + align:start position:0% +also what I noticed first of all, I may +have mentioned this the first time, and + + align:start position:0% +have mentioned this the first time, and + + + align:start position:0% +have mentioned this the first time, and +forgive me if I repeat myself + + align:start position:0% +forgive me if I repeat myself + + + align:start position:0% +forgive me if I repeat myself +occasionally, first time we met. + + align:start position:0% +occasionally, first time we met. + + + align:start position:0% +occasionally, first time we met. +Um the cinematography is superb and when + + align:start position:0% +Um the cinematography is superb and when + + + align:start position:0% +Um the cinematography is superb and when +I came out of the theater or seeing it + + align:start position:0% +I came out of the theater or seeing it + + + align:start position:0% +I came out of the theater or seeing it +before watching it on DVD um I said to + + align:start position:0% +before watching it on DVD um I said to + + + align:start position:0% +before watching it on DVD um I said to +myself she'll win an they'll win I'm + + align:start position:0% +myself she'll win an they'll win I'm + + + align:start position:0% +myself she'll win an they'll win I'm +sorry they'll win an Academy Award for + + align:start position:0% +sorry they'll win an Academy Award for + + + align:start position:0% +sorry they'll win an Academy Award for +the + + align:start position:0% +the + + + align:start position:0% +the +cinematography. So it's so imaginative. + + align:start position:0% +cinematography. So it's so imaginative. + + + align:start position:0% +cinematography. So it's so imaginative. +It was effects that I hadn't foreseen + + align:start position:0% +It was effects that I hadn't foreseen + + + align:start position:0% +It was effects that I hadn't foreseen +that I couldn't have imagined and it was + + align:start position:0% +that I couldn't have imagined and it was + + + align:start position:0% +that I couldn't have imagined and it was +very very fertile but absolutely right + + align:start position:0% +very very fertile but absolutely right + + + align:start position:0% +very very fertile but absolutely right +given the fact that the nature of + + align:start position:0% +given the fact that the nature of + + + align:start position:0% +given the fact that the nature of +imagination is what it's all + + align:start position:0% +imagination is what it's all + + + align:start position:0% +imagination is what it's all +about. On top of that there is also what + + align:start position:0% +about. On top of that there is also what + + + align:start position:0% +about. On top of that there is also what +Carrie was talking about in idealization + + align:start position:0% +Carrie was talking about in idealization + + + align:start position:0% +Carrie was talking about in idealization +in rel you um Carrie take the roll call. + + align:start position:0% +in rel you um Carrie take the roll call. + + + align:start position:0% +in rel you um Carrie take the roll call. +How many have read the two chapters for + + align:start position:0% +How many have read the two chapters for + + + align:start position:0% +How many have read the two chapters for +today? I'm not interested in name naming + + align:start position:0% +today? I'm not interested in name naming + + + align:start position:0% +today? I'm not interested in name naming +names. I just want to have an idea of + + align:start position:0% +names. I just want to have an idea of + + + align:start position:0% +names. I just want to have an idea of +what's going on. I think almost every + + align:start position:0% +what's going on. I think almost every + + + align:start position:0% +what's going on. I think almost every +almost everyone. Well, then you all know + + align:start position:0% +almost everyone. Well, then you all know + + + align:start position:0% +almost everyone. Well, then you all know +then you all know the uh short story + + align:start position:0% +then you all know the uh short story + + + align:start position:0% +then you all know the uh short story +that I discuss by check off. Remember um + + align:start position:0% +that I discuss by check off. Remember um + + + align:start position:0% +that I discuss by check off. Remember um +the point being that the structure of + + align:start position:0% +the point being that the structure of + + + align:start position:0% +the point being that the structure of +that narrative is built upon the way in + + align:start position:0% +that narrative is built upon the way in + + + align:start position:0% +that narrative is built upon the way in +which human beings make ideals and how + + align:start position:0% +which human beings make ideals and how + + + align:start position:0% +which human beings make ideals and how +the ideal of romantic love is the core + + align:start position:0% +the ideal of romantic love is the core + + + align:start position:0% +the ideal of romantic love is the core +of of the story. The man who's never had + + align:start position:0% +of of the story. The man who's never had + + + align:start position:0% +of of the story. The man who's never had +it and then through his imagination sort + + align:start position:0% +it and then through his imagination sort + + + align:start position:0% +it and then through his imagination sort +of creates it for himself. But since the + + align:start position:0% +of creates it for himself. But since the + + + align:start position:0% +of creates it for himself. But since the +ideal is so remote from his reality, uh + + align:start position:0% +ideal is so remote from his reality, uh + + + align:start position:0% +ideal is so remote from his reality, uh +it's fragile and then he ends up + + align:start position:0% +it's fragile and then he ends up + + + align:start position:0% +it's fragile and then he ends up +demoralized because it never comes into + + align:start position:0% +demoralized because it never comes into + + + align:start position:0% +demoralized because it never comes into +being. Now that for me is a very + + align:start position:0% +being. Now that for me is a very + + + align:start position:0% +being. Now that for me is a very +important aspect of human nature, the + + align:start position:0% +important aspect of human nature, the + + + align:start position:0% +important aspect of human nature, the +fact that we do make ideals and that + + align:start position:0% +fact that we do make ideals and that + + + align:start position:0% +fact that we do make ideals and that +I've written a great deal about because + + align:start position:0% +I've written a great deal about because + + + align:start position:0% +I've written a great deal about because +for some reason other people haven't. Uh + + align:start position:0% +for some reason other people haven't. Uh + + + align:start position:0% +for some reason other people haven't. Uh +there have been lots of um philosophers + + align:start position:0% +there have been lots of um philosophers + + + align:start position:0% +there have been lots of um philosophers +writing about ideals but they do it in a + + align:start position:0% +writing about ideals but they do it in a + + + align:start position:0% +writing about ideals but they do it in a +way that I felt uh was inadequate. Plato + + align:start position:0% +way that I felt uh was inadequate. Plato + + + align:start position:0% +way that I felt uh was inadequate. Plato +for instance thinks that all reality is + + align:start position:0% +for instance thinks that all reality is + + + align:start position:0% +for instance thinks that all reality is +struggling towards higher ideals the + + align:start position:0% +struggling towards higher ideals the + + + align:start position:0% +struggling towards higher ideals the +highest ideals. That's not what I'm + + align:start position:0% +highest ideals. That's not what I'm + + + align:start position:0% +highest ideals. That's not what I'm +talking about because often uh people do + + align:start position:0% +talking about because often uh people do + + + align:start position:0% +talking about because often uh people do +things for reasons that can't be + + align:start position:0% +things for reasons that can't be + + + align:start position:0% +things for reasons that can't be +explained in platonic terms. Um the um + + align:start position:0% +explained in platonic terms. Um the um + + + align:start position:0% +explained in platonic terms. Um the um +Freud thinks ideals are generally + + align:start position:0% +Freud thinks ideals are generally + + + align:start position:0% +Freud thinks ideals are generally +rationalizations and so when he talks + + align:start position:0% +rationalizations and so when he talks + + + align:start position:0% +rationalizations and so when he talks +about love uh for him that's what he + + align:start position:0% +about love uh for him that's what he + + + align:start position:0% +about love uh for him that's what he +calls idealization because it is an + + align:start position:0% +calls idealization because it is an + + + align:start position:0% +calls idealization because it is an +overvaluation. It is an overestimation + + align:start position:0% +overvaluation. It is an overestimation + + + align:start position:0% +overvaluation. It is an overestimation +of some of the beloved of the other + + align:start position:0% +of some of the beloved of the other + + + align:start position:0% +of some of the beloved of the other +person being overs it means it's + + align:start position:0% +person being overs it means it's + + + align:start position:0% +person being overs it means it's +inaccurate. it's erroneous and therefore + + align:start position:0% +inaccurate. it's erroneous and therefore + + + align:start position:0% +inaccurate. it's erroneous and therefore +to some extent at least it's going to be + + align:start position:0% +to some extent at least it's going to be + + + align:start position:0% +to some extent at least it's going to be +based on some kind of illusion. I don't + + align:start position:0% +based on some kind of illusion. I don't + + + align:start position:0% +based on some kind of illusion. I don't +think idealization is necessarily + + align:start position:0% +think idealization is necessarily + + + align:start position:0% +think idealization is necessarily +illusory. + + align:start position:0% +illusory. + + + align:start position:0% +illusory. +uh sometimes it is sometimes it's not + + align:start position:0% +uh sometimes it is sometimes it's not + + + align:start position:0% +uh sometimes it is sometimes it's not +but it isn't in the nature of + + align:start position:0% +but it isn't in the nature of + + + align:start position:0% +but it isn't in the nature of +idealization for it to be illusory and + + align:start position:0% +idealization for it to be illusory and + + + align:start position:0% +idealization for it to be illusory and +therefore I refuse to reduce it to + + align:start position:0% +therefore I refuse to reduce it to + + + align:start position:0% +therefore I refuse to reduce it to +rationalization or any other category of + + align:start position:0% +rationalization or any other category of + + + align:start position:0% +rationalization or any other category of +that sort that Freud um uses to explain + + align:start position:0% +that sort that Freud um uses to explain + + + align:start position:0% +that sort that Freud um uses to explain +his theor to form to construct his + + align:start position:0% +his theor to form to construct his + + + align:start position:0% +his theor to form to construct his +theory so my view is very different from + + align:start position:0% +theory so my view is very different from + + + align:start position:0% +theory so my view is very different from +Freud it's very different from + + align:start position:0% +Freud it's very different from + + + align:start position:0% +Freud it's very different from +Plato all that I mean is the making of + + align:start position:0% +Plato all that I mean is the making of + + + align:start position:0% +Plato all that I mean is the making of +ideals. This is a phenomenon, a + + align:start position:0% +ideals. This is a phenomenon, a + + + align:start position:0% +ideals. This is a phenomenon, a +universal phenomenon among human beings. + + align:start position:0% +universal phenomenon among human beings. + + + align:start position:0% +universal phenomenon among human beings. +The way you might say that um since we + + align:start position:0% +The way you might say that um since we + + + align:start position:0% +The way you might say that um since we +are dorphic creatures biologically, + + align:start position:0% +are dorphic creatures biologically, + + + align:start position:0% +are dorphic creatures biologically, +uh heterosexual impulse is a universal + + align:start position:0% +uh heterosexual impulse is a universal + + + align:start position:0% +uh heterosexual impulse is a universal +phenomenon. Doesn't mean that everybody + + align:start position:0% +phenomenon. Doesn't mean that everybody + + + align:start position:0% +phenomenon. Doesn't mean that everybody +has it on every occasion. + + align:start position:0% +has it on every occasion. + + + align:start position:0% +has it on every occasion. +uh and it doesn't mean that any other + + align:start position:0% +uh and it doesn't mean that any other + + + align:start position:0% +uh and it doesn't mean that any other +kind of attraction of a loving and + + align:start position:0% +kind of attraction of a loving and + + + align:start position:0% +kind of attraction of a loving and +sexual sort is wrong because I argue + + align:start position:0% +sexual sort is wrong because I argue + + + align:start position:0% +sexual sort is wrong because I argue +there isn't any fixed model. There isn't + + align:start position:0% +there isn't any fixed model. There isn't + + + align:start position:0% +there isn't any fixed model. There isn't +any biological model that establishes + + align:start position:0% +any biological model that establishes + + + align:start position:0% +any biological model that establishes +the ideal. So um I'm not trying to say + + align:start position:0% +the ideal. So um I'm not trying to say + + + align:start position:0% +the ideal. So um I'm not trying to say +that only heterosexual uh attraction is + + align:start position:0% +that only heterosexual uh attraction is + + + align:start position:0% +that only heterosexual uh attraction is +the norm but it is a universal thing + + align:start position:0% +the norm but it is a universal thing + + + align:start position:0% +the norm but it is a universal thing +that we all recognize and we can explain + + align:start position:0% +that we all recognize and we can explain + + + align:start position:0% +that we all recognize and we can explain +in terms of the fact that uh for the + + align:start position:0% +in terms of the fact that uh for the + + + align:start position:0% +in terms of the fact that uh for the +species to propagate there has to be an + + align:start position:0% +species to propagate there has to be an + + + align:start position:0% +species to propagate there has to be an +intimate congress between male and + + align:start position:0% +intimate congress between male and + + + align:start position:0% +intimate congress between male and +female. All right. Well in that sort of + + align:start position:0% +female. All right. Well in that sort of + + + align:start position:0% +female. All right. Well in that sort of +vein there are certain fundamentals and + + align:start position:0% +vein there are certain fundamentals and + + + align:start position:0% +vein there are certain fundamentals and +one of them in human nature. One of + + align:start position:0% +one of them in human nature. One of + + + align:start position:0% +one of them in human nature. One of +them, I argue, is the making of + + align:start position:0% +them, I argue, is the making of + + + align:start position:0% +them, I argue, is the making of +ideals. There wouldn't be all the + + align:start position:0% +ideals. There wouldn't be all the + + + align:start position:0% +ideals. There wouldn't be all the +millions, hundreds, and thousands of + + align:start position:0% +millions, hundreds, and thousands of + + + align:start position:0% +millions, hundreds, and thousands of +millions of people who have died because + + align:start position:0% +millions of people who have died because + + + align:start position:0% +millions of people who have died because +of some ideal fighting in warfare or + + align:start position:0% +of some ideal fighting in warfare or + + + align:start position:0% +of some ideal fighting in warfare or +because they're taking care of their + + align:start position:0% +because they're taking care of their + + + align:start position:0% +because they're taking care of their +family when they should be taking care + + align:start position:0% +family when they should be taking care + + + align:start position:0% +family when they should be taking care +of themselves. um or you know being + + align:start position:0% +of themselves. um or you know being + + + align:start position:0% +of themselves. um or you know being +artists who neglect uh to go to the + + align:start position:0% +artists who neglect uh to go to the + + + align:start position:0% +artists who neglect uh to go to the +doctors so that they can pursue their + + align:start position:0% +doctors so that they can pursue their + + + align:start position:0% +doctors so that they can pursue their +arts. All sorts of ways in which a + + align:start position:0% +arts. All sorts of ways in which a + + + align:start position:0% +arts. All sorts of ways in which a +certain ideal an ideal that could be + + align:start position:0% +certain ideal an ideal that could be + + + align:start position:0% +certain ideal an ideal that could be +aesthetic could mil military could be + + align:start position:0% +aesthetic could mil military could be + + + align:start position:0% +aesthetic could mil military could be +paternal could be nationalistic. Um it + + align:start position:0% +paternal could be nationalistic. Um it + + + align:start position:0% +paternal could be nationalistic. Um it +can be vain, it can be selfless. All + + align:start position:0% +can be vain, it can be selfless. All + + + align:start position:0% +can be vain, it can be selfless. All +these are possible uh + + align:start position:0% +these are possible uh + + + align:start position:0% +these are possible uh +ideals that they are built into us as + + align:start position:0% +ideals that they are built into us as + + + align:start position:0% +ideals that they are built into us as +human beings. We are makers of ideals. + + align:start position:0% +human beings. We are makers of ideals. + + + align:start position:0% +human beings. We are makers of ideals. +were a lot of other things too. That's + + align:start position:0% +were a lot of other things too. That's + + + align:start position:0% +were a lot of other things too. That's +what I mean by idealization. And in the + + align:start position:0% +what I mean by idealization. And in the + + + align:start position:0% +what I mean by idealization. And in the +case of the short story + + align:start position:0% +case of the short story + + + align:start position:0% +case of the short story +u it's this ideal + + align:start position:0% +u it's this ideal + + + align:start position:0% +u it's this ideal +of romantic love which is heterosexual + + align:start position:0% +of romantic love which is heterosexual + + + align:start position:0% +of romantic love which is heterosexual +and bourgeoa leading to marriage that + + align:start position:0% +and bourgeoa leading to marriage that + + + align:start position:0% +and bourgeoa leading to marriage that +propels that short story and it uh that + + align:start position:0% +propels that short story and it uh that + + + align:start position:0% +propels that short story and it uh that +the check off analyzes with exquisite + + align:start position:0% +the check off analyzes with exquisite + + + align:start position:0% +the check off analyzes with exquisite +precision and and realistic detail. So + + align:start position:0% +precision and and realistic detail. So + + + align:start position:0% +precision and and realistic detail. So +it's a great short story. All right. In + + align:start position:0% +it's a great short story. All right. In + + + align:start position:0% +it's a great short story. All right. In +the case of + + align:start position:0% +the case of + + + align:start position:0% +the case of +Ami, how does that come in? What how who + + align:start position:0% +Ami, how does that come in? What how who + + + align:start position:0% +Ami, how does that come in? What how who +is motivated by a comparable ideal? + + align:start position:0% + + + + align:start position:0% + +I I don't know how to see idealization + + align:start position:0% +I I don't know how to see idealization + + + align:start position:0% +I I don't know how to see idealization +in all. I mean, + + align:start position:0% +in all. I mean, + + + align:start position:0% +in all. I mean, +she idealizes her own independent self + + align:start position:0% +she idealizes her own independent self + + + align:start position:0% +she idealizes her own independent self +maybe at the beginning of the movie and + + align:start position:0% +maybe at the beginning of the movie and + + + align:start position:0% +maybe at the beginning of the movie and +her own I mean in the depictions of the + + align:start position:0% +her own I mean in the depictions of the + + + align:start position:0% +her own I mean in the depictions of the +lady die um and her uh imagination + + align:start position:0% +lady die um and her uh imagination + + + align:start position:0% +lady die um and her uh imagination +running on on that TV script. It talks + + align:start position:0% +running on on that TV script. It talks + + + align:start position:0% +running on on that TV script. It talks +very much about um how she's very and + + align:start position:0% +very much about um how she's very and + + + align:start position:0% +very much about um how she's very and +and and she she idealizes helping other + + align:start position:0% +and and she she idealizes helping other + + + align:start position:0% +and and she she idealizes helping other +people at some point in the movie. She + + align:start position:0% +people at some point in the movie. She + + + align:start position:0% +people at some point in the movie. She +has this realization that she should + + align:start position:0% +has this realization that she should + + + align:start position:0% +has this realization that she should +help other people and that she and she + + align:start position:0% +help other people and that she and she + + + align:start position:0% +help other people and that she and she +tries it out once and it works and and + + align:start position:0% +tries it out once and it works and and + + + align:start position:0% +tries it out once and it works and and +then it keeps going and it gets and like + + align:start position:0% +then it keeps going and it gets and like + + + align:start position:0% +then it keeps going and it gets and like +just but over overarching it all is that + + align:start position:0% +just but over overarching it all is that + + + align:start position:0% +just but over overarching it all is that +it's a love story. That's that's true. + + align:start position:0% +it's a love story. That's that's true. + + + align:start position:0% +it's a love story. That's that's true. +Yeah. There's the ideal of romantic + + align:start position:0% +Yeah. There's the ideal of romantic + + + align:start position:0% +Yeah. There's the ideal of romantic +love, finding the right man. And when uh + + align:start position:0% +love, finding the right man. And when uh + + + align:start position:0% +love, finding the right man. And when uh +the man reacts eventually, it's because + + align:start position:0% +the man reacts eventually, it's because + + + align:start position:0% +the man reacts eventually, it's because +he is driven by them the ideal of + + align:start position:0% +he is driven by them the ideal of + + + align:start position:0% +he is driven by them the ideal of +finding the right woman. And both of + + align:start position:0% +finding the right woman. And both of + + + align:start position:0% +finding the right woman. And both of +them, but particularly her because she + + align:start position:0% +them, but particularly her because she + + + align:start position:0% +them, but particularly her because she +is the great heroine, uh, does so + + align:start position:0% +is the great heroine, uh, does so + + + align:start position:0% +is the great heroine, uh, does so +through methods that are extremely + + align:start position:0% +through methods that are extremely + + + align:start position:0% +through methods that are extremely +imaginative and show how imagination and + + align:start position:0% +imaginative and show how imagination and + + + align:start position:0% +imaginative and show how imagination and +idealization go together. I I would say + + align:start position:0% +idealization go together. I I would say + + + align:start position:0% +idealization go together. I I would say +that she's not idealizing. I mean there + + align:start position:0% +that she's not idealizing. I mean there + + + align:start position:0% +that she's not idealizing. I mean there +is an idealization of love that takes + + align:start position:0% +is an idealization of love that takes + + + align:start position:0% +is an idealization of love that takes +place in the movie but um much more much + + align:start position:0% +place in the movie but um much more much + + + align:start position:0% +place in the movie but um much more much +more um I I I she's not going after the + + align:start position:0% +more um I I I she's not going after the + + + align:start position:0% +more um I I I she's not going after the +love just because it's love as much as + + align:start position:0% +love just because it's love as much as + + + align:start position:0% +love just because it's love as much as +it's this is a person that she sees who + + align:start position:0% +it's this is a person that she sees who + + + align:start position:0% +it's this is a person that she sees who +has I mean they they their inner persons + + align:start position:0% +has I mean they they their inner persons + + + align:start position:0% +has I mean they they their inner persons +connect we'll talk about it again next + + align:start position:0% +connect we'll talk about it again next + + + align:start position:0% +connect we'll talk about it again next +time but I want to leave plenty of time + + align:start position:0% +time but I want to leave plenty of time + + + align:start position:0% +time but I want to leave plenty of time +for the movie so we don't have much um + + align:start position:0% +for the movie so we don't have much um + + + align:start position:0% +for the movie so we don't have much um +time left for the class. So, let me + + align:start position:0% +time left for the class. So, let me + + + align:start position:0% +time left for the class. So, let me +quickly go through the rest and make any + + align:start position:0% +quickly go through the rest and make any + + + align:start position:0% +quickly go through the rest and make any +comment along the way and I'll try to be + + align:start position:0% +comment along the way and I'll try to be + + + align:start position:0% +comment along the way and I'll try to be +uh silent if that's conceivable. Uh, + + align:start position:0% +uh silent if that's conceivable. Uh, + + + align:start position:0% +uh silent if that's conceivable. Uh, +Mika Rivera. + + align:start position:0% +Mika Rivera. + + + align:start position:0% +Mika Rivera. +Um, I guess anomaly, there's this one + + align:start position:0% +Um, I guess anomaly, there's this one + + + align:start position:0% +Um, I guess anomaly, there's this one +scene with the blind guy that like + + align:start position:0% +scene with the blind guy that like + + + align:start position:0% +scene with the blind guy that like +strikes me every time I see the movie. + + align:start position:0% +strikes me every time I see the movie. + + + align:start position:0% +strikes me every time I see the movie. +Like, I think that's like my favorite + + align:start position:0% +Like, I think that's like my favorite + + + align:start position:0% +Like, I think that's like my favorite +part. What about that scene? Um, she + + align:start position:0% +part. What about that scene? Um, she + + + align:start position:0% +part. What about that scene? Um, she +pretty much I think she acts as his + + align:start position:0% +pretty much I think she acts as his + + + align:start position:0% +pretty much I think she acts as his +imagination. Like she's kind of like a + + align:start position:0% +imagination. Like she's kind of like a + + + align:start position:0% +imagination. Like she's kind of like a +guide. Everything's fastpaced colorful. + + align:start position:0% +guide. Everything's fastpaced colorful. + + + align:start position:0% +guide. Everything's fastpaced colorful. +But that's just one aspect because she's + + align:start position:0% +But that's just one aspect because she's + + + align:start position:0% +But that's just one aspect because she's +doing that all the time, right? She's + + align:start position:0% +doing that all the time, right? She's + + + align:start position:0% +doing that all the time, right? She's +doing that all the time. But that that + + align:start position:0% +doing that all the time. But that that + + + align:start position:0% +doing that all the time. But that that +scene in particular strikes me because + + align:start position:0% +scene in particular strikes me because + + + align:start position:0% +scene in particular strikes me because +I've had discussions with friends about + + align:start position:0% +I've had discussions with friends about + + + align:start position:0% +I've had discussions with friends about +like blind people and how do they have + + align:start position:0% +like blind people and how do they have + + + align:start position:0% +like blind people and how do they have +dreams or + + align:start position:0% +dreams or + + + align:start position:0% +dreams or +not? What do they say? Well, that will + + align:start position:0% +not? What do they say? Well, that will + + + align:start position:0% +not? What do they say? Well, that will +be later. Uh Lauren, um + + align:start position:0% +be later. Uh Lauren, um + + + align:start position:0% +be later. Uh Lauren, um +no, you don't have to say anything + + align:start position:0% +no, you don't have to say anything + + + align:start position:0% +no, you don't have to say anything +about Ali. What about the uh the + + align:start position:0% +about Ali. What about the uh the + + + align:start position:0% +about Ali. What about the uh the +chapters or reality transformed or the + + align:start position:0% +chapters or reality transformed or the + + + align:start position:0% +chapters or reality transformed or the +lady Eve? I guess something from the + + align:start position:0% +lady Eve? I guess something from the + + + align:start position:0% +lady Eve? I guess something from the +Lady Eve that's I've been thinking about + + align:start position:0% +Lady Eve that's I've been thinking about + + + align:start position:0% +Lady Eve that's I've been thinking about +a lot is I really like the character of + + align:start position:0% +a lot is I really like the character of + + + align:start position:0% +a lot is I really like the character of +the Eve and Jean. I really liked your + + align:start position:0% +the Eve and Jean. I really liked your + + + align:start position:0% +the Eve and Jean. I really liked your +character, but it just seemed I didn't + + align:start position:0% +character, but it just seemed I didn't + + + align:start position:0% +character, but it just seemed I didn't +like the end at all because it seemed + + align:start position:0% +like the end at all because it seemed + + + align:start position:0% +like the end at all because it seemed +like she was such a strong character and + + align:start position:0% +like she was such a strong character and + + + align:start position:0% +like she was such a strong character and +in the end she kind of almost sells out + + align:start position:0% +in the end she kind of almost sells out + + + align:start position:0% +in the end she kind of almost sells out +because Charles was he was the one that + + align:start position:0% +because Charles was he was the one that + + + align:start position:0% +because Charles was he was the one that +wasn't able to like understand her when + + align:start position:0% +wasn't able to like understand her when + + + align:start position:0% +wasn't able to like understand her when +she said that she had been with all + + align:start position:0% +she said that she had been with all + + + align:start position:0% +she said that she had been with all +these other men and he was the one who + + align:start position:0% +these other men and he was the one who + + + align:start position:0% +these other men and he was the one who +like freaked out and it just and then + + align:start position:0% +like freaked out and it just and then + + + align:start position:0% +like freaked out and it just and then +she was the one who basically let her + + align:start position:0% +she was the one who basically let her + + + align:start position:0% +she was the one who basically let her +back led him back and took him back and + + align:start position:0% +back led him back and took him back and + + + align:start position:0% +back led him back and took him back and +like it just well and you're right it's + + align:start position:0% +like it just well and you're right it's + + + align:start position:0% +like it just well and you're right it's +a it's + + align:start position:0% +a it's + + + align:start position:0% +a it's +kind of feminist movie. I mean, it's not + + align:start position:0% +kind of feminist movie. I mean, it's not + + + align:start position:0% +kind of feminist movie. I mean, it's not +only one of the greatest performances on + + align:start position:0% +only one of the greatest performances on + + + align:start position:0% +only one of the greatest performances on +film by Barbara Sandwick, who's a great + + align:start position:0% +film by Barbara Sandwick, who's a great + + + align:start position:0% +film by Barbara Sandwick, who's a great +movie actress, but also it's one in + + align:start position:0% +movie actress, but also it's one in + + + align:start position:0% +movie actress, but also it's one in +which the woman is the real center. It's + + align:start position:0% +which the woman is the real center. It's + + + align:start position:0% +which the woman is the real center. It's +about her. It's about the Lady Eve. It's + + align:start position:0% +about her. It's about the Lady Eve. It's + + + align:start position:0% +about her. It's about the Lady Eve. It's +not about Adam except in relation to + + align:start position:0% +not about Adam except in relation to + + + align:start position:0% +not about Adam except in relation to +Eve. Yeah. So, you're right about that. + + align:start position:0% +Eve. Yeah. So, you're right about that. + + + align:start position:0% +Eve. Yeah. So, you're right about that. +U let me go on. We can come back to any + + align:start position:0% +U let me go on. We can come back to any + + + align:start position:0% +U let me go on. We can come back to any +of these. Now, Katherine Chang is not + + align:start position:0% +of these. Now, Katherine Chang is not + + + align:start position:0% +of these. Now, Katherine Chang is not +here. + + align:start position:0% + + + + align:start position:0% + +Um, have we have I called every we is + + align:start position:0% +Um, have we have I called every we is + + + align:start position:0% +Um, have we have I called every we is +everybody told? All right. Um, about now + + align:start position:0% +everybody told? All right. Um, about now + + + align:start position:0% +everybody told? All right. Um, about now +we ought to stop, but I do want to give + + align:start position:0% +we ought to stop, but I do want to give + + + align:start position:0% +we ought to stop, but I do want to give +anybody a chance to say anything. + + align:start position:0% +anybody a chance to say anything. + + + align:start position:0% +anybody a chance to say anything. +Remember, every week you can catch up + + align:start position:0% +Remember, every week you can catch up + + + align:start position:0% +Remember, every week you can catch up +and say things that you didn't have time + + align:start position:0% +and say things that you didn't have time + + + align:start position:0% +and say things that you didn't have time +for before. Um, so let's go off to a le \ No newline at end of file diff --git a/rzg_CavQI_M.txt b/rzg_CavQI_M.txt new file mode 100644 index 0000000000000000000000000000000000000000..9baa7e8f6c0aedf2af8497ccde14af6dc85087f2 --- /dev/null +++ b/rzg_CavQI_M.txt @@ -0,0 +1,943 @@ +Hi. + +In this problem, we'll be +talking about communication + +across a noisy channel. + +But before we dive into the +problem itself, I wanted to + +first motivate the context a +little bit and talk more about + +what exactly a communication +channel is and + +what "noise" means. + +So in our everyday life, +we deal with a lot of + +communication channels, for +example, the internet, where + +we download data and we watch +videos online, or even just + +talking to a friend. + +And the air could be +your communication + +channel for our voice. + +But as you probably have +experienced, sometimes these + +channels have noise, which +just means that what the + +sender was trying to send isn't +necessarily exactly what + +the receiver receives. + +And so in probability, we try +to model these communication + +channels and noise and +try to understand the + +probability behind it. + +And so now, let's go into +the problem itself. + +In this problem, we're dealing +with a pretty simple + +communication channel. + +It's just a binary channel, +which means that what we're + +sending is just one +bit at a time. + +And here, a bit just means +either 0 or 1-- + +so essentially, the simplest +case of information that you + +could send. + +But sometimes when you send +a 0, the receiver actually + +receives a 1 instead, +or vice versa. + +And that is where +noise comes in. + +So here in this problem, we +actually have a probabilistic + +model of this channel and the +noise that hits the channel. + + + +What we're trying to send +is either 0 or a 1. + + + +And what we know is that on +the receiving end, a 0 can + +either be received when a 0 is +sent, or a 1 can be received + +when a 0 is sent. + +And when a 1 is sent, we +could also have noise + +that corrupts it. + +And you get a 0 instead. + +Or you can have a 1 being +successfully transmitted. + +And the problem actually +tells us what the + +probabilities here are. + +So we know that if a 0 is sent, +then with probability 1 + +minus epsilon naught, +a 0 is received. + +And with the remaining +probability, it actually gets + +corrupted and turned into a 1. + +And similarly, if a 1 is sent, +then with probability 1 minus + +epsilon 1, the 1 is correctly +transmitted. + +And with the remaining +probability epsilon 1, it's + +turned into a 0 instead. + +And the last bit of information +is that we know + +that with the probability p, any +random bit is actually is + +0 that is being sent. + +And with probability 1 minus +p, we're actually + +trying to send a 1. + +So that is the basic setup +for the problem. + +And the first part that the +problem asks us to find, what + +is the probability of a +successful transmission when + +you have just any arbitrary +bit that's being sent. + +So what we can do here is, use +this tree that we've already + +drawn and identify what are the +cases, the outcomes where + +a bit is actually successfully +transmitted. + +So if a 0 is sent and a 0 +is received, then that + +corresponds to a successful +transmission. + +Similarly, if a 1 is sent and +a 1 is received, that also + +corresponds to a successful +transmission. + +And then we can calculate what +these probabilities are, + +because we just calculate the + +probabilities along the branches. + +And so here implicitly, what +we're doing is invoking the + +multiplication rule. + +So we can calculate the +probabilities of these two + +individual outcomes and their +disjoint outcomes. + +So we can actually just sum the +two probabilities to find + +the answer. + +So the probability here is p +times 1 minus epsilon naught-- + +that's the probability of +a 0 being successfully + +transmitted-- + +plus 1 minus p times 1 minus +epsilon, 1, which is the + +probability that a 1 is +successfully transmitted. + +And so what we've done here is +actually just looked at this + +kind of diagram, this tree +to find the answer. + +What we also could have done +is been a little bit more + +methodical maybe and actually +apply the law of total + +probability, which is really +what we're trying to do here. + +So you can see that this +actually corresponds to-- + +the p corresponds to the +probability of 0 being sent. + +And 1 minus epsilon naught is +the probability of success, + +given that a 0 is sent. + +And this second term +is analogous. + +It's the probability that a 1 +was sent times the probability + +that you have a success, given +that a 1 was sent. + +And this is just an example of +applying the law of total + +probability, where we +partitioned into the two cases + +of a 0 being sent and a 1 being +sent and calculated the + +probabilities for each +of those two cases + +and added those up. + +So that's kind of a review of +the multiplication rule and + +law of total probability. + + + +So now, let's move on to part +B. Part B is asking, what is + +the probability that a +particular sequence of bits, + +not just a single one, but a +sequence of four bits in a row + +is successfully transmitted? + +And the sequence that we're +looking for is, 1, 0, 1, 1. + + + +So this is how I'll +denote this event. + +1, 0, 1, 1 gets successfully +transmitted into 1, 0, 1, 1. + + + +Now, instead of dealing with +single bits in isolation, we + +have a sequence of four bits. + +But we can really just break +this out into the four + +individual bits and look +at those one by one. + +So in order to transmit +successfully 1, 0, 1, 1, that + +whole sequence, we first need to +transmit a 1 successfully, + +then a 0 successfully, then +another 1 successfully, and + +then finally, the last +1 successfully. + +So really, this is the same as +the intersection of four + +different smaller events, a 1 +being successfully transmitted + +and a 0 being successfully +transmitted and two more 1's + +being successfully +transmitted. + + + +So why are we able to do +this, first of all? + +We are using an important +assumption that we make in the + +problem that each transmission +of an individual bit has the + +same probabilistic structure +so that no matter which bit + +you're talking about, they all +have the same [? error ?] + +probability, the same +probabilities of being either + +successfully transmitted or +having noise corrupt it. + +So because of that, it doesn't +really matter which particular + +1 or 0 we're talking about. + +And now, we'll make one more +step, and we'll invoke + +independence, which is +the third topic here. + +And the other important +assumption here we're making + +is that every single +bit is independent + +from any other bit. + +So the fact that this one was +successfully transmitted has + +no impact on the probability +of the 0 being successfully + +transmitted or not. + +And so because of that, we can +now break this down into a + +product of four probabilities. + +So this becomes the probability +of 1 transmitted + +into a 1 times the probability +of 0 transmitted into a 0, 1 + +to a 1, and 1 to 1. + + + +And that simplifies things, +because we know what each one + +of these are. + +The probability of 1 being +successful transmitted into a + +1, we know that's just +1 minus epsilon 1. + +And similarly, probability of +0 being transmitted into a 0 + +is 1 minus epsilon naught. + +So our final answer +then is just-- + +well, we have three of these +and one of these. + +So the answer is going to be 1 +minus epsilon naught times 1 + +minus epsilon 1 to +the third power. + + + +Now, let's move on go on to +part C, which adds another + +wrinkle to the problem. + +So now, maybe we're not +satisfied with the success + +rate of our current channel. + +And we want to improve +it somehow. + +And one way of doing this is +to add some redundancy. + +So instead of just sending a +single 0 and hoping that it + +gets successfully transmitted, +instead what we can do is, + +send three 0's in a row to +represent a single 0 and hope + +that because we've added some +redundancy, we can somehow + +improve our error rates. + +So in particular what we're +going to do is, for a 0, when + +we want to send a 0, which I'll +put in quotes here, what + +we're actually going to send +is a sequence of three 0s. + +And what's going to happen is, +this sequence of three 0s, + +each one of these bits +is going to go + +through the same channel. + +So the 0, 0, 0 can stay and get +transmitted successfully + +as a 0, 0, 0. + +Or maybe the last 0 gets turned +into a 1, or the second + +0 gets turned into a 1, or we +can have any one of these + +eight possible outcomes +on the receiving end. + + + +And then similarly, for a 1, +when we want to send a 1, what + +we'll actually send +is a sequence of + +three 1's, three bits. + +And just like above, this 1, 1, +1, due to the noise in the + +channel, it can get turned into +any one of these eight + +sequences on the +receiving end. + + + +So what we're going to do now +is, instead of sending just a + +single 0, we'll send three 0s, +and instead of sending a 1, + +we'll send three 1s. + +But now, the question is, this +is what you'll get on the + +receiving end. + +How do you interpret-- + +0, 0, 0, maybe intuitively +you'll say + +that's obviously a 0. + +But what if you get something +like 0, 1, 0 or 1, 0, 1, when + +there's both 0s and 1s in +the received message? + +What are you going to do? + +So one obvious thing to do is +to take a majority rule. + +So because there's three of +them, if there's two or more + +0s, we'll say that what +was meant to be sent + +was actually a 0. + +And if there's two or more 1s, +then we'll interpret that as a + +1 being sent. + +So in this case, let's look +at the case of 0. + +The majority rule here would say +that, well, if 0, 0, 0 was + +sent, then the majority is 0s. + +And similarly, in these two +cases, 0, 0, 1 or 0, 1, 0, the + +majority is also 0s. + +And then finally, in this last +case, 1, 0, 0, you get a + +majority of 0s. + +So in these four received +messages, we'll interpret that + +as a 0 have being set. + +So part C is asking, given this +majority rule and this + +redundancy, what is the +probability that a 0 is + +correctly transmitted? + +Well, to answer that, we've +already identified these are + +the four outcomes, where +a 0 would be correctly + +transmitted. + +So to find the answer to this +question, all we have to do is + +find the probability that a +sequence of 0, 0, 0 gets + +turned into one of these +four sequences. + +So let's do that. + +What is the probability that +a 0, 0, 0 gets turned + +into a 0, 0, 0? + +Well, that means that +all three of + +these 0s had no errors. + +So we would have the answer +being 1 minus epsilon 0 cubed, + +because all three of these +bits had to have been + +successfully transmitted. + +Now, let's consider +the other ones. + +For example, what's the +probability that a 0, 0, 0 + +gets turned into a 0, 0, 1? + +Well, in this case, we need two +successful transmissions + +of 0s, plus one transmission +of 0 that had an error. + +So that is going to be 1 minus +epsilon naught squared for the + +two successful transmissions of +0, times epsilon naught for + +the single one that was wrong. + +And if you think about it, that +was only for this case-- + +0, 0, 1. + +But the case where 0, 1, 0 and +1, 0, 0 are the same, because + +for all three of these, you +have two successful + +transmissions of 0, plus one +that was corrupted with noise. + +And so it turns out that all +three of those probabilities + +are going to be the same. + +So this is our final answer +for this part. + + + +Now, let's move on to part D. +Part D is asking now a type of + +inference problem. + +And we'll talk more +about inference + +later on in this course. + +The purpose of this problem-- + +what it's asking is, suppose +you received a 1, 0, 1. + +That's the sequence of +three messages, three + +bits that you received. + +Given that you received a 1, 0, +1, what's the probability + +that 0 was actually the thing +that was being sent. + + + +So if you look at this, you'll +look at it and say, this looks + +like something where we +can apply Bayes' rule. + +So that's the fourth +thing that we're + +covering in this problem. + +And if you apply Bayes' rule, +what you'll get is, this is + +equal to the probability of 0 +times the probability of 1, 0, + +1 being received, given that 0 +was what was sent, divided by + +the probability that 1, +0, 1 is received. + +So we have this basic +structure. + +And we also know that we can +use the law of total + +probability again on +this denominator. + +So we know that the probability +that 1, 0, 1 is + +received is equal to the +probability of 0 being sent + +times probability of 1, 0, 1 +being received, given that 0 + +was sent, plus the probability +that 1 was sent times the + +probability that 1, +0, 1 is received, + +given that 1 is sent. + +And as you'll notice in +applications of Bayes' rule, + +usually what you'll have is a +numerator is then repeated as + +one of the terms in the +denominator, because it's just + +an application of total +probability. + +So if you put these pieces +together, really, what we need + +is just these four terms. + +Once we have those four terms, +we can just plug them into + +this equation, and we'll +have our answer. + +So let's figure out what +those four terms are. + +The probability of 0 +being sent-- well, + +we said that earlier. + +Probability of 0 being +sent is just p. + +And the probability of 1 being +sent is 1 minus p. + +That's just from the +model that we're + +given in the problem. + +Now, let's figure +out this part. + +What is the probability of a 1, +0, 1 being received, given + +that 0 was sent? + +So if 0 was sent, then we know +that what really was sent was + +0, 0, 0, that sequence +of three bits. + +And now, what's the probability +that 0, 0, 0 got + +turned into 1, 0, 1? + +Wall, in this case, what we +have is one successful + +transmission of a 0, plus two +failed transmission of a 0. + +So that one successful +transmission of a 0, that + +probability is 1 minus +epsilon naught. + +And now, we have two failed +transmissions of a 0. + +So we have to multiply that +by epsilon naught squared. + +And now, for the last piece, +what's the probability of + +receiving the 1, 0, 1, given +that 1 was actually sent? + +Well, in that case, if a 1 was +sent, what was really sent was + +a sequence of three 1s. + +And now, we want the probability +that a 1, 1, 1 got + +turned into a 1, 0, 1. + +In this case, we have two +successful transmissions of + +the 1 with one failed +transmission. + +So the two successful +transmissions will have 1 + +minus epsilon 1 squared. + +And then the one failed +transmission will give us an + +extra term of epsilon 1. + +So just for completeness, let's +actually write out what + +this final answer would be. + +So probability of 0 is p. + +Probability of 1, 0, 1, given 0 +is, we calculated that as 1 + +minus epsilon naught times +epsilon naught squared. + +The same term appears again +in the denominator. + + + +Plus the other term is, +probability of 1 times the + +probability of 1, +0, 1, given 1. + +So that is 1 minus epsilon +squared times epsilon 1. + +So that is our final answer. + +And it's really just a +application of Bayes' rule. + +So this was a nice problem, +because it represents a real + +world phenomenon that happens. + +And we can see that you can +apply a pretty simple + +probabilistic model to it and +still be able to answer some + +interesting questions. + +And there are other extensions +that you can ask also. + +For example, we've talked about +adding redundancy by + +tripling the number of bits, +but tripling the number of + +bits also reduces the +throughputs, because instead + +of sending one, you have +to send three bits + +just to send one. + +So if there's a cost of that, at +what point does the benefit + +of having lower ever outweigh +the cost of having to send + +more things? + +And so that's a question that +you can answer with some more + +tools in probability. + +So we hope you enjoyed +this problem. + +And we'll see you +again next time. \ No newline at end of file diff --git a/s31hXhmhUws.txt b/s31hXhmhUws.txt new file mode 100644 index 0000000000000000000000000000000000000000..0a5939f9743b051d53288432fb44f25c9914cb0b --- /dev/null +++ b/s31hXhmhUws.txt @@ -0,0 +1,642 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: The artists tonight-- +this afternoon-- are of course, + +we'll start off with +Phil Scarff, Natraj, + +who plays all these +saxes in front of us. + +Phil is a stalwart of this area +who plays in jazz ensembles + +and also tours India with his +gifts as an Indian musician, + +and has just come back from +India, as a matter of fact. + +And his CD-- his Indian CD-- +is up on the table there. + +Mike Rivard, you +probably know Mike + +from several different +ensembles, especially + +Club d'Elf. + +He's playing bass. + +Jerry Leake, white pants +over there, plays tabla + +and he also plays the +various hand percussion. + +He is a member of the Cubist +Ensemble as well as Natraj. + +Bertrand Lehman +plays the trap sets + +and other percussion +over in the corner. + +They're going to open +the program today, + +but Ravikiranji-- Sangeet +[? Samrat ?] Chitravina N + +Ravikiran, to be +more exact-- is going + +to join them on the second item. + +And I hope you'll give him round +of applause when he appears. + +The program today will be in +two parts, roughly an hour long + +each, with a very short +intermission between, + +which will give you a chance +to go and look at the many CDs + +that the artists have +brought from all phases + +of their careers. + +So without further ado, Natraj. + +[APPLAUSE] + +[MUSIC - NATRAJ, "AVA DE SE"] + +[APPLAUSE] + +PHIL SCARFF: Thank +you very much. + +And we opened our +program this afternoon + +with a traditional +West African piece + +called "Ava De Se" from +the southern Ghanaian + +tradition of the Ewe people. + +Once again, Jerry Leake. + +On that piece he was +playing [INAUDIBLE]. + +Let's hear it for Jerry Leake. + +[APPLAUSE] + +PHIL SCARFF: And on drums and +percussion, Bertram Lehman. + +[APPLAUSE] + +PHIL SCARFF: And on +string bass Mike Rivard. + +[APPLAUSE] + +PHIL SCARFF: And I'm Phil +Scarff on saxophones. + +Thank you. + +Now we'd like to +welcome to the stage + +our special guest for this +evening's program, Sangeet + +[? Samrat ?] +Chitravina N Ravikiran. + +[APPLAUSE] + +PHIL SCARFF: So we're +going to continue + +with an original +composition by Ravikiran. + +This is a piece called +"River," and it's + +based on the Carnatic +rag [? Saraswati. ?] + +[MUSIC - NATRAJ, "RIVER"] + +[APPLAUSE] + +PHIL SCARFF: Thank +you very much. + +Once again, that was +the composition "River" + +by Ravikiran, arranged +by both Ravikiran + +and me for this program. + +And next we'd like to move +to a different tradition, + +and we're going to move +to the jazz tradition-- + +contemporary jazz +tradition-- and play + +a piece by the great saxophonist +and composer Ornette Coleman. + +And this is his classic piece +"Lonely Woman," which was first + +released on-- I believe-- Shape +of Jazz to Come back in 1959, + +I think. + +And so we thought we'd give this +a little different treatment + +today. + +This is Ornette +Coleman's "Lonely Woman." + +[MUSIC - NATRAJ, "LONELY WOMAN"] + +[APPLAUSE] + +RAVIKIRAN: Good afternoon. + +And I'd like to introduce +the next composition. + +It's titled "Red Swan." + +It's actually based on a +traditional composition + +of Carnatic music, and based +on a very popular mode of raga + +called Hamsandani, which is +well known in both North Indian + +and South Indian +classical music, + +but the composition has +been set for arrangement + +with this group, +Natraj, [INAUDIBLE] + +It's a great pleasure +for me to play with each + +and every one of +my friends here, + +and to play at MIT for MITHAS. + +So this is going +to be "Red Swan." + +[MUSIC - NATRAJ, "RED SWAN"] + +JERRY LEAKE: +[SINGING IN FOREIGN LANGUAGE] + +[MUSIC - NATRAJ, "RED SWAN" + CONTINUES] + +[APPLAUSE] + +PHIL SCARFF: Kiran, +thank you very much. + +Thank you. + +That was "Red Swan," +recomposed, decomposed, + +by Chitravina Ravikiran, +arranged by Ravikiran + +and me for this performance. + +Thank you very much. + +So you've been listening +to Bertam Lehmann + +on drums and percussion. + +Let's hear it for Bertram. + +[APPLAUSE] + +PHIL SCARFF: Jerry Leake, +tabla and multi-percussion. + +Jerry Leake. + +[APPLAUSE] + +PHIL SCARFF: Mike +Rivard on string bass. + +Mike Rivard. + +[APPLAUSE] + +PHIL SCARFF: And of +course our special guest + +for this performance, on +chitravina we have Sangeet + +[? Samrat ?] +Chitravina N Ravikiran. + +[APPLAUSE] + +PHIL SCARFF: And I'm Phil +Scarff on saxophones. + +Thank you. + +[APPLAUSE] + +PHIL SCARFF: And of +course we are Natraj. + +Thank you for coming out. + +We are going to take +a short intermission. + +And we're going to +begin our second set + +with a piece from West Africa. + +This is from the Dagomba +people of northern Ghana, + +as distinct from the Ewe +people of southern Ghana. + +The opening piece was a West +African piece, "Awa De Se." + +That is from the Ewe people of +southern Ghana and also Togo. + +And this is from the Dagomba +tradition of northern Ghana, + +and it's based on the-- I would +call it the-- rhythm called + +Damba [? So ?] [? Chandi, ?] +and there are two compositions. + +One is called "Wolenboli" and +the other one is "Bandanya." + +[MUSIC - NATRAJ, + "WOLENBOLI/BANDANYA"] + +[APPLAUSE] + +PHIL SCARFF: Thank +you very much. + +Thank you very much. + +That was Damba So Chandi, +"Wolenboli" and "Bandanya." + +Turn it over to Ravikiran. + +RAVIKIRAN: I've been requested +to play a short solo piece. + +This is going to be +a composition which + +I'll be playing on the +tabla, just me and the tabla. + +So it's going to be a +composition in seven beats, + +a time cycle of seven +counts known as [INAUDIBLE]. + +The composer of this is +a traditional composer + +in Carnatic music, +Shyama Shastri, + +who lived between 1762 and 1827. + +And the raga is ananda bhairavi. + +It is somewhat +like a minor scale. + +[MUSIC PLAYING] + +RAVIKIRAN: I would like +more of this and less + +of the [INAUDIBLE], please. + +[TUNING INSTRUMENT] + +[MUSIC - RAVIKIRAN, "MARIVERE + GATI"] + +RAVIKIRAN: Can you please +reduce the high ends somewhat? + +It's like-- + +[MUSIC - RAVIKIRAN, "MARIVERE + GATI" CONTINUES] + +[APPLAUSE] + +PHIL SCARFF: Next +we'd like to play + +another original +composition by Ravikiran. + +This one is called +"No Nonsense Fives," + +and it's in rag janaranjani. + +RAVIKIRAN: This +piece was actually + +born out of the-- +against the background + +that all my other pieces in five +had so much nonsense before it. + +So I thought, OK, at least +let me attempt something + +with no nonsense in fives. + +The concept behind some of these +compositions-- some of these + +are actually arranged for +Western classical symphony + +orchestras as well. + +We have a different arrangement +for the jazz groups like this. + +Some of them are even arranged +for quartets or quintets + +and chamber orchestras. + +The concept of this is +melharmony Basically, + +melharmony is harmony +with an emphasis + +on the melodic rules of +evolved melodic systems. + +For instance, the +Indian raga system + +is a very highly evolved +melodic system of music. + +So we do create harmony in +this-- you will actually + +notice it more when we +have symphonic arrangements + +presented by orchestras-- +but in this kind of thing + +you'll probably be able +to see some glimpses + +of meloharmonic principles. + +And in this we are +just going to start off + +with a very short +prelude by me, and then + +follow it by the composition. + +[MUSIC PLAYING] + +[MUSIC - NATRAJ, "NO NONSENSE + FIVES"] + +[APPLAUSE] + +[TUNING INSTRUMENTS] + +PHIL SCARFF: OK. + +Thank you very much. + +That last piece was, +again, "No Nonsense Fives." + +We'd like to conclude +our concert this evening + +with a composition +by Purandara Dasa. + +And this one is in +rag sindhu bhairavi, + +and it's called +"Tamburi Meetidava." + +And we've arranged this +in such a way of-- we've + +set this to more of +a West African feel. + +"Tamburi Meetidava." + +RAVIKIRAN: Just for +information, Purandara Dasa + +lived from 1484 to 1564. + +Many of his compositions, +they are traditional tunes, + +but some of it has also +been tuned by other people + +because some of the +original have been lost. + +But he's hailed as the +father of Carnatic music. + +He's had a lot of +students' lessons as well. + +[MUSIC - NATRAJ, "TAMBURI + MEETIDAVA"] + +[APPLAUSE] + +PHIL SCARFF: Thank +you very much. + +Thank you. + +That was "Tamburi Meetidava." + +Thank you once again. + +And you've been listening +to Bertram Lehmann + +on drums and percussion. + +Let's hear it for Bertram +Lehmann over there on drums. + +[APPLAUSE] + +PHIL SCARFF: All right. + +Laying it down on tabla +and multi-percussion + +we have Jerry Leake. + +Jerry Leake. + +[APPLAUSE] + +PHIL SCARFF: And back +here on string bass + +we have Mr. Mike Rivard. + +Mike Rivard on string bass. + +[APPLAUSE] + +PHIL SCARFF: Yeah, Mike Rivard. + +And of course our special +guest of the evening, + +Sangeet [? Samrat ?] +Chitravina N Ravikiran. + +Let's hear it for Ravikiran. + +[APPLAUSE] + +PHIL SCARFF: And I'm Phil +Scarff on saxophones. + +Thank you. + +[APPLAUSE] + +PHIL SCARFF: Thank +you very much. + +And of course we are Natraj. + +Thank you so much for coming +out this evening to the concert + +and thanks so much for MITHAS +and also Art of the Improvisers + +and Mark Harvey for +organizing this program today. + +And we hope to see you again. + +Please check us out on +the web, natrajmusic.com, + +check ou our Facebook page +and like us on Facebook. + +Check out the recordings on the +way out and the mailing list, + +and we look forward to +seeing you next time. + +Thank you. + +Good night. \ No newline at end of file diff --git a/s7TtenBwlYg.txt b/s7TtenBwlYg.txt new file mode 100644 index 0000000000000000000000000000000000000000..97cfa2fd6f79696aae0481a25aea9e7862a24331 --- /dev/null +++ b/s7TtenBwlYg.txt @@ -0,0 +1,9475 @@ +align:start position:0% + +I didn't get any new topics that people + + align:start position:0% +I didn't get any new topics that people + + + align:start position:0% +I didn't get any new topics that people +wanted uh throughout the day so I'm + + align:start position:0% +wanted uh throughout the day so I'm + + + align:start position:0% +wanted uh throughout the day so I'm +going to go through some topics that + + align:start position:0% +going to go through some topics that + + + align:start position:0% +going to go through some topics that +people have uh T talk asked about + + align:start position:0% +people have uh T talk asked about + + + align:start position:0% +people have uh T talk asked about +earlier in this semester and um that I + + align:start position:0% +earlier in this semester and um that I + + + align:start position:0% +earlier in this semester and um that I +think are are kind of fun and so they're + + align:start position:0% +think are are kind of fun and so they're + + + align:start position:0% +think are are kind of fun and so they're +sort of the the most fun things that + + align:start position:0% +sort of the the most fun things that + + + align:start position:0% +sort of the the most fun things that +from my perspective maybe I have a six + + align:start position:0% +from my perspective maybe I have a six + + + align:start position:0% +from my perspective maybe I have a six +sense of fun uh that that we didn't + + align:start position:0% +sense of fun uh that that we didn't + + + align:start position:0% +sense of fun uh that that we didn't +fully cover so one of the first things I + + align:start position:0% +fully cover so one of the first things I + + + align:start position:0% +fully cover so one of the first things I +want to talk about is a cool little + + align:start position:0% +want to talk about is a cool little + + + align:start position:0% +want to talk about is a cool little +two-part um uh you what do you call this + + align:start position:0% +two-part um uh you what do you call this + + + align:start position:0% +two-part um uh you what do you call this +a fable a moral uh moral story um that + + align:start position:0% +a fable a moral uh moral story um that + + + align:start position:0% +a fable a moral uh moral story um that +has a little conclusion at the end and + + align:start position:0% +has a little conclusion at the end and + + + align:start position:0% +has a little conclusion at the end and +something called Gap fill I'm pretty + + align:start position:0% +something called Gap fill I'm pretty + + + align:start position:0% +something called Gap fill I'm pretty +sure I've talked about this a couple + + align:start position:0% +sure I've talked about this a couple + + + align:start position:0% +sure I've talked about this a couple +times in different places but I'm pretty + + align:start position:0% +times in different places but I'm pretty + + + align:start position:0% +times in different places but I'm pretty +sure I did not do this this semester did + + align:start position:0% +sure I did not do this this semester did + + + align:start position:0% +sure I did not do this this semester did +I no good good okay because there + + align:start position:0% +I no good good okay because there + + + align:start position:0% +I no good good okay because there +there's three points in the semester + + align:start position:0% +there's three points in the semester + + + align:start position:0% +there's three points in the semester +where this could have gone one is + + align:start position:0% +where this could have gone one is + + + align:start position:0% +where this could have gone one is +anytime we started talking about David + + align:start position:0% +anytime we started talking about David + + + align:start position:0% +anytime we started talking about David +Hon's work um and this is one of the + + align:start position:0% +Hon's work um and this is one of the + + + align:start position:0% +Hon's work um and this is one of the +very cool papers he's the second author + + align:start position:0% +very cool papers he's the second author + + + align:start position:0% +very cool papers he's the second author +Paul Von hipple a very uh very well + + align:start position:0% +Paul Von hipple a very uh very well + + + align:start position:0% +Paul Von hipple a very uh very well +established uh scholar and of Music + + align:start position:0% +established uh scholar and of Music + + + align:start position:0% +established uh scholar and of Music +perception and cognition um did this + + align:start position:0% +perception and cognition um did this + + + align:start position:0% +perception and cognition um did this +study in around fall 2000 published in + + align:start position:0% +study in around fall 2000 published in + + + align:start position:0% +study in around fall 2000 published in +Fall 2000 so it's about uh 25 year 25 + + align:start position:0% +Fall 2000 so it's about uh 25 year 25 + + + align:start position:0% +Fall 2000 so it's about uh 25 year 25 +years since they did this and it's a one + + align:start position:0% +years since they did this and it's a one + + + align:start position:0% +years since they did this and it's a one +of these really cool things that got me + + align:start position:0% +of these really cool things that got me + + + align:start position:0% +of these really cool things that got me +into this field U so when I heard about + + align:start position:0% +into this field U so when I heard about + + + align:start position:0% +into this field U so when I heard about +this I was like this is why I want to + + align:start position:0% +this I was like this is why I want to + + + align:start position:0% +this I was like this is why I want to +use computers to do things so um has + + align:start position:0% +use computers to do things so um has + + + align:start position:0% +use computers to do things so um has +anybody ever uh you all have some + + align:start position:0% +anybody ever uh you all have some + + + align:start position:0% +anybody ever uh you all have some +encounter with species Counterpoint + + align:start position:0% +encounter with species Counterpoint + + + align:start position:0% +encounter with species Counterpoint +because you did uh you read the um the + + align:start position:0% +because you did uh you read the um the + + + align:start position:0% +because you did uh you read the um the +David Luen article on an interesting + + align:start position:0% +David Luen article on an interesting + + + align:start position:0% +David Luen article on an interesting +Global rule for Counterpoint so it's + + align:start position:0% +Global rule for Counterpoint so it's + + + align:start position:0% +Global rule for Counterpoint so it's +dealing with sort of 16th century + + align:start position:0% +dealing with sort of 16th century + + + align:start position:0% +dealing with sort of 16th century +musical style and how we can recreate it + + align:start position:0% +musical style and how we can recreate it + + + align:start position:0% +musical style and how we can recreate it +and one of the rules that I was taught + + align:start position:0% +and one of the rules that I was taught + + + align:start position:0% +and one of the rules that I was taught +when I learned uh species Counterpoint + + align:start position:0% +when I learned uh species Counterpoint + + + align:start position:0% +when I learned uh species Counterpoint +is that if you take a big leap and you + + align:start position:0% +is that if you take a big leap and you + + + align:start position:0% +is that if you take a big leap and you +go up you've created a gap and the most + + align:start position:0% +go up you've created a gap and the most + + + align:start position:0% +go up you've created a gap and the most +natural thing for your musical line to + + align:start position:0% +natural thing for your musical line to + + + align:start position:0% +natural thing for your musical line to +do is to go down after that fill in the + + align:start position:0% +do is to go down after that fill in the + + + align:start position:0% +do is to go down after that fill in the +Gap Gap fill uh some people spell it as + + align:start position:0% +Gap Gap fill uh some people spell it as + + + align:start position:0% +Gap Gap fill uh some people spell it as +one word some hyphen some as space it + + align:start position:0% +one word some hyphen some as space it + + + align:start position:0% +one word some hyphen some as space it +doesn't I don't really care Gap fill + + align:start position:0% +doesn't I don't really care Gap fill + + + align:start position:0% +doesn't I don't really care Gap fill +similarly you leap down a lot and you + + align:start position:0% +similarly you leap down a lot and you + + + align:start position:0% +similarly you leap down a lot and you +should go + + align:start position:0% +should go + + + align:start position:0% +should go +up and um so I immediately looked at um + + align:start position:0% +up and um so I immediately looked at um + + + align:start position:0% +up and um so I immediately looked at um +a piece by Giovani palestrina uh one of + + align:start position:0% +a piece by Giovani palestrina uh one of + + + align:start position:0% +a piece by Giovani palestrina uh one of +the most important composers in this + + align:start position:0% +the most important composers in this + + + align:start position:0% +the most important composers in this +period that species Counterpoint is + + align:start position:0% +period that species Counterpoint is + + + align:start position:0% +period that species Counterpoint is +based on uh around 1550 1570 or so um + + align:start position:0% +based on uh around 1550 1570 or so um + + + align:start position:0% +based on uh around 1550 1570 or so um +this is part of one of his masses and um + + align:start position:0% +this is part of one of his masses and um + + + align:start position:0% +this is part of one of his masses and um +here's the score you see it but I've + + align:start position:0% +here's the score you see it but I've + + + align:start position:0% +here's the score you see it but I've +also kind of colored things in that uh + + align:start position:0% +also kind of colored things in that uh + + + align:start position:0% +also kind of colored things in that uh +green notes are upward leaps that need a + + align:start position:0% +green notes are upward leaps that need a + + + align:start position:0% +green notes are upward leaps that need a +downward um thing after it so um things + + align:start position:0% +downward um thing after it so um things + + + align:start position:0% +downward um thing after it so um things +and then the Blue Notes a downward leap + + align:start position:0% +and then the Blue Notes a downward leap + + + align:start position:0% +and then the Blue Notes a downward leap +that needs an upward motion and all + + align:start position:0% +that needs an upward motion and all + + + align:start position:0% +that needs an upward motion and all +around here it's all stepwise so it can + + align:start position:0% +around here it's all stepwise so it can + + + align:start position:0% +around here it's all stepwise so it can +go any direction it wants so if Gap fill + + align:start position:0% +go any direction it wants so if Gap fill + + + align:start position:0% +go any direction it wants so if Gap fill +exists then then uh and every time + + align:start position:0% +exists then then uh and every time + + + align:start position:0% +exists then then uh and every time +there's Gap fill fulfilled every time it + + align:start position:0% +there's Gap fill fulfilled every time it + + + align:start position:0% +there's Gap fill fulfilled every time it +works there's um a little uh pink or + + align:start position:0% +works there's um a little uh pink or + + + align:start position:0% +works there's um a little uh pink or +Peach Dot and every time it's not + + align:start position:0% +Peach Dot and every time it's not + + + align:start position:0% +Peach Dot and every time it's not +there's a big yellow Dot and you can see + + align:start position:0% +there's a big yellow Dot and you can see + + + align:start position:0% +there's a big yellow Dot and you can see +there are no yellow dots up there so + + align:start position:0% +there are no yellow dots up there so + + + align:start position:0% +there are no yellow dots up there so +this is what this sounds + + align:start position:0% +this is what this sounds + + + align:start position:0% +this is what this sounds +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +like do that one more time so you can + + align:start position:0% +like do that one more time so you can + + + align:start position:0% +like do that one more time so you can +hear it + + align:start position:0% +hear it + + + align:start position:0% +hear it +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +I just had to add the last note + + align:start position:0% +I just had to add the last note + + + align:start position:0% +I just had to add the last note +otherwise it'd be kind of out there um + + align:start position:0% +otherwise it'd be kind of out there um + + + align:start position:0% +otherwise it'd be kind of out there um +so Gap fill seems to be a thing + + align:start position:0% +so Gap fill seems to be a thing + + + align:start position:0% +so Gap fill seems to be a thing +composers do this but um the really cool + + align:start position:0% +composers do this but um the really cool + + + align:start position:0% +composers do this but um the really cool +thing that uh that hippo Von hippo and + + align:start position:0% +thing that uh that hippo Von hippo and + + + align:start position:0% +thing that uh that hippo Von hippo and +hiron did was that they realized that + + align:start position:0% +hiron did was that they realized that + + + align:start position:0% +hiron did was that they realized that +there's two things happening when you + + align:start position:0% +there's two things happening when you + + + align:start position:0% +there's two things happening when you +leap up a lot one is you've you've + + align:start position:0% +leap up a lot one is you've you've + + + align:start position:0% +leap up a lot one is you've you've +created a big leap right the other is + + align:start position:0% +created a big leap right the other is + + + align:start position:0% +created a big leap right the other is +that you're higher in your voice + + align:start position:0% +that you're higher in your voice + + + align:start position:0% +that you're higher in your voice +range so + + align:start position:0% +range so + + + align:start position:0% +range so +um if if I'm down here and I leap up and + + align:start position:0% +um if if I'm down here and I leap up and + + + align:start position:0% +um if if I'm down here and I leap up and +then I leap up then I Le up you guys are + + align:start position:0% +then I leap up then I Le up you guys are + + + align:start position:0% +then I leap up then I Le up you guys are +going to bet that eventually I'm going + + align:start position:0% +going to bet that eventually I'm going + + + align:start position:0% +going to bet that eventually I'm going +to come down right yeah uh you can't + + align:start position:0% +to come down right yeah uh you can't + + + align:start position:0% +to come down right yeah uh you can't +really go up forever and so what they + + align:start position:0% +really go up forever and so what they + + + align:start position:0% +really go up forever and so what they +were wondering is does it have to do the + + align:start position:0% +were wondering is does it have to do the + + + align:start position:0% +were wondering is does it have to do the +fact that eventually when you get really + + align:start position:0% +fact that eventually when you get really + + + align:start position:0% +fact that eventually when you get really +high the only place to go is down + + align:start position:0% +high the only place to go is down + + + align:start position:0% +high the only place to go is down +especially if you're talking about vocal + + align:start position:0% +especially if you're talking about vocal + + + align:start position:0% +especially if you're talking about vocal +music or well I mean even on a piano + + align:start position:0% +music or well I mean even on a piano + + + align:start position:0% +music or well I mean even on a piano +eventually you got to come down so they + + align:start position:0% +eventually you got to come down so they + + + align:start position:0% +eventually you got to come down so they +looked at um what the median what the + + align:start position:0% +looked at um what the median what the + + + align:start position:0% +looked at um what the median what the +average pitch across a whole piece was + + align:start position:0% +average pitch across a whole piece was + + + align:start position:0% +average pitch across a whole piece was +and marked it as specific and then + + align:start position:0% +and marked it as specific and then + + + align:start position:0% +and marked it as specific and then +thought that hey there's um there's four + + align:start position:0% +thought that hey there's um there's four + + + align:start position:0% +thought that hey there's um there's four +kinds of leaps and can't um there's ones + + align:start position:0% +kinds of leaps and can't um there's ones + + + align:start position:0% +kinds of leaps and can't um there's ones +that start at or above the median and go + + align:start position:0% +that start at or above the median and go + + + align:start position:0% +that start at or above the median and go +even higher that's when I was doing this + + align:start position:0% +even higher that's when I was doing this + + + align:start position:0% +even higher that's when I was doing this +and I yeah up there then there's ones + + align:start position:0% +and I yeah up there then there's ones + + + align:start position:0% +and I yeah up there then there's ones +that start below the median and go above + + align:start position:0% +that start below the median and go above + + + align:start position:0% +that start below the median and go above +it there's ones that start below and + + align:start position:0% +it there's ones that start below and + + + align:start position:0% +it there's ones that start below and +reach the median and then like I started + + align:start position:0% +reach the median and then like I started + + + align:start position:0% +reach the median and then like I started +the ones that start below and after they + + align:start position:0% +the ones that start below and after they + + + align:start position:0% +the ones that start below and after they +leap up they're still pretty low so + + align:start position:0% +leap up they're still pretty low so + + + align:start position:0% +leap up they're still pretty low so +there's still below the + + align:start position:0% +there's still below the + + + align:start position:0% +there's still below the +median and + + align:start position:0% +median and + + + align:start position:0% +median and +that there might be something besides + + align:start position:0% +that there might be something besides + + + align:start position:0% +that there might be something besides +Gap fill that explains things for + + align:start position:0% +Gap fill that explains things for + + + align:start position:0% +Gap fill that explains things for +instance let's say you bought two + + align:start position:0% +instance let's say you bought two + + + align:start position:0% +instance let's say you bought two +domestic continental US + + align:start position:0% +domestic continental US + + + align:start position:0% +domestic continental US +flights first you flow from San + + align:start position:0% +flights first you flow from San + + + align:start position:0% +flights first you flow from San +Francisco to New York City now you have + + align:start position:0% +Francisco to New York City now you have + + + align:start position:0% +Francisco to New York City now you have +another + + align:start position:0% +another + + + align:start position:0% +another +flight just take a guess uh you've gone + + align:start position:0% +flight just take a guess uh you've gone + + + align:start position:0% +flight just take a guess uh you've gone +from well instead of up and down we'll + + align:start position:0% +from well instead of up and down we'll + + + align:start position:0% +from well instead of up and down we'll +say west east you've gone from west to a + + align:start position:0% +say west east you've gone from west to a + + + align:start position:0% +say west east you've gone from west to a +big thing on the East and now you board + + align:start position:0% +big thing on the East and now you board + + + align:start position:0% +big thing on the East and now you board +let's say a random flight after this + + align:start position:0% +let's say a random flight after this + + + align:start position:0% +let's say a random flight after this +it's it's pre 911 you could just board + + align:start position:0% +it's it's pre 911 you could just board + + + align:start position:0% +it's it's pre 911 you could just board +random flights you all don't remember + + align:start position:0% +random flights you all don't remember + + + align:start position:0% +random flights you all don't remember +that World um + + align:start position:0% +that World um + + + align:start position:0% +that World um +so what do you which direction do you + + align:start position:0% +so what do you which direction do you + + + align:start position:0% +so what do you which direction do you +think you're likely to go you you're not + + align:start position:0% +think you're likely to go you you're not + + + align:start position:0% +think you're likely to go you you're not +in the international section west or + + align:start position:0% +in the international section west or + + + align:start position:0% +in the international section west or +east west west why because there's so + + align:start position:0% +east west west why because there's so + + + align:start position:0% +east west west why because there's so +many more options of going west from New + + align:start position:0% +many more options of going west from New + + + align:start position:0% +many more options of going west from New +York than there are from um + + align:start position:0% +York than there are from um + + + align:start position:0% +York than there are from um +yeah then there are East I guess we + + align:start position:0% +yeah then there are East I guess we + + + align:start position:0% +yeah then there are East I guess we +that's that's a little too far for + + align:start position:0% +that's that's a little too far for + + + align:start position:0% +that's that's a little too far for +Portland I mean but yeah you can kind of + + align:start position:0% +Portland I mean but yeah you can kind of + + + align:start position:0% +Portland I mean but yeah you can kind of +get the picture um and so if + + align:start position:0% +get the picture um and so if + + + align:start position:0% +get the picture um and so if +you're if you're already above the + + align:start position:0% +you're if you're already above the + + + align:start position:0% +you're if you're already above the +median you have a lot more choices going + + align:start position:0% +median you have a lot more choices going + + + align:start position:0% +median you have a lot more choices going +down than up and what they + + align:start position:0% +down than up and what they + + + align:start position:0% +down than up and what they +predicted was that um a lot of these + + align:start position:0% +predicted was that um a lot of these + + + align:start position:0% +predicted was that um a lot of these +things would happen even by chance that + + align:start position:0% +things would happen even by chance that + + + align:start position:0% +things would happen even by chance that +if you went um if you you jumped up up + + align:start position:0% +if you went um if you you jumped up up + + + align:start position:0% +if you went um if you you jumped up up +above from a normal note and and you big + + align:start position:0% +above from a normal note and and you big + + + align:start position:0% +above from a normal note and and you big +do a big J Jump Up you're probably above + + align:start position:0% +do a big J Jump Up you're probably above + + + align:start position:0% +do a big J Jump Up you're probably above +the median and you're going to Gap fill + + align:start position:0% +the median and you're going to Gap fill + + + align:start position:0% +the median and you're going to Gap fill +just by the concept of regression to the + + align:start position:0% +just by the concept of regression to the + + + align:start position:0% +just by the concept of regression to the +mean and so I went and um took that + + align:start position:0% +mean and so I went and um took that + + + align:start position:0% +mean and so I went and um took that +exact same piece from uh pal I guess + + align:start position:0% +exact same piece from uh pal I guess + + + align:start position:0% +exact same piece from uh pal I guess +I've been doing the same thing I did + + align:start position:0% +I've been doing the same thing I did + + + align:start position:0% +I've been doing the same thing I did +with a bcde e f for a long time of just + + align:start position:0% +with a bcde e f for a long time of just + + + align:start position:0% +with a bcde e f for a long time of just +taking pieces and scrambling them + + align:start position:0% +taking pieces and scrambling them + + + align:start position:0% +taking pieces and scrambling them +remember when we were doing the + + align:start position:0% +remember when we were doing the + + + align:start position:0% +remember when we were doing the +similarity one I just scrambled all the + + align:start position:0% +similarity one I just scrambled all the + + + align:start position:0% +similarity one I just scrambled all the +notes so here's the exact same Melody + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +scrambled and again everything that that + + align:start position:0% +scrambled and again everything that that + + + align:start position:0% +scrambled and again everything that that +demands by the theory of Gap fill Motion + + align:start position:0% +demands by the theory of Gap fill Motion + + + align:start position:0% +demands by the theory of Gap fill Motion +in the opposite direction than where it + + align:start position:0% +in the opposite direction than where it + + + align:start position:0% +in the opposite direction than where it +just came I've marked um with a green or + + align:start position:0% +just came I've marked um with a green or + + + align:start position:0% +just came I've marked um with a green or +blue and I've marked with peach when it + + align:start position:0% +blue and I've marked with peach when it + + + align:start position:0% +blue and I've marked with peach when it +works I've marked with a big yellow dot + + align:start position:0% +works I've marked with a big yellow dot + + + align:start position:0% +works I've marked with a big yellow dot +when it doesn't and in this scrambled + + align:start position:0% +when it doesn't and in this scrambled + + + align:start position:0% +when it doesn't and in this scrambled +and this was the first random run I did + + align:start position:0% +and this was the first random run I did + + + align:start position:0% +and this was the first random run I did +I didn't run it a whole bunch of times + + align:start position:0% +I didn't run it a whole bunch of times + + + align:start position:0% +I didn't run it a whole bunch of times +until I got one that worked it works + + align:start position:0% +until I got one that worked it works + + + align:start position:0% +until I got one that worked it works +perfectly so there what they argued was + + align:start position:0% +perfectly so there what they argued was + + + align:start position:0% +perfectly so there what they argued was +that this concept of Gap fill as + + align:start position:0% +that this concept of Gap fill as + + + align:start position:0% +that this concept of Gap fill as +something un in music could actually + + align:start position:0% +something un in music could actually + + + align:start position:0% +something un in music could actually +just be explained by regression to the + + align:start position:0% +just be explained by regression to the + + + align:start position:0% +just be explained by regression to the +mean and I thought this is really really + + align:start position:0% +mean and I thought this is really really + + + align:start position:0% +mean and I thought this is really really +cool um the thing I noticed looking at + + align:start position:0% +cool um the thing I noticed looking at + + + align:start position:0% +cool um the thing I noticed looking at +this article for the first time you uh + + align:start position:0% +this article for the first time you uh + + + align:start position:0% +this article for the first time you uh +in the mid what do you call them the a + + align:start position:0% +in the mid what do you call them the a + + + align:start position:0% +in the mid what do you call them the a +the 2000 to 2009 something was looking + + align:start position:0% +the 2000 to 2009 something was looking + + + align:start position:0% +the 2000 to 2009 something was looking +at the data that they had um to do this + + align:start position:0% +at the data that they had um to do this + + + align:start position:0% +at the data that they had um to do this +and so they had um some uh songs Leader + + align:start position:0% +and so they had um some uh songs Leader + + + align:start position:0% +and so they had um some uh songs Leader +by Schubert they had European folk songs + + align:start position:0% +by Schubert they had European folk songs + + + align:start position:0% +by Schubert they had European folk songs +where do you think that came from from + + align:start position:0% +where do you think that came from from + + + align:start position:0% +where do you think that came from from +anybody European folk songs and Chinese + + align:start position:0% +anybody European folk songs and Chinese + + + align:start position:0% +anybody European folk songs and Chinese +folk songs that's always that's the ESS + + align:start position:0% +folk songs that's always that's the ESS + + + align:start position:0% +folk songs that's always that's the ESS +in data set so they had this data sets + + align:start position:0% +in data set so they had this data sets + + + align:start position:0% +in data set so they had this data sets +been around for a while and they had + + align:start position:0% +been around for a while and they had + + + align:start position:0% +been around for a while and they had +some other things South African and obj + + align:start position:0% +some other things South African and obj + + + align:start position:0% +some other things South African and obj +uh Native American folk songs and um you + + align:start position:0% +uh Native American folk songs and um you + + + align:start position:0% +uh Native American folk songs and um you +can kind of see when uh when you're + + align:start position:0% +can kind of see when uh when you're + + + align:start position:0% +can kind of see when uh when you're +going all the you're already high and + + align:start position:0% +going all the you're already high and + + + align:start position:0% +going all the you're already high and +you go even higher then the odds are + + align:start position:0% +you go even higher then the odds are + + + align:start position:0% +you go even higher then the odds are +you're going to turn down when you're + + align:start position:0% +you're going to turn down when you're + + + align:start position:0% +you're going to turn down when you're +here you you're going to come back down + + align:start position:0% +here you you're going to come back down + + + align:start position:0% +here you you're going to come back down +right and so that's very statically + + align:start position:0% +right and so that's very statically + + + align:start position:0% +right and so that's very statically +significant and when you start in a + + align:start position:0% +significant and when you start in a + + + align:start position:0% +significant and when you start in a +normal range and end in a high range + + align:start position:0% +normal range and end in a high range + + + align:start position:0% +normal range and end in a high range +you're still probably going to go down + + align:start position:0% +you're still probably going to go down + + + align:start position:0% +you're still probably going to go down +and they saw that a lot this is not just + + align:start position:0% +and they saw that a lot this is not just + + + align:start position:0% +and they saw that a lot this is not just +down this is other direction but I'll + + align:start position:0% +down this is other direction but I'll + + + align:start position:0% +down this is other direction but I'll +assume for a second that everything is + + align:start position:0% +assume for a second that everything is + + + align:start position:0% +assume for a second that everything is +leaping up but then when you get right + + align:start position:0% +leaping up but then when you get right + + + align:start position:0% +leaping up but then when you get right +to the median you kind of see that you + + align:start position:0% +to the median you kind of see that you + + + align:start position:0% +to the median you kind of see that you +go about 5050 in either direction and + + align:start position:0% +go about 5050 in either direction and + + + align:start position:0% +go about 5050 in either direction and +when you um when you start low and you + + align:start position:0% +when you um when you start low and you + + + align:start position:0% +when you um when you start low and you +go up but you're still + + align:start position:0% +go up but you're still + + + align:start position:0% +go up but you're still +low the that um more often than not you + + align:start position:0% +low the that um more often than not you + + + align:start position:0% +low the that um more often than not you +just continue going up there is no Gap + + align:start position:0% +just continue going up there is no Gap + + + align:start position:0% +just continue going up there is no Gap +fill or or it's kind of reverse Gap fill + + align:start position:0% +fill or or it's kind of reverse Gap fill + + + align:start position:0% +fill or or it's kind of reverse Gap fill +or some something like that um so I'm + + align:start position:0% +or some something like that um so I'm + + + align:start position:0% +or some something like that um so I'm +you know somebody uh developing music 21 + + align:start position:0% +you know somebody uh developing music 21 + + + align:start position:0% +you know somebody uh developing music 21 +and I I kind of look at these numbers + + align:start position:0% +and I I kind of look at these numbers + + + align:start position:0% +and I I kind of look at these numbers +which are probably from like 1998 or + + align:start position:0% +which are probably from like 1998 or + + + align:start position:0% +which are probably from like 1998 or +something now it's 2010 2012 I'm + + align:start position:0% +something now it's 2010 2012 I'm + + + align:start position:0% +something now it's 2010 2012 I'm +teaching here doing this type of stuff + + align:start position:0% +teaching here doing this type of stuff + + + align:start position:0% +teaching here doing this type of stuff +and I look at their sample size they + + align:start position:0% +and I look at their sample size they + + + align:start position:0% +and I look at their sample size they +have you know 60 86 examples of + + align:start position:0% +have you know 60 86 examples of + + + align:start position:0% +have you know 60 86 examples of +something like this and 101 of something + + align:start position:0% +something like this and 101 of something + + + align:start position:0% +something like this and 101 of something +else because it took a long time to + + align:start position:0% +else because it took a long time to + + + align:start position:0% +else because it took a long time to +encode music then it still takes a long + + align:start position:0% +encode music then it still takes a long + + + align:start position:0% +encode music then it still takes a long +time but we've gotten things better + + align:start position:0% +time but we've gotten things better + + + align:start position:0% +time but we've gotten things better +there's more data sets out there so I + + align:start position:0% +there's more data sets out there so I + + + align:start position:0% +there's more data sets out there so I +thought about running it for um think it + + align:start position:0% +thought about running it for um think it + + + align:start position:0% +thought about running it for um think it +was originally to think of as a problem + + align:start position:0% +was originally to think of as a problem + + + align:start position:0% +was originally to think of as a problem +set for this class to to you know let's + + align:start position:0% +set for this class to to you know let's + + + align:start position:0% +set for this class to to you know let's +validate Von hipple and Hon's work um + + align:start position:0% +validate Von hipple and Hon's work um + + + align:start position:0% +validate Von hipple and Hon's work um +but it turned into a little bit more and + + align:start position:0% +but it turned into a little bit more and + + + align:start position:0% +but it turned into a little bit more and +it turned into uh a paper that my friend + + align:start position:0% +it turned into uh a paper that my friend + + + align:start position:0% +it turned into uh a paper that my friend +Mark who's probably going to watch this + + align:start position:0% +Mark who's probably going to watch this + + + align:start position:0% +Mark who's probably going to watch this +at some point we do still need to finish + + align:start position:0% +at some point we do still need to finish + + + align:start position:0% +at some point we do still need to finish +publishing it we've presented it many + + align:start position:0% +publishing it we've presented it many + + + align:start position:0% +publishing it we've presented it many +times but + + align:start position:0% +times but + + + align:start position:0% +times but +published uh species or species on + + align:start position:0% +published uh species or species on + + + align:start position:0% +published uh species or species on +various rules for species Counterpoint + + align:start position:0% +various rules for species Counterpoint + + + align:start position:0% +various rules for species Counterpoint +that uh don't seem to actually exist in + + align:start position:0% +that uh don't seem to actually exist in + + + align:start position:0% +that uh don't seem to actually exist in +the literature uh + + align:start position:0% +the literature uh + + + align:start position:0% +the literature uh +because when we ran the same thing you + + align:start position:0% +because when we ran the same thing you + + + align:start position:0% +because when we ran the same thing you +can see we have a a lot more data + + align:start position:0% +can see we have a a lot more data + + + align:start position:0% +can see we have a a lot more data +examples and when we looked at the + + align:start position:0% +examples and when we looked at the + + + align:start position:0% +examples and when we looked at the +Chinese folk songs we also saw the same + + align:start position:0% +Chinese folk songs we also saw the same + + + align:start position:0% +Chinese folk songs we also saw the same +thing that Von hipple and hiron did that + + align:start position:0% +thing that Von hipple and hiron did that + + + align:start position:0% +thing that Von hipple and hiron did that +there is a lot more evidence for R to + + align:start position:0% +there is a lot more evidence for R to + + + align:start position:0% +there is a lot more evidence for R to +the mean regression to the mean than + + align:start position:0% +the mean regression to the mean than + + + align:start position:0% +the mean regression to the mean than +there is for Gap Phill and when uh we + + align:start position:0% +there is for Gap Phill and when uh we + + + align:start position:0% +there is for Gap Phill and when uh we +looked at the European Essen data set we + + align:start position:0% +looked at the European Essen data set we + + + align:start position:0% +looked at the European Essen data set we +still saw the same thing and all these + + align:start position:0% +still saw the same thing and all these + + + align:start position:0% +still saw the same thing and all these +things so um I get got to do the nice + + align:start position:0% +things so um I get got to do the nice + + + align:start position:0% +things so um I get got to do the nice +validation study that I thought we would + + align:start position:0% +validation study that I thought we would + + + align:start position:0% +validation study that I thought we would +do and I thought would' make a nice + + align:start position:0% +do and I thought would' make a nice + + + align:start position:0% +do and I thought would' make a nice +assignment for us all and everything + + align:start position:0% +assignment for us all and everything + + + align:start position:0% +assignment for us all and everything +until I looked at um music before Bach + + align:start position:0% +until I looked at um music before Bach + + + align:start position:0% +until I looked at um music before Bach +the music of the era that we do species + + align:start position:0% +the music of the era that we do species + + + align:start position:0% +the music of the era that we do species +Counterpoint on why we have species + + align:start position:0% +Counterpoint on why we have species + + + align:start position:0% +Counterpoint on why we have species +Counterpoint exercises and it turned out + + align:start position:0% +Counterpoint exercises and it turned out + + + align:start position:0% +Counterpoint exercises and it turned out +there that for these uh weird pieces + + align:start position:0% +there that for these uh weird pieces + + + align:start position:0% +there that for these uh weird pieces +where you're jumping up above the mean + + align:start position:0% +where you're jumping up above the mean + + + align:start position:0% +where you're jumping up above the mean +or something like that that Gap fill + + align:start position:0% +or something like that that Gap fill + + + align:start position:0% +or something like that that Gap fill +happens more often than regression to + + align:start position:0% +happens more often than regression to + + + align:start position:0% +happens more often than regression to +the + + align:start position:0% +the + + + align:start position:0% +the +mean and so for these like low going to + + align:start position:0% +mean and so for these like low going to + + + align:start position:0% +mean and so for these like low going to +here and then you would expect + + align:start position:0% +here and then you would expect + + + align:start position:0% +here and then you would expect +regression to mean you should still go + + align:start position:0% +regression to mean you should still go + + + align:start position:0% +regression to mean you should still go +up there did seem to be a period where + + align:start position:0% +up there did seem to be a period where + + + align:start position:0% +up there did seem to be a period where +people were actually doing Gap fill and + + align:start position:0% +people were actually doing Gap fill and + + + align:start position:0% +people were actually doing Gap fill and +so that was was pretty uh was pretty + + align:start position:0% +so that was was pretty uh was pretty + + + align:start position:0% +so that was was pretty uh was pretty +neat and um so it just shows that + + align:start position:0% +neat and um so it just shows that + + + align:start position:0% +neat and um so it just shows that +sometimes and you get a new data set you + + align:start position:0% +sometimes and you get a new data set you + + + align:start position:0% +sometimes and you get a new data set you +should be + + align:start position:0% +should be + + + align:start position:0% +should be +reexamining existing + + align:start position:0% +reexamining existing + + + align:start position:0% +reexamining existing +theories um but Von hipple and hon did + + align:start position:0% +theories um but Von hipple and hon did + + + align:start position:0% +theories um but Von hipple and hon did +cover their butts at the end they said + + align:start position:0% +cover their butts at the end they said + + + align:start position:0% +cover their butts at the end they said +that their conclusion and I agree with + + align:start position:0% +that their conclusion and I agree with + + + align:start position:0% +that their conclusion and I agree with +them completely so so they are actually + + align:start position:0% +them completely so so they are actually + + + align:start position:0% +them completely so so they are actually +and I are actually in agreement on this + + align:start position:0% +and I are actually in agreement on this + + + align:start position:0% +and I are actually in agreement on this +that their conclusion applied only to + + align:start position:0% +that their conclusion applied only to + + + align:start position:0% +that their conclusion applied only to +the sampled vocal repertories that they + + align:start position:0% +the sampled vocal repertories that they + + + align:start position:0% +the sampled vocal repertories that they +were looking at um that that other + + align:start position:0% +were looking at um that that other + + + align:start position:0% +were looking at um that that other +repertories may contain an excess of + + align:start position:0% +repertories may contain an excess of + + + align:start position:0% +repertories may contain an excess of +post skip reversals Gap fill uh given + + align:start position:0% +post skip reversals Gap fill uh given + + + align:start position:0% +post skip reversals Gap fill uh given +the centuries of Western composers who + + align:start position:0% +the centuries of Western composers who + + + align:start position:0% +the centuries of Western composers who +have been taught to write Gap fill it + + align:start position:0% +have been taught to write Gap fill it + + + align:start position:0% +have been taught to write Gap fill it +seems inevitable that some of them have + + align:start position:0% +seems inevitable that some of them have + + + align:start position:0% +seems inevitable that some of them have +actually done it in their compositions + + align:start position:0% +actually done it in their compositions + + + align:start position:0% +actually done it in their compositions +and now we can kind of see what eras + + align:start position:0% +and now we can kind of see what eras + + + align:start position:0% +and now we can kind of see what eras +composers were actually doing it though + + align:start position:0% +composers were actually doing it though + + + align:start position:0% +composers were actually doing it though +I I think it's kind of interesting that + + align:start position:0% +I I think it's kind of interesting that + + + align:start position:0% +I I think it's kind of interesting that +the era that um started teaching how to + + align:start position:0% +the era that um started teaching how to + + + align:start position:0% +the era that um started teaching how to +write music with gapville is closer to + + align:start position:0% +write music with gapville is closer to + + + align:start position:0% +write music with gapville is closer to +this period to Bach Mozart and + + align:start position:0% +this period to Bach Mozart and + + + align:start position:0% +this period to Bach Mozart and +everything talking about how music of + + align:start position:0% +everything talking about how music of + + + align:start position:0% +everything talking about how music of +that past worked so they weren't + + align:start position:0% +that past worked so they weren't + + + align:start position:0% +that past worked so they weren't +actually doing it in their own music but + + align:start position:0% +actually doing it in their own music but + + + align:start position:0% +actually doing it in their own music but +they had observed something um in the + + align:start position:0% +they had observed something um in the + + + align:start position:0% +they had observed something um in the +past and just shows for the 10 millionth + + align:start position:0% +past and just shows for the 10 millionth + + + align:start position:0% +past and just shows for the 10 millionth +time when we think we're Smarter Than + + align:start position:0% +time when we think we're Smarter Than + + + align:start position:0% +time when we think we're Smarter Than +People of the past were quite often + + align:start position:0% + + + + align:start position:0% + +wrong questions on Gap fill or this kind + + align:start position:0% +wrong questions on Gap fill or this kind + + + align:start position:0% +wrong questions on Gap fill or this kind +of work or or discussion points doesn't + + align:start position:0% +of work or or discussion points doesn't + + + align:start position:0% +of work or or discussion points doesn't +have to be a + + align:start position:0% + + + + align:start position:0% + +question cool eh do it again somewh + + align:start position:0% +question cool eh do it again somewh + + + align:start position:0% +question cool eh do it again somewh +something between yeah um can you talk a + + align:start position:0% +something between yeah um can you talk a + + + align:start position:0% +something between yeah um can you talk a +little bit through the numbers like what + + align:start position:0% +little bit through the numbers like what + + + align:start position:0% +little bit through the numbers like what +yeah what exactly does like how do you + + align:start position:0% +yeah what exactly does like how do you + + + align:start position:0% +yeah what exactly does like how do you +measure significance exactly yeah I + + align:start position:0% +measure significance exactly yeah I + + + align:start position:0% +measure significance exactly yeah I +can't I can't remember this is why I + + align:start position:0% +can't I can't remember this is why I + + + align:start position:0% +can't I can't remember this is why I +needs a little bit of time to come back + + align:start position:0% +needs a little bit of time to come back + + + align:start position:0% +needs a little bit of time to come back +to this how did this I think it was the + + align:start position:0% +to this how did this I think it was the + + + align:start position:0% +to this how did this I think it was the +um uh Scholars T Test um do you know + + align:start position:0% +um uh Scholars T Test um do you know + + + align:start position:0% +um uh Scholars T Test um do you know +what that is what the significance + + align:start position:0% +what that is what the significance + + + align:start position:0% +what that is what the significance +basically how far is this difference + + align:start position:0% +basically how far is this difference + + + align:start position:0% +basically how far is this difference +between these two things um how far is + + align:start position:0% +between these two things um how far is + + + align:start position:0% +between these two things um how far is +it compared to random chance so one of + + align:start position:0% +it compared to random chance so one of + + + align:start position:0% +it compared to random chance so one of +the one of the things that um it doesn't + + align:start position:0% +the one of the things that um it doesn't + + + align:start position:0% +the one of the things that um it doesn't +work this isn't a statistics class and I + + align:start position:0% +work this isn't a statistics class and I + + + align:start position:0% +work this isn't a statistics class and I +am not a professional statistician but + + align:start position:0% +am not a professional statistician but + + + align:start position:0% +am not a professional statistician but +um but one of the ways you can often + + align:start position:0% +um but one of the ways you can often + + + align:start position:0% +um but one of the ways you can often +test something is U if your null + + align:start position:0% +test something is U if your null + + + align:start position:0% +test something is U if your null +hypothesis if your hypothesis going into + + align:start position:0% +hypothesis if your hypothesis going into + + + align:start position:0% +hypothesis if your hypothesis going into +experiment is that um you know that Gap + + align:start position:0% +experiment is that um you know that Gap + + + align:start position:0% +experiment is that um you know that Gap +fill doesn't exist that there shouldn't + + align:start position:0% +fill doesn't exist that there shouldn't + + + align:start position:0% +fill doesn't exist that there shouldn't +be a difference between a gap fill and a + + align:start position:0% +be a difference between a gap fill and a + + + align:start position:0% +be a difference between a gap fill and a +random motion or motion toward the the + + align:start position:0% +random motion or motion toward the the + + + align:start position:0% +random motion or motion toward the the +um toward the mediant regression should + + align:start position:0% +um toward the mediant regression should + + + align:start position:0% +um toward the mediant regression should +say regression to mediant I suppose than + + align:start position:0% +say regression to mediant I suppose than + + + align:start position:0% +say regression to mediant I suppose than +to mean but we don't know that and so + + align:start position:0% +to mean but we don't know that and so + + + align:start position:0% +to mean but we don't know that and so +one of the things is that + + align:start position:0% +one of the things is that + + + align:start position:0% +one of the things is that +significance goes um the amount of + + align:start position:0% +significance goes um the amount of + + + align:start position:0% +significance goes um the amount of +difference between two hypotheses + + align:start position:0% +difference between two hypotheses + + + align:start position:0% +difference between two hypotheses +necessary to say that something is + + align:start position:0% +necessary to say that something is + + + align:start position:0% +necessary to say that something is +highly significant goes up uh the the + + align:start position:0% +highly significant goes up uh the the + + + align:start position:0% +highly significant goes up uh the the +amount of difference in percentage uh + + align:start position:0% +amount of difference in percentage uh + + + align:start position:0% +amount of difference in percentage uh +goes down a lot as the number of + + align:start position:0% +goes down a lot as the number of + + + align:start position:0% +goes down a lot as the number of +observations goes way way up um and one + + align:start position:0% +observations goes way way up um and one + + + align:start position:0% +observations goes way way up um and one +of the places I saw this on was on uh + + align:start position:0% +of the places I saw this on was on uh + + + align:start position:0% +of the places I saw this on was on uh +the article I wrote with Sophia sun on + + align:start position:0% +the article I wrote with Sophia sun on + + + align:start position:0% +the article I wrote with Sophia sun on +the lyrics uh emphasis you know like uh + + align:start position:0% +the lyrics uh emphasis you know like uh + + + align:start position:0% +the lyrics uh emphasis you know like uh +various are there high notes on + + align:start position:0% +various are there high notes on + + + align:start position:0% +various are there high notes on +anticipation or surprise when you when + + align:start position:0% +anticipation or surprise when you when + + + align:start position:0% +anticipation or surprise when you when +we're talking about oh anticipation is + + align:start position:0% +we're talking about oh anticipation is + + + align:start position:0% +we're talking about oh anticipation is +higher than discusted we're talking + + align:start position:0% +higher than discusted we're talking + + + align:start position:0% +higher than discusted we're talking +about an average I think those two were + + align:start position:0% +about an average I think those two were + + + align:start position:0% +about an average I think those two were +about one semitone the difference + + align:start position:0% +about one semitone the difference + + + align:start position:0% +about one semitone the difference +between F and FP this is not a huge + + align:start position:0% +between F and FP this is not a huge + + + align:start position:0% +between F and FP this is not a huge +difference but when you get um you know + + align:start position:0% +difference but when you get um you know + + + align:start position:0% +difference but when you get um you know +880,000 or I suppose that one was around + + align:start position:0% +880,000 or I suppose that one was around + + + align:start position:0% +880,000 or I suppose that one was around +10,000 observations one semitone starts + + align:start position:0% +10,000 observations one semitone starts + + + align:start position:0% +10,000 observations one semitone starts +becoming pretty significant um so that's + + align:start position:0% +becoming pretty significant um so that's + + + align:start position:0% +becoming pretty significant um so that's +one of the ways that sometimes you can + + align:start position:0% +one of the ways that sometimes you can + + + align:start position:0% +one of the ways that sometimes you can +um if you look at if you're just looking + + align:start position:0% +um if you look at if you're just looking + + + align:start position:0% +um if you look at if you're just looking +at like 10 pieces you might see that + + align:start position:0% +at like 10 pieces you might see that + + + align:start position:0% +at like 10 pieces you might see that +well six of them do this and four of + + align:start position:0% +well six of them do this and four of + + + align:start position:0% +well six of them do this and four of +them do the other thing that's probably + + align:start position:0% +them do the other thing that's probably + + + align:start position:0% +them do the other thing that's probably +not going to be a significant difference + + align:start position:0% +not going to be a significant difference + + + align:start position:0% +not going to be a significant difference +because if you flip a coin 10 times you + + align:start position:0% +because if you flip a coin 10 times you + + + align:start position:0% +because if you flip a coin 10 times you +might get sick heads and four tails or + + align:start position:0% +might get sick heads and four tails or + + + align:start position:0% +might get sick heads and four tails or +something um + + align:start position:0% +something um + + + align:start position:0% +something um +yeah the numbers for Gap fill and + + align:start position:0% +yeah the numbers for Gap fill and + + + align:start position:0% +yeah the numbers for Gap fill and +regression so I guess the median those + + align:start position:0% +regression so I guess the median those + + + align:start position:0% +regression so I guess the median those +are instances where this happens in the + + align:start position:0% +are instances where this happens in the + + + align:start position:0% +are instances where this happens in the +pieces of that specific um sometimes can + + align:start position:0% +pieces of that specific um sometimes can + + + align:start position:0% +pieces of that specific um sometimes can +it do both I guess like if if it starts + + align:start position:0% +it do both I guess like if if it starts + + + align:start position:0% +it do both I guess like if if it starts +above the above R median it will + + align:start position:0% +above the above R median it will + + + align:start position:0% +above the above R median it will +technically be both if it just goes down + + align:start position:0% +technically be both if it just goes down + + + align:start position:0% +technically be both if it just goes down +right yes so you can okay but some of + + align:start position:0% +right yes so you can okay but some of + + + align:start position:0% +right yes so you can okay but some of +them are one or the other right and and + + align:start position:0% +them are one or the other right and and + + + align:start position:0% +them are one or the other right and and +so the ones that cross over um I think + + align:start position:0% +so the ones that cross over um I think + + + align:start position:0% +so the ones that cross over um I think +it's only the ones that reach to the + + align:start position:0% +it's only the ones that reach to the + + + align:start position:0% +it's only the ones that reach to the +median or that don't reach it that end + + align:start position:0% +median or that don't reach it that end + + + align:start position:0% +median or that don't reach it that end +up having um being in the observation + + align:start position:0% +up having um being in the observation + + + align:start position:0% +up having um being in the observation +set okay because all the rest should + + align:start position:0% +set okay because all the rest should + + + align:start position:0% +set okay because all the rest should +always be the um should always be the + + align:start position:0% +always be the um should always be the + + + align:start position:0% +always be the um should always be the +same they should be the same the whether + + align:start position:0% +same they should be the same the whether + + + align:start position:0% +same they should be the same the whether +uh that is to say if if you + + align:start position:0% +uh that is to say if if you + + + align:start position:0% +uh that is to say if if you +start if you start middle or start + + align:start position:0% +start if you start middle or start + + + align:start position:0% +start if you start middle or start +middle high and go really high and then + + align:start position:0% +middle high and go really high and then + + + align:start position:0% +middle high and go really high and then +you go even higher well then you've + + align:start position:0% +you go even higher well then you've + + + align:start position:0% +you go even higher well then you've +broken Gap fill and broken regression to + + align:start position:0% +broken Gap fill and broken regression to + + + align:start position:0% +broken Gap fill and broken regression to +the mean and if you go down then you + + align:start position:0% +the mean and if you go down then you + + + align:start position:0% +the mean and if you go down then you +fulfilled Gap fill and regression to the + + align:start position:0% +fulfilled Gap fill and regression to the + + + align:start position:0% +fulfilled Gap fill and regression to the +mean so you haven't learned anything + + align:start position:0% +mean so you haven't learned anything + + + align:start position:0% +mean so you haven't learned anything +about your hypothesis so I think these + + align:start position:0% +about your hypothesis so I think these + + + align:start position:0% +about your hypothesis so I think these +were um only very um various these um + + align:start position:0% +were um only very um various these um + + + align:start position:0% +were um only very um various these um +particular cases where the two + + align:start position:0% +particular cases where the two + + + align:start position:0% +particular cases where the two +hypotheses would res uh result in + + align:start position:0% +hypotheses would res uh result in + + + align:start position:0% +hypotheses would res uh result in +different directions + + align:start position:0% +different directions + + + align:start position:0% +different directions +predicted yeah great question great + + align:start position:0% +predicted yeah great question great + + + align:start position:0% +predicted yeah great question great +question now we're getting on I just + + align:start position:0% +question now we're getting on I just + + + align:start position:0% +question now we're getting on I just +need to give more time + + align:start position:0% +need to give more time + + + align:start position:0% +need to give more time +any other things + + align:start position:0% + + + + align:start position:0% + +this isn't a statistics class so I'm not + + align:start position:0% +this isn't a statistics class so I'm not + + + align:start position:0% +this isn't a statistics class so I'm not +going to go into um things like this but + + align:start position:0% +going to go into um things like this but + + + align:start position:0% +going to go into um things like this but +there one of the one of the mistakes + + align:start position:0% +there one of the one of the mistakes + + + align:start position:0% +there one of the one of the mistakes +that people who dabble in statistics uh + + align:start position:0% +that people who dabble in statistics uh + + + align:start position:0% +that people who dabble in statistics uh +but whose main work is on Medieval music + + align:start position:0% +but whose main work is on Medieval music + + + align:start position:0% +but whose main work is on Medieval music +music theory programming all these other + + align:start position:0% +music theory programming all these other + + + align:start position:0% +music theory programming all these other +things we often get wrong is uh + + align:start position:0% +things we often get wrong is uh + + + align:start position:0% +things we often get wrong is uh +something called a multiple comparison + + align:start position:0% +something called a multiple comparison + + + align:start position:0% +something called a multiple comparison +test and that is to say the more if I + + align:start position:0% +test and that is to say the more if I + + + align:start position:0% +test and that is to say the more if I +did looked at you know 7,000 repertories + + align:start position:0% +did looked at you know 7,000 repertories + + + align:start position:0% +did looked at you know 7,000 repertories +and I'm only reporting the top 10 or the + + align:start position:0% +and I'm only reporting the top 10 or the + + + align:start position:0% +and I'm only reporting the top 10 or the +10 best or something like that um then + + align:start position:0% +10 best or something like that um then + + + align:start position:0% +10 best or something like that um then +my significance level needs to be much + + align:start position:0% +my significance level needs to be much + + + align:start position:0% +my significance level needs to be much +much much higher and sort of general + + align:start position:0% +much much higher and sort of general + + + align:start position:0% +much much higher and sort of general +rule if is if um who's heard of like P + + align:start position:0% +rule if is if um who's heard of like P + + + align:start position:0% +rule if is if um who's heard of like P +value 05 or 5% yeah as sort of a + + align:start position:0% +value 05 or 5% yeah as sort of a + + + align:start position:0% +value 05 or 5% yeah as sort of a +standard thing so if you look at five + + align:start position:0% +standard thing so if you look at five + + + align:start position:0% +standard thing so if you look at five +different things in uh you know five + + align:start position:0% +different things in uh you know five + + + align:start position:0% +different things in uh you know five +different hypotheses start with a P + + align:start position:0% +different hypotheses start with a P + + + align:start position:0% +different hypotheses start with a P +value instead of 05 divide that by five + + align:start position:0% +value instead of 05 divide that by five + + + align:start position:0% +value instead of 05 divide that by five +is + + align:start position:0% +is + + + align:start position:0% +is +01 um and so this was uh a criticism on + + align:start position:0% +01 um and so this was uh a criticism on + + + align:start position:0% +01 um and so this was uh a criticism on +some of the um some earlier work that I + + align:start position:0% +some of the um some earlier work that I + + + align:start position:0% +some of the um some earlier work that I +did where I was looking at you know + + align:start position:0% +did where I was looking at you know + + + align:start position:0% +did where I was looking at you know +there's uh what is it 10 different um 10 + + align:start position:0% +there's uh what is it 10 different um 10 + + + align:start position:0% +there's uh what is it 10 different um 10 +different emotions or sentiments that + + align:start position:0% +different emotions or sentiments that + + + align:start position:0% +different emotions or sentiments that +can be compared with nine other ones so + + align:start position:0% +can be compared with nine other ones so + + + align:start position:0% +can be compared with nine other ones so +I'm doing 90 comparisons for each uh + + align:start position:0% +I'm doing 90 comparisons for each uh + + + align:start position:0% +I'm doing 90 comparisons for each uh +attribute so I should be whatever 05 + + align:start position:0% +attribute so I should be whatever 05 + + + align:start position:0% +attribute so I should be whatever 05 +divided by 90 is some somewhere around + + align:start position:0% +divided by 90 is some somewhere around + + + align:start position:0% +divided by 90 is some somewhere around +01 we just looked at the number of zeros + + align:start position:0% +01 we just looked at the number of zeros + + + align:start position:0% +01 we just looked at the number of zeros +compared to the number of of hypotheses + + align:start position:0% +compared to the number of of hypotheses + + + align:start position:0% +compared to the number of of hypotheses +um yeah so so look out for things where + + align:start position:0% +um yeah so so look out for things where + + + align:start position:0% +um yeah so so look out for things where +people are reporting + + align:start position:0% +people are reporting + + + align:start position:0% +people are reporting +p + + align:start position:0% +p + + + align:start position:0% +p +046 as significant because it's lower + + align:start position:0% +046 as significant because it's lower + + + align:start position:0% +046 as significant because it's lower +than 05 but not not very much but on the + + align:start position:0% +than 05 but not not very much but on the + + + align:start position:0% +than 05 but not not very much but on the +other hand when you get something like e + + align:start position:0% +other hand when you get something like e + + + align:start position:0% +other hand when you get something like e +to the 45 you have 45 zeros before some + + align:start position:0% +to the 45 you have 45 zeros before some + + + align:start position:0% +to the 45 you have 45 zeros before some +digit that I don't even care what the + + align:start position:0% +digit that I don't even care what the + + + align:start position:0% +digit that I don't even care what the +digit is there's 45 zeros and that's + + align:start position:0% +digit is there's 45 zeros and that's + + + align:start position:0% +digit is there's 45 zeros and that's +what's important um that ends up being + + align:start position:0% +what's important um that ends up being + + + align:start position:0% +what's important um that ends up being +pretty good I like that the um European + + align:start position:0% +pretty good I like that the um European + + + align:start position:0% +pretty good I like that the um European +folk song we can actually do even better + + align:start position:0% +folk song we can actually do even better + + + align:start position:0% +folk song we can actually do even better +than um than uh you know they were + + align:start position:0% +than um than uh you know they were + + + align:start position:0% +than um than uh you know they were +giving two two stars for um for their + + align:start position:0% +giving two two stars for um for their + + + align:start position:0% +giving two two stars for um for their +work because they only had this many + + align:start position:0% +work because they only had this many + + + align:start position:0% +work because they only had this many +observations um but now we can give them + + align:start position:0% +observations um but now we can give them + + + align:start position:0% +observations um but now we can give them +a lot more observations and say yeah + + align:start position:0% +a lot more observations and say yeah + + + align:start position:0% +a lot more observations and say yeah +this is absolutely right um one once you + + align:start position:0% +this is absolutely right um one once you + + + align:start position:0% +this is absolutely right um one once you +get uh in 64-bit numbers once you get uh + + align:start position:0% +get uh in 64-bit numbers once you get uh + + + align:start position:0% +get uh in 64-bit numbers once you get uh +more than 308 zeros it just gets rounded + + align:start position:0% +more than 308 zeros it just gets rounded + + + align:start position:0% +more than 308 zeros it just gets rounded +to zero which uh ends up being a lot of + + align:start position:0% +to zero which uh ends up being a lot of + + + align:start position:0% +to zero which uh ends up being a lot of +zero division errors cool + + align:start position:0% +zero division errors cool + + + align:start position:0% +zero division errors cool +I'm going to move on to the second um + + align:start position:0% +I'm going to move on to the second um + + + align:start position:0% +I'm going to move on to the second um +second topic uh a little bit briefly and + + align:start position:0% +second topic uh a little bit briefly and + + + align:start position:0% +second topic uh a little bit briefly and +it's something I feel I rightly should + + align:start position:0% +it's something I feel I rightly should + + + align:start position:0% +it's something I feel I rightly should +feel apologetic for um we're moving into + + align:start position:0% +feel apologetic for um we're moving into + + + align:start position:0% +feel apologetic for um we're moving into +an era where uh where we where where + + align:start position:0% +an era where uh where we where where + + + align:start position:0% +an era where uh where we where where +people here in New England in Boston at + + align:start position:0% +people here in New England in Boston at + + + align:start position:0% +people here in New England in Boston at +MIT in the United States are recognizing + + align:start position:0% +MIT in the United States are recognizing + + + align:start position:0% +MIT in the United States are recognizing +finally that Western Europe is not the + + align:start position:0% +finally that Western Europe is not the + + + align:start position:0% +finally that Western Europe is not the +only place that does music or culture I + + align:start position:0% +only place that does music or culture I + + + align:start position:0% +only place that does music or culture I +know big big big shock so why has this + + align:start position:0% +know big big big shock so why has this + + + align:start position:0% +know big big big shock so why has this +class been primarily about western music + + align:start position:0% +class been primarily about western music + + + align:start position:0% +class been primarily about western music +in fact we can start um looking at other + + align:start position:0% +in fact we can start um looking at other + + + align:start position:0% +in fact we can start um looking at other +music as part of a music theory class + + align:start position:0% +music as part of a music theory class + + + align:start position:0% +music as part of a music theory class +there was just earlier this semester I + + align:start position:0% +there was just earlier this semester I + + + align:start position:0% +there was just earlier this semester I +think I emailed it to somebody it might + + align:start position:0% +think I emailed it to somebody it might + + + align:start position:0% +think I emailed it to somebody it might +have been Vincent even who just came + + align:start position:0% +have been Vincent even who just came + + + align:start position:0% +have been Vincent even who just came +came in um some maybe sure a new book + + align:start position:0% +came in um some maybe sure a new book + + + align:start position:0% +came in um some maybe sure a new book +that just came out it's I think it's + + align:start position:0% +that just came out it's I think it's + + + align:start position:0% +that just came out it's I think it's +like 600 Pages all on + + align:start position:0% +like 600 Pages all on + + + align:start position:0% +like 600 Pages all on +computational approaches to Indian art + + align:start position:0% +computational approaches to Indian art + + + align:start position:0% +computational approaches to Indian art +music uh that's say um music that's + + align:start position:0% +music uh that's say um music that's + + + align:start position:0% +music uh that's say um music that's +that's sort of in a high tradition that + + align:start position:0% +that's sort of in a high tradition that + + + align:start position:0% +that's sort of in a high tradition that +is not folk music or modern popular + + align:start position:0% +is not folk music or modern popular + + + align:start position:0% +is not folk music or modern popular +music and if you think about you or + + align:start position:0% +music and if you think about you or + + + align:start position:0% +music and if you think about you or +Bollywood or something like that if you + + align:start position:0% +Bollywood or something like that if you + + + align:start position:0% +Bollywood or something like that if you +think about if you can write 600 pages + + align:start position:0% +think about if you can write 600 pages + + + align:start position:0% +think about if you can write 600 pages +on Indian art music you could probably + + align:start position:0% +on Indian art music you could probably + + + align:start position:0% +on Indian art music you could probably +write 600 pages on computational + + align:start position:0% +write 600 pages on computational + + + align:start position:0% +write 600 pages on computational +approaches to any of those things too um + + align:start position:0% +approaches to any of those things too um + + + align:start position:0% +approaches to any of those things too um +and I'm really looking forward to seeing + + align:start position:0% +and I'm really looking forward to seeing + + + align:start position:0% +and I'm really looking forward to seeing +uh what one of my colleagues uh down in + + align:start position:0% +uh what one of my colleagues uh down in + + + align:start position:0% +uh what one of my colleagues uh down in +the um in South South as are doing but + + align:start position:0% +the um in South South as are doing but + + + align:start position:0% +the um in South South as are doing but +uh one of the things that's comes up + + align:start position:0% +uh one of the things that's comes up + + + align:start position:0% +uh one of the things that's comes up +here oh no I didn't highlight this is + + align:start position:0% +here oh no I didn't highlight this is + + + align:start position:0% +here oh no I didn't highlight this is +that most of my training my personal + + align:start position:0% +that most of my training my personal + + + align:start position:0% +that most of my training my personal +blinders I I'll say bias my although + + align:start position:0% +blinders I I'll say bias my although + + + align:start position:0% +blinders I I'll say bias my although +maybe it is also that has been that I + + align:start position:0% +maybe it is also that has been that I + + + align:start position:0% +maybe it is also that has been that I +was always interested in musical scores + + align:start position:0% +was always interested in musical scores + + + align:start position:0% +was always interested in musical scores +and now there's large parts of music + + align:start position:0% +and now there's large parts of music + + + align:start position:0% +and now there's large parts of music +theory that are interested in things + + align:start position:0% +theory that are interested in things + + + align:start position:0% +theory that are interested in things +that are not score-based and most of the + + align:start position:0% +that are not score-based and most of the + + + align:start position:0% +that are not score-based and most of the +rest of the world's music is not + + align:start position:0% +rest of the world's music is not + + + align:start position:0% +rest of the world's music is not +primarily score based just as shockingly + + align:start position:0% +primarily score based just as shockingly + + + align:start position:0% +primarily score based just as shockingly +most um most western music today is not + + align:start position:0% +most um most western music today is not + + + align:start position:0% +most um most western music today is not +primarily score based I mean it is + + align:start position:0% +primarily score based I mean it is + + + align:start position:0% +primarily score based I mean it is +really really great when you go see your + + align:start position:0% +really really great when you go see your + + + align:start position:0% +really really great when you go see your +favorite uh heavy metal band and they're + + align:start position:0% +favorite uh heavy metal band and they're + + + align:start position:0% +favorite uh heavy metal band and they're +all page turning for each other so no no + + align:start position:0% +all page turning for each other so no no + + + align:start position:0% +all page turning for each other so no no +that doesn't happen we're you know we're + + align:start position:0% +that doesn't happen we're you know we're + + + align:start position:0% +that doesn't happen we're you know we're +much more of an oral culture today so + + align:start position:0% +much more of an oral culture today so + + + align:start position:0% +much more of an oral culture today so +yeah so it says basically that um there + + align:start position:0% +yeah so it says basically that um there + + + align:start position:0% +yeah so it says basically that um there +are no standardized tools yet such as + + align:start position:0% +are no standardized tools yet such as + + + align:start position:0% +are no standardized tools yet such as +hum drum or music 21 for Indian art + + align:start position:0% +hum drum or music 21 for Indian art + + + align:start position:0% +hum drum or music 21 for Indian art +music scores and that still get need + + align:start position:0% +music scores and that still get need + + + align:start position:0% +music scores and that still get need +Collections and of scores whatever it is + + align:start position:0% +Collections and of scores whatever it is + + + align:start position:0% +Collections and of scores whatever it is +if we're going to be using these tools + + align:start position:0% +if we're going to be using these tools + + + align:start position:0% +if we're going to be using these tools +and I want us to always be trying to + + align:start position:0% +and I want us to always be trying to + + + align:start position:0% +and I want us to always be trying to +break out of the chicken and egg problem + + align:start position:0% +break out of the chicken and egg problem + + + align:start position:0% +break out of the chicken and egg problem +that I've done this semester with you + + align:start position:0% +that I've done this semester with you + + + align:start position:0% +that I've done this semester with you +we'll do another Buck cow I I really my + + align:start position:0% +we'll do another Buck cow I I really my + + + align:start position:0% +we'll do another Buck cow I I really my +apology to you all everybody is that I + + align:start position:0% +apology to you all everybody is that I + + + align:start position:0% +apology to you all everybody is that I +wanted to deemphasize more of those + + align:start position:0% +wanted to deemphasize more of those + + + align:start position:0% +wanted to deemphasize more of those +things and music 21 Version 9 has a + + align:start position:0% +things and music 21 Version 9 has a + + + align:start position:0% +things and music 21 Version 9 has a +bunch of other substitute scores that + + align:start position:0% +bunch of other substitute scores that + + + align:start position:0% +bunch of other substitute scores that +are designed for us to be using and uh + + align:start position:0% +are designed for us to be using and uh + + + align:start position:0% +are designed for us to be using and uh +it's just has continued to be too buggy + + align:start position:0% +it's just has continued to be too buggy + + + align:start position:0% +it's just has continued to be too buggy +to recommend for us all to use in this + + align:start position:0% +to recommend for us all to use in this + + + align:start position:0% +to recommend for us all to use in this +class not the scores the surrounding + + align:start position:0% +class not the scores the surrounding + + + align:start position:0% +class not the scores the surrounding +code um so we don't want the chicken and + + align:start position:0% +code um so we don't want the chicken and + + + align:start position:0% +code um so we don't want the chicken and +egg problem that well we don't study + + align:start position:0% +egg problem that well we don't study + + + align:start position:0% +egg problem that well we don't study +this music because there aren't enough + + align:start position:0% +this music because there aren't enough + + + align:start position:0% +this music because there aren't enough +scores in there well why don't we encode + + align:start position:0% +scores in there well why don't we encode + + + align:start position:0% +scores in there well why don't we encode +a whole bunch of scores well if we did + + align:start position:0% +a whole bunch of scores well if we did + + + align:start position:0% +a whole bunch of scores well if we did +that there's no software to analyze it + + align:start position:0% +that there's no software to analyze it + + + align:start position:0% +that there's no software to analyze it +right so these are some of the problems + + align:start position:0% +right so these are some of the problems + + + align:start position:0% +right so these are some of the problems +that are there um so um they're + + align:start position:0% +that are there um so um they're + + + align:start position:0% +that are there um so um they're +absolutely WR that these tools the + + align:start position:0% +absolutely WR that these tools the + + + align:start position:0% +absolutely WR that these tools the +authors of this book editors that these + + align:start position:0% +authors of this book editors that these + + + align:start position:0% +authors of this book editors that these +tools don't yet exist um + + align:start position:0% +tools don't yet exist um + + + align:start position:0% +tools don't yet exist um +but we wanted to those of us who are + + align:start position:0% +but we wanted to those of us who are + + + align:start position:0% +but we wanted to those of us who are +building music 21 first and many of us + + align:start position:0% +building music 21 first and many of us + + + align:start position:0% +building music 21 first and many of us +in scores we just never got there this + + align:start position:0% +in scores we just never got there this + + + align:start position:0% +in scores we just never got there this +is um one of the slides I know I haven't + + align:start position:0% +is um one of the slides I know I haven't + + + align:start position:0% +is um one of the slides I know I haven't +changed my font in a long time um from + + align:start position:0% +changed my font in a long time um from + + + align:start position:0% +changed my font in a long time um from +the original funding presentation to get + + align:start position:0% +the original funding presentation to get + + + align:start position:0% +the original funding presentation to get +funding to take music 21 from a little + + align:start position:0% +funding to take music 21 from a little + + + align:start position:0% +funding to take music 21 from a little +hobby europ project and to make it a + + align:start position:0% +hobby europ project and to make it a + + + align:start position:0% +hobby europ project and to make it a +bigger one and we talked about these are + + align:start position:0% +bigger one and we talked about these are + + + align:start position:0% +bigger one and we talked about these are +probably things doesn't exactly work + + align:start position:0% +probably things doesn't exactly work + + + align:start position:0% +probably things doesn't exactly work +like this but you know these were the + + align:start position:0% +like this but you know these were the + + + align:start position:0% +like this but you know these were the +types of things music 21 was going to be + + align:start position:0% +types of things music 21 was going to be + + + align:start position:0% +types of things music 21 was going to be +able to do generic intervals specific + + align:start position:0% +able to do generic intervals specific + + + align:start position:0% +able to do generic intervals specific +chromatic is Step you all have worked + + align:start position:0% +chromatic is Step you all have worked + + + align:start position:0% +chromatic is Step you all have worked +with this by now um but then I thought + + align:start position:0% +with this by now um but then I thought + + + align:start position:0% +with this by now um but then I thought +well you should be able to apply a + + align:start position:0% +well you should be able to apply a + + + align:start position:0% +well you should be able to apply a +context to any object and transform how + + align:start position:0% +context to any object and transform how + + + align:start position:0% +context to any object and transform how +that object Works uh so you could apply + + align:start position:0% +that object Works uh so you could apply + + + align:start position:0% +that object Works uh so you could apply +13th century France con uh con oh I + + align:start position:0% +13th century France con uh con oh I + + + align:start position:0% +13th century France con uh con oh I +didn't even make this consistent in the + + align:start position:0% +didn't even make this consistent in the + + + align:start position:0% +didn't even make this consistent in the +um you this is all pseudo code in 13th + + align:start position:0% +um you this is all pseudo code in 13th + + + align:start position:0% +um you this is all pseudo code in 13th +century France this major third would + + align:start position:0% +century France this major third would + + + align:start position:0% +century France this major third would +not be called a consonant only perfect + + align:start position:0% +not be called a consonant only perfect + + + align:start position:0% +not be called a consonant only perfect +intervals that's why they're called + + align:start position:0% +intervals that's why they're called + + + align:start position:0% +intervals that's why they're called +perfect or consonantes in fact this + + align:start position:0% +perfect or consonantes in fact this + + + align:start position:0% +perfect or consonantes in fact this +lower note wouldn't even exist there is + + align:start position:0% +lower note wouldn't even exist there is + + + align:start position:0% +lower note wouldn't even exist there is +no a flat back then so we could do that + + align:start position:0% +no a flat back then so we could do that + + + align:start position:0% +no a flat back then so we could do that +and then we could apply other things + + align:start position:0% +and then we could apply other things + + + align:start position:0% +and then we could apply other things +like 20th century Harmony apply an + + align:start position:0% +like 20th century Harmony apply an + + + align:start position:0% +like 20th century Harmony apply an +octatonic scale and count the number of + + align:start position:0% +octatonic scale and count the number of + + + align:start position:0% +octatonic scale and count the number of +um notes in this and we' get three + + align:start position:0% +um notes in this and we' get three + + + align:start position:0% +um notes in this and we' get three +instead of two and that one we can kind + + align:start position:0% +instead of two and that one we can kind + + + align:start position:0% +instead of two and that one we can kind +of do but I did think about oh wouldn't + + align:start position:0% +of do but I did think about oh wouldn't + + + align:start position:0% +of do but I did think about oh wouldn't +it be great to be able to take this + + align:start position:0% +it be great to be able to take this + + + align:start position:0% +it be great to be able to take this +interval which we started with calling + + align:start position:0% +interval which we started with calling + + + align:start position:0% +interval which we started with calling +it major 3D and convert it into the + + align:start position:0% +it major 3D and convert it into the + + + align:start position:0% +it major 3D and convert it into the +Indian farara and get seven shuti as the + + align:start position:0% +Indian farara and get seven shuti as the + + + align:start position:0% +Indian farara and get seven shuti as the +interval that these types of things + + align:start position:0% +interval that these types of things + + + align:start position:0% +interval that these types of things +should be able to be done and a lot of + + align:start position:0% +should be able to be done and a lot of + + + align:start position:0% +should be able to be done and a lot of +the basic design decisions some of the + + align:start position:0% +the basic design decisions some of the + + + align:start position:0% +the basic design decisions some of the +things are over complicated in what + + align:start position:0% +things are over complicated in what + + + align:start position:0% +things are over complicated in what +you're trying to do were in order to + + align:start position:0% +you're trying to do were in order to + + + align:start position:0% +you're trying to do were in order to +enable more of these U things or that um + + align:start position:0% +enable more of these U things or that um + + + align:start position:0% +enable more of these U things or that um +we can apply an IND okan pentatonic + + align:start position:0% +we can apply an IND okan pentatonic + + + align:start position:0% +we can apply an IND okan pentatonic +scale and say the a flat to C is a step + + align:start position:0% +scale and say the a flat to C is a step + + + align:start position:0% +scale and say the a flat to C is a step +it is not a skip is a leap because there + + align:start position:0% +it is not a skip is a leap because there + + + align:start position:0% +it is not a skip is a leap because there +is no note between those + + align:start position:0% +is no note between those + + + align:start position:0% +is no note between those +um or one of the last things in there + + align:start position:0% +um or one of the last things in there + + + align:start position:0% +um or one of the last things in there +that um you know one of the things music + + align:start position:0% +that um you know one of the things music + + + align:start position:0% +that um you know one of the things music +21 will be able to answer um I suppose I + + align:start position:0% +21 will be able to answer um I suppose I + + + align:start position:0% +21 will be able to answer um I suppose I +never put a timeline on that so maybe + + align:start position:0% +never put a timeline on that so maybe + + + align:start position:0% +never put a timeline on that so maybe +I'm still uh telling the truth you know + + align:start position:0% +I'm still uh telling the truth you know + + + align:start position:0% +I'm still uh telling the truth you know +is that West African cultures often hear + + align:start position:0% +is that West African cultures often hear + + + align:start position:0% +is that West African cultures often hear +the same rhythmic pattern and as having + + align:start position:0% +the same rhythmic pattern and as having + + + align:start position:0% +the same rhythmic pattern and as having +different strong beats different parts + + align:start position:0% +different strong beats different parts + + + align:start position:0% +different strong beats different parts +of the Bell pattern um what can we learn + + align:start position:0% +of the Bell pattern um what can we learn + + + align:start position:0% +of the Bell pattern um what can we learn +from analyzing more music to try to + + align:start position:0% +from analyzing more music to try to + + + align:start position:0% +from analyzing more music to try to +figure out what Clues give uh different + + align:start position:0% +figure out what Clues give uh different + + + align:start position:0% +figure out what Clues give uh different +of um of strong beat among different + + align:start position:0% +of um of strong beat among different + + + align:start position:0% +of um of strong beat among different +listeners so these are all ideas that + + align:start position:0% +listeners so these are all ideas that + + + align:start position:0% +listeners so these are all ideas that +computational music theory should be + + align:start position:0% +computational music theory should be + + + align:start position:0% +computational music theory should be +able to + + align:start position:0% + + + + align:start position:0% + +do so we wanted to get there originally + + align:start position:0% +do so we wanted to get there originally + + + align:start position:0% +do so we wanted to get there originally +a whole field has wanted to get there uh + + align:start position:0% +a whole field has wanted to get there uh + + + align:start position:0% +a whole field has wanted to get there uh +to be able to do some of these things + + align:start position:0% +to be able to do some of these things + + + align:start position:0% +to be able to do some of these things +but we're not there yet to really have + + align:start position:0% +but we're not there yet to really have + + + align:start position:0% +but we're not there yet to really have +cross-cultural symbolic music um an + + align:start position:0% +cross-cultural symbolic music um an + + + align:start position:0% +cross-cultural symbolic music um an +analysis but I want to keep trying I'm + + align:start position:0% +analysis but I want to keep trying I'm + + + align:start position:0% +analysis but I want to keep trying I'm +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +spending this is a summer coming up for + + align:start position:0% +spending this is a summer coming up for + + + align:start position:0% +spending this is a summer coming up for +me I'm going to be trying to this has + + align:start position:0% +me I'm going to be trying to this has + + + align:start position:0% +me I'm going to be trying to this has +really inspired me to make sure that at + + align:start position:0% +really inspired me to make sure that at + + + align:start position:0% +really inspired me to make sure that at +least one more of these things are + + align:start position:0% + + + + align:start position:0% + +possible so that's that's one more the + + align:start position:0% +possible so that's that's one more the + + + align:start position:0% +possible so that's that's one more the +second of three things I wanted to talk + + align:start position:0% +second of three things I wanted to talk + + + align:start position:0% +second of three things I wanted to talk +about today um discussion ideas anybody + + align:start position:0% +about today um discussion ideas anybody + + + align:start position:0% +about today um discussion ideas anybody +know of anything very cool happening in + + align:start position:0% +know of anything very cool happening in + + + align:start position:0% +know of anything very cool happening in +this sort of + + align:start position:0% +this sort of + + + align:start position:0% +this sort of +world oh I meant to talk about there is + + align:start position:0% +world oh I meant to talk about there is + + + align:start position:0% +world oh I meant to talk about there is +a project taros that um is specifically + + align:start position:0% +a project taros that um is specifically + + + align:start position:0% +a project taros that um is specifically +a music theory uh toolkit for looking at + + align:start position:0% +a music theory uh toolkit for looking at + + + align:start position:0% +a music theory uh toolkit for looking at +music throughout the world it's a little + + align:start position:0% +music throughout the world it's a little + + + align:start position:0% +music throughout the world it's a little +bit um uh older it's one of these things + + align:start position:0% +bit um uh older it's one of these things + + + align:start position:0% +bit um uh older it's one of these things +that you need to find your Java virtual + + align:start position:0% +that you need to find your Java virtual + + + align:start position:0% +that you need to find your Java virtual +machine to work uh properly on but it's + + align:start position:0% +machine to work uh properly on but it's + + + align:start position:0% +machine to work uh properly on but it's +very cool set um of tools for uh for + + align:start position:0% +very cool set um of tools for uh for + + + align:start position:0% +very cool set um of tools for uh for +analyzing especially scales and scale + + align:start position:0% +analyzing especially scales and scale + + + align:start position:0% +analyzing especially scales and scale +usage through the world that doesn't re + + align:start position:0% +usage through the world that doesn't re + + + align:start position:0% +usage through the world that doesn't re +that doesn't rely on saying oh well that + + align:start position:0% +that doesn't rely on saying oh well that + + + align:start position:0% +that doesn't rely on saying oh well that +not's kind of like an A and that notes a + + align:start position:0% +not's kind of like an A and that notes a + + + align:start position:0% +not's kind of like an A and that notes a +c but 20 cents high no no those are + + align:start position:0% +c but 20 cents high no no those are + + + align:start position:0% +c but 20 cents high no no those are +notes these are not alterations on some + + align:start position:0% +notes these are not alterations on some + + + align:start position:0% +notes these are not alterations on some +you know platonic correct note that just + + align:start position:0% +you know platonic correct note that just + + + align:start position:0% +you know platonic correct note that just +happens to be the Western scale so I + + align:start position:0% +happens to be the Western scale so I + + + align:start position:0% +happens to be the Western scale so I +think any conceptual system for + + align:start position:0% +think any conceptual system for + + + align:start position:0% +think any conceptual system for +nonwestern music needs to start with + + align:start position:0% +nonwestern music needs to start with + + + align:start position:0% +nonwestern music needs to start with +anything that is fundamental in that + + align:start position:0% +anything that is fundamental in that + + + align:start position:0% +anything that is fundamental in that +system is a fundamental object that + + align:start position:0% +system is a fundamental object that + + + align:start position:0% +system is a fundamental object that +maybe we can translate them to um to + + align:start position:0% +maybe we can translate them to um to + + + align:start position:0% +maybe we can translate them to um to +other systems objects like western music + + align:start position:0% +other systems objects like western music + + + align:start position:0% +other systems objects like western music +but first the manipulation should happen + + align:start position:0% +but first the manipulation should happen + + + align:start position:0% +but first the manipulation should happen +in the space that people are actually + + align:start position:0% + + + + align:start position:0% + +conceiving I know it's very B leury + + align:start position:0% +conceiving I know it's very B leury + + + align:start position:0% +conceiving I know it's very B leury +today for me but + + align:start position:0% +today for me but + + + align:start position:0% +today for me but +um I don't want you to have to do too + + align:start position:0% +um I don't want you to have to do too + + + align:start position:0% +um I don't want you to have to do too +much more work while you're doing many + + align:start position:0% +much more work while you're doing many + + + align:start position:0% +much more work while you're doing many +other things so I'm going to talk about + + align:start position:0% +other things so I'm going to talk about + + + align:start position:0% +other things so I'm going to talk about +um the last really cool area that I + + align:start position:0% +um the last really cool area that I + + + align:start position:0% +um the last really cool area that I +think there's still so much for music + + align:start position:0% +think there's still so much for music + + + align:start position:0% +think there's still so much for music +theory to be doing in order order to get + + align:start position:0% +theory to be doing in order order to get + + + align:start position:0% +theory to be doing in order order to get +us more scores and that is improving + + align:start position:0% +us more scores and that is improving + + + align:start position:0% +us more scores and that is improving +Optical music recognition so Optical + + align:start position:0% +Optical music recognition so Optical + + + align:start position:0% +Optical music recognition so Optical +music recognition process of changing a + + align:start position:0% +music recognition process of changing a + + + align:start position:0% +music recognition process of changing a +musical score into something that a + + align:start position:0% +musical score into something that a + + + align:start position:0% +musical score into something that a +computer can understand a symbolic score + + align:start position:0% +computer can understand a symbolic score + + + align:start position:0% +computer can understand a symbolic score +and this is uh done what is my name + + align:start position:0% +and this is uh done what is my name + + + align:start position:0% +and this is uh done what is my name +bigger on this I think we reset the that + + align:start position:0% +bigger on this I think we reset the that + + + align:start position:0% +bigger on this I think we reset the that +that is not supposed to happen I think + + align:start position:0% +that is not supposed to happen I think + + + align:start position:0% +that is not supposed to happen I think +there was something I think it was in an + + align:start position:0% +there was something I think it was in an + + + align:start position:0% +there was something I think it was in an +auto shrink um uh mode sorry about that + + align:start position:0% +auto shrink um uh mode sorry about that + + + align:start position:0% +auto shrink um uh mode sorry about that +sorry Mara uh doing amazing things out + + align:start position:0% +sorry Mara uh doing amazing things out + + + align:start position:0% +sorry Mara uh doing amazing things out +there at du lingo um okay um one of the + + align:start position:0% +there at du lingo um okay um one of the + + + align:start position:0% +there at du lingo um okay um one of the +opportunities is and this is from a + + align:start position:0% +opportunities is and this is from a + + + align:start position:0% +opportunities is and this is from a +presentation I'm reusing slides I don't + + align:start position:0% +presentation I'm reusing slides I don't + + + align:start position:0% +presentation I'm reusing slides I don't +update them every year uh because from + + align:start position:0% +update them every year uh because from + + + align:start position:0% +update them every year uh because from +2014 um + + align:start position:0% +2014 um + + + align:start position:0% +2014 um +that um that back when imslp had about + + align:start position:0% +that um that back when imslp had about + + + align:start position:0% +that um that back when imslp had about +300,000 scores I think it's over double + + align:start position:0% +300,000 scores I think it's over double + + + align:start position:0% +300,000 scores I think it's over double +that now and so we'd love to be able to + + align:start position:0% +that now and so we'd love to be able to + + + align:start position:0% +that now and so we'd love to be able to +convert all of them into music so I + + align:start position:0% +convert all of them into music so I + + + align:start position:0% +convert all of them into music so I +always you know might as well start with + + align:start position:0% +always you know might as well start with + + + align:start position:0% +always you know might as well start with +AA Klein KN music by wolf amas Mozart + + align:start position:0% +AA Klein KN music by wolf amas Mozart + + + align:start position:0% +AA Klein KN music by wolf amas Mozart +late 19th + + align:start position:0% +late 19th + + + align:start position:0% +late 19th +century and so if we want to convert it + + align:start position:0% +century and so if we want to convert it + + + align:start position:0% +century and so if we want to convert it +over this is um use from the + + align:start position:0% +over this is um use from the + + + align:start position:0% +over this is um use from the +state-of-the-art in 2014 it's gotten + + align:start position:0% +state-of-the-art in 2014 it's gotten + + + align:start position:0% +state-of-the-art in 2014 it's gotten +better but not a huge amount better so + + align:start position:0% +better but not a huge amount better so + + + align:start position:0% +better but not a huge amount better so +this is the original score of of one + + align:start position:0% +this is the original score of of one + + + align:start position:0% +this is the original score of of one +part and this is what the optical music + + align:start position:0% +part and this is what the optical music + + + align:start position:0% +part and this is what the optical music +recognition score came up with so you + + align:start position:0% +recognition score came up with so you + + + align:start position:0% +recognition score came up with so you +can see uh oops we've lost lost some + + align:start position:0% +can see uh oops we've lost lost some + + + align:start position:0% +can see uh oops we've lost lost some +notes Here uh somehow we have another + + align:start position:0% +notes Here uh somehow we have another + + + align:start position:0% +notes Here uh somehow we have another +rest here and a whole bunch of dots at + + align:start position:0% +rest here and a whole bunch of dots at + + + align:start position:0% +rest here and a whole bunch of dots at +the top and on the other hand you know a + + align:start position:0% +the top and on the other hand you know a + + + align:start position:0% +the top and on the other hand you know a +lot of it looks kind of kind of right + + align:start position:0% +lot of it looks kind of kind of right + + + align:start position:0% +lot of it looks kind of kind of right +but how do these errors add up + + align:start position:0% +but how do these errors add up + + + align:start position:0% +but how do these errors add up +especially rhythmic errors um and + + align:start position:0% +especially rhythmic errors um and + + + align:start position:0% +especially rhythmic errors um and +misidentified part names cffs can lead + + align:start position:0% +misidentified part names cffs can lead + + + align:start position:0% +misidentified part names cffs can lead +to Big differences in perception so I'm + + align:start position:0% +to Big differences in perception so I'm + + + align:start position:0% +to Big differences in perception so I'm +just going to remind us for the first + + align:start position:0% +just going to remind us for the first + + + align:start position:0% +just going to remind us for the first +couple bars of what I CL music knock + + align:start position:0% +couple bars of what I CL music knock + + + align:start position:0% +couple bars of what I CL music knock +music should sound like this is actually + + align:start position:0% +music should sound like this is actually + + + align:start position:0% +music should sound like this is actually +it shouldn't sound like this this is a + + align:start position:0% +it shouldn't sound like this this is a + + + align:start position:0% +it shouldn't sound like this this is a +un unretouched finale performance from + + align:start position:0% +un unretouched finale performance from + + + align:start position:0% +un unretouched finale performance from +um music EX + + align:start position:0% + + + + align:start position:0% + +okay y'all recognize it good so I don't + + align:start position:0% +okay y'all recognize it good so I don't + + + align:start position:0% +okay y'all recognize it good so I don't +need to play more let's listen to a + + align:start position:0% +need to play more let's listen to a + + + align:start position:0% +need to play more let's listen to a +little bit of what happens when you play + + align:start position:0% +little bit of what happens when you play + + + align:start position:0% +little bit of what happens when you play +back the state-of-the-art optical music + + align:start position:0% +back the state-of-the-art optical music + + + align:start position:0% +back the state-of-the-art optical music +recognition + + align:start position:0% +recognition + + + align:start position:0% +recognition +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +oh + + align:start position:0% + + + + align:start position:0% + +I have no idea how it got what + + align:start position:0% +I have no idea how it got what + + + align:start position:0% +I have no idea how it got what +instruments should be + + align:start position:0% +instruments should be + + + align:start position:0% +instruments should be +playing + + align:start position:0% +playing + + + align:start position:0% +playing +anyhow so one of the things I've been + + align:start position:0% +anyhow so one of the things I've been + + + align:start position:0% +anyhow so one of the things I've been +talking about especially since our sound + + align:start position:0% +talking about especially since our sound + + + align:start position:0% +talking about especially since our sound +discore lecture we didn't really do uh + + align:start position:0% +discore lecture we didn't really do uh + + + align:start position:0% +discore lecture we didn't really do uh +uh image discore lecture uh is how music + + align:start position:0% +uh image discore lecture uh is how music + + + align:start position:0% +uh image discore lecture uh is how music +theory knowledge can um work with + + align:start position:0% +theory knowledge can um work with + + + align:start position:0% +theory knowledge can um work with +inaccuracies in omr fortunately some + + align:start position:0% +inaccuracies in omr fortunately some + + + align:start position:0% +inaccuracies in omr fortunately some +other people have been thinking about it + + align:start position:0% +other people have been thinking about it + + + align:start position:0% +other people have been thinking about it +this is one um I should be citing my + + align:start position:0% +this is one um I should be citing my + + + align:start position:0% +this is one um I should be citing my +sources I can't uh remember exactly + + align:start position:0% +sources I can't uh remember exactly + + + align:start position:0% +sources I can't uh remember exactly +where it came from one uh pipeline for + + align:start position:0% +where it came from one uh pipeline for + + + align:start position:0% +where it came from one uh pipeline for +how scanned music can end up as a music + + align:start position:0% +how scanned music can end up as a music + + + align:start position:0% +how scanned music can end up as a music +encoded data file staff line DET + + align:start position:0% +encoded data file staff line DET + + + align:start position:0% +encoded data file staff line DET +identification object location so on but + + align:start position:0% +identification object location so on but + + + align:start position:0% +identification object location so on but +uh just like we saw in the sound of + + align:start position:0% +uh just like we saw in the sound of + + + align:start position:0% +uh just like we saw in the sound of +score things musical semantics and + + align:start position:0% +score things musical semantics and + + + align:start position:0% +score things musical semantics and +musical knowledge can be used to go back + + align:start position:0% +musical knowledge can be used to go back + + + align:start position:0% +musical knowledge can be used to go back +and forth in sort of a two-way Pipeline + + align:start position:0% +and forth in sort of a two-way Pipeline + + + align:start position:0% +and forth in sort of a two-way Pipeline +and that was the idea that almost + + align:start position:0% +and that was the idea that almost + + + align:start position:0% +and that was the idea that almost +everybody knew but but very few musical + + align:start position:0% +everybody knew but but very few musical + + + align:start position:0% +everybody knew but but very few musical +semantics have been brought in to um uh + + align:start position:0% +semantics have been brought in to um uh + + + align:start position:0% +semantics have been brought in to um uh +to to what we're uh doing so here's some + + align:start position:0% +to to what we're uh doing so here's some + + + align:start position:0% +to to what we're uh doing so here's some +things that errors that music theory can + + align:start position:0% +things that errors that music theory can + + + align:start position:0% +things that errors that music theory can +fix um you might have a pitch out of + + align:start position:0% +fix um you might have a pitch out of + + + align:start position:0% +fix um you might have a pitch out of +context and would figure out what we + + align:start position:0% +context and would figure out what we + + + align:start position:0% +context and would figure out what we +have + + align:start position:0% +have + + + align:start position:0% +have +misread probably that was intended to be + + align:start position:0% +misread probably that was intended to be + + + align:start position:0% +misread probably that was intended to be +a sharp and now it's been read as a + + align:start position:0% +a sharp and now it's been read as a + + + align:start position:0% +a sharp and now it's been read as a +natural instrument or cleff + + align:start position:0% +natural instrument or cleff + + + align:start position:0% +natural instrument or cleff +misidentification I mean this is + + align:start position:0% +misidentification I mean this is + + + align:start position:0% +misidentification I mean this is +something that you don't need very much + + align:start position:0% +something that you don't need very much + + + align:start position:0% +something that you don't need very much +programming to figure out Uh something's + + align:start position:0% +programming to figure out Uh something's + + + align:start position:0% +programming to figure out Uh something's +wrong + + align:start position:0% +wrong + + + align:start position:0% +wrong +the correction isn't necessarily the + + align:start position:0% +the correction isn't necessarily the + + + align:start position:0% +the correction isn't necessarily the +easiest thing should it be uh change + + align:start position:0% +easiest thing should it be uh change + + + align:start position:0% +easiest thing should it be uh change +that to a tuba or change the cluff to um + + align:start position:0% +that to a tuba or change the cluff to um + + + align:start position:0% +that to a tuba or change the cluff to um +to a treble cluff not sure but we can + + align:start position:0% +to a treble cluff not sure but we can + + + align:start position:0% +to a treble cluff not sure but we can +definitely point that out if we have + + align:start position:0% +definitely point that out if we have + + + align:start position:0% +definitely point that out if we have +music theory knowledge um to point + + align:start position:0% +music theory knowledge um to point + + + align:start position:0% +music theory knowledge um to point +something in um and then metrical + + align:start position:0% +something in um and then metrical + + + align:start position:0% +something in um and then metrical +inconsistencies is what we focused on + + align:start position:0% +inconsistencies is what we focused on + + + align:start position:0% +inconsistencies is what we focused on +because metrical inconsistencies have a + + align:start position:0% +because metrical inconsistencies have a + + + align:start position:0% +because metrical inconsistencies have a +really really nice thing that pitch + + align:start position:0% +really really nice thing that pitch + + + align:start position:0% +really really nice thing that pitch +inconsistencies don't there's um there's + + align:start position:0% +inconsistencies don't there's um there's + + + align:start position:0% +inconsistencies don't there's um there's +no answer key to whether you do it right + + align:start position:0% +no answer key to whether you do it right + + + align:start position:0% +no answer key to whether you do it right +or wrong but there is a check sum to + + align:start position:0% +or wrong but there is a check sum to + + + align:start position:0% +or wrong but there is a check sum to +check see if you've probably got it + + align:start position:0% +check see if you've probably got it + + + align:start position:0% +check see if you've probably got it +right or probably got it wrong and that + + align:start position:0% +right or probably got it wrong and that + + + align:start position:0% +right or probably got it wrong and that +is the time + + align:start position:0% +is the time + + + align:start position:0% +is the time +signature when everything that you've + + align:start position:0% +signature when everything that you've + + + align:start position:0% +signature when everything that you've +recognized does not add up to the time + + align:start position:0% +recognized does not add up to the time + + + align:start position:0% +recognized does not add up to the time +signature maybe it's a pickup bar maybe + + align:start position:0% +signature maybe it's a pickup bar maybe + + + align:start position:0% +signature maybe it's a pickup bar maybe +it's some other weird thing but most of + + align:start position:0% +it's some other weird thing but most of + + + align:start position:0% +it's some other weird thing but most of +the time you've gotten something wrong + + align:start position:0% +the time you've gotten something wrong + + + align:start position:0% +the time you've gotten something wrong +right so um we want to talk about um the + + align:start position:0% +right so um we want to talk about um the + + + align:start position:0% +right so um we want to talk about um the +Rhythm replacement and what we're doing + + align:start position:0% +Rhythm replacement and what we're doing + + + align:start position:0% +Rhythm replacement and what we're doing +all + + align:start position:0% +all + + + align:start position:0% +all +has begins with the assumption that + + align:start position:0% +has begins with the assumption that + + + align:start position:0% +has begins with the assumption that +context will give you an idea of the + + align:start position:0% +context will give you an idea of the + + + align:start position:0% +context will give you an idea of the +correct Rhythm so here's that measure + + align:start position:0% +correct Rhythm so here's that measure + + + align:start position:0% +correct Rhythm so here's that measure +that was screwed up and here it becomes + + align:start position:0% +that was screwed up and here it becomes + + + align:start position:0% +that was screwed up and here it becomes +very obvious that we have a DOT that's + + align:start position:0% +very obvious that we have a DOT that's + + + align:start position:0% +very obvious that we have a DOT that's +been + + align:start position:0% +been + + + align:start position:0% +been +added given this context but now we're + + align:start position:0% +added given this context but now we're + + + align:start position:0% +added given this context but now we're +going to come up with a different + + align:start position:0% +going to come up with a different + + + align:start position:0% +going to come up with a different +conclusion same middle + + align:start position:0% +conclusion same middle + + + align:start position:0% +conclusion same middle +measure but now what's wrong is almost + + align:start position:0% +measure but now what's wrong is almost + + + align:start position:0% +measure but now what's wrong is almost +is very very likely that we've lost a + + align:start position:0% +is very very likely that we've lost a + + + align:start position:0% +is very very likely that we've lost a +flag + + align:start position:0% +flag + + + align:start position:0% +flag +on the first eth + + align:start position:0% + + + + align:start position:0% + +note so we have the assumption that the + + align:start position:0% +note so we have the assumption that the + + + align:start position:0% +note so we have the assumption that the +context will give an idea about the + + align:start position:0% +context will give an idea about the + + + align:start position:0% +context will give an idea about the +correct Rhythm and that requires a + + align:start position:0% +correct Rhythm and that requires a + + + align:start position:0% +correct Rhythm and that requires a +certain amount of rhythmic repetition + + align:start position:0% +certain amount of rhythmic repetition + + + align:start position:0% +certain amount of rhythmic repetition +and metrical stability throughout a + + align:start position:0% +and metrical stability throughout a + + + align:start position:0% +and metrical stability throughout a +piece or across parts um there's some + + align:start position:0% +piece or across parts um there's some + + + align:start position:0% +piece or across parts um there's some +20th century music John Cage Pier bz uh + + align:start position:0% +20th century music John Cage Pier bz uh + + + align:start position:0% +20th century music John Cage Pier bz uh +Ruth Crawford Seager Gregorian chant + + align:start position:0% +Ruth Crawford Seager Gregorian chant + + + align:start position:0% +Ruth Crawford Seager Gregorian chant +that can't do it but most music doesn't + + align:start position:0% +that can't do it but most music doesn't + + + align:start position:0% +that can't do it but most music doesn't +behave like that most music works like + + align:start position:0% +behave like that most music works like + + + align:start position:0% +behave like that most music works like +inin and KN music so we're just tripping + + align:start position:0% +inin and KN music so we're just tripping + + + align:start position:0% +inin and KN music so we're just tripping +out all of the um Melody and just giving + + align:start position:0% +out all of the um Melody and just giving + + + align:start position:0% +out all of the um Melody and just giving +the computer a score that looks kind of + + align:start position:0% +the computer a score that looks kind of + + + align:start position:0% +the computer a score that looks kind of +like this it be a separate problem if + + align:start position:0% +like this it be a separate problem if + + + align:start position:0% +like this it be a separate problem if +there's a note deleted to try to figure + + align:start position:0% +there's a note deleted to try to figure + + + align:start position:0% +there's a note deleted to try to figure +out what pitch put it in but we're + + align:start position:0% +out what pitch put it in but we're + + + align:start position:0% +out what pitch put it in but we're +trying to figure out well at least what + + align:start position:0% +trying to figure out well at least what + + + align:start position:0% +trying to figure out well at least what +Rhythm it is so this is iined knock + + align:start position:0% +Rhythm it is so this is iined knock + + + align:start position:0% +Rhythm it is so this is iined knock +music the opening with just the + + align:start position:0% +music the opening with just the + + + align:start position:0% +music the opening with just the +rhythm so first thing work looked at was + + align:start position:0% +rhythm so first thing work looked at was + + + align:start position:0% +rhythm so first thing work looked at was +distance that the probability measure + + align:start position:0% +distance that the probability measure + + + align:start position:0% +distance that the probability measure +offers a solution based on its location + + align:start position:0% +offers a solution based on its location + + + align:start position:0% +offers a solution based on its location +and score something called distance + + align:start position:0% +and score something called distance + + + align:start position:0% +and score something called distance +probability um so distance can be + + align:start position:0% +probability um so distance can be + + + align:start position:0% +probability um so distance can be +partwise or horizont vertical or + + align:start position:0% +partwise or horizont vertical or + + + align:start position:0% +partwise or horizont vertical or +horizontal what do I mean by vertical um + + align:start position:0% +horizontal what do I mean by vertical um + + + align:start position:0% +horizontal what do I mean by vertical um +probability measure so we're just going + + align:start position:0% +probability measure so we're just going + + + align:start position:0% +probability measure so we're just going +to look at this third measure at the top + + align:start position:0% +to look at this third measure at the top + + + align:start position:0% +to look at this third measure at the top +of in music where there's an added well + + align:start position:0% +of in music where there's an added well + + + align:start position:0% +of in music where there's an added well +there's a there something doesn't add up + + align:start position:0% +there's a there something doesn't add up + + + align:start position:0% +there's a there something doesn't add up +here the computer doesn't yet know what + + align:start position:0% +here the computer doesn't yet know what + + + align:start position:0% +here the computer doesn't yet know what +you all know that there's a DOT that's + + align:start position:0% +you all know that there's a DOT that's + + + align:start position:0% +you all know that there's a DOT that's +been added dotted eighth note but it + + align:start position:0% +been added dotted eighth note but it + + + align:start position:0% +been added dotted eighth note but it +could be anything + + align:start position:0% +could be anything + + + align:start position:0% +could be anything +right so yeah there it is much so one of + + align:start position:0% +right so yeah there it is much so one of + + + align:start position:0% +right so yeah there it is much so one of +the things to do is to look at the + + align:start position:0% +the things to do is to look at the + + + align:start position:0% +the things to do is to look at the +rhythms in all the other parts at the + + align:start position:0% +rhythms in all the other parts at the + + + align:start position:0% +rhythms in all the other parts at the +same + + align:start position:0% +same + + + align:start position:0% +same +time what we can do is build a histogram + + align:start position:0% +time what we can do is build a histogram + + + align:start position:0% +time what we can do is build a histogram +of for the violin how often across the + + align:start position:0% +of for the violin how often across the + + + align:start position:0% +of for the violin how often across the +whole piece now again this is being + + align:start position:0% +whole piece now again this is being + + + align:start position:0% +whole piece now again this is being +built based on the incorrect possibly + + align:start position:0% +built based on the incorrect possibly + + + align:start position:0% +built based on the incorrect possibly +incorrect o omr so you're learning from + + align:start position:0% +incorrect o omr so you're learning from + + + align:start position:0% +incorrect o omr so you're learning from +you know from uh error PR scores to + + align:start position:0% +you know from uh error PR scores to + + + align:start position:0% +you know from uh error PR scores to +build other error prone scores perhaps + + align:start position:0% +build other error prone scores perhaps + + + align:start position:0% +build other error prone scores perhaps +but you hope that that this is act just + + align:start position:0% +but you hope that that this is act just + + + align:start position:0% +but you hope that that this is act just +a little bit close to reality so the + + align:start position:0% +a little bit close to reality so the + + + align:start position:0% +a little bit close to reality so the +violin mostly violin one mostly has the + + align:start position:0% +violin mostly violin one mostly has the + + + align:start position:0% +violin mostly violin one mostly has the +same Rhythm or has closest the same + + align:start position:0% +same Rhythm or has closest the same + + + align:start position:0% +same Rhythm or has closest the same +Rhythm violent 2 and the cello but for + + align:start position:0% +Rhythm violent 2 and the cello but for + + + align:start position:0% +Rhythm violent 2 and the cello but for +the most part it's doing its own thing + + align:start position:0% +the most part it's doing its own thing + + + align:start position:0% +the most part it's doing its own thing +when we look compared to the viola you + + align:start position:0% +when we look compared to the viola you + + + align:start position:0% +when we look compared to the viola you +can see hey when the viola is wrong 80% + + align:start position:0% +can see hey when the viola is wrong 80% + + + align:start position:0% +can see hey when the viola is wrong 80% +of the time if that measures like the + + align:start position:0% +of the time if that measures like the + + + align:start position:0% +of the time if that measures like the +other measures uh the the cello might + + align:start position:0% +other measures uh the the cello might + + + align:start position:0% +other measures uh the the cello might +have the same + + align:start position:0% +have the same + + + align:start position:0% +have the same +Rhythm so that gives the probability + + align:start position:0% +Rhythm so that gives the probability + + + align:start position:0% +Rhythm so that gives the probability +based on a horizontal a vertical and + + align:start position:0% +based on a horizontal a vertical and + + + align:start position:0% +based on a horizontal a vertical and +then the other thing you can do is look + + align:start position:0% +then the other thing you can do is look + + + align:start position:0% +then the other thing you can do is look +left and look right to see if that same + + align:start position:0% +left and look right to see if that same + + + align:start position:0% +left and look right to see if that same +rhythm is somewhere over there in this + + align:start position:0% +rhythm is somewhere over there in this + + + align:start position:0% +rhythm is somewhere over there in this +case it's not because uh it should have + + align:start position:0% +case it's not because uh it should have + + + align:start position:0% +case it's not because uh it should have +been but there's another mistake in the + + align:start position:0% +been but there's another mistake in the + + + align:start position:0% +been but there's another mistake in the +first measure and we can look throughout + + align:start position:0% +first measure and we can look throughout + + + align:start position:0% +first measure and we can look throughout +the whole score not just a what's cool + + align:start position:0% +the whole score not just a what's cool + + + align:start position:0% +the whole score not just a what's cool +about the horizontal thing is that + + align:start position:0% +about the horizontal thing is that + + + align:start position:0% +about the horizontal thing is that +scores tend to be wider than they are um + + align:start position:0% +scores tend to be wider than they are um + + + align:start position:0% +scores tend to be wider than they are um +tall other words more measures than + + align:start position:0% +tall other words more measures than + + + align:start position:0% +tall other words more measures than +there are parts so you have more things + + align:start position:0% +there are parts so you have more things + + + align:start position:0% +there are parts so you have more things +to do and we can look I'll skip over the + + align:start position:0% +to do and we can look I'll skip over the + + + align:start position:0% +to do and we can look I'll skip over the +violin I think it's more interesting to + + align:start position:0% +violin I think it's more interesting to + + + align:start position:0% +violin I think it's more interesting to +look at the cello um that obviously each + + align:start position:0% +look at the cello um that obviously each + + + align:start position:0% +look at the cello um that obviously each +measure is always exactly identical to + + align:start position:0% +measure is always exactly identical to + + + align:start position:0% +measure is always exactly identical to +itself so you have a one probability of + + align:start position:0% +itself so you have a one probability of + + + align:start position:0% +itself so you have a one probability of +one it's going to be but then um you can + + align:start position:0% +one it's going to be but then um you can + + + align:start position:0% +one it's going to be but then um you can +kind of see in a lot of the classical + + align:start position:0% +kind of see in a lot of the classical + + + align:start position:0% +kind of see in a lot of the classical +things the the most often similar + + align:start position:0% +things the the most often similar + + + align:start position:0% +things the the most often similar +measure is two measures on either side + + align:start position:0% +measure is two measures on either side + + + align:start position:0% +measure is two measures on either side +not one because of this sort of four bar + + align:start position:0% +not one because of this sort of four bar + + + align:start position:0% +not one because of this sort of four bar +structure and um the other thing that I + + align:start position:0% +structure and um the other thing that I + + + align:start position:0% +structure and um the other thing that I +learned from this is anybody know Sonata + + align:start position:0% +learned from this is anybody know Sonata + + + align:start position:0% +learned from this is anybody know Sonata +form uh yeah exposition + + align:start position:0% +form uh yeah exposition + + + align:start position:0% +form uh yeah exposition +development recapitulation at some point + + align:start position:0% +development recapitulation at some point + + + align:start position:0% +development recapitulation at some point +later the music comes back and so you + + align:start position:0% +later the music comes back and so you + + + align:start position:0% +later the music comes back and so you +can kind of see this temporary spike in + + align:start position:0% +can kind of see this temporary spike in + + + align:start position:0% +can kind of see this temporary spike in +that if you can't get it right look 97 + + align:start position:0% +that if you can't get it right look 97 + + + align:start position:0% +that if you can't get it right look 97 +measures later and you might also get it + + align:start position:0% +measures later and you might also get it + + + align:start position:0% +measures later and you might also get it +right so the computer can learn just + + align:start position:0% +right so the computer can learn just + + + align:start position:0% +right so the computer can learn just +from the scores what all the + + align:start position:0% +from the scores what all the + + + align:start position:0% +from the scores what all the +probabilities for this particular piece + + align:start position:0% +probabilities for this particular piece + + + align:start position:0% +probabilities for this particular piece +are and then hopefully apply them to put + + align:start position:0% +are and then hopefully apply them to put + + + align:start position:0% +are and then hopefully apply them to put +it in so now we know what measures what + + align:start position:0% +it in so now we know what measures what + + + align:start position:0% +it in so now we know what measures what +the probability of any measure having + + align:start position:0% +the probability of any measure having + + + align:start position:0% +the probability of any measure having +the same Rhythm would be ahead of time + + align:start position:0% +the same Rhythm would be ahead of time + + + align:start position:0% +the same Rhythm would be ahead of time +but then we need to look at second + + align:start position:0% +but then we need to look at second + + + align:start position:0% +but then we need to look at second +probability what's the probability that + + align:start position:0% +probability what's the probability that + + + align:start position:0% +probability what's the probability that +that measure that each other measure + + align:start position:0% +that measure that each other measure + + + align:start position:0% +that measure that each other measure +might have the solution based on how + + align:start position:0% +might have the solution based on how + + + align:start position:0% +might have the solution based on how +often certain errors happen and here's a + + align:start position:0% +often certain errors happen and here's a + + + align:start position:0% +often certain errors happen and here's a +chart that I think we need to keep + + align:start position:0% +chart that I think we need to keep + + + align:start position:0% +chart that I think we need to keep +looking at and keep judging but it was + + align:start position:0% +looking at and keep judging but it was + + + align:start position:0% +looking at and keep judging but it was +the only one that I knew of at the time + + align:start position:0% +the only one that I knew of at the time + + + align:start position:0% +the only one that I knew of at the time +where somebody looked at what the + + align:start position:0% +where somebody looked at what the + + + align:start position:0% +where somebody looked at what the +probability that something uh that any + + align:start position:0% +probability that something uh that any + + + align:start position:0% +probability that something uh that any +given musical object would be recognized + + align:start position:0% +given musical object would be recognized + + + align:start position:0% +given musical object would be recognized +properly so 97% + + align:start position:0% +properly so 97% + + + align:start position:0% +properly so 97% +99% some of them I don't believe + + align:start position:0% +99% some of them I don't believe + + + align:start position:0% +99% some of them I don't believe +anything that says 100. that means not + + align:start position:0% +anything that says 100. that means not + + + align:start position:0% +anything that says 100. that means not +enough data right but you know uh a lot + + align:start position:0% +enough data right but you know uh a lot + + + align:start position:0% +enough data right but you know uh a lot +of things so we can look at uh + + align:start position:0% +of things so we can look at uh + + + align:start position:0% +of things so we can look at uh +various uh probabilities the natural is + + align:start position:0% +various uh probabilities the natural is + + + align:start position:0% +various uh probabilities the natural is +that's quite quite quite + + align:start position:0% +that's quite quite quite + + + align:start position:0% +that's quite quite quite +low so then um this is where there + + align:start position:0% +low so then um this is where there + + + align:start position:0% +low so then um this is where there +should have been some gigantic formula + + align:start position:0% +should have been some gigantic formula + + + align:start position:0% +should have been some gigantic formula +with regressions but it turns out all + + align:start position:0% +with regressions but it turns out all + + + align:start position:0% +with regressions but it turns out all +you need to do is find the probability + + align:start position:0% +you need to do is find the probability + + + align:start position:0% +you need to do is find the probability +that of each measure being the same find + + align:start position:0% +that of each measure being the same find + + + align:start position:0% +that of each measure being the same find +the probability that it would how how + + align:start position:0% +the probability that it would how how + + + align:start position:0% +the probability that it would how how +many changes you would have to make and + + align:start position:0% +many changes you would have to make and + + + align:start position:0% +many changes you would have to make and +multiply those two probabilities and + + align:start position:0% +multiply those two probabilities and + + + align:start position:0% +multiply those two probabilities and +take the max value so and yeah it is + + align:start position:0% +take the max value so and yeah it is + + + align:start position:0% +take the max value so and yeah it is +that simple um so the workflow normally + + align:start position:0% +that simple um so the workflow normally + + + align:start position:0% +that simple um so the workflow normally +take a PDF turn it into music XML we + + align:start position:0% +take a PDF turn it into music XML we + + + align:start position:0% +take a PDF turn it into music XML we +kind of stuck ourselves in to in the + + align:start position:0% +kind of stuck ourselves in to in the + + + align:start position:0% +kind of stuck ourselves in to in the +middle take uh run it through one more + + align:start position:0% +middle take uh run it through one more + + + align:start position:0% +middle take uh run it through one more +time I would love to be able to send it + + align:start position:0% +time I would love to be able to send it + + + align:start position:0% +time I would love to be able to send it +all the way back into the omr pipeline + + align:start position:0% +all the way back into the omr pipeline + + + align:start position:0% +all the way back into the omr pipeline +and say no reject that now rerun the + + align:start position:0% +and say no reject that now rerun the + + + align:start position:0% +and say no reject that now rerun the +recognition with this being a + + align:start position:0% +recognition with this being a + + + align:start position:0% +recognition with this being a +possibility but didn't get to that um + + align:start position:0% +possibility but didn't get to that um + + + align:start position:0% +possibility but didn't get to that um +then had a whole bunch of scores where + + align:start position:0% +then had a whole bunch of scores where + + + align:start position:0% +then had a whole bunch of scores where +we had um not not as many as I would + + align:start position:0% +we had um not not as many as I would + + + align:start position:0% +we had um not not as many as I would +like but we had scanned Optical music + + align:start position:0% +like but we had scanned Optical music + + + align:start position:0% +like but we had scanned Optical music +recognition music XML and we had the + + align:start position:0% +recognition music XML and we had the + + + align:start position:0% +recognition music XML and we had the +correctly encoded one and we can look at + + align:start position:0% +correctly encoded one and we can look at + + + align:start position:0% +correctly encoded one and we can look at +the number of differences before run + + align:start position:0% +the number of differences before run + + + align:start position:0% +the number of differences before run +through the model and then look at the + + align:start position:0% +through the model and then look at the + + + align:start position:0% +through the model and then look at the +new number of + + align:start position:0% +new number of + + + align:start position:0% +new number of +differences um all of this code is in + + align:start position:0% +differences um all of this code is in + + + align:start position:0% +differences um all of this code is in +music 21 in case you want to use it to + + align:start position:0% +music 21 in case you want to use it to + + + align:start position:0% +music 21 in case you want to use it to +improve things how everything works and + + align:start position:0% +improve things how everything works and + + + align:start position:0% +improve things how everything works and +the music we looked at again too many + + align:start position:0% +the music we looked at again too many + + + align:start position:0% +the music we looked at again too many +canonical + + align:start position:0% +canonical + + + align:start position:0% +canonical +composers average about 19% decrease in + + align:start position:0% +composers average about 19% decrease in + + + align:start position:0% +composers average about 19% decrease in +error which made us very happy in a + + align:start position:0% +error which made us very happy in a + + + align:start position:0% +error which made us very happy in a +field where um usually you're trying to + + align:start position:0% +field where um usually you're trying to + + + align:start position:0% +field where um usually you're trying to +improve by 1% at a time or something and + + align:start position:0% +improve by 1% at a time or something and + + + align:start position:0% +improve by 1% at a time or something and +Got U well and Mora Church earned the + + align:start position:0% +Got U well and Mora Church earned the + + + align:start position:0% +Got U well and Mora Church earned the +best uh grad student paper award which + + align:start position:0% +best uh grad student paper award which + + + align:start position:0% +best uh grad student paper award which +was great because she wasn't technically + + align:start position:0% +was great because she wasn't technically + + + align:start position:0% +was great because she wasn't technically +qualified because she was still an + + align:start position:0% +qualified because she was still an + + + align:start position:0% +qualified because she was still an +undergrad but but um yeah so it worked + + align:start position:0% +undergrad but but um yeah so it worked + + + align:start position:0% +undergrad but but um yeah so it worked +worked pretty well um here and some of + + align:start position:0% +worked pretty well um here and some of + + + align:start position:0% +worked pretty well um here and some of +the pieces got as high as 36% error + + align:start position:0% +the pieces got as high as 36% error + + + align:start position:0% +the pieces got as high as 36% error +reduction so what happens you have all + + align:start position:0% +reduction so what happens you have all + + + align:start position:0% +reduction so what happens you have all +original score we've marked what's the + + align:start position:0% +original score we've marked what's the + + + align:start position:0% +original score we've marked what's the +errors we correct that and then post + + align:start position:0% +errors we correct that and then post + + + align:start position:0% +errors we correct that and then post +correction it's correct if we got the + + align:start position:0% +correction it's correct if we got the + + + align:start position:0% +correction it's correct if we got the +same Rhythm not if we um not necessarily + + align:start position:0% +same Rhythm not if we um not necessarily + + + align:start position:0% +same Rhythm not if we um not necessarily +the right pitch because we didn't work + + align:start position:0% +the right pitch because we didn't work + + + align:start position:0% +the right pitch because we didn't work +any time on that so these are all the + + align:start position:0% +any time on that so these are all the + + + align:start position:0% +any time on that so these are all the +places to be looking + + align:start position:0% +places to be looking + + + align:start position:0% +places to be looking +at here here's what the optical music + + align:start position:0% +at here here's what the optical music + + + align:start position:0% +at here here's what the optical music +recognition software got + + align:start position:0% +recognition software got + + + align:start position:0% +recognition software got +wrong and um the correction so it got in + + align:start position:0% +wrong and um the correction so it got in + + + align:start position:0% +wrong and um the correction so it got in +this case three out of five corrected + + align:start position:0% +this case three out of five corrected + + + align:start position:0% +this case three out of five corrected +see them all there um but the what what + + align:start position:0% +see them all there um but the what what + + + align:start position:0% +see them all there um but the what what +really um came out of this work for me + + align:start position:0% +really um came out of this work for me + + + align:start position:0% +really um came out of this work for me +that seemed very important was that we + + align:start position:0% +that seemed very important was that we + + + align:start position:0% +that seemed very important was that we +are evaluating the quality of our work a + + align:start position:0% +are evaluating the quality of our work a + + + align:start position:0% +are evaluating the quality of our work a +little bit wrong so there's um + + align:start position:0% +little bit wrong so there's um + + + align:start position:0% +little bit wrong so there's um +that we need to be looking at Optical + + align:start position:0% +that we need to be looking at Optical + + + align:start position:0% +that we need to be looking at Optical +music recognition that allows for + + align:start position:0% +music recognition that allows for + + + align:start position:0% +music recognition that allows for +musical semantics to go back and forth + + align:start position:0% +musical semantics to go back and forth + + + align:start position:0% +musical semantics to go back and forth +into things um that was a prop possible + + align:start position:0% +into things um that was a prop possible + + + align:start position:0% +into things um that was a prop possible +implementation for how you can um make + + align:start position:0% +implementation for how you can um make + + + align:start position:0% +implementation for how you can um make +it faster to do things but um so there's + + align:start position:0% +it faster to do things but um so there's + + + align:start position:0% +it faster to do things but um so there's +proposals for judging how good Optical + + align:start position:0% +proposals for judging how good Optical + + + align:start position:0% +proposals for judging how good Optical +music recognition software is that you + + align:start position:0% +music recognition software is that you + + + align:start position:0% +music recognition software is that you +feed in a bunch of scores and you see + + align:start position:0% +feed in a bunch of scores and you see + + + align:start position:0% +feed in a bunch of scores and you see +how you know how well does it do but + + align:start position:0% +how you know how well does it do but + + + align:start position:0% +how you know how well does it do but +some of the standard scores being used + + align:start position:0% +some of the standard scores being used + + + align:start position:0% +some of the standard scores being used +are ones that uh if we had to run our + + align:start position:0% +are ones that uh if we had to run our + + + align:start position:0% +are ones that uh if we had to run our +software through would run terribly on + + align:start position:0% +software through would run terribly on + + + align:start position:0% +software through would run terribly on +so this is one of the ones that you + + align:start position:0% +so this is one of the ones that you + + + align:start position:0% +so this is one of the ones that you +should be able to recognize but this + + align:start position:0% +should be able to recognize but this + + + align:start position:0% +should be able to recognize but this +particular score has no motivic + + align:start position:0% +particular score has no motivic + + + align:start position:0% +particular score has no motivic +repetition I mean I I've never even + + align:start position:0% +repetition I mean I I've never even + + + align:start position:0% +repetition I mean I I've never even +played it let me let me play it just + + align:start position:0% +played it let me let me play it just + + + align:start position:0% +played it let me let me play it just +here how unusual that score is + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so it doesn't really behave like a + + align:start position:0% +so it doesn't really behave like a + + + align:start position:0% +so it doesn't really behave like a +normal score and there's even things + + align:start position:0% +normal score and there's even things + + + align:start position:0% +normal score and there's even things +like if if I my Optical music + + align:start position:0% +like if if I my Optical music + + + align:start position:0% +like if if I my Optical music +recognition saw that c when it just + + align:start position:0% +recognition saw that c when it just + + + align:start position:0% +recognition saw that c when it just +recognized this key signature I would + + align:start position:0% +recognized this key signature I would + + + align:start position:0% +recognized this key signature I would +say you probably got it wrong that's + + align:start position:0% +say you probably got it wrong that's + + + align:start position:0% +say you probably got it wrong that's +probably a c natural or you've got your + + align:start position:0% +probably a c natural or you've got your + + + align:start position:0% +probably a c natural or you've got your +key signature wrong because there's no + + align:start position:0% +key signature wrong because there's no + + + align:start position:0% +key signature wrong because there's no +reason why you would write a sharp there + + align:start position:0% +reason why you would write a sharp there + + + align:start position:0% +reason why you would write a sharp there +immediately + + align:start position:0% + + + + align:start position:0% + +there are other things that are in the + + align:start position:0% +there are other things that are in the + + + align:start position:0% +there are other things that are in the +test beds I still think we need to do + + align:start position:0% +test beds I still think we need to do + + + align:start position:0% +test beds I still think we need to do +like being able to recognize properly + + align:start position:0% +like being able to recognize properly + + + align:start position:0% +like being able to recognize properly +this measure and I get that it's trying + + align:start position:0% +this measure and I get that it's trying + + + align:start position:0% +this measure and I get that it's trying +to test can you recognize a whole bunch + + align:start position:0% +to test can you recognize a whole bunch + + + align:start position:0% +to test can you recognize a whole bunch +of rests but if I saw this from an + + align:start position:0% +of rests but if I saw this from an + + + align:start position:0% +of rests but if I saw this from an +regular regular piece of music I would + + align:start position:0% +regular regular piece of music I would + + + align:start position:0% +regular regular piece of music I would +say those are probably notes in here + + align:start position:0% +say those are probably notes in here + + + align:start position:0% +say those are probably notes in here +right because there's no reason to not + + align:start position:0% +right because there's no reason to not + + + align:start position:0% +right because there's no reason to not +just write every measure like + + align:start position:0% +just write every measure like + + + align:start position:0% +just write every measure like +this and then other things if you get + + align:start position:0% +this and then other things if you get + + + align:start position:0% +this and then other things if you get +really smart you could okay well that's + + align:start position:0% +really smart you could okay well that's + + + align:start position:0% +really smart you could okay well that's +a pedal Mark and that's a cleff Mark I + + align:start position:0% +a pedal Mark and that's a cleff Mark I + + + align:start position:0% +a pedal Mark and that's a cleff Mark I +don't know a single Alto cff instrument + + align:start position:0% +don't know a single Alto cff instrument + + + align:start position:0% +don't know a single Alto cff instrument +that uses one staff and has pedals so I + + align:start position:0% +that uses one staff and has pedals so I + + + align:start position:0% +that uses one staff and has pedals so I +would send it back and say you got to + + align:start position:0% +would send it back and say you got to + + + align:start position:0% +would send it back and say you got to +change one of these things in your + + align:start position:0% +change one of these things in your + + + align:start position:0% +change one of these things in your +recognition um so I think in our quest + + align:start position:0% +recognition um so I think in our quest + + + align:start position:0% +recognition um so I think in our quest +to try to give simple tests that can be + + align:start position:0% +to try to give simple tests that can be + + + align:start position:0% +to try to give simple tests that can be +run very quickly we're ending up + + align:start position:0% +run very quickly we're ending up + + + align:start position:0% +run very quickly we're ending up +optimizing our models for things that + + align:start position:0% +optimizing our models for things that + + + align:start position:0% +optimizing our models for things that +don't resemble the music that most of us + + align:start position:0% +don't resemble the music that most of us + + + align:start position:0% +don't resemble the music that most of us +learn um yes so there's still a ton of + + align:start position:0% +learn um yes so there's still a ton of + + + align:start position:0% +learn um yes so there's still a ton of +work to be done on music theory and + + align:start position:0% +work to be done on music theory and + + + align:start position:0% +work to be done on music theory and +semantics in Optical music recognition + + align:start position:0% +semantics in Optical music recognition + + + align:start position:0% +semantics in Optical music recognition +choices and this is something that's + + align:start position:0% +choices and this is something that's + + + align:start position:0% +choices and this is something that's +getting a little bit harder now with the + + align:start position:0% +getting a little bit harder now with the + + + align:start position:0% +getting a little bit harder now with the +rise of most people who are trying to + + align:start position:0% +rise of most people who are trying to + + + align:start position:0% +rise of most people who are trying to +work in this field now obviously want to + + align:start position:0% +work in this field now obviously want to + + + align:start position:0% +work in this field now obviously want to +use machine learning artificial + + align:start position:0% +use machine learning artificial + + + align:start position:0% +use machine learning artificial +intelligence and deep learning models um + + align:start position:0% +intelligence and deep learning models um + + + align:start position:0% +intelligence and deep learning models um +which will be great once we get more + + align:start position:0% +which will be great once we get more + + + align:start position:0% +which will be great once we get more +ground truths encoded and we can do + + align:start position:0% +ground truths encoded and we can do + + + align:start position:0% +ground truths encoded and we can do +things right now that's the hardest part + + align:start position:0% +things right now that's the hardest part + + + align:start position:0% +things right now that's the hardest part +of having more things lined up so that + + align:start position:0% +of having more things lined up so that + + + align:start position:0% +of having more things lined up so that +the computer can learn but um it's it's + + align:start position:0% +the computer can learn but um it's it's + + + align:start position:0% +the computer can learn but um it's it's +going to be harder and harder as long as + + align:start position:0% +going to be harder and harder as long as + + + align:start position:0% +going to be harder and harder as long as +we're just using black boxes to be able + + align:start position:0% +we're just using black boxes to be able + + + align:start position:0% +we're just using black boxes to be able +to um to get this uh in into there uh I + + align:start position:0% +to um to get this uh in into there uh I + + + align:start position:0% +to um to get this uh in into there uh I +think uh you all have actually met the + + align:start position:0% +think uh you all have actually met the + + + align:start position:0% +think uh you all have actually met the +world's expert in doing this his name is + + align:start position:0% +world's expert in doing this his name is + + + align:start position:0% +world's expert in doing this his name is +Gus sha he h was here um when we moved + + align:start position:0% +Gus sha he h was here um when we moved + + + align:start position:0% +Gus sha he h was here um when we moved +in another place yeah so there are + + align:start position:0% +in another place yeah so there are + + + align:start position:0% +in another place yeah so there are +people who are trying to figure out a + + align:start position:0% +people who are trying to figure out a + + + align:start position:0% +people who are trying to figure out a +way to add uh not just not just in + + align:start position:0% +way to add uh not just not just in + + + align:start position:0% +way to add uh not just not just in +Optical music recognition but in any + + align:start position:0% +Optical music recognition but in any + + + align:start position:0% +Optical music recognition but in any +sort of artificial intelligence working + + align:start position:0% +sort of artificial intelligence working + + + align:start position:0% +sort of artificial intelligence working +with scores how that we can we can still + + align:start position:0% +with scores how that we can we can still + + + align:start position:0% +with scores how that we can we can still +use these big deep learning models but + + align:start position:0% +use these big deep learning models but + + + align:start position:0% +use these big deep learning models but +still but incorporate music theory into + + align:start position:0% +still but incorporate music theory into + + + align:start position:0% +still but incorporate music theory into +that so that's the big challenge for our + + align:start position:0% + + + + align:start position:0% + +time questions on this yeah what do you + + align:start position:0% +time questions on this yeah what do you + + + align:start position:0% +time questions on this yeah what do you +think the state of using deep Lear + + align:start position:0% +think the state of using deep Lear + + + align:start position:0% +think the state of using deep Lear +endtoend deep learning for + + align:start position:0% +endtoend deep learning for + + + align:start position:0% +endtoend deep learning for +optical yeah so what do I think this the + + align:start position:0% +optical yeah so what do I think this the + + + align:start position:0% +optical yeah so what do I think this the +state of the-art of using endend deep + + align:start position:0% +state of the-art of using endend deep + + + align:start position:0% +state of the-art of using endend deep +learning for optical music recognition I + + align:start position:0% +learning for optical music recognition I + + + align:start position:0% +learning for optical music recognition I +think it is a place um with great + + align:start position:0% +think it is a place um with great + + + align:start position:0% +think it is a place um with great +potential it is not nearly as good yet + + align:start position:0% +potential it is not nearly as good yet + + + align:start position:0% +potential it is not nearly as good yet +as the things you can buy um smart score + + align:start position:0% +as the things you can buy um smart score + + + align:start position:0% +as the things you can buy um smart score +sharpy uh the things that are there but + + align:start position:0% +sharpy uh the things that are there but + + + align:start position:0% +sharpy uh the things that are there but +it you know it's has a lot of potential + + align:start position:0% +it you know it's has a lot of potential + + + align:start position:0% +it you know it's has a lot of potential +and one of the things most of the work + + align:start position:0% +and one of the things most of the work + + + align:start position:0% +and one of the things most of the work +that I've seen on it is missing are the + + align:start position:0% +that I've seen on it is missing are the + + + align:start position:0% +that I've seen on it is missing are the +skills that you guys have here um I saw + + align:start position:0% +skills that you guys have here um I saw + + + align:start position:0% +skills that you guys have here um I saw +okay I'm going to forget you're going to + + align:start position:0% +okay I'm going to forget you're going to + + + align:start position:0% +okay I'm going to forget you're going to +tell me to put this back up in a second + + align:start position:0% +tell me to put this back up in a second + + + align:start position:0% +tell me to put this back up in a second +I just need a couple extra lines I I + + align:start position:0% +I just need a couple extra lines I I + + + align:start position:0% +I just need a couple extra lines I I +actually saw a model um + + align:start position:0% +actually saw a model um + + + align:start position:0% +actually saw a model um +where uh it was using generated scores + + align:start position:0% +where uh it was using generated scores + + + align:start position:0% +where uh it was using generated scores +which are a little bit different because + + align:start position:0% +which are a little bit different because + + + align:start position:0% +which are a little bit different because +they're always the same so you take an + + align:start position:0% +they're always the same so you take an + + + align:start position:0% +they're always the same so you take an +output from finale or M score or + + align:start position:0% +output from finale or M score or + + + align:start position:0% +output from finale or M score or +something you create a image file and + + align:start position:0% +something you create a image file and + + + align:start position:0% +something you create a image file and +then you know exactly where every note + + align:start position:0% +then you know exactly where every note + + + align:start position:0% +then you know exactly where every note +is because you wrote it and everything + + align:start position:0% +is because you wrote it and everything + + + align:start position:0% +is because you wrote it and everything +so you can generate a million ground + + align:start position:0% +so you can generate a million ground + + + align:start position:0% +so you can generate a million ground +truths and stuff like that and so it was + + align:start position:0% +truths and stuff like that and so it was + + + align:start position:0% +truths and stuff like that and so it was +you know running through a whole bunch + + align:start position:0% +you know running through a whole bunch + + + align:start position:0% +you know running through a whole bunch +of scores and + + align:start position:0% +of scores and + + + align:start position:0% +of scores and +things and this particular one it had a + + align:start position:0% +things and this particular one it had a + + + align:start position:0% +things and this particular one it had a +particular uh reinforcement learning + + align:start position:0% +particular uh reinforcement learning + + + align:start position:0% +particular uh reinforcement learning +problem that it successfully identified + + align:start position:0% +problem that it successfully identified + + + align:start position:0% +problem that it successfully identified +where all the notes were and where all + + align:start position:0% +where all the notes were and where all + + + align:start position:0% +where all the notes were and where all +the staff lines were it was getting + + align:start position:0% +the staff lines were it was getting + + + align:start position:0% +the staff lines were it was getting +incredibly incredibly good but could not + + align:start position:0% +incredibly incredibly good but could not + + + align:start position:0% +incredibly incredibly good but could not +break around 80% on then recognizing + + align:start position:0% +break around 80% on then recognizing + + + align:start position:0% +break around 80% on then recognizing +what the note was why because they had + + align:start position:0% +what the note was why because they had + + + align:start position:0% +what the note was why because they had +trained it on this is a this is D this + + align:start position:0% +trained it on this is a this is D this + + + align:start position:0% +trained it on this is a this is D this +is G this is F this is B flat + + align:start position:0% +is G this is F this is B flat + + + align:start position:0% +is G this is F this is B flat +uh this is B flat this is e actually + + align:start position:0% +uh this is B flat this is e actually + + + align:start position:0% +uh this is B flat this is e actually +we'll make it even even even + + align:start position:0% +we'll make it even even even + + + align:start position:0% +we'll make it even even even +better put that + + align:start position:0% + + + + align:start position:0% + +there that's an e + + align:start position:0% +there that's an e + + + align:start position:0% +there that's an e +sharp so these are all being + + align:start position:0% +sharp so these are all being + + + align:start position:0% +sharp so these are all being +recognized the fourth will also be right + + align:start position:0% +recognized the fourth will also be right + + + align:start position:0% +recognized the fourth will also be right +yeah that's oh sorry thank you yep um + + align:start position:0% +yeah that's oh sorry thank you yep um + + + align:start position:0% +yeah that's oh sorry thank you yep um +thank you very much Adam but now imagine + + align:start position:0% +thank you very much Adam but now imagine + + + align:start position:0% +thank you very much Adam but now imagine +you're the PO computer that's having to + + align:start position:0% +you're the PO computer that's having to + + + align:start position:0% +you're the PO computer that's having to +predict okay a I got it right d i got it + + align:start position:0% +predict okay a I got it right d i got it + + + align:start position:0% +predict okay a I got it right d i got it +right oh sorry I didn't mean that G and + + align:start position:0% +right oh sorry I didn't mean that G and + + + align:start position:0% +right oh sorry I didn't mean that G and +ignore that G I got it right uh I think + + align:start position:0% +ignore that G I got it right uh I think + + + align:start position:0% +ignore that G I got it right uh I think +that's + + align:start position:0% +that's + + + align:start position:0% +that's +F because it's only looking at sorry + + align:start position:0% +F because it's only looking at sorry + + + align:start position:0% +F because it's only looking at sorry +camera and people on this side because + + align:start position:0% +camera and people on this side because + + + align:start position:0% +camera and people on this side because +it's only looking at this amount of data + + align:start position:0% +it's only looking at this amount of data + + + align:start position:0% +it's only looking at this amount of data +whereas it needs some way to know that's + + align:start position:0% +whereas it needs some way to know that's + + + align:start position:0% +whereas it needs some way to know that's +sharp um yeah this this one could get + + align:start position:0% +sharp um yeah this this one could get + + + align:start position:0% +sharp um yeah this this one could get +right is B flat and then again it was + + align:start position:0% +right is B flat and then again it was + + + align:start position:0% +right is B flat and then again it was +saying uh I think that's G + + align:start position:0% +saying uh I think that's G + + + align:start position:0% +saying uh I think that's G +flat I think that's C and I think that's + + align:start position:0% +flat I think that's C and I think that's + + + align:start position:0% +flat I think that's C and I think that's +D because the training data had + + align:start position:0% +D because the training data had + + + align:start position:0% +D because the training data had +prioritized treble cff and once it's + + align:start position:0% +prioritized treble cff and once it's + + + align:start position:0% +prioritized treble cff and once it's +here has no way of getting back to here + + align:start position:0% +here has no way of getting back to here + + + align:start position:0% +here has no way of getting back to here +what what should the computer be trying + + align:start position:0% +what what should the computer be trying + + + align:start position:0% +what what should the computer be trying +to + + align:start position:0% +to + + + align:start position:0% +to +predict on this + + align:start position:0% + + + + align:start position:0% + +basis anyone take a guess B based on the + + align:start position:0% +basis anyone take a guess B based on the + + + align:start position:0% +basis anyone take a guess B based on the +amount of information you're trying to + + align:start position:0% +amount of information you're trying to + + + align:start position:0% +amount of information you're trying to +get the computer what would be uh an + + align:start position:0% +get the computer what would be uh an + + + align:start position:0% +get the computer what would be uh an +essentially incredibly good prediction + + align:start position:0% +essentially incredibly good prediction + + + align:start position:0% +essentially incredibly good prediction +model yeah maybe just have it predict + + align:start position:0% +model yeah maybe just have it predict + + + align:start position:0% +model yeah maybe just have it predict +like which line or space yeah what's + + align:start position:0% +like which line or space yeah what's + + + align:start position:0% +like which line or space yeah what's +yeah I see a quarter note on + + align:start position:0% +yeah I see a quarter note on + + + align:start position:0% +yeah I see a quarter note on +space + + align:start position:0% +space + + + align:start position:0% +space +three I see a 16th note on line five and + + align:start position:0% +three I see a 16th note on line five and + + + align:start position:0% +three I see a 16th note on line five and +then when you put all that together then + + align:start position:0% +then when you put all that together then + + + align:start position:0% +then when you put all that together then +have a separate detector trying to + + align:start position:0% +have a separate detector trying to + + + align:start position:0% +have a separate detector trying to +detect all the cffs or it can be the + + align:start position:0% +detect all the cffs or it can be the + + + align:start position:0% +detect all the cffs or it can be the +same one these things are pretty smart + + align:start position:0% +same one these things are pretty smart + + + align:start position:0% +same one these things are pretty smart +but yeah and try to do that and then + + align:start position:0% +but yeah and try to do that and then + + + align:start position:0% +but yeah and try to do that and then +only afterwards connect those two data + + align:start position:0% +only afterwards connect those two data + + + align:start position:0% +only afterwards connect those two data +to other things so that that was that + + align:start position:0% +to other things so that that was that + + + align:start position:0% +to other things so that that was that +was really nice that um that that was + + align:start position:0% +was really nice that um that that was + + + align:start position:0% +was really nice that um that that was +about I think four about four years ago + + align:start position:0% +about I think four about four years ago + + + align:start position:0% +about I think four about four years ago +that that this was shown to me as sort + + align:start position:0% +that that this was shown to me as sort + + + align:start position:0% +that that this was shown to me as sort +of the state-ofthe-art I think that + + align:start position:0% +of the state-ofthe-art I think that + + + align:start position:0% +of the state-ofthe-art I think that +they've gotten better since then but + + align:start position:0% +they've gotten better since then but + + + align:start position:0% +they've gotten better since then but +there's still if if these kind of + + align:start position:0% +there's still if if these kind of + + + align:start position:0% +there's still if if these kind of +mistakes were still being made four + + align:start position:0% +mistakes were still being made four + + + align:start position:0% +mistakes were still being made four +years ago I imagine that there's still + + align:start position:0% +years ago I imagine that there's still + + + align:start position:0% +years ago I imagine that there's still +many um stumbling blocks that you can uh + + align:start position:0% +many um stumbling blocks that you can uh + + + align:start position:0% +many um stumbling blocks that you can uh +put in for and I I think a team from + + align:start position:0% +put in for and I I think a team from + + + align:start position:0% +put in for and I I think a team from +here now with the knowledge that we have + + align:start position:0% +here now with the knowledge that we have + + + align:start position:0% +here now with the knowledge that we have +uh could you know in a year-long project + + align:start position:0% +uh could you know in a year-long project + + + align:start position:0% +uh could you know in a year-long project +produce a real State ofthe art tool yeah + + align:start position:0% +produce a real State ofthe art tool yeah + + + align:start position:0% +produce a real State ofthe art tool yeah +Misha with some of the best uh like + + align:start position:0% +Misha with some of the best uh like + + + align:start position:0% +Misha with some of the best uh like +language large language models they use + + align:start position:0% +language large language models they use + + + align:start position:0% +language large language models they use +like attention based models y so in this + + align:start position:0% +like attention based models y so in this + + + align:start position:0% +like attention based models y so in this +case this actually might um fix this + + align:start position:0% +case this actually might um fix this + + + align:start position:0% +case this actually might um fix this +problem because it would really + + align:start position:0% +problem because it would really + + + align:start position:0% +problem because it would really +priortize Stu at the beginning of the + + align:start position:0% +priortize Stu at the beginning of the + + + align:start position:0% +priortize Stu at the beginning of the +measure and and ignore the adg when + + align:start position:0% +measure and and ignore the adg when + + + align:start position:0% +measure and and ignore the adg when +evaluating half sharp yeah yeah some of + + align:start position:0% +evaluating half sharp yeah yeah some of + + + align:start position:0% +evaluating half sharp yeah yeah some of +you who are also taking um uh Aran Go's + + align:start position:0% +you who are also taking um uh Aran Go's + + + align:start position:0% +you who are also taking um uh Aran Go's +interactive music systems had um had a + + align:start position:0% +interactive music systems had um had a + + + align:start position:0% +interactive music systems had um had a +lecture from one of the experts Anna + + align:start position:0% +lecture from one of the experts Anna + + + align:start position:0% +lecture from one of the experts Anna +hang who is um an expert in the + + align:start position:0% +hang who is um an expert in the + + + align:start position:0% +hang who is um an expert in the +attention models and the the sort of + + align:start position:0% +attention models and the the sort of + + + align:start position:0% +attention models and the the sort of +things where you sort of have a memory + + align:start position:0% +things where you sort of have a memory + + + align:start position:0% +things where you sort of have a memory +and thinking back about what's what's + + align:start position:0% +and thinking back about what's what's + + + align:start position:0% +and thinking back about what's what's +important earlier in the data and so uh + + align:start position:0% +important earlier in the data and so uh + + + align:start position:0% +important earlier in the data and so uh +I think that that her work um and that's + + align:start position:0% +I think that that her work um and that's + + + align:start position:0% +I think that that her work um and that's +over at Google um project magenta I + + align:start position:0% +over at Google um project magenta I + + + align:start position:0% +over at Google um project magenta I +think that that could have a lot of of + + align:start position:0% +think that that could have a lot of of + + + align:start position:0% +think that that could have a lot of of +impact on the field and there's other + + align:start position:0% +impact on the field and there's other + + + align:start position:0% +impact on the field and there's other +people um naming naming a few people + + align:start position:0% +people um naming naming a few people + + + align:start position:0% +people um naming naming a few people +doesn't mean that these are the only + + align:start position:0% +doesn't mean that these are the only + + + align:start position:0% +doesn't mean that these are the only +people doing great things is just ones + + align:start position:0% +people doing great things is just ones + + + align:start position:0% +people doing great things is just ones +people who I seem to know but none of + + align:start position:0% +people who I seem to know but none of + + + align:start position:0% +people who I seem to know but none of +these people are are working + + align:start position:0% +these people are are working + + + align:start position:0% +these people are are working +particularly on the optical music + + align:start position:0% +particularly on the optical music + + + align:start position:0% +particularly on the optical music +recognition problem so again we need to + + align:start position:0% +recognition problem so again we need to + + + align:start position:0% +recognition problem so again we need to +someday have 21m 384 where we have a + + align:start position:0% +someday have 21m 384 where we have a + + + align:start position:0% +someday have 21m 384 where we have a +whole semester to just take our projects + + align:start position:0% +whole semester to just take our projects + + + align:start position:0% +whole semester to just take our projects +and do something bigger uh but we don't + + align:start position:0% +and do something bigger uh but we don't + + + align:start position:0% +and do something bigger uh but we don't +have something like that + + align:start position:0% +have something like that + + + align:start position:0% +have something like that +yet because that would be a great group + + align:start position:0% +yet because that would be a great group + + + align:start position:0% +yet because that would be a great group +project right we going to do all + + align:start position:0% +project right we going to do all + + + align:start position:0% +project right we going to do all +this any + + align:start position:0% +this any + + + align:start position:0% +this any +other question + + align:start position:0% + + + + align:start position:0% + +yeah you know are there any classes I + + align:start position:0% +yeah you know are there any classes I + + + align:start position:0% +yeah you know are there any classes I +know like that no right now and Paul are + + align:start position:0% +know like that no right now and Paul are + + + align:start position:0% +know like that no right now and Paul are +you + + align:start position:0% +you + + + align:start position:0% +you +senior you're junior there may be by the + + align:start position:0% +senior you're junior there may be by the + + + align:start position:0% +senior you're junior there may be by the +time you uh leave or M we are looking at + + align:start position:0% +time you uh leave or M we are looking at + + + align:start position:0% +time you uh leave or M we are looking at +creating more classes on U on artificial + + align:start position:0% +creating more classes on U on artificial + + + align:start position:0% +creating more classes on U on artificial +intelligence and music and and these + + align:start position:0% +intelligence and music and and these + + + align:start position:0% +intelligence and music and and these +kinds of problems um yeah so there's + + align:start position:0% +kinds of problems um yeah so there's + + + align:start position:0% +kinds of problems um yeah so there's +there's prob um but definitely well I + + align:start position:0% +there's prob um but definitely well I + + + align:start position:0% +there's prob um but definitely well I +suppose if you're junior yeah we're + + align:start position:0% +suppose if you're junior yeah we're + + + align:start position:0% +suppose if you're junior yeah we're +already too late right we're in the + + align:start position:0% +already too late right we're in the + + + align:start position:0% +already too late right we're in the +second semester it's just been so cold I + + align:start position:0% +second semester it's just been so cold I + + + align:start position:0% +second semester it's just been so cold I +still feel don't feel like it's Spring + + align:start position:0% +still feel don't feel like it's Spring + + + align:start position:0% +still feel don't feel like it's Spring +end of semester there but yeah there + + align:start position:0% +end of semester there but yeah there + + + align:start position:0% +end of semester there but yeah there +there should be more and and there are + + align:start position:0% +there should be more and and there are + + + align:start position:0% +there should be more and and there are +other schools that offer um some of + + align:start position:0% +other schools that offer um some of + + + align:start position:0% +other schools that offer um some of +these things and and various workshops + + align:start position:0% +these things and and various workshops + + + align:start position:0% +these things and and various workshops +that you could go to on some these + + align:start position:0% +that you could go to on some these + + + align:start position:0% +that you could go to on some these +techniques but we're all we're all still + + align:start position:0% +techniques but we're all we're all still + + + align:start position:0% +techniques but we're all we're all still +learning we're all still trying to + + align:start position:0% +learning we're all still trying to + + + align:start position:0% +learning we're all still trying to +create um the musical equivalent of for + + align:start position:0% +create um the musical equivalent of for + + + align:start position:0% +create um the musical equivalent of for +those who have done machine learning + + align:start position:0% +those who have done machine learning + + + align:start position:0% +those who have done machine learning +know the handwritten to to to to data + + align:start position:0% +know the handwritten to to to to data + + + align:start position:0% +know the handwritten to to to to data +set the classify thing which everybody + + align:start position:0% +set the classify thing which everybody + + + align:start position:0% +set the classify thing which everybody +does as their first artificial + + align:start position:0% +does as their first artificial + + + align:start position:0% +does as their first artificial +intelligence thing to here's all the + + align:start position:0% +intelligence thing to here's all the + + + align:start position:0% +intelligence thing to here's all the +different ways to's been written now + + align:start position:0% +different ways to's been written now + + + align:start position:0% +different ways to's been written now +here's a new number what is it um we + + align:start position:0% +here's a new number what is it um we + + + align:start position:0% +here's a new number what is it um we +still need that data set for optical + + align:start position:0% +still need that data set for optical + + + align:start position:0% +still need that data set for optical +music recognition here are 10,000 + + align:start position:0% +music recognition here are 10,000 + + + align:start position:0% +music recognition here are 10,000 +quarter notes on space three from all + + align:start position:0% +quarter notes on space three from all + + + align:start position:0% +quarter notes on space three from all +different things and now can your system + + align:start position:0% +different things and now can your system + + + align:start position:0% +different things and now can your system +do that + + align:start position:0% +do that + + + align:start position:0% +do that +cool else + + align:start position:0% + + + + align:start position:0% + +well I'm going to give you time to + + align:start position:0% +well I'm going to give you time to + + + align:start position:0% +well I'm going to give you time to +either work on your projects or stay + + align:start position:0% +either work on your projects or stay + + + align:start position:0% +either work on your projects or stay +here or take advantage of the fact that + + align:start position:0% +here or take advantage of the fact that + + + align:start position:0% +here or take advantage of the fact that +um you know finally I didn't make it uh + + align:start position:0% +um you know finally I didn't make it uh + + + align:start position:0% +um you know finally I didn't make it uh +use up every inch my time so just um + + align:start position:0% +use up every inch my time so just um + + + align:start position:0% +use up every inch my time so just um +this is the end for my teaching in this + + align:start position:0% +this is the end for my teaching in this + + + align:start position:0% +this is the end for my teaching in this +class uh and next week I'm excited + + align:start position:0% +class uh and next week I'm excited + + + align:start position:0% +class uh and next week I'm excited +because I get to learn a lot new now + + align:start position:0% +because I get to learn a lot new now + + + align:start position:0% +because I get to learn a lot new now +I've been learning from youall but I'll + + align:start position:0% +I've been learning from youall but I'll + + + align:start position:0% +I've been learning from youall but I'll +get to learn a lot more so I'm looking + + align:start position:0% +get to learn a lot more so I'm looking + + + align:start position:0% +get to learn a lot more so I'm looking +forward to that um I'll have office + + align:start position:0% +forward to that um I'll have office + + + align:start position:0% +forward to that um I'll have office +hours uh as soon as I'm done here and uh + + align:start position:0% +hours uh as soon as I'm done here and uh + + + align:start position:0% +hours uh as soon as I'm done here and uh +look forward to to projects so + + align:start position:0% +look forward to to projects so + + + align:start position:0% +look forward to to projects so +thanks thanks oh oh that's nice that's + + align:start position:0% +thanks thanks oh oh that's nice that's + + + align:start position:0% +thanks thanks oh oh that's nice that's +nice thank you \ No newline at end of file diff --git a/t-n4a18AW08.txt b/t-n4a18AW08.txt new file mode 100644 index 0000000000000000000000000000000000000000..9fbfe108d659ee003536caadeccaac7adeb23aee --- /dev/null +++ b/t-n4a18AW08.txt @@ -0,0 +1,1011 @@ +align:start position:0% + +hi guys my name is Nicola and in this + + align:start position:0% +hi guys my name is Nicola and in this + + + align:start position:0% +hi guys my name is Nicola and in this +video we're going to work out an example + + align:start position:0% +video we're going to work out an example + + + align:start position:0% +video we're going to work out an example +of an orthogonal projection matrix + + align:start position:0% +of an orthogonal projection matrix + + + align:start position:0% +of an orthogonal projection matrix +specifically we are gonna compute the + + align:start position:0% +specifically we are gonna compute the + + + align:start position:0% +specifically we are gonna compute the +projection matrix onto the plane given + + align:start position:0% +projection matrix onto the plane given + + + align:start position:0% +projection matrix onto the plane given +by the equation X plus y minus Z equals + + align:start position:0% +by the equation X plus y minus Z equals + + + align:start position:0% +by the equation X plus y minus Z equals +0 so before we start let me just recall + + align:start position:0% +0 so before we start let me just recall + + + align:start position:0% +0 so before we start let me just recall +what a projection matrix is so you've + + align:start position:0% +what a projection matrix is so you've + + + align:start position:0% +what a projection matrix is so you've +seen this sketch here a million times + + align:start position:0% +seen this sketch here a million times + + + align:start position:0% +seen this sketch here a million times +already + + align:start position:0% +already + + + align:start position:0% +already +a projection matrix takes any vector in + + align:start position:0% +a projection matrix takes any vector in + + + align:start position:0% +a projection matrix takes any vector in +three space well in just in this case we + + align:start position:0% +three space well in just in this case we + + + align:start position:0% +three space well in just in this case we +are dealing with a three space and + + align:start position:0% +are dealing with a three space and + + + align:start position:0% +are dealing with a three space and +projects it down onto the plane a + + align:start position:0% +projects it down onto the plane a + + + align:start position:0% +projects it down onto the plane a +two-dimensional space subspace of r3 so + + align:start position:0% +two-dimensional space subspace of r3 so + + + align:start position:0% +two-dimensional space subspace of r3 so +I'm going to give you a few moments to + + align:start position:0% +I'm going to give you a few moments to + + + align:start position:0% +I'm going to give you a few moments to +consider the problem for yourselves and + + align:start position:0% +consider the problem for yourselves and + + + align:start position:0% +consider the problem for yourselves and +then you'll see my take on it + + align:start position:0% + + + + align:start position:0% + +again okay so in in lecture professor + + align:start position:0% +again okay so in in lecture professor + + + align:start position:0% +again okay so in in lecture professor +Strang derived in meticulous detail the + + align:start position:0% +Strang derived in meticulous detail the + + + align:start position:0% +Strang derived in meticulous detail the +formula for the projection matrix so it + + align:start position:0% +formula for the projection matrix so it + + + align:start position:0% +formula for the projection matrix so it +was given by the following well slightly + + align:start position:0% +was given by the following well slightly + + + align:start position:0% +was given by the following well slightly +complicated expression it's a times a + + align:start position:0% +complicated expression it's a times a + + + align:start position:0% +complicated expression it's a times a +transpose a inverse a transpose where a + + align:start position:0% +transpose a inverse a transpose where a + + + align:start position:0% +transpose a inverse a transpose where a +is a matrix that somehow encodes the + + align:start position:0% +is a matrix that somehow encodes the + + + align:start position:0% +is a matrix that somehow encodes the +subspace we're projecting on it yeah in + + align:start position:0% +subspace we're projecting on it yeah in + + + align:start position:0% +subspace we're projecting on it yeah in +particular a is has as its columns a 1 a + + align:start position:0% +particular a is has as its columns a 1 a + + + align:start position:0% +particular a is has as its columns a 1 a +2 I'm going to denote them a basis for + + align:start position:0% +2 I'm going to denote them a basis for + + + align:start position:0% +2 I'm going to denote them a basis for +the plane we're projecting on so + + align:start position:0% +the plane we're projecting on so + + + align:start position:0% +the plane we're projecting on so +essentially what we need to do is find + + align:start position:0% +essentially what we need to do is find + + + align:start position:0% +essentially what we need to do is find +two such vectors let's bend the plane + + align:start position:0% +two such vectors let's bend the plane + + + align:start position:0% +two such vectors let's bend the plane +and start computing with the matrix it's + + align:start position:0% +and start computing with the matrix it's + + + align:start position:0% +and start computing with the matrix it's +yeah this is fairly straightforward one + + align:start position:0% +yeah this is fairly straightforward one + + + align:start position:0% +yeah this is fairly straightforward one +one choice that works for example is 1 + + align:start position:0% +one choice that works for example is 1 + + + align:start position:0% +one choice that works for example is 1 +negative 1 0 for the first column and 1 + + align:start position:0% +negative 1 0 for the first column and 1 + + + align:start position:0% +negative 1 0 for the first column and 1 +0 1 for the second column ok and let me + + align:start position:0% +0 1 for the second column ok and let me + + + align:start position:0% +0 1 for the second column ok and let me +write out the matrix a ok so in the + + align:start position:0% +write out the matrix a ok so in the + + + align:start position:0% +write out the matrix a ok so in the +formula the I guess the more slightly + + align:start position:0% +formula the I guess the more slightly + + + align:start position:0% +formula the I guess the more slightly +more complicated combination these a + + align:start position:0% +more complicated combination these a + + + align:start position:0% +more complicated combination these a +transpose a inverse so let me compute + + align:start position:0% +transpose a inverse so let me compute + + + align:start position:0% +transpose a inverse so let me compute +that first for you ok so a transpose a + + align:start position:0% +that first for you ok so a transpose a + + + align:start position:0% +that first for you ok so a transpose a +is a 2 by 2 matrix and it's not so hard + + align:start position:0% +is a 2 by 2 matrix and it's not so hard + + + align:start position:0% +is a 2 by 2 matrix and it's not so hard +to figure out it's like 2 & 1 1 2 ok now + + align:start position:0% +to figure out it's like 2 & 1 1 2 ok now + + + align:start position:0% +to figure out it's like 2 & 1 1 2 ok now +we shall invert it + + align:start position:0% + + + + align:start position:0% + +using the familiar formula 1 over the + + align:start position:0% +using the familiar formula 1 over the + + + align:start position:0% +using the familiar formula 1 over the +determinant 2 times 2 minus 1 is 3 and + + align:start position:0% + + + + align:start position:0% + +so we switch the diagonal entries and we + + align:start position:0% +so we switch the diagonal entries and we + + + align:start position:0% +so we switch the diagonal entries and we +flip the signs of the off diagonal bus + + align:start position:0% +flip the signs of the off diagonal bus + + + align:start position:0% +flip the signs of the off diagonal bus +ok right and therefore projection matrix + + align:start position:0% +ok right and therefore projection matrix + + + align:start position:0% +ok right and therefore projection matrix +is given by the following product of + + align:start position:0% +is given by the following product of + + + align:start position:0% +is given by the following product of +matrices one-third to negative 1/2 and + + align:start position:0% +matrices one-third to negative 1/2 and + + + align:start position:0% +matrices one-third to negative 1/2 and +then transpose of a which is okay I'm + + align:start position:0% +then transpose of a which is okay I'm + + + align:start position:0% +then transpose of a which is okay I'm +gonna carry out this multiplication in + + align:start position:0% +gonna carry out this multiplication in + + + align:start position:0% +gonna carry out this multiplication in +an humanly fast fashion so I'm just + + align:start position:0% +an humanly fast fashion so I'm just + + + align:start position:0% +an humanly fast fashion so I'm just +gonna write down the answer which is a + + align:start position:0% +gonna write down the answer which is a + + + align:start position:0% +gonna write down the answer which is a +third to one right so what you can do + + align:start position:0% +third to one right so what you can do + + + align:start position:0% +third to one right so what you can do +now is well you can check whether this + + align:start position:0% +now is well you can check whether this + + + align:start position:0% +now is well you can check whether this +answer actually makes sense one thing + + align:start position:0% +answer actually makes sense one thing + + + align:start position:0% +answer actually makes sense one thing +you can do is just well + + align:start position:0% +you can do is just well + + + align:start position:0% +you can do is just well +projection matrix is supposed to take + + align:start position:0% +projection matrix is supposed to take + + + align:start position:0% +projection matrix is supposed to take +the normal to the plane down to 0 so you + + align:start position:0% +the normal to the plane down to 0 so you + + + align:start position:0% +the normal to the plane down to 0 so you +can just multiply P and the normal + + align:start position:0% +can just multiply P and the normal + + + align:start position:0% +can just multiply P and the normal +vector 1 1 negative 1 and if you get 0 + + align:start position:0% +vector 1 1 negative 1 and if you get 0 + + + align:start position:0% +vector 1 1 negative 1 and if you get 0 +maybe you've done a good job another + + align:start position:0% +maybe you've done a good job another + + + align:start position:0% +maybe you've done a good job another +curious thing that I would like to point + + align:start position:0% +curious thing that I would like to point + + + align:start position:0% +curious thing that I would like to point +out here is so you see we had lots of + + align:start position:0% +out here is so you see we had lots of + + + align:start position:0% +out here is so you see we had lots of +freedom of choosing the matrix a I mean + + align:start position:0% +freedom of choosing the matrix a I mean + + + align:start position:0% +freedom of choosing the matrix a I mean +you could have we could have chosen any + + align:start position:0% +you could have we could have chosen any + + + align:start position:0% +you could have we could have chosen any +two columns that spent the subspace that + + align:start position:0% +two columns that spent the subspace that + + + align:start position:0% +two columns that spent the subspace that +spans the plane + + align:start position:0% +spans the plane + + + align:start position:0% +spans the plane +the beautiful thing about it is that in + + align:start position:0% +the beautiful thing about it is that in + + + align:start position:0% +the beautiful thing about it is that in +Indiana we will get the same same answer + + align:start position:0% +Indiana we will get the same same answer + + + align:start position:0% +Indiana we will get the same same answer +right so I hope there will be many of + + align:start position:0% +right so I hope there will be many of + + + align:start position:0% +right so I hope there will be many of +you who would say hey there is an easier + + align:start position:0% +you who would say hey there is an easier + + + align:start position:0% +you who would say hey there is an easier +way to the problem and I'll agree with + + align:start position:0% +way to the problem and I'll agree with + + + align:start position:0% +way to the problem and I'll agree with +these people + + align:start position:0% +these people + + + align:start position:0% +these people +so let's yeah let's see what would be an + + align:start position:0% +so let's yeah let's see what would be an + + + align:start position:0% +so let's yeah let's see what would be an +easier approach well let's go back to + + align:start position:0% +easier approach well let's go back to + + + align:start position:0% +easier approach well let's go back to +the sketch here all right and let's make + + align:start position:0% +the sketch here all right and let's make + + + align:start position:0% +the sketch here all right and let's make +the following observation that any + + align:start position:0% +the following observation that any + + + align:start position:0% +the following observation that any +vector is a sum of two components well + + align:start position:0% +vector is a sum of two components well + + + align:start position:0% +vector is a sum of two components well +the first component is its projection + + align:start position:0% +the first component is its projection + + + align:start position:0% +the first component is its projection +onto the plane and the other component + + align:start position:0% +onto the plane and the other component + + + align:start position:0% +onto the plane and the other component +is its projection onto the orthogonal + + align:start position:0% +is its projection onto the orthogonal + + + align:start position:0% +is its projection onto the orthogonal +complement to the plane in this case + + align:start position:0% +complement to the plane in this case + + + align:start position:0% +complement to the plane in this case +onto the normal vector to the plane so + + align:start position:0% +onto the normal vector to the plane so + + + align:start position:0% +onto the normal vector to the plane so +in the language of linear algebra this + + align:start position:0% +in the language of linear algebra this + + + align:start position:0% +in the language of linear algebra this +is just V equals to projection onto the + + align:start position:0% +is just V equals to projection onto the + + + align:start position:0% +is just V equals to projection onto the +plane plus its projection I'm going to + + align:start position:0% +plane plus its projection I'm going to + + + align:start position:0% +plane plus its projection I'm going to +call it P and onto the orthogonal + + align:start position:0% +call it P and onto the orthogonal + + + align:start position:0% +call it P and onto the orthogonal +complement of the plane + + align:start position:0% +complement of the plane + + + align:start position:0% +complement of the plane +okay I'm gonna suggestively right here + + align:start position:0% +okay I'm gonna suggestively right here + + + align:start position:0% +okay I'm gonna suggestively right here +the identity matrix so that you can + + align:start position:0% +the identity matrix so that you can + + + align:start position:0% +the identity matrix so that you can +immediately read off a matrix equality + + align:start position:0% +immediately read off a matrix equality + + + align:start position:0% +immediately read off a matrix equality +associated with this equality here it's + + align:start position:0% +associated with this equality here it's + + + align:start position:0% +associated with this equality here it's +the identity equals P plus and therefore + + align:start position:0% +the identity equals P plus and therefore + + + align:start position:0% +the identity equals P plus and therefore +the projection matrix is just the + + align:start position:0% +the projection matrix is just the + + + align:start position:0% +the projection matrix is just the +identity minus the projection matrix + + align:start position:0% +identity minus the projection matrix + + + align:start position:0% +identity minus the projection matrix +onto the normal vector now this object + + align:start position:0% +onto the normal vector now this object + + + align:start position:0% +onto the normal vector now this object +here PN is much easier to compute well + + align:start position:0% +here PN is much easier to compute well + + + align:start position:0% +here PN is much easier to compute well +for two reasons + + align:start position:0% +for two reasons + + + align:start position:0% +for two reasons +first one is that well projecting onto + + align:start position:0% +first one is that well projecting onto + + + align:start position:0% +first one is that well projecting onto +one dimensional subspace is infinitely + + align:start position:0% +one dimensional subspace is infinitely + + + align:start position:0% +one dimensional subspace is infinitely +easier than projection onto a higher + + align:start position:0% +easier than projection onto a higher + + + align:start position:0% +easier than projection onto a higher +dimensional subspace and second we + + align:start position:0% +dimensional subspace and second we + + + align:start position:0% +dimensional subspace and second we +already have well immediately we can + + align:start position:0% +already have well immediately we can + + + align:start position:0% +already have well immediately we can +read off from the equation of the plane + + align:start position:0% +read off from the equation of the plane + + + align:start position:0% +read off from the equation of the plane +or the normal vector is so we don't have + + align:start position:0% +or the normal vector is so we don't have + + + align:start position:0% +or the normal vector is so we don't have +to + + align:start position:0% +to + + + align:start position:0% +to +derive these guys like we don't have to + + align:start position:0% +derive these guys like we don't have to + + + align:start position:0% +derive these guys like we don't have to +do what we did here okay so essentially + + align:start position:0% +do what we did here okay so essentially + + + align:start position:0% +do what we did here okay so essentially +he and will be and and transpose and + + align:start position:0% +he and will be and and transpose and + + + align:start position:0% +he and will be and and transpose and +inverse and transpose that's equal to + + align:start position:0% + + + + align:start position:0% + +one one negative one and transpose and + + align:start position:0% +one one negative one and transpose and + + + align:start position:0% +one one negative one and transpose and +inverse this is just a number it's 1 + + align:start position:0% +inverse this is just a number it's 1 + + + align:start position:0% +inverse this is just a number it's 1 +over the magnitude of the normal vector + + align:start position:0% +over the magnitude of the normal vector + + + align:start position:0% +over the magnitude of the normal vector +so that's then the magnitude squared so + + align:start position:0% +so that's then the magnitude squared so + + + align:start position:0% +so that's then the magnitude squared so +that's three okay I'm gonna write the + + align:start position:0% +that's three okay I'm gonna write the + + + align:start position:0% +that's three okay I'm gonna write the +answer here it's third one negative one + + align:start position:0% + + + + align:start position:0% + +one thirty one and right so yeah you + + align:start position:0% +one thirty one and right so yeah you + + + align:start position:0% +one thirty one and right so yeah you +know and in order to get the projection + + align:start position:0% +know and in order to get the projection + + + align:start position:0% +know and in order to get the projection +matrix yes oh thank you thank you and in + + align:start position:0% +matrix yes oh thank you thank you and in + + + align:start position:0% +matrix yes oh thank you thank you and in +order to get the projection matrix we + + align:start position:0% +order to get the projection matrix we + + + align:start position:0% +order to get the projection matrix we +just subtract from the identity this + + align:start position:0% +just subtract from the identity this + + + align:start position:0% +just subtract from the identity this +expression and you can confirm that it's + + align:start position:0% +expression and you can confirm that it's + + + align:start position:0% +expression and you can confirm that it's +nice we got the same answer is here all + + align:start position:0% +nice we got the same answer is here all + + + align:start position:0% +nice we got the same answer is here all +right I think we're done here \ No newline at end of file diff --git a/t5EI5fXX8K0.txt b/t5EI5fXX8K0.txt new file mode 100644 index 0000000000000000000000000000000000000000..1943851ac5ba0a5b5f7ebebbea0ed32e322b192c --- /dev/null +++ b/t5EI5fXX8K0.txt @@ -0,0 +1,2391 @@ +[MUSIC PLAYING] + +PROFESSOR: Well, let's see. + +What we did so far was +a lot of fun, was + +it useful for anything? + +I suppose the answer +is going to be yes. + +If these metacircular +interpreters are a valuable + +thing to play with. + +Well, there have been times I +spend 50% of my time, over a + +year, trying various design +alternatives by experimenting + +with them with metacircular +interpreters-- + +metacircular interpreters like +the sort you just saw. + +Metacircular is because they +are defined in terms of + +themselves in such a way that +the language they interpret + +contains itself. + +Such interpreters are a +convenient medium for + +exploring language issues. + +If you want to try adding a new +feature, it's sort of a + +snap, it's easy, you just do +it and see what happens. + +You play with that language for +a while you say, gee, I'm + +didn't like that, you +throw it away. + +Or you might want to see what +the difference is if you'd + +make a slight difference in the +binding strategy, or some + +more complicated things +that might occur. + +In fact, these metacircular +interpreters are an excellent + +medium for people exchanging +ideas about language design, + +because they're pretty easy to +understand, and they're short, + +and compact, and simple. + +If I have some idea that I want +somebody to criticize + +like say, Dan Friedman at +Indiana, I'd write a little + +metacircular interpreter and +send him some network mail + +with this interpreter in it. + +He could whip it up on his +machine and play with it and + +say, that's no good. + +And then send it back to me and +say, well, why don't you + +try this one, it's +a little better. + +So I want to show you some +of that technology. + +See, because, really, it's the +essential, simple technology + +for getting started in designing +your own languages + +for particular purposes. + +Let's start by adding a very +simple feature to a Lisp. + +Now, one thing I want +to tell you about is + +features, before I start. + +There are many languages that +have made a mess of themselves + +by adding huge numbers +of features. + +Computer scientists have a joke +about bugs that transform + +it to features all the time. + +But I like to think of it is +that many systems suffer from + +what's called creeping +featurism. + +Which is that George has a pet +feature he'd like in the + +system, so he adds it. + +And then Harry says, gee, this +system is no longer what + +exactly I like, so I'm going +to add my favorite feature. + +And then Jim adds his +favorite feature. + +And, after a while, the thing +has a manual 500 pages long + +that no one can understand. + +And sometimes it's the same +person who writes all of these + +features and produces this +terribly complicated thing. + +In some cases, like editors, +it's sort of reasonable to + +have lots of features, because +there are a lot of things you + +want to be able to do and +many of them arbitrary. + +But in computer languages, I +think it's a disaster to have + +too much stuff in them. + +The other alternative you get +into is something called + +feeping creaturism, which is +where you have a box which has + +a display, a fancy display, and +a mouse, and there is all + +sorts of complexity associated +with all this fancy IO. + +And your computer language +becomes a dismal, little, tiny + +thing that barely works because +of all the swapping, + +and disk twitching, and so on, +caused by your Windows system. + +And every time you go near the +computer, the mouse process + +wakes up and says, gee do you +have something for me to do, + +and then it goes +back to sleep. + +And if you accidentally push +mouse with you elbow, a big + +puff of smoke comes out +of your computer + +and things like that. + +So two ways to disastrously +destroy a + +system by adding features. + +But try right now to add a +little, simple feature. + +This actually is a good +one, and in fact, + +real Lisps have it. + +As you've seen, there are +procedures like plus and times + +that take any number +of arguments. + +So we can write things like the +sum of the product of a + +and x and x, and the product +of b and x and c. + +As you can see here, addition +takes three arguments or two + +arguments, multiplication takes +two arguments or three + +arguments, taking numbers of +arguments all of which are to + +be treated in the same way. + +This is a valuable thing, + +indefinite numbers of arguments. + +Yet the particular Lisp system +that I showed you is one where + +the numbers of arguments is +fixed, because I had to match + +the arguments against the +formal parameters in the + +binder, where there's +a pairup. + +Well, I'd like to be able to +define new procedures like + +this that can have any +number of arguments. + +Well there's several parts +to this problem. + +The first part is coming +up with the syntactic + +specification, some way of +notating the additional + +arguments, of which you don't +know how many there are. + +And then there's the other +thing, which is once we've + +notated it, how are we going to +interpret that notation so + +as to do the right thing, +whatever the right thing is? + +So let's consider an example +of a sort of thing we might + +want to be able to do. + +So an example might be, that +I might want to be able to + +define a procedure which is a +procedure of one required + +argument x and a bunch of +arguments, I don't know how + +many there are, called y. + +So x is required, and there are +many y's, many argument-- + +y will be the list of them. + +Now, with such a thing, we might +be able to say something + +like, map-- + +I'm going to do something +to every one-- + +of that procedure of one +argument u, which multiplies x + +by u, and we'll apply +that to y. + +I've used a dot here to indicate +that the thing after + +this is a list of all the +rest of the arguments. + +I'm making a syntactic +specification. + +Now, what this depends upon, the +reason why this is sort of + +a reasonable thing to do, is +because this happens to be a + +syntax that's used in +the Lisp reader for + +representing conses. + +We've never introduced +that before. + +You may have seen when playing +with the system that if you + +cons two things together, you +get the first, space, dot, the + +second, space-- + +the first, space, dot, space, +the second with parentheses + +around the whole thing. + +So that, for example, this x dot +y corresponds to a pair, + +which has got an x in +it and a y in it. + +The other notations that you've +seen so far are things + +like a procedure of arguments x +and y and z which do things, + +and that looks like-- + +Just looking at the bound +variable list, it looks like + +this, x, y, z, and +the empty thing. + +If I have a list of arguments I +wish to match this against, + +supposing, I have a list of +arguments one, two, three, I + +want to match these against. So +I might have here a list of + +three things, one, two, three. + +And I want to match x, y, z +against one, two, three. + +Well, it's clear that the one +matches the x, because I can + +just sort of follow the +structure, and the two matches + +the y, and the three +matches the z. + +But now, supposing I were to +compare this x dot y-- + +this is x dot y-- + +supposing I compare that with +a list of three arguments, + +one, two, three. + +Let's look at that again. + +One, two, three-- + +Well, I can walk along here and +say, oh yes, x matches the + +one, the y matches the list, +which is two and three. + +So the notation I'm choosing +here is one that's very + +natural for Lisp system. + +But I'm going to choose this as +a notation for representing + +a bunch of arguments. + +Now, there's an alternative +possibility. + +If I don't want to take one +special out, or two special + +ones out or something like that, +if I don't want to do + +that, if I want to talk about +just the list of all the + +arguments like in addition, well +then the argument list + +I'm going to choose to be that +procedure of all the arguments + +x which does something with x. + +And which, for example, if I +take the procedure, which + +takes all the arguments x and +returned the list of them, + +that's list. That's the +procedure list. + +How does this work? + +Well, indeed what I had as the +bound variable list in this + +case, whatever it is, +is being matched + +against a list of arguments. + +This symbol now is all +of the arguments. + +And so this is the choice I'm +making for a particular + +syntactic specification, for the +description of procedures + +which take indefinite numbers +of arguments. + +There are two cases of it, +this one and this one. + +When you make syntactic +specifications, it's important + +that it's unambiguous, that +neither of these can be + +confused with a representation +we already have, this one. + +I can always tell whether +I have a fixed number of + +explicitly named arguments +made by these formal + +parameters, or a fixed number +of named formal parameters + +followed by a thing which picks +up all the rest of them, + +or a list of all the arguments +which will be matched against + +this particular formal parameter +called x, because + +these are syntactically +distinguishable. + +Many languages make terrible +errors in that form where + +whole segments of interpretation +are cut off, + +because there are syntactic +ambiguities in the language. + +They are the traditional +problems with ALGOL like + +languages having to do with +the nesting of ifs in the + +predicate part. + +In any case, now, so I've told +you about the syntax, now, + +what are we going to do about +the semantics of this? + +How do we interpret it? + +Well this is just super easy. + +I'm going to modify +the metacircular + +interpreter to do it. + +And that's a one liner. + +There it is. + +I'm changing the way +you pair things up. + +Here's the procedure that +pairs the variables, the + +formal parameters, with the +arguments that were passed + +from the last description of the +metacircular interpreter. + +And here's some things +that are the same + +as they were before. + +In other words, if the list of +variables is empty, then if + +the list of values is empty, +then I have an empty list. + +Otherwise, I have too many +arguments, that is, if I have + +empty variables but +not empty values. + +If I have empty values, but the +variables are not empty, I + +have too few arguments. + +The variables are a symbol-- + +interesting case-- + +then, what I should do is say, +oh yes, this is the special + +case that I have a +symbolic tail. + +I have here a thing just like +we looked over here. + +This is a tail which +is a symbol, y. + +It's not a nil. + +It's not the empty list. Here's +a symbolic tail that is + +just the very beginning +of the tail. + +There is nothing else. + +In that case, I wish to match +that variable with all the + +values and add that to the +pairing that I'm making. + +Otherwise, I go through the +normal arrangement of making + +up the whole pairing. + +I suppose that's very simple. + +And that's all there is to it. + +And now I'll answer +some questions. + +The first one-- + +Are there any questions? + +Yes? + +AUDIENCE: Could you explain +that third form? + +PROFESSOR: This one? + +Well, maybe we should look +at the thing as a + +piece of list structure. + +This is a procedure which +contains a lambda. + +I'm just looking at +the list structure + +which represents this. + +Here's x. + +These are our symbols. + +And then the body is +nothing but x. + +If I were looking for the bound +variable list part of + +this procedure, I would go +looking at the CADR, and I'd + +find a symbol. + +So the, naturally, which is +this pairup thing I just + +showed you, is going to be +matching a symbolic object + +against a list of arguments +that were passed. + +And it will bind that symbol +to the list of arguments. + +In this case, if I'm looking +for it, the match will be + +against this in the bound +variable list position. + +Now, if what this does is it +gets a list of arguments and + +returns it, that's list. That's +what the procedure is. + +Oh well, thank you. + +Let's take a break. + +[MUSIC PLAYING] + +PROFESSOR: Well let's see. + +Now, I'm going to tell you +about a rather more + +substantial variation, one +that's a famous variation that + +many early Lisps had. + +It's called dynamic binding +of variables. + +And we'll investigate a little +bit about that right now. + +I'm going to first introduce +this by showing you the sort + +of thing that would make +someone want this idea. + +I'm not going to tell what it is +yet, I'm going to show you + +why you might want it. + +Suppose, for example, we looked +at the sum procedure + +again for summing up +a bunch of things. + +To be that procedure, of a term, +lower bound, method of + +computing the next index, and +upper bound, such that, if a + +is greater than b then the +result is 0, otherwise, it's + +the sum, of the term, procedure, +applied to a and + +the result of adding up, terms, +with the next a being + +the a, the next procedure passed +along, and the upper + +bound being passed along. + +Blink, blink, blink-- + +Now, when I use this sum +procedure, I can use it, for + +example, like this. + +We can define the sum of the +powers to be, for example, sum + +of a bunch of powers x to the +n, to be that procedure + +of a, b, and n-- + +lower bound, the upper +bound, and n-- + +which is sum, of lambda of x, +the procedure of one argument + +x, which exponentiates x to +the n, with the a, the + +incrementer, and b, being +passed along. + +So we're adding up x +to n, given an x. + +x takes on values from a to +b, incrementing by one. + +I can also write the-- + +That's right. + +Product, excuse me. + +The product of a bunch +of powers. + +It's a strange name. + +I'm going to leave it there. + +Weird-- + +I write up what I have. +I'm sure that's right. + +And if I want the product +of a bunch of powers-- + +That was 12 brain cells, +that double-take. + +I can for example use the +procedure which is like sum, + +which is for making products, +but it's similar to that, that + +you've seen before. + +There's a procedure of three +arguments again. + +Which is the product of terms +that are constructed, or + +factors in this case, +constructed from + +exponentiating x to the n, +where I start with a, I + +increment, and I go to b. + +Now, there's some sort of thing +here that should disturb + +you immediately. + +These look the same. + +Why am I writing this +code so many times? + +Here I am, in the same boat +I've been in before. + +Wouldn't it be nice to make +an abstraction here? + +What's an example of a good +abstraction to make? + +Well, I see some codes +that's identical. + +Here's one, and here's +another. + +And so maybe I should be +able to pull that out. + +I should be able to say, oh +yes, the sum of the powers + +could be written in terms +of something called + +the nth power procedure. + +Imagine somebody wanted to write +a slightly different + +procedure that looks +like this. + +The sum powers to be a procedure +of a, b, and n, as + +the result of summing +up the nth power. + +We're going to give a name to +that idea, for starting at a, + +going by one, and ending at b. + +And similarly, I might want to +write the product powers this + +way, abstracting +out this idea. + +I might want this. + +Product powers, to be a +procedure of a, b, and n, + +which is the product of the nth +power operation on a with + +the incrementation and b being +my arguments for the + +analogous-thing product. + +And I'd like to be able to +define, I'd like to be able to + +define nth power-- + +I'll put it over here. + +I'll put it at the top. + +--to be, in fact, my procedure +of one argument x which is the + +result of exponentiating +x to the n. + +But I have a problem. + +My environment model, that is my +means of interpretation for + +the language that we've defined +so far, does not give + +me a meaning for this n. + +Because, as you know, this n +is free in this procedure. + +The environment model tells us +that the meaning of a free + +variable is determined in the +environment in which this + +procedure is defined. + +In a way I have written it, +assuming these things are + +defined on the blackboard as +is, this is defined in the + +global environment, where +there is no end. + +Therefore, n is unbound +variable. + +But it's perfectly clear, to +most of us, that we would like + +it to be this n and this n. + +On the other hand, +it would be nice. + +Certainly we've got to be +careful here of keeping this + +to be this, and this one +over here, wherever it + +is to be this one. + +Well, the desire to make +this work has led to + +a very famous bug. + +I'll tell you about +the famous bug. + +Look at this slide. + +This is an idea called +dynamic binding. + +Where, instead of the free +variable being interpreted in + +the environment of definition +of a procedure, the free + +variable is interpreted as +having its value in the + +environment of the caller +of the procedure. + +So what you have is a system +where you search up the chain + +of callers of a particular +procedure, and, of course, in + +this case, since nth power is +called from inside product + +whatever it is-- + +I had to write our own sum +which is the analogous + +procedure-- + +and product is presumably called +from product powers, as + +you see over here, then since +product powers bind with + +variable n , then nth powers +n would be derived + +through that chain. + +Similarly, this n, the nth power +in n in this case, would + +come through nth power here +being called from inside sum. + +You can see it being called +from inside sum here. + +It's called term here. + +But sum was called from inside +of sum powers, which bound n. + +Therefore, there would be an n +available for that n to get + +it's value from. + +What we have below this white +line plus over here, is what's + +called a dynamic binding +view of the world. + +If that works, that's a +dynamic binding view. + +Now, let's take a look, for +example, at just what it takes + +to implement that. + +That's real easy. + +In fact, the very first Lisps +that had any interpretations + +of the free variables at all, +had dynamic binding + +interpretations for the +free variables. + +APL has dynamic binding +interpretation for the free + +variables, not lexical +or static binding. + +So, of course, the change +is in eval. + +And it's really in two places. + +First of all, one thing we see, +is that things become a + +little simpler. + +If I don't have to have the +environment be the environment + +of definition for procedure, the +procedure need not capture + +the environment at the +time it's defined. + +And so if we look here at this +slide, we see that the clause + +for a lambda expression, which +is the way a procedure is + +defined, does not make up a +thing which has a type closure + +and a attached environment +structure. + +It's just the expression +itself. + +And we'll decompose that some +other way somewhere else. + +The other thing we see is the +applicator must be able to get + +the environment of the caller. + +The caller of a procedure +is right here. + +If the expression we're +evaluating is anpplication or + +a combination, then we're going +to call a procedure + +which is the value +of the operator. + +The environment of the caller +is the environment we have + +right here, available now. + +So all I have to do is pass +that environment to the + +applicator, to apply. + +And if we look at that here, +the only change we have to + +make is that fellow takes that +environment and uses that + +environment for the purpose of +extending that environment + +when abiding the formal +parameters of the procedure to + +the arguments that were passed, +not an environment + +that was captured in +the procedure. + +The reason why the first Lisps +were implemented this way, is + +the sort of the obvious, +accidental implementation. + +And, of course, as usual, +people got used to + +it and liked it. + +And there were some people +said, this is + +the way to do it. + +Unfortunately that causes some +serious problems. The most + +important, serious problem in +using dynamic binding is + +there's a modularity crisis +that's involved it. + +If two people are working +together on some big system, + +then an important thing to want +is that the names used by + +each one don't interfere with +the names of the other. + +It's important that when I +invent some segment of code + +that no one can make my code +stop working by using my names + +that I use internal to my code, +internal to his code. + +However, dynamic binding +violates that particular + +modularity constraint +in a clear way. + +Consider, for example, what +happens over here. + +Suppose it was the case +that I decided to + +change the word next. + +Supposing somebody is writing +sum, and somebody else is + +going to use sum. + +The writer of sum has a choice +of what names he may use. + +Let's say, I'm that writer. + +Well, by gosh, just happens I +didn't want to call this next. + +I called it n. + +So all places where you see +next, I called it n. + +Whoops. + +I changed nothing about the +specifications of this + +program, but this program +stops working. + +Not only that, unfortunately, +this one does too. + +Why do these programs +stop working? + +Well, it's sort of clear. + +Instead of chasing out the value +of the n that occurs in + +nth power over here or over +here, through the environment + +of definition, where this one is +always linked to this one, + +if it was through the +environment of definition, + +because here is the +definition. + +This lambda expression was +executed in the environment + +where that n was defined. + +If instead of doing that, I have +to chase through the call + +chain, then look what horrible +thing happens. + +Well, this was called from +inside sum as term, term a. + +I'm looking for a value of n. + +Instead of getting this +one, I get that one. + +So by changing the insides of +this program, this program + +stops working. + +So I no longer have +a quantifier, + +as I described before. + +The lambda symbol is supposed +to be a quantifier. + +A thing which has the property +that the names that are bound + +by it are unimportant, that I +can uniformly substitute any + +names for these throughout this +thing, so long as they + +don't occur in here, the new +names, and the meaning of this + +expression should remain +unchanged. + +I've just changed the meaning of +the expression by changing + +the one of the names. + +So lambda is no longer +a well defined idea. + +It's a very serious problem. + +So for that reason, I and my +buddies have given up this + +particular kind of abstraction, +which I would + +like to have, in favor of +a modularity principle. + +But this is the kind of +experiment you can do if you + +want to play with these +interpreters. + +You can try them out this way, +that way, and the other way. + +You see what makes +a nicer language. + +So that's a very important +thing to be able to do. + +Now, I would like to give you +a feeling for I think the + +right thing to do is here. + +How are you going to I get +this kind of power in a + +lexical system? + +And the answer is, of course, +what I really want is a + +something that makes up for +me an exponentiator for a + +particular n. + +Given an n, it will make +me an exponentiator. + +Oh, but that's easy too. + +In other words, I can write +my program this way. + +I'm going to define a thing +called PGEN, which is a + +procedure of n which produces +for me an exponentiator. + +--x to the n. + +Given that I have that, then I +can capture the abstraction I + +wanted even better, because now +it's encapsulated in a way + +where I can't be destroyed +by a change of names. + +I can define some powers to be a +procedure again of a, b, and + +n which is the sum of the term +function generated by using + +this generator, PGEN, n, with +a, incrementer, and b. + +And I can define the product of +powers to be a procedure of + +a, b, and n which is the product +PGEN, n, with a, + +increment, and b. + +Now, of course, this is a very +simple example where this + +object that I'm trying to +abstract over is small. + +But it could be a 100 +lines of code. + +And so, the purpose +of this is, of + +course, to make it simple. + +I'd give a name to it, it's +just that here it's a + +parameterized name. + +It's a name that depends upon, +explicitly, the lexically + +apparent value of n. + +So you can think of this +as a long name. + +And here, I've solved my problem +by naming the term + +generation procedures +within an n in them. + +Are there any questions? + +Oh, yes, David. + +AUDIENCE: Is the only solution +to the problem you raise to + +create another procedure? + +In other words, can this only +work in languages that are + +capable of defining objects +as procedures? + +PROFESSOR: Oh, I see. + +My solution to making this +abstraction, when I didn't + +want include the procedure +inside the body, depends upon + +my ability to return a procedure +or export one. + +And that's right. + +If I don't have that, then I +just don't have this ability + +to make an abstraction in +a way where I don't have + +possibilities of symbol +conflicts that were + +unanticipated. + +That's right. + +I consider being able to return +the procedural value + +and, therefore, to sort of have +first class procedures, + +in general, as being essential +to doing very good modular + +programming. + +Now, indeed there are many other +ways to skin this cat. + +What you can do is take for each +of the bad things that + +you have to worry about, you +can make a special feature + +that covers that thing. + +You can make a package system. + +You can make a module system +as in Ada, et cetera. + +And all of those work, or they +cover little regions of it. + +The thing is that returning +procedures as values cover all + +of those problems. And so it's +the simplest mechanism that + +gives you the best modularity, +gives you all of the known + +modularity mechanisms. + +Well, I suppose it's time for +the next break, thank you. + +[MUSIC PLAYING] + +PROFESSOR: Well, yesterday +when you learned about + +streams, Hal worried to you +about the order of evaluation + +and delayed arguments +to procedures. + +The way we played with streams +yesterday, it was the + +responsibility of the caller and +the callee to both agree + +that an argument was delayed, +and the callee must force the + +argument if it needs +the answer. + +So there had to be a lot of +hand shaking between the + +designer of a procedure and user +of it over delayedness. + +That turns out, of course, to +be a fairly bad thing, it + +works all right with streams. +But as a general thing, what + +you want is an idea to have a +locus, a decision, a design + +decision in general, to have +a place where it's made, + +explicitly, and notated +in a clear way. + +And so it's not a very good +idea to have to have an + +agreement, between the person +who writes a procedure and the + +person who calls it, about such +details as, maybe, the + +arguments of evaluation, the +order of evaluation. + +Although, that's not so bad. + +I mean, we have other such +agreements like, + +the input's a number. + +But it would be nice if only one +of these guys could take + +responsibility, completely. + +Now this is not a new idea. + +ALGOL 60 had two different ways +of calling a procedure. + +The arguments could be passed +by name or by value. + +And what that meant was that a +name argument was delayed. + +That when you passed an argument +by name, that its + +value would only be obtained if +you accessed that argument. + +So what I'd like to do now is +show you, first of all, a + +little bit about, again, we're +going to make a modification + +to a language. + +In this case, we're going +to add a feature. + +We're going to add the feature +of, by name parameters, if you + +will, or delayed parameters. + +Because, in fact, the default +in our Lisp system is by the + +value of a pointer. + +A pointer is copied, but +the data structure it + +points at is not. + +But I'd like to, in fact, show +you is how you add name + +arguments as well. + +Now again, why would we +need such a thing? + +Well supposing we wanted to +invent certain kinds of what + +otherwise would be special +forms, reserve words? + +But I'd rather not take +up reserve words. + +I want procedures that can +do things like if. + +If is special, or cond, +or whatever it is. + +It's the same thing. + +It's special in that it +determines whether or not to + +evaluate the consequent or the +alternative based on the value + +of the predicate part +of an expression. + +So taking the value of one thing +determines whether or + +not to do something else. + +Whereas all the procedures like +plus, the ones that we + +can define right now, evaluate +all of their arguments before + +application. + +So, for example, supposing I +wish to be able to define + +something like the reverse +of if in terms of if. + +Call it unless. + +We've a predicate, a +consequent, and an + +alternative. + +Now what I would like to sort of +be able to do is say-- oh, + +I'll do it in terms of cond. + +Cond, if not the predicate, +then take the consequent, + +otherwise, take the +alternative. + +Now, what I'd like this to +mean, is supposing I do + +something like this. + +I'd like this unless say if +equals one, 0, then the answer + +is two, otherwise, the quotient +of one and 0. + +What I'd like that to mean is +the result of substituting + +equal one, 0, and two, and +the quotient of one, 0 + +for p, c, and a. + +I'd like that to mean, and this +is funny, I'd like it to + +transform into or mean cond +not equal one, 0, then the + +result is two, otherwise +I want it to be the + +quotient one and 0. + +Now, you know that if I +were to type this into + +Lisp, I'd get a two. + +There's no problem with that. + +However, if I were to type this +into Lisp, because all + +the arguments are evaluated +before I start, then I'm going + +to get an error out of this. + +So that if the substitutions +work at all, of course, I + +would get the right answer. + +But here's a case where the +substitutions don't work. + +I don't get the wrong answer. + +I get no answer. + +I get an error. + +Now, however, I'd like to be +able to make my definition so + +that this kind of thing works. + +What I want to do +is say something + +special about c and a. + +I want them to be delayed +automatically. + +I don't want them to be +evaluated at the time I call. + +So I'm going to make a +declaration, and then I'm + +going to see how to implement +such a declaration. + +But again, I want you to say +to yourself, oh, this is an + +interesting kluge he's +adding in here. + +The piles of kluges make +a big complicated mess. + +And is this going to +foul up something + +else that might occur. + +First of all, is it +syntactically unambiguous? + +Well, it will be syntactically +unambiguous with what we've + +seen so far. + +But what I'm going to do may, +in fact, cause trouble. + +It may be that the thing I had +will conflict with type + +declarations I might want to add +in the future for giving + +some system, some compiler or +something, the ability to + +optimize given the +types are known. + +Or it might conflict with other +types of declarations I + +might want to make about +the formal parameters. + +So I'm not making a general +mechanism here where I can add + +declarations. + +And I would like to be +able to do that. + +But I don't want to talk +about that right now. + +So here I'm going to do, I'm +going to build a kluge. + +So we're going to define +unless of a predicate-- + +and I'm going to call +these by name-- + +the consequent, and name +the alternative. + +Huh, huh-- + +I got caught in the corner. + +If not p then the result +is c, else-- + +that's what I'd like. + +Where I can explicitly declare +certain of the parameters to + +be delayed, to be +computed later. + +Now, this is actually a very +complicated modification to an + +interpreter rather than +a simple one. + +The ones you saw before, dynamic +binding or adding + +indefinite argument procedures, + +is relatively simple. + +But this one changes +a basic strategy. + +The problem here is that our +interpreter, as written, + +evaluates a combination by +evaluating the procedure, the + +operator producing the +procedure, and evaluating the + +operands producing the +arguments, and then doing + +apply of the procedure +to the arguments. + +However, here, I don't want to +evaluate the operands to + +produce the arguments until +after I examined the procedure + +to see what the procedure's +declarations look like. + +So let's look at that. + +Here we have a changed +evaluator. + +I'm starting with the simple +lexical evaluator, not + +dynamic, but we're going to have +to do something sort of + +similar in some ways. + +Because of the fact that, +if I delay a procedure-- + +I'm sorry-- delay an argument +to a procedure, I'm going to + +have to attach and environment +to it. + +Remember how Hal implemented +delay. + +Hal implemented delay as being +a procedure of no arguments + +which does some expression. + +That's what delay of +the expression is. + +--of that expression. + +This turned into something +like this. + +Now, however, if I evaluate a +lambda expression, I have to + +capture the environment. + +The reason why is because there +are variables in there + +who's meaning I wish to derive +from the context where this + +was written. + +So that's why a lambda +does the job. + +It's the right thing. + +And such that the forcing of a +delayed expression was same + +thing as calling that +with no arguments. + +It's just the opposite +of this. + +Producing an environment of the +call which is, in fact, + +the environment where this was +defined with an extra frame in + +it that's empty. + +I don't care about that. + +Well, if we go back to this +slide, since it's the case, if + +we look at this for a second, +everything is the same as it + +was before except the case of +applications or combinations. + +And combinations are going +to do two things. + +One, is I have to evaluate +the procedure-- + +forget the procedure-- by +evaluating the operator. + +That's what you see +right here. + +I have to make sure that that's +current, that is not a + +delayed object, and evaluate +that to the point where it's + +forced now. + +And then I have to somehow apply +that to the operands. + +But I have to keep the +environment, pass that + +environmental along. + +So some of those operands +I may have to delay. + +I may have to attach that +environment to those operands. + +This is a rather complicated +thing happening here. + +Looking at that in apply. + +Apply, well it has a +primitive procedure + +thing just like before. + +But the compound one is a +little more interesting. + +I have to evaluate the body, +just as before, in an + +environment which is the result +of binding some formal + +parameters to arguments +in the environment. + +That's true. + +The environment is the +one that comes from + +the procedure now. + +It's a lexical language, +statically bound. + +However, one thing I have +to do is strip off the + +declarations to get the names +of the variables. + +That's what this guy +does, vnames. + +And the other thing I have +to do is process these + +declarations, deciding which +of these operands-- + +that's the operands now, as +opposed to the arguments-- + +which of these operands to +evaluate, and which of them + +are to be encapsulated in +delays of some sort. + +The other thing you see here is +that we got a primitive, a + +primitive like plus, had better + +get at the real operands. + +So here is a place where we're +going to have to force them. + +And we're going to look at what +evlist is going to have + +to do a bunch of forces. + +So we have two different +kinds of evlist now. + +We have evlist and gevlist. +Gevlist is going to wrap + +delays around some things and +force others, evaluate others. + +And this guy's going to do +some forcing of things. + +Just looking at this a little +bit, this is a game you must + +play for yourself, you know. + +It's not something that you're +going to see all possible + +variations on an evaluator +talking to me. + +What you have to do is +do this for yourself. + +And after you feel this, you +play this a bit, you get to + +see all the possible design +decisions and what they might + +mean, and how they interact +with each other. + +So what languages might +have in them. + +And what are some of the +consistent sets that make a + +legitimate language. + +Whereas what things are +complicated kluges that are + +just piles of junk. + +So evlist of course, over here, +just as I said, is a + +list of operands which are going +to be undelayed after + +evaluation. + +So these are going to +be forced, whatever + +that's going to mean. + +And gevlist, which is +the next thing-- + +Thank you. + +What we see here, well there's +a couple of possibilities. + +Either it's a normal, ordinary +thing, a symbol sitting there + +like the predicate in the +unless, and that's + +what we have here. + +In which case, this is intended +to be evaluated in + +applicative order. + +And it's, essentially, just +what we had before. + +It's mapping eval down the +list. In other words, I + +evaluate the first expression +and continue gevlisting the + +CDR of the expression +in the environment. + +However, it's possible that +this is a name parameter. + +If it's a name parameter, I want +to put a delay in which + +combines that expression, which +I'm calling by name, + +with the environment that's +available at this time and + +passing that as the parameter. + +And this is part of the +mapping process + +that you see here. + +The only other interesting +place in this + +interpreter is cond. + +People tend to write this thing, +and then they leave + +this one out. + +There's a place where +you have to force. + +Conditionals have to know +whether or not the answer is + +true or false. + +It's like a primitive. + +When you do a conditional, +you have to force. + +Now, I'm not going to +look at any more + +of this in any detail. + +It isn't very exciting. + +And what's left is how +you make delays. + +Well, delays are data structures +which contain an + +expression, an environment, +and a type on them. + +And it says they're a thunk. + +That comes from ALGOL language, +and it's claimed to + +be the sound of something +being pushed on a stack. + +I don't know. + +I was not an ALGOLician or an +ALGOLite or whatever, so I + +don't know. + +But that's what was claimed. + +And undelay is something which +will recursively undelay + +thunks until the thunk becomes +something which isn't a thunk. + +This is the way you implement +a call by name + +like thing in ALGOL. + +And that's about all there is. + +Are there any questions? + +AUDIENCE: Gerry? + +PROFESSOR: Yes, Vesko? + +AUDIENCE: I noticed you avoided +calling by name in the + +primitive procedures, +I was wondering what + +cause you have on that? + +You never need that? + +PROFESSOR: Vesko is asking if +it's ever reasonable to call a + +primitive procedure by name? + +The answer is, yes. + +There's one particular case +where it's reasonable, + +actually two. + +Construction of a data structure +like cons where + +making an array if you +have arrays with + +any number of elements. + +It's unnecessary to evaluate +those arguments. + +All you need is promises to +evaluate those arguments if + +you look at them. + +If I cons together two things, +then I could cons together the + +promises just as easily as I can +cons together the things. + +And it's not even when +I CAR CDR them that I + +have to look at them. + +That just gets out +the promises and + +passes them to somebody. + +That's why the lambda calculus +definition, the Alonzo Church + +definition of CAR, CDR, +and cons makes sense. + +It's because no work is done +in CAR, CDR, and cons, it's + +just shuffling data, it's just +routing, if you will. + +However, the things that do +have to look at data are + +things like plus. + +Because they have a look at the +bits that the numbers are + +made out of, unless they're +lambda calculus + +numbers which are funny. + +They have to look at the bits +to be able to crunch them + +together to do the add. + +So, in fact, data constructors, +data selectors, + +and, in fact, things that +side-effect data objects don't + +need to do any forcing in the +laziest possible interpreters. + +On the other hand predicates +on data structures have to. + +Is this a pair? + +Or is it a symbol? + +Well, you better find out. + +You got to look at it then. + +Any other questions? + +Oh, well, I suppose it's +time for a break. + +Thank you. + +[MUSIC PLAYING] + +and \ No newline at end of file diff --git a/tbWuyysnj9U.txt b/tbWuyysnj9U.txt new file mode 100644 index 0000000000000000000000000000000000000000..a1b2dbee125ea7f588131145412876de8512d10c --- /dev/null +++ b/tbWuyysnj9U.txt @@ -0,0 +1,1872 @@ +The following content is +provided by MIT OpenCourseWare + +under a Creative Commons +license. + +Additional information about +our license and MIT + +OpenCourseWare in general is +available at ocw.mit.edu. + +Today is a very big day for all +of you. + +Your first semester at MIT is +half over. + +And, in addition to that, +you have a lot of challenges + +remaining ahead of you for the +rest of this semester. + +I am going to help make the +chemical challenges fun for you. + +That is what I am here to do. +I love chemistry. + +I love teaching 5.112. +This is the best part of my + +week. +So, here we are. + +Do you guys know that chemistry +can be incredibly fun? + +Let me just show you how fun +chemistry can be. + +And that is just the gravy. +The fun part is actually making + +the molecules. +Any of you see this picture in + +U.S.A. +Today recently? + +Not reading that important +journal, I see. + +Well, this picture did appear +very recently in U.S.A. + +Today in a story that talked +about the recent Nobel Prize in + +chemistry that was awarded to +Professor Richard R. + +Schrock, of our department. +And, in fact, + +I don't know if you realize +this, but Professor Schrock was + +the first person ever awarded +the Nobel Prize in Chemistry at + +MIT for work conducted while at +MIT. + +That is a pretty amazing +accomplishment because we have + +so many tremendous chemists on +the faculty here, + +and he is the first one to +break through in that manner. + +And maybe you are here at a +very special time, + +and we will see a number more +of these in the next few years. + +May with you contributing, +so much the better because you + +are here. +And let me just explain + +something, too. +Chemistry is fun. + +And only on very rare occasions +like this would Professor + +Schrock be drinking champagne at +8:30 in the morning, + +when this picture was taken. +The Reuters reporter, + +Brian, who took this photo, +is actually a pretty good + +friend of Professor Nocera here. +And so he rode over from the + +Schrock household. +And Dick and Dan came in + +together in the same car, +as they often do, + +from Winchester on that +morning, which was a very + +exciting day. +If you come to see me for + +office hours maybe I will tell +you more about it in detail, + +but it was an exciting day. +And I am in here, + +too. +My name is Kit Cummins. + +Kit is my nickname. +My name is Christopher. + +You can call me Christopher or +Kit, or you can call me + +Professor Cummins, +or you can just say hey, + +chemistry guy. +That will be fine. + +I am in this picture primarily +because it is part of being in + +the right place at the right +time, just like I am here now in + +front of you. +But also I am in it because we + +three are three in one of the +areas in our department that + +really focus our research on +inorganic chemistry. + +And what is inorganic +chemistry? + +I will say more about this +during the semester. + +But inorganic chemistry is +really the chemistry of the + +elements of the Periodic Table +inclusively. + +So, a pretty broad topic. +And I like doing chemistry with + +lots of elements. +And so that is why these guys + +and I share an association with +each other. + +And, in fact, +I was a graduate student with + +Professor Schrock. +And I am very, + +very proud to be able to say +that. + +Hopefully, my computer will be +staying on, here. + +And I want to point out, +too, that people who love + +science want to know something +about its history. + +And part of all of that is +knowing the academic family from + +which you derive, +depending on the person you've + +studied with in learning about +chemistry. + +And I studied with Schrock. +And Schrock studied with + +Osborn, a fantastic chemist in +his own right, + +no longer alive, +sadly, to see his progeny, + +Professor Schrock, +win the Nobel Prize. + +And Osborn studied with +Wilkinson, and Wilkinson was + +also a Nobel Prize winner. +So, you do not have to go very + +far back in that lineage to +encounter that recognition, + +the Nobel Prize, +Schrock, and then it skipped + +Osborne, and if you go back to +Wilkinson, there is another one. + +And you can keep going back. +And I am not going to go + +through that whole history today +because I have another history + +that I am going to need to go +through with you today. + +And I am going to bring this +back over so it does not + +distract you. +And this other history that I + +need to impart to you today has +to do with some of the + +contributions of Gilbert Newton +Lewis. + +This is one of the most famous +of all chemists ever. + +And if you like chemistry, +I encourage you to think of the + +word Newton, as it is found +engraved in one of the pillars + +in Killian Court at MIT as the +middle name of Gilbert Newton + +Lewis. +It is conceivable that having + +that middle name weighed heavily +upon Gilbert during his + +lifetime. +But it remains a good moniker. + +And in the future, +when you have kids, + +I encourage you to consider +using it as a middle name. + +It worked well in this +particular case. + +When you get the notes for +today, which incidentally will + +be available on the website +after class today, + +so you don't need to write down +everything I am writing down. + +You are actually going to get a +little bit more in the online + +version than what I am writing +down here. + +And if you find that you forgot +something that I said during + +class, just email me. +I will tell you what I said. + +It is not a problem. +But if you want to write down + +notes while I am speaking just +to make notes that you can refer + +to later to refresh your memory, +that is fine. + +I think your taking in +information in lots of different + +ways. +We are going to use the + +computer and we are going to use +the blackboard today. + +And you are going to have +available stuff from the + +Internet a little bit later, +too. + +And all of that is good. +I think you should try to + +reinforce and not worry if some +of the information is a little + +redundant. +And never be afraid to ask + +questions, especially, +I like to take questions by + +email or if you come knock on my +office door. + +In 1916, Gilbert Lewis +published a landmark paper in + +chemistry in the journal of the +American Chemical Society which + +remains the flagship journal of +the American Chemical Society. + +And this paper was entitled +"The Atom and the Molecule." + +Besides being an incredibly +important and influential paper + +in the history of chemistry, +"The Atom and the Molecule" was + +also the basis for -- + +Like I said, +besides being a hugely + +influential manuscript, +"The Atom and the Molecule" + +also laid the foundations for +Lewis's thinking about + +electronic structure theory that +shaped the way we still today + +talk about valence and chemical +bonding. + +So, an incredibly important +paper from 1916. + +In the lecture notes today, +you will find the specific + +volume and page number for that +reference in the journal of the + +American Chemical Society. +And I encourage you in your + +copious free time to download +that paper. + +It is really great. +All the American Chemical + +Society journal articles are +available, from the very + +beginning. +And you can download it and + +read it. +And, having had this + +introduction today, +I think it will probably prove + +to be a very fascinating +exercise for you, + +if you choose to do so. +It also was the basis of a book + +that Gilbert Newton Lewis later +wrote on valance and on atoms + +and molecules. +That is also a classic in + +chemistry. +And, should you be shopping for + +chemistry books on e-bay or +something, you might find a rare + +copy of it. +And if you do and choose not to + +buy it, please alert me and I +will buy it. + +But Gilbert Newton Lewis, +"The Atom and the Molecule." + +In this paper you are going to +see, if you do choose to + +download it, that he was +thinking about polarity. + +And he was also thinking about +the relationship between the + +polarity of a molecule relates +to the polarity of a substance. + +And I mean, when I say a +polarity of a substance, + +that that would be a sample, +you could say a water molecule + +down here and liquid water up +here. + +And you will see this kind of +sigmoidal graph that Lewis made + +in thinking about how polar +condensed phase substances were + +as compared with the structure +of the molecules that comprise + +the substance. +Down here, in this region, + +you will find that there are +substances that are not terribly + +polar. +And what I have written here is + +the organic shorthand for the +hexane molecule. + +Liquid hexane is an alkane, +akin to methane, + +which is natural gas. +And so, if you are not familiar + +with this way of writing organic +molecules, I will just tell you + +briefly that this terminus is CH +three or a methyl group, + +and then it is CH two, +CH two, CH two, + +CH two, and then CH three, +another methyl group. + +So, that is some +organic shorthand. + +And I will go through that kind +of shorthand occasionally so + +that you become familiar with +it. + +And that is the hexane +molecule, a very non-polar + +molecule composed of elements, +carbon and hydrogen, + +that have very similar +electronegativity. + +And then he goes on up the +curve here, and you find this + +familiar molecule, +benzene, considered next, + +as being somehow more polar +than hexane, and liquid benzene + +accordingly in its solvating +properties in the condensed + +phase, being a more polar +medium, as it were. + +And then, as we continue +progress up this scale, + +he writes next molecules like +the diethyl ether molecule. + +No doubt you are familiar with +ether and its applications as an + +anesthetic. +The first use of ether as an + +anesthesia in an operation in +medicine was carried out just + +across the river in Boston. +There is this historical Ether + +Dome there that you can go and +look at. + +But, nonetheless, +we are just getting up a little + +bit more polar than benzene. +And then next you find + +molecules like this one. +That contains an organic + +functional group called an +ester. + +That is ethyl acetate, +which is a substance that you + +might have smelled if you ever +built models, + +because some of the glues that +you may have used would contain + +it, or the paints. +And so, it is a system that, + +in terms of its molecular +structure, is more polar. + +And, when you use it in the +condensed phase, + +it behaves in a manner that you +would describe as more polar. + +And then, finally, +you get up to some very polar + +systems, like the water +molecule. + +Like the ammonia molecule. +And, finally, + +Lewis talks about a species +like this, which is sodium twice + +sulfur. +That is actually called sodium + +sulfide. +And it is a salt analogous to + +table salt, sodium chloride. + +And being a salt, +it is obviously very polar + +because there is quite a large +degree of charge separation + +between the atoms in the +molecule. + +And, accordingly, +if you take that salt and heat + +it up until you have got it as +hot as its melting point and + +make it liquid, +that molten salt has + +individually charged ions moving +around in solution. + +And that provides a very polar +medium, which would be excellent + +at dissolving polar things. +You will notice here that on + +the non-polar side we have +elements, carbon and hydrogen, + +that are very close to each +other in electronegativity. + +And then, as we examine this +relationship, + +we start putting in elements +like oxygen or nitrogen, + +which are very electronegative +close to the upper right-hand + +side of the Periodic Table. +That introduces polarity both + +in the molecule and in +substances comprised of the + +molecule. +And then all the way over to + +the involved atoms, +sodium and sulfur are very + +different in electronegativity +and, therefore, + +have very strongly separated +charges. + +And, in thinking about this, +Lewis proposed the notion of a + +continuum. +And his musing on this are + +really quite lucid in that 1916 +paper, but the idea was that a + +molecule, or a part of a +molecule even, + +you can analyze molecules in +terms of smaller pieces of them + +that can be identified within +the larger molecule, + +can lie on either side of a +continuum in reference to a + +number of different properties. +And the section of class that + +we are launching into today +deals with acid-base properties. + +Let's mention that first, +acid and base. + +These are two ends of a +continuum. + +But he also recognized that you +could have a molecule that would + +be an oxidant. +And the counterpart to that is + +a reductant. +And then, here is a term that + +maybe those of you who have +studied organic chemistry in + +more detail than most would +recognize. + +This is electrophile. + +Electrophile has a counterpart +called a nucleophile. + +And then, the fourth one that I +would like to mention is + +acceptor. + +And, of course, +the counterpart to that is + +donor. + +Please remember those four +pairs because when you can + +understand and make predictions +about those four properties as a + +function of molecular structure, +then you will be a chemist. + +I mean that is a large part of +what it is all about, + +understanding all the different +chemical properties that will + +make it interested in terms of +acid-base, oxidant-reductant, + +electrophile-nucleophile, +and acceptor and donor. + +And the currency of chemistry +can be seen, with reference to + +this, to be the electron. +That is what chemistry is all + +about. +And so, we will be talking a + +lot about atoms and molecules +with reference to their + +properties and how the +properties stem from knowing + +something about the electrons in +the molecule. + +And I think you are going to +find this to be quite fun. + +With respect to the properties +of the medium, + +let's talk about a substance +like hydrogen chloride. + +This is just to illustrate what +I was saying over there. + +If you take a molecule like +hydrogen chloride, + +and it is a gas, +of course. + +And if you make a solution of +it in hexane, + +hexane is going to be our +solvent, and then what you find + +is that in this low polarity +medium hexane solution, + +liquid hexane, +the HCl molecule remains intact + +and floats around in solution, +interacting weakly with hexane + +molecules that surround it. +But if you take this HCl + +molecule and put it into a +solvent like water, + +then something on the other end +of the continuum transpires + +because we get ionization to +produce hydrogen ions. + +And they go off and are +separated in solution from + +chloride ions. +And we will talk more about + +just what is going on when you +separate H plus from Cl + +minus and let them +diffuse apart in aqueous + +solution. +But you can see, + +I think, the dichotomy. +Either the proton shares in the + +electrons of the chloride, +or it just pops off and ionizes + +and goes out into solution. +And Lewis wanted to understand + +this. +And, to understand it, + +he developed a theory. +And his theory was the "cube + +theory." In this part we get to +draw some cubes. + +And he decided that if you +thought of the nucleus, + +which he calls the kernel, +of an atom as being located at + +the center of the system, +then if you had an atom like + +neon, which is a noble gas with +eight valance electrons, + +that these valance electrons +would want to get away from each + +other as far as possible because +they repel each other. + +They are all negatively +charged. + +This could be, +here, the neon atom. + +Here, on that cube, +is how he would represent the + +electronic structure of the neon +atom, with the eight electrons + +here represented by +peach-colored circles, + +each the vertex of a cube. +So, they got far away from each + +other. +And you can see that in the + +historical archives, +some of his original sketch + +books containing these ideas are +there, and now you will know + +what they mean. +You will see that he progressed + +beyond understanding the atom to +understanding the molecule. + +And here is one of the +molecules that he talks about. + +Here we have a molecule +containing 14 valance electrons, + +all arranged in that manner. +And this could be, + +for example, +the I two molecule. + +And let me draw it in terms of +a dot structure, + +-- + +-- like that. +And there was known at the + +time, partly because of the +contributions of Lewis himself, + +something called the Rule of +Eight. + +And that was a reference to +this notion that most atoms want + +to have eight electrons in their +valance shell, + +and it is also something that +we call today the Octet Rule. + +So, when you see the Rule of +Eight mentioned in his paper, + +it is the familiar Octet Rule. +And you can see here that one + +of the key features is two +electrons shared equally. + +And when electrons are shared +equally like that, + +you have a molecule with +symmetrical charge distribution, + +charge referring to the +electrons where they are in + +space. +And then, he showed that you + +could think about this another +way. + +You could consider some kind of +a geometric distortion of the I + +two molecule, like this. + +Distorted, not only because of +my drawing, but because of the + +way the atoms themselves are +thought to be rearranging in + +this process. + +Notice that what has happened +here is that the I two + +molecule is doing something +electronically such that one + +iodine is starting to pull away +from the other. + +This one over here is carrying +with it the electron that came + +from over here. +And, in that case, + +what we have is a molecule in +which we are developing partial + +negative charge on the +right-hand side and partial + +positive charge on the left-hand +side. + +As I was talking up here, +I was thinking about what I was + +going to say here, +because the ideal is that + +molecules, even if they are +inherently non-polar like the I + +two molecule, +in their equilibrium structure + +they can have electron +fluctuations that lead to + +partial charges in the manner +shown here. + +And Lewis was working +beautifully toward the + +development of a theory like +this that would allow the + +description of electronic +structure to be made graphically + +apparent. +And this is something that + +chemists really like to do, +is we like to be able to see + +stuff. +I hope I am going to be able to + +show you some really cool stuff +this semester. + +And, in fact, +even some really cool stuff + +before we finish here today. +So, that is the development of + +charge as represented using the +Lewis cube theory in an I two + +molecule. +Next, one thing you could do is + +say, let's just continue this +process, and the right-hand + +iodine with its eight electrons +pops off. + +That would give you an ionized +situation in which you had an I + +minus floating away from +an I plus molecule. + +And that situation is drawn in +the notes, and because I am + +running out of space on this +board I am not going to draw + +that one up. +Instead I am going to go onto + +another triumph of the Lewis +cube theory, which was its + +ability to explain different +chemical bond orders. + +By the way, Lewis never got the +Nobel Prize. + +He certainly should have. +A dramatic oversight. + +He was born in Massachusetts. +He was a Harvard professor for + +a while and did not like it, +and came to MIT to be a + +professor for a while. +And, although he liked that, + +that was not far enough away +from Harvard, + +so he went to Berkeley, +where he became the department + +head and was very successful +over a long period of time in + +learning about chemistry and in +teaching chemistry. + +I will invite you, +and you will see this in the + +notes, too, to go ahead and see +if you can find a good biography + +of Lewis because it is very +instructive. + +Anyway, here is another +molecule considered by Lewis's + +cube theory. + +How many electrons are being +shared by the two nuclei or + +atoms involved? +Four electrons shared. + +We can circle them here. +That is four electrons shared. + +Therefore, that is not a single +bond. + +We call that a double bond. +And so, that might be a + +representation of, +for example, + +the O two molecule. +Here we have I two, + +here we have distorted I two +with charges developing, + +and here we have O two. +O two is a very + +interesting diatomic molecule. +We are going to talk about that + +later in the semester, +but for now let's just leave it + +at that. +But then, even though this was + +quite a successful theory, +the cube theory, + +it has certain problems, +certain shortcomings, + +such as, we can do single bonds +with it quite well, + +and now we can do double bonds +with the cube theory, + +but what do you do if you have +to make a triple bond? + +That was a problem for Lewis. +That should be a problem for + +you, too. +Cubes just don't fit together + +that way. +They have edges and faces, + +and that is it. +And they have vertices. + +You can do one vertex. +So, triple bond is a problem. + +And we know that there are +molecules that have triple + +bonds. +And we cannot handle them with + +the cube theory, +so we are going to have to + +something a little different, +for that reason. + +But there is also another +reason that had to do with just + +considering the chemistry of +light elements like hydrogen and + +helium. +Those elements tend to + +associate themselves with only +two electrons. + +And so, Lewis decided, +well, maybe the rule of two is + +more fundamental than the rule +of eight, and that we should be + +thinking about pairs of +electrons somehow. + +Because he looked at what was +known about chemistry and + +realized that in most molecules, +the number of electrons is + +always even, is always divisible +by two. + +That is something interesting +about two electrons at a time + +being important. +You take that together with the + +triple bond problem, +and Lewis started thinking in + +terms of electron pairs, +and this is where this + +"electron pair theory" comes +from. + +Although he spent a lot of time +on the cube theory, + +he was perfectly willing to +cast that theory aside in favor + +of something that maybe was +going to work a little better, + +the electron pair theory. +And how does that look? + +Well, of course, +his initial pictures still had + +the cube, which just shows that +once the human mind fixes on + +something, it fixes on it with +great tenacity and it can be + +hard to shake your way of +thinking about things. + +But hopefully you will be able +to do that. + +He still decided, +let's arrange these electron + +pairs on a cube with the nucleus +of the atom supposed to be at + +the center, and let's keep these +electrons, now, + +nicely collected in pairs. +And let's get these pairs as + +far away from each other as +possible, for the same reasons + +we used to be putting eight +electrons as far away from each + +other as possible, +namely, electron repulsion. + +Now, the problem of electron +repulsion between the pairs was + +not really solved. +And Lewis decided that the pair + +theory worked so well that he +was not going to worry about + +that, and so we won't worry +about it yet, + +either. +You have your four pairs of + +electrons arranged at the center +of four of the edges of the + +cube, and that geometry is what +we call a tetrahedron, + +which I am drawing the edges of +here in pink. + +You have a tetrahedral +disposition of four pairs of + +electrons, now, +for an atom. + +This might again be the neon +atom. + +But the nice thing about this +choice is that if you want to + +you can make single bonds with +this theory, and you can make + +double bonds -- + +-- with this theory, +like that. + +And then, due to the properties +of the tetrahedron, + +you can also make triple bonds. +This is marvelous. + +You can see that the famous +chemist Gilbert Newton Lewis was + +talking about electronic +structure in terms of + +symmetrical things, +like tetrahedra and cubes, + +as a way of arranging electrons +reasonably in space. + +This could, again, +be our iodine molecule. + +This could be, +now, our O two molecule. + +And, if we continue that +progression in the Periodic + +Table, what is this molecule? +Dinitrogen, N two, + +the major component of our +atmosphere, another interesting + +molecule that we will be talking +about as the semester progresses + +forward. +But chemical language and + +electronic structure theory are +very much still permeated with + +this affection for symmetry and +the problems that you can solve + +using symmetry to analyze +electronic structure theory. + +Let's talk next about another +molecule because we want to talk + +about Lewis's development of the +electron pair theory, + +but also we want to understand +how that relates to acid-base + +properties. +And so, let me draw here + +another molecule. + +And when you look at this +molecule, which is the aluminum + +trichloride molecule, +in which I am drawing out + +explicitly all of the electrons, +not forgetting these two. + +And having drawn the aluminum +trichloride molecule + +and looked at it like that, +you can ask yourself is the + +number of electrons divisible by +eight? + +Yes it is. +We have a 24 valance electron + +system here. +It is divisible by eight. + +Of course, it is also divisible +by two. + +You can also ask yourself is +this molecule, + +as written, one that satisfies +the rule of eight for all four + +of the atoms? +No. + +We have a problem there because +this thing is electron + +deficient. + +And if you were Lewis, +you would want to know, + +well, if it is electron +deficient, this molecule must be + +doing something about that to +get more electrons. + +Which atom is missing +electrons, here? + +The aluminum. +How can we give aluminum more + +electrons, in a structure like +this? + +Can we get it up to the rule of +eight? + +Double bonds, +awesome. + +Beautiful. +We can make a double bond. + +And, if we do that, +we can allow aluminum to + +satisfy the rule of eight, +or allow the rule of eight to + +satisfy aluminum. +Whichever way you want to look + +at it. +And see what we have done, + +here? +We have taken one of the + +electron pairs, +say, this one, + +and we have moved it in between +the aluminum and the chlorine, + +so it joins the other one in +there. + +And we get a double bond. +And now, everybody has an + +octet. +But what is the problem with + +that? +The problem with that is that + +chlorine is very +electronegative, + +and it does not want its +electrons stolen away by the + +very electropositive aluminum +center. + +There are other ways that +aluminum can ultimately satisfy + +its octet, and this is how we +get into the realm of "Lewis + +acid-base theory." +And I want to show you one of + +the other ways that aluminum can +satisfy its octet, + +and then, we are going to move +to the computer so we can + +visualize some of these +properties. + +If I put my aluminum here -- +and do you remember this + +molecule up here, +the ammonia molecule? + +I am going to say that if I +draw that ammonia molecule in + +place, here -- + +The ammonia molecule comes in, +and it has its eight electrons. + +It is sharing six of them with +three hydrogens. + +The idea is that it has an +extra pair of electrons on that + +nitrogen in the ammonia +molecule, that it can share with + +the aluminum. +And now we go ahead and + +complete the picture. +And we can have eight electrons + +around everybody. + +And so the rule of eight is now +satisfied for the three + +chlorines, for the aluminum, +and for the nitrogen of the + +ammonia molecule. +The ammonia molecule is what we + +call a "Lewis base." + +And the aluminum trichloride +molecule is what we + +call a "Lewis acid," +for reasons that should now be + +quite clear. +And I want to show you how we + +can look at these things. +And if you will give me just a + +second here, I am going to load +the aluminum trichloride + +molecule up onto the screen. + +What we are going to do is +remember that there are lots of + +different ways in which you can +visualize molecules. + +And I want to show you some of +the more interesting ways. + +All that is is a picture of the +aluminum trichloride + +molecule with spheres drawn at +kind of arbitrary radii. + +The size of these spheres is +not representative of any + +particular physical quantity, +but we can change that. + +And so now, what we are going +to do is draw the thing a + +slightly different way. +And what you can see is that + +the positions of those nuclei +are in this flat box. + +I made the box kind of flat. +It is kind of a slab because + +this AlCl three +molecule is conveniently kind of + +flat in its structure. +And what are we going to do + +now? +We are going to draw a contour + +surface. +And I like this. + +We are going to use the solid +surface method, + +first. +And can you see that now? + +These curves that enclose the +four nuclei of the aluminum + +trichloride molecule +do have some physical + +significance, +because what I have done here + +is taken results, +in this case from the quantum + +chemistry calculation, +but you could also take it from + +an X-ray crystallographic +structure determination study. + +And I have drawn a +three-dimensional contour map. + +The value of the electron +density at every point on the + +surface of one of those ovaloid +shapes is the same. + +Just like when you have a +contour map to describe in two + +dimensions an interesting +complicated surface, + +we can do this in three +dimensions as well. + +And one of the things you +notice, when you look at a + +surface like this, +is that the value of the + +electron density actually goes +down to some low value in + +between the nuclei, +for this. + +When you see molecules +represented as balls and sticks, + +or if you represent molecules +this way, just showing a pair of + +dots between the aluminum and +chloride, you may not be getting + +a physically complete picture of +the situation. + +You can get a much more +complete picture if you have + +access to the actual electron +density. + +And then, you can even go a +little further, + +and I want to show you +something very cool. + +First I am going to need to +load in a second molecule. + +And that will be the product of +the first "Lewis acid-base + +reaction" that we have +discussed. + +Because, I didn't say it over +there, but that was your first + +exposure to a Lewis acid-base +reaction, in which the ammonia + +molecule comes in and binds to +the aluminum trichloride + +molecule, +in order to satisfy the valence + +requirements of the respective +atom types. + +And so, here we are going to +look at that molecule, + +and we are going to look at its +electron density. + +And I think you are going to +like this very much. + +Here it comes. +And then I am going to + +represent this as a solid +surface. + +The value of the electron +density everywhere on this + +surface is 0.1 electron density +units. + +I want you to start thinking +about how that shape appears + +there because I am going to +underscore that a little bit + +more in just a second. +But one thing you should notice + +is that at the NH three +molecule, which is pictured at + +the top of that representation, +what you are seeing is that the + +value of the electron density +does not get very small as you + +go between the nitrogen and +hydrogen nuclei because both + +nitrogen and hydrogen are quite +similar in electronegativity as + +compared with the aluminum atom +in this system. + +The fascinating thing about +illustrating a molecule in this + +way is that we can actually +associate another property with + +the color on the surface. +Now what we are doing is + +looking at the aluminum +trichloride ammonia system. + +And let me see if I can make +this thing gradually spin, + +so that I can talk about it +without being pinned to my + +computer. +What we have on the surface on + +each of these electron density +isosurface enclosed regions is a + +color that corresponds with a +value of a function that tells + +us about the propensity of +electrons to be paired at that + +point in space. +The Lewis theory is now colored + +onto the electron density +isosurface of this Lewis acid, + +Lewis base complex molecule. +And the values that correspond + +to those regions in space where +electrons are most likely to be + +found paired up are colored +blue. + +Where they are least likely to +be found paired up are colored + +kind of red-orange, +here. + +And then an intermediate color +is this green. + +And so, you can see that you +have electron pairs associated + +with each of the three NH bonds, +up at the top. + +You have another electron pair +here in blue, + +which is very proximate to this +aluminum center, + +that is very electron deficient +as we had found right over here + +because it lacks an octet. +And then, each of these + +chlorines is able to attract +electron pairs. + +Because chlorine is very +electronegative, + +it attracts the electron pairs +to itself and sort of withholds + +them from the aluminum center, +but yet, that development of + +charge separation keeps +everything together in what we + +can call an ionic interaction, +an electrostatic interaction. + +You can see here covalent +bonding, donor-acceptor complex + +formation, and electrostatic +contributions to bonding. + +And all of this is just an +illustration of the brilliant + +ideas of Gilbert Newton Lewis. \ No newline at end of file diff --git a/tkU3bM_6YLk.txt b/tkU3bM_6YLk.txt new file mode 100644 index 0000000000000000000000000000000000000000..06b6c4e820ea0bf0d6ccd5a2cf8d0370b402f364 --- /dev/null +++ b/tkU3bM_6YLk.txt @@ -0,0 +1,2647 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation, or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Ladies +and gentlemen, + +welcome to lecture four. + +In the last lecture, I presented +to you a general + +formulation for finite +element analysis. + +In this lecture, I would like +to talk to you about the + +derivation of specific finite +element matrices. + +The formulation that we will be +using, or the derivation I + +should say, that we will be +using, leads us to generalized + +finite element models. + +I will be talking later on +about what we mean by + +generalized. + +Let's remember, let's recall +what we arrived + +at in the last lecture. + +We had that the element +stiffness matrix for element m + +is obtained by this integration +here where we + +integrate the product of a +strain-displacement matrix + +times a stress-strain matrix +times the strain-displacement + +matrix over the volume +of the element. + +We also had derived the +expression for a body force + +vector, B. m, again, +denoting element m. + +And here, we integrated over the +volume of the element the + +product of the displacement +interpolation matrix times the + +body forces in the element. + +We also had derived a surface +force vector of the element in + +which we integrate the product +of the surface interpolation + +matrix times the surface forces +applied to the element. + +So in essence, we see then if we +look at these expressions, + +we see that we need really a B +matrix, a strain-displacement + +matrix for the element. + +Of course, we need the + +stress-strain law for the element. + +And that will really be given to +us from the serial strength + +of materials. + +We also want the displacement +interpolation + +matrix for the element. + +Once we have this displacement +interpolation matrix, we can + +directly obtain the +interpolation matrix for the + +surface displacement of the +element by simply substituting + +into this matrix here, the +surface coordinates. + +In summary then, we need the H +matrix, the B matrix, and the + +stress-strain law for every +element that we have in the + +assemblage. + +Notice that the stress-strain +law, of course, must depend on + +what kind of element +we are looking at. + +How we have mechanically +idealized our system. + +In a truss structure, we will +have simply the Young's + +modulus in here. + +In a plane stress idealization, +we will have a + +plane stress law. + +In a plate bending idealization, +we will have the + +plate bending stress-strain +law in there, and so on. + +Well, I want to talk today +about these matrices. + +How do we obtain +these matrices? + +Once we have talked about that +subject, I finally want to + +also spend a little bit of +time talking about the + +convergence of the +analysis results. + +Of course, in finite element +analysis, we must be concerned + +about the accuracy of the +analysis results that we are + +obtaining, and about the +convergence of the results to + +the actual analytically, +theoretically accurate result + +that we want to obtain. + +Well, let us then first talk +about the derivation of the H, + +B, and C matrices. + +And the H, B, and C matrix, +of course, depend on the + +particular problem that +you're looking at. + +Let us therefore categorize +the different types of + +problems that we encounter +in structural analysis. + +Here we have a truss structure, +and a truss + +structure is really an +assemblage of truss elements. + +And in each truss element that +lies between the nodes, we + +have one-dimensional +stress conditions. + +In other words, the only stress +that we see on the + +section AA would be +the tau xx stress. + +And that is the only stress, no +other stress is involved. + +Of course, just going a little +bit ahead, we immediately + +would also say that the only +strain we would be interested + +in is epsilon xx and the +stress-strain law is simply + +Young's modulus. + +The second kind of analysis that +we might be performing is + +a plane stress analysis. + +In plane stress conditions, +the only stresses that are + +non-zero are tau xx, +tau yy, and tau xy. + +Remember in lectures three, I +had listed all six stress and + +strain components. + +And what I'm doing now is I take +out just those stress and + +strain components that are +really applicable for the kind + +of problem that I +want to look at. + +Plane stress situations we will +encounter in the analysis + +of a beam, for example. + +Here's a simple cantilever +beam subjected to + +surface loading p. + +And if we look at an element +here, it is redrawn here. + +We would find that +tau xx would be a + +stress into this direction. + +Tau xy is the shear +stress, and tau yy + +is that normal stress. + +The cantilever, of course, can +be subjected to a surface + +loading, a bending moment, tip +loading, whatever loading. + +The stress components, the only +stress components that we + +assume of course, act in the +structure would be these three + +stress components. + +In fact, of course, in the +actual physical situation, we + +would find that around here, +depending on the specific + +support conditions that we are +using, we would have a much + +more complicated stress +situation than the plane + +stress situation assumed. + +However, if we are only +interested in the tip + +displacement here, or the +displacements away from the + +support condition from +the support. + +Similarly, if we are only +interested in the stresses and + +strains away from the support, +certainly it is accurate + +enough to-- + +it yields an accurate enough +model to assume a + +plane stress situation. + +Another plane stress situation +occurs here, for example, + +where we have a sheet +with a hole. + +If the sheet is thin, the only +stresses that we would see on + +an element, such as shown here, +would be z stresses, the + +plane stress stresses. + +A next category of analysis +that we would encounter in + +practice is a plane +strain condition. + +Plane strain condition means +that in the space xyz shown + +here with the displacements uvw, +the displacement w is 0. + +It's identically 0 if our x, +y-coordinate system lies in + +the plane of a typical section +of the total problem. + +And let me show you +one such typical-- + +or describe to you one such +difficult problem. + +Here we have a dam that +is very long. + +In fact, we might assume +it infinitely long. + +And it is supported on this +face here, so that w, the + +displacement, normal +to that face is 0. + +And the same support +conditions are + +at the other face. + +If the dam is subject to uniform +water loading, water + +pressure loading all along its +side, then by symmetry it + +follows that w, the +displacement, at any section + +of the dam, the displacement +normal to that + +section must be 0. + +Therefore, we have w 0 meaning +directly epsilon zz 0. + +The strain into the z-direction +is also 0. + +Similarly, the shear stresses, +tau zx and tau zy are 0. + +And the only stresses that we +are left with which are + +non-zero are those shown here. + +These are the stresses acting on +a typical slice of the dam. + +A slice say, of unit length +would be subjected to just + +these stress conditions. + +Therefore, in that array of six +stresses and strains that + +I talked to you about in lecture +three, we really only + +are concerned-- + +you only need to calculate these +four components of those + +six that I talked about there. + +Another stress-strain condition +that we are + +interested in frequently in +practice is an axisymmetric + +analysis condition. + +This case we have an axis of +revolution for the structure, + +and here we look at a +cylinder, which is + +axisymmetric in geometry about +that center line here, the + +axis of revolution. + +And the loading is also assumed +in this particular + +case to be also axisymmetric. + +So typically, we are talking +about a cylinder, circular, of + +course, when looking from a +plane view subjected to + +internal pressure, which +is the same all around. + +And of course, the geometry is +also axisymmetric when we look + +at the axis of revolution, the +center line of the cylinder. + +In this particular case, the +only stress conditions that we + +need to calculate are +shown here for an + +element in that cylinder. + +We have tau xx, tau +yy, tau zz. + +This, of course, being +the hoop stress. + +And the shear stress, tau xy. + +These are the stress conditions +that we need to + +calculate for this +particular case. + +Similarity, because we are +talking about an axisymmetric + +condition, an axisymmetric +condition where really, every + +one of these elements behaves +in the same way, we can look + +at one radian of the total +circumference in the analysis. + +So this is an axisymmetric +analysis, which we also are + +concerned with frequently +in practice. + +Finally, the very large +number of analyses-- + +in a very large number of +analyses, we consider plates + +and shells. + +If we look at a plate, an +element in that plate, we + +would find that in general we +would have the tau xx, tau yy. + +These are the normal stresses. + +And tau xy shearing stresses +in the plane of the plate. + +We would also have transfer +shearing stresses, + +tau xz and tau yz. + +Sorry, tau yz, shown +here as the + +transfer shearing stresses. + +Of course, these transfers +shearing stresses give us + +shear forces. + +And these stresses here give +us membrane forces plus + +bending moments and +twisting moments. + +Elementary theory of plates +shows us, tells us, that these + +are the significant stresses +in a plate. + +The important point is that in +a plate, as well as in a + +shell, the stress normal +to the plate is 0. + +The same holds for the shell. + +The stress normal to the shell +is 0, and we have the stress + +components. + +However, we have to now remember +that the xx and yy + +axes are aligned with the +curvature of the shelf. + +Are aligned with the curvature +of the shell. + +And then these are the stress +components that are of + +interest in the analysis +of shells. + +In many cases, when we look at +the analysis of plates, the + +membrane forces-- + +the total membrane +forces are 0. + +In which case, of course, we +assume that tau yy has a + +linear variation through the +thickness of the plate. + +As stipulated, for example, in +the Kirchhoff plate theory. + +This much then for the static +components, or rather the + +stress components of plates and +shells when we look at the + +kinematics of plates +and shells. + +Just to remind you, we assume +that there's a normal to the + +mid-surface. + +And that normal in Kirchhoff +plate theory remains during + +deformation normal to +the plate surface. + +And all material particles on +that normal AB remain on a + +straight line. + +These are the two things. + +I repeat, all material particles +on the line AB + +remain during deformation on the +line AB, and the line AB + +remains normal to the +mid-surface in Kirchhoff plate + +theory, which does not exclude +shear deformations. + +However, if we use a theory +that does include shear + +deformations, we would still +have that the material + +particles on line AB will still +lie after deformations + +on the line A prime +B prime say. + +But the line A prime B prime-- + +B is still a straight line-- is +not anymore normal to the + +mid-surface. + +In this case, we have included +shear deformations. + +We will see in the next lecture +that, in fact, it is + +simpler to use a theory +including shear deformations + +to derive effective +finite elements. + +Well, this then is a review +for the kinds of stress + +components and strain components +that we are + +interested in. + +Of course, that information +which I discussed so far is + +available from the strengths +of material theory and + +continue mechanic theory. + +And as an engineer, however, we +have to be able to decide + +what kind of stress and strain + +situations you want to analyze. + +And there, of course, is already +one very important + +assumption. + +A very important assumption in +laying out or starting with + +the right model for the actual +physical structure. + +Whether we want to model the +actual physical structure as a + +truss assemblage, as an +assemblage of plates, beams, + +et cetera, all of those +situations can be covered in + +the finite element theory. + +But we have to make the right +assumptions right from the + +start in starting with +the right model. + +So here I listed ones. + +In one table, the particular +problems + +that we might encounter. + +We might have a bar. + +The displacement components +then being simply u. + +In a beam, which I have not +given earlier, but here we + +have a transverse +displacement, w. + +In plane stress situations, we +have two displacements, u and + +v. + +In a plane strain situation, +u and v. + +In an axisymmetric situation, +u and v. + +Three-dimensional situation, +we have u, v, and w. + +In plate bending, simply the +transverse displacements. + +In analysis of shells, in the +analysis of shells we would, + +of course, have the transverse +placements and also the + +membrane displacements +included. + +We will talk about that +in the next lecture. + +These are the displacement +components for the particular + +problem that we are +looking at. + +And correspondingly, we have +particular strains. + +The strains that we are talking +about are in the bar, + +simply the normals strains. + +In a beam, the second derivative +of the transverse + +displacements. + +Here we have kappa xx defined. + +This is kappa xx defined. + +In plane stress, we have +these three components. + +Plane strain, these +three components. + +Axisymmetric these three +components, and so on. + +And it is here, of course, +where the engineer has to + +decide what kind of problem he +has in hand when he actually-- + +when he looks at an actual +physical situation. + +Corresponding to these strains, + +we have also stresses. + +And here we are listing +the stresses. + +Notice that for the beam, we +are talking about a bending + +moment, which we might +consider to be + +a generalized stress. + +In plate bending, we talk +similarly about bending + +moments, which you also +might consider as + +being generalized stresses. + +Otherwise, we have the actual +stresses that correspond to + +the strains. + +Having decided what stresses +and strains we + +want to look at-- + +in other words, what kind of +problem we have at hand, we + +also have to select the +appropriate material matrix. + +Again, this one is given form +strengths of material. + +Here, for a bar, a truss +structure, we simply have + +Young's modulus. + +For a beam, we have the +flexural rigidity. + +In plane stress analysis, this +would be the material law that + +you would find in many +textbooks on + +strengths of materials. + +Well, having therefore resolved +the problem of how to + +establish the stress-strain +law, or the stress-strain + +matrix c, we now go on to +discuss the construction of + +the displacement interpolation +matrix. + +For a one-dimensional +bar element, + +we would have simply-- + +we can assume simply a +polynomial with unknown + +coefficients, alpha 1, +alpha 2, alpha 3. + +And this is simply +a polynomial nx. + +x being, of course, the +coordinate that is being used + +to describe the displacement +for the element. + +For two-dimensional elements, +here we're talking about plane + +stress, plane strain. + +Axisymmetric analysis, we would +have, similarly, these + +assumptions here. + +alphas for the u displacements +and betas for the v + +displacements. + +For the plate bending element +in which we only discretize + +the w displacement, the +transverse displacement, we + +would have this assumption +here. + +For three-dimensional solid +elements, similarly, we have + +these assumptions. + +Notice that these gammas, +alphas, betas are unknowns for + +the element. + +And we will actually relate +these coefficients to the + +nodal point displacements +of an element. + +If we look, therefore, in +general, at the description of + +an element, we really have on +the left-hand side here, the + +actual displacements, the +continuous displacements in + +the element being given by +matrix phi, which contains the + +constant and x, x squared, +x cubed terms, and so on. + +And this alpha vector here +contains the generalized + +coordinates, the alphas, +betas, gammas. + +Typically, therefore, just to +focus our attention on a + +particular case, we might have +if we say that u of x for a + +truss structure is equal to +alpha 0 plus alpha 1x plus + +alpha 2x squared. + +In this particular case, we +would have that we can write + +this, of course, as 1 x x +squared in matrix form times + +alpha 0 alpha 1, alpha 2. + +And here, I'm talking about this +being equal to the phi, + +and this being equal to +the vector alpha. + +So just to give you an example +for this particular case. + +If we now want to evaluate +the alpha values. + +Of course, in two-dimension +analysis as I shown earlier to + +you, we have also betas here. + +In three-dimensional analysis, +we also would have gammas in + +this vector. + +If you want to evaluate these +alpha values, then we can + +simply use this relation here, +or that relation here, and + +apply it to the element +nodal points. + +To the displacements at the +nodal points of the elements. + +If we do that, in other words, +we substitute into here, into + +the phi matrix, the actual +coordinate of the nodal + +points, and on the left-hand +side, of course, the + +displacement at that nodal +point, we directly generate + +this relation. + +We can then invert this relation +to obtain alpha. + +And here, we have now the +generalized coordinates in + +terms of the nodal point +displacements. + +This then would really complete +the evaluation of the + +continuous displacements u in +terms of the nodal points + +displacement u hat. + +If we have laid down this +assumption, we can directly + +also obtain the relation for the +strains of the elements. + +We have decided what kinds of +strains we want to look at + +that we have to include. + +And by proper differentiation of +the rows here, we directly + +generate this relation. + +Of course, this is a +[UNINTELLIGIBLE] + +relation then for the material +of the element. + +And we then directly have +tau in terms of alpha. + +But alpha was already given +in terms of u hat here. + +In summary, therefore, we have +our displacement interpolation + +matrix here, given as +phi times a inverse. + +This is obtained by simply +substituting from here, + +substitute from here, +directly into there. + +And you get that u is +equal to H u hat. + +And our H being phi a inverse. + +Once again, the u is the +continuous displacement in the + +elements. u hat has nodal point + +displacements in the elements. + +Similarly, if we substitute +from here into there and + +recognize that our epsilon +strain is equal to B times u + +hat, we directly obtain +that B must be equal + +to E times A inverse. + +Well, let us now look at a +particular case, a particular + +example to demonstrate how we +proceed for a particular case. + +Here I'm looking at the analysis +of a cantilever + +subjected to a load. + +And I've idealized that +cantilever as an assemblage of + +four elements. + +Each element is a four +nodal element. + +So for element 1, we have nodes +1, 2, 4, and 5 of the + +global assemblage. + +Notice that all together +we have 9 nodes. + +And once again, 4 elements. + +The cantilever structure is SiN +and we believe that it is + +appropriately modeled using +a plane stress analysis. + +In which case, the only stresses +that are of concern + +are the stresses in this +plane, tau yy, + +tau xx, and tau xy. + +So these other stress components +here are 0. + +If we look now at a particular +element to focus our attention + +on one element, because +all these elements + +are really the same. + +Basically, the same. + +Let's look at element 2. + +And we notice that element 2 +being a four nodal element is + +shown once more here with the +displacements U1, V1 at the + +local nodal point of +the element 1. + +V2, U2 being the displacements +of the local nodal point 2. + +And here, V3, U3 similarly +for nodal point 3. + +And V4, U4 for nodal point 4. + +We have taken this element of +the assemblage and what we + +want to really do is derive the +displacement and strain + +interpolation matrices for this +element corresponding to + +U1, V1; U2, V2; U3, +V3; and U4, V4. + +If we have done that, we +recognize, of course, that U1 + +corresponds to a global +displacement. + +Similarly, V1 corresponds +to a global placement. + +Then we can directly construct +the displacement and strain + +interpolations corresponding to +the global displacements. + +But the finite element procedure +is really to look + +locally at an element. + +Locally at an element. + +And work in terms of local +displacements. + +Later on then, we relate the +local displacements to the + +global displacements. + +The advantage of proceeding this +way is that we really-- + +in looking at one element, +we look at all four + +simultaneously. + +The procedure then is, once more +in summary, we want this + +matrix here, the H2 matrix +corresponding to element 2. + +The vector U lists all of the +displacements, all of the 18 + +displacements. + +However, we will look at the +element 2 with local nodal + +point displacements, forgetting +about the global + +nodal point displacement. + +And our objective is to derive +a relationship of u equals H + +times u hat, where u hat +lists U1, V1; U2, V2; + +U3, V3; U4 and V4. + +Once we have this H, which is, +of course, a 2 by 8 matrix, + +because there are 2 +displacements, u and v. The u + +and v displacement +for the element. + +And there are 8 entries +in u hat. + +Therefore, this H matrix +must be a 2 by 8. + +Once we have obtained this H +matrix, we can construct + +directly our H2 matrix that +we talked about earlier. + +Well, let's proceed then in the +way that I discussed in + +general form earlier. + +Since we have a four nodal +element, let me just sketch it + +once more here. + +Since we have a four nodal +element, and we are talking + +about u and v displacements, we +really can only have four + +constants, four generalized +coordinates. + +Generalized coordinates +corresponding to the u and + +corresponding to the +v displacements. + +Remember that the only unknown +u displacements are these 4. + +And these 4 u displacements will +give us alpha 1, alpha 2, + +alpha 3, and alpha 4. + +The same holds for the +v displacements. + +This is a bilinear approximation +of the u + +displacements in the element. + +We write this in matrix +form as shown here. + +Noting that this capital Phi, +notice this is a capital Phi + +because there are these +cross bars. + +It's easy to confuse the capital +Phi with the lowercase + +phi, which doesn't have +the cross bars. + +So this capital Phi was +the cross bars here + +is defined in here. + +Where the lowercase phi +is simply an array + +of 1, x, y, x, y. + +This relationship here is +nothing else than that + +relationship, but written +in matrix form. + +The alpha lists all the +generalized coordinates. + +The generalize coordinates. + +And this is the reason why we +call this the generalized + +coordinate finite element +formulation for this + +particular element. + +Let us now define the +u hat vector, + +which I refer to earlier. + +This case, the u hat vector +involves 4 u nodal point + +displacements and 4 v nodal +point displacements. + +Now if we apply-- + +and this is really one +important point. + +If we apply this relationship +here, which of course must + +hold all over the element. + +In particular, it must also hold +for the nodal points of + +the element. + +If we apply this relationship +for the nodal points of the + +elements, we can apply it eight +times because we have 8 + +nodal point displacements. + +We directly generate this +relationship here. + +u hat equals A times alpha, +where A involve the + +coordinates of the +nodal points. + +Hence, we have our H Phi times +A inverse the way I have + +derived it earlier. + +So this is a very systematic +approach of deriving the + +displacement interpolation +matrix. + +It consists of evaluating +the A matrix. + +And of course, we assume that +that A matrix can be inverted. + +This is, for this element, +certainly the case, as long as + +we are talking about the +rectangular element or not + +very highly distorted +elements. + +We can for the four nodal +element, invert this matrix + +and directly get this +relationship. + +Let's look now, once more back +at the analysis that we wanted + +to perform. + +Remember that we looked at this +element here, and we have + +now obtained the H matrix, the +displacement interpolation + +matrix for this element. + +Once more, here is +the H matrix. + +In fact, this H matrix here, +since we have no superscript + +attached to it yet, really holds +for every one of the 4 + +elements that we are +talking about. + +Provided we put into the u hat +here the appropriate nodal + +point displacements +of the elements. + +We can directly say that this +matrix here holds for any one + +of the elements. + +If the elements, if the 4 +elements are not completely + +identical, of course, the A +inverse will change from + +element to element. + +Having gone through that step +and having looked at element 2 + +once more, we directly recognize +how to establish now + +the H2 matrix. + +Remember our u1 will be related +to the global U11. + +Our v1 will be related +to the-- + +or will correspond I should +rather say, to the global U12. + +Let's look at why this +is the case. + +Why did I write down U11 +here and U12 there? + +Well, let's look at +this point there. + +Which is of course, the +local nodal point 1. + +The local nodal point 1, right +upperhand corner of element 1, + +corresponds here to +nodal point 6. + +Well, the global nodal point +displacements of + +nodal point 6 are U11. + +Let me put them in. + +And U12. + +Why is that the case? + +Well, if we start numbering +here-- and I'm going to + +include now, I'm going to +include now the displacement + +of these nodal points, although +we know that they are + +actually 0, that boundary +condition we can + +impose later on. + +So if I start numbering here, I +would have U1, U2, 3, 4, 5, + +6, 7, 8, 9, 10, 11, 12. + +So the global nodal point +displacements are U11, U12 + +corresponding to +nodal point 9. + +And those are the ones that +appear right here + +corresponding to the local +U1 and the local V1. + +Well, if we proceed in the same +way for all of the other + +nodal points for element 2, +and these are the results. + +You can look these up in the +textbook figure 4.6, or in the + +accompanying notes. + +We can directly construct the +H2 matrix for the element. + +And now the H2 matrix, of +course, involves as the vector + +the global nodal point +displacements, U1 to U18. + +The H matrix for element 2. + +And if the 4 elements are +identical, we will have the + +same H matrix for all +the elements. + +The H matrix here looks +as shown here. + +Notice that we have a +one quarter there. + +It's a little arrow here. + +The bracket should've +been there. + +Bracket should have +been there. + +So we have a one quarter +outside of the bracket. + +And we have as the first +entry, this one here. + +This corresponds to U1. + +This is the entry corresponding +to U1. + +I left the entries +corresponding + +to U2, U3, U4 out. + +This is the entry corresponding +to V1. + +And I left out the entries +corresponding to V2, V3, V4. + +This is our H matrix here. + +And now we basically want to +blow it up to obtain the H2 + +matrix corresponding +to element 2. + +Well, if we recognize as we just +did that U1, the local + +U1, the local V1, correspond +to capital U11 and capital + +U12, and I just showed you that +that is indeed the case. + +We would simply take the first +element here, this element + +here, and put it right there. + +This element here would +go right there. + +This element here would +go right there. + +And this element here would +go right there. + +In fact, H1 5 is 0 as +you can see here. + +And H2 1 is 0. + +So H1 1 is this term here. + +And H2 5 is that term here. + +Those are two non-zero entries +in the complete H matrix. + +Well, this is then the way how +we actually can proceed to + +construct the H2 matrix. + +I pointed out earlier in lecture +three already that we + +do not perform this step +computationally. + +In fact, what we do +computationally is we stay + +with this H matrix. + +We calculate a compacted +stiffness matrix, a compacted + +load vector, which the stiffness +matrix will be of + +order 8 by 8. + +And then we assemble these +element matrices with + +identification arrays and +connectivity arrays into the + +global structural stiffness +matrix, into + +the global load vectors. + +So we really don't perform +this step of + +blowing up the H matrix. + +And I will show you in the next +lecture how we actually + +perform the computations of +assembling element matrices. + +However, for theoretical +purposes, it is neat if you + +understand how we can construct +this H2 matrix from + +this H matrix. + +And of course, similarly, we +could construct H1, H3, and H4 + +from this basic H matrix. + +Once we have done that, we can +directly write that k being + +equal to the sum of the km. + +In other words, the global +structure stiffness matrix is + +equal to the sum of the element +matrices, stiffness + +matrices, where each of these +km's has the same order as the + +structure stiffness matrix k. + +Let us now look briefly at the +development of the strain + +displacement matrix. + +In plane stress conditions, +we have three entries. + +The strains are given +as shown here. + +Elementary strengths materials +tells us that + +these are the strains. + +And I showed earlier that the +B matrix is constructed by + +multiplying the E times +the A inverse. + +The A inverse was already used +in the calculation of the + +displacement interpolation +matrix. + +The E matrix is obtained by +appropriately differentiating + +the entries in the displacement +interpolations. + +And this differentiation is +performed on the phi matrix + +right here. + +Or rather, on these +entries here. + +By simply differentiating these +entries here, we would + +obtain the strains and writing +those in matrix form, we + +obtain the E matrix here. + +Once we have the B matrix, which +in this particular case + +is 3 by 8 matrix for a typical +element, we can, of course, + +construct the B2 matrix for +element 2 just in the same way + +as the H2 matrix. + +Of course, we would again, +blow up the B + +matrix from a 3 to 8. + +3 by 8 I should rather say, to +a 3 by 18 now because we have + +actually 18 degrees +of freedom in the + +complete structural model. + +This then completes what I +wanted to say about the + +construction of the +displacement and + +strain-displacement +interpolation matrix for the + +element, the H2 and +B2 matrices. + +However, let me just spend +a few moments on the + +construction of the surface +displacement + +interpolation matrix. + +In other words, the +interpolation of the + +displacements along the +surface of an element. + +Here, assume for example, that +this is a surface of the + +elements that we are +concerned with. + +And that there would be some +loading applied to that + +surface of the element. + +So that we need, in other words, +the HSM matrix the way + +I have been pointing +it out earlier. + +What we would do to obtain this +matrix here, is really + +simply use our earlier +results for the HS-- + +sorry, for the HM matrix. + +And here we have the +H matrix and the H2 + +matrix for element 2. + +What we would do is we would use +this matrix, or this one + +of course, this matrix is +contained in this one. + +And simply, substitute the +particular coordinates along + +the surface. + +Now, going back once more +to the element under + +consideration. + +If we are looking at this +surface, then y is constant + +and equal to this +distance here. + +So knowing y, we would simply +substitute that value of y + +into this function here, and +thus obtain the HS matrix. + +So, in general, therefore the +HS matrix is simply obtained + +from the H matrix, or the HS2 +matrix here would simply be + +obtained from the H2 matrix by +substituting the coordinates + +along the line, or along +the surface that we are + +considering. + +Let us now to look at the +overall process of the finite + +element solution. + +Here I have summarized what we +all are concerned about. + +Of course we have the actual +physical problem that we want + +to analyze. + +We have a geometric domain that +we have to discretize. + +A material that has to be +represented, a loading and the + +boundary conditions. + +All of those have to +be represented. + +In the mechanic idealization, +the idealization step that is + +a very important step that I +referred to earlier, we would + +idealize the kinematics as being +a truss, plane stress, + +three-dimensional, Kirchhoff +plate, kinematics. + +The material isotopic elastic, +the loading, and the boundary + +conditions. + +And this mechanical idealization +really gives us a + +differential equation +or equilibrium for + +one-dimensional stress +situation, a bar. + +We will have an equation +such as this one. + +In the finite element solution +then, we operate on this + +equation basically. + +We want to solve the governing +differential equation of the + +mechanical idealization. + +The errors that we are +therefore, concerned with are + +discretization errors by the +use of the finite element + +interpolations. + +And then, a number +of other errors. + +Numerical integration +in space. + +If we use numerical integration, +there would be + +other errors introduced. + +In the evaluation of the +constitutive relations, again, + +errors would be introduced. + +The solution of the dynamic +equilibrium equations, by + +[UNINTELLIGIBLE] time +integration, mode + +superposition further errors +would be introduced. + +If you solved the governing +equilibrium equations, ku + +equals r, by iteration there +would be further errors + +introduced. + +And of course, finally there +are round-off errors on the + +digital computer. + +What I want to do now in +discussing convergence, I want + +to say that all of these +errors are negligible. + +In other words, we are basically +evaluating the + +integrations in space exactly. + +There is no round-off because we +have an infinite precision + +machine, and so on. + +So all the errors that we are +looking at now are the + +discretization errors, + +And if we look only at +the discretization + +errors, we can say some-- + +make some very fundamental +remarks about the convergence + +of the finite elements scheme. + +I've summarized here on the +blackboard some of these very + +important concepts. + +When we talk about convergence, +let us assume + +first now that we are having a +compatible element layout. + +In other words, we're using a +compatible element layout. + +And then, we know that we have +monotonic convergence to the + +solution of the +problem-governing differential + +equations provided the elements +that we are using + +contain: + +Firstly, all required +rigid body modes. + +This means, for example, that +for in a plane stress + +analysis, the element must be +able to undergo three rigid + +body modes, two translations, +horizontally and vertically, + +and a rigid body rotation. + +And the element must be able +to represent the required + +constant strain states. + +In a plane stress analysis, +three constant strain states. + +Pulling this way, pulling that +way, and the constant shear. + +If these two conditions are +satisfied, we have monotonic + +convergence in a compatible +element layout. + +What do we mean by a compatible +element layout? + +Well, here I have show a small +picture showing two elements, + +a white and an orange element. + +And these elements are +compatible because we have + +three nodes along this line +for each of the elements. + +So the white element +displacements basically vary + +parabolically along this line, +and so do the orange element + +displacements. + +No gap can develop between +these two lines. + +Here we have an incompatible +element layout. + +Two nodes that describe only +a linear variation + +for the white element. + +But three nodes for the orange +element describing a parabolic + +variation in displacement. + +Therefore a gap can open up and +this is an incompatible + +element layout. + +Well, let us assume then that +we have a compatible element + +layout fist of all. + +Then, typically for an analysis +such as this one, a + +simple cantilever subjected to +a tip load, the convergence + +that we would observe would +be the following. + +As we increase the number of +elements that idealize the + +cantilever, the displacement +measured here would + +monotonically approach from +below the exact displacement. + +What do we mean by exact +displacement? + +Notice I put it into quotes. + +Well, the exact displacement +that I'm talking about here is + +the tip displacements that we +would calculate from the + +problem-governing differential +equation. + +Of course, that +problem-governing differential + +equation also corresponds to a +mechanical idealization of the + +actual physical situation. + +And depending on which +problem-governing differential + +equation we choose, we would +have a different dashed line. + +But assuming now that we have +made up our mind which one to + +choose, which mechanical +idealization to choose, and we + +are choosing a corresponding +finite element idealization, + +this would be the convergence +that we would observe. + +And it would be monotonically +from below. + +In other words, our finite +element model, + +actually is too stiff. + +It is stiffer than the actual +physical structure. + +Well, why I think we can +intuitively understand that + +quite well if we just recognize +that we are + +constraining the displacements +within each element to only be + +able to basically, take patterns +on that are contained + +in the element. + +In other words, for the four +nodal element here, we really + +have for the U displacements and +for the V displacements, + +only 4 displacement +patterns each that + +the element can undergo. + +So we are constraining the +exact displacements to be + +really, approximated by these +displacement patterns. + +And that makes the actual finite +element model stiffer + +than the actual physical +structure. + +If we have an incompatible +layout, and I showed earlier + +what we mean by that, +then, in addition, + +every patch of elements-- + +by patch of elements we mean +small assemblage of elements-- + +must be able to represent the +constant strain states. + +It's not just that each element +must be able to + +represent the constant +strain state, but + +each patch of elements. + +Also, then if this holds true, +then we have convergence. + +But non-monotonic convergence. + +By non-monotonic convergence, +I mean the following. + +We might get this result for +a certain set of elements. + +And as we increase the number +of elements, we are + +oscillating about the correct +result, the exact result in + +quotes again, and finally +we converge. + +This is non-monotonic +convergence because we can + +have solutions lying on either +side of the exact result. + +Well, let me now show to you +some of the facts that I just + +talked about on this +view graph. + +What do these mean? + +Well, I said already that each +element in every case must be + +able to represent the +rigid body modes. + +Here for a plane stress analysis +of a cantilever beam + +shown here, we have 3 +rigid body modes. + +And as I mentioned earlier +briefly already, the element + +must be able to go over, go up +as a rigid body and rotate as + +a rigid body. + +Why is this the case? + +Well, if we look at an analysis +of the cantilever + +where we have not a tip load, +but a load say, at this end + +here, we know that the bending +moment looks this way. + +Hence, these elements over here +must be able to freely + +rotate and displace. + +In other words, we know that the +exact condition, the exact + +physical condition, there should +be no stress here. + +The stress should be +0 in this element. + +And this means that the tip +element here must be able to + +translate freely as +a rigid body and + +rotate as a rigid body. + +If this were not the +case, then we would + +get stresses here. + +And of course, our analysis or +finite element model can never + +predict the actual physical +conditions accurately or + +closely, even if we take an +infinite number of elements. + +So this somehow explains to you +intuitively why the rigid + +body more criteria must +be satisfied. + +How about the constant strain +state criteria? + +Well, if we assume that we take +more and more elements-- + +and let me draw in here +such elements. + +For example, now we have gone +from a certain number of + +elements to a larger +number of elements. + +These elements, as we keep on +refining the mesh, would + +become very small, and +would go down. + +In fact, each element would +go down to a point. + +But at a point we only have one +constant stress basically. + +So the element must be able in +the limit, to represent the + +constant stress at a point. + +And therefore, we have the +constant stress criteria also. + +One way of finding out whether +an element satisfies these + +criteria, the constant stress +criteria and the rigid body + +mode criteria is to calculate +its eigenvalues. + +Here, we have taken ones. + +A four node plane stress element +and calculate the + +eigenvalues. + +Notice the lowest three +eigenvalues are 0, + +representing the rigid +body modes. + +And then, we have a flexural +mode here, the fourth + +eigenvalue. + +The fifth eigenvalue is again +the flexural mode. + +And here is the constant +sharing mode. + +And here are the two +constant, one + +compression and tension modes. + +So these are the constant strain +states that the element + +can represent therefore. + +And earlier I showed you the +three rigid body modes. + +So surely, this element +therefore satisfies both of + +the criteria. + +Let's look now at what happens +when we don't have a + +compatible mesh. + +We have an additional condition +that every patch of + +elements must also be able +to represent the + +constant strain states. + +Only then we will have +convergence. + +But we will not necessarily have +monotonic convergence. + +We can only talk about +non-monotonic convergence. + +Well, here I've taken +a patch of elements. + +Each element by itself satisfies +the constant strain + +criterion and the rigid +body more criterion. + +In this case here, we use a +compatible element layout. + +Compatible because along each +side, the adjacent elements + +shares the nodes. + +And we are subjecting this patch +of elements to a total + +stress here of 100 Newton +per square centimeters. + +Of course, the stress in each +of these elements would be + +simply a stress this +direction of 1,000. + +Excuse me, 1,000 not 100. + +The other stress, the vertical +stress and the shear stress is + +0 for this patch of elements. + +Let us now perform the +following experiment. + +Let us say that we are assigning +two nodes, two + +different nodes to element +4 and 5 at this location. + +Here they share the same node. + +Let us do the same +at this end. + +And let us say that node +17 only belongs to + +this element 4. + +Node 18 belongs only +to element 6. + +Node 20 and 19 belong +to element 5. + +In other words, node 17 can +basically gives this + +displacement pattern. + +And 19 gives this displacement +pattern. + +An incompatibility +can reside here. + +And similarly, along +this line. + +If we subject this patch of +elements to the stress state + +of the external forces that we +used here too, we would find + +that the stresses at the points +A, B, C, D, E shown + +along here, which here were, +of course, exactly equal to + +1,000 for this stress tau yy +and 0 in this direction. + +And the sheer stress was 0. + +If you look at the tau yy +at A, B, C, D, E now the + +incompatible element mesh +layout, we would find the + +following stress result. + +Notice that the stresses +now are not 1,000. + +In fact, they vary drastically +from 1,000. + +359 instead of 1,000. + +This means that this patch +of elements with the + +incompatibility here, does not +represent exactly the constant + +stress state that it should +represent because we are + +subjecting it to a constant +stress state. + +Therefore, this patch of element +does not satisfy the + +requirement for convergence. + +Not monotonic convergence and +not non-monotonic convergence. + +It just should not be used in an +actual practical analysis. + +This completes what I wanted to +say then in this lecture. + +Thank you very much for +your attention. \ No newline at end of file diff --git a/uskl5IFNM64.txt b/uskl5IFNM64.txt new file mode 100644 index 0000000000000000000000000000000000000000..036361007909f13b464879877ba0740f37866e0a --- /dev/null +++ b/uskl5IFNM64.txt @@ -0,0 +1,459 @@ +align:start position:0% + +We conduct the class entirely in Chinese + + align:start position:0% +We conduct the class entirely in Chinese + + + align:start position:0% +We conduct the class entirely in Chinese +starting from day two after orientation. + + align:start position:0% +starting from day two after orientation. + + + align:start position:0% +starting from day two after orientation. +So I think in the orientation we clearly + + align:start position:0% +So I think in the orientation we clearly + + + align:start position:0% +So I think in the orientation we clearly +tell students about rules and + + align:start position:0% +tell students about rules and + + + align:start position:0% +tell students about rules and +expectations. I would say there are a + + align:start position:0% +expectations. I would say there are a + + + align:start position:0% +expectations. I would say there are a +few key components here to make it + + align:start position:0% +few key components here to make it + + + align:start position:0% +few key components here to make it +happen. The first the first one + + align:start position:0% +happen. The first the first one + + + align:start position:0% +happen. The first the first one +is we tell students that our idea here + + align:start position:0% +is we tell students that our idea here + + + align:start position:0% +is we tell students that our idea here +is we try to create Chinese as an + + align:start position:0% +is we try to create Chinese as an + + + align:start position:0% +is we try to create Chinese as an +atmosphere as possible and if we were to + + align:start position:0% +atmosphere as possible and if we were to + + + align:start position:0% +atmosphere as possible and if we were to +refer to English every few minutes this + + align:start position:0% +refer to English every few minutes this + + + align:start position:0% +refer to English every few minutes this +goal is impossible to accomplish. So in + + align:start position:0% +goal is impossible to accomplish. So in + + + align:start position:0% +goal is impossible to accomplish. So in +order in order to do this there are a + + align:start position:0% +order in order to do this there are a + + + align:start position:0% +order in order to do this there are a +few key components. One is classroom + + align:start position:0% +few key components. One is classroom + + + align:start position:0% +few key components. One is classroom +expressions. So students they need to be + + align:start position:0% +expressions. So students they need to be + + + align:start position:0% +expressions. So students they need to be +familiar with those instructions you + + align:start position:0% +familiar with those instructions you + + + align:start position:0% +familiar with those instructions you +want them to do. For example, you want + + align:start position:0% +want them to do. For example, you want + + + align:start position:0% +want them to do. For example, you want +them to repeat after you or you want + + align:start position:0% +them to repeat after you or you want + + + align:start position:0% +them to repeat after you or you want +them to answer the questions. So that + + align:start position:0% +them to answer the questions. So that + + + align:start position:0% +them to answer the questions. So that +classroom expressions are very + + align:start position:0% +classroom expressions are very + + + align:start position:0% +classroom expressions are very +important. Second thing is they need to + + align:start position:0% +important. Second thing is they need to + + + align:start position:0% +important. Second thing is they need to +know what they are expected to do in + + align:start position:0% +know what they are expected to do in + + + align:start position:0% +know what they are expected to do in +class. So that is about your weekly + + align:start position:0% +class. So that is about your weekly + + + align:start position:0% +class. So that is about your weekly +schedules that detail everything you + + align:start position:0% +schedules that detail everything you + + + align:start position:0% +schedules that detail everything you +wanted to do in class. So for example, + + align:start position:0% +wanted to do in class. So for example, + + + align:start position:0% +wanted to do in class. So for example, +you need to tell students what they need + + align:start position:0% +you need to tell students what they need + + + align:start position:0% +you need to tell students what they need +to prepare before class. And in class, + + align:start position:0% +to prepare before class. And in class, + + + align:start position:0% +to prepare before class. And in class, +you only practice, you got only drill + + align:start position:0% +you only practice, you got only drill + + + align:start position:0% +you only practice, you got only drill +based on those materials. So what they + + align:start position:0% +based on those materials. So what they + + + align:start position:0% +based on those materials. So what they +do in class is what they prepared. And + + align:start position:0% +do in class is what they prepared. And + + + align:start position:0% +do in class is what they prepared. And +with the classroom expressions, they're + + align:start position:0% +with the classroom expressions, they're + + + align:start position:0% +with the classroom expressions, they're +pretty they're pretty easily guided by + + align:start position:0% +pretty they're pretty easily guided by + + + align:start position:0% +pretty they're pretty easily guided by +you. So that the whole interaction can + + align:start position:0% +you. So that the whole interaction can + + + align:start position:0% +you. So that the whole interaction can +be in Chinese. And of course we do + + align:start position:0% +be in Chinese. And of course we do + + + align:start position:0% +be in Chinese. And of course we do +understand that because of the anxieties + + align:start position:0% +understand that because of the anxieties + + + align:start position:0% +understand that because of the anxieties +or or + + align:start position:0% +or or + + + align:start position:0% +or or +sometimes students they cannot fully + + align:start position:0% +sometimes students they cannot fully + + + align:start position:0% +sometimes students they cannot fully +understand what you say. In that case we + + align:start position:0% +understand what you say. In that case we + + + align:start position:0% +understand what you say. In that case we +always tell students be a little bit + + align:start position:0% +always tell students be a little bit + + + align:start position:0% +always tell students be a little bit +patient. If you really have questions + + align:start position:0% +patient. If you really have questions + + + align:start position:0% +patient. If you really have questions +you need to ask in English. There are a + + align:start position:0% +you need to ask in English. There are a + + + align:start position:0% +you need to ask in English. There are a +couple things you can do. You can do it + + align:start position:0% +couple things you can do. You can do it + + + align:start position:0% +couple things you can do. You can do it +the last five minutes of class or you + + align:start position:0% +the last five minutes of class or you + + + align:start position:0% +the last five minutes of class or you +can do it after class or you can you can + + align:start position:0% +can do it after class or you can you can + + + align:start position:0% +can do it after class or you can you can +communicate with your instructor via + + align:start position:0% +communicate with your instructor via + + + align:start position:0% +communicate with your instructor via +email. But for the f for the first 45 + + align:start position:0% +email. But for the f for the first 45 + + + align:start position:0% +email. But for the f for the first 45 +minutes, we really want to create the + + align:start position:0% +minutes, we really want to create the + + + align:start position:0% +minutes, we really want to create the +Chinese atmosphere so that everybody can + + align:start position:0% +Chinese atmosphere so that everybody can + + + align:start position:0% +Chinese atmosphere so that everybody can +feel they're they're immersed in that in + + align:start position:0% +feel they're they're immersed in that in + + + align:start position:0% +feel they're they're immersed in that in +that culture. So this is what we're + + align:start position:0% +that culture. So this is what we're + + + align:start position:0% +that culture. So this is what we're +trying to do and I think for after I + + align:start position:0% +trying to do and I think for after I + + + align:start position:0% +trying to do and I think for after I +would say the two days or three + + align:start position:0% +would say the two days or three + + + align:start position:0% +would say the two days or three +days student as long as you stick to the + + align:start position:0% +days student as long as you stick to the + + + align:start position:0% +days student as long as you stick to the +principle and also be accommodating + + align:start position:0% +principle and also be accommodating + + + align:start position:0% +principle and also be accommodating +sometimes students they would know this + + align:start position:0% +sometimes students they would know this + + + align:start position:0% +sometimes students they would know this +is expectance and I would say after + + align:start position:0% +is expectance and I would say after + + + align:start position:0% +is expectance and I would say after +three days they usually can come they + + align:start position:0% +three days they usually can come they + + + align:start position:0% +three days they usually can come they +usually follow along very very well. \ No newline at end of file diff --git a/vMJshx7SO6Y.txt b/vMJshx7SO6Y.txt new file mode 100644 index 0000000000000000000000000000000000000000..e7e695d76e17f1ce67f1b462f3aa9f63be11939b --- /dev/null +++ b/vMJshx7SO6Y.txt @@ -0,0 +1,10419 @@ +align:start position:0% + +So um today we're going to continue our + + align:start position:0% +So um today we're going to continue our + + + align:start position:0% +So um today we're going to continue our +discussion of uh enforcing modularity + + align:start position:0% + + + + align:start position:0% + +and we're going to in particular if you + + align:start position:0% +and we're going to in particular if you + + + align:start position:0% +and we're going to in particular if you +remember last time we spent a lot of + + align:start position:0% +remember last time we spent a lot of + + + align:start position:0% +remember last time we spent a lot of +time talking about um + + align:start position:0% + + + + align:start position:0% + +last time we spent a lot of time talking + + align:start position:0% +last time we spent a lot of time talking + + + align:start position:0% +last time we spent a lot of time talking +about how we can create a virtual + + align:start position:0% +about how we can create a virtual + + + align:start position:0% +about how we can create a virtual +memory so that we can have multiple + + align:start position:0% +memory so that we can have multiple + + + align:start position:0% +memory so that we can have multiple +programs. + + align:start position:0% +programs. + + + align:start position:0% +programs. +running on top of one piece of hardware + + align:start position:0% +running on top of one piece of hardware + + + align:start position:0% +running on top of one piece of hardware +that all appear to have a separate + + align:start position:0% +that all appear to have a separate + + + align:start position:0% +that all appear to have a separate +address space or a separate memory. So, + + align:start position:0% +address space or a separate memory. So, + + + align:start position:0% +address space or a separate memory. So, +uh, two lectures ago we talked about + + align:start position:0% +uh, two lectures ago we talked about + + + align:start position:0% +uh, two lectures ago we talked about +having one module per computer. + + align:start position:0% + + + + align:start position:0% + +Um, and then last time we talked about + + align:start position:0% +Um, and then last time we talked about + + + align:start position:0% +Um, and then last time we talked about +this notion of wanting to have a module + + align:start position:0% + + + + align:start position:0% + +per + + align:start position:0% +per + + + align:start position:0% +per +virtual computer + + align:start position:0% + + + + align:start position:0% + +and we saw this notion of virtual + + align:start position:0% +and we saw this notion of virtual + + + align:start position:0% +and we saw this notion of virtual +memory. + + align:start position:0% +memory. + + + align:start position:0% +memory. +Okay. And now this time what we're going + + align:start position:0% +Okay. And now this time what we're going + + + align:start position:0% +Okay. And now this time what we're going +to do is we're going to talk about the + + align:start position:0% +to do is we're going to talk about the + + + align:start position:0% +to do is we're going to talk about the +other piece that our virtual computer + + align:start position:0% +other piece that our virtual computer + + + align:start position:0% +other piece that our virtual computer +needs which is a virtual processor. + + align:start position:0% + + + + align:start position:0% + +Okay. So the idea that we want here + + align:start position:0% +Okay. So the idea that we want here + + + align:start position:0% +Okay. So the idea that we want here +when we're designing a virtual processor + + align:start position:0% +when we're designing a virtual processor + + + align:start position:0% +when we're designing a virtual processor +is to create uh have our programs be + + align:start position:0% +is to create uh have our programs be + + + align:start position:0% +is to create uh have our programs be +able to run on one on on a single + + align:start position:0% +able to run on one on on a single + + + align:start position:0% +able to run on one on on a single +physical physical processor but have + + align:start position:0% +physical physical processor but have + + + align:start position:0% +physical physical processor but have +different programs be able to run as + + align:start position:0% +different programs be able to run as + + + align:start position:0% +different programs be able to run as +though they were the only program that + + align:start position:0% +though they were the only program that + + + align:start position:0% +though they were the only program that +was executing on that processor. So we + + align:start position:0% +was executing on that processor. So we + + + align:start position:0% +was executing on that processor. So we +want the programs to be written in a + + align:start position:0% +want the programs to be written in a + + + align:start position:0% +want the programs to be written in a +style where the programmer doesn't have + + align:start position:0% +style where the programmer doesn't have + + + align:start position:0% +style where the programmer doesn't have +to be aware of the other programs that + + align:start position:0% +to be aware of the other programs that + + + align:start position:0% +to be aware of the other programs that +are running on the machine and where the + + align:start position:0% +are running on the machine and where the + + + align:start position:0% +are running on the machine and where the +machine uh creates a sort of virtual + + align:start position:0% +machine uh creates a sort of virtual + + + align:start position:0% +machine uh creates a sort of virtual +processor for each one of these programs + + align:start position:0% +processor for each one of these programs + + + align:start position:0% +processor for each one of these programs +that's running. So that uh each program + + align:start position:0% +that's running. So that uh each program + + + align:start position:0% +that's running. So that uh each program +uh has its own sort of set of + + align:start position:0% +uh has its own sort of set of + + + align:start position:0% +uh has its own sort of set of +instructions that it's ex executes and + + align:start position:0% +instructions that it's ex executes and + + + align:start position:0% +instructions that it's ex executes and +those instructions appear to be + + align:start position:0% +those instructions appear to be + + + align:start position:0% +those instructions appear to be +independent of all the other programs + + align:start position:0% +independent of all the other programs + + + align:start position:0% +independent of all the other programs +that are running. So in order to create + + align:start position:0% +that are running. So in order to create + + + align:start position:0% +that are running. So in order to create +this illusion of a virtual processor, + + align:start position:0% + + + + align:start position:0% + +we're going to imple introduce a very + + align:start position:0% +we're going to imple introduce a very + + + align:start position:0% +we're going to imple introduce a very +simple concept. Um we're going to have + + align:start position:0% +simple concept. Um we're going to have + + + align:start position:0% +simple concept. Um we're going to have +each program run + + align:start position:0% +each program run + + + align:start position:0% +each program run +in what's known as a thread. + + align:start position:0% + + + + align:start position:0% + +Um and thread is really short for a + + align:start position:0% +Um and thread is really short for a + + + align:start position:0% +Um and thread is really short for a +thread of execution. + + align:start position:0% + + + + align:start position:0% + +And a thread is just uh a collection of + + align:start position:0% +And a thread is just uh a collection of + + + align:start position:0% +And a thread is just uh a collection of +all of the state that we need in order + + align:start position:0% +all of the state that we need in order + + + align:start position:0% +all of the state that we need in order +to keep track of what one single given + + align:start position:0% +to keep track of what one single given + + + align:start position:0% +to keep track of what one single given +program is doing at a particular point + + align:start position:0% +program is doing at a particular point + + + align:start position:0% +program is doing at a particular point +in time. So a thread is a collection of + + align:start position:0% +in time. So a thread is a collection of + + + align:start position:0% +in time. So a thread is a collection of +the instructions + + align:start position:0% + + + + align:start position:0% + +or the program that the module is + + align:start position:0% +or the program that the module is + + + align:start position:0% +or the program that the module is +running + + align:start position:0% +running + + + align:start position:0% +running +um as well as the state the current + + align:start position:0% +um as well as the state the current + + + align:start position:0% +um as well as the state the current +state of the program. In particular, + + align:start position:0% +state of the program. In particular, + + + align:start position:0% +state of the program. In particular, +it's the value of the registers on the + + align:start position:0% +it's the value of the registers on the + + + align:start position:0% +it's the value of the registers on the +processor. Um, including and of + + align:start position:0% +processor. Um, including and of + + + align:start position:0% +processor. Um, including and of +particular import for this lecture, the + + align:start position:0% +particular import for this lecture, the + + + align:start position:0% +particular import for this lecture, the +program counter and the stack pointer. + + align:start position:0% +program counter and the stack pointer. + + + align:start position:0% +program counter and the stack pointer. +Okay, so there's a bunch of registers on + + align:start position:0% +Okay, so there's a bunch of registers on + + + align:start position:0% +Okay, so there's a bunch of registers on +the processor, say you know your there's + + align:start position:0% +the processor, say you know your there's + + + align:start position:0% +the processor, say you know your there's +say 32 registers. Um, and it there also + + align:start position:0% +say 32 registers. Um, and it there also + + + align:start position:0% +say 32 registers. Um, and it there also +are these special registers. the program + + align:start position:0% +are these special registers. the program + + + align:start position:0% +are these special registers. the program +counter that keeps track of which + + align:start position:0% +counter that keeps track of which + + + align:start position:0% +counter that keeps track of which +instruction is currently being executed + + align:start position:0% +instruction is currently being executed + + + align:start position:0% +instruction is currently being executed +and the stack pointer which keeps track + + align:start position:0% +and the stack pointer which keeps track + + + align:start position:0% +and the stack pointer which keeps track +of uh where on the stack uh values are + + align:start position:0% +of uh where on the stack uh values are + + + align:start position:0% +of uh where on the stack uh values are +currently being pushed on pushed or + + align:start position:0% +currently being pushed on pushed or + + + align:start position:0% +currently being pushed on pushed or +popped from. Um + + align:start position:0% +popped from. Um + + + align:start position:0% +popped from. Um +so this is these are really the things + + align:start position:0% +so this is these are really the things + + + align:start position:0% +so this is these are really the things +that uh these things combined together + + align:start position:0% +that uh these things combined together + + + align:start position:0% +that uh these things combined together +with the stack are really the things + + align:start position:0% +with the stack are really the things + + + align:start position:0% +with the stack are really the things +that define one single thread. So um if + + align:start position:0% +that define one single thread. So um if + + + align:start position:0% +that define one single thread. So um if +you think so and the way to think about + + align:start position:0% +you think so and the way to think about + + + align:start position:0% +you think so and the way to think about +this is if you think about a program + + align:start position:0% +this is if you think about a program + + + align:start position:0% +this is if you think about a program +that's running you can really + + align:start position:0% +that's running you can really + + + align:start position:0% +that's running you can really +encapsulate almost everything about what + + align:start position:0% +encapsulate almost everything about what + + + align:start position:0% +encapsulate almost everything about what +that program is currently doing by the + + align:start position:0% +that program is currently doing by the + + + align:start position:0% +that program is currently doing by the +state of its by sort of uh the + + align:start position:0% +state of its by sort of uh the + + + align:start position:0% +state of its by sort of uh the +instructions that it has to execute the + + align:start position:0% +instructions that it has to execute the + + + align:start position:0% +instructions that it has to execute the +value of the registers that it is that + + align:start position:0% +value of the registers that it is that + + + align:start position:0% +value of the registers that it is that +that are currently set in the program + + align:start position:0% +that are currently set in the program + + + align:start position:0% +that are currently set in the program +and the state that's on the stack. Now + + align:start position:0% +and the state that's on the stack. Now + + + align:start position:0% +and the state that's on the stack. Now +programs may also have some sort of uh + + align:start position:0% +programs may also have some sort of uh + + + align:start position:0% +programs may also have some sort of uh +data that's stored in the global memory + + align:start position:0% +data that's stored in the global memory + + + align:start position:0% +data that's stored in the global memory +in the sort of say global variables or + + align:start position:0% +in the sort of say global variables or + + + align:start position:0% +in the sort of say global variables or +things that are stored on the heap that + + align:start position:0% +things that are stored on the heap that + + + align:start position:0% +things that are stored on the heap that +have been allocated via some memory + + align:start position:0% +have been allocated via some memory + + + align:start position:0% +have been allocated via some memory +allocation call. Um and so those things + + align:start position:0% +allocation call. Um and so those things + + + align:start position:0% +allocation call. Um and so those things +are a part of the program as well + + align:start position:0% +are a part of the program as well + + + align:start position:0% +are a part of the program as well +although I don't want to explicitly list + + align:start position:0% +although I don't want to explicitly list + + + align:start position:0% +although I don't want to explicitly list +them as being a part of a of a of a + + align:start position:0% +them as being a part of a of a of a + + + align:start position:0% +them as being a part of a of a of a +single thread because if two programs as + + align:start position:0% +single thread because if two programs as + + + align:start position:0% +single thread because if two programs as +we'll see two programs can share the + + align:start position:0% +we'll see two programs can share the + + + align:start position:0% +we'll see two programs can share the +same address space and if two programs + + align:start position:0% +same address space and if two programs + + + align:start position:0% +same address space and if two programs +are sharing the same address space then + + align:start position:0% +are sharing the same address space then + + + align:start position:0% +are sharing the same address space then +they're going to share those global + + align:start position:0% +they're going to share those global + + + align:start position:0% +they're going to share those global +variables the stuff that's stored on the + + align:start position:0% +variables the stuff that's stored on the + + + align:start position:0% +variables the stuff that's stored on the +heap of the program. So, um, think of a + + align:start position:0% +heap of the program. So, um, think of a + + + align:start position:0% +heap of the program. So, um, think of a +thread as the as these things, um, plus + + align:start position:0% +thread as the as these things, um, plus + + + align:start position:0% +thread as the as these things, um, plus +there's some additional, we'll call it a + + align:start position:0% +there's some additional, we'll call it a + + + align:start position:0% +there's some additional, we'll call it a +heap, uh, set of memory that maybe is + + align:start position:0% +heap, uh, set of memory that maybe is + + + align:start position:0% +heap, uh, set of memory that maybe is +shared between, uh, several different + + align:start position:0% +shared between, uh, several different + + + align:start position:0% +shared between, uh, several different +threads that are all running within the + + align:start position:0% +threads that are all running within the + + + align:start position:0% +threads that are all running within the +same address space. And I'll explain + + align:start position:0% +same address space. And I'll explain + + + align:start position:0% +same address space. And I'll explain +more about that as we go. Um, okay. So, + + align:start position:0% +more about that as we go. Um, okay. So, + + + align:start position:0% +more about that as we go. Um, okay. So, +as I said, now what we want is to create + + align:start position:0% +as I said, now what we want is to create + + + align:start position:0% +as I said, now what we want is to create +this illusion that each one of these + + align:start position:0% +this illusion that each one of these + + + align:start position:0% +this illusion that each one of these +threads has its own virtual processor + + align:start position:0% +threads has its own virtual processor + + + align:start position:0% +threads has its own virtual processor +upon which it's running. So, how are we + + align:start position:0% +upon which it's running. So, how are we + + + align:start position:0% +upon which it's running. So, how are we +going to accomplish that? + + align:start position:0% +going to accomplish that? + + + align:start position:0% +going to accomplish that? +So if you think about this for a second, + + align:start position:0% +So if you think about this for a second, + + + align:start position:0% +So if you think about this for a second, +um the way to accomplish this is simply + + align:start position:0% +um the way to accomplish this is simply + + + align:start position:0% +um the way to accomplish this is simply +to allow each one of these uh each + + align:start position:0% +to allow each one of these uh each + + + align:start position:0% +to allow each one of these uh each +thread to update these uh these various + + align:start position:0% +thread to update these uh these various + + + align:start position:0% +thread to update these uh these various +registers, push things onto the stack, + + align:start position:0% +registers, push things onto the stack, + + + align:start position:0% +registers, push things onto the stack, +and then to have some uh function which + + align:start position:0% +and then to have some uh function which + + + align:start position:0% +and then to have some uh function which +we can call which will save all of this + + align:start position:0% +we can call which will save all of this + + + align:start position:0% +we can call which will save all of this +current state off um for the current + + align:start position:0% +current state off um for the current + + + align:start position:0% +current state off um for the current +thread that's executing and then load + + align:start position:0% +thread that's executing and then load + + + align:start position:0% +thread that's executing and then load +the state in for another thread that + + align:start position:0% +the state in for another thread that + + + align:start position:0% +the state in for another thread that +might be executing and stop the current + + align:start position:0% +might be executing and stop the current + + + align:start position:0% +might be executing and stop the current +thread from executing and start the new + + align:start position:0% +thread from executing and start the new + + + align:start position:0% +thread from executing and start the new +one executing. So the idea is if you + + align:start position:0% +one executing. So the idea is if you + + + align:start position:0% +one executing. So the idea is if you +were to think about uh if you were to + + align:start position:0% +were to think about uh if you were to + + + align:start position:0% +were to think about uh if you were to +look at a a timeline of what the pro + + align:start position:0% +look at a a timeline of what the pro + + + align:start position:0% +look at a a timeline of what the pro +that the processor was doing um and if + + align:start position:0% +that the processor was doing um and if + + + align:start position:0% +that the processor was doing um and if +the processor is running two threads + + align:start position:0% +the processor is running two threads + + + align:start position:0% +the processor is running two threads +thread one and thread two you would see + + align:start position:0% +thread one and thread two you would see + + + align:start position:0% +thread one and thread two you would see +that uh during some period of time + + align:start position:0% +that uh during some period of time + + + align:start position:0% +that uh during some period of time +thread one would be running then the + + align:start position:0% +thread one would be running then the + + + align:start position:0% +thread one would be running then the +computer would switch over and thread + + align:start position:0% +computer would switch over and thread + + + align:start position:0% +computer would switch over and thread +two would start running and then again + + align:start position:0% +two would start running and then again + + + align:start position:0% +two would start running and then again +the computer would switch and thread one + + align:start position:0% +the computer would switch and thread one + + + align:start position:0% +the computer would switch and thread one +would start running. So we're going to + + align:start position:0% +would start running. So we're going to + + + align:start position:0% +would start running. So we're going to +multiplex the processor resource in this + + align:start position:0% +multiplex the processor resource in this + + + align:start position:0% +multiplex the processor resource in this +way. Okay, so we have one processor that + + align:start position:0% +way. Okay, so we have one processor that + + + align:start position:0% +way. Okay, so we have one processor that +can execute can be executing + + align:start position:0% +can execute can be executing + + + align:start position:0% +can execute can be executing +instructions. And at each point in time, + + align:start position:0% +instructions. And at each point in time, + + + align:start position:0% +instructions. And at each point in time, +that processor is going to be executing + + align:start position:0% +that processor is going to be executing + + + align:start position:0% +that processor is going to be executing +instructions from one of these two + + align:start position:0% +instructions from one of these two + + + align:start position:0% +instructions from one of these two +threads. And when we switch in these + + align:start position:0% +threads. And when we switch in these + + + align:start position:0% +threads. And when we switch in these +points in between threads, we're going + + align:start position:0% +points in between threads, we're going + + + align:start position:0% +points in between threads, we're going +to have to save off this state for the + + align:start position:0% +to have to save off this state for the + + + align:start position:0% +to have to save off this state for the +thread that was running and restore the + + align:start position:0% +thread that was running and restore the + + + align:start position:0% +thread that was running and restore the +state for the thread that is currently + + align:start position:0% +state for the thread that is currently + + + align:start position:0% +state for the thread that is currently +running. Okay, so that's a very high + + align:start position:0% +running. Okay, so that's a very high + + + align:start position:0% +running. Okay, so that's a very high +level picture of what we're going to be + + align:start position:0% +level picture of what we're going to be + + + align:start position:0% +level picture of what we're going to be +doing with threads. Um, + + align:start position:0% +doing with threads. Um, + + + align:start position:0% +doing with threads. Um, +and there's going to be a number of + + align:start position:0% +and there's going to be a number of + + + align:start position:0% +and there's going to be a number of +different ways, and that's what we're + + align:start position:0% +different ways, and that's what we're + + + align:start position:0% +different ways, and that's what we're +going to look at through this lecture as + + align:start position:0% +going to look at through this lecture as + + + align:start position:0% +going to look at through this lecture as +to how we can actually accomplish this + + align:start position:0% +to how we can actually accomplish this + + + align:start position:0% +to how we can actually accomplish this +switching, how we decide when to switch, + + align:start position:0% +switching, how we decide when to switch, + + + align:start position:0% +switching, how we decide when to switch, +uh, and what actually happens when this, + + align:start position:0% +uh, and what actually happens when this, + + + align:start position:0% +uh, and what actually happens when this, +uh, this switch takes place. + + align:start position:0% +uh, this switch takes place. + + + align:start position:0% +uh, this switch takes place. +Okay. So, um, we're going to look at + + align:start position:0% + + + + align:start position:0% + +several different methods. So, the first + + align:start position:0% +several different methods. So, the first + + + align:start position:0% +several different methods. So, the first +thing we're going to look at is an + + align:start position:0% +thing we're going to look at is an + + + align:start position:0% +thing we're going to look at is an +approach called cooperative scheduling + + align:start position:0% +approach called cooperative scheduling + + + align:start position:0% +approach called cooperative scheduling +or cooperative switching. So in a + + align:start position:0% +or cooperative switching. So in a + + + align:start position:0% +or cooperative switching. So in a +cooperative switching what happens is + + align:start position:0% +cooperative switching what happens is + + + align:start position:0% +cooperative switching what happens is +that each thread periodically decides + + align:start position:0% +that each thread periodically decides + + + align:start position:0% +that each thread periodically decides +that it's done processing and it's + + align:start position:0% +that it's done processing and it's + + + align:start position:0% +that it's done processing and it's +willing to let some other process run. + + align:start position:0% +willing to let some other process run. + + + align:start position:0% +willing to let some other process run. +Okay? So the thread says calls a routine + + align:start position:0% +Okay? So the thread says calls a routine + + + align:start position:0% +Okay? So the thread says calls a routine +that says I'm done please schedule + + align:start position:0% +that says I'm done please schedule + + + align:start position:0% +that says I'm done please schedule +another thread. So this cooperative + + align:start position:0% +another thread. So this cooperative + + + align:start position:0% +another thread. So this cooperative +approach is is simple and it's easy to + + align:start position:0% +approach is is simple and it's easy to + + + align:start position:0% +approach is is simple and it's easy to +think about. um in the sort of grand + + align:start position:0% +think about. um in the sort of grand + + + align:start position:0% +think about. um in the sort of grand +scheme of enforcing modularity of + + align:start position:0% +scheme of enforcing modularity of + + + align:start position:0% +scheme of enforcing modularity of +creating this illusion uh that each + + align:start position:0% +creating this illusion uh that each + + + align:start position:0% +creating this illusion uh that each +program really has its own computer uh + + align:start position:0% +program really has its own computer uh + + + align:start position:0% +program really has its own computer uh +that's running and where each program + + align:start position:0% +that's running and where each program + + + align:start position:0% +that's running and where each program +gets to run sort of no matter what any + + align:start position:0% +gets to run sort of no matter what any + + + align:start position:0% +gets to run sort of no matter what any +other program does. Cooperative + + align:start position:0% +other program does. Cooperative + + + align:start position:0% +other program does. Cooperative +scheduling has a bit of a problem + + align:start position:0% +scheduling has a bit of a problem + + + align:start position:0% +scheduling has a bit of a problem +because uh a if if we're doing + + align:start position:0% +because uh a if if we're doing + + + align:start position:0% +because uh a if if we're doing +cooperative scheduling then one process + + align:start position:0% +cooperative scheduling then one process + + + align:start position:0% +cooperative scheduling then one process +can just never call this function that + + align:start position:0% +can just never call this function that + + + align:start position:0% +can just never call this function that +says I give up time to the other + + align:start position:0% +says I give up time to the other + + + align:start position:0% +says I give up time to the other +processes running on the system. uh + + align:start position:0% +processes running on the system. uh + + + align:start position:0% +processes running on the system. uh +other one module may just never give up + + align:start position:0% +other one module may just never give up + + + align:start position:0% +other one module may just never give up +the processor and then uh we're in + + align:start position:0% +the processor and then uh we're in + + + align:start position:0% +the processor and then uh we're in +trouble because no other module ever + + align:start position:0% +trouble because no other module ever + + + align:start position:0% +trouble because no other module ever +gets to run. So instead what we're going + + align:start position:0% +gets to run. So instead what we're going + + + align:start position:0% +gets to run. So instead what we're going +to talk about the alternative to this is + + align:start position:0% +to talk about the alternative to this is + + + align:start position:0% +to talk about the alternative to this is +something we call preemptive scheduling. + + align:start position:0% +something we call preemptive scheduling. + + + align:start position:0% +something we call preemptive scheduling. +Um and in preemptive scheduling what + + align:start position:0% +Um and in preemptive scheduling what + + + align:start position:0% +Um and in preemptive scheduling what +happens is some part of the computer say + + align:start position:0% +happens is some part of the computer say + + + align:start position:0% +happens is some part of the computer say +the kernel periodically decides that it + + align:start position:0% +the kernel periodically decides that it + + + align:start position:0% +the kernel periodically decides that it +forces the currently running thread to + + align:start position:0% +forces the currently running thread to + + + align:start position:0% +forces the currently running thread to +give up the processor and starts a new + + align:start position:0% +give up the processor and starts a new + + + align:start position:0% +give up the processor and starts a new +thread running and we'll see how that + + align:start position:0% +thread running and we'll see how that + + + align:start position:0% +thread running and we'll see how that +works. Okay. Um, we're also we also I + + align:start position:0% +works. Okay. Um, we're also we also I + + + align:start position:0% +works. Okay. Um, we're also we also I +also want to draw a distinction between + + align:start position:0% +also want to draw a distinction between + + + align:start position:0% +also want to draw a distinction between +whether these threads are running in the + + align:start position:0% +whether these threads are running in the + + + align:start position:0% +whether these threads are running in the +same address space + + align:start position:0% +same address space + + + align:start position:0% +same address space +or in a different address space. + + align:start position:0% +or in a different address space. + + + align:start position:0% +or in a different address space. +Okay. So, uh we could for example have + + align:start position:0% +Okay. So, uh we could for example have + + + align:start position:0% +Okay. So, uh we could for example have +these two threads T1 and T2 um they + + align:start position:0% +these two threads T1 and T2 um they + + + align:start position:0% +these two threads T1 and T2 um they +might be running as a part of a single + + align:start position:0% +might be running as a part of a single + + + align:start position:0% +might be running as a part of a single +say application. So, for example, they + + align:start position:0% +say application. So, for example, they + + + align:start position:0% +say application. So, for example, they +might be um they they might be a part of + + align:start position:0% +might be um they they might be a part of + + + align:start position:0% +might be um they they might be a part of +a uh say for example a uh some computer + + align:start position:0% +a uh say for example a uh some computer + + + align:start position:0% +a uh say for example a uh some computer +game that we have running. So suppose we + + align:start position:0% +game that we have running. So suppose we + + + align:start position:0% +game that we have running. So suppose we +have a computer game like um let me just + + align:start position:0% +have a computer game like um let me just + + + align:start position:0% +have a computer game like um let me just +load up my computer here. Uh suppose we + + align:start position:0% +load up my computer here. Uh suppose we + + + align:start position:0% +load up my computer here. Uh suppose we +have a computer game like um I don't + + align:start position:0% +have a computer game like um I don't + + + align:start position:0% +have a computer game like um I don't +know pick your favorite computer game + + align:start position:0% +know pick your favorite computer game + + + align:start position:0% +know pick your favorite computer game +say uh Halo and we're running running + + align:start position:0% +say uh Halo and we're running running + + + align:start position:0% +say uh Halo and we're running running +this uh we're running this program uh + + align:start position:0% +this uh we're running this program uh + + + align:start position:0% +this uh we're running this program uh +we're running Halo and um Halo is going + + align:start position:0% +we're running Halo and um Halo is going + + + align:start position:0% +we're running Halo and um Halo is going +to consist of a um + + align:start position:0% +to consist of a um + + + align:start position:0% +to consist of a um +some set of threads that are responsible + + align:start position:0% +some set of threads that are responsible + + + align:start position:0% +some set of threads that are responsible +for running the ex running running this + + align:start position:0% +for running the ex running running this + + + align:start position:0% +for running the ex running running this +game. So we might have one main thread + + align:start position:0% +game. So we might have one main thread + + + align:start position:0% +game. So we might have one main thread +um which what it does when it runs is to + + align:start position:0% +um which what it does when it runs is to + + + align:start position:0% +um which what it does when it runs is to +simply uh update the it it simply uh + + align:start position:0% +simply uh update the it it simply uh + + + align:start position:0% +simply uh update the it it simply uh +waits for it it uh repeats in a loop + + align:start position:0% +waits for it it uh repeats in a loop + + + align:start position:0% +waits for it it uh repeats in a loop +over and over again uh wait for a little + + align:start position:0% +over and over again uh wait for a little + + + align:start position:0% +over and over again uh wait for a little +while check and see if there's any user + + align:start position:0% +while check and see if there's any user + + + align:start position:0% +while check and see if there's any user +input. Um, if there is any user input, + + align:start position:0% +input. Um, if there is any user input, + + + align:start position:0% +input. Um, if there is any user input, +update the state of the game and then + + align:start position:0% +update the state of the game and then + + + align:start position:0% +update the state of the game and then +say, for example, redart draw the + + align:start position:0% +say, for example, redart draw the + + + align:start position:0% +say, for example, redart draw the +display. And because Halo is a video + + align:start position:0% +display. And because Halo is a video + + + align:start position:0% +display. And because Halo is a video +game that somebody's staring at and + + align:start position:0% +game that somebody's staring at and + + + align:start position:0% +game that somebody's staring at and +looking at, it needs to update that + + align:start position:0% +looking at, it needs to update that + + + align:start position:0% +looking at, it needs to update that +display at some rate, say once every, + + align:start position:0% +display at some rate, say once every, + + + align:start position:0% +display at some rate, say once every, +you know, say 20 times a second in order + + align:start position:0% +you know, say 20 times a second in order + + + align:start position:0% +you know, say 20 times a second in order +to create the illusion of sort of + + align:start position:0% +to create the illusion of sort of + + + align:start position:0% +to create the illusion of sort of +natural animation in the game. So this + + align:start position:0% +natural animation in the game. So this + + + align:start position:0% +natural animation in the game. So this +weight step is going to wait say 20 20 + + align:start position:0% +weight step is going to wait say 20 20 + + + align:start position:0% +weight step is going to wait say 20 20 +uh, you know, a 20th of a second between + + align:start position:0% +uh, you know, a 20th of a second between + + + align:start position:0% +uh, you know, a 20th of a second between +every step. Okay, so this is this is + + align:start position:0% +every step. Okay, so this is this is + + + align:start position:0% +every step. Okay, so this is this is +might be one example of a thread, but um + + align:start position:0% +might be one example of a thread, but um + + + align:start position:0% +might be one example of a thread, but um +of course within Halo, there may be uh + + align:start position:0% +of course within Halo, there may be uh + + + align:start position:0% +of course within Halo, there may be uh +multiple other threads that are also + + align:start position:0% +multiple other threads that are also + + + align:start position:0% +multiple other threads that are also +running. So there may be a thread that's + + align:start position:0% +running. So there may be a thread that's + + + align:start position:0% +running. So there may be a thread that's +responsible for uh looking for input + + align:start position:0% +responsible for uh looking for input + + + align:start position:0% +responsible for uh looking for input +over the network, right? To see if + + align:start position:0% +over the network, right? To see if + + + align:start position:0% +over the network, right? To see if +there's additional data that's arrived + + align:start position:0% +there's additional data that's arrived + + + align:start position:0% +there's additional data that's arrived +from the user and from other users that + + align:start position:0% +from the user and from other users that + + + align:start position:0% +from the user and from other users that +are remote and updating the state of the + + align:start position:0% +are remote and updating the state of the + + + align:start position:0% +are remote and updating the state of the +game as other uh information comes in. + + align:start position:0% +game as other uh information comes in. + + + align:start position:0% +game as other uh information comes in. +And there may be a third thread that say + + align:start position:0% +And there may be a third thread that say + + + align:start position:0% +And there may be a third thread that say +for example is responsible for uh doing + + align:start position:0% +for example is responsible for uh doing + + + align:start position:0% +for example is responsible for uh doing +some cleanup work in the game like uh + + align:start position:0% +some cleanup work in the game like uh + + + align:start position:0% +some cleanup work in the game like uh +reclaiming memory after you know some + + align:start position:0% +reclaiming memory after you know some + + + align:start position:0% +reclaiming memory after you know some +monster that's running around in the + + align:start position:0% +monster that's running around in the + + + align:start position:0% +monster that's running around in the +game has died and we no longer need its + + align:start position:0% +game has died and we no longer need its + + + align:start position:0% +game has died and we no longer need its +state. Okay. Um + + align:start position:0% +state. Okay. Um + + + align:start position:0% +state. Okay. Um +so + + align:start position:0% +so + + + align:start position:0% +so +if we look at the state of this current + + align:start position:0% +if we look at the state of this current + + + align:start position:0% +if we look at the state of this current +th so if we look at just this say main + + align:start position:0% +th so if we look at just this say main + + + align:start position:0% +th so if we look at just this say main +thread within Halo as I said here we can + + align:start position:0% +thread within Halo as I said here we can + + + align:start position:0% +thread within Halo as I said here we can +encapsulate the state of this thread by + + align:start position:0% +encapsulate the state of this thread by + + + align:start position:0% +encapsulate the state of this thread by +a set of registers say R1 through Rn as + + align:start position:0% +a set of registers say R1 through Rn as + + + align:start position:0% +a set of registers say R1 through Rn as +well as a stack pointer and a program + + align:start position:0% +well as a stack pointer and a program + + + align:start position:0% +well as a stack pointer and a program +counter. Um and then there also will be + + align:start position:0% +counter. Um and then there also will be + + + align:start position:0% +counter. Um and then there also will be +a stack that represents the currently + + align:start position:0% +a stack that represents the currently + + + align:start position:0% +a stack that represents the currently +executing program. Um so for example + + align:start position:0% +executing program. Um so for example + + + align:start position:0% +executing program. Um so for example +this stack might if we just have entered + + align:start position:0% +this stack might if we just have entered + + + align:start position:0% +this stack might if we just have entered +into this procedure uh it might just + + align:start position:0% +into this procedure uh it might just + + + align:start position:0% +into this procedure uh it might just +have a return address which is sort of + + align:start position:0% +have a return address which is sort of + + + align:start position:0% +have a return address which is sort of +uh how we get how the address that we + + align:start position:0% +uh how we get how the address that we + + + align:start position:0% +uh how we get how the address that we +should jump to when we're done executing + + align:start position:0% +should jump to when we're done executing + + + align:start position:0% +should jump to when we're done executing +uh this this this Halo program here. Um + + align:start position:0% +uh this this this Halo program here. Um + + + align:start position:0% +uh this this this Halo program here. Um +and then finally we have a program + + align:start position:0% +and then finally we have a program + + + align:start position:0% +and then finally we have a program +counter that points to the sort of + + align:start position:0% +counter that points to the sort of + + + align:start position:0% +counter that points to the sort of +current place where we're executing + + align:start position:0% +current place where we're executing + + + align:start position:0% +current place where we're executing +this. So we might have started off we're + + align:start position:0% +this. So we might have started off we're + + + align:start position:0% +this. So we might have started off we're +just executing the first instruction + + align:start position:0% +just executing the first instruction + + + align:start position:0% +just executing the first instruction +here the init. + + align:start position:0% +here the init. + + + align:start position:0% +here the init. +Um okay so let's see how we can make + + align:start position:0% +Um okay so let's see how we can make + + + align:start position:0% +Um okay so let's see how we can make +this. So what so the the po so what + + align:start position:0% +this. So what so the the po so what + + + align:start position:0% +this. So what so the the po so what +we're going to look at now is this case + + align:start position:0% +we're going to look at now is this case + + + align:start position:0% +we're going to look at now is this case +where we have a bunch of threads say for + + align:start position:0% +where we have a bunch of threads say for + + + align:start position:0% +where we have a bunch of threads say for +example uh in Halo all running within + + align:start position:0% +example uh in Halo all running within + + + align:start position:0% +example uh in Halo all running within +the same address space. So they're all a + + align:start position:0% +the same address space. So they're all a + + + align:start position:0% +the same address space. So they're all a +part of the Halo program. They can all + + align:start position:0% +part of the Halo program. They can all + + + align:start position:0% +part of the Halo program. They can all +access the global variables of Halo. Um + + align:start position:0% +access the global variables of Halo. Um + + + align:start position:0% +access the global variables of Halo. Um +but they we want to have different + + align:start position:0% +but they we want to have different + + + align:start position:0% +but they we want to have different +threads to do sort of different + + align:start position:0% +threads to do sort of different + + + align:start position:0% +threads to do sort of different +operations that this program may need to + + align:start position:0% +operations that this program may need to + + + align:start position:0% +operations that this program may need to +take care of. So we want each of these + + align:start position:0% +take care of. So we want each of these + + + align:start position:0% +take care of. So we want each of these +threads to sort of have the illusion + + align:start position:0% +threads to sort of have the illusion + + + align:start position:0% +threads to sort of have the illusion +that it has its own processor. And then + + align:start position:0% +that it has its own processor. And then + + + align:start position:0% +that it has its own processor. And then +later we'll talk about a set of programs + + align:start position:0% +later we'll talk about a set of programs + + + align:start position:0% +later we'll talk about a set of programs +say that are running in different + + align:start position:0% +say that are running in different + + + align:start position:0% +say that are running in different +address spaces. and we'll talk about + + align:start position:0% +address spaces. and we'll talk about + + + align:start position:0% +address spaces. and we'll talk about +what's different about managing pro two + + align:start position:0% +what's different about managing pro two + + + align:start position:0% +what's different about managing pro two +program managing two threads each of + + align:start position:0% +program managing two threads each of + + + align:start position:0% +program managing two threads each of +which is running in a different address + + align:start position:0% +which is running in a different address + + + align:start position:0% +which is running in a different address +space. Um okay so the very simple idea + + align:start position:0% +space. Um okay so the very simple idea + + + align:start position:0% +space. Um okay so the very simple idea +that we're going to introduce uh in + + align:start position:0% +that we're going to introduce uh in + + + align:start position:0% +that we're going to introduce uh in +order to deal with in order to look at + + align:start position:0% +order to deal with in order to look at + + + align:start position:0% +order to deal with in order to look at +this situation where we have cooper + + align:start position:0% +this situation where we have cooper + + + align:start position:0% +this situation where we have cooper +we're going to start off by looking at + + align:start position:0% +we're going to start off by looking at + + + align:start position:0% +we're going to start off by looking at +cooperative scheduling in the same + + align:start position:0% +cooperative scheduling in the same + + + align:start position:0% +cooperative scheduling in the same +address space um we're going to + + align:start position:0% +address space um we're going to + + + align:start position:0% +address space um we're going to +introduce the notion of a uh program of + + align:start position:0% +introduce the notion of a uh program of + + + align:start position:0% +introduce the notion of a uh program of +a of a routine called yield. Okay. + + align:start position:0% + + + + align:start position:0% + +So yield is going to be the thing that + + align:start position:0% +So yield is going to be the thing that + + + align:start position:0% +So yield is going to be the thing that +the currently executing thread calls + + align:start position:0% +the currently executing thread calls + + + align:start position:0% +the currently executing thread calls +when it's ready to give up the the + + align:start position:0% +when it's ready to give up the the + + + align:start position:0% +when it's ready to give up the the +processor and let another thread run. So + + align:start position:0% +processor and let another thread run. So + + + align:start position:0% +processor and let another thread run. So +the thread is going to run for a while + + align:start position:0% +the thread is going to run for a while + + + align:start position:0% +the thread is going to run for a while +and then it's going to call yield and + + align:start position:0% +and then it's going to call yield and + + + align:start position:0% +and then it's going to call yield and +that's going to allow other threads to + + align:start position:0% +that's going to allow other threads to + + + align:start position:0% +that's going to allow other threads to +uh sort of do their execution. And this + + align:start position:0% +uh sort of do their execution. And this + + + align:start position:0% +uh sort of do their execution. And this +is cooperative because if a program + + align:start position:0% +is cooperative because if a program + + + align:start position:0% +is cooperative because if a program +doesn't call doesn't call yield then no + + align:start position:0% +doesn't call doesn't call yield then no + + + align:start position:0% +doesn't call doesn't call yield then no +other program will ever be allowed to + + align:start position:0% +other program will ever be allowed to + + + align:start position:0% +other program will ever be allowed to +run on the system. Um, + + align:start position:0% +run on the system. Um, + + + align:start position:0% +run on the system. Um, +so the basic idea is that when a program + + align:start position:0% +so the basic idea is that when a program + + + align:start position:0% +so the basic idea is that when a program +calls yield, what it's going to do is + + align:start position:0% +calls yield, what it's going to do is + + + align:start position:0% +calls yield, what it's going to do is +exactly what I described just a minute + + align:start position:0% +exactly what I described just a minute + + + align:start position:0% +exactly what I described just a minute +ago. So yield is going to + + align:start position:0% +ago. So yield is going to + + + align:start position:0% +ago. So yield is going to +save the state of the current thread. + + align:start position:0% +save the state of the current thread. + + + align:start position:0% +save the state of the current thread. +Um, and then it's going to + + align:start position:0% + + + + align:start position:0% + +schedule the next thread. So pick the + + align:start position:0% +schedule the next thread. So pick the + + + align:start position:0% +schedule the next thread. So pick the +next thread to run from all the + + align:start position:0% +next thread to run from all the + + + align:start position:0% +next thread to run from all the +available threads that are on the system + + align:start position:0% +available threads that are on the system + + + align:start position:0% +available threads that are on the system +and then it's going to dispatch the next + + align:start position:0% +and then it's going to dispatch the next + + + align:start position:0% +and then it's going to dispatch the next +thread. So it's going to in particular + + align:start position:0% +thread. So it's going to in particular + + + align:start position:0% +thread. So it's going to in particular +set up the state for the next thread so + + align:start position:0% +set up the state for the next thread so + + + align:start position:0% +set up the state for the next thread so +that it's ready to run and it's going to + + align:start position:0% +that it's ready to run and it's going to + + + align:start position:0% +that it's ready to run and it's going to +jump into the return address for that + + align:start position:0% +jump into the return address for that + + + align:start position:0% +jump into the return address for that +thread. + + align:start position:0% + + + + align:start position:0% + +Okay. So um we're going to look through + + align:start position:0% +Okay. So um we're going to look through + + + align:start position:0% +Okay. So um we're going to look through +I want to take you guys through a very + + align:start position:0% +I want to take you guys through a very + + + align:start position:0% +I want to take you guys through a very +simple example um of a sort of of a + + align:start position:0% +simple example um of a sort of of a + + + align:start position:0% +simple example um of a sort of of a +program that has multiple threads in it + + align:start position:0% +program that has multiple threads in it + + + align:start position:0% +program that has multiple threads in it +and we're going to have a simple simple + + align:start position:0% +and we're going to have a simple simple + + + align:start position:0% +and we're going to have a simple simple +threaduler. So the threadul is the thing + + align:start position:0% +threaduler. So the threadul is the thing + + + align:start position:0% +threaduler. So the threadul is the thing +that decides which thread to run next. + + align:start position:0% +that decides which thread to run next. + + + align:start position:0% +that decides which thread to run next. +This thread scheduler is going to keep + + align:start position:0% +This thread scheduler is going to keep + + + align:start position:0% +This thread scheduler is going to keep +um an array + + align:start position:0% +um an array + + + align:start position:0% +um an array +of size fixed size call it numbum + + align:start position:0% +of size fixed size call it numbum + + + align:start position:0% +of size fixed size call it numbum +threads + + align:start position:0% + + + + align:start position:0% + +that are all the threads that are + + align:start position:0% +that are all the threads that are + + + align:start position:0% +that are all the threads that are +currently running on the system. Um it's + + align:start position:0% +currently running on the system. Um it's + + + align:start position:0% +currently running on the system. Um it's +going to have an integer that is the + + align:start position:0% +going to have an integer that is the + + + align:start position:0% +going to have an integer that is the +next thread to run that that's going to + + align:start position:0% +next thread to run that that's going to + + + align:start position:0% +next thread to run that that's going to +tell us what the next thread to run is. + + align:start position:0% +tell us what the next thread to run is. + + + align:start position:0% +tell us what the next thread to run is. +And then for every one of our threads + + align:start position:0% +And then for every one of our threads + + + align:start position:0% +And then for every one of our threads +we're going to have a variable that we + + align:start position:0% +we're going to have a variable that we + + + align:start position:0% +we're going to have a variable that we +call me which is the ID of the currently + + align:start position:0% +call me which is the ID of the currently + + + align:start position:0% +call me which is the ID of the currently +executing thread. Okay, so this is local + + align:start position:0% +executing thread. Okay, so this is local + + + align:start position:0% +executing thread. Okay, so this is local +to the thread. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Okay, so let's look at an example of how + + align:start position:0% +Okay, so let's look at an example of how + + + align:start position:0% +Okay, so let's look at an example of how +this might work with our uh with with + + align:start position:0% +this might work with our uh with with + + + align:start position:0% +this might work with our uh with with +this Halo thread that we're talking + + align:start position:0% +this Halo thread that we're talking + + + align:start position:0% +this Halo thread that we're talking +about here. + + align:start position:0% +about here. + + + align:start position:0% +about here. +Okay, so suppose we have a Halo thread + + align:start position:0% +Okay, so suppose we have a Halo thread + + + align:start position:0% +Okay, so suppose we have a Halo thread +and we'll call this the main thread of + + align:start position:0% +and we'll call this the main thread of + + + align:start position:0% +and we'll call this the main thread of +execution. And as I said, uh we want to + + align:start position:0% +execution. And as I said, uh we want to + + + align:start position:0% +execution. And as I said, uh we want to +have a couple of other threads that are + + align:start position:0% +have a couple of other threads that are + + + align:start position:0% +have a couple of other threads that are +also running on the system at the same + + align:start position:0% +also running on the system at the same + + + align:start position:0% +also running on the system at the same +time. So we might have a network thread + + align:start position:0% +time. So we might have a network thread + + + align:start position:0% +time. So we might have a network thread +and a cleanup thread. Um now suppose so + + align:start position:0% +and a cleanup thread. Um now suppose so + + + align:start position:0% +and a cleanup thread. Um now suppose so +in this case what we're going to say is + + align:start position:0% +in this case what we're going to say is + + + align:start position:0% +in this case what we're going to say is +that the yield procedure um is is going + + align:start position:0% +that the yield procedure um is is going + + + align:start position:0% +that the yield procedure um is is going +to is going to do these three steps and + + align:start position:0% +to is going to do these three steps and + + + align:start position:0% +to is going to do these three steps and +I made these steps a little bit more + + align:start position:0% +I made these steps a little bit more + + + align:start position:0% +I made these steps a little bit more +concrete so that we can actually think + + align:start position:0% +concrete so that we can actually think + + + align:start position:0% +concrete so that we can actually think +about what might be happening on this on + + align:start position:0% +about what might be happening on this on + + + align:start position:0% +about what might be happening on this on +the stack as these things are executing. + + align:start position:0% +the stack as these things are executing. + + + align:start position:0% +the stack as these things are executing. +So uh the yield procedure is going to um + + align:start position:0% +So uh the yield procedure is going to um + + + align:start position:0% +So uh the yield procedure is going to um +when it runs the first thing it's going + + align:start position:0% +when it runs the first thing it's going + + + align:start position:0% +when it runs the first thing it's going +to do is save the state. So to save the + + align:start position:0% +to do is save the state. So to save the + + + align:start position:0% +to do is save the state. So to save the +state, it simply uh stores in this table + + align:start position:0% +state, it simply uh stores in this table + + + align:start position:0% +state, it simply uh stores in this table +the stack pointer of the currently + + align:start position:0% +the stack pointer of the currently + + + align:start position:0% +the stack pointer of the currently +executing program uh the stack pointer + + align:start position:0% +executing program uh the stack pointer + + + align:start position:0% +executing program uh the stack pointer +of the currently executing thread. Uh + + align:start position:0% +of the currently executing thread. Uh + + + align:start position:0% +of the currently executing thread. Uh +and then what it's going to do is it's + + align:start position:0% +and then what it's going to do is it's + + + align:start position:0% +and then what it's going to do is it's +going to pick the next thread to run. So + + align:start position:0% +going to pick the next thread to run. So + + + align:start position:0% +going to pick the next thread to run. So +in this case picking the next thread to + + align:start position:0% +in this case picking the next thread to + + + align:start position:0% +in this case picking the next thread to +run this threaduler is doing something + + align:start position:0% +run this threaduler is doing something + + + align:start position:0% +run this threaduler is doing something +extremely simple. It's just cycling + + align:start position:0% +extremely simple. It's just cycling + + + align:start position:0% +extremely simple. It's just cycling +through all the available threads one + + align:start position:0% +through all the available threads one + + + align:start position:0% +through all the available threads one +after the scheduling them. Right? So it + + align:start position:0% +after the scheduling them. Right? So it + + + align:start position:0% +after the scheduling them. Right? So it +says next gets next plus one and then + + align:start position:0% +says next gets next plus one and then + + + align:start position:0% +says next gets next plus one and then +modulo the total number of threads that + + align:start position:0% +modulo the total number of threads that + + + align:start position:0% +modulo the total number of threads that +are in the system. Um so this is going + + align:start position:0% +are in the system. Um so this is going + + + align:start position:0% +are in the system. Um so this is going +to when we reach so suppose you know num + + align:start position:0% +to when we reach so suppose you know num + + + align:start position:0% +to when we reach so suppose you know num +threads is equal to uh five as soon as + + align:start position:0% +threads is equal to uh five as soon as + + + align:start position:0% +threads is equal to uh five as soon as +next plus one is equal to five then five + + align:start position:0% +next plus one is equal to five then five + + + align:start position:0% +next plus one is equal to five then five +modulo 5 is zero and we're going to wrap + + align:start position:0% +modulo 5 is zero and we're going to wrap + + + align:start position:0% +modulo 5 is zero and we're going to wrap +back around so we sort of start execute + + align:start position:0% +back around so we sort of start execute + + + align:start position:0% +back around so we sort of start execute +once we've executed the fourth thread + + align:start position:0% +once we've executed the fourth thread + + + align:start position:0% +once we've executed the fourth thread +we're going to wrap around and start + + align:start position:0% +we're going to wrap around and start + + + align:start position:0% +we're going to wrap around and start +executing thread number zero and then + + align:start position:0% +executing thread number zero and then + + + align:start position:0% +executing thread number zero and then +finally what it's going to do is it's + + align:start position:0% +finally what it's going to do is it's + + + align:start position:0% +finally what it's going to do is it's +going to resto restore the stack pointer + + align:start position:0% +going to resto restore the stack pointer + + + align:start position:0% +going to resto restore the stack pointer +uh excuse me this this table should be + + align:start position:0% +uh excuse me this this table should be + + + align:start position:0% +uh excuse me this this table should be +uh here I'll just change this for you + + align:start position:0% +uh here I'll just change this for you + + + align:start position:0% +uh here I'll just change this for you +right now um this should be + + align:start position:0% +right now um this should be + + + align:start position:0% +right now um this should be +table sub next uh + + align:start position:0% +table sub next uh + + + align:start position:0% +table sub next uh +I didn't want to do that. + + align:start position:0% + + + + align:start position:0% + +So we have this table with table. So we + + align:start position:0% +So we have this table with table. So we + + + align:start position:0% +So we have this table with table. So we +restore the stack pointer for the next + + align:start position:0% +restore the stack pointer for the next + + + align:start position:0% +restore the stack pointer for the next +thread that we want to run uh from the + + align:start position:0% +thread that we want to run uh from the + + + align:start position:0% +thread that we want to run uh from the +uh from the table of stack pointers that + + align:start position:0% +uh from the table of stack pointers that + + + align:start position:0% +uh from the table of stack pointers that +are available. And then what's going to + + align:start position:0% +are available. And then what's going to + + + align:start position:0% +are available. And then what's going to +happen is that when we exit out of this + + align:start position:0% +happen is that when we exit out of this + + + align:start position:0% +happen is that when we exit out of this +yield routine, we're going to load the + + align:start position:0% +yield routine, we're going to load the + + + align:start position:0% +yield routine, we're going to load the +return address from the stack pointer uh + + align:start position:0% +return address from the stack pointer uh + + + align:start position:0% +return address from the stack pointer uh +that we just have set up. So you'll see + + align:start position:0% +that we just have set up. So you'll see + + + align:start position:0% +that we just have set up. So you'll see +how that works again in a second. But + + align:start position:0% +how that works again in a second. But + + + align:start position:0% +how that works again in a second. But +the basic process then is just going to + + align:start position:0% +the basic process then is just going to + + + align:start position:0% +the basic process then is just going to +be as follows. So this only works on a + + align:start position:0% +be as follows. So this only works on a + + + align:start position:0% +be as follows. So this only works on a +single processor. And uh I'm not going + + align:start position:0% +single processor. And uh I'm not going + + + align:start position:0% +single processor. And uh I'm not going +to have time to go into too much detail + + align:start position:0% +to have time to go into too much detail + + + align:start position:0% +to have time to go into too much detail +about what happens in a multipprocessor, + + align:start position:0% +about what happens in a multipprocessor, + + + align:start position:0% +about what happens in a multipprocessor, +but the book talks carefully about why + + align:start position:0% +but the book talks carefully about why + + + align:start position:0% +but the book talks carefully about why +this doesn't work on a single processor + + align:start position:0% +this doesn't work on a single processor + + + align:start position:0% +this doesn't work on a single processor +machine. Um okay. So + + align:start position:0% +machine. Um okay. So + + + align:start position:0% +machine. Um okay. So +the basic process then is going to be as + + align:start position:0% +the basic process then is going to be as + + + align:start position:0% +the basic process then is going to be as +follows. So uh we've got our yield + + align:start position:0% +follows. So uh we've got our yield + + + align:start position:0% +follows. So uh we've got our yield +procedure. We have our three threads. + + align:start position:0% +procedure. We have our three threads. + + + align:start position:0% +procedure. We have our three threads. +Say we've numbered them one, two, and + + align:start position:0% +Say we've numbered them one, two, and + + + align:start position:0% +Say we've numbered them one, two, and +three as shown up here. Um so num + + align:start position:0% +three as shown up here. Um so num + + + align:start position:0% +three as shown up here. Um so num +threads is equal to three and say we + + align:start position:0% +threads is equal to three and say we + + + align:start position:0% +threads is equal to three and say we +start off uh with next equal to one. Um + + align:start position:0% +start off uh with next equal to one. Um + + + align:start position:0% +start off uh with next equal to one. Um +so what's going to happen is that the + + align:start position:0% +so what's going to happen is that the + + + align:start position:0% +so what's going to happen is that the +first thread is going to yield is going + + align:start position:0% +first thread is going to yield is going + + + align:start position:0% +first thread is going to yield is going +to at some point is going to call the + + align:start position:0% +to at some point is going to call the + + + align:start position:0% +to at some point is going to call the +yield routine and that what that's going + + align:start position:0% +yield routine and that what that's going + + + align:start position:0% +yield routine and that what that's going +to do is it's going to cause this yield + + align:start position:0% +to do is it's going to cause this yield + + + align:start position:0% +to do is it's going to cause this yield +to execute. We're going to increment + + align:start position:0% +to execute. We're going to increment + + + align:start position:0% +to execute. We're going to increment +next um and we're going to schedule the + + align:start position:0% +next um and we're going to schedule the + + + align:start position:0% +next um and we're going to schedule the +network thread here. Okay. And then the + + align:start position:0% +network thread here. Okay. And then the + + + align:start position:0% +network thread here. Okay. And then the +next network thread is going to run for + + align:start position:0% +next network thread is going to run for + + + align:start position:0% +next network thread is going to run for +a little while and at some point it's + + align:start position:0% +a little while and at some point it's + + + align:start position:0% +a little while and at some point it's +going to call yield and that's going to + + align:start position:0% +going to call yield and that's going to + + + align:start position:0% +going to call yield and that's going to +sort of cause the next thread to be + + align:start position:0% +sort of cause the next thread to be + + + align:start position:0% +sort of cause the next thread to be +scheduled. We're going to call cleanup. + + align:start position:0% +scheduled. We're going to call cleanup. + + + align:start position:0% +scheduled. We're going to call cleanup. +And then finally, we're going to call + + align:start position:0% +And then finally, we're going to call + + + align:start position:0% +And then finally, we're going to call +yield. Uh, and the third thread is going + + align:start position:0% +yield. Uh, and the third thread is going + + + align:start position:0% +yield. Uh, and the third thread is going +to call yield and call cause the first + + align:start position:0% +to call yield and call cause the first + + + align:start position:0% +to call yield and call cause the first +thread to run again. And this process is + + align:start position:0% +thread to run again. And this process is + + + align:start position:0% +thread to run again. And this process is +just going to repeat over and over and + + align:start position:0% +just going to repeat over and over and + + + align:start position:0% +just going to repeat over and over and +over again. Okay. So, um, + + align:start position:0% + + + + align:start position:0% + +okay. So what I want to do now is to + + align:start position:0% +okay. So what I want to do now is to + + + align:start position:0% +okay. So what I want to do now is to +look at actually more carefully at + + align:start position:0% +look at actually more carefully at + + + align:start position:0% +look at actually more carefully at +what's happening with the uh with the + + align:start position:0% +what's happening with the uh with the + + + align:start position:0% +what's happening with the uh with the +stack on these on how this how this + + align:start position:0% +stack on these on how this how this + + + align:start position:0% +stack on these on how this how this +scheduling process is actually working + + align:start position:0% +scheduling process is actually working + + + align:start position:0% +scheduling process is actually working +so we can understand a little bit better + + align:start position:0% +so we can understand a little bit better + + + align:start position:0% +so we can understand a little bit better +what's happening to the stack pointer + + align:start position:0% +what's happening to the stack pointer + + + align:start position:0% +what's happening to the stack pointer +and how these various yields are + + align:start position:0% +and how these various yields are + + + align:start position:0% +and how these various yields are +actually executed. So um + + align:start position:0% +actually executed. So um + + + align:start position:0% +actually executed. So um +let's look at the uh + + align:start position:0% +let's look at the uh + + + align:start position:0% +let's look at the uh +so this is going to be a example of the + + align:start position:0% +so this is going to be a example of the + + + align:start position:0% +so this is going to be a example of the +stack on these say two of these threads. + + align:start position:0% +stack on these say two of these threads. + + + align:start position:0% +stack on these say two of these threads. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So suppose we have um thread number one + + align:start position:0% + + + + align:start position:0% + +call this thread one and this is our + + align:start position:0% +call this thread one and this is our + + + align:start position:0% +call this thread one and this is our +halo thread. Okay. Um and this is the + + align:start position:0% +halo thread. Okay. Um and this is the + + + align:start position:0% +halo thread. Okay. Um and this is the +stack + + align:start position:0% +stack + + + align:start position:0% +stack +for halo. Um we also have thread number + + align:start position:0% +for halo. Um we also have thread number + + + align:start position:0% +for halo. Um we also have thread number +two + + align:start position:0% + + + + align:start position:0% + +which is uh our network thread. Okay. + + align:start position:0% +which is uh our network thread. Okay. + + + align:start position:0% +which is uh our network thread. Okay. +And this is also some stack associated + + align:start position:0% +And this is also some stack associated + + + align:start position:0% +And this is also some stack associated +with this thing. So these are we're just + + align:start position:0% +with this thing. So these are we're just + + + align:start position:0% +with this thing. So these are we're just +looking at the current state of the + + align:start position:0% +looking at the current state of the + + + align:start position:0% +looking at the current state of the +stack on these two things uh these two + + align:start position:0% +stack on these two things uh these two + + + align:start position:0% +stack on these two things uh these two +threads. Um and if you remember + + align:start position:0% +threads. Um and if you remember + + + align:start position:0% +threads. Um and if you remember +typically we represent stacks as growing + + align:start position:0% +typically we represent stacks as growing + + + align:start position:0% +typically we represent stacks as growing +down in memory. So these are the + + align:start position:0% +down in memory. So these are the + + + align:start position:0% +down in memory. So these are the +different addresses of the uh the the + + align:start position:0% +different addresses of the uh the the + + + align:start position:0% +different addresses of the uh the the +different entries in this stack. Um that + + align:start position:0% +different entries in this stack. Um that + + + align:start position:0% +different entries in this stack. Um that +represent the current execution what + + align:start position:0% +represent the current execution what + + + align:start position:0% +represent the current execution what +what's going on currently in the + + align:start position:0% +what's going on currently in the + + + align:start position:0% +what's going on currently in the +processor. Um so we'll say that thread + + align:start position:0% +processor. Um so we'll say that thread + + + align:start position:0% +processor. Um so we'll say that thread +one perhaps is it stack starts at + + align:start position:0% +one perhaps is it stack starts at + + + align:start position:0% +one perhaps is it stack starts at +address 108. Um and maybe thread 2's + + align:start position:0% +address 108. Um and maybe thread 2's + + + align:start position:0% +address 108. Um and maybe thread 2's +starts at address 208. + + align:start position:0% + + + + align:start position:0% + +Okay. So when we uh suppose we start up + + align:start position:0% +Okay. So when we uh suppose we start up + + + align:start position:0% +Okay. So when we uh suppose we start up +this system and when we start it up the + + align:start position:0% +this system and when we start it up the + + + align:start position:0% +this system and when we start it up the +stack pointer is currently pointing here + + align:start position:0% +stack pointer is currently pointing here + + + align:start position:0% +stack pointer is currently pointing here +at we look at the system and this the + + align:start position:0% +at we look at the system and this the + + + align:start position:0% +at we look at the system and this the +the uh when so we take a snapshot of the + + align:start position:0% +the uh when so we take a snapshot of the + + + align:start position:0% +the uh when so we take a snapshot of the +system at a given point in time. Suppose + + align:start position:0% +system at a given point in time. Suppose + + + align:start position:0% +system at a given point in time. Suppose +the stack pointer is currently at + + align:start position:0% +the stack pointer is currently at + + + align:start position:0% +the stack pointer is currently at +pointing at 104. The currently executing + + align:start position:0% +pointing at 104. The currently executing + + + align:start position:0% +pointing at 104. The currently executing +thread is this one. The the is thread + + align:start position:0% +thread is this one. The the is thread + + + align:start position:0% +thread is this one. The the is thread +one. Um + + align:start position:0% +one. Um + + + align:start position:0% +one. Um +and we have our remember our threads t + + align:start position:0% +and we have our remember our threads t + + + align:start position:0% +and we have our remember our threads t +our our thread table that captures the + + align:start position:0% +our our thread table that captures the + + + align:start position:0% +our our thread table that captures the +current + + align:start position:0% +current + + + align:start position:0% +current +thread number + + align:start position:0% +thread number + + + align:start position:0% +thread number +uh and the saved stack pointer for each + + align:start position:0% +uh and the saved stack pointer for each + + + align:start position:0% +uh and the saved stack pointer for each +one of these threads. + + align:start position:0% +one of these threads. + + + align:start position:0% +one of these threads. +So we've got thread number one, thread + + align:start position:0% +So we've got thread number one, thread + + + align:start position:0% +So we've got thread number one, thread +number two. Okay. So let's suppose we + + align:start position:0% +number two. Okay. So let's suppose we + + + align:start position:0% +number two. Okay. So let's suppose we +start looking at this system at this + + align:start position:0% +start looking at this system at this + + + align:start position:0% +start looking at this system at this +point in time where the stack pointer is + + align:start position:0% +point in time where the stack pointer is + + + align:start position:0% +point in time where the stack pointer is +pointing here. Um + + align:start position:0% +pointing here. Um + + + align:start position:0% +pointing here. Um +and if we look at the if we look at this + + align:start position:0% +and if we look at the if we look at this + + + align:start position:0% +and if we look at the if we look at this +program um suppose so so if we start off + + align:start position:0% +program um suppose so so if we start off + + + align:start position:0% +program um suppose so so if we start off +with the program that we initially had + + align:start position:0% +with the program that we initially had + + + align:start position:0% +with the program that we initially had +in order to understand what happens to + + align:start position:0% +in order to understand what happens to + + + align:start position:0% +in order to understand what happens to +the stack we need to actually look at uh + + align:start position:0% +the stack we need to actually look at uh + + + align:start position:0% +the stack we need to actually look at uh +when the stack gets manipulated. So if + + align:start position:0% +when the stack gets manipulated. So if + + + align:start position:0% +when the stack gets manipulated. So if +we're just looking at C code typically + + align:start position:0% +we're just looking at C code typically + + + align:start position:0% +we're just looking at C code typically +the CC code isn't going to have we're + + align:start position:0% +the CC code isn't going to have we're + + + align:start position:0% +the CC code isn't going to have we're +not going to see the the changes to the + + align:start position:0% +not going to see the the changes to the + + + align:start position:0% +not going to see the the changes to the +stack uh occurring within the CC code. + + align:start position:0% +stack uh occurring within the CC code. + + + align:start position:0% +stack uh occurring within the CC code. +So what I've done here is in yellow I've + + align:start position:0% +So what I've done here is in yellow I've + + + align:start position:0% +So what I've done here is in yellow I've +annotated this with the sort of + + align:start position:0% +annotated this with the sort of + + + align:start position:0% +annotated this with the sort of +operations that are going to be hap that + + align:start position:0% +operations that are going to be hap that + + + align:start position:0% +operations that are going to be hap that +the additional operations the assembly + + align:start position:0% +the additional operations the assembly + + + align:start position:0% +the additional operations the assembly +operations that are happening on the + + align:start position:0% +operations that are happening on the + + + align:start position:0% +operations that are happening on the +entry and exit to these procedures. Um + + align:start position:0% +entry and exit to these procedures. Um + + + align:start position:0% +entry and exit to these procedures. Um +so what happens just before we call the + + align:start position:0% +so what happens just before we call the + + + align:start position:0% +so what happens just before we call the +yield procedure is that uh the Halo + + align:start position:0% +yield procedure is that uh the Halo + + + align:start position:0% +yield procedure is that uh the Halo +thread will push the return address onto + + align:start position:0% +thread will push the return address onto + + + align:start position:0% +thread will push the return address onto +the stack. Okay. Um so if we if we start + + align:start position:0% +the stack. Okay. Um so if we if we start + + + align:start position:0% +the stack. Okay. Um so if we if we start +executing the yield procedure, Halo is + + align:start position:0% +executing the yield procedure, Halo is + + + align:start position:0% +executing the yield procedure, Halo is +going to push the return address onto + + align:start position:0% +going to push the return address onto + + + align:start position:0% +going to push the return address onto +the stack. Excuse me. Um and then it's + + align:start position:0% +the stack. Excuse me. Um and then it's + + + align:start position:0% +the stack. Excuse me. Um and then it's +going to jump into the yield procedure. + + align:start position:0% +going to jump into the yield procedure. + + + align:start position:0% +going to jump into the yield procedure. +So uh suppose we come onto here now if + + align:start position:0% +So uh suppose we come onto here now if + + + align:start position:0% +So uh suppose we come onto here now if +we look at what the return address is + + align:start position:0% +we look at what the return address is + + + align:start position:0% +we look at what the return address is +after we execute the yield procedure + + align:start position:0% +after we execute the yield procedure + + + align:start position:0% +after we execute the yield procedure +it's going to be instruction number + + align:start position:0% +it's going to be instruction number + + + align:start position:0% +it's going to be instruction number +five. So we're going to push that + + align:start position:0% +five. So we're going to push that + + + align:start position:0% +five. So we're going to push that +address onto the stack. Um because + + align:start position:0% +address onto the stack. Um because + + + align:start position:0% +address onto the stack. Um because +instruction number five is labeled here + + align:start position:0% +instruction number five is labeled here + + + align:start position:0% +instruction number five is labeled here +on the left side um is where we're going + + align:start position:0% +on the left side um is where we're going + + + align:start position:0% +on the left side um is where we're going +to return to after the yield. And then + + align:start position:0% +to return to after the yield. And then + + + align:start position:0% +to return to after the yield. And then +the yield is going to execute. And + + align:start position:0% +the yield is going to execute. And + + + align:start position:0% +the yield is going to execute. And +what's going to happen as the yield + + align:start position:0% +what's going to happen as the yield + + + align:start position:0% +what's going to happen as the yield +executes is it's going to uh change the + + align:start position:0% +executes is it's going to uh change the + + + align:start position:0% +executes is it's going to uh change the +stack pointer to be the stack pointer of + + align:start position:0% +stack pointer to be the stack pointer of + + + align:start position:0% +stack pointer to be the stack pointer of +the next thread. Right? So I have this + + align:start position:0% +the next thread. Right? So I have this + + + align:start position:0% +the next thread. Right? So I have this +typo here again. So be careful about + + align:start position:0% +typo here again. So be careful about + + + align:start position:0% +typo here again. So be careful about +that. + + align:start position:0% +that. + + + align:start position:0% +that. +Um, we're going to change the stack + + align:start position:0% +Um, we're going to change the stack + + + align:start position:0% +Um, we're going to change the stack +pointer to be the stack pointer of the + + align:start position:0% +pointer to be the stack pointer of the + + + align:start position:0% +pointer to be the stack pointer of the +next thread. And so what it when it + + align:start position:0% +next thread. And so what it when it + + + align:start position:0% +next thread. And so what it when it +executes this pop RA instruction that we + + align:start position:0% +executes this pop RA instruction that we + + + align:start position:0% +executes this pop RA instruction that we +see here, it's actually going to be + + align:start position:0% +see here, it's actually going to be + + + align:start position:0% +see here, it's actually going to be +popping the return address from the + + align:start position:0% +popping the return address from the + + + align:start position:0% +popping the return address from the +network thread that it scheduled next as + + align:start position:0% +network thread that it scheduled next as + + + align:start position:0% +network thread that it scheduled next as +opposed to the the return address from + + align:start position:0% +opposed to the the return address from + + + align:start position:0% +opposed to the the return address from +this Halo thread. Okay. So uh suppose + + align:start position:0% +this Halo thread. Okay. So uh suppose + + + align:start position:0% +this Halo thread. Okay. So uh suppose +that the stack pointer the saved stack + + align:start position:0% +that the stack pointer the saved stack + + + align:start position:0% +that the stack pointer the saved stack +pointer for the network thread was + + align:start position:0% +pointer for the network thread was + + + align:start position:0% +pointer for the network thread was +pointing here at 204. Um, so there would + + align:start position:0% +pointing here at 204. Um, so there would + + + align:start position:0% +pointing here at 204. Um, so there would +have been an entry 204 here when it uh + + align:start position:0% +have been an entry 204 here when it uh + + + align:start position:0% +have been an entry 204 here when it uh +and the saved the the return address + + align:start position:0% +and the saved the the return address + + + align:start position:0% +and the saved the the return address +that it's going to jump to is going to + + align:start position:0% +that it's going to jump to is going to + + + align:start position:0% +that it's going to jump to is going to +be here. So suppose the return address + + align:start position:0% +be here. So suppose the return address + + + align:start position:0% +be here. So suppose the return address +that it jumps to is 1,00. Okay. So if we + + align:start position:0% +that it jumps to is 1,00. Okay. So if we + + + align:start position:0% +that it jumps to is 1,00. Okay. So if we +look at + + align:start position:0% +look at + + + align:start position:0% +look at +the state of these two threads as + + align:start position:0% +the state of these two threads as + + + align:start position:0% +the state of these two threads as +they've been running, we saw thread one + + align:start position:0% +they've been running, we saw thread one + + + align:start position:0% +they've been running, we saw thread one +ran for a little while and then at in it + + align:start position:0% +ran for a little while and then at in it + + + align:start position:0% +ran for a little while and then at in it +called yield and the instruction + + align:start position:0% +called yield and the instruction + + + align:start position:0% +called yield and the instruction +following yield was instruction number + + align:start position:0% +following yield was instruction number + + + align:start position:0% +following yield was instruction number +five. Okay, so that was that was the + + align:start position:0% +five. Okay, so that was that was the + + + align:start position:0% +five. Okay, so that was that was the +address that we pushed on to uh the + + align:start position:0% +address that we pushed on to uh the + + + align:start position:0% +address that we pushed on to uh the +stack pointer. Now we switched over here + + align:start position:0% +stack pointer. Now we switched over here + + + align:start position:0% +stack pointer. Now we switched over here +to thread two. Um and last time we ran + + align:start position:0% +to thread two. Um and last time we ran + + + align:start position:0% +to thread two. Um and last time we ran +thread two, it called yield and its + + align:start position:0% +thread two, it called yield and its + + + align:start position:0% +thread two, it called yield and its +return address was 1,00. So there was + + align:start position:0% +return address was 1,00. So there was + + + align:start position:0% +return address was 1,00. So there was +this 1,00 here. Okay. So now when we uh + + align:start position:0% +this 1,00 here. Okay. So now when we uh + + + align:start position:0% +this 1,00 here. Okay. So now when we uh +schedule thread 2, what's going to + + align:start position:0% +schedule thread 2, what's going to + + + align:start position:0% +schedule thread 2, what's going to +happen is that uh we're going to read + + align:start position:0% +happen is that uh we're going to read + + + align:start position:0% +happen is that uh we're going to read +the uh so this is instruction 1000. + + align:start position:0% +the uh so this is instruction 1000. + + + align:start position:0% +the uh so this is instruction 1000. +We're going to start executing from + + align:start position:0% +We're going to start executing from + + + align:start position:0% +We're going to start executing from +10,00 because we're going to execute + + align:start position:0% +10,00 because we're going to execute + + + align:start position:0% +10,00 because we're going to execute +this pop return address. So, we're going + + align:start position:0% +this pop return address. So, we're going + + + align:start position:0% +this pop return address. So, we're going +to pop the return address off the stack. + + align:start position:0% +to pop the return address off the stack. + + + align:start position:0% +to pop the return address off the stack. +Um, and we're going to start executing + + align:start position:0% +Um, and we're going to start executing + + + align:start position:0% +Um, and we're going to start executing +here at instruction 1000. Okay. So, you + + align:start position:0% +here at instruction 1000. Okay. So, you + + + align:start position:0% +here at instruction 1000. Okay. So, you +guys kind of see how how it is that + + align:start position:0% +guys kind of see how how it is that + + + align:start position:0% +guys kind of see how how it is that +we've switched now from one thread to + + align:start position:0% +we've switched now from one thread to + + + align:start position:0% +we've switched now from one thread to +the other by switching the stack pointer + + align:start position:0% +the other by switching the stack pointer + + + align:start position:0% +the other by switching the stack pointer +and restoring our return and grabbing + + align:start position:0% +and restoring our return and grabbing + + + align:start position:0% +and restoring our return and grabbing +our return address from the stack of + + align:start position:0% +our return address from the stack of + + + align:start position:0% +our return address from the stack of +thread two instead of from thread one. + + align:start position:0% +thread two instead of from thread one. + + + align:start position:0% +thread two instead of from thread one. +Okay. So now what's going to happen is + + align:start position:0% +Okay. So now what's going to happen is + + + align:start position:0% +Okay. So now what's going to happen is +this this thread two is going to start + + align:start position:0% +this this thread two is going to start + + + align:start position:0% +this this thread two is going to start +executing from this address. um and it's + + align:start position:0% +executing from this address. um and it's + + + align:start position:0% +executing from this address. um and it's +going to run for a little while and at + + align:start position:0% +going to run for a little while and at + + + align:start position:0% +going to run for a little while and at +some point later it's going to call + + align:start position:0% +some point later it's going to call + + + align:start position:0% +some point later it's going to call +yield again, right? Because it's run for + + align:start position:0% +yield again, right? Because it's run for + + + align:start position:0% +yield again, right? Because it's run for +a while and it's decided that it's time + + align:start position:0% +a while and it's decided that it's time + + + align:start position:0% +a while and it's decided that it's time +to yield. So suppose at uh instruction + + align:start position:0% +to yield. So suppose at uh instruction + + + align:start position:0% +to yield. So suppose at uh instruction +uh 1025 + + align:start position:0% +uh 1025 + + + align:start position:0% +uh 1025 +it calls y instruction 1024 it calls + + align:start position:0% +it calls y instruction 1024 it calls + + + align:start position:0% +it calls y instruction 1024 it calls +yield. So when it does that the same + + align:start position:0% +yield. So when it does that the same + + + align:start position:0% +yield. So when it does that the same +thing is going to happen. It's going to + + align:start position:0% +thing is going to happen. It's going to + + + align:start position:0% +thing is going to happen. It's going to +uh it's going to have run for a little + + align:start position:0% +uh it's going to have run for a little + + + align:start position:0% +uh it's going to have run for a little +while. So it stack is going to have + + align:start position:0% +while. So it stack is going to have + + + align:start position:0% +while. So it stack is going to have +grown but eventually it's going to push + + align:start position:0% +grown but eventually it's going to push + + + align:start position:0% +grown but eventually it's going to push +the return address onto the stack. say + + align:start position:0% +the return address onto the stack. say + + + align:start position:0% +the return address onto the stack. say +here 1,025 + + align:start position:0% +here 1,025 + + + align:start position:0% +here 1,025 +um and suppose this value of its stack + + align:start position:0% +um and suppose this value of its stack + + + align:start position:0% +um and suppose this value of its stack +pointer now is uh has grown down. So + + align:start position:0% +pointer now is uh has grown down. So + + + align:start position:0% +pointer now is uh has grown down. So +it's gone 208 204 it's run for a while + + align:start position:0% +it's gone 208 204 it's run for a while + + + align:start position:0% +it's gone 208 204 it's run for a while +pushed some things on the stack and you + + align:start position:0% +pushed some things on the stack and you + + + align:start position:0% +pushed some things on the stack and you +know maybe it's at the stack pointer is + + align:start position:0% +know maybe it's at the stack pointer is + + + align:start position:0% +know maybe it's at the stack pointer is +now at 148. So when it calls yield it's + + align:start position:0% +now at 148. So when it calls yield it's + + + align:start position:0% +now at 148. So when it calls yield it's +going to write into the stack pointer + + align:start position:0% +going to write into the stack pointer + + + align:start position:0% +going to write into the stack pointer +address in the thread table 148. Um and + + align:start position:0% +address in the thread table 148. Um and + + + align:start position:0% +address in the thread table 148. Um and +we're going to restore the stack pointer + + align:start position:0% +we're going to restore the stack pointer + + + align:start position:0% +we're going to restore the stack pointer +address from here which I forgot to show + + align:start position:0% +address from here which I forgot to show + + + align:start position:0% +address from here which I forgot to show +being written in but what I should have + + align:start position:0% +being written in but what I should have + + + align:start position:0% +being written in but what I should have +written in there was 104. So we're going + + align:start position:0% +written in there was 104. So we're going + + + align:start position:0% +written in there was 104. So we're going +to restore the stack address to 104. + + align:start position:0% +to restore the stack address to 104. + + + align:start position:0% +to restore the stack address to 104. +We're going to pop the next instruction + + align:start position:0% +We're going to pop the next instruction + + + align:start position:0% +We're going to pop the next instruction +to execute off of that stack five. And + + align:start position:0% +to execute off of that stack five. And + + + align:start position:0% +to execute off of that stack five. And +then we're going to keep executing. So + + align:start position:0% +then we're going to keep executing. So + + + align:start position:0% +then we're going to keep executing. So +we just switch back and forth in this + + align:start position:0% +we just switch back and forth in this + + + align:start position:0% +we just switch back and forth in this +way. + + align:start position:0% +way. + + + align:start position:0% +way. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Okay. So um + + align:start position:0% + + + + align:start position:0% + +okay. Okay. So what I want to do now is + + align:start position:0% +okay. Okay. So what I want to do now is + + + align:start position:0% +okay. Okay. So what I want to do now is +to uh so this is the the basic process + + align:start position:0% +to uh so this is the the basic process + + + align:start position:0% +to uh so this is the the basic process +now by whereby this yield uh instruction + + align:start position:0% +now by whereby this yield uh instruction + + + align:start position:0% +now by whereby this yield uh instruction +can be used to switch between the + + align:start position:0% +can be used to switch between the + + + align:start position:0% +can be used to switch between the +scheduling of these two procedures right + + align:start position:0% +scheduling of these two procedures right + + + align:start position:0% +scheduling of these two procedures right +um and this is sort of the the core of + + align:start position:0% +um and this is sort of the the core of + + + align:start position:0% +um and this is sort of the the core of +how it is. So we have these two threads + + align:start position:0% +how it is. So we have these two threads + + + align:start position:0% +how it is. So we have these two threads +of execution and they just sort of run + + align:start position:0% +of execution and they just sort of run + + + align:start position:0% +of execution and they just sort of run +through and they periodically call yield + + align:start position:0% +through and they periodically call yield + + + align:start position:0% +through and they periodically call yield +and that allows another thread to be + + align:start position:0% +and that allows another thread to be + + + align:start position:0% +and that allows another thread to be +written but to execute it but otherwise + + align:start position:0% +written but to execute it but otherwise + + + align:start position:0% +written but to execute it but otherwise +these two threads are essentially uh + + align:start position:0% +these two threads are essentially uh + + + align:start position:0% +these two threads are essentially uh +they've just been written in in this + + align:start position:0% +they've just been written in in this + + + align:start position:0% +they've just been written in in this +style where they don't actually have to + + align:start position:0% +style where they don't actually have to + + + align:start position:0% +style where they don't actually have to +know anything about the other threads + + align:start position:0% +know anything about the other threads + + + align:start position:0% +know anything about the other threads +that are running. um you know there + + align:start position:0% +that are running. um you know there + + + align:start position:0% +that are running. um you know there +could have been two other threads or 200 + + align:start position:0% +could have been two other threads or 200 + + + align:start position:0% +could have been two other threads or 200 +other threads running on the system at + + align:start position:0% +other threads running on the system at + + + align:start position:0% +other threads running on the system at +the same time and this approach that + + align:start position:0% +the same time and this approach that + + + align:start position:0% +the same time and this approach that +I've showed you would have caused all of + + align:start position:0% +I've showed you would have caused all of + + + align:start position:0% +I've showed you would have caused all of +those threads eventually to have been + + align:start position:0% +those threads eventually to have been + + + align:start position:0% +those threads eventually to have been +scheduled and to execute properly right + + align:start position:0% +scheduled and to execute properly right + + + align:start position:0% +scheduled and to execute properly right +um but as I as we said before uh the use + + align:start position:0% +um but as I as we said before uh the use + + + align:start position:0% +um but as I as we said before uh the use +of requiring these proced these + + align:start position:0% +of requiring these proced these + + + align:start position:0% +of requiring these proced these +functions to actually call yield + + align:start position:0% +functions to actually call yield + + + align:start position:0% +functions to actually call yield +periodically has sort of defeated the + + align:start position:0% +periodically has sort of defeated the + + + align:start position:0% +periodically has sort of defeated the +purpose of our enforcing modularity one + + align:start position:0% +purpose of our enforcing modularity one + + + align:start position:0% +purpose of our enforcing modularity one +of our goals of enforcing modularity + + align:start position:0% +of our goals of enforcing modularity + + + align:start position:0% +of our goals of enforcing modularity +which is to make it so that no one + + align:start position:0% +which is to make it so that no one + + + align:start position:0% +which is to make it so that no one +thread can interfere with the operation + + align:start position:0% +thread can interfere with the operation + + + align:start position:0% +thread can interfere with the operation +of the other thread or cause that other + + align:start position:0% +of the other thread or cause that other + + + align:start position:0% +of the other thread or cause that other +thread to crash, right? Because uh if + + align:start position:0% +thread to crash, right? Because uh if + + + align:start position:0% +thread to crash, right? Because uh if +the procedure never calls yield, then if + + align:start position:0% +the procedure never calls yield, then if + + + align:start position:0% +the procedure never calls yield, then if +a a function never call a module never + + align:start position:0% +a a function never call a module never + + + align:start position:0% +a a function never call a module never +calls yield, excuse me, the uh thread, + + align:start position:0% +calls yield, excuse me, the uh thread, + + + align:start position:0% +calls yield, excuse me, the uh thread, +you know, another thread will never be + + align:start position:0% +you know, another thread will never be + + + align:start position:0% +you know, another thread will never be +scheduled. And so that module will have + + align:start position:0% +scheduled. And so that module will have + + + align:start position:0% +scheduled. And so that module will have +the ability essentially to take over the + + align:start position:0% +the ability essentially to take over the + + + align:start position:0% +the ability essentially to take over the +whole computer, which is bad. So what + + align:start position:0% +whole computer, which is bad. So what + + + align:start position:0% +whole computer, which is bad. So what +we're going to look at now is how we go + + align:start position:0% +we're going to look at now is how we go + + + align:start position:0% +we're going to look at now is how we go +from this cooperative scheduling where + + align:start position:0% +from this cooperative scheduling where + + + align:start position:0% +from this cooperative scheduling where +procedures call where modules call yield + + align:start position:0% +procedures call where modules call yield + + + align:start position:0% +procedures call where modules call yield +to preemptive scheduling where modules + + align:start position:0% +to preemptive scheduling where modules + + + align:start position:0% +to preemptive scheduling where modules +are forced to yield the processor + + align:start position:0% +are forced to yield the processor + + + align:start position:0% +are forced to yield the processor +periodically. + + align:start position:0% + + + + align:start position:0% + +Okay, so this is the case where we have + + align:start position:0% +Okay, so this is the case where we have + + + align:start position:0% +Okay, so this is the case where we have +no explicit yield statements. + + align:start position:0% + + + + align:start position:0% + +All right. So, uh the idea here is it + + align:start position:0% +All right. So, uh the idea here is it + + + align:start position:0% +All right. So, uh the idea here is it +turns out it turns out to be very + + align:start position:0% +turns out it turns out to be very + + + align:start position:0% +turns out it turns out to be very +simple. So, we're in programs aren't + + align:start position:0% +simple. So, we're in programs aren't + + + align:start position:0% +simple. So, we're in programs aren't +going to have an explicit yield + + align:start position:0% +going to have an explicit yield + + + align:start position:0% +going to have an explicit yield +statement in them. But what we're going + + align:start position:0% +statement in them. But what we're going + + + align:start position:0% +statement in them. But what we're going +to do is we're going to have a special + + align:start position:0% +to do is we're going to have a special + + + align:start position:0% +to do is we're going to have a special +uh timer that runs periodically within + + align:start position:0% +uh timer that runs periodically within + + + align:start position:0% +uh timer that runs periodically within +say for example the kernel. So suppose + + align:start position:0% +say for example the kernel. So suppose + + + align:start position:0% +say for example the kernel. So suppose +the kernel has a timer that runs + + align:start position:0% +the kernel has a timer that runs + + + align:start position:0% +the kernel has a timer that runs +periodically that causes the causes the + + align:start position:0% +periodically that causes the causes the + + + align:start position:0% +periodically that causes the causes the +kernel uh to be sort of woken up and + + align:start position:0% +kernel uh to be sort of woken up and + + + align:start position:0% +kernel uh to be sort of woken up and +allowed to execute some code. Um, so + + align:start position:0% +allowed to execute some code. Um, so + + + align:start position:0% +allowed to execute some code. Um, so +this timer is going to be connected to + + align:start position:0% +this timer is going to be connected to + + + align:start position:0% +this timer is going to be connected to +what's called an interrupt. + + align:start position:0% +what's called an interrupt. + + + align:start position:0% +what's called an interrupt. +So we're going to introduce a timer + + align:start position:0% +So we're going to introduce a timer + + + align:start position:0% +So we're going to introduce a timer +interrupt. + + align:start position:0% + + + + align:start position:0% + +And almost all all processors + + align:start position:0% +And almost all all processors + + + align:start position:0% +And almost all all processors +essentially have some notion of a timer + + align:start position:0% +essentially have some notion of a timer + + + align:start position:0% +essentially have some notion of a timer +interrupt. And an interrupt is something + + align:start position:0% +interrupt. And an interrupt is something + + + align:start position:0% +interrupt. And an interrupt is something +that um when it fires, it causes the + + align:start position:0% +that um when it fires, it causes the + + + align:start position:0% +that um when it fires, it causes the +processor it causes the uh processor to + + align:start position:0% +processor it causes the uh processor to + + + align:start position:0% +processor it causes the uh processor to +run a special piece of code. Okay. So, + + align:start position:0% +run a special piece of code. Okay. So, + + + align:start position:0% +run a special piece of code. Okay. So, +um, + + align:start position:0% +um, + + + align:start position:0% +um, +basically + + align:start position:0% +basically + + + align:start position:0% +basically +this is going to be a some processor. + + align:start position:0% +this is going to be a some processor. + + + align:start position:0% +this is going to be a some processor. +Think of it if you like as some line on + + align:start position:0% +Think of it if you like as some line on + + + align:start position:0% +Think of it if you like as some line on +the processor. Okay, there's a wire + + align:start position:0% +the processor. Okay, there's a wire + + + align:start position:0% +the processor. Okay, there's a wire +that's coming off the processor. Um, and + + align:start position:0% +that's coming off the processor. Um, and + + + align:start position:0% +that's coming off the processor. Um, and +when this wire gets pulled high, when + + align:start position:0% +when this wire gets pulled high, when + + + align:start position:0% +when this wire gets pulled high, when +the timer goes off and fires, this line + + align:start position:0% +the timer goes off and fires, this line + + + align:start position:0% +the timer goes off and fires, this line +is going to be pulled high. Um, and when + + align:start position:0% +is going to be pulled high. Um, and when + + + align:start position:0% +is going to be pulled high. Um, and when +that happens, um, the microprocessor is + + align:start position:0% +that happens, um, the microprocessor is + + + align:start position:0% +that happens, um, the microprocessor is +going to notice that and is going to + + align:start position:0% +going to notice that and is going to + + + align:start position:0% +going to notice that and is going to +invoke a special function within the + + align:start position:0% +invoke a special function within the + + + align:start position:0% +invoke a special function within the +kernel. So uh + + align:start position:0% +kernel. So uh + + + align:start position:0% +kernel. So uh +this timer this this line is going to be + + align:start position:0% +this timer this this line is going to be + + + align:start position:0% +this timer this this line is going to be +uh checked by the microprocessor + + align:start position:0% + + + + align:start position:0% + +before it executes each instruction. + + align:start position:0% +before it executes each instruction. + + + align:start position:0% +before it executes each instruction. +Okay. And if the line is high, + + align:start position:0% + + + + align:start position:0% + +the timer is going to execute a uh the + + align:start position:0% +the timer is going to execute a uh the + + + align:start position:0% +the timer is going to execute a uh the +microprocessor is going to execute one + + align:start position:0% +microprocessor is going to execute one + + + align:start position:0% +microprocessor is going to execute one +of these special um gate functions. + + align:start position:0% +of these special um gate functions. + + + align:start position:0% +of these special um gate functions. +Okay, that's very much so we saw the + + align:start position:0% +Okay, that's very much so we saw the + + + align:start position:0% +Okay, that's very much so we saw the +notion of a gate function before that + + align:start position:0% +notion of a gate function before that + + + align:start position:0% +notion of a gate function before that +can be used to uh for a a procedure to + + align:start position:0% +can be used to uh for a a procedure to + + + align:start position:0% +can be used to uh for a a procedure to +execute to obtain entry into uh or for a + + align:start position:0% +execute to obtain entry into uh or for a + + + align:start position:0% +execute to obtain entry into uh or for a +module to obtain entry into the kernel. + + align:start position:0% +module to obtain entry into the kernel. + + + align:start position:0% +module to obtain entry into the kernel. +Essentially what's going to happen is + + align:start position:0% +Essentially what's going to happen is + + + align:start position:0% +Essentially what's going to happen is +that the when the timer interrupt f + + align:start position:0% +that the when the timer interrupt f + + + align:start position:0% +that the when the timer interrupt f +fires it's going to go execute one of + + align:start position:0% +fires it's going to go execute one of + + + align:start position:0% +fires it's going to go execute one of +these special gate functions as well and + + align:start position:0% +these special gate functions as well and + + + align:start position:0% +these special gate functions as well and +that's going to cause the kernel to then + + align:start position:0% +that's going to cause the kernel to then + + + align:start position:0% +that's going to cause the kernel to then +be uh in control of the processor. So + + align:start position:0% +be uh in control of the processor. So + + + align:start position:0% +be uh in control of the processor. So +remember when the gate function in when + + align:start position:0% +remember when the gate function in when + + + align:start position:0% +remember when the gate function in when +the gate function runs it uh causes the + + align:start position:0% +the gate function runs it uh causes the + + + align:start position:0% +the gate function runs it uh causes the +current it switches the user to user to + + align:start position:0% +current it switches the user to user to + + + align:start position:0% +current it switches the user to user to +kernel mode bit to kernel mode. It + + align:start position:0% +kernel mode bit to kernel mode. It + + + align:start position:0% +kernel mode bit to kernel mode. It +switches the page map address register + + align:start position:0% +switches the page map address register + + + align:start position:0% +switches the page map address register +to the kernel's page map so that the + + align:start position:0% +to the kernel's page map so that the + + + align:start position:0% +to the kernel's page map so that the +kernel is in control and it switches the + + align:start position:0% +kernel is in control and it switches the + + + align:start position:0% +kernel is in control and it switches the +stack pointer to the kernel saved stack + + align:start position:0% +stack pointer to the kernel saved stack + + + align:start position:0% +stack pointer to the kernel saved stack +pointer so that the kernel is in control + + align:start position:0% +pointer so that the kernel is in control + + + align:start position:0% +pointer so that the kernel is in control +of the system and can execute whatever + + align:start position:0% +of the system and can execute whatever + + + align:start position:0% +of the system and can execute whatever +code that it wants. So this is going to + + align:start position:0% +code that it wants. So this is going to + + + align:start position:0% +code that it wants. So this is going to +accomplish basically everything that we + + align:start position:0% +accomplish basically everything that we + + + align:start position:0% +accomplish basically everything that we +need right because if I can get if we + + align:start position:0% +need right because if I can get if we + + + align:start position:0% +need right because if I can get if we +can get the kernel in control of the + + align:start position:0% +can get the kernel in control of the + + + align:start position:0% +can get the kernel in control of the +process of the system now the kernel can + + align:start position:0% +process of the system now the kernel can + + + align:start position:0% +process of the system now the kernel can +do whatever it needs to do to uh for + + align:start position:0% +do whatever it needs to do to uh for + + + align:start position:0% +do whatever it needs to do to uh for +example schedule the next thread. So the + + align:start position:0% +example schedule the next thread. So the + + + align:start position:0% +example schedule the next thread. So the +way that that's going to work um is + + align:start position:0% +way that that's going to work um is + + + align:start position:0% +way that that's going to work um is +basically very simple. So when the + + align:start position:0% +basically very simple. So when the + + + align:start position:0% +basically very simple. So when the +kernel gets run uh it knows which thread + + align:start position:0% +kernel gets run uh it knows which thread + + + align:start position:0% +kernel gets run uh it knows which thread +is current it uh it knows which thread + + align:start position:0% +is current it uh it knows which thread + + + align:start position:0% +is current it uh it knows which thread +for example is currently running. Um and + + align:start position:0% +for example is currently running. Um and + + + align:start position:0% +for example is currently running. Um and +basically what it does is it just uh + + align:start position:0% +basically what it does is it just uh + + + align:start position:0% +basically what it does is it just uh +calls the appropriate yield function. It + + align:start position:0% +calls the appropriate yield function. It + + + align:start position:0% +calls the appropriate yield function. It +calls the yield function for the thread + + align:start position:0% +calls the yield function for the thread + + + align:start position:0% +calls the yield function for the thread +that is currently running forcing uh + + align:start position:0% +that is currently running forcing uh + + + align:start position:0% +that is currently running forcing uh +that thread to yield. So um + + align:start position:0% + + + + align:start position:0% + +kernel calls + + align:start position:0% + + + + align:start position:0% + +yield on current thread, right? + + align:start position:0% + + + + align:start position:0% + +Okay. So in order to do this, of course, + + align:start position:0% +Okay. So in order to do this, of course, + + + align:start position:0% +Okay. So in order to do this, of course, +the kernel needs to understand uh how + + align:start position:0% +the kernel needs to understand uh how + + + align:start position:0% +the kernel needs to understand uh how +the where where the current what uh it + + align:start position:0% +the where where the current what uh it + + + align:start position:0% +the where where the current what uh it +needs to needs to know how to get to the + + align:start position:0% +needs to needs to know how to get to the + + + align:start position:0% +needs to needs to know how to get to the +yield, needs to know how to capture the + + align:start position:0% +yield, needs to know how to capture the + + + align:start position:0% +yield, needs to know how to capture the +state for the currently running thread. + + align:start position:0% +state for the currently running thread. + + + align:start position:0% +state for the currently running thread. +But for the most part, that's pretty + + align:start position:0% +But for the most part, that's pretty + + + align:start position:0% +But for the most part, that's pretty +simple because the state is all + + align:start position:0% +simple because the state is all + + + align:start position:0% +simple because the state is all +encapsulated in the current values of + + align:start position:0% +encapsulated in the current values of + + + align:start position:0% +encapsulated in the current values of +the registers and the current value of + + align:start position:0% +the registers and the current value of + + + align:start position:0% +the registers and the current value of +the stack pointer. So the kernel is + + align:start position:0% +the stack pointer. So the kernel is + + + align:start position:0% +the stack pointer. So the kernel is +going to call yield on the currently + + align:start position:0% +going to call yield on the currently + + + align:start position:0% +going to call yield on the currently +executing thread and that's going to + + align:start position:0% +executing thread and that's going to + + + align:start position:0% +executing thread and that's going to +force that thread to go ahead and + + align:start position:0% +force that thread to go ahead and + + + align:start position:0% +force that thread to go ahead and +schedule the next to schedule to + + align:start position:0% +schedule the next to schedule to + + + align:start position:0% +schedule the next to schedule to +schedule another thread. So uh the + + align:start position:0% +schedule another thread. So uh the + + + align:start position:0% +schedule another thread. So uh the +module itself hasn't called yield but + + align:start position:0% +module itself hasn't called yield but + + + align:start position:0% +module itself hasn't called yield but +still the module has been forced to sort + + align:start position:0% +still the module has been forced to sort + + + align:start position:0% +still the module has been forced to sort +of give up its control of the processor. + + align:start position:0% +of give up its control of the processor. + + + align:start position:0% +of give up its control of the processor. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +so + + align:start position:0% +so + + + align:start position:0% +so +this is simply when it calls yield it's + + align:start position:0% +this is simply when it calls yield it's + + + align:start position:0% +this is simply when it calls yield it's +just going to do what we did before + + align:start position:0% +just going to do what we did before + + + align:start position:0% +just going to do what we did before +which is uh save our state and + + align:start position:0% + + + + align:start position:0% + +schedule and run + + align:start position:0% +schedule and run + + + align:start position:0% +schedule and run +the next thread. + + align:start position:0% +the next thread. + + + align:start position:0% +the next thread. +Okay. Um + + align:start position:0% + + + + align:start position:0% + +so the only last little detail that we + + align:start position:0% +so the only last little detail that we + + + align:start position:0% +so the only last little detail that we +have to think about is um what if the + + align:start position:0% +have to think about is um what if the + + + align:start position:0% +have to think about is um what if the +colonel wants to schedule a thread + + align:start position:0% +colonel wants to schedule a thread + + + align:start position:0% +colonel wants to schedule a thread +that's running in a different address + + align:start position:0% +that's running in a different address + + + align:start position:0% +that's running in a different address +space. So if a colonel wants to schedule + + align:start position:0% +space. So if a colonel wants to schedule + + + align:start position:0% +space. So if a colonel wants to schedule +a thread that's running in a different + + align:start position:0% +a thread that's running in a different + + + align:start position:0% +a thread that's running in a different +address space well it has to do what we + + align:start position:0% +address space well it has to do what we + + + align:start position:0% +address space well it has to do what we +did last time we saw last time when we + + align:start position:0% +did last time we saw last time when we + + + align:start position:0% +did last time we saw last time when we +saw about how we switch address spaces. + + align:start position:0% +saw about how we switch address spaces. + + + align:start position:0% +saw about how we switch address spaces. +it has to change the value of the PM + + align:start position:0% +it has to change the value of the PM + + + align:start position:0% +it has to change the value of the PM +register uh so that the next address + + align:start position:0% +register uh so that the next address + + + align:start position:0% +register uh so that the next address +space gets swapped in and then it can go + + align:start position:0% +space gets swapped in and then it can go + + + align:start position:0% +space gets swapped in and then it can go +ahead and jump into the and jump into + + align:start position:0% +ahead and jump into the and jump into + + + align:start position:0% +ahead and jump into the and jump into +the appropriate location in the sort of + + align:start position:0% +the appropriate location in the sort of + + + align:start position:0% +the appropriate location in the sort of +newly scheduled address space. So um + + align:start position:0% +newly scheduled address space. So um + + + align:start position:0% +newly scheduled address space. So um +that brings us to the next topic of + + align:start position:0% +that brings us to the next topic of + + + align:start position:0% +that brings us to the next topic of +discussion. So what we've seen so far + + align:start position:0% +discussion. So what we've seen so far + + + align:start position:0% +discussion. So what we've seen so far +now we saw cooperative in the same + + align:start position:0% +now we saw cooperative in the same + + + align:start position:0% +now we saw cooperative in the same +address space and I introduced the + + align:start position:0% +address space and I introduced the + + + align:start position:0% +address space and I introduced the +notion of a preemptive scheduling. Um + + align:start position:0% +notion of a preemptive scheduling. Um + + + align:start position:0% +notion of a preemptive scheduling. Um +and what we want to look at now is sort + + align:start position:0% +and what we want to look at now is sort + + + align:start position:0% +and what we want to look at now is sort +of uh what it means to run multiple + + align:start position:0% +of uh what it means to run multiple + + + align:start position:0% +of uh what it means to run multiple +threads run threads in different address + + align:start position:0% +threads run threads in different address + + + align:start position:0% +threads run threads in different address +spaces. So uh typically when we talk + + align:start position:0% +spaces. So uh typically when we talk + + + align:start position:0% +spaces. So uh typically when we talk +about a program that's running on a + + align:start position:0% +about a program that's running on a + + + align:start position:0% +about a program that's running on a +computer or uh in 6033 we like to call + + align:start position:0% +computer or uh in 6033 we like to call + + + align:start position:0% +computer or uh in 6033 we like to call +programs running on computers processes + + align:start position:0% +programs running on computers processes + + + align:start position:0% +programs running on computers processes +when we talk about a process we mean a + + align:start position:0% +when we talk about a process we mean a + + + align:start position:0% +when we talk about a process we mean a +address space + + align:start position:0% +address space + + + align:start position:0% +address space +plus some collection of threads. + + align:start position:0% +plus some collection of threads. + + + align:start position:0% +plus some collection of threads. +So this is our sort of the the the real + + align:start position:0% +So this is our sort of the the the real + + + align:start position:0% +So this is our sort of the the the real +definition of what we mean by a process. + + align:start position:0% +definition of what we mean by a process. + + + align:start position:0% +definition of what we mean by a process. +Um and you know alternately you'll see + + align:start position:0% +Um and you know alternately you'll see + + + align:start position:0% +Um and you know alternately you'll see +processes called things like + + align:start position:0% +processes called things like + + + align:start position:0% +processes called things like +applications or programs but anytime you + + align:start position:0% +applications or programs but anytime you + + + align:start position:0% +applications or programs but anytime you +see a word like that what people + + align:start position:0% +see a word like that what people + + + align:start position:0% +see a word like that what people +typically mean is it's some address + + align:start position:0% +typically mean is it's some address + + + align:start position:0% +typically mean is it's some address +space some uh virt some virtual address + + align:start position:0% +space some uh virt some virtual address + + + align:start position:0% +space some uh virt some virtual address +space in which we resolve memory + + align:start position:0% +space in which we resolve memory + + + align:start position:0% +space in which we resolve memory +addresses um and then a collection of + + align:start position:0% +addresses um and then a collection of + + + align:start position:0% +addresses um and then a collection of +threads that are currently executing + + align:start position:0% +threads that are currently executing + + + align:start position:0% +threads that are currently executing +within that address space. um and where + + align:start position:0% +within that address space. um and where + + + align:start position:0% +within that address space. um and where +each of those threads includes the set + + align:start position:0% +each of those threads includes the set + + + align:start position:0% +each of those threads includes the set +of instructions and registers uh and + + align:start position:0% +of instructions and registers uh and + + + align:start position:0% +of instructions and registers uh and +stack that correspond to it. Okay. + + align:start position:0% + + + + align:start position:0% + +So um + + align:start position:0% +So um + + + align:start position:0% +So um +the kernel has explicit support for + + align:start position:0% +the kernel has explicit support for + + + align:start position:0% +the kernel has explicit support for +these processes. + + align:start position:0% + + + + align:start position:0% + +So in particular what the kernel + + align:start position:0% +So in particular what the kernel + + + align:start position:0% +So in particular what the kernel +provides are uh routines to create a + + align:start position:0% +provides are uh routines to create a + + + align:start position:0% +provides are uh routines to create a +process + + align:start position:0% +process + + + align:start position:0% +process +uh and destroy a process. + + align:start position:0% + + + + align:start position:0% + +Okay. And this these create and destroy + + align:start position:0% +Okay. And this these create and destroy + + + align:start position:0% +Okay. And this these create and destroy +methods are going to do uh sort of do + + align:start position:0% +methods are going to do uh sort of do + + + align:start position:0% +methods are going to do uh sort of do +all the the create method is going to do + + align:start position:0% +all the the create method is going to do + + + align:start position:0% +all the the create method is going to do +all the initialization that we need to + + align:start position:0% +all the initialization that we need to + + + align:start position:0% +all the initialization that we need to +do in order to create a new address + + align:start position:0% +do in order to create a new address + + + align:start position:0% +do in order to create a new address +space and to create at least one thread + + align:start position:0% +space and to create at least one thread + + + align:start position:0% +space and to create at least one thread +that is running within that address + + align:start position:0% +that is running within that address + + + align:start position:0% +that is running within that address +space. So we've sort of seen all the + + align:start position:0% +space. So we've sort of seen all the + + + align:start position:0% +space. So we've sort of seen all the +pieces of this but uh basically what + + align:start position:0% +pieces of this but uh basically what + + + align:start position:0% +pieces of this but uh basically what +it's going to do is it's going to uh + + align:start position:0% +it's going to do is it's going to uh + + + align:start position:0% +it's going to do is it's going to uh +allocate the address space + + align:start position:0% +allocate the address space + + + align:start position:0% +allocate the address space +in its table of + + align:start position:0% +in its table of + + + align:start position:0% +in its table of +in the table of all the address bases + + align:start position:0% +in the table of all the address bases + + + align:start position:0% +in the table of all the address bases +that it that it knows about. We saw that + + align:start position:0% +that it that it knows about. We saw that + + + align:start position:0% +that it that it knows about. We saw that +in the la the last time. Um and it's + + align:start position:0% +in the la the last time. Um and it's + + + align:start position:0% +in the la the last time. Um and it's +going to allocate a uh piece of physical + + align:start position:0% +going to allocate a uh piece of physical + + + align:start position:0% +going to allocate a uh piece of physical +memory that corresponds to that address + + align:start position:0% +memory that corresponds to that address + + + align:start position:0% +memory that corresponds to that address +space in particular. Uh the sort of so + + align:start position:0% + + + + align:start position:0% + +it's going to create allocate a piece of + + align:start position:0% +it's going to create allocate a piece of + + + align:start position:0% +it's going to create allocate a piece of +physical memory that corresponds to that + + align:start position:0% +physical memory that corresponds to that + + + align:start position:0% +physical memory that corresponds to that +address space. It's going to allocate + + align:start position:0% +address space. It's going to allocate + + + align:start position:0% +address space. It's going to allocate +one of these page maps that the uh page + + align:start position:0% +one of these page maps that the uh page + + + align:start position:0% +one of these page maps that the uh page +map the the PM register is going to + + align:start position:0% +map the the PM register is going to + + + align:start position:0% +map the the PM register is going to +point to uh when this thing is that when + + align:start position:0% +point to uh when this thing is that when + + + align:start position:0% +point to uh when this thing is that when +this thing is running. + + align:start position:0% +this thing is running. + + + align:start position:0% +this thing is running. +Okay. And now the other thing that it's + + align:start position:0% +Okay. And now the other thing that it's + + + align:start position:0% +Okay. And now the other thing that it's +going to do is to go ahead and load the + + align:start position:0% +going to do is to go ahead and load the + + + align:start position:0% +going to do is to go ahead and load the +code + + align:start position:0% +code + + + align:start position:0% +code +for this thing into memory + + align:start position:0% + + + + align:start position:0% + +and map it into the address space. + + align:start position:0% + + + + align:start position:0% + +So it's going to add a point. It's going + + align:start position:0% +So it's going to add a point. It's going + + + align:start position:0% +So it's going to add a point. It's going +to add the code for this currently + + align:start position:0% +to add the code for this currently + + + align:start position:0% +to add the code for this currently +running module into the address space. + + align:start position:0% +running module into the address space. + + + align:start position:0% +running module into the address space. +And then it's going to create a thread + + align:start position:0% +And then it's going to create a thread + + + align:start position:0% +And then it's going to create a thread +for this + + align:start position:0% + + + + align:start position:0% + +new process. + + align:start position:0% +new process. + + + align:start position:0% +new process. +It's going to add it to the table, + + align:start position:0% + + + + align:start position:0% + +the thread table. + + align:start position:0% +the thread table. + + + align:start position:0% +the thread table. +And then it's going to set up the value + + align:start position:0% +And then it's going to set up the value + + + align:start position:0% +And then it's going to set up the value +of the stack pointer and the program + + align:start position:0% +of the stack pointer and the program + + + align:start position:0% +of the stack pointer and the program +counter for this process. So that uh + + align:start position:0% +counter for this process. So that uh + + + align:start position:0% +counter for this process. So that uh +when the process starts running, it you + + align:start position:0% +when the process starts running, it you + + + align:start position:0% +when the process starts running, it you +sort of enter the process at some well- + + align:start position:0% +sort of enter the process at some well- + + + align:start position:0% +sort of enter the process at some well- +definfined entry point. Say, you know, + + align:start position:0% +definfined entry point. Say, you know, + + + align:start position:0% +definfined entry point. Say, you know, +the main co the main routine in that + + align:start position:0% +the main co the main routine in that + + + align:start position:0% +the main co the main routine in that +process. so that that so that the you + + align:start position:0% +process. so that that so that the you + + + align:start position:0% +process. so that that so that the you +know thread can start executing at + + align:start position:0% +know thread can start executing at + + + align:start position:0% +know thread can start executing at +whatever starting point it has. Okay. + + align:start position:0% +whatever starting point it has. Okay. + + + align:start position:0% +whatever starting point it has. Okay. +And now destroy is just going to + + align:start position:0% +And now destroy is just going to + + + align:start position:0% +And now destroy is just going to +basically do the opposite. It's going to + + align:start position:0% +basically do the opposite. It's going to + + + align:start position:0% +basically do the opposite. It's going to +get rid of all this state that we've + + align:start position:0% +get rid of all this state that we've + + + align:start position:0% +get rid of all this state that we've +created. So it's going to destroy the + + align:start position:0% +created. So it's going to destroy the + + + align:start position:0% +created. So it's going to destroy the +it's going to uh remove the address + + align:start position:0% +it's going to uh remove the address + + + align:start position:0% +it's going to uh remove the address +space + + align:start position:0% +space + + + align:start position:0% +space +and it's going to remove + + align:start position:0% + + + + align:start position:0% + +the thread from the table. Okay. and it + + align:start position:0% +the thread from the table. Okay. and it + + + align:start position:0% +the thread from the table. Okay. and it +may also uh reclaim any memory that's + + align:start position:0% +may also uh reclaim any memory that's + + + align:start position:0% +may also uh reclaim any memory that's +associated exclusively with this + + align:start position:0% +associated exclusively with this + + + align:start position:0% +associated exclusively with this +process. + + align:start position:0% +process. + + + align:start position:0% +process. +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +okay. So, if we look at uh + + align:start position:0% +okay. So, if we look at uh + + + align:start position:0% +okay. So, if we look at uh +[Applause] + + align:start position:0% + + + + align:start position:0% + +so if you look at a computer system at + + align:start position:0% +so if you look at a computer system at + + + align:start position:0% +so if you look at a computer system at +any one point in time, what you'll see + + align:start position:0% +any one point in time, what you'll see + + + align:start position:0% +any one point in time, what you'll see +is a collection of + + align:start position:0% +is a collection of + + + align:start position:0% +is a collection of +uh processes. So I've drawn these here + + align:start position:0% +uh processes. So I've drawn these here + + + align:start position:0% +uh processes. So I've drawn these here +as these big boxes. So we might have a + + align:start position:0% +as these big boxes. So we might have a + + + align:start position:0% +as these big boxes. So we might have a +process that corresponds to Halo and say + + align:start position:0% +process that corresponds to Halo and say + + + align:start position:0% +process that corresponds to Halo and say +we're also editing our code. So we have + + align:start position:0% +we're also editing our code. So we have + + + align:start position:0% +we're also editing our code. So we have +a process that corresponds to Emacs. + + align:start position:0% +a process that corresponds to Emacs. + + + align:start position:0% +a process that corresponds to Emacs. +Okay. And each one of these processes is + + align:start position:0% +Okay. And each one of these processes is + + + align:start position:0% +Okay. And each one of these processes is +going to have is going to have an + + align:start position:0% +going to have is going to have an + + + align:start position:0% +going to have is going to have an +address space associated with it. Um + + align:start position:0% + + + + align:start position:0% + +and then there are going to be some set + + align:start position:0% +and then there are going to be some set + + + align:start position:0% +and then there are going to be some set +of uh threads that are running in + + align:start position:0% +of uh threads that are running in + + + align:start position:0% +of uh threads that are running in +association with this process. So in the + + align:start position:0% +association with this process. So in the + + + align:start position:0% +association with this process. So in the +case of Halo, I'm going to draw these + + align:start position:0% +case of Halo, I'm going to draw these + + + align:start position:0% +case of Halo, I'm going to draw these +threads as these little squiggly lines. + + align:start position:0% +threads as these little squiggly lines. + + + align:start position:0% +threads as these little squiggly lines. +So in the case of Halo, we saw that + + align:start position:0% +So in the case of Halo, we saw that + + + align:start position:0% +So in the case of Halo, we saw that +well, you know, maybe it has three + + align:start position:0% +well, you know, maybe it has three + + + align:start position:0% +well, you know, maybe it has three +threads that are running within it, + + align:start position:0% +threads that are running within it, + + + align:start position:0% +threads that are running within it, +right? So these are three threads that + + align:start position:0% +right? So these are three threads that + + + align:start position:0% +right? So these are three threads that +all run within the same address space. + + align:start position:0% +all run within the same address space. + + + align:start position:0% +all run within the same address space. +Now, Emacs might have just one thread + + align:start position:0% +Now, Emacs might have just one thread + + + align:start position:0% +Now, Emacs might have just one thread +that's running in it, say, um, although + + align:start position:0% +that's running in it, say, um, although + + + align:start position:0% +that's running in it, say, um, although +that's probably not true. Emacs is + + align:start position:0% +that's probably not true. Emacs is + + + align:start position:0% +that's probably not true. Emacs is +horribly complicated and probably has + + align:start position:0% +horribly complicated and probably has + + + align:start position:0% +horribly complicated and probably has +many threads that are running within it. + + align:start position:0% +many threads that are running within it. + + + align:start position:0% +many threads that are running within it. +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +and so we're going to have these sort of + + align:start position:0% +and so we're going to have these sort of + + + align:start position:0% +and so we're going to have these sort of +these two processes with these two + + align:start position:0% +these two processes with these two + + + align:start position:0% +these two processes with these two +collections of threads. + + align:start position:0% +collections of threads. + + + align:start position:0% +collections of threads. +So if you think about uh how the so if + + align:start position:0% +So if you think about uh how the so if + + + align:start position:0% +So if you think about uh how the so if +you think about the sort of modularity + + align:start position:0% +you think about the sort of modularity + + + align:start position:0% +you think about the sort of modularity +the enforcement of modularity that we + + align:start position:0% +the enforcement of modularity that we + + + align:start position:0% +the enforcement of modularity that we +have between these processes we can say + + align:start position:0% +have between these processes we can say + + + align:start position:0% +have between these processes we can say +some thing we can say some interesting + + align:start position:0% +some thing we can say some interesting + + + align:start position:0% +some thing we can say some interesting +things. So first of all we've enforced + + align:start position:0% +things. So first of all we've enforced + + + align:start position:0% +things. So first of all we've enforced +modularity we have hard enforced + + align:start position:0% +modularity we have hard enforced + + + align:start position:0% +modularity we have hard enforced +modularity between + + align:start position:0% + + + + align:start position:0% + +these two uh these two processes right + + align:start position:0% +these two uh these two processes right + + + align:start position:0% +these two uh these two processes right +because there's no way that the Halo + + align:start position:0% +because there's no way that the Halo + + + align:start position:0% +because there's no way that the Halo +process can uh muck with any of the + + align:start position:0% +process can uh muck with any of the + + + align:start position:0% +process can uh muck with any of the +memory that say the EMAC process has + + align:start position:0% +memory that say the EMAC process has + + + align:start position:0% +memory that say the EMAC process has +evalu has has executed um and if as long + + align:start position:0% +evalu has has executed um and if as long + + + align:start position:0% +evalu has has executed um and if as long +as we're using preemptive scheduling uh + + align:start position:0% +as we're using preemptive scheduling uh + + + align:start position:0% +as we're using preemptive scheduling uh +there's no way that the Halo process + + align:start position:0% +there's no way that the Halo process + + + align:start position:0% +there's no way that the Halo process +could completely uh can can completely + + align:start position:0% +could completely uh can can completely + + + align:start position:0% +could completely uh can can completely +maintain control of the processor. So + + align:start position:0% +maintain control of the processor. So + + + align:start position:0% +maintain control of the processor. So +the EMAC process is going to be allowed + + align:start position:0% +the EMAC process is going to be allowed + + + align:start position:0% +the EMAC process is going to be allowed +to run and its memory is going to be uh + + align:start position:0% +to run and its memory is going to be uh + + + align:start position:0% +to run and its memory is going to be uh +protected from the Halo process. Okay. + + align:start position:0% +protected from the Halo process. Okay. + + + align:start position:0% +protected from the Halo process. Okay. +Now within the Halo process, there's + + align:start position:0% +Now within the Halo process, there's + + + align:start position:0% +Now within the Halo process, there's +sort of a different story. So within the + + align:start position:0% +sort of a different story. So within the + + + align:start position:0% +sort of a different story. So within the +Halo process, these threads because + + align:start position:0% +Halo process, these threads because + + + align:start position:0% +Halo process, these threads because +they're all within the same address + + align:start position:0% +they're all within the same address + + + align:start position:0% +they're all within the same address +space can uh muck with each other's + + align:start position:0% +space can uh muck with each other's + + + align:start position:0% +space can uh muck with each other's +memory. Um so they're not isolated from + + align:start position:0% +memory. Um so they're not isolated from + + + align:start position:0% +memory. Um so they're not isolated from +each other in that way. And typically + + align:start position:0% +each other in that way. And typically + + + align:start position:0% +each other in that way. And typically +because these are all within one process + + align:start position:0% +because these are all within one process + + + align:start position:0% +because these are all within one process +um in that if we were to destroy that + + align:start position:0% +um in that if we were to destroy that + + + align:start position:0% +um in that if we were to destroy that +process in this step what the operating + + align:start position:0% +process in this step what the operating + + + align:start position:0% +process in this step what the operating +system would do is to destroy in + + align:start position:0% +system would do is to destroy in + + + align:start position:0% +system would do is to destroy in +addition to destroying the address space + + align:start position:0% +addition to destroying the address space + + + align:start position:0% +addition to destroying the address space +all of the running threads. So we say + + align:start position:0% +all of the running threads. So we say + + + align:start position:0% +all of the running threads. So we say +that these threads that are running + + align:start position:0% +that these threads that are running + + + align:start position:0% +that these threads that are running +within Halo um share fate. + + align:start position:0% +within Halo um share fate. + + + align:start position:0% +within Halo um share fate. +If one of them dies then or if one of + + align:start position:0% +If one of them dies then or if one of + + + align:start position:0% +If one of them dies then or if one of +these threads is uh fails then they're + + align:start position:0% +these threads is uh fails then they're + + + align:start position:0% +these threads is uh fails then they're +all going to if one of these threads + + align:start position:0% +all going to if one of these threads + + + align:start position:0% +all going to if one of these threads +fails or uh crashes or does something + + align:start position:0% +fails or uh crashes or does something + + + align:start position:0% +fails or uh crashes or does something +bad then they're essentially all going + + align:start position:0% +bad then they're essentially all going + + + align:start position:0% +bad then they're essentially all going +to crash or do something bad. If the + + align:start position:0% +to crash or do something bad. If the + + + align:start position:0% +to crash or do something bad. If the +operating system uh kills one it kills + + align:start position:0% +operating system uh kills one it kills + + + align:start position:0% +operating system uh kills one it kills +the process then all these threads are + + align:start position:0% +the process then all these threads are + + + align:start position:0% +the process then all these threads are +going to go away. + + align:start position:0% +going to go away. + + + align:start position:0% +going to go away. +Um + + align:start position:0% + + + + align:start position:0% + +so this is the basic picture of sort of + + align:start position:0% +so this is the basic picture of sort of + + + align:start position:0% +so this is the basic picture of sort of +what what's going on within within a + + align:start position:0% +what what's going on within within a + + + align:start position:0% +what what's going on within within a +computer system. I mean if you stare at + + align:start position:0% +computer system. I mean if you stare at + + + align:start position:0% +computer system. I mean if you stare at +this for a little bit you see that + + align:start position:0% +this for a little bit you see that + + + align:start position:0% +this for a little bit you see that +there's actually sort of a hierarchy of + + align:start position:0% +there's actually sort of a hierarchy of + + + align:start position:0% +there's actually sort of a hierarchy of +threads that are running on any one + + align:start position:0% +threads that are running on any one + + + align:start position:0% +threads that are running on any one +computer system at any one point in + + align:start position:0% +computer system at any one point in + + + align:start position:0% +computer system at any one point in +time. So uh we have these larger uh sort + + align:start position:0% +time. So uh we have these larger uh sort + + + align:start position:0% +time. So uh we have these larger uh sort +of processes that are running and then + + align:start position:0% +of processes that are running and then + + + align:start position:0% +of processes that are running and then +within these processes we have some set + + align:start position:0% +within these processes we have some set + + + align:start position:0% +within these processes we have some set +of threads that's also running right. Um + + align:start position:0% +of threads that's also running right. Um + + + align:start position:0% +of threads that's also running right. Um +and so there's a diagram that's sort of + + align:start position:0% +and so there's a diagram that's sort of + + + align:start position:0% +and so there's a diagram that's sort of +useful to help us to understand this + + align:start position:0% +useful to help us to understand this + + + align:start position:0% +useful to help us to understand this +hierarchy or layering of processes uh or + + align:start position:0% +hierarchy or layering of processes uh or + + + align:start position:0% +hierarchy or layering of processes uh or +threads on a on a computer system. I'm + + align:start position:0% +threads on a on a computer system. I'm + + + align:start position:0% +threads on a on a computer system. I'm +going to show that to you. + + align:start position:0% + + + + align:start position:0% + +Okay. So, if on our computer system, if + + align:start position:0% +Okay. So, if on our computer system, if + + + align:start position:0% +Okay. So, if on our computer system, if +we look at the lowest layer, we have + + align:start position:0% +we look at the lowest layer, we have + + + align:start position:0% +we look at the lowest layer, we have +this, we have our microprocessor down + + align:start position:0% +this, we have our microprocessor down + + + align:start position:0% +this, we have our microprocessor down +here. + + align:start position:0% +here. + + + align:start position:0% +here. +Okay. And this microprocessor + + align:start position:0% +Okay. And this microprocessor + + + align:start position:0% +Okay. And this microprocessor +um what we've seen is that the + + align:start position:0% +um what we've seen is that the + + + align:start position:0% +um what we've seen is that the +microprocessor has sort of uh two things + + align:start position:0% +microprocessor has sort of uh two things + + + align:start position:0% +microprocessor has sort of uh two things +that it can be doing. Either the + + align:start position:0% +that it can be doing. Either the + + + align:start position:0% +that it can be doing. Either the +microprocessor can be executing say some + + align:start position:0% +microprocessor can be executing say some + + + align:start position:0% +microprocessor can be executing say some +user program or the microprocessor can + + align:start position:0% +user program or the microprocessor can + + + align:start position:0% +user program or the microprocessor can +be interrupted and go execute one of + + align:start position:0% +be interrupted and go execute one of + + + align:start position:0% +be interrupted and go execute one of +these interrupt handler uh kinds the + + align:start position:0% +these interrupt handler uh kinds the + + + align:start position:0% +these interrupt handler uh kinds the +these interrupt handler functions. So uh + + align:start position:0% +these interrupt handler functions. So uh + + + align:start position:0% +these interrupt handler functions. So uh +these interrupts are going to do things + + align:start position:0% +these interrupts are going to do things + + + align:start position:0% +these interrupts are going to do things +like it's going to be this timer + + align:start position:0% +like it's going to be this timer + + + align:start position:0% +like it's going to be this timer +interrupt or when some special piece + + align:start position:0% +interrupt or when some special piece + + + align:start position:0% +interrupt or when some special piece +when some IO device say for example the + + align:start position:0% +when some IO device say for example the + + + align:start position:0% +when some IO device say for example the +disk finishes uh performing some IO + + align:start position:0% +disk finishes uh performing some IO + + + align:start position:0% +disk finishes uh performing some IO +operation like reading a block for + + align:start position:0% +operation like reading a block for + + + align:start position:0% +operation like reading a block for +memory then it's going to receive the + + align:start position:0% +memory then it's going to receive the + + + align:start position:0% +memory then it's going to receive the +processor receive an interrupt and the + + align:start position:0% +processor receive an interrupt and the + + + align:start position:0% +processor receive an interrupt and the +processor can do whatever it needs to do + + align:start position:0% +processor can do whatever it needs to do + + + align:start position:0% +processor can do whatever it needs to do +to service that piece of hardware so + + align:start position:0% +to service that piece of hardware so + + + align:start position:0% +to service that piece of hardware so +that uh the hardware can go and for + + align:start position:0% +that uh the hardware can go and for + + + align:start position:0% +that uh the hardware can go and for +example read the next block. So um in a + + align:start position:0% +example read the next block. So um in a + + + align:start position:0% +example read the next block. So um in a +sense you can think of the processor + + align:start position:0% +sense you can think of the processor + + + align:start position:0% +sense you can think of the processor +itself as having two sort of threads + + align:start position:0% +itself as having two sort of threads + + + align:start position:0% +itself as having two sort of threads +that are associated with it. One of them + + align:start position:0% +that are associated with it. One of them + + + align:start position:0% +that are associated with it. One of them +is an interrupt thread and one of them + + align:start position:0% +is an interrupt thread and one of them + + + align:start position:0% +is an interrupt thread and one of them +is the main thread. Now running on top + + align:start position:0% +is the main thread. Now running on top + + + align:start position:0% +is the main thread. Now running on top +of this. So this these + + align:start position:0% +of this. So this these + + + align:start position:0% +of this. So this these +these are sort of the sometimes you can + + align:start position:0% +these are sort of the sometimes you can + + + align:start position:0% +these are sort of the sometimes you can +think of these as being these these are + + align:start position:0% +think of these as being these these are + + + align:start position:0% +think of these as being these these are +threads that are really running within + + align:start position:0% +threads that are really running within + + + align:start position:0% +threads that are really running within +the kernel. But on top of these things + + align:start position:0% +the kernel. But on top of these things + + + align:start position:0% +the kernel. But on top of these things +there's this set of applications + + align:start position:0% +there's this set of applications + + + align:start position:0% +there's this set of applications +like Halo and + + align:start position:0% +like Halo and + + + align:start position:0% +like Halo and +Emacs and these are the kind of user + + align:start position:0% +Emacs and these are the kind of user + + + align:start position:0% +Emacs and these are the kind of user +programs that are all running on the + + align:start position:0% +programs that are all running on the + + + align:start position:0% +programs that are all running on the +system and there may be you know a whole + + align:start position:0% +system and there may be you know a whole + + + align:start position:0% +system and there may be you know a whole +bunch of these. It's not just two, but + + align:start position:0% +bunch of these. It's not just two, but + + + align:start position:0% +bunch of these. It's not just two, but +it's any number of threads that we can + + align:start position:0% +it's any number of threads that we can + + + align:start position:0% +it's any number of threads that we can +multiplex on top of this main thread. + + align:start position:0% +multiplex on top of this main thread. + + + align:start position:0% +multiplex on top of this main thread. +And then + + align:start position:0% +And then + + + align:start position:0% +And then +each one of these may in turn have + + align:start position:0% +each one of these may in turn have + + + align:start position:0% +each one of these may in turn have +subthreads that are running as a part of + + align:start position:0% +subthreads that are running as a part of + + + align:start position:0% +subthreads that are running as a part of +it. So if you think about uh this what + + align:start position:0% +it. So if you think about uh this what + + + align:start position:0% +it. So if you think about uh this what +what's going on in this computer in this + + align:start position:0% +what's going on in this computer in this + + + align:start position:0% +what's going on in this computer in this +system um you can see that at any one + + align:start position:0% +system um you can see that at any one + + + align:start position:0% +system um you can see that at any one +level these two threads don't these + + align:start position:0% +level these two threads don't these + + + align:start position:0% +level these two threads don't these +threads don't really need to know uh + + align:start position:0% +threads don't really need to know uh + + + align:start position:0% +threads don't really need to know uh +anything about the other threads that + + align:start position:0% +anything about the other threads that + + + align:start position:0% +anything about the other threads that +are running at that same level. So for + + align:start position:0% +are running at that same level. So for + + + align:start position:0% +are running at that same level. So for +example, these, you know, within Halo, + + align:start position:0% +example, these, you know, within Halo, + + + align:start position:0% +example, these, you know, within Halo, +these individual subthreads don't really + + align:start position:0% +these individual subthreads don't really + + + align:start position:0% +these individual subthreads don't really +know anything about what the other + + align:start position:0% +know anything about what the other + + + align:start position:0% +know anything about what the other +subthreads are doing. But it is the case + + align:start position:0% +subthreads are doing. But it is the case + + + align:start position:0% +subthreads are doing. But it is the case +that the threads at that the threads at + + align:start position:0% +that the threads at that the threads at + + + align:start position:0% +that the threads at that the threads at +a lower level need to know about the + + align:start position:0% +a lower level need to know about the + + + align:start position:0% +a lower level need to know about the +threads as they're running above them + + align:start position:0% +threads as they're running above them + + + align:start position:0% +threads as they're running above them +because the threads at the lower level + + align:start position:0% +because the threads at the lower level + + + align:start position:0% +because the threads at the lower level +implement this thread scheduling policy. + + align:start position:0% +implement this thread scheduling policy. + + + align:start position:0% +implement this thread scheduling policy. +Right? So it's the Halo program decides + + align:start position:0% +Right? So it's the Halo program decides + + + align:start position:0% +Right? So it's the Halo program decides +which of its sub subthreads to run next. + + align:start position:0% +which of its sub subthreads to run next. + + + align:start position:0% +which of its sub subthreads to run next. +So the Halo program in particular is so + + align:start position:0% +So the Halo program in particular is so + + + align:start position:0% +So the Halo program in particular is so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so the parent thread + + align:start position:0% + + + + align:start position:0% + +implements + + align:start position:0% +implements + + + align:start position:0% +implements +a uh scheduling + + align:start position:0% + + + + align:start position:0% + +a scheduling policy for all of its + + align:start position:0% +a scheduling policy for all of its + + + align:start position:0% +a scheduling policy for all of its +children threads. So Halo has some + + align:start position:0% +children threads. So Halo has some + + + align:start position:0% +children threads. So Halo has some +policy for deciding what thread to run + + align:start position:0% +policy for deciding what thread to run + + + align:start position:0% +policy for deciding what thread to run +next. The operating system has some the + + align:start position:0% +next. The operating system has some the + + + align:start position:0% +next. The operating system has some the +kernel has some policy for deciding + + align:start position:0% +kernel has some policy for deciding + + + align:start position:0% +kernel has some policy for deciding +which of these user level threads to run + + align:start position:0% +which of these user level threads to run + + + align:start position:0% +which of these user level threads to run +next. Um and the parent thread also + + align:start position:0% +next. Um and the parent thread also + + + align:start position:0% +next. Um and the parent thread also +provides some uh switching mechanism. + + align:start position:0% + + + + align:start position:0% + +So we studied two switching mechanisms. + + align:start position:0% +So we studied two switching mechanisms. + + + align:start position:0% +So we studied two switching mechanisms. +Uh today we looked at this notion of + + align:start position:0% +Uh today we looked at this notion of + + + align:start position:0% +Uh today we looked at this notion of +having this uh sort of uh this this + + align:start position:0% +having this uh sort of uh this this + + + align:start position:0% +having this uh sort of uh this this +cooperative switching where process + + align:start position:0% +cooperative switching where process + + + align:start position:0% +cooperative switching where process +where where threads call yield in order + + align:start position:0% +where where threads call yield in order + + + align:start position:0% +where where threads call yield in order +to allow the next thread to run. And we + + align:start position:0% +to allow the next thread to run. And we + + + align:start position:0% +to allow the next thread to run. And we +looked at this notion of uh preemptive + + align:start position:0% +looked at this notion of uh preemptive + + + align:start position:0% +looked at this notion of uh preemptive +scheduling that allows uh that forces + + align:start position:0% +scheduling that allows uh that forces + + + align:start position:0% +scheduling that allows uh that forces +the next thread in the in the schedule + + align:start position:0% +the next thread in the in the schedule + + + align:start position:0% +the next thread in the in the schedule +to run. So if you look at computer + + align:start position:0% +to run. So if you look at computer + + + align:start position:0% +to run. So if you look at computer +systems in fact it's a fairly common + + align:start position:0% +systems in fact it's a fairly common + + + align:start position:0% +systems in fact it's a fairly common +organization to see that there's + + align:start position:0% +organization to see that there's + + + align:start position:0% +organization to see that there's +preemptive scheduling at the kernel + + align:start position:0% +preemptive scheduling at the kernel + + + align:start position:0% +preemptive scheduling at the kernel +level that causes different user level + + align:start position:0% +level that causes different user level + + + align:start position:0% +level that causes different user level +applications to run. But that within a + + align:start position:0% +applications to run. But that within a + + + align:start position:0% +applications to run. But that within a +user level within a user a particular + + align:start position:0% +user level within a user a particular + + + align:start position:0% +user level within a user a particular +user program that program may use + + align:start position:0% +user program that program may use + + + align:start position:0% +user program that program may use +cooperative scheduling. So the + + align:start position:0% +cooperative scheduling. So the + + + align:start position:0% +cooperative scheduling. So the +individual threads of Halo may hand off + + align:start position:0% +individual threads of Halo may hand off + + + align:start position:0% +individual threads of Halo may hand off +control to the next thread only when + + align:start position:0% +control to the next thread only when + + + align:start position:0% +control to the next thread only when +they want to. And this sort of makes + + align:start position:0% +they want to. And this sort of makes + + + align:start position:0% +they want to. And this sort of makes +sense because if I'm a developer of a + + align:start position:0% +sense because if I'm a developer of a + + + align:start position:0% +sense because if I'm a developer of a +program, you know, I may very well trust + + align:start position:0% +program, you know, I may very well trust + + + align:start position:0% +program, you know, I may very well trust +that, you know, the other threads that I + + align:start position:0% +that, you know, the other threads that I + + + align:start position:0% +that, you know, the other threads that I +have running in the program at the same + + align:start position:0% +have running in the program at the same + + + align:start position:0% +have running in the program at the same +time, you know, I know when I want them + + align:start position:0% +time, you know, I know when I want them + + + align:start position:0% +time, you know, I know when I want them +to run. So, um, we can talk about sort + + align:start position:0% +to run. So, um, we can talk about sort + + + align:start position:0% +to run. So, um, we can talk about sort +of different switching mechanisms at + + align:start position:0% +of different switching mechanisms at + + + align:start position:0% +of different switching mechanisms at +different levels of this hierarchy. + + align:start position:0% + + + + align:start position:0% + +Okay. So uh what we've seen up to this + + align:start position:0% +Okay. So uh what we've seen up to this + + + align:start position:0% +Okay. So uh what we've seen up to this +point uh is this + + align:start position:0% +point uh is this + + + align:start position:0% +point uh is this +the sort of basic mechanism that we have + + align:start position:0% +the sort of basic mechanism that we have + + + align:start position:0% +the sort of basic mechanism that we have +for setting up a set of threads that are + + align:start position:0% +for setting up a set of threads that are + + + align:start position:0% +for setting up a set of threads that are +running on a computer system. And what + + align:start position:0% +running on a computer system. And what + + + align:start position:0% +running on a computer system. And what +we uh what we haven't really talked at + + align:start position:0% +we uh what we haven't really talked at + + + align:start position:0% +we uh what we haven't really talked at +all about is how if we we can actually + + align:start position:0% +all about is how if we we can actually + + + align:start position:0% +all about is how if we we can actually +share information between these threads + + align:start position:0% +share information between these threads + + + align:start position:0% +share information between these threads +or coordinate access to some shared + + align:start position:0% +or coordinate access to some shared + + + align:start position:0% +or coordinate access to some shared +resource between these threads. So what + + align:start position:0% +resource between these threads. So what + + + align:start position:0% +resource between these threads. So what +I want to do with the rest of the time + + align:start position:0% +I want to do with the rest of the time + + + align:start position:0% +I want to do with the rest of the time +today is to talk about this notion of + + align:start position:0% +today is to talk about this notion of + + + align:start position:0% +today is to talk about this notion of +coordinating access between threads. Um + + align:start position:0% +coordinating access between threads. Um + + + align:start position:0% +coordinating access between threads. Um +and we're going to talk about + + align:start position:0% +and we're going to talk about + + + align:start position:0% +and we're going to talk about +this in the context of a slightly + + align:start position:0% +this in the context of a slightly + + + align:start position:0% +this in the context of a slightly +different example. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% + + + + align:start position:0% + +let's suppose that I am building a web + + align:start position:0% +let's suppose that I am building a web + + + align:start position:0% +let's suppose that I am building a web +server + + align:start position:0% + + + + align:start position:0% + +and I decide that I want to structure my + + align:start position:0% +and I decide that I want to structure my + + + align:start position:0% +and I decide that I want to structure my +web server as follows. I want to have + + align:start position:0% +web server as follows. I want to have + + + align:start position:0% +web server as follows. I want to have +some + + align:start position:0% + + + + align:start position:0% + +network thread + + align:start position:0% + + + + align:start position:0% + +and I want to have some thread that + + align:start position:0% +and I want to have some thread that + + + align:start position:0% +and I want to have some thread that +services disk requests. + + align:start position:0% +services disk requests. + + + align:start position:0% +services disk requests. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +so the network thread is going to do + + align:start position:0% +so the network thread is going to do + + + align:start position:0% +so the network thread is going to do +things like accept incoming connections + + align:start position:0% +things like accept incoming connections + + + align:start position:0% +things like accept incoming connections +from the clients uh and process those + + align:start position:0% +from the clients uh and process those + + + align:start position:0% +from the clients uh and process those +connections um parse the HTTP requests + + align:start position:0% +connections um parse the HTTP requests + + + align:start position:0% +connections um parse the HTTP requests +and generate the HTML results that we + + align:start position:0% +and generate the HTML results that we + + + align:start position:0% +and generate the HTML results that we +send back to users. And the disk request + + align:start position:0% +send back to users. And the disk request + + + align:start position:0% +send back to users. And the disk request +thread is going to be in charge of doing + + align:start position:0% +thread is going to be in charge of doing + + + align:start position:0% +thread is going to be in charge of doing +these expensive operations where it goes + + align:start position:0% +these expensive operations where it goes + + + align:start position:0% +these expensive operations where it goes +out to disk and reads in some data that + + align:start position:0% +out to disk and reads in some data that + + + align:start position:0% +out to disk and reads in some data that +it may need to assemble uh these HTML + + align:start position:0% +it may need to assemble uh these HTML + + + align:start position:0% +it may need to assemble uh these HTML +pages that we generate. So um if all + + align:start position:0% +pages that we generate. So um if all + + + align:start position:0% +pages that we generate. So um if all +this doesn't so we're you're next uh for + + align:start position:0% +this doesn't so we're you're next uh for + + + align:start position:0% +this doesn't so we're you're next uh for +next restation you're going to read + + align:start position:0% +next restation you're going to read + + + align:start position:0% +next restation you're going to read +about a system called flash which is a + + align:start position:0% +about a system called flash which is a + + + align:start position:0% +about a system called flash which is a +multi-threaded web server. Um and so + + align:start position:0% +multi-threaded web server. Um and so + + + align:start position:0% +multi-threaded web server. Um and so +this should be a little taste of what + + align:start position:0% +this should be a little taste of what + + + align:start position:0% +this should be a little taste of what +you're going to see uh for tomorrow. + + align:start position:0% +you're going to see uh for tomorrow. + + + align:start position:0% +you're going to see uh for tomorrow. +So these two threads are likely to want + + align:start position:0% +So these two threads are likely to want + + + align:start position:0% +So these two threads are likely to want +to communicate with each other through + + align:start position:0% +to communicate with each other through + + + align:start position:0% +to communicate with each other through +some data structure, some queue of + + align:start position:0% +some data structure, some queue of + + + align:start position:0% +some data structure, some queue of +requests. Okay. So or queue queue of + + align:start position:0% +requests. Okay. So or queue queue of + + + align:start position:0% +requests. Okay. So or queue queue of +outstanding information. So uh + + align:start position:0% +outstanding information. So uh + + + align:start position:0% +outstanding information. So uh +suppose that what we're looking at in + + align:start position:0% +suppose that what we're looking at in + + + align:start position:0% +suppose that what we're looking at in +fact in in particular is a queue of disk + + align:start position:0% +fact in in particular is a queue of disk + + + align:start position:0% +fact in in particular is a queue of disk +blocks that are being sent from this is + + align:start position:0% +blocks that are being sent from this is + + + align:start position:0% +blocks that are being sent from this is +a disk request thread from the disk + + align:start position:0% +a disk request thread from the disk + + + align:start position:0% +a disk request thread from the disk +request thread out to the network + + align:start position:0% +request thread out to the network + + + align:start position:0% +request thread out to the network +thread. So whenever a whenever the disk + + align:start position:0% +thread. So whenever a whenever the disk + + + align:start position:0% +thread. So whenever a whenever the disk +finishes reading a block, it adds it + + align:start position:0% +finishes reading a block, it adds it + + + align:start position:0% +finishes reading a block, it adds it +incues a value into this uh into the + + align:start position:0% +incues a value into this uh into the + + + align:start position:0% +incues a value into this uh into the +network thread so that the network + + align:start position:0% +network thread so that the network + + + align:start position:0% +network thread so that the network +thread can then later pull that value + + align:start position:0% +thread can then later pull that value + + + align:start position:0% +thread can then later pull that value +off and deliver it uh out to the user. + + align:start position:0% +off and deliver it uh out to the user. + + + align:start position:0% +off and deliver it uh out to the user. +So in this case, these are two threads + + align:start position:0% +So in this case, these are two threads + + + align:start position:0% +So in this case, these are two threads +that are both running within the same + + align:start position:0% +that are both running within the same + + + align:start position:0% +that are both running within the same +address space within the same web + + align:start position:0% +address space within the same web + + + align:start position:0% +address space within the same web +server. So they both have direct access + + align:start position:0% +server. So they both have direct access + + + align:start position:0% +server. So they both have direct access +to this Q data structure. They can both + + align:start position:0% +to this Q data structure. They can both + + + align:start position:0% +to this Q data structure. They can both +read and write to it um at the same + + align:start position:0% +read and write to it um at the same + + + align:start position:0% +read and write to it um at the same +time. this Q data structure. Think of it + + align:start position:0% +time. this Q data structure. Think of it + + + align:start position:0% +time. this Q data structure. Think of it +as a global variable that's in the + + align:start position:0% +as a global variable that's in the + + + align:start position:0% +as a global variable that's in the +memory of the that's in the ad that's + + align:start position:0% +memory of the that's in the ad that's + + + align:start position:0% +memory of the that's in the ad that's +mapped into the address space and both + + align:start position:0% +mapped into the address space and both + + + align:start position:0% +mapped into the address space and both +threads can access it. + + align:start position:0% +threads can access it. + + + align:start position:0% +threads can access it. +So let's look at what happens uh when + + align:start position:0% +So let's look at what happens uh when + + + align:start position:0% +So let's look at what happens uh when +these two threads let's look at some + + align:start position:0% +these two threads let's look at some + + + align:start position:0% +these two threads let's look at some +pseudo code that shows what might be + + align:start position:0% +pseudo code that shows what might be + + + align:start position:0% +pseudo code that shows what might be +happening inside of these two threads. + + align:start position:0% +happening inside of these two threads. + + + align:start position:0% +happening inside of these two threads. +So um + + align:start position:0% +So um + + + align:start position:0% +So um +suppose within uh this this first this + + align:start position:0% +suppose within uh this this first this + + + align:start position:0% +suppose within uh this this first this +first thread here this network thread um + + align:start position:0% +first thread here this network thread um + + + align:start position:0% +first thread here this network thread um +we have a loop that says while + + align:start position:0% + + + + align:start position:0% + +true uh do the following dq a request + + align:start position:0% +true uh do the following dq a request + + + align:start position:0% +true uh do the following dq a request +call it m + + align:start position:0% +call it m + + + align:start position:0% +call it m +from the thread um and then + + align:start position:0% +from the thread um and then + + + align:start position:0% +from the thread um and then +process sorry dqa uh dq cue a a disk + + align:start position:0% +process sorry dqa uh dq cue a a disk + + + align:start position:0% +process sorry dqa uh dq cue a a disk +block that's in the queue and then go + + align:start position:0% +block that's in the queue and then go + + + align:start position:0% +block that's in the queue and then go +ahead and process that disc q that go + + align:start position:0% +ahead and process that disc q that go + + + align:start position:0% +ahead and process that disc q that go +ahead and process that. And now within + + align:start position:0% +ahead and process that. And now within + + + align:start position:0% +ahead and process that. And now within +the uh within the disk request thread, + + align:start position:0% +the uh within the disk request thread, + + + align:start position:0% +the uh within the disk request thread, +we also have a while loop that just + + align:start position:0% +we also have a while loop that just + + + align:start position:0% +we also have a while loop that just +loops forever. + + align:start position:0% +loops forever. + + + align:start position:0% +loops forever. +Um and what this does is it gets the + + align:start position:0% +Um and what this does is it gets the + + + align:start position:0% +Um and what this does is it gets the +next disk block to send however it does + + align:start position:0% +next disk block to send however it does + + + align:start position:0% +next disk block to send however it does +that goes off and reads the block from + + align:start position:0% +that goes off and reads the block from + + + align:start position:0% +that goes off and reads the block from +disk. uh and then infusees that block + + align:start position:0% + + + + align:start position:0% + +onto the key. Okay. + + align:start position:0% + + + + align:start position:0% + +Uh so if you like you can think of this + + align:start position:0% +Uh so if you like you can think of this + + + align:start position:0% +Uh so if you like you can think of this +as um + + align:start position:0% +as um + + + align:start position:0% +as um +simply you know the the disk request + + align:start position:0% +simply you know the the disk request + + + align:start position:0% +simply you know the the disk request +thread is going to is going to stick + + align:start position:0% +thread is going to is going to stick + + + align:start position:0% +thread is going to is going to stick +some blocks into here and then the + + align:start position:0% +some blocks into here and then the + + + align:start position:0% +some blocks into here and then the +network thread is going to sort of pull + + align:start position:0% +network thread is going to sort of pull + + + align:start position:0% +network thread is going to sort of pull +those pull those blocks off of the top + + align:start position:0% +those pull those blocks off of the top + + + align:start position:0% +those pull those blocks off of the top +of the queue. So if you think about uh + + align:start position:0% +of the queue. So if you think about uh + + + align:start position:0% +of the queue. So if you think about uh +this process running um there's kind of + + align:start position:0% +this process running um there's kind of + + + align:start position:0% +this process running um there's kind of +a problem with the way that I've written + + align:start position:0% +a problem with the way that I've written + + + align:start position:0% +a problem with the way that I've written +this right which is that uh suppose that + + align:start position:0% +this right which is that uh suppose that + + + align:start position:0% +this right which is that uh suppose that +the disk request thread uh that that + + align:start position:0% +the disk request thread uh that that + + + align:start position:0% +the disk request thread uh that that +this disk request thread runs much + + align:start position:0% +this disk request thread runs much + + + align:start position:0% +this disk request thread runs much +faster than the network thread. Suppose + + align:start position:0% +faster than the network thread. Suppose + + + align:start position:0% +faster than the network thread. Suppose +that for every you know one network one + + align:start position:0% +that for every you know one network one + + + align:start position:0% +that for every you know one network one +one uh one block that the network thread + + align:start position:0% +one uh one block that the network thread + + + align:start position:0% +one uh one block that the network thread +is able to pull off and process the disk + + align:start position:0% +is able to pull off and process the disk + + + align:start position:0% +is able to pull off and process the disk +thread can incue two blocks. Okay. Okay, + + align:start position:0% +thread can incue two blocks. Okay. Okay, + + + align:start position:0% +thread can incue two blocks. Okay. Okay, +so if you think about this for a while, + + align:start position:0% +so if you think about this for a while, + + + align:start position:0% +so if you think about this for a while, +if you run the system for a long time, + + align:start position:0% +if you run the system for a long time, + + + align:start position:0% +if you run the system for a long time, +eventually uh you're going to have + + align:start position:0% +eventually uh you're going to have + + + align:start position:0% +eventually uh you're going to have +incued a huge amount of stuff. And + + align:start position:0% +incued a huge amount of stuff. And + + + align:start position:0% +incued a huge amount of stuff. And +typically the way cues are implemented + + align:start position:0% +typically the way cues are implemented + + + align:start position:0% +typically the way cues are implemented +is they're sort of some fixed size. You + + align:start position:0% +is they're sort of some fixed size. You + + + align:start position:0% +is they're sort of some fixed size. You +don't want them to be able to grow to + + align:start position:0% +don't want them to be able to grow to + + + align:start position:0% +don't want them to be able to grow to +fill the whole memory of the processor. + + align:start position:0% +fill the whole memory of the processor. + + + align:start position:0% +fill the whole memory of the processor. +So you limit them to some particular + + align:start position:0% +So you limit them to some particular + + + align:start position:0% +So you limit them to some particular +fixed size. And eventually we're going + + align:start position:0% +fixed size. And eventually we're going + + + align:start position:0% +fixed size. And eventually we're going +to have this problem that the queue is + + align:start position:0% +to have this problem that the queue is + + + align:start position:0% +to have this problem that the queue is +going to fill up. It's going to overflow + + align:start position:0% +going to fill up. It's going to overflow + + + align:start position:0% +going to fill up. It's going to overflow +and we're going to have a disk block + + align:start position:0% +and we're going to have a disk block + + + align:start position:0% +and we're going to have a disk block +that we don't have anything we could do + + align:start position:0% +that we don't have anything we could do + + + align:start position:0% +that we don't have anything we could do +with. We we don't know what to do with + + align:start position:0% +with. We we don't know what to do with + + + align:start position:0% +with. We we don't know what to do with +it, right? So okay, you say that's easy. + + align:start position:0% +it, right? So okay, you say that's easy. + + + align:start position:0% +it, right? So okay, you say that's easy. +There's an easy way to fix this. Why + + align:start position:0% +There's an easy way to fix this. Why + + + align:start position:0% +There's an easy way to fix this. Why +don't we just um you know wait until + + align:start position:0% +don't we just um you know wait until + + + align:start position:0% +don't we just um you know wait until +there's some uh extra space + + align:start position:0% +there's some uh extra space + + + align:start position:0% +there's some uh extra space +here. So we'll test + + align:start position:0% + + + + align:start position:0% + +so we'll introduce a while uh full + + align:start position:0% +so we'll introduce a while uh full + + + align:start position:0% +so we'll introduce a while uh full +statement here that just sort of spins + + align:start position:0% +statement here that just sort of spins + + + align:start position:0% +statement here that just sort of spins +sits in a spin loop and waits until uh + + align:start position:0% +sits in a spin loop and waits until uh + + + align:start position:0% +sits in a spin loop and waits until uh +this full condition is not true. Okay, + + align:start position:0% +this full condition is not true. Okay, + + + align:start position:0% +this full condition is not true. Okay, +so as soon as the full condition is not + + align:start position:0% +so as soon as the full condition is not + + + align:start position:0% +so as soon as the full condition is not +true, we can go ahead and encue the next + + align:start position:0% +true, we can go ahead and encue the next + + + align:start position:0% +true, we can go ahead and encue the next +thing on the queue. And similarly, we're + + align:start position:0% +thing on the queue. And similarly, we're + + + align:start position:0% +thing on the queue. And similarly, we're +going to need to do something over here + + align:start position:0% +going to need to do something over here + + + align:start position:0% +going to need to do something over here +on the process side because we can't + + align:start position:0% +on the process side because we can't + + + align:start position:0% +on the process side because we can't +really dq a message if the queue is + + align:start position:0% +really dq a message if the queue is + + + align:start position:0% +really dq a message if the queue is +empty. So if the processing thread is + + align:start position:0% +empty. So if the processing thread is + + + align:start position:0% +empty. So if the processing thread is +running faster than the in the inquing + + align:start position:0% +running faster than the in the inquing + + + align:start position:0% +running faster than the in the inquing +thread, we're going to be in trouble. So + + align:start position:0% +thread, we're going to be in trouble. So + + + align:start position:0% +thread, we're going to be in trouble. So +uh we're going to also need to introduce + + align:start position:0% +uh we're going to also need to introduce + + + align:start position:0% +uh we're going to also need to introduce +a while loop here that says something + + align:start position:0% +a while loop here that says something + + + align:start position:0% +a while loop here that says something +like while empty. + + align:start position:0% +like while empty. + + + align:start position:0% +like while empty. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So um so this is fine. this uh it seems + + align:start position:0% +So um so this is fine. this uh it seems + + + align:start position:0% +So um so this is fine. this uh it seems +like it fixes our problem. But there's a + + align:start position:0% +like it fixes our problem. But there's a + + + align:start position:0% +like it fixes our problem. But there's a +little bit of a limitation to this + + align:start position:0% +little bit of a limitation to this + + + align:start position:0% +little bit of a limitation to this +approach which is that uh now what you + + align:start position:0% +approach which is that uh now what you + + + align:start position:0% +approach which is that uh now what you +see is suppose these two threads are + + align:start position:0% +see is suppose these two threads are + + + align:start position:0% +see is suppose these two threads are +running and they're being sort of + + align:start position:0% +running and they're being sort of + + + align:start position:0% +running and they're being sort of +scheduled in round robin. They're being + + align:start position:0% +scheduled in round robin. They're being + + + align:start position:0% +scheduled in round robin. They're being +scheduled one after the other. Now this + + align:start position:0% +scheduled one after the other. Now this + + + align:start position:0% +scheduled one after the other. Now this +thread runs and when it runs suppose + + align:start position:0% +thread runs and when it runs suppose + + + align:start position:0% +thread runs and when it runs suppose +that the queue is empty. Suppose the + + align:start position:0% +that the queue is empty. Suppose the + + + align:start position:0% +that the queue is empty. Suppose the +producer hasn't put anything on the + + align:start position:0% +producer hasn't put anything on the + + + align:start position:0% +producer hasn't put anything on the +queue yet. Now when this guy runs it's + + align:start position:0% +queue yet. Now when this guy runs it's + + + align:start position:0% +queue yet. Now when this guy runs it's +going to sit here and for the whole time + + align:start position:0% +going to sit here and for the whole time + + + align:start position:0% +going to sit here and for the whole time +that it's scheduled um it's just going + + align:start position:0% +that it's scheduled um it's just going + + + align:start position:0% +that it's scheduled um it's just going +to check this while loop and see if the + + align:start position:0% +to check this while loop and see if the + + + align:start position:0% +to check this while loop and see if the +thing is empty over and over and over + + align:start position:0% +thing is empty over and over and over + + + align:start position:0% +thing is empty over and over and over +and over and over again. Right? So + + align:start position:0% +and over and over again. Right? So + + + align:start position:0% +and over and over again. Right? So +that's a whole lot of wasted time that + + align:start position:0% +that's a whole lot of wasted time that + + + align:start position:0% +that's a whole lot of wasted time that +the processor could and should have been + + align:start position:0% +the processor could and should have been + + + align:start position:0% +the processor could and should have been +doing something else useful like perhaps + + align:start position:0% +doing something else useful like perhaps + + + align:start position:0% +doing something else useful like perhaps +letting the producer run so that it + + align:start position:0% +letting the producer run so that it + + + align:start position:0% +letting the producer run so that it +could incuse some data. So um in order + + align:start position:0% +could incuse some data. So um in order + + + align:start position:0% +could incuse some data. So um in order +to do this so in order to fix this + + align:start position:0% +to do this so in order to fix this + + + align:start position:0% +to do this so in order to fix this +problem we introduced this notion of + + align:start position:0% +problem we introduced this notion of + + + align:start position:0% +problem we introduced this notion of +sequence coordination operators. Um, and + + align:start position:0% +sequence coordination operators. Um, and + + + align:start position:0% +sequence coordination operators. Um, and +what sequence coordination operators do + + align:start position:0% + + + + align:start position:0% + +is they allow an uh if they they allow a + + align:start position:0% +is they allow an uh if they they allow a + + + align:start position:0% +is they allow an uh if they they allow a +thread to uh declare that it wants to + + align:start position:0% +thread to uh declare that it wants to + + + align:start position:0% +thread to uh declare that it wants to +wait until some condition is true and + + align:start position:0% +wait until some condition is true and + + + align:start position:0% +wait until some condition is true and +they allow other threads to signal that + + align:start position:0% +they allow other threads to signal that + + + align:start position:0% +they allow other threads to signal that +that condition has now been become true + + align:start position:0% +that condition has now been become true + + + align:start position:0% +that condition has now been become true +and uh sort of allow threads that are + + align:start position:0% +and uh sort of allow threads that are + + + align:start position:0% +and uh sort of allow threads that are +waiting for that condition to become + + align:start position:0% +waiting for that condition to become + + + align:start position:0% +waiting for that condition to become +true to run. So we have these two + + align:start position:0% +true to run. So we have these two + + + align:start position:0% +true to run. So we have these two +operations. Wait um on some variable + + align:start position:0% +operations. Wait um on some variable + + + align:start position:0% +operations. Wait um on some variable +until some condition is true um and + + align:start position:0% +until some condition is true um and + + + align:start position:0% +until some condition is true um and +signal + + align:start position:0% +signal + + + align:start position:0% +signal +on that variable. + + align:start position:0% + + + + align:start position:0% + +Okay. So um we're basically out of time + + align:start position:0% +Okay. So um we're basically out of time + + + align:start position:0% +Okay. So um we're basically out of time +now. So what I want to do is I'll come + + align:start position:0% +now. So what I want to do is I'll come + + + align:start position:0% +now. So what I want to do is I'll come +back and I'll finish going through this + + align:start position:0% +back and I'll finish going through this + + + align:start position:0% +back and I'll finish going through this +example uh for the next time. But what + + align:start position:0% +example uh for the next time. But what + + + align:start position:0% +example uh for the next time. But what +you should do is think about suppose you + + align:start position:0% +you should do is think about suppose you + + + align:start position:0% +you should do is think about suppose you +had these sequence coordination + + align:start position:0% +had these sequence coordination + + + align:start position:0% +had these sequence coordination +operators. How could we sort of modify + + align:start position:0% +operators. How could we sort of modify + + + align:start position:0% +operators. How could we sort of modify +these two while loops that we have for + + align:start position:0% +these two while loops that we have for + + + align:start position:0% +these two while loops that we have for +these two operators in order to be able + + align:start position:0% +these two operators in order to be able + + + align:start position:0% +these two operators in order to be able +to take advantage of the fact that uh in + + align:start position:0% +to take advantage of the fact that uh in + + + align:start position:0% +to take advantage of the fact that uh in +order to be able to make this so we + + align:start position:0% +order to be able to make this so we + + + align:start position:0% +order to be able to make this so we +don't sit in this spin loop forever and + + align:start position:0% +don't sit in this spin loop forever and + + + align:start position:0% +don't sit in this spin loop forever and +execute. So um that's it. Today we saw + + align:start position:0% +execute. So um that's it. Today we saw + + + align:start position:0% +execute. So um that's it. Today we saw +how to get these multiple processes to + + align:start position:0% +how to get these multiple processes to + + + align:start position:0% +how to get these multiple processes to +run on one computer. Um and next time + + align:start position:0% +run on one computer. Um and next time + + + align:start position:0% +run on one computer. Um and next time +we'll talk about sort of um making + + align:start position:0% +we'll talk about sort of um making + + + align:start position:0% +we'll talk about sort of um making +computer programs run more efficiently, + + align:start position:0% +computer programs run more efficiently, + + + align:start position:0% +computer programs run more efficiently, +getting good performance out of our out + + align:start position:0% +getting good performance out of our out + + + align:start position:0% +getting good performance out of our out +of this sort of architecture we've + + align:start position:0% +of this sort of architecture we've + + + align:start position:0% +of this sort of architecture we've +sketched. \ No newline at end of file diff --git a/vMaKx9fmJHE.txt b/vMaKx9fmJHE.txt new file mode 100644 index 0000000000000000000000000000000000000000..bcecdc0645a943f1918a8aefafcfc0333f40a298 --- /dev/null +++ b/vMaKx9fmJHE.txt @@ -0,0 +1,15176 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a creative common license. Your support + + align:start position:0% +a creative common license. Your support + + + align:start position:0% +a creative common license. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT + + align:start position:0% +hundreds of MIT courses, visit MIT + + + align:start position:0% +hundreds of MIT courses, visit MIT +OpenCourseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +We're talking about goodness of fit + + align:start position:0% +We're talking about goodness of fit + + + align:start position:0% +We're talking about goodness of fit +tests. Goodness of fit tests are is my + + align:start position:0% +tests. Goodness of fit tests are is my + + + align:start position:0% +tests. Goodness of fit tests are is my +does my data come from a particular + + align:start position:0% +does my data come from a particular + + + align:start position:0% +does my data come from a particular +distribution? And why we would want to + + align:start position:0% +distribution? And why we would want to + + + align:start position:0% +distribution? And why we would want to +know this? Well, maybe we're interested + + align:start position:0% +know this? Well, maybe we're interested + + + align:start position:0% +know this? Well, maybe we're interested +in, for example, uh, you know, knowing + + align:start position:0% +in, for example, uh, you know, knowing + + + align:start position:0% +in, for example, uh, you know, knowing +if the, uh, zodiac signs of the Fortune + + align:start position:0% +if the, uh, zodiac signs of the Fortune + + + align:start position:0% +if the, uh, zodiac signs of the Fortune +500 CEOs are uniformly distributed or + + align:start position:0% +500 CEOs are uniformly distributed or + + + align:start position:0% +500 CEOs are uniformly distributed or +maybe we actually have slightly more uh, + + align:start position:0% +maybe we actually have slightly more uh, + + + align:start position:0% +maybe we actually have slightly more uh, +slightly deeper, uh, endeavors uh, such + + align:start position:0% +slightly deeper, uh, endeavors uh, such + + + align:start position:0% +slightly deeper, uh, endeavors uh, such +as understanding if you can actually + + align:start position:0% +as understanding if you can actually + + + align:start position:0% +as understanding if you can actually +apply the t test by testing normality of + + align:start position:0% +apply the t test by testing normality of + + + align:start position:0% +apply the t test by testing normality of +your sample. All right, so we saw that + + align:start position:0% +your sample. All right, so we saw that + + + align:start position:0% +your sample. All right, so we saw that +there's the main result is the main + + align:start position:0% +there's the main result is the main + + + align:start position:0% +there's the main result is the main +standard test for this is called the + + align:start position:0% +standard test for this is called the + + + align:start position:0% +standard test for this is called the +korov smearinoff test that people uh, + + align:start position:0% +korov smearinoff test that people uh, + + + align:start position:0% +korov smearinoff test that people uh, +use quite a bit. is probably one of the + + align:start position:0% +use quite a bit. is probably one of the + + + align:start position:0% +use quite a bit. is probably one of the +most used test out there and uh there's + + align:start position:0% +most used test out there and uh there's + + + align:start position:0% +most used test out there and uh there's +other uh versions of it uh that I + + align:start position:0% +other uh versions of it uh that I + + + align:start position:0% +other uh versions of it uh that I +mentioned passing by there's the crime + + align:start position:0% +mentioned passing by there's the crime + + + align:start position:0% +mentioned passing by there's the crime +van mises and there's the Anderson + + align:start position:0% +van mises and there's the Anderson + + + align:start position:0% +van mises and there's the Anderson +darling test now how would you pick one + + align:start position:0% +darling test now how would you pick one + + + align:start position:0% +darling test now how would you pick one +of such tests well you know there always + + align:start position:0% +of such tests well you know there always + + + align:start position:0% +of such tests well you know there always +are going to h they're always going to + + align:start position:0% +are going to h they're always going to + + + align:start position:0% +are going to h they're always going to +have their advantages and disadvantages + + align:start position:0% +have their advantages and disadvantages + + + align:start position:0% +have their advantages and disadvantages +and uh komograph mirnoff is definitely + + align:start position:0% +and uh komograph mirnoff is definitely + + + align:start position:0% +and uh komograph mirnoff is definitely +the most uh uh widely used because well + + align:start position:0% +the most uh uh widely used because well + + + align:start position:0% +the most uh uh widely used because well +I guess because it's a natural notion of + + align:start position:0% +I guess because it's a natural notion of + + + align:start position:0% +I guess because it's a natural notion of +distance between function just look for + + align:start position:0% +distance between function just look for + + + align:start position:0% +distance between function just look for +each point how far they can be and you + + align:start position:0% +each point how far they can be and you + + + align:start position:0% +each point how far they can be and you +just look at the farthest they can be + + align:start position:0% +just look at the farthest they can be + + + align:start position:0% +just look at the farthest they can be +everywhere. Now you know crean mses + + align:start position:0% +everywhere. Now you know crean mses + + + align:start position:0% +everywhere. Now you know crean mses +involves l2 distance. So if you're not + + align:start position:0% +involves l2 distance. So if you're not + + + align:start position:0% +involves l2 distance. So if you're not +used to you know hbert spaces or uh + + align:start position:0% +used to you know hbert spaces or uh + + + align:start position:0% +used to you know hbert spaces or uh +notions of you know ukleian spaces at + + align:start position:0% +notions of you know ukleian spaces at + + + align:start position:0% +notions of you know ukleian spaces at +least it's a little more complicated and + + align:start position:0% +least it's a little more complicated and + + + align:start position:0% +least it's a little more complicated and +then dling is definitely even more + + align:start position:0% +then dling is definitely even more + + + align:start position:0% +then dling is definitely even more +complicated. Now each of this test is + + align:start position:0% +complicated. Now each of this test is + + + align:start position:0% +complicated. Now each of this test is +going to be more powerful against other + + align:start position:0% +going to be more powerful against other + + + align:start position:0% +going to be more powerful against other +alternatives. So unless you can really + + align:start position:0% +alternatives. So unless you can really + + + align:start position:0% +alternatives. So unless you can really +guess which alternative you're expecting + + align:start position:0% +guess which alternative you're expecting + + + align:start position:0% +guess which alternative you're expecting +to see, which you probably don't because + + align:start position:0% +to see, which you probably don't because + + + align:start position:0% +to see, which you probably don't because +again you're in a case where you want to + + align:start position:0% +again you're in a case where you want to + + + align:start position:0% +again you're in a case where you want to +typically declare H0 to be the correct + + align:start position:0% +typically declare H0 to be the correct + + + align:start position:0% +typically declare H0 to be the correct +one, then it's really, you know, a + + align:start position:0% +one, then it's really, you know, a + + + align:start position:0% +one, then it's really, you know, a +matter of tossing a coin. Um maybe you + + align:start position:0% +matter of tossing a coin. Um maybe you + + + align:start position:0% +matter of tossing a coin. Um maybe you +can run all three of them and just sleep + + align:start position:0% +can run all three of them and just sleep + + + align:start position:0% +can run all three of them and just sleep +with better at night because all three + + align:start position:0% +with better at night because all three + + + align:start position:0% +with better at night because all three +of them have failed to reject for + + align:start position:0% +of them have failed to reject for + + + align:start position:0% +of them have failed to reject for +example. All right. So as I mentioned + + align:start position:0% +example. All right. So as I mentioned + + + align:start position:0% +example. All right. So as I mentioned +one of the maybe primary goals to test + + align:start position:0% +one of the maybe primary goals to test + + + align:start position:0% +one of the maybe primary goals to test +uh goodness of fit is to is to be able + + align:start position:0% +uh goodness of fit is to is to be able + + + align:start position:0% +uh goodness of fit is to is to be able +to check whether we can apply students + + align:start position:0% +to check whether we can apply students + + + align:start position:0% +to check whether we can apply students +uh test right and if the student + + align:start position:0% +uh test right and if the student + + + align:start position:0% +uh test right and if the student +distribution is actually a valid + + align:start position:0% +distribution is actually a valid + + + align:start position:0% +distribution is actually a valid +distributions and for that we need to + + align:start position:0% +distributions and for that we need to + + + align:start position:0% +distributions and for that we need to +have normally distributed data now as I + + align:start position:0% +have normally distributed data now as I + + + align:start position:0% +have normally distributed data now as I +said several times normally distributed + + align:start position:0% +said several times normally distributed + + + align:start position:0% +said several times normally distributed +is not a specific distribution it's a + + align:start position:0% +is not a specific distribution it's a + + + align:start position:0% +is not a specific distribution it's a +family of distribution that's indexed by + + align:start position:0% +family of distribution that's indexed by + + + align:start position:0% +family of distribution that's indexed by +means and variances and the way I would + + align:start position:0% +means and variances and the way I would + + + align:start position:0% +means and variances and the way I would +want to test if a distribution is + + align:start position:0% +want to test if a distribution is + + + align:start position:0% +want to test if a distribution is +normally distributed is well I would + + align:start position:0% +normally distributed is well I would + + + align:start position:0% +normally distributed is well I would +just look at the most natural normal + + align:start position:0% +just look at the most natural normal + + + align:start position:0% +just look at the most natural normal +distribution or Gaussian distribution + + align:start position:0% +distribution or Gaussian distribution + + + align:start position:0% +distribution or Gaussian distribution +that my data could follow. That means + + align:start position:0% +that my data could follow. That means + + + align:start position:0% +that my data could follow. That means +that's the Gaussian distribution that + + align:start position:0% +that's the Gaussian distribution that + + + align:start position:0% +that's the Gaussian distribution that +has the same mean as my data and the + + align:start position:0% +has the same mean as my data and the + + + align:start position:0% +has the same mean as my data and the +same empirical variance as my data. All + + align:start position:0% +same empirical variance as my data. All + + + align:start position:0% +same empirical variance as my data. All +right. And so I'm going to be given some + + align:start position:0% +right. And so I'm going to be given some + + + align:start position:0% +right. And so I'm going to be given some +points X1 XN + + align:start position:0% +points X1 XN + + + align:start position:0% +points X1 XN +and I'm going to be asking are those + + align:start position:0% +and I'm going to be asking are those + + + align:start position:0% +and I'm going to be asking are those +Gaussian? + + align:start position:0% + + + + align:start position:0% + +That means this is equivalent to say are + + align:start position:0% +That means this is equivalent to say are + + + align:start position:0% +That means this is equivalent to say are +they n mu sigma square for some mu sigma + + align:start position:0% +they n mu sigma square for some mu sigma + + + align:start position:0% +they n mu sigma square for some mu sigma +squ. + + align:start position:0% +squ. + + + align:start position:0% +squ. +And of course the natural choice is to + + align:start position:0% +And of course the natural choice is to + + + align:start position:0% +And of course the natural choice is to +take mu hat to be uh mu to be equal to + + align:start position:0% +take mu hat to be uh mu to be equal to + + + align:start position:0% +take mu hat to be uh mu to be equal to +muhat which is xn bar and sigma squar to + + align:start position:0% +muhat which is xn bar and sigma squar to + + + align:start position:0% +muhat which is xn bar and sigma squar to +be sigma squar hat to be uh uh um well + + align:start position:0% +be sigma squar hat to be uh uh um well + + + align:start position:0% +be sigma squar hat to be uh uh um well +sn hat sn what we wrote sn which is 1 / + + align:start position:0% +sn hat sn what we wrote sn which is 1 / + + + align:start position:0% +sn hat sn what we wrote sn which is 1 / +n sum from i= 1 to n of x i minus xn bar + + align:start position:0% +n sum from i= 1 to n of x i minus xn bar + + + align:start position:0% +n sum from i= 1 to n of x i minus xn bar +2. Okay, so this is definitely the + + align:start position:0% +2. Okay, so this is definitely the + + + align:start position:0% +2. Okay, so this is definitely the +natural one you would want to test and + + align:start position:0% +natural one you would want to test and + + + align:start position:0% +natural one you would want to test and +maybe you could actually just close your + + align:start position:0% +maybe you could actually just close your + + + align:start position:0% +maybe you could actually just close your +eyes and just stuff that in a uh a uh + + align:start position:0% +eyes and just stuff that in a uh a uh + + + align:start position:0% +eyes and just stuff that in a uh a uh +chromograph smear enough test. Okay, so + + align:start position:0% +chromograph smear enough test. Okay, so + + + align:start position:0% +chromograph smear enough test. Okay, so +here there's a few things that don't + + align:start position:0% +here there's a few things that don't + + + align:start position:0% +here there's a few things that don't +work. The first one is that the donskers + + align:start position:0% +work. The first one is that the donskers + + + align:start position:0% +work. The first one is that the donskers +theorem does not work anymore, right? + + align:start position:0% +theorem does not work anymore, right? + + + align:start position:0% +theorem does not work anymore, right? +Donsker theorem was the one that told us + + align:start position:0% +Donsker theorem was the one that told us + + + align:start position:0% +Donsker theorem was the one that told us +that you know properly normalized this + + align:start position:0% +that you know properly normalized this + + + align:start position:0% +that you know properly normalized this +thing would actually converge to the + + align:start position:0% +thing would actually converge to the + + + align:start position:0% +thing would actually converge to the +supreum of a brownian bridge which is + + align:start position:0% +supreum of a brownian bridge which is + + + align:start position:0% +supreum of a brownian bridge which is +not true. So that's one problem. But + + align:start position:0% +not true. So that's one problem. But + + + align:start position:0% +not true. So that's one problem. But +there's actually an even bigger problem + + align:start position:0% +there's actually an even bigger problem + + + align:start position:0% +there's actually an even bigger problem +is that this distribution we will check + + align:start position:0% +is that this distribution we will check + + + align:start position:0% +is that this distribution we will check +in a second actually does not is pivotal + + align:start position:0% +in a second actually does not is pivotal + + + align:start position:0% +in a second actually does not is pivotal +itself. Right? This this this statistic + + align:start position:0% +itself. Right? This this this statistic + + + align:start position:0% +itself. Right? This this this statistic +is pivotal. It does not have a + + align:start position:0% +is pivotal. It does not have a + + + align:start position:0% +is pivotal. It does not have a +distribution that depends on the known + + align:start position:0% +distribution that depends on the known + + + align:start position:0% +distribution that depends on the known +parameters which is sort of nice at + + align:start position:0% +parameters which is sort of nice at + + + align:start position:0% +parameters which is sort of nice at +least under the null. However, the + + align:start position:0% +least under the null. However, the + + + align:start position:0% +least under the null. However, the +distribution is not the same as the one + + align:start position:0% +distribution is not the same as the one + + + align:start position:0% +distribution is not the same as the one +that had fix mu and sigma. The fact that + + align:start position:0% +that had fix mu and sigma. The fact that + + + align:start position:0% +that had fix mu and sigma. The fact that +they come from some random variables uh + + align:start position:0% +they come from some random variables uh + + + align:start position:0% +they come from some random variables uh +is actually distorting the distribution + + align:start position:0% +is actually distorting the distribution + + + align:start position:0% +is actually distorting the distribution +itself. And in particular the quentiles + + align:start position:0% +itself. And in particular the quentiles + + + align:start position:0% +itself. And in particular the quentiles +are going to be distorted and we hinted + + align:start position:0% +are going to be distorted and we hinted + + + align:start position:0% +are going to be distorted and we hinted +at it that last time. So one of the + + align:start position:0% +at it that last time. So one of the + + + align:start position:0% +at it that last time. So one of the +thing I need to tell you though is that + + align:start position:0% +thing I need to tell you though is that + + + align:start position:0% +thing I need to tell you though is that +this thing actually uh so I know there's + + align:start position:0% +this thing actually uh so I know there's + + + align:start position:0% +this thing actually uh so I know there's +uh some there's oh yeah that's where uh + + align:start position:0% +uh some there's oh yeah that's where uh + + + align:start position:0% +uh some there's oh yeah that's where uh +that's where there's a word missing. So + + align:start position:0% +that's where there's a word missing. So + + + align:start position:0% +that's where there's a word missing. So +we compute the quentiles for this test + + align:start position:0% +we compute the quentiles for this test + + + align:start position:0% +we compute the quentiles for this test +statistic. And so what I need to promise + + align:start position:0% +statistic. And so what I need to promise + + + align:start position:0% +statistic. And so what I need to promise +to you is that this quentiles + + align:start position:0% +to you is that this quentiles + + + align:start position:0% +to you is that this quentiles +do not depend on any unknown parameter. + + align:start position:0% +do not depend on any unknown parameter. + + + align:start position:0% +do not depend on any unknown parameter. +Right? I mean it's not clear + + align:start position:0% +Right? I mean it's not clear + + + align:start position:0% +Right? I mean it's not clear +this uh uh um right so I want to test + + align:start position:0% +this uh uh um right so I want to test + + + align:start position:0% +this uh uh um right so I want to test +whether my data has some Gaussian + + align:start position:0% +whether my data has some Gaussian + + + align:start position:0% +whether my data has some Gaussian +distribution so under the null all I + + align:start position:0% +distribution so under the null all I + + + align:start position:0% +distribution so under the null all I +know is that my my x i are gaussian with + + align:start position:0% +know is that my my x i are gaussian with + + + align:start position:0% +know is that my my x i are gaussian with +some mean mu and some variance sigma + + align:start position:0% +some mean mu and some variance sigma + + + align:start position:0% +some mean mu and some variance sigma +which I don't know so it could be the + + align:start position:0% +which I don't know so it could be the + + + align:start position:0% +which I don't know so it could be the +case that when I try to understand the + + align:start position:0% +case that when I try to understand the + + + align:start position:0% +case that when I try to understand the +distribution of this quantity under the + + align:start position:0% +distribution of this quantity under the + + + align:start position:0% +distribution of this quantity under the +null it depends on mu and sigma which I + + align:start position:0% +null it depends on mu and sigma which I + + + align:start position:0% +null it depends on mu and sigma which I +don't know + + align:start position:0% +don't know + + + align:start position:0% +don't know +so we need to check that this is the + + align:start position:0% +so we need to check that this is the + + + align:start position:0% +so we need to check that this is the +case and What's actually our uh uh uh + + align:start position:0% +case and What's actually our uh uh uh + + + align:start position:0% +case and What's actually our uh uh uh +redemption here is actually going to be + + align:start position:0% +redemption here is actually going to be + + + align:start position:0% +redemption here is actually going to be +the um uh supreum. The supreum is going + + align:start position:0% +the um uh supreum. The supreum is going + + + align:start position:0% +the um uh supreum. The supreum is going +to basically allow us to say soup out mu + + align:start position:0% +to basically allow us to say soup out mu + + + align:start position:0% +to basically allow us to say soup out mu +and and and sigma square. So let's check + + align:start position:0% +and and and sigma square. So let's check + + + align:start position:0% +and and and sigma square. So let's check +that. Right? So what I'm interested in + + align:start position:0% +that. Right? So what I'm interested in + + + align:start position:0% +that. Right? So what I'm interested in +is this quantity supreum over t and r + + align:start position:0% +is this quantity supreum over t and r + + + align:start position:0% +is this quantity supreum over t and r +of the difference between fn of t and uh + + align:start position:0% +of the difference between fn of t and uh + + + align:start position:0% +of the difference between fn of t and uh +what I write five mu hat sigma squar of + + align:start position:0% +what I write five mu hat sigma squar of + + + align:start position:0% +what I write five mu hat sigma squar of +t. So phi mu hat + + align:start position:0% +t. So phi mu hat + + + align:start position:0% +t. So phi mu hat +sigma hat squared sorry sigma hat + + align:start position:0% +sigma hat squared sorry sigma hat + + + align:start position:0% +sigma hat squared sorry sigma hat +squared is the cdf + + align:start position:0% +squared is the cdf + + + align:start position:0% +squared is the cdf +of some galsian with mean mu hat and + + align:start position:0% +of some galsian with mean mu hat and + + + align:start position:0% +of some galsian with mean mu hat and +variance sigma hat squared and so in + + align:start position:0% +variance sigma hat squared and so in + + + align:start position:0% +variance sigma hat squared and so in +particular this thing here + + align:start position:0% +particular this thing here + + + align:start position:0% +particular this thing here +fi hat of mu hat sorry fi hat of mu hat + + align:start position:0% +fi hat of mu hat sorry fi hat of mu hat + + + align:start position:0% +fi hat of mu hat sorry fi hat of mu hat +sigma hat squar + + align:start position:0% +sigma hat squar + + + align:start position:0% +sigma hat squar +of t is the probability that some x is + + align:start position:0% +of t is the probability that some x is + + + align:start position:0% +of t is the probability that some x is +less than t where x follows some n mu + + align:start position:0% +less than t where x follows some n mu + + + align:start position:0% +less than t where x follows some n mu +hat sigma hat squ. So what it means is + + align:start position:0% +hat sigma hat squ. So what it means is + + + align:start position:0% +hat sigma hat squ. So what it means is +that by just the translation and scaling + + align:start position:0% +that by just the translation and scaling + + + align:start position:0% +that by just the translation and scaling +trick that we typically do for galsian + + align:start position:0% +trick that we typically do for galsian + + + align:start position:0% +trick that we typically do for galsian +to turn it into some standard gaussian + + align:start position:0% +to turn it into some standard gaussian + + + align:start position:0% +to turn it into some standard gaussian +that implies that there exists some z + + align:start position:0% +that implies that there exists some z + + + align:start position:0% +that implies that there exists some z +which is standard Gaussian this time. So + + align:start position:0% +which is standard Gaussian this time. So + + + align:start position:0% +which is standard Gaussian this time. So +mean zero and variance one such that X + + align:start position:0% +mean zero and variance one such that X + + + align:start position:0% +mean zero and variance one such that X +is equal to sigma hat X sorry uh Z + + align:start position:0% +is equal to sigma hat X sorry uh Z + + + align:start position:0% +is equal to sigma hat X sorry uh Z +plus mu hat agreed that's that's + + align:start position:0% +plus mu hat agreed that's that's + + + align:start position:0% +plus mu hat agreed that's that's +basically saying that X has some uh uh + + align:start position:0% +basically saying that X has some uh uh + + + align:start position:0% +basically saying that X has some uh uh +Gaussian with mean mu and variance sigma + + align:start position:0% +Gaussian with mean mu and variance sigma + + + align:start position:0% +Gaussian with mean mu and variance sigma +square and I'm not going to say the hats + + align:start position:0% +square and I'm not going to say the hats + + + align:start position:0% +square and I'm not going to say the hats +every single times okay + + align:start position:0% +every single times okay + + + align:start position:0% +every single times okay +so + + align:start position:0% +so + + + align:start position:0% +so +okay so that's what it means so in + + align:start position:0% +okay so that's what it means so in + + + align:start position:0% +okay so that's what it means so in +particular uh maybe I shouldn't use uh x + + align:start position:0% +particular uh maybe I shouldn't use uh x + + + align:start position:0% +particular uh maybe I shouldn't use uh x +here because x is going to be my actual + + align:start position:0% +here because x is going to be my actual + + + align:start position:0% +here because x is going to be my actual +ual data. So let me write y. + + align:start position:0% + + + + align:start position:0% + +Okay. So now what is the what is this + + align:start position:0% +Okay. So now what is the what is this + + + align:start position:0% +Okay. So now what is the what is this +guy here? It's basically uh so phi hat. + + align:start position:0% +guy here? It's basically uh so phi hat. + + + align:start position:0% +guy here? It's basically uh so phi hat. +So this implies that phi mu hat sigma + + align:start position:0% +So this implies that phi mu hat sigma + + + align:start position:0% +So this implies that phi mu hat sigma +hat squar of t is equal to the + + align:start position:0% +hat squar of t is equal to the + + + align:start position:0% +hat squar of t is equal to the +probability that sigma hat z + mu hat is + + align:start position:0% +probability that sigma hat z + mu hat is + + + align:start position:0% +probability that sigma hat z + mu hat is +less than t which is equal to the + + align:start position:0% +less than t which is equal to the + + + align:start position:0% +less than t which is equal to the +probability that z is less than t minus + + align:start position:0% +probability that z is less than t minus + + + align:start position:0% +probability that z is less than t minus +mu hat divided by sigma hat. + + align:start position:0% +mu hat divided by sigma hat. + + + align:start position:0% +mu hat divided by sigma hat. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +But now when Z is a standard normal, + + align:start position:0% +But now when Z is a standard normal, + + + align:start position:0% +But now when Z is a standard normal, +this is really just the cumulative + + align:start position:0% +this is really just the cumulative + + + align:start position:0% +this is really just the cumulative +distribution function of a standard + + align:start position:0% +distribution function of a standard + + + align:start position:0% +distribution function of a standard +Gaussian but evaluated at a point which + + align:start position:0% +Gaussian but evaluated at a point which + + + align:start position:0% +Gaussian but evaluated at a point which +is not t but t minus mu hat divided by + + align:start position:0% +is not t but t minus mu hat divided by + + + align:start position:0% +is not t but t minus mu hat divided by +sigma hat. All right. So in particular + + align:start position:0% +sigma hat. All right. So in particular + + + align:start position:0% +sigma hat. All right. So in particular +what I know so from this what I get well + + align:start position:0% +what I know so from this what I get well + + + align:start position:0% +what I know so from this what I get well +maybe I'll remove that it's going to be + + align:start position:0% +maybe I'll remove that it's going to be + + + align:start position:0% +maybe I'll remove that it's going to be +annoying. I know that phi mu hat sigma + + align:start position:0% +annoying. I know that phi mu hat sigma + + + align:start position:0% +annoying. I know that phi mu hat sigma +hat squared + + align:start position:0% +hat squared + + + align:start position:0% +hat squared +sorry ph mu hat sigma hat squar of t is + + align:start position:0% +sorry ph mu hat sigma hat squar of t is + + + align:start position:0% +sorry ph mu hat sigma hat squar of t is +simply phi of say 01 + + align:start position:0% +simply phi of say 01 + + + align:start position:0% +simply phi of say 01 +and that's just a notation usually we + + align:start position:0% +and that's just a notation usually we + + + align:start position:0% +and that's just a notation usually we +don't put those but uh here it's more + + align:start position:0% +don't put those but uh here it's more + + + align:start position:0% +don't put those but uh here it's more +convenient so it's f 01 of t minus mu + + align:start position:0% +convenient so it's f 01 of t minus mu + + + align:start position:0% +convenient so it's f 01 of t minus mu +hat divided by sigma hat + + align:start position:0% +hat divided by sigma hat + + + align:start position:0% +hat divided by sigma hat +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that's just something you can quickly + + align:start position:0% +that's just something you can quickly + + + align:start position:0% +that's just something you can quickly +check. Uh there's this nice way of + + align:start position:0% +check. Uh there's this nice way of + + + align:start position:0% +check. Uh there's this nice way of +writing the cumulative distribution + + align:start position:0% +writing the cumulative distribution + + + align:start position:0% +writing the cumulative distribution +function for any mean and any uh + + align:start position:0% +function for any mean and any uh + + + align:start position:0% +function for any mean and any uh +variance in terms of the cumulative + + align:start position:0% +variance in terms of the cumulative + + + align:start position:0% +variance in terms of the cumulative +distribution function with mean zero and + + align:start position:0% +distribution function with mean zero and + + + align:start position:0% +distribution function with mean zero and +variance one. All right, not too + + align:start position:0% +variance one. All right, not too + + + align:start position:0% +variance one. All right, not too +complicated. All right. So now what I'm + + align:start position:0% +complicated. All right. So now what I'm + + + align:start position:0% +complicated. All right. So now what I'm +going to say is that okay I have this + + align:start position:0% +going to say is that okay I have this + + + align:start position:0% +going to say is that okay I have this +soup here. So what I can write is that + + align:start position:0% +soup here. So what I can write is that + + + align:start position:0% +soup here. So what I can write is that +this thing here is equal to the soup + + align:start position:0% +this thing here is equal to the soup + + + align:start position:0% +this thing here is equal to the soup +over t in r of 1 / n. Let me write what + + align:start position:0% +over t in r of 1 / n. Let me write what + + + align:start position:0% +over t in r of 1 / n. Let me write what +fn is. Sum from i= 1 to n of the + + align:start position:0% +fn is. Sum from i= 1 to n of the + + + align:start position:0% +fn is. Sum from i= 1 to n of the +indicator that x i is less than t minus + + align:start position:0% +indicator that x i is less than t minus + + + align:start position:0% +indicator that x i is less than t minus + + align:start position:0% + + + align:start position:0% +of t minus mu hat / sigma hat. + + align:start position:0% + + + + align:start position:0% + +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +I actually want to make a change of + + align:start position:0% +I actually want to make a change of + + + align:start position:0% +I actually want to make a change of +variable so that this thing I'm going to + + align:start position:0% +variable so that this thing I'm going to + + + align:start position:0% +variable so that this thing I'm going to +call mu u, sorry. Okay. And so I'm going + + align:start position:0% +call mu u, sorry. Okay. And so I'm going + + + align:start position:0% +call mu u, sorry. Okay. And so I'm going +to make my life easier and I'm going to + + align:start position:0% +to make my life easier and I'm going to + + + align:start position:0% +to make my life easier and I'm going to +make it appear here. And so I'm just + + align:start position:0% +make it appear here. And so I'm just + + + align:start position:0% +make it appear here. And so I'm just +going to replace this by indicator that + + align:start position:0% +going to replace this by indicator that + + + align:start position:0% +going to replace this by indicator that +x i minus mu hat / sigma hat less than t + + align:start position:0% +x i minus mu hat / sigma hat less than t + + + align:start position:0% +x i minus mu hat / sigma hat less than t +minus mu hat / sigma hat which is sort + + align:start position:0% +minus mu hat / sigma hat which is sort + + + align:start position:0% +minus mu hat / sigma hat which is sort +of useless at this point. I'm just + + align:start position:0% +of useless at this point. I'm just + + + align:start position:0% +of useless at this point. I'm just +making my formula more complicated. But + + align:start position:0% +making my formula more complicated. But + + + align:start position:0% +making my formula more complicated. But +now I see something here that shows up + + align:start position:0% +now I see something here that shows up + + + align:start position:0% +now I see something here that shows up +and I will call it u. And this is + + align:start position:0% +and I will call it u. And this is + + + align:start position:0% +and I will call it u. And this is +another u. + + align:start position:0% +another u. + + + align:start position:0% +another u. +Okay. So now what it means is that + + align:start position:0% +Okay. So now what it means is that + + + align:start position:0% +Okay. So now what it means is that +souping over t when t ranges from + + align:start position:0% +souping over t when t ranges from + + + align:start position:0% +souping over t when t ranges from +negative infinity to plus infinity then + + align:start position:0% +negative infinity to plus infinity then + + + align:start position:0% +negative infinity to plus infinity then +new ranges from negative infinity to + + align:start position:0% +new ranges from negative infinity to + + + align:start position:0% +new ranges from negative infinity to +plus infinity. Right? + + align:start position:0% +plus infinity. Right? + + + align:start position:0% +plus infinity. Right? +So this soup I can actually write this + + align:start position:0% +So this soup I can actually write this + + + align:start position:0% +So this soup I can actually write this +soup in t. I can write as a soup + + align:start position:0% +soup in t. I can write as a soup + + + align:start position:0% +soup in t. I can write as a soup +in u. + + align:start position:0% + + + + align:start position:0% + +So it's indicator that x i minus mu hat + + align:start position:0% +So it's indicator that x i minus mu hat + + + align:start position:0% +So it's indicator that x i minus mu hat +/ sigma hat is less than u minus 5 01 + + align:start position:0% +/ sigma hat is less than u minus 5 01 + + + align:start position:0% +/ sigma hat is less than u minus 5 01 +of u. + + align:start position:0% +of u. + + + align:start position:0% +of u. +Now let's pause for one second. Let's + + align:start position:0% +Now let's pause for one second. Let's + + + align:start position:0% +Now let's pause for one second. Let's +see where we're going. What we're trying + + align:start position:0% +see where we're going. What we're trying + + + align:start position:0% +see where we're going. What we're trying +to show that this thing does not depend + + align:start position:0% +to show that this thing does not depend + + + align:start position:0% +to show that this thing does not depend +on the unknown parameters say mu and + + align:start position:0% +on the unknown parameters say mu and + + + align:start position:0% +on the unknown parameters say mu and +sigma which are the mean and the + + align:start position:0% +sigma which are the mean and the + + + align:start position:0% +sigma which are the mean and the +variance of x under the null. + + align:start position:0% +variance of x under the null. + + + align:start position:0% +variance of x under the null. +To do that we basically need to make + + align:start position:0% +To do that we basically need to make + + + align:start position:0% +To do that we basically need to make +only quantities that are sort of + + align:start position:0% +only quantities that are sort of + + + align:start position:0% +only quantities that are sort of +invariant under these values. So I try + + align:start position:0% +invariant under these values. So I try + + + align:start position:0% +invariant under these values. So I try +to make this thing invariant under + + align:start position:0% +to make this thing invariant under + + + align:start position:0% +to make this thing invariant under +anything. It's just really something + + align:start position:0% +anything. It's just really something + + + align:start position:0% +anything. It's just really something +that depends on nothing. It's the CDF. + + align:start position:0% +that depends on nothing. It's the CDF. + + + align:start position:0% +that depends on nothing. It's the CDF. +It doesn't depend of sigma hat and mu + + align:start position:0% +It doesn't depend of sigma hat and mu + + + align:start position:0% +It doesn't depend of sigma hat and mu +hat anymore. But sigma hat and muhat + + align:start position:0% +hat anymore. But sigma hat and muhat + + + align:start position:0% +hat anymore. But sigma hat and muhat +will depend on mu and sigma, right? I + + align:start position:0% +will depend on mu and sigma, right? I + + + align:start position:0% +will depend on mu and sigma, right? I +mean they're actually good estimators of + + align:start position:0% +mean they're actually good estimators of + + + align:start position:0% +mean they're actually good estimators of +those guys. So they should be pretty + + align:start position:0% +those guys. So they should be pretty + + + align:start position:0% +those guys. So they should be pretty +close to them. And so I need to make + + align:start position:0% +close to them. And so I need to make + + + align:start position:0% +close to them. And so I need to make +sure that I'm not actually doing + + align:start position:0% +sure that I'm not actually doing + + + align:start position:0% +sure that I'm not actually doing +anything wrong here. So the key thing + + align:start position:0% +anything wrong here. So the key thing + + + align:start position:0% +anything wrong here. So the key thing +here is going to be to observe that 1 / + + align:start position:0% +here is going to be to observe that 1 / + + + align:start position:0% +here is going to be to observe that 1 / +n sum from i= 1 to n of indicator of x i + + align:start position:0% +n sum from i= 1 to n of indicator of x i + + + align:start position:0% +n sum from i= 1 to n of indicator of x i +minus mu hat / sigma hat less than u + + align:start position:0% +minus mu hat / sigma hat less than u + + + align:start position:0% +minus mu hat / sigma hat less than u +which is the first term that I have in + + align:start position:0% +which is the first term that I have in + + + align:start position:0% +which is the first term that I have in +this uh absolute value. + + align:start position:0% +this uh absolute value. + + + align:start position:0% +this uh absolute value. +Well this is what well this is uh equal + + align:start position:0% +Well this is what well this is uh equal + + + align:start position:0% +Well this is what well this is uh equal +to 1 / n sum from i= 1 to n of indicator + + align:start position:0% +to 1 / n sum from i= 1 to n of indicator + + + align:start position:0% +to 1 / n sum from i= 1 to n of indicator +that well now under the null + + align:start position:0% + + + + align:start position:0% + +which is that x follows n mu sigma squar + + align:start position:0% +which is that x follows n mu sigma squar + + + align:start position:0% +which is that x follows n mu sigma squar +for some mu and sigma squ that are + + align:start position:0% +for some mu and sigma squ that are + + + align:start position:0% +for some mu and sigma squ that are +unknown but they are here they exist I + + align:start position:0% +unknown but they are here they exist I + + + align:start position:0% +unknown but they are here they exist I +just don't know what they are then x i + + align:start position:0% +just don't know what they are then x i + + + align:start position:0% +just don't know what they are then x i +minus mu can be written as sigma z i + + + align:start position:0% +minus mu can be written as sigma z i + + + + align:start position:0% +minus mu can be written as sigma z i + +mu - muhat divided by sigma hat + + align:start position:0% +mu - muhat divided by sigma hat + + + align:start position:0% +mu - muhat divided by sigma hat +where z + + align:start position:0% +where z + + + align:start position:0% +where z +is equal to x - mu mu divided by sigma, + + align:start position:0% +is equal to x - mu mu divided by sigma, + + + align:start position:0% +is equal to x - mu mu divided by sigma, +right? That's just the same trick uh + + align:start position:0% +right? That's just the same trick uh + + + align:start position:0% +right? That's just the same trick uh +that I wrote here. Okay, everybody + + align:start position:0% +that I wrote here. Okay, everybody + + + align:start position:0% +that I wrote here. Okay, everybody +agrees? I just standardize + + align:start position:0% +agrees? I just standardize + + + align:start position:0% +agrees? I just standardize +uh sorry z yeah so zi is x i minus mui + + align:start position:0% +uh sorry z yeah so zi is x i minus mui + + + align:start position:0% +uh sorry z yeah so zi is x i minus mui +minus mu divided by sigma. All right, + + align:start position:0% +minus mu divided by sigma. All right, + + + align:start position:0% +minus mu divided by sigma. All right, +just the standardization. So now once I + + align:start position:0% +just the standardization. So now once I + + + align:start position:0% +just the standardization. So now once I +write this I can actually divide + + align:start position:0% +write this I can actually divide + + + align:start position:0% +write this I can actually divide +everybody by sigma, + + align:start position:0% + + + + align:start position:0% + +right? I just divided on top here and at + + align:start position:0% +right? I just divided on top here and at + + + align:start position:0% +right? I just divided on top here and at +the bottom here. + + align:start position:0% +the bottom here. + + + align:start position:0% +the bottom here. +So now what I need to check is that the + + align:start position:0% +So now what I need to check is that the + + + align:start position:0% +So now what I need to check is that the +distribution of this guy + + align:start position:0% +distribution of this guy + + + align:start position:0% +distribution of this guy +does not depend on mu or sigma. That's + + align:start position:0% +does not depend on mu or sigma. That's + + + align:start position:0% +does not depend on mu or sigma. That's +what I claim. What is the distribution + + align:start position:0% +what I claim. What is the distribution + + + align:start position:0% +what I claim. What is the distribution +of this indicator? + + align:start position:0% + + + + align:start position:0% + +It's a Bernoly, right? + + align:start position:0% +It's a Bernoly, right? + + + align:start position:0% +It's a Bernoly, right? +And so if I want to understand its + + align:start position:0% +And so if I want to understand its + + + align:start position:0% +And so if I want to understand its +distribution, all I need to do is to + + align:start position:0% +distribution, all I need to do is to + + + align:start position:0% +distribution, all I need to do is to +compute its expectation which is just + + align:start position:0% +compute its expectation which is just + + + align:start position:0% +compute its expectation which is just +the probability that this thing happens. + + align:start position:0% +the probability that this thing happens. + + + align:start position:0% +the probability that this thing happens. +But the probability that this thing + + align:start position:0% +But the probability that this thing + + + align:start position:0% +But the probability that this thing +happens is actually not depending on mu + + align:start position:0% +happens is actually not depending on mu + + + align:start position:0% +happens is actually not depending on mu +and sigma. And the reason is that mu + + align:start position:0% +and sigma. And the reason is that mu + + + align:start position:0% +and sigma. And the reason is that mu +is what? Well, it's xar sorry uh + + align:start position:0% + + + + align:start position:0% + +yeah so mu hat sorry is xn bar. + + align:start position:0% +yeah so mu hat sorry is xn bar. + + + align:start position:0% +yeah so mu hat sorry is xn bar. +So mu hat minus mu + + align:start position:0% +So mu hat minus mu + + + align:start position:0% +So mu hat minus mu +which under the null follows n mu sigma + + align:start position:0% +which under the null follows n mu sigma + + + align:start position:0% +which under the null follows n mu sigma +square overn right that's the property + + align:start position:0% +square overn right that's the property + + + align:start position:0% +square overn right that's the property +of the average so when I do mu hat minus + + align:start position:0% +of the average so when I do mu hat minus + + + align:start position:0% +of the average so when I do mu hat minus +mu divided by sigma this thing is what + + align:start position:0% +mu divided by sigma this thing is what + + + align:start position:0% +mu divided by sigma this thing is what +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +it's still a normal it's a linear + + align:start position:0% +it's still a normal it's a linear + + + align:start position:0% +it's still a normal it's a linear +transformation of a normal what are the + + align:start position:0% +transformation of a normal what are the + + + align:start position:0% +transformation of a normal what are the +parameters + + align:start position:0% + + + + align:start position:0% + +yeah 01 overn + + align:start position:0% + + + + align:start position:0% + +But this does not depend + + align:start position:0% + + + + align:start position:0% + +on mu or sigma. Right? + + align:start position:0% +on mu or sigma. Right? + + + align:start position:0% +on mu or sigma. Right? +Now I need to check that this guy does + + align:start position:0% +Now I need to check that this guy does + + + align:start position:0% +Now I need to check that this guy does +not depend on mu or sigma. + + align:start position:0% +not depend on mu or sigma. + + + align:start position:0% +not depend on mu or sigma. +What is the distribution of sigma hat + + align:start position:0% +What is the distribution of sigma hat + + + align:start position:0% +What is the distribution of sigma hat +minus over sigma? + + align:start position:0% + + + + align:start position:0% + +square. Yeah, it is a k square. So this + + align:start position:0% +square. Yeah, it is a k square. So this + + + align:start position:0% +square. Yeah, it is a k square. So this +is actually sorry sigma hat squ divided + + align:start position:0% +is actually sorry sigma hat squ divided + + + align:start position:0% +is actually sorry sigma hat squ divided +by sigma squ is a k^ 2 with n minus one + + align:start position:0% +by sigma squ is a k^ 2 with n minus one + + + align:start position:0% +by sigma squ is a k^ 2 with n minus one +degrees of freedom + + align:start position:0% +degrees of freedom + + + align:start position:0% +degrees of freedom +does not depend on your sigma. + + align:start position:0% + + + + align:start position:0% + +Uh yeah thank you. So this is actually + + align:start position:0% +Uh yeah thank you. So this is actually + + + align:start position:0% +Uh yeah thank you. So this is actually +divided by n. So maybe this guy let's + + align:start position:0% +divided by n. So maybe this guy let's + + + align:start position:0% +divided by n. So maybe this guy let's +write it like that. This is the proper + + align:start position:0% +write it like that. This is the proper + + + align:start position:0% +write it like that. This is the proper +way of writing it. Thank you. + + align:start position:0% + + + + align:start position:0% + +Right. So I have those two things. + + align:start position:0% +Right. So I have those two things. + + + align:start position:0% +Right. So I have those two things. +Neither of them depends on mu or sigma. + + align:start position:0% +Neither of them depends on mu or sigma. + + + align:start position:0% +Neither of them depends on mu or sigma. +I have those two those two things. + + align:start position:0% +I have those two those two things. + + + align:start position:0% +I have those two those two things. +There's just one more thing to check. + + align:start position:0% +There's just one more thing to check. + + + align:start position:0% +There's just one more thing to check. +What is it + + align:start position:0% + + + + align:start position:0% + +that they're independent, right? Because + + align:start position:0% +that they're independent, right? Because + + + align:start position:0% +that they're independent, right? Because +the dependence in mu and sigma could be + + align:start position:0% +the dependence in mu and sigma could be + + + align:start position:0% +the dependence in mu and sigma could be +hidden in the coariance. It could be the + + align:start position:0% +hidden in the coariance. It could be the + + + align:start position:0% +hidden in the coariance. It could be the +case that the marginal distribution of + + align:start position:0% +case that the marginal distribution of + + + align:start position:0% +case that the marginal distribution of +mu does not depend on mu or sigma. That + + align:start position:0% +mu does not depend on mu or sigma. That + + + align:start position:0% +mu does not depend on mu or sigma. That +the marginal distribution of sigma of mu + + align:start position:0% +the marginal distribution of sigma of mu + + + align:start position:0% +the marginal distribution of sigma of mu +hat does not depend on mu. The marginal + + align:start position:0% +hat does not depend on mu. The marginal + + + align:start position:0% +hat does not depend on mu. The marginal +distribution of sigma hat does not + + align:start position:0% +distribution of sigma hat does not + + + align:start position:0% +distribution of sigma hat does not +depend on mu or sigma. But their + + align:start position:0% +depend on mu or sigma. But their + + + align:start position:0% +depend on mu or sigma. But their +correlation could depend on mu and + + align:start position:0% +correlation could depend on mu and + + + align:start position:0% +correlation could depend on mu and +sigma. But we also have that if I look + + align:start position:0% +sigma. But we also have that if I look + + + align:start position:0% +sigma. But we also have that if I look +at uh the so if I look at uh uh um + + align:start position:0% +at uh the so if I look at uh uh um + + + align:start position:0% +at uh the so if I look at uh uh um +so since + + align:start position:0% +so since + + + align:start position:0% +so since +mu hat is independent of sigma hat it + + align:start position:0% +mu hat is independent of sigma hat it + + + align:start position:0% +mu hat is independent of sigma hat it +means that the joint distribution + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% +of + + + align:start position:0% +of +mu hats + + align:start position:0% + + + + align:start position:0% + +divided by sigma n sigma hat divided by + + align:start position:0% +divided by sigma n sigma hat divided by + + + align:start position:0% +divided by sigma n sigma hat divided by +sigma does not depend + + align:start position:0% + + + + align:start position:0% + +on blah blah blah on mu and sigma okay + + align:start position:0% + + + + align:start position:0% + +agreed + + align:start position:0% +agreed + + + align:start position:0% +agreed +it's not in the individual ones and It's + + align:start position:0% +it's not in the individual ones and It's + + + align:start position:0% +it's not in the individual ones and It's +not in their the way they interact with + + align:start position:0% +not in their the way they interact with + + + align:start position:0% +not in their the way they interact with +each other. It's nowhere. + + align:start position:0% + + + + align:start position:0% + +Yeah. Coherence theorem, right? So + + align:start position:0% +Yeah. Coherence theorem, right? So + + + align:start position:0% +Yeah. Coherence theorem, right? So +that's something we've been using over + + align:start position:0% +that's something we've been using over + + + align:start position:0% +that's something we've been using over +and again. That's all under the null. If + + align:start position:0% +and again. That's all under the null. If + + + align:start position:0% +and again. That's all under the null. If +my data is not Gaussian, nothing of the + + align:start position:0% +my data is not Gaussian, nothing of the + + + align:start position:0% +my data is not Gaussian, nothing of the +nothing actually holds. + + align:start position:0% +nothing actually holds. + + + align:start position:0% +nothing actually holds. +I just use the fact that under the null, + + align:start position:0% +I just use the fact that under the null, + + + align:start position:0% +I just use the fact that under the null, +I'm Gaussian for some mean mu and varian + + align:start position:0% +I'm Gaussian for some mean mu and varian + + + align:start position:0% +I'm Gaussian for some mean mu and varian +sigma square. But that's all I care + + align:start position:0% +sigma square. But that's all I care + + + align:start position:0% +sigma square. But that's all I care +about when I'm designing a test. I only + + align:start position:0% +about when I'm designing a test. I only + + + align:start position:0% +about when I'm designing a test. I only +care about the the distribution and the + + align:start position:0% +care about the the distribution and the + + + align:start position:0% +care about the the distribution and the +null at least to control the type one + + align:start position:0% +null at least to control the type one + + + align:start position:0% +null at least to control the type one +error. Uh then to control the type two + + align:start position:0% +error. Uh then to control the type two + + + align:start position:0% +error. Uh then to control the type two +error uh then you know I cross my + + align:start position:0% +error uh then you know I cross my + + + align:start position:0% +error uh then you know I cross my +fingers pretty hard. + + align:start position:0% +fingers pretty hard. + + + align:start position:0% +fingers pretty hard. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So um + + align:start position:0% +So um + + + align:start position:0% +So um +now this basically implies what's + + align:start position:0% +now this basically implies what's + + + align:start position:0% +now this basically implies what's +written on the board that this + + align:start position:0% +written on the board that this + + + align:start position:0% +written on the board that this +distribution this uh uh test statistic + + align:start position:0% +distribution this uh uh test statistic + + + align:start position:0% +distribution this uh uh test statistic +does not depend on any unknown + + align:start position:0% +does not depend on any unknown + + + align:start position:0% +does not depend on any unknown +parameters. It's just something that's + + align:start position:0% +parameters. It's just something that's + + + align:start position:0% +parameters. It's just something that's +pivotal. In particular, I could go at + + align:start position:0% +pivotal. In particular, I could go at + + + align:start position:0% +pivotal. In particular, I could go at +the back of a book and check if there's + + align:start position:0% +the back of a book and check if there's + + + align:start position:0% +the back of a book and check if there's +a table for the quentiles of the things. + + align:start position:0% +a table for the quentiles of the things. + + + align:start position:0% +a table for the quentiles of the things. +And indeed, there are. This is uh uh the + + align:start position:0% +And indeed, there are. This is uh uh the + + + align:start position:0% +And indeed, there are. This is uh uh the +table that you see. So, actually, this + + align:start position:0% +table that you see. So, actually, this + + + align:start position:0% +table that you see. So, actually, this +is not even in a book. This is in Ly + + align:start position:0% +is not even in a book. This is in Ly + + + align:start position:0% +is not even in a book. This is in Ly +Forest uh originals uh paper uh 1967, + + align:start position:0% +Forest uh originals uh paper uh 1967, + + + align:start position:0% +Forest uh originals uh paper uh 1967, +as you can tell from the typewriting. + + align:start position:0% +as you can tell from the typewriting. + + + align:start position:0% +as you can tell from the typewriting. +And uh and uh you know he actually you + + align:start position:0% +And uh and uh you know he actually you + + + align:start position:0% +And uh and uh you know he actually you +know probably was rolling some dice from + + align:start position:0% +know probably was rolling some dice from + + + align:start position:0% +know probably was rolling some dice from +his office back in the day and uh was + + align:start position:0% +his office back in the day and uh was + + + align:start position:0% +his office back in the day and uh was +checking that this was uh you know he + + align:start position:0% +checking that this was uh you know he + + + align:start position:0% +checking that this was uh you know he +simulated and this is how he computed + + align:start position:0% +simulated and this is how he computed + + + align:start position:0% +simulated and this is how he computed +those numbers. And here you also have + + align:start position:0% +those numbers. And here you also have + + + align:start position:0% +those numbers. And here you also have +some li limiting distribution which is + + align:start position:0% +some li limiting distribution which is + + + align:start position:0% +some li limiting distribution which is +not the soup of a brown motion over 01 + + align:start position:0% +not the soup of a brown motion over 01 + + + align:start position:0% +not the soup of a brown motion over 01 +uh uh of sorry of a brown bridge over 01 + + align:start position:0% +uh uh of sorry of a brown bridge over 01 + + + align:start position:0% +uh uh of sorry of a brown bridge over 01 +which is the one that you would see for + + align:start position:0% +which is the one that you would see for + + + align:start position:0% +which is the one that you would see for +the uh komograph smeirnoff test but it's + + align:start position:0% +the uh komograph smeirnoff test but it's + + + align:start position:0% +the uh komograph smeirnoff test but it's +something that's slightly different and + + align:start position:0% +something that's slightly different and + + + align:start position:0% +something that's slightly different and +uh as I said this numbers are actually + + align:start position:0% +uh as I said this numbers are actually + + + align:start position:0% +uh as I said this numbers are actually +typically much smaller than the numbers + + align:start position:0% +typically much smaller than the numbers + + + align:start position:0% +typically much smaller than the numbers +you would get right remember we got + + align:start position:0% +you would get right remember we got + + + align:start position:0% +you would get right remember we got +something that was about 0.5 I think or + + align:start position:0% +something that was about 0.5 I think or + + + align:start position:0% +something that was about 0.5 I think or +maybe 0.41 41 for the uh komograph + + align:start position:0% +maybe 0.41 41 for the uh komograph + + + align:start position:0% +maybe 0.41 41 for the uh komograph +mirnoff test at the same entrance which + + align:start position:0% +mirnoff test at the same entrance which + + + align:start position:0% +mirnoff test at the same entrance which +means that using komograph liforce test + + align:start position:0% +means that using komograph liforce test + + + align:start position:0% +means that using komograph liforce test +is going to be harder for you not to + + align:start position:0% +is going to be harder for you not to + + + align:start position:0% +is going to be harder for you not to +reject with the same data. It might be + + align:start position:0% +reject with the same data. It might be + + + align:start position:0% +reject with the same data. It might be +the case that in one case you reject and + + align:start position:0% +the case that in one case you reject and + + + align:start position:0% +the case that in one case you reject and +in the other one you fail to reject. But + + align:start position:0% +in the other one you fail to reject. But + + + align:start position:0% +in the other one you fail to reject. But +the ordering is always that if you fail + + align:start position:0% +the ordering is always that if you fail + + + align:start position:0% +the ordering is always that if you fail +to reject with komograph lily force you + + align:start position:0% +to reject with komograph lily force you + + + align:start position:0% +to reject with komograph lily force you +will fail to reject uh with komograph + + align:start position:0% +will fail to reject uh with komograph + + + align:start position:0% +will fail to reject uh with komograph +smeirnoff + + align:start position:0% +smeirnoff + + + align:start position:0% +smeirnoff +right there's always one. So that's why + + align:start position:0% +right there's always one. So that's why + + + align:start position:0% +right there's always one. So that's why +people tend to close their eyes and + + align:start position:0% +people tend to close their eyes and + + + align:start position:0% +people tend to close their eyes and +prefer komograph smeirnoff because it + + align:start position:0% +prefer komograph smeirnoff because it + + + align:start position:0% +prefer komograph smeirnoff because it +just makes their life easier. + + align:start position:0% +just makes their life easier. + + + align:start position:0% +just makes their life easier. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So uh this is called komograph lily + + align:start position:0% +So uh this is called komograph lily + + + align:start position:0% +So uh this is called komograph lily +force. I think there's actually an E + + align:start position:0% +force. I think there's actually an E + + + align:start position:0% +force. I think there's actually an E +here. + + align:start position:0% +here. + + + align:start position:0% +here. +Uh, sorry, an I before the E. + + align:start position:0% +Uh, sorry, an I before the E. + + + align:start position:0% +Uh, sorry, an I before the E. +Uh, + + align:start position:0% +Uh, + + + align:start position:0% +Uh, +doesn't matter too much. + + align:start position:0% +doesn't matter too much. + + + align:start position:0% +doesn't matter too much. +Okay. Are there any questions? Yes. + + align:start position:0% + + + + align:start position:0% + +Yeah. So, so the fact that it's actually + + align:start position:0% +Yeah. So, so the fact that it's actually + + + align:start position:0% +Yeah. So, so the fact that it's actually +a different distribution is that um + + align:start position:0% +a different distribution is that um + + + align:start position:0% +a different distribution is that um +here, so if I actually knew what mu and + + align:start position:0% +here, so if I actually knew what mu and + + + align:start position:0% +here, so if I actually knew what mu and +sigma were, I would do exactly the same + + align:start position:0% +sigma were, I would do exactly the same + + + align:start position:0% +sigma were, I would do exactly the same +thing. But here, rather than having this + + align:start position:0% +thing. But here, rather than having this + + + align:start position:0% +thing. But here, rather than having this +average with mu and sigma, I would just + + align:start position:0% +average with mu and sigma, I would just + + + align:start position:0% +average with mu and sigma, I would just +have the average with mu hat and sigma + + align:start position:0% +have the average with mu hat and sigma + + + align:start position:0% +have the average with mu hat and sigma +hat, I would just have the average with + + align:start position:0% +hat, I would just have the average with + + + align:start position:0% +hat, I would just have the average with +mu and sigma. Okay. So what it means is + + align:start position:0% +mu and sigma. Okay. So what it means is + + + align:start position:0% +mu and sigma. Okay. So what it means is +that the key thing is that what I would + + align:start position:0% +that the key thing is that what I would + + + align:start position:0% +that the key thing is that what I would +compare is the one overn sum of some + + align:start position:0% +compare is the one overn sum of some + + + align:start position:0% +compare is the one overn sum of some +Bernalies with parameter and the + + align:start position:0% +Bernalies with parameter and the + + + align:start position:0% +Bernalies with parameter and the +parameter here would be the probability + + align:start position:0% +parameter here would be the probability + + + align:start position:0% +parameter here would be the probability +that mu x i minus mu over sigma is less + + align:start position:0% +that mu x i minus mu over sigma is less + + + align:start position:0% +that mu x i minus mu over sigma is less +than u which is just the probability + + align:start position:0% +than u which is just the probability + + + align:start position:0% +than u which is just the probability +that fi uh sorry it's a bernly with + + align:start position:0% +that fi uh sorry it's a bernly with + + + align:start position:0% +that fi uh sorry it's a bernly with +probability f of t. Well let's rewrite + + align:start position:0% +probability f of t. Well let's rewrite + + + align:start position:0% +probability f of t. Well let's rewrite +that what it is + + align:start position:0% + + + + align:start position:0% + +right. So that's minus uh + + align:start position:0% + + + + align:start position:0% + +501 of t. + + align:start position:0% +501 of t. + + + align:start position:0% +501 of t. +Okay. So that's for the ks test + + align:start position:0% +Okay. So that's for the ks test + + + align:start position:0% +Okay. So that's for the ks test +and then I soup over t. Right? That's + + align:start position:0% +and then I soup over t. Right? That's + + + align:start position:0% +and then I soup over t. Right? That's +what I would have had because this is + + align:start position:0% +what I would have had because this is + + + align:start position:0% +what I would have had because this is +actually exactly the right thing here. I + + align:start position:0% +actually exactly the right thing here. I + + + align:start position:0% +actually exactly the right thing here. I +would remove the true mean. I would + + align:start position:0% +would remove the true mean. I would + + + align:start position:0% +would remove the true mean. I would +divide by the true standard deviation. + + align:start position:0% +divide by the true standard deviation. + + + align:start position:0% +divide by the true standard deviation. +So that would actually end up being a + + align:start position:0% +So that would actually end up being a + + + align:start position:0% +So that would actually end up being a +standard Gaussian. And that's why I'm + + align:start position:0% +standard Gaussian. And that's why I'm + + + align:start position:0% +standard Gaussian. And that's why I'm +allowed to use 501 here. Agreed. And + + align:start position:0% +allowed to use 501 here. Agreed. And + + + align:start position:0% +allowed to use 501 here. Agreed. And +these are Burnleys because they're just + + align:start position:0% +these are Burnleys because they're just + + + align:start position:0% +these are Burnleys because they're just +indicators. What happens in the uh + + align:start position:0% +indicators. What happens in the uh + + + align:start position:0% +indicators. What happens in the uh +Komogra Ley force test? + + align:start position:0% +Komogra Ley force test? + + + align:start position:0% +Komogra Ley force test? +Well, here the Burnley, the only thing + + align:start position:0% +Well, here the Burnley, the only thing + + + align:start position:0% +Well, here the Burnley, the only thing +that's going to change is this guy, + + align:start position:0% +that's going to change is this guy, + + + align:start position:0% +that's going to change is this guy, +right? They still have a Bernal. It's + + align:start position:0% +right? They still have a Bernal. It's + + + align:start position:0% +right? They still have a Bernal. It's +just that the parameters of the Bernley + + align:start position:0% +just that the parameters of the Bernley + + + align:start position:0% +just that the parameters of the Bernley +are weird. the the parameters of the + + align:start position:0% +are weird. the the parameters of the + + + align:start position:0% +are weird. the the parameters of the +Bernal looks like it's uh it becomes the + + align:start position:0% +Bernal looks like it's uh it becomes the + + + align:start position:0% +Bernal looks like it's uh it becomes the +probability that some uh n01 + + align:start position:0% + + + + align:start position:0% + +plus + + align:start position:0% +plus + + + align:start position:0% +plus +some uh n01 overn + + align:start position:0% + + + + align:start position:0% + +right divided by + + align:start position:0% +right divided by + + + align:start position:0% +right divided by +some uh square root of k^ 2 n -1 / n + + align:start position:0% +some uh square root of k^ 2 n -1 / n + + + align:start position:0% +some uh square root of k^ 2 n -1 / n +is less than t + + align:start position:0% +is less than t + + + align:start position:0% +is less than t +and uh those things are independent but + + align:start position:0% +and uh those things are independent but + + + align:start position:0% +and uh those things are independent but +those guys are not necessarily + + align:start position:0% +those guys are not necessarily + + + align:start position:0% +those guys are not necessarily +independent right and so what why is + + align:start position:0% +independent right and so what why is + + + align:start position:0% +independent right and so what why is +this probably changing well because this + + align:start position:0% +this probably changing well because this + + + align:start position:0% +this probably changing well because this +denominator is actually fluctuating a + + align:start position:0% +denominator is actually fluctuating a + + + align:start position:0% +denominator is actually fluctuating a +lot so that actually makes this + + align:start position:0% +lot so that actually makes this + + + align:start position:0% +lot so that actually makes this +probability different and so that's + + align:start position:0% +probability different and so that's + + + align:start position:0% +probability different and so that's +basically where it comes from right so + + align:start position:0% +basically where it comes from right so + + + align:start position:0% +basically where it comes from right so +you could probably convince yourself + + align:start position:0% +you could probably convince yourself + + + align:start position:0% +you could probably convince yourself +very quickly that uh this only makes + + align:start position:0% +very quickly that uh this only makes + + + align:start position:0% +very quickly that uh this only makes +those guys closer + + align:start position:0% +those guys closer + + + align:start position:0% +those guys closer +And um + + align:start position:0% + + + + align:start position:0% + +why does it make those guys closer? + + align:start position:0% +why does it make those guys closer? + + + align:start position:0% +why does it make those guys closer? +No, sorry. It makes those guys farther + + align:start position:0% +No, sorry. It makes those guys farther + + + align:start position:0% +No, sorry. It makes those guys farther +right and it makes those guys farther + + align:start position:0% +right and it makes those guys farther + + + align:start position:0% +right and it makes those guys farther +for a very clear reason is that this the + + align:start position:0% +for a very clear reason is that this the + + + align:start position:0% +for a very clear reason is that this the +expectation of this Bernal is exactly + + align:start position:0% +expectation of this Bernal is exactly + + + align:start position:0% +expectation of this Bernal is exactly +that guy here. It's all I think it's + + align:start position:0% +that guy here. It's all I think it's + + + align:start position:0% +that guy here. It's all I think it's +going to be true as well that the + + align:start position:0% +going to be true as well that the + + + align:start position:0% +going to be true as well that the +expectation of this Bernal is going to + + align:start position:0% +expectation of this Bernal is going to + + + align:start position:0% +expectation of this Bernal is going to +be that guy. But the fluctuations are + + align:start position:0% +be that guy. But the fluctuations are + + + align:start position:0% +be that guy. But the fluctuations are +going to be much bigger than just if I + + align:start position:0% +going to be much bigger than just if I + + + align:start position:0% +going to be much bigger than just if I +had the Bernly because the first thing I + + align:start position:0% +had the Bernly because the first thing I + + + align:start position:0% +had the Bernly because the first thing I +do is I have a random parameter for my + + align:start position:0% +do is I have a random parameter for my + + + align:start position:0% +do is I have a random parameter for my +Bernly and then I flip the Bernly. So + + align:start position:0% +Bernly and then I flip the Bernly. So + + + align:start position:0% +Bernly and then I flip the Bernly. So +the fluctuations are going to be bigger + + align:start position:0% +the fluctuations are going to be bigger + + + align:start position:0% +the fluctuations are going to be bigger +than a Bernie and so when I take the + + align:start position:0% +than a Bernie and so when I take the + + + align:start position:0% +than a Bernie and so when I take the +soup I'm going to have to pay them. So + + align:start position:0% +soup I'm going to have to pay them. So + + + align:start position:0% +soup I'm going to have to pay them. So +it makes things farther apart which + + align:start position:0% +it makes things farther apart which + + + align:start position:0% +it makes things farther apart which +makes it more likely for you to reject. + + align:start position:0% +makes it more likely for you to reject. + + + align:start position:0% +makes it more likely for you to reject. +Yeah. + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% + + + + align:start position:0% + +It means that lily force is harder not + + align:start position:0% +It means that lily force is harder not + + + align:start position:0% +It means that lily force is harder not +to reject. Yes. Because we reject when + + align:start position:0% +to reject. Yes. Because we reject when + + + align:start position:0% +to reject. Yes. Because we reject when +we're larger than the number. So the + + align:start position:0% +we're larger than the number. So the + + + align:start position:0% +we're larger than the number. So the +number being smaller we're with the same + + align:start position:0% +number being smaller we're with the same + + + align:start position:0% +number being smaller we're with the same +data we might be right. So basically it + + align:start position:0% +data we might be right. So basically it + + + align:start position:0% +data we might be right. So basically it +looks like this. uh what we run. + + align:start position:0% + + + + align:start position:0% + +So here we have the distribution for the + + align:start position:0% +So here we have the distribution for the + + + align:start position:0% +So here we have the distribution for the +uh so let's say this is the density + + align:start position:0% +uh so let's say this is the density + + + align:start position:0% +uh so let's say this is the density +for uh KS + + align:start position:0% + + + + align:start position:0% + +and then we have the density for uh L uh + + align:start position:0% +and then we have the density for uh L uh + + + align:start position:0% +and then we have the density for uh L uh +come lily force KL okay and what the + + align:start position:0% +come lily force KL okay and what the + + + align:start position:0% +come lily force KL okay and what the +density of KL looks like it looks like + + align:start position:0% +density of KL looks like it looks like + + + align:start position:0% +density of KL looks like it looks like +this + + align:start position:0% + + + + align:start position:0% + +Right? And so if I want to squeeze in + + align:start position:0% +Right? And so if I want to squeeze in + + + align:start position:0% +Right? And so if I want to squeeze in +alpha + + align:start position:0% + + + + align:start position:0% + +here, I'm going to have to squeeze in + + align:start position:0% +here, I'm going to have to squeeze in + + + align:start position:0% +here, I'm going to have to squeeze in +and I squeeze in alpha here. Then this + + align:start position:0% +and I squeeze in alpha here. Then this + + + align:start position:0% +and I squeeze in alpha here. Then this +is the quentile of order one minus + + align:start position:0% +is the quentile of order one minus + + + align:start position:0% +is the quentile of order one minus +alpha. Well, let's say alpha of the K L + + align:start position:0% +alpha. Well, let's say alpha of the K L + + + align:start position:0% +alpha. Well, let's say alpha of the K L +and this is the quentile alpha of KS. So + + align:start position:0% +and this is the quentile alpha of KS. So + + + align:start position:0% +and this is the quentile alpha of KS. So +now you give me data and what I do is + + align:start position:0% +now you give me data and what I do is + + + align:start position:0% +now you give me data and what I do is +that I check whether they're larger than + + align:start position:0% +that I check whether they're larger than + + + align:start position:0% +that I check whether they're larger than +this number. So if I apply KS, I check + + align:start position:0% +this number. So if I apply KS, I check + + + align:start position:0% +this number. So if I apply KS, I check +whether I'm larger or smaller than this + + align:start position:0% +whether I'm larger or smaller than this + + + align:start position:0% +whether I'm larger or smaller than this +thing. But if I apply comm force, I + + align:start position:0% +thing. But if I apply comm force, I + + + align:start position:0% +thing. But if I apply comm force, I +check whether I'm large or small in this + + align:start position:0% +check whether I'm large or small in this + + + align:start position:0% +check whether I'm large or small in this +thing. So for this entire range of + + align:start position:0% +thing. So for this entire range of + + + align:start position:0% +thing. So for this entire range of +values for my test statistic because it + + align:start position:0% +values for my test statistic because it + + + align:start position:0% +values for my test statistic because it +is the same test statistic. I just + + align:start position:0% +is the same test statistic. I just + + + align:start position:0% +is the same test statistic. I just +plugged in mu hat and sigma hat. For + + align:start position:0% +plugged in mu hat and sigma hat. For + + + align:start position:0% +plugged in mu hat and sigma hat. For +this entire range, the two tests have + + align:start position:0% +this entire range, the two tests have + + + align:start position:0% +this entire range, the two tests have +different outcomes. + + align:start position:0% +different outcomes. + + + align:start position:0% +different outcomes. +And this is a big range in practice, + + align:start position:0% +And this is a big range in practice, + + + align:start position:0% +And this is a big range in practice, +right? I mean it's between it's it's I + + align:start position:0% +right? I mean it's between it's it's I + + + align:start position:0% +right? I mean it's between it's it's I +mean it's pretty much on on at scale + + align:start position:0% +mean it's pretty much on on at scale + + + align:start position:0% +mean it's pretty much on on at scale +here. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Any any other? Yeah. + + align:start position:0% + + + + align:start position:0% + +Yeah, they should become the same very + + align:start position:0% +Yeah, they should become the same very + + + align:start position:0% +Yeah, they should become the same very +far. Um + + align:start position:0% +far. Um + + + align:start position:0% +far. Um +let me see though because right so here + + align:start position:0% +let me see though because right so here + + + align:start position:0% +let me see though because right so here +we have eight uh so here we have say for + + align:start position:0% +we have eight uh so here we have say for + + + align:start position:0% +we have eight uh so here we have say for +0.5 we get 886 + + align:start position:0% +0.5 we get 886 + + + align:start position:0% +0.5 we get 886 +and for oh I don't have it + + align:start position:0% + + + + align:start position:0% + +yeah actually sorry you're right you're + + align:start position:0% +yeah actually sorry you're right you're + + + align:start position:0% +yeah actually sorry you're right you're +totally right this is the brown and + + align:start position:0% +totally right this is the brown and + + + align:start position:0% +totally right this is the brown and +bridge uh values because in the limit by + + align:start position:0% +bridge uh values because in the limit by + + + align:start position:0% +bridge uh values because in the limit by +seeky + + align:start position:0% +seeky + + + align:start position:0% +seeky +Uh sorry uh I'm lost. Yeah, these are + + align:start position:0% +Uh sorry uh I'm lost. Yeah, these are + + + align:start position:0% +Uh sorry uh I'm lost. Yeah, these are +the values that you get for the brown + + align:start position:0% +the values that you get for the brown + + + align:start position:0% +the values that you get for the brown +and bridge because in the limit by + + align:start position:0% +and bridge because in the limit by + + + align:start position:0% +and bridge because in the limit by +sledsky this thing is going to have no + + align:start position:0% +sledsky this thing is going to have no + + + align:start position:0% +sledsky this thing is going to have no +fluctuation and this thing is going to + + align:start position:0% +fluctuation and this thing is going to + + + align:start position:0% +fluctuation and this thing is going to +have no fluctuation. So they're just + + align:start position:0% +have no fluctuation. So they're just + + + align:start position:0% +have no fluctuation. So they're just +going to be pinned down and it's going + + align:start position:0% +going to be pinned down and it's going + + + align:start position:0% +going to be pinned down and it's going +to look like as if I did not replace + + align:start position:0% +to look like as if I did not replace + + + align:start position:0% +to look like as if I did not replace +anything because in the limit I know + + align:start position:0% +anything because in the limit I know + + + align:start position:0% +anything because in the limit I know +those guys much faster. The mu hat and + + align:start position:0% +those guys much faster. The mu hat and + + + align:start position:0% +those guys much faster. The mu hat and +sigma hat converge much faster to mu and + + align:start position:0% +sigma hat converge much faster to mu and + + + align:start position:0% +sigma hat converge much faster to mu and +sigma than the distribution itself. + + align:start position:0% +sigma than the distribution itself. + + + align:start position:0% +sigma than the distribution itself. +Right? So those are actually going to be + + align:start position:0% +Right? So those are actually going to be + + + align:start position:0% +Right? So those are actually going to be +negligible. You're right. + + align:start position:0% +negligible. You're right. + + + align:start position:0% +negligible. You're right. +actually even I didn't have these are + + align:start position:0% +actually even I didn't have these are + + + align:start position:0% +actually even I didn't have these are +actually the numbers I showed you for + + align:start position:0% +actually the numbers I showed you for + + + align:start position:0% +actually the numbers I showed you for +the bridge the brown bridge last time + + align:start position:0% +the bridge the brown bridge last time + + + align:start position:0% +the bridge the brown bridge last time +because I didn't have it for the one + + align:start position:0% +because I didn't have it for the one + + + align:start position:0% +because I didn't have it for the one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so there's actually so those are + + align:start position:0% +so there's actually so those are + + + align:start position:0% +so there's actually so those are +numerical ways of checking things right + + align:start position:0% +numerical ways of checking things right + + + align:start position:0% +numerical ways of checking things right +I give you data you just crank the + + align:start position:0% +I give you data you just crank the + + + align:start position:0% +I give you data you just crank the +commemor usually you press F5 on mat lab + + align:start position:0% +commemor usually you press F5 on mat lab + + + align:start position:0% +commemor usually you press F5 on mat lab +but uh uh let's say you actually compute + + align:start position:0% +but uh uh let's say you actually compute + + + align:start position:0% +but uh uh let's say you actually compute +this entire thing and uh there's a + + align:start position:0% +this entire thing and uh there's a + + + align:start position:0% +this entire thing and uh there's a +number that comes out and uh you decide + + align:start position:0% +number that comes out and uh you decide + + + align:start position:0% +number that comes out and uh you decide +whether it's large enough or small + + align:start position:0% +whether it's large enough or small + + + align:start position:0% +whether it's large enough or small +enough. Of course, statistical software + + align:start position:0% +enough. Of course, statistical software + + + align:start position:0% +enough. Of course, statistical software +is going to make your life even simpler + + align:start position:0% +is going to make your life even simpler + + + align:start position:0% +is going to make your life even simpler +by spitting out a p value because you + + align:start position:0% +by spitting out a p value because you + + + align:start position:0% +by spitting out a p value because you +can I mean if you can compute quintiles + + align:start position:0% +can I mean if you can compute quintiles + + + align:start position:0% +can I mean if you can compute quintiles +you can also compute p values and so you + + align:start position:0% +you can also compute p values and so you + + + align:start position:0% +you can also compute p values and so you +know your life is just fairly easy. you + + align:start position:0% +know your life is just fairly easy. you + + + align:start position:0% +know your life is just fairly easy. you +just have, you know, red is bad, green + + align:start position:0% +just have, you know, red is bad, green + + + align:start position:0% +just have, you know, red is bad, green +is good, and uh then you can go. The + + align:start position:0% +is good, and uh then you can go. The + + + align:start position:0% +is good, and uh then you can go. The +problem is that uh those are numbers you + + align:start position:0% +problem is that uh those are numbers you + + + align:start position:0% +problem is that uh those are numbers you +want to rely on, but let's say you + + align:start position:0% +want to rely on, but let's say you + + + align:start position:0% +want to rely on, but let's say you +actually reject. Let's say you reject + + align:start position:0% +actually reject. Let's say you reject + + + align:start position:0% +actually reject. Let's say you reject +your p value is actually just like + + align:start position:0% +your p value is actually just like + + + align:start position:0% +your p value is actually just like +slightly below 5%. + + align:start position:0% +slightly below 5%. + + + align:start position:0% +slightly below 5%. +So you can say, well, maybe I'm just + + align:start position:0% +So you can say, well, maybe I'm just + + + align:start position:0% +So you can say, well, maybe I'm just +going to change my uh my uh uh my p + + align:start position:0% +going to change my uh my uh uh my p + + + align:start position:0% +going to change my uh my uh uh my p +value, my threshold to 1%. But you might + + align:start position:0% +value, my threshold to 1%. But you might + + + align:start position:0% +value, my threshold to 1%. But you might +want to see what's happening. And for + + align:start position:0% +want to see what's happening. And for + + + align:start position:0% +want to see what's happening. And for +that you need a visual diagnostics like + + align:start position:0% +that you need a visual diagnostics like + + + align:start position:0% +that you need a visual diagnostics like +how do I check if something departs from + + align:start position:0% +how do I check if something departs from + + + align:start position:0% +how do I check if something departs from +being normal for example how do I check + + align:start position:0% +being normal for example how do I check + + + align:start position:0% +being normal for example how do I check +if a distribution why is a distribution + + align:start position:0% +if a distribution why is a distribution + + + align:start position:0% +if a distribution why is a distribution +not a uniform distribution why is a + + align:start position:0% +not a uniform distribution why is a + + + align:start position:0% +not a uniform distribution why is a +distribution not an exponential + + align:start position:0% +distribution not an exponential + + + align:start position:0% +distribution not an exponential +distribution there's many ways right if + + align:start position:0% +distribution there's many ways right if + + + align:start position:0% +distribution there's many ways right if +I have an exponential distribution and I + + align:start position:0% +I have an exponential distribution and I + + + align:start position:0% +I have an exponential distribution and I +first half of my values are negative for + + align:start position:0% +first half of my values are negative for + + + align:start position:0% +first half of my values are negative for +example well there's like pretty obvious + + align:start position:0% +example well there's like pretty obvious + + + align:start position:0% +example well there's like pretty obvious +reasons why it should not be exponential + + align:start position:0% +reasons why it should not be exponential + + + align:start position:0% +reasons why it should not be exponential +but it could be the case that it's just + + align:start position:0% +but it could be the case that it's just + + + align:start position:0% +but it could be the case that it's just +the tails are a little heavier or the uh + + align:start position:0% +the tails are a little heavier or the uh + + + align:start position:0% +the tails are a little heavier or the uh +there's more concent concentration at + + align:start position:0% +there's more concent concentration at + + + align:start position:0% +there's more concent concentration at +some point. Maybe it has two modes. + + align:start position:0% +some point. Maybe it has two modes. + + + align:start position:0% +some point. Maybe it has two modes. +There's things like this. But the real + + align:start position:0% +There's things like this. But the real + + + align:start position:0% +There's things like this. But the real +thing, we don't believe that the + + align:start position:0% +thing, we don't believe that the + + + align:start position:0% +thing, we don't believe that the +Gaussian is so important because it + + align:start position:0% +Gaussian is so important because it + + + align:start position:0% +Gaussian is so important because it +looks like this close to zero. What we + + align:start position:0% +looks like this close to zero. What we + + + align:start position:0% +looks like this close to zero. What we +like about the Gaussian is that the + + align:start position:0% +like about the Gaussian is that the + + + align:start position:0% +like about the Gaussian is that the +tails here decay at this rate + + align:start position:0% +tails here decay at this rate + + + align:start position:0% +tails here decay at this rate +exponential minus x^2 over two that we + + align:start position:0% +exponential minus x^2 over two that we + + + align:start position:0% +exponential minus x^2 over two that we +described in the maybe first lecture. + + align:start position:0% +described in the maybe first lecture. + + + align:start position:0% +described in the maybe first lecture. +And in particular, if there were like + + align:start position:0% +And in particular, if there were like + + + align:start position:0% +And in particular, if there were like +kinks around here, it wouldn't matter + + align:start position:0% +kinks around here, it wouldn't matter + + + align:start position:0% +kinks around here, it wouldn't matter +too much. This is not what makes issues + + align:start position:0% +too much. This is not what makes issues + + + align:start position:0% +too much. This is not what makes issues +for the Gaussian. + + align:start position:0% +for the Gaussian. + + + align:start position:0% +for the Gaussian. +And so what we want is to have a visual + + align:start position:0% +And so what we want is to have a visual + + + align:start position:0% +And so what we want is to have a visual +diagnostic that tells us if the tails of + + align:start position:0% +diagnostic that tells us if the tails of + + + align:start position:0% +diagnostic that tells us if the tails of +my distribution + + align:start position:0% +my distribution + + + align:start position:0% +my distribution +are comparable to the tails of a + + align:start position:0% +are comparable to the tails of a + + + align:start position:0% +are comparable to the tails of a +Gaussian one for example. And those are + + align:start position:0% +Gaussian one for example. And those are + + + align:start position:0% +Gaussian one for example. And those are +uh uh what's called quentile quentile + + align:start position:0% +uh uh what's called quentile quentile + + + align:start position:0% +uh uh what's called quentile quentile +plots. And in particular or QQ plots and + + align:start position:0% +plots. And in particular or QQ plots and + + + align:start position:0% +plots. And in particular or QQ plots and +the very the the the basic Q plots we're + + align:start position:0% +the very the the the basic Q plots we're + + + align:start position:0% +the very the the the basic Q plots we're +going to be using are the ones that are + + align:start position:0% +going to be using are the ones that are + + + align:start position:0% +going to be using are the ones that are +called normal Q plots that are comparing + + align:start position:0% +called normal Q plots that are comparing + + + align:start position:0% +called normal Q plots that are comparing +your data to a Gaussian distribution or + + align:start position:0% +your data to a Gaussian distribution or + + + align:start position:0% +your data to a Gaussian distribution or +a normal distribution. But in general, + + align:start position:0% +a normal distribution. But in general, + + + align:start position:0% +a normal distribution. But in general, +you could be comparing your data to any + + align:start position:0% +you could be comparing your data to any + + + align:start position:0% +you could be comparing your data to any +distribution you want. And the way you + + align:start position:0% +distribution you want. And the way you + + + align:start position:0% +distribution you want. And the way you +do this is by comparing the quintiles of + + align:start position:0% +do this is by comparing the quintiles of + + + align:start position:0% +do this is by comparing the quintiles of +your data, the empirical quentiles to + + align:start position:0% +your data, the empirical quentiles to + + + align:start position:0% +your data, the empirical quentiles to +the quentiles of the actual distribution + + align:start position:0% +the quentiles of the actual distribution + + + align:start position:0% +the quentiles of the actual distribution +you're trying to compare yourself to. So + + align:start position:0% +you're trying to compare yourself to. So + + + align:start position:0% +you're trying to compare yourself to. So +this in a way is a visual way of + + align:start position:0% +this in a way is a visual way of + + + align:start position:0% +this in a way is a visual way of +performing this goodness of fit tests. + + align:start position:0% +performing this goodness of fit tests. + + + align:start position:0% +performing this goodness of fit tests. +And what's nice about visual is that + + align:start position:0% +And what's nice about visual is that + + + align:start position:0% +And what's nice about visual is that +there's room for debate. You can see + + align:start position:0% +there's room for debate. You can see + + + align:start position:0% +there's room for debate. You can see +something that somebody else cannot see. + + align:start position:0% +something that somebody else cannot see. + + + align:start position:0% +something that somebody else cannot see. +And you can always because you want to + + align:start position:0% +And you can always because you want to + + + align:start position:0% +And you can always because you want to +say that things are Gaussian and we'll + + align:start position:0% +say that things are Gaussian and we'll + + + align:start position:0% +say that things are Gaussian and we'll +see some examples where you can actually + + align:start position:0% +see some examples where you can actually + + + align:start position:0% +see some examples where you can actually +see it if you are you know good at + + align:start position:0% +see it if you are you know good at + + + align:start position:0% +see it if you are you know good at +debate uh but uh it's actually going to + + align:start position:0% +debate uh but uh it's actually going to + + + align:start position:0% +debate uh but uh it's actually going to +be clearly not true. + + align:start position:0% +be clearly not true. + + + align:start position:0% +be clearly not true. +All right. So this is a quick and easy + + align:start position:0% +All right. So this is a quick and easy + + + align:start position:0% +All right. So this is a quick and easy +check. That's something I do all the + + align:start position:0% +check. That's something I do all the + + + align:start position:0% +check. That's something I do all the +time. You give me data I'm just going to + + align:start position:0% +time. You give me data I'm just going to + + + align:start position:0% +time. You give me data I'm just going to +run this one of the first thing I do so + + align:start position:0% +run this one of the first thing I do so + + + align:start position:0% +run this one of the first thing I do so +I can check if I can start you know + + align:start position:0% +I can check if I can start you know + + + align:start position:0% +I can check if I can start you know +entering the Gaussian world without you + + align:start position:0% +entering the Gaussian world without you + + + align:start position:0% +entering the Gaussian world without you +know compromising myself too much. And + + align:start position:0% +know compromising myself too much. And + + + align:start position:0% +know compromising myself too much. And +um the idea is to say well if f is close + + align:start position:0% +um the idea is to say well if f is close + + + align:start position:0% +um the idea is to say well if f is close +to if f if my data comes from a f and if + + align:start position:0% +to if f if my data comes from a f and if + + + align:start position:0% +to if f if my data comes from a f and if +I know that fn is close to f then rather + + align:start position:0% +I know that fn is close to f then rather + + + align:start position:0% +I know that fn is close to f then rather +than computing some norm some number + + align:start position:0% +than computing some norm some number + + + align:start position:0% +than computing some norm some number +that tells me how far they are + + align:start position:0% +that tells me how far they are + + + align:start position:0% +that tells me how far they are +summarizing how far they are I could + + align:start position:0% +summarizing how far they are I could + + + align:start position:0% +summarizing how far they are I could +actually plot the two functions and see + + align:start position:0% +actually plot the two functions and see + + + align:start position:0% +actually plot the two functions and see +if they're far apart. So let's let's + + align:start position:0% +if they're far apart. So let's let's + + + align:start position:0% +if they're far apart. So let's let's +think for one second what uh uh this + + align:start position:0% +think for one second what uh uh this + + + align:start position:0% +think for one second what uh uh this +kind of a of plot would look like. Well + + align:start position:0% +kind of a of plot would look like. Well + + + align:start position:0% +kind of a of plot would look like. Well +I would go between zero and one. That's + + align:start position:0% +I would go between zero and one. That's + + + align:start position:0% +I would go between zero and one. That's +where everything would happen. Let's say + + align:start position:0% +where everything would happen. Let's say + + + align:start position:0% +where everything would happen. Let's say +my distribution is the Gaussian + + align:start position:0% +my distribution is the Gaussian + + + align:start position:0% +my distribution is the Gaussian +distribution. So this is the CDF + + align:start position:0% +distribution. So this is the CDF + + + align:start position:0% +distribution. So this is the CDF +of N01. + + align:start position:0% +of N01. + + + align:start position:0% +of N01. +And now I have this guy that shows up. + + align:start position:0% +And now I have this guy that shows up. + + + align:start position:0% +And now I have this guy that shows up. +And remember we had this peacewise + + align:start position:0% +And remember we had this peacewise + + + align:start position:0% +And remember we had this peacewise +constant + + align:start position:0% +constant + + + align:start position:0% +constant +um + + align:start position:0% + + + + align:start position:0% + +well okay let's say we get something + + align:start position:0% +well okay let's say we get something + + + align:start position:0% +well okay let's say we get something +like this. we get a peace-wise constant + + align:start position:0% +like this. we get a peace-wise constant + + + align:start position:0% +like this. we get a peace-wise constant +um uh distribution for uh for fn right + + align:start position:0% +um uh distribution for uh for fn right + + + align:start position:0% +um uh distribution for uh for fn right +just from this and even despite my bad + + align:start position:0% +just from this and even despite my bad + + + align:start position:0% +just from this and even despite my bad +scales at drawing it's clear that it's + + align:start position:0% +scales at drawing it's clear that it's + + + align:start position:0% +scales at drawing it's clear that it's +going to be hard for you to distinguish + + align:start position:0% +going to be hard for you to distinguish + + + align:start position:0% +going to be hard for you to distinguish +those two things even for a fairly large + + align:start position:0% +those two things even for a fairly large + + + align:start position:0% +those two things even for a fairly large +amount of points because the problem is + + align:start position:0% +amount of points because the problem is + + + align:start position:0% +amount of points because the problem is +going to happen here and those guys look + + align:start position:0% +going to happen here and those guys look + + + align:start position:0% +going to happen here and those guys look +pretty much the same everywhere you are + + align:start position:0% +pretty much the same everywhere you are + + + align:start position:0% +pretty much the same everywhere you are +here you're going to see differences + + align:start position:0% +here you're going to see differences + + + align:start position:0% +here you're going to see differences +maybe in the middle but we don't care + + align:start position:0% +maybe in the middle but we don't care + + + align:start position:0% +maybe in the middle but we don't care +too much about those differenc + + align:start position:0% +too much about those differenc + + + align:start position:0% +too much about those differenc +differences. And so what's going to + + align:start position:0% +differences. And so what's going to + + + align:start position:0% +differences. And so what's going to +happen is that you're going to want to + + align:start position:0% +happen is that you're going to want to + + + align:start position:0% +happen is that you're going to want to +compare those two things. And this is + + align:start position:0% +compare those two things. And this is + + + align:start position:0% +compare those two things. And this is +basically you have the information you + + align:start position:0% +basically you have the information you + + + align:start position:0% +basically you have the information you +want, but visually just doesn't render + + align:start position:0% +want, but visually just doesn't render + + + align:start position:0% +want, but visually just doesn't render +very well because you're not scaling + + align:start position:0% +very well because you're not scaling + + + align:start position:0% +very well because you're not scaling +things properly. And the way we actually + + align:start position:0% +things properly. And the way we actually + + + align:start position:0% +things properly. And the way we actually +do it is by flipping things around and + + align:start position:0% +do it is by flipping things around and + + + align:start position:0% +do it is by flipping things around and +rather than comparing the plot of f to + + align:start position:0% +rather than comparing the plot of f to + + + align:start position:0% +rather than comparing the plot of f to +the plot of fn, we compare the plot of + + align:start position:0% +the plot of fn, we compare the plot of + + + align:start position:0% +the plot of fn, we compare the plot of +fn inverse to the plot of f inverse. + + align:start position:0% +fn inverse to the plot of f inverse. + + + align:start position:0% +fn inverse to the plot of f inverse. +Now + + align:start position:0% +Now + + + align:start position:0% +Now +if f goes from the real line to the + + align:start position:0% +if f goes from the real line to the + + + align:start position:0% +if f goes from the real line to the +interval 01 f inverse goes through goes + + align:start position:0% +interval 01 f inverse goes through goes + + + align:start position:0% +interval 01 f inverse goes through goes +from uh 01 to the whole real line. So + + align:start position:0% +from uh 01 to the whole real line. So + + + align:start position:0% +from uh 01 to the whole real line. So +what's going to happen is that I'm going + + align:start position:0% +what's going to happen is that I'm going + + + align:start position:0% +what's going to happen is that I'm going +to compare things on some intervals + + align:start position:0% +to compare things on some intervals + + + align:start position:0% +to compare things on some intervals +which is the ent which are the entire + + align:start position:0% +which is the ent which are the entire + + + align:start position:0% +which is the ent which are the entire +real line and then what values should I + + align:start position:0% +real line and then what values should I + + + align:start position:0% +real line and then what values should I +be looking those things at? Well, + + align:start position:0% +be looking those things at? Well, + + + align:start position:0% +be looking those things at? Well, +technically for f, if f is continuous, I + + align:start position:0% +technically for f, if f is continuous, I + + + align:start position:0% +technically for f, if f is continuous, I +could look at at f inverse for any value + + align:start position:0% +could look at at f inverse for any value + + + align:start position:0% +could look at at f inverse for any value +that I place, right? So I have f + + align:start position:0% +that I place, right? So I have f + + + align:start position:0% +that I place, right? So I have f +and if I want to look at f inverse, I + + align:start position:0% +and if I want to look at f inverse, I + + + align:start position:0% +and if I want to look at f inverse, I +pick a point here and I look at the + + align:start position:0% +pick a point here and I look at the + + + align:start position:0% +pick a point here and I look at the +value that it gives me and that's f + + align:start position:0% +value that it gives me and that's f + + + align:start position:0% +value that it gives me and that's f +inverse of say u. Right? If this is u + + align:start position:0% +inverse of say u. Right? If this is u + + + align:start position:0% +inverse of say u. Right? If this is u +and I can pick any value I want, I'm + + align:start position:0% +and I can pick any value I want, I'm + + + align:start position:0% +and I can pick any value I want, I'm +going to be able to find it. The problem + + align:start position:0% +going to be able to find it. The problem + + + align:start position:0% +going to be able to find it. The problem +is that when I start to have this + + align:start position:0% +is that when I start to have this + + + align:start position:0% +is that when I start to have this +piewise constant thing, + + align:start position:0% +piewise constant thing, + + + align:start position:0% +piewise constant thing, +I need to decide what value I assign for + + align:start position:0% +I need to decide what value I assign for + + + align:start position:0% +I need to decide what value I assign for +anything that's in between two jumps, + + align:start position:0% +anything that's in between two jumps, + + + align:start position:0% +anything that's in between two jumps, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +And so I can choose whatever I want. But + + align:start position:0% +And so I can choose whatever I want. But + + + align:start position:0% +And so I can choose whatever I want. But +in practice, it's just going to be + + align:start position:0% +in practice, it's just going to be + + + align:start position:0% +in practice, it's just going to be +things that I myself decide. Maybe I can + + align:start position:0% +things that I myself decide. Maybe I can + + + align:start position:0% +things that I myself decide. Maybe I can +decide that this is the value. Maybe I + + align:start position:0% +decide that this is the value. Maybe I + + + align:start position:0% +decide that this is the value. Maybe I +can decide that the value is here. But + + align:start position:0% +can decide that the value is here. But + + + align:start position:0% +can decide that the value is here. But +for all these guys, I'm going to pretty + + align:start position:0% +for all these guys, I'm going to pretty + + + align:start position:0% +for all these guys, I'm going to pretty +much decide always the same value. + + align:start position:0% +much decide always the same value. + + + align:start position:0% +much decide always the same value. +Right? If I'm in between for this value + + align:start position:0% +Right? If I'm in between for this value + + + align:start position:0% +Right? If I'm in between for this value +u for this jump uh the jump is here. So + + align:start position:0% +u for this jump uh the jump is here. So + + + align:start position:0% +u for this jump uh the jump is here. So +if uh for for this value I'm going to be + + align:start position:0% +if uh for for this value I'm going to be + + + align:start position:0% +if uh for for this value I'm going to be +able to decide whether I want to go + + align:start position:0% +able to decide whether I want to go + + + align:start position:0% +able to decide whether I want to go +above or below but it's always this + + align:start position:0% +above or below but it's always this + + + align:start position:0% +above or below but it's always this +value that's going to come out. So + + align:start position:0% +value that's going to come out. So + + + align:start position:0% +value that's going to come out. So +rather than picking values that are in + + align:start position:0% +rather than picking values that are in + + + align:start position:0% +rather than picking values that are in +between I might as well just pick only + + align:start position:0% +between I might as well just pick only + + + align:start position:0% +between I might as well just pick only +values for which this is the value that + + align:start position:0% +values for which this is the value that + + + align:start position:0% +values for which this is the value that +it's going to get. And those values are + + align:start position:0% +it's going to get. And those values are + + + align:start position:0% +it's going to get. And those values are +exactly one overn + + align:start position:0% + + + + align:start position:0% + +right? That's exactly where the flat + + align:start position:0% +right? That's exactly where the flat + + + align:start position:0% +right? That's exactly where the flat +parts are. We know we jump from one + + align:start position:0% +parts are. We know we jump from one + + + align:start position:0% +parts are. We know we jump from one +overn every time. + + align:start position:0% +overn every time. + + + align:start position:0% +overn every time. +And so that's exactly the recipe. It + + align:start position:0% +And so that's exactly the recipe. It + + + align:start position:0% +And so that's exactly the recipe. It +says look at those values 1 overn 2 + + align:start position:0% +says look at those values 1 overn 2 + + + align:start position:0% +says look at those values 1 overn 2 +overn 3 overn until say n minus one + + align:start position:0% +overn 3 overn until say n minus one + + + align:start position:0% +overn 3 overn until say n minus one +overn. And for those values compute the + + align:start position:0% +overn. And for those values compute the + + + align:start position:0% +overn. And for those values compute the +inverse of both the empirical cdf and + + align:start position:0% +inverse of both the empirical cdf and + + + align:start position:0% +inverse of both the empirical cdf and +the true cdf. Now for the empirical cdf + + align:start position:0% +the true cdf. Now for the empirical cdf + + + align:start position:0% +the true cdf. Now for the empirical cdf +it's actually easy. I just told you this + + align:start position:0% +it's actually easy. I just told you this + + + align:start position:0% +it's actually easy. I just told you this +is basically where the points o where + + align:start position:0% +is basically where the points o where + + + align:start position:0% +is basically where the points o where +the jumps occur. And the jumps occur + + align:start position:0% +the jumps occur. And the jumps occur + + + align:start position:0% +the jumps occur. And the jumps occur +where? Well, exactly at my observations. + + align:start position:0% +where? Well, exactly at my observations. + + + align:start position:0% +where? Well, exactly at my observations. +Now remember, I need to sort those + + align:start position:0% +Now remember, I need to sort those + + + align:start position:0% +Now remember, I need to sort those +observations to to talk about them. So + + align:start position:0% +observations to to talk about them. So + + + align:start position:0% +observations to to talk about them. So +the one that occurs for the ice jump is + + align:start position:0% +the one that occurs for the ice jump is + + + align:start position:0% +the one that occurs for the ice jump is +the ice largest observation which we + + align:start position:0% +the ice largest observation which we + + + align:start position:0% +the ice largest observation which we +denoted by add x sub parenthesis i. + + align:start position:0% +denoted by add x sub parenthesis i. + + + align:start position:0% +denoted by add x sub parenthesis i. +Remember we had this formula that we + + align:start position:0% +Remember we had this formula that we + + + align:start position:0% +Remember we had this formula that we +said well we have x1 xn these are my + + align:start position:0% +said well we have x1 xn these are my + + + align:start position:0% +said well we have x1 xn these are my +data and what I'm going to sort them + + align:start position:0% +data and what I'm going to sort them + + + align:start position:0% +data and what I'm going to sort them +into is x sub1 parenthesis which is less + + align:start position:0% +into is x sub1 parenthesis which is less + + + align:start position:0% +into is x sub1 parenthesis which is less +than or equal to x sub2 parenthesis + + align:start position:0% +than or equal to x sub2 parenthesis + + + align:start position:0% +than or equal to x sub2 parenthesis +which is less than x subn parenthesis. + + align:start position:0% +which is less than x subn parenthesis. + + + align:start position:0% +which is less than x subn parenthesis. +Okay so we just ordered them from + + align:start position:0% +Okay so we just ordered them from + + + align:start position:0% +Okay so we just ordered them from +smallest to largest and to we've done + + align:start position:0% +smallest to largest and to we've done + + + align:start position:0% +smallest to largest and to we've done +that we just put this parenthesis + + align:start position:0% +that we just put this parenthesis + + + align:start position:0% +that we just put this parenthesis +notation. So in particular + + align:start position:0% +notation. So in particular + + + align:start position:0% +notation. So in particular +f n inverse of i / n is the location + + align:start position:0% +f n inverse of i / n is the location + + + align:start position:0% +f n inverse of i / n is the location +where the ice jumps occur which is the + + align:start position:0% +where the ice jumps occur which is the + + + align:start position:0% +where the ice jumps occur which is the +ice largest observation. Okay. + + align:start position:0% +ice largest observation. Okay. + + + align:start position:0% +ice largest observation. Okay. +So for this guy + + align:start position:0% +So for this guy + + + align:start position:0% +So for this guy +this values the y axis are actually + + align:start position:0% +this values the y axis are actually + + + align:start position:0% +this values the y axis are actually +fairly easy. I know it's basically my + + align:start position:0% +fairly easy. I know it's basically my + + + align:start position:0% +fairly easy. I know it's basically my +ordered observations. + + align:start position:0% +ordered observations. + + + align:start position:0% +ordered observations. +The x values + + align:start position:0% +The x values + + + align:start position:0% +The x values +are well that depends on the function f + + align:start position:0% +are well that depends on the function f + + + align:start position:0% +are well that depends on the function f +I'm trying to test. If it's the + + align:start position:0% +I'm trying to test. If it's the + + + align:start position:0% +I'm trying to test. If it's the +Gaussian, it's just the quintile of + + align:start position:0% +Gaussian, it's just the quintile of + + + align:start position:0% +Gaussian, it's just the quintile of +order + + align:start position:0% +order + + + align:start position:0% +order +1 - 1 /n, right? Is this q 1 - 1 /n here + + align:start position:0% +1 - 1 /n, right? Is this q 1 - 1 /n here + + + align:start position:0% +1 - 1 /n, right? Is this q 1 - 1 /n here +that I need to compute. It's the inverse + + align:start position:0% +that I need to compute. It's the inverse + + + align:start position:0% +that I need to compute. It's the inverse +of the cumulative distribution function, + + align:start position:0% +of the cumulative distribution function, + + + align:start position:0% +of the cumulative distribution function, +which given the formula for f, you can + + align:start position:0% +which given the formula for f, you can + + + align:start position:0% +which given the formula for f, you can +actually compute or maybe estimate + + align:start position:0% +actually compute or maybe estimate + + + align:start position:0% +actually compute or maybe estimate +fairly well, but it's something that you + + align:start position:0% +fairly well, but it's something that you + + + align:start position:0% +fairly well, but it's something that you +can find in tables. Those are basically + + align:start position:0% +can find in tables. Those are basically + + + align:start position:0% +can find in tables. Those are basically +quentiles. Inverse of cdfs are + + align:start position:0% +quentiles. Inverse of cdfs are + + + align:start position:0% +quentiles. Inverse of cdfs are +quentiles, right? And so that's + + align:start position:0% +quentiles, right? And so that's + + + align:start position:0% +quentiles, right? And so that's +basically uh uh the things we're + + align:start position:0% +basically uh uh the things we're + + + align:start position:0% +basically uh uh the things we're +interested in. That's why it's called + + align:start position:0% +interested in. That's why it's called + + + align:start position:0% +interested in. That's why it's called +quentile quentile. Those are the some + + align:start position:0% +quentile quentile. Those are the some + + + align:start position:0% +quentile quentile. Those are the some +refer sometimes referred to as + + align:start position:0% +refer sometimes referred to as + + + align:start position:0% +refer sometimes referred to as +theoretical quentiles, the one we're + + align:start position:0% +theoretical quentiles, the one we're + + + align:start position:0% +theoretical quentiles, the one we're +trying to test and empirical quentiles, + + align:start position:0% +trying to test and empirical quentiles, + + + align:start position:0% +trying to test and empirical quentiles, +the one that corresponds to the + + align:start position:0% +the one that corresponds to the + + + align:start position:0% +the one that corresponds to the +empirical CDF. And so I'm plotting a + + align:start position:0% +empirical CDF. And so I'm plotting a + + + align:start position:0% +empirical CDF. And so I'm plotting a +plot where the x-axis is quentile, the + + align:start position:0% +plot where the x-axis is quentile, the + + + align:start position:0% +plot where the x-axis is quentile, the +y-axis is quentile. And so I call this + + align:start position:0% +y-axis is quentile. And so I call this + + + align:start position:0% +y-axis is quentile. And so I call this +plot a quentile quentile plot or QQ plot + + align:start position:0% +plot a quentile quentile plot or QQ plot + + + align:start position:0% +plot a quentile quentile plot or QQ plot +because well just say 10 times quentile + + align:start position:0% +because well just say 10 times quentile + + + align:start position:0% +because well just say 10 times quentile +qual and then you'll see why. Yeah. + + align:start position:0% + + + + align:start position:0% + +Well, that's just that's we're back to + + align:start position:0% +Well, that's just that's we're back to + + + align:start position:0% +Well, that's just that's we're back to +the uh we're back to the uh goodness of + + align:start position:0% +the uh we're back to the uh goodness of + + + align:start position:0% +the uh we're back to the uh goodness of +fit test, right? So, if you look so you + + align:start position:0% +fit test, right? So, if you look so you + + + align:start position:0% +fit test, right? So, if you look so you +don't do it yourself. That's the simple + + align:start position:0% +don't do it yourself. That's the simple + + + align:start position:0% +don't do it yourself. That's the simple +answer to you don't I just I'm just + + align:start position:0% +answer to you don't I just I'm just + + + align:start position:0% +answer to you don't I just I'm just +telling you how those plots that you're + + align:start position:0% +telling you how those plots that you're + + + align:start position:0% +telling you how those plots that you're +going to be seeing spit out from a + + align:start position:0% +going to be seeing spit out from a + + + align:start position:0% +going to be seeing spit out from a +software are going to look like. Now, + + align:start position:0% +software are going to look like. Now, + + + align:start position:0% +software are going to look like. Now, +depending on the software, there's a + + align:start position:0% +depending on the software, there's a + + + align:start position:0% +depending on the software, there's a +different thing that's happening. Some + + align:start position:0% +different thing that's happening. Some + + + align:start position:0% +different thing that's happening. Some +softwares are actually plotting f with + + align:start position:0% +softwares are actually plotting f with + + + align:start position:0% +softwares are actually plotting f with +the right. Let's say you want to do qu + + align:start position:0% +the right. Let's say you want to do qu + + + align:start position:0% +the right. Let's say you want to do qu +normal as you asked. So you some + + align:start position:0% +normal as you asked. So you some + + + align:start position:0% +normal as you asked. So you some +software are just going to use f to be + + align:start position:0% +software are just going to use f to be + + + align:start position:0% +software are just going to use f to be +with mu hat and sigma hat and that's + + align:start position:0% +with mu hat and sigma hat and that's + + + align:start position:0% +with mu hat and sigma hat and that's +fine. Some software are actually not + + align:start position:0% +fine. Some software are actually not + + + align:start position:0% +fine. Some software are actually not +going to do this. They're just going to + + align:start position:0% +going to do this. They're just going to + + + align:start position:0% +going to do this. They're just going to +use a gaussian + + align:start position:0% +use a gaussian + + + align:start position:0% +use a gaussian +but then they're going to actually have + + align:start position:0% +but then they're going to actually have + + + align:start position:0% +but then they're going to actually have +a different uh reference point. So what + + align:start position:0% +a different uh reference point. So what + + + align:start position:0% +a different uh reference point. So what +do we want to see here? What should + + align:start position:0% +do we want to see here? What should + + + align:start position:0% +do we want to see here? What should +happen if all these points if all my + + align:start position:0% +happen if all these points if all my + + + align:start position:0% +happen if all these points if all my +points actually come from f from a + + align:start position:0% +points actually come from f from a + + + align:start position:0% +points actually come from f from a +distribution that has cdf? What should + + align:start position:0% +distribution that has cdf? What should + + + align:start position:0% +distribution that has cdf? What should +happen? What should I see? + + align:start position:0% + + + + align:start position:0% + +Well, since fn should be close to f, fn + + align:start position:0% +Well, since fn should be close to f, fn + + + align:start position:0% +Well, since fn should be close to f, fn +inverse should be close to f inverse + + align:start position:0% +inverse should be close to f inverse + + + align:start position:0% +inverse should be close to f inverse +which mean that this point should be + + align:start position:0% +which mean that this point should be + + + align:start position:0% +which mean that this point should be +close to that point. This point should + + align:start position:0% +close to that point. This point should + + + align:start position:0% +close to that point. This point should +be close to that point. So ideally, if I + + align:start position:0% +be close to that point. So ideally, if I + + + align:start position:0% +be close to that point. So ideally, if I +actually pick the right f, I should see + + align:start position:0% +actually pick the right f, I should see + + + align:start position:0% +actually pick the right f, I should see +a plot that looks like this. + + align:start position:0% + + + + align:start position:0% + +Something where all my points + + align:start position:0% +Something where all my points + + + align:start position:0% +Something where all my points +are very close to the line y is equal to + + align:start position:0% +are very close to the line y is equal to + + + align:start position:0% +are very close to the line y is equal to +x, right? + + align:start position:0% +x, right? + + + align:start position:0% +x, right? +And I'm going to have some fluctuations, + + align:start position:0% +And I'm going to have some fluctuations, + + + align:start position:0% +And I'm going to have some fluctuations, +but something very close to this. + + align:start position:0% +but something very close to this. + + + align:start position:0% +but something very close to this. +Now, that's if f is exactly the right + + align:start position:0% +Now, that's if f is exactly the right + + + align:start position:0% +Now, that's if f is exactly the right +one. If f is not exactly the right one + + align:start position:0% +one. If f is not exactly the right one + + + align:start position:0% +one. If f is not exactly the right one +in particular in the case of a gausian + + align:start position:0% +in particular in the case of a gausian + + + align:start position:0% +in particular in the case of a gausian +one if I actually plotted here the + + align:start position:0% +one if I actually plotted here the + + + align:start position:0% +one if I actually plotted here the +quentiles so if I plotted f + + align:start position:0% + + + + align:start position:0% + +f 01 + + align:start position:0% +f 01 + + + align:start position:0% +f 01 +of t right so let's say those are the + + align:start position:0% +of t right so let's say those are the + + + align:start position:0% +of t right so let's say those are the +ones I actually plot but I really don't + + align:start position:0% +ones I actually plot but I really don't + + + align:start position:0% +ones I actually plot but I really don't +know what mu hat is not zero and sigma + + align:start position:0% +know what mu hat is not zero and sigma + + + align:start position:0% +know what mu hat is not zero and sigma +hat is not zero and so this is not the + + align:start position:0% +hat is not zero and so this is not the + + + align:start position:0% +hat is not zero and so this is not the +one I should be getting since we + + align:start position:0% +one I should be getting since we + + + align:start position:0% +one I should be getting since we +actually know that I of mu hat sigma + + align:start position:0% +actually know that I of mu hat sigma + + + align:start position:0% +actually know that I of mu hat sigma +hat^ squar t is equal to 501 + + align:start position:0% +hat^ squar t is equal to 501 + + + align:start position:0% +hat^ squar t is equal to 501 +of t minus mu hat / sigma hat. There's + + align:start position:0% +of t minus mu hat / sigma hat. There's + + + align:start position:0% +of t minus mu hat / sigma hat. There's +just this change of axis which is + + align:start position:0% +just this change of axis which is + + + align:start position:0% +just this change of axis which is +actually very simple. This change of + + align:start position:0% +actually very simple. This change of + + + align:start position:0% +actually very simple. This change of +axis is just a simple translation + + align:start position:0% +axis is just a simple translation + + + align:start position:0% +axis is just a simple translation +scaling which means that this + + align:start position:0% +scaling which means that this + + + align:start position:0% +scaling which means that this +this line here is going to be + + align:start position:0% +this line here is going to be + + + align:start position:0% +this line here is going to be +transformed into another line with a + + align:start position:0% +transformed into another line with a + + + align:start position:0% +transformed into another line with a +different slope and a different + + align:start position:0% +different slope and a different + + + align:start position:0% +different slope and a different +intercept. + + align:start position:0% +intercept. + + + align:start position:0% +intercept. +And so some software will actually + + align:start position:0% +And so some software will actually + + + align:start position:0% +And so some software will actually +decide to go with this curve and just + + align:start position:0% +decide to go with this curve and just + + + align:start position:0% +decide to go with this curve and just +show you what the reference curve should + + align:start position:0% +show you what the reference curve should + + + align:start position:0% +show you what the reference curve should +be rather than actually putting + + align:start position:0% +be rather than actually putting + + + align:start position:0% +be rather than actually putting +everything back onto the uh 45deree + + align:start position:0% +everything back onto the uh 45deree + + + align:start position:0% +everything back onto the uh 45deree +curve. + + align:start position:0% +curve. + + + align:start position:0% +curve. +Any straight line, you're happy. I mean + + align:start position:0% +Any straight line, you're happy. I mean + + + align:start position:0% +Any straight line, you're happy. I mean +depending on the software because if the + + align:start position:0% +depending on the software because if the + + + align:start position:0% +depending on the software because if the +software actually really rescaled this + + align:start position:0% +software actually really rescaled this + + + align:start position:0% +software actually really rescaled this +thing to have new hat and sigma square + + align:start position:0% +thing to have new hat and sigma square + + + align:start position:0% +thing to have new hat and sigma square +and you find a different line then + + align:start position:0% +and you find a different line then + + + align:start position:0% +and you find a different line then +you're a different straight line. This + + align:start position:0% +you're a different straight line. This + + + align:start position:0% +you're a different straight line. This +is bad news, which is not going to + + align:start position:0% +is bad news, which is not going to + + + align:start position:0% +is bad news, which is not going to +happen actually. It's impossible that + + align:start position:0% +happen actually. It's impossible that + + + align:start position:0% +happen actually. It's impossible that +happens because you've actually said + + align:start position:0% +happens because you've actually said + + + align:start position:0% +happens because you've actually said +well no it could if you're if it's crazy + + align:start position:0% +well no it could if you're if it's crazy + + + align:start position:0% +well no it could if you're if it's crazy +it could it should be very crazy. Okay. + + align:start position:0% +it could it should be very crazy. Okay. + + + align:start position:0% +it could it should be very crazy. Okay. +So let's see what uh R does for us for + + align:start position:0% +So let's see what uh R does for us for + + + align:start position:0% +So let's see what uh R does for us for +example. + + align:start position:0% +example. + + + align:start position:0% +example. +So here in R uh R actually does this uh + + align:start position:0% +So here in R uh R actually does this uh + + + align:start position:0% +So here in R uh R actually does this uh +funny trick where so here I did not + + align:start position:0% +funny trick where so here I did not + + + align:start position:0% +funny trick where so here I did not +actually plot the lines. I should + + align:start position:0% +actually plot the lines. I should + + + align:start position:0% +actually plot the lines. I should +actually add the lines. So the command + + align:start position:0% +actually add the lines. So the command + + + align:start position:0% +actually add the lines. So the command +is like QQQ norm of my sample, right? + + align:start position:0% +is like QQQ norm of my sample, right? + + + align:start position:0% +is like QQQ norm of my sample, right? +And that's really simple. I just stack + + align:start position:0% +And that's really simple. I just stack + + + align:start position:0% +And that's really simple. I just stack +all my data into some vector say X and I + + align:start position:0% +all my data into some vector say X and I + + + align:start position:0% +all my data into some vector say X and I +say QQ norm + + align:start position:0% +say QQ norm + + + align:start position:0% +say QQ norm +of X and it just spits this thing out. + + align:start position:0% +of X and it just spits this thing out. + + + align:start position:0% +of X and it just spits this thing out. +Okay, very simple. But I could actually + + align:start position:0% +Okay, very simple. But I could actually + + + align:start position:0% +Okay, very simple. But I could actually +add another command which I can't + + align:start position:0% +add another command which I can't + + + align:start position:0% +add another command which I can't +remember. I think it's like QQ line + + align:start position:0% + + + + align:start position:0% + +and it's just going to add the line on + + align:start position:0% +and it's just going to add the line on + + + align:start position:0% +and it's just going to add the line on +top of it. But if you see actually what + + align:start position:0% +top of it. But if you see actually what + + + align:start position:0% +top of it. But if you see actually what +R does for us, it's actually doing the + + align:start position:0% +R does for us, it's actually doing the + + + align:start position:0% +R does for us, it's actually doing the +translation and scaling on the axis + + align:start position:0% +translation and scaling on the axis + + + align:start position:0% +translation and scaling on the axis +themselves. So it actually changes the + + align:start position:0% +themselves. So it actually changes the + + + align:start position:0% +themselves. So it actually changes the +uh x and y axis in such a way that when + + align:start position:0% +uh x and y axis in such a way that when + + + align:start position:0% +uh x and y axis in such a way that when +you look at your picture and you forget + + align:start position:0% +you look at your picture and you forget + + + align:start position:0% +you look at your picture and you forget +about what the meaning of the axis are, + + align:start position:0% +about what the meaning of the axis are, + + + align:start position:0% +about what the meaning of the axis are, +the relevant straight line is actually + + align:start position:0% +the relevant straight line is actually + + + align:start position:0% +the relevant straight line is actually +still the 45deree line. It's because + + align:start position:0% +still the 45deree line. It's because + + + align:start position:0% +still the 45deree line. It's because +it's actually done the change of uh of + + align:start position:0% +it's actually done the change of uh of + + + align:start position:0% +it's actually done the change of uh of +units for you. So you don't have to even + + align:start position:0% +units for you. So you don't have to even + + + align:start position:0% +units for you. So you don't have to even +see the line. know that in your mind + + align:start position:0% +see the line. know that in your mind + + + align:start position:0% +see the line. know that in your mind +that this is basically the reference + + align:start position:0% +that this is basically the reference + + + align:start position:0% +that this is basically the reference +line is still 45 degree + + align:start position:0% +line is still 45 degree + + + align:start position:0% +line is still 45 degree +uh because that's the way the the axes + + align:start position:0% +uh because that's the way the the axes + + + align:start position:0% +uh because that's the way the the axes +are made. But if I actually put my axis, + + align:start position:0% +are made. But if I actually put my axis, + + + align:start position:0% +are made. But if I actually put my axis, +right? So here, for example, it goes + + align:start position:0% +right? So here, for example, it goes + + + align:start position:0% +right? So here, for example, it goes +from uh let's look at some uh well, + + align:start position:0% +from uh let's look at some uh well, + + + align:start position:0% +from uh let's look at some uh well, +okay, those are all square. Um + + align:start position:0% +okay, those are all square. Um + + + align:start position:0% +okay, those are all square. Um +yeah, and that's probably because I + + align:start position:0% +yeah, and that's probably because I + + + align:start position:0% +yeah, and that's probably because I +actually have a the samples are actually + + align:start position:0% +actually have a the samples are actually + + + align:start position:0% +actually have a the samples are actually +from a standard normal. So uh I did not + + align:start position:0% +from a standard normal. So uh I did not + + + align:start position:0% +from a standard normal. So uh I did not +make my life very easy to illustrate + + align:start position:0% +make my life very easy to illustrate + + + align:start position:0% +make my life very easy to illustrate +your question, but of course I didn't + + align:start position:0% +your question, but of course I didn't + + + align:start position:0% +your question, but of course I didn't +know you were going to ask it. Next + + align:start position:0% +know you were going to ask it. Next + + + align:start position:0% +know you were going to ask it. Next +time, let's just prepare. Uh let's + + align:start position:0% +time, let's just prepare. Uh let's + + + align:start position:0% +time, let's just prepare. Uh let's +script more. Uh we'll see in another one + + align:start position:0% +script more. Uh we'll see in another one + + + align:start position:0% +script more. Uh we'll see in another one +in the next plot. But so here what you + + align:start position:0% +in the next plot. But so here what you + + + align:start position:0% +in the next plot. But so here what you +expect to see is that all the plots + + align:start position:0% +expect to see is that all the plots + + + align:start position:0% +expect to see is that all the plots +should be on the 45 degree line. Right? + + align:start position:0% +should be on the 45 degree line. Right? + + + align:start position:0% +should be on the 45 degree line. Right? +This is there should be the right one. + + align:start position:0% +This is there should be the right one. + + + align:start position:0% +This is there should be the right one. +And if you see when I start having + + align:start position:0% +And if you see when I start having + + + align:start position:0% +And if you see when I start having +10,000 samples this is exactly what's + + align:start position:0% +10,000 samples this is exactly what's + + + align:start position:0% +10,000 samples this is exactly what's +happening. So this is a good as good as + + align:start position:0% +happening. So this is a good as good as + + + align:start position:0% +happening. So this is a good as good as +it gets. This is an N01 plotted against + + align:start position:0% +it gets. This is an N01 plotted against + + + align:start position:0% +it gets. This is an N01 plotted against +the theoretical quantile of an N01. As + + align:start position:0% +the theoretical quantile of an N01. As + + + align:start position:0% +the theoretical quantile of an N01. As +good as it gets. Now if you see for the + + align:start position:0% +good as it gets. Now if you see for the + + + align:start position:0% +good as it gets. Now if you see for the +second one which is 50 sample size of + + align:start position:0% +second one which is 50 sample size of + + + align:start position:0% +second one which is 50 sample size of +size sample of size 50 there is some + + align:start position:0% +size sample of size 50 there is some + + + align:start position:0% +size sample of size 50 there is some +fudge factor right? I mean those things + + align:start position:0% +fudge factor right? I mean those things + + + align:start position:0% +fudge factor right? I mean those things +are doesn't look like there's a straight + + align:start position:0% +are doesn't look like there's a straight + + + align:start position:0% +are doesn't look like there's a straight +line, right? Sort of appears that + + align:start position:0% +line, right? Sort of appears that + + + align:start position:0% +line, right? Sort of appears that +there's some weird things happening here + + align:start position:0% +there's some weird things happening here + + + align:start position:0% +there's some weird things happening here +at the lower tail. + + align:start position:0% +at the lower tail. + + + align:start position:0% +at the lower tail. +And the reason why this is happening is + + align:start position:0% +And the reason why this is happening is + + + align:start position:0% +And the reason why this is happening is +because we're trying to compare the + + align:start position:0% +because we're trying to compare the + + + align:start position:0% +because we're trying to compare the +tails, right? When I look at this + + align:start position:0% +tails, right? When I look at this + + + align:start position:0% +tails, right? When I look at this +picture, the only thing that goes wrong + + align:start position:0% +picture, the only thing that goes wrong + + + align:start position:0% +picture, the only thing that goes wrong +somehow is always at the tip because + + align:start position:0% +somehow is always at the tip because + + + align:start position:0% +somehow is always at the tip because +those are sort of rare and extreme + + align:start position:0% +those are sort of rare and extreme + + + align:start position:0% +those are sort of rare and extreme +values and they're sort of all over the + + align:start position:0% +values and they're sort of all over the + + + align:start position:0% +values and they're sort of all over the +place. And so things are never really + + align:start position:0% +place. And so things are never really + + + align:start position:0% +place. And so things are never really +super smooth and super clean. So this is + + align:start position:0% +super smooth and super clean. So this is + + + align:start position:0% +super smooth and super clean. So this is +what your best shot is. This is what + + align:start position:0% +what your best shot is. This is what + + + align:start position:0% +what your best shot is. This is what +you've ever will ever hope to get. So + + align:start position:0% +you've ever will ever hope to get. So + + + align:start position:0% +you've ever will ever hope to get. So +size 10 right so you have 10 points + + align:start position:0% +size 10 right so you have 10 points + + + align:start position:0% +size 10 right so you have 10 points +remember we actually well I didn't + + align:start position:0% +remember we actually well I didn't + + + align:start position:0% +remember we actually well I didn't +really tell you how to deal with the + + align:start position:0% +really tell you how to deal with the + + + align:start position:0% +really tell you how to deal with the +extreme cases because the problem is + + align:start position:0% +extreme cases because the problem is + + + align:start position:0% +extreme cases because the problem is +that f inverse of one for the true f is + + align:start position:0% +that f inverse of one for the true f is + + + align:start position:0% +that f inverse of one for the true f is +plus infinity so you have to make some + + align:start position:0% +plus infinity so you have to make some + + + align:start position:0% +plus infinity so you have to make some +sort of weird boundary choices to decide + + align:start position:0% +sort of weird boundary choices to decide + + + align:start position:0% +sort of weird boundary choices to decide +what f inverse of one is and it's + + align:start position:0% +what f inverse of one is and it's + + + align:start position:0% +what f inverse of one is and it's +something that's like somewhere but you + + align:start position:0% +something that's like somewhere but you + + + align:start position:0% +something that's like somewhere but you +still want to put like 10 dots right one + + align:start position:0% +still want to put like 10 dots right one + + + align:start position:0% +still want to put like 10 dots right one +two three four five six seven eight nine + + align:start position:0% +two three four five six seven eight nine + + + align:start position:0% +two three four five six seven eight nine +10 dots so I have 10 observations you + + align:start position:0% +10 dots so I have 10 observations you + + + align:start position:0% +10 dots so I have 10 observations you +will see 10 dots I have 50 observations + + align:start position:0% +will see 10 dots I have 50 observations + + + align:start position:0% +will see 10 dots I have 50 observations +you will 50 dots remember right because + + align:start position:0% +you will 50 dots remember right because + + + align:start position:0% +you will 50 dots remember right because +I have there are one overn two overn all + + align:start position:0% +I have there are one overn two overn all + + + align:start position:0% +I have there are one overn two overn all +the way to n / n + + align:start position:0% +the way to n / n + + + align:start position:0% +the way to n / n +I didn't tell you the last one + + align:start position:0% +I didn't tell you the last one + + + align:start position:0% +I didn't tell you the last one +okay so this is when things go well and + + align:start position:0% +okay so this is when things go well and + + + align:start position:0% +okay so this is when things go well and +this is when things should not go well + + align:start position:0% +this is when things should not go well + + + align:start position:0% +this is when things should not go well +okay so here actually the distribution + + align:start position:0% +okay so here actually the distribution + + + align:start position:0% +okay so here actually the distribution +is a student t with 15 degrees of + + align:start position:0% +is a student t with 15 degrees of + + + align:start position:0% +is a student t with 15 degrees of +freedom which should depart somewhat + + align:start position:0% +freedom which should depart somewhat + + + align:start position:0% +freedom which should depart somewhat +from a Gaussian distribution the tails + + align:start position:0% +from a Gaussian distribution the tails + + + align:start position:0% +from a Gaussian distribution the tails +should be heavier + + align:start position:0% +should be heavier + + + align:start position:0% +should be heavier +and what you can see is basically the + + align:start position:0% +and what you can see is basically the + + + align:start position:0% +and what you can see is basically the +following is that uh for 10 you actually + + align:start position:0% +following is that uh for 10 you actually + + + align:start position:0% +following is that uh for 10 you actually +see something that's crazy right if I do + + align:start position:0% +see something that's crazy right if I do + + + align:start position:0% +see something that's crazy right if I do +10 observations but if I do 50 + + align:start position:0% +10 observations but if I do 50 + + + align:start position:0% +10 observations but if I do 50 +observations honestly it's kind of hard + + align:start position:0% +observations honestly it's kind of hard + + + align:start position:0% +observations honestly it's kind of hard +to say that it's different from the + + align:start position:0% +to say that it's different from the + + + align:start position:0% +to say that it's different from the +standard normal so you could still be + + align:start position:0% +standard normal so you could still be + + + align:start position:0% +standard normal so you could still be +happy with this for 100 and then this is + + align:start position:0% +happy with this for 100 and then this is + + + align:start position:0% +happy with this for 100 and then this is +what's happening for 10,000 and even + + align:start position:0% +what's happening for 10,000 and even + + + align:start position:0% +what's happening for 10,000 and even +here it's not the beautiful straight + + align:start position:0% +here it's not the beautiful straight + + + align:start position:0% +here it's not the beautiful straight +line but it feels like you would be + + align:start position:0% +line but it feels like you would be + + + align:start position:0% +line but it feels like you would be +still tempted to conclude that it's a + + align:start position:0% +still tempted to conclude that it's a + + + align:start position:0% +still tempted to conclude that it's a +beautiful straight line. So let's try to + + align:start position:0% +beautiful straight line. So let's try to + + + align:start position:0% +beautiful straight line. So let's try to +guess. So basically there's for each of + + align:start position:0% +guess. So basically there's for each of + + + align:start position:0% +guess. So basically there's for each of +those sides there's two phenomena either + + align:start position:0% +those sides there's two phenomena either + + + align:start position:0% +those sides there's two phenomena either +it goes like this or it goes like this + + align:start position:0% +it goes like this or it goes like this + + + align:start position:0% +it goes like this or it goes like this +and then it goes like this or goes like + + align:start position:0% +and then it goes like this or goes like + + + align:start position:0% +and then it goes like this or goes like +this. Each side corresponds to the left + + align:start position:0% +this. Each side corresponds to the left + + + align:start position:0% +this. Each side corresponds to the left +tail the all the smallest values. So + + align:start position:0% +tail the all the smallest values. So + + + align:start position:0% +tail the all the smallest values. So +that's the left side and that's the + + align:start position:0% +that's the left side and that's the + + + align:start position:0% +that's the left side and that's the +right side corresponds to the large + + align:start position:0% +right side corresponds to the large + + + align:start position:0% +right side corresponds to the large +values. Okay. And so basically you can + + align:start position:0% +values. Okay. And so basically you can + + + align:start position:0% +values. Okay. And so basically you can +actually think of um some sort of a + + align:start position:0% +actually think of um some sort of a + + + align:start position:0% +actually think of um some sort of a +table that tells you what your Q plot + + align:start position:0% +table that tells you what your Q plot + + + align:start position:0% +table that tells you what your Q plot +looks like. + + align:start position:0% + + + + align:start position:0% + +And so let's say it looks like so we + + align:start position:0% +And so let's say it looks like so we + + + align:start position:0% +And so let's say it looks like so we +have our reference 45 degree line. So + + align:start position:0% +have our reference 45 degree line. So + + + align:start position:0% +have our reference 45 degree line. So +let's say this is the QQ plot. That's + + align:start position:0% +let's say this is the QQ plot. That's + + + align:start position:0% +let's say this is the QQ plot. That's +that could be one thing. This could be + + align:start position:0% +that could be one thing. This could be + + + align:start position:0% +that could be one thing. This could be +the QQ plot where I have another thing + + align:start position:0% +the QQ plot where I have another thing + + + align:start position:0% +the QQ plot where I have another thing +that's uh then I can do um + + align:start position:0% +that's uh then I can do um + + + align:start position:0% +that's uh then I can do um +this guy + + align:start position:0% +this guy + + + align:start position:0% +this guy +and then I do this guy. Uh + + align:start position:0% +and then I do this guy. Uh + + + align:start position:0% +and then I do this guy. Uh +this is like this. Okay. + + align:start position:0% +this is like this. Okay. + + + align:start position:0% +this is like this. Okay. +the four cases. Okay. And here + + align:start position:0% +the four cases. Okay. And here + + + align:start position:0% +the four cases. Okay. And here +what's changing is the right tail. And + + align:start position:0% +what's changing is the right tail. And + + + align:start position:0% +what's changing is the right tail. And +here what's changing is the and when I + + align:start position:0% +here what's changing is the and when I + + + align:start position:0% +here what's changing is the and when I +go from here to here, what changes is + + align:start position:0% +go from here to here, what changes is + + + align:start position:0% +go from here to here, what changes is +the left tail. Uh is that true? + + align:start position:0% +the left tail. Uh is that true? + + + align:start position:0% +the left tail. Uh is that true? +No, sorry. What changes here is the + + align:start position:0% +No, sorry. What changes here is the + + + align:start position:0% +No, sorry. What changes here is the +right tail. That's this part that + + align:start position:0% +right tail. That's this part that + + + align:start position:0% +right tail. That's this part that +changes from uh uh top to bottom. So + + align:start position:0% +changes from uh uh top to bottom. So + + + align:start position:0% +changes from uh uh top to bottom. So +here it's something about right tail + + align:start position:0% + + + + align:start position:0% + +and here that's something about left + + align:start position:0% +and here that's something about left + + + align:start position:0% +and here that's something about left +tail. + + align:start position:0% + + + + align:start position:0% + +Everybody understands what I mean when I + + align:start position:0% +Everybody understands what I mean when I + + + align:start position:0% +Everybody understands what I mean when I +talk about tails? Okay. And so here is + + align:start position:0% +talk about tails? Okay. And so here is + + + align:start position:0% +talk about tails? Okay. And so here is +just going to be a question of whether + + align:start position:0% +just going to be a question of whether + + + align:start position:0% +just going to be a question of whether +the tails are heavier or lighter than + + align:start position:0% +the tails are heavier or lighter than + + + align:start position:0% +the tails are heavier or lighter than +the Gaussian. Everybody understand what + + align:start position:0% +the Gaussian. Everybody understand what + + + align:start position:0% +the Gaussian. Everybody understand what +I mean when I say heavy tails and light + + align:start position:0% +I mean when I say heavy tails and light + + + align:start position:0% +I mean when I say heavy tails and light +tails. Okay. So right. So heavy tails + + align:start position:0% +tails. Okay. So right. So heavy tails + + + align:start position:0% +tails. Okay. So right. So heavy tails +just means that basically here the tails + + align:start position:0% +just means that basically here the tails + + + align:start position:0% +just means that basically here the tails +of this guy are heavier than the tails + + align:start position:0% +of this guy are heavier than the tails + + + align:start position:0% +of this guy are heavier than the tails +of this guy. So it means that if I draw + + align:start position:0% +of this guy. So it means that if I draw + + + align:start position:0% +of this guy. So it means that if I draw +them they're going to be above. + + align:start position:0% +them they're going to be above. + + + align:start position:0% +them they're going to be above. +Actually, let me keep this picture + + align:start position:0% +Actually, let me keep this picture + + + align:start position:0% +Actually, let me keep this picture +because it's going to be very useful for + + align:start position:0% +because it's going to be very useful for + + + align:start position:0% +because it's going to be very useful for +me + + align:start position:0% + + + + align:start position:0% + +when I plot the quintiles + + align:start position:0% +when I plot the quintiles + + + align:start position:0% +when I plot the quintiles +at the same. So, let's look at the right + + align:start position:0% +at the same. So, let's look at the right + + + align:start position:0% +at the same. So, let's look at the right +tail for example. Right here, my picture + + align:start position:0% +tail for example. Right here, my picture + + + align:start position:0% +tail for example. Right here, my picture +is for right tails. When I look at the + + align:start position:0% +is for right tails. When I look at the + + + align:start position:0% +is for right tails. When I look at the +quentiles of my theoretical + + align:start position:0% +quentiles of my theoretical + + + align:start position:0% +quentiles of my theoretical +distribution, so here you can see the + + align:start position:0% +distribution, so here you can see the + + + align:start position:0% +distribution, so here you can see the +bottom curve, we have the theoretical + + align:start position:0% +bottom curve, we have the theoretical + + + align:start position:0% +bottom curve, we have the theoretical +quentiles + + align:start position:0% +quentiles + + + align:start position:0% +quentiles +and those are the empirical quentiles. + + align:start position:0% +and those are the empirical quentiles. + + + align:start position:0% +and those are the empirical quentiles. +the if I look to the right here + + align:start position:0% +the if I look to the right here + + + align:start position:0% +the if I look to the right here +are the theoretical quintiles larger or + + align:start position:0% +are the theoretical quintiles larger or + + + align:start position:0% +are the theoretical quintiles larger or +smaller than the empirical quentiles. + + align:start position:0% + + + + align:start position:0% + +Let me freeze it the other. Are the + + align:start position:0% +Let me freeze it the other. Are the + + + align:start position:0% +Let me freeze it the other. Are the +empirical quentiles larger or smaller + + align:start position:0% +empirical quentiles larger or smaller + + + align:start position:0% +empirical quentiles larger or smaller +than the theoretical quintiles? + + align:start position:0% + + + + align:start position:0% + +It should be smaller. right on this line + + align:start position:0% +It should be smaller. right on this line + + + align:start position:0% +It should be smaller. right on this line +they are equal. So if I see the + + align:start position:0% +they are equal. So if I see the + + + align:start position:0% +they are equal. So if I see the +empirical quintile showing up here, it + + align:start position:0% +empirical quintile showing up here, it + + + align:start position:0% +empirical quintile showing up here, it +means that here the empirical quentile + + align:start position:0% +means that here the empirical quentile + + + align:start position:0% +means that here the empirical quentile +is less than the theoretical quintile. + + align:start position:0% +is less than the theoretical quintile. + + + align:start position:0% +is less than the theoretical quintile. +Agreed? So that means that if I look at + + align:start position:0% +Agreed? So that means that if I look at + + + align:start position:0% +Agreed? So that means that if I look at +this thing and that's for the same + + align:start position:0% +this thing and that's for the same + + + align:start position:0% +this thing and that's for the same +values, right? So the quintiles are + + align:start position:0% +values, right? So the quintiles are + + + align:start position:0% +values, right? So the quintiles are +computed for the same values I over N. + + align:start position:0% +computed for the same values I over N. + + + align:start position:0% +computed for the same values I over N. +So it means that the empirical quintile + + align:start position:0% +So it means that the empirical quintile + + + align:start position:0% +So it means that the empirical quintile +should be looking uh so that should be + + align:start position:0% +should be looking uh so that should be + + + align:start position:0% +should be looking uh so that should be +the empirical quintile + + align:start position:0% +the empirical quintile + + + align:start position:0% +the empirical quintile +and that should be the theorical + + align:start position:0% +and that should be the theorical + + + align:start position:0% +and that should be the theorical +quintile. + + align:start position:0% +quintile. + + + align:start position:0% +quintile. +Agreed? Those are the smaller values for + + align:start position:0% +Agreed? Those are the smaller values for + + + align:start position:0% +Agreed? Those are the smaller values for +the same alpha. + + align:start position:0% +the same alpha. + + + align:start position:0% +the same alpha. +So that implies + + align:start position:0% +So that implies + + + align:start position:0% +So that implies +that the tails the right tail is it + + align:start position:0% +that the tails the right tail is it + + + align:start position:0% +that the tails the right tail is it +heavy or lighter? Heavier or lighter + + align:start position:0% +heavy or lighter? Heavier or lighter + + + align:start position:0% +heavy or lighter? Heavier or lighter +than the Gaussian. + + align:start position:0% + + + + align:start position:0% + +Yeah, lighter. Right? Because those are + + align:start position:0% +Yeah, lighter. Right? Because those are + + + align:start position:0% +Yeah, lighter. Right? Because those are +the tails of the Gaussian. Those are my + + align:start position:0% +the tails of the Gaussian. Those are my + + + align:start position:0% +the tails of the Gaussian. Those are my +theoretical quentiles. That means that + + align:start position:0% +theoretical quentiles. That means that + + + align:start position:0% +theoretical quentiles. That means that +this is the tail of my of my empirical + + align:start position:0% +this is the tail of my of my empirical + + + align:start position:0% +this is the tail of my of my empirical +distribution. So they are actually + + align:start position:0% +distribution. So they are actually + + + align:start position:0% +distribution. So they are actually +lighter. + + align:start position:0% + + + + align:start position:0% + +Okay. So here if I look at this thing, + + align:start position:0% +Okay. So here if I look at this thing, + + + align:start position:0% +Okay. So here if I look at this thing, +this means that the right tail + + align:start position:0% +this means that the right tail + + + align:start position:0% +this means that the right tail +is actually light. + + align:start position:0% +is actually light. + + + align:start position:0% +is actually light. +And by light I mean lighter than + + align:start position:0% +And by light I mean lighter than + + + align:start position:0% +And by light I mean lighter than +Gaussian. Heavy I mean heavier than + + align:start position:0% +Gaussian. Heavy I mean heavier than + + + align:start position:0% +Gaussian. Heavy I mean heavier than +Gaussian. Okay. Okay. Now we can + + align:start position:0% +Gaussian. Okay. Okay. Now we can + + + align:start position:0% +Gaussian. Okay. Okay. Now we can +probably do the entire thing. Well, if + + align:start position:0% +probably do the entire thing. Well, if + + + align:start position:0% +probably do the entire thing. Well, if +this is light, + + align:start position:0% +this is light, + + + align:start position:0% +this is light, +this is going to be heavy, right? That's + + align:start position:0% +this is going to be heavy, right? That's + + + align:start position:0% +this is going to be heavy, right? That's +when I'm above the curve. + + align:start position:0% + + + + align:start position:0% + +Exercise. Is this light or is this + + align:start position:0% +Exercise. Is this light or is this + + + align:start position:0% +Exercise. Is this light or is this +heavy? The first column. + + align:start position:0% + + + + align:start position:0% + +It's okay. Should take you at least 30 + + align:start position:0% +It's okay. Should take you at least 30 + + + align:start position:0% +It's okay. Should take you at least 30 +seconds. + + align:start position:0% + + + + align:start position:0% + +Yeah, this column, right? So this is + + align:start position:0% +Yeah, this column, right? So this is + + + align:start position:0% +Yeah, this column, right? So this is +something that pertains to this entire + + align:start position:0% +something that pertains to this entire + + + align:start position:0% +something that pertains to this entire +column is going to tell me whether the + + align:start position:0% +column is going to tell me whether the + + + align:start position:0% +column is going to tell me whether the +fact that this guy is above. Does this + + align:start position:0% +fact that this guy is above. Does this + + + align:start position:0% +fact that this guy is above. Does this +mean that I have lighter or heavier uh + + align:start position:0% +mean that I have lighter or heavier uh + + + align:start position:0% +mean that I have lighter or heavier uh +left tails + + align:start position:0% +left tails + + + align:start position:0% +left tails +on the left? It's heavier. + + align:start position:0% +on the left? It's heavier. + + + align:start position:0% +on the left? It's heavier. +Okay. So I I don't know actually I need + + align:start position:0% +Okay. So I I don't know actually I need + + + align:start position:0% +Okay. So I I don't know actually I need +to draw a picture. You guys are probably + + align:start position:0% +to draw a picture. You guys are probably + + + align:start position:0% +to draw a picture. You guys are probably +faster than I am. + + align:start position:0% + + + + align:start position:0% + +Actually let me check how much + + align:start position:0% +Actually let me check how much + + + align:start position:0% +Actually let me check how much +randomness is it? Who says it's lighter? + + align:start position:0% +randomness is it? Who says it's lighter? + + + align:start position:0% +randomness is it? Who says it's lighter? +Who says it's heavier? + + align:start position:0% + + + + align:start position:0% + +Yeah. Okay. Um, all right. So, let's see + + align:start position:0% +Yeah. Okay. Um, all right. So, let's see + + + align:start position:0% +Yeah. Okay. Um, all right. So, let's see +if it's heavier. + + align:start position:0% +if it's heavier. + + + align:start position:0% +if it's heavier. +So, we're on the left tail. And so, we + + align:start position:0% +So, we're on the left tail. And so, we + + + align:start position:0% +So, we're on the left tail. And so, we +have one looks like this, one looks like + + align:start position:0% +have one looks like this, one looks like + + + align:start position:0% +have one looks like this, one looks like +that, right? + + align:start position:0% + + + + align:start position:0% + +So, we know here that I'm looking at + + align:start position:0% +So, we know here that I'm looking at + + + align:start position:0% +So, we know here that I'm looking at +this part here. So it means that here my + + align:start position:0% +this part here. So it means that here my + + + align:start position:0% +this part here. So it means that here my +empirical quentile is larger than the + + align:start position:0% +empirical quentile is larger than the + + + align:start position:0% +empirical quentile is larger than the +theoretical quentile. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So are my tails heavier or lighter? + + align:start position:0% + + + + align:start position:0% + +They're lighter. That was a bad bias, + + align:start position:0% + + + + align:start position:0% + +right? That it's below. So it's lighter. + + align:start position:0% +right? That it's below. So it's lighter. + + + align:start position:0% +right? That it's below. So it's lighter. +is the problem is that larger for the + + align:start position:0% +is the problem is that larger for the + + + align:start position:0% +is the problem is that larger for the +negative ones means that it's smaller in + + align:start position:0% +negative ones means that it's smaller in + + + align:start position:0% +negative ones means that it's smaller in +absolute right. Yeah. + + align:start position:0% + + + + align:start position:0% + +CDF. + + align:start position:0% + + + + align:start position:0% + +Oh, did I put this inverse CDF? + + align:start position:0% + + + + align:start position:0% + +No, the inverse CDN. Yeah. So, I'm I + + align:start position:0% +No, the inverse CDN. Yeah. So, I'm I + + + align:start position:0% +No, the inverse CDN. Yeah. So, I'm I +mean putting + + align:start position:0% +mean putting + + + align:start position:0% +mean putting +Yeah. So, it's a scatter plot, right? + + align:start position:0% +Yeah. So, it's a scatter plot, right? + + + align:start position:0% +Yeah. So, it's a scatter plot, right? +So, each point is attached each point is + + align:start position:0% +So, each point is attached each point is + + + align:start position:0% +So, each point is attached each point is +attached one over n, two over n, three + + align:start position:0% +attached one over n, two over n, three + + + align:start position:0% +attached one over n, two over n, three +overn. Now for each point I'm plotting + + align:start position:0% +overn. Now for each point I'm plotting + + + align:start position:0% +overn. Now for each point I'm plotting +that's my x value which maps a number + + align:start position:0% +that's my x value which maps a number + + + align:start position:0% +that's my x value which maps a number +between zero and one back onto the + + align:start position:0% +between zero and one back onto the + + + align:start position:0% +between zero and one back onto the +entire real line and my y-value is the + + align:start position:0% +entire real line and my y-value is the + + + align:start position:0% +entire real line and my y-value is the +same. + + align:start position:0% +same. + + + align:start position:0% +same. +Okay. So what it means is that those two + + align:start position:0% +Okay. So what it means is that those two + + + align:start position:0% +Okay. So what it means is that those two +numbers this is in the entire this lives + + align:start position:0% +numbers this is in the entire this lives + + + align:start position:0% +numbers this is in the entire this lives +on the entire real line not on the + + align:start position:0% +on the entire real line not on the + + + align:start position:0% +on the entire real line not on the +interval. This lives on the entire real + + align:start position:0% +interval. This lives on the entire real + + + align:start position:0% +interval. This lives on the entire real +line not in the interval. And so my QQ + + align:start position:0% +line not in the interval. And so my QQ + + + align:start position:0% +line not in the interval. And so my QQ +plots + + align:start position:0% +plots + + + align:start position:0% +plots +take values on the entire real line. + + align:start position:0% +take values on the entire real line. + + + align:start position:0% +take values on the entire real line. +Entire real line right? So it's you + + align:start position:0% +Entire real line right? So it's you + + + align:start position:0% +Entire real line right? So it's you +think of it as a parameterized curve + + align:start position:0% +think of it as a parameterized curve + + + align:start position:0% +think of it as a parameterized curve +where the the time steps are one over n + + align:start position:0% +where the the time steps are one over n + + + align:start position:0% +where the the time steps are one over n +two over n two over n and I'm just like + + align:start position:0% +two over n two over n and I'm just like + + + align:start position:0% +two over n two over n and I'm just like +putting a dot every time I'm making one + + align:start position:0% +putting a dot every time I'm making one + + + align:start position:0% +putting a dot every time I'm making one +step. + + align:start position:0% +step. + + + align:start position:0% +step. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Okay. So what did we say that was + + align:start position:0% +Okay. So what did we say that was + + + align:start position:0% +Okay. So what did we say that was +lighter, right? + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +One of my favorite exercises is here's a + + align:start position:0% +One of my favorite exercises is here's a + + + align:start position:0% +One of my favorite exercises is here's a +bunch of densities. Here's a bunch of QQ + + align:start position:0% +bunch of densities. Here's a bunch of QQ + + + align:start position:0% +bunch of densities. Here's a bunch of QQ +plots. Map the correct QQ plot to its + + align:start position:0% +plots. Map the correct QQ plot to its + + + align:start position:0% +plots. Map the correct QQ plot to its +own density, right? And uh and there + + align:start position:0% +own density, right? And uh and there + + + align:start position:0% +own density, right? And uh and there +won't be mangled lines that allow you to + + align:start position:0% +won't be mangled lines that allow you to + + + align:start position:0% +won't be mangled lines that allow you to +do that. Then you just have to follow + + align:start position:0% +do that. Then you just have to follow + + + align:start position:0% +do that. Then you just have to follow +like at the back the back of serial + + align:start position:0% +like at the back the back of serial + + + align:start position:0% +like at the back the back of serial +boxes. All right. Um + + align:start position:0% +boxes. All right. Um + + + align:start position:0% +boxes. All right. Um +are there any questions? So one thing + + align:start position:0% +are there any questions? So one thing + + + align:start position:0% +are there any questions? So one thing +there's two things I'm trying to + + align:start position:0% +there's two things I'm trying to + + + align:start position:0% +there's two things I'm trying to +communicate here is if you see a Q plot + + align:start position:0% +communicate here is if you see a Q plot + + + align:start position:0% +communicate here is if you see a Q plot +now you should understand one how it was + + align:start position:0% +now you should understand one how it was + + + align:start position:0% +now you should understand one how it was +built and two uh whether it means that + + align:start position:0% +built and two uh whether it means that + + + align:start position:0% +built and two uh whether it means that +you have heavier tails or lighter tails. + + align:start position:0% +you have heavier tails or lighter tails. + + + align:start position:0% +you have heavier tails or lighter tails. +Now let's look at this guy. What should + + align:start position:0% +Now let's look at this guy. What should + + + align:start position:0% +Now let's look at this guy. What should +we see? We should see heavy on the left + + align:start position:0% +we see? We should see heavy on the left + + + align:start position:0% +we see? We should see heavy on the left +and heavy on the right. Right? We know + + align:start position:0% +and heavy on the right. Right? We know + + + align:start position:0% +and heavy on the right. Right? We know +that this should be the case. So this + + align:start position:0% +that this should be the case. So this + + + align:start position:0% +that this should be the case. So this +thing actually looks like this. + + align:start position:0% +thing actually looks like this. + + + align:start position:0% +thing actually looks like this. +It sort of does. Right? If I take this + + align:start position:0% +It sort of does. Right? If I take this + + + align:start position:0% +It sort of does. Right? If I take this +line going through here, I can see that + + align:start position:0% +line going through here, I can see that + + + align:start position:0% +line going through here, I can see that +this guy is tipping here and this guy is + + align:start position:0% +this guy is tipping here and this guy is + + + align:start position:0% +this guy is tipping here and this guy is +dipping here. But honestly, actually, I + + align:start position:0% +dipping here. But honestly, actually, I + + + align:start position:0% +dipping here. But honestly, actually, I +can't remember exactly, but T15, + + align:start position:0% +can't remember exactly, but T15, + + + align:start position:0% +can't remember exactly, but T15, +if I plotted the density + + align:start position:0% +if I plotted the density + + + align:start position:0% +if I plotted the density +on top of the Gaussian, you can see a + + align:start position:0% +on top of the Gaussian, you can see a + + + align:start position:0% +on top of the Gaussian, you can see a +difference, but if I just gave it to + + align:start position:0% +difference, but if I just gave it to + + + align:start position:0% +difference, but if I just gave it to +you, it would be very hard for you to + + align:start position:0% +you, it would be very hard for you to + + + align:start position:0% +you, it would be very hard for you to +tell me if there's an actual difference + + align:start position:0% +tell me if there's an actual difference + + + align:start position:0% +tell me if there's an actual difference +between T15 and Gaussian, right? Those + + align:start position:0% +between T15 and Gaussian, right? Those + + + align:start position:0% +between T15 and Gaussian, right? Those +things are actually very close. And so, + + align:start position:0% +things are actually very close. And so, + + + align:start position:0% +things are actually very close. And so, +in particular here, we're really trying + + align:start position:0% +in particular here, we're really trying + + + align:start position:0% +in particular here, we're really trying +to recognize what the shape is. the fact + + align:start position:0% +to recognize what the shape is. the fact + + + align:start position:0% +to recognize what the shape is. the fact +right so T15 compared to a standard + + align:start position:0% +right so T15 compared to a standard + + + align:start position:0% +right so T15 compared to a standard +Gaussian was diff different but T15 + + align:start position:0% +Gaussian was diff different but T15 + + + align:start position:0% +Gaussian was diff different but T15 +compared to a Gaussian with slightly + + align:start position:0% +compared to a Gaussian with slightly + + + align:start position:0% +compared to a Gaussian with slightly +larger variance is not going to actually + + align:start position:0% +larger variance is not going to actually + + + align:start position:0% +larger variance is not going to actually +see you're not going to see much of a + + align:start position:0% +see you're not going to see much of a + + + align:start position:0% +see you're not going to see much of a +difference so in a way + + align:start position:0% +difference so in a way + + + align:start position:0% +difference so in a way +you know such distributions are actually + + align:start position:0% +you know such distributions are actually + + + align:start position:0% +you know such distributions are actually +not too far from the Gaussian and it's + + align:start position:0% +not too far from the Gaussian and it's + + + align:start position:0% +not too far from the Gaussian and it's +not too it's still pretty benign to + + align:start position:0% +not too it's still pretty benign to + + + align:start position:0% +not too it's still pretty benign to +conclude that this was actually a + + align:start position:0% +conclude that this was actually a + + + align:start position:0% +conclude that this was actually a +Gaussian distribution because you can + + align:start position:0% +Gaussian distribution because you can + + + align:start position:0% +Gaussian distribution because you can +just you know use the variance at a + + align:start position:0% +just you know use the variance at a + + + align:start position:0% +just you know use the variance at a +little bit of a buffer I'm not going to + + align:start position:0% +little bit of a buffer I'm not going to + + + align:start position:0% +little bit of a buffer I'm not going to +go really into how you would use a t + + align:start position:0% +go really into how you would use a t + + + align:start position:0% +go really into how you would use a t +distribution into a t + + align:start position:0% +distribution into a t + + + align:start position:0% +distribution into a t +test because it's kind of like + + align:start position:0% +test because it's kind of like + + + align:start position:0% +test because it's kind of like +inception, right? So, uh but you could + + align:start position:0% +inception, right? So, uh but you could + + + align:start position:0% +inception, right? So, uh but you could +pretend that your data actually is uh is + + align:start position:0% +pretend that your data actually is uh is + + + align:start position:0% +pretend that your data actually is uh is +t distributed and then build a t + + align:start position:0% +t distributed and then build a t + + + align:start position:0% +t distributed and then build a t +distribution from it. But, uh let's not + + align:start position:0% +distribution from it. But, uh let's not + + + align:start position:0% +distribution from it. But, uh let's not +say that. Maybe that's that was a bad + + align:start position:0% +say that. Maybe that's that was a bad + + + align:start position:0% +say that. Maybe that's that was a bad +example. But, you know, there's like + + align:start position:0% +example. But, you know, there's like + + + align:start position:0% +example. But, you know, there's like +other heavy tail distributions like cowi + + align:start position:0% +other heavy tail distributions like cowi + + + align:start position:0% +other heavy tail distributions like cowi +distribution which doesn't even have a + + align:start position:0% +distribution which doesn't even have a + + + align:start position:0% +distribution which doesn't even have a +is not even integraable. So that's as + + align:start position:0% +is not even integraable. So that's as + + + align:start position:0% +is not even integraable. So that's as +heavy as the tails get. And uh this you + + align:start position:0% +heavy as the tails get. And uh this you + + + align:start position:0% +heavy as the tails get. And uh this you +can really tell it's going to look like + + align:start position:0% +can really tell it's going to look like + + + align:start position:0% +can really tell it's going to look like +this. + + align:start position:0% +this. + + + align:start position:0% +this. +It's going to be like + + align:start position:0% +It's going to be like + + + align:start position:0% +It's going to be like +what does a uniform distribution look + + align:start position:0% +what does a uniform distribution look + + + align:start position:0% +what does a uniform distribution look +like? + + align:start position:0% + + + + align:start position:0% + +Like this. It's going to be it's going + + align:start position:0% +Like this. It's going to be it's going + + + align:start position:0% +Like this. It's going to be it's going +to look like a Gaussian one. + + align:start position:0% + + + + align:start position:0% + +Right. So right. So a uniform district. + + align:start position:0% +Right. So right. So a uniform district. + + + align:start position:0% +Right. So right. So a uniform district. +So this is my Gaussian. The uniform is + + align:start position:0% +So this is my Gaussian. The uniform is + + + align:start position:0% +So this is my Gaussian. The uniform is +basically going to look like this once I + + align:start position:0% +basically going to look like this once I + + + align:start position:0% +basically going to look like this once I +take the right mean and the right + + align:start position:0% +take the right mean and the right + + + align:start position:0% +take the right mean and the right +variance, right? So the tails are + + align:start position:0% +variance, right? So the tails are + + + align:start position:0% +variance, right? So the tails are +definitely lighter. They're zero. That's + + align:start position:0% +definitely lighter. They're zero. That's + + + align:start position:0% +definitely lighter. They're zero. That's +as lighter as it gets. So the light + + align:start position:0% +as lighter as it gets. So the light + + + align:start position:0% +as lighter as it gets. So the light +light is going to look like this S + + align:start position:0% +light is going to look like this S + + + align:start position:0% +light is going to look like this S +shape. So an S light tail distribution + + align:start position:0% +shape. So an S light tail distribution + + + align:start position:0% +shape. So an S light tail distribution +has this S shape. Okay. Uh what is the + + align:start position:0% +has this S shape. Okay. Uh what is the + + + align:start position:0% +has this S shape. Okay. Uh what is the +um exponential going to look like? + + align:start position:0% + + + + align:start position:0% + +Right? So the exponential is positively + + align:start position:0% +Right? So the exponential is positively + + + align:start position:0% +Right? So the exponential is positively +supported. It only has positive numbers. + + align:start position:0% +supported. It only has positive numbers. + + + align:start position:0% +supported. It only has positive numbers. +So there's no left tail. This is also as + + align:start position:0% +So there's no left tail. This is also as + + + align:start position:0% +So there's no left tail. This is also as +as light as it gets. But the right tail, + + align:start position:0% +as light as it gets. But the right tail, + + + align:start position:0% +as light as it gets. But the right tail, +is it heavier or lighter than the + + align:start position:0% +is it heavier or lighter than the + + + align:start position:0% +is it heavier or lighter than the +Gaussian? + + align:start position:0% +Gaussian? + + + align:start position:0% +Gaussian? +It's heavier, right? It's only decays + + align:start position:0% +It's heavier, right? It's only decays + + + align:start position:0% +It's heavier, right? It's only decays +like e to the minus x rather than e to + + align:start position:0% +like e to the minus x rather than e to + + + align:start position:0% +like e to the minus x rather than e to +the minus x^2. So it's heavier. So it + + align:start position:0% +the minus x^2. So it's heavier. So it + + + align:start position:0% +the minus x^2. So it's heavier. So it +means that on the left it's going to be + + align:start position:0% +means that on the left it's going to be + + + align:start position:0% +means that on the left it's going to be +light + + align:start position:0% +light + + + align:start position:0% +light +and on the right it's going to be heavy. + + align:start position:0% +and on the right it's going to be heavy. + + + align:start position:0% +and on the right it's going to be heavy. +So it's going to be U-shaped. + + align:start position:0% +So it's going to be U-shaped. + + + align:start position:0% +So it's going to be U-shaped. +Okay, + + align:start position:0% + + + + align:start position:0% + +that'll be fun. + + align:start position:0% +that'll be fun. + + + align:start position:0% +that'll be fun. +All right, + + align:start position:0% +All right, + + + align:start position:0% +All right, +any other question? + + align:start position:0% +any other question? + + + align:start position:0% +any other question? +Again, two messages like more technical + + align:start position:0% +Again, two messages like more technical + + + align:start position:0% +Again, two messages like more technical +and you can sort of fiddle with it by + + align:start position:0% +and you can sort of fiddle with it by + + + align:start position:0% +and you can sort of fiddle with it by +looking at it. You can definitely + + align:start position:0% +looking at it. You can definitely + + + align:start position:0% +looking at it. You can definitely +conclude that this is okay enough to be + + align:start position:0% +conclude that this is okay enough to be + + + align:start position:0% +conclude that this is okay enough to be +Gaussian for your purposes. Yeah, + + align:start position:0% + + + + align:start position:0% + +I did not hear the if at the beginning + + align:start position:0% +I did not hear the if at the beginning + + + align:start position:0% +I did not hear the if at the beginning +of your sentence. + + align:start position:0% + + + + align:start position:0% + +So what is your purpose as a + + align:start position:0% + + + + align:start position:0% + +Yes. + + align:start position:0% + + + + align:start position:0% + +Yeah, in a way that's true, right? So + + align:start position:0% +Yeah, in a way that's true, right? So + + + align:start position:0% +Yeah, in a way that's true, right? So +once you've actually factored in the + + align:start position:0% +once you've actually factored in the + + + align:start position:0% +once you've actually factored in the +mean and the variance, the only thing + + align:start position:0% +mean and the variance, the only thing + + + align:start position:0% +mean and the variance, the only thing +that actually + + align:start position:0% +that actually + + + align:start position:0% +that actually +right. So if you have Gaussian tails or + + align:start position:0% +right. So if you have Gaussian tails or + + + align:start position:0% +right. So if you have Gaussian tails or +lighter even lighter tails, then it's + + align:start position:0% +lighter even lighter tails, then it's + + + align:start position:0% +lighter even lighter tails, then it's +harder for you to explain deviations + + align:start position:0% +harder for you to explain deviations + + + align:start position:0% +harder for you to explain deviations +from randomness only. Right? If you have + + align:start position:0% +from randomness only. Right? If you have + + + align:start position:0% +from randomness only. Right? If you have +a uniform distribution and you see + + align:start position:0% +a uniform distribution and you see + + + align:start position:0% +a uniform distribution and you see +something which is if you're uniform on + + align:start position:0% +something which is if you're uniform on + + + align:start position:0% +something which is if you're uniform on +01 plus some number and you see 25 you + + align:start position:0% +01 plus some number and you see 25 you + + + align:start position:0% +01 plus some number and you see 25 you +know this number is not going to be + + align:start position:0% +know this number is not going to be + + + align:start position:0% +know this number is not going to be +zero. Right? So that's basically as good + + align:start position:0% +zero. Right? So that's basically as good + + + align:start position:0% +zero. Right? So that's basically as good +as it gets and it's there's basically + + align:start position:0% +as it gets and it's there's basically + + + align:start position:0% +as it gets and it's there's basically +some smooth interpolation if you have + + align:start position:0% +some smooth interpolation if you have + + + align:start position:0% +some smooth interpolation if you have +lighter tails. Now if you start having + + align:start position:0% +lighter tails. Now if you start having + + + align:start position:0% +lighter tails. Now if you start having +something that has heavy tails then it's + + align:start position:0% +something that has heavy tails then it's + + + align:start position:0% +something that has heavy tails then it's +more likely that pure noise will + + align:start position:0% +more likely that pure noise will + + + align:start position:0% +more likely that pure noise will +generate larger observations and + + align:start position:0% +generate larger observations and + + + align:start position:0% +generate larger observations and +therefore discovery. So yes lighter + + align:start position:0% +therefore discovery. So yes lighter + + + align:start position:0% +therefore discovery. So yes lighter +tails is definitely + + align:start position:0% +tails is definitely + + + align:start position:0% +tails is definitely +the be better behaved noise. Let's put + + align:start position:0% +the be better behaved noise. Let's put + + + align:start position:0% +the be better behaved noise. Let's put +it this way. The lighter it is, the + + align:start position:0% +it this way. The lighter it is, the + + + align:start position:0% +it this way. The lighter it is, the +better behaved it is. Now for this is + + align:start position:0% +better behaved it is. Now for this is + + + align:start position:0% +better behaved it is. Now for this is +good in this is good for some purposes. + + align:start position:0% +good in this is good for some purposes. + + + align:start position:0% +good in this is good for some purposes. +But when you want to compute actual + + align:start position:0% +But when you want to compute actual + + + align:start position:0% +But when you want to compute actual +quentiles + + align:start position:0% + + + + align:start position:0% + +like exact quentiles, then it it is true + + align:start position:0% +like exact quentiles, then it it is true + + + align:start position:0% +like exact quentiles, then it it is true +in general that the quentiles of a + + align:start position:0% +in general that the quentiles of a + + + align:start position:0% +in general that the quentiles of a +lighter tail distributions are going to + + align:start position:0% +lighter tail distributions are going to + + + align:start position:0% +lighter tail distributions are going to +be dominated by the are going to + + align:start position:0% +be dominated by the are going to + + + align:start position:0% +be dominated by the are going to +be dominated by the uh let's say on the + + align:start position:0% +be dominated by the uh let's say on the + + + align:start position:0% +be dominated by the uh let's say on the +right tails are going to be dominated by + + align:start position:0% +right tails are going to be dominated by + + + align:start position:0% +right tails are going to be dominated by +those of a heavy distribution. uh that + + align:start position:0% +those of a heavy distribution. uh that + + + align:start position:0% +those of a heavy distribution. uh that +is true, but it's not always the case. + + align:start position:0% +is true, but it's not always the case. + + + align:start position:0% +is true, but it's not always the case. +And in particular, there's going to be + + align:start position:0% +And in particular, there's going to be + + + align:start position:0% +And in particular, there's going to be +some like sort of weird points where + + align:start position:0% +some like sort of weird points where + + + align:start position:0% +some like sort of weird points where +things are actually changing depending + + align:start position:0% +things are actually changing depending + + + align:start position:0% +things are actually changing depending +on what level you're actually looking at + + align:start position:0% +on what level you're actually looking at + + + align:start position:0% +on what level you're actually looking at +those things, maybe 5% or 10% in which + + align:start position:0% +those things, maybe 5% or 10% in which + + + align:start position:0% +those things, maybe 5% or 10% in which +case things might be changing a little + + align:start position:0% +case things might be changing a little + + + align:start position:0% +case things might be changing a little +bit. But if you start going really + + align:start position:0% +bit. But if you start going really + + + align:start position:0% +bit. But if you start going really +towards the tail, if you start looking + + align:start position:0% +towards the tail, if you start looking + + + align:start position:0% +towards the tail, if you start looking +at levels alpha, which are 1% or 0.1%, + + align:start position:0% +at levels alpha, which are 1% or 0.1%, + + + align:start position:0% +at levels alpha, which are 1% or 0.1%, +it is true that you're it's always if + + align:start position:0% +it is true that you're it's always if + + + align:start position:0% +it is true that you're it's always if +you can actually so if you see something + + align:start position:0% +you can actually so if you see something + + + align:start position:0% +you can actually so if you see something +that looks light tail, you definitely do + + align:start position:0% +that looks light tail, you definitely do + + + align:start position:0% +that looks light tail, you definitely do +not want to conclude that it's Gaussian. + + align:start position:0% +not want to conclude that it's Gaussian. + + + align:start position:0% +not want to conclude that it's Gaussian. +You want to actually change your + + align:start position:0% +You want to actually change your + + + align:start position:0% +You want to actually change your +modeling so that you're it makes your + + align:start position:0% +modeling so that you're it makes your + + + align:start position:0% +modeling so that you're it makes your +life even easier and uh and you actually + + align:start position:0% +life even easier and uh and you actually + + + align:start position:0% +life even easier and uh and you actually +factor in the fact that you can see that + + align:start position:0% +factor in the fact that you can see that + + + align:start position:0% +factor in the fact that you can see that +the the noise is actually more benign + + align:start position:0% +the the noise is actually more benign + + + align:start position:0% +the the noise is actually more benign +than you would like it to be. + + align:start position:0% +than you would like it to be. + + + align:start position:0% +than you would like it to be. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Stretching fingers. That's it. All + + align:start position:0% +Stretching fingers. That's it. All + + + align:start position:0% +Stretching fingers. That's it. All +right. Um Okay. So I want to I mentioned + + align:start position:0% +right. Um Okay. So I want to I mentioned + + + align:start position:0% +right. Um Okay. So I want to I mentioned +at some point that uh we had this uh + + align:start position:0% +at some point that uh we had this uh + + + align:start position:0% +at some point that uh we had this uh +kquare test that uh was showing up and I + + align:start position:0% +kquare test that uh was showing up and I + + + align:start position:0% +kquare test that uh was showing up and I +do not know what I did. Let's just Oh + + align:start position:0% +do not know what I did. Let's just Oh + + + align:start position:0% +do not know what I did. Let's just Oh +yeah. So you know we have this k square + + align:start position:0% +yeah. So you know we have this k square + + + align:start position:0% +yeah. So you know we have this k square +test that we uh we worked on uh last + + align:start position:0% +test that we uh we worked on uh last + + + align:start position:0% +test that we uh we worked on uh last +time right so the way we I introduce the + + align:start position:0% +time right so the way we I introduce the + + + align:start position:0% +time right so the way we I introduce the +k square test is by saying I am + + align:start position:0% +k square test is by saying I am + + + align:start position:0% +k square test is by saying I am +fascinated by this question let's check + + align:start position:0% +fascinated by this question let's check + + + align:start position:0% +fascinated by this question let's check +if it's correct okay or let's you know + + align:start position:0% +if it's correct okay or let's you know + + + align:start position:0% +if it's correct okay or let's you know +something maybe slightly deeper let's + + align:start position:0% +something maybe slightly deeper let's + + + align:start position:0% +something maybe slightly deeper let's +check if juries in this country are + + align:start position:0% +check if juries in this country are + + + align:start position:0% +check if juries in this country are +representative of uh uh uh racial + + align:start position:0% +representative of uh uh uh racial + + + align:start position:0% +representative of uh uh uh racial +distribution but uh uh you could + + align:start position:0% +distribution but uh uh you could + + + align:start position:0% +distribution but uh uh you could +actually those numbers here come from + + align:start position:0% +actually those numbers here come from + + + align:start position:0% +actually those numbers here come from +like very specific thing that was the + + align:start position:0% +like very specific thing that was the + + + align:start position:0% +like very specific thing that was the +uniform that was our benchmark here's + + align:start position:0% +uniform that was our benchmark here's + + + align:start position:0% +uniform that was our benchmark here's +the uniform + + align:start position:0% +the uniform + + + align:start position:0% +the uniform +And there was the uh this guy which was + + align:start position:0% +And there was the uh this guy which was + + + align:start position:0% +And there was the uh this guy which was +a benchmark which was you know the + + align:start position:0% +a benchmark which was you know the + + + align:start position:0% +a benchmark which was you know the +actual benchmark that we need to have + + align:start position:0% +actual benchmark that we need to have + + + align:start position:0% +actual benchmark that we need to have +for this problem and those things + + align:start position:0% +for this problem and those things + + + align:start position:0% +for this problem and those things +basically came out of my hat right those + + align:start position:0% +basically came out of my hat right those + + + align:start position:0% +basically came out of my hat right those +are numbers that exist but in practice + + align:start position:0% +are numbers that exist but in practice + + + align:start position:0% +are numbers that exist but in practice +you actually make those numbers yourself + + align:start position:0% +you actually make those numbers yourself + + + align:start position:0% +you actually make those numbers yourself +and the way you do it is by saying well + + align:start position:0% +and the way you do it is by saying well + + + align:start position:0% +and the way you do it is by saying well +if I have a binomial distribution + + align:start position:0% +if I have a binomial distribution + + + align:start position:0% +if I have a binomial distribution +and I want to test if my data comes from + + align:start position:0% +and I want to test if my data comes from + + + align:start position:0% +and I want to test if my data comes from +a binomial distribution you could ask + + align:start position:0% +a binomial distribution you could ask + + + align:start position:0% +a binomial distribution you could ask +this question right you have a bunch of + + align:start position:0% +this question right you have a bunch of + + + align:start position:0% +this question right you have a bunch of +data I did not promise to you that you + + align:start position:0% +data I did not promise to you that you + + + align:start position:0% +data I did not promise to you that you +know this was the sum of independent + + align:start position:0% +know this was the sum of independent + + + align:start position:0% +know this was the sum of independent +Bernal and law and then you can actually + + align:start position:0% +Bernal and law and then you can actually + + + align:start position:0% +Bernal and law and then you can actually +check that it's a binomial indeed and + + align:start position:0% +check that it's a binomial indeed and + + + align:start position:0% +check that it's a binomial indeed and +you have binomial if you think about + + align:start position:0% +you have binomial if you think about + + + align:start position:0% +you have binomial if you think about +where you've encountered binomials it + + align:start position:0% +where you've encountered binomials it + + + align:start position:0% +where you've encountered binomials it +was mostly when you were drawing balls + + align:start position:0% +was mostly when you were drawing balls + + + align:start position:0% +was mostly when you were drawing balls +from earns which you probably don't do + + align:start position:0% +from earns which you probably don't do + + + align:start position:0% +from earns which you probably don't do +that much in practice okay and so maybe + + align:start position:0% +that much in practice okay and so maybe + + + align:start position:0% +that much in practice okay and so maybe +one day you want to model things as a + + align:start position:0% +one day you want to model things as a + + + align:start position:0% +one day you want to model things as a +binomial or maybe you want to model as a + + align:start position:0% +binomial or maybe you want to model as a + + + align:start position:0% +binomial or maybe you want to model as a +as a limited binomial right people tell + + align:start position:0% +as a limited binomial right people tell + + + align:start position:0% +as a limited binomial right people tell +you you know photons arrive the rate of + + align:start position:0% +you you know photons arrive the rate of + + + align:start position:0% +you you know photons arrive the rate of +photon hitting some surface is actually + + align:start position:0% +photon hitting some surface is actually + + + align:start position:0% +photon hitting some surface is actually +a pson distribution right that's where + + align:start position:0% +a pson distribution right that's where + + + align:start position:0% +a pson distribution right that's where +they arise a lot in imaging + + align:start position:0% +they arise a lot in imaging + + + align:start position:0% +they arise a lot in imaging +Uh right. So if I you know I have a + + align:start position:0% +Uh right. So if I you know I have a + + + align:start position:0% +Uh right. So if I you know I have a +colleague who's taking pictures of the + + align:start position:0% +colleague who's taking pictures of the + + + align:start position:0% +colleague who's taking pictures of the +skies overnight and he's like following + + align:start position:0% +skies overnight and he's like following + + + align:start position:0% +skies overnight and he's like following +stars and it's just like moving around + + align:start position:0% +stars and it's just like moving around + + + align:start position:0% +stars and it's just like moving around +with the rotation of the earth and he + + align:start position:0% +with the rotation of the earth and he + + + align:start position:0% +with the rotation of the earth and he +has to do this for like you know eight + + align:start position:0% +has to do this for like you know eight + + + align:start position:0% +has to do this for like you know eight +hours because he needs to get enough + + align:start position:0% +hours because he needs to get enough + + + align:start position:0% +hours because he needs to get enough +photons for this picture to actually + + align:start position:0% +photons for this picture to actually + + + align:start position:0% +photons for this picture to actually +arise and he knows they arrive at you + + align:start position:0% +arise and he knows they arrive at you + + + align:start position:0% +arise and he knows they arrive at you +know pesson like a pesson process and + + align:start position:0% +know pesson like a pesson process and + + + align:start position:0% +know pesson like a pesson process and +you know yeah chapter seven of your + + align:start position:0% +you know yeah chapter seven of your + + + align:start position:0% +you know yeah chapter seven of your +probability class I guess and u and you + + align:start position:0% +probability class I guess and u and you + + + align:start position:0% +probability class I guess and u and you +know there's all these distributions + + align:start position:0% +know there's all these distributions + + + align:start position:0% +know there's all these distributions +that you know outside the classroom you + + align:start position:0% +that you know outside the classroom you + + + align:start position:0% +that you know outside the classroom you +probably want to check that they're + + align:start position:0% +probably want to check that they're + + + align:start position:0% +probably want to check that they're +actually correct and so the first one + + align:start position:0% +actually correct and so the first one + + + align:start position:0% +actually correct and so the first one +you I want to check for example is a is + + align:start position:0% +you I want to check for example is a is + + + align:start position:0% +you I want to check for example is a is +a binomial. So I give you a distribution + + align:start position:0% +a binomial. So I give you a distribution + + + align:start position:0% +a binomial. So I give you a distribution +a binomial distribution on say k trials + + align:start position:0% +a binomial distribution on say k trials + + + align:start position:0% +a binomial distribution on say k trials +and you have some number p and here I + + align:start position:0% +and you have some number p and here I + + + align:start position:0% +and you have some number p and here I +don't know typically what p should be + + align:start position:0% +don't know typically what p should be + + + align:start position:0% +don't know typically what p should be +but let's say I know it or I estimated + + align:start position:0% +but let's say I know it or I estimated + + + align:start position:0% +but let's say I know it or I estimated +from my data and here since we're only + + align:start position:0% +from my data and here since we're only + + + align:start position:0% +from my data and here since we're only +going to do asmtoics just like it was + + align:start position:0% +going to do asmtoics just like it was + + + align:start position:0% +going to do asmtoics just like it was +the case for the komograph smoff one in + + align:start position:0% +the case for the komograph smoff one in + + + align:start position:0% +the case for the komograph smoff one in +the asmtoic we're going to be able to + + align:start position:0% +the asmtoic we're going to be able to + + + align:start position:0% +the asmtoic we're going to be able to +think of the uh estimated p as being the + + align:start position:0% +think of the uh estimated p as being the + + + align:start position:0% +think of the uh estimated p as being the +true p okay under the null at least. So + + align:start position:0% +true p okay under the null at least. So + + + align:start position:0% +true p okay under the null at least. So +now for each outcome + + align:start position:0% +now for each outcome + + + align:start position:0% +now for each outcome +I can actually tell you what the + + align:start position:0% +I can actually tell you what the + + + align:start position:0% +I can actually tell you what the +probability of a binomial is this + + align:start position:0% +probability of a binomial is this + + + align:start position:0% +probability of a binomial is this +outcome. For a given K and a given P I + + align:start position:0% +outcome. For a given K and a given P I + + + align:start position:0% +outcome. For a given K and a given P I +can tell you exactly what a binomial + + align:start position:0% +can tell you exactly what a binomial + + + align:start position:0% +can tell you exactly what a binomial +should give you as a probability for the + + align:start position:0% +should give you as a probability for the + + + align:start position:0% +should give you as a probability for the +outcome. And that's what I actually use + + align:start position:0% +outcome. And that's what I actually use + + + align:start position:0% +outcome. And that's what I actually use +to replace the numbers uh you know uh uh + + align:start position:0% +to replace the numbers uh you know uh uh + + + align:start position:0% +to replace the numbers uh you know uh uh +1 over 12 one over 12 one over 12 one + + align:start position:0% +1 over 12 one over 12 one over 12 one + + + align:start position:0% +1 over 12 one over 12 one over 12 one +over 12 or the numbers uh 72.07 + + align:start position:0% +over 12 or the numbers uh 72.07 + + + align:start position:0% +over 12 or the numbers uh 72.07 +uh2.09 009 all these numbers I can + + align:start position:0% +uh2.09 009 all these numbers I can + + + align:start position:0% +uh2.09 009 all these numbers I can +actually compute using the probabilities + + align:start position:0% +actually compute using the probabilities + + + align:start position:0% +actually compute using the probabilities +of a binomial right so I know for + + align:start position:0% +of a binomial right so I know for + + + align:start position:0% +of a binomial right so I know for +example that the probability that a + + align:start position:0% +example that the probability that a + + + align:start position:0% +example that the probability that a +binomial np is equal to say k is uh n + + align:start position:0% +binomial np is equal to say k is uh n + + + align:start position:0% +binomial np is equal to say k is uh n +choose k + + align:start position:0% +choose k + + + align:start position:0% +choose k +uh p to the k uh 1 minus p to the n + + align:start position:0% +uh p to the k uh 1 minus p to the n + + + align:start position:0% +uh p to the k uh 1 minus p to the n +minus k okay + + align:start position:0% +minus k okay + + + align:start position:0% +minus k okay +and so these are numbers if you give me + + align:start position:0% +and so these are numbers if you give me + + + align:start position:0% +and so these are numbers if you give me +p and you give me n I can compute those + + align:start position:0% +p and you give me n I can compute those + + + align:start position:0% +p and you give me n I can compute those +numbers for all K from 0 to N and from + + align:start position:0% +numbers for all K from 0 to N and from + + + align:start position:0% +numbers for all K from 0 to N and from +this I can actually build a table + + align:start position:0% + + + + align:start position:0% + +right so for each k + + align:start position:0% +right so for each k + + + align:start position:0% +right so for each k +zero so k is here and uh from zero one + + align:start position:0% +zero so k is here and uh from zero one + + + align:start position:0% +zero so k is here and uh from zero one +etc all the way to n I can compute the + + align:start position:0% +etc all the way to n I can compute the + + + align:start position:0% +etc all the way to n I can compute the +true probability which is the + + align:start position:0% +true probability which is the + + + align:start position:0% +true probability which is the +probability that my binomial np is equal + + align:start position:0% +probability that my binomial np is equal + + + align:start position:0% +probability that my binomial np is equal +to zero the probability that my binomial + + align:start position:0% +to zero the probability that my binomial + + + align:start position:0% +to zero the probability that my binomial +is equal to one etc all the way to n I + + align:start position:0% +is equal to one etc all the way to n I + + + align:start position:0% +is equal to one etc all the way to n I +can compute those numbers those are + + align:start position:0% +can compute those numbers those are + + + align:start position:0% +can compute those numbers those are +actually going to be exact numbers right + + align:start position:0% +actually going to be exact numbers right + + + align:start position:0% +actually going to be exact numbers right +I just plug in uh in the formula that I + + align:start position:0% +I just plug in uh in the formula that I + + + align:start position:0% +I just plug in uh in the formula that I +had and then I'm going to have some + + align:start position:0% +had and then I'm going to have some + + + align:start position:0% +had and then I'm going to have some +observed + + align:start position:0% + + + + align:start position:0% + +so that's going to be p hat zero and + + align:start position:0% +so that's going to be p hat zero and + + + align:start position:0% +so that's going to be p hat zero and +that's basically the proportions + + align:start position:0% + + + + align:start position:0% + +of zeros + + align:start position:0% + + + + align:start position:0% + +Right. So here you have to remember + + align:start position:0% +Right. So here you have to remember + + + align:start position:0% +Right. So here you have to remember +it's not a one-time experiment like you + + align:start position:0% +it's not a one-time experiment like you + + + align:start position:0% +it's not a one-time experiment like you +do in probability where you say I'm + + align:start position:0% +do in probability where you say I'm + + + align:start position:0% +do in probability where you say I'm +going to draw + + align:start position:0% +going to draw + + + align:start position:0% +going to draw +uh uh n balls from an urn and I'm + + align:start position:0% +uh uh n balls from an urn and I'm + + + align:start position:0% +uh uh n balls from an urn and I'm +counting how many how many I have. This + + align:start position:0% +counting how many how many I have. This + + + align:start position:0% +counting how many how many I have. This +is statistics. I need to be able to do + + align:start position:0% +is statistics. I need to be able to do + + + align:start position:0% +is statistics. I need to be able to do +this experiment many times. So I can + + align:start position:0% +this experiment many times. So I can + + + align:start position:0% +this experiment many times. So I can +actually have in the end get an idea of + + align:start position:0% +actually have in the end get an idea of + + + align:start position:0% +actually have in the end get an idea of +what the proportion of PS is. So you + + align:start position:0% +what the proportion of PS is. So you + + + align:start position:0% +what the proportion of PS is. So you +have not just one binomial but you have + + align:start position:0% +have not just one binomial but you have + + + align:start position:0% +have not just one binomial but you have +n binomials. Oh, maybe I should not use + + align:start position:0% +n binomials. Oh, maybe I should not use + + + align:start position:0% +n binomials. Oh, maybe I should not use +N twice. So that's why it's a K here, + + align:start position:0% +N twice. So that's why it's a K here, + + + align:start position:0% +N twice. So that's why it's a K here, +right? So I have a binomial K KP and I + + align:start position:0% +right? So I have a binomial K KP and I + + + align:start position:0% +right? So I have a binomial K KP and I +just sees N of those guys. And with this + + align:start position:0% +just sees N of those guys. And with this + + + align:start position:0% +just sees N of those guys. And with this +N of those guys, I can actually estimate + + align:start position:0% +N of those guys, I can actually estimate + + + align:start position:0% +N of those guys, I can actually estimate +those probabilities. And what I'm going + + align:start position:0% +those probabilities. And what I'm going + + + align:start position:0% +those probabilities. And what I'm going +to want to check if is those two + + align:start position:0% +to want to check if is those two + + + align:start position:0% +to want to check if is those two +probabilities are actually close to each + + align:start position:0% +probabilities are actually close to each + + + align:start position:0% +probabilities are actually close to each +other. But I already know how to do + + align:start position:0% +other. But I already know how to do + + + align:start position:0% +other. But I already know how to do +this. + + align:start position:0% +this. + + + align:start position:0% +this. +All right. So here I'm going to test + + align:start position:0% +All right. So here I'm going to test + + + align:start position:0% +All right. So here I'm going to test +whether P is in some parametric family. + + align:start position:0% +whether P is in some parametric family. + + + align:start position:0% +whether P is in some parametric family. +For example, binomial or not binomial. + + align:start position:0% +For example, binomial or not binomial. + + + align:start position:0% +For example, binomial or not binomial. +And uh and uh uh testing. If I know that + + align:start position:0% +And uh and uh uh testing. If I know that + + + align:start position:0% +And uh and uh uh testing. If I know that +it's a binomial ship, I basically just + + align:start position:0% +it's a binomial ship, I basically just + + + align:start position:0% +it's a binomial ship, I basically just +have to test if P is the right thing. + + align:start position:0% +have to test if P is the right thing. + + + align:start position:0% +have to test if P is the right thing. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Oh, sorry. Uh I'm actually uh lying to + + align:start position:0% +Oh, sorry. Uh I'm actually uh lying to + + + align:start position:0% +Oh, sorry. Uh I'm actually uh lying to +you here. Okay. I don't want to test if + + align:start position:0% +you here. Okay. I don't want to test if + + + align:start position:0% +you here. Okay. I don't want to test if +it's binomial. I want to test the the + + align:start position:0% +it's binomial. I want to test the the + + + align:start position:0% +it's binomial. I want to test the the +the the probabil the parameter of the + + align:start position:0% +the the probabil the parameter of the + + + align:start position:0% +the the probabil the parameter of the +binomial here. Okay. So, I know right. + + align:start position:0% +binomial here. Okay. So, I know right. + + + align:start position:0% +binomial here. Okay. So, I know right. +So, no, sorry, that's sorry. Okay. So, I + + align:start position:0% +So, no, sorry, that's sorry. Okay. So, I + + + align:start position:0% +So, no, sorry, that's sorry. Okay. So, I +want to know if I'm in some family, the + + align:start position:0% +want to know if I'm in some family, the + + + align:start position:0% +want to know if I'm in some family, the +family of binomials or not in the family + + align:start position:0% +family of binomials or not in the family + + + align:start position:0% +family of binomials or not in the family +of binomials. Okay. So, that's what I + + align:start position:0% +of binomials. Okay. So, that's what I + + + align:start position:0% +of binomials. Okay. So, that's what I +want to do. And so here h0 is basically + + align:start position:0% +want to do. And so here h0 is basically + + + align:start position:0% +want to do. And so here h0 is basically +equivalent to testing if the pjs are the + + align:start position:0% +equivalent to testing if the pjs are the + + + align:start position:0% +equivalent to testing if the pjs are the +pjs that come from the binomial and the + + align:start position:0% +pjs that come from the binomial and the + + + align:start position:0% +pjs that come from the binomial and the +pjs here are the probabilities that my I + + align:start position:0% +pjs here are the probabilities that my I + + + align:start position:0% +pjs here are the probabilities that my I +get this is the probability that I get j + + align:start position:0% +get this is the probability that I get j + + + align:start position:0% +get this is the probability that I get j +uh successes uh that's my pj that's the + + align:start position:0% +uh successes uh that's my pj that's the + + + align:start position:0% +uh successes uh that's my pj that's the +j value here + + align:start position:0% +j value here + + + align:start position:0% +j value here +okay so this is the example and we know + + align:start position:0% +okay so this is the example and we know + + + align:start position:0% +okay so this is the example and we know +how to do this we construct p hat which + + align:start position:0% +how to do this we construct p hat which + + + align:start position:0% +how to do this we construct p hat which +is the estimated proportion of successes + + align:start position:0% +is the estimated proportion of successes + + + align:start position:0% +is the estimated proportion of successes +from the observation so here now I have + + align:start position:0% +from the observation so here now I have + + + align:start position:0% +from the observation so here now I have +n trials this is the actual ual maximum + + align:start position:0% +n trials this is the actual ual maximum + + + align:start position:0% +n trials this is the actual ual maximum +likelihood estimator. This becomes a b + + align:start position:0% +likelihood estimator. This becomes a b + + + align:start position:0% +likelihood estimator. This becomes a b +multinnomial experiment and uh right so + + align:start position:0% +multinnomial experiment and uh right so + + + align:start position:0% +multinnomial experiment and uh right so +it's kind of confusing. We have a + + align:start position:0% +it's kind of confusing. We have a + + + align:start position:0% +it's kind of confusing. We have a +multinnomial experiment for binomial + + align:start position:0% +multinnomial experiment for binomial + + + align:start position:0% +multinnomial experiment for binomial +distribution. The binomial here is just + + align:start position:0% +distribution. The binomial here is just + + + align:start position:0% +distribution. The binomial here is just +a recipe to create some test + + align:start position:0% +a recipe to create some test + + + align:start position:0% +a recipe to create some test +probabilities. That's all it is. + + align:start position:0% +probabilities. That's all it is. + + + align:start position:0% +probabilities. That's all it is. +Binomial here doesn't really matter. + + align:start position:0% +Binomial here doesn't really matter. + + + align:start position:0% +Binomial here doesn't really matter. +It's really to create the test + + align:start position:0% +It's really to create the test + + + align:start position:0% +It's really to create the test +probabilities. And then I'm going to + + align:start position:0% +probabilities. And then I'm going to + + + align:start position:0% +probabilities. And then I'm going to +define this test statistic which is + + align:start position:0% +define this test statistic which is + + + align:start position:0% +define this test statistic which is +known as + + align:start position:0% + + + + align:start position:0% + +the k square statistic. Right? + + align:start position:0% +the k square statistic. Right? + + + align:start position:0% +the k square statistic. Right? +This was the k square test. We just + + align:start position:0% +This was the k square test. We just + + + align:start position:0% +This was the k square test. We just +looked at the sum of the square of the + + align:start position:0% +looked at the sum of the square of the + + + align:start position:0% +looked at the sum of the square of the +differences in inverting the coarian + + align:start position:0% +differences in inverting the coarian + + + align:start position:0% +differences in inverting the coarian +matrix or using the fisher information + + align:start position:0% +matrix or using the fisher information + + + align:start position:0% +matrix or using the fisher information +with removing the part that was not + + align:start position:0% +with removing the part that was not + + + align:start position:0% +with removing the part that was not +invertible led us to actually use this + + align:start position:0% +invertible led us to actually use this + + + align:start position:0% +invertible led us to actually use this +particular value here. And then we had + + align:start position:0% +particular value here. And then we had + + + align:start position:0% +particular value here. And then we had +to multiply by n. + + align:start position:0% +to multiply by n. + + + align:start position:0% +to multiply by n. +Okay. And that we know converges to + + align:start position:0% +Okay. And that we know converges to + + + align:start position:0% +Okay. And that we know converges to +what? + + align:start position:0% +what? + + + align:start position:0% +what? +A k square distribution. So I'm not + + align:start position:0% +A k square distribution. So I'm not + + + align:start position:0% +A k square distribution. So I'm not +going to go through this again. And I'm + + align:start position:0% +going to go through this again. And I'm + + + align:start position:0% +going to go through this again. And I'm +just telling you, you can use the kai + + align:start position:0% +just telling you, you can use the kai + + + align:start position:0% +just telling you, you can use the kai +square that we've seen where we we just + + align:start position:0% +square that we've seen where we we just + + + align:start position:0% +square that we've seen where we we just +came up with the numbers we were testing + + align:start position:0% +came up with the numbers we were testing + + + align:start position:0% +came up with the numbers we were testing +those numbers that were in this row for + + align:start position:0% +those numbers that were in this row for + + + align:start position:0% +those numbers that were in this row for +the true probabilities. We came up with + + align:start position:0% +the true probabilities. We came up with + + + align:start position:0% +the true probabilities. We came up with +them out of thin air. And now I'm + + align:start position:0% +them out of thin air. And now I'm + + + align:start position:0% +them out of thin air. And now I'm +telling you, you can actually come up + + align:start position:0% +telling you, you can actually come up + + + align:start position:0% +telling you, you can actually come up +with those guys from a binomial + + align:start position:0% +with those guys from a binomial + + + align:start position:0% +with those guys from a binomial +distribution or a quest distribution or + + align:start position:0% +distribution or a quest distribution or + + + align:start position:0% +distribution or a quest distribution or +whatever distribution you're happy with. + + align:start position:0% + + + + align:start position:0% + +Any question? + + align:start position:0% + + + + align:start position:0% + +So now I'm creating this thing and I can + + align:start position:0% +So now I'm creating this thing and I can + + + align:start position:0% +So now I'm creating this thing and I can +apply the entire theory that I had for + + align:start position:0% +apply the entire theory that I had for + + + align:start position:0% +apply the entire theory that I had for +the K square and in particular that this + + align:start position:0% +the K square and in particular that this + + + align:start position:0% +the K square and in particular that this +thing converges to a K square. + + align:start position:0% +thing converges to a K square. + + + align:start position:0% +thing converges to a K square. +But if you see there's something that's + + align:start position:0% +But if you see there's something that's + + + align:start position:0% +But if you see there's something that's +different. What is different? + + align:start position:0% + + + + align:start position:0% + +The degrees of freedom. And if you think + + align:start position:0% +The degrees of freedom. And if you think + + + align:start position:0% +The degrees of freedom. And if you think +about it + + align:start position:0% +about it + + + align:start position:0% +about it +again the meaning of degrees of freedom. + + align:start position:0% +again the meaning of degrees of freedom. + + + align:start position:0% +again the meaning of degrees of freedom. +What does this word in these words + + align:start position:0% +What does this word in these words + + + align:start position:0% +What does this word in these words +actually mean? It means well to which + + align:start position:0% +actually mean? It means well to which + + + align:start position:0% +actually mean? It means well to which +extent can I play around with those + + align:start position:0% +extent can I play around with those + + + align:start position:0% +extent can I play around with those +values? what are the possible values + + align:start position:0% +values? what are the possible values + + + align:start position:0% +values? what are the possible values +that I can get? If I'm not equal to this + + align:start position:0% +that I can get? If I'm not equal to this + + + align:start position:0% +that I can get? If I'm not equal to this +particular value I'm testing, how many + + align:start position:0% +particular value I'm testing, how many + + + align:start position:0% +particular value I'm testing, how many +directions can I be different from this + + align:start position:0% +directions can I be different from this + + + align:start position:0% +directions can I be different from this +guy? And when we had like a given set of + + align:start position:0% +guy? And when we had like a given set of + + + align:start position:0% +guy? And when we had like a given set of +values, we could be any other set of + + align:start position:0% +values, we could be any other set of + + + align:start position:0% +values, we could be any other set of +values. Right? So here I had this, I'm + + align:start position:0% +values. Right? So here I had this, I'm + + + align:start position:0% +values. Right? So here I had this, I'm +going to represent this is the set of + + align:start position:0% +going to represent this is the set of + + + align:start position:0% +going to represent this is the set of +all probability distributions of vectors + + align:start position:0% +all probability distributions of vectors + + + align:start position:0% +all probability distributions of vectors +of a certain of size K. So here if I + + align:start position:0% +of a certain of size K. So here if I + + + align:start position:0% +of a certain of size K. So here if I +look at one point in this set this is + + align:start position:0% +look at one point in this set this is + + + align:start position:0% +look at one point in this set this is +something that looks like P1 to PK such + + align:start position:0% +something that looks like P1 to PK such + + + align:start position:0% +something that looks like P1 to PK such +that their sum such that they're non- + + align:start position:0% +that their sum such that they're non- + + + align:start position:0% +that their sum such that they're non- +negative and the sum P1 to PK + + align:start position:0% + + + + align:start position:0% + +is equal to one. Okay. So I have all + + align:start position:0% +is equal to one. Okay. So I have all + + + align:start position:0% +is equal to one. Okay. So I have all +those points here. Okay. + + align:start position:0% +those points here. Okay. + + + align:start position:0% +those points here. Okay. +So this is basically the set that I had + + align:start position:0% +So this is basically the set that I had + + + align:start position:0% +So this is basically the set that I had +before if I was testing whether I was + + align:start position:0% +before if I was testing whether I was + + + align:start position:0% +before if I was testing whether I was +equal to this one guy or if I was + + align:start position:0% +equal to this one guy or if I was + + + align:start position:0% +equal to this one guy or if I was +anything else. And there's many ways I + + align:start position:0% +anything else. And there's many ways I + + + align:start position:0% +anything else. And there's many ways I +can be anything else. What matters of + + align:start position:0% +can be anything else. What matters of + + + align:start position:0% +can be anything else. What matters of +course is what's around this guy that + + align:start position:0% +course is what's around this guy that + + + align:start position:0% +course is what's around this guy that +could I could actually confuse me myself + + align:start position:0% +could I could actually confuse me myself + + + align:start position:0% +could I could actually confuse me myself +with. But there's many ways I can move + + align:start position:0% +with. But there's many ways I can move + + + align:start position:0% +with. But there's many ways I can move +around this guy. Agreed? + + align:start position:0% +around this guy. Agreed? + + + align:start position:0% +around this guy. Agreed? +Now I'm actually just testing something + + align:start position:0% +Now I'm actually just testing something + + + align:start position:0% +Now I'm actually just testing something +very specific. I'm saying well now the + + align:start position:0% +very specific. I'm saying well now the + + + align:start position:0% +very specific. I'm saying well now the +piece that I have have to come from this + + align:start position:0% +piece that I have have to come from this + + + align:start position:0% +piece that I have have to come from this +have to be constructed from this uh + + align:start position:0% +have to be constructed from this uh + + + align:start position:0% +have to be constructed from this uh +formula this parametric family p of + + align:start position:0% +formula this parametric family p of + + + align:start position:0% +formula this parametric family p of +theta. And there's a very you know + + align:start position:0% +theta. And there's a very you know + + + align:start position:0% +theta. And there's a very you know +there's a fixed way for let's say this + + align:start position:0% +there's a fixed way for let's say this + + + align:start position:0% +there's a fixed way for let's say this +is theta. So I have a theta here. + + align:start position:0% +is theta. So I have a theta here. + + + align:start position:0% +is theta. So I have a theta here. +There's not that many ways this can + + align:start position:0% +There's not that many ways this can + + + align:start position:0% +There's not that many ways this can +actually give me a set of probabilities, + + align:start position:0% +actually give me a set of probabilities, + + + align:start position:0% +actually give me a set of probabilities, +right? I can I have to move to another + + align:start position:0% +right? I can I have to move to another + + + align:start position:0% +right? I can I have to move to another +theta to actually start being confused. + + align:start position:0% +theta to actually start being confused. + + + align:start position:0% +theta to actually start being confused. +And so here the number of degrees of + + align:start position:0% +And so here the number of degrees of + + + align:start position:0% +And so here the number of degrees of +freedom is basically how can I move + + align:start position:0% +freedom is basically how can I move + + + align:start position:0% +freedom is basically how can I move +along this family? And so here this is + + align:start position:0% +along this family? And so here this is + + + align:start position:0% +along this family? And so here this is +all the points but there might be just a + + align:start position:0% +all the points but there might be just a + + + align:start position:0% +all the points but there might be just a +subset of the points that looks like + + align:start position:0% +subset of the points that looks like + + + align:start position:0% +subset of the points that looks like +this just this curve not uh a half half + + align:start position:0% +this just this curve not uh a half half + + + align:start position:0% +this just this curve not uh a half half +of the same thing. And those guys on + + align:start position:0% +of the same thing. And those guys on + + + align:start position:0% +of the same thing. And those guys on +this curves are the p thetas + + align:start position:0% + + + + align:start position:0% + +and that's for all thetas when theta + + align:start position:0% +and that's for all thetas when theta + + + align:start position:0% +and that's for all thetas when theta +runs across theta. So in a way this is + + align:start position:0% +runs across theta. So in a way this is + + + align:start position:0% +runs across theta. So in a way this is +just a much smaller dimensional thing. + + align:start position:0% +just a much smaller dimensional thing. + + + align:start position:0% +just a much smaller dimensional thing. +It's a much smaller object. Those are + + align:start position:0% +It's a much smaller object. Those are + + + align:start position:0% +It's a much smaller object. Those are +the only the ones that I can create that + + align:start position:0% +the only the ones that I can create that + + + align:start position:0% +the only the ones that I can create that +are exactly of this very specific + + align:start position:0% +are exactly of this very specific + + + align:start position:0% +are exactly of this very specific +parametric form. + + align:start position:0% +parametric form. + + + align:start position:0% +parametric form. +And not of course not all are of this + + align:start position:0% +And not of course not all are of this + + + align:start position:0% +And not of course not all are of this +form. that all probability PMFs are of + + align:start position:0% +form. that all probability PMFs are of + + + align:start position:0% +form. that all probability PMFs are of +this form. And so that is going to have + + align:start position:0% +this form. And so that is going to have + + + align:start position:0% +this form. And so that is going to have +an effect on what my uh PMF is going to + + align:start position:0% +an effect on what my uh PMF is going to + + + align:start position:0% +an effect on what my uh PMF is going to +be on sorry on what my um my uh um uh + + align:start position:0% +be on sorry on what my um my uh um uh + + + align:start position:0% +be on sorry on what my um my uh um uh +sorry what my um + + align:start position:0% +sorry what my um + + + align:start position:0% +sorry what my um +uh degrees of freedoms are going to be + + align:start position:0% +uh degrees of freedoms are going to be + + + align:start position:0% +uh degrees of freedoms are going to be +because when this thing is very small + + align:start position:0% +because when this thing is very small + + + align:start position:0% +because when this thing is very small +right that means when that's happening + + align:start position:0% +right that means when that's happening + + + align:start position:0% +right that means when that's happening +when theta is actually say a + + align:start position:0% +when theta is actually say a + + + align:start position:0% +when theta is actually say a +one-dimensional space then there's still + + align:start position:0% +one-dimensional space then there's still + + + align:start position:0% +one-dimensional space then there's still +many ways I can escape right I can be + + align:start position:0% +many ways I can escape right I can be + + + align:start position:0% +many ways I can escape right I can be +different from this guy in pretty every + + align:start position:0% +different from this guy in pretty every + + + align:start position:0% +different from this guy in pretty every +other direction except for those two + + align:start position:0% +other direction except for those two + + + align:start position:0% +other direction except for those two +directions just when I move from here or + + align:start position:0% +directions just when I move from here or + + + align:start position:0% +directions just when I move from here or +when I move in this direction. But now + + align:start position:0% +when I move in this direction. But now + + + align:start position:0% +when I move in this direction. But now +if this thing becomes bigger + + align:start position:0% +if this thing becomes bigger + + + align:start position:0% +if this thing becomes bigger +here theta is say two-dimensional + + align:start position:0% +here theta is say two-dimensional + + + align:start position:0% +here theta is say two-dimensional +then when I'm here it's becoming harder + + align:start position:0% +then when I'm here it's becoming harder + + + align:start position:0% +then when I'm here it's becoming harder +for me to not be that guy. If I want to + + align:start position:0% +for me to not be that guy. If I want to + + + align:start position:0% +for me to not be that guy. If I want to +move away from it I have to move away + + align:start position:0% +move away from it I have to move away + + + align:start position:0% +move away from it I have to move away +from the board. + + align:start position:0% +from the board. + + + align:start position:0% +from the board. +And so that means that the bigger the + + align:start position:0% +And so that means that the bigger the + + + align:start position:0% +And so that means that the bigger the +dimension of my uh of my theta, the + + align:start position:0% +dimension of my uh of my theta, the + + + align:start position:0% +dimension of my uh of my theta, the +smaller the degrees of freedoms that I + + align:start position:0% +smaller the degrees of freedoms that I + + + align:start position:0% +smaller the degrees of freedoms that I +have. + + align:start position:0% +have. + + + align:start position:0% +have. +Okay? Because moving out of this + + align:start position:0% +Okay? Because moving out of this + + + align:start position:0% +Okay? Because moving out of this +parametric family is actually very + + align:start position:0% +parametric family is actually very + + + align:start position:0% +parametric family is actually very +difficult for me. So if you think for + + align:start position:0% +difficult for me. So if you think for + + + align:start position:0% +difficult for me. So if you think for +example as the at an extreme case, the + + align:start position:0% +example as the at an extreme case, the + + + align:start position:0% +example as the at an extreme case, the +parametric family that I have is + + align:start position:0% +parametric family that I have is + + + align:start position:0% +parametric family that I have is +basically all + + align:start position:0% +basically all + + + align:start position:0% +basically all +uh uh PMFs all of them. Right? So that's + + align:start position:0% +uh uh PMFs all of them. Right? So that's + + + align:start position:0% +uh uh PMFs all of them. Right? So that's +a stupid parametric family. I'm indexed + + align:start position:0% +a stupid parametric family. I'm indexed + + + align:start position:0% +a stupid parametric family. I'm indexed +by the distribution itself, but it's + + align:start position:0% +by the distribution itself, but it's + + + align:start position:0% +by the distribution itself, but it's +still finite dimensional. Then here I + + align:start position:0% +still finite dimensional. Then here I + + + align:start position:0% +still finite dimensional. Then here I +have basically no degrees of freedom. + + align:start position:0% +have basically no degrees of freedom. + + + align:start position:0% +have basically no degrees of freedom. +There's no way I can actually not be + + align:start position:0% +There's no way I can actually not be + + + align:start position:0% +There's no way I can actually not be +that guy because this is everything I + + align:start position:0% +that guy because this is everything I + + + align:start position:0% +that guy because this is everything I +have. And so you don't have to really + + align:start position:0% +have. And so you don't have to really + + + align:start position:0% +have. And so you don't have to really +understand what the how the computation + + align:start position:0% +understand what the how the computation + + + align:start position:0% +understand what the how the computation +comes in into into numbers of of + + align:start position:0% +comes in into into numbers of of + + + align:start position:0% +comes in into into numbers of of +dimension and what I mean by dimension + + align:start position:0% +dimension and what I mean by dimension + + + align:start position:0% +dimension and what I mean by dimension +of this curve space. But really what's + + align:start position:0% +of this curve space. But really what's + + + align:start position:0% +of this curve space. But really what's +important is that as the dimension of + + align:start position:0% +important is that as the dimension of + + + align:start position:0% +important is that as the dimension of +theta becomes bigger, I have less + + align:start position:0% +theta becomes bigger, I have less + + + align:start position:0% +theta becomes bigger, I have less +degrees of freedom to become to be away + + align:start position:0% +degrees of freedom to become to be away + + + align:start position:0% +degrees of freedom to become to be away +from this family. This family becomes + + align:start position:0% +from this family. This family becomes + + + align:start position:0% +from this family. This family becomes +big and it's very hard for me to violate + + align:start position:0% +big and it's very hard for me to violate + + + align:start position:0% +big and it's very hard for me to violate +this. So it's actually shrinking the + + align:start position:0% +this. So it's actually shrinking the + + + align:start position:0% +this. So it's actually shrinking the +number of degrees of freedom of my of my + + align:start position:0% +number of degrees of freedom of my of my + + + align:start position:0% +number of degrees of freedom of my of my +k square. And that's all you need to + + align:start position:0% +k square. And that's all you need to + + + align:start position:0% +k square. And that's all you need to +understand. When d increases, the number + + align:start position:0% +understand. When d increases, the number + + + align:start position:0% +understand. When d increases, the number +of degrees of freedom decreases. And if + + align:start position:0% +of degrees of freedom decreases. And if + + + align:start position:0% +of degrees of freedom decreases. And if +you I'd like to you to have an idea of + + align:start position:0% +you I'd like to you to have an idea of + + + align:start position:0% +you I'd like to you to have an idea of +why this is somewhat true. And this is + + align:start position:0% +why this is somewhat true. And this is + + + align:start position:0% +why this is somewhat true. And this is +basically the picture you should have in + + align:start position:0% +basically the picture you should have in + + + align:start position:0% +basically the picture you should have in +mind. + + align:start position:0% + + + + align:start position:0% + +Okay. So now once I have done this I can + + align:start position:0% +Okay. So now once I have done this I can + + + align:start position:0% +Okay. So now once I have done this I can +just construct. So here I need to check. + + align:start position:0% +just construct. So here I need to check. + + + align:start position:0% +just construct. So here I need to check. +So what is D in the case of the binomial + + align:start position:0% + + + + align:start position:0% + +one right? It's just a one-dimensional + + align:start position:0% +one right? It's just a one-dimensional + + + align:start position:0% +one right? It's just a one-dimensional +thing. And for most of the examples + + align:start position:0% +thing. And for most of the examples + + + align:start position:0% +thing. And for most of the examples +we're going to have it's going to be + + align:start position:0% +we're going to have it's going to be + + + align:start position:0% +we're going to have it's going to be +onedimensional. So we have this weird + + align:start position:0% +onedimensional. So we have this weird + + + align:start position:0% +onedimensional. So we have this weird +thing. We're going to have K minus two + + align:start position:0% +thing. We're going to have K minus two + + + align:start position:0% +thing. We're going to have K minus two +degrees of freedom. + + align:start position:0% + + + + align:start position:0% + +So uh now I have this thing and uh and + + align:start position:0% +So uh now I have this thing and uh and + + + align:start position:0% +So uh now I have this thing and uh and +uh I have this asmtoic then I can just + + align:start position:0% +uh I have this asmtoic then I can just + + + align:start position:0% +uh I have this asmtoic then I can just +basically use a test that has that uses + + align:start position:0% +basically use a test that has that uses + + + align:start position:0% +basically use a test that has that uses +the fact that the asmtoic distribution + + align:start position:0% +the fact that the asmtoic distribution + + + align:start position:0% +the fact that the asmtoic distribution +is this. So I compute my quintiles out + + align:start position:0% +is this. So I compute my quintiles out + + + align:start position:0% +is this. So I compute my quintiles out +of this. Again I made the same mistake. + + align:start position:0% +of this. Again I made the same mistake. + + + align:start position:0% +of this. Again I made the same mistake. +This should be q alpha and this should + + align:start position:0% +This should be q alpha and this should + + + align:start position:0% +This should be q alpha and this should +be q alpha. Uh so that's just the tail + + align:start position:0% +be q alpha. Uh so that's just the tail + + + align:start position:0% +be q alpha. Uh so that's just the tail +probability is equal to alpha when I'm + + align:start position:0% +probability is equal to alpha when I'm + + + align:start position:0% +probability is equal to alpha when I'm +on the right of q alpha. And so those + + align:start position:0% +on the right of q alpha. And so those + + + align:start position:0% +on the right of q alpha. And so those +are the tail probability of the + + align:start position:0% +are the tail probability of the + + + align:start position:0% +are the tail probability of the +appropriate k square with the + + align:start position:0% +appropriate k square with the + + + align:start position:0% +appropriate k square with the +appropriate number of degrees of + + align:start position:0% +appropriate number of degrees of + + + align:start position:0% +appropriate number of degrees of +freedom. And so I can compute p values + + align:start position:0% +freedom. And so I can compute p values + + + align:start position:0% +freedom. And so I can compute p values +and I can do whatever I want. Okay. So + + align:start position:0% +and I can do whatever I want. Okay. So + + + align:start position:0% +and I can do whatever I want. Okay. So +then I just like unfold my testing + + align:start position:0% +then I just like unfold my testing + + + align:start position:0% +then I just like unfold my testing +machinery. Okay. So now I know how to + + align:start position:0% +machinery. Okay. So now I know how to + + + align:start position:0% +machinery. Okay. So now I know how to +test a if I'm um binomial distribution + + align:start position:0% +test a if I'm um binomial distribution + + + align:start position:0% +test a if I'm um binomial distribution +or not. Again here I testing if I'm a + + align:start position:0% +or not. Again here I testing if I'm a + + + align:start position:0% +or not. Again here I testing if I'm a +binomial distribution is not a a simple + + align:start position:0% +binomial distribution is not a a simple + + + align:start position:0% +binomial distribution is not a a simple +goodness of fit. It's a composite one + + align:start position:0% +goodness of fit. It's a composite one + + + align:start position:0% +goodness of fit. It's a composite one +where I can actually there's many ways I + + align:start position:0% +where I can actually there's many ways I + + + align:start position:0% +where I can actually there's many ways I +can be a binomial distribution because + + align:start position:0% +can be a binomial distribution because + + + align:start position:0% +can be a binomial distribution because +there's as many as there is theta. And + + align:start position:0% +there's as many as there is theta. And + + + align:start position:0% +there's as many as there is theta. And +so I'm actually plugging in the theta + + align:start position:0% +so I'm actually plugging in the theta + + + align:start position:0% +so I'm actually plugging in the theta +hat which is estimated from the data. + + align:start position:0% +hat which is estimated from the data. + + + align:start position:0% +hat which is estimated from the data. +Right? And here since everything's + + align:start position:0% +Right? And here since everything's + + + align:start position:0% +Right? And here since everything's +happening in the asmtotics, I'm not + + align:start position:0% +happening in the asmtotics, I'm not + + + align:start position:0% +happening in the asmtotics, I'm not +claiming that tn has a pivotal + + align:start position:0% +claiming that tn has a pivotal + + + align:start position:0% +claiming that tn has a pivotal +distribution for finite n. This is + + align:start position:0% +distribution for finite n. This is + + + align:start position:0% +distribution for finite n. This is +actually not true. It's going to depend + + align:start position:0% +actually not true. It's going to depend + + + align:start position:0% +actually not true. It's going to depend +like crazy on what the actual + + align:start position:0% +like crazy on what the actual + + + align:start position:0% +like crazy on what the actual +distribution is. But asmtoically I have + + align:start position:0% +distribution is. But asmtoically I have + + + align:start position:0% +distribution is. But asmtoically I have +a k square which obviously does not + + align:start position:0% +a k square which obviously does not + + + align:start position:0% +a k square which obviously does not +depend on anything I done. + + align:start position:0% +depend on anything I done. + + + align:start position:0% +depend on anything I done. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Yeah. + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% + + + + align:start position:0% + +That's correct. And thank you for this + + align:start position:0% +That's correct. And thank you for this + + + align:start position:0% +That's correct. And thank you for this +beautiful segue into my next slide. Uh + + align:start position:0% +beautiful segue into my next slide. Uh + + + align:start position:0% +beautiful segue into my next slide. Uh +so we can actually deal with the case + + align:start position:0% +so we can actually deal with the case + + + align:start position:0% +so we can actually deal with the case +not only where it's infinite which would + + align:start position:0% +not only where it's infinite which would + + + align:start position:0% +not only where it's infinite which would +be the case of quason. I mean nobody + + align:start position:0% +be the case of quason. I mean nobody + + + align:start position:0% +be the case of quason. I mean nobody +believes I'm going to get an infinite + + align:start position:0% +believes I'm going to get an infinite + + + align:start position:0% +believes I'm going to get an infinite +number of of photons in a finite amount + + align:start position:0% +number of of photons in a finite amount + + + align:start position:0% +number of of photons in a finite amount +of time. But we just don't want to have + + align:start position:0% +of time. But we just don't want to have + + + align:start position:0% +of time. But we just don't want to have +to say there's going to be a large this + + align:start position:0% +to say there's going to be a large this + + + align:start position:0% +to say there's going to be a large this +is the largest possible number. We don't + + align:start position:0% +is the largest possible number. We don't + + + align:start position:0% +is the largest possible number. We don't +want to have to do that because if you + + align:start position:0% +want to have to do that because if you + + + align:start position:0% +want to have to do that because if you +start doing this then the probabilities + + align:start position:0% +start doing this then the probabilities + + + align:start position:0% +start doing this then the probabilities +become close to zero things become + + align:start position:0% +become close to zero things become + + + align:start position:0% +become close to zero things become +degenerate and it's an issue. So what we + + align:start position:0% +degenerate and it's an issue. So what we + + + align:start position:0% +degenerate and it's an issue. So what we +do is we bin we just bin stuff. Okay. + + align:start position:0% +do is we bin we just bin stuff. Okay. + + + align:start position:0% +do is we bin we just bin stuff. Okay. +And so maybe you know if I have a + + align:start position:0% +And so maybe you know if I have a + + + align:start position:0% +And so maybe you know if I have a +binomial distribution with say 200,000 + + align:start position:0% +binomial distribution with say 200,000 + + + align:start position:0% +binomial distribution with say 200,000 +uh uh possible values then it's actually + + align:start position:0% +uh uh possible values then it's actually + + + align:start position:0% +uh uh possible values then it's actually +maybe not the level of uh of uh uh + + align:start position:0% +maybe not the level of uh of uh uh + + + align:start position:0% +maybe not the level of uh of uh uh +precision I want to look at this. Maybe + + align:start position:0% +precision I want to look at this. Maybe + + + align:start position:0% +precision I want to look at this. Maybe +I want to bin. Maybe I want to say let's + + align:start position:0% +I want to bin. Maybe I want to say let's + + + align:start position:0% +I want to bin. Maybe I want to say let's +just think of all things that are + + align:start position:0% +just think of all things that are + + + align:start position:0% +just think of all things that are +between zero and 100 to be the same + + align:start position:0% +between zero and 100 to be the same + + + align:start position:0% +between zero and 100 to be the same +thing between 100 and and 200 the same + + align:start position:0% +thing between 100 and and 200 the same + + + align:start position:0% +thing between 100 and and 200 the same +thing etc. And so if I act I'm actually + + align:start position:0% +thing etc. And so if I act I'm actually + + + align:start position:0% +thing etc. And so if I act I'm actually +going to bin I don't even have to think + + align:start position:0% +going to bin I don't even have to think + + + align:start position:0% +going to bin I don't even have to think +about things that are discrete. I can + + align:start position:0% +about things that are discrete. I can + + + align:start position:0% +about things that are discrete. I can +even think about continuous cases. And + + align:start position:0% +even think about continuous cases. And + + + align:start position:0% +even think about continuous cases. And +so if I want to test if I have a + + align:start position:0% +so if I want to test if I have a + + + align:start position:0% +so if I want to test if I have a +Gaussian distribution for example, I can + + align:start position:0% +Gaussian distribution for example, I can + + + align:start position:0% +Gaussian distribution for example, I can +just approximate that by some say + + align:start position:0% +just approximate that by some say + + + align:start position:0% +just approximate that by some say +peacewise constant function + + align:start position:0% +peacewise constant function + + + align:start position:0% +peacewise constant function +that just says that well you know if I + + align:start position:0% +that just says that well you know if I + + + align:start position:0% +that just says that well you know if I +have a Gaussian distribution like this + + align:start position:0% +have a Gaussian distribution like this + + + align:start position:0% +have a Gaussian distribution like this +I'm going to bin it like this + + align:start position:0% +I'm going to bin it like this + + + align:start position:0% +I'm going to bin it like this +and I'm going to say well the + + align:start position:0% +and I'm going to say well the + + + align:start position:0% +and I'm going to say well the +probability that I'm less than this + + align:start position:0% +probability that I'm less than this + + + align:start position:0% +probability that I'm less than this +value is this. The probability that I'm + + align:start position:0% +value is this. The probability that I'm + + + align:start position:0% +value is this. The probability that I'm +between this and this value is this. The + + align:start position:0% +between this and this value is this. The + + + align:start position:0% +between this and this value is this. The +probability I'm between this and this + + align:start position:0% +probability I'm between this and this + + + align:start position:0% +probability I'm between this and this +value is this. And then this and then + + align:start position:0% +value is this. And then this and then + + + align:start position:0% +value is this. And then this and then +this. Right? And now I've turned I've + + align:start position:0% +this. Right? And now I've turned I've + + + align:start position:0% +this. Right? And now I've turned I've +discretized effectively my Gaussian into + + align:start position:0% +discretized effectively my Gaussian into + + + align:start position:0% +discretized effectively my Gaussian into +a PMF. The value that this is P1. The + + align:start position:0% +a PMF. The value that this is P1. The + + + align:start position:0% +a PMF. The value that this is P1. The +value here is P1. This is P2. + + align:start position:0% +value here is P1. This is P2. + + + align:start position:0% +value here is P1. This is P2. +This is P3. + + align:start position:0% +This is P3. + + + align:start position:0% +This is P3. +This is P4. + + align:start position:0% +This is P4. + + + align:start position:0% +This is P4. +This is P5 + + align:start position:0% +This is P5 + + + align:start position:0% +This is P5 +and P6. Right? I've discretized my + + align:start position:0% +and P6. Right? I've discretized my + + + align:start position:0% +and P6. Right? I've discretized my +Gaussian into six possible values. + + align:start position:0% +Gaussian into six possible values. + + + align:start position:0% +Gaussian into six possible values. +That's just the probability that they + + align:start position:0% +That's just the probability that they + + + align:start position:0% +That's just the probability that they +fall into a certain bin. + + align:start position:0% +fall into a certain bin. + + + align:start position:0% +fall into a certain bin. +And we can do this. If you if you don't + + align:start position:0% +And we can do this. If you if you don't + + + align:start position:0% +And we can do this. If you if you don't +know what key is, just stop at 10. You + + align:start position:0% +know what key is, just stop at 10. You + + + align:start position:0% +know what key is, just stop at 10. You +know, let's look you look at your data + + align:start position:0% +know, let's look you look at your data + + + align:start position:0% +know, let's look you look at your data +quickly and you say, well, you know, I + + align:start position:0% +quickly and you say, well, you know, I + + + align:start position:0% +quickly and you say, well, you know, I +have so few of them that are like I see + + align:start position:0% +have so few of them that are like I see + + + align:start position:0% +have so few of them that are like I see +maybe + + align:start position:0% +maybe + + + align:start position:0% +maybe +18, 11, and 115. Well, everything that's + + align:start position:0% +18, 11, and 115. Well, everything that's + + + align:start position:0% +18, 11, and 115. Well, everything that's +between 8 and 20, I'm just going to put + + align:start position:0% +between 8 and 20, I'm just going to put + + + align:start position:0% +between 8 and 20, I'm just going to put +in one bin because what else are you + + align:start position:0% +in one bin because what else are you + + + align:start position:0% +in one bin because what else are you +going to do? I mean, you just don't have + + align:start position:0% +going to do? I mean, you just don't have + + + align:start position:0% +going to do? I mean, you just don't have +enough observations. And so, what we do + + align:start position:0% +enough observations. And so, what we do + + + align:start position:0% +enough observations. And so, what we do +is we just bin everything. So, here I'm + + align:start position:0% +is we just bin everything. So, here I'm + + + align:start position:0% +is we just bin everything. So, here I'm +going to actually be slightly abstract. + + align:start position:0% +going to actually be slightly abstract. + + + align:start position:0% +going to actually be slightly abstract. +Our bins are going to be intervals. AJ, + + align:start position:0% +Our bins are going to be intervals. AJ, + + + align:start position:0% +Our bins are going to be intervals. AJ, +so here they don't even have to be + + align:start position:0% +so here they don't even have to be + + + align:start position:0% +so here they don't even have to be +intervals. I could go crazy and just + + align:start position:0% +intervals. I could go crazy and just + + + align:start position:0% +intervals. I could go crazy and just +like call a bin this guy and this guy, + + align:start position:0% +like call a bin this guy and this guy, + + + align:start position:0% +like call a bin this guy and this guy, +right? That would make no sense, but I + + align:start position:0% +right? That would make no sense, but I + + + align:start position:0% +right? That would make no sense, but I +could do that. And um and then um and of + + align:start position:0% +could do that. And um and then um and of + + + align:start position:0% +could do that. And um and then um and of +course, you know, you can do whatever + + align:start position:0% +course, you know, you can do whatever + + + align:start position:0% +course, you know, you can do whatever +you want, but there's going to be some + + align:start position:0% +you want, but there's going to be some + + + align:start position:0% +you want, but there's going to be some +consequences on the conclusions that you + + align:start position:0% +consequences on the conclusions that you + + + align:start position:0% +consequences on the conclusions that you +can take, right? All you're going to be + + align:start position:0% +can take, right? All you're going to be + + + align:start position:0% +can take, right? All you're going to be +able to say is that my distribution does + + align:start position:0% +able to say is that my distribution does + + + align:start position:0% +able to say is that my distribution does +not look like it could be binn in this + + align:start position:0% +not look like it could be binn in this + + + align:start position:0% +not look like it could be binn in this +way. That's all you're going to be able + + align:start position:0% +way. That's all you're going to be able + + + align:start position:0% +way. That's all you're going to be able +to say. So if you decide to just put all + + align:start position:0% +to say. So if you decide to just put all + + + align:start position:0% +to say. So if you decide to just put all +the negative numbers and the positive + + align:start position:0% +the negative numbers and the positive + + + align:start position:0% +the negative numbers and the positive +numbers then it's going to be very hard + + align:start position:0% +numbers then it's going to be very hard + + + align:start position:0% +numbers then it's going to be very hard +for you to distinguish a Gaussian from a + + align:start position:0% +for you to distinguish a Gaussian from a + + + align:start position:0% +for you to distinguish a Gaussian from a +random variable that takes values minus + + align:start position:0% +random variable that takes values minus + + + align:start position:0% +random variable that takes values minus +one and plus one only. You need to just + + align:start position:0% +one and plus one only. You need to just + + + align:start position:0% +one and plus one only. You need to just +you know be reasonable. Okay. So now I + + align:start position:0% +you know be reasonable. Okay. So now I + + + align:start position:0% +you know be reasonable. Okay. So now I +have my PG has become the probability + + align:start position:0% +have my PG has become the probability + + + align:start position:0% +have my PG has become the probability +that my random variable falls into being + + align:start position:0% +that my random variable falls into being + + + align:start position:0% +that my random variable falls into being +J. + + align:start position:0% +J. + + + align:start position:0% +J. +Um so that's PG of theta under the + + align:start position:0% +Um so that's PG of theta under the + + + align:start position:0% +Um so that's PG of theta under the +parametric distribution for the true one + + align:start position:0% +parametric distribution for the true one + + + align:start position:0% +parametric distribution for the true one +whether it's parametric or not I have a + + align:start position:0% +whether it's parametric or not I have a + + + align:start position:0% +whether it's parametric or not I have a +PJ and then I have a p hat j which is + + align:start position:0% +PJ and then I have a p hat j which is + + + align:start position:0% +PJ and then I have a p hat j which is +the proportion of observations that + + align:start position:0% +the proportion of observations that + + + align:start position:0% +the proportion of observations that +falls in this bin right so I have a + + align:start position:0% +falls in this bin right so I have a + + + align:start position:0% +falls in this bin right so I have a +bunch of observations I count how many + + align:start position:0% +bunch of observations I count how many + + + align:start position:0% +bunch of observations I count how many +of them fall in this bin I divide by n + + align:start position:0% +of them fall in this bin I divide by n + + + align:start position:0% +of them fall in this bin I divide by n +and that tells me what my estimated + + align:start position:0% +and that tells me what my estimated + + + align:start position:0% +and that tells me what my estimated +probability for this bin is and theta + + align:start position:0% +probability for this bin is and theta + + + align:start position:0% +probability for this bin is and theta +hat well is the same as before if I'm in + + align:start position:0% +hat well is the same as before if I'm in + + + align:start position:0% +hat well is the same as before if I'm in +a parametric family I'm just estimating + + align:start position:0% +a parametric family I'm just estimating + + + align:start position:0% +a parametric family I'm just estimating +theta hat maybe a maximum imum + + align:start position:0% +theta hat maybe a maximum imum + + + align:start position:0% +theta hat maybe a maximum imum +likelihood estimator plug it in and + + align:start position:0% +likelihood estimator plug it in and + + + align:start position:0% +likelihood estimator plug it in and +estimate those PG of theta hat from this + + align:start position:0% +estimate those PG of theta hat from this + + + align:start position:0% +estimate those PG of theta hat from this +I form my k square and I have exactly + + align:start position:0% +I form my k square and I have exactly + + + align:start position:0% +I form my k square and I have exactly +the same thing as before so the answer + + align:start position:0% +the same thing as before so the answer + + + align:start position:0% +the same thing as before so the answer +to your question is yes you've been and + + align:start position:0% +to your question is yes you've been and + + + align:start position:0% +to your question is yes you've been and +it's the answer to even more questions + + align:start position:0% +it's the answer to even more questions + + + align:start position:0% +it's the answer to even more questions +so that's why there you can actually use + + align:start position:0% +so that's why there you can actually use + + + align:start position:0% +so that's why there you can actually use +the k square test to test for normality + + align:start position:0% +the k square test to test for normality + + + align:start position:0% +the k square test to test for normality +now here it's going to be slightly + + align:start position:0% +now here it's going to be slightly + + + align:start position:0% +now here it's going to be slightly +weaker because there's only an asmtoic + + align:start position:0% +weaker because there's only an asmtoic + + + align:start position:0% +weaker because there's only an asmtoic +theory whereas komograph smeirnoff and + + align:start position:0% +theory whereas komograph smeirnoff and + + + align:start position:0% +theory whereas komograph smeirnoff and +komograph ley force work Actually even + + align:start position:0% +komograph ley force work Actually even + + + align:start position:0% +komograph ley force work Actually even +for finite samples for for the k square + + align:start position:0% +for finite samples for for the k square + + + align:start position:0% +for finite samples for for the k square +test it's only asmtoic. So you just + + align:start position:0% +test it's only asmtoic. So you just + + + align:start position:0% +test it's only asmtoic. So you just +pretend you actually know what the + + align:start position:0% +pretend you actually know what the + + + align:start position:0% +pretend you actually know what the +parameters are you just stuff them into + + align:start position:0% +parameters are you just stuff them into + + + align:start position:0% +parameters are you just stuff them into +uh uh theta mu hat and sigma square hat + + align:start position:0% +uh uh theta mu hat and sigma square hat + + + align:start position:0% +uh uh theta mu hat and sigma square hat +and uh you just go to you just cross + + align:start position:0% +and uh you just go to you just cross + + + align:start position:0% +and uh you just go to you just cross +your finger that n is large enough for + + align:start position:0% +your finger that n is large enough for + + + align:start position:0% +your finger that n is large enough for +everything to have converged by the time + + align:start position:0% +everything to have converged by the time + + + align:start position:0% +everything to have converged by the time +you make your decision. Okay. And then + + align:start position:0% +you make your decision. Okay. And then + + + align:start position:0% +you make your decision. Okay. And then +this is a copy paste with the same error + + align:start position:0% +this is a copy paste with the same error + + + align:start position:0% +this is a copy paste with the same error +actually uh as the previous slide where + + align:start position:0% +actually uh as the previous slide where + + + align:start position:0% +actually uh as the previous slide where +you just uh build your test based on + + align:start position:0% +you just uh build your test based on + + + align:start position:0% +you just uh build your test based on +whether you exceed or not some quentile + + align:start position:0% +whether you exceed or not some quentile + + + align:start position:0% +whether you exceed or not some quentile +and you can also compute some p value. + + align:start position:0% +and you can also compute some p value. + + + align:start position:0% +and you can also compute some p value. +Okay, I'm sorry + + align:start position:0% +Okay, I'm sorry + + + align:start position:0% +Okay, I'm sorry +what is the error? + + align:start position:0% + + + + align:start position:0% + +Oh the error is that this should be Q + + align:start position:0% +Oh the error is that this should be Q + + + align:start position:0% +Oh the error is that this should be Q +alpha, right? I've been calling this Q + + align:start position:0% +alpha, right? I've been calling this Q + + + align:start position:0% +alpha, right? I've been calling this Q +alpha. + + align:start position:0% +alpha. + + + align:start position:0% +alpha. +That's my personal uh choice because I + + align:start position:0% +That's my personal uh choice because I + + + align:start position:0% +That's my personal uh choice because I +don't want to I only use Q alpha. So I + + align:start position:0% +don't want to I only use Q alpha. So I + + + align:start position:0% +don't want to I only use Q alpha. So I +only use quentiles of degree where alpha + + align:start position:0% +only use quentiles of degree where alpha + + + align:start position:0% +only use quentiles of degree where alpha +is to the right. So that's what + + align:start position:0% +is to the right. So that's what + + + align:start position:0% +is to the right. So that's what +statisticians probabilist would use this + + align:start position:0% +statisticians probabilist would use this + + + align:start position:0% +statisticians probabilist would use this +uh this notation. + + align:start position:0% + + + + align:start position:0% + +Okay. And so uh some questions right so + + align:start position:0% +Okay. And so uh some questions right so + + + align:start position:0% +Okay. And so uh some questions right so +of course in practice you're going to + + align:start position:0% +of course in practice you're going to + + + align:start position:0% +of course in practice you're going to +have some issues which you know + + align:start position:0% +have some issues which you know + + + align:start position:0% +have some issues which you know +translate. I said well how do you pick + + align:start position:0% +translate. I said well how do you pick + + + align:start position:0% +translate. I said well how do you pick +this guy this case? So I gave you some + + align:start position:0% +this guy this case? So I gave you some + + + align:start position:0% +this guy this case? So I gave you some +sort of a you know I mean the way we + + align:start position:0% +sort of a you know I mean the way we + + + align:start position:0% +sort of a you know I mean the way we +discussed right you have eight and 10 + + align:start position:0% +discussed right you have eight and 10 + + + align:start position:0% +discussed right you have eight and 10 +and 20 then it's you know it's ad hoc + + align:start position:0% +and 20 then it's you know it's ad hoc + + + align:start position:0% +and 20 then it's you know it's ad hoc +and uh so depending on whether you want + + align:start position:0% +and uh so depending on whether you want + + + align:start position:0% +and uh so depending on whether you want +to stop K at 20 or if you want to bin + + align:start position:0% +to stop K at 20 or if you want to bin + + + align:start position:0% +to stop K at 20 or if you want to bin +those guys is really up to you and + + align:start position:0% +those guys is really up to you and + + + align:start position:0% +those guys is really up to you and +there's going to be some considerations + + align:start position:0% +there's going to be some considerations + + + align:start position:0% +there's going to be some considerations +about the particular problem at hand. I + + align:start position:0% +about the particular problem at hand. I + + + align:start position:0% +about the particular problem at hand. I +mean is it coarse too coarse for your + + align:start position:0% +mean is it coarse too coarse for your + + + align:start position:0% +mean is it coarse too coarse for your +problem to decide that the observations + + align:start position:0% +problem to decide that the observations + + + align:start position:0% +problem to decide that the observations +between eight and 20 are the same? It's + + align:start position:0% +between eight and 20 are the same? It's + + + align:start position:0% +between eight and 20 are the same? It's +really up to you. Maybe that's actually + + align:start position:0% +really up to you. Maybe that's actually + + + align:start position:0% +really up to you. Maybe that's actually +making a huge difference in terms of + + align:start position:0% +making a huge difference in terms of + + + align:start position:0% +making a huge difference in terms of +what phenomenon you're looking at. uh + + align:start position:0% +what phenomenon you're looking at. uh + + + align:start position:0% +what phenomenon you're looking at. uh +the choice of the bins, right? So here + + align:start position:0% +the choice of the bins, right? So here + + + align:start position:0% +the choice of the bins, right? So here +there's actually some sort of rules + + align:start position:0% +there's actually some sort of rules + + + align:start position:0% +there's actually some sort of rules +which are don't use only one bin and uh + + align:start position:0% +which are don't use only one bin and uh + + + align:start position:0% +which are don't use only one bin and uh +don't make sure there's actually at + + align:start position:0% +don't make sure there's actually at + + + align:start position:0% +don't make sure there's actually at +least don't use them too small so that + + align:start position:0% +least don't use them too small so that + + + align:start position:0% +least don't use them too small so that +there's at least one observation per + + align:start position:0% +there's at least one observation per + + + align:start position:0% +there's at least one observation per +bin, right? And it's basically the same + + align:start position:0% +bin, right? And it's basically the same + + + align:start position:0% +bin, right? And it's basically the same +kind of rules that you would have to + + align:start position:0% +kind of rules that you would have to + + + align:start position:0% +kind of rules that you would have to +build a histogram. If you were to build + + align:start position:0% +build a histogram. If you were to build + + + align:start position:0% +build a histogram. If you were to build +a histogram for your data, you still + + align:start position:0% +a histogram for your data, you still + + + align:start position:0% +a histogram for your data, you still +want to make sure that you've been in + + align:start position:0% +want to make sure that you've been in + + + align:start position:0% +want to make sure that you've been in +appropriate fashion. Okay? And there's a + + align:start position:0% +appropriate fashion. Okay? And there's a + + + align:start position:0% +appropriate fashion. Okay? And there's a +bunch of rule of thumbs. Um every time + + align:start position:0% +bunch of rule of thumbs. Um every time + + + align:start position:0% +bunch of rule of thumbs. Um every time +you ask someone, they're going to have a + + align:start position:0% +you ask someone, they're going to have a + + + align:start position:0% +you ask someone, they're going to have a +different rule of thumb. So, you know, + + align:start position:0% +different rule of thumb. So, you know, + + + align:start position:0% +different rule of thumb. So, you know, +just make your own. and uh and u then + + align:start position:0% +just make your own. and uh and u then + + + align:start position:0% +just make your own. and uh and u then +there's the computation of p g of theta + + align:start position:0% +there's the computation of p g of theta + + + align:start position:0% +there's the computation of p g of theta +which might be a bit complicated because + + align:start position:0% +which might be a bit complicated because + + + align:start position:0% +which might be a bit complicated because +in this case I would have to integrate + + align:start position:0% +in this case I would have to integrate + + + align:start position:0% +in this case I would have to integrate +the galsian between this number and this + + align:start position:0% +the galsian between this number and this + + + align:start position:0% +the galsian between this number and this +number. So for this case I could just + + align:start position:0% +number. So for this case I could just + + + align:start position:0% +number. So for this case I could just +say well it's difference of the cdf in + + align:start position:0% +say well it's difference of the cdf in + + + align:start position:0% +say well it's difference of the cdf in +that value and that value and then be + + align:start position:0% +that value and that value and then be + + + align:start position:0% +that value and that value and then be +happy with it. But you can imagine that + + align:start position:0% +happy with it. But you can imagine that + + + align:start position:0% +happy with it. But you can imagine that +you have some slightly more crazy + + align:start position:0% +you have some slightly more crazy + + + align:start position:0% +you have some slightly more crazy +distributions you're going to have to + + align:start position:0% +distributions you're going to have to + + + align:start position:0% +distributions you're going to have to +somewhat compute some integrals that + + align:start position:0% +somewhat compute some integrals that + + + align:start position:0% +somewhat compute some integrals that +might be unpleasant for you to compute. + + align:start position:0% +might be unpleasant for you to compute. + + + align:start position:0% +might be unpleasant for you to compute. +Okay. And in particular, I said the + + align:start position:0% +Okay. And in particular, I said the + + + align:start position:0% +Okay. And in particular, I said the +difference of the PDF between that value + + align:start position:0% +difference of the PDF between that value + + + align:start position:0% +difference of the PDF between that value +and that value of sorry, the CDF between + + align:start position:0% +and that value of sorry, the CDF between + + + align:start position:0% +and that value of sorry, the CDF between +that value and that value. It is true, + + align:start position:0% +that value and that value. It is true, + + + align:start position:0% +that value and that value. It is true, +but it's not like you actually have + + align:start position:0% +but it's not like you actually have + + + align:start position:0% +but it's not like you actually have +tables that compute the CDF at any value + + align:start position:0% +tables that compute the CDF at any value + + + align:start position:0% +tables that compute the CDF at any value +you like, right? You have to sort of, + + align:start position:0% +you like, right? You have to sort of, + + + align:start position:0% +you like, right? You have to sort of, +you know, well, there might be, but at + + align:start position:0% +you know, well, there might be, but at + + + align:start position:0% +you know, well, there might be, but at +some some degree, but you're going to + + align:start position:0% +some some degree, but you're going to + + + align:start position:0% +some some degree, but you're going to +have to use a computer typically to do + + align:start position:0% +have to use a computer typically to do + + + align:start position:0% +have to use a computer typically to do +that. + + align:start position:0% +that. + + + align:start position:0% +that. +Okay? And uh so for example, you could + + align:start position:0% +Okay? And uh so for example, you could + + + align:start position:0% +Okay? And uh so for example, you could +do the uh if I had time, if I had more + + align:start position:0% +do the uh if I had time, if I had more + + + align:start position:0% +do the uh if I had time, if I had more +than one minute, I would actually do it + + align:start position:0% +than one minute, I would actually do it + + + align:start position:0% +than one minute, I would actually do it +for you. But it's basically the same the + + align:start position:0% +for you. But it's basically the same the + + + align:start position:0% +for you. But it's basically the same the +you're going to have an infinite tail + + align:start position:0% +you're going to have an infinite tail + + + align:start position:0% +you're going to have an infinite tail +and you just say at some point I'm going + + align:start position:0% +and you just say at some point I'm going + + + align:start position:0% +and you just say at some point I'm going +to cut everything that's larger than + + align:start position:0% +to cut everything that's larger than + + + align:start position:0% +to cut everything that's larger than +some value. All right. So uh you can + + align:start position:0% +some value. All right. So uh you can + + + align:start position:0% +some value. All right. So uh you can +play around for some right I say well if + + align:start position:0% +play around for some right I say well if + + + align:start position:0% +play around for some right I say well if +you have extra knowledge about what you + + align:start position:0% +you have extra knowledge about what you + + + align:start position:0% +you have extra knowledge about what you +expect to see maybe you can cut at a + + align:start position:0% +expect to see maybe you can cut at a + + + align:start position:0% +expect to see maybe you can cut at a +certain number and then just fold all + + align:start position:0% +certain number and then just fold all + + + align:start position:0% +certain number and then just fold all +the largest values from k minus one to + + align:start position:0% +the largest values from k minus one to + + + align:start position:0% +the largest values from k minus one to +infinity + + align:start position:0% +infinity + + + align:start position:0% +infinity +uh so that uh you actually have um you + + align:start position:0% +uh so that uh you actually have um you + + + align:start position:0% +uh so that uh you actually have um you +have everything into one large bin. + + align:start position:0% +have everything into one large bin. + + + align:start position:0% +have everything into one large bin. +Okay, that's the entire tail. And that's + + align:start position:0% +Okay, that's the entire tail. And that's + + + align:start position:0% +Okay, that's the entire tail. And that's +the way people do it in insurance + + align:start position:0% +the way people do it in insurance + + + align:start position:0% +the way people do it in insurance +companies. For example, they assume that + + align:start position:0% +companies. For example, they assume that + + + align:start position:0% +companies. For example, they assume that +the number of accidents you're going to + + align:start position:0% +the number of accidents you're going to + + + align:start position:0% +the number of accidents you're going to +have is a question distribution. They + + align:start position:0% +have is a question distribution. They + + + align:start position:0% +have is a question distribution. They +have to fit it to you. They have to know + + align:start position:0% +have to fit it to you. They have to know + + + align:start position:0% +have to fit it to you. They have to know +or at least to your pool of insurance of + + align:start position:0% +or at least to your pool of insurance of + + + align:start position:0% +or at least to your pool of insurance of +injured people. So they just, you know, + + align:start position:0% +injured people. So they just, you know, + + + align:start position:0% +injured people. So they just, you know, +slice you into, you know, what your + + align:start position:0% +slice you into, you know, what your + + + align:start position:0% +slice you into, you know, what your +character relevant characteristics are + + align:start position:0% +character relevant characteristics are + + + align:start position:0% +character relevant characteristics are +and then they want to estimate what the + + align:start position:0% +and then they want to estimate what the + + + align:start position:0% +and then they want to estimate what the +distribution is and basically they they + + align:start position:0% +distribution is and basically they they + + + align:start position:0% +distribution is and basically they they +do they can do a k square test to check + + align:start position:0% +do they can do a k square test to check + + + align:start position:0% +do they can do a k square test to check +if it's indeed a distribution. + + align:start position:0% +if it's indeed a distribution. + + + align:start position:0% +if it's indeed a distribution. +All right. So uh that will be it for + + align:start position:0% +All right. So uh that will be it for + + + align:start position:0% +All right. So uh that will be it for +today and uh so I'll be I'll have your + + align:start position:0% +today and uh so I'll be I'll have your + + + align:start position:0% +today and uh so I'll be I'll have your +home \ No newline at end of file diff --git a/vPSWNkZ_WX0.txt b/vPSWNkZ_WX0.txt new file mode 100644 index 0000000000000000000000000000000000000000..fcebf6c0a88fae9c20181e429e9db24e2e477770 --- /dev/null +++ b/vPSWNkZ_WX0.txt @@ -0,0 +1,5395 @@ +align:start position:0% + +coming across people that are suffering + + align:start position:0% +coming across people that are suffering + + + align:start position:0% +coming across people that are suffering +from the same stuff that you're + + align:start position:0% +from the same stuff that you're + + + align:start position:0% +from the same stuff that you're +suffering from they've been affected by + + align:start position:0% +suffering from they've been affected by + + + align:start position:0% +suffering from they've been affected by +Wars they lost their homes they lost + + align:start position:0% +Wars they lost their homes they lost + + + align:start position:0% +Wars they lost their homes they lost +loved ones it sort of helped in my + + align:start position:0% +loved ones it sort of helped in my + + + align:start position:0% +loved ones it sort of helped in my +healing process or in my like + + align:start position:0% +healing process or in my like + + + align:start position:0% +healing process or in my like +understanding process of absorbing + + align:start position:0% +understanding process of absorbing + + + align:start position:0% +understanding process of absorbing +everything that is happening or + + align:start position:0% +everything that is happening or + + + align:start position:0% +everything that is happening or +currently happening in Sudan this is the + + align:start position:0% +currently happening in Sudan this is the + + + align:start position:0% +currently happening in Sudan this is the +part that is sentimental to this + + align:start position:0% +part that is sentimental to this + + + align:start position:0% +part that is sentimental to this +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +journey welcome to open Learners a + + align:start position:0% +journey welcome to open Learners a + + + align:start position:0% +journey welcome to open Learners a +podcast that tells the stories of + + align:start position:0% +podcast that tells the stories of + + + align:start position:0% +podcast that tells the stories of +Learners all over the world who use + + align:start position:0% +Learners all over the world who use + + + align:start position:0% +Learners all over the world who use +mit's open courseware I'm + + align:start position:0% +mit's open courseware I'm + + + align:start position:0% +mit's open courseware I'm +emmanueli an open learner from Cala + + align:start position:0% +emmanueli an open learner from Cala + + + align:start position:0% +emmanueli an open learner from Cala +Uganda and I'm Michael Jordan Pilgreen + + align:start position:0% +Uganda and I'm Michael Jordan Pilgreen + + + align:start position:0% +Uganda and I'm Michael Jordan Pilgreen +an open learner from Memphis + + align:start position:0% +an open learner from Memphis + + + align:start position:0% +an open learner from Memphis +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Tennessee hey Emanuel how are you doing + + align:start position:0% +Tennessee hey Emanuel how are you doing + + + align:start position:0% +Tennessee hey Emanuel how are you doing +I'm good Michael I'm good I'm enjoying + + align:start position:0% +I'm good Michael I'm good I'm enjoying + + + align:start position:0% +I'm good Michael I'm good I'm enjoying +summer I'm enjoying + + align:start position:0% +summer I'm enjoying + + + align:start position:0% +summer I'm enjoying +Toronto Emanuel you know this episode is + + align:start position:0% +Toronto Emanuel you know this episode is + + + align:start position:0% +Toronto Emanuel you know this episode is +really special Our Guest today is + + align:start position:0% +really special Our Guest today is + + + align:start position:0% +really special Our Guest today is +someone who has leveraged mit's open + + align:start position:0% +someone who has leveraged mit's open + + + align:start position:0% +someone who has leveraged mit's open +learning resources during a really + + align:start position:0% +learning resources during a really + + + align:start position:0% +learning resources during a really +difficult time for herself her family + + align:start position:0% +difficult time for herself her family + + + align:start position:0% +difficult time for herself her family +and her country that's right Michael + + align:start position:0% +and her country that's right Michael + + + align:start position:0% +and her country that's right Michael +today's guest is Saud khed Ahmed alumar + + align:start position:0% +today's guest is Saud khed Ahmed alumar + + + align:start position:0% +today's guest is Saud khed Ahmed alumar +an open learner from Kum Sudan she + + align:start position:0% +an open learner from Kum Sudan she + + + align:start position:0% +an open learner from Kum Sudan she +earned her bachelor's degree in + + align:start position:0% +earned her bachelor's degree in + + + align:start position:0% +earned her bachelor's degree in +electrical and electronic engineering + + align:start position:0% +electrical and electronic engineering + + + align:start position:0% +electrical and electronic engineering +from the University of katum in 2022 one + + align:start position:0% +from the University of katum in 2022 one + + + align:start position:0% +from the University of katum in 2022 one +year later in May of 2023 sadly sujud + + align:start position:0% +year later in May of 2023 sadly sujud + + + align:start position:0% +year later in May of 2023 sadly sujud +was forced to flee Sudan because of the + + align:start position:0% +was forced to flee Sudan because of the + + + align:start position:0% +was forced to flee Sudan because of the +ongoing war in her home country the + + align:start position:0% +ongoing war in her home country the + + + align:start position:0% +ongoing war in her home country the +company she was working for shut down + + align:start position:0% +company she was working for shut down + + + align:start position:0% +company she was working for shut down +and she was forced to leave her home and + + align:start position:0% +and she was forced to leave her home and + + + align:start position:0% +and she was forced to leave her home and +some of her family members behind she + + align:start position:0% +some of her family members behind she + + + align:start position:0% +some of her family members behind she +currently lives in Egypt where she's + + align:start position:0% +currently lives in Egypt where she's + + + align:start position:0% +currently lives in Egypt where she's +working on her certificate in computer + + align:start position:0% +working on her certificate in computer + + + align:start position:0% +working on her certificate in computer +and data science as part of mit's + + align:start position:0% +and data science as part of mit's + + + align:start position:0% +and data science as part of mit's +Imaging Talent program and she's working + + align:start position:0% +Imaging Talent program and she's working + + + align:start position:0% +Imaging Talent program and she's working +towards a micro Masters in statistics + + align:start position:0% +towards a micro Masters in statistics + + + align:start position:0% +towards a micro Masters in statistics +there are so many difficult and + + align:start position:0% +there are so many difficult and + + + align:start position:0% +there are so many difficult and +inspiring parts of saud's story but one + + align:start position:0% +inspiring parts of saud's story but one + + + align:start position:0% +inspiring parts of saud's story but one +thing that stuck out to me is that sujud + + align:start position:0% +thing that stuck out to me is that sujud + + + align:start position:0% +thing that stuck out to me is that sujud +applied to emerging talent because she + + align:start position:0% +applied to emerging talent because she + + + align:start position:0% +applied to emerging talent because she +felt like she had nothing left to + + align:start position:0% +felt like she had nothing left to + + + align:start position:0% +felt like she had nothing left to +lose now a year into the program she + + align:start position:0% +lose now a year into the program she + + + align:start position:0% +lose now a year into the program she +sees the skills that she's learned + + align:start position:0% +sees the skills that she's learned + + + align:start position:0% +sees the skills that she's learned +through MIT open learning as essential + + align:start position:0% +through MIT open learning as essential + + + align:start position:0% +through MIT open learning as essential +tools that will help her rebuild her + + align:start position:0% +tools that will help her rebuild her + + + align:start position:0% +tools that will help her rebuild her +home country sujud is deeply committed + + align:start position:0% +home country sujud is deeply committed + + + align:start position:0% +home country sujud is deeply committed +to building a prosperous future for + + align:start position:0% +to building a prosperous future for + + + align:start position:0% +to building a prosperous future for +Sudan and placing her home country at + + align:start position:0% +Sudan and placing her home country at + + + align:start position:0% +Sudan and placing her home country at +the Forefront of technological + + align:start position:0% +the Forefront of technological + + + align:start position:0% +the Forefront of technological +advancement her long-term goal is to + + align:start position:0% +advancement her long-term goal is to + + + align:start position:0% +advancement her long-term goal is to +establish a research center in Sudan + + align:start position:0% +establish a research center in Sudan + + + align:start position:0% +establish a research center in Sudan +which will use data science to address + + align:start position:0% +which will use data science to address + + + align:start position:0% +which will use data science to address +local social economical and + + align:start position:0% +local social economical and + + + align:start position:0% +local social economical and +environmental challenges by in the short + + align:start position:0% +environmental challenges by in the short + + + align:start position:0% +environmental challenges by in the short +time she's already putting her data + + align:start position:0% +time she's already putting her data + + + align:start position:0% +time she's already putting her data +science and program + + align:start position:0% +science and program + + + align:start position:0% +science and program +programming skills to good use she runs + + align:start position:0% +programming skills to good use she runs + + + align:start position:0% +programming skills to good use she runs +a database called NASA Al Sudan which + + align:start position:0% +a database called NASA Al Sudan which + + + align:start position:0% +a database called NASA Al Sudan which +curates a list of scholarships available + + align:start position:0% +curates a list of scholarships available + + + align:start position:0% +curates a list of scholarships available +to stanes students yes ajude is a really + + align:start position:0% +to stanes students yes ajude is a really + + + align:start position:0% +to stanes students yes ajude is a really +inspiring person and I admire her deep + + align:start position:0% +inspiring person and I admire her deep + + + align:start position:0% +inspiring person and I admire her deep +commitment to her country and her own + + align:start position:0% +commitment to her country and her own + + + align:start position:0% +commitment to her country and her own +learning I'm really excited for our + + align:start position:0% +learning I'm really excited for our + + + align:start position:0% +learning I'm really excited for our +listeners to hear our entire + + align:start position:0% +listeners to hear our entire + + + align:start position:0% +listeners to hear our entire +conversation with suude we talk about + + align:start position:0% +conversation with suude we talk about + + + align:start position:0% +conversation with suude we talk about +her hopes for Sudan along with how ocw + + align:start position:0% +her hopes for Sudan along with how ocw + + + align:start position:0% +her hopes for Sudan along with how ocw +helped her make lifelong friends and how + + align:start position:0% +helped her make lifelong friends and how + + + align:start position:0% +helped her make lifelong friends and how +she keeps herself motivated during the + + align:start position:0% +she keeps herself motivated during the + + + align:start position:0% +she keeps herself motivated during the +dark times this is a really really great + + align:start position:0% +dark times this is a really really great + + + align:start position:0% +dark times this is a really really great +episode Michael and the perfect story to + + align:start position:0% +episode Michael and the perfect story to + + + align:start position:0% +episode Michael and the perfect story to +end our first season with so without + + align:start position:0% +end our first season with so without + + + align:start position:0% +end our first season with so without +further Ado he's our conversation with + + align:start position:0% +further Ado he's our conversation with + + + align:start position:0% +further Ado he's our conversation with +Saud khed Ahmed alumar from Kum Sudan + + align:start position:0% +Saud khed Ahmed alumar from Kum Sudan + + + align:start position:0% +Saud khed Ahmed alumar from Kum Sudan +[Music] + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% + + + + align:start position:0% + +Sudan my name + + align:start position:0% +Sudan my name + + + align:start position:0% +Sudan my name +is um I'm 25 years old almost 26 I was + + align:start position:0% +is um I'm 25 years old almost 26 I was + + + align:start position:0% +is um I'm 25 years old almost 26 I was +missed by saying 25 but I'm almost 26 um + + align:start position:0% +missed by saying 25 but I'm almost 26 um + + + align:start position:0% +missed by saying 25 but I'm almost 26 um +I come from a country in Africa called + + align:start position:0% +I come from a country in Africa called + + + align:start position:0% +I come from a country in Africa called +Sudan and I graduated from University of + + align:start position:0% +Sudan and I graduated from University of + + + align:start position:0% +Sudan and I graduated from University of +Harum electrical and electronics + + align:start position:0% +Harum electrical and electronics + + + align:start position:0% +Harum electrical and electronics +engineering department and I specialized + + align:start position:0% +engineering department and I specialized + + + align:start position:0% +engineering department and I specialized +in control and instrumentation I've sort + + align:start position:0% +in control and instrumentation I've sort + + + align:start position:0% +in control and instrumentation I've sort +of drifted into data science and data + + align:start position:0% +of drifted into data science and data + + + align:start position:0% +of drifted into data science and data +and data related stuff and yeah I'm just + + align:start position:0% +and data related stuff and yeah I'm just + + + align:start position:0% +and data related stuff and yeah I'm just +exploring it and learning about it would + + align:start position:0% +exploring it and learning about it would + + + align:start position:0% +exploring it and learning about it would +you want to just uh start off with sort + + align:start position:0% +you want to just uh start off with sort + + + align:start position:0% +you want to just uh start off with sort +of how you grew up and your experience + + align:start position:0% +of how you grew up and your experience + + + align:start position:0% +of how you grew up and your experience +with education then I grew up in the + + align:start position:0% +with education then I grew up in the + + + align:start position:0% +with education then I grew up in the +capital city of + + align:start position:0% +capital city of + + + align:start position:0% +capital city of +Sudan basically Kum consists of three + + align:start position:0% +Sudan basically Kum consists of three + + + align:start position:0% +Sudan basically Kum consists of three +cities umman and bah I grew up in umman + + align:start position:0% +cities umman and bah I grew up in umman + + + align:start position:0% +cities umman and bah I grew up in umman +uh it's a lovely city and my childhood + + align:start position:0% +uh it's a lovely city and my childhood + + + align:start position:0% +uh it's a lovely city and my childhood +was was lovely I guess I grew up with + + align:start position:0% +was was lovely I guess I grew up with + + + align:start position:0% +was was lovely I guess I grew up with +four siblings they're all males also I + + align:start position:0% +four siblings they're all males also I + + + align:start position:0% +four siblings they're all males also I +shared a hoppy With My Father which is + + align:start position:0% +shared a hoppy With My Father which is + + + align:start position:0% +shared a hoppy With My Father which is +reading and I think it participated a + + align:start position:0% +reading and I think it participated a + + + align:start position:0% +reading and I think it participated a +lot into the person I am today and the + + align:start position:0% +lot into the person I am today and the + + + align:start position:0% +lot into the person I am today and the +personality I have we just like read + + align:start position:0% +personality I have we just like read + + + align:start position:0% +personality I have we just like read +books and discussed them as of my + + align:start position:0% +books and discussed them as of my + + + align:start position:0% +books and discussed them as of my +education in my basic school I went to a + + align:start position:0% +education in my basic school I went to a + + + align:start position:0% +education in my basic school I went to a +private school and then after that my + + align:start position:0% +private school and then after that my + + + align:start position:0% +private school and then after that my +experience like changed a lot because I + + align:start position:0% +experience like changed a lot because I + + + align:start position:0% +experience like changed a lot because I +moved from a private school into a + + align:start position:0% +moved from a private school into a + + + align:start position:0% +moved from a private school into a +public high school which had too many + + align:start position:0% +public high school which had too many + + + align:start position:0% +public high school which had too many +number of students there they all come + + align:start position:0% +number of students there they all come + + + align:start position:0% +number of students there they all come +from different backgrounds they all have + + align:start position:0% +from different backgrounds they all have + + + align:start position:0% +from different backgrounds they all have +different stories and different + + align:start position:0% +different stories and different + + + align:start position:0% +different stories and different +personalities I think it was around that + + align:start position:0% +personalities I think it was around that + + + align:start position:0% +personalities I think it was around that +time I started to realize that I'm + + align:start position:0% +time I started to realize that I'm + + + align:start position:0% +time I started to realize that I'm +interested in mathematics that and I + + align:start position:0% +interested in mathematics that and I + + + align:start position:0% +interested in mathematics that and I +love it I love mathematics so I started + + align:start position:0% +love it I love mathematics so I started + + + align:start position:0% +love it I love mathematics so I started +to explore it I did not have like much + + align:start position:0% +to explore it I did not have like much + + + align:start position:0% +to explore it I did not have like much +room to explore it I didn't know what + + align:start position:0% +room to explore it I didn't know what + + + align:start position:0% +room to explore it I didn't know what +where to look or I didn't have anyone in + + align:start position:0% +where to look or I didn't have anyone in + + + align:start position:0% +where to look or I didn't have anyone in +my circle who was also interested in + + align:start position:0% +my circle who was also interested in + + + align:start position:0% +my circle who was also interested in +math and I think it was around that time + + align:start position:0% +math and I think it was around that time + + + align:start position:0% +math and I think it was around that time +where I realized that I need to find + + align:start position:0% +where I realized that I need to find + + + align:start position:0% +where I realized that I need to find +other sources or I need to find one + + align:start position:0% +other sources or I need to find one + + + align:start position:0% +other sources or I need to find one +place to pursue this uh interest so I + + align:start position:0% +place to pursue this uh interest so I + + + align:start position:0% +place to pursue this uh interest so I +applied for University of Kum one of the + + align:start position:0% +applied for University of Kum one of the + + + align:start position:0% +applied for University of Kum one of the +prestigious universities in Sudan and I + + align:start position:0% +prestigious universities in Sudan and I + + + align:start position:0% +prestigious universities in Sudan and I +applied for the electrical and + + align:start position:0% +applied for the electrical and + + + align:start position:0% +applied for the electrical and +electronics engineering department I got + + align:start position:0% +electronics engineering department I got + + + align:start position:0% +electronics engineering department I got +in and I was really excited because all + + align:start position:0% +in and I was really excited because all + + + align:start position:0% +in and I was really excited because all +the things I heard about it was that + + align:start position:0% +the things I heard about it was that + + + align:start position:0% +the things I heard about it was that +engineering was embedded with these + + align:start position:0% +engineering was embedded with these + + + align:start position:0% +engineering was embedded with these +mathematic courses and that we get we'd + + align:start position:0% +mathematic courses and that we get we'd + + + align:start position:0% +mathematic courses and that we get we'd +get the chance to explore so many of the + + align:start position:0% +get the chance to explore so many of the + + + align:start position:0% +get the chance to explore so many of the +stuff in math but then then I think I + + align:start position:0% +stuff in math but then then I think I + + + align:start position:0% +stuff in math but then then I think I +was shocked because the content was not + + align:start position:0% +was shocked because the content was not + + + align:start position:0% +was shocked because the content was not +did not have like in-depth things about + + align:start position:0% +did not have like in-depth things about + + + align:start position:0% +did not have like in-depth things about +math or like too many Advanced topics + + align:start position:0% +math or like too many Advanced topics + + + align:start position:0% +math or like too many Advanced topics +about mathematics and I think it it was + + align:start position:0% +about mathematics and I think it it was + + + align:start position:0% +about mathematics and I think it it was +that there that I realized that it's not + + align:start position:0% +that there that I realized that it's not + + + align:start position:0% +that there that I realized that it's not +the answer maybe it's like the start of + + align:start position:0% +the answer maybe it's like the start of + + + align:start position:0% +the answer maybe it's like the start of +the answer but it's not it and I need to + + align:start position:0% +the answer but it's not it and I need to + + + align:start position:0% +the answer but it's not it and I need to +like seek my uh pursue my interest + + align:start position:0% +like seek my uh pursue my interest + + + align:start position:0% +like seek my uh pursue my interest +somewhere else I love your journey + + align:start position:0% +somewhere else I love your journey + + + align:start position:0% +somewhere else I love your journey +particularly because I understand and + + align:start position:0% +particularly because I understand and + + + align:start position:0% +particularly because I understand and +resonate with the fact you know when you + + align:start position:0% +resonate with the fact you know when you + + + align:start position:0% +resonate with the fact you know when you +come from a small + + align:start position:0% +come from a small + + + align:start position:0% +come from a small +a private school then you go to a big + + align:start position:0% +a private school then you go to a big + + + align:start position:0% +a private school then you go to a big +school and it's like oh look at all + + align:start position:0% +school and it's like oh look at all + + + align:start position:0% +school and it's like oh look at all +these people and it's a new experience + + align:start position:0% +these people and it's a new experience + + + align:start position:0% +these people and it's a new experience +and we I can also understand actually I + + align:start position:0% +and we I can also understand actually I + + + align:start position:0% +and we I can also understand actually I +can understand this as well I also + + align:start position:0% +can understand this as well I also + + + align:start position:0% +can understand this as well I also +wanted to take an engineering background + + align:start position:0% +wanted to take an engineering background + + + align:start position:0% +wanted to take an engineering background +I ended up taking a science uh so a + + align:start position:0% +I ended up taking a science uh so a + + + align:start position:0% +I ended up taking a science uh so a +computer science course as well but + + align:start position:0% +computer science course as well but + + + align:start position:0% +computer science course as well but +that's an interesting journey I just + + align:start position:0% +that's an interesting journey I just + + + align:start position:0% +that's an interesting journey I just +wanted you to shed some light on the + + align:start position:0% +wanted you to shed some light on the + + + align:start position:0% +wanted you to shed some light on the +difference between online learning when + + align:start position:0% +difference between online learning when + + + align:start position:0% +difference between online learning when +you first when you finally encountered + + align:start position:0% +you first when you finally encountered + + + align:start position:0% +you first when you finally encountered +it and traditional learning back home + + align:start position:0% +it and traditional learning back home + + + align:start position:0% +it and traditional learning back home +how was that for you so I think the + + align:start position:0% +how was that for you so I think the + + + align:start position:0% +how was that for you so I think the +difference between traditional uh + + align:start position:0% +difference between traditional uh + + + align:start position:0% +difference between traditional uh +learning or maybe the learning at school + + align:start position:0% +learning or maybe the learning at school + + + align:start position:0% +learning or maybe the learning at school +and then we had like structured content + + align:start position:0% +and then we had like structured content + + + align:start position:0% +and then we had like structured content +that was not always up to dat with what + + align:start position:0% +that was not always up to dat with what + + + align:start position:0% +that was not always up to dat with what +was happening in the world especially in + + align:start position:0% +was happening in the world especially in + + + align:start position:0% +was happening in the world especially in +specializations like engineering and uh + + align:start position:0% +specializations like engineering and uh + + + align:start position:0% +specializations like engineering and uh +that are like they're changing at the + + align:start position:0% +that are like they're changing at the + + + align:start position:0% +that are like they're changing at the +moment and they're evolving in too many + + align:start position:0% +moment and they're evolving in too many + + + align:start position:0% +moment and they're evolving in too many +Technologies are being Advanced every + + align:start position:0% +Technologies are being Advanced every + + + align:start position:0% +Technologies are being Advanced every +day and that was not reflected in the + + align:start position:0% +day and that was not reflected in the + + + align:start position:0% +day and that was not reflected in the +content that we had at the time but then + + align:start position:0% +content that we had at the time but then + + + align:start position:0% +content that we had at the time but then +on the other hand the online learning + + align:start position:0% +on the other hand the online learning + + + align:start position:0% +on the other hand the online learning +and the online material it's embedded + + align:start position:0% +and the online material it's embedded + + + align:start position:0% +and the online material it's embedded +with uh knowledge it's unlimited let me + + align:start position:0% +with uh knowledge it's unlimited let me + + + align:start position:0% +with uh knowledge it's unlimited let me +talk about YouTube you go to one link + + align:start position:0% +talk about YouTube you go to one link + + + align:start position:0% +talk about YouTube you go to one link +and then you start learning and then you + + align:start position:0% +and then you start learning and then you + + + align:start position:0% +and then you start learning and then you +find another one that takes you to + + align:start position:0% +find another one that takes you to + + + align:start position:0% +find another one that takes you to +another thing or another topic and it's + + align:start position:0% +another thing or another topic and it's + + + align:start position:0% +another thing or another topic and it's +just like it opens a world full of + + align:start position:0% +just like it opens a world full of + + + align:start position:0% +just like it opens a world full of +possibilities and you can get to explore + + align:start position:0% +possibilities and you can get to explore + + + align:start position:0% +possibilities and you can get to explore +everything you want so just a follow-up + + align:start position:0% +everything you want so just a follow-up + + + align:start position:0% +everything you want so just a follow-up +question there so when you first found + + align:start position:0% +question there so when you first found + + + align:start position:0% +question there so when you first found +MIT open course where was that through + + align:start position:0% +MIT open course where was that through + + + align:start position:0% +MIT open course where was that through +YouTube and was that during your + + align:start position:0% +YouTube and was that during your + + + align:start position:0% +YouTube and was that during your +undergraduate studies or was that during + + align:start position:0% +undergraduate studies or was that during + + + align:start position:0% +undergraduate studies or was that during +uh the time when you started becoming a + + align:start position:0% +uh the time when you started becoming a + + + align:start position:0% +uh the time when you started becoming a +teacher assistant my first experience + + align:start position:0% +teacher assistant my first experience + + + align:start position:0% +teacher assistant my first experience +with MIT open course s was during my + + align:start position:0% +with MIT open course s was during my + + + align:start position:0% +with MIT open course s was during my +undergrads actually it was through one + + align:start position:0% +undergrads actually it was through one + + + align:start position:0% +undergrads actually it was through one +of my Tas uh around the second year of + + align:start position:0% +of my Tas uh around the second year of + + + align:start position:0% +of my Tas uh around the second year of +my undergrads we were struggling with + + align:start position:0% +my undergrads we were struggling with + + + align:start position:0% +my undergrads we were struggling with +programming classes at that time it was + + align:start position:0% +programming classes at that time it was + + + align:start position:0% +programming classes at that time it was +like our first impression with it and we + + align:start position:0% +like our first impression with it and we + + + align:start position:0% +like our first impression with it and we +did not just fully understand it and we + + align:start position:0% +did not just fully understand it and we + + + align:start position:0% +did not just fully understand it and we +wanted something more to understand it + + align:start position:0% +wanted something more to understand it + + + align:start position:0% +wanted something more to understand it +and one of the T suggested that we look + + align:start position:0% +and one of the T suggested that we look + + + align:start position:0% +and one of the T suggested that we look +at one of the courses at MIT I think it + + align:start position:0% +at one of the courses at MIT I think it + + + align:start position:0% +at one of the courses at MIT I think it +was in YouTube the course was in YouTube + + align:start position:0% +was in YouTube the course was in YouTube + + + align:start position:0% +was in YouTube the course was in YouTube +it was recorded it was not just me I had + + align:start position:0% +it was recorded it was not just me I had + + + align:start position:0% +it was recorded it was not just me I had +like couple of other fellow students + + align:start position:0% +like couple of other fellow students + + + align:start position:0% +like couple of other fellow students +with me and we studied the course + + align:start position:0% +with me and we studied the course + + + align:start position:0% +with me and we studied the course +together and then after that we wanted + + align:start position:0% +together and then after that we wanted + + + align:start position:0% +together and then after that we wanted +to like okay there's this website it has + + align:start position:0% +to like okay there's this website it has + + + align:start position:0% +to like okay there's this website it has +so many courses not just about + + align:start position:0% +so many courses not just about + + + align:start position:0% +so many courses not just about +programming about too many other stuff + + align:start position:0% +programming about too many other stuff + + + align:start position:0% +programming about too many other stuff +some of which we had we already had in + + align:start position:0% +some of which we had we already had in + + + align:start position:0% +some of which we had we already had in +our undergrad or in our materials and + + align:start position:0% +our undergrad or in our materials and + + + align:start position:0% +our undergrad or in our materials and +it's just delivered differently + + align:start position:0% +it's just delivered differently + + + align:start position:0% +it's just delivered differently +structured in a different way and yes I + + align:start position:0% +structured in a different way and yes I + + + align:start position:0% +structured in a different way and yes I +owe MIT open course where a lot of my + + align:start position:0% +owe MIT open course where a lot of my + + + align:start position:0% +owe MIT open course where a lot of my +mathematical knowledge and mathematical + + align:start position:0% +mathematical knowledge and mathematical + + + align:start position:0% +mathematical knowledge and mathematical +understanding it comes from there I + + align:start position:0% +understanding it comes from there I + + + align:start position:0% +understanding it comes from there I +guess amazing amazing it's really cool + + align:start position:0% +guess amazing amazing it's really cool + + + align:start position:0% +guess amazing amazing it's really cool +that you were in a group too you know I + + align:start position:0% +that you were in a group too you know I + + + align:start position:0% +that you were in a group too you know I +think you might be the first learner + + align:start position:0% +think you might be the first learner + + + align:start position:0% +think you might be the first learner +that was using MIT open course where in + + align:start position:0% +that was using MIT open course where in + + + align:start position:0% +that was using MIT open course where in +a group would would you just maybe talk + + align:start position:0% +a group would would you just maybe talk + + + align:start position:0% +a group would would you just maybe talk +about how using open courseware + + align:start position:0% +about how using open courseware + + + align:start position:0% +about how using open courseware +especially in the group it sounded like + + align:start position:0% +especially in the group it sounded like + + + align:start position:0% +especially in the group it sounded like +it helped you academically but did it + + align:start position:0% +it helped you academically but did it + + + align:start position:0% +it helped you academically but did it +help you like with personal + + align:start position:0% +help you like with personal + + + align:start position:0% +help you like with personal +relationships with friendships I did not + + align:start position:0% +relationships with friendships I did not + + + align:start position:0% +relationships with friendships I did not +actually reflect on this throughout my + + align:start position:0% +actually reflect on this throughout my + + + align:start position:0% +actually reflect on this throughout my +life but now looking at it I think it + + align:start position:0% +life but now looking at it I think it + + + align:start position:0% +life but now looking at it I think it +did help me and uh especially when we + + align:start position:0% +did help me and uh especially when we + + + align:start position:0% +did help me and uh especially when we +were we were just like we were in the + + align:start position:0% +were we were just like we were in the + + + align:start position:0% +were we were just like we were in the +our second year of my undergrads and + + align:start position:0% +our second year of my undergrads and + + + align:start position:0% +our second year of my undergrads and +around that time the structure of + + align:start position:0% +around that time the structure of + + + align:start position:0% +around that time the structure of +University um like I applied for + + align:start position:0% +University um like I applied for + + + align:start position:0% +University um like I applied for +electrical and electronics engineering + + align:start position:0% +electrical and electronics engineering + + + align:start position:0% +electrical and electronics engineering +specialization but at first two years we + + align:start position:0% +specialization but at first two years we + + + align:start position:0% +specialization but at first two years we +study like from different + + align:start position:0% +study like from different + + + align:start position:0% +study like from different +specializations so we were too many + + align:start position:0% +specializations so we were too many + + + align:start position:0% +specializations so we were too many +students coming from different areas and + + align:start position:0% +students coming from different areas and + + + align:start position:0% +students coming from different areas and +going into different areas and I didn't + + align:start position:0% +going into different areas and I didn't + + + align:start position:0% +going into different areas and I didn't +like have the chance to meet for with + + align:start position:0% +like have the chance to meet for with + + + align:start position:0% +like have the chance to meet for with +with students from my patch or who we + + align:start position:0% +with students from my patch or who we + + + align:start position:0% +with students from my patch or who we +going to like spend the rest of my + + align:start position:0% +going to like spend the rest of my + + + align:start position:0% +going to like spend the rest of my +undergrads with and then when this came + + align:start position:0% +undergrads with and then when this came + + + align:start position:0% +undergrads with and then when this came +up and when we started like to form the + + align:start position:0% +up and when we started like to form the + + + align:start position:0% +up and when we started like to form the +groups and other students from my patch + + align:start position:0% +groups and other students from my patch + + + align:start position:0% +groups and other students from my patch +came in who are now are some of my best + + align:start position:0% +came in who are now are some of my best + + + align:start position:0% +came in who are now are some of my best +friends in my life even after like 10 + + align:start position:0% +friends in my life even after like 10 + + + align:start position:0% +friends in my life even after like 10 +years of graduating uh we spent too many + + align:start position:0% +years of graduating uh we spent too many + + + align:start position:0% +years of graduating uh we spent too many +time together we would like uh sit we + + align:start position:0% +time together we would like uh sit we + + + align:start position:0% +time together we would like uh sit we +maybe we would not just like attend the + + align:start position:0% +maybe we would not just like attend the + + + align:start position:0% +maybe we would not just like attend the +lectures or go through the content + + align:start position:0% +lectures or go through the content + + + align:start position:0% +lectures or go through the content +together but we would come and discuss + + align:start position:0% +together but we would come and discuss + + + align:start position:0% +together but we would come and discuss +it and uh share maybe some some people + + align:start position:0% +it and uh share maybe some some people + + + align:start position:0% +it and uh share maybe some some people +go through different course and then we + + align:start position:0% +go through different course and then we + + + align:start position:0% +go through different course and then we +would share it we would share the + + align:start position:0% +would share it we would share the + + + align:start position:0% +would share it we would share the +knowledge we had and in between this + + align:start position:0% +knowledge we had and in between this + + + align:start position:0% +knowledge we had and in between this +time of learning we would like just + + align:start position:0% +time of learning we would like just + + + align:start position:0% +time of learning we would like just +chitchat and exchange just like the + + align:start position:0% +chitchat and exchange just like the + + + align:start position:0% +chitchat and exchange just like the +basic human interaction and boom we + + align:start position:0% +basic human interaction and boom we + + + align:start position:0% +basic human interaction and boom we +became friends did you ever use ocw for + + align:start position:0% +became friends did you ever use ocw for + + + align:start position:0% +became friends did you ever use ocw for +other things outside career because they + + align:start position:0% +other things outside career because they + + + align:start position:0% +other things outside career because they +have so many topics on there that are + + align:start position:0% +have so many topics on there that are + + + align:start position:0% +have so many topics on there that are +outside so was it strictly for book + + align:start position:0% +outside so was it strictly for book + + + align:start position:0% +outside so was it strictly for book +purposes are you still using ocw right + + align:start position:0% +purposes are you still using ocw right + + + align:start position:0% +purposes are you still using ocw right +now in your life I think originally it + + align:start position:0% +now in your life I think originally it + + + align:start position:0% +now in your life I think originally it +was for the pure academic reasons that I + + align:start position:0% +was for the pure academic reasons that I + + + align:start position:0% +was for the pure academic reasons that I +started like going through and studying + + align:start position:0% +started like going through and studying + + + align:start position:0% +started like going through and studying +it it was just for pure mathematic + + align:start position:0% +it it was just for pure mathematic + + + align:start position:0% +it it was just for pure mathematic +content and other stuff related to my + + align:start position:0% +content and other stuff related to my + + + align:start position:0% +content and other stuff related to my +academic Journey but definitely in + + align:start position:0% +academic Journey but definitely in + + + align:start position:0% +academic Journey but definitely in +between then and there I did go through + + align:start position:0% +between then and there I did go through + + + align:start position:0% +between then and there I did go through +some of the courses that are not just + + align:start position:0% +some of the courses that are not just + + + align:start position:0% +some of the courses that are not just +related to my academic Life currently + + align:start position:0% +related to my academic Life currently + + + align:start position:0% +related to my academic Life currently +I'm using it to go through my uh MIT + + align:start position:0% +I'm using it to go through my uh MIT + + + align:start position:0% +I'm using it to go through my uh MIT +emerging learning uh program it's also + + align:start position:0% +emerging learning uh program it's also + + + align:start position:0% +emerging learning uh program it's also +academic but uh it's helping me a lot + + align:start position:0% +academic but uh it's helping me a lot + + + align:start position:0% +academic but uh it's helping me a lot +which brings me to this other thing + + align:start position:0% +which brings me to this other thing + + + align:start position:0% +which brings me to this other thing +that listening to these videos and + + align:start position:0% +that listening to these videos and + + + align:start position:0% +that listening to these videos and +attending these lectures had has helped + + align:start position:0% +attending these lectures had has helped + + + align:start position:0% +attending these lectures had has helped +me a lot with my English language and it + + align:start position:0% +me a lot with my English language and it + + + align:start position:0% +me a lot with my English language and it +was a challenge at first because as I + + align:start position:0% +was a challenge at first because as I + + + align:start position:0% +was a challenge at first because as I +said during my uh high school and before + + align:start position:0% +said during my uh high school and before + + + align:start position:0% +said during my uh high school and before +my undergrads I did not attend a school + + align:start position:0% +my undergrads I did not attend a school + + + align:start position:0% +my undergrads I did not attend a school +or university which was in full English + + align:start position:0% +or university which was in full English + + + align:start position:0% +or university which was in full English +and then when I joined my undergrads + + align:start position:0% +and then when I joined my undergrads + + + align:start position:0% +and then when I joined my undergrads +when I joined University it was like + + align:start position:0% +when I joined University it was like + + + align:start position:0% +when I joined University it was like +just pure English which was an extreme + + align:start position:0% +just pure English which was an extreme + + + align:start position:0% +just pure English which was an extreme +challenge but listening to these courses + + align:start position:0% +challenge but listening to these courses + + + align:start position:0% +challenge but listening to these courses +and going through them has helped me a + + align:start position:0% +and going through them has helped me a + + + align:start position:0% +and going through them has helped me a +lot in listening and understanding in + + align:start position:0% +lot in listening and understanding in + + + align:start position:0% +lot in listening and understanding in +the academic English and how to + + align:start position:0% +the academic English and how to + + + align:start position:0% +the academic English and how to +communicate with this language so this + + align:start position:0% +communicate with this language so this + + + align:start position:0% +communicate with this language so this +is one of the major parts that helped me + + align:start position:0% +is one of the major parts that helped me + + + align:start position:0% +is one of the major parts that helped me +with throughout my + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +life uh how did you find Imaging Talent + + align:start position:0% +life uh how did you find Imaging Talent + + + align:start position:0% +life uh how did you find Imaging Talent +first of all uh maybe you could give us + + align:start position:0% +first of all uh maybe you could give us + + + align:start position:0% +first of all uh maybe you could give us +a b brief background about that I was + + align:start position:0% +a b brief background about that I was + + + align:start position:0% +a b brief background about that I was +going through through really hard time + + align:start position:0% +going through through really hard time + + + align:start position:0% +going through through really hard time +in my life when I found out about the + + align:start position:0% +in my life when I found out about the + + + align:start position:0% +in my life when I found out about the +MIT emerging Talent program um if you + + align:start position:0% +MIT emerging Talent program um if you + + + align:start position:0% +MIT emerging Talent program um if you +don't know I come from Sudan and Sudan + + align:start position:0% +don't know I come from Sudan and Sudan + + + align:start position:0% +don't know I come from Sudan and Sudan +is currently suffering from uh a + + align:start position:0% +is currently suffering from uh a + + + align:start position:0% +is currently suffering from uh a +conflict which is it's it's a war it's + + align:start position:0% +conflict which is it's it's a war it's + + + align:start position:0% +conflict which is it's it's a war it's +not just a conflict it's a war that's + + align:start position:0% +not just a conflict it's a war that's + + + align:start position:0% +not just a conflict it's a war that's +happening in Sudan and in May of 2023 I + + align:start position:0% +happening in Sudan and in May of 2023 I + + + align:start position:0% +happening in Sudan and in May of 2023 I +was forced to flee Sudan and uh relocate + + align:start position:0% +was forced to flee Sudan and uh relocate + + + align:start position:0% +was forced to flee Sudan and uh relocate +to Egypt I lost like everything that I + + align:start position:0% +to Egypt I lost like everything that I + + + align:start position:0% +to Egypt I lost like everything that I +love I lost my home um some of my family + + align:start position:0% +love I lost my home um some of my family + + + align:start position:0% +love I lost my home um some of my family +were still stuck there and even at the + + align:start position:0% +were still stuck there and even at the + + + align:start position:0% +were still stuck there and even at the +moment I still have parts of my family + + align:start position:0% +moment I still have parts of my family + + + align:start position:0% +moment I still have parts of my family +still stuck there I have friends stuck + + align:start position:0% +still stuck there I have friends stuck + + + align:start position:0% +still stuck there I have friends stuck +there and we we all lost loved ones and + + align:start position:0% +there and we we all lost loved ones and + + + align:start position:0% +there and we we all lost loved ones and +I just couldn't find the purpose of my + + align:start position:0% +I just couldn't find the purpose of my + + + align:start position:0% +I just couldn't find the purpose of my +life or why am I doing anything or + + align:start position:0% +life or why am I doing anything or + + + align:start position:0% +life or why am I doing anything or +what's what's the reason I remember I + + align:start position:0% +what's what's the reason I remember I + + + align:start position:0% +what's what's the reason I remember I +met this one friend and she was talking + + align:start position:0% +met this one friend and she was talking + + + align:start position:0% +met this one friend and she was talking +to me and we were discussing just how + + align:start position:0% +to me and we were discussing just how + + + align:start position:0% +to me and we were discussing just how +this words affecting our lives and how + + align:start position:0% +this words affecting our lives and how + + + align:start position:0% +this words affecting our lives and how +we need to how we need to overcome it + + align:start position:0% +we need to how we need to overcome it + + + align:start position:0% +we need to how we need to overcome it +not just overcoming but we need to work + + align:start position:0% +not just overcoming but we need to work + + + align:start position:0% +not just overcoming but we need to work +on on ourselves so when the time comes + + align:start position:0% +on on ourselves so when the time comes + + + align:start position:0% +on on ourselves so when the time comes +for us to go back to Sudan and build it + + align:start position:0% +for us to go back to Sudan and build it + + + align:start position:0% +for us to go back to Sudan and build it +we have the knowledge and we have the + + align:start position:0% +we have the knowledge and we have the + + + align:start position:0% +we have the knowledge and we have the +power to do so at that time I was + + align:start position:0% +power to do so at that time I was + + + align:start position:0% +power to do so at that time I was +looking for materials and stuff and this + + align:start position:0% +looking for materials and stuff and this + + + align:start position:0% +looking for materials and stuff and this +same friend she sent me the application + + align:start position:0% +same friend she sent me the application + + + align:start position:0% +same friend she sent me the application +for MIT merging Talent is coming in like + + align:start position:0% +for MIT merging Talent is coming in like + + + align:start position:0% +for MIT merging Talent is coming in like +couple of hours and it was talking about + + align:start position:0% +couple of hours and it was talking about + + + align:start position:0% +couple of hours and it was talking about +the program and that Sudanese people are + + align:start position:0% +the program and that Sudanese people are + + + align:start position:0% +the program and that Sudanese people are +now eligible for it because it's + + align:start position:0% +now eligible for it because it's + + + align:start position:0% +now eligible for it because it's +directed toward people who are suffering + + align:start position:0% +directed toward people who are suffering + + + align:start position:0% +directed toward people who are suffering +from Wars conflicts and who are refugees + + align:start position:0% +from Wars conflicts and who are refugees + + + align:start position:0% +from Wars conflicts and who are refugees +and everything the deadline was + + align:start position:0% +and everything the deadline was + + + align:start position:0% +and everything the deadline was +approaching like couple of hours and I + + align:start position:0% +approaching like couple of hours and I + + + align:start position:0% +approaching like couple of hours and I +needed to prepare for it and write all + + align:start position:0% +needed to prepare for it and write all + + + align:start position:0% +needed to prepare for it and write all +the essays and it has like a + + align:start position:0% +the essays and it has like a + + + align:start position:0% +the essays and it has like a +mathematical tests and other programming + + align:start position:0% +mathematical tests and other programming + + + align:start position:0% +mathematical tests and other programming +tests and everything and then when I + + align:start position:0% +tests and everything and then when I + + + align:start position:0% +tests and everything and then when I +reached like the last part it needed a + + align:start position:0% +reached like the last part it needed a + + + align:start position:0% +reached like the last part it needed a +video recording this is really funny + + align:start position:0% +video recording this is really funny + + + align:start position:0% +video recording this is really funny +because every time I remember it I just + + align:start position:0% +because every time I remember it I just + + + align:start position:0% +because every time I remember it I just +I laugh about it um it had like a video + + align:start position:0% +I laugh about it um it had like a video + + + align:start position:0% +I laugh about it um it had like a video +recording thing and at that time I was + + align:start position:0% +recording thing and at that time I was + + + align:start position:0% +recording thing and at that time I was +in Egypt and it was summer and they had + + align:start position:0% +in Egypt and it was summer and they had + + + align:start position:0% +in Egypt and it was summer and they had +like this power outage that comes in + + align:start position:0% +like this power outage that comes in + + + align:start position:0% +like this power outage that comes in +Egypt for a couple of hours and I needed + + align:start position:0% +Egypt for a couple of hours and I needed + + + align:start position:0% +Egypt for a couple of hours and I needed +to record the video for this and I + + align:start position:0% +to record the video for this and I + + + align:start position:0% +to record the video for this and I +didn't know when will the electricity + + align:start position:0% +didn't know when will the electricity + + + align:start position:0% +didn't know when will the electricity +come back so I said okay I don't have + + align:start position:0% +come back so I said okay I don't have + + + align:start position:0% +come back so I said okay I don't have +anything to lose let's just try so + + align:start position:0% +anything to lose let's just try so + + + align:start position:0% +anything to lose let's just try so +instead of recording a video I sent a + + align:start position:0% +instead of recording a video I sent a + + + align:start position:0% +instead of recording a video I sent a +voice recording I didn't think they + + align:start position:0% +voice recording I didn't think they + + + align:start position:0% +voice recording I didn't think they +would accept it because why would MIT + + align:start position:0% +would accept it because why would MIT + + + align:start position:0% +would accept it because why would MIT +accept a voice memo when when they + + align:start position:0% +accept a voice memo when when they + + + align:start position:0% +accept a voice memo when when they +clearly stated that they wanted like a + + align:start position:0% +clearly stated that they wanted like a + + + align:start position:0% +clearly stated that they wanted like a +video recording but I sent it anyway I + + align:start position:0% +video recording but I sent it anyway I + + + align:start position:0% +video recording but I sent it anyway I +had nothing to lose and I didn't have + + align:start position:0% +had nothing to lose and I didn't have + + + align:start position:0% +had nothing to lose and I didn't have +Alternatives so I sent it and couple of + + align:start position:0% +Alternatives so I sent it and couple of + + + align:start position:0% +Alternatives so I sent it and couple of +weeks after that I got the email I got + + align:start position:0% +weeks after that I got the email I got + + + align:start position:0% +weeks after that I got the email I got +the acceptance email and I think the + + align:start position:0% +the acceptance email and I think the + + + align:start position:0% +the acceptance email and I think the +program has been really helpful for me + + align:start position:0% +program has been really helpful for me + + + align:start position:0% +program has been really helpful for me +coming across people that are suffering + + align:start position:0% +coming across people that are suffering + + + align:start position:0% +coming across people that are suffering +from the same stuff that you're + + align:start position:0% +from the same stuff that you're + + + align:start position:0% +from the same stuff that you're +suffering from or have been going + + align:start position:0% +suffering from or have been going + + + align:start position:0% +suffering from or have been going +through the same Journey the same things + + align:start position:0% +through the same Journey the same things + + + align:start position:0% +through the same Journey the same things +or not just maybe not just the same but + + align:start position:0% +or not just maybe not just the same but + + + align:start position:0% +or not just maybe not just the same but +something similar and they they've been + + align:start position:0% +something similar and they they've been + + + align:start position:0% +something similar and they they've been +affected by Wars they they lost their + + align:start position:0% +affected by Wars they they lost their + + + align:start position:0% +affected by Wars they they lost their +homes they lost loved ones like going + + align:start position:0% +homes they lost loved ones like going + + + align:start position:0% +homes they lost loved ones like going +live with people who understand the + + align:start position:0% +live with people who understand the + + + align:start position:0% +live with people who understand the +things that you are are going through it + + align:start position:0% +things that you are are going through it + + + align:start position:0% +things that you are are going through it +it sort of helped in my healing process + + align:start position:0% +it sort of helped in my healing process + + + align:start position:0% +it sort of helped in my healing process +or in my like understanding process of + + align:start position:0% +or in my like understanding process of + + + align:start position:0% +or in my like understanding process of +absorbing everything that is happening + + align:start position:0% +absorbing everything that is happening + + + align:start position:0% +absorbing everything that is happening +or currently happening in Sudan this is + + align:start position:0% +or currently happening in Sudan this is + + + align:start position:0% +or currently happening in Sudan this is +the part that is sentimental to this + + align:start position:0% +the part that is sentimental to this + + + align:start position:0% +the part that is sentimental to this +journey what project are you working on + + align:start position:0% +journey what project are you working on + + + align:start position:0% +journey what project are you working on +that side uh how is it important to you + + align:start position:0% +that side uh how is it important to you + + + align:start position:0% +that side uh how is it important to you +how did you arrive to that kind of + + align:start position:0% +how did you arrive to that kind of + + + align:start position:0% +how did you arrive to that kind of +project maybe if you can shed some light + + align:start position:0% +project maybe if you can shed some light + + + align:start position:0% +project maybe if you can shed some light +in that aspect as well the project that + + align:start position:0% +in that aspect as well the project that + + + align:start position:0% +in that aspect as well the project that +we're currently doing so our graduation + + align:start position:0% +we're currently doing so our graduation + + + align:start position:0% +we're currently doing so our graduation +project from the program uh we United me + + align:start position:0% +project from the program uh we United me + + + align:start position:0% +project from the program uh we United me +and another fellows from another MIT + + align:start position:0% +and another fellows from another MIT + + + align:start position:0% +and another fellows from another MIT +fellows from Sudan uh and we're doing + + align:start position:0% +fellows from Sudan uh and we're doing + + + align:start position:0% +fellows from Sudan uh and we're doing +this project which is directed toward + + align:start position:0% +this project which is directed toward + + + align:start position:0% +this project which is directed toward +education in Sudan the educational + + align:start position:0% +education in Sudan the educational + + + align:start position:0% +education in Sudan the educational +system basically just fell down the + + align:start position:0% +system basically just fell down the + + + align:start position:0% +system basically just fell down the +schools are not working universities are + + align:start position:0% +schools are not working universities are + + + align:start position:0% +schools are not working universities are +not working some of them are working + + align:start position:0% +not working some of them are working + + + align:start position:0% +not working some of them are working +online but the majority of the schools + + align:start position:0% +online but the majority of the schools + + + align:start position:0% +online but the majority of the schools +and universities in Sudan has not been + + align:start position:0% +and universities in Sudan has not been + + + align:start position:0% +and universities in Sudan has not been +working for more than a year now which + + align:start position:0% +working for more than a year now which + + + align:start position:0% +working for more than a year now which +is a disaster and we need to look at it + + align:start position:0% +is a disaster and we need to look at it + + + align:start position:0% +is a disaster and we need to look at it +and we need to like find solutions to it + + align:start position:0% +and we need to like find solutions to it + + + align:start position:0% +and we need to like find solutions to it +so our graduation project that we're + + align:start position:0% +so our graduation project that we're + + + align:start position:0% +so our graduation project that we're +trying to offer students with + + align:start position:0% +trying to offer students with + + + align:start position:0% +trying to offer students with +alternatives to this there is this uh + + align:start position:0% +alternatives to this there is this uh + + + align:start position:0% +alternatives to this there is this uh +there's this website called NASA Sudan + + align:start position:0% +there's this website called NASA Sudan + + + align:start position:0% +there's this website called NASA Sudan +it's an initiative that collects all the + + align:start position:0% +it's an initiative that collects all the + + + align:start position:0% +it's an initiative that collects all the +other Alternatives or all the other like + + align:start position:0% +other Alternatives or all the other like + + + align:start position:0% +other Alternatives or all the other like +scholarships universities that accept + + align:start position:0% +scholarships universities that accept + + + align:start position:0% +scholarships universities that accept +Sudanese people outside of Sudan and the + + align:start position:0% +Sudanese people outside of Sudan and the + + + align:start position:0% +Sudanese people outside of Sudan and the +requirements and all the process that + + align:start position:0% +requirements and all the process that + + + align:start position:0% +requirements and all the process that +they need to go through in order to + + align:start position:0% +they need to go through in order to + + + align:start position:0% +they need to go through in order to +apply for these universities so we're + + align:start position:0% +apply for these universities so we're + + + align:start position:0% +apply for these universities so we're +helping with their databases we're + + align:start position:0% +helping with their databases we're + + + align:start position:0% +helping with their databases we're +rebuilding the databases for this + + align:start position:0% +rebuilding the databases for this + + + align:start position:0% +rebuilding the databases for this +universities and the website and + + align:start position:0% +universities and the website and + + + align:start position:0% +universities and the website and +everything in between that I was just + + align:start position:0% +everything in between that I was just + + + align:start position:0% +everything in between that I was just +curious if you wanted to talk about you + + align:start position:0% +curious if you wanted to talk about you + + + align:start position:0% +curious if you wanted to talk about you +know after the + + align:start position:0% +know after the + + + align:start position:0% +know after the +program after all the learning on open + + align:start position:0% +program after all the learning on open + + + align:start position:0% +program after all the learning on open +course where if you have a vision for + + align:start position:0% +course where if you have a vision for + + + align:start position:0% +course where if you have a vision for +your own future or if you have an idea + + align:start position:0% +your own future or if you have an idea + + + align:start position:0% +your own future or if you have an idea +of where you want to go in in the future + + align:start position:0% +of where you want to go in in the future + + + align:start position:0% +of where you want to go in in the future +at this point in time well I'm still not + + align:start position:0% +at this point in time well I'm still not + + + align:start position:0% +at this point in time well I'm still not +quite sure I don't have like a clearer + + align:start position:0% +quite sure I don't have like a clearer + + + align:start position:0% +quite sure I don't have like a clearer +vision of where I want to go I think + + align:start position:0% +vision of where I want to go I think + + + align:start position:0% +vision of where I want to go I think +merely because the situation in Sudan is + + align:start position:0% +merely because the situation in Sudan is + + + align:start position:0% +merely because the situation in Sudan is +not quite clear yet and all my career + + align:start position:0% +not quite clear yet and all my career + + + align:start position:0% +not quite clear yet and all my career +plans and my life plans are oriented + + align:start position:0% +plans and my life plans are oriented + + + align:start position:0% +plans and my life plans are oriented +around Sudan and I think this past year + + align:start position:0% +around Sudan and I think this past year + + + align:start position:0% +around Sudan and I think this past year +has affirmed me that I really want to + + align:start position:0% +has affirmed me that I really want to + + + align:start position:0% +has affirmed me that I really want to +give back to Sudan and I want to help + + align:start position:0% +give back to Sudan and I want to help + + + align:start position:0% +give back to Sudan and I want to help +build San because I can't I can't belong + + align:start position:0% +build San because I can't I can't belong + + + align:start position:0% +build San because I can't I can't belong +anywhere I can't find anywhere to belong + + align:start position:0% +anywhere I can't find anywhere to belong + + + align:start position:0% +anywhere I can't find anywhere to belong +and I want to build Sudan for the other + + align:start position:0% +and I want to build Sudan for the other + + + align:start position:0% +and I want to build Sudan for the other +people the other Generations that will + + align:start position:0% +people the other Generations that will + + + align:start position:0% +people the other Generations that will +come to find some place to belong to + + align:start position:0% +come to find some place to belong to + + + align:start position:0% +come to find some place to belong to +because belonging is one of the it's one + + align:start position:0% +because belonging is one of the it's one + + + align:start position:0% +because belonging is one of the it's one +of the most + + align:start position:0% +of the most + + + align:start position:0% +of the most +important uh feelings for for human + + align:start position:0% +important uh feelings for for human + + + align:start position:0% +important uh feelings for for human +beings and I sort of want to contribute + + align:start position:0% +beings and I sort of want to contribute + + + align:start position:0% +beings and I sort of want to contribute +this knowledge I have or I think I have + + align:start position:0% +this knowledge I have or I think I have + + + align:start position:0% +this knowledge I have or I think I have +to building Sudan and + + align:start position:0% +to building Sudan and + + + align:start position:0% +to building Sudan and +to to its healing and it's its recovery + + align:start position:0% +to to its healing and it's its recovery + + + align:start position:0% +to to its healing and it's its recovery +so currently I'm just looking for + + align:start position:0% +so currently I'm just looking for + + + align:start position:0% +so currently I'm just looking for +opportunities uh throughout the program + + align:start position:0% +opportunities uh throughout the program + + + align:start position:0% +opportunities uh throughout the program +and after after finishing the program + + align:start position:0% +and after after finishing the program + + + align:start position:0% +and after after finishing the program +I'm looking for opportunities to + + align:start position:0% +I'm looking for opportunities to + + + align:start position:0% +I'm looking for opportunities to +contribute this that's perfect no we we + + align:start position:0% +contribute this that's perfect no we we + + + align:start position:0% +contribute this that's perfect no we we +understand that having certainty in the + + align:start position:0% +understand that having certainty in the + + + align:start position:0% +understand that having certainty in the +future um you know one final question + + align:start position:0% +future um you know one final question + + + align:start position:0% +future um you know one final question +from me and then I'll let Emanuel kind + + align:start position:0% +from me and then I'll let Emanuel kind + + + align:start position:0% +from me and then I'll let Emanuel kind +of take over is do you have any advice + + align:start position:0% +of take over is do you have any advice + + + align:start position:0% +of take over is do you have any advice +for anyone that may be in the same exact + + align:start position:0% +for anyone that may be in the same exact + + + align:start position:0% +for anyone that may be in the same exact +situation that you are if I can give + + align:start position:0% +situation that you are if I can give + + + align:start position:0% +situation that you are if I can give +like advice for people coming from not + + align:start position:0% +like advice for people coming from not + + + align:start position:0% +like advice for people coming from not +just the same background but from + + align:start position:0% +just the same background but from + + + align:start position:0% +just the same background but from +communities where they do not have + + align:start position:0% +communities where they do not have + + + align:start position:0% +communities where they do not have +access to maybe quality education or uh + + align:start position:0% +access to maybe quality education or uh + + + align:start position:0% +access to maybe quality education or uh +opportunities don't wait for them just + + align:start position:0% +opportunities don't wait for them just + + + align:start position:0% +opportunities don't wait for them just +seek these opportunities and do + + align:start position:0% +seek these opportunities and do + + + align:start position:0% +seek these opportunities and do +not I remember I read this somewhere + + align:start position:0% +not I remember I read this somewhere + + + align:start position:0% +not I remember I read this somewhere +that it was something about + + align:start position:0% +that it was something about + + + align:start position:0% +that it was something about +self-rejection and how we always like + + align:start position:0% +self-rejection and how we always like + + + align:start position:0% +self-rejection and how we always like +self reject ourselves and we do not give + + align:start position:0% +self reject ourselves and we do not give + + + align:start position:0% +self reject ourselves and we do not give +ourselves the opportunity to even even + + align:start position:0% +ourselves the opportunity to even even + + + align:start position:0% +ourselves the opportunity to even even +be considered for something and just do + + align:start position:0% +be considered for something and just do + + + align:start position:0% +be considered for something and just do +not self- reject yourselves you're not + + align:start position:0% +not self- reject yourselves you're not + + + align:start position:0% +not self- reject yourselves you're not +losing anything by trying but when + + align:start position:0% +losing anything by trying but when + + + align:start position:0% +losing anything by trying but when +you're not trying you're not even + + align:start position:0% +you're not trying you're not even + + + align:start position:0% +you're not trying you're not even +presenting yourself and you're not + + align:start position:0% +presenting yourself and you're not + + + align:start position:0% +presenting yourself and you're not +giving yourself the opportunity to being + + align:start position:0% +giving yourself the opportunity to being + + + align:start position:0% +giving yourself the opportunity to being +considered for something or to take + + align:start position:0% +considered for something or to take + + + align:start position:0% +considered for something or to take +something so self-rejection is the worst + + align:start position:0% +something so self-rejection is the worst + + + align:start position:0% +something so self-rejection is the worst +enemy for everyone so just don't self- + + align:start position:0% +enemy for everyone so just don't self- + + + align:start position:0% +enemy for everyone so just don't self- +reject yourself if there is opportunity + + align:start position:0% +reject yourself if there is opportunity + + + align:start position:0% +reject yourself if there is opportunity +and you're not going to to lose anything + + align:start position:0% +and you're not going to to lose anything + + + align:start position:0% +and you're not going to to lose anything +so why not just try it and why not just + + align:start position:0% +so why not just try it and why not just + + + align:start position:0% +so why not just try it and why not just +like take this + + align:start position:0% +like take this + + + align:start position:0% +like take this +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +opportunity if they gave you a magic one + + align:start position:0% +opportunity if they gave you a magic one + + + align:start position:0% +opportunity if they gave you a magic one +and they told you okay you could add + + align:start position:0% +and they told you okay you could add + + + align:start position:0% +and they told you okay you could add +something to the + + align:start position:0% +something to the + + + align:start position:0% +something to the +ocw movement like you could add + + align:start position:0% +ocw movement like you could add + + + align:start position:0% +ocw movement like you could add +something to this or remove something + + align:start position:0% +something to this or remove something + + + align:start position:0% +something to this or remove something +from it what would that be if I have a + + align:start position:0% +from it what would that be if I have a + + + align:start position:0% +from it what would that be if I have a +magical power and I am to add anything + + align:start position:0% +magical power and I am to add anything + + + align:start position:0% +magical power and I am to add anything +to MIT open course whereare what would + + align:start position:0% +to MIT open course whereare what would + + + align:start position:0% +to MIT open course whereare what would +it be I think the one thing that I would + + align:start position:0% +it be I think the one thing that I would + + + align:start position:0% +it be I think the one thing that I would +add and uh to find some medical way or + + align:start position:0% +add and uh to find some medical way or + + + align:start position:0% +add and uh to find some medical way or +some medical power just to to get rid of + + align:start position:0% +some medical power just to to get rid of + + + align:start position:0% +some medical power just to to get rid of +the language barrier and maybe give + + align:start position:0% +the language barrier and maybe give + + + align:start position:0% +the language barrier and maybe give +everyone the opportunity to benefit from + + align:start position:0% +everyone the opportunity to benefit from + + + align:start position:0% +everyone the opportunity to benefit from +from the material and from all the stuff + + align:start position:0% +from the material and from all the stuff + + + align:start position:0% +from the material and from all the stuff +that are out there without the language + + align:start position:0% +that are out there without the language + + + align:start position:0% +that are out there without the language +barrier that's awesome that's great s + + align:start position:0% +barrier that's awesome that's great s + + + align:start position:0% +barrier that's awesome that's great s +Jude I love your story and I would like + + align:start position:0% +Jude I love your story and I would like + + + align:start position:0% +Jude I love your story and I would like +to personally thank you for you know + + align:start position:0% +to personally thank you for you know + + + align:start position:0% +to personally thank you for you know +telling us your story and we hope + + align:start position:0% +telling us your story and we hope + + + align:start position:0% +telling us your story and we hope +that anyone else listening to this will + + align:start position:0% +that anyone else listening to this will + + + align:start position:0% +that anyone else listening to this will +get inspired you know will know that + + align:start position:0% +get inspired you know will know that + + + align:start position:0% +get inspired you know will know that +actually this is not just some online + + align:start position:0% +actually this is not just some online + + + align:start position:0% +actually this is not just some online +learning thing online it's actually + + align:start position:0% +learning thing online it's actually + + + align:start position:0% +learning thing online it's actually +helping lives it's helping people not + + align:start position:0% +helping lives it's helping people not + + + align:start position:0% +helping lives it's helping people not +just in school outside school in the + + align:start position:0% +just in school outside school in the + + + align:start position:0% +just in school outside school in the +toughest situations I guess my final + + align:start position:0% +toughest situations I guess my final + + + align:start position:0% +toughest situations I guess my final +question to you would be first of + + align:start position:0% +question to you would be first of + + + align:start position:0% +question to you would be first of +all as someone who has gone through all + + align:start position:0% +all as someone who has gone through all + + + align:start position:0% +all as someone who has gone through all +this I know it can't be easy maybe how + + align:start position:0% +this I know it can't be easy maybe how + + + align:start position:0% +this I know it can't be easy maybe how +do you + + align:start position:0% +do you + + + align:start position:0% +do you +stay focused how do you stay strong you + + align:start position:0% +stay focused how do you stay strong you + + + align:start position:0% +stay focused how do you stay strong you +say you mentioned don't self reject + + align:start position:0% +say you mentioned don't self reject + + + align:start position:0% +say you mentioned don't self reject +which is a powerful thing like what do + + align:start position:0% +which is a powerful thing like what do + + + align:start position:0% +which is a powerful thing like what do +you do to self motivate to self you know + + align:start position:0% +you do to self motivate to self you know + + + align:start position:0% +you do to self motivate to self you know +push to drive when in that moment when + + align:start position:0% +push to drive when in that moment when + + + align:start position:0% +push to drive when in that moment when +you feel like giving up what moves you + + align:start position:0% +you feel like giving up what moves you + + + align:start position:0% +you feel like giving up what moves you +well about staying focused I won't lie + + align:start position:0% +well about staying focused I won't lie + + + align:start position:0% +well about staying focused I won't lie +I'm not focused most of the times + + align:start position:0% +I'm not focused most of the times + + + align:start position:0% +I'm not focused most of the times +because like as you said the world is + + align:start position:0% +because like as you said the world is + + + align:start position:0% +because like as you said the world is +still happening and people are still + + align:start position:0% +still happening and people are still + + + align:start position:0% +still happening and people are still +suffering so most of the times that the + + align:start position:0% +suffering so most of the times that the + + + align:start position:0% +suffering so most of the times that the +all the news coming from Sudan just + + align:start position:0% +all the news coming from Sudan just + + + align:start position:0% +all the news coming from Sudan just +absorbs us and we find ourselves + + align:start position:0% +absorbs us and we find ourselves + + + align:start position:0% +absorbs us and we find ourselves +even though we're not in Sudan but we + + align:start position:0% +even though we're not in Sudan but we + + + align:start position:0% +even though we're not in Sudan but we +are in Sudan and even so we're not + + align:start position:0% +are in Sudan and even so we're not + + + align:start position:0% +are in Sudan and even so we're not +physically like there and we're not + + align:start position:0% +physically like there and we're not + + + align:start position:0% +physically like there and we're not +physically hurting and we're not hearing + + align:start position:0% +physically hurting and we're not hearing + + + align:start position:0% +physically hurting and we're not hearing +the bombings and everything but we are + + align:start position:0% +the bombings and everything but we are + + + align:start position:0% +the bombings and everything but we are +there and it's hard to stay focused and + + align:start position:0% +there and it's hard to stay focused and + + + align:start position:0% +there and it's hard to stay focused and +it's hard to to continue with our lives + + align:start position:0% +it's hard to to continue with our lives + + + align:start position:0% +it's hard to to continue with our lives +even though we know that a war is + + align:start position:0% +even though we know that a war is + + + align:start position:0% +even though we know that a war is +happening back there and people are + + align:start position:0% +happening back there and people are + + + align:start position:0% +happening back there and people are +dying back there so most of the times + + align:start position:0% +dying back there so most of the times + + + align:start position:0% +dying back there so most of the times +it's really hard most of the times it's + + align:start position:0% +it's really hard most of the times it's + + + align:start position:0% +it's really hard most of the times it's +impossible to focus or to study or to do + + align:start position:0% +impossible to focus or to study or to do + + + align:start position:0% +impossible to focus or to study or to do +anything productive so I could say that + + align:start position:0% +anything productive so I could say that + + + align:start position:0% +anything productive so I could say that +maybe every couple of productive days I + + align:start position:0% +maybe every couple of productive days I + + + align:start position:0% +maybe every couple of productive days I +just cvel in my bed and I don't do + + align:start position:0% +just cvel in my bed and I don't do + + + align:start position:0% +just cvel in my bed and I don't do +anything I don't find the energy in me + + align:start position:0% +anything I don't find the energy in me + + + align:start position:0% +anything I don't find the energy in me +to get out of my bed and do something + + align:start position:0% +to get out of my bed and do something + + + align:start position:0% +to get out of my bed and do something +productive and I understand that I + + align:start position:0% +productive and I understand that I + + + align:start position:0% +productive and I understand that I +understand the reason behind that but + + align:start position:0% +understand the reason behind that but + + + align:start position:0% +understand the reason behind that but +then I try to just remind myself with + + align:start position:0% +then I try to just remind myself with + + + align:start position:0% +then I try to just remind myself with +the whole purpose of it and why am I + + align:start position:0% +the whole purpose of it and why am I + + + align:start position:0% +the whole purpose of it and why am I +doing it and that there will come a time + + align:start position:0% +doing it and that there will come a time + + + align:start position:0% +doing it and that there will come a time +that we will build Sudan it will come + + align:start position:0% +that we will build Sudan it will come + + + align:start position:0% +that we will build Sudan it will come +even though we don't know when whether + + align:start position:0% +even though we don't know when whether + + + align:start position:0% +even though we don't know when whether +we are going to be alive to witness it + + align:start position:0% +we are going to be alive to witness it + + + align:start position:0% +we are going to be alive to witness it +or to participate in it but if we are + + align:start position:0% +or to participate in it but if we are + + + align:start position:0% +or to participate in it but if we are +Sudan will need us to be at a strong as + + align:start position:0% +Sudan will need us to be at a strong as + + + align:start position:0% +Sudan will need us to be at a strong as +possible to build it and to participate + + align:start position:0% +possible to build it and to participate + + + align:start position:0% +possible to build it and to participate +in it and this sort of gives me some + + align:start position:0% +in it and this sort of gives me some + + + align:start position:0% +in it and this sort of gives me some +peace it sort of helps me a lot with + + align:start position:0% +peace it sort of helps me a lot with + + + align:start position:0% +peace it sort of helps me a lot with +okay I'm not doing it just for myself + + align:start position:0% +okay I'm not doing it just for myself + + + align:start position:0% +okay I'm not doing it just for myself +I'm not doing it just for my family but + + align:start position:0% +I'm not doing it just for my family but + + + align:start position:0% +I'm not doing it just for my family but +in the bigger picture and with with a + + align:start position:0% +in the bigger picture and with with a + + + align:start position:0% +in the bigger picture and with with a +heart filled with hope I'm doing it for + + align:start position:0% +heart filled with hope I'm doing it for + + + align:start position:0% +heart filled with hope I'm doing it for +Sudan for when the time comes + + align:start position:0% +Sudan for when the time comes + + + align:start position:0% +Sudan for when the time comes +that Sudan needs to be built that I'm + + align:start position:0% +that Sudan needs to be built that I'm + + + align:start position:0% +that Sudan needs to be built that I'm +ready well thank you sujud again I think + + align:start position:0% +ready well thank you sujud again I think + + + align:start position:0% +ready well thank you sujud again I think +so many people around the world are + + align:start position:0% +so many people around the world are + + + align:start position:0% +so many people around the world are +going to be inspired by how powerful + + align:start position:0% +going to be inspired by how powerful + + + align:start position:0% +going to be inspired by how powerful +your story is and the knowledge you've + + align:start position:0% +your story is and the knowledge you've + + + align:start position:0% +your story is and the knowledge you've +shared so we are very grateful that you + + align:start position:0% +shared so we are very grateful that you + + + align:start position:0% +shared so we are very grateful that you +came on and were able to share your + + align:start position:0% +came on and were able to share your + + + align:start position:0% +came on and were able to share your +journey and you know I know it may not + + align:start position:0% +journey and you know I know it may not + + + align:start position:0% +journey and you know I know it may not +be complete uh representation of your + + align:start position:0% +be complete uh representation of your + + + align:start position:0% +be complete uh representation of your +journey but I hope it does capture a + + align:start position:0% +journey but I hope it does capture a + + + align:start position:0% +journey but I hope it does capture a +small piece of it that other people can + + align:start position:0% +small piece of it that other people can + + + align:start position:0% +small piece of it that other people can +find inspiration from thank you again + + align:start position:0% +find inspiration from thank you again + + + align:start position:0% +find inspiration from thank you again +thank you Emanuel Michael thank you for + + align:start position:0% +thank you Emanuel Michael thank you for + + + align:start position:0% +thank you Emanuel Michael thank you for +the opportunity and thank you for having + + align:start position:0% +the opportunity and thank you for having + + + align:start position:0% +the opportunity and thank you for having +me I'm really grateful for this + + align:start position:0% +me I'm really grateful for this + + + align:start position:0% +me I'm really grateful for this +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +opportunity wow sujud has really been + + align:start position:0% +opportunity wow sujud has really been + + + align:start position:0% +opportunity wow sujud has really been +able to do something extraordinary she + + align:start position:0% +able to do something extraordinary she + + + align:start position:0% +able to do something extraordinary she +spent the most most difficult moment in + + align:start position:0% +spent the most most difficult moment in + + + align:start position:0% +spent the most most difficult moment in +her life expanding her own knowledge so + + align:start position:0% +her life expanding her own knowledge so + + + align:start position:0% +her life expanding her own knowledge so +that she can rebuild her home country of + + align:start position:0% +that she can rebuild her home country of + + + align:start position:0% +that she can rebuild her home country of +Sudan it's very + + align:start position:0% +Sudan it's very + + + align:start position:0% +Sudan it's very +inspiring what's been on your mind since + + align:start position:0% +inspiring what's been on your mind since + + + align:start position:0% +inspiring what's been on your mind since +we spoke to suude Emanuel yeah Michael + + align:start position:0% +we spoke to suude Emanuel yeah Michael + + + align:start position:0% +we spoke to suude Emanuel yeah Michael +I've been thinking a lot about this + + align:start position:0% +I've been thinking a lot about this + + + align:start position:0% +I've been thinking a lot about this +episode because it's a very touching + + align:start position:0% +episode because it's a very touching + + + align:start position:0% +episode because it's a very touching +episode it's a very inspiring episode I + + align:start position:0% +episode it's a very inspiring episode I + + + align:start position:0% +episode it's a very inspiring episode I +like the part where she says never self- + + align:start position:0% +like the part where she says never self- + + + align:start position:0% +like the part where she says never self- +reject but here we have someone a young + + align:start position:0% +reject but here we have someone a young + + + align:start position:0% +reject but here we have someone a young +person in their mid 20s trying to start + + align:start position:0% +person in their mid 20s trying to start + + + align:start position:0% +person in their mid 20s trying to start +their life and the worst possible thing + + align:start position:0% +their life and the worst possible thing + + + align:start position:0% +their life and the worst possible thing +that could have happened to someone + + align:start position:0% +that could have happened to someone + + + align:start position:0% +that could have happened to someone +happens but in the midst of all that + + align:start position:0% +happens but in the midst of all that + + + align:start position:0% +happens but in the midst of all that +she pushes through she perseveres and + + align:start position:0% +she pushes through she perseveres and + + + align:start position:0% +she pushes through she perseveres and +what amazes me the most is somehow ocw + + align:start position:0% +what amazes me the most is somehow ocw + + + align:start position:0% +what amazes me the most is somehow ocw +was may not have solved all our problems + + align:start position:0% +was may not have solved all our problems + + + align:start position:0% +was may not have solved all our problems +but it kind of provided a Guiding Light + + align:start position:0% +but it kind of provided a Guiding Light + + + align:start position:0% +but it kind of provided a Guiding Light +it kind of provided a hope in the midst + + align:start position:0% +it kind of provided a hope in the midst + + + align:start position:0% +it kind of provided a hope in the midst +of all this glimmering Darkness so what + + align:start position:0% +of all this glimmering Darkness so what + + + align:start position:0% +of all this glimmering Darkness so what +about you Michael how was your takea + + align:start position:0% +about you Michael how was your takea + + + align:start position:0% +about you Michael how was your takea +away from this I found saud's + + align:start position:0% +away from this I found saud's + + + align:start position:0% +away from this I found saud's +honesty to be the most impactful thing + + align:start position:0% +honesty to be the most impactful thing + + + align:start position:0% +honesty to be the most impactful thing +to me she doesn't shy away from sharing + + align:start position:0% +to me she doesn't shy away from sharing + + + align:start position:0% +to me she doesn't shy away from sharing +that there's multiple days where she + + align:start position:0% +that there's multiple days where she + + + align:start position:0% +that there's multiple days where she +just can't find the energy to get out of + + align:start position:0% +just can't find the energy to get out of + + + align:start position:0% +just can't find the energy to get out of +bed and when you think about the + + align:start position:0% +bed and when you think about the + + + align:start position:0% +bed and when you think about the +separation from first her + + align:start position:0% +separation from first her + + + align:start position:0% +separation from first her +land but also her family and her + + align:start position:0% +land but also her family and her + + + align:start position:0% +land but also her family and her +language you should really just take a + + align:start position:0% +language you should really just take a + + + align:start position:0% +language you should really just take a +moment and pause and reflect on how that + + align:start position:0% +moment and pause and reflect on how that + + + align:start position:0% +moment and pause and reflect on how that +would be for you as well but despite all + + align:start position:0% +would be for you as well but despite all + + + align:start position:0% +would be for you as well but despite all +that she continues to improve herself + + align:start position:0% +that she continues to improve herself + + + align:start position:0% +that she continues to improve herself +she continues to hope for a better day I + + align:start position:0% +she continues to hope for a better day I + + + align:start position:0% +she continues to hope for a better day I +just find that so inspiring especially + + align:start position:0% +just find that so inspiring especially + + + align:start position:0% +just find that so inspiring especially +coming from a country like the United + + align:start position:0% +coming from a country like the United + + + align:start position:0% +coming from a country like the United +States where we've never had to worry + + align:start position:0% +States where we've never had to worry + + + align:start position:0% +States where we've never had to worry +about that type of separation from the + + align:start position:0% +about that type of separation from the + + + align:start position:0% +about that type of separation from the +ones we love so that was the most + + align:start position:0% +ones we love so that was the most + + + align:start position:0% +ones we love so that was the most +impactful thing for me and Michael how + + align:start position:0% +impactful thing for me and Michael how + + + align:start position:0% +impactful thing for me and Michael how +you feeling did this leave up to the + + align:start position:0% +you feeling did this leave up to the + + + align:start position:0% +you feeling did this leave up to the +dream we drummed up on that Zoom call so + + align:start position:0% +dream we drummed up on that Zoom call so + + + align:start position:0% +dream we drummed up on that Zoom call so +many months almost years ago now we + + align:start position:0% +many months almost years ago now we + + + align:start position:0% +many months almost years ago now we +surpassed any dream or Vision that I + + align:start position:0% +surpassed any dream or Vision that I + + + align:start position:0% +surpassed any dream or Vision that I +could have thought + + align:start position:0% +could have thought + + + align:start position:0% +could have thought +of all that time ago it was uh full of + + align:start position:0% +of all that time ago it was uh full of + + + align:start position:0% +of all that time ago it was uh full of +inspiring moments it was full of + + align:start position:0% +inspiring moments it was full of + + + align:start position:0% +inspiring moments it was full of +inspiring stories and inspiring people + + align:start position:0% +inspiring stories and inspiring people + + + align:start position:0% +inspiring stories and inspiring people +just seeing learning and all these + + align:start position:0% +just seeing learning and all these + + + align:start position:0% +just seeing learning and all these +different contexts how it affects people + + align:start position:0% +different contexts how it affects people + + + align:start position:0% +different contexts how it affects people +you know that are trying to get their + + align:start position:0% +you know that are trying to get their + + + align:start position:0% +you know that are trying to get their +degree and just want to add some more + + align:start position:0% +degree and just want to add some more + + + align:start position:0% +degree and just want to add some more +education or that are actually having to + + align:start position:0% +education or that are actually having to + + + align:start position:0% +education or that are actually having to +flee their countries and still try to + + align:start position:0% +flee their countries and still try to + + + align:start position:0% +flee their countries and still try to +figure out a way to make everything work + + align:start position:0% +figure out a way to make everything work + + + align:start position:0% +figure out a way to make everything work +out in their lives um I hope that + + align:start position:0% +out in their lives um I hope that + + + align:start position:0% +out in their lives um I hope that +highlighting these stories about humans + + align:start position:0% +highlighting these stories about humans + + + align:start position:0% +highlighting these stories about humans +just like all of us from all over the + + align:start position:0% +just like all of us from all over the + + + align:start position:0% +just like all of us from all over the +world really gives people a glass to + + align:start position:0% +world really gives people a glass to + + + align:start position:0% +world really gives people a glass to +look through and see what their life + + align:start position:0% +look through and see what their life + + + align:start position:0% +look through and see what their life +might be able to become I always + + align:start position:0% +might be able to become I always + + + align:start position:0% +might be able to become I always +remember the first one of the first + + align:start position:0% +remember the first one of the first + + + align:start position:0% +remember the first one of the first +calls we had with cat where he mentioned + + align:start position:0% +calls we had with cat where he mentioned + + + align:start position:0% +calls we had with cat where he mentioned +that when they started all this when + + align:start position:0% +that when they started all this when + + + align:start position:0% +that when they started all this when +they started ocw they thought their + + align:start position:0% +they started ocw they thought their + + + align:start position:0% +they started ocw they thought their +biggest clientele was going to be the + + align:start position:0% +biggest clientele was going to be the + + + align:start position:0% +biggest clientele was going to be the +teachers you know and it brings me back + + align:start position:0% +teachers you know and it brings me back + + + align:start position:0% +teachers you know and it brings me back +to a quot I read somewhere once where + + align:start position:0% +to a quot I read somewhere once where + + + align:start position:0% +to a quot I read somewhere once where +like when you create something and put + + align:start position:0% +like when you create something and put + + + align:start position:0% +like when you create something and put +it out in the world you never know you + + align:start position:0% +it out in the world you never know you + + + align:start position:0% +it out in the world you never know you +never know is going to use it you never + + align:start position:0% +never know is going to use it you never + + + align:start position:0% +never know is going to use it you never +know how it's going to impact them you + + align:start position:0% +know how it's going to impact them you + + + align:start position:0% +know how it's going to impact them you +never know and that's what I've Loved + + align:start position:0% +never know and that's what I've Loved + + + align:start position:0% +never know and that's what I've Loved +about what this podcast has brought to + + align:start position:0% +about what this podcast has brought to + + + align:start position:0% +about what this podcast has brought to +light in that his resources that are + + align:start position:0% +light in that his resources that are + + + align:start position:0% +light in that his resources that are +open to everyone in all over the world + + align:start position:0% +open to everyone in all over the world + + + align:start position:0% +open to everyone in all over the world +yes you know people are using them but + + align:start position:0% +yes you know people are using them but + + + align:start position:0% +yes you know people are using them but +you don't know what for you don't know + + align:start position:0% +you don't know what for you don't know + + + align:start position:0% +you don't know what for you don't know +how they're using them you don't know + + align:start position:0% +how they're using them you don't know + + + align:start position:0% +how they're using them you don't know +what they're developing you don't know + + align:start position:0% +what they're developing you don't know + + + align:start position:0% +what they're developing you don't know +how it's affecting their lives now that + + align:start position:0% +how it's affecting their lives now that + + + align:start position:0% +how it's affecting their lives now that +we have a platform for at least people + + align:start position:0% +we have a platform for at least people + + + align:start position:0% +we have a platform for at least people +to show us and tell us about that impact + + align:start position:0% +to show us and tell us about that impact + + + align:start position:0% +to show us and tell us about that impact +it's something really I'm really loving + + align:start position:0% +it's something really I'm really loving + + + align:start position:0% +it's something really I'm really loving +and I won't likee it's been a fun J it's + + align:start position:0% +and I won't likee it's been a fun J it's + + + align:start position:0% +and I won't likee it's been a fun J it's +been more than anything I could have + + align:start position:0% +been more than anything I could have + + + align:start position:0% +been more than anything I could have +expected more than anything I could have + + align:start position:0% +expected more than anything I could have + + + align:start position:0% +expected more than anything I could have +asked for I'm even shocked we got here + + align:start position:0% +asked for I'm even shocked we got here + + + align:start position:0% +asked for I'm even shocked we got here +I'm even shocked we actually did this so + + align:start position:0% +I'm even shocked we actually did this so + + + align:start position:0% +I'm even shocked we actually did this so +stay tuned into mit's channels to learn + + align:start position:0% +stay tuned into mit's channels to learn + + + align:start position:0% +stay tuned into mit's channels to learn +about other Learners and perhaps take a + + align:start position:0% +about other Learners and perhaps take a + + + align:start position:0% +about other Learners and perhaps take a +few courses yourself which I can + + align:start position:0% +few courses yourself which I can + + + align:start position:0% +few courses yourself which I can +guarantee you will change your life you + + align:start position:0% +guarantee you will change your life you + + + align:start position:0% +guarantee you will change your life you +may not know how you may not know when + + align:start position:0% +may not know how you may not know when + + + align:start position:0% +may not know how you may not know when +but take a course it will change your + + align:start position:0% +but take a course it will change your + + + align:start position:0% +but take a course it will change your +[Music] + + align:start position:0% + + + + align:start position:0% + +life open lers is produced by alexas hot + + align:start position:0% +life open lers is produced by alexas hot + + + align:start position:0% +life open lers is produced by alexas hot +special thanks to the supporters and + + align:start position:0% +special thanks to the supporters and + + + align:start position:0% +special thanks to the supporters and +donors who make ocw possible to learn + + align:start position:0% +donors who make ocw possible to learn + + + align:start position:0% +donors who make ocw possible to learn +more about mit's Open courseware and to + + align:start position:0% +more about mit's Open courseware and to + + + align:start position:0% +more about mit's Open courseware and to +check out the courses mentioned in this + + align:start position:0% +check out the courses mentioned in this + + + align:start position:0% +check out the courses mentioned in this +episode visit the ocw website at + + align:start position:0% +episode visit the ocw website at + + + align:start position:0% +episode visit the ocw website at +ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +[Music] \ No newline at end of file diff --git a/vfqPpai_9jI.txt b/vfqPpai_9jI.txt new file mode 100644 index 0000000000000000000000000000000000000000..3366b60d46c3b9ed9f532fa5da9aa69bba9cdfd0 --- /dev/null +++ b/vfqPpai_9jI.txt @@ -0,0 +1,1459 @@ +align:start position:0% + +we will now define the notion of a + + align:start position:0% +we will now define the notion of a + + + align:start position:0% +we will now define the notion of a +random variable very loosely speaking a + + align:start position:0% +random variable very loosely speaking a + + + align:start position:0% +random variable very loosely speaking a +random variable is a numerical quantity + + align:start position:0% +random variable is a numerical quantity + + + align:start position:0% +random variable is a numerical quantity +that takes random values but what does + + align:start position:0% +that takes random values but what does + + + align:start position:0% +that takes random values but what does +this mean we want to be a little more + + align:start position:0% +this mean we want to be a little more + + + align:start position:0% +this mean we want to be a little more +precise and I'm going to introduce the + + align:start position:0% +precise and I'm going to introduce the + + + align:start position:0% +precise and I'm going to introduce the +idea through an example suppose that our + + align:start position:0% +idea through an example suppose that our + + + align:start position:0% +idea through an example suppose that our +sample space is a set of students + + align:start position:0% +sample space is a set of students + + + align:start position:0% +sample space is a set of students +labelled according to their names or for + + align:start position:0% +labelled according to their names or for + + + align:start position:0% +labelled according to their names or for +simplicity let's just label them as a B + + align:start position:0% +simplicity let's just label them as a B + + + align:start position:0% +simplicity let's just label them as a B +C and D our probabilistic experiment is + + align:start position:0% +C and D our probabilistic experiment is + + + align:start position:0% +C and D our probabilistic experiment is +to pick a student at random according to + + align:start position:0% +to pick a student at random according to + + + align:start position:0% +to pick a student at random according to +some probability law and then record + + align:start position:0% +some probability law and then record + + + align:start position:0% +some probability law and then record +their weight in kilograms so for example + + align:start position:0% +their weight in kilograms so for example + + + align:start position:0% +their weight in kilograms so for example +suppose that the outcome of the + + align:start position:0% +suppose that the outcome of the + + + align:start position:0% +suppose that the outcome of the +experiment was this particular student + + align:start position:0% +experiment was this particular student + + + align:start position:0% +experiment was this particular student +and the weight of that student is 62 or + + align:start position:0% +and the weight of that student is 62 or + + + align:start position:0% +and the weight of that student is 62 or +it could be that the outcome of the + + align:start position:0% +it could be that the outcome of the + + + align:start position:0% +it could be that the outcome of the +experiment is this particular student + + align:start position:0% +experiment is this particular student + + + align:start position:0% +experiment is this particular student +and that particular student has a weight + + align:start position:0% +and that particular student has a weight + + + align:start position:0% +and that particular student has a weight +of 75 kilograms the weight of a + + align:start position:0% +of 75 kilograms the weight of a + + + align:start position:0% +of 75 kilograms the weight of a +particular student is a number little W + + align:start position:0% +particular student is a number little W + + + align:start position:0% +particular student is a number little W +but let us think of the abstract + + align:start position:0% +but let us think of the abstract + + + align:start position:0% +but let us think of the abstract +concepts of weight something that we + + align:start position:0% +concepts of weight something that we + + + align:start position:0% +concepts of weight something that we +will denote by capital W weight is an + + align:start position:0% +will denote by capital W weight is an + + + align:start position:0% +will denote by capital W weight is an +object whose value is determined once + + align:start position:0% +object whose value is determined once + + + align:start position:0% +object whose value is determined once +you tell me the outcome of the + + align:start position:0% +you tell me the outcome of the + + + align:start position:0% +you tell me the outcome of the +experiment once you tell me which + + align:start position:0% +experiment once you tell me which + + + align:start position:0% +experiment once you tell me which +student was picked in this sense weight + + align:start position:0% +student was picked in this sense weight + + + align:start position:0% +student was picked in this sense weight +is really a function of the outcome of + + align:start position:0% +is really a function of the outcome of + + + align:start position:0% +is really a function of the outcome of +the experiment so think of weight as an + + align:start position:0% +the experiment so think of weight as an + + + align:start position:0% +the experiment so think of weight as an +abstract box that takes as input a + + align:start position:0% +abstract box that takes as input a + + + align:start position:0% +abstract box that takes as input a +student and produces a number little W + + align:start position:0% +student and produces a number little W + + + align:start position:0% +student and produces a number little W +which is the weight of that particular + + align:start position:0% +which is the weight of that particular + + + align:start position:0% +which is the weight of that particular +student or more concretely think of + + align:start position:0% +student or more concretely think of + + + align:start position:0% +student or more concretely think of +weight with a capital W as a procedure + + align:start position:0% +weight with a capital W as a procedure + + + align:start position:0% +weight with a capital W as a procedure +that takes a student puts him or her on + + align:start position:0% +that takes a student puts him or her on + + + align:start position:0% +that takes a student puts him or her on +a scale and reports the result in this + + align:start position:0% +a scale and reports the result in this + + + align:start position:0% +a scale and reports the result in this +sense weight is an object of the same + + align:start position:0% +sense weight is an object of the same + + + align:start position:0% +sense weight is an object of the same +kind as the square root function that's + + align:start position:0% +kind as the square root function that's + + + align:start position:0% +kind as the square root function that's +setting inside your computer + + align:start position:0% +setting inside your computer + + + align:start position:0% +setting inside your computer +the square root function is a function + + align:start position:0% +the square root function is a function + + + align:start position:0% +the square root function is a function +it's a subroutine perhaps it is a piece + + align:start position:0% +it's a subroutine perhaps it is a piece + + + align:start position:0% +it's a subroutine perhaps it is a piece +of code that takes as input a number + + align:start position:0% +of code that takes as input a number + + + align:start position:0% +of code that takes as input a number +let's say the number nine and produces + + align:start position:0% +let's say the number nine and produces + + + align:start position:0% +let's say the number nine and produces +another number in this case it would be + + align:start position:0% +another number in this case it would be + + + align:start position:0% +another number in this case it would be +the number three which is the square + + align:start position:0% +the number three which is the square + + + align:start position:0% +the number three which is the square +root of nine + + align:start position:0% + + + + align:start position:0% + +notice here the distinction that we will + + align:start position:0% +notice here the distinction that we will + + + align:start position:0% +notice here the distinction that we will +keep emphasizing over and over square + + align:start position:0% +keep emphasizing over and over square + + + align:start position:0% +keep emphasizing over and over square +root of nine is a number it's the number + + align:start position:0% +root of nine is a number it's the number + + + align:start position:0% +root of nine is a number it's the number +three the Box square root is a function + + align:start position:0% +three the Box square root is a function + + + align:start position:0% +three the Box square root is a function +now let us go back to our probabilistic + + align:start position:0% +now let us go back to our probabilistic + + + align:start position:0% +now let us go back to our probabilistic +experiments + + align:start position:0% +experiments + + + align:start position:0% +experiments +note that the probabilistic experiment + + align:start position:0% +note that the probabilistic experiment + + + align:start position:0% +note that the probabilistic experiment +such as the one in our example can have + + align:start position:0% +such as the one in our example can have + + + align:start position:0% +such as the one in our example can have +several associated random variables for + + align:start position:0% +several associated random variables for + + + align:start position:0% +several associated random variables for +example we could have another random + + align:start position:0% +example we could have another random + + + align:start position:0% +example we could have another random +variable denoted by capital H which is + + align:start position:0% +variable denoted by capital H which is + + + align:start position:0% +variable denoted by capital H which is +the height of a student recorded in + + align:start position:0% +the height of a student recorded in + + + align:start position:0% +the height of a student recorded in +meters so if the outcome of the + + align:start position:0% +meters so if the outcome of the + + + align:start position:0% +meters so if the outcome of the +experiment for example was student a + + align:start position:0% +experiment for example was student a + + + align:start position:0% +experiment for example was student a +then this random variable would take a + + align:start position:0% +then this random variable would take a + + + align:start position:0% +then this random variable would take a +value which is the height of that + + align:start position:0% +value which is the height of that + + + align:start position:0% +value which is the height of that +student let's say it was point one point + + align:start position:0% +student let's say it was point one point + + + align:start position:0% +student let's say it was point one point +seven or if the outcome of the + + align:start position:0% +seven or if the outcome of the + + + align:start position:0% +seven or if the outcome of the +experiment was student C then we would + + align:start position:0% +experiment was student C then we would + + + align:start position:0% +experiment was student C then we would +record the height of that student and + + align:start position:0% +record the height of that student and + + + align:start position:0% +record the height of that student and +let us say that it turns out to be one + + align:start position:0% +let us say that it turns out to be one + + + align:start position:0% +let us say that it turns out to be one +point eight once again height with a + + align:start position:0% +point eight once again height with a + + + align:start position:0% +point eight once again height with a +capital H is an abstract object a + + align:start position:0% +capital H is an abstract object a + + + align:start position:0% +capital H is an abstract object a +function whose value is determined once + + align:start position:0% +function whose value is determined once + + + align:start position:0% +function whose value is determined once +you tell me the outcome of the + + align:start position:0% +you tell me the outcome of the + + + align:start position:0% +you tell me the outcome of the +experiments now given some random + + align:start position:0% +experiments now given some random + + + align:start position:0% +experiments now given some random +variables we can create new random + + align:start position:0% +variables we can create new random + + + align:start position:0% +variables we can create new random +variables as functions of the original + + align:start position:0% +variables as functions of the original + + + align:start position:0% +variables as functions of the original +random variables for example consider + + align:start position:0% +random variables for example consider + + + align:start position:0% +random variables for example consider +the quantity defined as weight divided + + align:start position:0% +the quantity defined as weight divided + + + align:start position:0% +the quantity defined as weight divided +by height squared this quantity is the + + align:start position:0% +by height squared this quantity is the + + + align:start position:0% +by height squared this quantity is the +so-called body mass index and it is also + + align:start position:0% +so-called body mass index and it is also + + + align:start position:0% +so-called body mass index and it is also +a function on the sample space why is it + + align:start position:0% +a function on the sample space why is it + + + align:start position:0% +a function on the sample space why is it +a function on the sample space well + + align:start position:0% +a function on the sample space well + + + align:start position:0% +a function on the sample space well +because once an outcome of the + + align:start position:0% +because once an outcome of the + + + align:start position:0% +because once an outcome of the +experiment is determined suppose that + + align:start position:0% +experiment is determined suppose that + + + align:start position:0% +experiment is determined suppose that +the outcome of the experiment was the + + align:start position:0% +the outcome of the experiment was the + + + align:start position:0% +the outcome of the experiment was the +blue student then + + align:start position:0% +blue student then + + + align:start position:0% +blue student then +these two numbers 62 and 1.7 are also + + align:start position:0% +these two numbers 62 and 1.7 are also + + + align:start position:0% +these two numbers 62 and 1.7 are also +determined and using those numbers we + + align:start position:0% +determined and using those numbers we + + + align:start position:0% +determined and using those numbers we +can carry out this calculation and find + + align:start position:0% +can carry out this calculation and find + + + align:start position:0% +can carry out this calculation and find +the body mass index of that particular + + align:start position:0% +the body mass index of that particular + + + align:start position:0% +the body mass index of that particular +student which in this case would be 21.5 + + align:start position:0% +student which in this case would be 21.5 + + + align:start position:0% +student which in this case would be 21.5 +or if it happened that this student was + + align:start position:0% +or if it happened that this student was + + + align:start position:0% +or if it happened that this student was +selected then the body mass index would + + align:start position:0% +selected then the body mass index would + + + align:start position:0% +selected then the body mass index would +turn out to be some other number in this + + align:start position:0% +turn out to be some other number in this + + + align:start position:0% +turn out to be some other number in this +case it would be 23 so again we see that + + align:start position:0% +case it would be 23 so again we see that + + + align:start position:0% +case it would be 23 so again we see that +the body mass index can be viewed as an + + align:start position:0% +the body mass index can be viewed as an + + + align:start position:0% +the body mass index can be viewed as an +abstract concept defined by this formula + + align:start position:0% +abstract concept defined by this formula + + + align:start position:0% +abstract concept defined by this formula +but once an outcome is determined then + + align:start position:0% +but once an outcome is determined then + + + align:start position:0% +but once an outcome is determined then +the body mass index is also determined + + align:start position:0% +the body mass index is also determined + + + align:start position:0% +the body mass index is also determined +and so the body mass index is really a + + align:start position:0% +and so the body mass index is really a + + + align:start position:0% +and so the body mass index is really a +function of which particular outcome was + + align:start position:0% +function of which particular outcome was + + + align:start position:0% +function of which particular outcome was +selected let us now abstract from the + + align:start position:0% +selected let us now abstract from the + + + align:start position:0% +selected let us now abstract from the +previous discussion we have seen that + + align:start position:0% +previous discussion we have seen that + + + align:start position:0% +previous discussion we have seen that +random variables are objects abstract + + align:start position:0% +random variables are objects abstract + + + align:start position:0% +random variables are objects abstract +objects that associate a specific value + + align:start position:0% +objects that associate a specific value + + + align:start position:0% +objects that associate a specific value +a particular number to any particular + + align:start position:0% +a particular number to any particular + + + align:start position:0% +a particular number to any particular +outcome of a of a probabilistic + + align:start position:0% +outcome of a of a probabilistic + + + align:start position:0% +outcome of a of a probabilistic +experiment so in that sense random + + align:start position:0% +experiment so in that sense random + + + align:start position:0% +experiment so in that sense random +variables are functions from the sample + + align:start position:0% +variables are functions from the sample + + + align:start position:0% +variables are functions from the sample +space to the real numbers there are + + align:start position:0% +space to the real numbers there are + + + align:start position:0% +space to the real numbers there are +numerical functions but as numerical + + align:start position:0% +numerical functions but as numerical + + + align:start position:0% +numerical functions but as numerical +functions they can either take discrete + + align:start position:0% +functions they can either take discrete + + + align:start position:0% +functions they can either take discrete +values for example the integers or they + + align:start position:0% +values for example the integers or they + + + align:start position:0% +values for example the integers or they +can take continuous values let's say on + + align:start position:0% +can take continuous values let's say on + + + align:start position:0% +can take continuous values let's say on +the real line for example if your random + + align:start position:0% +the real line for example if your random + + + align:start position:0% +the real line for example if your random +variable is the number of heads in 10 + + align:start position:0% +variable is the number of heads in 10 + + + align:start position:0% +variable is the number of heads in 10 +consecutive coin tosses this is a + + align:start position:0% +consecutive coin tosses this is a + + + align:start position:0% +consecutive coin tosses this is a +discrete random variable that takes + + align:start position:0% +discrete random variable that takes + + + align:start position:0% +discrete random variable that takes +values in the set from 0 to 10 if your + + align:start position:0% +values in the set from 0 to 10 if your + + + align:start position:0% +values in the set from 0 to 10 if your +random variable is a measurement of the + + align:start position:0% +random variable is a measurement of the + + + align:start position:0% +random variable is a measurement of the +time at which something happens and if + + align:start position:0% +time at which something happens and if + + + align:start position:0% +time at which something happens and if +your timer has infinite accuracy then + + align:start position:0% +your timer has infinite accuracy then + + + align:start position:0% +your timer has infinite accuracy then +the timer reports a real number and we + + align:start position:0% +the timer reports a real number and we + + + align:start position:0% +the timer reports a real number and we +would have a continuous random variable + + align:start position:0% +would have a continuous random variable + + + align:start position:0% +would have a continuous random variable +in the in this lecture sequence and in + + align:start position:0% +in the in this lecture sequence and in + + + align:start position:0% +in the in this lecture sequence and in +the next few ones we will concentrate on + + align:start position:0% +the next few ones we will concentrate on + + + align:start position:0% +the next few ones we will concentrate on +discrete random variables because they + + align:start position:0% +discrete random variables because they + + + align:start position:0% +discrete random variables because they +are easier to handle and then later on + + align:start position:0% +are easier to handle and then later on + + + align:start position:0% +are easier to handle and then later on +we will move to a discussion of + + align:start position:0% +we will move to a discussion of + + + align:start position:0% +we will move to a discussion of +continuous random variables throughout + + align:start position:0% +continuous random variables throughout + + + align:start position:0% +continuous random variables throughout +we want to keep noting this very + + align:start position:0% +we want to keep noting this very + + + align:start position:0% +we want to keep noting this very +important distinction that I already + + align:start position:0% +important distinction that I already + + + align:start position:0% +important distinction that I already +brought in the discussion of our + + align:start position:0% +brought in the discussion of our + + + align:start position:0% +brought in the discussion of our +particular example but it needs to be + + align:start position:0% +particular example but it needs to be + + + align:start position:0% +particular example but it needs to be +emphasized and reinforced that we make a + + align:start position:0% +emphasized and reinforced that we make a + + + align:start position:0% +emphasized and reinforced that we make a +distinction between random variables + + align:start position:0% +distinction between random variables + + + align:start position:0% +distinction between random variables +which are abstract objects their + + align:start position:0% +which are abstract objects their + + + align:start position:0% +which are abstract objects their +functions on the sample space and they + + align:start position:0% +functions on the sample space and they + + + align:start position:0% +functions on the sample space and they +are denoted by uppercase letters in + + align:start position:0% +are denoted by uppercase letters in + + + align:start position:0% +are denoted by uppercase letters in +contrast we will use lowercase letters + + align:start position:0% +contrast we will use lowercase letters + + + align:start position:0% +contrast we will use lowercase letters +to indicate numerical values of the + + align:start position:0% +to indicate numerical values of the + + + align:start position:0% +to indicate numerical values of the +random variables so little X is always a + + align:start position:0% +random variables so little X is always a + + + align:start position:0% +random variables so little X is always a +real number as opposed to the random + + align:start position:0% +real number as opposed to the random + + + align:start position:0% +real number as opposed to the random +variable which is a function one point + + align:start position:0% +variable which is a function one point + + + align:start position:0% +variable which is a function one point +that we made earlier is that for the + + align:start position:0% +that we made earlier is that for the + + + align:start position:0% +that we made earlier is that for the +same probabilistic experiment we can + + align:start position:0% +same probabilistic experiment we can + + + align:start position:0% +same probabilistic experiment we can +have several random variables associated + + align:start position:0% +have several random variables associated + + + align:start position:0% +have several random variables associated +with that experiment and we can also + + align:start position:0% +with that experiment and we can also + + + align:start position:0% +with that experiment and we can also +combine random variables to form new + + align:start position:0% +combine random variables to form new + + + align:start position:0% +combine random variables to form new +random variables in general a function + + align:start position:0% +random variables in general a function + + + align:start position:0% +random variables in general a function +of random variables has numerical values + + align:start position:0% +of random variables has numerical values + + + align:start position:0% +of random variables has numerical values +that are determined by the numerical + + align:start position:0% +that are determined by the numerical + + + align:start position:0% +that are determined by the numerical +values of the original random variables + + align:start position:0% +values of the original random variables + + + align:start position:0% +values of the original random variables +and so ultimately they are determined by + + align:start position:0% +and so ultimately they are determined by + + + align:start position:0% +and so ultimately they are determined by +the outcome of the experiment so a + + align:start position:0% +the outcome of the experiment so a + + + align:start position:0% +the outcome of the experiment so a +function of random variables has a + + align:start position:0% +function of random variables has a + + + align:start position:0% +function of random variables has a +numerical value which is completely + + align:start position:0% +numerical value which is completely + + + align:start position:0% +numerical value which is completely +determined by the outcome of the + + align:start position:0% +determined by the outcome of the + + + align:start position:0% +determined by the outcome of the +experiment and so a function of random + + align:start position:0% +experiment and so a function of random + + + align:start position:0% +experiment and so a function of random +variables is also a random variable as + + align:start position:0% +variables is also a random variable as + + + align:start position:0% +variables is also a random variable as +an example we could think of two random + + align:start position:0% +an example we could think of two random + + + align:start position:0% +an example we could think of two random +variables x and y associated with the + + align:start position:0% +variables x and y associated with the + + + align:start position:0% +variables x and y associated with the +same probabilistic experiment and then + + align:start position:0% +same probabilistic experiment and then + + + align:start position:0% +same probabilistic experiment and then +define a random variable let's say X + + align:start position:0% +define a random variable let's say X + + + align:start position:0% +define a random variable let's say X +plus y what does that mean X plus y is a + + align:start position:0% +plus y what does that mean X plus y is a + + + align:start position:0% +plus y what does that mean X plus y is a +random variable that takes the value + + align:start position:0% +random variable that takes the value + + + align:start position:0% +random variable that takes the value +little X plus little Y when the random + + align:start position:0% +little X plus little Y when the random + + + align:start position:0% +little X plus little Y when the random +variable capital X takes the value + + align:start position:0% +variable capital X takes the value + + + align:start position:0% +variable capital X takes the value +little X and capital y takes the value + + align:start position:0% +little X and capital y takes the value + + + align:start position:0% +little X and capital y takes the value +little Y so X and y are random variables + + align:start position:0% +little Y so X and y are random variables + + + align:start position:0% +little Y so X and y are random variables +X plus y is another random variable x + + align:start position:0% +X plus y is another random variable x + + + align:start position:0% +X plus y is another random variable x +and y will take numerical values once + + align:start position:0% +and y will take numerical values once + + + align:start position:0% +and y will take numerical values once +the outcome of the experiment has been + + align:start position:0% +the outcome of the experiment has been + + + align:start position:0% +the outcome of the experiment has been +obtained and if the numerical values + + align:start position:0% +obtained and if the numerical values + + + align:start position:0% +obtained and if the numerical values +that they take are lead + + align:start position:0% +that they take are lead + + + align:start position:0% +that they take are lead +X and little Y then the random variable + + align:start position:0% +X and little Y then the random variable + + + align:start position:0% +X and little Y then the random variable +X plus y we'll take the numerical value + + align:start position:0% +X plus y we'll take the numerical value + + + align:start position:0% +X plus y we'll take the numerical value +little X plus little Y so we can now + + align:start position:0% +little X plus little Y so we can now + + + align:start position:0% +little X plus little Y so we can now +move on and start doing some interesting + + align:start position:0% +move on and start doing some interesting + + + align:start position:0% +move on and start doing some interesting +things about random variables + + align:start position:0% +things about random variables + + + align:start position:0% +things about random variables +characterize them describe them give + + align:start position:0% +characterize them describe them give + + + align:start position:0% +characterize them describe them give +some examples and introduce some new + + align:start position:0% +some examples and introduce some new + + + align:start position:0% +some examples and introduce some new +concepts associated with them \ No newline at end of file diff --git a/w7HDA8gUbpQ.txt b/w7HDA8gUbpQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..1c8d82fa80716b5d5bd5d9cc5d3aee9b5e837b5c --- /dev/null +++ b/w7HDA8gUbpQ.txt @@ -0,0 +1,10379 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +hello everybody good weekend everybody's + + align:start position:0% +hello everybody good weekend everybody's + + + align:start position:0% +hello everybody good weekend everybody's +staying dry + + align:start position:0% +staying dry + + + align:start position:0% +staying dry +I hope so we're going to dive back into + + align:start position:0% +I hope so we're going to dive back into + + + align:start position:0% +I hope so we're going to dive back into +luck j-money and we didn't we didn't + + align:start position:0% +luck j-money and we didn't we didn't + + + align:start position:0% +luck j-money and we didn't we didn't +lose too many people when we did + + align:start position:0% +lose too many people when we did + + + align:start position:0% +lose too many people when we did +cryptographic hash functions and digital + + align:start position:0% +cryptographic hash functions and digital + + + align:start position:0% +cryptographic hash functions and digital +signatures last week so so I thank you + + align:start position:0% +signatures last week so so I thank you + + + align:start position:0% +signatures last week so so I thank you +for all being back so what were today's + + align:start position:0% +for all being back so what were today's + + + align:start position:0% +for all being back so what were today's +study questions again + + align:start position:0% +study questions again + + + align:start position:0% +study questions again +what's the Byzantine generals problem + + align:start position:0% +what's the Byzantine generals problem + + + align:start position:0% +what's the Byzantine generals problem +anybody want to tell me what the + + align:start position:0% +anybody want to tell me what the + + + align:start position:0% +anybody want to tell me what the +Byzantine general problem is there might + + align:start position:0% +Byzantine general problem is there might + + + align:start position:0% +Byzantine general problem is there might +be how to coordinate when somebody's not + + align:start position:0% +be how to coordinate when somebody's not + + + align:start position:0% +be how to coordinate when somebody's not +acting in good faith is a malicious + + align:start position:0% +acting in good faith is a malicious + + + align:start position:0% +acting in good faith is a malicious +actor but it also might be just somebody + + align:start position:0% +actor but it also might be just somebody + + + align:start position:0% +actor but it also might be just somebody +that doesn't get the communication + + align:start position:0% +that doesn't get the communication + + + align:start position:0% +that doesn't get the communication +somebody that is there's a thought + + align:start position:0% +somebody that is there's a thought + + + align:start position:0% +somebody that is there's a thought +whether it's malicious or not how are we + + align:start position:0% +whether it's malicious or not how are we + + + align:start position:0% +whether it's malicious or not how are we +doing allene yeah + + align:start position:0% + + + + align:start position:0% + +how does proof-of-work and mining in + + align:start position:0% +how does proof-of-work and mining in + + + align:start position:0% +how does proof-of-work and mining in +Bitcoin address it we're gonna walk + + align:start position:0% +Bitcoin address it we're gonna walk + + + align:start position:0% +Bitcoin address it we're gonna walk +through this I'm going to give you my + + align:start position:0% +through this I'm going to give you my + + + align:start position:0% +through this I'm going to give you my +sense of it but does anybody want to + + align:start position:0% +sense of it but does anybody want to + + + align:start position:0% +sense of it but does anybody want to +give a short short version prepared for + + align:start position:0% + + + + align:start position:0% + +British + + align:start position:0% + + + + align:start position:0% + +sparkly you know probably stick where + + align:start position:0% +sparkly you know probably stick where + + + align:start position:0% +sparkly you know probably stick where +antenna deterministic with I am using a + + align:start position:0% +antenna deterministic with I am using a + + + align:start position:0% +antenna deterministic with I am using a +amount of CPU power problem complexity + + align:start position:0% +amount of CPU power problem complexity + + + align:start position:0% +amount of CPU power problem complexity +to prove that a1 consensus has been + + align:start position:0% +to prove that a1 consensus has been + + + align:start position:0% +to prove that a1 consensus has been +reached by majority of the rotor said is + + align:start position:0% +reached by majority of the rotor said is + + + align:start position:0% +reached by majority of the rotor said is +its probabilistic instead of + + align:start position:0% +its probabilistic instead of + + + align:start position:0% +its probabilistic instead of +deterministic that you use CPU power to + + align:start position:0% +deterministic that you use CPU power to + + + align:start position:0% +deterministic that you use CPU power to +form some consensus I think that's what + + align:start position:0% +form some consensus I think that's what + + + align:start position:0% +form some consensus I think that's what +you said I'm going to walk through this + + align:start position:0% +you said I'm going to walk through this + + + align:start position:0% +you said I'm going to walk through this +in more detail but does anybody want to + + align:start position:0% +in more detail but does anybody want to + + + align:start position:0% +in more detail but does anybody want to +give a another shot at it + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so remind me your first name rehab rehab + + align:start position:0% +so remind me your first name rehab rehab + + + align:start position:0% +so remind me your first name rehab rehab +says it's about people called miners or + + align:start position:0% +says it's about people called miners or + + + align:start position:0% +says it's about people called miners or +computers called miners which we'll talk + + align:start position:0% +computers called miners which we'll talk + + + align:start position:0% +computers called miners which we'll talk +about today using computer power again + + align:start position:0% +about today using computer power again + + + align:start position:0% +about today using computer power again +but transactions were part of that as + + align:start position:0% +but transactions were part of that as + + + align:start position:0% +but transactions were part of that as +well as to how it comes together I'm not + + align:start position:0% +well as to how it comes together I'm not + + + align:start position:0% +well as to how it comes together I'm not +gonna torture you and he asked a bunch + + align:start position:0% +gonna torture you and he asked a bunch + + + align:start position:0% +gonna torture you and he asked a bunch +more but key point that yen DN raises is + + align:start position:0% +more but key point that yen DN raises is + + + align:start position:0% +more but key point that yen DN raises is +that when somebody solves the puzzle it + + align:start position:0% +that when somebody solves the puzzle it + + + align:start position:0% +that when somebody solves the puzzle it +can be propagated across a network and + + align:start position:0% +can be propagated across a network and + + + align:start position:0% +can be propagated across a network and +then others when the network can + + align:start position:0% +then others when the network can + + + align:start position:0% +then others when the network can +validate it so what we'll talk about a + + align:start position:0% +validate it so what we'll talk about a + + + align:start position:0% +validate it so what we'll talk about a +little bit later is that it's a hard + + align:start position:0% +little bit later is that it's a hard + + + align:start position:0% +little bit later is that it's a hard +puzzle to solve + + align:start position:0% +puzzle to solve + + + align:start position:0% +puzzle to solve +but an easy Puffs puzzle to verify and + + align:start position:0% +but an easy Puffs puzzle to verify and + + + align:start position:0% +but an easy Puffs puzzle to verify and +that this is an important asymmetry in + + align:start position:0% +that this is an important asymmetry in + + + align:start position:0% +that this is an important asymmetry in +essence that there's a lot of resources + + align:start position:0% +essence that there's a lot of resources + + + align:start position:0% +essence that there's a lot of resources +to solve a puzzle + + align:start position:0% +to solve a puzzle + + + align:start position:0% +to solve a puzzle +but once knowing the answer there's very + + align:start position:0% +but once knowing the answer there's very + + + align:start position:0% +but once knowing the answer there's very +limited resources to verify that it's + + align:start position:0% +limited resources to verify that it's + + + align:start position:0% +limited resources to verify that it's +the right answer if it was not + + align:start position:0% +the right answer if it was not + + + align:start position:0% +the right answer if it was not +asymmetric it would not work as well so + + align:start position:0% +asymmetric it would not work as well so + + + align:start position:0% +asymmetric it would not work as well so +it's a it's a key part of the design of + + align:start position:0% +it's a it's a key part of the design of + + + align:start position:0% +it's a it's a key part of the design of +many cryptographic things but + + align:start position:0% +many cryptographic things but + + + align:start position:0% +many cryptographic things but +particularly atom backs a sort of + + align:start position:0% +particularly atom backs a sort of + + + align:start position:0% +particularly atom backs a sort of +novelty in the 1990s of proof-of-work I + + align:start position:0% +novelty in the 1990s of proof-of-work I + + + align:start position:0% +novelty in the 1990s of proof-of-work I +don't know if that's just a relaxed bit + + align:start position:0% +don't know if that's just a relaxed bit + + + align:start position:0% +don't know if that's just a relaxed bit +for you or you have your hands up Derek + + align:start position:0% +for you or you have your hands up Derek + + + align:start position:0% +for you or you have your hands up Derek +that's just a relaxed expose I like it + + align:start position:0% +that's just a relaxed expose I like it + + + align:start position:0% +that's just a relaxed expose I like it +we're gonna talk about other consensus + + align:start position:0% +we're gonna talk about other consensus + + + align:start position:0% +we're gonna talk about other consensus +protocols as well proof-of-work is not + + align:start position:0% +protocols as well proof-of-work is not + + + align:start position:0% +protocols as well proof-of-work is not +the only consensus protocol but how to + + align:start position:0% +the only consensus protocol but how to + + + align:start position:0% +the only consensus protocol but how to +address ourselves to Byzantine thought + + align:start position:0% +address ourselves to Byzantine thought + + + align:start position:0% +address ourselves to Byzantine thought +tolerance and then some of the economic + + align:start position:0% +tolerance and then some of the economic + + + align:start position:0% +tolerance and then some of the economic +incentives so we'll talk about the + + align:start position:0% +incentives so we'll talk about the + + + align:start position:0% +incentives so we'll talk about the +native currency what's the native + + align:start position:0% +native currency what's the native + + + align:start position:0% +native currency what's the native +currency of the first blockchain + + align:start position:0% +currency of the first blockchain + + + align:start position:0% +currency of the first blockchain +application Bitcoin how many of you in + + align:start position:0% +application Bitcoin how many of you in + + + align:start position:0% +application Bitcoin how many of you in +this room owned a Bitcoin at some point + + align:start position:0% +this room owned a Bitcoin at some point + + + align:start position:0% +this room owned a Bitcoin at some point +in time so you've all owned the native + + align:start position:0% +in time so you've all owned the native + + + align:start position:0% +in time so you've all owned the native +currency that helps a blockchain you got + + align:start position:0% +currency that helps a blockchain you got + + + align:start position:0% +currency that helps a blockchain you got +the opportunity to read a paper that a + + align:start position:0% +the opportunity to read a paper that a + + + align:start position:0% +the opportunity to read a paper that a +group of us here at MIT co-authored I + + align:start position:0% +group of us here at MIT co-authored I + + + align:start position:0% +group of us here at MIT co-authored I +hope some of you actually were able to + + align:start position:0% +hope some of you actually were able to + + + align:start position:0% +hope some of you actually were able to +download it and and yeah go ahead + + align:start position:0% +download it and and yeah go ahead + + + align:start position:0% +download it and and yeah go ahead +apparently even when you write something + + align:start position:0% +apparently even when you write something + + + align:start position:0% +apparently even when you write something +it still goes behind a copyright law so + + align:start position:0% +it still goes behind a copyright law so + + + align:start position:0% +it still goes behind a copyright law so +I'm glad to know that it was actually + + align:start position:0% +I'm glad to know that it was actually + + + align:start position:0% +I'm glad to know that it was actually +available and then back to the the + + align:start position:0% +available and then back to the the + + + align:start position:0% +available and then back to the the +National Institute of Standards and + + align:start position:0% +National Institute of Standards and + + + align:start position:0% +National Institute of Standards and +Technology paper as well this time the + + align:start position:0% +Technology paper as well this time the + + + align:start position:0% +Technology paper as well this time the +next chapters and then a paper from + + align:start position:0% +next chapters and then a paper from + + + align:start position:0% +next chapters and then a paper from +about 25 years ago or on the Byzantine + + align:start position:0% +about 25 years ago or on the Byzantine + + + align:start position:0% +about 25 years ago or on the Byzantine +generals problem itself so what are we + + align:start position:0% +generals problem itself so what are we + + + align:start position:0% +generals problem itself so what are we +going to do today we're going to go back + + align:start position:0% +going to do today we're going to go back + + + align:start position:0% +going to do today we're going to go back +through the design we're gonna talk + + align:start position:0% +through the design we're gonna talk + + + align:start position:0% +through the design we're gonna talk +about consensus through proof of work + + align:start position:0% +about consensus through proof of work + + + align:start position:0% +about consensus through proof of work +Bitcoin mining it's important it's + + align:start position:0% +Bitcoin mining it's important it's + + + align:start position:0% +Bitcoin mining it's important it's +relevant but it's kind of some fun facts + + align:start position:0% +relevant but it's kind of some fun facts + + + align:start position:0% +relevant but it's kind of some fun facts +about that as well the native currency + + align:start position:0% +about that as well the native currency + + + align:start position:0% +about that as well the native currency +of course Bitcoin of the first but + + align:start position:0% +of course Bitcoin of the first but + + + align:start position:0% +of course Bitcoin of the first but +there's now at least 1600 different + + align:start position:0% +there's now at least 1600 different + + + align:start position:0% +there's now at least 1600 different +native currencies what does it mean to + + align:start position:0% +native currencies what does it mean to + + + align:start position:0% +native currencies what does it mean to +have a network and widen networks matter + + align:start position:0% +have a network and widen networks matter + + + align:start position:0% +have a network and widen networks matter +particularly for blockchain some of the + + align:start position:0% +particularly for blockchain some of the + + + align:start position:0% +particularly for blockchain some of the +other consensus protocols and then just + + align:start position:0% +other consensus protocols and then just + + + align:start position:0% +other consensus protocols and then just +wrap up so just going back to the review + + align:start position:0% +wrap up so just going back to the review + + + align:start position:0% +wrap up so just going back to the review +and this is what we talked about a bit + + align:start position:0% +and this is what we talked about a bit + + + align:start position:0% +and this is what we talked about a bit +on Thursday but I think it's relevant to + + align:start position:0% +on Thursday but I think it's relevant to + + + align:start position:0% +on Thursday but I think it's relevant to +just kind of bring it back I found when + + align:start position:0% +just kind of bring it back I found when + + + align:start position:0% +just kind of bring it back I found when +I was first learning this it's hard to + + align:start position:0% +I was first learning this it's hard to + + + align:start position:0% +I was first learning this it's hard to +keep all the moving parts + + align:start position:0% +keep all the moving parts + + + align:start position:0% +keep all the moving parts +remember there's how many's that graphic + + align:start position:0% +remember there's how many's that graphic + + + align:start position:0% +remember there's how many's that graphic +you'll see all semester but it's all the + + align:start position:0% +you'll see all semester but it's all the + + + align:start position:0% +you'll see all semester but it's all the +different blocks and it's append-only + + align:start position:0% +different blocks and it's append-only + + + align:start position:0% +different blocks and it's append-only +what does append-only mean Andrew was + + align:start position:0% +what does append-only mean Andrew was + + + align:start position:0% +what does append-only mean Andrew was +that matter this word a pendant that we + + align:start position:0% +that matter this word a pendant that we + + + align:start position:0% +that matter this word a pendant that we +talked about last Thursday immutable now + + align:start position:0% +talked about last Thursday immutable now + + + align:start position:0% +talked about last Thursday immutable now +of course because cryptography maybe can + + align:start position:0% +of course because cryptography maybe can + + + align:start position:0% +of course because cryptography maybe can +be broken but we use the word immutable + + align:start position:0% +be broken but we use the word immutable + + + align:start position:0% +be broken but we use the word immutable +that it cannot be changed except for + + align:start position:0% +that it cannot be changed except for + + + align:start position:0% +that it cannot be changed except for +maybe as a lien so right I like that's + + align:start position:0% +maybe as a lien so right I like that's + + + align:start position:0% +maybe as a lien so right I like that's +in his book you all have to see this + + align:start position:0% +in his book you all have to see this + + + align:start position:0% +in his book you all have to see this +this is very clever flag maybe it's + + align:start position:0% +this is very clever flag maybe it's + + + align:start position:0% +this is very clever flag maybe it's +immutable except for 1 out of 10 to the + + align:start position:0% +immutable except for 1 out of 10 to the + + + align:start position:0% +immutable except for 1 out of 10 to the +40th times it could be broken or + + align:start position:0% +40th times it could be broken or + + + align:start position:0% +40th times it could be broken or +something one way to attack them is to + + align:start position:0% +something one way to attack them is to + + + align:start position:0% +something one way to attack them is to +come on but another way to attack them + + align:start position:0% +come on but another way to attack them + + + align:start position:0% +come on but another way to attack them +is to just take control over the actual + + align:start position:0% +is to just take control over the actual + + + align:start position:0% +is to just take control over the actual +network like the internet cuz you're an + + align:start position:0% +network like the internet cuz you're an + + + align:start position:0% +network like the internet cuz you're an +Internet service provider or if you're + + align:start position:0% +Internet service provider or if you're + + + align:start position:0% +Internet service provider or if you're +China you can actually import mid-point + + align:start position:0% +China you can actually import mid-point + + + align:start position:0% +China you can actually import mid-point +with C remaining powers by just + + align:start position:0% +with C remaining powers by just + + + align:start position:0% +with C remaining powers by just +controlling the network so it's actually + + align:start position:0% +controlling the network so it's actually + + + align:start position:0% +controlling the network so it's actually +an assumption behind how this thing + + align:start position:0% +an assumption behind how this thing + + + align:start position:0% +an assumption behind how this thing +works which is that the network works I + + align:start position:0% +works which is that the network works I + + + align:start position:0% +works which is that the network works I +agree with you but there's also some + + align:start position:0% +agree with you but there's also some + + + align:start position:0% +agree with you but there's also some +assumptions let's say that China or any + + align:start position:0% +assumptions let's say that China or any + + + align:start position:0% +assumptions let's say that China or any +state actor chose to fork one of these + + align:start position:0% +state actor chose to fork one of these + + + align:start position:0% +state actor chose to fork one of these +if it's considerably less than a + + align:start position:0% +if it's considerably less than a + + + align:start position:0% +if it's considerably less than a +majority + + align:start position:0% + + + + align:start position:0% + +if you control the worldwide network or + + align:start position:0% +if you control the worldwide network or + + + align:start position:0% +if you control the worldwide network or +just the network I understand are you + + align:start position:0% +just the network I understand are you + + + align:start position:0% +just the network I understand are you +talking about the worldwide Internet or + + align:start position:0% +talking about the worldwide Internet or + + + align:start position:0% +talking about the worldwide Internet or +you're talking about one country's so + + align:start position:0% +you're talking about one country's so + + + align:start position:0% +you're talking about one country's so +we're going to talk about Forks a little + + align:start position:0% +we're going to talk about Forks a little + + + align:start position:0% +we're going to talk about Forks a little +later can we hold a leads point until + + align:start position:0% +later can we hold a leads point until + + + align:start position:0% +later can we hold a leads point until +then and then I'm going to share with + + align:start position:0% +then and then I'm going to share with + + + align:start position:0% +then and then I'm going to share with +you with Satoshi Nakamoto wrote about + + align:start position:0% +you with Satoshi Nakamoto wrote about + + + align:start position:0% +you with Satoshi Nakamoto wrote about +this very issue back in 2010 aleene's + + align:start position:0% +this very issue back in 2010 aleene's + + + align:start position:0% +this very issue back in 2010 aleene's +raising a point as to whether somebody + + align:start position:0% +raising a point as to whether somebody + + + align:start position:0% +raising a point as to whether somebody +captures part of the Internet and if the + + align:start position:0% +captures part of the Internet and if the + + + align:start position:0% +captures part of the Internet and if the +internet itself by capturing part of the + + align:start position:0% +internet itself by capturing part of the + + + align:start position:0% +internet itself by capturing part of the +Internet you fork the blockchain and + + align:start position:0% +Internet you fork the blockchain and + + + align:start position:0% +Internet you fork the blockchain and +what I was just said I was hold for + + align:start position:0% +what I was just said I was hold for + + + align:start position:0% +what I was just said I was hold for +later but instead I'll cover now is this + + align:start position:0% +later but instead I'll cover now is this + + + align:start position:0% +later but instead I'll cover now is this +question was raised in an email exchange + + align:start position:0% +question was raised in an email exchange + + + align:start position:0% +question was raised in an email exchange +with whomever Satoshi Nakamoto was back + + align:start position:0% +with whomever Satoshi Nakamoto was back + + + align:start position:0% +with whomever Satoshi Nakamoto was back +in around 2010 and his his answer to + + align:start position:0% +in around 2010 and his his answer to + + + align:start position:0% +in around 2010 and his his answer to +Lena's question that I'm just helping + + align:start position:0% +Lena's question that I'm just helping + + + align:start position:0% +Lena's question that I'm just helping +share with you all is that as long as is + + align:start position:0% +share with you all is that as long as is + + + align:start position:0% +share with you all is that as long as is +that part of the internet that was + + align:start position:0% +that part of the internet that was + + + align:start position:0% +that part of the internet that was +walled off was less than a majority and + + align:start position:0% +walled off was less than a majority and + + + align:start position:0% +walled off was less than a majority and +in fact if it was China because that was + + align:start position:0% +in fact if it was China because that was + + + align:start position:0% +in fact if it was China because that was +in in the example even eight years ago + + align:start position:0% +in in the example even eight years ago + + + align:start position:0% +in in the example even eight years ago +it would be considerably less than 50% + + align:start position:0% +it would be considerably less than 50% + + + align:start position:0% +it would be considerably less than 50% +that within a reasonable amount of time + + align:start position:0% +that within a reasonable amount of time + + + align:start position:0% +that within a reasonable amount of time +maybe it would take a few hours but + + align:start position:0% +maybe it would take a few hours but + + + align:start position:0% +maybe it would take a few hours but +within a reasonable amount of time one + + align:start position:0% +within a reasonable amount of time one + + + align:start position:0% +within a reasonable amount of time one +chain would be where the majority of the + + align:start position:0% +chain would be where the majority of the + + + align:start position:0% +chain would be where the majority of the +mining power was and that that that it + + align:start position:0% +mining power was and that that that it + + + align:start position:0% +mining power was and that that that it +could take a while but the the other one + + align:start position:0% +could take a while but the the other one + + + align:start position:0% +could take a while but the the other one +would would probably stop that people + + align:start position:0% +would would probably stop that people + + + align:start position:0% +would would probably stop that people +would stop investing a + + align:start position:0% +would stop investing a + + + align:start position:0% +would stop investing a +electricity and CPU time within China + + align:start position:0% +electricity and CPU time within China + + + align:start position:0% +electricity and CPU time within China +because they would realize some way now + + align:start position:0% +because they would realize some way now + + + align:start position:0% +because they would realize some way now +that was the theory at least that + + align:start position:0% +that was the theory at least that + + + align:start position:0% +that was the theory at least that +something to realize it's like you yeah + + align:start position:0% +something to realize it's like you yeah + + + align:start position:0% +something to realize it's like you yeah +you said well going to Forks but just + + align:start position:0% +you said well going to Forks but just + + + align:start position:0% +you said well going to Forks but just +for people who don't know one pork so + + align:start position:0% +for people who don't know one pork so + + + align:start position:0% +for people who don't know one pork so +it's like if you lose connection to the + + align:start position:0% +it's like if you lose connection to the + + + align:start position:0% +it's like if you lose connection to the +main Bitcoin network so if somebody I'm + + align:start position:0% +main Bitcoin network so if somebody I'm + + + align:start position:0% +main Bitcoin network so if somebody I'm +trying to realize is that they're on the + + align:start position:0% +trying to realize is that they're on the + + + align:start position:0% +trying to realize is that they're on the +wrong chain it's not like you've lost + + align:start position:0% +wrong chain it's not like you've lost + + + align:start position:0% +wrong chain it's not like you've lost +your actually no that's correct they + + align:start position:0% +your actually no that's correct they + + + align:start position:0% +your actually no that's correct they +don't lose it up to and what if I can + + align:start position:0% +don't lose it up to and what if I can + + + align:start position:0% +don't lose it up to and what if I can +use the term prior to the fork there's a + + align:start position:0% +use the term prior to the fork there's a + + + align:start position:0% +use the term prior to the fork there's a +question varnish the wavy point actually + + align:start position:0% +question varnish the wavy point actually + + + align:start position:0% +question varnish the wavy point actually +so this assumption underlying assumption + + align:start position:0% +so this assumption underlying assumption + + + align:start position:0% +so this assumption underlying assumption +for the Byzantine general problem in the + + align:start position:0% +for the Byzantine general problem in the + + + align:start position:0% +for the Byzantine general problem in the +context of blockchain is you have what + + align:start position:0% +context of blockchain is you have what + + + align:start position:0% +context of blockchain is you have what +is being is actually a valid information + + align:start position:0% +is being is actually a valid information + + + align:start position:0% +is being is actually a valid information +so that is kind of an underlying + + align:start position:0% +so that is kind of an underlying + + + align:start position:0% +so that is kind of an underlying +assumption if the network is + + align:start position:0% +assumption if the network is + + + align:start position:0% +assumption if the network is +contaminated then the three mites on + + align:start position:0% +contaminated then the three mites on + + + align:start position:0% +contaminated then the three mites on +which the problem is being solved also + + align:start position:0% +which the problem is being solved also + + + align:start position:0% +which the problem is being solved also +the protocol that is being given here as + + align:start position:0% +the protocol that is being given here as + + + align:start position:0% +the protocol that is being given here as +a solution to the problem is actually + + align:start position:0% +a solution to the problem is actually + + + align:start position:0% +a solution to the problem is actually +not valid if the network is so I think + + align:start position:0% +not valid if the network is so I think + + + align:start position:0% +not valid if the network is so I think +because I didn't pick up every word + + align:start position:0% +because I didn't pick up every word + + + align:start position:0% +because I didn't pick up every word +you're just saying that there's an + + align:start position:0% +you're just saying that there's an + + + align:start position:0% +you're just saying that there's an +underlying assumption that the network + + align:start position:0% +underlying assumption that the network + + + align:start position:0% +underlying assumption that the network +protocol the communication protocol of + + align:start position:0% +protocol the communication protocol of + + + align:start position:0% +protocol the communication protocol of +the Internet is not compromised or + + align:start position:0% +the Internet is not compromised or + + + align:start position:0% +the Internet is not compromised or +walled off but also that it's working it + + align:start position:0% +walled off but also that it's working it + + + align:start position:0% +walled off but also that it's working it +creates a database we've talked about it + + align:start position:0% +creates a database we've talked about it + + + align:start position:0% +creates a database we've talked about it +through hash functions and digital + + align:start position:0% +through hash functions and digital + + + align:start position:0% +through hash functions and digital +signatures and then consensus so what + + align:start position:0% +signatures and then consensus so what + + + align:start position:0% +signatures and then consensus so what +were the technical features I I thought + + align:start position:0% +were the technical features I I thought + + + align:start position:0% +were the technical features I I thought +about it a little bit from our last + + align:start position:0% +about it a little bit from our last + + + align:start position:0% +about it a little bit from our last +class to help just thinking through in + + align:start position:0% +class to help just thinking through in + + + align:start position:0% +class to help just thinking through in +three buckets the cryptography and time + + align:start position:0% +three buckets the cryptography and time + + + align:start position:0% +three buckets the cryptography and time +stamping that we talked about last + + align:start position:0% +stamping that we talked about last + + + align:start position:0% +stamping that we talked about last +Thursday + + align:start position:0% +Thursday + + + align:start position:0% +Thursday +what we're gonna talk about today that + + align:start position:0% +what we're gonna talk about today that + + + align:start position:0% +what we're gonna talk about today that +decentralized consensus protocols and + + align:start position:0% +decentralized consensus protocols and + + + align:start position:0% +decentralized consensus protocols and +the network of course in the native + + align:start position:0% +the network of course in the native + + + align:start position:0% +the network of course in the native +currency and then lastly transaction + + align:start position:0% +currency and then lastly transaction + + + align:start position:0% +currency and then lastly transaction +script that we're gonna talk about this + + align:start position:0% +script that we're gonna talk about this + + + align:start position:0% +script that we're gonna talk about this +coming Thursday now it's not just three + + align:start position:0% +coming Thursday now it's not just three + + + align:start position:0% +coming Thursday now it's not just three +buckets because it's three lectures but + + align:start position:0% +buckets because it's three lectures but + + + align:start position:0% +buckets because it's three lectures but +it's three buckets because they have + + align:start position:0% +it's three buckets because they have + + + align:start position:0% +it's three buckets because they have +something to do with each other the + + align:start position:0% +something to do with each other the + + + align:start position:0% +something to do with each other the +cryptography which is at the core of + + align:start position:0% +cryptography which is at the core of + + + align:start position:0% +cryptography which is at the core of +crypto currencies and blockchains and + + align:start position:0% +crypto currencies and blockchains and + + + align:start position:0% +crypto currencies and blockchains and +it's at the core of a lot of things on + + align:start position:0% +it's at the core of a lot of things on + + + align:start position:0% +it's at the core of a lot of things on +the Internet today + + align:start position:0% +the Internet today + + + align:start position:0% +the Internet today +the consensus mechanism and then the + + align:start position:0% +the consensus mechanism and then the + + + align:start position:0% +the consensus mechanism and then the +transaction script itself cryptography + + align:start position:0% +transaction script itself cryptography + + + align:start position:0% +transaction script itself cryptography +is as as we've talked about + + align:start position:0% +is as as we've talked about + + + align:start position:0% +is as as we've talked about +communications in the presence of + + align:start position:0% +communications in the presence of + + + align:start position:0% +communications in the presence of +adversaries also a form of ways to make + + align:start position:0% +adversaries also a form of ways to make + + + align:start position:0% +adversaries also a form of ways to make +commitments and and secure computation + + align:start position:0% +commitments and and secure computation + + + align:start position:0% +commitments and and secure computation +hash functions if you recall what we + + align:start position:0% +hash functions if you recall what we + + + align:start position:0% +hash functions if you recall what we +talked about + + align:start position:0% +talked about + + + align:start position:0% +talked about +what's the key of a hash function here + + align:start position:0% +what's the key of a hash function here + + + align:start position:0% +what's the key of a hash function here +jokin one the elevator pitch you just + + align:start position:0% +jokin one the elevator pitch you just + + + align:start position:0% +jokin one the elevator pitch you just +have to you know make sure that your + + align:start position:0% +have to you know make sure that your + + + align:start position:0% +have to you know make sure that your +sibling knows you what's that yeah to + + align:start position:0% +sibling knows you what's that yeah to + + + align:start position:0% +sibling knows you what's that yeah to +the private in the public key all right + + align:start position:0% +the private in the public key all right + + + align:start position:0% +the private in the public key all right +that that that's a good that's + + align:start position:0% +that that that's a good that's + + + align:start position:0% +that that that's a good that's +cryptography but not a hash function + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +like that one-way data compression a + + align:start position:0% +like that one-way data compression a + + + align:start position:0% +like that one-way data compression a +crossword puzzle anybody here dude that + + align:start position:0% +crossword puzzle anybody here dude that + + + align:start position:0% +crossword puzzle anybody here dude that +New York Times crossword puzzle and a + + align:start position:0% +New York Times crossword puzzle and a + + + align:start position:0% +New York Times crossword puzzle and a +mobile app good so if you do a + + align:start position:0% +mobile app good so if you do a + + + align:start position:0% +mobile app good so if you do a +Wednesday's New York Times crossword + + align:start position:0% +Wednesday's New York Times crossword + + + align:start position:0% +Wednesday's New York Times crossword +puzzle does it tell you whether you're + + align:start position:0% +puzzle does it tell you whether you're + + + align:start position:0% +puzzle does it tell you whether you're +correct on Wednesday or does it not tell + + align:start position:0% +correct on Wednesday or does it not tell + + + align:start position:0% +correct on Wednesday or does it not tell +you you're correct when when does it I + + align:start position:0% +you you're correct when when does it I + + + align:start position:0% +you you're correct when when does it I +don't do the New York Times crossword + + align:start position:0% +don't do the New York Times crossword + + + align:start position:0% +don't do the New York Times crossword +puzzles but + + align:start position:0% + + + + align:start position:0% + +or maybe as soon as you have any errors + + align:start position:0% +or maybe as soon as you have any errors + + + align:start position:0% +or maybe as soon as you have any errors +but it won't but you can't actually + + align:start position:0% +but it won't but you can't actually + + + align:start position:0% +but it won't but you can't actually +check what the errors are unless you + + align:start position:0% +check what the errors are unless you + + + align:start position:0% +check what the errors are unless you +want to like invalidate your streak I + + align:start position:0% + + + + align:start position:0% + +don't actually know if the New York + + align:start position:0% +don't actually know if the New York + + + align:start position:0% +don't actually know if the New York +Times used hash functions but they could + + align:start position:0% +Times used hash functions but they could + + + align:start position:0% +Times used hash functions but they could +they could because they could stick the + + align:start position:0% +they could because they could stick the + + + align:start position:0% +they could because they could stick the +the whole entire crossword puzzle into a + + align:start position:0% +the whole entire crossword puzzle into a + + + align:start position:0% +the whole entire crossword puzzle into a +hash and it's a commitment scheme and + + align:start position:0% +hash and it's a commitment scheme and + + + align:start position:0% +hash and it's a commitment scheme and +remember if you change even one thing in + + align:start position:0% +remember if you change even one thing in + + + align:start position:0% +remember if you change even one thing in +the input data the hash will come out + + align:start position:0% +the input data the hash will come out + + + align:start position:0% +the input data the hash will come out +differently so the New York Times could + + align:start position:0% +differently so the New York Times could + + + align:start position:0% +differently so the New York Times could +use a hash function so that Stephanie + + align:start position:0% +use a hash function so that Stephanie + + + align:start position:0% +use a hash function so that Stephanie +could find out right because you can + + align:start position:0% +could find out right because you can + + + align:start position:0% +could find out right because you can +only push to see if it's correct when + + align:start position:0% +only push to see if it's correct when + + + align:start position:0% +only push to see if it's correct when +you finish the whole and it either tells + + align:start position:0% +you finish the whole and it either tells + + + align:start position:0% +you finish the whole and it either tells +you you have it or not right it's so I'm + + align:start position:0% +you you have it or not right it's so I'm + + + align:start position:0% +you you have it or not right it's so I'm +just I'm bringing it to real life that a + + align:start position:0% +just I'm bringing it to real life that a + + + align:start position:0% +just I'm bringing it to real life that a +hash function just think of the New York + + align:start position:0% +hash function just think of the New York + + + align:start position:0% +hash function just think of the New York +Times crossword puzzle and if you don't + + align:start position:0% +Times crossword puzzle and if you don't + + + align:start position:0% +Times crossword puzzle and if you don't +remember ask Stephanie we talked about + + align:start position:0% +remember ask Stephanie we talked about + + + align:start position:0% +remember ask Stephanie we talked about +append-only logs and recall that in + + align:start position:0% +append-only logs and recall that in + + + align:start position:0% +append-only logs and recall that in +blockchain and Bitcoin there's a bunch + + align:start position:0% +blockchain and Bitcoin there's a bunch + + + align:start position:0% +blockchain and Bitcoin there's a bunch +of information and the head of the block + + align:start position:0% +of information and the head of the block + + + align:start position:0% +of information and the head of the block +and that which is in the head of the + + align:start position:0% +and that which is in the head of the + + + align:start position:0% +and that which is in the head of the +block is put together like the New York + + align:start position:0% +block is put together like the New York + + + align:start position:0% +block is put together like the New York +Times crossword puzzle and we have a + + align:start position:0% +Times crossword puzzle and we have a + + + align:start position:0% +Times crossword puzzle and we have a +chain of blocks most of the data though + + align:start position:0% +chain of blocks most of the data though + + + align:start position:0% +chain of blocks most of the data though +is stored efficiently in something + + align:start position:0% +is stored efficiently in something + + + align:start position:0% +is stored efficiently in something +called a Merkel tree again it uses a + + align:start position:0% +called a Merkel tree again it uses a + + + align:start position:0% +called a Merkel tree again it uses a +whole lot of hash functions and and so + + align:start position:0% +whole lot of hash functions and and so + + + align:start position:0% +whole lot of hash functions and and so +it's a way to be efficient but it's also + + align:start position:0% +it's a way to be efficient but it's also + + + align:start position:0% +it's a way to be efficient but it's also +a way to secure the data so now we're + + align:start position:0% +a way to secure the data so now we're + + + align:start position:0% +a way to secure the data so now we're +gonna get back to your favorite thing + + align:start position:0% +gonna get back to your favorite thing + + + align:start position:0% +gonna get back to your favorite thing +digital signatures so what's a digital + + align:start position:0% +digital signatures so what's a digital + + + align:start position:0% +digital signatures so what's a digital +signature do + + align:start position:0% + + + + align:start position:0% + +that you're signing something like a + + align:start position:0% +that you're signing something like a + + + align:start position:0% +that you're signing something like a +transaction with the private key and the + + align:start position:0% +transaction with the private key and the + + + align:start position:0% +transaction with the private key and the +other person on the other side could + + align:start position:0% +other person on the other side could + + + align:start position:0% +other person on the other side could +prove that you are the one to sign it + + align:start position:0% +prove that you are the one to sign it + + + align:start position:0% +prove that you are the one to sign it +with your public key perfect so it + + align:start position:0% +with your public key perfect so it + + + align:start position:0% +with your public key perfect so it +guards against tampering and + + align:start position:0% +guards against tampering and + + + align:start position:0% +guards against tampering and +impersonation I didn't go through this + + align:start position:0% +impersonation I didn't go through this + + + align:start position:0% +impersonation I didn't go through this +last Thursday but think of digital + + align:start position:0% +last Thursday but think of digital + + + align:start position:0% +last Thursday but think of digital +signatures two different ways a digital + + align:start position:0% +signatures two different ways a digital + + + align:start position:0% +signatures two different ways a digital +signature that you use without a hash + + align:start position:0% +signature that you use without a hash + + + align:start position:0% +signature that you use without a hash +and in Bitcoin and blockchain and often + + align:start position:0% +and in Bitcoin and blockchain and often + + + align:start position:0% +and in Bitcoin and blockchain and often +it's actually it's combined with a hash + + align:start position:0% +it's actually it's combined with a hash + + + align:start position:0% +it's actually it's combined with a hash +so as Joe Quinn just went through you + + align:start position:0% +so as Joe Quinn just went through you + + + align:start position:0% +so as Joe Quinn just went through you +can have a private key that you sign + + align:start position:0% +can have a private key that you sign + + + align:start position:0% +can have a private key that you sign +something with the sender's public key + + align:start position:0% +something with the sender's public key + + + align:start position:0% +something with the sender's public key +and a signature and exactly that but + + align:start position:0% +and a signature and exactly that but + + + align:start position:0% +and a signature and exactly that but +it's also able to do it where you have a + + align:start position:0% +it's also able to do it where you have a + + + align:start position:0% +it's also able to do it where you have a +hash as well you take all the data all + + align:start position:0% +hash as well you take all the data all + + + align:start position:0% +hash as well you take all the data all +the message and you put it into into it + + align:start position:0% +the message and you put it into into it + + + align:start position:0% +the message and you put it into into it +with a signature and this is a little + + align:start position:0% +with a signature and this is a little + + + align:start position:0% +with a signature and this is a little +bit too complex and it was last + + align:start position:0% +bit too complex and it was last + + + align:start position:0% +bit too complex and it was last +Thursday's lecture but it's important to + + align:start position:0% +Thursday's lecture but it's important to + + + align:start position:0% +Thursday's lecture but it's important to +know that what blockchain is basically + + align:start position:0% +know that what blockchain is basically + + + align:start position:0% +know that what blockchain is basically +doing most block chains do is they take + + align:start position:0% +doing most block chains do is they take + + + align:start position:0% +doing most block chains do is they take +a lot of information a transaction for + + align:start position:0% +a lot of information a transaction for + + + align:start position:0% +a lot of information a transaction for +instance hash that information and why + + align:start position:0% +instance hash that information and why + + + align:start position:0% +instance hash that information and why +do we hash it again and it also + + align:start position:0% +do we hash it again and it also + + + align:start position:0% +do we hash it again and it also +compresses some of the data but it's a + + align:start position:0% +compresses some of the data but it's a + + + align:start position:0% +compresses some of the data but it's a +it's a commitment scheme it's it's like + + align:start position:0% +it's a commitment scheme it's it's like + + + align:start position:0% +it's a commitment scheme it's it's like +this is it this is actually the the New + + align:start position:0% +this is it this is actually the the New + + + align:start position:0% +this is it this is actually the the New +York Times crossword puzzle that answers + + align:start position:0% +York Times crossword puzzle that answers + + + align:start position:0% +York Times crossword puzzle that answers +all the questions so usually it first + + align:start position:0% +all the questions so usually it first + + + align:start position:0% +all the questions so usually it first +hashes it meaning it's a commitment and + + align:start position:0% +hashes it meaning it's a commitment and + + + align:start position:0% +hashes it meaning it's a commitment and +then put a digital signature on it and + + align:start position:0% +then put a digital signature on it and + + + align:start position:0% +then put a digital signature on it and +there was one last thing we talked about + + align:start position:0% +there was one last thing we talked about + + + align:start position:0% +there was one last thing we talked about +last week what our Bitcoin addresses + + align:start position:0% + + + + align:start position:0% + +Isabella can you tell me what a Bitcoin + + align:start position:0% +Isabella can you tell me what a Bitcoin + + + align:start position:0% +Isabella can you tell me what a Bitcoin +address is + + align:start position:0% + + + + align:start position:0% + +tells you where bitcoin is being said + + align:start position:0% +tells you where bitcoin is being said + + + align:start position:0% +tells you where bitcoin is being said +fan you want to help out a little so + + align:start position:0% +fan you want to help out a little so + + + align:start position:0% +fan you want to help out a little so +it's the clothes so it's basically that + + align:start position:0% +it's the clothes so it's basically that + + + align:start position:0% +it's the clothes so it's basically that +between Isabel and Penn you've got it + + align:start position:0% +between Isabel and Penn you've got it + + + align:start position:0% +between Isabel and Penn you've got it +it's basically how any of the native + + align:start position:0% +it's basically how any of the native + + + align:start position:0% +it's basically how any of the native +currency Bitcoin can be identified but + + align:start position:0% +currency Bitcoin can be identified but + + + align:start position:0% +currency Bitcoin can be identified but +it is a public key with a couple extra + + align:start position:0% +it is a public key with a couple extra + + + align:start position:0% +it is a public key with a couple extra +hashes and a little bit other fancy + + align:start position:0% +hashes and a little bit other fancy + + + align:start position:0% +hashes and a little bit other fancy +footwork to make it compressed and + + align:start position:0% +footwork to make it compressed and + + + align:start position:0% +footwork to make it compressed and +smaller but it is literally what you can + + align:start position:0% +smaller but it is literally what you can + + + align:start position:0% +smaller but it is literally what you can +send bitcoins to so it's determined by + + align:start position:0% +send bitcoins to so it's determined by + + + align:start position:0% +send bitcoins to so it's determined by +the public key but it's not identical to + + align:start position:0% +the public key but it's not identical to + + + align:start position:0% +the public key but it's not identical to +and I found a fancy little Charter chart + + align:start position:0% +and I found a fancy little Charter chart + + + align:start position:0% +and I found a fancy little Charter chart +to define it a private key leads to a + + align:start position:0% +to define it a private key leads to a + + + align:start position:0% +to define it a private key leads to a +public key through some form and in + + align:start position:0% +public key through some form and in + + + align:start position:0% +public key through some form and in +Bitcoin it's called elliptic curve + + align:start position:0% +Bitcoin it's called elliptic curve + + + align:start position:0% +Bitcoin it's called elliptic curve +multiplication but there are other forms + + align:start position:0% +multiplication but there are other forms + + + align:start position:0% +multiplication but there are other forms +of public and private keys the public + + align:start position:0% +of public and private keys the public + + + align:start position:0% +of public and private keys the public +key then it gets hashed and then it goes + + align:start position:0% +key then it gets hashed and then it goes + + + align:start position:0% +key then it gets hashed and then it goes +through a code that makes it shorter + + align:start position:0% +through a code that makes it shorter + + + align:start position:0% +through a code that makes it shorter +which is the Bitcoin address part of the + + align:start position:0% +which is the Bitcoin address part of the + + + align:start position:0% +which is the Bitcoin address part of the +reason it was hashed and part of the + + align:start position:0% +reason it was hashed and part of the + + + align:start position:0% +reason it was hashed and part of the +reason it goes through that extra code + + align:start position:0% +reason it goes through that extra code + + + align:start position:0% +reason it goes through that extra code +is to make it even more secure it's not + + align:start position:0% +is to make it even more secure it's not + + + align:start position:0% +is to make it even more secure it's not +the only reason it also compresses it a + + align:start position:0% +the only reason it also compresses it a + + + align:start position:0% +the only reason it also compresses it a +bit more but those of you who have ever + + align:start position:0% +bit more but those of you who have ever + + + align:start position:0% +bit more but those of you who have ever +owned Bitcoin and you have a wallet and + + align:start position:0% +owned Bitcoin and you have a wallet and + + + align:start position:0% +owned Bitcoin and you have a wallet and +the wallet keeps those big Bitcoin + + align:start position:0% +the wallet keeps those big Bitcoin + + + align:start position:0% +the wallet keeps those big Bitcoin +addresses alright so now let's talk + + align:start position:0% +addresses alright so now let's talk + + + align:start position:0% +addresses alright so now let's talk +about decentralized networks the topic + + align:start position:0% +about decentralized networks the topic + + + align:start position:0% +about decentralized networks the topic +of today any questions about the review + + align:start position:0% +of today any questions about the review + + + align:start position:0% +of today any questions about the review +for last Thursday I know it was quick a + + align:start position:0% +for last Thursday I know it was quick a + + + align:start position:0% +for last Thursday I know it was quick a +lot + + align:start position:0% + + + + align:start position:0% + +options I think that your the question + + align:start position:0% +options I think that your the question + + + align:start position:0% +options I think that your the question +is is this if if the output of a hash + + align:start position:0% +is is this if if the output of a hash + + + align:start position:0% +is is this if if the output of a hash +function is shorter is it possibly more + + align:start position:0% +function is shorter is it possibly more + + + align:start position:0% +function is shorter is it possibly more +breakable I think mathematically that + + align:start position:0% +breakable I think mathematically that + + + align:start position:0% +breakable I think mathematically that +might be correct + + align:start position:0% +might be correct + + + align:start position:0% +might be correct +however this actually goes through two + + align:start position:0% +however this actually goes through two + + + align:start position:0% +however this actually goes through two +hashes one which is this mechanism + + align:start position:0% +hashes one which is this mechanism + + + align:start position:0% +hashes one which is this mechanism +called sha-256 and the other one I'm + + align:start position:0% +called sha-256 and the other one I'm + + + align:start position:0% +called sha-256 and the other one I'm +gonna mispronounce but down to 160 so I + + align:start position:0% +gonna mispronounce but down to 160 so I + + + align:start position:0% +gonna mispronounce but down to 160 so I +think because it's going through two + + align:start position:0% +think because it's going through two + + + align:start position:0% +think because it's going through two +different hashes the answer is it's even + + align:start position:0% +different hashes the answer is it's even + + + align:start position:0% +different hashes the answer is it's even +harder to break both that any other + + align:start position:0% +harder to break both that any other + + + align:start position:0% +harder to break both that any other +questions about the review no please + + align:start position:0% +questions about the review no please + + + align:start position:0% +questions about the review no please +Derek I'm just wondering the public key + + align:start position:0% +Derek I'm just wondering the public key + + + align:start position:0% +Derek I'm just wondering the public key +is for what is the the only thing that + + align:start position:0% +is for what is the the only thing that + + + align:start position:0% +is for what is the the only thing that +you're actually showing is a Bitcoin + + align:start position:0% +you're actually showing is a Bitcoin + + + align:start position:0% +you're actually showing is a Bitcoin +address until later and we'll talk a lot + + align:start position:0% +address until later and we'll talk a lot + + + align:start position:0% +address until later and we'll talk a lot +about this on Thursday when you actually + + align:start position:0% +about this on Thursday when you actually + + + align:start position:0% +about this on Thursday when you actually +do a transaction you have to then + + align:start position:0% +do a transaction you have to then + + + align:start position:0% +do a transaction you have to then +disclose your public key so initially + + align:start position:0% +disclose your public key so initially + + + align:start position:0% +disclose your public key so initially +the storage is around Bitcoin addresses + + align:start position:0% +the storage is around Bitcoin addresses + + + align:start position:0% +the storage is around Bitcoin addresses +and some some will advise and it's why + + align:start position:0% +and some some will advise and it's why + + + align:start position:0% +and some some will advise and it's why +many wallets do this that you should + + align:start position:0% +many wallets do this that you should + + + align:start position:0% +many wallets do this that you should +never use the same public key twice + + align:start position:0% +never use the same public key twice + + + align:start position:0% +never use the same public key twice +though numerous people do on block + + align:start position:0% +though numerous people do on block + + + align:start position:0% +though numerous people do on block +chains but to be most secure you would + + align:start position:0% +chains but to be most secure you would + + + align:start position:0% +chains but to be most secure you would +constantly be creating new public key + + align:start position:0% +constantly be creating new public key + + + align:start position:0% +constantly be creating new public key +private key pairs and once you've used + + align:start position:0% +private key pairs and once you've used + + + align:start position:0% +private key pairs and once you've used +it move on and get a new set of keys got + + align:start position:0% +it move on and get a new set of keys got + + + align:start position:0% +it move on and get a new set of keys got +it + + align:start position:0% +it + + + align:start position:0% +it +so distributed networks we talked about + + align:start position:0% +so distributed networks we talked about + + + align:start position:0% +so distributed networks we talked about +Byzantine generals problem so I've found + + align:start position:0% +Byzantine generals problem so I've found + + + align:start position:0% +Byzantine generals problem so I've found +some Byzantine generals they want to all + + align:start position:0% +some Byzantine generals they want to all + + + align:start position:0% +some Byzantine generals they want to all +attack that cat castle or what if only + + align:start position:0% +attack that cat castle or what if only + + + align:start position:0% +attack that cat castle or what if only +three of them do and two of them say + + align:start position:0% +three of them do and two of them say + + + align:start position:0% +three of them do and two of them say +retreat that that's the visual that's + + align:start position:0% +retreat that that's the visual that's + + + align:start position:0% +retreat that that's the visual that's +that's the problem the only way to win + + align:start position:0% +that's the problem the only way to win + + + align:start position:0% +that's the problem the only way to win +it and in this mathematical game theory + + align:start position:0% +it and in this mathematical game theory + + + align:start position:0% +it and in this mathematical game theory +paper that was written some twenty five + + align:start position:0% +paper that was written some twenty five + + + align:start position:0% +paper that was written some twenty five +years ago was if they all said attack or + + align:start position:0% +years ago was if they all said attack or + + + align:start position:0% +years ago was if they all said attack or +all said retreat but the same thing sort + + align:start position:0% +all said retreat but the same thing sort + + + align:start position:0% +all said retreat but the same thing sort +of came to computers and the core thing + + align:start position:0% +of came to computers and the core thing + + + align:start position:0% +of came to computers and the core thing +about a permissionless system is there + + align:start position:0% +about a permissionless system is there + + + align:start position:0% +about a permissionless system is there +is no central authority and if there's + + align:start position:0% +is no central authority and if there's + + + align:start position:0% +is no central authority and if there's +no central authority had as a + + align:start position:0% +no central authority had as a + + + align:start position:0% +no central authority had as a +distributed network like the distributed + + align:start position:0% +distributed network like the distributed + + + align:start position:0% +distributed network like the distributed +set of generals come to some agreement + + align:start position:0% +set of generals come to some agreement + + + align:start position:0% +set of generals come to some agreement +do we attack do we retreat well it's + + align:start position:0% +do we attack do we retreat well it's + + + align:start position:0% +do we attack do we retreat well it's +based on a consensus protocol and a + + align:start position:0% +based on a consensus protocol and a + + + align:start position:0% +based on a consensus protocol and a +native currency though that's the key + + align:start position:0% +native currency though that's the key + + + align:start position:0% +native currency though that's the key +innovation of satoshi nakamoto is to + + align:start position:0% +innovation of satoshi nakamoto is to + + + align:start position:0% +innovation of satoshi nakamoto is to +pull it all together but it was built on + + align:start position:0% +pull it all together but it was built on + + + align:start position:0% +pull it all together but it was built on +the backs of other people Adam back in + + align:start position:0% +the backs of other people Adam back in + + + align:start position:0% +the backs of other people Adam back in +1997 he proposed a way to address email + + align:start position:0% +1997 he proposed a way to address email + + + align:start position:0% +1997 he proposed a way to address email +spam and other types of computer + + align:start position:0% +spam and other types of computer + + + align:start position:0% +spam and other types of computer +problems called denial service attacks + + align:start position:0% + + + + align:start position:0% + +now it ultimately wasn't used I mean he + + align:start position:0% +now it ultimately wasn't used I mean he + + + align:start position:0% +now it ultimately wasn't used I mean he +proposed it it was used for short while + + align:start position:0% +proposed it it was used for short while + + + align:start position:0% +proposed it it was used for short while +and then it wasn't subsequently used but + + align:start position:0% +and then it wasn't subsequently used but + + + align:start position:0% +and then it wasn't subsequently used but +it's important to understand that the + + align:start position:0% +it's important to understand that the + + + align:start position:0% +it's important to understand that the +proof of work in the middle of Bitcoin + + align:start position:0% +proof of work in the middle of Bitcoin + + + align:start position:0% +proof of work in the middle of Bitcoin +was created eleven or twelve years + + align:start position:0% +was created eleven or twelve years + + + align:start position:0% +was created eleven or twelve years +before the Bitcoin paper and and the key + + align:start position:0% +before the Bitcoin paper and and the key + + + align:start position:0% +before the Bitcoin paper and and the key +was basically require a bunch of + + align:start position:0% +was basically require a bunch of + + + align:start position:0% +was basically require a bunch of +computational work using hash functions + + align:start position:0% +computational work using hash functions + + + align:start position:0% +computational work using hash functions +and so the email or the header of the + + align:start position:0% +and so the email or the header of the + + + align:start position:0% +and so the email or the header of the +email this is Adam backs not Bitcoin but + + align:start position:0% +email this is Adam backs not Bitcoin but + + + align:start position:0% +email this is Adam backs not Bitcoin but +the email or the head of the email went + + align:start position:0% +the email or the head of the email went + + + align:start position:0% +the email or the head of the email went +into the hash function creates a hash + + align:start position:0% +into the hash function creates a hash + + + align:start position:0% +into the hash function creates a hash +but the difficulty of finding + + align:start position:0% +but the difficulty of finding + + + align:start position:0% +but the difficulty of finding +whether it's confirmed was was it in a + + align:start position:0% +whether it's confirmed was was it in a + + + align:start position:0% +whether it's confirmed was was it in a +certain range of hashes and he did that + + align:start position:0% +certain range of hashes and he did that + + + align:start position:0% +certain range of hashes and he did that +by the quote leading zeros does anybody + + align:start position:0% +by the quote leading zeros does anybody + + + align:start position:0% +by the quote leading zeros does anybody +want to guess why he did it this way or + + align:start position:0% +want to guess why he did it this way or + + + align:start position:0% +want to guess why he did it this way or +her leans just gonna tell us probably + + align:start position:0% +her leans just gonna tell us probably + + + align:start position:0% +her leans just gonna tell us probably +and not yes but who hasn't spoken yet + + align:start position:0% + + + + align:start position:0% + +Emily you want to try it out + + align:start position:0% + + + + align:start position:0% + +Daniel preserves see around the email + + align:start position:0% +Daniel preserves see around the email + + + align:start position:0% +Daniel preserves see around the email +well so it definitely preserved privacy + + align:start position:0% +well so it definitely preserved privacy + + + align:start position:0% +well so it definitely preserved privacy +but he was trying to put some + + align:start position:0% +but he was trying to put some + + + align:start position:0% +but he was trying to put some +computational work every email that + + align:start position:0% +computational work every email that + + + align:start position:0% +computational work every email that +would set be sent would take one to two + + align:start position:0% +would set be sent would take one to two + + + align:start position:0% +would set be sent would take one to two +or three seconds of computational work + + align:start position:0% +or three seconds of computational work + + + align:start position:0% +or three seconds of computational work +that was his paper a few seconds what + + align:start position:0% +that was his paper a few seconds what + + + align:start position:0% +that was his paper a few seconds what +you get is to modify a small piece of + + align:start position:0% +you get is to modify a small piece of + + + align:start position:0% +you get is to modify a small piece of +the whole information and try and try + + align:start position:0% +the whole information and try and try + + + align:start position:0% +the whole information and try and try +until you get that specific hash and + + align:start position:0% +until you get that specific hash and + + + align:start position:0% +until you get that specific hash and +that makes it really computationally + + align:start position:0% +that makes it really computationally + + + align:start position:0% +that makes it really computationally +intensive but validating is just running + + align:start position:0% +intensive but validating is just running + + + align:start position:0% +intensive but validating is just running +what we talked about last time with the + + align:start position:0% +what we talked about last time with the + + + align:start position:0% +what we talked about last time with the +nonce is right you need to try out a + + align:start position:0% +nonce is right you need to try out a + + + align:start position:0% +nonce is right you need to try out a +bunch of different random numbers in + + align:start position:0% +bunch of different random numbers in + + + align:start position:0% +bunch of different random numbers in +order to get the right number of leading + + align:start position:0% +order to get the right number of leading + + + align:start position:0% +order to get the right number of leading +zeroes and it could be I don't know I + + align:start position:0% +zeroes and it could be I don't know I + + + align:start position:0% +zeroes and it could be I don't know I +think it could be like leaving anything + + align:start position:0% +think it could be like leaving anything + + + align:start position:0% +think it could be like leaving anything +but he chose zero because it's nice + + align:start position:0% +but he chose zero because it's nice + + + align:start position:0% +but he chose zero because it's nice +right + + align:start position:0% +right + + + align:start position:0% +right +but like you need to try + + align:start position:0% +but like you need to try + + + align:start position:0% +but like you need to try +in order to get the right number and in + + align:start position:0% +in order to get the right number and in + + + align:start position:0% +in order to get the right number and in +the email circumstance his thought was + + align:start position:0% +the email circumstance his thought was + + + align:start position:0% +the email circumstance his thought was +it will take two or three seconds for + + align:start position:0% +it will take two or three seconds for + + + align:start position:0% +it will take two or three seconds for +anyone sending an email to do this proof + + align:start position:0% +anyone sending an email to do this proof + + + align:start position:0% +anyone sending an email to do this proof +of work but it will take a nano second + + align:start position:0% +of work but it will take a nano second + + + align:start position:0% +of work but it will take a nano second +or less to confirm it but if you were + + align:start position:0% +or less to confirm it but if you were + + + align:start position:0% +or less to confirm it but if you were +sending spam and you had a computer to + + align:start position:0% +sending spam and you had a computer to + + + align:start position:0% +sending spam and you had a computer to +said millions of spam times two or three + + align:start position:0% +said millions of spam times two or three + + + align:start position:0% +said millions of spam times two or three +seconds of peace that would be too much + + align:start position:0% +seconds of peace that would be too much + + + align:start position:0% +seconds of peace that would be too much +for the spammer that that was it so any + + align:start position:0% +for the spammer that that was it so any + + + align:start position:0% +for the spammer that that was it so any +one person sending one email it won't be + + align:start position:0% +one person sending one email it won't be + + + align:start position:0% +one person sending one email it won't be +too bad + + align:start position:0% +too bad + + + align:start position:0% +too bad +anyone sending millions of emails it + + align:start position:0% +anyone sending millions of emails it + + + align:start position:0% +anyone sending millions of emails it +would be lousy and so that's why this + + align:start position:0% +would be lousy and so that's why this + + + align:start position:0% +would be lousy and so that's why this +concept was in the midst of emails and + + align:start position:0% +concept was in the midst of emails and + + + align:start position:0% +concept was in the midst of emails and +and it could be efficiently proved so + + align:start position:0% +and it could be efficiently proved so + + + align:start position:0% +and it could be efficiently proved so +back to blockchain the innovation was + + align:start position:0% +back to blockchain the innovation was + + + align:start position:0% +back to blockchain the innovation was +basically how do we do this with a chain + + align:start position:0% +basically how do we do this with a chain + + + align:start position:0% +basically how do we do this with a chain +how do we do this with a chain set of + + align:start position:0% +how do we do this with a chain set of + + + align:start position:0% +how do we do this with a chain set of +works and remember Stuart Haber that + + align:start position:0% +works and remember Stuart Haber that + + + align:start position:0% +works and remember Stuart Haber that +whole thing about the blockchain and the + + align:start position:0% +whole thing about the blockchain and the + + + align:start position:0% +whole thing about the blockchain and the +what's in the New York Times this was + + align:start position:0% +what's in the New York Times this was + + + align:start position:0% +what's in the New York Times this was +was that chain of information but here + + align:start position:0% +was that chain of information but here + + + align:start position:0% +was that chain of information but here +why don't we do a proof of work between + + align:start position:0% +why don't we do a proof of work between + + + align:start position:0% +why don't we do a proof of work between +the chain and I found a little graphic + + align:start position:0% +the chain and I found a little graphic + + + align:start position:0% +the chain and I found a little graphic +but but the sha-256 that's the formula + + align:start position:0% +but but the sha-256 that's the formula + + + align:start position:0% +but but the sha-256 that's the formula +which is is used to hash the header the + + align:start position:0% +which is is used to hash the header the + + + align:start position:0% +which is is used to hash the header the +previous hash the transaction hash a + + align:start position:0% +previous hash the transaction hash a + + + align:start position:0% +previous hash the transaction hash a +timestamp and a nonce + + align:start position:0% + + + + align:start position:0% + +can you find a hash that has a certain + + align:start position:0% +can you find a hash that has a certain + + + align:start position:0% +can you find a hash that has a certain +number of leading zeroes + + align:start position:0% +number of leading zeroes + + + align:start position:0% +number of leading zeroes +this was the key innovation in a sense + + align:start position:0% +this was the key innovation in a sense + + + align:start position:0% +this was the key innovation in a sense +or maybe Satoshi Nakamoto was just + + align:start position:0% +or maybe Satoshi Nakamoto was just + + + align:start position:0% +or maybe Satoshi Nakamoto was just +taking Adam Beck's email proof of work + + align:start position:0% + + + + align:start position:0% + +remember the reading for last week + + align:start position:0% +remember the reading for last week + + + align:start position:0% +remember the reading for last week +blocks this this is colored green + + align:start position:0% +blocks this this is colored green + + + align:start position:0% +blocks this this is colored green +because each of them have hashes that in + + align:start position:0% +because each of them have hashes that in + + + align:start position:0% +because each of them have hashes that in +this case have leading if I'm right is + + align:start position:0% +this case have leading if I'm right is + + + align:start position:0% +this case have leading if I'm right is +this leading four zeros leaving four + + align:start position:0% +this leading four zeros leaving four + + + align:start position:0% +this leading four zeros leaving four +zeros what if we change one thing what's + + align:start position:0% +zeros what if we change one thing what's + + + align:start position:0% +zeros what if we change one thing what's +going to happen + + align:start position:0% + + + + align:start position:0% + +is it alpha what happens if we change + + align:start position:0% +is it alpha what happens if we change + + + align:start position:0% +is it alpha what happens if we change +one thing that has to change completely + + align:start position:0% +one thing that has to change completely + + + align:start position:0% +one thing that has to change completely +the hash will change completely so what + + align:start position:0% +the hash will change completely so what + + + align:start position:0% +the hash will change completely so what +happened what did we change here I'll go + + align:start position:0% +happened what did we change here I'll go + + + align:start position:0% +happened what did we change here I'll go +back and forth what's that why should I + + align:start position:0% +back and forth what's that why should I + + + align:start position:0% +back and forth what's that why should I +be able to get a hundred dollars for + + align:start position:0% +be able to get a hundred dollars for + + + align:start position:0% +be able to get a hundred dollars for +free well in this example I guess the + + align:start position:0% +free well in this example I guess the + + + align:start position:0% +free well in this example I guess the +coin basis for the minor right there's + + align:start position:0% +coin basis for the minor right there's + + + align:start position:0% +coin basis for the minor right there's +one transaction dedicated for whoever's + + align:start position:0% +one transaction dedicated for whoever's + + + align:start position:0% +one transaction dedicated for whoever's +validates the block gets right now + + align:start position:0% +validates the block gets right now + + + align:start position:0% +validates the block gets right now +twelve and a half Bitcoin and so you add + + align:start position:0% +twelve and a half Bitcoin and so you add + + + align:start position:0% +twelve and a half Bitcoin and so you add +that in addition to all the other + + align:start position:0% +that in addition to all the other + + + align:start position:0% +that in addition to all the other +transactions that you're validating but + + align:start position:0% +transactions that you're validating but + + + align:start position:0% +transactions that you're validating but +in this case you're not actually this + + align:start position:0% +in this case you're not actually this + + + align:start position:0% +in this case you're not actually this +minor so you know so the little eighteen + + align:start position:0% +minor so you know so the little eighteen + + + align:start position:0% +minor so you know so the little eighteen +minute video that was aside for last + + align:start position:0% +minute video that was aside for last + + + align:start position:0% +minute video that was aside for last +Thursday I just went in and I was trying + + align:start position:0% +Thursday I just went in and I was trying + + + align:start position:0% +Thursday I just went in and I was trying +to I was trying to get I was trying to + + align:start position:0% +to I was trying to get I was trying to + + + align:start position:0% +to I was trying to get I was trying to +get the money for me and and it it + + align:start position:0% +get the money for me and and it it + + + align:start position:0% +get the money for me and and it it +invalidated the rest of the chain and + + align:start position:0% +invalidated the rest of the chain and + + + align:start position:0% +invalidated the rest of the chain and +that's really that's the that's the sort + + align:start position:0% +that's really that's the that's the sort + + + align:start position:0% +that's really that's the that's the sort +of innovation or genius is if you try to + + align:start position:0% +of innovation or genius is if you try to + + + align:start position:0% +of innovation or genius is if you try to +go into a former block whether it's the + + align:start position:0% +go into a former block whether it's the + + + align:start position:0% +go into a former block whether it's the +last block or block a hundred thousand + + align:start position:0% +last block or block a hundred thousand + + + align:start position:0% +last block or block a hundred thousand +blocks away and change one little + + align:start position:0% +blocks away and change one little + + + align:start position:0% +blocks away and change one little +whisker of information or one letter on + + align:start position:0% +whisker of information or one letter on + + + align:start position:0% +whisker of information or one letter on +that crossword puzzle it's going to + + align:start position:0% +that crossword puzzle it's going to + + + align:start position:0% +that crossword puzzle it's going to +change the entire blockchain and I bring + + align:start position:0% +change the entire blockchain and I bring + + + align:start position:0% +change the entire blockchain and I bring +it back to the crossword puzzles or + + align:start position:0% +it back to the crossword puzzles or + + + align:start position:0% +it back to the crossword puzzles or +whisker on a cat it's just any little + + align:start position:0% +whisker on a cat it's just any little + + + align:start position:0% +whisker on a cat it's just any little +bit of information so an innovation + + align:start position:0% +bit of information so an innovation + + + align:start position:0% +bit of information so an innovation +about hash functions became and an + + align:start position:0% +about hash functions became and an + + + align:start position:0% +about hash functions became and an +innovation about time stamp blocks all + + align:start position:0% +innovation about time stamp blocks all + + + align:start position:0% +innovation about time stamp blocks all +the sudden came together with this proof + + align:start position:0% +the sudden came together with this proof + + + align:start position:0% +the sudden came together with this proof +of work innovation so now to the chains + + align:start position:0% +of work innovation so now to the chains + + + align:start position:0% +of work innovation so now to the chains +themselves the consensus of block chains + + align:start position:0% +themselves the consensus of block chains + + + align:start position:0% +themselves the consensus of block chains +and many people would say that in fact + + align:start position:0% +and many people would say that in fact + + + align:start position:0% +and many people would say that in fact +the reality of blocked + + align:start position:0% +the reality of blocked + + + align:start position:0% +the reality of blocked +only the longest chain is the one that + + align:start position:0% +only the longest chain is the one that + + + align:start position:0% +only the longest chain is the one that +other miners other people will build a + + align:start position:0% +other miners other people will build a + + + align:start position:0% +other miners other people will build a +pod as I understand though it's not + + align:start position:0% +pod as I understand though it's not + + + align:start position:0% +pod as I understand though it's not +written into the base computational code + + align:start position:0% +written into the base computational code + + + align:start position:0% +written into the base computational code +it's really just a consensus that comes + + align:start position:0% +it's really just a consensus that comes + + + align:start position:0% +it's really just a consensus that comes +about this is an example the purple + + align:start position:0% +about this is an example the purple + + + align:start position:0% +about this is an example the purple +block and the black blocks the purple + + align:start position:0% +block and the black blocks the purple + + + align:start position:0% +block and the black blocks the purple +blocks are kind of stale blocks they + + align:start position:0% +blocks are kind of stale blocks they + + + align:start position:0% +blocks are kind of stale blocks they +were mined they were computationally + + align:start position:0% +were mined they were computationally + + + align:start position:0% +were mined they were computationally +solved a proof of work but nobody mined + + align:start position:0% +solved a proof of work but nobody mined + + + align:start position:0% +solved a proof of work but nobody mined +on top of that and if somebody doesn't + + align:start position:0% +on top of that and if somebody doesn't + + + align:start position:0% +on top of that and if somebody doesn't +mind on top of them then eventually + + align:start position:0% +mind on top of them then eventually + + + align:start position:0% +mind on top of them then eventually +they're ignored some people call them + + align:start position:0% +they're ignored some people call them + + + align:start position:0% +they're ignored some people call them +orphan blocks but I'll call them stale + + align:start position:0% +orphan blocks but I'll call them stale + + + align:start position:0% +orphan blocks but I'll call them stale +blocks because they were actually + + align:start position:0% +blocks because they were actually + + + align:start position:0% +blocks because they were actually +created but the information that's in + + align:start position:0% +created but the information that's in + + + align:start position:0% +created but the information that's in +them or is kind of worthless it's not + + align:start position:0% +them or is kind of worthless it's not + + + align:start position:0% +them or is kind of worthless it's not +needed in the actual Bitcoin technology + + align:start position:0% +needed in the actual Bitcoin technology + + + align:start position:0% +needed in the actual Bitcoin technology +this happens from time to time but it + + align:start position:0% +this happens from time to time but it + + + align:start position:0% +this happens from time to time but it +hasn't happened in over a year + + align:start position:0% +hasn't happened in over a year + + + align:start position:0% +hasn't happened in over a year +the technology it's and you can look on + + align:start position:0% +the technology it's and you can look on + + + align:start position:0% +the technology it's and you can look on +various websites to find this out + + align:start position:0% +various websites to find this out + + + align:start position:0% +various websites to find this out +probably at the maximum the longest + + align:start position:0% +probably at the maximum the longest + + + align:start position:0% +probably at the maximum the longest +stale chained get it out to two or three + + align:start position:0% +stale chained get it out to two or three + + + align:start position:0% +stale chained get it out to two or three +blocks but it's very very rare so back + + align:start position:0% +blocks but it's very very rare so back + + + align:start position:0% +blocks but it's very very rare so back +to aliens question of what if China + + align:start position:0% +to aliens question of what if China + + + align:start position:0% +to aliens question of what if China +carved off and and had the presumption + + align:start position:0% +carved off and and had the presumption + + + align:start position:0% +carved off and and had the presumption +it may not work but the presumption is + + align:start position:0% +it may not work but the presumption is + + + align:start position:0% +it may not work but the presumption is +let's say China is the purple blocks + + align:start position:0% +let's say China is the purple blocks + + + align:start position:0% +let's say China is the purple blocks +because China's walled off its entire + + align:start position:0% +because China's walled off its entire + + + align:start position:0% +because China's walled off its entire +network is the presumption is there'll + + align:start position:0% +network is the presumption is there'll + + + align:start position:0% +network is the presumption is there'll +be some communication outside of the + + align:start position:0% +be some communication outside of the + + + align:start position:0% +be some communication outside of the +network it might be on television it + + align:start position:0% +network it might be on television it + + + align:start position:0% +network it might be on television it +might be by by courier that the Chinese + + align:start position:0% +might be by by courier that the Chinese + + + align:start position:0% +might be by by courier that the Chinese +miners would know that they're not in + + align:start position:0% +miners would know that they're not in + + + align:start position:0% +miners would know that they're not in +the majority and they would stop + + align:start position:0% +the majority and they would stop + + + align:start position:0% +the majority and they would stop +expending electricity to even mine in + + align:start position:0% +expending electricity to even mine in + + + align:start position:0% +expending electricity to even mine in +that circumstance because whether it's a + + align:start position:0% +that circumstance because whether it's a + + + align:start position:0% +that circumstance because whether it's a +few hours or a few weeks or a few months + + align:start position:0% +few hours or a few weeks or a few months + + + align:start position:0% +few hours or a few weeks or a few months +they know that their expenditures would + + align:start position:0% +they know that their expenditures would + + + align:start position:0% +they know that their expenditures would +be be worth + + align:start position:0% + + + + align:start position:0% + +Tom still watches porn are the + + align:start position:0% +Tom still watches porn are the + + + align:start position:0% +Tom still watches porn are the +miners receiving bitcoins so in the + + align:start position:0% +miners receiving bitcoins so in the + + + align:start position:0% +miners receiving bitcoins so in the +purple blocks there will be if I can go + + align:start position:0% +purple blocks there will be if I can go + + + align:start position:0% +purple blocks there will be if I can go +back to this there will be a coinbase + + align:start position:0% +back to this there will be a coinbase + + + align:start position:0% +back to this there will be a coinbase +transaction but it will be worthless + + align:start position:0% +transaction but it will be worthless + + + align:start position:0% +transaction but it will be worthless +because it's a coinbase transaction in a + + align:start position:0% +because it's a coinbase transaction in a + + + align:start position:0% +because it's a coinbase transaction in a +block that's not on the main block and + + align:start position:0% +block that's not on the main block and + + + align:start position:0% +block that's not on the main block and +it won't be usable later but in Bitcoin + + align:start position:0% +it won't be usable later but in Bitcoin + + + align:start position:0% +it won't be usable later but in Bitcoin +itself there's software that says you + + align:start position:0% +itself there's software that says you + + + align:start position:0% +itself there's software that says you +cannot use a coin base output for a + + align:start position:0% +cannot use a coin base output for a + + + align:start position:0% +cannot use a coin base output for a +hundred blocks it's written right into + + align:start position:0% +hundred blocks it's written right into + + + align:start position:0% +hundred blocks it's written right into +the base code and it has been since the + + align:start position:0% +the base code and it has been since the + + + align:start position:0% +the base code and it has been since the +beginning let me just go back to the I'm + + align:start position:0% +beginning let me just go back to the I'm + + + align:start position:0% +beginning let me just go back to the I'm +sorry the chain you're saying if the + + align:start position:0% +sorry the chain you're saying if the + + + align:start position:0% +sorry the chain you're saying if the +Tom's question is is what if the purple + + align:start position:0% +Tom's question is is what if the purple + + + align:start position:0% +Tom's question is is what if the purple +side chain goes on for a hundred blocks + + align:start position:0% +side chain goes on for a hundred blocks + + + align:start position:0% +side chain goes on for a hundred blocks +what happens then in fact we have + + align:start position:0% +what happens then in fact we have + + + align:start position:0% +what happens then in fact we have +circumstances of that Bitcoin has split + + align:start position:0% +circumstances of that Bitcoin has split + + + align:start position:0% +circumstances of that Bitcoin has split +between Bitcoin and Bitcoin cash it's + + align:start position:0% +between Bitcoin and Bitcoin cash it's + + + align:start position:0% +between Bitcoin and Bitcoin cash it's +called a hard fork last year and and for + + align:start position:0% +called a hard fork last year and and for + + + align:start position:0% +called a hard fork last year and and for +a moment let's call the purple jay and + + align:start position:0% +a moment let's call the purple jay and + + + align:start position:0% +a moment let's call the purple jay and +Bitcoin cash it's not only going on four + + align:start position:0% +Bitcoin cash it's not only going on four + + + align:start position:0% +Bitcoin cash it's not only going on four +hundred blocks it's now going on for + + align:start position:0% +hundred blocks it's now going on for + + + align:start position:0% +hundred blocks it's now going on for +tens of thousands of blocks it is now + + align:start position:0% +tens of thousands of blocks it is now + + + align:start position:0% +tens of thousands of blocks it is now +its own native currency within that + + align:start position:0% +its own native currency within that + + + align:start position:0% +its own native currency within that +community that purple blockchain is so + + align:start position:0% +community that purple blockchain is so + + + align:start position:0% +community that purple blockchain is so +long now that people have found value in + + align:start position:0% +long now that people have found value in + + + align:start position:0% +long now that people have found value in +that and it is its own native currency + + align:start position:0% +that and it is its own native currency + + + align:start position:0% +that and it is its own native currency +and the reason I share that is + + align:start position:0% +and the reason I share that is + + + align:start position:0% +and the reason I share that is +Tom's question of well what if China was + + align:start position:0% +Tom's question of well what if China was + + + align:start position:0% +Tom's question of well what if China was +walled off so long it's plausible + + align:start position:0% +walled off so long it's plausible + + + align:start position:0% +walled off so long it's plausible +unlikely but plausible that there would + + align:start position:0% +unlikely but plausible that there would + + + align:start position:0% +unlikely but plausible that there would +become some value and call it the + + align:start position:0% +become some value and call it the + + + align:start position:0% +become some value and call it the +Bitcoin China blockchain versus the + + align:start position:0% +Bitcoin China blockchain versus the + + + align:start position:0% +Bitcoin China blockchain versus the +Bitcoin global blockchain there would be + + align:start position:0% +Bitcoin global blockchain there would be + + + align:start position:0% +Bitcoin global blockchain there would be +as what is money but a social consensus + + align:start position:0% + + + + align:start position:0% + +the the question is of the reward I'm + + align:start position:0% +the the question is of the reward I'm + + + align:start position:0% +the the question is of the reward I'm +going to hold a part a part of it for a + + align:start position:0% +going to hold a part a part of it for a + + + align:start position:0% +going to hold a part a part of it for a +little bit when we talk about native + + align:start position:0% +little bit when we talk about native + + + align:start position:0% +little bit when we talk about native +currents see but the reward is in nearly + + align:start position:0% +currents see but the reward is in nearly + + + align:start position:0% +currents see but the reward is in nearly +every blockchain is is a new native + + align:start position:0% +every blockchain is is a new native + + + align:start position:0% +every blockchain is is a new native +currency of that blockchain Bitcoin for + + align:start position:0% +currency of that blockchain Bitcoin for + + + align:start position:0% +currency of that blockchain Bitcoin for +Bitcoin earth or ETH for if the etherium + + align:start position:0% + + + + align:start position:0% + +XRP or for each blockchain there's a + + align:start position:0% +XRP or for each blockchain there's a + + + align:start position:0% +XRP or for each blockchain there's a +native currency who did the second + + align:start position:0% +native currency who did the second + + + align:start position:0% +native currency who did the second +question was who decides it it's + + align:start position:0% +question was who decides it it's + + + align:start position:0% +question was who decides it it's +generally but not always hard programmed + + align:start position:0% +generally but not always hard programmed + + + align:start position:0% +generally but not always hard programmed +into the first release of that to the + + align:start position:0% +into the first release of that to the + + + align:start position:0% +into the first release of that to the +Bitcoin chain does that make the + + align:start position:0% +Bitcoin chain does that make the + + + align:start position:0% +Bitcoin chain does that make the +assumption of the the majority consensus + + align:start position:0% + + + + align:start position:0% + +is if it's shorter does it there's no + + align:start position:0% +is if it's shorter does it there's no + + + align:start position:0% +is if it's shorter does it there's no +there's no about the validity in that in + + align:start position:0% +there's no about the validity in that in + + + align:start position:0% +there's no about the validity in that in +that chain so there's there's two in + + align:start position:0% +that chain so there's there's two in + + + align:start position:0% +that chain so there's there's two in +using this short just as an example + + align:start position:0% +using this short just as an example + + + align:start position:0% +using this short just as an example +there's two ways there was the main + + align:start position:0% +there's two ways there was the main + + + align:start position:0% +there's two ways there was the main +point of this chart was to say that the + + align:start position:0% +point of this chart was to say that the + + + align:start position:0% +point of this chart was to say that the +the black the + + align:start position:0% +the black the + + + align:start position:0% +the black the +black chain is represented in black is + + align:start position:0% +black chain is represented in black is + + + align:start position:0% +black chain is represented in black is +the main chain and that is where the + + align:start position:0% +the main chain and that is where the + + + align:start position:0% +the main chain and that is where the +social consensus will stay that's where + + align:start position:0% +social consensus will stay that's where + + + align:start position:0% +social consensus will stay that's where +the consensus is and generally speaking + + align:start position:0% +the consensus is and generally speaking + + + align:start position:0% +the consensus is and generally speaking +the stale blocks don't mean anything and + + align:start position:0% +the stale blocks don't mean anything and + + + align:start position:0% +the stale blocks don't mean anything and +the steel blocks go away occasionally + + align:start position:0% +the steel blocks go away occasionally + + + align:start position:0% +the steel blocks go away occasionally +there is something called a hard fork + + align:start position:0% +there is something called a hard fork + + + align:start position:0% +there is something called a hard fork +where the social consensus continues to + + align:start position:0% +where the social consensus continues to + + + align:start position:0% +where the social consensus continues to +maintain and I was using this chart as a + + align:start position:0% +maintain and I was using this chart as a + + + align:start position:0% +maintain and I was using this chart as a +rough answer to Tom's earlier question + + align:start position:0% +rough answer to Tom's earlier question + + + align:start position:0% +rough answer to Tom's earlier question +about Bitcoin cash and if the purple + + align:start position:0% +about Bitcoin cash and if the purple + + + align:start position:0% +about Bitcoin cash and if the purple +chain kept going for thousands of blocks + + align:start position:0% +chain kept going for thousands of blocks + + + align:start position:0% +chain kept going for thousands of blocks +and there was a social consensus to keep + + align:start position:0% +and there was a social consensus to keep + + + align:start position:0% +and there was a social consensus to keep +both chains going you'd start to see + + align:start position:0% +both chains going you'd start to see + + + align:start position:0% +both chains going you'd start to see +separate currencies and as you've seen + + align:start position:0% +separate currencies and as you've seen + + + align:start position:0% +separate currencies and as you've seen +with Bitcoin cash does that help so I + + align:start position:0% +with Bitcoin cash does that help so I + + + align:start position:0% +with Bitcoin cash does that help so I +was I was using a graphic to answer a + + align:start position:0% +was I was using a graphic to answer a + + + align:start position:0% +was I was using a graphic to answer a +separate question I'm going to take two + + align:start position:0% +separate question I'm going to take two + + + align:start position:0% +separate question I'm going to take two +more questions and then go to native + + align:start position:0% +more questions and then go to native + + + align:start position:0% +more questions and then go to native +currencies I haven't heard from Daniel + + align:start position:0% +currencies I haven't heard from Daniel + + + align:start position:0% +currencies I haven't heard from Daniel +yet transaction it's not so much void + + align:start position:0% +yet transaction it's not so much void + + + align:start position:0% +yet transaction it's not so much void +it's just it's meaningless it's yes in a + + align:start position:0% +it's just it's meaningless it's yes in a + + + align:start position:0% +it's just it's meaningless it's yes in a +sense of effectively it's void very good + + align:start position:0% +sense of effectively it's void very good + + + align:start position:0% +sense of effectively it's void very good +question the the transactions will still + + align:start position:0% +question the the transactions will still + + + align:start position:0% +question the the transactions will still +be in what's called the memory pool of + + align:start position:0% +be in what's called the memory pool of + + + align:start position:0% +be in what's called the memory pool of +anybody who's mining on the on the main + + align:start position:0% +anybody who's mining on the on the main + + + align:start position:0% +anybody who's mining on the on the main +chain so transactions which we'll talk a + + align:start position:0% +chain so transactions which we'll talk a + + + align:start position:0% +chain so transactions which we'll talk a +lot about on Thursday this coming + + align:start position:0% +lot about on Thursday this coming + + + align:start position:0% +lot about on Thursday this coming +lecture go in through the network + + align:start position:0% +lecture go in through the network + + + align:start position:0% +lecture go in through the network +they're propagated through the network + + align:start position:0% +they're propagated through the network + + + align:start position:0% +they're propagated through the network +to the entire node network and Bitcoin + + align:start position:0% +to the entire node network and Bitcoin + + + align:start position:0% +to the entire node network and Bitcoin +there's about 10,000 nodes and they will + + align:start position:0% +there's about 10,000 nodes and they will + + + align:start position:0% +there's about 10,000 nodes and they will +receive those coins and there's true + + align:start position:0% +receive those coins and there's true + + + align:start position:0% +receive those coins and there's true +those proposed transactions so anything + + align:start position:0% +those proposed transactions so anything + + + align:start position:0% +those proposed transactions so anything +in the purple chain will still be in the + + align:start position:0% +in the purple chain will still be in the + + + align:start position:0% +in the purple chain will still be in the +other chains memory pool one more than + + align:start position:0% +other chains memory pool one more than + + + align:start position:0% +other chains memory pool one more than +I'm going to + + align:start position:0% +I'm going to + + + align:start position:0% +I'm going to +yes yes in the case of the heart foot + + align:start position:0% +yes yes in the case of the heart foot + + + align:start position:0% +yes yes in the case of the heart foot +so between Bitcoin and Bitcoin cash what + + align:start position:0% +so between Bitcoin and Bitcoin cash what + + + align:start position:0% +so between Bitcoin and Bitcoin cash what +are the differences and what about the + + align:start position:0% +are the differences and what about the + + + align:start position:0% +are the differences and what about the +differences in value that's a much + + align:start position:0% +differences in value that's a much + + + align:start position:0% +differences in value that's a much +longer question the question is is what + + align:start position:0% +longer question the question is is what + + + align:start position:0% +longer question the question is is what +are the differences of value between + + align:start position:0% +are the differences of value between + + + align:start position:0% +are the differences of value between +Bitcoin and Bitcoin cash and though I + + align:start position:0% +Bitcoin and Bitcoin cash and though I + + + align:start position:0% +Bitcoin and Bitcoin cash and though I +think bitcoin is trading around sixty + + align:start position:0% +think bitcoin is trading around sixty + + + align:start position:0% +think bitcoin is trading around sixty +three hundred dollars and Bitcoin cash + + align:start position:0% +three hundred dollars and Bitcoin cash + + + align:start position:0% +three hundred dollars and Bitcoin cash +is for thirty four hundred and + + align:start position:0% +is for thirty four hundred and + + + align:start position:0% +is for thirty four hundred and +thirty-five thank you Zann that gives + + align:start position:0% +thirty-five thank you Zann that gives + + + align:start position:0% +thirty-five thank you Zann that gives +you the monetary difference of about + + align:start position:0% +you the monetary difference of about + + + align:start position:0% +you the monetary difference of about +fifteen to one but it would take more + + align:start position:0% +fifteen to one but it would take more + + + align:start position:0% +fifteen to one but it would take more +conversations about why that happened in + + align:start position:0% +conversations about why that happened in + + + align:start position:0% +conversations about why that happened in +background depends and so forth so let + + align:start position:0% +background depends and so forth so let + + + align:start position:0% +background depends and so forth so let +me let me talk about the difficulty + + align:start position:0% +me let me talk about the difficulty + + + align:start position:0% +me let me talk about the difficulty +factor so proof-of-work at least in + + align:start position:0% +factor so proof-of-work at least in + + + align:start position:0% +factor so proof-of-work at least in +bitcoins case has a difficulty factor + + align:start position:0% +bitcoins case has a difficulty factor + + + align:start position:0% +bitcoins case has a difficulty factor +with regard to these leading zeros in + + align:start position:0% +with regard to these leading zeros in + + + align:start position:0% +with regard to these leading zeros in +the hash and Satoshi Nakamoto said let's + + align:start position:0% +the hash and Satoshi Nakamoto said let's + + + align:start position:0% +the hash and Satoshi Nakamoto said let's +change that every 10 minutes let's let's + + align:start position:0% +change that every 10 minutes let's let's + + + align:start position:0% +change that every 10 minutes let's let's +ensure that every block comes on average + + align:start position:0% +ensure that every block comes on average + + + align:start position:0% +ensure that every block comes on average +every 10 minutes and to do that define + + align:start position:0% +every 10 minutes and to do that define + + + align:start position:0% +every 10 minutes and to do that define +how many leading zeros there needs to be + + align:start position:0% +how many leading zeros there needs to be + + + align:start position:0% +how many leading zeros there needs to be +an data just about every two weeks every + + align:start position:0% +an data just about every two weeks every + + + align:start position:0% +an data just about every two weeks every +blockchain can be different it doesn't + + align:start position:0% +blockchain can be different it doesn't + + + align:start position:0% +blockchain can be different it doesn't +have to adjust every two weeks + + align:start position:0% +have to adjust every two weeks + + + align:start position:0% +have to adjust every two weeks +this is just what Bitcoin did this is + + align:start position:0% +this is just what Bitcoin did this is + + + align:start position:0% +this is just what Bitcoin did this is +what Nakamoto did to maintain an average + + align:start position:0% +what Nakamoto did to maintain an average + + + align:start position:0% +what Nakamoto did to maintain an average +of 10 minutes so what what has happened + + align:start position:0% +of 10 minutes so what what has happened + + + align:start position:0% +of 10 minutes so what what has happened +currently it takes 18 leading zeros and + + align:start position:0% +currently it takes 18 leading zeros and + + + align:start position:0% +currently it takes 18 leading zeros and +because this is in a 60 it's in a + + align:start position:0% +because this is in a 60 it's in a + + + align:start position:0% +because this is in a 60 it's in a +hexadecimal character system every + + align:start position:0% +hexadecimal character system every + + + align:start position:0% +hexadecimal character system every +decimal is what's that so it's 2 to the + + align:start position:0% +decimal is what's that so it's 2 to the + + + align:start position:0% +decimal is what's that so it's 2 to the +64 so what a lien just said was that + + align:start position:0% +64 so what a lien just said was that + + + align:start position:0% +64 so what a lien just said was that +it's very small chance of finding a + + align:start position:0% +it's very small chance of finding a + + + align:start position:0% +it's very small chance of finding a +block because this is the equivalent of + + align:start position:0% +block because this is the equivalent of + + + align:start position:0% +block because this is the equivalent of +18 leading zeros so it's more than 64 + + align:start position:0% +18 leading zeros so it's more than 64 + + + align:start position:0% +18 leading zeros so it's more than 64 +it's 18 times for PhD in computer + + align:start position:0% +it's 18 times for PhD in computer + + + align:start position:0% +it's 18 times for PhD in computer +science so this is the most recent block + + align:start position:0% +science so this is the most recent block + + + align:start position:0% +science so this is the most recent block +I grabbed off the blockchain this + + align:start position:0% +I grabbed off the blockchain this + + + align:start position:0% +I grabbed off the blockchain this +morning and it has 18 leading zeros and + + align:start position:0% +morning and it has 18 leading zeros and + + + align:start position:0% +morning and it has 18 leading zeros and +then all those other digits that's block + + align:start position:0% +then all those other digits that's block + + + align:start position:0% +then all those other digits that's block +number 540 1974 18 leading zeros the + + align:start position:0% +number 540 1974 18 leading zeros the + + + align:start position:0% +number 540 1974 18 leading zeros the +Genesis block the very first block in + + align:start position:0% +Genesis block the very first block in + + + align:start position:0% +Genesis block the very first block in +January of 2009 had 10 leading zeros but + + align:start position:0% +January of 2009 had 10 leading zeros but + + + align:start position:0% +January of 2009 had 10 leading zeros but +the requirement that Satoshi Nakamoto + + align:start position:0% +the requirement that Satoshi Nakamoto + + + align:start position:0% +the requirement that Satoshi Nakamoto +actually put into the computer code was + + align:start position:0% +actually put into the computer code was + + + align:start position:0% +actually put into the computer code was +you only needed 8 leading zeros so the + + align:start position:0% +you only needed 8 leading zeros so the + + + align:start position:0% +you only needed 8 leading zeros so the +probabilities have gone way up so let me + + align:start position:0% +probabilities have gone way up so let me + + + align:start position:0% +probabilities have gone way up so let me +take it off of a fancy you know numbers + + align:start position:0% +take it off of a fancy you know numbers + + + align:start position:0% +take it off of a fancy you know numbers +like that and just say this is the + + align:start position:0% +like that and just say this is the + + + align:start position:0% +like that and just say this is the +actual Bitcoin mining difficulties on a + + align:start position:0% +actual Bitcoin mining difficulties on a + + + align:start position:0% +actual Bitcoin mining difficulties on a +logarithmic scale because if it weren't + + align:start position:0% +logarithmic scale because if it weren't + + + align:start position:0% +logarithmic scale because if it weren't +logarithmic you couldn't really read it + + align:start position:0% +logarithmic you couldn't really read it + + + align:start position:0% +logarithmic you couldn't really read it +the difficulty was set at 1 this is all + + align:start position:0% +the difficulty was set at 1 this is all + + + align:start position:0% +the difficulty was set at 1 this is all +scaled to how difficult was it for the + + align:start position:0% +scaled to how difficult was it for the + + + align:start position:0% +scaled to how difficult was it for the +first year and a half of mining in 2009 + + align:start position:0% +first year and a half of mining in 2009 + + + align:start position:0% +first year and a half of mining in 2009 +and early 2010 won and now it is at 1 + + align:start position:0% +and early 2010 won and now it is at 1 + + + align:start position:0% +and early 2010 won and now it is at 1 +trillion it's actually more than 1 + + align:start position:0% +trillion it's actually more than 1 + + + align:start position:0% +trillion it's actually more than 1 +trillion because it's logarithmic it's + + align:start position:0% +trillion because it's logarithmic it's + + + align:start position:0% +trillion because it's logarithmic it's +at about 7 trillion + + align:start position:0% +at about 7 trillion + + + align:start position:0% +at about 7 trillion +it is currently 7 trillion times harder + + align:start position:0% +it is currently 7 trillion times harder + + + align:start position:0% +it is currently 7 trillion times harder +to find the answer to the puzzle than it + + align:start position:0% +to find the answer to the puzzle than it + + + align:start position:0% +to find the answer to the puzzle than it +was in 2009 + + align:start position:0% + + + + align:start position:0% + +and that's because there's a lot of + + align:start position:0% +and that's because there's a lot of + + + align:start position:0% +and that's because there's a lot of +computers trying to hash all of this + + align:start position:0% +computers trying to hash all of this + + + align:start position:0% +computers trying to hash all of this +stuff correct and the hash rate is now + + align:start position:0% +stuff correct and the hash rate is now + + + align:start position:0% +stuff correct and the hash rate is now +somewhere around 50 it's not Tara hashes + + align:start position:0% +somewhere around 50 it's not Tara hashes + + + align:start position:0% +somewhere around 50 it's not Tara hashes +I'm trying to remember what what's that + + align:start position:0% +I'm trying to remember what what's that + + + align:start position:0% +I'm trying to remember what what's that +50 hexa hash per second which is like a + + align:start position:0% +50 hexa hash per second which is like a + + + align:start position:0% +50 hexa hash per second which is like a +thousand trillion hashes because a Tara + + align:start position:0% +thousand trillion hashes because a Tara + + + align:start position:0% +thousand trillion hashes because a Tara +hashes a trillion hashes Dan I think + + align:start position:0% +hashes a trillion hashes Dan I think + + + align:start position:0% +hashes a trillion hashes Dan I think +it's worth noting though it didn't scale + + align:start position:0% +it's worth noting though it didn't scale + + + align:start position:0% +it's worth noting though it didn't scale +linearly as like number of computers got + + align:start position:0% +linearly as like number of computers got + + + align:start position:0% +linearly as like number of computers got +on the network it's also the hardware + + align:start position:0% +on the network it's also the hardware + + + align:start position:0% +on the network it's also the hardware +has gotten incredibly more sophisticated + + align:start position:0% +has gotten incredibly more sophisticated + + + align:start position:0% +has gotten incredibly more sophisticated +so it's not that you can just assume + + align:start position:0% +so it's not that you can just assume + + + align:start position:0% +so it's not that you can just assume +there's you know fifteen trillion number + + align:start position:0% +there's you know fifteen trillion number + + + align:start position:0% +there's you know fifteen trillion number +of people that are mining Bitcoin it's + + align:start position:0% +of people that are mining Bitcoin it's + + + align:start position:0% +of people that are mining Bitcoin it's +just the same people that are doing it + + align:start position:0% +just the same people that are doing it + + + align:start position:0% +just the same people that are doing it +better I can't ask for a better setup + + align:start position:0% +better I can't ask for a better setup + + + align:start position:0% +better I can't ask for a better setup +than that + + align:start position:0% +than that + + + align:start position:0% +than that +Bitcoin mining evolution did you did you + + align:start position:0% +Bitcoin mining evolution did you did you + + + align:start position:0% +Bitcoin mining evolution did you did you +see my slides you know so what what's + + align:start position:0% +see my slides you know so what what's + + + align:start position:0% +see my slides you know so what what's +the evolution so it started with central + + align:start position:0% +the evolution so it started with central + + + align:start position:0% +the evolution so it started with central +processing units and CPUs and I'm not + + align:start position:0% +processing units and CPUs and I'm not + + + align:start position:0% +processing units and CPUs and I'm not +sure my numbers are accurate because I + + align:start position:0% +sure my numbers are accurate because I + + + align:start position:0% +sure my numbers are accurate because I +might be using CPU power today and not + + align:start position:0% +might be using CPU power today and not + + + align:start position:0% +might be using CPU power today and not +CPU power in 2009 apologies for those + + align:start position:0% +CPU power in 2009 apologies for those + + + align:start position:0% +CPU power in 2009 apologies for those +who know CPU power better than mine you + + align:start position:0% +who know CPU power better than mine you + + + align:start position:0% +who know CPU power better than mine you +could do about 2 to 20 million hashes a + + align:start position:0% +could do about 2 to 20 million hashes a + + + align:start position:0% +could do about 2 to 20 million hashes a +second on a CPU properly geared + + align:start position:0% +second on a CPU properly geared + + + align:start position:0% +second on a CPU properly geared +apparently they didn't last that long + + align:start position:0% +apparently they didn't last that long + + + align:start position:0% +apparently they didn't last that long +by 2010 some folks figured out there was + + align:start position:0% +by 2010 some folks figured out there was + + + align:start position:0% +by 2010 some folks figured out there was +something faster and it's caught a + + align:start position:0% +something faster and it's caught a + + + align:start position:0% +something faster and it's caught a +graphics processing unit we all use GPUs + + align:start position:0% +graphics processing unit we all use GPUs + + + align:start position:0% +graphics processing unit we all use GPUs +all day long because that's what gives + + align:start position:0% +all day long because that's what gives + + + align:start position:0% +all day long because that's what gives +us all our quick graphics if you + + align:start position:0% +us all our quick graphics if you + + + align:start position:0% +us all our quick graphics if you +livestream something that one your + + align:start position:0% +livestream something that one your + + + align:start position:0% +livestream something that one your +laptop and graphics processing units + + align:start position:0% +laptop and graphics processing units + + + align:start position:0% +laptop and graphics processing units +somebody figure it out + + align:start position:0% +somebody figure it out + + + align:start position:0% +somebody figure it out +you can use that and you could hash + + align:start position:0% +you can use that and you could hash + + + align:start position:0% +you can use that and you could hash +faster and then all of a sudden + + align:start position:0% +faster and then all of a sudden + + + align:start position:0% +faster and then all of a sudden +hobbyists started to wire the GPUs + + align:start position:0% +hobbyists started to wire the GPUs + + + align:start position:0% +hobbyists started to wire the GPUs +together and they could figure out a way + + align:start position:0% +together and they could figure out a way + + + align:start position:0% +together and they could figure out a way +to get between 20 million hashes to 300 + + align:start position:0% +to get between 20 million hashes to 300 + + + align:start position:0% +to get between 20 million hashes to 300 +million hashes a second I'm told that + + align:start position:0% +million hashes a second I'm told that + + + align:start position:0% +million hashes a second I'm told that +even today you could maybe get up closer + + align:start position:0% +even today you could maybe get up closer + + + align:start position:0% +even today you could maybe get up closer +to a thousand million hashes a second or + + align:start position:0% +to a thousand million hashes a second or + + + align:start position:0% +to a thousand million hashes a second or +a billion hash as a second if you did a + + align:start position:0% +a billion hash as a second if you did a + + + align:start position:0% +a billion hash as a second if you did a +GPU rig but that's yesteryear or Bitcoin + + align:start position:0% +GPU rig but that's yesteryear or Bitcoin + + + align:start position:0% +GPU rig but that's yesteryear or Bitcoin +now there's something called an + + align:start position:0% +now there's something called an + + + align:start position:0% +now there's something called an +application-specific integrated circuit + + align:start position:0% +application-specific integrated circuit + + + align:start position:0% +application-specific integrated circuit +an ASIC just think about a circuit that + + align:start position:0% +an ASIC just think about a circuit that + + + align:start position:0% +an ASIC just think about a circuit that +the only thing the circuit does is + + align:start position:0% +the only thing the circuit does is + + + align:start position:0% +the only thing the circuit does is +create hashes in fact the circuit is + + align:start position:0% +create hashes in fact the circuit is + + + align:start position:0% +create hashes in fact the circuit is +wired I use the word wired because I'm + + align:start position:0% +wired I use the word wired because I'm + + + align:start position:0% +wired I use the word wired because I'm +old enough to remember wires but it's + + align:start position:0% +old enough to remember wires but it's + + + align:start position:0% +old enough to remember wires but it's +the circuit board is manufactured in a + + align:start position:0% +the circuit board is manufactured in a + + + align:start position:0% +the circuit board is manufactured in a +way that all it does is the sha-256 hash + + align:start position:0% +way that all it does is the sha-256 hash + + + align:start position:0% +way that all it does is the sha-256 hash +function to Bitcoin mine and the first + + align:start position:0% +function to Bitcoin mine and the first + + + align:start position:0% +function to Bitcoin mine and the first +Asics which are dedicated circuit boards + + align:start position:0% +Asics which are dedicated circuit boards + + + align:start position:0% +Asics which are dedicated circuit boards +to do this mining came out in 2013 and + + align:start position:0% +to do this mining came out in 2013 and + + + align:start position:0% +to do this mining came out in 2013 and +even since then they have moved up the + + align:start position:0% +even since then they have moved up the + + + align:start position:0% +even since then they have moved up the +scale the most expensive that sells for + + align:start position:0% +scale the most expensive that sells for + + + align:start position:0% +scale the most expensive that sells for +about three or four thousand dollars an + + align:start position:0% +about three or four thousand dollars an + + + align:start position:0% +about three or four thousand dollars an +ASIC can do sixteen tera hashes per + + align:start position:0% +ASIC can do sixteen tera hashes per + + + align:start position:0% +ASIC can do sixteen tera hashes per +second or at least that's what it's + + align:start position:0% +second or at least that's what it's + + + align:start position:0% +second or at least that's what it's +rated for if you go on Amazon and try to + + align:start position:0% +rated for if you go on Amazon and try to + + + align:start position:0% +rated for if you go on Amazon and try to +buy it and you can do that but you'd be + + align:start position:0% +buy it and you can do that but you'd be + + + align:start position:0% +buy it and you can do that but you'd be +competing with something like that looks + + align:start position:0% +competing with something like that looks + + + align:start position:0% +competing with something like that looks +like this a modern map mining factory + + align:start position:0% +like this a modern map mining factory + + + align:start position:0% +like this a modern map mining factory +for Bitcoin has thousands of a six they + + align:start position:0% +for Bitcoin has thousands of a six they + + + align:start position:0% +for Bitcoin has thousands of a six they +have water cooling systems to keep it + + align:start position:0% +have water cooling systems to keep it + + + align:start position:0% +have water cooling systems to keep it +cooled down and they're probably buying + + align:start position:0% +cooled down and they're probably buying + + + align:start position:0% +cooled down and they're probably buying +their electricity for less than three + + align:start position:0% +their electricity for less than three + + + align:start position:0% +their electricity for less than three +kilowatts a three cents per kilowatt and + + align:start position:0% +kilowatts a three cents per kilowatt and + + + align:start position:0% +kilowatts a three cents per kilowatt and +they might even be paying off the local + + align:start position:0% +they might even be paying off the local + + + align:start position:0% +they might even be paying off the local +government officials and not even paying + + align:start position:0% +government officials and not even paying + + + align:start position:0% +government officials and not even paying +the electricity company and just bribing + + align:start position:0% +the electricity company and just bribing + + + align:start position:0% +the electricity company and just bribing +to get their electricity Emily like is + + align:start position:0% +to get their electricity Emily like is + + + align:start position:0% +to get their electricity Emily like is +there a more efficient allocation + + align:start position:0% + + + + align:start position:0% + +there are certainly trade-offs here and + + align:start position:0% +there are certainly trade-offs here and + + + align:start position:0% +there are certainly trade-offs here and +and the aggregate electricity for all of + + align:start position:0% +and the aggregate electricity for all of + + + align:start position:0% +and the aggregate electricity for all of +Bitcoin mining now that it's seven + + align:start position:0% +Bitcoin mining now that it's seven + + + align:start position:0% +Bitcoin mining now that it's seven +trillion times harder than it was in + + align:start position:0% +trillion times harder than it was in + + + align:start position:0% +trillion times harder than it was in +2009 has been compared to the + + align:start position:0% +2009 has been compared to the + + + align:start position:0% +2009 has been compared to the +electricity use of countries like + + align:start position:0% +electricity use of countries like + + + align:start position:0% +electricity use of countries like +Ireland on the way to they electricity + + align:start position:0% +Ireland on the way to they electricity + + + align:start position:0% +Ireland on the way to they electricity +use of countries like Denmark I think + + align:start position:0% +use of countries like Denmark I think + + + align:start position:0% +use of countries like Denmark I think +it's somewhere between Ireland and + + align:start position:0% +it's somewhere between Ireland and + + + align:start position:0% +it's somewhere between Ireland and +Denmark Larry the reward is in bitcoins + + align:start position:0% +Denmark Larry the reward is in bitcoins + + + align:start position:0% +Denmark Larry the reward is in bitcoins +volatility of Bitcoin makes it hard to + + align:start position:0% +volatility of Bitcoin makes it hard to + + + align:start position:0% +volatility of Bitcoin makes it hard to +answer that question because you don't + + align:start position:0% +answer that question because you don't + + + align:start position:0% +answer that question because you don't +know if there's an autonomic value for + + align:start position:0% +know if there's an autonomic value for + + + align:start position:0% +know if there's an autonomic value for +you so I I said in our first class I'm + + align:start position:0% +you so I I said in our first class I'm + + + align:start position:0% +you so I I said in our first class I'm +neither blockchain maximalist or + + align:start position:0% +neither blockchain maximalist or + + + align:start position:0% +neither blockchain maximalist or +blockchain minimalist and you all will + + align:start position:0% +blockchain minimalist and you all will + + + align:start position:0% +blockchain minimalist and you all will +have a chance through this course to + + align:start position:0% +have a chance through this course to + + + align:start position:0% +have a chance through this course to +form your own views but one of the + + align:start position:0% +form your own views but one of the + + + align:start position:0% +form your own views but one of the +debates is all right Emily's to pay is + + align:start position:0% +debates is all right Emily's to pay is + + + align:start position:0% +debates is all right Emily's to pay is +this a good use of economic a good use + + align:start position:0% +this a good use of economic a good use + + + align:start position:0% +this a good use of economic a good use +of resources but I would note that all + + align:start position:0% + + + + align:start position:0% + +strong currencies strong monies for + + align:start position:0% +strong currencies strong monies for + + + align:start position:0% +strong currencies strong monies for +centuries have had something to limit + + align:start position:0% +centuries have had something to limit + + + align:start position:0% +centuries have had something to limit +the supply and so now we're doing it + + align:start position:0% +the supply and so now we're doing it + + + align:start position:0% +the supply and so now we're doing it +electronically and through this mining + + align:start position:0% +electronically and through this mining + + + align:start position:0% +electronically and through this mining +it doesn't mean it's the best use I'm + + align:start position:0% +it doesn't mean it's the best use I'm + + + align:start position:0% +it doesn't mean it's the best use I'm +just saying it's another way so + + align:start position:0% +just saying it's another way so + + + align:start position:0% +just saying it's another way so +extracting gold out of the ground is + + align:start position:0% +extracting gold out of the ground is + + + align:start position:0% +extracting gold out of the ground is +very hard and in the 19th century to + + align:start position:0% +very hard and in the 19th century to + + + align:start position:0% +very hard and in the 19th century to +have big vault doors and and and + + align:start position:0% +have big vault doors and and and + + + align:start position:0% +have big vault doors and and and +security guards with rifles was a way to + + align:start position:0% +security guards with rifles was a way to + + + align:start position:0% +security guards with rifles was a way to +ensure it and one could even say that + + align:start position:0% +ensure it and one could even say that + + + align:start position:0% +ensure it and one could even say that +having central banks takes cost so I + + align:start position:0% +having central banks takes cost so I + + + align:start position:0% +having central banks takes cost so I +think of it as is a trade-off of how you + + align:start position:0% +think of it as is a trade-off of how you + + + align:start position:0% +think of it as is a trade-off of how you +ensure a currency is a hard or currency + + align:start position:0% +ensure a currency is a hard or currency + + + align:start position:0% +ensure a currency is a hard or currency +to to create but it doesn't mean that + + align:start position:0% +to to create but it doesn't mean that + + + align:start position:0% +to to create but it doesn't mean that +proof of work is the best way which is + + align:start position:0% +proof of work is the best way which is + + + align:start position:0% +proof of work is the best way which is +of course then the set up to + + align:start position:0% + + + + align:start position:0% + +the question of are there other ways to + + align:start position:0% +the question of are there other ways to + + + align:start position:0% +the question of are there other ways to +do consensus so one other thing is all + + align:start position:0% +do consensus so one other thing is all + + + align:start position:0% +do consensus so one other thing is all +of this hashing how is it distributed + + align:start position:0% +of this hashing how is it distributed + + + align:start position:0% +of this hashing how is it distributed +and this I pulled off the internet this + + align:start position:0% +and this I pulled off the internet this + + + align:start position:0% +and this I pulled off the internet this +morning you can see these statistics + + align:start position:0% +morning you can see these statistics + + + align:start position:0% +morning you can see these statistics +every day proof of work and mining has + + align:start position:0% + + + + align:start position:0% + +formed mining pools and these mining + + align:start position:0% +formed mining pools and these mining + + + align:start position:0% +formed mining pools and these mining +pools come together for a simple + + align:start position:0% +pools come together for a simple + + + align:start position:0% +pools come together for a simple +economic reason that it's so unlikely to + + align:start position:0% +economic reason that it's so unlikely to + + + align:start position:0% +economic reason that it's so unlikely to +solve the riddle solve the puzzle of + + align:start position:0% +solve the riddle solve the puzzle of + + + align:start position:0% +solve the riddle solve the puzzle of +mining that if you can only solve it + + align:start position:0% +mining that if you can only solve it + + + align:start position:0% +mining that if you can only solve it +once a year or maybe even once every 10 + + align:start position:0% +once a year or maybe even once every 10 + + + align:start position:0% +once a year or maybe even once every 10 +years you weren't going to invest in + + align:start position:0% +years you weren't going to invest in + + + align:start position:0% +years you weren't going to invest in +mining so mining pools started around + + align:start position:0% +mining so mining pools started around + + + align:start position:0% +mining so mining pools started around +2010 to smooth out the revenue so if + + align:start position:0% +2010 to smooth out the revenue so if + + + align:start position:0% +2010 to smooth out the revenue so if +Amanda doesn't want to get it once every + + align:start position:0% +Amanda doesn't want to get it once every + + + align:start position:0% +Amanda doesn't want to get it once every +10 years she might say well why doesn't + + align:start position:0% +10 years she might say well why doesn't + + + align:start position:0% +10 years she might say well why doesn't +all the 80 people in this room you might + + align:start position:0% +all the 80 people in this room you might + + + align:start position:0% +all the 80 people in this room you might +Amanda I don't know say why don't we all + + align:start position:0% +Amanda I don't know say why don't we all + + + align:start position:0% +Amanda I don't know say why don't we all +form a pool and we'll are going to use + + align:start position:0% +form a pool and we'll are going to use + + + align:start position:0% +form a pool and we'll are going to use +our laptops and now this is still 2009 + + align:start position:0% +our laptops and now this is still 2009 + + + align:start position:0% +our laptops and now this is still 2009 +or 2010 when you could mined Bitcoin on + + align:start position:0% +or 2010 when you could mined Bitcoin on + + + align:start position:0% +or 2010 when you could mined Bitcoin on +your laptop but we could say why don't + + align:start position:0% +your laptop but we could say why don't + + + align:start position:0% +your laptop but we could say why don't +we all do that together and then all of + + align:start position:0% +we all do that together and then all of + + + align:start position:0% +we all do that together and then all of +us could say well Amanda that's a great + + align:start position:0% +us could say well Amanda that's a great + + + align:start position:0% +us could say well Amanda that's a great +idea but could you create the the the + + align:start position:0% +idea but could you create the the the + + + align:start position:0% +idea but could you create the the the +Merkel route for us could you do some + + align:start position:0% +Merkel route for us could you do some + + + align:start position:0% +Merkel route for us could you do some +other things so that our computer + + align:start position:0% +other things so that our computer + + + align:start position:0% +other things so that our computer +doesn't have to do all that other fancy + + align:start position:0% +doesn't have to do all that other fancy + + + align:start position:0% +doesn't have to do all that other fancy +stuff so then Amanda might say well I + + align:start position:0% +stuff so then Amanda might say well I + + + align:start position:0% +stuff so then Amanda might say well I +want to charge all of you a little bit + + align:start position:0% +want to charge all of you a little bit + + + align:start position:0% +want to charge all of you a little bit +how about if I charge you 1% of the they + + align:start position:0% +how about if I charge you 1% of the they + + + align:start position:0% +how about if I charge you 1% of the they +take and Amanda would call herself a + + align:start position:0% +take and Amanda would call herself a + + + align:start position:0% +take and Amanda would call herself a +mining pool operator that's what's + + align:start position:0% +mining pool operator that's what's + + + align:start position:0% +mining pool operator that's what's +happened is basically the economics of + + align:start position:0% +happened is basically the economics of + + + align:start position:0% +happened is basically the economics of +mining have clumped around mining pool + + align:start position:0% +mining have clumped around mining pool + + + align:start position:0% +mining have clumped around mining pool +operators and the standard fees range + + align:start position:0% +operators and the standard fees range + + + align:start position:0% +operators and the standard fees range +from 1 to 3% that the mining pool + + align:start position:0% +from 1 to 3% that the mining pool + + + align:start position:0% +from 1 to 3% that the mining pool +operator provides a number of services + + align:start position:0% +operator provides a number of services + + + align:start position:0% +operator provides a number of services +to the miners themselves and those + + align:start position:0% +to the miners themselves and those + + + align:start position:0% +to the miners themselves and those +services are compensated as I say + + align:start position:0% +services are compensated as I say + + + align:start position:0% +services are compensated as I say +somewhere between 1 and 3% + + align:start position:0% +somewhere between 1 and 3% + + + align:start position:0% +somewhere between 1 and 3% +of their returns but mostly it smoothes + + align:start position:0% +of their returns but mostly it smoothes + + + align:start position:0% +of their returns but mostly it smoothes +out the economics for all the miners it + + align:start position:0% +out the economics for all the miners it + + + align:start position:0% +out the economics for all the miners it +does some other things as well but + + align:start position:0% +does some other things as well but + + + align:start position:0% +does some other things as well but +that's the primary and the cost of the + + align:start position:0% +that's the primary and the cost of the + + + align:start position:0% +that's the primary and the cost of the +electrode it's a breaking but the + + align:start position:0% +electrode it's a breaking but the + + + align:start position:0% +electrode it's a breaking but the +break-even point has actually becoming + + align:start position:0% +break-even point has actually becoming + + + align:start position:0% +break-even point has actually becoming +odd lower lower electricity cost so with + + align:start position:0% +odd lower lower electricity cost so with + + + align:start position:0% +odd lower lower electricity cost so with +that in mind over the next couple of + + align:start position:0% +that in mind over the next couple of + + + align:start position:0% +that in mind over the next couple of +years if that's the case people will + + align:start position:0% +years if that's the case people will + + + align:start position:0% +years if that's the case people will +start to lose incentive and keep doing + + align:start position:0% +start to lose incentive and keep doing + + + align:start position:0% +start to lose incentive and keep doing +the mining + + align:start position:0% +the mining + + + align:start position:0% +the mining +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +well it could go either way + + align:start position:0% +well it could go either way + + + align:start position:0% +well it could go either way +as we said just Bitcoin this is Bitcoin + + align:start position:0% +as we said just Bitcoin this is Bitcoin + + + align:start position:0% +as we said just Bitcoin this is Bitcoin +adjusts the difficulty of mining every + + align:start position:0% +adjusts the difficulty of mining every + + + align:start position:0% +adjusts the difficulty of mining every +two weeks so if there's fewer people + + align:start position:0% +two weeks so if there's fewer people + + + align:start position:0% +two weeks so if there's fewer people +mining the difficulty will go down and + + align:start position:0% +mining the difficulty will go down and + + + align:start position:0% +mining the difficulty will go down and +if you remember I said you have to have + + align:start position:0% +if you remember I said you have to have + + + align:start position:0% +if you remember I said you have to have +18 leading zeros it might go back to 17 + + align:start position:0% +18 leading zeros it might go back to 17 + + + align:start position:0% +18 leading zeros it might go back to 17 +leading zeros or 16 leading zeros and + + align:start position:0% +leading zeros or 16 leading zeros and + + + align:start position:0% +leading zeros or 16 leading zeros and +every two weeks it adjusts based upon + + align:start position:0% +every two weeks it adjusts based upon + + + align:start position:0% +every two weeks it adjusts based upon +the prior 2016 blocks did it average 10 + + align:start position:0% +the prior 2016 blocks did it average 10 + + + align:start position:0% +the prior 2016 blocks did it average 10 +minutes if it averaged for instance 14 + + align:start position:0% +minutes if it averaged for instance 14 + + + align:start position:0% +minutes if it averaged for instance 14 +minutes then it will lower the + + align:start position:0% +minutes then it will lower the + + + align:start position:0% +minutes then it will lower the +difficulty if it averages 6 minutes it + + align:start position:0% +difficulty if it averages 6 minutes it + + + align:start position:0% +difficulty if it averages 6 minutes it +will increase the difficulty + + align:start position:0% + + + + align:start position:0% + +so Kelly is asking whether this is where + + align:start position:0% +so Kelly is asking whether this is where + + + align:start position:0% +so Kelly is asking whether this is where +proof of steak comes in what is proof of + + align:start position:0% +proof of steak comes in what is proof of + + + align:start position:0% +proof of steak comes in what is proof of +steak anybody who read the coin desk + + align:start position:0% +steak anybody who read the coin desk + + + align:start position:0% +steak anybody who read the coin desk +article see when you hide your first + + align:start position:0% +article see when you hide your first + + + align:start position:0% +article see when you hide your first +name I can just call you US air force + + align:start position:0% +name I can just call you US air force + + + align:start position:0% +name I can just call you US air force +it's true Bo's Bo's name card says US + + align:start position:0% +it's true Bo's Bo's name card says US + + + align:start position:0% +it's true Bo's Bo's name card says US +Air Force that's so pretty steak is the + + align:start position:0% +Air Force that's so pretty steak is the + + + align:start position:0% +Air Force that's so pretty steak is the +coins all the coins are dispersed so + + align:start position:0% +coins all the coins are dispersed so + + + align:start position:0% +coins all the coins are dispersed so +proof of steak is an alternative + + align:start position:0% +proof of steak is an alternative + + + align:start position:0% +proof of steak is an alternative +consensus mechanism and Bo described it + + align:start position:0% +consensus mechanism and Bo described it + + + align:start position:0% +consensus mechanism and Bo described it +well but Kelly it's not related to this + + align:start position:0% +well but Kelly it's not related to this + + + align:start position:0% +well but Kelly it's not related to this +chart here this is all proof of work BTC + + align:start position:0% +chart here this is all proof of work BTC + + + align:start position:0% +chart here this is all proof of work BTC +has 19% of the hash rate that that means + + align:start position:0% +has 19% of the hash rate that that means + + + align:start position:0% +has 19% of the hash rate that that means +that they literally have about if the + + align:start position:0% +that they literally have about if the + + + align:start position:0% +that they literally have about if the +total hash power on Bitcoin is 60 hexa + + align:start position:0% +total hash power on Bitcoin is 60 hexa + + + align:start position:0% +total hash power on Bitcoin is 60 hexa +do I have this word hexa hash then 19 + + align:start position:0% +do I have this word hexa hash then 19 + + + align:start position:0% +do I have this word hexa hash then 19 +percent of that are about 12 correct + + align:start position:0% +percent of that are about 12 correct + + + align:start position:0% +percent of that are about 12 correct +most Bitcoin miners sell their coins so + + align:start position:0% +most Bitcoin miners sell their coins so + + + align:start position:0% +most Bitcoin miners sell their coins so +the the coins that are created the the + + align:start position:0% +the the coins that are created the the + + + align:start position:0% +the the coins that are created the the +coins that are created each year are + + align:start position:0% +coins that are created each year are + + + align:start position:0% +coins that are created each year are +sold into the broad community very few + + align:start position:0% +sold into the broad community very few + + + align:start position:0% +sold into the broad community very few +miners hold on to their coins for great + + align:start position:0% +miners hold on to their coins for great + + + align:start position:0% +miners hold on to their coins for great +lengths of time I mean they might for + + align:start position:0% +lengths of time I mean they might for + + + align:start position:0% +lengths of time I mean they might for +days then wait for they might keep some + + align:start position:0% +days then wait for they might keep some + + + align:start position:0% +days then wait for they might keep some +for all sorts of reasons and as I truly + + align:start position:0% +for all sorts of reasons and as I truly + + + align:start position:0% +for all sorts of reasons and as I truly +believe but can't factually prove a + + align:start position:0% +believe but can't factually prove a + + + align:start position:0% +believe but can't factually prove a +number of the biggest mining pools or + + align:start position:0% +number of the biggest mining pools or + + + align:start position:0% +number of the biggest mining pools or +miners are in places where they're doing + + align:start position:0% +miners are in places where they're doing + + + align:start position:0% +miners are in places where they're doing +illicit activity they're getting their + + align:start position:0% +illicit activity they're getting their + + + align:start position:0% +illicit activity they're getting their +electricity for less than what it's + + align:start position:0% +electricity for less than what it's + + + align:start position:0% +electricity for less than what it's +really costing on the grid by bad act + + align:start position:0% +really costing on the grid by bad act + + + align:start position:0% +really costing on the grid by bad act +actor but nonetheless they they have a + + align:start position:0% +actor but nonetheless they they have a + + + align:start position:0% +actor but nonetheless they they have a +choice whether to sell their coins or + + align:start position:0% +choice whether to sell their coins or + + + align:start position:0% +choice whether to sell their coins or +keep their coins + + align:start position:0% +keep their coins + + + align:start position:0% +keep their coins +question over here and then I want to + + align:start position:0% +question over here and then I want to + + + align:start position:0% +question over here and then I want to +keep going if the mining industry is + + align:start position:0% +keep going if the mining industry is + + + align:start position:0% +keep going if the mining industry is +like so formalized like you've got so + + align:start position:0% +like so formalized like you've got so + + + align:start position:0% +like so formalized like you've got so +many foods what prevents all the foods + + align:start position:0% +many foods what prevents all the foods + + + align:start position:0% +many foods what prevents all the foods +from coming together and saying that + + align:start position:0% +from coming together and saying that + + + align:start position:0% +from coming together and saying that +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +becomes lower and then the charges must + + align:start position:0% +becomes lower and then the charges must + + + align:start position:0% +becomes lower and then the charges must +not reach in everyone so the question is + + align:start position:0% +not reach in everyone so the question is + + + align:start position:0% +not reach in everyone so the question is +is is what happens if the mining poles + + align:start position:0% +is is what happens if the mining poles + + + align:start position:0% +is is what happens if the mining poles +collude and come together either as a G + + align:start position:0% +collude and come together either as a G + + + align:start position:0% +collude and come together either as a G +DM says to let's say well why should we + + align:start position:0% +DM says to let's say well why should we + + + align:start position:0% +DM says to let's say well why should we +have so much mining capacity + + align:start position:0% +have so much mining capacity + + + align:start position:0% +have so much mining capacity +let's as a cartel like OPEC the oil + + align:start position:0% +let's as a cartel like OPEC the oil + + + align:start position:0% +let's as a cartel like OPEC the oil +cartel say we should constrain supply + + align:start position:0% +cartel say we should constrain supply + + + align:start position:0% +cartel say we should constrain supply +and and so forth I think what can + + align:start position:0% +and and so forth I think what can + + + align:start position:0% +and and so forth I think what can +constrains that is is it's an open + + align:start position:0% +constrains that is is it's an open + + + align:start position:0% +constrains that is is it's an open +system but it's possible it's plausible + + align:start position:0% +system but it's possible it's plausible + + + align:start position:0% +system but it's possible it's plausible +I think the bigger question and there's + + align:start position:0% +I think the bigger question and there's + + + align:start position:0% +I think the bigger question and there's +been a numerous Eckener murus academic + + align:start position:0% +been a numerous Eckener murus academic + + + align:start position:0% +been a numerous Eckener murus academic +papers around this is what happens if + + align:start position:0% +papers around this is what happens if + + + align:start position:0% +papers around this is what happens if +the mining pools come together and try + + align:start position:0% +the mining pools come together and try + + + align:start position:0% +the mining pools come together and try +to do what's called a 51% attack and try + + align:start position:0% +to do what's called a 51% attack and try + + + align:start position:0% +to do what's called a 51% attack and try +to take over the blockchain and that's a + + align:start position:0% +to take over the blockchain and that's a + + + align:start position:0% +to take over the blockchain and that's a +more interesting challenge and and we'll + + align:start position:0% +more interesting challenge and and we'll + + + align:start position:0% +more interesting challenge and and we'll +talk about that throughout this semester + + align:start position:0% +talk about that throughout this semester + + + align:start position:0% +talk about that throughout this semester +it hasn't happened as of yet let me talk + + align:start position:0% +it hasn't happened as of yet let me talk + + + align:start position:0% +it hasn't happened as of yet let me talk +about the native currencies native + + align:start position:0% +about the native currencies native + + + align:start position:0% +about the native currencies native +currency helps do all this what's + + align:start position:0% +currency helps do all this what's + + + align:start position:0% +currency helps do all this what's +Nakamoto said is it was an incentive + + align:start position:0% +Nakamoto said is it was an incentive + + + align:start position:0% +Nakamoto said is it was an incentive +system it was an incentive system but it + + align:start position:0% +system it was an incentive system but it + + + align:start position:0% +system it was an incentive system but it +was also a peer-to-peer way to create a + + align:start position:0% +was also a peer-to-peer way to create a + + + align:start position:0% +was also a peer-to-peer way to create a +new money and embedded in most + + align:start position:0% +new money and embedded in most + + + align:start position:0% +new money and embedded in most +blockchains not a hundred percent of + + align:start position:0% +blockchains not a hundred percent of + + + align:start position:0% +blockchains not a hundred percent of +them there is something I put quotes + + align:start position:0% +them there is something I put quotes + + + align:start position:0% +them there is something I put quotes +around it monetary policy in essence + + align:start position:0% +around it monetary policy in essence + + + align:start position:0% +around it monetary policy in essence +that limits the supply of the currency + + align:start position:0% +that limits the supply of the currency + + + align:start position:0% +that limits the supply of the currency +not every blockchain has this but the + + align:start position:0% +not every blockchain has this but the + + + align:start position:0% +not every blockchain has this but the +vast majority do and when we start + + align:start position:0% +vast majority do and when we start + + + align:start position:0% +vast majority do and when we start +talking about it initial coin offerings + + align:start position:0% +talking about it initial coin offerings + + + align:start position:0% +talking about it initial coin offerings +you'll find some that don't + + align:start position:0% +you'll find some that don't + + + align:start position:0% +you'll find some that don't +but Bitcoin limits it and I'm just going + + align:start position:0% +but Bitcoin limits it and I'm just going + + + align:start position:0% +but Bitcoin limits it and I'm just going +to say what it is it's created in a + + align:start position:0% +to say what it is it's created in a + + + align:start position:0% +to say what it is it's created in a +coinbase transaction in each block it + + align:start position:0% +coinbase transaction in each block it + + + align:start position:0% +coinbase transaction in each block it +was initially 50 bitcoins per block but + + align:start position:0% +was initially 50 bitcoins per block but + + + align:start position:0% +was initially 50 bitcoins per block but +now now because it's haft every 210,000 + + align:start position:0% +now now because it's haft every 210,000 + + + align:start position:0% +now now because it's haft every 210,000 +blow + + align:start position:0% +blow + + + align:start position:0% +blow +it's just 12 and a half bitcoins that's + + align:start position:0% +it's just 12 and a half bitcoins that's + + + align:start position:0% +it's just 12 and a half bitcoins that's +that's the number of bitcoins you earn + + align:start position:0% +that's the number of bitcoins you earn + + + align:start position:0% +that's the number of bitcoins you earn +each time if you mine a block that's + + align:start position:0% +each time if you mine a block that's + + + align:start position:0% +each time if you mine a block that's +approximately seventy-five thousand US + + align:start position:0% +approximately seventy-five thousand US + + + align:start position:0% +approximately seventy-five thousand US +dollars in value today + + align:start position:0% +dollars in value today + + + align:start position:0% +dollars in value today +give or take or eighty thousand roughly + + align:start position:0% +give or take or eighty thousand roughly + + + align:start position:0% +give or take or eighty thousand roughly +to mine a block the inflation rate for + + align:start position:0% +to mine a block the inflation rate for + + + align:start position:0% +to mine a block the inflation rate for +Bitcoin right now is four point one + + align:start position:0% +Bitcoin right now is four point one + + + align:start position:0% +Bitcoin right now is four point one +percent so think for any of you that + + align:start position:0% +percent so think for any of you that + + + align:start position:0% +percent so think for any of you that +have taken monetary policy courses or + + align:start position:0% +have taken monetary policy courses or + + + align:start position:0% +have taken monetary policy courses or +financial courses that talk about the + + align:start position:0% +financial courses that talk about the + + + align:start position:0% +financial courses that talk about the +Federal Reserve Bitcoin is growing about + + align:start position:0% +Federal Reserve Bitcoin is growing about + + + align:start position:0% +Federal Reserve Bitcoin is growing about +four percent a year right now but it + + align:start position:0% +four percent a year right now but it + + + align:start position:0% +four percent a year right now but it +haves every two hundred and ten thousand + + align:start position:0% +haves every two hundred and ten thousand + + + align:start position:0% +haves every two hundred and ten thousand +blocks so the inflation rate will go + + align:start position:0% +blocks so the inflation rate will go + + + align:start position:0% +blocks so the inflation rate will go +down to two percent and then later to + + align:start position:0% +down to two percent and then later to + + + align:start position:0% +down to two percent and then later to +about 1% and later about a half a + + align:start position:0% +about 1% and later about a half a + + + align:start position:0% +about 1% and later about a half a +percent and it caps around the year 2040 + + align:start position:0% +percent and it caps around the year 2040 + + + align:start position:0% +percent and it caps around the year 2040 +so whether Satoshi was one person or a + + align:start position:0% +so whether Satoshi was one person or a + + + align:start position:0% +so whether Satoshi was one person or a +team of people back in 2008 they put in + + align:start position:0% +team of people back in 2008 they put in + + + align:start position:0% +team of people back in 2008 they put in +place a monetary policy that is + + align:start position:0% +place a monetary policy that is + + + align:start position:0% +place a monetary policy that is +hard-coded into the computer base code + + align:start position:0% +hard-coded into the computer base code + + + align:start position:0% +hard-coded into the computer base code +and is supposedly going to be there + + align:start position:0% +and is supposedly going to be there + + + align:start position:0% +and is supposedly going to be there +forever + + align:start position:0% +forever + + + align:start position:0% +forever +to cap Bitcoin at 21 million Bitcoin I'm + + align:start position:0% +to cap Bitcoin at 21 million Bitcoin I'm + + + align:start position:0% +to cap Bitcoin at 21 million Bitcoin I'm +going to throw up + + align:start position:0% +going to throw up + + + align:start position:0% +going to throw up +ether just because it's an alternative + + align:start position:0% +ether just because it's an alternative + + + align:start position:0% +ether just because it's an alternative +currently that Minds 3/8 per block and + + align:start position:0% +currently that Minds 3/8 per block and + + + align:start position:0% +currently that Minds 3/8 per block and +the inflation rates about seven and a + + align:start position:0% +the inflation rates about seven and a + + + align:start position:0% +the inflation rates about seven and a +half percent it's a different stage a + + align:start position:0% +half percent it's a different stage a + + + align:start position:0% +half percent it's a different stage a +development different inflation rate but + + align:start position:0% +development different inflation rate but + + + align:start position:0% +development different inflation rate but +there's been a proposal recently to + + align:start position:0% +there's been a proposal recently to + + + align:start position:0% +there's been a proposal recently to +literally it was a proposal by the + + align:start position:0% +literally it was a proposal by the + + + align:start position:0% +literally it was a proposal by the +programmers we should really lower the + + align:start position:0% +programmers we should really lower the + + + align:start position:0% +programmers we should really lower the +inflation rate and if it's accepted it + + align:start position:0% +inflation rate and if it's accepted it + + + align:start position:0% +inflation rate and if it's accepted it +will be adopted in November the fees the + + align:start position:0% +will be adopted in November the fees the + + + align:start position:0% +will be adopted in November the fees the +fees in in aetherium or largely paid in + + align:start position:0% +fees in in aetherium or largely paid in + + + align:start position:0% +fees in in aetherium or largely paid in +something called gas gas is just a small + + align:start position:0% +something called gas gas is just a small + + + align:start position:0% +something called gas gas is just a small +unit of aetherium what's the small unit + + align:start position:0% +unit of aetherium what's the small unit + + + align:start position:0% +unit of aetherium what's the small unit +of Bitcoin Satoshi so gas as Satoshi are + + align:start position:0% +of Bitcoin Satoshi so gas as Satoshi are + + + align:start position:0% +of Bitcoin Satoshi so gas as Satoshi are +very similar British + + align:start position:0% + + + + align:start position:0% + +wait it's not 2040 yes wait you think + + align:start position:0% +wait it's not 2040 yes wait you think + + + align:start position:0% +wait it's not 2040 yes wait you think +it's 21 40 what's that all right so I + + align:start position:0% +it's 21 40 what's that all right so I + + + align:start position:0% +it's 21 40 what's that all right so I +typed poorly Aviva did you have a + + align:start position:0% +typed poorly Aviva did you have a + + + align:start position:0% +typed poorly Aviva did you have a +question well aleem says is Bitcoin a + + align:start position:0% +question well aleem says is Bitcoin a + + + align:start position:0% +question well aleem says is Bitcoin a +deflationary currency depending upon + + align:start position:0% +deflationary currency depending upon + + + align:start position:0% +deflationary currency depending upon +your use of that word but others have + + align:start position:0% +your use of that word but others have + + + align:start position:0% +your use of that word but others have +written that bitcoin is a deflationary + + align:start position:0% +written that bitcoin is a deflationary + + + align:start position:0% +written that bitcoin is a deflationary +currency because it's not growing if the + + align:start position:0% +currency because it's not growing if the + + + align:start position:0% +currency because it's not growing if the +economy is growing at X percent and X + + align:start position:0% +economy is growing at X percent and X + + + align:start position:0% +economy is growing at X percent and X +percent is bigger than how bitcoin is + + align:start position:0% +percent is bigger than how bitcoin is + + + align:start position:0% +percent is bigger than how bitcoin is +growing that would that would sort of + + align:start position:0% +growing that would that would sort of + + + align:start position:0% +growing that would that would sort of +define it as deflationary I would just + + align:start position:0% +define it as deflationary I would just + + + align:start position:0% +define it as deflationary I would just +know that those who are fond and there's + + align:start position:0% +know that those who are fond and there's + + + align:start position:0% +know that those who are fond and there's +a lot of academic literature and this + + align:start position:0% +a lot of academic literature and this + + + align:start position:0% +a lot of academic literature and this +goes back decades if not centuries for + + align:start position:0% +goes back decades if not centuries for + + + align:start position:0% +goes back decades if not centuries for +hard currencies where monetary policy is + + align:start position:0% +hard currencies where monetary policy is + + + align:start position:0% +hard currencies where monetary policy is +absolutely formula driven whether it's + + align:start position:0% +absolutely formula driven whether it's + + + align:start position:0% +absolutely formula driven whether it's +the Taylor rule or other rules rule + + align:start position:0% +the Taylor rule or other rules rule + + + align:start position:0% +the Taylor rule or other rules rule +based monetary policy would have a + + align:start position:0% +based monetary policy would have a + + + align:start position:0% +based monetary policy would have a +fondness for what you could maybe put in + + align:start position:0% +fondness for what you could maybe put in + + + align:start position:0% +fondness for what you could maybe put in +computer code those who think that + + align:start position:0% +computer code those who think that + + + align:start position:0% +computer code those who think that +humans should be involved and many + + align:start position:0% +humans should be involved and many + + + align:start position:0% +humans should be involved and many +people think there's a need for some + + align:start position:0% +people think there's a need for some + + + align:start position:0% +people think there's a need for some +human involvement would say this is too + + align:start position:0% +human involvement would say this is too + + + align:start position:0% +human involvement would say this is too +hard coded and you'd want something + + align:start position:0% +hard coded and you'd want something + + + align:start position:0% +hard coded and you'd want something +where you can modify and change it and + + align:start position:0% +where you can modify and change it and + + + align:start position:0% +where you can modify and change it and +it would be dangerous in times of war + + align:start position:0% +it would be dangerous in times of war + + + align:start position:0% +it would be dangerous in times of war +and times of stress and times of + + align:start position:0% +and times of stress and times of + + + align:start position:0% +and times of stress and times of +economic peril or like the 2008 crisis + + align:start position:0% +economic peril or like the 2008 crisis + + + align:start position:0% +economic peril or like the 2008 crisis +that this would make a crisis worse and + + align:start position:0% +that this would make a crisis worse and + + + align:start position:0% +that this would make a crisis worse and +so the academic literature and the real + + align:start position:0% +so the academic literature and the real + + + align:start position:0% +so the academic literature and the real +life reality of the last couple hundred + + align:start position:0% +life reality of the last couple hundred + + + align:start position:0% +life reality of the last couple hundred +years of hard currencies hard monetary + + align:start position:0% +years of hard currencies hard monetary + + + align:start position:0% +years of hard currencies hard monetary +policies versus human involvement and + + align:start position:0% +policies versus human involvement and + + + align:start position:0% +policies versus human involvement and +some judgment it's kind of an + + align:start position:0% +some judgment it's kind of an + + + align:start position:0% +some judgment it's kind of an +interesting debate that goes right in + + align:start position:0% +interesting debate that goes right in + + + align:start position:0% +interesting debate that goes right in +the middle of all of this + + align:start position:0% + + + + align:start position:0% + +so the question is is this is a real + + align:start position:0% +so the question is is this is a real + + + align:start position:0% +so the question is is this is a real +currency or is it just a asset that has + + align:start position:0% +currency or is it just a asset that has + + + align:start position:0% +currency or is it just a asset that has +aspects of currency Ben what do you + + align:start position:0% +aspects of currency Ben what do you + + + align:start position:0% +aspects of currency Ben what do you +think so they were the three roles of + + align:start position:0% +think so they were the three roles of + + + align:start position:0% +think so they were the three roles of +well three places upon ignorance it was + + align:start position:0% +well three places upon ignorance it was + + + align:start position:0% +well three places upon ignorance it was +to the unit of accounts store value + + align:start position:0% +to the unit of accounts store value + + + align:start position:0% +to the unit of accounts store value +medium of exchange accounts you're + + align:start position:0% +medium of exchange accounts you're + + + align:start position:0% +medium of exchange accounts you're +saying if it has all of those it does + + align:start position:0% +saying if it has all of those it does + + + align:start position:0% +saying if it has all of those it does +all right so then thinks yes how many + + align:start position:0% +all right so then thinks yes how many + + + align:start position:0% +all right so then thinks yes how many +people were with then as of September + + align:start position:0% +people were with then as of September + + + align:start position:0% +people were with then as of September +eighteenth 2018 not 21 18 so Isabella's + + align:start position:0% +eighteenth 2018 not 21 18 so Isabella's + + + align:start position:0% +eighteenth 2018 not 21 18 so Isabella's +there Xan how many people that Tom how + + align:start position:0% +there Xan how many people that Tom how + + + align:start position:0% +there Xan how many people that Tom how +many people think not right I don't I + + align:start position:0% +many people think not right I don't I + + + align:start position:0% +many people think not right I don't I +think that you all get to decide + + align:start position:0% +think that you all get to decide + + + align:start position:0% +think that you all get to decide +yourself + + align:start position:0% +yourself + + + align:start position:0% +yourself +Mark Carney who's the governor of the + + align:start position:0% +Mark Carney who's the governor of the + + + align:start position:0% +Mark Carney who's the governor of the +Bank of England gave a speech earlier in + + align:start position:0% +Bank of England gave a speech earlier in + + + align:start position:0% +Bank of England gave a speech earlier in +the year which is assigned at a later + + align:start position:0% +the year which is assigned at a later + + + align:start position:0% +the year which is assigned at a later +class and he says I don't think we + + align:start position:0% +class and he says I don't think we + + + align:start position:0% +class and he says I don't think we +should call him cryptocurrency so they + + align:start position:0% +should call him cryptocurrency so they + + + align:start position:0% +should call him cryptocurrency so they +should be called crypto assets they're + + align:start position:0% +should be called crypto assets they're + + + align:start position:0% +should be called crypto assets they're +not yet evidencing all three of these so + + align:start position:0% +not yet evidencing all three of these so + + + align:start position:0% +not yet evidencing all three of these so +that's Mark Carney who I have great + + align:start position:0% +that's Mark Carney who I have great + + + align:start position:0% +that's Mark Carney who I have great +respect for but there are others that + + align:start position:0% +respect for but there are others that + + + align:start position:0% +respect for but there are others that +say no it's evidencing enough I would + + align:start position:0% +say no it's evidencing enough I would + + + align:start position:0% +say no it's evidencing enough I would +say this though it's plausible that they + + align:start position:0% +say this though it's plausible that they + + + align:start position:0% +say this though it's plausible that they +will they and this this if you take + + align:start position:0% +will they and this this if you take + + + align:start position:0% +will they and this this if you take +nothing else from the class it's + + align:start position:0% +nothing else from the class it's + + + align:start position:0% +nothing else from the class it's +plausible in my view that they could + + align:start position:0% +plausible in my view that they could + + + align:start position:0% +plausible in my view that they could +provide you could have digital currency + + align:start position:0% +provide you could have digital currency + + + align:start position:0% +provide you could have digital currency +that does not have a central authority I + + align:start position:0% +that does not have a central authority I + + + align:start position:0% +that does not have a central authority I +mean I think that innovation is there + + align:start position:0% +mean I think that innovation is there + + + align:start position:0% +mean I think that innovation is there +whether you call it a crypto currency or + + align:start position:0% +whether you call it a crypto currency or + + + align:start position:0% +whether you call it a crypto currency or +crypto acid at this point in time I + + align:start position:0% +crypto acid at this point in time I + + + align:start position:0% +crypto acid at this point in time I +leave to all of you there won't be a + + align:start position:0% +leave to all of you there won't be a + + + align:start position:0% +leave to all of you there won't be a +right answer to that on any paper you + + align:start position:0% +right answer to that on any paper you + + + align:start position:0% +right answer to that on any paper you +submit you can use whichever term you + + align:start position:0% +submit you can use whichever term you + + + align:start position:0% +submit you can use whichever term you +you think it's fits you're thinking I + + align:start position:0% +you think it's fits you're thinking I + + + align:start position:0% +you think it's fits you're thinking I +want to talk about the network we only + + align:start position:0% +want to talk about the network we only + + + align:start position:0% +want to talk about the network we only +have ten minutes but the network is + + align:start position:0% +have ten minutes but the network is + + + align:start position:0% +have ten minutes but the network is +important and a lot of times when you + + align:start position:0% +important and a lot of times when you + + + align:start position:0% +important and a lot of times when you +talk about Bitcoin and blockchain folks + + align:start position:0% +talk about Bitcoin and blockchain folks + + + align:start position:0% +talk about Bitcoin and blockchain folks +aren't going to talk about it but I'm + + align:start position:0% +aren't going to talk about it but I'm + + + align:start position:0% +aren't going to talk about it but I'm +going to quickly hit a tour + + align:start position:0% +going to quickly hit a tour + + + align:start position:0% +going to quickly hit a tour +players on the network there are full + + align:start position:0% +players on the network there are full + + + align:start position:0% +players on the network there are full +nodes a full node is is group is a + + align:start position:0% +nodes a full node is is group is a + + + align:start position:0% +nodes a full node is is group is a +computer I should say that stores the + + align:start position:0% +computer I should say that stores the + + + align:start position:0% +computer I should say that stores the +full blockchain and is able to validate + + align:start position:0% +full blockchain and is able to validate + + + align:start position:0% +full blockchain and is able to validate +all transactions it doesn't have to it's + + align:start position:0% +all transactions it doesn't have to it's + + + align:start position:0% +all transactions it doesn't have to it's +a volunteer thing but it can validate + + align:start position:0% +a volunteer thing but it can validate + + + align:start position:0% +a volunteer thing but it can validate +all transactions a pruning node you're + + align:start position:0% +all transactions a pruning node you're + + + align:start position:0% +all transactions a pruning node you're +not gonna read a lot about it but I just + + align:start position:0% +not gonna read a lot about it but I just + + + align:start position:0% +not gonna read a lot about it but I just +have it it prints transactions once + + align:start position:0% +have it it prints transactions once + + + align:start position:0% +have it it prints transactions once +they've validated and they have a + + align:start position:0% +they've validated and they have a + + + align:start position:0% +they've validated and they have a +certain age you're saying you know all + + align:start position:0% +certain age you're saying you know all + + + align:start position:0% +certain age you're saying you know all +of those early transactions we're not + + align:start position:0% +of those early transactions we're not + + + align:start position:0% +of those early transactions we're not +going to focus there's been probably six + + align:start position:0% +going to focus there's been probably six + + + align:start position:0% +going to focus there's been probably six +times the number of transactions that + + align:start position:0% +times the number of transactions that + + + align:start position:0% +times the number of transactions that +have happened compared to the actual + + align:start position:0% +have happened compared to the actual + + + align:start position:0% +have happened compared to the actual +extent transactions right now so all the + + align:start position:0% +extent transactions right now so all the + + + align:start position:0% +extent transactions right now so all the +transactions that have ever happened + + align:start position:0% +transactions that have ever happened + + + align:start position:0% +transactions that have ever happened +five six of them have already been used + + align:start position:0% +five six of them have already been used + + + align:start position:0% +five six of them have already been used +they're not around anymore why do we + + align:start position:0% +they're not around anymore why do we + + + align:start position:0% +they're not around anymore why do we +have to lug it around in our data set so + + align:start position:0% +have to lug it around in our data set so + + + align:start position:0% +have to lug it around in our data set so +you could have a pruning node + + align:start position:0% +you could have a pruning node + + + align:start position:0% +you could have a pruning node +lightweight nodes which if any of you + + align:start position:0% +lightweight nodes which if any of you + + + align:start position:0% +lightweight nodes which if any of you +have a Bitcoin wallet or any other + + align:start position:0% +have a Bitcoin wallet or any other + + + align:start position:0% +have a Bitcoin wallet or any other +wallet you probably have a lightweight + + align:start position:0% +wallet you probably have a lightweight + + + align:start position:0% +wallet you probably have a lightweight +some form of lightweight node or what's + + align:start position:0% +some form of lightweight node or what's + + + align:start position:0% +some form of lightweight node or what's +called an S PV node it stores just those + + align:start position:0% +called an S PV node it stores just those + + + align:start position:0% +called an S PV node it stores just those +blockchain headers rather than all this + + align:start position:0% +blockchain headers rather than all this + + + align:start position:0% +blockchain headers rather than all this +detail underneath a lot less storage but + + align:start position:0% +detail underneath a lot less storage but + + + align:start position:0% +detail underneath a lot less storage but +a lightweight node has to rely on the + + align:start position:0% +a lightweight node has to rely on the + + + align:start position:0% +a lightweight node has to rely on the +full nodes for verification because the + + align:start position:0% +full nodes for verification because the + + + align:start position:0% +full nodes for verification because the +lightweight nodes not going to be doing + + align:start position:0% +lightweight nodes not going to be doing + + + align:start position:0% +lightweight nodes not going to be doing +that and so on miners we talked about + + align:start position:0% +that and so on miners we talked about + + + align:start position:0% +that and so on miners we talked about +miners I want to just mention miners + + align:start position:0% +miners I want to just mention miners + + + align:start position:0% +miners I want to just mention miners +don't have to be full nodes Amanda + + align:start position:0% +don't have to be full nodes Amanda + + + align:start position:0% +don't have to be full nodes Amanda +you're running this mining operation for + + align:start position:0% +you're running this mining operation for + + + align:start position:0% +you're running this mining operation for +the whole class and we're paying you one + + align:start position:0% +the whole class and we're paying you one + + + align:start position:0% +the whole class and we're paying you one +two three percent but you're you're + + align:start position:0% +two three percent but you're you're + + + align:start position:0% +two three percent but you're you're +slowing right you're probably charging + + align:start position:0% +slowing right you're probably charging + + + align:start position:0% +slowing right you're probably charging +at the high end right so do you think + + align:start position:0% +at the high end right so do you think + + + align:start position:0% +at the high end right so do you think +that Amanda as a mining pool operator is + + align:start position:0% +that Amanda as a mining pool operator is + + + align:start position:0% +that Amanda as a mining pool operator is +operating a full node + + align:start position:0% + + + + align:start position:0% + +saying it tentatively but Tom you're + + align:start position:0% +saying it tentatively but Tom you're + + + align:start position:0% +saying it tentatively but Tom you're +paying a man to 2% of your fees don't + + align:start position:0% +paying a man to 2% of your fees don't + + + align:start position:0% +paying a man to 2% of your fees don't +you want to make sure she's validating + + align:start position:0% +you want to make sure she's validating + + + align:start position:0% +you want to make sure she's validating +everything what's that + + align:start position:0% +everything what's that + + + align:start position:0% +everything what's that +she thinks 3% yes but but any of you who + + align:start position:0% +she thinks 3% yes but but any of you who + + + align:start position:0% +she thinks 3% yes but but any of you who +are just minors remember Amanda's air + + align:start position:0% +are just minors remember Amanda's air + + + align:start position:0% +are just minors remember Amanda's air +pool operator anybody is my Andrew do + + align:start position:0% +pool operator anybody is my Andrew do + + + align:start position:0% +pool operator anybody is my Andrew do +you think you need a full node if if if + + align:start position:0% +you think you need a full node if if if + + + align:start position:0% +you think you need a full node if if if +Amanda know so a lot of minors are not + + align:start position:0% +Amanda know so a lot of minors are not + + + align:start position:0% +Amanda know so a lot of minors are not +operating full nodes + + align:start position:0% +operating full nodes + + + align:start position:0% +operating full nodes +they've got all those racks of Asics + + align:start position:0% +they've got all those racks of Asics + + + align:start position:0% +they've got all those racks of Asics +they're running all their electricity + + align:start position:0% +they're running all their electricity + + + align:start position:0% +they're running all their electricity +and they're paying Amanda to check on it + + align:start position:0% +and they're paying Amanda to check on it + + + align:start position:0% +and they're paying Amanda to check on it +don't let them down so I might start + + align:start position:0% +don't let them down so I might start + + + align:start position:0% +don't let them down so I might start +calling you Nouriel Roubini but I won't + + align:start position:0% +calling you Nouriel Roubini but I won't + + + align:start position:0% +calling you Nouriel Roubini but I won't +but Nouriel Roubini here's an economist + + align:start position:0% +but Nouriel Roubini here's an economist + + + align:start position:0% +but Nouriel Roubini here's an economist +he sometimes called dr. doom and he + + align:start position:0% +he sometimes called dr. doom and he + + + align:start position:0% +he sometimes called dr. doom and he +likes that phrase because he caused down + + align:start position:0% +likes that phrase because he caused down + + + align:start position:0% +likes that phrase because he caused down +terms in the market there's there's a + + align:start position:0% +terms in the market there's there's a + + + align:start position:0% +terms in the market there's there's a +later reading and I might have even done + + align:start position:0% +later reading and I might have even done + + + align:start position:0% +later reading and I might have even done +a video of Rubini has this view that + + align:start position:0% +a video of Rubini has this view that + + + align:start position:0% +a video of Rubini has this view that +it's not decentralized in mining polls + + align:start position:0% +it's not decentralized in mining polls + + + align:start position:0% +it's not decentralized in mining polls +or an Achilles heel of the system but + + align:start position:0% +or an Achilles heel of the system but + + + align:start position:0% +or an Achilles heel of the system but +the full nodes the 10,000 nodes actually + + align:start position:0% +the full nodes the 10,000 nodes actually + + + align:start position:0% +the full nodes the 10,000 nodes actually +still do validation and there's an + + align:start position:0% +still do validation and there's an + + + align:start position:0% +still do validation and there's an +interesting social construct where + + align:start position:0% +interesting social construct where + + + align:start position:0% +interesting social construct where +there's a lot of nodes doing an + + align:start position:0% +there's a lot of nodes doing an + + + align:start position:0% +there's a lot of nodes doing an +innocence non compensated work + + align:start position:0% +innocence non compensated work + + + align:start position:0% +innocence non compensated work +validating transactions beyond Amanda + + align:start position:0% +validating transactions beyond Amanda + + + align:start position:0% +validating transactions beyond Amanda +and any miner Andrew could could + + align:start position:0% +and any miner Andrew could could + + + align:start position:0% +and any miner Andrew could could +validate if he wants to so there's a lot + + align:start position:0% +validate if he wants to so there's a lot + + + align:start position:0% +validate if he wants to so there's a lot +of free writing that goes law and the + + align:start position:0% +of free writing that goes law and the + + + align:start position:0% +of free writing that goes law and the +economics of free riding and then + + align:start position:0% +economics of free riding and then + + + align:start position:0% +economics of free riding and then +there's wallets which probably 30 or 40 + + align:start position:0% +there's wallets which probably 30 or 40 + + + align:start position:0% +there's wallets which probably 30 or 40 +of you have when your computer somewhere + + align:start position:0% +of you have when your computer somewhere + + + align:start position:0% +of you have when your computer somewhere +they store and view and send all the + + align:start position:0% +they store and view and send all the + + + align:start position:0% +they store and view and send all the +transactions but it importantly also + + align:start position:0% +transactions but it importantly also + + + align:start position:0% +transactions but it importantly also +create the key pairs so a lot to cover + + align:start position:0% +create the key pairs so a lot to cover + + + align:start position:0% +create the key pairs so a lot to cover +there's one that's not a node itself at + + align:start position:0% +there's one that's not a node itself at + + + align:start position:0% +there's one that's not a node itself at +all it's called the mem pull + + align:start position:0% +all it's called the mem pull + + + align:start position:0% +all it's called the mem pull +or the memory pool and we're gonna talk + + align:start position:0% +or the memory pool and we're gonna talk + + + align:start position:0% +or the memory pool and we're gonna talk +about this more on Thursday but the + + align:start position:0% +about this more on Thursday but the + + + align:start position:0% +about this more on Thursday but the +memory pulls stores all the unconformity + + align:start position:0% +memory pulls stores all the unconformity + + + align:start position:0% +memory pulls stores all the unconformity +ette already validated so they've been + + align:start position:0% +ette already validated so they've been + + + align:start position:0% +ette already validated so they've been +validated by somebody a transaction goes + + align:start position:0% +validated by somebody a transaction goes + + + align:start position:0% +validated by somebody a transaction goes +out into the network a full node + + align:start position:0% +out into the network a full node + + + align:start position:0% +out into the network a full node +validates it and it's put in a memory + + align:start position:0% +validates it and it's put in a memory + + + align:start position:0% +validates it and it's put in a memory +pool and a man that grabs the memory + + align:start position:0% +pool and a man that grabs the memory + + + align:start position:0% +pool and a man that grabs the memory +pool and sends it out to everybody in + + align:start position:0% +pool and sends it out to everybody in + + + align:start position:0% +pool and sends it out to everybody in +this class in a block and then we mine + + align:start position:0% +this class in a block and then we mine + + + align:start position:0% +this class in a block and then we mine +it we're not going to chat much about + + align:start position:0% +it we're not going to chat much about + + + align:start position:0% +it we're not going to chat much about +these right now but we talked about + + align:start position:0% +these right now but we talked about + + + align:start position:0% +these right now but we talked about +there was a coin desk article how many + + align:start position:0% +there was a coin desk article how many + + + align:start position:0% +there was a coin desk article how many +of you actually skimmed it looked at it + + align:start position:0% +of you actually skimmed it looked at it + + + align:start position:0% +of you actually skimmed it looked at it +did it mean anything to you or just met + + align:start position:0% +did it mean anything to you or just met + + + align:start position:0% +did it mean anything to you or just met +that there's some alternative what's + + align:start position:0% +that there's some alternative what's + + + align:start position:0% +that there's some alternative what's +that Priya there's some alternative + + align:start position:0% +that Priya there's some alternative + + + align:start position:0% +that Priya there's some alternative +that's what it meant to me the first + + align:start position:0% +that's what it meant to me the first + + + align:start position:0% +that's what it meant to me the first +time I looked into this about six months + + align:start position:0% +time I looked into this about six months + + + align:start position:0% +time I looked into this about six months +ago but I want to just mention what the + + align:start position:0% +ago but I want to just mention what the + + + align:start position:0% +ago but I want to just mention what the +alternatives come down to they generally + + align:start position:0% +alternatives come down to they generally + + + align:start position:0% +alternatives come down to they generally +randomized or delegate the selection so + + align:start position:0% +randomized or delegate the selection so + + + align:start position:0% +randomized or delegate the selection so +rather than rather than saying any one + + align:start position:0% +rather than rather than saying any one + + + align:start position:0% +rather than rather than saying any one +of 10,000 nodes can prove that this + + align:start position:0% +of 10,000 nodes can prove that this + + + align:start position:0% +of 10,000 nodes can prove that this +works they've they use various + + align:start position:0% +works they've they use various + + + align:start position:0% +works they've they use various +mathematical means randomized or + + align:start position:0% +mathematical means randomized or + + + align:start position:0% +mathematical means randomized or +delegated and sometimes they do a little + + align:start position:0% +delegated and sometimes they do a little + + + align:start position:0% +delegated and sometimes they do a little +bit of delegation and randomization to + + align:start position:0% +bit of delegation and randomization to + + + align:start position:0% +bit of delegation and randomization to +pick who's gonna validate the next block + + align:start position:0% +pick who's gonna validate the next block + + + align:start position:0% +pick who's gonna validate the next block +it all comes down to who is picking the + + align:start position:0% +it all comes down to who is picking the + + + align:start position:0% +it all comes down to who is picking the +next block is it by Adam Beck's + + align:start position:0% +next block is it by Adam Beck's + + + align:start position:0% +next block is it by Adam Beck's +sort of as Satoshi Nakamoto put out + + align:start position:0% +sort of as Satoshi Nakamoto put out + + + align:start position:0% +sort of as Satoshi Nakamoto put out +there we'll call it Nakamoto consensus + + align:start position:0% +there we'll call it Nakamoto consensus + + + align:start position:0% +there we'll call it Nakamoto consensus +proof-of-work + + align:start position:0% +proof-of-work + + + align:start position:0% +proof-of-work +and you'll you'll have a paper for + + align:start position:0% +and you'll you'll have a paper for + + + align:start position:0% +and you'll you'll have a paper for +Thursday that talks about Nakamoto + + align:start position:0% +Thursday that talks about Nakamoto + + + align:start position:0% +Thursday that talks about Nakamoto +consensus the Clarke paper but or is + + align:start position:0% +consensus the Clarke paper but or is + + + align:start position:0% +consensus the Clarke paper but or is +there some other randomize delegated way + + align:start position:0% +there some other randomize delegated way + + + align:start position:0% +there some other randomize delegated way +to do it in some of them they have a + + align:start position:0% +to do it in some of them they have a + + + align:start position:0% +to do it in some of them they have a +second check if there's a delegated + + align:start position:0% +second check if there's a delegated + + + align:start position:0% +second check if there's a delegated +person to validate something they put a + + align:start position:0% +person to validate something they put a + + + align:start position:0% +person to validate something they put a +second check in there that there's + + align:start position:0% +second check in there that there's + + + align:start position:0% +second check in there that there's +another group that that officiates and + + align:start position:0% +another group that that officiates and + + + align:start position:0% +another group that that officiates and +says whether it's correct and so there's + + align:start position:0% +says whether it's correct and so there's + + + align:start position:0% +says whether it's correct and so there's +proof of stake which is based on the + + align:start position:0% +proof of stake which is based on the + + + align:start position:0% +proof of stake which is based on the +you have in the underlying currency + + align:start position:0% +you have in the underlying currency + + + align:start position:0% +you have in the underlying currency +there's proof of activity which is kind + + align:start position:0% +there's proof of activity which is kind + + + align:start position:0% +there's proof of activity which is kind +of a high-bred of proof of work and + + align:start position:0% +of a high-bred of proof of work and + + + align:start position:0% +of a high-bred of proof of work and +proof of stake proof of burn are you + + align:start position:0% +proof of stake proof of burn are you + + + align:start position:0% +proof of stake proof of burn are you +willing to give up coins proof of + + align:start position:0% +willing to give up coins proof of + + + align:start position:0% +willing to give up coins proof of +capacity do you have storage capacity + + align:start position:0% +capacity do you have storage capacity + + + align:start position:0% +capacity do you have storage capacity +and you might have a tiered system the + + align:start position:0% +and you might have a tiered system the + + + align:start position:0% +and you might have a tiered system the +major permissionless block chains all + + align:start position:0% +major permissionless block chains all + + + align:start position:0% +major permissionless block chains all +use proof of work and the reason is + + align:start position:0% +use proof of work and the reason is + + + align:start position:0% +use proof of work and the reason is +nobody's really solved all of these + + align:start position:0% +nobody's really solved all of these + + + align:start position:0% +nobody's really solved all of these +other alternatives no one's really + + align:start position:0% +other alternatives no one's really + + + align:start position:0% +other alternatives no one's really +solved for a couple of problems in them + + align:start position:0% +solved for a couple of problems in them + + + align:start position:0% +solved for a couple of problems in them +but they usually find a way to be more + + align:start position:0% +but they usually find a way to be more + + + align:start position:0% +but they usually find a way to be more +efficient through delegation and + + align:start position:0% +efficient through delegation and + + + align:start position:0% +efficient through delegation and +randomization and might have a backup + + align:start position:0% +randomization and might have a backup + + + align:start position:0% +randomization and might have a backup +set of checks on it + + align:start position:0% +set of checks on it + + + align:start position:0% +set of checks on it +- and neo will say that they use proof + + align:start position:0% +- and neo will say that they use proof + + + align:start position:0% +- and neo will say that they use proof +of stake but they're actually kind of + + align:start position:0% +of stake but they're actually kind of + + + align:start position:0% +of stake but they're actually kind of +using some form of masternodes or setup + + align:start position:0% +using some form of masternodes or setup + + + align:start position:0% +using some form of masternodes or setup +professional nodes but - and neo are + + align:start position:0% +professional nodes but - and neo are + + + align:start position:0% +professional nodes but - and neo are +kind of like think the 13th and 15th + + align:start position:0% +kind of like think the 13th and 15th + + + align:start position:0% +kind of like think the 13th and 15th +largest market value Kryptos which means + + align:start position:0% +largest market value Kryptos which means + + + align:start position:0% +largest market value Kryptos which means +everything else kind of and ripple + + align:start position:0% +everything else kind of and ripple + + + align:start position:0% +everything else kind of and ripple +doesn't ripples really almost like a + + align:start position:0% +doesn't ripples really almost like a + + + align:start position:0% +doesn't ripples really almost like a +permission system rather than + + align:start position:0% +permission system rather than + + + align:start position:0% +permission system rather than +permissionless I mean they would say + + align:start position:0% +permissionless I mean they would say + + + align:start position:0% +permissionless I mean they would say +they're permissionless but it's it's a + + align:start position:0% +they're permissionless but it's it's a + + + align:start position:0% +they're permissionless but it's it's a +confirm set of notes that in the system + + align:start position:0% +confirm set of notes that in the system + + + align:start position:0% +confirm set of notes that in the system +so that's it for today we're gonna do + + align:start position:0% +so that's it for today we're gonna do + + + align:start position:0% +so that's it for today we're gonna do +transactions on Thursday I move that + + align:start position:0% +transactions on Thursday I move that + + + align:start position:0% +transactions on Thursday I move that +study question and and then I'm gonna + + align:start position:0% +study question and and then I'm gonna + + + align:start position:0% +study question and and then I'm gonna +ask you to read through the Clarke paper + + align:start position:0% +ask you to read through the Clarke paper + + + align:start position:0% +ask you to read through the Clarke paper +which is really the academic pedigree + + align:start position:0% +which is really the academic pedigree + + + align:start position:0% +which is really the academic pedigree +where is this bill - and what's the + + align:start position:0% +where is this bill - and what's the + + + align:start position:0% +where is this bill - and what's the +background but I think it's a good way + + align:start position:0% +background but I think it's a good way + + + align:start position:0% +background but I think it's a good way +to bring it all together and remember on + + align:start position:0% +to bring it all together and remember on + + + align:start position:0% +to bring it all together and remember on +Thursday you all come in to answer this + + align:start position:0% +Thursday you all come in to answer this + + + align:start position:0% +Thursday you all come in to answer this +question your own view as to who's + + align:start position:0% +question your own view as to who's + + + align:start position:0% +question your own view as to who's +Satoshi Nakamoto is there is no right + + align:start position:0% +Satoshi Nakamoto is there is no right + + + align:start position:0% +Satoshi Nakamoto is there is no right +answer but if mi t--'s block shaded + + align:start position:0% +answer but if mi t--'s block shaded + + + align:start position:0% +answer but if mi t--'s block shaded +money class can answer that I'm sure + + align:start position:0% +money class can answer that I'm sure + + + align:start position:0% +money class can answer that I'm sure +that we'll get a write-up somewhere + + align:start position:0% +that we'll get a write-up somewhere + + + align:start position:0% +that we'll get a write-up somewhere +about it + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/xRWGiK2SMrw.txt b/xRWGiK2SMrw.txt new file mode 100644 index 0000000000000000000000000000000000000000..10dd558394dec5c9fe33f3ae0bad5158de9089f1 --- /dev/null +++ b/xRWGiK2SMrw.txt @@ -0,0 +1,1643 @@ +PROFESSOR: Examine every +possible means for combining + +the symmetry at once, but +there is a seemingly + +paradoxical trick that +we can yet pull. + +And let me indicate what +is true here for 2mm. + +OK, so this is a twofold axis. + +Has mirror planes perpendicular +to it. + +If one of these is a mirror +plane, the other one has to be + +a mirror plane as well. + +So there's no way we could make +one a mirror plane and + +one a glide plane. + +OK, that requires a net that +is exactly rectangular. + +So let's put in the +twofold axis. + +And I add one to the +corner of the cell. + +As we well know we have to have +twofold axes at all of + +these other locations. + +We want to put a mirror +plane in the cell. + +We could pass it through the +twofold axis, and that would + +be the same as P getting +to P2mn back again. + +But why do we have to put the +mirror plane through the + +twofold axis? + +We have to have the twofold axis +left unchanged when we + +add the mirror plane, because +if we created a new twofold + +axis we create a new lattice +and we'd wreck the lattice + +that we've constructed. + +But why, why, oh why couldn't +we put the mirror + +plane in like this? + +That's going to leave the +twofold axis alone. + +It's going to leave the +translations invariant. + +Why don't we do that? + +Why not? + +So here, trick number five, +or wherever we are now. + +You can add the symmetry +elements of a point group to a + +lattice, but not necessarily +at the same point. + +You can interweave them. + +But the constraint is that this +addition must leave the + +axis invariant. + +Let's leave the twofold +axis invariant. + +And vice versa. + +That is to say the mirror +planes can't create new + +twofold axes, the twofold +axis can't + +create new mirror planes. + +And let's make sure we +understand the reason why. + +If I've got a twofold axis here +and a twofold axis here, + +I have to have a translation +that's twice their separation. + +If this distance is delta, +then I have to have a + +translation that's +automatically + +created at twice delta. + +This is the same as saying +twofold axis with a + +translation gives you a twofold +axis halfway along. + +If I take the twofold axis, I +get the translation back as a + +consequence. + +So what I'm saying is if we take +the first twofold axis + +and repeat number one to number +two, and then add + +another twofold axis which +repeats number two to number + +three, you have a third one that +is related by translation + +of twice delta. + +So if you're going to interweave +the symmetry + +elements, you have to leave the +arrangement of symmetry + +elements at the same intervals, +otherwise you would + +have created a translation or +more that is incommensurate + +and incompatible with +the other ones. + +So this is a third trick. + +And we are going to need +a new theorem. + +Let's first of all look +at the possibilities. + +We can have the twofold +axis interweave + +with a mirror plane. + +How about putting +a glide plane in + +between the twofold axis. + +In other words, replace the +mirror plane by a glide plane. + +This twofold axis hangs off +here, reflect it across and + +slide it down to here, and you +get this twofold axis here. + +So that's also a self consistent +compatible + +arrangement. + +How about a centered net? + +And that's more difficult. + +A centered net has twofold axis +and all the places of C2, + +and then twofold axes at +locations like one quarter, + +one quarter as well. + +We can't put a mirror +plane in here. + +That's not going to work, +because it will generate a new + +twofold axis, and that changes +the translation + +T1 to half its value. + +We can't even put a glide plane +here because this would + +slide down to here, reflect +across, and that's + +not going to work. + +So the number of possibilities +is limited, but we'll see that + +there's one other case as well +for a fourfold axis. + +OK, we need a new combination +theorem that says if you have + +an operation a, pi, and combine +it with a reflection + +operation that's removed from +it by some distance delta, + +what is the result? + +That general theorem has worked +out for you on the + +notes, but I think what I'll do +it in the interest of time + +is simply look at how this +arrangement of symmetry + +elements would move +things around. + +And here I've taken the motif +and hung it at the lattice + +point, and repeated it +by the twofold axis. + +The mirror plane would take this +and reflected it across + +to here, then take this one and +reflect it across to here. + +And do the same thing down at +the bottom of the cell. + +Let me now ask you what sort of +plane has arisen that would + +be perpendicular to +the mirror plane? + +Could be interweaved or passed +through the twofold axis. + +Anybody want to hazard +an answer? + +OK. + +We have to have some sort of +correspondence theorem that + +says if you've got a twofold +axis, have one plane, you've + +got to have another plane +90 degrees away. + +Do I know how everything +is related? + +I know how this is +related to this. + +I know this is related +to this. + +That's by a reflection plane. + +I know how the twofold +axes relate things. + +How is this pair related +to this pair? + +And the answer is that the way +they are related is by rights + +and lefts on here. + +This is right, this is right. + +Reflection changes handedness +to left, so I've got to have + +some way of getting from this +pair to this pair that + +involves a change +of handedness. + +And I see nobody is really +jumping out of their seat, but + +there is a glide +plane in here. + +Take this pair, slide it along +by half of T2, and flip it + +across by reflection. + +And there is a glide +plane right here. + +And therefore of necessity +there's a glide plane here. + +And this glide combined with the +perpendicular translation + +will put a glide plane +in here as well. + +And you look in your tables. + +This is plane group +number seven. + +And this one has +a twofold axis. + +It has a primitive rectangular +neck, so this is called P2m, + +and now the second plane at +right angles is not an mirror + +plane, it's a glide plane. + +So this is called P2mg, or +there's a shorthand form that + +leaves out the two. + +PMG is the shorthand +symbol for it. + +So there's a new plane group +that is based on orthogonal + +symmetry planes. + +One a mirror, one a glide, +and twofold axes. + +Let me ask you now what is the +point group of a crystal that + +would have this relation between +the atoms that are + +down in the guts +of the crystal? + +What would be the point +group of the crystal? + +We've got two different +point groups. + +We've got point M, we've +got point group two. + +What would be the point +group of the crystal? + +And this is a new problem, +a new concept. + +All of the plane groups that we +looked at until this point, + +the symmetry elements on an +atomic scale down inside the + +plane group were exactly the +same as the point group that + +we had added to the +lattice points. + +But here we've got two different +point groups that + +had been put into the lattice. + +So do we say that this +crystal has symmetry + +two or symmetry M? + +Or just point group 2m. + +That won't work because if you +have one mirror plane in a + +point group, you have +to have another. + +What this introduces is +a very subtle point. + +The point group is inherently +a macroscopic symmetry. + +When I say a crystal has a +particular point group, what I + +mean is that if I look at the +exterior faces of the crystal, + +I would say there's a +twofold axis here. + +And that's about all, if these +spaces are pair wise distinct. + +I have a crystal that looks +like this externally. + +I would say that that crystal +has symmetry 2mm + +based on the faces. + +If I found that the etch pits on +the surfaces were not quite + +the same on this face and this +face, I would have to throw + +out the twofold axis, perhaps, +which means this mirror plane + +would go out as well. + +But also I would do things +like look at the optical + +properties. + +I would measure the +conductivity as + +a function of direction. + +I would look at the slip systems +and yield stresses in + +different directions, and the +assignment of a point group is + +an experimental observation that +requires that you look at + +all possible properties. + +Not only shape, but properties +like conductivity and the + +magnetic susceptibility, and +also perhaps the way the + +crystal diffracts X-Rays. + +That's another physical +property. + +And then when you've done as +many measurements as you + +choose to make, you say as far +as I can tell, all behavior of + +this crystal is determined +inconsistent with this + +particular point group. + +But you're doing macroscopic +things. + +You're doing macroscopic +things. + +When you talk about the plane +group or space group, you're + +talking what goes on on +a local atomistic + +scale in the unit cell. + +So what would be the point +group of this crystal? + +It would have a twofold axis +that would be manifested + +externally. + +It would have a mirror plane, +which makes the left hand side + +want to be the same as +the right hand side. + +And if this were not a mirror +plane here, but a glide plane, + +what you would say is that this +face, if I reflect it and + +slide it along by one angstrom +is going to become this face. + +And this face here, if I reflect +it and slide it back + +by one angstrom is going +to become this face. + +But what will that do to +the external shape? + +I just extend all these +surfaces, and it's going to be + +exactly what I've drawn here. + +How would you distinguish +a mirror plane + +from a glide plane? + +If a crystal has a mirror plane, +a face that sits here + +passes through some atoms. + +Those atoms are repeated +by reflection. + +And being slit up by an amount +tau which is on the scale of + +atomic dimensions, and +that would give + +rise to a face here. + +But can you macroscopically +assign any difference to the + +fact that two faces +atomistically don't meet, but + +are separated by +3.2 angstroms? + +No. + +What you see is one face like +this, and one face inclined to + +it with a slope that is the same +for either a glide plane + +or a mirror plane. + +So another truth about +crystals is that + +macroscopically a glide line +plane manifests itself as a + +mirror plane. + +So paradoxically this crystal, +which only has a twofold axis + +and one mirror plane down in its +guts is going to look as + +though it has point group two in +it, even though there is no + +sight, atomistically within this +arrangement of atoms that + +has symmetry 2mm. + +AUDIENCE: I have a question. + +PROFESSOR: Yeah? + +Sorry. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: That's a very +good question. + +And actually, to answer it +properly requires knowing + +something about diffraction. + +The symmetry of the diffraction +pattern that you + +observed would look as though +it had a mirror plane in it. + +Which is to say if we put a beam +of white radiation down + +along this direction of a +crystal, imagine these things + +all extending out in a third +dimension, that what we would + +see among the arrangement of +spots is a twofold axis in the + +center of [INAUDIBLE] + +photograph we'd see a mirror +plane running this way, and a + +mirror plane running this way. + +So we would see spots on the +[INAUDIBLE] pattern, which + +would look like this. + +So the glide plane would +also behave it + +were a mirrored plane. + +And, maybe, if you +think of what + +goes on with the fraction. + +If you ask yourself, if I +brought in x-rays this way and + +diffracted them off a layer of +atoms related by this glide + +plane, and then I can't do this +actually to the crystal. + +But, suppose I then inverted the +direction of the incoming + +beam, and slitted along +by five angstroms. + +Doesn't make any sense. + +The diffraction from these +planes is going to look the + +same whether I bring in from +one side or the other. + +So a glide plane, in diffraction +symmetry, + +manifests itself as +a mirror plane. + +So how can you determine the +presence of glide planes using + +diffraction? + +And you can. + +And the answer is, that the +glide plane causes the + +intensity diffracted it from +planes with certain indices to + +be identically zero. + +You've probably heard of these +magical extinction rules + +they're called. + +And it says that if h plus k, +plus three times L is two pi + +plus four, and the crystal is +green, then you've got such + +and such, the reflection +being absent. + +Actually it is-- + +I'm getting distracted-- but, it +turns out that glide planes + +affect just a sheet +of reflections + +in reciprocal space. + +And the reason some reflections +are absent is that + +that sheet of reflections +corresponds to what the + +projection of the structure +onto that plane would do. + +And, if you project a structure +that has a glide + +operation onto the plane of the +glide plane, the structure + +looks like the lattice +translation is half as big. + +And, if that's the case, the +diffraction spots are twice as + +widely separated. + +And it turns out that all of the +reflections that have an + +index corresponding to the +direction of tau are absent if + +that index is odd. + +So, if you knew a little bit +about it to begin with, that + +perhaps answers the question. + +So yes, you can determine the +presence of glide planes. + +And later on, we'll talk +about screw axes. + +You can determine their presence +unambiguously, but + +you do that not the symmetry +of the diffraction effects, + +but from systematic absences. + +OK, another thing I suggested we +could do is to put a glide + +plane in between the +two-fold axes + +instead of a mirror plane. + +And this says that I have a pair +of atoms repeated by the + +two-fold axis, the glide plane +would take that pair, shift + +them down by half of the cell, +and reflect them over. + +So this would be the +pattern of objects. + +This is not a lattice point, +because if these are right + +handed, that's a right-handed +pair, this is + +a left-handed pair. + +Now let me try you again. + +I know how these guys left +and right to this + +glide plane are related. + +How about these ones that are +up, to the ones that are down + +here in the middle +of the cell? + +There's got to be, from our +correspondence principle, some + +plane going in this direction. + +Anybody want to hazard a +guess at what it is? + +The answer to that question +resoundingly is, no, not at + +this hour the afternoon, +thank you. + +Yeah? + +AUDIENCE: Left one. + +PROFESSOR: Yeah, very good. + +Right ones have to go left ones, +and they're going to go + +left and right about +these planes here. + +And, if I combine this glide +plane with t2, there has to be + +another glide plane in here. + +If I combine this glide plane +with t1, there'll have to be + +another glide plane in here. + +OK, and that turns out to be +plane group number eight, + +P2gg, not P2mm, both mirror +planes have become glide. + +All right, we're almost there. + +If you look at the hexagonal +symmetries, there is just no + +way that you can interweave +things, and an attempt is made + +in the notes that +I handed out. + +You just cannot do it. + +But with P4M, P4, there is +one final possibility. + +And I'll just set that up +and not carry them out. + +OK, I'm going to put on just P4 +with twofold axes in here. + +Now we have planes that go in +orientations like this. + +And then there is another plane +45 degrees away that is + +a symmetry independent plane. + +And the question now, I'll let +you have a crack at it, is + +there any way in which I could +take planes in the diagonal + +orientation or parallel to the +cell edge and interweave them + +in between the rotation axes +in such a fashion that the + +rotation axes were +left invariant? + +Again, conversely if they're +not left invariant, we will + +have created new translations +and wreck the lattice. + +So how could we slip in planes, +either reflection or + +glide, and leave the +axes invariant? + +AUDIENCE: One quarter +and three quarters? + +PROFESSOR: Yeah. + +Do you want parallel +to the cell edge? + +AUDIENCE: Horizontal. + +PROFESSOR: Horizontal? + +Yeah. + +This [INAUDIBLE] + +here has a fourfold axis up, +a fourfold axis down, a + +fourfold axis up. + +Twofold axis down, twofold axis +up, twofold axis down. + +So this would be a lovely +location for a glide plane. + +So that's one. + +From the fact that I am placing +the same diagram on + +the board yet again suggests +that there's another way. + +That's a perfectly good +suggestion, and that's one of + +the things we would +have to examine. + +Is there any other way I could +put in a mirror plane or a + +glide plane and leave +the axes invariant? + +Yeah? + +AUDIENCE: [INAUDIBLE] + +45 degrees? + +PROFESSOR: 45 degrees. + +Through here. + +I don't want to do it through +here because the fourfold axes + +sit on the same side, but you +want to put it in like this? + +I don't think you can do that. + +Glide plane won't work here. + +How about a mirror plane? + +There's no mirror plane that +goes through these twofold + +axes for P4mm. + +What we had there were mirror +planes here, and then going + +this way were glide planes. + +We've already got that. + +How about putting in a mirror +plane like that? + +This goes into this. + +Halfway along there would have +to be another mirror plane in + +that orientation. + +Here's a twofold axis that +demands that there has to be + +another one if it has a mirror +plane passing through it. + +So there's another way. + +One final one, and I will not +keep you guessing anymore, + +sneaking a peak at the answer. + +There is another way you could +do it, and that would be to + +put the glide plane down +diagonally through the cell. + +That is put the glide +plane here. + +That and take this twofold axis, +reflect it across to + +here, and slide it +down to here. + +So this twofold axis would be +related to this one by glide. + +So those three possibilities are +available for point group + +4mm and a square net. + +If you try them, and the simple +way of doing it without + +any general theorem would be +to draw in the way the + +symmetry elements repeat the +motifs, and then ask what they + +require for the remaining +symmetry elements. + +All of these give the +final result. + +So they yield the same result. + +You can develop a general +theorem for what you obtain if + +you have an operation a, alpha +combined with a plane, and + +make it a general plan, a glide +plane that is removed + +from the axis by some +distance delta. + +And that theorem is written out +for you in the notes on + +the very first page. + +You take a glide plane, and this +is a specific example, a, + +pi, if you have a glide plane +that misses a twofold axis by + +some distance delta, then the +effect of those two successive + +operations is a glide plane at +90 degrees to the first, and + +it's removed from the twofold +axis by two delta. + +It has a glide component, +excuse me, has a glide + +component two delta. + +So there's a general theorem +for the twofold rotation. + +The general theorem for a +fourfold or a threefold + +rotation is considerably more +complex to derive, but that's + +contained for you in +the notes as well. + +All right, we've come to the end +of one other major part of + +our story of symmetry. + +These are the periodic +patterns in a + +two dimensional space. + +And these are then the 17 +crystallographic plane groups. + +Crystallographic is rather +redundant because they are + +groups that have [? in ?] +translation and therefore + +these are the symmetries, the +two dimensional symmetries + +that are suitable +for the atomic + +arrangements in crystals. + +As a little bonus, we also have, +as a result, 17 of the + +three dimensional +space groups. + +Just imagine each of these +plane groups with a + +translation perpendicular to the +plane of the plane group, + +and that would leave all the +symmetry elements coincidence. + +So you could pick a third +translation at right angles to + +the blackboard of any arbitrary +length, and you + +would have a three dimensional +lattice that contain the + +symmetries of a plane group. + +I think I mentioned earlier that +the way you distinguish a + +plane group with a twofold axis +in it from a space group + +with a twofold axis is that +a lowercase letter for the + +lattice type implies plane +group, and an uppercase + +symbol, capital P stands +for a primitive + +lattice in a space group. + +So something like lowercase p4mm +is a plane group, capital + +P4mm is a space group with a +third translation of arbitrary + +length at right angles +to the plane group. + +We talked about plane groups and +space groups, let's take a + +giant leap backwards. + +How about the one dimensional +space groups? + +Bet you were wondering about +them all along and + +were afraid to ask. + +So what would be the story +for one dimension? + +It's nontrivial. + +A one dimensional space group +would be a lattice row. + +You have just one dimension to +play with, and you can make + +that space periodic +by translation. + +So there's one lattice type. + +Just the lattice row. + +And what sort of symmetries +could you + +place in that lattice? + +Now you have to define +your ground rules. + +In our two dimensional +symmetries, we did not permit + +any operation which would pick +the two dimensional space up + +and rotate it and flip it over +and put it down again, because + +that is a transformation that +takes you out of that space + +and pops you back into it. + +And we will not in our +discussion of three + +dimensional crystallography +consider symmetries operations + +that take something, suck it +up into a fourth dimension + +that we can't comprehend, and +then all of a sudden pop it + +down in again, and suddenly +it appears. + +I mean, that sounds bizarre. + +We wouldn't want to do that. + +So for plane groups, we did not +allow for any operation, + +say a twofold axis that would +flip the object over and turn + +it upside down. + +But why not? + +I mean this, is mathematics. + +If it's your ballgame, you +can make up the rules. + +So why couldn't we have a +twofold axis in the plane or + +the plane group? + +It would have to leave +the net invariant. + +Well actually such entities +do exist, and + +they have been derived. + +They're called the two +sided plane groups. + +And if you want to allow that +when you make up the game, you + +can actually do that if +you wish to allow it. + +And also there could be a mirror +plane in the plane of + +the space that would take the +top side and relate it to the + +bottom side. + +So you can do that, you +can permit that. + +That's a different beast +entirely, but you can allow + +that to be one of the +transformations. + +So for our one dimensional +space, I would submit to be + +consistent with what we've done +and just finished in two + +dimensions. + +And what we will do in three, +we will not allow for any + +operation that will take the +space and transform it into a + +second or third dimension, and +then put it down again. + +So that being the case, the +only operation that is + +possible is a mirror point +that would reflect + +things left to right. + +And let me illustrate now +with some patterns. + +There's the lattice point. + +So let me put in some motifs. + +and I have to make a one +dimensional motif, but to + +distinguish the ends I'll take +a little artistic license and + +make one end of the motif a +little fatter than the other. + +Or alternatively, I could put +a little one dimensional + +headlight on this +thing that would + +shine just in one direction. + +So here's a motif hung on every +lattice point, and so + +this is no symmetry at all. + +So the symmetry part of the +symbol would be one, and the + +lattice is primitive, and what +do you think people use? + +We've used lowercase symbols, +we used uppercase symbols, + +what's left? + +Yes? + +AUDIENCE: Greek? + +PROFESSOR: Good try. + +Gothic. + +Actually, what you do is you use +a Gothic symbol with all + +these nice little shaded +angular shapes. + +That's a Gothich P, isn't it? + +Yeah, that's a Gothic +P. It is. + +It actually has thick and +thin parts, curved parts + +[INAUDIBLE]. + +So that's P1. + +What about another symmetry? + +Well if we have a mirror point +in there, another possibility + +would be to have these +motifs point + +alternately left and right. + +So I'll take some non one +dimensional license and say + +that there would be mirror +points at these locations. + +Really nice symmetry, but +actually it would be totally + +wasted on these poor denizens +in a one dimensional world. + +Life would be dull and +uninteresting because they + +couldn't see anything except +the motif on either side of + +them, because everything is +constrained to one dimension. + +There's an old saying about sled +dogs that says if you are + +not the lead dog, the scenery +is not very interesting. + +And the same is true for these +poor people in a one + +dimensional world. + +They could never see the +elegance and beauty of that. + +But in any case, that would be +Gothic P, no snickers, please, + +and that would be m. + +And those are the only two +possibilities and a one + +dimensional space. + +We have a couple minutes to go, +but I think this is a good + +place to pause. + +And I'll give just a brief +indication of coming + +attractions. + +We're now going to look at +point groups in three + +dimensions, and a good way of +entering this much more + +complex situation is to go back +to something analogous to + +what we did for two dimensional +symmetries. + +And I'm going to first consider +the arrangement of + +rotation axes in three +dimensions. + +We do not have the constraint +that all the rotation axes be + +perpendicular to the plane of a +two dimensional space, being + +therefore more properly +rotation points. + +We've got three dimensions we +have to view a rotation axis + +as extending infinitely in a +direction, and there's no + +reason why we can't have another +rotation axis at an + +angle to it. + +But you know that already. + +Everybody's heard about +cubic crystals. + +Even if you think all crystals +are either body centered + +cubic, primitive cubic, face +centered cubic, or complex, + +four kinds of lattices. + +But you've heard of cubic +crystals, in the cubic + +crystals clearly the rotation +axes are inclined to one + +another and arranged +spacially. + +So we're going to ask the +nontrivial question, how can + +we combine more than one +rotation axis at a time about + +a common point in space? + +And the constraint is going to +be that a rotation about the + +first axis followed by a +rotation about the second + +axis, wherever it is, is going +to have to turn out to be + +something that is +crystallographically + +compatible with a lattice. + +So that's the constraint. + +It's not an easy question. + +And just to make you feel proud +of yourself when we get + +through this, this uses a +geometry that is due to one of + +the great mathematicians of +all time, Leonhard Euler. + +Probably the most remarkable +thing about Euler was that + +he's Swiss. + +How many world class scientists +have you heard of + +that come from Switzerland? + +Not very many, and the reason is +it's such a small country, + +and if genius occurs as a +certain fraction of the + +population, that's not going +to happen very often in a + +country like Lichtenstein +or Switzerland. + +Have you ever heard of anybody +prominent in science who came + +from Lichtenstein? + +No, probably not. + +OK, this then is going to +be a nontrivial piece of + +mathematics for us, largely +because it involves spherical + +trigonometry. + +Which I'm sure if you've ever +heard of, you've forgotten, + +and probably don't see +any utility in it. + +OK, with that exciting prospect +in hand, I look + +forward to seeing +you on Thursday. \ No newline at end of file diff --git a/xmImNoDc9Z4.txt b/xmImNoDc9Z4.txt new file mode 100644 index 0000000000000000000000000000000000000000..2c63b6670f8ca0f62eebb77a0f445c2da267e045 --- /dev/null +++ b/xmImNoDc9Z4.txt @@ -0,0 +1,16731 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay so today today's lecture right is + + align:start position:0% +okay so today today's lecture right is + + + align:start position:0% +okay so today today's lecture right is +relevant for a couple reasons but we're + + align:start position:0% +relevant for a couple reasons but we're + + + align:start position:0% +relevant for a couple reasons but we're +going to be talking about about probably + + align:start position:0% +going to be talking about about probably + + + align:start position:0% +going to be talking about about probably +planning later right and in these cases + + align:start position:0% +planning later right and in these cases + + + align:start position:0% +planning later right and in these cases +were you doing in planning a large state + + align:start position:0% +were you doing in planning a large state + + + align:start position:0% +were you doing in planning a large state +spaces Frank this is very difficult if + + align:start position:0% +spaces Frank this is very difficult if + + + align:start position:0% +spaces Frank this is very difficult if +one of the main thing you can do it + + align:start position:0% +one of the main thing you can do it + + + align:start position:0% +one of the main thing you can do it +could be MVP planning it would be you + + align:start position:0% +could be MVP planning it would be you + + + align:start position:0% +could be MVP planning it would be you +know stressful activity planning of the + + align:start position:0% +know stressful activity planning of the + + + align:start position:0% +know stressful activity planning of the +lights but you have to deal with spaces + + align:start position:0% +lights but you have to deal with spaces + + + align:start position:0% +lights but you have to deal with spaces +so money Carla researches is one of the + + align:start position:0% +so money Carla researches is one of the + + + align:start position:0% +so money Carla researches is one of the +techniques that people kind of + + align:start position:0% +techniques that people kind of + + + align:start position:0% +techniques that people kind of +identified over the last five years as + + align:start position:0% +identified over the last five years as + + + align:start position:0% +identified over the last five years as +having an amazing performance + + align:start position:0% +having an amazing performance + + + align:start position:0% +having an amazing performance +improvement over other kinds of + + align:start position:0% +improvement over other kinds of + + + align:start position:0% +improvement over other kinds of +Saturday's Republican so MCT is very + + align:start position:0% +Saturday's Republican so MCT is very + + + align:start position:0% +Saturday's Republican so MCT is very +interesting in that standpoint and then + + align:start position:0% +interesting in that standpoint and then + + + align:start position:0% +interesting in that standpoint and then +if we leave the last lecture right then + + align:start position:0% +if we leave the last lecture right then + + + align:start position:0% +if we leave the last lecture right then +the combination of something which is + + align:start position:0% +the combination of something which is + + + align:start position:0% +the combination of something which is +trying to learn about policy combining + + align:start position:0% +trying to learn about policy combining + + + align:start position:0% +trying to learn about policy combining +with surf is very powerful in this case + + align:start position:0% +with surf is very powerful in this case + + + align:start position:0% +with surf is very powerful in this case +through the state of art my techniques + + align:start position:0% +through the state of art my techniques + + + align:start position:0% +through the state of art my techniques +for that is research the other + + align:start position:0% + + + + align:start position:0% + +good morning everyone as Professor + + align:start position:0% +good morning everyone as Professor + + + align:start position:0% +good morning everyone as Professor +leontius said we are going to be talking + + align:start position:0% +leontius said we are going to be talking + + + align:start position:0% +leontius said we are going to be talking +about Monte Carlo tree search today by + + align:start position:0% +about Monte Carlo tree search today by + + + align:start position:0% +about Monte Carlo tree search today by +the end of this presentation you will + + align:start position:0% +the end of this presentation you will + + + align:start position:0% +the end of this presentation you will +know not only why we care about money + + align:start position:0% +know not only why we care about money + + + align:start position:0% +know not only why we care about money +college district is as Professor + + align:start position:0% +college district is as Professor + + + align:start position:0% +college district is as Professor +Williams said there's so many algorithms + + align:start position:0% +Williams said there's so many algorithms + + + align:start position:0% +Williams said there's so many algorithms +out there + + align:start position:0% +out there + + + align:start position:0% +out there +why to the care of this specific one and + + align:start position:0% +why to the care of this specific one and + + + align:start position:0% +why to the care of this specific one and +second we have will be going to the pros + + align:start position:0% +second we have will be going to the pros + + + align:start position:0% +second we have will be going to the pros +and cons of MCTS as well as the + + align:start position:0% +and cons of MCTS as well as the + + + align:start position:0% +and cons of MCTS as well as the +algorithm itself and then lastly we will + + align:start position:0% +algorithm itself and then lastly we will + + + align:start position:0% +algorithm itself and then lastly we will +have a pretty cool demo on how it's + + align:start position:0% +have a pretty cool demo on how it's + + + align:start position:0% +have a pretty cool demo on how it's +applied to Super Mario Brothers and the + + align:start position:0% +applied to Super Mario Brothers and the + + + align:start position:0% +applied to Super Mario Brothers and the +latest alphago AI that built the second + + align:start position:0% +latest alphago AI that built the second + + + align:start position:0% +latest alphago AI that built the second +best feeding of Latino player for + + align:start position:0% +best feeding of Latino player for + + + align:start position:0% +best feeding of Latino player for +today's presentation is first we're + + align:start position:0% +today's presentation is first we're + + + align:start position:0% +today's presentation is first we're +going to talk about pre and CTS + + align:start position:0% +going to talk about pre and CTS + + + align:start position:0% +going to talk about pre and CTS +algorithms the other algorithms that + + align:start position:0% +algorithms the other algorithms that + + + align:start position:0% +algorithms the other algorithms that +currently exist out there and just a few + + align:start position:0% +currently exist out there and just a few + + + align:start position:0% +currently exist out there and just a few +of them to lead into why we do care + + align:start position:0% +of them to lead into why we do care + + + align:start position:0% +of them to lead into why we do care +about MCTS and why these other + + align:start position:0% +about MCTS and why these other + + + align:start position:0% +about MCTS and why these other +algorithms failed and ii will talk about + + align:start position:0% +algorithms failed and ii will talk about + + + align:start position:0% +algorithms failed and ii will talk about +Monte Carlo tree search itself with you + + align:start position:0% +Monte Carlo tree search itself with you + + + align:start position:0% +Monte Carlo tree search itself with you +and lastly tip will tell you more about + + align:start position:0% +and lastly tip will tell you more about + + + align:start position:0% +and lastly tip will tell you more about +the applications of Monte Carlo tree + + align:start position:0% +the applications of Monte Carlo tree + + + align:start position:0% +the applications of Monte Carlo tree +search so the motivation of of these + + align:start position:0% +search so the motivation of of these + + + align:start position:0% +search so the motivation of of these +kinds of algorithms is you want to be + + align:start position:0% +kinds of algorithms is you want to be + + + align:start position:0% +kinds of algorithms is you want to be +able to play games and we want to be + + align:start position:0% +able to play games and we want to be + + + align:start position:0% +able to play games and we want to be +able to create programs to play these + + align:start position:0% +able to create programs to play these + + + align:start position:0% +able to create programs to play these +games but we want to play them optimally + + align:start position:0% +games but we want to play them optimally + + + align:start position:0% +games but we want to play them optimally +we want to be able to win but we also + + align:start position:0% +we want to be able to win but we also + + + align:start position:0% +we want to be able to win but we also +want to be able to do this in a + + align:start position:0% +want to be able to do this in a + + + align:start position:0% +want to be able to do this in a +reasonable amount of time so these three + + align:start position:0% +reasonable amount of time so these three + + + align:start position:0% +reasonable amount of time so these three +constraints itself lead to different + + align:start position:0% +constraints itself lead to different + + + align:start position:0% +constraints itself lead to different +kinds of algorithms and different + + align:start position:0% +kinds of algorithms and different + + + align:start position:0% +kinds of algorithms and different +algorithms with different complexities + + align:start position:0% +algorithms with different complexities + + + align:start position:0% +algorithms with different complexities +and time or ties to search and so that's + + align:start position:0% +and time or ties to search and so that's + + + align:start position:0% +and time or ties to search and so that's +why would a we're going to be talking + + align:start position:0% +why would a we're going to be talking + + + align:start position:0% +why would a we're going to be talking +about Monte Carlo tree search and you'll + + align:start position:0% +about Monte Carlo tree search and you'll + + + align:start position:0% +about Monte Carlo tree search and you'll +figure out it and a few slides why they + + align:start position:0% +figure out it and a few slides why they + + + align:start position:0% +figure out it and a few slides why they +do care so these are the types of games + + align:start position:0% +do care so these are the types of games + + + align:start position:0% +do care so these are the types of games +we have you have this chart where + + align:start position:0% +we have you have this chart where + + + align:start position:0% +we have you have this chart where +there's fully observable of cervical + + align:start position:0% +there's fully observable of cervical + + + align:start position:0% +there's fully observable of cervical +games partially observable games + + align:start position:0% +games partially observable games + + + align:start position:0% +games partially observable games +deterministic and games with chance and + + align:start position:0% +deterministic and games with chance and + + + align:start position:0% +deterministic and games with chance and +so today that games that we care about + + align:start position:0% +so today that games that we care about + + + align:start position:0% +so today that games that we care about +are the games that are fully observable + + align:start position:0% +are the games that are fully observable + + + align:start position:0% +are the games that are fully observable +and deterministic and these games + + align:start position:0% +and deterministic and these games + + + align:start position:0% +and deterministic and these games +include games like chess and checkers + + align:start position:0% +include games like chess and checkers + + + align:start position:0% +include games like chess and checkers +and Co and we'll also be talking about + + align:start position:0% +and Co and we'll also be talking about + + + align:start position:0% +and Co and we'll also be talking about +another example with tic-tac-toe + + align:start position:0% +another example with tic-tac-toe + + + align:start position:0% +another example with tic-tac-toe +so these three MCTS algorithms include + + align:start position:0% +so these three MCTS algorithms include + + + align:start position:0% +so these three MCTS algorithms include +deterministic fully observable games + + align:start position:0% +deterministic fully observable games + + + align:start position:0% +deterministic fully observable games +like we said earlier and the idea of + + align:start position:0% +like we said earlier and the idea of + + + align:start position:0% +like we said earlier and the idea of +this and me the nice thing about these + + align:start position:0% +this and me the nice thing about these + + + align:start position:0% +this and me the nice thing about these +games is that they're they have perfect + + align:start position:0% +games is that they're they have perfect + + + align:start position:0% +games is that they're they have perfect +information and that you have all of the + + align:start position:0% +information and that you have all of the + + + align:start position:0% +information and that you have all of the +states that you need and there's no + + align:start position:0% +states that you need and there's no + + + align:start position:0% +states that you need and there's no +opportunity for chance and so the idea + + align:start position:0% +opportunity for chance and so the idea + + + align:start position:0% +opportunity for chance and so the idea +is that we can construct a dream that + + align:start position:0% +is that we can construct a dream that + + + align:start position:0% +is that we can construct a dream that +contains all possible outcomes because + + align:start position:0% +contains all possible outcomes because + + + align:start position:0% +contains all possible outcomes because +everything is fully determined and so + + align:start position:0% +everything is fully determined and so + + + align:start position:0% +everything is fully determined and so +one of these algorithms to address this + + align:start position:0% +one of these algorithms to address this + + + align:start position:0% +one of these algorithms to address this +if you have here the minimax which you + + align:start position:0% +if you have here the minimax which you + + + align:start position:0% +if you have here the minimax which you +might might have heard before and the + + align:start position:0% +might might have heard before and the + + + align:start position:0% +might might have heard before and the +idea of minimax is to minimize the + + align:start position:0% +idea of minimax is to minimize the + + + align:start position:0% +idea of minimax is to minimize the +maximum possible bus then it sounds a + + align:start position:0% +maximum possible bus then it sounds a + + + align:start position:0% +maximum possible bus then it sounds a +little weird in the beginning but if you + + align:start position:0% +little weird in the beginning but if you + + + align:start position:0% +little weird in the beginning but if you +take a look at this tree this red dot + + align:start position:0% +take a look at this tree this red dot + + + align:start position:0% +take a look at this tree this red dot +for example is the computer and so in + + align:start position:0% +for example is the computer and so in + + + align:start position:0% +for example is the computer and so in +the computer's eyes it wants to beat its + + align:start position:0% +the computer's eyes it wants to beat its + + + align:start position:0% +the computer's eyes it wants to beat its +opponent and we're assuming the opponent + + align:start position:0% +opponent and we're assuming the opponent + + + align:start position:0% +opponent and we're assuming the opponent +wants to win also so they're playing + + align:start position:0% +wants to win also so they're playing + + + align:start position:0% +wants to win also so they're playing +their best game as well and so the + + align:start position:0% +their best game as well and so the + + + align:start position:0% +their best game as well and so the +computer wants to maximize his or her + + align:start position:0% +computer wants to maximize his or her + + + align:start position:0% +computer wants to maximize his or her +points but also things also knowing that + + align:start position:0% +points but also things also knowing that + + + align:start position:0% +points but also things also knowing that +the opponent or the human wants to + + align:start position:0% +the opponent or the human wants to + + + align:start position:0% +the opponent or the human wants to +maximize their own win as well and so in + + align:start position:0% +maximize their own win as well and so in + + + align:start position:0% +maximize their own win as well and so in +the computer's eyes it wants to minimize + + align:start position:0% +the computer's eyes it wants to minimize + + + align:start position:0% +the computer's eyes it wants to minimize +the maximum possible months does that + + align:start position:0% +the maximum possible months does that + + + align:start position:0% +the maximum possible months does that +mean sensor + + align:start position:0% + + + + align:start position:0% + +and so in the example of minimax we're + + align:start position:0% +and so in the example of minimax we're + + + align:start position:0% +and so in the example of minimax we're +gonna start with a Kinect or a + + align:start position:0% +gonna start with a Kinect or a + + + align:start position:0% +gonna start with a Kinect or a +tic-tac-toe board where the computer is + + align:start position:0% +tic-tac-toe board where the computer is + + + align:start position:0% +tic-tac-toe board where the computer is +this order right here and the blue and + + align:start position:0% +this order right here and the blue and + + + align:start position:0% +this order right here and the blue and +the blue tic-tac-toe Awards are the + + align:start position:0% +the blue tic-tac-toe Awards are the + + + align:start position:0% +the blue tic-tac-toe Awards are the +states that the computer clinic chooses + + align:start position:0% +states that the computer clinic chooses + + + align:start position:0% +states that the computer clinic chooses +it's anticipating what the moves the + + align:start position:0% +it's anticipating what the moves the + + + align:start position:0% +it's anticipating what the moves the +human could play so if you take a look + + align:start position:0% +human could play so if you take a look + + + align:start position:0% +human could play so if you take a look +up here so if you take a look up here + + align:start position:0% +up here so if you take a look up here + + + align:start position:0% +up here so if you take a look up here +here's the current state of the board + + align:start position:0% +here's the current state of the board + + + align:start position:0% +here's the current state of the board +current state of the board and the + + align:start position:0% +current state of the board and the + + + align:start position:0% +current state of the board and the +possible options for human are this guy + + align:start position:0% +possible options for human are this guy + + + align:start position:0% +possible options for human are this guy +this guy no possible options for the + + align:start position:0% +this guy no possible options for the + + + align:start position:0% +this guy no possible options for the +computer we have three different options + + align:start position:0% +computer we have three different options + + + align:start position:0% +computer we have three different options +and so you'll notice that this is + + align:start position:0% +and so you'll notice that this is + + + align:start position:0% +and so you'll notice that this is +clearly the obvious winner but in the + + align:start position:0% +clearly the obvious winner but in the + + + align:start position:0% +clearly the obvious winner but in the +state of mini max it goes through the + + align:start position:0% +state of mini max it goes through the + + + align:start position:0% +state of mini max it goes through the +entire tree which is different from + + align:start position:0% +entire tree which is different from + + + align:start position:0% +entire tree which is different from +depth or search it goes into the entire + + align:start position:0% +depth or search it goes into the entire + + + align:start position:0% +depth or search it goes into the entire +tree until it finds the winning move and + + align:start position:0% +tree until it finds the winning move and + + + align:start position:0% +tree until it finds the winning move and +the max minimize of the maximum possible + + align:start position:0% +the max minimize of the maximum possible + + + align:start position:0% +the max minimize of the maximum possible +point second way so is there a way we + + align:start position:0% +point second way so is there a way we + + + align:start position:0% +point second way so is there a way we +can make this better yes I'm sure you + + align:start position:0% +can make this better yes I'm sure you + + + align:start position:0% +can make this better yes I'm sure you +thought it you've heard about pruning or + + align:start position:0% +thought it you've heard about pruning or + + + align:start position:0% +thought it you've heard about pruning or +in our human and our human intuition it + + align:start position:0% +in our human and our human intuition it + + + align:start position:0% +in our human and our human intuition it +makes sense well why don't you just stop + + align:start position:0% +makes sense well why don't you just stop + + + align:start position:0% +makes sense well why don't you just stop +when we win or when we know that we're + + align:start position:0% +when we win or when we know that we're + + + align:start position:0% +when we win or when we know that we're +going to have a game that that allows us + + align:start position:0% +going to have a game that that allows us + + + align:start position:0% +going to have a game that that allows us +to win and tonight is the idea of simple + + align:start position:0% +to win and tonight is the idea of simple + + + align:start position:0% +to win and tonight is the idea of simple +tree and so when we combine minimax and + + align:start position:0% +tree and so when we combine minimax and + + + align:start position:0% +tree and so when we combine minimax and +simple pruney + + align:start position:0% +simple pruney + + + align:start position:0% +simple pruney +we have anyone know yes or 6:03 for a + + align:start position:0% +we have anyone know yes or 6:03 for a + + + align:start position:0% +we have anyone know yes or 6:03 for a +genius + + align:start position:0% +genius + + + align:start position:0% +genius +we have alpha beta pruning where you + + align:start position:0% +we have alpha beta pruning where you + + + align:start position:0% +we have alpha beta pruning where you +prune away any branches that cannot + + align:start position:0% +prune away any branches that cannot + + + align:start position:0% +prune away any branches that cannot +influence the final decision so in other + + align:start position:0% +influence the final decision so in other + + + align:start position:0% +influence the final decision so in other +words you wouldn't keep exploring the + + align:start position:0% +words you wouldn't keep exploring the + + + align:start position:0% +words you wouldn't keep exploring the +tree if you already knew that a previous + + align:start position:0% +tree if you already knew that a previous + + + align:start position:0% +tree if you already knew that a previous +turn would allow you to win and so this + + align:start position:0% +turn would allow you to win and so this + + + align:start position:0% +turn would allow you to win and so this +idea in alpha beta pruning we have the + + align:start position:0% +idea in alpha beta pruning we have the + + + align:start position:0% +idea in alpha beta pruning we have the +Alpha and the beta and so if the details + + align:start position:0% +Alpha and the beta and so if the details + + + align:start position:0% +Alpha and the beta and so if the details +aren't missed aren't important for you + + align:start position:0% +aren't missed aren't important for you + + + align:start position:0% +aren't missed aren't important for you +to know right now but the idea is that + + align:start position:0% +to know right now but the idea is that + + + align:start position:0% +to know right now but the idea is that +we stop whenever we know we don't need + + align:start position:0% +we stop whenever we know we don't need + + + align:start position:0% +we stop whenever we know we don't need +to go on any further so in the means of + + align:start position:0% +to go on any further so in the means of + + + align:start position:0% +to go on any further so in the means of +tic-tac-toe in Connect or in chess we + + align:start position:0% +tic-tac-toe in Connect or in chess we + + + align:start position:0% +tic-tac-toe in Connect or in chess we +have relatively low rating factors so in + + align:start position:0% +have relatively low rating factors so in + + + align:start position:0% +have relatively low rating factors so in +the case of tic-tac-toe we have 2 to the + + align:start position:0% +the case of tic-tac-toe we have 2 to the + + + align:start position:0% +the case of tic-tac-toe we have 2 to the +fourth ranking factor but what if we + + align:start position:0% +fourth ranking factor but what if we + + + align:start position:0% +fourth ranking factor but what if we +have really large branching factors like + + align:start position:0% +have really large branching factors like + + + align:start position:0% +have really large branching factors like +alphago in alphago we have 2 to the + + align:start position:0% +alphago in alphago we have 2 to the + + + align:start position:0% +alphago in alphago we have 2 to the +215th do you think that minimax or even + + align:start position:0% +215th do you think that minimax or even + + + align:start position:0% +215th do you think that minimax or even +alpha beta for me would be an optimal + + align:start position:0% +alpha beta for me would be an optimal + + + align:start position:0% +alpha beta for me would be an optimal +algorithm the answer is no and this + + align:start position:0% +algorithm the answer is no and this + + + align:start position:0% +algorithm the answer is no and this +leads us to our next presentation to our + + align:start position:0% +leads us to our next presentation to our + + + align:start position:0% +leads us to our next presentation to our +next section where yo is going to talk + + align:start position:0% +next section where yo is going to talk + + + align:start position:0% +next section where yo is going to talk +about how we can use the Monte Carlo + + align:start position:0% +about how we can use the Monte Carlo + + + align:start position:0% +about how we can use the Monte Carlo +tree search algorithm for games with + + align:start position:0% +tree search algorithm for games with + + + align:start position:0% +tree search algorithm for games with +really high branching factors and using + + align:start position:0% +really high branching factors and using + + + align:start position:0% +really high branching factors and using +the random expansion to allow us to see + + align:start position:0% +the random expansion to allow us to see + + + align:start position:0% +the random expansion to allow us to see +ultimately how alphago which is google's + + align:start position:0% +ultimately how alphago which is google's + + + align:start position:0% +ultimately how alphago which is google's +AI was able to eat e leading go player + + align:start position:0% +AI was able to eat e leading go player + + + align:start position:0% +AI was able to eat e leading go player +in the world + + align:start position:0% + + + + align:start position:0% + +okay so this is the part where we do we + + align:start position:0% +okay so this is the part where we do we + + + align:start position:0% +okay so this is the part where we do we +explain the algorithm some and - before + + align:start position:0% +explain the algorithm some and - before + + + align:start position:0% +explain the algorithm some and - before +we dive into this I wanna make something + + align:start position:0% +we dive into this I wanna make something + + + align:start position:0% +we dive into this I wanna make something +really clear which is that like because + + align:start position:0% +really clear which is that like because + + + align:start position:0% +really clear which is that like because +these are technical details and because + + align:start position:0% +these are technical details and because + + + align:start position:0% +these are technical details and because +we actually want you to understand them + + align:start position:0% +we actually want you to understand them + + + align:start position:0% +we actually want you to understand them +and because I didn't even understand + + align:start position:0% +and because I didn't even understand + + + align:start position:0% +and because I didn't even understand +this the first one three times that are + + align:start position:0% +this the first one three times that are + + + align:start position:0% +this the first one three times that are +at the paper I really want you to feel + + align:start position:0% +at the paper I really want you to feel + + + align:start position:0% +at the paper I really want you to feel +free to ask any questions on your mind + + align:start position:0% +free to ask any questions on your mind + + + align:start position:0% +free to ask any questions on your mind +with the knowledge that like as in my + + align:start position:0% +with the knowledge that like as in my + + + align:start position:0% +with the knowledge that like as in my +experience it is very rare that someone + + align:start position:0% +experience it is very rare that someone + + + align:start position:0% +experience it is very rare that someone +asks a question in class that's missing + + align:start position:0% +asks a question in class that's missing + + + align:start position:0% +asks a question in class that's missing +okay so whenever you have okay so why + + align:start position:0% +okay so whenever you have okay so why + + + align:start position:0% +okay so whenever you have okay so why +are we doing this well the ideal goal + + align:start position:0% +are we doing this well the ideal goal + + + align:start position:0% +are we doing this well the ideal goal +behind ncts is that we want to + + align:start position:0% +behind ncts is that we want to + + + align:start position:0% +behind ncts is that we want to +selectively build out different parts of + + align:start position:0% +selectively build out different parts of + + + align:start position:0% +selectively build out different parts of +the tree so the sort of the diamond the + + align:start position:0% +the tree so the sort of the diamond the + + + align:start position:0% +the tree so the sort of the diamond the +depth-first search + + align:start position:0% +depth-first search + + + align:start position:0% +depth-first search +kind of way the exhaustive sort of + + align:start position:0% +kind of way the exhaustive sort of + + + align:start position:0% +kind of way the exhaustive sort of +search would have us explore in the + + align:start position:0% +search would have us explore in the + + + align:start position:0% +search would have us explore in the +entirety of the tree and that our depth + + align:start position:0% +entirety of the tree and that our depth + + + align:start position:0% +entirety of the tree and that our depth +is limited by you know looking all the + + align:start position:0% +is limited by you know looking all the + + + align:start position:0% +is limited by you know looking all the +possible nodes at that level but what we + + align:start position:0% +possible nodes at that level but what we + + + align:start position:0% +possible nodes at that level but what we +want is we want that because like that + + align:start position:0% +want is we want that because like that + + + align:start position:0% +want is we want that because like that +need another computation of fire - that + + align:start position:0% +need another computation of fire - that + + + align:start position:0% +need another computation of fire - that +explodes really quickly you know with + + align:start position:0% +explodes really quickly you know with + + + align:start position:0% +explodes really quickly you know with +the number of moves that you're + + align:start position:0% +the number of moves that you're + + + align:start position:0% +the number of moves that you're +basically looking into the future we + + align:start position:0% +basically looking into the future we + + + align:start position:0% +basically looking into the future we +want to be able to search selectively in + + align:start position:0% +want to be able to search selectively in + + + align:start position:0% +want to be able to search selectively in +certain parts of the tree and so for + + align:start position:0% +certain parts of the tree and so for + + + align:start position:0% +certain parts of the tree and so for +example if there are less promising + + align:start position:0% +example if there are less promising + + + align:start position:0% +example if there are less promising +parts over here then we care less about + + align:start position:0% +parts over here then we care less about + + + align:start position:0% +parts over here then we care less about +looking into the future in those areas + + align:start position:0% +looking into the future in those areas + + + align:start position:0% +looking into the future in those areas +but if we have you know a certain move + + align:start position:0% +but if we have you know a certain move + + + align:start position:0% +but if we have you know a certain move +in chests for example there's a certain + + align:start position:0% +in chests for example there's a certain + + + align:start position:0% +in chests for example there's a certain +move where in two moves I'm gonna be + + align:start position:0% +move where in two moves I'm gonna be + + + align:start position:0% +move where in two moves I'm gonna be +able to take the opponent's Queen right + + align:start position:0% +able to take the opponent's Queen right + + + align:start position:0% +able to take the opponent's Queen right +but I really want to search that region + + align:start position:0% +but I really want to search that region + + + align:start position:0% +but I really want to search that region +and figure out whether that's going to + + align:start position:0% +and figure out whether that's going to + + + align:start position:0% +and figure out whether that's going to +end up being like a significantly + + align:start position:0% +end up being like a significantly + + + align:start position:0% +end up being like a significantly +positive move for me and so the cold + + align:start position:0% +positive move for me and so the cold + + + align:start position:0% +positive move for me and so the cold +goal of our algorithm is going to be + + align:start position:0% +goal of our algorithm is going to be + + + align:start position:0% +goal of our algorithm is going to be +growing assassin monitoring how is the + + align:start position:0% +growing assassin monitoring how is the + + + align:start position:0% +growing assassin monitoring how is the +presence of + + align:start position:0% + + + + align:start position:0% + +okay great + + align:start position:0% +okay great + + + align:start position:0% +okay great +so how do we actually do this um we're + + align:start position:0% +so how do we actually do this um we're + + + align:start position:0% +so how do we actually do this um we're +gonna be going over a high-level outline + + align:start position:0% +gonna be going over a high-level outline + + + align:start position:0% +gonna be going over a high-level outline +before we do that let's talk about our + + align:start position:0% +before we do that let's talk about our + + + align:start position:0% +before we do that let's talk about our +tree which you are going to get very + + align:start position:0% +tree which you are going to get very + + + align:start position:0% +tree which you are going to get very +familiar with um the it's a little bit + + align:start position:0% +familiar with um the it's a little bit + + + align:start position:0% +familiar with um the it's a little bit +watch out can people see that this is + + align:start position:0% +watch out can people see that this is + + + align:start position:0% +watch out can people see that this is +red and this is blue okay um so this is + + align:start position:0% +red and this is blue okay um so this is + + + align:start position:0% +red and this is blue okay um so this is +our game state when we start when we + + align:start position:0% +our game state when we start when we + + + align:start position:0% +our game state when we start when we +start our game you know can be a given + + align:start position:0% +start our game you know can be a given + + + align:start position:0% +start our game you know can be a given +let's exacto board with a few movies + + align:start position:0% +let's exacto board with a few movies + + + align:start position:0% +let's exacto board with a few movies +place um a game of chess with the moves + + align:start position:0% +place um a game of chess with the moves + + + align:start position:0% +place um a game of chess with the moves +configured in a certain way and so our + + align:start position:0% +configured in a certain way and so our + + + align:start position:0% +configured in a certain way and so our +player which is the computer has three + + align:start position:0% +player which is the computer has three + + + align:start position:0% +player which is the computer has three +separate moves that they dictate and so + + align:start position:0% +separate moves that they dictate and so + + + align:start position:0% +separate moves that they dictate and so +each of those moves are represented by a + + align:start position:0% +each of those moves are represented by a + + + align:start position:0% +each of those moves are represented by a +node and each of those moves have + + align:start position:0% +node and each of those moves have + + + align:start position:0% +node and each of those moves have +response moves by the opponent okay + + align:start position:0% +response moves by the opponent okay + + + align:start position:0% +response moves by the opponent okay +so you can imagine that if one of these + + align:start position:0% +so you can imagine that if one of these + + + align:start position:0% +so you can imagine that if one of these +is a tic-tac-toe board with just a + + align:start position:0% +is a tic-tac-toe board with just a + + + align:start position:0% +is a tic-tac-toe board with just a +circle but one of these is with that + + align:start position:0% +circle but one of these is with that + + + align:start position:0% +circle but one of these is with that +circle and connects placement right by + + align:start position:0% +circle and connects placement right by + + + align:start position:0% +circle and connects placement right by +it and as you sort of go down this tree + + align:start position:0% +it and as you sort of go down this tree + + + align:start position:0% +it and as you sort of go down this tree +we start unused you start understanding + + align:start position:0% +we start unused you start understanding + + + align:start position:0% +we start unused you start understanding +that you know okay basically it's the + + align:start position:0% +that you know okay basically it's the + + + align:start position:0% +that you know okay basically it's the +way that humans think that's all about + + align:start position:0% +way that humans think that's all about + + + align:start position:0% +way that humans think that's all about +playing these games you know if I look + + align:start position:0% +playing these games you know if I look + + + align:start position:0% +playing these games you know if I look +here well then then what if they go + + align:start position:0% +here well then then what if they go + + + align:start position:0% +here well then then what if they go +there and then you know what if I go + + align:start position:0% +there and then you know what if I go + + + align:start position:0% +there and then you know what if I go +what if I go here you're trying to think + + align:start position:0% +what if I go here you're trying to think + + + align:start position:0% +what if I go here you're trying to think +through the set of future moves and try + + align:start position:0% +through the set of future moves and try + + + align:start position:0% +through the set of future moves and try +and evaluate like whether your move will + + align:start position:0% +and evaluate like whether your move will + + + align:start position:0% +and evaluate like whether your move will +be good in a long-term sense + + align:start position:0% +be good in a long-term sense + + + align:start position:0% +be good in a long-term sense +okay so the way that we are going to + + align:start position:0% +okay so the way that we are going to + + + align:start position:0% +okay so the way that we are going to +expand our tree as we said to create an + + align:start position:0% +expand our tree as we said to create an + + + align:start position:0% +expand our tree as we said to create an +isometric at a symmetric tree is first + + align:start position:0% +isometric at a symmetric tree is first + + + align:start position:0% +isometric at a symmetric tree is first +of all we're going to decide through the + + align:start position:0% +of all we're going to decide through the + + + align:start position:0% +of all we're going to decide through the +tree you're going to start at the top + + align:start position:0% +tree you're going to start at the top + + + align:start position:0% +tree you're going to start at the top +and we're going to basically jump down + + align:start position:0% +and we're going to basically jump down + + + align:start position:0% +and we're going to basically jump down +some sequences of branches until we + + align:start position:0% +some sequences of branches until we + + + align:start position:0% +some sequences of branches until we +figure out where we're going to where + + align:start position:0% +figure out where we're going to where + + + align:start position:0% +figure out where we're going to where +we're going to play for any node which + + align:start position:0% +we're going to play for any node which + + + align:start position:0% +we're going to play for any node which +seems like kind of a key operation here + + align:start position:0% +seems like kind of a key operation here + + + align:start position:0% +seems like kind of a key operation here +right to create a symmetric tree that's + + align:start position:0% +right to create a symmetric tree that's + + + align:start position:0% +right to create a symmetric tree that's +all that how to build um and so for + + align:start position:0% +all that how to build um and so for + + + align:start position:0% +all that how to build um and so for +example in this case we're going to + + align:start position:0% +example in this case we're going to + + + align:start position:0% +example in this case we're going to +picked this sequence of notes + + align:start position:0% +picked this sequence of notes + + + align:start position:0% +picked this sequence of notes +and once we get to the bottom and find a + + align:start position:0% +and once we get to the bottom and find a + + + align:start position:0% +and once we get to the bottom and find a +new location we're going to create a do + + align:start position:0% +new location we're going to create a do + + + align:start position:0% +new location we're going to create a do +you know it's not very hard um then + + align:start position:0% +you know it's not very hard um then + + + align:start position:0% +you know it's not very hard um then +we're going to simulate a game for this + + align:start position:0% +we're going to simulate a game for this + + + align:start position:0% +we're going to simulate a game for this +video and this is sort of the key part + + align:start position:0% +video and this is sort of the key part + + + align:start position:0% +video and this is sort of the key part +of MCTS is that once you get to a new + + align:start position:0% +of MCTS is that once you get to a new + + + align:start position:0% +of MCTS is that once you get to a new +location what you're going to be doing + + align:start position:0% +location what you're going to be doing + + + align:start position:0% +location what you're going to be doing +then is you're going to be simulating a + + align:start position:0% +then is you're going to be simulating a + + + align:start position:0% +then is you're going to be simulating a +game from that new location we're going + + align:start position:0% +game from that new location we're going + + + align:start position:0% +game from that new location we're going +to talk about how you go about + + align:start position:0% +to talk about how you go about + + + align:start position:0% +to talk about how you go about +simulating a game from this like this + + align:start position:0% +simulating a game from this like this + + + align:start position:0% +simulating a game from this like this +more more advanced game state than you + + align:start position:0% +more more advanced game state than you + + + align:start position:0% +more more advanced game state than you +know what we started out with many + + align:start position:0% +know what we started out with many + + + align:start position:0% +know what we started out with many +questions right now we will be going to + + align:start position:0% +questions right now we will be going to + + + align:start position:0% +questions right now we will be going to +end up into all of these steps but just + + align:start position:0% + + + + align:start position:0% + +know you're creating some unit we'll + + align:start position:0% +know you're creating some unit we'll + + + align:start position:0% +know you're creating some unit we'll +talk about how we pick that new node but + + align:start position:0% +talk about how we pick that new node but + + + align:start position:0% +talk about how we pick that new node but +we're just making a new ok the next + + align:start position:0% +we're just making a new ok the next + + + align:start position:0% +we're just making a new ok the next +thing is that we're gonna update the + + align:start position:0% +thing is that we're gonna update the + + + align:start position:0% +thing is that we're gonna update the +tree so whatever the value of the + + align:start position:0% +tree so whatever the value of the + + + align:start position:0% +tree so whatever the value of the +simulation Delta was um was we're going + + align:start position:0% +simulation Delta was um was we're going + + + align:start position:0% +simulation Delta was um was we're going +to like propagate that up and basically + + align:start position:0% +to like propagate that up and basically + + + align:start position:0% +to like propagate that up and basically +add that to all of the nodes that are + + align:start position:0% +add that to all of the nodes that are + + + align:start position:0% +add that to all of the nodes that are +the parents of that node in the tree and + + align:start position:0% +the parents of that node in the tree and + + + align:start position:0% +the parents of that node in the tree and +update some information that goes known + + align:start position:0% +update some information that goes known + + + align:start position:0% +update some information that goes known +to story um this is going to be good + + align:start position:0% +to story um this is going to be good + + + align:start position:0% +to story um this is going to be good +because it's going to mean that there + + align:start position:0% +because it's going to mean that there + + + align:start position:0% +because it's going to mean that there +it's a lot like you know the search + + align:start position:0% +it's a lot like you know the search + + + align:start position:0% +it's a lot like you know the search +Ogdensburg of trees but then the the + + align:start position:0% +Ogdensburg of trees but then the the + + + align:start position:0% +Ogdensburg of trees but then the the +entirely the tree remains not to take + + align:start position:0% +entirely the tree remains not to take + + + align:start position:0% +entirely the tree remains not to take +with the information from every + + align:start position:0% +with the information from every + + + align:start position:0% +with the information from every +container and we're just gonna repeat + + align:start position:0% +container and we're just gonna repeat + + + align:start position:0% +container and we're just gonna repeat +this over and over and over again and + + align:start position:0% +this over and over and over again and + + + align:start position:0% +this over and over and over again and +slowly our tree will grow out until + + align:start position:0% +slowly our tree will grow out until + + + align:start position:0% +slowly our tree will grow out until +whenever we feel like stopping this is + + align:start position:0% +whenever we feel like stopping this is + + + align:start position:0% +whenever we feel like stopping this is +actually one of the nice things about + + align:start position:0% +actually one of the nice things about + + + align:start position:0% +actually one of the nice things about +CTS is that whenever we decide um we + + align:start position:0% +CTS is that whenever we decide um we + + + align:start position:0% +CTS is that whenever we decide um we +that were out of time like for example + + align:start position:0% +that were out of time like for example + + + align:start position:0% +that were out of time like for example +hearing a couple + + align:start position:0% +hearing a couple + + + align:start position:0% +hearing a couple +playing a tendon go player um you can + + align:start position:0% +playing a tendon go player um you can + + + align:start position:0% +playing a tendon go player um you can +you can stop the simulation and then all + + align:start position:0% +you can stop the simulation and then all + + + align:start position:0% +you can stop the simulation and then all +you have to do is pick between one of + + align:start position:0% +you have to do is pick between one of + + + align:start position:0% +you have to do is pick between one of +the best first moves that you're going + + align:start position:0% +the best first moves that you're going + + + align:start position:0% +the best first moves that you're going +to make because you know at the end of + + align:start position:0% +to make because you know at the end of + + + align:start position:0% +to make because you know at the end of +the day after doing all this simulation + + align:start position:0% +the day after doing all this simulation + + + align:start position:0% +the day after doing all this simulation +we're still right here right and we're + + align:start position:0% +we're still right here right and we're + + + align:start position:0% +we're still right here right and we're +still only picking between the movements + + align:start position:0% +still only picking between the movements + + + align:start position:0% +still only picking between the movements +they go from immediately where we + + align:start position:0% +they go from immediately where we + + + align:start position:0% +they go from immediately where we +started yeah + + align:start position:0% + + + + align:start position:0% + +a conservatively our Treasuries + + align:start position:0% +a conservatively our Treasuries + + + align:start position:0% +a conservatively our Treasuries +yes so we'll go through how you pick + + align:start position:0% +yes so we'll go through how you pick + + + align:start position:0% +yes so we'll go through how you pick +word in asunder' a.m. um but I guess + + align:start position:0% +word in asunder' a.m. um but I guess + + + align:start position:0% +word in asunder' a.m. um but I guess +it's any possible any possible move that + + align:start position:0% +it's any possible any possible move that + + + align:start position:0% +it's any possible any possible move that +starts at your starting names day okay + + align:start position:0% +starts at your starting names day okay + + + align:start position:0% +starts at your starting names day okay +great so before we move on to the + + align:start position:0% +great so before we move on to the + + + align:start position:0% +great so before we move on to the +algorithm itself let's talk about what + + align:start position:0% +algorithm itself let's talk about what + + + align:start position:0% +algorithm itself let's talk about what +we store in each one of these notes so + + align:start position:0% +we store in each one of these notes so + + + align:start position:0% +we store in each one of these notes so +now we've added these numbers and what + + align:start position:0% +now we've added these numbers and what + + + align:start position:0% +now we've added these numbers and what +these numbers represent is that NK as in + + align:start position:0% +these numbers represent is that NK as in + + + align:start position:0% +these numbers represent is that NK as in +the value on the right is the number of + + align:start position:0% +the value on the right is the number of + + + align:start position:0% +the value on the right is the number of +games that have been played that involve + + align:start position:0% +games that have been played that involve + + + align:start position:0% +games that have been played that involve +a certain note so for example if I look + + align:start position:0% +a certain note so for example if I look + + + align:start position:0% +a certain note so for example if I look +at this node that means that four games + + align:start position:0% +at this node that means that four games + + + align:start position:0% +at this node that means that four games +have been played that involve this note + + align:start position:0% +have been played that involve this note + + + align:start position:0% +have been played that involve this note +but even that has been played that + + align:start position:0% +but even that has been played that + + + align:start position:0% +but even that has been played that +involves this member just means that one + + align:start position:0% +involves this member just means that one + + + align:start position:0% +involves this member just means that one +of the states of the board at some point + + align:start position:0% +of the states of the board at some point + + + align:start position:0% +of the states of the board at some point +in the game was the state of the board + + align:start position:0% +in the game was the state of the board + + + align:start position:0% +in the game was the state of the board +that this represents um and so like for + + align:start position:0% +that this represents um and so like for + + + align:start position:0% +that this represents um and so like for +example if I have a game that was played + + align:start position:0% +example if I have a game that was played + + + align:start position:0% +example if I have a game that was played +here right if I if I know that I played + + align:start position:0% +here right if I if I know that I played + + + align:start position:0% +here right if I if I know that I played +this game once the Nick you're + + align:start position:0% +this game once the Nick you're + + + align:start position:0% +this game once the Nick you're +interested me that I played this game + + align:start position:0% +interested me that I played this game + + + align:start position:0% +interested me that I played this game +once because this is a precursor state + + align:start position:0% +once because this is a precursor state + + + align:start position:0% +once because this is a precursor state +like this make sense yeah ah okay that + + align:start position:0% +like this make sense yeah ah okay that + + + align:start position:0% +like this make sense yeah ah okay that +will come when we we started spending + + align:start position:0% +will come when we we started spending + + + align:start position:0% +will come when we we started spending +our game but that's a great question and + + align:start position:0% +our game but that's a great question and + + + align:start position:0% +our game but that's a great question and +like intuitively speaking it should know + + align:start position:0% +like intuitively speaking it should know + + + align:start position:0% +like intuitively speaking it should know +using your storing data from past games + + align:start position:0% +using your storing data from past games + + + align:start position:0% +using your storing data from past games +we know you're asking in the script yeah + + align:start position:0% +we know you're asking in the script yeah + + + align:start position:0% +we know you're asking in the script yeah +um and then the other value is the + + align:start position:0% +um and then the other value is the + + + align:start position:0% +um and then the other value is the +number of wins associated with a certain + + align:start position:0% +number of wins associated with a certain + + + align:start position:0% +number of wins associated with a certain +level and these are going to be wins for + + align:start position:0% +level and these are going to be wins for + + + align:start position:0% +level and these are going to be wins for +player one which is read in this case + + align:start position:0% +player one which is read in this case + + + align:start position:0% +player one which is read in this case +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um it would get confusing if we put both + + align:start position:0% +um it would get confusing if we put both + + + align:start position:0% +um it would get confusing if we put both +of them but they're complementary right + + align:start position:0% +of them but they're complementary right + + + align:start position:0% +of them but they're complementary right +so for example three out of four times + + align:start position:0% +so for example three out of four times + + + align:start position:0% +so for example three out of four times +that red the red player visited this + + align:start position:0% +that red the red player visited this + + + align:start position:0% +that red the red player visited this +node they won in that note okay and so + + align:start position:0% +node they won in that note okay and so + + + align:start position:0% +node they won in that note okay and so +and these are the two numbers that were + + align:start position:0% +and these are the two numbers that were + + + align:start position:0% +and these are the two numbers that were +in store and we're gonna see why there's + + align:start position:0% +in store and we're gonna see why there's + + + align:start position:0% +in store and we're gonna see why there's +even two major store later great + + align:start position:0% +even two major store later great + + + align:start position:0% +even two major store later great +so first descending the you know key + + align:start position:0% +so first descending the you know key + + + align:start position:0% +so first descending the you know key +part of our algorithm who they're + + align:start position:0% +part of our algorithm who they're + + + align:start position:0% +part of our algorithm who they're +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +and when descending there are these two + + align:start position:0% +and when descending there are these two + + + align:start position:0% +and when descending there are these two +sort of counter balance desires that we + + align:start position:0% +sort of counter balance desires that we + + + align:start position:0% +sort of counter balance desires that we +have the first of them is that we want + + align:start position:0% +have the first of them is that we want + + + align:start position:0% +have the first of them is that we want +to you know explore + + align:start position:0% +to you know explore + + + align:start position:0% +to you know explore +into our tree right we want to think + + align:start position:0% +into our tree right we want to think + + + align:start position:0% +into our tree right we want to think +about you know okay if if they do this + + align:start position:0% +about you know okay if if they do this + + + align:start position:0% +about you know okay if if they do this +then I'll do this and then well then + + align:start position:0% +then I'll do this and then well then + + + align:start position:0% +then I'll do this and then well then +I'll do that and then so on and so forth + + align:start position:0% +I'll do that and then so on and so forth + + + align:start position:0% +I'll do that and then so on and so forth +and we want to think through a long term + + align:start position:0% +and we want to think through a long term + + + align:start position:0% +and we want to think through a long term +strategy but at the same time you don't + + align:start position:0% +strategy but at the same time you don't + + + align:start position:0% +strategy but at the same time you don't +want to get caught on none um what we + + align:start position:0% +want to get caught on none um what we + + + align:start position:0% +want to get caught on none um what we +want to make sure that you know we're + + align:start position:0% +want to make sure that you know we're + + + align:start position:0% +want to make sure that you know we're +not missing a really promising other + + align:start position:0% +not missing a really promising other + + + align:start position:0% +not missing a really promising other +move that we weren't even considering + + align:start position:0% +move that we weren't even considering + + + align:start position:0% +move that we weren't even considering +these are really going down this certain + + align:start position:0% +these are really going down this certain + + + align:start position:0% +these are really going down this certain +rabbit hole of the move that we have + + align:start position:0% +rabbit hole of the move that we have + + + align:start position:0% +rabbit hole of the move that we have +thought about before this is illustrated + + align:start position:0% +thought about before this is illustrated + + + align:start position:0% +thought about before this is illustrated +by the xkc MSNBC um the SME see comic + + align:start position:0% +by the xkc MSNBC um the SME see comic + + + align:start position:0% +by the xkc MSNBC um the SME see comic +about you know academia and how if + + align:start position:0% +about you know academia and how if + + + align:start position:0% +about you know academia and how if +someone tells you that a lot of really + + align:start position:0% +someone tells you that a lot of really + + + align:start position:0% +someone tells you that a lot of really +great work has been done in an area that + + align:start position:0% +great work has been done in an area that + + + align:start position:0% +great work has been done in an area that +means nothing about how promising the + + align:start position:0% +means nothing about how promising the + + + align:start position:0% +means nothing about how promising the +future work um okay so it's all that + + align:start position:0% +future work um okay so it's all that + + + align:start position:0% +future work um okay so it's all that +expansion and exploration and the way + + align:start position:0% +expansion and exploration and the way + + + align:start position:0% +expansion and exploration and the way +that we're going to balance expansion + + align:start position:0% +that we're going to balance expansion + + + align:start position:0% +that we're going to balance expansion +and exploration in order to create a + + align:start position:0% +and exploration in order to create a + + + align:start position:0% +and exploration in order to create a +really nice s metric tree is the + + align:start position:0% +really nice s metric tree is the + + + align:start position:0% +really nice s metric tree is the +following formula and it's fine if that + + align:start position:0% +following formula and it's fine if that + + + align:start position:0% +following formula and it's fine if that +looks really confusing and messy but um + + align:start position:0% +looks really confusing and messy but um + + + align:start position:0% +looks really confusing and messy but um +but actually it breaks down quite nicely + + align:start position:0% +but actually it breaks down quite nicely + + + align:start position:0% +but actually it breaks down quite nicely +into two parts so um that this formula + + align:start position:0% +into two parts so um that this formula + + + align:start position:0% +into two parts so um that this formula +is known as the UCPD you don't need to + + align:start position:0% +is known as the UCPD you don't need to + + + align:start position:0% +is known as the UCPD you don't need to +know why it's an upper confidence value + + align:start position:0% +know why it's an upper confidence value + + + align:start position:0% +know why it's an upper confidence value +let's just talk about what's inside so + + align:start position:0% +let's just talk about what's inside so + + + align:start position:0% +let's just talk about what's inside so +first of all you have this term on the + + align:start position:0% +first of all you have this term on the + + + align:start position:0% +first of all you have this term on the +left and this term on the left is the + + align:start position:0% +left and this term on the left is the + + + align:start position:0% +left and this term on the left is the +expansion term it's basically + + align:start position:0% +expansion term it's basically + + + align:start position:0% +expansion term it's basically +proportional to the likelihood that if + + align:start position:0% +proportional to the likelihood that if + + + align:start position:0% +proportional to the likelihood that if +the expected number of times that you're + + align:start position:0% +the expected number of times that you're + + + align:start position:0% +the expected number of times that you're +going to win given that you are in a + + align:start position:0% +going to win given that you are in a + + + align:start position:0% +going to win given that you are in a +certain node um and that you were a + + align:start position:0% +certain node um and that you were a + + + align:start position:0% +certain node um and that you were a +certain player and so that it's + + align:start position:0% +certain player and so that it's + + + align:start position:0% +certain player and so that it's +basically the quality of your sting in + + align:start position:0% +basically the quality of your sting in + + + align:start position:0% +basically the quality of your sting in +some abstract level if we knew this + + align:start position:0% +some abstract level if we knew this + + + align:start position:0% +some abstract level if we knew this +perfectly then we would be doing great + + align:start position:0% +perfectly then we would be doing great + + + align:start position:0% +perfectly then we would be doing great +things like that's the thing that we're + + align:start position:0% +things like that's the thing that we're + + + align:start position:0% +things like that's the thing that we're +looking for on some granular break the + + align:start position:0% +looking for on some granular break the + + + align:start position:0% +looking for on some granular break the +expected likelihood of winning from a + + align:start position:0% +expected likelihood of winning from a + + + align:start position:0% +expected likelihood of winning from a +certain state on the other hand you have + + align:start position:0% +certain state on the other hand you have + + + align:start position:0% +certain state on the other hand you have +this exploration term and you might not + + align:start position:0% +this exploration term and you might not + + + align:start position:0% +this exploration term and you might not +be able to read the font there but what + + align:start position:0% +be able to read the font there but what + + + align:start position:0% +be able to read the font there but what +this is basically saying is that it + + align:start position:0% +this is basically saying is that it + + + align:start position:0% +this is basically saying is that it +looks at the number of games that month + + align:start position:0% +looks at the number of games that month + + + align:start position:0% +looks at the number of games that month +that I have I have been talking + + align:start position:0% +that I have I have been talking + + + align:start position:0% +that I have I have been talking +playthrough and it looks at the number + + align:start position:0% +playthrough and it looks at the number + + + align:start position:0% +playthrough and it looks at the number +of games that my parent has been played + + align:start position:0% +of games that my parent has been played + + + align:start position:0% +of games that my parent has been played +and it tries to preserve that that those + + align:start position:0% +and it tries to preserve that that those + + + align:start position:0% +and it tries to preserve that that those +refers at a certain ratio at a log ratio + + align:start position:0% +refers at a certain ratio at a log ratio + + + align:start position:0% +refers at a certain ratio at a log ratio +and with that effectively means is that + + align:start position:0% +and with that effectively means is that + + + align:start position:0% +and with that effectively means is that +um is that the number of times that I + + align:start position:0% +um is that the number of times that I + + + align:start position:0% +um is that the number of times that I +have been bit like if I have been + + align:start position:0% +have been bit like if I have been + + + align:start position:0% +have been bit like if I have been +visited relatively few times and if the + + align:start position:0% +visited relatively few times and if the + + + align:start position:0% +visited relatively few times and if the +the denominator is small whereas my my + + align:start position:0% +the denominator is small whereas my my + + + align:start position:0% +the denominator is small whereas my my +parent has been visited many times which + + align:start position:0% +parent has been visited many times which + + + align:start position:0% +parent has been visited many times which +means that my siblings have gotten much + + align:start position:0% +means that my siblings have gotten much + + + align:start position:0% +means that my siblings have gotten much +more attention then the likelihood that + + align:start position:0% +more attention then the likelihood that + + + align:start position:0% +more attention then the likelihood that +I will be visited again actually + + align:start position:0% +I will be visited again actually + + + align:start position:0% +I will be visited again actually +increases so this this is biased on one + + align:start position:0% +increases so this this is biased on one + + + align:start position:0% +increases so this this is biased on one +hand towards young notes that are really + + align:start position:0% +hand towards young notes that are really + + + align:start position:0% +hand towards young notes that are really +promising and then they are the other + + align:start position:0% +promising and then they are the other + + + align:start position:0% +promising and then they are the other +hand on towards nodes that haven't been + + align:start position:0% +hand on towards nodes that haven't been + + + align:start position:0% +hand on towards nodes that haven't been +explored yet you know where there's a + + align:start position:0% +explored yet you know where there's a + + + align:start position:0% +explored yet you know where there's a +goldmine and all you need to do is look + + align:start position:0% +goldmine and all you need to do is look + + + align:start position:0% +goldmine and all you need to do is look +to think a little bit potentially and we + + align:start position:0% +to think a little bit potentially and we + + + align:start position:0% +to think a little bit potentially and we +don't actually have analytical + + align:start position:0% +don't actually have analytical + + + align:start position:0% +don't actually have analytical +expression for this but we can + + align:start position:0% +expression for this but we can + + + align:start position:0% +expression for this but we can +approximate it because you can think + + align:start position:0% +approximate it because you can think + + + align:start position:0% +approximate it because you can think +that the expected value from a certain + + align:start position:0% +that the expected value from a certain + + + align:start position:0% +that the expected value from a certain +node is roughly speaking approximately + + align:start position:0% +node is roughly speaking approximately + + + align:start position:0% +node is roughly speaking approximately +the ratio of winds at that node to the + + align:start position:0% +the ratio of winds at that node to the + + + align:start position:0% +the ratio of winds at that node to the +ratio times of that node has been + + align:start position:0% +ratio times of that node has been + + + align:start position:0% +ratio times of that node has been +visited at all okay so let's talk about + + align:start position:0% +visited at all okay so let's talk about + + + align:start position:0% +visited at all okay so let's talk about +actually applying the sting right + + align:start position:0% +actually applying the sting right + + + align:start position:0% +actually applying the sting right +because what the stigma is going to give + + align:start position:0% +because what the stigma is going to give + + + align:start position:0% +because what the stigma is going to give +you is it's going to give you a value it + + align:start position:0% +you is it's going to give you a value it + + + align:start position:0% +you is it's going to give you a value it +like some number for here it's a number + + align:start position:0% +like some number for here it's a number + + + align:start position:0% +like some number for here it's a number +for here and some number for here and so + + align:start position:0% +for here and some number for here and so + + + align:start position:0% +for here and some number for here and so +on so when we start descending through + + align:start position:0% +on so when we start descending through + + + align:start position:0% +on so when we start descending through +the tree we're gonna start at the top + + align:start position:0% +the tree we're gonna start at the top + + + align:start position:0% +the tree we're gonna start at the top +node and then we're going to look at the + + align:start position:0% +node and then we're going to look at the + + + align:start position:0% +node and then we're going to look at the +three children of that node and we're + + align:start position:0% +three children of that node and we're + + + align:start position:0% +three children of that node and we're +going to compute this ucv values for + + align:start position:0% +going to compute this ucv values for + + + align:start position:0% +going to compute this ucv values for +each of these children and pick + + align:start position:0% +each of these children and pick + + + align:start position:0% +each of these children and pick +whichever one is the highest so just as + + align:start position:0% +whichever one is the highest so just as + + + align:start position:0% +whichever one is the highest so just as +a thought for a moment what if we + + align:start position:0% +a thought for a moment what if we + + + align:start position:0% +a thought for a moment what if we +ignored this one and what if we're just + + align:start position:0% +ignored this one and what if we're just + + + align:start position:0% +ignored this one and what if we're just +computing the UCB of these two does + + align:start position:0% +computing the UCB of these two does + + + align:start position:0% +computing the UCB of these two does +anyone have any intuition on whether the + + align:start position:0% +anyone have any intuition on whether the + + + align:start position:0% +anyone have any intuition on whether the +UCB + + align:start position:0% +UCB + + + align:start position:0% +UCB +would be higher for this node or for + + align:start position:0% +would be higher for this node or for + + + align:start position:0% +would be higher for this node or for +this node the love note okay so why is + + align:start position:0% +this node the love note okay so why is + + + align:start position:0% +this node the love note okay so why is +that + + align:start position:0% + + + + align:start position:0% + +yeah it has a winner + + align:start position:0% +yeah it has a winner + + + align:start position:0% +yeah it has a winner +exactly and so clearly the exploration + + align:start position:0% +exactly and so clearly the exploration + + + align:start position:0% +exactly and so clearly the exploration +term is going to be the same because you + + align:start position:0% +term is going to be the same because you + + + align:start position:0% +term is going to be the same because you +know it's not that one child has been + + align:start position:0% +know it's not that one child has been + + + align:start position:0% +know it's not that one child has been +loved less than the other but the + + align:start position:0% +loved less than the other but the + + + align:start position:0% +loved less than the other but the +expansion term is going to be different + + align:start position:0% +expansion term is going to be different + + + align:start position:0% +expansion term is going to be different +and so it's definitely gonna pick this + + align:start position:0% +and so it's definitely gonna pick this + + + align:start position:0% +and so it's definitely gonna pick this +one although in this case what we're + + align:start position:0% +one although in this case what we're + + + align:start position:0% +one although in this case what we're +gonna say is actually that this is so + + align:start position:0% +gonna say is actually that this is so + + + align:start position:0% +gonna say is actually that this is so +much more promising than the others but + + align:start position:0% +much more promising than the others but + + + align:start position:0% +much more promising than the others but +it's actually going to pick this letter + + align:start position:0% +it's actually going to pick this letter + + + align:start position:0% +it's actually going to pick this letter +and so it's going to expand it's gonna + + align:start position:0% +and so it's going to expand it's gonna + + + align:start position:0% +and so it's going to expand it's gonna +look down and now when it looks down + + align:start position:0% +look down and now when it looks down + + + align:start position:0% +look down and now when it looks down +it's going to compare between these two + + align:start position:0% +it's going to compare between these two + + + align:start position:0% +it's going to compare between these two +and this time remember that this is our + + align:start position:0% +and this time remember that this is our + + + align:start position:0% +and this time remember that this is our +point right and so a parent wants to + + align:start position:0% +point right and so a parent wants to + + + align:start position:0% +point right and so a parent wants to +minimize the number of wins than we have + + align:start position:0% +minimize the number of wins than we have + + + align:start position:0% +minimize the number of wins than we have +right which means that our opponent is + + align:start position:0% +right which means that our opponent is + + + align:start position:0% +right which means that our opponent is +going to want to UM to pick the one that + + align:start position:0% +going to want to UM to pick the one that + + + align:start position:0% +going to want to UM to pick the one that +were less likely to win in and they're + + align:start position:0% +were less likely to win in and they're + + + align:start position:0% +were less likely to win in and they're +more likely this is the idea of minimax + + align:start position:0% +more likely this is the idea of minimax + + + align:start position:0% +more likely this is the idea of minimax +you know I'm minimizing how don't like + + align:start position:0% +you know I'm minimizing how don't like + + + align:start position:0% +you know I'm minimizing how don't like +enemy does anyway so so now although + + align:start position:0% +enemy does anyway so so now although + + + align:start position:0% +enemy does anyway so so now although +again the exploration term might counter + + align:start position:0% +again the exploration term might counter + + + align:start position:0% +again the exploration term might counter +balance in a little bit right because + + align:start position:0% +balance in a little bit right because + + + align:start position:0% +balance in a little bit right because +technically this is been explored more + + align:start position:0% +technically this is been explored more + + + align:start position:0% +technically this is been explored more +but we're going to anyway we're gonna + + align:start position:0% +but we're going to anyway we're gonna + + + align:start position:0% +but we're going to anyway we're gonna +pick the one on the left again and we're + + align:start position:0% +pick the one on the left again and we're + + + align:start position:0% +pick the one on the left again and we're +going to get to that location that we + + align:start position:0% +going to get to that location that we + + + align:start position:0% +going to get to that location that we +got to originally now when we're + + align:start position:0% +got to originally now when we're + + + align:start position:0% +got to originally now when we're +comparing between these two between a + + align:start position:0% +comparing between these two between a + + + align:start position:0% +comparing between these two between a +node that has been visited once and a + + align:start position:0% +node that has been visited once and a + + + align:start position:0% +node that has been visited once and a +note that has never been visited can + + align:start position:0% +note that has never been visited can + + + align:start position:0% +note that has never been visited can +anyone guess which one is just going to + + align:start position:0% +anyone guess which one is just going to + + + align:start position:0% +anyone guess which one is just going to +pick yeah + + align:start position:0% +pick yeah + + + align:start position:0% +pick yeah +yeah exactly because this number is zero + + align:start position:0% +yeah exactly because this number is zero + + + align:start position:0% +yeah exactly because this number is zero +and so if the parent has ever been + + align:start position:0% +and so if the parent has ever been + + + align:start position:0% +and so if the parent has ever been +visited but the no it hasn't + + align:start position:0% +visited but the no it hasn't + + + align:start position:0% +visited but the no it hasn't +this is going to be infinite and it's + + align:start position:0% +this is going to be infinite and it's + + + align:start position:0% +this is going to be infinite and it's +gonna have to pick the note what that is + + align:start position:0% +gonna have to pick the note what that is + + + align:start position:0% +gonna have to pick the note what that is +never seen before + + align:start position:0% +never seen before + + + align:start position:0% +never seen before +okay so that's how we just send through + + align:start position:0% +okay so that's how we just send through + + + align:start position:0% +okay so that's how we just send through +the tree does anyone have any questions + + align:start position:0% +the tree does anyone have any questions + + + align:start position:0% +the tree does anyone have any questions +on that + + align:start position:0% +on that + + + align:start position:0% +on that +really it's totally fine like yeah so no + + align:start position:0% +really it's totally fine like yeah so no + + + align:start position:0% +really it's totally fine like yeah so no +because of the way that we're going to + + align:start position:0% +because of the way that we're going to + + + align:start position:0% +because of the way that we're going to +be updating the tree actual talked about + + align:start position:0% +be updating the tree actual talked about + + + align:start position:0% +be updating the tree actual talked about +so yeah I mean I like the concept but if + + align:start position:0% +so yeah I mean I like the concept but if + + + align:start position:0% +so yeah I mean I like the concept but if +it's a deterministic game that's the + + align:start position:0% +it's a deterministic game that's the + + + align:start position:0% +it's a deterministic game that's the +real question + + align:start position:0% +real question + + + align:start position:0% +real question +um that's really up to computer memory + + align:start position:0% +um that's really up to computer memory + + + align:start position:0% +um that's really up to computer memory +limits um as I think the image and it + + align:start position:0% +limits um as I think the image and it + + + align:start position:0% +limits um as I think the image and it +the number of states in a game of go + + align:start position:0% +the number of states in a game of go + + + align:start position:0% +the number of states in a game of go +it's a 19-5 19 board and this something + + align:start position:0% +it's a 19-5 19 board and this something + + + align:start position:0% +it's a 19-5 19 board and this something +every state is only 2 to the what 250 it + + align:start position:0% +every state is only 2 to the what 250 it + + + align:start position:0% +every state is only 2 to the what 250 it +gets kind of you you could never explore + + align:start position:0% +gets kind of you you could never explore + + + align:start position:0% +gets kind of you you could never explore +the entire search + + align:start position:0% + + + + align:start position:0% + +there are many except you're trying to + + align:start position:0% +there are many except you're trying to + + + align:start position:0% +there are many except you're trying to +do that it's really awkward + + align:start position:0% +do that it's really awkward + + + align:start position:0% +do that it's really awkward +so it's simply true um if you if you + + align:start position:0% +so it's simply true um if you if you + + + align:start position:0% +so it's simply true um if you if you +know a state you're gonna write that + + align:start position:0% +know a state you're gonna write that + + + align:start position:0% +know a state you're gonna write that +ahead of time then you can totally do + + align:start position:0% +ahead of time then you can totally do + + + align:start position:0% +ahead of time then you can totally do +that but in a game that sort of large + + align:start position:0% +that but in a game that sort of large + + + align:start position:0% +that but in a game that sort of large +enough then you know it'll to do that + + align:start position:0% +enough then you know it'll to do that + + + align:start position:0% +enough then you know it'll to do that +for all of the possible states would + + align:start position:0% +for all of the possible states would + + + align:start position:0% +for all of the possible states would +take that much more time to take that + + align:start position:0% +take that much more time to take that + + + align:start position:0% +take that much more time to take that +much Montgomery um it doesn't end up + + align:start position:0% +much Montgomery um it doesn't end up + + + align:start position:0% +much Montgomery um it doesn't end up +making that much sense and also + + align:start position:0% +making that much sense and also + + + align:start position:0% +making that much sense and also +something to point out here is that for + + align:start position:0% +something to point out here is that for + + + align:start position:0% +something to point out here is that for +most of the games that we're talking + + align:start position:0% +most of the games that we're talking + + + align:start position:0% +most of the games that we're talking +about simulating a single run-through of + + align:start position:0% +about simulating a single run-through of + + + align:start position:0% +about simulating a single run-through of +a game is really fast so if you think + + align:start position:0% +a game is really fast so if you think + + + align:start position:0% +a game is really fast so if you think +about it you know how long well let's + + align:start position:0% +about it you know how long well let's + + + align:start position:0% +about it you know how long well let's +actually get to that in the next piece + + align:start position:0% +actually get to that in the next piece + + + align:start position:0% +actually get to that in the next piece +but the point is that building up this + + align:start position:0% +but the point is that building up this + + + align:start position:0% +but the point is that building up this +many levels of a tree for computer takes + + align:start position:0% +many levels of a tree for computer takes + + + align:start position:0% +many levels of a tree for computer takes +probably on the order of less than a + + align:start position:0% +probably on the order of less than a + + + align:start position:0% +probably on the order of less than a +millisecond great and so doing this for + + align:start position:0% +millisecond great and so doing this for + + + align:start position:0% +millisecond great and so doing this for +a really really huge tree is also just + + align:start position:0% +a really really huge tree is also just + + + align:start position:0% +a really really huge tree is also just +kind of its peanuts because there's such + + align:start position:0% +kind of its peanuts because there's such + + + align:start position:0% +kind of its peanuts because there's such +simple operations but it would get + + align:start position:0% +simple operations but it would get + + + align:start position:0% +simple operations but it would get +expensive when we start building up the + + align:start position:0% +expensive when we start building up the + + + align:start position:0% +expensive when we start building up the +tree the like serious deaths + + align:start position:0% +tree the like serious deaths + + + align:start position:0% +tree the like serious deaths +well I mean but a game like go how many + + align:start position:0% +well I mean but a game like go how many + + + align:start position:0% +well I mean but a game like go how many +nodes would you have so on each level in + + align:start position:0% +nodes would you have so on each level in + + + align:start position:0% +nodes would you have so on each level in +the beginning we have something on the + + align:start position:0% +the beginning we have something on the + + + align:start position:0% +the beginning we have something on the +order of 400 nodes and we have a depth + + align:start position:0% +order of 400 nodes and we have a depth + + + align:start position:0% +order of 400 nodes and we have a depth +of about I think most games ever after + + align:start position:0% +of about I think most games ever after + + + align:start position:0% +of about I think most games ever after +250 steps or something like that so like + + align:start position:0% +250 steps or something like that so like + + + align:start position:0% +250 steps or something like that so like +just the middle if you go in there blank + + align:start position:0% +just the middle if you go in there blank + + + align:start position:0% +just the middle if you go in there blank +without any notes built you have to + + align:start position:0% +without any notes built you have to + + + align:start position:0% +without any notes built you have to +computer like you said if it has a visit + + align:start position:0% +computer like you said if it has a visit + + + align:start position:0% +computer like you said if it has a visit +of note it has to go there before it's + + align:start position:0% +of note it has to go there before it's + + + align:start position:0% +of note it has to go there before it's +further right yeah basically like + + align:start position:0% +further right yeah basically like + + + align:start position:0% +further right yeah basically like +reading first so it's sort of like + + align:start position:0% +reading first so it's sort of like + + + align:start position:0% +reading first so it's sort of like +breath strips but not quite and there's + + align:start position:0% +breath strips but not quite and there's + + + align:start position:0% +breath strips but not quite and there's +an important distinction which is that + + align:start position:0% +an important distinction which is that + + + align:start position:0% +an important distinction which is that +it doesn't have to build that this or + + align:start position:0% +it doesn't have to build that this or + + + align:start position:0% +it doesn't have to build that this or +this you know well or or any it doesn't + + align:start position:0% +this you know well or or any it doesn't + + + align:start position:0% +this you know well or or any it doesn't +have to build up all of the nodes that a + + align:start position:0% +have to build up all of the nodes that a + + + align:start position:0% +have to build up all of the nodes that a +certain level all has to do is if it + + align:start position:0% +certain level all has to do is if it + + + align:start position:0% +certain level all has to do is if it +branches down to a certain like sub + + align:start position:0% +branches down to a certain like sub + + + align:start position:0% +branches down to a certain like sub +region that it can't descend in that + + align:start position:0% +region that it can't descend in that + + + align:start position:0% +region that it can't descend in that +step region below one of its siblings + + align:start position:0% +step region below one of its siblings + + + align:start position:0% +step region below one of its siblings +without putting at least look once than + + align:start position:0% +without putting at least look once than + + + align:start position:0% +without putting at least look once than +all the siblings after it looks once it + + align:start position:0% +all the siblings after it looks once it + + + align:start position:0% +all the siblings after it looks once it +can do whatever it wants and the point + + align:start position:0% +can do whatever it wants and the point + + + align:start position:0% +can do whatever it wants and the point +is but it doesn't mean that the tree has + + align:start position:0% +is but it doesn't mean that the tree has + + + align:start position:0% +is but it doesn't mean that the tree has +to be kept in an equal level all that + + align:start position:0% +to be kept in an equal level all that + + + align:start position:0% +to be kept in an equal level all that +means is that the tree like is that in + + align:start position:0% +means is that the tree like is that in + + + align:start position:0% +means is that the tree like is that in +order to descend on a specific part of + + align:start position:0% +order to descend on a specific part of + + + align:start position:0% +order to descend on a specific part of +the tree it has to at least have visited + + align:start position:0% +the tree it has to at least have visited + + + align:start position:0% +the tree it has to at least have visited +the direct + + align:start position:0% +the direct + + + align:start position:0% +the direct +neighbors + + align:start position:0% + + + + align:start position:0% + +all right any more questions on this + + align:start position:0% +all right any more questions on this + + + align:start position:0% +all right any more questions on this +week of work yeah what's the event + + align:start position:0% +week of work yeah what's the event + + + align:start position:0% +week of work yeah what's the event +necessarily of having to visit every + + align:start position:0% +necessarily of having to visit every + + + align:start position:0% +necessarily of having to visit every +single um well one of them is that this + + align:start position:0% +single um well one of them is that this + + + align:start position:0% +single um well one of them is that this +is the advantage of having to visit or + + align:start position:0% +is the advantage of having to visit or + + + align:start position:0% +is the advantage of having to visit or +something the way that I think of it is + + align:start position:0% +something the way that I think of it is + + + align:start position:0% +something the way that I think of it is +that you don't want to be missing out on + + align:start position:0% +that you don't want to be missing out on + + + align:start position:0% +that you don't want to be missing out on +you know potentially being interested in + + align:start position:0% +you know potentially being interested in + + + align:start position:0% +you know potentially being interested in +some things and not and not others and + + align:start position:0% +some things and not and not others and + + + align:start position:0% +some things and not and not others and +this sort of comes back to the + + align:start position:0% +this sort of comes back to the + + + align:start position:0% +this sort of comes back to the +exploration versus versus expectation + + align:start position:0% +exploration versus versus expectation + + + align:start position:0% +exploration versus versus expectation +distinction but you know we we do want + + align:start position:0% +distinction but you know we we do want + + + align:start position:0% +distinction but you know we we do want +to descend into the region of the tree + + align:start position:0% +to descend into the region of the tree + + + align:start position:0% +to descend into the region of the tree +that's really valuable to us but like at + + align:start position:0% +that's really valuable to us but like at + + + align:start position:0% +that's really valuable to us but like at +least having explored a little bit at + + align:start position:0% +least having explored a little bit at + + + align:start position:0% +least having explored a little bit at +least maintaining some baseline which + + align:start position:0% +least maintaining some baseline which + + + align:start position:0% +least maintaining some baseline which +really isn't isn't that costly compared + + align:start position:0% +really isn't isn't that costly compared + + + align:start position:0% +really isn't isn't that costly compared +with the size of the journey rate 400 + + align:start position:0% +with the size of the journey rate 400 + + + align:start position:0% +with the size of the journey rate 400 +years is not that bad compared to 400 to + + align:start position:0% +years is not that bad compared to 400 to + + + align:start position:0% +years is not that bad compared to 400 to +250 are these simulations they're just + + align:start position:0% +250 are these simulations they're just + + + align:start position:0% +250 are these simulations they're just +random simulations super ready to talk + + align:start position:0% +random simulations super ready to talk + + + align:start position:0% +random simulations super ready to talk +about that minute anymore crushed before + + align:start position:0% +about that minute anymore crushed before + + + align:start position:0% +about that minute anymore crushed before +and under that okay so next step is + + align:start position:0% +and under that okay so next step is + + + align:start position:0% +and under that okay so next step is +expanding and this is very simple it is + + align:start position:0% +expanding and this is very simple it is + + + align:start position:0% +expanding and this is very simple it is +create a node and you set the two + + align:start position:0% +create a node and you set the two + + + align:start position:0% +create a node and you set the two +initial values and the initial values + + align:start position:0% +initial values and the initial values + + + align:start position:0% +initial values and the initial values +are in to the number of times it's been + + align:start position:0% +are in to the number of times it's been + + + align:start position:0% +are in to the number of times it's been +visited to zero and then over time to + + align:start position:0% +visited to zero and then over time to + + + align:start position:0% +visited to zero and then over time to +someone is blowing from their experiment + + align:start position:0% +someone is blowing from their experiment + + + align:start position:0% +someone is blowing from their experiment +that yeah easy breaking something + + align:start position:0% +that yeah easy breaking something + + + align:start position:0% +that yeah easy breaking something +right now I'm simulating um so + + align:start position:0% +right now I'm simulating um so + + + align:start position:0% +right now I'm simulating um so +simulating is really hard you can + + align:start position:0% +simulating is really hard you can + + + align:start position:0% +simulating is really hard you can +imagine that if you get to a certain + + align:start position:0% +imagine that if you get to a certain + + + align:start position:0% +imagine that if you get to a certain +node and you've never seen that node + + align:start position:0% +node and you've never seen that node + + + align:start position:0% +node and you've never seen that node +before and you don't know what to do + + align:start position:0% +before and you don't know what to do + + + align:start position:0% +before and you don't know what to do +from this node onward that you know if + + align:start position:0% +from this node onward that you know if + + + align:start position:0% +from this node onward that you know if +we knew how the game was going to play + + align:start position:0% +we knew how the game was going to play + + + align:start position:0% +we knew how the game was going to play +out that is exactly what we're searching + + align:start position:0% +out that is exactly what we're searching + + + align:start position:0% +out that is exactly what we're searching +for and we would be done but we don't + + align:start position:0% +for and we would be done but we don't + + + align:start position:0% +for and we would be done but we don't +and in fact we have no idea like how to + + align:start position:0% +and in fact we have no idea like how to + + + align:start position:0% +and in fact we have no idea like how to +go about simulating a realistic game and + + align:start position:0% +go about simulating a realistic game and + + + align:start position:0% +go about simulating a realistic game and +a game that will tell us something + + align:start position:0% +a game that will tell us something + + + align:start position:0% +a game that will tell us something +meaningful but the quality of a certain + + align:start position:0% +meaningful but the quality of a certain + + + align:start position:0% +meaningful but the quality of a certain +state and so as you correctly guessed + + align:start position:0% +state and so as you correctly guessed + + + align:start position:0% +state and so as you correctly guessed +randomly we're just going to pick we're + + align:start position:0% +randomly we're just going to pick we're + + + align:start position:0% +randomly we're just going to pick we're +going to be a certain state and then + + align:start position:0% +going to be a certain state and then + + + align:start position:0% +going to be a certain state and then +from that state we're just going to pick + + align:start position:0% +from that state we're just going to pick + + + align:start position:0% +from that state we're just going to pick +random moves for each of the players + + align:start position:0% +random moves for each of the players + + + align:start position:0% +random moves for each of the players +until the game has + + align:start position:0% +until the game has + + + align:start position:0% +until the game has +and if we if we as player one win then + + align:start position:0% +and if we if we as player one win then + + + align:start position:0% +and if we if we as player one win then +we're gonna add one this is that then + + align:start position:0% +we're gonna add one this is that then + + + align:start position:0% +we're gonna add one this is that then +we're gonna say Delta equals plus 1 and + + align:start position:0% +we're gonna say Delta equals plus 1 and + + + align:start position:0% +we're gonna say Delta equals plus 1 and +if we don't win or you know yeah if we + + align:start position:0% +if we don't win or you know yeah if we + + + align:start position:0% +if we don't win or you know yeah if we +tie or lose then we're gonna call it a + + align:start position:0% +tie or lose then we're gonna call it a + + + align:start position:0% +tie or lose then we're gonna call it a +zero um you can see in this graphic + + align:start position:0% +zero um you can see in this graphic + + + align:start position:0% +zero um you can see in this graphic +we're just sort of descending randomly + + align:start position:0% +we're just sort of descending randomly + + + align:start position:0% +we're just sort of descending randomly +not gonna be better it turns out that + + align:start position:0% +not gonna be better it turns out that + + + align:start position:0% +not gonna be better it turns out that +this is actually great because it's + + align:start position:0% +this is actually great because it's + + + align:start position:0% +this is actually great because it's +really bleep up additionally efficient + + align:start position:0% +really bleep up additionally efficient + + + align:start position:0% +really bleep up additionally efficient +um you know if you have a board even if + + align:start position:0% +um you know if you have a board even if + + + align:start position:0% +um you know if you have a board even if +it has 400 open squares populating it by + + align:start position:0% +it has 400 open squares populating it by + + + align:start position:0% +it has 400 open squares populating it by +like a bunch of random moves doesn't + + align:start position:0% +like a bunch of random moves doesn't + + + align:start position:0% +like a bunch of random moves doesn't +take you very long like on the order of + + align:start position:0% +take you very long like on the order of + + + align:start position:0% +take you very long like on the order of +not that many machines that's why you + + align:start position:0% +not that many machines that's why you + + + align:start position:0% +not that many machines that's why you +don't I mean if you go down a tree + + align:start position:0% +don't I mean if you go down a tree + + + align:start position:0% +don't I mean if you go down a tree +randomly yeah you already have + + align:start position:0% +randomly yeah you already have + + + align:start position:0% +randomly yeah you already have +simulations for those sometimes + + align:start position:0% +simulations for those sometimes + + + align:start position:0% +simulations for those sometimes +listen I just or it so you're you're + + align:start position:0% +listen I just or it so you're you're + + + align:start position:0% +listen I just or it so you're you're +totally right actually in this case um + + align:start position:0% +totally right actually in this case um + + + align:start position:0% +totally right actually in this case um +there I've thought through this and I + + align:start position:0% +there I've thought through this and I + + + align:start position:0% +there I've thought through this and I +can't come up with a reason why you + + align:start position:0% +can't come up with a reason why you + + + align:start position:0% +can't come up with a reason why you +wouldn't store good sort of temporary + + align:start position:0% +wouldn't store good sort of temporary + + + align:start position:0% +wouldn't store good sort of temporary +values that you find all the way down + + align:start position:0% +values that you find all the way down + + + align:start position:0% +values that you find all the way down +the tree but they don't realize but + + align:start position:0% +the tree but they don't realize but + + + align:start position:0% +the tree but they don't realize but +you're totally right about that + + align:start position:0% +you're totally right about that + + + align:start position:0% +you're totally right about that +understand the distinction the fact that + + align:start position:0% +understand the distinction the fact that + + + align:start position:0% +understand the distinction the fact that +we only hold on to you know the result + + align:start position:0% +we only hold on to you know the result + + + align:start position:0% +we only hold on to you know the result +here and don't theoretically make notes + + align:start position:0% +here and don't theoretically make notes + + + align:start position:0% +here and don't theoretically make notes +for every place down in the tree just + + align:start position:0% +for every place down in the tree just + + + align:start position:0% +for every place down in the tree just +because we could just because we've seen + + align:start position:0% +because we could just because we've seen + + + align:start position:0% +because we could just because we've seen +them before we don't mean it doesn't + + align:start position:0% +them before we don't mean it doesn't + + + align:start position:0% +them before we don't mean it doesn't +really matter in this case but it's + + align:start position:0% +really matter in this case but it's + + + align:start position:0% +really matter in this case but it's +theoretically a slight yeah okay so we + + align:start position:0% +theoretically a slight yeah okay so we + + + align:start position:0% +theoretically a slight yeah okay so we +can look at an example of simulating at + + align:start position:0% +can look at an example of simulating at + + + align:start position:0% +can look at an example of simulating at +a random game and get maybe some + + align:start position:0% +a random game and get maybe some + + + align:start position:0% +a random game and get maybe some +intuition for why a random game would be + + align:start position:0% +intuition for why a random game would be + + + align:start position:0% +intuition for why a random game would be +correlated with you know how good your + + align:start position:0% +correlated with you know how good your + + + align:start position:0% +correlated with you know how good your +board positions so for example you know + + align:start position:0% +board positions so for example you know + + + align:start position:0% +board positions so for example you know +here we have a detective game circle is + + align:start position:0% +here we have a detective game circle is + + + align:start position:0% +here we have a detective game circle is +going to move next + + align:start position:0% +going to move next + + + align:start position:0% +going to move next +but as hopefully you can see because you + + align:start position:0% +but as hopefully you can see because you + + + align:start position:0% +but as hopefully you can see because you +clicked effect important this is not a + + align:start position:0% +clicked effect important this is not a + + + align:start position:0% +clicked effect important this is not a +particularly promising board for for X + + align:start position:0% +particularly promising board for for X + + + align:start position:0% +particularly promising board for for X +because um because you know no matter + + align:start position:0% +because um because you know no matter + + + align:start position:0% +because um because you know no matter +what circle does if X is an intelligent + + align:start position:0% +what circle does if X is an intelligent + + + align:start position:0% +what circle does if X is an intelligent +player I just been going right now it + + align:start position:0% +player I just been going right now it + + + align:start position:0% +player I just been going right now it +has two different options for one and so + + align:start position:0% +has two different options for one and so + + + align:start position:0% +has two different options for one and so +if you simulate this forward + + align:start position:0% +if you simulate this forward + + + align:start position:0% +if you simulate this forward +what randomly what you'll get + + align:start position:0% +what randomly what you'll get + + + align:start position:0% +what randomly what you'll get +the 2/3 of the time x11 back to win even + + align:start position:0% +the 2/3 of the time x11 back to win even + + + align:start position:0% +the 2/3 of the time x11 back to win even +if the players aren't really thinking + + align:start position:0% +if the players aren't really thinking + + + align:start position:0% +if the players aren't really thinking +the other left oh yeah simulation + + align:start position:0% +the other left oh yeah simulation + + + align:start position:0% +the other left oh yeah simulation +totally can't do that that's in fact + + align:start position:0% +totally can't do that that's in fact + + + align:start position:0% +totally can't do that that's in fact +something that makes sense to do and + + align:start position:0% +something that makes sense to do and + + + align:start position:0% +something that makes sense to do and +that some people do although what you'll + + align:start position:0% +that some people do although what you'll + + + align:start position:0% +that some people do although what you'll +find somewhat soon is that considering + + align:start position:0% +find somewhat soon is that considering + + + align:start position:0% +find somewhat soon is that considering +that we're going down the tree and that + + align:start position:0% +that we're going down the tree and that + + + align:start position:0% +that we're going down the tree and that +you know sometime soon we're going to + + align:start position:0% +you know sometime soon we're going to + + + align:start position:0% +you know sometime soon we're going to +explore all of its children there's a + + align:start position:0% +explore all of its children there's a + + + align:start position:0% +explore all of its children there's a +good question of why do men simulations + + align:start position:0% +good question of why do men simulations + + + align:start position:0% +good question of why do men simulations +now when you can just do the Sun through + + align:start position:0% +now when you can just do the Sun through + + + align:start position:0% +now when you can just do the Sun through +the tree and times and thereby do men + + align:start position:0% +the tree and times and thereby do men + + + align:start position:0% +the tree and times and thereby do men +simulations by going through the thing + + align:start position:0% +simulations by going through the thing + + + align:start position:0% +simulations by going through the thing +and also building up the children okay + + align:start position:0% +and also building up the children okay + + + align:start position:0% +and also building up the children okay +now this this case is oh yeah this gives + + align:start position:0% +now this this case is oh yeah this gives + + + align:start position:0% +now this this case is oh yeah this gives +more importance to why you did read + + align:start position:0% +more importance to why you did read + + + align:start position:0% +more importance to why you did read +verse because if you're doing random + + align:start position:0% +verse because if you're doing random + + + align:start position:0% +verse because if you're doing random +simulations in order possibly the best + + align:start position:0% +simulations in order possibly the best + + + align:start position:0% +simulations in order possibly the best +one if you're first ranking simulation + + align:start position:0% +one if you're first ranking simulation + + + align:start position:0% +one if you're first ranking simulation +here was that + + align:start position:0% +here was that + + + align:start position:0% +here was that +like or that's no great absolutely + + align:start position:0% +like or that's no great absolutely + + + align:start position:0% +like or that's no great absolutely +better which is which is why it matters + + align:start position:0% +better which is which is why it matters + + + align:start position:0% +better which is which is why it matters +that we do there's so many times that we + + align:start position:0% +that we do there's so many times that we + + + align:start position:0% +that we do there's so many times that we +sort of drown out all of the noise that + + align:start position:0% +sort of drown out all of the noise that + + + align:start position:0% +sort of drown out all of the noise that +is associated with playing game ever and + + align:start position:0% +is associated with playing game ever and + + + align:start position:0% +is associated with playing game ever and +actually let's talk about that if this + + align:start position:0% +actually let's talk about that if this + + + align:start position:0% +actually let's talk about that if this +if there's a lot of distance between + + align:start position:0% +if there's a lot of distance between + + + align:start position:0% +if there's a lot of distance between +where we are right now and you know our + + align:start position:0% +where we are right now and you know our + + + align:start position:0% +where we are right now and you know our +end result like for example in this game + + align:start position:0% +end result like for example in this game + + + align:start position:0% +end result like for example in this game +if I were to tell you like how good is + + align:start position:0% +if I were to tell you like how good is + + + align:start position:0% +if I were to tell you like how good is +this board position if you were one of + + align:start position:0% +this board position if you were one of + + + align:start position:0% +this board position if you were one of +those people who's played out in every + + align:start position:0% +those people who's played out in every + + + align:start position:0% +those people who's played out in every +game of tic-tac-toe you'll know that + + align:start position:0% +game of tic-tac-toe you'll know that + + + align:start position:0% +game of tic-tac-toe you'll know that +like this is great if you want it to be + + align:start position:0% +like this is great if you want it to be + + + align:start position:0% +like this is great if you want it to be +actually coming over anyway the point is + + align:start position:0% +actually coming over anyway the point is + + + align:start position:0% +actually coming over anyway the point is +that that is not easy to do if you are + + align:start position:0% +that that is not easy to do if you are + + + align:start position:0% +that that is not easy to do if you are +doing random simulations from where you + + align:start position:0% +doing random simulations from where you + + + align:start position:0% +doing random simulations from where you +started right but the correlation + + align:start position:0% +started right but the correlation + + + align:start position:0% +started right but the correlation +between your current board state and the + + align:start position:0% +between your current board state and the + + + align:start position:0% +between your current board state and the +quality of that state actually observed + + align:start position:0% +quality of that state actually observed + + + align:start position:0% +quality of that state actually observed +drops precipitously and this for me is + + align:start position:0% +drops precipitously and this for me is + + + align:start position:0% +drops precipitously and this for me is +one of the hardest parts to stomach + + align:start position:0% +one of the hardest parts to stomach + + + align:start position:0% +one of the hardest parts to stomach +about Monte Carlo tree search although + + align:start position:0% +about Monte Carlo tree search although + + + align:start position:0% +about Monte Carlo tree search although +as new people explain to you it actually + + align:start position:0% +as new people explain to you it actually + + + align:start position:0% +as new people explain to you it actually +works quite well um and one of the + + align:start position:0% +works quite well um and one of the + + + align:start position:0% +works quite well um and one of the +reasons that works correctly well in + + align:start position:0% +reasons that works correctly well in + + + align:start position:0% +reasons that works correctly well in +practice for more complicated + + align:start position:0% +practice for more complicated + + + align:start position:0% +practice for more complicated +applications is that they sort of do + + align:start position:0% +applications is that they sort of do + + + align:start position:0% +applications is that they sort of do +away with this assumption of random + + align:start position:0% +away with this assumption of random + + + align:start position:0% +away with this assumption of random +stimulation because even though random + + align:start position:0% +stimulation because even though random + + + align:start position:0% +stimulation because even though random +stimulation does allow you to explore + + align:start position:0% +stimulation does allow you to explore + + + align:start position:0% +stimulation does allow you to explore +all the states if you have some idea you + + align:start position:0% +all the states if you have some idea you + + + align:start position:0% +all the states if you have some idea you +know what a reasonable quality approach + + align:start position:0% +know what a reasonable quality approach + + + align:start position:0% +know what a reasonable quality approach +would be then using that as long as it's + + align:start position:0% +would be then using that as long as it's + + + align:start position:0% +would be then using that as long as it's +not that much more expensive comfort + + align:start position:0% +not that much more expensive comfort + + + align:start position:0% +not that much more expensive comfort +Lincoln differently um can help you in + + align:start position:0% +Lincoln differently um can help you in + + + align:start position:0% +Lincoln differently um can help you in +your summation right now we're still + + align:start position:0% +your summation right now we're still + + + align:start position:0% +your summation right now we're still +talking about total randoms okay all + + align:start position:0% +talking about total randoms okay all + + + align:start position:0% +talking about total randoms okay all +right great now we're gonna update the + + align:start position:0% +right great now we're gonna update the + + + align:start position:0% +right great now we're gonna update the +tree with the result for simulation so + + align:start position:0% +tree with the result for simulation so + + + align:start position:0% +tree with the result for simulation so +given that we had some result lined up + + align:start position:0% +given that we had some result lined up + + + align:start position:0% +given that we had some result lined up +we're going to propagate up the parents + + align:start position:0% +we're going to propagate up the parents + + + align:start position:0% +we're going to propagate up the parents +um and for each parent you know we're + + align:start position:0% +um and for each parent you know we're + + + align:start position:0% +um and for each parent you know we're +gonna add the game has been played there + + align:start position:0% +gonna add the game has been played there + + + align:start position:0% +gonna add the game has been played there +once end that the that the result of + + align:start position:0% +once end that the that the result of + + + align:start position:0% +once end that the that the result of +that simulation gets you know added if + + align:start position:0% +that simulation gets you know added if + + + align:start position:0% +that simulation gets you know added if +if it was a one in so for example you + + align:start position:0% +if it was a one in so for example you + + + align:start position:0% +if it was a one in so for example you +know if there was a win in this game + + align:start position:0% +know if there was a win in this game + + + align:start position:0% +know if there was a win in this game +then this becomes 1 1 because now it's + + align:start position:0% +then this becomes 1 1 because now it's + + + align:start position:0% +then this becomes 1 1 because now it's +one once and two invisible ones and this + + align:start position:0% +one once and two invisible ones and this + + + align:start position:0% +one once and two invisible ones and this +these two get agreement by one + + align:start position:0% +these two get agreement by one + + + align:start position:0% +these two get agreement by one +and these are been agreed by one and + + align:start position:0% +and these are been agreed by one and + + + align:start position:0% +and these are been agreed by one and +that event in itself comprises a + + align:start position:0% +that event in itself comprises a + + + align:start position:0% +that event in itself comprises a +complete iteration a complete single + + align:start position:0% +complete iteration a complete single + + + align:start position:0% +complete iteration a complete single +iteration of running a Monte Carlo tree + + align:start position:0% +iteration of running a Monte Carlo tree + + + align:start position:0% +iteration of running a Monte Carlo tree +search which means that that now we can + + align:start position:0% +search which means that that now we can + + + align:start position:0% +search which means that that now we can +keep doing this over and over again + + align:start position:0% +keep doing this over and over again + + + align:start position:0% +keep doing this over and over again +building up the tree and you know slowly + + align:start position:0% +building up the tree and you know slowly + + + align:start position:0% +building up the tree and you know slowly +making it deeper and making a deeper and + + align:start position:0% +making it deeper and making a deeper and + + + align:start position:0% +making it deeper and making a deeper and +selective areas and having these numbers + + align:start position:0% +selective areas and having these numbers + + + align:start position:0% +selective areas and having these numbers +increase and increase and be more and + + align:start position:0% +increase and increase and be more and + + + align:start position:0% +increase and increase and be more and +more proportional to you know the actual + + align:start position:0% +more proportional to you know the actual + + + align:start position:0% +more proportional to you know the actual +like expected value of the quality of + + align:start position:0% +like expected value of the quality of + + + align:start position:0% +like expected value of the quality of +the state until zenu any questions about + + align:start position:0% +the state until zenu any questions about + + + align:start position:0% +the state until zenu any questions about +this this okay so until we terminate you + + align:start position:0% +this this okay so until we terminate you + + + align:start position:0% +this this okay so until we terminate you +need to come up with a way of + + align:start position:0% +need to come up with a way of + + + align:start position:0% +need to come up with a way of +terminating now again we said we're + + align:start position:0% +terminating now again we said we're + + + align:start position:0% +terminating now again we said we're +going to pick what the best child base + + align:start position:0% +going to pick what the best child base + + + align:start position:0% +going to pick what the best child base +is going to be great what the best + + align:start position:0% +is going to be great what the best + + + align:start position:0% +is going to be great what the best +immediate move from the start state has + + align:start position:0% +immediate move from the start state has + + + align:start position:0% +immediate move from the start state has +gonna be and that is what we're gonna + + align:start position:0% +gonna be and that is what we're gonna + + + align:start position:0% +gonna be and that is what we're gonna +that's the move that we're actually + + align:start position:0% +that's the move that we're actually + + + align:start position:0% +that's the move that we're actually +going to play and so how do we determine + + align:start position:0% +going to play and so how do we determine + + + align:start position:0% +going to play and so how do we determine +what the best is well the trivial + + align:start position:0% +what the best is well the trivial + + + align:start position:0% +what the best is well the trivial +solution is just the highest expected + + align:start position:0% +solution is just the highest expected + + + align:start position:0% +solution is just the highest expected +win given K right and ends up with that + + align:start position:0% +win given K right and ends up with that + + + align:start position:0% +win given K right and ends up with that +in our case is going to be is you know + + align:start position:0% +in our case is going to be is you know + + + align:start position:0% +in our case is going to be is you know +the ratio of number of times that I won + + align:start position:0% +the ratio of number of times that I won + + + align:start position:0% +the ratio of number of times that I won +from a given early state to however this + + align:start position:0% +from a given early state to however this + + + align:start position:0% +from a given early state to however this +doesn't actually work as well as we + + align:start position:0% +doesn't actually work as well as we + + + align:start position:0% +doesn't actually work as well as we +might hope let's because the following + + align:start position:0% +might hope let's because the following + + + align:start position:0% +might hope let's because the following +scenario which is that you have this + + align:start position:0% +scenario which is that you have this + + + align:start position:0% +scenario which is that you have this +exact so game like this and you have + + align:start position:0% +exact so game like this and you have + + + align:start position:0% +exact so game like this and you have +been exploring the tree for a while and + + align:start position:0% +been exploring the tree for a while and + + + align:start position:0% +been exploring the tree for a while and +you've been really mostly like looking + + align:start position:0% +you've been really mostly like looking + + + align:start position:0% +you've been really mostly like looking +at these two nodes and one of these + + align:start position:0% +at these two nodes and one of these + + + align:start position:0% +at these two nodes and one of these +nodes have them if if you sort of think + + align:start position:0% +nodes have them if if you sort of think + + + align:start position:0% +nodes have them if if you sort of think +it through this node is quite promising + + align:start position:0% +it through this node is quite promising + + + align:start position:0% +it through this node is quite promising +and you've been exploring it for a while + + align:start position:0% +and you've been exploring it for a while + + + align:start position:0% +and you've been exploring it for a while +there is a there is a winning strategy + + align:start position:0% +there is a there is a winning strategy + + + align:start position:0% +there is a there is a winning strategy +for the code it's that circle goes here + + align:start position:0% +for the code it's that circle goes here + + + align:start position:0% +for the code it's that circle goes here +and the next goes here and then circle + + align:start position:0% +and the next goes here and then circle + + + align:start position:0% +and the next goes here and then circle +loses because the XS two options to win + + align:start position:0% +loses because the XS two options to win + + + align:start position:0% +loses because the XS two options to win +um however however its explore this a + + align:start position:0% +um however however its explore this a + + + align:start position:0% +um however however its explore this a +bunch of times and for some reason due + + align:start position:0% +bunch of times and for some reason due + + + align:start position:0% +bunch of times and for some reason due +to the randomness this is at 11:00 at + + align:start position:0% +to the randomness this is at 11:00 at + + + align:start position:0% +to the randomness this is at 11:00 at +night of 20 where is this state which is + + align:start position:0% +night of 20 where is this state which is + + + align:start position:0% +night of 20 where is this state which is +inherently inferior um is it is a 3 out + + align:start position:0% +inherently inferior um is it is a 3 out + + + align:start position:0% +inherently inferior um is it is a 3 out +of 5 because it when children + + align:start position:0% +of 5 because it when children + + + align:start position:0% +of 5 because it when children +it hasn't been explored as much and if + + align:start position:0% +it hasn't been explored as much and if + + + align:start position:0% +it hasn't been explored as much and if +we get looked at this one as + + align:start position:0% +we get looked at this one as + + + align:start position:0% +we get looked at this one as +exhaustively as we have it this one then + + align:start position:0% +exhaustively as we have it this one then + + + align:start position:0% +exhaustively as we have it this one then +they probably would you probably would + + align:start position:0% +they probably would you probably would + + + align:start position:0% +they probably would you probably would +actually say that this state is better + + align:start position:0% +actually say that this state is better + + + align:start position:0% +actually say that this state is better +and so you can create an alternative + + align:start position:0% +and so you can create an alternative + + + align:start position:0% +and so you can create an alternative +criteria which is that it's the highest + + align:start position:0% +criteria which is that it's the highest + + + align:start position:0% +criteria which is that it's the highest +expected win value of the children but + + align:start position:0% +expected win value of the children but + + + align:start position:0% +expected win value of the children but +also that that value has to be the node + + align:start position:0% +also that that value has to be the node + + + align:start position:0% +also that that value has to be the node +that has been most visited so that they + + align:start position:0% +that has been most visited so that they + + + align:start position:0% +that has been most visited so that they +aren't explored different different + + align:start position:0% +aren't explored different different + + + align:start position:0% +aren't explored different different +amounts um what this sacrifices however + + align:start position:0% +amounts um what this sacrifices however + + + align:start position:0% +amounts um what this sacrifices however +is that mean this means that we can't + + align:start position:0% +is that mean this means that we can't + + + align:start position:0% +is that mean this means that we can't +terminate on demand you know it's it's + + align:start position:0% +terminate on demand you know it's it's + + + align:start position:0% +terminate on demand you know it's it's +this is not always going to be true and + + align:start position:0% +this is not always going to be true and + + + align:start position:0% +this is not always going to be true and +therefore we're gonna have to let the + + align:start position:0% +therefore we're gonna have to let the + + + align:start position:0% +therefore we're gonna have to let the +algorithm run until that's true for some + + align:start position:0% +algorithm run until that's true for some + + + align:start position:0% +algorithm run until that's true for some +start state which means that maybe it's + + align:start position:0% +start state which means that maybe it's + + + align:start position:0% +start state which means that maybe it's +not a criteria that we want to apply + + align:start position:0% +not a criteria that we want to apply + + + align:start position:0% +not a criteria that we want to apply +even though we know that it would be + + align:start position:0% +even though we know that it would be + + + align:start position:0% +even though we know that it would be +wise to music right are there any + + align:start position:0% +wise to music right are there any + + + align:start position:0% +wise to music right are there any +questions about how we pick the training + + align:start position:0% +questions about how we pick the training + + + align:start position:0% +questions about how we pick the training +okay so that was the whole thing and now + + align:start position:0% +okay so that was the whole thing and now + + + align:start position:0% +okay so that was the whole thing and now +we're going to do it lots and lots of + + align:start position:0% +we're going to do it lots and lots of + + + align:start position:0% +we're going to do it lots and lots of +times until you guys think of month of + + align:start position:0% +times until you guys think of month of + + + align:start position:0% +times until you guys think of month of +garlic music um so this is our treat + + align:start position:0% +garlic music um so this is our treat + + + align:start position:0% +garlic music um so this is our treat +it's more or less what we've had before + + align:start position:0% +it's more or less what we've had before + + + align:start position:0% +it's more or less what we've had before +and the first thing we're gonna do is + + align:start position:0% +and the first thing we're gonna do is + + + align:start position:0% +and the first thing we're gonna do is +we're going to look at the topic area + + align:start position:0% +we're going to look at the topic area + + + align:start position:0% +we're going to look at the topic area +and we're gonna pick one of these + + align:start position:0% +and we're gonna pick one of these + + + align:start position:0% +and we're gonna pick one of these +children um now let's say that we looked + + align:start position:0% +children um now let's say that we looked + + + align:start position:0% +children um now let's say that we looked +at this and it turns out the one on the + + align:start position:0% +at this and it turns out the one on the + + + align:start position:0% +at this and it turns out the one on the +left is really valuable drunk so that + + align:start position:0% +left is really valuable drunk so that + + + align:start position:0% +left is really valuable drunk so that +one of the left has been explored a + + align:start position:0% +one of the left has been explored a + + + align:start position:0% +one of the left has been explored a +whole bunch of times remember that it's + + align:start position:0% +whole bunch of times remember that it's + + + align:start position:0% +whole bunch of times remember that it's +that this term starts becoming larger + + align:start position:0% +that this term starts becoming larger + + + align:start position:0% +that this term starts becoming larger +for the ones that haven't been visited + + align:start position:0% +for the ones that haven't been visited + + + align:start position:0% +for the ones that haven't been visited +about this much and so we're going to + + align:start position:0% +about this much and so we're going to + + + align:start position:0% +about this much and so we're going to +descend from this one oh and now we're + + align:start position:0% +descend from this one oh and now we're + + + align:start position:0% +descend from this one oh and now we're +going to just we're going to descend and + + align:start position:0% +going to just we're going to descend and + + + align:start position:0% +going to just we're going to descend and +we have these two options now given what + + align:start position:0% +we have these two options now given what + + + align:start position:0% +we have these two options now given what +you know would you expect that the node + + align:start position:0% +you know would you expect that the node + + + align:start position:0% +you know would you expect that the node +that this is going to pick is going to + + align:start position:0% +that this is going to pick is going to + + + align:start position:0% +that this is going to pick is going to +be the one on the right or the one below + + align:start position:0% +be the one on the right or the one below + + + align:start position:0% +be the one on the right or the one below +on the right because it's never been + + align:start position:0% +on the right because it's never been + + + align:start position:0% +on the right because it's never been +visited before and so this term is going + + align:start position:0% +visited before and so this term is going + + + align:start position:0% +visited before and so this term is going +to explode + + align:start position:0% +to explode + + + align:start position:0% +to explode +and so we're gonna build it on there and + + align:start position:0% +and so we're gonna build it on there and + + + align:start position:0% +and so we're gonna build it on there and +then we're gonna stimulate a game and + + align:start position:0% +then we're gonna stimulate a game and + + + align:start position:0% +then we're gonna stimulate a game and +the result is a win which is bad for + + align:start position:0% +the result is a win which is bad for + + + align:start position:0% +the result is a win which is bad for +this player that means that they partly + + align:start position:0% +this player that means that they partly + + + align:start position:0% +this player that means that they partly +didn't want to make that move and so + + align:start position:0% +didn't want to make that move and so + + + align:start position:0% +didn't want to make that move and so +we're going to propagate that value up + + align:start position:0% +we're going to propagate that value up + + + align:start position:0% +we're going to propagate that value up +and we're going to start the oven again + + align:start position:0% +and we're going to start the oven again + + + align:start position:0% +and we're going to start the oven again +and it's going to + + align:start position:0% +and it's going to + + + align:start position:0% +and it's going to +between these three and now it's going + + align:start position:0% +between these three and now it's going + + + align:start position:0% +between these three and now it's going +to pick the one on the left + + align:start position:0% +to pick the one on the left + + + align:start position:0% +to pick the one on the left +yeah um and and now that it picked the + + align:start position:0% +yeah um and and now that it picked the + + + align:start position:0% +yeah um and and now that it picked the +one on the left it's going to tween + + align:start position:0% +one on the left it's going to tween + + + align:start position:0% +one on the left it's going to tween +these two states know which which of the + + align:start position:0% +these two states know which which of the + + + align:start position:0% +these two states know which which of the +two is going to have a higher expansion + + align:start position:0% +two is going to have a higher expansion + + + align:start position:0% +two is going to have a higher expansion +factor exactly if you do because you + + align:start position:0% +factor exactly if you do because you + + + align:start position:0% +factor exactly if you do because you +know 203 is actually better because it's + + align:start position:0% +know 203 is actually better because it's + + + align:start position:0% +know 203 is actually better because it's +one out of three for the opponent who's + + align:start position:0% +one out of three for the opponent who's + + + align:start position:0% +one out of three for the opponent who's +currently so the one on the left is + + align:start position:0% +currently so the one on the left is + + + align:start position:0% +currently so the one on the left is +gonna have a higher expansion factor and + + align:start position:0% +gonna have a higher expansion factor and + + + align:start position:0% +gonna have a higher expansion factor and +the one of the rights can have a higher + + align:start position:0% +the one of the rights can have a higher + + + align:start position:0% +the one of the rights can have a higher +exploration factor that makes sense for + + align:start position:0% +exploration factor that makes sense for + + + align:start position:0% +exploration factor that makes sense for +people it's okay though okay so we're + + align:start position:0% +people it's okay though okay so we're + + + align:start position:0% +people it's okay though okay so we're +seeing that the one on the right because + + align:start position:0% +seeing that the one on the right because + + + align:start position:0% +seeing that the one on the right because +you know the other one is doing three + + align:start position:0% +you know the other one is doing three + + + align:start position:0% +you know the other one is doing three +and has lots of its mother's love notes + + align:start position:0% +and has lots of its mother's love notes + + + align:start position:0% +and has lots of its mother's love notes +and so we're going to expand that note + + align:start position:0% +and so we're going to expand that note + + + align:start position:0% +and so we're going to expand that note +it doesn't matter if they're both + + align:start position:0% +it doesn't matter if they're both + + + align:start position:0% +it doesn't matter if they're both +equally likely things edit we're going + + align:start position:0% +equally likely things edit we're going + + + align:start position:0% +equally likely things edit we're going +to simulate forward and it's going to be + + align:start position:0% +to simulate forward and it's going to be + + + align:start position:0% +to simulate forward and it's going to be +one which means that that was probably a + + align:start position:0% +one which means that that was probably a + + + align:start position:0% +one which means that that was probably a +wise comfortable um Rick okay yeah so + + align:start position:0% +wise comfortable um Rick okay yeah so + + + align:start position:0% +wise comfortable um Rick okay yeah so +when it's the opponent's turn versus + + align:start position:0% +when it's the opponent's turn versus + + + align:start position:0% +when it's the opponent's turn versus +your train but the exploration factor is + + align:start position:0% +your train but the exploration factor is + + + align:start position:0% +your train but the exploration factor is +the same but we invert or like + + align:start position:0% +the same but we invert or like + + + align:start position:0% +the same but we invert or like +complement the expansion factor yes + + align:start position:0% +complement the expansion factor yes + + + align:start position:0% +complement the expansion factor yes +so the key here being that this takes in + + align:start position:0% +so the key here being that this takes in + + + align:start position:0% +so the key here being that this takes in +both the the state that you're talking + + align:start position:0% +both the the state that you're talking + + + align:start position:0% +both the the state that you're talking +about and player there's but regardless + + align:start position:0% +about and player there's but regardless + + + align:start position:0% +about and player there's but regardless +of the player the excavation factor will + + align:start position:0% +of the player the excavation factor will + + + align:start position:0% +of the player the excavation factor will +always be like this because it's only + + align:start position:0% +always be like this because it's only + + + align:start position:0% +always be like this because it's only +the number of business and not has + + align:start position:0% +the number of business and not has + + + align:start position:0% +the number of business and not has +nothing to do with the recession yeah + + align:start position:0% + + + + align:start position:0% + +so when your love did you + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah so if the opponent wins then what + + align:start position:0% +yeah so if the opponent wins then what + + + align:start position:0% +yeah so if the opponent wins then what +you do is you propagate up a zero which + + align:start position:0% +you do is you propagate up a zero which + + + align:start position:0% +you do is you propagate up a zero which +means that that this that sorry that wk + + align:start position:0% +means that that this that sorry that wk + + + align:start position:0% +means that that this that sorry that wk +is not incremented but but NK is isn't + + align:start position:0% +is not incremented but but NK is isn't + + + align:start position:0% +is not incremented but but NK is isn't +so you know I think we actually did have + + align:start position:0% +so you know I think we actually did have + + + align:start position:0% +so you know I think we actually did have +we seen a missouria there's one sir + + align:start position:0% +we seen a missouria there's one sir + + + align:start position:0% +we seen a missouria there's one sir +but yeah but the idea is that rather + + align:start position:0% +but yeah but the idea is that rather + + + align:start position:0% +but yeah but the idea is that rather +than rather than subtracting or anything + + align:start position:0% +than rather than subtracting or anything + + + align:start position:0% +than rather than subtracting or anything +all you do is propagate off the result + + align:start position:0% +all you do is propagate off the result + + + align:start position:0% +all you do is propagate off the result +of the game which in this case is is + + align:start position:0% +of the game which in this case is is + + + align:start position:0% +of the game which in this case is is +zero which means that which means that + + align:start position:0% +zero which means that which means that + + + align:start position:0% +zero which means that which means that +all of those states seem to become more + + align:start position:0% +all of those states seem to become more + + + align:start position:0% +all of those states seem to become more +valuable to the blue and less valuable + + align:start position:0% +valuable to the blue and less valuable + + + align:start position:0% +valuable to the blue and less valuable +to the red because these numbers are + + align:start position:0% +to the red because these numbers are + + + align:start position:0% +to the red because these numbers are +lower so yeah so we propagate this up + + align:start position:0% +lower so yeah so we propagate this up + + + align:start position:0% +lower so yeah so we propagate this up +and you know this becomes better but + + align:start position:0% +and you know this becomes better but + + + align:start position:0% +and you know this becomes better but +we've sort of done here is we've figured + + align:start position:0% +we've sort of done here is we've figured + + + align:start position:0% +we've sort of done here is we've figured +out a theoretical counter move to blue + + align:start position:0% +out a theoretical counter move to blue + + + align:start position:0% +out a theoretical counter move to blue +moving here right that's how you should + + align:start position:0% +moving here right that's how you should + + + align:start position:0% +moving here right that's how you should +think about this whole tree it's really + + align:start position:0% +think about this whole tree it's really + + + align:start position:0% +think about this whole tree it's really +a lot like the way the huge thing about + + align:start position:0% +a lot like the way the huge thing about + + + align:start position:0% +a lot like the way the huge thing about +these things you know if I do this then + + align:start position:0% +these things you know if I do this then + + + align:start position:0% +these things you know if I do this then +what if they do this well then I'll do + + align:start position:0% +what if they do this well then I'll do + + + align:start position:0% +what if they do this well then I'll do +this and I see that I'm sort of + + align:start position:0% +this and I see that I'm sort of + + + align:start position:0% +this and I see that I'm sort of +successful right okay so now we're look + + align:start position:0% +successful right okay so now we're look + + + align:start position:0% +successful right okay so now we're look +again at the top um and we're going to + + align:start position:0% +again at the top um and we're going to + + + align:start position:0% +again at the top um and we're going to +pick one on the left because it's really + + align:start position:0% +pick one on the left because it's really + + + align:start position:0% +pick one on the left because it's really +promising five out of six is like a good + + align:start position:0% +promising five out of six is like a good + + + align:start position:0% +promising five out of six is like a good +number then we're gonna look at both + + align:start position:0% +number then we're gonna look at both + + + align:start position:0% +number then we're gonna look at both +sides and which one is going to move + + align:start position:0% +sides and which one is going to move + + + align:start position:0% +sides and which one is going to move +blue gonna pick now well it's gonna pick + + align:start position:0% +blue gonna pick now well it's gonna pick + + + align:start position:0% +blue gonna pick now well it's gonna pick +the ones then it's going to be more + + align:start position:0% +the ones then it's going to be more + + + align:start position:0% +the ones then it's going to be more +successful in which is to every I + + align:start position:0% +successful in which is to every I + + + align:start position:0% +successful in which is to every I +realize that this is actually not the + + align:start position:0% +realize that this is actually not the + + + align:start position:0% +realize that this is actually not the +kind of thing where you necessarily ask + + align:start position:0% +kind of thing where you necessarily ask + + + align:start position:0% +kind of thing where you necessarily ask +me okay + + align:start position:0% +me okay + + + align:start position:0% +me okay +I'm the one who's this + + align:start position:0% +I'm the one who's this + + + align:start position:0% +I'm the one who's this +but okay so so then we go that gear and + + align:start position:0% +but okay so so then we go that gear and + + + align:start position:0% +but okay so so then we go that gear and +there's an equal likelihood of picking + + align:start position:0% +there's an equal likelihood of picking + + + align:start position:0% +there's an equal likelihood of picking +either of those notes and so we're gonna + + align:start position:0% +either of those notes and so we're gonna + + + align:start position:0% +either of those notes and so we're gonna +pick my random that's going to be a lot + + align:start position:0% +pick my random that's going to be a lot + + + align:start position:0% +pick my random that's going to be a lot +fun and we're going to create an empty + + align:start position:0% +fun and we're going to create an empty + + + align:start position:0% +fun and we're going to create an empty +node the roof laid out and what's the + + align:start position:0% +node the roof laid out and what's the + + + align:start position:0% +node the roof laid out and what's the +success for blue she's amazing + + align:start position:0% +success for blue she's amazing + + + align:start position:0% +success for blue she's amazing +because what this means now is that + + align:start position:0% +because what this means now is that + + + align:start position:0% +because what this means now is that +suddenly in this tree of you knows + + align:start position:0% +suddenly in this tree of you knows + + + align:start position:0% +suddenly in this tree of you knows +really good move that red can make that + + align:start position:0% +really good move that red can make that + + + align:start position:0% +really good move that red can make that +blue wasn't finding any response to + + align:start position:0% +blue wasn't finding any response to + + + align:start position:0% +blue wasn't finding any response to +suddenly there's hope because we're + + align:start position:0% +suddenly there's hope because we're + + + align:start position:0% +suddenly there's hope because we're +gonna propagate this back and that means + + align:start position:0% +gonna propagate this back and that means + + + align:start position:0% +gonna propagate this back and that means +that move actually has a response move + + align:start position:0% +that move actually has a response move + + + align:start position:0% +that move actually has a response move +to that sequence of Reds moves and so + + align:start position:0% +to that sequence of Reds moves and so + + + align:start position:0% +to that sequence of Reds moves and so +it's going to propagate up and this + + align:start position:0% +it's going to propagate up and this + + + align:start position:0% +it's going to propagate up and this +states going to be more promising to + + align:start position:0% +states going to be more promising to + + + align:start position:0% +states going to be more promising to +blue and less promising for red and so + + align:start position:0% +blue and less promising for red and so + + + align:start position:0% +blue and less promising for red and so +that region the tree that we had dug + + align:start position:0% +that region the tree that we had dug + + + align:start position:0% +that region the tree that we had dug +into is a little less less less + + align:start position:0% +into is a little less less less + + + align:start position:0% +into is a little less less less +promising so we're gonna look back up + + align:start position:0% +promising so we're gonna look back up + + + align:start position:0% +promising so we're gonna look back up +and this time instead we're going to + + align:start position:0% +and this time instead we're going to + + + align:start position:0% +and this time instead we're going to +evaluate the thing that is both + + align:start position:0% +evaluate the thing that is both + + + align:start position:0% +evaluate the thing that is both +promising from you know being the + + align:start position:0% +promising from you know being the + + + align:start position:0% +promising from you know being the +expansion factor and also promising + + align:start position:0% +expansion factor and also promising + + + align:start position:0% +expansion factor and also promising +because we haven't looked at it very + + align:start position:0% +because we haven't looked at it very + + + align:start position:0% +because we haven't looked at it very +much we're gonna pick between these two + + align:start position:0% +much we're gonna pick between these two + + + align:start position:0% +much we're gonna pick between these two +which one is gonna be picked here + + align:start position:0% + + + + align:start position:0% + +didn't because the expiration factor is + + align:start position:0% +didn't because the expiration factor is + + + align:start position:0% +didn't because the expiration factor is +the same with the expansion factor is + + align:start position:0% +the same with the expansion factor is + + + align:start position:0% +the same with the expansion factor is +higher a little for money left over to + + align:start position:0% +higher a little for money left over to + + + align:start position:0% +higher a little for money left over to +look down and it's going to show us + + align:start position:0% +look down and it's going to show us + + + align:start position:0% +look down and it's going to show us +annuity and the result it's going to be + + align:start position:0% +annuity and the result it's going to be + + + align:start position:0% +annuity and the result it's going to be +a win for red which means that redness + + align:start position:0% +a win for red which means that redness + + + align:start position:0% +a win for red which means that redness +found a good counter move to the thing + + align:start position:0% +found a good counter move to the thing + + + align:start position:0% +found a good counter move to the thing +that was previously from save Rebecca + + align:start position:0% +that was previously from save Rebecca + + + align:start position:0% +that was previously from save Rebecca +and finally we're going to pick the one + + align:start position:0% +and finally we're going to pick the one + + + align:start position:0% +and finally we're going to pick the one +furthest on the right because even + + align:start position:0% +furthest on the right because even + + + align:start position:0% +furthest on the right because even +though it's terrible for red and even + + align:start position:0% +though it's terrible for red and even + + + align:start position:0% +though it's terrible for red and even +though it's number one when it's private + + align:start position:0% +though it's number one when it's private + + + align:start position:0% +though it's number one when it's private +it has to obey this idea of the + + align:start position:0% +it has to obey this idea of the + + + align:start position:0% +it has to obey this idea of the +exploration the exploration component to + + align:start position:0% +exploration the exploration component to + + + align:start position:0% +exploration the exploration component to +find out whether maybe there isn't + + align:start position:0% +find out whether maybe there isn't + + + align:start position:0% +find out whether maybe there isn't +something promising in there so it + + align:start position:0% +something promising in there so it + + + align:start position:0% +something promising in there so it +explores and it goes down and it has to + + align:start position:0% +explores and it goes down and it has to + + + align:start position:0% +explores and it goes down and it has to +pick the one on the right and so it does + + align:start position:0% +pick the one on the right and so it does + + + align:start position:0% +pick the one on the right and so it does +and plays this game out and it's a loss + + align:start position:0% +and plays this game out and it's a loss + + + align:start position:0% +and plays this game out and it's a loss +again um which sort of goes to show you + + align:start position:0% +again um which sort of goes to show you + + + align:start position:0% +again um which sort of goes to show you +that you know blue this phone give + + align:start position:0% +that you know blue this phone give + + + align:start position:0% +that you know blue this phone give +another severe move to this really bad + + align:start position:0% +another severe move to this really bad + + + align:start position:0% +another severe move to this really bad +movie to bread we're probably this move + + align:start position:0% +movie to bread we're probably this move + + + align:start position:0% +movie to bread we're probably this move +of red you know if this is a game of + + align:start position:0% +of red you know if this is a game of + + + align:start position:0% +of red you know if this is a game of +chess is that like that like running + + align:start position:0% +chess is that like that like running + + + align:start position:0% +chess is that like that like running +directly in front of the opponent's + + align:start position:0% +directly in front of the opponent's + + + align:start position:0% +directly in front of the opponent's +grove of pawns and I just leave it there + + align:start position:0% +grove of pawns and I just leave it there + + + align:start position:0% +grove of pawns and I just leave it there +right and like there's nothing that's + + align:start position:0% +right and like there's nothing that's + + + align:start position:0% +right and like there's nothing that's +ever gonna come of it but we have to + + align:start position:0% +ever gonna come of it but we have to + + + align:start position:0% +ever gonna come of it but we have to +explore it just to find out whether you + + align:start position:0% +explore it just to find out whether you + + + align:start position:0% +explore it just to find out whether you +know there isn't some magical way that I + + align:start position:0% +know there isn't some magical way that I + + + align:start position:0% +know there isn't some magical way that I +can protect me and as you can see we've + + align:start position:0% +can protect me and as you can see we've + + + align:start position:0% +can protect me and as you can see we've +built up this tree over and over and + + align:start position:0% +built up this tree over and over and + + + align:start position:0% +built up this tree over and over and +over again + + align:start position:0% +over again + + + align:start position:0% +over again +and it's starting to look a symmetric + + align:start position:0% +and it's starting to look a symmetric + + + align:start position:0% +and it's starting to look a symmetric +and we're starting to see that there's + + align:start position:0% +and we're starting to see that there's + + + align:start position:0% +and we're starting to see that there's +really this disparate the disparity + + align:start position:0% +really this disparate the disparity + + + align:start position:0% +really this disparate the disparity +between you know exploring the regions + + align:start position:0% +between you know exploring the regions + + + align:start position:0% +between you know exploring the regions +that are promising this tree and + + align:start position:0% +that are promising this tree and + + + align:start position:0% +that are promising this tree and +exploring the regions that are not and + + align:start position:0% +exploring the regions that are not and + + + align:start position:0% +exploring the regions that are not and +that don't really matter to us very much + + align:start position:0% +that don't really matter to us very much + + + align:start position:0% +that don't really matter to us very much +and that and that this is exactly what + + align:start position:0% +and that and that this is exactly what + + + align:start position:0% +and that and that this is exactly what +we wanted from other cultures that was + + align:start position:0% +we wanted from other cultures that was + + + align:start position:0% +we wanted from other cultures that was +like why destroy the whole different + + align:start position:0% +like why destroy the whole different + + + align:start position:0% +like why destroy the whole different +first base alright the next thing I'm + + align:start position:0% +first base alright the next thing I'm + + + align:start position:0% +first base alright the next thing I'm +gonna talk about is pros and cons but + + align:start position:0% +gonna talk about is pros and cons but + + + align:start position:0% +gonna talk about is pros and cons but +before we do that does anyone have any + + align:start position:0% +before we do that does anyone have any + + + align:start position:0% +before we do that does anyone have any +more questions about the algorithm + + align:start position:0% +more questions about the algorithm + + + align:start position:0% +more questions about the algorithm +yeah it's still not clear how we're + + align:start position:0% +yeah it's still not clear how we're + + + align:start position:0% +yeah it's still not clear how we're +getting know + + align:start position:0% + + + + align:start position:0% + +okay so the reason for that is that + + align:start position:0% +okay so the reason for that is that + + + align:start position:0% +okay so the reason for that is that +because because of the way that we're + + align:start position:0% +because because of the way that we're + + + align:start position:0% +because because of the way that we're +simulating it through we're actually + + align:start position:0% +simulating it through we're actually + + + align:start position:0% +simulating it through we're actually +we're not holding on to the results the + + align:start position:0% +we're not holding on to the results the + + + align:start position:0% +we're not holding on to the results the +simulation as we've been going and + + align:start position:0% +simulation as we've been going and + + + align:start position:0% +simulation as we've been going and +farther down the river than the lowest + + align:start position:0% +farther down the river than the lowest + + + align:start position:0% +farther down the river than the lowest +numbers and so for example when you + + align:start position:0% +numbers and so for example when you + + + align:start position:0% +numbers and so for example when you +simulate we're here um you're going to + + align:start position:0% +simulate we're here um you're going to + + + align:start position:0% +simulate we're here um you're going to +you know propagate that value here and + + align:start position:0% +you know propagate that value here and + + + align:start position:0% +you know propagate that value here and +here and so on + + align:start position:0% +here and so on + + + align:start position:0% +here and so on +but then when we expend below even if in + + align:start position:0% +but then when we expend below even if in + + + align:start position:0% +but then when we expend below even if in +the course of this guy's simulation it + + align:start position:0% +the course of this guy's simulation it + + + align:start position:0% +the course of this guy's simulation it +happened to go through one of the states + + align:start position:0% +happened to go through one of the states + + + align:start position:0% +happened to go through one of the states +that we expected below it will not have + + align:start position:0% +that we expected below it will not have + + + align:start position:0% +that we expected below it will not have +incremented the value for that state + + align:start position:0% +incremented the value for that state + + + align:start position:0% +incremented the value for that state +because we weren't getting track of it + + align:start position:0% +because we weren't getting track of it + + + align:start position:0% +because we weren't getting track of it +yet and so theoretically if we were to + + align:start position:0% +yet and so theoretically if we were to + + + align:start position:0% +yet and so theoretically if we were to +be in track of all of this English ins + + align:start position:0% +be in track of all of this English ins + + + align:start position:0% +be in track of all of this English ins +that we have in fact run the numbers + + align:start position:0% +that we have in fact run the numbers + + + align:start position:0% +that we have in fact run the numbers +beneath these things would be higher + + align:start position:0% +beneath these things would be higher + + + align:start position:0% +beneath these things would be higher +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +like what do you brought us in Malaysia + + align:start position:0% +like what do you brought us in Malaysia + + + align:start position:0% +like what do you brought us in Malaysia +from that note we first built it and + + align:start position:0% +from that note we first built it and + + + align:start position:0% +from that note we first built it and +then of when you created by those two + + align:start position:0% +then of when you created by those two + + + align:start position:0% +then of when you created by those two +ones each of those have solutions so + + align:start position:0% +ones each of those have solutions so + + + align:start position:0% +ones each of those have solutions so +you're like totally up and so forth the + + align:start position:0% +you're like totally up and so forth the + + + align:start position:0% +you're like totally up and so forth the +denominator always be one more than the + + align:start position:0% +denominator always be one more than the + + + align:start position:0% +denominator always be one more than the +sum of the children oh yeah in the + + align:start position:0% +sum of the children oh yeah in the + + + align:start position:0% +sum of the children oh yeah in the +transition okay yeah so with your yeah + + align:start position:0% +transition okay yeah so with your yeah + + + align:start position:0% +transition okay yeah so with your yeah +how can you is it like a rule of thumb + + align:start position:0% +how can you is it like a rule of thumb + + + align:start position:0% +how can you is it like a rule of thumb +like it's time to choose a move and it + + align:start position:0% +like it's time to choose a move and it + + + align:start position:0% +like it's time to choose a move and it +seems like you have very low numbers + + align:start position:0% +seems like you have very low numbers + + + align:start position:0% +seems like you have very low numbers +here okay mister places they're both on + + align:start position:0% +here okay mister places they're both on + + + align:start position:0% +here okay mister places they're both on +you know given game for 2015 whatever + + align:start position:0% +you know given game for 2015 whatever + + + align:start position:0% +you know given game for 2015 whatever +what kind of numbers you need + + align:start position:0% +what kind of numbers you need + + + align:start position:0% +what kind of numbers you need +first row before using console um so + + align:start position:0% +first row before using console um so + + + align:start position:0% +first row before using console um so +what we'll get to students that there + + align:start position:0% +what we'll get to students that there + + + align:start position:0% +what we'll get to students that there +isn't and that that's one of the + + align:start position:0% +isn't and that that's one of the + + + align:start position:0% +isn't and that that's one of the +problems with ncts um but the in terms + + align:start position:0% +problems with ncts um but the in terms + + + align:start position:0% +problems with ncts um but the in terms +of which of the moves you will choose + + align:start position:0% +of which of the moves you will choose + + + align:start position:0% +of which of the moves you will choose +there there are actually very incidents + + align:start position:0% +there there are actually very incidents + + + align:start position:0% +there there are actually very incidents +yes that suggest that you you know more + + align:start position:0% +yes that suggest that you you know more + + + align:start position:0% +yes that suggest that you you know more +selectively aimed toward certain + + align:start position:0% +selectively aimed toward certain + + + align:start position:0% +selectively aimed toward certain +children but based on something more + + align:start position:0% +children but based on something more + + + align:start position:0% +children but based on something more +than just the this sort of blind look + + align:start position:0% +than just the this sort of blind look + + + align:start position:0% +than just the this sort of blind look +right now in terms of like you know if + + align:start position:0% +right now in terms of like you know if + + + align:start position:0% +right now in terms of like you know if +I'm here it's our time here and it's you + + align:start position:0% +I'm here it's our time here and it's you + + + align:start position:0% +I'm here it's our time here and it's you +know creating my next children is + + align:start position:0% +know creating my next children is + + + align:start position:0% +know creating my next children is +equivalent then there are some + + align:start position:0% +equivalent then there are some + + + align:start position:0% +equivalent then there are some +intelligent guesses that you workers + + align:start position:0% +intelligent guesses that you workers + + + align:start position:0% +intelligent guesses that you workers +yeah I'm just saying like computational + + align:start position:0% +yeah I'm just saying like computational + + + align:start position:0% +yeah I'm just saying like computational +time in what it is you might say okay if + + align:start position:0% +time in what it is you might say okay if + + + align:start position:0% +time in what it is you might say okay if +this is the timeline of this game yeah I + + align:start position:0% +this is the timeline of this game yeah I + + + align:start position:0% +this is the timeline of this game yeah I +can expect to do a million simulations + + align:start position:0% +can expect to do a million simulations + + + align:start position:0% +can expect to do a million simulations +which will give me if there's 400 nodes + + align:start position:0% +which will give me if there's 400 nodes + + + align:start position:0% +which will give me if there's 400 nodes +you know I'm gonna have so much you know + + align:start position:0% +you know I'm gonna have so much you know + + + align:start position:0% +you know I'm gonna have so much you know +yeah is that enough time to say that I + + align:start position:0% +yeah is that enough time to say that I + + + align:start position:0% +yeah is that enough time to say that I +could play for a game I couldn't play + + align:start position:0% +could play for a game I couldn't play + + + align:start position:0% +could play for a game I couldn't play +through a game 400 options if I've got + + align:start position:0% +through a game 400 options if I've got + + + align:start position:0% +through a game 400 options if I've got +like five out of seven absolutely and I + + align:start position:0% +like five out of seven absolutely and I + + + align:start position:0% +like five out of seven absolutely and I +would say that this that's surprise I + + align:start position:0% +would say that this that's surprise I + + + align:start position:0% +would say that this that's surprise I +know we've got something that's + + align:start position:0% +know we've got something that's + + + align:start position:0% +know we've got something that's +basically four apparently yeah um so + + align:start position:0% +basically four apparently yeah um so + + + align:start position:0% +basically four apparently yeah um so +let's get the first comments because + + align:start position:0% +let's get the first comments because + + + align:start position:0% +let's get the first comments because +that is particularly um so why should + + align:start position:0% +that is particularly um so why should + + + align:start position:0% +that is particularly um so why should +you use this under them even though you + + align:start position:0% +you use this under them even though you + + + align:start position:0% +you use this under them even though you +know we've seen tremendous breakthroughs + + align:start position:0% +know we've seen tremendous breakthroughs + + + align:start position:0% +know we've seen tremendous breakthroughs +in this algorithm and you know you're + + align:start position:0% +in this algorithm and you know you're + + + align:start position:0% +in this algorithm and you know you're +gonna have to ignore everything they + + align:start position:0% +gonna have to ignore everything they + + + align:start position:0% +gonna have to ignore everything they +tell you remember this does actually + + align:start position:0% +tell you remember this does actually + + + align:start position:0% +tell you remember this does actually +work quite well in certain scenarios um + + align:start position:0% +work quite well in certain scenarios um + + + align:start position:0% +work quite well in certain scenarios um +should we use it or not okay the pros + + align:start position:0% +should we use it or not okay the pros + + + align:start position:0% +should we use it or not okay the pros +are that it actually does the thing a + + align:start position:0% +are that it actually does the thing a + + + align:start position:0% +are that it actually does the thing a +large bruise the tree a symmetrically it + + align:start position:0% +large bruise the tree a symmetrically it + + + align:start position:0% +large bruise the tree a symmetrically it +means that we do not have to explore you + + align:start position:0% +means that we do not have to explore you + + + align:start position:0% +means that we do not have to explore you +know and that it doesn't actually + + align:start position:0% +know and that it doesn't actually + + + align:start position:0% +know and that it doesn't actually +explode exponentially with the number of + + align:start position:0% +explode exponentially with the number of + + + align:start position:0% +explode exponentially with the number of +the number of moves that we're looking + + align:start position:0% +the number of moves that we're looking + + + align:start position:0% +the number of moves that we're looking +into + + align:start position:0% +into + + + align:start position:0% +into +future and that it's you know + + align:start position:0% +future and that it's you know + + + align:start position:0% +future and that it's you know +selectively grows the tree towards the + + align:start position:0% +selectively grows the tree towards the + + + align:start position:0% +selectively grows the tree towards the +areas that are most promising okay um + + align:start position:0% +areas that are most promising okay um + + + align:start position:0% +areas that are most promising okay um +the other huge benefit if you'll notice + + align:start position:0% +the other huge benefit if you'll notice + + + align:start position:0% +the other huge benefit if you'll notice +from what we've just talked through is + + align:start position:0% +from what we've just talked through is + + + align:start position:0% +from what we've just talked through is +that it never relies on anything other + + align:start position:0% +that it never relies on anything other + + + align:start position:0% +that it never relies on anything other +than the strict rules of the game what + + align:start position:0% +than the strict rules of the game what + + + align:start position:0% +than the strict rules of the game what +that means is that the only way the game + + align:start position:0% +that means is that the only way the game + + + align:start position:0% +that means is that the only way the game +is factored in is that the game is what + + align:start position:0% +is factored in is that the game is what + + + align:start position:0% +is factored in is that the game is what +tells us what the next moves we can make + + align:start position:0% +tells us what the next moves we can make + + + align:start position:0% +tells us what the next moves we can make +from a given state are and what and + + align:start position:0% +from a given state are and what and + + + align:start position:0% +from a given state are and what and +whether a given state is like a victory + + align:start position:0% +whether a given state is like a victory + + + align:start position:0% +whether a given state is like a victory +or a defeat um and that's that's kind of + + align:start position:0% +or a defeat um and that's that's kind of + + + align:start position:0% +or a defeat um and that's that's kind of +amazing because you know we had no + + align:start position:0% +amazing because you know we had no + + + align:start position:0% +amazing because you know we had no +external heuristic information about + + align:start position:0% +external heuristic information about + + + align:start position:0% +external heuristic information about +this game which means that if I took a + + align:start position:0% +this game which means that if I took a + + + align:start position:0% +this game which means that if I took a +completely new game but someone had just + + align:start position:0% +completely new game but someone had just + + + align:start position:0% +completely new game but someone had just +invented for me and I plugged MCTS into + + align:start position:0% +invented for me and I plugged MCTS into + + + align:start position:0% +invented for me and I plugged MCTS into +it + + align:start position:0% +it + + + align:start position:0% +it +MCTS would be a like slightly or + + align:start position:0% +MCTS would be a like slightly or + + + align:start position:0% +MCTS would be a like slightly or +somewhat competitive in a player for + + align:start position:0% +somewhat competitive in a player for + + + align:start position:0% +somewhat competitive in a player for +this game which is a powerful idea it + + align:start position:0% +this game which is a powerful idea it + + + align:start position:0% +this game which is a powerful idea it +leads to our next two groups for the + + align:start position:0% +leads to our next two groups for the + + + align:start position:0% +leads to our next two groups for the +first of which is that it's very easy to + + align:start position:0% +first of which is that it's very easy to + + + align:start position:0% +first of which is that it's very easy to +add eyes to new games that you know it + + align:start position:0% +add eyes to new games that you know it + + + align:start position:0% +add eyes to new games that you know it +hasn't seen before or even that people + + align:start position:0% +hasn't seen before or even that people + + + align:start position:0% +hasn't seen before or even that people +haven't seen before and the others and I + + align:start position:0% +haven't seen before and the others and I + + + align:start position:0% +haven't seen before and the others and I +mean this is clearly valuable but the + + align:start position:0% +mean this is clearly valuable but the + + + align:start position:0% +mean this is clearly valuable but the +other nice thing about it is that even + + align:start position:0% +other nice thing about it is that even + + + align:start position:0% +other nice thing about it is that even +though heuristics are not required to + + align:start position:0% +though heuristics are not required to + + + align:start position:0% +though heuristics are not required to +make MCTS um make MCTS permanent in wine + + align:start position:0% +make MCTS um make MCTS permanent in wine + + + align:start position:0% +make MCTS um make MCTS permanent in wine +there are a number and these places in + + align:start position:0% +there are a number and these places in + + + align:start position:0% +there are a number and these places in +the algorithm that you can actually + + align:start position:0% +the algorithm that you can actually + + + align:start position:0% +the algorithm that you can actually +incorporate your estates into Nikki's + + align:start position:0% +incorporate your estates into Nikki's + + + align:start position:0% +incorporate your estates into Nikki's +going to talk about how alphago uses + + align:start position:0% +going to talk about how alphago uses + + + align:start position:0% +going to talk about how alphago uses +this very heavily alphago is not vanilla + + align:start position:0% +this very heavily alphago is not vanilla + + + align:start position:0% +this very heavily alphago is not vanilla +go it has a lot of external information + + align:start position:0% +go it has a lot of external information + + + align:start position:0% +go it has a lot of external information +that's built into the way that it works + + align:start position:0% +that's built into the way that it works + + + align:start position:0% +that's built into the way that it works +but mc2 can MCTS as a framework you can + + align:start position:0% +but mc2 can MCTS as a framework you can + + + align:start position:0% +but mc2 can MCTS as a framework you can +imagine you know is it your purest + + align:start position:0% +imagine you know is it your purest + + + align:start position:0% +imagine you know is it your purest +exceed can apply in the simulation there + + align:start position:0% +exceed can apply in the simulation there + + + align:start position:0% +exceed can apply in the simulation there +here's because you can apply in the UCB + + align:start position:0% +here's because you can apply in the UCB + + + align:start position:0% +here's because you can apply in the UCB +and the like wave it and choose the next + + align:start position:0% +and the like wave it and choose the next + + + align:start position:0% +and the like wave it and choose the next +note um there are places that are + + align:start position:0% +note um there are places that are + + + align:start position:0% +note um there are places that are +getting to can fit in and then this + + align:start position:0% +getting to can fit in and then this + + + align:start position:0% +getting to can fit in and then this +serves as a nice infrastructure reducer + + align:start position:0% +serves as a nice infrastructure reducer + + + align:start position:0% +serves as a nice infrastructure reducer +alright um + + align:start position:0% +alright um + + + align:start position:0% +alright um +few other benefit is that you know it's + + align:start position:0% +few other benefit is that you know it's + + + align:start position:0% +few other benefit is that you know it's +an on-demand algorithm which is + + align:start position:0% +an on-demand algorithm which is + + + align:start position:0% +an on-demand algorithm which is +particularly valuable when you're under + + align:start position:0% +particularly valuable when you're under + + + align:start position:0% +particularly valuable when you're under +some sort of time pressure the limiter + + align:start position:0% +some sort of time pressure the limiter + + + align:start position:0% +some sort of time pressure the limiter +competing against someone it's a + + align:start position:0% +competing against someone it's a + + + align:start position:0% +competing against someone it's a +competition + + align:start position:0% +competition + + + align:start position:0% +competition +when something is better explode you + + align:start position:0% +when something is better explode you + + + align:start position:0% +when something is better explode you +have to like make a decision on which + + align:start position:0% +have to like make a decision on which + + + align:start position:0% +have to like make a decision on which +you actively shut down um + + align:start position:0% +you actively shut down um + + + align:start position:0% +you actively shut down um +and lastly or not it's completely which + + align:start position:0% +and lastly or not it's completely which + + + align:start position:0% +and lastly or not it's completely which +is really nice because you know that you + + align:start position:0% +is really nice because you know that you + + + align:start position:0% +is really nice because you know that you +know if you run the same for long enough + + align:start position:0% +know if you run the same for long enough + + + align:start position:0% +know if you run the same for long enough +it's gonna start looking a lot like like + + align:start position:0% +it's gonna start looking a lot like like + + + align:start position:0% +it's gonna start looking a lot like like +a BFS tree + + align:start position:0% +a BFS tree + + + align:start position:0% +a BFS tree +we're actually no to certainly be enough + + align:start position:0% +we're actually no to certainly be enough + + + align:start position:0% +we're actually no to certainly be enough +of a trim is what a furnace to which + + align:start position:0% +of a trim is what a furnace to which + + + align:start position:0% +of a trim is what a furnace to which +means they you know it's it's a nice + + align:start position:0% +means they you know it's it's a nice + + + align:start position:0% +means they you know it's it's a nice +property to have although this property + + align:start position:0% +property to have although this property + + + align:start position:0% +property to have although this property +some does slightly get compromised if + + align:start position:0% +some does slightly get compromised if + + + align:start position:0% +some does slightly get compromised if +you lose the random aside together and + + align:start position:0% +you lose the random aside together and + + + align:start position:0% +you lose the random aside together and +if you only simulate these mister soon + + align:start position:0% +if you only simulate these mister soon + + + align:start position:0% +if you only simulate these mister soon +okay + + align:start position:0% +okay + + + align:start position:0% +okay +oh yeah so you made an interesting + + align:start position:0% +oh yeah so you made an interesting + + + align:start position:0% +oh yeah so you made an interesting +comment when he said oh looks like + + align:start position:0% +comment when he said oh looks like + + + align:start position:0% +comment when he said oh looks like +another beta treat so so it looked like + + align:start position:0% +another beta treat so so it looked like + + + align:start position:0% +another beta treat so so it looked like +a minimax treat right but have they also + + align:start position:0% +a minimax treat right but have they also + + + align:start position:0% +a minimax treat right but have they also +incorporating notions of pruning and + + align:start position:0% +incorporating notions of pruning and + + + align:start position:0% +incorporating notions of pruning and +MCTS which would make it look like an + + align:start position:0% +MCTS which would make it look like an + + + align:start position:0% +MCTS which would make it look like an +alpha beta me sooo sorry you're + + align:start position:0% +alpha beta me sooo sorry you're + + + align:start position:0% +alpha beta me sooo sorry you're +completely right it does look immunity + + align:start position:0% +completely right it does look immunity + + + align:start position:0% +completely right it does look immunity +ministry oh I think I've seen variants + + align:start position:0% + + + + align:start position:0% + +but they but people have explored + + align:start position:0% +but they but people have explored + + + align:start position:0% +but they but people have explored +incorporating pruning into MCPS I think + + align:start position:0% +incorporating pruning into MCPS I think + + + align:start position:0% +incorporating pruning into MCPS I think +so I can't say okay and then lastly it's + + align:start position:0% +so I can't say okay and then lastly it's + + + align:start position:0% +so I can't say okay and then lastly it's +really paralyzing + + align:start position:0% +really paralyzing + + + align:start position:0% +really paralyzing +if you'll notice none of the brent none + + align:start position:0% +if you'll notice none of the brent none + + + align:start position:0% +if you'll notice none of the brent none +of the regions of this tree other than + + align:start position:0% +of the regions of this tree other than + + + align:start position:0% +of the regions of this tree other than +you know the original choice ever have + + align:start position:0% +you know the original choice ever have + + + align:start position:0% +you know the original choice ever have +to interact with each other so if you + + align:start position:0% +to interact with each other so if you + + + align:start position:0% +to interact with each other so if you +have like two hundred processors and you + + align:start position:0% +have like two hundred processors and you + + + align:start position:0% +have like two hundred processors and you +decide okay I'm going to break up this + + align:start position:0% +decide okay I'm going to break up this + + + align:start position:0% +decide okay I'm going to break up this +tree and the first like to hunt antigens + + align:start position:0% +tree and the first like to hunt antigens + + + align:start position:0% +tree and the first like to hunt antigens +and then have each one of those flesh + + align:start position:0% +and then have each one of those flesh + + + align:start position:0% +and then have each one of those flesh +out one of those decisions that actually + + align:start position:0% +out one of those decisions that actually + + + align:start position:0% +out one of those decisions that actually +means that you know they can all combine + + align:start position:0% +means that you know they can all combine + + + align:start position:0% +means that you know they can all combine +the information right at the end and + + align:start position:0% +the information right at the end and + + + align:start position:0% +the information right at the end and +make a decision which is a really nice + + align:start position:0% +make a decision which is a really nice + + + align:start position:0% +make a decision which is a really nice +nice power principle as okay it does + + align:start position:0% +nice power principle as okay it does + + + align:start position:0% +nice power principle as okay it does +have its fair share of problems the + + align:start position:0% +have its fair share of problems the + + + align:start position:0% +have its fair share of problems the +first problem being that it does sort of + + align:start position:0% +first problem being that it does sort of + + + align:start position:0% +first problem being that it does sort of +break down under extreme tree death and + + align:start position:0% +break down under extreme tree death and + + + align:start position:0% +break down under extreme tree death and +one of the main reason for this being + + align:start position:0% +one of the main reason for this being + + + align:start position:0% +one of the main reason for this being +that you know that as you increase more + + align:start position:0% +that you know that as you increase more + + + align:start position:0% +that you know that as you increase more +moves between + + align:start position:0% +moves between + + + align:start position:0% +moves between +you and in the end of the game you're + + align:start position:0% +you and in the end of the game you're + + + align:start position:0% +you and in the end of the game you're +increasing the probability that you're + + align:start position:0% +increasing the probability that you're + + + align:start position:0% +increasing the probability that you're +decreasing the correlation between your + + align:start position:0% +decreasing the correlation between your + + + align:start position:0% +decreasing the correlation between your +gained state and whether a wreck and + + align:start position:0% +gained state and whether a wreck and + + + align:start position:0% +gained state and whether a wreck and +playoff would suggests that you're in a + + align:start position:0% +playoff would suggests that you're in a + + + align:start position:0% +playoff would suggests that you're in a +good position for a bad position the + + align:start position:0% +good position for a bad position the + + + align:start position:0% +good position for a bad position the +same sort of goes for branching factors + + align:start position:0% +same sort of goes for branching factors + + + align:start position:0% +same sort of goes for branching factors +one of the things that people suppress + + align:start position:0% +one of the things that people suppress + + + align:start position:0% +one of the things that people suppress +our medicine pensiero ncts hey guys + + align:start position:0% +our medicine pensiero ncts hey guys + + + align:start position:0% +our medicine pensiero ncts hey guys +cannot play first person peters because + + align:start position:0% +cannot play first person peters because + + + align:start position:0% +cannot play first person peters because +the like distance between the lake + + align:start position:0% +the like distance between the lake + + + align:start position:0% +the like distance between the lake +number of things that you can do with + + align:start position:0% +number of things that you can do with + + + align:start position:0% +number of things that you can do with +every given moment and the what would be + + align:start position:0% +every given moment and the what would be + + + align:start position:0% +every given moment and the what would be +a successful approach you know in the + + align:start position:0% +a successful approach you know in the + + + align:start position:0% +a successful approach you know in the +long term after making many many many + + align:start position:0% +long term after making many many many + + + align:start position:0% +long term after making many many many +moves that each have many branching + + align:start position:0% +moves that each have many branching + + + align:start position:0% +moves that each have many branching +factors is that it never means again + + align:start position:0% +factors is that it never means again + + + align:start position:0% +factors is that it never means again +stirs explore the size of the surgery + + align:start position:0% +stirs explore the size of the surgery + + + align:start position:0% +stirs explore the size of the surgery +it's not like for the most part it's not + + align:start position:0% +it's not like for the most part it's not + + + align:start position:0% +it's not like for the most part it's not +really coming up with a long term policy + + align:start position:0% +really coming up with a long term policy + + + align:start position:0% +really coming up with a long term policy +right it's really thinking about what + + align:start position:0% +right it's really thinking about what + + + align:start position:0% +right it's really thinking about what +are the sort of next sequence of food + + align:start position:0% +are the sort of next sequence of food + + + align:start position:0% +are the sort of next sequence of food +obsession okay another another problem + + align:start position:0% +obsession okay another another problem + + + align:start position:0% +obsession okay another another problem +is that requires stimulation to be very + + align:start position:0% +is that requires stimulation to be very + + + align:start position:0% +is that requires stimulation to be very +easy and very repeatable + + align:start position:0% +easy and very repeatable + + + align:start position:0% +easy and very repeatable +so for example if if we wanted to tell + + align:start position:0% +so for example if if we wanted to tell + + + align:start position:0% +so for example if if we wanted to tell +rai to you know how do I take over + + align:start position:0% +rai to you know how do I take over + + + align:start position:0% +rai to you know how do I take over +Ontario right there's not a particularly + + align:start position:0% +Ontario right there's not a particularly + + + align:start position:0% +Ontario right there's not a particularly +good way that you can simulate taking + + align:start position:0% +good way that you can simulate taking + + + align:start position:0% +good way that you can simulate taking +over Ontario if you do it once or if you + + align:start position:0% +over Ontario if you do it once or if you + + + align:start position:0% +over Ontario if you do it once or if you +try it once you're like not gonna have + + align:start position:0% +try it once you're like not gonna have + + + align:start position:0% +try it once you're like not gonna have +an opportunity to try it again + + align:start position:0% +an opportunity to try it again + + + align:start position:0% +an opportunity to try it again +at least we're the same you know set of + + align:start position:0% +at least we're the same you know set of + + + align:start position:0% +at least we're the same you know set of +configurations and and actually you know + + align:start position:0% +configurations and and actually you know + + + align:start position:0% +configurations and and actually you know +one of the things that we really take + + align:start position:0% +one of the things that we really take + + + align:start position:0% +one of the things that we really take +thank you Joe is that random simulation + + align:start position:0% +thank you Joe is that random simulation + + + align:start position:0% +thank you Joe is that random simulation +happens really quickly in the order of + + align:start position:0% +happens really quickly in the order of + + + align:start position:0% +happens really quickly in the order of +microseconds um and on the other hand + + align:start position:0% +microseconds um and on the other hand + + + align:start position:0% +microseconds um and on the other hand +you know this it does require you know + + align:start position:0% +you know this it does require you know + + + align:start position:0% +you know this it does require you know +the finger your computational resources + + align:start position:0% +the finger your computational resources + + + align:start position:0% +the finger your computational resources +that you have access to you the better + + align:start position:0% +that you have access to you the better + + + align:start position:0% +that you have access to you the better +the algorithm works that means that I + + align:start position:0% +the algorithm works that means that I + + + align:start position:0% +the algorithm works that means that I +can't run it off my network particularly + + align:start position:0% +can't run it off my network particularly + + + align:start position:0% +can't run it off my network particularly +well large games um it it relies on this + + align:start position:0% +well large games um it it relies on this + + + align:start position:0% +well large games um it it relies on this +you know ten years assumption of random + + align:start position:0% +you know ten years assumption of random + + + align:start position:0% +you know ten years assumption of random +play being weakly correlated with the + + align:start position:0% +play being weakly correlated with the + + + align:start position:0% +play being weakly correlated with the +quality of our game state this is one of + + align:start position:0% +quality of our game state this is one of + + + align:start position:0% +quality of our game state this is one of +the first assumption that's going to be + + align:start position:0% +the first assumption that's going to be + + + align:start position:0% +the first assumption that's going to be +thrown out the window for a lot of the + + align:start position:0% +thrown out the window for a lot of the + + + align:start position:0% +thrown out the window for a lot of the +more advanced + + align:start position:0% +more advanced + + + align:start position:0% +more advanced +ts approaches which are going to have + + align:start position:0% +ts approaches which are going to have + + + align:start position:0% +ts approaches which are going to have +you know more more intelligent play outs + + align:start position:0% +you know more more intelligent play outs + + + align:start position:0% +you know more more intelligent play outs +but those are going to lose some of the + + align:start position:0% +but those are going to lose some of the + + + align:start position:0% +but those are going to lose some of the +generality that we had before um another + + align:start position:0% +generality that we had before um another + + + align:start position:0% +generality that we had before um another +sort of something that goes off of that + + align:start position:0% +sort of something that goes off of that + + + align:start position:0% +sort of something that goes off of that +is that MCTS is a framework but in order + + align:start position:0% +is that MCTS is a framework but in order + + + align:start position:0% +is that MCTS is a framework but in order +to actually make it effective for a lot + + align:start position:0% +to actually make it effective for a lot + + + align:start position:0% +to actually make it effective for a lot +of games it does require a lot of you + + align:start position:0% +of games it does require a lot of you + + + align:start position:0% +of games it does require a lot of you +know tuning in the sense that there are + + align:start position:0% +know tuning in the sense that there are + + + align:start position:0% +know tuning in the sense that there are +a whole bunch of variants and then you + + align:start position:0% +a whole bunch of variants and then you + + + align:start position:0% +a whole bunch of variants and then you +need to be able to implement whatever + + align:start position:0% +need to be able to implement whatever + + + align:start position:0% +need to be able to implement whatever +flavor is best suited for you which + + align:start position:0% +flavor is best suited for you which + + + align:start position:0% +flavor is best suited for you which +means that it's not quite as nice and + + align:start position:0% +means that it's not quite as nice and + + + align:start position:0% +means that it's not quite as nice and +black boxy as we would want it to be and + + align:start position:0% +black boxy as we would want it to be and + + + align:start position:0% +black boxy as we would want it to be and +as far as you know give it the rules and + + align:start position:0% +as far as you know give it the rules and + + + align:start position:0% +as far as you know give it the rules and +like have it magically come up with the + + align:start position:0% +like have it magically come up with the + + + align:start position:0% +like have it magically come up with the +strategy goes oh and then lastly as you + + align:start position:0% +strategy goes oh and then lastly as you + + + align:start position:0% +strategy goes oh and then lastly as you +mentioned there is not a great amount of + + align:start position:0% +mentioned there is not a great amount of + + + align:start position:0% +mentioned there is not a great amount of +literature right now about the + + align:start position:0% +literature right now about the + + + align:start position:0% +literature right now about the +properties of ncts and its convert this + + align:start position:0% +properties of ncts and its convert this + + + align:start position:0% +properties of ncts and its convert this +and you know what the actual proportion + + align:start position:0% +and you know what the actual proportion + + + align:start position:0% +and you know what the actual proportion +of time to quality of solution is I mean + + align:start position:0% +of time to quality of solution is I mean + + + align:start position:0% +of time to quality of solution is I mean +this is sort of true all modern machine + + align:start position:0% +this is sort of true all modern machine + + + align:start position:0% +this is sort of true all modern machine +learning the thing is rate is it either + + align:start position:0% +learning the thing is rate is it either + + + align:start position:0% +learning the thing is rate is it either +certainly a lot more work that can be + + align:start position:0% +certainly a lot more work that can be + + + align:start position:0% +certainly a lot more work that can be +done but right now that's sort of a gap + + align:start position:0% +done but right now that's sort of a gap + + + align:start position:0% +done but right now that's sort of a gap +in terms of using this for us I mean + + align:start position:0% +in terms of using this for us I mean + + + align:start position:0% +in terms of using this for us I mean +it's supposed to be unreliable okay + + align:start position:0% +it's supposed to be unreliable okay + + + align:start position:0% +it's supposed to be unreliable okay +anyone have any questions on the pros + + align:start position:0% +anyone have any questions on the pros + + + align:start position:0% +anyone have any questions on the pros +and cons all right + + align:start position:0% +and cons all right + + + align:start position:0% +and cons all right +Before we jump to dive into applications + + align:start position:0% +Before we jump to dive into applications + + + align:start position:0% +Before we jump to dive into applications +let's talk through a few examples of you + + align:start position:0% +let's talk through a few examples of you + + + align:start position:0% +let's talk through a few examples of you +know what games could be solved and + + align:start position:0% +know what games could be solved and + + + align:start position:0% +know what games could be solved and +could not be solved by an GPS so do you + + align:start position:0% +could not be solved by an GPS so do you + + + align:start position:0% +could not be solved by an GPS so do you +guys think the checkers is okay it's + + align:start position:0% +guys think the checkers is okay it's + + + align:start position:0% +guys think the checkers is okay it's +completely deterministic its two-player + + align:start position:0% +completely deterministic its two-player + + + align:start position:0% +completely deterministic its two-player +its upsizing + + align:start position:0% +its upsizing + + + align:start position:0% +its upsizing +all of the great hearing that we played + + align:start position:0% +all of the great hearing that we played + + + align:start position:0% +all of the great hearing that we played +out before it checkers is definitely a + + align:start position:0% +out before it checkers is definitely a + + + align:start position:0% +out before it checkers is definitely a +game that can and has been solved I'd + + align:start position:0% +game that can and has been solved I'd + + + align:start position:0% +game that can and has been solved I'd +say yes well they're not sold to be + + align:start position:0% +say yes well they're not sold to be + + + align:start position:0% +say yes well they're not sold to be +extended like you know + + align:start position:0% +extended like you know + + + align:start position:0% +extended like you know +defeat the thing that actually has the + + align:start position:0% +defeat the thing that actually has the + + + align:start position:0% +defeat the thing that actually has the +solution effect oh okay + + align:start position:0% +solution effect oh okay + + + align:start position:0% +solution effect oh okay +how about sub layers of Catan this was a + + align:start position:0% +how about sub layers of Catan this was a + + + align:start position:0% +how about sub layers of Catan this was a +little bit trickier do you guys think + + align:start position:0% +little bit trickier do you guys think + + + align:start position:0% +little bit trickier do you guys think +that I'm CGS is likely to be able to + + align:start position:0% +that I'm CGS is likely to be able to + + + align:start position:0% +that I'm CGS is likely to be able to +replace uppers + + align:start position:0% +replace uppers + + + align:start position:0% +replace uppers +if not let's throw our reasons why or + + align:start position:0% +if not let's throw our reasons why or + + + align:start position:0% +if not let's throw our reasons why or +why not yeah so yes that is absolutely + + align:start position:0% +why not yeah so yes that is absolutely + + + align:start position:0% +why not yeah so yes that is absolutely +criticism and that's why we can't apply + + align:start position:0% +criticism and that's why we can't apply + + + align:start position:0% +criticism and that's why we can't apply +it vanilla I sort of put this on here is + + align:start position:0% +it vanilla I sort of put this on here is + + + align:start position:0% +it vanilla I sort of put this on here is +it you as a trick question though + + align:start position:0% +it you as a trick question though + + + align:start position:0% +it you as a trick question though +because it turns out that that ncts is + + align:start position:0% +because it turns out that that ncts is + + + align:start position:0% +because it turns out that that ncts is +robust your animus um that you can + + align:start position:0% +robust your animus um that you can + + + align:start position:0% +robust your animus um that you can +actually plate and I realize me but you + + align:start position:0% +actually plate and I realize me but you + + + align:start position:0% +actually plate and I realize me but you +can actually play it through um through + + align:start position:0% +can actually play it through um through + + + align:start position:0% +can actually play it through um through +games and if you think about the + + align:start position:0% +games and if you think about the + + + align:start position:0% +games and if you think about the +simulation the simulation is actually + + align:start position:0% +simulation the simulation is actually + + + align:start position:0% +simulation the simulation is actually +applicable even if even if the game is + + align:start position:0% +applicable even if even if the game is + + + align:start position:0% +applicable even if even if the game is +not as her monistic because it does give + + align:start position:0% +not as her monistic because it does give + + + align:start position:0% +not as her monistic because it does give +you a sense of the quality of your + + align:start position:0% +you a sense of the quality of your + + + align:start position:0% +you a sense of the quality of your +position and that the the ncts based AI + + align:start position:0% +position and that the the ncts based AI + + + align:start position:0% +position and that the the ncts based AI +to play settlers is I think it's like + + align:start position:0% +to play settlers is I think it's like + + + align:start position:0% +to play settlers is I think it's like +49% competitive with these like AI so it + + align:start position:0% +49% competitive with these like AI so it + + + align:start position:0% +49% competitive with these like AI so it +does sort of work alright let's talk + + align:start position:0% +does sort of work alright let's talk + + + align:start position:0% +does sort of work alright let's talk +about the war operations and plan + + align:start position:0% +about the war operations and plan + + + align:start position:0% +about the war operations and plan +response so here to see movie for games + + align:start position:0% +response so here to see movie for games + + + align:start position:0% +response so here to see movie for games +okay well it should be more you but the + + align:start position:0% +okay well it should be more you but the + + + align:start position:0% +okay well it should be more you but the +the idea of more games is that you know + + align:start position:0% +the idea of more games is that you know + + + align:start position:0% +the idea of more games is that you know +the core characters in this in this + + align:start position:0% +the core characters in this in this + + + align:start position:0% +the core characters in this in this +world is this computer that has been put + + align:start position:0% +world is this computer that has been put + + + align:start position:0% +world is this computer that has been put +in charge of like the United States + + align:start position:0% +in charge of like the United States + + + align:start position:0% +in charge of like the United States +national defense strategy with respect + + align:start position:0% +national defense strategy with respect + + + align:start position:0% +national defense strategy with respect +to Russia and that it needs to you know + + align:start position:0% +to Russia and that it needs to you know + + + align:start position:0% +to Russia and that it needs to you know +think through possible future scenarios + + align:start position:0% +think through possible future scenarios + + + align:start position:0% +think through possible future scenarios +and decide whether it's going to launch + + align:start position:0% +and decide whether it's going to launch + + + align:start position:0% +and decide whether it's going to launch +the nukes or not um and so do you think + + align:start position:0% +the nukes or not um and so do you think + + + align:start position:0% +the nukes or not um and so do you think +that the Whopper can be MCTS B's and so + + align:start position:0% +that the Whopper can be MCTS B's and so + + + align:start position:0% +that the Whopper can be MCTS B's and so +you can't particularly singling through + + align:start position:0% +you can't particularly singling through + + + align:start position:0% +you can't particularly singling through +what the possible scenarios gonna be + + align:start position:0% +what the possible scenarios gonna be + + + align:start position:0% +what the possible scenarios gonna be +like yeah so what if you had I agree you + + align:start position:0% +like yeah so what if you had I agree you + + + align:start position:0% +like yeah so what if you had I agree you +can't like simulated in the real world + + align:start position:0% +can't like simulated in the real world + + + align:start position:0% +can't like simulated in the real world +but what if we have teens there's a + + align:start position:0% +but what if we have teens there's a + + + align:start position:0% +but what if we have teens there's a +really good model and you just simulated + + align:start position:0% +really good model and you just simulated + + + align:start position:0% +really good model and you just simulated +based on that model so in that case it + + align:start position:0% +based on that model so in that case it + + + align:start position:0% +based on that model so in that case it +probably depends on the quality of your + + align:start position:0% +probably depends on the quality of your + + + align:start position:0% +probably depends on the quality of your +model it is the case that the military + + align:start position:0% +model it is the case that the military + + + align:start position:0% +model it is the case that the military +does have simulators and they do + + align:start position:0% +does have simulators and they do + + + align:start position:0% +does have simulators and they do +workings and simulation answer them yes + + align:start position:0% +workings and simulation answer them yes + + + align:start position:0% +workings and simulation answer them yes +they could certainly try it and runs it + + align:start position:0% +they could certainly try it and runs it + + + align:start position:0% +they could certainly try it and runs it +yes a big one that's what happened in + + align:start position:0% +yes a big one that's what happened in + + + align:start position:0% +yes a big one that's what happened in +the movie + + align:start position:0% + + + + align:start position:0% + +yeah it's definitely it's simply about + + align:start position:0% +yeah it's definitely it's simply about + + + align:start position:0% +yeah it's definitely it's simply about +putting money into the simulation really + + align:start position:0% +putting money into the simulation really + + + align:start position:0% +putting money into the simulation really +good solution if you have a really good + + align:start position:0% +good solution if you have a really good + + + align:start position:0% +good solution if you have a really good +simulation right yeah in fact two + + align:start position:0% +simulation right yeah in fact two + + + align:start position:0% +simulation right yeah in fact two +settlers for a second isn't there like a + + align:start position:0% +settlers for a second isn't there like a + + + align:start position:0% +settlers for a second isn't there like a +way to code the whole like player + + align:start position:0% +way to code the whole like player + + + align:start position:0% +way to code the whole like player +training resources thing or like would + + align:start position:0% +training resources thing or like would + + + align:start position:0% +training resources thing or like would +it have to be only like if it's just + + align:start position:0% +it have to be only like if it's just + + + align:start position:0% +it have to be only like if it's just +playing a two-player game but if they + + align:start position:0% +playing a two-player game but if they + + + align:start position:0% +playing a two-player game but if they +weren't I bet that you can program the + + align:start position:0% +weren't I bet that you can program the + + + align:start position:0% +weren't I bet that you can program the +weather no no no in fact there are lots + + align:start position:0% +weather no no no in fact there are lots + + + align:start position:0% +weather no no no in fact there are lots +of approaches that you only want their + + align:start position:0% +of approaches that you only want their + + + align:start position:0% +of approaches that you only want their +games where you just you know think of + + align:start position:0% +games where you just you know think of + + + align:start position:0% +games where you just you know think of +think of what's the best move that you + + align:start position:0% +think of what's the best move that you + + + align:start position:0% +think of what's the best move that you +can make well know what I mean yeah + + align:start position:0% +can make well know what I mean yeah + + + align:start position:0% +can make well know what I mean yeah +absolutely + + align:start position:0% +absolutely + + + align:start position:0% +absolutely +I'm not sure what how they computed + + align:start position:0% +I'm not sure what how they computed + + + align:start position:0% +I'm not sure what how they computed +their head-to-head yeah that might be a + + align:start position:0% +their head-to-head yeah that might be a + + + align:start position:0% +their head-to-head yeah that might be a +people who fly phrases I'm not sure how + + align:start position:0% +people who fly phrases I'm not sure how + + + align:start position:0% +people who fly phrases I'm not sure how +the zippers errant okay yeah but + + align:start position:0% +the zippers errant okay yeah but + + + align:start position:0% +the zippers errant okay yeah but +question so what ice personally you are + + align:start position:0% +question so what ice personally you are + + + align:start position:0% +question so what ice personally you are +Battista chess board + + align:start position:0% +Battista chess board + + + align:start position:0% +Battista chess board +four-pack 4/5 from brother mcs versus + + align:start position:0% +four-pack 4/5 from brother mcs versus + + + align:start position:0% +four-pack 4/5 from brother mcs versus +the traditional theory so the thing + + align:start position:0% +the traditional theory so the thing + + + align:start position:0% +the traditional theory so the thing +about the way that deep blue is + + align:start position:0% +about the way that deep blue is + + + align:start position:0% +about the way that deep blue is +implemented which is the AI of being + + align:start position:0% +implemented which is the AI of being + + + align:start position:0% +implemented which is the AI of being +chess grandmasters is that it has a + + align:start position:0% +chess grandmasters is that it has a + + + align:start position:0% +chess grandmasters is that it has a +tremendous amount of heuristic + + align:start position:0% +tremendous amount of heuristic + + + align:start position:0% +tremendous amount of heuristic +information there's a lot of external + + align:start position:0% +information there's a lot of external + + + align:start position:0% +information there's a lot of external +stuff that's incorporated into the + + align:start position:0% +stuff that's incorporated into the + + + align:start position:0% +stuff that's incorporated into the +system that makes it able to you know + + align:start position:0% +system that makes it able to you know + + + align:start position:0% +system that makes it able to you know +explore the best paths and so what I + + align:start position:0% +explore the best paths and so what I + + + align:start position:0% +explore the best paths and so what I +would say is that like knowledge this + + align:start position:0% +would say is that like knowledge this + + + align:start position:0% +would say is that like knowledge this +MCTS + + align:start position:0% +MCTS + + + align:start position:0% +MCTS +based on randomness would take a very + + align:start position:0% +based on randomness would take a very + + + align:start position:0% +based on randomness would take a very +long computational time feasibly never + + align:start position:0% +long computational time feasibly never + + + align:start position:0% +long computational time feasibly never +win but if you incorporate your estate + + align:start position:0% +win but if you incorporate your estate + + + align:start position:0% +win but if you incorporate your estate +information I think that there's a bunch + + align:start position:0% +information I think that there's a bunch + + + align:start position:0% +information I think that there's a bunch +of bull in terms of GPS to start and you + + align:start position:0% +of bull in terms of GPS to start and you + + + align:start position:0% +of bull in terms of GPS to start and you +can look at when gonna talk about + + align:start position:0% +can look at when gonna talk about + + + align:start position:0% +can look at when gonna talk about +alphago to take some inspiration it + + align:start position:0% +alphago to take some inspiration it + + + align:start position:0% +alphago to take some inspiration it +definitely seems like if you have a + + align:start position:0% +definitely seems like if you have a + + + align:start position:0% +definitely seems like if you have a +really rooted heuristic model for for + + align:start position:0% +really rooted heuristic model for for + + + align:start position:0% +really rooted heuristic model for for +how like what good states in the game + + align:start position:0% +how like what good states in the game + + + align:start position:0% +how like what good states in the game +are then there are men that like if it's + + align:start position:0% +are then there are men that like if it's + + + align:start position:0% +are then there are men that like if it's +a smaller you know search space that + + align:start position:0% +a smaller you know search space that + + + align:start position:0% +a smaller you know search space that +some other models although one less game + + align:start position:0% +some other models although one less game + + + align:start position:0% +some other models although one less game +but does anyone know what this payment + + align:start position:0% +but does anyone know what this payment + + + align:start position:0% +but does anyone know what this payment +yes nice um this is rome total war ii + + align:start position:0% +yes nice um this is rome total war ii + + + align:start position:0% +yes nice um this is rome total war ii +it's a simulator for a trip like this + + align:start position:0% +it's a simulator for a trip like this + + + align:start position:0% +it's a simulator for a trip like this +tremendous realtime strategy game where + + align:start position:0% +tremendous realtime strategy game where + + + align:start position:0% +tremendous realtime strategy game where +you play + + align:start position:0% +you play + + + align:start position:0% +you play +I think the Roman Empire and you know + + align:start position:0% +I think the Roman Empire and you know + + + align:start position:0% +I think the Roman Empire and you know +you're controlling armies and you know + + align:start position:0% +you're controlling armies and you know + + + align:start position:0% +you're controlling armies and you know +huge infrastructure systems that move + + align:start position:0% +huge infrastructure systems that move + + + align:start position:0% +huge infrastructure systems that move +and conquer and like States and + + align:start position:0% +and conquer and like States and + + + align:start position:0% +and conquer and like States and +continents and meet in the field and + + align:start position:0% +continents and meet in the field and + + + align:start position:0% +continents and meet in the field and +punic manage resources and do all these + + align:start position:0% +punic manage resources and do all these + + + align:start position:0% +punic manage resources and do all these +incredible diplomacy feats and so do you + + align:start position:0% +incredible diplomacy feats and so do you + + + align:start position:0% +incredible diplomacy feats and so do you +think that this game could be solved by + + align:start position:0% +think that this game could be solved by + + + align:start position:0% +think that this game could be solved by +GPS let's see no but I guess I put on + + align:start position:0% +GPS let's see no but I guess I put on + + + align:start position:0% +GPS let's see no but I guess I put on +here so that's good on you um the way + + align:start position:0% +here so that's good on you um the way + + + align:start position:0% +here so that's good on you um the way +that the AI in rome total war ii is + + align:start position:0% +that the AI in rome total war ii is + + + align:start position:0% +that the AI in rome total war ii is +built is that it's built on an MCTS + + align:start position:0% +built is that it's built on an MCTS + + + align:start position:0% +built is that it's built on an MCTS +structure and it in fact does do + + align:start position:0% +structure and it in fact does do + + + align:start position:0% +structure and it in fact does do +research allocation and like a lot of + + align:start position:0% +research allocation and like a lot of + + + align:start position:0% +research allocation and like a lot of +its political maneuvers based on + + align:start position:0% +its political maneuvers based on + + + align:start position:0% +its political maneuvers based on +Montecarlo evisceration moves there are + + align:start position:0% +Montecarlo evisceration moves there are + + + align:start position:0% +Montecarlo evisceration moves there are +a bunch of reasons that they explain in + + align:start position:0% +a bunch of reasons that they explain in + + + align:start position:0% +a bunch of reasons that they explain in +the game for why they do this for + + align:start position:0% +the game for why they do this for + + + align:start position:0% +the game for why they do this for +the game but one of the nice ones is + + align:start position:0% +the game but one of the nice ones is + + + align:start position:0% +the game but one of the nice ones is +that it's random which means that you're + + align:start position:0% +that it's random which means that you're + + + align:start position:0% +that it's random which means that you're +never gonna play against the same kind + + align:start position:0% +never gonna play against the same kind + + + align:start position:0% +never gonna play against the same kind +of a twice because you know every time + + align:start position:0% +of a twice because you know every time + + + align:start position:0% +of a twice because you know every time +the set of decisions that is going to + + align:start position:0% +the set of decisions that is going to + + + align:start position:0% +the set of decisions that is going to +think about this people we never fought + + align:start position:0% +think about this people we never fought + + + align:start position:0% +think about this people we never fought +or anything yes does it have to be that + + align:start position:0% +or anything yes does it have to be that + + + align:start position:0% +or anything yes does it have to be that +here the actions I play that game has be + + align:start position:0% +here the actions I play that game has be + + + align:start position:0% +here the actions I play that game has be +they go to this great house + + align:start position:0% +they go to this great house + + + align:start position:0% +they go to this great house +yes so so far as I know I haven't seen + + align:start position:0% +yes so so far as I know I haven't seen + + + align:start position:0% +yes so so far as I know I haven't seen +many continuous very inception to guess + + align:start position:0% +many continuous very inception to guess + + + align:start position:0% +many continuous very inception to guess +um and so I think that it is about + + align:start position:0% +um and so I think that it is about + + + align:start position:0% +um and so I think that it is about +choosing mystery disc reactions which on + + align:start position:0% +choosing mystery disc reactions which on + + + align:start position:0% +choosing mystery disc reactions which on +there against its most narrow level it + + align:start position:0% +there against its most narrow level it + + + align:start position:0% +there against its most narrow level it +does actually bring it down to here um I + + align:start position:0% +does actually bring it down to here um I + + + align:start position:0% +does actually bring it down to here um I +think one of the reasons that this is + + align:start position:0% +think one of the reasons that this is + + + align:start position:0% +think one of the reasons that this is +nice is that there are so many different + + align:start position:0% +nice is that there are so many different + + + align:start position:0% +nice is that there are so many different +decisions that could be made that MCTS + + align:start position:0% +decisions that could be made that MCTS + + + align:start position:0% +decisions that could be made that MCTS +is really the only approach that can + + align:start position:0% +is really the only approach that can + + + align:start position:0% +is really the only approach that can +even begin to handle the massive + + align:start position:0% +even begin to handle the massive + + + align:start position:0% +even begin to handle the massive +branching factor that's associated with + + align:start position:0% +branching factor that's associated with + + + align:start position:0% +branching factor that's associated with +a game yeah consequences that's it + + align:start position:0% +a game yeah consequences that's it + + + align:start position:0% +a game yeah consequences that's it +that's interesting that's probably + + align:start position:0% +that's interesting that's probably + + + align:start position:0% +that's interesting that's probably +totally it that's cool okay so that's + + align:start position:0% +totally it that's cool okay so that's + + + align:start position:0% +totally it that's cool okay so that's +everything about how the algorithm + + align:start position:0% +everything about how the algorithm + + + align:start position:0% +everything about how the algorithm +actually works + + align:start position:0% +actually works + + + align:start position:0% +actually works +no it's he's going to talk to us about + + align:start position:0% +no it's he's going to talk to us about + + + align:start position:0% +no it's he's going to talk to us about +some actual implementations for this + + align:start position:0% +some actual implementations for this + + + align:start position:0% +some actual implementations for this +game all right so start diving into some + + align:start position:0% +game all right so start diving into some + + + align:start position:0% +game all right so start diving into some +applications here and it's not only + + align:start position:0% +applications here and it's not only + + + align:start position:0% +applications here and it's not only +applications but also some modifications + + align:start position:0% +applications but also some modifications + + + align:start position:0% +applications but also some modifications +or augmentations of entities yes it + + align:start position:0% +or augmentations of entities yes it + + + align:start position:0% +or augmentations of entities yes it +should hopefully clarify some of the + + align:start position:0% +should hopefully clarify some of the + + + align:start position:0% +should hopefully clarify some of the +side questions all been having on slight + + align:start position:0% +side questions all been having on slight + + + align:start position:0% +side questions all been having on slight +tweaks time since yes and that let's get + + align:start position:0% +tweaks time since yes and that let's get + + + align:start position:0% +tweaks time since yes and that let's get +started okay wait for it now it's either + + align:start position:0% +started okay wait for it now it's either + + + align:start position:0% +started okay wait for it now it's either +part three application first thing we're + + align:start position:0% +part three application first thing we're + + + align:start position:0% +part three application first thing we're +gonna look at is an MTTF based mario + + align:start position:0% +gonna look at is an MTTF based mario + + + align:start position:0% +gonna look at is an MTTF based mario +controller and mario it might seem like + + align:start position:0% +controller and mario it might seem like + + + align:start position:0% +controller and mario it might seem like +some weird thing to test a eye on but + + align:start position:0% +some weird thing to test a eye on but + + + align:start position:0% +some weird thing to test a eye on but +there actually is a super mario bros AI + + align:start position:0% +there actually is a super mario bros AI + + + align:start position:0% +there actually is a super mario bros AI +benchmark used to test a lot of AI I + + align:start position:0% +benchmark used to test a lot of AI I + + + align:start position:0% +benchmark used to test a lot of AI I +thought well they can play this platform + + align:start position:0% +thought well they can play this platform + + + align:start position:0% +thought well they can play this platform +and in case I need you don't know what + + align:start position:0% +and in case I need you don't know what + + + align:start position:0% +and in case I need you don't know what +Super Mario Bros is this is a screen + + align:start position:0% +Super Mario Bros is this is a screen + + + align:start position:0% +Super Mario Bros is this is a screen +shot basically you control this one + + align:start position:0% +shot basically you control this one + + + align:start position:0% +shot basically you control this one +character it's a single player game and + + align:start position:0% +character it's a single player game and + + + align:start position:0% +character it's a single player game and +you can do the ultimate goal is to reach + + align:start position:0% +you can do the ultimate goal is to reach + + + align:start position:0% +you can do the ultimate goal is to reach +this flag again but along the way + + align:start position:0% +this flag again but along the way + + + align:start position:0% +this flag again but along the way +there's enemies there's some bonus + + align:start position:0% +there's enemies there's some bonus + + + align:start position:0% +there's enemies there's some bonus +shrooms you can get if you break open + + align:start position:0% +shrooms you can get if you break open + + + align:start position:0% +shrooms you can get if you break open +some boxes you Michael + + align:start position:0% +some boxes you Michael + + + align:start position:0% +some boxes you Michael +things like that but first let's just + + align:start position:0% +things like that but first let's just + + + align:start position:0% +things like that but first let's just +highlight some of the modifications that + + align:start position:0% +highlight some of the modifications that + + + align:start position:0% +highlight some of the modifications that +need to be made or some of the + + align:start position:0% +need to be made or some of the + + + align:start position:0% +need to be made or some of the +differences between vanilla ncts and an + + align:start position:0% +differences between vanilla ncts and an + + + align:start position:0% +differences between vanilla ncts and an +MCTS that's going to be able to work for + + align:start position:0% +MCTS that's going to be able to work for + + + align:start position:0% +MCTS that's going to be able to work for +Mario first thing to that single player + + align:start position:0% +Mario first thing to that single player + + + align:start position:0% +Mario first thing to that single player +the second is we use a slightly + + align:start position:0% +the second is we use a slightly + + + align:start position:0% +the second is we use a slightly +different simulation strategy than the + + align:start position:0% +different simulation strategy than the + + + align:start position:0% +different simulation strategy than the +initial just vanilla simulation and + + align:start position:0% +initial just vanilla simulation and + + + align:start position:0% +initial just vanilla simulation and +someone actually can't do that doing + + align:start position:0% +someone actually can't do that doing + + + align:start position:0% +someone actually can't do that doing +more than one simulation because you + + align:start position:0% +more than one simulation because you + + + align:start position:0% +more than one simulation because you +you're like what can you do and + + align:start position:0% +you're like what can you do and + + + align:start position:0% +you're like what can you do and +simulations I think yeah so would touch + + align:start position:0% +simulations I think yeah so would touch + + + align:start position:0% +simulations I think yeah so would touch +on that then this also introduces what I + + align:start position:0% +on that then this also introduces what I + + + align:start position:0% +on that then this also introduces what I +would consider to be domain knowledge + + align:start position:0% +would consider to be domain knowledge + + + align:start position:0% +would consider to be domain knowledge +and finally there's a 50 to 40 + + align:start position:0% +and finally there's a 50 to 40 + + + align:start position:0% +and finally there's a 50 to 40 +milliseconds computation time in that + + align:start position:0% +milliseconds computation time in that + + + align:start position:0% +milliseconds computation time in that +suit with the frames per second of the + + align:start position:0% +suit with the frames per second of the + + + align:start position:0% +suit with the frames per second of the +game so you would think that mario is a + + align:start position:0% +game so you would think that mario is a + + + align:start position:0% +game so you would think that mario is a +continuous game but if you disparate + + align:start position:0% +continuous game but if you disparate + + + align:start position:0% +continuous game but if you disparate +eyes time into these chunks that we can + + align:start position:0% +eyes time into these chunks that we can + + + align:start position:0% +eyes time into these chunks that we can +use unto TS all right now let's just + + align:start position:0% +use unto TS all right now let's just + + + align:start position:0% +use unto TS all right now let's just +think about how we could possibly + + align:start position:0% +think about how we could possibly + + + align:start position:0% +think about how we could possibly +formulate this problem can I even think + + align:start position:0% +formulate this problem can I even think + + + align:start position:0% +formulate this problem can I even think +of what each of these nodes would be for + + align:start position:0% +of what each of these nodes would be for + + + align:start position:0% +of what each of these nodes would be for +playing Super Mario okay that might be a + + align:start position:0% +playing Super Mario okay that might be a + + + align:start position:0% +playing Super Mario okay that might be a +way to formulate it but I think that you + + align:start position:0% +way to formulate it but I think that you + + + align:start position:0% +way to formulate it but I think that you +did right so the node itself isn't going + + align:start position:0% +did right so the node itself isn't going + + + align:start position:0% +did right so the node itself isn't going +to be an action + + align:start position:0% + + + + align:start position:0% + +no prank yeah basically so it's going to + + align:start position:0% +no prank yeah basically so it's going to + + + align:start position:0% +no prank yeah basically so it's going to +be the state of a game when we fall a + + align:start position:0% +be the state of a game when we fall a + + + align:start position:0% +be the state of a game when we fall a +state so it's been just a spring map and + + align:start position:0% +state so it's been just a spring map and + + + align:start position:0% +state so it's been just a spring map and +it takes it in this case it's a 15 by 19 + + align:start position:0% +it takes it in this case it's a 15 by 19 + + + align:start position:0% +it takes it in this case it's a 15 by 19 +grid screen grab of the game and it'll + + align:start position:0% +grid screen grab of the game and it'll + + + align:start position:0% +grid screen grab of the game and it'll +have information about in those Mario's + + align:start position:0% +have information about in those Mario's + + + align:start position:0% +have information about in those Mario's +position it was the enemy's position + + align:start position:0% +position it was the enemy's position + + + align:start position:0% +position it was the enemy's position +position of the blocks etc and then at + + align:start position:0% +position of the blocks etc and then at + + + align:start position:0% +position of the blocks etc and then at +yo was saying yes if you have values + + align:start position:0% +yo was saying yes if you have values + + + align:start position:0% +yo was saying yes if you have values +associated with our nodes and so it will + + align:start position:0% +associated with our nodes and so it will + + + align:start position:0% +associated with our nodes and so it will +also have a value but we'll get into the + + align:start position:0% +also have a value but we'll get into the + + + align:start position:0% +also have a value but we'll get into the +value in the next slide because I can't + + align:start position:0% +value in the next slide because I can't + + + align:start position:0% +value in the next slide because I can't +really fit over you but then with that + + align:start position:0% +really fit over you but then with that + + + align:start position:0% +really fit over you but then with that +being said for our node being the + + align:start position:0% +being said for our node being the + + + align:start position:0% +being said for our node being the +statement game what would make sense for + + align:start position:0% +statement game what would make sense for + + + align:start position:0% +statement game what would make sense for +the head so how do we transition from + + align:start position:0% +the head so how do we transition from + + + align:start position:0% +the head so how do we transition from +one state to another state yeah yeah + + align:start position:0% +one state to another state yeah yeah + + + align:start position:0% +one state to another state yeah yeah +exactly so this really jump it all that + + align:start position:0% +exactly so this really jump it all that + + + align:start position:0% +exactly so this really jump it all that +comes in play so the actions that you + + align:start position:0% +comes in play so the actions that you + + + align:start position:0% +comes in play so the actions that you +take but I've never list all the actions + + align:start position:0% +take but I've never list all the actions + + + align:start position:0% +take but I've never list all the actions +you thought that would jump up jump + + align:start position:0% +you thought that would jump up jump + + + align:start position:0% +you thought that would jump up jump +right all these things but basically the + + align:start position:0% +right all these things but basically the + + + align:start position:0% +right all these things but basically the +actions are what take from state to + + align:start position:0% +actions are what take from state to + + + align:start position:0% +actions are what take from state to +state so I just drew out what could + + align:start position:0% +state so I just drew out what could + + + align:start position:0% +state so I just drew out what could +possibly what a node might look like if + + align:start position:0% +possibly what a node might look like if + + + align:start position:0% +possibly what a node might look like if +you use the jump action you might have + + align:start position:0% +you use the jump action you might have + + + align:start position:0% +you use the jump action you might have +my you up in the sky alright that's it + + align:start position:0% +my you up in the sky alright that's it + + + align:start position:0% +my you up in the sky alright that's it +just run the rest of it well it's not + + align:start position:0% +just run the rest of it well it's not + + + align:start position:0% +just run the rest of it well it's not +moving in this moment in time like we're + + align:start position:0% +moving in this moment in time like we're + + + align:start position:0% +moving in this moment in time like we're +just eyes economy yeah but I'm saying + + align:start position:0% +just eyes economy yeah but I'm saying + + + align:start position:0% +just eyes economy yeah but I'm saying +like if your action is jump you would + + align:start position:0% +like if your action is jump you would + + + align:start position:0% +like if your action is jump you would +get your I have a thousand nodes because + + align:start position:0% +get your I have a thousand nodes because + + + align:start position:0% +get your I have a thousand nodes because +if you didn't plan out where that things + + align:start position:0% +if you didn't plan out where that things + + + align:start position:0% +if you didn't plan out where that things +moving left or right yeah right so in + + align:start position:0% +moving left or right yeah right so in + + + align:start position:0% +moving left or right yeah right so in +each state we have the enemy's position + + align:start position:0% +each state we have the enemy's position + + + align:start position:0% +each state we have the enemy's position +and we know even direction and so you + + align:start position:0% +and we know even direction and so you + + + align:start position:0% +and we know even direction and so you +know let me go from this node to one + + align:start position:0% +know let me go from this node to one + + + align:start position:0% +know let me go from this node to one +time step later we'll know where the + + align:start position:0% + + + + align:start position:0% + +all right moving on + + align:start position:0% +all right moving on + + + align:start position:0% +all right moving on +oh sorry let me just preface this part + + align:start position:0% +oh sorry let me just preface this part + + + align:start position:0% +oh sorry let me just preface this part +real quick so in our other simulations + + align:start position:0% +real quick so in our other simulations + + + align:start position:0% +real quick so in our other simulations +at the end of the simulation we would + + align:start position:0% +at the end of the simulation we would + + + align:start position:0% +at the end of the simulation we would +get either a 1 or a 0 but we won + + align:start position:0% +get either a 1 or a 0 but we won + + + align:start position:0% +get either a 1 or a 0 but we won +tic-tac-toe or most effective right but + + align:start position:0% +tic-tac-toe or most effective right but + + + align:start position:0% +tic-tac-toe or most effective right but +that won't really work too well here + + align:start position:0% +that won't really work too well here + + + align:start position:0% +that won't really work too well here +because there's a lot of other factors + + align:start position:0% +because there's a lot of other factors + + + align:start position:0% +because there's a lot of other factors +that go into play when you're playing + + align:start position:0% +that go into play when you're playing + + + align:start position:0% +that go into play when you're playing +Mario and also if you're doing a + + align:start position:0% +Mario and also if you're doing a + + + align:start position:0% +Mario and also if you're doing a +simulation more than likely you're going + + align:start position:0% +simulation more than likely you're going + + + align:start position:0% +simulation more than likely you're going +to end up hitting an enemy and dying or + + align:start position:0% +to end up hitting an enemy and dying or + + + align:start position:0% +to end up hitting an enemy and dying or +falling into a gap and dying so a lot of + + align:start position:0% +falling into a gap and dying so a lot of + + + align:start position:0% +falling into a gap and dying so a lot of +these simulations might all return zero + + align:start position:0% +these simulations might all return zero + + + align:start position:0% +these simulations might all return zero +and in fact is you can't really + + align:start position:0% +and in fact is you can't really + + + align:start position:0% +and in fact is you can't really +distinguish between them so this is why + + align:start position:0% +distinguish between them so this is why + + + align:start position:0% +distinguish between them so this is why +I say this version of MC chess + + align:start position:0% +I say this version of MC chess + + + align:start position:0% +I say this version of MC chess +introduces what I would consider to be + + align:start position:0% +introduces what I would consider to be + + + align:start position:0% +introduces what I would consider to be +domain knowledge basically they're + + align:start position:0% +domain knowledge basically they're + + + align:start position:0% +domain knowledge basically they're +signing scores to potential things that + + align:start position:0% +signing scores to potential things that + + + align:start position:0% +signing scores to potential things that +could happen along the way and this is + + align:start position:0% +could happen along the way and this is + + + align:start position:0% +could happen along the way and this is +basically telling the AI that collecting + + align:start position:0% +basically telling the AI that collecting + + + align:start position:0% +basically telling the AI that collecting +a flower is a little bit better than + + align:start position:0% +a flower is a little bit better than + + + align:start position:0% +a flower is a little bit better than +collecting a mushroom he's telling if + + align:start position:0% +collecting a mushroom he's telling if + + + align:start position:0% +collecting a mushroom he's telling if +that getting hurt is bad right off the + + align:start position:0% +that getting hurt is bad right off the + + + align:start position:0% +that getting hurt is bad right off the +bat all these things in the store are + + align:start position:0% +bat all these things in the store are + + + align:start position:0% +bat all these things in the store are +giving the AI some sort of domain + + align:start position:0% +giving the AI some sort of domain + + + align:start position:0% +giving the AI some sort of domain +knowledge about Super Mario Bros that is + + align:start position:0% +knowledge about Super Mario Bros that is + + + align:start position:0% +knowledge about Super Mario Bros that is +helping it calculate the simulation + + align:start position:0% +helping it calculate the simulation + + + align:start position:0% +helping it calculate the simulation +results and as it says here is just + + align:start position:0% +results and as it says here is just + + + align:start position:0% +results and as it says here is just +doing a multi objective weighted sum of + + align:start position:0% +doing a multi objective weighted sum of + + + align:start position:0% +doing a multi objective weighted sum of +all these things so throughout the + + align:start position:0% +all these things so throughout the + + + align:start position:0% +all these things so throughout the +simulation it's just adding up your + + align:start position:0% +simulation it's just adding up your + + + align:start position:0% +simulation it's just adding up your +score and then that's the score that is + + align:start position:0% +score and then that's the score that is + + + align:start position:0% +score and then that's the score that is +going to be prompted other questions not + + align:start position:0% +going to be prompted other questions not + + + align:start position:0% +going to be prompted other questions not +the score + + align:start position:0% +the score + + + align:start position:0% +the score +that he said the adds up all these + + align:start position:0% +that he said the adds up all these + + + align:start position:0% +that he said the adds up all these +values human propagates in our it's + + align:start position:0% +values human propagates in our it's + + + align:start position:0% +values human propagates in our it's +impossible to stop it but won't be only + + align:start position:0% +impossible to stop it but won't be only + + + align:start position:0% +impossible to stop it but won't be only +part some as a public TV individual bags + + align:start position:0% +part some as a public TV individual bags + + + align:start position:0% +part some as a public TV individual bags +as opposed to propagating one value that + + align:start position:0% +as opposed to propagating one value that + + + align:start position:0% +as opposed to propagating one value that +you create like are you interviews and + + align:start position:0% +you create like are you interviews and + + + align:start position:0% +you create like are you interviews and +you're propagating all what is this 15 + + align:start position:0% +you're propagating all what is this 15 + + + align:start position:0% +you're propagating all what is this 15 +values upwards at every note where you + + align:start position:0% +values upwards at every note where you + + + align:start position:0% +values upwards at every note where you +propagating one that would be one value + + align:start position:0% +propagating one that would be one value + + + align:start position:0% +propagating one that would be one value +is good that you make that like a dinner + + align:start position:0% +is good that you make that like a dinner + + + align:start position:0% +is good that you make that like a dinner +each of them with some background + + align:start position:0% +each of them with some background + + + align:start position:0% +each of them with some background +all right and also just one thing to + + align:start position:0% +all right and also just one thing to + + + align:start position:0% +all right and also just one thing to +note here is distance you get 21 and + + align:start position:0% +note here is distance you get 21 and + + + align:start position:0% +note here is distance you get 21 and +these are all parameters that have been + + align:start position:0% +these are all parameters that have been + + + align:start position:0% +these are all parameters that have been +tuned so in the initial version distance + + align:start position:0% +tuned so in the initial version distance + + + align:start position:0% +tuned so in the initial version distance +was I think a reward of like five but + + align:start position:0% +was I think a reward of like five but + + + align:start position:0% +was I think a reward of like five but +probably realized that that made Mario + + align:start position:0% +probably realized that that made Mario + + + align:start position:0% +probably realized that that made Mario +skip past a lot of coins and things and + + align:start position:0% +skip past a lot of coins and things and + + + align:start position:0% +skip past a lot of coins and things and +so you tweet the score for that and also + + align:start position:0% +so you tweet the score for that and also + + + align:start position:0% +so you tweet the score for that and also +time left is to so there's some weight + + align:start position:0% +time left is to so there's some weight + + + align:start position:0% +time left is to so there's some weight +there you want to get to the very end of + + align:start position:0% +there you want to get to the very end of + + + align:start position:0% +there you want to get to the very end of +the game + + align:start position:0% +the game + + + align:start position:0% +the game +yeah if you're pushing up this like + + align:start position:0% +yeah if you're pushing up this like + + + align:start position:0% +yeah if you're pushing up this like +score it's no longer like I win over + + align:start position:0% +score it's no longer like I win over + + + align:start position:0% +score it's no longer like I win over +lots of not coming over and misses what + + align:start position:0% +lots of not coming over and misses what + + + align:start position:0% +lots of not coming over and misses what +is the vector you can just use the score + + align:start position:0% +is the vector you can just use the score + + + align:start position:0% +is the vector you can just use the score +facilities yeah so in MTTs you have this + + align:start position:0% +facilities yeah so in MTTs you have this + + + align:start position:0% +facilities yeah so in MTTs you have this +idea of like when you're propagating + + align:start position:0% +idea of like when you're propagating + + + align:start position:0% +idea of like when you're propagating +like your Q value and so in you could + + align:start position:0% +like your Q value and so in you could + + + align:start position:0% +like your Q value and so in you could +have that zero one but like sum of all + + align:start position:0% +have that zero one but like sum of all + + + align:start position:0% +have that zero one but like sum of all +the scores on the notes below over the + + align:start position:0% +the scores on the notes below over the + + + align:start position:0% +the scores on the notes below over the +number of games you play so basically + + align:start position:0% +number of games you play so basically + + + align:start position:0% +number of games you play so basically +what you would be getting when you + + align:start position:0% +what you would be getting when you + + + align:start position:0% +what you would be getting when you +divide by the number of simulations is + + align:start position:0% +divide by the number of simulations is + + + align:start position:0% +divide by the number of simulations is +like your average score + + align:start position:0% + + + + align:start position:0% + +by fire + + align:start position:0% + + + + align:start position:0% + +oh this is killing ahead of you by five + + align:start position:0% +oh this is killing ahead of you by five + + + align:start position:0% +oh this is killing ahead of you by five +wait Mario if you collect a certain + + align:start position:0% +wait Mario if you collect a certain + + + align:start position:0% +wait Mario if you collect a certain +flower or a flower then you have a party + + align:start position:0% +flower or a flower then you have a party + + + align:start position:0% +flower or a flower then you have a party +established in the day no Marius status + + align:start position:0% +established in the day no Marius status + + + align:start position:0% +established in the day no Marius status +is life I believe my statute is the fact + + align:start position:0% +is life I believe my statute is the fact + + + align:start position:0% +is life I believe my statute is the fact +that you can upgrade Mario by excitons + + align:start position:0% +that you can upgrade Mario by excitons + + + align:start position:0% +that you can upgrade Mario by excitons +good luck even like a fire Mario so that + + align:start position:0% +good luck even like a fire Mario so that + + + align:start position:0% +good luck even like a fire Mario so that +could do a lot of points because if + + align:start position:0% +could do a lot of points because if + + + align:start position:0% +could do a lot of points because if +you've done fire Mario then you're like + + align:start position:0% +you've done fire Mario then you're like + + + align:start position:0% +you've done fire Mario then you're like +you're more likely to not die by running + + align:start position:0% +you're more likely to not die by running + + + align:start position:0% +you're more likely to not die by running +into enemies is your father skewing you + + align:start position:0% +into enemies is your father skewing you + + + align:start position:0% +into enemies is your father skewing you +simply spend a lot of time using these + + align:start position:0% +simply spend a lot of time using these + + + align:start position:0% +simply spend a lot of time using these +parameters sort of isn't it generally + + align:start position:0% +parameters sort of isn't it generally + + + align:start position:0% +parameters sort of isn't it generally +though just an optimization framework + + align:start position:0% +though just an optimization framework + + + align:start position:0% +though just an optimization framework +and that's some formula so make it the + + align:start position:0% +and that's some formula so make it the + + + align:start position:0% +and that's some formula so make it the +way that we think it's nice but if you + + align:start position:0% +way that we think it's nice but if you + + + align:start position:0% +way that we think it's nice but if you +came to evaluate don't do the right + + align:start position:0% +came to evaluate don't do the right + + + align:start position:0% +came to evaluate don't do the right +thing before that wait yeah yeah but + + align:start position:0% +thing before that wait yeah yeah but + + + align:start position:0% +thing before that wait yeah yeah but +they were tuning this to make it plain + + align:start position:0% +they were tuning this to make it plain + + + align:start position:0% +they were tuning this to make it plain +how they wanted synergies these values + + align:start position:0% +how they wanted synergies these values + + + align:start position:0% +how they wanted synergies these values +can't just be a reflection of anything + + align:start position:0% +can't just be a reflection of anything + + + align:start position:0% +can't just be a reflection of anything +I mean that subscribe you can shoot up + + align:start position:0% +I mean that subscribe you can shoot up + + + align:start position:0% +I mean that subscribe you can shoot up +to I not yet that might affect certain + + align:start position:0% +to I not yet that might affect certain + + + align:start position:0% +to I not yet that might affect certain +things I mean obviously you can change + + align:start position:0% +things I mean obviously you can change + + + align:start position:0% +things I mean obviously you can change +it to whatever you want it'll slightly + + align:start position:0% +it to whatever you want it'll slightly + + + align:start position:0% +it to whatever you want it'll slightly +tweak which simulations us to work even + + align:start position:0% +tweak which simulations us to work even + + + align:start position:0% +tweak which simulations us to work even +better which will check in Turnitin for + + align:start position:0% +better which will check in Turnitin for + + + align:start position:0% +better which will check in Turnitin for +two nodes we have a cheap labor - yeah + + align:start position:0% +two nodes we have a cheap labor - yeah + + + align:start position:0% +two nodes we have a cheap labor - yeah +alright so we'll move on to the next so + + align:start position:0% +alright so we'll move on to the next so + + + align:start position:0% +alright so we'll move on to the next so +we go about scoring simulations and now + + align:start position:0% +we go about scoring simulations and now + + + align:start position:0% +we go about scoring simulations and now +we're gonna look at exactly the + + align:start position:0% +we're gonna look at exactly the + + + align:start position:0% +we're gonna look at exactly the +simulation type let's use it to play + + align:start position:0% +simulation type let's use it to play + + + align:start position:0% +simulation type let's use it to play +this MTTs controller so the regular + + align:start position:0% +this MTTs controller so the regular + + + align:start position:0% +this MTTs controller so the regular +version that yo talked about is just + + align:start position:0% +version that yo talked about is just + + + align:start position:0% +version that yo talked about is just +choosing a random node at each level in + + align:start position:0% +choosing a random node at each level in + + + align:start position:0% +choosing a random node at each level in +your simulation but there are some other + + align:start position:0% +your simulation but there are some other + + + align:start position:0% +your simulation but there are some other +strategies and someone brought went up + + align:start position:0% +strategies and someone brought went up + + + align:start position:0% +strategies and someone brought went up +but first let's look at the best of n so + + align:start position:0% +but first let's look at the best of n so + + + align:start position:0% +but first let's look at the best of n so +in this one you choose three random + + align:start position:0% +in this one you choose three random + + + align:start position:0% +in this one you choose three random +nodes at each level except you stick + + align:start position:0% +nodes at each level except you stick + + + align:start position:0% +nodes at each level except you stick +with the best of those three so no you + + align:start position:0% +with the best of those three so no you + + + align:start position:0% +with the best of those three so no you +stick with this one go to the next one + + align:start position:0% +stick with this one go to the next one + + + align:start position:0% +stick with this one go to the next one +you would choose free like n randoms me + + align:start position:0% +you would choose free like n randoms me + + + align:start position:0% +you would choose free like n randoms me +take the best one and then go to the + + align:start position:0% +take the best one and then go to the + + + align:start position:0% +take the best one and then go to the +next level and you're able to do that in + + align:start position:0% +next level and you're able to do that in + + + align:start position:0% +next level and you're able to do that in +this game because you can because of the + + align:start position:0% +this game because you can because of the + + + align:start position:0% +this game because you can because of the +way the scoring works you don't have to + + align:start position:0% +way the scoring works you don't have to + + + align:start position:0% +way the scoring works you don't have to +get to the end of the game for you score + + align:start position:0% +get to the end of the game for you score + + + align:start position:0% +get to the end of the game for you score +actually could collect a coin along the + + align:start position:0% +actually could collect a coin along the + + + align:start position:0% +actually could collect a coin along the +way so like if this if I jumped and it + + align:start position:0% +way so like if this if I jumped and it + + + align:start position:0% +way so like if this if I jumped and it +gets me a coin versus moving left and + + align:start position:0% +gets me a coin versus moving left and + + + align:start position:0% +gets me a coin versus moving left and +right that don't give me any points then + + align:start position:0% +right that don't give me any points then + + + align:start position:0% +right that don't give me any points then +this is the node that would give you the + + align:start position:0% +this is the node that would give you the + + + align:start position:0% +this is the node that would give you the +highest score so I choose that one we + + align:start position:0% +highest score so I choose that one we + + + align:start position:0% +highest score so I choose that one we +said and then the final one which is the + + align:start position:0% +said and then the final one which is the + + + align:start position:0% +said and then the final one which is the +one that's actually used for this + + align:start position:0% +one that's actually used for this + + + align:start position:0% +one that's actually used for this +controller is multi simulation this was + + align:start position:0% +controller is multi simulation this was + + + align:start position:0% +controller is multi simulation this was +brought up by imitating subject but + + align:start position:0% +brought up by imitating subject but + + + align:start position:0% +brought up by imitating subject but +basically you run multiple random + + align:start position:0% +basically you run multiple random + + + align:start position:0% +basically you run multiple random +simulations from your note and then you + + align:start position:0% +simulations from your note and then you + + + align:start position:0% +simulations from your note and then you +propagate up whichever of those + + align:start position:0% +propagate up whichever of those + + + align:start position:0% +propagate up whichever of those +simulations gave you the highest value + + align:start position:0% +simulations gave you the highest value + + + align:start position:0% +simulations gave you the highest value +and the reason to do multiple + + align:start position:0% +and the reason to do multiple + + + align:start position:0% +and the reason to do multiple +simulations is to attempt to increase + + align:start position:0% +simulations is to attempt to increase + + + align:start position:0% +simulations is to attempt to increase +the accuracy of your simulations so if + + align:start position:0% +the accuracy of your simulations so if + + + align:start position:0% +the accuracy of your simulations so if +you just do one simulation you might + + align:start position:0% +you just do one simulation you might + + + align:start position:0% +you just do one simulation you might +just get really unlucky but if you do + + align:start position:0% +just get really unlucky but if you do + + + align:start position:0% +just get really unlucky but if you do +three then you can take the highest + + align:start position:0% +three then you can take the highest + + + align:start position:0% +three then you can take the highest +value and use that as your value and + + align:start position:0% +value and use that as your value and + + + align:start position:0% +value and use that as your value and +then since the whole point of this is to + + align:start position:0% +then since the whole point of this is to + + + align:start position:0% +then since the whole point of this is to +try to make moves that get you the + + align:start position:0% +try to make moves that get you the + + + align:start position:0% +try to make moves that get you the +highest values and that'll make + + align:start position:0% + + + + align:start position:0% + +so there's a trade-off here so the more + + align:start position:0% +so there's a trade-off here so the more + + + align:start position:0% +so there's a trade-off here so the more +simulations you do the more accurate + + align:start position:0% +simulations you do the more accurate + + + align:start position:0% +simulations you do the more accurate +your simulation the more representative + + align:start position:0% +your simulation the more representative + + + align:start position:0% +your simulation the more representative +your simulation will be at the endgame + + align:start position:0% +your simulation will be at the endgame + + + align:start position:0% +your simulation will be at the endgame +like you could technically do every you + + align:start position:0% +like you could technically do every you + + + align:start position:0% +like you could technically do every you +could run like to to look whatever the + + align:start position:0% +could run like to to look whatever the + + + align:start position:0% +could run like to to look whatever the +simulations to try to get every single + + align:start position:0% +simulations to try to get every single + + + align:start position:0% +simulations to try to get every single +possible action and then take them back + + align:start position:0% +possible action and then take them back + + + align:start position:0% +possible action and then take them back +to that and that would give you the + + align:start position:0% +to that and that would give you the + + + align:start position:0% +to that and that would give you the +maximum value way that would be ideal + + align:start position:0% +maximum value way that would be ideal + + + align:start position:0% +maximum value way that would be ideal +but obviously that takes more time so + + align:start position:0% +but obviously that takes more time so + + + align:start position:0% +but obviously that takes more time so +there's a trade-off between computation + + align:start position:0% +there's a trade-off between computation + + + align:start position:0% +there's a trade-off between computation +time and the number of simulations to + + align:start position:0% +time and the number of simulations to + + + align:start position:0% +time and the number of simulations to +run and that's just something that they + + align:start position:0% +run and that's just something that they + + + align:start position:0% +run and that's just something that they +probably just play around + + align:start position:0% + + + + align:start position:0% + +frankly have a + + align:start position:0% + + + + align:start position:0% + +losing five minutes or evidence + + align:start position:0% +losing five minutes or evidence + + + align:start position:0% +losing five minutes or evidence +yes so in this competition there's + + align:start position:0% +yes so in this competition there's + + + align:start position:0% +yes so in this competition there's +different computation times budgets that + + align:start position:0% +different computation times budgets that + + + align:start position:0% +different computation times budgets that +you get and I believe the reason for the + + align:start position:0% +you get and I believe the reason for the + + + align:start position:0% +you get and I believe the reason for the +different computation time budgets is + + align:start position:0% +different computation time budgets is + + + align:start position:0% +different computation time budgets is +the frames per second of the game oh + + align:start position:0% + + + + align:start position:0% + +okay so I told you all all about how + + align:start position:0% +okay so I told you all all about how + + + align:start position:0% +okay so I told you all all about how +this is I don't we went over the scoring + + align:start position:0% +this is I don't we went over the scoring + + + align:start position:0% +this is I don't we went over the scoring +the knows what the edges are what this + + align:start position:0% +the knows what the edges are what this + + + align:start position:0% +the knows what the edges are what this +simulation grab you use and so you + + align:start position:0% +simulation grab you use and so you + + + align:start position:0% +simulation grab you use and so you +probably want to see it in action so + + align:start position:0% +probably want to see it in action so + + + align:start position:0% +probably want to see it in action so +this is always a risky move trying to + + align:start position:0% +this is always a risky move trying to + + + align:start position:0% +this is always a risky move trying to +shoot video at play it's actually in the + + align:start position:0% +shoot video at play it's actually in the + + + align:start position:0% +shoot video at play it's actually in the +background oh okay got it + + align:start position:0% + + + + align:start position:0% + +Latinas Washington right alright so + + align:start position:0% +Latinas Washington right alright so + + + align:start position:0% +Latinas Washington right alright so +here's this ncts based modeling + + align:start position:0% +here's this ncts based modeling + + + align:start position:0% +here's this ncts based modeling +controller you can see he's actually + + align:start position:0% +controller you can see he's actually + + + align:start position:0% +controller you can see he's actually +wrecking doing some serious damage here + + align:start position:0% +wrecking doing some serious damage here + + + align:start position:0% +wrecking doing some serious damage here +but those lines that you see the reason + + align:start position:0% +but those lines that you see the reason + + + align:start position:0% +but those lines that you see the reason +they're different colors is not showing + + align:start position:0% +they're different colors is not showing + + + align:start position:0% +they're different colors is not showing +it's not showing like different players + + align:start position:0% +it's not showing like different players + + + align:start position:0% +it's not showing like different players +or anything like that be just using + + align:start position:0% +or anything like that be just using + + + align:start position:0% +or anything like that be just using +different colors so you can see the + + align:start position:0% +different colors so you can see the + + + align:start position:0% +different colors so you can see the +different layers of history search and + + align:start position:0% +different layers of history search and + + + align:start position:0% +different layers of history search and +so you can see they actually went + + align:start position:0% +so you can see they actually went + + + align:start position:0% +so you can see they actually went +backwards there and that's because in + + align:start position:0% +backwards there and that's because in + + + align:start position:0% +backwards there and that's because in +his simulation one of the backwards ones + + align:start position:0% +his simulation one of the backwards ones + + + align:start position:0% +his simulation one of the backwards ones +landed on an enemy and that gives you + + align:start position:0% +landed on an enemy and that gives you + + + align:start position:0% +landed on an enemy and that gives you +points from our scoring system versus if + + align:start position:0% +points from our scoring system versus if + + + align:start position:0% +points from our scoring system versus if +he had just gone forward he would have + + align:start position:0% +he had just gone forward he would have + + + align:start position:0% +he had just gone forward he would have +got in some distance points but not all + + align:start position:0% +got in some distance points but not all + + + align:start position:0% +got in some distance points but not all +so here's of tons of enemies to the + + align:start position:0% +so here's of tons of enemies to the + + + align:start position:0% +so here's of tons of enemies to the +connection this simulation is quickly + + align:start position:0% +connection this simulation is quickly + + + align:start position:0% +connection this simulation is quickly +being able to figure out that come all + + align:start position:0% +being able to figure out that come all + + + align:start position:0% +being able to figure out that come all +these enemies so you're just wrecking + + align:start position:0% +these enemies so you're just wrecking + + + align:start position:0% +these enemies so you're just wrecking +all these guys not two points here + + align:start position:0% +all these guys not two points here + + + align:start position:0% +all these guys not two points here +collecting the coin et cetera you did + + align:start position:0% +collecting the coin et cetera you did + + + align:start position:0% +collecting the coin et cetera you did +the idea it's pretty awesome to watch oh + + align:start position:0% +the idea it's pretty awesome to watch oh + + + align:start position:0% +the idea it's pretty awesome to watch oh +there's that flower we were talking + + align:start position:0% +there's that flower we were talking + + + align:start position:0% +there's that flower we were talking +about so now he's actually a five + + align:start position:0% +about so now he's actually a five + + + align:start position:0% +about so now he's actually a five +viewing bar you demon and he's doing + + align:start position:0% +viewing bar you demon and he's doing + + + align:start position:0% +viewing bar you demon and he's doing +some serious damage with that step with + + align:start position:0% +some serious damage with that step with + + + align:start position:0% +some serious damage with that step with +all the missiles I even know you can + + align:start position:0% +all the missiles I even know you can + + + align:start position:0% +all the missiles I even know you can +step on the missiles all right okay you + + align:start position:0% +step on the missiles all right okay you + + + align:start position:0% +step on the missiles all right okay you +could watch this for a while well thanks + + align:start position:0% +could watch this for a while well thanks + + + align:start position:0% +could watch this for a while well thanks +it now so it looks super promising in + + align:start position:0% +it now so it looks super promising in + + + align:start position:0% +it now so it looks super promising in +this video I don't know how to close + + align:start position:0% +this video I don't know how to close + + + align:start position:0% +this video I don't know how to close +match there it is okay so the demo looks + + align:start position:0% +match there it is okay so the demo looks + + + align:start position:0% +match there it is okay so the demo looks +really cool it's really promising let's + + align:start position:0% +really cool it's really promising let's + + + align:start position:0% +really cool it's really promising let's +take a look at the Sharks here we all + + align:start position:0% +take a look at the Sharks here we all + + + align:start position:0% +take a look at the Sharks here we all +want some quantitative stuff this is the + + align:start position:0% +want some quantitative stuff this is the + + + align:start position:0% +want some quantitative stuff this is the +chart the scores on the y-axis the + + align:start position:0% +chart the scores on the y-axis the + + + align:start position:0% +chart the scores on the y-axis the +bottom is computation budget which is + + align:start position:0% +bottom is computation budget which is + + + align:start position:0% +bottom is computation budget which is +something that you were talking about + + align:start position:0% +something that you were talking about + + + align:start position:0% +something that you were talking about +and I just want to highlight to make + + align:start position:0% +and I just want to highlight to make + + + align:start position:0% +and I just want to highlight to make +this a little more visually appealing + + align:start position:0% +this a little more visually appealing + + + align:start position:0% +this a little more visually appealing +here all of these things that I + + align:start position:0% +here all of these things that I + + + align:start position:0% +here all of these things that I +highlighted are using this juice it's + + align:start position:0% +highlighted are using this juice it's + + + align:start position:0% +highlighted are using this juice it's +labeled suc team that's + + align:start position:0% +labeled suc team that's + + + align:start position:0% +labeled suc team that's +upper confidence bound tree remember you + + align:start position:0% +upper confidence bound tree remember you + + + align:start position:0% +upper confidence bound tree remember you +know talk about upper confidence bands + + align:start position:0% +know talk about upper confidence bands + + + align:start position:0% +know talk about upper confidence bands +that's just essentially what's used in + + align:start position:0% +that's just essentially what's used in + + + align:start position:0% +that's just essentially what's used in +ncts for guiding your tree search so + + align:start position:0% +ncts for guiding your tree search so + + + align:start position:0% +ncts for guiding your tree search so +these are all the methods but then you + + align:start position:0% +these are all the methods but then you + + + align:start position:0% +these are all the methods but then you +see T multi + + align:start position:0% +see T multi + + + align:start position:0% +see T multi +which is this purple square that's + + align:start position:0% +which is this purple square that's + + + align:start position:0% +which is this purple square that's +saying it's using ncts but it's doing + + align:start position:0% +saying it's using ncts but it's doing + + + align:start position:0% +saying it's using ncts but it's doing +the multiple simulations and you can see + + align:start position:0% +the multiple simulations and you can see + + + align:start position:0% +the multiple simulations and you can see +this multi plus care is also at the top + + align:start position:0% +this multi plus care is also at the top + + + align:start position:0% +this multi plus care is also at the top +so both these use the multi simulation + + align:start position:0% +so both these use the multi simulation + + + align:start position:0% +so both these use the multi simulation +technique and then the plus car is + + align:start position:0% +technique and then the plus car is + + + align:start position:0% +technique and then the plus car is +actually they added an extra scoring + + align:start position:0% +actually they added an extra scoring + + + align:start position:0% +actually they added an extra scoring +mechanism for carries I believe that's + + align:start position:0% +mechanism for carries I believe that's + + + align:start position:0% +mechanism for carries I believe that's +probably like carrying a shell and that + + align:start position:0% +probably like carrying a shell and that + + + align:start position:0% +probably like carrying a shell and that +if you made it do better than these ones + + align:start position:0% +if you made it do better than these ones + + + align:start position:0% +if you made it do better than these ones +that are highlighted are using playing a + + align:start position:0% +that are highlighted are using playing a + + + align:start position:0% +that are highlighted are using playing a +star and then a refined version of a + + align:start position:0% +star and then a refined version of a + + + align:start position:0% +star and then a refined version of a +star so with increasing time they do + + align:start position:0% +star so with increasing time they do + + + align:start position:0% +star so with increasing time they do +increase score but they're even worse + + align:start position:0% +increase score but they're even worse + + + align:start position:0% +increase score but they're even worse +than just your UCT with just random + + align:start position:0% +than just your UCT with just random + + + align:start position:0% +than just your UCT with just random +simulation no multi simulations oh I + + align:start position:0% +simulation no multi simulations oh I + + + align:start position:0% +simulation no multi simulations oh I +guess we're kind of running low on time + + align:start position:0% +guess we're kind of running low on time + + + align:start position:0% +guess we're kind of running low on time +it's not ideal but another thing I want + + align:start position:0% +it's not ideal but another thing I want + + + align:start position:0% +it's not ideal but another thing I want +to point out is down at the bottom here + + align:start position:0% +to point out is down at the bottom here + + + align:start position:0% +to point out is down at the bottom here +these are the multi simulations they + + align:start position:0% +these are the multi simulations they + + + align:start position:0% +these are the multi simulations they +actually have the lowest maximal search + + align:start position:0% +actually have the lowest maximal search + + + align:start position:0% +actually have the lowest maximal search +depth in which at first would seem like + + align:start position:0% +depth in which at first would seem like + + + align:start position:0% +depth in which at first would seem like +what light I have the lowest search + + align:start position:0% +what light I have the lowest search + + + align:start position:0% +what light I have the lowest search +depth but my scores the most but that + + align:start position:0% +depth but my scores the most but that + + + align:start position:0% +depth but my scores the most but that +comes into play with what you were + + align:start position:0% +comes into play with what you were + + + align:start position:0% +comes into play with what you were +saying about the trade-off between those + + align:start position:0% +saying about the trade-off between those + + + align:start position:0% +saying about the trade-off between those +simulations and the amount of time it + + align:start position:0% +simulations and the amount of time it + + + align:start position:0% +simulations and the amount of time it +takes so because I'm doing multiple + + align:start position:0% +takes so because I'm doing multiple + + + align:start position:0% +takes so because I'm doing multiple +simulations I'm taking more time at each + + align:start position:0% +simulations I'm taking more time at each + + + align:start position:0% +simulations I'm taking more time at each +node but that's giving me a more + + align:start position:0% +node but that's giving me a more + + + align:start position:0% +node but that's giving me a more +accurate value assessment and so that + + align:start position:0% +accurate value assessment and so that + + + align:start position:0% +accurate value assessment and so that +lets me choose my action more carefully + + align:start position:0% +lets me choose my action more carefully + + + align:start position:0% +lets me choose my action more carefully +or with more information and so that's + + align:start position:0% +or with more information and so that's + + + align:start position:0% +or with more information and so that's +what's able to give me this better score + + align:start position:0% +what's able to give me this better score + + + align:start position:0% +what's able to give me this better score +okay that's all Mario so we're gonna + + align:start position:0% +okay that's all Mario so we're gonna + + + align:start position:0% +okay that's all Mario so we're gonna +move on to half ago I guess other + + align:start position:0% +move on to half ago I guess other + + + align:start position:0% +move on to half ago I guess other +questions about Mario before I get up + + align:start position:0% +questions about Mario before I get up + + + align:start position:0% +questions about Mario before I get up +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah that's a good question I have a + + align:start position:0% +yeah that's a good question I have a + + + align:start position:0% +yeah that's a good question I have a +feeling it's because if you're doing the + + align:start position:0% +feeling it's because if you're doing the + + + align:start position:0% +feeling it's because if you're doing the +best of n that's really heavily relying + + align:start position:0% +best of n that's really heavily relying + + + align:start position:0% +best of n that's really heavily relying +on your scoring metrics and so if let's + + align:start position:0% +on your scoring metrics and so if let's + + + align:start position:0% +on your scoring metrics and so if let's +say I have one step I collect + + align:start position:0% +say I have one step I collect + + + align:start position:0% +say I have one step I collect +accomplished by jumping reflect a coin + + align:start position:0% +accomplished by jumping reflect a coin + + + align:start position:0% +accomplished by jumping reflect a coin +purse if I go a lot right but I get more + + align:start position:0% +purse if I go a lot right but I get more + + + align:start position:0% +purse if I go a lot right but I get more +points I get that point + + align:start position:0% +points I get that point + + + align:start position:0% +points I get that point +but maybe like a missile is gonna hit me + + align:start position:0% +but maybe like a missile is gonna hit me + + + align:start position:0% +but maybe like a missile is gonna hit me +in the face but do that I should get rid + + align:start position:0% +in the face but do that I should get rid + + + align:start position:0% +in the face but do that I should get rid +of some of the it's kind of like forcing + + align:start position:0% +of some of the it's kind of like forcing + + + align:start position:0% +of some of the it's kind of like forcing +you to do certain moves yes do they + + align:start position:0% +you to do certain moves yes do they + + + align:start position:0% +you to do certain moves yes do they +start using the same value yeah so I'm + + align:start position:0% +start using the same value yeah so I'm + + + align:start position:0% +start using the same value yeah so I'm +not exactly sure what the a-star + + align:start position:0% +not exactly sure what the a-star + + + align:start position:0% +not exactly sure what the a-star +heuristic is the whole reason that a + + align:start position:0% +heuristic is the whole reason that a + + + align:start position:0% +heuristic is the whole reason that a +star is difficult is because coming up + + align:start position:0% +star is difficult is because coming up + + + align:start position:0% +star is difficult is because coming up +with a heuristic to these types of games + + align:start position:0% +with a heuristic to these types of games + + + align:start position:0% +with a heuristic to these types of games +sorry yeah but this is not his version + + align:start position:0% +sorry yeah but this is not his version + + + align:start position:0% +sorry yeah but this is not his version +of a star I believe this is the a star + + align:start position:0% +of a star I believe this is the a star + + + align:start position:0% +of a star I believe this is the a star +that was used by I've read the name of + + align:start position:0% +that was used by I've read the name of + + + align:start position:0% +that was used by I've read the name of +the guy but if one the AI competition + + align:start position:0% +the guy but if one the AI competition + + + align:start position:0% +the guy but if one the AI competition +like a couple years ago okay but I'm + + align:start position:0% +like a couple years ago okay but I'm + + + align:start position:0% +like a couple years ago okay but I'm +gonna kind of move on to up ago does + + align:start position:0% +gonna kind of move on to up ago does + + + align:start position:0% +gonna kind of move on to up ago does +someone have that minute time for okay + + align:start position:0% +someone have that minute time for okay + + + align:start position:0% +someone have that minute time for okay +we're gonna power Bruce so here's + + align:start position:0% +we're gonna power Bruce so here's + + + align:start position:0% +we're gonna power Bruce so here's +alphago hopefully you all know the rules + + align:start position:0% +alphago hopefully you all know the rules + + + align:start position:0% +alphago hopefully you all know the rules +just in case I'll just go through a + + align:start position:0% +just in case I'll just go through a + + + align:start position:0% +just in case I'll just go through a +paper 19 by 19 you alternate black + + align:start position:0% +paper 19 by 19 you alternate black + + + align:start position:0% +paper 19 by 19 you alternate black +stones white stones you collect enemies + + align:start position:0% +stones white stones you collect enemies + + + align:start position:0% +stones white stones you collect enemies +stones bison completely surrounding them + + align:start position:0% +stones bison completely surrounding them + + + align:start position:0% +stones bison completely surrounding them +you can surround a single stone groups + + align:start position:0% +you can surround a single stone groups + + + align:start position:0% +you can surround a single stone groups +of stones and your score is your + + align:start position:0% +of stones and your score is your + + + align:start position:0% +of stones and your score is your +territory + + align:start position:0% +territory + + + align:start position:0% +territory +plus the number of captured pieces so + + align:start position:0% +plus the number of captured pieces so + + + align:start position:0% +plus the number of captured pieces so +your territory is just the area that was + + align:start position:0% +your territory is just the area that was + + + align:start position:0% +your territory is just the area that was +surrounding and then you just add the + + align:start position:0% +surrounding and then you just add the + + + align:start position:0% +surrounding and then you just add the +stones you collected the main emphasis + + align:start position:0% +stones you collected the main emphasis + + + align:start position:0% +stones you collected the main emphasis +year the rules are super important the + + align:start position:0% +year the rules are super important the + + + align:start position:0% +year the rules are super important the +main emphasis is the rule there's very + + align:start position:0% +main emphasis is the rule there's very + + + align:start position:0% +main emphasis is the rule there's very +few rules so you would think it's really + + align:start position:0% +few rules so you would think it's really + + + align:start position:0% +few rules so you would think it's really +simple but the complexity of the game is + + align:start position:0% +simple but the complexity of the game is + + + align:start position:0% +simple but the complexity of the game is +quite extreme at each level and each + + align:start position:0% +quite extreme at each level and each + + + align:start position:0% +quite extreme at each level and each +turn you have about 250 options you can + + align:start position:0% +turn you have about 250 options you can + + + align:start position:0% +turn you have about 250 options you can +play each go game lasts about 150 turns + + align:start position:0% +play each go game lasts about 150 turns + + + align:start position:0% +play each go game lasts about 150 turns +so they can do a total of 10 to the 761 + + align:start position:0% +so they can do a total of 10 to the 761 + + + align:start position:0% +so they can do a total of 10 to the 761 +games of approximately and to put that + + align:start position:0% +games of approximately and to put that + + + align:start position:0% +games of approximately and to put that +in comparison here's chess and read + + align:start position:0% +in comparison here's chess and read + + + align:start position:0% +in comparison here's chess and read +those numbers chess is also pretty + + align:start position:0% +those numbers chess is also pretty + + + align:start position:0% +those numbers chess is also pretty +complex but there's 35 options per turn + + align:start position:0% +complex but there's 35 options per turn + + + align:start position:0% +complex but there's 35 options per turn +deep blue it would actually I think you + + align:start position:0% +deep blue it would actually I think you + + + align:start position:0% +deep blue it would actually I think you +were talking about building out the + + align:start position:0% +were talking about building out the + + + align:start position:0% +were talking about building out the +whole tree so deep blue would build out + + align:start position:0% +whole tree so deep blue would build out + + + align:start position:0% +whole tree so deep blue would build out +the tree for six levels + + align:start position:0% +the tree for six levels + + + align:start position:0% +the tree for six levels +then use this parkour chess master + + align:start position:0% +then use this parkour chess master + + + align:start position:0% +then use this parkour chess master +inputted like heuristic the evaluation + + align:start position:0% +inputted like heuristic the evaluation + + + align:start position:0% +inputted like heuristic the evaluation +that it used to find the best move they + + align:start position:0% +that it used to find the best move they + + + align:start position:0% +that it used to find the best move they +said would go you have 250 options which + + align:start position:0% +said would go you have 250 options which + + + align:start position:0% +said would go you have 250 options which +already is adding a lot more complexity + + align:start position:0% +already is adding a lot more complexity + + + align:start position:0% +already is adding a lot more complexity +and so that strategy won't work quite as + + align:start position:0% +and so that strategy won't work quite as + + + align:start position:0% +and so that strategy won't work quite as +nicely so what do we do we use a + + align:start position:0% +nicely so what do we do we use a + + + align:start position:0% +nicely so what do we do we use a +modified version of empties yes well + + align:start position:0% +modified version of empties yes well + + + align:start position:0% +modified version of empties yes well +it's not what we do that's what Alec + + align:start position:0% +it's not what we do that's what Alec + + + align:start position:0% +it's not what we do that's what Alec +that's what google's deepmind team to + + align:start position:0% +that's what google's deepmind team to + + + align:start position:0% +that's what google's deepmind team to +the top ago they combined neural + + align:start position:0% +the top ago they combined neural + + + align:start position:0% +the top ago they combined neural +networks with MC GS coincidentally we + + align:start position:0% +networks with MC GS coincidentally we + + + align:start position:0% +networks with MC GS coincidentally we +learned about neural networks last class + + align:start position:0% +learned about neural networks last class + + + align:start position:0% +learned about neural networks last class +probably not a coincidence but it's not + + align:start position:0% +probably not a coincidence but it's not + + + align:start position:0% +probably not a coincidence but it's not +a good policy network in the alphago and + + align:start position:0% +a good policy network in the alphago and + + + align:start position:0% +a good policy network in the alphago and +one value network and another big + + align:start position:0% +one value network and another big + + + align:start position:0% +one value network and another big +coincidence here the two policy numbers + + align:start position:0% +coincidence here the two policy numbers + + + align:start position:0% +coincidence here the two policy numbers +rocky CN NS which we learned + + align:start position:0% +rocky CN NS which we learned + + + align:start position:0% +rocky CN NS which we learned +specifically about less less + + align:start position:0% +specifically about less less + + + align:start position:0% +specifically about less less +convolutional neural nets and the reason + + align:start position:0% +convolutional neural nets and the reason + + + align:start position:0% +convolutional neural nets and the reason +for that is the input to the the policy + + align:start position:0% +for that is the input to the the policy + + + align:start position:0% +for that is the input to the the policy +neural networks is an image of the game + + align:start position:0% +neural networks is an image of the game + + + align:start position:0% +neural networks is an image of the game +the remembered convolutional neural nets + + align:start position:0% +the remembered convolutional neural nets + + + align:start position:0% +the remembered convolutional neural nets +work really well with images and so it + + align:start position:0% +work really well with images and so it + + + align:start position:0% +work really well with images and so it +outputs though is a probability + + align:start position:0% +outputs though is a probability + + + align:start position:0% +outputs though is a probability +distribution over the legal moves and + + align:start position:0% +distribution over the legal moves and + + + align:start position:0% +distribution over the legal moves and +the idea is that if a move has a higher + + align:start position:0% +the idea is that if a move has a higher + + + align:start position:0% +the idea is that if a move has a higher +probability it'll be a more promising + + align:start position:0% +probability it'll be a more promising + + + align:start position:0% +probability it'll be a more promising +move for you to take but but another key + + align:start position:0% +move for you to take but but another key + + + align:start position:0% +move for you to take but but another key +point of that is not deterministic it's + + align:start position:0% +point of that is not deterministic it's + + + align:start position:0% +point of that is not deterministic it's +not telling you to take this move this + + align:start position:0% +not telling you to take this move this + + + align:start position:0% +not telling you to take this move this +is assigning a higher probability to + + align:start position:0% +is assigning a higher probability to + + + align:start position:0% +is assigning a higher probability to +this move and this network generated by + + align:start position:0% +this move and this network generated by + + + align:start position:0% +this move and this network generated by +doing supervised learning on 30 million + + align:start position:0% +doing supervised learning on 30 million + + + align:start position:0% +doing supervised learning on 30 million +positions from human expert games but + + align:start position:0% +positions from human expert games but + + + align:start position:0% +positions from human expert games but +apparently there's a giant database of + + align:start position:0% +apparently there's a giant database of + + + align:start position:0% +apparently there's a giant database of +go expert games so that came in handy + + align:start position:0% +go expert games so that came in handy + + + align:start position:0% +go expert games so that came in handy +and there were two different networks + + align:start position:0% +and there were two different networks + + + align:start position:0% +and there were two different networks +training one of them was a slow policy + + align:start position:0% +training one of them was a slow policy + + + align:start position:0% +training one of them was a slow policy +the other was the fast policy the slow + + align:start position:0% +the other was the fast policy the slow + + + align:start position:0% +the other was the fast policy the slow +was able to predict an expert move with + + align:start position:0% +was able to predict an expert move with + + + align:start position:0% +was able to predict an expert move with +57 percent accuracy which to me was + + align:start position:0% +57 percent accuracy which to me was + + + align:start position:0% +57 percent accuracy which to me was +mind-blowing + + align:start position:0% +mind-blowing + + + align:start position:0% +mind-blowing +like using this neural network 57 + + align:start position:0% +like using this neural network 57 + + + align:start position:0% +like using this neural network 57 +percent imma kick in where the expert + + align:start position:0% +percent imma kick in where the expert + + + align:start position:0% +percent imma kick in where the expert +would place his move but that took 3,000 + + align:start position:0% +would place his move but that took 3,000 + + + align:start position:0% +would place his move but that took 3,000 +microseconds versus the fast policy + + align:start position:0% +microseconds versus the fast policy + + + align:start position:0% +microseconds versus the fast policy +which suffers a bit in the + + align:start position:0% +which suffers a bit in the + + + align:start position:0% +which suffers a bit in the +it's a thousand five hundred times + + align:start position:0% +it's a thousand five hundred times + + + align:start position:0% +it's a thousand five hundred times +faster and we'll see where they use each + + align:start position:0% +faster and we'll see where they use each + + + align:start position:0% +faster and we'll see where they use each +mr. policies later on but yeah expert + + align:start position:0% +mr. policies later on but yeah expert + + + align:start position:0% +mr. policies later on but yeah expert +movement with 57% accuracy the Alpha + + align:start position:0% +movement with 57% accuracy the Alpha + + + align:start position:0% +movement with 57% accuracy the Alpha +Team is like we don't that's not our + + align:start position:0% +Team is like we don't that's not our + + + align:start position:0% +Team is like we don't that's not our +goal we don't have predict an expert + + align:start position:0% +goal we don't have predict an expert + + + align:start position:0% +goal we don't have predict an expert +move we want to predict a winning move + + align:start position:0% +move we want to predict a winning move + + + align:start position:0% +move we want to predict a winning move +and so to do that they took their policy + + align:start position:0% +and so to do that they took their policy + + + align:start position:0% +and so to do that they took their policy +Network and then they would use + + align:start position:0% +Network and then they would use + + + align:start position:0% +Network and then they would use +reinforcement learning so that's where + + align:start position:0% +reinforcement learning so that's where + + + align:start position:0% +reinforcement learning so that's where +you played the network against what + + align:start position:0% +you played the network against what + + + align:start position:0% +you played the network against what +iterations of itself in order to hone in + + align:start position:0% +iterations of itself in order to hone in + + + align:start position:0% +iterations of itself in order to hone in +a better policy of a year towards + + align:start position:0% +a better policy of a year towards + + + align:start position:0% +a better policy of a year towards +winning moves and then they tested this + + align:start position:0% +winning moves and then they tested this + + + align:start position:0% +winning moves and then they tested this +against patchy which uses for the camera + + align:start position:0% +against patchy which uses for the camera + + + align:start position:0% +against patchy which uses for the camera +no idea if that's how you pronounce pots + + align:start position:0% +no idea if that's how you pronounce pots + + + align:start position:0% +no idea if that's how you pronounce pots +you might be patchy I'm not sure but who + + align:start position:0% +you might be patchy I'm not sure but who + + + align:start position:0% +you might be patchy I'm not sure but who +this a hundred and thousand ncts + + align:start position:0% +this a hundred and thousand ncts + + + align:start position:0% +this a hundred and thousand ncts +simulation that each turn so this is + + align:start position:0% +simulation that each turn so this is + + + align:start position:0% +simulation that each turn so this is +purely MTTs okay + + align:start position:0% +purely MTTs okay + + + align:start position:0% +purely MTTs okay +they've been playing just the alphago + + align:start position:0% +they've been playing just the alphago + + + align:start position:0% +they've been playing just the alphago +policy network the policy number one + + align:start position:0% +policy network the policy number one + + + align:start position:0% +policy network the policy number one +eighty-five percent of the games so + + align:start position:0% +eighty-five percent of the games so + + + align:start position:0% +eighty-five percent of the games so +without any sort of trained search or + + align:start position:0% +without any sort of trained search or + + + align:start position:0% +without any sort of trained search or +anything involved one eighty-five + + align:start position:0% +anything involved one eighty-five + + + align:start position:0% +anything involved one eighty-five +percent which is pretty great and that + + align:start position:0% +percent which is pretty great and that + + + align:start position:0% +percent which is pretty great and that +suggests that maybe intuition wins over + + align:start position:0% +suggests that maybe intuition wins over + + + align:start position:0% +suggests that maybe intuition wins over +long reflections and go and + + align:start position:0% +long reflections and go and + + + align:start position:0% +long reflections and go and +interestingly if you talk to expert go + + align:start position:0% +interestingly if you talk to expert go + + + align:start position:0% +interestingly if you talk to expert go +players and ask them why they do certain + + align:start position:0% +players and ask them why they do certain + + + align:start position:0% +players and ask them why they do certain +new let us say like it felt good I had a + + align:start position:0% +new let us say like it felt good I had a + + + align:start position:0% +new let us say like it felt good I had a +bunch of this and so that's kind of + + align:start position:0% +bunch of this and so that's kind of + + + align:start position:0% +bunch of this and so that's kind of +indicative they're complete up going + + align:start position:0% +indicative they're complete up going + + + align:start position:0% +indicative they're complete up going +over time sorry but the then there's + + align:start position:0% +over time sorry but the then there's + + + align:start position:0% +over time sorry but the then there's +those little two policy numbers there's + + align:start position:0% +those little two policy numbers there's + + + align:start position:0% +those little two policy numbers there's +also value network but the value number + + align:start position:0% +also value network but the value number + + + align:start position:0% +also value network but the value number +does is it takes in a board and they'll + + align:start position:0% +does is it takes in a board and they'll + + + align:start position:0% +does is it takes in a board and they'll +give you a value of like how good is + + align:start position:0% +give you a value of like how good is + + + align:start position:0% +give you a value of like how good is +this board the wind point you know give + + align:start position:0% +this board the wind point you know give + + + align:start position:0% +this board the wind point you know give +you a win probability number so it's 77% + + align:start position:0% +you a win probability number so it's 77% + + + align:start position:0% +you a win probability number so it's 77% +it would say like seventy seven percent + + align:start position:0% +it would say like seventy seven percent + + + align:start position:0% +it would say like seventy seven percent +of time you + + align:start position:0% +of time you + + + align:start position:0% +of time you +from the sport and so that's similar to + + align:start position:0% +from the sport and so that's similar to + + + align:start position:0% +from the sport and so that's similar to +the evaluation election deep-blue but + + align:start position:0% +the evaluation election deep-blue but + + + align:start position:0% +the evaluation election deep-blue but +rather than a go master coming in and + + align:start position:0% +rather than a go master coming in and + + + align:start position:0% +rather than a go master coming in and +telling you like well if these are + + align:start position:0% +telling you like well if these are + + + align:start position:0% +telling you like well if these are +connected in this way and like down here + + align:start position:0% +connected in this way and like down here + + + align:start position:0% +connected in this way and like down here +we have this certain thing then here's + + align:start position:0% +we have this certain thing then here's + + + align:start position:0% +we have this certain thing then here's +the sort of score we should expect white + + align:start position:0% +the sort of score we should expect white + + + align:start position:0% +the sort of score we should expect white +in chess though they had a chess match + + align:start position:0% +in chess though they had a chess match + + + align:start position:0% +in chess though they had a chess match +was like if the knight is here and the + + align:start position:0% +was like if the knight is here and the + + + align:start position:0% +was like if the knight is here and the +queen is here all these specific things + + align:start position:0% +queen is here all these specific things + + + align:start position:0% +queen is here all these specific things +this was actually learned from the + + align:start position:0% +this was actually learned from the + + + align:start position:0% +this was actually learned from the +reinforcement learning that was + + align:start position:0% +reinforcement learning that was + + + align:start position:0% +reinforcement learning that was +happening when the policy number two + + align:start position:0% +happening when the policy number two + + + align:start position:0% +happening when the policy number two +playing another the value number was + + align:start position:0% +playing another the value number was + + + align:start position:0% +playing another the value number was +learning about those positions during + + align:start position:0% +learning about those positions during + + + align:start position:0% +learning about those positions during +that time and the predictions get better + + align:start position:0% +that time and the predictions get better + + + align:start position:0% +that time and the predictions get better +towards the end of the game which I + + align:start position:0% +towards the end of the game which I + + + align:start position:0% +towards the end of the game which I +think Jo mentioned in his talking all + + align:start position:0% +think Jo mentioned in his talking all + + + align:start position:0% +think Jo mentioned in his talking all +right so how do you combine all these + + align:start position:0% +right so how do you combine all these + + + align:start position:0% +right so how do you combine all these +contentions yes well the slow policy + + align:start position:0% +contentions yes well the slow policy + + + align:start position:0% +contentions yes well the slow policy +never could remember is slower but + + align:start position:0% +never could remember is slower but + + + align:start position:0% +never could remember is slower but +should give us stronger moves is used to + + align:start position:0% +should give us stronger moves is used to + + + align:start position:0% +should give us stronger moves is used to +guide our research in order to help us + + align:start position:0% +guide our research in order to help us + + + align:start position:0% +guide our research in order to help us +decide which you know to expand next + + align:start position:0% +decide which you know to expand next + + + align:start position:0% +decide which you know to expand next +when we expand that note to get the + + align:start position:0% +when we expand that note to get the + + + align:start position:0% +when we expand that note to get the +value the value of the state is the + + align:start position:0% +value the value of the state is the + + + align:start position:0% +value the value of the state is the +simulation like before like normal NTTS + + align:start position:0% +simulation like before like normal NTTS + + + align:start position:0% +simulation like before like normal NTTS +except it's not a completely random + + align:start position:0% +except it's not a completely random + + + align:start position:0% +except it's not a completely random +simulation we use our fast policy + + align:start position:0% +simulation we use our fast policy + + + align:start position:0% +simulation we use our fast policy +Network do you miss a more educated + + align:start position:0% +Network do you miss a more educated + + + align:start position:0% +Network do you miss a more educated +simulation here but we're using a fast + + align:start position:0% +simulation here but we're using a fast + + + align:start position:0% +simulation here but we're using a fast +one obviously to save some computation + + align:start position:0% +one obviously to save some computation + + + align:start position:0% +one obviously to save some computation +time so it's giving us a more app + + align:start position:0% +time so it's giving us a more app + + + align:start position:0% +time so it's giving us a more app +probably a more indicative random + + align:start position:0% +probably a more indicative random + + + align:start position:0% +probably a more indicative random +simulation of what's going to actually + + align:start position:0% +simulation of what's going to actually + + + align:start position:0% +simulation of what's going to actually +happen and then we also combine that + + align:start position:0% +happen and then we also combine that + + + align:start position:0% +happen and then we also combine that +with our value network output so we run + + align:start position:0% +with our value network output so we run + + + align:start position:0% +with our value network output so we run +our value network on this node as well + + align:start position:0% +our value network on this node as well + + + align:start position:0% +our value network on this node as well +and we add that to our simulation value + + align:start position:0% +and we add that to our simulation value + + + align:start position:0% +and we add that to our simulation value +can propagate it interestingly the Alpha + + align:start position:0% +can propagate it interestingly the Alpha + + + align:start position:0% +can propagate it interestingly the Alpha +go seemed tested out just using the fast + + align:start position:0% +go seemed tested out just using the fast + + + align:start position:0% +go seemed tested out just using the fast +policy simulation value and scrapping + + align:start position:0% +policy simulation value and scrapping + + + align:start position:0% +policy simulation value and scrapping +the value network and they also just use + + align:start position:0% +the value network and they also just use + + + align:start position:0% +the value network and they also just use +the value network and scrapped the + + align:start position:0% +the value network and scrapped the + + + align:start position:0% +the value network and scrapped the +simulation value and those both + + align:start position:0% +simulation value and those both + + + align:start position:0% +simulation value and those both +performed worse than if it had these and + + align:start position:0% +performed worse than if it had these and + + + align:start position:0% +performed worse than if it had these and +another added interesting point here + + align:start position:0% +another added interesting point here + + + align:start position:0% +another added interesting point here +that these two factors and our value + + align:start position:0% +that these two factors and our value + + + align:start position:0% +that these two factors and our value +have about the same weight they were + + align:start position:0% +have about the same weight they were + + + align:start position:0% +have about the same weight they were +both about equally important and I think + + align:start position:0% +both about equally important and I think + + + align:start position:0% +both about equally important and I think +I'll give into that later but first + + align:start position:0% +I'll give into that later but first + + + align:start position:0% +I'll give into that later but first +assessment yeah don't what but so when + + align:start position:0% +assessment yeah don't what but so when + + + align:start position:0% +assessment yeah don't what but so when +you said the policy network is use is + + align:start position:0% +you said the policy network is use is + + + align:start position:0% +you said the policy network is use is +that use when you're navigating to the + + align:start position:0% +that use when you're navigating to the + + + align:start position:0% +that use when you're navigating to the +tree to get to a leaf or as a policy + + align:start position:0% +tree to get to a leaf or as a policy + + + align:start position:0% +tree to get to a leaf or as a policy +network being used to do the simulation + + align:start position:0% +network being used to do the simulation + + + align:start position:0% +network being used to do the simulation +once your athlete or so the fast policy + + align:start position:0% +once your athlete or so the fast policy + + + align:start position:0% +once your athlete or so the fast policy +so the slow policy is using + + align:start position:0% +so the slow policy is using + + + align:start position:0% +so the slow policy is using +done for this part then the fastball C + + align:start position:0% +done for this part then the fastball C + + + align:start position:0% +done for this part then the fastball C +is used for the simulation because the + + align:start position:0% +is used for the simulation because the + + + align:start position:0% +is used for the simulation because the +slope LC does take a thousand five + + align:start position:0% +slope LC does take a thousand five + + + align:start position:0% +slope LC does take a thousand five +hundred times faster than writing the + + align:start position:0% +hundred times faster than writing the + + + align:start position:0% +hundred times faster than writing the +slope takes a thousand five hundred + + align:start position:0% +slope takes a thousand five hundred + + + align:start position:0% +slope takes a thousand five hundred +times longer than the fast policy you + + align:start position:0% +times longer than the fast policy you + + + align:start position:0% +times longer than the fast policy you +don't want to use that in your + + align:start position:0% +don't want to use that in your + + + align:start position:0% +don't want to use that in your +simulations that would just take away + + align:start position:0% +simulations that would just take away + + + align:start position:0% +simulations that would just take away +too long + + align:start position:0% +too long + + + align:start position:0% +too long +listen it's basically just a way of + + align:start position:0% +listen it's basically just a way of + + + align:start position:0% +listen it's basically just a way of +making it so our simulation isn't + + align:start position:0% +making it so our simulation isn't + + + align:start position:0% +making it so our simulation isn't +completely random it's had some sort of + + align:start position:0% +completely random it's had some sort of + + + align:start position:0% +completely random it's had some sort of +educated news all right so why use your + + align:start position:0% +educated news all right so why use your + + + align:start position:0% +educated news all right so why use your +policy am ninety numbers in Turkey why + + align:start position:0% +policy am ninety numbers in Turkey why + + + align:start position:0% +policy am ninety numbers in Turkey why +can we just use the policy network why + + align:start position:0% +can we just use the policy network why + + + align:start position:0% +can we just use the policy network why +can't we just use a value memory well we + + align:start position:0% +can't we just use a value memory well we + + + align:start position:0% +can't we just use a value memory well we +have a value now that alone well + + align:start position:0% +have a value now that alone well + + + align:start position:0% +have a value now that alone well +actually it's this side point remember + + align:start position:0% +actually it's this side point remember + + + align:start position:0% +actually it's this side point remember +the value number to learn from the + + align:start position:0% +the value number to learn from the + + + align:start position:0% +the value number to learn from the +policy network and then also later on + + align:start position:0% +policy network and then also later on + + + align:start position:0% +policy network and then also later on +the policy network is improved by our + + align:start position:0% +the policy network is improved by our + + + align:start position:0% +the policy network is improved by our +values and so they kind of work hand in + + align:start position:0% +values and so they kind of work hand in + + + align:start position:0% +values and so they kind of work hand in +hand but if you have the value nugget + + align:start position:0% +hand but if you have the value nugget + + + align:start position:0% +hand but if you have the value nugget +alone when we're deciding on the next + + align:start position:0% +alone when we're deciding on the next + + + align:start position:0% +alone when we're deciding on the next +move we would have to evaluate every + + align:start position:0% +move we would have to evaluate every + + + align:start position:0% +move we would have to evaluate every +single move which would take forever and + + align:start position:0% +single move which would take forever and + + + align:start position:0% +single move which would take forever and +so what the policy network does is + + align:start position:0% +so what the policy network does is + + + align:start position:0% +so what the policy network does is +predict busy predicts the best move with + + align:start position:0% +predict busy predicts the best move with + + + align:start position:0% +predict busy predicts the best move with +this probability distribution and it + + align:start position:0% +this probability distribution and it + + + align:start position:0% +this probability distribution and it +narrows our search space and then if you + + align:start position:0% +narrows our search space and then if you + + + align:start position:0% +narrows our search space and then if you +have the policy network alone we unable + + align:start position:0% +have the policy network alone we unable + + + align:start position:0% +have the policy network alone we unable +to compare nodes in different parts of + + align:start position:0% +to compare nodes in different parts of + + + align:start position:0% +to compare nodes in different parts of +our tree right so the pulse in our + + align:start position:0% +our tree right so the pulse in our + + + align:start position:0% +our tree right so the pulse in our +network is able to tell us a + + align:start position:0% +network is able to tell us a + + + align:start position:0% +network is able to tell us a +distribution over which movie should + + align:start position:0% +distribution over which movie should + + + align:start position:0% +distribution over which movie should +take from a certain node but then if I + + align:start position:0% +take from a certain node but then if I + + + align:start position:0% +take from a certain node but then if I +ask if I've been a better position here + + align:start position:0% +ask if I've been a better position here + + + align:start position:0% +ask if I've been a better position here +than in some other place it won't know + + align:start position:0% +than in some other place it won't know + + + align:start position:0% +than in some other place it won't know +and that's where the value that would + + align:start position:0% +and that's where the value that would + + + align:start position:0% +and that's where the value that would +come in to give us a estimated number + + align:start position:0% +come in to give us a estimated number + + + align:start position:0% +come in to give us a estimated number +was of a value assignment of an + + align:start position:0% +was of a value assignment of an + + + align:start position:0% +was of a value assignment of an +evaluation of that node and then these + + align:start position:0% +evaluation of that node and then these + + + align:start position:0% +evaluation of that node and then these +values are later used to direct our tree + + align:start position:0% +values are later used to direct our tree + + + align:start position:0% +values are later used to direct our tree +searches based on updating the policy + + align:start position:0% +searches based on updating the policy + + + align:start position:0% +searches based on updating the policy +once it realizes like I thought this + + align:start position:0% +once it realizes like I thought this + + + align:start position:0% +once it realizes like I thought this +would be a good path but the value is + + align:start position:0% +would be a good path but the value is + + + align:start position:0% +would be a good path but the value is +this so update on that then why do we + + align:start position:0% +this so update on that then why do we + + + align:start position:0% +this so update on that then why do we +combine neural networks with medicines + + align:start position:0% +combine neural networks with medicines + + + align:start position:0% +combine neural networks with medicines +yes remember the policy dr. Bowen played + + align:start position:0% +yes remember the policy dr. Bowen played + + + align:start position:0% +yes remember the policy dr. Bowen played +against Pachi which was purely MCTS and + + align:start position:0% +against Pachi which was purely MCTS and + + + align:start position:0% +against Pachi which was purely MCTS and +it did pretty well all right + + align:start position:0% +it did pretty well all right + + + align:start position:0% +it did pretty well all right +so how does that teach us improve our + + align:start position:0% +so how does that teach us improve our + + + align:start position:0% +so how does that teach us improve our +policy network well remember NCGS did + + align:start position:0% +policy network well remember NCGS did + + + align:start position:0% +policy network well remember NCGS did +win a 15% of those games so already that + + align:start position:0% +win a 15% of those games so already that + + + align:start position:0% +win a 15% of those games so already that +means you think there's some something + + align:start position:0% +means you think there's some something + + + align:start position:0% +means you think there's some something +there that maybe the policy network is + + align:start position:0% +there that maybe the policy network is + + + align:start position:0% +there that maybe the policy network is +missing also the policy network is just + + align:start position:0% +missing also the policy network is just + + + align:start position:0% +missing also the policy network is just +prediction so by using this tree + + align:start position:0% +prediction so by using this tree + + + align:start position:0% +prediction so by using this tree +structure we're able to use these months + + align:start position:0% +structure we're able to use these months + + + align:start position:0% +structure we're able to use these months +power rollouts to adjust our policy to + + align:start position:0% +power rollouts to adjust our policy to + + + align:start position:0% +power rollouts to adjust our policy to +move towards notes that are actually + + align:start position:0% +move towards notes that are actually + + + align:start position:0% +move towards notes that are actually +evaluated to be good and then had a + + align:start position:0% +evaluated to be good and then had a + + + align:start position:0% +evaluated to be good and then had a +neural network events yes this point + + align:start position:0% +neural network events yes this point + + + align:start position:0% +neural network events yes this point +should probably be clear by now the were + + align:start position:0% +should probably be clear by now the were + + + align:start position:0% +should probably be clear by now the were +a bit more intelligently made our 2d + + align:start position:0% +a bit more intelligently made our 2d + + + align:start position:0% +a bit more intelligently made our 2d +exploration our simulations are more + + align:start position:0% +exploration our simulations are more + + + align:start position:0% +exploration our simulations are more +reflective of actual games and the value + + align:start position:0% +reflective of actual games and the value + + + align:start position:0% +reflective of actual games and the value +network in the value network and our + + align:start position:0% +network in the value network and our + + + align:start position:0% +network in the value network and our +simulation value are complementary which + + align:start position:0% +simulation value are complementary which + + + align:start position:0% +simulation value are complementary which +I mentioned before and just sort of + + align:start position:0% +I mentioned before and just sort of + + + align:start position:0% +I mentioned before and just sort of +highlight that basically the value + + align:start position:0% +highlight that basically the value + + + align:start position:0% +highlight that basically the value +number is going to give us a value that + + align:start position:0% +number is going to give us a value that + + + align:start position:0% +number is going to give us a value that +is reflective of as if we played the SLO + + align:start position:0% +is reflective of as if we played the SLO + + + align:start position:0% +is reflective of as if we played the SLO +policy the whole time and the simulation + + align:start position:0% +policy the whole time and the simulation + + + align:start position:0% +policy the whole time and the simulation +is if we use the faster of policy so + + align:start position:0% +is if we use the faster of policy so + + + align:start position:0% +is if we use the faster of policy so +they kind of are complimentary and I + + align:start position:0% +they kind of are complimentary and I + + + align:start position:0% +they kind of are complimentary and I +know I'm over time so just want to skim + + align:start position:0% +know I'm over time so just want to skim + + + align:start position:0% +know I'm over time so just want to skim +through the statue of alphago + + align:start position:0% +through the statue of alphago + + + align:start position:0% +through the statue of alphago +distributed alphago 177 percent of the + + align:start position:0% +distributed alphago 177 percent of the + + + align:start position:0% +distributed alphago 177 percent of the +games against regular alphago so it's + + align:start position:0% +games against regular alphago so it's + + + align:start position:0% +games against regular alphago so it's +the only thing that he dragged off ago + + align:start position:0% +the only thing that he dragged off ago + + + align:start position:0% +the only thing that he dragged off ago +and then distributed alphago won 100 + + align:start position:0% +and then distributed alphago won 100 + + + align:start position:0% +and then distributed alphago won 100 +percent of the games against all these + + align:start position:0% +percent of the games against all these + + + align:start position:0% +percent of the games against all these +so in a rematch against Pocky now that + + align:start position:0% +so in a rematch against Pocky now that + + + align:start position:0% +so in a rematch against Pocky now that +we've added MCTS to our policy number + + align:start position:0% +we've added MCTS to our policy number + + + align:start position:0% +we've added MCTS to our policy number +can we have our value network we + + align:start position:0% +can we have our value network we + + + align:start position:0% +can we have our value network we +slaughtered plot to you hundred percent + + align:start position:0% +slaughtered plot to you hundred percent + + + align:start position:0% +slaughtered plot to you hundred percent +then we decided to see how we fare + + align:start position:0% +then we decided to see how we fare + + + align:start position:0% +then we decided to see how we fare +against humans and by we I mean not me I + + align:start position:0% +against humans and by we I mean not me I + + + align:start position:0% +against humans and by we I mean not me I +mean + + align:start position:0% +mean + + + align:start position:0% +mean +Google and they won 4 to 1 and VC all + + align:start position:0% +Google and they won 4 to 1 and VC all + + + align:start position:0% +Google and they won 4 to 1 and VC all +greeting was 3520 and so now he goes + + align:start position:0% +greeting was 3520 and so now he goes + + + align:start position:0% +greeting was 3520 and so now he goes +raiding accustomed to be about 3586 to + + align:start position:0% +raiding accustomed to be about 3586 to + + + align:start position:0% +raiding accustomed to be about 3586 to +like eat the best dude except we did it + + align:start position:0% +like eat the best dude except we did it + + + align:start position:0% +like eat the best dude except we did it +because there's another dude who has an + + align:start position:0% +because there's another dude who has an + + + align:start position:0% +because there's another dude who has an +even higher score can't we 3621 and I + + align:start position:0% +even higher score can't we 3621 and I + + + align:start position:0% +even higher score can't we 3621 and I +think this ok this should be the last + + align:start position:0% +think this ok this should be the last + + + align:start position:0% +think this ok this should be the last +part because this a time line basically + + align:start position:0% +part because this a time line basically + + + align:start position:0% +part because this a time line basically +EXO checkers were conquered in 50 looks + + align:start position:0% +EXO checkers were conquered in 50 looks + + + align:start position:0% +EXO checkers were conquered in 50 looks +like about 40 years later conquered + + align:start position:0% +like about 40 years later conquered + + + align:start position:0% +like about 40 years later conquered +checkers chess then we scroll down to + + align:start position:0% +checkers chess then we scroll down to + + + align:start position:0% +checkers chess then we scroll down to +2015 is when alphago was able to beat + + align:start position:0% +2015 is when alphago was able to beat + + + align:start position:0% +2015 is when alphago was able to beat +fan McCree there was a - damn player + + align:start position:0% +fan McCree there was a - damn player + + + align:start position:0% +fan McCree there was a - damn player +which is considered lower down in the + + align:start position:0% +which is considered lower down in the + + + align:start position:0% +which is considered lower down in the +tier of professional go but then we see + + align:start position:0% +tier of professional go but then we see + + + align:start position:0% +tier of professional go but then we see +all his nine damage to the pipe and he + + align:start position:0% +all his nine damage to the pipe and he + + + align:start position:0% +all his nine damage to the pipe and he +was able to beat him like literally last + + align:start position:0% +was able to beat him like literally last + + + align:start position:0% +was able to beat him like literally last +month good job we're done + + align:start position:0% +month good job we're done + + + align:start position:0% +month good job we're done +[Applause] + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/y81AhLQN-NI.txt b/y81AhLQN-NI.txt new file mode 100644 index 0000000000000000000000000000000000000000..f7ebaef00a7d8a706243c0a16deec3f3ad44c715 --- /dev/null +++ b/y81AhLQN-NI.txt @@ -0,0 +1,2754 @@ +OPERATOR: The following content +is provided under a + +Creative Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free, To make a + +donation or view additional +materials from hundreds of MIT + +courses, visit MIT +OpenCourseWare at ocw.mit.edu. + +PROFESSOR: Last time, Professor +Guttag introduced + +the idea of objects and classes +and this wonderful + +phrase called object-oriented +programming. + +And it's a topic I want to pick +up on today, we're going + +to do for the next few lectures, +and it's a topic I + +want to spend some time on +because this idea of capturing + +data and methods, the term we're +going to use for it, but + +data and functions that belong +to that data, things that can + +be used to manipulate them, +is a really powerful one. + +What we're really getting at is +the idea of saying I want + +to have a way of grouping +together information into + +units that make sense. + +So I can go back to one of those +topics we had at the + +beginning, which is the idea +of abstraction, that I can + +create one of those units as a +simple entity, bury away the + +details and write really +modular code. + +And so we're going to +talk about that a + +lot as we go along. + +What we're really doing, or +I shouldn't say what we're + +really doing, a basic piece of +what we're doing, when we talk + +about classes or objects, is +we're doing something that + +Professor Guttag mentioned, +we're defining an + +abstract data type. + +Now what in the world +does that mean? + +Well basically what we're +doing is we're giving + +ourselves the ability to create +data types the same way + +that we have some built-ins, +so we have things like int, + +float, string, these are +built-in data types. + +And if you think about it, +associated with each one of + +those data types is a set +of functions it's + +intended to apply to. + +Sometimes the functions -- +sometimes a function can be + +used on multiple data types, +plus, for example, we saw + +could add strings, or could +add ints, but each one of + +those data types has associated +with it a set of + +functions that are geared +to handling them. + +We want to do the same thing, +but with our data types. + +We want to create data types and +functions, or we're going + +to call them methods, that +are specifically aimed at + +manipulating those +kinds of objects. + +And our goal is then to +basically see how we can build + +systems that take advantage +of that modularity. + +Right, so the fundamental idea +then, is, I want to glue + +together information, I want +to take pieces of data that + +naturally belong together, glue +them together, and attach + +some methods to it. + +And that's, you know, saying +a lot of words, let's do an + +example because it's probably +easiest to see this by looking + +at a specific example. + +So here's the example I'm +going to start with. + +Suppose I want to do little +piece of code that's going to + +do planar geometry, points +in the plane. + +All right, so I want to have +some way of gluing those + +things together. + +Well you know what a point is, +it's got an x- and a y- + +coordinate, it's natural to +think about those two things + +as belonging as a +single entity. + +So an easy way to do this would +be to say, let's just + +represent them as a list. +Just as a 2-list, + +or a list of 2 elements. + +It's easy to think of a point as +just a list of an x- and a + +y- coordinate. + +OK, for example, I might say +point p1 is that list, x is 1, + +y is 2. in fact, if I draw +a little simple -- it's + +basically pointing to that point +in the plane, right, x + +is 1, y is 2. + +OK, fine, there's another way +to represent points on the + +plane now, and that's in +polar form, so this, if + +you like, is Cartesian. + +Another way to represent a point +in a plane is I've got a + +radius and I've got an angle +from the x-axis, right, and + +that's a standard thing +you might do. + +So I might define, for example, +in polar form p 2, + +and let me see, which example +did I do here, we'll make this + +the point of radius 2 and at +angle pi by 2, I'm going to + +make it easy because pi by 2 +is up along this axis, and + +that's basically that point. + +Ok, just fine, it's +no big deal. + +But here now becomes +the problem. + +I've glued things together but +just using a list. Suppose I + +hand you one of these lists. + +How do you know which +kind it is? + +How do you know whether +it's in Cartesian + +form or in polar form? + +You have nothing that identifies +that there, you + +have no way of saying what this +grouping actually means. + +Right, and just to get a sense +of this, let's look at a + +simple little example, so on +your hand-out, you'll see I've + +got a little piece of code that +says assuming I've got + +one of these points, I want to +do things with it, for example + +I might want to add +them together. + +So this first little piece of +code right here says, ok you + +give me 2 points, I'll create +another 1 of these lists and + +I'll simply take the x, sorry +I shouldn't say x, I'm going + +to assume it's the x, the +x-values are the two points, + +add them together, just right +there, the y-values, add them + +together and return that list. +And if I actually run this, + +which I'm going to do -- excuse +me, do it again -- + +OK, you can see that I've +added together and I've + +printed out the value of r, and +I'll just show you that in + +fact that's what I've got. + +This looks fine, right, I'm +doing the right thing. + +Another way of saying it is, +I've actually said, what did I + +use there, (1,2) and (3,1), It's +basically saying there is + +the first point, there's the +second point, add them + +together and I get that point. + +OK, that sounds fine. + +Now, suppose in fact these +weren't x and y glued + +together, these were radius +and angle glued together. + +In that case point p 1 doesn't +correspond to this point, it + +actually corresponds to the +point of radius 2 and angle 1, + +which is about here. + +I think I wrote this down +carefully so I would make sure + +I did it right. + +Sorry, said that wrong, radius +1 and angle 2, 2 radians is a + +little bit more than pi half. + +And the second point is of +radius 3 and angle 1, which is + +up about there. + +So what point, sorry, bad +pun, what point am I + +trying to make here? + +Different understandings of what +that piece means gives + +you different values, and that's +a bit of a problem. + +The second problem is, suppose +actually I had p 1 and p 2 + +were in polar form, and I +ran add points on them. + +This little piece of code +here that I did. + +Does that even make any sense? + +Course not, right? + +You know when you add 2 polar +forms, you add the radii + +together, you don't add the +angles together, you need to + +do it in Cartesian form. + +So what I'm leading up to here +is that we've got a problem. + +And the problem is, that we want +to build this abstract + +data type, but we'd like to +basically know what kind of + +object is it, and what functions +actually belong to + +it, how do we use them? + +And so I'm going to go back to +this idea of a class, and + +let's build the first of these, +and that is shown right + +here on this piece +of your handout. + +I'm going to define a class, +and in particular, what I'm + +going to do, is walk through +what that says. + +So I'm going to now build +an object, it's going to + +represent a point. + +So what does that thing +say up there? + +It's got this funky looking +form, right, it says, I've got + +something that I'm going to +call a class, got that key + +word class right here. + +And I'm going to give it a name, +and right now I'm just + +building a simple piece of it -- +but first of all, what does + +a class do? + +Think of this as, this is +a template for creating + +instances of an object. + +At the moment, it's a really +dumb template. + +I'm going to add to it in +a second, but I want + +to build up to this. + +Right now it's got that second +key word there called pass, + +which is just Python's way +of saying there's an + +empty body in here. + +Right,, we're going to add to +it in a second, but the idea + +is class is going +to be a template + +for creating instances. + +How do I use it? + +Well, I call class just like +a function, and you + +can see that below. + +Having created this thing called +Cartesian point, I'm + +going to create two instances +of it. c p 1 and c p 2. + +Notice the form of it, it's +just the name of the class + +followed by open paren, +close paren, + +treating it like a function. + +What that does, is that it +creates, c p 1 and c p 2 are + +both instances of this +type, specific + +versions of this type. + +For now the way to think about +this is, when I call that + +class definition, it goes off +and allocates a specific spot + +in memory that corresponds +to that instance. + +Right now it's empty, actually +it's not quite empty, it has a + +pointer back to the class. + +And I can give a name to that, +so c p 1 and c p 2 are both + +going to point to that. + +Once I've got that, I can now +start giving some variable + +names, sorry not, rephrase +that, I can give some + +attributes, I can give some + +characteristics to these classes. + +So each instance has some +internal, or will have some + +internal attributes. + +Notice how I did +that up there. + +Having created c p 1 and +c p 2, I had this weird + +looking form here. + +Not so weird, you've actually +seen it before. + +In which I said c p 1 +dot x equals 1.0. + +What's this doing? c p 1 points +to an instance, it + +points to a particular version +of this class. + +And I have now given an internal +variable name x and a + +value associated with that. + +So I've just given +it an x variable. + +All right, c p 1 dot y, I've +said assign that to + +the value 2, 2,0. + +So now c p 1 has inside of +it an x and y value. + +Did the same thing with +c p 2, give it a + +different x and y value. + +Again, remind you, c p 2 +is a different instance + +of this data type. + +All right, when I call the class +definition it goes off + +and finds another spot in +memory, says that the spot I'm + +going to give you a pointer back +to that, give it the name + +c p 2, and then by running these +2 little assignments + +statements here, I've given it +an x and a y value for c p 2. + +So you see why I say it's +a template, right? + +Right now it's a simple +template, but it's a template + +for creating what a class looks +like, and I now have an + +x- and y- value associated with +each instance of this. + +OK, and if I wanted to look at +it, we can come back over + +here, and we can see what does +c p 1 look like, interesting. + +It says some funky stuff, +and says it's a kind + +of Cartesian point. + +And that's going to be valuable +to me when I want to + +get back to using these +things, right? + +You see that little thing says +dot Cartesian point in there. + +If I want to get out right now +the versions of these things, + +I can ask what's the value +of c p 1 x, and it + +returns it back out. + +I could say c p 2 dot x, that +was a bad one to use because + +they use the same valuable +in both places, didn't I? + +So let's do c p 1 dot +y, c p 2 dot y. + +OK, so I've just created local +versions of variables with + +each one of these objects. + +I can get at them just like I +would before, I can assign + +them in as I might +have done before. + +OK, now that I've got that, we +could think about what would I + +want to do with these points? + +Well one thing I might want to +do is say, is this the same + +point or not? + +So the next little piece of code +I've written here, just + +move down to it slightly. + +I've got a little piece of +code called same point. + +And you can look at it. + +What does it say to do? + +It says, if you give me two of +these data objects, I'm going + +to call them p 1 and p 2. + +I'm going to say, gee, is the +x value the same in both of + +them, and if it is, and the y +value's the same, then this is + +the same point, I'm going +to return true. + +Notice the form. + +This is saying, that's a class, +or sorry, an instance + +of a class, and I'm going +to get the x value + +associated with it. + +I going to come back in a second +to how it actually does + +that, but it basically says, get +me x value for p 1, get me + +the x value for p 2, +compare them, just + +as you would normally. + +I've got another little thing +here that I'm going to use a + +little later on that just prints +out values of things. + +OK, let's see what happens +if I do this. + +Let me show you simple +little example. + +I'm going to go over here, and +let me define a couple of + +these things. + +I'm going to say p 1, try it +again, p 1 is a Cartesian, it + +would help if I could type, +Cartesian point, and I'm going + +to say p 1 of x is 3, p 1 of y +is 4, and I'm going to make p + +2 another Cartesian point. + +And I'll give it an x value +of 3 and a y value of 4. + +OK, now I want to say, +are these the same? + +Thing I've got a little +procedure that could do that, + +but you know the simplest thing +I could do is to say + +well, gee, wait a minute, why +don't I just check to see if + +these are the same thing? + +So I can say is p 1 the same +as p 2, using Scheme's + +built-in is comparator. + +Say -- sorry? + +PROFESSOR 2: Part of Python? + +PROFESSOR: Part of Scheme, whoa, +there's a Freudian slip, + +thank you, John. + +I'm showing my age, and my +history here, is p 1 and p 2 + +the same thing? + +Hey, there's a bad English +sentence even worse, now I'm + +really thrown off. + +I'm using Python's is comparator +to say is it the + +same thing? + +It says no. + +But if I say, are p 1 and p 2 +the same point, it says yes. + +And this is a point I +want to stress here. + +So what's going on in this case +is, I want to distinguish + +between shallow equality +and deep equality. + +The first thing is testing +shallow equality. + +What it is doing, that's another +bad English sentence, + +but what it is doing? + +Is is essentially saying, given +2 things, do they point + +to exactly the same referent? + +Or another way of thinking about +it, is remember I said + +when I call that class +definition it creates an + +instance, that's a pointer to +some spot in memory that's got + +some local information +around it. + +Is is saying, do these things +point to exactly the same spot + +in memory, the same instance. + +Deep equality, we get to define, +that's what I did by + +writing same point. + +OK, as I said, I want equality +in the case of points to be, + +are the x- and y- coordinates +the same? + +And I'm actually going to change +it. just to show you + +this point. + +If I do the following, and +I say, I'm going to + +assign p 1 to be p 2. + +What's that doing? + +It's taking the name p 1 and +it's changing its value to + +point to exactly what +p 2 points to. + +And then I say, are they +the same thing? + +Answer's yes, because now they +are pointing to exactly the + +same spot in memory. + +The same instance. + +OK, the reason I'm saying this +is, we have one class + +definition, is a cookie cutter, +it's a template that's + +going to let us build versions +of these things. + +Every time I use it, I'm +creating a new instance, + +that's a different thing +inside of memory. + +And I want to have that because +I want to have lots of + +versions of points. + +OK, now, let's go back +to where I was. + +I said one of the things I want +to do is, I want to have + +different versions of points. + +So I've got now things that +are Cartesian points. + +I could do the same thing, I +could build polar point. + +I wanted to show +it to you here. + +I've got a class called polar +point, which is right there, + +and same kind of thing, I can +create instances of it, and + +then assign to them things like +a radius and an angle, + +make instances of those. + +OK, John? + +PROFESSOR 2: I just want to +maybe mention that in some of + +the reading, you'll see terms +like object equality and value + +equality, instead of shallow +equality and deep equality. + +PROFESSOR: Right, so, this +object, this is, + +right, value quality. + +Right. + +And you will see both +terms used. + +Some people like to use shallow +and deep, object and + +value, but they're talking about +the same thing, which is + +it the same object or is it the +same, in this case, set of + +values, depending on what you +want to define as you use it. + +OK, so as I said, now I can go +off and I could create a + +different class. + +I've got Cartesian points, I +could create a polar points. + +And I'm going to run it in a +sec, but you can see, the same + +kind of idea. + +I define a class call polar +point, I create a couple of + +them, and I give them a +radius and an angle. + +And then I could do things like +again, say, okay having + +done, that let me just run it +here, run that, so I've now + +got polar point 1, and +polar point 2. + +I can say is polar point 1 the +same as polar point 2, and the + +answer should be no. + +And then I could say well, gee, +are they the same point? + +Oops. + +What happened? + +Well it bombed out. + +Because, what was I +expecting to do? + +I was expecting to compare +x- and y- values, + +not radius and angle. + +And so this doesn't know how +to do it, it doesn't have a + +method to deal with it, +so it complains. + +So what's my problem here, and +this is what I want to now + +lead up to. + +I could imagine writing another +function for same + +point, and I have to give it a +name like same point polar, + +and same point Cartesian. + +A different function to compare +polar versions of + +these points. + +But that's starting to +get to be a nuisance. + +What I'd really like to do is to +have 1 representation for a + +point that supports different +ways of getting information + +out, but has gathered within it, +a method or a function for + +dealing with things like how +do I know if it's the same + +point or not. + +So I want to take this idea +classes now, and I want to + +generalize it. + +Right, and that is going to +lead us then to this funky + +looking thing. + +Right there, and I'd +like you to look at + +that in your handout. + +OK, I'm going to go back +and rebuild the class. + +Ok, and again, I'm going +to remind you, the + +class is this template. + +But now I'm going to change +it, so what is that new + +version of class say. + +I'm going to call it +c point just to + +make it a little shorter. + +You can see inside of it, it's +got a set of definitions for + +things like functions. + +And that first one is this kind +of interesting thing, + +it's two underbars, init, +and two underbars. + +Underscores, I guess +is the right way + +to say it, not underbars. + +Right that's a specific name, +and what it basically says is, + +when I call the class +instance. + +That's a bad mistake. + +When I call the class +definition, that is I call c + +point, I'm going to +call it with a + +specific set of arguments. + +And what is it going to +happen is that init is + +going to then apply. + +It's going to apply to +those arguments. + +So let me in fact show +you an example. + +I've got a definition of +Cartesian point, I've got a + +definition of polar point. + +Let me just run these to +get them in there. + +Now let's do the following. + +Let's let p be Cartesian point, +and we'll give it a + +couple of values. + +OK? + +So what happened? + +Notice in the class definition +here, is there, this is the + +first thing that's got called, +and I just called with the + +value for x and the value for +y, and it went off and did + +something for me. + +Does that look right? + +This is where you all hate it, I +get no eye contact anywhere. + +Anything look odd about that? + +I said. + +When I call this class +definition, it calls init, and + +I give it an x and a y value. + +How many arguments +does init take? + +Three. + +How many arguments +did I give it? + +Two. + +What in the world's going on? + +Well, this is a piece of +object-oriented coding that we + +get to talk about +a little bit. + +There's this weird extra +variable in there called self. + +So what is self? + +And I have to admit, I did the +standard thing you do every + +time you run across something +you don't know about, you go + +to Wikipedia. + +So I went and looked up self +in Wikipedia, and I have to + +read it out. + +Wikipedia informs us that the +self is the idea of a unified + +being, which is the source +of an idiosyncratic + +consciousness. + +Moreover, this self is the +agent responsible for the + +thoughts and actions +of an individual to + +which they are ascribed. + +It is a substance which +therefore endures through + +time, thus thoughts and actions +at different moments + +of time may pertain +to the same self. + +OK, how do we code that up? + +Sounds like an AI problem, +I guess right? + +But there's actually hidden in +there an important element, + +and that is, when I create an +instance, I have to be able to + +get access to the things that +characterize that instance. + +I won't say that they're +thoughts and emotions or + +things, but what characterizes +an instance here, it's the + +internal parameters that specify +what is going on. + +So in fact what happens inside +of an object-oriented system, + +and particularly in Python's +object-oriented + +system, is the following. + +When we call init, it's going +to create the instance, all + +right, just as we said before. + +But in particular, it's +going to use self to + +refer to that instance. + +Right, so let me say this +a little differently. + +I have a class definition. + +It's actually an object +somewhere. + +It has inside of it all those +internal definitions. + +When I call that class +definition, it calls init. + +Init creates a pointer +to the instance. + +And then it needs to have access +to that, so it calls + +it, passing in self as the +pointer to the instance. + +That is, it says it has access +to that piece in memory, and + +now inside of that piece of +memory, I can do things like, + +as you see here, define self +dot x to be the value + +passed in for x. + +What's that doing? + +It's saying where's +self pointing to? + +Inside of that structure, create +a variable name x, and + +a value associated with it. + +Notice what I also do here, I +create self dot y, give it a + +value, and then, oh cool, I +can also set up what's the + +radius and angle for this point, +by just doing a little + +bit of work. + +OK, in fact if you look at what +it does there, just put + +the pointer over here, it says, +get the value of x that + +I just stored away, square it, +add it to the value of y + +squared that I just stored away, +and then take square + +root, pass it back out. + +So I just computed the radius +of that particular thing. + +Right? + +Compute the angle the same +way, just using the + +appropriate things. + +So the idea is that self +will always point to + +the particular instance. + +Now you might say, why? + +Why do it this way? + +Well, basically because it was +a design choice when the + +creators of Python decided to +create the language, they + +basically said, we're always +going to have an explicit + +pointer to the instance. + +Some other object-oriented +programming languages do not + +provide that pointer. + +This is kind of nice in my view, +I don't know if John, + +you'd agree, but this +is explicit. + +It actually lets you see how to +get access to that pointer + +so you know what you're +referring to. + +But it's simply design choice. + +So another way saying it again +is, when I call the class + +definition, by default I'm going +to look to see is there + +an init method there, and if +there is, I'm going to use it. + +First argument by convention is +always self, because it has + +to point to the instance, and +then I pass, in this case, + +another couple of +arguments in. + +OK, now, if I actually do this, +and I'm going to show + +you the example, I just, what +did I type over there, I got p + +was a c point. + +If I want to get values back +out, I could in fact simply + +send to that instance a message, +in this case I could + +say p dot x. + +In fact let's do it. + +If I do that over here -- aha -- +it gets me back the value. + +Now let me spend just a second +to say, what was this actually + +doing? p is an instance. + +It knows, or has stored away, +and in fact let's look at it, + +if we look at what p does, +p says -- it says reading + +through a little bit of this +stuff here, it says -- it's a + +kind of Cartesian point, it's an +instance, there's actually + +the memory location that it's +at, that's why I say this idea + +of it's an instant at +a specific spot. + +It knows that it came from +this class, c point. + +So when I type, I'm sorry, I +shouldn't say type, when I + +write, although I would have +typed it, p dot x, here's what + +basically happens. p is an +instance, it's being sent a + +message, in this case the +message x, it says I want the + +x-value back out. p knows that +it is a kind of Cartesian + +point, it actually goes and +gets, if you like, the class + +definition up here. + +And is able to then say, +inside of that class + +definition, find +the value of x. + +All right, now, that's one of +the ways we could get things + +out, but in fact it's really +not a good way. + +A better way to do this would +be the following. + +If I could type. + +What did I just do there? + +One of the things that I +defined inside my class + +definition here was an +internal method. + +That method has a name, +obviously, and + +what does it do? + +It's going to go off and get the +values of x and y attached + +to this thing and return +them to me. + +And that's one of the +things I want. + +I would like my classes +to have methods. + +So you can access the values +of the specific instance. + +Now, this is still a nuance, why +would I like to do this? + +Well this is leading up to why +I want to gather things + +together in classes +to start with. + +It's perfectly legal in Python +to type that in and get the + +value back out. + +As I said, I would prefer to +do something that uses an + +accessor that I just wrote. + +So p dot Cartesian is a kind +of accessor, it's getting + +access to the data. + +And here's why I'd +like to have it. + +Right now, I still have the +problem that those classes, + +those instances of classes, +are exposed. + +What do I mean by that? + +Here's something I could do. + +Let's do it in fact. + +OK. + +What point in the plane +does p now point to? + +X-axis is foobar y-axis +ought to be foobass + +something else, right? + +I know it looks like a simple +and silly little example, but + +at the moment, I still have +the ability to go in and + +change the values of the +parameters by that little + +definition. + +And this makes no sense. + +And this is because I don't have +something I would really + +like to have, which +is data hiding. + +So you'll see lots of +definitions of this. + +I think of data hiding as +basically saying, one can only + +access instance values, or, +we'll call them that, instance + +values through defined +methods. + +And that's a wonderful thing to +have because it gives you + +that modularity, that +encapsulation that basically + +says, when I create a point, the +only way I can get at the + +values, is by using one of the +defined methods, in this case + +it could be Cartesian, and get +all the pieces of that. + +Unfortunately, Python +doesn't do this. + +Which is really a shame. + +Or another way of saying it +is, please don't do that. + +Don't go in and change the +values of things by using the + +direct access. + +Have the computational hygiene, +if you like, to only + +go through accessors, only go +through methods that are + +actually provided to +you as you do this. + +I actually don't remember, +John, C++ does have data + +hiding, I think, right? + +PROFESSOR 2: And not only +shouldn't you change it, you + +shouldn't even read it. + +PROFESSOR: Exactly. + +What you're going to see in a +second I violated in some of + +my code, which Professor Guttag +is going to yell at me + +shortly because I should have +done it through accessors, + +but, he's exactly right. + +A good, hygienic way of doing +this is, not only do I not go + +in and change things except +through a pre-defined method, + +I shouldn't read it other than +through a pre-defined method. + +I should use Cartesian +or polar to pull out + +those pieces of it. + +Once I've got that, you notice +I can now define a polar + +point, same way. + +Notice I've now solved one of my +problems, which is, in each + +one of these cases here, I'm +creating both x y and radius + +angle values inside of there. + +If it's in polar form I passed +in a radius and angle and I'll + +compute what the x- +and y- value is. + +If its in Cartesian form I'll +pass in an x and y and compute + +what a radius and angle is. + +But it now says that in any, in +no matter what kind of form + +I made it from, I can get out +that kind of information. + +So for example I defined p, +remember back over here, as a + +Cartesian point, but +I can actually ask + +for its polar form. + +It's there accessible to me. + +OK, this is great. + +Just to drive home one more +reason why I don't want to + +have changes to the +values other than + +through pre-defined things. + +Notice what happens if +I do the following. + +I could say I want to +change the radius of + +this particular thing. + +OK, perfectly reasonable +thing to do. + +And if I go look at the polar +form of this, OK, good, looks + +right, right? + +It's now got a different radius, +same angle, so I just + +changed the radius of it. + +Oh, but what happened to +the Cartesian form. + +I should have done this +earlier by typing the + +Cartesian form earlier, so let +me go back to where I was, + +sorry for that, let me go +make this a 1 again. + +If I look at the Cartesian, oh, +I did have the Cartesian + +form, don't mind me while I +mutter to myself here quietly. + +Yeah, that's right, I did +screw that up badly. + +All right, we try one more time, +here we go, let's try + +one more time. + +We'll make p a new point, ok? + +There's the Cartesian +representation of it, which is + +right, (1,2). + +Here's the polar representation +of it, some + +random set of numbers +which makes sense. + +If I now say, I'm going to go +ahead and change the radius of + +this, something, my polar form +did it right, but what + +happened to the Cartesian +form? + +Ah yes, didn't change. + +Which makes sense if you +think of my code. + +I didn't have anything in there +that says, if you change + +one of these values, other +values depend on it, and I + +want to make that +change to it. + +So this is one more example of +stressing why I only want to + +come access to the instances +through defined methods. + +Because I could've built that +in, it says if you change the + +value of this thing, by the +way you need to change + +recompute those other values in +order to make this hold up. + +OK, so what else do I have +then in my little class + +definitions here? + +So, I've got an init +in both cases. + +I don't have to put an init in, +but it's again, usually a + +good idea to put that +in originally. + +I've got and init that says, +when you create an instance, + +here's what you do. + +Notice that that typically also +defines for me what the + +internal variables are, what the +internal characteristics + +of the class are going to be. + +Again, I could have some other +functions to compute things, + +but this is typically +the place where I'm + +going to put them in. + +So this is giving me now that +template, better way of saying + +it, all right, a template +now, for a point is + +x, y, radius, angle. + +And I can see that in +those pieces there. + +And then I've got some things +that get me back out + +information about them. + +But I got a couple of other of +these strange looking things + +in there with underbars +to them. + +So let's look at what some of +the traditional methods for + +classes are in Python. + +I have init. + +This is what's actually going +to create the instance, + +instantiate it, create what +the set of variable + +values are for it. + +OK, I have another +one in there, + +underbar, underbar, str. + +Anybody have a sense of +what that's doing? + +What's s -- sorry, I heard +something, sorry go ahead. + +STUDENT: Display what I have. + +PROFESSOR: Displaying what +I have. Thank you. + +Yeah, I was going to say, think +about what does str do, + +in general? + +It converts things into +a string type. + +How do we typically +print things, we + +convert them to strings. + +So str is basically telling +us how we want to + +have it printed out. + +OK, in fact if we look at this, +if I say, print of p, it + +prints it out in that form. + +Now this is actually a poor +way to do it, because you + +might say, well, it's just the +list. But remember, it wasn't + +a list. What does it do? + +It says, if I want to print +out something I built in + +Cartesian form up here, says, +again, I'm going to pass it in + +a pointer to the instance, that +self thing, and then I'm + +going to return a string that +I combine together with an + +open and close paren, a comma in +the middle, and getting the + +x-value and the y-value and +converting them into strings + +before I put the whole +thing together. + +So it gives me basically my +printed representation. + +OK. + +What else do I have in here? + +Well, I have cmp. + +My handout's wrong, which I +discovered this morning after + +I printed them all out. + +So the version I'd like you to +have uses, that, greater than + +rather than equals that +I had in my handout. + +What's cmp doing as a method? + +Yeah? + +STUDENT: Comparing values? + +PROFESSOR: Yeah, comparing +values, right? + +And again, it's similar +to what cmp would do + +generically in Python. + +It's a way of doing +comparisons. + +So this is doing comparisons. + +Now, I put a version up there, +I have no idea if this is the + +right way to do comparisons +or not. + +I said both the x- and y- +coordinates are bigger, then + +I'm going to return +something to it. + +And I think in the polar one I +said, if, what did I do there, + +I said, yeah, again if the x +and y are greater than the + +other one, I'm going to +return them to it. + +The version in the handout, what +was that actually doing? + +You could look at the handout. + +Well I think it was comparing, +are they the same? + +So that would actually be +another method I could put in. + +Underbar underbar eq, +underbar underbar. + +Would be a default or generic +way of doing, are + +these things the same? + +OK, in each case, what these +things are doing, is they're + +doing, what sometimes gets +referred to as operator + +overloading. + +I know you don't remember that +far back, but in about the + +second lecture I made a joke of +Professor Guttag which, you + +know, you didn't laugh at, he +didn't laugh at, that's okay. + +In which I said, you know, I +didn't like the fact that + +things like plus are overloaded, +because you can + +use plus to add strings, you can +use plus to add numbers, + +you can use plus +to add floats. + +And he quite correctly, because +he's more senior than + +I am, more experienced +than I am, said it's + +actually a good thing. + +And he's right. + +Most of the time. + +The reason I say that is, by +having operator overloading I + +can use 1 generic interface +to all of the objects + +that I want to use. + +So it makes sense to be able to +say, look for many methods + +I do want to have a way of doing +comparison, and I don't + +have to remember, at top level, +what the name of the + +comparison method was. + +I can simply use the built-in +Sc -- about to say Scheme + +again -- the built-in Python +comparison operation. + +Say, are these 2 things +the same? + +Same thing with cmp, that's just +saying greater than, and + +greater than now can apply to +strings, it can apply to + +floats, it could apply to +points, it could add other + +pieces into it. + +So there are some downsides, in +my view, to doing operator + +overloading, but there's +some real pluses. + +And the main one is, I get to +just decide, how do I want to + +use this, and call it. + +Yes, ma'am? + +STUDENT: [INAUDIBLE] + +PROFESSOR: Right, cmp other, +so how would I call this? + +A good question. + +Here's the way I +would call it. + +Let me give you, I'm going to +create, a polar point, I'm + +going to call it q, and we'll +give it some random values. + +OK, and now I want to know, +is p greater than q? + +Now happens to return true here, +but the question is, + +where's the other come from? + +P is a particular object type. + +When I try and evaluate that +expression of greater than, is + +going to go into the class +to say greater + +than is a comp method. + +So let me say it very +carefully here. + +When I evaluate, yeah, when +I evaluate this, p is an + +instance of a point, in this +case it was actually a + +Cartesian point, it sends a +message to the instance, which + +sends a message to the +class, to get the cmp + +method from the class. + +And that then gets applied to +itself, just p, and one other + +argument, which is the second +piece there, so other points + +to the second argument +that was present. + +OK. + +John? + +PROFESSOR 2: -- other, +it could have said + +who or zort or -- + +PROFESSOR: Yeah, sorry, that +was part of the question, I + +could have a picked foobar could +put anything in here. + +It's simply, notice the form of +it here is, it's going to + +take two arguments, and +you're right, self is + +the original instance. + +This says, I need a second +argument to it, and that + +second argument better be +a point so I can do the + +comparison. + +Yes ma'am? + +STUDENT: [INAUDIBLE] + +PROFESSOR: What do you +think happens? + +Sorry, the question was, what +happens if I said p + +is less than q? + +Got it, yes? + +Seems pretty obvious, right? + +Next time I bring the +right glasses. + +It's still calling cmp, but it's +knowing that cmp is just + +reversing the order +of the arguments. + +Ok, which makes sense. + +If greater than takes, expects, +arguments in order x + +y, less than simply takes +greater than, but with the + +arguments reversed. + +OK, so I don't have to, it's a +great question, I don't have + +to create a second +one for cmp. + +Cmp is just saying, is this +bigger than, and if I want to + +reverse it, it goes +the other way. + +Question? + +STUDENT: [INAUDIBLE] + +PROFESSOR: Or equal equal? + +Let's try equal equal because +I didn't define it here. + +It says they're not the same, +and boy, I need help on this + +one, John, it's not, there's +no pre-defined eq in there. + +PROFESSOR 2: So, what cmp does, +and maybe this isn't + +exactly the right way to write +is, is cmp actually returns 1 + +of 3 values. + +A 0, minus a positive value, +zero or a negative value, + +depending upon whether +it's less than, + +equal, or greater than. + +PROFESSOR: Right. + +PROFESSOR2: So it's not really +a Boolean-valued function. + +It has 3 possible values +it could return. + +PROFESSOR: And so in this case, +it's using the same + +piece, but it's returning that +middle value that says they're + +actually the same. + +Right, one the things you can +see now is, we start building + +up classes, we get +these methods. + +So you can actually say, how +do I know which methods are + +associated with the class? + +For that, we can call dir. + +And what it does, is it gives +me back a listing of all the + +things, all the methods, that +are associated with it. + +Some of which I built: +cmp, init, str. + +And there, notice, are the +internal definitions and there + +are the internal variables. + +And in fact I should've +said, we often call + +those things fields. + +So inside of an instance, +associated with an instance, + +we have both methods +and fields. + +These are both altogether +called + +attributes of the instance. + +And then there were a couple of +other ones in there that I + +hadn't actually dealt with. + +The reason I want to point this +out to you is, if we go + +back up to the kinds of data +objects we started with, + +floats, ints, strings, they +actually behave the same way. + +They are instances of a class, +and associated with that class + +is a set of methods. + +So for example, I can say, +what are all the methods + +associated with the number, +or the integer 1? + +And you probably recognize some +of them in there, right, + +absolute value, add, comp, cors, +well we didn't do cors, + +we did a bunch of +other things. + +It could also say, what are the +methods associated with + +the string, 1. + +I'm sure you can quickly +graph it, but notice + +they aren't the same. + +That makes sense. + +We have some set of things we +want to do with strings, and + +different set of things we +want to do with numbers. + +But underlying Python +is the same idea. + +These are instances of a class, +and associated with + +that class are a set +of methods, things + +that I can deal with. + +So this is a handy way of being +able to see, what are in + +fact the methods that are +available if I don't happen to + +remember them, and want +to go back to them. + +OK, I want to spend the last few +minutes just showing you a + +couple of other things that +we can do in here. + +Let me see where I want +to go with this. + +So let's add one more +piece to this. + +OK, now that I've got points, +I might want to do something + +with points. + +So an easy thing to do in planar +geometry is I want to + +make a line segment. + +It's got a start point, +it's got an end point. + +Right, if you want to think +of it back over here. + +There's a line segment, it's +got a starting point and + +ending point. + +Well, I can do the same thing. + +And the reason I want to use +this as an example is, here's + +my little definition +of segment. + +Again, it's got an initializer, +or an instance + +creator, right there. + +Takes a start and an end point, +just going to bind + +local variable names start +and end to those pieces. + +But notice now, those aren't +just simple things like + +numbers, those are +actually points. + +And that's where the modularity +comes in. + +Now I have the ability to say, +I've got a new class, I can + +create instances of a line +segment, and it's elements are + +themselves instances of points. + +OK? + +And then what might I want +to do with the segment? + +I might want to get the +length of the segment. + +And I know it's kind of, you can +see it on your handout, it + +has the rest of the +pieces over here. + +Ok, what's the geometry say? + +The length of a line segment? + +Well, it's Pythagoras, right? + +I take the difference in the +x-values, squared, the + +difference in the y-values, +squared, add them up, take the + +square root of that. + +Notice what this says to do. + +It says if I want to get the +length of a segment, going to + +pass in that instance, it says +from that instance, get the + +start point, that's the +thing I just found. + +And then from that start +point, get the x-value. + +Same thing, from that instance, +get the endpoint, + +from that end point get +the x-value, square. + +Add the same thing to the +y-values, squared, take the + +square root. + +Yes, ma'am? + +STUDENT: So are you entering a +tuple in for start and end? + +PROFESSOR: No. + +I'm entering -- well, +let's look at the + +example right down here. + +In fact, let me uncomment +it so we can look at it. + +All right. + +I'm going to uncomment that. + +So notice what I'm +going to do. + +I'm going to build, this case, +a Cartesian point, I'm going + +to build a second Cartesian +point, and my segment passes + +in those class instances. + +All right, they're not tuples, +they're simply an instance + +with some structuring. + +And in fact if I go off and +run this, OK, what I was + +printing here was s 1 dot +length, and that's -- + +What is it doing? + +S 1 is a segment. + +It has inside of it +pointers to 2 + +points which are instances. + +And when I call length on this, +it takes that starting + +point, sends it the message +saying give me your + +x-coordinate, takes the +endpoint, says give me your + +x-coordinate, and add +them together. + +Now, I prefaced this a few +minutes ago about saying + +Professor Guttag wasn't +going to like me. + +He doesn't like me generally, +but that's between he and I. + +He beats me regularly at +tennis, which is why + +I don't like him. + +Sorry, John. + +This is being taped, which +is really good, isn't it? + +So why am I saying that? + +I said that if I was really +hygienic, and you can now + +wonder about how often +do I shower? + +If I was really hygienic. + +I would only ever access the +values through a method. + +And I'm cheating here, right, +because what am I doing? + +I'm taking advantage of the fact +that start is going to be + +a point, and I'm just directly +saying, give me your x-value. + +So I don't know don't, John, I +would argue if I'd written + +this better, I would have had a +method that returned the x- + +and the y- value, and it +would be cleaner to go + +after it that way. + +This is nice shorthand, all +right, but it's something that + +in fact I probably would +want to do differently. + +Why would I want to +do it differently? + +Imagine that I've written +code like this, + +written a bunch of code. + +And I originally decided I was +going to have as points, it's + +going to have internal values +of an x and a y. + +And then somewhere along the +line, I decide to store things + +in a different representation. + +If I had had a clean interface, +that I had a + +specific method to get those +values out, I wouldn't have to + +change anything. + +Other than that interface. + +But here, if I decide I'm going +to store things not in x + +and y, but with some other set +of names, for example, I've + +gotta go back into these pieces +of code that use the + +points, and change them. + +So I've lost modularity. + +I'd really like to have that +modularity that says, I'm only + +going to get access to the +values, not by calling their + +names, but by calling some +specific method to get access + +to their names. + +You could argue, well, x is +in some sense inherently a + +method, but it's not nearly as +clean as what I would like. + +And the last piece I want you to +see here, and then I'll let + +you go is, notice now how that +encapsulation, that binding + +things together has +really helped me. + +Given the abstraction, the +notion of a point as an + +instance with some +values, I can now + +start building segments. + +And I could now extend that. + +I could have, you know, +polygonal figures, that are a + +sequence of segments. + +And I would be able to simply +bury away the details of how + +those other instances are +created from how I want to use + +them by simply calling methods +on the classes. + +We'll come back to +this next time. \ No newline at end of file diff --git a/ysQ9jcF04Nw.txt b/ysQ9jcF04Nw.txt new file mode 100644 index 0000000000000000000000000000000000000000..7d17d06a27ff00da7b9dec09f51d32283830eb42 --- /dev/null +++ b/ysQ9jcF04Nw.txt @@ -0,0 +1,17835 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +So today we're going to kind of continue + + align:start position:0% +So today we're going to kind of continue + + + align:start position:0% +So today we're going to kind of continue +the story uh that we were looking at + + align:start position:0% +the story uh that we were looking at + + + align:start position:0% +the story uh that we were looking at +um in on Monday's class some of these + + align:start position:0% +um in on Monday's class some of these + + + align:start position:0% +um in on Monday's class some of these +early developments after the end of the + + align:start position:0% +early developments after the end of the + + + align:start position:0% +early developments after the end of the +second World War uh to Grapple with + + align:start position:0% +second World War uh to Grapple with + + + align:start position:0% +second World War uh to Grapple with +Quantum field Theory I try to trying to + + align:start position:0% +Quantum field Theory I try to trying to + + + align:start position:0% +Quantum field Theory I try to trying to +piece together a quantized treatment of + + align:start position:0% +piece together a quantized treatment of + + + align:start position:0% +piece together a quantized treatment of +things like the Maxwell field or + + align:start position:0% +things like the Maxwell field or + + + align:start position:0% +things like the Maxwell field or +electrons and positrons and we saw last + + align:start position:0% +electrons and positrons and we saw last + + + align:start position:0% +electrons and positrons and we saw last +time there were a lot of puzzles some of + + align:start position:0% +time there were a lot of puzzles some of + + + align:start position:0% +time there were a lot of puzzles some of +which had been identified as puzzles uh + + align:start position:0% +which had been identified as puzzles uh + + + align:start position:0% +which had been identified as puzzles uh +well before the war going all the way + + align:start position:0% +well before the war going all the way + + + align:start position:0% +well before the war going all the way +back to the 1920s and 30s like virtual + + align:start position:0% +back to the 1920s and 30s like virtual + + + align:start position:0% +back to the 1920s and 30s like virtual +particles that could borrow energy for + + align:start position:0% +particles that could borrow energy for + + + align:start position:0% +particles that could borrow energy for +temporary periods of time uh which led + + align:start position:0% +temporary periods of time uh which led + + + align:start position:0% +temporary periods of time uh which led +to these sort of infinite + + align:start position:0% +to these sort of infinite + + + align:start position:0% +to these sort of infinite +um Quantum Corrections that when people + + align:start position:0% +um Quantum Corrections that when people + + + align:start position:0% +um Quantum Corrections that when people +try to take into account quantitatively + + align:start position:0% +try to take into account quantitatively + + + align:start position:0% +try to take into account quantitatively +the impact of those virtual particles + + align:start position:0% +the impact of those virtual particles + + + align:start position:0% +the impact of those virtual particles +their equations would blow up they would + + align:start position:0% +their equations would blow up they would + + + align:start position:0% +their equations would blow up they would +encounter these divergences and those + + align:start position:0% +encounter these divergences and those + + + align:start position:0% +encounter these divergences and those +were a big big puzzle uh for for really + + align:start position:0% +were a big big puzzle uh for for really + + + align:start position:0% +were a big big puzzle uh for for really +for for decades it was only very soon + + align:start position:0% +for for decades it was only very soon + + + align:start position:0% +for for decades it was only very soon +after the end of the second world war + + align:start position:0% +after the end of the second world war + + + align:start position:0% +after the end of the second world war +when a newer generation of physicists + + align:start position:0% +when a newer generation of physicists + + + align:start position:0% +when a newer generation of physicists +came back to those older questions but + + align:start position:0% +came back to those older questions but + + + align:start position:0% +came back to those older questions but +now with some new skills new sometimes + + align:start position:0% +now with some new skills new sometimes + + + align:start position:0% +now with some new skills new sometimes +literally new instruments and new ideas + + align:start position:0% +literally new instruments and new ideas + + + align:start position:0% +literally new instruments and new ideas +about how to organize their their + + align:start position:0% +about how to organize their their + + + align:start position:0% +about how to organize their their +calculations so near the end of last + + align:start position:0% +calculations so near the end of last + + + align:start position:0% +calculations so near the end of last +class we looked at some of Julian + + align:start position:0% +class we looked at some of Julian + + + align:start position:0% +class we looked at some of Julian +schwinger's efforts + + align:start position:0% +schwinger's efforts + + + align:start position:0% +schwinger's efforts +in that and today we'll look at some uh + + align:start position:0% +in that and today we'll look at some uh + + + align:start position:0% +in that and today we'll look at some uh +efforts by his contemporary uh Richard + + align:start position:0% +efforts by his contemporary uh Richard + + + align:start position:0% +efforts by his contemporary uh Richard +Feynman and fireman's Circle + + align:start position:0% +Feynman and fireman's Circle + + + align:start position:0% +Feynman and fireman's Circle +so today today's class draws on a book I + + align:start position:0% +so today today's class draws on a book I + + + align:start position:0% +so today today's class draws on a book I +wrote + + align:start position:0% +wrote + + + align:start position:0% +wrote +um 15 years ago it's actually hard to + + align:start position:0% +um 15 years ago it's actually hard to + + + align:start position:0% +um 15 years ago it's actually hard to +believe he's been out for 15 years + + align:start position:0% +believe he's been out for 15 years + + + align:start position:0% +believe he's been out for 15 years +um + + align:start position:0% +um + + + align:start position:0% +um +and so we'll talk + + align:start position:0% +and so we'll talk + + + align:start position:0% +and so we'll talk +um about the book and how it fits into + + align:start position:0% +um about the book and how it fits into + + + align:start position:0% +um about the book and how it fits into +the kind of series of developments we've + + align:start position:0% +the kind of series of developments we've + + + align:start position:0% +the kind of series of developments we've +been talking about throughout uh + + align:start position:0% +been talking about throughout uh + + + align:start position:0% +been talking about throughout uh +throughout the semester and so as usual + + align:start position:0% +throughout the semester and so as usual + + + align:start position:0% +throughout the semester and so as usual +the the class has three main sections + + align:start position:0% +the the class has three main sections + + + align:start position:0% +the the class has three main sections +for today the first is how did these new + + align:start position:0% +for today the first is how did these new + + + align:start position:0% +for today the first is how did these new +Tools in this case Simon's particular + + align:start position:0% +Tools in this case Simon's particular + + + align:start position:0% +Tools in this case Simon's particular +approach to Quantum field Theory + + align:start position:0% +approach to Quantum field Theory + + + align:start position:0% +approach to Quantum field Theory +um how do these new tools enter into + + align:start position:0% +um how do these new tools enter into + + + align:start position:0% +um how do these new tools enter into +circulation how do they become kind of + + align:start position:0% +circulation how do they become kind of + + + align:start position:0% +circulation how do they become kind of +second nature or a standard technique + + align:start position:0% +second nature or a standard technique + + + align:start position:0% +second nature or a standard technique +for um ultimately for essentially the + + align:start position:0% +for um ultimately for essentially the + + + align:start position:0% +for um ultimately for essentially the +entire profession so how did these new + + align:start position:0% +entire profession so how did these new + + + align:start position:0% +entire profession so how did these new +tools be begin to get picked up by + + align:start position:0% +tools be begin to get picked up by + + + align:start position:0% +tools be begin to get picked up by +people other than uh Feynman himself + + align:start position:0% +people other than uh Feynman himself + + + align:start position:0% +people other than uh Feynman himself +and we'll spend a good chunk of time on + + align:start position:0% +and we'll spend a good chunk of time on + + + align:start position:0% +and we'll spend a good chunk of time on +on that today + + align:start position:0% +on that today + + + align:start position:0% +on that today +and then we'll see that once some people + + align:start position:0% +and then we'll see that once some people + + + align:start position:0% +and then we'll see that once some people +did start using them they would often + + align:start position:0% +did start using them they would often + + + align:start position:0% +did start using them they would often +deploy these new tools these paper + + align:start position:0% +deploy these new tools these paper + + + align:start position:0% +deploy these new tools these paper +techniques uh pencil and paper + + align:start position:0% +techniques uh pencil and paper + + + align:start position:0% +techniques uh pencil and paper +techniques often in quite different ways + + align:start position:0% +techniques often in quite different ways + + + align:start position:0% +techniques often in quite different ways +than what Feynman himself had had in + + align:start position:0% +than what Feynman himself had had in + + + align:start position:0% +than what Feynman himself had had in +mind so it's not just that new people + + align:start position:0% +mind so it's not just that new people + + + align:start position:0% +mind so it's not just that new people +had to start using the tools new people + + align:start position:0% +had to start using the tools new people + + + align:start position:0% +had to start using the tools new people +began adapting the tools toward new or + + align:start position:0% +began adapting the tools toward new or + + + align:start position:0% +began adapting the tools toward new or +different ends and what did that mean + + align:start position:0% +different ends and what did that mean + + + align:start position:0% +different ends and what did that mean +for the continuing um conceptual puzzles + + align:start position:0% +for the continuing um conceptual puzzles + + + align:start position:0% +for the continuing um conceptual puzzles +they were they were wrestling with as + + align:start position:0% +they were they were wrestling with as + + + align:start position:0% +they were they were wrestling with as +they tried to continue to make sense of + + align:start position:0% +they tried to continue to make sense of + + + align:start position:0% +they tried to continue to make sense of +high energy physics phenomena and then + + align:start position:0% +high energy physics phenomena and then + + + align:start position:0% +high energy physics phenomena and then +finally we'll ask you just very briefly + + align:start position:0% +finally we'll ask you just very briefly + + + align:start position:0% +finally we'll ask you just very briefly +near the end why did this particular set + + align:start position:0% +near the end why did this particular set + + + align:start position:0% +near the end why did this particular set +of tools actually stick why was it + + align:start position:0% +of tools actually stick why was it + + + align:start position:0% +of tools actually stick why was it +that these tools really became the + + align:start position:0% +that these tools really became the + + + align:start position:0% +that these tools really became the +standard way uh to this to this day that + + align:start position:0% +standard way uh to this to this day that + + + align:start position:0% +standard way uh to this to this day that +physicists all around the world try to + + align:start position:0% +physicists all around the world try to + + + align:start position:0% +physicists all around the world try to +make sense of uh of nature when it + + align:start position:0% +make sense of uh of nature when it + + + align:start position:0% +make sense of uh of nature when it +wasn't so clear they were going to take + + align:start position:0% +wasn't so clear they were going to take + + + align:start position:0% +wasn't so clear they were going to take +off at all so why did this tool come to + + align:start position:0% +off at all so why did this tool come to + + + align:start position:0% +off at all so why did this tool come to +seem like such a natural or winning + + align:start position:0% +seem like such a natural or winning + + + align:start position:0% +seem like such a natural or winning +strategy and that's our kind of + + align:start position:0% +strategy and that's our kind of + + + align:start position:0% +strategy and that's our kind of +three-part + + align:start position:0% +three-part + + + align:start position:0% +three-part +um scope for today + + align:start position:0% +um scope for today + + + align:start position:0% +um scope for today +so some of you many of you by now might + + align:start position:0% +so some of you many of you by now might + + + align:start position:0% +so some of you many of you by now might +might recognize these things you might + + align:start position:0% +might recognize these things you might + + + align:start position:0% +might recognize these things you might +have already had them in some classes if + + align:start position:0% +have already had them in some classes if + + + align:start position:0% +have already had them in some classes if +not you've probably seen them you know + + align:start position:0% +not you've probably seen them you know + + + align:start position:0% +not you've probably seen them you know +uh around these things that we now call + + align:start position:0% +uh around these things that we now call + + + align:start position:0% +uh around these things that we now call +feymen diagrams they are really + + align:start position:0% +feymen diagrams they are really + + + align:start position:0% +feymen diagrams they are really +unavoidable today they are they are + + align:start position:0% +unavoidable today they are they are + + + align:start position:0% +unavoidable today they are they are +literally ubiquitous in fact not only + + align:start position:0% +literally ubiquitous in fact not only + + + align:start position:0% +literally ubiquitous in fact not only +are they all over the place they become + + align:start position:0% +are they all over the place they become + + + align:start position:0% +are they all over the place they become +automatic or automated so there are now + + align:start position:0% +automatic or automated so there are now + + + align:start position:0% +automatic or automated so there are now +um computer routines that will both + + align:start position:0% +um computer routines that will both + + + align:start position:0% +um computer routines that will both +evaluate tens of thousands of them now + + align:start position:0% +evaluate tens of thousands of them now + + + align:start position:0% +evaluate tens of thousands of them now +even on not very fancy laptops + + align:start position:0% +even on not very fancy laptops + + + align:start position:0% +even on not very fancy laptops +um so you have these algorithms to + + align:start position:0% +um so you have these algorithms to + + + align:start position:0% +um so you have these algorithms to +compute very large numbers of finding + + align:start position:0% +compute very large numbers of finding + + + align:start position:0% +compute very large numbers of finding +diagrams quantitatively and also + + align:start position:0% +diagrams quantitatively and also + + + align:start position:0% +diagrams quantitatively and also +routines to draw them they literally + + align:start position:0% +routines to draw them they literally + + + align:start position:0% +routines to draw them they literally +have um the way they look has now become + + align:start position:0% +have um the way they look has now become + + + align:start position:0% +have um the way they look has now become +automated or subject to computer routine + + align:start position:0% +automated or subject to computer routine + + + align:start position:0% +automated or subject to computer routine +as well they're all over the place + + align:start position:0% +as well they're all over the place + + + align:start position:0% +as well they're all over the place +in virtually every subfield of the + + align:start position:0% +in virtually every subfield of the + + + align:start position:0% +in virtually every subfield of the +discipline but many many subfields + + align:start position:0% +discipline but many many subfields + + + align:start position:0% +discipline but many many subfields +anyway and yet of course they have a + + align:start position:0% +anyway and yet of course they have a + + + align:start position:0% +anyway and yet of course they have a +history wasn't always that way our kind + + align:start position:0% +history wasn't always that way our kind + + + align:start position:0% +history wasn't always that way our kind +of present day saturation with these + + align:start position:0% +of present day saturation with these + + + align:start position:0% +of present day saturation with these +things uh is of relatively recent um + + align:start position:0% +things uh is of relatively recent um + + + align:start position:0% +things uh is of relatively recent um +vintage and when they were first + + align:start position:0% +vintage and when they were first + + + align:start position:0% +vintage and when they were first +introduced in in the Years soon after + + align:start position:0% +introduced in in the Years soon after + + + align:start position:0% +introduced in in the Years soon after +the second world war some people thought + + align:start position:0% +the second world war some people thought + + + align:start position:0% +the second world war some people thought +they didn't make any sense others + + align:start position:0% +they didn't make any sense others + + + align:start position:0% +they didn't make any sense others +thought they must be all wrong and a + + align:start position:0% +thought they must be all wrong and a + + + align:start position:0% +thought they must be all wrong and a +small number of people began using a + + align:start position:0% +small number of people began using a + + + align:start position:0% +small number of people began using a +couple of them at a time so it was a + + align:start position:0% +couple of them at a time so it was a + + + align:start position:0% +couple of them at a time so it was a +publishable feat to evaluate sort of + + align:start position:0% +publishable feat to evaluate sort of + + + align:start position:0% +publishable feat to evaluate sort of +five of them by hand not ten thousand on + + align:start position:0% +five of them by hand not ten thousand on + + + align:start position:0% +five of them by hand not ten thousand on +your laptop you could get your PhD + + align:start position:0% +your laptop you could get your PhD + + + align:start position:0% +your laptop you could get your PhD +dissertation by evaluating you know a + + align:start position:0% +dissertation by evaluating you know a + + + align:start position:0% +dissertation by evaluating you know a +few dozen at most + + align:start position:0% +few dozen at most + + + align:start position:0% +few dozen at most +um by hand in the into the uh 19 early + + align:start position:0% +um by hand in the into the uh 19 early + + + align:start position:0% +um by hand in the into the uh 19 early +1950s so these things weren't these kind + + align:start position:0% +1950s so these things weren't these kind + + + align:start position:0% +1950s so these things weren't these kind +of automated tools from the beginning in + + align:start position:0% +of automated tools from the beginning in + + + align:start position:0% +of automated tools from the beginning in +fact they were kind of suspect + + align:start position:0% +fact they were kind of suspect + + + align:start position:0% +fact they were kind of suspect +um at least to some people for quite a + + align:start position:0% +um at least to some people for quite a + + + align:start position:0% +um at least to some people for quite a +while as I mentioned already + + align:start position:0% +while as I mentioned already + + + align:start position:0% +while as I mentioned already +they're kind of single use the fact that + + align:start position:0% +they're kind of single use the fact that + + + align:start position:0% +they're kind of single use the fact that +now you can train computer algorithm + + align:start position:0% +now you can train computer algorithm + + + align:start position:0% +now you can train computer algorithm +algorithms to evaluate these things + + align:start position:0% +algorithms to evaluate these things + + + align:start position:0% +algorithms to evaluate these things +unambiguously that again took quite a + + align:start position:0% +unambiguously that again took quite a + + + align:start position:0% +unambiguously that again took quite a +while to kind of settle into place and + + align:start position:0% +while to kind of settle into place and + + + align:start position:0% +while to kind of settle into place and +what in fact for two decades or more + + align:start position:0% +what in fact for two decades or more + + + align:start position:0% +what in fact for two decades or more +even arguably about close to three + + align:start position:0% +even arguably about close to three + + + align:start position:0% +even arguably about close to three +decades what the diagrams were used for + + align:start position:0% +decades what the diagrams were used for + + + align:start position:0% +decades what the diagrams were used for +how they would be turned into elements + + align:start position:0% +how they would be turned into elements + + + align:start position:0% +how they would be turned into elements +of calculations and Quantified that was + + align:start position:0% +of calculations and Quantified that was + + + align:start position:0% +of calculations and Quantified that was +actually pretty malleable for for to me + + align:start position:0% +actually pretty malleable for for to me + + + align:start position:0% +actually pretty malleable for for to me +what seemed at least to be surprisingly + + align:start position:0% +what seemed at least to be surprisingly + + + align:start position:0% +what seemed at least to be surprisingly +long period of time they were adapted as + + align:start position:0% +long period of time they were adapted as + + + align:start position:0% +long period of time they were adapted as +well as adopted + + align:start position:0% +well as adopted + + + align:start position:0% +well as adopted +and so before I started working on this + + align:start position:0% +and so before I started working on this + + + align:start position:0% +and so before I started working on this +kind of series of puzzles how the + + align:start position:0% +kind of series of puzzles how the + + + align:start position:0% +kind of series of puzzles how the +diagram spread why did they um come to + + align:start position:0% +diagram spread why did they um come to + + + align:start position:0% +diagram spread why did they um come to +be used uh and so on very little had + + align:start position:0% +be used uh and so on very little had + + + align:start position:0% +be used uh and so on very little had +been written about the spread of the + + align:start position:0% +been written about the spread of the + + + align:start position:0% +been written about the spread of the +diagrams I used to tease that there had + + align:start position:0% +diagrams I used to tease that there had + + + align:start position:0% +diagrams I used to tease that there had +been more written at that point + + align:start position:0% +been more written at that point + + + align:start position:0% +been more written at that point +about the search for Richard feynman's + + align:start position:0% +about the search for Richard feynman's + + + align:start position:0% +about the search for Richard feynman's +actual van this is fine and his then + + align:start position:0% +actual van this is fine and his then + + + align:start position:0% +actual van this is fine and his then +very young children + + align:start position:0% +very young children + + + align:start position:0% +very young children +with this van that needs to drive around + + align:start position:0% +with this van that needs to drive around + + + align:start position:0% +with this van that needs to drive around +Southern California and with large + + align:start position:0% +Southern California and with large + + + align:start position:0% +Southern California and with large +in-life finding diagrams on the side uh + + align:start position:0% +in-life finding diagrams on the side uh + + + align:start position:0% +in-life finding diagrams on the side uh +there was more written about his van + + align:start position:0% +there was more written about his van + + + align:start position:0% +there was more written about his van +than about the diagrams that you know + + align:start position:0% +than about the diagrams that you know + + + align:start position:0% +than about the diagrams that you know +detect the van and so how was it that + + align:start position:0% +detect the van and so how was it that + + + align:start position:0% +detect the van and so how was it that +this was even something you'd paint on + + align:start position:0% +this was even something you'd paint on + + + align:start position:0% +this was even something you'd paint on +your van in the first place not only + + align:start position:0% +your van in the first place not only + + + align:start position:0% +your van in the first place not only +because it was The Groovy 70s and you're + + align:start position:0% +because it was The Groovy 70s and you're + + + align:start position:0% +because it was The Groovy 70s and you're +in California why would these become + + align:start position:0% +in California why would these become + + + align:start position:0% +in California why would these become +something to paint on your you know + + align:start position:0% +something to paint on your you know + + + align:start position:0% +something to paint on your you know +personal vehicle and so that's what I + + align:start position:0% +personal vehicle and so that's what I + + + align:start position:0% +personal vehicle and so that's what I +was really kind of curious to try to + + align:start position:0% +was really kind of curious to try to + + + align:start position:0% +was really kind of curious to try to +learn more about + + align:start position:0% +learn more about + + + align:start position:0% +learn more about +so to make sense of that + + align:start position:0% +so to make sense of that + + + align:start position:0% +so to make sense of that +I wound up thinking a lot about this + + align:start position:0% +I wound up thinking a lot about this + + + align:start position:0% +I wound up thinking a lot about this +this word dispersion I think it's I + + align:start position:0% +this word dispersion I think it's I + + + align:start position:0% +this word dispersion I think it's I +still think it's helpful to organize the + + align:start position:0% +still think it's helpful to organize the + + + align:start position:0% +still think it's helpful to organize the +kind of different layers of this study + + align:start position:0% +kind of different layers of this study + + + align:start position:0% +kind of different layers of this study +so disperse means many different things + + align:start position:0% +so disperse means many different things + + + align:start position:0% +so disperse means many different things +the verb to disperse where there's there + + align:start position:0% +the verb to disperse where there's there + + + align:start position:0% +the verb to disperse where there's there +are two main clusters of meanings if you + + align:start position:0% +are two main clusters of meanings if you + + + align:start position:0% +are two main clusters of meanings if you +go look up for example in the Oxford + + align:start position:0% +go look up for example in the Oxford + + + align:start position:0% +go look up for example in the Oxford +English Dictionary or your favorite you + + align:start position:0% +English Dictionary or your favorite you + + + align:start position:0% +English Dictionary or your favorite you +know Merriam-Webster or whatever you + + align:start position:0% +know Merriam-Webster or whatever you + + + align:start position:0% +know Merriam-Webster or whatever you +like there are kind of two basic sets of + + align:start position:0% +like there are kind of two basic sets of + + + align:start position:0% +like there are kind of two basic sets of +meanings for the verb to disperse one of + + align:start position:0% +meanings for the verb to disperse one of + + + align:start position:0% +meanings for the verb to disperse one of +the means to put into circulation think + + align:start position:0% +the means to put into circulation think + + + align:start position:0% +the means to put into circulation think +about you dispersing things to to people + + align:start position:0% +about you dispersing things to to people + + + align:start position:0% +about you dispersing things to to people +and but that's really the first part for + + align:start position:0% +and but that's really the first part for + + + align:start position:0% +and but that's really the first part for +today's class that we'll focus on + + align:start position:0% +today's class that we'll focus on + + + align:start position:0% +today's class that we'll focus on +disperse also means to cause to become + + align:start position:0% +disperse also means to cause to become + + + align:start position:0% +disperse also means to cause to become +basically more and more different think + + align:start position:0% +basically more and more different think + + + align:start position:0% +basically more and more different think +about Optical dispersion taking uh light + + align:start position:0% +about Optical dispersion taking uh light + + + align:start position:0% +about Optical dispersion taking uh light +and dispersing it into the distinct + + align:start position:0% +and dispersing it into the distinct + + + align:start position:0% +and dispersing it into the distinct +colors of the rainbow and I think that + + align:start position:0% +colors of the rainbow and I think that + + + align:start position:0% +colors of the rainbow and I think that +also captures a lot of what was going on + + align:start position:0% +also captures a lot of what was going on + + + align:start position:0% +also captures a lot of what was going on +with these new theoretical tools uh not + + align:start position:0% +with these new theoretical tools uh not + + + align:start position:0% +with these new theoretical tools uh not +just for a month or a year but really + + align:start position:0% +just for a month or a year but really + + + align:start position:0% +just for a month or a year but really +over decades uh even after Feynman had + + align:start position:0% +over decades uh even after Feynman had + + + align:start position:0% +over decades uh even after Feynman had +had introduced + + align:start position:0% +had introduced + + + align:start position:0% +had introduced +because that's what set up these three + + align:start position:0% +because that's what set up these three + + + align:start position:0% +because that's what set up these three +questions that I mentioned earlier how + + align:start position:0% +questions that I mentioned earlier how + + + align:start position:0% +questions that I mentioned earlier how +do they spread so fast what do people + + align:start position:0% +do they spread so fast what do people + + + align:start position:0% +do they spread so fast what do people +actually use them for and then given + + align:start position:0% +actually use them for and then given + + + align:start position:0% +actually use them for and then given +that variety why did they stick so let's + + align:start position:0% +that variety why did they stick so let's + + + align:start position:0% +that variety why did they stick so let's +talk about how they start entering + + align:start position:0% +talk about how they start entering + + + align:start position:0% +talk about how they start entering +circulation in the first place let's dig + + align:start position:0% +circulation in the first place let's dig + + + align:start position:0% +circulation in the first place let's dig +into that a bit more + + align:start position:0% +into that a bit more + + + align:start position:0% +into that a bit more +these were introduced at the second of + + align:start position:0% +these were introduced at the second of + + + align:start position:0% +these were introduced at the second of +this uh three sets of annual meetings + + align:start position:0% +this uh three sets of annual meetings + + + align:start position:0% +this uh three sets of annual meetings +that we talked a little bit about in the + + align:start position:0% +that we talked a little bit about in the + + + align:start position:0% +that we talked a little bit about in the +previous class you might remember on + + align:start position:0% +previous class you might remember on + + + align:start position:0% +previous class you might remember on +Monday I talked a bit about the June + + align:start position:0% +Monday I talked a bit about the June + + + align:start position:0% +Monday I talked a bit about the June +1947 Shelter Island meeting in fact this + + align:start position:0% +1947 Shelter Island meeting in fact this + + + align:start position:0% +1947 Shelter Island meeting in fact this +Photograph was from that Shelter Island + + align:start position:0% +Photograph was from that Shelter Island + + + align:start position:0% +Photograph was from that Shelter Island +one from the first of them uh held just + + align:start position:0% +one from the first of them uh held just + + + align:start position:0% +one from the first of them uh held just +on a tiny Island near Long Island + + align:start position:0% +on a tiny Island near Long Island + + + align:start position:0% +on a tiny Island near Long Island +and the Rams Head it I've never been + + align:start position:0% +and the Rams Head it I've never been + + + align:start position:0% +and the Rams Head it I've never been +there I don't know if it still exists if + + align:start position:0% +there I don't know if it still exists if + + + align:start position:0% +there I don't know if it still exists if +you're going to go to the actual bed and + + align:start position:0% +you're going to go to the actual bed and + + + align:start position:0% +you're going to go to the actual bed and +breakfast where they all stayed and that + + align:start position:0% +breakfast where they all stayed and that + + + align:start position:0% +breakfast where they all stayed and that +was the meeting at which + + align:start position:0% +was the meeting at which + + + align:start position:0% +was the meeting at which +um 24 kind of personally selected + + align:start position:0% +um 24 kind of personally selected + + + align:start position:0% +um 24 kind of personally selected +participants selected by Robert + + align:start position:0% +participants selected by Robert + + + align:start position:0% +participants selected by Robert +Oppenheimer got together for a week to + + align:start position:0% +Oppenheimer got together for a week to + + + align:start position:0% +Oppenheimer got together for a week to +talk about theoretical physics including + + align:start position:0% +talk about theoretical physics including + + + align:start position:0% +talk about theoretical physics including +these sort of puzzles of quantum field + + align:start position:0% +these sort of puzzles of quantum field + + + align:start position:0% +these sort of puzzles of quantum field +Theory that's where Willis lamb first + + align:start position:0% +Theory that's where Willis lamb first + + + align:start position:0% +Theory that's where Willis lamb first +presented uh his his results on what + + align:start position:0% +presented uh his his results on what + + + align:start position:0% +presented uh his his results on what +would come to be called the lamb shift + + align:start position:0% +would come to be called the lamb shift + + + align:start position:0% +would come to be called the lamb shift +is it a Robbie talked about the new + + align:start position:0% +is it a Robbie talked about the new + + + align:start position:0% +is it a Robbie talked about the new +experimental measurements + + align:start position:0% +experimental measurements + + + align:start position:0% +experimental measurements +on the anomalous Magnetic Moment + + align:start position:0% +on the anomalous Magnetic Moment + + + align:start position:0% +on the anomalous Magnetic Moment +electron and they were there were three + + align:start position:0% +electron and they were there were three + + + align:start position:0% +electron and they were there were three +in a row so every annual meetings the + + align:start position:0% +in a row so every annual meetings the + + + align:start position:0% +in a row so every annual meetings the +second of them was held not uh in Long + + align:start position:0% +second of them was held not uh in Long + + + align:start position:0% +second of them was held not uh in Long +Island but in the Pocono area sort of + + align:start position:0% +Island but in the Pocono area sort of + + + align:start position:0% +Island but in the Pocono area sort of +due north of Philadelphia Due West of + + align:start position:0% +due north of Philadelphia Due West of + + + align:start position:0% +due north of Philadelphia Due West of +Manhattan to kind of short bus ride out + + align:start position:0% +Manhattan to kind of short bus ride out + + + align:start position:0% +Manhattan to kind of short bus ride out +of Manhattan again organized by + + align:start position:0% +of Manhattan again organized by + + + align:start position:0% +of Manhattan again organized by +Oppenheimer very similar format roughly + + align:start position:0% +Oppenheimer very similar format roughly + + + align:start position:0% +Oppenheimer very similar format roughly +24 or 25 kind of hand selected + + align:start position:0% +24 or 25 kind of hand selected + + + align:start position:0% +24 or 25 kind of hand selected +participants many of whom had come to + + align:start position:0% +participants many of whom had come to + + + align:start position:0% +participants many of whom had come to +the previous one + + align:start position:0% +the previous one + + + align:start position:0% +the previous one +uh so this is the first meeting of its + + align:start position:0% +uh so this is the first meeting of its + + + align:start position:0% +uh so this is the first meeting of its +kind after the um experimental results + + align:start position:0% +kind after the um experimental results + + + align:start position:0% +kind after the um experimental results +for thing that seemed to suggest at + + align:start position:0% +for thing that seemed to suggest at + + + align:start position:0% +for thing that seemed to suggest at +least to some people that virtual + + align:start position:0% +least to some people that virtual + + + align:start position:0% +least to some people that virtual +particles might actually have have some + + align:start position:0% +particles might actually have have some + + + align:start position:0% +particles might actually have have some +hefts to them they might actually affect + + align:start position:0% +hefts to them they might actually affect + + + align:start position:0% +hefts to them they might actually affect +measurable quantities + + align:start position:0% +measurable quantities + + + align:start position:0% +measurable quantities +so it was at this meeting the second in + + align:start position:0% +so it was at this meeting the second in + + + align:start position:0% +so it was at this meeting the second in +the series where fireman introduced his + + align:start position:0% +the series where fireman introduced his + + + align:start position:0% +the series where fireman introduced his +new techniques he was one of the um + + align:start position:0% +new techniques he was one of the um + + + align:start position:0% +new techniques he was one of the um +informal speakers + + align:start position:0% +informal speakers + + + align:start position:0% +informal speakers +this was actually from his his first + + align:start position:0% +this was actually from his his first + + + align:start position:0% +this was actually from his his first +published example we know from notes + + align:start position:0% +published example we know from notes + + + align:start position:0% +published example we know from notes +that were taken he was scribbling very + + align:start position:0% +that were taken he was scribbling very + + + align:start position:0% +that were taken he was scribbling very +similar things on the Blackboard and he + + align:start position:0% +similar things on the Blackboard and he + + + align:start position:0% +similar things on the Blackboard and he +was trying to motivate for his + + align:start position:0% +was trying to motivate for his + + + align:start position:0% +was trying to motivate for his +colleagues how they could try to + + align:start position:0% +colleagues how they could try to + + + align:start position:0% +colleagues how they could try to +understand at a quantum mechanical level + + align:start position:0% +understand at a quantum mechanical level + + + align:start position:0% +understand at a quantum mechanical level +why it is that for example electrons + + align:start position:0% +why it is that for example electrons + + + align:start position:0% +why it is that for example electrons +repel each other we all learn in high + + align:start position:0% +repel each other we all learn in high + + + align:start position:0% +repel each other we all learn in high +school that like Chargers repel and + + align:start position:0% +school that like Chargers repel and + + + align:start position:0% +school that like Chargers repel and +office of charges attract he said well + + align:start position:0% +office of charges attract he said well + + + align:start position:0% +office of charges attract he said well +why is it if we think at this quantum + + align:start position:0% +why is it if we think at this quantum + + + align:start position:0% +why is it if we think at this quantum +mechanical level that charges with the + + align:start position:0% +mechanical level that charges with the + + + align:start position:0% +mechanical level that charges with the +same sign of their electric charge would + + align:start position:0% +same sign of their electric charge would + + + align:start position:0% +same sign of their electric charge would +push each other apart would repel each + + align:start position:0% +push each other apart would repel each + + + align:start position:0% +push each other apart would repel each +other + + align:start position:0% +other + + + align:start position:0% +other +and so here's the kind of story that we + + align:start position:0% +and so here's the kind of story that we + + + align:start position:0% +and so here's the kind of story that we +could that we could imagine unfolding + + align:start position:0% +could that we could imagine unfolding + + + align:start position:0% +could that we could imagine unfolding +there'd be some electron coming in here + + align:start position:0% +there'd be some electron coming in here + + + align:start position:0% +there'd be some electron coming in here +from the right hand side it would have + + align:start position:0% +from the right hand side it would have + + + align:start position:0% +from the right hand side it would have +some likelihood to travel from here to + + align:start position:0% +some likelihood to travel from here to + + + align:start position:0% +some likelihood to travel from here to +here it has some separate but calculable + + align:start position:0% +here it has some separate but calculable + + + align:start position:0% +here it has some separate but calculable +likelihood to emit a virtual Photon at + + align:start position:0% +likelihood to emit a virtual Photon at + + + align:start position:0% +likelihood to emit a virtual Photon at +this point in space you can't turn off + + align:start position:0% +this point in space you can't turn off + + + align:start position:0% +this point in space you can't turn off +there in certain principle the vacuum is + + align:start position:0% +there in certain principle the vacuum is + + + align:start position:0% +there in certain principle the vacuum is +roiling with virtual particles by this + + align:start position:0% +roiling with virtual particles by this + + + align:start position:0% +roiling with virtual particles by this +that by this time that had become kind + + align:start position:0% +that by this time that had become kind + + + align:start position:0% +that by this time that had become kind +of familiar um set of ideas so he wanted + + align:start position:0% +of familiar um set of ideas so he wanted + + + align:start position:0% +of familiar um set of ideas so he wanted +to have a way to kind of calculate those + + align:start position:0% +to have a way to kind of calculate those + + + align:start position:0% +to have a way to kind of calculate those +effects a little while later that + + align:start position:0% +effects a little while later that + + + align:start position:0% +effects a little while later that +virtual Photon would have zoomed across + + align:start position:0% +virtual Photon would have zoomed across + + + align:start position:0% +virtual Photon would have zoomed across +space and it could smack into this other + + align:start position:0% +space and it could smack into this other + + + align:start position:0% +space and it could smack into this other +electron the second electron which had + + align:start position:0% +electron the second electron which had + + + align:start position:0% +electron the second electron which had +been otherwise traveling all by its + + align:start position:0% +been otherwise traveling all by its + + + align:start position:0% +been otherwise traveling all by its +Lonesome unsuspected going from say 0.1 + + align:start position:0% +Lonesome unsuspected going from say 0.1 + + + align:start position:0% +Lonesome unsuspected going from say 0.1 +to 0.5 all of a sudden it'll get smacked + + align:start position:0% +to 0.5 all of a sudden it'll get smacked + + + align:start position:0% +to 0.5 all of a sudden it'll get smacked +by this virtual Photon that is carrying + + align:start position:0% +by this virtual Photon that is carrying + + + align:start position:0% +by this virtual Photon that is carrying +some energy and some momentum it is + + align:start position:0% +some energy and some momentum it is + + + align:start position:0% +some energy and some momentum it is +getting + + align:start position:0% +getting + + + align:start position:0% +getting +um + + align:start position:0% +um + + + align:start position:0% +um +it's absorbing that that momentum so + + align:start position:0% +it's absorbing that that momentum so + + + align:start position:0% +it's absorbing that that momentum so +after it absorbs that virtual Photon + + align:start position:0% +after it absorbs that virtual Photon + + + align:start position:0% +after it absorbs that virtual Photon +it'll be knocked off its course imagine + + align:start position:0% +it'll be knocked off its course imagine + + + align:start position:0% +it'll be knocked off its course imagine +you know getting hit with a dodgeball uh + + align:start position:0% +you know getting hit with a dodgeball uh + + + align:start position:0% +you know getting hit with a dodgeball uh +not that I want to trigger bad memories + + align:start position:0% +not that I want to trigger bad memories + + + align:start position:0% +not that I want to trigger bad memories +in elementary school anyway you get you + + align:start position:0% +in elementary school anyway you get you + + + align:start position:0% +in elementary school anyway you get you +knocked off your course you get hit with + + align:start position:0% +knocked off your course you get hit with + + + align:start position:0% +knocked off your course you get hit with +some uh object carrying momentum so so + + align:start position:0% +some uh object carrying momentum so so + + + align:start position:0% +some uh object carrying momentum so so +it's direction of travel will change + + align:start position:0% +it's direction of travel will change + + + align:start position:0% +it's direction of travel will change +meanwhile the original electron has shot + + align:start position:0% +meanwhile the original electron has shot + + + align:start position:0% +meanwhile the original electron has shot +out that that virtual Photon it recoils + + align:start position:0% +out that that virtual Photon it recoils + + + align:start position:0% +out that that virtual Photon it recoils +like a hunter firing a rifle it's going + + align:start position:0% +like a hunter firing a rifle it's going + + + align:start position:0% +like a hunter firing a rifle it's going +to have some equal and opposite Kickback + + align:start position:0% +to have some equal and opposite Kickback + + + align:start position:0% +to have some equal and opposite Kickback +so its direction of travel will change + + align:start position:0% +so its direction of travel will change + + + align:start position:0% +so its direction of travel will change +as well so finally says here's the kind + + align:start position:0% +as well so finally says here's the kind + + + align:start position:0% +as well so finally says here's the kind +of fundamental process or the reason + + align:start position:0% +of fundamental process or the reason + + + align:start position:0% +of fundamental process or the reason +Quantum mechanically why like charges + + align:start position:0% +Quantum mechanically why like charges + + + align:start position:0% +Quantum mechanically why like charges +repel because they're trading back and + + align:start position:0% +repel because they're trading back and + + + align:start position:0% +repel because they're trading back and +forth these virtual force carrying + + align:start position:0% +forth these virtual force carrying + + + align:start position:0% +forth these virtual force carrying +particles in this case the photon the + + align:start position:0% +particles in this case the photon the + + + align:start position:0% +particles in this case the photon the +virtual Photon + + align:start position:0% +virtual Photon + + + align:start position:0% +virtual Photon +now he could use this kind of map of + + align:start position:0% +now he could use this kind of map of + + + align:start position:0% +now he could use this kind of map of +that interaction and relate every single + + align:start position:0% +that interaction and relate every single + + + align:start position:0% +that interaction and relate every single +part of this little squiggle this line + + align:start position:0% +part of this little squiggle this line + + + align:start position:0% +part of this little squiggle this line +drawing to particular parts of the + + align:start position:0% +drawing to particular parts of the + + + align:start position:0% +drawing to particular parts of the +integrals uh and so he would map this + + align:start position:0% +integrals uh and so he would map this + + + align:start position:0% +integrals uh and so he would map this +try to explain this at the Blackboard + + align:start position:0% +try to explain this at the Blackboard + + + align:start position:0% +try to explain this at the Blackboard +the electron has some likelihood to + + align:start position:0% +the electron has some likelihood to + + + align:start position:0% +the electron has some likelihood to +travel unimpeded from point two to point + + align:start position:0% +travel unimpeded from point two to point + + + align:start position:0% +travel unimpeded from point two to point +six here it is the other electron + + align:start position:0% +six here it is the other electron + + + align:start position:0% +six here it is the other electron +electron a let's say has some likelihood + + align:start position:0% +electron a let's say has some likelihood + + + align:start position:0% +electron a let's say has some likelihood +to travel from 0.1 to 0.5 they have a + + align:start position:0% +to travel from 0.1 to 0.5 they have a + + + align:start position:0% +to travel from 0.1 to 0.5 they have a +likelihood to both Emit and absorb a + + align:start position:0% +likelihood to both Emit and absorb a + + + align:start position:0% +likelihood to both Emit and absorb a +photon Each of which is proportional to + + align:start position:0% +photon Each of which is proportional to + + + align:start position:0% +photon Each of which is proportional to +the charge electron the photon itself + + align:start position:0% +the charge electron the photon itself + + + align:start position:0% +the charge electron the photon itself +has a likely to travel from 0.6 to 0.5 + + align:start position:0% +has a likely to travel from 0.6 to 0.5 + + + align:start position:0% +has a likely to travel from 0.6 to 0.5 +you just piece it all together like kind + + align:start position:0% +you just piece it all together like kind + + + align:start position:0% +you just piece it all together like kind +of Lego bricks + + align:start position:0% +of Lego bricks + + + align:start position:0% +of Lego bricks +so now you have a kind of road map to + + align:start position:0% +so now you have a kind of road map to + + + align:start position:0% +so now you have a kind of road map to +the corresponding equations to map out + + align:start position:0% +the corresponding equations to map out + + + align:start position:0% +the corresponding equations to map out +this series of of steps between + + align:start position:0% +this series of of steps between + + + align:start position:0% +this series of of steps between +electrons and their traded virtual + + align:start position:0% +electrons and their traded virtual + + + align:start position:0% +electrons and their traded virtual +particle + + align:start position:0% +particle + + + align:start position:0% +particle +and Feynman said this is going to be + + align:start position:0% +and Feynman said this is going to be + + + align:start position:0% +and Feynman said this is going to be +important not just because this is one + + align:start position:0% +important not just because this is one + + + align:start position:0% +important not just because this is one +thing that could happen but because all + + align:start position:0% +thing that could happen but because all + + + align:start position:0% +thing that could happen but because all +kinds of things could happen when we + + align:start position:0% +kinds of things could happen when we + + + align:start position:0% +kinds of things could happen when we +start thinking about virtual particles + + align:start position:0% +start thinking about virtual particles + + + align:start position:0% +start thinking about virtual particles +it had already become clear well before + + align:start position:0% +it had already become clear well before + + + align:start position:0% +it had already become clear well before +the second world war that these virtual + + align:start position:0% +the second world war that these virtual + + + align:start position:0% +the second world war that these virtual +particles could borrow any amount of + + align:start position:0% +particles could borrow any amount of + + + align:start position:0% +particles could borrow any amount of +energy and momentum consistent with uh + + align:start position:0% +energy and momentum consistent with uh + + + align:start position:0% +energy and momentum consistent with uh +with paying it back sufficiently quickly + + align:start position:0% +with paying it back sufficiently quickly + + + align:start position:0% +with paying it back sufficiently quickly +given the uncertainty principle but but + + align:start position:0% +given the uncertainty principle but but + + + align:start position:0% +given the uncertainty principle but but +it was even more complicated the + + align:start position:0% +it was even more complicated the + + + align:start position:0% +it was even more complicated the +electrons could trade more than one + + align:start position:0% +electrons could trade more than one + + + align:start position:0% +electrons could trade more than one +virtual particle so instead of just + + align:start position:0% +virtual particle so instead of just + + + align:start position:0% +virtual particle so instead of just +saying the amount of energy that this + + align:start position:0% +saying the amount of energy that this + + + align:start position:0% +saying the amount of energy that this +one virtual particle borrowed was + + align:start position:0% +one virtual particle borrowed was + + + align:start position:0% +one virtual particle borrowed was +uncertain and the principle could be + + align:start position:0% +uncertain and the principle could be + + + align:start position:0% +uncertain and the principle could be +infinite what if the electrons had + + align:start position:0% +infinite what if the electrons had + + + align:start position:0% +infinite what if the electrons had +traded two photons + + align:start position:0% +traded two photons + + + align:start position:0% +traded two photons +two virtual photons Each of which had + + align:start position:0% +two virtual photons Each of which had + + + align:start position:0% +two virtual photons Each of which had +temporarily borrowed + + align:start position:0% +temporarily borrowed + + + align:start position:0% +temporarily borrowed +energy and momentum from the vacuum well + + align:start position:0% +energy and momentum from the vacuum well + + + align:start position:0% +energy and momentum from the vacuum well +now it starts getting pretty tricky + + align:start position:0% +now it starts getting pretty tricky + + + align:start position:0% +now it starts getting pretty tricky +because there are actually several + + align:start position:0% +because there are actually several + + + align:start position:0% +because there are actually several +topologically distinct ways in which two + + align:start position:0% +topologically distinct ways in which two + + + align:start position:0% +topologically distinct ways in which two +incoming electrons could trade two + + align:start position:0% +incoming electrons could trade two + + + align:start position:0% +incoming electrons could trade two +photons and leave only two electrons + + align:start position:0% +photons and leave only two electrons + + + align:start position:0% +photons and leave only two electrons +coming out so instead of only one sort + + align:start position:0% +coming out so instead of only one sort + + + align:start position:0% +coming out so instead of only one sort +of storyline that you have to map into a + + align:start position:0% +of storyline that you have to map into a + + + align:start position:0% +of storyline that you have to map into a +line of algebra you actually have all + + align:start position:0% +line of algebra you actually have all + + + align:start position:0% +line of algebra you actually have all +these different ways in which two + + align:start position:0% +these different ways in which two + + + align:start position:0% +these different ways in which two +electrons come in two electrons go out + + align:start position:0% +electrons come in two electrons go out + + + align:start position:0% +electrons come in two electrons go out +and in between they've traded two + + align:start position:0% +and in between they've traded two + + + align:start position:0% +and in between they've traded two +virtual photons and so the diagrams were + + align:start position:0% +virtual photons and so the diagrams were + + + align:start position:0% +virtual photons and so the diagrams were +literally a form of bookkeeping and + + align:start position:0% +literally a form of bookkeeping and + + + align:start position:0% +literally a form of bookkeeping and +again you could walk through the same + + align:start position:0% +again you could walk through the same + + + align:start position:0% +again you could walk through the same +series of steps to map every element of + + align:start position:0% +series of steps to map every element of + + + align:start position:0% +series of steps to map every element of +these slightly more complicated Feynman + + align:start position:0% +these slightly more complicated Feynman + + + align:start position:0% +these slightly more complicated Feynman +diagrams to the Scott to the + + align:start position:0% +diagrams to the Scott to the + + + align:start position:0% +diagrams to the Scott to the +corresponding algebra and you can do the + + align:start position:0% +corresponding algebra and you can do the + + + align:start position:0% +corresponding algebra and you can do the +same with three virtual photons or four + + align:start position:0% +same with three virtual photons or four + + + align:start position:0% +same with three virtual photons or four +in principle there could be an infinite + + align:start position:0% +in principle there could be an infinite + + + align:start position:0% +in principle there could be an infinite +number of virtual photons Each of which + + align:start position:0% +number of virtual photons Each of which + + + align:start position:0% +number of virtual photons Each of which +could carry in principle an infinite + + align:start position:0% +could carry in principle an infinite + + + align:start position:0% +could carry in principle an infinite +albeit short-lived energy momentum so + + align:start position:0% +albeit short-lived energy momentum so + + + align:start position:0% +albeit short-lived energy momentum so +you see the bookkeeping becomes like + + align:start position:0% +you see the bookkeeping becomes like + + + align:start position:0% +you see the bookkeeping becomes like +mind-boggling right so this is a kind of + + align:start position:0% +mind-boggling right so this is a kind of + + + align:start position:0% +mind-boggling right so this is a kind of +way to March through the corresponding + + align:start position:0% +way to March through the corresponding + + + align:start position:0% +way to March through the corresponding +equations make sure you don't omit any + + align:start position:0% +equations make sure you don't omit any + + + align:start position:0% +equations make sure you don't omit any +terms make sure you don't double count + + align:start position:0% +terms make sure you don't double count + + + align:start position:0% +terms make sure you don't double count +certain terms which have been bedeviling + + align:start position:0% +certain terms which have been bedeviling + + + align:start position:0% +certain terms which have been bedeviling +these calculations throughout the 30s + + align:start position:0% +these calculations throughout the 30s + + + align:start position:0% +these calculations throughout the 30s +and so now you have a map to make sure + + align:start position:0% +and so now you have a map to make sure + + + align:start position:0% +and so now you have a map to make sure +you at least have the equations the + + align:start position:0% +you at least have the equations the + + + align:start position:0% +you at least have the equations the +correct set of equations to worry about + + align:start position:0% +correct set of equations to worry about + + + align:start position:0% +correct set of equations to worry about +and then by this point uh in late spring + + align:start position:0% +and then by this point uh in late spring + + + align:start position:0% +and then by this point uh in late spring +early summer of 1948 finally could show + + align:start position:0% +early summer of 1948 finally could show + + + align:start position:0% +early summer of 1948 finally could show +that if you have the right bookkeeping + + align:start position:0% +that if you have the right bookkeeping + + + align:start position:0% +that if you have the right bookkeeping +you see some of these Infinities + + align:start position:0% +you see some of these Infinities + + + align:start position:0% +you see some of these Infinities +actually exactly cancel each other so + + align:start position:0% +actually exactly cancel each other so + + + align:start position:0% +actually exactly cancel each other so +some of the Infinities that it cropped + + align:start position:0% +some of the Infinities that it cropped + + + align:start position:0% +some of the Infinities that it cropped +up in these earlier calculations not all + + align:start position:0% +up in these earlier calculations not all + + + align:start position:0% +up in these earlier calculations not all +but some of them would exactly cancel + + align:start position:0% +but some of them would exactly cancel + + + align:start position:0% +but some of them would exactly cancel +even before you got Fancy with + + align:start position:0% +even before you got Fancy with + + + align:start position:0% +even before you got Fancy with +renormalization just because you have to + + align:start position:0% +renormalization just because you have to + + + align:start position:0% +renormalization just because you have to +remember that for every diagram like + + align:start position:0% +remember that for every diagram like + + + align:start position:0% +remember that for every diagram like +this there's a corresponding one like + + align:start position:0% +this there's a corresponding one like + + + align:start position:0% +this there's a corresponding one like +that and so on and some of these have + + align:start position:0% +that and so on and some of these have + + + align:start position:0% +that and so on and some of these have +exact cancellation + + align:start position:0% +exact cancellation + + + align:start position:0% +exact cancellation +so the challenge of taming those + + align:start position:0% +so the challenge of taming those + + + align:start position:0% +so the challenge of taming those +Infinities would become a bit more + + align:start position:0% +Infinities would become a bit more + + + align:start position:0% +Infinities would become a bit more +manageable if you can make sure you have + + align:start position:0% +manageable if you can make sure you have + + + align:start position:0% +manageable if you can make sure you have +the right set of equations to work with + + align:start position:0% +the right set of equations to work with + + + align:start position:0% +the right set of equations to work with +from the start + + align:start position:0% +from the start + + + align:start position:0% +from the start +so how did that go that sounds awesome + + align:start position:0% +so how did that go that sounds awesome + + + align:start position:0% +so how did that go that sounds awesome +you have this amazing kind of intuitive + + align:start position:0% +you have this amazing kind of intuitive + + + align:start position:0% +you have this amazing kind of intuitive +very simple looking technique this used + + align:start position:0% +very simple looking technique this used + + + align:start position:0% +very simple looking technique this used +to occupy literally 30 and 40 page + + align:start position:0% +to occupy literally 30 and 40 page + + + align:start position:0% +to occupy literally 30 and 40 page +Journal articles when people try to do + + align:start position:0% +Journal articles when people try to do + + + align:start position:0% +Journal articles when people try to do +this without the diagrams throughout the + + align:start position:0% +this without the diagrams throughout the + + + align:start position:0% +this without the diagrams throughout the +1930s they'd always find these + + align:start position:0% +1930s they'd always find these + + + align:start position:0% +1930s they'd always find these +Infinities you think Oh Our Heroes in + + align:start position:0% +Infinities you think Oh Our Heroes in + + + align:start position:0% +Infinities you think Oh Our Heroes in +town finally help us on the way it + + align:start position:0% +town finally help us on the way it + + + align:start position:0% +town finally help us on the way it +didn't play out that way for our poor + + align:start position:0% +didn't play out that way for our poor + + + align:start position:0% +didn't play out that way for our poor +MIT alumnus Richard fine + + align:start position:0% +MIT alumnus Richard fine + + + align:start position:0% +MIT alumnus Richard fine +the first thing to keep in mind is that + + align:start position:0% +the first thing to keep in mind is that + + + align:start position:0% +the first thing to keep in mind is that +he his presentation followed an + + align:start position:0% +he his presentation followed an + + + align:start position:0% +he his presentation followed an +eight-hour lecture by Julian schwinger + + align:start position:0% +eight-hour lecture by Julian schwinger + + + align:start position:0% +eight-hour lecture by Julian schwinger +I'd want to let that settle in for a + + align:start position:0% +I'd want to let that settle in for a + + + align:start position:0% +I'd want to let that settle in for a +second an eight hour lecture that's like + + align:start position:0% +second an eight hour lecture that's like + + + align:start position:0% +second an eight hour lecture that's like +unlawful imprisonment right now I often + + align:start position:0% +unlawful imprisonment right now I often + + + align:start position:0% +unlawful imprisonment right now I often +run along with my lectures here and I + + align:start position:0% +run along with my lectures here and I + + + align:start position:0% +run along with my lectures here and I +feel bad I go like three minutes late + + align:start position:0% +feel bad I go like three minutes late + + + align:start position:0% +feel bad I go like three minutes late +and you're all busy + + align:start position:0% +and you're all busy + + + align:start position:0% +and you're all busy +but you know anyway there are limits so + + align:start position:0% +but you know anyway there are limits so + + + align:start position:0% +but you know anyway there are limits so +schwinger why was schwinger given so + + align:start position:0% +schwinger why was schwinger given so + + + align:start position:0% +schwinger why was schwinger given so +much space + + align:start position:0% +much space + + + align:start position:0% +much space +in between the Shelter Island meeting + + align:start position:0% +in between the Shelter Island meeting + + + align:start position:0% +in between the Shelter Island meeting +and this follow-up one in Pocono it was + + align:start position:0% +and this follow-up one in Pocono it was + + + align:start position:0% +and this follow-up one in Pocono it was +schwinger who had first found a way to + + align:start position:0% +schwinger who had first found a way to + + + align:start position:0% +schwinger who had first found a way to +tame these Infinities he first + + align:start position:0% +tame these Infinities he first + + + align:start position:0% +tame these Infinities he first +calculated with his new techniques that + + align:start position:0% +calculated with his new techniques that + + + align:start position:0% +calculated with his new techniques that +did not involve any of these + + align:start position:0% +did not involve any of these + + + align:start position:0% +did not involve any of these +diagrammatic methods he had not only + + align:start position:0% +diagrammatic methods he had not only + + + align:start position:0% +diagrammatic methods he had not only +found a way in principle to respect the + + align:start position:0% +found a way in principle to respect the + + + align:start position:0% +found a way in principle to respect the +symmetries of Relativity and find finite + + align:start position:0% +symmetries of Relativity and find finite + + + align:start position:0% +symmetries of Relativity and find finite +answers with his renew normalization + + align:start position:0% +answers with his renew normalization + + + align:start position:0% +answers with his renew normalization +program he'd also found right in between + + align:start position:0% +program he'd also found right in between + + + align:start position:0% +program he'd also found right in between +sort of six months between these + + align:start position:0% +sort of six months between these + + + align:start position:0% +sort of six months between these +meetings in December 47 he published the + + align:start position:0% +meetings in December 47 he published the + + + align:start position:0% +meetings in December 47 he published the +first kind of successful + + align:start position:0% +first kind of successful + + + align:start position:0% +first kind of successful +demonstration that renormalization could + + align:start position:0% +demonstration that renormalization could + + + align:start position:0% +demonstration that renormalization could +yield finer results that actually match + + align:start position:0% +yield finer results that actually match + + + align:start position:0% +yield finer results that actually match +unbelievably closely to these latest + + align:start position:0% +unbelievably closely to these latest + + + align:start position:0% +unbelievably closely to these latest +High Precision experiments schwenger was + + align:start position:0% +High Precision experiments schwenger was + + + align:start position:0% +High Precision experiments schwenger was +you know the person of the hour or + + align:start position:0% +you know the person of the hour or + + + align:start position:0% +you know the person of the hour or +rather the eight hours so it was after + + align:start position:0% +rather the eight hours so it was after + + + align:start position:0% +rather the eight hours so it was after +that they had a brief break for lunch + + align:start position:0% +that they had a brief break for lunch + + + align:start position:0% +that they had a brief break for lunch +and came back and trying to talk earlier + + align:start position:0% +and came back and trying to talk earlier + + + align:start position:0% +and came back and trying to talk earlier +four hours afterwards then finally had + + align:start position:0% +four hours afterwards then finally had + + + align:start position:0% +four hours afterwards then finally had +had 30 minutes of the blackboard at the + + align:start position:0% +had 30 minutes of the blackboard at the + + + align:start position:0% +had 30 minutes of the blackboard at the +end of that day all right so it's not + + align:start position:0% +end of that day all right so it's not + + + align:start position:0% +end of that day all right so it's not +like great setup + + align:start position:0% +like great setup + + + align:start position:0% +like great setup +moreover he like was completely + + align:start position:0% +moreover he like was completely + + + align:start position:0% +moreover he like was completely +unprepared he did not have a + + align:start position:0% +unprepared he did not have a + + + align:start position:0% +unprepared he did not have a +well-polished presentation in hand he + + align:start position:0% +well-polished presentation in hand he + + + align:start position:0% +well-polished presentation in hand he +just wanted to kind of wing it which is + + align:start position:0% +just wanted to kind of wing it which is + + + align:start position:0% +just wanted to kind of wing it which is +not a good thing to do at the end of a + + align:start position:0% +not a good thing to do at the end of a + + + align:start position:0% +not a good thing to do at the end of a +busy day + + align:start position:0% +busy day + + + align:start position:0% +busy day +it was so it seemed at least to some of + + align:start position:0% +it was so it seemed at least to some of + + + align:start position:0% +it was so it seemed at least to some of +his listeners to be so scatter shot and + + align:start position:0% +his listeners to be so scatter shot and + + + align:start position:0% +his listeners to be so scatter shot and +so disorganized that Not only was he + + align:start position:0% +so disorganized that Not only was he + + + align:start position:0% +so disorganized that Not only was he +repeated all the time at one point Niels + + align:start position:0% +repeated all the time at one point Niels + + + align:start position:0% +repeated all the time at one point Niels +Bohr who had been invited to participate + + align:start position:0% +Bohr who had been invited to participate + + + align:start position:0% +Bohr who had been invited to participate +one of the few older European physicists + + align:start position:0% +one of the few older European physicists + + + align:start position:0% +one of the few older European physicists +Bohr got out of his chair walked up to + + align:start position:0% +Bohr got out of his chair walked up to + + + align:start position:0% +Bohr got out of his chair walked up to +the Blackboard and took the chalk out of + + align:start position:0% +the Blackboard and took the chalk out of + + + align:start position:0% +the Blackboard and took the chalk out of +Simon's hands and you don't understand + + align:start position:0% +Simon's hands and you don't understand + + + align:start position:0% +Simon's hands and you don't understand +quantum physics not great God I wish I + + align:start position:0% +quantum physics not great God I wish I + + + align:start position:0% +quantum physics not great God I wish I +had been able to see that + + align:start position:0% +had been able to see that + + + align:start position:0% +had been able to see that +so Bohr says not just this is like a + + align:start position:0% +so Bohr says not just this is like a + + + align:start position:0% +so Bohr says not just this is like a +disorganized presentation he says your + + align:start position:0% +disorganized presentation he says your + + + align:start position:0% +disorganized presentation he says your +whole framework is violates the + + align:start position:0% +whole framework is violates the + + + align:start position:0% +whole framework is violates the +uncertainty principle what does it mean + + align:start position:0% +uncertainty principle what does it mean + + + align:start position:0% +uncertainty principle what does it mean +to draw a picture of an electron moving + + align:start position:0% +to draw a picture of an electron moving + + + align:start position:0% +to draw a picture of an electron moving +from here to here bore says in effect + + align:start position:0% +from here to here bore says in effect + + + align:start position:0% +from here to here bore says in effect +you've assumed that the electron has a + + align:start position:0% +you've assumed that the electron has a + + + align:start position:0% +you've assumed that the electron has a +well-defined trajectory but no Quantum + + align:start position:0% +well-defined trajectory but no Quantum + + + align:start position:0% +well-defined trajectory but no Quantum +object has a well-defined trajectory + + align:start position:0% +object has a well-defined trajectory + + + align:start position:0% +object has a well-defined trajectory +because to do so it would need to have + + align:start position:0% +because to do so it would need to have + + + align:start position:0% +because to do so it would need to have +arbitrarily precise position and + + align:start position:0% +arbitrarily precise position and + + + align:start position:0% +arbitrarily precise position and +momentum at the same time but we can't + + align:start position:0% +momentum at the same time but we can't + + + align:start position:0% +momentum at the same time but we can't +have that because it's interesting + + align:start position:0% +have that because it's interesting + + + align:start position:0% +have that because it's interesting +support is like this is a non-starter + + align:start position:0% +support is like this is a non-starter + + + align:start position:0% +support is like this is a non-starter +from the beginning okay five is a little + + align:start position:0% +from the beginning okay five is a little + + + align:start position:0% +from the beginning okay five is a little +fluster though it's not literally a + + align:start position:0% +fluster though it's not literally a + + + align:start position:0% +fluster though it's not literally a +trajectory oh let me go on + + align:start position:0% +trajectory oh let me go on + + + align:start position:0% +trajectory oh let me go on +okay Paul Dirac was there Dirac says + + align:start position:0% +okay Paul Dirac was there Dirac says + + + align:start position:0% +okay Paul Dirac was there Dirac says +well when you calculate the + + align:start position:0% +well when you calculate the + + + align:start position:0% +well when you calculate the +probabilities with these new diagrams do + + align:start position:0% +probabilities with these new diagrams do + + + align:start position:0% +probabilities with these new diagrams do +they obey unitarity to which feynman's + + align:start position:0% +they obey unitarity to which feynman's + + + align:start position:0% +they obey unitarity to which feynman's +response was what's unitarity not not + + align:start position:0% +response was what's unitarity not not + + + align:start position:0% +response was what's unitarity not not +good okay this was not a great + + align:start position:0% +good okay this was not a great + + + align:start position:0% +good okay this was not a great +presentation for for + + align:start position:0% +presentation for for + + + align:start position:0% +presentation for for +um unitarity is again some of you might + + align:start position:0% +um unitarity is again some of you might + + + align:start position:0% +um unitarity is again some of you might +might know we might have found in other + + align:start position:0% +might know we might have found in other + + + align:start position:0% +might know we might have found in other +classes it's really a fancy way of + + align:start position:0% +classes it's really a fancy way of + + + align:start position:0% +classes it's really a fancy way of +asking does the sum of all these + + align:start position:0% +asking does the sum of all these + + + align:start position:0% +asking does the sum of all these +probabilities add up to what there's a + + align:start position:0% +probabilities add up to what there's a + + + align:start position:0% +probabilities add up to what there's a +100 chance that something will happen + + align:start position:0% +100 chance that something will happen + + + align:start position:0% +100 chance that something will happen +and it might be 35 chance of that and 42 + + align:start position:0% +and it might be 35 chance of that and 42 + + + align:start position:0% +and it might be 35 chance of that and 42 +chance of that you have to add all these + + align:start position:0% +chance of that you have to add all these + + + align:start position:0% +chance of that you have to add all these +up does the sum of all these + + align:start position:0% +up does the sum of all these + + + align:start position:0% +up does the sum of all these +probabilities obey the conservation of + + align:start position:0% +probabilities obey the conservation of + + + align:start position:0% +probabilities obey the conservation of +probability does it add up to one that's + + align:start position:0% +probability does it add up to one that's + + + align:start position:0% +probability does it add up to one that's +the fancy way that's the simpler version + + align:start position:0% +the fancy way that's the simpler version + + + align:start position:0% +the fancy way that's the simpler version +of what Dirac was asking and Feynman + + align:start position:0% +of what Dirac was asking and Feynman + + + align:start position:0% +of what Dirac was asking and Feynman +hadn't even thought about the question + + align:start position:0% +hadn't even thought about the question + + + align:start position:0% +hadn't even thought about the question +they certainly had no answer ready yet + + align:start position:0% +they certainly had no answer ready yet + + + align:start position:0% +they certainly had no answer ready yet +Edward Teller was there he says what + + align:start position:0% +Edward Teller was there he says what + + + align:start position:0% +Edward Teller was there he says what +about when you have a pair of electrons + + align:start position:0% +about when you have a pair of electrons + + + align:start position:0% +about when you have a pair of electrons +in these intermediate States two virtual + + align:start position:0% +in these intermediate States two virtual + + + align:start position:0% +in these intermediate States two virtual +electrons that say do they obey the + + align:start position:0% +electrons that say do they obey the + + + align:start position:0% +electrons that say do they obey the +palette Exclusion Principle another kind + + align:start position:0% +palette Exclusion Principle another kind + + + align:start position:0% +palette Exclusion Principle another kind +of Cornerstone of quantum physics and + + align:start position:0% +of Cornerstone of quantum physics and + + + align:start position:0% +of Cornerstone of quantum physics and +fireman's response was that's a really + + align:start position:0% +fireman's response was that's a really + + + align:start position:0% +fireman's response was that's a really +interesting question I'll go think about + + align:start position:0% +interesting question I'll go think about + + + align:start position:0% +interesting question I'll go think about +again he had no answer so in general + + align:start position:0% +again he had no answer so in general + + + align:start position:0% +again he had no answer so in general +what this very esteemed about small kind + + align:start position:0% +what this very esteemed about small kind + + + align:start position:0% +what this very esteemed about small kind +of elite audience kept asking during + + align:start position:0% +of elite audience kept asking during + + + align:start position:0% +of elite audience kept asking during +this scattered presentation of Finance + + align:start position:0% +this scattered presentation of Finance + + + align:start position:0% +this scattered presentation of Finance +was what rules govern their use it + + align:start position:0% +was what rules govern their use it + + + align:start position:0% +was what rules govern their use it +really looked like he was kind of making + + align:start position:0% +really looked like he was kind of making + + + align:start position:0% +really looked like he was kind of making +it up as it went along and he was not + + align:start position:0% +it up as it went along and he was not + + + align:start position:0% +it up as it went along and he was not +able at least at that moment to + + align:start position:0% +able at least at that moment to + + + align:start position:0% +able at least at that moment to +articulate the kind of rule-bound + + align:start position:0% +articulate the kind of rule-bound + + + align:start position:0% +articulate the kind of rule-bound +techniques that would that would perhaps + + align:start position:0% +techniques that would that would perhaps + + + align:start position:0% +techniques that would that would perhaps +yield as a comparable set of calculating + + align:start position:0% +yield as a comparable set of calculating + + + align:start position:0% +yield as a comparable set of calculating +techniques to schwinger's very pristine + + align:start position:0% +techniques to schwinger's very pristine + + + align:start position:0% +techniques to schwinger's very pristine +very precise algebraic approach + + align:start position:0% +very precise algebraic approach + + + align:start position:0% +very precise algebraic approach +so by many many accounts fine and left + + align:start position:0% +so by many many accounts fine and left + + + align:start position:0% +so by many many accounts fine and left +this meeting disappointed maybe even + + align:start position:0% +this meeting disappointed maybe even + + + align:start position:0% +this meeting disappointed maybe even +depressed that was uh he really was it + + align:start position:0% +depressed that was uh he really was it + + + align:start position:0% +depressed that was uh he really was it +was was not a great start for these new + + align:start position:0% +was was not a great start for these new + + + align:start position:0% +was was not a great start for these new +techniques and he was really down + + align:start position:0% +techniques and he was really down + + + align:start position:0% +techniques and he was really down +now one might have thought that all he + + align:start position:0% +now one might have thought that all he + + + align:start position:0% +now one might have thought that all he +had to do was kind of collect himself + + align:start position:0% +had to do was kind of collect himself + + + align:start position:0% +had to do was kind of collect himself +write up some clear articles just say + + align:start position:0% +write up some clear articles just say + + + align:start position:0% +write up some clear articles just say +Point by Point first do this and then do + + align:start position:0% +Point by Point first do this and then do + + + align:start position:0% +Point by Point first do this and then do +that here's where this comes from give a + + align:start position:0% +that here's where this comes from give a + + + align:start position:0% +that here's where this comes from give a +derivation give a demonstration he could + + align:start position:0% +derivation give a demonstration he could + + + align:start position:0% +derivation give a demonstration he could +have cleared this up one might have + + align:start position:0% +have cleared this up one might have + + + align:start position:0% +have cleared this up one might have +thought by writing some kind of clear + + align:start position:0% +thought by writing some kind of clear + + + align:start position:0% +thought by writing some kind of clear +articles + + align:start position:0% +articles + + + align:start position:0% +articles +well he did write some clear articles + + align:start position:0% +well he did write some clear articles + + + align:start position:0% +well he did write some clear articles +and yet what what again I found really + + align:start position:0% +and yet what what again I found really + + + align:start position:0% +and yet what what again I found really +fascinating was that that kind of + + align:start position:0% +fascinating was that that kind of + + + align:start position:0% +fascinating was that that kind of +confusion about the diagrams lingered + + align:start position:0% +confusion about the diagrams lingered + + + align:start position:0% +confusion about the diagrams lingered +for years afterwards not just for days + + align:start position:0% +for years afterwards not just for days + + + align:start position:0% +for years afterwards not just for days +weeks or months even years after his + + align:start position:0% +weeks or months even years after his + + + align:start position:0% +weeks or months even years after his +articles had been in print + + align:start position:0% +articles had been in print + + + align:start position:0% +articles had been in print +and so I won't go through all of these + + align:start position:0% +and so I won't go through all of these + + + align:start position:0% +and so I won't go through all of these +examples just some some examples I write + + align:start position:0% +examples just some some examples I write + + + align:start position:0% +examples just some some examples I write +about in more detail in the book but you + + align:start position:0% +about in more detail in the book but you + + + align:start position:0% +about in more detail in the book but you +have people either writing directly to + + align:start position:0% +have people either writing directly to + + + align:start position:0% +have people either writing directly to +Feynman saying I can't do this + + align:start position:0% +Feynman saying I can't do this + + + align:start position:0% +Feynman saying I can't do this +calculation will you do it for me with + + align:start position:0% +calculation will you do it for me with + + + align:start position:0% +calculation will you do it for me with +your trick and tell me what you get and + + align:start position:0% +your trick and tell me what you get and + + + align:start position:0% +your trick and tell me what you get and +then they thank him in the + + align:start position:0% +then they thank him in the + + + align:start position:0% +then they thank him in the +acknowledgments there's some interesting + + align:start position:0% +acknowledgments there's some interesting + + + align:start position:0% +acknowledgments there's some interesting +correspondent circles with people not + + align:start position:0% +correspondent circles with people not + + + align:start position:0% +correspondent circles with people not +including fighting from a very very um + + align:start position:0% +including fighting from a very very um + + + align:start position:0% +including fighting from a very very um +Elite very well-trained experts in in + + align:start position:0% +Elite very well-trained experts in in + + + align:start position:0% +Elite very well-trained experts in in +the field who three of them try to do + + align:start position:0% +the field who three of them try to do + + + align:start position:0% +the field who three of them try to do +the same calculation with the same + + align:start position:0% +the same calculation with the same + + + align:start position:0% +the same calculation with the same +diagrams and they keep getting different + + align:start position:0% +diagrams and they keep getting different + + + align:start position:0% +diagrams and they keep getting different +answers from each other so you have this + + align:start position:0% +answers from each other so you have this + + + align:start position:0% +answers from each other so you have this +wonderful series of letters because it + + align:start position:0% +wonderful series of letters because it + + + align:start position:0% +wonderful series of letters because it +was you know pre-email and they were in + + align:start position:0% +was you know pre-email and they were in + + + align:start position:0% +was you know pre-email and they were in +fact in different countries they weren't + + align:start position:0% +fact in different countries they weren't + + + align:start position:0% +fact in different countries they weren't +going to pick up you know make + + align:start position:0% +going to pick up you know make + + + align:start position:0% +going to pick up you know make +long-distance telephone calls so you + + align:start position:0% +long-distance telephone calls so you + + + align:start position:0% +long-distance telephone calls so you +have these letters of of them trying to + + align:start position:0% +have these letters of of them trying to + + + align:start position:0% +have these letters of of them trying to +figure out what keeps going wrong when + + align:start position:0% +figure out what keeps going wrong when + + + align:start position:0% +figure out what keeps going wrong when +they try to do the same calculation + + align:start position:0% +they try to do the same calculation + + + align:start position:0% +they try to do the same calculation +that's as late as 1950. + + align:start position:0% +that's as late as 1950. + + + align:start position:0% +that's as late as 1950. +a few years later my favorite example + + align:start position:0% +a few years later my favorite example + + + align:start position:0% +a few years later my favorite example +actually comes from a letter of + + align:start position:0% +actually comes from a letter of + + + align:start position:0% +actually comes from a letter of +recommendation for young physicist who + + align:start position:0% +recommendation for young physicist who + + + align:start position:0% +recommendation for young physicist who +is finishing his PhD at Stanford and the + + align:start position:0% +is finishing his PhD at Stanford and the + + + align:start position:0% +is finishing his PhD at Stanford and the +students advisor Leonard Schiff wrote to + + align:start position:0% +students advisor Leonard Schiff wrote to + + + align:start position:0% +students advisor Leonard Schiff wrote to +to to recommend the students and you + + align:start position:0% +to to recommend the students and you + + + align:start position:0% +to to recommend the students and you +should hire my student for the new + + align:start position:0% +should hire my student for the new + + + align:start position:0% +should hire my student for the new +professorship because he actually does + + align:start position:0% +professorship because he actually does + + + align:start position:0% +professorship because he actually does +understand filament diagrams and + + align:start position:0% +understand filament diagrams and + + + align:start position:0% +understand filament diagrams and +actually use them in his thesis that was + + align:start position:0% +actually use them in his thesis that was + + + align:start position:0% +actually use them in his thesis that was +five years after this Pocono conference + + align:start position:0% +five years after this Pocono conference + + + align:start position:0% +five years after this Pocono conference +roughly four years after feynman's uh + + align:start position:0% +roughly four years after feynman's uh + + + align:start position:0% +roughly four years after feynman's uh +attempt to clarify the techniques with + + align:start position:0% +attempt to clarify the techniques with + + + align:start position:0% +attempt to clarify the techniques with +his articles so if four or five years + + align:start position:0% +his articles so if four or five years + + + align:start position:0% +his articles so if four or five years +later your advisor says my student is + + align:start position:0% +later your advisor says my student is + + + align:start position:0% +later your advisor says my student is +unusual because he does understand them + + align:start position:0% +unusual because he does understand them + + + align:start position:0% +unusual because he does understand them +that seems to suggest these were not + + align:start position:0% +that seems to suggest these were not + + + align:start position:0% +that seems to suggest these were not +universally cleared everyone so they + + align:start position:0% +universally cleared everyone so they + + + align:start position:0% +universally cleared everyone so they +were clearly not so obvious or automatic + + align:start position:0% +were clearly not so obvious or automatic + + + align:start position:0% +were clearly not so obvious or automatic +even after finding did have a chance to + + align:start position:0% +even after finding did have a chance to + + + align:start position:0% +even after finding did have a chance to +try to clarify and yet you can see + + align:start position:0% +try to clarify and yet you can see + + + align:start position:0% +try to clarify and yet you can see +evidence that they're taking off like + + align:start position:0% +evidence that they're taking off like + + + align:start position:0% +evidence that they're taking off like +gangbusters if you go through the + + align:start position:0% +gangbusters if you go through the + + + align:start position:0% +gangbusters if you go through the +physical review and + + align:start position:0% +physical review and + + + align:start position:0% +physical review and +in the book I talk about similar + + align:start position:0% +in the book I talk about similar + + + align:start position:0% +in the book I talk about similar +searches in other uh journals throughout + + align:start position:0% +searches in other uh journals throughout + + + align:start position:0% +searches in other uh journals throughout +many parts of the world in fact not just + + align:start position:0% +many parts of the world in fact not just + + + align:start position:0% +many parts of the world in fact not just +in the United States you see an + + align:start position:0% +in the United States you see an + + + align:start position:0% +in the United States you see an +exponential rise that these diagram + + align:start position:0% +exponential rise that these diagram + + + align:start position:0% +exponential rise that these diagram +techniques are getting picked up the + + align:start position:0% +techniques are getting picked up the + + + align:start position:0% +techniques are getting picked up the +doubling time I forgot is something like + + align:start position:0% +doubling time I forgot is something like + + + align:start position:0% +doubling time I forgot is something like +two and a half years or three years + + align:start position:0% +two and a half years or three years + + + align:start position:0% +two and a half years or three years +where that where they're really growing + + align:start position:0% +where that where they're really growing + + + align:start position:0% +where that where they're really growing +literally exponentially uh over the + + align:start position:0% +literally exponentially uh over the + + + align:start position:0% +literally exponentially uh over the +first sort of half decade or so so yeah + + align:start position:0% +first sort of half decade or so so yeah + + + align:start position:0% +first sort of half decade or so so yeah +on the one hand you have people saying I + + align:start position:0% +on the one hand you have people saying I + + + align:start position:0% +on the one hand you have people saying I +don't get it I can't do it and yet you + + align:start position:0% +don't get it I can't do it and yet you + + + align:start position:0% +don't get it I can't do it and yet you +find there's growing evidence that at + + align:start position:0% +find there's growing evidence that at + + + align:start position:0% +find there's growing evidence that at +least some people have become kind of + + align:start position:0% +least some people have become kind of + + + align:start position:0% +least some people have become kind of +early adopters of the techniques + + align:start position:0% +early adopters of the techniques + + + align:start position:0% +early adopters of the techniques +you can then do the usual trick and and + + align:start position:0% +you can then do the usual trick and and + + + align:start position:0% +you can then do the usual trick and and +not just say how many articles use the + + align:start position:0% +not just say how many articles use the + + + align:start position:0% +not just say how many articles use the +diagrams but who wrote those articles + + align:start position:0% +diagrams but who wrote those articles + + + align:start position:0% +diagrams but who wrote those articles +where were they what were they up to and + + align:start position:0% +where were they what were they up to and + + + align:start position:0% +where were they what were they up to and +you start seeing some pretty interesting + + align:start position:0% +you start seeing some pretty interesting + + + align:start position:0% +you start seeing some pretty interesting +um traits some common features among the + + align:start position:0% +um traits some common features among the + + + align:start position:0% +um traits some common features among the +people who were who were beginning to + + align:start position:0% +people who were who were beginning to + + + align:start position:0% +people who were who were beginning to +use these techniques uh in their own + + align:start position:0% +use these techniques uh in their own + + + align:start position:0% +use these techniques uh in their own +papers so firsthand they were all young + + align:start position:0% +papers so firsthand they were all young + + + align:start position:0% +papers so firsthand they were all young +in their careers which is say they were + + align:start position:0% +in their careers which is say they were + + + align:start position:0% +in their careers which is say they were +all either graduate students or + + align:start position:0% +all either graduate students or + + + align:start position:0% +all either graduate students or +post-docs uh for the vast majority a few + + align:start position:0% +post-docs uh for the vast majority a few + + + align:start position:0% +post-docs uh for the vast majority a few +of them were kind of assistant + + align:start position:0% +of them were kind of assistant + + + align:start position:0% +of them were kind of assistant +professors they were all still fairly + + align:start position:0% +professors they were all still fairly + + + align:start position:0% +professors they were all still fairly +early in their training or careers they + + align:start position:0% +early in their training or careers they + + + align:start position:0% +early in their training or careers they +were all theoretical physicists in this + + align:start position:0% +were all theoretical physicists in this + + + align:start position:0% +were all theoretical physicists in this +early period + + align:start position:0% +early period + + + align:start position:0% +early period +nowadays these diagrams are just as + + align:start position:0% +nowadays these diagrams are just as + + + align:start position:0% +nowadays these diagrams are just as +ubiquitous among experimental physicists + + align:start position:0% +ubiquitous among experimental physicists + + + align:start position:0% +ubiquitous among experimental physicists +as theorists but in this early phases + + align:start position:0% +as theorists but in this early phases + + + align:start position:0% +as theorists but in this early phases +early kind of exponential rise it was + + align:start position:0% +early kind of exponential rise it was + + + align:start position:0% +early kind of exponential rise it was +young theoretical physicists and the + + align:start position:0% +young theoretical physicists and the + + + align:start position:0% +young theoretical physicists and the +last part was that they were really in + + align:start position:0% +last part was that they were really in + + + align:start position:0% +last part was that they were really in +contact with each other you can do a + + align:start position:0% +contact with each other you can do a + + + align:start position:0% +contact with each other you can do a +kind of network study and trace it + + align:start position:0% +kind of network study and trace it + + + align:start position:0% +kind of network study and trace it +through by co-authorship by + + align:start position:0% +through by co-authorship by + + + align:start position:0% +through by co-authorship by +acknowledgments by unpublished uh + + align:start position:0% +acknowledgments by unpublished uh + + + align:start position:0% +acknowledgments by unpublished uh +correspondence that I was able to find + + align:start position:0% +correspondence that I was able to find + + + align:start position:0% +correspondence that I was able to find +and piece together that they knew each + + align:start position:0% +and piece together that they knew each + + + align:start position:0% +and piece together that they knew each +other it was a network that had come + + align:start position:0% +other it was a network that had come + + + align:start position:0% +other it was a network that had come +together to learn these techniques and + + align:start position:0% +together to learn these techniques and + + + align:start position:0% +together to learn these techniques and +then they began to spread out so + + align:start position:0% +then they began to spread out so + + + align:start position:0% +then they began to spread out so +something pedagogical was going on the + + align:start position:0% +something pedagogical was going on the + + + align:start position:0% +something pedagogical was going on the +majority of these of these early users + + align:start position:0% +majority of these of these early users + + + align:start position:0% +majority of these of these early users +were in the still in the formal phase of + + align:start position:0% +were in the still in the formal phase of + + + align:start position:0% +were in the still in the formal phase of +their training they were literally still + + align:start position:0% +their training they were literally still + + + align:start position:0% +their training they were literally still +being taught to be physicists and yet it + + align:start position:0% +being taught to be physicists and yet it + + + align:start position:0% +being taught to be physicists and yet it +wasn't a story of like write a textbook + + align:start position:0% +wasn't a story of like write a textbook + + + align:start position:0% +wasn't a story of like write a textbook +teach some classes it'll spread this + + align:start position:0% +teach some classes it'll spread this + + + align:start position:0% +teach some classes it'll spread this +entire all of the data points shown on + + align:start position:0% +entire all of the data points shown on + + + align:start position:0% +entire all of the data points shown on +this uh early plot uh represent articles + + align:start position:0% +this uh early plot uh represent articles + + + align:start position:0% +this uh early plot uh represent articles +that came out before the very first + + align:start position:0% +that came out before the very first + + + align:start position:0% +that came out before the very first +English language textbooks have been + + align:start position:0% +English language textbooks have been + + + align:start position:0% +English language textbooks have been +published that incorporated the new + + align:start position:0% +published that incorporated the new + + + align:start position:0% +published that incorporated the new +technique so the first textbook + + align:start position:0% +technique so the first textbook + + + align:start position:0% +technique so the first textbook +treatments of how to calculate with + + align:start position:0% +treatments of how to calculate with + + + align:start position:0% +treatments of how to calculate with +these new Feynman diagrams weren't + + align:start position:0% +these new Feynman diagrams weren't + + + align:start position:0% +these new Feynman diagrams weren't +published until 1955 by which time there + + align:start position:0% +published until 1955 by which time there + + + align:start position:0% +published until 1955 by which time there +was already evidence of this + + align:start position:0% +was already evidence of this + + + align:start position:0% +was already evidence of this +fast-growing exponential rise + + align:start position:0% +fast-growing exponential rise + + + align:start position:0% +fast-growing exponential rise +so how does that happen a lot of it + + align:start position:0% +so how does that happen a lot of it + + + align:start position:0% +so how does that happen a lot of it +comes down to this gentleman uh Freeman + + align:start position:0% +comes down to this gentleman uh Freeman + + + align:start position:0% +comes down to this gentleman uh Freeman +Dyson + + align:start position:0% + + + + align:start position:0% + +Dyson you might know his name he just + + align:start position:0% +Dyson you might know his name he just + + + align:start position:0% +Dyson you might know his name he just +passed away this past March + + align:start position:0% +passed away this past March + + + align:start position:0% +passed away this past March +just before quarantine in fact he died + + align:start position:0% +just before quarantine in fact he died + + + align:start position:0% +just before quarantine in fact he died +in the very early March at the age of 96 + + align:start position:0% +in the very early March at the age of 96 + + + align:start position:0% +in the very early March at the age of 96 +quite a remarkable life and career + + align:start position:0% +quite a remarkable life and career + + + align:start position:0% +quite a remarkable life and career +at this point he was quite a young + + align:start position:0% +at this point he was quite a young + + + align:start position:0% +at this point he was quite a young +person he was in fact still in graduate + + align:start position:0% +person he was in fact still in graduate + + + align:start position:0% +person he was in fact still in graduate +school he was originally from Britain + + align:start position:0% +school he was originally from Britain + + + align:start position:0% +school he was originally from Britain +he got a very competitive Fellowship + + align:start position:0% +he got a very competitive Fellowship + + + align:start position:0% +he got a very competitive Fellowship +very soon after the end of the second + + align:start position:0% +very soon after the end of the second + + + align:start position:0% +very soon after the end of the second +World War called a commonwealth + + align:start position:0% +World War called a commonwealth + + + align:start position:0% +World War called a commonwealth +Fellowship reserved at the time for + + align:start position:0% +Fellowship reserved at the time for + + + align:start position:0% +Fellowship reserved at the time for +British students to study abroad mostly + + align:start position:0% +British students to study abroad mostly + + + align:start position:0% +British students to study abroad mostly +in commonwealth countries like Canada or + + align:start position:0% +in commonwealth countries like Canada or + + + align:start position:0% +in commonwealth countries like Canada or +Australia but also to the United States + + align:start position:0% +Australia but also to the United States + + + align:start position:0% +Australia but also to the United States +so he got a fellowship he came to + + align:start position:0% +so he got a fellowship he came to + + + align:start position:0% +so he got a fellowship he came to +Cornell University because he really + + align:start position:0% +Cornell University because he really + + + align:start position:0% +Cornell University because he really +wanted to study with Hans beta whose + + align:start position:0% +wanted to study with Hans beta whose + + + align:start position:0% +wanted to study with Hans beta whose +work even in the 30s it seemed super + + align:start position:0% +work even in the 30s it seemed super + + + align:start position:0% +work even in the 30s it seemed super +exciting and this young grad student + + align:start position:0% +exciting and this young grad student + + + align:start position:0% +exciting and this young grad student +said I want to go study with beta so he + + align:start position:0% +said I want to go study with beta so he + + + align:start position:0% +said I want to go study with beta so he +gets the fellowship comes to Cornell he + + align:start position:0% +gets the fellowship comes to Cornell he + + + align:start position:0% +gets the fellowship comes to Cornell he +starts working with the beta but also + + align:start position:0% +starts working with the beta but also + + + align:start position:0% +starts working with the beta but also +very quickly meets Feynman who at this + + align:start position:0% +very quickly meets Feynman who at this + + + align:start position:0% +very quickly meets Feynman who at this +point was a very young Professor whom + + align:start position:0% +point was a very young Professor whom + + + align:start position:0% +point was a very young Professor whom +Beta had recruited + + align:start position:0% +Beta had recruited + + + align:start position:0% +Beta had recruited +as soon as Los Alamos uh as soon as they + + align:start position:0% +as soon as Los Alamos uh as soon as they + + + align:start position:0% +as soon as Los Alamos uh as soon as they +were done at Los Alamos for the war so + + align:start position:0% +were done at Los Alamos for the war so + + + align:start position:0% +were done at Los Alamos for the war so +beta and Feynman had interacted at Los + + align:start position:0% +beta and Feynman had interacted at Los + + + align:start position:0% +beta and Feynman had interacted at Los +Alamos beta as the senior theoretical + + align:start position:0% +Alamos beta as the senior theoretical + + + align:start position:0% +Alamos beta as the senior theoretical +physicist in Cornell hired Feynman this + + align:start position:0% +physicist in Cornell hired Feynman this + + + align:start position:0% +physicist in Cornell hired Feynman this +even younger physicist Dyson meets fine + + align:start position:0% +even younger physicist Dyson meets fine + + + align:start position:0% +even younger physicist Dyson meets fine +in there the summer after his first year + + align:start position:0% +in there the summer after his first year + + + align:start position:0% +in there the summer after his first year +grad school Dyson and Feynman Drive + + align:start position:0% +grad school Dyson and Feynman Drive + + + align:start position:0% +grad school Dyson and Feynman Drive +cross-country together + + align:start position:0% +cross-country together + + + align:start position:0% +cross-country together +Dyson wanted to just see the country he + + align:start position:0% +Dyson wanted to just see the country he + + + align:start position:0% +Dyson wanted to just see the country he +was from Britain he was sending these + + align:start position:0% +was from Britain he was sending these + + + align:start position:0% +was from Britain he was sending these +really kind of delicious letters back to + + align:start position:0% +really kind of delicious letters back to + + + align:start position:0% +really kind of delicious letters back to +his family often writing to his mother + + align:start position:0% +his family often writing to his mother + + + align:start position:0% +his family often writing to his mother +on a manual typewrit or a small portable + + align:start position:0% +on a manual typewrit or a small portable + + + align:start position:0% +on a manual typewrit or a small portable +manual typewriter often more than once a + + align:start position:0% +manual typewriter often more than once a + + + align:start position:0% +manual typewriter often more than once a +week + + align:start position:0% +week + + + align:start position:0% +week +and he just wanted to explore the + + align:start position:0% +and he just wanted to explore the + + + align:start position:0% +and he just wanted to explore the +country because no member of his + + align:start position:0% +country because no member of his + + + align:start position:0% +country because no member of his +immediate family had ever visited the + + align:start position:0% +immediate family had ever visited the + + + align:start position:0% +immediate family had ever visited the +United States he was very curious and + + align:start position:0% +United States he was very curious and + + + align:start position:0% +United States he was very curious and +Feynman wanted to go back to um New + + align:start position:0% +Feynman wanted to go back to um New + + + align:start position:0% +Feynman wanted to go back to um New +Mexico yeah girlfriend out there maybe + + align:start position:0% +Mexico yeah girlfriend out there maybe + + + align:start position:0% +Mexico yeah girlfriend out there maybe +was gonna do some Consulting by Los + + align:start position:0% +was gonna do some Consulting by Los + + + align:start position:0% +was gonna do some Consulting by Los +Alamos so they basically drove + + align:start position:0% +Alamos so they basically drove + + + align:start position:0% +Alamos so they basically drove +cross-country together that summer of + + align:start position:0% +cross-country together that summer of + + + align:start position:0% +cross-country together that summer of +48. + + align:start position:0% +48. + + + align:start position:0% +48. +um + + align:start position:0% +um + + + align:start position:0% +um +which is say just just weeks after the + + align:start position:0% +which is say just just weeks after the + + + align:start position:0% +which is say just just weeks after the +Pocono meeting so Dyson had not been at + + align:start position:0% +Pocono meeting so Dyson had not been at + + + align:start position:0% +Pocono meeting so Dyson had not been at +Pocono he'd been hearing about these + + align:start position:0% +Pocono he'd been hearing about these + + + align:start position:0% +Pocono he'd been hearing about these +things in in Ithaca from from his uh new + + align:start position:0% +things in in Ithaca from from his uh new + + + align:start position:0% +things in in Ithaca from from his uh new +friend but now he had several days long + + align:start position:0% +friend but now he had several days long + + + align:start position:0% +friend but now he had several days long +drive to just pick his brain + + align:start position:0% +drive to just pick his brain + + + align:start position:0% +drive to just pick his brain +uh meanwhile once once they get to New + + align:start position:0% +uh meanwhile once once they get to New + + + align:start position:0% +uh meanwhile once once they get to New +Mexico then Dyson took the bus to go to + + align:start position:0% +Mexico then Dyson took the bus to go to + + + align:start position:0% +Mexico then Dyson took the bus to go to +Ann Arbor Michigan again he was like + + align:start position:0% +Ann Arbor Michigan again he was like + + + align:start position:0% +Ann Arbor Michigan again he was like +being a tourist he then spent about six + + align:start position:0% +being a tourist he then spent about six + + + align:start position:0% +being a tourist he then spent about six +weeks at uh at the University of + + align:start position:0% +weeks at uh at the University of + + + align:start position:0% +weeks at uh at the University of +Michigan attending summer school + + align:start position:0% +Michigan attending summer school + + + align:start position:0% +Michigan attending summer school +lectures by none other than Julian + + align:start position:0% +lectures by none other than Julian + + + align:start position:0% +lectures by none other than Julian +schwinger where again he had a chance to + + align:start position:0% +schwinger where again he had a chance to + + + align:start position:0% +schwinger where again he had a chance to +talk directly with schwinger at some + + align:start position:0% +talk directly with schwinger at some + + + align:start position:0% +talk directly with schwinger at some +length and some detail where schwinger + + align:start position:0% +length and some detail where schwinger + + + align:start position:0% +length and some detail where schwinger +was lecturing on his own approach to + + align:start position:0% +was lecturing on his own approach to + + + align:start position:0% +was lecturing on his own approach to +Quantum field Theory under normalization + + align:start position:0% +Quantum field Theory under normalization + + + align:start position:0% +Quantum field Theory under normalization +so at this point by the end of the + + align:start position:0% +so at this point by the end of the + + + align:start position:0% +so at this point by the end of the +summer of 1948 Freeman Dyson was the + + align:start position:0% +summer of 1948 Freeman Dyson was the + + + align:start position:0% +summer of 1948 Freeman Dyson was the +only person in the universe who had + + align:start position:0% +only person in the universe who had + + + align:start position:0% +only person in the universe who had +spent extensive close informal personal + + align:start position:0% +spent extensive close informal personal + + + align:start position:0% +spent extensive close informal personal +time with both Richard Feynman and + + align:start position:0% +time with both Richard Feynman and + + + align:start position:0% +time with both Richard Feynman and +Julian schwinger just at the time they + + align:start position:0% +Julian schwinger just at the time they + + + align:start position:0% +Julian schwinger just at the time they +were each working on their separate and + + align:start position:0% +were each working on their separate and + + + align:start position:0% +were each working on their separate and +very different looking approaches to + + align:start position:0% +very different looking approaches to + + + align:start position:0% +very different looking approaches to +Quantum field Theory and renew + + align:start position:0% +Quantum field Theory and renew + + + align:start position:0% +Quantum field Theory and renew +normalization they take this now famous + + align:start position:0% +normalization they take this now famous + + + align:start position:0% +normalization they take this now famous +bus ride back from Michigan uh back to + + align:start position:0% +bus ride back from Michigan uh back to + + + align:start position:0% +bus ride back from Michigan uh back to +the east coast where he was going to + + align:start position:0% +the east coast where he was going to + + + align:start position:0% +the east coast where he was going to +start for the second year of his + + align:start position:0% +start for the second year of his + + + align:start position:0% +start for the second year of his +fellowship at The Institute for that + + align:start position:0% +fellowship at The Institute for that + + + align:start position:0% +fellowship at The Institute for that +study in Princeton + + align:start position:0% +study in Princeton + + + align:start position:0% +study in Princeton +by the way he never finished his PhD to + + align:start position:0% +by the way he never finished his PhD to + + + align:start position:0% +by the way he never finished his PhD to +the day that he died he was Mr Dyson uh + + align:start position:0% +the day that he died he was Mr Dyson uh + + + align:start position:0% +the day that he died he was Mr Dyson uh +so and he thought phds were a horrible + + align:start position:0% +so and he thought phds were a horrible + + + align:start position:0% +so and he thought phds were a horrible +waste of time + + align:start position:0% +waste of time + + + align:start position:0% +waste of time +he might be right I don't know anyway so + + align:start position:0% +he might be right I don't know anyway so + + + align:start position:0% +he might be right I don't know anyway so +so he he spent one year as a grad + + align:start position:0% +so he he spent one year as a grad + + + align:start position:0% +so he he spent one year as a grad +student Cornell then one year on + + align:start position:0% +student Cornell then one year on + + + align:start position:0% +student Cornell then one year on +fellowship at The Institute and then was + + align:start position:0% +fellowship at The Institute and then was + + + align:start position:0% +fellowship at The Institute and then was +hired as a full Professor Cornell like + + align:start position:0% +hired as a full Professor Cornell like + + + align:start position:0% +hired as a full Professor Cornell like +four years later this + + align:start position:0% + + + + align:start position:0% + +this on the bus ride he has this amazing + + align:start position:0% +this on the bus ride he has this amazing + + + align:start position:0% +this on the bus ride he has this amazing +epiphany + + align:start position:0% +epiphany + + + align:start position:0% +epiphany +uh that he starts seeing you know how + + align:start position:0% +uh that he starts seeing you know how + + + align:start position:0% +uh that he starts seeing you know how +the two very different looking + + align:start position:0% +the two very different looking + + + align:start position:0% +the two very different looking +approaches might fit together + + align:start position:0% +approaches might fit together + + + align:start position:0% +approaches might fit together +schwinger's very formal looking approach + + align:start position:0% +schwinger's very formal looking approach + + + align:start position:0% +schwinger's very formal looking approach +to a kind of algebraic almost axiomatic + + align:start position:0% +to a kind of algebraic almost axiomatic + + + align:start position:0% +to a kind of algebraic almost axiomatic +approach to Quantum field Theory and + + align:start position:0% +approach to Quantum field Theory and + + + align:start position:0% +approach to Quantum field Theory and +renewalization and feynman's diagram + + align:start position:0% +renewalization and feynman's diagram + + + align:start position:0% +renewalization and feynman's diagram +based bookkeeping sort of more pictorial + + align:start position:0% +based bookkeeping sort of more pictorial + + + align:start position:0% +based bookkeeping sort of more pictorial +somewhat more intuitive approach the two + + align:start position:0% +somewhat more intuitive approach the two + + + align:start position:0% +somewhat more intuitive approach the two +of them meaning fine and swinger + + align:start position:0% +of them meaning fine and swinger + + + align:start position:0% +of them meaning fine and swinger +couldn't understand what each other was + + align:start position:0% +couldn't understand what each other was + + + align:start position:0% +couldn't understand what each other was +doing yet + + align:start position:0% +doing yet + + + align:start position:0% +doing yet +uh and so Dyson is the one who actually + + align:start position:0% +uh and so Dyson is the one who actually + + + align:start position:0% +uh and so Dyson is the one who actually +sort of puts it together uh a a good + + align:start position:0% +sort of puts it together uh a a good + + + align:start position:0% +sort of puts it together uh a a good +chunk of it literally on the bus heading + + align:start position:0% +chunk of it literally on the bus heading + + + align:start position:0% +chunk of it literally on the bus heading +back East once he gets to The Institute + + align:start position:0% +back East once he gets to The Institute + + + align:start position:0% +back East once he gets to The Institute +he then submits two articles that Autumn + + align:start position:0% +he then submits two articles that Autumn + + + align:start position:0% +he then submits two articles that Autumn +sends both of them to the physical + + align:start position:0% +sends both of them to the physical + + + align:start position:0% +sends both of them to the physical +review these were published before + + align:start position:0% +review these were published before + + + align:start position:0% +review these were published before +fireman's own articles had come out fine + + align:start position:0% +fireman's own articles had come out fine + + + align:start position:0% +fireman's own articles had come out fine +was actually quite slow to write up his + + align:start position:0% +was actually quite slow to write up his + + + align:start position:0% +was actually quite slow to write up his +articles it came out a little bit later + + align:start position:0% +articles it came out a little bit later + + + align:start position:0% +articles it came out a little bit later +also in 1949 + + align:start position:0% +also in 1949 + + + align:start position:0% +also in 1949 +in the early years Dyson's papers were + + align:start position:0% +in the early years Dyson's papers were + + + align:start position:0% +in the early years Dyson's papers were +cited more often than firemens they were + + align:start position:0% +cited more often than firemens they were + + + align:start position:0% +cited more often than firemens they were +they were getting a lot of attention in + + align:start position:0% +they were getting a lot of attention in + + + align:start position:0% +they were getting a lot of attention in +part because he was so methodical in + + align:start position:0% +part because he was so methodical in + + + align:start position:0% +part because he was so methodical in +laying out a kind of point-by-point + + align:start position:0% +laying out a kind of point-by-point + + + align:start position:0% +laying out a kind of point-by-point +almost recipe book a rule book for how + + align:start position:0% +almost recipe book a rule book for how + + + align:start position:0% +almost recipe book a rule book for how +to use them exactly the stuff that + + align:start position:0% +to use them exactly the stuff that + + + align:start position:0% +to use them exactly the stuff that +seemed to be missing from feynman's + + align:start position:0% +seemed to be missing from feynman's + + + align:start position:0% +seemed to be missing from feynman's +presentation at least at Pocono Dyson + + align:start position:0% +presentation at least at Pocono Dyson + + + align:start position:0% +presentation at least at Pocono Dyson +was able to kind of ground the diagrams + + align:start position:0% +was able to kind of ground the diagrams + + + align:start position:0% +was able to kind of ground the diagrams +in more first principles derivations and + + align:start position:0% +in more first principles derivations and + + + align:start position:0% +in more first principles derivations and +really go through worked examples + + align:start position:0% +really go through worked examples + + + align:start position:0% +really go through worked examples +and it was in these papers uh where + + align:start position:0% +and it was in these papers uh where + + + align:start position:0% +and it was in these papers uh where +Dyson demonstrates the mathematical + + align:start position:0% +Dyson demonstrates the mathematical + + + align:start position:0% +Dyson demonstrates the mathematical +equivalence of the three separate + + align:start position:0% +equivalence of the three separate + + + align:start position:0% +equivalence of the three separate +methods that by this point were on offer + + align:start position:0% +methods that by this point were on offer + + + align:start position:0% +methods that by this point were on offer +those by Feynman schwinger and then + + align:start position:0% +those by Feynman schwinger and then + + + align:start position:0% +those by Feynman schwinger and then +separately by sinitiro tomanaga whom I + + align:start position:0% +separately by sinitiro tomanaga whom I + + + align:start position:0% +separately by sinitiro tomanaga whom I +mentioned briefly last time tomanaga was + + align:start position:0% +mentioned briefly last time tomanaga was + + + align:start position:0% +mentioned briefly last time tomanaga was +still in Tokyo Japan was under U.S + + align:start position:0% +still in Tokyo Japan was under U.S + + + align:start position:0% +still in Tokyo Japan was under U.S +occupation after the war + + align:start position:0% +occupation after the war + + + align:start position:0% +occupation after the war +chomanage had worked out a method + + align:start position:0% +chomanage had worked out a method + + + align:start position:0% +chomanage had worked out a method +remarkably similar to what schwinger + + align:start position:0% +remarkably similar to what schwinger + + + align:start position:0% +remarkably similar to what schwinger +later came up with they were working + + align:start position:0% +later came up with they were working + + + align:start position:0% +later came up with they were working +totally independent of each other partly + + align:start position:0% +totally independent of each other partly + + + align:start position:0% +totally independent of each other partly +because of the war + + align:start position:0% +because of the war + + + align:start position:0% +because of the war +had gotten there to many parts not not + + align:start position:0% +had gotten there to many parts not not + + + align:start position:0% +had gotten there to many parts not not +all the things schwinger did but very + + align:start position:0% +all the things schwinger did but very + + + align:start position:0% +all the things schwinger did but very +similar framework and many of the same + + align:start position:0% +similar framework and many of the same + + + align:start position:0% +similar framework and many of the same +insights along the way tomanaga had done + + align:start position:0% +insights along the way tomanaga had done + + + align:start position:0% +insights along the way tomanaga had done +this starting in 1943 but the results + + align:start position:0% +this starting in 1943 but the results + + + align:start position:0% +this starting in 1943 but the results +were not known outside of Japan partly + + align:start position:0% +were not known outside of Japan partly + + + align:start position:0% +were not known outside of Japan partly +because of you know the naval blockade + + align:start position:0% +because of you know the naval blockade + + + align:start position:0% +because of you know the naval blockade +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +one of the first packages sent overseas + + align:start position:0% +one of the first packages sent overseas + + + align:start position:0% +one of the first packages sent overseas +out of Japan after the end of the war + + align:start position:0% +out of Japan after the end of the war + + + align:start position:0% +out of Japan after the end of the war +was actually a package of manuscripts + + align:start position:0% +was actually a package of manuscripts + + + align:start position:0% +was actually a package of manuscripts +and reprints the tomanaga sent to Robert + + align:start position:0% +and reprints the tomanaga sent to Robert + + + align:start position:0% +and reprints the tomanaga sent to Robert +Oppenheimer and it was actually ferried + + align:start position:0% +Oppenheimer and it was actually ferried + + + align:start position:0% +Oppenheimer and it was actually ferried +in official kind of um uh U.S uh + + align:start position:0% +in official kind of um uh U.S uh + + + align:start position:0% +in official kind of um uh U.S uh +delivery was from from U.S occupied + + align:start position:0% +delivery was from from U.S occupied + + + align:start position:0% +delivery was from from U.S occupied +Tokyo back to the United States because + + align:start position:0% +Tokyo back to the United States because + + + align:start position:0% +Tokyo back to the United States because +tobunaga had read in one of the new + + align:start position:0% +tobunaga had read in one of the new + + + align:start position:0% +tobunaga had read in one of the new +libraries in a new subscription to + + align:start position:0% +libraries in a new subscription to + + + align:start position:0% +libraries in a new subscription to +Newsweek magazine about the lamb shift + + align:start position:0% +Newsweek magazine about the lamb shift + + + align:start position:0% +Newsweek magazine about the lamb shift +because the magazine had covered + + align:start position:0% +because the magazine had covered + + + align:start position:0% +because the magazine had covered +everything about Robert Oppenheimer he + + align:start position:0% +everything about Robert Oppenheimer he + + + align:start position:0% +everything about Robert Oppenheimer he +was amazingly famous in the United + + align:start position:0% +was amazingly famous in the United + + + align:start position:0% +was amazingly famous in the United +States after the war the fact that he + + align:start position:0% +States after the war the fact that he + + + align:start position:0% +States after the war the fact that he +was talking about the Shelter Island + + align:start position:0% +was talking about the Shelter Island + + + align:start position:0% +was talking about the Shelter Island +conference became newsworthy he + + align:start position:0% +conference became newsworthy he + + + align:start position:0% +conference became newsworthy he +mentioned the lamb shift this gets all + + align:start position:0% +mentioned the lamb shift this gets all + + + align:start position:0% +mentioned the lamb shift this gets all +the way back to Tokyo through this kind + + align:start position:0% +the way back to Tokyo through this kind + + + align:start position:0% +the way back to Tokyo through this kind +of crazy uh um convoluted system + + align:start position:0% +of crazy uh um convoluted system + + + align:start position:0% +of crazy uh um convoluted system +tomanaga reads about it says Hey wow and + + align:start position:0% +tomanaga reads about it says Hey wow and + + + align:start position:0% +tomanaga reads about it says Hey wow and +it digs back through some of his old + + align:start position:0% +it digs back through some of his old + + + align:start position:0% +it digs back through some of his old +wartime manuscripts and reprints and + + align:start position:0% +wartime manuscripts and reprints and + + + align:start position:0% +wartime manuscripts and reprints and +sends materials to opponent had them + + align:start position:0% +sends materials to opponent had them + + + align:start position:0% +sends materials to opponent had them +effectively mimeographed and shared with + + align:start position:0% +effectively mimeographed and shared with + + + align:start position:0% +effectively mimeographed and shared with +all the participants who've been Shelter + + align:start position:0% +all the participants who've been Shelter + + + align:start position:0% +all the participants who've been Shelter +Island so the U.S based in some of the + + align:start position:0% +Island so the U.S based in some of the + + + align:start position:0% +Island so the U.S based in some of the +Western European physicists who had + + align:start position:0% +Western European physicists who had + + + align:start position:0% +Western European physicists who had +heard about the lamb shift and Robbie's + + align:start position:0% +heard about the lamb shift and Robbie's + + + align:start position:0% +heard about the lamb shift and Robbie's +group's measurements and so on + + align:start position:0% +group's measurements and so on + + + align:start position:0% +group's measurements and so on +they learned in the days after Shelter + + align:start position:0% +they learned in the days after Shelter + + + align:start position:0% +they learned in the days after Shelter +Island about some of tomonaga's work + + align:start position:0% +Island about some of tomonaga's work + + + align:start position:0% +Island about some of tomonaga's work +then they helped arrange for English + + align:start position:0% +then they helped arrange for English + + + align:start position:0% +then they helped arrange for English +language Publications they were very + + align:start position:0% +language Publications they were very + + + align:start position:0% +language Publications they were very +very eager in fact to try to get + + align:start position:0% +very eager in fact to try to get + + + align:start position:0% +very eager in fact to try to get +tomonaga credit + + align:start position:0% +tomonaga credit + + + align:start position:0% +tomonaga credit +um partly because it was remarkable + + align:start position:0% +um partly because it was remarkable + + + align:start position:0% +um partly because it was remarkable +partly I think because there was a a + + align:start position:0% +partly I think because there was a a + + + align:start position:0% +partly I think because there was a a +sense that this was a dramatic + + align:start position:0% +sense that this was a dramatic + + + align:start position:0% +sense that this was a dramatic +Development coming from uh the city that + + align:start position:0% +Development coming from uh the city that + + + align:start position:0% +Development coming from uh the city that +had just been uh subjected to Relentless + + align:start position:0% +had just been uh subjected to Relentless + + + align:start position:0% +had just been uh subjected to Relentless +firebombing during the war that + + align:start position:0% +firebombing during the war that + + + align:start position:0% +firebombing during the war that +nonetheless this work somehow got done + + align:start position:0% +nonetheless this work somehow got done + + + align:start position:0% +nonetheless this work somehow got done +in the midst of horrible conditions so + + align:start position:0% +in the midst of horrible conditions so + + + align:start position:0% +in the midst of horrible conditions so +Oppenheimer worked hard to get + + align:start position:0% +Oppenheimer worked hard to get + + + align:start position:0% +Oppenheimer worked hard to get +tomanaga's work into circulation so + + align:start position:0% +tomanaga's work into circulation so + + + align:start position:0% +tomanaga's work into circulation so +Dyson learned of it and Dyson was able + + align:start position:0% +Dyson learned of it and Dyson was able + + + align:start position:0% +Dyson learned of it and Dyson was able +to show in this pair of Articles from + + align:start position:0% +to show in this pair of Articles from + + + align:start position:0% +to show in this pair of Articles from +1949 that these three distinct + + align:start position:0% +1949 that these three distinct + + + align:start position:0% +1949 that these three distinct +approaches to Quantum electronamics were + + align:start position:0% +approaches to Quantum electronamics were + + + align:start position:0% +approaches to Quantum electronamics were +in fact mathematically equivalent very + + align:start position:0% +in fact mathematically equivalent very + + + align:start position:0% +in fact mathematically equivalent very +very much like what had happened 20 + + align:start position:0% +very much like what had happened 20 + + + align:start position:0% +very much like what had happened 20 +years earlier between Heisenberg's and + + align:start position:0% +years earlier between Heisenberg's and + + + align:start position:0% +years earlier between Heisenberg's and +Schrodinger's approaches to quantum + + align:start position:0% +Schrodinger's approaches to quantum + + + align:start position:0% +Schrodinger's approaches to quantum +theory + + align:start position:0% + + + + align:start position:0% + +timer at this point had become director + + align:start position:0% +timer at this point had become director + + + align:start position:0% +timer at this point had become director +of The Institute for advanced study he + + align:start position:0% +of The Institute for advanced study he + + + align:start position:0% +of The Institute for advanced study he +was now basically in effect Dyson the + + align:start position:0% +was now basically in effect Dyson the + + + align:start position:0% +was now basically in effect Dyson the +supervisor for the second year of the + + align:start position:0% +supervisor for the second year of the + + + align:start position:0% +supervisor for the second year of the +fellowship Oppenheimer was not that + + align:start position:0% +fellowship Oppenheimer was not that + + + align:start position:0% +fellowship Oppenheimer was not that +impressed with the Feynman diagrams at + + align:start position:0% +impressed with the Feynman diagrams at + + + align:start position:0% +impressed with the Feynman diagrams at +first in fact he used to come to Dyson's + + align:start position:0% +first in fact he used to come to Dyson's + + + align:start position:0% +first in fact he used to come to Dyson's +informal presentations and interrupt + + align:start position:0% +informal presentations and interrupt + + + align:start position:0% +informal presentations and interrupt +and basically show that he was still the + + align:start position:0% +and basically show that he was still the + + + align:start position:0% +and basically show that he was still the +smartest person in the room + + align:start position:0% +smartest person in the room + + + align:start position:0% +smartest person in the room +so the postdocs at The Institute asked + + align:start position:0% +so the postdocs at The Institute asked + + + align:start position:0% +so the postdocs at The Institute asked +Dyson to repeat each of his many hour + + align:start position:0% +Dyson to repeat each of his many hour + + + align:start position:0% +Dyson to repeat each of his many hour +seminars in private and they just + + align:start position:0% +seminars in private and they just + + + align:start position:0% +seminars in private and they just +wouldn't tell Oppenheimer so if Dyson + + align:start position:0% +wouldn't tell Oppenheimer so if Dyson + + + align:start position:0% +wouldn't tell Oppenheimer so if Dyson +would give these sort of announced + + align:start position:0% +would give these sort of announced + + + align:start position:0% +would give these sort of announced +seminars oppenheim would come and + + align:start position:0% +seminars oppenheim would come and + + + align:start position:0% +seminars oppenheim would come and +essentially kind of Heckle and disrupt + + align:start position:0% +essentially kind of Heckle and disrupt + + + align:start position:0% +essentially kind of Heckle and disrupt +and they'd have Dyson give the exact + + align:start position:0% +and they'd have Dyson give the exact + + + align:start position:0% +and they'd have Dyson give the exact +same talk the next day sort of in secret + + align:start position:0% +same talk the next day sort of in secret + + + align:start position:0% +same talk the next day sort of in secret +and finally after Hans beta intervened + + align:start position:0% +and finally after Hans beta intervened + + + align:start position:0% +and finally after Hans beta intervened +Oppenheimer said okay okay I relent in + + align:start position:0% +Oppenheimer said okay okay I relent in + + + align:start position:0% +Oppenheimer said okay okay I relent in +fact he literally wrote no low Contender + + align:start position:0% +fact he literally wrote no low Contender + + + align:start position:0% +fact he literally wrote no low Contender +like I I don't contest the charge I I I + + align:start position:0% +like I I don't contest the charge I I I + + + align:start position:0% +like I I don't contest the charge I I I +give up uh and uh by a few weeks into + + align:start position:0% +give up uh and uh by a few weeks into + + + align:start position:0% +give up uh and uh by a few weeks into +Dyson's fellowship and after that uh the + + align:start position:0% +Dyson's fellowship and after that uh the + + + align:start position:0% +Dyson's fellowship and after that uh the +diagrams really began to take off at The + + align:start position:0% +diagrams really began to take off at The + + + align:start position:0% +diagrams really began to take off at The +Institute + + align:start position:0% +Institute + + + align:start position:0% +Institute +so to understand what's going on in this + + align:start position:0% +so to understand what's going on in this + + + align:start position:0% +so to understand what's going on in this +very specific setting at The Institute + + align:start position:0% +very specific setting at The Institute + + + align:start position:0% +very specific setting at The Institute +for event study and all these new + + align:start position:0% +for event study and all these new + + + align:start position:0% +for event study and all these new +postdocs again it's important to step + + align:start position:0% +postdocs again it's important to step + + + align:start position:0% +postdocs again it's important to step +back and understand this is happening in + + align:start position:0% +back and understand this is happening in + + + align:start position:0% +back and understand this is happening in +a very particular institutional setting + + align:start position:0% +a very particular institutional setting + + + align:start position:0% +a very particular institutional setting +and again I found this really kind of + + align:start position:0% +and again I found this really kind of + + + align:start position:0% +and again I found this really kind of +fun to dig into when I was working on + + align:start position:0% +fun to dig into when I was working on + + + align:start position:0% +fun to dig into when I was working on +the book + + align:start position:0% +the book + + + align:start position:0% +the book +the idea that young scientists will + + align:start position:0% +the idea that young scientists will + + + align:start position:0% +the idea that young scientists will +typically do one or two are now not + + align:start position:0% +typically do one or two are now not + + + align:start position:0% +typically do one or two are now not +infrequently three separate + + align:start position:0% +infrequently three separate + + + align:start position:0% +infrequently three separate +post-doctoral appointments after their + + align:start position:0% +post-doctoral appointments after their + + + align:start position:0% +post-doctoral appointments after their +PHD but before they take on either a + + align:start position:0% +PHD but before they take on either a + + + align:start position:0% +PHD but before they take on either a +faculty job or a research job in + + align:start position:0% +faculty job or a research job in + + + align:start position:0% +faculty job or a research job in +industry or anything else that's now + + align:start position:0% +industry or anything else that's now + + + align:start position:0% +industry or anything else that's now +pretty routine today Across The Sciences + + align:start position:0% +pretty routine today Across The Sciences + + + align:start position:0% +pretty routine today Across The Sciences +in fact even in more and more of the + + align:start position:0% +in fact even in more and more of the + + + align:start position:0% +in fact even in more and more of the +humanities and social sciences the + + align:start position:0% +humanities and social sciences the + + + align:start position:0% +humanities and social sciences the +post-doc stage is pretty kind of + + align:start position:0% +post-doc stage is pretty kind of + + + align:start position:0% +post-doc stage is pretty kind of +self-evident or we've come we've gotten + + align:start position:0% +self-evident or we've come we've gotten + + + align:start position:0% +self-evident or we've come we've gotten +used to it uh by and large but again + + align:start position:0% +used to it uh by and large but again + + + align:start position:0% +used to it uh by and large but again +that that has a history and it's not a + + align:start position:0% +that that has a history and it's not a + + + align:start position:0% +that that has a history and it's not a +very very long history + + align:start position:0% +very very long history + + + align:start position:0% +very very long history +the idea of the post-doctoral fellowship + + align:start position:0% +the idea of the post-doctoral fellowship + + + align:start position:0% +the idea of the post-doctoral fellowship +really dates to the early years of the + + align:start position:0% +really dates to the early years of the + + + align:start position:0% +really dates to the early years of the +20th century very soon after the end of + + align:start position:0% +20th century very soon after the end of + + + align:start position:0% +20th century very soon after the end of +the first world war but they were still + + align:start position:0% +the first world war but they were still + + + align:start position:0% +the first world war but they were still +pretty rare they were very elite it was + + align:start position:0% +pretty rare they were very elite it was + + + align:start position:0% +pretty rare they were very elite it was +a big deal if you got this fancy + + align:start position:0% +a big deal if you got this fancy + + + align:start position:0% +a big deal if you got this fancy +post-doctoral Fellowship after finishing + + align:start position:0% +post-doctoral Fellowship after finishing + + + align:start position:0% +post-doctoral Fellowship after finishing +a PhD in fact even after the second + + align:start position:0% +a PhD in fact even after the second + + + align:start position:0% +a PhD in fact even after the second +World War + + align:start position:0% +World War + + + align:start position:0% +World War +only roughly 16 percent of the us-based + + align:start position:0% +only roughly 16 percent of the us-based + + + align:start position:0% +only roughly 16 percent of the us-based +phds actually did a postdoc just did one + + align:start position:0% +phds actually did a postdoc just did one + + + align:start position:0% +phds actually did a postdoc just did one +postdoc let alone two or three + + align:start position:0% +postdoc let alone two or three + + + align:start position:0% +postdoc let alone two or three +but the numbers began to grow very + + align:start position:0% +but the numbers began to grow very + + + align:start position:0% +but the numbers began to grow very +rapidly after the war they became more + + align:start position:0% +rapidly after the war they became more + + + align:start position:0% +rapidly after the war they became more +and more common + + align:start position:0% +and more common + + + align:start position:0% +and more common +the idea going right back to the 19 uh + + align:start position:0% +the idea going right back to the 19 uh + + + align:start position:0% +the idea going right back to the 19 uh +1918 proposals in 1920s and so on was + + align:start position:0% +1918 proposals in 1920s and so on was + + + align:start position:0% +1918 proposals in 1920s and so on was +these post-doc positions were designed + + align:start position:0% +these post-doc positions were designed + + + align:start position:0% +these post-doc positions were designed +to foster a different kind of training + + align:start position:0% +to foster a different kind of training + + + align:start position:0% +to foster a different kind of training +compared to the PHD that was the that + + align:start position:0% +compared to the PHD that was the that + + + align:start position:0% +compared to the PHD that was the that +was the the hope the ambition + + align:start position:0% +was the the hope the ambition + + + align:start position:0% +was the the hope the ambition +but they should foster what uh + + align:start position:0% +but they should foster what uh + + + align:start position:0% +but they should foster what uh +historians and sociologists often call + + align:start position:0% +historians and sociologists often call + + + align:start position:0% +historians and sociologists often call +tacit knowledge not explicit kind of + + align:start position:0% +tacit knowledge not explicit kind of + + + align:start position:0% +tacit knowledge not explicit kind of +book learning but actually stuff that + + align:start position:0% +book learning but actually stuff that + + + align:start position:0% +book learning but actually stuff that +you kind of know by doing even for + + align:start position:0% +you kind of know by doing even for + + + align:start position:0% +you kind of know by doing even for +theoretical physicists who aren't like + + align:start position:0% +theoretical physicists who aren't like + + + align:start position:0% +theoretical physicists who aren't like +building apparatus or glass blowing or + + align:start position:0% +building apparatus or glass blowing or + + + align:start position:0% +building apparatus or glass blowing or +eventually learning to solder there's a + + align:start position:0% +eventually learning to solder there's a + + + align:start position:0% +eventually learning to solder there's a +kind of knowledge that comes at a kind + + align:start position:0% +kind of knowledge that comes at a kind + + + align:start position:0% +kind of knowledge that comes at a kind +of intuitive level by practice which is + + align:start position:0% +of intuitive level by practice which is + + + align:start position:0% +of intuitive level by practice which is +why we work on uh you know problem sets + + align:start position:0% +why we work on uh you know problem sets + + + align:start position:0% +why we work on uh you know problem sets +all the time rather than only kind of + + align:start position:0% +all the time rather than only kind of + + + align:start position:0% +all the time rather than only kind of +reading textbooks and um and dealing + + align:start position:0% +reading textbooks and um and dealing + + + align:start position:0% +reading textbooks and um and dealing +with kind of uh uh formal levels or + + align:start position:0% +with kind of uh uh formal levels or + + + align:start position:0% +with kind of uh uh formal levels or +explicit levels of instruction so the + + align:start position:0% +explicit levels of instruction so the + + + align:start position:0% +explicit levels of instruction so the +postdoc was meant to complement the kind + + align:start position:0% +postdoc was meant to complement the kind + + + align:start position:0% +postdoc was meant to complement the kind +of more formal more book learning + + align:start position:0% +of more formal more book learning + + + align:start position:0% +of more formal more book learning +explicit uh training of a PhD with his + + align:start position:0% +explicit uh training of a PhD with his + + + align:start position:0% +explicit uh training of a PhD with his +more informal tacit knowledge moreover + + align:start position:0% +more informal tacit knowledge moreover + + + align:start position:0% +more informal tacit knowledge moreover +they were especially in the United + + align:start position:0% +they were especially in the United + + + align:start position:0% +they were especially in the United +States they were often funded by private + + align:start position:0% +States they were often funded by private + + + align:start position:0% +States they were often funded by private +foundations and again a kind of + + align:start position:0% +foundations and again a kind of + + + align:start position:0% +foundations and again a kind of +patriotic ambition to to improve and + + align:start position:0% +patriotic ambition to to improve and + + + align:start position:0% +patriotic ambition to to improve and +build up uh U.S domestic scientific + + align:start position:0% +build up uh U.S domestic scientific + + + align:start position:0% +build up uh U.S domestic scientific +talent and to share the wealth so you'd + + align:start position:0% +talent and to share the wealth so you'd + + + align:start position:0% +talent and to share the wealth so you'd +have these young people getting phds at + + align:start position:0% +have these young people getting phds at + + + align:start position:0% +have these young people getting phds at +one school they would get a fellowship + + align:start position:0% +one school they would get a fellowship + + + align:start position:0% +one school they would get a fellowship +to become a postdoc at a second school + + align:start position:0% +to become a postdoc at a second school + + + align:start position:0% +to become a postdoc at a second school +they could bring what they've learned to + + align:start position:0% +they could bring what they've learned to + + + align:start position:0% +they could bring what they've learned to +the new place they'll learn new things + + align:start position:0% +the new place they'll learn new things + + + align:start position:0% +the new place they'll learn new things +at the new place themselves then they'll + + align:start position:0% +at the new place themselves then they'll + + + align:start position:0% +at the new place themselves then they'll +hopefully get a job at a third place so + + align:start position:0% +hopefully get a job at a third place so + + + align:start position:0% +hopefully get a job at a third place so +you start building in an emphasis on + + align:start position:0% +you start building in an emphasis on + + + align:start position:0% +you start building in an emphasis on +circulation so that was it was hope + + align:start position:0% +circulation so that was it was hope + + + align:start position:0% +circulation so that was it was hope +would help knit together the U.S + + align:start position:0% +would help knit together the U.S + + + align:start position:0% +would help knit together the U.S +scientific Community even more tightly + + align:start position:0% +scientific Community even more tightly + + + align:start position:0% +scientific Community even more tightly +and build in this kind of sharing of + + align:start position:0% +and build in this kind of sharing of + + + align:start position:0% +and build in this kind of sharing of +skills especially this tacit knowledge + + align:start position:0% +skills especially this tacit knowledge + + + align:start position:0% +skills especially this tacit knowledge +stuff + + align:start position:0% +stuff + + + align:start position:0% +stuff +so after the second world war this + + align:start position:0% +so after the second world war this + + + align:start position:0% +so after the second world war this +became especially pertinent for training + + align:start position:0% +became especially pertinent for training + + + align:start position:0% +became especially pertinent for training +young physicists in theoretical physics + + align:start position:0% +young physicists in theoretical physics + + + align:start position:0% +young physicists in theoretical physics +in the United States which had still + + align:start position:0% +in the United States which had still + + + align:start position:0% +in the United States which had still +been it was felt at the time kind of + + align:start position:0% +been it was felt at the time kind of + + + align:start position:0% +been it was felt at the time kind of +lacking and not nearly so developed as + + align:start position:0% +lacking and not nearly so developed as + + + align:start position:0% +lacking and not nearly so developed as +in other parts of the world mostly uh + + align:start position:0% +in other parts of the world mostly uh + + + align:start position:0% +in other parts of the world mostly uh +they had their eyes on Western Europe + + align:start position:0% +they had their eyes on Western Europe + + + align:start position:0% +they had their eyes on Western Europe +so the most important place where this + + align:start position:0% +so the most important place where this + + + align:start position:0% +so the most important place where this +begins to really change uh soon after + + align:start position:0% +begins to really change uh soon after + + + align:start position:0% +begins to really change uh soon after +the war is this place where Dyson had + + align:start position:0% +the war is this place where Dyson had + + + align:start position:0% +the war is this place where Dyson had +wound up the institute for vet study in + + align:start position:0% +wound up the institute for vet study in + + + align:start position:0% +wound up the institute for vet study in +Princeton New Jersey it's near Princeton + + align:start position:0% +Princeton New Jersey it's near Princeton + + + align:start position:0% +Princeton New Jersey it's near Princeton +University though it's independent from + + align:start position:0% +University though it's independent from + + + align:start position:0% +University though it's independent from +the University + + align:start position:0% +the University + + + align:start position:0% +the University +Oppenheimer moved there just soon after + + align:start position:0% +Oppenheimer moved there just soon after + + + align:start position:0% +Oppenheimer moved there just soon after +the end of the war + + align:start position:0% +the end of the war + + + align:start position:0% +the end of the war +he became the new director for The + + align:start position:0% +he became the new director for The + + + align:start position:0% +he became the new director for The +Institute starting in 1947. partly so + + align:start position:0% +Institute starting in 1947. partly so + + + align:start position:0% +Institute starting in 1947. partly so +he'd be closer to Washington DC he was + + align:start position:0% +he'd be closer to Washington DC he was + + + align:start position:0% +he'd be closer to Washington DC he was +still doing a lot of Consulting for the + + align:start position:0% +still doing a lot of Consulting for the + + + align:start position:0% +still doing a lot of Consulting for the +government and so on so one of the first + + align:start position:0% +government and so on so one of the first + + + align:start position:0% +government and so on so one of the first +things he did when he moved was it was + + align:start position:0% +things he did when he moved was it was + + + align:start position:0% +things he did when he moved was it was +Jack up the number of theory postdocs by + + align:start position:0% +Jack up the number of theory postdocs by + + + align:start position:0% +Jack up the number of theory postdocs by +60 in one year he really said I'm in + + align:start position:0% +60 in one year he really said I'm in + + + align:start position:0% +60 in one year he really said I'm in +charge now and rather than support other + + align:start position:0% +charge now and rather than support other + + + align:start position:0% +charge now and rather than support other +things that he might have done with the + + align:start position:0% +things that he might have done with the + + + align:start position:0% +things that he might have done with the +institute's budget he said the most + + align:start position:0% +institute's budget he said the most + + + align:start position:0% +institute's budget he said the most +important thing we can do for the + + align:start position:0% +important thing we can do for the + + + align:start position:0% +important thing we can do for the +scientific Community is really kind of + + align:start position:0% +scientific Community is really kind of + + + align:start position:0% +scientific Community is really kind of +rapidly expand the number of slots for + + align:start position:0% +rapidly expand the number of slots for + + + align:start position:0% +rapidly expand the number of slots for +young postdocs in theoretical physics + + align:start position:0% +young postdocs in theoretical physics + + + align:start position:0% +young postdocs in theoretical physics +not coincidentally his own field + + align:start position:0% +not coincidentally his own field + + + align:start position:0% +not coincidentally his own field +a lot of people with the Institute + + align:start position:0% +a lot of people with the Institute + + + align:start position:0% +a lot of people with the Institute +didn't like that at all + + align:start position:0% +didn't like that at all + + + align:start position:0% +didn't like that at all +but that's what he did + + align:start position:0% + + + + align:start position:0% + +and he did that year after year + + align:start position:0% +and he did that year after year + + + align:start position:0% +and he did that year after year +and it was uh I love this letter he + + align:start position:0% +and it was uh I love this letter he + + + align:start position:0% +and it was uh I love this letter he +wrote to Wolfgang Paoli who at this + + align:start position:0% +wrote to Wolfgang Paoli who at this + + + align:start position:0% +wrote to Wolfgang Paoli who at this +point was back in Europe Paladin spent a + + align:start position:0% +point was back in Europe Paladin spent a + + + align:start position:0% +point was back in Europe Paladin spent a +good chunk of the War years at The + + align:start position:0% +good chunk of the War years at The + + + align:start position:0% +good chunk of the War years at The +Institute in fact visiting and avoiding + + align:start position:0% +Institute in fact visiting and avoiding + + + align:start position:0% +Institute in fact visiting and avoiding +some of the worst parts of uh fighting + + align:start position:0% +some of the worst parts of uh fighting + + + align:start position:0% +some of the worst parts of uh fighting +in Europe by this point he was back in + + align:start position:0% +in Europe by this point he was back in + + + align:start position:0% +in Europe by this point he was back in +Europe and Panama explained that the + + align:start position:0% +Europe and Panama explained that the + + + align:start position:0% +Europe and Panama explained that the +Institute by this point is not a school + + align:start position:0% +Institute by this point is not a school + + + align:start position:0% +Institute by this point is not a school +in the sense that even the younger + + align:start position:0% +in the sense that even the younger + + + align:start position:0% +in the sense that even the younger +people are not listening to lectures or + + align:start position:0% +people are not listening to lectures or + + + align:start position:0% +people are not listening to lectures or +working for doctors degrees but it is a + + align:start position:0% +working for doctors degrees but it is a + + + align:start position:0% +working for doctors degrees but it is a +school in the sense that everyone who + + align:start position:0% +school in the sense that everyone who + + + align:start position:0% +school in the sense that everyone who +comes learns of parts of physics which + + align:start position:0% +comes learns of parts of physics which + + + align:start position:0% +comes learns of parts of physics which +are new to him and it turns out that was + + align:start position:0% +are new to him and it turns out that was + + + align:start position:0% +are new to him and it turns out that was +especially happening once Dyson arrived + + align:start position:0% +especially happening once Dyson arrived + + + align:start position:0% +especially happening once Dyson arrived +among the very first of these new + + align:start position:0% +among the very first of these new + + + align:start position:0% +among the very first of these new +cohorts the very first of these rapid + + align:start position:0% +cohorts the very first of these rapid + + + align:start position:0% +cohorts the very first of these rapid +expanded groups of 8 to 10 to 12 Theory + + align:start position:0% +expanded groups of 8 to 10 to 12 Theory + + + align:start position:0% +expanded groups of 8 to 10 to 12 Theory +post-docs at a time as opposed to only + + align:start position:0% +post-docs at a time as opposed to only + + + align:start position:0% +post-docs at a time as opposed to only +one or two as before + + align:start position:0% +one or two as before + + + align:start position:0% +one or two as before +so by the time Dyson and his first + + align:start position:0% +so by the time Dyson and his first + + + align:start position:0% +so by the time Dyson and his first +cohort arrived as the new post-docs + + align:start position:0% +cohort arrived as the new post-docs + + + align:start position:0% +cohort arrived as the new post-docs +although Dyson was actually + + align:start position:0% +although Dyson was actually + + + align:start position:0% +although Dyson was actually +not a post-documented a doc but he was + + align:start position:0% +not a post-documented a doc but he was + + + align:start position:0% +not a post-documented a doc but he was +he was joining these postdocs + + align:start position:0% +he was joining these postdocs + + + align:start position:0% +he was joining these postdocs +uh the new building uh that that would + + align:start position:0% +uh the new building uh that that would + + + align:start position:0% +uh the new building uh that that would +house them actually was still under + + align:start position:0% +house them actually was still under + + + align:start position:0% +house them actually was still under +construction so they all shared one + + align:start position:0% +construction so they all shared one + + + align:start position:0% +construction so they all shared one +office in fact they shared oppenheimer's + + align:start position:0% +office in fact they shared oppenheimer's + + + align:start position:0% +office in fact they shared oppenheimer's +office the director's office was big + + align:start position:0% +office the director's office was big + + + align:start position:0% +office the director's office was big +enough for 12 postdocs so some things + + align:start position:0% +enough for 12 postdocs so some things + + + align:start position:0% +enough for 12 postdocs so some things +don't change Oppenheimer was in Europe + + align:start position:0% +don't change Oppenheimer was in Europe + + + align:start position:0% +don't change Oppenheimer was in Europe +for much of that fall so they were + + align:start position:0% +for much of that fall so they were + + + align:start position:0% +for much of that fall so they were +literally kind of sharing desk space + + align:start position:0% +literally kind of sharing desk space + + + align:start position:0% +literally kind of sharing desk space +they were completely kind of elbow to + + align:start position:0% +they were completely kind of elbow to + + + align:start position:0% +they were completely kind of elbow to +Elbow informally sharing space + + align:start position:0% +Elbow informally sharing space + + + align:start position:0% +Elbow informally sharing space +and then the postdocs would circulate + + align:start position:0% +and then the postdocs would circulate + + + align:start position:0% +and then the postdocs would circulate +through what Oppenheimer loved to call + + align:start position:0% +through what Oppenheimer loved to call + + + align:start position:0% +through what Oppenheimer loved to call +his intellectual Hotel you you don't + + align:start position:0% +his intellectual Hotel you you don't + + + align:start position:0% +his intellectual Hotel you you don't +move there you stay there for a visit + + align:start position:0% +move there you stay there for a visit + + + align:start position:0% +move there you stay there for a visit +and then you go somewhere else + + align:start position:0% +and then you go somewhere else + + + align:start position:0% +and then you go somewhere else +they would tend to stay for two-year + + align:start position:0% +they would tend to stay for two-year + + + align:start position:0% +they would tend to stay for two-year +stays and while they were there in these + + align:start position:0% +stays and while they were there in these + + + align:start position:0% +stays and while they were there in these +early years Dyson would coordinate these + + align:start position:0% +early years Dyson would coordinate these + + + align:start position:0% +early years Dyson would coordinate these +kind of little teams or groups of + + align:start position:0% +kind of little teams or groups of + + + align:start position:0% +kind of little teams or groups of +calculations because he was coaching + + align:start position:0% +calculations because he was coaching + + + align:start position:0% +calculations because he was coaching +them in these new techniques uh for the + + align:start position:0% +them in these new techniques uh for the + + + align:start position:0% +them in these new techniques uh for the +finding doctors and again the word of + + align:start position:0% +finding doctors and again the word of + + + align:start position:0% +finding doctors and again the word of +that began to spread so Paulie writes + + align:start position:0% +that began to spread so Paulie writes + + + align:start position:0% +that began to spread so Paulie writes +back from Europe what are Dyson the rest + + align:start position:0% +back from Europe what are Dyson the rest + + + align:start position:0% +back from Europe what are Dyson the rest +of the Feynman School working on it was + + align:start position:0% +of the Feynman School working on it was + + + align:start position:0% +of the Feynman School working on it was +already becoming clear that they were + + align:start position:0% +already becoming clear that they were + + + align:start position:0% +already becoming clear that they were +working very hard on that so when you go + + align:start position:0% +working very hard on that so when you go + + + align:start position:0% +working very hard on that so when you go +back to that curve of these exponential + + align:start position:0% +back to that curve of these exponential + + + align:start position:0% +back to that curve of these exponential +rise of who's using the diagrams it + + align:start position:0% +rise of who's using the diagrams it + + + align:start position:0% +rise of who's using the diagrams it +starts to make a little more sense it + + align:start position:0% +starts to make a little more sense it + + + align:start position:0% +starts to make a little more sense it +really was a social network the + + align:start position:0% +really was a social network the + + + align:start position:0% +really was a social network the +overwhelming majority of those early + + align:start position:0% +overwhelming majority of those early + + + align:start position:0% +overwhelming majority of those early +users were either direct members of + + align:start position:0% +users were either direct members of + + + align:start position:0% +users were either direct members of +these of these post-doc cohorts at The + + align:start position:0% +these of these post-doc cohorts at The + + + align:start position:0% +these of these post-doc cohorts at The +Institute who learned and practiced the + + align:start position:0% +Institute who learned and practiced the + + + align:start position:0% +Institute who learned and practiced the +techniques directly from Freeman Dyson + + align:start position:0% +techniques directly from Freeman Dyson + + + align:start position:0% +techniques directly from Freeman Dyson +just as he was working about himself + + align:start position:0% +just as he was working about himself + + + align:start position:0% +just as he was working about himself +himself + + align:start position:0% +himself + + + align:start position:0% +himself +or they were students or immediate + + align:start position:0% +or they were students or immediate + + + align:start position:0% +or they were students or immediate +colleagues of those postdocs once they + + align:start position:0% +colleagues of those postdocs once they + + + align:start position:0% +colleagues of those postdocs once they +took up their first teaching jobs and + + align:start position:0% +took up their first teaching jobs and + + + align:start position:0% +took up their first teaching jobs and +moved to other universities around the + + align:start position:0% +moved to other universities around the + + + align:start position:0% +moved to other universities around the +country the remaining 20 or I mean not + + align:start position:0% +country the remaining 20 or I mean not + + + align:start position:0% +country the remaining 20 or I mean not +much more than rounding error of those + + align:start position:0% +much more than rounding error of those + + + align:start position:0% +much more than rounding error of those +early of those early articles that use + + align:start position:0% +early of those early articles that use + + + align:start position:0% +early of those early articles that use +the diagrams had come from Feynman or + + align:start position:0% +the diagrams had come from Feynman or + + + align:start position:0% +the diagrams had come from Feynman or +from fyman's immediate circles so we + + align:start position:0% +from fyman's immediate circles so we + + + align:start position:0% +from fyman's immediate circles so we +really have kind of two lightly + + align:start position:0% +really have kind of two lightly + + + align:start position:0% +really have kind of two lightly +connected networks that dominate the + + align:start position:0% +connected networks that dominate the + + + align:start position:0% +connected networks that dominate the +early adopters + + align:start position:0% +early adopters + + + align:start position:0% +early adopters +and so you get these sort of like Air + + align:start position:0% +and so you get these sort of like Air + + + align:start position:0% +and so you get these sort of like Air +Airline flight Maps um this is not + + align:start position:0% +Airline flight Maps um this is not + + + align:start position:0% +Airline flight Maps um this is not +literally the find a diagram case I just + + align:start position:0% +literally the find a diagram case I just + + + align:start position:0% +literally the find a diagram case I just +took it from Google Images it is a map + + align:start position:0% +took it from Google Images it is a map + + + align:start position:0% +took it from Google Images it is a map +of like you know domestic air travel + + align:start position:0% +of like you know domestic air travel + + + align:start position:0% +of like you know domestic air travel +route but it was very similar how the + + align:start position:0% +route but it was very similar how the + + + align:start position:0% +route but it was very similar how the +digraphs itself spread out you can trace + + align:start position:0% +digraphs itself spread out you can trace + + + align:start position:0% +digraphs itself spread out you can trace +through who's publishing with the + + align:start position:0% +through who's publishing with the + + + align:start position:0% +through who's publishing with the +diagrams we have their articles we can + + align:start position:0% +diagrams we have their articles we can + + + align:start position:0% +diagrams we have their articles we can +see where they were from their kind of + + align:start position:0% +see where they were from their kind of + + + align:start position:0% +see where they were from their kind of +byline then look up well where were they + + align:start position:0% +byline then look up well where were they + + + align:start position:0% +byline then look up well where were they +when do they interact with uh say + + align:start position:0% +when do they interact with uh say + + + align:start position:0% +when do they interact with uh say +Freeman Dyson when do they uh attend + + align:start position:0% +Freeman Dyson when do they uh attend + + + align:start position:0% +Freeman Dyson when do they uh attend +this lengthy set of summer school + + align:start position:0% +this lengthy set of summer school + + + align:start position:0% +this lengthy set of summer school +lectures and so on and you start getting + + align:start position:0% +lectures and so on and you start getting + + + align:start position:0% +lectures and so on and you start getting +this kind of connected graph of how the + + align:start position:0% +this kind of connected graph of how the + + + align:start position:0% +this kind of connected graph of how the +diagrams spread throughout the United + + align:start position:0% +diagrams spread throughout the United + + + align:start position:0% +diagrams spread throughout the United +States let me say a little bit more + + align:start position:0% +States let me say a little bit more + + + align:start position:0% +States let me say a little bit more +about the spread and then we'll pause uh + + align:start position:0% +about the spread and then we'll pause uh + + + align:start position:0% +about the spread and then we'll pause uh +and for some discussion so that works I + + align:start position:0% +and for some discussion so that works I + + + align:start position:0% +and for some discussion so that works I +think that helps account for how these + + align:start position:0% +think that helps account for how these + + + align:start position:0% +think that helps account for how these +techniques spread so kind of anomalously + + align:start position:0% +techniques spread so kind of anomalously + + + align:start position:0% +techniques spread so kind of anomalously +quickly within the United States go to + + align:start position:0% +quickly within the United States go to + + + align:start position:0% +quickly within the United States go to +the physical review at that point most + + align:start position:0% +the physical review at that point most + + + align:start position:0% +the physical review at that point most +articles in the physical review were + + align:start position:0% +articles in the physical review were + + + align:start position:0% +articles in the physical review were +contributed by physicists in the United + + align:start position:0% +contributed by physicists in the United + + + align:start position:0% +contributed by physicists in the United +States that's certainly not the case now + + align:start position:0% +States that's certainly not the case now + + + align:start position:0% +States that's certainly not the case now +but back then it was a pretty good + + align:start position:0% +but back then it was a pretty good + + + align:start position:0% +but back then it was a pretty good +reflection of us-based physics we get a + + align:start position:0% +reflection of us-based physics we get a + + + align:start position:0% +reflection of us-based physics we get a +sense of how the USB users of the + + align:start position:0% +sense of how the USB users of the + + + align:start position:0% +sense of how the USB users of the +diagrams began to Fan out but very + + align:start position:0% +diagrams began to Fan out but very + + + align:start position:0% +diagrams began to Fan out but very +quickly + + align:start position:0% +quickly + + + align:start position:0% +quickly +the diagrams were showing up in the + + align:start position:0% +the diagrams were showing up in the + + + align:start position:0% +the diagrams were showing up in the +journals from other countries as well so + + align:start position:0% +journals from other countries as well so + + + align:start position:0% +journals from other countries as well so +it turns out in the United Kingdom we + + align:start position:0% +it turns out in the United Kingdom we + + + align:start position:0% +it turns out in the United Kingdom we +have a very replay of the same story The + + align:start position:0% +have a very replay of the same story The + + + align:start position:0% +have a very replay of the same story The +the rules of that Fellowship that had + + align:start position:0% +the rules of that Fellowship that had + + + align:start position:0% +the rules of that Fellowship that had +allowed Dyson to come over to Cornell + + align:start position:0% +allowed Dyson to come over to Cornell + + + align:start position:0% +allowed Dyson to come over to Cornell +and to Princeton The Institute required + + align:start position:0% +and to Princeton The Institute required + + + align:start position:0% +and to Princeton The Institute required +that the recipients returned to Britain + + align:start position:0% +that the recipients returned to Britain + + + align:start position:0% +that the recipients returned to Britain +for a couple years so you could go for + + align:start position:0% +for a couple years so you could go for + + + align:start position:0% +for a couple years so you could go for +two or three years on the fellowship but + + align:start position:0% +two or three years on the fellowship but + + + align:start position:0% +two or three years on the fellowship but +you had to return to Britain and you had + + align:start position:0% +you had to return to Britain and you had + + + align:start position:0% +you had to return to Britain and you had +to stay in Britain for at least two + + align:start position:0% +to stay in Britain for at least two + + + align:start position:0% +to stay in Britain for at least two +years those were the rules + + align:start position:0% +years those were the rules + + + align:start position:0% +years those were the rules +so when Dyson's Fellowship expired he + + align:start position:0% +so when Dyson's Fellowship expired he + + + align:start position:0% +so when Dyson's Fellowship expired he +went back to Britain he began teaching + + align:start position:0% +went back to Britain he began teaching + + + align:start position:0% +went back to Britain he began teaching +at um first at Cambridge but eventually + + align:start position:0% +at um first at Cambridge but eventually + + + align:start position:0% +at um first at Cambridge but eventually +at Birmingham again no PhD he was a + + align:start position:0% +at Birmingham again no PhD he was a + + + align:start position:0% +at Birmingham again no PhD he was a +professor with no PhD + + align:start position:0% +professor with no PhD + + + align:start position:0% +professor with no PhD +and when you look at who was using the + + align:start position:0% +and when you look at who was using the + + + align:start position:0% +and when you look at who was using the +diagrams in Britain they were people who + + align:start position:0% +diagrams in Britain they were people who + + + align:start position:0% +diagrams in Britain they were people who +learned from Dyson once Dyson went back + + align:start position:0% +learned from Dyson once Dyson went back + + + align:start position:0% +learned from Dyson once Dyson went back +to Britain so like no mystery there it's + + align:start position:0% +to Britain so like no mystery there it's + + + align:start position:0% +to Britain so like no mystery there it's +kind of the same story + + align:start position:0% +kind of the same story + + + align:start position:0% +kind of the same story +this next part I found really + + align:start position:0% +this next part I found really + + + align:start position:0% +this next part I found really +interesting I didn't know about this + + align:start position:0% +interesting I didn't know about this + + + align:start position:0% +interesting I didn't know about this +until my friend Kenji Ito helped me a + + align:start position:0% +until my friend Kenji Ito helped me a + + + align:start position:0% +until my friend Kenji Ito helped me a +lot with this because uh he's originally + + align:start position:0% +lot with this because uh he's originally + + + align:start position:0% +lot with this because uh he's originally +from Tokyo he is uh he knows the + + align:start position:0% +from Tokyo he is uh he knows the + + + align:start position:0% +from Tokyo he is uh he knows the +language and he's also an expert in the + + align:start position:0% +language and he's also an expert in the + + + align:start position:0% +language and he's also an expert in the +history of quantum physics we read some + + align:start position:0% +history of quantum physics we read some + + + align:start position:0% +history of quantum physics we read some +of kenji's stuff I think for uh for + + align:start position:0% +of kenji's stuff I think for uh for + + + align:start position:0% +of kenji's stuff I think for uh for +paper two assignment so Kenji helped me + + align:start position:0% +paper two assignment so Kenji helped me + + + align:start position:0% +paper two assignment so Kenji helped me +a lot with this I really learned work + + align:start position:0% +a lot with this I really learned work + + + align:start position:0% +a lot with this I really learned work +with him so what happens with the spread + + align:start position:0% +with him so what happens with the spread + + + align:start position:0% +with him so what happens with the spread +of the diagrams in Japan after the + + align:start position:0% +of the diagrams in Japan after the + + + align:start position:0% +of the diagrams in Japan after the +second world war here's tomanaga whose + + align:start position:0% +second world war here's tomanaga whose + + + align:start position:0% +second world war here's tomanaga whose +work I was describing earlier turns out + + align:start position:0% +work I was describing earlier turns out + + + align:start position:0% +work I was describing earlier turns out +tomanaga was doing I think just + + align:start position:0% +tomanaga was doing I think just + + + align:start position:0% +tomanaga was doing I think just +extraordinary kind of superhuman efforts + + align:start position:0% +extraordinary kind of superhuman efforts + + + align:start position:0% +extraordinary kind of superhuman efforts +I think superhuman efforts to try to + + align:start position:0% +I think superhuman efforts to try to + + + align:start position:0% +I think superhuman efforts to try to +rebuild the Japanese community in + + align:start position:0% +rebuild the Japanese community in + + + align:start position:0% +rebuild the Japanese community in +theoretical physics after the war the + + align:start position:0% +theoretical physics after the war the + + + align:start position:0% +theoretical physics after the war the +University where he was hired had been + + align:start position:0% +University where he was hired had been + + + align:start position:0% +University where he was hired had been +leveled most of buildings have been + + align:start position:0% +leveled most of buildings have been + + + align:start position:0% +leveled most of buildings have been +destroyed in the saturation firebombing + + align:start position:0% +destroyed in the saturation firebombing + + + align:start position:0% +destroyed in the saturation firebombing +of Tokyo so they he and his little group + + align:start position:0% +of Tokyo so they he and his little group + + + align:start position:0% +of Tokyo so they he and his little group +of students and advisees would meet in + + align:start position:0% +of students and advisees would meet in + + + align:start position:0% +of students and advisees would meet in +his home but his home had been bombed + + align:start position:0% +his home but his home had been bombed + + + align:start position:0% +his home but his home had been bombed +out so they were meeting his in his + + align:start position:0% +out so they were meeting his in his + + + align:start position:0% +out so they were meeting his in his +Quonset hut he literally had temporary + + align:start position:0% +Quonset hut he literally had temporary + + + align:start position:0% +Quonset hut he literally had temporary +shelter that was not meant to outlive + + align:start position:0% +shelter that was not meant to outlive + + + align:start position:0% +shelter that was not meant to outlive +the war and soon after the war amid + + align:start position:0% +the war and soon after the war amid + + + align:start position:0% +the war and soon after the war amid +shortages of food and paper and clothing + + align:start position:0% +shortages of food and paper and clothing + + + align:start position:0% +shortages of food and paper and clothing +and much else he was working to kind of + + align:start position:0% +and much else he was working to kind of + + + align:start position:0% +and much else he was working to kind of +get his own students back on track and + + align:start position:0% +get his own students back on track and + + + align:start position:0% +get his own students back on track and +and uh and they would meet together in + + align:start position:0% +and uh and they would meet together in + + + align:start position:0% +and uh and they would meet together in +his residence which itself was a + + align:start position:0% +his residence which itself was a + + + align:start position:0% +his residence which itself was a +temporary literally kind of a shell + + align:start position:0% +temporary literally kind of a shell + + + align:start position:0% +temporary literally kind of a shell +and they returned to questions they've + + align:start position:0% +and they returned to questions they've + + + align:start position:0% +and they returned to questions they've +been thinking about together even during + + align:start position:0% +been thinking about together even during + + + align:start position:0% +been thinking about together even during +the war things like uh Quantum + + align:start position:0% +the war things like uh Quantum + + + align:start position:0% +the war things like uh Quantum +electronamics virtual particles and + + align:start position:0% +electronamics virtual particles and + + + align:start position:0% +electronamics virtual particles and +infinities + + align:start position:0% +infinities + + + align:start position:0% +infinities +uh and they have developed soon after + + align:start position:0% +uh and they have developed soon after + + + align:start position:0% +uh and they have developed soon after +the war these kinds of their own kinds + + align:start position:0% +the war these kinds of their own kinds + + + align:start position:0% +the war these kinds of their own kinds +of pencil and paper diagram bookkeepers + + align:start position:0% +of pencil and paper diagram bookkeepers + + + align:start position:0% +of pencil and paper diagram bookkeepers +which Kenji found for me we wrote about + + align:start position:0% +which Kenji found for me we wrote about + + + align:start position:0% +which Kenji found for me we wrote about +them together that these were in in some + + align:start position:0% +them together that these were in in some + + + align:start position:0% +them together that these were in in some +of the kind of mini graphs early uh + + align:start position:0% +of the kind of mini graphs early uh + + + align:start position:0% +of the kind of mini graphs early uh +post-war Publications from the uh the + + align:start position:0% +post-war Publications from the uh the + + + align:start position:0% +post-war Publications from the uh the +circuit in Japan + + align:start position:0% +circuit in Japan + + + align:start position:0% +circuit in Japan +and these were in momentum space they + + align:start position:0% +and these were in momentum space they + + + align:start position:0% +and these were in momentum space they +weren't space-time diagrams but they + + align:start position:0% +weren't space-time diagrams but they + + + align:start position:0% +weren't space-time diagrams but they +were trying to do similar things you + + align:start position:0% +were trying to do similar things you + + + align:start position:0% +were trying to do similar things you +have all these ways that virtual + + align:start position:0% +have all these ways that virtual + + + align:start position:0% +have all these ways that virtual +particles could be involved your example + + align:start position:0% +particles could be involved your example + + + align:start position:0% +particles could be involved your example +examples of a single electron that's + + align:start position:0% +examples of a single electron that's + + + align:start position:0% +examples of a single electron that's +interacting with two separate virtual + + align:start position:0% +interacting with two separate virtual + + + align:start position:0% +interacting with two separate virtual +photons sorry how do you keep track of + + align:start position:0% +photons sorry how do you keep track of + + + align:start position:0% +photons sorry how do you keep track of +it so tamanagan his group had invented + + align:start position:0% +it so tamanagan his group had invented + + + align:start position:0% +it so tamanagan his group had invented +their own techniques then they began + + align:start position:0% +their own techniques then they began + + + align:start position:0% +their own techniques then they began +getting news back from the United States + + align:start position:0% +getting news back from the United States + + + align:start position:0% +getting news back from the United States +after the war + + align:start position:0% +after the war + + + align:start position:0% +after the war +about Dyson's new work not only from + + align:start position:0% +about Dyson's new work not only from + + + align:start position:0% +about Dyson's new work not only from +Reading Newsweek magazine in the new uh + + align:start position:0% +Reading Newsweek magazine in the new uh + + + align:start position:0% +Reading Newsweek magazine in the new uh +occupation uh libraries but also because + + align:start position:0% +occupation uh libraries but also because + + + align:start position:0% +occupation uh libraries but also because +of the more senior Japanese physicist + + align:start position:0% +of the more senior Japanese physicist + + + align:start position:0% +of the more senior Japanese physicist +tudeka yukawa was actually invited to + + align:start position:0% +tudeka yukawa was actually invited to + + + align:start position:0% +tudeka yukawa was actually invited to +spend um two years at The Institute for + + align:start position:0% +spend um two years at The Institute for + + + align:start position:0% +spend um two years at The Institute for +event study invited the personal + + align:start position:0% +event study invited the personal + + + align:start position:0% +event study invited the personal +limitation of Robert Oppenheimer while + + align:start position:0% +limitation of Robert Oppenheimer while + + + align:start position:0% +limitation of Robert Oppenheimer while +yukawa was visiting is when he won the + + align:start position:0% +yukawa was visiting is when he won the + + + align:start position:0% +yukawa was visiting is when he won the +Nobel Prize for his work on nuclear + + align:start position:0% +Nobel Prize for his work on nuclear + + + align:start position:0% +Nobel Prize for his work on nuclear +physics and he was unable to send + + align:start position:0% +physics and he was unable to send + + + align:start position:0% +physics and he was unable to send +pre-prints and news back to his younger + + align:start position:0% +pre-prints and news back to his younger + + + align:start position:0% +pre-prints and news back to his younger +colleagues in Japan so yokawa was + + align:start position:0% +colleagues in Japan so yokawa was + + + align:start position:0% +colleagues in Japan so yokawa was +learning he was among the people who + + align:start position:0% +learning he was among the people who + + + align:start position:0% +learning he was among the people who +could learn directly from Freeman Dyson + + align:start position:0% +could learn directly from Freeman Dyson + + + align:start position:0% +could learn directly from Freeman Dyson +then this very active group at The + + align:start position:0% +then this very active group at The + + + align:start position:0% +then this very active group at The +Institute and is able to share news back + + align:start position:0% +Institute and is able to share news back + + + align:start position:0% +Institute and is able to share news back +with this incredible tight-knit but + + align:start position:0% +with this incredible tight-knit but + + + align:start position:0% +with this incredible tight-knit but +somewhat separated group in Tokyo and + + align:start position:0% +somewhat separated group in Tokyo and + + + align:start position:0% +somewhat separated group in Tokyo and +they basically after a few months + + align:start position:0% +they basically after a few months + + + align:start position:0% +they basically after a few months +kind of ditched their own uh kind of + + align:start position:0% +kind of ditched their own uh kind of + + + align:start position:0% +kind of ditched their own uh kind of +momentum space diagrams and began + + align:start position:0% +momentum space diagrams and began + + + align:start position:0% +momentum space diagrams and began +adopting the finding diagrams because + + align:start position:0% +adopting the finding diagrams because + + + align:start position:0% +adopting the finding diagrams because +they were already kind of primed for + + align:start position:0% +they were already kind of primed for + + + align:start position:0% +they were already kind of primed for +they're already immersed in a lot of + + align:start position:0% +they're already immersed in a lot of + + + align:start position:0% +they're already immersed in a lot of +these details they already recognize + + align:start position:0% +these details they already recognize + + + align:start position:0% +these details they already recognize +that some kind of diagrammatic + + align:start position:0% +that some kind of diagrammatic + + + align:start position:0% +that some kind of diagrammatic +bookkeeping would be important and then + + align:start position:0% +bookkeeping would be important and then + + + align:start position:0% +bookkeeping would be important and then +they were kind of quick to go + + align:start position:0% +they were kind of quick to go + + + align:start position:0% +they were kind of quick to go +uh so now you have a group in Tokyo + + align:start position:0% +uh so now you have a group in Tokyo + + + align:start position:0% +uh so now you have a group in Tokyo +that's really getting very intensively + + align:start position:0% +that's really getting very intensively + + + align:start position:0% +that's really getting very intensively +into this stuff how do you spread it + + align:start position:0% +into this stuff how do you spread it + + + align:start position:0% +into this stuff how do you spread it +throughout the rest of Japan again + + align:start position:0% +throughout the rest of Japan again + + + align:start position:0% +throughout the rest of Japan again +remarkable kind of coincidence + + align:start position:0% +remarkable kind of coincidence + + + align:start position:0% +remarkable kind of coincidence +under U.S occupation the General + + align:start position:0% +under U.S occupation the General + + + align:start position:0% +under U.S occupation the General +headquarters which is what the occupying + + align:start position:0% +headquarters which is what the occupying + + + align:start position:0% +headquarters which is what the occupying +uh uh forest was called they issued a + + align:start position:0% +uh uh forest was called they issued a + + + align:start position:0% +uh uh forest was called they issued a +decree right at this time to try to + + align:start position:0% +decree right at this time to try to + + + align:start position:0% +decree right at this time to try to +weaken the hold of the traditional the + + align:start position:0% +weaken the hold of the traditional the + + + align:start position:0% +weaken the hold of the traditional the +so-called Imperial University system + + align:start position:0% +so-called Imperial University system + + + align:start position:0% +so-called Imperial University system +throughout Japan + + align:start position:0% +throughout Japan + + + align:start position:0% +throughout Japan +so the uh the U.S Ally occupying + + align:start position:0% +so the uh the U.S Ally occupying + + + align:start position:0% +so the uh the U.S Ally occupying +authorities + + align:start position:0% +authorities + + + align:start position:0% +authorities +kind of by Fiat said that every prefect + + align:start position:0% +kind of by Fiat said that every prefect + + + align:start position:0% +kind of by Fiat said that every prefect +kind of like roughly speaking every + + align:start position:0% +kind of like roughly speaking every + + + align:start position:0% +kind of like roughly speaking every +state within Japan will have at least + + align:start position:0% +state within Japan will have at least + + + align:start position:0% +state within Japan will have at least +one new University + + align:start position:0% +one new University + + + align:start position:0% +one new University +like much like the United States we have + + align:start position:0% +like much like the United States we have + + + align:start position:0% +like much like the United States we have +you know Most states have um at least + + align:start position:0% +you know Most states have um at least + + + align:start position:0% +you know Most states have um at least +two public universities you know + + align:start position:0% +two public universities you know + + + align:start position:0% +two public universities you know +Michigan State and University of + + align:start position:0% +Michigan State and University of + + + align:start position:0% +Michigan State and University of +Michigan and so on they want to do a + + align:start position:0% +Michigan and so on they want to do a + + + align:start position:0% +Michigan and so on they want to do a +similar thing in Japan partly to help + + align:start position:0% +similar thing in Japan partly to help + + + align:start position:0% +similar thing in Japan partly to help +rebuild the country and expand higher + + align:start position:0% +rebuild the country and expand higher + + + align:start position:0% +rebuild the country and expand higher +education partly as a kind of political + + align:start position:0% +education partly as a kind of political + + + align:start position:0% +education partly as a kind of political +move to break the hold of the Elites at + + align:start position:0% +move to break the hold of the Elites at + + + align:start position:0% +move to break the hold of the Elites at +these Imperial universities so suddenly + + align:start position:0% +these Imperial universities so suddenly + + + align:start position:0% +these Imperial universities so suddenly +have tenfold increase in the number of + + align:start position:0% +have tenfold increase in the number of + + + align:start position:0% +have tenfold increase in the number of +universities that need to hire young + + align:start position:0% +universities that need to hire young + + + align:start position:0% +universities that need to hire young +physicists because they suddenly have to + + align:start position:0% +physicists because they suddenly have to + + + align:start position:0% +physicists because they suddenly have to +teach young students physics so + + align:start position:0% +teach young students physics so + + + align:start position:0% +teach young students physics so +basically Tom and August students + + align:start position:0% +basically Tom and August students + + + align:start position:0% +basically Tom and August students +disperse all through Japan because + + align:start position:0% +disperse all through Japan because + + + align:start position:0% +disperse all through Japan because +they're now getting hired in these newly + + align:start position:0% +they're now getting hired in these newly + + + align:start position:0% +they're now getting hired in these newly +created physics apprenticeships and + + align:start position:0% +created physics apprenticeships and + + + align:start position:0% +created physics apprenticeships and +again you can chart when do the diagrams + + align:start position:0% +again you can chart when do the diagrams + + + align:start position:0% +again you can chart when do the diagrams +show up in Osaka oh that's because this + + align:start position:0% +show up in Osaka oh that's because this + + + align:start position:0% +show up in Osaka oh that's because this +person just moved from Tokyo to Osaka or + + align:start position:0% +person just moved from Tokyo to Osaka or + + + align:start position:0% +person just moved from Tokyo to Osaka or +Kyoto and so on + + align:start position:0% +Kyoto and so on + + + align:start position:0% +Kyoto and so on +last example what about in the Soviet + + align:start position:0% +last example what about in the Soviet + + + align:start position:0% +last example what about in the Soviet +Union this is now the Feynman introduces + + align:start position:0% +Union this is now the Feynman introduces + + + align:start position:0% +Union this is now the Feynman introduces +these diagrams and Dyson really helps + + align:start position:0% +these diagrams and Dyson really helps + + + align:start position:0% +these diagrams and Dyson really helps +make sense of them + + align:start position:0% +make sense of them + + + align:start position:0% +make sense of them +exactly the time that the kind of + + align:start position:0% +exactly the time that the kind of + + + align:start position:0% +exactly the time that the kind of +broader Cold War rivalry begins to + + align:start position:0% +broader Cold War rivalry begins to + + + align:start position:0% +broader Cold War rivalry begins to +really kind of Harden uh into a kind of + + align:start position:0% +really kind of Harden uh into a kind of + + + align:start position:0% +really kind of Harden uh into a kind of +standoff that would come to dominate the + + align:start position:0% +standoff that would come to dominate the + + + align:start position:0% +standoff that would come to dominate the +next roughly 20 years or more so this is + + align:start position:0% +next roughly 20 years or more so this is + + + align:start position:0% +next roughly 20 years or more so this is +exactly the time in other words when it + + align:start position:0% +exactly the time in other words when it + + + align:start position:0% +exactly the time in other words when it +was very hard for journals to get back + + align:start position:0% +was very hard for journals to get back + + + align:start position:0% +was very hard for journals to get back +and forth and even much more difficult + + align:start position:0% +and forth and even much more difficult + + + align:start position:0% +and forth and even much more difficult +for individuals to travel back and forth + + align:start position:0% +for individuals to travel back and forth + + + align:start position:0% +for individuals to travel back and forth +in fact in this earliest period between + + align:start position:0% +in fact in this earliest period between + + + align:start position:0% +in fact in this earliest period between +1948 until the death of Stalin uh he + + align:start position:0% +1948 until the death of Stalin uh he + + + align:start position:0% +1948 until the death of Stalin uh he +died in March of 53 and about a year + + align:start position:0% +died in March of 53 and about a year + + + align:start position:0% +died in March of 53 and about a year +later there was a the first kind of + + align:start position:0% +later there was a the first kind of + + + align:start position:0% +later there was a the first kind of +tentative person-to-person exchanges + + align:start position:0% +tentative person-to-person exchanges + + + align:start position:0% +tentative person-to-person exchanges +again between scientists there was no + + align:start position:0% +again between scientists there was no + + + align:start position:0% +again between scientists there was no +possibility for the kinds of personal + + align:start position:0% +possibility for the kinds of personal + + + align:start position:0% +possibility for the kinds of personal +contact that have been so important for + + align:start position:0% +contact that have been so important for + + + align:start position:0% +contact that have been so important for +spreading the diagrams in the United + + align:start position:0% +spreading the diagrams in the United + + + align:start position:0% +spreading the diagrams in the United +States and Britain + + align:start position:0% +States and Britain + + + align:start position:0% +States and Britain +so and and maybe therefore it helps us + + align:start position:0% +so and and maybe therefore it helps us + + + align:start position:0% +so and and maybe therefore it helps us +make sense the fact that no diagrams are + + align:start position:0% +make sense the fact that no diagrams are + + + align:start position:0% +make sense the fact that no diagrams are +published in any of the Soviet physics + + align:start position:0% +published in any of the Soviet physics + + + align:start position:0% +published in any of the Soviet physics +journals for several years there was a + + align:start position:0% +journals for several years there was a + + + align:start position:0% +journals for several years there was a +few months delay in Japan which sort of + + align:start position:0% +few months delay in Japan which sort of + + + align:start position:0% +few months delay in Japan which sort of +makes sense and we saw how that um um + + align:start position:0% +makes sense and we saw how that um um + + + align:start position:0% +makes sense and we saw how that um um +was kind of overcome or what changed it + + align:start position:0% +was kind of overcome or what changed it + + + align:start position:0% +was kind of overcome or what changed it +was actually multiple years in the case + + align:start position:0% +was actually multiple years in the case + + + align:start position:0% +was actually multiple years in the case +of the Soviet Union + + align:start position:0% +of the Soviet Union + + + align:start position:0% +of the Soviet Union +between when they did start showing up + + align:start position:0% +between when they did start showing up + + + align:start position:0% +between when they did start showing up +they were just a trickle they were + + align:start position:0% +they were just a trickle they were + + + align:start position:0% +they were just a trickle they were +literally 12 articles over the span of + + align:start position:0% +literally 12 articles over the span of + + + align:start position:0% +literally 12 articles over the span of +two years at a time when they're more + + align:start position:0% +two years at a time when they're more + + + align:start position:0% +two years at a time when they're more +than a hundred you know in the in the + + align:start position:0% +than a hundred you know in the in the + + + align:start position:0% +than a hundred you know in the in the +U.S term + + align:start position:0% +U.S term + + + align:start position:0% +U.S term +and it turns out six of those 12 were + + align:start position:0% +and it turns out six of those 12 were + + + align:start position:0% +and it turns out six of those 12 were +submitted by one physicist this was not + + align:start position:0% +submitted by one physicist this was not + + + align:start position:0% +submitted by one physicist this was not +an exponential rise uh in the same way + + align:start position:0% +an exponential rise uh in the same way + + + align:start position:0% +an exponential rise uh in the same way +at the same time + + align:start position:0% +at the same time + + + align:start position:0% +at the same time +that one person who did submit to Alexi + + align:start position:0% +that one person who did submit to Alexi + + + align:start position:0% +that one person who did submit to Alexi +galanian had very particular reasons to + + align:start position:0% +galanian had very particular reasons to + + + align:start position:0% +galanian had very particular reasons to +learn how to calculate radius + + align:start position:0% +learn how to calculate radius + + + align:start position:0% +learn how to calculate radius +corrections to comps and scattering + + align:start position:0% +corrections to comps and scattering + + + align:start position:0% +corrections to comps and scattering +because he was working on the top secret + + align:start position:0% +because he was working on the top secret + + + align:start position:0% +because he was working on the top secret +h-bomb project and had to worry about + + align:start position:0% +h-bomb project and had to worry about + + + align:start position:0% +h-bomb project and had to worry about +shielding for that high + + align:start position:0% +shielding for that high + + + align:start position:0% +shielding for that high +radiation pressure inside of a various H + + align:start position:0% +radiation pressure inside of a various H + + + align:start position:0% +radiation pressure inside of a various H +bone designs yeah let's just say special + + align:start position:0% +bone designs yeah let's just say special + + + align:start position:0% +bone designs yeah let's just say special +incentive uh to learn how to uh to learn + + align:start position:0% +incentive uh to learn how to uh to learn + + + align:start position:0% +incentive uh to learn how to uh to learn +from Dyson's articles + + align:start position:0% +from Dyson's articles + + + align:start position:0% +from Dyson's articles +when he did here's an example of uh one + + align:start position:0% +when he did here's an example of uh one + + + align:start position:0% +when he did here's an example of uh one +of kalanian's early papers he's stuck + + align:start position:0% +of kalanian's early papers he's stuck + + + align:start position:0% +of kalanian's early papers he's stuck +and this is not to fall to him he did + + align:start position:0% +and this is not to fall to him he did + + + align:start position:0% +and this is not to fall to him he did +exactly what Dyson's articles had + + align:start position:0% +exactly what Dyson's articles had + + + align:start position:0% +exactly what Dyson's articles had +prepped him to do but he didn't do any + + align:start position:0% +prepped him to do but he didn't do any + + + align:start position:0% +prepped him to do but he didn't do any +of the or neither galanian or any of his + + align:start position:0% +of the or neither galanian or any of his + + + align:start position:0% +of the or neither galanian or any of his +immediate uh colleagues in the Soviet + + align:start position:0% +immediate uh colleagues in the Soviet + + + align:start position:0% +immediate uh colleagues in the Soviet +Union did any of the kind of broader + + align:start position:0% +Union did any of the kind of broader + + + align:start position:0% +Union did any of the kind of broader +more let's just say improvisational or + + align:start position:0% +more let's just say improvisational or + + + align:start position:0% +more let's just say improvisational or +more adaptive uses of the diagrams that + + align:start position:0% +more adaptive uses of the diagrams that + + + align:start position:0% +more adaptive uses of the diagrams that +were already becoming quite common in + + align:start position:0% +were already becoming quite common in + + + align:start position:0% +were already becoming quite common in +the United States in Britain and even in + + align:start position:0% +the United States in Britain and even in + + + align:start position:0% +the United States in Britain and even in +Japan so you have a kind of transmission + + align:start position:0% +Japan so you have a kind of transmission + + + align:start position:0% +Japan so you have a kind of transmission +by text it takes a lot longer and then + + align:start position:0% +by text it takes a lot longer and then + + + align:start position:0% +by text it takes a lot longer and then +and the range of applications remains + + align:start position:0% +and the range of applications remains + + + align:start position:0% +and the range of applications remains +rather narrow okay let me pause that it + + align:start position:0% +rather narrow okay let me pause that it + + + align:start position:0% +rather narrow okay let me pause that it +was a long chunk but let me pause there + + align:start position:0% +was a long chunk but let me pause there + + + align:start position:0% +was a long chunk but let me pause there +I see some questions popping up in the + + align:start position:0% +I see some questions popping up in the + + + align:start position:0% +I see some questions popping up in the +chat + + align:start position:0% +chat + + + align:start position:0% +chat +Lucas tells me the Rams Head and is + + align:start position:0% +Lucas tells me the Rams Head and is + + + align:start position:0% +Lucas tells me the Rams Head and is +still in business so once we any of us + + align:start position:0% +still in business so once we any of us + + + align:start position:0% +still in business so once we any of us +can travel we should all arrange a field + + align:start position:0% +can travel we should all arrange a field + + + align:start position:0% +can travel we should all arrange a field +trip I'd love to see that place with my + + align:start position:0% +trip I'd love to see that place with my + + + align:start position:0% +trip I'd love to see that place with my +own eyes thank you Lucas for confirming + + align:start position:0% +own eyes thank you Lucas for confirming + + + align:start position:0% +own eyes thank you Lucas for confirming +uh Alex says it's like when you get a + + align:start position:0% +uh Alex says it's like when you get a + + + align:start position:0% +uh Alex says it's like when you get a +speaking ticket you have to take the + + align:start position:0% +speaking ticket you have to take the + + + align:start position:0% +speaking ticket you have to take the +class I'm not sure what that was about + + align:start position:0% +class I'm not sure what that was about + + + align:start position:0% +class I'm not sure what that was about +but um + + align:start position:0% +but um + + + align:start position:0% +but um +but yes Fisher says had five received as + + align:start position:0% +but yes Fisher says had five received as + + + align:start position:0% +but yes Fisher says had five received as +professorship postdoc oh very good so uh + + align:start position:0% +professorship postdoc oh very good so uh + + + align:start position:0% +professorship postdoc oh very good so uh +Feynman was indeed um so Feynman was a a + + align:start position:0% +Feynman was indeed um so Feynman was a a + + + align:start position:0% +Feynman was indeed um so Feynman was a a +professor uh at Cornell he um had + + align:start position:0% +professor uh at Cornell he um had + + + align:start position:0% +professor uh at Cornell he um had +finished his PhD it's actually a little + + align:start position:0% +finished his PhD it's actually a little + + + align:start position:0% +finished his PhD it's actually a little +funny he finished the work for his PhD + + align:start position:0% +funny he finished the work for his PhD + + + align:start position:0% +funny he finished the work for his PhD +before leaving Princeton he was in grad + + align:start position:0% +before leaving Princeton he was in grad + + + align:start position:0% +before leaving Princeton he was in grad +school in Princeton uh before leaving + + align:start position:0% +school in Princeton uh before leaving + + + align:start position:0% +school in Princeton uh before leaving +for Los Alamos for the war but he hadn't + + align:start position:0% +for Los Alamos for the war but he hadn't + + + align:start position:0% +for Los Alamos for the war but he hadn't +formally written up his thesis yet and + + align:start position:0% +formally written up his thesis yet and + + + align:start position:0% +formally written up his thesis yet and +then he got really busy yeah working uh + + align:start position:0% +then he got really busy yeah working uh + + + align:start position:0% +then he got really busy yeah working uh +in the theory group at Los Alamos so he + + align:start position:0% +in the theory group at Los Alamos so he + + + align:start position:0% +in the theory group at Los Alamos so he +didn't formally file his PhD + + align:start position:0% +didn't formally file his PhD + + + align:start position:0% +didn't formally file his PhD +dissertation until basically a few weeks + + align:start position:0% +dissertation until basically a few weeks + + + align:start position:0% +dissertation until basically a few weeks +after the end of the war very soon + + align:start position:0% +after the end of the war very soon + + + align:start position:0% +after the end of the war very soon +afterwards so he officially got his PhD + + align:start position:0% +afterwards so he officially got his PhD + + + align:start position:0% +afterwards so he officially got his PhD +but everyone knew it was all but done + + align:start position:0% +but everyone knew it was all but done + + + align:start position:0% +but everyone knew it was all but done +remember post-doc stages were not all + + align:start position:0% +remember post-doc stages were not all + + + align:start position:0% +remember post-doc stages were not all +that common it was not that unusual to + + align:start position:0% +that common it was not that unusual to + + + align:start position:0% +that common it was not that unusual to +be hired straight into a faculty + + align:start position:0% +be hired straight into a faculty + + + align:start position:0% +be hired straight into a faculty +position from one's PhD and everyone + + align:start position:0% +position from one's PhD and everyone + + + align:start position:0% +position from one's PhD and everyone +knew at that point that feynman's PhD + + align:start position:0% +knew at that point that feynman's PhD + + + align:start position:0% +knew at that point that feynman's PhD +was was essentially done + + align:start position:0% +was was essentially done + + + align:start position:0% +was was essentially done +moreover he had really impressed people + + align:start position:0% +moreover he had really impressed people + + + align:start position:0% +moreover he had really impressed people +like Hans beta and Robert Oppenheimer + + align:start position:0% +like Hans beta and Robert Oppenheimer + + + align:start position:0% +like Hans beta and Robert Oppenheimer +during the war and so he was actually + + align:start position:0% +during the war and so he was actually + + + align:start position:0% +during the war and so he was actually +being multiply recruited I found letters + + align:start position:0% +being multiply recruited I found letters + + + align:start position:0% +being multiply recruited I found letters +uh he was made multiple faculty offers + + align:start position:0% +uh he was made multiple faculty offers + + + align:start position:0% +uh he was made multiple faculty offers +Berkeley so Oppenheimer first went back + + align:start position:0% +Berkeley so Oppenheimer first went back + + + align:start position:0% +Berkeley so Oppenheimer first went back +to Berkeley he tried to hire Feynman + + align:start position:0% +to Berkeley he tried to hire Feynman + + + align:start position:0% +to Berkeley he tried to hire Feynman +beta made it basically a better offer so + + align:start position:0% +beta made it basically a better offer so + + + align:start position:0% +beta made it basically a better offer so +he was in high demand as many many of + + align:start position:0% +he was in high demand as many many of + + + align:start position:0% +he was in high demand as many many of +these young physicists were so he was + + align:start position:0% +these young physicists were so he was + + + align:start position:0% +these young physicists were so he was +starting uh formerly as a member of The + + align:start position:0% +starting uh formerly as a member of The + + + align:start position:0% +starting uh formerly as a member of The +Faculty he was still rather Young and he + + align:start position:0% +Faculty he was still rather Young and he + + + align:start position:0% +Faculty he was still rather Young and he +was relatively close in age to Freeman + + align:start position:0% +was relatively close in age to Freeman + + + align:start position:0% +was relatively close in age to Freeman +Dyson because Dyson had also had his + + align:start position:0% +Dyson because Dyson had also had his + + + align:start position:0% +Dyson because Dyson had also had his +studies kind of interrupted by the war + + align:start position:0% +studies kind of interrupted by the war + + + align:start position:0% +studies kind of interrupted by the war +he'd worked for a couple years uh in + + align:start position:0% +he'd worked for a couple years uh in + + + align:start position:0% +he'd worked for a couple years uh in +uh in the British kind of military + + align:start position:0% +uh in the British kind of military + + + align:start position:0% +uh in the British kind of military +um basically part of the the Royal Air + + align:start position:0% +um basically part of the the Royal Air + + + align:start position:0% +um basically part of the the Royal Air +Force doing statistical analyzes of + + align:start position:0% +Force doing statistical analyzes of + + + align:start position:0% +Force doing statistical analyzes of +bombing runs so they hired a lot of + + align:start position:0% +bombing runs so they hired a lot of + + + align:start position:0% +bombing runs so they hired a lot of +mathematically gifted young people to + + align:start position:0% +mathematically gifted young people to + + + align:start position:0% +mathematically gifted young people to +say what's the most effective way to use + + align:start position:0% +say what's the most effective way to use + + + align:start position:0% +say what's the most effective way to use +bombers what's the highest you know like + + align:start position:0% +bombers what's the highest you know like + + + align:start position:0% +bombers what's the highest you know like +kill ratio so to speak uh and what's + + align:start position:0% +kill ratio so to speak uh and what's + + + align:start position:0% +kill ratio so to speak uh and what's +what yields the least losses to the + + align:start position:0% +what yields the least losses to the + + + align:start position:0% +what yields the least losses to the +British planes so dice was doing a lot + + align:start position:0% +British planes so dice was doing a lot + + + align:start position:0% +British planes so dice was doing a lot +of statistical stuff during the war so + + align:start position:0% +of statistical stuff during the war so + + + align:start position:0% +of statistical stuff during the war so +his own studies were delayed so they + + align:start position:0% +his own studies were delayed so they + + + align:start position:0% +his own studies were delayed so they +were pretty close in age uh even though + + align:start position:0% +were pretty close in age uh even though + + + align:start position:0% +were pretty close in age uh even though +they were kind of different career + + align:start position:0% +they were kind of different career + + + align:start position:0% +they were kind of different career +stages and Alex confirms that the uh you + + align:start position:0% +stages and Alex confirms that the uh you + + + align:start position:0% +stages and Alex confirms that the uh you +have to take a classic uh we'll be like + + align:start position:0% +have to take a classic uh we'll be like + + + align:start position:0% +have to take a classic uh we'll be like +having to sit through schwinger's + + align:start position:0% +having to sit through schwinger's + + + align:start position:0% +having to sit through schwinger's +eight-hour lecture that's right I've + + align:start position:0% +eight-hour lecture that's right I've + + + align:start position:0% +eight-hour lecture that's right I've +seen the lecture notes that um I think + + align:start position:0% +seen the lecture notes that um I think + + + align:start position:0% +seen the lecture notes that um I think +it was John Wheeler took on trainer's + + align:start position:0% +it was John Wheeler took on trainer's + + + align:start position:0% +it was John Wheeler took on trainer's +lecture there and they really were + + align:start position:0% +lecture there and they really were + + + align:start position:0% +lecture there and they really were +they were they were beautiful polished + + align:start position:0% +they were they were beautiful polished + + + align:start position:0% +they were they were beautiful polished +like schwinger had thought this through + + align:start position:0% +like schwinger had thought this through + + + align:start position:0% +like schwinger had thought this through +he wasn't having it hauling for eight + + align:start position:0% +he wasn't having it hauling for eight + + + align:start position:0% +he wasn't having it hauling for eight +hours so the contrast with fine and just + + align:start position:0% +hours so the contrast with fine and just + + + align:start position:0% +hours so the contrast with fine and just +like winging it for 30 minutes is all + + align:start position:0% +like winging it for 30 minutes is all + + + align:start position:0% +like winging it for 30 minutes is all +was I think all the more Stark + + align:start position:0% +was I think all the more Stark + + + align:start position:0% +was I think all the more Stark +but any other questions on any of that + + align:start position:0% +but any other questions on any of that + + + align:start position:0% +but any other questions on any of that +material the early uh kind of post-doc + + align:start position:0% +material the early uh kind of post-doc + + + align:start position:0% +material the early uh kind of post-doc +cascade or anything like that + + align:start position:0% + + + + align:start position:0% + +okay I will press on but as usual please + + align:start position:0% +okay I will press on but as usual please + + + align:start position:0% +okay I will press on but as usual please +uh jump in if other questions come up + + align:start position:0% +uh jump in if other questions come up + + + align:start position:0% +uh jump in if other questions come up +I'm going to talk next about what were + + align:start position:0% +I'm going to talk next about what were + + + align:start position:0% +I'm going to talk next about what were +people actually doing with these + + align:start position:0% +people actually doing with these + + + align:start position:0% +people actually doing with these +diagrams and this will connect with one + + align:start position:0% +diagrams and this will connect with one + + + align:start position:0% +diagrams and this will connect with one +of the articles that I designed for uh + + align:start position:0% +of the articles that I designed for uh + + + align:start position:0% +of the articles that I designed for uh +for today's reading + + align:start position:0% +for today's reading + + + align:start position:0% +for today's reading +so remember that second meaning of + + align:start position:0% +so remember that second meaning of + + + align:start position:0% +so remember that second meaning of +dispersion is to get sort of more and + + align:start position:0% +dispersion is to get sort of more and + + + align:start position:0% +dispersion is to get sort of more and +more distinct from each other like like + + align:start position:0% +more distinct from each other like like + + + align:start position:0% +more distinct from each other like like +the single beam of light separating into + + align:start position:0% +the single beam of light separating into + + + align:start position:0% +the single beam of light separating into +the distinct colors of the rainbow + + align:start position:0% +the distinct colors of the rainbow + + + align:start position:0% +the distinct colors of the rainbow +so this picture how they spread doesn't + + align:start position:0% +so this picture how they spread doesn't + + + align:start position:0% +so this picture how they spread doesn't +really capture what people were doing + + align:start position:0% +really capture what people were doing + + + align:start position:0% +really capture what people were doing +with it in fact as as I'll as we'll talk + + align:start position:0% +with it in fact as as I'll as we'll talk + + + align:start position:0% +with it in fact as as I'll as we'll talk +about in this part people got actually + + align:start position:0% +about in this part people got actually + + + align:start position:0% +about in this part people got actually +pretty creative uh in making putting the + + align:start position:0% +pretty creative uh in making putting the + + + align:start position:0% +pretty creative uh in making putting the +diagrams to a range of different uses + + align:start position:0% +diagrams to a range of different uses + + + align:start position:0% +diagrams to a range of different uses +uh and so that had a few different seeds + + align:start position:0% +uh and so that had a few different seeds + + + align:start position:0% +uh and so that had a few different seeds +what was driving the kind of + + align:start position:0% +what was driving the kind of + + + align:start position:0% +what was driving the kind of +distinctiveness of what people did with + + align:start position:0% +distinctiveness of what people did with + + + align:start position:0% +distinctiveness of what people did with +the diagrams there were a couple + + align:start position:0% +the diagrams there were a couple + + + align:start position:0% +the diagrams there were a couple +ingredients + + align:start position:0% +ingredients + + + align:start position:0% +ingredients +one of them was that firemen and Dyson + + align:start position:0% +one of them was that firemen and Dyson + + + align:start position:0% +one of them was that firemen and Dyson +themselves actually held pretty + + align:start position:0% +themselves actually held pretty + + + align:start position:0% +themselves actually held pretty +different ideas about what the diagrams + + align:start position:0% +different ideas about what the diagrams + + + align:start position:0% +different ideas about what the diagrams +really represented or how they should + + align:start position:0% +really represented or how they should + + + align:start position:0% +really represented or how they should +sort of properly be interpreted so + + align:start position:0% +sort of properly be interpreted so + + + align:start position:0% +sort of properly be interpreted so +Feynman always talked about them as + + align:start position:0% +Feynman always talked about them as + + + align:start position:0% +Feynman always talked about them as +intuitive pictures and I think that's + + align:start position:0% +intuitive pictures and I think that's + + + align:start position:0% +intuitive pictures and I think that's +fair we can sort of see where it's + + align:start position:0% +fair we can sort of see where it's + + + align:start position:0% +fair we can sort of see where it's +coming from this is sort of a story that + + align:start position:0% +coming from this is sort of a story that + + + align:start position:0% +coming from this is sort of a story that +he would often act out as I tried to do + + align:start position:0% +he would often act out as I tried to do + + + align:start position:0% +he would often act out as I tried to do +in my little Zoom chair you know the + + align:start position:0% +in my little Zoom chair you know the + + + align:start position:0% +in my little Zoom chair you know the +electron spits out a photon it recoils + + align:start position:0% +electron spits out a photon it recoils + + + align:start position:0% +electron spits out a photon it recoils +here they were very very kind of + + align:start position:0% +here they were very very kind of + + + align:start position:0% +here they were very very kind of +animated Tales of things unfolding + + align:start position:0% +animated Tales of things unfolding + + + align:start position:0% +animated Tales of things unfolding +through space and time Dyson whose + + align:start position:0% +through space and time Dyson whose + + + align:start position:0% +through space and time Dyson whose +original training was actually in pure + + align:start position:0% +original training was actually in pure + + + align:start position:0% +original training was actually in pure +mathematics not in physics and + + align:start position:0% +mathematics not in physics and + + + align:start position:0% +mathematics not in physics and +throughout his his career was always + + align:start position:0% +throughout his his career was always + + + align:start position:0% +throughout his his career was always +much more formal much more a + + align:start position:0% +much more formal much more a + + + align:start position:0% +much more formal much more a +mathematical physicist than Feynman + + align:start position:0% +mathematical physicist than Feynman + + + align:start position:0% +mathematical physicist than Feynman +Dyson cautions in his very first article + + align:start position:0% +Dyson cautions in his very first article + + + align:start position:0% +Dyson cautions in his very first article +on the new techniques that these are + + align:start position:0% +on the new techniques that these are + + + align:start position:0% +on the new techniques that these are +merely graphs on paper that's the phrase + + align:start position:0% +merely graphs on paper that's the phrase + + + align:start position:0% +merely graphs on paper that's the phrase +uses these are not pictures they're not + + align:start position:0% +uses these are not pictures they're not + + + align:start position:0% +uses these are not pictures they're not +minkowski diagrams these are not literal + + align:start position:0% +minkowski diagrams these are not literal + + + align:start position:0% +minkowski diagrams these are not literal +depictions of events unfolding in space + + align:start position:0% +depictions of events unfolding in space + + + align:start position:0% +depictions of events unfolding in space +and time what's relevant is their kind + + align:start position:0% +and time what's relevant is their kind + + + align:start position:0% +and time what's relevant is their kind +of topology that some two lines connect + + align:start position:0% +of topology that some two lines connect + + + align:start position:0% +of topology that some two lines connect +here in a Vertex two other lines connect + + align:start position:0% +here in a Vertex two other lines connect + + + align:start position:0% +here in a Vertex two other lines connect +over here and there are only so many + + align:start position:0% +over here and there are only so many + + + align:start position:0% +over here and there are only so many +ways to arrange various lines and + + align:start position:0% +ways to arrange various lines and + + + align:start position:0% +ways to arrange various lines and +vertices it was for him more like a kind + + align:start position:0% +vertices it was for him more like a kind + + + align:start position:0% +vertices it was for him more like a kind +of mathematician's graph Theory so from + + align:start position:0% +of mathematician's graph Theory so from + + + align:start position:0% +of mathematician's graph Theory so from +the beginning you're getting kind of + + align:start position:0% +the beginning you're getting kind of + + + align:start position:0% +the beginning you're getting kind of +mixed signals about what these diagrams + + align:start position:0% +mixed signals about what these diagrams + + + align:start position:0% +mixed signals about what these diagrams +are all about even more important that + + align:start position:0% +are all about even more important that + + + align:start position:0% +are all about even more important that +is what we'll talk more about in this in + + align:start position:0% +is what we'll talk more about in this in + + + align:start position:0% +is what we'll talk more about in this in +this uh this next part + + align:start position:0% +this uh this next part + + + align:start position:0% +this uh this next part +was that the questions that seemed most + + align:start position:0% +was that the questions that seemed most + + + align:start position:0% +was that the questions that seemed most +pressing toward which many many people + + align:start position:0% +pressing toward which many many people + + + align:start position:0% +pressing toward which many many people +tried to put these diagrams for use + + align:start position:0% +tried to put these diagrams for use + + + align:start position:0% +tried to put these diagrams for use +actually were not the problem area for + + align:start position:0% +actually were not the problem area for + + + align:start position:0% +actually were not the problem area for +which they had first been introduced so + + align:start position:0% +which they had first been introduced so + + + align:start position:0% +which they had first been introduced so +these were introduced in the context of + + align:start position:0% +these were introduced in the context of + + + align:start position:0% +these were introduced in the context of +quantum electrodynamics meaning + + align:start position:0% +quantum electrodynamics meaning + + + align:start position:0% +quantum electrodynamics meaning +electrons positrons photons every + + align:start position:0% +electrons positrons photons every + + + align:start position:0% +electrons positrons photons every +interaction of which is governed by the + + align:start position:0% +interaction of which is governed by the + + + align:start position:0% +interaction of which is governed by the +electric charge when I say that the + + align:start position:0% +electric charge when I say that the + + + align:start position:0% +electric charge when I say that the +electron has a certain likelihood to + + align:start position:0% +electron has a certain likelihood to + + + align:start position:0% +electron has a certain likelihood to +emit a virtual Photon that likelihood + + align:start position:0% +emit a virtual Photon that likelihood + + + align:start position:0% +emit a virtual Photon that likelihood +quantitatively is governed by what we + + align:start position:0% +quantitatively is governed by what we + + + align:start position:0% +quantitatively is governed by what we +call its coupling constant which is just + + align:start position:0% +call its coupling constant which is just + + + align:start position:0% +call its coupling constant which is just +to say it's electric charge so every + + align:start position:0% +to say it's electric charge so every + + + align:start position:0% +to say it's electric charge so every +what that means pictorially is everyone + + align:start position:0% +what that means pictorially is everyone + + + align:start position:0% +what that means pictorially is everyone +has red dots where say electron lines + + align:start position:0% +has red dots where say electron lines + + + align:start position:0% +has red dots where say electron lines +meet a photon line every time these + + align:start position:0% +meet a photon line every time these + + + align:start position:0% +meet a photon line every time these +lines literally connect in a Vertex the + + align:start position:0% +lines literally connect in a Vertex the + + + align:start position:0% +lines literally connect in a Vertex the +corresponding algebraic expression is + + align:start position:0% +corresponding algebraic expression is + + + align:start position:0% +corresponding algebraic expression is +multiplied by one factor of that + + align:start position:0% +multiplied by one factor of that + + + align:start position:0% +multiplied by one factor of that +coefficient the electric charge and then + + align:start position:0% +coefficient the electric charge and then + + + align:start position:0% +coefficient the electric charge and then +the lines meet again here's the second + + align:start position:0% +the lines meet again here's the second + + + align:start position:0% +the lines meet again here's the second +Factor this is an e-squared diagram we + + align:start position:0% +Factor this is an e-squared diagram we + + + align:start position:0% +Factor this is an e-squared diagram we +tell you our second order diagram this + + align:start position:0% +tell you our second order diagram this + + + align:start position:0% +tell you our second order diagram this +one is a more complicated diagram there + + align:start position:0% +one is a more complicated diagram there + + + align:start position:0% +one is a more complicated diagram there +are four spots where electron lines hit + + align:start position:0% +are four spots where electron lines hit + + + align:start position:0% +are four spots where electron lines hit +Photon lines or vice versa four red + + align:start position:0% +Photon lines or vice versa four red + + + align:start position:0% +Photon lines or vice versa four red +circles that's an e to the fourth + + align:start position:0% +circles that's an e to the fourth + + + align:start position:0% +circles that's an e to the fourth +diagram the algebra in front of the long + + align:start position:0% +diagram the algebra in front of the long + + + align:start position:0% +diagram the algebra in front of the long +uh excuse me the coefficient I should + + align:start position:0% +uh excuse me the coefficient I should + + + align:start position:0% +uh excuse me the coefficient I should +say in front of the long algebra would + + align:start position:0% +say in front of the long algebra would + + + align:start position:0% +say in front of the long algebra would +have four factors of this constant + + align:start position:0% +have four factors of this constant + + + align:start position:0% +have four factors of this constant +number e here's an example with a tenth + + align:start position:0% +number e here's an example with a tenth + + + align:start position:0% +number e here's an example with a tenth +order diagram where you're trading five + + align:start position:0% +order diagram where you're trading five + + + align:start position:0% +order diagram where you're trading five +virtual photons as an e to the 10th now + + align:start position:0% +virtual photons as an e to the 10th now + + + align:start position:0% +virtual photons as an e to the 10th now +it turns out that in in natural units + + align:start position:0% +it turns out that in in natural units + + + align:start position:0% +it turns out that in in natural units +the charge electron is small electricity + + align:start position:0% +the charge electron is small electricity + + + align:start position:0% +the charge electron is small electricity +is a weak weakly coupled force in + + align:start position:0% +is a weak weakly coupled force in + + + align:start position:0% +is a weak weakly coupled force in +particular e squared is about 1 over 137 + + align:start position:0% +particular e squared is about 1 over 137 + + + align:start position:0% +particular e squared is about 1 over 137 +in these kind of natural units less so + + align:start position:0% +in these kind of natural units less so + + + align:start position:0% +in these kind of natural units less so +it's uh it's um it's smaller than one + + align:start position:0% +it's uh it's um it's smaller than one + + + align:start position:0% +it's uh it's um it's smaller than one +over a hundred so this diagram is + + align:start position:0% +over a hundred so this diagram is + + + align:start position:0% +over a hundred so this diagram is +multiplied by a number that's a hundred + + align:start position:0% +multiplied by a number that's a hundred + + + align:start position:0% +multiplied by a number that's a hundred +times smaller than this diagram no + + align:start position:0% +times smaller than this diagram no + + + align:start position:0% +times smaller than this diagram no +matter what the algebra is its + + align:start position:0% +matter what the algebra is its + + + align:start position:0% +matter what the algebra is its +coefficient is a parametrically smaller + + align:start position:0% +coefficient is a parametrically smaller + + + align:start position:0% +coefficient is a parametrically smaller +which means this diagram is + + align:start position:0% +which means this diagram is + + + align:start position:0% +which means this diagram is +exponentially smaller still so that's + + align:start position:0% +exponentially smaller still so that's + + + align:start position:0% +exponentially smaller still so that's +why these things became so useful in QED + + align:start position:0% +why these things became so useful in QED + + + align:start position:0% +why these things became so useful in QED +you didn't have to calculate to Infinity + + align:start position:0% +you didn't have to calculate to Infinity + + + align:start position:0% +you didn't have to calculate to Infinity +these two electrons could have traded an + + align:start position:0% +these two electrons could have traded an + + + align:start position:0% +these two electrons could have traded an +infinite number of virtual particles but + + align:start position:0% +infinite number of virtual particles but + + + align:start position:0% +infinite number of virtual particles but +the more complicated the interaction the + + align:start position:0% +the more complicated the interaction the + + + align:start position:0% +the more complicated the interaction the +more places where blue electron lines + + align:start position:0% +more places where blue electron lines + + + align:start position:0% +more places where blue electron lines +would connect with these kind of neon + + align:start position:0% +would connect with these kind of neon + + + align:start position:0% +would connect with these kind of neon +green Photon lines the more powers of + + align:start position:0% +green Photon lines the more powers of + + + align:start position:0% +green Photon lines the more powers of +that small number would come out in + + align:start position:0% +that small number would come out in + + + align:start position:0% +that small number would come out in +front so as a practical matter you could + + align:start position:0% +front so as a practical matter you could + + + align:start position:0% +front so as a practical matter you could +stop this is a perturbation Theory + + align:start position:0% +stop this is a perturbation Theory + + + align:start position:0% +stop this is a perturbation Theory +calculation + + align:start position:0% +calculation + + + align:start position:0% +calculation +got a tailor expanding and each + + align:start position:0% +got a tailor expanding and each + + + align:start position:0% +got a tailor expanding and each +additional contribution weighs less + + align:start position:0% +additional contribution weighs less + + + align:start position:0% +additional contribution weighs less +quantitative okay so that's great it's a + + align:start position:0% +quantitative okay so that's great it's a + + + align:start position:0% +quantitative okay so that's great it's a +great bookkeeper none of that works none + + align:start position:0% +great bookkeeper none of that works none + + + align:start position:0% +great bookkeeper none of that works none +of that works when you apply these to + + align:start position:0% +of that works when you apply these to + + + align:start position:0% +of that works when you apply these to +strongly interacting particles and guess + + align:start position:0% +strongly interacting particles and guess + + + align:start position:0% +strongly interacting particles and guess +what most physicists in the United + + align:start position:0% +what most physicists in the United + + + align:start position:0% +what most physicists in the United +States apply them to strongly + + align:start position:0% +States apply them to strongly + + + align:start position:0% +States apply them to strongly +interacting particles it makes no sense + + align:start position:0% +interacting particles it makes no sense + + + align:start position:0% +interacting particles it makes no sense +at all they applied it to the scattering + + align:start position:0% +at all they applied it to the scattering + + + align:start position:0% +at all they applied it to the scattering +of say protons off of Pi mesons or + + align:start position:0% +of say protons off of Pi mesons or + + + align:start position:0% +of say protons off of Pi mesons or +neutrons off of other kind of particles + + align:start position:0% +neutrons off of other kind of particles + + + align:start position:0% +neutrons off of other kind of particles +coming out of the new accelerators + + align:start position:0% +coming out of the new accelerators + + + align:start position:0% +coming out of the new accelerators +the equivalent the analog of the + + align:start position:0% +the equivalent the analog of the + + + align:start position:0% +the equivalent the analog of the +electric charge for those nuclear forces + + align:start position:0% +electric charge for those nuclear forces + + + align:start position:0% +electric charge for those nuclear forces +was strong in the same natural units + + align:start position:0% +was strong in the same natural units + + + align:start position:0% +was strong in the same natural units +it's larger in fact it's larger than 10 + + align:start position:0% +it's larger in fact it's larger than 10 + + + align:start position:0% +it's larger in fact it's larger than 10 +which means that this diagram counts + + align:start position:0% +which means that this diagram counts + + + align:start position:0% +which means that this diagram counts +exponentially More Than This diagram and + + align:start position:0% +exponentially More Than This diagram and + + + align:start position:0% +exponentially More Than This diagram and +there's an infinite number of them so + + align:start position:0% +there's an infinite number of them so + + + align:start position:0% +there's an infinite number of them so +they're not doing perturbation Theory + + align:start position:0% +they're not doing perturbation Theory + + + align:start position:0% +they're not doing perturbation Theory +and yet they're still using diagrams + + align:start position:0% +and yet they're still using diagrams + + + align:start position:0% +and yet they're still using diagrams +that is pretty strange + + align:start position:0% +that is pretty strange + + + align:start position:0% +that is pretty strange +so that leads to this kind of + + align:start position:0% +so that leads to this kind of + + + align:start position:0% +so that leads to this kind of +real kind of explosion + + align:start position:0% +real kind of explosion + + + align:start position:0% +real kind of explosion +and how people adapted the Tigers often + + align:start position:0% +and how people adapted the Tigers often + + + align:start position:0% +and how people adapted the Tigers often +even just the pictorial form of the + + align:start position:0% +even just the pictorial form of the + + + align:start position:0% +even just the pictorial form of the +diagrams themselves because they weren't + + align:start position:0% +diagrams themselves because they weren't + + + align:start position:0% +diagrams themselves because they weren't +just doing one cookie cutter thing they + + align:start position:0% +just doing one cookie cutter thing they + + + align:start position:0% +just doing one cookie cutter thing they +weren't all doing fine and Dyson + + align:start position:0% +weren't all doing fine and Dyson + + + align:start position:0% +weren't all doing fine and Dyson +perturbation theory for electromagnetism + + align:start position:0% +perturbation theory for electromagnetism + + + align:start position:0% +perturbation theory for electromagnetism +they were mostly applying it to nuclear + + align:start position:0% +they were mostly applying it to nuclear + + + align:start position:0% +they were mostly applying it to nuclear +forces you can't just do the same trick + + align:start position:0% +forces you can't just do the same trick + + + align:start position:0% +forces you can't just do the same trick +for nuclear forces because the coupling + + align:start position:0% +for nuclear forces because the coupling + + + align:start position:0% +for nuclear forces because the coupling +constant is so large but people still + + align:start position:0% +constant is so large but people still + + + align:start position:0% +constant is so large but people still +found useful things so the diagrams are + + align:start position:0% +found useful things so the diagrams are + + + align:start position:0% +found useful things so the diagrams are +taking off exponentially even though + + align:start position:0% +taking off exponentially even though + + + align:start position:0% +taking off exponentially even though +they're applying them to new and + + align:start position:0% +they're applying them to new and + + + align:start position:0% +they're applying them to new and +different kinds of applications so this + + align:start position:0% +different kinds of applications so this + + + align:start position:0% +different kinds of applications so this +looks kind of scatter shy it's meant to + + align:start position:0% +looks kind of scatter shy it's meant to + + + align:start position:0% +looks kind of scatter shy it's meant to +be scatter shot + + align:start position:0% +be scatter shot + + + align:start position:0% +be scatter shot +we begin to get some order once we come + + align:start position:0% +we begin to get some order once we come + + + align:start position:0% +we begin to get some order once we come +back to ask about who knew whom in + + align:start position:0% +back to ask about who knew whom in + + + align:start position:0% +back to ask about who knew whom in +particular who is learning from whom who + + align:start position:0% +particular who is learning from whom who + + + align:start position:0% +particular who is learning from whom who +is studying with whom so I call these + + align:start position:0% +is studying with whom so I call these + + + align:start position:0% +is studying with whom so I call these +kind of family resemblances + + align:start position:0% +kind of family resemblances + + + align:start position:0% +kind of family resemblances +in each of these colored um um you know + + align:start position:0% +in each of these colored um um you know + + + align:start position:0% +in each of these colored um um you know +rectangles the diagram that's a little + + align:start position:0% +rectangles the diagram that's a little + + + align:start position:0% +rectangles the diagram that's a little +elevated on the left comes from the PHD + + align:start position:0% +elevated on the left comes from the PHD + + + align:start position:0% +elevated on the left comes from the PHD +advisor of the person whose diagram + + align:start position:0% +advisor of the person whose diagram + + + align:start position:0% +advisor of the person whose diagram +appears on the right these are literally + + align:start position:0% +appears on the right these are literally + + + align:start position:0% +appears on the right these are literally +Mentor student relationships I used to + + align:start position:0% +Mentor student relationships I used to + + + align:start position:0% +Mentor student relationships I used to +try to play this kind of parlor game + + align:start position:0% +try to play this kind of parlor game + + + align:start position:0% +try to play this kind of parlor game +when I could go to parlors like choose + + align:start position:0% +when I could go to parlors like choose + + + align:start position:0% +when I could go to parlors like choose +any random find a diagram from the + + align:start position:0% +any random find a diagram from the + + + align:start position:0% +any random find a diagram from the +physical review at least up through the + + align:start position:0% +physical review at least up through the + + + align:start position:0% +physical review at least up through the +mid 50s and with reasonable accuracy at + + align:start position:0% +mid 50s and with reasonable accuracy at + + + align:start position:0% +mid 50s and with reasonable accuracy at +least would claim I could tell you who + + align:start position:0% +least would claim I could tell you who + + + align:start position:0% +least would claim I could tell you who +drew it or at least what PhD program + + align:start position:0% +drew it or at least what PhD program + + + align:start position:0% +drew it or at least what PhD program +they came from I had pretty it was + + align:start position:0% +they came from I had pretty it was + + + align:start position:0% +they came from I had pretty it was +pretty good now they're maybe more + + align:start position:0% +pretty good now they're maybe more + + + align:start position:0% +pretty good now they're maybe more +useful life skills to train oneself on + + align:start position:0% +useful life skills to train oneself on + + + align:start position:0% +useful life skills to train oneself on +but that was like way into this so you + + align:start position:0% +but that was like way into this so you + + + align:start position:0% +but that was like way into this so you +could literally see oh that's um that's + + align:start position:0% +could literally see oh that's um that's + + + align:start position:0% +could literally see oh that's um that's +a a + + align:start position:0% +a a + + + align:start position:0% +a a +Richard Feynman student oh but this over + + align:start position:0% +Richard Feynman student oh but this over + + + align:start position:0% +Richard Feynman student oh but this over +here that's actually you know a Norman + + align:start position:0% +here that's actually you know a Norman + + + align:start position:0% +here that's actually you know a Norman +Kroll suit or this one over here that + + align:start position:0% +Kroll suit or this one over here that + + + align:start position:0% +Kroll suit or this one over here that +person was trained by Robert Marshall + + align:start position:0% +person was trained by Robert Marshall + + + align:start position:0% +person was trained by Robert Marshall +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +you can see these local adaptations + + align:start position:0% +you can see these local adaptations + + + align:start position:0% +you can see these local adaptations +because these different departments or + + align:start position:0% +because these different departments or + + + align:start position:0% +because these different departments or +members of these different departments + + align:start position:0% +members of these different departments + + + align:start position:0% +members of these different departments +we're actually doing different things + + align:start position:0% +we're actually doing different things + + + align:start position:0% +we're actually doing different things +with the diagrams often set by local + + align:start position:0% +with the diagrams often set by local + + + align:start position:0% +with the diagrams often set by local +demands for priorities so for example at + + align:start position:0% +demands for priorities so for example at + + + align:start position:0% +demands for priorities so for example at +Rochester uh in Upstate New York not too + + align:start position:0% +Rochester uh in Upstate New York not too + + + align:start position:0% +Rochester uh in Upstate New York not too +too far from Ithaca but far enough they + + align:start position:0% +too far from Ithaca but far enough they + + + align:start position:0% +too far from Ithaca but far enough they +had just received um it was like MIT had + + align:start position:0% +had just received um it was like MIT had + + + align:start position:0% +had just received um it was like MIT had +done funding to build their own small + + align:start position:0% +done funding to build their own small + + + align:start position:0% +done funding to build their own small +particle accelerator much like MIT + + align:start position:0% +particle accelerator much like MIT + + + align:start position:0% +particle accelerator much like MIT +synchrotron + + align:start position:0% +synchrotron + + + align:start position:0% +synchrotron +so they were the theorists there their + + align:start position:0% +so they were the theorists there their + + + align:start position:0% +so they were the theorists there their +main task was to help make sense of all + + align:start position:0% +main task was to help make sense of all + + + align:start position:0% +main task was to help make sense of all +the new kinds of particles that kept + + align:start position:0% +the new kinds of particles that kept + + + align:start position:0% +the new kinds of particles that kept +shooting out every time they turned that + + align:start position:0% +shooting out every time they turned that + + + align:start position:0% +shooting out every time they turned that +machine on they weren't worrying about + + align:start position:0% +machine on they weren't worrying about + + + align:start position:0% +machine on they weren't worrying about +these very fancy virtual particle + + align:start position:0% +these very fancy virtual particle + + + align:start position:0% +these very fancy virtual particle +Corrections there are no single virtual + + align:start position:0% +Corrections there are no single virtual + + + align:start position:0% +Corrections there are no single virtual +particle they're not these so-called + + align:start position:0% +particle they're not these so-called + + + align:start position:0% +particle they're not these so-called +Loop Corrections that led to all the + + align:start position:0% +Loop Corrections that led to all the + + + align:start position:0% +Loop Corrections that led to all the +trouble it was really a way of + + align:start position:0% +trouble it was really a way of + + + align:start position:0% +trouble it was really a way of +classifying what goes with what when + + align:start position:0% +classifying what goes with what when + + + align:start position:0% +classifying what goes with what when +these two things smash into each other + + align:start position:0% +these two things smash into each other + + + align:start position:0% +these two things smash into each other +what kinds of detritus comes out it's + + align:start position:0% +what kinds of detritus comes out it's + + + align:start position:0% +what kinds of detritus comes out it's +classification rather than kind of + + align:start position:0% +classification rather than kind of + + + align:start position:0% +classification rather than kind of +Dynamics these people were applying the + + align:start position:0% +Dynamics these people were applying the + + + align:start position:0% +Dynamics these people were applying the +diagrams not to high energy physics but + + align:start position:0% +diagrams not to high energy physics but + + + align:start position:0% +diagrams not to high energy physics but +actually to kind of many body Theory and + + align:start position:0% +actually to kind of many body Theory and + + + align:start position:0% +actually to kind of many body Theory and +what would become known as condensed + + align:start position:0% +what would become known as condensed + + + align:start position:0% +what would become known as condensed +matter physics what happens when two + + align:start position:0% +matter physics what happens when two + + + align:start position:0% +matter physics what happens when two +things are near each other and keep + + align:start position:0% +things are near each other and keep + + + align:start position:0% +things are near each other and keep +trading the same two particles keep + + align:start position:0% +trading the same two particles keep + + + align:start position:0% +trading the same two particles keep +trading uh Force carrying particles over + + align:start position:0% +trading uh Force carrying particles over + + + align:start position:0% +trading uh Force carrying particles over +and over again how do you add up that + + align:start position:0% +and over again how do you add up that + + + align:start position:0% +and over again how do you add up that +effect that might be something like a + + align:start position:0% +effect that might be something like a + + + align:start position:0% +effect that might be something like a +kind of bound state or some stable + + align:start position:0% +kind of bound state or some stable + + + align:start position:0% +kind of bound state or some stable +system different kind of challenge they + + align:start position:0% +system different kind of challenge they + + + align:start position:0% +system different kind of challenge they +were working for so you can start seeing + + align:start position:0% +were working for so you can start seeing + + + align:start position:0% +were working for so you can start seeing +the kind of local variation + + align:start position:0% +the kind of local variation + + + align:start position:0% +the kind of local variation +and who's using the diagrams toward what + + align:start position:0% +and who's using the diagrams toward what + + + align:start position:0% +and who's using the diagrams toward what +ends and now let me talk briefly about + + align:start position:0% +ends and now let me talk briefly about + + + align:start position:0% +ends and now let me talk briefly about +one of the even further kind of + + align:start position:0% +one of the even further kind of + + + align:start position:0% +one of the even further kind of +excursions or even more creative + + align:start position:0% +excursions or even more creative + + + align:start position:0% +excursions or even more creative +reinterpretations that I wrote about in + + align:start position:0% +reinterpretations that I wrote about in + + + align:start position:0% +reinterpretations that I wrote about in +one of the articles for um for today a + + align:start position:0% +one of the articles for um for today a + + + align:start position:0% +one of the articles for um for today a +little bit uh later in time + + align:start position:0% +little bit uh later in time + + + align:start position:0% +little bit uh later in time +and this focuses on the work from + + align:start position:0% +and this focuses on the work from + + + align:start position:0% +and this focuses on the work from +Jeffrey Chu he's one shown here at the + + align:start position:0% +Jeffrey Chu he's one shown here at the + + + align:start position:0% +Jeffrey Chu he's one shown here at the +Blackboard he was the kind of main + + align:start position:0% +Blackboard he was the kind of main + + + align:start position:0% +Blackboard he was the kind of main +um uh theoretical energy physicist at + + align:start position:0% +um uh theoretical energy physicist at + + + align:start position:0% +um uh theoretical energy physicist at +the University of California Berkeley + + align:start position:0% +the University of California Berkeley + + + align:start position:0% +the University of California Berkeley +over + + align:start position:0% +over + + + align:start position:0% +over +um the 50s and into the 60s + + align:start position:0% +um the 50s and into the 60s + + + align:start position:0% +um the 50s and into the 60s +uh most of the 60s so what he was like + + align:start position:0% +uh most of the 60s so what he was like + + + align:start position:0% +uh most of the 60s so what he was like +many of his colleagues really interested + + align:start position:0% +many of his colleagues really interested + + + align:start position:0% +many of his colleagues really interested +in nuclear forces not electrodynamics + + align:start position:0% +in nuclear forces not electrodynamics + + + align:start position:0% +in nuclear forces not electrodynamics +but all these many particles coming out + + align:start position:0% +but all these many particles coming out + + + align:start position:0% +but all these many particles coming out +of these big accelerators and all + + align:start position:0% +of these big accelerators and all + + + align:start position:0% +of these big accelerators and all +different ways they could interact with + + align:start position:0% +different ways they could interact with + + + align:start position:0% +different ways they could interact with +each other he knew as well as all of + + align:start position:0% +each other he knew as well as all of + + + align:start position:0% +each other he knew as well as all of +them did the faced with a large coupling + + align:start position:0% +them did the faced with a large coupling + + + align:start position:0% +them did the faced with a large coupling +constant you can't do this kind of + + align:start position:0% +constant you can't do this kind of + + + align:start position:0% +constant you can't do this kind of +perturbation Theory um and yet there's + + align:start position:0% +perturbation Theory um and yet there's + + + align:start position:0% +perturbation Theory um and yet there's +all this uh other things that one might + + align:start position:0% +all this uh other things that one might + + + align:start position:0% +all this uh other things that one might +try to do to make sense of the + + align:start position:0% +try to do to make sense of the + + + align:start position:0% +try to do to make sense of the +of all the new empirical riches coming + + align:start position:0% +of all the new empirical riches coming + + + align:start position:0% +of all the new empirical riches coming +from the from the new machines so he + + align:start position:0% +from the from the new machines so he + + + align:start position:0% +from the from the new machines so he +actually become so frustrated with + + align:start position:0% +actually become so frustrated with + + + align:start position:0% +actually become so frustrated with +Quantum field Theory precisely because + + align:start position:0% +Quantum field Theory precisely because + + + align:start position:0% +Quantum field Theory precisely because +it seems not up to the task of handling + + align:start position:0% +it seems not up to the task of handling + + + align:start position:0% +it seems not up to the task of handling +these strong nuclear forces it says + + align:start position:0% +these strong nuclear forces it says + + + align:start position:0% +these strong nuclear forces it says +Quantum field theory is dead in fact he + + align:start position:0% +Quantum field theory is dead in fact he + + + align:start position:0% +Quantum field theory is dead in fact he +says it's sterile and destined not to + + align:start position:0% +says it's sterile and destined not to + + + align:start position:0% +says it's sterile and destined not to +die but just to fade away and yet the + + align:start position:0% +die but just to fade away and yet the + + + align:start position:0% +die but just to fade away and yet the +diagrams he says hold a real key to + + align:start position:0% +diagrams he says hold a real key to + + + align:start position:0% +diagrams he says hold a real key to +moving forward so he tries to lift the + + align:start position:0% +moving forward so he tries to lift the + + + align:start position:0% +moving forward so he tries to lift the +diagrams out of quantum fuel Theory and + + align:start position:0% +diagrams out of quantum fuel Theory and + + + align:start position:0% +diagrams out of quantum fuel Theory and +toss away what have been used actually + + align:start position:0% +toss away what have been used actually + + + align:start position:0% +toss away what have been used actually +to derive them in the first place + + align:start position:0% +to derive them in the first place + + + align:start position:0% +to derive them in the first place +that's a pretty interesting move + + align:start position:0% + + + + align:start position:0% + +in its place + + align:start position:0% +in its place + + + align:start position:0% +in its place +he starts talking about something he + + align:start position:0% +he starts talking about something he + + + align:start position:0% +he starts talking about something he +called heinous students called a nuclear + + align:start position:0% +called heinous students called a nuclear + + + align:start position:0% +called heinous students called a nuclear +democracy and eventually the bootstrap + + align:start position:0% +democracy and eventually the bootstrap + + + align:start position:0% +democracy and eventually the bootstrap +and the idea was to treat all of these + + align:start position:0% +and the idea was to treat all of these + + + align:start position:0% +and the idea was to treat all of these +nuclear particles by this point more + + align:start position:0% +nuclear particles by this point more + + + align:start position:0% +nuclear particles by this point more +than a hundred of them have been + + align:start position:0% +than a hundred of them have been + + + align:start position:0% +than a hundred of them have been +identified + + align:start position:0% +identified + + + align:start position:0% +identified +treat them all as being on an equal + + align:start position:0% +treat them all as being on an equal + + + align:start position:0% +treat them all as being on an equal +footing + + align:start position:0% +footing + + + align:start position:0% +footing +why was that so radical according to + + align:start position:0% +why was that so radical according to + + + align:start position:0% +why was that so radical according to +ordinary Quantum field Theory you start + + align:start position:0% +ordinary Quantum field Theory you start + + + align:start position:0% +ordinary Quantum field Theory you start +out with a very different picture you + + align:start position:0% +out with a very different picture you + + + align:start position:0% +out with a very different picture you +have certain so-called Elementary + + align:start position:0% +have certain so-called Elementary + + + align:start position:0% +have certain so-called Elementary +particles and some of them might stick + + align:start position:0% +particles and some of them might stick + + + align:start position:0% +particles and some of them might stick +together and make bound States or + + align:start position:0% +together and make bound States or + + + align:start position:0% +together and make bound States or +Composites but some are sort of more + + align:start position:0% +Composites but some are sort of more + + + align:start position:0% +Composites but some are sort of more +special than others he actually called + + align:start position:0% +special than others he actually called + + + align:start position:0% +special than others he actually called +that an aristocracy or a kind of elitism + + align:start position:0% +that an aristocracy or a kind of elitism + + + align:start position:0% +that an aristocracy or a kind of elitism +or hierarchy I said maybe with a hundred + + align:start position:0% +or hierarchy I said maybe with a hundred + + + align:start position:0% +or hierarchy I said maybe with a hundred +plus nuclear particles let's not try to + + align:start position:0% +plus nuclear particles let's not try to + + + align:start position:0% +plus nuclear particles let's not try to +sort them into which ones are really + + align:start position:0% +sort them into which ones are really + + + align:start position:0% +sort them into which ones are really +special which ones are they all seem to + + align:start position:0% +special which ones are they all seem to + + + align:start position:0% +special which ones are they all seem to +fly out together let's assume they're + + align:start position:0% +fly out together let's assume they're + + + align:start position:0% +fly out together let's assume they're +all equally special treat them all on + + align:start position:0% +all equally special treat them all on + + + align:start position:0% +all equally special treat them all on +the same footing a democracy now this + + align:start position:0% +the same footing a democracy now this + + + align:start position:0% +the same footing a democracy now this +was unfolding as I wrote about it in the + + align:start position:0% +was unfolding as I wrote about it in the + + + align:start position:0% +was unfolding as I wrote about it in the +essay at a time when he was very + + align:start position:0% +essay at a time when he was very + + + align:start position:0% +essay at a time when he was very +concerned about other forms of democracy + + align:start position:0% +concerned about other forms of democracy + + + align:start position:0% +concerned about other forms of democracy +a slightly more literal form involving + + align:start position:0% +a slightly more literal form involving + + + align:start position:0% +a slightly more literal form involving +people and fair fair treatment of people + + align:start position:0% +people and fair fair treatment of people + + + align:start position:0% +people and fair fair treatment of people +amid the early stages of domestic + + align:start position:0% +amid the early stages of domestic + + + align:start position:0% +amid the early stages of domestic +anti-communism the so-called McCarthy + + align:start position:0% +anti-communism the so-called McCarthy + + + align:start position:0% +anti-communism the so-called McCarthy +era which we talked about some some + + align:start position:0% +era which we talked about some some + + + align:start position:0% +era which we talked about some some +weeks ago in this class + + align:start position:0% +weeks ago in this class + + + align:start position:0% +weeks ago in this class +in fact he was the first Professor to + + align:start position:0% +in fact he was the first Professor to + + + align:start position:0% +in fact he was the first Professor to +resign from the physics department and + + align:start position:0% +resign from the physics department and + + + align:start position:0% +resign from the physics department and +perhaps the first one from the entire + + align:start position:0% +perhaps the first one from the entire + + + align:start position:0% +perhaps the first one from the entire +University of California Berkeley campus + + align:start position:0% +University of California Berkeley campus + + + align:start position:0% +University of California Berkeley campus +to resign in 1949 over a kind of um + + align:start position:0% +to resign in 1949 over a kind of um + + + align:start position:0% +to resign in 1949 over a kind of um +loyalty oath um uh controversy he was uh + + align:start position:0% +loyalty oath um uh controversy he was uh + + + align:start position:0% +loyalty oath um uh controversy he was uh +he worked + + align:start position:0% +he worked + + + align:start position:0% +he worked +he gotten clearance during the War uh he + + align:start position:0% +he gotten clearance during the War uh he + + + align:start position:0% +he gotten clearance during the War uh he +there was no question that he had any + + align:start position:0% +there was no question that he had any + + + align:start position:0% +there was no question that he had any +kind of communist + + align:start position:0% +kind of communist + + + align:start position:0% +kind of communist +um you know Association just passed but + + align:start position:0% +um you know Association just passed but + + + align:start position:0% +um you know Association just passed but +about on principle it was simply + + align:start position:0% +about on principle it was simply + + + align:start position:0% +about on principle it was simply +Un-American in his estimation to demand + + align:start position:0% +Un-American in his estimation to demand + + + align:start position:0% +Un-American in his estimation to demand +that people swear kind of political + + align:start position:0% +that people swear kind of political + + + align:start position:0% +that people swear kind of political +allegiance uh that was a violation of of + + align:start position:0% +allegiance uh that was a violation of of + + + align:start position:0% +allegiance uh that was a violation of of +people's kind of free political + + align:start position:0% +people's kind of free political + + + align:start position:0% +people's kind of free political +consciences so he resigned because the + + align:start position:0% +consciences so he resigned because the + + + align:start position:0% +consciences so he resigned because the +university started um requiring these + + align:start position:0% +university started um requiring these + + + align:start position:0% +university started um requiring these +these sort of anti-communist loyalty + + align:start position:0% +these sort of anti-communist loyalty + + + align:start position:0% +these sort of anti-communist loyalty +Odes and he said forget it he was + + align:start position:0% +Odes and he said forget it he was + + + align:start position:0% +Odes and he said forget it he was +immediately hired at the University of + + align:start position:0% +immediately hired at the University of + + + align:start position:0% +immediately hired at the University of +Urbana-Champaign University of Illinois + + align:start position:0% +Urbana-Champaign University of Illinois + + + align:start position:0% +Urbana-Champaign University of Illinois +Urbana-Champaign and he got more and + + align:start position:0% +Urbana-Champaign and he got more and + + + align:start position:0% +Urbana-Champaign and he got more and +more involved with political efforts on + + align:start position:0% +more involved with political efforts on + + + align:start position:0% +more involved with political efforts on +behalf of similar physics groups he + + align:start position:0% +behalf of similar physics groups he + + + align:start position:0% +behalf of similar physics groups he +testified before the U.S Congress and so + + align:start position:0% +testified before the U.S Congress and so + + + align:start position:0% +testified before the U.S Congress and so +on and what's interesting is we go + + align:start position:0% +on and what's interesting is we go + + + align:start position:0% +on and what's interesting is we go +through his testimony and his op-eds and + + align:start position:0% +through his testimony and his op-eds and + + + align:start position:0% +through his testimony and his op-eds and +his other Publications from this period + + align:start position:0% +his other Publications from this period + + + align:start position:0% +his other Publications from this period +you see that same language recur + + align:start position:0% +you see that same language recur + + + align:start position:0% +you see that same language recur +about a kind of democratic treatment no + + align:start position:0% +about a kind of democratic treatment no + + + align:start position:0% +about a kind of democratic treatment no +one and no nuclear particle deserves + + align:start position:0% +one and no nuclear particle deserves + + + align:start position:0% +one and no nuclear particle deserves +special status they should all be + + align:start position:0% +special status they should all be + + + align:start position:0% +special status they should all be +treated as equal Partners under the law + + align:start position:0% +treated as equal Partners under the law + + + align:start position:0% +treated as equal Partners under the law +and I write more about that in the essay + + align:start position:0% +and I write more about that in the essay + + + align:start position:0% +and I write more about that in the essay +but that's the kind of gist he's using + + align:start position:0% +but that's the kind of gist he's using + + + align:start position:0% +but that's the kind of gist he's using +this language of treat everyone the same + + align:start position:0% +this language of treat everyone the same + + + align:start position:0% +this language of treat everyone the same +in a lot of domains around the same time + + align:start position:0% +in a lot of domains around the same time + + + align:start position:0% +in a lot of domains around the same time +so why does he think these filament + + align:start position:0% +so why does he think these filament + + + align:start position:0% +so why does he think these filament +diagrams might be the way forward what + + align:start position:0% +diagrams might be the way forward what + + + align:start position:0% +diagrams might be the way forward what +do you want to do with them in this new + + align:start position:0% +do you want to do with them in this new + + + align:start position:0% +do you want to do with them in this new +kind of so-called democracy well he says + + align:start position:0% +kind of so-called democracy well he says + + + align:start position:0% +kind of so-called democracy well he says +that the diagrams seem to hold more + + align:start position:0% +that the diagrams seem to hold more + + + align:start position:0% +that the diagrams seem to hold more +content than Quantum field Theory so + + align:start position:0% +content than Quantum field Theory so + + + align:start position:0% +content than Quantum field Theory so +let's let's see where the diagrams of + + align:start position:0% +let's let's see where the diagrams of + + + align:start position:0% +let's let's see where the diagrams of +the cells will lead us in this + + align:start position:0% +the cells will lead us in this + + + align:start position:0% +the cells will lead us in this +orientation of a simple looking finding + + align:start position:0% +orientation of a simple looking finding + + + align:start position:0% +orientation of a simple looking finding +diagram this row Maison which had + + align:start position:0% +diagram this row Maison which had + + + align:start position:0% +diagram this row Maison which had +actually just been identified by some of + + align:start position:0% +actually just been identified by some of + + + align:start position:0% +actually just been identified by some of +his experimentalist colleagues uh not + + align:start position:0% +his experimentalist colleagues uh not + + + align:start position:0% +his experimentalist colleagues uh not +long before + + align:start position:0% +long before + + + align:start position:0% +long before +this shows two pions exchanging aromason + + align:start position:0% +this shows two pions exchanging aromason + + + align:start position:0% +this shows two pions exchanging aromason +so the row is a kind of force carrier + + align:start position:0% +so the row is a kind of force carrier + + + align:start position:0% +so the row is a kind of force carrier +much like say a virtual Photon would be + + align:start position:0% +much like say a virtual Photon would be + + + align:start position:0% +much like say a virtual Photon would be +a force carrier in a QED diagram + + align:start position:0% +a force carrier in a QED diagram + + + align:start position:0% +a force carrier in a QED diagram +but if you just rotate that Diagon + + align:start position:0% +but if you just rotate that Diagon + + + align:start position:0% +but if you just rotate that Diagon +literally turn it on its side then it + + align:start position:0% +literally turn it on its side then it + + + align:start position:0% +literally turn it on its side then it +you tell a very different story you see + + align:start position:0% +you tell a very different story you see + + + align:start position:0% +you tell a very different story you see +two pie mesons brought together they + + align:start position:0% +two pie mesons brought together they + + + align:start position:0% +two pie mesons brought together they +were attracted because they felt a force + + align:start position:0% +were attracted because they felt a force + + + align:start position:0% +were attracted because they felt a force +once they approach each other they + + align:start position:0% +once they approach each other they + + + align:start position:0% +once they approach each other they +actually can create a temporary bound + + align:start position:0% +actually can create a temporary bound + + + align:start position:0% +actually can create a temporary bound +state of the romazon it's a it's an + + align:start position:0% +state of the romazon it's a it's an + + + align:start position:0% +state of the romazon it's a it's an +unstable article so the Rome is on later + + align:start position:0% +unstable article so the Rome is on later + + + align:start position:0% +unstable article so the Rome is on later +with a Decay into a pair of pions and + + align:start position:0% +with a Decay into a pair of pions and + + + align:start position:0% +with a Decay into a pair of pions and +that just comes from rotating the same + + align:start position:0% +that just comes from rotating the same + + + align:start position:0% +that just comes from rotating the same +diagram + + align:start position:0% +diagram + + + align:start position:0% +diagram +meanwhile once you create some romeisons + + align:start position:0% +meanwhile once you create some romeisons + + + align:start position:0% +meanwhile once you create some romeisons +this way they can be involved in all + + align:start position:0% +this way they can be involved in all + + + align:start position:0% +this way they can be involved in all +kinds of other interactions where they + + align:start position:0% +kinds of other interactions where they + + + align:start position:0% +kinds of other interactions where they +would appear as a so-called elementary + + align:start position:0% +would appear as a so-called elementary + + + align:start position:0% +would appear as a so-called elementary +particle so the status of the particle + + align:start position:0% +particle so the status of the particle + + + align:start position:0% +particle so the status of the particle +type seems to change just by rotating + + align:start position:0% +type seems to change just by rotating + + + align:start position:0% +type seems to change just by rotating +these very simple looking line drives + + align:start position:0% +these very simple looking line drives + + + align:start position:0% +these very simple looking line drives +and so Jeffrey Chu said basically let's + + align:start position:0% +and so Jeffrey Chu said basically let's + + + align:start position:0% +and so Jeffrey Chu said basically let's +take the diagrams at face value if they + + align:start position:0% +take the diagrams at face value if they + + + align:start position:0% +take the diagrams at face value if they +make no distinction between these + + align:start position:0% +make no distinction between these + + + align:start position:0% +make no distinction between these +different kinds of roles or hierarchies + + align:start position:0% +different kinds of roles or hierarchies + + + align:start position:0% +different kinds of roles or hierarchies +what's truly Elementary versus composite + + align:start position:0% +what's truly Elementary versus composite + + + align:start position:0% +what's truly Elementary versus composite +then why should our equations so we + + align:start position:0% +then why should our equations so we + + + align:start position:0% +then why should our equations so we +wanted to build a new approach to a + + align:start position:0% +wanted to build a new approach to a + + + align:start position:0% +wanted to build a new approach to a +quantitative approach + + align:start position:0% +quantitative approach + + + align:start position:0% +quantitative approach +to the nuclear forces following these + + align:start position:0% +to the nuclear forces following these + + + align:start position:0% +to the nuclear forces following these +kind of diagram based symmetries rather + + align:start position:0% +kind of diagram based symmetries rather + + + align:start position:0% +kind of diagram based symmetries rather +than Quantum filtering and they went + + align:start position:0% +than Quantum filtering and they went + + + align:start position:0% +than Quantum filtering and they went +even further said what if every single + + align:start position:0% +even further said what if every single + + + align:start position:0% +even further said what if every single +particle was a kind of self-consistent + + align:start position:0% +particle was a kind of self-consistent + + + align:start position:0% +particle was a kind of self-consistent +state they would each pull itself up by + + align:start position:0% +state they would each pull itself up by + + + align:start position:0% +state they would each pull itself up by +its own bootstraps using a well-known + + align:start position:0% +its own bootstraps using a well-known + + + align:start position:0% +its own bootstraps using a well-known +kind of American + + align:start position:0% +kind of American + + + align:start position:0% +kind of American +idiomatic expression they were all they + + align:start position:0% +idiomatic expression they were all they + + + align:start position:0% +idiomatic expression they were all they +would all be kind of self-made people uh + + align:start position:0% +would all be kind of self-made people uh + + + align:start position:0% +would all be kind of self-made people uh +no one was was born being more + + align:start position:0% +no one was was born being more + + + align:start position:0% +no one was was born being more +Elementary or more elitist than others + + align:start position:0% +Elementary or more elitist than others + + + align:start position:0% +Elementary or more elitist than others +was the idea + + align:start position:0% +was the idea + + + align:start position:0% +was the idea +what if every particle like that Rome is + + align:start position:0% +what if every particle like that Rome is + + + align:start position:0% +what if every particle like that Rome is +on would generate the forces that would + + align:start position:0% +on would generate the forces that would + + + align:start position:0% +on would generate the forces that would +give rise to its own production pretty + + align:start position:0% +give rise to its own production pretty + + + align:start position:0% +give rise to its own production pretty +that's pretty cool could there be one + + align:start position:0% +that's pretty cool could there be one + + + align:start position:0% +that's pretty cool could there be one +unique self-consistent solution to all + + align:start position:0% +unique self-consistent solution to all + + + align:start position:0% +unique self-consistent solution to all +these equations going back to this kind + + align:start position:0% +these equations going back to this kind + + + align:start position:0% +these equations going back to this kind +of rotated diagrams in this example you + + align:start position:0% +of rotated diagrams in this example you + + + align:start position:0% +of rotated diagrams in this example you +have some expression some quantitative + + align:start position:0% +have some expression some quantitative + + + align:start position:0% +have some expression some quantitative +expression for the force that this row + + align:start position:0% +expression for the force that this row + + + align:start position:0% +expression for the force that this row +Maison exerts an attractive force + + align:start position:0% +Maison exerts an attractive force + + + align:start position:0% +Maison exerts an attractive force +between these pie mesons that expression + + align:start position:0% +between these pie mesons that expression + + + align:start position:0% +between these pie mesons that expression +will depend on the mass of the particle + + align:start position:0% +will depend on the mass of the particle + + + align:start position:0% +will depend on the mass of the particle +that the exchange and this coupling + + align:start position:0% +that the exchange and this coupling + + + align:start position:0% +that the exchange and this coupling +constant the factor that appears at + + align:start position:0% +constant the factor that appears at + + + align:start position:0% +constant the factor that appears at +every vertex rotate your piece of paper + + align:start position:0% +every vertex rotate your piece of paper + + + align:start position:0% +every vertex rotate your piece of paper +by um 90 degrees now you see that once + + align:start position:0% +by um 90 degrees now you see that once + + + align:start position:0% +by um 90 degrees now you see that once +these two pions have attracted each + + align:start position:0% +these two pions have attracted each + + + align:start position:0% +these two pions have attracted each +other thanks to that Rhodes Mason they + + align:start position:0% +other thanks to that Rhodes Mason they + + + align:start position:0% +other thanks to that Rhodes Mason they +form this bound State the odds for that + + align:start position:0% +form this bound State the odds for that + + + align:start position:0% +form this bound State the odds for that +to happen also has some distinct + + align:start position:0% +to happen also has some distinct + + + align:start position:0% +to happen also has some distinct +expression still only depends on two + + align:start position:0% +expression still only depends on two + + + align:start position:0% +expression still only depends on two +quantities the mass of the pound State + + align:start position:0% +quantities the mass of the pound State + + + align:start position:0% +quantities the mass of the pound State +they produce and this coupling constant + + align:start position:0% +they produce and this coupling constant + + + align:start position:0% +they produce and this coupling constant +so now you have two equations for two + + align:start position:0% +so now you have two equations for two + + + align:start position:0% +so now you have two equations for two +unknowns + + align:start position:0% +unknowns + + + align:start position:0% +unknowns +so you can look for self-consistent + + align:start position:0% +so you can look for self-consistent + + + align:start position:0% +so you can look for self-consistent +Solutions and in fact heinous students + + align:start position:0% +Solutions and in fact heinous students + + + align:start position:0% +Solutions and in fact heinous students +were able to publish + + align:start position:0% +were able to publish + + + align:start position:0% +were able to publish +the first compelling theoretical account + + align:start position:0% +the first compelling theoretical account + + + align:start position:0% +the first compelling theoretical account +of why these nuclear particles have the + + align:start position:0% +of why these nuclear particles have the + + + align:start position:0% +of why these nuclear particles have the +quantitative properties they did at a + + align:start position:0% +quantitative properties they did at a + + + align:start position:0% +quantitative properties they did at a +time when no one else could come even + + align:start position:0% +time when no one else could come even + + + align:start position:0% +time when no one else could come even +close this is far outside the regime of + + align:start position:0% +close this is far outside the regime of + + + align:start position:0% +close this is far outside the regime of +perturbation Theory and here is this + + align:start position:0% +perturbation Theory and here is this + + + align:start position:0% +perturbation Theory and here is this +kind of very clever self-consistent way + + align:start position:0% +kind of very clever self-consistent way + + + align:start position:0% +kind of very clever self-consistent way +of using their so-called bootstrap to + + align:start position:0% +of using their so-called bootstrap to + + + align:start position:0% +of using their so-called bootstrap to +try to account for why the romazon was + + align:start position:0% +try to account for why the romazon was + + + align:start position:0% +try to account for why the romazon was +particularly heavy uh and why it had + + align:start position:0% +particularly heavy uh and why it had + + + align:start position:0% +particularly heavy uh and why it had +this particular interaction strength + + align:start position:0% +this particular interaction strength + + + align:start position:0% +this particular interaction strength +with uh with ions + + align:start position:0% +with uh with ions + + + align:start position:0% +with uh with ions +so let me pause there any questions on + + align:start position:0% +so let me pause there any questions on + + + align:start position:0% +so let me pause there any questions on +that + + align:start position:0% + + + + align:start position:0% + +it's just too awesome you're so you're + + align:start position:0% +it's just too awesome you're so you're + + + align:start position:0% +it's just too awesome you're so you're +stunned into you're just shocked into + + align:start position:0% +stunned into you're just shocked into + + + align:start position:0% +stunned into you're just shocked into +silence I I mean I get that way too it's + + align:start position:0% +silence I I mean I get that way too it's + + + align:start position:0% +silence I I mean I get that way too it's +okay + + align:start position:0% +okay + + + align:start position:0% +okay +what I mostly want to emphasize with + + align:start position:0% +what I mostly want to emphasize with + + + align:start position:0% +what I mostly want to emphasize with +that part hopefully was clear + + align:start position:0% +that part hopefully was clear + + + align:start position:0% +that part hopefully was clear +was that even after Dyson did such a + + align:start position:0% +was that even after Dyson did such a + + + align:start position:0% +was that even after Dyson did such a +kind of uh um celebrated job of + + align:start position:0% +kind of uh um celebrated job of + + + align:start position:0% +kind of uh um celebrated job of +clarifying exactly what Simon diagrams + + align:start position:0% +clarifying exactly what Simon diagrams + + + align:start position:0% +clarifying exactly what Simon diagrams +should mean exactly how they should be + + align:start position:0% +should mean exactly how they should be + + + align:start position:0% +should mean exactly how they should be +used in a calculation in the years after + + align:start position:0% +used in a calculation in the years after + + + align:start position:0% +used in a calculation in the years after +that that led to more different uses + + align:start position:0% +that that led to more different uses + + + align:start position:0% +that that led to more different uses +rather than collapsing to only one I + + align:start position:0% +rather than collapsing to only one I + + + align:start position:0% +rather than collapsing to only one I +found that really pretty cool actually + + align:start position:0% +found that really pretty cool actually + + + align:start position:0% +found that really pretty cool actually +pretty neat uh and then some people got + + align:start position:0% +pretty neat uh and then some people got + + + align:start position:0% +pretty neat uh and then some people got +even more ambitious with them like the + + align:start position:0% +even more ambitious with them like the + + + align:start position:0% +even more ambitious with them like the +more extreme example from the birthday + + align:start position:0% +more extreme example from the birthday + + + align:start position:0% +more extreme example from the birthday +group but even at Rochester or Urbana or + + align:start position:0% +group but even at Rochester or Urbana or + + + align:start position:0% +group but even at Rochester or Urbana or +in Cambridge England people were being + + align:start position:0% +in Cambridge England people were being + + + align:start position:0% +in Cambridge England people were being +very kind of um they treated the + + align:start position:0% +very kind of um they treated the + + + align:start position:0% +very kind of um they treated the +diagrams as pretty malleable for for a + + align:start position:0% +diagrams as pretty malleable for for a + + + align:start position:0% +diagrams as pretty malleable for for a +long time I thought and that was you + + align:start position:0% +long time I thought and that was you + + + align:start position:0% +long time I thought and that was you +know that was neat it's hard to get + + align:start position:0% +know that was neat it's hard to get + + + align:start position:0% +know that was neat it's hard to get +computers to do that computers do one + + align:start position:0% +computers to do that computers do one + + + align:start position:0% +computers to do that computers do one +thing with these diagrams now but for + + align:start position:0% +thing with these diagrams now but for + + + align:start position:0% +thing with these diagrams now but for +much of their history the diagrams meant + + align:start position:0% +much of their history the diagrams meant + + + align:start position:0% +much of their history the diagrams meant +a variety of things or could be used in + + align:start position:0% +a variety of things or could be used in + + + align:start position:0% +a variety of things or could be used in +a variety of ways + + align:start position:0% +a variety of ways + + + align:start position:0% +a variety of ways +um + + align:start position:0% + + + + align:start position:0% + +yeah go ahead Fishers so so Fisher asks + + align:start position:0% +yeah go ahead Fishers so so Fisher asks + + + align:start position:0% +yeah go ahead Fishers so so Fisher asks +when when we're talking about + + align:start position:0% +when when we're talking about + + + align:start position:0% +when when we're talking about +perturbation Theory uh they're referring + + align:start position:0% +perturbation Theory uh they're referring + + + align:start position:0% +perturbation Theory uh they're referring +to everything beyond the second order + + align:start position:0% +to everything beyond the second order + + + align:start position:0% +to everything beyond the second order +Beyond e squared or everything including + + align:start position:0% +Beyond e squared or everything including + + + align:start position:0% +Beyond e squared or everything including +e squared + + align:start position:0% +e squared + + + align:start position:0% +e squared +I guess technically we would even + + align:start position:0% +I guess technically we would even + + + align:start position:0% +I guess technically we would even +include the E squared the the first term + + align:start position:0% +include the E squared the the first term + + + align:start position:0% +include the E squared the the first term +would be one which that nothing happens + + align:start position:0% +would be one which that nothing happens + + + align:start position:0% +would be one which that nothing happens +well I should say nothing changes so + + align:start position:0% +well I should say nothing changes so + + + align:start position:0% +well I should say nothing changes so +your first term in What's called the S + + align:start position:0% +your first term in What's called the S + + + align:start position:0% +your first term in What's called the S +Matrix expansion is one plus everything + + align:start position:0% +Matrix expansion is one plus everything + + + align:start position:0% +Matrix expansion is one plus everything +else + + align:start position:0% +else + + + align:start position:0% +else +and so the next term the the the first + + align:start position:0% +and so the next term the the the first + + + align:start position:0% +and so the next term the the the first +term to enter would that be e squared + + align:start position:0% +term to enter would that be e squared + + + align:start position:0% +term to enter would that be e squared +that'd be the first correction to + + align:start position:0% +that'd be the first correction to + + + align:start position:0% +that'd be the first correction to +nothing happening is you could add two + + align:start position:0% +nothing happening is you could add two + + + align:start position:0% +nothing happening is you could add two +electrons scatter then it could have + + align:start position:0% +electrons scatter then it could have + + + align:start position:0% +electrons scatter then it could have +scattered in more complicated ways uh so + + align:start position:0% +scattered in more complicated ways uh so + + + align:start position:0% +scattered in more complicated ways uh so +it is really like to like Taylor you can + + align:start position:0% +it is really like to like Taylor you can + + + align:start position:0% +it is really like to like Taylor you can +think of it like Taylor expanding + + align:start position:0% +think of it like Taylor expanding + + + align:start position:0% +think of it like Taylor expanding +and it's you know it is remarkable uh + + align:start position:0% +and it's you know it is remarkable uh + + + align:start position:0% +and it's you know it is remarkable uh +because it works because the the you + + align:start position:0% +because it works because the the you + + + align:start position:0% +because it works because the the you +have a controlled parameter you can + + align:start position:0% +have a controlled parameter you can + + + align:start position:0% +have a controlled parameter you can +really do a controlled uh perturbation + + align:start position:0% +really do a controlled uh perturbation + + + align:start position:0% +really do a controlled uh perturbation +expansion so even without calculating an + + align:start position:0% +expansion so even without calculating an + + + align:start position:0% +expansion so even without calculating an +arbitrarily complicated diagram you can + + align:start position:0% +arbitrarily complicated diagram you can + + + align:start position:0% +arbitrarily complicated diagram you can +estimate how much would that matter + + align:start position:0% +estimate how much would that matter + + + align:start position:0% +estimate how much would that matter +quantitatively what would be your error + + align:start position:0% +quantitatively what would be your error + + + align:start position:0% +quantitatively what would be your error +budget if you left it out so to speak + + align:start position:0% +budget if you left it out so to speak + + + align:start position:0% +budget if you left it out so to speak +and you can't do any of that using these + + align:start position:0% +and you can't do any of that using these + + + align:start position:0% +and you can't do any of that using these +techniques for the nuclear force + + align:start position:0% +techniques for the nuclear force + + + align:start position:0% +techniques for the nuclear force +all right let me press on I'll talk + + align:start position:0% +all right let me press on I'll talk + + + align:start position:0% +all right let me press on I'll talk +about this last part it'll be pretty + + align:start position:0% +about this last part it'll be pretty + + + align:start position:0% +about this last part it'll be pretty +quick I'll try not to go for eight hours + + align:start position:0% +quick I'll try not to go for eight hours + + + align:start position:0% +quick I'll try not to go for eight hours +uh no promises but this last part is so + + align:start position:0% +uh no promises but this last part is so + + + align:start position:0% +uh no promises but this last part is so +why do they stick if they're if they're + + align:start position:0% +why do they stick if they're if they're + + + align:start position:0% +why do they stick if they're if they're +being used in so many different ways uh + + align:start position:0% +being used in so many different ways uh + + + align:start position:0% +being used in so many different ways uh +why do people stick with them instead of + + align:start position:0% +why do people stick with them instead of + + + align:start position:0% +why do people stick with them instead of +you know design other uh techniques + + align:start position:0% +you know design other uh techniques + + + align:start position:0% +you know design other uh techniques +along the way so within perturbation + + align:start position:0% +along the way so within perturbation + + + align:start position:0% +along the way so within perturbation +Theory when doing these electrodynamic + + align:start position:0% +Theory when doing these electrodynamic + + + align:start position:0% +Theory when doing these electrodynamic +calculations I think it's pretty clear + + align:start position:0% +calculations I think it's pretty clear + + + align:start position:0% +calculations I think it's pretty clear +and people spoke of it even at the time + + align:start position:0% +and people spoke of it even at the time + + + align:start position:0% +and people spoke of it even at the time +that these were just an extraordinary + + align:start position:0% +that these were just an extraordinary + + + align:start position:0% +that these were just an extraordinary +um extraordinarily useful tool + + align:start position:0% +um extraordinarily useful tool + + + align:start position:0% +um extraordinarily useful tool +um Dyson remarked years later the + + align:start position:0% +um Dyson remarked years later the + + + align:start position:0% +um Dyson remarked years later the +calculation he first did for Hans beta + + align:start position:0% +calculation he first did for Hans beta + + + align:start position:0% +calculation he first did for Hans beta +as a grad student before learning about + + align:start position:0% +as a grad student before learning about + + + align:start position:0% +as a grad student before learning about +the diagrams took him several months of + + align:start position:0% +the diagrams took him several months of + + + align:start position:0% +the diagrams took him several months of +work and several hundred sheets of paper + + align:start position:0% +work and several hundred sheets of paper + + + align:start position:0% +work and several hundred sheets of paper +there dick Feynman Richard Feynman could + + align:start position:0% +there dick Feynman Richard Feynman could + + + align:start position:0% +there dick Feynman Richard Feynman could +get the same answer calculated on the + + align:start position:0% +get the same answer calculated on the + + + align:start position:0% +get the same answer calculated on the +Blackboard in half an hour and that was + + align:start position:0% +Blackboard in half an hour and that was + + + align:start position:0% +Blackboard in half an hour and that was +indeed what became more and more common + + align:start position:0% +indeed what became more and more common + + + align:start position:0% +indeed what became more and more common +Julian schwinger said a bit more + + align:start position:0% +Julian schwinger said a bit more + + + align:start position:0% +Julian schwinger said a bit more +um snarkily a swinger and finally were + + align:start position:0% +um snarkily a swinger and finally were + + + align:start position:0% +um snarkily a swinger and finally were +kind of like frenemies uh he said find a + + align:start position:0% +kind of like frenemies uh he said find a + + + align:start position:0% +kind of like frenemies uh he said find a +dog has brought computation to the + + align:start position:0% +dog has brought computation to the + + + align:start position:0% +dog has brought computation to the +masses which was you can almost see + + align:start position:0% +masses which was you can almost see + + + align:start position:0% +masses which was you can almost see +schwinger sniffing like my students + + align:start position:0% +schwinger sniffing like my students + + + align:start position:0% +schwinger sniffing like my students +learn really how to calculate but any + + align:start position:0% +learn really how to calculate but any + + + align:start position:0% +learn really how to calculate but any +old slob could calculate using Finance + + align:start position:0% +old slob could calculate using Finance + + + align:start position:0% +old slob could calculate using Finance +techniques that's what I that's the + + align:start position:0% +techniques that's what I that's the + + + align:start position:0% +techniques that's what I that's the +spirit in which I take that remark that + + align:start position:0% +spirit in which I take that remark that + + + align:start position:0% +spirit in which I take that remark that +these really were effective and many + + align:start position:0% +these really were effective and many + + + align:start position:0% +these really were effective and many +many people could calculate even people + + align:start position:0% +many people could calculate even people + + + align:start position:0% +many people could calculate even people +who weren't blessed to have had Julian + + align:start position:0% +who weren't blessed to have had Julian + + + align:start position:0% +who weren't blessed to have had Julian +schwinger as their PHD advisor + + align:start position:0% +schwinger as their PHD advisor + + + align:start position:0% +schwinger as their PHD advisor +this cartoon here ran in physics today + + align:start position:0% +this cartoon here ran in physics today + + + align:start position:0% +this cartoon here ran in physics today +uh many years ago basically saying if + + align:start position:0% +uh many years ago basically saying if + + + align:start position:0% +uh many years ago basically saying if +you're going to go through these + + align:start position:0% +you're going to go through these + + + align:start position:0% +you're going to go through these +dangerous thickets of perturbation + + align:start position:0% +dangerous thickets of perturbation + + + align:start position:0% +dangerous thickets of perturbation +Theory as if you were kind of Explorer + + align:start position:0% +Theory as if you were kind of Explorer + + + align:start position:0% +Theory as if you were kind of Explorer +in the Amazonian jungle it helps to have + + align:start position:0% +in the Amazonian jungle it helps to have + + + align:start position:0% +in the Amazonian jungle it helps to have +a reliable map and so the fireman + + align:start position:0% +a reliable map and so the fireman + + + align:start position:0% +a reliable map and so the fireman +diagrams would be a reliable map to this + + align:start position:0% +diagrams would be a reliable map to this + + + align:start position:0% +diagrams would be a reliable map to this +complicated seemingly dangerous or + + align:start position:0% +complicated seemingly dangerous or + + + align:start position:0% +complicated seemingly dangerous or +forbidding terrain so I think that makes + + align:start position:0% +forbidding terrain so I think that makes + + + align:start position:0% +forbidding terrain so I think that makes +sense except as I was just emphasizing + + align:start position:0% +sense except as I was just emphasizing + + + align:start position:0% +sense except as I was just emphasizing +that can hardly be the whole story + + align:start position:0% +that can hardly be the whole story + + + align:start position:0% +that can hardly be the whole story +because most physicists weren't using + + align:start position:0% +because most physicists weren't using + + + align:start position:0% +because most physicists weren't using +them in the early days for what they + + align:start position:0% +them in the early days for what they + + + align:start position:0% +them in the early days for what they +were sort of most good at for what the + + align:start position:0% +were sort of most good at for what the + + + align:start position:0% +were sort of most good at for what the +diagrams are most efficacious for so + + align:start position:0% +diagrams are most efficacious for so + + + align:start position:0% +diagrams are most efficacious for so +sure that would explain why people use + + align:start position:0% +sure that would explain why people use + + + align:start position:0% +sure that would explain why people use +them in weekly coupled situations but + + align:start position:0% +them in weekly coupled situations but + + + align:start position:0% +them in weekly coupled situations but +what about all these other applications + + align:start position:0% +what about all these other applications + + + align:start position:0% +what about all these other applications +so to make sense of that I found it very + + align:start position:0% +so to make sense of that I found it very + + + align:start position:0% +so to make sense of that I found it very +helpful actually very fun + + align:start position:0% +helpful actually very fun + + + align:start position:0% +helpful actually very fun +to go back and took some classic studies + + align:start position:0% +to go back and took some classic studies + + + align:start position:0% +to go back and took some classic studies +in art history these are after all a + + align:start position:0% +in art history these are after all a + + + align:start position:0% +in art history these are after all a +kind of visual representation scheme and + + align:start position:0% +kind of visual representation scheme and + + + align:start position:0% +kind of visual representation scheme and +art historians have been arguing for a + + align:start position:0% +art historians have been arguing for a + + + align:start position:0% +art historians have been arguing for a +long long long time about why various um + + align:start position:0% +long long long time about why various um + + + align:start position:0% +long long long time about why various um +styles and art modes of depiction have + + align:start position:0% +styles and art modes of depiction have + + + align:start position:0% +styles and art modes of depiction have +come to seem natural or have a kind of + + align:start position:0% +come to seem natural or have a kind of + + + align:start position:0% +come to seem natural or have a kind of +staying power and why what happens when + + align:start position:0% +staying power and why what happens when + + + align:start position:0% +staying power and why what happens when +they change so the art historian Eris + + align:start position:0% +they change so the art historian Eris + + + align:start position:0% +they change so the art historian Eris +gomrich wrote this really lovely very + + align:start position:0% +gomrich wrote this really lovely very + + + align:start position:0% +gomrich wrote this really lovely very +influential book many years ago + + align:start position:0% +influential book many years ago + + + align:start position:0% +influential book many years ago +where he says that basically his his + + align:start position:0% +where he says that basically his his + + + align:start position:0% +where he says that basically his his +catchphrase was that + + align:start position:0% +catchphrase was that + + + align:start position:0% +catchphrase was that +um painters + + align:start position:0% +um painters + + + align:start position:0% +um painters +um How does it go they + + align:start position:0% +um How does it go they + + + align:start position:0% +um How does it go they +see what they paint they don't paint + + align:start position:0% +see what they paint they don't paint + + + align:start position:0% +see what they paint they don't paint +what they see they have an idea of what + + align:start position:0% +what they see they have an idea of what + + + align:start position:0% +what they see they have an idea of what +they want to convey and that structure's + + align:start position:0% +they want to convey and that structure's + + + align:start position:0% +they want to convey and that structure's +not even take in the world is it he kind + + align:start position:0% +not even take in the world is it he kind + + + align:start position:0% +not even take in the world is it he kind +of flips the story you don't just look + + align:start position:0% +of flips the story you don't just look + + + align:start position:0% +of flips the story you don't just look +out your window and say oh I'll paint a + + align:start position:0% +out your window and say oh I'll paint a + + + align:start position:0% +out your window and say oh I'll paint a +landscape you can learn techniques and + + align:start position:0% +landscape you can learn techniques and + + + align:start position:0% +landscape you can learn techniques and +then you come to see the world through + + align:start position:0% +then you come to see the world through + + + align:start position:0% +then you come to see the world through +the lens of those techniques not unlike + + align:start position:0% +the lens of those techniques not unlike + + + align:start position:0% +the lens of those techniques not unlike +what say the historian of science Thomas + + align:start position:0% +what say the historian of science Thomas + + + align:start position:0% +what say the historian of science Thomas +Conan argued around the same time so + + align:start position:0% +Conan argued around the same time so + + + align:start position:0% +Conan argued around the same time so +these are examples of the kinds of + + align:start position:0% +these are examples of the kinds of + + + align:start position:0% +these are examples of the kinds of +things that godbridge talks about these + + align:start position:0% +things that godbridge talks about these + + + align:start position:0% +things that godbridge talks about these +were from training manuals in the early + + align:start position:0% +were from training manuals in the early + + + align:start position:0% +were from training manuals in the early +modern period to learn how to draw say a + + align:start position:0% +modern period to learn how to draw say a + + + align:start position:0% +modern period to learn how to draw say a +human face you break it down and you + + align:start position:0% +human face you break it down and you + + + align:start position:0% +human face you break it down and you +literally practice drawing an eyeball + + align:start position:0% +literally practice drawing an eyeball + + + align:start position:0% +literally practice drawing an eyeball +over and over and over again until you + + align:start position:0% +over and over and over again until you + + + align:start position:0% +over and over and over again until you +see you know actual people through this + + align:start position:0% +see you know actual people through this + + + align:start position:0% +see you know actual people through this +kind of schema of how you draw an + + align:start position:0% +kind of schema of how you draw an + + + align:start position:0% +kind of schema of how you draw an +eyeball or if you're employed by the + + align:start position:0% +eyeball or if you're employed by the + + + align:start position:0% +eyeball or if you're employed by the +local church which most of them were + + align:start position:0% +local church which most of them were + + + align:start position:0% +local church which most of them were +here's how you draw like the adorable + + align:start position:0% +here's how you draw like the adorable + + + align:start position:0% +here's how you draw like the adorable +little you know cherubs and little baby + + align:start position:0% +little you know cherubs and little baby + + + align:start position:0% +little you know cherubs and little baby +Angels you practice drawing these chubby + + align:start position:0% +Angels you practice drawing these chubby + + + align:start position:0% +Angels you practice drawing these chubby +cheek faces and you break it down and + + align:start position:0% +cheek faces and you break it down and + + + align:start position:0% +cheek faces and you break it down and +you practice and practice like doing + + align:start position:0% +you practice and practice like doing + + + align:start position:0% +you practice and practice like doing +problem sets before you go paint you + + align:start position:0% +problem sets before you go paint you + + + align:start position:0% +problem sets before you go paint you +know the the kind of latest picture for + + align:start position:0% +know the the kind of latest picture for + + + align:start position:0% +know the the kind of latest picture for +the to decorate the local church + + align:start position:0% +the to decorate the local church + + + align:start position:0% +the to decorate the local church +and so it seems a similar thing was + + align:start position:0% +and so it seems a similar thing was + + + align:start position:0% +and so it seems a similar thing was +happening with these scientific images + + align:start position:0% +happening with these scientific images + + + align:start position:0% +happening with these scientific images +that the physicists kind of Prior habits + + align:start position:0% +that the physicists kind of Prior habits + + + align:start position:0% +that the physicists kind of Prior habits +help them seem in a new way just as you + + align:start position:0% +help them seem in a new way just as you + + + align:start position:0% +help them seem in a new way just as you +know if you stare if you practice this + + align:start position:0% +know if you stare if you practice this + + + align:start position:0% +know if you stare if you practice this +technique over and over again you you + + align:start position:0% +technique over and over again you you + + + align:start position:0% +technique over and over again you you +structure your in your newer experiences + + align:start position:0% +structure your in your newer experiences + + + align:start position:0% +structure your in your newer experiences +with it with a kind of scheme that + + align:start position:0% +with it with a kind of scheme that + + + align:start position:0% +with it with a kind of scheme that +you've already worked hard to master + + align:start position:0% +you've already worked hard to master + + + align:start position:0% +you've already worked hard to master +and so these pictorial conventions can + + align:start position:0% +and so these pictorial conventions can + + + align:start position:0% +and so these pictorial conventions can +actually help us map a kind of + + align:start position:0% +actually help us map a kind of + + + align:start position:0% +actually help us map a kind of +pedagogical lineage not necessarily A + + align:start position:0% +pedagogical lineage not necessarily A + + + align:start position:0% +pedagogical lineage not necessarily A +conceptual one they were they were often + + align:start position:0% +conceptual one they were they were often + + + align:start position:0% +conceptual one they were they were often +kind of irrelevant to the New Uses but + + align:start position:0% +kind of irrelevant to the New Uses but + + + align:start position:0% +kind of irrelevant to the New Uses but +they were more kind of social or + + align:start position:0% +they were more kind of social or + + + align:start position:0% +they were more kind of social or +pedagogical value they helped you get up + + align:start position:0% +pedagogical value they helped you get up + + + align:start position:0% +pedagogical value they helped you get up +to speed or help you make sense of the + + align:start position:0% +to speed or help you make sense of the + + + align:start position:0% +to speed or help you make sense of the +newer things you then wanted to do + + align:start position:0% +newer things you then wanted to do + + + align:start position:0% +newer things you then wanted to do +and the most significant at least as it + + align:start position:0% +and the most significant at least as it + + + align:start position:0% +and the most significant at least as it +makes sense to me was that people were + + align:start position:0% +makes sense to me was that people were + + + align:start position:0% +makes sense to me was that people were +were slotting these things into a very + + align:start position:0% +were slotting these things into a very + + + align:start position:0% +were slotting these things into a very +well established tradition by that point + + align:start position:0% +well established tradition by that point + + + align:start position:0% +well established tradition by that point +these minkowski daggers which of course + + align:start position:0% +these minkowski daggers which of course + + + align:start position:0% +these minkowski daggers which of course +many of you had already seen probably + + align:start position:0% +many of you had already seen probably + + + align:start position:0% +many of you had already seen probably +before this term we spent some time + + align:start position:0% +before this term we spent some time + + + align:start position:0% +before this term we spent some time +looking at them together early in this + + align:start position:0% +looking at them together early in this + + + align:start position:0% +looking at them together early in this +semester + + align:start position:0% +semester + + + align:start position:0% +semester +we talked about special relativity + + align:start position:0% +we talked about special relativity + + + align:start position:0% +we talked about special relativity +literally space-time diagrams Feynman + + align:start position:0% +literally space-time diagrams Feynman + + + align:start position:0% +literally space-time diagrams Feynman +was not shy about adopting the exact + + align:start position:0% +was not shy about adopting the exact + + + align:start position:0% +was not shy about adopting the exact +same conventions + + align:start position:0% +same conventions + + + align:start position:0% +same conventions +he began drawing his little Doodles his + + align:start position:0% +he began drawing his little Doodles his + + + align:start position:0% +he began drawing his little Doodles his +at first kind of private sketches not + + align:start position:0% +at first kind of private sketches not + + + align:start position:0% +at first kind of private sketches not +just that you have one dimension of + + align:start position:0% +just that you have one dimension of + + + align:start position:0% +just that you have one dimension of +space and one of time he oriented space + + align:start position:0% +space and one of time he oriented space + + + align:start position:0% +space and one of time he oriented space +along horizontals no law that says you + + align:start position:0% +along horizontals no law that says you + + + align:start position:0% +along horizontals no law that says you +have to do that he tacitly starts + + align:start position:0% +have to do that he tacitly starts + + + align:start position:0% +have to do that he tacitly starts +scaling the speed of light to be one so + + align:start position:0% +scaling the speed of light to be one so + + + align:start position:0% +scaling the speed of light to be one so +light travels along 45 degree diagonals + + align:start position:0% +light travels along 45 degree diagonals + + + align:start position:0% +light travels along 45 degree diagonals +and there's not literally drawing + + align:start position:0% +and there's not literally drawing + + + align:start position:0% +and there's not literally drawing +space-time diagrams these had been + + align:start position:0% +space-time diagrams these had been + + + align:start position:0% +space-time diagrams these had been +completely kind of pedagogical second + + align:start position:0% +completely kind of pedagogical second + + + align:start position:0% +completely kind of pedagogical second +nature for generations of physicists in + + align:start position:0% +nature for generations of physicists in + + + align:start position:0% +nature for generations of physicists in +many many parts of the world not just + + align:start position:0% +many many parts of the world not just + + + align:start position:0% +many many parts of the world not just +the United States uh before Feynman and + + align:start position:0% +the United States uh before Feynman and + + + align:start position:0% +the United States uh before Feynman and +Dyson introduced their work this was a + + align:start position:0% +Dyson introduced their work this was a + + + align:start position:0% +Dyson introduced their work this was a +kind of context in which students could + + align:start position:0% +kind of context in which students could + + + align:start position:0% +kind of context in which students could +then encounter Feynman diagrams these + + align:start position:0% +then encounter Feynman diagrams these + + + align:start position:0% +then encounter Feynman diagrams these +are examples + + align:start position:0% +are examples + + + align:start position:0% +are examples +from fireman's own work uh this one and + + align:start position:0% +from fireman's own work uh this one and + + + align:start position:0% +from fireman's own work uh this one and +this one from his early Publications + + align:start position:0% +this one from his early Publications + + + align:start position:0% +this one from his early Publications +this is my favorite this comes from one + + align:start position:0% +this is my favorite this comes from one + + + align:start position:0% +this is my favorite this comes from one +of his uh lecture notes at Cornell when + + align:start position:0% +of his uh lecture notes at Cornell when + + + align:start position:0% +of his uh lecture notes at Cornell when +he was lecturing in 1949 uh at uh in the + + align:start position:0% +he was lecturing in 1949 uh at uh in the + + + align:start position:0% +he was lecturing in 1949 uh at uh in the +department what I love is that he + + align:start position:0% +department what I love is that he + + + align:start position:0% +department what I love is that he +actually gets his own filing diagrams + + align:start position:0% +actually gets his own filing diagrams + + + align:start position:0% +actually gets his own filing diagrams +wrong he's so enamored of this kind of + + align:start position:0% +wrong he's so enamored of this kind of + + + align:start position:0% +wrong he's so enamored of this kind of +Storytelling space-time structure that + + align:start position:0% +Storytelling space-time structure that + + + align:start position:0% +Storytelling space-time structure that +he draws diagrams that literally could + + align:start position:0% +he draws diagrams that literally could + + + align:start position:0% +he draws diagrams that literally could +not be calculated in QED they have the + + align:start position:0% +not be calculated in QED they have the + + + align:start position:0% +not be calculated in QED they have the +wrong number of legs entering each + + align:start position:0% +wrong number of legs entering each + + + align:start position:0% +wrong number of legs entering each +vertex but he was caught up trying to + + align:start position:0% +vertex but he was caught up trying to + + + align:start position:0% +vertex but he was caught up trying to +tell his students about how you could + + align:start position:0% +tell his students about how you could + + + align:start position:0% +tell his students about how you could +have pear production in QED and try to + + align:start position:0% +have pear production in QED and try to + + + align:start position:0% +have pear production in QED and try to +narrate that story through space and + + align:start position:0% +narrate that story through space and + + + align:start position:0% +narrate that story through space and +time and we can forgive him forgetting + + align:start position:0% +time and we can forgive him forgetting + + + align:start position:0% +time and we can forgive him forgetting +that in the theory for which he'd + + align:start position:0% +that in the theory for which he'd + + + align:start position:0% +that in the theory for which he'd +eventually win the Nobel Prize only two + + align:start position:0% +eventually win the Nobel Prize only two + + + align:start position:0% +eventually win the Nobel Prize only two +uh straight legs and one curvy leg can + + align:start position:0% +uh straight legs and one curvy leg can + + + align:start position:0% +uh straight legs and one curvy leg can +meet at each point oops right because + + align:start position:0% +meet at each point oops right because + + + align:start position:0% +meet at each point oops right because +there's so much bound up I think for + + align:start position:0% +there's so much bound up I think for + + + align:start position:0% +there's so much bound up I think for +store for Feynman in this kind of + + align:start position:0% +store for Feynman in this kind of + + + align:start position:0% +store for Feynman in this kind of +space-time narrative and the + + align:start position:0% +space-time narrative and the + + + align:start position:0% +space-time narrative and the +trajectories I think moving to space and + + align:start position:0% +trajectories I think moving to space and + + + align:start position:0% +trajectories I think moving to space and +time it wasn't only fun if you look at + + align:start position:0% +time it wasn't only fun if you look at + + + align:start position:0% +time it wasn't only fun if you look at +the earliest textbooks they keep + + align:start position:0% +the earliest textbooks they keep + + + align:start position:0% +the earliest textbooks they keep +repeating the same scheme even when they + + align:start position:0% +repeating the same scheme even when they + + + align:start position:0% +repeating the same scheme even when they +move into momentum space for which + + align:start position:0% +move into momentum space for which + + + align:start position:0% +move into momentum space for which +there's absolutely no meaning no + + align:start position:0% +there's absolutely no meaning no + + + align:start position:0% +there's absolutely no meaning no +relevance whatsoever to the kind of 45 + + align:start position:0% +relevance whatsoever to the kind of 45 + + + align:start position:0% +relevance whatsoever to the kind of 45 +degree diagonal that only means + + align:start position:0% +degree diagonal that only means + + + align:start position:0% +degree diagonal that only means +something if you're actually working in + + align:start position:0% +something if you're actually working in + + + align:start position:0% +something if you're actually working in +space-time and scaling the speed of + + align:start position:0% +space-time and scaling the speed of + + + align:start position:0% +space-time and scaling the speed of +light to be one they it means nothing if + + align:start position:0% +light to be one they it means nothing if + + + align:start position:0% +light to be one they it means nothing if +you're even if you're in momentum space + + align:start position:0% +you're even if you're in momentum space + + + align:start position:0% +you're even if you're in momentum space +and yet in these examples and many of + + align:start position:0% +and yet in these examples and many of + + + align:start position:0% +and yet in these examples and many of +these physicists working explicitly in + + align:start position:0% +these physicists working explicitly in + + + align:start position:0% +these physicists working explicitly in +momentous space nonetheless kept using + + align:start position:0% +momentous space nonetheless kept using + + + align:start position:0% +momentous space nonetheless kept using +the space-time minkowski conventions and + + align:start position:0% +the space-time minkowski conventions and + + + align:start position:0% +the space-time minkowski conventions and +I argue that that was kind of what they + + align:start position:0% +I argue that that was kind of what they + + + align:start position:0% +I argue that that was kind of what they +were used to and it also probably helped + + align:start position:0% +were used to and it also probably helped + + + align:start position:0% +were used to and it also probably helped +some of the students get up get kind of + + align:start position:0% +some of the students get up get kind of + + + align:start position:0% +some of the students get up get kind of +comfortable with them as well + + align:start position:0% +comfortable with them as well + + + align:start position:0% +comfortable with them as well +there was another visual feature that + + align:start position:0% +there was another visual feature that + + + align:start position:0% +there was another visual feature that +again in in terms of which these these + + align:start position:0% +again in in terms of which these these + + + align:start position:0% +again in in terms of which these these +physicists were immersed at the time + + align:start position:0% +physicists were immersed at the time + + + align:start position:0% +physicists were immersed at the time +and that was comes from this explosion + + align:start position:0% +and that was comes from this explosion + + + align:start position:0% +and that was comes from this explosion +of the very large and Rapid production + + align:start position:0% +of the very large and Rapid production + + + align:start position:0% +of the very large and Rapid production +of particle particle accelerators after + + align:start position:0% +of particle particle accelerators after + + + align:start position:0% +of particle particle accelerators after +the war funded by the atomic energy + + align:start position:0% +the war funded by the atomic energy + + + align:start position:0% +the war funded by the atomic energy +commission where many many universities + + align:start position:0% +commission where many many universities + + + align:start position:0% +commission where many many universities +like MIT had their own local atom + + align:start position:0% +like MIT had their own local atom + + + align:start position:0% +like MIT had their own local atom +smasher + + align:start position:0% +smasher + + + align:start position:0% +smasher +so what became common was to draw these + + align:start position:0% +so what became common was to draw these + + + align:start position:0% +so what became common was to draw these +freehand reconstructions based on the + + align:start position:0% +freehand reconstructions based on the + + + align:start position:0% +freehand reconstructions based on the +bubble chamber photographs this was not + + align:start position:0% +bubble chamber photographs this was not + + + align:start position:0% +bubble chamber photographs this was not +meant to be filing diagram + + align:start position:0% +meant to be filing diagram + + + align:start position:0% +meant to be filing diagram +but it became clear because it was + + align:start position:0% +but it became clear because it was + + + align:start position:0% +but it became clear because it was +actually fairly expensive to keep trying + + align:start position:0% +actually fairly expensive to keep trying + + + align:start position:0% +actually fairly expensive to keep trying +to reprint the photographs you'll just + + align:start position:0% +to reprint the photographs you'll just + + + align:start position:0% +to reprint the photographs you'll just +reprint these hand often hand-drawn + + align:start position:0% +reprint these hand often hand-drawn + + + align:start position:0% +reprint these hand often hand-drawn +um align sketch reconstructions which + + align:start position:0% +um align sketch reconstructions which + + + align:start position:0% +um align sketch reconstructions which +consist like these fiber diagrams of + + align:start position:0% +consist like these fiber diagrams of + + + align:start position:0% +consist like these fiber diagrams of +propagation lines and vertices so there + + align:start position:0% +propagation lines and vertices so there + + + align:start position:0% +propagation lines and vertices so there +was in some sense a kind of + + align:start position:0% +was in some sense a kind of + + + align:start position:0% +was in some sense a kind of +reinforcement of a kind of realism that + + align:start position:0% +reinforcement of a kind of realism that + + + align:start position:0% +reinforcement of a kind of realism that +had nothing to do with Freeman Dyson's + + align:start position:0% +had nothing to do with Freeman Dyson's + + + align:start position:0% +had nothing to do with Freeman Dyson's +very careful kind of derivation uh or or + + align:start position:0% +very careful kind of derivation uh or or + + + align:start position:0% +very careful kind of derivation uh or or +anything about perturbation Theory so + + align:start position:0% +anything about perturbation Theory so + + + align:start position:0% +anything about perturbation Theory so +there's a kind of realism and you see + + align:start position:0% +there's a kind of realism and you see + + + align:start position:0% +there's a kind of realism and you see +that in this quotation for example some + + align:start position:0% +that in this quotation for example some + + + align:start position:0% +that in this quotation for example some +years later in a very influential + + align:start position:0% +years later in a very influential + + + align:start position:0% +years later in a very influential +textbook but these filament diagrams + + align:start position:0% +textbook but these filament diagrams + + + align:start position:0% +textbook but these filament diagrams +Richard Matic wrote are so vividly + + align:start position:0% +Richard Matic wrote are so vividly + + + align:start position:0% +Richard Matic wrote are so vividly +physical looking that it seems a bit + + align:start position:0% +physical looking that it seems a bit + + + align:start position:0% +physical looking that it seems a bit +extreme to completely reject any sort of + + align:start position:0% +extreme to completely reject any sort of + + + align:start position:0% +extreme to completely reject any sort of +physical interpretation whatsoever so he + + align:start position:0% +physical interpretation whatsoever so he + + + align:start position:0% +physical interpretation whatsoever so he +does this funny kind of um uh cheat we + + align:start position:0% +does this funny kind of um uh cheat we + + + align:start position:0% +does this funny kind of um uh cheat we +will therefore talk about the diagrams + + align:start position:0% +will therefore talk about the diagrams + + + align:start position:0% +will therefore talk about the diagrams +as if they were physical but remember + + align:start position:0% +as if they were physical but remember + + + align:start position:0% +as if they were physical but remember +they're not right so he can't he can't + + align:start position:0% +they're not right so he can't he can't + + + align:start position:0% +they're not right so he can't he can't +help himself but describe them as real + + align:start position:0% +help himself but describe them as real + + + align:start position:0% +help himself but describe them as real +things moving through space and time + + align:start position:0% +things moving through space and time + + + align:start position:0% +things moving through space and time +other textbooks at the time reinforce + + align:start position:0% +other textbooks at the time reinforce + + + align:start position:0% +other textbooks at the time reinforce +that visually + + align:start position:0% +that visually + + + align:start position:0% +that visually +if we could look if we could really kind + + align:start position:0% +if we could look if we could really kind + + + align:start position:0% +if we could look if we could really kind +of zoom in with our own eye + + align:start position:0% +of zoom in with our own eye + + + align:start position:0% +of zoom in with our own eye +and watch these Elementary processes we + + align:start position:0% +and watch these Elementary processes we + + + align:start position:0% +and watch these Elementary processes we +would see Simon diagrams we wouldn't see + + align:start position:0% +would see Simon diagrams we wouldn't see + + + align:start position:0% +would see Simon diagrams we wouldn't see +you know um uh cathode rays skittering + + align:start position:0% +you know um uh cathode rays skittering + + + align:start position:0% +you know um uh cathode rays skittering +on a scintillation screen we would + + align:start position:0% +on a scintillation screen we would + + + align:start position:0% +on a scintillation screen we would +literally see nature as finding diagrams + + align:start position:0% +literally see nature as finding diagrams + + + align:start position:0% +literally see nature as finding diagrams +if we had a big microscope + + align:start position:0% +if we had a big microscope + + + align:start position:0% +if we had a big microscope +okay so let me wrap + + align:start position:0% +okay so let me wrap + + + align:start position:0% +okay so let me wrap +so scientists then and as now always + + align:start position:0% +so scientists then and as now always + + + align:start position:0% +so scientists then and as now always +have to practice using their tools our + + align:start position:0% +have to practice using their tools our + + + align:start position:0% +have to practice using their tools our +tools don't come for free that's why it + + align:start position:0% +tools don't come for free that's why it + + + align:start position:0% +tools don't come for free that's why it +takes many years of training many + + align:start position:0% +takes many years of training many + + + align:start position:0% +takes many years of training many +problem sets many late nights many lab + + align:start position:0% +problem sets many late nights many lab + + + align:start position:0% +problem sets many late nights many lab +reports and the tools aren't automatic + + align:start position:0% +reports and the tools aren't automatic + + + align:start position:0% +reports and the tools aren't automatic +uh the tools themselves can change and + + align:start position:0% +uh the tools themselves can change and + + + align:start position:0% +uh the tools themselves can change and +can be put um to New Uses how do they + + align:start position:0% +can be put um to New Uses how do they + + + align:start position:0% +can be put um to New Uses how do they +spread how these new techniques spread + + align:start position:0% +spread how these new techniques spread + + + align:start position:0% +spread how these new techniques spread +writing a really great textbook or + + align:start position:0% +writing a really great textbook or + + + align:start position:0% +writing a really great textbook or +nowadays may be making a great you know + + align:start position:0% +nowadays may be making a great you know + + + align:start position:0% +nowadays may be making a great you know +viral YouTube video that can certainly + + align:start position:0% +viral YouTube video that can certainly + + + align:start position:0% +viral YouTube video that can certainly +help but at least in his early days it + + align:start position:0% +help but at least in his early days it + + + align:start position:0% +help but at least in his early days it +took much more than only kind of + + align:start position:0% +took much more than only kind of + + + align:start position:0% +took much more than only kind of +um text-based means of of propagation it + + align:start position:0% +um text-based means of of propagation it + + + align:start position:0% +um text-based means of of propagation it +really took very specific social + + align:start position:0% +really took very specific social + + + align:start position:0% +really took very specific social +institutions like post-docs and their + + align:start position:0% +institutions like post-docs and their + + + align:start position:0% +institutions like post-docs and their +dispersal to help move these techniques + + align:start position:0% +dispersal to help move these techniques + + + align:start position:0% +dispersal to help move these techniques +around + + align:start position:0% +around + + + align:start position:0% +around +moreover even the kind of fanciest new + + align:start position:0% +moreover even the kind of fanciest new + + + align:start position:0% +moreover even the kind of fanciest new +techniques will be will be incorporated + + align:start position:0% +techniques will be will be incorporated + + + align:start position:0% +techniques will be will be incorporated +made sense of in the context of what + + align:start position:0% +made sense of in the context of what + + + align:start position:0% +made sense of in the context of what +Generations had already become + + align:start position:0% +Generations had already become + + + align:start position:0% +Generations had already become +comfortable with so I think we can make + + align:start position:0% +comfortable with so I think we can make + + + align:start position:0% +comfortable with so I think we can make +sense of the particular rhythms of the + + align:start position:0% +sense of the particular rhythms of the + + + align:start position:0% +sense of the particular rhythms of the +history of these diagrams by thinking + + align:start position:0% +history of these diagrams by thinking + + + align:start position:0% +history of these diagrams by thinking +about pedagogically what had previous + + align:start position:0% +about pedagogically what had previous + + + align:start position:0% +about pedagogically what had previous +generations already become used to and + + align:start position:0% +generations already become used to and + + + align:start position:0% +generations already become used to and +so in that sense you can see the + + align:start position:0% +so in that sense you can see the + + + align:start position:0% +so in that sense you can see the +diagrams and their users kind of being + + align:start position:0% +diagrams and their users kind of being + + + align:start position:0% +diagrams and their users kind of being +forged together that the early users of + + align:start position:0% +forged together that the early users of + + + align:start position:0% +forged together that the early users of +the techniques were themselves being + + align:start position:0% +the techniques were themselves being + + + align:start position:0% +the techniques were themselves being +molded in these formal training stages + + align:start position:0% +molded in these formal training stages + + + align:start position:0% +molded in these formal training stages +of their career and they're often + + align:start position:0% +of their career and they're often + + + align:start position:0% +of their career and they're often +molding the diagrams at this same time + + align:start position:0% +molding the diagrams at this same time + + + align:start position:0% +molding the diagrams at this same time +so I will stop there \ No newline at end of file diff --git a/z9JJp8DHMYc.txt b/z9JJp8DHMYc.txt new file mode 100644 index 0000000000000000000000000000000000000000..e47de9ae1bb6d5913c10b1398c708755c4441f49 --- /dev/null +++ b/z9JJp8DHMYc.txt @@ -0,0 +1,1107 @@ +align:start position:0% + +we're a team phonezilla + + align:start position:0% + + + + align:start position:0% + +hi we're team ponzola and we're here + + align:start position:0% +hi we're team ponzola and we're here + + + align:start position:0% +hi we're team ponzola and we're here +today to present to you our prototype + + align:start position:0% +today to present to you our prototype + + + align:start position:0% +today to present to you our prototype +for a nebulizer + + align:start position:0% +for a nebulizer + + + align:start position:0% +for a nebulizer +there are three major systems of this + + align:start position:0% +there are three major systems of this + + + align:start position:0% +there are three major systems of this +nebulizer there's the motor + + align:start position:0% +nebulizer there's the motor + + + align:start position:0% +nebulizer there's the motor +there's the nozzle + + align:start position:0% +there's the nozzle + + + align:start position:0% +there's the nozzle +and there's the various mouth or face + + align:start position:0% +and there's the various mouth or face + + + align:start position:0% +and there's the various mouth or face +pieces that attach to the nozzle + + align:start position:0% +pieces that attach to the nozzle + + + align:start position:0% +pieces that attach to the nozzle +I'm going to talk about talking about + + align:start position:0% +I'm going to talk about talking about + + + align:start position:0% +I'm going to talk about talking about +the motor section + + align:start position:0% +the motor section + + + align:start position:0% +the motor section +what we have is instead of pounded by an + + align:start position:0% +what we have is instead of pounded by an + + + align:start position:0% +what we have is instead of pounded by an +electric motor which is costly and + + align:start position:0% +electric motor which is costly and + + + align:start position:0% +electric motor which is costly and +breaks easily we're powering it with CO2 + + align:start position:0% +breaks easily we're powering it with CO2 + + + align:start position:0% +breaks easily we're powering it with CO2 +gas which is readily available in the + + align:start position:0% +gas which is readily available in the + + + align:start position:0% +gas which is readily available in the +developing world + + align:start position:0% +developing world + + + align:start position:0% +developing world +the pressurized CO2 gas is spread into + + align:start position:0% +the pressurized CO2 gas is spread into + + + align:start position:0% +the pressurized CO2 gas is spread into +this moment system what I've done that + + align:start position:0% +this moment system what I've done that + + + align:start position:0% +this moment system what I've done that +on the board + + align:start position:0% +on the board + + + align:start position:0% +on the board +CO2 feeds into an air motor + + align:start position:0% +CO2 feeds into an air motor + + + align:start position:0% +CO2 feeds into an air motor +which turns turning the shaft attached + + align:start position:0% +which turns turning the shaft attached + + + align:start position:0% +which turns turning the shaft attached +to a pump the pump moves up and down + + align:start position:0% +to a pump the pump moves up and down + + + align:start position:0% +to a pump the pump moves up and down +generating oxygen which moves + + align:start position:0% +generating oxygen which moves + + + align:start position:0% +generating oxygen which moves +the reason we even + + align:start position:0% + + + + align:start position:0% + +seemed to be flowing through the nozzle + + align:start position:0% +seemed to be flowing through the nozzle + + + align:start position:0% +seemed to be flowing through the nozzle +we can't have CO2 flowing through the + + align:start position:0% +we can't have CO2 flowing through the + + + align:start position:0% +we can't have CO2 flowing through the +nozzle + + align:start position:0% + + + + align:start position:0% + +the tubes connecting the nozzle to the + + align:start position:0% +the tubes connecting the nozzle to the + + + align:start position:0% +the tubes connecting the nozzle to the +motor are detachable although they + + align:start position:0% +motor are detachable although they + + + align:start position:0% +motor are detachable although they +aren't in this model + + align:start position:0% +aren't in this model + + + align:start position:0% +aren't in this model +and levana who's up next we'll be + + align:start position:0% +and levana who's up next we'll be + + + align:start position:0% +and levana who's up next we'll be +talking about the nozzle subsystem oh go + + align:start position:0% +talking about the nozzle subsystem oh go + + + align:start position:0% +talking about the nozzle subsystem oh go +so this is a nozzle to the nebulizer and + + align:start position:0% +so this is a nozzle to the nebulizer and + + + align:start position:0% +so this is a nozzle to the nebulizer and +it works just the same way as the + + align:start position:0% +it works just the same way as the + + + align:start position:0% +it works just the same way as the +traditional nebulizer + + align:start position:0% +traditional nebulizer + + + align:start position:0% +traditional nebulizer +changes + + align:start position:0% +changes + + + align:start position:0% +changes +um I'll first explain and go through and + + align:start position:0% +um I'll first explain and go through and + + + align:start position:0% +um I'll first explain and go through and +tell you what's different along the way + + align:start position:0% +tell you what's different along the way + + + align:start position:0% +tell you what's different along the way +so you would actually pour the medicine + + align:start position:0% +so you would actually pour the medicine + + + align:start position:0% +so you would actually pour the medicine +into the cup + + align:start position:0% +into the cup + + + align:start position:0% +into the cup +and as you can see inside there's + + align:start position:0% +and as you can see inside there's + + + align:start position:0% +and as you can see inside there's +actually the centerpiece and + + align:start position:0% +actually the centerpiece and + + + align:start position:0% +actually the centerpiece and +theoretically it'll be removable however + + align:start position:0% +theoretically it'll be removable however + + + align:start position:0% +theoretically it'll be removable however +in this uh + + align:start position:0% +in this uh + + + align:start position:0% +in this uh +SketchUp model it's not just simply + + align:start position:0% +SketchUp model it's not just simply + + + align:start position:0% +SketchUp model it's not just simply +because of the way we had to tape it so + + align:start position:0% +because of the way we had to tape it so + + + align:start position:0% +because of the way we had to tape it so +it could be removable and then there + + align:start position:0% +it could be removable and then there + + + align:start position:0% +it could be removable and then there +would be another + + align:start position:0% + + + + align:start position:0% + +you would have actually the cap to it + + align:start position:0% +you would have actually the cap to it + + + align:start position:0% +you would have actually the cap to it +which would snap into place + + align:start position:0% +which would snap into place + + + align:start position:0% +which would snap into place +and + + align:start position:0% +and + + + align:start position:0% +and +a Tight Seal and attached to this cap + + align:start position:0% +a Tight Seal and attached to this cap + + + align:start position:0% +a Tight Seal and attached to this cap +and actually connected to it is a small + + align:start position:0% +and actually connected to it is a small + + + align:start position:0% +and actually connected to it is a small +segment of tube that would lead to a + + align:start position:0% +segment of tube that would lead to a + + + align:start position:0% +segment of tube that would lead to a +longer through and then + + align:start position:0% +longer through and then + + + align:start position:0% +longer through and then +lead to uh + + align:start position:0% +lead to uh + + + align:start position:0% +lead to uh +the readout for uh + + align:start position:0% + + + + align:start position:0% + +and I'll explain more about how this + + align:start position:0% +and I'll explain more about how this + + + align:start position:0% +and I'll explain more about how this +nozzle works so as you can see here + + align:start position:0% + + + + align:start position:0% + +and show the tips here + + align:start position:0% +and show the tips here + + + align:start position:0% +and show the tips here +allowing it to be a high velocity and + + align:start position:0% +allowing it to be a high velocity and + + + align:start position:0% +allowing it to be a high velocity and +also the liquid and the medication will + + align:start position:0% +also the liquid and the medication will + + + align:start position:0% +also the liquid and the medication will +flow up between the center + + align:start position:0% +flow up between the center + + + align:start position:0% +flow up between the center +the original signal nozzle itself and + + align:start position:0% +the original signal nozzle itself and + + + align:start position:0% +the original signal nozzle itself and +then it will create a mixing effect with + + align:start position:0% +then it will create a mixing effect with + + + align:start position:0% +then it will create a mixing effect with +the gas to aerosolidize it and this will + + align:start position:0% +the gas to aerosolidize it and this will + + + align:start position:0% +the gas to aerosolidize it and this will +be pushed through this top of the center + + align:start position:0% +be pushed through this top of the center + + + align:start position:0% +be pushed through this top of the center +piece which is actually on the design + + align:start position:0% +piece which is actually on the design + + + align:start position:0% +piece which is actually on the design +change here is that we remove the scope + + align:start position:0% +change here is that we remove the scope + + + align:start position:0% +change here is that we remove the scope +of our previously on it and instead it's + + align:start position:0% +of our previously on it and instead it's + + + align:start position:0% +of our previously on it and instead it's +being tested in place to place of the + + align:start position:0% +being tested in place to place of the + + + align:start position:0% +being tested in place to place of the +pressure of the lack of distance applies + + align:start position:0% +pressure of the lack of distance applies + + + align:start position:0% +pressure of the lack of distance applies +between the the collaborative and the + + align:start position:0% +between the the collaborative and the + + + align:start position:0% +between the the collaborative and the +tip of the novels and its connections + + align:start position:0% +tip of the novels and its connections + + + align:start position:0% +tip of the novels and its connections +is a funnel safe that is the tips here + + align:start position:0% +is a funnel safe that is the tips here + + + align:start position:0% +is a funnel safe that is the tips here +is actually smaller than the text yes so + + align:start position:0% +is actually smaller than the text yes so + + + align:start position:0% +is actually smaller than the text yes so +then this will allows us to go through + + align:start position:0% +then this will allows us to go through + + + align:start position:0% +then this will allows us to go through +and then expand outwards where it enters + + align:start position:0% +and then expand outwards where it enters + + + align:start position:0% +and then expand outwards where it enters +the Thousand allows for + + align:start position:0% +the Thousand allows for + + + align:start position:0% +the Thousand allows for +um + + align:start position:0% + + + + align:start position:0% + +time just for the design of the valve + + align:start position:0% +time just for the design of the valve + + + align:start position:0% +time just for the design of the valve +and the mouth + + align:start position:0% + + + + align:start position:0% + +this part that's detachable and then so + + align:start position:0% +this part that's detachable and then so + + + align:start position:0% +this part that's detachable and then so +after the medication gets mixed right + + align:start position:0% +after the medication gets mixed right + + + align:start position:0% +after the medication gets mixed right +here it's going to come up through this + + align:start position:0% +here it's going to come up through this + + + align:start position:0% +here it's going to come up through this +channel into this tube and then actually + + align:start position:0% +channel into this tube and then actually + + + align:start position:0% +channel into this tube and then actually +and then eventually you either have a + + align:start position:0% +and then eventually you either have a + + + align:start position:0% +and then eventually you either have a +mouthpiece that connects to the end of + + align:start position:0% +mouthpiece that connects to the end of + + + align:start position:0% +mouthpiece that connects to the end of +the tube + + align:start position:0% +the tube + + + align:start position:0% +the tube +or you can have a mask + + align:start position:0% +or you can have a mask + + + align:start position:0% +or you can have a mask +and then just the patient's mouth would + + align:start position:0% +and then just the patient's mouth would + + + align:start position:0% +and then just the patient's mouth would +end up right here and then kind of be + + align:start position:0% +end up right here and then kind of be + + + align:start position:0% +end up right here and then kind of be +like look like this + + align:start position:0% + + + + align:start position:0% + +so to try to prevent infection we put a + + align:start position:0% +so to try to prevent infection we put a + + + align:start position:0% +so to try to prevent infection we put a +little a one-way valve about right here + + align:start position:0% +little a one-way valve about right here + + + align:start position:0% +little a one-way valve about right here +in the tube about three inches away from + + align:start position:0% +in the tube about three inches away from + + + align:start position:0% +in the tube about three inches away from +where the mouthpiece or the mask would + + align:start position:0% +where the mouthpiece or the mask would + + + align:start position:0% +where the mouthpiece or the mask would +attach so the way the winery valve works + + align:start position:0% +attach so the way the winery valve works + + + align:start position:0% +attach so the way the winery valve works +is um + + align:start position:0% +is um + + + align:start position:0% +is um +it would allow the medicine to come up + + align:start position:0% +it would allow the medicine to come up + + + align:start position:0% +it would allow the medicine to come up +through this tube and then into + + align:start position:0% +through this tube and then into + + + align:start position:0% +through this tube and then into +towards the mask or the mouthpiece + + align:start position:0% +towards the mask or the mouthpiece + + + align:start position:0% +towards the mask or the mouthpiece +however + + align:start position:0% +however + + + align:start position:0% +however +if sometimes when the patient's using it + + align:start position:0% +if sometimes when the patient's using it + + + align:start position:0% +if sometimes when the patient's using it +they will cough back into the tube and + + align:start position:0% +they will cough back into the tube and + + + align:start position:0% +they will cough back into the tube and +this is valve will prevent anything that + + align:start position:0% +this is valve will prevent anything that + + + align:start position:0% +this is valve will prevent anything that +comes from the patient's body it will + + align:start position:0% +comes from the patient's body it will + + + align:start position:0% +comes from the patient's body it will +prevent that those particles from going + + align:start position:0% +prevent that those particles from going + + + align:start position:0% +prevent that those particles from going +back down into the tubing contaminating + + align:start position:0% +back down into the tubing contaminating + + + align:start position:0% +back down into the tubing contaminating +the tube so this we hope will decrease + + align:start position:0% +the tube so this we hope will decrease + + + align:start position:0% +the tube so this we hope will decrease +the rate of infection for people using + + align:start position:0% +the rate of infection for people using + + + align:start position:0% +the rate of infection for people using +it the reason well before + + align:start position:0% +it the reason well before + + + align:start position:0% +it the reason well before +the standard treatment was to use a mask + + align:start position:0% +the standard treatment was to use a mask + + + align:start position:0% +the standard treatment was to use a mask +and have the patients apply the mask to + + align:start position:0% +and have the patients apply the mask to + + + align:start position:0% +and have the patients apply the mask to +the base + + align:start position:0% +the base + + + align:start position:0% +the base +um a lot of children didn't like this + + align:start position:0% +um a lot of children didn't like this + + + align:start position:0% +um a lot of children didn't like this +because it was uncomfortable for them + + align:start position:0% +because it was uncomfortable for them + + + align:start position:0% +because it was uncomfortable for them +so we decided to to use a mouthpiece + + align:start position:0% +so we decided to to use a mouthpiece + + + align:start position:0% +so we decided to to use a mouthpiece +instead because what we did found was + + align:start position:0% +instead because what we did found was + + + align:start position:0% +instead because what we did found was +that a lot of children would instead of + + align:start position:0% +that a lot of children would instead of + + + align:start position:0% +that a lot of children would instead of +using the mask they would actually put + + align:start position:0% +using the mask they would actually put + + + align:start position:0% +using the mask they would actually put +the tube directly to their mouth and try + + align:start position:0% +the tube directly to their mouth and try + + + align:start position:0% +the tube directly to their mouth and try +to breathe it in that way so that was + + align:start position:0% +to breathe it in that way so that was + + + align:start position:0% +to breathe it in that way so that was +one cause for an infection among + + align:start position:0% +one cause for an infection among + + + align:start position:0% +one cause for an infection among +different patients was because it gets + + align:start position:0% +different patients was because it gets + + + align:start position:0% +different patients was because it gets +contaminated from other people's + + align:start position:0% +contaminated from other people's + + + align:start position:0% +contaminated from other people's +other people's germs so we created this + + align:start position:0% +other people's germs so we created this + + + align:start position:0% +other people's germs so we created this +mouthpiece that will attach to the end + + align:start position:0% +mouthpiece that will attach to the end + + + align:start position:0% +mouthpiece that will attach to the end +of the tube and then + + align:start position:0% +of the tube and then + + + align:start position:0% +of the tube and then +this is this mouthpiece can be cleaned + + align:start position:0% +this is this mouthpiece can be cleaned + + + align:start position:0% +this is this mouthpiece can be cleaned +in between each patient so that will + + align:start position:0% +in between each patient so that will + + + align:start position:0% +in between each patient so that will +help with controlling infection and it's + + align:start position:0% +help with controlling infection and it's + + + align:start position:0% +help with controlling infection and it's +also a great distance away from the + + align:start position:0% +also a great distance away from the + + + align:start position:0% +also a great distance away from the +filter the filter would be right here so + + align:start position:0% +filter the filter would be right here so + + + align:start position:0% +filter the filter would be right here so +the end from the end of the mouthpiece + + align:start position:0% +the end from the end of the mouthpiece + + + align:start position:0% +the end from the end of the mouthpiece +to the culture there's about three + + align:start position:0% +to the culture there's about three + + + align:start position:0% +to the culture there's about three +inches of tubing so that's also meant to + + align:start position:0% +inches of tubing so that's also meant to + + + align:start position:0% +inches of tubing so that's also meant to +help decrease infection + + align:start position:0% +help decrease infection + + + align:start position:0% +help decrease infection +and yeah \ No newline at end of file diff --git a/zYgkr0KfWM0.txt b/zYgkr0KfWM0.txt new file mode 100644 index 0000000000000000000000000000000000000000..4be75f252ea847eb99ca5f367d392a6ac0c4a85e --- /dev/null +++ b/zYgkr0KfWM0.txt @@ -0,0 +1,11667 @@ +align:start position:0% + +okay so a little over a year ago I got a + + align:start position:0% +okay so a little over a year ago I got a + + + align:start position:0% +okay so a little over a year ago I got a +call from from this committee nay some + + align:start position:0% +call from from this committee nay some + + + align:start position:0% +call from from this committee nay some +is the national academy of science + + align:start position:0% +is the national academy of science + + + align:start position:0% +is the national academy of science +engineering and medicine so this is an + + align:start position:0% +engineering and medicine so this is an + + + align:start position:0% +engineering and medicine so this is an +august body of old people with lots of + + align:start position:0% +august body of old people with lots of + + + align:start position:0% +august body of old people with lots of +gray hair who have done something + + align:start position:0% +gray hair who have done something + + + align:start position:0% +gray hair who have done something +important enough to get elected to these + + align:start position:0% +important enough to get elected to these + + + align:start position:0% +important enough to get elected to these +academies and their research arm is + + align:start position:0% +academies and their research arm is + + + align:start position:0% +academies and their research arm is +called the national research council and + + align:start position:0% +called the national research council and + + + align:start position:0% +called the national research council and +has a bunch of different committees one + + align:start position:0% +has a bunch of different committees one + + + align:start position:0% +has a bunch of different committees one +of them is this committee on science + + align:start position:0% +of them is this committee on science + + + align:start position:0% +of them is this committee on science +technology on the law it's a very + + align:start position:0% +technology on the law it's a very + + + align:start position:0% +technology on the law it's a very +interesting committee it's chaired by + + align:start position:0% +interesting committee it's chaired by + + + align:start position:0% +interesting committee it's chaired by +David Baltimore who used to be an MIT + + align:start position:0% +David Baltimore who used to be an MIT + + + align:start position:0% +David Baltimore who used to be an MIT +professor until he went and became + + align:start position:0% +professor until he went and became + + + align:start position:0% +professor until he went and became +president of Caltech and he also happens + + align:start position:0% +president of Caltech and he also happens + + + align:start position:0% +president of Caltech and he also happens +to have a Nobel Prize in his pocket and + + align:start position:0% +to have a Nobel Prize in his pocket and + + + align:start position:0% +to have a Nobel Prize in his pocket and +you know he's a pretty famous guy and + + align:start position:0% +you know he's a pretty famous guy and + + + align:start position:0% +you know he's a pretty famous guy and +Judge David Tatel is a member of the US + + align:start position:0% +Judge David Tatel is a member of the US + + + align:start position:0% +Judge David Tatel is a member of the US +Court of Appeals for the District of + + align:start position:0% +Court of Appeals for the District of + + + align:start position:0% +Court of Appeals for the District of +Columbia Circuit so this is probably the + + align:start position:0% +Columbia Circuit so this is probably the + + + align:start position:0% +Columbia Circuit so this is probably the +most important Circuit Court it's one + + align:start position:0% +most important Circuit Court it's one + + + align:start position:0% +most important Circuit Court it's one +level below the Supreme Court and he + + align:start position:0% +level below the Supreme Court and he + + + align:start position:0% +level below the Supreme Court and he +happens to sit in the seat that Ruth + + align:start position:0% +happens to sit in the seat that Ruth + + + align:start position:0% +happens to sit in the seat that Ruth +Bader Ginsburg occupied before she was + + align:start position:0% +Bader Ginsburg occupied before she was + + + align:start position:0% +Bader Ginsburg occupied before she was +elevated to the Supreme Court from that + + align:start position:0% +elevated to the Supreme Court from that + + + align:start position:0% +elevated to the Supreme Court from that +that Court of Appeals so this is a + + align:start position:0% +that Court of Appeals so this is a + + + align:start position:0% +that Court of Appeals so this is a +pretty big deal so these are heavy + + align:start position:0% +pretty big deal so these are heavy + + + align:start position:0% +pretty big deal so these are heavy +hitters and they convened a a meeting to + + align:start position:0% +hitters and they convened a a meeting to + + + align:start position:0% +hitters and they convened a a meeting to +talk about the the set of topics that + + align:start position:0% +talk about the the set of topics that + + + align:start position:0% +talk about the the set of topics that +I've listed here so blockchain and + + align:start position:0% +I've listed here so blockchain and + + + align:start position:0% +I've listed here so blockchain and +distributer trust artificial + + align:start position:0% +distributer trust artificial + + + align:start position:0% +distributer trust artificial +intelligence on decision-making which is + + align:start position:0% +intelligence on decision-making which is + + + align:start position:0% +intelligence on decision-making which is +obviously the part that I got invited to + + align:start position:0% +obviously the part that I got invited to + + + align:start position:0% +obviously the part that I got invited to +talk about privacy and informed consent + + align:start position:0% +talk about privacy and informed consent + + + align:start position:0% +talk about privacy and informed consent +in an era of big data science curricula + + align:start position:0% +in an era of big data science curricula + + + align:start position:0% +in an era of big data science curricula +for law schools emerging issues in + + align:start position:0% +for law schools emerging issues in + + + align:start position:0% +for law schools emerging issues in +science technology and law the issue of + + align:start position:0% +science technology and law the issue of + + + align:start position:0% +science technology and law the issue of +using litigation to target scientists + + align:start position:0% +using litigation to target scientists + + + align:start position:0% +using litigation to target scientists +who have opinions that you don't like + + align:start position:0% +who have opinions that you don't like + + + align:start position:0% +who have opinions that you don't like +and a more general issue of how do you + + align:start position:0% +and a more general issue of how do you + + + align:start position:0% +and a more general issue of how do you +communicate advances in life sciences to + + align:start position:0% +communicate advances in life sciences to + + + align:start position:0% +communicate advances in life sciences to +a skeptical public so this is dealing + + align:start position:0% +a skeptical public so this is dealing + + + align:start position:0% +a skeptical public so this is dealing +with the sort of anti science of tenor + + align:start position:0% +with the sort of anti science of tenor + + + align:start position:0% +with the sort of anti science of tenor +of the times + + align:start position:0% +of the times + + + align:start position:0% +of the times +so the group of us that talked about AI + + align:start position:0% +so the group of us that talked about AI + + + align:start position:0% +so the group of us that talked about AI +and decision-making I was a little bit + + align:start position:0% +and decision-making I was a little bit + + + align:start position:0% +and decision-making I was a little bit +surprised by the focus because Hank + + align:start position:0% +surprised by the focus because Hank + + + align:start position:0% +surprised by the focus because Hank +really is a law school professor at + + align:start position:0% +really is a law school professor at + + + align:start position:0% +really is a law school professor at +Stanford who's done a lot of work on + + align:start position:0% +Stanford who's done a lot of work on + + + align:start position:0% +Stanford who's done a lot of work on +unfairness and Prejudice in in health + + align:start position:0% +unfairness and Prejudice in in health + + + align:start position:0% +unfairness and Prejudice in in health +care Charisse Bertie is at something + + align:start position:0% +care Charisse Bertie is at something + + + align:start position:0% +care Charisse Bertie is at something +called the pretrial justice Institute + + align:start position:0% +called the pretrial justice Institute + + + align:start position:0% +called the pretrial justice Institute +and her issue is a legal one which is + + align:start position:0% +and her issue is a legal one which is + + + align:start position:0% +and her issue is a legal one which is +that there are now a lot of companies + + align:start position:0% +that there are now a lot of companies + + + align:start position:0% +that there are now a lot of companies +that have software that predict if you + + align:start position:0% +that have software that predict if you + + + align:start position:0% +that have software that predict if you +get bail while you're awaiting trial are + + align:start position:0% +get bail while you're awaiting trial are + + + align:start position:0% +get bail while you're awaiting trial are +you likely to skip bail or not and so + + align:start position:0% +you likely to skip bail or not and so + + + align:start position:0% +you likely to skip bail or not and so +this is influential in the decision that + + align:start position:0% +this is influential in the decision that + + + align:start position:0% +this is influential in the decision that +judges make about how much bail to + + align:start position:0% +judges make about how much bail to + + + align:start position:0% +judges make about how much bail to +impose and and whether to let you out on + + align:start position:0% +impose and and whether to let you out on + + + align:start position:0% +impose and and whether to let you out on +bail at all or to keep you in prison + + align:start position:0% +bail at all or to keep you in prison + + + align:start position:0% +bail at all or to keep you in prison +awaiting your trial Matt Lundgren is a + + align:start position:0% +awaiting your trial Matt Lundgren is a + + + align:start position:0% +awaiting your trial Matt Lundgren is a +radiology professor at Stanford and has + + align:start position:0% +radiology professor at Stanford and has + + + align:start position:0% +radiology professor at Stanford and has +done some of the really cool work on + + align:start position:0% +done some of the really cool work on + + + align:start position:0% +done some of the really cool work on +building convolutional neural network + + align:start position:0% +building convolutional neural network + + + align:start position:0% +building convolutional neural network +models to detect pulmonary emboli and + + align:start position:0% +models to detect pulmonary emboli and + + + align:start position:0% +models to detect pulmonary emboli and +various other things in in in imaging + + align:start position:0% +various other things in in in imaging + + + align:start position:0% +various other things in in in imaging +data you know that X Guy and Suresh man + + align:start position:0% +data you know that X Guy and Suresh man + + + align:start position:0% +data you know that X Guy and Suresh man +Venkatasubramanian as a professor he was + + align:start position:0% +Venkatasubramanian as a professor he was + + + align:start position:0% +Venkatasubramanian as a professor he was +originally a theorist at the University + + align:start position:0% +originally a theorist at the University + + + align:start position:0% +originally a theorist at the University +of Utah but has also gotten into + + align:start position:0% +of Utah but has also gotten into + + + align:start position:0% +of Utah but has also gotten into +thinking a lot about privacy and and + + align:start position:0% +thinking a lot about privacy and and + + + align:start position:0% +thinking a lot about privacy and and +fairness and so that that was our panel + + align:start position:0% +fairness and so that that was our panel + + + align:start position:0% +fairness and so that that was our panel +and we each gave a brief talk and then + + align:start position:0% +and we each gave a brief talk and then + + + align:start position:0% +and we each gave a brief talk and then +had a very interesting discussion one of + + align:start position:0% +had a very interesting discussion one of + + + align:start position:0% +had a very interesting discussion one of +the things that I was very surprised by + + align:start position:0% +the things that I was very surprised by + + + align:start position:0% +the things that I was very surprised by +is somebody raised the question of + + align:start position:0% +is somebody raised the question of + + + align:start position:0% +is somebody raised the question of +shouldn't title as a as a judge on the + + align:start position:0% +shouldn't title as a as a judge on the + + + align:start position:0% +shouldn't title as a as a judge on the +Circuit Court of Appeals hire people + + align:start position:0% +Circuit Court of Appeals hire people + + + align:start position:0% +Circuit Court of Appeals hire people +like you guys to be clerks in his court + + align:start position:0% +like you guys to be clerks in his court + + + align:start position:0% +like you guys to be clerks in his court +so people like you guys who also happen + + align:start position:0% +so people like you guys who also happen + + + align:start position:0% +so people like you guys who also happen +to go to law school of which there are a + + align:start position:0% +to go to law school of which there are a + + + align:start position:0% +to go to law school of which there are a +number now of people who are trained in + + align:start position:0% +number now of people who are trained in + + + align:start position:0% +number now of people who are trained in +sort of computational methods and + + align:start position:0% +sort of computational methods and + + + align:start position:0% +sort of computational methods and +machine learning but also have the legal + + align:start position:0% +machine learning but also have the legal + + + align:start position:0% +machine learning but also have the legal +background + + align:start position:0% +background + + + align:start position:0% +background +and he said something very interesting + + align:start position:0% +and he said something very interesting + + + align:start position:0% +and he said something very interesting +to me he said no he wouldn't want people + + align:start position:0% +to me he said no he wouldn't want people + + + align:start position:0% +to me he said no he wouldn't want people +like that which kind of shocked me and + + align:start position:0% +like that which kind of shocked me and + + + align:start position:0% +like that which kind of shocked me and +and so we quizzed him a little bit on + + align:start position:0% +and so we quizzed him a little bit on + + + align:start position:0% +and so we quizzed him a little bit on +why and he said well because he views + + align:start position:0% +why and he said well because he views + + + align:start position:0% +why and he said well because he views +the role of the judge not to be an + + align:start position:0% +the role of the judge not to be an + + + align:start position:0% +the role of the judge not to be an +expert but to be a judge to be a + + align:start position:0% +expert but to be a judge to be a + + + align:start position:0% +expert but to be a judge to be a +balancer of arguments on both sides of + + align:start position:0% +balancer of arguments on both sides of + + + align:start position:0% +balancer of arguments on both sides of +an issue and he was afraid that if he + + align:start position:0% +an issue and he was afraid that if he + + + align:start position:0% +an issue and he was afraid that if he +had a clerk who had a strong technical + + align:start position:0% +had a clerk who had a strong technical + + + align:start position:0% +had a clerk who had a strong technical +background that person would have strong + + align:start position:0% +background that person would have strong + + + align:start position:0% +background that person would have strong +technical opinions which would bias his + + align:start position:0% +technical opinions which would bias his + + + align:start position:0% +technical opinions which would bias his +decision one way or another so this + + align:start position:0% +decision one way or another so this + + + align:start position:0% +decision one way or another so this +reminded me my wife was a lawyer and I + + align:start position:0% +reminded me my wife was a lawyer and I + + + align:start position:0% +reminded me my wife was a lawyer and I +remember when she was in law school she + + align:start position:0% +remember when she was in law school she + + + align:start position:0% +remember when she was in law school she +would tell me about the classes that she + + align:start position:0% +would tell me about the classes that she + + + align:start position:0% +would tell me about the classes that she +was taking and and it became obvious + + align:start position:0% +was taking and and it became obvious + + + align:start position:0% +was taking and and it became obvious +that studying law was learning how to + + align:start position:0% +that studying law was learning how to + + + align:start position:0% +that studying law was learning how to +win not learning how to find the truth + + align:start position:0% +win not learning how to find the truth + + + align:start position:0% +win not learning how to find the truth +and there's this philosophical notion in + + align:start position:0% +and there's this philosophical notion in + + + align:start position:0% +and there's this philosophical notion in +the law that says that the truth will + + align:start position:0% +the law that says that the truth will + + + align:start position:0% +the law that says that the truth will +come out from spirited argument on two + + align:start position:0% +come out from spirited argument on two + + + align:start position:0% +come out from spirited argument on two +sides of a question but your duty as a + + align:start position:0% +sides of a question but your duty as a + + + align:start position:0% +sides of a question but your duty as a +lawyer is to argue as hard as you can + + align:start position:0% +lawyer is to argue as hard as you can + + + align:start position:0% +lawyer is to argue as hard as you can +for your side of the argument and in + + align:start position:0% +for your side of the argument and in + + + align:start position:0% +for your side of the argument and in +fact in law school they teach them like + + align:start position:0% +fact in law school they teach them like + + + align:start position:0% +fact in law school they teach them like +in debate that you should be able to + + align:start position:0% +in debate that you should be able to + + + align:start position:0% +in debate that you should be able to +take either side of any case and be able + + align:start position:0% +take either side of any case and be able + + + align:start position:0% +take either side of any case and be able +to make a cogent argument for it and so + + align:start position:0% +to make a cogent argument for it and so + + + align:start position:0% +to make a cogent argument for it and so +titled sort of reinforced that that + + align:start position:0% +titled sort of reinforced that that + + + align:start position:0% +titled sort of reinforced that that +notion in what he said which I thought + + align:start position:0% +notion in what he said which I thought + + + align:start position:0% +notion in what he said which I thought +was interesting well just to talk a + + align:start position:0% +was interesting well just to talk a + + + align:start position:0% +was interesting well just to talk a +little bit about the justice area + + align:start position:0% +little bit about the justice area + + + align:start position:0% +little bit about the justice area +because this is the one that has gotten + + align:start position:0% +because this is the one that has gotten + + + align:start position:0% +because this is the one that has gotten +the most public attention government's + + align:start position:0% +the most public attention government's + + + align:start position:0% +the most public attention government's +use decision automation for determining + + align:start position:0% +use decision automation for determining + + + align:start position:0% +use decision automation for determining +eligibility for various kinds of + + align:start position:0% +eligibility for various kinds of + + + align:start position:0% +eligibility for various kinds of +services evaluating where to deploy + + align:start position:0% +services evaluating where to deploy + + + align:start position:0% +services evaluating where to deploy +health inspectors and law enforcement + + align:start position:0% +health inspectors and law enforcement + + + align:start position:0% +health inspectors and law enforcement +personnel defining boundaries or along + + align:start position:0% +personnel defining boundaries or along + + + align:start position:0% +personnel defining boundaries or along +voting districts so all of the + + align:start position:0% +voting districts so all of the + + + align:start position:0% +voting districts so all of the +gerrymandering discussion that you hear + + align:start position:0% +gerrymandering discussion that you hear + + + align:start position:0% +gerrymandering discussion that you hear +about is is all about using computers + + align:start position:0% +about is is all about using computers + + + align:start position:0% +about is is all about using computers +and actually machine learning tech + + align:start position:0% +and actually machine learning tech + + + align:start position:0% +and actually machine learning tech +to try to figure out how to you know + + align:start position:0% +to try to figure out how to you know + + + align:start position:0% +to try to figure out how to you know +your objective function is to get + + align:start position:0% +your objective function is to get + + + align:start position:0% +your objective function is to get +Republicans or Democrats elected + + align:start position:0% +Republicans or Democrats elected + + + align:start position:0% +Republicans or Democrats elected +depending on who's in charge of the + + align:start position:0% +depending on who's in charge of the + + + align:start position:0% +depending on who's in charge of the +redistricting and then you tailor these + + align:start position:0% +redistricting and then you tailor these + + + align:start position:0% +redistricting and then you tailor these +gerrymandered districts in order to + + align:start position:0% +gerrymandered districts in order to + + + align:start position:0% +gerrymandered districts in order to +maximize the probability that you're + + align:start position:0% +maximize the probability that you're + + + align:start position:0% +maximize the probability that you're +going to have a majority and whatever + + align:start position:0% +going to have a majority and whatever + + + align:start position:0% +going to have a majority and whatever +congressional races or or state + + align:start position:0% +congressional races or or state + + + align:start position:0% +congressional races or or state +legislative races so in the law people + + align:start position:0% +legislative races so in the law people + + + align:start position:0% +legislative races so in the law people +are in favor of these ideas to the + + align:start position:0% +are in favor of these ideas to the + + + align:start position:0% +are in favor of these ideas to the +extent that they inject clarity and + + align:start position:0% +extent that they inject clarity and + + + align:start position:0% +extent that they inject clarity and +precision in to bail parole and + + align:start position:0% +precision in to bail parole and + + + align:start position:0% +precision in to bail parole and +sentencing decisions algorithmic + + align:start position:0% +sentencing decisions algorithmic + + + align:start position:0% +sentencing decisions algorithmic +technologies may minimize harms that are + + align:start position:0% +technologies may minimize harms that are + + + align:start position:0% +technologies may minimize harms that are +the products of human judgement so we + + align:start position:0% +the products of human judgement so we + + + align:start position:0% +the products of human judgement so we +know that people are in fact prejudiced + + align:start position:0% +know that people are in fact prejudiced + + + align:start position:0% +know that people are in fact prejudiced +and so there are prejudices by judges + + align:start position:0% +and so there are prejudices by judges + + + align:start position:0% +and so there are prejudices by judges +and by juries that play into the + + align:start position:0% +and by juries that play into the + + + align:start position:0% +and by juries that play into the +decisions made in the legal system and + + align:start position:0% +decisions made in the legal system and + + + align:start position:0% +decisions made in the legal system and +also by formalizing it you might win + + align:start position:0% +also by formalizing it you might win + + + align:start position:0% +also by formalizing it you might win +however conversely the use of technology + + align:start position:0% +however conversely the use of technology + + + align:start position:0% +however conversely the use of technology +to determine whose Liberty is deprived + + align:start position:0% +to determine whose Liberty is deprived + + + align:start position:0% +to determine whose Liberty is deprived +and on what terms raises significant + + align:start position:0% +and on what terms raises significant + + + align:start position:0% +and on what terms raises significant +concerns about transparency and + + align:start position:0% +concerns about transparency and + + + align:start position:0% +concerns about transparency and +interpretability so next week we're + + align:start position:0% +interpretability so next week we're + + + align:start position:0% +interpretability so next week we're +gonna talk some about transparency and + + align:start position:0% +gonna talk some about transparency and + + + align:start position:0% +gonna talk some about transparency and +interpretability + + align:start position:0% +interpretability + + + align:start position:0% +interpretability +but today's is really about fairness so + + align:start position:0% +but today's is really about fairness so + + + align:start position:0% +but today's is really about fairness so +here's an article from October of last + + align:start position:0% +here's an article from October of last + + + align:start position:0% +here's an article from October of last +year and now September of last year + + align:start position:0% +year and now September of last year + + + align:start position:0% +year and now September of last year +saying that as of October of this year + + align:start position:0% +saying that as of October of this year + + + align:start position:0% +saying that as of October of this year +if you get arrested in California the + + align:start position:0% +if you get arrested in California the + + + align:start position:0% +if you get arrested in California the +decision of whether you get bail or not + + align:start position:0% +decision of whether you get bail or not + + + align:start position:0% +decision of whether you get bail or not +is going to be made by a computer + + align:start position:0% +is going to be made by a computer + + + align:start position:0% +is going to be made by a computer +algorithm not by a human being + + align:start position:0% +algorithm not by a human being + + + align:start position:0% +algorithm not by a human being +okay so it's not a hundred percent so + + align:start position:0% +okay so it's not a hundred percent so + + + align:start position:0% +okay so it's not a hundred percent so +there is some discretion on the part of + + align:start position:0% +there is some discretion on the part of + + + align:start position:0% +there is some discretion on the part of +this county official who will make a + + align:start position:0% +this county official who will make a + + + align:start position:0% +this county official who will make a +recommendation and the judge ultimately + + align:start position:0% +recommendation and the judge ultimately + + + align:start position:0% +recommendation and the judge ultimately +decides but I suspect that on until + + align:start position:0% +decides but I suspect that on until + + + align:start position:0% +decides but I suspect that on until +there are some egregious outcomes from + + align:start position:0% +there are some egregious outcomes from + + + align:start position:0% +there are some egregious outcomes from +doing this it will probably be quite + + align:start position:0% +doing this it will probably be quite + + + align:start position:0% +doing this it will probably be quite +commonly used + + align:start position:0% + + + + align:start position:0% + +now the critique of these bail + + align:start position:0% +now the critique of these bail + + + align:start position:0% +now the critique of these bail +algorithms is is based on a number of + + align:start position:0% +algorithms is is based on a number of + + + align:start position:0% +algorithms is is based on a number of +different factors one is that the + + align:start position:0% +different factors one is that the + + + align:start position:0% +different factors one is that the +algorithms reflect a severe racial bias + + align:start position:0% +algorithms reflect a severe racial bias + + + align:start position:0% +algorithms reflect a severe racial bias +so for example if you are two identical + + align:start position:0% +so for example if you are two identical + + + align:start position:0% +so for example if you are two identical +people but one of you happens to be + + align:start position:0% +people but one of you happens to be + + + align:start position:0% +people but one of you happens to be +white and one of them have you happens + + align:start position:0% +white and one of them have you happens + + + align:start position:0% +white and one of them have you happens +to be black the chances of you getting + + align:start position:0% +to be black the chances of you getting + + + align:start position:0% +to be black the chances of you getting +bail are much lower if you're black than + + align:start position:0% +bail are much lower if you're black than + + + align:start position:0% +bail are much lower if you're black than +if you're white now you say well how + + align:start position:0% +if you're white now you say well how + + + align:start position:0% +if you're white now you say well how +could that be given that we're learning + + align:start position:0% +could that be given that we're learning + + + align:start position:0% +could that be given that we're learning +this algorithmically well it's a + + align:start position:0% +this algorithmically well it's a + + + align:start position:0% +this algorithmically well it's a +complicated feedback loop because the + + align:start position:0% +complicated feedback loop because the + + + align:start position:0% +complicated feedback loop because the +algorithm is learning from historical + + align:start position:0% +algorithm is learning from historical + + + align:start position:0% +algorithm is learning from historical +data and if historically judges have + + align:start position:0% +data and if historically judges have + + + align:start position:0% +data and if historically judges have +been less likely to grant bail to an + + align:start position:0% +been less likely to grant bail to an + + + align:start position:0% +been less likely to grant bail to an +african-american than to a Caucasian + + align:start position:0% +african-american than to a Caucasian + + + align:start position:0% +african-american than to a Caucasian +American then the algorithm will learn + + align:start position:0% +American then the algorithm will learn + + + align:start position:0% +American then the algorithm will learn +that that's the right thing to do and + + align:start position:0% +that that's the right thing to do and + + + align:start position:0% +that that's the right thing to do and +will nicely incorporate exactly that + + align:start position:0% +will nicely incorporate exactly that + + + align:start position:0% +will nicely incorporate exactly that +prejudice and then the second problem + + align:start position:0% +prejudice and then the second problem + + + align:start position:0% +prejudice and then the second problem +which I consider to be really horrendous + + align:start position:0% +which I consider to be really horrendous + + + align:start position:0% +which I consider to be really horrendous +is that in this particular field the + + align:start position:0% +is that in this particular field the + + + align:start position:0% +is that in this particular field the +algorithms are developed privately by + + align:start position:0% +algorithms are developed privately by + + + align:start position:0% +algorithms are developed privately by +private companies which will not tell + + align:start position:0% +private companies which will not tell + + + align:start position:0% +private companies which will not tell +you what the what their algorithm is you + + align:start position:0% +you what the what their algorithm is you + + + align:start position:0% +you what the what their algorithm is you +can just pay them and they will tell you + + align:start position:0% +can just pay them and they will tell you + + + align:start position:0% +can just pay them and they will tell you +the answer but they won't tell you how + + align:start position:0% +the answer but they won't tell you how + + + align:start position:0% +the answer but they won't tell you how +they compute it they won't tell you what + + align:start position:0% +they compute it they won't tell you what + + + align:start position:0% +they compute it they won't tell you what +data they used to train the algorithm + + align:start position:0% +data they used to train the algorithm + + + align:start position:0% +data they used to train the algorithm +and so it's really a black box and so + + align:start position:0% +and so it's really a black box and so + + + align:start position:0% +and so it's really a black box and so +you have no idea what's going on in that + + align:start position:0% +you have no idea what's going on in that + + + align:start position:0% +you have no idea what's going on in that +box other than by looking at its at its + + align:start position:0% +box other than by looking at its at its + + + align:start position:0% +box other than by looking at its at its +decisions well and so the data + + align:start position:0% +decisions well and so the data + + + align:start position:0% +decisions well and so the data +collection system is flawed in the same + + align:start position:0% +collection system is flawed in the same + + + align:start position:0% +collection system is flawed in the same +way as the judicial system itself so not + + align:start position:0% +way as the judicial system itself so not + + + align:start position:0% +way as the judicial system itself so not +only are there algorithms that decide + + align:start position:0% +only are there algorithms that decide + + + align:start position:0% +only are there algorithms that decide +whether you get bail or not which is + + align:start position:0% +whether you get bail or not which is + + + align:start position:0% +whether you get bail or not which is +after all a relatively temporary + + align:start position:0% +after all a relatively temporary + + + align:start position:0% +after all a relatively temporary +question until your trial comes up + + align:start position:0% +question until your trial comes up + + + align:start position:0% +question until your trial comes up +although that may be a long time but + + align:start position:0% +although that may be a long time but + + + align:start position:0% +although that may be a long time but +there are also algorithms that advise + + align:start position:0% +there are also algorithms that advise + + + align:start position:0% +there are also algorithms that advise +on things like sentencing so they say + + align:start position:0% +on things like sentencing so they say + + + align:start position:0% +on things like sentencing so they say +how likely is this patient to be a + + align:start position:0% +how likely is this patient to be a + + + align:start position:0% +how likely is this patient to be a +recidivist somebody who when they get + + align:start position:0% +recidivist somebody who when they get + + + align:start position:0% +recidivist somebody who when they get +out of jail they're going to offend + + align:start position:0% +out of jail they're going to offend + + + align:start position:0% +out of jail they're going to offend +again and therefore they deserve a + + align:start position:0% +again and therefore they deserve a + + + align:start position:0% +again and therefore they deserve a +longer jail sentence because you want to + + align:start position:0% +longer jail sentence because you want to + + + align:start position:0% +longer jail sentence because you want to +keep them off the streets or if you're + + align:start position:0% +keep them off the streets or if you're + + + align:start position:0% +keep them off the streets or if you're +well so this is a particular story about + + align:start position:0% +well so this is a particular story about + + + align:start position:0% +well so this is a particular story about +a particular person in Wisconsin and + + align:start position:0% +a particular person in Wisconsin and + + + align:start position:0% +a particular person in Wisconsin and +shockingly the state Supreme Court ruled + + align:start position:0% +shockingly the state Supreme Court ruled + + + align:start position:0% +shockingly the state Supreme Court ruled +against the sky saying that knowledge of + + align:start position:0% +against the sky saying that knowledge of + + + align:start position:0% +against the sky saying that knowledge of +the algorithms output was a sufficient + + align:start position:0% +the algorithms output was a sufficient + + + align:start position:0% +the algorithms output was a sufficient +level of transparency in order to not + + align:start position:0% +level of transparency in order to not + + + align:start position:0% +level of transparency in order to not +violate his rights which I think many + + align:start position:0% +violate his rights which I think many + + + align:start position:0% +violate his rights which I think many +people consider to be kind of an + + align:start position:0% +people consider to be kind of an + + + align:start position:0% +people consider to be kind of an +outrageous decision I'm sure it'll be + + align:start position:0% +outrageous decision I'm sure it'll be + + + align:start position:0% +outrageous decision I'm sure it'll be +appealed and may be overturned + + align:start position:0% +appealed and may be overturned + + + align:start position:0% +appealed and may be overturned +conversely I keep doing you know on the + + align:start position:0% +conversely I keep doing you know on the + + + align:start position:0% +conversely I keep doing you know on the +one hand and on the other algorithms + + align:start position:0% +one hand and on the other algorithms + + + align:start position:0% +one hand and on the other algorithms +could help keep people out of jail so + + align:start position:0% +could help keep people out of jail so + + + align:start position:0% +could help keep people out of jail so +there's a a wired article not long ago + + align:start position:0% +there's a a wired article not long ago + + + align:start position:0% +there's a a wired article not long ago +that says we can use algorithms to + + align:start position:0% +that says we can use algorithms to + + + align:start position:0% +that says we can use algorithms to +analyze people's cases and say oh this + + align:start position:0% +analyze people's cases and say oh this + + + align:start position:0% +analyze people's cases and say oh this +person looks like they're really in need + + align:start position:0% +person looks like they're really in need + + + align:start position:0% +person looks like they're really in need +of psychiatric help rather than in need + + align:start position:0% +of psychiatric help rather than in need + + + align:start position:0% +of psychiatric help rather than in need +of jail time and so perhaps we can + + align:start position:0% +of jail time and so perhaps we can + + + align:start position:0% +of jail time and so perhaps we can +divert him from the from the penal + + align:start position:0% +divert him from the from the penal + + + align:start position:0% +divert him from the from the penal +system into psychiatric care and keep + + align:start position:0% +system into psychiatric care and keep + + + align:start position:0% +system into psychiatric care and keep +him out of prison and get him help and + + align:start position:0% +him out of prison and get him help and + + + align:start position:0% +him out of prison and get him help and +so on so that that's the positive side + + align:start position:0% +so on so that that's the positive side + + + align:start position:0% +so on so that that's the positive side +of being able to use these kinds of + + align:start position:0% +of being able to use these kinds of + + + align:start position:0% +of being able to use these kinds of +algorithms now it's not only in + + align:start position:0% +algorithms now it's not only in + + + align:start position:0% +algorithms now it's not only in +criminality there's also a long + + align:start position:0% +criminality there's also a long + + + align:start position:0% +criminality there's also a long +discussion you can find this all over + + align:start position:0% +discussion you can find this all over + + + align:start position:0% +discussion you can find this all over +the web for example can an algorithm + + align:start position:0% +the web for example can an algorithm + + + align:start position:0% +the web for example can an algorithm +hire better than a human being so if + + align:start position:0% +hire better than a human being so if + + + align:start position:0% +hire better than a human being so if +you're a big company and you have a lot + + align:start position:0% +you're a big company and you have a lot + + + align:start position:0% +you're a big company and you have a lot +of people that you're trying to hire for + + align:start position:0% +of people that you're trying to hire for + + + align:start position:0% +of people that you're trying to hire for +various jobs it's very tempting to say + + align:start position:0% +various jobs it's very tempting to say + + + align:start position:0% +various jobs it's very tempting to say +hey I've made lots and lots of hiring + + align:start position:0% +hey I've made lots and lots of hiring + + + align:start position:0% +hey I've made lots and lots of hiring +decisions and we have some outcome data + + align:start position:0% +decisions and we have some outcome data + + + align:start position:0% +decisions and we have some outcome data +I know which people have turned out to + + align:start position:0% +I know which people have turned out to + + + align:start position:0% +I know which people have turned out to +be good employees and which people have + + align:start position:0% +be good employees and which people have + + + align:start position:0% +be good employees and which people have +turned out to be bad employees + + align:start position:0% +turned out to be bad employees + + + align:start position:0% +turned out to be bad employees +and therefore we can base a first cut + + align:start position:0% +and therefore we can base a first cut + + + align:start position:0% +and therefore we can base a first cut +screening method on using such + + align:start position:0% +screening method on using such + + + align:start position:0% +screening method on using such +unlearning such an algorithm and using + + align:start position:0% +unlearning such an algorithm and using + + + align:start position:0% +unlearning such an algorithm and using +it on people who apply for jobs and say + + align:start position:0% +it on people who apply for jobs and say + + + align:start position:0% +it on people who apply for jobs and say +okay these are the ones that we're going + + align:start position:0% +okay these are the ones that we're going + + + align:start position:0% +okay these are the ones that we're going +to interview and maybe hire because they + + align:start position:0% +to interview and maybe hire because they + + + align:start position:0% +to interview and maybe hire because they +look like they're a better bet now I + + align:start position:0% +look like they're a better bet now I + + + align:start position:0% +look like they're a better bet now I +have to tell you a personal story when I + + align:start position:0% +have to tell you a personal story when I + + + align:start position:0% +have to tell you a personal story when I +was an undergraduate at Caltech + + align:start position:0% +was an undergraduate at Caltech + + + align:start position:0% +was an undergraduate at Caltech +the Caltech faculty decided that they + + align:start position:0% +the Caltech faculty decided that they + + + align:start position:0% +the Caltech faculty decided that they +wanted to include student members of all + + align:start position:0% +wanted to include student members of all + + + align:start position:0% +wanted to include student members of all +the faculty committees and so I was + + align:start position:0% +the faculty committees and so I was + + + align:start position:0% +the faculty committees and so I was +lucky enough that I served for three + + align:start position:0% +lucky enough that I served for three + + + align:start position:0% +lucky enough that I served for three +years as a member of the undergraduate + + align:start position:0% +years as a member of the undergraduate + + + align:start position:0% +years as a member of the undergraduate +admissions committee at Caltech and in + + align:start position:0% +admissions committee at Caltech and in + + + align:start position:0% +admissions committee at Caltech and in +those days + + align:start position:0% +those days + + + align:start position:0% +those days +Caltech only took about 220 230 students + + align:start position:0% +Caltech only took about 220 230 students + + + align:start position:0% +Caltech only took about 220 230 students +a year it's a very small school and we + + align:start position:0% +a year it's a very small school and we + + + align:start position:0% +a year it's a very small school and we +would actually fly around the country + + align:start position:0% +would actually fly around the country + + + align:start position:0% +would actually fly around the country +and interview about the top half of all + + align:start position:0% +and interview about the top half of all + + + align:start position:0% +and interview about the top half of all +the applicants in the applicant pool so + + align:start position:0% +the applicants in the applicant pool so + + + align:start position:0% +the applicants in the applicant pool so +we would talk not only to the students + + align:start position:0% +we would talk not only to the students + + + align:start position:0% +we would talk not only to the students +but also to their teachers and their + + align:start position:0% +but also to their teachers and their + + + align:start position:0% +but also to their teachers and their +counselors and see what the environment + + align:start position:0% +counselors and see what the environment + + + align:start position:0% +counselors and see what the environment +was like and I think we got a very good + + align:start position:0% +was like and I think we got a very good + + + align:start position:0% +was like and I think we got a very good +sense of how good a student was likely + + align:start position:0% +sense of how good a student was likely + + + align:start position:0% +sense of how good a student was likely +to be based on that so + + align:start position:0% +to be based on that so + + + align:start position:0% +to be based on that so +one day after the admissions decisions + + align:start position:0% +one day after the admissions decisions + + + align:start position:0% +one day after the admissions decisions +had been made one of the professor's + + align:start position:0% +had been made one of the professor's + + + align:start position:0% +had been made one of the professor's +kind of as a thought experiment said + + align:start position:0% +kind of as a thought experiment said + + + align:start position:0% +kind of as a thought experiment said +here's what we ought to do we ought to + + align:start position:0% +here's what we ought to do we ought to + + + align:start position:0% +here's what we ought to do we ought to +take the 230 people that we've just + + align:start position:0% +take the 230 people that we've just + + + align:start position:0% +take the 230 people that we've just +offered admission to and we should + + align:start position:0% +offered admission to and we should + + + align:start position:0% +offered admission to and we should +reject them all and take the next 230 + + align:start position:0% +reject them all and take the next 230 + + + align:start position:0% +reject them all and take the next 230 +people and then see whether the faculty + + align:start position:0% +people and then see whether the faculty + + + align:start position:0% +people and then see whether the faculty +notices because it seemed like a fairly + + align:start position:0% +notices because it seemed like a fairly + + + align:start position:0% +notices because it seemed like a fairly +flat distribution now of course I and + + align:start position:0% +flat distribution now of course I and + + + align:start position:0% +flat distribution now of course I and +others argued that this would be unfair + + align:start position:0% +others argued that this would be unfair + + + align:start position:0% +others argued that this would be unfair +and unethical and would be you know a + + align:start position:0% +and unethical and would be you know a + + + align:start position:0% +and unethical and would be you know a +waste of all the time that we had put + + align:start position:0% +waste of all the time that we had put + + + align:start position:0% +waste of all the time that we had put +into selecting these people so we didn't + + align:start position:0% +into selecting these people so we didn't + + + align:start position:0% +into selecting these people so we didn't +do that but then this guy went out and + + align:start position:0% +do that but then this guy went out and + + + align:start position:0% +do that but then this guy went out and +he looked at the data we had on people's + + align:start position:0% +he looked at the data we had on people's + + + align:start position:0% +he looked at the data we had on people's +rank in class SAT scores + + align:start position:0% +rank in class SAT scores + + + align:start position:0% +rank in class SAT scores +grade point average the check marks on + + align:start position:0% +grade point average the check marks on + + + align:start position:0% +grade point average the check marks on +their recommendation letters about + + align:start position:0% +their recommendation letters about + + + align:start position:0% +their recommendation letters about +whether they were truly exceptional or + + align:start position:0% +whether they were truly exceptional or + + + align:start position:0% +whether they were truly exceptional or +merely outstanding and and he built a + + align:start position:0% +merely outstanding and and he built a + + + align:start position:0% +merely outstanding and and he built a +logistic regression model that's no it + + align:start position:0% +logistic regression model that's no it + + + align:start position:0% +logistic regression model that's no it +was a linear regression model that + + align:start position:0% +was a linear regression model that + + + align:start position:0% +was a linear regression model that +predicted the person's sophomore level a + + align:start position:0% +predicted the person's sophomore level a + + + align:start position:0% +predicted the person's sophomore level a +grade point average which seemed like a + + align:start position:0% +grade point average which seemed like a + + + align:start position:0% +grade point average which seemed like a +reasonable thing to try to predict and + + align:start position:0% +reasonable thing to try to predict and + + + align:start position:0% +reasonable thing to try to predict and +he got a reasonably good fit but what + + align:start position:0% +he got a reasonably good fit but what + + + align:start position:0% +he got a reasonably good fit but what +was disturbing about it is that at in + + align:start position:0% +was disturbing about it is that at in + + + align:start position:0% +was disturbing about it is that at in +the Caltech population of students it + + align:start position:0% +the Caltech population of students it + + + align:start position:0% +the Caltech population of students it +turned out that the beta for your SAT + + align:start position:0% +turned out that the beta for your SAT + + + align:start position:0% +turned out that the beta for your SAT +English performance was negative okay so + + align:start position:0% +English performance was negative okay so + + + align:start position:0% +English performance was negative okay so +if you did particularly well in English + + align:start position:0% +if you did particularly well in English + + + align:start position:0% +if you did particularly well in English +on the SAT you were likely to do worse + + align:start position:0% +on the SAT you were likely to do worse + + + align:start position:0% +on the SAT you were likely to do worse +as a sophomore at Caltech than if you + + align:start position:0% +as a sophomore at Caltech than if you + + + align:start position:0% +as a sophomore at Caltech than if you +didn't do as well and so we we thought + + align:start position:0% +didn't do as well and so we we thought + + + align:start position:0% +didn't do as well and so we we thought +about that a lot of course we decided + + align:start position:0% +about that a lot of course we decided + + + align:start position:0% +about that a lot of course we decided +that that would be really unfair to + + align:start position:0% +that that would be really unfair to + + + align:start position:0% +that that would be really unfair to +penalize somebody for being good at + + align:start position:0% +penalize somebody for being good at + + + align:start position:0% +penalize somebody for being good at +something + + align:start position:0% +something + + + align:start position:0% +something +especially when the school had this + + align:start position:0% +especially when the school had this + + + align:start position:0% +especially when the school had this +philosophical orientation that said we + + align:start position:0% +philosophical orientation that said we + + + align:start position:0% +philosophical orientation that said we +ought to look for people with broad + + align:start position:0% +ought to look for people with broad + + + align:start position:0% +ought to look for people with broad +education so that's a just an example + + align:start position:0% +education so that's a just an example + + + align:start position:0% +education so that's a just an example +and more Science Friday had a nice show + + align:start position:0% +and more Science Friday had a nice show + + + align:start position:0% +and more Science Friday had a nice show +that you can listen to about this issue + + align:start position:0% +that you can listen to about this issue + + + align:start position:0% +that you can listen to about this issue +so let me ask you what do you mean by + + align:start position:0% +so let me ask you what do you mean by + + + align:start position:0% +so let me ask you what do you mean by +fairness what you know if we're going to + + align:start position:0% +fairness what you know if we're going to + + + align:start position:0% +fairness what you know if we're going to +define the concept + + align:start position:0% + + + + align:start position:0% + +what is fair + + align:start position:0% + + + + align:start position:0% + +what characteristics would you like to + + align:start position:0% +what characteristics would you like to + + + align:start position:0% +what characteristics would you like to +have an algorithm have that judges you + + align:start position:0% +have an algorithm have that judges you + + + align:start position:0% +have an algorithm have that judges you +for some particular purpose yeah okay so + + align:start position:0% +for some particular purpose yeah okay so + + + align:start position:0% +for some particular purpose yeah okay so +similar error rates is definitely one of + + align:start position:0% +similar error rates is definitely one of + + + align:start position:0% +similar error rates is definitely one of +the criteria that people use in talking + + align:start position:0% +the criteria that people use in talking + + + align:start position:0% +the criteria that people use in talking +about fairness and you'll see later + + align:start position:0% +about fairness and you'll see later + + + align:start position:0% +about fairness and you'll see later +Irene where's Irene right there + + align:start position:0% +Irene where's Irene right there + + + align:start position:0% +Irene where's Irene right there +Irene is is a master of that notion of + + align:start position:0% +Irene is is a master of that notion of + + + align:start position:0% +Irene is is a master of that notion of +fairness yeah when the model says + + align:start position:0% +fairness yeah when the model says + + + align:start position:0% +fairness yeah when the model says +observation that causally shouldn't be + + align:start position:0% +observation that causally shouldn't be + + + align:start position:0% +observation that causally shouldn't be +true and what I want to say + + align:start position:0% + + + + align:start position:0% + +so I'm not sure how to capture that and + + align:start position:0% +so I'm not sure how to capture that and + + + align:start position:0% +so I'm not sure how to capture that and +a short phrase societal goals but that's + + align:start position:0% +a short phrase societal goals but that's + + + align:start position:0% +a short phrase societal goals but that's +tricky right I mean suppose that I would + + align:start position:0% +tricky right I mean suppose that I would + + + align:start position:0% +tricky right I mean suppose that I would +like it to be the case that the fraction + + align:start position:0% +like it to be the case that the fraction + + + align:start position:0% +like it to be the case that the fraction +of people of different ethnicity who are + + align:start position:0% +of people of different ethnicity who are + + + align:start position:0% +of people of different ethnicity who are +criminals should be the same right that + + align:start position:0% +criminals should be the same right that + + + align:start position:0% +criminals should be the same right that +seems like a good goal for fairness how + + align:start position:0% +seems like a good goal for fairness how + + + align:start position:0% +seems like a good goal for fairness how +do I achieve that I mean I could pretend + + align:start position:0% +do I achieve that I mean I could pretend + + + align:start position:0% +do I achieve that I mean I could pretend +that it's the same but it isn't the same + + align:start position:0% +that it's the same but it isn't the same + + + align:start position:0% +that it's the same but it isn't the same +today + + align:start position:0% +today + + + align:start position:0% +today +objectively and the data wouldn't + + align:start position:0% +objectively and the data wouldn't + + + align:start position:0% +objectively and the data wouldn't +support that so that that's an issue + + align:start position:0% +support that so that that's an issue + + + align:start position:0% +support that so that that's an issue +yeah similar people should lead to + + align:start position:0% +yeah similar people should lead to + + + align:start position:0% +yeah similar people should lead to +similar treatment yeah I like that + + align:start position:0% +similar treatment yeah I like that + + + align:start position:0% +similar treatment yeah I like that +I know it's another it's another of the + + align:start position:0% +I know it's another it's another of the + + + align:start position:0% +I know it's another it's another of the +classic sort of notions of fairness that + + align:start position:0% +classic sort of notions of fairness that + + + align:start position:0% +classic sort of notions of fairness that +puts a lot of weight on the on the + + align:start position:0% +puts a lot of weight on the on the + + + align:start position:0% +puts a lot of weight on the on the +distance function right in what way are + + align:start position:0% +distance function right in what way are + + + align:start position:0% +distance function right in what way are +two people similar and what + + align:start position:0% +two people similar and what + + + align:start position:0% +two people similar and what +characteristics you obviously don't want + + align:start position:0% +characteristics you obviously don't want + + + align:start position:0% +characteristics you obviously don't want +to use the sensitive characteristics the + + align:start position:0% +to use the sensitive characteristics the + + + align:start position:0% +to use the sensitive characteristics the +forbidden characteristics in order to + + align:start position:0% +forbidden characteristics in order to + + + align:start position:0% +forbidden characteristics in order to +decide similarity because then people + + align:start position:0% +decide similarity because then people + + + align:start position:0% +decide similarity because then people +will be dissimilar in ways that you + + align:start position:0% +will be dissimilar in ways that you + + + align:start position:0% +will be dissimilar in ways that you +don't want but defining that function is + + align:start position:0% +don't want but defining that function is + + + align:start position:0% +don't want but defining that function is +a challenge all right well let me let me + + align:start position:0% +a challenge all right well let me let me + + + align:start position:0% +a challenge all right well let me let me +show you a more technical approach to + + align:start position:0% +show you a more technical approach to + + + align:start position:0% +show you a more technical approach to +thinking about this so we all know about + + align:start position:0% +thinking about this so we all know about + + + align:start position:0% +thinking about this so we all know about +biases like selection by a sampling bias + + align:start position:0% +biases like selection by a sampling bias + + + align:start position:0% +biases like selection by a sampling bias +reporting bias etc these are in the + + align:start position:0% +reporting bias etc these are in the + + + align:start position:0% +reporting bias etc these are in the +conventional sense of the term bias but + + align:start position:0% +conventional sense of the term bias but + + + align:start position:0% +conventional sense of the term bias but +I'll show you an example that + + align:start position:0% +I'll show you an example that + + + align:start position:0% +I'll show you an example that +I got involved in Raj man ray is was a + + align:start position:0% +I got involved in Raj man ray is was a + + + align:start position:0% +I got involved in Raj man ray is was a +MIT Harvard HST student and he started + + align:start position:0% +MIT Harvard HST student and he started + + + align:start position:0% +MIT Harvard HST student and he started +looking at the question of the genetics + + align:start position:0% +looking at the question of the genetics + + + align:start position:0% +looking at the question of the genetics +that was used in order to determine + + align:start position:0% +that was used in order to determine + + + align:start position:0% +that was used in order to determine +whether somebody is at risk for cardio + + align:start position:0% +whether somebody is at risk for cardio + + + align:start position:0% +whether somebody is at risk for cardio +Maya for cardiomyopathy hypertrophic + + align:start position:0% +Maya for cardiomyopathy hypertrophic + + + align:start position:0% +Maya for cardiomyopathy hypertrophic +cardiomyopathy that's a big word it + + align:start position:0% +cardiomyopathy that's a big word it + + + align:start position:0% +cardiomyopathy that's a big word it +means that your heart gets too big and + + align:start position:0% +means that your heart gets too big and + + + align:start position:0% +means that your heart gets too big and +it becomes sort of flabby and it starts + + align:start position:0% +it becomes sort of flabby and it starts + + + align:start position:0% +it becomes sort of flabby and it starts +it stops pumping well and eventually you + + align:start position:0% +it stops pumping well and eventually you + + + align:start position:0% +it stops pumping well and eventually you +die of this disease at a relatively + + align:start position:0% +die of this disease at a relatively + + + align:start position:0% +die of this disease at a relatively +young age if in fact you have it and so + + align:start position:0% +young age if in fact you have it and so + + + align:start position:0% +young age if in fact you have it and so +what happened is that there was a a + + align:start position:0% +what happened is that there was a a + + + align:start position:0% +what happened is that there was a a +study that was done mostly with European + + align:start position:0% +study that was done mostly with European + + + align:start position:0% +study that was done mostly with European +populations where they discovered that a + + align:start position:0% +populations where they discovered that a + + + align:start position:0% +populations where they discovered that a +lot of people who had this disease had a + + align:start position:0% +lot of people who had this disease had a + + + align:start position:0% +lot of people who had this disease had a +certain genetic variant and they said + + align:start position:0% +certain genetic variant and they said + + + align:start position:0% +certain genetic variant and they said +well that must be the cause of this + + align:start position:0% +well that must be the cause of this + + + align:start position:0% +well that must be the cause of this +disease and so it became accepted wisdom + + align:start position:0% +disease and so it became accepted wisdom + + + align:start position:0% +disease and so it became accepted wisdom +that if you had that genetic variant + + align:start position:0% +that if you had that genetic variant + + + align:start position:0% +that if you had that genetic variant +people would counsel you to not plan on + + align:start position:0% +people would counsel you to not plan on + + + align:start position:0% +people would counsel you to not plan on +living along life and you know this has + + align:start position:0% +living along life and you know this has + + + align:start position:0% +living along life and you know this has +all kinds of consequences imagine if + + align:start position:0% +all kinds of consequences imagine if + + + align:start position:0% +all kinds of consequences imagine if +you're thinking about having a kid when + + align:start position:0% +you're thinking about having a kid when + + + align:start position:0% +you're thinking about having a kid when +you're in your early 40s and your life + + align:start position:0% +you're in your early 40s and your life + + + align:start position:0% +you're in your early 40s and your life +expectancy is 55 would you want to die + + align:start position:0% +expectancy is 55 would you want to die + + + align:start position:0% +expectancy is 55 would you want to die +when you have a teenager that you leave + + align:start position:0% +when you have a teenager that you leave + + + align:start position:0% +when you have a teenager that you leave +to your spouse so this is a + + align:start position:0% +to your spouse so this is a + + + align:start position:0% +to your spouse so this is a +consequential set of decisions that + + align:start position:0% +consequential set of decisions that + + + align:start position:0% +consequential set of decisions that +people have to make now what happened is + + align:start position:0% +people have to make now what happened is + + + align:start position:0% +people have to make now what happened is +that in the u.s. there were tests of + + align:start position:0% +that in the u.s. there were tests of + + + align:start position:0% +that in the u.s. there were tests of +this sort done but the problem was that + + align:start position:0% +this sort done but the problem was that + + + align:start position:0% +this sort done but the problem was that +a lot of African and African American + + align:start position:0% +a lot of African and African American + + + align:start position:0% +a lot of African and African American +populations turn out to have this + + align:start position:0% +populations turn out to have this + + + align:start position:0% +populations turn out to have this +genetic variant frequently without + + align:start position:0% +genetic variant frequently without + + + align:start position:0% +genetic variant frequently without +developing this terrible disease but + + align:start position:0% +developing this terrible disease but + + + align:start position:0% +developing this terrible disease but +they were all told that they were going + + align:start position:0% +they were all told that they were going + + + align:start position:0% +they were all told that they were going +to die basically and it was only after + + align:start position:0% +to die basically and it was only after + + + align:start position:0% +to die basically and it was only after +years when people noticed that these + + align:start position:0% +years when people noticed that these + + + align:start position:0% +years when people noticed that these +people who were supposed to die + + align:start position:0% +people who were supposed to die + + + align:start position:0% +people who were supposed to die +genetically weren't dying that they said + + align:start position:0% +genetically weren't dying that they said + + + align:start position:0% +genetically weren't dying that they said +hmm maybe we've misunderstood something + + align:start position:0% +hmm maybe we've misunderstood something + + + align:start position:0% +hmm maybe we've misunderstood something +and what they misunderstood was that the + + align:start position:0% +and what they misunderstood was that the + + + align:start position:0% +and what they misunderstood was that the +population that was used to develop the + + align:start position:0% +population that was used to develop the + + + align:start position:0% +population that was used to develop the +model was a Europe was a European + + align:start position:0% +model was a Europe was a European + + + align:start position:0% +model was a Europe was a European +ancestry population and not an African + + align:start position:0% +ancestry population and not an African + + + align:start position:0% +ancestry population and not an African +ancestry population so you go well we + + align:start position:0% +ancestry population so you go well we + + + align:start position:0% +ancestry population so you go well we +must have learned that lesson so this + + align:start position:0% +must have learned that lesson so this + + + align:start position:0% +must have learned that lesson so this +paper was published in 2016 and this was + + align:start position:0% +paper was published in 2016 and this was + + + align:start position:0% +paper was published in 2016 and this was +one of the first in this area here's a + + align:start position:0% +one of the first in this area here's a + + + align:start position:0% +one of the first in this area here's a +paper that was published three weeks ago + + align:start position:0% +paper that was published three weeks ago + + + align:start position:0% +paper that was published three weeks ago +in Nature scientific reports that says + + align:start position:0% +in Nature scientific reports that says + + + align:start position:0% +in Nature scientific reports that says +hmm genetic risk factors identified in + + align:start position:0% +hmm genetic risk factors identified in + + + align:start position:0% +hmm genetic risk factors identified in +populations of European descent do not + + align:start position:0% +populations of European descent do not + + + align:start position:0% +populations of European descent do not +improve the prediction of osteoporotic + + align:start position:0% +improve the prediction of osteoporotic + + + align:start position:0% +improve the prediction of osteoporotic +fracture and bone mineral density in + + align:start position:0% +fracture and bone mineral density in + + + align:start position:0% +fracture and bone mineral density in +Chinese populations so it's the same + + align:start position:0% +Chinese populations so it's the same + + + align:start position:0% +Chinese populations so it's the same +story it's exactly the same story + + align:start position:0% +story it's exactly the same story + + + align:start position:0% +story it's exactly the same story +different disease the consequence is + + align:start position:0% +different disease the consequence is + + + align:start position:0% +different disease the consequence is +probably less dire because being told + + align:start position:0% +probably less dire because being told + + + align:start position:0% +probably less dire because being told +that you're gonna break your bones when + + align:start position:0% +that you're gonna break your bones when + + + align:start position:0% +that you're gonna break your bones when +you're old is not as bad as being told + + align:start position:0% +you're old is not as bad as being told + + + align:start position:0% +you're old is not as bad as being told +that your heart's gonna stop working + + align:start position:0% +that your heart's gonna stop working + + + align:start position:0% +that your heart's gonna stop working +when you're in your 50s but there we + + align:start position:0% +when you're in your 50s but there we + + + align:start position:0% +when you're in your 50s but there we +have it okay so technically where does + + align:start position:0% +have it okay so technically where does + + + align:start position:0% +have it okay so technically where does +bias come from well I mentioned the + + align:start position:0% +bias come from well I mentioned the + + + align:start position:0% +bias come from well I mentioned the +standard sources but here's an + + align:start position:0% +standard sources but here's an + + + align:start position:0% +standard sources but here's an +interesting analysis this comes from + + align:start position:0% +interesting analysis this comes from + + + align:start position:0% +interesting analysis this comes from +Constantin Alif Eris from a number of + + align:start position:0% +Constantin Alif Eris from a number of + + + align:start position:0% +Constantin Alif Eris from a number of +years ago 2006 and he says well look in + + align:start position:0% +years ago 2006 and he says well look in + + + align:start position:0% +years ago 2006 and he says well look in +a perfect world if I give you a data set + + align:start position:0% +a perfect world if I give you a data set + + + align:start position:0% +a perfect world if I give you a data set +there's an uncountably infinite number + + align:start position:0% +there's an uncountably infinite number + + + align:start position:0% +there's an uncountably infinite number +of models that might possibly explain + + align:start position:0% +of models that might possibly explain + + + align:start position:0% +of models that might possibly explain +the relationships and that data okay + + align:start position:0% +the relationships and that data okay + + + align:start position:0% +the relationships and that data okay +I cannot enumerate an uncountable number + + align:start position:0% +I cannot enumerate an uncountable number + + + align:start position:0% +I cannot enumerate an uncountable number +of models and so what I'm going to do is + + align:start position:0% +of models and so what I'm going to do is + + + align:start position:0% +of models and so what I'm going to do is +choose some family of models to try to + + align:start position:0% +choose some family of models to try to + + + align:start position:0% +choose some family of models to try to +fit and then I'm gonna use some fitting + + align:start position:0% +fit and then I'm gonna use some fitting + + + align:start position:0% +fit and then I'm gonna use some fitting +technique like stochastic gradient + + align:start position:0% +technique like stochastic gradient + + + align:start position:0% +technique like stochastic gradient +descent or something that will find + + align:start position:0% +descent or something that will find + + + align:start position:0% +descent or something that will find +maybe a global optimum but maybe not + + align:start position:0% +maybe a global optimum but maybe not + + + align:start position:0% +maybe a global optimum but maybe not +maybe it'll + + align:start position:0% +maybe it'll + + + align:start position:0% +maybe it'll +find the local optimum and then there's + + align:start position:0% +find the local optimum and then there's + + + align:start position:0% +find the local optimum and then there's +noise and so his observation is that if + + align:start position:0% +noise and so his observation is that if + + + align:start position:0% +noise and so his observation is that if +you count oh as the optimal possible + + align:start position:0% +you count oh as the optimal possible + + + align:start position:0% +you count oh as the optimal possible +model overall possible model families + + align:start position:0% +model overall possible model families + + + align:start position:0% +model overall possible model families +and if you count L as the best model + + align:start position:0% +and if you count L as the best model + + + align:start position:0% +and if you count L as the best model +that's learn about by a particular + + align:start position:0% +that's learn about by a particular + + + align:start position:0% +that's learn about by a particular +learning mechanism and you call and you + + align:start position:0% +learning mechanism and you call and you + + + align:start position:0% +learning mechanism and you call and you +call a the actual model that's learned + + align:start position:0% +call a the actual model that's learned + + + align:start position:0% +call a the actual model that's learned +then the bias is essentially o minus L + + align:start position:0% +then the bias is essentially o minus L + + + align:start position:0% +then the bias is essentially o minus L +so its limitation of learning method + + align:start position:0% +so its limitation of learning method + + + align:start position:0% +so its limitation of learning method +related to the target model the the + + align:start position:0% +related to the target model the the + + + align:start position:0% +related to the target model the the +variance is like L minus a it's the + + align:start position:0% +variance is like L minus a it's the + + + align:start position:0% +variance is like L minus a it's the +error that's due to the particular way + + align:start position:0% +error that's due to the particular way + + + align:start position:0% +error that's due to the particular way +in which you learned things like + + align:start position:0% +in which you learned things like + + + align:start position:0% +in which you learned things like +sampling and so on okay and you can + + align:start position:0% +sampling and so on okay and you can + + + align:start position:0% +sampling and so on okay and you can +estimate the significance of differences + + align:start position:0% +estimate the significance of differences + + + align:start position:0% +estimate the significance of differences +between different models by just + + align:start position:0% +between different models by just + + + align:start position:0% +between different models by just +permuting the data randomizing + + align:start position:0% +permuting the data randomizing + + + align:start position:0% +permuting the data randomizing +essentially the relationships and the + + align:start position:0% +essentially the relationships and the + + + align:start position:0% +essentially the relationships and the +data and then you get a curve of + + align:start position:0% +data and then you get a curve of + + + align:start position:0% +data and then you get a curve of +performance of those models and if yours + + align:start position:0% +performance of those models and if yours + + + align:start position:0% +performance of those models and if yours +lies outside the 95 percent confidence + + align:start position:0% +lies outside the 95 percent confidence + + + align:start position:0% +lies outside the 95 percent confidence +interval then you have a P equal point + + align:start position:0% +interval then you have a P equal point + + + align:start position:0% +interval then you have a P equal point +zero 5 result that this model is not + + align:start position:0% +zero 5 result that this model is not + + + align:start position:0% +zero 5 result that this model is not +random okay so that's the typical way of + + align:start position:0% +random okay so that's the typical way of + + + align:start position:0% +random okay so that's the typical way of +doing about this now you might say but + + align:start position:0% + + + + align:start position:0% + +isn't discrimination the very reason we + + align:start position:0% +isn't discrimination the very reason we + + + align:start position:0% +isn't discrimination the very reason we +do machine learning not discrimination + + align:start position:0% +do machine learning not discrimination + + + align:start position:0% +do machine learning not discrimination +in the legal sense but discrimination in + + align:start position:0% +in the legal sense but discrimination in + + + align:start position:0% +in the legal sense but discrimination in +the sense of separating different + + align:start position:0% +the sense of separating different + + + align:start position:0% +the sense of separating different +populations and so you could say well + + align:start position:0% +populations and so you could say well + + + align:start position:0% +populations and so you could say well +yes but some basis for differentiation + + align:start position:0% +yes but some basis for differentiation + + + align:start position:0% +yes but some basis for differentiation +are justified and some basis for + + align:start position:0% +are justified and some basis for + + + align:start position:0% +are justified and some basis for +differentiation are not justified so + + align:start position:0% +differentiation are not justified so + + + align:start position:0% +differentiation are not justified so +they're either practically irrelevant or + + align:start position:0% +they're either practically irrelevant or + + + align:start position:0% +they're either practically irrelevant or +we decide for societal goals that we + + align:start position:0% +we decide for societal goals that we + + + align:start position:0% +we decide for societal goals that we +want them to be irrelevant and we're not + + align:start position:0% +want them to be irrelevant and we're not + + + align:start position:0% +want them to be irrelevant and we're not +going to take them into account + + align:start position:0% +going to take them into account + + + align:start position:0% +going to take them into account +so one lesson from people who + + align:start position:0% +so one lesson from people who + + + align:start position:0% +so one lesson from people who +this for a while is that discrimination + + align:start position:0% +this for a while is that discrimination + + + align:start position:0% +this for a while is that discrimination +is domain-specific so you can't define a + + align:start position:0% +is domain-specific so you can't define a + + + align:start position:0% +is domain-specific so you can't define a +universal notion of what it means to + + align:start position:0% +universal notion of what it means to + + + align:start position:0% +universal notion of what it means to +discriminate because it's very much tied + + align:start position:0% +discriminate because it's very much tied + + + align:start position:0% +discriminate because it's very much tied +to these questions of what is + + align:start position:0% +to these questions of what is + + + align:start position:0% +to these questions of what is +practically and morally irrelevant in + + align:start position:0% +practically and morally irrelevant in + + + align:start position:0% +practically and morally irrelevant in +the decisions that you're making and so + + align:start position:0% +the decisions that you're making and so + + + align:start position:0% +the decisions that you're making and so +it's going to be different in criminal + + align:start position:0% +it's going to be different in criminal + + + align:start position:0% +it's going to be different in criminal +law than it is in medicine than it is in + + align:start position:0% +law than it is in medicine than it is in + + + align:start position:0% +law than it is in medicine than it is in +hiring than it is in various other + + align:start position:0% +hiring than it is in various other + + + align:start position:0% +hiring than it is in various other +fields college admissions for example + + align:start position:0% +fields college admissions for example + + + align:start position:0% +fields college admissions for example +and its feature specific as well so you + + align:start position:0% +and its feature specific as well so you + + + align:start position:0% +and its feature specific as well so you +have to take the individual features + + align:start position:0% +have to take the individual features + + + align:start position:0% +have to take the individual features +into account well historically the + + align:start position:0% +into account well historically the + + + align:start position:0% +into account well historically the +government has tried to regulate these + + align:start position:0% +government has tried to regulate these + + + align:start position:0% +government has tried to regulate these +domains and so credit is regulated by + + align:start position:0% +domains and so credit is regulated by + + + align:start position:0% +domains and so credit is regulated by +the Equal Credit Opportunity Act + + align:start position:0% +the Equal Credit Opportunity Act + + + align:start position:0% +the Equal Credit Opportunity Act +education by the Civil Rights Act and + + align:start position:0% +education by the Civil Rights Act and + + + align:start position:0% +education by the Civil Rights Act and +various amendments employment by the + + align:start position:0% +various amendments employment by the + + + align:start position:0% +various amendments employment by the +Civil Rights Act housing by the Fair + + align:start position:0% +Civil Rights Act housing by the Fair + + + align:start position:0% +Civil Rights Act housing by the Fair +Housing Act public accommodation by the + + align:start position:0% +Housing Act public accommodation by the + + + align:start position:0% +Housing Act public accommodation by the +Civil Rights Act + + align:start position:0% +Civil Rights Act + + + align:start position:0% +Civil Rights Act +more recently marriage is regulated by + + align:start position:0% +more recently marriage is regulated by + + + align:start position:0% +more recently marriage is regulated by +the originally by the Defense of + + align:start position:0% +the originally by the Defense of + + + align:start position:0% +the originally by the Defense of +Marriage Act which as you might tell + + align:start position:0% +Marriage Act which as you might tell + + + align:start position:0% +Marriage Act which as you might tell +from its title was against things like + + align:start position:0% +from its title was against things like + + + align:start position:0% +from its title was against things like +people being able to marry who were not + + align:start position:0% +people being able to marry who were not + + + align:start position:0% +people being able to marry who were not +the traditional marriage that they + + align:start position:0% +the traditional marriage that they + + + align:start position:0% +the traditional marriage that they +wanted to defend but it was struck down + + align:start position:0% +wanted to defend but it was struck down + + + align:start position:0% +wanted to defend but it was struck down +by the Supreme Court about six years ago + + align:start position:0% +by the Supreme Court about six years ago + + + align:start position:0% +by the Supreme Court about six years ago +as being discriminatory it's interesting + + align:start position:0% +as being discriminatory it's interesting + + + align:start position:0% +as being discriminatory it's interesting +if you look back to probably before you + + align:start position:0% +if you look back to probably before you + + + align:start position:0% +if you look back to probably before you +guys who were born in 1967 until 1967 it + + align:start position:0% +guys who were born in 1967 until 1967 it + + + align:start position:0% +guys who were born in 1967 until 1967 it +was illegal for a an African American + + align:start position:0% +was illegal for a an African American + + + align:start position:0% +was illegal for a an African American +and a white to marry each other in + + align:start position:0% +and a white to marry each other in + + + align:start position:0% +and a white to marry each other in +Virginia okay it was literally illegal + + align:start position:0% +Virginia okay it was literally illegal + + + align:start position:0% +Virginia okay it was literally illegal +if you want to get a marriage license + + align:start position:0% +if you want to get a marriage license + + + align:start position:0% +if you want to get a marriage license +you you were denied and if you got + + align:start position:0% +you you were denied and if you got + + + align:start position:0% +you you were denied and if you got +married out of state and came back you + + align:start position:0% +married out of state and came back you + + + align:start position:0% +married out of state and came back you +could be arrested this happened much + + align:start position:0% +could be arrested this happened much + + + align:start position:0% +could be arrested this happened much +later Trevor Noah if you know him from + + align:start position:0% +later Trevor Noah if you know him from + + + align:start position:0% +later Trevor Noah if you know him from +The Daily Show wrote a book called born + + align:start position:0% +The Daily Show wrote a book called born + + + align:start position:0% +The Daily Show wrote a book called born +born a crime I think + + align:start position:0% +born a crime I think + + + align:start position:0% +born a crime I think +and his father is white Swiss guy and + + align:start position:0% +and his father is white Swiss guy and + + + align:start position:0% +and his father is white Swiss guy and +his mother is a South African plaque and + + align:start position:0% +his mother is a South African plaque and + + + align:start position:0% +his mother is a South African plaque and +so it was literally illegal for him to + + align:start position:0% +so it was literally illegal for him to + + + align:start position:0% +so it was literally illegal for him to +exist under the apartheid laws that they + + align:start position:0% +exist under the apartheid laws that they + + + align:start position:0% +exist under the apartheid laws that they +had and he had to pretend to be his + + align:start position:0% +had and he had to pretend to be his + + + align:start position:0% +had and he had to pretend to be his +mother was his caretaker or rather than + + align:start position:0% +mother was his caretaker or rather than + + + align:start position:0% +mother was his caretaker or rather than +rather than his mother in order to be + + align:start position:0% +rather than his mother in order to be + + + align:start position:0% +rather than his mother in order to be +able to go out in public because + + align:start position:0% +able to go out in public because + + + align:start position:0% +able to go out in public because +otherwise they would get arrested so + + align:start position:0% +otherwise they would get arrested so + + + align:start position:0% +otherwise they would get arrested so +this is recently of course also + + align:start position:0% +this is recently of course also + + + align:start position:0% +this is recently of course also +disappeared but these are some of the of + + align:start position:0% +disappeared but these are some of the of + + + align:start position:0% +disappeared but these are some of the of +the regulatory issues so here are some + + align:start position:0% +the regulatory issues so here are some + + + align:start position:0% +the regulatory issues so here are some +of the legally recognized protected + + align:start position:0% +of the legally recognized protected + + + align:start position:0% +of the legally recognized protected +classes race color sex religion national + + align:start position:0% +classes race color sex religion national + + + align:start position:0% +classes race color sex religion national +origin citizenship age pregnancy + + align:start position:0% +origin citizenship age pregnancy + + + align:start position:0% +origin citizenship age pregnancy +familial status disability veteran + + align:start position:0% +familial status disability veteran + + + align:start position:0% +familial status disability veteran +status and more recently sexual + + align:start position:0% +status and more recently sexual + + + align:start position:0% +status and more recently sexual +orientation in certain jurisdictions but + + align:start position:0% +orientation in certain jurisdictions but + + + align:start position:0% +orientation in certain jurisdictions but +not everywhere around the country okay + + align:start position:0% +not everywhere around the country okay + + + align:start position:0% +not everywhere around the country okay +so given those examples there are two + + align:start position:0% +so given those examples there are two + + + align:start position:0% +so given those examples there are two +legal doctrines about discrimination and + + align:start position:0% +legal doctrines about discrimination and + + + align:start position:0% +legal doctrines about discrimination and +one of them talks about disparate + + align:start position:0% +one of them talks about disparate + + + align:start position:0% +one of them talks about disparate +treatment which is sort of related to + + align:start position:0% +treatment which is sort of related to + + + align:start position:0% +treatment which is sort of related to +this one and the other talks about + + align:start position:0% +this one and the other talks about + + + align:start position:0% +this one and the other talks about +disparate impact and says no matter what + + align:start position:0% +disparate impact and says no matter what + + + align:start position:0% +disparate impact and says no matter what +the mechanism is if the outcome is very + + align:start position:0% +the mechanism is if the outcome is very + + + align:start position:0% +the mechanism is if the outcome is very +different for different racial groups + + align:start position:0% +different for different racial groups + + + align:start position:0% +different for different racial groups +typically or gender groups then there's + + align:start position:0% +typically or gender groups then there's + + + align:start position:0% +typically or gender groups then there's +prima facie evidence that there's + + align:start position:0% +prima facie evidence that there's + + + align:start position:0% +prima facie evidence that there's +something not right that there's some + + align:start position:0% +something not right that there's some + + + align:start position:0% +something not right that there's some +sort of discrimination now the problem + + align:start position:0% +sort of discrimination now the problem + + + align:start position:0% +sort of discrimination now the problem +is how do you defend yourself against + + align:start position:0% +is how do you defend yourself against + + + align:start position:0% +is how do you defend yourself against +for example a disparate impact argument + + align:start position:0% +for example a disparate impact argument + + + align:start position:0% +for example a disparate impact argument +well you say it's it it in order to be a + + align:start position:0% +well you say it's it it in order to be a + + + align:start position:0% +well you say it's it it in order to be a +disparate impact that's illegal + + align:start position:0% +disparate impact that's illegal + + + align:start position:0% +disparate impact that's illegal +it has to be unjustified or avoidable so + + align:start position:0% +it has to be unjustified or avoidable so + + + align:start position:0% +it has to be unjustified or avoidable so +for example suppose I'm trying to hire + + align:start position:0% +for example suppose I'm trying to hire + + + align:start position:0% +for example suppose I'm trying to hire +people to + + align:start position:0% +people to + + + align:start position:0% +people to +climb 50 storey buildings that are under + + align:start position:0% +climb 50 storey buildings that are under + + + align:start position:0% +climb 50 storey buildings that are under +construction and you apply but it turns + + align:start position:0% +construction and you apply but it turns + + + align:start position:0% +construction and you apply but it turns +out you have a medical condition which + + align:start position:0% +out you have a medical condition which + + + align:start position:0% +out you have a medical condition which +is that you get dizzy at times right I + + align:start position:0% +is that you get dizzy at times right I + + + align:start position:0% +is that you get dizzy at times right I +might say you know what I don't want to + + align:start position:0% +might say you know what I don't want to + + + align:start position:0% +might say you know what I don't want to +hire you because I don't want you + + align:start position:0% +hire you because I don't want you + + + align:start position:0% +hire you because I don't want you +plopping off the 50th floor of a + + align:start position:0% +plopping off the 50th floor of a + + + align:start position:0% +plopping off the 50th floor of a +building that's under construction and + + align:start position:0% +building that's under construction and + + + align:start position:0% +building that's under construction and +that's probably a reasonable defense if + + align:start position:0% +that's probably a reasonable defense if + + + align:start position:0% +that's probably a reasonable defense if +I brought suit against you and said hey + + align:start position:0% +I brought suit against you and said hey + + + align:start position:0% +I brought suit against you and said hey +you're discriminating against me on the + + align:start position:0% +you're discriminating against me on the + + + align:start position:0% +you're discriminating against me on the +basis of this medical disability a + + align:start position:0% +basis of this medical disability a + + + align:start position:0% +basis of this medical disability a +perfectly good defense is yeah it's true + + align:start position:0% +perfectly good defense is yeah it's true + + + align:start position:0% +perfectly good defense is yeah it's true +but it's relevant to the job so that's + + align:start position:0% +but it's relevant to the job so that's + + + align:start position:0% +but it's relevant to the job so that's +one way of dealing with it now how do + + align:start position:0% +one way of dealing with it now how do + + + align:start position:0% +one way of dealing with it now how do +you demonstrate this brute impact well + + align:start position:0% +you demonstrate this brute impact well + + + align:start position:0% +you demonstrate this brute impact well +the court has decided that you need to + + align:start position:0% +the court has decided that you need to + + + align:start position:0% +the court has decided that you need to +be able to show about a 20% difference + + align:start position:0% +be able to show about a 20% difference + + + align:start position:0% +be able to show about a 20% difference +in order to call something disparate + + align:start position:0% +in order to call something disparate + + + align:start position:0% +in order to call something disparate +impact so the question of course is can + + align:start position:0% +impact so the question of course is can + + + align:start position:0% +impact so the question of course is can +we change our hiring policies or + + align:start position:0% +we change our hiring policies or + + + align:start position:0% +we change our hiring policies or +whatever policies we're using in order + + align:start position:0% +whatever policies we're using in order + + + align:start position:0% +whatever policies we're using in order +to achieve the same goals but with less + + align:start position:0% +to achieve the same goals but with less + + + align:start position:0% +to achieve the same goals but with less +of a disparity in the impact so that's + + align:start position:0% +of a disparity in the impact so that's + + + align:start position:0% +of a disparity in the impact so that's +the challenge now what's interesting is + + align:start position:0% +the challenge now what's interesting is + + + align:start position:0% +the challenge now what's interesting is +that disparate treatment and disparate + + align:start position:0% +that disparate treatment and disparate + + + align:start position:0% +that disparate treatment and disparate +impact are really in conflict with each + + align:start position:0% +impact are really in conflict with each + + + align:start position:0% +impact are really in conflict with each +other and you'll find that this is true + + align:start position:0% +other and you'll find that this is true + + + align:start position:0% +other and you'll find that this is true +in almost everything in this domain so + + align:start position:0% +in almost everything in this domain so + + + align:start position:0% +in almost everything in this domain so +disparate impact is about distributive + + align:start position:0% +disparate impact is about distributive + + + align:start position:0% +disparate impact is about distributive +justice and minimizing equality of + + align:start position:0% +justice and minimizing equality of + + + align:start position:0% +justice and minimizing equality of +outcome disparate treatment is about + + align:start position:0% +outcome disparate treatment is about + + + align:start position:0% +outcome disparate treatment is about +procedural fairness and equality of + + align:start position:0% +procedural fairness and equality of + + + align:start position:0% +procedural fairness and equality of +opportunity and those don't always mesh + + align:start position:0% +opportunity and those don't always mesh + + + align:start position:0% +opportunity and those don't always mesh +in other words it may well be that + + align:start position:0% +in other words it may well be that + + + align:start position:0% +in other words it may well be that +equality of opportunity still leads to + + align:start position:0% +equality of opportunity still leads to + + + align:start position:0% +equality of opportunity still leads to +differences in outcome and you can't + + align:start position:0% +differences in outcome and you can't + + + align:start position:0% +differences in outcome and you can't +square that circle easily + + align:start position:0% + + + + align:start position:0% + +well there's a lot of discrimination + + align:start position:0% +well there's a lot of discrimination + + + align:start position:0% +well there's a lot of discrimination +that keeps persisting there's plenty of + + align:start position:0% +that keeps persisting there's plenty of + + + align:start position:0% +that keeps persisting there's plenty of +evidence in the literature and one of + + align:start position:0% +evidence in the literature and one of + + + align:start position:0% +evidence in the literature and one of +the problems is that for example take an + + align:start position:0% +the problems is that for example take an + + + align:start position:0% +the problems is that for example take an +issue like the disparity between + + align:start position:0% +issue like the disparity between + + + align:start position:0% +issue like the disparity between +different different races or different + + align:start position:0% +different different races or different + + + align:start position:0% +different different races or different +ethnicities it turns out that we don't + + align:start position:0% +ethnicities it turns out that we don't + + + align:start position:0% +ethnicities it turns out that we don't +have a nicely balanced set where the + + align:start position:0% +have a nicely balanced set where the + + + align:start position:0% +have a nicely balanced set where the +number of people of European descent is + + align:start position:0% +number of people of European descent is + + + align:start position:0% +number of people of European descent is +equal to the number of people of African + + align:start position:0% +equal to the number of people of African + + + align:start position:0% +equal to the number of people of African +American or Hispanic or Asian or + + align:start position:0% +American or Hispanic or Asian or + + + align:start position:0% +American or Hispanic or Asian or +whatever population you choose descent + + align:start position:0% +whatever population you choose descent + + + align:start position:0% +whatever population you choose descent +and therefore we tend to know a lot more + + align:start position:0% +and therefore we tend to know a lot more + + + align:start position:0% +and therefore we tend to know a lot more +about the majority class than we know + + align:start position:0% +about the majority class than we know + + + align:start position:0% +about the majority class than we know +about these minority classes and just + + align:start position:0% +about these minority classes and just + + + align:start position:0% +about these minority classes and just +that additional data and that additional + + align:start position:0% +that additional data and that additional + + + align:start position:0% +that additional data and that additional +knowledge might mean that we're able to + + align:start position:0% +knowledge might mean that we're able to + + + align:start position:0% +knowledge might mean that we're able to +reduce the error rate simply because we + + align:start position:0% +reduce the error rate simply because we + + + align:start position:0% +reduce the error rate simply because we +have a larger sample size okay so if you + + align:start position:0% +have a larger sample size okay so if you + + + align:start position:0% +have a larger sample size okay so if you +want to formalize this this is Moritz + + align:start position:0% +want to formalize this this is Moritz + + + align:start position:0% +want to formalize this this is Moritz +Hart's part of the tutorial that I'm + + align:start position:0% +Hart's part of the tutorial that I'm + + + align:start position:0% +Hart's part of the tutorial that I'm +stealin from in this talk this was given + + align:start position:0% +stealin from in this talk this was given + + + align:start position:0% +stealin from in this talk this was given +at kdd about a year and a half ago I + + align:start position:0% +at kdd about a year and a half ago I + + + align:start position:0% +at kdd about a year and a half ago I +think and Moritz is a professor at + + align:start position:0% +think and Moritz is a professor at + + + align:start position:0% +think and Moritz is a professor at +Berkeley who actually teaches an entire + + align:start position:0% +Berkeley who actually teaches an entire + + + align:start position:0% +Berkeley who actually teaches an entire +semester long course on fairness and + + align:start position:0% +semester long course on fairness and + + + align:start position:0% +semester long course on fairness and +machine learning so there's a lot of + + align:start position:0% +machine learning so there's a lot of + + + align:start position:0% +machine learning so there's a lot of +material here and so he formalizes the + + align:start position:0% +material here and so he formalizes the + + + align:start position:0% +material here and so he formalizes the +problem this way he says look a decision + + align:start position:0% +problem this way he says look a decision + + + align:start position:0% +problem this way he says look a decision +problem a model in our were in our terms + + align:start position:0% +problem a model in our were in our terms + + + align:start position:0% +problem a model in our were in our terms +is that we have some X which is the set + + align:start position:0% +is that we have some X which is the set + + + align:start position:0% +is that we have some X which is the set +of features we know about an individual + + align:start position:0% +of features we know about an individual + + + align:start position:0% +of features we know about an individual +and we have some set a which is the set + + align:start position:0% +and we have some set a which is the set + + + align:start position:0% +and we have some set a which is the set +of protected features like your race or + + align:start position:0% +of protected features like your race or + + + align:start position:0% +of protected features like your race or +your gender or your age or whatever it + + align:start position:0% +your gender or your age or whatever it + + + align:start position:0% +your gender or your age or whatever it +is we're trying to prevent from + + align:start position:0% +is we're trying to prevent from + + + align:start position:0% +is we're trying to prevent from +discriminating on and then we have + + align:start position:0% +discriminating on and then we have + + + align:start position:0% +discriminating on and then we have +either a classifier or some score or + + align:start position:0% +either a classifier or some score or + + + align:start position:0% +either a classifier or some score or +predictive function that's a function of + + align:start position:0% +predictive function that's a function of + + + align:start position:0% +predictive function that's a function of +X + + align:start position:0% +X + + + align:start position:0% +X +in either case and then we have some why + + align:start position:0% +in either case and then we have some why + + + align:start position:0% +in either case and then we have some why +which is the outcome that we're + + align:start position:0% +which is the outcome that we're + + + align:start position:0% +which is the outcome that we're +interested in predicting so now you can + + align:start position:0% +interested in predicting so now you can + + + align:start position:0% +interested in predicting so now you can +begin to tease apart some different + + align:start position:0% +begin to tease apart some different + + + align:start position:0% +begin to tease apart some different +notions of fairness by looking at the + + align:start position:0% +notions of fairness by looking at the + + + align:start position:0% +notions of fairness by looking at the +relationships between these elements so + + align:start position:0% +relationships between these elements so + + + align:start position:0% +relationships between these elements so +there are three criteria that appear in + + align:start position:0% +there are three criteria that appear in + + + align:start position:0% +there are three criteria that appear in +the literature one of them is the notion + + align:start position:0% +the literature one of them is the notion + + + align:start position:0% +the literature one of them is the notion +of Independence of the scoring function + + align:start position:0% +of Independence of the scoring function + + + align:start position:0% +of Independence of the scoring function +from sensitive attributes so this says + + align:start position:0% +from sensitive attributes so this says + + + align:start position:0% +from sensitive attributes so this says +that R is independent from a in other + + align:start position:0% +that R is independent from a in other + + + align:start position:0% +that R is independent from a in other +words the previous slide I said that R + + align:start position:0% +words the previous slide I said that R + + + align:start position:0% +words the previous slide I said that R +is a function of oops R as a function of + + align:start position:0% +is a function of oops R as a function of + + + align:start position:0% +is a function of oops R as a function of +X and ay so obviously that criterion + + align:start position:0% +X and ay so obviously that criterion + + + align:start position:0% +X and ay so obviously that criterion +says that it can't be a function of a + + align:start position:0% +says that it can't be a function of a + + + align:start position:0% +says that it can't be a function of a +the null function another notion is + + align:start position:0% +the null function another notion is + + + align:start position:0% +the null function another notion is +separation of score and the sensitive + + align:start position:0% +separation of score and the sensitive + + + align:start position:0% +separation of score and the sensitive +attribute given the outcome so this is + + align:start position:0% +attribute given the outcome so this is + + + align:start position:0% +attribute given the outcome so this is +the one that says the different groups + + align:start position:0% +the one that says the different groups + + + align:start position:0% +the one that says the different groups +are going to be treated similarly in + + align:start position:0% +are going to be treated similarly in + + + align:start position:0% +are going to be treated similarly in +other words if I tell you the group the + + align:start position:0% +other words if I tell you the group the + + + align:start position:0% +other words if I tell you the group the +outcome you know the people who did well + + align:start position:0% +outcome you know the people who did well + + + align:start position:0% +outcome you know the people who did well +at the job and the people who did poorly + + align:start position:0% +at the job and the people who did poorly + + + align:start position:0% +at the job and the people who did poorly +at the job then the scoring function is + + align:start position:0% +at the job then the scoring function is + + + align:start position:0% +at the job then the scoring function is +independent of the protected attribute + + align:start position:0% +independent of the protected attribute + + + align:start position:0% +independent of the protected attribute +right so that allows a little more + + align:start position:0% +right so that allows a little more + + + align:start position:0% +right so that allows a little more +wiggle room because it says that the + + align:start position:0% +wiggle room because it says that the + + + align:start position:0% +wiggle room because it says that the +protected attribute can still predict + + align:start position:0% +protected attribute can still predict + + + align:start position:0% +protected attribute can still predict +something about the outcome it's just + + align:start position:0% +something about the outcome it's just + + + align:start position:0% +something about the outcome it's just +that you can't use it in the scoring + + align:start position:0% +that you can't use it in the scoring + + + align:start position:0% +that you can't use it in the scoring +function given that the category of + + align:start position:0% +function given that the category of + + + align:start position:0% +function given that the category of +which outcome category that individual + + align:start position:0% +which outcome category that individual + + + align:start position:0% +which outcome category that individual +belongs to and then sufficiency is the + + align:start position:0% +belongs to and then sufficiency is the + + + align:start position:0% +belongs to and then sufficiency is the +inverse of that it says that given the + + align:start position:0% +inverse of that it says that given the + + + align:start position:0% +inverse of that it says that given the +scoring function the outcome is + + align:start position:0% +scoring function the outcome is + + + align:start position:0% +scoring function the outcome is +independent of the protected attribute + + align:start position:0% +independent of the protected attribute + + + align:start position:0% +independent of the protected attribute +so that says can we build a fair scoring + + align:start position:0% +so that says can we build a fair scoring + + + align:start position:0% +so that says can we build a fair scoring +function that separates the outcome from + + align:start position:0% +function that separates the outcome from + + + align:start position:0% +function that separates the outcome from +the protected attribute so here's some + + align:start position:0% +the protected attribute so here's some + + + align:start position:0% +the protected attribute so here's some +detail on those if you look at + + align:start position:0% +detail on those if you look at + + + align:start position:0% +detail on those if you look at +Independence this is also called by + + align:start position:0% +Independence this is also called by + + + align:start position:0% +Independence this is also called by +various other names basically what it + + align:start position:0% +various other names basically what it + + + align:start position:0% +various other names basically what it +says is that + + align:start position:0% +says is that + + + align:start position:0% +says is that +the probability of a particular result + + align:start position:0% +the probability of a particular result + + + align:start position:0% +the probability of a particular result +are equal one is the same whether you're + + align:start position:0% +are equal one is the same whether you're + + + align:start position:0% +are equal one is the same whether you're +in Class A or Class B in the protected + + align:start position:0% +in Class A or Class B in the protected + + + align:start position:0% +in Class A or Class B in the protected +attribute okay so what does that tell + + align:start position:0% +attribute okay so what does that tell + + + align:start position:0% +attribute okay so what does that tell +you that tells you that the scoring + + align:start position:0% +you that tells you that the scoring + + + align:start position:0% +you that tells you that the scoring +function has to be universal over the + + align:start position:0% +function has to be universal over the + + + align:start position:0% +function has to be universal over the +entire data set and has to not + + align:start position:0% +entire data set and has to not + + + align:start position:0% +entire data set and has to not +distinguish between people in Class A + + align:start position:0% +distinguish between people in Class A + + + align:start position:0% +distinguish between people in Class A +versus Class B alright that's a pretty + + align:start position:0% +versus Class B alright that's a pretty + + + align:start position:0% +versus Class B alright that's a pretty +strong requirement and then you can + + align:start position:0% +strong requirement and then you can + + + align:start position:0% +strong requirement and then you can +operationalize the notion of unfairness + + align:start position:0% +operationalize the notion of unfairness + + + align:start position:0% +operationalize the notion of unfairness +either by looking for an absolute + + align:start position:0% +either by looking for an absolute + + + align:start position:0% +either by looking for an absolute +difference between those probabilities + + align:start position:0% +difference between those probabilities + + + align:start position:0% +difference between those probabilities +if it's greater than some epsilon then + + align:start position:0% +if it's greater than some epsilon then + + + align:start position:0% +if it's greater than some epsilon then +you have evidence that this is not a + + align:start position:0% +you have evidence that this is not a + + + align:start position:0% +you have evidence that this is not a +fair scoring function or a ratio test + + align:start position:0% +fair scoring function or a ratio test + + + align:start position:0% +fair scoring function or a ratio test +that says we look at the ratio and if it + + align:start position:0% +that says we look at the ratio and if it + + + align:start position:0% +that says we look at the ratio and if it +differs from one significantly then you + + align:start position:0% +differs from one significantly then you + + + align:start position:0% +differs from one significantly then you +have evidence that this is an unfair + + align:start position:0% +have evidence that this is an unfair + + + align:start position:0% +have evidence that this is an unfair +scoring function and by the way this + + align:start position:0% +scoring function and by the way this + + + align:start position:0% +scoring function and by the way this +relates to the 4/5 rule because if you + + align:start position:0% +relates to the 4/5 rule because if you + + + align:start position:0% +relates to the 4/5 rule because if you +make epsilon a 20% then then that's the + + align:start position:0% +make epsilon a 20% then then that's the + + + align:start position:0% +make epsilon a 20% then then that's the +same as the 4/5 rule now the problem + + align:start position:0% +same as the 4/5 rule now the problem + + + align:start position:0% +same as the 4/5 rule now the problem +there are problems with this notion of + + align:start position:0% +there are problems with this notion of + + + align:start position:0% +there are problems with this notion of +Independence so it only requires equal + + align:start position:0% +Independence so it only requires equal + + + align:start position:0% +Independence so it only requires equal +rates of decisions for hiring or giving + + align:start position:0% +rates of decisions for hiring or giving + + + align:start position:0% +rates of decisions for hiring or giving +somebody a liver for transplant or + + align:start position:0% +somebody a liver for transplant or + + + align:start position:0% +somebody a liver for transplant or +whatever topic you're interested in and + + align:start position:0% +whatever topic you're interested in and + + + align:start position:0% +whatever topic you're interested in and +so what if hiring is based on a good + + align:start position:0% +so what if hiring is based on a good + + + align:start position:0% +so what if hiring is based on a good +scoring group a but random in B so for + + align:start position:0% +scoring group a but random in B so for + + + align:start position:0% +scoring group a but random in B so for +example what if we know a lot more + + align:start position:0% +example what if we know a lot more + + + align:start position:0% +example what if we know a lot more +information about Group A than we do + + align:start position:0% +information about Group A than we do + + + align:start position:0% +information about Group A than we do +about Group B so we have a better way of + + align:start position:0% +about Group B so we have a better way of + + + align:start position:0% +about Group B so we have a better way of +scoring them than we do of scoring Group + + align:start position:0% +scoring them than we do of scoring Group + + + align:start position:0% +scoring them than we do of scoring Group +B so you might wind up with the + + align:start position:0% +B so you might wind up with the + + + align:start position:0% +B so you might wind up with the +situation where you wind up hiring the + + align:start position:0% +situation where you wind up hiring the + + + align:start position:0% +situation where you wind up hiring the +same number of people with the same + + align:start position:0% +same number of people with the same + + + align:start position:0% +same number of people with the same +ratio of people in both groups but in + + align:start position:0% +ratio of people in both groups but in + + + align:start position:0% +ratio of people in both groups but in +one group you've done a good job of + + align:start position:0% +one group you've done a good job of + + + align:start position:0% +one group you've done a good job of +selecting out the good candidates + + align:start position:0% +selecting out the good candidates + + + align:start position:0% +selecting out the good candidates +and in the other group you've + + align:start position:0% +and in the other group you've + + + align:start position:0% +and in the other group you've +essentially done done it at random + + align:start position:0% +essentially done done it at random + + + align:start position:0% +essentially done done it at random +well the outcomes are likely to be + + align:start position:0% +well the outcomes are likely to be + + + align:start position:0% +well the outcomes are likely to be +better for a group a than for Group B + + align:start position:0% +better for a group a than for Group B + + + align:start position:0% +better for a group a than for Group B +which means that you're developing more + + align:start position:0% +which means that you're developing more + + + align:start position:0% +which means that you're developing more +data for the future that says we really + + align:start position:0% +data for the future that says we really + + + align:start position:0% +data for the future that says we really +ought to be hiring people in Group A + + align:start position:0% +ought to be hiring people in Group A + + + align:start position:0% +ought to be hiring people in Group A +because they have better outcomes so + + align:start position:0% +because they have better outcomes so + + + align:start position:0% +because they have better outcomes so +there's this feedback loop or + + align:start position:0% +there's this feedback loop or + + + align:start position:0% +there's this feedback loop or +alternatively well of course it could be + + align:start position:0% +alternatively well of course it could be + + + align:start position:0% +alternatively well of course it could be +caused by malice also so you know I + + align:start position:0% +caused by malice also so you know I + + + align:start position:0% +caused by malice also so you know I +could just decide as a hiring manager + + align:start position:0% +could just decide as a hiring manager + + + align:start position:0% +could just decide as a hiring manager +I'm not hiring enough african-americans + + align:start position:0% +I'm not hiring enough african-americans + + + align:start position:0% +I'm not hiring enough african-americans +so I'm just gonna take some random + + align:start position:0% +so I'm just gonna take some random + + + align:start position:0% +so I'm just gonna take some random +sample of african-americans and hire + + align:start position:0% +sample of african-americans and hire + + + align:start position:0% +sample of african-americans and hire +them and then maybe they'll do badly and + + align:start position:0% +them and then maybe they'll do badly and + + + align:start position:0% +them and then maybe they'll do badly and +then I'll have more data to demonstrate + + align:start position:0% +then I'll have more data to demonstrate + + + align:start position:0% +then I'll have more data to demonstrate +that this was a bad idea okay so that + + align:start position:0% +that this was a bad idea okay so that + + + align:start position:0% +that this was a bad idea okay so that +would be malicious there's also a + + align:start position:0% +would be malicious there's also a + + + align:start position:0% +would be malicious there's also a +technical problem which is it's possible + + align:start position:0% +technical problem which is it's possible + + + align:start position:0% +technical problem which is it's possible +that the category the group is a perfect + + align:start position:0% +that the category the group is a perfect + + + align:start position:0% +that the category the group is a perfect +predictor of the outcome in which case + + align:start position:0% +predictor of the outcome in which case + + + align:start position:0% +predictor of the outcome in which case +of course they can't be separated they + + align:start position:0% +of course they can't be separated they + + + align:start position:0% +of course they can't be separated they +can't be independent of each other now + + align:start position:0% +can't be independent of each other now + + + align:start position:0% +can't be independent of each other now +how do you achieve independence well + + align:start position:0% +how do you achieve independence well + + + align:start position:0% +how do you achieve independence well +there are a number of different + + align:start position:0% +there are a number of different + + + align:start position:0% +there are a number of different +techniques one of them is there's this + + align:start position:0% +techniques one of them is there's this + + + align:start position:0% +techniques one of them is there's this +article by Zemel that's about learning + + align:start position:0% +article by Zemel that's about learning + + + align:start position:0% +article by Zemel that's about learning +fair representations and what it says is + + align:start position:0% +fair representations and what it says is + + + align:start position:0% +fair representations and what it says is +you create a new representation Z which + + align:start position:0% +you create a new representation Z which + + + align:start position:0% +you create a new representation Z which +is some combination of X and ay and you + + align:start position:0% +is some combination of X and ay and you + + + align:start position:0% +is some combination of X and ay and you +do this by maximizing the mutual + + align:start position:0% +do this by maximizing the mutual + + + align:start position:0% +do this by maximizing the mutual +information between X and Z and by + + align:start position:0% +information between X and Z and by + + + align:start position:0% +information between X and Z and by +minimizing the mutual information + + align:start position:0% +minimizing the mutual information + + + align:start position:0% +minimizing the mutual information +between ay and Z so this is an idea that + + align:start position:0% +between ay and Z so this is an idea that + + + align:start position:0% +between ay and Z so this is an idea that +I've seen used in machine learning in + + align:start position:0% +I've seen used in machine learning in + + + align:start position:0% +I've seen used in machine learning in +for robustness rather than for fairness + + align:start position:0% +for robustness rather than for fairness + + + align:start position:0% +for robustness rather than for fairness +where people say you know the problem is + + align:start position:0% +where people say you know the problem is + + + align:start position:0% +where people say you know the problem is +that given a particular data set you can + + align:start position:0% +that given a particular data set you can + + + align:start position:0% +that given a particular data set you can +over fit to that data set and so one of + + align:start position:0% +over fit to that data set and so one of + + + align:start position:0% +over fit to that data set and so one of +the ideas is to do again like method + + align:start position:0% +the ideas is to do again like method + + + align:start position:0% +the ideas is to do again like method +where you say I want to train my + + align:start position:0% +where you say I want to train my + + + align:start position:0% +where you say I want to train my +classifier let's say not only to work + + align:start position:0% +classifier let's say not only to work + + + align:start position:0% +classifier let's say not only to work +well + + align:start position:0% +well + + + align:start position:0% +well +getting the right answer but also to + + align:start position:0% +getting the right answer but also to + + + align:start position:0% +getting the right answer but also to +work as poorly as possible on + + align:start position:0% +work as poorly as possible on + + + align:start position:0% +work as poorly as possible on +identifying which part which data set my + + align:start position:0% +identifying which part which data set my + + + align:start position:0% +identifying which part which data set my +example came from so this is the same + + align:start position:0% +example came from so this is the same + + + align:start position:0% +example came from so this is the same +sort of idea it's a representation + + align:start position:0% +sort of idea it's a representation + + + align:start position:0% +sort of idea it's a representation +learning idea and then you build your + + align:start position:0% +learning idea and then you build your + + + align:start position:0% +learning idea and then you build your +predictor are based on this + + align:start position:0% +predictor are based on this + + + align:start position:0% +predictor are based on this +representation which is perhaps not + + align:start position:0% +representation which is perhaps not + + + align:start position:0% +representation which is perhaps not +perfectly independent of the protected + + align:start position:0% +perfectly independent of the protected + + + align:start position:0% +perfectly independent of the protected +attribute but is as independent as + + align:start position:0% +attribute but is as independent as + + + align:start position:0% +attribute but is as independent as +possible and usually there are knobs in + + align:start position:0% +possible and usually there are knobs in + + + align:start position:0% +possible and usually there are knobs in +these learning algorithms and depending + + align:start position:0% +these learning algorithms and depending + + + align:start position:0% +these learning algorithms and depending +on how you turn the knob you can affect + + align:start position:0% +on how you turn the knob you can affect + + + align:start position:0% +on how you turn the knob you can affect +which effect whether you're gonna get a + + align:start position:0% +which effect whether you're gonna get a + + + align:start position:0% +which effect whether you're gonna get a +better classifier that's more + + align:start position:0% +better classifier that's more + + + align:start position:0% +better classifier that's more +discriminatory or worse classifier + + align:start position:0% +discriminatory or worse classifier + + + align:start position:0% +discriminatory or worse classifier +that's less discriminatory so you can do + + align:start position:0% +that's less discriminatory so you can do + + + align:start position:0% +that's less discriminatory so you can do +that in pre-processing you can do some + + align:start position:0% +that in pre-processing you can do some + + + align:start position:0% +that in pre-processing you can do some +kind of incorporating in the loss + + align:start position:0% +kind of incorporating in the loss + + + align:start position:0% +kind of incorporating in the loss +function a dependence notion or an + + align:start position:0% +function a dependence notion or an + + + align:start position:0% +function a dependence notion or an +independence notion and say we're gonna + + align:start position:0% +independence notion and say we're gonna + + + align:start position:0% +independence notion and say we're gonna +train on a particular data set imposing + + align:start position:0% +train on a particular data set imposing + + + align:start position:0% +train on a particular data set imposing +this notion of wanting this independence + + align:start position:0% +this notion of wanting this independence + + + align:start position:0% +this notion of wanting this independence +between a and R as part of our desert + + align:start position:0% +between a and R as part of our desert + + + align:start position:0% +between a and R as part of our desert +errata and so you again are making + + align:start position:0% +errata and so you again are making + + + align:start position:0% +errata and so you again are making +trade-offs against other characteristics + + align:start position:0% +trade-offs against other characteristics + + + align:start position:0% +trade-offs against other characteristics +or you can do post-processing so suppose + + align:start position:0% +or you can do post-processing so suppose + + + align:start position:0% +or you can do post-processing so suppose +I've built an optimal are not worrying + + align:start position:0% +I've built an optimal are not worrying + + + align:start position:0% +I've built an optimal are not worrying +about discrimination then I can do + + align:start position:0% +about discrimination then I can do + + + align:start position:0% +about discrimination then I can do +another learning problem that says I'm + + align:start position:0% +another learning problem that says I'm + + + align:start position:0% +another learning problem that says I'm +now going to build a new F which takes R + + align:start position:0% +now going to build a new F which takes R + + + align:start position:0% +now going to build a new F which takes R +and the protected attribute into account + + align:start position:0% +and the protected attribute into account + + + align:start position:0% +and the protected attribute into account +and it's going to minimize the cost of + + align:start position:0% +and it's going to minimize the cost of + + + align:start position:0% +and it's going to minimize the cost of +misclassification and again there's a + + align:start position:0% +misclassification and again there's a + + + align:start position:0% +misclassification and again there's a +knob where you can say how much do I + + align:start position:0% +knob where you can say how much do I + + + align:start position:0% +knob where you can say how much do I +want to emphasize misclassifications for + + align:start position:0% +want to emphasize misclassifications for + + + align:start position:0% +want to emphasize misclassifications for +the protected attribute were based on + + align:start position:0% +the protected attribute were based on + + + align:start position:0% +the protected attribute were based on +the protected attribute so this this was + + align:start position:0% +the protected attribute so this this was + + + align:start position:0% +the protected attribute so this this was +still talking about independence the + + align:start position:0% +still talking about independence the + + + align:start position:0% +still talking about independence the +next notion is separation that says + + align:start position:0% +next notion is separation that says + + + align:start position:0% +next notion is separation that says +given the outcome I want to separate a + + align:start position:0% +given the outcome I want to separate a + + + align:start position:0% +given the outcome I want to separate a +and R so that graphical model shows it + + align:start position:0% +and R so that graphical model shows it + + + align:start position:0% +and R so that graphical model shows it +to you that + + align:start position:0% +to you that + + + align:start position:0% +to you that +protected attribute is only related to + + align:start position:0% +protected attribute is only related to + + + align:start position:0% +protected attribute is only related to +the scoring function through the outcome + + align:start position:0% +the scoring function through the outcome + + + align:start position:0% +the scoring function through the outcome +so there's nothing else that you can + + align:start position:0% +so there's nothing else that you can + + + align:start position:0% +so there's nothing else that you can +learn from one to the other other than + + align:start position:0% +learn from one to the other other than + + + align:start position:0% +learn from one to the other other than +through the outcome so this recognizes + + align:start position:0% +through the outcome so this recognizes + + + align:start position:0% +through the outcome so this recognizes +that the protected attribute may in fact + + align:start position:0% +that the protected attribute may in fact + + + align:start position:0% +that the protected attribute may in fact +be correlated with the target variable + + align:start position:0% +be correlated with the target variable + + + align:start position:0% +be correlated with the target variable +and so an example might be different + + align:start position:0% +and so an example might be different + + + align:start position:0% +and so an example might be different +success rates in a drug trial for + + align:start position:0% +success rates in a drug trial for + + + align:start position:0% +success rates in a drug trial for +different ethnic populations there there + + align:start position:0% +different ethnic populations there there + + + align:start position:0% +different ethnic populations there there +are now some cardiac drugs where the + + align:start position:0% +are now some cardiac drugs where the + + + align:start position:0% +are now some cardiac drugs where the +manufacturer has determined that this + + align:start position:0% +manufacturer has determined that this + + + align:start position:0% +manufacturer has determined that this +drug works much better in certain + + align:start position:0% +drug works much better in certain + + + align:start position:0% +drug works much better in certain +subpopulations than it does in other + + align:start position:0% +subpopulations than it does in other + + + align:start position:0% +subpopulations than it does in other +populations and the FDA has actually + + align:start position:0% +populations and the FDA has actually + + + align:start position:0% +populations and the FDA has actually +approved the marketing of that drug to + + align:start position:0% +approved the marketing of that drug to + + + align:start position:0% +approved the marketing of that drug to +those subpopulations so you're not + + align:start position:0% +those subpopulations so you're not + + + align:start position:0% +those subpopulations so you're not +supposed to market it to the people for + + align:start position:0% +supposed to market it to the people for + + + align:start position:0% +supposed to market it to the people for +whom it doesn't work as well but you're + + align:start position:0% +whom it doesn't work as well but you're + + + align:start position:0% +whom it doesn't work as well but you're +allowed to market it specifically for + + align:start position:0% +allowed to market it specifically for + + + align:start position:0% +allowed to market it specifically for +the people for whom it does work well + + align:start position:0% +the people for whom it does work well + + + align:start position:0% +the people for whom it does work well +and if you think about the personalized + + align:start position:0% +and if you think about the personalized + + + align:start position:0% +and if you think about the personalized +medicine idea which we've talked about + + align:start position:0% +medicine idea which we've talked about + + + align:start position:0% +medicine idea which we've talked about +earlier the populations that were + + align:start position:0% +earlier the populations that were + + + align:start position:0% +earlier the populations that were +interested in becomes smaller and + + align:start position:0% +interested in becomes smaller and + + + align:start position:0% +interested in becomes smaller and +smaller until it may just be you and so + + align:start position:0% +smaller until it may just be you and so + + + align:start position:0% +smaller until it may just be you and so +there might be a drug that works for you + + align:start position:0% +there might be a drug that works for you + + + align:start position:0% +there might be a drug that works for you +and not for anybody else in the class + + align:start position:0% +and not for anybody else in the class + + + align:start position:0% +and not for anybody else in the class +but it's exactly the right drug for you + + align:start position:0% +but it's exactly the right drug for you + + + align:start position:0% +but it's exactly the right drug for you +and we may get to the point where that + + align:start position:0% +and we may get to the point where that + + + align:start position:0% +and we may get to the point where that +will happen and where we can build such + + align:start position:0% +will happen and where we can build such + + + align:start position:0% +will happen and where we can build such +drugs and where we can approve their use + + align:start position:0% +drugs and where we can approve their use + + + align:start position:0% +drugs and where we can approve their use +in human populations now the idea here + + align:start position:0% +in human populations now the idea here + + + align:start position:0% +in human populations now the idea here +is that if I have two populations blue + + align:start position:0% +is that if I have two populations blue + + + align:start position:0% +is that if I have two populations blue +and green and I draw ROC curves for both + + align:start position:0% +and green and I draw ROC curves for both + + + align:start position:0% +and green and I draw ROC curves for both +of these populations they're not going + + align:start position:0% +of these populations they're not going + + + align:start position:0% +of these populations they're not going +to be the same because the drug will + + align:start position:0% +to be the same because the drug will + + + align:start position:0% +to be the same because the drug will +work differently for those two + + align:start position:0% +work differently for those two + + + align:start position:0% +work differently for those two +populations but on the other hand I can + + align:start position:0% +populations but on the other hand I can + + + align:start position:0% +populations but on the other hand I can +draw them on the same axis and I can say + + align:start position:0% +draw them on the same axis and I can say + + + align:start position:0% +draw them on the same axis and I can say +look any place within this colored + + align:start position:0% +look any place within this colored + + + align:start position:0% +look any place within this colored +region can be a fair region in that I'm + + align:start position:0% +region can be a fair region in that I'm + + + align:start position:0% +region can be a fair region in that I'm +going to get the same + + align:start position:0% +going to get the same + + + align:start position:0% +going to get the same +come for both populations so I can't + + align:start position:0% +come for both populations so I can't + + + align:start position:0% +come for both populations so I can't +achieve this outcome for the blue + + align:start position:0% +achieve this outcome for the blue + + + align:start position:0% +achieve this outcome for the blue +population or this outcome for the green + + align:start position:0% +population or this outcome for the green + + + align:start position:0% +population or this outcome for the green +population but I can achieve any of + + align:start position:0% +population but I can achieve any of + + + align:start position:0% +population but I can achieve any of +these outcomes for both populations + + align:start position:0% +these outcomes for both populations + + + align:start position:0% +these outcomes for both populations +simultaneously and the so that's one way + + align:start position:0% +simultaneously and the so that's one way + + + align:start position:0% +simultaneously and the so that's one way +of going about satisfying this + + align:start position:0% +of going about satisfying this + + + align:start position:0% +of going about satisfying this +requirement when it is not easily + + align:start position:0% +requirement when it is not easily + + + align:start position:0% +requirement when it is not easily +satisfied so the advantage of separation + + align:start position:0% +satisfied so the advantage of separation + + + align:start position:0% +satisfied so the advantage of separation +over independence is that it allows + + align:start position:0% +over independence is that it allows + + + align:start position:0% +over independence is that it allows +correlation between R and Y even a + + align:start position:0% +correlation between R and Y even a + + + align:start position:0% +correlation between R and Y even a +perfect predictor so why are could be a + + align:start position:0% +perfect predictor so why are could be a + + + align:start position:0% +perfect predictor so why are could be a +perfect predictor for Y and it gives you + + align:start position:0% +perfect predictor for Y and it gives you + + + align:start position:0% +perfect predictor for Y and it gives you +incentives to learn to reduce the errors + + align:start position:0% +incentives to learn to reduce the errors + + + align:start position:0% +incentives to learn to reduce the errors +in all groups so that issue about + + align:start position:0% +in all groups so that issue about + + + align:start position:0% +in all groups so that issue about +randomly choosing members of the + + align:start position:0% +randomly choosing members of the + + + align:start position:0% +randomly choosing members of the +minority group doesn't work here because + + align:start position:0% +minority group doesn't work here because + + + align:start position:0% +minority group doesn't work here because +that would suppress the ROC curve to the + + align:start position:0% +that would suppress the ROC curve to the + + + align:start position:0% +that would suppress the ROC curve to the +point where there would be no feasible + + align:start position:0% +point where there would be no feasible + + + align:start position:0% +point where there would be no feasible +region that you would like so for + + align:start position:0% +region that you would like so for + + + align:start position:0% +region that you would like so for +example if it's a coin flip then you'd + + align:start position:0% +example if it's a coin flip then you'd + + + align:start position:0% +example if it's a coin flip then you'd +have the diagonal line and the only + + align:start position:0% +have the diagonal line and the only + + + align:start position:0% +have the diagonal line and the only +feasible region would be below that + + align:start position:0% +feasible region would be below that + + + align:start position:0% +feasible region would be below that +diagonal no matter how good the + + align:start position:0% +diagonal no matter how good the + + + align:start position:0% +diagonal no matter how good the +predictor was for the other class so + + align:start position:0% +predictor was for the other class so + + + align:start position:0% +predictor was for the other class so +that's a nice characteristic and then + + align:start position:0% +that's a nice characteristic and then + + + align:start position:0% +that's a nice characteristic and then +the final criterion is sufficiency which + + align:start position:0% +the final criterion is sufficiency which + + + align:start position:0% +the final criterion is sufficiency which +flips r and y so it says that the + + align:start position:0% +flips r and y so it says that the + + + align:start position:0% +flips r and y so it says that the +regressor the predictive variable can + + align:start position:0% +regressor the predictive variable can + + + align:start position:0% +regressor the predictive variable can +depend on the protected class but it's + + align:start position:0% +depend on the protected class but it's + + + align:start position:0% +depend on the protected class but it's +but the protected class is separated + + align:start position:0% +but the protected class is separated + + + align:start position:0% +but the protected class is separated +from the outcome so for example the + + align:start position:0% +from the outcome so for example the + + + align:start position:0% +from the outcome so for example the +probability of a in a binary case of a + + align:start position:0% +probability of a in a binary case of a + + + align:start position:0% +probability of a in a binary case of a +true outcome for y given that r is some + + align:start position:0% +true outcome for y given that r is some + + + align:start position:0% +true outcome for y given that r is some +particular value r and a is is a + + align:start position:0% +particular value r and a is is a + + + align:start position:0% +particular value r and a is is a +particular class is the same as the + + align:start position:0% +particular class is the same as the + + + align:start position:0% +particular class is the same as the +probability of that same outcome given + + align:start position:0% +probability of that same outcome given + + + align:start position:0% +probability of that same outcome given +the same r value but the different class + + align:start position:0% +the same r value but the different class + + + align:start position:0% +the same r value but the different class +okay so that's related to the sort of + + align:start position:0% +okay so that's related to the sort of + + + align:start position:0% +okay so that's related to the sort of +similar people similar treatment notion + + align:start position:0% +similar people similar treatment notion + + + align:start position:0% +similar people similar treatment notion +qualitative notion again + + align:start position:0% +qualitative notion again + + + align:start position:0% +qualitative notion again +so it requires the parity of both the + + align:start position:0% +so it requires the parity of both the + + + align:start position:0% +so it requires the parity of both the +positive and the negative predictive + + align:start position:0% +positive and the negative predictive + + + align:start position:0% +positive and the negative predictive +values across different groups okay so + + align:start position:0% +values across different groups okay so + + + align:start position:0% +values across different groups okay so +that's another popular way of looking at + + align:start position:0% +that's another popular way of looking at + + + align:start position:0% +that's another popular way of looking at +this so for example if the scoring + + align:start position:0% +this so for example if the scoring + + + align:start position:0% +this so for example if the scoring +function is a probability or the set of + + align:start position:0% +function is a probability or the set of + + + align:start position:0% +function is a probability or the set of +all instances assigned the score R has + + align:start position:0% +all instances assigned the score R has + + + align:start position:0% +all instances assigned the score R has +an R fraction of positive instances + + align:start position:0% +an R fraction of positive instances + + + align:start position:0% +an R fraction of positive instances +among them then the scoring function is + + align:start position:0% +among them then the scoring function is + + + align:start position:0% +among them then the scoring function is +set to be well calibrated so we've + + align:start position:0% +set to be well calibrated so we've + + + align:start position:0% +set to be well calibrated so we've +talked about that before in the class if + + align:start position:0% +talked about that before in the class if + + + align:start position:0% +talked about that before in the class if +it turns out that R is not well + + align:start position:0% +it turns out that R is not well + + + align:start position:0% +it turns out that R is not well +calibrated you can hack it and you can + + align:start position:0% +calibrated you can hack it and you can + + + align:start position:0% +calibrated you can hack it and you can +make it well calibrated by putting it + + align:start position:0% +make it well calibrated by putting it + + + align:start position:0% +make it well calibrated by putting it +through a logistic function that will + + align:start position:0% +through a logistic function that will + + + align:start position:0% +through a logistic function that will +then approximate the appropriately + + align:start position:0% +then approximate the appropriately + + + align:start position:0% +then approximate the appropriately +calibrated score and then you hope that + + align:start position:0% +calibrated score and then you hope that + + + align:start position:0% +calibrated score and then you hope that +that calibration will give the degree of + + align:start position:0% +that calibration will give the degree of + + + align:start position:0% +that calibration will give the degree of +calibration will give you a good + + align:start position:0% +calibration will give you a good + + + align:start position:0% +calibration will give you a good +approximation to this notion of + + align:start position:0% +approximation to this notion of + + + align:start position:0% +approximation to this notion of +sufficiency these guys in the tutorial + + align:start position:0% +sufficiency these guys in the tutorial + + + align:start position:0% +sufficiency these guys in the tutorial +also point out that some datasets + + align:start position:0% +also point out that some datasets + + + align:start position:0% +also point out that some datasets +actually lead to good calibration + + align:start position:0% +actually lead to good calibration + + + align:start position:0% +actually lead to good calibration +without even trying very hard so for + + align:start position:0% +without even trying very hard so for + + + align:start position:0% +without even trying very hard so for +example this is the UCI census data set + + align:start position:0% +example this is the UCI census data set + + + align:start position:0% +example this is the UCI census data set +and it's a binary prediction of whether + + align:start position:0% +and it's a binary prediction of whether + + + align:start position:0% +and it's a binary prediction of whether +somebody makes more than $50,000 a year + + align:start position:0% +somebody makes more than $50,000 a year + + + align:start position:0% +somebody makes more than $50,000 a year +if you have any income at all and if + + align:start position:0% +if you have any income at all and if + + + align:start position:0% +if you have any income at all and if +you're over 16 years old and the feature + + align:start position:0% +you're over 16 years old and the feature + + + align:start position:0% +you're over 16 years old and the feature +there 14 features age type of work + + align:start position:0% +there 14 features age type of work + + + align:start position:0% +there 14 features age type of work +weight of sample of some statistical + + align:start position:0% +weight of sample of some statistical + + + align:start position:0% +weight of sample of some statistical +hack from the Census Bureau your + + align:start position:0% +hack from the Census Bureau your + + + align:start position:0% +hack from the Census Bureau your +education level marital status etc and + + align:start position:0% +education level marital status etc and + + + align:start position:0% +education level marital status etc and +what you see is that the calibration for + + align:start position:0% +what you see is that the calibration for + + + align:start position:0% +what you see is that the calibration for +males and females is pretty decent it's + + align:start position:0% +males and females is pretty decent it's + + + align:start position:0% +males and females is pretty decent it's +almost exactly along the 45-degree line + + align:start position:0% +almost exactly along the 45-degree line + + + align:start position:0% +almost exactly along the 45-degree line +without having done anything + + align:start position:0% +without having done anything + + + align:start position:0% +without having done anything +particularly dramatic in order to + + align:start position:0% +particularly dramatic in order to + + + align:start position:0% +particularly dramatic in order to +achieve that on the other hand if you + + align:start position:0% +achieve that on the other hand if you + + + align:start position:0% +achieve that on the other hand if you +look at the calibration curve by race + + align:start position:0% +look at the calibration curve by race + + + align:start position:0% +look at the calibration curve by race +for whites versus blacks the whites not + + align:start position:0% +for whites versus blacks the whites not + + + align:start position:0% +for whites versus blacks the whites not +surprisingly are reasonably well + + align:start position:0% +surprisingly are reasonably well + + + align:start position:0% +surprisingly are reasonably well +calibrated and the blacks are not as + + align:start position:0% +calibrated and the blacks are not as + + + align:start position:0% +calibrated and the blacks are not as +well calibrated so you could imagine + + align:start position:0% +well calibrated so you could imagine + + + align:start position:0% +well calibrated so you could imagine +building some kind of a transformation + + align:start position:0% +building some kind of a transformation + + + align:start position:0% +building some kind of a transformation +function to improve that calibration and + + align:start position:0% +function to improve that calibration and + + + align:start position:0% +function to improve that calibration and +that would get you separation + + align:start position:0% +that would get you separation + + + align:start position:0% +that would get you separation +now there's a terrible piece of news + + align:start position:0% +now there's a terrible piece of news + + + align:start position:0% +now there's a terrible piece of news +which is that you can prove as they do + + align:start position:0% +which is that you can prove as they do + + + align:start position:0% +which is that you can prove as they do +in this tutorial that it's not possible + + align:start position:0% +in this tutorial that it's not possible + + + align:start position:0% +in this tutorial that it's not possible +to jointly achieve any pair of these + + align:start position:0% +to jointly achieve any pair of these + + + align:start position:0% +to jointly achieve any pair of these +conditions so you have three reasonable + + align:start position:0% +conditions so you have three reasonable + + + align:start position:0% +conditions so you have three reasonable +technical notions of what fairness means + + align:start position:0% +technical notions of what fairness means + + + align:start position:0% +technical notions of what fairness means +and they're incompatible with each other + + align:start position:0% +and they're incompatible with each other + + + align:start position:0% +and they're incompatible with each other +except in some trivial cases this is not + + align:start position:0% +except in some trivial cases this is not + + + align:start position:0% +except in some trivial cases this is not +good and I'm not gonna have time to go + + align:start position:0% +good and I'm not gonna have time to go + + + align:start position:0% +good and I'm not gonna have time to go +into it but there's a very nice thing + + align:start position:0% +into it but there's a very nice thing + + + align:start position:0% +into it but there's a very nice thing +from Google where they illustrate the + + align:start position:0% +from Google where they illustrate the + + + align:start position:0% +from Google where they illustrate the +results of adopting one or another of + + align:start position:0% +results of adopting one or another of + + + align:start position:0% +results of adopting one or another of +these notions of fairness on a + + align:start position:0% +these notions of fairness on a + + + align:start position:0% +these notions of fairness on a +synthesized population of people and you + + align:start position:0% +synthesized population of people and you + + + align:start position:0% +synthesized population of people and you +can see how the trade-offs vary and what + + align:start position:0% +can see how the trade-offs vary and what + + + align:start position:0% +can see how the trade-offs vary and what +the results are of choosing different + + align:start position:0% +the results are of choosing different + + + align:start position:0% +the results are of choosing different +notions of fairness so it's a kind of + + align:start position:0% +notions of fairness so it's a kind of + + + align:start position:0% +notions of fairness so it's a kind of +nice graphical hack again it'll be in + + align:start position:0% +nice graphical hack again it'll be in + + + align:start position:0% +nice graphical hack again it'll be in +the slides and I urge you to check that + + align:start position:0% +the slides and I urge you to check that + + + align:start position:0% +the slides and I urge you to check that +out but I'm not going to have time to go + + align:start position:0% +out but I'm not going to have time to go + + + align:start position:0% +out but I'm not going to have time to go +into it there's one other problem that + + align:start position:0% +into it there's one other problem that + + + align:start position:0% +into it there's one other problem that +they point out which is interesting + + align:start position:0% +they point out which is interesting + + + align:start position:0% +they point out which is interesting +so this was a scenario where you're + + align:start position:0% +so this was a scenario where you're + + + align:start position:0% +so this was a scenario where you're +trying to hire computer programmers and + + align:start position:0% +trying to hire computer programmers and + + + align:start position:0% +trying to hire computer programmers and +you don't want to take gender into + + align:start position:0% +you don't want to take gender into + + + align:start position:0% +you don't want to take gender into +account because we know that women are + + align:start position:0% +account because we know that women are + + + align:start position:0% +account because we know that women are +underrepresented among computer people + + align:start position:0% +underrepresented among computer people + + + align:start position:0% +underrepresented among computer people +and so we would like that not to be an + + align:start position:0% +and so we would like that not to be an + + + align:start position:0% +and so we would like that not to be an +aloud attribute in order to decide to + + align:start position:0% +aloud attribute in order to decide to + + + align:start position:0% +aloud attribute in order to decide to +hire someone so they say well there are + + align:start position:0% +hire someone so they say well there are + + + align:start position:0% +hire someone so they say well there are +two scenarios one of them is that gender + + align:start position:0% +two scenarios one of them is that gender + + + align:start position:0% +two scenarios one of them is that gender +a influences whether you're a programmer + + align:start position:0% +a influences whether you're a programmer + + + align:start position:0% +a influences whether you're a programmer +or not this is empirically true there + + align:start position:0% +or not this is empirically true there + + + align:start position:0% +or not this is empirically true there +are fewer women who are programmers it + + align:start position:0% +are fewer women who are programmers it + + + align:start position:0% +are fewer women who are programmers it +turns out that visiting Pinterest is + + align:start position:0% +turns out that visiting Pinterest is + + + align:start position:0% +turns out that visiting Pinterest is +slightly more common among women than + + align:start position:0% +slightly more common among women than + + + align:start position:0% +slightly more common among women than +men who knew + + align:start position:0% +men who knew + + + align:start position:0% +men who knew +and then visiting github is much more + + align:start position:0% +and then visiting github is much more + + + align:start position:0% +and then visiting github is much more +common among programmers than among not + + align:start position:0% +common among programmers than among not + + + align:start position:0% +common among programmers than among not +programmers that one's pretty obvious so + + align:start position:0% +programmers that one's pretty obvious so + + + align:start position:0% +programmers that one's pretty obvious so +what they say is you know if you want a + + align:start position:0% +what they say is you know if you want a + + + align:start position:0% +what they say is you know if you want a +optimal predictor of whether somebody's + + align:start position:0% +optimal predictor of whether somebody's + + + align:start position:0% +optimal predictor of whether somebody's +gonna get hired it should actually take + + align:start position:0% +gonna get hired it should actually take + + + align:start position:0% +gonna get hired it should actually take +both Pinterest visits and github visits + + align:start position:0% +both Pinterest visits and github visits + + + align:start position:0% +both Pinterest visits and github visits +into account but because those go back + + align:start position:0% +into account but because those go back + + + align:start position:0% +into account but because those go back +to gender which is an unusable attribute + + align:start position:0% +to gender which is an unusable attribute + + + align:start position:0% +to gender which is an unusable attribute +they don't like this model and so they + + align:start position:0% +they don't like this model and so they + + + align:start position:0% +they don't like this model and so they +say well we could use an optimal + + align:start position:0% +say well we could use an optimal + + + align:start position:0% +say well we could use an optimal +separated score because now being a + + align:start position:0% +separated score because now being a + + + align:start position:0% +separated score because now being a +programmer separates your gender from + + align:start position:0% +programmer separates your gender from + + + align:start position:0% +programmer separates your gender from +the scoring function and so we can + + align:start position:0% +the scoring function and so we can + + + align:start position:0% +the scoring function and so we can +create a different score which is not + + align:start position:0% +create a different score which is not + + + align:start position:0% +create a different score which is not +the same as the optimal score but is + + align:start position:0% +the same as the optimal score but is + + + align:start position:0% +the same as the optimal score but is +permitted because it's no longer + + align:start position:0% +permitted because it's no longer + + + align:start position:0% +permitted because it's no longer +dependent on on your on your sex on your + + align:start position:0% +dependent on on your on your sex on your + + + align:start position:0% +dependent on on your on your sex on your +gender here's another scenario that + + align:start position:0% +gender here's another scenario that + + + align:start position:0% +gender here's another scenario that +again starts with gender and says oh + + align:start position:0% +again starts with gender and says oh + + + align:start position:0% +again starts with gender and says oh +look we know that there are more men + + align:start position:0% +look we know that there are more men + + + align:start position:0% +look we know that there are more men +than women who obtain college degrees in + + align:start position:0% +than women who obtain college degrees in + + + align:start position:0% +than women who obtain college degrees in +computer science and so there's an + + align:start position:0% +computer science and so there's an + + + align:start position:0% +computer science and so there's an +influence there and computer scientists + + align:start position:0% +influence there and computer scientists + + + align:start position:0% +influence there and computer scientists +are much more likely to be programmers + + align:start position:0% +are much more likely to be programmers + + + align:start position:0% +are much more likely to be programmers +than non computer science majors if + + align:start position:0% +than non computer science majors if + + + align:start position:0% +than non computer science majors if +you're a woman has anybody visited the + + align:start position:0% +you're a woman has anybody visited the + + + align:start position:0% +you're a woman has anybody visited the +grace Murray hopper conference a couple + + align:start position:0% +grace Murray hopper conference a couple + + + align:start position:0% +grace Murray hopper conference a couple +of few of you yeah so this is a really + + align:start position:0% +of few of you yeah so this is a really + + + align:start position:0% +of few of you yeah so this is a really +cool conference grace Murray hopper + + align:start position:0% +cool conference grace Murray hopper + + + align:start position:0% +cool conference grace Murray hopper +invented the notion bug or the term bug + + align:start position:0% +invented the notion bug or the term bug + + + align:start position:0% +invented the notion bug or the term bug +and was a really famous computer + + align:start position:0% +and was a really famous computer + + + align:start position:0% +and was a really famous computer +scientist starting back in the 1940s + + align:start position:0% +scientist starting back in the 1940s + + + align:start position:0% +scientist starting back in the 1940s +when there were very few of them and + + align:start position:0% +when there were very few of them and + + + align:start position:0% +when there were very few of them and +there's a yearly conference for women + + align:start position:0% +there's a yearly conference for women + + + align:start position:0% +there's a yearly conference for women +computer scientists in her honor + + align:start position:0% +computer scientists in her honor + + + align:start position:0% +computer scientists in her honor +so clearly the probability that you + + align:start position:0% +so clearly the probability that you + + + align:start position:0% +so clearly the probability that you +visited + + align:start position:0% +visited + + + align:start position:0% +visited +the Grace Hopper conference is dependent + + align:start position:0% +the Grace Hopper conference is dependent + + + align:start position:0% +the Grace Hopper conference is dependent +on your gender it's also dependent on + + align:start position:0% +on your gender it's also dependent on + + + align:start position:0% +on your gender it's also dependent on +whether you're a computer scientist + + align:start position:0% +whether you're a computer scientist + + + align:start position:0% +whether you're a computer scientist +because if you're a historian and you're + + align:start position:0% +because if you're a historian and you're + + + align:start position:0% +because if you're a historian and you're +not likely to be interested in going to + + align:start position:0% +not likely to be interested in going to + + + align:start position:0% +not likely to be interested in going to +that conference and so in this story the + + align:start position:0% +that conference and so in this story the + + + align:start position:0% +that conference and so in this story the +optimal score is going to depend + + align:start position:0% +optimal score is going to depend + + + align:start position:0% +optimal score is going to depend +basically on whether you have a computer + + align:start position:0% +basically on whether you have a computer + + + align:start position:0% +basically on whether you have a computer +science degree or not right but the + + align:start position:0% +science degree or not right but the + + + align:start position:0% +science degree or not right but the +separated score will depend only on your + + align:start position:0% +separated score will depend only on your + + + align:start position:0% +separated score will depend only on your +gender which is kind of funny because + + align:start position:0% +gender which is kind of funny because + + + align:start position:0% +gender which is kind of funny because +that's the protected attribute and what + + align:start position:0% +that's the protected attribute and what + + + align:start position:0% +that's the protected attribute and what +what these guys point out is that + + align:start position:0% +what these guys point out is that + + + align:start position:0% +what these guys point out is that +despite the fact that you have these two + + align:start position:0% +despite the fact that you have these two + + + align:start position:0% +despite the fact that you have these two +scenarios it could well turn out that + + align:start position:0% +scenarios it could well turn out that + + + align:start position:0% +scenarios it could well turn out that +the numerical data the statistics from + + align:start position:0% +the numerical data the statistics from + + + align:start position:0% +the numerical data the statistics from +which you estimate these models are + + align:start position:0% +which you estimate these models are + + + align:start position:0% +which you estimate these models are +absolutely identical in other words the + + align:start position:0% +absolutely identical in other words the + + + align:start position:0% +absolutely identical in other words the +same fraction of people are men and + + align:start position:0% +same fraction of people are men and + + + align:start position:0% +same fraction of people are men and +women the same fraction of people are + + align:start position:0% +women the same fraction of people are + + + align:start position:0% +women the same fraction of people are +programmers they have the same + + align:start position:0% +programmers they have the same + + + align:start position:0% +programmers they have the same +relationship to those other factors and + + align:start position:0% +relationship to those other factors and + + + align:start position:0% +relationship to those other factors and +so from a purely observational viewpoint + + align:start position:0% +so from a purely observational viewpoint + + + align:start position:0% +so from a purely observational viewpoint +you can't tell which of these styles of + + align:start position:0% +you can't tell which of these styles of + + + align:start position:0% +you can't tell which of these styles of +model is correct or which version of + + align:start position:0% +model is correct or which version of + + + align:start position:0% +model is correct or which version of +fairness your data can support so that's + + align:start position:0% +fairness your data can support so that's + + + align:start position:0% +fairness your data can support so that's +a problem because we know that that + + align:start position:0% +a problem because we know that that + + + align:start position:0% +a problem because we know that that +these different notions of fairness are + + align:start position:0% +these different notions of fairness are + + + align:start position:0% +these different notions of fairness are +in conflict with each other so I wanted + + align:start position:0% +in conflict with each other so I wanted + + + align:start position:0% +in conflict with each other so I wanted +to finish by showing you a couple of + + align:start position:0% +to finish by showing you a couple of + + + align:start position:0% +to finish by showing you a couple of +examples so this was a paper based on + + align:start position:0% +examples so this was a paper based on + + + align:start position:0% +examples so this was a paper based on +Irene's work so Irene shout if I'm + + align:start position:0% +Irene's work so Irene shout if I'm + + + align:start position:0% +Irene's work so Irene shout if I'm +butchering the discussion I got a an + + align:start position:0% +butchering the discussion I got a an + + + align:start position:0% +butchering the discussion I got a an +invitation last year from the the + + align:start position:0% +invitation last year from the the + + + align:start position:0% +invitation last year from the the +American Medical Association's journal + + align:start position:0% +American Medical Association's journal + + + align:start position:0% +American Medical Association's journal +of ethics which I didn't know existed to + + align:start position:0% +of ethics which I didn't know existed to + + + align:start position:0% +of ethics which I didn't know existed to +write a think piece for them about + + align:start position:0% +write a think piece for them about + + + align:start position:0% +write a think piece for them about +fairness and machine learning and I + + align:start position:0% +fairness and machine learning and I + + + align:start position:0% +fairness and machine learning and I +decided that rather than just bloviate I + + align:start position:0% +decided that rather than just bloviate I + + + align:start position:0% +decided that rather than just bloviate I +wanted to present some real work + + align:start position:0% +wanted to present some real work + + + align:start position:0% +wanted to present some real work +and Irene had been doing some real work + + align:start position:0% +and Irene had been doing some real work + + + align:start position:0% +and Irene had been doing some real work +and so Marcia who was one of my students + + align:start position:0% +and so Marcia who was one of my students + + + align:start position:0% +and so Marcia who was one of my students +and I convinced her to get into this and + + align:start position:0% +and I convinced her to get into this and + + + align:start position:0% +and I convinced her to get into this and +we started looking at the question of + + align:start position:0% +we started looking at the question of + + + align:start position:0% +we started looking at the question of +how these machine learning models can + + align:start position:0% +how these machine learning models can + + + align:start position:0% +how these machine learning models can +identify and perhaps reduce disparities + + align:start position:0% +identify and perhaps reduce disparities + + + align:start position:0% +identify and perhaps reduce disparities +in general medical and mental health + + align:start position:0% +in general medical and mental health + + + align:start position:0% +in general medical and mental health +now why those two areas because we had + + align:start position:0% +now why those two areas because we had + + + align:start position:0% +now why those two areas because we had +access to data in those areas so general + + align:start position:0% +access to data in those areas so general + + + align:start position:0% +access to data in those areas so general +medical was actually not that general + + align:start position:0% +medical was actually not that general + + + align:start position:0% +medical was actually not that general +it's intensive care data from mimic and + + align:start position:0% +it's intensive care data from mimic and + + + align:start position:0% +it's intensive care data from mimic and +mental healthcare is some data that we + + align:start position:0% +mental healthcare is some data that we + + + align:start position:0% +mental healthcare is some data that we +had access to from Mass General and + + align:start position:0% +had access to from Mass General and + + + align:start position:0% +had access to from Mass General and +McLain's Hospital here in Boston which + + align:start position:0% +McLain's Hospital here in Boston which + + + align:start position:0% +McLain's Hospital here in Boston which +both have big psychiatric clinics so + + align:start position:0% +both have big psychiatric clinics so + + + align:start position:0% +both have big psychiatric clinics so +yeah this is what I just said so the + + align:start position:0% +yeah this is what I just said so the + + + align:start position:0% +yeah this is what I just said so the +question we were asking is is there bias + + align:start position:0% +question we were asking is is there bias + + + align:start position:0% +question we were asking is is there bias +based on race gender and insurance type + + align:start position:0% +based on race gender and insurance type + + + align:start position:0% +based on race gender and insurance type +so we were really interested in + + align:start position:0% +so we were really interested in + + + align:start position:0% +so we were really interested in +socioeconomic status but we didn't have + + align:start position:0% +socioeconomic status but we didn't have + + + align:start position:0% +socioeconomic status but we didn't have +that in the database but the type of + + align:start position:0% +that in the database but the type of + + + align:start position:0% +that in the database but the type of +insurance you have correlates pretty + + align:start position:0% +insurance you have correlates pretty + + + align:start position:0% +insurance you have correlates pretty +well with whether you're rich or poor if + + align:start position:0% +well with whether you're rich or poor if + + + align:start position:0% +well with whether you're rich or poor if +you have Medicaid insurance for example + + align:start position:0% +you have Medicaid insurance for example + + + align:start position:0% +you have Medicaid insurance for example +you were poor and if you have private + + align:start position:0% +you were poor and if you have private + + + align:start position:0% +you were poor and if you have private +insurance the first approximation you're + + align:start position:0% +insurance the first approximation you're + + + align:start position:0% +insurance the first approximation you're +rich so we did that and then we looked + + align:start position:0% +rich so we did that and then we looked + + + align:start position:0% +rich so we did that and then we looked +at the notes so we wanted to see not the + + align:start position:0% +at the notes so we wanted to see not the + + + align:start position:0% +at the notes so we wanted to see not the +coded data but whether the things that + + align:start position:0% +coded data but whether the things that + + + align:start position:0% +coded data but whether the things that +nurses and doctors said about you as you + + align:start position:0% +nurses and doctors said about you as you + + + align:start position:0% +nurses and doctors said about you as you +were in the hospital were predictive of + + align:start position:0% +were in the hospital were predictive of + + + align:start position:0% +were in the hospital were predictive of +readmission of 30-day readmission of + + align:start position:0% +readmission of 30-day readmission of + + + align:start position:0% +readmission of 30-day readmission of +whether you were likely to come back to + + align:start position:0% +whether you were likely to come back to + + + align:start position:0% +whether you were likely to come back to +the hospital so these are some of the + + align:start position:0% +the hospital so these are some of the + + + align:start position:0% +the hospital so these are some of the +topics we used LD a standard topic + + align:start position:0% +topics we used LD a standard topic + + + align:start position:0% +topics we used LD a standard topic +modeling framework and the topics as + + align:start position:0% +modeling framework and the topics as + + + align:start position:0% +modeling framework and the topics as +usual include some garbage but also + + align:start position:0% +usual include some garbage but also + + + align:start position:0% +usual include some garbage but also +include a lot of recognizably useful + + align:start position:0% +include a lot of recognizably useful + + + align:start position:0% +include a lot of recognizably useful +topics so for example mass cancer + + align:start position:0% +topics so for example mass cancer + + + align:start position:0% +topics so for example mass cancer +metastatic clearly associated with + + align:start position:0% +metastatic clearly associated with + + + align:start position:0% +metastatic clearly associated with +cancer + + align:start position:0% +cancer + + + align:start position:0% +cancer +a-fib atrial coumadin fibrillation + + align:start position:0% +a-fib atrial coumadin fibrillation + + + align:start position:0% +a-fib atrial coumadin fibrillation +associated with with heart function etc + + align:start position:0% +associated with with heart function etc + + + align:start position:0% +associated with with heart function etc +in the ICU domain in the psychiatric + + align:start position:0% +in the ICU domain in the psychiatric + + + align:start position:0% +in the ICU domain in the psychiatric +domain you + + align:start position:0% +domain you + + + align:start position:0% +domain you +things like bipolar lithium manic + + align:start position:0% +things like bipolar lithium manic + + + align:start position:0% +things like bipolar lithium manic +episode clearly associated with bipolar + + align:start position:0% +episode clearly associated with bipolar + + + align:start position:0% +episode clearly associated with bipolar +disease pain chronic milligrams the drug + + align:start position:0% +disease pain chronic milligrams the drug + + + align:start position:0% +disease pain chronic milligrams the drug +quantity associated with chronic pain + + align:start position:0% +quantity associated with chronic pain + + + align:start position:0% +quantity associated with chronic pain +etc so these were were the topics that + + align:start position:0% +etc so these were were the topics that + + + align:start position:0% +etc so these were were the topics that +we used and so we we said what happens + + align:start position:0% +we used and so we we said what happens + + + align:start position:0% +we used and so we we said what happens +when you look at how the the different + + align:start position:0% +when you look at how the the different + + + align:start position:0% +when you look at how the the different +topics how often the different topics + + align:start position:0% +topics how often the different topics + + + align:start position:0% +topics how often the different topics +arise in different subpopulations and so + + align:start position:0% +arise in different subpopulations and so + + + align:start position:0% +arise in different subpopulations and so +what we found is that for example white + + align:start position:0% +what we found is that for example white + + + align:start position:0% +what we found is that for example white +patients have more topics that are + + align:start position:0% +patients have more topics that are + + + align:start position:0% +patients have more topics that are +enriched for anxiety and chronic pain + + align:start position:0% +enriched for anxiety and chronic pain + + + align:start position:0% +enriched for anxiety and chronic pain +whereas black Hispanic and Asian + + align:start position:0% +whereas black Hispanic and Asian + + + align:start position:0% +whereas black Hispanic and Asian +patients had higher tropic enrichment + + align:start position:0% +patients had higher tropic enrichment + + + align:start position:0% +patients had higher tropic enrichment +for psychosis okay it's interesting male + + align:start position:0% +for psychosis okay it's interesting male + + + align:start position:0% +for psychosis okay it's interesting male +patients had more substance abuse + + align:start position:0% +patients had more substance abuse + + + align:start position:0% +patients had more substance abuse +problems female patients had more + + align:start position:0% +problems female patients had more + + + align:start position:0% +problems female patients had more +general depression and treatment + + align:start position:0% +general depression and treatment + + + align:start position:0% +general depression and treatment +resistant depression so you know if you + + align:start position:0% +resistant depression so you know if you + + + align:start position:0% +resistant depression so you know if you +want to create a stereotype men or + + align:start position:0% +want to create a stereotype men or + + + align:start position:0% +want to create a stereotype men or +druggies and women are depressed okay + + align:start position:0% +druggies and women are depressed okay + + + align:start position:0% +druggies and women are depressed okay +according to to this data what about + + align:start position:0% +according to to this data what about + + + align:start position:0% +according to to this data what about +insurance type well private insurance + + align:start position:0% +insurance type well private insurance + + + align:start position:0% +insurance type well private insurance +patients had higher levels of anxiety + + align:start position:0% +patients had higher levels of anxiety + + + align:start position:0% +patients had higher levels of anxiety +and depression and poorer patients were + + align:start position:0% +and depression and poorer patients were + + + align:start position:0% +and depression and poorer patients were +public insurance patients had more + + align:start position:0% +public insurance patients had more + + + align:start position:0% +public insurance patients had more +problems with substance abuse again + + align:start position:0% +problems with substance abuse again + + + align:start position:0% +problems with substance abuse again +another stereotype that you could form + + align:start position:0% +another stereotype that you could form + + + align:start position:0% +another stereotype that you could form +and then you could look at that that was + + align:start position:0% +and then you could look at that that was + + + align:start position:0% +and then you could look at that that was +in the psychiatric population in the ICU + + align:start position:0% +in the psychiatric population in the ICU + + + align:start position:0% +in the psychiatric population in the ICU +population men still have substance + + align:start position:0% +population men still have substance + + + align:start position:0% +population men still have substance +substance abuse problems women have more + + align:start position:0% +substance abuse problems women have more + + + align:start position:0% +substance abuse problems women have more +pulmonary disease and we were + + align:start position:0% +pulmonary disease and we were + + + align:start position:0% +pulmonary disease and we were +speculating on how this relates to sort + + align:start position:0% +speculating on how this relates to sort + + + align:start position:0% +speculating on how this relates to sort +of known data about under diagnosis of + + align:start position:0% +of known data about under diagnosis of + + + align:start position:0% +of known data about under diagnosis of +COPD and women by race Asian patients + + align:start position:0% +COPD and women by race Asian patients + + + align:start position:0% +COPD and women by race Asian patients +have a lot of discussion of cancer black + + align:start position:0% +have a lot of discussion of cancer black + + + align:start position:0% +have a lot of discussion of cancer black +patients have a lot of discussion of + + align:start position:0% +patients have a lot of discussion of + + + align:start position:0% +patients have a lot of discussion of +kidney problems Hispanics of liver + + align:start position:0% +kidney problems Hispanics of liver + + + align:start position:0% +kidney problems Hispanics of liver +problems and whites have a + + align:start position:0% +problems and whites have a + + + align:start position:0% +problems and whites have a +in relation so again stereotypes of + + align:start position:0% +in relation so again stereotypes of + + + align:start position:0% +in relation so again stereotypes of +what's most common in these different + + align:start position:0% +what's most common in these different + + + align:start position:0% +what's most common in these different +groups and by insurance type those with + + align:start position:0% +groups and by insurance type those with + + + align:start position:0% +groups and by insurance type those with +public insurance often have multiple + + align:start position:0% +public insurance often have multiple + + + align:start position:0% +public insurance often have multiple +chronic conditions and so public + + align:start position:0% +chronic conditions and so public + + + align:start position:0% +chronic conditions and so public +insurance patients have atrial + + align:start position:0% +insurance patients have atrial + + + align:start position:0% +insurance patients have atrial +fibrillation pacemakers dialysis these + + align:start position:0% +fibrillation pacemakers dialysis these + + + align:start position:0% +fibrillation pacemakers dialysis these +are indications of chronic heart disease + + align:start position:0% +are indications of chronic heart disease + + + align:start position:0% +are indications of chronic heart disease +and chronic kidney disease and private + + align:start position:0% +and chronic kidney disease and private + + + align:start position:0% +and chronic kidney disease and private +insurance patients have higher topic + + align:start position:0% +insurance patients have higher topic + + + align:start position:0% +insurance patients have higher topic +enrichment values for fractures so maybe + + align:start position:0% +enrichment values for fractures so maybe + + + align:start position:0% +enrichment values for fractures so maybe +they're richer they play more sports and + + align:start position:0% +they're richer they play more sports and + + + align:start position:0% +they're richer they play more sports and +break their arms or something lymphoma + + align:start position:0% +break their arms or something lymphoma + + + align:start position:0% +break their arms or something lymphoma +and aneurysms right just reporting the + + align:start position:0% +and aneurysms right just reporting the + + + align:start position:0% +and aneurysms right just reporting the +data just the facts so these results are + + align:start position:0% +data just the facts so these results are + + + align:start position:0% +data just the facts so these results are +actually consistent with lots of + + align:start position:0% +actually consistent with lots of + + + align:start position:0% +actually consistent with lots of +analyses that have been done of this + + align:start position:0% +analyses that have been done of this + + + align:start position:0% +analyses that have been done of this +kind of data + + align:start position:0% +kind of data + + + align:start position:0% +kind of data +now what Irene wanted to look at was + + align:start position:0% +now what Irene wanted to look at was + + + align:start position:0% +now what Irene wanted to look at was +this question of can we get similar + + align:start position:0% +this question of can we get similar + + + align:start position:0% +this question of can we get similar +error rates or how similar are the error + + align:start position:0% +error rates or how similar are the error + + + align:start position:0% +error rates or how similar are the error +rates that we get and the answer is in + + align:start position:0% +rates that we get and the answer is in + + + align:start position:0% +rates that we get and the answer is in +not so much so for example if you look + + align:start position:0% +not so much so for example if you look + + + align:start position:0% +not so much so for example if you look +at the ICU data we find that the error + + align:start position:0% +at the ICU data we find that the error + + + align:start position:0% +at the ICU data we find that the error +rates on a 0 1 loss metric are much + + align:start position:0% +rates on a 0 1 loss metric are much + + + align:start position:0% +rates on a 0 1 loss metric are much +lower for men than they are for women + + align:start position:0% +lower for men than they are for women + + + align:start position:0% +lower for men than they are for women +statistically significantly lower so + + align:start position:0% +statistically significantly lower so + + + align:start position:0% +statistically significantly lower so +we're able to more accurately model male + + align:start position:0% +we're able to more accurately model male + + + align:start position:0% +we're able to more accurately model male +response or male prediction of 30-day + + align:start position:0% +response or male prediction of 30-day + + + align:start position:0% +response or male prediction of 30-day +readmission and we are no sorry of ICU + + align:start position:0% +readmission and we are no sorry of ICU + + + align:start position:0% +readmission and we are no sorry of ICU +mortality for the ICU than we are for + + align:start position:0% +mortality for the ICU than we are for + + + align:start position:0% +mortality for the ICU than we are for +women + + align:start position:0% +women + + + align:start position:0% +women +similarly we have much tighter ability + + align:start position:0% +similarly we have much tighter ability + + + align:start position:0% +similarly we have much tighter ability +to predict outcomes for private + + align:start position:0% +to predict outcomes for private + + + align:start position:0% +to predict outcomes for private +insurance patients than for public + + align:start position:0% +insurance patients than for public + + + align:start position:0% +insurance patients than for public +insurance patients with a huge gap in in + + align:start position:0% +insurance patients with a huge gap in in + + + align:start position:0% +insurance patients with a huge gap in in +the confidence intervals between them so + + align:start position:0% +the confidence intervals between them so + + + align:start position:0% +the confidence intervals between them so +this indicates that there is in fact a + + align:start position:0% +this indicates that there is in fact a + + + align:start position:0% +this indicates that there is in fact a +racial bias in the data that we have and + + align:start position:0% +racial bias in the data that we have and + + + align:start position:0% +racial bias in the data that we have and +in the models that were + + align:start position:0% +in the models that were + + + align:start position:0% +in the models that were +holding these are particularly simple + + align:start position:0% +holding these are particularly simple + + + align:start position:0% +holding these are particularly simple +models in psychiatry when you look at + + align:start position:0% +models in psychiatry when you look at + + + align:start position:0% +models in psychiatry when you look at +the comparison for different ethnic + + align:start position:0% +the comparison for different ethnic + + + align:start position:0% +the comparison for different ethnic +populations you see a fair amount of + + align:start position:0% +populations you see a fair amount of + + + align:start position:0% +populations you see a fair amount of +overlap one reason we speculate is that + + align:start position:0% +overlap one reason we speculate is that + + + align:start position:0% +overlap one reason we speculate is that +we have a lot less data about + + align:start position:0% +we have a lot less data about + + + align:start position:0% +we have a lot less data about +psychiatric patients than we do about + + align:start position:0% +psychiatric patients than we do about + + + align:start position:0% +psychiatric patients than we do about +ICU patients so the models are not going + + align:start position:0% +ICU patients so the models are not going + + + align:start position:0% +ICU patients so the models are not going +to give us as accurate predictions but + + align:start position:0% +to give us as accurate predictions but + + + align:start position:0% +to give us as accurate predictions but +you still see for example a + + align:start position:0% +you still see for example a + + + align:start position:0% +you still see for example a +statistically significant difference + + align:start position:0% +statistically significant difference + + + align:start position:0% +statistically significant difference +between blacks and and other and whites + + align:start position:0% +between blacks and and other and whites + + + align:start position:0% +between blacks and and other and whites +and other races although there's a lot + + align:start position:0% +and other races although there's a lot + + + align:start position:0% +and other races although there's a lot +of overlap here again between males and + + align:start position:0% +of overlap here again between males and + + + align:start position:0% +of overlap here again between males and +females we get fewer errors in making + + align:start position:0% +females we get fewer errors in making + + + align:start position:0% +females we get fewer errors in making +predictions for males but there's not a + + align:start position:0% +predictions for males but there's not a + + + align:start position:0% +predictions for males but there's not a +95% confidence separation between them + + align:start position:0% +95% confidence separation between them + + + align:start position:0% +95% confidence separation between them +and for private versus public insurance + + align:start position:0% +and for private versus public insurance + + + align:start position:0% +and for private versus public insurance +we do see that separation where for some + + align:start position:0% +we do see that separation where for some + + + align:start position:0% +we do see that separation where for some +reason in fact we're able to make better + + align:start position:0% +reason in fact we're able to make better + + + align:start position:0% +reason in fact we're able to make better +predictions for the people on Medicare + + align:start position:0% +predictions for the people on Medicare + + + align:start position:0% +predictions for the people on Medicare +than we are or Medicaid than we are for + + align:start position:0% +than we are or Medicaid than we are for + + + align:start position:0% +than we are or Medicaid than we are for +patients and private insurance so just + + align:start position:0% +patients and private insurance so just + + + align:start position:0% +patients and private insurance so just +to wrap that up this is not a solution + + align:start position:0% +to wrap that up this is not a solution + + + align:start position:0% +to wrap that up this is not a solution +to the problem but it's it's an + + align:start position:0% +to the problem but it's it's an + + + align:start position:0% +to the problem but it's it's an +examination of the problem and and this + + align:start position:0% +examination of the problem and and this + + + align:start position:0% +examination of the problem and and this +Journal of ethics considered it + + align:start position:0% +Journal of ethics considered it + + + align:start position:0% +Journal of ethics considered it +interesting enough to publish just a + + align:start position:0% +interesting enough to publish just a + + + align:start position:0% +interesting enough to publish just a +couple of months ago the last thing I + + align:start position:0% +couple of months ago the last thing I + + + align:start position:0% +couple of months ago the last thing I +want to talk about is some work of + + align:start position:0% +want to talk about is some work of + + + align:start position:0% +want to talk about is some work of +Willie's so I'm I'm taking the risk of + + align:start position:0% +Willie's so I'm I'm taking the risk of + + + align:start position:0% +Willie's so I'm I'm taking the risk of +speaking before the people who actually + + align:start position:0% +speaking before the people who actually + + + align:start position:0% +speaking before the people who actually +did the work here and embarrassing + + align:start position:0% +did the work here and embarrassing + + + align:start position:0% +did the work here and embarrassing +myself so this is modeling mistrust in + + align:start position:0% +myself so this is modeling mistrust in + + + align:start position:0% +myself so this is modeling mistrust in +end-of-life care and it's based on on + + align:start position:0% +end-of-life care and it's based on on + + + align:start position:0% +end-of-life care and it's based on on +Willie's master's thesis and then some + + align:start position:0% +Willie's master's thesis and then some + + + align:start position:0% +Willie's master's thesis and then some +papers that came as a result of that so + + align:start position:0% +papers that came as a result of that so + + + align:start position:0% +papers that came as a result of that so +here's the interesting data if you look + + align:start position:0% +here's the interesting data if you look + + + align:start position:0% +here's the interesting data if you look +at african-american patients and these + + align:start position:0% +at african-american patients and these + + + align:start position:0% +at african-american patients and these +are patients in in the mimic data set + + align:start position:0% +are patients in in the mimic data set + + + align:start position:0% +are patients in in the mimic data set +what you find + + align:start position:0% + + + + align:start position:0% + +for mechanical ventilation blacks are on + + align:start position:0% +for mechanical ventilation blacks are on + + + align:start position:0% +for mechanical ventilation blacks are on +mechanical ventilation a lot longer than + + align:start position:0% +mechanical ventilation a lot longer than + + + align:start position:0% +mechanical ventilation a lot longer than +whites on average and there's a pretty + + align:start position:0% +whites on average and there's a pretty + + + align:start position:0% +whites on average and there's a pretty +decent separation at the P equal point + + align:start position:0% +decent separation at the P equal point + + + align:start position:0% +decent separation at the P equal point +0:05 level so half percent level between + + align:start position:0% +0:05 level so half percent level between + + + align:start position:0% +0:05 level so half percent level between +those two populations so there's + + align:start position:0% +those two populations so there's + + + align:start position:0% +those two populations so there's +something going on we're black patients + + align:start position:0% +something going on we're black patients + + + align:start position:0% +something going on we're black patients +are kept on mechanical ventilation + + align:start position:0% +are kept on mechanical ventilation + + + align:start position:0% +are kept on mechanical ventilation +longer than white patients now of course + + align:start position:0% +longer than white patients now of course + + + align:start position:0% +longer than white patients now of course +we don't know exactly why we don't know + + align:start position:0% +we don't know exactly why we don't know + + + align:start position:0% +we don't know exactly why we don't know +whether it's because there's a + + align:start position:0% +whether it's because there's a + + + align:start position:0% +whether it's because there's a +physiological difference or because it + + align:start position:0% +physiological difference or because it + + + align:start position:0% +physiological difference or because it +has something to do with their insurance + + align:start position:0% +has something to do with their insurance + + + align:start position:0% +has something to do with their insurance +or because God knows it could be any of + + align:start position:0% +or because God knows it could be any of + + + align:start position:0% +or because God knows it could be any of +a lot of different factors but that's + + align:start position:0% +a lot of different factors but that's + + + align:start position:0% +a lot of different factors but that's +the case the II ICU data set we've + + align:start position:0% +the case the II ICU data set we've + + + align:start position:0% +the case the II ICU data set we've +mentioned it's a larger but less + + align:start position:0% +mentioned it's a larger but less + + + align:start position:0% +mentioned it's a larger but less +detailed data set also of intensive care + + align:start position:0% +detailed data set also of intensive care + + + align:start position:0% +detailed data set also of intensive care +patients that was donated to Roger marks + + align:start position:0% +patients that was donated to Roger marks + + + align:start position:0% +patients that was donated to Roger marks +lab by Phillips corporation and there we + + align:start position:0% +lab by Phillips corporation and there we + + + align:start position:0% +lab by Phillips corporation and there we +see again a separation of mechanical + + align:start position:0% +see again a separation of mechanical + + + align:start position:0% +see again a separation of mechanical +ventilation duration roughly comparable + + align:start position:0% +ventilation duration roughly comparable + + + align:start position:0% +ventilation duration roughly comparable +to what we saw in the mimic data sets so + + align:start position:0% +to what we saw in the mimic data sets so + + + align:start position:0% +to what we saw in the mimic data sets so +these are consistent with each other on + + align:start position:0% +these are consistent with each other on + + + align:start position:0% +these are consistent with each other on +the other hand if you look at at the use + + align:start position:0% +the other hand if you look at at the use + + + align:start position:0% +the other hand if you look at at the use +of vasopressors in blacks versus whites + + align:start position:0% +of vasopressors in blacks versus whites + + + align:start position:0% +of vasopressors in blacks versus whites +at the P equal point 12 level you say + + align:start position:0% +at the P equal point 12 level you say + + + align:start position:0% +at the P equal point 12 level you say +well there's a little bit of evidence + + align:start position:0% +well there's a little bit of evidence + + + align:start position:0% +well there's a little bit of evidence +but not strong enough to reach any + + align:start position:0% +but not strong enough to reach any + + + align:start position:0% +but not strong enough to reach any +conclusions or in this in the II ICU + + align:start position:0% +conclusions or in this in the II ICU + + + align:start position:0% +conclusions or in this in the II ICU +data P equal point 4 2 is clearly quite + + align:start position:0% +data P equal point 4 2 is clearly quite + + + align:start position:0% +data P equal point 4 2 is clearly quite +insignificant so we're not making any + + align:start position:0% +insignificant so we're not making any + + + align:start position:0% +insignificant so we're not making any +claims there so the question that Willie + + align:start position:0% +claims there so the question that Willie + + + align:start position:0% +claims there so the question that Willie +was asking which i think is a really + + align:start position:0% +was asking which i think is a really + + + align:start position:0% +was asking which i think is a really +good question is could this difference + + align:start position:0% +good question is could this difference + + + align:start position:0% +good question is could this difference +be due not to physiological differences + + align:start position:0% +be due not to physiological differences + + + align:start position:0% +be due not to physiological differences +or even the these sort of socio-economic + + align:start position:0% +or even the these sort of socio-economic + + + align:start position:0% +or even the these sort of socio-economic +or social differences but to a + + align:start position:0% +or social differences but to a + + + align:start position:0% +or social differences but to a +difference in the degree of trust + + align:start position:0% +difference in the degree of trust + + + align:start position:0% +difference in the degree of trust +between the patient and their doctors + + align:start position:0% +between the patient and their doctors + + + align:start position:0% +between the patient and their doctors +okay interesting idea and of course I + + align:start position:0% +okay interesting idea and of course I + + + align:start position:0% +okay interesting idea and of course I +wouldn't be telling you telling you + + align:start position:0% +wouldn't be telling you telling you + + + align:start position:0% +wouldn't be telling you telling you +about this if the answer were no and so + + align:start position:0% +about this if the answer were no and so + + + align:start position:0% +about this if the answer were no and so +the approach that he took was to look + + align:start position:0% +the approach that he took was to look + + + align:start position:0% +the approach that he took was to look +for cases where there's clearly mistrust + + align:start position:0% +for cases where there's clearly mistrust + + + align:start position:0% +for cases where there's clearly mistrust +so there are red flags if you read the + + align:start position:0% +so there are red flags if you read the + + + align:start position:0% +so there are red flags if you read the +notes for example if a patient leaves + + align:start position:0% +notes for example if a patient leaves + + + align:start position:0% +notes for example if a patient leaves +the hospital against medical advice that + + align:start position:0% +the hospital against medical advice that + + + align:start position:0% +the hospital against medical advice that +is a pretty good indication that they + + align:start position:0% +is a pretty good indication that they + + + align:start position:0% +is a pretty good indication that they +don't trust the medical system if the + + align:start position:0% +don't trust the medical system if the + + + align:start position:0% +don't trust the medical system if the +family if the person dies and the family + + align:start position:0% +family if the person dies and the family + + + align:start position:0% +family if the person dies and the family +refuses to allow them to do an autopsy + + align:start position:0% +refuses to allow them to do an autopsy + + + align:start position:0% +refuses to allow them to do an autopsy +this is another indication that maybe + + align:start position:0% +this is another indication that maybe + + + align:start position:0% +this is another indication that maybe +they don't trust the medical system so + + align:start position:0% +they don't trust the medical system so + + + align:start position:0% +they don't trust the medical system so +there are these sort of red letter + + align:start position:0% +there are these sort of red letter + + + align:start position:0% +there are these sort of red letter +indicators of mistrust for example + + align:start position:0% +indicators of mistrust for example + + + align:start position:0% +indicators of mistrust for example +patient refused to sign ICU consent and + + align:start position:0% +patient refused to sign ICU consent and + + + align:start position:0% +patient refused to sign ICU consent and +expressed wishes to be do not + + align:start position:0% +expressed wishes to be do not + + + align:start position:0% +expressed wishes to be do not +resuscitate do not intubate seemingly + + align:start position:0% +resuscitate do not intubate seemingly + + + align:start position:0% +resuscitate do not intubate seemingly +very frustrated and mistrusting of the + + align:start position:0% +very frustrated and mistrusting of the + + + align:start position:0% +very frustrated and mistrusting of the +health care system also with the history + + align:start position:0% +health care system also with the history + + + align:start position:0% +health care system also with the history +of poor medication compliance and + + align:start position:0% +of poor medication compliance and + + + align:start position:0% +of poor medication compliance and +follow-up so that's a pretty clear + + align:start position:0% +follow-up so that's a pretty clear + + + align:start position:0% +follow-up so that's a pretty clear +indication and you can build a + + align:start position:0% +indication and you can build a + + + align:start position:0% +indication and you can build a +relatively simple extraction or + + align:start position:0% +relatively simple extraction or + + + align:start position:0% +relatively simple extraction or +interpretation model that identifies + + align:start position:0% +interpretation model that identifies + + + align:start position:0% +interpretation model that identifies +those clear cases this is what I was + + align:start position:0% +those clear cases this is what I was + + + align:start position:0% +those clear cases this is what I was +saying about autopsies so the problem of + + align:start position:0% +saying about autopsies so the problem of + + + align:start position:0% +saying about autopsies so the problem of +course is that not every patient has + + align:start position:0% +course is that not every patient has + + + align:start position:0% +course is that not every patient has +such an obvious label in fact most of + + align:start position:0% +such an obvious label in fact most of + + + align:start position:0% +such an obvious label in fact most of +them don't and so Willie's idea was can + + align:start position:0% +them don't and so Willie's idea was can + + + align:start position:0% +them don't and so Willie's idea was can +we learn a model from these obvious + + align:start position:0% +we learn a model from these obvious + + + align:start position:0% +we learn a model from these obvious +examples and then apply them to less + + align:start position:0% +examples and then apply them to less + + + align:start position:0% +examples and then apply them to less +obvious examples in order to get a kind + + align:start position:0% +obvious examples in order to get a kind + + + align:start position:0% +obvious examples in order to get a kind +of bronze standard or remote supervision + + align:start position:0% +of bronze standard or remote supervision + + + align:start position:0% +of bronze standard or remote supervision +notion of a larger population that has a + + align:start position:0% +notion of a larger population that has a + + + align:start position:0% +notion of a larger population that has a +tendency to be mistrustful according to + + align:start position:0% +tendency to be mistrustful according to + + + align:start position:0% +tendency to be mistrustful according to +our model without having as explicit a + + align:start position:0% +our model without having as explicit a + + + align:start position:0% +our model without having as explicit a +clear case of mistrust as in those + + align:start position:0% +clear case of mistrust as in those + + + align:start position:0% +clear case of mistrust as in those +examples and so if you look at chart + + align:start position:0% +examples and so if you look at chart + + + align:start position:0% +examples and so if you look at chart +events in mimic for example you discover + + align:start position:0% +events in mimic for example you discover + + + align:start position:0% +events in mimic for example you discover +that associated with those cases of + + align:start position:0% +that associated with those cases of + + + align:start position:0% +that associated with those cases of +obvious mistrust our features like the + + align:start position:0% +obvious mistrust our features like the + + + align:start position:0% +obvious mistrust our features like the +person was in restraints right they were + + align:start position:0% +person was in restraints right they were + + + align:start position:0% +person was in restraints right they were +literally locked down to their bed + + align:start position:0% +literally locked down to their bed + + + align:start position:0% +literally locked down to their bed +because the nurses were afraid they + + align:start position:0% +because the nurses were afraid they + + + align:start position:0% +because the nurses were afraid they +would get up and do something bad bad + + align:start position:0% +would get up and do something bad bad + + + align:start position:0% +would get up and do something bad bad +not necessarily like attack a nurse but + + align:start position:0% +not necessarily like attack a nurse but + + + align:start position:0% +not necessarily like attack a nurse but +more like fall out of bed or go + + align:start position:0% +more like fall out of bed or go + + + align:start position:0% +more like fall out of bed or go +wandering off off the floor or something + + align:start position:0% +wandering off off the floor or something + + + align:start position:0% +wandering off off the floor or something +like that if a person is in pain that + + align:start position:0% +like that if a person is in pain that + + + align:start position:0% +like that if a person is in pain that +correlated with these mistrust measures + + align:start position:0% +correlated with these mistrust measures + + + align:start position:0% +correlated with these mistrust measures +as well and conversely if you saw that + + align:start position:0% +as well and conversely if you saw that + + + align:start position:0% +as well and conversely if you saw that +somebody had their hair washed or that + + align:start position:0% +somebody had their hair washed or that + + + align:start position:0% +somebody had their hair washed or that +there was a discussion of their status + + align:start position:0% +there was a discussion of their status + + + align:start position:0% +there was a discussion of their status +and comfort then they were probably less + + align:start position:0% +and comfort then they were probably less + + + align:start position:0% +and comfort then they were probably less +likely to be mistrustful of the system + + align:start position:0% +likely to be mistrustful of the system + + + align:start position:0% +likely to be mistrustful of the system +and so the approach that that Willie + + align:start position:0% +and so the approach that that Willie + + + align:start position:0% +and so the approach that that Willie +took was to say well let's code the 620 + + align:start position:0% +took was to say well let's code the 620 + + + align:start position:0% +took was to say well let's code the 620 +binary indicators of trust and build a + + align:start position:0% +binary indicators of trust and build a + + + align:start position:0% +binary indicators of trust and build a +logistic regression model to the labeled + + align:start position:0% +logistic regression model to the labeled + + + align:start position:0% +logistic regression model to the labeled +examples and then apply it to the + + align:start position:0% +examples and then apply it to the + + + align:start position:0% +examples and then apply it to the +unlabeled examples the people for whom + + align:start position:0% +unlabeled examples the people for whom + + + align:start position:0% +unlabeled examples the people for whom +we don't have such a clear indication + + align:start position:0% +we don't have such a clear indication + + + align:start position:0% +we don't have such a clear indication +and this gives us another population of + + align:start position:0% +and this gives us another population of + + + align:start position:0% +and this gives us another population of +people who are likely to be mistrustful + + align:start position:0% +people who are likely to be mistrustful + + + align:start position:0% +people who are likely to be mistrustful +and therefore enough people that we can + + align:start position:0% +and therefore enough people that we can + + + align:start position:0% +and therefore enough people that we can +do further analysis on it so if you look + + align:start position:0% +do further analysis on it so if you look + + + align:start position:0% +do further analysis on it so if you look +at the mistrust metrics you have things + + align:start position:0% +at the mistrust metrics you have things + + + align:start position:0% +at the mistrust metrics you have things +like you know if the patient is agitated + + align:start position:0% +like you know if the patient is agitated + + + align:start position:0% +like you know if the patient is agitated +on some agitation scale they're more + + align:start position:0% +on some agitation scale they're more + + + align:start position:0% +on some agitation scale they're more +likely to be mistrustful if conversely + + align:start position:0% +likely to be mistrustful if conversely + + + align:start position:0% +likely to be mistrustful if conversely +they're alert they're less likely to be + + align:start position:0% +they're alert they're less likely to be + + + align:start position:0% +they're alert they're less likely to be +mistrustful so that means they're in + + align:start position:0% +mistrustful so that means they're in + + + align:start position:0% +mistrustful so that means they're in +some better mental shape if they're not + + align:start position:0% +some better mental shape if they're not + + + align:start position:0% +some better mental shape if they're not +in pain they're less likely to be + + align:start position:0% +in pain they're less likely to be + + + align:start position:0% +in pain they're less likely to be +mistrustful etc and if the patient was + + align:start position:0% +mistrustful etc and if the patient was + + + align:start position:0% +mistrustful etc and if the patient was +restrained then trustful patients have + + align:start position:0% +restrained then trustful patients have + + + align:start position:0% +restrained then trustful patients have +no pain or they have a spokesperson who + + align:start position:0% +no pain or they have a spokesperson who + + + align:start position:0% +no pain or they have a spokesperson who +is their health care proxy or there is a + + align:start position:0% +is their health care proxy or there is a + + + align:start position:0% +is their health care proxy or there is a +lot of family communication but + + align:start position:0% +lot of family communication but + + + align:start position:0% +lot of family communication but +conversely if constraint if restraints + + align:start position:0% +conversely if constraint if restraints + + + align:start position:0% +conversely if constraint if restraints +have to be reapplied or if they're you + + align:start position:0% +have to be reapplied or if they're you + + + align:start position:0% +have to be reapplied or if they're you +know various other factors then they're + + align:start position:0% +know various other factors then they're + + + align:start position:0% +know various other factors then they're +more likely to be mistrustful so if you + + align:start position:0% +more likely to be mistrustful so if you + + + align:start position:0% +more likely to be mistrustful so if you +look at that prediction + + align:start position:0% +look at that prediction + + + align:start position:0% + +what you find is that for both + + align:start position:0% +what you find is that for both + + + align:start position:0% +what you find is that for both +predicting the use of mechanical + + align:start position:0% +predicting the use of mechanical + + + align:start position:0% +predicting the use of mechanical +ventilation and vasopressors the + + align:start position:0% +ventilation and vasopressors the + + + align:start position:0% +ventilation and vasopressors the +disparity between a population of black + + align:start position:0% +disparity between a population of black + + + align:start position:0% +disparity between a population of black +and white and white patients is actually + + align:start position:0% +and white and white patients is actually + + + align:start position:0% +and white and white patients is actually +less significant than the disparity + + align:start position:0% +less significant than the disparity + + + align:start position:0% +less significant than the disparity +between a population of high trust and + + align:start position:0% +between a population of high trust and + + + align:start position:0% +between a population of high trust and +low trust patients so what this suggests + + align:start position:0% +low trust patients so what this suggests + + + align:start position:0% +low trust patients so what this suggests +is that the fundamental feature here + + align:start position:0% +is that the fundamental feature here + + + align:start position:0% +is that the fundamental feature here +that may be leading to that difference + + align:start position:0% +that may be leading to that difference + + + align:start position:0% +that may be leading to that difference +is in fact not race but is something + + align:start position:0% +is in fact not race but is something + + + align:start position:0% +is in fact not race but is something +that correlates with race because blacks + + align:start position:0% +that correlates with race because blacks + + + align:start position:0% +that correlates with race because blacks +are more likely to be distrustful of the + + align:start position:0% +are more likely to be distrustful of the + + + align:start position:0% +are more likely to be distrustful of the +medical system than whites now why might + + align:start position:0% +medical system than whites now why might + + + align:start position:0% +medical system than whites now why might +that be what do you know about history + + align:start position:0% + + + + align:start position:0% + +right I mean you you took the city + + align:start position:0% +right I mean you you took the city + + + align:start position:0% +right I mean you you took the city +training course that had you read the + + align:start position:0% +training course that had you read the + + + align:start position:0% +training course that had you read the +Belmont report talking about things like + + align:start position:0% +Belmont report talking about things like + + + align:start position:0% +Belmont report talking about things like +the Tuskegee Experiment you know I'm + + align:start position:0% +the Tuskegee Experiment you know I'm + + + align:start position:0% +the Tuskegee Experiment you know I'm +sure that leaves a significant + + align:start position:0% +sure that leaves a significant + + + align:start position:0% +sure that leaves a significant +impression in people's minds about how + + align:start position:0% +impression in people's minds about how + + + align:start position:0% +impression in people's minds about how +the health care system is going to treat + + align:start position:0% +the health care system is going to treat + + + align:start position:0% +the health care system is going to treat +people of their race I'm Jewish my + + align:start position:0% +people of their race I'm Jewish my + + + align:start position:0% +people of their race I'm Jewish my +mother barely lived through Auschwitz + + align:start position:0% +mother barely lived through Auschwitz + + + align:start position:0% +mother barely lived through Auschwitz +and so I understand some of the strong + + align:start position:0% +and so I understand some of the strong + + + align:start position:0% +and so I understand some of the strong +family feelings that happened as a + + align:start position:0% +family feelings that happened as a + + + align:start position:0% +family feelings that happened as a +result of some of these historical + + align:start position:0% +result of some of these historical + + + align:start position:0% +result of some of these historical +events and there were medical people + + align:start position:0% +events and there were medical people + + + align:start position:0% +events and there were medical people +doing experiments on on prisoners in the + + align:start position:0% +doing experiments on on prisoners in the + + + align:start position:0% +doing experiments on on prisoners in the +concentration camps as well so I would + + align:start position:0% +concentration camps as well so I would + + + align:start position:0% +concentration camps as well so I would +expect that people in my status might + + align:start position:0% +expect that people in my status might + + + align:start position:0% +expect that people in my status might +also have similar issues of mistrust now + + align:start position:0% +also have similar issues of mistrust now + + + align:start position:0% +also have similar issues of mistrust now +it turns out you might ask well is + + align:start position:0% +it turns out you might ask well is + + + align:start position:0% +it turns out you might ask well is +mistrust in fact just a proxy for + + align:start position:0% +mistrust in fact just a proxy for + + + align:start position:0% +mistrust in fact just a proxy for +severity are sicker people just simply + + align:start position:0% +severity are sicker people just simply + + + align:start position:0% +severity are sicker people just simply +more mistrustful and is what we're + + align:start position:0% +more mistrustful and is what we're + + + align:start position:0% +more mistrustful and is what we're +seeing just a reflection of the fact + + align:start position:0% +seeing just a reflection of the fact + + + align:start position:0% +seeing just a reflection of the fact +that they're sicker and the answer seems + + align:start position:0% +that they're sicker and the answer seems + + + align:start position:0% +that they're sicker and the answer seems +to be not so much so if you look at + + align:start position:0% +to be not so much so if you look at + + + align:start position:0% +to be not so much so if you look at +these severity scores like Oasis and + + align:start position:0% +these severity scores like Oasis and + + + align:start position:0% +these severity scores like Oasis and +saps + + align:start position:0% +saps + + + align:start position:0% +saps +and look at their correlation with + + align:start position:0% +and look at their correlation with + + + align:start position:0% +and look at their correlation with +non-compliance and autopsy those are + + align:start position:0% +non-compliance and autopsy those are + + + align:start position:0% +non-compliance and autopsy those are +pretty low correlation values + + align:start position:0% +pretty low correlation values + + + align:start position:0% +pretty low correlation values +so they're not they're not explanatory + + align:start position:0% +so they're not they're not explanatory + + + align:start position:0% +so they're not they're not explanatory +of this phenomenon and then in the + + align:start position:0% +of this phenomenon and then in the + + + align:start position:0% +of this phenomenon and then in the +population you see that again there's a + + align:start position:0% +population you see that again there's a + + + align:start position:0% +population you see that again there's a +significant difference in in sentiment + + align:start position:0% +significant difference in in sentiment + + + align:start position:0% +significant difference in in sentiment +expressed in the notes between black and + + align:start position:0% +expressed in the notes between black and + + + align:start position:0% +expressed in the notes between black and +white + + align:start position:0% +white + + + align:start position:0% +white +patients the autopsy derived mistrust + + align:start position:0% +patients the autopsy derived mistrust + + + align:start position:0% +patients the autopsy derived mistrust +metrics don't show a strong relationship + + align:start position:0% +metrics don't show a strong relationship + + + align:start position:0% +metrics don't show a strong relationship +a strong difference between them but the + + align:start position:0% +a strong difference between them but the + + + align:start position:0% +a strong difference between them but the +non-compliance derived mistrust metrics + + align:start position:0% +non-compliance derived mistrust metrics + + + align:start position:0% +non-compliance derived mistrust metrics +do so I'm out of time I'll just leave + + align:start position:0% +do so I'm out of time I'll just leave + + + align:start position:0% +do so I'm out of time I'll just leave +you with the final word there's a lot + + align:start position:0% +you with the final word there's a lot + + + align:start position:0% +you with the final word there's a lot +more work that needs to be done in this + + align:start position:0% +more work that needs to be done in this + + + align:start position:0% +more work that needs to be done in this +area and it's a very rich area both for + + align:start position:0% +area and it's a very rich area both for + + + align:start position:0% +area and it's a very rich area both for +for technical work and for trying to + + align:start position:0% +for technical work and for trying to + + + align:start position:0% +for technical work and for trying to +understand what the desiderata are and + + align:start position:0% +understand what the desiderata are and + + + align:start position:0% +understand what the desiderata are and +how to match them to technical + + align:start position:0% +how to match them to technical + + + align:start position:0% +how to match them to technical +capabilities there are these various + + align:start position:0% +capabilities there are these various + + + align:start position:0% +capabilities there are these various +conferences one of the people active in + + align:start position:0% +conferences one of the people active in + + + align:start position:0% +conferences one of the people active in +this area well one of the pairs of + + align:start position:0% +this area well one of the pairs of + + + align:start position:0% +this area well one of the pairs of +people my Kern's and Aaron Roth that pen + + align:start position:0% +people my Kern's and Aaron Roth that pen + + + align:start position:0% +people my Kern's and Aaron Roth that pen +are coming out with a book called the + + align:start position:0% +are coming out with a book called the + + + align:start position:0% +are coming out with a book called the +ethical algorithm which is coming out + + align:start position:0% +ethical algorithm which is coming out + + + align:start position:0% +ethical algorithm which is coming out +this fall my it's a popular press book + + align:start position:0% +this fall my it's a popular press book + + + align:start position:0% +this fall my it's a popular press book +I've not read it but it looks like it + + align:start position:0% +I've not read it but it looks like it + + + align:start position:0% +I've not read it but it looks like it +should be should be quite interesting + + align:start position:0% +should be should be quite interesting + + + align:start position:0% +should be should be quite interesting +and then we're starting to see whole + + align:start position:0% +and then we're starting to see whole + + + align:start position:0% +and then we're starting to see whole +classes in fairness popping up at + + align:start position:0% +classes in fairness popping up at + + + align:start position:0% +classes in fairness popping up at +different universities University of + + align:start position:0% +different universities University of + + + align:start position:0% +different universities University of +Pennsylvania has the science of data + + align:start position:0% +Pennsylvania has the science of data + + + align:start position:0% +Pennsylvania has the science of data +ethics and I've mentioned already this + + align:start position:0% +ethics and I've mentioned already this + + + align:start position:0% +ethics and I've mentioned already this +fairness and machine learning class at + + align:start position:0% +fairness and machine learning class at + + + align:start position:0% +fairness and machine learning class at +Berkeley this is in fact one of the + + align:start position:0% +Berkeley this is in fact one of the + + + align:start position:0% +Berkeley this is in fact one of the +topics we've talked about I'm on a + + align:start position:0% +topics we've talked about I'm on a + + + align:start position:0% +topics we've talked about I'm on a +committee that is planning the + + align:start position:0% +committee that is planning the + + + align:start position:0% +committee that is planning the +activities of the new Schwartzman + + align:start position:0% +activities of the new Schwartzman + + + align:start position:0% +activities of the new Schwartzman +College of Computing and this notion of + + align:start position:0% +College of Computing and this notion of + + + align:start position:0% +College of Computing and this notion of +infusing ideas about fairness and ethics + + align:start position:0% +infusing ideas about fairness and ethics + + + align:start position:0% +infusing ideas about fairness and ethics +into the technical curriculum is one of + + align:start position:0% +into the technical curriculum is one of + + + align:start position:0% +into the technical curriculum is one of +the things that we've been discussing + + align:start position:0% +the things that we've been discussing + + + align:start position:0% +the things that we've been discussing +the college obviously hasn't started yet + + align:start position:0% +the college obviously hasn't started yet + + + align:start position:0% +the college obviously hasn't started yet +so we don't have anything other than + + align:start position:0% +so we don't have anything other than + + + align:start position:0% +so we don't have anything other than +this lecture and a few other things like + + align:start position:0% +this lecture and a few other things like + + + align:start position:0% +this lecture and a few other things like +that in the works but the plan is there + + align:start position:0% +that in the works but the plan is there + + + align:start position:0% +that in the works but the plan is there +to expand more in the + + align:start position:0% +to expand more in the + + + align:start position:0% +to expand more in the +Uriel + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/zYzEmBlJ77s.txt b/zYzEmBlJ77s.txt new file mode 100644 index 0000000000000000000000000000000000000000..be3e72c207ba0607acf21e01fd488d242d6752da --- /dev/null +++ b/zYzEmBlJ77s.txt @@ -0,0 +1,15923 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so to start we're gonna recap what + + align:start position:0% +so to start we're gonna recap what + + + align:start position:0% +so to start we're gonna recap what +happened last class and last class we + + align:start position:0% +happened last class and last class we + + + align:start position:0% +happened last class and last class we +were talking about how traditional + + align:start position:0% +were talking about how traditional + + + align:start position:0% +were talking about how traditional +payment systems work and some of the + + align:start position:0% +payment systems work and some of the + + + align:start position:0% +payment systems work and some of the +downsides when you had a bank in the + + align:start position:0% +downsides when you had a bank in the + + + align:start position:0% +downsides when you had a bank in the +middle even if you were using techniques + + align:start position:0% +middle even if you were using techniques + + + align:start position:0% +middle even if you were using techniques +like Chow me and E cash to try to manage + + align:start position:0% +like Chow me and E cash to try to manage + + + align:start position:0% +like Chow me and E cash to try to manage +what the bank was doing so just as a + + align:start position:0% +what the bank was doing so just as a + + + align:start position:0% +what the bank was doing so just as a +quick reminder we had this kind of setup + + align:start position:0% +quick reminder we had this kind of setup + + + align:start position:0% +quick reminder we had this kind of setup +where there was Alice and there was Bob + + align:start position:0% +where there was Alice and there was Bob + + + align:start position:0% +where there was Alice and there was Bob +Alice with in order to actually make + + align:start position:0% +Alice with in order to actually make + + + align:start position:0% +Alice with in order to actually make +transfers Alice had to interact with the + + align:start position:0% +transfers Alice had to interact with the + + + align:start position:0% +transfers Alice had to interact with the +bank and in the case of sort of the + + align:start position:0% +bank and in the case of sort of the + + + align:start position:0% +bank and in the case of sort of the +traditional payment system we saw that + + align:start position:0% +traditional payment system we saw that + + + align:start position:0% +traditional payment system we saw that +the bank could basically just say no + + align:start position:0% +the bank could basically just say no + + + align:start position:0% +the bank could basically just say no +right that it was always possible that a + + align:start position:0% +right that it was always possible that a + + + align:start position:0% +right that it was always possible that a +bank could decide that it didn't like + + align:start position:0% +bank could decide that it didn't like + + + align:start position:0% +bank could decide that it didn't like +Alice and it didn't want to process + + align:start position:0% +Alice and it didn't want to process + + + align:start position:0% +Alice and it didn't want to process +Alice's transactions we got a little + + align:start position:0% +Alice's transactions we got a little + + + align:start position:0% +Alice's transactions we got a little +better than this with Chow me and E cash + + align:start position:0% +better than this with Chow me and E cash + + + align:start position:0% +better than this with Chow me and E cash +but even with Tommy and ecash the bank + + align:start position:0% +but even with Tommy and ecash the bank + + + align:start position:0% +but even with Tommy and ecash the bank +was required to do something they were + + align:start position:0% +was required to do something they were + + + align:start position:0% +was required to do something they were +the ones minting the tokens and they + + align:start position:0% +the ones minting the tokens and they + + + align:start position:0% +the ones minting the tokens and they +were the ones redeeming the token so the + + align:start position:0% +were the ones redeeming the token so the + + + align:start position:0% +were the ones redeeming the token so the +banks still played an integral part in + + align:start position:0% +banks still played an integral part in + + + align:start position:0% +banks still played an integral part in +this system and you know that actually + + align:start position:0% +this system and you know that actually + + + align:start position:0% +this system and you know that actually +really does make a difference it's not + + align:start position:0% +really does make a difference it's not + + + align:start position:0% +really does make a difference it's not +just a theoretical problem + + align:start position:0% +just a theoretical problem + + + align:start position:0% +just a theoretical problem +there are many accounts of people with + + align:start position:0% +there are many accounts of people with + + + align:start position:0% +there are many accounts of people with +for example PayPal accounts who have + + align:start position:0% +for example PayPal accounts who have + + + align:start position:0% +for example PayPal accounts who have +their who have their funds frozen so + + align:start position:0% +their who have their funds frozen so + + + align:start position:0% +their who have their funds frozen so +they can't access the money that they + + align:start position:0% +they can't access the money that they + + + align:start position:0% +they can't access the money that they +have in PayPal so you know this often + + align:start position:0% +have in PayPal so you know this often + + + align:start position:0% +have in PayPal so you know this often +happens to merchants actually who end up + + align:start position:0% +happens to merchants actually who end up + + + align:start position:0% +happens to merchants actually who end up +accepting customers from different + + align:start position:0% +accepting customers from different + + + align:start position:0% +accepting customers from different +countries or things like this they can + + align:start position:0% +countries or things like this they can + + + align:start position:0% +countries or things like this they can +get flagged by PayPal's algorithms as + + align:start position:0% +get flagged by PayPal's algorithms as + + + align:start position:0% +get flagged by PayPal's algorithms as +being potentially fraudulent and that + + align:start position:0% +being potentially fraudulent and that + + + align:start position:0% +being potentially fraudulent and that +can put a hold on their funds in the + + align:start position:0% +can put a hold on their funds in the + + + align:start position:0% +can put a hold on their funds in the +case of Chow me and E cash you'll notice + + align:start position:0% +case of Chow me and E cash you'll notice + + + align:start position:0% +case of Chow me and E cash you'll notice +that we're not all running around using + + align:start position:0% +that we're not all running around using + + + align:start position:0% +that we're not all running around using +digital tokens issued by banks chummy me + + align:start position:0% +digital tokens issued by banks chummy me + + + align:start position:0% +digital tokens issued by banks chummy me +cash didn't really work out and that was + + align:start position:0% +cash didn't really work out and that was + + + align:start position:0% +cash didn't really work out and that was +in part due to the fact that banks + + align:start position:0% +in part due to the fact that banks + + + align:start position:0% +in part due to the fact that banks +weren't really interested in + + align:start position:0% +weren't really interested in + + + align:start position:0% +weren't really interested in +implementing this technique so okay so + + align:start position:0% +implementing this technique so okay so + + + align:start position:0% +implementing this technique so okay so +this is where we ended last class which + + align:start position:0% +this is where we ended last class which + + + align:start position:0% +this is where we ended last class which +was we're in this situation where the + + align:start position:0% +was we're in this situation where the + + + align:start position:0% +was we're in this situation where the +bank sort of has a lot of control over + + align:start position:0% +bank sort of has a lot of control over + + + align:start position:0% +bank sort of has a lot of control over +payments and how payments happen and and + + align:start position:0% +payments and how payments happen and and + + + align:start position:0% +payments and how payments happen and and +something I want to emphasize here as + + align:start position:0% +something I want to emphasize here as + + + align:start position:0% +something I want to emphasize here as +well is you know this isn't it's not + + align:start position:0% +well is you know this isn't it's not + + + align:start position:0% +well is you know this isn't it's not +just that we worry about this + + align:start position:0% +just that we worry about this + + + align:start position:0% +just that we worry about this +because we want to do a legal activity + + align:start position:0% +because we want to do a legal activity + + + align:start position:0% +because we want to do a legal activity +having an institution in the middle of + + align:start position:0% +having an institution in the middle of + + + align:start position:0% +having an institution in the middle of +payments and sort of being able to + + align:start position:0% +payments and sort of being able to + + + align:start position:0% +payments and sort of being able to +facilitate payments can can be a problem + + align:start position:0% +facilitate payments can can be a problem + + + align:start position:0% +facilitate payments can can be a problem +in other ways as well because it can + + align:start position:0% +in other ways as well because it can + + + align:start position:0% +in other ways as well because it can +just simply make things slower it can + + align:start position:0% +just simply make things slower it can + + + align:start position:0% +just simply make things slower it can +make things it's harder to innovate it's + + align:start position:0% +make things it's harder to innovate it's + + + align:start position:0% +make things it's harder to innovate it's +harder to introduce new features there's + + align:start position:0% +harder to introduce new features there's + + + align:start position:0% +harder to introduce new features there's +a sign-up process so you know there are + + align:start position:0% +a sign-up process so you know there are + + + align:start position:0% +a sign-up process so you know there are +reasons why we don't want to have an + + align:start position:0% +reasons why we don't want to have an + + + align:start position:0% +reasons why we don't want to have an +institution in the middle even if we're + + align:start position:0% +institution in the middle even if we're + + + align:start position:0% +institution in the middle even if we're +totally honest actors so the question so + + align:start position:0% +totally honest actors so the question so + + + align:start position:0% +totally honest actors so the question so +where we ended up was how do we build a + + align:start position:0% +where we ended up was how do we build a + + + align:start position:0% +where we ended up was how do we build a +decentralized digital token transfer so + + align:start position:0% +decentralized digital token transfer so + + + align:start position:0% +decentralized digital token transfer so +we ended with tell me Andy cash and now + + align:start position:0% +we ended with tell me Andy cash and now + + + align:start position:0% +we ended with tell me Andy cash and now +we're in this position where what we + + align:start position:0% +we're in this position where what we + + + align:start position:0% +we're in this position where what we +want to do is we want to figure out how + + align:start position:0% +want to do is we want to figure out how + + + align:start position:0% +want to do is we want to figure out how +to make payments without a bank in the + + align:start position:0% +to make payments without a bank in the + + + align:start position:0% +to make payments without a bank in the +middle so there's a few problems that + + align:start position:0% +middle so there's a few problems that + + + align:start position:0% +middle so there's a few problems that +we're gonna have to address in order to + + align:start position:0% +we're gonna have to address in order to + + + align:start position:0% +we're gonna have to address in order to +make this happen okay + + align:start position:0% +make this happen okay + + + align:start position:0% +make this happen okay +so first of all we really don't want it + + align:start position:0% +so first of all we really don't want it + + + align:start position:0% +so first of all we really don't want it +to be possible for other users to + + align:start position:0% +to be possible for other users to + + + align:start position:0% +to be possible for other users to +intercept a transfer of payment and + + align:start position:0% +intercept a transfer of payment and + + + align:start position:0% +intercept a transfer of payment and +steal funds if our system can't support + + align:start position:0% +steal funds if our system can't support + + + align:start position:0% +steal funds if our system can't support +this sort of very basic thing then no + + align:start position:0% +this sort of very basic thing then no + + + align:start position:0% +this sort of very basic thing then no +one's gonna use it no one's gonna trust + + align:start position:0% +one's gonna use it no one's gonna trust + + + align:start position:0% +one's gonna use it no one's gonna trust +it no one's going to rely on it so it's + + align:start position:0% +it no one's going to rely on it so it's + + + align:start position:0% +it no one's going to rely on it so it's +very important that we have security + + align:start position:0% +very important that we have security + + + align:start position:0% +very important that we have security +right another aspect of security is that + + align:start position:0% +right another aspect of security is that + + + align:start position:0% +right another aspect of security is that +we don't want to allow people to spend + + align:start position:0% +we don't want to allow people to spend + + + align:start position:0% +we don't want to allow people to spend +money without authorization there has to + + align:start position:0% +money without authorization there has to + + + align:start position:0% +money without authorization there has to +be some mechanism by which we're really + + align:start position:0% +be some mechanism by which we're really + + + align:start position:0% +be some mechanism by which we're really +sure it's Alice when Alice wants to make + + align:start position:0% +sure it's Alice when Alice wants to make + + + align:start position:0% +sure it's Alice when Alice wants to make +a payment another thing another problem + + align:start position:0% +a payment another thing another problem + + + align:start position:0% +a payment another thing another problem +that we want to avoid is a double spend + + align:start position:0% +that we want to avoid is a double spend + + + align:start position:0% +that we want to avoid is a double spend +problem so what is the double spend + + align:start position:0% +problem so what is the double spend + + + align:start position:0% +problem so what is the double spend +problem well oh and and equivocation + + align:start position:0% +problem well oh and and equivocation + + + align:start position:0% +problem well oh and and equivocation +problem so what is the double spend + + align:start position:0% +problem so what is the double spend + + + align:start position:0% +problem so what is the double spend +problem well when you have digital + + align:start position:0% +problem well when you have digital + + + align:start position:0% +problem well when you have digital +tokens the problem with with digital + + align:start position:0% +tokens the problem with with digital + + + align:start position:0% +tokens the problem with with digital +information is that it can really easily + + align:start position:0% +information is that it can really easily + + + align:start position:0% +information is that it can really easily +be replicated right so you actually need + + align:start position:0% +be replicated right so you actually need + + + align:start position:0% +be replicated right so you actually need +to think pretty carefully + + align:start position:0% +to think pretty carefully + + + align:start position:0% +to think pretty carefully +it's the naive solution of just having a + + align:start position:0% +it's the naive solution of just having a + + + align:start position:0% +it's the naive solution of just having a +unique string that you blast around at + + align:start position:0% +unique string that you blast around at + + + align:start position:0% +unique string that you blast around at +your digital token doesn't really work + + align:start position:0% +your digital token doesn't really work + + + align:start position:0% +your digital token doesn't really work +you have to do something extra to think + + align:start position:0% +you have to do something extra to think + + + align:start position:0% +you have to do something extra to think +about how to ensure that these once a + + align:start position:0% +about how to ensure that these once a + + + align:start position:0% +about how to ensure that these once a +token is spent it cannot be spent again + + align:start position:0% +token is spent it cannot be spent again + + + align:start position:0% +token is spent it cannot be spent again +now what I mean by the equivocation + + align:start position:0% +now what I mean by the equivocation + + + align:start position:0% +now what I mean by the equivocation +problem is you want to make sure that + + align:start position:0% +problem is you want to make sure that + + + align:start position:0% +problem is you want to make sure that +once a spend happens it can + + align:start position:0% +once a spend happens it can + + + align:start position:0% +once a spend happens it can +be taken back very easily right so if + + align:start position:0% +be taken back very easily right so if + + + align:start position:0% +be taken back very easily right so if +I'm being paid by Alice I have some + + align:start position:0% +I'm being paid by Alice I have some + + + align:start position:0% +I'm being paid by Alice I have some +confidence that once I actually receive + + align:start position:0% +confidence that once I actually receive + + + align:start position:0% +confidence that once I actually receive +the money I've received the money Alice + + align:start position:0% +the money I've received the money Alice + + + align:start position:0% +the money I've received the money Alice +can't renege on that promise okay so + + align:start position:0% +can't renege on that promise okay so + + + align:start position:0% +can't renege on that promise okay so +these are some of the problems that we + + align:start position:0% +these are some of the problems that we + + + align:start position:0% +these are some of the problems that we +want to solve with a with a + + align:start position:0% +want to solve with a with a + + + align:start position:0% +want to solve with a with a +decentralized digital payment system and + + align:start position:0% +decentralized digital payment system and + + + align:start position:0% +decentralized digital payment system and +here are some of the features that we + + align:start position:0% +here are some of the features that we + + + align:start position:0% +here are some of the features that we +want to have which is kind of related to + + align:start position:0% +want to have which is kind of related to + + + align:start position:0% +want to have which is kind of related to +some of the problems so first of all we + + align:start position:0% +some of the problems so first of all we + + + align:start position:0% +some of the problems so first of all we +want to make sure that anyone can use it + + align:start position:0% +want to make sure that anyone can use it + + + align:start position:0% +want to make sure that anyone can use it +that's what we mean by the word do you + + align:start position:0% +that's what we mean by the word do you + + + align:start position:0% +that's what we mean by the word do you +centralized there's no single point of + + align:start position:0% +centralized there's no single point of + + + align:start position:0% +centralized there's no single point of +control there's no one metering access + + align:start position:0% +control there's no one metering access + + + align:start position:0% +control there's no one metering access +to this system if you want to make + + align:start position:0% +to this system if you want to make + + + align:start position:0% +to this system if you want to make +payments if you want to join the system + + align:start position:0% +payments if you want to join the system + + + align:start position:0% +payments if you want to join the system +you can join the system so anyone can + + align:start position:0% +you can join the system so anyone can + + + align:start position:0% +you can join the system so anyone can +use it + + align:start position:0% +use it + + + align:start position:0% +use it +we need a Thorat ativ transfer so that + + align:start position:0% +we need a Thorat ativ transfer so that + + + align:start position:0% +we need a Thorat ativ transfer so that +we can be sure that when Alice produces + + align:start position:0% +we can be sure that when Alice produces + + + align:start position:0% +we can be sure that when Alice produces +a transaction it's really her and we + + align:start position:0% +a transaction it's really her and we + + + align:start position:0% +a transaction it's really her and we +believe that and we want to make it so + + align:start position:0% +believe that and we want to make it so + + + align:start position:0% +believe that and we want to make it so +that you can't equivocate you can't undo + + align:start position:0% +that you can't equivocate you can't undo + + + align:start position:0% +that you can't equivocate you can't undo +Spence so that translates into the + + align:start position:0% +Spence so that translates into the + + + align:start position:0% +Spence so that translates into the +following sort of terminology that we + + align:start position:0% +following sort of terminology that we + + + align:start position:0% +following sort of terminology that we +often use with these systems we want it + + align:start position:0% +often use with these systems we want it + + + align:start position:0% +often use with these systems we want it +to be permissionless it doesn't require + + align:start position:0% +to be permissionless it doesn't require + + + align:start position:0% +to be permissionless it doesn't require +permission to enter the system anyone + + align:start position:0% +permission to enter the system anyone + + + align:start position:0% +permission to enter the system anyone +can join authoritative transfer no + + align:start position:0% +can join authoritative transfer no + + + align:start position:0% +can join authoritative transfer no +double spends and can't undo we call + + align:start position:0% +double spends and can't undo we call + + + align:start position:0% +double spends and can't undo we call +that being tamper proof so we don't want + + align:start position:0% +that being tamper proof so we don't want + + + align:start position:0% +that being tamper proof so we don't want +it to be the case that someone could go + + align:start position:0% +it to be the case that someone could go + + + align:start position:0% +it to be the case that someone could go +back and undo a spend another way to + + align:start position:0% +back and undo a spend another way to + + + align:start position:0% +back and undo a spend another way to +think about that is we don't want people + + align:start position:0% +think about that is we don't want people + + + align:start position:0% +think about that is we don't want people +tampering with history something that + + align:start position:0% +tampering with history something that + + + align:start position:0% +tampering with history something that +would be really useful here and + + align:start position:0% +would be really useful here and + + + align:start position:0% +would be really useful here and +something that the bank was kind of + + align:start position:0% +something that the bank was kind of + + + align:start position:0% +something that the bank was kind of +keeping implicitly was a database of who + + align:start position:0% +keeping implicitly was a database of who + + + align:start position:0% +keeping implicitly was a database of who +was transferring money to whom right + + align:start position:0% +was transferring money to whom right + + + align:start position:0% +was transferring money to whom right +that was sort of the little the little + + align:start position:0% +that was sort of the little the little + + + align:start position:0% +that was sort of the little the little +thing in the corner which said how much + + align:start position:0% +thing in the corner which said how much + + + align:start position:0% +thing in the corner which said how much +was in Alice's account and how much was + + align:start position:0% +was in Alice's account and how much was + + + align:start position:0% +was in Alice's account and how much was +in Bob's account um there are actually + + align:start position:0% +in Bob's account um there are actually + + + align:start position:0% +in Bob's account um there are actually +techniques out there for maintaining a + + align:start position:0% +techniques out there for maintaining a + + + align:start position:0% +techniques out there for maintaining a +decentralized database among a set of + + align:start position:0% +decentralized database among a set of + + + align:start position:0% +decentralized database among a set of +participants this problem of needing to + + align:start position:0% +participants this problem of needing to + + + align:start position:0% +participants this problem of needing to +agree on a value amongst many different + + align:start position:0% +agree on a value amongst many different + + + align:start position:0% +agree on a value amongst many different +participants is a problem known as + + align:start position:0% +participants is a problem known as + + + align:start position:0% +participants is a problem known as +distributed consensus so here's what + + align:start position:0% +distributed consensus so here's what + + + align:start position:0% +distributed consensus so here's what +distributed consensus means and if + + align:start position:0% +distributed consensus means and if + + + align:start position:0% +distributed consensus means and if +you've taken 8 to 4 then you've probably + + align:start position:0% +you've taken 8 to 4 then you've probably + + + align:start position:0% +you've taken 8 to 4 then you've probably +seen this before but distributed + + align:start position:0% +seen this before but distributed + + + align:start position:0% +seen this before but distributed +consensus is a problem of multiple + + align:start position:0% +consensus is a problem of multiple + + + align:start position:0% +consensus is a problem of multiple +computers agreeing on a value + + align:start position:0% +computers agreeing on a value + + + align:start position:0% +computers agreeing on a value +particularly in the presence of faults + + align:start position:0% +particularly in the presence of faults + + + align:start position:0% +particularly in the presence of faults +so some of these computers might + + align:start position:0% +so some of these computers might + + + align:start position:0% +so some of these computers might +or go away you can use this technique + + align:start position:0% +or go away you can use this technique + + + align:start position:0% +or go away you can use this technique +distributed consensus to build a log of + + align:start position:0% +distributed consensus to build a log of + + + align:start position:0% +distributed consensus to build a log of +operations with something called state + + align:start position:0% +operations with something called state + + + align:start position:0% +operations with something called state +machine replication and essentially what + + align:start position:0% +machine replication and essentially what + + + align:start position:0% +machine replication and essentially what +you have when you do this is a + + align:start position:0% +you have when you do this is a + + + align:start position:0% +you have when you do this is a +distributed database which is what we're + + align:start position:0% +distributed database which is what we're + + + align:start position:0% +distributed database which is what we're +trying to obtain here we need to keep + + align:start position:0% +trying to obtain here we need to keep + + + align:start position:0% +trying to obtain here we need to keep +track of accounts and who's spending + + align:start position:0% +track of accounts and who's spending + + + align:start position:0% +track of accounts and who's spending +what and what payments have happened in + + align:start position:0% +what and what payments have happened in + + + align:start position:0% +what and what payments have happened in +the system and so distributed consensus + + align:start position:0% +the system and so distributed consensus + + + align:start position:0% +the system and so distributed consensus +is a tool that we might be able to use + + align:start position:0% +is a tool that we might be able to use + + + align:start position:0% +is a tool that we might be able to use +to do this so the reason that we might + + align:start position:0% +to do this so the reason that we might + + + align:start position:0% +to do this so the reason that we might +be able to use distributed consensus to + + align:start position:0% +be able to use distributed consensus to + + + align:start position:0% +be able to use distributed consensus to +do this is we could keep a log of all of + + align:start position:0% +do this is we could keep a log of all of + + + align:start position:0% +do this is we could keep a log of all of +the transactions in the system so Alice + + align:start position:0% +the transactions in the system so Alice + + + align:start position:0% +the transactions in the system so Alice +pays Bob David pace charlie and what + + align:start position:0% +pays Bob David pace charlie and what + + + align:start position:0% +pays Bob David pace charlie and what +this log provides it provides ordering + + align:start position:0% +this log provides it provides ordering + + + align:start position:0% +this log provides it provides ordering +so if Alice tries to pay Carol the same + + align:start position:0% +so if Alice tries to pay Carol the same + + + align:start position:0% +so if Alice tries to pay Carol the same +thing that Alice pays Bob because we + + align:start position:0% +thing that Alice pays Bob because we + + + align:start position:0% +thing that Alice pays Bob because we +have this primitive this log this + + align:start position:0% +have this primitive this log this + + + align:start position:0% +have this primitive this log this +globally ordered log everyone can see + + align:start position:0% +globally ordered log everyone can see + + + align:start position:0% +globally ordered log everyone can see +that this came after that one right + + align:start position:0% +that this came after that one right + + + align:start position:0% +that this came after that one right +everyone can see that Alice was trying + + align:start position:0% +everyone can see that Alice was trying + + + align:start position:0% +everyone can see that Alice was trying +to double spend Alice was trying to + + align:start position:0% +to double spend Alice was trying to + + + align:start position:0% +to double spend Alice was trying to +spend the same coin twice so this + + align:start position:0% +spend the same coin twice so this + + + align:start position:0% +spend the same coin twice so this +primitive is going to be really useful + + align:start position:0% +primitive is going to be really useful + + + align:start position:0% +primitive is going to be really useful +this idea of this globally ordered log + + align:start position:0% +this idea of this globally ordered log + + + align:start position:0% +this idea of this globally ordered log +of transactions it's kind of what + + align:start position:0% +of transactions it's kind of what + + + align:start position:0% +of transactions it's kind of what +fundamentally underlines underlies all + + align:start position:0% +fundamentally underlines underlies all + + + align:start position:0% +fundamentally underlines underlies all +of these things so you know we could we + + align:start position:0% +of these things so you know we could we + + + align:start position:0% +of these things so you know we could we +could say if we were to see this log and + + align:start position:0% +could say if we were to see this log and + + + align:start position:0% +could say if we were to see this log and +we were to see this transaction pop up + + align:start position:0% +we were to see this transaction pop up + + + align:start position:0% +we were to see this transaction pop up +we can decide that this doesn't really + + align:start position:0% +we can decide that this doesn't really + + + align:start position:0% +we can decide that this doesn't really +count that this is you know Alice + + align:start position:0% +count that this is you know Alice + + + align:start position:0% +count that this is you know Alice +already spent her coin a property that + + align:start position:0% +already spent her coin a property that + + + align:start position:0% +already spent her coin a property that +we want to maintain with these things is + + align:start position:0% +we want to maintain with these things is + + + align:start position:0% +we want to maintain with these things is +that you can only spend a coin once so + + align:start position:0% +that you can only spend a coin once so + + + align:start position:0% +that you can only spend a coin once so +therefore we're not really gonna allow + + align:start position:0% +therefore we're not really gonna allow + + + align:start position:0% +therefore we're not really gonna allow +this to happen so as I said the the + + align:start position:0% +this to happen so as I said the the + + + align:start position:0% +this to happen so as I said the the +problem of distributed consensus is that + + align:start position:0% +problem of distributed consensus is that + + + align:start position:0% +problem of distributed consensus is that +when you have a whole bunch of people + + align:start position:0% +when you have a whole bunch of people + + + align:start position:0% +when you have a whole bunch of people +working on this log you can tolerate + + align:start position:0% +working on this log you can tolerate + + + align:start position:0% +working on this log you can tolerate +false so if some of the people go away + + align:start position:0% +false so if some of the people go away + + + align:start position:0% +false so if some of the people go away +if it's only up to a certain number it's + + align:start position:0% +if it's only up to a certain number it's + + + align:start position:0% +if it's only up to a certain number it's +okay you still have a consistent + + align:start position:0% +okay you still have a consistent + + + align:start position:0% +okay you still have a consistent +globally order log so there's a lot of + + align:start position:0% +globally order log so there's a lot of + + + align:start position:0% +globally order log so there's a lot of +existing systems that actually provide + + align:start position:0% +existing systems that actually provide + + + align:start position:0% +existing systems that actually provide +this property some of them are Paxos + + align:start position:0% +this property some of them are Paxos + + + align:start position:0% +this property some of them are Paxos +zookeeper and raft if you've ever heard + + align:start position:0% +zookeeper and raft if you've ever heard + + + align:start position:0% +zookeeper and raft if you've ever heard +of them so the way that these protocols + + align:start position:0% +of them so the way that these protocols + + + align:start position:0% +of them so the way that these protocols +work is that all of these participants + + align:start position:0% +work is that all of these participants + + + align:start position:0% +work is that all of these participants +are executing the protocol to agree on + + align:start position:0% +are executing the protocol to agree on + + + align:start position:0% +are executing the protocol to agree on +the log if if you fail the protocol can + + align:start position:0% +the log if if you fail the protocol can + + + align:start position:0% +the log if if you fail the protocol can +so operate usually they can tolerate up + + align:start position:0% +so operate usually they can tolerate up + + + align:start position:0% +so operate usually they can tolerate up +to + + align:start position:0% +to + + + align:start position:0% +to +or a failing so these protocols the ones + + align:start position:0% +or a failing so these protocols the ones + + + align:start position:0% +or a failing so these protocols the ones +that I just listed operating something + + align:start position:0% +that I just listed operating something + + + align:start position:0% +that I just listed operating something +called the crash fault tolerance model + + align:start position:0% +called the crash fault tolerance model + + + align:start position:0% +called the crash fault tolerance model +meaning they can handle computers going + + align:start position:0% +meaning they can handle computers going + + + align:start position:0% +meaning they can handle computers going +away but not really much else and when + + align:start position:0% +away but not really much else and when + + + align:start position:0% +away but not really much else and when +we're operating in decentralized digital + + align:start position:0% +we're operating in decentralized digital + + + align:start position:0% +we're operating in decentralized digital +payment land we want to be able to + + align:start position:0% +payment land we want to be able to + + + align:start position:0% +payment land we want to be able to +tolerate more than crashes we want to be + + align:start position:0% +tolerate more than crashes we want to be + + + align:start position:0% +tolerate more than crashes we want to be +able to tolerate actively malicious + + align:start position:0% +able to tolerate actively malicious + + + align:start position:0% +able to tolerate actively malicious +behavior because if you're gonna create + + align:start position:0% +behavior because if you're gonna create + + + align:start position:0% +behavior because if you're gonna create +a digital payment system and it's money + + align:start position:0% +a digital payment system and it's money + + + align:start position:0% +a digital payment system and it's money +then people are gonna try to steal that + + align:start position:0% +then people are gonna try to steal that + + + align:start position:0% +then people are gonna try to steal that +money so like I said if people go away + + align:start position:0% +money so like I said if people go away + + + align:start position:0% +money so like I said if people go away +if it's up to a minority you can still + + align:start position:0% +if it's up to a minority you can still + + + align:start position:0% +if it's up to a minority you can still +have the log so there's stuff from the + + align:start position:0% +have the log so there's stuff from the + + + align:start position:0% +have the log so there's stuff from the +literature that actually supports + + align:start position:0% +literature that actually supports + + + align:start position:0% +literature that actually supports +something close to this there's + + align:start position:0% +something close to this there's + + + align:start position:0% +something close to this there's +something called Byzantine fault + + align:start position:0% +something called Byzantine fault + + + align:start position:0% +something called Byzantine fault +tolerance and Byzantine fault tolerance + + align:start position:0% +tolerance and Byzantine fault tolerance + + + align:start position:0% +tolerance and Byzantine fault tolerance +tolerates more than crashes it actually + + align:start position:0% +tolerates more than crashes it actually + + + align:start position:0% +tolerates more than crashes it actually +tolerates actively malicious + + align:start position:0% +tolerates actively malicious + + + align:start position:0% +tolerates actively malicious +participants it can tolerate a smaller + + align:start position:0% +participants it can tolerate a smaller + + + align:start position:0% +participants it can tolerate a smaller +number of actively participants up to a + + align:start position:0% +number of actively participants up to a + + + align:start position:0% +number of actively participants up to a +third so here nodes might not just fail + + align:start position:0% +third so here nodes might not just fail + + + align:start position:0% +third so here nodes might not just fail +they might actually try to subvert the + + align:start position:0% +they might actually try to subvert the + + + align:start position:0% +they might actually try to subvert the +protocol to to keep from landing on a + + align:start position:0% +protocol to to keep from landing on a + + + align:start position:0% +protocol to to keep from landing on a +single globally ordered log and like I + + align:start position:0% +single globally ordered log and like I + + + align:start position:0% +single globally ordered log and like I +said we have protocols that can tolerate + + align:start position:0% +said we have protocols that can tolerate + + + align:start position:0% +said we have protocols that can tolerate +this great however and these protocols + + align:start position:0% +this great however and these protocols + + + align:start position:0% +this great however and these protocols +are very very old okay like visit the + + align:start position:0% +are very very old okay like visit the + + + align:start position:0% +are very very old okay like visit the +Byzantine generals problem which was + + align:start position:0% +Byzantine generals problem which was + + + align:start position:0% +Byzantine generals problem which was +sort of a basic formulation of what led + + align:start position:0% +sort of a basic formulation of what led + + + align:start position:0% +sort of a basic formulation of what led +to Byzantine fault tolerance was + + align:start position:0% +to Byzantine fault tolerance was + + + align:start position:0% +to Byzantine fault tolerance was +formulated in nineteen eighty-two Paxos + + align:start position:0% +formulated in nineteen eighty-two Paxos + + + align:start position:0% +formulated in nineteen eighty-two Paxos +and view stamp replication also came + + align:start position:0% +and view stamp replication also came + + + align:start position:0% +and view stamp replication also came +about in the eighties those are to + + align:start position:0% +about in the eighties those are to + + + align:start position:0% +about in the eighties those are to +distribute consensus program protocols + + align:start position:0% +distribute consensus program protocols + + + align:start position:0% +distribute consensus program protocols +practical Byzantine fault tolerance so + + align:start position:0% +practical Byzantine fault tolerance so + + + align:start position:0% +practical Byzantine fault tolerance so +an actual like very practical protocol + + align:start position:0% +an actual like very practical protocol + + + align:start position:0% +an actual like very practical protocol +that you can implement and that you can + + align:start position:0% +that you can implement and that you can + + + align:start position:0% +that you can implement and that you can +use to create a globally ordered log + + align:start position:0% +use to create a globally ordered log + + + align:start position:0% +use to create a globally ordered log +that was in the 90s and you know ever + + align:start position:0% +that was in the 90s and you know ever + + + align:start position:0% +that was in the 90s and you know ever +since then we've had a lot of different + + align:start position:0% +since then we've had a lot of different + + + align:start position:0% +since then we've had a lot of different +protocols so and then in 2009 Bitcoin so + + align:start position:0% +protocols so and then in 2009 Bitcoin so + + + align:start position:0% +protocols so and then in 2009 Bitcoin so +this idea this idea of a globally + + align:start position:0% +this idea this idea of a globally + + + align:start position:0% +this idea this idea of a globally +ordered log that can tolerate malicious + + align:start position:0% +ordered log that can tolerate malicious + + + align:start position:0% +ordered log that can tolerate malicious +participants the thing I want to impress + + align:start position:0% +participants the thing I want to impress + + + align:start position:0% +participants the thing I want to impress +upon you is that it's an old idea + + align:start position:0% +upon you is that it's an old idea + + + align:start position:0% +upon you is that it's an old idea +decades old so what's new what happened + + align:start position:0% +decades old so what's new what happened + + + align:start position:0% +decades old so what's new what happened +with Bitcoin well a downside the + + align:start position:0% +with Bitcoin well a downside the + + + align:start position:0% +with Bitcoin well a downside the +all of these systems have is that you + + align:start position:0% +all of these systems have is that you + + + align:start position:0% +all of these systems have is that you +need to know exactly who is + + align:start position:0% +need to know exactly who is + + + align:start position:0% +need to know exactly who is +participating in the protocol so the way + + align:start position:0% +participating in the protocol so the way + + + align:start position:0% +participating in the protocol so the way +that these systems work is as the + + align:start position:0% +that these systems work is as the + + + align:start position:0% +that these systems work is as the +protocol works based on identity so you + + align:start position:0% +protocol works based on identity so you + + + align:start position:0% +protocol works based on identity so you +have to know who is involved you need to + + align:start position:0% +have to know who is involved you need to + + + align:start position:0% +have to know who is involved you need to +know everybody in the system you know + + align:start position:0% +know everybody in the system you know + + + align:start position:0% +know everybody in the system you know +everybody in the system you can tell you + + align:start position:0% +everybody in the system you can tell you + + + align:start position:0% +everybody in the system you can tell you +know as who's sending you messages and + + align:start position:0% +know as who's sending you messages and + + + align:start position:0% +know as who's sending you messages and +who's not sending you messages and you + + align:start position:0% +who's not sending you messages and you + + + align:start position:0% +who's not sending you messages and you +can make decisions about what everybody + + align:start position:0% +can make decisions about what everybody + + + align:start position:0% +can make decisions about what everybody +else thinks the globally ordered log + + align:start position:0% +else thinks the globally ordered log + + + align:start position:0% +else thinks the globally ordered log +looks like the thing that these + + align:start position:0% +looks like the thing that these + + + align:start position:0% +looks like the thing that these +protocols did not tolerate was when you + + align:start position:0% +protocols did not tolerate was when you + + + align:start position:0% +protocols did not tolerate was when you +don't know everybody in the system and + + align:start position:0% +don't know everybody in the system and + + + align:start position:0% +don't know everybody in the system and +the problem when you don't know + + align:start position:0% +the problem when you don't know + + + align:start position:0% +the problem when you don't know +everybody in the system + + align:start position:0% +everybody in the system + + + align:start position:0% +everybody in the system +and you're not doing participation based + + align:start position:0% +and you're not doing participation based + + + align:start position:0% +and you're not doing participation based +on identity is that an attacker could + + align:start position:0% +on identity is that an attacker could + + + align:start position:0% +on identity is that an attacker could +create a whole bunch of identities + + align:start position:0% +create a whole bunch of identities + + + align:start position:0% +create a whole bunch of identities +there's nothing preventing an attacker + + align:start position:0% +there's nothing preventing an attacker + + + align:start position:0% +there's nothing preventing an attacker +from creating identities and remember we + + align:start position:0% +from creating identities and remember we + + + align:start position:0% +from creating identities and remember we +want a permissionless decentralized + + align:start position:0% +want a permissionless decentralized + + + align:start position:0% +want a permissionless decentralized +system we don't want to have some + + align:start position:0% +system we don't want to have some + + + align:start position:0% +system we don't want to have some +gatekeeper saying who can enter into and + + align:start position:0% +gatekeeper saying who can enter into and + + + align:start position:0% +gatekeeper saying who can enter into and +out of the system and given that we + + align:start position:0% +out of the system and given that we + + + align:start position:0% +out of the system and given that we +don't want to have that gatekeeper we + + align:start position:0% +don't want to have that gatekeeper we + + + align:start position:0% +don't want to have that gatekeeper we +can't just let people join willy-nilly + + align:start position:0% +can't just let people join willy-nilly + + + align:start position:0% +can't just let people join willy-nilly +and manufacture their own identities + + align:start position:0% +and manufacture their own identities + + + align:start position:0% +and manufacture their own identities +because if they do all of these + + align:start position:0% +because if they do all of these + + + align:start position:0% +because if they do all of these +protocols all of a sudden no longer work + + align:start position:0% +protocols all of a sudden no longer work + + + align:start position:0% +protocols all of a sudden no longer work +this is what's known as a Sybil attack + + align:start position:0% +this is what's known as a Sybil attack + + + align:start position:0% +this is what's known as a Sybil attack +okay when an attacker can create + + align:start position:0% +okay when an attacker can create + + + align:start position:0% +okay when an attacker can create +identities essentially for free and can + + align:start position:0% +identities essentially for free and can + + + align:start position:0% +identities essentially for free and can +swarm the good guys and take over the + + align:start position:0% +swarm the good guys and take over the + + + align:start position:0% +swarm the good guys and take over the +protocol so we're I'm gonna leave you is + + align:start position:0% +protocol so we're I'm gonna leave you is + + + align:start position:0% +protocol so we're I'm gonna leave you is +with this problem which is we want to + + align:start position:0% +with this problem which is we want to + + + align:start position:0% +with this problem which is we want to +figure out how to address the Sybil + + align:start position:0% +figure out how to address the Sybil + + + align:start position:0% +figure out how to address the Sybil +attack problem when creating a globally + + align:start position:0% +attack problem when creating a globally + + + align:start position:0% +attack problem when creating a globally +ordered log and and one way of doing + + align:start position:0% +ordered log and and one way of doing + + + align:start position:0% +ordered log and and one way of doing +that is to think about making identities + + align:start position:0% +that is to think about making identities + + + align:start position:0% +that is to think about making identities +costly so good guys can create new + + align:start position:0% +costly so good guys can create new + + + align:start position:0% +costly so good guys can create new +identities and can join the system and + + align:start position:0% +identities and can join the system and + + + align:start position:0% +identities and can join the system and +can execute the protocol bad guys could + + align:start position:0% +can execute the protocol bad guys could + + + align:start position:0% +can execute the protocol bad guys could +potentially create identities and join + + align:start position:0% +potentially create identities and join + + + align:start position:0% +potentially create identities and join +the system and execute the protocol but + + align:start position:0% +the system and execute the protocol but + + + align:start position:0% +the system and execute the protocol but +because identities actually cost + + align:start position:0% +because identities actually cost + + + align:start position:0% +because identities actually cost +something there's a limit there's an + + align:start position:0% +something there's a limit there's an + + + align:start position:0% +something there's a limit there's an +inherent limit they don't come for free + + align:start position:0% +inherent limit they don't come for free + + + align:start position:0% +inherent limit they don't come for free +the bad guys can only create so many and + + align:start position:0% +the bad guys can only create so many and + + + align:start position:0% +the bad guys can only create so many and +that's where I want to end are there any + + align:start position:0% +that's where I want to end are there any + + + align:start position:0% +that's where I want to end are there any +questions about that as we transfer over + + align:start position:0% +questions about that as we transfer over + + + align:start position:0% +questions about that as we transfer over +to attach + + align:start position:0% + + + + align:start position:0% + +yeah this percentage to deal with the + + align:start position:0% +yeah this percentage to deal with the + + + align:start position:0% +yeah this percentage to deal with the +security consensus that's you have + + align:start position:0% +security consensus that's you have + + + align:start position:0% +security consensus that's you have +synchronicity not necessarily so that + + align:start position:0% +synchronicity not necessarily so that + + + align:start position:0% +synchronicity not necessarily so that +problem is unsolvable in the case where + + align:start position:0% +problem is unsolvable in the case where + + + align:start position:0% +problem is unsolvable in the case where +there it a totally asynchronous system + + align:start position:0% +there it a totally asynchronous system + + + align:start position:0% +there it a totally asynchronous system +but there's there's a lot of different + + align:start position:0% +but there's there's a lot of different + + + align:start position:0% +but there's there's a lot of different +ways to create a model where for example + + align:start position:0% +ways to create a model where for example + + + align:start position:0% +ways to create a model where for example +if you have random coins then it is + + align:start position:0% +if you have random coins then it is + + + align:start position:0% +if you have random coins then it is +solvable in an asynchronous system so + + align:start position:0% +solvable in an asynchronous system so + + + align:start position:0% +solvable in an asynchronous system so +this is something that you might have + + align:start position:0% +this is something that you might have + + + align:start position:0% +this is something that you might have +heard of something called the cap + + align:start position:0% +heard of something called the cap + + + align:start position:0% +heard of something called the cap +theorem this is sort of a predecessor to + + align:start position:0% +theorem this is sort of a predecessor to + + + align:start position:0% +theorem this is sort of a predecessor to +that which indicates that in a totally + + align:start position:0% +that which indicates that in a totally + + + align:start position:0% +that which indicates that in a totally +asynchronous system without random coins + + align:start position:0% +asynchronous system without random coins + + + align:start position:0% +asynchronous system without random coins +consensus is actually impossible but + + align:start position:0% +consensus is actually impossible but + + + align:start position:0% +consensus is actually impossible but +that's there's there's different ways to + + align:start position:0% +that's there's there's different ways to + + + align:start position:0% +that's there's there's different ways to +sort of get around that and oftentimes + + align:start position:0% +sort of get around that and oftentimes + + + align:start position:0% +sort of get around that and oftentimes +people assume that the system is semi + + align:start position:0% +people assume that the system is semi + + + align:start position:0% +people assume that the system is semi +synchronous what oh sorry yeah + + align:start position:0% + + + + align:start position:0% + +exactly and that's what Taj is going to + + align:start position:0% +exactly and that's what Taj is going to + + + align:start position:0% +exactly and that's what Taj is going to +talk about yes okay everyone I'm gonna + + align:start position:0% +talk about yes okay everyone I'm gonna + + + align:start position:0% +talk about yes okay everyone I'm gonna +talk about proof work which is in my Tim + + align:start position:0% +talk about proof work which is in my Tim + + + align:start position:0% +talk about proof work which is in my Tim +in my estimation sort of the thing that + + align:start position:0% +in my estimation sort of the thing that + + + align:start position:0% +in my estimation sort of the thing that +started all of this that you know + + align:start position:0% +started all of this that you know + + + align:start position:0% +started all of this that you know +there's all sorts of cool cryptography + + align:start position:0% +there's all sorts of cool cryptography + + + align:start position:0% +there's all sorts of cool cryptography +involved in Bitcoin and different + + align:start position:0% +involved in Bitcoin and different + + + align:start position:0% +involved in Bitcoin and different +cryptocurrencies but it was the proven + + align:start position:0% +cryptocurrencies but it was the proven + + + align:start position:0% +cryptocurrencies but it was the proven +where consensus that sort of kicked all + + align:start position:0% +where consensus that sort of kicked all + + + align:start position:0% +where consensus that sort of kicked all +this off and it was the big difference + + align:start position:0% +this off and it was the big difference + + + align:start position:0% +this off and it was the big difference +so we want to cost anyhow was mentioning + + align:start position:0% +so we want to cost anyhow was mentioning + + + align:start position:0% +so we want to cost anyhow was mentioning +we want some kind of cost to create + + align:start position:0% +we want some kind of cost to create + + + align:start position:0% +we want some kind of cost to create +identities or cost to participate in the + + align:start position:0% +identities or cost to participate in the + + + align:start position:0% +identities or cost to participate in the +system how do we prevent civil attacks + + align:start position:0% +system how do we prevent civil attacks + + + align:start position:0% +system how do we prevent civil attacks +and this is a very hard problem because + + align:start position:0% +and this is a very hard problem because + + + align:start position:0% +and this is a very hard problem because +it tends to be an arms race in many in + + align:start position:0% +it tends to be an arms race in many in + + + align:start position:0% +it tends to be an arms race in many in +many ways we're like you know Twitter or + + align:start position:0% +many ways we're like you know Twitter or + + + align:start position:0% +many ways we're like you know Twitter or +Facebook or things like that have those + + align:start position:0% +Facebook or things like that have those + + + align:start position:0% +Facebook or things like that have those +tons of bots because as soon as Twitter + + align:start position:0% +tons of bots because as soon as Twitter + + + align:start position:0% +tons of bots because as soon as Twitter +makes a cool new algorithm to identify + + align:start position:0% +makes a cool new algorithm to identify + + + align:start position:0% +makes a cool new algorithm to identify +what's a bot and kick them off the + + align:start position:0% +what's a bot and kick them off the + + + align:start position:0% +what's a bot and kick them off the +system the various people who are trying + + align:start position:0% +system the various people who are trying + + + align:start position:0% +system the various people who are trying +to make millions of Twitter BOTS start + + align:start position:0% +to make millions of Twitter BOTS start + + + align:start position:0% +to make millions of Twitter BOTS start +to figure it out they're like hey they + + align:start position:0% +to figure it out they're like hey they + + + align:start position:0% +to figure it out they're like hey they +banned all these BOTS well I'll switch + + align:start position:0% +banned all these BOTS well I'll switch + + + align:start position:0% +banned all these BOTS well I'll switch +this around and you know make my BOTS + + align:start position:0% +this around and you know make my BOTS + + + align:start position:0% +this around and you know make my BOTS +more human-like and better + + align:start position:0% +more human-like and better + + + align:start position:0% +more human-like and better +I was actually kicked off of Twitter for + + align:start position:0% +I was actually kicked off of Twitter for + + + align:start position:0% +I was actually kicked off of Twitter for +being a bot and I totally they say that + + align:start position:0% +being a bot and I totally they say that + + + align:start position:0% +being a bot and I totally they say that +it exhibited automated activity so so + + align:start position:0% +it exhibited automated activity so so + + + align:start position:0% +it exhibited automated activity so so +this is a hard problem and this is sort + + align:start position:0% +this is a hard problem and this is sort + + + align:start position:0% +this is a hard problem and this is sort +of you know gets into like Turing test + + align:start position:0% +of you know gets into like Turing test + + + align:start position:0% +of you know gets into like Turing test +CAPTCHA kind of thing as well but this + + align:start position:0% +CAPTCHA kind of thing as well but this + + + align:start position:0% +CAPTCHA kind of thing as well but this +is Bitcoin is a fairly different + + align:start position:0% +is Bitcoin is a fairly different + + + align:start position:0% +is Bitcoin is a fairly different +solution and as I said you don't want + + align:start position:0% +solution and as I said you don't want + + + align:start position:0% +solution and as I said you don't want +really anyone in charge you don't want a + + align:start position:0% +really anyone in charge you don't want a + + + align:start position:0% +really anyone in charge you don't want a +set identity list of people who can + + align:start position:0% +set identity list of people who can + + + align:start position:0% +set identity list of people who can +participate so that rules out things + + align:start position:0% +participate so that rules out things + + + align:start position:0% +participate so that rules out things +that that other systems use like let's + + align:start position:0% +that that other systems use like let's + + + align:start position:0% +that that other systems use like let's +use Social Security numbers let's use + + align:start position:0% +use Social Security numbers let's use + + + align:start position:0% +use Social Security numbers let's use +phone numbers let's use CAPTCHAs well + + align:start position:0% +phone numbers let's use CAPTCHAs well + + + align:start position:0% +phone numbers let's use CAPTCHAs well +those don't really apply like what's a + + align:start position:0% +those don't really apply like what's a + + + align:start position:0% +those don't really apply like what's a +social security number what if I mean + + align:start position:0% +social security number what if I mean + + + align:start position:0% +social security number what if I mean +you know Germany and I want to use it + + align:start position:0% +you know Germany and I want to use it + + + align:start position:0% +you know Germany and I want to use it +what if I'm in somewhere else you know + + align:start position:0% +what if I'm in somewhere else you know + + + align:start position:0% +what if I'm in somewhere else you know +phone numbers as well phone numbers are + + align:start position:0% +phone numbers as well phone numbers are + + + align:start position:0% +phone numbers as well phone numbers are +just administrated by a phone company + + align:start position:0% +just administrated by a phone company + + + align:start position:0% +just administrated by a phone company +who would then become the de-facto + + align:start position:0% +who would then become the de-facto + + + align:start position:0% +who would then become the de-facto +controller of the system and CAPTCHAs + + align:start position:0% +controller of the system and CAPTCHAs + + + align:start position:0% +controller of the system and CAPTCHAs +are kind of an interesting idea and but + + align:start position:0% +are kind of an interesting idea and but + + + align:start position:0% +are kind of an interesting idea and but +they you know the like identify the + + align:start position:0% +they you know the like identify the + + + align:start position:0% +they you know the like identify the +signs in this picture or the cars in + + align:start position:0% +signs in this picture or the cars in + + + align:start position:0% +signs in this picture or the cars in +this picture or whatever but it doesn't + + align:start position:0% +this picture or whatever but it doesn't + + + align:start position:0% +this picture or whatever but it doesn't +really apply because it's not sort of + + align:start position:0% +really apply because it's not sort of + + + align:start position:0% +really apply because it's not sort of +easy for people to verify and not easy + + align:start position:0% +easy for people to verify and not easy + + + align:start position:0% +easy for people to verify and not easy +for computers to verify that like the + + align:start position:0% +for computers to verify that like the + + + align:start position:0% +for computers to verify that like the +people were actually doing it so those + + align:start position:0% +people were actually doing it so those + + + align:start position:0% +people were actually doing it so those +don't work so what does work is work so + + align:start position:0% +don't work so what does work is work so + + + align:start position:0% +don't work so what does work is work so +I don't know if I think some people have + + align:start position:0% +I don't know if I think some people have + + + align:start position:0% +I don't know if I think some people have +said they've they've some people said + + align:start position:0% +said they've they've some people said + + + align:start position:0% +said they've they've some people said +like the first day oh I did problems + + align:start position:0% +like the first day oh I did problems + + + align:start position:0% +like the first day oh I did problems +that one's like oh okay cool + + align:start position:0% +that one's like oh okay cool + + + align:start position:0% +that one's like oh okay cool +some people have yet to start which is + + align:start position:0% +some people have yet to start which is + + + align:start position:0% +some people have yet to start which is +fine as well but if you have started and + + align:start position:0% +fine as well but if you have started and + + + align:start position:0% +fine as well but if you have started and +looked into problem set one great I will + + align:start position:0% +looked into problem set one great I will + + + align:start position:0% +looked into problem set one great I will +talk about it a little bit in the next + + align:start position:0% +talk about it a little bit in the next + + + align:start position:0% +talk about it a little bit in the next +few minutes the problem set needs many + + align:start position:0% +few minutes the problem set needs many + + + align:start position:0% +few minutes the problem set needs many +attempts to forge a signature so if + + align:start position:0% +attempts to forge a signature so if + + + align:start position:0% +attempts to forge a signature so if +you've done it you've I don't know what + + align:start position:0% +you've done it you've I don't know what + + + align:start position:0% +you've done it you've I don't know what +the fastest probably someone got it to + + align:start position:0% +the fastest probably someone got it to + + + align:start position:0% +the fastest probably someone got it to +work really fast when I completed it it + + align:start position:0% +work really fast when I completed it it + + + align:start position:0% +work really fast when I completed it it +took I got it to run on a course of a + + align:start position:0% +took I got it to run on a course of a + + + align:start position:0% +took I got it to run on a course of a +fairly fast machine and I got it to run + + align:start position:0% +fairly fast machine and I got it to run + + + align:start position:0% +fairly fast machine and I got it to run +in like three minutes and it took me + + align:start position:0% +in like three minutes and it took me + + + align:start position:0% +in like three minutes and it took me +something like two billion attempts + + align:start position:0% +something like two billion attempts + + + align:start position:0% +something like two billion attempts +which it should write two billion is + + align:start position:0% +which it should write two billion is + + + align:start position:0% +which it should write two billion is +around so this is because the hash + + align:start position:0% +around so this is because the hash + + + align:start position:0% +around so this is because the hash +functions have random output right I'm + + align:start position:0% +functions have random output right I'm + + + align:start position:0% +functions have random output right I'm +looking for a string where certain bits + + align:start position:0% +looking for a string where certain bits + + + align:start position:0% +looking for a string where certain bits +are set and certain bits are free and + + align:start position:0% +are set and certain bits are free and + + + align:start position:0% +are set and certain bits are free and +since the hash functions have random + + align:start position:0% +since the hash functions have random + + + align:start position:0% +since the hash functions have random +output I have no shortcut this to be + + align:start position:0% +output I have no shortcut this to be + + + align:start position:0% +output I have no shortcut this to be +like well I want an output where these + + align:start position:0% +like well I want an output where these + + + align:start position:0% +like well I want an output where these +bits are ones and these bits are zeros + + align:start position:0% +bits are ones and these bits are zeros + + + align:start position:0% +bits are ones and these bits are zeros +and the rest I don't care I can't really + + align:start position:0% +and the rest I don't care I can't really + + + align:start position:0% +and the rest I don't care I can't really +specify that as the input to my hash + + align:start position:0% +specify that as the input to my hash + + + align:start position:0% +specify that as the input to my hash +function so I just have to keep trying + + align:start position:0% +function so I just have to keep trying + + + align:start position:0% +function so I just have to keep trying +different numbers right we know what we + + align:start position:0% +different numbers right we know what we + + + align:start position:0% +different numbers right we know what we +want but the only way to get it is just + + align:start position:0% +want but the only way to get it is just + + + align:start position:0% +want but the only way to get it is just +keep throwing in different numbers to + + align:start position:0% +keep throwing in different numbers to + + + align:start position:0% +keep throwing in different numbers to +this hash function getting the output + + align:start position:0% +this hash function getting the output + + + align:start position:0% +this hash function getting the output +and checking if it matches our criteria + + align:start position:0% +and checking if it matches our criteria + + + align:start position:0% +and checking if it matches our criteria +so what do you want out of work in this + + align:start position:0% +so what do you want out of work in this + + + align:start position:0% +so what do you want out of work in this +case you want it to be time consuming so + + align:start position:0% +case you want it to be time consuming so + + + align:start position:0% +case you want it to be time consuming so +I'm kind of like the homework but the + + align:start position:0% +I'm kind of like the homework but the + + + align:start position:0% +I'm kind of like the homework but the +example of the homework has some + + align:start position:0% +example of the homework has some + + + align:start position:0% +example of the homework has some +problems because it's this weird trusted + + align:start position:0% +problems because it's this weird trusted + + + align:start position:0% +problems because it's this weird trusted +set up right in fact it's so in the + + align:start position:0% +set up right in fact it's so in the + + + align:start position:0% +set up right in fact it's so in the +homework case you're trying to forge a + + align:start position:0% +homework case you're trying to forge a + + + align:start position:0% +homework case you're trying to forge a +signature where I have the private key + + align:start position:0% +signature where I have the private key + + + align:start position:0% +signature where I have the private key +I've made four signatures and you want + + align:start position:0% +I've made four signatures and you want + + + align:start position:0% +I've made four signatures and you want +to forge a fifth signature without my + + align:start position:0% +to forge a fifth signature without my + + + align:start position:0% +to forge a fifth signature without my +private key the problem is it seems like + + align:start position:0% +private key the problem is it seems like + + + align:start position:0% +private key the problem is it seems like +I would have an advantage in this work I + + align:start position:0% +I would have an advantage in this work I + + + align:start position:0% +I would have an advantage in this work I +actually don't because you can verify + + align:start position:0% +actually don't because you can verify + + + align:start position:0% +actually don't because you can verify +that I haven't revealed any new bits but + + align:start position:0% +that I haven't revealed any new bits but + + + align:start position:0% +that I haven't revealed any new bits but +it but there's it's a weird setup right + + align:start position:0% +it but there's it's a weird setup right + + + align:start position:0% +it but there's it's a weird setup right +where it's like okay well there's one + + align:start position:0% +where it's like okay well there's one + + + align:start position:0% +where it's like okay well there's one +certain actor that like sets up this + + align:start position:0% +certain actor that like sets up this + + + align:start position:0% +certain actor that like sets up this +whole work and like we shouldn't have + + align:start position:0% +whole work and like we shouldn't have + + + align:start position:0% +whole work and like we shouldn't have +that kind + + align:start position:0% +that kind + + + align:start position:0% +that kind +so you want it to be deterministic you + + align:start position:0% +so you want it to be deterministic you + + + align:start position:0% +so you want it to be deterministic you +also want it to be scalable and you want + + align:start position:0% +also want it to be scalable and you want + + + align:start position:0% +also want it to be scalable and you want +it to be memoryless where everyone sort + + align:start position:0% +it to be memoryless where everyone sort + + + align:start position:0% +it to be memoryless where everyone sort +of gets a chance and you're not making + + align:start position:0% +of gets a chance and you're not making + + + align:start position:0% +of gets a chance and you're not making +progress because if you are I'll get to + + align:start position:0% +progress because if you are I'll get to + + + align:start position:0% +progress because if you are I'll get to +that later but if you're making progress + + align:start position:0% +that later but if you're making progress + + + align:start position:0% +that later but if you're making progress +it tends to be that the fastest person + + align:start position:0% +it tends to be that the fastest person + + + align:start position:0% +it tends to be that the fastest person +always wins + + align:start position:0% +always wins + + + align:start position:0% +always wins +right it's if there's no randomness + + align:start position:0% +right it's if there's no randomness + + + align:start position:0% +right it's if there's no randomness +involved like if it's you know let's + + align:start position:0% +involved like if it's you know let's + + + align:start position:0% +involved like if it's you know let's +have a race between a bicycle and + + align:start position:0% +have a race between a bicycle and + + + align:start position:0% +have a race between a bicycle and +someone running it's like well that's + + align:start position:0% +someone running it's like well that's + + + align:start position:0% +someone running it's like well that's +not really a race ever the bicycle is + + align:start position:0% +not really a race ever the bicycle is + + + align:start position:0% +not really a race ever the bicycle is +always gonna win whereas in this case if + + align:start position:0% +always gonna win whereas in this case if + + + align:start position:0% +always gonna win whereas in this case if +it's memoryless every attempt is a new + + align:start position:0% +it's memoryless every attempt is a new + + + align:start position:0% +it's memoryless every attempt is a new +shot at getting it and so someone who's + + align:start position:0% +shot at getting it and so someone who's + + + align:start position:0% +shot at getting it and so someone who's +10% is fast will still win 10% of the + + align:start position:0% +10% is fast will still win 10% of the + + + align:start position:0% +10% is fast will still win 10% of the +time okay so in the case of the homework + + align:start position:0% +time okay so in the case of the homework + + + align:start position:0% +time okay so in the case of the homework +so here's an example where five bits of + + align:start position:0% +so here's an example where five bits of + + + align:start position:0% +so here's an example where five bits of +eight are constrained so let's say these + + align:start position:0% +eight are constrained so let's say these + + + align:start position:0% +eight are constrained so let's say these +first two you've got the preimages for + + align:start position:0% +first two you've got the preimages for + + + align:start position:0% +first two you've got the preimages for +both the one you know this is the zero + + align:start position:0% +both the one you know this is the zero + + + align:start position:0% +both the one you know this is the zero +row this is the one row and the the + + align:start position:0% +row this is the one row and the the + + + align:start position:0% +row this is the one row and the the +signatures I've revealed okay you get + + align:start position:0% +signatures I've revealed okay you get + + + align:start position:0% +signatures I've revealed okay you get +both bits here however here in this + + align:start position:0% +both bits here however here in this + + + align:start position:0% +both bits here however here in this +place you only have the one bit being + + align:start position:0% +place you only have the one bit being + + + align:start position:0% +place you only have the one bit being +the one preimage here you only have a + + align:start position:0% +the one preimage here you only have a + + + align:start position:0% +the one preimage here you only have a +zero here you only have the one here + + align:start position:0% +zero here you only have the one here + + + align:start position:0% +zero here you only have the one here +you've got both and then you're also + + align:start position:0% +you've got both and then you're also + + + align:start position:0% +you've got both and then you're also +here one zero so the idea is these three + + align:start position:0% +here one zero so the idea is these three + + + align:start position:0% +here one zero so the idea is these three +bits are like X like don't care either + + align:start position:0% +bits are like X like don't care either + + + align:start position:0% +bits are like X like don't care either +either a 1 or a 0 will will work these 5 + + align:start position:0% +either a 1 or a 0 will will work these 5 + + + align:start position:0% +either a 1 or a 0 will will work these 5 +bits are constrained so it must match 1 + + align:start position:0% +bits are constrained so it must match 1 + + + align:start position:0% +bits are constrained so it must match 1 +0 1 and then 1 so you're gonna have to + + align:start position:0% +0 1 and then 1 so you're gonna have to + + + align:start position:0% +0 1 and then 1 so you're gonna have to +keep trying messages and since 5 bits + + align:start position:0% +keep trying messages and since 5 bits + + + align:start position:0% +keep trying messages and since 5 bits +are constrained you're gonna have to try + + align:start position:0% +are constrained you're gonna have to try + + + align:start position:0% +are constrained you're gonna have to try +to the 5 messages which is about 64 yeah + + align:start position:0% +to the 5 messages which is about 64 yeah + + + align:start position:0% +to the 5 messages which is about 64 yeah +which is totally doable right 64 tries + + align:start position:0% +which is totally doable right 64 tries + + + align:start position:0% +which is totally doable right 64 tries +and you'll probably get it so for + + align:start position:0% +and you'll probably get it so for + + + align:start position:0% +and you'll probably get it so for +example you try once and you say ok I + + align:start position:0% +example you try once and you say ok I + + + align:start position:0% +example you try once and you say ok I +got 1 1 0 0 1 1 0 0 doesn't work these + + align:start position:0% +got 1 1 0 0 1 1 0 0 doesn't work these + + + align:start position:0% +got 1 1 0 0 1 1 0 0 doesn't work these +are ok because they're ok no matter what + + align:start position:0% +are ok because they're ok no matter what + + + align:start position:0% +are ok because they're ok no matter what +this one's wrong this one's ok this + + align:start position:0% +this one's wrong this one's ok this + + + align:start position:0% +this one's wrong this one's ok this +one's okay this one's wrong let me try + + align:start position:0% +one's okay this one's wrong let me try + + + align:start position:0% +one's okay this one's wrong let me try +again + + align:start position:0% +again + + + align:start position:0% +again +but you okay I got it right these can be + + align:start position:0% +but you okay I got it right these can be + + + align:start position:0% +but you okay I got it right these can be +anything + + align:start position:0% +anything + + + align:start position:0% +anything +I got a 0 & 1 sure these all line up the + + align:start position:0% +I got a 0 & 1 sure these all line up the + + + align:start position:0% +I got a 0 & 1 sure these all line up the +red ones all line up so I found a valid + + align:start position:0% +red ones all line up so I found a valid + + + align:start position:0% +red ones all line up so I found a valid +solution and so that works as a + + align:start position:0% +solution and so that works as a + + + align:start position:0% +solution and so that works as a +proof-of-work and in this case I found a + + align:start position:0% +proof-of-work and in this case I found a + + + align:start position:0% +proof-of-work and in this case I found a +solution which was a tag forge + + align:start position:0% +solution which was a tag forge + + + align:start position:0% +solution which was a tag forge +154 million two hundred sixty two + + align:start position:0% +154 million two hundred sixty two + + + align:start position:0% +154 million two hundred sixty two +thousand one hundred seven and that's a + + align:start position:0% +thousand one hundred seven and that's a + + + align:start position:0% +thousand one hundred seven and that's a +message that can be forged given those + + align:start position:0% +message that can be forged given those + + + align:start position:0% +message that can be forged given those +four signatures in the problem set and + + align:start position:0% +four signatures in the problem set and + + + align:start position:0% +four signatures in the problem set and +anyone can you know whatever homework + + align:start position:0% +anyone can you know whatever homework + + + align:start position:0% +anyone can you know whatever homework +solution you have you can probably copy + + align:start position:0% +solution you have you can probably copy + + + align:start position:0% +solution you have you can probably copy +and paste that string and check that you + + align:start position:0% +and paste that string and check that you + + + align:start position:0% +and paste that string and check that you +know if you hash that you'll get a hash + + align:start position:0% +know if you hash that you'll get a hash + + + align:start position:0% +know if you hash that you'll get a hash +that like matches up and can be signed + + align:start position:0% +that like matches up and can be signed + + + align:start position:0% +that like matches up and can be signed +with those four signatures so the + + align:start position:0% +with those four signatures so the + + + align:start position:0% +with those four signatures so the +question is did I do + + align:start position:0% +question is did I do + + + align:start position:0% +question is did I do +one hundred and fifty-four million tries + + align:start position:0% +one hundred and fifty-four million tries + + + align:start position:0% +one hundred and fifty-four million tries +to get that like did I start at zero + + align:start position:0% +to get that like did I start at zero + + + align:start position:0% +to get that like did I start at zero +maybe I did more maybe it was random + + align:start position:0% +maybe I did more maybe it was random + + + align:start position:0% +maybe I did more maybe it was random +maybe I got lucky and I started counting + + align:start position:0% +maybe I got lucky and I started counting + + + align:start position:0% +maybe I got lucky and I started counting +at 150 million so it's not really a + + align:start position:0% +at 150 million so it's not really a + + + align:start position:0% +at 150 million so it's not really a +proof is the thing like you're not + + align:start position:0% +proof is the thing like you're not + + + align:start position:0% +proof is the thing like you're not +exactly sure how many attempts someone + + align:start position:0% +exactly sure how many attempts someone + + + align:start position:0% +exactly sure how many attempts someone +did not quite approve right there's a + + align:start position:0% +did not quite approve right there's a + + + align:start position:0% +did not quite approve right there's a +lot of chance however over many proofs + + align:start position:0% +lot of chance however over many proofs + + + align:start position:0% +lot of chance however over many proofs +it's sort of averages out and you can be + + align:start position:0% +it's sort of averages out and you can be + + + align:start position:0% +it's sort of averages out and you can be +pretty sure that someone's doing all the + + align:start position:0% +pretty sure that someone's doing all the + + + align:start position:0% +pretty sure that someone's doing all the +work right so if you know if someone + + align:start position:0% +work right so if you know if someone + + + align:start position:0% +work right so if you know if someone +gets lucky once fine like maybe they + + align:start position:0% +gets lucky once fine like maybe they + + + align:start position:0% +gets lucky once fine like maybe they +they you know try it a couple times and + + align:start position:0% +they you know try it a couple times and + + + align:start position:0% +they you know try it a couple times and +got a valid proof of work but eventually + + align:start position:0% +got a valid proof of work but eventually + + + align:start position:0% +got a valid proof of work but eventually +if they keep doing proof of work and + + align:start position:0% +if they keep doing proof of work and + + + align:start position:0% +if they keep doing proof of work and +they're you know + + align:start position:0% +they're you know + + + align:start position:0% +they're you know +iteratively showing them then you can be + + align:start position:0% +iteratively showing them then you can be + + + align:start position:0% +iteratively showing them then you can be +pretty sure that they're not they're not + + align:start position:0% +pretty sure that they're not they're not + + + align:start position:0% +pretty sure that they're not they're not +gonna be lucky the whole time right and + + align:start position:0% +gonna be lucky the whole time right and + + + align:start position:0% +gonna be lucky the whole time right and +so you have to kind of estimate the + + align:start position:0% +so you have to kind of estimate the + + + align:start position:0% +so you have to kind of estimate the +collision difficulty the best way to + + align:start position:0% +collision difficulty the best way to + + + align:start position:0% +collision difficulty the best way to +estimate the difficulty and the amount + + align:start position:0% +estimate the difficulty and the amount + + + align:start position:0% +estimate the difficulty and the amount +of work that people have done isn't to + + align:start position:0% +of work that people have done isn't to + + + align:start position:0% +of work that people have done isn't to +look at their proof isn't to look at + + align:start position:0% +look at their proof isn't to look at + + + align:start position:0% +look at their proof isn't to look at +their nuts but to look at the + + align:start position:0% +their nuts but to look at the + + + align:start position:0% +their nuts but to look at the +constraints of the system before they + + align:start position:0% +constraints of the system before they + + + align:start position:0% +constraints of the system before they +start right so in the case of the + + align:start position:0% +start right so in the case of the + + + align:start position:0% +start right so in the case of the +homework 31 bits are are specified right + + align:start position:0% +homework 31 bits are are specified right + + + align:start position:0% +homework 31 bits are are specified right +so with four signatures you'd you'd + + align:start position:0% +so with four signatures you'd you'd + + + align:start position:0% +so with four signatures you'd you'd +guess that about 32 bits would be and in + + align:start position:0% +guess that about 32 bits would be and in + + + align:start position:0% +guess that about 32 bits would be and in +this case there's one bit difference so + + align:start position:0% +this case there's one bit difference so + + + align:start position:0% +this case there's one bit difference so +in the case of the homework there's 31 + + align:start position:0% +in the case of the homework there's 31 + + + align:start position:0% +in the case of the homework there's 31 +bits that are specified so that means + + align:start position:0% +bits that are specified so that means + + + align:start position:0% +bits that are specified so that means +you're gonna have to do about to be + + align:start position:0% +you're gonna have to do about to be + + + align:start position:0% +you're gonna have to do about to be +billion hashes right two to thirty ones + + align:start position:0% +billion hashes right two to thirty ones + + + align:start position:0% +billion hashes right two to thirty ones +like 2.1 billion or something and so + + align:start position:0% +like 2.1 billion or something and so + + + align:start position:0% +like 2.1 billion or something and so +that's the best estimate of how long it + + align:start position:0% +that's the best estimate of how long it + + + align:start position:0% +that's the best estimate of how long it +took regardless of what the nan says + + align:start position:0% +took regardless of what the nan says + + + align:start position:0% +took regardless of what the nan says +regardless of what it looks like they + + align:start position:0% +regardless of what it looks like they + + + align:start position:0% +regardless of what it looks like they +did you could say well it's gonna take + + align:start position:0% +did you could say well it's gonna take + + + align:start position:0% +did you could say well it's gonna take +on average two to thirty one attempts + + align:start position:0% +on average two to thirty one attempts + + + align:start position:0% +on average two to thirty one attempts +let's just and so if any valid solution + + align:start position:0% +let's just and so if any valid solution + + + align:start position:0% +let's just and so if any valid solution +they give me I'm gonna sort of credit + + align:start position:0% +they give me I'm gonna sort of credit + + + align:start position:0% +they give me I'm gonna sort of credit +that with two to thirty one work + + align:start position:0% +that with two to thirty one work + + + align:start position:0% +that with two to thirty one work +so actually in the case of mine the one + + align:start position:0% +so actually in the case of mine the one + + + align:start position:0% +so actually in the case of mine the one +is the thread number and there were + + align:start position:0% +is the thread number and there were + + + align:start position:0% +is the thread number and there were +eight threads so this Taj Forge one 154 + + align:start position:0% +eight threads so this Taj Forge one 154 + + + align:start position:0% +eight threads so this Taj Forge one 154 +million so I had eight threads going in + + align:start position:0% +million so I had eight threads going in + + + align:start position:0% +million so I had eight threads going in +parallel and that happened to be thread + + align:start position:0% +parallel and that happened to be thread + + + align:start position:0% +parallel and that happened to be thread +one and so they all they all went about + + align:start position:0% +one and so they all they all went about + + + align:start position:0% +one and so they all they all went about +the same speed so it's really like + + align:start position:0% +the same speed so it's really like + + + align:start position:0% +the same speed so it's really like +hundred fifty four million times eight + + align:start position:0% +hundred fifty four million times eight + + + align:start position:0% +hundred fifty four million times eight +which is about 1.2 billion and so that's + + align:start position:0% +which is about 1.2 billion and so that's + + + align:start position:0% +which is about 1.2 billion and so that's +actually kind of lucky right like it + + align:start position:0% +actually kind of lucky right like it + + + align:start position:0% +actually kind of lucky right like it +should it you would you would estimate + + align:start position:0% +should it you would you would estimate + + + align:start position:0% +should it you would you would estimate +on average it would take two billion and + + align:start position:0% +on average it would take two billion and + + + align:start position:0% +on average it would take two billion and +I got in like 1.2 billion so like pretty + + align:start position:0% +I got in like 1.2 billion so like pretty + + + align:start position:0% +I got in like 1.2 billion so like pretty +good luck + + align:start position:0% +good luck + + + align:start position:0% +good luck +but within you know within 2x of what + + align:start position:0% +but within you know within 2x of what + + + align:start position:0% +but within you know within 2x of what +you'd expect and and since you can look + + align:start position:0% +you'd expect and and since you can look + + + align:start position:0% +you'd expect and and since you can look +at like the probability distributions of + + align:start position:0% +at like the probability distributions of + + + align:start position:0% +at like the probability distributions of +like that might be kind of interesting + + align:start position:0% +like that might be kind of interesting + + + align:start position:0% +like that might be kind of interesting +with the homework like okay everyone's + + align:start position:0% +with the homework like okay everyone's + + + align:start position:0% +with the homework like okay everyone's +attempt some people it takes to billions + + align:start position:0% +attempt some people it takes to billions + + + align:start position:0% +attempt some people it takes to billions +some people get lucky and it takes 1 + + align:start position:0% +some people get lucky and it takes 1 + + + align:start position:0% +some people get lucky and it takes 1 +billion some people get unlucky and it + + align:start position:0% +billion some people get unlucky and it + + + align:start position:0% +billion some people get unlucky and it +takes 5 billion and you're gonna have + + align:start position:0% +takes 5 billion and you're gonna have + + + align:start position:0% +takes 5 billion and you're gonna have +this sort of curve to see it but this is + + align:start position:0% +this sort of curve to see it but this is + + + align:start position:0% +this sort of curve to see it but this is +that's a kind of weird application of + + align:start position:0% +that's a kind of weird application of + + + align:start position:0% +that's a kind of weird application of +this signature forging algorithm alright + + align:start position:0% +this signature forging algorithm alright + + + align:start position:0% +this signature forging algorithm alright +it's it's sort of not what it's made for + + align:start position:0% +it's it's sort of not what it's made for + + + align:start position:0% +it's it's sort of not what it's made for +it we can have a simpler proof of work + + align:start position:0% +it we can have a simpler proof of work + + + align:start position:0% +it we can have a simpler proof of work +that has a specific target that's reused + + align:start position:0% +that has a specific target that's reused + + + align:start position:0% +that has a specific target that's reused +forever and it's sort of more universal + + align:start position:0% +forever and it's sort of more universal + + + align:start position:0% +forever and it's sort of more universal +and that it's not like oh here's this + + align:start position:0% +and that it's not like oh here's this + + + align:start position:0% +and that it's not like oh here's this +private key you know here's this key + + align:start position:0% +private key you know here's this key + + + align:start position:0% +private key you know here's this key +pair and here are these four signatures + + align:start position:0% +pair and here are these four signatures + + + align:start position:0% +pair and here are these four signatures +where are these things coming from + + align:start position:0% +where are these things coming from + + + align:start position:0% +where are these things coming from +that's weird we have to like match these + + align:start position:0% +that's weird we have to like match these + + + align:start position:0% +that's weird we have to like match these +weird strings of bits and stuff that's + + align:start position:0% +weird strings of bits and stuff that's + + + align:start position:0% +weird strings of bits and stuff that's +kind of annoying so it's better to do + + align:start position:0% +kind of annoying so it's better to do + + + align:start position:0% +kind of annoying so it's better to do +something similar but much simpler we'll + + align:start position:0% +something similar but much simpler we'll + + + align:start position:0% +something similar but much simpler we'll +just try to collide with a fixed string + + align:start position:0% +just try to collide with a fixed string + + + align:start position:0% +just try to collide with a fixed string +so there's some defined string of ones + + align:start position:0% +so there's some defined string of ones + + + align:start position:0% +so there's some defined string of ones +and zeroes and we just say okay well + + align:start position:0% +and zeroes and we just say okay well + + + align:start position:0% +and zeroes and we just say okay well +let's try to have a collision with this + + align:start position:0% +let's try to have a collision with this + + + align:start position:0% +let's try to have a collision with this +and the simplest is collide with zero or + + align:start position:0% +and the simplest is collide with zero or + + + align:start position:0% +and the simplest is collide with zero or +you could also collide with like ffff + + align:start position:0% +you could also collide with like ffff + + + align:start position:0% +you could also collide with like ffff +but in the case of Bitcoin in the case + + align:start position:0% +but in the case of Bitcoin in the case + + + align:start position:0% +but in the case of Bitcoin in the case +of many of these systems we say well + + align:start position:0% +of many of these systems we say well + + + align:start position:0% +of many of these systems we say well +let's just try to have a low number + + align:start position:0% +let's just try to have a low number + + + align:start position:0% +let's just try to have a low number +so let's interpret the hash output as an + + align:start position:0% +so let's interpret the hash output as an + + + align:start position:0% +so let's interpret the hash output as an +actual number in most cases do I have + + align:start position:0% +actual number in most cases do I have + + + align:start position:0% +actual number in most cases do I have +any cashes out here no you know it's a + + align:start position:0% +any cashes out here no you know it's a + + + align:start position:0% +any cashes out here no you know it's a +it's a 32 byte string and we think of it + + align:start position:0% +it's a 32 byte string and we think of it + + + align:start position:0% +it's a 32 byte string and we think of it +as just like here's a blob of bytes but + + align:start position:0% +as just like here's a blob of bytes but + + + align:start position:0% +as just like here's a blob of bytes but +you could cast that into like an integer + + align:start position:0% +you could cast that into like an integer + + + align:start position:0% +you could cast that into like an integer +right you could say oh let's let's + + align:start position:0% +right you could say oh let's let's + + + align:start position:0% +right you could say oh let's let's +interpret these 32 bytes as a you end + + align:start position:0% +interpret these 32 bytes as a you end + + + align:start position:0% +interpret these 32 bytes as a you end +256 write a 256 bit unsigned integer + + align:start position:0% +256 write a 256 bit unsigned integer + + + align:start position:0% +256 write a 256 bit unsigned integer +and let's look for really low once and + + align:start position:0% +and let's look for really low once and + + + align:start position:0% +and let's look for really low once and +and you can do that I think with some + + align:start position:0% +and you can do that I think with some + + + align:start position:0% +and you can do that I think with some +CPUs they'll actually like let you do + + align:start position:0% +CPUs they'll actually like let you do + + + align:start position:0% +CPUs they'll actually like let you do +giant integers that way but even if not + + align:start position:0% +giant integers that way but even if not + + + align:start position:0% +giant integers that way but even if not +you have like some kind of big int + + align:start position:0% +you have like some kind of big int + + + align:start position:0% +you have like some kind of big int +library in your computer which just + + align:start position:0% +library in your computer which just + + + align:start position:0% +library in your computer which just +interprets it that way and says okay + + align:start position:0% +interprets it that way and says okay + + + align:start position:0% +interprets it that way and says okay +let's try to find collisions with zero + + align:start position:0% +let's try to find collisions with zero + + + align:start position:0% +let's try to find collisions with zero +basically let's try to find low numbers + + align:start position:0% +basically let's try to find low numbers + + + align:start position:0% +basically let's try to find low numbers +okay so this this idea there's a paper + + align:start position:0% +okay so this this idea there's a paper + + + align:start position:0% +okay so this this idea there's a paper +before hashcash but I don't think cache + + align:start position:0% +before hashcash but I don't think cache + + + align:start position:0% +before hashcash but I don't think cache +cache was the first software this idea + + align:start position:0% +cache was the first software this idea + + + align:start position:0% +cache was the first software this idea +is actually really old in 1997 + + align:start position:0% +is actually really old in 1997 + + + align:start position:0% +is actually really old in 1997 +Adam back who still works on this kind + + align:start position:0% +Adam back who still works on this kind + + + align:start position:0% +Adam back who still works on this kind +of stuff now with Bitcoin the idea was + + align:start position:0% +of stuff now with Bitcoin the idea was + + + align:start position:0% +of stuff now with Bitcoin the idea was +to stop email spam which I don't know if + + align:start position:0% +to stop email spam which I don't know if + + + align:start position:0% +to stop email spam which I don't know if +you know in the late 90s was actually a + + align:start position:0% +you know in the late 90s was actually a + + + align:start position:0% +you know in the late 90s was actually a +huge problem they didn't have all the + + align:start position:0% +huge problem they didn't have all the + + + align:start position:0% +huge problem they didn't have all the +cool like different machine learning + + align:start position:0% +cool like different machine learning + + + align:start position:0% +cool like different machine learning +stuff and there's tons of spam and the + + align:start position:0% +stuff and there's tons of spam and the + + + align:start position:0% +stuff and there's tons of spam and the +idea was okay put a nonce and a nun says + + align:start position:0% +idea was okay put a nonce and a nun says + + + align:start position:0% +idea was okay put a nonce and a nun says +this we call this a nonce right the sort + + align:start position:0% +this we call this a nonce right the sort + + + align:start position:0% +this we call this a nonce right the sort +of random number you're throwing in to + + align:start position:0% +of random number you're throwing in to + + + align:start position:0% +of random number you're throwing in to +keep changing things put it nuns in your + + align:start position:0% +keep changing things put it nuns in your + + + align:start position:0% +keep changing things put it nuns in your +email header and you try to get a low + + align:start position:0% +email header and you try to get a low + + + align:start position:0% +email header and you try to get a low +hash output when you hash the whole + + align:start position:0% +hash output when you hash the whole + + + align:start position:0% +hash output when you hash the whole +thing so you know within the UI for + + align:start position:0% +thing so you know within the UI for + + + align:start position:0% +thing so you know within the UI for +email you don't necessarily have to see + + align:start position:0% +email you don't necessarily have to see + + + align:start position:0% +email you don't necessarily have to see +okay what's this person's nuts + + align:start position:0% +okay what's this person's nuts + + + align:start position:0% +okay what's this person's nuts +the computer just does it all + + align:start position:0% +the computer just does it all + + + align:start position:0% +the computer just does it all +automatically for you but the idea is + + align:start position:0% +automatically for you but the idea is + + + align:start position:0% +automatically for you but the idea is +you need a partial collision with zero + + align:start position:0% +you need a partial collision with zero + + + align:start position:0% +you need a partial collision with zero +you need a low out hash output for your + + align:start position:0% +you need a low out hash output for your + + + align:start position:0% +you need a low out hash output for your +email before your email the receiving + + align:start position:0% +email before your email the receiving + + + align:start position:0% +email before your email the receiving +person will display the email and since + + align:start position:0% +person will display the email and since + + + align:start position:0% +person will display the email and since +the header includes the like destination + + align:start position:0% +the header includes the like destination + + + align:start position:0% +the header includes the like destination +address if you're a spammer and you want + + align:start position:0% +address if you're a spammer and you want + + + align:start position:0% +address if you're a spammer and you want +to spam a million different people + + align:start position:0% +to spam a million different people + + + align:start position:0% +to spam a million different people +you're gonna have to come up with a + + align:start position:0% +you're gonna have to come up with a + + + align:start position:0% +you're gonna have to come up with a +million different proofs of work and + + align:start position:0% +million different proofs of work and + + + align:start position:0% +million different proofs of work and +that could take quite a while like let's + + align:start position:0% +that could take quite a while like let's + + + align:start position:0% +that could take quite a while like let's +say you know let's say an average CPU + + align:start position:0% +say you know let's say an average CPU + + + align:start position:0% +say you know let's say an average CPU +can do it in two or three seconds that + + align:start position:0% +can do it in two or three seconds that + + + align:start position:0% +can do it in two or three seconds that +means you're gonna have to be waiting + + align:start position:0% +means you're gonna have to be waiting + + + align:start position:0% +means you're gonna have to be waiting +you know months to spam all these emails + + align:start position:0% +you know months to spam all these emails + + + align:start position:0% +you know months to spam all these emails +however for a normal person if you're + + align:start position:0% +however for a normal person if you're + + + align:start position:0% +however for a normal person if you're +just sending an email to your friend + + align:start position:0% +just sending an email to your friend + + + align:start position:0% +just sending an email to your friend +takes a few seconds right takes two + + align:start position:0% +takes a few seconds right takes two + + + align:start position:0% +takes a few seconds right takes two +seconds for your CPU time which is not a + + align:start position:0% +seconds for your CPU time which is not a + + + align:start position:0% +seconds for your CPU time which is not a +huge deal um so this was a cool idea it + + align:start position:0% +huge deal um so this was a cool idea it + + + align:start position:0% +huge deal um so this was a cool idea it +never really got off the ground just + + align:start position:0% +never really got off the ground just + + + align:start position:0% +never really got off the ground just +because I don't know Gmail happened + + align:start position:0% +because I don't know Gmail happened + + + align:start position:0% +because I don't know Gmail happened +hotmail happened a lot of webmail things + + align:start position:0% +hotmail happened a lot of webmail things + + + align:start position:0% +hotmail happened a lot of webmail things +happen people don't really use yeah + + align:start position:0% + + + + align:start position:0% + +yeah I mean spammers often have botnets + + align:start position:0% +yeah I mean spammers often have botnets + + + align:start position:0% +yeah I mean spammers often have botnets +so yeah there's there's a lot of other + + align:start position:0% +so yeah there's there's a lot of other + + + align:start position:0% +so yeah there's there's a lot of other +issues right like there's it didn't it + + align:start position:0% +issues right like there's it didn't it + + + align:start position:0% +issues right like there's it didn't it +didn't take off for for various reasons + + align:start position:0% +didn't take off for for various reasons + + + align:start position:0% +didn't take off for for various reasons +but yeah also spare some violence which + + align:start position:0% +but yeah also spare some violence which + + + align:start position:0% +but yeah also spare some violence which +which also sort of hurts the whole idea + + align:start position:0% +which also sort of hurts the whole idea + + + align:start position:0% +which also sort of hurts the whole idea +of proof-of-work in some cases which + + align:start position:0% +of proof-of-work in some cases which + + + align:start position:0% +of proof-of-work in some cases which +we'll talk about in a second okay so the + + align:start position:0% +we'll talk about in a second okay so the + + + align:start position:0% +we'll talk about in a second okay so the +simpler proving work so for example if + + align:start position:0% +simpler proving work so for example if + + + align:start position:0% +simpler proving work so for example if +you go onto your computers and you say + + align:start position:0% +you go onto your computers and you say + + + align:start position:0% +you go onto your computers and you say +echo + + align:start position:0% +echo + + + align:start position:0% +echo +Tadgh four to three three nine six four + + align:start position:0% +Tadgh four to three three nine six four + + + align:start position:0% +Tadgh four to three three nine six four +oh two four and pipe that to shock to + + align:start position:0% +oh two four and pipe that to shock to + + + align:start position:0% +oh two four and pipe that to shock to +five six some you will get this output + + align:start position:0% +five six some you will get this output + + + align:start position:0% +five six some you will get this output +and that's zeros in the front so that's + + align:start position:0% +and that's zeros in the front so that's + + + align:start position:0% +and that's zeros in the front so that's +four bytes i did two to the thirty to + + align:start position:0% +four bytes i did two to the thirty to + + + align:start position:0% +four bytes i did two to the thirty to +work and it you know that's me right and + + align:start position:0% +work and it you know that's me right and + + + align:start position:0% +work and it you know that's me right and +so that proves that I'm a hard worker + + align:start position:0% +so that proves that I'm a hard worker + + + align:start position:0% +so that proves that I'm a hard worker +and I'm gonna put this nonce on my + + align:start position:0% +and I'm gonna put this nonce on my + + + align:start position:0% +and I'm gonna put this nonce on my +resume and everyone can see that like I + + align:start position:0% +resume and everyone can see that like I + + + align:start position:0% +resume and everyone can see that like I +do work that you know it's kind of silly + + align:start position:0% +do work that you know it's kind of silly + + + align:start position:0% +do work that you know it's kind of silly +but it's a really easy sort of universal + + align:start position:0% +but it's a really easy sort of universal + + + align:start position:0% +but it's a really easy sort of universal +way to have a proof-of-work anyone can + + align:start position:0% +way to have a proof-of-work anyone can + + + align:start position:0% +way to have a proof-of-work anyone can +put their name or any message and any + + align:start position:0% +put their name or any message and any + + + align:start position:0% +put their name or any message and any +kind of months and we all just pipe it + + align:start position:0% +kind of months and we all just pipe it + + + align:start position:0% +kind of months and we all just pipe it +into the sha-256 function and see how + + align:start position:0% +into the sha-256 function and see how + + + align:start position:0% +into the sha-256 function and see how +low the output is in this case it's + + align:start position:0% +low the output is in this case it's + + + align:start position:0% +low the output is in this case it's +actually two to the thirty three right + + align:start position:0% +actually two to the thirty three right + + + align:start position:0% +actually two to the thirty three right +because the first digits of seven so + + align:start position:0% +because the first digits of seven so + + + align:start position:0% +because the first digits of seven so +that's zero one one one but this is this + + align:start position:0% +that's zero one one one but this is this + + + align:start position:0% +that's zero one one one but this is this +is what we use in Bitcoin it's what they + + align:start position:0% +is what we use in Bitcoin it's what they + + + align:start position:0% +is what we use in Bitcoin it's what they +use in like a lot of these things I mean + + align:start position:0% +use in like a lot of these things I mean + + + align:start position:0% +use in like a lot of these things I mean +it's really straightforward + + align:start position:0% +it's really straightforward + + + align:start position:0% +it's really straightforward +okay so partial collision worth it it + + align:start position:0% +okay so partial collision worth it it + + + align:start position:0% +okay so partial collision worth it it +has a lot of the properties what we're + + align:start position:0% +has a lot of the properties what we're + + + align:start position:0% +has a lot of the properties what we're +looking for then when we want this + + align:start position:0% +looking for then when we want this + + + align:start position:0% +looking for then when we want this +consensus system right it increases the + + align:start position:0% +consensus system right it increases the + + + align:start position:0% +consensus system right it increases the +costs of equivocation and you know helps + + align:start position:0% +costs of equivocation and you know helps + + + align:start position:0% +costs of equivocation and you know helps +with civil resistance in that if I want + + align:start position:0% +with civil resistance in that if I want + + + align:start position:0% +with civil resistance in that if I want +to fool you I'm still gonna have to do a + + align:start position:0% +to fool you I'm still gonna have to do a + + + align:start position:0% +to fool you I'm still gonna have to do a +lot of work and I need time to do that I + + align:start position:0% +lot of work and I need time to do that I + + + align:start position:0% +lot of work and I need time to do that I +need electricity due to that I need a + + align:start position:0% +need electricity due to that I need a + + + align:start position:0% +need electricity due to that I need a +bunch of computers to do that with also + + align:start position:0% +bunch of computers to do that with also + + + align:start position:0% +bunch of computers to do that with also +scalable because a ton of work still + + align:start position:0% +scalable because a ton of work still + + + align:start position:0% +scalable because a ton of work still +takes the same amount of time to verify + + align:start position:0% +takes the same amount of time to verify + + + align:start position:0% +takes the same amount of time to verify +and space to verify as a little bit of + + align:start position:0% +and space to verify as a little bit of + + + align:start position:0% +and space to verify as a little bit of +work right so I can do o of n work right + + align:start position:0% +work right so I can do o of n work right + + + align:start position:0% +work right so I can do o of n work right +I can put as many zeros as I want and + + align:start position:0% +I can put as many zeros as I want and + + + align:start position:0% +I can put as many zeros as I want and +the nonce doesn't really get any bigger + + align:start position:0% +the nonce doesn't really get any bigger + + + align:start position:0% +the nonce doesn't really get any bigger +the nones never has to get bigger than + + align:start position:0% +the nones never has to get bigger than + + + align:start position:0% +the nones never has to get bigger than +the hash output certainly and time to + + align:start position:0% +the hash output certainly and time to + + + align:start position:0% +the hash output certainly and time to +verify is the same no matter what so + + align:start position:0% +verify is the same no matter what so + + + align:start position:0% +verify is the same no matter what so +that's really cool + + align:start position:0% +that's really cool + + + align:start position:0% +that's really cool +so why do we do work in the case of + + align:start position:0% +so why do we do work in the case of + + + align:start position:0% +so why do we do work in the case of +Bitcoin + + align:start position:0% +Bitcoin + + + align:start position:0% +Bitcoin +the idea is you used a chained proof of + + align:start position:0% +the idea is you used a chained proof of + + + align:start position:0% +the idea is you used a chained proof of +work as a distributed time stamping + + align:start position:0% +work as a distributed time stamping + + + align:start position:0% +work as a distributed time stamping +mechanism so it's to determine what + + align:start position:0% +mechanism so it's to determine what + + + align:start position:0% +mechanism so it's to determine what +happened first so in the case of a + + align:start position:0% +happened first so in the case of a + + + align:start position:0% +happened first so in the case of a +double spend where someone's saying oh + + align:start position:0% +double spend where someone's saying oh + + + align:start position:0% +double spend where someone's saying oh +transaction a happened first and someone + + align:start position:0% +transaction a happened first and someone + + + align:start position:0% +transaction a happened first and someone +else says well I think transaction B + + align:start position:0% +else says well I think transaction B + + + align:start position:0% +else says well I think transaction B +happened first you can't just rely on + + align:start position:0% +happened first you can't just rely on + + + align:start position:0% +happened first you can't just rely on +what other people are telling you + + align:start position:0% +what other people are telling you + + + align:start position:0% +what other people are telling you +because who are these other people you + + align:start position:0% +because who are these other people you + + + align:start position:0% +because who are these other people you +know there's no real identities here so + + align:start position:0% +know there's no real identities here so + + + align:start position:0% +know there's no real identities here so +you look at what got into the chain of + + align:start position:0% +you look at what got into the chain of + + + align:start position:0% +you look at what got into the chain of +hashes first and you say okay well that + + align:start position:0% +hashes first and you say okay well that + + + align:start position:0% +hashes first and you say okay well that +one you know this one this data has a + + align:start position:0% +one you know this one this data has a + + + align:start position:0% +one you know this one this data has a +hash of this data so it must have + + align:start position:0% +hash of this data so it must have + + + align:start position:0% +hash of this data so it must have +happened after it right and the things + + align:start position:0% +happened after it right and the things + + + align:start position:0% +happened after it right and the things +that happened before are pointed to by + + align:start position:0% +that happened before are pointed to by + + + align:start position:0% +that happened before are pointed to by +the things that happened Africa because + + align:start position:0% +the things that happened Africa because + + + align:start position:0% +the things that happened Africa because +the idea is I can't include the hash of + + align:start position:0% +the idea is I can't include the hash of + + + align:start position:0% +the idea is I can't include the hash of +something that I haven't seen yet right + + align:start position:0% +something that I haven't seen yet right + + + align:start position:0% +something that I haven't seen yet right +it should be impossible to do that so + + align:start position:0% +it should be impossible to do that so + + + align:start position:0% +it should be impossible to do that so +the idea of the blockchain you've got + + align:start position:0% +the idea of the blockchain you've got + + + align:start position:0% +the idea of the blockchain you've got +some message M some nuns let's call it R + + align:start position:0% +some message M some nuns let's call it R + + + align:start position:0% +some message M some nuns let's call it R +and some target T and this actually + + align:start position:0% +and some target T and this actually + + + align:start position:0% +and some target T and this actually +changes but we're not going to talk + + align:start position:0% +changes but we're not going to talk + + + align:start position:0% +changes but we're not going to talk +about the changes yet so you tack the + + align:start position:0% +about the changes yet so you tack the + + + align:start position:0% +about the changes yet so you tack the +hash of your message and the nonce like + + align:start position:0% +hash of your message and the nonce like + + + align:start position:0% +hash of your message and the nonce like +I was doing with you note add in the + + align:start position:0% +I was doing with you note add in the + + + align:start position:0% +I was doing with you note add in the +number and you say okay that's H and H + + align:start position:0% +number and you say okay that's H and H + + + align:start position:0% +number and you say okay that's H and H +has to be less than some number T so in + + align:start position:0% +has to be less than some number T so in + + + align:start position:0% +has to be less than some number T so in +the case where I just said you know my + + align:start position:0% +the case where I just said you know my + + + align:start position:0% +the case where I just said you know my +notes I had to to the 33 work so you + + align:start position:0% +notes I had to to the 33 work so you + + + align:start position:0% +notes I had to to the 33 work so you +know say say the same thing here in the + + align:start position:0% +know say say the same thing here in the + + + align:start position:0% +know say say the same thing here in the +example I mean only require two bytes + + align:start position:0% +example I mean only require two bytes + + + align:start position:0% +example I mean only require two bytes +for the target so that target needs to + + align:start position:0% +for the target so that target needs to + + + align:start position:0% +for the target so that target needs to +be fairly large and then the message for + + align:start position:0% +be fairly large and then the message for + + + align:start position:0% +be fairly large and then the message for +blah you know for block n includes some + + align:start position:0% +blah you know for block n includes some + + + align:start position:0% +blah you know for block n includes some +data and also the hash of block n minus + + align:start position:0% +data and also the hash of block n minus + + + align:start position:0% +data and also the hash of block n minus +1 so you refer to your previous block + + align:start position:0% +1 so you refer to your previous block + + + align:start position:0% +1 so you refer to your previous block +hash in your current block data so for + + align:start position:0% +hash in your current block data so for + + + align:start position:0% +hash in your current block data so for +example the message number 2 would be + + align:start position:0% +example the message number 2 would be + + + align:start position:0% +example the message number 2 would be +data to concatenated with the hash of + + align:start position:0% +data to concatenated with the hash of + + + align:start position:0% +data to concatenated with the hash of +data 1 + R there should be like R 1 + + align:start position:0% +data 1 + R there should be like R 1 + + + align:start position:0% +data 1 + R there should be like R 1 +there so I'll show you a little diagram + + align:start position:0% +there so I'll show you a little diagram + + + align:start position:0% +there so I'll show you a little diagram +of this the idea of a block chain which + + align:start position:0% + + + + align:start position:0% + +in this case we want low numbers as the + + align:start position:0% +in this case we want low numbers as the + + + align:start position:0% +in this case we want low numbers as the +hash output you could do greater than + + align:start position:0% +hash output you could do greater than + + + align:start position:0% +hash output you could do greater than +you could have I want something that + + align:start position:0% +you could have I want something that + + + align:start position:0% +you could have I want something that +starts with a lot of F's it would + + align:start position:0% +starts with a lot of F's it would + + + align:start position:0% +starts with a lot of F's it would +work the same there you know you could + + align:start position:0% +work the same there you know you could + + + align:start position:0% +work the same there you know you could +yeah you want to constrain yeah so you + + align:start position:0% +yeah you want to constrain yeah so you + + + align:start position:0% +yeah you want to constrain yeah so you +can you can do that with greater then + + align:start position:0% +can you can do that with greater then + + + align:start position:0% +can you can do that with greater then +you can do that with a fixed sort of + + align:start position:0% +you can do that with a fixed sort of + + + align:start position:0% +you can do that with a fixed sort of +yeah you know bits have to be well + + align:start position:0% +yeah you know bits have to be well + + + align:start position:0% +yeah you know bits have to be well +there's something okay so less than and + + align:start position:0% +there's something okay so less than and + + + align:start position:0% +there's something okay so less than and +greater than or actually nicer than just + + align:start position:0% +greater than or actually nicer than just + + + align:start position:0% +greater than or actually nicer than just +fixed bit so you could say I want it to + + align:start position:0% +fixed bit so you could say I want it to + + + align:start position:0% +fixed bit so you could say I want it to +start with the repeating pattern one + + align:start position:0% +start with the repeating pattern one + + + align:start position:0% +start with the repeating pattern one +zero one zero one zero one zero that + + align:start position:0% +zero one zero one zero one zero that + + + align:start position:0% +zero one zero one zero one zero that +would work too but then you're sort of + + align:start position:0% +would work too but then you're sort of + + + align:start position:0% +would work too but then you're sort of +constrained in how fine-tuned you can + + align:start position:0% +constrained in how fine-tuned you can + + + align:start position:0% +constrained in how fine-tuned you can +turn the knob and that you're gonna + + align:start position:0% +turn the knob and that you're gonna + + + align:start position:0% +turn the knob and that you're gonna +either have to add another bit of + + align:start position:0% +either have to add another bit of + + + align:start position:0% +either have to add another bit of +constraint or remove a bit of constraint + + align:start position:0% +constraint or remove a bit of constraint + + + align:start position:0% +constraint or remove a bit of constraint +and so that you know you have to go in + + align:start position:0% +and so that you know you have to go in + + + align:start position:0% +and so that you know you have to go in +to X jumps if what's nice with this is + + align:start position:0% +to X jumps if what's nice with this is + + + align:start position:0% +to X jumps if what's nice with this is +you actually have very fine-grained + + align:start position:0% +you actually have very fine-grained + + + align:start position:0% +you actually have very fine-grained +control over how or how much work you're + + align:start position:0% +control over how or how much work you're + + + align:start position:0% +control over how or how much work you're +requiring because you don't so in this + + align:start position:0% +requiring because you don't so in this + + + align:start position:0% +requiring because you don't so in this +example I've said hey I have you know + + align:start position:0% +example I've said hey I have you know + + + align:start position:0% +example I've said hey I have you know +this many zero bits but I can also say + + align:start position:0% +this many zero bits but I can also say + + + align:start position:0% +this many zero bits but I can also say +well I have I needed to have a number + + align:start position:0% +well I have I needed to have a number + + + align:start position:0% +well I have I needed to have a number +less than seven F like less than seven F + + align:start position:0% +less than seven F like less than seven F + + + align:start position:0% +less than seven F like less than seven F +0 0 0 0 here and this satisfies it + + align:start position:0% +0 0 0 0 here and this satisfies it + + + align:start position:0% +0 0 0 0 here and this satisfies it +because hey that's 7e that's less than + + align:start position:0% +because hey that's 7e that's less than + + + align:start position:0% +because hey that's 7e that's less than +7f right so I can I can actually have a + + align:start position:0% +7f right so I can I can actually have a + + + align:start position:0% +7f right so I can I can actually have a +pretty like specific thing not just in + + align:start position:0% +pretty like specific thing not just in + + + align:start position:0% +pretty like specific thing not just in +terms of number of bits specified so + + align:start position:0% +terms of number of bits specified so + + + align:start position:0% +terms of number of bits specified so +like a greater than or less than it's + + align:start position:0% +like a greater than or less than it's + + + align:start position:0% +like a greater than or less than it's +kind of nice in that sense because you + + align:start position:0% +kind of nice in that sense because you + + + align:start position:0% +kind of nice in that sense because you +can have very small changes to the + + align:start position:0% +can have very small changes to the + + + align:start position:0% +can have very small changes to the +target oh okay any questions about all + + align:start position:0% +target oh okay any questions about all + + + align:start position:0% +target oh okay any questions about all +this crazy stuff + + align:start position:0% + + + + align:start position:0% + +cool okay um yeah so you could you can + + align:start position:0% +cool okay um yeah so you could you can + + + align:start position:0% +cool okay um yeah so you could you can +special in the in the case of the + + align:start position:0% +special in the in the case of the + + + align:start position:0% +special in the in the case of the +homework it's just number of bits right + + align:start position:0% +homework it's just number of bits right + + + align:start position:0% +homework it's just number of bits right +because they're all sort of scattered + + align:start position:0% +because they're all sort of scattered + + + align:start position:0% +because they're all sort of scattered +throughout the field whereas in this one + + align:start position:0% +throughout the field whereas in this one + + + align:start position:0% +throughout the field whereas in this one +you can say well it's the targets + + align:start position:0% +you can say well it's the targets + + + align:start position:0% +you can say well it's the targets +greater than or less than in this case + + align:start position:0% +greater than or less than in this case + + + align:start position:0% +greater than or less than in this case +less than so I have kind of find two + + align:start position:0% +less than so I have kind of find two + + + align:start position:0% +less than so I have kind of find two +fine grained control which we're not + + align:start position:0% +fine grained control which we're not + + + align:start position:0% +fine grained control which we're not +going to we will get into later but yeah + + align:start position:0% +going to we will get into later but yeah + + + align:start position:0% +going to we will get into later but yeah +in in the actual case of Bitcoin the the + + align:start position:0% +in in the actual case of Bitcoin the the + + + align:start position:0% +in in the actual case of Bitcoin the the +target can vary right so the you know + + align:start position:0% +target can vary right so the you know + + + align:start position:0% +target can vary right so the you know +when Bitcoin started you needed four + + align:start position:0% +when Bitcoin started you needed four + + + align:start position:0% +when Bitcoin started you needed four +bytes of zeros right you needed to do + + align:start position:0% +bytes of zeros right you needed to do + + + align:start position:0% +bytes of zeros right you needed to do +two to the 32 work now you need to do + + align:start position:0% +two to the 32 work now you need to do + + + align:start position:0% +two to the 32 work now you need to do +way way way more and there's an + + align:start position:0% +way way way more and there's an + + + align:start position:0% +way way way more and there's an +algorithm in Bitcoin that sort of + + align:start position:0% +algorithm in Bitcoin that sort of + + + align:start position:0% +algorithm in Bitcoin that sort of +adjusts what that target is and I'll + + align:start position:0% +adjusts what that target is and I'll + + + align:start position:0% +adjusts what that target is and I'll +show at the end of this like a current + + align:start position:0% +show at the end of this like a current + + + align:start position:0% +show at the end of this like a current +Bitcoin approved work + + align:start position:0% + + + + align:start position:0% + +right right so time is sort of a tricky + + align:start position:0% +right right so time is sort of a tricky + + + align:start position:0% +right right so time is sort of a tricky +semi ugly subject in Bitcoin it'd be + + align:start position:0% +semi ugly subject in Bitcoin it'd be + + + align:start position:0% +semi ugly subject in Bitcoin it'd be +really cool to get rid of it but there + + align:start position:0% +really cool to get rid of it but there + + + align:start position:0% +really cool to get rid of it but there +eight-time is used and only to vary that + + align:start position:0% +eight-time is used and only to vary that + + + align:start position:0% +eight-time is used and only to vary that +target right so when you mine a block + + align:start position:0% +target right so when you mine a block + + + align:start position:0% +target right so when you mine a block +you say I'm gonna put what time it is + + align:start position:0% +you say I'm gonna put what time it is + + + align:start position:0% +you say I'm gonna put what time it is +and you look at the last two hunts when + + align:start position:0% +and you look at the last two hunts when + + + align:start position:0% +and you look at the last two hunts when +every two weeks or so every 2016 blocks + + align:start position:0% +every two weeks or so every 2016 blocks + + + align:start position:0% +every two weeks or so every 2016 blocks +you look at them and say okay what are + + align:start position:0% +you look at them and say okay what are + + + align:start position:0% +you look at them and say okay what are +the what's the first time stamp of this + + align:start position:0% +the what's the first time stamp of this + + + align:start position:0% +the what's the first time stamp of this +2016 period and the current time stamp + + align:start position:0% +2016 period and the current time stamp + + + align:start position:0% +2016 period and the current time stamp +and if that took two weeks cool we don't + + align:start position:0% +and if that took two weeks cool we don't + + + align:start position:0% +and if that took two weeks cool we don't +have to vary the target if it took less + + align:start position:0% +have to vary the target if it took less + + + align:start position:0% +have to vary the target if it took less +than two weeks let's crank up the + + align:start position:0% +than two weeks let's crank up the + + + align:start position:0% +than two weeks let's crank up the +difficulty or lower the target and it + + align:start position:0% +difficulty or lower the target and it + + + align:start position:0% +difficulty or lower the target and it +and if it took too long let's make it + + align:start position:0% +and if it took too long let's make it + + + align:start position:0% +and if it took too long let's make it +easier by raising the target and so + + align:start position:0% +easier by raising the target and so + + + align:start position:0% +easier by raising the target and so +really you're only comparing the first + + align:start position:0% +really you're only comparing the first + + + align:start position:0% +really you're only comparing the first +and last thing during the process when + + align:start position:0% +and last thing during the process when + + + align:start position:0% +and last thing during the process when +everyone's downloading stuff if I think + + align:start position:0% +everyone's downloading stuff if I think + + + align:start position:0% +everyone's downloading stuff if I think +the general rule is if you see something + + align:start position:0% +the general rule is if you see something + + + align:start position:0% +the general rule is if you see something +that's off by more than two hours you + + align:start position:0% +that's off by more than two hours you + + + align:start position:0% +that's off by more than two hours you +reject it but it's very lacks in terms + + align:start position:0% +reject it but it's very lacks in terms + + + align:start position:0% +reject it but it's very lacks in terms +of synchronization right if someone's if + + align:start position:0% +of synchronization right if someone's if + + + align:start position:0% +of synchronization right if someone's if +someone's 10 minutes off you're like + + align:start position:0% +someone's 10 minutes off you're like + + + align:start position:0% +someone's 10 minutes off you're like +yeah sure I'll take it even if a block + + align:start position:0% +yeah sure I'll take it even if a block + + + align:start position:0% +yeah sure I'll take it even if a block +even if like block 8 says it happened + + align:start position:0% +even if like block 8 says it happened + + + align:start position:0% +even if like block 8 says it happened +before block 7 right refers to block 7 + + align:start position:0% +before block 7 right refers to block 7 + + + align:start position:0% +before block 7 right refers to block 7 +and yet has a time stamp that's before + + align:start position:0% +and yet has a time stamp that's before + + + align:start position:0% +and yet has a time stamp that's before +it you're still like yeah ok fine + + align:start position:0% +it you're still like yeah ok fine + + + align:start position:0% +it you're still like yeah ok fine +whatever + + align:start position:0% +whatever + + + align:start position:0% +whatever +people's clocks are off so that the time + + align:start position:0% +people's clocks are off so that the time + + + align:start position:0% +people's clocks are off so that the time +is fairly lacks you just the the person + + align:start position:0% +is fairly lacks you just the the person + + + align:start position:0% +is fairly lacks you just the the person +who's doing the work time stamps it + + align:start position:0% + + + + align:start position:0% + +you're fairly constrained right so like + + align:start position:0% +you're fairly constrained right so like + + + align:start position:0% +you're fairly constrained right so like +it should be 2 weeks and you can say + + align:start position:0% +it should be 2 weeks and you can say + + + align:start position:0% +it should be 2 weeks and you can say +well I bet if I am I'm off by 20 minutes + + align:start position:0% +well I bet if I am I'm off by 20 minutes + + + align:start position:0% +well I bet if I am I'm off by 20 minutes +they'll everyone will be ok with it but + + align:start position:0% +they'll everyone will be ok with it but + + + align:start position:0% +they'll everyone will be ok with it but +that's not a ton of control right if + + align:start position:0% +that's not a ton of control right if + + + align:start position:0% +that's not a ton of control right if +you're if you're the last one of this + + align:start position:0% +you're if you're the last one of this + + + align:start position:0% +you're if you're the last one of this +difficulty adjustment thing you could + + align:start position:0% +difficulty adjustment thing you could + + + align:start position:0% +difficulty adjustment thing you could +say hey I'm gonna you know say it's I'm + + align:start position:0% +say hey I'm gonna you know say it's I'm + + + align:start position:0% +say hey I'm gonna you know say it's I'm +gonna say what would you probably want + + align:start position:0% +gonna say what would you probably want + + + align:start position:0% +gonna say what would you probably want +to do I'm gonna say it's 20 minutes in + + align:start position:0% +to do I'm gonna say it's 20 minutes in + + + align:start position:0% +to do I'm gonna say it's 20 minutes in +the future because I want the difficulty + + align:start position:0% +the future because I want the difficulty + + + align:start position:0% +the future because I want the difficulty +to not go up too much because I'm trying + + align:start position:0% +to not go up too much because I'm trying + + + align:start position:0% +to not go up too much because I'm trying +to get more blocks so you could try to + + align:start position:0% +to get more blocks so you could try to + + + align:start position:0% +to get more blocks so you could try to +push it to like 20 minutes in the future + + align:start position:0% +push it to like 20 minutes in the future + + + align:start position:0% +push it to like 20 minutes in the future +from what it actually is and people all + + align:start position:0% +from what it actually is and people all + + + align:start position:0% +from what it actually is and people all +the rest of the nodes in the network + + align:start position:0% +the rest of the nodes in the network + + + align:start position:0% +the rest of the nodes in the network +will probably accept it but you get 20 + + align:start position:0% +will probably accept it but you get 20 + + + align:start position:0% +will probably accept it but you get 20 +you know 20 minutes + + align:start position:0% +you know 20 minutes + + + align:start position:0% +you know 20 minutes +prints over a two-week period which is + + align:start position:0% +prints over a two-week period which is + + + align:start position:0% +prints over a two-week period which is +like less way you know less than a + + align:start position:0% +like less way you know less than a + + + align:start position:0% +like less way you know less than a +percent so yeah so so jet in the thing + + align:start position:0% +percent so yeah so so jet in the thing + + + align:start position:0% +percent so yeah so so jet in the thing +is it's hard to like you don't really + + align:start position:0% +is it's hard to like you don't really + + + align:start position:0% +is it's hard to like you don't really +necessarily know everyone's consensus + + align:start position:0% +necessarily know everyone's consensus + + + align:start position:0% +necessarily know everyone's consensus +rules in these systems but I think the + + align:start position:0% +rules in these systems but I think the + + + align:start position:0% +rules in these systems but I think the +default is two hours from your clock and + + align:start position:0% +default is two hours from your clock and + + + align:start position:0% +default is two hours from your clock and +you like you know every client I've seen + + align:start position:0% +you like you know every client I've seen + + + align:start position:0% +you like you know every client I've seen +will reject something that seems to be + + align:start position:0% +will reject something that seems to be + + + align:start position:0% +will reject something that seems to be +more than two hours off but which is + + align:start position:0% +more than two hours off but which is + + + align:start position:0% +more than two hours off but which is +really lacks right for most types of + + align:start position:0% +really lacks right for most types of + + + align:start position:0% +really lacks right for most types of +distributed systems like two hours is + + align:start position:0% +distributed systems like two hours is + + + align:start position:0% +distributed systems like two hours is +crazy like most of the time they're + + align:start position:0% +crazy like most of the time they're + + + align:start position:0% +crazy like most of the time they're +gonna be within a few seconds so in AI + + align:start position:0% +gonna be within a few seconds so in AI + + + align:start position:0% +gonna be within a few seconds so in AI +in general I don't think it ever is a + + align:start position:0% +in general I don't think it ever is a + + + align:start position:0% +in general I don't think it ever is a +problem in terms of that so like yeah + + align:start position:0% +problem in terms of that so like yeah + + + align:start position:0% +problem in terms of that so like yeah +but but people do okay so one of the + + align:start position:0% +but but people do okay so one of the + + + align:start position:0% +but but people do okay so one of the +things they do which I can get to here + + align:start position:0% +things they do which I can get to here + + + align:start position:0% +things they do which I can get to here +since there's a timestamp in the message + + align:start position:0% +since there's a timestamp in the message + + + align:start position:0% +since there's a timestamp in the message +being hashed some chips that are + + align:start position:0% +being hashed some chips that are + + + align:start position:0% +being hashed some chips that are +purpose-built for doing this work will + + align:start position:0% +purpose-built for doing this work will + + + align:start position:0% +purpose-built for doing this work will +actually flip bits in the time stamp + + align:start position:0% +actually flip bits in the time stamp + + + align:start position:0% +actually flip bits in the time stamp +flip the low-order bits because they're + + align:start position:0% +flip the low-order bits because they're + + + align:start position:0% +flip the low-order bits because they're +like well no one cares what second it is + + align:start position:0% +like well no one cares what second it is + + + align:start position:0% +like well no one cares what second it is +so I have a bit here that I can just + + align:start position:0% +so I have a bit here that I can just + + + align:start position:0% +so I have a bit here that I can just +turn on and off and use as a nuns so + + align:start position:0% +turn on and off and use as a nuns so + + + align:start position:0% +turn on and off and use as a nuns so +like the last the the lowest few bits + + align:start position:0% +like the last the the lowest few bits + + + align:start position:0% +like the last the the lowest few bits +they just sort of randomize they're like + + align:start position:0% +they just sort of randomize they're like + + + align:start position:0% +they just sort of randomize they're like +well if I'm off by five seconds no one + + align:start position:0% +well if I'm off by five seconds no one + + + align:start position:0% +well if I'm off by five seconds no one +cares whether future fast so I'll just + + align:start position:0% +cares whether future fast so I'll just + + + align:start position:0% +cares whether future fast so I'll just +use this as note space okay so but I'll + + align:start position:0% +use this as note space okay so but I'll + + + align:start position:0% +use this as note space okay so but I'll +get into that a little more later so + + align:start position:0% +get into that a little more later so + + + align:start position:0% +get into that a little more later so +anyway so so a block let's call this a + + align:start position:0% +anyway so so a block let's call this a + + + align:start position:0% +anyway so so a block let's call this a +block has a bunch of data and then we + + align:start position:0% +block has a bunch of data and then we + + + align:start position:0% +block has a bunch of data and then we +hash it right and in this case it's got + + align:start position:0% +hash it right and in this case it's got + + + align:start position:0% +hash it right and in this case it's got +three things it's got a previous hash so + + align:start position:0% +three things it's got a previous hash so + + + align:start position:0% +three things it's got a previous hash so +a pointer you know it specifies the + + align:start position:0% +a pointer you know it specifies the + + + align:start position:0% +a pointer you know it specifies the +thing it's building off of it's got a + + align:start position:0% +thing it's building off of it's got a + + + align:start position:0% +thing it's building off of it's got a +message so that you can add your message + + align:start position:0% +message so that you can add your message + + + align:start position:0% +message so that you can add your message +that you're adding to the blockchain and + + align:start position:0% +that you're adding to the blockchain and + + + align:start position:0% +that you're adding to the blockchain and +it's got a nuns so that you can prove + + align:start position:0% +it's got a nuns so that you can prove + + + align:start position:0% +it's got a nuns so that you can prove +you're doing work and then these are the + + align:start position:0% +you're doing work and then these are the + + + align:start position:0% +you're doing work and then these are the +things the actual data but then the + + align:start position:0% +things the actual data but then the + + + align:start position:0% +things the actual data but then the +block itself has a hash right and this + + align:start position:0% +block itself has a hash right and this + + + align:start position:0% +block itself has a hash right and this +hash is not included anywhere in the + + align:start position:0% +hash is not included anywhere in the + + + align:start position:0% +hash is not included anywhere in the +block because it couldn't be right this + + align:start position:0% +block because it couldn't be right this + + + align:start position:0% +block because it couldn't be right this +is the hash of this data and so we can + + align:start position:0% +is the hash of this data and so we can + + + align:start position:0% +is the hash of this data and so we can +compute it but we can't we can't stick + + align:start position:0% +compute it but we can't we can't stick + + + align:start position:0% +compute it but we can't we can't stick +this 0 0 DB thing here because that + + align:start position:0% +this 0 0 DB thing here because that + + + align:start position:0% +this 0 0 DB thing here because that +would then change the data itself so the + + align:start position:0% +would then change the data itself so the + + + align:start position:0% +would then change the data itself so the +idea is use these block hashes as + + align:start position:0% +idea is use these block hashes as + + + align:start position:0% +idea is use these block hashes as +identifiers and in most of these systems + + align:start position:0% +identifiers and in most of these systems + + + align:start position:0% +identifiers and in most of these systems +in general the hash of something is its + + align:start position:0% +in general the hash of something is its + + + align:start position:0% +in general the hash of something is its +identifier is it sort of named the way + + align:start position:0% +identifier is it sort of named the way + + + align:start position:0% +identifier is it sort of named the way +to point to it okay so the next block + + align:start position:0% +to point to it okay so the next block + + + align:start position:0% +to point to it okay so the next block +includes a hash of the last block right + + align:start position:0% +includes a hash of the last block right + + + align:start position:0% +includes a hash of the last block right +so here you saying okay the previous + + align:start position:0% +so here you saying okay the previous + + + align:start position:0% +so here you saying okay the previous +block is zero zero dB you know you're + + align:start position:0% +block is zero zero dB you know you're + + + align:start position:0% +block is zero zero dB you know you're +pointing to it and then you're adding + + align:start position:0% +pointing to it and then you're adding + + + align:start position:0% +pointing to it and then you're adding +your own message oh hi + + align:start position:0% +your own message oh hi + + + align:start position:0% +your own message oh hi +and you're adding your own nuts to make + + align:start position:0% +and you're adding your own nuts to make + + + align:start position:0% +and you're adding your own nuts to make +you know and so you're when you these + + align:start position:0% +you know and so you're when you these + + + align:start position:0% +you know and so you're when you these +two things you start out with you start + + align:start position:0% +two things you start out with you start + + + align:start position:0% +two things you start out with you start +out with the pointer to the previous + + align:start position:0% +out with the pointer to the previous + + + align:start position:0% +out with the pointer to the previous +block and then you say okay the message + + align:start position:0% +block and then you say okay the message + + + align:start position:0% +block and then you say okay the message +I'm gonna try to add here is oh hi and + + align:start position:0% +I'm gonna try to add here is oh hi and + + + align:start position:0% +I'm gonna try to add here is oh hi and +then you start grinding through these + + align:start position:0% +then you start grinding through these + + + align:start position:0% +then you start grinding through these +right you start iterating or randomly + + align:start position:0% +right you start iterating or randomly + + + align:start position:0% +right you start iterating or randomly +attempting different nonces until do you + + align:start position:0% +attempting different nonces until do you + + + align:start position:0% +attempting different nonces until do you +found one where it's it's low right it's + + align:start position:0% +found one where it's it's low right it's + + + align:start position:0% +found one where it's it's low right it's +got a bunch of zeros and you found and + + align:start position:0% +got a bunch of zeros and you found and + + + align:start position:0% +got a bunch of zeros and you found and +so this is the nonce you need to specify + + align:start position:0% +so this is the nonce you need to specify + + + align:start position:0% +so this is the nonce you need to specify +to get a lot of service and in this case + + align:start position:0% +to get a lot of service and in this case + + + align:start position:0% +to get a lot of service and in this case +there's four characters of nonce and you + + align:start position:0% +there's four characters of nonce and you + + + align:start position:0% +there's four characters of nonce and you +only need two characters of zero so like + + align:start position:0% +only need two characters of zero so like + + + align:start position:0% +only need two characters of zero so like +it's way more non-space than you need + + align:start position:0% +it's way more non-space than you need + + + align:start position:0% +it's way more non-space than you need +yes in this case there would be on + + align:start position:0% +yes in this case there would be on + + + align:start position:0% +yes in this case there would be on +average 255 nan says that would work + + align:start position:0% +average 255 nan says that would work + + + align:start position:0% +average 255 nan says that would work +right because I'm okay I haven't + + align:start position:0% +right because I'm okay I haven't + + + align:start position:0% +right because I'm okay I haven't +actually specified these things but + + align:start position:0% +actually specified these things but + + + align:start position:0% +actually specified these things but +assuming the target here is must be less + + align:start position:0% +assuming the target here is must be less + + + align:start position:0% +assuming the target here is must be less +than oh oh ffs right so you need eight + + align:start position:0% +than oh oh ffs right so you need eight + + + align:start position:0% +than oh oh ffs right so you need eight +zero bits in the front and all the rest + + align:start position:0% +zero bits in the front and all the rest + + + align:start position:0% +zero bits in the front and all the rest +can be apps and you can have any notes + + align:start position:0% +can be apps and you can have any notes + + + align:start position:0% +can be apps and you can have any notes +you want and this is an actual hash + + align:start position:0% +you want and this is an actual hash + + + align:start position:0% +you want and this is an actual hash +function which is two bytes long that + + align:start position:0% +function which is two bytes long that + + + align:start position:0% +function which is two bytes long that +means you've got two bytes here and only + + align:start position:0% +means you've got two bytes here and only + + + align:start position:0% +means you've got two bytes here and only +one byte specified so you've got two to + + align:start position:0% +one byte specified so you've got two to + + + align:start position:0% +one byte specified so you've got two to +the sixteen none space and your output + + align:start position:0% +the sixteen none space and your output + + + align:start position:0% +the sixteen none space and your output +is constrained in two to the eighth so + + align:start position:0% +is constrained in two to the eighth so + + + align:start position:0% +is constrained in two to the eighth so +you're gonna have two to the eight + + align:start position:0% +you're gonna have two to the eight + + + align:start position:0% +you're gonna have two to the eight +different nonces that will work in the + + align:start position:0% +different nonces that will work in the + + + align:start position:0% +different nonces that will work in the +case of Bitcoin + + align:start position:0% +case of Bitcoin + + + align:start position:0% +case of Bitcoin +there's nowhere near enough nan says no + + align:start position:0% +there's nowhere near enough nan says no + + + align:start position:0% +there's nowhere near enough nan says no +space right because your actual + + align:start position:0% +space right because your actual + + + align:start position:0% +space right because your actual +constraint on your proof-of-work is a + + align:start position:0% +constraint on your proof-of-work is a + + + align:start position:0% +constraint on your proof-of-work is a +lot of bits and you only have four bytes + + align:start position:0% +lot of bits and you only have four bytes + + + align:start position:0% +lot of bits and you only have four bytes +or 32 bits of none space so what you + + align:start position:0% +or 32 bits of none space so what you + + + align:start position:0% +or 32 bits of none space so what you +actually end up doing is using your + + align:start position:0% +actually end up doing is using your + + + align:start position:0% +actually end up doing is using your +message as further none space right so + + align:start position:0% +message as further none space right so + + + align:start position:0% +message as further none space right so +the thing is I could put oh hi - and now + + align:start position:0% +the thing is I could put oh hi - and now + + + align:start position:0% +the thing is I could put oh hi - and now +I've changed my message which will + + align:start position:0% +I've changed my message which will + + + align:start position:0% +I've changed my message which will +change my hash and so I if I if I go + + align:start position:0% +change my hash and so I if I if I go + + + align:start position:0% +change my hash and so I if I if I go +through my entire nan space and don't + + align:start position:0% +through my entire nan space and don't + + + align:start position:0% +through my entire nan space and don't +find a valid + + align:start position:0% +find a valid + + + align:start position:0% +find a valid +of work I can edit my message and then + + align:start position:0% +of work I can edit my message and then + + + align:start position:0% +of work I can edit my message and then +go through it again + + align:start position:0% +go through it again + + + align:start position:0% +go through it again +so that it's a little ugly right it'd be + + align:start position:0% +so that it's a little ugly right it'd be + + + align:start position:0% +so that it's a little ugly right it'd be +nicer if your non-space was big enough + + align:start position:0% +nicer if your non-space was big enough + + + align:start position:0% +nicer if your non-space was big enough +that you've never had to do that in the + + align:start position:0% +that you've never had to do that in the + + + align:start position:0% +that you've never had to do that in the +case of Bitcoin we don't know who + + align:start position:0% +case of Bitcoin we don't know who + + + align:start position:0% +case of Bitcoin we don't know who +designed it and whoever designed it + + align:start position:0% +designed it and whoever designed it + + + align:start position:0% +designed it and whoever designed it +didn't put enough in on space and so + + align:start position:0% +didn't put enough in on space and so + + + align:start position:0% +didn't put enough in on space and so +it's kind of annoying but you can get + + align:start position:0% +it's kind of annoying but you can get + + + align:start position:0% +it's kind of annoying but you can get +around it in theory you could just + + align:start position:0% +around it in theory you could just + + + align:start position:0% +around it in theory you could just +eliminate the null space entirely and + + align:start position:0% +eliminate the null space entirely and + + + align:start position:0% +eliminate the null space entirely and +say well just put it in the message + + align:start position:0% +say well just put it in the message + + + align:start position:0% +say well just put it in the message +right but it's nice it's much easier to + + align:start position:0% +right but it's nice it's much easier to + + + align:start position:0% +right but it's nice it's much easier to +think of when you're like here these + + align:start position:0% +think of when you're like here these + + + align:start position:0% +think of when you're like here these +separate things like this is random and + + align:start position:0% +separate things like this is random and + + + align:start position:0% +separate things like this is random and +has no real meaning this is the thing + + align:start position:0% +has no real meaning this is the thing + + + align:start position:0% +has no real meaning this is the thing +that has meaning that we're going to use + + align:start position:0% +that has meaning that we're going to use + + + align:start position:0% +that has meaning that we're going to use +see yeah the chain keeps building you + + align:start position:0% +see yeah the chain keeps building you + + + align:start position:0% +see yeah the chain keeps building you +add work each time right bye okay + + align:start position:0% +add work each time right bye okay + + + align:start position:0% +add work each time right bye okay +finding different notes is that that + + align:start position:0% +finding different notes is that that + + + align:start position:0% +finding different notes is that that +match up with your message how are you + + align:start position:0% +match up with your message how are you + + + align:start position:0% +match up with your message how are you +I'm good okay and the idea is if you + + align:start position:0% +I'm good okay and the idea is if you + + + align:start position:0% +I'm good okay and the idea is if you +flip a bit in any block that's come out + + align:start position:0% +flip a bit in any block that's come out + + + align:start position:0% +flip a bit in any block that's come out +so for example you change oh hi - oh hey + + align:start position:0% +so for example you change oh hi - oh hey + + + align:start position:0% +so for example you change oh hi - oh hey +and try to leave everything the same + + align:start position:0% +and try to leave everything the same + + + align:start position:0% +and try to leave everything the same +you're gonna change the hash so most + + align:start position:0% +you're gonna change the hash so most + + + align:start position:0% +you're gonna change the hash so most +likely the proof-of-work will no longer + + align:start position:0% +likely the proof-of-work will no longer + + + align:start position:0% +likely the proof-of-work will no longer +be valid right you know this starts with + + align:start position:0% +be valid right you know this starts with + + + align:start position:0% +be valid right you know this starts with +a 9 now that's no one's gonna point use + + align:start position:0% +a 9 now that's no one's gonna point use + + + align:start position:0% +a 9 now that's no one's gonna point use +it and and more importantly actually + + align:start position:0% +it and and more importantly actually + + + align:start position:0% +it and and more importantly actually +these pointers stop working right + + align:start position:0% +these pointers stop working right + + + align:start position:0% +these pointers stop working right +because I was this block was pointing + + align:start position:0% +because I was this block was pointing + + + align:start position:0% +because I was this block was pointing +200 - see that's not this that's this + + align:start position:0% +200 - see that's not this that's this + + + align:start position:0% +200 - see that's not this that's this +other one so basically you flip any bit + + align:start position:0% +other one so basically you flip any bit + + + align:start position:0% +other one so basically you flip any bit +in the entire history of this chain and + + align:start position:0% +in the entire history of this chain and + + + align:start position:0% +in the entire history of this chain and +it breaks right so you can't go back and + + align:start position:0% +it breaks right so you can't go back and + + + align:start position:0% +it breaks right so you can't go back and +edit things you can't change messages + + align:start position:0% +edit things you can't change messages + + + align:start position:0% +edit things you can't change messages +after the fact so it gives you the nice + + align:start position:0% +after the fact so it gives you the nice + + + align:start position:0% +after the fact so it gives you the nice +property of immutability that once once + + align:start position:0% +property of immutability that once once + + + align:start position:0% +property of immutability that once once +the message is included in the system so + + align:start position:0% +the message is included in the system so + + + align:start position:0% +the message is included in the system so +in the case of money once a transaction + + align:start position:0% +in the case of money once a transaction + + + align:start position:0% +in the case of money once a transaction +has moved funds from one place to + + align:start position:0% +has moved funds from one place to + + + align:start position:0% +has moved funds from one place to +another you can't go back and change it + + align:start position:0% +another you can't go back and change it + + + align:start position:0% +another you can't go back and change it +you can't undo something unless unless + + align:start position:0% +you can't undo something unless unless + + + align:start position:0% +you can't undo something unless unless +you fork the chain so the idea is + + align:start position:0% +you fork the chain so the idea is + + + align:start position:0% +you fork the chain so the idea is +everyone you know is running this system + + align:start position:0% +everyone you know is running this system + + + align:start position:0% +everyone you know is running this system +sometimes inadvertently or sometimes on + + align:start position:0% +sometimes inadvertently or sometimes on + + + align:start position:0% +sometimes inadvertently or sometimes on +purpose you can have two branches right + + align:start position:0% +purpose you can have two branches right + + + align:start position:0% +purpose you can have two branches right +you can't have something point to two + + align:start position:0% +you can't have something point to two + + + align:start position:0% +you can't have something point to two +different previous blocks right there's + + align:start position:0% +different previous blocks right there's + + + align:start position:0% +different previous blocks right there's +one specified so in this case when I say + + align:start position:0% +one specified so in this case when I say + + + align:start position:0% +one specified so in this case when I say +previous block it's a single specific + + align:start position:0% +previous block it's a single specific + + + align:start position:0% +previous block it's a single specific +hash that I'm pointing to + + align:start position:0% +hash that I'm pointing to + + + align:start position:0% +hash that I'm pointing to +and since we're pretty sure we can't + + align:start position:0% +and since we're pretty sure we can't + + + align:start position:0% +and since we're pretty sure we can't +find collisions that means if I'm + + align:start position:0% +find collisions that means if I'm + + + align:start position:0% +find collisions that means if I'm +pointing to zero zero dB it's only this + + align:start position:0% +pointing to zero zero dB it's only this + + + align:start position:0% +pointing to zero zero dB it's only this +one which has the message hi I should + + align:start position:0% +one which has the message hi I should + + + align:start position:0% +one which has the message hi I should +not be able to find two different blocks + + align:start position:0% +not be able to find two different blocks + + + align:start position:0% +not be able to find two different blocks +which hash to zero zero DB because then + + align:start position:0% +which hash to zero zero DB because then + + + align:start position:0% +which hash to zero zero DB because then +it's ambiguous and like wait which am i + + align:start position:0% +it's ambiguous and like wait which am i + + + align:start position:0% +it's ambiguous and like wait which am i +pointing to so I shouldn't be able to do + + align:start position:0% +pointing to so I shouldn't be able to do + + + align:start position:0% +pointing to so I shouldn't be able to do +that however it's easy to have two + + align:start position:0% +that however it's easy to have two + + + align:start position:0% +that however it's easy to have two +blocks here that both point to the same + + align:start position:0% +blocks here that both point to the same + + + align:start position:0% +blocks here that both point to the same +ancestor the post we call this a parent + + align:start position:0% +ancestor the post we call this a parent + + + align:start position:0% +ancestor the post we call this a parent +well that's a child + + align:start position:0% +well that's a child + + + align:start position:0% +well that's a child +plus a brand any so so this is easy to + + align:start position:0% +plus a brand any so so this is easy to + + + align:start position:0% +plus a brand any so so this is easy to +do right - but different people can just + + align:start position:0% +do right - but different people can just + + + align:start position:0% +do right - but different people can just +come up with their own messages and own + + align:start position:0% +come up with their own messages and own + + + align:start position:0% +come up with their own messages and own +nonsense and point to the same ancestor + + align:start position:0% +nonsense and point to the same ancestor + + + align:start position:0% +nonsense and point to the same ancestor +they could do this inadvertently because + + align:start position:0% +they could do this inadvertently because + + + align:start position:0% +they could do this inadvertently because +they're not aware of each other's work + + align:start position:0% +they're not aware of each other's work + + + align:start position:0% +they're not aware of each other's work +right where maybe these two things + + align:start position:0% +right where maybe these two things + + + align:start position:0% +right where maybe these two things +happen at the same time and they're like + + align:start position:0% +happen at the same time and they're like + + + align:start position:0% +happen at the same time and they're like +oh well we both found the answers at + + align:start position:0% +oh well we both found the answers at + + + align:start position:0% +oh well we both found the answers at +about the same time or they could do it + + align:start position:0% +about the same time or they could do it + + + align:start position:0% +about the same time or they could do it +maliciously where I saw that you made + + align:start position:0% +maliciously where I saw that you made + + + align:start position:0% +maliciously where I saw that you made +this block and I saw that you made this + + align:start position:0% +this block and I saw that you made this + + + align:start position:0% +this block and I saw that you made this +block and I'm gonna make these two + + align:start position:0% +block and I'm gonna make these two + + + align:start position:0% +block and I'm gonna make these two +that's you know to try to confuse things + + align:start position:0% +that's you know to try to confuse things + + + align:start position:0% +that's you know to try to confuse things +so this can happen in the rule in + + align:start position:0% +so this can happen in the rule in + + + align:start position:0% +so this can happen in the rule in +Bitcoin and most all these systems is + + align:start position:0% +Bitcoin and most all these systems is + + + align:start position:0% +Bitcoin and most all these systems is +okay well the highest walk chain wins + + align:start position:0% +okay well the highest walk chain wins + + + align:start position:0% +okay well the highest walk chain wins +the most work wins so that's just our + + align:start position:0% +the most work wins so that's just our + + + align:start position:0% +the most work wins so that's just our +metric for what we all determine is the + + align:start position:0% +metric for what we all determine is the + + + align:start position:0% +metric for what we all determine is the +state of this system so everyone uses + + align:start position:0% +state of this system so everyone uses + + + align:start position:0% +state of this system so everyone uses +the chain with the most work and that + + align:start position:0% +the chain with the most work and that + + + align:start position:0% +the chain with the most work and that +can change right let's say we started + + align:start position:0% +can change right let's say we started + + + align:start position:0% +can change right let's say we started +off with the eight zero zero eight a + + align:start position:0% +off with the eight zero zero eight a + + + align:start position:0% +off with the eight zero zero eight a +being the chain tip that's what we call + + align:start position:0% +being the chain tip that's what we call + + + align:start position:0% +being the chain tip that's what we call +the you know the current state of the + + align:start position:0% +the you know the current state of the + + + align:start position:0% +the you know the current state of the +system and then someone came along and + + align:start position:0% +system and then someone came along and + + + align:start position:0% +system and then someone came along and +said well I'm gonna I'm gonna get rid of + + align:start position:0% +said well I'm gonna I'm gonna get rid of + + + align:start position:0% +said well I'm gonna I'm gonna get rid of +this thing + + align:start position:0% +this thing + + + align:start position:0% +this thing +something happens in 94 that I want to + + align:start position:0% +something happens in 94 that I want to + + + align:start position:0% +something happens in 94 that I want to +rewrite right I want to get rid of the + + align:start position:0% +rewrite right I want to get rid of the + + + align:start position:0% +rewrite right I want to get rid of the +how are you message and I'm gonna + + align:start position:0% +how are you message and I'm gonna + + + align:start position:0% +how are you message and I'm gonna +replace it with my own message and so + + align:start position:0% +replace it with my own message and so + + + align:start position:0% +replace it with my own message and so +the way I do it is I branch off from o2c + + align:start position:0% +the way I do it is I branch off from o2c + + + align:start position:0% +the way I do it is I branch off from o2c +make this one make this one and now drew + + align:start position:0% +make this one make this one and now drew + + + align:start position:0% +make this one make this one and now drew +I've made another one so now this this + + align:start position:0% +I've made another one so now this this + + + align:start position:0% +I've made another one so now this this +branch here has the most work and + + align:start position:0% +branch here has the most work and + + + align:start position:0% +branch here has the most work and +everyone's gonna use it do and they sort + + align:start position:0% +everyone's gonna use it do and they sort + + + align:start position:0% +everyone's gonna use it do and they sort +of forget about these two things like + + align:start position:0% +of forget about these two things like + + + align:start position:0% +of forget about these two things like +yeah that was the tip you know that was + + align:start position:0% +yeah that was the tip you know that was + + + align:start position:0% +yeah that was the tip you know that was +the most work state of the system but + + align:start position:0% +the most work state of the system but + + + align:start position:0% +the most work state of the system but +now this is so now we have to go back we + + align:start position:0% +now this is so now we have to go back we + + + align:start position:0% +now this is so now we have to go back we +have to erase these two messages and + + align:start position:0% +have to erase these two messages and + + + align:start position:0% +have to erase these two messages and +these three messages and now everyone + + align:start position:0% +these three messages and now everyone + + + align:start position:0% +these three messages and now everyone +agrees that that's the next state of the + + align:start position:0% +agrees that that's the next state of the + + + align:start position:0% +agrees that that's the next state of the +system and this is called a reorg a + + align:start position:0% +system and this is called a reorg a + + + align:start position:0% +system and this is called a reorg a +reorganization of the block this is sort + + align:start position:0% +reorganization of the block this is sort + + + align:start position:0% +reorganization of the block this is sort +of bad but yeah they request it or + + align:start position:0% +of bad but yeah they request it or + + + align:start position:0% +of bad but yeah they request it or +basically like someone says hey I have + + align:start position:0% +basically like someone says hey I have + + + align:start position:0% +basically like someone says hey I have +these three and you're like really what + + align:start position:0% +these three and you're like really what + + + align:start position:0% +these three and you're like really what +are those three and they give them to + + align:start position:0% +are those three and they give them to + + + align:start position:0% +are those three and they give them to +you you're like okay + + align:start position:0% +you you're like okay + + + align:start position:0% +you you're like okay +yep that works so the actual Network I + + align:start position:0% +yep that works so the actual Network I + + + align:start position:0% +yep that works so the actual Network I +think in a few weeks we're going to the + + align:start position:0% +think in a few weeks we're going to the + + + align:start position:0% +think in a few weeks we're going to the +actual like Network messages that are + + align:start position:0% +actual like Network messages that are + + + align:start position:0% +actual like Network messages that are +used in Bitcoin but they're not they're + + align:start position:0% +used in Bitcoin but they're not they're + + + align:start position:0% +used in Bitcoin but they're not they're +not like you actually if you wrote it + + align:start position:0% +not like you actually if you wrote it + + + align:start position:0% +not like you actually if you wrote it +yourself you'd probably write something + + align:start position:0% +yourself you'd probably write something + + + align:start position:0% +yourself you'd probably write something +more sensible and better it's a little + + align:start position:0% +more sensible and better it's a little + + + align:start position:0% +more sensible and better it's a little +weird but basically you sort of knows + + align:start position:0% +weird but basically you sort of knows + + + align:start position:0% +weird but basically you sort of knows +nodes in this network all are all + + align:start position:0% +nodes in this network all are all + + + align:start position:0% +nodes in this network all are all +connected to each other and they report + + align:start position:0% +connected to each other and they report + + + align:start position:0% +connected to each other and they report +on what they have and they say hey I + + align:start position:0% +on what they have and they say hey I + + + align:start position:0% +on what they have and they say hey I +have oh oh six one and you're like + + align:start position:0% +have oh oh six one and you're like + + + align:start position:0% +have oh oh six one and you're like +really I don't have a low six one and + + align:start position:0% +really I don't have a low six one and + + + align:start position:0% +really I don't have a low six one and +you think maybe you owe six one builds + + align:start position:0% +you think maybe you owe six one builds + + + align:start position:0% +you think maybe you owe six one builds +off here you request oh six one and + + align:start position:0% +off here you request oh six one and + + + align:start position:0% +off here you request oh six one and +you're like oh it built off of here and + + align:start position:0% +you're like oh it built off of here and + + + align:start position:0% +you're like oh it built off of here and +then they're like Oh ffff - I have a + + align:start position:0% +then they're like Oh ffff - I have a + + + align:start position:0% +then they're like Oh ffff - I have a +three and so they build these you know + + align:start position:0% +three and so they build these you know + + + align:start position:0% +three and so they build these you know +they request them all and build them and + + align:start position:0% +they request them all and build them and + + + align:start position:0% +they request them all and build them and +then they actually keep these on in + + align:start position:0% +then they actually keep these on in + + + align:start position:0% +then they actually keep these on in +memory for a little while and then event + + align:start position:0% +memory for a little while and then event + + + align:start position:0% +memory for a little while and then event +but they don't think they save them on + + align:start position:0% +but they don't think they save them on + + + align:start position:0% +but they don't think they save them on +disk so so you can have multiple like + + align:start position:0% +disk so so you can have multiple like + + + align:start position:0% +disk so so you can have multiple like +different branches and concurrently in + + align:start position:0% +different branches and concurrently in + + + align:start position:0% +different branches and concurrently in +your software and you just you know use + + align:start position:0% +your software and you just you know use + + + align:start position:0% +your software and you just you know use +this and show this to DUI if one person + + align:start position:0% +this and show this to DUI if one person + + + align:start position:0% +this and show this to DUI if one person +had a longer chain and + + align:start position:0% +had a longer chain and + + + align:start position:0% +had a longer chain and +and everyone's out there getting it then + + align:start position:0% +and everyone's out there getting it then + + + align:start position:0% +and everyone's out there getting it then +the network starts believing it great + + align:start position:0% +the network starts believing it great + + + align:start position:0% +the network starts believing it great +yeah so so it's a gossip network so + + align:start position:0% +yeah so so it's a gossip network so + + + align:start position:0% +yeah so so it's a gossip network so +basically there's no real identity for + + align:start position:0% +basically there's no real identity for + + + align:start position:0% +basically there's no real identity for +all the different nodes of computers you + + align:start position:0% +all the different nodes of computers you + + + align:start position:0% +all the different nodes of computers you +you also will report all the IE you + + align:start position:0% +you also will report all the IE you + + + align:start position:0% +you also will report all the IE you +basically do it by IP address right so + + align:start position:0% +basically do it by IP address right so + + + align:start position:0% +basically do it by IP address right so +when I connect to a node I don't think I + + align:start position:0% +when I connect to a node I don't think I + + + align:start position:0% +when I connect to a node I don't think I +asked I think they just tell me like hey + + align:start position:0% +asked I think they just tell me like hey + + + align:start position:0% +asked I think they just tell me like hey +here's a thousand IP addresses that I + + align:start position:0% +here's a thousand IP addresses that I + + + align:start position:0% +here's a thousand IP addresses that I +know of that I've connected to that are + + align:start position:0% +know of that I've connected to that are + + + align:start position:0% +know of that I've connected to that are +running this software and you're like + + align:start position:0% +running this software and you're like + + + align:start position:0% +running this software and you're like +okay I'll add that into my list and then + + align:start position:0% +okay I'll add that into my list and then + + + align:start position:0% +okay I'll add that into my list and then +you just sort of randomly connect to + + align:start position:0% +you just sort of randomly connect to + + + align:start position:0% +you just sort of randomly connect to +people I think the default is randomly + + align:start position:0% +people I think the default is randomly + + + align:start position:0% +people I think the default is randomly +connect to seven years and then when you + + align:start position:0% +connect to seven years and then when you + + + align:start position:0% +connect to seven years and then when you +when anything comes in hey I got a new + + align:start position:0% +when anything comes in hey I got a new + + + align:start position:0% +when anything comes in hey I got a new +message you know I got a new block + + align:start position:0% +message you know I got a new block + + + align:start position:0% +message you know I got a new block +message you will tell all seven of your + + align:start position:0% +message you will tell all seven of your + + + align:start position:0% +message you will tell all seven of your +peers hey I got a three and if they + + align:start position:0% +peers hey I got a three and if they + + + align:start position:0% +peers hey I got a three and if they +request you know what what the data is + + align:start position:0% +request you know what what the data is + + + align:start position:0% +request you know what what the data is +you'll give it to them so in in practice + + align:start position:0% +you'll give it to them so in in practice + + + align:start position:0% +you'll give it to them so in in practice +things get propagated pretty well but + + align:start position:0% +things get propagated pretty well but + + + align:start position:0% +things get propagated pretty well but +yeah partition attacks if you can + + align:start position:0% +yeah partition attacks if you can + + + align:start position:0% +yeah partition attacks if you can +isolate so like if you can isolate this + + align:start position:0% +isolate so like if you can isolate this + + + align:start position:0% +isolate so like if you can isolate this +off the network you may be able to + + align:start position:0% +off the network you may be able to + + + align:start position:0% +off the network you may be able to +prevent this kind of thing from + + align:start position:0% +prevent this kind of thing from + + + align:start position:0% +prevent this kind of thing from +happening so if you know someone built + + align:start position:0% +happening so if you know someone built + + + align:start position:0% +happening so if you know someone built +these three blocks but isn't able to + + align:start position:0% +these three blocks but isn't able to + + + align:start position:0% +these three blocks but isn't able to +broadcast it to the network then people + + align:start position:0% +broadcast it to the network then people + + + align:start position:0% +broadcast it to the network then people +will still think that this is the most + + align:start position:0% +will still think that this is the most + + + align:start position:0% +will still think that this is the most +the most work and build off of this so + + align:start position:0% +the most work and build off of this so + + + align:start position:0% +the most work and build off of this so +yeah those are those are attacks that + + align:start position:0% +yeah those are those are attacks that + + + align:start position:0% +yeah those are those are attacks that +can happen yeah + + align:start position:0% + + + + align:start position:0% + +yeah um they stop being you know they + + align:start position:0% +yeah um they stop being you know they + + + align:start position:0% +yeah um they stop being you know they +get undone so this is a very real risk + + align:start position:0% +get undone so this is a very real risk + + + align:start position:0% +get undone so this is a very real risk +if you you know if you have a sort of + + align:start position:0% +if you you know if you have a sort of + + + align:start position:0% +if you you know if you have a sort of +I'm you know alice is sending Bob five + + align:start position:0% +I'm you know alice is sending Bob five + + + align:start position:0% +I'm you know alice is sending Bob five +bitcoins in this block and in this block + + align:start position:0% +bitcoins in this block and in this block + + + align:start position:0% +bitcoins in this block and in this block +you have a conflicting transaction alice + + align:start position:0% +you have a conflicting transaction alice + + + align:start position:0% +you have a conflicting transaction alice +is sending Carol five bitcoins you know + + align:start position:0% +is sending Carol five bitcoins you know + + + align:start position:0% +is sending Carol five bitcoins you know +the same five bitcoins + + align:start position:0% +the same five bitcoins + + + align:start position:0% +the same five bitcoins +Bob could think at this point hey I got + + align:start position:0% +Bob could think at this point hey I got + + + align:start position:0% +Bob could think at this point hey I got +some money I have some money + + align:start position:0% +some money I have some money + + + align:start position:0% +some money I have some money +oh shoot I don't have the money anymore + + align:start position:0% +oh shoot I don't have the money anymore + + + align:start position:0% +oh shoot I don't have the money anymore +when this gets reorg doubt so that's + + align:start position:0% +when this gets reorg doubt so that's + + + align:start position:0% +when this gets reorg doubt so that's +that is an attack right ends and you + + align:start position:0% +that is an attack right ends and you + + + align:start position:0% +that is an attack right ends and you +have to be aware of that in using + + align:start position:0% +have to be aware of that in using + + + align:start position:0% +have to be aware of that in using +Bitcoin or any of these kinds of systems + + align:start position:0% +Bitcoin or any of these kinds of systems + + + align:start position:0% +Bitcoin or any of these kinds of systems +they're not you have consensus but I + + align:start position:0% +they're not you have consensus but I + + + align:start position:0% +they're not you have consensus but I +think it's sort of like eventually + + align:start position:0% +think it's sort of like eventually + + + align:start position:0% +think it's sort of like eventually +consent like so so generally the the + + align:start position:0% +consent like so so generally the the + + + align:start position:0% +consent like so so generally the the +rule of thumb people use is like wait + + align:start position:0% +rule of thumb people use is like wait + + + align:start position:0% +rule of thumb people use is like wait +six blocks I think that's in the + + align:start position:0% +six blocks I think that's in the + + + align:start position:0% +six blocks I think that's in the +original Bitcoin white paper which is + + align:start position:0% +original Bitcoin white paper which is + + + align:start position:0% +original Bitcoin white paper which is +fairly arbitrary like you know the + + align:start position:0% +fairly arbitrary like you know the + + + align:start position:0% +fairly arbitrary like you know the +longer you wait the more certain it is + + align:start position:0% +longer you wait the more certain it is + + + align:start position:0% +longer you wait the more certain it is +the more difficult it will be to perform + + align:start position:0% +the more difficult it will be to perform + + + align:start position:0% +the more difficult it will be to perform +this kind of attack because you're gonna + + align:start position:0% +this kind of attack because you're gonna + + + align:start position:0% +this kind of attack because you're gonna +have to do more work right and the idea + + align:start position:0% +have to do more work right and the idea + + + align:start position:0% +have to do more work right and the idea +is everyone's building off of the one + + align:start position:0% +is everyone's building off of the one + + + align:start position:0% +is everyone's building off of the one +that they think is the tip so everyone's + + align:start position:0% +that they think is the tip so everyone's + + + align:start position:0% +that they think is the tip so everyone's +gonna you know you have to sort of get + + align:start position:0% +gonna you know you have to sort of get + + + align:start position:0% +gonna you know you have to sort of get +pretty lucky or outrun everyone else to + + align:start position:0% +pretty lucky or outrun everyone else to + + + align:start position:0% +pretty lucky or outrun everyone else to +perform this kind of attack so like in + + align:start position:0% +perform this kind of attack so like in + + + align:start position:0% +perform this kind of attack so like in +aetherium and some other systems they + + align:start position:0% +aetherium and some other systems they + + + align:start position:0% +aetherium and some other systems they +have uncles where you can point to + + align:start position:0% +have uncles where you can point to + + + align:start position:0% +have uncles where you can point to +multiple ancestors which is weird + + align:start position:0% +multiple ancestors which is weird + + + align:start position:0% +multiple ancestors which is weird +because your uncle's not really um the + + align:start position:0% +because your uncle's not really um the + + + align:start position:0% +because your uncle's not really um the +so like that would that would let for + + align:start position:0% +so like that would that would let for + + + align:start position:0% +so like that would that would let for +example that would let of' to point to + + align:start position:0% +example that would let of' to point to + + + align:start position:0% +example that would let of' to point to +both oh six one and oh nine four + + align:start position:0% +both oh six one and oh nine four + + + align:start position:0% +both oh six one and oh nine four +the answer is no these are not uncles + + align:start position:0% +the answer is no these are not uncles + + + align:start position:0% +the answer is no these are not uncles +yeah there's a separate thing this is + + align:start position:0% +yeah there's a separate thing this is + + + align:start position:0% +yeah there's a separate thing this is +not uncle's but related right you could + + align:start position:0% +not uncle's but related right you could + + + align:start position:0% +not uncle's but related right you could +draw like you could draw an arrow there + + align:start position:0% +draw like you could draw an arrow there + + + align:start position:0% +draw like you could draw an arrow there +okay so I'll talk about sort of pros and + + align:start position:0% +okay so I'll talk about sort of pros and + + + align:start position:0% +okay so I'll talk about sort of pros and +cons and some of this gets into not as + + align:start position:0% +cons and some of this gets into not as + + + align:start position:0% +cons and some of this gets into not as +objective and somewhat subjective ideas + + align:start position:0% +objective and somewhat subjective ideas + + + align:start position:0% +objective and somewhat subjective ideas +but it's an interesting thing to talk + + align:start position:0% +but it's an interesting thing to talk + + + align:start position:0% +but it's an interesting thing to talk +about especially in contests of money + + align:start position:0% +about especially in contests of money + + + align:start position:0% +about especially in contests of money +okay so pros anonymous memoryless + + align:start position:0% +okay so pros anonymous memoryless + + + align:start position:0% +okay so pros anonymous memoryless +scalable non interactive I'll go through + + align:start position:0% +scalable non interactive I'll go through + + + align:start position:0% +scalable non interactive I'll go through +all these kind of the real world + + align:start position:0% +all these kind of the real world + + + align:start position:0% +all these kind of the real world +Conn's pretty much all Monza's fail it + + align:start position:0% +Conn's pretty much all Monza's fail it + + + align:start position:0% +Conn's pretty much all Monza's fail it +uses watts uses chips + + align:start position:0% +uses watts uses chips + + + align:start position:0% +uses watts uses chips +there's 51% attacks and people hate it + + align:start position:0% +there's 51% attacks and people hate it + + + align:start position:0% +there's 51% attacks and people hate it +so the pros there's they're quite good + + align:start position:0% +so the pros there's they're quite good + + + align:start position:0% +so the pros there's they're quite good +it is anonymous right you can mine + + align:start position:0% +it is anonymous right you can mine + + + align:start position:0% +it is anonymous right you can mine +without any kind of identity even after + + align:start position:0% +without any kind of identity even after + + + align:start position:0% +without any kind of identity even after +you've mined you don't really have to + + align:start position:0% +you've mined you don't really have to + + + align:start position:0% +you've mined you don't really have to +say who you are + + align:start position:0% +say who you are + + + align:start position:0% +say who you are +there's no pre known keys there's + + align:start position:0% +there's no pre known keys there's + + + align:start position:0% +there's no pre known keys there's +there's actually no signatures involved + + align:start position:0% +there's actually no signatures involved + + + align:start position:0% +there's actually no signatures involved +right there's no public key system at + + align:start position:0% +right there's no public key system at + + + align:start position:0% +right there's no public key system at +all you're just you know trying + + align:start position:0% +all you're just you know trying + + + align:start position:0% +all you're just you know trying +different notices anyone can go for it + + align:start position:0% +different notices anyone can go for it + + + align:start position:0% +different notices anyone can go for it +every attempt is equally likely to + + align:start position:0% +every attempt is equally likely to + + + align:start position:0% +every attempt is equally likely to +succeed since it's random and it's not + + align:start position:0% +succeed since it's random and it's not + + + align:start position:0% +succeed since it's random and it's not +limited to humans so you could have you + + align:start position:0% +limited to humans so you could have you + + + align:start position:0% +limited to humans so you could have you +know you don't need a social security + + align:start position:0% +know you don't need a social security + + + align:start position:0% +know you don't need a social security +number bots are welcome any anything can + + align:start position:0% +number bots are welcome any anything can + + + align:start position:0% +number bots are welcome any anything can +mine and everyone you know doesn't + + align:start position:0% +mine and everyone you know doesn't + + + align:start position:0% +mine and everyone you know doesn't +really care who mined it it's not about + + align:start position:0% +really care who mined it it's not about + + + align:start position:0% +really care who mined it it's not about +who it's just oh there's a none stairs + + align:start position:0% +who it's just oh there's a none stairs + + + align:start position:0% +who it's just oh there's a none stairs +work okay this is valid so that's really + + align:start position:0% +work okay this is valid so that's really + + + align:start position:0% +work okay this is valid so that's really +cool it's memoryless this is important + + align:start position:0% +cool it's memoryless this is important + + + align:start position:0% +cool it's memoryless this is important +and a little counterintuitive in some + + align:start position:0% +and a little counterintuitive in some + + + align:start position:0% +and a little counterintuitive in some +ways there's no progress so if you have + + align:start position:0% +ways there's no progress so if you have + + + align:start position:0% +ways there's no progress so if you have +10 trillion failed nonces your next + + align:start position:0% +10 trillion failed nonces your next + + + align:start position:0% +10 trillion failed nonces your next +month's is just as likely to fail which + + align:start position:0% +month's is just as likely to fail which + + + align:start position:0% +month's is just as likely to fail which +is extremely likely so that makes it a + + align:start position:0% +is extremely likely so that makes it a + + + align:start position:0% +is extremely likely so that makes it a +possible process right which is you know + + align:start position:0% +possible process right which is you know + + + align:start position:0% +possible process right which is you know +it's a certain probability distribution + + align:start position:0% +it's a certain probability distribution + + + align:start position:0% +it's a certain probability distribution +kind of thing you will always expect the + + align:start position:0% +kind of thing you will always expect the + + + align:start position:0% +kind of thing you will always expect the +next block in ten minutes from now so + + align:start position:0% +next block in ten minutes from now so + + + align:start position:0% +next block in ten minutes from now so +hey it's been 20 minutes since the last + + align:start position:0% +hey it's been 20 minutes since the last + + + align:start position:0% +hey it's been 20 minutes since the last +block came out when's the next one + + align:start position:0% +block came out when's the next one + + + align:start position:0% +block came out when's the next one +coming out probably 10 minutes there you + + align:start position:0% +coming out probably 10 minutes there you + + + align:start position:0% +coming out probably 10 minutes there you +know and there's no it's sort of like + + align:start position:0% +know and there's no it's sort of like + + + align:start position:0% +know and there's no it's sort of like +you know there's no progress being made + + align:start position:0% +you know there's no progress being made + + + align:start position:0% +you know there's no progress being made +you you always you have no memory of + + align:start position:0% +you you always you have no memory of + + + align:start position:0% +you you always you have no memory of +what the last few minutes have had so + + align:start position:0% +what the last few minutes have had so + + + align:start position:0% +what the last few minutes have had so +the fact that it's been 10 minutes the + + align:start position:0% +the fact that it's been 10 minutes the + + + align:start position:0% +the fact that it's been 10 minutes the +fact that I miss or it's been 2 seconds + + align:start position:0% +fact that I miss or it's been 2 seconds + + + align:start position:0% +fact that I miss or it's been 2 seconds +you still think it's gonna take about 10 + + align:start position:0% +you still think it's gonna take about 10 + + + align:start position:0% +you still think it's gonna take about 10 +minutes which is nice because it means + + align:start position:0% +minutes which is nice because it means + + + align:start position:0% +minutes which is nice because it means +like there's a linear trade-off between + + align:start position:0% +like there's a linear trade-off between + + + align:start position:0% +like there's a linear trade-off between +how many attempts you're making and what + + align:start position:0% +how many attempts you're making and what + + + align:start position:0% +how many attempts you're making and what +your chances of finding in the next + + align:start position:0% +your chances of finding in the next + + + align:start position:0% +your chances of finding in the next +block are so if you attempt twice as + + align:start position:0% +block are so if you attempt twice as + + + align:start position:0% +block are so if you attempt twice as +many you have twice as good a chance of + + align:start position:0% +many you have twice as good a chance of + + + align:start position:0% +many you have twice as good a chance of +finding the next block which is good + + align:start position:0% +finding the next block which is good + + + align:start position:0% +finding the next block which is good +because if there is progress right if + + align:start position:0% +because if there is progress right if + + + align:start position:0% +because if there is progress right if +you had some kind of function where the + + align:start position:0% +you had some kind of function where the + + + align:start position:0% +you had some kind of function where the +probability was non not just linear a + + align:start position:0% +probability was non not just linear a + + + align:start position:0% +probability was non not just linear a +number of chances but if it was like + + align:start position:0% +number of chances but if it was like + + + align:start position:0% +number of chances but if it was like +super linear exponential + + align:start position:0% +super linear exponential + + + align:start position:0% +super linear exponential +or something like that you the fastest + + align:start position:0% +or something like that you the fastest + + + align:start position:0% +or something like that you the fastest +person would always win right so if it's + + align:start position:0% +person would always win right so if it's + + + align:start position:0% +person would always win right so if it's +like okay I need to compute this thing + + align:start position:0% +like okay I need to compute this thing + + + align:start position:0% +like okay I need to compute this thing +and it takes a couple trillion + + align:start position:0% +and it takes a couple trillion + + + align:start position:0% +and it takes a couple trillion +computations and so for some computers + + align:start position:0% +computations and so for some computers + + + align:start position:0% +computations and so for some computers +it takes five minutes for some computers + + align:start position:0% +it takes five minutes for some computers + + + align:start position:0% +it takes five minutes for some computers +it only takes two minutes the computers + + align:start position:0% +it only takes two minutes the computers + + + align:start position:0% +it only takes two minutes the computers +that can do it in two minutes + + align:start position:0% +that can do it in two minutes + + + align:start position:0% +that can do it in two minutes +are just always going to win because the + + align:start position:0% +are just always going to win because the + + + align:start position:0% +are just always going to win because the +people who take five minutes to finish + + align:start position:0% +people who take five minutes to finish + + + align:start position:0% +people who take five minutes to finish +it well they just did it in two minutes + + align:start position:0% +it well they just did it in two minutes + + + align:start position:0% +it well they just did it in two minutes +and like I can't keep up with them so + + align:start position:0% +and like I can't keep up with them so + + + align:start position:0% +and like I can't keep up with them so +this is really nice and it makes it + + align:start position:0% +this is really nice and it makes it + + + align:start position:0% +this is really nice and it makes it +competitive otherwise it would end up + + align:start position:0% +competitive otherwise it would end up + + + align:start position:0% +competitive otherwise it would end up +being like whoever's fastest just + + align:start position:0% +being like whoever's fastest just + + + align:start position:0% +being like whoever's fastest just +consistently can perform the work any + + align:start position:0% +consistently can perform the work any + + + align:start position:0% +consistently can perform the work any +questions about memory lists it's kind + + align:start position:0% +questions about memory lists it's kind + + + align:start position:0% +questions about memory lists it's kind +of this is this I mean you guys actually + + align:start position:0% +of this is this I mean you guys actually + + + align:start position:0% +of this is this I mean you guys actually +know computers and stuff and math you + + align:start position:0% +know computers and stuff and math you + + + align:start position:0% +know computers and stuff and math you +know MIT but this is like a fairly + + align:start position:0% +know MIT but this is like a fairly + + + align:start position:0% +know MIT but this is like a fairly +common misconception in Bitcoin and + + align:start position:0% +common misconception in Bitcoin and + + + align:start position:0% +common misconception in Bitcoin and +other systems like this where people get + + align:start position:0% +other systems like this where people get + + + align:start position:0% +other systems like this where people get +mad like it's been an hour and no blocks + + align:start position:0% +mad like it's been an hour and no blocks + + + align:start position:0% +mad like it's been an hour and no blocks +come out it's like well yeah you know + + align:start position:0% +come out it's like well yeah you know + + + align:start position:0% +come out it's like well yeah you know +awesome process on average every day and + + align:start position:0% +awesome process on average every day and + + + align:start position:0% +awesome process on average every day and +a half there will be a one-hour gap and + + align:start position:0% +a half there will be a one-hour gap and + + + align:start position:0% +a half there will be a one-hour gap and +then people have been like well the last + + align:start position:0% +then people have been like well the last + + + align:start position:0% +then people have been like well the last +three blocks came out and like you know + + align:start position:0% +three blocks came out and like you know + + + align:start position:0% +three blocks came out and like you know +two minutes so there's gonna be awhile + + align:start position:0% +two minutes so there's gonna be awhile + + + align:start position:0% +two minutes so there's gonna be awhile +before the next block it's like no no + + align:start position:0% +before the next block it's like no no + + + align:start position:0% +before the next block it's like no no +there's there's no memory so so there's + + align:start position:0% +there's there's no memory so so there's + + + align:start position:0% +there's there's no memory so so there's +a lot of you know it's misconceptions + + align:start position:0% +a lot of you know it's misconceptions + + + align:start position:0% +a lot of you know it's misconceptions +when it's a purely random system that + + align:start position:0% +when it's a purely random system that + + + align:start position:0% +when it's a purely random system that +people are not used to this kind of + + align:start position:0% +people are not used to this kind of + + + align:start position:0% +people are not used to this kind of +thing so but it but it's kind of + + align:start position:0% +thing so but it but it's kind of + + + align:start position:0% +thing so but it but it's kind of +intuitive right like even I sort of + + align:start position:0% +intuitive right like even I sort of + + + align:start position:0% +intuitive right like even I sort of +think like oh you know and like no no + + align:start position:0% +think like oh you know and like no no + + + align:start position:0% +think like oh you know and like no no +memoryless got to remember that got to + + align:start position:0% +memoryless got to remember that got to + + + align:start position:0% +memoryless got to remember that got to +remember in this memory loss + + align:start position:0% +remember in this memory loss + + + align:start position:0% +remember in this memory loss +okay so scalability is actually kind of + + align:start position:0% +okay so scalability is actually kind of + + + align:start position:0% +okay so scalability is actually kind of +amazing so this is a block hash from + + align:start position:0% +amazing so this is a block hash from + + + align:start position:0% +amazing so this is a block hash from +this morning or late last night that + + align:start position:0% +this morning or late last night that + + + align:start position:0% +this morning or late last night that +actually happened in Bitcoin and there's + + align:start position:0% +actually happened in Bitcoin and there's + + + align:start position:0% +actually happened in Bitcoin and there's +a lot of zeroes there's 18 of them and 9 + + align:start position:0% +a lot of zeroes there's 18 of them and 9 + + + align:start position:0% +a lot of zeroes there's 18 of them and 9 +bytes and actually more because it + + align:start position:0% +bytes and actually more because it + + + align:start position:0% +bytes and actually more because it +starts with a 3 instead of a math for + + align:start position:0% +starts with a 3 instead of a math for + + + align:start position:0% +starts with a 3 instead of a math for +something so what's really cool about + + align:start position:0% +something so what's really cool about + + + align:start position:0% +something so what's really cool about +this is it takes just as long to verify + + align:start position:0% +this is it takes just as long to verify + + + align:start position:0% +this is it takes just as long to verify +this work as it did with the one with my + + align:start position:0% +this work as it did with the one with my + + + align:start position:0% +this work as it did with the one with my +name right which only had 4 bytes of + + align:start position:0% +name right which only had 4 bytes of + + + align:start position:0% +name right which only had 4 bytes of +work you know and the one with my name + + align:start position:0% +work you know and the one with my name + + + align:start position:0% +work you know and the one with my name +it took my computer I don't know 20 + + align:start position:0% +it took my computer I don't know 20 + + + align:start position:0% +it took my computer I don't know 20 +minutes or whatever to do this took + + align:start position:0% +minutes or whatever to do this took + + + align:start position:0% +minutes or whatever to do this took +computer you know this one took + + align:start position:0% +computer you know this one took + + + align:start position:0% +computer you know this one took +ten minutes right but it took the + + align:start position:0% +ten minutes right but it took the + + + align:start position:0% +ten minutes right but it took the +network ten minutes because everyone's + + align:start position:0% +network ten minutes because everyone's + + + align:start position:0% +network ten minutes because everyone's +participating at the same time so yeah + + align:start position:0% +participating at the same time so yeah + + + align:start position:0% +participating at the same time so yeah +it's and it's a trillion times we're + + align:start position:0% +it's and it's a trillion times we're + + + align:start position:0% +it's and it's a trillion times we're +working takes no more time to verify + + align:start position:0% +working takes no more time to verify + + + align:start position:0% +working takes no more time to verify +that's really cool and it is kind of + + align:start position:0% +that's really cool and it is kind of + + + align:start position:0% +that's really cool and it is kind of +like amazing because this is almost a + + align:start position:0% +like amazing because this is almost a + + + align:start position:0% +like amazing because this is almost a +mole of attempts like Avogadro's number + + align:start position:0% +mole of attempts like Avogadro's number + + + align:start position:0% +mole of attempts like Avogadro's number +so you're getting into numbers that like + + align:start position:0% +so you're getting into numbers that like + + + align:start position:0% +so you're getting into numbers that like +you never deal with these scales of + + align:start position:0% +you never deal with these scales of + + + align:start position:0% +you never deal with these scales of +numbers in I mean you do it in my + + align:start position:0% +numbers in I mean you do it in my + + + align:start position:0% +numbers in I mean you do it in my +chemistry but so so that's that's a nice + + align:start position:0% +chemistry but so so that's that's a nice + + + align:start position:0% +chemistry but so so that's that's a nice +property also it's not interactive in + + align:start position:0% +property also it's not interactive in + + + align:start position:0% +property also it's not interactive in +that that helps as well so you never + + align:start position:0% +that that helps as well so you never + + + align:start position:0% +that that helps as well so you never +have to report your failed attempts + + align:start position:0% +have to report your failed attempts + + + align:start position:0% +have to report your failed attempts +right so you can have a thousand + + align:start position:0% +right so you can have a thousand + + + align:start position:0% +right so you can have a thousand +different computers all trying one nones + + align:start position:0% +different computers all trying one nones + + + align:start position:0% +different computers all trying one nones +with you know different messages or one + + align:start position:0% +with you know different messages or one + + + align:start position:0% +with you know different messages or one +chip trying a thousand times and you + + align:start position:0% +chip trying a thousand times and you + + + align:start position:0% +chip trying a thousand times and you +don't need any communication between + + align:start position:0% +don't need any communication between + + + align:start position:0% +don't need any communication between +them so the only communication between + + align:start position:0% +them so the only communication between + + + align:start position:0% +them so the only communication between +the network is when a block has actually + + align:start position:0% +the network is when a block has actually + + + align:start position:0% +the network is when a block has actually +found so there's no real setup + + align:start position:0% +found so there's no real setup + + + align:start position:0% +found so there's no real setup +needed so it's a very simple message + + align:start position:0% +needed so it's a very simple message + + + align:start position:0% +needed so it's a very simple message +protocol where you just say hey here's a + + align:start position:0% +protocol where you just say hey here's a + + + align:start position:0% +protocol where you just say hey here's a +block everyone just sort of broadcasts + + align:start position:0% +block everyone just sort of broadcasts + + + align:start position:0% +block everyone just sort of broadcasts +so that's really cool too + + align:start position:0% +so that's really cool too + + + align:start position:0% +so that's really cool too +so these are all really useful + + align:start position:0% +so these are all really useful + + + align:start position:0% +so these are all really useful +properties for our network in our + + align:start position:0% +properties for our network in our + + + align:start position:0% +properties for our network in our +consensus system also it uses real world + + align:start position:0% +consensus system also it uses real world + + + align:start position:0% +consensus system also it uses real world +resources so when you want to go back + + align:start position:0% +resources so when you want to go back + + + align:start position:0% +resources so when you want to go back +and rewrite history even if a majority + + align:start position:0% +and rewrite history even if a majority + + + align:start position:0% +and rewrite history even if a majority +of participants want to do that they're + + align:start position:0% +of participants want to do that they're + + + align:start position:0% +of participants want to do that they're +still going to be a cost so that's + + align:start position:0% +still going to be a cost so that's + + + align:start position:0% +still going to be a cost so that's +that's pretty unique compared to many + + align:start position:0% +that's pretty unique compared to many + + + align:start position:0% +that's pretty unique compared to many +different sets consensus systems in many + + align:start position:0% +different sets consensus systems in many + + + align:start position:0% +different sets consensus systems in many +systems say okay well we have unanimous + + align:start position:0% +systems say okay well we have unanimous + + + align:start position:0% +systems say okay well we have unanimous +agreement all participants in the system + + align:start position:0% +agreement all participants in the system + + + align:start position:0% +agreement all participants in the system +are going to rewrite history we're gonna + + align:start position:0% +are going to rewrite history we're gonna + + + align:start position:0% +are going to rewrite history we're gonna +go back for 10 that never happened and + + align:start position:0% +go back for 10 that never happened and + + + align:start position:0% +go back for 10 that never happened and +you know branch off and create a new + + align:start position:0% +you know branch off and create a new + + + align:start position:0% +you know branch off and create a new +history even if everyone in Bitcoin + + align:start position:0% +history even if everyone in Bitcoin + + + align:start position:0% +history even if everyone in Bitcoin +every participant tries to do that + + align:start position:0% +every participant tries to do that + + + align:start position:0% +every participant tries to do that +they're still gonna have to spend that + + align:start position:0% +they're still gonna have to spend that + + + align:start position:0% +they're still gonna have to spend that +that energy and that work and so that + + align:start position:0% +that energy and that work and so that + + + align:start position:0% +that energy and that work and so that +really discourages reorganize history + + align:start position:0% +really discourages reorganize history + + + align:start position:0% +really discourages reorganize history +even when everyone wants to so that's + + align:start position:0% +even when everyone wants to so that's + + + align:start position:0% +even when everyone wants to so that's +kind of cool and that like you're you're + + align:start position:0% +kind of cool and that like you're you're + + + align:start position:0% +kind of cool and that like you're you're +tied down not just by the other + + align:start position:0% +tied down not just by the other + + + align:start position:0% +tied down not just by the other +participants in the system but by sort + + align:start position:0% +participants in the system but by sort + + + align:start position:0% +participants in the system but by sort +of physics itself and like the way the + + align:start position:0% +of physics itself and like the way the + + + align:start position:0% +of physics itself and like the way the +world works like we are gonna have to do + + align:start position:0% +world works like we are gonna have to do + + + align:start position:0% +world works like we are gonna have to do +work to rewrite this so that's and and + + align:start position:0% +work to rewrite this so that's and and + + + align:start position:0% +work to rewrite this so that's and and +also it shows that people are sort of + + align:start position:0% +also it shows that people are sort of + + + align:start position:0% +also it shows that people are sort of +invested and they've done work so that's + + align:start position:0% +invested and they've done work so that's + + + align:start position:0% +invested and they've done work so that's +kind of cool - okay so any any + + align:start position:0% +kind of cool - okay so any any + + + align:start position:0% +kind of cool - okay so any any +about all these pros or if you want to + + align:start position:0% +about all these pros or if you want to + + + align:start position:0% +about all these pros or if you want to +say some of these pros are actually cons + + align:start position:0% +say some of these pros are actually cons + + + align:start position:0% +say some of these pros are actually cons +before I get to the cons okay go to cons + + align:start position:0% +before I get to the cons okay go to cons + + + align:start position:0% +before I get to the cons okay go to cons +and this is all oh it's always more fun + + align:start position:0% +and this is all oh it's always more fun + + + align:start position:0% +and this is all oh it's always more fun +to complain about stuff so we can go + + align:start position:0% +to complain about stuff so we can go + + + align:start position:0% +to complain about stuff so we can go +into cons and and I'm sure people can + + align:start position:0% +into cons and and I'm sure people can + + + align:start position:0% +into cons and and I'm sure people can +jump in with other things like yeah this + + align:start position:0% +jump in with other things like yeah this + + + align:start position:0% +jump in with other things like yeah this +is bad so one problem is that it's + + align:start position:0% +is bad so one problem is that it's + + + align:start position:0% +is bad so one problem is that it's +inefficient almost every attempt fails + + align:start position:0% +inefficient almost every attempt fails + + + align:start position:0% +inefficient almost every attempt fails +so that's no fun right so the proof of + + align:start position:0% +so that's no fun right so the proof of + + + align:start position:0% +so that's no fun right so the proof of +work from a few hours ago + + align:start position:0% +work from a few hours ago + + + align:start position:0% +work from a few hours ago +this is ten to the twenty two attempts + + align:start position:0% +this is ten to the twenty two attempts + + + align:start position:0% +this is ten to the twenty two attempts +and all - you know there's ten to twenty + + align:start position:0% +and all - you know there's ten to twenty + + + align:start position:0% +and all - you know there's ten to twenty +two failed attempts that were required + + align:start position:0% +two failed attempts that were required + + + align:start position:0% +two failed attempts that were required +you know that will happened in order to + + align:start position:0% +you know that will happened in order to + + + align:start position:0% +you know that will happened in order to +get that one so that's like extremely + + align:start position:0% +get that one so that's like extremely + + + align:start position:0% +get that one so that's like extremely +inefficient you know your I don't know + + align:start position:0% +inefficient you know your I don't know + + + align:start position:0% +inefficient you know your I don't know +how to express that as a percentage but + + align:start position:0% +how to express that as a percentage but + + + align:start position:0% +how to express that as a percentage but +the actual like things moving the system + + align:start position:0% +the actual like things moving the system + + + align:start position:0% +the actual like things moving the system +are some incredibly small percentage of + + align:start position:0% +are some incredibly small percentage of + + + align:start position:0% +are some incredibly small percentage of +the actual things happening it's also + + align:start position:0% +the actual things happening it's also + + + align:start position:0% +the actual things happening it's also +problem because you're not gonna be able + + align:start position:0% +problem because you're not gonna be able + + + align:start position:0% +problem because you're not gonna be able +to get a valid block right if you have + + align:start position:0% +to get a valid block right if you have + + + align:start position:0% +to get a valid block right if you have +to do two to the 72 attempts like you're + + align:start position:0% +to do two to the 72 attempts like you're + + + align:start position:0% +to do two to the 72 attempts like you're +just not gonna do it like ever you can + + align:start position:0% +just not gonna do it like ever you can + + + align:start position:0% +just not gonna do it like ever you can +run your laptop for your entire life and + + align:start position:0% +run your laptop for your entire life and + + + align:start position:0% +run your laptop for your entire life and +you will not be able to do two of the 72 + + align:start position:0% +you will not be able to do two of the 72 + + + align:start position:0% +you will not be able to do two of the 72 +work which is kind of depressing even if + + align:start position:0% +work which is kind of depressing even if + + + align:start position:0% +work which is kind of depressing even if +you buy specialized hardware yeah you're + + align:start position:0% +you buy specialized hardware yeah you're + + + align:start position:0% +you buy specialized hardware yeah you're +not gonna you're not gonna find a block + + align:start position:0% +not gonna you're not gonna find a block + + + align:start position:0% +not gonna you're not gonna find a block +it sort of consolidates until you need a + + align:start position:0% +it sort of consolidates until you need a + + + align:start position:0% +it sort of consolidates until you need a +you need a factory you need a warehouse + + align:start position:0% +you need a factory you need a warehouse + + + align:start position:0% +you need a factory you need a warehouse +full of equipment basically in order to + + align:start position:0% +full of equipment basically in order to + + + align:start position:0% +full of equipment basically in order to +do this now so that's kind of annoying + + align:start position:0% +do this now so that's kind of annoying + + + align:start position:0% +do this now so that's kind of annoying +right it's not as fun like the small + + align:start position:0% +right it's not as fun like the small + + + align:start position:0% +right it's not as fun like the small +players have been pushed out of the game + + align:start position:0% +players have been pushed out of the game + + + align:start position:0% +players have been pushed out of the game +because you need to do so much work in + + align:start position:0% +because you need to do so much work in + + + align:start position:0% +because you need to do so much work in +order to have you know you can't get + + align:start position:0% +order to have you know you can't get + + + align:start position:0% +order to have you know you can't get +sort of hey I came close can I get like + + align:start position:0% +sort of hey I came close can I get like + + + align:start position:0% +sort of hey I came close can I get like +partial credit can I you know I did I + + align:start position:0% +partial credit can I you know I did I + + + align:start position:0% +partial credit can I you know I did I +did to to the fifty work and I get + + align:start position:0% +did to to the fifty work and I get + + + align:start position:0% +did to to the fifty work and I get +anything for that the system doesn't + + align:start position:0% +anything for that the system doesn't + + + align:start position:0% +anything for that the system doesn't +recognize partial work okay + + align:start position:0% +recognize partial work okay + + + align:start position:0% +recognize partial work okay +other cons it uses wats and chips uses + + align:start position:0% +other cons it uses wats and chips uses + + + align:start position:0% +other cons it uses wats and chips uses +lots of electricity you could use that + + align:start position:0% +lots of electricity you could use that + + + align:start position:0% +lots of electricity you could use that +electricity to charge your car or do + + align:start position:0% +electricity to charge your car or do + + + align:start position:0% +electricity to charge your car or do +something cool it uses fabs to make + + align:start position:0% +something cool it uses fabs to make + + + align:start position:0% +something cool it uses fabs to make +microchips which could make more CPUs or + + align:start position:0% +microchips which could make more CPUs or + + + align:start position:0% +microchips which could make more CPUs or +make cool phones or something + + align:start position:0% +make cool phones or something + + + align:start position:0% +make cool phones or something +once it gets big enough it actually + + align:start position:0% +once it gets big enough it actually + + + align:start position:0% +once it gets big enough it actually +starts affecting markets so I don't know + + align:start position:0% +starts affecting markets so I don't know + + + align:start position:0% +starts affecting markets so I don't know +if I just know in micro Center + + align:start position:0% +if I just know in micro Center + + + align:start position:0% +if I just know in micro Center +they're like many times that because I + + align:start position:0% +they're like many times that because I + + + align:start position:0% +they're like many times that because I +live near there and like you go around + + align:start position:0% +live near there and like you go around + + + align:start position:0% +live near there and like you go around +and like there's the GPU section and + + align:start position:0% +and like there's the GPU section and + + + align:start position:0% +and like there's the GPU section and +like everyone complains about Bitcoin in + + align:start position:0% +like everyone complains about Bitcoin in + + + align:start position:0% +like everyone complains about Bitcoin in +micro Center near the GPUs it's not + + align:start position:0% +micro Center near the GPUs it's not + + + align:start position:0% +micro Center near the GPUs it's not +Bitcoin aside it's usually like + + align:start position:0% +Bitcoin aside it's usually like + + + align:start position:0% +Bitcoin aside it's usually like +aetherium another other coins that that + + align:start position:0% +aetherium another other coins that that + + + align:start position:0% +aetherium another other coins that that +use GPUs for mining what that has had a + + align:start position:0% +use GPUs for mining what that has had a + + + align:start position:0% +use GPUs for mining what that has had a +really big effect on the market for GPUs + + align:start position:0% +really big effect on the market for GPUs + + + align:start position:0% +really big effect on the market for GPUs +a lot of people because you can make + + align:start position:0% +a lot of people because you can make + + + align:start position:0% +a lot of people because you can make +money with them so people are like yeah + + align:start position:0% +money with them so people are like yeah + + + align:start position:0% +money with them so people are like yeah +buy one of these things for 500 bucks + + align:start position:0% +buy one of these things for 500 bucks + + + align:start position:0% +buy one of these things for 500 bucks +because I'll make back my 500 bucks in a + + align:start position:0% +because I'll make back my 500 bucks in a + + + align:start position:0% +because I'll make back my 500 bucks in a +year and then I'll you know still have + + align:start position:0% +year and then I'll you know still have + + + align:start position:0% +year and then I'll you know still have +the chitin still have the GPU that maybe + + align:start position:0% +the chitin still have the GPU that maybe + + + align:start position:0% +the chitin still have the GPU that maybe +I can sell it used and get a couple + + align:start position:0% +I can sell it used and get a couple + + + align:start position:0% +I can sell it used and get a couple +hundred bucks back and then I profited + + align:start position:0% +hundred bucks back and then I profited + + + align:start position:0% +hundred bucks back and then I profited +so so these things affect you know it's + + align:start position:0% +so so these things affect you know it's + + + align:start position:0% +so so these things affect you know it's +big enough that it affects markets + + align:start position:0% +big enough that it affects markets + + + align:start position:0% +big enough that it affects markets +initially it didn't because it was just + + align:start position:0% +initially it didn't because it was just + + + align:start position:0% +initially it didn't because it was just +a couple nerds running Bitcoin and so + + align:start position:0% +a couple nerds running Bitcoin and so + + + align:start position:0% +a couple nerds running Bitcoin and so +like who cares you know a couple people + + align:start position:0% +like who cares you know a couple people + + + align:start position:0% +like who cares you know a couple people +buying GPUs but now it's big enough you + + align:start position:0% +buying GPUs but now it's big enough you + + + align:start position:0% +buying GPUs but now it's big enough you +know these are like billion-dollar + + align:start position:0% +know these are like billion-dollar + + + align:start position:0% +know these are like billion-dollar +markets and it's getting to be the same + + align:start position:0% +markets and it's getting to be the same + + + align:start position:0% +markets and it's getting to be the same +sort of scale as the you know gamer + + align:start position:0% +sort of scale as the you know gamer + + + align:start position:0% +sort of scale as the you know gamer +market your gamer or like whatever CUDA + + align:start position:0% +market your gamer or like whatever CUDA + + + align:start position:0% +market your gamer or like whatever CUDA +or whatever people use GPUs for but it + + align:start position:0% +or whatever people use GPUs for but it + + + align:start position:0% +or whatever people use GPUs for but it +you know mining is significant and so it + + align:start position:0% +you know mining is significant and so it + + + align:start position:0% +you know mining is significant and so it +affects the market who knows someday you + + align:start position:0% +affects the market who knows someday you + + + align:start position:0% +affects the market who knows someday you +could start to affect electricity prices + + align:start position:0% +could start to affect electricity prices + + + align:start position:0% +could start to affect electricity prices +if you get big enough where a + + align:start position:0% +if you get big enough where a + + + align:start position:0% +if you get big enough where a +significant portion of all the + + align:start position:0% +significant portion of all the + + + align:start position:0% +significant portion of all the +electrical usage in the world or the + + align:start position:0% +electrical usage in the world or the + + + align:start position:0% +electrical usage in the world or the +country is going into doing this sha-256 + + align:start position:0% +country is going into doing this sha-256 + + + align:start position:0% +country is going into doing this sha-256 +and so that makes electricity prices go + + align:start position:0% +and so that makes electricity prices go + + + align:start position:0% +and so that makes electricity prices go +up and then everyone starts complaining + + align:start position:0% +up and then everyone starts complaining + + + align:start position:0% +up and then everyone starts complaining +like me and electricity is twice as much + + align:start position:0% +like me and electricity is twice as much + + + align:start position:0% +like me and electricity is twice as much +as it used to be because all these + + align:start position:0% +as it used to be because all these + + + align:start position:0% +as it used to be because all these +people mining bitcoins and it's possible + + align:start position:0% +people mining bitcoins and it's possible + + + align:start position:0% +people mining bitcoins and it's possible +if it gets big enough instead of just + + align:start position:0% +if it gets big enough instead of just + + + align:start position:0% +if it gets big enough instead of just +people complaining about GPS so that's + + align:start position:0% +people complaining about GPS so that's + + + align:start position:0% +people complaining about GPS so that's +sort of a con right that's it starts + + align:start position:0% +sort of a con right that's it starts + + + align:start position:0% +sort of a con right that's it starts +affecting the real world in big ways the + + align:start position:0% +affecting the real world in big ways the + + + align:start position:0% +affecting the real world in big ways the +corollary of that being a memoryless + + align:start position:0% +corollary of that being a memoryless + + + align:start position:0% +corollary of that being a memoryless +process is that it's irregular + + align:start position:0% +process is that it's irregular + + + align:start position:0% +process is that it's irregular +it's a Poisson process which means + + align:start position:0% +it's a Poisson process which means + + + align:start position:0% +it's a Poisson process which means +sometimes you get in a few seconds and + + align:start position:0% +sometimes you get in a few seconds and + + + align:start position:0% +sometimes you get in a few seconds and +sometimes it takes an hour and people + + align:start position:0% +sometimes it takes an hour and people + + + align:start position:0% +sometimes it takes an hour and people +don't like that right you you I can see + + align:start position:0% +don't like that right you you I can see + + + align:start position:0% +don't like that right you you I can see +how you'd rather have something come out + + align:start position:0% +how you'd rather have something come out + + + align:start position:0% +how you'd rather have something come out +regularly a lot of people think yeah + + align:start position:0% +regularly a lot of people think yeah + + + align:start position:0% +regularly a lot of people think yeah +blocks come out every 10 minutes well on + + align:start position:0% +blocks come out every 10 minutes well on + + + align:start position:0% +blocks come out every 10 minutes well on +average every 10 minutes but it can be + + align:start position:0% +average every 10 minutes but it can be + + + align:start position:0% +average every 10 minutes but it can be +hours it can be seconds and so that + + align:start position:0% +hours it can be seconds and so that + + + align:start position:0% +hours it can be seconds and so that +that's hard in some cases you can't + + align:start position:0% +that's hard in some cases you can't + + + align:start position:0% +that's hard in some cases you can't +really use it like hey I want a you know + + align:start position:0% +really use it like hey I want a you know + + + align:start position:0% +really use it like hey I want a you know +regular clock or I want message + + align:start position:0% +regular clock or I want message + + + align:start position:0% +regular clock or I want message +that come out in some kind of I want + + align:start position:0% +that come out in some kind of I want + + + align:start position:0% +that come out in some kind of I want +some assurance right if I make a mess + + align:start position:0% +some assurance right if I make a mess + + + align:start position:0% +some assurance right if I make a mess +you know I make a transaction I want it + + align:start position:0% +you know I make a transaction I want it + + + align:start position:0% +you know I make a transaction I want it +to be included in this system I want + + align:start position:0% +to be included in this system I want + + + align:start position:0% +to be included in this system I want +some assurance it will be included in + + align:start position:0% +some assurance it will be included in + + + align:start position:0% +some assurance it will be included in +the next 20 minutes you don't get that + + align:start position:0% +the next 20 minutes you don't get that + + + align:start position:0% +the next 20 minutes you don't get that +assurance right it can be 30 minutes + + align:start position:0% +assurance right it can be 30 minutes + + + align:start position:0% +assurance right it can be 30 minutes +before anything gets included and in + + align:start position:0% +before anything gets included and in + + + align:start position:0% +before anything gets included and in +fact we'll get into later but there's + + align:start position:0% +fact we'll get into later but there's + + + align:start position:0% +fact we'll get into later but there's +even worse assurance properties in that + + align:start position:0% +even worse assurance properties in that + + + align:start position:0% +even worse assurance properties in that +like just because five blocks came out + + align:start position:0% +like just because five blocks came out + + + align:start position:0% +like just because five blocks came out +doesn't mean your transaction got into + + align:start position:0% +doesn't mean your transaction got into + + + align:start position:0% +doesn't mean your transaction got into +any of them they might have been ignored + + align:start position:0% +any of them they might have been ignored + + + align:start position:0% +any of them they might have been ignored +it might you know there's all sorts of + + align:start position:0% +it might you know there's all sorts of + + + align:start position:0% +it might you know there's all sorts of +reasons so you can deal with this but it + + align:start position:0% +reasons so you can deal with this but it + + + align:start position:0% +reasons so you can deal with this but it +is kind of annoying and it precludes + + align:start position:0% +is kind of annoying and it precludes + + + align:start position:0% +is kind of annoying and it precludes +some use cases and other consensus + + align:start position:0% +some use cases and other consensus + + + align:start position:0% +some use cases and other consensus +systems do not have this problem other + + align:start position:0% +systems do not have this problem other + + + align:start position:0% +systems do not have this problem other +consensus systems can have much more + + align:start position:0% +consensus systems can have much more + + + align:start position:0% +consensus systems can have much more +regular clocks so this is kind of + + align:start position:0% +regular clocks so this is kind of + + + align:start position:0% +regular clocks so this is kind of +annoying as well any questions about the + + align:start position:0% +annoying as well any questions about the + + + align:start position:0% +annoying as well any questions about the +irregularity aspects okay big con 51% + + align:start position:0% +irregularity aspects okay big con 51% + + + align:start position:0% +irregularity aspects okay big con 51% +attacks okay part of the problem with + + align:start position:0% +attacks okay part of the problem with + + + align:start position:0% +attacks okay part of the problem with +anonymity is you have no idea who's + + align:start position:0% +anonymity is you have no idea who's + + + align:start position:0% +anonymity is you have no idea who's +doing this stuff right even if they say + + align:start position:0% +doing this stuff right even if they say + + + align:start position:0% +doing this stuff right even if they say +who you know even if they claim so the + + align:start position:0% +who you know even if they claim so the + + + align:start position:0% +who you know even if they claim so the +one interesting part of anonymity + + align:start position:0% +one interesting part of anonymity + + + align:start position:0% +one interesting part of anonymity +despite this being designed as a really + + align:start position:0% +despite this being designed as a really + + + align:start position:0% +despite this being designed as a really +cool hackery cyberpunk anonymous system + + align:start position:0% +cool hackery cyberpunk anonymous system + + + align:start position:0% +cool hackery cyberpunk anonymous system +one of the first things people did was + + align:start position:0% +one of the first things people did was + + + align:start position:0% +one of the first things people did was +put their name in it right so if you + + align:start position:0% +put their name in it right so if you + + + align:start position:0% +put their name in it right so if you +mind a block you've got space where you + + align:start position:0% +mind a block you've got space where you + + + align:start position:0% +mind a block you've got space where you +you know you can put 32 bytes or so that + + align:start position:0% +you know you can put 32 bytes or so that + + + align:start position:0% +you know you can put 32 bytes or so that +are undefined and people would just + + align:start position:0% +are undefined and people would just + + + align:start position:0% +are undefined and people would just +start putting the names of their mining + + align:start position:0% +start putting the names of their mining + + + align:start position:0% +start putting the names of their mining +pools or their names of their cat or + + align:start position:0% +pools or their names of their cat or + + + align:start position:0% +pools or their names of their cat or +whatever they just put their names in it + + align:start position:0% +whatever they just put their names in it + + + align:start position:0% +whatever they just put their names in it +so it's kind of like they're showing who + + align:start position:0% +so it's kind of like they're showing who + + + align:start position:0% +so it's kind of like they're showing who +they are and you can look at like + + align:start position:0% +they are and you can look at like + + + align:start position:0% +they are and you can look at like +distribution of like who are the + + align:start position:0% +distribution of like who are the + + + align:start position:0% +distribution of like who are the +different miners and stuff like that's + + align:start position:0% +different miners and stuff like that's + + + align:start position:0% +different miners and stuff like that's +like even though it's supposed to be + + align:start position:0% +like even though it's supposed to be + + + align:start position:0% +like even though it's supposed to be +anonymous so they claim but they can + + align:start position:0% +anonymous so they claim but they can + + + align:start position:0% +anonymous so they claim but they can +claim a name and they can claim this + + align:start position:0% +claim a name and they can claim this + + + align:start position:0% +claim a name and they can claim this +block was mined by f2 pool or this MOC + + align:start position:0% +block was mined by f2 pool or this MOC + + + align:start position:0% +block was mined by f2 pool or this MOC +was mined by BTC com but you're not a + + align:start position:0% +was mined by BTC com but you're not a + + + align:start position:0% +was mined by BTC com but you're not a +hundred percent sure right it's all I + + align:start position:0% +hundred percent sure right it's all I + + + align:start position:0% +hundred percent sure right it's all I +could also mine a block and claim that + + align:start position:0% +could also mine a block and claim that + + + align:start position:0% +could also mine a block and claim that +it's from f2 pool and it's hard to + + align:start position:0% +it's from f2 pool and it's hard to + + + align:start position:0% +it's from f2 pool and it's hard to +disprove so you don't really know who's + + align:start position:0% +disprove so you don't really know who's + + + align:start position:0% +disprove so you don't really know who's +mining and an attacker with 51% of the + + align:start position:0% +mining and an attacker with 51% of the + + + align:start position:0% +mining and an attacker with 51% of the +total network power can write a chain + + align:start position:0% +total network power can write a chain + + + align:start position:0% +total network power can write a chain +faster than everyone else combined so + + align:start position:0% +faster than everyone else combined so + + + align:start position:0% +faster than everyone else combined so +that means they can rewrite history + + align:start position:0% +that means they can rewrite history + + + align:start position:0% +that means they can rewrite history +right so like in the example before + + align:start position:0% +right so like in the example before + + + align:start position:0% +right so like in the example before +where hey + + align:start position:0% +where hey + + + align:start position:0% +where hey +made this three blocks longer than these + + align:start position:0% +made this three blocks longer than these + + + align:start position:0% +made this three blocks longer than these +two blocks + + align:start position:0% +two blocks + + + align:start position:0% +two blocks +I had to either get lucky or you know + + align:start position:0% +I had to either get lucky or you know + + + align:start position:0% +I had to either get lucky or you know +everyone else stopped mining for a + + align:start position:0% +everyone else stopped mining for a + + + align:start position:0% +everyone else stopped mining for a +second + + align:start position:0% +second + + + align:start position:0% +second +but that's not really possible long term + + align:start position:0% +but that's not really possible long term + + + align:start position:0% +but that's not really possible long term +if I have a minority of the hash power + + align:start position:0% +if I have a minority of the hash power + + + align:start position:0% +if I have a minority of the hash power +right because everyone's just gonna + + align:start position:0% +right because everyone's just gonna + + + align:start position:0% +right because everyone's just gonna +start you know if the money if the + + align:start position:0% +start you know if the money if the + + + align:start position:0% +start you know if the money if the +majority is sort of honest and playing + + align:start position:0% +majority is sort of honest and playing + + + align:start position:0% +majority is sort of honest and playing +by the right rules they're just gonna + + align:start position:0% +by the right rules they're just gonna + + + align:start position:0% +by the right rules they're just gonna +see what the most you know the longest + + align:start position:0% +see what the most you know the longest + + + align:start position:0% +see what the most you know the longest +work the most work the longest chain is + + align:start position:0% +work the most work the longest chain is + + + align:start position:0% +work the most work the longest chain is +and start throwing blocks on top of that + + align:start position:0% +and start throwing blocks on top of that + + + align:start position:0% +and start throwing blocks on top of that +and if I go back and try to make a + + align:start position:0% +and if I go back and try to make a + + + align:start position:0% +and if I go back and try to make a +branch the main branch will grow faster + + align:start position:0% +branch the main branch will grow faster + + + align:start position:0% +branch the main branch will grow faster +than my sub branch and so I'll never + + align:start position:0% +than my sub branch and so I'll never + + + align:start position:0% +than my sub branch and so I'll never +overtake the main branch and so I'll + + align:start position:0% +overtake the main branch and so I'll + + + align:start position:0% +overtake the main branch and so I'll +never be able to reorg + + align:start position:0% +never be able to reorg + + + align:start position:0% +never be able to reorg +however if I am faster than everyone + + align:start position:0% +however if I am faster than everyone + + + align:start position:0% +however if I am faster than everyone +else put together its assured that I + + align:start position:0% +else put together its assured that I + + + align:start position:0% +else put together its assured that I +will eventually you know catch up and + + align:start position:0% +will eventually you know catch up and + + + align:start position:0% +will eventually you know catch up and +overtake the rest of the network and + + align:start position:0% +overtake the rest of the network and + + + align:start position:0% +overtake the rest of the network and +then everyone will have to reorder on to + + align:start position:0% +then everyone will have to reorder on to + + + align:start position:0% +then everyone will have to reorder on to +mine so you know here's the main chain + + align:start position:0% +mine so you know here's the main chain + + + align:start position:0% +mine so you know here's the main chain +and then I branch off here and I'm + + align:start position:0% +and then I branch off here and I'm + + + align:start position:0% +and then I branch off here and I'm +faster so I you know overtake them and + + align:start position:0% +faster so I you know overtake them and + + + align:start position:0% +faster so I you know overtake them and +then that's sort of everyone's stuck + + align:start position:0% +then that's sort of everyone's stuck + + + align:start position:0% +then that's sort of everyone's stuck +right even if they want to keep mining I + + align:start position:0% +right even if they want to keep mining I + + + align:start position:0% +right even if they want to keep mining I +can just reorder them out every time + + align:start position:0% +can just reorder them out every time + + + align:start position:0% +can just reorder them out every time +because I'm bigger this is a this is + + align:start position:0% +because I'm bigger this is a this is + + + align:start position:0% +because I'm bigger this is a this is +called a 51% attack it's pretty bad an + + align:start position:0% +called a 51% attack it's pretty bad an + + + align:start position:0% +called a 51% attack it's pretty bad an +attacker can rewrite history can undo + + align:start position:0% +attacker can rewrite history can undo + + + align:start position:0% +attacker can rewrite history can undo +transactions they can't Forge + + align:start position:0% +transactions they can't Forge + + + align:start position:0% +transactions they can't Forge +transactions right so they can't + + align:start position:0% +transactions right so they can't + + + align:start position:0% +transactions right so they can't +necessarily reorg out a message and + + align:start position:0% +necessarily reorg out a message and + + + align:start position:0% +necessarily reorg out a message and +replace it with a message of their + + align:start position:0% +replace it with a message of their + + + align:start position:0% +replace it with a message of their +choosing all they can do is you know if + + align:start position:0% +choosing all they can do is you know if + + + align:start position:0% +choosing all they can do is you know if +they can but they can do that with their + + align:start position:0% +they can but they can do that with their + + + align:start position:0% +they can but they can do that with their +own messages so you sort of need to to + + align:start position:0% +own messages so you sort of need to to + + + align:start position:0% +own messages so you sort of need to to +have this as part of an attack where + + align:start position:0% +have this as part of an attack where + + + align:start position:0% +have this as part of an attack where +they reorg their own messages out by + + align:start position:0% +they reorg their own messages out by + + + align:start position:0% +they reorg their own messages out by +default when a reorg occurs so like I + + align:start position:0% +default when a reorg occurs so like I + + + align:start position:0% +default when a reorg occurs so like I +can go here so by default when a reorg + + align:start position:0% +can go here so by default when a reorg + + + align:start position:0% +can go here so by default when a reorg +occurs and like say these two blocks of + + align:start position:0% +occurs and like say these two blocks of + + + align:start position:0% +occurs and like say these two blocks of +messages have been invalidated software + + align:start position:0% +messages have been invalidated software + + + align:start position:0% +messages have been invalidated software +will attempt to include all the + + align:start position:0% +will attempt to include all the + + + align:start position:0% +will attempt to include all the +transactions in these blocks into the + + align:start position:0% +transactions in these blocks into the + + + align:start position:0% +transactions in these blocks into the +next blocks right it's not just because + + align:start position:0% +next blocks right it's not just because + + + align:start position:0% +next blocks right it's not just because +this got reordered out doesn't mean it + + align:start position:0% +this got reordered out doesn't mean it + + + align:start position:0% +this got reordered out doesn't mean it +was invalid it just means it didn't you + + align:start position:0% +was invalid it just means it didn't you + + + align:start position:0% +was invalid it just means it didn't you +know it didn't get into a block and so + + align:start position:0% +know it didn't get into a block and so + + + align:start position:0% +know it didn't get into a block and so +we can try to include the + + align:start position:0% +we can try to include the + + + align:start position:0% +we can try to include the +message later as long as nothing in here + + align:start position:0% +message later as long as nothing in here + + + align:start position:0% +message later as long as nothing in here +conflicts with it so just doing a 51% + + align:start position:0% +conflicts with it so just doing a 51% + + + align:start position:0% +conflicts with it so just doing a 51% +attack to reorg doesn't on its own + + align:start position:0% +attack to reorg doesn't on its own + + + align:start position:0% +attack to reorg doesn't on its own +doesn't actually do very much damage + + align:start position:0% +doesn't actually do very much damage + + + align:start position:0% +doesn't actually do very much damage +however you it's not too hard to cook to + + align:start position:0% +however you it's not too hard to cook to + + + align:start position:0% +however you it's not too hard to cook to +sort of combine that with other attacks + + align:start position:0% +sort of combine that with other attacks + + + align:start position:0% +sort of combine that with other attacks +where you know whoever's doing this + + align:start position:0% +where you know whoever's doing this + + + align:start position:0% +where you know whoever's doing this +mining says oh I'll pay someone here and + + align:start position:0% +mining says oh I'll pay someone here and + + + align:start position:0% +mining says oh I'll pay someone here and +then pay myself here and then you know + + align:start position:0% +then pay myself here and then you know + + + align:start position:0% +then pay myself here and then you know +undo the payment that they made to solve + + align:start position:0% +undo the payment that they made to solve + + + align:start position:0% +undo the payment that they made to solve +so that's a big big con 51 percent of + + align:start position:0% +so that's a big big con 51 percent of + + + align:start position:0% +so that's a big big con 51 percent of +tax not only is it like very disruptive + + align:start position:0% +tax not only is it like very disruptive + + + align:start position:0% +tax not only is it like very disruptive +to the system you it's very hard to + + align:start position:0% +to the system you it's very hard to + + + align:start position:0% +to the system you it's very hard to +predict when it'll happen since it's + + align:start position:0% +predict when it'll happen since it's + + + align:start position:0% +predict when it'll happen since it's +anonymous you know it could be the case + + align:start position:0% +anonymous you know it could be the case + + + align:start position:0% +anonymous you know it could be the case +that all the people mining Bitcoin now + + align:start position:0% +that all the people mining Bitcoin now + + + align:start position:0% +that all the people mining Bitcoin now +are friends and they're you know a 51% + + align:start position:0% +are friends and they're you know a 51% + + + align:start position:0% +are friends and they're you know a 51% +group and they could just you know get + + align:start position:0% +group and they could just you know get + + + align:start position:0% +group and they could just you know get +together and say hey let's read about + + align:start position:0% +together and say hey let's read about + + + align:start position:0% +together and say hey let's read about +these things that said there's there's a + + align:start position:0% +these things that said there's there's a + + + align:start position:0% +these things that said there's there's a +cost to do so so if you have you can see + + align:start position:0% +cost to do so so if you have you can see + + + align:start position:0% +cost to do so so if you have you can see +it must be much much easier there's very + + align:start position:0% +it must be much much easier there's very + + + align:start position:0% +it must be much much easier there's very +little work being done in the system + + align:start position:0% +little work being done in the system + + + align:start position:0% +little work being done in the system +it's probably pretty cheap to get a + + align:start position:0% +it's probably pretty cheap to get a + + + align:start position:0% +it's probably pretty cheap to get a +bunch of hardware and be 51% of that + + align:start position:0% +bunch of hardware and be 51% of that + + + align:start position:0% +bunch of hardware and be 51% of that +system true so like and in the case of + + align:start position:0% +system true so like and in the case of + + + align:start position:0% +system true so like and in the case of +Bitcoin if you have to do two to the 72 + + align:start position:0% +Bitcoin if you have to do two to the 72 + + + align:start position:0% +Bitcoin if you have to do two to the 72 +work well in every ten minutes that + + align:start position:0% +work well in every ten minutes that + + + align:start position:0% +work well in every ten minutes that +means if I want to be 51% I have to do + + align:start position:0% +means if I want to be 51% I have to do + + + align:start position:0% +means if I want to be 51% I have to do +two to the 71 work every 10 minutes + + align:start position:0% +two to the 71 work every 10 minutes + + + align:start position:0% +two to the 71 work every 10 minutes +which that's a lot of work and so you + + align:start position:0% +which that's a lot of work and so you + + + align:start position:0% +which that's a lot of work and so you +know you're gonna need enormous amounts + + align:start position:0% +know you're gonna need enormous amounts + + + align:start position:0% +know you're gonna need enormous amounts +of resources to become a 51% attacker + + align:start position:0% +of resources to become a 51% attacker + + + align:start position:0% +of resources to become a 51% attacker +there's sort of two ways this this + + align:start position:0% +there's sort of two ways this this + + + align:start position:0% +there's sort of two ways this this +attack can happen either some attacker + + align:start position:0% +attack can happen either some attacker + + + align:start position:0% +attack can happen either some attacker +comes out of nowhere and says okay I'm + + align:start position:0% +comes out of nowhere and says okay I'm + + + align:start position:0% +comes out of nowhere and says okay I'm +just gonna build up an enormous amount + + align:start position:0% +just gonna build up an enormous amount + + + align:start position:0% +just gonna build up an enormous amount +of attack power or the existing actors + + align:start position:0% +of attack power or the existing actors + + + align:start position:0% +of attack power or the existing actors +in the system sort of go bad which seems + + align:start position:0% +in the system sort of go bad which seems + + + align:start position:0% +in the system sort of go bad which seems +more likely where they're like okay + + align:start position:0% +more likely where they're like okay + + + align:start position:0% +more likely where they're like okay +we're we already you know I'm five + + align:start position:0% +we're we already you know I'm five + + + align:start position:0% +we're we already you know I'm five +percent he's ten percent and she is 20 + + align:start position:0% +percent he's ten percent and she is 20 + + + align:start position:0% +percent he's ten percent and she is 20 +percent and they all sort of get + + align:start position:0% +percent and they all sort of get + + + align:start position:0% +percent and they all sort of get +together and try to do an attack so both + + align:start position:0% +together and try to do an attack so both + + + align:start position:0% +together and try to do an attack so both +of those different ways are possible + + align:start position:0% + + + + align:start position:0% + +joining from my pool we said who does + + align:start position:0% +joining from my pool we said who does + + + align:start position:0% +joining from my pool we said who does +like small players yes like and fishes + + align:start position:0% + + + + align:start position:0% + +yes pools we didn't haven't mentioned + + align:start position:0% +yes pools we didn't haven't mentioned + + + align:start position:0% +yes pools we didn't haven't mentioned +pools but the idea part of the the con + + align:start position:0% +pools but the idea part of the the con + + + align:start position:0% +pools but the idea part of the the con +of you're never going to find a valid + + align:start position:0% +of you're never going to find a valid + + + align:start position:0% +of you're never going to find a valid +proof of work is the way they mitigate + + align:start position:0% +proof of work is the way they mitigate + + + align:start position:0% +proof of work is the way they mitigate +that is then people sort of get together + + align:start position:0% +that is then people sort of get together + + + align:start position:0% +that is then people sort of get together +in pools and they will prove partial + + align:start position:0% +in pools and they will prove partial + + + align:start position:0% +in pools and they will prove partial +work to each other and sort of there's + + align:start position:0% +work to each other and sort of there's + + + align:start position:0% +work to each other and sort of there's +one entity that's then sort of controls + + align:start position:0% +one entity that's then sort of controls + + + align:start position:0% +one entity that's then sort of controls +a lot of different minors and gives out + + align:start position:0% +a lot of different minors and gives out + + + align:start position:0% +a lot of different minors and gives out +the room give us out partial rewards so + + align:start position:0% +the room give us out partial rewards so + + + align:start position:0% +the room give us out partial rewards so +ok there's a thousand different people + + align:start position:0% +ok there's a thousand different people + + + align:start position:0% +ok there's a thousand different people +mining and one of them found the block + + align:start position:0% +mining and one of them found the block + + + align:start position:0% +mining and one of them found the block +but I'll I'll distribute that reward to + + align:start position:0% +but I'll I'll distribute that reward to + + + align:start position:0% +but I'll I'll distribute that reward to +all the thousand people for all the work + + align:start position:0% +all the thousand people for all the work + + + align:start position:0% +all the thousand people for all the work +they've done and so that that does + + align:start position:0% +they've done and so that that does + + + align:start position:0% +they've done and so that that does +concentrate power in that you know sort + + align:start position:0% +concentrate power in that you know sort + + + align:start position:0% +concentrate power in that you know sort +of mining pool whoever's running it so + + align:start position:0% +of mining pool whoever's running it so + + + align:start position:0% +of mining pool whoever's running it so +that's all that can also be a big + + align:start position:0% +that's all that can also be a big + + + align:start position:0% +that's all that can also be a big +problem yeah and and because if you're + + align:start position:0% +problem yeah and and because if you're + + + align:start position:0% +problem yeah and and because if you're +doing it solo now he's so sort of solo + + align:start position:0% +doing it solo now he's so sort of solo + + + align:start position:0% +doing it solo now he's so sort of solo +mining is saying I'm just mining on my + + align:start position:0% +mining is saying I'm just mining on my + + + align:start position:0% +mining is saying I'm just mining on my +own I'm gonna try to find a valid proof + + align:start position:0% +own I'm gonna try to find a valid proof + + + align:start position:0% +own I'm gonna try to find a valid proof +of work that's very difficult because of + + align:start position:0% +of work that's very difficult because of + + + align:start position:0% +of work that's very difficult because of +the amount of work needed so many people + + align:start position:0% +the amount of work needed so many people + + + align:start position:0% +the amount of work needed so many people +pool together so yeah that's another + + align:start position:0% +pool together so yeah that's another + + + align:start position:0% +pool together so yeah that's another +issue + + align:start position:0% + + + + align:start position:0% + +yeah there's also protocols one called + + align:start position:0% +yeah there's also protocols one called + + + align:start position:0% +yeah there's also protocols one called +p2 pool where you can sort of have + + align:start position:0% +p2 pool where you can sort of have + + + align:start position:0% +p2 pool where you can sort of have +another layer of blockchain II kind of + + align:start position:0% +another layer of blockchain II kind of + + + align:start position:0% +another layer of blockchain II kind of +messages which allows you to pool + + align:start position:0% +messages which allows you to pool + + + align:start position:0% +messages which allows you to pool +together resources without having a + + align:start position:0% +together resources without having a + + + align:start position:0% +together resources without having a +single entity responsible for like + + align:start position:0% +single entity responsible for like + + + align:start position:0% +single entity responsible for like +getting the rewards and distributing + + align:start position:0% +getting the rewards and distributing + + + align:start position:0% +getting the rewards and distributing +them back out I mean I've really talked + + align:start position:0% +them back out I mean I've really talked + + + align:start position:0% +them back out I mean I've really talked +about the like rewards and like the + + align:start position:0% +about the like rewards and like the + + + align:start position:0% +about the like rewards and like the +Bitcoin specific stuff will be in next + + align:start position:0% +Bitcoin specific stuff will be in next + + + align:start position:0% +Bitcoin specific stuff will be in next +week probably but but yeah there's all + + align:start position:0% +week probably but but yeah there's all + + + align:start position:0% +week probably but but yeah there's all +sorts of this gets really complicated + + align:start position:0% +sorts of this gets really complicated + + + align:start position:0% +sorts of this gets really complicated +and crazy in like pools there's so many + + align:start position:0% +and crazy in like pools there's so many + + + align:start position:0% +and crazy in like pools there's so many +attacks on pools and it's it's a mess + + align:start position:0% +attacks on pools and it's it's a mess + + + align:start position:0% +attacks on pools and it's it's a mess +okay + + align:start position:0% +okay + + + align:start position:0% +okay +last con people hate it and this is not + + align:start position:0% +last con people hate it and this is not + + + align:start position:0% +last con people hate it and this is not +a quantitative objective reason but it + + align:start position:0% +a quantitative objective reason but it + + + align:start position:0% +a quantitative objective reason but it +is a problem and people don't like + + align:start position:0% +is a problem and people don't like + + + align:start position:0% +is a problem and people don't like +proof-of-work + + align:start position:0% +proof-of-work + + + align:start position:0% +proof-of-work +some people are fine with it but a lot + + align:start position:0% +some people are fine with it but a lot + + + align:start position:0% +some people are fine with it but a lot +of like especially in academia that I've + + align:start position:0% +of like especially in academia that I've + + + align:start position:0% +of like especially in academia that I've +talked a lot of people they're just like + + align:start position:0% +talked a lot of people they're just like + + + align:start position:0% +talked a lot of people they're just like +ah this is horrible you know the whole + + align:start position:0% +ah this is horrible you know the whole + + + align:start position:0% +ah this is horrible you know the whole +point of shot to v6 is you can't find + + align:start position:0% +point of shot to v6 is you can't find + + + align:start position:0% +point of shot to v6 is you can't find +collisions and you design an entire + + align:start position:0% +collisions and you design an entire + + + align:start position:0% +collisions and you design an entire +system we're all we're doing is trying + + align:start position:0% +system we're all we're doing is trying + + + align:start position:0% +system we're all we're doing is trying +to find collisions in this non + + align:start position:0% +to find collisions in this non + + + align:start position:0% +to find collisions in this non +collidable system and you've got you + + align:start position:0% +collidable system and you've got you + + + align:start position:0% +collidable system and you've got you +know giant warehouses full you know uses + + align:start position:0% +know giant warehouses full you know uses + + + align:start position:0% +know giant warehouses full you know uses +so much electricity and you've got giant + + align:start position:0% +so much electricity and you've got giant + + + align:start position:0% +so much electricity and you've got giant +warehouses full of chips that are just + + align:start position:0% +warehouses full of chips that are just + + + align:start position:0% +warehouses full of chips that are just +doing this pointless thing but it's you + + align:start position:0% +doing this pointless thing but it's you + + + align:start position:0% +doing this pointless thing but it's you +know it offends the sensibilities of + + align:start position:0% +know it offends the sensibilities of + + + align:start position:0% +know it offends the sensibilities of +many people and it and it probably is + + align:start position:0% +many people and it and it probably is + + + align:start position:0% +many people and it and it probably is +getting worse because it keeps getting + + align:start position:0% +getting worse because it keeps getting + + + align:start position:0% +getting worse because it keeps getting +bigger and so a lot of people don't like + + align:start position:0% +bigger and so a lot of people don't like + + + align:start position:0% +bigger and so a lot of people don't like +it and I I can understand that like when + + align:start position:0% +it and I I can understand that like when + + + align:start position:0% +it and I I can understand that like when +I first read about this stuff I was like + + align:start position:0% +I first read about this stuff I was like + + + align:start position:0% +I first read about this stuff I was like +that's kind of cool that's kind of + + align:start position:0% +that's kind of cool that's kind of + + + align:start position:0% +that's kind of cool that's kind of +stupid and then I was like oh man what + + align:start position:0% +stupid and then I was like oh man what + + + align:start position:0% +stupid and then I was like oh man what +if this gets really takes off there's + + align:start position:0% +if this gets really takes off there's + + + align:start position:0% +if this gets really takes off there's +just gonna be so much power usage and so + + align:start position:0% +just gonna be so much power usage and so + + + align:start position:0% +just gonna be so much power usage and so +many chips dedicated to like kind of a + + align:start position:0% +many chips dedicated to like kind of a + + + align:start position:0% +many chips dedicated to like kind of a +pointless thing I I would say that like + + align:start position:0% +pointless thing I I would say that like + + + align:start position:0% +pointless thing I I would say that like +I acknowledge this is a big problem and + + align:start position:0% +I acknowledge this is a big problem and + + + align:start position:0% +I acknowledge this is a big problem and +I think the best analogy is something + + align:start position:0% +I think the best analogy is something + + + align:start position:0% +I think the best analogy is something +like gold or silver they know precious + + align:start position:0% +like gold or silver they know precious + + + align:start position:0% +like gold or silver they know precious +metal mining where you could make very + + align:start position:0% +metal mining where you could make very + + + align:start position:0% +metal mining where you could make very +similar arguments that you know like all + + align:start position:0% +similar arguments that you know like all + + + align:start position:0% +similar arguments that you know like all +these you know Spanish or Portuguese + + align:start position:0% +these you know Spanish or Portuguese + + + align:start position:0% +these you know Spanish or Portuguese +people sailed over to South America five + + align:start position:0% +people sailed over to South America five + + + align:start position:0% +people sailed over to South America five +hundred years ago and it was sort of it + + align:start position:0% +hundred years ago and it was sort of it + + + align:start position:0% +hundred years ago and it was sort of it +was you know horrible and all these + + align:start position:0% +was you know horrible and all these + + + align:start position:0% +was you know horrible and all these +people are like working in these mines + + align:start position:0% +people are like working in these mines + + + align:start position:0% +people are like working in these mines +and it's like a mess just to get silver + + align:start position:0% +and it's like a mess just to get silver + + + align:start position:0% +and it's like a mess just to get silver +or gold or whatever it's like why + + align:start position:0% +or gold or whatever it's like why + + + align:start position:0% +or gold or whatever it's like why +why are you doing this right just to get + + align:start position:0% +why are you doing this right just to get + + + align:start position:0% +why are you doing this right just to get +some gold so similarly the the Bitcoin + + align:start position:0% +some gold so similarly the the Bitcoin + + + align:start position:0% +some gold so similarly the the Bitcoin +and the proof of work in general has a + + align:start position:0% +and the proof of work in general has a + + + align:start position:0% +and the proof of work in general has a +lot of people who don't like it and so + + align:start position:0% +lot of people who don't like it and so + + + align:start position:0% +lot of people who don't like it and so +that's why there's a lot of research in + + align:start position:0% +that's why there's a lot of research in + + + align:start position:0% +that's why there's a lot of research in +okay can we have the same kind of system + + align:start position:0% +okay can we have the same kind of system + + + align:start position:0% +okay can we have the same kind of system +but without the work or alternatively + + align:start position:0% +but without the work or alternatively + + + align:start position:0% +but without the work or alternatively +can we have some kind of proof of work + + align:start position:0% +can we have some kind of proof of work + + + align:start position:0% +can we have some kind of proof of work +that's also useful for other things so + + align:start position:0% +that's also useful for other things so + + + align:start position:0% +that's also useful for other things so +can we have some kind of proof of work + + align:start position:0% +can we have some kind of proof of work + + + align:start position:0% +can we have some kind of proof of work +that like cures cancer it's like wow I + + align:start position:0% +that like cures cancer it's like wow I + + + align:start position:0% +that like cures cancer it's like wow I +mean there's there's actually write + + align:start position:0% +mean there's there's actually write + + + align:start position:0% +mean there's there's actually write +papers about like protein folding proof + + align:start position:0% +papers about like protein folding proof + + + align:start position:0% +papers about like protein folding proof +of work and I don't I don't I haven't + + align:start position:0% +of work and I don't I don't I haven't + + + align:start position:0% +of work and I don't I don't I haven't +seen a ton there's one where you like + + align:start position:0% +seen a ton there's one where you like + + + align:start position:0% +seen a ton there's one where you like +find sequences of prime numbers and it's + + align:start position:0% +find sequences of prime numbers and it's + + + align:start position:0% +find sequences of prime numbers and it's +sort of work it sort of has most of the + + align:start position:0% +sort of work it sort of has most of the + + + align:start position:0% +sort of work it sort of has most of the +properties you want and it's like okay + + align:start position:0% +properties you want and it's like okay + + + align:start position:0% +properties you want and it's like okay +but it's like well you found five prime + + align:start position:0% +but it's like well you found five prime + + + align:start position:0% +but it's like well you found five prime +numbers in a row like yeah so that's + + align:start position:0% +numbers in a row like yeah so that's + + + align:start position:0% +numbers in a row like yeah so that's +another yeah people want useful proof + + align:start position:0% +another yeah people want useful proof + + + align:start position:0% +another yeah people want useful proof +work a lot of times with useful proof of + + align:start position:0% +work a lot of times with useful proof of + + + align:start position:0% +work a lot of times with useful proof of +work it's hard to tell that it's a valid + + align:start position:0% +work it's hard to tell that it's a valid + + + align:start position:0% +work it's hard to tell that it's a valid +proof or you know there's not as much of + + align:start position:0% +proof or you know there's not as much of + + + align:start position:0% +proof or you know there's not as much of +a gap like the gap in in Bitcoin is + + align:start position:0% +a gap like the gap in in Bitcoin is + + + align:start position:0% +a gap like the gap in in Bitcoin is +enormous right + + align:start position:0% +enormous right + + + align:start position:0% +enormous right +Oh of n takes o of one to verify which + + align:start position:0% +Oh of n takes o of one to verify which + + + align:start position:0% +Oh of n takes o of one to verify which +is like perfect + + align:start position:0% +is like perfect + + + align:start position:0% +is like perfect +yeah you can't get better than that + + align:start position:0% +yeah you can't get better than that + + + align:start position:0% +yeah you can't get better than that +so so yeah it's hard to verify there's + + align:start position:0% +so so yeah it's hard to verify there's + + + align:start position:0% +so so yeah it's hard to verify there's +also that also applies to many different + + align:start position:0% +also that also applies to many different + + + align:start position:0% +also that also applies to many different +proofs of work so so one of the things + + align:start position:0% +proofs of work so so one of the things + + + align:start position:0% +proofs of work so so one of the things +with 51 percent of tax is if like you're + + align:start position:0% +with 51 percent of tax is if like you're + + + align:start position:0% +with 51 percent of tax is if like you're +saying if you want to build your own + + align:start position:0% +saying if you want to build your own + + + align:start position:0% +saying if you want to build your own +coin if you use the same proof of work + + align:start position:0% +coin if you use the same proof of work + + + align:start position:0% +coin if you use the same proof of work +algorithm as Bitcoin you are in a very + + align:start position:0% +algorithm as Bitcoin you are in a very + + + align:start position:0% +algorithm as Bitcoin you are in a very +risky situation because you've started + + align:start position:0% +risky situation because you've started + + + align:start position:0% +risky situation because you've started +your own new coin that like you know + + align:start position:0% +your own new coin that like you know + + + align:start position:0% +your own new coin that like you know +your own new message network that very + + align:start position:0% +your own new message network that very + + + align:start position:0% +your own new message network that very +few people are using and there's very + + align:start position:0% +few people are using and there's very + + + align:start position:0% +few people are using and there's very +little work being done in this network + + align:start position:0% +little work being done in this network + + + align:start position:0% +little work being done in this network +and then there's this huge Bitcoin + + align:start position:0% +and then there's this huge Bitcoin + + + align:start position:0% +and then there's this huge Bitcoin +network and as soon as they see your + + align:start position:0% +network and as soon as they see your + + + align:start position:0% +network and as soon as they see your +network they could easily overpower it + + align:start position:0% +network they could easily overpower it + + + align:start position:0% +network they could easily overpower it +right one one actor one person who's + + align:start position:0% +right one one actor one person who's + + + align:start position:0% +right one one actor one person who's +mining could become more than 51 percent + + align:start position:0% +mining could become more than 51 percent + + + align:start position:0% +mining could become more than 51 percent +of your network just with a flip of us + + align:start position:0% +of your network just with a flip of us + + + align:start position:0% +of your network just with a flip of us +you know pressing a button and so it's + + align:start position:0% +you know pressing a button and so it's + + + align:start position:0% +you know pressing a button and so it's +very dangerous to be running a very + + align:start position:0% +very dangerous to be running a very + + + align:start position:0% +very dangerous to be running a very +small network that shares a + + align:start position:0% +small network that shares a + + + align:start position:0% +small network that shares a +proof-of-work with the larger network + + align:start position:0% +proof-of-work with the larger network + + + align:start position:0% +proof-of-work with the larger network +and so most of the different coins when + + align:start position:0% +and so most of the different coins when + + + align:start position:0% +and so most of the different coins when +people say hey I'm gonna make my own you + + align:start position:0% +people say hey I'm gonna make my own you + + + align:start position:0% +people say hey I'm gonna make my own you +know derivative of Bitcoin or my own new + + align:start position:0% +know derivative of Bitcoin or my own new + + + align:start position:0% +know derivative of Bitcoin or my own new +coin I'm gonna have a different proof of + + align:start position:0% +coin I'm gonna have a different proof of + + + align:start position:0% +coin I'm gonna have a different proof of +work and so there's all sorts of + + align:start position:0% +work and so there's all sorts of + + + align:start position:0% +work and so there's all sorts of +different hash you know maybe I'll use + + align:start position:0% +different hash you know maybe I'll use + + + align:start position:0% +different hash you know maybe I'll use +shot three instead of shot 256 okay or + + align:start position:0% +shot three instead of shot 256 okay or + + + align:start position:0% +shot three instead of shot 256 okay or +I'll use some other hash function or + + align:start position:0% +I'll use some other hash function or + + + align:start position:0% +I'll use some other hash function or +some other like usually iterative hash + + align:start position:0% +some other like usually iterative hash + + + align:start position:0% +some other like usually iterative hash +function like for password hashing are + + align:start position:0% +function like for password hashing are + + + align:start position:0% +function like for password hashing are +you actually in a passion several + + align:start position:0% +you actually in a passion several + + + align:start position:0% +you actually in a passion several +million times and the disadvantage there + + align:start position:0% +million times and the disadvantage there + + + align:start position:0% +million times and the disadvantage there +as well as it can take quite a while to + + align:start position:0% +as well as it can take quite a while to + + + align:start position:0% +as well as it can take quite a while to +verify the the work not too much but + + align:start position:0% +verify the the work not too much but + + + align:start position:0% +verify the the work not too much but +noticeable where if you're running + + align:start position:0% +noticeable where if you're running + + + align:start position:0% +noticeable where if you're running +different clients like litecoin for + + align:start position:0% +different clients like litecoin for + + + align:start position:0% +different clients like litecoin for +example it uses a proof-of-work which + + align:start position:0% +example it uses a proof-of-work which + + + align:start position:0% +example it uses a proof-of-work which +takes thousands of times longer to + + align:start position:0% +takes thousands of times longer to + + + align:start position:0% +takes thousands of times longer to +verify still fast enough but some of + + align:start position:0% +verify still fast enough but some of + + + align:start position:0% +verify still fast enough but some of +them are pretty heavy so so those are + + align:start position:0% +them are pretty heavy so so those are + + + align:start position:0% +them are pretty heavy so so those are +all the different you know it gets + + align:start position:0% +all the different you know it gets + + + align:start position:0% +all the different you know it gets +pretty messy and I'm you know if you ask + + align:start position:0% +pretty messy and I'm you know if you ask + + + align:start position:0% +pretty messy and I'm you know if you ask +probably James and some other people are + + align:start position:0% +probably James and some other people are + + + align:start position:0% +probably James and some other people are +much more familiar with all the like + + align:start position:0% +much more familiar with all the like + + + align:start position:0% +much more familiar with all the like +horrible intricacies of proof of work + + align:start position:0% + + + + align:start position:0% + +yeah yeah so there's one wait + + align:start position:0% +yeah yeah so there's one wait + + + align:start position:0% +yeah yeah so there's one wait +so I said the longest so if you say the + + align:start position:0% +so I said the longest so if you say the + + + align:start position:0% +so I said the longest so if you say the +longest chain is the valid one I think I + + align:start position:0% +longest chain is the valid one I think I + + + align:start position:0% +longest chain is the valid one I think I +mostly said most work right they're not + + align:start position:0% +mostly said most work right they're not + + + align:start position:0% +mostly said most work right they're not +necessarily the same right in this case + + align:start position:0% +necessarily the same right in this case + + + align:start position:0% +necessarily the same right in this case +where we have a fixed target you know + + align:start position:0% +where we have a fixed target you know + + + align:start position:0% +where we have a fixed target you know +fix the amount of work per block they + + align:start position:0% +fix the amount of work per block they + + + align:start position:0% +fix the amount of work per block they +are the same but in the case of Bitcoin + + align:start position:0% +are the same but in the case of Bitcoin + + + align:start position:0% +are the same but in the case of Bitcoin +and most of these networks the the + + align:start position:0% +and most of these networks the the + + + align:start position:0% +and most of these networks the the +target and the amount of work required + + align:start position:0% +target and the amount of work required + + + align:start position:0% +target and the amount of work required +for a block can change right with that + + align:start position:0% +for a block can change right with that + + + align:start position:0% +for a block can change right with that +2016 period and so there are attacks + + align:start position:0% +2016 period and so there are attacks + + + align:start position:0% +2016 period and so there are attacks +where you can say well I'm gonna make + + align:start position:0% +where you can say well I'm gonna make + + + align:start position:0% +where you can say well I'm gonna make +something that's longer but actually has + + align:start position:0% +something that's longer but actually has + + + align:start position:0% +something that's longer but actually has +less work because I've forged all these + + align:start position:0% +less work because I've forged all these + + + align:start position:0% +less work because I've forged all these +times that you know I go back in time I + + align:start position:0% +times that you know I go back in time I + + + align:start position:0% +times that you know I go back in time I +pretend it took me a long time and I + + align:start position:0% +pretend it took me a long time and I + + + align:start position:0% +pretend it took me a long time and I +change the time stamps so that it looks + + align:start position:0% +change the time stamps so that it looks + + + align:start position:0% +change the time stamps so that it looks +like it took a long time and the + + align:start position:0% +like it took a long time and the + + + align:start position:0% +like it took a long time and the +difficulty decreased and then but I + + align:start position:0% +difficulty decreased and then but I + + + align:start position:0% +difficulty decreased and then but I +actually have more blocks but less total + + align:start position:0% +actually have more blocks but less total + + + align:start position:0% +actually have more blocks but less total +work and then I can have some weird + + align:start position:0% +work and then I can have some weird + + + align:start position:0% +work and then I can have some weird +attacks where I like reorg out things so + + align:start position:0% +attacks where I like reorg out things so + + + align:start position:0% +attacks where I like reorg out things so +in the case of Bitcoin I think yeah + + align:start position:0% +in the case of Bitcoin I think yeah + + + align:start position:0% +in the case of Bitcoin I think yeah +pretty early version 1.0 version 0.1 it + + align:start position:0% +pretty early version 1.0 version 0.1 it + + + align:start position:0% +pretty early version 1.0 version 0.1 it +actually just looked at + + align:start position:0% +actually just looked at + + + align:start position:0% +actually just looked at +of blocks because it's so much easier in + + align:start position:0% +of blocks because it's so much easier in + + + align:start position:0% +of blocks because it's so much easier in +the code to just do number of blocks you + + align:start position:0% +the code to just do number of blocks you + + + align:start position:0% +the code to just do number of blocks you +know otherwise you have to like treat + + align:start position:0% +know otherwise you have to like treat + + + align:start position:0% +know otherwise you have to like treat +all the hashes as bigots and like figure + + align:start position:0% +all the hashes as bigots and like figure + + + align:start position:0% +all the hashes as bigots and like figure +out how much work was done on each one + + align:start position:0% +out how much work was done on each one + + + align:start position:0% +out how much work was done on each one +and this annoying stuff but that attack + + align:start position:0% +and this annoying stuff but that attack + + + align:start position:0% +and this annoying stuff but that attack +was sort of thought of it I don't think + + align:start position:0% +was sort of thought of it I don't think + + + align:start position:0% +was sort of thought of it I don't think +the attack ever happened but the whoever + + align:start position:0% +the attack ever happened but the whoever + + + align:start position:0% +the attack ever happened but the whoever +designed it was like oh wait yeah + + align:start position:0% +designed it was like oh wait yeah + + + align:start position:0% +designed it was like oh wait yeah +longest is not quite right it has to be + + align:start position:0% +longest is not quite right it has to be + + + align:start position:0% +longest is not quite right it has to be +most work and so they changed the code + + align:start position:0% +most work and so they changed the code + + + align:start position:0% +most work and so they changed the code +okay so proof worked we played it yeah + + align:start position:0% +okay so proof worked we played it yeah + + + align:start position:0% +okay so proof worked we played it yeah +but the thing is it does work it's been + + align:start position:0% +but the thing is it does work it's been + + + align:start position:0% +but the thing is it does work it's been +working for nine years the blocks keep + + align:start position:0% +working for nine years the blocks keep + + + align:start position:0% +working for nine years the blocks keep +on coming not regularly but you know + + align:start position:0% +on coming not regularly but you know + + + align:start position:0% +on coming not regularly but you know +over the course of a day about a hundred + + align:start position:0% +over the course of a day about a hundred + + + align:start position:0% +over the course of a day about a hundred +and forty four will come out in practice + + align:start position:0% +and forty four will come out in practice + + + align:start position:0% +and forty four will come out in practice +it's infeasible to write old messages + + align:start position:0% +it's infeasible to write old messages + + + align:start position:0% +it's infeasible to write old messages +right you you there are all these known + + align:start position:0% +right you you there are all these known + + + align:start position:0% +right you you there are all these known +attacks but they're very costly and and + + align:start position:0% +attacks but they're very costly and and + + + align:start position:0% +attacks but they're very costly and and +either you have to do an enormous amount + + align:start position:0% +either you have to do an enormous amount + + + align:start position:0% +either you have to do an enormous amount +of work and get all these resources or + + align:start position:0% +of work and get all these resources or + + + align:start position:0% +of work and get all these resources or +you have to sort of have a lot of + + align:start position:0% +you have to sort of have a lot of + + + align:start position:0% +you have to sort of have a lot of +collusion between the different actors + + align:start position:0% +collusion between the different actors + + + align:start position:0% +collusion between the different actors +one nice part is that in these systems + + align:start position:0% +one nice part is that in these systems + + + align:start position:0% +one nice part is that in these systems +people are very adversarial and so they + + align:start position:0% +people are very adversarial and so they + + + align:start position:0% +people are very adversarial and so they +don't want to collude they always are + + align:start position:0% +don't want to collude they always are + + + align:start position:0% +don't want to collude they always are +attacking each other and hate each other + + align:start position:0% +attacking each other and hate each other + + + align:start position:0% +attacking each other and hate each other +so it's so that sort of keeps the system + + align:start position:0% +so it's so that sort of keeps the system + + + align:start position:0% +so it's so that sort of keeps the system +working in practice with Bitcoin there + + align:start position:0% +working in practice with Bitcoin there + + + align:start position:0% +working in practice with Bitcoin there +are very few blocker York's this happens + + align:start position:0% +are very few blocker York's this happens + + + align:start position:0% +are very few blocker York's this happens +I don't know when's the last time actual + + align:start position:0% +I don't know when's the last time actual + + + align:start position:0% +I don't know when's the last time actual +reorg happened instead of just two like + + align:start position:0% +reorg happened instead of just two like + + + align:start position:0% +reorg happened instead of just two like +years it just never happens most one or + + align:start position:0% +years it just never happens most one or + + + align:start position:0% +years it just never happens most one or +two blocks so you can have a one block + + align:start position:0% +two blocks so you can have a one block + + + align:start position:0% +two blocks so you can have a one block +where two blocks + + align:start position:0% +where two blocks + + + align:start position:0% +where two blocks +come out at the same time and point to + + align:start position:0% +come out at the same time and point to + + + align:start position:0% +come out at the same time and point to +the same parent but that's not a reorg + + align:start position:0% +the same parent but that's not a reorg + + + align:start position:0% +the same parent but that's not a reorg +right because then your software sees it + + align:start position:0% +right because then your software sees it + + + align:start position:0% +right because then your software sees it +it's like well which is gonna be right + + align:start position:0% +it's like well which is gonna be right + + + align:start position:0% +it's like well which is gonna be right +and then one of them pulls ahead so that + + align:start position:0% +and then one of them pulls ahead so that + + + align:start position:0% +and then one of them pulls ahead so that +happens every couple days it used to be + + align:start position:0% +happens every couple days it used to be + + + align:start position:0% +happens every couple days it used to be +more frequently but now it's fairly + + align:start position:0% +more frequently but now it's fairly + + + align:start position:0% +more frequently but now it's fairly +infrequent and like two blocks reorg it + + align:start position:0% +infrequent and like two blocks reorg it + + + align:start position:0% +infrequent and like two blocks reorg it +has happened but it's it's very rare now + + align:start position:0% +has happened but it's it's very rare now + + + align:start position:0% +has happened but it's it's very rare now +so you can build on these things + + align:start position:0% +so you can build on these things + + + align:start position:0% +so you can build on these things +okay I'm almost done new one last fun + + align:start position:0% +okay I'm almost done new one last fun + + + align:start position:0% +okay I'm almost done new one last fun +facts and then questions ok so fun facts + + align:start position:0% +facts and then questions ok so fun facts + + + align:start position:0% +facts and then questions ok so fun facts +how to estimate the total work done + + align:start position:0% +how to estimate the total work done + + + align:start position:0% +how to estimate the total work done +throughout history of the network well + + align:start position:0% +throughout history of the network well + + + align:start position:0% +throughout history of the network well +you just look at the lowest - this is a + + align:start position:0% +you just look at the lowest - this is a + + + align:start position:0% +you just look at the lowest - this is a +kind of like counterintuitive like whoa + + align:start position:0% +kind of like counterintuitive like whoa + + + align:start position:0% +kind of like counterintuitive like whoa +kind of thing you can prove all the work + + align:start position:0% +kind of thing you can prove all the work + + + align:start position:0% +kind of thing you can prove all the work +ever done in the history of the system + + align:start position:0% +ever done in the history of the system + + + align:start position:0% +ever done in the history of the system +with just one + + align:start position:0% +with just one + + + align:start position:0% +with just one +the lowest because probabilistically + + align:start position:0% +the lowest because probabilistically + + + align:start position:0% +the lowest because probabilistically +like well I've been doing work the whole + + align:start position:0% +like well I've been doing work the whole + + + align:start position:0% +like well I've been doing work the whole +time probabilistically I guess the the + + align:start position:0% +time probabilistically I guess the the + + + align:start position:0% +time probabilistically I guess the the +way this works is that whether we were + + align:start position:0% +way this works is that whether we were + + + align:start position:0% +way this works is that whether we were +all trying for the same block or whether + + align:start position:0% +all trying for the same block or whether + + + align:start position:0% +all trying for the same block or whether +we are trying for all these different + + align:start position:0% +we are trying for all these different + + + align:start position:0% +we are trying for all these different +blocks it doesn't matter right we're + + align:start position:0% +blocks it doesn't matter right we're + + + align:start position:0% +blocks it doesn't matter right we're +still doing attempts and the best + + align:start position:0% +still doing attempts and the best + + + align:start position:0% +still doing attempts and the best +attempt will have the most zeroes in + + align:start position:0% +attempt will have the most zeroes in + + + align:start position:0% +attempt will have the most zeroes in +front of it and that holds true for + + align:start position:0% +front of it and that holds true for + + + align:start position:0% +front of it and that holds true for +whatever kind of configuration graph + + align:start position:0% +whatever kind of configuration graph + + + align:start position:0% +whatever kind of configuration graph +configuration whether there's Forks + + align:start position:0% +configuration whether there's Forks + + + align:start position:0% +configuration whether there's Forks +whether this a single chain whether we + + align:start position:0% +whether this a single chain whether we + + + align:start position:0% +whether this a single chain whether we +all just work on the same thing and you + + align:start position:0% +all just work on the same thing and you + + + align:start position:0% +all just work on the same thing and you +know never make any progress and just + + align:start position:0% +know never make any progress and just + + + align:start position:0% +know never make any progress and just +submit the best hash so that's kind of + + align:start position:0% +submit the best hash so that's kind of + + + align:start position:0% +submit the best hash so that's kind of +cool you can just look at a single hash + + align:start position:0% +cool you can just look at a single hash + + + align:start position:0% +cool you can just look at a single hash +and see all the work that's ever been + + align:start position:0% +and see all the work that's ever been + + + align:start position:0% +and see all the work that's ever been +done in the system kind of cool with + + align:start position:0% +done in the system kind of cool with + + + align:start position:0% +done in the system kind of cool with +with pretty crummy accuracy of course + + align:start position:0% +with pretty crummy accuracy of course + + + align:start position:0% +with pretty crummy accuracy of course +but but actually not too bad and so + + align:start position:0% +but but actually not too bad and so + + + align:start position:0% +but but actually not too bad and so +there's a paper that's pretty + + align:start position:0% +there's a paper that's pretty + + + align:start position:0% +there's a paper that's pretty +interesting if you're interested in like + + align:start position:0% +interesting if you're interested in like + + + align:start position:0% +interesting if you're interested in like +this and want to look into the math + + align:start position:0% +this and want to look into the math + + + align:start position:0% +this and want to look into the math +there's a paper called hyper log log + + align:start position:0% +there's a paper called hyper log log + + + align:start position:0% +there's a paper called hyper log log +that uses this fact for something + + align:start position:0% +that uses this fact for something + + + align:start position:0% +that uses this fact for something +completely different to like count set + + align:start position:0% +completely different to like count set + + + align:start position:0% +completely different to like count set +cardinalities and stuff and it's kind of + + align:start position:0% +cardinalities and stuff and it's kind of + + + align:start position:0% +cardinalities and stuff and it's kind of +a cool math paper but but I think the + + align:start position:0% +a cool math paper but but I think the + + + align:start position:0% +a cool math paper but but I think the +Bitcoin software does do that and it'll + + align:start position:0% +Bitcoin software does do that and it'll + + + align:start position:0% +Bitcoin software does do that and it'll +say like best hash and it's in there you + + align:start position:0% +say like best hash and it's in there you + + + align:start position:0% +say like best hash and it's in there you +can say like well this is how much work + + align:start position:0% +can say like well this is how much work + + + align:start position:0% +can say like well this is how much work +we've all done there's also some papers + + align:start position:0% +we've all done there's also some papers + + + align:start position:0% +we've all done there's also some papers +in Bitcoin where you can try to use + + align:start position:0% +in Bitcoin where you can try to use + + + align:start position:0% +in Bitcoin where you can try to use +these facts like the lucky blocks that + + align:start position:0% +these facts like the lucky blocks that + + + align:start position:0% +these facts like the lucky blocks that +happen to have much more work than they + + align:start position:0% +happen to have much more work than they + + + align:start position:0% +happen to have much more work than they +needed and you can look back through + + align:start position:0% +needed and you can look back through + + + align:start position:0% +needed and you can look back through +history and sort of given a bridged + + align:start position:0% +history and sort of given a bridged + + + align:start position:0% +history and sort of given a bridged +version of history that still took as + + align:start position:0% +version of history that still took as + + + align:start position:0% +version of history that still took as +much that would still take about as much + + align:start position:0% +much that would still take about as much + + + align:start position:0% +much that would still take about as much +work to rewrite without providing all of + + align:start position:0% +work to rewrite without providing all of + + + align:start position:0% +work to rewrite without providing all of +the different headers the different + + align:start position:0% +the different headers the different + + + align:start position:0% +the different headers the different +blocks and stuff you can also prove + + align:start position:0% +blocks and stuff you can also prove + + + align:start position:0% +blocks and stuff you can also prove +close calls so like with pools and + + align:start position:0% +close calls so like with pools and + + + align:start position:0% +close calls so like with pools and +mining one way you can do it is you can + + align:start position:0% +mining one way you can do it is you can + + + align:start position:0% +mining one way you can do it is you can +prove that you are trying but didn't + + align:start position:0% +prove that you are trying but didn't + + + align:start position:0% +prove that you are trying but didn't +quite make it so if the if the + + align:start position:0% +quite make it so if the if the + + + align:start position:0% +quite make it so if the if the +requirement is you need two to the forty + + align:start position:0% +requirement is you need two to the forty + + + align:start position:0% +requirement is you need two to the forty +leading zeros and you get two to the + + align:start position:0% +leading zeros and you get two to the + + + align:start position:0% +leading zeros and you get two to the +thirty-nine you can show like hey I got + + align:start position:0% +thirty-nine you can show like hey I got + + + align:start position:0% +thirty-nine you can show like hey I got +two to the thirty-nine and I didn't + + align:start position:0% +two to the thirty-nine and I didn't + + + align:start position:0% +two to the thirty-nine and I didn't +quite make it but you know I tried and + + align:start position:0% +quite make it but you know I tried and + + + align:start position:0% +quite make it but you know I tried and +then people can verify that work as well + + align:start position:0% +then people can verify that work as well + + + align:start position:0% +then people can verify that work as well +and like credit you for that so the way + + align:start position:0% +and like credit you for that so the way + + + align:start position:0% +and like credit you for that so the way +a mining pool works will be you give + + align:start position:0% +a mining pool works will be you give + + + align:start position:0% +a mining pool works will be you give +what's called shares which is like you + + align:start position:0% +what's called shares which is like you + + + align:start position:0% +what's called shares which is like you +know close calls that it were were not + + align:start position:0% +know close calls that it were were not + + + align:start position:0% +know close calls that it were were not +sufficient to meet the proof of work but + + align:start position:0% +sufficient to meet the proof of work but + + + align:start position:0% +sufficient to meet the proof of work but +you keep you keep giving them every few + + align:start position:0% +you keep you keep giving them every few + + + align:start position:0% +you keep you keep giving them every few +seconds or every few minutes and then + + align:start position:0% +seconds or every few minutes and then + + + align:start position:0% +seconds or every few minutes and then +the central pool operator says okay well + + align:start position:0% +the central pool operator says okay well + + + align:start position:0% +the central pool operator says okay well +this person did this many shares this + + align:start position:0% +this person did this many shares this + + + align:start position:0% +this person did this many shares this +person did this many shares I have you + + align:start position:0% +person did this many shares I have you + + + align:start position:0% +person did this many shares I have you +know the central operator has a very + + align:start position:0% +know the central operator has a very + + + align:start position:0% +know the central operator has a very +good estimation of how much work + + align:start position:0% +good estimation of how much work + + + align:start position:0% +good estimation of how much work +different people are doing and so + + align:start position:0% +different people are doing and so + + + align:start position:0% +different people are doing and so +credits them and said okay well he's + + align:start position:0% +credits them and said okay well he's + + + align:start position:0% +credits them and said okay well he's +doing this much work he's doing this + + align:start position:0% +doing this much work he's doing this + + + align:start position:0% +doing this much work he's doing this +work and then when someone actually + + align:start position:0% +work and then when someone actually + + + align:start position:0% +work and then when someone actually +finds the block distributes the rewards + + align:start position:0% +finds the block distributes the rewards + + + align:start position:0% +finds the block distributes the rewards +from the block proportionally to how + + align:start position:0% +from the block proportionally to how + + + align:start position:0% +from the block proportionally to how +much work everyone's been doing + + align:start position:0% +much work everyone's been doing + + + align:start position:0% +much work everyone's been doing +so that's trusted and not great and + + align:start position:0% +so that's trusted and not great and + + + align:start position:0% +so that's trusted and not great and +there's also a bunch of attacks the sort + + align:start position:0% +there's also a bunch of attacks the sort + + + align:start position:0% +there's also a bunch of attacks the sort +of sneakiest of which is keep submitting + + align:start position:0% +of sneakiest of which is keep submitting + + + align:start position:0% +of sneakiest of which is keep submitting +shares submitting close calls but when + + align:start position:0% +shares submitting close calls but when + + + align:start position:0% +shares submitting close calls but when +you actually do find a valid proof of + + align:start position:0% +you actually do find a valid proof of + + + align:start position:0% +you actually do find a valid proof of +work immediately forget about it drop it + + align:start position:0% +work immediately forget about it drop it + + + align:start position:0% +work immediately forget about it drop it +and never tell anyone the reason that's + + align:start position:0% +and never tell anyone the reason that's + + + align:start position:0% +and never tell anyone the reason that's +a good attack is fairly counterintuitive + + align:start position:0% +a good attack is fairly counterintuitive + + + align:start position:0% +a good attack is fairly counterintuitive +but it's a good attack even though it + + align:start position:0% +but it's a good attack even though it + + + align:start position:0% +but it's a good attack even though it +seems like well you just found the block + + align:start position:0% +seems like well you just found the block + + + align:start position:0% +seems like well you just found the block +you know tell everyone you get this you + + align:start position:0% +you know tell everyone you get this you + + + align:start position:0% +you know tell everyone you get this you +know reward you get it's like nope no I + + align:start position:0% +know reward you get it's like nope no I + + + align:start position:0% +know reward you get it's like nope no I +found a block throw it away but oh I got + + align:start position:0% +found a block throw it away but oh I got + + + align:start position:0% +found a block throw it away but oh I got +a close call okay keep telling the + + align:start position:0% +a close call okay keep telling the + + + align:start position:0% +a close call okay keep telling the +central operator what that does is that + + align:start position:0% +central operator what that does is that + + + align:start position:0% +central operator what that does is that +really screws over the central operator + + align:start position:0% +really screws over the central operator + + + align:start position:0% +really screws over the central operator +who now thinks you're doing a lot of + + align:start position:0% +who now thinks you're doing a lot of + + + align:start position:0% +who now thinks you're doing a lot of +work but you never find an actual block + + align:start position:0% +work but you never find an actual block + + + align:start position:0% +work but you never find an actual block +and eventually the central operator like + + align:start position:0% +and eventually the central operator like + + + align:start position:0% +and eventually the central operator like +this person's really unlucky huh he's + + align:start position:0% +this person's really unlucky huh he's + + + align:start position:0% +this person's really unlucky huh he's +found so many close calls but never + + align:start position:0% +found so many close calls but never + + + align:start position:0% +found so many close calls but never +seems to actually get over the line and + + align:start position:0% +seems to actually get over the line and + + + align:start position:0% +seems to actually get over the line and +find a valid proof of work + + align:start position:0% +find a valid proof of work + + + align:start position:0% +find a valid proof of work +and so maybe they can kick you off + + align:start position:0% +and so maybe they can kick you off + + + align:start position:0% +and so maybe they can kick you off +eventually but it's it's not something + + align:start position:0% +eventually but it's it's not something + + + align:start position:0% +eventually but it's it's not something +you can prove you're like well I got + + align:start position:0% +you can prove you're like well I got + + + align:start position:0% +you can prove you're like well I got +unlucky so there's all sorts of things + + align:start position:0% +unlucky so there's all sorts of things + + + align:start position:0% +unlucky so there's all sorts of things +there's all sorts of fun things you can + + align:start position:0% +there's all sorts of fun things you can + + + align:start position:0% +there's all sorts of fun things you can +do with the proof of work and this you + + align:start position:0% +do with the proof of work and this you + + + align:start position:0% +do with the proof of work and this you +know just these hash functions + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/zasCvIWLyRA.txt b/zasCvIWLyRA.txt new file mode 100644 index 0000000000000000000000000000000000000000..b117776ba9b5a049d0e586b37aedd099b9b42c90 --- /dev/null +++ b/zasCvIWLyRA.txt @@ -0,0 +1,843 @@ +align:start position:0% + +the process by which Google determines + + align:start position:0% +the process by which Google determines + + + align:start position:0% +the process by which Google determines +which ads to display for which queries + + align:start position:0% +which ads to display for which queries + + + align:start position:0% +which ads to display for which queries +consists of three key steps first Google + + align:start position:0% +consists of three key steps first Google + + + align:start position:0% +consists of three key steps first Google +runs an auction where advertisers place + + align:start position:0% +runs an auction where advertisers place + + + align:start position:0% +runs an auction where advertisers place +bids for different queries that they + + align:start position:0% +bids for different queries that they + + + align:start position:0% +bids for different queries that they +want to display their ads on next Google + + align:start position:0% +want to display their ads on next Google + + + align:start position:0% +want to display their ads on next Google +uses each bid and a metric known as the + + align:start position:0% +uses each bid and a metric known as the + + + align:start position:0% +uses each bid and a metric known as the +quality score which basically measures + + align:start position:0% +quality score which basically measures + + + align:start position:0% +quality score which basically measures +how well a particular ad fits a + + align:start position:0% +how well a particular ad fits a + + + align:start position:0% +how well a particular ad fits a +particular query to decide a quantity + + align:start position:0% +particular query to decide a quantity + + + align:start position:0% +particular query to decide a quantity +known as the price per click Google does + + align:start position:0% +known as the price per click Google does + + + align:start position:0% +known as the price per click Google does +this for each advertiser in each query + + align:start position:0% +this for each advertiser in each query + + + align:start position:0% +this for each advertiser in each query +finally and this is where optimization + + align:start position:0% +finally and this is where optimization + + + align:start position:0% +finally and this is where optimization +plays a key role Google decides how + + align:start position:0% +plays a key role Google decides how + + + align:start position:0% +plays a key role Google decides how +often to display each ad for each query + + align:start position:0% +often to display each ad for each query + + + align:start position:0% +often to display each ad for each query +this problem as we'll see shortly can be + + align:start position:0% +this problem as we'll see shortly can be + + + align:start position:0% +this problem as we'll see shortly can be +formulated as a linear optimization + + align:start position:0% +formulated as a linear optimization + + + align:start position:0% +formulated as a linear optimization +model let's begin by thinking about the + + align:start position:0% +model let's begin by thinking about the + + + align:start position:0% +model let's begin by thinking about the +data that we need for this model in + + align:start position:0% +data that we need for this model in + + + align:start position:0% +data that we need for this model in +particular let's think about the price + + align:start position:0% +particular let's think about the price + + + align:start position:0% +particular let's think about the price +per click so as we just discussed Google + + align:start position:0% +per click so as we just discussed Google + + + align:start position:0% +per click so as we just discussed Google +decides each advertisers price per click + + align:start position:0% +decides each advertisers price per click + + + align:start position:0% +decides each advertisers price per click +the price per click is how much each + + align:start position:0% +the price per click is how much each + + + align:start position:0% +the price per click is how much each +advertiser pays Google when a user + + align:start position:0% +advertiser pays Google when a user + + + align:start position:0% +advertiser pays Google when a user +clicks on the ad for that query each + + align:start position:0% +clicks on the ad for that query each + + + align:start position:0% +clicks on the ad for that query each +advertiser also specifies a budget this + + align:start position:0% +advertiser also specifies a budget this + + + align:start position:0% +advertiser also specifies a budget this +is the total amount of money that the + + align:start position:0% +is the total amount of money that the + + + align:start position:0% +is the total amount of money that the +advertiser has available to pay for all + + align:start position:0% +advertiser has available to pay for all + + + align:start position:0% +advertiser has available to pay for all +the clicks to their ad every time a user + + align:start position:0% +the clicks to their ad every time a user + + + align:start position:0% +the clicks to their ad every time a user +clicks on the advertisers ad the + + align:start position:0% +clicks on the advertisers ad the + + + align:start position:0% +clicks on the advertisers ad the +advertisers budget is depleted by the + + align:start position:0% +advertisers budget is depleted by the + + + align:start position:0% +advertisers budget is depleted by the +price per click for that ad before that + + align:start position:0% +price per click for that ad before that + + + align:start position:0% +price per click for that ad before that +users query let's illustrate this with a + + align:start position:0% +users query let's illustrate this with a + + + align:start position:0% +users query let's illustrate this with a +small example so suppose that we are + + align:start position:0% +small example so suppose that we are + + + align:start position:0% +small example so suppose that we are +Google and three of the major wireless + + align:start position:0% +Google and three of the major wireless + + + align:start position:0% +Google and three of the major wireless +service providers in the United States + + align:start position:0% +service providers in the United States + + + align:start position:0% +service providers in the United States +AT&T t-mobile and Verizon come to us + + align:start position:0% +AT&T t-mobile and Verizon come to us + + + align:start position:0% +AT&T t-mobile and Verizon come to us +wanting to place ads on three different + + align:start position:0% +wanting to place ads on three different + + + align:start position:0% +wanting to place ads on three different +search queries query one which is 4G LTE + + align:start position:0% +search queries query one which is 4G LTE + + + align:start position:0% +search queries query one which is 4G LTE +query two which is largest LTE and query + + align:start position:0% +query two which is largest LTE and query + + + align:start position:0% +query two which is largest LTE and query +three which is best LTE network if + + align:start position:0% +three which is best LTE network if + + + align:start position:0% +three which is best LTE network if +you're not familiar with these terms 4G + + align:start position:0% +you're not familiar with these terms 4G + + + align:start position:0% +you're not familiar with these terms 4G +and LTE basically refer to different + + align:start position:0% +and LTE basically refer to different + + + align:start position:0% +and LTE basically refer to different +standards of high-speed wireless data + + align:start position:0% +standards of high-speed wireless data + + + align:start position:0% +standards of high-speed wireless data +communication + + align:start position:0% + + + + align:start position:0% + +the table here shows the price per click + + align:start position:0% +the table here shows the price per click + + + align:start position:0% +the table here shows the price per click +of each advertiser in each query so for + + align:start position:0% +of each advertiser in each query so for + + + align:start position:0% +of each advertiser in each query so for +example this 10 here means the t-mobile + + align:start position:0% +example this 10 here means the t-mobile + + + align:start position:0% +example this 10 here means the t-mobile +will pay Google $10 every time a user + + align:start position:0% +will pay Google $10 every time a user + + + align:start position:0% +will pay Google $10 every time a user +searches for query 1 and click some + + align:start position:0% +searches for query 1 and click some + + + align:start position:0% +searches for query 1 and click some +t-mobile's advertisement in this example + + align:start position:0% +t-mobile's advertisement in this example + + + align:start position:0% +t-mobile's advertisement in this example +t-mobile's budget is $100 if t-mobile + + align:start position:0% +t-mobile's budget is $100 if t-mobile + + + align:start position:0% +t-mobile's budget is $100 if t-mobile +begins advertising and by some point + + align:start position:0% +begins advertising and by some point + + + align:start position:0% +begins advertising and by some point +five people have clicked and t-mobile's + + align:start position:0% +five people have clicked and t-mobile's + + + align:start position:0% +five people have clicked and t-mobile's +ad when they search for 4G LTE then + + align:start position:0% +ad when they search for 4G LTE then + + + align:start position:0% +ad when they search for 4G LTE then +t-mobile will need to pay five times ten + + align:start position:0% +t-mobile will need to pay five times ten + + + align:start position:0% +t-mobile will need to pay five times ten +dollars or a total of $50 if t-mobile's + + align:start position:0% +dollars or a total of $50 if t-mobile's + + + align:start position:0% +dollars or a total of $50 if t-mobile's +budget is $100 + + align:start position:0% +budget is $100 + + + align:start position:0% +budget is $100 +this means the t-mobile is left with + + align:start position:0% +this means the t-mobile is left with + + + align:start position:0% +this means the t-mobile is left with +$100 minus $50 for remaining budget of + + align:start position:0% +$100 minus $50 for remaining budget of + + + align:start position:0% +$100 minus $50 for remaining budget of +$50 now well the price per click is + + align:start position:0% +$50 now well the price per click is + + + align:start position:0% +$50 now well the price per click is +important to know we must remember that + + align:start position:0% +important to know we must remember that + + + align:start position:0% +important to know we must remember that +the price per click is exactly that the + + align:start position:0% +the price per click is exactly that the + + + align:start position:0% +the price per click is exactly that the +price that the advertiser pays of Google + + align:start position:0% +price that the advertiser pays of Google + + + align:start position:0% +price that the advertiser pays of Google +for a single click of a given ad on a + + align:start position:0% +for a single click of a given ad on a + + + align:start position:0% +for a single click of a given ad on a +given query this price is paid only if + + align:start position:0% +given query this price is paid only if + + + align:start position:0% +given query this price is paid only if +the user clicks on the ad but typically + + align:start position:0% +the user clicks on the ad but typically + + + align:start position:0% +the user clicks on the ad but typically +the people who use Google search engine + + align:start position:0% +the people who use Google search engine + + + align:start position:0% +the people who use Google search engine +who are you and me will not click on + + align:start position:0% +who are you and me will not click on + + + align:start position:0% +who are you and me will not click on +every adit that is shown to them + + align:start position:0% +every adit that is shown to them + + + align:start position:0% +every adit that is shown to them +therefore we need a way to capture how + + align:start position:0% +therefore we need a way to capture how + + + align:start position:0% +therefore we need a way to capture how +often users click on ads this is where + + align:start position:0% +often users click on ads this is where + + + align:start position:0% +often users click on ads this is where +the idea of click-through rate becomes + + align:start position:0% +the idea of click-through rate becomes + + + align:start position:0% +the idea of click-through rate becomes +useful the click-through rate is the + + align:start position:0% +useful the click-through rate is the + + + align:start position:0% +useful the click-through rate is the +probability that a user clicks on an + + align:start position:0% +probability that a user clicks on an + + + align:start position:0% +probability that a user clicks on an +advertisers ad for a given query you can + + align:start position:0% +advertisers ad for a given query you can + + + align:start position:0% +advertisers ad for a given query you can +also think of this as the average number + + align:start position:0% +also think of this as the average number + + + align:start position:0% +also think of this as the average number +of clicks that we expect per user and + + align:start position:0% +of clicks that we expect per user and + + + align:start position:0% +of clicks that we expect per user and +this quantity is defined as we said per + + align:start position:0% +this quantity is defined as we said per + + + align:start position:0% +this quantity is defined as we said per +advertiser and per query so to + + align:start position:0% +advertiser and per query so to + + + align:start position:0% +advertiser and per query so to +illustrate this for the example that we + + align:start position:0% +illustrate this for the example that we + + + align:start position:0% +illustrate this for the example that we +just introduced a few slides ago suppose + + align:start position:0% +just introduced a few slides ago suppose + + + align:start position:0% +just introduced a few slides ago suppose +that we have to fall in quick + + align:start position:0% +that we have to fall in quick + + + align:start position:0% +that we have to fall in quick +click-through rates the number 0.08 here + + align:start position:0% +click-through rates the number 0.08 here + + + align:start position:0% +click-through rates the number 0.08 here +means that there is an 8% chance that a + + align:start position:0% +means that there is an 8% chance that a + + + align:start position:0% +means that there is an 8% chance that a +user who searches for best LTE network + + align:start position:0% +user who searches for best LTE network + + + align:start position:0% +user who searches for best LTE network +will click an AT&T Zaid if it is shown + + align:start position:0% +will click an AT&T Zaid if it is shown + + + align:start position:0% +will click an AT&T Zaid if it is shown +to them in terms of the number of users + + align:start position:0% +to them in terms of the number of users + + + align:start position:0% +to them in terms of the number of users +who click on an ad for a given query + + align:start position:0% +who click on an ad for a given query + + + align:start position:0% +who click on an ad for a given query +this means that for 50 users + + align:start position:0% + + + + align:start position:0% + +if the click-through rate is point zero + + align:start position:0% +if the click-through rate is point zero + + + align:start position:0% +if the click-through rate is point zero +eight we expect to see four users + + align:start position:0% +eight we expect to see four users + + + align:start position:0% +eight we expect to see four users +clicking on the ad similarly if there + + align:start position:0% +clicking on the ad similarly if there + + + align:start position:0% +clicking on the ad similarly if there +are hundred users who viewed the ad and + + align:start position:0% +are hundred users who viewed the ad and + + + align:start position:0% +are hundred users who viewed the ad and +eight percent of them click on the ad we + + align:start position:0% +eight percent of them click on the ad we + + + align:start position:0% +eight percent of them click on the ad we +expect to see eight users clicking on + + align:start position:0% +expect to see eight users clicking on + + + align:start position:0% +expect to see eight users clicking on +ATT's ad for query three in the next + + align:start position:0% +ATT's ad for query three in the next + + + align:start position:0% +ATT's ad for query three in the next +video we will define additional data + + align:start position:0% +video we will define additional data + + + align:start position:0% +video we will define additional data +that we will need to formulate the + + align:start position:0% +that we will need to formulate the + + + align:start position:0% +that we will need to formulate the +problem in particular we will see how + + align:start position:0% +problem in particular we will see how + + + align:start position:0% +problem in particular we will see how +the click-through rate and the price per + + align:start position:0% +the click-through rate and the price per + + + align:start position:0% +the click-through rate and the price per +click can be combined together to obtain + + align:start position:0% +click can be combined together to obtain + + + align:start position:0% +click can be combined together to obtain +a new quantity called the prior Burrage + + align:start position:0% +a new quantity called the prior Burrage + + + align:start position:0% +a new quantity called the prior Burrage +price per display this derived quantity + + align:start position:0% +price per display this derived quantity + + + align:start position:0% +price per display this derived quantity +will form a crucial part of our linear + + align:start position:0% +will form a crucial part of our linear + + + align:start position:0% +will form a crucial part of our linear +optimization model \ No newline at end of file